ConnectPP---0.7.2.THM-Prf.s

%------------------------------------------------------------------------------
% File     : ConnectPP---0.7.2
% Problem  : SWW311+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n017.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Sep 24 09:06:00 AM UTC 2026

% Result   : Theorem 166.34s 166.64s
% Output   : Proof 166.55s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
fof(fact_ext,axiom,
    ! [V_g_2,V_f_2] :
      ( ! [B_x] : hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x)
     => V_f_2 = V_g_2 ),
    file('theBenchmark.p',fact_ext) ).

fof(fact_asm,axiom,
    ! [V_G_2,V_tsa_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_tsa_2),V_G_2))
     => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_tsa_2) ),
    file('theBenchmark.p',fact_asm) ).

fof(fact_weaken,axiom,
    ! [V_tsa_2,V_ts_H_2,V_G_2,T_b] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_ts_H_2)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_tsa_2),V_ts_H_2))
       => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_tsa_2) ) ),
    file('theBenchmark.p',fact_weaken) ).

fof(fact_cut,axiom,
    ! [V_G_2,V_tsa_2,V_G_Ha_2,T_b] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_Ha_2,V_tsa_2)
     => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_G_Ha_2)
       => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_tsa_2) ) ),
    file('theBenchmark.p',fact_cut) ).

fof(fact_equalityI,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
       => V_A_2 = V_B_2 ) ),
    file('theBenchmark.p',fact_equalityI) ).

fof(fact_order__refl,axiom,
    ! [V_x,T_a] :
      ( class_Orderings_Opreorder(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_x)) ),
    file('theBenchmark.p',fact_order__refl) ).

fof(fact_le__fun__def,axiom,
    ! [V_g_2,V_f_2,T_b,T_c] :
      ( class_Orderings_Oord(T_c)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
      <=> ! [B_x] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) ),
    file('theBenchmark.p',fact_le__fun__def) ).

fof(fact_le__funD,axiom,
    ! [V_x_2,V_g_2,V_f_2,T_b,T_c] :
      ( class_Orderings_Oord(T_c)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))) ) ),
    file('theBenchmark.p',fact_le__funD) ).

fof(fact_le__funE,axiom,
    ! [V_x_2,V_g_2,V_f_2,T_b,T_c] :
      ( class_Orderings_Oord(T_c)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))) ) ),
    file('theBenchmark.p',fact_le__funE) ).

fof(fact_subset__refl,axiom,
    ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_A_2)),
    file('theBenchmark.p',fact_subset__refl) ).

fof(fact_set__eq__subset,axiom,
    ! [T_b,V_B_2,V_A_2] :
      ( V_A_2 = V_B_2
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
    file('theBenchmark.p',fact_set__eq__subset) ).

fof(fact_rev__predicate1D,axiom,
    ! [V_Q_2,T_b,V_x_2,V_P_2] :
      ( hBOOL(hAPP(V_P_2,V_x_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_P_2),V_Q_2))
       => hBOOL(hAPP(V_Q_2,V_x_2)) ) ),
    file('theBenchmark.p',fact_rev__predicate1D) ).

fof(fact_equalityD1,axiom,
    ! [T_b,V_B_2,V_A_2] :
      ( V_A_2 = V_B_2
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    file('theBenchmark.p',fact_equalityD1) ).

fof(fact_equalityD2,axiom,
    ! [T_b,V_B_2,V_A_2] :
      ( V_A_2 = V_B_2
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ),
    file('theBenchmark.p',fact_equalityD2) ).

fof(fact_predicate1D,axiom,
    ! [V_x_2,V_Q_2,V_P_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_P_2),V_Q_2))
     => ( hBOOL(hAPP(V_P_2,V_x_2))
       => hBOOL(hAPP(V_Q_2,V_x_2)) ) ),
    file('theBenchmark.p',fact_predicate1D) ).

fof(fact_subset__trans,axiom,
    ! [V_C_2,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ),
    file('theBenchmark.p',fact_subset__trans) ).

fof(fact_linorder__le__cases,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ),
    file('theBenchmark.p',fact_linorder__le__cases) ).

fof(fact_xt1_I6_J,axiom,
    ! [V_z,V_x,V_y,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) ) ) ),
    file('theBenchmark.p',fact_xt1_I6_J) ).

fof(fact_xt1_I5_J,axiom,
    ! [V_x,V_y,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
         => V_x = V_y ) ) ),
    file('theBenchmark.p',fact_xt1_I5_J) ).

fof(fact_order__trans,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Orderings_Opreorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) ) ) ),
    file('theBenchmark.p',fact_order__trans) ).

fof(fact_order__antisym,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
         => V_x = V_y ) ) ),
    file('theBenchmark.p',fact_order__antisym) ).

fof(fact_xt1_I4_J,axiom,
    ! [V_c,V_a,V_b,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
       => ( V_b = V_c
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ),
    file('theBenchmark.p',fact_xt1_I4_J) ).

fof(fact_ord__le__eq__trans,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Orderings_Oord(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
       => ( V_b = V_c
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ),
    file('theBenchmark.p',fact_ord__le__eq__trans) ).

fof(fact_xt1_I3_J,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( V_a = V_b
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_b))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ),
    file('theBenchmark.p',fact_xt1_I3_J) ).

fof(fact_ord__eq__le__trans,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Orderings_Oord(T_a)
     => ( V_a = V_b
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ),
    file('theBenchmark.p',fact_ord__eq__le__trans) ).

fof(fact_order__antisym__conv,axiom,
    ! [V_x_2,V_y_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
        <=> V_x_2 = V_y_2 ) ) ),
    file('theBenchmark.p',fact_order__antisym__conv) ).

fof(fact_order__eq__refl,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Opreorder(T_a)
     => ( V_x = V_y
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ),
    file('theBenchmark.p',fact_order__eq__refl) ).

fof(fact_order__eq__iff,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => ( V_x_2 = V_y_2
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ),
    file('theBenchmark.p',fact_order__eq__iff) ).

fof(fact_linorder__linear,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ),
    file('theBenchmark.p',fact_linorder__linear) ).

fof(fact_equalityE,axiom,
    ! [T_b,V_B_2,V_A_2] :
      ( V_A_2 = V_B_2
     => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
         => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_equalityE) ).

fof(fact_Powp__mono,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(T_b,V_A_2)),c_Predicate_OPowp(T_b,V_B_2))) ),
    file('theBenchmark.p',fact_Powp__mono) ).

fof(fact_le__funI,axiom,
    ! [T_b,V_g_2,V_f_2,T_c] :
      ( class_Orderings_Oord(T_c)
     => ( ! [B_x] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) ) ),
    file('theBenchmark.p',fact_le__funI) ).

fof(fact_strict__mono__less__eq,axiom,
    ! [V_y_2,V_x_2,V_f_2,T_b,T_c] :
      ( ( class_Orderings_Olinorder(T_b)
        & class_Orderings_Oorder(T_c) )
     => ( c_Orderings_Oorder__class_Ostrict__mono(T_b,T_c,V_f_2)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ),
    file('theBenchmark.p',fact_strict__mono__less__eq) ).

fof(fact_greaterThan__subset__iff,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_y_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ),
    file('theBenchmark.p',fact_greaterThan__subset__iff) ).

fof(fact_lessThan__subset__iff,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_y_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ),
    file('theBenchmark.p',fact_lessThan__subset__iff) ).

fof(fact_atLeast__subset__iff,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_y_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ),
    file('theBenchmark.p',fact_atLeast__subset__iff) ).

fof(fact_atMost__subset__iff,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_y_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ),
    file('theBenchmark.p',fact_atMost__subset__iff) ).

fof(fact_SUP__subset,axiom,
    ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_c)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),V_f_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_B_2),V_f_2))) ) ),
    file('theBenchmark.p',fact_SUP__subset) ).

fof(fact_INF__subset,axiom,
    ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_c)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_B_2),V_f_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),V_f_2))) ) ),
    file('theBenchmark.p',fact_INF__subset) ).

fof(fact_top__greatest,axiom,
    ! [V_x,T_a] :
      ( class_Orderings_Otop(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Orderings_Otop__class_Otop(T_a))) ),
    file('theBenchmark.p',fact_top__greatest) ).

fof(fact_bot__least,axiom,
    ! [V_x,T_a] :
      ( class_Orderings_Obot(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x)) ),
    file('theBenchmark.p',fact_bot__least) ).

fof(fact_empty__subsetI,axiom,
    ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),
    file('theBenchmark.p',fact_empty__subsetI) ).

fof(fact_UNIV__not__empty,axiom,
    ! [T_b] : c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_UNIV__not__empty) ).

fof(fact_bot__apply,axiom,
    ! [V_x_2,T_c,T_b] :
      ( class_Orderings_Obot(T_b)
     => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b) ),
    file('theBenchmark.p',fact_bot__apply) ).

fof(fact_top__apply,axiom,
    ! [V_x_2,T_c,T_b] :
      ( class_Orderings_Otop(T_b)
     => hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Otop__class_Otop(T_b) ),
    file('theBenchmark.p',fact_top__apply) ).

fof(fact_greaterThan__eq__iff,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_y_2)
      <=> V_x_2 = V_y_2 ) ),
    file('theBenchmark.p',fact_greaterThan__eq__iff) ).

fof(fact_lessThan__eq__iff,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_y_2)
      <=> V_x_2 = V_y_2 ) ),
    file('theBenchmark.p',fact_lessThan__eq__iff) ).

fof(fact_atLeast__eq__iff,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_y_2)
      <=> V_x_2 = V_y_2 ) ),
    file('theBenchmark.p',fact_atLeast__eq__iff) ).

fof(fact_atMost__eq__iff,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_y_2)
      <=> V_x_2 = V_y_2 ) ),
    file('theBenchmark.p',fact_atMost__eq__iff) ).

fof(fact_strict__mono__eq,axiom,
    ! [V_y_2,V_x_2,V_f_2,T_b,T_c] :
      ( ( class_Orderings_Olinorder(T_b)
        & class_Orderings_Oorder(T_c) )
     => ( c_Orderings_Oorder__class_Ostrict__mono(T_b,T_c,V_f_2)
       => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
        <=> V_x_2 = V_y_2 ) ) ),
    file('theBenchmark.p',fact_strict__mono__eq) ).

fof(fact_subset__UNIV,axiom,
    ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))),
    file('theBenchmark.p',fact_subset__UNIV) ).

fof(fact_subset__empty,axiom,
    ! [V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
    <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_subset__empty) ).

fof(fact_empty,axiom,
    ! [V_G_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))),
    file('theBenchmark.p',fact_empty) ).

fof(fact_hoare__derivs_Oequations_I1_J,axiom,
    ! [V_a_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))),
    file('theBenchmark.p',fact_hoare__derivs_Oequations_I1_J) ).

fof(fact_Inf__empty,axiom,
    ! [T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => c_Complete__Lattice_OInf__class_OInf(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(T_b) ),
    file('theBenchmark.p',fact_Inf__empty) ).

fof(fact_Sup__empty,axiom,
    ! [T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => c_Complete__Lattice_OSup__class_OSup(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(T_b) ),
    file('theBenchmark.p',fact_Sup__empty) ).

fof(fact_Pow__mono,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)),hAPP(c_Set_OPow(T_b),V_B_2))) ),
    file('theBenchmark.p',fact_Pow__mono) ).

fof(fact_greaterThanLessThan__empty,axiom,
    ! [V_k_2,V_l_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_k_2))
       => c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_greaterThanLessThan__empty) ).

fof(fact_greaterThanAtMost__empty,axiom,
    ! [V_k_2,V_l_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_k_2))
       => c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_greaterThanAtMost__empty) ).

fof(fact_Inter__anti__mono,axiom,
    ! [V_A_2,V_B_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_B_2),V_A_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2))) ),
    file('theBenchmark.p',fact_Inter__anti__mono) ).

fof(fact_atLeastLessThan__subset__iff,axiom,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)))
       => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2)) )
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2)) ) ) ),
    file('theBenchmark.p',fact_atLeastLessThan__subset__iff) ).

fof(fact_Compl__greaterThan,axiom,
    ! [V_k_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2) ),
    file('theBenchmark.p',fact_Compl__greaterThan) ).

fof(fact_Compl__atMost,axiom,
    ! [V_k_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2) ),
    file('theBenchmark.p',fact_Compl__atMost) ).

fof(fact_atLeastLessThan__empty,axiom,
    ! [V_a_2,V_b_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2))
       => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_atLeastLessThan__empty) ).

fof(fact_atLeastatMost__subset__iff,axiom,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ),
    file('theBenchmark.p',fact_atLeastatMost__subset__iff) ).

fof(fact_Compl__lessThan,axiom,
    ! [V_k_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_k_2) ),
    file('theBenchmark.p',fact_Compl__lessThan) ).

fof(fact_top1I,axiom,
    ! [V_x_2,T_b] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_x_2)),
    file('theBenchmark.p',fact_top1I) ).

fof(fact_Pow__not__empty,axiom,
    ! [V_A_2,T_b] : hAPP(c_Set_OPow(T_b),V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),
    file('theBenchmark.p',fact_Pow__not__empty) ).

fof(fact_Pow__UNIV,axiom,
    ! [T_b] : hAPP(c_Set_OPow(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),
    file('theBenchmark.p',fact_Pow__UNIV) ).

fof(fact_Union__Pow__eq,axiom,
    ! [V_A_2,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_OPow(T_b),V_A_2)) = V_A_2,
    file('theBenchmark.p',fact_Union__Pow__eq) ).

fof(fact_Union__UNIV,axiom,
    ! [T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Union__UNIV) ).

fof(fact_Inter__empty,axiom,
    ! [T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Inter__empty) ).

fof(fact_Compl__eq__Compl__iff,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)
    <=> V_A_2 = V_B_2 ),
    file('theBenchmark.p',fact_Compl__eq__Compl__iff) ).

fof(fact_double__complement,axiom,
    ! [V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = V_A_2,
    file('theBenchmark.p',fact_double__complement) ).

fof(fact_subset__Pow__Union,axiom,
    ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)))),
    file('theBenchmark.p',fact_subset__Pow__Union) ).

fof(fact_Compl__UNIV__eq,axiom,
    ! [T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Compl__UNIV__eq) ).

fof(fact_Compl__empty__eq,axiom,
    ! [T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Compl__empty__eq) ).

fof(fact_Union__empty,axiom,
    ! [T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Union__empty) ).

fof(fact_Compl__anti__mono,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) ),
    file('theBenchmark.p',fact_Compl__anti__mono) ).

fof(fact_Compl__subset__Compl__iff,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ),
    file('theBenchmark.p',fact_Compl__subset__Compl__iff) ).

fof(fact_Inter__UNIV,axiom,
    ! [T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Inter__UNIV) ).

fof(fact_Sup__le__iff,axiom,
    ! [V_b_2,V_A_2,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2)),V_b_2))
      <=> ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) ) ) ),
    file('theBenchmark.p',fact_Sup__le__iff) ).

fof(fact_le__Inf__iff,axiom,
    ! [V_A_2,V_b_2,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2)))
      <=> ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) ) ) ),
    file('theBenchmark.p',fact_le__Inf__iff) ).

fof(fact_Inf__UNIV,axiom,
    ! [T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => c_Complete__Lattice_OInf__class_OInf(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(T_b) ),
    file('theBenchmark.p',fact_Inf__UNIV) ).

fof(fact_Sup__UNIV,axiom,
    ! [T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => c_Complete__Lattice_OSup__class_OSup(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(T_b) ),
    file('theBenchmark.p',fact_Sup__UNIV) ).

fof(fact_subset__Compl__self__eq,axiom,
    ! [V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
    <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_subset__Compl__self__eq) ).

fof(fact_Union__mono,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2))) ),
    file('theBenchmark.p',fact_Union__mono) ).

fof(fact_atLeastatMost__empty__iff,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => ( c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ),
    file('theBenchmark.p',fact_atLeastatMost__empty__iff) ).

fof(fact_atLeastatMost__empty__iff2,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ),
    file('theBenchmark.p',fact_atLeastatMost__empty__iff2) ).

fof(fact_Compl__atLeast,axiom,
    ! [V_k_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_k_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2) ),
    file('theBenchmark.p',fact_Compl__atLeast) ).

fof(fact_compl__bot__eq,axiom,
    ! [T_a] :
      ( class_Lattices_Oboolean__algebra(T_a)
     => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Otop__class_Otop(T_a) ),
    file('theBenchmark.p',fact_compl__bot__eq) ).

fof(fact_compl__top__eq,axiom,
    ! [T_a] :
      ( class_Lattices_Oboolean__algebra(T_a)
     => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Otop__class_Otop(T_a)) = c_Orderings_Obot__class_Obot(T_a) ),
    file('theBenchmark.p',fact_compl__top__eq) ).

fof(fact_uminus__apply,axiom,
    ! [V_x_2,V_A_2,T_c,T_b] :
      ( class_Groups_Ouminus(T_b)
     => hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,T_b)),V_A_2),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(V_A_2,V_x_2)) ),
    file('theBenchmark.p',fact_uminus__apply) ).

fof(fact_compl__mono,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Lattices_Oboolean__algebra(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x))) ) ),
    file('theBenchmark.p',fact_compl__mono) ).

fof(fact_le__imp__neg__le,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Oordered__ab__group__add(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a))) ) ),
    file('theBenchmark.p',fact_le__imp__neg__le) ).

fof(fact_compl__le__compl__iff,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Lattices_Oboolean__algebra(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ),
    file('theBenchmark.p',fact_compl__le__compl__iff) ).

fof(fact_neg__le__iff__le,axiom,
    ! [V_a_2,V_b_2,T_b] :
      ( class_Groups_Oordered__ab__group__add(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ),
    file('theBenchmark.p',fact_neg__le__iff__le) ).

fof(fact_minus__le__iff,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( class_Groups_Oordered__ab__group__add(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),V_a_2)) ) ),
    file('theBenchmark.p',fact_minus__le__iff) ).

fof(fact_le__minus__iff,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( class_Groups_Oordered__ab__group__add(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) ) ),
    file('theBenchmark.p',fact_le__minus__iff) ).

fof(fact_ivl__disj__un_I13_J,axiom,
    ! [V_u_2,V_l_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_l_2) ) ),
    file('theBenchmark.p',fact_ivl__disj__un_I13_J) ).

fof(fact_ivl__disj__un_I10_J,axiom,
    ! [V_u_2,V_l_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_l_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_u_2) ) ),
    file('theBenchmark.p',fact_ivl__disj__un_I10_J) ).

fof(fact_ivl__disj__int_I5_J,axiom,
    ! [V_u_2,V_l_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_ivl__disj__int_I5_J) ).

fof(fact_sup1E,axiom,
    ! [V_x_2,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2))
     => ( ~ hBOOL(hAPP(V_A_2,V_x_2))
       => hBOOL(hAPP(V_B_2,V_x_2)) ) ),
    file('theBenchmark.p',fact_sup1E) ).

fof(fact_sup1CI,axiom,
    ! [T_b,V_A_2,V_x_2,V_B_2] :
      ( ( ~ hBOOL(hAPP(V_B_2,V_x_2))
       => hBOOL(hAPP(V_A_2,V_x_2)) )
     => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ),
    file('theBenchmark.p',fact_sup1CI) ).

fof(fact_inf1I,axiom,
    ! [T_b,V_B_2,V_x_2,V_A_2] :
      ( hBOOL(hAPP(V_A_2,V_x_2))
     => ( hBOOL(hAPP(V_B_2,V_x_2))
       => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ) ),
    file('theBenchmark.p',fact_inf1I) ).

fof(fact_inf1E,axiom,
    ! [V_x_2,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2))
     => ~ ( hBOOL(hAPP(V_A_2,V_x_2))
         => ~ hBOOL(hAPP(V_B_2,V_x_2)) ) ),
    file('theBenchmark.p',fact_inf1E) ).

fof(fact_Union__Un__distrib,axiom,
    ! [V_B_2,V_A_2,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)),
    file('theBenchmark.p',fact_Union__Un__distrib) ).

fof(fact_compl__inf,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Lattices_Oboolean__algebra(T_a)
     => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ),
    file('theBenchmark.p',fact_compl__inf) ).

fof(fact_compl__sup,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Lattices_Oboolean__algebra(T_a)
     => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ),
    file('theBenchmark.p',fact_compl__sup) ).

fof(fact_Int__absorb,axiom,
    ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_A_2) = V_A_2,
    file('theBenchmark.p',fact_Int__absorb) ).

fof(fact_Un__absorb,axiom,
    ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_A_2) = V_A_2,
    file('theBenchmark.p',fact_Un__absorb) ).

fof(fact_Int__commute,axiom,
    ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2),
    file('theBenchmark.p',fact_Int__commute) ).

fof(fact_Un__commute,axiom,
    ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2),
    file('theBenchmark.p',fact_Un__commute) ).

fof(fact_Int__left__absorb,axiom,
    ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),
    file('theBenchmark.p',fact_Int__left__absorb) ).

fof(fact_Un__left__absorb,axiom,
    ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),
    file('theBenchmark.p',fact_Un__left__absorb) ).

fof(fact_Int__left__commute,axiom,
    ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),
    file('theBenchmark.p',fact_Int__left__commute) ).

fof(fact_Un__left__commute,axiom,
    ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),
    file('theBenchmark.p',fact_Un__left__commute) ).

fof(fact_Int__Un__distrib,axiom,
    ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),
    file('theBenchmark.p',fact_Int__Un__distrib) ).

fof(fact_Un__Int__distrib,axiom,
    ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),
    file('theBenchmark.p',fact_Un__Int__distrib) ).

fof(fact_Int__assoc,axiom,
    ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)),
    file('theBenchmark.p',fact_Int__assoc) ).

fof(fact_Un__assoc,axiom,
    ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)),
    file('theBenchmark.p',fact_Un__assoc) ).

fof(fact_Int__Un__distrib2,axiom,
    ! [V_A_2,V_C_2,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),
    file('theBenchmark.p',fact_Int__Un__distrib2) ).

fof(fact_Un__Int__distrib2,axiom,
    ! [V_A_2,V_C_2,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),
    file('theBenchmark.p',fact_Un__Int__distrib2) ).

fof(fact_bex__Un,axiom,
    ! [V_P_2,V_B_2,V_A_2,T_b] :
      ( ? [B_x] :
          ( hBOOL(hAPP(V_P_2,B_x))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) )
    <=> ( ? [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) )
        | ? [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ),
    file('theBenchmark.p',fact_bex__Un) ).

fof(fact_ball__Un,axiom,
    ! [V_P_2,V_B_2,V_A_2,T_b] :
      ( ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
         => hBOOL(hAPP(V_P_2,B_x)) )
    <=> ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2))
           => hBOOL(hAPP(V_P_2,B_x)) )
        & ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
           => hBOOL(hAPP(V_P_2,B_x)) ) ) ),
    file('theBenchmark.p',fact_ball__Un) ).

fof(fact_Un__Int__crazy,axiom,
    ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),
    file('theBenchmark.p',fact_Un__Int__crazy) ).

fof(fact_sup1I1,axiom,
    ! [V_B_2,T_b,V_x_2,V_A_2] :
      ( hBOOL(hAPP(V_A_2,V_x_2))
     => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ),
    file('theBenchmark.p',fact_sup1I1) ).

fof(fact_sup1I2,axiom,
    ! [V_A_2,T_b,V_x_2,V_B_2] :
      ( hBOOL(hAPP(V_B_2,V_x_2))
     => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ),
    file('theBenchmark.p',fact_sup1I2) ).

fof(fact_inf1D1,axiom,
    ! [V_x_2,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2))
     => hBOOL(hAPP(V_A_2,V_x_2)) ),
    file('theBenchmark.p',fact_inf1D1) ).

fof(fact_inf1D2,axiom,
    ! [V_x_2,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2))
     => hBOOL(hAPP(V_B_2,V_x_2)) ),
    file('theBenchmark.p',fact_inf1D2) ).

fof(fact_sup__apply,axiom,
    ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
      ( class_Lattices_Olattice(T_b)
     => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,T_b)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ),
    file('theBenchmark.p',fact_sup__apply) ).

fof(fact_inf__apply,axiom,
    ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
      ( class_Lattices_Olattice(T_b)
     => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,T_b)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ),
    file('theBenchmark.p',fact_inf__apply) ).

fof(fact_sup__inf__distrib2,axiom,
    ! [V_x,V_z,V_y,T_a] :
      ( class_Lattices_Odistrib__lattice(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)),V_x) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_x)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_z),V_x)) ),
    file('theBenchmark.p',fact_sup__inf__distrib2) ).

fof(fact_inf__sup__distrib2,axiom,
    ! [V_x,V_z,V_y,T_a] :
      ( class_Lattices_Odistrib__lattice(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)),V_x) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_x)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_z),V_x)) ),
    file('theBenchmark.p',fact_inf__sup__distrib2) ).

fof(fact_sup__assoc,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Lattices_Osemilattice__sup(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)) ),
    file('theBenchmark.p',fact_sup__assoc) ).

fof(fact_inf__sup__aci_I6_J,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Lattices_Olattice(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)) ),
    file('theBenchmark.p',fact_inf__sup__aci_I6_J) ).

fof(fact_sup_Oassoc,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Lattices_Osemilattice__sup(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b),V_c)) ),
    file('theBenchmark.p',fact_sup_Oassoc) ).

fof(fact_inf__assoc,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) ),
    file('theBenchmark.p',fact_inf__assoc) ).

fof(fact_inf__sup__aci_I2_J,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Lattices_Olattice(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) ),
    file('theBenchmark.p',fact_inf__sup__aci_I2_J) ).

fof(fact_inf_Oassoc,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b),V_c)) ),
    file('theBenchmark.p',fact_inf_Oassoc) ).

fof(fact_sup__inf__distrib1,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Lattices_Odistrib__lattice(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_z)) ),
    file('theBenchmark.p',fact_sup__inf__distrib1) ).

fof(fact_inf__sup__distrib1,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Lattices_Odistrib__lattice(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_z)) ),
    file('theBenchmark.p',fact_inf__sup__distrib1) ).

fof(fact_sup__left__commute,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Lattices_Osemilattice__sup(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_z)) ),
    file('theBenchmark.p',fact_sup__left__commute) ).

fof(fact_inf__sup__aci_I7_J,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Lattices_Olattice(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_z)) ),
    file('theBenchmark.p',fact_inf__sup__aci_I7_J) ).

fof(fact_sup_Oleft__commute,axiom,
    ! [V_c,V_a,V_b,T_a] :
      ( class_Lattices_Osemilattice__sup(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_c)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b),V_c)) ),
    file('theBenchmark.p',fact_sup_Oleft__commute) ).

fof(fact_inf__left__commute,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_z)) ),
    file('theBenchmark.p',fact_inf__left__commute) ).

fof(fact_inf__sup__aci_I3_J,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Lattices_Olattice(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_z)) ),
    file('theBenchmark.p',fact_inf__sup__aci_I3_J) ).

fof(fact_inf_Oleft__commute,axiom,
    ! [V_c,V_a,V_b,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_c)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b),V_c)) ),
    file('theBenchmark.p',fact_inf_Oleft__commute) ).

fof(fact_sup__left__idem,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Lattices_Osemilattice__sup(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) ),
    file('theBenchmark.p',fact_sup__left__idem) ).

fof(fact_inf__sup__aci_I8_J,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Lattices_Olattice(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) ),
    file('theBenchmark.p',fact_inf__sup__aci_I8_J) ).

fof(fact_sup_Oleft__idem,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Lattices_Osemilattice__sup(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b) ),
    file('theBenchmark.p',fact_sup_Oleft__idem) ).

fof(fact_inf__left__idem,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) ),
    file('theBenchmark.p',fact_inf__left__idem) ).

fof(fact_inf__sup__aci_I4_J,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Lattices_Olattice(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) ),
    file('theBenchmark.p',fact_inf__sup__aci_I4_J) ).

fof(fact_inf_Oleft__idem,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b) ),
    file('theBenchmark.p',fact_inf_Oleft__idem) ).

fof(fact_sup__inf__absorb,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Lattices_Olattice(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)) = V_x ),
    file('theBenchmark.p',fact_sup__inf__absorb) ).

fof(fact_inf__sup__absorb,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Lattices_Olattice(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)) = V_x ),
    file('theBenchmark.p',fact_inf__sup__absorb) ).

fof(fact_sup__commute,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Lattices_Osemilattice__sup(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_x) ),
    file('theBenchmark.p',fact_sup__commute) ).

fof(fact_inf__sup__aci_I5_J,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Lattices_Olattice(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_x) ),
    file('theBenchmark.p',fact_inf__sup__aci_I5_J) ).

fof(fact_sup_Ocommute,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Lattices_Osemilattice__sup(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b),V_a) ),
    file('theBenchmark.p',fact_sup_Ocommute) ).

fof(fact_inf__commute,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_x) ),
    file('theBenchmark.p',fact_inf__commute) ).

fof(fact_inf__sup__aci_I1_J,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Lattices_Olattice(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_x) ),
    file('theBenchmark.p',fact_inf__sup__aci_I1_J) ).

fof(fact_inf_Ocommute,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b),V_a) ),
    file('theBenchmark.p',fact_inf_Ocommute) ).

fof(fact_sup__idem,axiom,
    ! [V_x,T_a] :
      ( class_Lattices_Osemilattice__sup(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ),
    file('theBenchmark.p',fact_sup__idem) ).

fof(fact_sup_Oidem,axiom,
    ! [V_a,T_a] :
      ( class_Lattices_Osemilattice__sup(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_a) = V_a ),
    file('theBenchmark.p',fact_sup_Oidem) ).

fof(fact_inf__idem,axiom,
    ! [V_x,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ),
    file('theBenchmark.p',fact_inf__idem) ).

fof(fact_inf_Oidem,axiom,
    ! [V_a,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_a) = V_a ),
    file('theBenchmark.p',fact_inf_Oidem) ).

fof(fact_distrib__inf__le,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Lattices_Olattice(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_z))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)))) ),
    file('theBenchmark.p',fact_distrib__inf__le) ).

fof(fact_distrib__sup__le,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Lattices_Olattice(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_z)))) ),
    file('theBenchmark.p',fact_distrib__sup__le) ).

fof(fact_Un__Int__assoc__eq,axiom,
    ! [V_C_2,V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) ),
    file('theBenchmark.p',fact_Un__Int__assoc__eq) ).

fof(fact_Union__Int__subset,axiom,
    ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)))),
    file('theBenchmark.p',fact_Union__Int__subset) ).

fof(fact_inf__sup__ord_I3_J,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Lattices_Olattice(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y))) ),
    file('theBenchmark.p',fact_inf__sup__ord_I3_J) ).

fof(fact_sup__ge1,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Lattices_Osemilattice__sup(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y))) ),
    file('theBenchmark.p',fact_sup__ge1) ).

fof(fact_inf__sup__ord_I4_J,axiom,
    ! [V_x,V_y,T_a] :
      ( class_Lattices_Olattice(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y))) ),
    file('theBenchmark.p',fact_inf__sup__ord_I4_J) ).

fof(fact_sup__ge2,axiom,
    ! [V_x,V_y,T_a] :
      ( class_Lattices_Osemilattice__sup(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y))) ),
    file('theBenchmark.p',fact_sup__ge2) ).

fof(fact_inf__sup__ord_I1_J,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Lattices_Olattice(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_x)) ),
    file('theBenchmark.p',fact_inf__sup__ord_I1_J) ).

fof(fact_inf__le1,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_x)) ),
    file('theBenchmark.p',fact_inf__le1) ).

fof(fact_inf__sup__ord_I2_J,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Lattices_Olattice(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_y)) ),
    file('theBenchmark.p',fact_inf__sup__ord_I2_J) ).

fof(fact_inf__le2,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_y)) ),
    file('theBenchmark.p',fact_inf__le2) ).

fof(fact_le__iff__inf,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Lattices_Osemilattice__inf(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
      <=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) = V_x_2 ) ),
    file('theBenchmark.p',fact_le__iff__inf) ).

fof(fact_le__iff__sup,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Lattices_Osemilattice__sup(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
      <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) = V_y_2 ) ),
    file('theBenchmark.p',fact_le__iff__sup) ).

fof(fact_le__inf__iff,axiom,
    ! [V_z_2,V_y_2,V_x_2,T_b] :
      ( class_Lattices_Osemilattice__inf(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_y_2),V_z_2)))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ),
    file('theBenchmark.p',fact_le__inf__iff) ).

fof(fact_le__sup__iff,axiom,
    ! [V_z_2,V_y_2,V_x_2,T_b] :
      ( class_Lattices_Osemilattice__sup(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2)),V_z_2))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) ) ) ),
    file('theBenchmark.p',fact_le__sup__iff) ).

fof(fact_le__supI1,axiom,
    ! [V_b,V_a,V_x,T_a] :
      ( class_Lattices_Osemilattice__sup(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b))) ) ),
    file('theBenchmark.p',fact_le__supI1) ).

fof(fact_le__supI2,axiom,
    ! [V_a,V_b,V_x,T_a] :
      ( class_Lattices_Osemilattice__sup(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b))) ) ),
    file('theBenchmark.p',fact_le__supI2) ).

fof(fact_le__infI1,axiom,
    ! [V_b,V_x,V_a,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_x)) ) ),
    file('theBenchmark.p',fact_le__infI1) ).

fof(fact_le__infI2,axiom,
    ! [V_a,V_x,V_b,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_x)) ) ),
    file('theBenchmark.p',fact_le__infI2) ).

fof(fact_inf__absorb1,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_x ) ),
    file('theBenchmark.p',fact_inf__absorb1) ).

fof(fact_sup__absorb2,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Lattices_Osemilattice__sup(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_y ) ),
    file('theBenchmark.p',fact_sup__absorb2) ).

fof(fact_inf__absorb2,axiom,
    ! [V_x,V_y,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_y ) ),
    file('theBenchmark.p',fact_inf__absorb2) ).

fof(fact_sup__absorb1,axiom,
    ! [V_x,V_y,T_a] :
      ( class_Lattices_Osemilattice__sup(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_x ) ),
    file('theBenchmark.p',fact_sup__absorb1) ).

fof(fact_le__infI,axiom,
    ! [V_b,V_a,V_x,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b))) ) ) ),
    file('theBenchmark.p',fact_le__infI) ).

fof(fact_inf__greatest,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z))) ) ) ),
    file('theBenchmark.p',fact_inf__greatest) ).

fof(fact_le__supI,axiom,
    ! [V_b,V_x,V_a,T_a] :
      ( class_Lattices_Osemilattice__sup(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)),V_x)) ) ) ),
    file('theBenchmark.p',fact_le__supI) ).

fof(fact_sup__least,axiom,
    ! [V_z,V_x,V_y,T_a] :
      ( class_Lattices_Osemilattice__sup(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)),V_x)) ) ) ),
    file('theBenchmark.p',fact_sup__least) ).

fof(fact_inf__mono,axiom,
    ! [V_d,V_b,V_c,V_a,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_c),V_d))) ) ) ),
    file('theBenchmark.p',fact_inf__mono) ).

fof(fact_sup__mono,axiom,
    ! [V_d,V_b,V_c,V_a,T_a] :
      ( class_Lattices_Osemilattice__sup(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_c),V_d))) ) ) ),
    file('theBenchmark.p',fact_sup__mono) ).

fof(fact_le__infE,axiom,
    ! [V_b,V_a,V_x,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)))
       => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
           => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ),
    file('theBenchmark.p',fact_le__infE) ).

fof(fact_le__supE,axiom,
    ! [V_x,V_b,V_a,T_a] :
      ( class_Lattices_Osemilattice__sup(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)),V_x))
       => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
           => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ),
    file('theBenchmark.p',fact_le__supE) ).

fof(fact_sup__eq__bot__iff,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Lattices_Obounded__lattice__bot(T_b)
     => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) = c_Orderings_Obot__class_Obot(T_b)
      <=> ( V_y_2 = c_Orderings_Obot__class_Obot(T_b)
          & V_x_2 = c_Orderings_Obot__class_Obot(T_b) ) ) ),
    file('theBenchmark.p',fact_sup__eq__bot__iff) ).

fof(fact_sup__bot__right,axiom,
    ! [V_x,T_a] :
      ( class_Lattices_Obounded__lattice__bot(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)) = V_x ),
    file('theBenchmark.p',fact_sup__bot__right) ).

fof(fact_inf__bot__right,axiom,
    ! [V_x,T_a] :
      ( class_Lattices_Obounded__lattice__bot(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Obot__class_Obot(T_a) ),
    file('theBenchmark.p',fact_inf__bot__right) ).

fof(fact_sup__bot__left,axiom,
    ! [V_x,T_a] :
      ( class_Lattices_Obounded__lattice__bot(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = V_x ),
    file('theBenchmark.p',fact_sup__bot__left) ).

fof(fact_inf__bot__left,axiom,
    ! [V_x,T_a] :
      ( class_Lattices_Obounded__lattice__bot(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = c_Orderings_Obot__class_Obot(T_a) ),
    file('theBenchmark.p',fact_inf__bot__left) ).

fof(fact_Compl__Int,axiom,
    ! [V_B_2,V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)),
    file('theBenchmark.p',fact_Compl__Int) ).

fof(fact_Compl__Un,axiom,
    ! [V_B_2,V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)),
    file('theBenchmark.p',fact_Compl__Un) ).

fof(fact_inf__eq__top__iff,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Lattices_Obounded__lattice__top(T_b)
     => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) = c_Orderings_Otop__class_Otop(T_b)
      <=> ( V_y_2 = c_Orderings_Otop__class_Otop(T_b)
          & V_x_2 = c_Orderings_Otop__class_Otop(T_b) ) ) ),
    file('theBenchmark.p',fact_inf__eq__top__iff) ).

fof(fact_inf__top__right,axiom,
    ! [V_x,T_a] :
      ( class_Lattices_Obounded__lattice__top(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)) = V_x ),
    file('theBenchmark.p',fact_inf__top__right) ).

fof(fact_sup__top__right,axiom,
    ! [V_x,T_a] :
      ( class_Lattices_Obounded__lattice__top(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)) = c_Orderings_Otop__class_Otop(T_a) ),
    file('theBenchmark.p',fact_sup__top__right) ).

fof(fact_inf__top__left,axiom,
    ! [V_x,T_a] :
      ( class_Lattices_Obounded__lattice__top(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Otop__class_Otop(T_a)),V_x) = V_x ),
    file('theBenchmark.p',fact_inf__top__left) ).

fof(fact_sup__top__left,axiom,
    ! [V_x,T_a] :
      ( class_Lattices_Obounded__lattice__top(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Orderings_Otop__class_Otop(T_a)),V_x) = c_Orderings_Otop__class_Otop(T_a) ),
    file('theBenchmark.p',fact_sup__top__left) ).

fof(fact_Pow__Int__eq,axiom,
    ! [V_B_2,V_A_2,T_b] : hAPP(c_Set_OPow(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)),hAPP(c_Set_OPow(T_b),V_B_2)),
    file('theBenchmark.p',fact_Pow__Int__eq) ).

fof(fact_Inter__Un__distrib,axiom,
    ! [V_B_2,V_A_2,T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2)),
    file('theBenchmark.p',fact_Inter__Un__distrib) ).

fof(fact_compl__unique,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Lattices_Oboolean__algebra(T_a)
     => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = c_Orderings_Obot__class_Obot(T_a)
       => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = c_Orderings_Otop__class_Otop(T_a)
         => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) = V_y ) ) ),
    file('theBenchmark.p',fact_compl__unique) ).

fof(fact_Inter__Un__subset,axiom,
    ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2))),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)))),
    file('theBenchmark.p',fact_Inter__Un__subset) ).

fof(fact_Un__empty__left,axiom,
    ! [V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = V_B_2,
    file('theBenchmark.p',fact_Un__empty__left) ).

fof(fact_Un__empty__right,axiom,
    ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_A_2,
    file('theBenchmark.p',fact_Un__empty__right) ).

fof(fact_Un__empty,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
    <=> ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
        & V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_Un__empty) ).

fof(fact_Int__empty__left,axiom,
    ! [V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Int__empty__left) ).

fof(fact_Int__empty__right,axiom,
    ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Int__empty__right) ).

fof(fact_disjoint__iff__not__equal,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
         => ! [B_xa] :
              ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_B_2))
             => B_x != B_xa ) ) ),
    file('theBenchmark.p',fact_disjoint__iff__not__equal) ).

fof(fact_Union__disjoint,axiom,
    ! [V_A_2,V_C_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_C_2))
         => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),B_x),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_Union__disjoint) ).

fof(fact_Un__upper1,axiom,
    ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),
    file('theBenchmark.p',fact_Un__upper1) ).

fof(fact_Un__upper2,axiom,
    ! [V_A_2,V_B_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),
    file('theBenchmark.p',fact_Un__upper2) ).

fof(fact_subset__Un__eq,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
    <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ),
    file('theBenchmark.p',fact_subset__Un__eq) ).

fof(fact_Un__absorb1,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ),
    file('theBenchmark.p',fact_Un__absorb1) ).

fof(fact_Un__absorb2,axiom,
    ! [V_A_2,V_B_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ),
    file('theBenchmark.p',fact_Un__absorb2) ).

fof(fact_Un__least,axiom,
    ! [V_B_2,V_C_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2)) ) ),
    file('theBenchmark.p',fact_Un__least) ).

fof(fact_Un__mono,axiom,
    ! [V_D_2,V_B_2,V_C_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2))) ) ),
    file('theBenchmark.p',fact_Un__mono) ).

fof(fact_Un__UNIV__right,axiom,
    ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Un__UNIV__right) ).

fof(fact_Un__UNIV__left,axiom,
    ! [V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Un__UNIV__left) ).

fof(fact_Int__lower1,axiom,
    ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_A_2)),
    file('theBenchmark.p',fact_Int__lower1) ).

fof(fact_Int__lower2,axiom,
    ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_B_2)),
    file('theBenchmark.p',fact_Int__lower2) ).

fof(fact_Int__absorb2,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ),
    file('theBenchmark.p',fact_Int__absorb2) ).

fof(fact_Int__absorb1,axiom,
    ! [V_A_2,V_B_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ),
    file('theBenchmark.p',fact_Int__absorb1) ).

fof(fact_Int__greatest,axiom,
    ! [V_B_2,V_A_2,V_C_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ),
    file('theBenchmark.p',fact_Int__greatest) ).

fof(fact_Int__mono,axiom,
    ! [V_D_2,V_B_2,V_C_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2))) ) ),
    file('theBenchmark.p',fact_Int__mono) ).

fof(fact_Int__UNIV__right,axiom,
    ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = V_A_2,
    file('theBenchmark.p',fact_Int__UNIV__right) ).

fof(fact_Int__UNIV__left,axiom,
    ! [V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = V_B_2,
    file('theBenchmark.p',fact_Int__UNIV__left) ).

fof(fact_Un__Pow__subset,axiom,
    ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)),hAPP(c_Set_OPow(T_b),V_B_2))),hAPP(c_Set_OPow(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))),
    file('theBenchmark.p',fact_Un__Pow__subset) ).

fof(fact_inf__compl__bot,axiom,
    ! [V_x,T_a] :
      ( class_Lattices_Oboolean__algebra(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = c_Orderings_Obot__class_Obot(T_a) ),
    file('theBenchmark.p',fact_inf__compl__bot) ).

fof(fact_compl__inf__bot,axiom,
    ! [V_x,T_a] :
      ( class_Lattices_Oboolean__algebra(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),V_x) = c_Orderings_Obot__class_Obot(T_a) ),
    file('theBenchmark.p',fact_compl__inf__bot) ).

fof(fact_sup__compl__top,axiom,
    ! [V_x,T_a] :
      ( class_Lattices_Oboolean__algebra(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = c_Orderings_Otop__class_Otop(T_a) ),
    file('theBenchmark.p',fact_sup__compl__top) ).

fof(fact_compl__sup__top,axiom,
    ! [V_x,T_a] :
      ( class_Lattices_Oboolean__algebra(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),V_x) = c_Orderings_Otop__class_Otop(T_a) ),
    file('theBenchmark.p',fact_compl__sup__top) ).

fof(fact_ivl__disj__un_I17_J,axiom,
    ! [V_u_2,V_m_2,V_l_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_m_2),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2) ) ) ),
    file('theBenchmark.p',fact_ivl__disj__un_I17_J) ).

fof(fact_ivl__disj__int_I11_J,axiom,
    ! [V_u_2,V_m_2,V_l_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_m_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_ivl__disj__int_I11_J) ).

fof(fact_Compl__disjoint,axiom,
    ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Compl__disjoint) ).

fof(fact_Compl__disjoint2,axiom,
    ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Compl__disjoint2) ).

fof(fact_Compl__partition2,axiom,
    ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Compl__partition2) ).

fof(fact_Compl__partition,axiom,
    ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Compl__partition) ).

fof(fact_ivl__disj__un_I20_J,axiom,
    ! [V_u_2,V_m_2,V_l_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2) ) ) ),
    file('theBenchmark.p',fact_ivl__disj__un_I20_J) ).

fof(fact_ivl__disj__int_I14_J,axiom,
    ! [V_u_2,V_m_2,V_l_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_ivl__disj__int_I14_J) ).

fof(fact_ivl__disj__un_I21_J,axiom,
    ! [V_u_2,V_m_2,V_l_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2) ) ) ),
    file('theBenchmark.p',fact_ivl__disj__un_I21_J) ).

fof(fact_disjoint__eq__subset__Compl,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2))) ),
    file('theBenchmark.p',fact_disjoint__eq__subset__Compl) ).

fof(fact_ivl__disj__int_I15_J,axiom,
    ! [V_u_2,V_m_2,V_l_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_ivl__disj__int_I15_J) ).

fof(fact_ivl__disj__un_I8_J,axiom,
    ! [V_u_2,V_l_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_l_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_u_2) ) ),
    file('theBenchmark.p',fact_ivl__disj__un_I8_J) ).

fof(fact_ivl__disj__un_I22_J,axiom,
    ! [V_u_2,V_m_2,V_l_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2) ) ) ),
    file('theBenchmark.p',fact_ivl__disj__un_I22_J) ).

fof(fact_ivl__disj__int_I4_J,axiom,
    ! [V_u_2,V_l_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_l_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_ivl__disj__int_I4_J) ).

fof(fact_ivl__disj__int_I2_J,axiom,
    ! [V_u_2,V_l_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_l_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_ivl__disj__int_I2_J) ).

fof(fact_ivl__disj__int_I16_J,axiom,
    ! [V_u_2,V_m_2,V_l_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_ivl__disj__int_I16_J) ).

fof(fact_ivl__disj__int_I12_J,axiom,
    ! [V_u_2,V_m_2,V_l_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_ivl__disj__int_I12_J) ).

fof(fact_ivl__disj__int_I13_J,axiom,
    ! [V_u_2,V_m_2,V_l_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_ivl__disj__int_I13_J) ).

fof(fact_ivl__disj__un_I14_J,axiom,
    ! [V_u_2,V_l_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_l_2) ) ),
    file('theBenchmark.p',fact_ivl__disj__un_I14_J) ).

fof(fact_ivl__disj__int_I9_J,axiom,
    ! [V_u_2,V_m_2,V_l_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_m_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_ivl__disj__int_I9_J) ).

fof(fact_ivl__disj__int_I8_J,axiom,
    ! [V_u_2,V_l_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_ivl__disj__int_I8_J) ).

fof(fact_ivl__disj__int_I7_J,axiom,
    ! [V_u_2,V_l_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_ivl__disj__int_I7_J) ).

fof(fact_ivl__disj__un_I9_J,axiom,
    ! [V_u_2,V_l_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_l_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_u_2) ) ),
    file('theBenchmark.p',fact_ivl__disj__un_I9_J) ).

fof(fact_ivl__disj__int_I3_J,axiom,
    ! [V_u_2,V_l_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_l_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_ivl__disj__int_I3_J) ).

fof(fact_ivl__disj__int_I1_J,axiom,
    ! [V_u_2,V_l_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_l_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_ivl__disj__int_I1_J) ).

fof(fact_ivl__disj__int_I10_J,axiom,
    ! [V_u_2,V_m_2,V_l_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_ivl__disj__int_I10_J) ).

fof(fact_compl__eq__compl__iff,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Lattices_Oboolean__algebra(T_b)
     => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)
      <=> V_x_2 = V_y_2 ) ),
    file('theBenchmark.p',fact_compl__eq__compl__iff) ).

fof(fact_neg__equal__iff__equal,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( class_Groups_Ogroup__add(T_b)
     => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
      <=> V_a_2 = V_b_2 ) ),
    file('theBenchmark.p',fact_neg__equal__iff__equal) ).

fof(fact_minus__equation__iff,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( class_Groups_Ogroup__add(T_b)
     => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = V_b_2
      <=> hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) = V_a_2 ) ),
    file('theBenchmark.p',fact_minus__equation__iff) ).

fof(fact_equation__minus__iff,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( class_Groups_Ogroup__add(T_b)
     => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
      <=> V_b_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) ) ),
    file('theBenchmark.p',fact_equation__minus__iff) ).

fof(fact_double__compl,axiom,
    ! [V_x,T_a] :
      ( class_Lattices_Oboolean__algebra(T_a)
     => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = V_x ),
    file('theBenchmark.p',fact_double__compl) ).

fof(fact_minus__minus,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Ogroup__add(T_a)
     => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = V_a ),
    file('theBenchmark.p',fact_minus__minus) ).

fof(fact_ivl__disj__un_I11_J,axiom,
    ! [V_u_2,V_l_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_u_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_l_2) ) ),
    file('theBenchmark.p',fact_ivl__disj__un_I11_J) ).

fof(fact_ivl__disj__int_I6_J,axiom,
    ! [V_u_2,V_l_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_ivl__disj__int_I6_J) ).

fof(fact_ivl__disj__un_I19_J,axiom,
    ! [V_u_2,V_m_2,V_l_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_m_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2) ) ) ),
    file('theBenchmark.p',fact_ivl__disj__un_I19_J) ).

fof(fact_ivl__disj__un_I18_J,axiom,
    ! [V_u_2,V_m_2,V_l_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_u_2))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_m_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2) ) ) ),
    file('theBenchmark.p',fact_ivl__disj__un_I18_J) ).

fof(fact_ivl__disj__un_I5_J,axiom,
    ! [V_u_2,V_l_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2) ) ),
    file('theBenchmark.p',fact_ivl__disj__un_I5_J) ).

fof(fact_ivl__disj__un_I6_J,axiom,
    ! [V_u_2,V_l_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2) ) ),
    file('theBenchmark.p',fact_ivl__disj__un_I6_J) ).

fof(fact_ivl__disj__un_I12_J,axiom,
    ! [V_u_2,V_l_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_u_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_l_2) ) ),
    file('theBenchmark.p',fact_ivl__disj__un_I12_J) ).

fof(fact_ivl__disj__un_I7_J,axiom,
    ! [V_u_2,V_l_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_l_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_u_2) ) ),
    file('theBenchmark.p',fact_ivl__disj__un_I7_J) ).

fof(fact_ivl__disj__un_I1_J,axiom,
    ! [V_l_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_l_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_l_2) ),
    file('theBenchmark.p',fact_ivl__disj__un_I1_J) ).

fof(fact_ivl__disj__un_I16_J,axiom,
    ! [V_u_2,V_m_2,V_l_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_u_2))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2) ) ) ),
    file('theBenchmark.p',fact_ivl__disj__un_I16_J) ).

fof(fact_atMost__Int__atLeast,axiom,
    ! [V_n_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_n_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_n_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_n_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ),
    file('theBenchmark.p',fact_atMost__Int__atLeast) ).

fof(fact_ivl__disj__un_I2_J,axiom,
    ! [V_u_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_u_2) ),
    file('theBenchmark.p',fact_ivl__disj__un_I2_J) ).

fof(fact_ivl__disj__un_I15_J,axiom,
    ! [V_u_2,V_m_2,V_l_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_m_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_m_2),V_u_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2) ) ) ),
    file('theBenchmark.p',fact_ivl__disj__un_I15_J) ).

fof(fact_linorder__cases,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
       => ( V_x != V_y
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ),
    file('theBenchmark.p',fact_linorder__cases) ).

fof(fact_order__less__asym,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Opreorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ),
    file('theBenchmark.p',fact_order__less__asym) ).

fof(fact_xt1_I10_J,axiom,
    ! [V_z,V_x,V_y,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ),
    file('theBenchmark.p',fact_xt1_I10_J) ).

fof(fact_order__less__trans,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Orderings_Opreorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ),
    file('theBenchmark.p',fact_order__less__trans) ).

fof(fact_xt1_I2_J,axiom,
    ! [V_c,V_a,V_b,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
       => ( V_b = V_c
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ),
    file('theBenchmark.p',fact_xt1_I2_J) ).

fof(fact_ord__less__eq__trans,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Orderings_Oord(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
       => ( V_b = V_c
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ),
    file('theBenchmark.p',fact_ord__less__eq__trans) ).

fof(fact_xt1_I1_J,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( V_a = V_b
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_b))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ),
    file('theBenchmark.p',fact_xt1_I1_J) ).

fof(fact_ord__eq__less__trans,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Orderings_Oord(T_a)
     => ( V_a = V_b
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ),
    file('theBenchmark.p',fact_ord__eq__less__trans) ).

fof(fact_xt1_I9_J,axiom,
    ! [V_a,V_b,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ),
    file('theBenchmark.p',fact_xt1_I9_J) ).

fof(fact_order__less__asym_H,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Orderings_Opreorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ),
    file('theBenchmark.p',fact_order__less__asym_H) ).

fof(fact_order__less__imp__not__eq2,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
       => V_y != V_x ) ),
    file('theBenchmark.p',fact_order__less__imp__not__eq2) ).

fof(fact_order__less__imp__not__eq,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
       => V_x != V_y ) ),
    file('theBenchmark.p',fact_order__less__imp__not__eq) ).

fof(fact_order__less__imp__not__less,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Opreorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ),
    file('theBenchmark.p',fact_order__less__imp__not__less) ).

fof(fact_order__less__not__sym,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Opreorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ),
    file('theBenchmark.p',fact_order__less__not__sym) ).

fof(fact_less__imp__neq,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
       => V_x != V_y ) ),
    file('theBenchmark.p',fact_less__imp__neq) ).

fof(fact_linorder__neqE,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( V_x != V_y
       => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ),
    file('theBenchmark.p',fact_linorder__neqE) ).

fof(fact_linorder__antisym__conv3,axiom,
    ! [V_x_2,V_y_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2))
       => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
        <=> V_x_2 = V_y_2 ) ) ),
    file('theBenchmark.p',fact_linorder__antisym__conv3) ).

fof(fact_insert__code,axiom,
    ! [V_x_2,V_A_2,V_y_2,T_b] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),V_A_2),V_x_2))
    <=> ( hBOOL(hAPP(V_A_2,V_x_2))
        | V_y_2 = V_x_2 ) ),
    file('theBenchmark.p',fact_insert__code) ).

fof(fact_insert__commute,axiom,
    ! [V_A_2,V_y_2,V_x_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),V_A_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),
    file('theBenchmark.p',fact_insert__commute) ).

fof(fact_insert__absorb2,axiom,
    ! [V_A_2,V_x_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2),
    file('theBenchmark.p',fact_insert__absorb2) ).

fof(fact_linorder__less__linear,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
        | V_x = V_y
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ),
    file('theBenchmark.p',fact_linorder__less__linear) ).

fof(fact_not__less__iff__gr__or__eq,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
      <=> ( V_x_2 = V_y_2
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) ) ) ),
    file('theBenchmark.p',fact_not__less__iff__gr__or__eq) ).

fof(fact_linorder__neq__iff,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( V_x_2 != V_y_2
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) ) ) ),
    file('theBenchmark.p',fact_linorder__neq__iff) ).

fof(fact_order__less__irrefl,axiom,
    ! [V_x,T_a] :
      ( class_Orderings_Opreorder(T_a)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_x)) ),
    file('theBenchmark.p',fact_order__less__irrefl) ).

fof(fact_lessThan__strict__subset__iff,axiom,
    ! [V_n_2,V_m_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_m_2)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_n_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_n_2)) ) ),
    file('theBenchmark.p',fact_lessThan__strict__subset__iff) ).

fof(fact_atLeastatMost__psubset__iff,axiom,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2)))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_d_2))
          & ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_d_2))
                | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_a_2)) )
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ) ),
    file('theBenchmark.p',fact_atLeastatMost__psubset__iff) ).

fof(fact_less__fun__def,axiom,
    ! [V_g_2,V_f_2,T_b,T_c] :
      ( class_Orderings_Oord(T_c)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,T_c)),V_f_2),V_g_2))
      <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_g_2),V_f_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) ) ) ),
    file('theBenchmark.p',fact_less__fun__def) ).

fof(fact_xt1_I8_J,axiom,
    ! [V_z,V_x,V_y,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ),
    file('theBenchmark.p',fact_xt1_I8_J) ).

fof(fact_order__le__less__trans,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Orderings_Opreorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ),
    file('theBenchmark.p',fact_order__le__less__trans) ).

fof(fact_xt1_I7_J,axiom,
    ! [V_z,V_x,V_y,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ),
    file('theBenchmark.p',fact_xt1_I7_J) ).

fof(fact_order__less__le__trans,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Orderings_Opreorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ),
    file('theBenchmark.p',fact_order__less__le__trans) ).

fof(fact_xt1_I11_J,axiom,
    ! [V_a,V_b,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
       => ( V_a != V_b
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ),
    file('theBenchmark.p',fact_xt1_I11_J) ).

fof(fact_order__le__neq__trans,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
       => ( V_a != V_b
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ),
    file('theBenchmark.p',fact_order__le__neq__trans) ).

fof(fact_order__le__imp__less__or__eq,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
       => ( V_x = V_y
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ),
    file('theBenchmark.p',fact_order__le__imp__less__or__eq) ).

fof(fact_linorder__antisym__conv2,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
       => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
        <=> V_x_2 = V_y_2 ) ) ),
    file('theBenchmark.p',fact_linorder__antisym__conv2) ).

fof(fact_order__less__imp__le,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Opreorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ),
    file('theBenchmark.p',fact_order__less__imp__le) ).

fof(fact_leD,axiom,
    ! [V_x,V_y,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ),
    file('theBenchmark.p',fact_leD) ).

fof(fact_xt1_I12_J,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( V_a != V_b
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ),
    file('theBenchmark.p',fact_xt1_I12_J) ).

fof(fact_order__neq__le__trans,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( V_a != V_b
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ),
    file('theBenchmark.p',fact_order__neq__le__trans) ).

fof(fact_linorder__antisym__conv1,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
        <=> V_x_2 = V_y_2 ) ) ),
    file('theBenchmark.p',fact_linorder__antisym__conv1) ).

fof(fact_not__leE,axiom,
    ! [V_x,V_y,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ),
    file('theBenchmark.p',fact_not__leE) ).

fof(fact_leI,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ),
    file('theBenchmark.p',fact_leI) ).

fof(fact_order__le__less,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
      <=> ( V_x_2 = V_y_2
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) ) ) ),
    file('theBenchmark.p',fact_order__le__less) ).

fof(fact_less__le__not__le,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Orderings_Opreorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
      <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ),
    file('theBenchmark.p',fact_less__le__not__le) ).

fof(fact_order__less__le,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
      <=> ( V_x_2 != V_y_2
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ),
    file('theBenchmark.p',fact_order__less__le) ).

fof(fact_linorder__le__less__linear,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ),
    file('theBenchmark.p',fact_linorder__le__less__linear) ).

fof(fact_linorder__not__le,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) ) ),
    file('theBenchmark.p',fact_linorder__not__le) ).

fof(fact_linorder__not__less,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ),
    file('theBenchmark.p',fact_linorder__not__less) ).

fof(fact_singleton__inject,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))
     => V_a_2 = V_b_2 ),
    file('theBenchmark.p',fact_singleton__inject) ).

fof(fact_doubleton__eq__iff,axiom,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
      ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(T_b),V_c_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_d_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
    <=> ( ( V_b_2 = V_c_2
          & V_a_2 = V_d_2 )
        | ( V_b_2 = V_d_2
          & V_a_2 = V_c_2 ) ) ),
    file('theBenchmark.p',fact_doubleton__eq__iff) ).

fof(fact_insert__not__empty,axiom,
    ! [V_A_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_insert__not__empty) ).

fof(fact_empty__not__insert,axiom,
    ! [V_A_2,V_a_2,T_b] : c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2),
    file('theBenchmark.p',fact_empty__not__insert) ).

fof(fact_insert__mono,axiom,
    ! [V_a_2,V_D_2,V_C_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_C_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_D_2))) ),
    file('theBenchmark.p',fact_insert__mono) ).

fof(fact_subset__insertI2,axiom,
    ! [V_b_2,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) ),
    file('theBenchmark.p',fact_subset__insertI2) ).

fof(fact_subset__insertI,axiom,
    ! [V_a_2,V_B_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2))),
    file('theBenchmark.p',fact_subset__insertI) ).

fof(fact_not__psubset__empty,axiom,
    ! [V_A_2,T_b] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),
    file('theBenchmark.p',fact_not__psubset__empty) ).

fof(fact_Un__insert__left,axiom,
    ! [V_C_2,V_B_2,V_a_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)),
    file('theBenchmark.p',fact_Un__insert__left) ).

fof(fact_Un__insert__right,axiom,
    ! [V_B_2,V_a_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),
    file('theBenchmark.p',fact_Un__insert__right) ).

fof(fact_insert__inter__insert,axiom,
    ! [V_B_2,V_A_2,V_a_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),
    file('theBenchmark.p',fact_insert__inter__insert) ).

fof(fact_less__supI1,axiom,
    ! [V_b,V_a,V_x,T_a] :
      ( class_Lattices_Osemilattice__sup(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b))) ) ),
    file('theBenchmark.p',fact_less__supI1) ).

fof(fact_less__supI2,axiom,
    ! [V_a,V_b,V_x,T_a] :
      ( class_Lattices_Osemilattice__sup(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b))) ) ),
    file('theBenchmark.p',fact_less__supI2) ).

fof(fact_less__infI1,axiom,
    ! [V_b,V_x,V_a,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_x)) ) ),
    file('theBenchmark.p',fact_less__infI1) ).

fof(fact_less__infI2,axiom,
    ! [V_a,V_x,V_b,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_x)) ) ),
    file('theBenchmark.p',fact_less__infI2) ).

fof(fact_less__minus__iff,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( class_Groups_Oordered__ab__group__add(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) ) ),
    file('theBenchmark.p',fact_less__minus__iff) ).

fof(fact_minus__less__iff,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( class_Groups_Oordered__ab__group__add(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),V_a_2)) ) ),
    file('theBenchmark.p',fact_minus__less__iff) ).

fof(fact_neg__less__iff__less,axiom,
    ! [V_a_2,V_b_2,T_b] :
      ( class_Groups_Oordered__ab__group__add(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ),
    file('theBenchmark.p',fact_neg__less__iff__less) ).

fof(fact_subset__psubset__trans,axiom,
    ! [V_C_2,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ),
    file('theBenchmark.p',fact_subset__psubset__trans) ).

fof(fact_psubset__subset__trans,axiom,
    ! [V_C_2,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ),
    file('theBenchmark.p',fact_psubset__subset__trans) ).

fof(fact_psubset__imp__subset,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    file('theBenchmark.p',fact_psubset__imp__subset) ).

fof(fact_subset__iff__psubset__eq,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
    <=> ( V_A_2 = V_B_2
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
    file('theBenchmark.p',fact_subset__iff__psubset__eq) ).

fof(fact_psubset__eq,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
    <=> ( V_A_2 != V_B_2
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
    file('theBenchmark.p',fact_psubset__eq) ).

fof(fact_atLeastLessThan__inj_I2_J,axiom,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2))
           => V_b_2 = V_d_2 ) ) ) ),
    file('theBenchmark.p',fact_atLeastLessThan__inj_I2_J) ).

fof(fact_atLeastLessThan__inj_I1_J,axiom,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2))
           => V_a_2 = V_c_2 ) ) ) ),
    file('theBenchmark.p',fact_atLeastLessThan__inj_I1_J) ).

fof(fact_atLeastLessThan__eq__iff,axiom,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2))
         => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)
          <=> ( V_b_2 = V_d_2
              & V_a_2 = V_c_2 ) ) ) ) ),
    file('theBenchmark.p',fact_atLeastLessThan__eq__iff) ).

fof(fact_less__Sup__iff,axiom,
    ! [V_S_2,V_a_2,T_b] :
      ( ( class_Orderings_Olinorder(T_b)
        & class_Complete__Lattice_Ocomplete__lattice(T_b) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_S_2)))
      <=> ? [B_x] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),B_x))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) ) ) ),
    file('theBenchmark.p',fact_less__Sup__iff) ).

fof(fact_Inf__less__iff,axiom,
    ! [V_a_2,V_S_2,T_b] :
      ( ( class_Orderings_Olinorder(T_b)
        & class_Complete__Lattice_Ocomplete__lattice(T_b) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Complete__Lattice_OInf__class_OInf(T_b,V_S_2)),V_a_2))
      <=> ? [B_x] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_a_2))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) ) ) ),
    file('theBenchmark.p',fact_Inf__less__iff) ).

fof(fact_strict__monoD,axiom,
    ! [V_y_2,V_x_2,V_f_2,T_b,T_c] :
      ( ( class_Orderings_Oorder(T_b)
        & class_Orderings_Oorder(T_c) )
     => ( c_Orderings_Oorder__class_Ostrict__mono(T_b,T_c,V_f_2)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) ) ) ),
    file('theBenchmark.p',fact_strict__monoD) ).

fof(fact_strict__mono__less,axiom,
    ! [V_y_2,V_x_2,V_f_2,T_b,T_c] :
      ( ( class_Orderings_Olinorder(T_b)
        & class_Orderings_Oorder(T_c) )
     => ( c_Orderings_Oorder__class_Ostrict__mono(T_b,T_c,V_f_2)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) ) ) ),
    file('theBenchmark.p',fact_strict__mono__less) ).

fof(fact_ivl__disj__un_I3_J,axiom,
    ! [V_u_2,V_l_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2) ) ),
    file('theBenchmark.p',fact_ivl__disj__un_I3_J) ).

fof(fact_subset__singletonD,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))
     => ( V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))
        | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_subset__singletonD) ).

fof(fact_insert__is__Un,axiom,
    ! [V_A_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_A_2),
    file('theBenchmark.p',fact_insert__is__Un) ).

fof(fact_ivl__disj__un_I4_J,axiom,
    ! [V_u_2,V_l_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2) ) ),
    file('theBenchmark.p',fact_ivl__disj__un_I4_J) ).

fof(fact_atLeastAtMost__singleton,axiom,
    ! [V_a_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_a_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ),
    file('theBenchmark.p',fact_atLeastAtMost__singleton) ).

fof(fact_atLeastAtMost__singleton__iff,axiom,
    ! [V_c_2,V_b_2,V_a_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => ( c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))
      <=> ( V_b_2 = V_c_2
          & V_a_2 = V_b_2 ) ) ),
    file('theBenchmark.p',fact_atLeastAtMost__singleton__iff) ).

fof(fact_atLeastAtMost__singleton_H,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => ( V_a_2 = V_b_2
       => c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ),
    file('theBenchmark.p',fact_atLeastAtMost__singleton_H) ).

fof(fact_Sup__singleton,axiom,
    ! [V_a_2,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_a_2 ),
    file('theBenchmark.p',fact_Sup__singleton) ).

fof(fact_Sup__insert,axiom,
    ! [V_A_2,V_a_2,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2)) ),
    file('theBenchmark.p',fact_Sup__insert) ).

fof(fact_atLeastatMost__empty,axiom,
    ! [V_a_2,V_b_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2))
       => c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_atLeastatMost__empty) ).

fof(fact_atLeastLessThan__empty__iff2,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ),
    file('theBenchmark.p',fact_atLeastLessThan__empty__iff2) ).

fof(fact_atLeastLessThan__empty__iff,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ),
    file('theBenchmark.p',fact_atLeastLessThan__empty__iff) ).

fof(fact_Inf__singleton,axiom,
    ! [V_a_2,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_a_2 ),
    file('theBenchmark.p',fact_Inf__singleton) ).

fof(fact_Inf__insert,axiom,
    ! [V_A_2,V_a_2,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2)) ),
    file('theBenchmark.p',fact_Inf__insert) ).

fof(fact_Union__insert,axiom,
    ! [V_B_2,V_a_2,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_a_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)),
    file('theBenchmark.p',fact_Union__insert) ).

fof(fact_greaterThanAtMost__empty__iff2,axiom,
    ! [V_l_2,V_k_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_k_2,V_l_2)
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2)) ) ),
    file('theBenchmark.p',fact_greaterThanAtMost__empty__iff2) ).

fof(fact_greaterThanAtMost__empty__iff,axiom,
    ! [V_l_2,V_k_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => ( c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2)) ) ),
    file('theBenchmark.p',fact_greaterThanAtMost__empty__iff) ).

fof(fact_Inter__insert,axiom,
    ! [V_B_2,V_a_2,T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_a_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2)),
    file('theBenchmark.p',fact_Inter__insert) ).

fof(fact_hoare__derivs_Oinsert,axiom,
    ! [V_tsa_2,V_t_2,V_G_2,T_b] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),V_t_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
     => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_tsa_2)
       => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),V_t_2),V_tsa_2)) ) ),
    file('theBenchmark.p',fact_hoare__derivs_Oinsert) ).

fof(fact_Sup__binary,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),V_b_2) ),
    file('theBenchmark.p',fact_Sup__binary) ).

fof(fact_Inf__binary,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),V_b_2) ),
    file('theBenchmark.p',fact_Inf__binary) ).

fof(fact_Un__eq__Union,axiom,
    ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_B_2),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))))),
    file('theBenchmark.p',fact_Un__eq__Union) ).

fof(fact_Pow__empty,axiom,
    ! [T_b] : hAPP(c_Set_OPow(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))),
    file('theBenchmark.p',fact_Pow__empty) ).

fof(fact_Int__eq__Inter,axiom,
    ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_B_2),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))))),
    file('theBenchmark.p',fact_Int__eq__Inter) ).

fof(fact_the__elem__eq,axiom,
    ! [V_x_2,T_b] : c_Set_Othe__elem(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2,
    file('theBenchmark.p',fact_the__elem__eq) ).

fof(fact_Pow__insert,axiom,
    ! [V_A_2,V_a_2,T_b] : hAPP(c_Set_OPow(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)),hAPP(c_Set_Oimage(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oinsert(T_b),V_a_2)),hAPP(c_Set_OPow(T_b),V_A_2))),
    file('theBenchmark.p',fact_Pow__insert) ).

fof(fact_Inf__fin_Oidem,axiom,
    ! [V_x,T_a] :
      ( class_Lattices_Olattice(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ),
    file('theBenchmark.p',fact_Inf__fin_Oidem) ).

fof(fact_Sup__fin_Oidem,axiom,
    ! [V_x,T_a] :
      ( class_Lattices_Olattice(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ),
    file('theBenchmark.p',fact_Sup__fin_Oidem) ).

fof(fact_linorder__neqE__linordered__idom,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => ( V_x != V_y
       => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ),
    file('theBenchmark.p',fact_linorder__neqE__linordered__idom) ).

fof(fact_Int__atLeastAtMostL2,axiom,
    ! [V_c_2,V_b_2,V_a_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_c_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),V_b_2) ),
    file('theBenchmark.p',fact_Int__atLeastAtMostL2) ).

fof(fact_Int__atLeastAtMostR2,axiom,
    ! [V_d_2,V_c_2,V_a_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_a_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),V_d_2) ),
    file('theBenchmark.p',fact_Int__atLeastAtMostR2) ).

fof(fact_image__uminus__atMost,axiom,
    ! [V_x_2,T_b] :
      ( class_Groups_Oordered__ab__group__add(T_b)
     => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ),
    file('theBenchmark.p',fact_image__uminus__atMost) ).

fof(fact_image__uminus__atLeast,axiom,
    ! [V_x_2,T_b] :
      ( class_Groups_Oordered__ab__group__add(T_b)
     => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ),
    file('theBenchmark.p',fact_image__uminus__atLeast) ).

fof(fact_image__uminus__lessThan,axiom,
    ! [V_x_2,T_b] :
      ( class_Groups_Oordered__ab__group__add(T_b)
     => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ),
    file('theBenchmark.p',fact_image__uminus__lessThan) ).

fof(fact_psubset__trans,axiom,
    ! [V_C_2,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ),
    file('theBenchmark.p',fact_psubset__trans) ).

fof(fact_Max_Oidem,axiom,
    ! [V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_x) = V_x ),
    file('theBenchmark.p',fact_Max_Oidem) ).

fof(fact_min__max_Osup_Oidem,axiom,
    ! [V_a,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_a) = V_a ),
    file('theBenchmark.p',fact_min__max_Osup_Oidem) ).

fof(fact_min__max_Osup_Ocommute,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b),V_a) ),
    file('theBenchmark.p',fact_min__max_Osup_Ocommute) ).

fof(fact_min__max_Osup__commute,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_x) ),
    file('theBenchmark.p',fact_min__max_Osup__commute) ).

fof(fact_min__max_Osup_Oleft__idem,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b) ),
    file('theBenchmark.p',fact_min__max_Osup_Oleft__idem) ).

fof(fact_min__max_Osup__left__idem,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) ),
    file('theBenchmark.p',fact_min__max_Osup__left__idem) ).

fof(fact_min__max_Osup_Oleft__commute,axiom,
    ! [V_c,V_a,V_b,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_c)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b),V_c)) ),
    file('theBenchmark.p',fact_min__max_Osup_Oleft__commute) ).

fof(fact_min__max_Osup__left__commute,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_z)) ),
    file('theBenchmark.p',fact_min__max_Osup__left__commute) ).

fof(fact_min__max_Osup_Oassoc,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b),V_c)) ),
    file('theBenchmark.p',fact_min__max_Osup_Oassoc) ).

fof(fact_min__max_Osup__assoc,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)) ),
    file('theBenchmark.p',fact_min__max_Osup__assoc) ).

fof(fact_image__Pow__surj,axiom,
    ! [V_B_2,V_A_2,V_f_2,T_b,T_c] :
      ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_B_2
     => hAPP(c_Set_Oimage(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_c,T_b,V_f_2)),hAPP(c_Set_OPow(T_c),V_A_2)) = hAPP(c_Set_OPow(T_b),V_B_2) ),
    file('theBenchmark.p',fact_image__Pow__surj) ).

fof(fact_empty__is__image,axiom,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)
    <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_empty__is__image) ).

fof(fact_image__empty,axiom,
    ! [V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_image__empty) ).

fof(fact_image__is__empty,axiom,
    ! [V_A_2,V_f_2,T_b,T_c] :
      ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
    <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_image__is__empty) ).

fof(fact_image__insert,axiom,
    ! [V_B_2,V_a_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_B_2)),
    file('theBenchmark.p',fact_image__insert) ).

fof(fact_le__maxI1,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y))) ),
    file('theBenchmark.p',fact_le__maxI1) ).

fof(fact_le__maxI2,axiom,
    ! [V_x,V_y,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y))) ),
    file('theBenchmark.p',fact_le__maxI2) ).

fof(fact_min__max_Ole__iff__sup,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
      <=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2) = V_y_2 ) ),
    file('theBenchmark.p',fact_min__max_Ole__iff__sup) ).

fof(fact_min__max_Ole__sup__iff,axiom,
    ! [V_z_2,V_y_2,V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2)),V_z_2))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) ) ) ),
    file('theBenchmark.p',fact_min__max_Ole__sup__iff) ).

fof(fact_min__max_Ole__supI1,axiom,
    ! [V_b,V_a,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b))) ) ),
    file('theBenchmark.p',fact_min__max_Ole__supI1) ).

fof(fact_min__max_Ole__supI2,axiom,
    ! [V_a,V_b,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b))) ) ),
    file('theBenchmark.p',fact_min__max_Ole__supI2) ).

fof(fact_min__max_Osup__absorb2,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
       => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_y ) ),
    file('theBenchmark.p',fact_min__max_Osup__absorb2) ).

fof(fact_min__max_Osup__absorb1,axiom,
    ! [V_x,V_y,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
       => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_x ) ),
    file('theBenchmark.p',fact_min__max_Osup__absorb1) ).

fof(fact_min__max_Ole__supI,axiom,
    ! [V_b,V_x,V_a,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)),V_x)) ) ) ),
    file('theBenchmark.p',fact_min__max_Ole__supI) ).

fof(fact_min__max_Osup__least,axiom,
    ! [V_z,V_x,V_y,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)),V_x)) ) ) ),
    file('theBenchmark.p',fact_min__max_Osup__least) ).

fof(fact_min__max_Osup__mono,axiom,
    ! [V_d,V_b,V_c,V_a,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_c),V_d))) ) ) ),
    file('theBenchmark.p',fact_min__max_Osup__mono) ).

fof(fact_min__max_Ole__supE,axiom,
    ! [V_x,V_b,V_a,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)),V_x))
       => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
           => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ),
    file('theBenchmark.p',fact_min__max_Ole__supE) ).

fof(fact_le__max__iff__disj,axiom,
    ! [V_y_2,V_x_2,V_z_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2)))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_y_2))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_x_2)) ) ) ),
    file('theBenchmark.p',fact_le__max__iff__disj) ).

fof(fact_less__max__iff__disj,axiom,
    ! [V_y_2,V_x_2,V_z_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2)))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2)) ) ) ),
    file('theBenchmark.p',fact_less__max__iff__disj) ).

fof(fact_max__less__iff__conj,axiom,
    ! [V_z_2,V_y_2,V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2)),V_z_2))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2)) ) ) ),
    file('theBenchmark.p',fact_max__less__iff__conj) ).

fof(fact_min__max_Oless__supI1,axiom,
    ! [V_b,V_a,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b))) ) ),
    file('theBenchmark.p',fact_min__max_Oless__supI1) ).

fof(fact_min__max_Oless__supI2,axiom,
    ! [V_a,V_b,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b))) ) ),
    file('theBenchmark.p',fact_min__max_Oless__supI2) ).

fof(fact_subset__image__iff,axiom,
    ! [V_A_2,V_f_2,T_c,V_B_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
    <=> ? [B_AA] :
          ( V_B_2 = hAPP(c_Set_Oimage(T_c,T_b,V_f_2),B_AA)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),B_AA),V_A_2)) ) ),
    file('theBenchmark.p',fact_subset__image__iff) ).

fof(fact_image__mono,axiom,
    ! [V_f_2,T_c,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2))) ),
    file('theBenchmark.p',fact_image__mono) ).

fof(fact_image__Un,axiom,
    ! [V_B_2,V_A_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_B_2)),
    file('theBenchmark.p',fact_image__Un) ).

fof(fact_sup__max,axiom,
    ! [T_b] :
      ( ( class_Orderings_Olinorder(T_b)
        & class_Lattices_Osemilattice__sup(T_b) )
     => c_Lattices_Osemilattice__sup__class_Osup(T_b) = c_Orderings_Oord__class_Omax(T_b) ),
    file('theBenchmark.p',fact_sup__max) ).

fof(fact_image__Pow__mono,axiom,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),V_B_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_c,T_b,V_f_2)),hAPP(c_Set_OPow(T_c),V_A_2))),hAPP(c_Set_OPow(T_b),V_B_2))) ),
    file('theBenchmark.p',fact_image__Pow__mono) ).

fof(fact_image__Int__subset,axiom,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_B_2)))),
    file('theBenchmark.p',fact_image__Int__subset) ).

fof(fact_image__uminus__atLeastAtMost,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Groups_Oordered__ab__group__add(T_b)
     => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_x_2,V_y_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ),
    file('theBenchmark.p',fact_image__uminus__atLeastAtMost) ).

fof(fact_image__uminus__greaterThanLessThan,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Groups_Oordered__ab__group__add(T_b)
     => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_x_2,V_y_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ),
    file('theBenchmark.p',fact_image__uminus__greaterThanLessThan) ).

fof(fact_image__uminus__atLeastLessThan,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Groups_Oordered__ab__group__add(T_b)
     => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_x_2),V_y_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ),
    file('theBenchmark.p',fact_image__uminus__atLeastLessThan) ).

fof(fact_image__uminus__greaterThanAtMost,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Groups_Oordered__ab__group__add(T_b)
     => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_x_2,V_y_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ),
    file('theBenchmark.p',fact_image__uminus__greaterThanAtMost) ).

fof(fact_image__uminus__greaterThan,axiom,
    ! [V_x_2,T_b] :
      ( class_Groups_Oordered__ab__group__add(T_b)
     => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ),
    file('theBenchmark.p',fact_image__uminus__greaterThan) ).

fof(fact_surj__Compl__image__subset,axiom,
    ! [V_A_2,V_f_2,T_b,T_c] :
      ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)))) ),
    file('theBenchmark.p',fact_surj__Compl__image__subset) ).

fof(fact_Cantors__paradox,axiom,
    ! [V_A_2,T_b] :
      ~ ? [B_f] : hAPP(c_Set_Oimage(T_b,tc_fun(T_b,tc_HOL_Obool),B_f),V_A_2) = hAPP(c_Set_OPow(T_b),V_A_2),
    file('theBenchmark.p',fact_Cantors__paradox) ).

fof(fact_max__ord__max,axiom,
    ! [T_b] :
      ( class_Orderings_Oord(T_b)
     => c_Orderings_Oord__class_Omax(T_b) = c_Orderings_Oord_Omax(T_b,c_Orderings_Oord__class_Oless__eq(T_b)) ),
    file('theBenchmark.p',fact_max__ord__max) ).

fof(fact_min__max_Omono__sup,axiom,
    ! [V_B_2,V_A_2,V_f_2,T_b,T_c] :
      ( ( class_Orderings_Olinorder(T_b)
        & class_Lattices_Osemilattice__sup(T_c) )
     => ( c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),hAPP(V_f_2,V_A_2)),hAPP(V_f_2,V_B_2))),hAPP(V_f_2,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_A_2),V_B_2)))) ) ),
    file('theBenchmark.p',fact_min__max_Omono__sup) ).

fof(fact_min__max_OSup__fin_Osingleton,axiom,
    ! [V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ),
    file('theBenchmark.p',fact_min__max_OSup__fin_Osingleton) ).

fof(fact_Int__atLeastAtMostR1,axiom,
    ! [V_d_2,V_c_2,V_b_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ),
    file('theBenchmark.p',fact_Int__atLeastAtMostR1) ).

fof(fact_Int__atLeastAtMostL1,axiom,
    ! [V_d_2,V_b_2,V_a_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ),
    file('theBenchmark.p',fact_Int__atLeastAtMostL1) ).

fof(fact_Int__greaterThanLessThan,axiom,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ),
    file('theBenchmark.p',fact_Int__greaterThanLessThan) ).

fof(fact_strict__monoI,axiom,
    ! [V_f_2,T_b,T_c] :
      ( ( class_Orderings_Oorder(T_b)
        & class_Orderings_Oorder(T_c) )
     => ( ! [B_x,B_y] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),B_y))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(V_f_2,B_x)),hAPP(V_f_2,B_y))) )
       => c_Orderings_Oorder__class_Ostrict__mono(T_b,T_c,V_f_2) ) ),
    file('theBenchmark.p',fact_strict__monoI) ).

fof(fact_Int__greaterThanAtMost,axiom,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ),
    file('theBenchmark.p',fact_Int__greaterThanAtMost) ).

fof(fact_Min_Oidem,axiom,
    ! [V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_x) = V_x ),
    file('theBenchmark.p',fact_Min_Oidem) ).

fof(fact_min__max_Oinf__assoc,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z)) ),
    file('theBenchmark.p',fact_min__max_Oinf__assoc) ).

fof(fact_min__max_Oinf_Oassoc,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b),V_c)) ),
    file('theBenchmark.p',fact_min__max_Oinf_Oassoc) ).

fof(fact_min__max_Oinf__left__commute,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_z)) ),
    file('theBenchmark.p',fact_min__max_Oinf__left__commute) ).

fof(fact_min__max_Oinf_Oleft__commute,axiom,
    ! [V_c,V_a,V_b,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_c)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b),V_c)) ),
    file('theBenchmark.p',fact_min__max_Oinf_Oleft__commute) ).

fof(fact_min__max_Oinf__left__idem,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) ),
    file('theBenchmark.p',fact_min__max_Oinf__left__idem) ).

fof(fact_min__max_Oinf_Oleft__idem,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b) ),
    file('theBenchmark.p',fact_min__max_Oinf_Oleft__idem) ).

fof(fact_min__max_Oinf__commute,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_x) ),
    file('theBenchmark.p',fact_min__max_Oinf__commute) ).

fof(fact_min__max_Oinf_Ocommute,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b),V_a) ),
    file('theBenchmark.p',fact_min__max_Oinf_Ocommute) ).

fof(fact_min__max_Oinf_Oidem,axiom,
    ! [V_a,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_a) = V_a ),
    file('theBenchmark.p',fact_min__max_Oinf_Oidem) ).

fof(fact_min__of__mono,axiom,
    ! [V_n_2,V_m_2,V_f_2,T_b,T_c] :
      ( ( class_Orderings_Olinorder(T_b)
        & class_Orderings_Olinorder(T_c) )
     => ( c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
       => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),hAPP(V_f_2,V_m_2)),hAPP(V_f_2,V_n_2)) = hAPP(V_f_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_m_2),V_n_2)) ) ),
    file('theBenchmark.p',fact_min__of__mono) ).

fof(fact_min__le__iff__disj,axiom,
    ! [V_z_2,V_y_2,V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2)),V_z_2))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) ) ) ),
    file('theBenchmark.p',fact_min__le__iff__disj) ).

fof(fact_min__max_Ole__infE,axiom,
    ! [V_b,V_a,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)))
       => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
           => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ),
    file('theBenchmark.p',fact_min__max_Ole__infE) ).

fof(fact_min__max_Oinf__mono,axiom,
    ! [V_d,V_b,V_c,V_a,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_c),V_d))) ) ) ),
    file('theBenchmark.p',fact_min__max_Oinf__mono) ).

fof(fact_min__max_Oinf__greatest,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z))) ) ) ),
    file('theBenchmark.p',fact_min__max_Oinf__greatest) ).

fof(fact_min__max_Ole__infI,axiom,
    ! [V_b,V_a,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b))) ) ) ),
    file('theBenchmark.p',fact_min__max_Ole__infI) ).

fof(fact_min__max_Oinf__absorb2,axiom,
    ! [V_x,V_y,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
       => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_y ) ),
    file('theBenchmark.p',fact_min__max_Oinf__absorb2) ).

fof(fact_min__max_Oinf__absorb1,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
       => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_x ) ),
    file('theBenchmark.p',fact_min__max_Oinf__absorb1) ).

fof(fact_min__max_Ole__infI2,axiom,
    ! [V_a,V_x,V_b,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_x)) ) ),
    file('theBenchmark.p',fact_min__max_Ole__infI2) ).

fof(fact_min__max_Ole__infI1,axiom,
    ! [V_b,V_x,V_a,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_x)) ) ),
    file('theBenchmark.p',fact_min__max_Ole__infI1) ).

fof(fact_min__max_Ole__inf__iff,axiom,
    ! [V_z_2,V_y_2,V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_y_2),V_z_2)))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ),
    file('theBenchmark.p',fact_min__max_Ole__inf__iff) ).

fof(fact_min__max_Ole__iff__inf,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
      <=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2) = V_x_2 ) ),
    file('theBenchmark.p',fact_min__max_Ole__iff__inf) ).

fof(fact_min__max_Oinf__le2,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_y)) ),
    file('theBenchmark.p',fact_min__max_Oinf__le2) ).

fof(fact_min__max_Oinf__le1,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_x)) ),
    file('theBenchmark.p',fact_min__max_Oinf__le1) ).

fof(fact_min__max_Oless__infI2,axiom,
    ! [V_a,V_x,V_b,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_x)) ) ),
    file('theBenchmark.p',fact_min__max_Oless__infI2) ).

fof(fact_min__max_Oless__infI1,axiom,
    ! [V_b,V_x,V_a,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_x)) ) ),
    file('theBenchmark.p',fact_min__max_Oless__infI1) ).

fof(fact_min__less__iff__disj,axiom,
    ! [V_z_2,V_y_2,V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2)),V_z_2))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2)) ) ) ),
    file('theBenchmark.p',fact_min__less__iff__disj) ).

fof(fact_min__less__iff__conj,axiom,
    ! [V_y_2,V_x_2,V_z_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2)))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2)) ) ) ),
    file('theBenchmark.p',fact_min__less__iff__conj) ).

fof(fact_min__max_Omono__inf,axiom,
    ! [V_B_2,V_A_2,V_f_2,T_b,T_c] :
      ( ( class_Orderings_Olinorder(T_b)
        & class_Lattices_Osemilattice__inf(T_c) )
     => ( c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),hAPP(V_f_2,V_A_2)),hAPP(V_f_2,V_B_2)))) ) ),
    file('theBenchmark.p',fact_min__max_Omono__inf) ).

fof(fact_inf__min,axiom,
    ! [T_b] :
      ( ( class_Orderings_Olinorder(T_b)
        & class_Lattices_Osemilattice__inf(T_b) )
     => c_Lattices_Osemilattice__inf__class_Oinf(T_b) = c_Orderings_Oord__class_Omin(T_b) ),
    file('theBenchmark.p',fact_inf__min) ).

fof(fact_min__max_Oinf__sup__distrib2,axiom,
    ! [V_x,V_z,V_y,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)),V_x) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_x)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_z),V_x)) ),
    file('theBenchmark.p',fact_min__max_Oinf__sup__distrib2) ).

fof(fact_min__max_Osup__inf__distrib2,axiom,
    ! [V_x,V_z,V_y,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z)),V_x) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_x)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_z),V_x)) ),
    file('theBenchmark.p',fact_min__max_Osup__inf__distrib2) ).

fof(fact_min__max_Oinf__sup__distrib1,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_z)) ),
    file('theBenchmark.p',fact_min__max_Oinf__sup__distrib1) ).

fof(fact_min__max_Osup__inf__distrib1,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_z)) ),
    file('theBenchmark.p',fact_min__max_Osup__inf__distrib1) ).

fof(fact_min__max_Oinf__sup__absorb,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)) = V_x ),
    file('theBenchmark.p',fact_min__max_Oinf__sup__absorb) ).

fof(fact_min__max_Osup__inf__absorb,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)) = V_x ),
    file('theBenchmark.p',fact_min__max_Osup__inf__absorb) ).

fof(fact_monoD,axiom,
    ! [V_y_2,V_x_2,V_f_2,T_b,T_c] :
      ( ( class_Orderings_Oorder(T_b)
        & class_Orderings_Oorder(T_c) )
     => ( c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) ) ) ),
    file('theBenchmark.p',fact_monoD) ).

fof(fact_max__of__mono,axiom,
    ! [V_n_2,V_m_2,V_f_2,T_b,T_c] :
      ( ( class_Orderings_Olinorder(T_b)
        & class_Orderings_Olinorder(T_c) )
     => ( c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
       => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),hAPP(V_f_2,V_m_2)),hAPP(V_f_2,V_n_2)) = hAPP(V_f_2,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_m_2),V_n_2)) ) ),
    file('theBenchmark.p',fact_max__of__mono) ).

fof(fact_min__max_Odistrib__inf__le,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_z))),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)))) ),
    file('theBenchmark.p',fact_min__max_Odistrib__inf__le) ).

fof(fact_min__max_Odistrib__sup__le,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z))),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_z)))) ),
    file('theBenchmark.p',fact_min__max_Odistrib__sup__le) ).

fof(fact_minus__max__eq__min,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Groups_Olinordered__ab__group__add(T_a)
     => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ),
    file('theBenchmark.p',fact_minus__max__eq__min) ).

fof(fact_minus__min__eq__max,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Groups_Olinordered__ab__group__add(T_a)
     => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ),
    file('theBenchmark.p',fact_minus__min__eq__max) ).

fof(fact_strict__mono__mono,axiom,
    ! [V_f_2,T_b,T_c] :
      ( ( class_Orderings_Oorder(T_b)
        & class_Orderings_Oorder(T_c) )
     => ( c_Orderings_Oorder__class_Ostrict__mono(T_b,T_c,V_f_2)
       => c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2) ) ),
    file('theBenchmark.p',fact_strict__mono__mono) ).

fof(fact_mono__Un,axiom,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),V_f_2)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_f_2,V_A_2)),hAPP(V_f_2,V_B_2))),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))) ),
    file('theBenchmark.p',fact_mono__Un) ).

fof(fact_mono__Int,axiom,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),V_f_2)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_f_2,V_A_2)),hAPP(V_f_2,V_B_2)))) ),
    file('theBenchmark.p',fact_mono__Int) ).

fof(fact_mono__sup,axiom,
    ! [V_B_2,V_A_2,V_f_2,T_b,T_c] :
      ( ( class_Lattices_Osemilattice__sup(T_b)
        & class_Lattices_Osemilattice__sup(T_c) )
     => ( c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),hAPP(V_f_2,V_A_2)),hAPP(V_f_2,V_B_2))),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_A_2),V_B_2)))) ) ),
    file('theBenchmark.p',fact_mono__sup) ).

fof(fact_mono__inf,axiom,
    ! [V_B_2,V_A_2,V_f_2,T_b,T_c] :
      ( ( class_Lattices_Osemilattice__inf(T_b)
        & class_Lattices_Osemilattice__inf(T_c) )
     => ( c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),hAPP(V_f_2,V_A_2)),hAPP(V_f_2,V_B_2)))) ) ),
    file('theBenchmark.p',fact_mono__inf) ).

fof(fact_Int__atLeastAtMost,axiom,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ),
    file('theBenchmark.p',fact_Int__atLeastAtMost) ).

fof(fact_Int__atLeastLessThan,axiom,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ),
    file('theBenchmark.p',fact_Int__atLeastLessThan) ).

fof(fact_min__ord__min,axiom,
    ! [T_b] :
      ( class_Orderings_Oord(T_b)
     => c_Orderings_Oord__class_Omin(T_b) = c_Orderings_Oord_Omin(T_b,c_Orderings_Oord__class_Oless__eq(T_b)) ),
    file('theBenchmark.p',fact_min__ord__min) ).

fof(fact_min__max_OSup__fin_Ounion__inter,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2)) ) ) ) ),
    file('theBenchmark.p',fact_min__max_OSup__fin_Ounion__inter) ).

fof(fact_min__max_OSup__fin_Ounion__disjoint,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
           => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
             => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
               => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2)) ) ) ) ) ) ),
    file('theBenchmark.p',fact_min__max_OSup__fin_Ounion__disjoint) ).

fof(fact_min__max_OSup__fin_Ounion__idem,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
           => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
             => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2)) ) ) ) ) ),
    file('theBenchmark.p',fact_min__max_OSup__fin_Ounion__idem) ).

fof(fact_min__max_OSup__fin_Osubset__idem,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
           => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) ) ) ) ),
    file('theBenchmark.p',fact_min__max_OSup__fin_Osubset__idem) ).

fof(fact_min__max_OSup__fin_Oinsert__idem,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) ) ) ),
    file('theBenchmark.p',fact_min__max_OSup__fin_Oinsert__idem) ).

fof(fact_inj__image__Compl__subset,axiom,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))) ),
    file('theBenchmark.p',fact_inj__image__Compl__subset) ).

fof(fact_min__max_OInf__fin_Osingleton,axiom,
    ! [V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ),
    file('theBenchmark.p',fact_min__max_OInf__fin_Osingleton) ).

fof(fact_single__Diff__lessThan,axiom,
    ! [V_k_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_k_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_k_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ),
    file('theBenchmark.p',fact_single__Diff__lessThan) ).

fof(fact_override__on__emptyset,axiom,
    ! [V_g_2,V_f_2,T_c,T_b] : c_Fun_Ooverride__on(T_b,T_c,V_f_2,V_g_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_f_2,
    file('theBenchmark.p',fact_override__on__emptyset) ).

fof(fact_inj__on__empty,axiom,
    ! [V_f_2,T_c,T_b] : c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),
    file('theBenchmark.p',fact_inj__on__empty) ).

fof(fact_inj__uminus,axiom,
    ! [V_A_2,T_b] :
      ( class_Groups_Oordered__ab__group__add(T_b)
     => c_Fun_Oinj__on(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b),V_A_2) ),
    file('theBenchmark.p',fact_inj__uminus) ).

fof(fact_inj__on__def,axiom,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
         => ! [B_xa] :
              ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
             => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_xa)
               => B_x = B_xa ) ) ) ),
    file('theBenchmark.p',fact_inj__on__def) ).

fof(fact_inj__on__diff,axiom,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
     => c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    file('theBenchmark.p',fact_inj__on__diff) ).

fof(fact_Diff__idemp,axiom,
    ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),
    file('theBenchmark.p',fact_Diff__idemp) ).

fof(fact_minus__apply,axiom,
    ! [V_x_2,V_B_2,V_A_2,T_c,T_b] :
      ( class_Groups_Ominus(T_b)
     => hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,T_b)),V_A_2),V_B_2),V_x_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(V_A_2,V_x_2)),hAPP(V_B_2,V_x_2)) ),
    file('theBenchmark.p',fact_minus__apply) ).

fof(fact_diff__eq__diff__eq,axiom,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
      ( class_Groups_Oab__group__add(T_b)
     => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_c_2),V_d_2)
       => ( V_a_2 = V_b_2
        <=> V_c_2 = V_d_2 ) ) ),
    file('theBenchmark.p',fact_diff__eq__diff__eq) ).

fof(fact_inj__on__image__set__diff,axiom,
    ! [V_B_2,V_A_2,V_C_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
         => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) ) ) ),
    file('theBenchmark.p',fact_inj__on__image__set__diff) ).

fof(fact_image__set__diff,axiom,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
     => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) ),
    file('theBenchmark.p',fact_image__set__diff) ).

fof(fact_min__max_OInf__fin_Oinsert__remove,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) )
          & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 ) ) ) ),
    file('theBenchmark.p',fact_min__max_OInf__fin_Oinsert__remove) ).

fof(fact_diff__eq__diff__less__eq,axiom,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
      ( class_Groups_Oordered__ab__group__add(T_b)
     => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_c_2),V_d_2)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_d_2)) ) ) ),
    file('theBenchmark.p',fact_diff__eq__diff__less__eq) ).

fof(fact_diff__eq__diff__less,axiom,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
      ( class_Groups_Oordered__ab__group__add(T_b)
     => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_c_2),V_d_2)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2)) ) ) ),
    file('theBenchmark.p',fact_diff__eq__diff__less) ).

fof(fact_subset__inj__on,axiom,
    ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
       => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ),
    file('theBenchmark.p',fact_subset__inj__on) ).

fof(fact_inj__eq,axiom,
    ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
     => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
      <=> V_x_2 = V_y_2 ) ),
    file('theBenchmark.p',fact_inj__eq) ).

fof(fact_injD,axiom,
    ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
     => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
       => V_x_2 = V_y_2 ) ),
    file('theBenchmark.p',fact_injD) ).

fof(fact_inj__on__Int,axiom,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
     => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
       => c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
    file('theBenchmark.p',fact_inj__on__Int) ).

fof(fact_minus__diff__eq,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Oab__group__add(T_a)
     => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_a) ),
    file('theBenchmark.p',fact_minus__diff__eq) ).

fof(fact_min__diff__distrib__left,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Groups_Oordered__ab__group__add(T_a)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_y),V_z)) ),
    file('theBenchmark.p',fact_min__diff__distrib__left) ).

fof(fact_max__diff__distrib__left,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Groups_Oordered__ab__group__add(T_a)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_y),V_z)) ),
    file('theBenchmark.p',fact_max__diff__distrib__left) ).

fof(fact_empty__Diff,axiom,
    ! [V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_empty__Diff) ).

fof(fact_Diff__empty,axiom,
    ! [V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_A_2,
    file('theBenchmark.p',fact_Diff__empty) ).

fof(fact_Diff__cancel,axiom,
    ! [V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Diff__cancel) ).

fof(fact_Diff__subset,axiom,
    ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_A_2)),
    file('theBenchmark.p',fact_Diff__subset) ).

fof(fact_Diff__mono,axiom,
    ! [V_B_2,V_D_2,V_C_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_D_2),V_B_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2))) ) ),
    file('theBenchmark.p',fact_Diff__mono) ).

fof(fact_double__diff,axiom,
    ! [V_C_2,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) = V_A_2 ) ),
    file('theBenchmark.p',fact_double__diff) ).

fof(fact_Un__Diff__cancel,axiom,
    ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),
    file('theBenchmark.p',fact_Un__Diff__cancel) ).

fof(fact_Un__Diff__cancel2,axiom,
    ! [V_A_2,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2),
    file('theBenchmark.p',fact_Un__Diff__cancel2) ).

fof(fact_Un__Diff,axiom,
    ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)),
    file('theBenchmark.p',fact_Un__Diff) ).

fof(fact_Diff__Int__distrib,axiom,
    ! [V_B_2,V_A_2,V_C_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)),
    file('theBenchmark.p',fact_Diff__Int__distrib) ).

fof(fact_Int__Diff,axiom,
    ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)),
    file('theBenchmark.p',fact_Int__Diff) ).

fof(fact_Diff__Int__distrib2,axiom,
    ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)),
    file('theBenchmark.p',fact_Diff__Int__distrib2) ).

fof(fact_Diff__Int2,axiom,
    ! [V_B_2,V_C_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),V_B_2),
    file('theBenchmark.p',fact_Diff__Int2) ).

fof(fact_strict__mono__imp__inj__on,axiom,
    ! [V_A_2,V_f_2,T_b,T_c] :
      ( ( class_Orderings_Olinorder(T_b)
        & class_Orderings_Oorder(T_c) )
     => ( c_Orderings_Oorder__class_Ostrict__mono(T_b,T_c,V_f_2)
       => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ),
    file('theBenchmark.p',fact_strict__mono__imp__inj__on) ).

fof(fact_min__max_OInf__fin_Oinsert__idem,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) ) ) ),
    file('theBenchmark.p',fact_min__max_OInf__fin_Oinsert__idem) ).

fof(fact_min__max_OInf__fin_Osubset__idem,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
           => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) ) ) ) ),
    file('theBenchmark.p',fact_min__max_OInf__fin_Osubset__idem) ).

fof(fact_min__max_OInf__fin_Ounion__idem,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
           => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
             => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2)) ) ) ) ) ),
    file('theBenchmark.p',fact_min__max_OInf__fin_Ounion__idem) ).

fof(fact_inj__on__Un,axiom,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
    <=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
        & c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
        & c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ),
    file('theBenchmark.p',fact_inj__on__Un) ).

fof(fact_inj__image__eq__iff,axiom,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
     => ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)
      <=> V_A_2 = V_B_2 ) ),
    file('theBenchmark.p',fact_inj__image__eq__iff) ).

fof(fact_inj__on__Un__image__eq__iff,axiom,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
     => ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)
      <=> V_A_2 = V_B_2 ) ),
    file('theBenchmark.p',fact_inj__on__Un__image__eq__iff) ).

fof(fact_diff__eq,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Lattices_Oboolean__algebra(T_a)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ),
    file('theBenchmark.p',fact_diff__eq) ).

fof(fact_Diff__insert,axiom,
    ! [V_B_2,V_a_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),
    file('theBenchmark.p',fact_Diff__insert) ).

fof(fact_Diff__insert2,axiom,
    ! [V_B_2,V_a_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_B_2),
    file('theBenchmark.p',fact_Diff__insert2) ).

fof(fact_insert__Diff__single,axiom,
    ! [V_A_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2),
    file('theBenchmark.p',fact_insert__Diff__single) ).

fof(fact_inj__on__strict__subset,axiom,
    ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2))) ) ),
    file('theBenchmark.p',fact_inj__on__strict__subset) ).

fof(fact_min__max_OSup__fin_Oinsert__remove,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) )
          & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 ) ) ) ),
    file('theBenchmark.p',fact_min__max_OSup__fin_Oinsert__remove) ).

fof(fact_Diff__UNIV,axiom,
    ! [V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Diff__UNIV) ).

fof(fact_Diff__disjoint,axiom,
    ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Diff__disjoint) ).

fof(fact_Diff__triv,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ),
    file('theBenchmark.p',fact_Diff__triv) ).

fof(fact_image__diff__subset,axiom,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_B_2))),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))),
    file('theBenchmark.p',fact_image__diff__subset) ).

fof(fact_Diff__partition,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) = V_B_2 ),
    file('theBenchmark.p',fact_Diff__partition) ).

fof(fact_Diff__subset__conv,axiom,
    ! [V_C_2,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))) ),
    file('theBenchmark.p',fact_Diff__subset__conv) ).

fof(fact_Diff__Int,axiom,
    ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),
    file('theBenchmark.p',fact_Diff__Int) ).

fof(fact_Diff__Un,axiom,
    ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),
    file('theBenchmark.p',fact_Diff__Un) ).

fof(fact_Un__Diff__Int,axiom,
    ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = V_A_2,
    file('theBenchmark.p',fact_Un__Diff__Int) ).

fof(fact_ivl__diff,axiom,
    ! [V_m_2,V_n_2,V_i_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_n_2))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_i_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_i_2),V_n_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_n_2),V_m_2) ) ),
    file('theBenchmark.p',fact_ivl__diff) ).

fof(fact_min__max_OInf__fin_Ounion__disjoint,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
           => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
             => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
               => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2)) ) ) ) ) ) ),
    file('theBenchmark.p',fact_min__max_OInf__fin_Ounion__disjoint) ).

fof(fact_min__max_OInf__fin_Ounion__inter,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2)) ) ) ) ),
    file('theBenchmark.p',fact_min__max_OInf__fin_Ounion__inter) ).

fof(fact_Compl__eq__Diff__UNIV,axiom,
    ! [V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_A_2),
    file('theBenchmark.p',fact_Compl__eq__Diff__UNIV) ).

fof(fact_Compl__Diff__eq,axiom,
    ! [V_B_2,V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2),
    file('theBenchmark.p',fact_Compl__Diff__eq) ).

fof(fact_Diff__eq,axiom,
    ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)),
    file('theBenchmark.p',fact_Diff__eq) ).

fof(fact_Diff__Compl,axiom,
    ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),
    file('theBenchmark.p',fact_Diff__Compl) ).

fof(fact_min__max_OInf__le__Sup,axiom,
    ! [V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2))) ) ) ),
    file('theBenchmark.p',fact_min__max_OInf__le__Sup) ).

fof(fact_inj__image__subset__iff,axiom,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
    file('theBenchmark.p',fact_inj__image__subset__iff) ).

fof(fact_inj__on__image__Int,axiom,
    ! [V_B_2,V_A_2,V_C_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
         => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) ) ) ),
    file('theBenchmark.p',fact_inj__on__image__Int) ).

fof(fact_image__Int,axiom,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
     => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) ),
    file('theBenchmark.p',fact_image__Int) ).

fof(fact_finite__Inter,axiom,
    ! [V_M_2,T_b] :
      ( ? [B_x] :
          ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_x))
          & hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_M_2)) )
     => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_M_2))) ),
    file('theBenchmark.p',fact_finite__Inter) ).

fof(fact_finite__Diff,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ),
    file('theBenchmark.p',fact_finite__Diff) ).

fof(fact_finite__Int,axiom,
    ! [V_G_2,V_F_2,T_b] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_G_2))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) )
     => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_G_2))) ),
    file('theBenchmark.p',fact_finite__Int) ).

fof(fact_finite__imageI,axiom,
    ! [V_h_2,T_c,V_F_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_h_2),V_F_2))) ),
    file('theBenchmark.p',fact_finite__imageI) ).

fof(fact_finite_OinsertI,axiom,
    ! [V_a_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2))) ),
    file('theBenchmark.p',fact_finite_OinsertI) ).

fof(fact_finite_OemptyI,axiom,
    ! [T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),
    file('theBenchmark.p',fact_finite_OemptyI) ).

fof(fact_finite__UNIV__inj__surj,axiom,
    ! [V_f_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
     => ( c_Fun_Oinj__on(T_b,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
       => hAPP(c_Set_Oimage(T_b,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_finite__UNIV__inj__surj) ).

fof(fact_finite__UNIV__surj__inj,axiom,
    ! [V_f_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
     => ( hAPP(c_Set_Oimage(T_b,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
       => c_Fun_Oinj__on(T_b,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ),
    file('theBenchmark.p',fact_finite__UNIV__surj__inj) ).

fof(fact_endo__inj__surj,axiom,
    ! [V_f_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_b,V_f_2),V_A_2)),V_A_2))
       => ( c_Fun_Oinj__on(T_b,T_b,V_f_2,V_A_2)
         => hAPP(c_Set_Oimage(T_b,T_b,V_f_2),V_A_2) = V_A_2 ) ) ),
    file('theBenchmark.p',fact_endo__inj__surj) ).

fof(fact_finite__UN,axiom,
    ! [V_B_2,T_c,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))
      <=> ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
           => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) ) ) ),
    file('theBenchmark.p',fact_finite__UN) ).

fof(fact_finite,axiom,
    ! [V_A_2,T_b] :
      ( class_Finite__Set_Ofinite(T_b)
     => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    file('theBenchmark.p',fact_finite) ).

fof(fact_finite__code,axiom,
    ! [V_A_2,T_b] :
      ( class_Finite__Set_Ofinite(T_b)
     => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    file('theBenchmark.p',fact_finite__code) ).

fof(fact_finite_Oequations_I1_J,axiom,
    ! [T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),
    file('theBenchmark.p',fact_finite_Oequations_I1_J) ).

fof(fact_finite__insert,axiom,
    ! [V_A_2,V_a_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)))
    <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    file('theBenchmark.p',fact_finite__insert) ).

fof(fact_finite__subset,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ),
    file('theBenchmark.p',fact_finite__subset) ).

fof(fact_rev__finite__subset,axiom,
    ! [V_A_2,V_B_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ),
    file('theBenchmark.p',fact_rev__finite__subset) ).

fof(fact_finite__UNIV,axiom,
    ! [T_b] :
      ( class_Finite__Set_Ofinite(T_b)
     => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ),
    file('theBenchmark.p',fact_finite__UNIV) ).

fof(fact_finite__Prod__UNIV,axiom,
    ! [T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)))) ) ),
    file('theBenchmark.p',fact_finite__Prod__UNIV) ).

fof(fact_finite__Plus__UNIV__iff,axiom,
    ! [T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(T_b,T_c),tc_HOL_Obool))))
    <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ),
    file('theBenchmark.p',fact_finite__Plus__UNIV__iff) ).

fof(fact_finite__option__UNIV,axiom,
    ! [T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_b)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(T_b),tc_HOL_Obool))))
    <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ),
    file('theBenchmark.p',fact_finite__option__UNIV) ).

fof(fact_finite__Un,axiom,
    ! [V_G_2,V_F_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_G_2)))
    <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_G_2))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) ) ),
    file('theBenchmark.p',fact_finite__Un) ).

fof(fact_finite__UnI,axiom,
    ! [V_G_2,V_F_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_G_2))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_G_2))) ) ),
    file('theBenchmark.p',fact_finite__UnI) ).

fof(fact_finite__Diff2,axiom,
    ! [V_A_2,V_B_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
      <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ),
    file('theBenchmark.p',fact_finite__Diff2) ).

fof(fact_finite__UnionD,axiom,
    ! [V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) ),
    file('theBenchmark.p',fact_finite__UnionD) ).

fof(fact_finite__Pow__iff,axiom,
    ! [V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)))
    <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    file('theBenchmark.p',fact_finite__Pow__iff) ).

fof(fact_finite__surj,axiom,
    ! [V_f_2,V_B_2,T_c,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ),
    file('theBenchmark.p',fact_finite__surj) ).

fof(fact_finite__Diff__insert,axiom,
    ! [V_B_2,V_a_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2))))
    <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ),
    file('theBenchmark.p',fact_finite__Diff__insert) ).

fof(fact_finite__imageD,axiom,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
     => ( c_Fun_Oinj__on(T_c,T_b,V_f_2,V_A_2)
       => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ) ),
    file('theBenchmark.p',fact_finite__imageD) ).

fof(fact_finite__compl,axiom,
    ! [V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
      <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ),
    file('theBenchmark.p',fact_finite__compl) ).

fof(fact_finite__fun__UNIVD2,axiom,
    ! [T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,T_c),tc_HOL_Obool))))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ),
    file('theBenchmark.p',fact_finite__fun__UNIVD2) ).

fof(fact_finite__surj__inj,axiom,
    ! [V_f_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_Oimage(T_b,T_b,V_f_2),V_A_2)))
       => c_Fun_Oinj__on(T_b,T_b,V_f_2,V_A_2) ) ),
    file('theBenchmark.p',fact_finite__surj__inj) ).

fof(fact_inj__on__iff__surj,axiom,
    ! [V_A_H_2,T_c,T_b,V_A_2] :
      ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
     => ( ? [B_f] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,B_f),V_A_2)),V_A_H_2))
            & c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2) )
      <=> ? [B_g] : hAPP(c_Set_Oimage(T_c,T_b,B_g),V_A_H_2) = V_A_2 ) ),
    file('theBenchmark.p',fact_inj__on__iff__surj) ).

fof(fact_folding__one_Ounion__inter,axiom,
    ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
      ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => hAPP(hAPP(V_f_2,hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ),
    file('theBenchmark.p',fact_folding__one_Ounion__inter) ).

fof(fact_folding__one_Ounion__disjoint,axiom,
    ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
      ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
           => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
             => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
               => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ) ) ),
    file('theBenchmark.p',fact_folding__one_Ounion__disjoint) ).

fof(fact_folding__image__simple_Ounion__disjoint,axiom,
    ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
           => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ),
    file('theBenchmark.p',fact_folding__image__simple_Ounion__disjoint) ).

fof(fact_folding__one_Oinsert__remove,axiom,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
      ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) )
          & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 ) ) ) ),
    file('theBenchmark.p',fact_folding__one_Oinsert__remove) ).

fof(fact_folding__image__simple_Oinsert__remove,axiom,
    ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
       => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))) ) ),
    file('theBenchmark.p',fact_folding__image__simple_Oinsert__remove) ).

fof(fact_min__max_OSup__fin_Ohom__commute,axiom,
    ! [V_N_2,V_h_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
         => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => hAPP(V_h_2,c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_N_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ),
    file('theBenchmark.p',fact_min__max_OSup__fin_Ohom__commute) ).

fof(fact_min__max_OInf__fin_Ohom__commute,axiom,
    ! [V_N_2,V_h_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
         => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => hAPP(V_h_2,c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_N_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ),
    file('theBenchmark.p',fact_min__max_OInf__fin_Ohom__commute) ).

fof(fact_min__max_OSup__fin_Oremove,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
             => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) )
            & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
             => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) = V_x_2 ) ) ) ) ),
    file('theBenchmark.p',fact_min__max_OSup__fin_Oremove) ).

fof(fact_equalityCE,axiom,
    ! [V_c_2,T_b,V_B_2,V_A_2] :
      ( V_A_2 = V_B_2
     => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
         => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) )
       => ~ ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
           => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ),
    file('theBenchmark.p',fact_equalityCE) ).

fof(fact_emptyE,axiom,
    ! [V_a_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),
    file('theBenchmark.p',fact_emptyE) ).

fof(fact_insertE,axiom,
    ! [V_A_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2)))
     => ( V_a_2 != V_b_2
       => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_insertE) ).

fof(fact_insertCI,axiom,
    ! [V_b_2,V_B_2,V_a_2,T_b] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
       => V_a_2 = V_b_2 )
     => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) ),
    file('theBenchmark.p',fact_insertCI) ).

fof(fact_subsetD,axiom,
    ! [V_c_2,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
       => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ),
    file('theBenchmark.p',fact_subsetD) ).

fof(fact_UNIV__I,axiom,
    ! [V_x_2,T_b] : hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))),
    file('theBenchmark.p',fact_UNIV__I) ).

fof(fact_image__eqI,axiom,
    ! [T_b,V_A_2,T_c,V_x_2,V_f_2,V_b_2] :
      ( V_b_2 = hAPP(V_f_2,V_x_2)
     => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
       => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) ) ),
    file('theBenchmark.p',fact_image__eqI) ).

fof(fact_UnE,axiom,
    ! [V_B_2,V_A_2,V_c_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
     => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
       => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ),
    file('theBenchmark.p',fact_UnE) ).

fof(fact_UnCI,axiom,
    ! [V_A_2,V_B_2,V_c_2,T_b] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
       => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) )
     => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ),
    file('theBenchmark.p',fact_UnCI) ).

fof(fact_IntI,axiom,
    ! [V_B_2,V_A_2,V_c_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
       => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ),
    file('theBenchmark.p',fact_IntI) ).

fof(fact_IntE,axiom,
    ! [V_B_2,V_A_2,V_c_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
     => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
         => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ),
    file('theBenchmark.p',fact_IntE) ).

fof(fact_DiffI,axiom,
    ! [V_B_2,V_A_2,V_c_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
     => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
       => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ),
    file('theBenchmark.p',fact_DiffI) ).

fof(fact_DiffE,axiom,
    ! [V_B_2,V_A_2,V_c_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
     => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
         => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ),
    file('theBenchmark.p',fact_DiffE) ).

fof(fact_ComplI,axiom,
    ! [V_A_2,V_c_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
     => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) ),
    file('theBenchmark.p',fact_ComplI) ).

fof(fact_UnionI,axiom,
    ! [V_A_2,V_C_2,V_X_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2))
       => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2))) ) ),
    file('theBenchmark.p',fact_UnionI) ).

fof(fact_InterD,axiom,
    ! [V_X_2,V_C_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_C_2)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
       => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2)) ) ),
    file('theBenchmark.p',fact_InterD) ).

fof(fact_InterE,axiom,
    ! [V_X_2,V_C_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_C_2)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
       => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2)) ) ),
    file('theBenchmark.p',fact_InterE) ).

fof(fact_PowI,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
     => hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2))) ),
    file('theBenchmark.p',fact_PowI) ).

fof(fact_mem__def,axiom,
    ! [V_A_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
    <=> hBOOL(hAPP(V_A_2,V_x_2)) ),
    file('theBenchmark.p',fact_mem__def) ).

fof(fact_eq__mem,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_fequal,V_y_2)))
    <=> V_x_2 = V_y_2 ),
    file('theBenchmark.p',fact_eq__mem) ).

fof(fact_eqset__imp__iff,axiom,
    ! [V_x_2,T_b,V_B_2,V_A_2] :
      ( V_A_2 = V_B_2
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ),
    file('theBenchmark.p',fact_eqset__imp__iff) ).

fof(fact_eqelem__imp__iff,axiom,
    ! [V_A_2,T_b,V_y_2,V_x_2] :
      ( V_x_2 = V_y_2
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      <=> hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_eqelem__imp__iff) ).

fof(fact_eq__mem__trans,axiom,
    ! [V_A_2,T_b,V_b_2,V_a_2] :
      ( V_a_2 = V_b_2
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
       => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_eq__mem__trans) ).

fof(fact_ball__UN,axiom,
    ! [V_P_2,V_B_2,V_A_2,T_c,T_b] :
      ( ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
         => hBOOL(hAPP(V_P_2,B_x)) )
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
         => ! [B_xa] :
              ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(V_B_2,B_x)))
             => hBOOL(hAPP(V_P_2,B_xa)) ) ) ),
    file('theBenchmark.p',fact_ball__UN) ).

fof(fact_all__not__in__conv,axiom,
    ! [V_A_2,T_b] :
      ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
    <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_all__not__in__conv) ).

fof(fact_ex__in__conv,axiom,
    ! [V_A_2,T_b] :
      ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
    <=> V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_ex__in__conv) ).

fof(fact_empty__iff,axiom,
    ! [V_c_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),
    file('theBenchmark.p',fact_empty__iff) ).

fof(fact_equals0D,axiom,
    ! [V_a_2,T_b,V_A_2] :
      ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
     => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ),
    file('theBenchmark.p',fact_equals0D) ).

fof(fact_insertI1,axiom,
    ! [V_B_2,V_a_2,T_b] : hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2))),
    file('theBenchmark.p',fact_insertI1) ).

fof(fact_insert__iff,axiom,
    ! [V_A_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2)))
    <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
        | V_a_2 = V_b_2 ) ),
    file('theBenchmark.p',fact_insert__iff) ).

fof(fact_insert__ident,axiom,
    ! [V_B_2,V_A_2,V_x_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
     => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
       => ( hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2)
        <=> V_A_2 = V_B_2 ) ) ),
    file('theBenchmark.p',fact_insert__ident) ).

fof(fact_insertI2,axiom,
    ! [V_b_2,V_B_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
     => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) ),
    file('theBenchmark.p',fact_insertI2) ).

fof(fact_insert__absorb,axiom,
    ! [V_A_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
     => hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) = V_A_2 ),
    file('theBenchmark.p',fact_insert__absorb) ).

fof(fact_in__mono,axiom,
    ! [V_x_2,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
       => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ),
    file('theBenchmark.p',fact_in__mono) ).

fof(fact_set__rev__mp,axiom,
    ! [V_B_2,V_A_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
       => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ),
    file('theBenchmark.p',fact_set__rev__mp) ).

fof(fact_set__mp,axiom,
    ! [V_x_2,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
       => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ),
    file('theBenchmark.p',fact_set__mp) ).

fof(fact_image__iff,axiom,
    ! [V_A_2,V_f_2,T_c,V_z_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
    <=> ? [B_x] :
          ( V_z_2 = hAPP(V_f_2,B_x)
          & hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ),
    file('theBenchmark.p',fact_image__iff) ).

fof(fact_imageI,axiom,
    ! [V_f_2,T_c,V_A_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
     => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) ),
    file('theBenchmark.p',fact_imageI) ).

fof(fact_rev__image__eqI,axiom,
    ! [T_c,V_f_2,V_b_2,V_A_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
     => ( V_b_2 = hAPP(V_f_2,V_x_2)
       => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) ) ),
    file('theBenchmark.p',fact_rev__image__eqI) ).

fof(fact_Un__iff,axiom,
    ! [V_B_2,V_A_2,V_c_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
    <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
        | hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_Un__iff) ).

fof(fact_UnI1,axiom,
    ! [V_B_2,V_A_2,V_c_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
     => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ),
    file('theBenchmark.p',fact_UnI1) ).

fof(fact_UnI2,axiom,
    ! [V_A_2,V_B_2,V_c_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
     => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ),
    file('theBenchmark.p',fact_UnI2) ).

fof(fact_Int__iff,axiom,
    ! [V_B_2,V_A_2,V_c_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
    <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
        & hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_Int__iff) ).

fof(fact_IntD1,axiom,
    ! [V_B_2,V_A_2,V_c_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
     => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ),
    file('theBenchmark.p',fact_IntD1) ).

fof(fact_IntD2,axiom,
    ! [V_B_2,V_A_2,V_c_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
     => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ),
    file('theBenchmark.p',fact_IntD2) ).

fof(fact_Diff__iff,axiom,
    ! [V_B_2,V_A_2,V_c_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
    <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
        & hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_Diff__iff) ).

fof(fact_DiffD1,axiom,
    ! [V_B_2,V_A_2,V_c_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
     => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ),
    file('theBenchmark.p',fact_DiffD1) ).

fof(fact_DiffD2,axiom,
    ! [V_B_2,V_A_2,V_c_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
     => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ),
    file('theBenchmark.p',fact_DiffD2) ).

fof(fact_inj__on__contraD,axiom,
    ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
     => ( V_x_2 != V_y_2
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
           => hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) ) ) ) ),
    file('theBenchmark.p',fact_inj__on__contraD) ).

fof(fact_inj__on__iff,axiom,
    ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
         => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
          <=> V_x_2 = V_y_2 ) ) ) ),
    file('theBenchmark.p',fact_inj__on__iff) ).

fof(fact_inj__onD,axiom,
    ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
     => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
           => V_x_2 = V_y_2 ) ) ) ),
    file('theBenchmark.p',fact_inj__onD) ).

fof(fact_folding__image__simple_Oinsert,axiom,
    ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
         => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,V_A_2)) ) ) ),
    file('theBenchmark.p',fact_folding__image__simple_Oinsert) ).

fof(fact_Compl__iff,axiom,
    ! [V_A_2,V_c_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
    <=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ),
    file('theBenchmark.p',fact_Compl__iff) ).

fof(fact_ComplD,axiom,
    ! [V_A_2,V_c_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
     => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ),
    file('theBenchmark.p',fact_ComplD) ).

fof(fact_ComplE,axiom,
    ! [V_A_2,V_c_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
     => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ),
    file('theBenchmark.p',fact_ComplE) ).

fof(fact_Pow__top,axiom,
    ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_A_2))),
    file('theBenchmark.p',fact_Pow__top) ).

fof(fact_psubsetD,axiom,
    ! [V_c_2,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
       => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ),
    file('theBenchmark.p',fact_psubsetD) ).

fof(fact_override__on__apply__notin,axiom,
    ! [V_g_2,V_f_2,T_c,V_A_2,V_a_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
     => hAPP(c_Fun_Ooverride__on(T_b,T_c,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_f_2,V_a_2) ),
    file('theBenchmark.p',fact_override__on__apply__notin) ).

fof(fact_override__on__apply__in,axiom,
    ! [V_g_2,V_f_2,T_c,V_A_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
     => hAPP(c_Fun_Ooverride__on(T_b,T_c,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_g_2,V_a_2) ),
    file('theBenchmark.p',fact_override__on__apply__in) ).

fof(fact_folding__one_Oinsert,axiom,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
      ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) ) ) ) ),
    file('theBenchmark.p',fact_folding__one_Oinsert) ).

fof(fact_folding__image__simple_Oempty,axiom,
    ! [V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
     => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_z_2 ),
    file('theBenchmark.p',fact_folding__image__simple_Oempty) ).

fof(fact_singleton__iff,axiom,
    ! [V_a_2,V_b_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))
    <=> V_b_2 = V_a_2 ),
    file('theBenchmark.p',fact_singleton__iff) ).

fof(fact_singletonE,axiom,
    ! [V_a_2,V_b_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))
     => V_b_2 = V_a_2 ),
    file('theBenchmark.p',fact_singletonE) ).

fof(fact_subset__insert,axiom,
    ! [V_B_2,V_A_2,V_x_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
    file('theBenchmark.p',fact_subset__insert) ).

fof(fact_insert__subset,axiom,
    ! [V_B_2,V_A_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
        & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ),
    file('theBenchmark.p',fact_insert__subset) ).

fof(fact_insert__image,axiom,
    ! [V_f_2,T_c,V_A_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
     => hAPP(hAPP(c_Set_Oinsert(T_c),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) ),
    file('theBenchmark.p',fact_insert__image) ).

fof(fact_Int__insert__right,axiom,
    ! [V_B_2,V_A_2,V_a_2,T_b] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) )
      & ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
    file('theBenchmark.p',fact_Int__insert__right) ).

fof(fact_Int__insert__left,axiom,
    ! [V_B_2,V_C_2,V_a_2,T_b] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2) )
      & ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) ) ),
    file('theBenchmark.p',fact_Int__insert__left) ).

fof(fact_Int__insert__right__if0,axiom,
    ! [V_B_2,V_A_2,V_a_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ),
    file('theBenchmark.p',fact_Int__insert__right__if0) ).

fof(fact_Int__insert__left__if0,axiom,
    ! [V_B_2,V_C_2,V_a_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2) ),
    file('theBenchmark.p',fact_Int__insert__left__if0) ).

fof(fact_Int__insert__right__if1,axiom,
    ! [V_B_2,V_A_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    file('theBenchmark.p',fact_Int__insert__right__if1) ).

fof(fact_Int__insert__left__if1,axiom,
    ! [V_B_2,V_C_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) ),
    file('theBenchmark.p',fact_Int__insert__left__if1) ).

fof(fact_range__eqI,axiom,
    ! [T_c,T_b,V_x_2,V_f_2,V_b_2] :
      ( V_b_2 = hAPP(V_f_2,V_x_2)
     => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) ),
    file('theBenchmark.p',fact_range__eqI) ).

fof(fact_rangeI,axiom,
    ! [T_c,V_x_2,V_f_2,T_b] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))),
    file('theBenchmark.p',fact_rangeI) ).

fof(fact_insert__Diff1,axiom,
    ! [V_A_2,V_B_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ),
    file('theBenchmark.p',fact_insert__Diff1) ).

fof(fact_insert__Diff__if,axiom,
    ! [V_A_2,V_B_2,V_x_2,T_b] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
      & ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ) ),
    file('theBenchmark.p',fact_insert__Diff__if) ).

fof(fact_Sup__upper,axiom,
    ! [V_A_2,V_x_2,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2))) ) ),
    file('theBenchmark.p',fact_Sup__upper) ).

fof(fact_Inf__lower,axiom,
    ! [V_A_2,V_x_2,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2)),V_x_2)) ) ),
    file('theBenchmark.p',fact_Inf__lower) ).

fof(fact_lessThan__iff,axiom,
    ! [V_k_2,V_i_2,T_b] :
      ( class_Orderings_Oord(T_b)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_i_2),V_k_2)) ) ),
    file('theBenchmark.p',fact_lessThan__iff) ).

fof(fact_atMost__iff,axiom,
    ! [V_k_2,V_i_2,T_b] :
      ( class_Orderings_Oord(T_b)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_k_2)) ) ),
    file('theBenchmark.p',fact_atMost__iff) ).

fof(fact_Union__upper,axiom,
    ! [V_A_2,V_B_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2))) ),
    file('theBenchmark.p',fact_Union__upper) ).

fof(fact_Pow__bottom,axiom,
    ! [V_B_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),hAPP(c_Set_OPow(T_b),V_B_2))),
    file('theBenchmark.p',fact_Pow__bottom) ).

fof(fact_atLeast__iff,axiom,
    ! [V_k_2,V_i_2,T_b] :
      ( class_Orderings_Oord(T_b)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_k_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_k_2),V_i_2)) ) ),
    file('theBenchmark.p',fact_atLeast__iff) ).

fof(fact_PowD,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2)))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    file('theBenchmark.p',fact_PowD) ).

fof(fact_Pow__iff,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    file('theBenchmark.p',fact_Pow__iff) ).

fof(fact_greaterThan__iff,axiom,
    ! [V_k_2,V_i_2,T_b] :
      ( class_Orderings_Oord(T_b)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_i_2)) ) ),
    file('theBenchmark.p',fact_greaterThan__iff) ).

fof(fact_Inter__lower,axiom,
    ! [V_A_2,V_B_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),V_B_2)) ),
    file('theBenchmark.p',fact_Inter__lower) ).

fof(fact_folding__one_Oremove,axiom,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
      ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
             => hAPP(V_F_2,V_A_2) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) )
            & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
             => hAPP(V_F_2,V_A_2) = V_x_2 ) ) ) ) ),
    file('theBenchmark.p',fact_folding__one_Oremove) ).

fof(fact_folding__image__simple_Oremove,axiom,
    ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
         => hAPP(V_F_2,V_A_2) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))) ) ) ),
    file('theBenchmark.p',fact_folding__image__simple_Oremove) ).

fof(fact_insert__Diff,axiom,
    ! [V_A_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
     => hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = V_A_2 ),
    file('theBenchmark.p',fact_insert__Diff) ).

fof(fact_Diff__insert__absorb,axiom,
    ! [V_A_2,V_x_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_A_2 ),
    file('theBenchmark.p',fact_Diff__insert__absorb) ).

fof(fact_range__ex1__eq,axiom,
    ! [V_b_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
     => ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))))
      <=> ? [B_x] :
            ( ! [B_y] :
                ( V_b_2 = hAPP(V_f_2,B_y)
               => B_y = B_x )
            & V_b_2 = hAPP(V_f_2,B_x) ) ) ),
    file('theBenchmark.p',fact_range__ex1__eq) ).

fof(fact_inj__image__mem__iff,axiom,
    ! [V_A_2,V_a_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
     => ( hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
      <=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_inj__image__mem__iff) ).

fof(fact_min__max_OInf__fin_Oin__idem,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) ) ) ),
    file('theBenchmark.p',fact_min__max_OInf__fin_Oin__idem) ).

fof(fact_min__max_OSup__fin_Oin__idem,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) ) ) ),
    file('theBenchmark.p',fact_min__max_OSup__fin_Oin__idem) ).

fof(fact_folding__one_Osingleton,axiom,
    ! [V_x_2,V_F_2,V_f_2,T_b] :
      ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
     => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ),
    file('theBenchmark.p',fact_folding__one_Osingleton) ).

fof(fact_subset__insert__iff,axiom,
    ! [V_B_2,V_x_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2)))
    <=> ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
        & ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_B_2)) ) ) ),
    file('theBenchmark.p',fact_subset__insert__iff) ).

fof(fact_diff__single__insert,axiom,
    ! [V_B_2,V_x_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_B_2))
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2))) ) ),
    file('theBenchmark.p',fact_diff__single__insert) ).

fof(fact_min__max_Osup__Inf__absorb,axiom,
    ! [V_a_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
         => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) = V_a_2 ) ) ),
    file('theBenchmark.p',fact_min__max_Osup__Inf__absorb) ).

fof(fact_min__max_Oinf__Sup__absorb,axiom,
    ! [V_a_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
         => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_a_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) = V_a_2 ) ) ),
    file('theBenchmark.p',fact_min__max_Oinf__Sup__absorb) ).

fof(fact_inj__on__insert,axiom,
    ! [V_A_2,V_a_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2))
    <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))))
        & c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ),
    file('theBenchmark.p',fact_inj__on__insert) ).

fof(fact_min__max_OInf__fin_Oinsert,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) ) ) ) ),
    file('theBenchmark.p',fact_min__max_OInf__fin_Oinsert) ).

fof(fact_min__max_OSup__fin_Oinsert,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) ) ) ) ),
    file('theBenchmark.p',fact_min__max_OSup__fin_Oinsert) ).

fof(fact_psubset__insert__iff,axiom,
    ! [V_B_2,V_x_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2)))
    <=> ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
         => ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
            & ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_B_2)) ) ) )
        & ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ),
    file('theBenchmark.p',fact_psubset__insert__iff) ).

fof(fact_folding__image__simple_Ounion__inter,axiom,
    ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
         => hAPP(hAPP(V_f_2,hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ),
    file('theBenchmark.p',fact_folding__image__simple_Ounion__inter) ).

fof(fact_min__max_OInf__fin_Oremove,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
             => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) )
            & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
             => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) = V_x_2 ) ) ) ) ),
    file('theBenchmark.p',fact_min__max_OInf__fin_Oremove) ).

fof(fact_min__max_OSup__fin_Oclosed,axiom,
    ! [V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
           => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),V_A_2)) ) ) ) ),
    file('theBenchmark.p',fact_min__max_OSup__fin_Oclosed) ).

fof(fact_min__max_OInf__fin_Oclosed,axiom,
    ! [V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
           => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),V_A_2)) ) ) ) ),
    file('theBenchmark.p',fact_min__max_OInf__fin_Oclosed) ).

fof(fact_ord_OatMost__iff,axiom,
    ! [V_k_2,V_less__eq_2,V_i_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatMost(T_b,V_less__eq_2,V_k_2)))
    <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_k_2)) ),
    file('theBenchmark.p',fact_ord_OatMost__iff) ).

fof(fact_ord_OatLeast__iff,axiom,
    ! [V_k_2,V_less__eq_2,V_i_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeast(T_b,V_less__eq_2,V_k_2)))
    <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_k_2),V_i_2)) ),
    file('theBenchmark.p',fact_ord_OatLeast__iff) ).

fof(fact_ord_OlessThan__iff,axiom,
    ! [V_k_2,V_less_2,V_i_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OlessThan(T_b,V_less_2,V_k_2)))
    <=> hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_k_2)) ),
    file('theBenchmark.p',fact_ord_OlessThan__iff) ).

fof(fact_ord_OgreaterThan__iff,axiom,
    ! [V_k_2,V_less_2,V_i_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThan(T_b,V_less_2,V_k_2)))
    <=> hBOOL(hAPP(hAPP(V_less_2,V_k_2),V_i_2)) ),
    file('theBenchmark.p',fact_ord_OgreaterThan__iff) ).

fof(fact_ord_OatLeastAtMost__iff,axiom,
    ! [V_u_2,V_l_2,V_less__eq_2,V_i_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeastAtMost(T_b,V_less__eq_2,V_l_2,V_u_2)))
    <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2))
        & hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2)) ) ),
    file('theBenchmark.p',fact_ord_OatLeastAtMost__iff) ).

fof(fact_ord_OgreaterThanLessThan__iff,axiom,
    ! [V_u_2,V_l_2,V_less_2,V_i_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThanLessThan(T_b,V_less_2,V_l_2,V_u_2)))
    <=> ( hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2))
        & hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)) ) ),
    file('theBenchmark.p',fact_ord_OgreaterThanLessThan__iff) ).

fof(fact_ord_OatLeastLessThan__iff,axiom,
    ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeastLessThan(T_b,V_less__eq_2,V_less_2,V_l_2,V_u_2)))
    <=> ( hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2))
        & hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2)) ) ),
    file('theBenchmark.p',fact_ord_OatLeastLessThan__iff) ).

fof(fact_ord_OgreaterThanAtMost__iff,axiom,
    ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThanAtMost(T_b,V_less__eq_2,V_less_2,V_l_2,V_u_2)))
    <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2))
        & hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)) ) ),
    file('theBenchmark.p',fact_ord_OgreaterThanAtMost__iff) ).

fof(fact_finite__Union,axiom,
    ! [V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_A_2))
     => ( ! [B_M] :
            ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_M),V_A_2))
           => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_M)) )
       => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2))) ) ),
    file('theBenchmark.p',fact_finite__Union) ).

fof(fact_Inf__fin_Oremove,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Lattices_Olattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
             => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) )
            & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
             => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = V_x_2 ) ) ) ) ),
    file('theBenchmark.p',fact_Inf__fin_Oremove) ).

fof(fact_Sup__fin_Oremove,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Lattices_Olattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
             => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) )
            & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
             => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = V_x_2 ) ) ) ) ),
    file('theBenchmark.p',fact_Sup__fin_Oremove) ).

fof(fact_Max_Oremove,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
             => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) )
            & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
             => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = V_x_2 ) ) ) ) ),
    file('theBenchmark.p',fact_Max_Oremove) ).

fof(fact_Min_Oremove,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
             => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) )
            & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
             => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = V_x_2 ) ) ) ) ),
    file('theBenchmark.p',fact_Min_Oremove) ).

fof(fact_iso__tuple__UNIV__I,axiom,
    ! [V_x_2,T_b] : hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))),
    file('theBenchmark.p',fact_iso__tuple__UNIV__I) ).

fof(fact_insert__partition,axiom,
    ! [V_F_2,V_x_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_F_2))
     => ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_F_2)))
           => ! [B_xa] :
                ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_xa),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_F_2)))
               => ( B_x != B_xa
                 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),B_x),B_xa) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) )
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_x_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_F_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_insert__partition) ).

fof(fact_folding__one_Oclosed,axiom,
    ! [V_A_2,V_F_2,V_f_2,T_b] :
      ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(V_f_2,B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
           => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_F_2,V_A_2)),V_A_2)) ) ) ) ),
    file('theBenchmark.p',fact_folding__one_Oclosed) ).

fof(fact_Inf__le__Sup,axiom,
    ! [V_A_2,T_b] :
      ( class_Lattices_Olattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2))) ) ) ),
    file('theBenchmark.p',fact_Inf__le__Sup) ).

fof(fact_minus__Max__eq__Min,axiom,
    ! [V_S_2,T_b] :
      ( class_Groups_Olinordered__ab__group__add(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
       => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_S_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),V_S_2)) ) ) ),
    file('theBenchmark.p',fact_minus__Max__eq__Min) ).

fof(fact_minus__Min__eq__Max,axiom,
    ! [V_S_2,T_b] :
      ( class_Groups_Olinordered__ab__group__add(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
       => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_S_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),V_S_2)) ) ) ),
    file('theBenchmark.p',fact_minus__Min__eq__Max) ).

fof(fact_Max_Osingleton,axiom,
    ! [V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ),
    file('theBenchmark.p',fact_Max_Osingleton) ).

fof(fact_Min_Osingleton,axiom,
    ! [V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ),
    file('theBenchmark.p',fact_Min_Osingleton) ).

fof(fact_Inf__fin_Osingleton,axiom,
    ! [V_x_2,T_b] :
      ( class_Lattices_Olattice(T_b)
     => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ),
    file('theBenchmark.p',fact_Inf__fin_Osingleton) ).

fof(fact_Sup__fin_Osingleton,axiom,
    ! [V_x_2,T_b] :
      ( class_Lattices_Olattice(T_b)
     => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ),
    file('theBenchmark.p',fact_Sup__fin_Osingleton) ).

fof(fact_Max__ge,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2))) ) ) ),
    file('theBenchmark.p',fact_Max__ge) ).

fof(fact_Min__le,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_x_2)) ) ) ),
    file('theBenchmark.p',fact_Min__le) ).

fof(fact_Min__in,axiom,
    ! [V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_A_2)) ) ) ),
    file('theBenchmark.p',fact_Min__in) ).

fof(fact_Max__in,axiom,
    ! [V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),V_A_2)) ) ) ),
    file('theBenchmark.p',fact_Max__in) ).

fof(fact_sup__Inf__absorb,axiom,
    ! [V_a_2,V_A_2,T_b] :
      ( class_Lattices_Olattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) = V_a_2 ) ) ),
    file('theBenchmark.p',fact_sup__Inf__absorb) ).

fof(fact_Sup__fin_Oin__idem,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Lattices_Olattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) ) ) ),
    file('theBenchmark.p',fact_Sup__fin_Oin__idem) ).

fof(fact_inf__Sup__absorb,axiom,
    ! [V_a_2,V_A_2,T_b] :
      ( class_Lattices_Olattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
         => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) = V_a_2 ) ) ),
    file('theBenchmark.p',fact_inf__Sup__absorb) ).

fof(fact_Inf__fin_Oin__idem,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Lattices_Olattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) ) ) ),
    file('theBenchmark.p',fact_Inf__fin_Oin__idem) ).

fof(fact_Min_Oin__idem,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) ) ) ),
    file('theBenchmark.p',fact_Min_Oin__idem) ).

fof(fact_Max_Oin__idem,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) ) ) ),
    file('theBenchmark.p',fact_Max_Oin__idem) ).

fof(fact_Sup__fin__Sup,axiom,
    ! [V_A_2,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2) ) ) ),
    file('theBenchmark.p',fact_Sup__fin__Sup) ).

fof(fact_Inf__fin__Inf,axiom,
    ! [V_A_2,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2) ) ) ),
    file('theBenchmark.p',fact_Inf__fin__Inf) ).

fof(fact_Max__mono,axiom,
    ! [V_N_2,V_M_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_M_2),V_N_2))
       => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_M_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_N_2))) ) ) ) ),
    file('theBenchmark.p',fact_Max__mono) ).

fof(fact_Min__antimono,axiom,
    ! [V_N_2,V_M_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_M_2),V_N_2))
       => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_N_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_M_2))) ) ) ) ),
    file('theBenchmark.p',fact_Min__antimono) ).

fof(fact_Sup__fin_Oinsert__idem,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Lattices_Olattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) ) ) ),
    file('theBenchmark.p',fact_Sup__fin_Oinsert__idem) ).

fof(fact_Inf__fin_Oinsert__idem,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Lattices_Olattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) ) ) ),
    file('theBenchmark.p',fact_Inf__fin_Oinsert__idem) ).

fof(fact_Min__insert,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)) ) ) ),
    file('theBenchmark.p',fact_Min__insert) ).

fof(fact_Sup__fin_Osubset__idem,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( class_Lattices_Olattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
           => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) ) ) ) ),
    file('theBenchmark.p',fact_Sup__fin_Osubset__idem) ).

fof(fact_Max__insert,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)) ) ) ),
    file('theBenchmark.p',fact_Max__insert) ).

fof(fact_Inf__fin_Osubset__idem,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( class_Lattices_Olattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
           => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) ) ) ) ),
    file('theBenchmark.p',fact_Inf__fin_Osubset__idem) ).

fof(fact_Min_Osubset__idem,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
           => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_B_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) ) ) ) ),
    file('theBenchmark.p',fact_Min_Osubset__idem) ).

fof(fact_Sup__fin_Ounion__idem,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( class_Lattices_Olattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
           => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
             => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2)) ) ) ) ) ),
    file('theBenchmark.p',fact_Sup__fin_Ounion__idem) ).

fof(fact_Max_Osubset__idem,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
           => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_B_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) ) ) ) ),
    file('theBenchmark.p',fact_Max_Osubset__idem) ).

fof(fact_Inf__fin_Ounion__idem,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( class_Lattices_Olattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
           => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
             => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2)) ) ) ) ) ),
    file('theBenchmark.p',fact_Inf__fin_Ounion__idem) ).

fof(fact_Min__Un,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
           => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
             => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_B_2)) ) ) ) ) ),
    file('theBenchmark.p',fact_Min__Un) ).

fof(fact_Max__Un,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
           => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
             => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_B_2)) ) ) ) ) ),
    file('theBenchmark.p',fact_Max__Un) ).

fof(fact_Sup__fin_Oinsert,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Lattices_Olattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) ) ) ) ),
    file('theBenchmark.p',fact_Sup__fin_Oinsert) ).

fof(fact_Inf__fin_Oinsert,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Lattices_Olattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) ) ) ) ),
    file('theBenchmark.p',fact_Inf__fin_Oinsert) ).

fof(fact_Min_Oinsert,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)) ) ) ) ),
    file('theBenchmark.p',fact_Min_Oinsert) ).

fof(fact_Max_Oinsert,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)) ) ) ) ),
    file('theBenchmark.p',fact_Max_Oinsert) ).

fof(fact_Sup__fin_Oinsert__remove,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Lattices_Olattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) )
          & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 ) ) ) ),
    file('theBenchmark.p',fact_Sup__fin_Oinsert__remove) ).

fof(fact_Inf__fin_Oinsert__remove,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Lattices_Olattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) )
          & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 ) ) ) ),
    file('theBenchmark.p',fact_Inf__fin_Oinsert__remove) ).

fof(fact_Min_Oinsert__remove,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) )
          & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 ) ) ) ),
    file('theBenchmark.p',fact_Min_Oinsert__remove) ).

fof(fact_Sup__fin_Ounion__disjoint,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( class_Lattices_Olattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
           => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
             => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
               => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2)) ) ) ) ) ) ),
    file('theBenchmark.p',fact_Sup__fin_Ounion__disjoint) ).

fof(fact_Sup__fin_Ounion__inter,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( class_Lattices_Olattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2)) ) ) ) ),
    file('theBenchmark.p',fact_Sup__fin_Ounion__inter) ).

fof(fact_Max_Oinsert__remove,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) )
          & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 ) ) ) ),
    file('theBenchmark.p',fact_Max_Oinsert__remove) ).

fof(fact_Inf__fin_Ounion__disjoint,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( class_Lattices_Olattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
           => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
             => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
               => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2)) ) ) ) ) ) ),
    file('theBenchmark.p',fact_Inf__fin_Ounion__disjoint) ).

fof(fact_Inf__fin_Ounion__inter,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( class_Lattices_Olattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2)) ) ) ) ),
    file('theBenchmark.p',fact_Inf__fin_Ounion__inter) ).

fof(fact_Min_Ounion__disjoint,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
           => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
             => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
               => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_B_2)) ) ) ) ) ) ),
    file('theBenchmark.p',fact_Min_Ounion__disjoint) ).

fof(fact_Min_Ounion__inter,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_B_2)) ) ) ) ),
    file('theBenchmark.p',fact_Min_Ounion__inter) ).

fof(fact_Max_Ounion__disjoint,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
           => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
             => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
               => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_B_2)) ) ) ) ) ) ),
    file('theBenchmark.p',fact_Max_Ounion__disjoint) ).

fof(fact_Max_Ounion__inter,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_B_2)) ) ) ) ),
    file('theBenchmark.p',fact_Max_Ounion__inter) ).

fof(fact_Max_Oclosed,axiom,
    ! [V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
           => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),V_A_2)) ) ) ) ),
    file('theBenchmark.p',fact_Max_Oclosed) ).

fof(fact_Min_Oclosed,axiom,
    ! [V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
           => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_A_2)) ) ) ) ),
    file('theBenchmark.p',fact_Min_Oclosed) ).

fof(fact_Inf__fin_Oclosed,axiom,
    ! [V_A_2,T_b] :
      ( class_Lattices_Olattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
           => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),V_A_2)) ) ) ) ),
    file('theBenchmark.p',fact_Inf__fin_Oclosed) ).

fof(fact_Sup__fin_Oclosed,axiom,
    ! [V_A_2,T_b] :
      ( class_Lattices_Olattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
           => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),V_A_2)) ) ) ) ),
    file('theBenchmark.p',fact_Sup__fin_Oclosed) ).

fof(fact_fun__upd__image,axiom,
    ! [V_y_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
       => hAPP(c_Set_Oimage(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2)),V_A_2) = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) )
      & ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
       => hAPP(c_Set_Oimage(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ),
    file('theBenchmark.p',fact_fun__upd__image) ).

fof(fact_the__inv__into__into,axiom,
    ! [V_B_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
     => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
         => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_x_2)),V_B_2)) ) ) ),
    file('theBenchmark.p',fact_the__inv__into__into) ).

fof(fact_Max_Ohom__commute,axiom,
    ! [V_N_2,V_h_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
         => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => hAPP(V_h_2,c_Big__Operators_Olinorder__class_OMax(T_b,V_N_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ),
    file('theBenchmark.p',fact_Max_Ohom__commute) ).

fof(fact_Min_Ohom__commute,axiom,
    ! [V_N_2,V_h_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
         => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => hAPP(V_h_2,c_Big__Operators_Olinorder__class_OMin(T_b,V_N_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ),
    file('theBenchmark.p',fact_Min_Ohom__commute) ).

fof(fact_fun__upd__triv,axiom,
    ! [V_x_2,V_f_2,T_c,T_b] : c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,hAPP(V_f_2,V_x_2)) = V_f_2,
    file('theBenchmark.p',fact_fun__upd__triv) ).

fof(fact_fun__upd__idem,axiom,
    ! [T_b,T_c,V_y_2,V_x_2,V_f_2] :
      ( hAPP(V_f_2,V_x_2) = V_y_2
     => c_Fun_Ofun__upd(T_c,T_b,V_f_2,V_x_2,V_y_2) = V_f_2 ),
    file('theBenchmark.p',fact_fun__upd__idem) ).

fof(fact_fun__upd__other,axiom,
    ! [V_y_2,V_f_2,T_c,T_b,V_x_2,V_z_2] :
      ( V_z_2 != V_x_2
     => hAPP(c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2),V_z_2) = hAPP(V_f_2,V_z_2) ),
    file('theBenchmark.p',fact_fun__upd__other) ).

fof(fact_fun__upd__twist,axiom,
    ! [V_d_2,V_b_2,V_m_2,T_c,T_b,V_c_2,V_a_2] :
      ( V_a_2 != V_c_2
     => c_Fun_Ofun__upd(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_m_2,V_a_2,V_b_2),V_c_2,V_d_2) = c_Fun_Ofun__upd(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_m_2,V_c_2,V_d_2),V_a_2,V_b_2) ),
    file('theBenchmark.p',fact_fun__upd__twist) ).

fof(fact_fun__upd__apply,axiom,
    ! [V_y_2,V_f_2,T_c,T_b,V_x_2,V_z_2] :
      ( ( V_z_2 != V_x_2
       => hAPP(c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2),V_z_2) = hAPP(V_f_2,V_z_2) )
      & ( V_z_2 = V_x_2
       => hAPP(c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2),V_z_2) = V_y_2 ) ),
    file('theBenchmark.p',fact_fun__upd__apply) ).

fof(fact_fun__upd__same,axiom,
    ! [V_y_2,V_x_2,V_f_2,T_b,T_c] : hAPP(c_Fun_Ofun__upd(T_c,T_b,V_f_2,V_x_2,V_y_2),V_x_2) = V_y_2,
    file('theBenchmark.p',fact_fun__upd__same) ).

fof(fact_fun__upd__upd,axiom,
    ! [V_z_2,V_y_2,V_x_2,V_f_2,T_c,T_b] : c_Fun_Ofun__upd(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2),V_x_2,V_z_2) = c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_z_2),
    file('theBenchmark.p',fact_fun__upd__upd) ).

fof(fact_fun__upd__idem__iff,axiom,
    ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
      ( c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2) = V_f_2
    <=> hAPP(V_f_2,V_x_2) = V_y_2 ),
    file('theBenchmark.p',fact_fun__upd__idem__iff) ).

fof(fact_the__inv__into__f__eq,axiom,
    ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
     => ( hAPP(V_f_2,V_x_2) = V_y_2
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ),
    file('theBenchmark.p',fact_the__inv__into__f__eq) ).

fof(fact_the__inv__into__f__f,axiom,
    ! [V_x_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
       => hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2 ) ),
    file('theBenchmark.p',fact_the__inv__into__f__f) ).

fof(fact_the__inv__f__f,axiom,
    ! [V_x_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
     => hAPP(c_Fun_Othe__inv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2 ),
    file('theBenchmark.p',fact_the__inv__f__f) ).

fof(fact_the__inv__into__onto,axiom,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
     => hAPP(c_Set_Oimage(T_c,T_b,c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = V_A_2 ),
    file('theBenchmark.p',fact_the__inv__into__onto) ).

fof(fact_inj__on__the__inv__into,axiom,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
     => c_Fun_Oinj__on(T_c,T_b,c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) ),
    file('theBenchmark.p',fact_inj__on__the__inv__into) ).

fof(fact_inj__on__fun__updI,axiom,
    ! [V_x_2,V_y_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
     => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
       => c_Fun_Oinj__on(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2),V_A_2) ) ),
    file('theBenchmark.p',fact_inj__on__fun__updI) ).

fof(fact_f__the__inv__into__f,axiom,
    ! [V_y_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
     => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
       => hAPP(V_f_2,hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_y_2)) = V_y_2 ) ),
    file('theBenchmark.p',fact_f__the__inv__into__f) ).

fof(fact_Inf__fin_Ohom__commute,axiom,
    ! [V_N_2,V_h_2,T_b] :
      ( class_Lattices_Olattice(T_b)
     => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),B_x),B_y)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
         => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => hAPP(V_h_2,c_Big__Operators_Olattice__class_OInf__fin(T_b,V_N_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ),
    file('theBenchmark.p',fact_Inf__fin_Ohom__commute) ).

fof(fact_Sup__fin_Ohom__commute,axiom,
    ! [V_N_2,V_h_2,T_b] :
      ( class_Lattices_Olattice(T_b)
     => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),B_x),B_y)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
         => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => hAPP(V_h_2,c_Big__Operators_Olattice__class_OSup__fin(T_b,V_N_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ),
    file('theBenchmark.p',fact_Sup__fin_Ohom__commute) ).

fof(fact_finite__empty__induct,axiom,
    ! [V_P_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( hBOOL(hAPP(V_P_2,V_A_2))
       => ( ! [B_a,B_A] :
              ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_A))
             => ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A))
               => ( hBOOL(hAPP(V_P_2,B_A))
                 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),B_A),hAPP(hAPP(c_Set_Oinsert(T_b),B_a),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) )
         => hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ) ),
    file('theBenchmark.p',fact_finite__empty__induct) ).

fof(fact_folding__one__idem_Ounion__idem,axiom,
    ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
      ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
           => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
             => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ) ),
    file('theBenchmark.p',fact_folding__one__idem_Ounion__idem) ).

fof(fact_finite__subset__induct,axiom,
    ! [V_P_2,V_A_2,V_F_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_A_2))
       => ( hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
         => ( ! [B_a,B_F] :
                ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_F))
               => ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
                 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_F))
                   => ( hBOOL(hAPP(V_P_2,B_F))
                     => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_F))) ) ) ) )
           => hBOOL(hAPP(V_P_2,V_F_2)) ) ) ) ),
    file('theBenchmark.p',fact_finite__subset__induct) ).

fof(fact_folding__one__idem_Osubset__idem,axiom,
    ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
      ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
           => hAPP(hAPP(V_f_2,hAPP(V_F_2,V_B_2)),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ),
    file('theBenchmark.p',fact_folding__one__idem_Osubset__idem) ).

fof(fact_folding__one__idem_Oinsert__idem,axiom,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
      ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) ) ) ),
    file('theBenchmark.p',fact_folding__one__idem_Oinsert__idem) ).

fof(fact_inj__on__Inter,axiom,
    ! [V_f_2,T_c,T_b,V_S_2] :
      ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))
     => ( ! [B_A] :
            ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_A),V_S_2))
           => c_Fun_Oinj__on(T_b,T_c,V_f_2,B_A) )
       => c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_S_2)) ) ),
    file('theBenchmark.p',fact_inj__on__Inter) ).

fof(fact_folding__one__idem_Oidem,axiom,
    ! [V_x_2,V_F_2,V_f_2,T_b] :
      ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
     => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ),
    file('theBenchmark.p',fact_folding__one__idem_Oidem) ).

fof(fact_folding__one__idem_Oin__idem,axiom,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
      ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ),
    file('theBenchmark.p',fact_folding__one__idem_Oin__idem) ).

fof(fact_Inter__subset,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( ! [B_X] :
          ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_A_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_X),V_B_2)) )
     => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),V_B_2)) ) ),
    file('theBenchmark.p',fact_Inter__subset) ).

fof(fact_fold1__antimono,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_B_2)),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2))) ) ) ) ),
    file('theBenchmark.p',fact_fold1__antimono) ).

fof(fact_folding__one__idem_Ohom__commute,axiom,
    ! [V_N_2,V_h_2,V_F_2,V_f_2,T_b] :
      ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
     => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(V_f_2,B_x),B_y)) = hAPP(hAPP(V_f_2,hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
         => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => hAPP(V_h_2,hAPP(V_F_2,V_N_2)) = hAPP(V_F_2,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ),
    file('theBenchmark.p',fact_folding__one__idem_Ohom__commute) ).

fof(fact_folding__image__simple_Ounion__inter__neutral,axiom,
    ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
         => ( ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))
               => hAPP(V_g_2,B_x) = V_z_2 )
           => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ),
    file('theBenchmark.p',fact_folding__image__simple_Ounion__inter__neutral) ).

fof(fact_setsum__diff1,axiom,
    ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
      ( class_Groups_Oab__group__add(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2) )
          & ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) ) ) ) ),
    file('theBenchmark.p',fact_setsum__diff1) ).

fof(fact_setsum__diff1__ring,axiom,
    ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
      ( class_Rings_Oring(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) ) ) ),
    file('theBenchmark.p',fact_setsum__diff1__ring) ).

fof(fact_InterI,axiom,
    ! [V_A_2,V_C_2,T_b] :
      ( ! [B_X] :
          ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2))
         => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),B_X)) )
     => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_C_2))) ),
    file('theBenchmark.p',fact_InterI) ).

fof(fact_Min__eqI,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ! [B_y] :
              ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_y)) )
         => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
           => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = V_x_2 ) ) ) ),
    file('theBenchmark.p',fact_Min__eqI) ).

fof(fact_setsum__diff__nat__ivl,axiom,
    ! [V_f_2,V_p_2,V_n_2,V_m_2,T_b] :
      ( class_Groups_Oab__group__add(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2))
         => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_p_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_n_2),V_p_2)) ) ) ),
    file('theBenchmark.p',fact_setsum__diff__nat__ivl) ).

fof(fact_fold1__singleton__def,axiom,
    ! [V_a_2,V_f_2,T_b,V_g_2] :
      ( V_g_2 = c_Finite__Set_Ofold1(T_b,V_f_2)
     => hAPP(V_g_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_a_2 ),
    file('theBenchmark.p',fact_fold1__singleton__def) ).

fof(fact_fold1__singleton,axiom,
    ! [V_a_2,V_f_2,T_b] : hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_a_2,
    file('theBenchmark.p',fact_fold1__singleton) ).

fof(fact_setsum__diff__nat,axiom,
    ! [V_f_2,V_A_2,V_B_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_B_2)) ) ),
    file('theBenchmark.p',fact_setsum__diff__nat) ).

fof(fact_folding__one_Oeq__fold,axiom,
    ! [V_A_2,V_F_2,V_f_2,T_b] :
      ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) ) ),
    file('theBenchmark.p',fact_folding__one_Oeq__fold) ).

fof(fact_Sup__fin_OF__eq,axiom,
    ! [V_A_2,T_b] :
      ( class_Lattices_Olattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_A_2) ) ),
    file('theBenchmark.p',fact_Sup__fin_OF__eq) ).

fof(fact_Inf__fin_OF__eq,axiom,
    ! [V_A_2,T_b] :
      ( class_Lattices_Olattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_A_2) ) ),
    file('theBenchmark.p',fact_Inf__fin_OF__eq) ).

fof(fact_setsum__diff1__nat,axiom,
    ! [V_f_2,V_A_2,V_a_2,T_b] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) )
      & ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) ) ),
    file('theBenchmark.p',fact_setsum__diff1__nat) ).

fof(fact_setsum__diff,axiom,
    ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
      ( class_Groups_Oab__group__add(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2)) ) ) ),
    file('theBenchmark.p',fact_setsum__diff) ).

fof(fact_Min_OF__eq,axiom,
    ! [V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2) ) ),
    file('theBenchmark.p',fact_Min_OF__eq) ).

fof(fact_Max_OF__eq,axiom,
    ! [V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omax(T_b)),V_A_2) ) ),
    file('theBenchmark.p',fact_Max_OF__eq) ).

fof(fact_min__max_OInf__fin_OF__eq,axiom,
    ! [V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2) ) ),
    file('theBenchmark.p',fact_min__max_OInf__fin_OF__eq) ).

fof(fact_min__max_OSup__fin_OF__eq,axiom,
    ! [V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omax(T_b)),V_A_2) ) ),
    file('theBenchmark.p',fact_min__max_OSup__fin_OF__eq) ).

fof(fact_fold1__belowI,axiom,
    ! [V_a_2,V_A_2,T_b] :
      ( class_Lattices_Osemilattice__inf(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_A_2)),V_a_2)) ) ) ),
    file('theBenchmark.p',fact_fold1__belowI) ).

fof(fact_below__fold1__iff,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Lattices_Osemilattice__inf(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_A_2)))
          <=> ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ),
    file('theBenchmark.p',fact_below__fold1__iff) ).

fof(fact_min__max_Ofold1__belowI,axiom,
    ! [V_a_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)),V_a_2)) ) ) ),
    file('theBenchmark.p',fact_min__max_Ofold1__belowI) ).

fof(fact_min__max_Obelow__fold1__iff,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)))
          <=> ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ),
    file('theBenchmark.p',fact_min__max_Obelow__fold1__iff) ).

fof(fact_fold1__below__iff,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)),V_x_2))
          <=> ? [B_x] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_x_2))
                & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ) ) ),
    file('theBenchmark.p',fact_fold1__below__iff) ).

fof(fact_strict__below__fold1__iff,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)))
          <=> ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),B_x)) ) ) ) ) ),
    file('theBenchmark.p',fact_strict__below__fold1__iff) ).

fof(fact_fold1__strict__below__iff,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)),V_x_2))
          <=> ? [B_x] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_x_2))
                & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ) ) ),
    file('theBenchmark.p',fact_fold1__strict__below__iff) ).

fof(fact_semilattice__big_OF__eq,axiom,
    ! [V_A_2,V_F_2,V_f_2,T_b] :
      ( c_Big__Operators_Osemilattice__big(T_b,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) ) ),
    file('theBenchmark.p',fact_semilattice__big_OF__eq) ).

fof(fact_setsum__strict__mono,axiom,
    ! [V_g_2,V_f_2,V_A_2,T_b,T_c] :
      ( ( class_Groups_Oordered__cancel__ab__semigroup__add(T_c)
        & class_Groups_Ocomm__monoid__add(T_c) )
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2))) ) ) ) ),
    file('theBenchmark.p',fact_setsum__strict__mono) ).

fof(fact_setsum_Oremove,axiom,
    ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__add(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ),
    file('theBenchmark.p',fact_setsum_Oremove) ).

fof(fact_setsum__diff1_H,axiom,
    ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__add(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ),
    file('theBenchmark.p',fact_setsum__diff1_H) ).

fof(fact_fold1__Un,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( class_Groups_Oab__semigroup__mult(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
           => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
             => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
               => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2)),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_B_2)) ) ) ) ) ) ),
    file('theBenchmark.p',fact_fold1__Un) ).

fof(fact_fold1__insert,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Groups_Oab__semigroup__mult(T_b)
     => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
         => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
           => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2)) ) ) ) ),
    file('theBenchmark.p',fact_fold1__insert) ).

fof(fact_Max__eqI,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ! [B_y] :
              ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_y),V_x_2)) )
         => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
           => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = V_x_2 ) ) ) ),
    file('theBenchmark.p',fact_Max__eqI) ).

fof(fact_setsum__reindex__cong,axiom,
    ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
      ( class_Groups_Ocomm__monoid__add(T_d)
     => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
       => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
         => ( ! [B_a] :
                ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
               => hAPP(V_g_2,B_a) = hAPP(V_h_2,hAPP(V_f_2,B_a)) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),V_g_2),V_A_2) ) ) ) ),
    file('theBenchmark.p',fact_setsum__reindex__cong) ).

fof(fact_finite__atLeastLessThan,axiom,
    ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_l_2),V_u_2))),
    file('theBenchmark.p',fact_finite__atLeastLessThan) ).

fof(fact_setsum__add__nat__ivl,axiom,
    ! [V_f_2,V_p_2,V_n_2,V_m_2,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2))
         => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_n_2),V_p_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_p_2)) ) ) ),
    file('theBenchmark.p',fact_setsum__add__nat__ivl) ).

fof(fact_eq__add__iff2,axiom,
    ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
      ( class_Rings_Oring(T_b)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)
      <=> V_c_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2) ) ),
    file('theBenchmark.p',fact_eq__add__iff2) ).

fof(fact_eq__add__iff1,axiom,
    ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
      ( class_Rings_Oring(T_b)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)
      <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_c_2) = V_d_2 ) ),
    file('theBenchmark.p',fact_eq__add__iff1) ).

fof(fact_atLeastLessThan__add__Un,axiom,
    ! [V_k_2,V_j_2,V_i_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
     => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),V_k_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_j_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),V_k_2))) ),
    file('theBenchmark.p',fact_atLeastLessThan__add__Un) ).

fof(fact_times_Oidem,axiom,
    ! [V_a,T_a] :
      ( class_Lattices_Oab__semigroup__idem__mult(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) = V_a ),
    file('theBenchmark.p',fact_times_Oidem) ).

fof(fact_mult__idem,axiom,
    ! [V_x,T_a] :
      ( class_Lattices_Oab__semigroup__idem__mult(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = V_x ),
    file('theBenchmark.p',fact_mult__idem) ).

fof(fact_mult__left__idem,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Lattices_Oab__semigroup__idem__mult(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) ),
    file('theBenchmark.p',fact_mult__left__idem) ).

fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Groups_Oab__semigroup__add(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)) ),
    file('theBenchmark.p',fact_ab__semigroup__add__class_Oadd__ac_I1_J) ).

fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Groups_Oab__semigroup__mult(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ),
    file('theBenchmark.p',fact_ab__semigroup__mult__class_Omult__ac_I1_J) ).

fof(fact_add__left__cancel,axiom,
    ! [V_c_2,V_b_2,V_a_2,T_b] :
      ( class_Groups_Ocancel__semigroup__add(T_b)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_c_2)
      <=> V_b_2 = V_c_2 ) ),
    file('theBenchmark.p',fact_add__left__cancel) ).

fof(fact_add__right__cancel,axiom,
    ! [V_c_2,V_a_2,V_b_2,T_b] :
      ( class_Groups_Ocancel__semigroup__add(T_b)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_a_2)
      <=> V_b_2 = V_c_2 ) ),
    file('theBenchmark.p',fact_add__right__cancel) ).

fof(fact_add__left__imp__eq,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Groups_Ocancel__semigroup__add(T_a)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)
       => V_b = V_c ) ),
    file('theBenchmark.p',fact_add__left__imp__eq) ).

fof(fact_add__imp__eq,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Groups_Ocancel__ab__semigroup__add(T_a)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)
       => V_b = V_c ) ),
    file('theBenchmark.p',fact_add__imp__eq) ).

fof(fact_add__right__imp__eq,axiom,
    ! [V_c,V_a,V_b,T_a] :
      ( class_Groups_Ocancel__semigroup__add(T_a)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)
       => V_b = V_c ) ),
    file('theBenchmark.p',fact_add__right__imp__eq) ).

fof(fact_comm__semiring__class_Odistrib,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Rings_Ocomm__semiring(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ),
    file('theBenchmark.p',fact_comm__semiring__class_Odistrib) ).

fof(fact_combine__common__factor,axiom,
    ! [V_c,V_b,V_e,V_a,T_a] :
      ( class_Rings_Osemiring(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_e)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_e)),V_c)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_e)),V_c) ),
    file('theBenchmark.p',fact_combine__common__factor) ).

fof(fact_finite__nat__set__iff__bounded__le,axiom,
    ! [V_N_2] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2))
    <=> ? [B_m] :
        ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_x),B_m)) ) ),
    file('theBenchmark.p',fact_finite__nat__set__iff__bounded__le) ).

fof(fact_le__add__iff2,axiom,
    ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
      ( class_Rings_Oordered__ring(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2))) ) ),
    file('theBenchmark.p',fact_le__add__iff2) ).

fof(fact_le__add__iff1,axiom,
    ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
      ( class_Rings_Oordered__ring(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_c_2)),V_d_2)) ) ),
    file('theBenchmark.p',fact_le__add__iff1) ).

fof(fact_less__add__iff1,axiom,
    ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
      ( class_Rings_Oordered__ring(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_c_2)),V_d_2)) ) ),
    file('theBenchmark.p',fact_less__add__iff1) ).

fof(fact_less__add__iff2,axiom,
    ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
      ( class_Rings_Oordered__ring(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2))) ) ),
    file('theBenchmark.p',fact_less__add__iff2) ).

fof(fact_add__le__cancel__right,axiom,
    ! [V_b_2,V_c_2,V_a_2,T_b] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_c_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ),
    file('theBenchmark.p',fact_add__le__cancel__right) ).

fof(fact_add__le__cancel__left,axiom,
    ! [V_b_2,V_a_2,V_c_2,T_b] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_b_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ),
    file('theBenchmark.p',fact_add__le__cancel__left) ).

fof(fact_add__right__mono,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Groups_Oordered__ab__semigroup__add(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))) ) ),
    file('theBenchmark.p',fact_add__right__mono) ).

fof(fact_add__left__mono,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Groups_Oordered__ab__semigroup__add(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b))) ) ),
    file('theBenchmark.p',fact_add__left__mono) ).

fof(fact_add__mono,axiom,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( class_Groups_Oordered__ab__semigroup__add(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))) ) ) ),
    file('theBenchmark.p',fact_add__mono) ).

fof(fact_add__le__imp__le__right,axiom,
    ! [V_b,V_c,V_a,T_a] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ),
    file('theBenchmark.p',fact_add__le__imp__le__right) ).

fof(fact_add__le__imp__le__left,axiom,
    ! [V_b,V_a,V_c,T_a] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ),
    file('theBenchmark.p',fact_add__le__imp__le__left) ).

fof(fact_add__less__cancel__right,axiom,
    ! [V_b_2,V_c_2,V_a_2,T_b] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_c_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ),
    file('theBenchmark.p',fact_add__less__cancel__right) ).

fof(fact_add__less__cancel__left,axiom,
    ! [V_b_2,V_a_2,V_c_2,T_b] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_b_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ),
    file('theBenchmark.p',fact_add__less__cancel__left) ).

fof(fact_add__strict__right__mono,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))) ) ),
    file('theBenchmark.p',fact_add__strict__right__mono) ).

fof(fact_add__strict__left__mono,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b))) ) ),
    file('theBenchmark.p',fact_add__strict__left__mono) ).

fof(fact_add__strict__mono,axiom,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))) ) ) ),
    file('theBenchmark.p',fact_add__strict__mono) ).

fof(fact_add__less__imp__less__right,axiom,
    ! [V_b,V_c,V_a,T_a] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ),
    file('theBenchmark.p',fact_add__less__imp__less__right) ).

fof(fact_add__less__imp__less__left,axiom,
    ! [V_b,V_a,V_c,T_a] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ),
    file('theBenchmark.p',fact_add__less__imp__less__left) ).

fof(fact_diff__add__cancel,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Ogroup__add(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)),V_b) = V_a ),
    file('theBenchmark.p',fact_diff__add__cancel) ).

fof(fact_add__diff__cancel,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Ogroup__add(T_a)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_b) = V_a ),
    file('theBenchmark.p',fact_add__diff__cancel) ).

fof(fact_minus__add__cancel,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Ogroup__add(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)) = V_b ),
    file('theBenchmark.p',fact_minus__add__cancel) ).

fof(fact_add__minus__cancel,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Ogroup__add(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) = V_b ),
    file('theBenchmark.p',fact_add__minus__cancel) ).

fof(fact_minus__add,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Ogroup__add(T_a)
     => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) ),
    file('theBenchmark.p',fact_minus__add) ).

fof(fact_minus__add__distrib,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Oab__group__add(T_a)
     => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ),
    file('theBenchmark.p',fact_minus__add__distrib) ).

fof(fact_square__eq__iff,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( class_Rings_Oidom(T_b)
     => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_a_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_b_2)
      <=> ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
          | V_a_2 = V_b_2 ) ) ),
    file('theBenchmark.p',fact_square__eq__iff) ).

fof(fact_minus__mult__minus,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Oring(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) ),
    file('theBenchmark.p',fact_minus__mult__minus) ).

fof(fact_minus__mult__commute,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Oring(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ),
    file('theBenchmark.p',fact_minus__mult__commute) ).

fof(fact_minus__mult__left,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Oring(T_a)
     => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b) ),
    file('theBenchmark.p',fact_minus__mult__left) ).

fof(fact_minus__mult__right,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Oring(T_a)
     => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ),
    file('theBenchmark.p',fact_minus__mult__right) ).

fof(fact_min__add__distrib__left,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),V_z)) ),
    file('theBenchmark.p',fact_min__add__distrib__left) ).

fof(fact_max__add__distrib__left,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),V_z)) ),
    file('theBenchmark.p',fact_max__add__distrib__left) ).

fof(fact_add__le__less__mono,axiom,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))) ) ) ),
    file('theBenchmark.p',fact_add__le__less__mono) ).

fof(fact_add__less__le__mono,axiom,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))) ) ) ),
    file('theBenchmark.p',fact_add__less__le__mono) ).

fof(fact_diff__minus__eq__add,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Ogroup__add(T_a)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) ),
    file('theBenchmark.p',fact_diff__minus__eq__add) ).

fof(fact_ab__diff__minus,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Oab__group__add(T_a)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ),
    file('theBenchmark.p',fact_ab__diff__minus) ).

fof(fact_diff__def,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Ogroup__add(T_a)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ),
    file('theBenchmark.p',fact_diff__def) ).

fof(fact_setsum__Un__nat,axiom,
    ! [V_f_2,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ),
    file('theBenchmark.p',fact_setsum__Un__nat) ).

fof(fact_setsum_Oinsert,axiom,
    ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__add(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)) ) ) ),
    file('theBenchmark.p',fact_setsum_Oinsert) ).

fof(fact_setsum__insert,axiom,
    ! [V_f_2,V_a_2,V_F_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__add(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_F_2))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_F_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_F_2)) ) ) ),
    file('theBenchmark.p',fact_setsum__insert) ).

fof(fact_setsum__Un__Int,axiom,
    ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__add(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
         => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_B_2)) ) ) ),
    file('theBenchmark.p',fact_setsum__Un__Int) ).

fof(fact_fold1__insert__idem,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Lattices_Oab__semigroup__idem__mult(T_b)
     => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
         => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2)) ) ) ),
    file('theBenchmark.p',fact_fold1__insert__idem) ).

fof(fact_fold1__Un2,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( class_Lattices_Oab__semigroup__idem__mult(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
           => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
             => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2)),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_B_2)) ) ) ) ) ),
    file('theBenchmark.p',fact_fold1__Un2) ).

fof(fact_setsum_Oinsert__remove,axiom,
    ! [V_x_2,V_g_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__add(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ),
    file('theBenchmark.p',fact_setsum_Oinsert__remove) ).

fof(fact_setsum__Un__disjoint,axiom,
    ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__add(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_B_2)) ) ) ) ),
    file('theBenchmark.p',fact_setsum__Un__disjoint) ).

fof(fact_setsum__Un,axiom,
    ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
      ( class_Groups_Oab__group__add(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ),
    file('theBenchmark.p',fact_setsum__Un) ).

fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Rings_Ocomm__ring__1(T_a)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_y) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ),
    file('theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J) ).

fof(fact_fold1__in,axiom,
    ! [V_A_2,T_b] :
      ( class_Groups_Oab__semigroup__mult(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
           => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2)),V_A_2)) ) ) ) ),
    file('theBenchmark.p',fact_fold1__in) ).

fof(fact_le__diff__iff,axiom,
    ! [V_n_2,V_m_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_k_2)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ),
    file('theBenchmark.p',fact_le__diff__iff) ).

fof(fact_Nat_Odiff__diff__eq,axiom,
    ! [V_n,V_m,V_k] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_m))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) ) ),
    file('theBenchmark.p',fact_Nat_Odiff__diff__eq) ).

fof(fact_eq__diff__iff,axiom,
    ! [V_n_2,V_m_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
       => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_k_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_k_2)
        <=> V_m_2 = V_n_2 ) ) ),
    file('theBenchmark.p',fact_eq__diff__iff) ).

fof(fact_nat__le__add__iff1,axiom,
    ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i_2),V_j_2)),V_u_2)),V_m_2)),V_n_2)) ) ),
    file('theBenchmark.p',fact_nat__le__add__iff1) ).

fof(fact_nat__diff__add__eq1,axiom,
    ! [V_n,V_m,V_u,V_i,V_j] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_j)),V_u)),V_m)),V_n) ),
    file('theBenchmark.p',fact_nat__diff__add__eq1) ).

fof(fact_nat__eq__add__iff1,axiom,
    ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)
      <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i_2),V_j_2)),V_u_2)),V_m_2) = V_n_2 ) ),
    file('theBenchmark.p',fact_nat__eq__add__iff1) ).

fof(fact_finite__lessThan,axiom,
    ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_k_2))),
    file('theBenchmark.p',fact_finite__lessThan) ).

fof(fact_finite__atMost,axiom,
    ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2))),
    file('theBenchmark.p',fact_finite__atMost) ).

fof(fact_finite__atLeastAtMost,axiom,
    ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_l_2,V_u_2))),
    file('theBenchmark.p',fact_finite__atLeastAtMost) ).

fof(fact_finite__greaterThanAtMost,axiom,
    ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_l_2,V_u_2))),
    file('theBenchmark.p',fact_finite__greaterThanAtMost) ).

fof(fact_finite__greaterThanLessThan,axiom,
    ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,V_l_2,V_u_2))),
    file('theBenchmark.p',fact_finite__greaterThanLessThan) ).

fof(fact_left__add__mult__distrib,axiom,
    ! [V_k,V_j,V_u,V_i] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_u)),V_k),
    file('theBenchmark.p',fact_left__add__mult__distrib) ).

fof(fact_nat__add__right__cancel,axiom,
    ! [V_n_2,V_k_2,V_m_2] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_k_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2)
    <=> V_m_2 = V_n_2 ),
    file('theBenchmark.p',fact_nat__add__right__cancel) ).

fof(fact_nat__add__left__cancel,axiom,
    ! [V_n_2,V_m_2,V_k_2] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2)
    <=> V_m_2 = V_n_2 ),
    file('theBenchmark.p',fact_nat__add__left__cancel) ).

fof(fact_add__mult__distrib,axiom,
    ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)),
    file('theBenchmark.p',fact_add__mult__distrib) ).

fof(fact_nat__mult__assoc,axiom,
    ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)),
    file('theBenchmark.p',fact_nat__mult__assoc) ).

fof(fact_nat__add__assoc,axiom,
    ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_k)),
    file('theBenchmark.p',fact_nat__add__assoc) ).

fof(fact_add__mult__distrib2,axiom,
    ! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)),
    file('theBenchmark.p',fact_add__mult__distrib2) ).

fof(fact_nat__add__left__commute,axiom,
    ! [V_z,V_y,V_x] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),V_z)),
    file('theBenchmark.p',fact_nat__add__left__commute) ).

fof(fact_nat__mult__commute,axiom,
    ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m),
    file('theBenchmark.p',fact_nat__mult__commute) ).

fof(fact_nat__add__commute,axiom,
    ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m),
    file('theBenchmark.p',fact_nat__add__commute) ).

fof(fact_add__lessD1,axiom,
    ! [V_k,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_k))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_k)) ),
    file('theBenchmark.p',fact_add__lessD1) ).

fof(fact_less__add__eq__less,axiom,
    ! [V_n,V_m,V_l,V_k] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l))
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_l) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_n)
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ),
    file('theBenchmark.p',fact_less__add__eq__less) ).

fof(fact_add__less__mono,axiom,
    ! [V_l,V_k,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_l))) ) ),
    file('theBenchmark.p',fact_add__less__mono) ).

fof(fact_add__less__mono1,axiom,
    ! [V_k,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k))) ),
    file('theBenchmark.p',fact_add__less__mono1) ).

fof(fact_trans__less__add2,axiom,
    ! [V_m,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_j))) ),
    file('theBenchmark.p',fact_trans__less__add2) ).

fof(fact_trans__less__add1,axiom,
    ! [V_m,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_m))) ),
    file('theBenchmark.p',fact_trans__less__add1) ).

fof(fact_nat__add__left__cancel__less,axiom,
    ! [V_n_2,V_m_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ),
    file('theBenchmark.p',fact_nat__add__left__cancel__less) ).

fof(fact_not__add__less2,axiom,
    ! [V_i,V_j] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i)),V_i)),
    file('theBenchmark.p',fact_not__add__less2) ).

fof(fact_not__add__less1,axiom,
    ! [V_j,V_i] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_i)),
    file('theBenchmark.p',fact_not__add__less1) ).

fof(fact_infinite__UNIV__nat,axiom,
    ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    file('theBenchmark.p',fact_infinite__UNIV__nat) ).

fof(fact_finite__nat__set__iff__bounded,axiom,
    ! [V_N_2] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2))
    <=> ? [B_m] :
        ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_x),B_m)) ) ),
    file('theBenchmark.p',fact_finite__nat__set__iff__bounded) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
    ! [V_c,V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
    ! [V_d,V_c,V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_d)) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
    ! [V_d,V_c,V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),V_d) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),V_b) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d)) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
    ! [V_ry,V_rx,V_lx,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ry)) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
    ! [V_ry,V_rx,V_lx,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ry) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
    ! [V_rx,V_ly,V_lx,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_rx)) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
    ! [V_rx,V_ly,V_lx,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ly) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
    ! [V_ry,V_rx,V_ly,V_lx,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
    ! [V_ry,V_rx,V_ly,V_lx,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_ry)) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
    ! [V_ry,V_rx,V_ly,V_lx,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_ry)) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).

fof(fact_nat__less__le,axiom,
    ! [V_n_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
    <=> ( V_m_2 != V_n_2
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ),
    file('theBenchmark.p',fact_nat__less__le) ).

fof(fact_le__eq__less__or__eq,axiom,
    ! [V_n_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
    <=> ( V_m_2 = V_n_2
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ),
    file('theBenchmark.p',fact_le__eq__less__or__eq) ).

fof(fact_less__imp__le__nat,axiom,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ),
    file('theBenchmark.p',fact_less__imp__le__nat) ).

fof(fact_le__neq__implies__less,axiom,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
     => ( V_m != V_n
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ),
    file('theBenchmark.p',fact_le__neq__implies__less) ).

fof(fact_less__or__eq__imp__le,axiom,
    ! [V_n,V_m] :
      ( ( V_m = V_n
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) )
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ),
    file('theBenchmark.p',fact_less__or__eq__imp__le) ).

fof(fact_le__refl,axiom,
    ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_n)),
    file('theBenchmark.p',fact_le__refl) ).

fof(fact_le__square,axiom,
    ! [V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m))),
    file('theBenchmark.p',fact_le__square) ).

fof(fact_le__add2,axiom,
    ! [V_m,V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))),
    file('theBenchmark.p',fact_le__add2) ).

fof(fact_le__add1,axiom,
    ! [V_m,V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m))),
    file('theBenchmark.p',fact_le__add1) ).

fof(fact_le__cube,axiom,
    ! [V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m)))),
    file('theBenchmark.p',fact_le__cube) ).

fof(fact_le__iff__add,axiom,
    ! [V_n_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
    <=> ? [B_k] : V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k) ),
    file('theBenchmark.p',fact_le__iff__add) ).

fof(fact_nat__le__linear,axiom,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ),
    file('theBenchmark.p',fact_nat__le__linear) ).

fof(fact_nat__add__left__cancel__le,axiom,
    ! [V_n_2,V_m_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ),
    file('theBenchmark.p',fact_nat__add__left__cancel__le) ).

fof(fact_eq__imp__le,axiom,
    ! [V_n,V_m] :
      ( V_m = V_n
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ),
    file('theBenchmark.p',fact_eq__imp__le) ).

fof(fact_trans__le__add1,axiom,
    ! [V_m,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_m))) ),
    file('theBenchmark.p',fact_trans__le__add1) ).

fof(fact_trans__le__add2,axiom,
    ! [V_m,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_j))) ),
    file('theBenchmark.p',fact_trans__le__add2) ).

fof(fact_add__le__mono1,axiom,
    ! [V_k,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k))) ),
    file('theBenchmark.p',fact_add__le__mono1) ).

fof(fact_mult__le__mono1,axiom,
    ! [V_k,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k))) ),
    file('theBenchmark.p',fact_mult__le__mono1) ).

fof(fact_mult__le__mono2,axiom,
    ! [V_k,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j))) ),
    file('theBenchmark.p',fact_mult__le__mono2) ).

fof(fact_le__trans,axiom,
    ! [V_k,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_k))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_k)) ) ),
    file('theBenchmark.p',fact_le__trans) ).

fof(fact_le__antisym,axiom,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
       => V_m = V_n ) ),
    file('theBenchmark.p',fact_le__antisym) ).

fof(fact_add__le__mono,axiom,
    ! [V_l,V_k,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_l))) ) ),
    file('theBenchmark.p',fact_add__le__mono) ).

fof(fact_mult__le__mono,axiom,
    ! [V_l,V_k,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_l))) ) ),
    file('theBenchmark.p',fact_mult__le__mono) ).

fof(fact_add__leD2,axiom,
    ! [V_n,V_k,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ),
    file('theBenchmark.p',fact_add__leD2) ).

fof(fact_add__leD1,axiom,
    ! [V_n,V_k,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ),
    file('theBenchmark.p',fact_add__leD1) ).

fof(fact_add__leE,axiom,
    ! [V_n,V_k,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n))
     => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
         => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ),
    file('theBenchmark.p',fact_add__leE) ).

fof(fact_less__diff__conv,axiom,
    ! [V_k_2,V_j_2,V_i_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_k_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),V_j_2)) ),
    file('theBenchmark.p',fact_less__diff__conv) ).

fof(fact_add__diff__inverse,axiom,
    ! [V_n,V_m] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = V_m ),
    file('theBenchmark.p',fact_add__diff__inverse) ).

fof(fact_less__imp__diff__less,axiom,
    ! [V_n,V_k,V_j] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_n)),V_k)) ),
    file('theBenchmark.p',fact_less__imp__diff__less) ).

fof(fact_diff__less__mono2,axiom,
    ! [V_l,V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_l))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_n)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_m))) ) ),
    file('theBenchmark.p',fact_diff__less__mono2) ).

fof(fact_nat__minus__add__max,axiom,
    ! [V_m,V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m)),V_m) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n),V_m),
    file('theBenchmark.p',fact_nat__minus__add__max) ).

fof(fact_diff__mult__distrib2,axiom,
    ! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)),
    file('theBenchmark.p',fact_diff__mult__distrib2) ).

fof(fact_diff__add__inverse2,axiom,
    ! [V_n,V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_n) = V_m,
    file('theBenchmark.p',fact_diff__add__inverse2) ).

fof(fact_diff__add__inverse,axiom,
    ! [V_m,V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),V_n) = V_m,
    file('theBenchmark.p',fact_diff__add__inverse) ).

fof(fact_diff__diff__left,axiom,
    ! [V_k,V_j,V_i] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_j)),V_k) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k)),
    file('theBenchmark.p',fact_diff__diff__left) ).

fof(fact_diff__commute,axiom,
    ! [V_k,V_j,V_i] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_j)),V_k) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_k)),V_j),
    file('theBenchmark.p',fact_diff__commute) ).

fof(fact_diff__mult__distrib,axiom,
    ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)),
    file('theBenchmark.p',fact_diff__mult__distrib) ).

fof(fact_diff__cancel,axiom,
    ! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),
    file('theBenchmark.p',fact_diff__cancel) ).

fof(fact_diff__cancel2,axiom,
    ! [V_n,V_k,V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),
    file('theBenchmark.p',fact_diff__cancel2) ).

fof(fact_min__diff,axiom,
    ! [V_n,V_i,V_m] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_i)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_i)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_m),V_n)),V_i),
    file('theBenchmark.p',fact_min__diff) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).

fof(fact_crossproduct__noteq,axiom,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
      ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)
     => ( ( V_c_2 != V_d_2
          & V_a_2 != V_b_2 )
      <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_d_2)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_d_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_c_2)) ) ),
    file('theBenchmark.p',fact_crossproduct__noteq) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
    ! [V_b,V_m,V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_m)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_m) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).

fof(fact_crossproduct__eq,axiom,
    ! [V_z_2,V_x_2,V_y_2,V_w_2,T_b] :
      ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_y_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_z_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_z_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_y_2))
      <=> ( V_y_2 = V_z_2
          | V_w_2 = V_x_2 ) ) ),
    file('theBenchmark.p',fact_crossproduct__eq) ).

fof(fact_nat__less__add__iff2,axiom,
    ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2)),V_u_2)),V_n_2))) ) ),
    file('theBenchmark.p',fact_nat__less__add__iff2) ).

fof(fact_nat__less__add__iff1,axiom,
    ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i_2),V_j_2)),V_u_2)),V_m_2)),V_n_2)) ) ),
    file('theBenchmark.p',fact_nat__less__add__iff1) ).

fof(fact_diff__less__mono,axiom,
    ! [V_c,V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a),V_b))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_c),V_a))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a),V_c)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_b),V_c))) ) ),
    file('theBenchmark.p',fact_diff__less__mono) ).

fof(fact_less__diff__iff,axiom,
    ! [V_n_2,V_m_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_k_2)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ),
    file('theBenchmark.p',fact_less__diff__iff) ).

fof(fact_diff__le__self,axiom,
    ! [V_n,V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_m)),
    file('theBenchmark.p',fact_diff__le__self) ).

fof(fact_diff__diff__right,axiom,
    ! [V_i,V_j,V_k] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),V_j) ),
    file('theBenchmark.p',fact_diff__diff__right) ).

fof(fact_le__diff__conv,axiom,
    ! [V_i_2,V_k_2,V_j_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_k_2)),V_i_2))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2))) ),
    file('theBenchmark.p',fact_le__diff__conv) ).

fof(fact_le__add__diff,axiom,
    ! [V_m,V_n,V_k] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),V_k))) ),
    file('theBenchmark.p',fact_le__add__diff) ).

fof(fact_diff__le__mono2,axiom,
    ! [V_l,V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_n)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_m))) ),
    file('theBenchmark.p',fact_diff__le__mono2) ).

fof(fact_diff__le__mono,axiom,
    ! [V_l,V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_l)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_l))) ),
    file('theBenchmark.p',fact_diff__le__mono) ).

fof(fact_diff__diff__cancel,axiom,
    ! [V_n,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_n))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_i)) = V_i ),
    file('theBenchmark.p',fact_diff__diff__cancel) ).

fof(fact_le__add__diff__inverse,axiom,
    ! [V_m,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = V_m ),
    file('theBenchmark.p',fact_le__add__diff__inverse) ).

fof(fact_add__diff__assoc,axiom,
    ! [V_i,V_j,V_k] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_k) ),
    file('theBenchmark.p',fact_add__diff__assoc) ).

fof(fact_le__diff__conv2,axiom,
    ! [V_i_2,V_j_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_j_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_k_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),V_j_2)) ) ),
    file('theBenchmark.p',fact_le__diff__conv2) ).

fof(fact_le__add__diff__inverse2,axiom,
    ! [V_m,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n) = V_m ),
    file('theBenchmark.p',fact_le__add__diff__inverse2) ).

fof(fact_le__imp__diff__is__add,axiom,
    ! [V_k_2,V_j_2,V_i_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
     => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2) = V_k_2
      <=> V_j_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2) ) ),
    file('theBenchmark.p',fact_le__imp__diff__is__add) ).

fof(fact_diff__add__assoc,axiom,
    ! [V_i,V_j,V_k] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)) ),
    file('theBenchmark.p',fact_diff__add__assoc) ).

fof(fact_add__diff__assoc2,axiom,
    ! [V_i,V_j,V_k] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)),V_i) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i)),V_k) ),
    file('theBenchmark.p',fact_add__diff__assoc2) ).

fof(fact_diff__add__assoc2,axiom,
    ! [V_i,V_j,V_k] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)),V_i) ),
    file('theBenchmark.p',fact_diff__add__assoc2) ).

fof(fact_nat__eq__add__iff2,axiom,
    ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)
      <=> V_m_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2)),V_u_2)),V_n_2) ) ),
    file('theBenchmark.p',fact_nat__eq__add__iff2) ).

fof(fact_nat__diff__add__eq2,axiom,
    ! [V_n,V_m,V_u,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_i)),V_u)),V_n)) ),
    file('theBenchmark.p',fact_nat__diff__add__eq2) ).

fof(fact_nat__le__add__iff2,axiom,
    ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2)),V_u_2)),V_n_2))) ) ),
    file('theBenchmark.p',fact_nat__le__add__iff2) ).

fof(fact_termination__basic__simps_I3_J,axiom,
    ! [V_z,V_y,V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))) ),
    file('theBenchmark.p',fact_termination__basic__simps_I3_J) ).

fof(fact_termination__basic__simps_I4_J,axiom,
    ! [V_y,V_z,V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_z))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))) ),
    file('theBenchmark.p',fact_termination__basic__simps_I4_J) ).

fof(fact_hom__fold1__commute,axiom,
    ! [V_N_2,V_h_2,T_b] :
      ( class_Lattices_Oab__semigroup__idem__mult(T_b)
     => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_x),B_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
         => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => hAPP(V_h_2,hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_N_2)) = hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ),
    file('theBenchmark.p',fact_hom__fold1__commute) ).

fof(fact_fold__graph__permute__diff,axiom,
    ! [V_a_2,V_x_2,V_A_2,V_b_2,T_b] :
      ( class_Groups_Oab__semigroup__mult(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_b_2,V_A_2),V_x_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
         => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
           => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_a_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),V_x_2)) ) ) ) ),
    file('theBenchmark.p',fact_fold__graph__permute__diff) ).

fof(fact_setprod_Oremove,axiom,
    ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__mult(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ),
    file('theBenchmark.p',fact_setprod_Oremove) ).

fof(fact_setsum__ivl__cong,axiom,
    ! [V_g_2,V_f_2,V_d_2,V_b_2,V_c_2,V_a_2,T_b,T_c] :
      ( ( class_Orderings_Oord(T_b)
        & class_Groups_Ocomm__monoid__add(T_c) )
     => ( V_a_2 = V_c_2
       => ( V_b_2 = V_d_2
         => ( ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),B_x))
               => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_d_2))
                 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)) ) ) ) ),
    file('theBenchmark.p',fact_setsum__ivl__cong) ).

fof(fact_min__max_OSup__fin_Oeq__fold_H,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_x_2),V_A_2) ) ) ),
    file('theBenchmark.p',fact_min__max_OSup__fin_Oeq__fold_H) ).

fof(fact_min__max_OInf__fin_Oeq__fold_H,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_x_2),V_A_2) ) ) ),
    file('theBenchmark.p',fact_min__max_OInf__fin_Oeq__fold_H) ).

fof(fact_sup__nat__def,axiom,
    c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat),
    file('theBenchmark.p',fact_sup__nat__def) ).

fof(fact_less__not__refl,axiom,
    ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)),
    file('theBenchmark.p',fact_less__not__refl) ).

fof(fact_nat__neq__iff,axiom,
    ! [V_n_2,V_m_2] :
      ( V_m_2 != V_n_2
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ),
    file('theBenchmark.p',fact_nat__neq__iff) ).

fof(fact_linorder__neqE__nat,axiom,
    ! [V_y,V_x] :
      ( V_x != V_y
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y),V_x)) ) ),
    file('theBenchmark.p',fact_linorder__neqE__nat) ).

fof(fact_less__irrefl__nat,axiom,
    ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)),
    file('theBenchmark.p',fact_less__irrefl__nat) ).

fof(fact_less__not__refl2,axiom,
    ! [V_m,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m))
     => V_m != V_n ),
    file('theBenchmark.p',fact_less__not__refl2) ).

fof(fact_less__not__refl3,axiom,
    ! [V_t,V_s] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s),V_t))
     => V_s != V_t ),
    file('theBenchmark.p',fact_less__not__refl3) ).

fof(fact_nat__less__cases,axiom,
    ! [V_P_2,V_n_2,V_m_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
       => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
     => ( ( V_m_2 = V_n_2
         => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
       => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
           => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
         => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) ) ),
    file('theBenchmark.p',fact_nat__less__cases) ).

fof(fact_inf__nat__def,axiom,
    c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat),
    file('theBenchmark.p',fact_inf__nat__def) ).

fof(fact_fold__empty,axiom,
    ! [V_z_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_b,V_f_2),V_z_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_z_2,
    file('theBenchmark.p',fact_fold__empty) ).

fof(fact_empty__fold__graphE,axiom,
    ! [V_x_2,V_z_2,V_f_2,T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_x_2))
     => V_x_2 = V_z_2 ),
    file('theBenchmark.p',fact_empty__fold__graphE) ).

fof(fact_fold__graph_OemptyI,axiom,
    ! [V_z_2,V_f_2,T_c,T_b] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_z_2)),
    file('theBenchmark.p',fact_fold__graph_OemptyI) ).

fof(fact_fold__graph_Oequations_I1_J,axiom,
    ! [V_z_2,V_f_2,T_c,T_b] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_z_2)),
    file('theBenchmark.p',fact_fold__graph_Oequations_I1_J) ).

fof(fact_fold__graph__imp__finite,axiom,
    ! [V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_x_2))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    file('theBenchmark.p',fact_fold__graph__imp__finite) ).

fof(fact_fold__graph_OinsertI,axiom,
    ! [V_y_2,V_z_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
     => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
       => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),hAPP(hAPP(V_f_2,V_x_2),V_y_2))) ) ),
    file('theBenchmark.p',fact_fold__graph_OinsertI) ).

fof(fact_union__fold__insert,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,tc_fun(T_b,tc_HOL_Obool),c_Set_Oinsert(T_b)),V_B_2),V_A_2) ),
    file('theBenchmark.p',fact_union__fold__insert) ).

fof(fact_fold__sup__insert,axiom,
    ! [V_a_2,V_b_2,V_A_2,T_b] :
      ( class_Lattices_Osemilattice__sup(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_b_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_fold__sup__insert) ).

fof(fact_fold__inf__insert,axiom,
    ! [V_a_2,V_b_2,V_A_2,T_b] :
      ( class_Lattices_Osemilattice__inf(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_b_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_fold__inf__insert) ).

fof(fact_min__max_Ofold__inf__insert,axiom,
    ! [V_a_2,V_b_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_b_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_min__max_Ofold__inf__insert) ).

fof(fact_min__max_Ofold__sup__insert,axiom,
    ! [V_a_2,V_b_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_b_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_min__max_Ofold__sup__insert) ).

fof(fact_sup__Sup__fold__sup,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_B_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_B_2),V_A_2) ) ),
    file('theBenchmark.p',fact_sup__Sup__fold__sup) ).

fof(fact_inf__Inf__fold__inf,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_B_2),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_B_2),V_A_2) ) ),
    file('theBenchmark.p',fact_inf__Inf__fold__inf) ).

fof(fact_termination__basic__simps_I1_J,axiom,
    ! [V_z,V_y,V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))) ),
    file('theBenchmark.p',fact_termination__basic__simps_I1_J) ).

fof(fact_termination__basic__simps_I2_J,axiom,
    ! [V_y,V_z,V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_z))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))) ),
    file('theBenchmark.p',fact_termination__basic__simps_I2_J) ).

fof(fact_folding__one__idem_Oeq__fold__idem_H,axiom,
    ! [V_a_2,V_A_2,V_F_2,V_f_2,T_b] :
      ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,V_f_2),V_a_2),V_A_2) ) ),
    file('theBenchmark.p',fact_folding__one__idem_Oeq__fold__idem_H) ).

fof(fact_termination__basic__simps_I5_J,axiom,
    ! [V_y,V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y)) ),
    file('theBenchmark.p',fact_termination__basic__simps_I5_J) ).

fof(fact_setprod__insert,axiom,
    ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__mult(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)) ) ) ),
    file('theBenchmark.p',fact_setprod__insert) ).

fof(fact_setprod_Oinsert,axiom,
    ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__mult(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)) ) ) ),
    file('theBenchmark.p',fact_setprod_Oinsert) ).

fof(fact_setprod__Un__Int,axiom,
    ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__mult(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
         => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2)) ) ) ),
    file('theBenchmark.p',fact_setprod__Un__Int) ).

fof(fact_setprod_Ounion__inter,axiom,
    ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__mult(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
         => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2)) ) ) ),
    file('theBenchmark.p',fact_setprod_Ounion__inter) ).

fof(fact_fold__graph__insert__swap,axiom,
    ! [V_z_2,V_y_2,V_A_2,V_b_2,T_b] :
      ( class_Groups_Oab__semigroup__mult(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_b_2,V_A_2),V_y_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
         => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_z_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_z_2),V_y_2))) ) ) ),
    file('theBenchmark.p',fact_fold__graph__insert__swap) ).

fof(fact_sup__le__fold__sup,axiom,
    ! [V_b_2,V_a_2,V_A_2,T_b] :
      ( class_Lattices_Osemilattice__sup(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_b_2),V_A_2))) ) ) ),
    file('theBenchmark.p',fact_sup__le__fold__sup) ).

fof(fact_fold__inf__le__inf,axiom,
    ! [V_b_2,V_a_2,V_A_2,T_b] :
      ( class_Lattices_Osemilattice__inf(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_b_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),V_b_2))) ) ) ),
    file('theBenchmark.p',fact_fold__inf__le__inf) ).

fof(fact_min__max_Ofold__inf__le__inf,axiom,
    ! [V_b_2,V_a_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_b_2),V_A_2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_a_2),V_b_2))) ) ) ),
    file('theBenchmark.p',fact_min__max_Ofold__inf__le__inf) ).

fof(fact_min__max_Osup__le__fold__sup,axiom,
    ! [V_b_2,V_a_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_b_2),V_A_2))) ) ) ),
    file('theBenchmark.p',fact_min__max_Osup__le__fold__sup) ).

fof(fact_Sup__fold__sup,axiom,
    ! [V_A_2,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),c_Orderings_Obot__class_Obot(T_b)),V_A_2) ) ),
    file('theBenchmark.p',fact_Sup__fold__sup) ).

fof(fact_Inf__fold__inf,axiom,
    ! [V_A_2,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),c_Orderings_Otop__class_Otop(T_b)),V_A_2) ) ),
    file('theBenchmark.p',fact_Inf__fold__inf) ).

fof(fact_fold1__eq__fold__idem,axiom,
    ! [V_a_2,V_A_2,T_b] :
      ( class_Lattices_Oab__semigroup__idem__mult(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)),V_a_2),V_A_2) ) ),
    file('theBenchmark.p',fact_fold1__eq__fold__idem) ).

fof(fact_Sup__fin_Oeq__fold__idem_H,axiom,
    ! [V_a_2,V_A_2,T_b] :
      ( class_Lattices_Olattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_a_2),V_A_2) ) ),
    file('theBenchmark.p',fact_Sup__fin_Oeq__fold__idem_H) ).

fof(fact_Inf__fin_Oeq__fold__idem_H,axiom,
    ! [V_a_2,V_A_2,T_b] :
      ( class_Lattices_Olattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_a_2),V_A_2) ) ),
    file('theBenchmark.p',fact_Inf__fin_Oeq__fold__idem_H) ).

fof(fact_Min_Oeq__fold__idem_H,axiom,
    ! [V_a_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_a_2),V_A_2) ) ),
    file('theBenchmark.p',fact_Min_Oeq__fold__idem_H) ).

fof(fact_Max_Oeq__fold__idem_H,axiom,
    ! [V_a_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_a_2),V_A_2) ) ),
    file('theBenchmark.p',fact_Max_Oeq__fold__idem_H) ).

fof(fact_min__max_OInf__fin_Oeq__fold__idem_H,axiom,
    ! [V_a_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_a_2),V_A_2) ) ),
    file('theBenchmark.p',fact_min__max_OInf__fin_Oeq__fold__idem_H) ).

fof(fact_min__max_OSup__fin_Oeq__fold__idem_H,axiom,
    ! [V_a_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_a_2),V_A_2) ) ),
    file('theBenchmark.p',fact_min__max_OSup__fin_Oeq__fold__idem_H) ).

fof(fact_folding__one_Oeq__fold_H,axiom,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
      ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,V_f_2),V_x_2),V_A_2) ) ) ),
    file('theBenchmark.p',fact_folding__one_Oeq__fold_H) ).

fof(fact_setprod_Oinsert__remove,axiom,
    ! [V_x_2,V_g_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__mult(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ),
    file('theBenchmark.p',fact_setprod_Oinsert__remove) ).

fof(fact_setprod_Ounion__disjoint,axiom,
    ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__mult(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2)) ) ) ) ),
    file('theBenchmark.p',fact_setprod_Ounion__disjoint) ).

fof(fact_setprod__Un__disjoint,axiom,
    ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__mult(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2)) ) ) ) ),
    file('theBenchmark.p',fact_setprod__Un__disjoint) ).

fof(fact_Diff1__fold__graph,axiom,
    ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_y_2))
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
       => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),hAPP(hAPP(V_f_2,V_x_2),V_y_2))) ) ),
    file('theBenchmark.p',fact_Diff1__fold__graph) ).

fof(fact_fold1__eq__fold,axiom,
    ! [V_a_2,V_A_2,T_b] :
      ( class_Groups_Oab__semigroup__mult(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
         => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)),V_a_2),V_A_2) ) ) ),
    file('theBenchmark.p',fact_fold1__eq__fold) ).

fof(fact_Sup__fin_Oeq__fold_H,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Lattices_Olattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_x_2),V_A_2) ) ) ),
    file('theBenchmark.p',fact_Sup__fin_Oeq__fold_H) ).

fof(fact_Inf__fin_Oeq__fold_H,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Lattices_Olattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_x_2),V_A_2) ) ) ),
    file('theBenchmark.p',fact_Inf__fin_Oeq__fold_H) ).

fof(fact_Min_Oeq__fold_H,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_x_2),V_A_2) ) ) ),
    file('theBenchmark.p',fact_Min_Oeq__fold_H) ).

fof(fact_Max_Oeq__fold_H,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_x_2),V_A_2) ) ) ),
    file('theBenchmark.p',fact_Max_Oeq__fold_H) ).

fof(fact_fun__left__comm_Ofold__rec,axiom,
    ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ),
    file('theBenchmark.p',fact_fun__left__comm_Ofold__rec) ).

fof(fact_fold1Set_Ointros,axiom,
    ! [V_x_2,V_A_2,V_a_2,V_f_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,V_a_2,V_A_2),V_x_2))
     => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
       => hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),V_x_2)) ) ),
    file('theBenchmark.p',fact_fold1Set_Ointros) ).

fof(fact_fun__left__comm_Ofold__insert__remove,axiom,
    ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ),
    file('theBenchmark.p',fact_fun__left__comm_Ofold__insert__remove) ).

fof(fact_fun__left__comm_Ofold__insert,axiom,
    ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2)) ) ) ),
    file('theBenchmark.p',fact_fun__left__comm_Ofold__insert) ).

fof(fact_fun__left__comm_Ofold__insert2,axiom,
    ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2) ) ) ),
    file('theBenchmark.p',fact_fun__left__comm_Ofold__insert2) ).

fof(fact_card__Diff1__less,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ) ),
    file('theBenchmark.p',fact_card__Diff1__less) ).

fof(fact_card__Diff2__less,axiom,
    ! [V_y_2,V_x_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ) ) ),
    file('theBenchmark.p',fact_card__Diff2__less) ).

fof(fact_fun__left__comm_Ofun__left__comm,axiom,
    ! [V_z_2,V_y_2,V_x_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
     => hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(V_f_2,V_y_2),V_z_2)) = hAPP(hAPP(V_f_2,V_y_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)) ),
    file('theBenchmark.p',fact_fun__left__comm_Ofun__left__comm) ).

fof(fact_card__lessThan,axiom,
    ! [V_u_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_u_2)) = V_u_2,
    file('theBenchmark.p',fact_card__lessThan) ).

fof(fact_fun__left__comm,axiom,
    ! [T_b] :
      ( class_Groups_Oab__semigroup__mult(T_b)
     => c_Finite__Set_Ofun__left__comm(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)) ),
    file('theBenchmark.p',fact_fun__left__comm) ).

fof(fact_card__eq__UNIV__imp__eq__UNIV,axiom,
    ! [V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
     => ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
       => V_A_2 = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_card__eq__UNIV__imp__eq__UNIV) ).

fof(fact_card__image,axiom,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
     => hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) ),
    file('theBenchmark.p',fact_card__image) ).

fof(fact_fun__left__comm_Ofold__graph__determ,axiom,
    ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_x_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
         => V_y_2 = V_x_2 ) ) ),
    file('theBenchmark.p',fact_fun__left__comm_Ofold__graph__determ) ).

fof(fact_empty__fold1SetE,axiom,
    ! [V_x_2,V_f_2,T_b] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_x_2)),
    file('theBenchmark.p',fact_empty__fold1SetE) ).

fof(fact_fold1Set__nonempty,axiom,
    ! [V_x_2,V_A_2,V_f_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,V_A_2),V_x_2))
     => V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_fold1Set__nonempty) ).

fof(fact_subset__card__intvl__is__intvl,axiom,
    ! [V_k_2,V_A_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),V_A_2)))))
     => V_A_2 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),V_A_2))) ),
    file('theBenchmark.p',fact_subset__card__intvl__is__intvl) ).

fof(fact_card__atLeastLessThan,axiom,
    ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_l_2),V_u_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_u_2),V_l_2),
    file('theBenchmark.p',fact_card__atLeastLessThan) ).

fof(fact_card__greaterThanAtMost,axiom,
    ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_l_2,V_u_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_u_2),V_l_2),
    file('theBenchmark.p',fact_card__greaterThanAtMost) ).

fof(fact_card__insert__le,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)))) ),
    file('theBenchmark.p',fact_card__insert__le) ).

fof(fact_card__mono,axiom,
    ! [V_A_2,V_B_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))) ) ),
    file('theBenchmark.p',fact_card__mono) ).

fof(fact_card__seteq,axiom,
    ! [V_A_2,V_B_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)))
         => V_A_2 = V_B_2 ) ) ),
    file('theBenchmark.p',fact_card__seteq) ).

fof(fact_card__image__le,axiom,
    ! [V_f_2,T_c,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ),
    file('theBenchmark.p',fact_card__image__le) ).

fof(fact_inj__on__iff__eq__card,axiom,
    ! [V_f_2,T_c,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
      <=> hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) ) ),
    file('theBenchmark.p',fact_inj__on__iff__eq__card) ).

fof(fact_eq__card__imp__inj__on,axiom,
    ! [V_f_2,T_c,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2)
       => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ),
    file('theBenchmark.p',fact_eq__card__imp__inj__on) ).

fof(fact_pigeonhole,axiom,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))),hAPP(c_Finite__Set_Ocard(T_c),V_A_2)))
     => ~ c_Fun_Oinj__on(T_c,T_b,V_f_2,V_A_2) ),
    file('theBenchmark.p',fact_pigeonhole) ).

fof(fact_psubset__card__mono,axiom,
    ! [V_A_2,V_B_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))) ) ),
    file('theBenchmark.p',fact_psubset__card__mono) ).

fof(fact_fun__left__comm_Ofold__fun__comm,axiom,
    ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2) ) ),
    file('theBenchmark.p',fact_fun__left__comm_Ofold__fun__comm) ).

fof(fact_fun__left__comm_Ofold__equality,axiom,
    ! [V_y_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
       => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2) = V_y_2 ) ),
    file('theBenchmark.p',fact_fun__left__comm_Ofold__equality) ).

fof(fact_fold1Set__sing,axiom,
    ! [V_b_2,V_a_2,V_f_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_b_2))
    <=> V_a_2 = V_b_2 ),
    file('theBenchmark.p',fact_fold1Set__sing) ).

fof(fact_card_Ounion__inter,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) ) ),
    file('theBenchmark.p',fact_card_Ounion__inter) ).

fof(fact_card__Un__Int,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ),
    file('theBenchmark.p',fact_card__Un__Int) ).

fof(fact_card__bij__eq,axiom,
    ! [V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),V_B_2))
       => ( c_Fun_Oinj__on(T_c,T_b,V_g_2,V_B_2)
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_g_2),V_B_2)),V_A_2))
           => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
             => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
               => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2) ) ) ) ) ) ),
    file('theBenchmark.p',fact_card__bij__eq) ).

fof(fact_card__Diff__subset,axiom,
    ! [V_A_2,V_B_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
       => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) ) ),
    file('theBenchmark.p',fact_card__Diff__subset) ).

fof(fact_card__Diff__subset__Int,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
     => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ),
    file('theBenchmark.p',fact_card__Diff__subset__Int) ).

fof(fact_diff__card__le__card__Diff,axiom,
    ! [V_A_2,V_B_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))) ),
    file('theBenchmark.p',fact_diff__card__le__card__Diff) ).

fof(fact_card__psubset,axiom,
    ! [V_A_2,V_B_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ),
    file('theBenchmark.p',fact_card__psubset) ).

fof(fact_card__Un__disjoint,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
       => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) ) ) ),
    file('theBenchmark.p',fact_card__Un__disjoint) ).

fof(fact_card__Diff1__le,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ),
    file('theBenchmark.p',fact_card__Diff1__le) ).

fof(fact_card__inj__on__le,axiom,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),V_B_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2))) ) ) ),
    file('theBenchmark.p',fact_card__inj__on__le) ).

fof(fact_inj__on__iff__card__le,axiom,
    ! [V_B_2,T_c,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
       => ( ? [B_f] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,B_f),V_A_2)),V_B_2))
              & c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2) )
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2))) ) ) ),
    file('theBenchmark.p',fact_inj__on__iff__card__le) ).

fof(fact_fun__left__comm_Ofold__graph__fold,axiom,
    ! [V_z_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2))) ) ),
    file('theBenchmark.p',fact_fun__left__comm_Ofold__graph__fold) ).

fof(fact_fun__left__comm_Ofold__graph__insertE__aux,axiom,
    ! [V_a_2,V_y_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
         => ? [B_y_H] :
              ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),B_y_H))
              & V_y_2 = hAPP(hAPP(V_f_2,V_a_2),B_y_H) ) ) ) ),
    file('theBenchmark.p',fact_fun__left__comm_Ofold__graph__insertE__aux) ).

fof(fact_card__Diff__singleton,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
       => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
    file('theBenchmark.p',fact_card__Diff__singleton) ).

fof(fact_card__Diff__singleton__if,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) )
        & ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ) ),
    file('theBenchmark.p',fact_card__Diff__singleton__if) ).

fof(fact_card_Oremove,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
       => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ),
    file('theBenchmark.p',fact_card_Oremove) ).

fof(fact_card_Oinsert__remove,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ),
    file('theBenchmark.p',fact_card_Oinsert__remove) ).

fof(fact_card__Diff__insert,axiom,
    ! [V_B_2,V_a_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
         => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ) ),
    file('theBenchmark.p',fact_card__Diff__insert) ).

fof(fact_card__Suc__Diff1,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
       => hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) ) ),
    file('theBenchmark.p',fact_card__Suc__Diff1) ).

fof(fact_lessI,axiom,
    ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_n))),
    file('theBenchmark.p',fact_lessI) ).

fof(fact_Suc__mono,axiom,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) ),
    file('theBenchmark.p',fact_Suc__mono) ).

fof(fact_card__UNIV__unit,axiom,
    hAPP(c_Finite__Set_Ocard(tc_Product__Type_Ounit),c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
    file('theBenchmark.p',fact_card__UNIV__unit) ).

fof(fact_diff__Suc__1,axiom,
    ! [V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n,
    file('theBenchmark.p',fact_diff__Suc__1) ).

fof(fact_mono__Suc,axiom,
    c_Orderings_Oorder__class_Omono(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),
    file('theBenchmark.p',fact_mono__Suc) ).

fof(fact_inj__Suc,axiom,
    ! [V_N_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,V_N_2),
    file('theBenchmark.p',fact_inj__Suc) ).

fof(fact_n__not__Suc__n,axiom,
    ! [V_n] : V_n != hAPP(c_Nat_OSuc,V_n),
    file('theBenchmark.p',fact_n__not__Suc__n) ).

fof(fact_Suc__n__not__n,axiom,
    ! [V_n] : hAPP(c_Nat_OSuc,V_n) != V_n,
    file('theBenchmark.p',fact_Suc__n__not__n) ).

fof(fact_nat_Oinject,axiom,
    ! [V_nat_H_2,V_nat_2] :
      ( hAPP(c_Nat_OSuc,V_nat_2) = hAPP(c_Nat_OSuc,V_nat_H_2)
    <=> V_nat_2 = V_nat_H_2 ),
    file('theBenchmark.p',fact_nat_Oinject) ).

fof(fact_Suc__inject,axiom,
    ! [V_y,V_x] :
      ( hAPP(c_Nat_OSuc,V_x) = hAPP(c_Nat_OSuc,V_y)
     => V_x = V_y ),
    file('theBenchmark.p',fact_Suc__inject) ).

fof(fact_atLeast__Suc__greaterThan,axiom,
    ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),V_k_2),
    file('theBenchmark.p',fact_atLeast__Suc__greaterThan) ).

fof(fact_one__reorient,axiom,
    ! [V_x_2,T_b] :
      ( class_Groups_Oone(T_b)
     => ( c_Groups_Oone__class_Oone(T_b) = V_x_2
      <=> V_x_2 = c_Groups_Oone__class_Oone(T_b) ) ),
    file('theBenchmark.p',fact_one__reorient) ).

fof(fact_greaterThan__Suc,axiom,
    ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),V_k_2)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    file('theBenchmark.p',fact_greaterThan__Suc) ).

fof(fact_atLeast__Suc,axiom,
    ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),V_k_2)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_k_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    file('theBenchmark.p',fact_atLeast__Suc) ).

fof(fact_mono__iff__le__Suc,axiom,
    ! [V_f_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => ( c_Orderings_Oorder__class_Omono(tc_Nat_Onat,T_b,V_f_2)
      <=> ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_n)),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_n)))) ) ),
    file('theBenchmark.p',fact_mono__iff__le__Suc) ).

fof(fact_mult__1__left,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Omonoid__mult(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ),
    file('theBenchmark.p',fact_mult__1__left) ).

fof(fact_mult__1,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Ocomm__monoid__mult(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ),
    file('theBenchmark.p',fact_mult__1) ).

fof(fact_mult__1__right,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Omonoid__mult(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ),
    file('theBenchmark.p',fact_mult__1__right) ).

fof(fact_mult_Ocomm__neutral,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Ocomm__monoid__mult(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ),
    file('theBenchmark.p',fact_mult_Ocomm__neutral) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).

fof(fact_not__less__eq,axiom,
    ! [V_n_2,V_m_2] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) ),
    file('theBenchmark.p',fact_not__less__eq) ).

fof(fact_less__Suc__eq,axiom,
    ! [V_n_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
    <=> ( V_m_2 = V_n_2
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ),
    file('theBenchmark.p',fact_less__Suc__eq) ).

fof(fact_Suc__less__eq,axiom,
    ! [V_n_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),hAPP(c_Nat_OSuc,V_n_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ),
    file('theBenchmark.p',fact_Suc__less__eq) ).

fof(fact_not__less__less__Suc__eq,axiom,
    ! [V_m_2,V_n_2] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2)))
      <=> V_n_2 = V_m_2 ) ),
    file('theBenchmark.p',fact_not__less__less__Suc__eq) ).

fof(fact_less__antisym,axiom,
    ! [V_m,V_n] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_m)))
       => V_m = V_n ) ),
    file('theBenchmark.p',fact_less__antisym) ).

fof(fact_less__SucI,axiom,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ),
    file('theBenchmark.p',fact_less__SucI) ).

fof(fact_Suc__lessI,axiom,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
     => ( hAPP(c_Nat_OSuc,V_m) != V_n
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ),
    file('theBenchmark.p',fact_Suc__lessI) ).

fof(fact_less__trans__Suc,axiom,
    ! [V_k,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_i)),V_k)) ) ),
    file('theBenchmark.p',fact_less__trans__Suc) ).

fof(fact_less__SucE,axiom,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)))
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
       => V_m = V_n ) ),
    file('theBenchmark.p',fact_less__SucE) ).

fof(fact_Suc__lessD,axiom,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ),
    file('theBenchmark.p',fact_Suc__lessD) ).

fof(fact_Suc__less__SucD,axiom,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ),
    file('theBenchmark.p',fact_Suc__less__SucD) ).

fof(fact_add__Suc__right,axiom,
    ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),
    file('theBenchmark.p',fact_add__Suc__right) ).

fof(fact_add__Suc,axiom,
    ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),
    file('theBenchmark.p',fact_add__Suc) ).

fof(fact_add__Suc__shift,axiom,
    ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)),
    file('theBenchmark.p',fact_add__Suc__shift) ).

fof(fact_Suc__n__not__le__n,axiom,
    ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)),V_n)),
    file('theBenchmark.p',fact_Suc__n__not__le__n) ).

fof(fact_not__less__eq__eq,axiom,
    ! [V_n_2,V_m_2] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ),
    file('theBenchmark.p',fact_not__less__eq__eq) ).

fof(fact_le__Suc__eq,axiom,
    ! [V_n_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
    <=> ( V_m_2 = hAPP(c_Nat_OSuc,V_n_2)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ),
    file('theBenchmark.p',fact_le__Suc__eq) ).

fof(fact_Suc__le__mono,axiom,
    ! [V_m_2,V_n_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Nat_OSuc,V_m_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ),
    file('theBenchmark.p',fact_Suc__le__mono) ).

fof(fact_le__SucI,axiom,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ),
    file('theBenchmark.p',fact_le__SucI) ).

fof(fact_le__SucE,axiom,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)))
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
       => V_m = hAPP(c_Nat_OSuc,V_n) ) ),
    file('theBenchmark.p',fact_le__SucE) ).

fof(fact_Suc__leD,axiom,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ),
    file('theBenchmark.p',fact_Suc__leD) ).

fof(fact_setprod__eq__1__iff,axiom,
    ! [V_f_2,V_F_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
     => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_F_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
      <=> ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2))
           => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ),
    file('theBenchmark.p',fact_setprod__eq__1__iff) ).

fof(fact_diff__Suc__Suc,axiom,
    ! [V_n,V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),
    file('theBenchmark.p',fact_diff__Suc__Suc) ).

fof(fact_Suc__diff__diff,axiom,
    ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)),hAPP(c_Nat_OSuc,V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_k),
    file('theBenchmark.p',fact_Suc__diff__diff) ).

fof(fact_Suc__mult__cancel1,axiom,
    ! [V_n_2,V_m_2,V_k_2] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_n_2)
    <=> V_m_2 = V_n_2 ),
    file('theBenchmark.p',fact_Suc__mult__cancel1) ).

fof(fact_nat__mult__1,axiom,
    ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n,
    file('theBenchmark.p',fact_nat__mult__1) ).

fof(fact_nat__1__eq__mult__iff,axiom,
    ! [V_n_2,V_m_2] :
      ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)
    <=> ( V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        & V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_nat__1__eq__mult__iff) ).

fof(fact_nat__mult__1__right,axiom,
    ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n,
    file('theBenchmark.p',fact_nat__mult__1__right) ).

fof(fact_nat__mult__eq__1__iff,axiom,
    ! [V_n_2,V_m_2] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    <=> ( V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        & V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_nat__mult__eq__1__iff) ).

fof(fact_image__Suc__atLeastLessThan,axiom,
    ! [V_j_2,V_i_2] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_i_2)),hAPP(c_Nat_OSuc,V_j_2)),
    file('theBenchmark.p',fact_image__Suc__atLeastLessThan) ).

fof(fact_atLeastLessThan__singleton,axiom,
    ! [V_m_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_m_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_m_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    file('theBenchmark.p',fact_atLeastLessThan__singleton) ).

fof(fact_image__Suc__atLeastAtMost,axiom,
    ! [V_j_2,V_i_2] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_i_2,V_j_2)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_i_2),hAPP(c_Nat_OSuc,V_j_2)),
    file('theBenchmark.p',fact_image__Suc__atLeastAtMost) ).

fof(fact_min__Suc__Suc,axiom,
    ! [V_n,V_m] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_m),V_n)),
    file('theBenchmark.p',fact_min__Suc__Suc) ).

fof(fact_lessThan__Suc,axiom,
    ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_k_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_k_2)),
    file('theBenchmark.p',fact_lessThan__Suc) ).

fof(fact_max__Suc__Suc,axiom,
    ! [V_n,V_m] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_m),V_n)),
    file('theBenchmark.p',fact_max__Suc__Suc) ).

fof(fact_atMost__Suc,axiom,
    ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2)),
    file('theBenchmark.p',fact_atMost__Suc) ).

fof(fact_card__atMost,axiom,
    ! [V_u_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_u_2)) = hAPP(c_Nat_OSuc,V_u_2),
    file('theBenchmark.p',fact_card__atMost) ).

fof(fact_less__add__one,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))) ),
    file('theBenchmark.p',fact_less__add__one) ).

fof(fact_less__1__mult,axiom,
    ! [V_n,V_m,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_m))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_n))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_m),V_n))) ) ) ),
    file('theBenchmark.p',fact_less__1__mult) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
    ! [V_m,V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)),V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a))),V_m) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
    ! [V_a,V_m,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a))),V_m) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
    ! [V_m,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_m),V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a))),V_m) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).

fof(fact_square__eq__1__iff,axiom,
    ! [V_x_2,T_b] :
      ( class_Rings_Oring__1__no__zero__divisors(T_b)
     => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_b)
      <=> ( V_x_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b))
          | V_x_2 = c_Groups_Oone__class_Oone(T_b) ) ) ),
    file('theBenchmark.p',fact_square__eq__1__iff) ).

fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,axiom,
    ! [V_x,T_a] :
      ( class_Rings_Ocomm__ring__1(T_a)
     => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),V_x) ),
    file('theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J) ).

fof(fact_less__add__Suc1,axiom,
    ! [V_m,V_i] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m)))),
    file('theBenchmark.p',fact_less__add__Suc1) ).

fof(fact_less__add__Suc2,axiom,
    ! [V_m,V_i] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_i)))),
    file('theBenchmark.p',fact_less__add__Suc2) ).

fof(fact_less__iff__Suc__add,axiom,
    ! [V_n_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
    <=> ? [B_k] : V_n_2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)) ),
    file('theBenchmark.p',fact_less__iff__Suc__add) ).

fof(fact_less__eq__Suc__le,axiom,
    ! [V_m_2,V_n_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ),
    file('theBenchmark.p',fact_less__eq__Suc__le) ).

fof(fact_less__Suc__eq__le,axiom,
    ! [V_n_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ),
    file('theBenchmark.p',fact_less__Suc__eq__le) ).

fof(fact_Suc__le__eq,axiom,
    ! [V_n_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ),
    file('theBenchmark.p',fact_Suc__le__eq) ).

fof(fact_le__imp__less__Suc,axiom,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ),
    file('theBenchmark.p',fact_le__imp__less__Suc) ).

fof(fact_Suc__leI,axiom,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ),
    file('theBenchmark.p',fact_Suc__leI) ).

fof(fact_le__less__Suc__eq,axiom,
    ! [V_n_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2)))
      <=> V_n_2 = V_m_2 ) ),
    file('theBenchmark.p',fact_le__less__Suc__eq) ).

fof(fact_Suc__le__lessD,axiom,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ),
    file('theBenchmark.p',fact_Suc__le__lessD) ).

fof(fact_diff__less__Suc,axiom,
    ! [V_n,V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),hAPP(c_Nat_OSuc,V_m))),
    file('theBenchmark.p',fact_diff__less__Suc) ).

fof(fact_Suc__mult__less__cancel1,axiom,
    ! [V_n_2,V_m_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_n_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ),
    file('theBenchmark.p',fact_Suc__mult__less__cancel1) ).

fof(fact_mult__Suc__right,axiom,
    ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),
    file('theBenchmark.p',fact_mult__Suc__right) ).

fof(fact_mult__Suc,axiom,
    ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),
    file('theBenchmark.p',fact_mult__Suc) ).

fof(fact_Suc__diff__le,axiom,
    ! [V_m,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) ),
    file('theBenchmark.p',fact_Suc__diff__le) ).

fof(fact_Suc__mult__le__cancel1,axiom,
    ! [V_n_2,V_m_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_n_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ),
    file('theBenchmark.p',fact_Suc__mult__le__cancel1) ).

fof(fact_setprod_Oempty,axiom,
    ! [V_g_2,T_c,T_b] :
      ( class_Groups_Ocomm__monoid__mult(T_b)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_g_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(T_b) ),
    file('theBenchmark.p',fact_setprod_Oempty) ).

fof(fact_setprod__empty,axiom,
    ! [V_f_2,T_c,T_b] :
      ( class_Groups_Ocomm__monoid__mult(T_b)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(T_b) ),
    file('theBenchmark.p',fact_setprod__empty) ).

fof(fact_setprod_Oinfinite,axiom,
    ! [V_g_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__mult(T_c)
     => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = c_Groups_Oone__class_Oone(T_c) ) ),
    file('theBenchmark.p',fact_setprod_Oinfinite) ).

fof(fact_setprod__infinite,axiom,
    ! [V_f_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__mult(T_c)
     => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2) = c_Groups_Oone__class_Oone(T_c) ) ),
    file('theBenchmark.p',fact_setprod__infinite) ).

fof(fact_atLeastLessThanSuc,axiom,
    ! [V_n_2,V_m_2] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
       => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
       => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_n_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)) ) ),
    file('theBenchmark.p',fact_atLeastLessThanSuc) ).

fof(fact_atLeastAtMostSuc__conv,axiom,
    ! [V_n_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
     => c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) ),
    file('theBenchmark.p',fact_atLeastAtMostSuc__conv) ).

fof(fact_card__atLeastAtMost,axiom,
    ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_l_2,V_u_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_u_2)),V_l_2),
    file('theBenchmark.p',fact_card__atLeastAtMost) ).

fof(fact_atLeastLessThanSuc__atLeastAtMost,axiom,
    ! [V_u_2,V_l_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_l_2),hAPP(c_Nat_OSuc,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_l_2,V_u_2),
    file('theBenchmark.p',fact_atLeastLessThanSuc__atLeastAtMost) ).

fof(fact_lessThan__Suc__atMost,axiom,
    ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2),
    file('theBenchmark.p',fact_lessThan__Suc__atMost) ).

fof(fact_card__greaterThanLessThan,axiom,
    ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,V_l_2,V_u_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_u_2),hAPP(c_Nat_OSuc,V_l_2)),
    file('theBenchmark.p',fact_card__greaterThanLessThan) ).

fof(fact_atLeastSucAtMost__greaterThanAtMost,axiom,
    ! [V_u_2,V_l_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_l_2),V_u_2) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_l_2,V_u_2),
    file('theBenchmark.p',fact_atLeastSucAtMost__greaterThanAtMost) ).

fof(fact_atLeastSucLessThan__greaterThanLessThan,axiom,
    ! [V_u_2,V_l_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_l_2)),V_u_2) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,V_l_2,V_u_2),
    file('theBenchmark.p',fact_atLeastSucLessThan__greaterThanLessThan) ).

fof(fact_diff__Suc__diff__eq2,axiom,
    ! [V_m,V_j,V_k] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k))),V_m) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_j)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_m)) ),
    file('theBenchmark.p',fact_diff__Suc__diff__eq2) ).

fof(fact_diff__Suc__diff__eq1,axiom,
    ! [V_m,V_j,V_k] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),hAPP(c_Nat_OSuc,V_j)) ),
    file('theBenchmark.p',fact_diff__Suc__diff__eq1) ).

fof(fact_card__insert__disjoint,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
       => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_b),V_A_2)) ) ),
    file('theBenchmark.p',fact_card__insert__disjoint) ).

fof(fact_card__insert__if,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_b),V_A_2)) )
        & ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) ) ) ),
    file('theBenchmark.p',fact_card__insert__if) ).

fof(fact_setsum__head__upt__Suc,axiom,
    ! [V_f_2,V_n_2,V_m_2,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_f_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2)),V_n_2))) ) ),
    file('theBenchmark.p',fact_setsum__head__upt__Suc) ).

fof(fact_setsum__head__Suc,axiom,
    ! [V_f_2,V_n_2,V_m_2,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_f_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2),V_n_2))) ) ),
    file('theBenchmark.p',fact_setsum__head__Suc) ).

fof(fact_card__insert,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ),
    file('theBenchmark.p',fact_card__insert) ).

fof(fact_card_Oinsert,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
       => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)) ) ),
    file('theBenchmark.p',fact_card_Oinsert) ).

fof(fact_setsum__ub__add__nat,axiom,
    ! [V_p_2,V_f_2,V_n_2,V_m_2,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_p_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_p_2)))) ) ),
    file('theBenchmark.p',fact_setsum__ub__add__nat) ).

fof(fact_diff__Suc__eq__diff__pred,axiom,
    ! [V_n,V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n),
    file('theBenchmark.p',fact_diff__Suc__eq__diff__pred) ).

fof(fact_Suc__eq__plus1,axiom,
    ! [V_n] : hAPP(c_Nat_OSuc,V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    file('theBenchmark.p',fact_Suc__eq__plus1) ).

fof(fact_Suc__eq__plus1__left,axiom,
    ! [V_n] : hAPP(c_Nat_OSuc,V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n),
    file('theBenchmark.p',fact_Suc__eq__plus1__left) ).

fof(fact_setprod__Un__one,axiom,
    ! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__mult(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
         => ( ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)))
               => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_S_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_T_2)) ) ) ) ),
    file('theBenchmark.p',fact_setprod__Un__one) ).

fof(fact_setprod_Ounion__inter__neutral,axiom,
    ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__mult(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
         => ( ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
               => hAPP(V_g_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2)) ) ) ) ),
    file('theBenchmark.p',fact_setprod_Ounion__inter__neutral) ).

fof(fact_finite__fun__UNIVD1,axiom,
    ! [T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,T_c),tc_HOL_Obool))))
     => ( hAPP(c_Finite__Set_Ocard(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ),
    file('theBenchmark.p',fact_finite__fun__UNIVD1) ).

fof(fact_less__zeroE,axiom,
    ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('theBenchmark.p',fact_less__zeroE) ).

fof(fact_le0,axiom,
    ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)),
    file('theBenchmark.p',fact_le0) ).

fof(fact_zero__less__Suc,axiom,
    ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,V_n))),
    file('theBenchmark.p',fact_zero__less__Suc) ).

fof(fact_zero__reorient,axiom,
    ! [V_x_2,T_b] :
      ( class_Groups_Ozero(T_b)
     => ( c_Groups_Ozero__class_Ozero(T_b) = V_x_2
      <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_b) ) ),
    file('theBenchmark.p',fact_zero__reorient) ).

fof(fact_bot__nat__def,axiom,
    c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_bot__nat__def) ).

fof(fact_add__0__iff,axiom,
    ! [V_a_2,V_b_2,T_b] :
      ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)
     => ( V_b_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2)
      <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ),
    file('theBenchmark.p',fact_add__0__iff) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).

fof(fact_add_Ocomm__neutral,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Ocomm__monoid__add(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ),
    file('theBenchmark.p',fact_add_Ocomm__neutral) ).

fof(fact_add__0__right,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Omonoid__add(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ),
    file('theBenchmark.p',fact_add__0__right) ).

fof(fact_double__zero__sym,axiom,
    ! [V_a_2,T_b] :
      ( class_Groups_Olinordered__ab__group__add(T_b)
     => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)
      <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ),
    file('theBenchmark.p',fact_double__zero__sym) ).

fof(fact_add__0,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Ocomm__monoid__add(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ),
    file('theBenchmark.p',fact_add__0) ).

fof(fact_add__0__left,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Omonoid__add(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ),
    file('theBenchmark.p',fact_add__0__left) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).

fof(fact_divisors__zero,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Ono__zero__divisors(T_a)
     => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
       => ( V_b = c_Groups_Ozero__class_Ozero(T_a)
          | V_a = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
    file('theBenchmark.p',fact_divisors__zero) ).

fof(fact_no__zero__divisors,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Ono__zero__divisors(T_a)
     => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
       => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
         => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a) ) ) ),
    file('theBenchmark.p',fact_no__zero__divisors) ).

fof(fact_mult__eq__0__iff,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( class_Rings_Oring__no__zero__divisors(T_b)
     => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b)
      <=> ( V_b_2 = c_Groups_Ozero__class_Ozero(T_b)
          | V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ),
    file('theBenchmark.p',fact_mult__eq__0__iff) ).

fof(fact_mult__zero__right,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Omult__zero(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_mult__zero__right) ).

fof(fact_mult__zero__left,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Omult__zero(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_mult__zero__left) ).

fof(fact_right__minus__eq,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( class_Groups_Ogroup__add(T_b)
     => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b)
      <=> V_a_2 = V_b_2 ) ),
    file('theBenchmark.p',fact_right__minus__eq) ).

fof(fact_eq__iff__diff__eq__0,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( class_Groups_Oab__group__add(T_b)
     => ( V_a_2 = V_b_2
      <=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b) ) ),
    file('theBenchmark.p',fact_eq__iff__diff__eq__0) ).

fof(fact_diff__self,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Ogroup__add(T_a)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_diff__self) ).

fof(fact_diff__0__right,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Ogroup__add(T_a)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ),
    file('theBenchmark.p',fact_diff__0__right) ).

fof(fact_zero__neq__one,axiom,
    ! [T_a] :
      ( class_Rings_Ozero__neq__one(T_a)
     => c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ),
    file('theBenchmark.p',fact_zero__neq__one) ).

fof(fact_one__neq__zero,axiom,
    ! [T_a] :
      ( class_Rings_Ozero__neq__one(T_a)
     => c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_one__neq__zero) ).

fof(fact_minus__zero,axiom,
    ! [T_a] :
      ( class_Groups_Ogroup__add(T_a)
     => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_minus__zero) ).

fof(fact_neg__0__equal__iff__equal,axiom,
    ! [V_a_2,T_b] :
      ( class_Groups_Ogroup__add(T_b)
     => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)
      <=> c_Groups_Ozero__class_Ozero(T_b) = V_a_2 ) ),
    file('theBenchmark.p',fact_neg__0__equal__iff__equal) ).

fof(fact_equal__neg__zero,axiom,
    ! [V_a_2,T_b] :
      ( class_Groups_Olinordered__ab__group__add(T_b)
     => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)
      <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ),
    file('theBenchmark.p',fact_equal__neg__zero) ).

fof(fact_neg__equal__0__iff__equal,axiom,
    ! [V_a_2,T_b] :
      ( class_Groups_Ogroup__add(T_b)
     => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
      <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ),
    file('theBenchmark.p',fact_neg__equal__0__iff__equal) ).

fof(fact_neg__equal__zero,axiom,
    ! [V_a_2,T_b] :
      ( class_Groups_Olinordered__ab__group__add(T_b)
     => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = V_a_2
      <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ),
    file('theBenchmark.p',fact_neg__equal__zero) ).

fof(fact_Suc__neq__Zero,axiom,
    ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_Suc__neq__Zero) ).

fof(fact_Zero__neq__Suc,axiom,
    ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m),
    file('theBenchmark.p',fact_Zero__neq__Suc) ).

fof(fact_nat_Osimps_I3_J,axiom,
    ! [V_nat_H_1] : hAPP(c_Nat_OSuc,V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_nat_Osimps_I3_J) ).

fof(fact_Suc__not__Zero,axiom,
    ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_Suc__not__Zero) ).

fof(fact_nat_Osimps_I2_J,axiom,
    ! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_nat_H),
    file('theBenchmark.p',fact_nat_Osimps_I2_J) ).

fof(fact_Zero__not__Suc,axiom,
    ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m),
    file('theBenchmark.p',fact_Zero__not__Suc) ).

fof(fact_gr0I,axiom,
    ! [V_n] :
      ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ),
    file('theBenchmark.p',fact_gr0I) ).

fof(fact_gr__implies__not0,axiom,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
     => V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('theBenchmark.p',fact_gr__implies__not0) ).

fof(fact_less__nat__zero__code,axiom,
    ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('theBenchmark.p',fact_less__nat__zero__code) ).

fof(fact_neq0__conv,axiom,
    ! [V_n_2] :
      ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ),
    file('theBenchmark.p',fact_neq0__conv) ).

fof(fact_not__less0,axiom,
    ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('theBenchmark.p',fact_not__less0) ).

fof(fact_add__eq__self__zero,axiom,
    ! [V_n,V_m] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_m
     => V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('theBenchmark.p',fact_add__eq__self__zero) ).

fof(fact_add__is__0,axiom,
    ! [V_n_2,V_m_2] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_add__is__0) ).

fof(fact_Nat_Oadd__0__right,axiom,
    ! [V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m,
    file('theBenchmark.p',fact_Nat_Oadd__0__right) ).

fof(fact_plus__nat_Oadd__0,axiom,
    ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n,
    file('theBenchmark.p',fact_plus__nat_Oadd__0) ).

fof(fact_le__0__eq,axiom,
    ! [V_n_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('theBenchmark.p',fact_le__0__eq) ).

fof(fact_less__eq__nat_Osimps_I1_J,axiom,
    ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)),
    file('theBenchmark.p',fact_less__eq__nat_Osimps_I1_J) ).

fof(fact_diffs0__imp__equal,axiom,
    ! [V_n,V_m] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
     => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => V_m = V_n ) ),
    file('theBenchmark.p',fact_diffs0__imp__equal) ).

fof(fact_diff__self__eq__0,axiom,
    ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_diff__self__eq__0) ).

fof(fact_minus__nat_Odiff__0,axiom,
    ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m,
    file('theBenchmark.p',fact_minus__nat_Odiff__0) ).

fof(fact_diff__0__eq__0,axiom,
    ! [V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_diff__0__eq__0) ).

fof(fact_mult__cancel2,axiom,
    ! [V_n_2,V_k_2,V_m_2] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)
    <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | V_m_2 = V_n_2 ) ),
    file('theBenchmark.p',fact_mult__cancel2) ).

fof(fact_mult__cancel1,axiom,
    ! [V_n_2,V_m_2,V_k_2] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)
    <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | V_m_2 = V_n_2 ) ),
    file('theBenchmark.p',fact_mult__cancel1) ).

fof(fact_nat__mult__eq__cancel__disj,axiom,
    ! [V_n_2,V_m_2,V_k_2] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)
    <=> ( V_m_2 = V_n_2
        | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_nat__mult__eq__cancel__disj) ).

fof(fact_mult__is__0,axiom,
    ! [V_n_2,V_m_2] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_mult__is__0) ).

fof(fact_mult__0__right,axiom,
    ! [V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_mult__0__right) ).

fof(fact_mult__0,axiom,
    ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_mult__0) ).

fof(fact_sum__squares__eq__zero__iff,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Rings_Olinordered__ring__strict(T_b)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2)) = c_Groups_Ozero__class_Ozero(T_b)
      <=> ( V_y_2 = c_Groups_Ozero__class_Ozero(T_b)
          & V_x_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ),
    file('theBenchmark.p',fact_sum__squares__eq__zero__iff) ).

fof(fact_atLeastLessThan0,axiom,
    ! [V_m_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
    file('theBenchmark.p',fact_atLeastLessThan0) ).

fof(fact_atLeast__0,axiom,
    hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
    file('theBenchmark.p',fact_atLeast__0) ).

fof(fact_min__0L,axiom,
    ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_min__0L) ).

fof(fact_min__0R,axiom,
    ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_min__0R) ).

fof(fact_lessThan__0,axiom,
    hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
    file('theBenchmark.p',fact_lessThan__0) ).

fof(fact_max__0L,axiom,
    ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n,
    file('theBenchmark.p',fact_max__0L) ).

fof(fact_max__0R,axiom,
    ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_n,
    file('theBenchmark.p',fact_max__0R) ).

fof(fact_atMost__0,axiom,
    hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    file('theBenchmark.p',fact_atMost__0) ).

fof(fact_setsum__shift__lb__Suc0__0__upt,axiom,
    ! [V_k_2,V_f_2,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(T_b)
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) ) ),
    file('theBenchmark.p',fact_setsum__shift__lb__Suc0__0__upt) ).

fof(fact_sum__squares__ge__zero,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Rings_Olinordered__ring(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y)))) ),
    file('theBenchmark.p',fact_sum__squares__ge__zero) ).

fof(fact_sum__squares__le__zero__iff,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Rings_Olinordered__ring__strict(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2))),c_Groups_Ozero__class_Ozero(T_b)))
      <=> ( V_y_2 = c_Groups_Ozero__class_Ozero(T_b)
          & V_x_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ),
    file('theBenchmark.p',fact_sum__squares__le__zero__iff) ).

fof(fact_not__sum__squares__lt__zero,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Rings_Olinordered__ring(T_a)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y))),c_Groups_Ozero__class_Ozero(T_a))) ),
    file('theBenchmark.p',fact_not__sum__squares__lt__zero) ).

fof(fact_sum__squares__gt__zero__iff,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Rings_Olinordered__ring__strict(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2))))
      <=> ( V_y_2 != c_Groups_Ozero__class_Ozero(T_b)
          | V_x_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ),
    file('theBenchmark.p',fact_sum__squares__gt__zero__iff) ).

fof(fact_add__nonpos__nonpos,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Oordered__comm__monoid__add(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ),
    file('theBenchmark.p',fact_add__nonpos__nonpos) ).

fof(fact_add__increasing2,axiom,
    ! [V_a,V_b,V_c,T_a] :
      ( class_Groups_Oordered__comm__monoid__add(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ),
    file('theBenchmark.p',fact_add__increasing2) ).

fof(fact_add__increasing,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Groups_Oordered__comm__monoid__add(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ),
    file('theBenchmark.p',fact_add__increasing) ).

fof(fact_add__nonneg__eq__0__iff,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Groups_Oordered__comm__monoid__add(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_x_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_y_2))
         => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_y_2) = c_Groups_Ozero__class_Ozero(T_b)
          <=> ( V_y_2 = c_Groups_Ozero__class_Ozero(T_b)
              & V_x_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ),
    file('theBenchmark.p',fact_add__nonneg__eq__0__iff) ).

fof(fact_add__nonneg__nonneg,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Oordered__comm__monoid__add(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ),
    file('theBenchmark.p',fact_add__nonneg__nonneg) ).

fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
    ! [V_a_2,T_b] :
      ( class_Groups_Olinordered__ab__group__add(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ),
    file('theBenchmark.p',fact_double__add__le__zero__iff__single__add__le__zero) ).

fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
    ! [V_a_2,T_b] :
      ( class_Groups_Olinordered__ab__group__add(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ),
    file('theBenchmark.p',fact_zero__le__double__add__iff__zero__le__single__add) ).

fof(fact_split__mult__neg__le,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Oordered__cancel__semiring(T_a)
     => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) ) )
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ),
    file('theBenchmark.p',fact_split__mult__neg__le) ).

fof(fact_split__mult__pos__le,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Oordered__ring(T_a)
     => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) ) )
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ) ),
    file('theBenchmark.p',fact_split__mult__pos__le) ).

fof(fact_mult__mono,axiom,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( class_Rings_Oordered__semiring(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ),
    file('theBenchmark.p',fact_mult__mono) ).

fof(fact_mult__mono_H,axiom,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( class_Rings_Oordered__semiring(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ),
    file('theBenchmark.p',fact_mult__mono_H) ).

fof(fact_mult__left__mono__neg,axiom,
    ! [V_c,V_a,V_b,T_a] :
      ( class_Rings_Oordered__ring(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ),
    file('theBenchmark.p',fact_mult__left__mono__neg) ).

fof(fact_mult__right__mono__neg,axiom,
    ! [V_c,V_a,V_b,T_a] :
      ( class_Rings_Oordered__ring(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ),
    file('theBenchmark.p',fact_mult__right__mono__neg) ).

fof(fact_comm__mult__left__mono,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Rings_Oordered__comm__semiring(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ),
    file('theBenchmark.p',fact_comm__mult__left__mono) ).

fof(fact_mult__left__mono,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Rings_Oordered__semiring(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ),
    file('theBenchmark.p',fact_mult__left__mono) ).

fof(fact_mult__right__mono,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Rings_Oordered__semiring(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ),
    file('theBenchmark.p',fact_mult__right__mono) ).

fof(fact_mult__nonpos__nonpos,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Oordered__ring(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ) ) ),
    file('theBenchmark.p',fact_mult__nonpos__nonpos) ).

fof(fact_mult__nonpos__nonneg,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Oordered__cancel__semiring(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ),
    file('theBenchmark.p',fact_mult__nonpos__nonneg) ).

fof(fact_mult__nonneg__nonpos2,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Oordered__cancel__semiring(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ),
    file('theBenchmark.p',fact_mult__nonneg__nonpos2) ).

fof(fact_mult__nonneg__nonpos,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Oordered__cancel__semiring(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ),
    file('theBenchmark.p',fact_mult__nonneg__nonpos) ).

fof(fact_mult__nonneg__nonneg,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Oordered__cancel__semiring(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ) ) ),
    file('theBenchmark.p',fact_mult__nonneg__nonneg) ).

fof(fact_mult__le__0__iff,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( class_Rings_Olinordered__ring__strict(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ),
    file('theBenchmark.p',fact_mult__le__0__iff) ).

fof(fact_zero__le__mult__iff,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( class_Rings_Olinordered__ring__strict(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ),
    file('theBenchmark.p',fact_zero__le__mult__iff) ).

fof(fact_zero__le__square,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Olinordered__ring(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a))) ),
    file('theBenchmark.p',fact_zero__le__square) ).

fof(fact_pos__add__strict,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ),
    file('theBenchmark.p',fact_pos__add__strict) ).

fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
    ! [V_a_2,T_b] :
      ( class_Groups_Olinordered__ab__group__add(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ),
    file('theBenchmark.p',fact_zero__less__double__add__iff__zero__less__single__add) ).

fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
    ! [V_a_2,T_b] :
      ( class_Groups_Olinordered__ab__group__add(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ),
    file('theBenchmark.p',fact_double__add__less__zero__iff__single__add__less__zero) ).

fof(fact_add__pos__pos,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Oordered__comm__monoid__add(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ),
    file('theBenchmark.p',fact_add__pos__pos) ).

fof(fact_add__neg__neg,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Oordered__comm__monoid__add(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ),
    file('theBenchmark.p',fact_add__neg__neg) ).

fof(fact_not__square__less__zero,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Olinordered__ring(T_a)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)),c_Groups_Ozero__class_Ozero(T_a))) ),
    file('theBenchmark.p',fact_not__square__less__zero) ).

fof(fact_mult__less__cancel__right__disj,axiom,
    ! [V_b_2,V_c_2,V_a_2,T_b] :
      ( class_Rings_Olinordered__ring__strict(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_c_2)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) ) ) ),
    file('theBenchmark.p',fact_mult__less__cancel__right__disj) ).

fof(fact_mult__less__cancel__left__disj,axiom,
    ! [V_b_2,V_a_2,V_c_2,T_b] :
      ( class_Rings_Olinordered__ring__strict(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) ) ) ),
    file('theBenchmark.p',fact_mult__less__cancel__left__disj) ).

fof(fact_mult__less__cancel__left__pos,axiom,
    ! [V_b_2,V_a_2,V_c_2,T_b] :
      ( class_Rings_Olinordered__ring__strict(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ),
    file('theBenchmark.p',fact_mult__less__cancel__left__pos) ).

fof(fact_mult__pos__pos,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Olinordered__semiring__strict(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ) ) ),
    file('theBenchmark.p',fact_mult__pos__pos) ).

fof(fact_mult__pos__neg,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Olinordered__semiring__strict(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ),
    file('theBenchmark.p',fact_mult__pos__neg) ).

fof(fact_mult__pos__neg2,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Olinordered__semiring__strict(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ),
    file('theBenchmark.p',fact_mult__pos__neg2) ).

fof(fact_zero__less__mult__pos,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Olinordered__semiring__strict(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ),
    file('theBenchmark.p',fact_zero__less__mult__pos) ).

fof(fact_zero__less__mult__pos2,axiom,
    ! [V_a,V_b,T_a] :
      ( class_Rings_Olinordered__semiring__strict(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ),
    file('theBenchmark.p',fact_zero__less__mult__pos2) ).

fof(fact_mult__less__cancel__left__neg,axiom,
    ! [V_b_2,V_a_2,V_c_2,T_b] :
      ( class_Rings_Olinordered__ring__strict(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) ) ) ),
    file('theBenchmark.p',fact_mult__less__cancel__left__neg) ).

fof(fact_mult__neg__pos,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Olinordered__semiring__strict(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ),
    file('theBenchmark.p',fact_mult__neg__pos) ).

fof(fact_mult__neg__neg,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Olinordered__ring__strict(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ) ) ),
    file('theBenchmark.p',fact_mult__neg__neg) ).

fof(fact_mult__strict__right__mono,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Rings_Olinordered__semiring__strict(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ),
    file('theBenchmark.p',fact_mult__strict__right__mono) ).

fof(fact_mult__strict__left__mono,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Rings_Olinordered__semiring__strict(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ),
    file('theBenchmark.p',fact_mult__strict__left__mono) ).

fof(fact_comm__mult__strict__left__mono,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Rings_Olinordered__comm__semiring__strict(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ),
    file('theBenchmark.p',fact_comm__mult__strict__left__mono) ).

fof(fact_mult__strict__right__mono__neg,axiom,
    ! [V_c,V_a,V_b,T_a] :
      ( class_Rings_Olinordered__ring__strict(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ),
    file('theBenchmark.p',fact_mult__strict__right__mono__neg) ).

fof(fact_mult__strict__left__mono__neg,axiom,
    ! [V_c,V_a,V_b,T_a] :
      ( class_Rings_Olinordered__ring__strict(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))) ) ) ),
    file('theBenchmark.p',fact_mult__strict__left__mono__neg) ).

fof(fact_le__iff__diff__le__0,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( class_Groups_Oordered__ab__group__add(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))) ) ),
    file('theBenchmark.p',fact_le__iff__diff__le__0) ).

fof(fact_less__iff__diff__less__0,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( class_Groups_Oordered__ab__group__add(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))) ) ),
    file('theBenchmark.p',fact_less__iff__diff__less__0) ).

fof(fact_add__scale__eq__noteq,axiom,
    ! [V_d,V_c,V_b,V_a,V_r,T_a] :
      ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
     => ( V_r != c_Groups_Ozero__class_Ozero(T_a)
       => ( ( V_c != V_d
            & V_a = V_b )
         => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_c)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_d)) ) ) ),
    file('theBenchmark.p',fact_add__scale__eq__noteq) ).

fof(fact_not__one__le__zero,axiom,
    ! [T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ),
    file('theBenchmark.p',fact_not__one__le__zero) ).

fof(fact_zero__le__one,axiom,
    ! [T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ),
    file('theBenchmark.p',fact_zero__le__one) ).

fof(fact_zero__less__one,axiom,
    ! [T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ),
    file('theBenchmark.p',fact_zero__less__one) ).

fof(fact_not__one__less__zero,axiom,
    ! [T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ),
    file('theBenchmark.p',fact_not__one__less__zero) ).

fof(fact_neg__0__le__iff__le,axiom,
    ! [V_a_2,T_b] :
      ( class_Groups_Oordered__ab__group__add(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ),
    file('theBenchmark.p',fact_neg__0__le__iff__le) ).

fof(fact_le__minus__self__iff,axiom,
    ! [V_a_2,T_b] :
      ( class_Groups_Olinordered__ab__group__add(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ),
    file('theBenchmark.p',fact_le__minus__self__iff) ).

fof(fact_neg__le__0__iff__le,axiom,
    ! [V_a_2,T_b] :
      ( class_Groups_Oordered__ab__group__add(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ),
    file('theBenchmark.p',fact_neg__le__0__iff__le) ).

fof(fact_minus__le__self__iff,axiom,
    ! [V_a_2,T_b] :
      ( class_Groups_Olinordered__ab__group__add(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_a_2))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ),
    file('theBenchmark.p',fact_minus__le__self__iff) ).

fof(fact_neg__less__nonneg,axiom,
    ! [V_a_2,T_b] :
      ( class_Groups_Olinordered__ab__group__add(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_a_2))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ),
    file('theBenchmark.p',fact_neg__less__nonneg) ).

fof(fact_neg__less__0__iff__less,axiom,
    ! [V_a_2,T_b] :
      ( class_Groups_Oordered__ab__group__add(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ),
    file('theBenchmark.p',fact_neg__less__0__iff__less) ).

fof(fact_neg__0__less__iff__less,axiom,
    ! [V_a_2,T_b] :
      ( class_Groups_Oordered__ab__group__add(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ),
    file('theBenchmark.p',fact_neg__0__less__iff__less) ).

fof(fact_less__minus__self__iff,axiom,
    ! [V_a_2,T_b] :
      ( class_Rings_Olinordered__idom(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ),
    file('theBenchmark.p',fact_less__minus__self__iff) ).

fof(fact_right__minus,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Ogroup__add(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_right__minus) ).

fof(fact_eq__neg__iff__add__eq__0,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( class_Groups_Ogroup__add(T_b)
     => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
      <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b) ) ),
    file('theBenchmark.p',fact_eq__neg__iff__add__eq__0) ).

fof(fact_left__minus,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Ogroup__add(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_left__minus) ).

fof(fact_ab__left__minus,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Oab__group__add(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_ab__left__minus) ).

fof(fact_minus__unique,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Ogroup__add(T_a)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
       => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) = V_b ) ),
    file('theBenchmark.p',fact_minus__unique) ).

fof(fact_diff__0,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Ogroup__add(T_a)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ),
    file('theBenchmark.p',fact_diff__0) ).

fof(fact_setsum__empty,axiom,
    ! [V_f_2,T_c,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(T_b) ),
    file('theBenchmark.p',fact_setsum__empty) ).

fof(fact_setsum_Oempty,axiom,
    ! [V_g_2,T_c,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_g_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(T_b) ),
    file('theBenchmark.p',fact_setsum_Oempty) ).

fof(fact_setsum_Oinfinite,axiom,
    ! [V_g_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__add(T_c)
     => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c) ) ),
    file('theBenchmark.p',fact_setsum_Oinfinite) ).

fof(fact_setsum__infinite,axiom,
    ! [V_f_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__add(T_c)
     => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c) ) ),
    file('theBenchmark.p',fact_setsum__infinite) ).

fof(fact_setprod__pos__nat__iff,axiom,
    ! [V_f_2,V_S_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_S_2)))
      <=> ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(V_f_2,B_x))) ) ) ),
    file('theBenchmark.p',fact_setprod__pos__nat__iff) ).

fof(fact_setprod__zero__iff,axiom,
    ! [V_f_2,V_A_2,T_b,T_c] :
      ( ( class_Rings_Ono__zero__divisors(T_c)
        & class_Rings_Ocomm__semiring__1(T_c) )
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c)
        <=> ? [B_x] :
              ( hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c)
              & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ) ),
    file('theBenchmark.p',fact_setprod__zero__iff) ).

fof(fact_setprod__zero,axiom,
    ! [V_f_2,V_A_2,T_b,T_c] :
      ( class_Rings_Ocomm__semiring__1(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ? [B_x] :
              ( hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c)
              & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ),
    file('theBenchmark.p',fact_setprod__zero) ).

fof(fact_gr0__conv__Suc,axiom,
    ! [V_n_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
    <=> ? [B_m] : V_n_2 = hAPP(c_Nat_OSuc,B_m) ),
    file('theBenchmark.p',fact_gr0__conv__Suc) ).

fof(fact_less__Suc0,axiom,
    ! [V_n_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
    <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('theBenchmark.p',fact_less__Suc0) ).

fof(fact_less__Suc__eq__0__disj,axiom,
    ! [V_n_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
    <=> ( ? [B_j] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_n_2))
            & V_m_2 = hAPP(c_Nat_OSuc,B_j) )
        | V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_less__Suc__eq__0__disj) ).

fof(fact_one__is__add,axiom,
    ! [V_n_2,V_m_2] :
      ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)
    <=> ( ( V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ),
    file('theBenchmark.p',fact_one__is__add) ).

fof(fact_add__is__1,axiom,
    ! [V_n_2,V_m_2] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    <=> ( ( V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ),
    file('theBenchmark.p',fact_add__is__1) ).

fof(fact_add__gr__0,axiom,
    ! [V_n_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) ) ),
    file('theBenchmark.p',fact_add__gr__0) ).

fof(fact_card_Oempty,axiom,
    ! [T_b] : hAPP(c_Finite__Set_Ocard(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_card_Oempty) ).

fof(fact_card__infinite,axiom,
    ! [V_A_2,T_b] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('theBenchmark.p',fact_card__infinite) ).

fof(fact_mult__eq__1__iff,axiom,
    ! [V_n_2,V_m_2] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    <=> ( V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        & V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    file('theBenchmark.p',fact_mult__eq__1__iff) ).

fof(fact_diff__less,axiom,
    ! [V_m,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_m)) ) ),
    file('theBenchmark.p',fact_diff__less) ).

fof(fact_zero__less__diff,axiom,
    ! [V_m_2,V_n_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_m_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ),
    file('theBenchmark.p',fact_zero__less__diff) ).

fof(fact_mult__less__mono2,axiom,
    ! [V_k,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j))) ) ),
    file('theBenchmark.p',fact_mult__less__mono2) ).

fof(fact_mult__less__mono1,axiom,
    ! [V_k,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k))) ) ),
    file('theBenchmark.p',fact_mult__less__mono1) ).

fof(fact_nat__mult__less__cancel1,axiom,
    ! [V_n_2,V_m_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ),
    file('theBenchmark.p',fact_nat__mult__less__cancel1) ).

fof(fact_nat__mult__eq__cancel1,axiom,
    ! [V_n_2,V_m_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
     => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)
      <=> V_m_2 = V_n_2 ) ),
    file('theBenchmark.p',fact_nat__mult__eq__cancel1) ).

fof(fact_mult__less__cancel2,axiom,
    ! [V_n_2,V_k_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) ) ),
    file('theBenchmark.p',fact_mult__less__cancel2) ).

fof(fact_mult__less__cancel1,axiom,
    ! [V_n_2,V_m_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) ) ),
    file('theBenchmark.p',fact_mult__less__cancel1) ).

fof(fact_nat__0__less__mult__iff,axiom,
    ! [V_n_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) ) ),
    file('theBenchmark.p',fact_nat__0__less__mult__iff) ).

fof(fact_diff__add__0,axiom,
    ! [V_m,V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_diff__add__0) ).

fof(fact_diff__is__0__eq,axiom,
    ! [V_n_2,V_m_2] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ),
    file('theBenchmark.p',fact_diff__is__0__eq) ).

fof(fact_diff__is__0__eq_H,axiom,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('theBenchmark.p',fact_diff__is__0__eq_H) ).

fof(fact_One__nat__def,axiom,
    c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('theBenchmark.p',fact_One__nat__def) ).

fof(fact_mult__eq__self__implies__10,axiom,
    ! [V_n,V_m] :
      ( V_m = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)
     => ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_mult__eq__self__implies__10) ).

fof(fact_setsum__shift__lb__Suc0__0,axiom,
    ! [V_k_2,V_f_2] :
      ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)) ),
    file('theBenchmark.p',fact_setsum__shift__lb__Suc0__0) ).

fof(fact_setsum__eq__0__iff,axiom,
    ! [V_f_2,V_F_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
     => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_F_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      <=> ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2))
           => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
    file('theBenchmark.p',fact_setsum__eq__0__iff) ).

fof(fact_greaterThan__0,axiom,
    hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    file('theBenchmark.p',fact_greaterThan__0) ).

fof(fact_lessThan__Suc__eq__insert__0,axiom,
    ! [V_n_2] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))),
    file('theBenchmark.p',fact_lessThan__Suc__eq__insert__0) ).

fof(fact_atLeast0LessThan,axiom,
    ! [V_n_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2),
    file('theBenchmark.p',fact_atLeast0LessThan) ).

fof(fact_atLeast0AtMost,axiom,
    ! [V_n_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2),
    file('theBenchmark.p',fact_atLeast0AtMost) ).

fof(fact_Suc__pred_H,axiom,
    ! [V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
     => V_n = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    file('theBenchmark.p',fact_Suc__pred_H) ).

fof(fact_add__eq__if,axiom,
    ! [V_n,V_m] :
      ( ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n)) )
      & ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_n ) ),
    file('theBenchmark.p',fact_add__eq__if) ).

fof(fact_add__nonpos__neg,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Oordered__comm__monoid__add(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ),
    file('theBenchmark.p',fact_add__nonpos__neg) ).

fof(fact_add__neg__nonpos,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Oordered__comm__monoid__add(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ),
    file('theBenchmark.p',fact_add__neg__nonpos) ).

fof(fact_add__strict__increasing2,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Groups_Oordered__comm__monoid__add(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ),
    file('theBenchmark.p',fact_add__strict__increasing2) ).

fof(fact_add__strict__increasing,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Groups_Oordered__comm__monoid__add(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ),
    file('theBenchmark.p',fact_add__strict__increasing) ).

fof(fact_add__nonneg__pos,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Oordered__comm__monoid__add(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ),
    file('theBenchmark.p',fact_add__nonneg__pos) ).

fof(fact_add__pos__nonneg,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Oordered__comm__monoid__add(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ),
    file('theBenchmark.p',fact_add__pos__nonneg) ).

fof(fact_mult__le__cancel__left__pos,axiom,
    ! [V_b_2,V_a_2,V_c_2,T_b] :
      ( class_Rings_Olinordered__ring__strict(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ),
    file('theBenchmark.p',fact_mult__le__cancel__left__pos) ).

fof(fact_mult__le__cancel__left__neg,axiom,
    ! [V_b_2,V_a_2,V_c_2,T_b] :
      ( class_Rings_Olinordered__ring__strict(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2)) ) ) ),
    file('theBenchmark.p',fact_mult__le__cancel__left__neg) ).

fof(fact_mult__strict__mono,axiom,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( class_Rings_Olinordered__semiring__strict(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ),
    file('theBenchmark.p',fact_mult__strict__mono) ).

fof(fact_mult__strict__mono_H,axiom,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( class_Rings_Olinordered__semiring__strict(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ),
    file('theBenchmark.p',fact_mult__strict__mono_H) ).

fof(fact_mult__less__le__imp__less,axiom,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( class_Rings_Olinordered__semiring__strict(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ),
    file('theBenchmark.p',fact_mult__less__le__imp__less) ).

fof(fact_mult__le__less__imp__less,axiom,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( class_Rings_Olinordered__semiring__strict(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))) ) ) ) ) ),
    file('theBenchmark.p',fact_mult__le__less__imp__less) ).

fof(fact_mult__right__less__imp__less,axiom,
    ! [V_b,V_c,V_a,T_a] :
      ( class_Rings_Olinordered__semiring(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ),
    file('theBenchmark.p',fact_mult__right__less__imp__less) ).

fof(fact_mult__less__imp__less__right,axiom,
    ! [V_b,V_c,V_a,T_a] :
      ( class_Rings_Olinordered__semiring__strict(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ),
    file('theBenchmark.p',fact_mult__less__imp__less__right) ).

fof(fact_mult__left__less__imp__less,axiom,
    ! [V_b,V_a,V_c,T_a] :
      ( class_Rings_Olinordered__semiring(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ),
    file('theBenchmark.p',fact_mult__left__less__imp__less) ).

fof(fact_mult__less__imp__less__left,axiom,
    ! [V_b,V_a,V_c,T_a] :
      ( class_Rings_Olinordered__semiring__strict(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ),
    file('theBenchmark.p',fact_mult__less__imp__less__left) ).

fof(fact_mult__right__le__imp__le,axiom,
    ! [V_b,V_c,V_a,T_a] :
      ( class_Rings_Olinordered__semiring__strict(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ),
    file('theBenchmark.p',fact_mult__right__le__imp__le) ).

fof(fact_mult__left__le__imp__le,axiom,
    ! [V_b,V_a,V_c,T_a] :
      ( class_Rings_Olinordered__semiring__strict(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ),
    file('theBenchmark.p',fact_mult__left__le__imp__le) ).

fof(fact_mult__eq__if,axiom,
    ! [V_n,V_m] :
      ( ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n)) )
      & ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_mult__eq__if) ).

fof(fact_mult__left__le__one__le,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x)),V_x)) ) ) ) ),
    file('theBenchmark.p',fact_mult__left__le__one__le) ).

fof(fact_mult__right__le__one__le,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),V_x)) ) ) ) ),
    file('theBenchmark.p',fact_mult__right__le__one__le) ).

fof(fact_zero__less__two,axiom,
    ! [T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a)))) ),
    file('theBenchmark.p',fact_zero__less__two) ).

fof(fact_card__eq__0__iff,axiom,
    ! [V_A_2,T_b] :
      ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
        | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_card__eq__0__iff) ).

fof(fact_card__ge__0__finite,axiom,
    ! [V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    file('theBenchmark.p',fact_card__ge__0__finite) ).

fof(fact_Suc__pred,axiom,
    ! [V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
     => hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = V_n ),
    file('theBenchmark.p',fact_Suc__pred) ).

fof(fact_diff__Suc__less,axiom,
    ! [V_i,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_i))),V_n)) ),
    file('theBenchmark.p',fact_diff__Suc__less) ).

fof(fact_n__less__m__mult__n,axiom,
    ! [V_m,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))) ) ),
    file('theBenchmark.p',fact_n__less__m__mult__n) ).

fof(fact_n__less__n__mult__m,axiom,
    ! [V_m,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m))) ) ),
    file('theBenchmark.p',fact_n__less__n__mult__m) ).

fof(fact_one__less__mult,axiom,
    ! [V_m,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))) ) ),
    file('theBenchmark.p',fact_one__less__mult) ).

fof(fact_nat__diff__split,axiom,
    ! [V_b_2,V_a_2,V_P_2] :
      ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
    <=> ( ! [B_d] :
            ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d)
           => hBOOL(hAPP(V_P_2,B_d)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
         => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ),
    file('theBenchmark.p',fact_nat__diff__split) ).

fof(fact_nat__diff__split__asm,axiom,
    ! [V_b_2,V_a_2,V_P_2] :
      ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
    <=> ~ ( ? [B_d] :
              ( ~ hBOOL(hAPP(V_P_2,B_d))
              & V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) )
          | ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) ) ) ),
    file('theBenchmark.p',fact_nat__diff__split__asm) ).

fof(fact_one__le__mult__iff,axiom,
    ! [V_n_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n_2))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m_2)) ) ),
    file('theBenchmark.p',fact_one__le__mult__iff) ).

fof(fact_nat__mult__le__cancel1,axiom,
    ! [V_n_2,V_m_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ),
    file('theBenchmark.p',fact_nat__mult__le__cancel1) ).

fof(fact_mult__le__cancel2,axiom,
    ! [V_n_2,V_k_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ),
    file('theBenchmark.p',fact_mult__le__cancel2) ).

fof(fact_mult__le__cancel1,axiom,
    ! [V_n_2,V_m_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ),
    file('theBenchmark.p',fact_mult__le__cancel1) ).

fof(fact_setsum__eq__Suc0__iff,axiom,
    ! [V_f_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
      <=> ? [B_x] :
            ( ! [B_xa] :
                ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
               => ( B_x != B_xa
                 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
            & hAPP(V_f_2,B_x) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ),
    file('theBenchmark.p',fact_setsum__eq__Suc0__iff) ).

fof(fact_setsum__eq__1__iff,axiom,
    ! [V_f_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
      <=> ? [B_x] :
            ( ! [B_xa] :
                ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
               => ( B_x != B_xa
                 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
            & hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ),
    file('theBenchmark.p',fact_setsum__eq__1__iff) ).

fof(fact_convex__bound__le,axiom,
    ! [V_v,V_u,V_y,V_a,V_x,T_a] :
      ( class_Rings_Olinordered__semiring__1(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_a))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v))
             => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a)
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y))),V_a)) ) ) ) ) ) ),
    file('theBenchmark.p',fact_convex__bound__le) ).

fof(fact_card__gt__0__iff,axiom,
    ! [V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)))
    <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
        & V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_card__gt__0__iff) ).

fof(fact_finite__UNIV__card__ge__0,axiom,
    ! [T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) ),
    file('theBenchmark.p',fact_finite__UNIV__card__ge__0) ).

fof(fact_Suc__diff__1,axiom,
    ! [V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
     => hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = V_n ),
    file('theBenchmark.p',fact_Suc__diff__1) ).

fof(fact_convex__bound__lt,axiom,
    ! [V_v,V_u,V_y,V_a,V_x,T_a] :
      ( class_Rings_Olinordered__semiring__1__strict(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_a))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v))
             => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a)
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y))),V_a)) ) ) ) ) ) ),
    file('theBenchmark.p',fact_convex__bound__lt) ).

fof(fact_setsum__op__ivl__Suc,axiom,
    ! [V_f_2,V_m_2,V_n_2,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2))),hAPP(V_f_2,V_n_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2))) = c_Groups_Ozero__class_Ozero(T_b) ) ) ),
    file('theBenchmark.p',fact_setsum__op__ivl__Suc) ).

fof(fact_setsum__cl__ivl__Suc,axiom,
    ! [V_f_2,V_m_2,V_n_2,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2))),hAPP(V_f_2,hAPP(c_Nat_OSuc,V_n_2))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2))) = c_Groups_Ozero__class_Ozero(T_b) ) ) ),
    file('theBenchmark.p',fact_setsum__cl__ivl__Suc) ).

fof(fact_ex__nat__less,axiom,
    ! [V_P_2,V_n_2] :
      ( ? [B_m] :
          ( hBOOL(hAPP(V_P_2,B_m))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2)) )
    <=> ? [B_x] :
          ( hBOOL(hAPP(V_P_2,B_x))
          & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2))) ) ),
    file('theBenchmark.p',fact_ex__nat__less) ).

fof(fact_all__nat__less,axiom,
    ! [V_P_2,V_n_2] :
      ( ! [B_m] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2))
         => hBOOL(hAPP(V_P_2,B_m)) )
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)))
         => hBOOL(hAPP(V_P_2,B_x)) ) ),
    file('theBenchmark.p',fact_all__nat__less) ).

fof(fact_all__nat__less__eq,axiom,
    ! [V_P_2,V_n_2] :
      ( ! [B_m] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2))
         => hBOOL(hAPP(V_P_2,B_m)) )
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)))
         => hBOOL(hAPP(V_P_2,B_x)) ) ),
    file('theBenchmark.p',fact_all__nat__less__eq) ).

fof(fact_ex__nat__less__eq,axiom,
    ! [V_P_2,V_n_2] :
      ( ? [B_m] :
          ( hBOOL(hAPP(V_P_2,B_m))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2)) )
    <=> ? [B_x] :
          ( hBOOL(hAPP(V_P_2,B_x))
          & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))) ) ),
    file('theBenchmark.p',fact_ex__nat__less__eq) ).

fof(fact_even__less__0__iff,axiom,
    ! [V_a_2,T_b] :
      ( class_Rings_Olinordered__idom(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ),
    file('theBenchmark.p',fact_even__less__0__iff) ).

fof(fact_card_Ounion__inter__neutral,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
       => ( ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
           => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
         => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) ) ) ),
    file('theBenchmark.p',fact_card_Ounion__inter__neutral) ).

fof(fact_setsum__mono2,axiom,
    ! [V_f_2,V_A_2,V_B_2,T_b,T_c] :
      ( class_Groups_Oordered__comm__monoid__add(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
         => ( ! [B_b] :
                ( hBOOL(hAPP(hAPP(c_member(T_b),B_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_b))) )
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2))) ) ) ) ),
    file('theBenchmark.p',fact_setsum__mono2) ).

fof(fact_double__eq__0__iff,axiom,
    ! [V_a_2,T_b] :
      ( class_Groups_Olinordered__ab__group__add(T_b)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
      <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ),
    file('theBenchmark.p',fact_double__eq__0__iff) ).

fof(fact_setsum_Ounion__inter__neutral,axiom,
    ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__add(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
         => ( ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
               => hAPP(V_g_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_B_2)) ) ) ) ),
    file('theBenchmark.p',fact_setsum_Ounion__inter__neutral) ).

fof(fact_setsum__Un__zero,axiom,
    ! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__add(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
         => ( ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)))
               => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_S_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_T_2)) ) ) ) ),
    file('theBenchmark.p',fact_setsum__Un__zero) ).

fof(fact_card__Suc__eq,axiom,
    ! [V_k_2,V_A_2,T_b] :
      ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Nat_OSuc,V_k_2)
    <=> ? [B_b,B_B] :
          ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
           => B_B = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
          & hAPP(c_Finite__Set_Ocard(T_b),B_B) = V_k_2
          & ~ hBOOL(hAPP(hAPP(c_member(T_b),B_b),B_B))
          & V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_b),B_b),B_B) ) ),
    file('theBenchmark.p',fact_card__Suc__eq) ).

fof(fact_setsum__mono3,axiom,
    ! [V_f_2,V_A_2,V_B_2,T_b,T_c] :
      ( ( class_Groups_Oordered__ab__semigroup__add(T_c)
        & class_Groups_Ocomm__monoid__add(T_c) )
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
         => ( ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) )
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2))) ) ) ) ),
    file('theBenchmark.p',fact_setsum__mono3) ).

fof(fact_Ints__odd__less__0,axiom,
    ! [V_a_2,T_b] :
      ( class_Rings_Olinordered__idom(T_b)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),c_Groups_Oone__class_Oone(T_b)),V_a_2)),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ),
    file('theBenchmark.p',fact_Ints__odd__less__0) ).

fof(fact_card__Plus__conv__if,axiom,
    ! [V_B_2,T_c,V_A_2,T_b] :
      ( ( ~ ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
            & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) )
       => hAPP(c_Finite__Set_Ocard(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) )
       => hAPP(c_Finite__Set_Ocard(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2)) ) ),
    file('theBenchmark.p',fact_card__Plus__conv__if) ).

fof(fact_Ints__0,axiom,
    ! [T_b] :
      ( class_Rings_Oring__1(T_b)
     => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Int_Oring__1__class_OInts(T_b))) ),
    file('theBenchmark.p',fact_Ints__0) ).

fof(fact_Ints__add,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( class_Rings_Oring__1(T_b)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
         => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_b))) ) ) ),
    file('theBenchmark.p',fact_Ints__add) ).

fof(fact_Ints__mult,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( class_Rings_Oring__1(T_b)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
         => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_b))) ) ) ),
    file('theBenchmark.p',fact_Ints__mult) ).

fof(fact_Ints__diff,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( class_Rings_Oring__1(T_b)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
         => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_b))) ) ) ),
    file('theBenchmark.p',fact_Ints__diff) ).

fof(fact_Ints__1,axiom,
    ! [T_b] :
      ( class_Rings_Oring__1(T_b)
     => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Oone__class_Oone(T_b)),c_Int_Oring__1__class_OInts(T_b))) ),
    file('theBenchmark.p',fact_Ints__1) ).

fof(fact_Ints__minus,axiom,
    ! [V_a_2,T_b] :
      ( class_Rings_Oring__1(T_b)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
       => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),c_Int_Oring__1__class_OInts(T_b))) ) ),
    file('theBenchmark.p',fact_Ints__minus) ).

fof(fact_Ints__double__eq__0__iff,axiom,
    ! [V_a_2,T_b] :
      ( class_Int_Oring__char__0(T_b)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
       => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
        <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ),
    file('theBenchmark.p',fact_Ints__double__eq__0__iff) ).

fof(fact_finite__Plus__iff,axiom,
    ! [V_B_2,V_A_2,T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)))
    <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ),
    file('theBenchmark.p',fact_finite__Plus__iff) ).

fof(fact_finite__Plus,axiom,
    ! [V_B_2,T_c,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2))) ) ),
    file('theBenchmark.p',fact_finite__Plus) ).

fof(fact_finite__PlusD_I1_J,axiom,
    ! [V_B_2,V_A_2,T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    file('theBenchmark.p',fact_finite__PlusD_I1_J) ).

fof(fact_finite__PlusD_I2_J,axiom,
    ! [V_B_2,V_A_2,T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ),
    file('theBenchmark.p',fact_finite__PlusD_I2_J) ).

fof(fact_card__Plus,axiom,
    ! [V_B_2,T_c,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
       => hAPP(c_Finite__Set_Ocard(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2)) ) ),
    file('theBenchmark.p',fact_card__Plus) ).

fof(fact_Ints__odd__nonzero,axiom,
    ! [V_a_2,T_b] :
      ( class_Int_Oring__char__0(T_b)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),c_Groups_Oone__class_Oone(T_b)),V_a_2)),V_a_2) != c_Groups_Ozero__class_Ozero(T_b) ) ),
    file('theBenchmark.p',fact_Ints__odd__nonzero) ).

fof(fact_UNIV__Plus__UNIV,axiom,
    ! [T_c,T_b] : c_Sum__Type_OPlus(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(T_b,T_c),tc_HOL_Obool)),
    file('theBenchmark.p',fact_UNIV__Plus__UNIV) ).

fof(fact_Plus__eq__empty__conv,axiom,
    ! [V_B_2,V_A_2,T_c,T_b] :
      ( c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(T_b,T_c),tc_HOL_Obool))
    <=> ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
        & V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_Plus__eq__empty__conv) ).

fof(fact_setprod__diff1,axiom,
    ! [V_a_2,V_f_2,V_A_2,T_b,T_c] :
      ( class_Fields_Ofield(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hAPP(V_f_2,V_a_2) != c_Groups_Ozero__class_Ozero(T_c)
         => ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
             => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2) )
            & ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
             => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) ) ) ) ) ),
    file('theBenchmark.p',fact_setprod__diff1) ).

fof(fact_fold__Un__disjoint,axiom,
    ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__mult(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_A_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_B_2)) ) ) ) ),
    file('theBenchmark.p',fact_fold__Un__disjoint) ).

fof(fact_ex__least__nat__less,axiom,
    ! [V_n_2,V_P_2] :
      ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
     => ( hBOOL(hAPP(V_P_2,V_n_2))
       => ? [B_k] :
            ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_k),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
            & ! [B_i] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_k))
               => ~ hBOOL(hAPP(V_P_2,B_i)) )
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_k),V_n_2)) ) ) ),
    file('theBenchmark.p',fact_ex__least__nat__less) ).

fof(fact_setprod__mono__one__right,axiom,
    ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__mult(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
         => ( ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_T_2),V_S_2)))
               => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_T_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_S_2) ) ) ) ),
    file('theBenchmark.p',fact_setprod__mono__one__right) ).

fof(fact_divide__zero__left,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Odivision__ring(T_a)
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_divide__zero__left) ).

fof(fact_divide__zero,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Odivision__ring__inverse__zero(T_a)
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_divide__zero) ).

fof(fact_add__divide__distrib,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Rings_Odivision__ring(T_a)
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)) ),
    file('theBenchmark.p',fact_add__divide__distrib) ).

fof(fact_times__divide__eq__right,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Rings_Odivision__ring(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c) ),
    file('theBenchmark.p',fact_times__divide__eq__right) ).

fof(fact_diff__divide__distrib,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Rings_Odivision__ring(T_a)
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)) ),
    file('theBenchmark.p',fact_diff__divide__distrib) ).

fof(fact_divide__1,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Odivision__ring(T_a)
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ),
    file('theBenchmark.p',fact_divide__1) ).

fof(fact_minus__divide__left,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Odivision__ring(T_a)
     => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b) ),
    file('theBenchmark.p',fact_minus__divide__left) ).

fof(fact_fold__image__empty,axiom,
    ! [V_z_2,V_g_2,V_f_2,T_c,T_b] : hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2),V_z_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_z_2,
    file('theBenchmark.p',fact_fold__image__empty) ).

fof(fact_nonzero__eq__divide__eq,axiom,
    ! [V_b_2,V_a_2,V_c_2,T_b] :
      ( class_Rings_Odivision__ring(T_b)
     => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
       => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)
        <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) = V_b_2 ) ) ),
    file('theBenchmark.p',fact_nonzero__eq__divide__eq) ).

fof(fact_nonzero__divide__eq__eq,axiom,
    ! [V_a_2,V_b_2,V_c_2,T_b] :
      ( class_Rings_Odivision__ring(T_b)
     => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
       => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) = V_a_2
        <=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) ) ) ),
    file('theBenchmark.p',fact_nonzero__divide__eq__eq) ).

fof(fact_divide__eq__imp,axiom,
    ! [V_a,V_b,V_c,T_a] :
      ( class_Rings_Odivision__ring(T_a)
     => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
       => ( V_b = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)
         => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) = V_a ) ) ),
    file('theBenchmark.p',fact_divide__eq__imp) ).

fof(fact_eq__divide__imp,axiom,
    ! [V_b,V_a,V_c,T_a] :
      ( class_Rings_Odivision__ring(T_a)
     => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
       => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) = V_b
         => V_a = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) ) ) ),
    file('theBenchmark.p',fact_eq__divide__imp) ).

fof(fact_right__inverse__eq,axiom,
    ! [V_a_2,V_b_2,T_b] :
      ( class_Rings_Odivision__ring(T_b)
     => ( V_b_2 != c_Groups_Ozero__class_Ozero(T_b)
       => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2) = c_Groups_Oone__class_Oone(T_b)
        <=> V_a_2 = V_b_2 ) ) ),
    file('theBenchmark.p',fact_right__inverse__eq) ).

fof(fact_divide__self,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Odivision__ring(T_a)
     => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
       => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ),
    file('theBenchmark.p',fact_divide__self) ).

fof(fact_divide__self__if,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Odivision__ring__inverse__zero(T_a)
     => ( ( V_a != c_Groups_Ozero__class_Ozero(T_a)
         => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) )
        & ( V_a = c_Groups_Ozero__class_Ozero(T_a)
         => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
    file('theBenchmark.p',fact_divide__self__if) ).

fof(fact_nonzero__minus__divide__right,axiom,
    ! [V_a,V_b,T_a] :
      ( class_Rings_Odivision__ring(T_a)
     => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
       => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ) ),
    file('theBenchmark.p',fact_nonzero__minus__divide__right) ).

fof(fact_nonzero__minus__divide__divide,axiom,
    ! [V_a,V_b,T_a] :
      ( class_Rings_Odivision__ring(T_a)
     => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
       => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b) ) ),
    file('theBenchmark.p',fact_nonzero__minus__divide__divide) ).

fof(fact_folding__image__simple_Oeq__fold__g,axiom,
    ! [V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
       => hAPP(V_F_2,V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2),V_z_2),V_A_2) ) ),
    file('theBenchmark.p',fact_folding__image__simple_Oeq__fold__g) ).

fof(fact_fold__image__insert,axiom,
    ! [V_z_2,V_g_2,V_a_2,V_A_2,T_b,T_c] :
      ( class_Groups_Oab__semigroup__mult(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
         => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_g_2,V_a_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),V_z_2),V_A_2)) ) ) ),
    file('theBenchmark.p',fact_fold__image__insert) ).

fof(fact_setsum_Oeq__fold,axiom,
    ! [V_g_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__add(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Oplus__class_Oplus(T_c)),V_g_2),c_Groups_Ozero__class_Ozero(T_c)),V_A_2) ) ),
    file('theBenchmark.p',fact_setsum_Oeq__fold) ).

fof(fact_setsum_OF__eq,axiom,
    ! [V_g_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__add(T_c)
     => ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c) )
        & ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Oplus__class_Oplus(T_c)),V_g_2),c_Groups_Ozero__class_Ozero(T_c)),V_A_2) ) ) ),
    file('theBenchmark.p',fact_setsum_OF__eq) ).

fof(fact_setprod_OF__eq,axiom,
    ! [V_g_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__mult(T_c)
     => ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = c_Groups_Oone__class_Oone(T_c) )
        & ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_A_2) ) ) ),
    file('theBenchmark.p',fact_setprod_OF__eq) ).

fof(fact_setprod_Oeq__fold,axiom,
    ! [V_g_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__mult(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_A_2) ) ),
    file('theBenchmark.p',fact_setprod_Oeq__fold) ).

fof(fact_fold__image__Un__Int,axiom,
    ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__mult(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
         => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_A_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ),
    file('theBenchmark.p',fact_fold__image__Un__Int) ).

fof(fact_divide__left__mono__neg,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Fields_Olinordered__field__inverse__zero(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_b))) ) ) ) ),
    file('theBenchmark.p',fact_divide__left__mono__neg) ).

fof(fact_divide__left__mono,axiom,
    ! [V_c,V_a,V_b,T_a] :
      ( class_Fields_Olinordered__field(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_b))) ) ) ) ),
    file('theBenchmark.p',fact_divide__left__mono) ).

fof(fact_neg__divide__le__eq,axiom,
    ! [V_a_2,V_b_2,V_c_2,T_b] :
      ( class_Fields_Olinordered__field(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) ) ),
    file('theBenchmark.p',fact_neg__divide__le__eq) ).

fof(fact_neg__le__divide__eq,axiom,
    ! [V_b_2,V_a_2,V_c_2,T_b] :
      ( class_Fields_Olinordered__field(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) ) ) ),
    file('theBenchmark.p',fact_neg__le__divide__eq) ).

fof(fact_mult__imp__le__div__pos,axiom,
    ! [V_x,V_z,V_y,T_a] :
      ( class_Fields_Olinordered__field(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)),V_x))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))) ) ) ),
    file('theBenchmark.p',fact_mult__imp__le__div__pos) ).

fof(fact_mult__imp__div__pos__le,axiom,
    ! [V_z,V_x,V_y,T_a] :
      ( class_Fields_Olinordered__field(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),V_z)) ) ) ),
    file('theBenchmark.p',fact_mult__imp__div__pos__le) ).

fof(fact_times__divide__times__eq,axiom,
    ! [V_w,V_z,V_y,V_x,T_a] :
      ( class_Fields_Ofield__inverse__zero(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_z),V_w)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_w)) ),
    file('theBenchmark.p',fact_times__divide__times__eq) ).

fof(fact_minus__divide__divide,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Fields_Ofield__inverse__zero(T_a)
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b) ),
    file('theBenchmark.p',fact_minus__divide__divide) ).

fof(fact_minus__divide__right,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Fields_Ofield__inverse__zero(T_a)
     => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ),
    file('theBenchmark.p',fact_minus__divide__right) ).

fof(fact_zero__le__divide__iff,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( class_Fields_Olinordered__field__inverse__zero(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ),
    file('theBenchmark.p',fact_zero__le__divide__iff) ).

fof(fact_divide__le__0__iff,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( class_Fields_Olinordered__field__inverse__zero(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ),
    file('theBenchmark.p',fact_divide__le__0__iff) ).

fof(fact_divide__right__mono,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Fields_Olinordered__field__inverse__zero(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c))) ) ) ),
    file('theBenchmark.p',fact_divide__right__mono) ).

fof(fact_divide__right__mono__neg,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Fields_Olinordered__field__inverse__zero(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c))) ) ) ),
    file('theBenchmark.p',fact_divide__right__mono__neg) ).

fof(fact_divide__strict__right__mono__neg,axiom,
    ! [V_c,V_a,V_b,T_a] :
      ( class_Fields_Olinordered__field(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c))) ) ) ),
    file('theBenchmark.p',fact_divide__strict__right__mono__neg) ).

fof(fact_divide__strict__right__mono,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Fields_Olinordered__field(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c))) ) ) ),
    file('theBenchmark.p',fact_divide__strict__right__mono) ).

fof(fact_divide__neg__neg,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Fields_Olinordered__field(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))) ) ) ),
    file('theBenchmark.p',fact_divide__neg__neg) ).

fof(fact_divide__neg__pos,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Fields_Olinordered__field(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ),
    file('theBenchmark.p',fact_divide__neg__pos) ).

fof(fact_divide__pos__neg,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Fields_Olinordered__field(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ),
    file('theBenchmark.p',fact_divide__pos__neg) ).

fof(fact_divide__pos__pos,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Fields_Olinordered__field(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))) ) ) ),
    file('theBenchmark.p',fact_divide__pos__pos) ).

fof(fact_divide__less__0__iff,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( class_Fields_Olinordered__field__inverse__zero(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ),
    file('theBenchmark.p',fact_divide__less__0__iff) ).

fof(fact_zero__less__divide__iff,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( class_Fields_Olinordered__field__inverse__zero(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ),
    file('theBenchmark.p',fact_zero__less__divide__iff) ).

fof(fact_eq__divide__eq,axiom,
    ! [V_c_2,V_b_2,V_a_2,T_b] :
      ( class_Fields_Ofield__inverse__zero(T_b)
     => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)
      <=> ( ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
           => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) )
          & ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
           => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) = V_b_2 ) ) ) ),
    file('theBenchmark.p',fact_eq__divide__eq) ).

fof(fact_divide__eq__eq,axiom,
    ! [V_a_2,V_c_2,V_b_2,T_b] :
      ( class_Fields_Ofield__inverse__zero(T_b)
     => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) = V_a_2
      <=> ( ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
           => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) )
          & ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
           => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) ) ) ) ),
    file('theBenchmark.p',fact_divide__eq__eq) ).

fof(fact_mult__divide__mult__cancel__right,axiom,
    ! [V_b,V_a,V_c,T_a] :
      ( class_Fields_Ofield__inverse__zero(T_a)
     => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
       => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b) ) ),
    file('theBenchmark.p',fact_mult__divide__mult__cancel__right) ).

fof(fact_mult__divide__mult__cancel__left,axiom,
    ! [V_b,V_a,V_c,T_a] :
      ( class_Fields_Ofield__inverse__zero(T_a)
     => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
       => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b) ) ),
    file('theBenchmark.p',fact_mult__divide__mult__cancel__left) ).

fof(fact_frac__eq__eq,axiom,
    ! [V_w_2,V_x_2,V_z_2,V_y_2,T_b] :
      ( class_Fields_Ofield(T_b)
     => ( V_y_2 != c_Groups_Ozero__class_Ozero(T_b)
       => ( V_z_2 != c_Groups_Ozero__class_Ozero(T_b)
         => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_x_2),V_y_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_w_2),V_z_2)
          <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_z_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_y_2) ) ) ) ),
    file('theBenchmark.p',fact_frac__eq__eq) ).

fof(fact_divide__nonneg__pos,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Fields_Olinordered__field(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))) ) ) ),
    file('theBenchmark.p',fact_divide__nonneg__pos) ).

fof(fact_divide__nonneg__neg,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Fields_Olinordered__field(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ),
    file('theBenchmark.p',fact_divide__nonneg__neg) ).

fof(fact_frac__less2,axiom,
    ! [V_z,V_w,V_y,V_x,T_a] :
      ( class_Fields_Olinordered__field(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_w),V_z))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_w))) ) ) ) ) ),
    file('theBenchmark.p',fact_frac__less2) ).

fof(fact_frac__less,axiom,
    ! [V_z,V_w,V_y,V_x,T_a] :
      ( class_Fields_Olinordered__field(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_w))) ) ) ) ) ),
    file('theBenchmark.p',fact_frac__less) ).

fof(fact_frac__le,axiom,
    ! [V_z,V_w,V_y,V_x,T_a] :
      ( class_Fields_Olinordered__field(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_w))) ) ) ) ) ),
    file('theBenchmark.p',fact_frac__le) ).

fof(fact_divide__nonpos__pos,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Fields_Olinordered__field(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ),
    file('theBenchmark.p',fact_divide__nonpos__pos) ).

fof(fact_divide__nonpos__neg,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Fields_Olinordered__field(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))) ) ) ),
    file('theBenchmark.p',fact_divide__nonpos__neg) ).

fof(fact_divide__strict__left__mono__neg,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Fields_Olinordered__field(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_b))) ) ) ) ),
    file('theBenchmark.p',fact_divide__strict__left__mono__neg) ).

fof(fact_divide__strict__left__mono,axiom,
    ! [V_c,V_a,V_b,T_a] :
      ( class_Fields_Olinordered__field(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_b))) ) ) ) ),
    file('theBenchmark.p',fact_divide__strict__left__mono) ).

fof(fact_neg__divide__less__eq,axiom,
    ! [V_a_2,V_b_2,V_c_2,T_b] :
      ( class_Fields_Olinordered__field(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) ) ),
    file('theBenchmark.p',fact_neg__divide__less__eq) ).

fof(fact_neg__less__divide__eq,axiom,
    ! [V_b_2,V_a_2,V_c_2,T_b] :
      ( class_Fields_Olinordered__field(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) ) ) ),
    file('theBenchmark.p',fact_neg__less__divide__eq) ).

fof(fact_mult__imp__less__div__pos,axiom,
    ! [V_x,V_z,V_y,T_a] :
      ( class_Fields_Olinordered__field(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)),V_x))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))) ) ) ),
    file('theBenchmark.p',fact_mult__imp__less__div__pos) ).

fof(fact_mult__imp__div__pos__less,axiom,
    ! [V_z,V_x,V_y,T_a] :
      ( class_Fields_Olinordered__field(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),V_z)) ) ) ),
    file('theBenchmark.p',fact_mult__imp__div__pos__less) ).

fof(fact_pos__divide__less__eq,axiom,
    ! [V_a_2,V_b_2,V_c_2,T_b] :
      ( class_Fields_Olinordered__field(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) ) ) ),
    file('theBenchmark.p',fact_pos__divide__less__eq) ).

fof(fact_pos__less__divide__eq,axiom,
    ! [V_b_2,V_a_2,V_c_2,T_b] :
      ( class_Fields_Olinordered__field(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) ) ),
    file('theBenchmark.p',fact_pos__less__divide__eq) ).

fof(fact_divide__less__eq,axiom,
    ! [V_a_2,V_c_2,V_b_2,T_b] :
      ( class_Fields_Olinordered__field__inverse__zero(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
      <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
           => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) )
              & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) ) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) ) ) ) ),
    file('theBenchmark.p',fact_divide__less__eq) ).

fof(fact_less__divide__eq,axiom,
    ! [V_c_2,V_b_2,V_a_2,T_b] :
      ( class_Fields_Olinordered__field__inverse__zero(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
      <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
           => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
              & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) ) ) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) ) ) ),
    file('theBenchmark.p',fact_less__divide__eq) ).

fof(fact_add__num__frac,axiom,
    ! [V_x,V_z,V_y,T_a] :
      ( class_Fields_Ofield__inverse__zero(T_a)
     => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_z),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))),V_y) ) ),
    file('theBenchmark.p',fact_add__num__frac) ).

fof(fact_add__divide__eq__iff,axiom,
    ! [V_y,V_x,V_z,T_a] :
      ( class_Fields_Ofield(T_a)
     => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_x)),V_y)),V_z) ) ),
    file('theBenchmark.p',fact_add__divide__eq__iff) ).

fof(fact_add__frac__num,axiom,
    ! [V_z,V_x,V_y,T_a] :
      ( class_Fields_Ofield__inverse__zero(T_a)
     => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))),V_y) ) ),
    file('theBenchmark.p',fact_add__frac__num) ).

fof(fact_divide__add__eq__iff,axiom,
    ! [V_y,V_x,V_z,T_a] :
      ( class_Fields_Ofield(T_a)
     => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),V_y) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))),V_z) ) ),
    file('theBenchmark.p',fact_divide__add__eq__iff) ).

fof(fact_add__frac__eq,axiom,
    ! [V_w,V_x,V_z,V_y,T_a] :
      ( class_Fields_Ofield(T_a)
     => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
       => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
         => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_w),V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w),V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z)) ) ) ),
    file('theBenchmark.p',fact_add__frac__eq) ).

fof(fact_diff__divide__eq__iff,axiom,
    ! [V_y,V_x,V_z,T_a] :
      ( class_Fields_Ofield(T_a)
     => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_x)),V_y)),V_z) ) ),
    file('theBenchmark.p',fact_diff__divide__eq__iff) ).

fof(fact_divide__diff__eq__iff,axiom,
    ! [V_y,V_x,V_z,T_a] :
      ( class_Fields_Ofield(T_a)
     => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),V_y) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))),V_z) ) ),
    file('theBenchmark.p',fact_divide__diff__eq__iff) ).

fof(fact_diff__frac__eq,axiom,
    ! [V_w,V_x,V_z,V_y,T_a] :
      ( class_Fields_Ofield(T_a)
     => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
       => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
         => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_w),V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w),V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z)) ) ) ),
    file('theBenchmark.p',fact_diff__frac__eq) ).

fof(fact_gt__half__sum,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Fields_Olinordered__field(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a)))),V_b)) ) ),
    file('theBenchmark.p',fact_gt__half__sum) ).

fof(fact_less__half__sum,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Fields_Olinordered__field(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a))))) ) ),
    file('theBenchmark.p',fact_less__half__sum) ).

fof(fact_le__divide__eq,axiom,
    ! [V_c_2,V_b_2,V_a_2,T_b] :
      ( class_Fields_Olinordered__field__inverse__zero(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
      <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
           => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
              & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) ) ) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) ) ) ),
    file('theBenchmark.p',fact_le__divide__eq) ).

fof(fact_divide__le__eq,axiom,
    ! [V_a_2,V_c_2,V_b_2,T_b] :
      ( class_Fields_Olinordered__field__inverse__zero(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
      <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
           => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) )
              & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) ) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) ) ) ) ),
    file('theBenchmark.p',fact_divide__le__eq) ).

fof(fact_pos__le__divide__eq,axiom,
    ! [V_b_2,V_a_2,V_c_2,T_b] :
      ( class_Fields_Olinordered__field(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) ) ),
    file('theBenchmark.p',fact_pos__le__divide__eq) ).

fof(fact_pos__divide__le__eq,axiom,
    ! [V_a_2,V_b_2,V_c_2,T_b] :
      ( class_Fields_Olinordered__field(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) ) ) ),
    file('theBenchmark.p',fact_pos__divide__le__eq) ).

fof(fact_comm__monoid__big_OF__eq,axiom,
    ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
      ( c_Big__Operators_Ocomm__monoid__big(T_b,T_c,V_f_2,V_z_2,V_F_2)
     => ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
         => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 )
        & ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
         => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2),V_z_2),V_A_2) ) ) ),
    file('theBenchmark.p',fact_comm__monoid__big_OF__eq) ).

fof(fact_setprod__Un,axiom,
    ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
      ( class_Fields_Ofield(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
         => ( ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
               => hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_c) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ) ),
    file('theBenchmark.p',fact_setprod__Un) ).

fof(fact_fold__image__Un__one,axiom,
    ! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__mult(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
         => ( ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)))
               => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
           => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_f_2),c_Groups_Oone__class_Oone(T_c)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_f_2),c_Groups_Oone__class_Oone(T_c)),V_S_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_f_2),c_Groups_Oone__class_Oone(T_c)),V_T_2)) ) ) ) ),
    file('theBenchmark.p',fact_fold__image__Un__one) ).

fof(fact_setprod__mono__one__left,axiom,
    ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__mult(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
         => ( ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_T_2),V_S_2)))
               => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_T_2) ) ) ) ),
    file('theBenchmark.p',fact_setprod__mono__one__left) ).

fof(fact_setsum__mono__zero__right,axiom,
    ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__add(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
         => ( ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_T_2),V_S_2)))
               => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_T_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_S_2) ) ) ) ),
    file('theBenchmark.p',fact_setsum__mono__zero__right) ).

fof(fact_setsum__mono__zero__left,axiom,
    ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__add(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
         => ( ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_T_2),V_S_2)))
               => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_T_2) ) ) ) ),
    file('theBenchmark.p',fact_setsum__mono__zero__left) ).

fof(fact_comm__monoid__big_Oinfinite,axiom,
    ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
      ( c_Big__Operators_Ocomm__monoid__big(T_b,T_c,V_f_2,V_z_2,V_F_2)
     => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
       => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ),
    file('theBenchmark.p',fact_comm__monoid__big_Oinfinite) ).

fof(fact_field__le__mult__one__interval,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Fields_Olinordered__field__inverse__zero(T_a)
     => ( ! [B_z] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_z))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_z),c_Groups_Oone__class_Oone(T_a)))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_z),V_x)),V_y)) ) )
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ),
    file('theBenchmark.p',fact_field__le__mult__one__interval) ).

fof(fact_sgn__neg,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
       => c_Groups_Osgn__class_Osgn(T_a,V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ),
    file('theBenchmark.p',fact_sgn__neg) ).

fof(fact_sgn__1__neg,axiom,
    ! [V_a_2,T_b] :
      ( class_Rings_Olinordered__idom(T_b)
     => ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ),
    file('theBenchmark.p',fact_sgn__1__neg) ).

fof(fact_sgn__if,axiom,
    ! [V_x,T_a] :
      ( class_Groups_Osgn__if(T_a)
     => ( ( V_x != c_Groups_Ozero__class_Ozero(T_a)
         => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
             => c_Groups_Osgn__class_Osgn(T_a,V_x) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
             => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Oone__class_Oone(T_a) ) ) )
        & ( V_x = c_Groups_Ozero__class_Ozero(T_a)
         => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
    file('theBenchmark.p',fact_sgn__if) ).

fof(fact_fold1Set_Oequations,axiom,
    ! [V_a3_2,V_a2_2,V_a1_2,V_f_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),V_a2_2)),V_a3_2))
    <=> ? [B_a,B_A] :
          ( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A))
          & hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_a3_2))
          & hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),V_a2_2) = hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A) ) ),
    file('theBenchmark.p',fact_fold1Set_Oequations) ).

fof(fact_insert__fold1SetE,axiom,
    ! [V_x_2,V_X_2,V_a_2,V_f_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_X_2)),V_x_2))
     => ~ ! [B_a,B_A] :
            ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_X_2) = hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A)
           => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_x_2))
             => hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A)) ) ) ),
    file('theBenchmark.p',fact_insert__fold1SetE) ).

fof(fact_sgn__sgn,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Osgn__class_Osgn(T_a,V_a)) = c_Groups_Osgn__class_Osgn(T_a,V_a) ),
    file('theBenchmark.p',fact_sgn__sgn) ).

fof(fact_sgn__0__0,axiom,
    ! [V_a_2,T_b] :
      ( class_Rings_Olinordered__idom(T_b)
     => ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
      <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ),
    file('theBenchmark.p',fact_sgn__0__0) ).

fof(fact_sgn0,axiom,
    ! [T_a] :
      ( class_Groups_Osgn__if(T_a)
     => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_sgn0) ).

fof(fact_sgn__times,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => c_Groups_Osgn__class_Osgn(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_a)),c_Groups_Osgn__class_Osgn(T_a,V_b)) ),
    file('theBenchmark.p',fact_sgn__times) ).

fof(fact_sgn__less,axiom,
    ! [V_a_2,T_b] :
      ( class_Rings_Olinordered__idom(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Osgn__class_Osgn(T_b,V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ),
    file('theBenchmark.p',fact_sgn__less) ).

fof(fact_sgn__greater,axiom,
    ! [V_a_2,T_b] :
      ( class_Rings_Olinordered__idom(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Groups_Osgn__class_Osgn(T_b,V_a_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ),
    file('theBenchmark.p',fact_sgn__greater) ).

fof(fact_sgn__pos,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
       => c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ),
    file('theBenchmark.p',fact_sgn__pos) ).

fof(fact_sgn__1__pos,axiom,
    ! [V_a_2,T_b] :
      ( class_Rings_Olinordered__idom(T_b)
     => ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Oone__class_Oone(T_b)
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ),
    file('theBenchmark.p',fact_sgn__1__pos) ).

fof(fact_setprod__pos__nat,axiom,
    ! [V_f_2,V_S_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
     => ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(V_f_2,B_x))) )
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_S_2))) ) ),
    file('theBenchmark.p',fact_setprod__pos__nat) ).

fof(fact_fun__left__comm_Ofold__graph__insertE,axiom,
    ! [V_v_2,V_A_2,V_x_2,V_z_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_v_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => ~ ! [B_y] :
                ( V_v_2 = hAPP(hAPP(V_f_2,V_x_2),B_y)
               => ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),B_y)) ) ) ) ),
    file('theBenchmark.p',fact_fun__left__comm_Ofold__graph__insertE) ).

fof(fact_fun__left__comm__idem_Ofold__insert__idem,axiom,
    ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_fun__left__comm__idem_Ofold__insert__idem) ).

fof(fact_fun__left__comm__idem_Ofold__insert__idem2,axiom,
    ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2) ) ),
    file('theBenchmark.p',fact_fun__left__comm__idem_Ofold__insert__idem2) ).

fof(fact_setsum__SucD,axiom,
    ! [V_n_2,V_A_2,V_f_2,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Nat_OSuc,V_n_2)
     => ? [B_x] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(V_f_2,B_x)))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ),
    file('theBenchmark.p',fact_setsum__SucD) ).

fof(fact_card__partition,axiom,
    ! [V_k_2,V_C_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_C_2))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2)))
       => ( ! [B_c] :
              ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c),V_C_2))
             => hAPP(c_Finite__Set_Ocard(T_b),B_c) = V_k_2 )
         => ( ! [B_c1] :
                ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c1),V_C_2))
               => ! [B_c2] :
                    ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c2),V_C_2))
                   => ( B_c1 != B_c2
                     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),B_c1),B_c2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) )
           => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(tc_fun(T_b,tc_HOL_Obool)),V_C_2)) = hAPP(c_Finite__Set_Ocard(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2)) ) ) ) ),
    file('theBenchmark.p',fact_card__partition) ).

fof(fact_fun__left__comm__idem_Ofun__left__idem,axiom,
    ! [V_z_2,V_x_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
     => hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)) = hAPP(hAPP(V_f_2,V_x_2),V_z_2) ),
    file('theBenchmark.p',fact_fun__left__comm__idem_Ofun__left__idem) ).

fof(fact_fun__left__comm__idem__insert,axiom,
    ! [T_b] : c_Finite__Set_Ofun__left__comm__idem(T_b,tc_fun(T_b,tc_HOL_Obool),c_Set_Oinsert(T_b)),
    file('theBenchmark.p',fact_fun__left__comm__idem__insert) ).

fof(fact_fun__left__comm__idem,axiom,
    ! [T_b] :
      ( class_Lattices_Oab__semigroup__idem__mult(T_b)
     => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)) ),
    file('theBenchmark.p',fact_fun__left__comm__idem) ).

fof(fact_fun__left__comm__idem__sup,axiom,
    ! [T_b] :
      ( class_Lattices_Osemilattice__sup(T_b)
     => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)) ),
    file('theBenchmark.p',fact_fun__left__comm__idem__sup) ).

fof(fact_fun__left__comm__idem__inf,axiom,
    ! [T_b] :
      ( class_Lattices_Osemilattice__inf(T_b)
     => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)) ),
    file('theBenchmark.p',fact_fun__left__comm__idem__inf) ).

fof(fact_min__max_Ofun__left__comm__idem__inf,axiom,
    ! [T_b] :
      ( class_Orderings_Olinorder(T_b)
     => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)) ),
    file('theBenchmark.p',fact_min__max_Ofun__left__comm__idem__inf) ).

fof(fact_min__max_Ofun__left__comm__idem__sup,axiom,
    ! [T_b] :
      ( class_Orderings_Olinorder(T_b)
     => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)) ),
    file('theBenchmark.p',fact_min__max_Ofun__left__comm__idem__sup) ).

fof(fact_card__Pow,axiom,
    ! [V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => hAPP(c_Finite__Set_Ocard(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)) ),
    file('theBenchmark.p',fact_card__Pow) ).

fof(fact_fold__image__1,axiom,
    ! [V_f_2,V_S_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__mult(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
       => ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
             => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
         => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_f_2),c_Groups_Oone__class_Oone(T_c)),V_S_2) = c_Groups_Oone__class_Oone(T_c) ) ) ),
    file('theBenchmark.p',fact_fold__image__1) ).

fof(fact_card_Oneutral,axiom,
    ! [V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
         => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
       => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_card_Oneutral) ).

fof(fact_min__max_Ofold__sup__le__sup,axiom,
    ! [V_c_2,V_b_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) )
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_c_2),V_A_2)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_b_2),V_c_2))) ) ) ),
    file('theBenchmark.p',fact_min__max_Ofold__sup__le__sup) ).

fof(fact_min__max_Oinf__le__fold__inf,axiom,
    ! [V_c_2,V_b_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) )
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_c_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_c_2),V_A_2))) ) ) ),
    file('theBenchmark.p',fact_min__max_Oinf__le__fold__inf) ).

fof(fact_fold__image__cong,axiom,
    ! [V_z_2,V_h_2,V_g_2,V_A_2,T_b,T_c] :
      ( class_Groups_Oab__semigroup__mult(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
             => hAPP(V_g_2,B_x) = hAPP(V_h_2,B_x) )
         => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),V_z_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_h_2),V_z_2),V_A_2) ) ) ),
    file('theBenchmark.p',fact_fold__image__cong) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
    ! [V_q,V_y,V_x,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),V_q) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_q)) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
    ! [V_q,V_p,V_x,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),V_q) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),V_q)) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
    ! [V_x,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,axiom,
    ! [V_q,V_x,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Nat_OSuc,V_q)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,axiom,
    ! [V_q,V_x,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Nat_OSuc,V_q)) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,axiom,
    ! [V_q,V_x,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)),V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Nat_OSuc,V_q)) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
    ! [V_x,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
    ! [V_q,V_p,V_x,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_p),V_q)) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).

fof(fact_Ints__power,axiom,
    ! [V_n_2,V_a_2,T_b] :
      ( class_Rings_Oring__1(T_b)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
       => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2)),c_Int_Oring__1__class_OInts(T_b))) ) ),
    file('theBenchmark.p',fact_Ints__power) ).

fof(fact_power__eq__if,axiom,
    ! [V_p,V_m] :
      ( ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
      & ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_power__eq__if) ).

fof(fact_power__strict__mono,axiom,
    ! [V_n,V_b,V_a,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))) ) ) ) ),
    file('theBenchmark.p',fact_power__strict__mono) ).

fof(fact_power__diff,axiom,
    ! [V_m,V_n,V_a,T_a] :
      ( class_Fields_Ofield(T_a)
     => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
         => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ) ),
    file('theBenchmark.p',fact_power__diff) ).

fof(fact_one__less__power,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ),
    file('theBenchmark.p',fact_one__less__power) ).

fof(fact_power__le__imp__le__exp,axiom,
    ! [V_n,V_m,V_a,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ) ),
    file('theBenchmark.p',fact_power__le__imp__le__exp) ).

fof(fact_power__increasing__iff,axiom,
    ! [V_y_2,V_x_2,V_b_2,T_b] :
      ( class_Rings_Olinordered__semidom(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_b_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_y_2)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ),
    file('theBenchmark.p',fact_power__increasing__iff) ).

fof(fact_power__decreasing,axiom,
    ! [V_a,V_N,V_n,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ) ),
    file('theBenchmark.p',fact_power__decreasing) ).

fof(fact_zpower__zadd__distrib,axiom,
    ! [V_z,V_y,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_z)),
    file('theBenchmark.p',fact_zpower__zadd__distrib) ).

fof(fact_zpower__zpower,axiom,
    ! [V_z,V_y,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),V_z) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_y),V_z)),
    file('theBenchmark.p',fact_zpower__zpower) ).

fof(fact_field__power__not__zero,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Rings_Oring__1__no__zero__divisors(T_a)
     => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
       => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) ) ),
    file('theBenchmark.p',fact_field__power__not__zero) ).

fof(fact_power__mult__distrib,axiom,
    ! [V_n,V_b,V_a,T_a] :
      ( class_Groups_Ocomm__monoid__mult(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ),
    file('theBenchmark.p',fact_power__mult__distrib) ).

fof(fact_power__commutes,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Groups_Omonoid__mult(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ),
    file('theBenchmark.p',fact_power__commutes) ).

fof(fact_power__one,axiom,
    ! [V_n,T_a] :
      ( class_Groups_Omonoid__mult(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),V_n) = c_Groups_Oone__class_Oone(T_a) ),
    file('theBenchmark.p',fact_power__one) ).

fof(fact_power__mult,axiom,
    ! [V_n,V_m,V_a,T_a] :
      ( class_Groups_Omonoid__mult(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),V_n) ),
    file('theBenchmark.p',fact_power__mult) ).

fof(fact_power__divide,axiom,
    ! [V_n,V_b,V_a,T_a] :
      ( class_Fields_Ofield__inverse__zero(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)),V_n) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ),
    file('theBenchmark.p',fact_power__divide) ).

fof(fact_power__one__right,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Omonoid__mult(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a ),
    file('theBenchmark.p',fact_power__one__right) ).

fof(fact_power__mono,axiom,
    ! [V_n,V_b,V_a,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))) ) ) ),
    file('theBenchmark.p',fact_power__mono) ).

fof(fact_zero__le__power,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ),
    file('theBenchmark.p',fact_zero__le__power) ).

fof(fact_zero__less__power,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ),
    file('theBenchmark.p',fact_zero__less__power) ).

fof(fact_power__eq__0__iff,axiom,
    ! [V_n_2,V_a_2,T_b] :
      ( ( class_Rings_Ozero__neq__one(T_b)
        & class_Rings_Ono__zero__divisors(T_b)
        & class_Rings_Omult__zero(T_b)
        & class_Power_Opower(T_b) )
     => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_b)
      <=> ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ),
    file('theBenchmark.p',fact_power__eq__0__iff) ).

fof(fact_one__le__power,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ),
    file('theBenchmark.p',fact_one__le__power) ).

fof(fact_power__0__Suc,axiom,
    ! [V_n,T_a] :
      ( ( class_Rings_Osemiring__0(T_a)
        & class_Power_Opower(T_a) )
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Nat_OSuc,V_n)) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_power__0__Suc) ).

fof(fact_power__inject__exp,axiom,
    ! [V_n_2,V_m_2,V_a_2,T_b] :
      ( class_Rings_Olinordered__semidom(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_a_2))
       => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_m_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2)
        <=> V_m_2 = V_n_2 ) ) ),
    file('theBenchmark.p',fact_power__inject__exp) ).

fof(fact_power__Suc2,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Groups_Omonoid__mult(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a) ),
    file('theBenchmark.p',fact_power__Suc2) ).

fof(fact_power__Suc,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Power_Opower(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ),
    file('theBenchmark.p',fact_power__Suc) ).

fof(fact_power__0,axiom,
    ! [V_a,T_a] :
      ( class_Power_Opower(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ),
    file('theBenchmark.p',fact_power__0) ).

fof(fact_power__add,axiom,
    ! [V_n,V_m,V_a,T_a] :
      ( class_Groups_Omonoid__mult(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ),
    file('theBenchmark.p',fact_power__add) ).

fof(fact_nonzero__power__divide,axiom,
    ! [V_n,V_a,V_b,T_a] :
      ( class_Fields_Ofield(T_a)
     => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
       => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)),V_n) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ) ),
    file('theBenchmark.p',fact_nonzero__power__divide) ).

fof(fact_power__one__over,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Fields_Ofield__inverse__zero(T_a)
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)),V_n) ),
    file('theBenchmark.p',fact_power__one__over) ).

fof(fact_power__Suc__0,axiom,
    ! [V_n] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('theBenchmark.p',fact_power__Suc__0) ).

fof(fact_nat__power__eq__Suc__0__iff,axiom,
    ! [V_m_2,V_x_2] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_m_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    <=> ( V_x_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_nat__power__eq__Suc__0__iff) ).

fof(fact_nat__zero__less__power__iff,axiom,
    ! [V_n_2,V_x_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2)))
    <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2)) ) ),
    file('theBenchmark.p',fact_nat__zero__less__power__iff) ).

fof(fact_nat__power__less__imp__less,axiom,
    ! [V_n,V_m,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ),
    file('theBenchmark.p',fact_nat__power__less__imp__less) ).

fof(fact_power__less__imp__less__base,axiom,
    ! [V_b,V_n,V_a,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ),
    file('theBenchmark.p',fact_power__less__imp__less__base) ).

fof(fact_power__inject__base,axiom,
    ! [V_b,V_n,V_a,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),hAPP(c_Nat_OSuc,V_n))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
           => V_a = V_b ) ) ) ),
    file('theBenchmark.p',fact_power__inject__base) ).

fof(fact_power__le__imp__le__base,axiom,
    ! [V_b,V_n,V_a,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),hAPP(c_Nat_OSuc,V_n))))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ),
    file('theBenchmark.p',fact_power__le__imp__le__base) ).

fof(fact_power__gt1__lemma,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))) ) ),
    file('theBenchmark.p',fact_power__gt1__lemma) ).

fof(fact_power__less__power__Suc,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))) ) ),
    file('theBenchmark.p',fact_power__less__power__Suc) ).

fof(fact_power__0__left,axiom,
    ! [V_n,T_a] :
      ( ( class_Rings_Osemiring__0(T_a)
        & class_Power_Opower(T_a) )
     => ( ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n) = c_Groups_Ozero__class_Ozero(T_a) )
        & ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n) = c_Groups_Oone__class_Oone(T_a) ) ) ),
    file('theBenchmark.p',fact_power__0__left) ).

fof(fact_power__gt1,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n)))) ) ),
    file('theBenchmark.p',fact_power__gt1) ).

fof(fact_power__strict__increasing__iff,axiom,
    ! [V_y_2,V_x_2,V_b_2,T_b] :
      ( class_Rings_Olinordered__semidom(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_b_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_y_2)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ),
    file('theBenchmark.p',fact_power__strict__increasing__iff) ).

fof(fact_power__less__imp__less__exp,axiom,
    ! [V_n,V_m,V_a,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ),
    file('theBenchmark.p',fact_power__less__imp__less__exp) ).

fof(fact_power__strict__increasing,axiom,
    ! [V_a,V_N,V_n,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N))) ) ) ),
    file('theBenchmark.p',fact_power__strict__increasing) ).

fof(fact_power__increasing,axiom,
    ! [V_a,V_N,V_n,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N))) ) ) ),
    file('theBenchmark.p',fact_power__increasing) ).

fof(fact_power__minus,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Rings_Oring__1(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ),
    file('theBenchmark.p',fact_power__minus) ).

fof(fact_nat__one__le__power,axiom,
    ! [V_n,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_i))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n))) ),
    file('theBenchmark.p',fact_nat__one__le__power) ).

fof(fact_power__Suc__less,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ),
    file('theBenchmark.p',fact_power__Suc__less) ).

fof(fact_power__eq__imp__eq__base,axiom,
    ! [V_b,V_n,V_a,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
             => V_a = V_b ) ) ) ) ),
    file('theBenchmark.p',fact_power__eq__imp__eq__base) ).

fof(fact_power__Suc__less__one,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n))),c_Groups_Oone__class_Oone(T_a))) ) ) ),
    file('theBenchmark.p',fact_power__Suc__less__one) ).

fof(fact_power__strict__decreasing,axiom,
    ! [V_a,V_N,V_n,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ) ),
    file('theBenchmark.p',fact_power__strict__decreasing) ).

fof(fact_power__power__power,axiom,
    ! [T_b] :
      ( class_Power_Opower(T_b)
     => c_Power_Opower__class_Opower(T_b) = c_Power_Opower_Opower(T_b,c_Groups_Oone__class_Oone(T_b),c_Groups_Otimes__class_Otimes(T_b)) ),
    file('theBenchmark.p',fact_power__power__power) ).

fof(fact_inf__le__fold__inf,axiom,
    ! [V_c_2,V_b_2,V_A_2,T_b] :
      ( class_Lattices_Osemilattice__inf(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) )
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_b_2),V_c_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_c_2),V_A_2))) ) ) ),
    file('theBenchmark.p',fact_inf__le__fold__inf) ).

fof(fact_fold__sup__le__sup,axiom,
    ! [V_c_2,V_b_2,V_A_2,T_b] :
      ( class_Lattices_Osemilattice__sup(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) )
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_c_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_b_2),V_c_2))) ) ) ),
    file('theBenchmark.p',fact_fold__sup__le__sup) ).

fof(fact_expand__Suc,axiom,
    ! [V_v] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)))
     => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    file('theBenchmark.p',fact_expand__Suc) ).

fof(fact_folding__image__simple__idem_Ounion__idem,axiom,
    ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
         => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ),
    file('theBenchmark.p',fact_folding__image__simple__idem_Ounion__idem) ).

fof(fact_UnionE,axiom,
    ! [V_C_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2)))
     => ~ ! [B_X] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),B_X))
           => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2)) ) ),
    file('theBenchmark.p',fact_UnionE) ).

fof(fact_zmult__1__right,axiom,
    ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z,
    file('theBenchmark.p',fact_zmult__1__right) ).

fof(fact_zmult__1,axiom,
    ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z,
    file('theBenchmark.p',fact_zmult__1) ).

fof(fact_pos__zmult__eq__1__iff,axiom,
    ! [V_n_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m_2))
     => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
      <=> ( V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
          & V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ),
    file('theBenchmark.p',fact_pos__zmult__eq__1__iff) ).

fof(fact_zmult__zless__mono2,axiom,
    ! [V_k,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_j))) ) ),
    file('theBenchmark.p',fact_zmult__zless__mono2) ).

fof(fact_zdiff__zmult__distrib2,axiom,
    ! [V_z2,V_z1,V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z1),V_z2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2)),
    file('theBenchmark.p',fact_zdiff__zmult__distrib2) ).

fof(fact_zdiff__zmult__distrib,axiom,
    ! [V_w,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z1),V_z2)),V_w) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w)),
    file('theBenchmark.p',fact_zdiff__zmult__distrib) ).

fof(fact_zadd__zmult__distrib,axiom,
    ! [V_w,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)),V_w) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w)),
    file('theBenchmark.p',fact_zadd__zmult__distrib) ).

fof(fact_zmult__assoc,axiom,
    ! [V_z3,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_z2)),V_z3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_z3)),
    file('theBenchmark.p',fact_zmult__assoc) ).

fof(fact_zadd__zmult__distrib2,axiom,
    ! [V_z2,V_z1,V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2)),
    file('theBenchmark.p',fact_zadd__zmult__distrib2) ).

fof(fact_zmult__commute,axiom,
    ! [V_w,V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_w) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z),
    file('theBenchmark.p',fact_zmult__commute) ).

fof(fact_zmult__zminus,axiom,
    ! [V_w,V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)),V_w) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_w)),
    file('theBenchmark.p',fact_zmult__zminus) ).

fof(fact_eq__number__of,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( ( class_Int_Oring__char__0(T_b)
        & class_Int_Onumber__ring(T_b) )
     => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
      <=> V_x_2 = V_y_2 ) ),
    file('theBenchmark.p',fact_eq__number__of) ).

fof(fact_number__of__reorient,axiom,
    ! [V_x_2,V_w_2,T_b] :
      ( class_Int_Onumber(T_b)
     => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = V_x_2
      <=> V_x_2 = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) ) ),
    file('theBenchmark.p',fact_number__of__reorient) ).

fof(fact_folding__image__simple__idem_Oidem,axiom,
    ! [V_x_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
     => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ),
    file('theBenchmark.p',fact_folding__image__simple__idem_Oidem) ).

fof(fact_le__number__of,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( ( class_Rings_Olinordered__idom(T_b)
        & class_Int_Onumber__ring(T_b) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ),
    file('theBenchmark.p',fact_le__number__of) ).

fof(fact_less__number__of,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( ( class_Rings_Olinordered__idom(T_b)
        & class_Int_Onumber__ring(T_b) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ),
    file('theBenchmark.p',fact_less__number__of) ).

fof(fact_number__of__add,axiom,
    ! [V_w,V_v,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ),
    file('theBenchmark.p',fact_number__of__add) ).

fof(fact_add__number__of__eq,axiom,
    ! [V_w,V_v,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w)) ),
    file('theBenchmark.p',fact_add__number__of__eq) ).

fof(fact_add__number__of__left,axiom,
    ! [V_z,V_w,V_v,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w))),V_z) ),
    file('theBenchmark.p',fact_add__number__of__left) ).

fof(fact_number__of__mult,axiom,
    ! [V_w,V_v,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ),
    file('theBenchmark.p',fact_number__of__mult) ).

fof(fact_arith__simps_I32_J,axiom,
    ! [V_w,V_v,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w)) ),
    file('theBenchmark.p',fact_arith__simps_I32_J) ).

fof(fact_mult__number__of__left,axiom,
    ! [V_z,V_w,V_v,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)),V_z)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w))),V_z) ),
    file('theBenchmark.p',fact_mult__number__of__left) ).

fof(fact_diff__number__of__eq,axiom,
    ! [V_w,V_v,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w))) ),
    file('theBenchmark.p',fact_diff__number__of__eq) ).

fof(fact_number__of__diff,axiom,
    ! [V_w,V_v,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_v),V_w)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ),
    file('theBenchmark.p',fact_number__of__diff) ).

fof(fact_number__of__minus,axiom,
    ! [V_w,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ),
    file('theBenchmark.p',fact_number__of__minus) ).

fof(fact_arith__simps_I30_J,axiom,
    ! [V_w,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)) ),
    file('theBenchmark.p',fact_arith__simps_I30_J) ).

fof(fact_le__number__of__eq__not__less,axiom,
    ! [V_w_2,V_v_2,T_b] :
      ( ( class_Orderings_Olinorder(T_b)
        & class_Int_Onumber(T_b) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2))) ) ),
    file('theBenchmark.p',fact_le__number__of__eq__not__less) ).

fof(fact_right__distrib__number__of,axiom,
    ! [V_c,V_b,V_v,T_b] :
      ( ( class_Rings_Osemiring(T_b)
        & class_Int_Onumber(T_b) )
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b),V_c)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),V_c)) ),
    file('theBenchmark.p',fact_right__distrib__number__of) ).

fof(fact_left__distrib__number__of,axiom,
    ! [V_v,V_b,V_a,T_b] :
      ( ( class_Rings_Osemiring(T_b)
        & class_Int_Onumber(T_b) )
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a),V_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))) ),
    file('theBenchmark.p',fact_left__distrib__number__of) ).

fof(fact_add__number__of__diff2,axiom,
    ! [V_w,V_c,V_v,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_c),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)))),V_c) ),
    file('theBenchmark.p',fact_add__number__of__diff2) ).

fof(fact_add__number__of__diff1,axiom,
    ! [V_c,V_w,V_v,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)),V_c)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w))),V_c) ),
    file('theBenchmark.p',fact_add__number__of__diff1) ).

fof(fact_right__diff__distrib__number__of,axiom,
    ! [V_c,V_b,V_v,T_b] :
      ( ( class_Rings_Oring(T_b)
        & class_Int_Onumber(T_b) )
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b),V_c)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),V_c)) ),
    file('theBenchmark.p',fact_right__diff__distrib__number__of) ).

fof(fact_left__diff__distrib__number__of,axiom,
    ! [V_v,V_b,V_a,T_b] :
      ( ( class_Rings_Oring(T_b)
        & class_Int_Onumber(T_b) )
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a),V_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))) ),
    file('theBenchmark.p',fact_left__diff__distrib__number__of) ).

fof(fact_minus__number__of__mult,axiom,
    ! [V_z,V_w,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))),V_z) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w))),V_z) ),
    file('theBenchmark.p',fact_minus__number__of__mult) ).

fof(fact_min__number__of,axiom,
    ! [V_v,V_u,T_b] :
      ( ( class_Orderings_Oord(T_b)
        & class_Int_Onumber(T_b) )
     => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)))
         => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)))
         => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u) ) ) ),
    file('theBenchmark.p',fact_min__number__of) ).

fof(fact_max__number__of,axiom,
    ! [V_v,V_u,T_b] :
      ( ( class_Orderings_Oord(T_b)
        & class_Int_Onumber(T_b) )
     => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)))
         => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)))
         => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v) ) ) ),
    file('theBenchmark.p',fact_max__number__of) ).

fof(fact_Ints__number__of,axiom,
    ! [V_w_2,T_b] :
      ( class_Int_Onumber__ring(T_b)
     => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Int_Oring__1__class_OInts(T_b))) ),
    file('theBenchmark.p',fact_Ints__number__of) ).

fof(fact_eq__divide__eq__number__of1,axiom,
    ! [V_w_2,V_b_2,V_a_2,T_b] :
      ( ( class_Int_Onumber(T_b)
        & class_Fields_Ofield__inverse__zero(T_b) )
     => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))
      <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b)
           => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) )
          & ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b)
           => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) = V_b_2 ) ) ) ),
    file('theBenchmark.p',fact_eq__divide__eq__number__of1) ).

fof(fact_eq__divide__eq__number__of,axiom,
    ! [V_c_2,V_b_2,V_w_2,T_b] :
      ( ( class_Int_Onumber(T_b)
        & class_Fields_Ofield__inverse__zero(T_b) )
     => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)
      <=> ( ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
           => hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) )
          & ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
           => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2) = V_b_2 ) ) ) ),
    file('theBenchmark.p',fact_eq__divide__eq__number__of) ).

fof(fact_divide__eq__eq__number__of,axiom,
    ! [V_w_2,V_c_2,V_b_2,T_b] :
      ( ( class_Int_Onumber(T_b)
        & class_Fields_Ofield__inverse__zero(T_b) )
     => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)
      <=> ( ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
           => hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) )
          & ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
           => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2) ) ) ) ),
    file('theBenchmark.p',fact_divide__eq__eq__number__of) ).

fof(fact_divide__eq__eq__number__of1,axiom,
    ! [V_a_2,V_w_2,V_b_2,T_b] :
      ( ( class_Int_Onumber(T_b)
        & class_Fields_Ofield__inverse__zero(T_b) )
     => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) = V_a_2
      <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b)
           => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) )
          & ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b)
           => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) ) ) ) ),
    file('theBenchmark.p',fact_divide__eq__eq__number__of1) ).

fof(fact_power_Opower_Opower__0,axiom,
    ! [V_a_2,V_times_2,V_one_2,T_b] : hAPP(hAPP(c_Power_Opower_Opower(T_b,V_one_2,V_times_2),V_a_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_one_2,
    file('theBenchmark.p',fact_power_Opower_Opower__0) ).

fof(fact_power_Opower_Opower__Suc,axiom,
    ! [V_n_2,V_a_2,V_times_2,V_one_2,T_b] : hAPP(hAPP(c_Power_Opower_Opower(T_b,V_one_2,V_times_2),V_a_2),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(V_times_2,V_a_2),hAPP(hAPP(c_Power_Opower_Opower(T_b,V_one_2,V_times_2),V_a_2),V_n_2)),
    file('theBenchmark.p',fact_power_Opower_Opower__Suc) ).

fof(fact_divide__less__eq__number__of1,axiom,
    ! [V_a_2,V_w_2,V_b_2,T_b] :
      ( ( class_Int_Onumber(T_b)
        & class_Fields_Olinordered__field__inverse__zero(T_b) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_a_2))
      <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
           => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) )
              & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2)) ) ) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))) ) ) ) ),
    file('theBenchmark.p',fact_divide__less__eq__number__of1) ).

fof(fact_divide__less__eq__number__of,axiom,
    ! [V_w_2,V_c_2,V_b_2,T_b] :
      ( ( class_Int_Onumber(T_b)
        & class_Fields_Olinordered__field__inverse__zero(T_b) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
      <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
           => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) )
              & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2)) ) ) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2))) ) ) ) ),
    file('theBenchmark.p',fact_divide__less__eq__number__of) ).

fof(fact_less__divide__eq__number__of,axiom,
    ! [V_c_2,V_b_2,V_w_2,T_b] :
      ( ( class_Int_Onumber(T_b)
        & class_Fields_Olinordered__field__inverse__zero(T_b) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
      <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
           => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) )
              & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2))) ) ) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2)) ) ) ) ),
    file('theBenchmark.p',fact_less__divide__eq__number__of) ).

fof(fact_less__divide__eq__number__of1,axiom,
    ! [V_w_2,V_b_2,V_a_2,T_b] :
      ( ( class_Int_Onumber(T_b)
        & class_Fields_Olinordered__field__inverse__zero(T_b) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))))
      <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
           => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
              & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))) ) ) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2)) ) ) ) ),
    file('theBenchmark.p',fact_less__divide__eq__number__of1) ).

fof(fact_le__divide__eq__number__of1,axiom,
    ! [V_w_2,V_b_2,V_a_2,T_b] :
      ( ( class_Int_Onumber(T_b)
        & class_Fields_Olinordered__field__inverse__zero(T_b) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))))
      <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
           => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
              & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))) ) ) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2)) ) ) ) ),
    file('theBenchmark.p',fact_le__divide__eq__number__of1) ).

fof(fact_le__divide__eq__number__of,axiom,
    ! [V_c_2,V_b_2,V_w_2,T_b] :
      ( ( class_Int_Onumber(T_b)
        & class_Fields_Olinordered__field__inverse__zero(T_b) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
      <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
           => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) )
              & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2))) ) ) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2)) ) ) ) ),
    file('theBenchmark.p',fact_le__divide__eq__number__of) ).

fof(fact_divide__le__eq__number__of,axiom,
    ! [V_w_2,V_c_2,V_b_2,T_b] :
      ( ( class_Int_Onumber(T_b)
        & class_Fields_Olinordered__field__inverse__zero(T_b) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
      <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
           => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) )
              & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2)) ) ) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2))) ) ) ) ),
    file('theBenchmark.p',fact_divide__le__eq__number__of) ).

fof(fact_divide__le__eq__number__of1,axiom,
    ! [V_a_2,V_w_2,V_b_2,T_b] :
      ( ( class_Int_Onumber(T_b)
        & class_Fields_Olinordered__field__inverse__zero(T_b) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_a_2))
      <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
           => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) )
              & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2)) ) ) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))) ) ) ) ),
    file('theBenchmark.p',fact_divide__le__eq__number__of1) ).

fof(fact_folding__image__simple__idem_Oin__idem,axiom,
    ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
         => hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ),
    file('theBenchmark.p',fact_folding__image__simple__idem_Oin__idem) ).

fof(fact_folding__image__simple__idem_Oinsert__idem,axiom,
    ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
       => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,V_A_2)) ) ),
    file('theBenchmark.p',fact_folding__image__simple__idem_Oinsert__idem) ).

fof(fact_folding__image__simple__idem_Osubset__idem,axiom,
    ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2))
         => hAPP(hAPP(V_f_2,hAPP(V_F_2,V_B_2)),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ),
    file('theBenchmark.p',fact_folding__image__simple__idem_Osubset__idem) ).

fof(fact_number__of__pred,axiom,
    ! [V_w,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_Opred(V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ),
    file('theBenchmark.p',fact_number__of__pred) ).

fof(fact_setprod__pos,axiom,
    ! [V_f_2,V_A_2,T_b,T_c] :
      ( class_Rings_Olinordered__semidom(T_c)
     => ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) )
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2))) ) ),
    file('theBenchmark.p',fact_setprod__pos) ).

fof(fact_setprod__nonneg,axiom,
    ! [V_f_2,V_A_2,T_b,T_c] :
      ( class_Rings_Olinordered__semidom(T_c)
     => ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) )
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2))) ) ),
    file('theBenchmark.p',fact_setprod__nonneg) ).

fof(fact_finite__induct,axiom,
    ! [V_P_2,V_F_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
     => ( hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
       => ( ! [B_x,B_F] :
              ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_F))
             => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_F))
               => ( hBOOL(hAPP(V_P_2,B_F))
                 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Set_Oinsert(T_b),B_x),B_F))) ) ) )
         => hBOOL(hAPP(V_P_2,V_F_2)) ) ) ),
    file('theBenchmark.p',fact_finite__induct) ).

fof(fact_fold__graph_H_Ointros_I2_J,axiom,
    ! [V_y_2,V_z_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
     => ( c_Nitpick_Ofold__graph_H(T_b,T_c,V_f_2,V_z_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_y_2)
       => c_Nitpick_Ofold__graph_H(T_b,T_c,V_f_2,V_z_2,V_A_2,hAPP(hAPP(V_f_2,V_x_2),V_y_2)) ) ),
    file('theBenchmark.p',fact_fold__graph_H_Ointros_I2_J) ).

fof(fact_number__of__succ,axiom,
    ! [V_k,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_Osucc(V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_k)) ),
    file('theBenchmark.p',fact_number__of__succ) ).

fof(fact_minus__numeral__code_I6_J,axiom,
    ! [V_w,V_v] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w))),
    file('theBenchmark.p',fact_minus__numeral__code_I6_J) ).

fof(fact_plus__numeral__code_I9_J,axiom,
    ! [V_w,V_v] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w)),
    file('theBenchmark.p',fact_plus__numeral__code_I9_J) ).

fof(fact_minus__numeral__code_I5_J,axiom,
    ! [V_w] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)),
    file('theBenchmark.p',fact_minus__numeral__code_I5_J) ).

fof(fact_less__number__of__int__code,axiom,
    ! [V_l_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_l_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ),
    file('theBenchmark.p',fact_less__number__of__int__code) ).

fof(fact_less__eq__number__of__int__code,axiom,
    ! [V_l_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_l_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ),
    file('theBenchmark.p',fact_less__eq__number__of__int__code) ).

fof(fact_zsgn__def,axiom,
    ! [V_i] :
      ( ( V_i != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i))
           => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i))
           => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) )
      & ( V_i = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    file('theBenchmark.p',fact_zsgn__def) ).

fof(fact_atLeastLessThanPlusOne__atLeastAtMost__int,axiom,
    ! [V_u_2,V_l_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_l_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_u_2),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_l_2,V_u_2),
    file('theBenchmark.p',fact_atLeastLessThanPlusOne__atLeastAtMost__int) ).

fof(fact_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom,
    ! [V_u_2,V_l_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_l_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_u_2) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,V_l_2,V_u_2),
    file('theBenchmark.p',fact_atLeastPlusOneAtMost__greaterThanAtMost__int) ).

fof(fact_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom,
    ! [V_u_2,V_l_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_l_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_u_2) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,V_l_2,V_u_2),
    file('theBenchmark.p',fact_atLeastPlusOneLessThan__greaterThanLessThan__int) ).

fof(fact_zadd__left__mono,axiom,
    ! [V_k,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_i)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_j))) ),
    file('theBenchmark.p',fact_zadd__left__mono) ).

fof(fact_zle__refl,axiom,
    ! [V_w] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_w)),
    file('theBenchmark.p',fact_zle__refl) ).

fof(fact_zle__linear,axiom,
    ! [V_w,V_z] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w)) ),
    file('theBenchmark.p',fact_zle__linear) ).

fof(fact_zle__trans,axiom,
    ! [V_k,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_j),V_k))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_k)) ) ),
    file('theBenchmark.p',fact_zle__trans) ).

fof(fact_zle__antisym,axiom,
    ! [V_w,V_z] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z))
       => V_z = V_w ) ),
    file('theBenchmark.p',fact_zle__antisym) ).

fof(fact_zless__le,axiom,
    ! [V_w_2,V_z_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),V_w_2))
    <=> ( V_z_2 != V_w_2
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),V_w_2)) ) ),
    file('theBenchmark.p',fact_zless__le) ).

fof(fact_le__iff__pred__less,axiom,
    ! [V_l_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(V_k_2)),V_l_2)) ),
    file('theBenchmark.p',fact_le__iff__pred__less) ).

fof(fact_zadd__zless__mono,axiom,
    ! [V_z,V_z_H,V_w,V_w_H] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_H),V_w))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_H),V_z_H)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),V_z))) ) ),
    file('theBenchmark.p',fact_zadd__zless__mono) ).

fof(fact_zadd__strict__right__mono,axiom,
    ! [V_k,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_j),V_k))) ),
    file('theBenchmark.p',fact_zadd__strict__right__mono) ).

fof(fact_zless__linear,axiom,
    ! [V_y,V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_x))
      | V_x = V_y
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),V_y)) ),
    file('theBenchmark.p',fact_zless__linear) ).

fof(fact_zminus__zminus,axiom,
    ! [V_z] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)) = V_z,
    file('theBenchmark.p',fact_zminus__zminus) ).

fof(fact_succ__pred,axiom,
    ! [V_x] : c_Int_Osucc(c_Int_Opred(V_x)) = V_x,
    file('theBenchmark.p',fact_succ__pred) ).

fof(fact_zminus__zadd__distrib,axiom,
    ! [V_w,V_z] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)),
    file('theBenchmark.p',fact_zminus__zadd__distrib) ).

fof(fact_zadd__commute,axiom,
    ! [V_w,V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),V_w) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),V_z),
    file('theBenchmark.p',fact_zadd__commute) ).

fof(fact_zadd__left__commute,axiom,
    ! [V_z,V_y,V_x] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_y),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_y),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_z)),
    file('theBenchmark.p',fact_zadd__left__commute) ).

fof(fact_zadd__assoc,axiom,
    ! [V_z3,V_z2,V_z1] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)),V_z3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z2),V_z3)),
    file('theBenchmark.p',fact_zadd__assoc) ).

fof(fact_diff__int__def__symmetric,axiom,
    ! [V_w,V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z),V_w),
    file('theBenchmark.p',fact_diff__int__def__symmetric) ).

fof(fact_diff__int__def,axiom,
    ! [V_w,V_z] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z),V_w) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)),
    file('theBenchmark.p',fact_diff__int__def) ).

fof(fact_zadd__0__right,axiom,
    ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z,
    file('theBenchmark.p',fact_zadd__0__right) ).

fof(fact_zadd__0,axiom,
    ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z) = V_z,
    file('theBenchmark.p',fact_zadd__0) ).

fof(fact_zadd__zminus__inverse2,axiom,
    ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)),V_z) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    file('theBenchmark.p',fact_zadd__zminus__inverse2) ).

fof(fact_finite__atLeastZeroLessThan__int,axiom,
    ! [V_u_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2))),
    file('theBenchmark.p',fact_finite__atLeastZeroLessThan__int) ).

fof(fact_zminus__0,axiom,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    file('theBenchmark.p',fact_zminus__0) ).

fof(fact_less__bin__lemma,axiom,
    ! [V_l_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k_2),V_l_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    file('theBenchmark.p',fact_less__bin__lemma) ).

fof(fact_odd__less__0,axiom,
    ! [V_z_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)),V_z_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    file('theBenchmark.p',fact_odd__less__0) ).

fof(fact_zless__add1__eq,axiom,
    ! [V_z_2,V_w_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    <=> ( V_w_2 = V_z_2
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ),
    file('theBenchmark.p',fact_zless__add1__eq) ).

fof(fact_zless__imp__add1__zle,axiom,
    ! [V_z,V_w] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w),V_z))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_z)) ),
    file('theBenchmark.p',fact_zless__imp__add1__zle) ).

fof(fact_le__imp__0__less,axiom,
    ! [V_z] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z))) ),
    file('theBenchmark.p',fact_le__imp__0__less) ).

fof(fact_add1__zle__eq,axiom,
    ! [V_z_2,V_w_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_z_2))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ),
    file('theBenchmark.p',fact_add1__zle__eq) ).

fof(fact_zle__add1__eq__le,axiom,
    ! [V_z_2,V_w_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ),
    file('theBenchmark.p',fact_zle__add1__eq__le) ).

fof(fact_int__0__less__1,axiom,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    file('theBenchmark.p',fact_int__0__less__1) ).

fof(fact_int__one__le__iff__zero__less,axiom,
    ! [V_z_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ),
    file('theBenchmark.p',fact_int__one__le__iff__zero__less) ).

fof(fact_zle__diff1__eq,axiom,
    ! [V_z_2,V_w_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ),
    file('theBenchmark.p',fact_zle__diff1__eq) ).

fof(fact_pred__def,axiom,
    ! [V_k] : c_Int_Opred(V_k) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    file('theBenchmark.p',fact_pred__def) ).

fof(fact_int__0__neq__1,axiom,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
    file('theBenchmark.p',fact_int__0__neq__1) ).

fof(fact_odd__nonzero,axiom,
    ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z)),V_z) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    file('theBenchmark.p',fact_odd__nonzero) ).

fof(fact_succ__def,axiom,
    ! [V_k] : c_Int_Osucc(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    file('theBenchmark.p',fact_succ__def) ).

fof(fact_fold__graph_H_Ointros_I1_J,axiom,
    ! [V_z_2,V_f_2,T_c,T_b] : c_Nitpick_Ofold__graph_H(T_b,T_c,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_z_2),
    file('theBenchmark.p',fact_fold__graph_H_Ointros_I1_J) ).

fof(fact_fold__graph_H_Oequations_I1_J,axiom,
    ! [V_a2_2,V_a1_2,T_c,T_b] : c_Nitpick_Ofold__graph_H(T_b,T_c,V_a1_2,V_a2_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_a2_2),
    file('theBenchmark.p',fact_fold__graph_H_Oequations_I1_J) ).

fof(fact_times__numeral__code_I5_J,axiom,
    ! [V_w,V_v] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w)),
    file('theBenchmark.p',fact_times__numeral__code_I5_J) ).

fof(fact_self__quotient__aux1,axiom,
    ! [V_q,V_r,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
     => ( V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_a))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_q)) ) ) ),
    file('theBenchmark.p',fact_self__quotient__aux1) ).

fof(fact_self__quotient__aux2,axiom,
    ! [V_q,V_r,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
     => ( V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ) ),
    file('theBenchmark.p',fact_self__quotient__aux2) ).

fof(fact_zdiv__mono2__neg__lemma,axiom,
    ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
             => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ) ),
    file('theBenchmark.p',fact_zdiv__mono2__neg__lemma) ).

fof(fact_unique__quotient__lemma__neg,axiom,
    ! [V_r,V_q,V_r_H,V_q_H,V_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H)),V_r_H)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r_H))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ),
    file('theBenchmark.p',fact_unique__quotient__lemma__neg) ).

fof(fact_zdiv__mono2__lemma,axiom,
    ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
             => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ) ),
    file('theBenchmark.p',fact_zdiv__mono2__lemma) ).

fof(fact_finite__atLeastAtMost__int,axiom,
    ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_l_2,V_u_2))),
    file('theBenchmark.p',fact_finite__atLeastAtMost__int) ).

fof(fact_finite__atLeastLessThan__int,axiom,
    ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_l_2),V_u_2))),
    file('theBenchmark.p',fact_finite__atLeastLessThan__int) ).

fof(fact_finite__greaterThanAtMost__int,axiom,
    ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,V_l_2,V_u_2))),
    file('theBenchmark.p',fact_finite__greaterThanAtMost__int) ).

fof(fact_finite__greaterThanLessThan__int,axiom,
    ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,V_l_2,V_u_2))),
    file('theBenchmark.p',fact_finite__greaterThanLessThan__int) ).

fof(fact_number__of__is__id,axiom,
    ! [V_k] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k) = V_k,
    file('theBenchmark.p',fact_number__of__is__id) ).

fof(fact_infinite__UNIV__int,axiom,
    ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))),
    file('theBenchmark.p',fact_infinite__UNIV__int) ).

fof(fact_q__pos__lemma,axiom,
    ! [V_r_H,V_q_H,V_b_H] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_q_H)) ) ) ),
    file('theBenchmark.p',fact_q__pos__lemma) ).

fof(fact_q__neg__lemma,axiom,
    ! [V_r_H,V_q_H,V_b_H] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ),
    file('theBenchmark.p',fact_q__neg__lemma) ).

fof(fact_unique__quotient__lemma,axiom,
    ! [V_r,V_q,V_r_H,V_q_H,V_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H)),V_r_H)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ),
    file('theBenchmark.p',fact_unique__quotient__lemma) ).

fof(fact_simp__from__to,axiom,
    ! [V_i_2,V_j_2] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2))
       => c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),V_i_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_j_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2))
       => c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_simp__from__to) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom,
    ! [V_n,V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n))) ),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom,
    ! [V_y,V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y))) ) ),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom,
    ! [V_y,V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y))) ) ),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J) ).

fof(fact_bset_I8_J,axiom,
    ! [V_B_2,V_t_2,V_D_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
     => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_B_2))
       => ! [B_x] :
            ( ! [B_xa] :
                ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
               => ! [B_xb] :
                    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
                   => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2))) ) ) ) ),
    file('theBenchmark.p',fact_bset_I8_J) ).

fof(fact_aset_I6_J,axiom,
    ! [V_A_2,V_t_2,V_D_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
     => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_A_2))
       => ! [B_x] :
            ( ! [B_xa] :
                ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
               => ! [B_xb] :
                    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
                   => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2)),V_t_2)) ) ) ) ),
    file('theBenchmark.p',fact_aset_I6_J) ).

fof(fact_aset_I8_J,axiom,
    ! [V_t_2,V_A_2,V_D_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
     => ! [B_x] :
          ( ! [B_xa] :
              ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
             => ! [B_xb] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
                 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2))) ) ) ),
    file('theBenchmark.p',fact_aset_I8_J) ).

fof(fact_bset_I6_J,axiom,
    ! [V_t_2,V_B_2,V_D_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
     => ! [B_x] :
          ( ! [B_xa] :
              ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
             => ! [B_xb] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
                 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2)),V_t_2)) ) ) ),
    file('theBenchmark.p',fact_bset_I6_J) ).

fof(fact_periodic__finite__ex,axiom,
    ! [V_P_2,V_d_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
     => ( ! [B_x,B_k] :
            ( hBOOL(hAPP(V_P_2,B_x))
          <=> hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B_k),V_d_2)))) )
       => ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
        <=> ? [B_x] :
              ( hBOOL(hAPP(V_P_2,B_x))
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_d_2))) ) ) ) ),
    file('theBenchmark.p',fact_periodic__finite__ex) ).

fof(fact_bset_I3_J,axiom,
    ! [V_B_2,V_t_2,V_D_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
     => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_B_2))
       => ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
             => ! [B_xa] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_B_2))
                 => V_t_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xa),B_x) ) )
         => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ),
    file('theBenchmark.p',fact_bset_I3_J) ).

fof(fact_aset_I3_J,axiom,
    ! [V_A_2,V_t_2,V_D_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
     => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_A_2))
       => ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
             => ! [B_xa] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_A_2))
                 => V_t_2 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xa),B_x) ) )
         => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ),
    file('theBenchmark.p',fact_aset_I3_J) ).

fof(fact_aset_I5_J,axiom,
    ! [V_A_2,V_t_2,V_D_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
     => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2))
       => ! [B_x] :
            ( ! [B_xa] :
                ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
               => ! [B_xb] :
                    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
                   => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2)),V_t_2)) ) ) ) ),
    file('theBenchmark.p',fact_aset_I5_J) ).

fof(fact_bset_I7_J,axiom,
    ! [V_B_2,V_t_2,V_D_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
     => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2))
       => ! [B_x] :
            ( ! [B_xa] :
                ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
               => ! [B_xb] :
                    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
                   => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2))) ) ) ) ),
    file('theBenchmark.p',fact_bset_I7_J) ).

fof(fact_bset_I4_J,axiom,
    ! [V_B_2,V_t_2,V_D_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
     => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2))
       => ! [B_x] :
            ( ! [B_xa] :
                ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
               => ! [B_xb] :
                    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
                   => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
           => ( B_x != V_t_2
             => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ),
    file('theBenchmark.p',fact_bset_I4_J) ).

fof(fact_aset_I4_J,axiom,
    ! [V_A_2,V_t_2,V_D_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
     => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2))
       => ! [B_x] :
            ( ! [B_xa] :
                ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
               => ! [B_xb] :
                    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
                   => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
           => ( B_x != V_t_2
             => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ),
    file('theBenchmark.p',fact_aset_I4_J) ).

fof(fact_aset_I7_J,axiom,
    ! [V_t_2,V_A_2,V_D_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
     => ! [B_x] :
          ( ! [B_xa] :
              ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
             => ! [B_xb] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
                 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2))) ) ) ),
    file('theBenchmark.p',fact_aset_I7_J) ).

fof(fact_bset_I5_J,axiom,
    ! [V_t_2,V_B_2,V_D_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
     => ! [B_x] :
          ( ! [B_xa] :
              ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
             => ! [B_xb] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
                 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2)),V_t_2)) ) ) ),
    file('theBenchmark.p',fact_bset_I5_J) ).

fof(fact_Suc__nat__number__of__add,axiom,
    ! [V_n,V_v] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
       => hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(V_v))),V_n) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
       => hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) ) ),
    file('theBenchmark.p',fact_Suc__nat__number__of__add) ).

fof(fact_tsub__def,axiom,
    ! [V_x,V_y] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
       => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
       => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) ) ),
    file('theBenchmark.p',fact_tsub__def) ).

fof(fact_not__neg__0,axiom,
    ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    file('theBenchmark.p',fact_not__neg__0) ).

fof(fact_not__neg__1,axiom,
    ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))),
    file('theBenchmark.p',fact_not__neg__1) ).

fof(fact_not__neg__eq__ge__0,axiom,
    ! [V_x_2] :
      ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_x_2))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ),
    file('theBenchmark.p',fact_not__neg__eq__ge__0) ).

fof(fact_neg__def,axiom,
    ! [V_Z_2] :
      ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_Z_2))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_Z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    file('theBenchmark.p',fact_neg__def) ).

fof(fact_neg__imp__number__of__eq__0,axiom,
    ! [V_v] :
      ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
     => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('theBenchmark.p',fact_neg__imp__number__of__eq__0) ).

fof(fact_eq__nat__number__of,axiom,
    ! [V_v_H_2,V_v_2] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2)
    <=> ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)))
         => ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2)))
             => V_v_2 = V_v_H_2 )
            & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2)))
             => hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) )
        & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ),
    file('theBenchmark.p',fact_eq__nat__number__of) ).

fof(fact_nat__number__of__add__left,axiom,
    ! [V_k,V_v_H,V_v] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
       => ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
           => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_v_H))),V_k) )
          & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
           => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),V_k) ) ) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k) ) ),
    file('theBenchmark.p',fact_nat__number__of__add__left) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom,
    ! [V_y,V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Nat__Transfer_Otsub(V_x,V_y))) ) ),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J) ).

fof(fact_neg__number__of__pred__iff__0,axiom,
    ! [V_v_2] :
      ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))))
    <=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('theBenchmark.p',fact_neg__number__of__pred__iff__0) ).

fof(fact_tsub__eq,axiom,
    ! [V_x,V_y] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
     => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) ),
    file('theBenchmark.p',fact_tsub__eq) ).

fof(fact_Suc__nat__number__of,axiom,
    ! [V_v] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
       => hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(V_v)) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
       => hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_Suc__nat__number__of) ).

fof(fact_fold__graph_H_Oequations_I2_J,axiom,
    ! [V_a5_2,V_a1_2,V_a2_2,V_a4_2,V_a3_2,T_c,T_b] :
      ( c_Nitpick_Ofold__graph_H(T_b,T_c,V_a3_2,V_a4_2,V_a2_2,hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2))
    <=> ( ? [B_x,B_y] :
            ( c_Nitpick_Ofold__graph_H(T_b,T_c,V_a3_2,V_a4_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_a2_2),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),B_y)
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a2_2))
            & hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = hAPP(hAPP(V_a3_2,B_x),B_y) )
        | ( hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = V_a4_2
          & V_a2_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ),
    file('theBenchmark.p',fact_fold__graph_H_Oequations_I2_J) ).

fof(fact_int__power__div__base,axiom,
    ! [V_k,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_k),V_m)),V_k) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
    file('theBenchmark.p',fact_int__power__div__base) ).

fof(fact_nat__number__of__diff__1,axiom,
    ! [V_v] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(V_v)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_nat__number__of__diff__1) ).

fof(fact_decr__mult__lemma,axiom,
    ! [V_k_2,V_P_2,V_d_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
     => ( ! [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
           => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_d_2))) )
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
         => ! [B_x] :
              ( hBOOL(hAPP(V_P_2,B_x))
             => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2)))) ) ) ) ),
    file('theBenchmark.p',fact_decr__mult__lemma) ).

fof(fact_incr__mult__lemma,axiom,
    ! [V_k_2,V_P_2,V_d_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
     => ( ! [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
           => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_d_2))) )
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
         => ! [B_x] :
              ( hBOOL(hAPP(V_P_2,B_x))
             => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2)))) ) ) ) ),
    file('theBenchmark.p',fact_incr__mult__lemma) ).

fof(fact_zdiv__zero,axiom,
    ! [V_b] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    file('theBenchmark.p',fact_zdiv__zero) ).

fof(fact_zdiv__zminus2,axiom,
    ! [V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a)),V_b),
    file('theBenchmark.p',fact_zdiv__zminus2) ).

fof(fact_zdiv__zminus__zminus,axiom,
    ! [V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b),
    file('theBenchmark.p',fact_zdiv__zminus__zminus) ).

fof(fact_Pls__def,axiom,
    c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    file('theBenchmark.p',fact_Pls__def) ).

fof(fact_rel__simps_I19_J,axiom,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),
    file('theBenchmark.p',fact_rel__simps_I19_J) ).

fof(fact_rel__simps_I2_J,axiom,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),
    file('theBenchmark.p',fact_rel__simps_I2_J) ).

fof(fact_add__Pls,axiom,
    ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),V_k) = V_k,
    file('theBenchmark.p',fact_add__Pls) ).

fof(fact_add__Pls__right,axiom,
    ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OPls) = V_k,
    file('theBenchmark.p',fact_add__Pls__right) ).

fof(fact_div__0,axiom,
    ! [V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_div__0) ).

fof(fact_div__by__0,axiom,
    ! [V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_div__by__0) ).

fof(fact_mult__Pls,axiom,
    ! [V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),V_w) = c_Int_OPls,
    file('theBenchmark.p',fact_mult__Pls) ).

fof(fact_diff__bin__simps_I1_J,axiom,
    ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OPls) = V_k,
    file('theBenchmark.p',fact_diff__bin__simps_I1_J) ).

fof(fact_minus__Pls,axiom,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls,
    file('theBenchmark.p',fact_minus__Pls) ).

fof(fact_div__by__1,axiom,
    ! [V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ),
    file('theBenchmark.p',fact_div__by__1) ).

fof(fact_Divides_Otransfer__nat__int__function__closures_I1_J,axiom,
    ! [V_y,V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y))) ) ),
    file('theBenchmark.p',fact_Divides_Otransfer__nat__int__function__closures_I1_J) ).

fof(fact_pos__imp__zdiv__neg__iff,axiom,
    ! [V_a_2,V_b_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    file('theBenchmark.p',fact_pos__imp__zdiv__neg__iff) ).

fof(fact_neg__imp__zdiv__neg__iff,axiom,
    ! [V_a_2,V_b_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ),
    file('theBenchmark.p',fact_neg__imp__zdiv__neg__iff) ).

fof(fact_div__neg__pos__less0,axiom,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    file('theBenchmark.p',fact_div__neg__pos__less0) ).

fof(fact_zdiv__self,axiom,
    ! [V_a] :
      ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_a) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    file('theBenchmark.p',fact_zdiv__self) ).

fof(fact_number__of__Pls,axiom,
    ! [T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_number__of__Pls) ).

fof(fact_semiring__norm_I112_J,axiom,
    ! [T_a] :
      ( class_Int_Onumber__ring(T_a)
     => c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) ),
    file('theBenchmark.p',fact_semiring__norm_I112_J) ).

fof(fact_add__numeral__0__right,axiom,
    ! [V_a,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) = V_a ),
    file('theBenchmark.p',fact_add__numeral__0__right) ).

fof(fact_add__numeral__0,axiom,
    ! [V_a,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)),V_a) = V_a ),
    file('theBenchmark.p',fact_add__numeral__0) ).

fof(fact_bin__less__0__simps_I1_J,axiom,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    file('theBenchmark.p',fact_bin__less__0__simps_I1_J) ).

fof(fact_nat__number__of__Pls,axiom,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_nat__number__of__Pls) ).

fof(fact_semiring__norm_I113_J,axiom,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls),
    file('theBenchmark.p',fact_semiring__norm_I113_J) ).

fof(fact_zero__is__num__zero,axiom,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls),
    file('theBenchmark.p',fact_zero__is__num__zero) ).

fof(fact_div__mult__mult1,axiom,
    ! [V_b,V_a,V_c,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b) ) ),
    file('theBenchmark.p',fact_div__mult__mult1) ).

fof(fact_div__mult__mult2,axiom,
    ! [V_b,V_a,V_c,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b) ) ),
    file('theBenchmark.p',fact_div__mult__mult2) ).

fof(fact_div__mult__self1__is__id,axiom,
    ! [V_a,V_b,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)),V_b) = V_a ) ),
    file('theBenchmark.p',fact_div__mult__self1__is__id) ).

fof(fact_div__mult__self2__is__id,axiom,
    ! [V_a,V_b,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_b) = V_a ) ),
    file('theBenchmark.p',fact_div__mult__self2__is__id) ).

fof(fact_div__mult__mult1__if,axiom,
    ! [V_b,V_a,V_c,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => ( ( V_c != c_Groups_Ozero__class_Ozero(T_a)
         => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b) )
        & ( V_c = c_Groups_Ozero__class_Ozero(T_a)
         => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
    file('theBenchmark.p',fact_div__mult__mult1__if) ).

fof(fact_div__self,axiom,
    ! [V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ),
    file('theBenchmark.p',fact_div__self) ).

fof(fact_not__neg__number__of__Pls,axiom,
    ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))),
    file('theBenchmark.p',fact_not__neg__number__of__Pls) ).

fof(fact_zdiv__eq__0__iff,axiom,
    ! [V_k_2,V_i_2] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_i_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),V_k_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2)) )
        | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    file('theBenchmark.p',fact_zdiv__eq__0__iff) ).

fof(fact_pos__imp__zdiv__nonneg__iff,axiom,
    ! [V_a_2,V_b_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ),
    file('theBenchmark.p',fact_pos__imp__zdiv__nonneg__iff) ).

fof(fact_pos__imp__zdiv__pos__iff,axiom,
    ! [V_i_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_i_2)) ) ),
    file('theBenchmark.p',fact_pos__imp__zdiv__pos__iff) ).

fof(fact_nonneg1__imp__zdiv__pos__iff,axiom,
    ! [V_b_2,V_a_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),V_a_2)) ) ) ),
    file('theBenchmark.p',fact_nonneg1__imp__zdiv__pos__iff) ).

fof(fact_zdiv__mono2,axiom,
    ! [V_b,V_b_H,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b_H))) ) ) ),
    file('theBenchmark.p',fact_zdiv__mono2) ).

fof(fact_div__nonneg__neg__le0,axiom,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    file('theBenchmark.p',fact_div__nonneg__neg__le0) ).

fof(fact_div__pos__pos__trivial,axiom,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    file('theBenchmark.p',fact_div__pos__pos__trivial) ).

fof(fact_neg__imp__zdiv__nonneg__iff,axiom,
    ! [V_a_2,V_b_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    file('theBenchmark.p',fact_neg__imp__zdiv__nonneg__iff) ).

fof(fact_div__nonpos__pos__le0,axiom,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    file('theBenchmark.p',fact_div__nonpos__pos__le0) ).

fof(fact_zdiv__mono2__neg,axiom,
    ! [V_b,V_b_H,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b_H)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))) ) ) ),
    file('theBenchmark.p',fact_zdiv__mono2__neg) ).

fof(fact_div__neg__neg__trivial,axiom,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    file('theBenchmark.p',fact_div__neg__neg__trivial) ).

fof(fact_zdiv__mono1,axiom,
    ! [V_b,V_a_H,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_H),V_b))) ) ),
    file('theBenchmark.p',fact_zdiv__mono1) ).

fof(fact_zdiv__mono1__neg,axiom,
    ! [V_b,V_a_H,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_H),V_b)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))) ) ),
    file('theBenchmark.p',fact_zdiv__mono1__neg) ).

fof(fact_int__div__less__self,axiom,
    ! [V_k,V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_k)),V_x)) ) ),
    file('theBenchmark.p',fact_int__div__less__self) ).

fof(fact_zdiv__zmult2__eq,axiom,
    ! [V_b,V_a,V_c] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),V_c) ),
    file('theBenchmark.p',fact_zdiv__zmult2__eq) ).

fof(fact_divide__Numeral0,axiom,
    ! [V_x,T_a] :
      ( ( class_Int_Onumber__ring(T_a)
        & class_Fields_Ofield__inverse__zero(T_a) )
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_divide__Numeral0) ).

fof(fact_eq__number__of__0,axiom,
    ! [V_v_2] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ),
    file('theBenchmark.p',fact_eq__number__of__0) ).

fof(fact_eq__0__number__of,axiom,
    ! [V_v_2] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ),
    file('theBenchmark.p',fact_eq__0__number__of) ).

fof(fact_number__of2,axiom,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))),
    file('theBenchmark.p',fact_number__of2) ).

fof(fact_less__nat__number__of,axiom,
    ! [V_v_H_2,V_v_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2)))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2))
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_H_2)) ) ) ),
    file('theBenchmark.p',fact_less__nat__number__of) ).

fof(fact_le__nat__number__of,axiom,
    ! [V_v_H_2,V_v_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2)))
    <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),V_v_H_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ),
    file('theBenchmark.p',fact_le__nat__number__of) ).

fof(fact_div__mult__self2,axiom,
    ! [V_c,V_a,V_b,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)) ) ),
    file('theBenchmark.p',fact_div__mult__self2) ).

fof(fact_div__mult__self1,axiom,
    ! [V_c,V_a,V_b,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)) ) ),
    file('theBenchmark.p',fact_div__mult__self1) ).

fof(fact_div__add__self2,axiom,
    ! [V_a,V_b,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),c_Groups_Oone__class_Oone(T_a)) ) ),
    file('theBenchmark.p',fact_div__add__self2) ).

fof(fact_div__add__self1,axiom,
    ! [V_a,V_b,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a)),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),c_Groups_Oone__class_Oone(T_a)) ) ),
    file('theBenchmark.p',fact_div__add__self1) ).

fof(fact_le__special_I3_J,axiom,
    ! [V_x_2,T_b] :
      ( ( class_Rings_Olinordered__idom(T_b)
        & class_Int_Onumber__ring(T_b) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Ozero__class_Ozero(T_b)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ),
    file('theBenchmark.p',fact_le__special_I3_J) ).

fof(fact_le__special_I1_J,axiom,
    ! [V_y_2,T_b] :
      ( ( class_Rings_Olinordered__idom(T_b)
        & class_Int_Onumber__ring(T_b) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ),
    file('theBenchmark.p',fact_le__special_I1_J) ).

fof(fact_less__special_I1_J,axiom,
    ! [V_y_2,T_b] :
      ( ( class_Rings_Olinordered__idom(T_b)
        & class_Int_Onumber__ring(T_b) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ),
    file('theBenchmark.p',fact_less__special_I1_J) ).

fof(fact_less__special_I3_J,axiom,
    ! [V_x_2,T_b] :
      ( ( class_Rings_Olinordered__idom(T_b)
        & class_Int_Onumber__ring(T_b) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Ozero__class_Ozero(T_b)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ),
    file('theBenchmark.p',fact_less__special_I3_J) ).

fof(fact_less__0__number__of,axiom,
    ! [V_v_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_2)) ),
    file('theBenchmark.p',fact_less__0__number__of) ).

fof(fact_add__nat__number__of,axiom,
    ! [V_v_H,V_v] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
       => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls))
           => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_v_H)) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls))
           => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) ) ) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H) ) ),
    file('theBenchmark.p',fact_add__nat__number__of) ).

fof(fact_split__zdiv,axiom,
    ! [V_k_2,V_n_2,V_P_2] :
      ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)))
    <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => ! [B_i] :
              ( ? [B_j] :
                  ( V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) )
             => hBOOL(hAPP(V_P_2,B_i)) ) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
         => ! [B_i] :
              ( ? [B_j] :
                  ( V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) )
             => hBOOL(hAPP(V_P_2,B_i)) ) )
        & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ),
    file('theBenchmark.p',fact_split__zdiv) ).

fof(fact_divmod__int__rel__div__eq,axiom,
    ! [V_r_1,V_y,V_b_1,V_a_1] :
      ( V_a_1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_1),V_y)),V_r_1)
     => ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r_1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_r_1)) ) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_1),V_b_1))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_1)) ) ) )
       => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_1),V_b_1) = V_y ) ) ),
    file('theBenchmark.p',fact_divmod__int__rel__div__eq) ).

fof(fact_nat__number__of__mult__left,axiom,
    ! [V_k,V_v_H,V_v] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_v_H))),V_k) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_nat__number__of__mult__left) ).

fof(fact_mult__nat__number__of,axiom,
    ! [V_v_H,V_v] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_v_H)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_mult__nat__number__of) ).

fof(fact_Suc__diff__number__of,axiom,
    ! [V_m,V_v] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(V_v))) ),
    file('theBenchmark.p',fact_Suc__diff__number__of) ).

fof(fact_nat__1__add__number__of,axiom,
    ! [V_v] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(V_v)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_nat__1__add__number__of) ).

fof(fact_nat__number__of__add__1,axiom,
    ! [V_v] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(V_v)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_nat__number__of__add__1) ).

fof(fact_z3div__def,axiom,
    ! [V_k,V_l] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
       => c_SMT_Oz3div(V_k,V_l) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_l))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
       => c_SMT_Oz3div(V_k,V_l) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l) ) ),
    file('theBenchmark.p',fact_z3div__def) ).

fof(fact_eq__special_I3_J,axiom,
    ! [V_x_2,T_b] :
      ( class_Int_Onumber__ring(T_b)
     => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = c_Groups_Ozero__class_Ozero(T_b)
      <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls)))) ) ),
    file('theBenchmark.p',fact_eq__special_I3_J) ).

fof(fact_eq__special_I1_J,axiom,
    ! [V_y_2,T_b] :
      ( class_Int_Onumber__ring(T_b)
     => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
      <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_y_2)))) ) ),
    file('theBenchmark.p',fact_eq__special_I1_J) ).

fof(fact_Nats__number__of,axiom,
    ! [V_w_2,T_b] :
      ( class_Int_Onumber__ring(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_w_2))
       => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ),
    file('theBenchmark.p',fact_Nats__number__of) ).

fof(fact_power__nat__number__of__number__of,axiom,
    ! [V_w,V_v] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w))) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w)) ) ),
    file('theBenchmark.p',fact_power__nat__number__of__number__of) ).

fof(fact_div__le__mono,axiom,
    ! [V_k,V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n),V_k))) ),
    file('theBenchmark.p',fact_div__le__mono) ).

fof(fact_div__le__dividend,axiom,
    ! [V_n,V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),V_m)),
    file('theBenchmark.p',fact_div__le__dividend) ).

fof(fact_div__mult2__eq,axiom,
    ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),V_b)),V_c),
    file('theBenchmark.p',fact_div__mult2__eq) ).

fof(fact_nat__div__distrib,axiom,
    ! [V_y,V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
     => hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)) ),
    file('theBenchmark.p',fact_nat__div__distrib) ).

fof(fact_Divides_Otransfer__nat__int__functions_I1_J,axiom,
    ! [V_y,V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) ) ),
    file('theBenchmark.p',fact_Divides_Otransfer__nat__int__functions_I1_J) ).

fof(fact_iszero__0,axiom,
    ! [T_a] :
      ( class_Rings_Osemiring__1(T_a)
     => c_Int_Oiszero(T_a,c_Groups_Ozero__class_Ozero(T_a)) ),
    file('theBenchmark.p',fact_iszero__0) ).

fof(fact_iszero__def,axiom,
    ! [V_z_2,T_b] :
      ( class_Rings_Osemiring__1(T_b)
     => ( c_Int_Oiszero(T_b,V_z_2)
      <=> V_z_2 = c_Groups_Ozero__class_Ozero(T_b) ) ),
    file('theBenchmark.p',fact_iszero__def) ).

fof(fact_div__1,axiom,
    ! [V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = V_m,
    file('theBenchmark.p',fact_div__1) ).

fof(fact_div__less,axiom,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('theBenchmark.p',fact_div__less) ).

fof(fact_nat__mult__div__cancel__disj,axiom,
    ! [V_n,V_m,V_k] :
      ( ( V_k != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) )
      & ( V_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_nat__mult__div__cancel__disj) ).

fof(fact_nat__0,axiom,
    hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_nat__0) ).

fof(fact_transfer__nat__int__numerals_I1_J,axiom,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    file('theBenchmark.p',fact_transfer__nat__int__numerals_I1_J) ).

fof(fact_not__iszero__1,axiom,
    ! [T_a] :
      ( class_Rings_Osemiring__1(T_a)
     => ~ c_Int_Oiszero(T_a,c_Groups_Oone__class_Oone(T_a)) ),
    file('theBenchmark.p',fact_not__iszero__1) ).

fof(fact_eq__nat__nat__iff,axiom,
    ! [V_z_H_2,V_z_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H_2))
       => ( hAPP(c_Int_Onat,V_z_2) = hAPP(c_Int_Onat,V_z_H_2)
        <=> V_z_2 = V_z_H_2 ) ) ),
    file('theBenchmark.p',fact_eq__nat__nat__iff) ).

fof(fact_ex__nat,axiom,
    ! [V_P_2] :
      ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
    <=> ? [B_x] :
          ( hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) ),
    file('theBenchmark.p',fact_ex__nat) ).

fof(fact_all__nat,axiom,
    ! [V_P_2] :
      ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
         => hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x))) ) ),
    file('theBenchmark.p',fact_all__nat) ).

fof(fact_transfer__nat__int__relations_I1_J,axiom,
    ! [V_y_2,V_x_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
       => ( hAPP(c_Int_Onat,V_x_2) = hAPP(c_Int_Onat,V_y_2)
        <=> V_x_2 = V_y_2 ) ) ),
    file('theBenchmark.p',fact_transfer__nat__int__relations_I1_J) ).

fof(fact_nat__number__of__def,axiom,
    ! [V_v] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),
    file('theBenchmark.p',fact_nat__number__of__def) ).

fof(fact_nat__number__of,axiom,
    ! [V_w] : hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w),
    file('theBenchmark.p',fact_nat__number__of) ).

fof(fact_transfer__nat__int__numerals_I2_J,axiom,
    c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)),
    file('theBenchmark.p',fact_transfer__nat__int__numerals_I2_J) ).

fof(fact_neg__nat,axiom,
    ! [V_z] :
      ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z))
     => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('theBenchmark.p',fact_neg__nat) ).

fof(fact_card__atLeastZeroLessThan__int,axiom,
    ! [V_u_2] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2)) = hAPP(c_Int_Onat,V_u_2),
    file('theBenchmark.p',fact_card__atLeastZeroLessThan__int) ).

fof(fact_div__nat__number__of,axiom,
    ! [V_v_H,V_v] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_div__nat__number__of) ).

fof(fact_card__atLeastLessThan__int,axiom,
    ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_l_2),V_u_2)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_u_2),V_l_2)),
    file('theBenchmark.p',fact_card__atLeastLessThan__int) ).

fof(fact_card__greaterThanAtMost__int,axiom,
    ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,V_l_2,V_u_2)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_u_2),V_l_2)),
    file('theBenchmark.p',fact_card__greaterThanAtMost__int) ).

fof(fact_one__div__nat__number__of,axiom,
    ! [V_v_H] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))),
    file('theBenchmark.p',fact_one__div__nat__number__of) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I2_J,axiom,
    c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__set__functions_I2_J) ).

fof(fact_div__le__mono2,axiom,
    ! [V_k,V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_k),V_n)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_k),V_m))) ) ),
    file('theBenchmark.p',fact_div__le__mono2) ).

fof(fact_div__mult__self1__is__m,axiom,
    ! [V_m,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m)),V_n) = V_m ),
    file('theBenchmark.p',fact_div__mult__self1__is__m) ).

fof(fact_div__mult__self__is__m,axiom,
    ! [V_m,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),V_n) = V_m ),
    file('theBenchmark.p',fact_div__mult__self__is__m) ).

fof(fact_nat__mult__div__cancel1,axiom,
    ! [V_n,V_m,V_k] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) ),
    file('theBenchmark.p',fact_nat__mult__div__cancel1) ).

fof(fact_div__less__dividend,axiom,
    ! [V_m,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),V_m)) ) ),
    file('theBenchmark.p',fact_div__less__dividend) ).

fof(fact_nat__le__0,axiom,
    ! [V_z] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('theBenchmark.p',fact_nat__le__0) ).

fof(fact_nat__0__iff,axiom,
    ! [V_i_2] :
      ( hAPP(c_Int_Onat,V_i_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    file('theBenchmark.p',fact_nat__0__iff) ).

fof(fact_zless__nat__conj,axiom,
    ! [V_z_2,V_w_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),hAPP(c_Int_Onat,V_z_2)))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ),
    file('theBenchmark.p',fact_zless__nat__conj) ).

fof(fact_nat__mono__iff,axiom,
    ! [V_w_2,V_z_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),hAPP(c_Int_Onat,V_z_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ),
    file('theBenchmark.p',fact_nat__mono__iff) ).

fof(fact_transfer__nat__int__relations_I3_J,axiom,
    ! [V_y_2,V_x_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,V_x_2)),hAPP(c_Int_Onat,V_y_2)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ),
    file('theBenchmark.p',fact_transfer__nat__int__relations_I3_J) ).

fof(fact_nat__1,axiom,
    hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('theBenchmark.p',fact_nat__1) ).

fof(fact_iszero__Numeral0,axiom,
    ! [T_a] :
      ( class_Int_Onumber__ring(T_a)
     => c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) ),
    file('theBenchmark.p',fact_iszero__Numeral0) ).

fof(fact_Nats__0,axiom,
    ! [T_b] :
      ( class_Rings_Osemiring__1(T_b)
     => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Nat_Osemiring__1__class_ONats(T_b))) ),
    file('theBenchmark.p',fact_Nats__0) ).

fof(fact_Nats__add,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( class_Rings_Osemiring__1(T_b)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Nat_Osemiring__1__class_ONats(T_b)))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Nat_Osemiring__1__class_ONats(T_b)))
         => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ) ),
    file('theBenchmark.p',fact_Nats__add) ).

fof(fact_Nats__mult,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( class_Rings_Osemiring__1(T_b)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Nat_Osemiring__1__class_ONats(T_b)))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Nat_Osemiring__1__class_ONats(T_b)))
         => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ) ),
    file('theBenchmark.p',fact_Nats__mult) ).

fof(fact_Nats__1,axiom,
    ! [T_b] :
      ( class_Rings_Osemiring__1(T_b)
     => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Oone__class_Oone(T_b)),c_Nat_Osemiring__1__class_ONats(T_b))) ),
    file('theBenchmark.p',fact_Nats__1) ).

fof(fact_div__if,axiom,
    ! [V_m,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
     => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
         => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
         => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
    file('theBenchmark.p',fact_div__if) ).

fof(fact_div__geq,axiom,
    ! [V_m,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n)) ) ),
    file('theBenchmark.p',fact_div__geq) ).

fof(fact_split__div,axiom,
    ! [V_k_2,V_n_2,V_P_2] :
      ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n_2),V_k_2)))
    <=> ( ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => ! [B_i,B_j] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2))
             => ( V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),B_i)),B_j)
               => hBOOL(hAPP(V_P_2,B_i)) ) ) )
        & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ),
    file('theBenchmark.p',fact_split__div) ).

fof(fact_zero__less__nat__eq,axiom,
    ! [V_z_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,V_z_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ),
    file('theBenchmark.p',fact_zero__less__nat__eq) ).

fof(fact_nat__less__eq__zless,axiom,
    ! [V_z_2,V_w_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),hAPP(c_Int_Onat,V_z_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ),
    file('theBenchmark.p',fact_nat__less__eq__zless) ).

fof(fact_transfer__nat__int__relations_I2_J,axiom,
    ! [V_y_2,V_x_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_x_2)),hAPP(c_Int_Onat,V_y_2)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ),
    file('theBenchmark.p',fact_transfer__nat__int__relations_I2_J) ).

fof(fact_nat__le__eq__zle,axiom,
    ! [V_z_2,V_w_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),hAPP(c_Int_Onat,V_z_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ),
    file('theBenchmark.p',fact_nat__le__eq__zle) ).

fof(fact_nat__add__distrib,axiom,
    ! [V_z_H,V_z] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H))
       => hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),V_z_H)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,V_z)),hAPP(c_Int_Onat,V_z_H)) ) ),
    file('theBenchmark.p',fact_nat__add__distrib) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J,axiom,
    ! [V_y,V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y)) ) ),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J) ).

fof(fact_nat__mult__distrib,axiom,
    ! [V_z_H,V_z] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
     => hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_z_H)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,V_z)),hAPP(c_Int_Onat,V_z_H)) ),
    file('theBenchmark.p',fact_nat__mult__distrib) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J,axiom,
    ! [V_y,V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)) ) ),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J) ).

fof(fact_nat__diff__distrib,axiom,
    ! [V_z,V_z_H] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z))
       => hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z),V_z_H)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,V_z)),hAPP(c_Int_Onat,V_z_H)) ) ),
    file('theBenchmark.p',fact_nat__diff__distrib) ).

fof(fact_card__atLeastAtMost__int,axiom,
    ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_l_2,V_u_2)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_u_2),V_l_2)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    file('theBenchmark.p',fact_card__atLeastAtMost__int) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J,axiom,
    ! [V_n,V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
     => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),V_n) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)) ),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J) ).

fof(fact_nat__power__eq,axiom,
    ! [V_n,V_z] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
     => hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,V_z)),V_n) ),
    file('theBenchmark.p',fact_nat__power__eq) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J,axiom,
    ! [V_y,V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,c_Nat__Transfer_Otsub(V_x,V_y)) ) ),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J) ).

fof(fact_card__greaterThanLessThan__int,axiom,
    ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,V_l_2,V_u_2)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_u_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_l_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    file('theBenchmark.p',fact_card__greaterThanLessThan__int) ).

fof(fact_le__div__geq,axiom,
    ! [V_m,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n)) ) ),
    file('theBenchmark.p',fact_le__div__geq) ).

fof(fact_split__div__lemma,axiom,
    ! [V_m_2,V_q_2,V_n_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_q_2))))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_q_2)),V_m_2)) )
      <=> V_q_2 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2) ) ),
    file('theBenchmark.p',fact_split__div__lemma) ).

fof(fact_split__div_H,axiom,
    ! [V_n_2,V_m_2,V_P_2] :
      ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2)))
    <=> ( ? [B_q] :
            ( hBOOL(hAPP(V_P_2,B_q))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,B_q))))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),B_q)),V_m_2)) )
        | ( hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
    file('theBenchmark.p',fact_split__div_H) ).

fof(fact_one__less__nat__eq,axiom,
    ! [V_z_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onat,V_z_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) ),
    file('theBenchmark.p',fact_one__less__nat__eq) ).

fof(fact_Suc__nat__eq__nat__zadd1,axiom,
    ! [V_z] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
     => hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,V_z)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z)) ),
    file('theBenchmark.p',fact_Suc__nat__eq__nat__zadd1) ).

fof(fact_nat__mult__distrib__neg,axiom,
    ! [V_z_H,V_z] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_z_H)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z))),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z_H))) ),
    file('theBenchmark.p',fact_nat__mult__distrib__neg) ).

fof(fact_eq__number__of__eq,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Int_Onumber__ring(T_b)
     => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
      <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_y_2)))) ) ),
    file('theBenchmark.p',fact_eq__number__of__eq) ).

fof(fact_power__nat__number__of,axiom,
    ! [V_n,V_v] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),V_n) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),V_n)) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),V_n) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) ) ),
    file('theBenchmark.p',fact_power__nat__number__of) ).

fof(fact_nat__aux__def,axiom,
    ! [V_n,V_i] : c_Int_Onat__aux(V_i,V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,V_i)),V_n),
    file('theBenchmark.p',fact_nat__aux__def) ).

fof(fact_transfer__morphism__nat__int,axiom,
    c_Nat__Transfer_Otransfer__morphism(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    file('theBenchmark.p',fact_transfer__morphism__nat__int) ).

fof(fact_eq__special_I2_J,axiom,
    ! [V_y_2,T_b] :
      ( class_Int_Onumber__ring(T_b)
     => ( c_Groups_Oone__class_Oone(T_b) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
      <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_y_2)))) ) ),
    file('theBenchmark.p',fact_eq__special_I2_J) ).

fof(fact_eq__special_I4_J,axiom,
    ! [V_x_2,T_b] :
      ( class_Int_Onumber__ring(T_b)
     => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = c_Groups_Oone__class_Oone(T_b)
      <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls))))) ) ),
    file('theBenchmark.p',fact_eq__special_I4_J) ).

fof(fact_of__nat__number__of__lemma,axiom,
    ! [V_v,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
         => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Ozero__class_Ozero(T_a) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
         => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v) ) ) ),
    file('theBenchmark.p',fact_of__nat__number__of__lemma) ).

fof(fact_negative__zle,axiom,
    ! [V_m,V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m))),
    file('theBenchmark.p',fact_negative__zle) ).

fof(fact_negative__zless,axiom,
    ! [V_m,V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,V_n)))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m))),
    file('theBenchmark.p',fact_negative__zless) ).

fof(fact_transfer__int__nat__set__return__embed,axiom,
    ! [V_A_2] : hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)) = V_A_2,
    file('theBenchmark.p',fact_transfer__int__nat__set__return__embed) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J,axiom,
    ! [V_B_2,V_A_2] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2))),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J) ).

fof(fact_nat__int,axiom,
    ! [V_n] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = V_n,
    file('theBenchmark.p',fact_nat__int) ).

fof(fact_rel__simps_I46_J,axiom,
    ! [V_k] : c_Int_OBit1(V_k) != c_Int_OPls,
    file('theBenchmark.p',fact_rel__simps_I46_J) ).

fof(fact_rel__simps_I39_J,axiom,
    ! [V_l] : c_Int_OPls != c_Int_OBit1(V_l),
    file('theBenchmark.p',fact_rel__simps_I39_J) ).

fof(fact_of__nat__eq__iff,axiom,
    ! [V_n_2,V_m_2,T_b] :
      ( class_Nat_Osemiring__char__0(T_b)
     => ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_m_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)
      <=> V_m_2 = V_n_2 ) ),
    file('theBenchmark.p',fact_of__nat__eq__iff) ).

fof(fact_rel__simps_I51_J,axiom,
    ! [V_l_2,V_k_2] :
      ( c_Int_OBit1(V_k_2) = c_Int_OBit1(V_l_2)
    <=> V_k_2 = V_l_2 ),
    file('theBenchmark.p',fact_rel__simps_I51_J) ).

fof(fact_rel__simps_I17_J,axiom,
    ! [V_l_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ),
    file('theBenchmark.p',fact_rel__simps_I17_J) ).

fof(fact_less__int__code_I16_J,axiom,
    ! [V_k2_2,V_k1_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ),
    file('theBenchmark.p',fact_less__int__code_I16_J) ).

fof(fact_less__eq__int__code_I16_J,axiom,
    ! [V_k2_2,V_k1_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ),
    file('theBenchmark.p',fact_less__eq__int__code_I16_J) ).

fof(fact_rel__simps_I34_J,axiom,
    ! [V_l_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ),
    file('theBenchmark.p',fact_rel__simps_I34_J) ).

fof(fact_Divides_Otransfer__int__nat__functions_I1_J,axiom,
    ! [V_y,V_x] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_x),V_y)),
    file('theBenchmark.p',fact_Divides_Otransfer__int__nat__functions_I1_J) ).

fof(fact_zdiv__int,axiom,
    ! [V_b,V_a] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_a)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_b)),
    file('theBenchmark.p',fact_zdiv__int) ).

fof(fact_not__neg__int,axiom,
    ! [V_n] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))),
    file('theBenchmark.p',fact_not__neg__int) ).

fof(fact_inj__int,axiom,
    c_Fun_Oinj__on(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    file('theBenchmark.p',fact_inj__int) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J,axiom,
    ! [V_A_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),V_A_2) = hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J) ).

fof(fact_transfer__nat__int__set__relations_I2_J,axiom,
    ! [V_A_2,V_x_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),V_A_2))
    <=> hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2))) ),
    file('theBenchmark.p',fact_transfer__nat__int__set__relations_I2_J) ).

fof(fact_transfer__int__nat__numerals_I4_J,axiom,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),
    file('theBenchmark.p',fact_transfer__int__nat__numerals_I4_J) ).

fof(fact_transfer__nat__int__set__relations_I5_J,axiom,
    ! [V_B_2,V_A_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2))) ),
    file('theBenchmark.p',fact_transfer__nat__int__set__relations_I5_J) ).

fof(fact_transfer__int__nat__numerals_I1_J,axiom,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('theBenchmark.p',fact_transfer__int__nat__numerals_I1_J) ).

fof(fact_int__0,axiom,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    file('theBenchmark.p',fact_int__0) ).

fof(fact_int__eq__0__conv,axiom,
    ! [V_n_2] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('theBenchmark.p',fact_int__eq__0__conv) ).

fof(fact_transfer__int__nat__quantifiers_I1_J,axiom,
    ! [V_P_2] :
      ( ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
         => hBOOL(hAPP(V_P_2,B_x)) )
    <=> ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ),
    file('theBenchmark.p',fact_transfer__int__nat__quantifiers_I1_J) ).

fof(fact_transfer__int__nat__quantifiers_I2_J,axiom,
    ! [V_P_2] :
      ( ? [B_x] :
          ( hBOOL(hAPP(V_P_2,B_x))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) )
    <=> ? [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ),
    file('theBenchmark.p',fact_transfer__int__nat__quantifiers_I2_J) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J,axiom,
    ! [V_z] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z))),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J) ).

fof(fact_zero__zle__int,axiom,
    ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))),
    file('theBenchmark.p',fact_zero__zle__int) ).

fof(fact_int__less__0__conv,axiom,
    ! [V_k] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_k)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    file('theBenchmark.p',fact_int__less__0__conv) ).

fof(fact_transfer__int__nat__relations_I2_J,axiom,
    ! [V_y_2,V_x_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ),
    file('theBenchmark.p',fact_transfer__int__nat__relations_I2_J) ).

fof(fact_zless__int,axiom,
    ! [V_n_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ),
    file('theBenchmark.p',fact_zless__int) ).

fof(fact_bin__less__0__simps_I4_J,axiom,
    ! [V_w_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_w_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    file('theBenchmark.p',fact_bin__less__0__simps_I4_J) ).

fof(fact_transfer__int__nat__relations_I3_J,axiom,
    ! [V_y_2,V_x_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ),
    file('theBenchmark.p',fact_transfer__int__nat__relations_I3_J) ).

fof(fact_zle__int,axiom,
    ! [V_n_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ),
    file('theBenchmark.p',fact_zle__int) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J,axiom,
    ! [V_y,V_x] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),V_y)),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J) ).

fof(fact_zadd__int__left,axiom,
    ! [V_z,V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))),V_z),
    file('theBenchmark.p',fact_zadd__int__left) ).

fof(fact_zadd__int,axiom,
    ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),
    file('theBenchmark.p',fact_zadd__int) ).

fof(fact_zle__iff__zadd,axiom,
    ! [V_z_2,V_w_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2))
    <=> ? [B_n] : V_z_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n)) ),
    file('theBenchmark.p',fact_zle__iff__zadd) ).

fof(fact_rel__simps_I22_J,axiom,
    ! [V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ),
    file('theBenchmark.p',fact_rel__simps_I22_J) ).

fof(fact_rel__simps_I12_J,axiom,
    ! [V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ),
    file('theBenchmark.p',fact_rel__simps_I12_J) ).

fof(fact_zero__le__imp__of__nat,axiom,
    ! [V_m,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m))) ),
    file('theBenchmark.p',fact_zero__le__imp__of__nat) ).

fof(fact_of__nat__0__le__iff,axiom,
    ! [V_n,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n))) ),
    file('theBenchmark.p',fact_of__nat__0__le__iff) ).

fof(fact_negative__eq__positive,axiom,
    ! [V_m_2,V_n_2] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)
    <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_negative__eq__positive) ).

fof(fact_of__nat__less__0__iff,axiom,
    ! [V_m,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),c_Groups_Ozero__class_Ozero(T_a))) ),
    file('theBenchmark.p',fact_of__nat__less__0__iff) ).

fof(fact_Bit1__def,axiom,
    ! [V_k] : c_Int_OBit1(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k)),V_k),
    file('theBenchmark.p',fact_Bit1__def) ).

fof(fact_not__int__zless__negative,axiom,
    ! [V_m,V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)))),
    file('theBenchmark.p',fact_not__int__zless__negative) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J,axiom,
    ! [V_y,V_x] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_x),V_y)),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J) ).

fof(fact_zmult__int,axiom,
    ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),
    file('theBenchmark.p',fact_zmult__int) ).

fof(fact_int__mult,axiom,
    ! [V_n,V_m] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)),
    file('theBenchmark.p',fact_int__mult) ).

fof(fact_of__nat__0,axiom,
    ! [T_a] :
      ( class_Rings_Osemiring__1(T_a)
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_of__nat__0) ).

fof(fact_of__nat__less__iff,axiom,
    ! [V_n_2,V_m_2,T_b] :
      ( class_Rings_Olinordered__semidom(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ),
    file('theBenchmark.p',fact_of__nat__less__iff) ).

fof(fact_less__imp__of__nat__less,axiom,
    ! [V_n,V_m,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n))) ) ),
    file('theBenchmark.p',fact_less__imp__of__nat__less) ).

fof(fact_of__nat__less__imp__less,axiom,
    ! [V_n,V_m,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ),
    file('theBenchmark.p',fact_of__nat__less__imp__less) ).

fof(fact_transfer__int__nat__numerals_I2_J,axiom,
    c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    file('theBenchmark.p',fact_transfer__int__nat__numerals_I2_J) ).

fof(fact_int__1,axiom,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Int_Oint),
    file('theBenchmark.p',fact_int__1) ).

fof(fact_of__nat__le__iff,axiom,
    ! [V_n_2,V_m_2,T_b] :
      ( class_Rings_Olinordered__semidom(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ),
    file('theBenchmark.p',fact_of__nat__le__iff) ).

fof(fact_of__nat__add,axiom,
    ! [V_n,V_m,T_a] :
      ( class_Rings_Osemiring__1(T_a)
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)) ),
    file('theBenchmark.p',fact_of__nat__add) ).

fof(fact_of__nat__mult,axiom,
    ! [V_n,V_m,T_a] :
      ( class_Rings_Osemiring__1(T_a)
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)) ),
    file('theBenchmark.p',fact_of__nat__mult) ).

fof(fact_neg__number__of__Bit1,axiom,
    ! [V_w_2] :
      ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_w_2))))
    <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ),
    file('theBenchmark.p',fact_neg__number__of__Bit1) ).

fof(fact_not__neg__nat,axiom,
    ! [V_z] :
      ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z))
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ),
    file('theBenchmark.p',fact_not__neg__nat) ).

fof(fact_of__nat__1,axiom,
    ! [T_a] :
      ( class_Rings_Osemiring__1(T_a)
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ),
    file('theBenchmark.p',fact_of__nat__1) ).

fof(fact_minus__Bit1,axiom,
    ! [V_k] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(V_k)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k))),
    file('theBenchmark.p',fact_minus__Bit1) ).

fof(fact_iszero__number__of__Bit1,axiom,
    ! [V_w,T_a] :
      ( ( class_Int_Oring__char__0(T_a)
        & class_Int_Onumber__ring(T_a) )
     => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(V_w))) ),
    file('theBenchmark.p',fact_iszero__number__of__Bit1) ).

fof(fact_Ints__of__nat,axiom,
    ! [V_n_2,T_b] :
      ( class_Rings_Oring__1(T_b)
     => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)),c_Int_Oring__1__class_OInts(T_b))) ),
    file('theBenchmark.p',fact_Ints__of__nat) ).

fof(fact_succ__Pls,axiom,
    c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls),
    file('theBenchmark.p',fact_succ__Pls) ).

fof(fact_of__nat__power,axiom,
    ! [V_n,V_m,T_a] :
      ( class_Rings_Osemiring__1(T_a)
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),V_n) ),
    file('theBenchmark.p',fact_of__nat__power) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J,axiom,
    ! [V_n,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x)),V_n) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x),V_n)),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J) ).

fof(fact_zpower__int,axiom,
    ! [V_n,V_m] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),V_n) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)),
    file('theBenchmark.p',fact_zpower__int) ).

fof(fact_int__power,axiom,
    ! [V_n,V_m] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),V_n),
    file('theBenchmark.p',fact_int__power) ).

fof(fact_of__nat__in__Nats,axiom,
    ! [V_n_2,T_b] :
      ( class_Rings_Osemiring__1(T_b)
     => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)),c_Nat_Osemiring__1__class_ONats(T_b))) ),
    file('theBenchmark.p',fact_of__nat__in__Nats) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J,axiom,
    ! [V_y,V_x] : c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x),V_y)),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J) ).

fof(fact_transfer__nat__int__set__relations_I1_J,axiom,
    ! [V_A_2] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_A_2))
    <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2))) ),
    file('theBenchmark.p',fact_transfer__nat__int__set__relations_I1_J) ).

fof(fact_inj__of__nat,axiom,
    ! [T_b] :
      ( class_Nat_Osemiring__char__0(T_b)
     => c_Fun_Oinj__on(tc_Nat_Onat,T_b,c_Nat_Osemiring__1__class_Oof__nat(T_b),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ),
    file('theBenchmark.p',fact_inj__of__nat) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I3_J,axiom,
    ! [V_B_2,V_A_2] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2))),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__set__functions_I3_J) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J,axiom,
    c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J) ).

fof(fact_number__of__Bit1,axiom,
    ! [V_w,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ),
    file('theBenchmark.p',fact_number__of__Bit1) ).

fof(fact_mult__numeral__1,axiom,
    ! [V_a,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))),V_a) = V_a ),
    file('theBenchmark.p',fact_mult__numeral__1) ).

fof(fact_mult__numeral__1__right,axiom,
    ! [V_a,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) = V_a ),
    file('theBenchmark.p',fact_mult__numeral__1__right) ).

fof(fact_int__le__0__conv,axiom,
    ! [V_n_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('theBenchmark.p',fact_int__le__0__conv) ).

fof(fact_numeral__1__eq__1,axiom,
    ! [T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(T_a) ),
    file('theBenchmark.p',fact_numeral__1__eq__1) ).

fof(fact_semiring__norm_I110_J,axiom,
    ! [T_a] :
      ( class_Int_Onumber__ring(T_a)
     => c_Groups_Oone__class_Oone(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) ),
    file('theBenchmark.p',fact_semiring__norm_I110_J) ).

fof(fact_int__Suc0__eq__1,axiom,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_Int_Oint),
    file('theBenchmark.p',fact_int__Suc0__eq__1) ).

fof(fact_zless__iff__Suc__zadd,axiom,
    ! [V_z_2,V_w_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
    <=> ? [B_n] : V_z_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,B_n))) ),
    file('theBenchmark.p',fact_zless__iff__Suc__zadd) ).

fof(fact_int__nat__eq,axiom,
    ! [V_z] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
       => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
       => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ),
    file('theBenchmark.p',fact_int__nat__eq) ).

fof(fact_int__eq__iff,axiom,
    ! [V_z_2,V_m_2] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = V_z_2
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
        & V_m_2 = hAPP(c_Int_Onat,V_z_2) ) ),
    file('theBenchmark.p',fact_int__eq__iff) ).

fof(fact_nat__0__le,axiom,
    ! [V_z] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ),
    file('theBenchmark.p',fact_nat__0__le) ).

fof(fact_zless__nat__eq__int__zless,axiom,
    ! [V_z_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Int_Onat,V_z_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)),V_z_2)) ),
    file('theBenchmark.p',fact_zless__nat__eq__int__zless) ).

fof(fact_rel__simps_I5_J,axiom,
    ! [V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ),
    file('theBenchmark.p',fact_rel__simps_I5_J) ).

fof(fact_rel__simps_I29_J,axiom,
    ! [V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ),
    file('theBenchmark.p',fact_rel__simps_I29_J) ).

fof(fact_int__zle__neg,axiom,
    ! [V_m_2,V_n_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2))))
    <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_int__zle__neg) ).

fof(fact_int__Suc,axiom,
    ! [V_m] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,V_m)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),
    file('theBenchmark.p',fact_int__Suc) ).

fof(fact_divide__numeral__1,axiom,
    ! [V_a,T_a] :
      ( ( class_Int_Onumber__ring(T_a)
        & class_Fields_Ofield(T_a) )
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) = V_a ),
    file('theBenchmark.p',fact_divide__numeral__1) ).

fof(fact_divide__Numeral1,axiom,
    ! [V_x,T_a] :
      ( ( class_Int_Onumber__ring(T_a)
        & class_Fields_Ofield(T_a) )
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) = V_x ),
    file('theBenchmark.p',fact_divide__Numeral1) ).

fof(fact_negative__zle__0,axiom,
    ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    file('theBenchmark.p',fact_negative__zle__0) ).

fof(fact_nat__zminus__int,axiom,
    ! [V_n] : hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_nat__zminus__int) ).

fof(fact_one__is__num__one,axiom,
    c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),
    file('theBenchmark.p',fact_one__is__num__one) ).

fof(fact_zdiff__int,axiom,
    ! [V_m,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) ),
    file('theBenchmark.p',fact_zdiff__int) ).

fof(fact_Numeral1__eq1__nat,axiom,
    c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)),
    file('theBenchmark.p',fact_Numeral1__eq1__nat) ).

fof(fact_nat__numeral__1__eq__1,axiom,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
    file('theBenchmark.p',fact_nat__numeral__1__eq__1) ).

fof(fact_of__nat__Suc,axiom,
    ! [V_m,T_a] :
      ( class_Rings_Osemiring__1(T_a)
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Nat_OSuc,V_m)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)) ),
    file('theBenchmark.p',fact_of__nat__Suc) ).

fof(fact_neg__zminus__int,axiom,
    ! [V_n] : hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,V_n))))),
    file('theBenchmark.p',fact_neg__zminus__int) ).

fof(fact_of__nat__diff,axiom,
    ! [V_m,V_n,T_a] :
      ( class_Rings_Oring__1(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
       => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)) ) ),
    file('theBenchmark.p',fact_of__nat__diff) ).

fof(fact_not__iszero__Numeral1,axiom,
    ! [T_a] :
      ( class_Int_Onumber__ring(T_a)
     => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) ),
    file('theBenchmark.p',fact_not__iszero__Numeral1) ).

fof(fact_SetInterval_Otransfer__nat__int__set__functions_I2_J,axiom,
    ! [V_n_2,V_m_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2))),
    file('theBenchmark.p',fact_SetInterval_Otransfer__nat__int__set__functions_I2_J) ).

fof(fact_zero__less__int__conv,axiom,
    ! [V_n_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ),
    file('theBenchmark.p',fact_zero__less__int__conv) ).

fof(fact_nat__eq__iff,axiom,
    ! [V_m_2,V_w_2] :
      ( hAPP(c_Int_Onat,V_w_2) = V_m_2
    <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
         => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
         => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) ) ) ),
    file('theBenchmark.p',fact_nat__eq__iff) ).

fof(fact_nat__eq__iff2,axiom,
    ! [V_w_2,V_m_2] :
      ( V_m_2 = hAPP(c_Int_Onat,V_w_2)
    <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
         => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
         => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) ) ) ),
    file('theBenchmark.p',fact_nat__eq__iff2) ).

fof(fact_split__nat,axiom,
    ! [V_i_2,V_P_2] :
      ( hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,V_i_2)))
    <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
        & ! [B_n] :
            ( V_i_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n)
           => hBOOL(hAPP(V_P_2,B_n)) ) ) ),
    file('theBenchmark.p',fact_split__nat) ).

fof(fact_zmult__zless__mono2__lemma,axiom,
    ! [V_k,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_k)),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_k)),V_j))) ) ),
    file('theBenchmark.p',fact_zmult__zless__mono2__lemma) ).

fof(fact_numeral__1__eq__Suc__0,axiom,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('theBenchmark.p',fact_numeral__1__eq__Suc__0) ).

fof(fact_numeral__3__eq__3,axiom,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
    file('theBenchmark.p',fact_numeral__3__eq__3) ).

fof(fact_not__zle__0__negative,axiom,
    ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,V_n))))),
    file('theBenchmark.p',fact_not__zle__0__negative) ).

fof(fact_negative__zless__0,axiom,
    ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,V_n)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    file('theBenchmark.p',fact_negative__zless__0) ).

fof(fact_power3__eq__cube,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Omonoid__mult(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)),V_a) ),
    file('theBenchmark.p',fact_power3__eq__cube) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J,axiom,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))))),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J) ).

fof(fact_Suc3__eq__add__3,axiom,
    ! [V_n] : hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_n),
    file('theBenchmark.p',fact_Suc3__eq__add__3) ).

fof(fact_Suc__div__eq__add3__div__number__of,axiom,
    ! [V_v,V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),
    file('theBenchmark.p',fact_Suc__div__eq__add3__div__number__of) ).

fof(fact_Suc__div__eq__add3__div,axiom,
    ! [V_n,V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m)))),V_n) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_m)),V_n),
    file('theBenchmark.p',fact_Suc__div__eq__add3__div) ).

fof(fact_div__Suc__eq__div__add3,axiom,
    ! [V_n,V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_n)),
    file('theBenchmark.p',fact_div__Suc__eq__div__add3) ).

fof(fact_int__eq__iff__number__of,axiom,
    ! [V_v_2,V_m_2] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)))
        & V_m_2 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)) ) ),
    file('theBenchmark.p',fact_int__eq__iff__number__of) ).

fof(fact_transfer__nat__int__numerals_I4_J,axiom,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),
    file('theBenchmark.p',fact_transfer__nat__int__numerals_I4_J) ).

fof(fact_of__nat__0__less__iff,axiom,
    ! [V_n_2,T_b] :
      ( class_Rings_Olinordered__semidom(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ),
    file('theBenchmark.p',fact_of__nat__0__less__iff) ).

fof(fact_int__nat__number__of,axiom,
    ! [V_v] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
       => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
       => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    file('theBenchmark.p',fact_int__nat__number__of) ).

fof(fact_SetInterval_Otransfer__nat__int__set__functions_I1_J,axiom,
    ! [V_n_2] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2))),
    file('theBenchmark.p',fact_SetInterval_Otransfer__nat__int__set__functions_I1_J) ).

fof(fact_le__special_I4_J,axiom,
    ! [V_x_2,T_b] :
      ( ( class_Rings_Olinordered__idom(T_b)
        & class_Int_Onumber__ring(T_b) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Oone__class_Oone(T_b)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ),
    file('theBenchmark.p',fact_le__special_I4_J) ).

fof(fact_le__special_I2_J,axiom,
    ! [V_y_2,T_b] :
      ( ( class_Rings_Olinordered__idom(T_b)
        & class_Int_Onumber__ring(T_b) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Oone__class_Oone(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ),
    file('theBenchmark.p',fact_le__special_I2_J) ).

fof(fact_less__special_I4_J,axiom,
    ! [V_x_2,T_b] :
      ( ( class_Rings_Olinordered__idom(T_b)
        & class_Int_Onumber__ring(T_b) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Oone__class_Oone(T_b)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ),
    file('theBenchmark.p',fact_less__special_I4_J) ).

fof(fact_less__special_I2_J,axiom,
    ! [V_y_2,T_b] :
      ( ( class_Rings_Olinordered__idom(T_b)
        & class_Int_Onumber__ring(T_b) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ),
    file('theBenchmark.p',fact_less__special_I2_J) ).

fof(fact_add__special_I2_J,axiom,
    ! [V_w,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_w)) ),
    file('theBenchmark.p',fact_add__special_I2_J) ).

fof(fact_add__special_I3_J,axiom,
    ! [V_v,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),c_Groups_Oone__class_Oone(T_a)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),c_Int_OBit1(c_Int_OPls))) ),
    file('theBenchmark.p',fact_add__special_I3_J) ).

fof(fact_nat__less__iff,axiom,
    ! [V_m_2,V_w_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),V_m_2))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2))) ) ),
    file('theBenchmark.p',fact_nat__less__iff) ).

fof(fact_Suc__diff__eq__diff__pred,axiom,
    ! [V_m,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls)),V_n))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)))) ),
    file('theBenchmark.p',fact_Suc__diff__eq__diff__pred) ).

fof(fact_zdiff__int__split,axiom,
    ! [V_y_2,V_x_2,V_P_2] :
      ( hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_y_2))))
    <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
         => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),V_x_2))
         => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2)))) ) ) ),
    file('theBenchmark.p',fact_zdiff__int__split) ).

fof(fact_of__nat__number__of__eq,axiom,
    ! [V_v,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
         => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v) )
        & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
         => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
    file('theBenchmark.p',fact_of__nat__number__of__eq) ).

fof(fact_image__atLeastZeroLessThan__int,axiom,
    ! [V_u_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2))
     => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Int_Onat,V_u_2))) ),
    file('theBenchmark.p',fact_image__atLeastZeroLessThan__int) ).

fof(fact_diff__special_I1_J,axiom,
    ! [V_w,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w))) ),
    file('theBenchmark.p',fact_diff__special_I1_J) ).

fof(fact_diff__special_I2_J,axiom,
    ! [V_v,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),c_Groups_Oone__class_Oone(T_a)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))) ),
    file('theBenchmark.p',fact_diff__special_I2_J) ).

fof(fact_pos__zdiv__mult__2,axiom,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b),V_a) ),
    file('theBenchmark.p',fact_pos__zdiv__mult__2) ).

fof(fact_neg__zdiv__mult__2,axiom,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_b),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_a) ),
    file('theBenchmark.p',fact_neg__zdiv__mult__2) ).

fof(fact_of__nat__double,axiom,
    ! [V_x,T_a] :
      ( class_Rings_Osemiring__1(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
       => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,V_x))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,V_x))) ) ),
    file('theBenchmark.p',fact_of__nat__double) ).

fof(fact_Suc__n__div__2__gt__zero,axiom,
    ! [V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ),
    file('theBenchmark.p',fact_Suc__n__div__2__gt__zero) ).

fof(fact_power__minus1__odd,axiom,
    ! [V_n,T_a] :
      ( class_Rings_Oring__1(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ),
    file('theBenchmark.p',fact_power__minus1__odd) ).

fof(fact_rel__simps_I49_J,axiom,
    ! [V_l,V_k] : c_Int_OBit0(V_k) != c_Int_OBit1(V_l),
    file('theBenchmark.p',fact_rel__simps_I49_J) ).

fof(fact_rel__simps_I50_J,axiom,
    ! [V_l,V_k] : c_Int_OBit1(V_k) != c_Int_OBit0(V_l),
    file('theBenchmark.p',fact_rel__simps_I50_J) ).

fof(fact_int__int__eq,axiom,
    ! [V_n_2,V_m_2] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)
    <=> V_m_2 = V_n_2 ),
    file('theBenchmark.p',fact_int__int__eq) ).

fof(fact_transfer__nat__int__set__relations_I4_J,axiom,
    ! [V_B_2,V_A_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2))) ),
    file('theBenchmark.p',fact_transfer__nat__int__set__relations_I4_J) ).

fof(fact_transfer__int__nat__relations_I1_J,axiom,
    ! [V_y_2,V_x_2] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2)
    <=> V_x_2 = V_y_2 ),
    file('theBenchmark.p',fact_transfer__int__nat__relations_I1_J) ).

fof(fact_transfer__nat__int__set__relations_I3_J,axiom,
    ! [V_B_2,V_A_2] :
      ( V_A_2 = V_B_2
    <=> hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2) ),
    file('theBenchmark.p',fact_transfer__nat__int__set__relations_I3_J) ).

fof(fact_Bit0__Pls,axiom,
    c_Int_OBit0(c_Int_OPls) = c_Int_OPls,
    file('theBenchmark.p',fact_Bit0__Pls) ).

fof(fact_rel__simps_I38_J,axiom,
    ! [V_l_2] :
      ( c_Int_OPls = c_Int_OBit0(V_l_2)
    <=> c_Int_OPls = V_l_2 ),
    file('theBenchmark.p',fact_rel__simps_I38_J) ).

fof(fact_rel__simps_I44_J,axiom,
    ! [V_k_2] :
      ( c_Int_OBit0(V_k_2) = c_Int_OPls
    <=> V_k_2 = c_Int_OPls ),
    file('theBenchmark.p',fact_rel__simps_I44_J) ).

fof(fact_Bit0__def,axiom,
    ! [V_k] : c_Int_OBit0(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_k),
    file('theBenchmark.p',fact_Bit0__def) ).

fof(fact_add__Bit0__Bit0,axiom,
    ! [V_l,V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(V_k)),c_Int_OBit0(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_l)),
    file('theBenchmark.p',fact_add__Bit0__Bit0) ).

fof(fact_rel__simps_I31_J,axiom,
    ! [V_l_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ),
    file('theBenchmark.p',fact_rel__simps_I31_J) ).

fof(fact_less__eq__int__code_I13_J,axiom,
    ! [V_k2_2,V_k1_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ),
    file('theBenchmark.p',fact_less__eq__int__code_I13_J) ).

fof(fact_less__int__code_I13_J,axiom,
    ! [V_k2_2,V_k1_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ),
    file('theBenchmark.p',fact_less__int__code_I13_J) ).

fof(fact_rel__simps_I14_J,axiom,
    ! [V_l_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ),
    file('theBenchmark.p',fact_rel__simps_I14_J) ).

fof(fact_rel__simps_I48_J,axiom,
    ! [V_l_2,V_k_2] :
      ( c_Int_OBit0(V_k_2) = c_Int_OBit0(V_l_2)
    <=> V_k_2 = V_l_2 ),
    file('theBenchmark.p',fact_rel__simps_I48_J) ).

fof(fact_minus__Bit0,axiom,
    ! [V_k] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit0(V_k)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k)),
    file('theBenchmark.p',fact_minus__Bit0) ).

fof(fact_diff__bin__simps_I7_J,axiom,
    ! [V_l,V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(V_k)),c_Int_OBit0(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),V_l)),
    file('theBenchmark.p',fact_diff__bin__simps_I7_J) ).

fof(fact_mult__Bit0,axiom,
    ! [V_l,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit0(V_k)),V_l) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_l)),
    file('theBenchmark.p',fact_mult__Bit0) ).

fof(fact_bin__less__0__simps_I3_J,axiom,
    ! [V_w_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_w_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    file('theBenchmark.p',fact_bin__less__0__simps_I3_J) ).

fof(fact_rel__simps_I21_J,axiom,
    ! [V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ),
    file('theBenchmark.p',fact_rel__simps_I21_J) ).

fof(fact_rel__simps_I27_J,axiom,
    ! [V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OPls)) ),
    file('theBenchmark.p',fact_rel__simps_I27_J) ).

fof(fact_rel__simps_I32_J,axiom,
    ! [V_l_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ),
    file('theBenchmark.p',fact_rel__simps_I32_J) ).

fof(fact_less__eq__int__code_I14_J,axiom,
    ! [V_k2_2,V_k1_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ),
    file('theBenchmark.p',fact_less__eq__int__code_I14_J) ).

fof(fact_rel__simps_I10_J,axiom,
    ! [V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ),
    file('theBenchmark.p',fact_rel__simps_I10_J) ).

fof(fact_rel__simps_I4_J,axiom,
    ! [V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_k_2)) ),
    file('theBenchmark.p',fact_rel__simps_I4_J) ).

fof(fact_less__int__code_I15_J,axiom,
    ! [V_k2_2,V_k1_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ),
    file('theBenchmark.p',fact_less__int__code_I15_J) ).

fof(fact_rel__simps_I16_J,axiom,
    ! [V_l_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ),
    file('theBenchmark.p',fact_rel__simps_I16_J) ).

fof(fact_add__Bit0__Bit1,axiom,
    ! [V_l,V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(V_k)),c_Int_OBit1(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_l)),
    file('theBenchmark.p',fact_add__Bit0__Bit1) ).

fof(fact_add__Bit1__Bit0,axiom,
    ! [V_l,V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(V_k)),c_Int_OBit0(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_l)),
    file('theBenchmark.p',fact_add__Bit1__Bit0) ).

fof(fact_diff__bin__simps_I3_J,axiom,
    ! [V_l] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),V_l)),
    file('theBenchmark.p',fact_diff__bin__simps_I3_J) ).

fof(fact_diff__bin__simps_I9_J,axiom,
    ! [V_l,V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(V_k)),c_Int_OBit0(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),V_l)),
    file('theBenchmark.p',fact_diff__bin__simps_I9_J) ).

fof(fact_diff__bin__simps_I10_J,axiom,
    ! [V_l,V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(V_k)),c_Int_OBit1(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),V_l)),
    file('theBenchmark.p',fact_diff__bin__simps_I10_J) ).

fof(fact_zdiv__number__of__Bit0,axiom,
    ! [V_w,V_v] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_v))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),
    file('theBenchmark.p',fact_zdiv__number__of__Bit0) ).

fof(fact_neg__number__of__Bit0,axiom,
    ! [V_w_2] :
      ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w_2))))
    <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ),
    file('theBenchmark.p',fact_neg__number__of__Bit0) ).

fof(fact_pred__Bit1,axiom,
    ! [V_k] : c_Int_Opred(c_Int_OBit1(V_k)) = c_Int_OBit0(V_k),
    file('theBenchmark.p',fact_pred__Bit1) ).

fof(fact_pred__Bit0,axiom,
    ! [V_k] : c_Int_Opred(c_Int_OBit0(V_k)) = c_Int_OBit1(c_Int_Opred(V_k)),
    file('theBenchmark.p',fact_pred__Bit0) ).

fof(fact_iszero__number__of__Bit0,axiom,
    ! [V_w_2,T_b] :
      ( ( class_Int_Oring__char__0(T_b)
        & class_Int_Onumber__ring(T_b) )
     => ( c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),c_Int_OBit0(V_w_2)))
      <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) ) ),
    file('theBenchmark.p',fact_iszero__number__of__Bit0) ).

fof(fact_succ__Bit0,axiom,
    ! [V_k] : c_Int_Osucc(c_Int_OBit0(V_k)) = c_Int_OBit1(V_k),
    file('theBenchmark.p',fact_succ__Bit0) ).

fof(fact_succ__Bit1,axiom,
    ! [V_k] : c_Int_Osucc(c_Int_OBit1(V_k)) = c_Int_OBit0(c_Int_Osucc(V_k)),
    file('theBenchmark.p',fact_succ__Bit1) ).

fof(fact_number__of__Bit0,axiom,
    ! [V_w,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ),
    file('theBenchmark.p',fact_number__of__Bit0) ).

fof(fact_less__eq__int__code_I15_J,axiom,
    ! [V_k2_2,V_k1_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ),
    file('theBenchmark.p',fact_less__eq__int__code_I15_J) ).

fof(fact_rel__simps_I33_J,axiom,
    ! [V_l_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ),
    file('theBenchmark.p',fact_rel__simps_I33_J) ).

fof(fact_less__int__code_I14_J,axiom,
    ! [V_k2_2,V_k1_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ),
    file('theBenchmark.p',fact_less__int__code_I14_J) ).

fof(fact_rel__simps_I15_J,axiom,
    ! [V_l_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ),
    file('theBenchmark.p',fact_rel__simps_I15_J) ).

fof(fact_card__UNIV__bool,axiom,
    hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
    file('theBenchmark.p',fact_card__UNIV__bool) ).

fof(fact_mult__Bit1,axiom,
    ! [V_l,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit1(V_k)),V_l) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_l))),V_l),
    file('theBenchmark.p',fact_mult__Bit1) ).

fof(fact_diff__bin__simps_I8_J,axiom,
    ! [V_l,V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(V_k)),c_Int_OBit1(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_Opred(V_k)),V_l)),
    file('theBenchmark.p',fact_diff__bin__simps_I8_J) ).

fof(fact_add__Bit1__Bit1,axiom,
    ! [V_l,V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(V_k)),c_Int_OBit1(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_Osucc(V_l))),
    file('theBenchmark.p',fact_add__Bit1__Bit1) ).

fof(fact_double__number__of__Bit0,axiom,
    ! [V_w,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a))),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(V_w)) ),
    file('theBenchmark.p',fact_double__number__of__Bit0) ).

fof(fact_number__of1,axiom,
    ! [V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_n))))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_n)))) ) ),
    file('theBenchmark.p',fact_number__of1) ).

fof(fact_transfer__int__nat__numerals_I3_J,axiom,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
    file('theBenchmark.p',fact_transfer__int__nat__numerals_I3_J) ).

fof(fact_mult__2__right,axiom,
    ! [V_z,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_z),V_z) ),
    file('theBenchmark.p',fact_mult__2__right) ).

fof(fact_mult__2,axiom,
    ! [V_z,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_z) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_z),V_z) ),
    file('theBenchmark.p',fact_mult__2) ).

fof(fact_one__add__one__is__two,axiom,
    ! [T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ),
    file('theBenchmark.p',fact_one__add__one__is__two) ).

fof(fact_zero__eq__power2,axiom,
    ! [V_a_2,T_b] :
      ( class_Rings_Oring__1__no__zero__divisors(T_b)
     => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(T_b)
      <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ),
    file('theBenchmark.p',fact_zero__eq__power2) ).

fof(fact_zero__power2,axiom,
    ! [T_a] :
      ( class_Rings_Osemiring__1(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_zero__power2) ).

fof(fact_semiring__norm_I115_J,axiom,
    hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
    file('theBenchmark.p',fact_semiring__norm_I115_J) ).

fof(fact_numeral__2__eq__2,axiom,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('theBenchmark.p',fact_numeral__2__eq__2) ).

fof(fact_power2__eq__square,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Omonoid__mult(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ),
    file('theBenchmark.p',fact_power2__eq__square) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
    ! [V_x,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J,axiom,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J) ).

fof(fact_add__2__eq__Suc,axiom,
    ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n)),
    file('theBenchmark.p',fact_add__2__eq__Suc) ).

fof(fact_add__2__eq__Suc_H,axiom,
    ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n)),
    file('theBenchmark.p',fact_add__2__eq__Suc_H) ).

fof(fact_one__power2,axiom,
    ! [T_a] :
      ( class_Rings_Osemiring__1(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(T_a) ),
    file('theBenchmark.p',fact_one__power2) ).

fof(fact_power2__minus,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Oring__1(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
    file('theBenchmark.p',fact_power2__minus) ).

fof(fact_nat__mult__2__right,axiom,
    ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_z),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_z),V_z),
    file('theBenchmark.p',fact_nat__mult__2__right) ).

fof(fact_nat__mult__2,axiom,
    ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_z) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_z),V_z),
    file('theBenchmark.p',fact_nat__mult__2) ).

fof(fact_power__even__eq,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Groups_Omonoid__mult(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
    file('theBenchmark.p',fact_power__even__eq) ).

fof(fact_transfer__nat__int__numerals_I3_J,axiom,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
    file('theBenchmark.p',fact_transfer__nat__int__numerals_I3_J) ).

fof(fact_nat__1__add__1,axiom,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
    file('theBenchmark.p',fact_nat__1__add__1) ).

fof(fact_div2__Suc__Suc,axiom,
    ! [V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
    file('theBenchmark.p',fact_div2__Suc__Suc) ).

fof(fact_add__self__div__2,axiom,
    ! [V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = V_m,
    file('theBenchmark.p',fact_add__self__div__2) ).

fof(fact_half__gt__zero__iff,axiom,
    ! [V_r_2,T_b] :
      ( ( class_Int_Onumber__ring(T_b)
        & class_Fields_Olinordered__field__inverse__zero(T_b) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_r_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_r_2)) ) ),
    file('theBenchmark.p',fact_half__gt__zero__iff) ).

fof(fact_half__gt__zero,axiom,
    ! [V_r,T_a] :
      ( ( class_Int_Onumber__ring(T_a)
        & class_Fields_Olinordered__field__inverse__zero(T_a) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_r))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_r),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ),
    file('theBenchmark.p',fact_half__gt__zero) ).

fof(fact_zero__le__power2,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ),
    file('theBenchmark.p',fact_zero__le__power2) ).

fof(fact_power2__le__imp__le,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ),
    file('theBenchmark.p',fact_power2__le__imp__le) ).

fof(fact_power2__eq__imp__eq,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
           => V_x = V_y ) ) ) ),
    file('theBenchmark.p',fact_power2__eq__imp__eq) ).

fof(fact_zero__less__power2,axiom,
    ! [V_a_2,T_b] :
      ( class_Rings_Olinordered__idom(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
      <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_b) ) ),
    file('theBenchmark.p',fact_zero__less__power2) ).

fof(fact_power2__less__0,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(T_a))) ),
    file('theBenchmark.p',fact_power2__less__0) ).

fof(fact_sum__power2__eq__zero__iff,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Rings_Olinordered__idom(T_b)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(T_b)
      <=> ( V_y_2 = c_Groups_Ozero__class_Ozero(T_b)
          & V_x_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ),
    file('theBenchmark.p',fact_sum__power2__eq__zero__iff) ).

fof(fact_power2__eq__square__number__of,axiom,
    ! [V_w,T_b] :
      ( ( class_Int_Onumber(T_b)
        & class_Groups_Omonoid__mult(T_b) )
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w)) ),
    file('theBenchmark.p',fact_power2__eq__square__number__of) ).

fof(fact_less__2__cases,axiom,
    ! [V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
     => ( V_n = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_less__2__cases) ).

fof(fact_nat__2,axiom,
    hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('theBenchmark.p',fact_nat__2) ).

fof(fact_power2__eq__1__iff,axiom,
    ! [V_a_2,T_b] :
      ( class_Rings_Oring__1__no__zero__divisors(T_b)
     => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(T_b)
      <=> ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b))
          | V_a_2 = c_Groups_Oone__class_Oone(T_b) ) ) ),
    file('theBenchmark.p',fact_power2__eq__1__iff) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom,
    ! [V_n,V_x,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) ).

fof(fact_power__minus__even,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Rings_Oring__1(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) ),
    file('theBenchmark.p',fact_power__minus__even) ).

fof(fact_power2__less__imp__less,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ),
    file('theBenchmark.p',fact_power2__less__imp__less) ).

fof(fact_sum__power2__le__zero__iff,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Rings_Olinordered__idom(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(T_b)))
      <=> ( V_y_2 = c_Groups_Ozero__class_Ozero(T_b)
          & V_x_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ),
    file('theBenchmark.p',fact_sum__power2__le__zero__iff) ).

fof(fact_sum__power2__ge__zero,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) ),
    file('theBenchmark.p',fact_sum__power2__ge__zero) ).

fof(fact_sum__power2__gt__zero__iff,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Rings_Olinordered__idom(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
      <=> ( V_y_2 != c_Groups_Ozero__class_Ozero(T_b)
          | V_x_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ),
    file('theBenchmark.p',fact_sum__power2__gt__zero__iff) ).

fof(fact_not__sum__power2__lt__zero,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(T_a))) ),
    file('theBenchmark.p',fact_not__sum__power2__lt__zero) ).

fof(fact_power2__sum,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x)),V_y)) ),
    file('theBenchmark.p',fact_power2__sum) ).

fof(fact_zero__le__even__power_H,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)))) ),
    file('theBenchmark.p',fact_zero__le__even__power_H) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J,axiom,
    ! [V_n,V_x,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n))) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J) ).

fof(fact_power__odd__eq,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Groups_Omonoid__mult(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
    file('theBenchmark.p',fact_power__odd__eq) ).

fof(fact_power__minus1__even,axiom,
    ! [V_n,T_a] :
      ( class_Rings_Oring__1(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = c_Groups_Oone__class_Oone(T_a) ),
    file('theBenchmark.p',fact_power__minus1__even) ).

fof(fact_zdiv__number__of__Bit1,axiom,
    ! [V_v,V_w] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_v))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_v))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) ) ),
    file('theBenchmark.p',fact_zdiv__number__of__Bit1) ).

fof(fact_div__2__gt__zero,axiom,
    ! [V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ),
    file('theBenchmark.p',fact_div__2__gt__zero) ).

fof(fact_power2__diff,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_y)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x)),V_y)) ),
    file('theBenchmark.p',fact_power2__diff) ).

fof(fact_odd__0__le__power__imp__0__le,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)))))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) ) ),
    file('theBenchmark.p',fact_odd__0__le__power__imp__0__le) ).

fof(fact_odd__power__less__zero,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)))),c_Groups_Ozero__class_Ozero(T_a))) ) ),
    file('theBenchmark.p',fact_odd__power__less__zero) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J,axiom,
    ! [V_B_2,V_A_2] :
      ( c_Nat__Transfer_Onat__set(V_A_2)
     => ( c_Nat__Transfer_Onat__set(V_B_2)
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2))) ) ),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J,axiom,
    ! [V_B_2,V_A_2] :
      ( c_Nat__Transfer_Onat__set(V_A_2)
     => ( c_Nat__Transfer_Onat__set(V_B_2)
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2))) ) ),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J) ).

fof(fact_zmod__number__of__Bit1,axiom,
    ! [V_v,V_w] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ),
    file('theBenchmark.p',fact_zmod__number__of__Bit1) ).

fof(fact_neg__zmod__mult__2,axiom,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_b),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_a))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
    file('theBenchmark.p',fact_neg__zmod__mult__2) ).

fof(fact_pos__zmod__mult__2,axiom,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
     => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_a))) ),
    file('theBenchmark.p',fact_pos__zmod__mult__2) ).

fof(fact_zmod__simps_I3_J,axiom,
    ! [V_c,V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c)),V_c) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b),V_c),
    file('theBenchmark.p',fact_zmod__simps_I3_J) ).

fof(fact_zmod__zmult1__eq,axiom,
    ! [V_c,V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c)),V_c),
    file('theBenchmark.p',fact_zmod__zmult1__eq) ).

fof(fact_zdiff__zmod__left,axiom,
    ! [V_y,V_m,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_m)),V_y),V_m) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y),V_m),
    file('theBenchmark.p',fact_zdiff__zmod__left) ).

fof(fact_zdiff__zmod__right,axiom,
    ! [V_m,V_y,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_y,V_m)),V_m) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y),V_m),
    file('theBenchmark.p',fact_zdiff__zmod__right) ).

fof(fact_zminus__zmod,axiom,
    ! [V_m,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_m)),V_m) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_x),V_m),
    file('theBenchmark.p',fact_zminus__zmod) ).

fof(fact_zmod__zminus__zminus,axiom,
    ! [V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),
    file('theBenchmark.p',fact_zmod__zminus__zminus) ).

fof(fact_zmod__zminus2,axiom,
    ! [V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),V_b)),
    file('theBenchmark.p',fact_zmod__zminus2) ).

fof(fact_mod__diff__cong,axiom,
    ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
      ( class_Divides_Oring__div(T_a)
     => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
       => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
         => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_H),V_b_H),V_c) ) ) ),
    file('theBenchmark.p',fact_mod__diff__cong) ).

fof(fact_mod__diff__eq,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Divides_Oring__div(T_a)
     => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ),
    file('theBenchmark.p',fact_mod__diff__eq) ).

fof(fact_mod__diff__left__eq,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Divides_Oring__div(T_a)
     => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) ),
    file('theBenchmark.p',fact_mod__diff__left__eq) ).

fof(fact_mod__diff__right__eq,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Divides_Oring__div(T_a)
     => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ),
    file('theBenchmark.p',fact_mod__diff__right__eq) ).

fof(fact_mod__add__cong,axiom,
    ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
       => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
         => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_H),V_b_H),V_c) ) ) ),
    file('theBenchmark.p',fact_mod__add__cong) ).

fof(fact_zmod__simps_I1_J,axiom,
    ! [V_b,V_c,V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) ),
    file('theBenchmark.p',fact_zmod__simps_I1_J) ).

fof(fact_zmod__simps_I2_J,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) ),
    file('theBenchmark.p',fact_zmod__simps_I2_J) ).

fof(fact_mod__add__eq,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ),
    file('theBenchmark.p',fact_mod__add__eq) ).

fof(fact_mod__add__left__eq,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) ),
    file('theBenchmark.p',fact_mod__add__left__eq) ).

fof(fact_mod__add__right__eq,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ),
    file('theBenchmark.p',fact_mod__add__right__eq) ).

fof(fact_mod__add__self1,axiom,
    ! [V_a,V_b,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ),
    file('theBenchmark.p',fact_mod__add__self1) ).

fof(fact_mod__add__self2,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ),
    file('theBenchmark.p',fact_mod__add__self2) ).

fof(fact_mod__minus__eq,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Divides_Oring__div(T_a)
     => c_Divides_Odiv__class_Omod(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a),V_b) = c_Divides_Odiv__class_Omod(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_b) ),
    file('theBenchmark.p',fact_mod__minus__eq) ).

fof(fact_mod__minus__cong,axiom,
    ! [V_a_H,V_b,V_a,T_a] :
      ( class_Divides_Oring__div(T_a)
     => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_b) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_b)
       => c_Divides_Odiv__class_Omod(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a),V_b) = c_Divides_Odiv__class_Omod(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_H),V_b) ) ),
    file('theBenchmark.p',fact_mod__minus__cong) ).

fof(fact_zmod__self,axiom,
    ! [V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_a) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    file('theBenchmark.p',fact_zmod__self) ).

fof(fact_mod__self,axiom,
    ! [V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => c_Divides_Odiv__class_Omod(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_mod__self) ).

fof(fact_mod__by__0,axiom,
    ! [V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ),
    file('theBenchmark.p',fact_mod__by__0) ).

fof(fact_zmod__zero,axiom,
    ! [V_b] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    file('theBenchmark.p',fact_zmod__zero) ).

fof(fact_mod__0,axiom,
    ! [V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => c_Divides_Odiv__class_Omod(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_mod__0) ).

fof(fact_mod__mod__trivial,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => c_Divides_Odiv__class_Omod(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ),
    file('theBenchmark.p',fact_mod__mod__trivial) ).

fof(fact_mod__mult__cong,axiom,
    ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
       => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
         => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_H),V_b_H),V_c) ) ) ),
    file('theBenchmark.p',fact_mod__mult__cong) ).

fof(fact_zmod__simps_I4_J,axiom,
    ! [V_b,V_c,V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) ),
    file('theBenchmark.p',fact_zmod__simps_I4_J) ).

fof(fact_mod__mult__mult2,axiom,
    ! [V_b,V_c,V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_c) ),
    file('theBenchmark.p',fact_mod__mult__mult2) ).

fof(fact_mod__mult__mult1,axiom,
    ! [V_b,V_a,V_c,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) ),
    file('theBenchmark.p',fact_mod__mult__mult1) ).

fof(fact_mod__mult__eq,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ),
    file('theBenchmark.p',fact_mod__mult__eq) ).

fof(fact_mod__mult__left__eq,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) ),
    file('theBenchmark.p',fact_mod__mult__left__eq) ).

fof(fact_mod__mult__right__eq,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ),
    file('theBenchmark.p',fact_mod__mult__right__eq) ).

fof(fact_zpower__zmod,axiom,
    ! [V_y,V_m,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_m)),V_y),V_m) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y),V_m),
    file('theBenchmark.p',fact_zpower__zmod) ).

fof(fact_mod__mult__self1__is__0,axiom,
    ! [V_a,V_b,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_mod__mult__self1__is__0) ).

fof(fact_mod__mult__self2__is__0,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_b) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_mod__mult__self2__is__0) ).

fof(fact_mod__mult__self1,axiom,
    ! [V_b,V_c,V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ),
    file('theBenchmark.p',fact_mod__mult__self1) ).

fof(fact_mod__mult__self2,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ),
    file('theBenchmark.p',fact_mod__mult__self2) ).

fof(fact_mod__by__1,axiom,
    ! [V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_mod__by__1) ).

fof(fact_mod__div__trivial,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_b) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_mod__div__trivial) ).

fof(fact_Divides_Otransfer__nat__int__function__closures_I2_J,axiom,
    ! [V_y,V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y))) ) ),
    file('theBenchmark.p',fact_Divides_Otransfer__nat__int__function__closures_I2_J) ).

fof(fact_zmod__le__nonneg__dividend,axiom,
    ! [V_k,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_k)),V_m)) ),
    file('theBenchmark.p',fact_zmod__le__nonneg__dividend) ).

fof(fact_pos__mod__bound,axiom,
    ! [V_a,V_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_b)) ),
    file('theBenchmark.p',fact_pos__mod__bound) ).

fof(fact_neg__mod__bound,axiom,
    ! [V_a,V_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))) ),
    file('theBenchmark.p',fact_neg__mod__bound) ).

fof(fact_zmod__eq__0__iff,axiom,
    ! [V_d_2,V_m_2] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_d_2),B_q) ),
    file('theBenchmark.p',fact_zmod__eq__0__iff) ).

fof(fact_zmod__zminus1__not__zero,axiom,
    ! [V_l,V_k] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k),V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
     => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    file('theBenchmark.p',fact_zmod__zminus1__not__zero) ).

fof(fact_zmod__zminus2__not__zero,axiom,
    ! [V_l,V_k] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_l)) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
     => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    file('theBenchmark.p',fact_zmod__zminus2__not__zero) ).

fof(fact_zmod__zdiv__trivial,axiom,
    ! [V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    file('theBenchmark.p',fact_zmod__zdiv__trivial) ).

fof(fact_DIVISION__BY__ZERO,axiom,
    ! [V_a] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_a
      & hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    file('theBenchmark.p',fact_DIVISION__BY__ZERO) ).

fof(fact_zdiv__zadd1__eq,axiom,
    ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_c)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b),V_c))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_c)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c))),V_c)),
    file('theBenchmark.p',fact_zdiv__zadd1__eq) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J,axiom,
    c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J,axiom,
    ! [V_B_2,V_A_2] :
      ( c_Nat__Transfer_Onat__set(V_A_2)
     => ( c_Nat__Transfer_Onat__set(V_B_2)
       => c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J,axiom,
    ! [V_B_2,V_A_2] :
      ( c_Nat__Transfer_Onat__set(V_A_2)
     => ( c_Nat__Transfer_Onat__set(V_B_2)
       => c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J) ).

fof(fact_nat__set__def,axiom,
    ! [V_S_2] :
      ( c_Nat__Transfer_Onat__set(V_S_2)
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),V_S_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) ),
    file('theBenchmark.p',fact_nat__set__def) ).

fof(fact_semiring__div__class_Omod__div__equality_H,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),V_b)) = V_a ),
    file('theBenchmark.p',fact_semiring__div__class_Omod__div__equality_H) ).

fof(fact_mod__div__equality2,axiom,
    ! [V_a,V_b,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b))),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) = V_a ),
    file('theBenchmark.p',fact_mod__div__equality2) ).

fof(fact_mod__div__equality,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),V_b)),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) = V_a ),
    file('theBenchmark.p',fact_mod__div__equality) ).

fof(fact_div__mod__equality2,axiom,
    ! [V_c,V_a,V_b,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b))),c_Divides_Odiv__class_Omod(T_a,V_a,V_b))),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c) ),
    file('theBenchmark.p',fact_div__mod__equality2) ).

fof(fact_div__mod__equality,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),V_b)),c_Divides_Odiv__class_Omod(T_a,V_a,V_b))),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c) ),
    file('theBenchmark.p',fact_div__mod__equality) ).

fof(fact_pos__mod__sign,axiom,
    ! [V_a,V_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))) ),
    file('theBenchmark.p',fact_pos__mod__sign) ).

fof(fact_pos__mod__conj,axiom,
    ! [V_a,V_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_b))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))) ) ),
    file('theBenchmark.p',fact_pos__mod__conj) ).

fof(fact_mod__pos__pos__trivial,axiom,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ),
    file('theBenchmark.p',fact_mod__pos__pos__trivial) ).

fof(fact_neg__mod__sign,axiom,
    ! [V_a,V_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    file('theBenchmark.p',fact_neg__mod__sign) ).

fof(fact_neg__mod__conj,axiom,
    ! [V_a,V_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    file('theBenchmark.p',fact_neg__mod__conj) ).

fof(fact_mod__neg__neg__trivial,axiom,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a))
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ),
    file('theBenchmark.p',fact_mod__neg__neg__trivial) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J,axiom,
    ! [V_C_2] : c_Nat__Transfer_Onat__set(hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_C_2)),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J) ).

fof(fact_transfer__int__nat__set__relations_I4_J,axiom,
    ! [V_B_2,V_A_2] :
      ( c_Nat__Transfer_Onat__set(V_A_2)
     => ( c_Nat__Transfer_Onat__set(V_B_2)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2))) ) ) ),
    file('theBenchmark.p',fact_transfer__int__nat__set__relations_I4_J) ).

fof(fact_transfer__int__nat__set__relations_I3_J,axiom,
    ! [V_B_2,V_A_2] :
      ( c_Nat__Transfer_Onat__set(V_A_2)
     => ( c_Nat__Transfer_Onat__set(V_B_2)
       => ( V_A_2 = V_B_2
        <=> hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2) ) ) ),
    file('theBenchmark.p',fact_transfer__int__nat__set__relations_I3_J) ).

fof(fact_zmod__zminus2__eq__if,axiom,
    ! [V_b,V_a] :
      ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_b) )
      & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    file('theBenchmark.p',fact_zmod__zminus2__eq__if) ).

fof(fact_zmod__zminus1__eq__if,axiom,
    ! [V_b,V_a] :
      ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),V_b) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)) )
      & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    file('theBenchmark.p',fact_zmod__zminus1__eq__if) ).

fof(fact_zmod__zdiv__equality,axiom,
    ! [V_b,V_a] : V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),
    file('theBenchmark.p',fact_zmod__zdiv__equality) ).

fof(fact_zdiv__zmult1__eq,axiom,
    ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b),V_c))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c))),V_c)),
    file('theBenchmark.p',fact_zdiv__zmult1__eq) ).

fof(fact_zdiv__zmod__equality,axiom,
    ! [V_k,V_a,V_b] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_k),
    file('theBenchmark.p',fact_zdiv__zmod__equality) ).

fof(fact_zdiv__zmod__equality2,axiom,
    ! [V_k,V_b,V_a] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),V_b)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_k),
    file('theBenchmark.p',fact_zdiv__zmod__equality2) ).

fof(fact_zmult__div__cancel,axiom,
    ! [V_m,V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_n),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_m),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_m),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n)),
    file('theBenchmark.p',fact_zmult__div__cancel) ).

fof(fact_zmod__zdiv__equality_H,axiom,
    ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_m),V_n)),V_n)),
    file('theBenchmark.p',fact_zmod__zdiv__equality_H) ).

fof(fact_mod__pos__neg__trivial,axiom,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b) ) ),
    file('theBenchmark.p',fact_mod__pos__neg__trivial) ).

fof(fact_SetInterval_Otransfer__nat__int__set__function__closures,axiom,
    ! [V_y_2,V_x_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
     => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ),
    file('theBenchmark.p',fact_SetInterval_Otransfer__nat__int__set__function__closures) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J,axiom,
    ! [V_x_2,V_A_2] :
      ( c_Nat__Transfer_Onat__set(V_A_2)
     => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J) ).

fof(fact_split__zmod,axiom,
    ! [V_k_2,V_n_2,V_P_2] :
      ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
    <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => ! [B_i,B_j] :
              ( ( V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) )
             => hBOOL(hAPP(V_P_2,B_j)) ) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
         => ! [B_i,B_j] :
              ( ( V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) )
             => hBOOL(hAPP(V_P_2,B_j)) ) )
        & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hBOOL(hAPP(V_P_2,V_n_2)) ) ) ),
    file('theBenchmark.p',fact_split__zmod) ).

fof(fact_zmult2__lemma__aux3,axiom,
    ! [V_q,V_b,V_r,V_c] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r))) ) ) ),
    file('theBenchmark.p',fact_zmult2__lemma__aux3) ).

fof(fact_zmult2__lemma__aux4,axiom,
    ! [V_q,V_b,V_r,V_c] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c))) ) ) ),
    file('theBenchmark.p',fact_zmult2__lemma__aux4) ).

fof(fact_zmult2__lemma__aux1,axiom,
    ! [V_q,V_r,V_b,V_c] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r))) ) ) ),
    file('theBenchmark.p',fact_zmult2__lemma__aux1) ).

fof(fact_zmult2__lemma__aux2,axiom,
    ! [V_q,V_r,V_b,V_c] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ),
    file('theBenchmark.p',fact_zmult2__lemma__aux2) ).

fof(fact_divmod__int__rel__mod__eq,axiom,
    ! [V_y,V_q_1,V_b_1,V_a_1] :
      ( V_a_1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_1),V_q_1)),V_y)
     => ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_y)) ) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_b_1))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) ) ) )
       => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a_1,V_b_1) = V_y ) ) ),
    file('theBenchmark.p',fact_divmod__int__rel__mod__eq) ).

fof(fact_zmod__number__of__Bit0,axiom,
    ! [V_w,V_v] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))),
    file('theBenchmark.p',fact_zmod__number__of__Bit0) ).

fof(fact_zmod__zmult2__eq,axiom,
    ! [V_b,V_a,V_c] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
     => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b),V_c))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)) ),
    file('theBenchmark.p',fact_zmod__zmult2__eq) ).

fof(fact_zdiv__zminus1__eq__if,axiom,
    ! [V_a,V_b] :
      ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
     => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a)),V_b) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
        & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a)),V_b) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)) ) ) ),
    file('theBenchmark.p',fact_zdiv__zminus1__eq__if) ).

fof(fact_zdiv__zminus2__eq__if,axiom,
    ! [V_a,V_b] :
      ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
     => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
        & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)) ) ) ),
    file('theBenchmark.p',fact_zdiv__zminus2__eq__if) ).

fof(fact_transfer__nat__int__set__return__embed,axiom,
    ! [V_A_2] :
      ( c_Nat__Transfer_Onat__set(V_A_2)
     => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)) = V_A_2 ),
    file('theBenchmark.p',fact_transfer__nat__int__set__return__embed) ).

fof(fact_split__pos__lemma,axiom,
    ! [V_n_2,V_P_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
     => ( hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
      <=> ! [B_i,B_j] :
            ( ( V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) )
           => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) ),
    file('theBenchmark.p',fact_split__pos__lemma) ).

fof(fact_split__neg__lemma,axiom,
    ! [V_n_2,V_P_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
      <=> ! [B_i,B_j] :
            ( ( V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) )
           => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) ),
    file('theBenchmark.p',fact_split__neg__lemma) ).

fof(fact_transfer__int__nat__set__relations_I1_J,axiom,
    ! [V_A_2] :
      ( c_Nat__Transfer_Onat__set(V_A_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),V_A_2))
      <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2))) ) ),
    file('theBenchmark.p',fact_transfer__int__nat__set__relations_I1_J) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J,axiom,
    ! [V_A_2] :
      ( c_Nat__Transfer_Onat__set(V_A_2)
     => hAPP(c_Finite__Set_Ocard(tc_Int_Oint),V_A_2) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)) ),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J) ).

fof(fact_transfer__int__nat__set__relations_I5_J,axiom,
    ! [V_B_2,V_A_2] :
      ( c_Nat__Transfer_Onat__set(V_A_2)
     => ( c_Nat__Transfer_Onat__set(V_B_2)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2))) ) ) ),
    file('theBenchmark.p',fact_transfer__int__nat__set__relations_I5_J) ).

fof(fact_z3mod__def,axiom,
    ! [V_k,V_l] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
       => c_SMT_Oz3mod(V_k,V_l) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_l)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
       => c_SMT_Oz3mod(V_k,V_l) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) ) ),
    file('theBenchmark.p',fact_z3mod__def) ).

fof(fact_power__m1__odd,axiom,
    ! [V_n,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin) ),
    file('theBenchmark.p',fact_power__m1__odd) ).

fof(fact_power__m1__even,axiom,
    ! [V_n,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = c_Groups_Oone__class_Oone(T_a) ),
    file('theBenchmark.p',fact_power__m1__even) ).

fof(fact_one__mod__nat__number__of,axiom,
    ! [V_v_H] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
       => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
       => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    file('theBenchmark.p',fact_one__mod__nat__number__of) ).

fof(fact_mod__less__eq__dividend,axiom,
    ! [V_n,V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_m)),
    file('theBenchmark.p',fact_mod__less__eq__dividend) ).

fof(fact_rel__simps_I7_J,axiom,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),
    file('theBenchmark.p',fact_rel__simps_I7_J) ).

fof(fact_mod__less,axiom,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
     => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ),
    file('theBenchmark.p',fact_mod__less) ).

fof(fact_mod__Suc__eq__Suc__mod,axiom,
    ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_n),
    file('theBenchmark.p',fact_mod__Suc__eq__Suc__mod) ).

fof(fact_mod__mult__distrib,axiom,
    ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_k) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)),
    file('theBenchmark.p',fact_mod__mult__distrib) ).

fof(fact_mod__mult__distrib2,axiom,
    ! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)),
    file('theBenchmark.p',fact_mod__mult__distrib2) ).

fof(fact_Bit1__Min,axiom,
    c_Int_OBit1(c_Int_OMin) = c_Int_OMin,
    file('theBenchmark.p',fact_Bit1__Min) ).

fof(fact_rel__simps_I43_J,axiom,
    ! [V_l_2] :
      ( c_Int_OMin = c_Int_OBit1(V_l_2)
    <=> c_Int_OMin = V_l_2 ),
    file('theBenchmark.p',fact_rel__simps_I43_J) ).

fof(fact_rel__simps_I47_J,axiom,
    ! [V_k_2] :
      ( c_Int_OBit1(V_k_2) = c_Int_OMin
    <=> V_k_2 = c_Int_OMin ),
    file('theBenchmark.p',fact_rel__simps_I47_J) ).

fof(fact_rel__simps_I40_J,axiom,
    c_Int_OMin != c_Int_OPls,
    file('theBenchmark.p',fact_rel__simps_I40_J) ).

fof(fact_rel__simps_I37_J,axiom,
    c_Int_OPls != c_Int_OMin,
    file('theBenchmark.p',fact_rel__simps_I37_J) ).

fof(fact_rel__simps_I24_J,axiom,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),
    file('theBenchmark.p',fact_rel__simps_I24_J) ).

fof(fact_rel__simps_I42_J,axiom,
    ! [V_l] : c_Int_OMin != c_Int_OBit0(V_l),
    file('theBenchmark.p',fact_rel__simps_I42_J) ).

fof(fact_rel__simps_I45_J,axiom,
    ! [V_k] : c_Int_OBit0(V_k) != c_Int_OMin,
    file('theBenchmark.p',fact_rel__simps_I45_J) ).

fof(fact_mod__Suc,axiom,
    ! [V_n,V_m] :
      ( ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) != V_n
       => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) )
      & ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = V_n
       => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_mod__Suc) ).

fof(fact_mod__1,axiom,
    ! [V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_mod__1) ).

fof(fact_mod__less__divisor,axiom,
    ! [V_m,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_n)) ),
    file('theBenchmark.p',fact_mod__less__divisor) ).

fof(fact_mod__eq__0__iff,axiom,
    ! [V_d_2,V_m_2] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_d_2),B_q) ),
    file('theBenchmark.p',fact_mod__eq__0__iff) ).

fof(fact_mod__geq,axiom,
    ! [V_n,V_m] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
     => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_n) ),
    file('theBenchmark.p',fact_mod__geq) ).

fof(fact_mod__if,axiom,
    ! [V_n,V_m] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
       => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_n) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
       => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ) ),
    file('theBenchmark.p',fact_mod__if) ).

fof(fact_mod__mult__self3,axiom,
    ! [V_m,V_n,V_k] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)),V_m),V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n),
    file('theBenchmark.p',fact_mod__mult__self3) ).

fof(fact_le__mod__geq,axiom,
    ! [V_m,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
     => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_n) ),
    file('theBenchmark.p',fact_le__mod__geq) ).

fof(fact_bin__less__0__simps_I2_J,axiom,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    file('theBenchmark.p',fact_bin__less__0__simps_I2_J) ).

fof(fact_rel__simps_I23_J,axiom,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
    file('theBenchmark.p',fact_rel__simps_I23_J) ).

fof(fact_rel__simps_I20_J,axiom,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
    file('theBenchmark.p',fact_rel__simps_I20_J) ).

fof(fact_rel__simps_I26_J,axiom,
    ! [V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),V_k_2)) ),
    file('theBenchmark.p',fact_rel__simps_I26_J) ).

fof(fact_rel__simps_I30_J,axiom,
    ! [V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ),
    file('theBenchmark.p',fact_rel__simps_I30_J) ).

fof(fact_rel__simps_I3_J,axiom,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
    file('theBenchmark.p',fact_rel__simps_I3_J) ).

fof(fact_rel__simps_I6_J,axiom,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
    file('theBenchmark.p',fact_rel__simps_I6_J) ).

fof(fact_rel__simps_I13_J,axiom,
    ! [V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OMin)) ),
    file('theBenchmark.p',fact_rel__simps_I13_J) ).

fof(fact_rel__simps_I9_J,axiom,
    ! [V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ),
    file('theBenchmark.p',fact_rel__simps_I9_J) ).

fof(fact_rel__simps_I28_J,axiom,
    ! [V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ),
    file('theBenchmark.p',fact_rel__simps_I28_J) ).

fof(fact_rel__simps_I8_J,axiom,
    ! [V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ),
    file('theBenchmark.p',fact_rel__simps_I8_J) ).

fof(fact_Divides_Otransfer__int__nat__functions_I2_J,axiom,
    ! [V_y,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_y)),
    file('theBenchmark.p',fact_Divides_Otransfer__int__nat__functions_I2_J) ).

fof(fact_zmod__int,axiom,
    ! [V_b,V_a] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,V_b)) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_b)),
    file('theBenchmark.p',fact_zmod__int) ).

fof(fact_eq__number__of__Pls__Min,axiom,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),
    file('theBenchmark.p',fact_eq__number__of__Pls__Min) ).

fof(fact_div__add1__eq,axiom,
    ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),V_c)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_b),V_c))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,V_c)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_b,V_c))),V_c)),
    file('theBenchmark.p',fact_div__add1__eq) ).

fof(fact_Int_OMin__def,axiom,
    c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    file('theBenchmark.p',fact_Int_OMin__def) ).

fof(fact_mult__Min,axiom,
    ! [V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),V_k) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k),
    file('theBenchmark.p',fact_mult__Min) ).

fof(fact_neg__number__of__Min,axiom,
    hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))),
    file('theBenchmark.p',fact_neg__number__of__Min) ).

fof(fact_pred__Pls,axiom,
    c_Int_Opred(c_Int_OPls) = c_Int_OMin,
    file('theBenchmark.p',fact_pred__Pls) ).

fof(fact_add__Min__right,axiom,
    ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Opred(V_k),
    file('theBenchmark.p',fact_add__Min__right) ).

fof(fact_add__Min,axiom,
    ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),V_k) = c_Int_Opred(V_k),
    file('theBenchmark.p',fact_add__Min) ).

fof(fact_pred__Min,axiom,
    c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin),
    file('theBenchmark.p',fact_pred__Min) ).

fof(fact_nonzero__number__of__Min,axiom,
    ! [T_a] :
      ( class_Int_Onumber__ring(T_a)
     => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) ),
    file('theBenchmark.p',fact_nonzero__number__of__Min) ).

fof(fact_succ__Min,axiom,
    c_Int_Osucc(c_Int_OMin) = c_Int_OPls,
    file('theBenchmark.p',fact_succ__Min) ).

fof(fact_diff__bin__simps_I2_J,axiom,
    ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Osucc(V_k),
    file('theBenchmark.p',fact_diff__bin__simps_I2_J) ).

fof(fact_mod__le__divisor,axiom,
    ! [V_m,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_n)) ),
    file('theBenchmark.p',fact_mod__le__divisor) ).

fof(fact_mod__mult__self4,axiom,
    ! [V_m,V_n,V_k] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)),V_m)),V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n),
    file('theBenchmark.p',fact_mod__mult__self4) ).

fof(fact_mult__minus1,axiom,
    ! [V_z,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)),V_z) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_z) ),
    file('theBenchmark.p',fact_mult__minus1) ).

fof(fact_mult__minus1__right,axiom,
    ! [V_z,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_z) ),
    file('theBenchmark.p',fact_mult__minus1__right) ).

fof(fact_number__of__Min,axiom,
    ! [T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ),
    file('theBenchmark.p',fact_number__of__Min) ).

fof(fact_arith__simps_I31_J,axiom,
    ! [T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin) ),
    file('theBenchmark.p',fact_arith__simps_I31_J) ).

fof(fact_divide__minus1,axiom,
    ! [V_x,T_a] :
      ( ( class_Int_Onumber__ring(T_a)
        & class_Fields_Ofield__inverse__zero(T_a) )
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) ),
    file('theBenchmark.p',fact_divide__minus1) ).

fof(fact_rel__simps_I11_J,axiom,
    ! [V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ),
    file('theBenchmark.p',fact_rel__simps_I11_J) ).

fof(fact_rel__simps_I25_J,axiom,
    ! [V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ),
    file('theBenchmark.p',fact_rel__simps_I25_J) ).

fof(fact_mod__mult2__eq,axiom,
    ! [V_c,V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),V_b),V_c))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,V_b)),
    file('theBenchmark.p',fact_mod__mult2__eq) ).

fof(fact_div__mult1__eq,axiom,
    ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_b),V_c))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_b,V_c))),V_c)),
    file('theBenchmark.p',fact_div__mult1__eq) ).

fof(fact_div__mod__equality_H,axiom,
    ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),
    file('theBenchmark.p',fact_div__mod__equality_H) ).

fof(fact_mult__div__cancel,axiom,
    ! [V_m,V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),
    file('theBenchmark.p',fact_mult__div__cancel) ).

fof(fact_Divides_Omod__div__equality_H,axiom,
    ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),V_n)),
    file('theBenchmark.p',fact_Divides_Omod__div__equality_H) ).

fof(fact_zmod__minus1__right,axiom,
    ! [V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    file('theBenchmark.p',fact_zmod__minus1__right) ).

fof(fact_diff__bin__simps_I4_J,axiom,
    ! [V_l] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),V_l)),
    file('theBenchmark.p',fact_diff__bin__simps_I4_J) ).

fof(fact_minus__Min,axiom,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = c_Int_OBit1(c_Int_OPls),
    file('theBenchmark.p',fact_minus__Min) ).

fof(fact_zmult__eq__1__iff,axiom,
    ! [V_n_2,V_m_2] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
    <=> ( ( V_n_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
          & V_m_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) )
        | ( V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
          & V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ),
    file('theBenchmark.p',fact_zmult__eq__1__iff) ).

fof(fact_pos__zmult__eq__1__iff__lemma,axiom,
    ! [V_n,V_m] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n) = c_Groups_Oone__class_Oone(tc_Int_Oint)
     => ( V_m = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
        | V_m = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
    file('theBenchmark.p',fact_pos__zmult__eq__1__iff__lemma) ).

fof(fact_diff__bin__simps_I6_J,axiom,
    ! [V_l] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),V_l)),
    file('theBenchmark.p',fact_diff__bin__simps_I6_J) ).

fof(fact_diff__bin__simps_I5_J,axiom,
    ! [V_l] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),V_l)),
    file('theBenchmark.p',fact_diff__bin__simps_I5_J) ).

fof(fact_zdiv__minus1__right,axiom,
    ! [V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),
    file('theBenchmark.p',fact_zdiv__minus1__right) ).

fof(fact_split__mod,axiom,
    ! [V_k_2,V_n_2,V_P_2] :
      ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2)))
    <=> ( ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => ! [B_i,B_j] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2))
             => ( V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),B_i)),B_j)
               => hBOOL(hAPP(V_P_2,B_j)) ) ) )
        & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => hBOOL(hAPP(V_P_2,V_n_2)) ) ) ),
    file('theBenchmark.p',fact_split__mod) ).

fof(fact_mod__lemma,axiom,
    ! [V_q,V_b,V_r,V_c] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_r),V_b))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_q,V_c))),V_r)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c))) ) ),
    file('theBenchmark.p',fact_mod__lemma) ).

fof(fact_Suc__times__mod__eq,axiom,
    ! [V_m,V_k] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_k))
     => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),V_k) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    file('theBenchmark.p',fact_Suc__times__mod__eq) ).

fof(fact_nat__mod__distrib,axiom,
    ! [V_y,V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
       => hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,V_x),hAPP(c_Int_Onat,V_y)) ) ),
    file('theBenchmark.p',fact_nat__mod__distrib) ).

fof(fact_Divides_Otransfer__nat__int__functions_I2_J,axiom,
    ! [V_y,V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
       => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,V_x),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) ) ),
    file('theBenchmark.p',fact_Divides_Otransfer__nat__int__functions_I2_J) ).

fof(fact_minus1__divide,axiom,
    ! [V_x,T_a] :
      ( ( class_Int_Onumber__ring(T_a)
        & class_Fields_Ofield__inverse__zero(T_a) )
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)),V_x) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Oone__class_Oone(T_a)),V_x)) ),
    file('theBenchmark.p',fact_minus1__divide) ).

fof(fact_div__eq__minus1,axiom,
    ! [V_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),V_b) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ),
    file('theBenchmark.p',fact_div__eq__minus1) ).

fof(fact_mod__Suc__eq__mod__add3,axiom,
    ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_n)),
    file('theBenchmark.p',fact_mod__Suc__eq__mod__add3) ).

fof(fact_Suc__mod__eq__add3__mod,axiom,
    ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m))),V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_m),V_n),
    file('theBenchmark.p',fact_Suc__mod__eq__add3__mod) ).

fof(fact_Suc__mod__eq__add3__mod__number__of,axiom,
    ! [V_v,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),
    file('theBenchmark.p',fact_Suc__mod__eq__add3__mod__number__of) ).

fof(fact_mod2__Suc__Suc,axiom,
    ! [V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
    file('theBenchmark.p',fact_mod2__Suc__Suc) ).

fof(fact_mod__nat__number__of,axiom,
    ! [V_v_H,V_v] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
       => ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
           => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) )
          & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
           => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) ) ) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
       => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_mod__nat__number__of) ).

fof(fact_div__pos__neg__trivial,axiom,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ),
    file('theBenchmark.p',fact_div__pos__neg__trivial) ).

fof(fact_zmod__minus1,axiom,
    ! [V_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
     => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),V_b) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_b),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
    file('theBenchmark.p',fact_zmod__minus1) ).

fof(fact_mod2__gr__0,axiom,
    ! [V_m_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    <=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    file('theBenchmark.p',fact_mod2__gr__0) ).

fof(fact_int__of__code,axiom,
    ! [V_k] :
      ( ( V_k != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => ( ( c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,V_k,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
           => hAPP(c_Code__Numeral_Oint__of,V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_k),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
          & ( c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,V_k,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
           => hAPP(c_Code__Numeral_Oint__of,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_k),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ) )
      & ( V_k = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => hAPP(c_Code__Numeral_Oint__of,V_k) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    file('theBenchmark.p',fact_int__of__code) ).

fof(fact_transfer__int__nat__set__relations_I2_J,axiom,
    ! [V_A_2,V_x_2] :
      ( c_Nat__Transfer_Ois__nat(V_x_2)
     => ( c_Nat__Transfer_Onat__set(V_A_2)
       => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
        <=> hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,V_x_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2))) ) ) ),
    file('theBenchmark.p',fact_transfer__int__nat__set__relations_I2_J) ).

fof(fact_setsum__bounded,axiom,
    ! [V_K_2,V_f_2,V_A_2,T_b,T_c] :
      ( ( class_Rings_Osemiring__1(T_c)
        & class_Groups_Oordered__ab__semigroup__add(T_c) )
     => ( ! [B_i] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_A_2))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_i)),V_K_2)) )
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))),V_K_2))) ) ),
    file('theBenchmark.p',fact_setsum__bounded) ).

fof(fact_SetInterval_Otransfer__int__nat__set__functions,axiom,
    ! [V_n_2,V_m_2] :
      ( c_Nat__Transfer_Ois__nat(V_m_2)
     => ( c_Nat__Transfer_Ois__nat(V_n_2)
       => c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_m_2,V_n_2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Int_Onat,V_m_2),hAPP(c_Int_Onat,V_n_2))) ) ),
    file('theBenchmark.p',fact_SetInterval_Otransfer__int__nat__set__functions) ).

fof(fact_code__numeral__zero__minus__one,axiom,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',fact_code__numeral__zero__minus__one) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J,axiom,
    c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J,axiom,
    ! [V_y,V_x] :
      ( c_Nat__Transfer_Ois__nat(V_x)
     => ( c_Nat__Transfer_Ois__nat(V_y)
       => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y)) ) ),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J,axiom,
    ! [V_z] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z)),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J,axiom,
    c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J,axiom,
    ! [V_y,V_x] :
      ( c_Nat__Transfer_Ois__nat(V_x)
     => ( c_Nat__Transfer_Ois__nat(V_y)
       => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)) ) ),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J) ).

fof(fact_Divides_Otransfer__int__nat__function__closures_I2_J,axiom,
    ! [V_y,V_x] :
      ( c_Nat__Transfer_Ois__nat(V_x)
     => ( c_Nat__Transfer_Ois__nat(V_y)
       => c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) ) ),
    file('theBenchmark.p',fact_Divides_Otransfer__int__nat__function__closures_I2_J) ).

fof(fact_Divides_Otransfer__int__nat__function__closures_I1_J,axiom,
    ! [V_y,V_x] :
      ( c_Nat__Transfer_Ois__nat(V_x)
     => ( c_Nat__Transfer_Ois__nat(V_y)
       => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) ) ),
    file('theBenchmark.p',fact_Divides_Otransfer__int__nat__function__closures_I1_J) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J,axiom,
    ! [V_n,V_x] :
      ( c_Nat__Transfer_Ois__nat(V_x)
     => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)) ),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J,axiom,
    ! [V_y,V_x] :
      ( c_Nat__Transfer_Ois__nat(V_x)
     => ( c_Nat__Transfer_Ois__nat(V_y)
       => c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(V_x,V_y)) ) ),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J) ).

fof(fact_is__nat__def,axiom,
    ! [V_x_2] :
      ( c_Nat__Transfer_Ois__nat(V_x_2)
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ),
    file('theBenchmark.p',fact_is__nat__def) ).

fof(fact_SetInterval_Otransfer__int__nat__set__function__closures,axiom,
    ! [V_y_2,V_x_2] :
      ( c_Nat__Transfer_Ois__nat(V_x_2)
     => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ),
    file('theBenchmark.p',fact_SetInterval_Otransfer__int__nat__set__function__closures) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J,axiom,
    ! [V_x_2,V_A_2] :
      ( c_Nat__Transfer_Onat__set(V_A_2)
     => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
       => c_Nat__Transfer_Ois__nat(V_x_2) ) ),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J) ).

fof(fact_zero__code__numeral__code,axiom,
    c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OPls),
    file('theBenchmark.p',fact_zero__code__numeral__code) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I8_J,axiom,
    c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I8_J) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I7_J,axiom,
    c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I7_J) ).

fof(fact_one__code__numeral__code,axiom,
    c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit1(c_Int_OPls)),
    file('theBenchmark.p',fact_one__code__numeral__code) ).

fof(fact_code__numeral_Osize_I1_J,axiom,
    c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_code__numeral_Osize_I1_J) ).

fof(fact_of__int__of__nat,axiom,
    ! [V_k,T_a] :
      ( class_Rings_Oring__1(T_a)
     => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,V_k)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k)))) ) ) ),
    file('theBenchmark.p',fact_of__int__of__nat) ).

fof(fact_nat__of__aux__code,axiom,
    ! [V_n,V_i] :
      ( ( V_i != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => c_Code__Numeral_Onat__of__aux(V_i,V_n) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_i),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,V_n)) )
      & ( V_i = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => c_Code__Numeral_Onat__of__aux(V_i,V_n) = V_n ) ),
    file('theBenchmark.p',fact_nat__of__aux__code) ).

fof(fact_negD,axiom,
    ! [V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ? [B_n] : V_x = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,B_n))) ),
    file('theBenchmark.p',fact_negD) ).

fof(fact_number__of__eq,axiom,
    ! [V_k,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_k) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) ),
    file('theBenchmark.p',fact_number__of__eq) ).

fof(fact_int__number__of__def,axiom,
    ! [V_w] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),V_w),
    file('theBenchmark.p',fact_int__number__of__def) ).

fof(fact_of__int__int__eq,axiom,
    ! [V_n] : hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n),
    file('theBenchmark.p',fact_of__int__int__eq) ).

fof(fact_of__int__eq__iff,axiom,
    ! [V_z_2,V_w_2,T_b] :
      ( class_Int_Oring__char__0(T_b)
     => ( hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_w_2) = hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)
      <=> V_w_2 = V_z_2 ) ),
    file('theBenchmark.p',fact_of__int__eq__iff) ).

fof(fact_of__int__eq__0__iff,axiom,
    ! [V_z_2,T_b] :
      ( class_Int_Oring__char__0(T_b)
     => ( hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2) = c_Groups_Ozero__class_Ozero(T_b)
      <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    file('theBenchmark.p',fact_of__int__eq__0__iff) ).

fof(fact_of__int__0__eq__iff,axiom,
    ! [V_z_2,T_b] :
      ( class_Int_Oring__char__0(T_b)
     => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)
      <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    file('theBenchmark.p',fact_of__int__0__eq__iff) ).

fof(fact_of__int__0,axiom,
    ! [T_a] :
      ( class_Rings_Oring__1(T_a)
     => hAPP(c_Int_Oring__1__class_Oof__int(T_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_of__int__0) ).

fof(fact_of__int__le__iff,axiom,
    ! [V_z_2,V_w_2,T_b] :
      ( class_Rings_Olinordered__idom(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_w_2)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ),
    file('theBenchmark.p',fact_of__int__le__iff) ).

fof(fact_of__int__less__iff,axiom,
    ! [V_z_2,V_w_2,T_b] :
      ( class_Rings_Olinordered__idom(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_w_2)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ),
    file('theBenchmark.p',fact_of__int__less__iff) ).

fof(fact_of__int__add,axiom,
    ! [V_z,V_w,T_a] :
      ( class_Rings_Oring__1(T_a)
     => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_w)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z)) ),
    file('theBenchmark.p',fact_of__int__add) ).

fof(fact_of__int__number__of__eq,axiom,
    ! [V_v,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v) ),
    file('theBenchmark.p',fact_of__int__number__of__eq) ).

fof(fact_of__int__mult,axiom,
    ! [V_z,V_w,T_a] :
      ( class_Rings_Oring__1(T_a)
     => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_w)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z)) ),
    file('theBenchmark.p',fact_of__int__mult) ).

fof(fact_of__int__1,axiom,
    ! [T_a] :
      ( class_Rings_Oring__1(T_a)
     => hAPP(c_Int_Oring__1__class_Oof__int(T_a),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(T_a) ),
    file('theBenchmark.p',fact_of__int__1) ).

fof(fact_of__int__diff,axiom,
    ! [V_z,V_w,T_a] :
      ( class_Rings_Oring__1(T_a)
     => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_w),V_z)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_w)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z)) ),
    file('theBenchmark.p',fact_of__int__diff) ).

fof(fact_of__int__of__nat__eq,axiom,
    ! [V_n,T_a] :
      ( class_Rings_Oring__1(T_a)
     => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n) ),
    file('theBenchmark.p',fact_of__int__of__nat__eq) ).

fof(fact_of__int__minus,axiom,
    ! [V_z,T_a] :
      ( class_Rings_Oring__1(T_a)
     => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z)) ),
    file('theBenchmark.p',fact_of__int__minus) ).

fof(fact_Ints__of__int,axiom,
    ! [V_z_2,T_b] :
      ( class_Rings_Oring__1(T_b)
     => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)),c_Int_Oring__1__class_OInts(T_b))) ),
    file('theBenchmark.p',fact_Ints__of__int) ).

fof(fact_of__int__power,axiom,
    ! [V_n,V_z,T_a] :
      ( class_Rings_Oring__1(T_a)
     => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z)),V_n) ),
    file('theBenchmark.p',fact_of__int__power) ).

fof(fact_of__int__m1,axiom,
    ! [T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin) ),
    file('theBenchmark.p',fact_of__int__m1) ).

fof(fact_of__int__0__le__iff,axiom,
    ! [V_z_2,T_b] :
      ( class_Rings_Olinordered__idom(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ),
    file('theBenchmark.p',fact_of__int__0__le__iff) ).

fof(fact_of__int__le__0__iff,axiom,
    ! [V_z_2,T_b] :
      ( class_Rings_Olinordered__idom(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)),c_Groups_Ozero__class_Ozero(T_b)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    file('theBenchmark.p',fact_of__int__le__0__iff) ).

fof(fact_of__int__less__0__iff,axiom,
    ! [V_z_2,T_b] :
      ( class_Rings_Olinordered__idom(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)),c_Groups_Ozero__class_Ozero(T_b)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    file('theBenchmark.p',fact_of__int__less__0__iff) ).

fof(fact_of__int__0__less__iff,axiom,
    ! [V_z_2,T_b] :
      ( class_Rings_Olinordered__idom(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ),
    file('theBenchmark.p',fact_of__int__0__less__iff) ).

fof(fact_of__nat__nat,axiom,
    ! [V_z,T_a] :
      ( class_Rings_Oring__1(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
       => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,V_z)) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z) ) ),
    file('theBenchmark.p',fact_of__nat__nat) ).

fof(fact_code__numeral_Osize_I2_J,axiom,
    ! [V_code__numeral] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(V_code__numeral)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(V_code__numeral)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('theBenchmark.p',fact_code__numeral_Osize_I2_J) ).

fof(fact_code__numeral_Osize_I3_J,axiom,
    hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_code__numeral_Osize_I3_J) ).

fof(fact_zero__less__imp__eq__int,axiom,
    ! [V_k] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
     => ? [B_n] :
          ( V_k = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)) ) ),
    file('theBenchmark.p',fact_zero__less__imp__eq__int) ).

fof(fact_decr__lemma,axiom,
    ! [V_z,V_x,V_d] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_z))),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_d))),V_z)) ),
    file('theBenchmark.p',fact_decr__lemma) ).

fof(fact_abs__minus__commute,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)) = hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_a)) ),
    file('theBenchmark.p',fact_abs__minus__commute) ).

fof(fact_abs__one,axiom,
    ! [T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ),
    file('theBenchmark.p',fact_abs__one) ).

fof(fact_abs__of__nat,axiom,
    ! [V_n,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n) ),
    file('theBenchmark.p',fact_abs__of__nat) ).

fof(fact_abs__int__eq,axiom,
    ! [V_m] : hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m),
    file('theBenchmark.p',fact_abs__int__eq) ).

fof(fact_abs__le__D1,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ),
    file('theBenchmark.p',fact_abs__le__D1) ).

fof(fact_abs__ge__self,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) ),
    file('theBenchmark.p',fact_abs__ge__self) ).

fof(fact_abs__divide,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Fields_Olinordered__field__inverse__zero(T_a)
     => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)) ),
    file('theBenchmark.p',fact_abs__divide) ).

fof(fact_abs__mult__self,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ),
    file('theBenchmark.p',fact_abs__mult__self) ).

fof(fact_abs__mult,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)) ),
    file('theBenchmark.p',fact_abs__mult) ).

fof(fact_abs__idempotent,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)) = hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) ),
    file('theBenchmark.p',fact_abs__idempotent) ).

fof(fact_power__abs,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_n) ),
    file('theBenchmark.p',fact_power__abs) ).

fof(fact_abs__minus__cancel,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) ),
    file('theBenchmark.p',fact_abs__minus__cancel) ).

fof(fact_abs__add__abs,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)) ),
    file('theBenchmark.p',fact_abs__add__abs) ).

fof(fact_abs__eq__0,axiom,
    ! [V_a_2,T_b] :
      ( class_Groups_Oordered__ab__group__add__abs(T_b)
     => ( hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
      <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ),
    file('theBenchmark.p',fact_abs__eq__0) ).

fof(fact_abs__zero,axiom,
    ! [T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_abs__zero) ).

fof(fact_code__numeral_Oinject,axiom,
    ! [V_code__numeral_H_2,V_code__numeral_2] :
      ( c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2) = c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H_2)
    <=> V_code__numeral_2 = V_code__numeral_H_2 ),
    file('theBenchmark.p',fact_code__numeral_Oinject) ).

fof(fact_abs__ge__zero,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) ),
    file('theBenchmark.p',fact_abs__ge__zero) ).

fof(fact_abs__le__zero__iff,axiom,
    ! [V_a_2,T_b] :
      ( class_Groups_Oordered__ab__group__add__abs(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
      <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ),
    file('theBenchmark.p',fact_abs__le__zero__iff) ).

fof(fact_abs__of__nonneg,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
       => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ),
    file('theBenchmark.p',fact_abs__of__nonneg) ).

fof(fact_abs__of__pos,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
       => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ),
    file('theBenchmark.p',fact_abs__of__pos) ).

fof(fact_zero__less__abs__iff,axiom,
    ! [V_a_2,T_b] :
      ( class_Groups_Oordered__ab__group__add__abs(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)))
      <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_b) ) ),
    file('theBenchmark.p',fact_zero__less__abs__iff) ).

fof(fact_abs__not__less__zero,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),c_Groups_Ozero__class_Ozero(T_a))) ),
    file('theBenchmark.p',fact_abs__not__less__zero) ).

fof(fact_abs__triangle__ineq,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)))) ),
    file('theBenchmark.p',fact_abs__triangle__ineq) ).

fof(fact_abs__mult__less,axiom,
    ! [V_d,V_b,V_c,V_a,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_c))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)),V_d))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_d))) ) ) ),
    file('theBenchmark.p',fact_abs__mult__less) ).

fof(fact_abs__triangle__ineq3,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)))),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)))) ),
    file('theBenchmark.p',fact_abs__triangle__ineq3) ).

fof(fact_abs__triangle__ineq2,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)))) ),
    file('theBenchmark.p',fact_abs__triangle__ineq2) ).

fof(fact_abs__triangle__ineq2__sym,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_a)))) ),
    file('theBenchmark.p',fact_abs__triangle__ineq2__sym) ).

fof(fact_abs__le__D2,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) ) ),
    file('theBenchmark.p',fact_abs__le__D2) ).

fof(fact_abs__leI,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) ) ) ),
    file('theBenchmark.p',fact_abs__leI) ).

fof(fact_abs__le__iff,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( class_Groups_Oordered__ab__group__add__abs(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),V_b_2))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ),
    file('theBenchmark.p',fact_abs__le__iff) ).

fof(fact_abs__ge__minus__self,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) ),
    file('theBenchmark.p',fact_abs__ge__minus__self) ).

fof(fact_abs__less__iff,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( class_Rings_Olinordered__idom(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),V_b_2))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ),
    file('theBenchmark.p',fact_abs__less__iff) ).

fof(fact_nonzero__abs__divide,axiom,
    ! [V_a,V_b,T_a] :
      ( class_Fields_Olinordered__field(T_a)
     => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
       => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)) ) ),
    file('theBenchmark.p',fact_nonzero__abs__divide) ).

fof(fact_abs__power__minus,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_n)) = hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ),
    file('theBenchmark.p',fact_abs__power__minus) ).

fof(fact_abs__zmult__eq__1,axiom,
    ! [V_n,V_m] :
      ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n)) = c_Groups_Oone__class_Oone(tc_Int_Oint)
     => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_m) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    file('theBenchmark.p',fact_abs__zmult__eq__1) ).

fof(fact_abs__sgn,axiom,
    ! [V_k,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ),
    file('theBenchmark.p',fact_abs__sgn) ).

fof(fact_mult__sgn__abs,axiom,
    ! [V_x,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_x)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_x)) = V_x ),
    file('theBenchmark.p',fact_mult__sgn__abs) ).

fof(fact_code__numeral_Osimps_I2_J,axiom,
    ! [V_code__numeral_H] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H),
    file('theBenchmark.p',fact_code__numeral_Osimps_I2_J) ).

fof(fact_code__numeral_Osimps_I3_J,axiom,
    ! [V_code__numeral_H_1] : c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H_1) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',fact_code__numeral_Osimps_I3_J) ).

fof(fact_abs__mult__pos,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_y)),V_x) = hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x)) ) ),
    file('theBenchmark.p',fact_abs__mult__pos) ).

fof(fact_abs__eq__mult,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Oordered__ring__abs(T_a)
     => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) ) )
       => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)) ) ),
    file('theBenchmark.p',fact_abs__eq__mult) ).

fof(fact_abs__triangle__ineq4,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)))) ),
    file('theBenchmark.p',fact_abs__triangle__ineq4) ).

fof(fact_abs__diff__triangle__ineq,axiom,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_c))),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_d))))) ),
    file('theBenchmark.p',fact_abs__diff__triangle__ineq) ).

fof(fact_abs__of__nonpos,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
       => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ),
    file('theBenchmark.p',fact_abs__of__nonpos) ).

fof(fact_abs__minus__le__zero,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))),c_Groups_Ozero__class_Ozero(T_a))) ),
    file('theBenchmark.p',fact_abs__minus__le__zero) ).

fof(fact_abs__of__neg,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
       => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ),
    file('theBenchmark.p',fact_abs__of__neg) ).

fof(fact_abs__if,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Oabs__if(T_a)
     => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
         => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
         => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ),
    file('theBenchmark.p',fact_abs__if) ).

fof(fact_zero__le__power__abs,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_n))) ),
    file('theBenchmark.p',fact_zero__le__power__abs) ).

fof(fact_abs__div__pos,axiom,
    ! [V_x,V_y,T_a] :
      ( class_Fields_Olinordered__field__inverse__zero(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
       => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_x)),V_y) = hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)) ) ),
    file('theBenchmark.p',fact_abs__div__pos) ).

fof(fact_abs__minus__one,axiom,
    ! [T_a] :
      ( ( class_Rings_Olinordered__idom(T_a)
        & class_Int_Onumber__ring(T_a) )
     => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) = c_Groups_Oone__class_Oone(T_a) ),
    file('theBenchmark.p',fact_abs__minus__one) ).

fof(fact_zabs__less__one__iff,axiom,
    ! [V_z_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_z_2)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    file('theBenchmark.p',fact_zabs__less__one__iff) ).

fof(fact_zabs__def,axiom,
    ! [V_i] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = V_i )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_i) ) ),
    file('theBenchmark.p',fact_zabs__def) ).

fof(fact_nat__abs__mult__distrib,axiom,
    ! [V_z,V_w] : hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_w))),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_z))),
    file('theBenchmark.p',fact_nat__abs__mult__distrib) ).

fof(fact_code__numeral_Osize_I4_J,axiom,
    ! [V_code__numeral] : hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(V_code__numeral)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),V_code__numeral)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('theBenchmark.p',fact_code__numeral_Osize_I4_J) ).

fof(fact_zero__le__zpower__abs,axiom,
    ! [V_n,V_x] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x)),V_n))),
    file('theBenchmark.p',fact_zero__le__zpower__abs) ).

fof(fact_abs__number__of,axiom,
    ! [V_x,T_a] :
      ( ( class_Rings_Olinordered__idom(T_a)
        & class_Int_Onumber__ring(T_a) )
     => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)),c_Groups_Ozero__class_Ozero(T_a)))
         => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)),c_Groups_Ozero__class_Ozero(T_a)))
         => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)) ) ) ),
    file('theBenchmark.p',fact_abs__number__of) ).

fof(fact_abs__power__minus__one,axiom,
    ! [V_n,T_a] :
      ( ( class_Rings_Olinordered__idom(T_a)
        & class_Int_Onumber__ring(T_a) )
     => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)),V_n)) = c_Groups_Oone__class_Oone(T_a) ),
    file('theBenchmark.p',fact_abs__power__minus__one) ).

fof(fact_zero__less__zpower__abs__iff,axiom,
    ! [V_n_2,V_x_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x_2)),V_n_2)))
    <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | V_x_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    file('theBenchmark.p',fact_zero__less__zpower__abs__iff) ).

fof(fact_Suc__code__numeral__minus__one,axiom,
    ! [V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(V_n)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = V_n,
    file('theBenchmark.p',fact_Suc__code__numeral__minus__one) ).

fof(fact_abs__power2,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
    file('theBenchmark.p',fact_abs__power2) ).

fof(fact_power2__abs,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
    file('theBenchmark.p',fact_power2__abs) ).

fof(fact_incr__lemma,axiom,
    ! [V_x,V_z,V_d] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_z))),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_d)))) ),
    file('theBenchmark.p',fact_incr__lemma) ).

fof(fact_Nitpick_Oint__lcm__def,axiom,
    ! [V_y,V_x] : c_Nitpick_Oint__lcm(V_x,V_y) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nitpick_Onat__lcm(hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_y)))),
    file('theBenchmark.p',fact_Nitpick_Oint__lcm__def) ).

fof(fact_code__numeral_Osimps_I5_J,axiom,
    ! [V_code__numeral_2,V_f2_2,V_f1_2,T_b] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(T_b,V_f1_2,V_f2_2,c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2)) = hAPP(V_f2_2,V_code__numeral_2),
    file('theBenchmark.p',fact_code__numeral_Osimps_I5_J) ).

fof(fact_nat0__intermed__int__val,axiom,
    ! [V_k_2,V_f_2,V_n_2] :
      ( ! [B_i] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_i),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(V_f_2,B_i)))),c_Groups_Oone__class_Oone(tc_Int_Oint))) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
         => ? [B_i] :
              ( hAPP(V_f_2,B_i) = V_k_2
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) ) ) ) ),
    file('theBenchmark.p',fact_nat0__intermed__int__val) ).

fof(fact_int__val__lemma,axiom,
    ! [V_k_2,V_f_2,V_n_2] :
      ( ! [B_i] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_i),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(V_f_2,B_i)))),c_Groups_Oone__class_Oone(tc_Int_Oint))) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
         => ? [B_i] :
              ( hAPP(V_f_2,B_i) = V_k_2
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) ) ) ) ),
    file('theBenchmark.p',fact_int__val__lemma) ).

fof(fact_code__numeral_Osimps_I4_J,axiom,
    ! [V_f2_2,V_f1_2,T_b] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(T_b,V_f1_2,V_f2_2,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = V_f1_2,
    file('theBenchmark.p',fact_code__numeral_Osimps_I4_J) ).

fof(fact_Nitpick_Onat__lcm__def,axiom,
    ! [V_y,V_x] : c_Nitpick_Onat__lcm(V_x,V_y) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_x),V_y)),c_Nitpick_Onat__gcd(V_x,V_y)),
    file('theBenchmark.p',fact_Nitpick_Onat__lcm__def) ).

fof(fact_nat__mod__eq__lemma,axiom,
    ! [V_y,V_n,V_x] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_y,V_n)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y),V_x))
       => ? [B_q] : V_x = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),B_q)) ) ),
    file('theBenchmark.p',fact_nat__mod__eq__lemma) ).

fof(fact_mod__induct__0,axiom,
    ! [V_i_2,V_P_2,V_p_2] :
      ( ! [B_i] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_p_2))
         => ( hBOOL(hAPP(V_P_2,B_i))
           => hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,B_i),V_p_2))) ) )
     => ( hBOOL(hAPP(V_P_2,V_i_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_p_2))
         => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ),
    file('theBenchmark.p',fact_mod__induct__0) ).

fof(fact_nat__intermed__int__val,axiom,
    ! [V_k_2,V_f_2,V_n_2,V_m_2] :
      ( ! [B_i] :
          ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i)) )
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_i),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(V_f_2,B_i)))),c_Groups_Oone__class_Oone(tc_Int_Oint))) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,V_m_2)),V_k_2))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
           => ? [B_i] :
                ( hAPP(V_f_2,B_i) = V_k_2
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i)) ) ) ) ) ),
    file('theBenchmark.p',fact_nat__intermed__int__val) ).

fof(fact_nat__gcd_Osimps,axiom,
    ! [V_x,V_y] :
      ( ( V_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => c_Nitpick_Onat__gcd(V_x,V_y) = c_Nitpick_Onat__gcd(V_y,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_y)) )
      & ( V_y = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => c_Nitpick_Onat__gcd(V_x,V_y) = V_x ) ),
    file('theBenchmark.p',fact_nat__gcd_Osimps) ).

fof(fact_Nitpick_Oint__gcd__def,axiom,
    ! [V_y,V_x] : hAPP(hAPP(c_Nitpick_Oint__gcd,V_x),V_y) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nitpick_Onat__gcd(hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_y)))),
    file('theBenchmark.p',fact_Nitpick_Oint__gcd__def) ).

fof(fact_log_Osimps,axiom,
    ! [V_i,V_b] :
      ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_b),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) )
       => c_Random_Olog(V_b,V_i) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),c_Random_Olog(V_b,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_i),V_b))) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_b),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) )
       => c_Random_Olog(V_b,V_i) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) ) ),
    file('theBenchmark.p',fact_log_Osimps) ).

fof(fact_mod__div__decomp,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),V_b)),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) ),
    file('theBenchmark.p',fact_mod__div__decomp) ).

fof(fact_field__le__epsilon,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Fields_Olinordered__field(T_a)
     => ( ! [B_e] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_e))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),B_e))) )
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ),
    file('theBenchmark.p',fact_field__le__epsilon) ).

fof(fact_minus__shift__def,axiom,
    ! [V_r,V_l,V_k] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
       => c_Random_Ominus__shift(V_r,V_k,V_l) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_k),V_l) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
       => c_Random_Ominus__shift(V_r,V_k,V_l) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),V_r),V_k)),V_l) ) ),
    file('theBenchmark.p',fact_minus__shift__def) ).

fof(fact_inc__shift__def,axiom,
    ! [V_k,V_v] :
      ( ( V_v != V_k
       => c_Random_Oinc__shift(V_v,V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),V_k),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) )
      & ( V_v = V_k
       => c_Random_Oinc__shift(V_v,V_k) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) ) ),
    file('theBenchmark.p',fact_inc__shift__def) ).

fof(fact_subtract__code__numeral__def,axiom,
    c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',fact_subtract__code__numeral__def) ).

fof(fact_minus__code__numeral__code,axiom,
    ! [V_m,V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_n),V_m) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,V_n),V_m),
    file('theBenchmark.p',fact_minus__code__numeral__code) ).

fof(fact_pair__box_Osize_I1_J,axiom,
    ! [V_b_2,V_a_2,V_fb_2,V_fa_2,T_c,T_b] : c_Nitpick_Opair__box_Opair__box__size(T_b,T_c,V_fa_2,V_fb_2,c_Nitpick_Opair__box_OPairBox(T_b,T_c,V_a_2,V_b_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_fa_2,V_a_2)),hAPP(V_fb_2,V_b_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('theBenchmark.p',fact_pair__box_Osize_I1_J) ).

fof(fact_arith__series__int,axiom,
    ! [V_n_2,V_d_2,V_a_2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),V_d_2))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_d_2)))),
    file('theBenchmark.p',fact_arith__series__int) ).

fof(fact_negDivAlg__eqn__1__number__of,axiom,
    ! [V_w] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
     => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))))
         => c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))))
         => c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) ) ) ),
    file('theBenchmark.p',fact_negDivAlg__eqn__1__number__of) ).

fof(fact_fold__image__reindex,axiom,
    ! [V_z_2,V_g_2,V_h_2,T_c,V_A_2,T_b,T_d] :
      ( class_Groups_Oab__semigroup__mult(T_d)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( c_Fun_Oinj__on(T_b,T_c,V_h_2,V_A_2)
         => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Otimes__class_Otimes(T_d)),V_g_2),V_z_2),hAPP(c_Set_Oimage(T_b,T_c,V_h_2),V_A_2)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_b,c_Groups_Otimes__class_Otimes(T_d)),hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_g_2),V_h_2)),V_z_2),V_A_2) ) ) ),
    file('theBenchmark.p',fact_fold__image__reindex) ).

fof(fact_SUP2__I,axiom,
    ! [T_d,T_c,V_c_2,V_b_2,V_B_2,V_A_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
     => ( hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2))
       => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) ) ),
    file('theBenchmark.p',fact_SUP2__I) ).

fof(fact_INF1__D,axiom,
    ! [V_a_2,V_b_2,V_B_2,V_A_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2))
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
       => hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) ) ),
    file('theBenchmark.p',fact_INF1__D) ).

fof(fact_INF1__E,axiom,
    ! [V_a_2,V_b_2,V_B_2,V_A_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2))
     => ( ~ hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2))
       => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_INF1__E) ).

fof(fact_INF2__D,axiom,
    ! [V_a_2,V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2))
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
       => hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2)) ) ),
    file('theBenchmark.p',fact_INF2__D) ).

fof(fact_INF2__E,axiom,
    ! [V_a_2,V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2))
     => ( ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2))
       => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_INF2__E) ).

fof(fact_INT__E,axiom,
    ! [V_a_2,V_B_2,V_A_2,T_c,V_b_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
     => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2)))
       => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_INT__E) ).

fof(fact_INT__D,axiom,
    ! [V_a_2,V_B_2,V_A_2,T_c,V_b_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
     => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
       => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ),
    file('theBenchmark.p',fact_INT__D) ).

fof(fact_finite__INT,axiom,
    ! [V_A_2,T_c,V_I_2,T_b] :
      ( ? [B_x] :
          ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_A_2,B_x)))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2)) )
     => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2))) ),
    file('theBenchmark.p',fact_finite__INT) ).

fof(fact_UN__I,axiom,
    ! [V_B_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
     => ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2)))
       => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ) ),
    file('theBenchmark.p',fact_UN__I) ).

fof(fact_SUP1__I,axiom,
    ! [T_c,V_b_2,V_B_2,V_A_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
     => ( hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2))
       => hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2)) ) ),
    file('theBenchmark.p',fact_SUP1__I) ).

fof(fact_setsum__abs,axiom,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( class_Groups_Oordered__ab__group__add__abs(T_b)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2))) ),
    file('theBenchmark.p',fact_setsum__abs) ).

fof(fact_setsum__abs__ge__zero,axiom,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( class_Groups_Oordered__ab__group__add__abs(T_b)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2))) ),
    file('theBenchmark.p',fact_setsum__abs__ge__zero) ).

fof(fact_of__int__setprod,axiom,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( ( class_Rings_Oring__1(T_b)
        & class_Groups_Ocomm__monoid__mult(T_b) )
     => hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,tc_Int_Oint),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_b,T_c),c_Int_Oring__1__class_Oof__int(T_b)),V_f_2)),V_A_2) ),
    file('theBenchmark.p',fact_of__int__setprod) ).

fof(fact_of__int__setsum,axiom,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( class_Rings_Oring__1(T_b)
     => hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Int_Oint),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_b,T_c),c_Int_Oring__1__class_Oof__int(T_b)),V_f_2)),V_A_2) ),
    file('theBenchmark.p',fact_of__int__setsum) ).

fof(fact_setsum__0,axiom,
    ! [V_A_2,T_c,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(c_COMBK(T_b,T_c),c_Groups_Ozero__class_Ozero(T_b))),V_A_2) = c_Groups_Ozero__class_Ozero(T_b) ),
    file('theBenchmark.p',fact_setsum__0) ).

fof(fact_of__nat__setsum,axiom,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( class_Rings_Osemiring__1(T_b)
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,T_c),c_Nat_Osemiring__1__class_Oof__nat(T_b)),V_f_2)),V_A_2) ),
    file('theBenchmark.p',fact_of__nat__setsum) ).

fof(fact_setsum__shift__bounds__Suc__ivl,axiom,
    ! [V_n_2,V_m_2,V_f_2,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2)),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)) ),
    file('theBenchmark.p',fact_setsum__shift__bounds__Suc__ivl) ).

fof(fact_transfer__nat__int__sum__prod2_I1_J,axiom,
    ! [V_A_2,V_f_2,T_b] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_b),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2)),
    file('theBenchmark.p',fact_transfer__nat__int__sum__prod2_I1_J) ).

fof(fact_range__composition,axiom,
    ! [V_g_2,V_f_2,T_d,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,hAPP(hAPP(c_COMBB(T_d,T_b,T_c),V_f_2),V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = hAPP(c_Set_Oimage(T_d,T_b,V_f_2),hAPP(c_Set_Oimage(T_c,T_d,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))),
    file('theBenchmark.p',fact_range__composition) ).

fof(fact_inj__fun,axiom,
    ! [T_d,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
     => c_Fun_Oinj__on(T_b,tc_fun(T_d,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_d,T_c),T_b),c_COMBK(T_c,T_d)),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
    file('theBenchmark.p',fact_inj__fun) ).

fof(fact_INF__INT__eq,axiom,
    ! [V_x_2,V_r_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c))),V_r_2)),V_x_2))
    <=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2))) ),
    file('theBenchmark.p',fact_INF__INT__eq) ).

fof(fact_INF__INT__eq2,axiom,
    ! [V_y_2,V_x_2,V_r_2,T_d,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),T_b),hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_c,T_d)))),c_Product__Type_OPair(T_c,T_d))))),V_r_2)),V_x_2),V_y_2))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2))) ),
    file('theBenchmark.p',fact_INF__INT__eq2) ).

fof(fact_SUP__UN__eq2,axiom,
    ! [V_y_2,V_x_2,V_r_2,T_d,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),T_b),hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_c,T_d)))),c_Product__Type_OPair(T_c,T_d))))),V_r_2)),V_x_2),V_y_2))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2))) ),
    file('theBenchmark.p',fact_SUP__UN__eq2) ).

fof(fact_UN__atLeast__UNIV,axiom,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
    file('theBenchmark.p',fact_UN__atLeast__UNIV) ).

fof(fact_UN__lessThan__UNIV,axiom,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
    file('theBenchmark.p',fact_UN__lessThan__UNIV) ).

fof(fact_INT__empty,axiom,
    ! [V_B_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_INT__empty) ).

fof(fact_INT__constant,axiom,
    ! [V_c_2,T_c,T_b,V_A_2] :
      ( ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_c_2)) = V_c_2 )
      & ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_c_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_INT__constant) ).

fof(fact_INTER__UNIV__conv_I2_J,axiom,
    ! [V_B_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
         => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_INTER__UNIV__conv_I2_J) ).

fof(fact_INTER__UNIV__conv_I1_J,axiom,
    ! [V_B_2,V_A_2,T_c,T_b] :
      ( c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
         => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_INTER__UNIV__conv_I1_J) ).

fof(fact_UN__atMost__UNIV,axiom,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OatMost(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
    file('theBenchmark.p',fact_UN__atMost__UNIV) ).

fof(fact_fun__left__comm__idem_Ofun__comp__idem,axiom,
    ! [V_x_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
     => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_x_2)) = hAPP(V_f_2,V_x_2) ),
    file('theBenchmark.p',fact_fun__left__comm__idem_Ofun__comp__idem) ).

fof(fact_inj__singleton,axiom,
    ! [T_b] : c_Fun_Oinj__on(T_b,tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),
    file('theBenchmark.p',fact_inj__singleton) ).

fof(fact_UN__insert__distrib,axiom,
    ! [V_B_2,V_a_2,T_c,V_A_2,V_u_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_u_2),V_A_2))
     => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    file('theBenchmark.p',fact_UN__insert__distrib) ).

fof(fact_image__constant__conv,axiom,
    ! [V_c_2,T_c,T_b,V_A_2] :
      ( ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_c_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) )
      & ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_c_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_image__constant__conv) ).

fof(fact_SUP__UN__eq,axiom,
    ! [V_x_2,V_r_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c))),V_r_2)),V_x_2))
    <=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2))) ),
    file('theBenchmark.p',fact_SUP__UN__eq) ).

fof(fact_finite__range__imageI,axiom,
    ! [V_f_2,T_d,V_g_2,T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_c,T_b,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),hAPP(c_Set_Oimage(T_c,T_d,hAPP(hAPP(c_COMBB(T_b,T_d,T_c),V_f_2),V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) ),
    file('theBenchmark.p',fact_finite__range__imageI) ).

fof(fact_UN__absorb,axiom,
    ! [V_A_2,T_c,V_I_2,V_k_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_k_2),V_I_2))
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_A_2,V_k_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2) ),
    file('theBenchmark.p',fact_UN__absorb) ).

fof(fact_INT__simps_I2_J,axiom,
    ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
      ( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) )
      & ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_INT__simps_I2_J) ).

fof(fact_INT__simps_I1_J,axiom,
    ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
      ( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) )
      & ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_INT__simps_I1_J) ).

fof(fact_UN__simps_I1_J,axiom,
    ! [V_B_2,V_a_2,T_c,T_b,V_C_2] :
      ( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) )
      & ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_UN__simps_I1_J) ).

fof(fact_UN__singleton,axiom,
    ! [V_A_2,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_A_2,
    file('theBenchmark.p',fact_UN__singleton) ).

fof(fact_UN__extend__simps_I1_J,axiom,
    ! [V_B_2,V_a_2,T_c,T_b,V_C_2] :
      ( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) )
      & ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) ) ),
    file('theBenchmark.p',fact_UN__extend__simps_I1_J) ).

fof(fact_setprod_Odistrib,axiom,
    ! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__mult(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Groups_Otimes__class_Otimes(T_c)),V_g_2)),V_h_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_h_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_setprod_Odistrib) ).

fof(fact_UN__extend__simps_I2_J,axiom,
    ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
      ( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) )
      & ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = V_B_2 ) ),
    file('theBenchmark.p',fact_UN__extend__simps_I2_J) ).

fof(fact_UN__extend__simps_I3_J,axiom,
    ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
      ( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) )
      & ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2 ) ),
    file('theBenchmark.p',fact_UN__extend__simps_I3_J) ).

fof(fact_UN__simps_I2_J,axiom,
    ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
      ( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) )
      & ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_UN__simps_I2_J) ).

fof(fact_UN__simps_I3_J,axiom,
    ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
      ( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) )
      & ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_UN__simps_I3_J) ).

fof(fact_UN__insert,axiom,
    ! [V_B_2,V_A_2,V_a_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_B_2,V_a_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),
    file('theBenchmark.p',fact_UN__insert) ).

fof(fact_INT__extend__simps_I5_J,axiom,
    ! [V_B_2,V_C_2,T_c,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Set_Oinsert(T_b),V_a_2)),V_B_2)),
    file('theBenchmark.p',fact_INT__extend__simps_I5_J) ).

fof(fact_INT__simps_I5_J,axiom,
    ! [V_B_2,V_a_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Set_Oinsert(T_b),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)),
    file('theBenchmark.p',fact_INT__simps_I5_J) ).

fof(fact_bot__fun__def,axiom,
    ! [V_x_2,T_c,T_b] :
      ( class_Orderings_Obot(T_b)
     => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b) ),
    file('theBenchmark.p',fact_bot__fun__def) ).

fof(fact_SUP__const,axiom,
    ! [V_M_2,T_b,V_A_2,T_c] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_c)
     => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),hAPP(c_COMBK(T_c,T_b),V_M_2)) = V_M_2 ) ),
    file('theBenchmark.p',fact_SUP__const) ).

fof(fact_UNION__empty__conv_I1_J,axiom,
    ! [V_B_2,V_A_2,T_c,T_b] :
      ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
         => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_UNION__empty__conv_I1_J) ).

fof(fact_UN__empty2,axiom,
    ! [V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_UN__empty2) ).

fof(fact_UN__constant,axiom,
    ! [V_c_2,T_c,T_b,V_A_2] :
      ( ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_c_2)) = V_c_2 )
      & ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_c_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_UN__constant) ).

fof(fact_UNION__empty__conv_I2_J,axiom,
    ! [V_B_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
         => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_UNION__empty__conv_I2_J) ).

fof(fact_INF__const,axiom,
    ! [V_M_2,T_b,V_A_2,T_c] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_c)
     => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),hAPP(c_COMBK(T_c,T_b),V_M_2)) = V_M_2 ) ),
    file('theBenchmark.p',fact_INF__const) ).

fof(fact_pair__box_Oinject,axiom,
    ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
      ( c_Nitpick_Opair__box_OPairBox(T_b,T_c,V_a_2,V_b_2) = c_Nitpick_Opair__box_OPairBox(T_b,T_c,V_a_H_2,V_b_H_2)
    <=> ( V_b_2 = V_b_H_2
        & V_a_2 = V_a_H_2 ) ),
    file('theBenchmark.p',fact_pair__box_Oinject) ).

fof(fact_Compl__INT,axiom,
    ! [V_B_2,V_A_2,T_c,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool))),V_B_2)),
    file('theBenchmark.p',fact_Compl__INT) ).

fof(fact_Compl__UN,axiom,
    ! [V_B_2,V_A_2,T_c,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool))),V_B_2)),
    file('theBenchmark.p',fact_Compl__UN) ).

fof(fact_fun__Compl__def,axiom,
    ! [V_x_2,V_A_2,T_c,T_b] :
      ( class_Groups_Ouminus(T_b)
     => hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,T_b)),V_A_2),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(V_A_2,V_x_2)) ),
    file('theBenchmark.p',fact_fun__Compl__def) ).

fof(fact_setsum__negf,axiom,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( class_Groups_Oab__group__add(T_b)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Ouminus__class_Ouminus(T_b)),V_f_2)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)) ),
    file('theBenchmark.p',fact_setsum__negf) ).

fof(fact_fold__image__def,axiom,
    ! [V_g_2,V_f_2,T_c,T_b] : hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2) = c_Finite__Set_Ofold(T_c,T_b,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),V_f_2),V_g_2)),
    file('theBenchmark.p',fact_fold__image__def) ).

fof(fact_setsum__divide__distrib,axiom,
    ! [V_r_2,V_A_2,V_f_2,T_c,T_b] :
      ( class_Fields_Ofield(T_b)
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),V_r_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Rings_Oinverse__class_Odivide(T_b)),V_f_2)),V_r_2)),V_A_2) ),
    file('theBenchmark.p',fact_setsum__divide__distrib) ).

fof(fact_UN__extend__simps_I8_J,axiom,
    ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)),V_B_2),
    file('theBenchmark.p',fact_UN__extend__simps_I8_J) ).

fof(fact_UN__simps_I8_J,axiom,
    ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),
    file('theBenchmark.p',fact_UN__simps_I8_J) ).

fof(fact_setsum__commute,axiom,
    ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_b),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_b),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_b),T_d),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b)),hAPP(c_COMBC(T_c,T_d,T_b),V_f_2))),V_A_2)),V_B_2) ),
    file('theBenchmark.p',fact_setsum__commute) ).

fof(fact_SUPR__apply,axiom,
    ! [V_x_2,V_f_2,V_A_2,T_d,T_c,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,T_b)),V_A_2),V_f_2),V_x_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2),hAPP(hAPP(c_COMBC(T_c,T_d,T_b),V_f_2),V_x_2)) ),
    file('theBenchmark.p',fact_SUPR__apply) ).

fof(fact_comp__cong,axiom,
    ! [T_f,T_e,T_d,T_b,T_c,V_x_H_2,V_g_H_2,V_f_H_2,V_x_2,V_g_2,V_f_2] :
      ( hAPP(V_f_2,hAPP(V_g_2,V_x_2)) = hAPP(V_f_H_2,hAPP(V_g_H_2,V_x_H_2))
     => hAPP(hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Fun_Ocomp(T_e,T_b,T_f,V_f_H_2),V_g_H_2),V_x_H_2) ),
    file('theBenchmark.p',fact_comp__cong) ).

fof(fact_o__eq__dest__lhs,axiom,
    ! [V_v_2,V_c_2,V_b_2,V_a_2,T_b,T_c,T_d] :
      ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = V_c_2
     => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,V_v_2) ),
    file('theBenchmark.p',fact_o__eq__dest__lhs) ).

fof(fact_K__record__comp,axiom,
    ! [V_x_2,V_f_2,V_c_2,T_d,T_b,T_c] : hAPP(hAPP(c_Fun_Ocomp(T_c,T_b,T_d,hAPP(c_COMBK(T_b,T_c),V_c_2)),V_f_2),V_x_2) = V_c_2,
    file('theBenchmark.p',fact_K__record__comp) ).

fof(fact_SUP__commute,axiom,
    ! [V_f_2,V_B_2,T_d,V_A_2,T_c,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),T_b,T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,T_b),V_B_2)),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,T_b),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_b),T_b,T_d),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2)),hAPP(c_COMBC(T_c,T_d,T_b),V_f_2))) ),
    file('theBenchmark.p',fact_SUP__commute) ).

fof(fact_INT__extend__simps_I9_J,axiom,
    ! [V_C_2,V_B_2,T_d,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2),
    file('theBenchmark.p',fact_INT__extend__simps_I9_J) ).

fof(fact_UN__extend__simps_I9_J,axiom,
    ! [V_C_2,V_B_2,T_d,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2),
    file('theBenchmark.p',fact_UN__extend__simps_I9_J) ).

fof(fact_INT__simps_I9_J,axiom,
    ! [V_C_2,V_B_2,V_A_2,T_d,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_d),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2)),
    file('theBenchmark.p',fact_INT__simps_I9_J) ).

fof(fact_UN__simps_I9_J,axiom,
    ! [V_C_2,V_B_2,V_A_2,T_d,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_d),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2)),
    file('theBenchmark.p',fact_UN__simps_I9_J) ).

fof(fact_UN__UN__flatten,axiom,
    ! [V_C_2,V_B_2,V_A_2,T_d,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_d),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2)),
    file('theBenchmark.p',fact_UN__UN__flatten) ).

fof(fact_SUP1__iff,axiom,
    ! [V_b_2,V_B_2,V_A_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2))
    <=> ? [B_x] :
          ( hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ),
    file('theBenchmark.p',fact_SUP1__iff) ).

fof(fact_Union__def,axiom,
    ! [V_S_2,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_S_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_COMBI(tc_fun(T_b,tc_HOL_Obool))),
    file('theBenchmark.p',fact_Union__def) ).

fof(fact_INT__simps_I8_J,axiom,
    ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),
    file('theBenchmark.p',fact_INT__simps_I8_J) ).

fof(fact_INT__extend__simps_I8_J,axiom,
    ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)),V_B_2),
    file('theBenchmark.p',fact_INT__extend__simps_I8_J) ).

fof(fact_INFI__apply,axiom,
    ! [V_x_2,V_f_2,V_A_2,T_d,T_c,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,T_b)),V_A_2),V_f_2),V_x_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2),hAPP(hAPP(c_COMBC(T_c,T_d,T_b),V_f_2),V_x_2)) ),
    file('theBenchmark.p',fact_INFI__apply) ).

fof(fact_INF__commute,axiom,
    ! [V_f_2,V_B_2,T_d,V_A_2,T_c,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),T_b,T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,T_b),V_B_2)),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,T_b),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_b),T_b,T_d),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2)),hAPP(c_COMBC(T_c,T_d,T_b),V_f_2))) ),
    file('theBenchmark.p',fact_INF__commute) ).

fof(fact_Inter__def,axiom,
    ! [V_S_2,T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_S_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_COMBI(tc_fun(T_b,tc_HOL_Obool))),
    file('theBenchmark.p',fact_Inter__def) ).

fof(fact_Pow__INT__eq,axiom,
    ! [V_B_2,V_A_2,T_c,T_b] : hAPP(c_Set_OPow(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),T_c),c_Set_OPow(T_b)),V_B_2)),
    file('theBenchmark.p',fact_Pow__INT__eq) ).

fof(fact_o__eq__elim,axiom,
    ! [V_d_2,V_c_2,T_e,V_b_2,V_a_2,T_b,T_c,T_d] :
      ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_e,T_c,T_b,V_c_2),V_d_2)
     => ! [B_v] : hAPP(V_a_2,hAPP(V_b_2,B_v)) = hAPP(V_c_2,hAPP(V_d_2,B_v)) ),
    file('theBenchmark.p',fact_o__eq__elim) ).

fof(fact_o__eq__dest,axiom,
    ! [V_v_2,V_d_2,V_c_2,T_e,V_b_2,V_a_2,T_b,T_c,T_d] :
      ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_e,T_c,T_b,V_c_2),V_d_2)
     => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,hAPP(V_d_2,V_v_2)) ),
    file('theBenchmark.p',fact_o__eq__dest) ).

fof(fact_o__apply,axiom,
    ! [V_x_2,V_g_2,V_f_2,T_d,T_b,T_c] : hAPP(hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2),V_x_2) = hAPP(V_f_2,hAPP(V_g_2,V_x_2)),
    file('theBenchmark.p',fact_o__apply) ).

fof(fact_o__assoc,axiom,
    ! [V_h_2,V_g_2,T_e,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),hAPP(c_Fun_Ocomp(T_e,T_d,T_b,V_g_2),V_h_2)) = hAPP(c_Fun_Ocomp(T_e,T_c,T_b,hAPP(c_Fun_Ocomp(T_d,T_c,T_e,V_f_2),V_g_2)),V_h_2),
    file('theBenchmark.p',fact_o__assoc) ).

fof(fact_o__def,axiom,
    ! [V_x_2,V_g_2,V_f_2,T_d,T_b,T_c] : hAPP(hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2),V_x_2) = hAPP(V_f_2,hAPP(V_g_2,V_x_2)),
    file('theBenchmark.p',fact_o__def) ).

fof(fact_fun__upd__def,axiom,
    ! [V_b_2,V_f_2,T_c,T_b,V_a_2,V_x_2] :
      ( ( V_x_2 != V_a_2
       => hAPP(c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_a_2,V_b_2),V_x_2) = hAPP(V_f_2,V_x_2) )
      & ( V_x_2 = V_a_2
       => hAPP(c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_a_2,V_b_2),V_x_2) = V_b_2 ) ),
    file('theBenchmark.p',fact_fun__upd__def) ).

fof(fact_fun__left__comm_Ofun__left__comm__apply,axiom,
    ! [V_g_2,T_d,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
     => c_Finite__Set_Ofun__left__comm(T_d,T_c,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,T_c),T_d),V_f_2),V_g_2)) ),
    file('theBenchmark.p',fact_fun__left__comm_Ofun__left__comm__apply) ).

fof(fact_fun__left__comm__idem_Ofun__left__comm__idem__apply,axiom,
    ! [V_g_2,T_d,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
     => c_Finite__Set_Ofun__left__comm__idem(T_d,T_c,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,T_c),T_d),V_f_2),V_g_2)) ),
    file('theBenchmark.p',fact_fun__left__comm__idem_Ofun__left__comm__idem__apply) ).

fof(fact_setprod__timesf,axiom,
    ! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
      ( class_Groups_Ocomm__monoid__mult(T_b)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Otimes__class_Otimes(T_b)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_g_2),V_A_2)) ),
    file('theBenchmark.p',fact_setprod__timesf) ).

fof(fact_setsum__right__distrib,axiom,
    ! [V_A_2,V_f_2,T_c,V_r_2,T_b] :
      ( class_Rings_Osemiring__0(T_b)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_r_2),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),hAPP(c_Groups_Otimes__class_Otimes(T_b),V_r_2)),V_f_2)),V_A_2) ),
    file('theBenchmark.p',fact_setsum__right__distrib) ).

fof(fact_setsum__left__distrib,axiom,
    ! [V_r_2,V_A_2,V_f_2,T_c,T_b] :
      ( class_Rings_Osemiring__0(T_b)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),V_r_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Otimes__class_Otimes(T_b)),V_f_2)),V_r_2)),V_A_2) ),
    file('theBenchmark.p',fact_setsum__left__distrib) ).

fof(fact_setsum__product,axiom,
    ! [V_B_2,V_g_2,T_d,V_A_2,V_f_2,T_c,T_b] :
      ( class_Rings_Osemiring__0(T_b)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b),V_g_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_b),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,T_b),tc_fun(T_d,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_b),tc_fun(tc_fun(T_d,T_b),tc_fun(T_d,T_b)),T_c),c_COMBB(T_b,T_b,T_d)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Otimes__class_Otimes(T_b)),V_f_2))),V_g_2))),V_B_2)),V_A_2) ),
    file('theBenchmark.p',fact_setsum__product) ).

fof(fact_fun__upd__comp,axiom,
    ! [V_y_2,V_x_2,V_g_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),c_Fun_Ofun__upd(T_b,T_d,V_g_2,V_x_2,V_y_2)) = c_Fun_Ofun__upd(T_b,T_c,hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),V_g_2),V_x_2,hAPP(V_f_2,V_y_2)),
    file('theBenchmark.p',fact_fun__upd__comp) ).

fof(fact_fun__left__comm_Ofun__comp__comm,axiom,
    ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
     => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_y_2)),hAPP(V_f_2,V_x_2)) ),
    file('theBenchmark.p',fact_fun__left__comm_Ofun__comp__comm) ).

fof(fact_INT__insert__distrib,axiom,
    ! [V_B_2,V_a_2,T_c,V_A_2,V_u_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_u_2),V_A_2))
     => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    file('theBenchmark.p',fact_INT__insert__distrib) ).

fof(fact_bot__empty__eq2,axiom,
    ! [V_y_2,V_x_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_x_2),V_y_2))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)))) ),
    file('theBenchmark.p',fact_bot__empty__eq2) ).

fof(fact_bot__empty__eq,axiom,
    ! [V_x_2,T_b] :
      ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_x_2))
    <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ),
    file('theBenchmark.p',fact_bot__empty__eq) ).

fof(fact_sup__Un__eq,axiom,
    ! [V_x_2,V_S_2,V_R_2,T_b] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)),V_x_2))
    <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2))) ),
    file('theBenchmark.p',fact_sup__Un__eq) ).

fof(fact_inf__Int__eq,axiom,
    ! [V_x_2,V_S_2,V_R_2,T_b] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)),V_x_2))
    <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2))) ),
    file('theBenchmark.p',fact_inf__Int__eq) ).

fof(fact_INT__absorb,axiom,
    ! [V_A_2,T_c,V_I_2,V_k_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_k_2),V_I_2))
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_A_2,V_k_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2) ),
    file('theBenchmark.p',fact_INT__absorb) ).

fof(fact_UN__iff,axiom,
    ! [V_B_2,V_A_2,T_c,V_b_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
    <=> ? [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,B_x)))
          & hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ),
    file('theBenchmark.p',fact_UN__iff) ).

fof(fact_INT__iff,axiom,
    ! [V_B_2,V_A_2,T_c,V_b_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
         => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,B_x))) ) ),
    file('theBenchmark.p',fact_INT__iff) ).

fof(fact_pred__equals__eq,axiom,
    ! [V_S_2,V_R_2,T_b] :
      ( hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2) = hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)
    <=> V_R_2 = V_S_2 ),
    file('theBenchmark.p',fact_pred__equals__eq) ).

fof(fact_pred__equals__eq2,axiom,
    ! [V_S_2,V_R_2,T_c,T_b] :
      ( hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_R_2) = hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_S_2)
    <=> V_R_2 = V_S_2 ),
    file('theBenchmark.p',fact_pred__equals__eq2) ).

fof(fact_sup__Un__eq2,axiom,
    ! [V_y_2,V_x_2,V_S_2,V_R_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_S_2)),V_x_2),V_y_2))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_R_2),V_S_2))) ),
    file('theBenchmark.p',fact_sup__Un__eq2) ).

fof(fact_inf__Int__eq2,axiom,
    ! [V_y_2,V_x_2,V_S_2,V_R_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_S_2)),V_x_2),V_y_2))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_R_2),V_S_2))) ),
    file('theBenchmark.p',fact_inf__Int__eq2) ).

fof(fact_Un__Inter,axiom,
    ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),
    file('theBenchmark.p',fact_Un__Inter) ).

fof(fact_inj__on__id2,axiom,
    ! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,T_b,c_COMBI(T_b),V_A_2),
    file('theBenchmark.p',fact_inj__on__id2) ).

fof(fact_INT__Int__distrib,axiom,
    ! [V_B_2,V_A_2,V_I_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_B_2)),
    file('theBenchmark.p',fact_INT__Int__distrib) ).

fof(fact_Un__INT__distrib2,axiom,
    ! [V_B_2,V_J_2,T_d,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_J_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_J_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool))),T_c),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2))),V_B_2))),
    file('theBenchmark.p',fact_Un__INT__distrib2) ).

fof(fact_INT__extend__simps_I6_J,axiom,
    ! [V_B_2,V_A_2,V_C_2,T_c,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)),
    file('theBenchmark.p',fact_INT__extend__simps_I6_J) ).

fof(fact_Un__INT__distrib,axiom,
    ! [V_A_2,V_I_2,T_c,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2)),V_A_2)),
    file('theBenchmark.p',fact_Un__INT__distrib) ).

fof(fact_INT__extend__simps_I7_J,axiom,
    ! [V_B_2,V_C_2,T_c,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)),
    file('theBenchmark.p',fact_INT__extend__simps_I7_J) ).

fof(fact_INT__simps_I6_J,axiom,
    ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2),
    file('theBenchmark.p',fact_INT__simps_I6_J) ).

fof(fact_INT__simps_I7_J,axiom,
    ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)),
    file('theBenchmark.p',fact_INT__simps_I7_J) ).

fof(fact_Int__Union,axiom,
    ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),
    file('theBenchmark.p',fact_Int__Union) ).

fof(fact_Int__Union2,axiom,
    ! [V_A_2,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),
    file('theBenchmark.p',fact_Int__Union2) ).

fof(fact_UN__simps_I5_J,axiom,
    ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)),
    file('theBenchmark.p',fact_UN__simps_I5_J) ).

fof(fact_UN__simps_I4_J,axiom,
    ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2),
    file('theBenchmark.p',fact_UN__simps_I4_J) ).

fof(fact_UN__extend__simps_I5_J,axiom,
    ! [V_B_2,V_C_2,T_c,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)),
    file('theBenchmark.p',fact_UN__extend__simps_I5_J) ).

fof(fact_Int__UN__distrib,axiom,
    ! [V_A_2,V_I_2,T_c,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2)),V_A_2)),
    file('theBenchmark.p',fact_Int__UN__distrib) ).

fof(fact_UN__extend__simps_I4_J,axiom,
    ! [V_B_2,V_A_2,V_C_2,T_c,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)),
    file('theBenchmark.p',fact_UN__extend__simps_I4_J) ).

fof(fact_Int__UN__distrib2,axiom,
    ! [V_B_2,V_J_2,T_d,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_J_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_J_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool))),T_c),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2))),V_B_2))),
    file('theBenchmark.p',fact_Int__UN__distrib2) ).

fof(fact_UN__Un__distrib,axiom,
    ! [V_B_2,V_A_2,V_I_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_B_2)),
    file('theBenchmark.p',fact_UN__Un__distrib) ).

fof(fact_UN__Un,axiom,
    ! [V_M_2,V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_M_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_M_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_M_2)),
    file('theBenchmark.p',fact_UN__Un) ).

fof(fact_INT__Un,axiom,
    ! [V_M_2,V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_M_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_M_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_M_2)),
    file('theBenchmark.p',fact_INT__Un) ).

fof(fact_inf__fun__def,axiom,
    ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
      ( class_Lattices_Olattice(T_b)
     => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,T_b)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ),
    file('theBenchmark.p',fact_inf__fun__def) ).

fof(fact_sup__fun__def,axiom,
    ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
      ( class_Lattices_Olattice(T_b)
     => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,T_b)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ),
    file('theBenchmark.p',fact_sup__fun__def) ).

fof(fact_inj__on__imageI2,axiom,
    ! [V_A_2,V_f_2,V_f_H_2,T_d,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_H_2),V_f_2),V_A_2)
     => c_Fun_Oinj__on(T_b,T_d,V_f_2,V_A_2) ),
    file('theBenchmark.p',fact_inj__on__imageI2) ).

fof(fact_INT__extend__simps_I2_J,axiom,
    ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
      ( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) )
      & ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2 ) ),
    file('theBenchmark.p',fact_INT__extend__simps_I2_J) ).

fof(fact_INT__extend__simps_I1_J,axiom,
    ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
      ( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) )
      & ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = V_B_2 ) ),
    file('theBenchmark.p',fact_INT__extend__simps_I1_J) ).

fof(fact_INT__insert,axiom,
    ! [V_B_2,V_A_2,V_a_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_B_2,V_a_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),
    file('theBenchmark.p',fact_INT__insert) ).

fof(fact_override__on__def,axiom,
    ! [V_g_2,V_f_2,T_c,V_A_2,V_a_2,T_b] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
       => hAPP(c_Fun_Ooverride__on(T_b,T_c,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_f_2,V_a_2) )
      & ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
       => hAPP(c_Fun_Ooverride__on(T_b,T_c,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_g_2,V_a_2) ) ),
    file('theBenchmark.p',fact_override__on__def) ).

fof(fact_int__setprod,axiom,
    ! [V_A_2,V_f_2,T_b] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_b),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2),
    file('theBenchmark.p',fact_int__setprod) ).

fof(fact_int__setsum,axiom,
    ! [V_A_2,V_f_2,T_b] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_b),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2),
    file('theBenchmark.p',fact_int__setsum) ).

fof(fact_UN__extend__simps_I10_J,axiom,
    ! [V_f_2,V_B_2,T_d,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),V_B_2),
    file('theBenchmark.p',fact_UN__extend__simps_I10_J) ).

fof(fact_image__UN,axiom,
    ! [V_B_2,V_A_2,T_d,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Set_Oimage(T_c,T_b,V_f_2)),V_B_2)),
    file('theBenchmark.p',fact_image__UN) ).

fof(fact_UN__simps_I10_J,axiom,
    ! [V_B_2,V_A_2,V_f_2,T_d,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_b,tc_HOL_Obool),T_d),V_B_2),V_f_2)),
    file('theBenchmark.p',fact_UN__simps_I10_J) ).

fof(fact_image__Union,axiom,
    ! [V_S_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_Set_Oimage(T_c,T_b,V_f_2)),
    file('theBenchmark.p',fact_image__Union) ).

fof(fact_image__image,axiom,
    ! [V_A_2,V_g_2,T_d,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Oimage(T_d,T_c,V_g_2),V_A_2)) = hAPP(c_Set_Oimage(T_d,T_b,hAPP(hAPP(c_COMBB(T_c,T_b,T_d),V_f_2),V_g_2)),V_A_2),
    file('theBenchmark.p',fact_image__image) ).

fof(fact_image__ident,axiom,
    ! [V_Y_2,T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_COMBI(T_b)),V_Y_2) = V_Y_2,
    file('theBenchmark.p',fact_image__ident) ).

fof(fact_INT__extend__simps_I10_J,axiom,
    ! [V_f_2,V_B_2,T_d,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),V_B_2),
    file('theBenchmark.p',fact_INT__extend__simps_I10_J) ).

fof(fact_INT__simps_I10_J,axiom,
    ! [V_B_2,V_A_2,V_f_2,T_d,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_b,tc_HOL_Obool),T_d),V_B_2),V_f_2)),
    file('theBenchmark.p',fact_INT__simps_I10_J) ).

fof(fact_image__compose,axiom,
    ! [V_r_2,V_g_2,V_f_2,T_d,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,hAPP(c_Fun_Ocomp(T_d,T_b,T_c,V_f_2),V_g_2)),V_r_2) = hAPP(c_Set_Oimage(T_d,T_b,V_f_2),hAPP(c_Set_Oimage(T_c,T_d,V_g_2),V_r_2)),
    file('theBenchmark.p',fact_image__compose) ).

fof(fact_INTER__eq__Inter__image,axiom,
    ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_A_2)),
    file('theBenchmark.p',fact_INTER__eq__Inter__image) ).

fof(fact_Inter__image__eq,axiom,
    ! [V_A_2,V_B_2,T_c,T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),
    file('theBenchmark.p',fact_Inter__image__eq) ).

fof(fact_setprod__dividef,axiom,
    ! [V_g_2,V_f_2,V_A_2,T_b,T_c] :
      ( class_Fields_Ofield__inverse__zero(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Rings_Oinverse__class_Odivide(T_c)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_setprod__dividef) ).

fof(fact_transfer__nat__int__sum__prod_I2_J,axiom,
    ! [V_A_2,V_f_2,T_b] :
      ( ( class_Groups_Ocomm__monoid__mult(T_b)
        & class_Groups_Ocomm__monoid__add(T_b) )
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),V_f_2),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)) ),
    file('theBenchmark.p',fact_transfer__nat__int__sum__prod_I2_J) ).

fof(fact_setsum__shift__bounds__cl__Suc__ivl,axiom,
    ! [V_n_2,V_m_2,V_f_2,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),c_Nat_OSuc)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) ),
    file('theBenchmark.p',fact_setsum__shift__bounds__cl__Suc__ivl) ).

fof(fact_UN__UN__finite__eq,axiom,
    ! [V_A_2,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),tc_Nat_Onat),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2),
    file('theBenchmark.p',fact_UN__UN__finite__eq) ).

fof(fact_card__eq__setsum,axiom,
    ! [V_A_2,T_b] : hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,T_b),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_A_2),
    file('theBenchmark.p',fact_card__eq__setsum) ).

fof(fact_setsum__subtractf,axiom,
    ! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
      ( class_Groups_Oab__group__add(T_b)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Ominus__class_Ominus(T_b)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_g_2),V_A_2)) ),
    file('theBenchmark.p',fact_setsum__subtractf) ).

fof(fact_fun__diff__def,axiom,
    ! [V_x_2,V_B_2,V_A_2,T_c,T_b] :
      ( class_Groups_Ominus(T_b)
     => hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,T_b)),V_A_2),V_B_2),V_x_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(V_A_2,V_x_2)),hAPP(V_B_2,V_x_2)) ),
    file('theBenchmark.p',fact_fun__diff__def) ).

fof(fact_setprod__1,axiom,
    ! [V_A_2,T_c,T_b] :
      ( class_Groups_Ocomm__monoid__mult(T_b)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(c_COMBK(T_b,T_c),c_Groups_Oone__class_Oone(T_b))),V_A_2) = c_Groups_Oone__class_Oone(T_b) ),
    file('theBenchmark.p',fact_setprod__1) ).

fof(fact_UN__simps_I7_J,axiom,
    ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)),
    file('theBenchmark.p',fact_UN__simps_I7_J) ).

fof(fact_UN__simps_I6_J,axiom,
    ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2),
    file('theBenchmark.p',fact_UN__simps_I6_J) ).

fof(fact_UN__extend__simps_I7_J,axiom,
    ! [V_B_2,V_C_2,T_c,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)),
    file('theBenchmark.p',fact_UN__extend__simps_I7_J) ).

fof(fact_UN__extend__simps_I6_J,axiom,
    ! [V_B_2,V_A_2,V_C_2,T_c,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)),
    file('theBenchmark.p',fact_UN__extend__simps_I6_J) ).

fof(fact_INT__extend__simps_I4_J,axiom,
    ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
      ( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) )
      & ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2 ) ),
    file('theBenchmark.p',fact_INT__extend__simps_I4_J) ).

fof(fact_INT__extend__simps_I3_J,axiom,
    ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
      ( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) )
      & ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))),V_B_2) ) ),
    file('theBenchmark.p',fact_INT__extend__simps_I3_J) ).

fof(fact_INT__simps_I3_J,axiom,
    ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
      ( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) )
      & ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_INT__simps_I3_J) ).

fof(fact_Union__image__eq,axiom,
    ! [V_A_2,V_B_2,T_c,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),
    file('theBenchmark.p',fact_Union__image__eq) ).

fof(fact_UNION__eq__Union__image,axiom,
    ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_A_2)),
    file('theBenchmark.p',fact_UNION__eq__Union__image) ).

fof(fact_abs__setsum__abs,axiom,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( class_Groups_Oordered__ab__group__add__abs(T_b)
     => hAPP(c_Groups_Oabs__class_Oabs(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2) ),
    file('theBenchmark.p',fact_abs__setsum__abs) ).

fof(fact_abs__setprod,axiom,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( class_Fields_Olinordered__field(T_b)
     => hAPP(c_Groups_Oabs__class_Oabs(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2) ),
    file('theBenchmark.p',fact_abs__setprod) ).

fof(fact_setsum__shift__bounds__cl__nat__ivl,axiom,
    ! [V_n_2,V_k_2,V_m_2,V_f_2,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) ),
    file('theBenchmark.p',fact_setsum__shift__bounds__cl__nat__ivl) ).

fof(fact_INT__subset__iff,axiom,
    ! [V_A_2,V_I_2,T_c,V_B_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)))
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(V_A_2,B_x))) ) ),
    file('theBenchmark.p',fact_INT__subset__iff) ).

fof(fact_UN__subset__iff,axiom,
    ! [V_B_2,V_A_2,V_I_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),V_B_2))
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_A_2,B_x)),V_B_2)) ) ),
    file('theBenchmark.p',fact_UN__subset__iff) ).

fof(fact_le__INF__iff,axiom,
    ! [V_M_2,V_A_2,T_c,V_u_2,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_u_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2),V_M_2)))
      <=> ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_u_2),hAPP(V_M_2,B_x))) ) ) ),
    file('theBenchmark.p',fact_le__INF__iff) ).

fof(fact_SUP__le__iff,axiom,
    ! [V_u_2,V_M_2,V_A_2,T_c,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2),V_M_2)),V_u_2))
      <=> ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_M_2,B_x)),V_u_2)) ) ) ),
    file('theBenchmark.p',fact_SUP__le__iff) ).

fof(fact_INT__lower,axiom,
    ! [V_B_2,T_c,V_A_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(V_B_2,V_a_2))) ),
    file('theBenchmark.p',fact_INT__lower) ).

fof(fact_pred__subset__eq,axiom,
    ! [V_S_2,V_R_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2)) ),
    file('theBenchmark.p',fact_pred__subset__eq) ).

fof(fact_pred__subset__eq2,axiom,
    ! [V_S_2,V_R_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_S_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_R_2),V_S_2)) ),
    file('theBenchmark.p',fact_pred__subset__eq2) ).

fof(fact_inj__on__add__nat,axiom,
    ! [V_N_2,V_k_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2),V_N_2),
    file('theBenchmark.p',fact_inj__on__add__nat) ).

fof(fact_setsum__addf,axiom,
    ! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Oplus__class_Oplus(T_b)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_g_2),V_A_2)) ),
    file('theBenchmark.p',fact_setsum__addf) ).

fof(fact_less__eq__Suc__le__raw,axiom,
    ! [V_n_2] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),
    file('theBenchmark.p',fact_less__eq__Suc__le__raw) ).

fof(fact_UN__upper,axiom,
    ! [V_B_2,T_c,V_A_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_B_2,V_a_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ),
    file('theBenchmark.p',fact_UN__upper) ).

fof(fact_setsum_Odistrib,axiom,
    ! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__add(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Groups_Oplus__class_Oplus(T_c)),V_g_2)),V_h_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_h_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_setsum_Odistrib) ).

fof(fact_INF__leI,axiom,
    ! [V_M_2,V_A_2,V_i_2,T_b,T_c] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_c)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),V_M_2)),hAPP(V_M_2,V_i_2))) ) ),
    file('theBenchmark.p',fact_INF__leI) ).

fof(fact_le__SUPI,axiom,
    ! [V_M_2,V_A_2,V_i_2,T_b,T_c] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_c)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_M_2,V_i_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),V_M_2))) ) ),
    file('theBenchmark.p',fact_le__SUPI) ).

fof(fact_INF__less__iff,axiom,
    ! [V_a_2,V_f_2,V_A_2,T_c,T_b] :
      ( ( class_Orderings_Olinorder(T_b)
        & class_Complete__Lattice_Ocomplete__lattice(T_b) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2),V_f_2)),V_a_2))
      <=> ? [B_x] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_x)),V_a_2))
            & hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ) ),
    file('theBenchmark.p',fact_INF__less__iff) ).

fof(fact_less__SUP__iff,axiom,
    ! [V_f_2,V_A_2,T_c,V_a_2,T_b] :
      ( ( class_Orderings_Olinorder(T_b)
        & class_Complete__Lattice_Ocomplete__lattice(T_b) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2),V_f_2)))
      <=> ? [B_x] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(V_f_2,B_x)))
            & hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ) ),
    file('theBenchmark.p',fact_less__SUP__iff) ).

fof(fact_setsum__shift__bounds__nat__ivl,axiom,
    ! [V_n_2,V_k_2,V_m_2,V_f_2,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)) ),
    file('theBenchmark.p',fact_setsum__shift__bounds__nat__ivl) ).

fof(fact_nat__number__of__Bit0,axiom,
    ! [V_w_2] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(V_w_2)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat))),
    file('theBenchmark.p',fact_nat__number__of__Bit0) ).

fof(fact_Int__Inter__image,axiom,
    ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_A_2),V_C_2))),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_C_2))),
    file('theBenchmark.p',fact_Int__Inter__image) ).

fof(fact_UN__le__add__shift,axiom,
    ! [V_k_2,V_M_2,V_n_2,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool),tc_Nat_Onat),V_M_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_k_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2))),V_M_2),
    file('theBenchmark.p',fact_UN__le__add__shift) ).

fof(fact_UN__Pow__subset,axiom,
    ! [V_B_2,V_A_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),T_c),c_Set_OPow(T_b)),V_B_2))),hAPP(c_Set_OPow(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))),
    file('theBenchmark.p',fact_UN__Pow__subset) ).

fof(fact_of__nat__setprod,axiom,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( ( class_Rings_Osemiring__1(T_b)
        & class_Groups_Ocomm__monoid__mult(T_b) )
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,T_c),c_Nat_Osemiring__1__class_Oof__nat(T_b)),V_f_2)),V_A_2) ),
    file('theBenchmark.p',fact_of__nat__setprod) ).

fof(fact_transfer__nat__int__sum__prod2_I2_J,axiom,
    ! [V_A_2,V_f_2,T_b] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_b),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2)),
    file('theBenchmark.p',fact_transfer__nat__int__sum__prod2_I2_J) ).

fof(fact_image__add__atLeastLessThan,axiom,
    ! [V_j_2,V_i_2,V_k_2] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),V_k_2)),
    file('theBenchmark.p',fact_image__add__atLeastLessThan) ).

fof(fact_image__add__atLeastAtMost,axiom,
    ! [V_j_2,V_i_2,V_k_2] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_i_2,V_j_2)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),V_k_2)),
    file('theBenchmark.p',fact_image__add__atLeastAtMost) ).

fof(fact_setsum__delta_H,axiom,
    ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__add(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
       => ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = c_Groups_Ozero__class_Ozero(T_c) )
          & ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = hAPP(V_b_2,V_a_2) ) ) ) ),
    file('theBenchmark.p',fact_setsum__delta_H) ).

fof(fact_setsum__delta,axiom,
    ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__add(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
       => ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = c_Groups_Ozero__class_Ozero(T_c) )
          & ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = hAPP(V_b_2,V_a_2) ) ) ) ),
    file('theBenchmark.p',fact_setsum__delta) ).

fof(fact_image__constant,axiom,
    ! [V_c_2,T_c,V_A_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
     => hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_c_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) ),
    file('theBenchmark.p',fact_image__constant) ).

fof(fact_INT__greaterThan__UNIV,axiom,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
    file('theBenchmark.p',fact_INT__greaterThan__UNIV) ).

fof(fact_setprod__delta,axiom,
    ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__mult(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
       => ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = c_Groups_Oone__class_Oone(T_c) )
          & ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = hAPP(V_b_2,V_a_2) ) ) ) ),
    file('theBenchmark.p',fact_setprod__delta) ).

fof(fact_setprod__delta_H,axiom,
    ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__mult(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
       => ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = c_Groups_Oone__class_Oone(T_c) )
          & ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = hAPP(V_b_2,V_a_2) ) ) ) ),
    file('theBenchmark.p',fact_setprod__delta_H) ).

fof(fact_image__eq__UN,axiom,
    ! [V_A_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Set_Oinsert(T_b)),V_f_2)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),
    file('theBenchmark.p',fact_image__eq__UN) ).

fof(fact_INT__simps_I4_J,axiom,
    ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
      ( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) )
      & ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_INT__simps_I4_J) ).

fof(fact_setsum__constant,axiom,
    ! [V_A_2,V_y_2,T_c,T_b] :
      ( class_Rings_Osemiring__1(T_b)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(c_COMBK(T_b,T_c),V_y_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(c_Finite__Set_Ocard(T_c),V_A_2))),V_y_2) ),
    file('theBenchmark.p',fact_setsum__constant) ).

fof(fact_power__number__of__even,axiom,
    ! [V_w_2,V_z_2,T_b] :
      ( class_Int_Onumber__ring(T_b)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(V_w_2))) = hAPP(hAPP(c_HOL_OLet(T_b,T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),c_Groups_Otimes__class_Otimes(T_b)),c_COMBI(T_b))) ),
    file('theBenchmark.p',fact_power__number__of__even) ).

fof(fact_fold__image__distrib,axiom,
    ! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__mult(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Groups_Otimes__class_Otimes(T_c)),V_g_2)),V_h_2)),c_Groups_Oone__class_Oone(T_c)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_A_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_h_2),c_Groups_Oone__class_Oone(T_c)),V_A_2)) ) ),
    file('theBenchmark.p',fact_fold__image__distrib) ).

fof(fact_dual__max,axiom,
    ! [T_b] :
      ( class_Orderings_Olinorder(T_b)
     => c_Orderings_Oord_Omax(T_b,hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_b))) = c_Orderings_Oord__class_Omin(T_b) ),
    file('theBenchmark.p',fact_dual__max) ).

fof(fact_dual__min,axiom,
    ! [T_b] :
      ( class_Orderings_Olinorder(T_b)
     => c_Orderings_Oord_Omin(T_b,hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_b))) = c_Orderings_Oord__class_Omax(T_b) ),
    file('theBenchmark.p',fact_dual__min) ).

fof(fact_setprod__constant,axiom,
    ! [V_y_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__mult(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(c_COMBK(T_c,T_b),V_y_2)),V_A_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_y_2),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)) ) ),
    file('theBenchmark.p',fact_setprod__constant) ).

fof(fact_sup__SUPR__fold__sup,axiom,
    ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),V_f_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Lattices_Osemilattice__sup__class_Osup(T_c)),V_f_2)),V_B_2),V_A_2) ) ),
    file('theBenchmark.p',fact_sup__SUPR__fold__sup) ).

fof(fact_inf__INFI__fold__inf,axiom,
    ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),V_f_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Lattices_Osemilattice__inf__class_Oinf(T_c)),V_f_2)),V_B_2),V_A_2) ) ),
    file('theBenchmark.p',fact_inf__INFI__fold__inf) ).

fof(fact_zpower__number__of__even,axiom,
    ! [V_w_2,V_z_2] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(V_w_2))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_COMBI(tc_Int_Oint))),
    file('theBenchmark.p',fact_zpower__number__of__even) ).

fof(fact_comp__surj,axiom,
    ! [V_g_2,T_d,V_f_2,T_b,T_c] :
      ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
     => ( hAPP(c_Set_Oimage(T_b,T_d,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))
       => hAPP(c_Set_Oimage(T_c,T_d,hAPP(c_Fun_Ocomp(T_b,T_d,T_c,V_g_2),V_f_2)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_comp__surj) ).

fof(fact_setsum__lessThan__Suc,axiom,
    ! [V_n_2,V_f_2,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))),hAPP(V_f_2,V_n_2)) ),
    file('theBenchmark.p',fact_setsum__lessThan__Suc) ).

fof(fact_UN__o,axiom,
    ! [V_f_2,V_g_2,T_d,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Fun_Ocomp(T_d,tc_fun(T_b,tc_HOL_Obool),T_c,V_g_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),V_g_2),
    file('theBenchmark.p',fact_UN__o) ).

fof(fact_inj__comp,axiom,
    ! [V_g_2,T_d,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
     => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)))
       => c_Fun_Oinj__on(T_d,T_c,hAPP(c_Fun_Ocomp(T_b,T_c,T_d,V_f_2),V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) ) ),
    file('theBenchmark.p',fact_inj__comp) ).

fof(fact_comp__inj__on__iff,axiom,
    ! [V_f_H_2,T_d,V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
     => ( c_Fun_Oinj__on(T_c,T_d,V_f_H_2,hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))
      <=> c_Fun_Oinj__on(T_b,T_d,hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_f_H_2),V_f_2),V_A_2) ) ),
    file('theBenchmark.p',fact_comp__inj__on__iff) ).

fof(fact_comp__inj__on,axiom,
    ! [V_g_2,T_d,V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
     => ( c_Fun_Oinj__on(T_c,T_d,V_g_2,hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))
       => c_Fun_Oinj__on(T_b,T_d,hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_g_2),V_f_2),V_A_2) ) ),
    file('theBenchmark.p',fact_comp__inj__on) ).

fof(fact_inj__on__imageI,axiom,
    ! [V_A_2,V_f_2,V_g_2,T_d,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_g_2),V_f_2),V_A_2)
     => c_Fun_Oinj__on(T_d,T_c,V_g_2,hAPP(c_Set_Oimage(T_b,T_d,V_f_2),V_A_2)) ),
    file('theBenchmark.p',fact_inj__on__imageI) ).

fof(fact_setsum__atMost__Suc,axiom,
    ! [V_n_2,V_f_2,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2))),hAPP(V_f_2,hAPP(c_Nat_OSuc,V_n_2))) ),
    file('theBenchmark.p',fact_setsum__atMost__Suc) ).

fof(fact_transfer__nat__int__sum__prod_I1_J,axiom,
    ! [V_A_2,V_f_2,T_b] :
      ( ( class_Groups_Ocomm__monoid__mult(T_b)
        & class_Groups_Ocomm__monoid__add(T_b) )
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),V_f_2),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)) ),
    file('theBenchmark.p',fact_transfer__nat__int__sum__prod_I1_J) ).

fof(fact_Un__Union__image,axiom,
    ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_A_2),V_C_2))),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_C_2))),
    file('theBenchmark.p',fact_Un__Union__image) ).

fof(fact_image__add__int__atLeastLessThan,axiom,
    ! [V_u_2,V_l_2] : hAPP(c_Set_Oimage(tc_Int_Oint,tc_Int_Oint,hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),V_l_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_u_2),V_l_2))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_l_2),V_u_2),
    file('theBenchmark.p',fact_image__add__int__atLeastLessThan) ).

fof(fact_transfer__int__nat__sum__prod_I2_J,axiom,
    ! [V_f_2,V_A_2,T_b] :
      ( ( class_Groups_Ocomm__monoid__mult(T_b)
        & class_Groups_Ocomm__monoid__add(T_b) )
     => ( c_Nat__Transfer_Onat__set(V_A_2)
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_b,tc_Nat_Onat),V_f_2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)) ) ),
    file('theBenchmark.p',fact_transfer__int__nat__sum__prod_I2_J) ).

fof(fact_Powp__Pow__eq,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Predicate_OPowp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)),V_x_2))
    <=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),hAPP(c_Set_OPow(T_b),V_A_2))) ),
    file('theBenchmark.p',fact_Powp__Pow__eq) ).

fof(fact_setsum__restrict__set,axiom,
    ! [V_B_2,V_f_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__add(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_f_2)),c_Groups_Ozero__class_Ozero(T_c))),V_A_2) ) ),
    file('theBenchmark.p',fact_setsum__restrict__set) ).

fof(fact_image__eq__fold__image,axiom,
    ! [V_f_2,T_c,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(T_c,tc_HOL_Obool),T_b,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(T_c,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Set_Oinsert(T_c)),V_f_2)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))),V_A_2) ),
    file('theBenchmark.p',fact_image__eq__fold__image) ).

fof(fact_power__number__of__even__number__of,axiom,
    ! [V_w_2,V_v_2,T_b] :
      ( class_Int_Onumber__ring(T_b)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(V_w_2))) = hAPP(hAPP(c_HOL_OLet(T_b,T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),c_Groups_Otimes__class_Otimes(T_b)),c_COMBI(T_b))) ),
    file('theBenchmark.p',fact_power__number__of__even__number__of) ).

fof(fact_SUPR__fold__sup,axiom,
    ! [V_f_2,V_A_2,T_b,T_c] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),V_f_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Lattices_Osemilattice__sup__class_Osup(T_c)),V_f_2)),c_Orderings_Obot__class_Obot(T_c)),V_A_2) ) ),
    file('theBenchmark.p',fact_SUPR__fold__sup) ).

fof(fact_card__def,axiom,
    ! [V_A_2,T_b] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,T_b,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,T_b),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2) ) ),
    file('theBenchmark.p',fact_card__def) ).

fof(fact_card_Oeq__fold__g,axiom,
    ! [V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,T_b,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,T_b),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2) ),
    file('theBenchmark.p',fact_card_Oeq__fold__g) ).

fof(fact_fun__left__comm__idem__remove,axiom,
    ! [T_b] : c_Finite__Set_Ofun__left__comm__idem(T_b,tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),
    file('theBenchmark.p',fact_fun__left__comm__idem__remove) ).

fof(fact_INFI__fold__inf,axiom,
    ! [V_f_2,V_A_2,T_b,T_c] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),V_f_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Lattices_Osemilattice__inf__class_Oinf(T_c)),V_f_2)),c_Orderings_Otop__class_Otop(T_c)),V_A_2) ) ),
    file('theBenchmark.p',fact_INFI__fold__inf) ).

fof(fact_diff__nat__eq__if,axiom,
    ! [V_z_2,V_z_H_2] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,V_z_2)),hAPP(c_Int_Onat,V_z_H_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z_2),V_z_H_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat)) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,V_z_2)),hAPP(c_Int_Onat,V_z_H_2)) = hAPP(c_Int_Onat,V_z_2) ) ),
    file('theBenchmark.p',fact_diff__nat__eq__if) ).

fof(fact_negDivAlg__div__mod,axiom,
    ! [V_l,V_k] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
       => c_Divides_OnegDivAlg(V_k,V_l) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l)) ) ),
    file('theBenchmark.p',fact_negDivAlg__div__mod) ).

fof(fact_negDivAlg__minus1,axiom,
    ! [V_b] : c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_b),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    file('theBenchmark.p',fact_negDivAlg__minus1) ).

fof(fact_UN__le__eq__Un0,axiom,
    ! [V_M_2,V_n_2,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2)),V_M_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n_2)),V_M_2)),hAPP(V_M_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('theBenchmark.p',fact_UN__le__eq__Un0) ).

fof(fact_transfer__int__nat__sum__prod_I1_J,axiom,
    ! [V_f_2,V_A_2,T_b] :
      ( ( class_Groups_Ocomm__monoid__mult(T_b)
        & class_Groups_Ocomm__monoid__add(T_b) )
     => ( c_Nat__Transfer_Onat__set(V_A_2)
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_b,tc_Nat_Onat),V_f_2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)) ) ),
    file('theBenchmark.p',fact_transfer__int__nat__sum__prod_I1_J) ).

fof(fact_adjust__eq,axiom,
    ! [V_r_2,V_q_2,V_b_2] : hAPP(c_Divides_Oadjust(V_b_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q_2),V_r_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_r_2),V_b_2)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_q_2)),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_q_2)),V_r_2))),
    file('theBenchmark.p',fact_adjust__eq) ).

fof(fact_setsum__head,axiom,
    ! [V_P_2,V_n_2,V_m_2,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_P_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_P_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_P_2),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_m_2,V_n_2))) ) ),
    file('theBenchmark.p',fact_setsum__head) ).

fof(fact_minus__fold__remove,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_B_2),V_A_2) ),
    file('theBenchmark.p',fact_minus__fold__remove) ).

fof(fact_setsum__reindex,axiom,
    ! [V_h_2,V_B_2,V_f_2,T_c,T_b,T_d] :
      ( class_Groups_Ocomm__monoid__add(T_d)
     => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_h_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)),V_B_2) ) ),
    file('theBenchmark.p',fact_setsum__reindex) ).

fof(fact_eq__number__of__Suc,axiom,
    ! [V_n_2,V_v_2] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = hAPP(c_Nat_OSuc,V_n_2)
    <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),V_n_2))))) ),
    file('theBenchmark.p',fact_eq__number__of__Suc) ).

fof(fact_Suc__eq__number__of,axiom,
    ! [V_v_2,V_n_2] :
      ( hAPP(c_Nat_OSuc,V_n_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)
    <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),V_n_2))))) ),
    file('theBenchmark.p',fact_Suc__eq__number__of) ).

fof(fact_setprod__reindex,axiom,
    ! [V_h_2,V_B_2,V_f_2,T_c,T_b,T_d] :
      ( class_Groups_Ocomm__monoid__mult(T_d)
     => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_h_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_d),hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)),V_B_2) ) ),
    file('theBenchmark.p',fact_setprod__reindex) ).

fof(fact_setprod__reindex__cong,axiom,
    ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
      ( class_Groups_Ocomm__monoid__mult(T_d)
     => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
       => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
         => ( V_g_2 = hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_d),V_g_2),V_A_2) ) ) ) ),
    file('theBenchmark.p',fact_setprod__reindex__cong) ).

fof(fact_nat__number__of__Bit1,axiom,
    ! [V_w_2] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
       => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat)))) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
       => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_nat__number__of__Bit1) ).

fof(fact_geometric__sum,axiom,
    ! [V_n_2,V_x_2,T_b] :
      ( class_Fields_Ofield(T_b)
     => ( V_x_2 != c_Groups_Oone__class_Oone(T_b)
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(c_Power_Opower__class_Opower(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),V_n_2)),c_Groups_Oone__class_Oone(T_b))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_x_2),c_Groups_Oone__class_Oone(T_b))) ) ),
    file('theBenchmark.p',fact_geometric__sum) ).

fof(fact_gauss__sum,axiom,
    ! [V_n_2,T_b] :
      ( class_Rings_Ocomm__semiring__1(T_b)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),c_Groups_Oone__class_Oone(T_b)),c_Groups_Oone__class_Oone(T_b))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),c_Nat_Osemiring__1__class_Oof__nat(T_b)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)),c_Groups_Oone__class_Oone(T_b))) ),
    file('theBenchmark.p',fact_gauss__sum) ).

fof(fact_setsum__natinterval__difff,axiom,
    ! [V_f_2,V_n_2,V_m_2,T_b] :
      ( class_Groups_Oab__group__add(T_b)
     => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(T_b)),V_f_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) = c_Groups_Ozero__class_Ozero(T_b) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(T_b)),V_f_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(V_f_2,V_m_2)),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ),
    file('theBenchmark.p',fact_setsum__natinterval__difff) ).

fof(fact_less__number__of__Suc,axiom,
    ! [V_n_2,V_v_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Nat_OSuc,V_n_2)))
    <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Int_Onat)),V_n_2)))) ),
    file('theBenchmark.p',fact_less__number__of__Suc) ).

fof(fact_less__Suc__number__of,axiom,
    ! [V_v_2,V_n_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)))
    <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2)),c_Int_Onat))))) ),
    file('theBenchmark.p',fact_less__Suc__number__of) ).

fof(fact_le__number__of__Suc,axiom,
    ! [V_n_2,V_v_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Nat_OSuc,V_n_2)))
    <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Int_Onat)),V_n_2)))) ),
    file('theBenchmark.p',fact_le__number__of__Suc) ).

fof(fact_le__Suc__number__of,axiom,
    ! [V_v_2,V_n_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)))
    <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2)),c_Int_Onat))))) ),
    file('theBenchmark.p',fact_le__Suc__number__of) ).

fof(fact_max__number__of__Suc,axiom,
    ! [V_v_2,V_n_2] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_OSuc,V_n_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n_2)),c_Int_Onat)))),
    file('theBenchmark.p',fact_max__number__of__Suc) ).

fof(fact_max__Suc__number__of,axiom,
    ! [V_n_2,V_v_2] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_OSuc,V_n_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Int_Onat)),V_n_2)))),
    file('theBenchmark.p',fact_max__Suc__number__of) ).

fof(fact_power__number__of__odd,axiom,
    ! [V_z_2,V_w_2,T_b] :
      ( class_Int_Onumber__ring(T_b)
     => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
         => hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = c_Groups_Oone__class_Oone(T_b) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
         => hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = hAPP(hAPP(c_HOL_OLet(T_b,T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_b),c_Groups_Otimes__class_Otimes(T_b)),hAPP(c_Groups_Otimes__class_Otimes(T_b),V_z_2))),c_COMBI(T_b))) ) ) ),
    file('theBenchmark.p',fact_power__number__of__odd) ).

fof(fact_setprod__gen__delta,axiom,
    ! [V_c_2,V_b_2,V_a_2,V_S_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__mult(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
       => ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),V_c_2)),V_S_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_c_2),hAPP(c_Finite__Set_Ocard(T_b),V_S_2)) )
          & ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),V_c_2)),V_S_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_b_2,V_a_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_S_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ) ),
    file('theBenchmark.p',fact_setprod__gen__delta) ).

fof(fact_image__minus__const__atLeastLessThan__nat,axiom,
    ! [V_x_2,V_y_2,V_c_2] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_c_2),V_y_2))
       => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
           => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_c_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
           => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_c_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ) ) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_c_2),V_y_2))
       => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_c_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_c_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_y_2),V_c_2)) ) ),
    file('theBenchmark.p',fact_image__minus__const__atLeastLessThan__nat) ).

fof(fact_setsum_Oreindex,axiom,
    ! [V_g_2,V_h_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__add(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2)
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(c_Fun_Ocomp(T_b,T_c,T_b,V_g_2),V_h_2)),V_A_2) ) ) ),
    file('theBenchmark.p',fact_setsum_Oreindex) ).

fof(fact_zpower__number__of__odd,axiom,
    ! [V_z_2,V_w_2] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = c_Groups_Oone__class_Oone(tc_Int_Oint) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z_2))),c_COMBI(tc_Int_Oint))) ) ),
    file('theBenchmark.p',fact_zpower__number__of__odd) ).

fof(fact_setprod_Oreindex,axiom,
    ! [V_g_2,V_h_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__mult(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2)
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(c_Fun_Ocomp(T_b,T_c,T_b,V_g_2),V_h_2)),V_A_2) ) ) ),
    file('theBenchmark.p',fact_setprod_Oreindex) ).

fof(fact_arith__series__general,axiom,
    ! [V_n_2,V_d_2,V_a_2,T_b] :
      ( class_Rings_Ocomm__semiring__1(T_b)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),c_Groups_Oone__class_Oone(T_b)),c_Groups_Oone__class_Oone(T_b))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(T_b)),c_Nat_Osemiring__1__class_Oof__nat(T_b))),V_d_2))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_d_2)))) ),
    file('theBenchmark.p',fact_arith__series__general) ).

fof(fact_negDivAlg_Osimps,axiom,
    ! [V_b,V_a] :
      ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b))) )
       => c_Divides_OnegDivAlg(V_a,V_b) = hAPP(c_Divides_Oadjust(V_b),c_Divides_OnegDivAlg(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b))) )
       => c_Divides_OnegDivAlg(V_a,V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)) ) ),
    file('theBenchmark.p',fact_negDivAlg_Osimps) ).

fof(fact_min__number__of__Suc,axiom,
    ! [V_v_2,V_n_2] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_n_2)),c_Int_Onat)))),
    file('theBenchmark.p',fact_min__number__of__Suc) ).

fof(fact_min__Suc__number__of,axiom,
    ! [V_n_2,V_v_2] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Orderings_Oord__class_Omin(tc_Nat_Onat)),c_Int_Onat)),V_n_2)))),
    file('theBenchmark.p',fact_min__Suc__number__of) ).

fof(fact_arith__series__nat,axiom,
    ! [V_n_2,V_d_2,V_a_2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),V_d_2))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_d_2)))),
    file('theBenchmark.p',fact_arith__series__nat) ).

fof(fact_the__inv__into__comp,axiom,
    ! [V_x_2,V_A_2,V_g_2,T_d,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2))
     => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,V_A_2)
       => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2))))
         => hAPP(c_Fun_Othe__inv__into(T_d,T_c,V_A_2,hAPP(c_Fun_Ocomp(T_b,T_c,T_d,V_f_2),V_g_2)),V_x_2) = hAPP(hAPP(c_Fun_Ocomp(T_b,T_d,T_c,c_Fun_Othe__inv__into(T_d,T_b,V_A_2,V_g_2)),c_Fun_Othe__inv__into(T_b,T_c,hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2),V_f_2)),V_x_2) ) ) ),
    file('theBenchmark.p',fact_the__inv__into__comp) ).

fof(fact_power__number__of__odd__number__of,axiom,
    ! [V_v_2,V_w_2,T_b] :
      ( class_Int_Onumber__ring(T_b)
     => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
         => hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = c_Groups_Oone__class_Oone(T_b) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
         => hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = hAPP(hAPP(c_HOL_OLet(T_b,T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_b),c_Groups_Otimes__class_Otimes(T_b)),hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)))),c_COMBI(T_b))) ) ) ),
    file('theBenchmark.p',fact_power__number__of__odd__number__of) ).

fof(fact_negDivAlg__eqn,axiom,
    ! [V_a,V_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
     => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)))
         => c_Divides_OnegDivAlg(V_a,V_b) = hAPP(c_Divides_Oadjust(V_b),c_Divides_OnegDivAlg(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)))
         => c_Divides_OnegDivAlg(V_a,V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)) ) ) ),
    file('theBenchmark.p',fact_negDivAlg__eqn) ).

fof(fact_negDivAlg__eqn__number__of,axiom,
    ! [V_w,V_v] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
     => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))))
         => c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))))
         => c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) ) ) ),
    file('theBenchmark.p',fact_negDivAlg__eqn__number__of) ).

fof(fact_diff__nat__number__of,axiom,
    ! [V_v_2,V_v_H_2] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_v_H_2)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) ) ),
    file('theBenchmark.p',fact_diff__nat__number__of) ).

fof(fact_norm__frac_Osimps,axiom,
    ! [V_a_2,V_b_2] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => ( ( ~ ( V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
                | V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
           => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,V_a_2),V_b_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b_2))) )
          & ( ( V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
              | V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
           => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b_2)) ) ),
    file('theBenchmark.p',fact_norm__frac_Osimps) ).

fof(fact_nat__case__add__eq__if,axiom,
    ! [V_n_2,V_v_2,V_f_2,V_a_2,T_b] : c_Nat_Onat_Onat__case(T_b,V_a_2,V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),V_n_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_b),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),tc_Int_Oint),c_If(T_b)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(T_b,V_a_2,V_f_2,V_n_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),V_f_2),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),V_n_2)))),
    file('theBenchmark.p',fact_nat__case__add__eq__if) ).

fof(fact_posDivAlg__eqn__1__number__of,axiom,
    ! [V_w] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
     => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
         => c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
         => c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ),
    file('theBenchmark.p',fact_posDivAlg__eqn__1__number__of) ).

fof(fact_posDivAlg_Osimps,axiom,
    ! [V_b,V_a] :
      ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) )
       => c_Divides_OposDivAlg(V_a,V_b) = hAPP(c_Divides_Oadjust(V_b),c_Divides_OposDivAlg(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) )
       => c_Divides_OposDivAlg(V_a,V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a) ) ),
    file('theBenchmark.p',fact_posDivAlg_Osimps) ).

fof(fact_sup2CI,axiom,
    ! [T_c,T_b,V_A_2,V_y_2,V_x_2,V_B_2] :
      ( ( ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
       => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) )
     => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ),
    file('theBenchmark.p',fact_sup2CI) ).

fof(fact_sup2E,axiom,
    ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2))
     => ( ~ hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
       => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ),
    file('theBenchmark.p',fact_sup2E) ).

fof(fact_inf2I,axiom,
    ! [T_c,T_b,V_B_2,V_y_2,V_x_2,V_A_2] :
      ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
     => ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
       => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ) ),
    file('theBenchmark.p',fact_inf2I) ).

fof(fact_inf2E,axiom,
    ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2))
     => ~ ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
         => ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ),
    file('theBenchmark.p',fact_inf2E) ).

fof(fact_bot2E,axiom,
    ! [V_y_2,V_x_2,T_c,T_b] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_x_2),V_y_2)),
    file('theBenchmark.p',fact_bot2E) ).

fof(fact_SUP2__iff,axiom,
    ! [V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2))
    <=> ? [B_x] :
          ( hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ),
    file('theBenchmark.p',fact_SUP2__iff) ).

fof(fact_INF1__iff,axiom,
    ! [V_b_2,V_B_2,V_A_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2))
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
         => hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ),
    file('theBenchmark.p',fact_INF1__iff) ).

fof(fact_INF2__iff,axiom,
    ! [V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2))
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
         => hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) ) ),
    file('theBenchmark.p',fact_INF2__iff) ).

fof(fact_predicate2D,axiom,
    ! [V_y_2,V_x_2,V_Q_2,V_P_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_P_2),V_Q_2))
     => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
       => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ),
    file('theBenchmark.p',fact_predicate2D) ).

fof(fact_rev__predicate2D,axiom,
    ! [V_Q_2,T_c,T_b,V_y_2,V_x_2,V_P_2] :
      ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_P_2),V_Q_2))
       => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ),
    file('theBenchmark.p',fact_rev__predicate2D) ).

fof(fact_less__by__empty,axiom,
    ! [V_B_2,T_b,V_A_2] :
      ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_A_2),V_B_2)) ),
    file('theBenchmark.p',fact_less__by__empty) ).

fof(fact_sup2I2,axiom,
    ! [V_A_2,T_c,T_b,V_y_2,V_x_2,V_B_2] :
      ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
     => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ),
    file('theBenchmark.p',fact_sup2I2) ).

fof(fact_sup2I1,axiom,
    ! [V_B_2,T_c,T_b,V_y_2,V_x_2,V_A_2] :
      ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
     => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ),
    file('theBenchmark.p',fact_sup2I1) ).

fof(fact_inf2D1,axiom,
    ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2))
     => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ),
    file('theBenchmark.p',fact_inf2D1) ).

fof(fact_inf2D2,axiom,
    ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2))
     => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ),
    file('theBenchmark.p',fact_inf2D2) ).

fof(fact_nat__case__0,axiom,
    ! [V_f2_2,V_f1_2,T_b] : c_Nat_Onat_Onat__case(T_b,V_f1_2,V_f2_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_f1_2,
    file('theBenchmark.p',fact_nat__case__0) ).

fof(fact_nat__case__Suc,axiom,
    ! [V_nat_2,V_f2_2,V_f1_2,T_b] : c_Nat_Onat_Onat__case(T_b,V_f1_2,V_f2_2,hAPP(c_Nat_OSuc,V_nat_2)) = hAPP(V_f2_2,V_nat_2),
    file('theBenchmark.p',fact_nat__case__Suc) ).

fof(fact_posDivAlg__0,axiom,
    ! [V_b] : c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    file('theBenchmark.p',fact_posDivAlg__0) ).

fof(fact_max__Suc1,axiom,
    ! [V_m_2,V_n_2] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n_2),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n_2)),V_m_2),
    file('theBenchmark.p',fact_max__Suc1) ).

fof(fact_max__Suc2,axiom,
    ! [V_n_2,V_m_2] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n_2),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),V_n_2)),V_m_2),
    file('theBenchmark.p',fact_max__Suc2) ).

fof(fact_less__eq__nat_Osimps_I2_J,axiom,
    ! [V_n_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2))
    <=> hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ),
    file('theBenchmark.p',fact_less__eq__nat_Osimps_I2_J) ).

fof(fact_diff__Suc,axiom,
    ! [V_n_2,V_m_2] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_COMBI(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2)),
    file('theBenchmark.p',fact_diff__Suc) ).

fof(fact_min__Suc1,axiom,
    ! [V_m_2,V_n_2] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_n_2)),V_m_2),
    file('theBenchmark.p',fact_min__Suc1) ).

fof(fact_min__Suc2,axiom,
    ! [V_n_2,V_m_2] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Oord__class_Omin(tc_Nat_Onat)),V_n_2)),V_m_2),
    file('theBenchmark.p',fact_min__Suc2) ).

fof(fact_posDivAlg__div__mod,axiom,
    ! [V_l,V_k] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
       => c_Divides_OposDivAlg(V_k,V_l) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l)) ) ),
    file('theBenchmark.p',fact_posDivAlg__div__mod) ).

fof(fact_nat__case__number__of,axiom,
    ! [V_v_2,V_f_2,V_a_2,T_b] : c_Nat_Onat_Onat__case(T_b,V_a_2,V_f_2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_b),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),tc_Int_Oint),c_If(T_b)),c_Nat__Numeral_Oneg)),V_a_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),V_f_2),c_Int_Onat))),
    file('theBenchmark.p',fact_nat__case__number__of) ).

fof(fact_posDivAlg__eqn,axiom,
    ! [V_a,V_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
     => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
         => c_Divides_OposDivAlg(V_a,V_b) = hAPP(c_Divides_Oadjust(V_b),c_Divides_OposDivAlg(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
         => c_Divides_OposDivAlg(V_a,V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a) ) ) ),
    file('theBenchmark.p',fact_posDivAlg__eqn) ).

fof(fact_posDivAlg__eqn__number__of,axiom,
    ! [V_w,V_v] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
     => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
         => c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
         => c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) ) ) ),
    file('theBenchmark.p',fact_posDivAlg__eqn__number__of) ).

fof(fact_in__rel__def,axiom,
    ! [V_y_2,V_x_2,V_R_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(T_b,T_c,V_R_2),V_x_2),V_y_2))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),V_R_2)) ),
    file('theBenchmark.p',fact_in__rel__def) ).

fof(fact_div__mod__code__numeral__def,axiom,
    ! [V_m,V_n] : c_Code__Numeral_Odiv__mod__code__numeral(V_n,V_m) = hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_n),V_m)),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,V_n,V_m)),
    file('theBenchmark.p',fact_div__mod__code__numeral__def) ).

fof(fact_Nitpick_Orefl_H__def,axiom,
    ! [V_r_2,T_b] :
      ( c_Nitpick_Orefl_H(T_b,V_r_2)
    <=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) ),
    file('theBenchmark.p',fact_Nitpick_Orefl_H__def) ).

fof(fact_adjust__def,axiom,
    ! [V_b_2] : c_Divides_Oadjust(V_b_2) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),V_b_2))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),V_b_2))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
    file('theBenchmark.p',fact_adjust__def) ).

fof(fact_divmod__nat__step,axiom,
    ! [V_m,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
       => c_Divides_Odivmod__nat(V_m,V_n) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_n)) ) ),
    file('theBenchmark.p',fact_divmod__nat__step) ).

fof(fact_nat__rec__add__eq__if,axiom,
    ! [V_n_2,V_v_2,V_f_2,V_a_2,T_b] : hAPP(c_Nat_Onat_Onat__rec(T_b,V_a_2,V_f_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),V_n_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_b),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),tc_Int_Oint),c_If(T_b)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(T_b,V_a_2,V_f_2),V_n_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_b,T_b),tc_Int_Oint),V_f_2),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),V_n_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),c_Nat_Onat_Onat__rec(T_b,V_a_2,V_f_2)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),V_n_2))))),
    file('theBenchmark.p',fact_nat__rec__add__eq__if) ).

fof(fact_nat__rec__0,axiom,
    ! [V_f2_2,V_f1_2,T_b] : hAPP(c_Nat_Onat_Onat__rec(T_b,V_f1_2,V_f2_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_f1_2,
    file('theBenchmark.p',fact_nat__rec__0) ).

fof(fact_nat__rec__Suc,axiom,
    ! [V_nat_2,V_f2_2,V_f1_2,T_b] : hAPP(c_Nat_Onat_Onat__rec(T_b,V_f1_2,V_f2_2),hAPP(c_Nat_OSuc,V_nat_2)) = hAPP(hAPP(V_f2_2,V_nat_2),hAPP(c_Nat_Onat_Onat__rec(T_b,V_f1_2,V_f2_2),V_nat_2)),
    file('theBenchmark.p',fact_nat__rec__Suc) ).

fof(fact_divmod__nat__zero,axiom,
    ! [V_m] : c_Divides_Odivmod__nat(V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m),
    file('theBenchmark.p',fact_divmod__nat__zero) ).

fof(fact_divmod__nat__base,axiom,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
     => c_Divides_Odivmod__nat(V_m,V_n) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m) ),
    file('theBenchmark.p',fact_divmod__nat__base) ).

fof(fact_divmod__nat__div__mod,axiom,
    ! [V_n,V_m] : c_Divides_Odivmod__nat(V_m,V_n) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),
    file('theBenchmark.p',fact_divmod__nat__div__mod) ).

fof(fact_nat__rec__number__of,axiom,
    ! [V_v_2,V_f_2,V_a_2,T_b] : hAPP(c_Nat_Onat_Onat__rec(T_b,V_a_2,V_f_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_b),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),tc_Int_Oint),c_If(T_b)),c_Nat__Numeral_Oneg)),V_a_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_b,T_b),tc_Int_Oint),V_f_2),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),c_Nat_Onat_Onat__rec(T_b,V_a_2,V_f_2)),c_Int_Onat)))),
    file('theBenchmark.p',fact_nat__rec__number__of) ).

fof(fact_pair__imageI,axiom,
    ! [V_f_2,T_d,V_A_2,V_b_2,V_a_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_A_2))
     => hBOOL(hAPP(hAPP(c_member(T_d),hAPP(hAPP(V_f_2,V_a_2),V_b_2)),hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_d,hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_f_2)),V_A_2))) ),
    file('theBenchmark.p',fact_pair__imageI) ).

fof(fact_of__int__num,axiom,
    ! [V_k_2,T_b] :
      ( class_Rings_Oring__1(T_b)
     => ( ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
             => hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_k_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(T_b,T_b)),tc_fun(tc_Int_Oint,T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),T_b),tc_fun(tc_fun(tc_Int_Oint,tc_fun(T_b,T_b)),tc_fun(tc_Int_Oint,T_b)),tc_Int_Oint),c_COMBB(tc_fun(T_b,T_b),T_b,tc_Int_Oint)),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_fun(T_b,T_b),T_b),tc_Int_Oint),c_HOL_OLet(T_b,T_b)),c_Int_Oring__1__class_Oof__int(T_b)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(T_b,T_b),tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,T_b)),tc_Int_Oint),c_COMBS(T_b,T_b,T_b)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(T_b,T_b),tc_fun(T_b,tc_fun(T_b,T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_fun(T_b,T_b))),tc_Int_Oint),c_COMBB(T_b,tc_fun(T_b,T_b),T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),tc_Int_Oint),c_If(T_b)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),c_Groups_Oplus__class_Oplus(T_b)),c_COMBI(T_b))))),hAPP(hAPP(c_COMBC(T_b,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_b),c_Groups_Oplus__class_Oplus(T_b)),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),c_Groups_Oplus__class_Oplus(T_b)),c_COMBI(T_b)))),c_Groups_Oone__class_Oone(T_b))))),c_Divides_Odivmod__int(V_k_2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
             => hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_k_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k_2))) ) ) )
        & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_k_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ),
    file('theBenchmark.p',fact_of__int__num) ).

fof(fact_semiring__1__class_Oof__nat__code,axiom,
    ! [V_n_2,T_b] :
      ( class_Rings_Osemiring__1(T_b)
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2) = c_Nat_Osemiring__1__class_Oof__nat__aux(T_b,hAPP(hAPP(c_COMBC(T_b,T_b,T_b),c_Groups_Oplus__class_Oplus(T_b)),c_Groups_Oone__class_Oone(T_b)),V_n_2,c_Groups_Ozero__class_Ozero(T_b)) ),
    file('theBenchmark.p',fact_semiring__1__class_Oof__nat__code) ).

fof(fact_splitI,axiom,
    ! [T_c,T_b,V_b_2,V_a_2,V_f_2] :
      ( hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2))
     => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ),
    file('theBenchmark.p',fact_splitI) ).

fof(fact_prod__caseI,axiom,
    ! [T_c,T_b,V_b_2,V_a_2,V_f1_2] :
      ( hBOOL(hAPP(hAPP(V_f1_2,V_a_2),V_b_2))
     => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_f1_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ),
    file('theBenchmark.p',fact_prod__caseI) ).

fof(fact_mem__splitI,axiom,
    ! [T_d,T_c,V_b_2,V_a_2,V_c_2,V_z_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_c_2,V_a_2),V_b_2)))
     => hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_fun(T_b,tc_HOL_Obool)),V_c_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)))) ),
    file('theBenchmark.p',fact_mem__splitI) ).

fof(fact_splitD,axiom,
    ! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)))
     => hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2)) ),
    file('theBenchmark.p',fact_splitD) ).

fof(fact_splitD_H,axiom,
    ! [V_c_2,V_b_2,V_a_2,V_R_2,T_d,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_d,tc_HOL_Obool)),V_R_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_c_2))
     => hBOOL(hAPP(hAPP(hAPP(V_R_2,V_a_2),V_b_2),V_c_2)) ),
    file('theBenchmark.p',fact_splitD_H) ).

fof(fact_of__nat__aux_Osimps_I1_J,axiom,
    ! [V_i_2,V_inc_2,T_b] :
      ( class_Rings_Osemiring__1(T_b)
     => c_Nat_Osemiring__1__class_Oof__nat__aux(T_b,V_inc_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i_2) = V_i_2 ),
    file('theBenchmark.p',fact_of__nat__aux_Osimps_I1_J) ).

fof(fact_of__nat__aux_Osimps_I2_J,axiom,
    ! [V_i_2,V_n_2,V_inc_2,T_b] :
      ( class_Rings_Osemiring__1(T_b)
     => c_Nat_Osemiring__1__class_Oof__nat__aux(T_b,V_inc_2,hAPP(c_Nat_OSuc,V_n_2),V_i_2) = c_Nat_Osemiring__1__class_Oof__nat__aux(T_b,V_inc_2,V_n_2,hAPP(V_inc_2,V_i_2)) ),
    file('theBenchmark.p',fact_of__nat__aux_Osimps_I2_J) ).

fof(fact_split__paired__All,axiom,
    ! [T_c,T_b,V_P_2] :
      ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
    <=> ! [B_a,B_b] : hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b))) ),
    file('theBenchmark.p',fact_split__paired__All) ).

fof(fact_Pair__eq,axiom,
    ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
      ( hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_H_2),V_b_H_2)
    <=> ( V_b_2 = V_b_H_2
        & V_a_2 = V_a_H_2 ) ),
    file('theBenchmark.p',fact_Pair__eq) ).

fof(fact_Pair__inject,axiom,
    ! [V_b_H,V_a_H,V_b,V_a,T_b,T_a] :
      ( hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a),V_b) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_H),V_b_H)
     => ~ ( V_a = V_a_H
         => V_b != V_b_H ) ),
    file('theBenchmark.p',fact_Pair__inject) ).

fof(fact_split__weak__cong,axiom,
    ! [V_c_2,T_d,T_c,T_b,V_q_2,V_p_2] :
      ( V_p_2 = V_q_2
     => hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_c_2),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_c_2),V_q_2) ),
    file('theBenchmark.p',fact_split__weak__cong) ).

fof(fact_divmod__int__mod__div,axiom,
    ! [V_q,V_p] : c_Divides_Odivmod__int(V_p,V_q) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_p),V_q)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_p,V_q)),
    file('theBenchmark.p',fact_divmod__int__mod__div) ).

fof(fact_prod_Osimps_I2_J,axiom,
    ! [V_b_2,V_a_2,V_f1_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f1_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2),
    file('theBenchmark.p',fact_prod_Osimps_I2_J) ).

fof(fact_split__conv,axiom,
    ! [V_b_2,V_a_2,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(V_f_2,V_a_2),V_b_2),
    file('theBenchmark.p',fact_split__conv) ).

fof(fact_divmod__nat__if,axiom,
    ! [V_m_2,V_n_2] :
      ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
            | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
       => c_Divides_Odivmod__nat(V_m_2,V_n_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat)),c_Nat_OSuc)),c_Divides_Odivmod__nat(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2),V_n_2)) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
          | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
       => c_Divides_Odivmod__nat(V_m_2,V_n_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2) ) ),
    file('theBenchmark.p',fact_divmod__nat__if) ).

fof(fact_split__eta,axiom,
    ! [V_f_2,T_d,T_c,T_b] : hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,T_d),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),T_d,T_c),V_f_2)),c_Product__Type_OPair(T_b,T_c))) = V_f_2,
    file('theBenchmark.p',fact_split__eta) ).

fof(fact_swap__inj__on,axiom,
    ! [V_A_2,T_c,T_b] : c_Fun_Oinj__on(tc_prod(T_b,T_c),tc_prod(T_c,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_prod(T_c,T_b)),hAPP(c_COMBC(T_c,T_b,tc_prod(T_c,T_b)),c_Product__Type_OPair(T_c,T_b))),V_A_2),
    file('theBenchmark.p',fact_swap__inj__on) ).

fof(fact_split__twice,axiom,
    ! [V_p_2,V_g_2,T_f,T_e,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_e,T_f,tc_prod(T_c,T_d)),V_g_2),V_p_2)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_e,T_f,T_b),hAPP(hAPP(c_COMBB(tc_fun(T_f,tc_prod(T_c,T_d)),tc_fun(T_f,T_b),T_e),hAPP(c_COMBB(tc_prod(T_c,T_d),T_b,T_f),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2))),V_g_2)),V_p_2),
    file('theBenchmark.p',fact_split__twice) ).

fof(fact_Nitpick_OFrac__def,axiom,
    c_Nitpick_OFrac = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),c_fequal)),c_Nitpick_Oint__gcd))),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    file('theBenchmark.p',fact_Nitpick_OFrac__def) ).

fof(fact_divmod__int__def,axiom,
    ! [V_b,V_a] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
       => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
           => c_Divides_Odivmod__int(V_a,V_b) = hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b))) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
           => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OnegDivAlg(V_a,V_b) ) ) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
       => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
           => ( ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
               => c_Divides_Odivmod__int(V_a,V_b) = hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b))) )
              & ( V_a = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
               => c_Divides_Odivmod__int(V_a,V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
           => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OposDivAlg(V_a,V_b) ) ) ) ),
    file('theBenchmark.p',fact_divmod__int__def) ).

fof(fact_divmod__int__pdivmod,axiom,
    ! [V_l_2,V_k_2] :
      ( ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => ( ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
           => c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_l_2))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fdisj,hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l_2)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_l_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(V_k_2,V_l_2)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_l_2))))),c_Divides_Opdivmod(V_k_2,V_l_2)))) )
          & ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
           => c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2) ) ) )
      & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
    file('theBenchmark.p',fact_divmod__int__pdivmod) ).

fof(fact_apsnd__conv,axiom,
    ! [V_y_2,V_x_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),V_x_2),V_y_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),hAPP(V_f_2,V_y_2)),
    file('theBenchmark.p',fact_apsnd__conv) ).

fof(fact_negateSnd__def,axiom,
    c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)),
    file('theBenchmark.p',fact_negateSnd__def) ).

fof(fact_apsnd__compose,axiom,
    ! [V_x_2,V_g_2,T_e,V_f_2,T_b,T_c,T_d] : hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),hAPP(c_Product__Type_Oapsnd(T_e,T_d,T_b,V_g_2),V_x_2)) = hAPP(c_Product__Type_Oapsnd(T_e,T_c,T_b,hAPP(c_Fun_Ocomp(T_d,T_c,T_e,V_f_2),V_g_2)),V_x_2),
    file('theBenchmark.p',fact_apsnd__compose) ).

fof(fact_negateSnd__eq,axiom,
    ! [V_r,V_q] : hAPP(c_Divides_OnegateSnd,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_r)),
    file('theBenchmark.p',fact_negateSnd__eq) ).

fof(fact_pdivmod__def,axiom,
    ! [V_l,V_k] : c_Divides_Opdivmod(V_k,V_l) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_k)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_l))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_k),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_l))),
    file('theBenchmark.p',fact_pdivmod__def) ).

fof(fact_pdivmod__posDivAlg,axiom,
    ! [V_k,V_l] :
      ( ( V_l != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => c_Divides_Opdivmod(V_k,V_l) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_k),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_l)) )
      & ( V_l = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => c_Divides_Opdivmod(V_k,V_l) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_k)) ) ),
    file('theBenchmark.p',fact_pdivmod__posDivAlg) ).

fof(fact_divmod__int__code,axiom,
    ! [V_l_2,V_k_2] :
      ( ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => ( ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
           => c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_l_2))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fequal,c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_k_2)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_l_2))),c_Divides_Opdivmod(V_k_2,V_l_2)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_l_2))))),c_Divides_Opdivmod(V_k_2,V_l_2)))) )
          & ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
           => c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2) ) ) )
      & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
    file('theBenchmark.p',fact_divmod__int__code) ).

fof(fact_divmod__nat__rel__mult1__eq,axiom,
    ! [V_a,V_r,V_q,V_c,V_b] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_b,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_q),V_r)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
       => hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_b),V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_q)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_r)),V_c))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_r),V_c)))) ) ),
    file('theBenchmark.p',fact_divmod__nat__rel__mult1__eq) ).

fof(fact_divmod__nat__rel__mult2__eq,axiom,
    ! [V_c,V_r,V_q,V_b,V_a] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_q),V_r)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_b))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
         => hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_q),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_q,V_c))),V_r)))) ) ) ),
    file('theBenchmark.p',fact_divmod__nat__rel__mult2__eq) ).

fof(fact_pair__box_Osize_I2_J,axiom,
    ! [V_b,V_a,T_b,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(T_a,T_b)),c_Nitpick_Opair__box_OPairBox(T_a,T_b,V_a,V_b)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_pair__box_Osize_I2_J) ).

fof(fact_divmod__nat__rel__unique,axiom,
    ! [V_qr_H,V_qr,V_n,V_m] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr))
     => ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr_H))
       => V_qr = V_qr_H ) ),
    file('theBenchmark.p',fact_divmod__nat__rel__unique) ).

fof(fact_divmod__nat__eq,axiom,
    ! [V_qr,V_n,V_m] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr))
     => c_Divides_Odivmod__nat(V_m,V_n) = V_qr ),
    file('theBenchmark.p',fact_divmod__nat__eq) ).

fof(fact_divmod__nat__rel__divmod__nat,axiom,
    ! [V_n,V_m] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),c_Divides_Odivmod__nat(V_m,V_n))),
    file('theBenchmark.p',fact_divmod__nat__rel__divmod__nat) ).

fof(fact_mod__eq,axiom,
    ! [V_r,V_q,V_n,V_m] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_q),V_r)))
     => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_r ),
    file('theBenchmark.p',fact_mod__eq) ).

fof(fact_div__eq,axiom,
    ! [V_r,V_q,V_n,V_m] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_q),V_r)))
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = V_q ),
    file('theBenchmark.p',fact_div__eq) ).

fof(fact_divmod__nat__rel,axiom,
    ! [V_n,V_m] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)))),
    file('theBenchmark.p',fact_divmod__nat__rel) ).

fof(fact_divmod__nat__rel__add1__eq,axiom,
    ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_a,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_aq),V_ar)))
     => ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_b,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_bq),V_br)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
         => hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a),V_b),V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_aq),V_bq)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_ar),V_br)),V_c))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_ar),V_br),V_c)))) ) ) ),
    file('theBenchmark.p',fact_divmod__nat__rel__add1__eq) ).

fof(fact_pair__box_Osimps_I2_J,axiom,
    ! [V_b_2,V_a_2,V_f1_2,T_b,T_d,T_c] : c_Nitpick_Opair__box_Opair__box__case(T_c,T_d,T_b,V_f1_2,c_Nitpick_Opair__box_OPairBox(T_c,T_d,V_a_2,V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2),
    file('theBenchmark.p',fact_pair__box_Osimps_I2_J) ).

fof(fact_pair__box_Orecs,axiom,
    ! [V_b_2,V_a_2,V_f1_2,T_b,T_d,T_c] : c_Nitpick_Opair__box_Opair__box__rec(T_c,T_d,T_b,V_f1_2,c_Nitpick_Opair__box_OPairBox(T_c,T_d,V_a_2,V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2),
    file('theBenchmark.p',fact_pair__box_Orecs) ).

fof(fact_negDivAlg_Opsimps,axiom,
    ! [V_b_2,V_a_2] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a_2),V_b_2)))
     => ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),V_b_2))) )
         => c_Divides_OnegDivAlg(V_a_2,V_b_2) = hAPP(c_Divides_Oadjust(V_b_2),c_Divides_OnegDivAlg(V_a_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b_2))) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),V_b_2))) )
         => c_Divides_OnegDivAlg(V_a_2,V_b_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),V_b_2)) ) ) ),
    file('theBenchmark.p',fact_negDivAlg_Opsimps) ).

fof(fact_posDivAlg_Opsimps,axiom,
    ! [V_b_2,V_a_2] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a_2),V_b_2)))
     => ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2)) )
         => c_Divides_OposDivAlg(V_a_2,V_b_2) = hAPP(c_Divides_Oadjust(V_b_2),c_Divides_OposDivAlg(V_a_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b_2))) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2)) )
         => c_Divides_OposDivAlg(V_a_2,V_b_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2) ) ) ),
    file('theBenchmark.p',fact_posDivAlg_Opsimps) ).

fof(fact_norm__frac_Opsimps,axiom,
    ! [V_b_2,V_a_2] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a_2),V_b_2)))
     => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => ( ( ~ ( V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
                  | V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
             => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,V_a_2),V_b_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b_2))) )
            & ( ( V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
                | V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
             => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b_2)) ) ) ),
    file('theBenchmark.p',fact_norm__frac_Opsimps) ).

fof(fact_negDivAlg_Opinduct,axiom,
    ! [V_P_2,V_a1_2,V_a0_2] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2)))
     => ( ! [B_a,B_b] :
            ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_a),B_b)))
           => ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_a),B_b))) )
               => hBOOL(hAPP(hAPP(V_P_2,B_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),B_b))) )
             => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) )
       => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ),
    file('theBenchmark.p',fact_negDivAlg_Opinduct) ).

fof(fact_posDivAlg_Opinduct,axiom,
    ! [V_P_2,V_a1_2,V_a0_2] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2)))
     => ( ! [B_a,B_b] :
            ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_a),B_b)))
           => ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_a),B_b)) )
               => hBOOL(hAPP(hAPP(V_P_2,B_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),B_b))) )
             => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) )
       => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ),
    file('theBenchmark.p',fact_posDivAlg_Opinduct) ).

fof(fact_accp__subset,axiom,
    ! [V_R2_2,V_R1_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),V_R1_2),V_R2_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Wellfounded_Oaccp(T_b,V_R2_2)),c_Wellfounded_Oaccp(T_b,V_R1_2))) ),
    file('theBenchmark.p',fact_accp__subset) ).

fof(fact_zmult2__lemma,axiom,
    ! [V_c,V_r,V_q,V_b,V_a] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r)))
     => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
         => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_q),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r)))) ) ) ),
    file('theBenchmark.p',fact_zmult2__lemma) ).

fof(fact_divmod__int__rel__0,axiom,
    ! [V_b] :
      ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
     => hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) ),
    file('theBenchmark.p',fact_divmod__int__rel__0) ).

fof(fact_self__remainder,axiom,
    ! [V_r,V_q,V_a] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_a),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r)))
     => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => V_r = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    file('theBenchmark.p',fact_self__remainder) ).

fof(fact_unique__quotient,axiom,
    ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r)))
     => ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q_H),V_r_H)))
       => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => V_q = V_q_H ) ) ),
    file('theBenchmark.p',fact_unique__quotient) ).

fof(fact_unique__remainder,axiom,
    ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r)))
     => ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q_H),V_r_H)))
       => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => V_r = V_r_H ) ) ),
    file('theBenchmark.p',fact_unique__remainder) ).

fof(fact_divmod__int__rel__neg,axiom,
    ! [V_qr,V_b,V_a] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)),V_qr))
     => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(c_Divides_OnegateSnd,V_qr))) ),
    file('theBenchmark.p',fact_divmod__int__rel__neg) ).

fof(fact_divmod__int__correct,axiom,
    ! [V_a,V_b] :
      ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
     => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_Odivmod__int(V_a,V_b))) ),
    file('theBenchmark.p',fact_divmod__int__correct) ).

fof(fact_accp__downward,axiom,
    ! [V_a_2,V_b_2,V_r_2,T_b] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_b_2))
     => ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
       => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2)) ) ),
    file('theBenchmark.p',fact_accp__downward) ).

fof(fact_accp_Oequations,axiom,
    ! [V_a_2,V_r_2,T_b] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2))
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2))
         => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x)) ) ),
    file('theBenchmark.p',fact_accp_Oequations) ).

fof(fact_accp_Osimps,axiom,
    ! [V_a_2,V_r_2,T_b] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2))
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2))
         => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x)) ) ),
    file('theBenchmark.p',fact_accp_Osimps) ).

fof(fact_self__quotient,axiom,
    ! [V_r,V_q,V_a] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_a),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r)))
     => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => V_q = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
    file('theBenchmark.p',fact_self__quotient) ).

fof(fact_divmod__int__rel__mod,axiom,
    ! [V_r,V_q,V_b,V_a] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r)))
     => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_r ) ),
    file('theBenchmark.p',fact_divmod__int__rel__mod) ).

fof(fact_divmod__int__rel__div,axiom,
    ! [V_r,V_q,V_b,V_a] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r)))
     => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = V_q ) ),
    file('theBenchmark.p',fact_divmod__int__rel__div) ).

fof(fact_negDivAlg__correct,axiom,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
       => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OnegDivAlg(V_a,V_b))) ) ),
    file('theBenchmark.p',fact_negDivAlg__correct) ).

fof(fact_divmod__int__rel__div__mod,axiom,
    ! [V_a,V_b] :
      ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
     => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)))) ),
    file('theBenchmark.p',fact_divmod__int__rel__div__mod) ).

fof(fact_posDivAlg__correct,axiom,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
       => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OposDivAlg(V_a,V_b))) ) ),
    file('theBenchmark.p',fact_posDivAlg__correct) ).

fof(fact_zadd1__lemma,axiom,
    ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_aq),V_ar)))
     => ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_b,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_bq),V_br)))
       => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b),V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_aq),V_bq)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_ar),V_br)),V_c))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_ar),V_br),V_c)))) ) ) ),
    file('theBenchmark.p',fact_zadd1__lemma) ).

fof(fact_zminus1__lemma,axiom,
    ! [V_r_2,V_q_2,V_b_2,V_a_2] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a_2,V_b_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q_2),V_r_2)))
     => hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a_2),V_b_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,V_r_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_q_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_q_2)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,V_r_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_b_2),V_r_2))))) ),
    file('theBenchmark.p',fact_zminus1__lemma) ).

fof(fact_divmod__int__relI,axiom,
    ! [V_r,V_q,V_b,V_a] :
      ( V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r)
     => ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) ) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) ) ) )
       => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r))) ) ),
    file('theBenchmark.p',fact_divmod__int__relI) ).

fof(fact_zmult1__lemma,axiom,
    ! [V_a,V_r,V_q,V_c,V_b] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_b,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r)))
     => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b),V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_r)),V_c))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_r),V_c)))) ) ),
    file('theBenchmark.p',fact_zmult1__lemma) ).

fof(fact_divmod__int__rel__def,axiom,
    ! [V_b_2,V_a_2] : c_Divides_Odivmod__int__rel(V_a_2,V_b_2) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fequal,V_a_2))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_2)))))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fimplies,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Int_Oint)),V_b_2))))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fimplies,hAPP(c_fNot,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))))),
    file('theBenchmark.p',fact_divmod__int__rel__def) ).

fof(fact_nat__gcd_Opsimps,axiom,
    ! [V_y_2,V_x_2] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)))
     => ( ( V_y_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => c_Nitpick_Onat__gcd(V_x_2,V_y_2) = c_Nitpick_Onat__gcd(V_y_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x_2,V_y_2)) )
        & ( V_y_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => c_Nitpick_Onat__gcd(V_x_2,V_y_2) = V_x_2 ) ) ),
    file('theBenchmark.p',fact_nat__gcd_Opsimps) ).

fof(fact_nat_Osize_I2_J,axiom,
    ! [V_nat] : c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,V_nat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(V_nat)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('theBenchmark.p',fact_nat_Osize_I2_J) ).

fof(fact_coinduct3__mono__lemma,axiom,
    ! [V_B_2,V_X_2,V_f_2,T_c,T_b] :
      ( class_Orderings_Oorder(T_b)
     => ( c_Orderings_Oorder__class_Omono(T_b,tc_fun(T_c,tc_HOL_Obool),V_f_2)
       => c_Orderings_Oorder__class_Omono(T_b,tc_fun(T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_f_2)),V_X_2))),V_B_2)) ) ),
    file('theBenchmark.p',fact_coinduct3__mono__lemma) ).

fof(fact_nat_Osize_I1_J,axiom,
    c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_nat_Osize_I1_J) ).

fof(fact_transfer__int__nat__sum__prod2_I2_J,axiom,
    ! [V_f_2,V_A_2,T_b] :
      ( ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
         => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) )
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Int_Oint),V_f_2),V_A_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,T_b),c_Int_Onat),V_f_2)),V_A_2)) ),
    file('theBenchmark.p',fact_transfer__int__nat__sum__prod2_I2_J) ).

fof(fact_mod__pos__neg__1__number__of,axiom,
    ! [V_w] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))))) ),
    file('theBenchmark.p',fact_mod__pos__neg__1__number__of) ).

fof(fact_in__measure,axiom,
    ! [V_f_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(c_Wellfounded_Omeasure(T_b),V_f_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) ),
    file('theBenchmark.p',fact_in__measure) ).

fof(fact_snd__apsnd,axiom,
    ! [V_x_2,V_f_2,T_d,T_b,T_c] : hAPP(c_Product__Type_Osnd(T_c,T_b),hAPP(c_Product__Type_Oapsnd(T_d,T_b,T_c,V_f_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_c,T_d),V_x_2)),
    file('theBenchmark.p',fact_snd__apsnd) ).

fof(fact_apsnd__eq__conv,axiom,
    ! [V_g_2,V_x_2,V_f_2,T_b,T_c,T_d] :
      ( hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),V_x_2) = hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_g_2),V_x_2)
    <=> hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_b,T_d),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_b,T_d),V_x_2)) ),
    file('theBenchmark.p',fact_apsnd__eq__conv) ).

fof(fact_snd__conv,axiom,
    ! [V_b,V_a,T_a,T_b] : hAPP(c_Product__Type_Osnd(T_b,T_a),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_a),V_b)) = V_b,
    file('theBenchmark.p',fact_snd__conv) ).

fof(fact_snd__eqD,axiom,
    ! [V_a,V_y,V_x,T_a,T_b] :
      ( hAPP(c_Product__Type_Osnd(T_b,T_a),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_x),V_y)) = V_a
     => V_y = V_a ),
    file('theBenchmark.p',fact_snd__eqD) ).

fof(fact_snd__def,axiom,
    ! [V_p_2,T_b,T_c] : hAPP(c_Product__Type_Osnd(T_c,T_b),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,T_b),hAPP(c_COMBK(tc_fun(T_b,T_b),T_c),c_COMBI(T_b))),V_p_2),
    file('theBenchmark.p',fact_snd__def) ).

fof(fact_mod__int__def,axiom,
    ! [V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(V_a,V_b)),
    file('theBenchmark.p',fact_mod__int__def) ).

fof(fact_mod__neg__pos,axiom,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(V_a,V_b)) ) ),
    file('theBenchmark.p',fact_mod__neg__pos) ).

fof(fact_mod__pos__pos,axiom,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(V_a,V_b)) ) ),
    file('theBenchmark.p',fact_mod__pos__pos) ).

fof(fact_mod__pos__pos__1__number__of,axiom,
    ! [V_w] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
     => c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) ),
    file('theBenchmark.p',fact_mod__pos__pos__1__number__of) ).

fof(fact_mod__pos__neg,axiom,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)))) ) ),
    file('theBenchmark.p',fact_mod__pos__neg) ).

fof(fact_mod__neg__neg,axiom,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)))) ) ),
    file('theBenchmark.p',fact_mod__neg__neg) ).

fof(fact_transfer__int__nat__sum__prod2_I1_J,axiom,
    ! [V_f_2,V_A_2,T_b] :
      ( ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
         => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) )
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Int_Oint),V_f_2),V_A_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,T_b),c_Int_Onat),V_f_2)),V_A_2)) ),
    file('theBenchmark.p',fact_transfer__int__nat__sum__prod2_I1_J) ).

fof(fact_folding_Oremove,axiom,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => hAPP(V_F_2,V_A_2) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(V_f_2,V_x_2)) ) ) ),
    file('theBenchmark.p',fact_folding_Oremove) ).

fof(fact_norm__frac_Opinduct,axiom,
    ! [V_P_2,V_a1_2,V_a0_2] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2)))
     => ( ! [B_a,B_b] :
            ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_a),B_b)))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
               => hBOOL(hAPP(hAPP(V_P_2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B_a)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B_b))) )
             => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) )
       => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ),
    file('theBenchmark.p',fact_norm__frac_Opinduct) ).

fof(fact_folding_Ocommute__left__comp,axiom,
    ! [V_g_2,V_x_2,V_y_2,T_d,V_F_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
     => hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_y_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_y_2)),V_g_2)) ),
    file('theBenchmark.p',fact_folding_Ocommute__left__comp) ).

fof(fact_folding_Ocommute__comp,axiom,
    ! [V_x_2,V_y_2,V_F_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
     => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_y_2)),hAPP(V_f_2,V_x_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)) ),
    file('theBenchmark.p',fact_folding_Ocommute__comp) ).

fof(fact_folding_Ocommute__comps_I1_J,axiom,
    ! [V_h_2,V_g_2,T_g,V_f_2,T_d,T_e,T_f,V_F_2,V_fa_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding(T_b,T_c,V_fa_2,V_F_2)
     => hAPP(c_Fun_Ocomp(T_f,T_e,T_d,V_f_2),hAPP(c_Fun_Ocomp(T_g,T_f,T_d,V_g_2),V_h_2)) = hAPP(c_Fun_Ocomp(T_g,T_e,T_d,hAPP(c_Fun_Ocomp(T_f,T_e,T_g,V_f_2),V_g_2)),V_h_2) ),
    file('theBenchmark.p',fact_folding_Ocommute__comps_I1_J) ).

fof(fact_mod__nat__def,axiom,
    ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(V_m,V_n)),
    file('theBenchmark.p',fact_mod__nat__def) ).

fof(fact_folding_Ocommute__left__comp_H_H,axiom,
    ! [V_g_2,T_d,V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
         => hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_B_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_A_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_A_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_B_2)),V_g_2)) ) ) ),
    file('theBenchmark.p',fact_folding_Ocommute__left__comp_H_H) ).

fof(fact_folding_Ocommute__comp_H_H,axiom,
    ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
         => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_B_2)),hAPP(V_F_2,V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ),
    file('theBenchmark.p',fact_folding_Ocommute__comp_H_H) ).

fof(fact_folding_Ocommute__left__comp_H,axiom,
    ! [V_g_2,V_x_2,T_d,V_A_2,V_F_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_A_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_A_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),V_g_2)) ) ),
    file('theBenchmark.p',fact_folding_Ocommute__left__comp_H) ).

fof(fact_folding_Ocommute__comp_H,axiom,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_F_2,V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) ) ),
    file('theBenchmark.p',fact_folding_Ocommute__comp_H) ).

fof(fact_folding_Oeq__fold,axiom,
    ! [V_s_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(hAPP(V_F_2,V_A_2),V_s_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_s_2),V_A_2) ) ),
    file('theBenchmark.p',fact_folding_Oeq__fold) ).

fof(fact_folding_Oinsert,axiom,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) ) ) ),
    file('theBenchmark.p',fact_folding_Oinsert) ).

fof(fact_folding_Ounion__inter,axiom,
    ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
         => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ),
    file('theBenchmark.p',fact_folding_Ounion__inter) ).

fof(fact_folding_Oinsert__remove,axiom,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(V_f_2,V_x_2)) ) ),
    file('theBenchmark.p',fact_folding_Oinsert__remove) ).

fof(fact_folding_Ounion,axiom,
    ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ),
    file('theBenchmark.p',fact_folding_Ounion) ).

fof(fact_div__pos__neg__1__number__of,axiom,
    ! [V_w] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))))) ),
    file('theBenchmark.p',fact_div__pos__neg__1__number__of) ).

fof(fact_nat__def,axiom,
    ! [V_z_2] : hAPP(c_Int_Onat,V_z_2) = c_Set_Othe__elem(tc_Nat_Onat,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,V_z_2)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_Set_Oinsert(tc_Nat_Onat))),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))))),
    file('theBenchmark.p',fact_nat__def) ).

fof(fact_UN__finite2__subset,axiom,
    ! [V_B_2,V_k_2,V_A_2,T_b] :
      ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_n),V_k_2))),V_B_2)))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_B_2))) ),
    file('theBenchmark.p',fact_UN__finite2__subset) ).

fof(fact_Pair__fst__snd__eq,axiom,
    ! [T_c,T_b,V_t_2,V_s_2] :
      ( V_s_2 = V_t_2
    <=> ( hAPP(c_Product__Type_Osnd(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Osnd(T_b,T_c),V_t_2)
        & hAPP(c_Product__Type_Ofst(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Ofst(T_b,T_c),V_t_2) ) ),
    file('theBenchmark.p',fact_Pair__fst__snd__eq) ).

fof(fact_prod__eqI,axiom,
    ! [V_q,V_p,T_b,T_a] :
      ( hAPP(c_Product__Type_Ofst(T_a,T_b),V_p) = hAPP(c_Product__Type_Ofst(T_a,T_b),V_q)
     => ( hAPP(c_Product__Type_Osnd(T_a,T_b),V_p) = hAPP(c_Product__Type_Osnd(T_a,T_b),V_q)
       => V_p = V_q ) ),
    file('theBenchmark.p',fact_prod__eqI) ).

fof(fact_fst__apsnd,axiom,
    ! [V_x_2,V_f_2,T_d,T_c,T_b] : hAPP(c_Product__Type_Ofst(T_b,T_c),hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),V_x_2)) = hAPP(c_Product__Type_Ofst(T_b,T_d),V_x_2),
    file('theBenchmark.p',fact_fst__apsnd) ).

fof(fact_fst__conv,axiom,
    ! [V_b,V_a,T_b,T_a] : hAPP(c_Product__Type_Ofst(T_a,T_b),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a),V_b)) = V_a,
    file('theBenchmark.p',fact_fst__conv) ).

fof(fact_fst__eqD,axiom,
    ! [V_a,V_y,V_x,T_b,T_a] :
      ( hAPP(c_Product__Type_Ofst(T_a,T_b),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x),V_y)) = V_a
     => V_x = V_a ),
    file('theBenchmark.p',fact_fst__eqD) ).

fof(fact_Rep__Integ__inject,axiom,
    ! [V_y_2,V_x_2] :
      ( hAPP(c_Int_ORep__Integ,V_x_2) = hAPP(c_Int_ORep__Integ,V_y_2)
    <=> V_x_2 = V_y_2 ),
    file('theBenchmark.p',fact_Rep__Integ__inject) ).

fof(fact_fst__def,axiom,
    ! [V_p_2,T_c,T_b] : hAPP(c_Product__Type_Ofst(T_b,T_c),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_b),c_COMBK(T_b,T_c)),V_p_2),
    file('theBenchmark.p',fact_fst__def) ).

fof(fact_surjective__pairing,axiom,
    ! [T_b,T_a,V_t] : V_t = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(c_Product__Type_Ofst(T_a,T_b),V_t)),hAPP(c_Product__Type_Osnd(T_a,T_b),V_t)),
    file('theBenchmark.p',fact_surjective__pairing) ).

fof(fact_pair__collapse,axiom,
    ! [V_p,T_b,T_a] : hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(c_Product__Type_Ofst(T_a,T_b),V_p)),hAPP(c_Product__Type_Osnd(T_a,T_b),V_p)) = V_p,
    file('theBenchmark.p',fact_pair__collapse) ).

fof(fact_prod__case__beta,axiom,
    ! [V_p_2,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2),V_p_2) = hAPP(hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_p_2)),hAPP(c_Product__Type_Osnd(T_c,T_d),V_p_2)),
    file('theBenchmark.p',fact_prod__case__beta) ).

fof(fact_div__int__def,axiom,
    ! [V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(V_a,V_b)),
    file('theBenchmark.p',fact_div__int__def) ).

fof(fact_split__beta,axiom,
    ! [V_z_2,V_P_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_P_2),V_z_2) = hAPP(hAPP(V_P_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_z_2)),hAPP(c_Product__Type_Osnd(T_c,T_d),V_z_2)),
    file('theBenchmark.p',fact_split__beta) ).

fof(fact_split__comp__eq,axiom,
    ! [V_g_2,V_f_2,T_e,T_d,T_c,T_b] : hAPP(hAPP(c_COMBS(tc_prod(T_b,T_c),T_c,T_d),hAPP(hAPP(c_COMBB(T_e,tc_fun(T_c,T_d),tc_prod(T_b,T_c)),V_f_2),hAPP(hAPP(c_COMBB(T_b,T_e,tc_prod(T_b,T_c)),V_g_2),c_Product__Type_Ofst(T_b,T_c)))),c_Product__Type_Osnd(T_b,T_c)) = hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),hAPP(hAPP(c_COMBB(T_e,tc_fun(T_c,T_d),T_b),V_f_2),V_g_2)),
    file('theBenchmark.p',fact_split__comp__eq) ).

fof(fact_split__def,axiom,
    ! [V_p_2,V_c_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_c_2),V_p_2) = hAPP(hAPP(V_c_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_p_2)),hAPP(c_Product__Type_Osnd(T_c,T_d),V_p_2)),
    file('theBenchmark.p',fact_split__def) ).

fof(fact_split__comp,axiom,
    ! [V_x_2,V_g_2,V_f_2,T_e,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),hAPP(c_Fun_Ocomp(T_e,tc_fun(T_d,T_b),T_c,V_f_2),V_g_2)),V_x_2) = hAPP(hAPP(V_f_2,hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_x_2))),hAPP(c_Product__Type_Osnd(T_c,T_d),V_x_2)),
    file('theBenchmark.p',fact_split__comp) ).

fof(fact_div__neg__pos,axiom,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(V_a,V_b)) ) ),
    file('theBenchmark.p',fact_div__neg__pos) ).

fof(fact_div__pos__pos,axiom,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(V_a,V_b)) ) ),
    file('theBenchmark.p',fact_div__pos__pos) ).

fof(fact_div__pos__pos__1__number__of,axiom,
    ! [V_w] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) ),
    file('theBenchmark.p',fact_div__pos__pos__1__number__of) ).

fof(fact_div__pos__neg,axiom,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)))) ) ),
    file('theBenchmark.p',fact_div__pos__neg) ).

fof(fact_div__neg__neg,axiom,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)))) ) ),
    file('theBenchmark.p',fact_div__neg__neg) ).

fof(fact_prod__size__simp,axiom,
    ! [V_p_2,V_g_2,V_f_2,T_c,T_b] : c_Product__Type_Oprod_Oprod__size(T_b,T_c,V_f_2,V_g_2,V_p_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_b,T_c),V_p_2))),hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_b,T_c),V_p_2)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('theBenchmark.p',fact_prod__size__simp) ).

fof(fact_exI__realizer,axiom,
    ! [T_b,T_c,V_x_2,V_y_2,V_P_2] :
      ( hBOOL(hAPP(hAPP(V_P_2,V_y_2),V_x_2))
     => hBOOL(hAPP(hAPP(V_P_2,hAPP(c_Product__Type_Osnd(T_c,T_b),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2),V_y_2))),hAPP(c_Product__Type_Ofst(T_c,T_b),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2),V_y_2)))) ),
    file('theBenchmark.p',fact_exI__realizer) ).

fof(fact_conjI__realizer,axiom,
    ! [T_c,T_b,V_q_2,V_Q_2,V_p_2,V_P_2] :
      ( hBOOL(hAPP(V_P_2,V_p_2))
     => ( hBOOL(hAPP(V_Q_2,V_q_2))
       => ( hBOOL(hAPP(V_Q_2,hAPP(c_Product__Type_Osnd(T_b,T_c),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_p_2),V_q_2))))
          & hBOOL(hAPP(V_P_2,hAPP(c_Product__Type_Ofst(T_b,T_c),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_p_2),V_q_2)))) ) ) ),
    file('theBenchmark.p',fact_conjI__realizer) ).

fof(fact_div__nat__def,axiom,
    ! [V_n,V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(V_m,V_n)),
    file('theBenchmark.p',fact_div__nat__def) ).

fof(fact_divmod__nat__rel__def,axiom,
    ! [V_qr_2,V_n_2,V_m_2] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m_2,V_n_2),V_qr_2))
    <=> ( ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
             => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2))) ) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
             => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)),V_n_2))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2))) ) ) ) )
        & ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),V_qr_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        & V_m_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)),V_n_2)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)) ) ),
    file('theBenchmark.p',fact_divmod__nat__rel__def) ).

fof(fact_nat__gcd_Opinduct,axiom,
    ! [V_P_2,V_a1_2,V_a0_2] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a0_2),V_a1_2)))
     => ( ! [B_x,B_y] :
            ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),B_x),B_y)))
           => ( ( B_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
               => hBOOL(hAPP(hAPP(V_P_2,B_y),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B_x,B_y))) )
             => hBOOL(hAPP(hAPP(V_P_2,B_x),B_y)) ) )
       => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ),
    file('theBenchmark.p',fact_nat__gcd_Opinduct) ).

fof(fact_range,axiom,
    ! [V_s,V_k] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),V_k))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Orange(V_k),V_s))),V_k)) ),
    file('theBenchmark.p',fact_range) ).

fof(fact_mlex__leq,axiom,
    ! [V_R_2,T_b,V_y_2,V_x_2,V_f_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_R_2))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2))) ) ),
    file('theBenchmark.p',fact_mlex__leq) ).

fof(fact_mlex__less,axiom,
    ! [V_R_2,T_b,V_y_2,V_x_2,V_f_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2))) ),
    file('theBenchmark.p',fact_mlex__less) ).

fof(fact_Least__mono,axiom,
    ! [V_S_2,V_f_2,T_b,T_c] :
      ( ( class_Orderings_Oorder(T_b)
        & class_Orderings_Oorder(T_c) )
     => ( c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
       => ( ? [B_x] :
              ( ! [B_xa] :
                  ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_S_2))
                 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),B_xa)) )
              & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) )
         => c_Orderings_Oord__class_OLeast(T_c,hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_S_2))) = hAPP(V_f_2,c_Orderings_Oord__class_OLeast(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2))) ) ) ),
    file('theBenchmark.p',fact_Least__mono) ).

fof(fact_folding__image_Oreindex,axiom,
    ! [V_g_2,V_h_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
       => ( c_Fun_Oinj__on(T_c,T_c,V_h_2,V_A_2)
         => hAPP(hAPP(V_F_2,V_g_2),hAPP(c_Set_Oimage(T_c,T_c,V_h_2),V_A_2)) = hAPP(hAPP(V_F_2,hAPP(c_Fun_Ocomp(T_c,T_b,T_c,V_g_2),V_h_2)),V_A_2) ) ) ),
    file('theBenchmark.p',fact_folding__image_Oreindex) ).

fof(fact_nat_Osize_I4_J,axiom,
    ! [V_nat] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_nat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),V_nat)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('theBenchmark.p',fact_nat_Osize_I4_J) ).

fof(fact_nat__size,axiom,
    ! [V_n] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),V_n) = V_n,
    file('theBenchmark.p',fact_nat__size) ).

fof(fact_LeastI__ex,axiom,
    ! [V_P_2,T_b] :
      ( class_Orderings_Owellorder(T_b)
     => ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
       => hBOOL(hAPP(V_P_2,c_Orderings_Oord__class_OLeast(T_b,V_P_2))) ) ),
    file('theBenchmark.p',fact_LeastI__ex) ).

fof(fact_LeastI,axiom,
    ! [V_k_2,V_P_2,T_b] :
      ( class_Orderings_Owellorder(T_b)
     => ( hBOOL(hAPP(V_P_2,V_k_2))
       => hBOOL(hAPP(V_P_2,c_Orderings_Oord__class_OLeast(T_b,V_P_2))) ) ),
    file('theBenchmark.p',fact_LeastI) ).

fof(fact_Least__le,axiom,
    ! [V_k_2,V_P_2,T_b] :
      ( class_Orderings_Owellorder(T_b)
     => ( hBOOL(hAPP(V_P_2,V_k_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Orderings_Oord__class_OLeast(T_b,V_P_2)),V_k_2)) ) ),
    file('theBenchmark.p',fact_Least__le) ).

fof(fact_not__less__Least,axiom,
    ! [V_P_2,V_k_2,T_b] :
      ( class_Orderings_Owellorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),c_Orderings_Oord__class_OLeast(T_b,V_P_2)))
       => ~ hBOOL(hAPP(V_P_2,V_k_2)) ) ),
    file('theBenchmark.p',fact_not__less__Least) ).

fof(fact_folding__image_Odistrib,axiom,
    ! [V_h_2,V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
       => hAPP(hAPP(V_F_2,hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),V_f_2),V_g_2)),V_h_2)),V_A_2) = hAPP(hAPP(V_f_2,hAPP(hAPP(V_F_2,V_g_2),V_A_2)),hAPP(hAPP(V_F_2,V_h_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_folding__image_Odistrib) ).

fof(fact_nat_Osize_I3_J,axiom,
    hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_nat_Osize_I3_J) ).

fof(fact_Least__Suc,axiom,
    ! [V_n_2,V_P_2] :
      ( hBOOL(hAPP(V_P_2,V_n_2))
     => ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
       => c_Orderings_Oord__class_OLeast(tc_Nat_Onat,V_P_2) = hAPP(c_Nat_OSuc,c_Orderings_Oord__class_OLeast(tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Nat_Onat),V_P_2),c_Nat_OSuc))) ) ),
    file('theBenchmark.p',fact_Least__Suc) ).

fof(fact_folding__image_Oeq__fold,axiom,
    ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
       => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2),V_z_2),V_A_2) ) ),
    file('theBenchmark.p',fact_folding__image_Oeq__fold) ).

fof(fact_prod_Orecs,axiom,
    ! [V_b_2,V_a_2,V_f1_2,T_b,T_d,T_c] : c_Product__Type_Oprod_Oprod__rec(T_c,T_d,T_b,V_f1_2,hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2),
    file('theBenchmark.p',fact_prod_Orecs) ).

fof(fact_setsum__reindex__nonzero,axiom,
    ! [T_c,V_h_2,V_f_2,V_S_2,T_b,T_d] :
      ( class_Groups_Ocomm__monoid__add(T_d)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
       => ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
             => ! [B_y] :
                  ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_S_2))
                 => ( B_x != B_y
                   => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y)
                     => hAPP(V_h_2,hAPP(V_f_2,B_x)) = c_Groups_Ozero__class_Ozero(T_d) ) ) ) )
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_h_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_S_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)),V_S_2) ) ) ),
    file('theBenchmark.p',fact_setsum__reindex__nonzero) ).

fof(fact_UN__finite2__eq,axiom,
    ! [V_B_2,V_k_2,V_A_2,T_b] :
      ( ! [B_n] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_n),V_k_2))),V_B_2)
     => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_B_2) ),
    file('theBenchmark.p',fact_UN__finite2__eq) ).

fof(fact_UN__finite__subset,axiom,
    ! [V_C_2,V_A_2,T_b] :
      ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)),V_A_2)),V_C_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2)),V_C_2)) ),
    file('theBenchmark.p',fact_UN__finite__subset) ).

fof(fact_image__INT,axiom,
    ! [V_j_2,V_B_2,V_A_2,T_d,V_C_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2)
     => ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_B_2,B_x)),V_C_2)) )
       => ( hBOOL(hAPP(hAPP(c_member(T_d),V_j_2),V_A_2))
         => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_d),c_Set_Oimage(T_b,T_c,V_f_2)),V_B_2)) ) ) ),
    file('theBenchmark.p',fact_image__INT) ).

fof(fact_in__lex__prod,axiom,
    ! [V_s_2,V_r_2,V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_H_2),V_b_H_2))),c_Wellfounded_Olex__prod(T_b,T_c,V_r_2,V_s_2)))
    <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_b_2),V_b_H_2)),V_s_2))
          & V_a_2 = V_a_H_2 )
        | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_H_2)),V_r_2)) ) ),
    file('theBenchmark.p',fact_in__lex__prod) ).

fof(fact_same__fstI,axiom,
    ! [T_b,V_R_2,V_y_2,V_y_H_2,T_c,V_x_2,V_P_2] :
      ( hBOOL(hAPP(V_P_2,V_x_2))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_y_H_2),V_y_2)),hAPP(V_R_2,V_x_2)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_H_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2))),c_Recdef_Osame__fst(T_b,T_c,V_P_2,V_R_2))) ) ),
    file('theBenchmark.p',fact_same__fstI) ).

fof(fact_in__finite__psubset,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),c_Wellfounded_Ofinite__psubset(T_b)))
    <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
    file('theBenchmark.p',fact_in__finite__psubset) ).

fof(fact_folding__idem_Ounion__idem,axiom,
    ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
         => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ),
    file('theBenchmark.p',fact_folding__idem_Ounion__idem) ).

fof(fact_folding__idem_Oidem__comp,axiom,
    ! [V_x_2,V_F_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
     => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_x_2)) = hAPP(V_f_2,V_x_2) ),
    file('theBenchmark.p',fact_folding__idem_Oidem__comp) ).

fof(fact_folding__idem_Oidem__left__comp,axiom,
    ! [V_g_2,V_x_2,T_d,V_F_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
     => hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),V_g_2) ),
    file('theBenchmark.p',fact_folding__idem_Oidem__left__comp) ).

fof(fact_folding__idem_Oin__comp__idem,axiom,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) = hAPP(V_F_2,V_A_2) ) ) ),
    file('theBenchmark.p',fact_folding__idem_Oin__comp__idem) ).

fof(fact_folding__idem_Oinsert__idem,axiom,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) ) ),
    file('theBenchmark.p',fact_folding__idem_Oinsert__idem) ).

fof(fact_folding__idem_Osubset__comp__idem,axiom,
    ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
         => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) = hAPP(V_F_2,V_A_2) ) ) ),
    file('theBenchmark.p',fact_folding__idem_Osubset__comp__idem) ).

fof(fact_setsum__nonneg__leq__bound,axiom,
    ! [V_i_2,V_B_2,V_f_2,V_s_2,T_b,T_c] :
      ( class_Groups_Oordered__ab__group__add(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
       => ( ! [B_i] :
              ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_s_2))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_i))) )
         => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_s_2) = V_B_2
           => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_s_2))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_i_2)),V_B_2)) ) ) ) ) ),
    file('theBenchmark.p',fact_setsum__nonneg__leq__bound) ).

fof(fact_setsum__nonneg__0,axiom,
    ! [V_i_2,V_f_2,V_s_2,T_b,T_c] :
      ( class_Groups_Oordered__ab__group__add(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
       => ( ! [B_i] :
              ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_s_2))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_i))) )
         => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_s_2) = c_Groups_Ozero__class_Ozero(T_c)
           => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_s_2))
             => hAPP(V_f_2,V_i_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ),
    file('theBenchmark.p',fact_setsum__nonneg__0) ).

fof(fact_sum__diff__distrib,axiom,
    ! [V_n_2,V_P_2,V_Q_2] :
      ( ! [B_x] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_Q_2,B_x)),hAPP(V_P_2,B_x)))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_P_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_Q_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_P_2)),V_Q_2)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2)) ),
    file('theBenchmark.p',fact_sum__diff__distrib) ).

fof(fact_apsnd__apfst,axiom,
    ! [V_x_2,V_g_2,T_e,V_f_2,T_b,T_c,T_d] : hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),hAPP(c_Product__Type_Oapfst(T_e,T_b,T_d,V_g_2),V_x_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_e,T_d),V_x_2))),hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_e,T_d),V_x_2))),
    file('theBenchmark.p',fact_apsnd__apfst) ).

fof(fact_apfst__apsnd,axiom,
    ! [V_x_2,V_g_2,T_e,V_f_2,T_c,T_b,T_d] : hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),hAPP(c_Product__Type_Oapsnd(T_e,T_c,T_d,V_g_2),V_x_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_d,T_e),V_x_2))),hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_d,T_e),V_x_2))),
    file('theBenchmark.p',fact_apfst__apsnd) ).

fof(fact_pair__lessI2,axiom,
    ! [V_t_2,V_s_2,V_b_2,V_a_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s_2),V_t_2))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_b_2),V_t_2))),c_FunDef_Opair__less)) ) ),
    file('theBenchmark.p',fact_pair__lessI2) ).

fof(fact_apfst__eq__conv,axiom,
    ! [V_g_2,V_x_2,V_f_2,T_c,T_b,T_d] :
      ( hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),V_x_2) = hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_g_2),V_x_2)
    <=> hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_d,T_c),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_d,T_c),V_x_2)) ),
    file('theBenchmark.p',fact_apfst__eq__conv) ).

fof(fact_fst__apfst,axiom,
    ! [V_x_2,V_f_2,T_d,T_c,T_b] : hAPP(c_Product__Type_Ofst(T_b,T_c),hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_d,T_c),V_x_2)),
    file('theBenchmark.p',fact_fst__apfst) ).

fof(fact_apfst__compose,axiom,
    ! [V_x_2,V_g_2,T_e,V_f_2,T_c,T_b,T_d] : hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),hAPP(c_Product__Type_Oapfst(T_e,T_d,T_c,V_g_2),V_x_2)) = hAPP(c_Product__Type_Oapfst(T_e,T_b,T_c,hAPP(c_Fun_Ocomp(T_d,T_b,T_e,V_f_2),V_g_2)),V_x_2),
    file('theBenchmark.p',fact_apfst__compose) ).

fof(fact_apfst__conv,axiom,
    ! [V_y_2,V_x_2,V_f_2,T_c,T_b,T_d] : hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_d,T_c),V_x_2),V_y_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,V_x_2)),V_y_2),
    file('theBenchmark.p',fact_apfst__conv) ).

fof(fact_snd__apfst,axiom,
    ! [V_x_2,V_f_2,T_d,T_b,T_c] : hAPP(c_Product__Type_Osnd(T_c,T_b),hAPP(c_Product__Type_Oapfst(T_d,T_c,T_b,V_f_2),V_x_2)) = hAPP(c_Product__Type_Osnd(T_d,T_b),V_x_2),
    file('theBenchmark.p',fact_snd__apfst) ).

fof(fact_apsnd__apfst__commute,axiom,
    ! [V_p_2,V_g_2,T_e,V_f_2,T_b,T_c,T_d] : hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),hAPP(c_Product__Type_Oapfst(T_e,T_b,T_d,V_g_2),V_p_2)) = hAPP(c_Product__Type_Oapfst(T_e,T_b,T_c,V_g_2),hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_e,V_f_2),V_p_2)),
    file('theBenchmark.p',fact_apsnd__apfst__commute) ).

fof(fact_pair__lessI1,axiom,
    ! [V_t_2,V_s_2,V_b_2,V_a_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_b_2),V_t_2))),c_FunDef_Opair__less)) ),
    file('theBenchmark.p',fact_pair__lessI1) ).

fof(fact_pair__leqI2,axiom,
    ! [V_t_2,V_s_2,V_b_2,V_a_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_s_2),V_t_2))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_b_2),V_t_2))),c_FunDef_Opair__leq)) ) ),
    file('theBenchmark.p',fact_pair__leqI2) ).

fof(fact_smin__insertI,axiom,
    ! [V_YS_2,V_y_2,V_XS_2,V_x_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_FunDef_Opair__less))
       => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),V_YS_2)),c_FunDef_Omin__strict))
         => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2))),c_FunDef_Omin__strict)) ) ) ),
    file('theBenchmark.p',fact_smin__insertI) ).

fof(fact_smax__insertI,axiom,
    ! [V_X_2,V_x_2,V_Y_2,V_y_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_Y_2))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_FunDef_Opair__less))
       => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_X_2),V_Y_2)),c_FunDef_Omax__strict))
         => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_X_2)),V_Y_2)),c_FunDef_Omax__strict)) ) ) ),
    file('theBenchmark.p',fact_smax__insertI) ).

fof(fact_smin__emptyI,axiom,
    ! [V_X_2] :
      ( V_X_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_X_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__strict)) ),
    file('theBenchmark.p',fact_smin__emptyI) ).

fof(fact_smax__emptyI,axiom,
    ! [V_Y_2] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_Y_2))
     => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),V_Y_2)),c_FunDef_Omax__strict)) ) ),
    file('theBenchmark.p',fact_smax__emptyI) ).

fof(fact_pair__leqI1,axiom,
    ! [V_t_2,V_s_2,V_b_2,V_a_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_b_2),V_t_2))),c_FunDef_Opair__leq)) ),
    file('theBenchmark.p',fact_pair__leqI1) ).

fof(fact_wmax__insertI,axiom,
    ! [V_XS_2,V_x_2,V_YS_2,V_y_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_FunDef_Opair__leq))
       => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),V_YS_2)),c_FunDef_Omax__weak))
         => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2)),V_YS_2)),c_FunDef_Omax__weak)) ) ) ),
    file('theBenchmark.p',fact_wmax__insertI) ).

fof(fact_wmin__insertI,axiom,
    ! [V_YS_2,V_y_2,V_XS_2,V_x_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_FunDef_Opair__leq))
       => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),V_YS_2)),c_FunDef_Omin__weak))
         => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2))),c_FunDef_Omin__weak)) ) ) ),
    file('theBenchmark.p',fact_wmin__insertI) ).

fof(fact_wmin__emptyI,axiom,
    ! [V_X_2] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_X_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__weak)),
    file('theBenchmark.p',fact_wmin__emptyI) ).

fof(fact_wmax__emptyI,axiom,
    ! [V_X_2] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_X_2))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),V_X_2)),c_FunDef_Omax__weak)) ),
    file('theBenchmark.p',fact_wmax__emptyI) ).

fof(fact_min__weak__def,axiom,
    c_FunDef_Omin__weak = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)))),
    file('theBenchmark.p',fact_min__weak__def) ).

fof(fact_max__weak__def,axiom,
    c_FunDef_Omax__weak = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)))),
    file('theBenchmark.p',fact_max__weak__def) ).

fof(fact_min__rpair__set,axiom,
    c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_FunDef_Omin__strict),c_FunDef_Omin__weak)),
    file('theBenchmark.p',fact_min__rpair__set) ).

fof(fact_max__strict__def,axiom,
    c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
    file('theBenchmark.p',fact_max__strict__def) ).

fof(fact_max__ext__additive,axiom,
    ! [V_D_2,V_C_2,V_R_2,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),c_Wellfounded_Omax__ext(T_b,V_R_2)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2)),c_Wellfounded_Omax__ext(T_b,V_R_2)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2))),c_Wellfounded_Omax__ext(T_b,V_R_2))) ) ),
    file('theBenchmark.p',fact_max__ext__additive) ).

fof(fact_min__strict__def,axiom,
    c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
    file('theBenchmark.p',fact_min__strict__def) ).

fof(fact_max__rpair__set,axiom,
    c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_FunDef_Omax__strict),c_FunDef_Omax__weak)),
    file('theBenchmark.p',fact_max__rpair__set) ).

fof(fact_max__extp__max__ext__eq,axiom,
    ! [V_xa_2,V_x_2,V_R_2,T_b] :
      ( c_Wellfounded_Omax__extp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_R_2),V_x_2,V_xa_2)
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_xa_2)),c_Wellfounded_Omax__ext(T_b,V_R_2))) ),
    file('theBenchmark.p',fact_max__extp__max__ext__eq) ).

fof(fact_less__than__iff,axiom,
    ! [V_y_2,V_x_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Wellfounded_Oless__than))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ),
    file('theBenchmark.p',fact_less__than__iff) ).

fof(fact_intrel__iff,axiom,
    ! [V_v_2,V_u_2,V_y_2,V_x_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2))),c_Int_Ointrel))
    <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_v_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_u_2),V_y_2) ),
    file('theBenchmark.p',fact_intrel__iff) ).

fof(fact_pair__less__def,axiom,
    c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than),
    file('theBenchmark.p',fact_pair__less__def) ).

fof(fact_mlex__prod__def,axiom,
    ! [V_R_2,V_f_2,T_b] : c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,T_b),T_b),c_Wellfounded_Olex__prod(tc_Nat_Onat,T_b,c_Wellfounded_Oless__than,V_R_2)),hAPP(hAPP(c_COMBS(T_b,T_b,tc_prod(tc_Nat_Onat,T_b)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_b,tc_prod(tc_Nat_Onat,T_b)),T_b),c_Product__Type_OPair(tc_Nat_Onat,T_b)),V_f_2)),c_COMBI(T_b))),
    file('theBenchmark.p',fact_mlex__prod__def) ).

fof(fact_rp__inv__image__rp,axiom,
    ! [V_f_2,T_c,V_P_2,T_b] :
      ( c_FunDef_Oreduction__pair(T_b,V_P_2)
     => c_FunDef_Oreduction__pair(T_c,hAPP(hAPP(c_FunDef_Orp__inv__image(T_b,T_c),V_P_2),V_f_2)) ),
    file('theBenchmark.p',fact_rp__inv__image__rp) ).

fof(fact_strong__setprod__reindex__cong,axiom,
    ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
      ( class_Groups_Ocomm__monoid__mult(T_d)
     => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
       => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
         => ( ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
               => hAPP(V_g_2,B_x) = hAPP(hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2),B_x) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_d),V_g_2),V_A_2) ) ) ) ),
    file('theBenchmark.p',fact_strong__setprod__reindex__cong) ).

fof(fact_rp__inv__image__def,axiom,
    ! [T_c,T_b] : c_FunDef_Orp__inv__image(T_b,T_c) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))))),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_COMBS(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_c,T_b),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))),tc_fun(T_c,T_b)),c_Product__Type_OPair(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),c_Relation_Oinv__image(T_b,T_c))))),c_Relation_Oinv__image(T_b,T_c))),
    file('theBenchmark.p',fact_rp__inv__image__def) ).

fof(fact_in__inv__image,axiom,
    ! [V_f_2,V_r_2,T_c,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Relation_Oinv__image(T_c,T_b),V_r_2),V_f_2)))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))),V_r_2)) ),
    file('theBenchmark.p',fact_in__inv__image) ).

fof(fact_equiv__intrel__iff,axiom,
    ! [V_y_2,V_x_2] :
      ( hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) = hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_Int_Ointrel)) ),
    file('theBenchmark.p',fact_equiv__intrel__iff) ).

fof(fact_transfer__nat__int__sum__prod__cong_I2_J,axiom,
    ! [V_g_2,V_f_2,V_B_2,V_A_2,T_b] :
      ( ( class_Groups_Ocomm__monoid__mult(T_b)
        & class_Groups_Ocomm__monoid__add(T_b) )
     => ( V_A_2 = V_B_2
       => ( c_Nat__Transfer_Onat__set(V_B_2)
         => ( ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
               => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_b),V_g_2),V_B_2) ) ) ) ),
    file('theBenchmark.p',fact_transfer__nat__int__sum__prod__cong_I2_J) ).

fof(fact_Image__empty,axiom,
    ! [V_R_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,V_R_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Image__empty) ).

fof(fact_Un__Image,axiom,
    ! [V_A_2,V_S_2,V_R_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_R_2),V_S_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_c,T_b,V_S_2),V_A_2)),
    file('theBenchmark.p',fact_Un__Image) ).

fof(fact_Image__Un,axiom,
    ! [V_B_2,V_A_2,V_R_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_B_2)),
    file('theBenchmark.p',fact_Image__Un) ).

fof(fact_Image__UN,axiom,
    ! [V_B_2,V_A_2,T_d,V_r_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Relation_OImage(T_c,T_b,V_r_2)),V_B_2)),
    file('theBenchmark.p',fact_Image__UN) ).

fof(fact_Image__INT__subset,axiom,
    ! [V_B_2,V_A_2,T_d,V_r_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Relation_OImage(T_c,T_b,V_r_2)),V_B_2)))),
    file('theBenchmark.p',fact_Image__INT__subset) ).

fof(fact_Image__Int__subset,axiom,
    ! [V_B_2,V_A_2,V_R_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_B_2)))),
    file('theBenchmark.p',fact_Image__Int__subset) ).

fof(fact_Image__mono,axiom,
    ! [V_A_2,V_A_H_2,V_r_2,V_r_H_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_H_2),V_r_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_H_2),V_A_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_c,V_r_H_2),V_A_H_2)),hAPP(c_Relation_OImage(T_b,T_c,V_r_2),V_A_2))) ) ),
    file('theBenchmark.p',fact_Image__mono) ).

fof(fact_Image__iff,axiom,
    ! [V_A_2,V_r_2,T_c,V_b_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2)))
    <=> ? [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),V_b_2)),V_r_2))
          & hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ),
    file('theBenchmark.p',fact_Image__iff) ).

fof(fact_rev__ImageI,axiom,
    ! [V_r_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2))
       => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Relation_OImage(T_b,T_c,V_r_2),V_A_2))) ) ),
    file('theBenchmark.p',fact_rev__ImageI) ).

fof(fact_Image__eq__UN,axiom,
    ! [V_B_2,V_r_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Relation_OImage(T_c,T_b,V_r_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),c_Set_Oinsert(T_c)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))),
    file('theBenchmark.p',fact_Image__eq__UN) ).

fof(fact_Image__singleton__iff,axiom,
    ! [V_a_2,V_r_2,T_c,V_b_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_a_2),V_b_2)),V_r_2)) ),
    file('theBenchmark.p',fact_Image__singleton__iff) ).

fof(fact_measure__def,axiom,
    ! [T_b] : c_Wellfounded_Omeasure(T_b) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,T_b),c_Wellfounded_Oless__than),
    file('theBenchmark.p',fact_measure__def) ).

fof(fact_of__int,axiom,
    ! [V_j_2,V_i_2,T_b] :
      ( class_Rings_Oring__1(T_b)
     => hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_i_2),V_j_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_i_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_j_2)) ),
    file('theBenchmark.p',fact_of__int) ).

fof(fact_One__int__def,axiom,
    c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    file('theBenchmark.p',fact_One__int__def) ).

fof(fact_mult,axiom,
    ! [V_v_2,V_u_2,V_y_2,V_x_2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_x_2),V_u_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_y_2),V_v_2))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_x_2),V_v_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_y_2),V_u_2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    file('theBenchmark.p',fact_mult) ).

fof(fact_Rep__Integ__inverse,axiom,
    ! [V_x_2] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,V_x_2)) = V_x_2,
    file('theBenchmark.p',fact_Rep__Integ__inverse) ).

fof(fact_minus,axiom,
    ! [V_y_2,V_x_2] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_y_2),V_x_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    file('theBenchmark.p',fact_minus) ).

fof(fact_Zero__int__def,axiom,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    file('theBenchmark.p',fact_Zero__int__def) ).

fof(fact_int__def,axiom,
    ! [V_m_2] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_m_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    file('theBenchmark.p',fact_int__def) ).

fof(fact_add,axiom,
    ! [V_v_2,V_u_2,V_y_2,V_x_2] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_u_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y_2),V_v_2))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    file('theBenchmark.p',fact_add) ).

fof(fact_nat,axiom,
    ! [V_y_2,V_x_2] : hAPP(c_Int_Onat,hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_y_2),
    file('theBenchmark.p',fact_nat) ).

fof(fact_minus__int__def,axiom,
    ! [V_z_2] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z_2) = hAPP(c_Int_OAbs__Integ,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,V_z_2)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_Nat_Onat),c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_Nat_Onat),c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_Nat_Onat),c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)))),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat))))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))),
    file('theBenchmark.p',fact_minus__int__def) ).

fof(fact_less,axiom,
    ! [V_v_2,V_u_2,V_y_2,V_x_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_v_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_u_2),V_y_2))) ),
    file('theBenchmark.p',fact_less) ).

fof(fact_le,axiom,
    ! [V_v_2,V_u_2,V_y_2,V_x_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_v_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_u_2),V_y_2))) ),
    file('theBenchmark.p',fact_le) ).

fof(fact_irrefl__def,axiom,
    ! [V_r_2,T_b] :
      ( c_Relation_Oirrefl(T_b,V_r_2)
    <=> ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) ),
    file('theBenchmark.p',fact_irrefl__def) ).

fof(fact_eq__Abs__Integ,axiom,
    ! [V_z_2] :
      ~ ! [B_x,B_y] : V_z_2 != hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),B_x),B_y)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    file('theBenchmark.p',fact_eq__Abs__Integ) ).

fof(fact_Field__insert,axiom,
    ! [V_r_2,V_b_2,V_a_2,T_b] : hAPP(c_Relation_OField(T_b),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(c_Relation_OField(T_b),V_r_2)),
    file('theBenchmark.p',fact_Field__insert) ).

fof(fact_Field__Union,axiom,
    ! [V_R_2,T_b] : hAPP(c_Relation_OField(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),V_R_2)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),c_Relation_OField(T_b)),V_R_2)),
    file('theBenchmark.p',fact_Field__Union) ).

fof(fact_Field__empty,axiom,
    ! [T_b] : hAPP(c_Relation_OField(T_b),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Field__empty) ).

fof(fact_mono__Field,axiom,
    ! [V_s_2,V_r_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OField(T_b),V_r_2)),hAPP(c_Relation_OField(T_b),V_s_2))) ),
    file('theBenchmark.p',fact_mono__Field) ).

fof(fact_Field__Un,axiom,
    ! [V_s_2,V_r_2,T_b] : hAPP(c_Relation_OField(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OField(T_b),V_r_2)),hAPP(c_Relation_OField(T_b),V_s_2)),
    file('theBenchmark.p',fact_Field__Un) ).

fof(fact_finite__Field,axiom,
    ! [V_r_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_OField(T_b),V_r_2))) ),
    file('theBenchmark.p',fact_finite__Field) ).

fof(fact_Id__on__def,axiom,
    ! [V_A_2,T_b] : c_Relation_OId__on(T_b,V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),T_b),c_Set_Oinsert(tc_prod(T_b,T_b))),hAPP(hAPP(c_COMBS(T_b,T_b,tc_prod(T_b,T_b)),c_Product__Type_OPair(T_b,T_b)),c_COMBI(T_b)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)))),
    file('theBenchmark.p',fact_Id__on__def) ).

fof(fact_quotient__def,axiom,
    ! [V_r_2,V_A_2,T_b] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),T_b),c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),c_Relation_OImage(T_b,T_b,V_r_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)))),
    file('theBenchmark.p',fact_quotient__def) ).

fof(fact_ImageE,axiom,
    ! [V_A_2,V_r_2,T_c,V_b_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2)))
     => ~ ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),V_b_2)),V_r_2))
           => ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ),
    file('theBenchmark.p',fact_ImageE) ).

fof(fact_quotient__empty,axiom,
    ! [V_r_2,T_b] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),
    file('theBenchmark.p',fact_quotient__empty) ).

fof(fact_quotient__is__empty2,axiom,
    ! [V_r_2,V_A_2,T_b] :
      ( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)
    <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_quotient__is__empty2) ).

fof(fact_quotient__is__empty,axiom,
    ! [V_r_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))
    <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_quotient__is__empty) ).

fof(fact_Id__on__def_H,axiom,
    ! [V_A_2,T_b] : c_Relation_OId__on(T_b,V_A_2) = hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),c_fequal))),V_A_2)),
    file('theBenchmark.p',fact_Id__on__def_H) ).

fof(fact_Id__on__empty,axiom,
    ! [T_b] : c_Relation_OId__on(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),
    file('theBenchmark.p',fact_Id__on__empty) ).

fof(fact_Image__Id__on,axiom,
    ! [V_B_2,V_A_2,T_b] : hAPP(c_Relation_OImage(T_b,T_b,c_Relation_OId__on(T_b,V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),
    file('theBenchmark.p',fact_Image__Id__on) ).

fof(fact_quotient__diff1,axiom,
    ! [V_a_2,V_A_2,V_r_2,T_b] :
      ( c_Fun_Oinj__on(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),T_b),c_Equiv__Relations_Oquotient(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_r_2),V_A_2)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
       => hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_r_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_r_2)) ) ),
    file('theBenchmark.p',fact_quotient__diff1) ).

fof(fact_quotientI,axiom,
    ! [V_r_2,V_A_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
     => hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) ),
    file('theBenchmark.p',fact_quotientI) ).

fof(fact_Id__on__eqI,axiom,
    ! [V_A_2,T_b,V_b_2,V_a_2] :
      ( V_a_2 = V_b_2
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Relation_OId__on(T_b,V_A_2))) ) ),
    file('theBenchmark.p',fact_Id__on__eqI) ).

fof(fact_Id__on__iff,axiom,
    ! [V_A_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Relation_OId__on(T_b,V_A_2)))
    <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
        & V_x_2 = V_y_2 ) ),
    file('theBenchmark.p',fact_Id__on__iff) ).

fof(fact_singleton__quotient,axiom,
    ! [V_r_2,V_x_2,T_b] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_r_2) = hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))),
    file('theBenchmark.p',fact_singleton__quotient) ).

fof(fact_card__quotient__disjoint,axiom,
    ! [V_r_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( c_Fun_Oinj__on(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),T_b),c_Equiv__Relations_Oquotient(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_r_2),V_A_2)
       => hAPP(c_Finite__Set_Ocard(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) ) ),
    file('theBenchmark.p',fact_card__quotient__disjoint) ).

fof(fact_equiv__class__nondisjoint,axiom,
    ! [V_b_2,V_a_2,V_x_2,V_r_2,V_A_2,T_b] :
      ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) ) ),
    file('theBenchmark.p',fact_equiv__class__nondisjoint) ).

fof(fact_subset__equiv__class,axiom,
    ! [V_a_2,V_b_2,V_r_2,V_A_2,T_b] :
      ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
         => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) ) ) ),
    file('theBenchmark.p',fact_subset__equiv__class) ).

fof(fact_quotientE,axiom,
    ! [V_r_2,V_A_2,V_X_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
     => ~ ! [B_x] :
            ( V_X_2 = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
           => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ),
    file('theBenchmark.p',fact_quotientE) ).

fof(fact_equiv__intrel,axiom,
    c_Equiv__Relations_Oequiv(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Int_Ointrel),
    file('theBenchmark.p',fact_equiv__intrel) ).

fof(fact_Union__quotient,axiom,
    ! [V_r_2,V_A_2,T_b] :
      ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
     => c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)) = V_A_2 ),
    file('theBenchmark.p',fact_Union__quotient) ).

fof(fact_equiv__class__self,axiom,
    ! [V_a_2,V_r_2,V_A_2,T_b] :
      ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
       => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ),
    file('theBenchmark.p',fact_equiv__class__self) ).

fof(fact_quotient__disj,axiom,
    ! [V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
      ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
     => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
       => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_Y_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
            | V_X_2 = V_Y_2 ) ) ) ),
    file('theBenchmark.p',fact_quotient__disj) ).

fof(fact_equiv__class__eq,axiom,
    ! [V_b_2,V_a_2,V_r_2,V_A_2,T_b] :
      ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
       => hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ),
    file('theBenchmark.p',fact_equiv__class__eq) ).

fof(fact_quotient__eq__iff,axiom,
    ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
      ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
     => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
       => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
         => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_X_2))
           => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_Y_2))
             => ( V_X_2 = V_Y_2
              <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) ) ) ) ) ) ),
    file('theBenchmark.p',fact_quotient__eq__iff) ).

fof(fact_quotient__eqI,axiom,
    ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
      ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
     => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
       => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
         => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_X_2))
           => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_Y_2))
             => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
               => V_X_2 = V_Y_2 ) ) ) ) ) ),
    file('theBenchmark.p',fact_quotient__eqI) ).

fof(fact_equiv__class__eq__iff,axiom,
    ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
      ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
      <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
          & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
          & hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ) ),
    file('theBenchmark.p',fact_equiv__class__eq__iff) ).

fof(fact_eq__equiv__class,axiom,
    ! [V_A_2,V_b_2,V_a_2,V_r_2,T_b] :
      ( hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
     => ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
         => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) ) ) ),
    file('theBenchmark.p',fact_eq__equiv__class) ).

fof(fact_eq__equiv__class__iff,axiom,
    ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
      ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
         => ( hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
          <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) ) ) ) ),
    file('theBenchmark.p',fact_eq__equiv__class__iff) ).

fof(fact_equiv__class__subset,axiom,
    ! [V_b_2,V_a_2,V_r_2,V_A_2,T_b] :
      ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ),
    file('theBenchmark.p',fact_equiv__class__subset) ).

fof(fact_eq__equiv__class__iff2,axiom,
    ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
      ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
         => ( hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_r_2) = hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_r_2)
          <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) ) ) ) ),
    file('theBenchmark.p',fact_eq__equiv__class__iff2) ).

fof(fact_UN__equiv__class2,axiom,
    ! [V_a2_2,V_a1_2,V_f_2,T_d,V_r2_2,V_A2_2,T_c,V_r1_2,V_A1_2,T_b] :
      ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2)
     => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
       => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
         => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a1_2),V_A1_2))
           => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a2_2),V_A2_2))
             => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r1_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_c,V_r2_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a2_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))),V_f_2)) = hAPP(hAPP(V_f_2,V_a1_2),V_a2_2) ) ) ) ) ),
    file('theBenchmark.p',fact_UN__equiv__class2) ).

fof(fact_UN__equiv__class,axiom,
    ! [V_a_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
      ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
     => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
         => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_f_2) = hAPP(V_f_2,V_a_2) ) ) ),
    file('theBenchmark.p',fact_UN__equiv__class) ).

fof(fact_equivp__equiv,axiom,
    ! [V_A_2,T_b] :
      ( c_Equiv__Relations_Oequiv(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_A_2)
    <=> c_Equiv__Relations_Oequivp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_A_2)) ),
    file('theBenchmark.p',fact_equivp__equiv) ).

fof(fact_equivp__transp,axiom,
    ! [V_z_2,V_y_2,V_x_2,V_R_2,T_b] :
      ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
     => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
       => ( hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_z_2))
         => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_z_2)) ) ) ),
    file('theBenchmark.p',fact_equivp__transp) ).

fof(fact_equivp__symp,axiom,
    ! [V_y_2,V_x_2,V_R_2,T_b] :
      ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
     => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
       => hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ),
    file('theBenchmark.p',fact_equivp__symp) ).

fof(fact_equivp__reflp,axiom,
    ! [V_x_2,V_R_2,T_b] :
      ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
     => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ),
    file('theBenchmark.p',fact_equivp__reflp) ).

fof(fact_equivp__def,axiom,
    ! [V_R_2,T_b] :
      ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
    <=> ! [B_x,B_y] :
          ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_y))
        <=> hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y) ) ),
    file('theBenchmark.p',fact_equivp__def) ).

fof(fact_identity__equivp,axiom,
    ! [T_b] : c_Equiv__Relations_Oequivp(T_b,c_fequal),
    file('theBenchmark.p',fact_identity__equivp) ).

fof(fact_congruent2__implies__congruent,axiom,
    ! [V_a_2,V_f_2,V_r2_2,T_d,T_c,V_r1_2,V_A_2,T_b] :
      ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r1_2)
     => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2)
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
         => c_Equiv__Relations_Ocongruent(T_c,T_d,V_r2_2,hAPP(V_f_2,V_a_2)) ) ) ),
    file('theBenchmark.p',fact_congruent2__implies__congruent) ).

fof(fact_congruent2D,axiom,
    ! [V_z2_2,V_y2_2,V_z1_2,V_y1_2,V_f_2,V_r2_2,V_r1_2,T_d,T_c,T_b] :
      ( c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y1_2),V_z1_2)),V_r1_2))
       => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_y2_2),V_z2_2)),V_r2_2))
         => hAPP(hAPP(V_f_2,V_y1_2),V_y2_2) = hAPP(hAPP(V_f_2,V_z1_2),V_z2_2) ) ) ),
    file('theBenchmark.p',fact_congruent2D) ).

fof(fact_congruentD,axiom,
    ! [V_z_2,V_y_2,V_f_2,V_r_2,T_c,T_b] :
      ( c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),V_r_2))
       => hAPP(V_f_2,V_y_2) = hAPP(V_f_2,V_z_2) ) ),
    file('theBenchmark.p',fact_congruentD) ).

fof(fact_congruent2__implies__congruent__UN,axiom,
    ! [V_a_2,V_f_2,T_d,V_r2_2,V_A2_2,T_c,V_r1_2,V_A1_2,T_b] :
      ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2)
     => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
       => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
         => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A2_2))
           => c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_d,tc_HOL_Obool),V_r1_2,hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_c,V_r2_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))),V_f_2)) ) ) ) ),
    file('theBenchmark.p',fact_congruent2__implies__congruent__UN) ).

fof(fact_UN__equiv__class__inject,axiom,
    ! [V_Y_2,V_X_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
      ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
     => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
       => ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_X_2),V_f_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_Y_2),V_f_2)
         => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
           => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
             => ( ! [B_x] :
                    ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
                   => ! [B_y] :
                        ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2))
                       => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y)
                         => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_r_2)) ) ) )
               => V_X_2 = V_Y_2 ) ) ) ) ) ),
    file('theBenchmark.p',fact_UN__equiv__class__inject) ).

fof(fact_UN__equiv__class__type2,axiom,
    ! [V_B_2,V_X2_2,V_X1_2,V_f_2,T_d,V_r2_2,V_A2_2,T_c,V_r1_2,V_A1_2,T_b] :
      ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2)
     => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
       => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
         => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X1_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A1_2),V_r1_2)))
           => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_X2_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),V_A2_2),V_r2_2)))
             => ( ! [B_x1] :
                    ( hBOOL(hAPP(hAPP(c_member(T_b),B_x1),V_A1_2))
                   => ! [B_x2] :
                        ( hBOOL(hAPP(hAPP(c_member(T_c),B_x2),V_A2_2))
                       => hBOOL(hAPP(hAPP(c_member(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(V_f_2,B_x1),B_x2)),V_B_2)) ) )
               => hBOOL(hAPP(hAPP(c_member(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_d,tc_HOL_Obool)),V_X1_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_X2_2)),V_f_2))),V_B_2)) ) ) ) ) ) ),
    file('theBenchmark.p',fact_UN__equiv__class__type2) ).

fof(fact_UN__equiv__class__type,axiom,
    ! [V_B_2,V_X_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
      ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
     => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
       => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
         => ( ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
               => hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_f_2,B_x)),V_B_2)) )
           => hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_X_2),V_f_2)),V_B_2)) ) ) ) ),
    file('theBenchmark.p',fact_UN__equiv__class__type) ).

fof(fact_Integ__def,axiom,
    c_Int_OInteg = hAPP(hAPP(c_Equiv__Relations_Oquotient(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Int_Ointrel),
    file('theBenchmark.p',fact_Integ__def) ).

fof(fact_Id__onE,axiom,
    ! [V_A_2,V_c_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_c_2),c_Relation_OId__on(T_b,V_A_2)))
     => ~ ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
           => V_c_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x) ) ),
    file('theBenchmark.p',fact_Id__onE) ).

fof(fact_transfer__nat__int__sum__prod__cong_I1_J,axiom,
    ! [V_g_2,V_f_2,V_B_2,V_A_2,T_b] :
      ( ( class_Groups_Ocomm__monoid__mult(T_b)
        & class_Groups_Ocomm__monoid__add(T_b) )
     => ( V_A_2 = V_B_2
       => ( c_Nat__Transfer_Onat__set(V_B_2)
         => ( ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
               => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),V_g_2),V_B_2) ) ) ) ),
    file('theBenchmark.p',fact_transfer__nat__int__sum__prod__cong_I1_J) ).

fof(fact_Rep__Integ,axiom,
    ! [V_x_2] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,V_x_2)),c_Int_OInteg)),
    file('theBenchmark.p',fact_Rep__Integ) ).

fof(fact_type__definition__Integ,axiom,
    c_Typedef_Otype__definition(tc_Int_Oint,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Int_ORep__Integ,c_Int_OAbs__Integ,c_Int_OInteg),
    file('theBenchmark.p',fact_type__definition__Integ) ).

fof(fact_accp__acc__eq,axiom,
    ! [V_x_2,V_r_2,T_b] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2)),V_x_2))
    <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ),
    file('theBenchmark.p',fact_accp__acc__eq) ).

fof(fact_max__extp_Oequations,axiom,
    ! [V_a2_2,V_a1_2,V_R_2,T_b] :
      ( c_Wellfounded_Omax__extp(T_b,V_R_2,V_a1_2,V_a2_2)
    <=> ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2))
           => ? [B_xa] :
                ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa))
                & hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2)) ) )
        & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2)) ) ),
    file('theBenchmark.p',fact_max__extp_Oequations) ).

fof(fact_acc__subset,axiom,
    ! [V_R2_2,V_R1_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R1_2),V_R2_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Wellfounded_Oacc(T_b,V_R2_2)),c_Wellfounded_Oacc(T_b,V_R1_2))) ),
    file('theBenchmark.p',fact_acc__subset) ).

fof(fact_acc__downward,axiom,
    ! [V_a_2,V_r_2,V_b_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
       => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ),
    file('theBenchmark.p',fact_acc__downward) ).

fof(fact_acc_Osimps,axiom,
    ! [V_r_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),V_a_2)),V_r_2))
         => hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2))) ) ),
    file('theBenchmark.p',fact_acc_Osimps) ).

fof(fact_type__definition_ORep__range,axiom,
    ! [V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
      ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
     => hAPP(c_Set_Oimage(T_b,T_c,V_Rep_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = V_A_2 ),
    file('theBenchmark.p',fact_type__definition_ORep__range) ).

fof(fact_type__definition_OAbs__image,axiom,
    ! [V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
      ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
     => hAPP(c_Set_Oimage(T_c,T_b,V_Abs_2),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_type__definition_OAbs__image) ).

fof(fact_type__definition_OAbs__inject,axiom,
    ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
      ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
     => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2))
         => ( hAPP(V_Abs_2,V_x_2) = hAPP(V_Abs_2,V_y_2)
          <=> V_x_2 = V_y_2 ) ) ) ),
    file('theBenchmark.p',fact_type__definition_OAbs__inject) ).

fof(fact_type__definition_ORep__inverse,axiom,
    ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
      ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
     => hAPP(V_Abs_2,hAPP(V_Rep_2,V_x_2)) = V_x_2 ),
    file('theBenchmark.p',fact_type__definition_ORep__inverse) ).

fof(fact_type__definition_ORep__inject,axiom,
    ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
      ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
     => ( hAPP(V_Rep_2,V_x_2) = hAPP(V_Rep_2,V_y_2)
      <=> V_x_2 = V_y_2 ) ),
    file('theBenchmark.p',fact_type__definition_ORep__inject) ).

fof(fact_type__definition_ORep,axiom,
    ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
      ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
     => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_Rep_2,V_x_2)),V_A_2)) ),
    file('theBenchmark.p',fact_type__definition_ORep) ).

fof(fact_type__definition_OAbs__inverse,axiom,
    ! [V_y_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
      ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
     => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2))
       => hAPP(V_Rep_2,hAPP(V_Abs_2,V_y_2)) = V_y_2 ) ),
    file('theBenchmark.p',fact_type__definition_OAbs__inverse) ).

fof(fact_max__ext_Ointros,axiom,
    ! [V_R_2,V_Y_2,V_X_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Y_2))
       => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_X_2))
               => ? [B_xa] :
                    ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_xa)),V_R_2))
                    & hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_Y_2)) ) )
           => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_Y_2)),c_Wellfounded_Omax__ext(T_b,V_R_2))) ) ) ) ),
    file('theBenchmark.p',fact_max__ext_Ointros) ).

fof(fact_Nitpick_Ozero__frac__def,axiom,
    ! [T_a] : c_Nitpick_Ozero__frac(T_a) = c_Nitpick_OAbs__Frac(T_a,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    file('theBenchmark.p',fact_Nitpick_Ozero__frac__def) ).

fof(fact_the__elem__def,axiom,
    ! [V_X_2,T_b] : c_Set_Othe__elem(T_b,V_X_2) = c_HOL_OThe(T_b,hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),hAPP(c_fequal,V_X_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),
    file('theBenchmark.p',fact_the__elem__def) ).

fof(fact_The__split__eq,axiom,
    ! [V_y_2,V_x_2,T_c,T_b] : c_HOL_OThe(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_x_2)))),hAPP(c_fequal,V_y_2)))) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2),
    file('theBenchmark.p',fact_The__split__eq) ).

fof(fact_split__paired__The,axiom,
    ! [V_P_2,T_c,T_b] : c_HOL_OThe(tc_prod(T_b,T_c),V_P_2) = c_HOL_OThe(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,T_c),V_P_2)),c_Product__Type_OPair(T_b,T_c)))),
    file('theBenchmark.p',fact_split__paired__The) ).

fof(fact_the__inv__into__def,axiom,
    ! [V_x_2,V_f_2,V_A_2,T_c,T_b] : hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_x_2) = c_HOL_OThe(T_b,hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),V_x_2))),
    file('theBenchmark.p',fact_the__inv__into__def) ).

fof(fact_fold__def,axiom,
    ! [V_A_2,V_z_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_b,V_f_2),V_z_2),V_A_2) = c_HOL_OThe(T_b,c_Finite__Set_Ofold__graph(T_c,T_b,V_f_2,V_z_2,V_A_2)),
    file('theBenchmark.p',fact_fold__def) ).

fof(fact_divmod__nat__def,axiom,
    ! [V_n_2,V_m_2] : c_Divides_Odivmod__nat(V_m_2,V_n_2) = c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(V_m_2,V_n_2)),
    file('theBenchmark.p',fact_divmod__nat__def) ).

fof(fact_fold1__def,axiom,
    ! [V_A_2,V_f_2,T_b] : hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) = c_HOL_OThe(T_b,c_Finite__Set_Ofold1Set(T_b,V_f_2,V_A_2)),
    file('theBenchmark.p',fact_fold1__def) ).

fof(fact_The__split,axiom,
    ! [V_P_2,T_c,T_b] : c_HOL_OThe(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_P_2)) = c_HOL_OThe(tc_prod(T_b,T_c),hAPP(hAPP(c_COMBS(tc_prod(T_b,T_c),T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_HOL_Obool),tc_prod(T_b,T_c)),V_P_2),c_Product__Type_Ofst(T_b,T_c))),c_Product__Type_Osnd(T_b,T_c))),
    file('theBenchmark.p',fact_The__split) ).

fof(fact_Nitpick_Oone__frac__def,axiom,
    ! [T_a] : c_Nitpick_Oone__frac(T_a) = c_Nitpick_OAbs__Frac(T_a,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    file('theBenchmark.p',fact_Nitpick_Oone__frac__def) ).

fof(fact_Nitpick_Onumber__of__frac__def,axiom,
    ! [V_n,T_a] : c_Nitpick_Onumber__of__frac(T_a,V_n) = c_Nitpick_OAbs__Frac(T_a,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_n),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    file('theBenchmark.p',fact_Nitpick_Onumber__of__frac__def) ).

fof(fact_Nitpick_Ofrac__def,axiom,
    ! [V_b,V_a,T_a] : hAPP(hAPP(c_Nitpick_Ofrac(T_a),V_a),V_b) = c_Nitpick_OAbs__Frac(T_a,c_Nitpick_Onorm__frac(V_a,V_b)),
    file('theBenchmark.p',fact_Nitpick_Ofrac__def) ).

fof(fact_flat__lub__def,axiom,
    ! [V_b_2,V_A_2,T_b] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))
       => c_Partial__Function_Oflat__lub(T_b,V_b_2,V_A_2) = c_HOL_OThe(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))
       => c_Partial__Function_Oflat__lub(T_b,V_b_2,V_A_2) = V_b_2 ) ),
    file('theBenchmark.p',fact_flat__lub__def) ).

fof(fact_inj__vimage__singleton,axiom,
    ! [V_a_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(T_b),c_HOL_OThe(T_b,hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),V_a_2))),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) ),
    file('theBenchmark.p',fact_inj__vimage__singleton) ).

fof(fact_Rep__Integ__cases,axiom,
    ! [V_y_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg))
     => ~ ! [B_x] : V_y_2 != hAPP(c_Int_ORep__Integ,B_x) ),
    file('theBenchmark.p',fact_Rep__Integ__cases) ).

fof(fact_vimageI,axiom,
    ! [T_c,V_B_2,T_b,V_b_2,V_a_2,V_f_2] :
      ( hAPP(V_f_2,V_a_2) = V_b_2
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_B_2))
       => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_B_2))) ) ),
    file('theBenchmark.p',fact_vimageI) ).

fof(fact_vimage__UNIV,axiom,
    ! [V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_vimage__UNIV) ).

fof(fact_vimage__empty,axiom,
    ! [V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_vimage__empty) ).

fof(fact_vimage__Un,axiom,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)),
    file('theBenchmark.p',fact_vimage__Un) ).

fof(fact_vimage__INT,axiom,
    ! [V_B_2,V_A_2,T_d,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Set_Ovimage(T_b,T_c,V_f_2)),V_B_2)),
    file('theBenchmark.p',fact_vimage__INT) ).

fof(fact_vimage__compose,axiom,
    ! [V_x_2,V_f_2,V_g_2,T_d,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_g_2),V_f_2)),V_x_2) = hAPP(c_Set_Ovimage(T_b,T_d,V_f_2),hAPP(c_Set_Ovimage(T_d,T_c,V_g_2),V_x_2)),
    file('theBenchmark.p',fact_vimage__compose) ).

fof(fact_vimage__ident,axiom,
    ! [V_Y_2,T_b] : hAPP(c_Set_Ovimage(T_b,T_b,c_COMBI(T_b)),V_Y_2) = V_Y_2,
    file('theBenchmark.p',fact_vimage__ident) ).

fof(fact_vimage__Compl,axiom,
    ! [V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)),
    file('theBenchmark.p',fact_vimage__Compl) ).

fof(fact_vimage__code,axiom,
    ! [V_x_2,V_A_2,V_f_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2),V_x_2))
    <=> hBOOL(hAPP(V_A_2,hAPP(V_f_2,V_x_2))) ),
    file('theBenchmark.p',fact_vimage__code) ).

fof(fact_vimage__Int,axiom,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)),
    file('theBenchmark.p',fact_vimage__Int) ).

fof(fact_vimage__mono,axiom,
    ! [V_f_2,T_c,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_B_2))) ),
    file('theBenchmark.p',fact_vimage__mono) ).

fof(fact_vimage__UN,axiom,
    ! [V_B_2,V_A_2,T_d,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Set_Ovimage(T_b,T_c,V_f_2)),V_B_2)),
    file('theBenchmark.p',fact_vimage__UN) ).

fof(fact_vimage__Diff,axiom,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)),
    file('theBenchmark.p',fact_vimage__Diff) ).

fof(fact_vimageI2,axiom,
    ! [T_c,V_A_2,V_a_2,V_f_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_A_2))
     => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2))) ),
    file('theBenchmark.p',fact_vimageI2) ).

fof(fact_vimageD,axiom,
    ! [V_A_2,V_f_2,T_c,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)))
     => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_A_2)) ),
    file('theBenchmark.p',fact_vimageD) ).

fof(fact_vimage__eq,axiom,
    ! [V_B_2,V_f_2,T_c,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)))
    <=> hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_B_2)) ),
    file('theBenchmark.p',fact_vimage__eq) ).

fof(fact_image__vimage__subset,axiom,
    ! [V_A_2,V_f_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2))),V_A_2)),
    file('theBenchmark.p',fact_image__vimage__subset) ).

fof(fact_surj__image__vimage__eq,axiom,
    ! [V_A_2,V_f_2,T_b,T_c] :
      ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
     => hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2)) = V_A_2 ),
    file('theBenchmark.p',fact_surj__image__vimage__eq) ).

fof(fact_vimage__Union,axiom,
    ! [V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Set_Ovimage(T_b,T_c,V_f_2)),
    file('theBenchmark.p',fact_vimage__Union) ).

fof(fact_vimage__singleton__eq,axiom,
    ! [V_b_2,V_f_2,T_c,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))))
    <=> hAPP(V_f_2,V_a_2) = V_b_2 ),
    file('theBenchmark.p',fact_vimage__singleton__eq) ).

fof(fact_vimage__insert,axiom,
    ! [V_B_2,V_a_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)),
    file('theBenchmark.p',fact_vimage__insert) ).

fof(fact_finite__vimageD,axiom,
    ! [V_F_2,V_h_2,T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_c,V_h_2),V_F_2)))
     => ( hAPP(c_Set_Oimage(T_b,T_c,V_h_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2)) ) ),
    file('theBenchmark.p',fact_finite__vimageD) ).

fof(fact_vimage__subsetD,axiom,
    ! [V_A_2,V_B_2,V_f_2,T_b,T_c] :
      ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_B_2)),V_A_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) ) ),
    file('theBenchmark.p',fact_vimage__subsetD) ).

fof(fact_image__vimage__eq,axiom,
    ! [V_A_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))),
    file('theBenchmark.p',fact_image__vimage__eq) ).

fof(fact_finite__vimageI,axiom,
    ! [V_h_2,T_c,V_F_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
     => ( c_Fun_Oinj__on(T_c,T_b,V_h_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Ovimage(T_c,T_b,V_h_2),V_F_2))) ) ),
    file('theBenchmark.p',fact_finite__vimageI) ).

fof(fact_inj__vimage__image__eq,axiom,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
     => hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = V_A_2 ),
    file('theBenchmark.p',fact_inj__vimage__image__eq) ).

fof(fact_vimage__const,axiom,
    ! [T_c,V_A_2,V_c_2,T_b] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
       => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(c_COMBK(T_b,T_c),V_c_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
      & ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
       => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(c_COMBK(T_b,T_c),V_c_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_vimage__const) ).

fof(fact_vimage__eq__UN,axiom,
    ! [V_B_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Set_Ovimage(T_b,T_c,V_f_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),c_Set_Oinsert(T_c)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))),
    file('theBenchmark.p',fact_vimage__eq__UN) ).

fof(fact_vimage__subsetI,axiom,
    ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)),V_A_2)) ) ),
    file('theBenchmark.p',fact_vimage__subsetI) ).

fof(fact_vimage__if,axiom,
    ! [V_B_2,T_c,V_d_2,V_A_2,V_c_2,T_b] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
       => ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
           => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
          & ( hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
           => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_B_2) ) ) )
      & ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
       => ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
           => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = V_B_2 )
          & ( hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
           => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) ) ) ),
    file('theBenchmark.p',fact_vimage__if) ).

fof(fact_image__split__eq__Sigma,axiom,
    ! [V_A_2,V_g_2,V_f_2,T_c,T_b,T_d] : hAPP(c_Set_Oimage(T_d,tc_prod(T_b,T_c),hAPP(hAPP(c_COMBS(T_d,T_c,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_prod(T_b,T_c)),T_d),c_Product__Type_OPair(T_b,T_c)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_Oimage(T_d,T_b,V_f_2),V_A_2)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_Oimage(T_d,T_c,V_g_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_b),c_Set_Ovimage(T_d,T_b,V_f_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),V_A_2))),
    file('theBenchmark.p',fact_image__split__eq__Sigma) ).

fof(fact_Rep__Integ__induct,axiom,
    ! [V_P_2,V_y_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg))
     => ( ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Int_ORep__Integ,B_x)))
       => hBOOL(hAPP(V_P_2,V_y_2)) ) ),
    file('theBenchmark.p',fact_Rep__Integ__induct) ).

fof(fact_inj__on__INTER,axiom,
    ! [V_A_2,V_f_2,T_d,T_c,T_b,V_I_2] :
      ( V_I_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
     => ( ! [B_i] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_I_2))
           => c_Fun_Oinj__on(T_c,T_d,V_f_2,hAPP(V_A_2,B_i)) )
       => c_Fun_Oinj__on(T_c,T_d,V_f_2,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_inj__on__INTER) ).

fof(fact_SigmaI,axiom,
    ! [V_B_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
     => ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))) ) ),
    file('theBenchmark.p',fact_SigmaI) ).

fof(fact_Times__eq__cancel2,axiom,
    ! [V_B_2,V_A_2,T_c,V_C_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_C_2))
     => ( hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_C_2)) = hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_B_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_C_2))
      <=> V_A_2 = V_B_2 ) ),
    file('theBenchmark.p',fact_Times__eq__cancel2) ).

fof(fact_Sigma__Diff__distrib2,axiom,
    ! [V_B_2,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_B_2)),
    file('theBenchmark.p',fact_Sigma__Diff__distrib2) ).

fof(fact_Times__Diff__distrib1,axiom,
    ! [V_C_2,V_B_2,V_A_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_B_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))),
    file('theBenchmark.p',fact_Times__Diff__distrib1) ).

fof(fact_Sigma__Diff__distrib1,axiom,
    ! [V_C_2,V_J_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_J_2)),V_C_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_J_2),V_C_2)),
    file('theBenchmark.p',fact_Sigma__Diff__distrib1) ).

fof(fact_Sigma__empty1,axiom,
    ! [V_B_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),
    file('theBenchmark.p',fact_Sigma__empty1) ).

fof(fact_Sigma__Union,axiom,
    ! [V_B_2,V_X_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_X_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),c_Product__Type_OSigma(T_b,T_c)),V_B_2)),
    file('theBenchmark.p',fact_Sigma__Union) ).

fof(fact_card__cartesian__product,axiom,
    ! [V_B_2,V_A_2,T_c,T_b] : hAPP(c_Finite__Set_Ocard(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2)),
    file('theBenchmark.p',fact_card__cartesian__product) ).

fof(fact_setsum__cartesian__product,axiom,
    ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_b),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(T_c,T_d),T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_B_2))) ),
    file('theBenchmark.p',fact_setsum__cartesian__product) ).

fof(fact_Times__empty,axiom,
    ! [V_B_2,V_A_2,T_c,T_b] :
      ( hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))
    <=> ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
        | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_Times__empty) ).

fof(fact_Sigma__empty2,axiom,
    ! [V_A_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),
    file('theBenchmark.p',fact_Sigma__empty2) ).

fof(fact_Compl__Times__UNIV2,axiom,
    ! [V_A_2,T_c,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))),
    file('theBenchmark.p',fact_Compl__Times__UNIV2) ).

fof(fact_Compl__Times__UNIV1,axiom,
    ! [V_A_2,T_c,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_A_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2))),
    file('theBenchmark.p',fact_Compl__Times__UNIV1) ).

fof(fact_setprod__cartesian__product,axiom,
    ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
      ( class_Groups_Ocomm__monoid__mult(T_b)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_b),T_c),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_d,T_b)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(T_c,T_d),T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_B_2))) ),
    file('theBenchmark.p',fact_setprod__cartesian__product) ).

fof(fact_Sigma__Un__distrib1,axiom,
    ! [V_C_2,V_J_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_J_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_J_2),V_C_2)),
    file('theBenchmark.p',fact_Sigma__Un__distrib1) ).

fof(fact_Times__Un__distrib1,axiom,
    ! [V_C_2,V_B_2,V_A_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_B_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))),
    file('theBenchmark.p',fact_Times__Un__distrib1) ).

fof(fact_Sigma__Un__distrib2,axiom,
    ! [V_B_2,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_B_2)),
    file('theBenchmark.p',fact_Sigma__Un__distrib2) ).

fof(fact_swap__product,axiom,
    ! [V_B_2,V_A_2,T_b,T_c] : hAPP(c_Set_Oimage(tc_prod(T_c,T_b),tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,tc_prod(T_b,T_c)),hAPP(c_COMBC(T_b,T_c,tc_prod(T_b,T_c)),c_Product__Type_OPair(T_b,T_c)))),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_B_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_A_2)),
    file('theBenchmark.p',fact_swap__product) ).

fof(fact_finite__cartesian__product,axiom,
    ! [V_B_2,T_c,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2)))) ) ),
    file('theBenchmark.p',fact_finite__cartesian__product) ).

fof(fact_equiv__type,axiom,
    ! [V_r_2,V_A_2,T_b] :
      ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) ),
    file('theBenchmark.p',fact_equiv__type) ).

fof(fact_Sigma__Int__distrib2,axiom,
    ! [V_B_2,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_B_2)),
    file('theBenchmark.p',fact_Sigma__Int__distrib2) ).

fof(fact_Times__Int__distrib1,axiom,
    ! [V_C_2,V_B_2,V_A_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_B_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))),
    file('theBenchmark.p',fact_Times__Int__distrib1) ).

fof(fact_Sigma__Int__distrib1,axiom,
    ! [V_C_2,V_J_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_J_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_J_2),V_C_2)),
    file('theBenchmark.p',fact_Sigma__Int__distrib1) ).

fof(fact_Id__on__subset__Times,axiom,
    ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Relation_OId__on(T_b,V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))),
    file('theBenchmark.p',fact_Id__on__subset__Times) ).

fof(fact_UNIV__Times__UNIV,axiom,
    ! [T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),
    file('theBenchmark.p',fact_UNIV__Times__UNIV) ).

fof(fact_SigmaE2,axiom,
    ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)))
     => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
         => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ) ),
    file('theBenchmark.p',fact_SigmaE2) ).

fof(fact_SigmaD2,axiom,
    ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)))
     => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ),
    file('theBenchmark.p',fact_SigmaD2) ).

fof(fact_SigmaD1,axiom,
    ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)))
     => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ),
    file('theBenchmark.p',fact_SigmaD1) ).

fof(fact_mem__Sigma__iff,axiom,
    ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)))
    <=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2)))
        & hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_mem__Sigma__iff) ).

fof(fact_card__cartesian__product__singleton,axiom,
    ! [V_A_2,V_x_2,T_c,T_b] : hAPP(c_Finite__Set_Ocard(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_A_2))) = hAPP(c_Finite__Set_Ocard(T_c),V_A_2),
    file('theBenchmark.p',fact_card__cartesian__product__singleton) ).

fof(fact_Times__subset__cancel2,axiom,
    ! [V_B_2,V_A_2,T_c,V_C_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_C_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_B_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_C_2))))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
    file('theBenchmark.p',fact_Times__subset__cancel2) ).

fof(fact_Image__subset,axiom,
    ! [V_C_2,V_B_2,V_A_2,V_r_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_c,V_r_2),V_C_2)),V_B_2)) ),
    file('theBenchmark.p',fact_Image__subset) ).

fof(fact_finite__cartesian__productD1,axiom,
    ! [V_B_2,V_A_2,T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))))
     => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ),
    file('theBenchmark.p',fact_finite__cartesian__productD1) ).

fof(fact_finite__cartesian__productD2,axiom,
    ! [V_B_2,V_A_2,T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))))
     => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ),
    file('theBenchmark.p',fact_finite__cartesian__productD2) ).

fof(fact_fst__image__times,axiom,
    ! [V_A_2,T_c,T_b,V_B_2] :
      ( ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(c_Set_Oimage(tc_prod(T_c,T_b),T_c,c_Product__Type_Ofst(T_c,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2))) = V_A_2 )
      & ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(c_Set_Oimage(tc_prod(T_c,T_b),T_c,c_Product__Type_Ofst(T_c,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_fst__image__times) ).

fof(fact_snd__image__times,axiom,
    ! [V_B_2,T_c,T_b,V_A_2] :
      ( ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_c,c_Product__Type_Osnd(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))) = V_B_2 )
      & ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_c,c_Product__Type_Osnd(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_snd__image__times) ).

fof(fact_insert__times__insert,axiom,
    ! [V_B_2,V_b_2,V_A_2,V_a_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),V_B_2))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),V_B_2)))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2)))),
    file('theBenchmark.p',fact_insert__times__insert) ).

fof(fact_finite__equiv__class,axiom,
    ! [V_X_2,V_r_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
       => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
         => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2)) ) ) ),
    file('theBenchmark.p',fact_finite__equiv__class) ).

fof(fact_vimage__Times,axiom,
    ! [V_B_2,V_A_2,V_f_2,T_d,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,tc_prod(T_c,T_d),V_f_2),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,hAPP(c_Fun_Ocomp(tc_prod(T_c,T_d),T_c,T_b,c_Product__Type_Ofst(T_c,T_d)),V_f_2)),V_A_2)),hAPP(c_Set_Ovimage(T_b,T_d,hAPP(c_Fun_Ocomp(tc_prod(T_c,T_d),T_d,T_b,c_Product__Type_Osnd(T_c,T_d)),V_f_2)),V_B_2)),
    file('theBenchmark.p',fact_vimage__Times) ).

fof(fact_UN__Times__distrib,axiom,
    ! [V_F_2,V_E_2,V_B_2,V_A_2,T_c,T_b,T_e,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(T_d,T_e),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_d,T_e),V_A_2),hAPP(c_COMBK(tc_fun(T_e,tc_HOL_Obool),T_d),V_B_2))),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_e,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),tc_fun(T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_e,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),tc_fun(T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),T_d),c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),T_e)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),T_d),c_Product__Type_OSigma(T_b,T_c)),V_E_2))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),T_e),c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b)),V_F_2)))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_E_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_F_2))),
    file('theBenchmark.p',fact_UN__Times__distrib) ).

fof(fact_Sigma__def,axiom,
    ! [V_B_2,V_A_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),T_b),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),V_B_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),T_c),c_Set_Oinsert(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))))),
    file('theBenchmark.p',fact_Sigma__def) ).

fof(fact_finite__quotient,axiom,
    ! [V_r_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) ) ),
    file('theBenchmark.p',fact_finite__quotient) ).

fof(fact_Ex__inj__on__UNION__Sigma,axiom,
    ! [V_A_2,V_I_2,T_c,T_b] :
    ? [B_f] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,tc_prod(T_c,T_b),B_f),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2))),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_I_2),V_A_2)))
      & c_Fun_Oinj__on(T_b,tc_prod(T_c,T_b),B_f,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)) ),
    file('theBenchmark.p',fact_Ex__inj__on__UNION__Sigma) ).

fof(fact_fold__image__Sigma,axiom,
    ! [V_g_2,V_B_2,T_c,V_A_2,T_b,T_d] :
      ( class_Groups_Ocomm__monoid__mult(T_d)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
             => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
         => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_b,c_Groups_Otimes__class_Otimes(T_d)),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBC(T_b,T_d,tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_d),tc_fun(T_d,tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d)),T_b),c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Otimes__class_Otimes(T_d))),V_g_2)),c_Groups_Oone__class_Oone(T_d))),V_B_2)),c_Groups_Oone__class_Oone(T_d)),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,tc_prod(T_b,T_c),c_Groups_Otimes__class_Otimes(T_d)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_g_2)),c_Groups_Oone__class_Oone(T_d)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)) ) ) ),
    file('theBenchmark.p',fact_fold__image__Sigma) ).

fof(fact_finite__SigmaI,axiom,
    ! [V_B_2,T_c,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( ! [B_a] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
           => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_a))) )
       => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))) ) ),
    file('theBenchmark.p',fact_finite__SigmaI) ).

fof(fact_setprod__Sigma,axiom,
    ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] :
      ( class_Groups_Ocomm__monoid__mult(T_d)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
             => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_d),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_d),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d),T_b),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(T_b,T_c),T_d),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)) ) ) ),
    file('theBenchmark.p',fact_setprod__Sigma) ).

fof(fact_setsum__Sigma,axiom,
    ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] :
      ( class_Groups_Ocomm__monoid__add(T_d)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
             => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_d),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d),T_b),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(T_b,T_c),T_d),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)) ) ) ),
    file('theBenchmark.p',fact_setsum__Sigma) ).

fof(fact_card__SigmaI,axiom,
    ! [V_B_2,T_c,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
           => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
       => hAPP(c_Finite__Set_Ocard(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_Nat_Onat,T_b),c_Finite__Set_Ocard(T_c)),V_B_2)),V_A_2) ) ),
    file('theBenchmark.p',fact_card__SigmaI) ).

fof(fact_SigmaE,axiom,
    ! [V_B_2,V_A_2,V_c_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_c_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)))
     => ~ ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
           => ! [B_y] :
                ( hBOOL(hAPP(hAPP(c_member(T_c),B_y),hAPP(V_B_2,B_x)))
               => V_c_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y) ) ) ),
    file('theBenchmark.p',fact_SigmaE) ).

fof(fact_map__pair__surj,axiom,
    ! [V_g_2,T_d,T_e,V_f_2,T_b,T_c] :
      ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
     => ( hAPP(c_Set_Oimage(T_e,T_d,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_e,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))
       => hAPP(c_Set_Oimage(tc_prod(T_c,T_e),tc_prod(T_b,T_d),c_Product__Type_Omap__pair(T_c,T_b,T_e,T_d,V_f_2,V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_c,T_e),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_map__pair__surj) ).

fof(fact_map__pair__inj__on,axiom,
    ! [V_B_2,V_g_2,T_e,T_d,V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
     => ( c_Fun_Oinj__on(T_d,T_e,V_g_2,V_B_2)
       => c_Fun_Oinj__on(tc_prod(T_b,T_d),tc_prod(T_c,T_e),c_Product__Type_Omap__pair(T_b,T_c,T_d,T_e,V_f_2,V_g_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_b),V_B_2))) ) ),
    file('theBenchmark.p',fact_map__pair__inj__on) ).

fof(fact_map__pair__imageI,axiom,
    ! [V_g_2,V_f_2,T_e,T_d,V_R_2,V_b_2,V_a_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_R_2))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_e)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),hAPP(V_f_2,V_a_2)),hAPP(V_g_2,V_b_2))),hAPP(c_Set_Oimage(tc_prod(T_b,T_c),tc_prod(T_d,T_e),c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,V_f_2,V_g_2)),V_R_2))) ),
    file('theBenchmark.p',fact_map__pair__imageI) ).

fof(fact_map__pair__ident,axiom,
    ! [V_z_2,T_c,T_b] : hAPP(c_Product__Type_Omap__pair(T_b,T_b,T_c,T_c,c_COMBI(T_b),c_COMBI(T_c)),V_z_2) = V_z_2,
    file('theBenchmark.p',fact_map__pair__ident) ).

fof(fact_snd__prod__fun,axiom,
    ! [V_x_2,V_g_2,V_f_2,T_e,T_d,T_b,T_c] : hAPP(c_Product__Type_Osnd(T_c,T_b),hAPP(c_Product__Type_Omap__pair(T_d,T_c,T_e,T_b,V_f_2,V_g_2),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_d,T_e),V_x_2)),
    file('theBenchmark.p',fact_snd__prod__fun) ).

fof(fact_fst__map__pair,axiom,
    ! [V_x_2,V_g_2,V_f_2,T_e,T_d,T_c,T_b] : hAPP(c_Product__Type_Ofst(T_b,T_c),hAPP(c_Product__Type_Omap__pair(T_d,T_b,T_e,T_c,V_f_2,V_g_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_d,T_e),V_x_2)),
    file('theBenchmark.p',fact_fst__map__pair) ).

fof(fact_map__pair__simp,axiom,
    ! [V_b_2,V_a_2,V_g_2,V_f_2,T_c,T_e,T_b,T_d] : hAPP(c_Product__Type_Omap__pair(T_d,T_b,T_e,T_c,V_f_2,V_g_2),hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),V_a_2),V_b_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,V_a_2)),hAPP(V_g_2,V_b_2)),
    file('theBenchmark.p',fact_map__pair__simp) ).

fof(fact_fst__comp__map__pair,axiom,
    ! [V_g_2,V_f_2,T_c,T_b,T_e,T_d] : hAPP(c_Fun_Ocomp(tc_prod(T_d,T_e),T_d,tc_prod(T_b,T_c),c_Product__Type_Ofst(T_d,T_e)),c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,V_f_2,V_g_2)) = hAPP(c_Fun_Ocomp(T_b,T_d,tc_prod(T_b,T_c),V_f_2),c_Product__Type_Ofst(T_b,T_c)),
    file('theBenchmark.p',fact_fst__comp__map__pair) ).

fof(fact_map__pair_Ocomp,axiom,
    ! [V_i_2,V_h_2,V_g_2,V_f_2,T_c,T_b,T_e,T_d,T_g,T_f] : hAPP(c_Fun_Ocomp(tc_prod(T_f,T_g),tc_prod(T_d,T_e),tc_prod(T_b,T_c),c_Product__Type_Omap__pair(T_f,T_d,T_g,T_e,V_f_2,V_g_2)),c_Product__Type_Omap__pair(T_b,T_f,T_c,T_g,V_h_2,V_i_2)) = c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,hAPP(c_Fun_Ocomp(T_f,T_d,T_b,V_f_2),V_h_2),hAPP(c_Fun_Ocomp(T_g,T_e,T_c,V_g_2),V_i_2)),
    file('theBenchmark.p',fact_map__pair_Ocomp) ).

fof(fact_map__pair__compose,axiom,
    ! [V_g2_2,V_g1_2,T_g,V_f2_2,V_f1_2,T_f,T_e,T_c,T_d,T_b] : c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,hAPP(c_Fun_Ocomp(T_f,T_d,T_b,V_f1_2),V_f2_2),hAPP(c_Fun_Ocomp(T_g,T_e,T_c,V_g1_2),V_g2_2)) = hAPP(c_Fun_Ocomp(tc_prod(T_f,T_g),tc_prod(T_d,T_e),tc_prod(T_b,T_c),c_Product__Type_Omap__pair(T_f,T_d,T_g,T_e,V_f1_2,V_g1_2)),c_Product__Type_Omap__pair(T_b,T_f,T_c,T_g,V_f2_2,V_g2_2)),
    file('theBenchmark.p',fact_map__pair__compose) ).

fof(fact_map__pair_Ocompositionality,axiom,
    ! [V_prod_2,V_i_2,V_h_2,T_g,T_f,V_g_2,V_f_2,T_c,T_e,T_b,T_d] : hAPP(c_Product__Type_Omap__pair(T_d,T_b,T_e,T_c,V_f_2,V_g_2),hAPP(c_Product__Type_Omap__pair(T_f,T_d,T_g,T_e,V_h_2,V_i_2),V_prod_2)) = hAPP(c_Product__Type_Omap__pair(T_f,T_b,T_g,T_c,hAPP(c_Fun_Ocomp(T_d,T_b,T_f,V_f_2),V_h_2),hAPP(c_Fun_Ocomp(T_e,T_c,T_g,V_g_2),V_i_2)),V_prod_2),
    file('theBenchmark.p',fact_map__pair_Ocompositionality) ).

fof(fact_snd__comp__map__pair,axiom,
    ! [V_g_2,V_f_2,T_c,T_b,T_d,T_e] : hAPP(c_Fun_Ocomp(tc_prod(T_e,T_d),T_d,tc_prod(T_b,T_c),c_Product__Type_Osnd(T_e,T_d)),c_Product__Type_Omap__pair(T_b,T_e,T_c,T_d,V_f_2,V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_d,tc_prod(T_b,T_c),V_g_2),c_Product__Type_Osnd(T_b,T_c)),
    file('theBenchmark.p',fact_snd__comp__map__pair) ).

fof(fact_map__pair__def,axiom,
    ! [V_g_2,V_f_2,T_e,T_c,T_d,T_b] : c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,V_f_2,V_g_2) = hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_prod(T_d,T_e)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,T_e),tc_fun(T_c,tc_prod(T_d,T_e))),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_prod(T_d,T_e)),tc_fun(tc_fun(T_c,T_e),tc_fun(T_c,tc_prod(T_d,T_e))),T_b),c_COMBB(T_e,tc_prod(T_d,T_e),T_c)),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_e,tc_prod(T_d,T_e)),T_b),c_Product__Type_OPair(T_d,T_e)),V_f_2))),V_g_2)),
    file('theBenchmark.p',fact_map__pair__def) ).

fof(fact_map__pair__surj__on,axiom,
    ! [V_B_H_2,V_B_2,V_g_2,T_d,T_e,V_A_H_2,V_A_2,V_f_2,T_b,T_c] :
      ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_A_H_2
     => ( hAPP(c_Set_Oimage(T_e,T_d,V_g_2),V_B_2) = V_B_H_2
       => hAPP(c_Set_Oimage(tc_prod(T_c,T_e),tc_prod(T_b,T_d),c_Product__Type_Omap__pair(T_c,T_b,T_e,T_d,V_f_2,V_g_2)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_e),V_A_2),hAPP(c_COMBK(tc_fun(T_e,tc_HOL_Obool),T_c),V_B_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_d),V_A_H_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_b),V_B_H_2)) ) ),
    file('theBenchmark.p',fact_map__pair__surj__on) ).

fof(fact_prod__fun__imageE,axiom,
    ! [V_R_2,V_g_2,V_f_2,T_e,T_d,V_c_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_c_2),hAPP(c_Set_Oimage(tc_prod(T_d,T_e),tc_prod(T_b,T_c),c_Product__Type_Omap__pair(T_d,T_b,T_e,T_c,V_f_2,V_g_2)),V_R_2)))
     => ~ ! [B_x,B_y] :
            ( V_c_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_y))
           => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_e)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),B_x),B_y)),V_R_2)) ) ),
    file('theBenchmark.p',fact_prod__fun__imageE) ).

fof(fact_refl__on__def,axiom,
    ! [V_r_2,V_A_2,T_b] :
      ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
    <=> ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
           => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) )
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) ) ),
    file('theBenchmark.p',fact_refl__on__def) ).

fof(fact_card__less__Suc2,axiom,
    ! [V_i_2,V_M_2] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
     => hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),V_M_2))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_i_2)))) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_M_2))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,V_i_2))))) ),
    file('theBenchmark.p',fact_card__less__Suc2) ).

fof(fact_CollectI,axiom,
    ! [T_b,V_a_2,V_P_2] :
      ( hBOOL(hAPP(V_P_2,V_a_2))
     => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2))) ),
    file('theBenchmark.p',fact_CollectI) ).

fof(fact_finite__Collect__conjI,axiom,
    ! [V_Q_2,V_P_2,T_b] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Q_2)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2))) )
     => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_P_2)),V_Q_2)))) ),
    file('theBenchmark.p',fact_finite__Collect__conjI) ).

fof(fact_finite__Collect__less__nat,axiom,
    ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_k_2)))),
    file('theBenchmark.p',fact_finite__Collect__less__nat) ).

fof(fact_finite__Collect__le__nat,axiom,
    ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),V_k_2)))),
    file('theBenchmark.p',fact_finite__Collect__le__nat) ).

fof(fact_Collect__split,axiom,
    ! [V_Q_2,V_P_2,T_c,T_b] : hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_P_2))),V_Q_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_OCollect(T_b),V_P_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_OCollect(T_c),V_Q_2))),
    file('theBenchmark.p',fact_Collect__split) ).

fof(fact_SetCompr__Sigma__eq,axiom,
    ! [V_Q_2,V_P_2,T_c,T_b] : hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_P_2))),V_Q_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_OCollect(T_b),V_P_2)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_OCollect(T_c)),V_Q_2)),
    file('theBenchmark.p',fact_SetCompr__Sigma__eq) ).

fof(fact_Collect__neg__eq,axiom,
    ! [V_P_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_P_2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_P_2)),
    file('theBenchmark.p',fact_Collect__neg__eq) ).

fof(fact_vimage__Collect__eq,axiom,
    ! [V_P_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(c_Set_OCollect(T_c),V_P_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(T_c,tc_HOL_Obool,T_b),V_P_2),V_f_2)),
    file('theBenchmark.p',fact_vimage__Collect__eq) ).

fof(fact_CollectE,axiom,
    ! [V_P_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2)))
     => hBOOL(hAPP(V_P_2,V_a_2)) ),
    file('theBenchmark.p',fact_CollectE) ).

fof(fact_CollectD,axiom,
    ! [V_P_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2)))
     => hBOOL(hAPP(V_P_2,V_a_2)) ),
    file('theBenchmark.p',fact_CollectD) ).

fof(fact_mem__Collect__eq,axiom,
    ! [V_P_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2)))
    <=> hBOOL(hAPP(V_P_2,V_a_2)) ),
    file('theBenchmark.p',fact_mem__Collect__eq) ).

fof(fact_Collect__mem__eq,axiom,
    ! [V_A_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)) = V_A_2,
    file('theBenchmark.p',fact_Collect__mem__eq) ).

fof(fact_insert__Collect,axiom,
    ! [V_P_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2)))),V_P_2)),
    file('theBenchmark.p',fact_insert__Collect) ).

fof(fact_finite__Collect__disjI,axiom,
    ! [V_Q_2,V_P_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),V_P_2)),V_Q_2))))
    <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Q_2)))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2))) ) ),
    file('theBenchmark.p',fact_finite__Collect__disjI) ).

fof(fact_Collect__def,axiom,
    ! [V_P_2,T_b] : hAPP(c_Set_OCollect(T_b),V_P_2) = V_P_2,
    file('theBenchmark.p',fact_Collect__def) ).

fof(fact_Collect__conj__eq,axiom,
    ! [V_Q_2,V_P_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_P_2)),V_Q_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_P_2)),hAPP(c_Set_OCollect(T_b),V_Q_2)),
    file('theBenchmark.p',fact_Collect__conj__eq) ).

fof(fact_Collect__disj__eq,axiom,
    ! [V_Q_2,V_P_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),V_P_2)),V_Q_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_P_2)),hAPP(c_Set_OCollect(T_b),V_Q_2)),
    file('theBenchmark.p',fact_Collect__disj__eq) ).

fof(fact_empty__Collect__eq,axiom,
    ! [V_P_2,T_b] :
      ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),V_P_2)
    <=> ! [B_x] : ~ hBOOL(hAPP(V_P_2,B_x)) ),
    file('theBenchmark.p',fact_empty__Collect__eq) ).

fof(fact_Collect__empty__eq,axiom,
    ! [V_P_2,T_b] :
      ( hAPP(c_Set_OCollect(T_b),V_P_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
    <=> ! [B_x] : ~ hBOOL(hAPP(V_P_2,B_x)) ),
    file('theBenchmark.p',fact_Collect__empty__eq) ).

fof(fact_empty__def,axiom,
    ! [T_b] : c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),hAPP(c_COMBK(tc_HOL_Obool,T_b),c_fFalse)),
    file('theBenchmark.p',fact_empty__def) ).

fof(fact_refl__on__Id__on,axiom,
    ! [V_A_2,T_b] : c_Relation_Orefl__on(T_b,V_A_2,c_Relation_OId__on(T_b,V_A_2)),
    file('theBenchmark.p',fact_refl__on__Id__on) ).

fof(fact_UNIV__def,axiom,
    ! [T_b] : c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),hAPP(c_COMBK(tc_HOL_Obool,T_b),c_fTrue)),
    file('theBenchmark.p',fact_UNIV__def) ).

fof(fact_insert__compr__raw,axiom,
    ! [V_B_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),
    file('theBenchmark.p',fact_insert__compr__raw) ).

fof(fact_insert__compr,axiom,
    ! [V_B_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),
    file('theBenchmark.p',fact_insert__compr) ).

fof(fact_Un__def,axiom,
    ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),
    file('theBenchmark.p',fact_Un__def) ).

fof(fact_Int__def,axiom,
    ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),
    file('theBenchmark.p',fact_Int__def) ).

fof(fact_Int__Collect,axiom,
    ! [V_P_2,V_A_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_P_2))))
    <=> ( hBOOL(hAPP(V_P_2,V_x_2))
        & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_Int__Collect) ).

fof(fact_Collect__conv__if,axiom,
    ! [T_b,V_a_2,V_P_2] :
      ( ( ~ hBOOL(hAPP(V_P_2,V_a_2))
       => hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_P_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
      & ( hBOOL(hAPP(V_P_2,V_a_2))
       => hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_P_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ),
    file('theBenchmark.p',fact_Collect__conv__if) ).

fof(fact_Collect__conv__if2,axiom,
    ! [T_b,V_a_2,V_P_2] :
      ( ( ~ hBOOL(hAPP(V_P_2,V_a_2))
       => hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_a_2))),V_P_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
      & ( hBOOL(hAPP(V_P_2,V_a_2))
       => hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_a_2))),V_P_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ),
    file('theBenchmark.p',fact_Collect__conv__if2) ).

fof(fact_singleton__conv,axiom,
    ! [V_a_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),
    file('theBenchmark.p',fact_singleton__conv) ).

fof(fact_singleton__conv2,axiom,
    ! [V_a_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(c_fequal,V_a_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),
    file('theBenchmark.p',fact_singleton__conv2) ).

fof(fact_set__diff__eq,axiom,
    ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2)))),
    file('theBenchmark.p',fact_set__diff__eq) ).

fof(fact_finite__Collect__not,axiom,
    ! [V_P_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2)))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_P_2))))
      <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ),
    file('theBenchmark.p',fact_finite__Collect__not) ).

fof(fact_insert__def,axiom,
    ! [V_B_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_B_2),
    file('theBenchmark.p',fact_insert__def) ).

fof(fact_Compl__eq,axiom,
    ! [V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),
    file('theBenchmark.p',fact_Compl__eq) ).

fof(fact_vimage__def,axiom,
    ! [V_B_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(T_c)),V_f_2)),V_B_2)),
    file('theBenchmark.p',fact_vimage__def) ).

fof(fact_Collect__imp__eq,axiom,
    ! [V_Q_2,V_P_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),V_P_2)),V_Q_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_P_2))),hAPP(c_Set_OCollect(T_b),V_Q_2)),
    file('theBenchmark.p',fact_Collect__imp__eq) ).

fof(fact_finite__M__bounded__by__nat,axiom,
    ! [V_i_2,V_P_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),V_P_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_i_2))))),
    file('theBenchmark.p',fact_finite__M__bounded__by__nat) ).

fof(fact_refl__on__empty,axiom,
    ! [T_b] : c_Relation_Orefl__on(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))),
    file('theBenchmark.p',fact_refl__on__empty) ).

fof(fact_refl__on__Un,axiom,
    ! [V_s_2,V_B_2,V_r_2,V_A_2,T_b] :
      ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
     => ( c_Relation_Orefl__on(T_b,V_B_2,V_s_2)
       => c_Relation_Orefl__on(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ) ),
    file('theBenchmark.p',fact_refl__on__Un) ).

fof(fact_refl__on__Int,axiom,
    ! [V_s_2,V_B_2,V_r_2,V_A_2,T_b] :
      ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
     => ( c_Relation_Orefl__on(T_b,V_B_2,V_s_2)
       => c_Relation_Orefl__on(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ) ),
    file('theBenchmark.p',fact_refl__on__Int) ).

fof(fact_setsum__setsum__restrict,axiom,
    ! [V_R_2,V_f_2,V_T_2,T_c,V_S_2,T_b,T_d] :
      ( class_Groups_Ocomm__monoid__add(T_d)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_d),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d),T_b),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d)),V_f_2)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_OCollect(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_T_2)))),V_R_2)))),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_b,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_d),tc_fun(tc_fun(T_b,tc_HOL_Obool),T_d),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d)),hAPP(c_COMBC(T_b,T_c,T_d),V_f_2))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Set_OCollect(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)))),hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),V_R_2))))),V_T_2) ) ) ),
    file('theBenchmark.p',fact_setsum__setsum__restrict) ).

fof(fact_if__image__distrib,axiom,
    ! [V_S_2,V_g_2,V_f_2,V_P_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),V_P_2)),V_f_2)),V_g_2)),V_S_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_S_2),hAPP(c_Set_OCollect(T_c),V_P_2)))),hAPP(c_Set_Oimage(T_c,T_b,V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_S_2),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c),c_fNot),V_P_2))))),
    file('theBenchmark.p',fact_if__image__distrib) ).

fof(fact_nat__seg__image__imp__finite,axiom,
    ! [V_n_2,V_f_2,T_b,V_A_2] :
      ( V_A_2 = hAPP(c_Set_Oimage(tc_Nat_Onat,T_b,V_f_2),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_n_2)))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    file('theBenchmark.p',fact_nat__seg__image__imp__finite) ).

fof(fact_refl__onD,axiom,
    ! [V_a_2,V_r_2,V_A_2,T_b] :
      ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),V_r_2)) ) ),
    file('theBenchmark.p',fact_refl__onD) ).

fof(fact_refl__onD1,axiom,
    ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
      ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
       => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_refl__onD1) ).

fof(fact_refl__onD2,axiom,
    ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
      ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
       => hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_refl__onD2) ).

fof(fact_setsum__restrict__set_H,axiom,
    ! [V_B_2,V_f_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__add(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_f_2)),c_Groups_Ozero__class_Ozero(T_c))),V_A_2) ) ),
    file('theBenchmark.p',fact_setsum__restrict__set_H) ).

fof(fact_setsum__image__gen,axiom,
    ! [V_f_2,T_d,V_g_2,V_S_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__add(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),T_c,T_d),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Set_OCollect(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)))),hAPP(c_COMBC(T_b,T_d,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,tc_HOL_Obool),T_b),c_fequal),V_f_2)))))),hAPP(c_Set_Oimage(T_b,T_d,V_f_2),V_S_2)) ) ),
    file('theBenchmark.p',fact_setsum__image__gen) ).

fof(fact_Image__singleton,axiom,
    ! [V_a_2,V_r_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(T_c,T_b),tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_c,T_b))),hAPP(c_Product__Type_OPair(T_c,T_b),V_a_2))),V_r_2)),
    file('theBenchmark.p',fact_Image__singleton) ).

fof(fact_setsum__cases,axiom,
    ! [V_g_2,V_f_2,V_P_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__add(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),V_P_2)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_P_2)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_P_2))))) ) ),
    file('theBenchmark.p',fact_setsum__cases) ).

fof(fact_card__less__Suc,axiom,
    ! [V_i_2,V_M_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
     => hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),V_M_2))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_i_2))))) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_M_2))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,V_i_2))))) ),
    file('theBenchmark.p',fact_card__less__Suc) ).

fof(fact_card__less,axiom,
    ! [V_i_2,V_M_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
     => hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_M_2))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,V_i_2))))) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('theBenchmark.p',fact_card__less) ).

fof(fact_refl__onI,axiom,
    ! [V_A_2,V_r_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
     => ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
           => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) )
       => c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ) ),
    file('theBenchmark.p',fact_refl__onI) ).

fof(fact_setsum__multicount,axiom,
    ! [V_k_2,V_R_2,V_T_2,T_c,V_S_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2))
       => ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_T_2))
             => hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),V_R_2),B_x)))) = V_k_2 )
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_Nat_Onat,T_b),c_Finite__Set_Ocard(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_OCollect(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_T_2)))),V_R_2)))),V_S_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(T_c),V_T_2)) ) ) ),
    file('theBenchmark.p',fact_setsum__multicount) ).

fof(fact_min__max_Osup__Inf1__distrib,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))))) ) ) ),
    file('theBenchmark.p',fact_min__max_Osup__Inf1__distrib) ).

fof(fact_finite__Collect__subsets,axiom,
    ! [V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),V_A_2)))) ),
    file('theBenchmark.p',fact_finite__Collect__subsets) ).

fof(fact_Pow__Compl,axiom,
    ! [V_A_2,T_b] : hAPP(c_Set_OPow(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = hAPP(c_Set_OCollect(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),c_HOL_OEx(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBS(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),c_Set_OPow(T_b))))),
    file('theBenchmark.p',fact_Pow__Compl) ).

fof(fact_Pow__def,axiom,
    ! [V_A_2,T_b] : hAPP(c_Set_OPow(T_b),V_A_2) = hAPP(c_Set_OCollect(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),
    file('theBenchmark.p',fact_Pow__def) ).

fof(fact_finite__Collect__bounded__ex,axiom,
    ! [V_Q_2,T_c,V_P_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2)))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_P_2))),V_Q_2)))))
      <=> ! [B_y] :
            ( hBOOL(hAPP(V_P_2,B_y))
           => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),V_Q_2),B_y)))) ) ) ),
    file('theBenchmark.p',fact_finite__Collect__bounded__ex) ).

fof(fact_finite__image__set,axiom,
    ! [V_f_2,T_c,V_P_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2)))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),T_c),c_COMBB(T_c,tc_HOL_Obool,T_b)),c_fequal)),V_f_2)))),V_P_2))))) ),
    file('theBenchmark.p',fact_finite__image__set) ).

fof(fact_inj__graph,axiom,
    ! [T_c,T_b] : c_Fun_Oinj__on(tc_fun(T_b,T_c),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_b,T_c)),c_Set_OCollect(tc_prod(T_b,T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_b,T_c)),c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool)),hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBC(T_c,T_c,tc_HOL_Obool),c_fequal)))),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,T_c),tc_HOL_Obool))),
    file('theBenchmark.p',fact_inj__graph) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J,axiom,
    ! [V_P_2] : c_Nat__Transfer_Onat__set(hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_P_2))),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J) ).

fof(fact_finite__psubset__def,axiom,
    ! [T_b] : c_Wellfounded_Ofinite__psubset(T_b) = hAPP(c_Set_OCollect(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBS(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_fconj)),c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool))))),c_Finite__Set_Ofinite(T_b)))),
    file('theBenchmark.p',fact_finite__psubset__def) ).

fof(fact_inv__image__def,axiom,
    ! [V_f_2,V_r_2,T_b,T_c] : hAPP(hAPP(c_Relation_Oinv__image(T_c,T_b),V_r_2),V_f_2) = hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_c,T_c)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_c,T_c),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_c,T_c)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_c),tc_fun(T_b,tc_prod(T_c,T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_c,T_c)),tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,tc_prod(T_c,T_c))),T_b),c_COMBB(T_c,tc_prod(T_c,T_c),T_b)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_prod(T_c,T_c)),T_b),c_Product__Type_OPair(T_c,T_c)),V_f_2))),V_f_2)))),V_r_2))),
    file('theBenchmark.p',fact_inv__image__def) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J,axiom,
    ! [V_P_2] : hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_P_2)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Nat_Onat),V_P_2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J,axiom,
    ! [V_P_2] : hAPP(c_Set_OCollect(tc_Nat_Onat),V_P_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),V_P_2),c_Int_Onat)))),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J) ).

fof(fact_add__Min__commute,axiom,
    ! [V_k_2,V_N_2,T_b] :
      ( class_Groups_Olinordered__ab__semigroup__add(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
       => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_k_2),c_Big__Operators_Olinorder__class_OMin(T_b,V_N_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(T_b),V_k_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_N_2))))) ) ) ),
    file('theBenchmark.p',fact_add__Min__commute) ).

fof(fact_add__Max__commute,axiom,
    ! [V_k_2,V_N_2,T_b] :
      ( class_Groups_Olinordered__ab__semigroup__add(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
       => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_k_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_N_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(T_b),V_k_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_N_2))))) ) ) ),
    file('theBenchmark.p',fact_add__Max__commute) ).

fof(fact_sup__Inf1__distrib,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Lattices_Odistrib__lattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))))) ) ) ),
    file('theBenchmark.p',fact_sup__Inf1__distrib) ).

fof(fact_sup__Inf2__distrib,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( class_Lattices_Odistrib__lattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
           => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
             => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBS(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal))),c_Lattices_Osemilattice__sup__class_Osup(T_b)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))))))) ) ) ) ) ),
    file('theBenchmark.p',fact_sup__Inf2__distrib) ).

fof(fact_inf__Sup1__distrib,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Lattices_Odistrib__lattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))))) ) ) ),
    file('theBenchmark.p',fact_inf__Sup1__distrib) ).

fof(fact_inf__Sup2__distrib,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( class_Lattices_Odistrib__lattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
           => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
             => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBS(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(T_b)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))))))) ) ) ) ) ),
    file('theBenchmark.p',fact_inf__Sup2__distrib) ).

fof(fact_min__max_Oinf__Sup1__distrib,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))))) ) ) ),
    file('theBenchmark.p',fact_min__max_Oinf__Sup1__distrib) ).

fof(fact_min__max_Oinf__Sup2__distrib,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
           => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
             => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBS(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal))),c_Orderings_Oord__class_Omin(T_b)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))))))) ) ) ) ) ),
    file('theBenchmark.p',fact_min__max_Oinf__Sup2__distrib) ).

fof(fact_min__max_Osup__Inf2__distrib,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
           => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
             => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBS(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal))),c_Orderings_Oord__class_Omax(T_b)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))))))) ) ) ) ) ),
    file('theBenchmark.p',fact_min__max_Osup__Inf2__distrib) ).

fof(fact_Nitpick_Oprod__def,axiom,
    ! [V_B_2,V_A_2,T_c,T_b] : c_Nitpick_Oprod(T_b,T_c,V_A_2,V_B_2) = hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2)))),
    file('theBenchmark.p',fact_Nitpick_Oprod__def) ).

fof(fact_int__ge__less__than__def,axiom,
    ! [V_d_2] : c_Int_Oint__ge__less__than(V_d_2) = hAPP(c_Set_OCollect(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_d_2)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
    file('theBenchmark.p',fact_int__ge__less__than__def) ).

fof(fact_int__ge__less__than2__def,axiom,
    ! [V_d_2] : c_Int_Oint__ge__less__than2(V_d_2) = hAPP(c_Set_OCollect(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_d_2)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
    file('theBenchmark.p',fact_int__ge__less__than2__def) ).

fof(fact_reflp__def,axiom,
    ! [V_r_2,T_b] :
      ( c_Predicate_Oreflp(T_b,V_r_2)
    <=> c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))) ),
    file('theBenchmark.p',fact_reflp__def) ).

fof(fact_setsum__mult__setsum__if__inj,axiom,
    ! [V_B_2,V_A_2,V_g_2,V_f_2,T_c,T_b,T_d] :
      ( class_Rings_Osemiring__0(T_d)
     => ( c_Fun_Oinj__on(tc_prod(T_b,T_c),T_d,hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,T_d),tc_fun(T_c,T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_d),tc_fun(tc_fun(T_c,T_d),tc_fun(T_c,T_d)),T_b),c_COMBB(T_d,T_d,T_c)),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,T_d),T_b),c_Groups_Otimes__class_Otimes(T_d)),V_f_2))),V_g_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2)))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_d),c_Fun_Oid(T_d)),hAPP(c_Set_OCollect(T_d),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_d),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_d),hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c))),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),T_d),c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),T_d),hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_d),hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj))),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_b,tc_fun(T_c,T_d)),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_d),tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_c,T_d)),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),T_d),c_COMBB(tc_fun(T_c,T_d),tc_fun(T_c,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_c,T_d),tc_fun(T_c,tc_HOL_Obool)),T_d),c_COMBB(T_d,tc_HOL_Obool,T_c)),c_fequal))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,T_d),tc_fun(T_c,T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_d),tc_fun(tc_fun(T_c,T_d),tc_fun(T_c,T_d)),T_b),c_COMBB(T_d,T_d,T_c)),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,T_d),T_b),c_Groups_Otimes__class_Otimes(T_d)),V_f_2))),V_g_2)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))))))) ) ),
    file('theBenchmark.p',fact_setsum__mult__setsum__if__inj) ).

fof(fact_setsum__multicount__gen,axiom,
    ! [V_k_2,V_R_2,V_t_2,T_c,V_s_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_t_2))
       => ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_t_2))
             => hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_s_2))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),V_R_2),B_x)))) = hAPP(V_k_2,B_x) )
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_Nat_Onat,T_b),c_Finite__Set_Ocard(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_OCollect(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_t_2)))),V_R_2)))),V_s_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),V_k_2),V_t_2) ) ) ),
    file('theBenchmark.p',fact_setsum__multicount__gen) ).

fof(fact_inj__on__id,axiom,
    ! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,T_b,c_Fun_Oid(T_b),V_A_2),
    file('theBenchmark.p',fact_inj__on__id) ).

fof(fact_of__int__eq__id,axiom,
    c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint),
    file('theBenchmark.p',fact_of__int__eq__id) ).

fof(fact_o__eq__id__dest,axiom,
    ! [V_v_2,V_c_2,V_b_2,V_a_2,T_b,T_c,T_d] :
      ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_c,T_c,T_b,c_Fun_Oid(T_c)),V_c_2)
     => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,V_v_2) ),
    file('theBenchmark.p',fact_o__eq__id__dest) ).

fof(fact_o__id,axiom,
    ! [V_f_2,T_c,T_b] : hAPP(c_Fun_Ocomp(T_b,T_c,T_b,V_f_2),c_Fun_Oid(T_b)) = V_f_2,
    file('theBenchmark.p',fact_o__id) ).

fof(fact_id__o,axiom,
    ! [V_g_2,T_b,T_c] : hAPP(c_Fun_Ocomp(T_c,T_c,T_b,c_Fun_Oid(T_c)),V_g_2) = V_g_2,
    file('theBenchmark.p',fact_id__o) ).

fof(fact_id__def,axiom,
    ! [V_x_1,T_a] : hAPP(c_Fun_Oid(T_a),V_x_1) = V_x_1,
    file('theBenchmark.p',fact_id__def) ).

fof(fact_apsnd__id,axiom,
    ! [T_b,T_c] : c_Product__Type_Oapsnd(T_c,T_c,T_b,c_Fun_Oid(T_c)) = c_Fun_Oid(tc_prod(T_b,T_c)),
    file('theBenchmark.p',fact_apsnd__id) ).

fof(fact_reflpE,axiom,
    ! [V_x_2,V_r_2,T_b] :
      ( c_Predicate_Oreflp(T_b,V_r_2)
     => hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_x_2)) ),
    file('theBenchmark.p',fact_reflpE) ).

fof(fact_id__apply,axiom,
    ! [V_x,T_a] : hAPP(c_Fun_Oid(T_a),V_x) = V_x,
    file('theBenchmark.p',fact_id__apply) ).

fof(fact_apfst__id,axiom,
    ! [T_c,T_b] : c_Product__Type_Oapfst(T_b,T_b,T_c,c_Fun_Oid(T_b)) = c_Fun_Oid(tc_prod(T_b,T_c)),
    file('theBenchmark.p',fact_apfst__id) ).

fof(fact_vimage__id,axiom,
    ! [V_A_2,T_b] : hAPP(c_Set_Ovimage(T_b,T_b,c_Fun_Oid(T_b)),V_A_2) = V_A_2,
    file('theBenchmark.p',fact_vimage__id) ).

fof(fact_map__pair_Oid,axiom,
    ! [T_c,T_b] : c_Product__Type_Omap__pair(T_b,T_b,T_c,T_c,c_Fun_Oid(T_b),c_Fun_Oid(T_c)) = c_Fun_Oid(tc_prod(T_b,T_c)),
    file('theBenchmark.p',fact_map__pair_Oid) ).

fof(fact_map__pair_Oidentity,axiom,
    ! [T_c,T_b] : c_Product__Type_Omap__pair(T_b,T_b,T_c,T_c,c_COMBI(T_b),c_COMBI(T_c)) = c_Fun_Oid(tc_prod(T_b,T_c)),
    file('theBenchmark.p',fact_map__pair_Oidentity) ).

fof(fact_image__id,axiom,
    ! [V_Y_2,T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_Fun_Oid(T_b)),V_Y_2) = V_Y_2,
    file('theBenchmark.p',fact_image__id) ).

fof(fact_surj__id,axiom,
    ! [T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_Fun_Oid(T_b)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_surj__id) ).

fof(fact_folding_Oempty,axiom,
    ! [V_F_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
     => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Fun_Oid(T_c) ),
    file('theBenchmark.p',fact_folding_Oempty) ).

fof(fact_apsnd__def,axiom,
    ! [V_f_2,T_b,T_d,T_c] : c_Product__Type_Oapsnd(T_c,T_d,T_b,V_f_2) = c_Product__Type_Omap__pair(T_b,T_b,T_c,T_d,c_Fun_Oid(T_b),V_f_2),
    file('theBenchmark.p',fact_apsnd__def) ).

fof(fact_apfst__def,axiom,
    ! [V_f_2,T_c,T_d,T_b] : c_Product__Type_Oapfst(T_b,T_d,T_c,V_f_2) = c_Product__Type_Omap__pair(T_b,T_d,T_c,T_c,V_f_2,c_Fun_Oid(T_c)),
    file('theBenchmark.p',fact_apfst__def) ).

fof(fact_split__Pair,axiom,
    ! [T_c,T_b] : hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_prod(T_b,T_c)),c_Product__Type_OPair(T_b,T_c)) = c_Fun_Oid(tc_prod(T_b,T_c)),
    file('theBenchmark.p',fact_split__Pair) ).

fof(fact_setsum__reindex__id,axiom,
    ! [V_B_2,V_f_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__add(T_c)
     => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_c),c_Fun_Oid(T_c)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) ) ),
    file('theBenchmark.p',fact_setsum__reindex__id) ).

fof(fact_setprod__reindex__id,axiom,
    ! [V_B_2,V_f_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__mult(T_c)
     => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_c),c_Fun_Oid(T_c)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) ) ),
    file('theBenchmark.p',fact_setprod__reindex__id) ).

fof(fact_finite__conv__nat__seg__image,axiom,
    ! [V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
    <=> ? [B_n,B_f] : V_A_2 = hAPP(c_Set_Oimage(tc_Nat_Onat,T_b,B_f),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),B_n))) ),
    file('theBenchmark.p',fact_finite__conv__nat__seg__image) ).

fof(fact_rel__comp__def,axiom,
    ! [V_s_2,V_r_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_r_2),V_s_2) = hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_d))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_b),c_COMBS(T_d,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_d),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_b),c_COMBC(T_d,tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_b,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_d),tc_fun(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_b,T_d)))),c_Product__Type_OPair(T_b,T_d)))),V_r_2))))),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_d,T_c)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_d,T_c),tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_d,T_c)))),hAPP(c_COMBC(T_d,T_c,tc_prod(T_d,T_c)),c_Product__Type_OPair(T_d,T_c))))),V_s_2))))),
    file('theBenchmark.p',fact_rel__comp__def) ).

fof(fact_Range__Collect__split,axiom,
    ! [V_P_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),hAPP(c_Set_OCollect(tc_prod(T_c,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,tc_HOL_Obool),V_P_2))) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c)),hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),V_P_2))),
    file('theBenchmark.p',fact_Range__Collect__split) ).

fof(fact_rel__compI,axiom,
    ! [V_s_2,V_c_2,T_d,V_r_2,V_b_2,V_a_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_b_2),V_c_2)),V_s_2))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),V_a_2),V_c_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2))) ) ),
    file('theBenchmark.p',fact_rel__compI) ).

fof(fact_RangeI,axiom,
    ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2))
     => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ),
    file('theBenchmark.p',fact_RangeI) ).

fof(fact_rel__comp__UNION__distrib2,axiom,
    ! [V_s_2,V_r_2,V_I_2,T_e,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)),V_I_2),V_r_2)),V_s_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBC(T_e,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),T_e),c_Relation_Orel__comp(T_b,T_d,T_c)),V_r_2)),V_s_2)),
    file('theBenchmark.p',fact_rel__comp__UNION__distrib2) ).

fof(fact_rel__comp__UNION__distrib,axiom,
    ! [V_r_2,V_I_2,T_e,V_s_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_s_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool)),V_I_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),T_e),hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_s_2)),V_r_2)),
    file('theBenchmark.p',fact_rel__comp__UNION__distrib) ).

fof(fact_rel__comp__empty2,axiom,
    ! [V_R_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_R_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),
    file('theBenchmark.p',fact_rel__comp__empty2) ).

fof(fact_rel__comp__empty1,axiom,
    ! [V_R_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool))),V_R_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),
    file('theBenchmark.p',fact_rel__comp__empty1) ).

fof(fact_rel__comp__distrib,axiom,
    ! [V_T_2,V_S_2,V_R_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_R_2),V_S_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_R_2),V_T_2)),
    file('theBenchmark.p',fact_rel__comp__distrib) ).

fof(fact_rel__comp__distrib2,axiom,
    ! [V_R_2,V_T_2,V_S_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)),V_S_2),V_T_2)),V_R_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_S_2),V_R_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_T_2),V_R_2)),
    file('theBenchmark.p',fact_rel__comp__distrib2) ).

fof(fact_O__assoc,axiom,
    ! [V_T_2,V_S_2,V_R_2,T_e,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_e,T_d),V_R_2),V_S_2)),V_T_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_e,T_c),V_R_2),hAPP(hAPP(c_Relation_Orel__comp(T_e,T_d,T_c),V_S_2),V_T_2)),
    file('theBenchmark.p',fact_O__assoc) ).

fof(fact_rel__comp__mono,axiom,
    ! [V_s_2,V_s_H_2,T_d,V_r_2,V_r_H_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_H_2),V_r_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),V_s_H_2),V_s_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_H_2),V_s_H_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2))) ) ),
    file('theBenchmark.p',fact_rel__comp__mono) ).

fof(fact_Range__Id__on,axiom,
    ! [V_A_2,T_b] : hAPP(c_Relation_ORange(T_b,T_b),c_Relation_OId__on(T_b,V_A_2)) = V_A_2,
    file('theBenchmark.p',fact_Range__Id__on) ).

fof(fact_union__comp__emptyR,axiom,
    ! [V_C_2,V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
     => ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_A_2),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
       => hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_B_2),V_C_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_union__comp__emptyR) ).

fof(fact_union__comp__emptyL,axiom,
    ! [V_B_2,V_C_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_A_2),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
     => ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_B_2),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
       => hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_union__comp__emptyL) ).

fof(fact_Range__Union,axiom,
    ! [V_S_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_Relation_ORange(T_c,T_b)),
    file('theBenchmark.p',fact_Range__Union) ).

fof(fact_Range__empty,axiom,
    ! [T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Range__empty) ).

fof(fact_Range__empty__iff,axiom,
    ! [V_r_2,T_b,T_c] :
      ( hAPP(c_Relation_ORange(T_c,T_b),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
    <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_Range__empty__iff) ).

fof(fact_rel__comp__subset__Sigma,axiom,
    ! [V_C_2,V_s_2,T_d,V_B_2,V_A_2,V_r_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),V_s_2),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_B_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_C_2))))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_b),V_C_2)))) ) ),
    file('theBenchmark.p',fact_rel__comp__subset__Sigma) ).

fof(fact_Range__Un__eq,axiom,
    ! [V_B_2,V_A_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_c,T_b),V_A_2)),hAPP(c_Relation_ORange(T_c,T_b),V_B_2)),
    file('theBenchmark.p',fact_Range__Un__eq) ).

fof(fact_finite__Range,axiom,
    ! [V_r_2,T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),V_r_2))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ),
    file('theBenchmark.p',fact_finite__Range) ).

fof(fact_snd__eq__Range,axiom,
    ! [V_R_2,T_b,T_c] : hAPP(c_Set_Oimage(tc_prod(T_c,T_b),T_b,c_Product__Type_Osnd(T_c,T_b)),V_R_2) = hAPP(c_Relation_ORange(T_c,T_b),V_R_2),
    file('theBenchmark.p',fact_snd__eq__Range) ).

fof(fact_Range__iff,axiom,
    ! [V_r_2,T_c,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2)))
    <=> ? [B_y] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_y),V_a_2)),V_r_2)) ),
    file('theBenchmark.p',fact_Range__iff) ).

fof(fact_Range__insert,axiom,
    ! [V_r_2,V_b_2,V_a_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2)),
    file('theBenchmark.p',fact_Range__insert) ).

fof(fact_Range__Int__subset,axiom,
    ! [V_B_2,V_A_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_c,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_c,T_b),V_A_2)),hAPP(c_Relation_ORange(T_c,T_b),V_B_2)))),
    file('theBenchmark.p',fact_Range__Int__subset) ).

fof(fact_Range__Diff__subset,axiom,
    ! [V_B_2,V_A_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_c,T_b),V_A_2)),hAPP(c_Relation_ORange(T_c,T_b),V_B_2))),hAPP(c_Relation_ORange(T_c,T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_A_2),V_B_2)))),
    file('theBenchmark.p',fact_Range__Diff__subset) ).

fof(fact_max__ext__compat,axiom,
    ! [V_S_2,V_R_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_S_2)),V_R_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Wellfounded_Omax__ext(T_b,V_R_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(T_b,V_S_2)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omax__ext(T_b,V_R_2))) ),
    file('theBenchmark.p',fact_max__ext__compat) ).

fof(fact_min__ext__compat,axiom,
    ! [V_S_2,V_R_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_S_2)),V_R_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Wellfounded_Omin__ext(T_b,V_R_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(T_b,V_S_2)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omin__ext(T_b,V_R_2))) ),
    file('theBenchmark.p',fact_min__ext__compat) ).

fof(fact_RangeP__Range__eq,axiom,
    ! [V_x_2,V_r_2,T_c,T_b] :
      ( hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_r_2)),V_x_2))
    <=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ),
    file('theBenchmark.p',fact_RangeP__Range__eq) ).

fof(fact_RangeE,axiom,
    ! [V_r_2,T_c,V_b_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2)))
     => ~ ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),V_b_2)),V_r_2)) ),
    file('theBenchmark.p',fact_RangeE) ).

fof(fact_pred__comp__rel__comp__eq,axiom,
    ! [V_y_2,V_x_2,V_s_2,V_r_2,T_d,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_b,T_c,T_d,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_r_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_c,T_d)))),c_Product__Type_OPair(T_c,T_d)))),V_s_2)),V_x_2),V_y_2))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),V_x_2),V_y_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2))) ),
    file('theBenchmark.p',fact_pred__comp__rel__comp__eq) ).

fof(fact_pred__comp_Ointros,axiom,
    ! [T_d,T_c,T_b,V_c_2,V_s_2,V_b_2,V_a_2,V_r_2] :
      ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
     => ( hBOOL(hAPP(hAPP(V_s_2,V_b_2),V_c_2))
       => hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_b,T_c,T_d,V_r_2,V_s_2),V_a_2),V_c_2)) ) ),
    file('theBenchmark.p',fact_pred__comp_Ointros) ).

fof(fact_RangeP_Ointros,axiom,
    ! [T_c,T_b,V_b_2,V_a_2,V_r_2] :
      ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
     => hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_b_2)) ),
    file('theBenchmark.p',fact_RangeP_Ointros) ).

fof(fact_pred__comp_Oequations,axiom,
    ! [V_a3_2,V_a1_2,V_s_2,V_r_2,T_d,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_b,T_c,T_d,V_r_2,V_s_2),V_a1_2),V_a3_2))
    <=> ? [B_b] :
          ( hBOOL(hAPP(hAPP(V_s_2,B_b),V_a3_2))
          & hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_b)) ) ),
    file('theBenchmark.p',fact_pred__comp_Oequations) ).

fof(fact_RangeP_Oequations,axiom,
    ! [V_a2_2,V_r_2,T_c,T_b] :
      ( hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_a2_2))
    <=> ? [B_a] : hBOOL(hAPP(hAPP(V_r_2,B_a),V_a2_2)) ),
    file('theBenchmark.p',fact_RangeP_Oequations) ).

fof(fact_reduction__pairI,axiom,
    ! [V_S_2,V_R_2,T_b] :
      ( c_Wellfounded_Owf(T_b,V_R_2)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_S_2)),V_R_2))
       => c_FunDef_Oreduction__pair(T_b,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)) ) ),
    file('theBenchmark.p',fact_reduction__pairI) ).

fof(fact_Domain__Collect__split,axiom,
    ! [V_P_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_P_2))) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c)),V_P_2)),
    file('theBenchmark.p',fact_Domain__Collect__split) ).

fof(fact_the__eq__trivial,axiom,
    ! [V_a_2,T_b] : c_HOL_OThe(T_b,hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2)) = V_a_2,
    file('theBenchmark.p',fact_the__eq__trivial) ).

fof(fact_wf__less__than,axiom,
    c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than),
    file('theBenchmark.p',fact_wf__less__than) ).

fof(fact_wf__empty,axiom,
    ! [T_b] : c_Wellfounded_Owf(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))),
    file('theBenchmark.p',fact_wf__empty) ).

fof(fact_wf__inv__image,axiom,
    ! [V_f_2,T_c,V_r_2,T_b] :
      ( c_Wellfounded_Owf(T_b,V_r_2)
     => c_Wellfounded_Owf(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2)) ),
    file('theBenchmark.p',fact_wf__inv__image) ).

fof(fact_wf__lex__prod,axiom,
    ! [V_rb_2,T_c,V_ra_2,T_b] :
      ( c_Wellfounded_Owf(T_b,V_ra_2)
     => ( c_Wellfounded_Owf(T_c,V_rb_2)
       => c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Wellfounded_Olex__prod(T_b,T_c,V_ra_2,V_rb_2)) ) ),
    file('theBenchmark.p',fact_wf__lex__prod) ).

fof(fact_wf__measure,axiom,
    ! [V_f_2,T_b] : c_Wellfounded_Owf(T_b,hAPP(c_Wellfounded_Omeasure(T_b),V_f_2)),
    file('theBenchmark.p',fact_wf__measure) ).

fof(fact_DomainI,axiom,
    ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2))
     => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ),
    file('theBenchmark.p',fact_DomainI) ).

fof(fact_wf__comp__self,axiom,
    ! [V_R_2,T_b] :
      ( c_Wellfounded_Owf(T_b,V_R_2)
    <=> c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2)) ),
    file('theBenchmark.p',fact_wf__comp__self) ).

fof(fact_min__ext__wf,axiom,
    ! [V_r_2,T_b] :
      ( c_Wellfounded_Owf(T_b,V_r_2)
     => c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Omin__ext(T_b,V_r_2)) ),
    file('theBenchmark.p',fact_min__ext__wf) ).

fof(fact_wf__subset,axiom,
    ! [V_p_2,V_r_2,T_b] :
      ( c_Wellfounded_Owf(T_b,V_r_2)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_p_2),V_r_2))
       => c_Wellfounded_Owf(T_b,V_p_2) ) ),
    file('theBenchmark.p',fact_wf__subset) ).

fof(fact_wf__irrefl,axiom,
    ! [V_a_2,V_r_2,T_b] :
      ( c_Wellfounded_Owf(T_b,V_r_2)
     => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),V_r_2)) ),
    file('theBenchmark.p',fact_wf__irrefl) ).

fof(fact_wf__asym,axiom,
    ! [V_x_2,V_a_2,V_r_2,T_b] :
      ( c_Wellfounded_Owf(T_b,V_r_2)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_x_2)),V_r_2))
       => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_a_2)),V_r_2)) ) ),
    file('theBenchmark.p',fact_wf__asym) ).

fof(fact_wf__not__sym,axiom,
    ! [V_x_2,V_a_2,V_r_2,T_b] :
      ( c_Wellfounded_Owf(T_b,V_r_2)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_x_2)),V_r_2))
       => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_a_2)),V_r_2)) ) ),
    file('theBenchmark.p',fact_wf__not__sym) ).

fof(fact_wf__not__refl,axiom,
    ! [V_a_2,V_r_2,T_b] :
      ( c_Wellfounded_Owf(T_b,V_r_2)
     => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),V_r_2)) ),
    file('theBenchmark.p',fact_wf__not__refl) ).

fof(fact_max__ext__wf,axiom,
    ! [V_r_2,T_b] :
      ( c_Wellfounded_Owf(T_b,V_r_2)
     => c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Omax__ext(T_b,V_r_2)) ),
    file('theBenchmark.p',fact_max__ext__wf) ).

fof(fact_wf__pair__less,axiom,
    c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
    file('theBenchmark.p',fact_wf__pair__less) ).

fof(fact_wf__finite__psubset,axiom,
    ! [T_b] : c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_b)),
    file('theBenchmark.p',fact_wf__finite__psubset) ).

fof(fact_wf__mlex,axiom,
    ! [V_f_2,V_R_2,T_b] :
      ( c_Wellfounded_Owf(T_b,V_R_2)
     => c_Wellfounded_Owf(T_b,c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2)) ),
    file('theBenchmark.p',fact_wf__mlex) ).

fof(fact_wf__Int1,axiom,
    ! [V_r_H_2,V_r_2,T_b] :
      ( c_Wellfounded_Owf(T_b,V_r_2)
     => c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_r_H_2)) ),
    file('theBenchmark.p',fact_wf__Int1) ).

fof(fact_wf__Int2,axiom,
    ! [V_r_H_2,V_r_2,T_b] :
      ( c_Wellfounded_Owf(T_b,V_r_2)
     => c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_H_2),V_r_2)) ),
    file('theBenchmark.p',fact_wf__Int2) ).

fof(fact_Domain__Id__on,axiom,
    ! [V_A_2,T_b] : hAPP(c_Relation_ODomain(T_b,T_b),c_Relation_OId__on(T_b,V_A_2)) = V_A_2,
    file('theBenchmark.p',fact_Domain__Id__on) ).

fof(fact_wf__less,axiom,
    c_Wellfounded_Owf(tc_Nat_Onat,hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)))),
    file('theBenchmark.p',fact_wf__less) ).

fof(fact_wf__int__ge__less__than2,axiom,
    ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(V_d_2)),
    file('theBenchmark.p',fact_wf__int__ge__less__than2) ).

fof(fact_wf__int__ge__less__than,axiom,
    ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(V_d_2)),
    file('theBenchmark.p',fact_wf__int__ge__less__than) ).

fof(fact_wf__Un,axiom,
    ! [V_s_2,V_r_2,T_b] :
      ( c_Wellfounded_Owf(T_b,V_r_2)
     => ( c_Wellfounded_Owf(T_b,V_s_2)
       => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_b),V_r_2)),hAPP(c_Relation_ORange(T_b,T_b),V_s_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ) ) ),
    file('theBenchmark.p',fact_wf__Un) ).

fof(fact_wf__acc__iff,axiom,
    ! [V_r_2,T_b] :
      ( c_Wellfounded_Owf(T_b,V_r_2)
    <=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2))) ),
    file('theBenchmark.p',fact_wf__acc__iff) ).

fof(fact_acc__wfD,axiom,
    ! [V_x_2,V_r_2,T_b] :
      ( c_Wellfounded_Owf(T_b,V_r_2)
     => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ),
    file('theBenchmark.p',fact_acc__wfD) ).

fof(fact_wf__no__loop,axiom,
    ! [V_R_2,T_b] :
      ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
     => c_Wellfounded_Owf(T_b,V_R_2) ),
    file('theBenchmark.p',fact_wf__no__loop) ).

fof(fact_wf__union__merge,axiom,
    ! [V_S_2,V_R_2,T_b] :
      ( c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2))
    <=> c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_S_2),V_R_2))),V_S_2)) ),
    file('theBenchmark.p',fact_wf__union__merge) ).

fof(fact_Domain__empty,axiom,
    ! [T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Domain__empty) ).

fof(fact_Domain__empty__iff,axiom,
    ! [V_r_2,T_c,T_b] :
      ( hAPP(c_Relation_ODomain(T_b,T_c),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
    <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_Domain__empty__iff) ).

fof(fact_Domain__mono,axiom,
    ! [V_s_2,V_r_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_2),V_s_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)),hAPP(c_Relation_ODomain(T_b,T_c),V_s_2))) ),
    file('theBenchmark.p',fact_Domain__mono) ).

fof(fact_Domain__Un__eq,axiom,
    ! [V_B_2,V_A_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_c),V_A_2)),hAPP(c_Relation_ODomain(T_b,T_c),V_B_2)),
    file('theBenchmark.p',fact_Domain__Un__eq) ).

fof(fact_finite__Domain,axiom,
    ! [V_r_2,T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),V_r_2))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ),
    file('theBenchmark.p',fact_finite__Domain) ).

fof(fact_fst__eq__Domain,axiom,
    ! [V_R_2,T_c,T_b] : hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_b,c_Product__Type_Ofst(T_b,T_c)),V_R_2) = hAPP(c_Relation_ODomain(T_b,T_c),V_R_2),
    file('theBenchmark.p',fact_fst__eq__Domain) ).

fof(fact_wf__iff__no__infinite__down__chain,axiom,
    ! [V_r_2,T_b] :
      ( c_Wellfounded_Owf(T_b,V_r_2)
    <=> ~ ? [B_f] :
          ! [B_i] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(B_f,hAPP(c_Nat_OSuc,B_i))),hAPP(B_f,B_i))),V_r_2)) ),
    file('theBenchmark.p',fact_wf__iff__no__infinite__down__chain) ).

fof(fact_wfE__pf,axiom,
    ! [V_A_2,V_R_2,T_b] :
      ( c_Wellfounded_Owf(T_b,V_R_2)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Relation_OImage(T_b,T_b,V_R_2),V_A_2)))
       => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_wfE__pf) ).

fof(fact_wf__union__compatible,axiom,
    ! [V_S_2,V_R_2,T_b] :
      ( c_Wellfounded_Owf(T_b,V_R_2)
     => ( c_Wellfounded_Owf(T_b,V_S_2)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_S_2)),V_R_2))
         => c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)) ) ) ),
    file('theBenchmark.p',fact_wf__union__compatible) ).

fof(fact_Domain__iff,axiom,
    ! [V_r_2,T_c,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)))
    <=> ? [B_y] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),B_y)),V_r_2)) ),
    file('theBenchmark.p',fact_Domain__iff) ).

fof(fact_wf,axiom,
    ! [T_b] :
      ( class_Orderings_Owellorder(T_b)
     => c_Wellfounded_Owf(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),c_Orderings_Oord__class_Oless(T_b)))) ),
    file('theBenchmark.p',fact_wf) ).

fof(fact_Domain__insert,axiom,
    ! [V_r_2,V_b_2,V_a_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)),
    file('theBenchmark.p',fact_Domain__insert) ).

fof(fact_reduction__pair__def,axiom,
    ! [V_P_2,T_b] :
      ( c_FunDef_Oreduction__pair(T_b,V_P_2)
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2)))
        & c_Wellfounded_Owf(T_b,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2)) ) ),
    file('theBenchmark.p',fact_reduction__pair__def) ).

fof(fact_reduction__pair__lemma,axiom,
    ! [V_S_2,V_R_2,V_P_2,T_b] :
      ( c_FunDef_Oreduction__pair(T_b,V_P_2)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_S_2),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2)))
         => ( c_Wellfounded_Owf(T_b,V_S_2)
           => c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)) ) ) ) ),
    file('theBenchmark.p',fact_reduction__pair__lemma) ).

fof(fact_Domain__Int__subset,axiom,
    ! [V_B_2,V_A_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_c),V_A_2)),hAPP(c_Relation_ODomain(T_b,T_c),V_B_2)))),
    file('theBenchmark.p',fact_Domain__Int__subset) ).

fof(fact_Domain__Diff__subset,axiom,
    ! [V_B_2,V_A_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_c),V_A_2)),hAPP(c_Relation_ODomain(T_b,T_c),V_B_2))),hAPP(c_Relation_ODomain(T_b,T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_A_2),V_B_2)))),
    file('theBenchmark.p',fact_Domain__Diff__subset) ).

fof(fact_Field__def,axiom,
    ! [V_r_2,T_b] : hAPP(c_Relation_OField(T_b),V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_b),V_r_2)),hAPP(c_Relation_ORange(T_b,T_b),V_r_2)),
    file('theBenchmark.p',fact_Field__def) ).

fof(fact_wf__map__pair__image,axiom,
    ! [V_f_2,T_c,V_r_2,T_b] :
      ( c_Wellfounded_Owf(T_b,V_r_2)
     => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
       => c_Wellfounded_Owf(T_c,hAPP(c_Set_Oimage(tc_prod(T_b,T_b),tc_prod(T_c,T_c),c_Product__Type_Omap__pair(T_b,T_c,T_b,T_c,V_f_2,V_f_2)),V_r_2)) ) ),
    file('theBenchmark.p',fact_wf__map__pair__image) ).

fof(fact_Domain__Union,axiom,
    ! [V_S_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_Relation_ODomain(T_b,T_c)),
    file('theBenchmark.p',fact_Domain__Union) ).

fof(fact_the__sym__eq__trivial,axiom,
    ! [V_x_2,T_b] : c_HOL_OThe(T_b,hAPP(c_fequal,V_x_2)) = V_x_2,
    file('theBenchmark.p',fact_the__sym__eq__trivial) ).

fof(fact_DomainP__Domain__eq,axiom,
    ! [V_x_2,V_r_2,T_c,T_b] :
      ( hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_r_2)),V_x_2))
    <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ),
    file('theBenchmark.p',fact_DomainP__Domain__eq) ).

fof(fact_wf__lenlex,axiom,
    ! [V_r_2,T_b] :
      ( c_Wellfounded_Owf(T_b,V_r_2)
     => c_Wellfounded_Owf(tc_List_Olist(T_b),c_List_Olenlex(T_b,V_r_2)) ),
    file('theBenchmark.p',fact_wf__lenlex) ).

fof(fact_DomainE,axiom,
    ! [V_r_2,T_c,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)))
     => ~ ! [B_y] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),B_y)),V_r_2)) ),
    file('theBenchmark.p',fact_DomainE) ).

fof(fact_DomainP_Ointros,axiom,
    ! [T_c,T_b,V_b_2,V_a_2,V_r_2] :
      ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
     => hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a_2)) ),
    file('theBenchmark.p',fact_DomainP_Ointros) ).

fof(fact_DomainP_Oequations,axiom,
    ! [V_a1_2,V_r_2,T_c,T_b] :
      ( hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a1_2))
    <=> ? [B_x1] : hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_x1)) ),
    file('theBenchmark.p',fact_DomainP_Oequations) ).

fof(fact_pred__nat__def,axiom,
    c_Wellfounded_Opred__nat = hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_fequal)),c_Nat_OSuc))),
    file('theBenchmark.p',fact_pred__nat__def) ).

fof(fact_wf__lex,axiom,
    ! [V_r_2,T_b] :
      ( c_Wellfounded_Owf(T_b,V_r_2)
     => c_Wellfounded_Owf(tc_List_Olist(T_b),c_List_Olex(T_b,V_r_2)) ),
    file('theBenchmark.p',fact_wf__lex) ).

fof(fact_wf__lexn,axiom,
    ! [V_n_2,V_r_2,T_b] :
      ( c_Wellfounded_Owf(T_b,V_r_2)
     => c_Wellfounded_Owf(tc_List_Olist(T_b),hAPP(c_List_Olexn(T_b,V_r_2),V_n_2)) ),
    file('theBenchmark.p',fact_wf__lexn) ).

fof(fact_lex__def,axiom,
    ! [V_r_2,T_b] : c_List_Olex(T_b,V_r_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_List_Olexn(T_b,V_r_2)),
    file('theBenchmark.p',fact_lex__def) ).

fof(fact_lexn_Osimps_I1_J,axiom,
    ! [V_r_2,T_b] : hAPP(c_List_Olexn(T_b,V_r_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),
    file('theBenchmark.p',fact_lexn_Osimps_I1_J) ).

fof(fact_wf__pred__nat,axiom,
    c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat),
    file('theBenchmark.p',fact_wf__pred__nat) ).

fof(fact_wf__same__fst,axiom,
    ! [T_b,V_R_2,T_c,V_P_2] :
      ( ! [B_x] :
          ( hBOOL(hAPP(V_P_2,B_x))
         => c_Wellfounded_Owf(T_c,hAPP(V_R_2,B_x)) )
     => c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Recdef_Osame__fst(T_b,T_c,V_P_2,V_R_2)) ),
    file('theBenchmark.p',fact_wf__same__fst) ).

fof(fact_wf__if__measure,axiom,
    ! [T_b,V_g_2,V_f_2,V_P_2] :
      ( ! [B_x] :
          ( hBOOL(hAPP(V_P_2,B_x))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,hAPP(V_g_2,B_x))),hAPP(V_f_2,B_x))) )
     => c_Wellfounded_Owf(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_P_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),V_g_2))))) ),
    file('theBenchmark.p',fact_wf__if__measure) ).

fof(fact_wfP__def,axiom,
    ! [V_r_2,T_b] :
      ( c_Wellfounded_OwfP(T_b,V_r_2)
    <=> c_Wellfounded_Owf(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))) ),
    file('theBenchmark.p',fact_wfP__def) ).

fof(fact_wfP__empty,axiom,
    ! [T_b] : c_Wellfounded_OwfP(T_b,hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBK(tc_HOL_Obool,T_b),c_fFalse))),
    file('theBenchmark.p',fact_wfP__empty) ).

fof(fact_accp__wfPD,axiom,
    ! [V_x_2,V_r_2,T_b] :
      ( c_Wellfounded_OwfP(T_b,V_r_2)
     => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_x_2)) ),
    file('theBenchmark.p',fact_accp__wfPD) ).

fof(fact_wfP__accp__iff,axiom,
    ! [V_r_2,T_b] :
      ( c_Wellfounded_OwfP(T_b,V_r_2)
    <=> ! [B_x1] : hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x1)) ),
    file('theBenchmark.p',fact_wfP__accp__iff) ).

fof(fact_wfP__subset,axiom,
    ! [V_p_2,V_r_2,T_b] :
      ( c_Wellfounded_OwfP(T_b,V_r_2)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),V_p_2),V_r_2))
       => c_Wellfounded_OwfP(T_b,V_p_2) ) ),
    file('theBenchmark.p',fact_wfP__subset) ).

fof(fact_wf__in__rel,axiom,
    ! [V_R_2,T_b] :
      ( c_Wellfounded_Owf(T_b,V_R_2)
     => c_Wellfounded_OwfP(T_b,c_FunDef_Oin__rel(T_b,T_b,V_R_2)) ),
    file('theBenchmark.p',fact_wf__in__rel) ).

fof(fact_wfP__wf__eq,axiom,
    ! [V_r_2,T_b] :
      ( c_Wellfounded_OwfP(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2))
    <=> c_Wellfounded_Owf(T_b,V_r_2) ),
    file('theBenchmark.p',fact_wfP__wf__eq) ).

fof(fact_wfP__acyclicP,axiom,
    ! [V_r_2,T_b] :
      ( c_Wellfounded_OwfP(T_b,V_r_2)
     => c_Wellfounded_Oacyclic(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))) ),
    file('theBenchmark.p',fact_wfP__acyclicP) ).

fof(fact_pigeonhole__infinite,axiom,
    ! [V_f_2,T_c,V_A_2,T_b] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
       => ? [B_x] :
            ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),hAPP(V_f_2,B_x))))))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ),
    file('theBenchmark.p',fact_pigeonhole__infinite) ).

fof(fact_refl__on__def_H,axiom,
    ! [V_r_2,V_A_2,T_b] :
      ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
    <=> ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
           => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) )
        & ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2))
           => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),B_x)) ) ) ),
    file('theBenchmark.p',fact_refl__on__def_H) ).

fof(fact_ball__empty,axiom,
    ! [V_P_2,T_b,B_x] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
     => hBOOL(hAPP(V_P_2,B_x)) ),
    file('theBenchmark.p',fact_ball__empty) ).

fof(fact_wf__acyclic,axiom,
    ! [V_r_2,T_b] :
      ( c_Wellfounded_Owf(T_b,V_r_2)
     => c_Wellfounded_Oacyclic(T_b,V_r_2) ),
    file('theBenchmark.p',fact_wf__acyclic) ).

fof(fact_acyclic__subset,axiom,
    ! [V_r_2,V_s_2,T_b] :
      ( c_Wellfounded_Oacyclic(T_b,V_s_2)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
       => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ),
    file('theBenchmark.p',fact_acyclic__subset) ).

fof(fact_INFI__bool__eq,axiom,
    ! [T_b] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_HOL_Obool) = c_Set_OBall(T_b),
    file('theBenchmark.p',fact_INFI__bool__eq) ).

fof(fact_Powp__def,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Predicate_OPowp(T_b,V_A_2),V_B_2))
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2))
         => hBOOL(hAPP(V_A_2,B_x)) ) ),
    file('theBenchmark.p',fact_Powp__def) ).

fof(fact_Collect__ball__eq,axiom,
    ! [V_P_2,V_A_2,T_c,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fimplies),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)))),V_P_2))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Set_OCollect(T_b)),hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),V_P_2))),
    file('theBenchmark.p',fact_Collect__ball__eq) ).

fof(fact_congruent__def,axiom,
    ! [V_f_2,V_r_2,T_c,T_b] :
      ( c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2)
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2))
         => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_c,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2))),V_f_2)),B_x)) ) ),
    file('theBenchmark.p',fact_congruent__def) ).

fof(fact_INTER__def,axiom,
    ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fimplies),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c)),c_member(T_b))),V_B_2)))),
    file('theBenchmark.p',fact_INTER__def) ).

fof(fact_wf__iff__acyclic__if__finite,axiom,
    ! [V_r_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
     => ( c_Wellfounded_Owf(T_b,V_r_2)
      <=> c_Wellfounded_Oacyclic(T_b,V_r_2) ) ),
    file('theBenchmark.p',fact_wf__iff__acyclic__if__finite) ).

fof(fact_finite__acyclic__wf,axiom,
    ! [V_r_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
     => ( c_Wellfounded_Oacyclic(T_b,V_r_2)
       => c_Wellfounded_Owf(T_b,V_r_2) ) ),
    file('theBenchmark.p',fact_finite__acyclic__wf) ).

fof(fact_Sup__Inf,axiom,
    ! [V_A_2,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_b)))))) ),
    file('theBenchmark.p',fact_Sup__Inf) ).

fof(fact_Inf__Sup,axiom,
    ! [V_A_2,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),c_Orderings_Oord__class_Oless__eq(T_b))))) ),
    file('theBenchmark.p',fact_Inf__Sup) ).

fof(fact_Nitpick_Owf_H__def,axiom,
    ! [V_r_2,T_b] :
      ( c_Nitpick_Owf_H(T_b,V_r_2)
    <=> ( ( c_Nitpick_Ounknown(tc_HOL_Obool)
          | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) )
        & c_Wellfounded_Oacyclic(T_b,V_r_2) ) ),
    file('theBenchmark.p',fact_Nitpick_Owf_H__def) ).

fof(fact_Abs__Integ__induct,axiom,
    ! [V_x_2,V_P_2] :
      ( ! [B_y] :
          ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg))
         => hBOOL(hAPP(V_P_2,hAPP(c_Int_OAbs__Integ,B_y))) )
     => hBOOL(hAPP(V_P_2,V_x_2)) ),
    file('theBenchmark.p',fact_Abs__Integ__induct) ).

fof(fact_Abs__Integ__cases,axiom,
    ! [V_x_2] :
      ~ ! [B_y] :
          ( V_x_2 = hAPP(c_Int_OAbs__Integ,B_y)
         => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg)) ),
    file('theBenchmark.p',fact_Abs__Integ__cases) ).

fof(fact_Inter__eq,axiom,
    ! [V_A_2,T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_fimplies),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_b,tc_HOL_Obool))),V_A_2)))),c_member(T_b)))),
    file('theBenchmark.p',fact_Inter__eq) ).

fof(fact_finite__UN__I,axiom,
    ! [V_B_2,T_c,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( ! [B_a] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
           => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_a))) )
       => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ) ),
    file('theBenchmark.p',fact_finite__UN__I) ).

fof(fact_inj__on__diff__nat,axiom,
    ! [V_k_2,V_N_2] :
      ( ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),B_x)) )
     => c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_k_2),V_N_2) ),
    file('theBenchmark.p',fact_inj__on__diff__nat) ).

fof(fact_wfP__SUP,axiom,
    ! [T_b,V_r_2,T_c] :
      ( ! [B_i] : c_Wellfounded_OwfP(T_c,hAPP(V_r_2,B_i))
     => ( ! [B_i,B_j] :
            ( hAPP(V_r_2,B_i) != hAPP(V_r_2,B_j)
           => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_Predicate_ODomainP(T_c,T_c,hAPP(V_r_2,B_i))),c_Predicate_ORangeP(T_c,T_c,hAPP(V_r_2,B_j))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
       => c_Wellfounded_OwfP(T_c,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2)) ) ),
    file('theBenchmark.p',fact_wfP__SUP) ).

fof(fact_mem__splitI2,axiom,
    ! [V_c_2,V_z_2,T_d,T_c,T_b,V_p_2] :
      ( ! [B_a,B_b] :
          ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b)
         => hBOOL(hAPP(hAPP(c_member(T_d),V_z_2),hAPP(hAPP(V_c_2,B_a),B_b))) )
     => hBOOL(hAPP(hAPP(c_member(T_d),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_d,tc_HOL_Obool)),V_c_2),V_p_2))) ),
    file('theBenchmark.p',fact_mem__splitI2) ).

fof(fact_mem__splitE,axiom,
    ! [V_p_2,V_c_2,T_d,T_c,V_z_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_fun(T_b,tc_HOL_Obool)),V_c_2),V_p_2)))
     => ~ ! [B_x,B_y] :
            ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),B_x),B_y)
           => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_c_2,B_x),B_y))) ) ),
    file('theBenchmark.p',fact_mem__splitE) ).

fof(fact_Eps__split,axiom,
    ! [V_P_2,T_c,T_b] : c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_P_2)) = c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(hAPP(c_COMBS(tc_prod(T_b,T_c),T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_HOL_Obool),tc_prod(T_b,T_c)),V_P_2),c_Product__Type_Ofst(T_b,T_c))),c_Product__Type_Osnd(T_b,T_c))),
    file('theBenchmark.p',fact_Eps__split) ).

fof(fact_exE__some,axiom,
    ! [T_b,V_c_2,V_P_2] :
      ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
     => ( V_c_2 = c_Hilbert__Choice_OEps(T_b,V_P_2)
       => hBOOL(hAPP(V_P_2,V_c_2)) ) ),
    file('theBenchmark.p',fact_exE__some) ).

fof(fact_some__sym__eq__trivial,axiom,
    ! [V_x_2,T_b] : c_Hilbert__Choice_OEps(T_b,hAPP(c_fequal,V_x_2)) = V_x_2,
    file('theBenchmark.p',fact_some__sym__eq__trivial) ).

fof(fact_some__eq__trivial,axiom,
    ! [V_x_2,T_b] : c_Hilbert__Choice_OEps(T_b,hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)) = V_x_2,
    file('theBenchmark.p',fact_some__eq__trivial) ).

fof(fact_some__eq__ex,axiom,
    ! [T_b,V_P_2] :
      ( hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_b,V_P_2)))
    <=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ),
    file('theBenchmark.p',fact_some__eq__ex) ).

fof(fact_someI__ex,axiom,
    ! [T_b,V_P_2] :
      ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
     => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_b,V_P_2))) ),
    file('theBenchmark.p',fact_someI__ex) ).

fof(fact_tfl__some,axiom,
    ! [T_b,B_P] :
      ( ? [B_x] : hBOOL(hAPP(B_P,B_x))
     => hBOOL(hAPP(B_P,c_Hilbert__Choice_OEps(T_b,B_P))) ),
    file('theBenchmark.p',fact_tfl__some) ).

fof(fact_someI,axiom,
    ! [T_b,V_x_2,V_P_2] :
      ( hBOOL(hAPP(V_P_2,V_x_2))
     => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_b,V_P_2))) ),
    file('theBenchmark.p',fact_someI) ).

fof(fact_split__paired__Eps,axiom,
    ! [V_P_2,T_c,T_b] : c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),V_P_2) = c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,T_c),V_P_2)),c_Product__Type_OPair(T_b,T_c)))),
    file('theBenchmark.p',fact_split__paired__Eps) ).

fof(fact_Eps__split__eq,axiom,
    ! [V_y_2,V_x_2,T_c,T_b] : c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_x_2)))),hAPP(c_fequal,V_y_2)))) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2),
    file('theBenchmark.p',fact_Eps__split__eq) ).

fof(fact_wfI__pf,axiom,
    ! [V_R_2,T_b] :
      ( ! [B_A] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_A),hAPP(c_Relation_OImage(T_b,T_b,V_R_2),B_A)))
         => B_A = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
     => c_Wellfounded_Owf(T_b,V_R_2) ),
    file('theBenchmark.p',fact_wfI__pf) ).

fof(fact_Sigma__mono,axiom,
    ! [V_D_2,V_B_2,T_c,V_C_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
     => ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_B_2,B_x)),hAPP(V_D_2,B_x))) )
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_C_2),V_D_2))) ) ),
    file('theBenchmark.p',fact_Sigma__mono) ).

fof(fact_not__acc__down,axiom,
    ! [V_R_2,V_x_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_R_2)))
     => ~ ! [B_z] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_z),V_x_2)),V_R_2))
           => hBOOL(hAPP(hAPP(c_member(T_b),B_z),c_Wellfounded_Oacc(T_b,V_R_2))) ) ),
    file('theBenchmark.p',fact_not__acc__down) ).

fof(fact_acc_OaccI,axiom,
    ! [V_r_2,V_x_2,T_b] :
      ( ! [B_y] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_x_2)),V_r_2))
         => hBOOL(hAPP(hAPP(c_member(T_b),B_y),c_Wellfounded_Oacc(T_b,V_r_2))) )
     => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ),
    file('theBenchmark.p',fact_acc_OaccI) ).

fof(fact_max__ext_Osimps,axiom,
    ! [V_R_2,V_a2_2,V_a1_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_a1_2),V_a2_2)),c_Wellfounded_Omax__ext(T_b,V_R_2)))
    <=> ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2))
           => ? [B_xa] :
                ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_xa)),V_R_2))
                & hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2)) ) )
        & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2)) ) ),
    file('theBenchmark.p',fact_max__ext_Osimps) ).

fof(fact_def__coinduct__set,axiom,
    ! [V_X_2,V_a_2,V_f_2,T_b,V_A_2] :
      ( V_A_2 = c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)
     => ( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_A_2))))
           => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ) ),
    file('theBenchmark.p',fact_def__coinduct__set) ).

fof(fact_def__gfp__unfold,axiom,
    ! [V_f_2,V_A_2,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => ( V_A_2 = c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2)
       => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
         => V_A_2 = hAPP(V_f_2,V_A_2) ) ) ),
    file('theBenchmark.p',fact_def__gfp__unfold) ).

fof(fact_gfp__unfold,axiom,
    ! [V_f_2,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
       => c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2) = hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2)) ) ),
    file('theBenchmark.p',fact_gfp__unfold) ).

fof(fact_gfp__upperbound,axiom,
    ! [V_f_2,V_X_2,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_X_2),hAPP(V_f_2,V_X_2)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_X_2),c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2))) ) ),
    file('theBenchmark.p',fact_gfp__upperbound) ).

fof(fact_weak__coinduct,axiom,
    ! [V_f_2,V_X_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(V_f_2,V_X_2)))
       => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2))) ) ),
    file('theBenchmark.p',fact_weak__coinduct) ).

fof(fact_gfp__lemma3,axiom,
    ! [V_f_2,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2))),c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2))) ) ),
    file('theBenchmark.p',fact_gfp__lemma3) ).

fof(fact_gfp__lemma2,axiom,
    ! [V_f_2,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2)),hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2)))) ) ),
    file('theBenchmark.p',fact_gfp__lemma2) ).

fof(fact_weak__coinduct__image,axiom,
    ! [V_f_2,V_g_2,T_c,V_X_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_g_2),V_X_2)),hAPP(V_f_2,hAPP(c_Set_Oimage(T_b,T_c,V_g_2),V_X_2))))
       => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_g_2,V_a_2)),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_c,tc_HOL_Obool),V_f_2))) ) ),
    file('theBenchmark.p',fact_weak__coinduct__image) ).

fof(fact_gfp__fun__UnI2,axiom,
    ! [V_X_2,V_a_2,V_f_2,T_b] :
      ( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)))
       => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_X_2),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2))))) ) ),
    file('theBenchmark.p',fact_gfp__fun__UnI2) ).

fof(fact_def__coinduct,axiom,
    ! [V_X_2,V_f_2,V_A_2,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => ( V_A_2 = c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2)
       => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_X_2),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_X_2),V_A_2))))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_X_2),V_A_2)) ) ) ) ),
    file('theBenchmark.p',fact_def__coinduct) ).

fof(fact_coinduct__lemma,axiom,
    ! [V_f_2,V_X_2,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_X_2),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_X_2),c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2)))))
       => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_X_2),c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2))),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_X_2),c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2))))) ) ) ),
    file('theBenchmark.p',fact_coinduct__lemma) ).

fof(fact_coinduct,axiom,
    ! [V_X_2,V_f_2,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_X_2),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_X_2),c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2)))))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_X_2),c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2))) ) ) ),
    file('theBenchmark.p',fact_coinduct) ).

fof(fact_coinduct__set,axiom,
    ! [V_X_2,V_a_2,V_f_2,T_b] :
      ( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_X_2),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)))))
         => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2))) ) ) ),
    file('theBenchmark.p',fact_coinduct__set) ).

fof(fact_coinduct3,axiom,
    ! [V_X_2,V_a_2,V_f_2,T_b] :
      ( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_f_2)),V_X_2))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2))))))
         => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2))) ) ) ),
    file('theBenchmark.p',fact_coinduct3) ).

fof(fact_def__coinduct3,axiom,
    ! [V_X_2,V_a_2,V_f_2,T_b,V_A_2] :
      ( V_A_2 = c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)
     => ( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_f_2)),V_X_2))),V_A_2)))))
           => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ) ),
    file('theBenchmark.p',fact_def__coinduct3) ).

fof(fact_def__Collect__coinduct,axiom,
    ! [V_X_2,V_a_2,V_P_2,T_b,V_A_2] :
      ( V_A_2 = c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_OCollect(T_b)),V_P_2))
     => ( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_OCollect(T_b)),V_P_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2))
         => ( ! [B_z] :
                ( hBOOL(hAPP(hAPP(c_member(T_b),B_z),V_X_2))
               => hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_A_2)),B_z)) )
           => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ) ),
    file('theBenchmark.p',fact_def__Collect__coinduct) ).

fof(fact_lfp__lowerbound,axiom,
    ! [V_A_2,V_f_2,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_A_2)),V_A_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2)),V_A_2)) ) ),
    file('theBenchmark.p',fact_lfp__lowerbound) ).

fof(fact_lfp__unfold,axiom,
    ! [V_f_2,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
       => c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2) = hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2)) ) ),
    file('theBenchmark.p',fact_lfp__unfold) ).

fof(fact_def__lfp__unfold,axiom,
    ! [V_f_2,V_h_2,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => ( V_h_2 = c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2)
       => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
         => V_h_2 = hAPP(V_f_2,V_h_2) ) ) ),
    file('theBenchmark.p',fact_def__lfp__unfold) ).

fof(fact_lfp__const,axiom,
    ! [V_t_2,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => c_Inductive_Ocomplete__lattice__class_Olfp(T_b,hAPP(c_COMBK(T_b,T_b),V_t_2)) = V_t_2 ),
    file('theBenchmark.p',fact_lfp__const) ).

fof(fact_lfp__lemma3,axiom,
    ! [V_f_2,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2)),hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2)))) ) ),
    file('theBenchmark.p',fact_lfp__lemma3) ).

fof(fact_lfp__lemma2,axiom,
    ! [V_f_2,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2))),c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2))) ) ),
    file('theBenchmark.p',fact_lfp__lemma2) ).

fof(fact_lfp__induct,axiom,
    ! [V_P_2,V_f_2,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2)),V_P_2))),V_P_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2)),V_P_2)) ) ) ),
    file('theBenchmark.p',fact_lfp__induct) ).

fof(fact_def__lfp__induct,axiom,
    ! [V_P_2,V_f_2,V_A_2,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => ( V_A_2 = c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2)
       => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_A_2),V_P_2))),V_P_2))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_A_2),V_P_2)) ) ) ) ),
    file('theBenchmark.p',fact_def__lfp__induct) ).

fof(fact_coinduct3__lemma,axiom,
    ! [V_f_2,V_X_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_f_2)),V_X_2))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2))))))
     => ( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_f_2)),V_X_2))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)))),hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_f_2)),V_X_2))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)))))) ) ),
    file('theBenchmark.p',fact_coinduct3__lemma) ).

fof(fact_def__lfp__induct__set,axiom,
    ! [V_P_2,V_a_2,V_f_2,T_b,V_A_2] :
      ( V_A_2 = c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)
     => ( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
         => ( ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_P_2)))))
               => hBOOL(hAPP(V_P_2,B_x)) )
           => hBOOL(hAPP(V_P_2,V_a_2)) ) ) ) ),
    file('theBenchmark.p',fact_def__lfp__induct__set) ).

fof(fact_lfp__induct__set,axiom,
    ! [V_P_2,V_f_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)))
     => ( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
       => ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)),hAPP(c_Set_OCollect(T_b),V_P_2)))))
             => hBOOL(hAPP(V_P_2,B_x)) )
         => hBOOL(hAPP(V_P_2,V_a_2)) ) ) ),
    file('theBenchmark.p',fact_lfp__induct__set) ).

fof(fact_lfp__induct2,axiom,
    ! [V_P_2,V_f_2,V_b_2,V_a_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),V_f_2)))
     => ( c_Orderings_Oorder__class_Omono(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),V_f_2)
       => ( ! [B_a,B_b] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b)),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),V_f_2)),hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_P_2))))))
             => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) )
         => hBOOL(hAPP(hAPP(V_P_2,V_a_2),V_b_2)) ) ) ),
    file('theBenchmark.p',fact_lfp__induct2) ).

fof(fact_wf__no__infinite__down__chainE,axiom,
    ! [V_f_2,V_r_2,T_b] :
      ( c_Wellfounded_Owf(T_b,V_r_2)
     => ~ ! [B_k] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_k))),hAPP(V_f_2,B_k))),V_r_2)) ),
    file('theBenchmark.p',fact_wf__no__infinite__down__chainE) ).

fof(fact_iterate_Osimps,axiom,
    ! [V_x_2,V_f_2,T_b,T_c,V_k_2] :
      ( ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => hAPP(c_Random_Oiterate(T_c,T_b,V_k_2,V_f_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_c,T_b,tc_prod(T_c,T_b)),hAPP(V_f_2,V_x_2)),c_Random_Oiterate(T_c,T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_k_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),V_f_2)) )
      & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => hAPP(c_Random_Oiterate(T_c,T_b,V_k_2,V_f_2),V_x_2) = hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2) ) ),
    file('theBenchmark.p',fact_iterate_Osimps) ).

fof(fact_scomp__unfold,axiom,
    ! [V_x_2,V_g_2,V_f_2,T_b,T_e,T_d,T_c] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_c,T_d,T_e,T_b),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_d,T_e),hAPP(V_f_2,V_x_2))),hAPP(c_Product__Type_Osnd(T_d,T_e),hAPP(V_f_2,V_x_2))),
    file('theBenchmark.p',fact_scomp__unfold) ).

fof(fact_scomp__scomp,axiom,
    ! [V_h_2,V_g_2,V_f_2,T_g,T_f,T_c,T_e,T_d,T_b] : hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_d,T_e,T_c),hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_f,T_g,tc_prod(T_d,T_e)),V_f_2),V_g_2)),V_h_2) = hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_f,T_g,T_c),V_f_2),hAPP(hAPP(c_COMBC(T_f,tc_fun(T_d,tc_fun(T_e,T_c)),tc_fun(T_g,T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_g,tc_prod(T_d,T_e)),tc_fun(tc_fun(T_d,tc_fun(T_e,T_c)),tc_fun(T_g,T_c)),T_f),c_Product__Type_Oscomp(T_g,T_d,T_e,T_c)),V_g_2)),V_h_2)),
    file('theBenchmark.p',fact_scomp__scomp) ).

fof(fact_scomp__Pair,axiom,
    ! [V_x_2,T_d,T_c,T_b] : hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_c,T_d,tc_prod(T_c,T_d)),V_x_2),c_Product__Type_OPair(T_c,T_d)) = V_x_2,
    file('theBenchmark.p',fact_scomp__Pair) ).

fof(fact_Pair__scomp,axiom,
    ! [V_f_2,V_x_2,T_c,T_d,T_b] : hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_d,T_b,T_c),hAPP(c_Product__Type_OPair(T_d,T_b),V_x_2)),V_f_2) = hAPP(V_f_2,V_x_2),
    file('theBenchmark.p',fact_Pair__scomp) ).

fof(fact_scomp__apply,axiom,
    ! [V_x_2,V_g_2,V_f_2,T_b,T_e,T_d,T_c] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_c,T_d,T_e,T_b),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,T_b),V_g_2),hAPP(V_f_2,V_x_2)),
    file('theBenchmark.p',fact_scomp__apply) ).

fof(fact_scomp__def,axiom,
    ! [V_x_2,V_g_2,V_f_2,T_b,T_e,T_d,T_c] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_c,T_d,T_e,T_b),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,T_b),V_g_2),hAPP(V_f_2,V_x_2)),
    file('theBenchmark.p',fact_scomp__def) ).

fof(fact_less__eq,axiom,
    ! [V_n_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_m_2),V_n_2)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ),
    file('theBenchmark.p',fact_less__eq) ).

fof(fact_wf__eq__minimal,axiom,
    ! [V_r_2,T_b] :
      ( c_Wellfounded_Owf(T_b,V_r_2)
    <=> ! [B_Q] :
          ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q))
         => ? [B_x] :
              ( ! [B_y] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_x)),V_r_2))
                 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_y),B_Q)) )
              & hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q)) ) ) ),
    file('theBenchmark.p',fact_wf__eq__minimal) ).

fof(fact_wf__trancl,axiom,
    ! [V_r_2,T_b] :
      ( c_Wellfounded_Owf(T_b,V_r_2)
     => c_Wellfounded_Owf(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)) ),
    file('theBenchmark.p',fact_wf__trancl) ).

fof(fact_less__than__def,axiom,
    c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat),
    file('theBenchmark.p',fact_less__than__def) ).

fof(fact_acyclic__def,axiom,
    ! [V_r_2,T_b] :
      ( c_Wellfounded_Oacyclic(T_b,V_r_2)
    <=> ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ),
    file('theBenchmark.p',fact_acyclic__def) ).

fof(fact_trancl_Or__into__trancl,axiom,
    ! [V_r_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ),
    file('theBenchmark.p',fact_trancl_Or__into__trancl) ).

fof(fact_trancl__subset__Field2,axiom,
    ! [V_r_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),hAPP(c_Relation_OField(T_b),V_r_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_Relation_OField(T_b),V_r_2))))),
    file('theBenchmark.p',fact_trancl__subset__Field2) ).

fof(fact_r__into__trancl_H,axiom,
    ! [V_r_2,V_p_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),V_r_2))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ),
    file('theBenchmark.p',fact_r__into__trancl_H) ).

fof(fact_trancl__empty,axiom,
    ! [T_b] : c_Transitive__Closure_Otrancl(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),
    file('theBenchmark.p',fact_trancl__empty) ).

fof(fact_trancl__domain,axiom,
    ! [V_r_2,T_b] : hAPP(c_Relation_ODomain(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)) = hAPP(c_Relation_ODomain(T_b,T_b),V_r_2),
    file('theBenchmark.p',fact_trancl__domain) ).

fof(fact_trancl__range,axiom,
    ! [V_r_2,T_b] : hAPP(c_Relation_ORange(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)) = hAPP(c_Relation_ORange(T_b,T_b),V_r_2),
    file('theBenchmark.p',fact_trancl__range) ).

fof(fact_finite__trancl,axiom,
    ! [V_r_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
    <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) ),
    file('theBenchmark.p',fact_finite__trancl) ).

fof(fact_trancl__trans,axiom,
    ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ),
    file('theBenchmark.p',fact_trancl__trans) ).

fof(fact_Transitive__Closure_Otrancl__into__trancl,axiom,
    ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),V_r_2))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ),
    file('theBenchmark.p',fact_Transitive__Closure_Otrancl__into__trancl) ).

fof(fact_trancl__into__trancl2,axiom,
    ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ),
    file('theBenchmark.p',fact_trancl__into__trancl2) ).

fof(fact_r__r__into__trancl,axiom,
    ! [V_c_2,V_R_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_R_2))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),V_R_2))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2))) ) ),
    file('theBenchmark.p',fact_r__r__into__trancl) ).

fof(fact_trancl__mono,axiom,
    ! [V_s_2,V_r_2,V_p_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_s_2))) ) ),
    file('theBenchmark.p',fact_trancl__mono) ).

fof(fact_trancl__unfold,axiom,
    ! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)),V_r_2)),
    file('theBenchmark.p',fact_trancl__unfold) ).

fof(fact_trancl__subset__Sigma,axiom,
    ! [V_A_2,V_r_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) ),
    file('theBenchmark.p',fact_trancl__subset__Sigma) ).

fof(fact_trancl__Int__subset,axiom,
    ! [V_s_2,V_r_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),V_s_2)),V_r_2)),V_s_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),V_s_2)) ) ),
    file('theBenchmark.p',fact_trancl__Int__subset) ).

fof(fact_trancl__insert,axiom,
    ! [V_r_2,V_x_2,V_y_2,T_b] : c_Transitive__Closure_Otrancl(T_b,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),V_r_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b))),hAPP(hAPP(c_COMBC(T_b,T_b,tc_prod(T_b,T_b)),c_Product__Type_OPair(T_b,T_b)),V_y_2))),c_Transitive__Closure_Ortrancl(T_b,V_r_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b))),hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2))),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))))),
    file('theBenchmark.p',fact_trancl__insert) ).

fof(fact_reflcl__set__eq,axiom,
    ! [V_y_2,V_x_2,V_r_2,T_b] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2)),c_fequal),V_x_2),V_y_2))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b)))) ),
    file('theBenchmark.p',fact_reflcl__set__eq) ).

fof(fact_r__into__rtrancl,axiom,
    ! [V_r_2,V_p_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),V_r_2))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ),
    file('theBenchmark.p',fact_r__into__rtrancl) ).

fof(fact_rtrancl_Ortrancl__refl,axiom,
    ! [V_r_2,V_a_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))),
    file('theBenchmark.p',fact_rtrancl_Ortrancl__refl) ).

fof(fact_IdI,axiom,
    ! [V_a_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),c_Relation_OId(T_b))),
    file('theBenchmark.p',fact_IdI) ).

fof(fact_trancl__into__rtrancl,axiom,
    ! [V_r_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ),
    file('theBenchmark.p',fact_trancl__into__rtrancl) ).

fof(fact_trancl__unfold__left,axiom,
    ! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,V_r_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_r_2),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),
    file('theBenchmark.p',fact_trancl__unfold__left) ).

fof(fact_trancl__unfold__right,axiom,
    ! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,V_r_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_r_2),
    file('theBenchmark.p',fact_trancl__unfold__right) ).

fof(fact_trancl__reflcl,axiom,
    ! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))) = c_Transitive__Closure_Ortrancl(T_b,V_r_2),
    file('theBenchmark.p',fact_trancl__reflcl) ).

fof(fact_reflcl__trancl,axiom,
    ! [V_r_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),c_Relation_OId(T_b)) = c_Transitive__Closure_Ortrancl(T_b,V_r_2),
    file('theBenchmark.p',fact_reflcl__trancl) ).

fof(fact_rtrancl__trancl__absorb,axiom,
    ! [V_R_2,T_b] : c_Transitive__Closure_Otrancl(T_b,c_Transitive__Closure_Ortrancl(T_b,V_R_2)) = c_Transitive__Closure_Ortrancl(T_b,V_R_2),
    file('theBenchmark.p',fact_rtrancl__trancl__absorb) ).

fof(fact_trancl__rtrancl__absorb,axiom,
    ! [V_R_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,c_Transitive__Closure_Otrancl(T_b,V_R_2)) = c_Transitive__Closure_Ortrancl(T_b,V_R_2),
    file('theBenchmark.p',fact_trancl__rtrancl__absorb) ).

fof(fact_Domain__rtrancl,axiom,
    ! [V_R_2,T_b] : hAPP(c_Relation_ODomain(T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_R_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Domain__rtrancl) ).

fof(fact_Range__rtrancl,axiom,
    ! [V_R_2,T_b] : hAPP(c_Relation_ORange(T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_R_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Range__rtrancl) ).

fof(fact_refl__rtrancl,axiom,
    ! [V_r_2,T_b] : c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),
    file('theBenchmark.p',fact_refl__rtrancl) ).

fof(fact_rtrancl__idemp,axiom,
    ! [V_r_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) = c_Transitive__Closure_Ortrancl(T_b,V_r_2),
    file('theBenchmark.p',fact_rtrancl__idemp) ).

fof(fact_rtrancl__trans,axiom,
    ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ),
    file('theBenchmark.p',fact_rtrancl__trans) ).

fof(fact_rtrancl_Ortrancl__into__rtrancl,axiom,
    ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),V_r_2))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ),
    file('theBenchmark.p',fact_rtrancl_Ortrancl__into__rtrancl) ).

fof(fact_converse__rtrancl__into__rtrancl,axiom,
    ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ),
    file('theBenchmark.p',fact_converse__rtrancl__into__rtrancl) ).

fof(fact_rtrancl__r__diff__Id,axiom,
    ! [V_r_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))) = c_Transitive__Closure_Ortrancl(T_b,V_r_2),
    file('theBenchmark.p',fact_rtrancl__r__diff__Id) ).

fof(fact_in__rtrancl__UnI,axiom,
    ! [V_S_2,V_R_2,V_x_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,V_S_2)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) )
     => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)))) ),
    file('theBenchmark.p',fact_in__rtrancl__UnI) ).

fof(fact_rtrancl__mono,axiom,
    ! [V_s_2,V_r_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),c_Transitive__Closure_Ortrancl(T_b,V_s_2))) ),
    file('theBenchmark.p',fact_rtrancl__mono) ).

fof(fact_rtrancl__subset,axiom,
    ! [V_S_2,V_R_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_S_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
       => c_Transitive__Closure_Ortrancl(T_b,V_S_2) = c_Transitive__Closure_Ortrancl(T_b,V_R_2) ) ),
    file('theBenchmark.p',fact_rtrancl__subset) ).

fof(fact_rtrancl__subset__rtrancl,axiom,
    ! [V_s_2,V_r_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Transitive__Closure_Ortrancl(T_b,V_s_2)))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),c_Transitive__Closure_Ortrancl(T_b,V_s_2))) ),
    file('theBenchmark.p',fact_rtrancl__subset__rtrancl) ).

fof(fact_rtrancl__reflcl__absorb,axiom,
    ! [V_R_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)),c_Relation_OId(T_b)) = c_Transitive__Closure_Ortrancl(T_b,V_R_2),
    file('theBenchmark.p',fact_rtrancl__reflcl__absorb) ).

fof(fact_rtrancl__Un__rtrancl,axiom,
    ! [V_S_2,V_R_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)),c_Transitive__Closure_Ortrancl(T_b,V_S_2))) = c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)),
    file('theBenchmark.p',fact_rtrancl__Un__rtrancl) ).

fof(fact_rtrancl__reflcl,axiom,
    ! [V_R_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),c_Relation_OId(T_b))) = c_Transitive__Closure_Ortrancl(T_b,V_R_2),
    file('theBenchmark.p',fact_rtrancl__reflcl) ).

fof(fact_rtrancl__Un__subset,axiom,
    ! [V_S_2,V_R_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)),c_Transitive__Closure_Ortrancl(T_b,V_S_2))),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)))),
    file('theBenchmark.p',fact_rtrancl__Un__subset) ).

fof(fact_Image__closed__trancl,axiom,
    ! [V_X_2,V_r_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),V_X_2)),V_X_2))
     => hAPP(c_Relation_OImage(T_b,T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_X_2) = V_X_2 ),
    file('theBenchmark.p',fact_Image__closed__trancl) ).

fof(fact_rtrancl__unfold,axiom,
    ! [V_r_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Relation_OId(T_b)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_r_2)),
    file('theBenchmark.p',fact_rtrancl__unfold) ).

fof(fact_rtrancl__idemp__self__comp,axiom,
    ! [V_R_2,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_R_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)) = c_Transitive__Closure_Ortrancl(T_b,V_R_2),
    file('theBenchmark.p',fact_rtrancl__idemp__self__comp) ).

fof(fact_r__comp__rtrancl__eq,axiom,
    ! [V_r_2,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_r_2),c_Transitive__Closure_Ortrancl(T_b,V_r_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_r_2),
    file('theBenchmark.p',fact_r__comp__rtrancl__eq) ).

fof(fact_rtrancl__Int__subset,axiom,
    ! [V_r_2,V_s_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Relation_OId(T_b)),V_s_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_s_2)),V_r_2)),V_s_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_s_2)) ) ),
    file('theBenchmark.p',fact_rtrancl__Int__subset) ).

fof(fact_rtrancl__empty,axiom,
    ! [T_b] : c_Transitive__Closure_Ortrancl(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) = c_Relation_OId(T_b),
    file('theBenchmark.p',fact_rtrancl__empty) ).

fof(fact_R__O__Id,axiom,
    ! [V_R_2,T_c,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_c),V_R_2),c_Relation_OId(T_c)) = V_R_2,
    file('theBenchmark.p',fact_R__O__Id) ).

fof(fact_Id__O__R,axiom,
    ! [V_R_2,T_c,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_c),c_Relation_OId(T_b)),V_R_2) = V_R_2,
    file('theBenchmark.p',fact_Id__O__R) ).

fof(fact_Image__Id,axiom,
    ! [V_A_2,T_b] : hAPP(c_Relation_OImage(T_b,T_b,c_Relation_OId(T_b)),V_A_2) = V_A_2,
    file('theBenchmark.p',fact_Image__Id) ).

fof(fact_pair__in__Id__conv,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Relation_OId(T_b)))
    <=> V_a_2 = V_b_2 ),
    file('theBenchmark.p',fact_pair__in__Id__conv) ).

fof(fact_rtrancl__trancl__trancl,axiom,
    ! [V_z_2,V_r_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ),
    file('theBenchmark.p',fact_rtrancl__trancl__trancl) ).

fof(fact_trancl__rtrancl__trancl,axiom,
    ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ),
    file('theBenchmark.p',fact_trancl__rtrancl__trancl) ).

fof(fact_rtrancl__into__trancl1,axiom,
    ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),V_r_2))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ),
    file('theBenchmark.p',fact_rtrancl__into__trancl1) ).

fof(fact_rtranclD,axiom,
    ! [V_R_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
     => ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2)))
          & V_a_2 != V_b_2 )
        | V_a_2 = V_b_2 ) ),
    file('theBenchmark.p',fact_rtranclD) ).

fof(fact_rtrancl__into__trancl2,axiom,
    ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ),
    file('theBenchmark.p',fact_rtrancl__into__trancl2) ).

fof(fact_rtrancl__eq__or__trancl,axiom,
    ! [V_R_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
    <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2)))
          & V_x_2 != V_y_2 )
        | V_x_2 = V_y_2 ) ),
    file('theBenchmark.p',fact_rtrancl__eq__or__trancl) ).

fof(fact_Domain__Id,axiom,
    ! [T_b] : hAPP(c_Relation_ODomain(T_b,T_b),c_Relation_OId(T_b)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Domain__Id) ).

fof(fact_Range__Id,axiom,
    ! [T_b] : hAPP(c_Relation_ORange(T_b,T_b),c_Relation_OId(T_b)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Range__Id) ).

fof(fact_refl__Id,axiom,
    ! [T_b] : c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Relation_OId(T_b)),
    file('theBenchmark.p',fact_refl__Id) ).

fof(fact_pair__leq__def,axiom,
    c_FunDef_Opair__leq = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_HOL_Obool)),c_FunDef_Opair__less),c_Relation_OId(tc_prod(tc_Nat_Onat,tc_Nat_Onat))),
    file('theBenchmark.p',fact_pair__leq__def) ).

fof(fact_Not__Domain__rtrancl,axiom,
    ! [V_y_2,V_R_2,V_x_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_b),V_R_2)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
      <=> V_x_2 = V_y_2 ) ),
    file('theBenchmark.p',fact_Not__Domain__rtrancl) ).

fof(fact_acc__downwards,axiom,
    ! [V_b_2,V_r_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
       => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ),
    file('theBenchmark.p',fact_acc__downwards) ).

fof(fact_acc__downwards__aux,axiom,
    ! [V_r_2,V_a_2,V_b_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
       => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ),
    file('theBenchmark.p',fact_acc__downwards__aux) ).

fof(fact_wf__insert,axiom,
    ! [V_r_2,V_x_2,V_y_2,T_b] :
      ( c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),V_r_2))
    <=> ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
        & c_Wellfounded_Owf(T_b,V_r_2) ) ),
    file('theBenchmark.p',fact_wf__insert) ).

fof(fact_acyclic__insert,axiom,
    ! [V_r_2,V_x_2,V_y_2,T_b] :
      ( c_Wellfounded_Oacyclic(T_b,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),V_r_2))
    <=> ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
        & c_Wellfounded_Oacyclic(T_b,V_r_2) ) ),
    file('theBenchmark.p',fact_acyclic__insert) ).

fof(fact_refl__reflcl,axiom,
    ! [V_r_2,T_b] : c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))),
    file('theBenchmark.p',fact_refl__reflcl) ).

fof(fact_Id__def,axiom,
    ! [T_b] : c_Relation_OId(T_b) = hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_prod(T_b,T_b)),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(tc_prod(T_b,T_b),tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_HOL_Obool)),tc_prod(T_b,T_b)),c_COMBB(tc_prod(T_b,T_b),tc_HOL_Obool,T_b)),c_fequal)),hAPP(hAPP(c_COMBS(T_b,T_b,tc_prod(T_b,T_b)),c_Product__Type_OPair(T_b,T_b)),c_COMBI(T_b))))),
    file('theBenchmark.p',fact_Id__def) ).

fof(fact_irrefl__diff__Id,axiom,
    ! [V_r_2,T_b] : c_Relation_Oirrefl(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))),
    file('theBenchmark.p',fact_irrefl__diff__Id) ).

fof(fact_pred__nat__trancl__eq__le,axiom,
    ! [V_n_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_m_2),V_n_2)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ),
    file('theBenchmark.p',fact_pred__nat__trancl__eq__le) ).

fof(fact_trancl__subset__Sigma__aux,axiom,
    ! [V_A_2,V_r_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
          | V_a_2 = V_b_2 ) ) ),
    file('theBenchmark.p',fact_trancl__subset__Sigma__aux) ).

fof(fact_irrefl__tranclI,axiom,
    ! [V_x_2,V_r_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
     => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_x_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ),
    file('theBenchmark.p',fact_irrefl__tranclI) ).

fof(fact_sequence__trans,axiom,
    ! [V_k_2,V_i_2,V_r_2,V_f_2,T_b] :
      ( ! [B_i] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_i))),hAPP(V_f_2,B_i))),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2))),hAPP(V_f_2,V_i_2))),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ),
    file('theBenchmark.p',fact_sequence__trans) ).

fof(fact_rtrancl__converse,axiom,
    ! [V_r_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) = hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),
    file('theBenchmark.p',fact_rtrancl__converse) ).

fof(fact_converse__Id,axiom,
    ! [T_b] : hAPP(c_Relation_Oconverse(T_b,T_b),c_Relation_OId(T_b)) = c_Relation_OId(T_b),
    file('theBenchmark.p',fact_converse__Id) ).

fof(fact_acyclic__converse,axiom,
    ! [V_r_2,T_b] :
      ( c_Wellfounded_Oacyclic(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
    <=> c_Wellfounded_Oacyclic(T_b,V_r_2) ),
    file('theBenchmark.p',fact_acyclic__converse) ).

fof(fact_refl__on__converse,axiom,
    ! [V_r_2,V_A_2,T_b] :
      ( c_Relation_Orefl__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
    <=> c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ),
    file('theBenchmark.p',fact_refl__on__converse) ).

fof(fact_converse__Id__on,axiom,
    ! [V_A_2,T_b] : hAPP(c_Relation_Oconverse(T_b,T_b),c_Relation_OId__on(T_b,V_A_2)) = c_Relation_OId__on(T_b,V_A_2),
    file('theBenchmark.p',fact_converse__Id__on) ).

fof(fact_converse__inv__image,axiom,
    ! [V_f_2,V_R_2,T_c,T_b] : hAPP(c_Relation_Oconverse(T_b,T_b),hAPP(hAPP(c_Relation_Oinv__image(T_c,T_b),V_R_2),V_f_2)) = hAPP(hAPP(c_Relation_Oinv__image(T_c,T_b),hAPP(c_Relation_Oconverse(T_c,T_c),V_R_2)),V_f_2),
    file('theBenchmark.p',fact_converse__inv__image) ).

fof(fact_finite__converse,axiom,
    ! [V_r_2,T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)))
    <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_c,T_b)),V_r_2)) ),
    file('theBenchmark.p',fact_finite__converse) ).

fof(fact_converse__Int,axiom,
    ! [V_s_2,V_r_2,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_s_2)),
    file('theBenchmark.p',fact_converse__Int) ).

fof(fact_converse__converse,axiom,
    ! [V_r_2,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2)) = V_r_2,
    file('theBenchmark.p',fact_converse__converse) ).

fof(fact_Field__converse,axiom,
    ! [V_r_2,T_b] : hAPP(c_Relation_OField(T_b),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) = hAPP(c_Relation_OField(T_b),V_r_2),
    file('theBenchmark.p',fact_Field__converse) ).

fof(fact_converse__iff,axiom,
    ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_b_2),V_a_2)),V_r_2)) ),
    file('theBenchmark.p',fact_converse__iff) ).

fof(fact_converseI,axiom,
    ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_b_2),V_a_2)),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2))) ),
    file('theBenchmark.p',fact_converseI) ).

fof(fact_converseD,axiom,
    ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_b_2),V_a_2)),V_r_2)) ),
    file('theBenchmark.p',fact_converseD) ).

fof(fact_converse__Un,axiom,
    ! [V_s_2,V_r_2,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_s_2)),
    file('theBenchmark.p',fact_converse__Un) ).

fof(fact_converse__rel__comp,axiom,
    ! [V_s_2,V_r_2,T_d,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Relation_Orel__comp(T_c,T_d,T_b),V_r_2),V_s_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),hAPP(c_Relation_Oconverse(T_d,T_b),V_s_2)),hAPP(c_Relation_Oconverse(T_c,T_d),V_r_2)),
    file('theBenchmark.p',fact_converse__rel__comp) ).

fof(fact_converse__UNION,axiom,
    ! [V_r_2,V_S_2,T_d,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_S_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_S_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),T_d),c_Relation_Oconverse(T_c,T_b)),V_r_2)),
    file('theBenchmark.p',fact_converse__UNION) ).

fof(fact_converse__INTER,axiom,
    ! [V_r_2,V_S_2,T_d,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_S_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_S_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),T_d),c_Relation_Oconverse(T_c,T_b)),V_r_2)),
    file('theBenchmark.p',fact_converse__INTER) ).

fof(fact_trancl__converse,axiom,
    ! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) = hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)),
    file('theBenchmark.p',fact_trancl__converse) ).

fof(fact_wf__converse__trancl,axiom,
    ! [V_r_2,T_b] :
      ( c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
     => c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ),
    file('theBenchmark.p',fact_wf__converse__trancl) ).

fof(fact_equiv__comp__eq,axiom,
    ! [V_r_2,V_A_2,T_b] :
      ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
     => hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),V_r_2) = V_r_2 ),
    file('theBenchmark.p',fact_equiv__comp__eq) ).

fof(fact_Range__def,axiom,
    ! [V_r_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),V_r_2) = hAPP(c_Relation_ODomain(T_b,T_c),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)),
    file('theBenchmark.p',fact_Range__def) ).

fof(fact_Domain__converse,axiom,
    ! [V_r_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)) = hAPP(c_Relation_ORange(T_c,T_b),V_r_2),
    file('theBenchmark.p',fact_Domain__converse) ).

fof(fact_Range__converse,axiom,
    ! [V_r_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2)) = hAPP(c_Relation_ODomain(T_b,T_c),V_r_2),
    file('theBenchmark.p',fact_Range__converse) ).

fof(fact_rtrancl__converseI,axiom,
    ! [V_r_2,V_x_2,V_y_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)))) ),
    file('theBenchmark.p',fact_rtrancl__converseI) ).

fof(fact_rtrancl__converseD,axiom,
    ! [V_r_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ),
    file('theBenchmark.p',fact_rtrancl__converseD) ).

fof(fact_trancl__converseI,axiom,
    ! [V_r_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2))))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)))) ),
    file('theBenchmark.p',fact_trancl__converseI) ).

fof(fact_trancl__converseD,axiom,
    ! [V_r_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)))) ),
    file('theBenchmark.p',fact_trancl__converseD) ).

fof(fact_Image__subset__eq,axiom,
    ! [V_B_2,V_A_2,V_r_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2)),V_B_2))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2))))) ),
    file('theBenchmark.p',fact_Image__subset__eq) ).

fof(fact_refl__on__comp__subset,axiom,
    ! [V_r_2,V_A_2,T_b] :
      ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),V_r_2))) ),
    file('theBenchmark.p',fact_refl__on__comp__subset) ).

fof(fact_comp__equivI,axiom,
    ! [V_A_2,V_r_2,T_b] :
      ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),V_r_2) = V_r_2
     => ( hAPP(c_Relation_ODomain(T_b,T_b),V_r_2) = V_A_2
       => c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ) ),
    file('theBenchmark.p',fact_comp__equivI) ).

fof(fact_finite__acyclic__wf__converse,axiom,
    ! [V_r_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
     => ( c_Wellfounded_Oacyclic(T_b,V_r_2)
       => c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) ) ),
    file('theBenchmark.p',fact_finite__acyclic__wf__converse) ).

fof(fact_converse__def,axiom,
    ! [V_r_2,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2) = hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_c,T_b)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_c,T_b),tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_c,T_b)))),hAPP(c_COMBC(T_c,T_b,tc_prod(T_c,T_b)),c_Product__Type_OPair(T_c,T_b))))),V_r_2))),
    file('theBenchmark.p',fact_converse__def) ).

fof(fact_Image__INT__eq,axiom,
    ! [V_B_2,T_d,V_A_2,V_r_2,T_c,T_b] :
      ( c_Relation_Osingle__valued(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2))
     => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))
       => hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Relation_OImage(T_c,T_b,V_r_2)),V_B_2)) ) ),
    file('theBenchmark.p',fact_Image__INT__eq) ).

fof(fact_total__on__diff__Id,axiom,
    ! [V_r_2,V_A_2,T_b] :
      ( c_Relation_Ototal__on(T_b,V_A_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b)))
    <=> c_Relation_Ototal__on(T_b,V_A_2,V_r_2) ),
    file('theBenchmark.p',fact_total__on__diff__Id) ).

fof(fact_single__valued__Id,axiom,
    ! [T_b] : c_Relation_Osingle__valued(T_b,T_b,c_Relation_OId(T_b)),
    file('theBenchmark.p',fact_single__valued__Id) ).

fof(fact_single__valued__subset,axiom,
    ! [V_s_2,V_r_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_2),V_s_2))
     => ( c_Relation_Osingle__valued(T_b,T_c,V_s_2)
       => c_Relation_Osingle__valued(T_b,T_c,V_r_2) ) ),
    file('theBenchmark.p',fact_single__valued__subset) ).

fof(fact_single__valued__rel__comp,axiom,
    ! [V_s_2,T_d,V_r_2,T_c,T_b] :
      ( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
     => ( c_Relation_Osingle__valued(T_c,T_d,V_s_2)
       => c_Relation_Osingle__valued(T_b,T_d,hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2)) ) ),
    file('theBenchmark.p',fact_single__valued__rel__comp) ).

fof(fact_single__valued__Id__on,axiom,
    ! [V_A_2,T_b] : c_Relation_Osingle__valued(T_b,T_b,c_Relation_OId__on(T_b,V_A_2)),
    file('theBenchmark.p',fact_single__valued__Id__on) ).

fof(fact_total__on__empty,axiom,
    ! [V_r_2,T_b] : c_Relation_Ototal__on(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_r_2),
    file('theBenchmark.p',fact_total__on__empty) ).

fof(fact_total__on__converse,axiom,
    ! [V_r_2,V_A_2,T_b] :
      ( c_Relation_Ototal__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
    <=> c_Relation_Ototal__on(T_b,V_A_2,V_r_2) ),
    file('theBenchmark.p',fact_total__on__converse) ).

fof(fact_single__valuedD,axiom,
    ! [V_z_2,V_y_2,V_x_2,V_r_2,T_c,T_b] :
      ( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),V_r_2))
       => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_z_2)),V_r_2))
         => V_y_2 = V_z_2 ) ) ),
    file('theBenchmark.p',fact_single__valuedD) ).

fof(fact_single__valued__def,axiom,
    ! [V_r_2,T_c,T_b] :
      ( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
    <=> ! [B_x,B_y] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y)),V_r_2))
         => ! [B_z] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_z)),V_r_2))
             => B_y = B_z ) ) ),
    file('theBenchmark.p',fact_single__valued__def) ).

fof(fact_total__on__def,axiom,
    ! [V_r_2,V_A_2,T_b] :
      ( c_Relation_Ototal__on(T_b,V_A_2,V_r_2)
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
         => ! [B_xa] :
              ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
             => ( B_x != B_xa
               => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_xa),B_x)),V_r_2))
                  | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_xa)),V_r_2)) ) ) ) ) ),
    file('theBenchmark.p',fact_total__on__def) ).

fof(fact_single__valued__confluent,axiom,
    ! [V_z_2,V_y_2,V_x_2,V_r_2,T_b] :
      ( c_Relation_Osingle__valued(T_b,T_b,V_r_2)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
       => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
         => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_z_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
            | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ) ),
    file('theBenchmark.p',fact_single__valued__confluent) ).

fof(fact_Image__Int__eq,axiom,
    ! [V_B_2,V_A_2,V_R_2,T_c,T_b] :
      ( c_Relation_Osingle__valued(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_R_2))
     => hAPP(c_Relation_OImage(T_c,T_b,V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_B_2)) ),
    file('theBenchmark.p',fact_Image__Int__eq) ).

fof(fact_rtrancl__imp__UN__rel__pow,axiom,
    ! [V_R_2,V_p_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2)))) ),
    file('theBenchmark.p',fact_rtrancl__imp__UN__rel__pow) ).

fof(fact_acyclicI,axiom,
    ! [V_r_2,T_b] :
      ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
     => c_Wellfounded_Oacyclic(T_b,V_r_2) ),
    file('theBenchmark.p',fact_acyclicI) ).

fof(fact_single__valued__rel__pow,axiom,
    ! [V_n_2,V_R_2,T_b] :
      ( c_Relation_Osingle__valued(T_b,T_b,V_R_2)
     => c_Relation_Osingle__valued(T_b,T_b,hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)) ),
    file('theBenchmark.p',fact_single__valued__rel__pow) ).

fof(fact_comp__funpow,axiom,
    ! [V_f_2,V_n_2,T_c,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_fun(T_b,T_c),tc_fun(T_b,T_c)),V_n_2),c_Fun_Ocomp(T_c,T_c,T_b,V_f_2)) = c_Fun_Ocomp(T_c,T_c,T_b,hAPP(hAPP(c_Nat_Ocompow(T_c,T_c),V_n_2),V_f_2)),
    file('theBenchmark.p',fact_comp__funpow) ).

fof(fact_funpow__swap1,axiom,
    ! [V_x_2,V_n_2,T_b,V_f_2] : hAPP(V_f_2,hAPP(hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),V_f_2),V_x_2)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),V_f_2),hAPP(V_f_2,V_x_2)),
    file('theBenchmark.p',fact_funpow__swap1) ).

fof(fact_funpow__mult,axiom,
    ! [V_f_2,V_m_2,V_n_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_m_2),V_f_2)) = hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)),V_f_2),
    file('theBenchmark.p',fact_funpow__mult) ).

fof(fact_wf__exp,axiom,
    ! [V_R_2,V_n_2,T_b] :
      ( c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2))
     => c_Wellfounded_Owf(T_b,V_R_2) ),
    file('theBenchmark.p',fact_wf__exp) ).

fof(fact_rel__pow__commute,axiom,
    ! [V_n_2,V_R_2,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)),V_R_2),
    file('theBenchmark.p',fact_rel__pow__commute) ).

fof(fact_rel__pow__1,axiom,
    ! [V_R_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_R_2) = V_R_2,
    file('theBenchmark.p',fact_rel__pow__1) ).

fof(fact_rtrancl__power,axiom,
    ! [V_R_2,V_p_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
    <=> ? [B_n] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),B_n),V_R_2))) ),
    file('theBenchmark.p',fact_rtrancl__power) ).

fof(fact_rel__pow__imp__rtrancl,axiom,
    ! [V_R_2,V_n_2,V_p_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) ),
    file('theBenchmark.p',fact_rel__pow__imp__rtrancl) ).

fof(fact_relpow_Osimps_I2_J,axiom,
    ! [V_R_2,V_n_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)),V_R_2),
    file('theBenchmark.p',fact_relpow_Osimps_I2_J) ).

fof(fact_rel__pow__add,axiom,
    ! [V_R_2,V_n_2,V_m_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)),V_R_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_m_2),V_R_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)),
    file('theBenchmark.p',fact_rel__pow__add) ).

fof(fact_relpow_Osimps_I1_J,axiom,
    ! [V_R_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_R_2) = c_Relation_OId(T_b),
    file('theBenchmark.p',fact_relpow_Osimps_I1_J) ).

fof(fact_rel__pow__0__E,axiom,
    ! [V_R_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_R_2)))
     => V_x_2 = V_y_2 ),
    file('theBenchmark.p',fact_rel__pow__0__E) ).

fof(fact_rel__pow__0__I,axiom,
    ! [V_R_2,V_x_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_R_2))),
    file('theBenchmark.p',fact_rel__pow__0__I) ).

fof(fact_rel__pow__Suc__I2,axiom,
    ! [V_n_2,V_z_2,V_R_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_R_2))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) ) ),
    file('theBenchmark.p',fact_rel__pow__Suc__I2) ).

fof(fact_rel__pow__Suc__I,axiom,
    ! [V_z_2,V_R_2,V_n_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),V_R_2))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) ) ),
    file('theBenchmark.p',fact_rel__pow__Suc__I) ).

fof(fact_funpow_Osimps_I2_J,axiom,
    ! [V_f_2,V_n_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),hAPP(c_Nat_OSuc,V_n_2)),V_f_2) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,V_f_2),hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),V_f_2)),
    file('theBenchmark.p',fact_funpow_Osimps_I2_J) ).

fof(fact_funpow__add,axiom,
    ! [V_f_2,V_n_2,V_m_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)),V_f_2) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_m_2),V_f_2)),hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),V_f_2)),
    file('theBenchmark.p',fact_funpow__add) ).

fof(fact_funpow_Osimps_I1_J,axiom,
    ! [V_f_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_f_2) = c_Fun_Oid(T_b),
    file('theBenchmark.p',fact_funpow_Osimps_I1_J) ).

fof(fact_trancl__power,axiom,
    ! [V_R_2,V_p_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_R_2)))
    <=> ? [B_n] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),B_n),V_R_2)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)) ) ),
    file('theBenchmark.p',fact_trancl__power) ).

fof(fact_rtrancl__is__UN__rel__pow,axiom,
    ! [V_R_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,V_R_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2)),
    file('theBenchmark.p',fact_rtrancl__is__UN__rel__pow) ).

fof(fact_funpow__code__def,axiom,
    ! [T_b] : c_Nat_Ofunpow(T_b) = c_Nat_Ocompow(T_b,T_b),
    file('theBenchmark.p',fact_funpow__code__def) ).

fof(fact_rel__pow__E2,axiom,
    ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))
     => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => V_x_2 != V_z_2 )
       => ~ ! [B_y,B_m] :
              ( V_n_2 = hAPP(c_Nat_OSuc,B_m)
             => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),V_R_2))
               => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),B_m),V_R_2))) ) ) ) ),
    file('theBenchmark.p',fact_rel__pow__E2) ).

fof(fact_rel__pow__E,axiom,
    ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))
     => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => V_x_2 != V_z_2 )
       => ~ ! [B_y,B_m] :
              ( V_n_2 = hAPP(c_Nat_OSuc,B_m)
             => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),B_m),V_R_2)))
               => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),V_R_2)) ) ) ) ),
    file('theBenchmark.p',fact_rel__pow__E) ).

fof(fact_rtrancl__Un__separatorE,axiom,
    ! [V_Q_2,V_P_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2),V_Q_2))))
     => ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),B_x)),c_Transitive__Closure_Ortrancl(T_b,V_P_2)))
           => ! [B_y] :
                ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_Q_2))
               => B_x = B_y ) )
       => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_P_2))) ) ),
    file('theBenchmark.p',fact_rtrancl__Un__separatorE) ).

fof(fact_rtrancl__Un__separator__converseE,axiom,
    ! [V_Q_2,V_P_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2),V_Q_2))))
     => ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_P_2)))
           => ! [B_y] :
                ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_x)),V_Q_2))
               => B_y = B_x ) )
       => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_P_2))) ) ),
    file('theBenchmark.p',fact_rtrancl__Un__separator__converseE) ).

fof(fact_rel__pow__Suc__E,axiom,
    ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2)))
     => ~ ! [B_y] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))
           => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),V_R_2)) ) ),
    file('theBenchmark.p',fact_rel__pow__Suc__E) ).

fof(fact_rel__pow__Suc__D2,axiom,
    ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2)))
     => ? [B_y] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),V_R_2)) ) ),
    file('theBenchmark.p',fact_rel__pow__Suc__D2) ).

fof(fact_rel__pow__Suc__E2,axiom,
    ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2)))
     => ~ ! [B_y] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),V_R_2))
           => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2))) ) ),
    file('theBenchmark.p',fact_rel__pow__Suc__E2) ).

fof(fact_tranclD2,axiom,
    ! [V_R_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2)))
     => ? [B_z] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_z),V_y_2)),V_R_2))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_z)),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) ) ),
    file('theBenchmark.p',fact_tranclD2) ).

fof(fact_tranclD,axiom,
    ! [V_R_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2)))
     => ? [B_z] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_z),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_z)),V_R_2)) ) ),
    file('theBenchmark.p',fact_tranclD) ).

fof(fact_IdE,axiom,
    ! [V_p_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Relation_OId(T_b)))
     => ~ ! [B_x] : V_p_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x) ),
    file('theBenchmark.p',fact_IdE) ).

fof(fact_transfer__nat__int__set__cong,axiom,
    ! [V_P_H_2,V_P_2] :
      ( ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
         => ( hBOOL(hAPP(V_P_2,B_x))
          <=> hBOOL(hAPP(V_P_H_2,B_x)) ) )
     => hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_P_2)) = hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_P_H_2)) ),
    file('theBenchmark.p',fact_transfer__nat__int__set__cong) ).

fof(fact_Int__Collect__mono,axiom,
    ! [V_Q_2,V_P_2,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
     => ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
           => ( hBOOL(hAPP(V_P_2,B_x))
             => hBOOL(hAPP(V_Q_2,B_x)) ) )
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_P_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_OCollect(T_b),V_Q_2)))) ) ),
    file('theBenchmark.p',fact_Int__Collect__mono) ).

fof(fact_converseE,axiom,
    ! [V_r_2,V_yx_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_yx_2),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)))
     => ~ ! [B_x,B_y] :
            ( V_yx_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_y),B_x)
           => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),B_y)),V_r_2)) ) ),
    file('theBenchmark.p',fact_converseE) ).

fof(fact_rel__compE,axiom,
    ! [V_s_2,V_r_2,T_d,V_xz_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_xz_2),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_r_2),V_s_2)))
     => ~ ! [B_x,B_y,B_z] :
            ( V_xz_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_z)
           => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),B_x),B_y)),V_r_2))
             => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_c),B_y),B_z)),V_s_2)) ) ) ),
    file('theBenchmark.p',fact_rel__compE) ).

fof(fact_Nitpick_Oplus__frac__def,axiom,
    ! [V_r_2,V_q_2,T_b] : c_Nitpick_Oplus__frac(T_b,V_q_2,V_r_2) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_b),c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(T_b),V_q_2),hAPP(c_Nitpick_Odenom(T_b),V_r_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,T_b),tc_Int_Oint),c_Nitpick_Ofrac(T_b)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_b),V_q_2))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(c_Nitpick_Odenom(T_b),V_q_2))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_b),V_r_2))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(c_Nitpick_Odenom(T_b),V_r_2)))))),c_COMBI(tc_Int_Oint))),
    file('theBenchmark.p',fact_Nitpick_Oplus__frac__def) ).

fof(fact_Nitpick_Otimes__frac__def,axiom,
    ! [V_r,V_q,T_a] : c_Nitpick_Otimes__frac(T_a,V_q,V_r) = hAPP(hAPP(c_Nitpick_Ofrac(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_a),V_q)),hAPP(c_Nitpick_Onum(T_a),V_r))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Odenom(T_a),V_q)),hAPP(c_Nitpick_Odenom(T_a),V_r))),
    file('theBenchmark.p',fact_Nitpick_Otimes__frac__def) ).

fof(fact_Nitpick_Oof__frac__def,axiom,
    ! [V_q,T_a,T_b] :
      ( ( class_Rings_Oring__1(T_b)
        & class_Rings_Oinverse(T_b) )
     => c_Nitpick_Oof__frac(T_a,T_b,V_q) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(c_Nitpick_Onum(T_a),V_q))),hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(c_Nitpick_Odenom(T_a),V_q))) ),
    file('theBenchmark.p',fact_Nitpick_Oof__frac__def) ).

fof(fact_Nitpick_Oinverse__frac__def,axiom,
    ! [V_q,T_a] : c_Nitpick_Oinverse__frac(T_a,V_q) = hAPP(hAPP(c_Nitpick_Ofrac(T_a),hAPP(c_Nitpick_Odenom(T_a),V_q)),hAPP(c_Nitpick_Onum(T_a),V_q)),
    file('theBenchmark.p',fact_Nitpick_Oinverse__frac__def) ).

fof(fact_Nitpick_Ouminus__frac__def,axiom,
    ! [V_q,T_a] : c_Nitpick_Ouminus__frac(T_a,V_q) = c_Nitpick_OAbs__Frac(T_a,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_a),V_q))),hAPP(c_Nitpick_Odenom(T_a),V_q))),
    file('theBenchmark.p',fact_Nitpick_Ouminus__frac__def) ).

fof(fact_Nitpick_Oless__frac__def,axiom,
    ! [V_r_2,V_q_2,T_b] :
      ( c_Nitpick_Oless__frac(T_b,V_q_2,V_r_2)
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_b),c_Nitpick_Oplus__frac(T_b,V_q_2,c_Nitpick_Ouminus__frac(T_b,V_r_2)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    file('theBenchmark.p',fact_Nitpick_Oless__frac__def) ).

fof(fact_Nitpick_Oless__eq__frac__def,axiom,
    ! [V_r_2,V_q_2,T_b] :
      ( c_Nitpick_Oless__eq__frac(T_b,V_q_2,V_r_2)
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_b),c_Nitpick_Oplus__frac(T_b,V_q_2,c_Nitpick_Ouminus__frac(T_b,V_r_2)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    file('theBenchmark.p',fact_Nitpick_Oless__eq__frac__def) ).

fof(fact_Nitpick_Odenom__def,axiom,
    ! [T_b] : c_Nitpick_Odenom(T_b) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,T_b,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(T_b)),
    file('theBenchmark.p',fact_Nitpick_Odenom__def) ).

fof(fact_Nitpick_Onum__def,axiom,
    ! [T_b] : c_Nitpick_Onum(T_b) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,T_b,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(T_b)),
    file('theBenchmark.p',fact_Nitpick_Onum__def) ).

fof(fact_internal__split__def,axiom,
    ! [T_d,T_c,T_b] : c_Product__Type_Ointernal__split(T_b,T_c,T_d) = c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),
    file('theBenchmark.p',fact_internal__split__def) ).

fof(fact_bool_Osize_I1_J,axiom,
    c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_bool_Osize_I1_J) ).

fof(fact_internal__split__conv,axiom,
    ! [V_b_2,V_a_2,V_c_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Ointernal__split(T_c,T_d,T_b),V_c_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(V_c_2,V_a_2),V_b_2),
    file('theBenchmark.p',fact_internal__split__conv) ).

fof(fact_bool_Osize_I2_J,axiom,
    c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_bool_Osize_I2_J) ).

fof(fact_finite__less__ub,axiom,
    ! [V_u_2,V_f_2] :
      ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_n),hAPP(V_f_2,B_n)))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),V_f_2)),V_u_2)))) ),
    file('theBenchmark.p',fact_finite__less__ub) ).

fof(fact_lenlex__def,axiom,
    ! [V_r_2,T_b] : c_List_Olenlex(T_b,V_r_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_List_Olist(T_b)),tc_List_Olist(T_b)),c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_List_Olist(T_b),c_Wellfounded_Oless__than,c_List_Olex(T_b,V_r_2))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_prod(tc_Nat_Onat,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_List_Olist(T_b),tc_prod(tc_Nat_Onat,tc_List_Olist(T_b))),tc_List_Olist(T_b)),c_Product__Type_OPair(tc_Nat_Onat,tc_List_Olist(T_b))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),c_COMBI(tc_List_Olist(T_b)))),
    file('theBenchmark.p',fact_lenlex__def) ).

fof(fact_lexn__length,axiom,
    ! [V_n_2,V_r_2,V_ys_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),hAPP(c_List_Olexn(T_b,V_r_2),V_n_2)))
     => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = V_n_2
        & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = V_n_2 ) ),
    file('theBenchmark.p',fact_lexn__length) ).

fof(fact_neq__if__length__neq,axiom,
    ! [V_ys,V_xs,T_a] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys)
     => V_xs != V_ys ),
    file('theBenchmark.p',fact_neq__if__length__neq) ).

fof(fact_lenlex__conv,axiom,
    ! [V_r_2,T_b] : c_List_Olenlex(T_b,V_r_2) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fdisj)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBC(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_HOL_Obool)),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))))),c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b))))),c_List_Olex(T_b,V_r_2)))))),
    file('theBenchmark.p',fact_lenlex__conv) ).

fof(fact_length__sublist,axiom,
    ! [V_I_2,V_xs_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Osublist(T_b,V_xs_2,V_I_2)) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_I_2)))),
    file('theBenchmark.p',fact_length__sublist) ).

fof(fact_lexn_Osimps_I2_J,axiom,
    ! [V_n_2,V_r_2,T_b] : hAPP(c_List_Olexn(T_b,V_r_2),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_prod(tc_prod(T_b,tc_List_Olist(T_b)),tc_prod(T_b,tc_List_Olist(T_b))),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_Product__Type_Omap__pair(tc_prod(T_b,tc_List_Olist(T_b)),tc_List_Olist(T_b),tc_prod(T_b,tc_List_Olist(T_b)),tc_List_Olist(T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)))),c_Wellfounded_Olex__prod(T_b,tc_List_Olist(T_b),V_r_2,hAPP(c_List_Olexn(T_b,V_r_2),V_n_2)))),hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),hAPP(c_Nat_OSuc,V_n_2))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),hAPP(c_Nat_OSuc,V_n_2)))))),
    file('theBenchmark.p',fact_lexn_Osimps_I2_J) ).

fof(fact_impossible__Cons,axiom,
    ! [V_x,V_ys,V_xs,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys)))
     => V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys) ),
    file('theBenchmark.p',fact_impossible__Cons) ).

fof(fact_list_Oinject,axiom,
    ! [V_list_H_2,V_a_H_2,V_list_2,V_a_2,T_b] :
      ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_list_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_H_2),V_list_H_2)
    <=> ( V_list_2 = V_list_H_2
        & V_a_2 = V_a_H_2 ) ),
    file('theBenchmark.p',fact_list_Oinject) ).

fof(fact_not__Cons__self2,axiom,
    ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) != V_xs,
    file('theBenchmark.p',fact_not__Cons__self2) ).

fof(fact_not__Cons__self,axiom,
    ! [V_x,T_a,V_xs] : V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs),
    file('theBenchmark.p',fact_not__Cons__self) ).

fof(fact_list_Osize_I4_J,axiom,
    ! [V_list,V_a,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a),V_list)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_list)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('theBenchmark.p',fact_list_Osize_I4_J) ).

fof(fact_Cons__in__lex,axiom,
    ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olex(T_b,V_r_2)))
    <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olex(T_b,V_r_2)))
          & V_x_2 = V_y_2 )
        | ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) ) ) ),
    file('theBenchmark.p',fact_Cons__in__lex) ).

fof(fact_set__Cons__def,axiom,
    ! [V_XS_2,V_A_2,T_b] : c_List_Oset__Cons(T_b,V_A_2,V_XS_2) = hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_List_Olist(T_b)),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),tc_List_Olist(T_b)),c_COMBS(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),T_b),c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),tc_List_Olist(T_b)),c_COMBB(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_List_Olist(T_b),tc_HOL_Obool,tc_List_Olist(T_b))),c_fequal))),c_List_Olist_OCons(T_b)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(T_b))),V_XS_2)))))),
    file('theBenchmark.p',fact_set__Cons__def) ).

fof(fact_pick_Osimps,axiom,
    ! [V_xs,V_x,T_a,V_i] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a),V_x)))
       => hAPP(c_Random_Opick(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a)),V_x),V_xs)),V_i) = hAPP(c_Random_Opick(T_a,V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_i),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a),V_x))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a),V_x)))
       => hAPP(c_Random_Opick(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a)),V_x),V_xs)),V_i) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,T_a),V_x) ) ),
    file('theBenchmark.p',fact_pick_Osimps) ).

fof(fact_select__weight__cons__zero,axiom,
    ! [V_xs_2,V_x_2,T_b] : c_Random_Oselect__weight(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b)),hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_b),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),V_x_2)),V_xs_2)) = c_Random_Oselect__weight(T_b,V_xs_2),
    file('theBenchmark.p',fact_select__weight__cons__zero) ).

fof(fact_lexord__cons__cons,axiom,
    ! [V_r_2,V_y_2,V_b_2,V_x_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_x_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_b_2),V_y_2))),c_List_Olexord(T_b,V_r_2)))
    <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2)))
          & V_a_2 = V_b_2 )
        | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) ) ),
    file('theBenchmark.p',fact_lexord__cons__cons) ).

fof(fact_lexord__lex,axiom,
    ! [V_r_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olex(T_b,V_r_2)))
    <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_y_2)
        & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2))) ) ),
    file('theBenchmark.p',fact_lexord__lex) ).

fof(fact_rtrancl__listrel1__ConsI2,axiom,
    ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ) ),
    file('theBenchmark.p',fact_rtrancl__listrel1__ConsI2) ).

fof(fact_list_Osize_I2_J,axiom,
    ! [V_list_2,V_a_2,V_fa_2,T_b] : c_List_Olist_Olist__size(T_b,V_fa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_list_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_fa_2,V_a_2)),c_List_Olist_Olist__size(T_b,V_fa_2,V_list_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('theBenchmark.p',fact_list_Osize_I2_J) ).

fof(fact_Cons__acc__listrel1I,axiom,
    ! [V_xs_2,V_r_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))
       => hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),c_Wellfounded_Oacc(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ) ),
    file('theBenchmark.p',fact_Cons__acc__listrel1I) ).

fof(fact_listrel1__mono,axiom,
    ! [V_s_2,V_r_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel1(T_b,V_r_2)),c_List_Olistrel1(T_b,V_s_2))) ),
    file('theBenchmark.p',fact_listrel1__mono) ).

fof(fact_listrel1__converse,axiom,
    ! [V_r_2,T_b] : c_List_Olistrel1(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) = hAPP(c_Relation_Oconverse(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olistrel1(T_b,V_r_2)),
    file('theBenchmark.p',fact_listrel1__converse) ).

fof(fact_listrel1__rtrancl__subset__rtrancl__listrel1,axiom,
    ! [V_r_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel1(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))),
    file('theBenchmark.p',fact_listrel1__rtrancl__subset__rtrancl__listrel1) ).

fof(fact_rtrancl__listrel1__ConsI1,axiom,
    ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_ys_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ),
    file('theBenchmark.p',fact_rtrancl__listrel1__ConsI1) ).

fof(fact_listrel1I2,axiom,
    ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_ys_2))),c_List_Olistrel1(T_b,V_r_2))) ),
    file('theBenchmark.p',fact_listrel1I2) ).

fof(fact_rtrancl__listrel1__eq__len,axiom,
    ! [V_r_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))
     => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_y_2) ),
    file('theBenchmark.p',fact_rtrancl__listrel1__eq__len) ).

fof(fact_listrel1__eq__len,axiom,
    ! [V_r_2,V_ys_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
     => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) ),
    file('theBenchmark.p',fact_listrel1__eq__len) ).

fof(fact_in__listrel1__converse,axiom,
    ! [V_r_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olistrel1(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olistrel1(T_b,V_r_2)))) ),
    file('theBenchmark.p',fact_in__listrel1__converse) ).

fof(fact_listrel1I1,axiom,
    ! [V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_xs_2))),c_List_Olistrel1(T_b,V_r_2))) ),
    file('theBenchmark.p',fact_listrel1I1) ).

fof(fact_Cons__listrel1__Cons,axiom,
    ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olistrel1(T_b,V_r_2)))
    <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
          & V_x_2 = V_y_2 )
        | ( V_xs_2 = V_ys_2
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) ) ) ),
    file('theBenchmark.p',fact_Cons__listrel1__Cons) ).

fof(fact_listrel__Cons,axiom,
    ! [V_xs_2,V_x_2,V_r_2,T_b] : hAPP(c_Relation_OImage(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))) = c_List_Oset__Cons(T_b,hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),hAPP(c_Relation_OImage(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),V_xs_2),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))))),
    file('theBenchmark.p',fact_listrel__Cons) ).

fof(fact_lexord__irreflexive,axiom,
    ! [V_y_2,V_r_2,T_b] :
      ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2))
     => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_y_2),V_y_2)),c_List_Olexord(T_b,V_r_2))) ),
    file('theBenchmark.p',fact_lexord__irreflexive) ).

fof(fact_listrel__rtrancl__refl,axiom,
    ! [V_r_2,V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_xs_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)))),
    file('theBenchmark.p',fact_listrel__rtrancl__refl) ).

fof(fact_listrel__mono,axiom,
    ! [V_s_2,V_r_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel(T_b,V_r_2)),c_List_Olistrel(T_b,V_s_2))) ),
    file('theBenchmark.p',fact_listrel__mono) ).

fof(fact_listrel__subset__rtrancl__listrel1,axiom,
    ! [V_r_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel(T_b,V_r_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))),
    file('theBenchmark.p',fact_listrel__subset__rtrancl__listrel1) ).

fof(fact_listrel__eq__len,axiom,
    ! [V_r_2,V_ys_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2)))
     => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) ),
    file('theBenchmark.p',fact_listrel__eq__len) ).

fof(fact_listrel__rtrancl__trans,axiom,
    ! [V_zs_2,V_r_2,V_ys_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2))))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_ys_2),V_zs_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2))))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_zs_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)))) ) ),
    file('theBenchmark.p',fact_listrel__rtrancl__trans) ).

fof(fact_listrel__rtrancl__eq__rtrancl__listrel1,axiom,
    ! [V_r_2,T_b] : c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)),
    file('theBenchmark.p',fact_listrel__rtrancl__eq__rtrancl__listrel1) ).

fof(fact_listrel__reflcl__if__listrel1,axiom,
    ! [V_r_2,V_ys_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)))) ),
    file('theBenchmark.p',fact_listrel__reflcl__if__listrel1) ).

fof(fact_listrel1__subset__listrel,axiom,
    ! [V_r_H_2,V_r_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_r_H_2))
     => ( c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_r_H_2)
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel1(T_b,V_r_2)),c_List_Olistrel(T_b,V_r_H_2))) ) ),
    file('theBenchmark.p',fact_listrel1__subset__listrel) ).

fof(fact_rtrancl__listrel1__if__listrel,axiom,
    ! [V_r_2,V_ys_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ),
    file('theBenchmark.p',fact_rtrancl__listrel1__if__listrel) ).

fof(fact_listrel_OCons,axiom,
    ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olistrel(T_b,V_r_2))) ) ),
    file('theBenchmark.p',fact_listrel_OCons) ).

fof(fact_listrelp__listrel__eq,axiom,
    ! [V_xa_2,V_x_2,V_r_2,T_b] :
      ( c_List_Olistrelp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2),V_x_2,V_xa_2)
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_xa_2)),c_List_Olistrel(T_b,V_r_2))) ),
    file('theBenchmark.p',fact_listrelp__listrel__eq) ).

fof(fact_listrel__Cons2,axiom,
    ! [V_r_2,V_ys_2,V_y_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olistrel(T_b,V_r_2)))
     => ~ ! [B_x,B_xs] :
            ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_xs)
           => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),V_y_2)),V_r_2))
             => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),B_xs),V_ys_2)),c_List_Olistrel(T_b,V_r_2))) ) ) ),
    file('theBenchmark.p',fact_listrel__Cons2) ).

fof(fact_listrelp_Oequations_I2_J,axiom,
    ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2,V_r_2,T_b] :
      ( c_List_Olistrelp(T_b,V_r_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a1_2),V_a3_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a2_2),V_a4_2))
    <=> ( c_List_Olistrelp(T_b,V_r_2,V_a3_2,V_a4_2)
        & hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2)) ) ),
    file('theBenchmark.p',fact_listrelp_Oequations_I2_J) ).

fof(fact_listrelp_OCons,axiom,
    ! [V_ys_2,V_xs_2,T_b,V_y_2,V_x_2,V_r_2] :
      ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2))
     => ( c_List_Olistrelp(T_b,V_r_2,V_xs_2,V_ys_2)
       => c_List_Olistrelp(T_b,V_r_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)) ) ),
    file('theBenchmark.p',fact_listrelp_OCons) ).

fof(fact_listrel__Cons1,axiom,
    ! [V_r_2,V_xs_2,V_ys_2,V_y_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)),V_xs_2)),c_List_Olistrel(T_b,V_r_2)))
     => ~ ! [B_y,B_ys] :
            ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_y),B_ys)
           => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),B_y)),V_r_2))
             => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_ys_2),B_ys)),c_List_Olistrel(T_b,V_r_2))) ) ) ),
    file('theBenchmark.p',fact_listrel__Cons1) ).

fof(fact_listrel__subset,axiom,
    ! [V_A_2,V_r_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel(T_b,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olists(T_b,V_A_2)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_List_Olist(T_b)),c_List_Olists(T_b,V_A_2))))) ),
    file('theBenchmark.p',fact_listrel__subset) ).

fof(fact_lists__UNIV,axiom,
    ! [T_b] : c_List_Olists(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),
    file('theBenchmark.p',fact_lists__UNIV) ).

fof(fact_lists__mono,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),c_List_Olists(T_b,V_A_2)),c_List_Olists(T_b,V_B_2))) ),
    file('theBenchmark.p',fact_lists__mono) ).

fof(fact_equiv__listrel,axiom,
    ! [V_r_2,V_A_2,T_b] :
      ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
     => c_Equiv__Relations_Oequiv(tc_List_Olist(T_b),c_List_Olists(T_b,V_A_2),c_List_Olistrel(T_b,V_r_2)) ),
    file('theBenchmark.p',fact_equiv__listrel) ).

fof(fact_listrel__refl__on,axiom,
    ! [V_r_2,V_A_2,T_b] :
      ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
     => c_Relation_Orefl__on(tc_List_Olist(T_b),c_List_Olists(T_b,V_A_2),c_List_Olistrel(T_b,V_r_2)) ),
    file('theBenchmark.p',fact_listrel__refl__on) ).

fof(fact_Cons__in__lists__iff,axiom,
    ! [V_A_2,V_xs_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),c_List_Olists(T_b,V_A_2)))
    <=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2)))
        & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_Cons__in__lists__iff) ).

fof(fact_lists__accI,axiom,
    ! [V_r_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))
     => hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,c_Wellfounded_Oacc(T_b,V_r_2)))) ),
    file('theBenchmark.p',fact_lists__accI) ).

fof(fact_lists__accD,axiom,
    ! [V_r_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,c_Wellfounded_Oacc(T_b,V_r_2))))
     => hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ),
    file('theBenchmark.p',fact_lists__accD) ).

fof(fact_listrel__iff__nth,axiom,
    ! [V_r_2,V_ys_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2)))
    <=> ( ! [B_n] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
           => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n)),hAPP(hAPP(c_List_Onth(T_b),V_ys_2),B_n))),V_r_2)) )
        & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) ) ),
    file('theBenchmark.p',fact_listrel__iff__nth) ).

fof(fact_lexord__linear,axiom,
    ! [V_y_2,V_x_2,V_r_2,T_b] :
      ( ! [B_a,B_b] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_b),B_a)),V_r_2))
          | B_a = B_b
          | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_a),B_b)),V_r_2)) )
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_y_2),V_x_2)),c_List_Olexord(T_b,V_r_2)))
        | V_x_2 = V_y_2
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2))) ) ),
    file('theBenchmark.p',fact_lexord__linear) ).

fof(fact_infinite__UNIV__listI,axiom,
    ! [T_b] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_b)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))),
    file('theBenchmark.p',fact_infinite__UNIV__listI) ).

fof(fact_list__eq__iff__nth__eq,axiom,
    ! [T_b,V_ys_2,V_xs_2] :
      ( V_xs_2 = V_ys_2
    <=> ( ! [B_i] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
           => hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) = hAPP(hAPP(c_List_Onth(T_b),V_ys_2),B_i) )
        & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) ) ),
    file('theBenchmark.p',fact_list__eq__iff__nth__eq) ).

fof(fact_nth__Cons__Suc,axiom,
    ! [V_n,V_xs,V_x,T_a] : hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n),
    file('theBenchmark.p',fact_nth__Cons__Suc) ).

fof(fact_nth__Cons__0,axiom,
    ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_x,
    file('theBenchmark.p',fact_nth__Cons__0) ).

fof(fact_nth_Osimps,axiom,
    ! [V_n_2,V_xs_2,V_x_2,T_b] : hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_n_2) = c_Nat_Onat_Onat__case(T_b,V_x_2,hAPP(c_List_Onth(T_b),V_xs_2),V_n_2),
    file('theBenchmark.p',fact_nth_Osimps) ).

fof(fact_nth__Cons_H,axiom,
    ! [V_xs,V_x,T_a,V_n] :
      ( ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_n) = hAPP(hAPP(c_List_Onth(T_a),V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))) )
      & ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_n) = V_x ) ),
    file('theBenchmark.p',fact_nth__Cons_H) ).

fof(fact_nth__Cons__number__of,axiom,
    ! [V_xs,V_x,T_a,V_v] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(hAPP(c_List_Onth(T_a),V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = V_x ) ),
    file('theBenchmark.p',fact_nth__Cons__number__of) ).

fof(fact_lexord__take__index__conv,axiom,
    ! [V_r_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2)))
    <=> ( ? [B_i] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(hAPP(c_List_Onth(T_b),V_x_2),B_i)),hAPP(hAPP(c_List_Onth(T_b),V_y_2),B_i))),V_r_2))
            & hAPP(hAPP(c_List_Otake(T_b),B_i),V_x_2) = hAPP(hAPP(c_List_Otake(T_b),B_i),V_y_2)
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_y_2)))) )
        | ( hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2)),V_y_2) = V_x_2
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_y_2))) ) ) ),
    file('theBenchmark.p',fact_lexord__take__index__conv) ).

fof(fact_set__sublist,axiom,
    ! [V_I_2,V_xs_2,T_b] : hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_b),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(T_b),V_xs_2))))),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_I_2))))),
    file('theBenchmark.p',fact_set__sublist) ).

fof(fact_finite__set,axiom,
    ! [V_xs_2,T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_List_Oset(T_b),V_xs_2))),
    file('theBenchmark.p',fact_finite__set) ).

fof(fact_set__subset__Cons,axiom,
    ! [V_x_2,V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)))),
    file('theBenchmark.p',fact_set__subset__Cons) ).

fof(fact_take__all,axiom,
    ! [V_n,V_xs,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n))
     => hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs) = V_xs ),
    file('theBenchmark.p',fact_take__all) ).

fof(fact_set__take__subset,axiom,
    ! [V_xs_2,V_n_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2))),
    file('theBenchmark.p',fact_set__take__subset) ).

fof(fact_set__take__subset__set__take,axiom,
    ! [V_xs_2,T_b,V_n_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),V_m_2),V_xs_2))),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2)))) ),
    file('theBenchmark.p',fact_set__take__subset__set__take) ).

fof(fact_set__sublist__subset,axiom,
    ! [V_I_2,V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2))),hAPP(c_List_Oset(T_b),V_xs_2))),
    file('theBenchmark.p',fact_set__sublist__subset) ).

fof(fact_nth__take,axiom,
    ! [V_xs,T_a,V_n,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n))
     => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),V_i) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i) ),
    file('theBenchmark.p',fact_nth__take) ).

fof(fact_set__ConsD,axiom,
    ! [V_xs_2,V_x_2,V_y_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))))
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2)))
        | V_y_2 = V_x_2 ) ),
    file('theBenchmark.p',fact_set__ConsD) ).

fof(fact_in__set__sublistD,axiom,
    ! [V_I_2,V_xs_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2))))
     => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ),
    file('theBenchmark.p',fact_in__set__sublistD) ).

fof(fact_in__set__takeD,axiom,
    ! [V_xs_2,V_n_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2))))
     => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ),
    file('theBenchmark.p',fact_in__set__takeD) ).

fof(fact_notin__set__sublistI,axiom,
    ! [V_I_2,V_xs_2,V_x_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
     => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2)))) ),
    file('theBenchmark.p',fact_notin__set__sublistI) ).

fof(fact_take__Suc__Cons,axiom,
    ! [V_xs,V_x,V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_n)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),
    file('theBenchmark.p',fact_take__Suc__Cons) ).

fof(fact_length__take,axiom,
    ! [V_xs,V_n,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n),
    file('theBenchmark.p',fact_length__take) ).

fof(fact_take__take,axiom,
    ! [V_xs,V_m,V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(hAPP(c_List_Otake(T_a),V_m),V_xs)) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_n),V_m)),V_xs),
    file('theBenchmark.p',fact_take__take) ).

fof(fact_List_Oset_Osimps_I2_J,axiom,
    ! [V_xs_2,V_x_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)),
    file('theBenchmark.p',fact_List_Oset_Osimps_I2_J) ).

fof(fact_sublist__upt__eq__take,axiom,
    ! [V_n_2,V_l_2,T_b] : c_List_Osublist(T_b,V_l_2,hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2)) = hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_l_2),
    file('theBenchmark.p',fact_sublist__upt__eq__take) ).

fof(fact_card__length,axiom,
    ! [V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_List_Oset(T_b),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))),
    file('theBenchmark.p',fact_card__length) ).

fof(fact_all__set__conv__all__nth,axiom,
    ! [V_P_2,V_xs_2,T_b] :
      ( ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
         => hBOOL(hAPP(V_P_2,B_x)) )
    <=> ! [B_i] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
         => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) ) ),
    file('theBenchmark.p',fact_all__set__conv__all__nth) ).

fof(fact_list__size__estimation,axiom,
    ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),c_List_Olist_Olist__size(T_b,V_f_2,V_xs_2))) ) ),
    file('theBenchmark.p',fact_list__size__estimation) ).

fof(fact_list__size__estimation_H,axiom,
    ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),c_List_Olist_Olist__size(T_b,V_f_2,V_xs_2))) ) ),
    file('theBenchmark.p',fact_list__size__estimation_H) ).

fof(fact_in__lists__conv__set,axiom,
    ! [V_A_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2)))
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
         => hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ),
    file('theBenchmark.p',fact_in__lists__conv__set) ).

fof(fact_length__pos__if__in__set,axiom,
    ! [V_xs_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ),
    file('theBenchmark.p',fact_length__pos__if__in__set) ).

fof(fact_nth__mem,axiom,
    ! [V_xs_2,T_b,V_n_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
     => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2)),hAPP(c_List_Oset(T_b),V_xs_2))) ),
    file('theBenchmark.p',fact_nth__mem) ).

fof(fact_in__set__conv__nth,axiom,
    ! [V_xs_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
    <=> ? [B_i] :
          ( hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) = V_x_2
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ) ),
    file('theBenchmark.p',fact_in__set__conv__nth) ).

fof(fact_lists__eq__set,axiom,
    ! [V_A_2,T_b] : c_List_Olists(T_b,V_A_2) = hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),c_List_Oset(T_b))),V_A_2)),
    file('theBenchmark.p',fact_lists__eq__set) ).

fof(fact_set__conv__nth,axiom,
    ! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_b),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(T_b),V_xs_2))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))))),
    file('theBenchmark.p',fact_set__conv__nth) ).

fof(fact_finite__lists__length__eq,axiom,
    ! [V_n_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_b)),hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),c_List_Oset(T_b))),V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_n_2))))) ),
    file('theBenchmark.p',fact_finite__lists__length__eq) ).

fof(fact_finite__lists__length__le,axiom,
    ! [V_n_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_b)),hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),c_List_Oset(T_b))),V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_n_2))))) ),
    file('theBenchmark.p',fact_finite__lists__length__le) ).

fof(fact_listrel__iff__zip,axiom,
    ! [V_r_2,V_ys_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2)))
    <=> ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),hAPP(c_List_Oset(tc_prod(T_b,T_b)),hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_ys_2))))
           => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2)),B_x)) )
        & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) ) ),
    file('theBenchmark.p',fact_listrel__iff__zip) ).

fof(fact_set__zip,axiom,
    ! [V_ys_2,V_xs_2,T_c,T_b] : hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) = hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_prod(T_b,T_c)),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(T_b,T_c),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(T_b,T_c)),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_prod(T_b,T_c)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(tc_prod(T_b,T_c),tc_fun(tc_Nat_Onat,tc_prod(T_b,T_c)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_prod(T_b,T_c)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(T_b,T_c)),c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_c,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_prod(T_b,T_c)),tc_Nat_Onat),c_Product__Type_OPair(T_b,T_c)),hAPP(c_List_Onth(T_b),V_xs_2))),hAPP(c_List_Onth(T_c),V_ys_2)))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)))))),
    file('theBenchmark.p',fact_set__zip) ).

fof(fact_take__zip,axiom,
    ! [V_ys,V_xs,V_n,T_b,T_a] : hAPP(hAPP(c_List_Otake(tc_prod(T_a,T_b)),V_n),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)) = hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Otake(T_b),V_n),V_ys)),
    file('theBenchmark.p',fact_take__zip) ).

fof(fact_length__zip,axiom,
    ! [V_ys,V_xs,T_b,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(T_a,T_b))),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys)),
    file('theBenchmark.p',fact_length__zip) ).

fof(fact_zip__Cons__Cons,axiom,
    ! [V_ys,V_y,V_xs,V_x,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y),V_ys)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x),V_y)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)),
    file('theBenchmark.p',fact_zip__Cons__Cons) ).

fof(fact_list__eq__iff__zip__eq,axiom,
    ! [T_b,V_ys_2,V_xs_2] :
      ( V_xs_2 = V_ys_2
    <=> ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),hAPP(c_List_Oset(tc_prod(T_b,T_b)),hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_ys_2))))
           => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),c_fequal),B_x)) )
        & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) ) ),
    file('theBenchmark.p',fact_list__eq__iff__zip__eq) ).

fof(fact_zip__same,axiom,
    ! [V_xs_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),hAPP(c_List_Oset(tc_prod(T_b,T_b)),hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_xs_2))))
    <=> ( V_a_2 = V_b_2
        & hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ),
    file('theBenchmark.p',fact_zip__same) ).

fof(fact_set__zip__leftD,axiom,
    ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))))
     => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ),
    file('theBenchmark.p',fact_set__zip__leftD) ).

fof(fact_set__zip__rightD,axiom,
    ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))))
     => hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_ys_2))) ),
    file('theBenchmark.p',fact_set__zip__rightD) ).

fof(fact_in__set__zipE,axiom,
    ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))))
     => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
         => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_ys_2))) ) ),
    file('theBenchmark.p',fact_in__set__zipE) ).

fof(fact_nth__zip,axiom,
    ! [V_ys,T_b,V_xs,T_a,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys)))
       => hAPP(hAPP(c_List_Onth(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)),V_i) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)),hAPP(hAPP(c_List_Onth(T_b),V_ys),V_i)) ) ),
    file('theBenchmark.p',fact_nth__zip) ).

fof(fact_greaterThanLessThan__upto,axiom,
    ! [V_j_2,V_i_2] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,V_i_2,V_j_2) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_j_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    file('theBenchmark.p',fact_greaterThanLessThan__upto) ).

fof(fact_listsum__setsum__nth,axiom,
    ! [V_xs_2,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),V_xs_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(c_List_Onth(T_b),V_xs_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ),
    file('theBenchmark.p',fact_listsum__setsum__nth) ).

fof(fact_listsum__eq__0__nat__iff__nat,axiom,
    ! [V_ns_2] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
         => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_listsum__eq__0__nat__iff__nat) ).

fof(fact_set__upto,axiom,
    ! [V_j_2,V_i_2] : hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_i_2,V_j_2)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2),
    file('theBenchmark.p',fact_set__upto) ).

fof(fact_atLeastAtMost__upto,axiom,
    ! [V_j_2,V_i_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_i_2,V_j_2)),
    file('theBenchmark.p',fact_atLeastAtMost__upto) ).

fof(fact_elem__le__listsum__nat,axiom,
    ! [V_ns,V_k] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),V_ns)))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),V_ns),V_k)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns))) ),
    file('theBenchmark.p',fact_elem__le__listsum__nat) ).

fof(fact_listsum__simps_I2_J,axiom,
    ! [V_xs,V_x,T_a] :
      ( class_Groups_Omonoid__add(T_a)
     => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs)) ),
    file('theBenchmark.p',fact_listsum__simps_I2_J) ).

fof(fact_atLeastLessThan__upto,axiom,
    ! [V_j_2,V_i_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_i_2),V_j_2) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_i_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_j_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    file('theBenchmark.p',fact_atLeastLessThan__upto) ).

fof(fact_greaterThanAtMost__upto,axiom,
    ! [V_j_2,V_i_2] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,V_i_2,V_j_2) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_j_2)),
    file('theBenchmark.p',fact_greaterThanAtMost__upto) ).

fof(fact_nat__list__def,axiom,
    ! [V_l_2] :
      ( c_List_Onat__list(V_l_2)
    <=> c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),V_l_2)) ),
    file('theBenchmark.p',fact_nat__list__def) ).

fof(fact_list__size__pointwise,axiom,
    ! [V_g_2,V_f_2,V_xs_2,T_b] :
      ( ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(T_b,V_f_2,V_xs_2)),c_List_Olist_Olist__size(T_b,V_g_2,V_xs_2))) ),
    file('theBenchmark.p',fact_list__size__pointwise) ).

fof(fact_listsum__update__nat,axiom,
    ! [V_n,V_ns,V_k] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),V_ns)))
     => hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat,V_ns),V_k),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns)),V_n)),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),V_ns),V_k)) ),
    file('theBenchmark.p',fact_listsum__update__nat) ).

fof(fact_butlast__take,axiom,
    ! [V_xs,T_a,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
     => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs) ),
    file('theBenchmark.p',fact_butlast__take) ).

fof(fact_list__update__beyond,axiom,
    ! [V_x,V_i,V_xs,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_i))
     => hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x) = V_xs ),
    file('theBenchmark.p',fact_list__update__beyond) ).

fof(fact_list__update__id,axiom,
    ! [V_i,V_xs,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)) = V_xs,
    file('theBenchmark.p',fact_list__update__id) ).

fof(fact_nth__list__update__neq,axiom,
    ! [V_x,V_xs,T_a,V_j,V_i] :
      ( V_i != V_j
     => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_j) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_j) ),
    file('theBenchmark.p',fact_nth__list__update__neq) ).

fof(fact_length__list__update,axiom,
    ! [V_x,V_i,V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs),
    file('theBenchmark.p',fact_length__list__update) ).

fof(fact_butlast__list__update,axiom,
    ! [V_x,V_xs,T_a,V_k] :
      ( ( V_k != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
       => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = hAPP(hAPP(c_List_Olist__update(T_a,c_List_Obutlast(T_a,V_xs)),V_k),V_x) )
      & ( V_k = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
       => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = c_List_Obutlast(T_a,V_xs) ) ),
    file('theBenchmark.p',fact_butlast__list__update) ).

fof(fact_zip__update,axiom,
    ! [V_y,V_ys,V_x,V_i,V_xs,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),hAPP(hAPP(c_List_Olist__update(T_b,V_ys),V_i),V_y)) = hAPP(hAPP(c_List_Olist__update(tc_prod(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)),V_i),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x),V_y)),
    file('theBenchmark.p',fact_zip__update) ).

fof(fact_update__zip,axiom,
    ! [V_xy,V_i,V_ys,V_xs,T_b,T_a] : hAPP(hAPP(c_List_Olist__update(tc_prod(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)),V_i),V_xy) = hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),hAPP(c_Product__Type_Ofst(T_a,T_b),V_xy))),hAPP(hAPP(c_List_Olist__update(T_b,V_ys),V_i),hAPP(c_Product__Type_Osnd(T_a,T_b),V_xy))),
    file('theBenchmark.p',fact_update__zip) ).

fof(fact_list__update__swap,axiom,
    ! [V_x_H,V_x,V_xs,T_a,V_i_H,V_i] :
      ( V_i != V_i_H
     => hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_i_H),V_x_H) = hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i_H),V_x_H)),V_i),V_x) ),
    file('theBenchmark.p',fact_list__update__swap) ).

fof(fact_list__update__overwrite,axiom,
    ! [V_y,V_x,V_i,V_xs,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_i),V_y) = hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_y),
    file('theBenchmark.p',fact_list__update__overwrite) ).

fof(fact_list__update_Osimps_I2_J,axiom,
    ! [V_v_2,V_i_2,V_xs_2,V_x_2,T_b] : hAPP(hAPP(c_List_Olist__update(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_i_2),V_v_2) = c_Nat_Onat_Onat__case(tc_List_Olist(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_v_2),V_xs_2),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_Nat_Onat),hAPP(c_List_Olist_OCons(T_b),V_x_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,T_b,tc_List_Olist(T_b)),c_List_Olist__update(T_b,V_xs_2)),V_v_2)),V_i_2),
    file('theBenchmark.p',fact_list__update_Osimps_I2_J) ).

fof(fact_list__update__code_I3_J,axiom,
    ! [V_y,V_i,V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(c_Nat_OSuc,V_i)),V_y) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_y)),
    file('theBenchmark.p',fact_list__update__code_I3_J) ).

fof(fact_list__update__code_I2_J,axiom,
    ! [V_y,V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_y) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs),
    file('theBenchmark.p',fact_list__update__code_I2_J) ).

fof(fact_in__set__butlastD,axiom,
    ! [V_xs_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_xs_2))))
     => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ),
    file('theBenchmark.p',fact_in__set__butlastD) ).

fof(fact_set__update__subsetI,axiom,
    ! [V_i_2,V_x_2,V_A_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),V_A_2))
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2))),V_A_2)) ) ),
    file('theBenchmark.p',fact_set__update__subsetI) ).

fof(fact_set__update__subset__insert,axiom,
    ! [V_x_2,V_i_2,V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2))),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))),
    file('theBenchmark.p',fact_set__update__subset__insert) ).

fof(fact_nth__list__update,axiom,
    ! [V_x,V_j,V_xs,T_a,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
     => ( ( V_i != V_j
         => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_j) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_j) )
        & ( V_i = V_j
         => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_j) = V_x ) ) ),
    file('theBenchmark.p',fact_nth__list__update) ).

fof(fact_list__update__same__conv,axiom,
    ! [V_x_2,V_xs_2,T_b,V_i_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
     => ( hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2) = V_xs_2
      <=> hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_i_2) = V_x_2 ) ),
    file('theBenchmark.p',fact_list__update__same__conv) ).

fof(fact_nth__list__update__eq,axiom,
    ! [V_x,V_xs,T_a,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
     => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_i) = V_x ),
    file('theBenchmark.p',fact_nth__list__update__eq) ).

fof(fact_take__butlast,axiom,
    ! [V_xs,T_a,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
     => hAPP(hAPP(c_List_Otake(T_a),V_n),c_List_Obutlast(T_a,V_xs)) = hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs) ),
    file('theBenchmark.p',fact_take__butlast) ).

fof(fact_length__butlast,axiom,
    ! [V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Obutlast(T_a,V_xs)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    file('theBenchmark.p',fact_length__butlast) ).

fof(fact_set__update__memI,axiom,
    ! [V_x_2,V_xs_2,T_b,V_n_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
     => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_n_2),V_x_2)))) ),
    file('theBenchmark.p',fact_set__update__memI) ).

fof(fact_butlast__conv__take,axiom,
    ! [V_xs,T_a] : c_List_Obutlast(T_a,V_xs) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs),
    file('theBenchmark.p',fact_butlast__conv__take) ).

fof(fact_listrel1__iff__update,axiom,
    ! [V_r_2,V_ys_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
    <=> ? [B_y,B_n] :
          ( V_ys_2 = hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),B_n),B_y)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n)),B_y)),V_r_2)) ) ),
    file('theBenchmark.p',fact_listrel1__iff__update) ).

fof(fact_distinct__list__update,axiom,
    ! [V_i_2,V_a_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
     => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_i_2)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
       => hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_a_2))) ) ),
    file('theBenchmark.p',fact_distinct__list__update) ).

fof(fact_distinct__upto,axiom,
    ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(V_i,V_j))),
    file('theBenchmark.p',fact_distinct__upto) ).

fof(fact_distinct__take,axiom,
    ! [V_i,V_xs,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
     => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs))) ),
    file('theBenchmark.p',fact_distinct__take) ).

fof(fact_distinct__sublistI,axiom,
    ! [V_I_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
     => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2))) ),
    file('theBenchmark.p',fact_distinct__sublistI) ).

fof(fact_distinct__zipI2,axiom,
    ! [V_xs,T_b,V_ys,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),V_ys))
     => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_b,T_a)),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs),V_ys))) ),
    file('theBenchmark.p',fact_distinct__zipI2) ).

fof(fact_distinct__zipI1,axiom,
    ! [V_ys,T_b,V_xs,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
     => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys))) ),
    file('theBenchmark.p',fact_distinct__zipI1) ).

fof(fact_distinct_Osimps_I2_J,axiom,
    ! [V_xs_2,V_x_2,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)))
    <=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
        & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ),
    file('theBenchmark.p',fact_distinct_Osimps_I2_J) ).

fof(fact_distinct__card,axiom,
    ! [V_xs_2,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
     => hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) ),
    file('theBenchmark.p',fact_distinct__card) ).

fof(fact_card__distinct,axiom,
    ! [V_xs_2,T_b] :
      ( hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)
     => hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ),
    file('theBenchmark.p',fact_card__distinct) ).

fof(fact_distinct__conv__nth,axiom,
    ! [V_xs_2,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
    <=> ! [B_i] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
         => ! [B_j] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
             => ( B_i != B_j
               => hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) != hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_j) ) ) ) ),
    file('theBenchmark.p',fact_distinct__conv__nth) ).

fof(fact_nth__eq__iff__index__eq,axiom,
    ! [V_j_2,V_i_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
         => ( hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_i_2) = hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_j_2)
          <=> V_i_2 = V_j_2 ) ) ) ),
    file('theBenchmark.p',fact_nth__eq__iff__index__eq) ).

fof(fact_distinct__listsum__conv__Setsum,axiom,
    ! [V_xs_2,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
       => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),V_xs_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_b),c_COMBI(T_b)),hAPP(c_List_Oset(T_b),V_xs_2)) ) ),
    file('theBenchmark.p',fact_distinct__listsum__conv__Setsum) ).

fof(fact_Nitpick_Ocard_H__def,axiom,
    ! [V_A_2,T_b] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => c_Nitpick_Ocard_H(T_b,V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => c_Nitpick_Ocard_H(T_b,V_A_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_Hilbert__Choice_OEps(tc_List_Olist(T_b),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_List_Oset(T_b))),V_A_2))),c_List_Odistinct(T_b)))) ) ),
    file('theBenchmark.p',fact_Nitpick_Ocard_H__def) ).

fof(fact_nth__take__lemma,axiom,
    ! [V_ys,V_xs,T_a,V_k] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys)))
       => ( ! [B_i] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_k))
             => hAPP(hAPP(c_List_Onth(T_a),V_xs),B_i) = hAPP(hAPP(c_List_Onth(T_a),V_ys),B_i) )
         => hAPP(hAPP(c_List_Otake(T_a),V_k),V_xs) = hAPP(hAPP(c_List_Otake(T_a),V_k),V_ys) ) ) ),
    file('theBenchmark.p',fact_nth__take__lemma) ).

fof(fact_set__remove1__eq,axiom,
    ! [V_x_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
     => hAPP(c_List_Oset(T_b),c_List_Oremove1(T_b,V_x_2,V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ),
    file('theBenchmark.p',fact_set__remove1__eq) ).

fof(fact_take__Cons__number__of,axiom,
    ! [V_xs,V_x,T_a,V_v] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs)) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a) ) ),
    file('theBenchmark.p',fact_take__Cons__number__of) ).

fof(fact_lists_ONil,axiom,
    ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_List_Olists(T_b,V_A_2))),
    file('theBenchmark.p',fact_lists_ONil) ).

fof(fact_listrel__Nil1,axiom,
    ! [V_r_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_xs_2)),c_List_Olistrel(T_b,V_r_2)))
     => V_xs_2 = c_List_Olist_ONil(T_b) ),
    file('theBenchmark.p',fact_listrel__Nil1) ).

fof(fact_listrel__Nil2,axiom,
    ! [V_r_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),c_List_Olist_ONil(T_b))),c_List_Olistrel(T_b,V_r_2)))
     => V_xs_2 = c_List_Olist_ONil(T_b) ),
    file('theBenchmark.p',fact_listrel__Nil2) ).

fof(fact_distinct__butlast,axiom,
    ! [T_a,V_xs] :
      ( V_xs != c_List_Olist_ONil(T_a)
     => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
       => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Obutlast(T_a,V_xs))) ) ),
    file('theBenchmark.p',fact_distinct__butlast) ).

fof(fact_distinct_Osimps_I1_J,axiom,
    ! [T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olist_ONil(T_a))),
    file('theBenchmark.p',fact_distinct_Osimps_I1_J) ).

fof(fact_distinct__remove1,axiom,
    ! [V_x,V_xs,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
     => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremove1(T_a,V_x,V_xs))) ),
    file('theBenchmark.p',fact_distinct__remove1) ).

fof(fact_butlast_Osimps_I1_J,axiom,
    ! [T_a] : c_List_Obutlast(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a),
    file('theBenchmark.p',fact_butlast_Osimps_I1_J) ).

fof(fact_butlast_Osimps_I2_J,axiom,
    ! [V_x,T_a,V_xs] :
      ( ( V_xs != c_List_Olist_ONil(T_a)
       => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Obutlast(T_a,V_xs)) )
      & ( V_xs = c_List_Olist_ONil(T_a)
       => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a) ) ),
    file('theBenchmark.p',fact_butlast_Osimps_I2_J) ).

fof(fact_remove1_Osimps_I2_J,axiom,
    ! [V_xs,T_a,V_y,V_x] :
      ( ( V_x != V_y
       => c_List_Oremove1(T_a,V_x,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),c_List_Oremove1(T_a,V_x,V_xs)) )
      & ( V_x = V_y
       => c_List_Oremove1(T_a,V_x,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = V_xs ) ),
    file('theBenchmark.p',fact_remove1_Osimps_I2_J) ).

fof(fact_list_Osimps_I3_J,axiom,
    ! [V_list_H,V_a_H,T_a] : hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_H),V_list_H) != c_List_Olist_ONil(T_a),
    file('theBenchmark.p',fact_list_Osimps_I3_J) ).

fof(fact_list_Osimps_I2_J,axiom,
    ! [V_list_H,V_a_H,T_a] : c_List_Olist_ONil(T_a) != hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_H),V_list_H),
    file('theBenchmark.p',fact_list_Osimps_I2_J) ).

fof(fact_upto__empty,axiom,
    ! [V_i,V_j] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j),V_i))
     => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ),
    file('theBenchmark.p',fact_upto__empty) ).

fof(fact_take__Nil,axiom,
    ! [V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a),
    file('theBenchmark.p',fact_take__Nil) ).

fof(fact_take__eq__Nil,axiom,
    ! [V_xs_2,V_n_2,T_b] :
      ( hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2) = c_List_Olist_ONil(T_b)
    <=> ( V_xs_2 = c_List_Olist_ONil(T_b)
        | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_take__eq__Nil) ).

fof(fact_take__0,axiom,
    ! [V_xs,T_a] : hAPP(hAPP(c_List_Otake(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_xs) = c_List_Olist_ONil(T_a),
    file('theBenchmark.p',fact_take__0) ).

fof(fact_sublist__nil,axiom,
    ! [V_A_2,T_b] : c_List_Osublist(T_b,c_List_Olist_ONil(T_b),V_A_2) = c_List_Olist_ONil(T_b),
    file('theBenchmark.p',fact_sublist__nil) ).

fof(fact_remove1_Osimps_I1_J,axiom,
    ! [V_x,T_a] : c_List_Oremove1(T_a,V_x,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a),
    file('theBenchmark.p',fact_remove1_Osimps_I1_J) ).

fof(fact_remove1__commute,axiom,
    ! [V_zs,V_y,V_x,T_a] : c_List_Oremove1(T_a,V_x,c_List_Oremove1(T_a,V_y,V_zs)) = c_List_Oremove1(T_a,V_y,c_List_Oremove1(T_a,V_x,V_zs)),
    file('theBenchmark.p',fact_remove1__commute) ).

fof(fact_listrelp_ONil,axiom,
    ! [V_r_2,T_b] : c_List_Olistrelp(T_b,V_r_2,c_List_Olist_ONil(T_b),c_List_Olist_ONil(T_b)),
    file('theBenchmark.p',fact_listrelp_ONil) ).

fof(fact_listrelp_Oequations_I1_J,axiom,
    ! [V_r_2,T_b] : c_List_Olistrelp(T_b,V_r_2,c_List_Olist_ONil(T_b),c_List_Olist_ONil(T_b)),
    file('theBenchmark.p',fact_listrelp_Oequations_I1_J) ).

fof(fact_zip_Osimps_I1_J,axiom,
    ! [V_xs,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(tc_prod(T_a,T_b)),
    file('theBenchmark.p',fact_zip_Osimps_I1_J) ).

fof(fact_zip__Nil,axiom,
    ! [V_ys,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),c_List_Olist_ONil(T_a)),V_ys) = c_List_Olist_ONil(tc_prod(T_a,T_b)),
    file('theBenchmark.p',fact_zip__Nil) ).

fof(fact_list_Osize_I1_J,axiom,
    ! [V_fa_2,T_b] : c_List_Olist_Olist__size(T_b,V_fa_2,c_List_Olist_ONil(T_b)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_list_Osize_I1_J) ).

fof(fact_listsum__simps_I1_J,axiom,
    ! [T_a] :
      ( class_Groups_Omonoid__add(T_a)
     => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),c_List_Olist_ONil(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_listsum__simps_I1_J) ).

fof(fact_length__0__conv,axiom,
    ! [V_xs_2,T_b] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> V_xs_2 = c_List_Olist_ONil(T_b) ),
    file('theBenchmark.p',fact_length__0__conv) ).

fof(fact_list_Osize_I3_J,axiom,
    ! [T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_list_Osize_I3_J) ).

fof(fact_List_Oset_Osimps_I1_J,axiom,
    ! [T_b] : hAPP(c_List_Oset(T_b),c_List_Olist_ONil(T_b)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_List_Oset_Osimps_I1_J) ).

fof(fact_set__empty2,axiom,
    ! [V_xs_2,T_b] :
      ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_List_Oset(T_b),V_xs_2)
    <=> V_xs_2 = c_List_Olist_ONil(T_b) ),
    file('theBenchmark.p',fact_set__empty2) ).

fof(fact_set__empty,axiom,
    ! [V_xs_2,T_b] :
      ( hAPP(c_List_Oset(T_b),V_xs_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
    <=> V_xs_2 = c_List_Olist_ONil(T_b) ),
    file('theBenchmark.p',fact_set__empty) ).

fof(fact_list__update__nonempty,axiom,
    ! [V_x_2,V_k_2,V_xs_2,T_b] :
      ( hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_k_2),V_x_2) = c_List_Olist_ONil(T_b)
    <=> V_xs_2 = c_List_Olist_ONil(T_b) ),
    file('theBenchmark.p',fact_list__update__nonempty) ).

fof(fact_list__update_Osimps_I1_J,axiom,
    ! [V_v,V_i,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,c_List_Olist_ONil(T_a)),V_i),V_v) = c_List_Olist_ONil(T_a),
    file('theBenchmark.p',fact_list__update_Osimps_I1_J) ).

fof(fact_list__update__code_I1_J,axiom,
    ! [V_y,V_i,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,c_List_Olist_ONil(T_a)),V_i),V_y) = c_List_Olist_ONil(T_a),
    file('theBenchmark.p',fact_list__update__code_I1_J) ).

fof(fact_in__set__remove1,axiom,
    ! [V_xs_2,T_b,V_b_2,V_a_2] :
      ( V_a_2 != V_b_2
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),c_List_Oremove1(T_b,V_b_2,V_xs_2))))
      <=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ),
    file('theBenchmark.p',fact_in__set__remove1) ).

fof(fact_notin__set__remove1,axiom,
    ! [V_y_2,V_xs_2,V_x_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
     => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Oremove1(T_b,V_y_2,V_xs_2)))) ),
    file('theBenchmark.p',fact_notin__set__remove1) ).

fof(fact_remove1__idem,axiom,
    ! [V_xs_2,V_x_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
     => c_List_Oremove1(T_b,V_x_2,V_xs_2) = V_xs_2 ),
    file('theBenchmark.p',fact_remove1__idem) ).

fof(fact_sublist__empty,axiom,
    ! [V_xs_2,T_b] : c_List_Osublist(T_b,V_xs_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) = c_List_Olist_ONil(T_b),
    file('theBenchmark.p',fact_sublist__empty) ).

fof(fact_set__remove1__subset,axiom,
    ! [V_xs_2,V_x_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),c_List_Oremove1(T_b,V_x_2,V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2))),
    file('theBenchmark.p',fact_set__remove1__subset) ).

fof(fact_length__greater__0__conv,axiom,
    ! [V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
    <=> V_xs_2 != c_List_Olist_ONil(T_b) ),
    file('theBenchmark.p',fact_length__greater__0__conv) ).

fof(fact_take__1__Cons,axiom,
    ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Otake(T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a)),
    file('theBenchmark.p',fact_take__1__Cons) ).

fof(fact_not__Nil__listrel1,axiom,
    ! [V_r_2,V_xs_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_xs_2)),c_List_Olistrel1(T_b,V_r_2))),
    file('theBenchmark.p',fact_not__Nil__listrel1) ).

fof(fact_not__listrel1__Nil,axiom,
    ! [V_r_2,V_xs_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),c_List_Olist_ONil(T_b))),c_List_Olistrel1(T_b,V_r_2))),
    file('theBenchmark.p',fact_not__listrel1__Nil) ).

fof(fact_listrel_ONil,axiom,
    ! [V_r_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_List_Olist_ONil(T_b))),c_List_Olistrel(T_b,V_r_2))),
    file('theBenchmark.p',fact_listrel_ONil) ).

fof(fact_lexord__Nil__right,axiom,
    ! [V_r_2,V_x_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),c_List_Olist_ONil(T_b))),c_List_Olexord(T_b,V_r_2))),
    file('theBenchmark.p',fact_lexord__Nil__right) ).

fof(fact_Nil__notin__lex,axiom,
    ! [V_r_2,V_ys_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_ys_2)),c_List_Olex(T_b,V_r_2))),
    file('theBenchmark.p',fact_Nil__notin__lex) ).

fof(fact_Nil2__notin__lex,axiom,
    ! [V_r_2,V_xs_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),c_List_Olist_ONil(T_b))),c_List_Olex(T_b,V_r_2))),
    file('theBenchmark.p',fact_Nil2__notin__lex) ).

fof(fact_take__Cons,axiom,
    ! [V_xs_2,V_x_2,V_n_2,T_b] : hAPP(hAPP(c_List_Otake(T_b),V_n_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_Nat_Onat_Onat__case(tc_List_Olist(T_b),c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_Nat_Onat),hAPP(c_List_Olist_OCons(T_b),V_x_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Otake(T_b)),V_xs_2)),V_n_2),
    file('theBenchmark.p',fact_take__Cons) ).

fof(fact_upto_Osimps,axiom,
    ! [V_j,V_i] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
       => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
       => c_List_Oupto(V_i,V_j) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),V_i),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_j)) ) ),
    file('theBenchmark.p',fact_upto_Osimps) ).

fof(fact_sublist__singleton,axiom,
    ! [V_x_2,T_b,V_A_2] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2))
       => c_List_Osublist(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)),V_A_2) = c_List_Olist_ONil(T_b) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2))
       => c_List_Osublist(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)),V_A_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ) ),
    file('theBenchmark.p',fact_sublist__singleton) ).

fof(fact_lists__empty,axiom,
    ! [T_b] : c_List_Olists(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),
    file('theBenchmark.p',fact_lists__empty) ).

fof(fact_take__Cons_H,axiom,
    ! [V_xs,V_x,T_a,V_n] :
      ( ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs)) )
      & ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a) ) ),
    file('theBenchmark.p',fact_take__Cons_H) ).

fof(fact_upto__rec__number__of,axiom,
    ! [V_n,V_m] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n)))
       => c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n)) = c_List_Olist_ONil(tc_Int_Oint) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n)))
       => c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m)),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n))) ) ),
    file('theBenchmark.p',fact_upto__rec__number__of) ).

fof(fact_listrel__Nil,axiom,
    ! [V_r_2,T_b] : hAPP(c_Relation_OImage(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),
    file('theBenchmark.p',fact_listrel__Nil) ).

fof(fact_set__Cons__sing__Nil,axiom,
    ! [V_A_2,T_b] : c_List_Oset__Cons(T_b,V_A_2,hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))) = hAPP(c_Set_Oimage(T_b,tc_List_Olist(T_b),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b))),V_A_2),
    file('theBenchmark.p',fact_set__Cons__sing__Nil) ).

fof(fact_length__remove1,axiom,
    ! [V_xs_2,V_x_2,T_b] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
       => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremove1(T_b,V_x_2,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) )
      & ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
       => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremove1(T_b,V_x_2,V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
    file('theBenchmark.p',fact_length__remove1) ).

fof(fact_upto_Opsimps,axiom,
    ! [V_j_2,V_i_2] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_i_2),V_j_2)))
     => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2))
         => c_List_Oupto(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Int_Oint) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2))
         => c_List_Oupto(V_i_2,V_j_2) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),V_i_2),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_j_2)) ) ) ),
    file('theBenchmark.p',fact_upto_Opsimps) ).

fof(fact_select,axiom,
    ! [V_s_2,T_b,V_xs_2] :
      ( V_xs_2 != c_List_Olist_ONil(T_b)
     => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Product__Type_Ofst(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect(T_b,V_xs_2),V_s_2))),hAPP(c_List_Oset(T_b),V_xs_2))) ),
    file('theBenchmark.p',fact_select) ).

fof(fact_listset_Osimps_I1_J,axiom,
    ! [T_b] : c_List_Olistset(T_b,c_List_Olist_ONil(tc_fun(T_b,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),
    file('theBenchmark.p',fact_listset_Osimps_I1_J) ).

fof(fact_zip__Cons1,axiom,
    ! [V_ys_2,V_xs_2,V_x_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_ys_2) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(T_b,T_c)),T_c,c_List_Olist_ONil(tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c)))),T_c),c_COMBB(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(T_c))),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c))),T_c),c_List_Olist_OCons(tc_prod(T_b,T_c))),hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2)))),hAPP(c_List_Ozip(T_b,T_c),V_xs_2))),V_ys_2),
    file('theBenchmark.p',fact_zip__Cons1) ).

fof(fact_list_Osimps_I5_J,axiom,
    ! [V_list_2,V_a_2,V_f2_2,V_f1_2,T_c,T_b] : hAPP(c_List_Olist_Olist__case(T_b,T_c,V_f1_2,V_f2_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_a_2),V_list_2)) = hAPP(hAPP(V_f2_2,V_a_2),V_list_2),
    file('theBenchmark.p',fact_list_Osimps_I5_J) ).

fof(fact_list_Osimps_I4_J,axiom,
    ! [V_f2_2,V_f1_2,T_c,T_b] : hAPP(c_List_Olist_Olist__case(T_b,T_c,V_f1_2,V_f2_2),c_List_Olist_ONil(T_c)) = V_f1_2,
    file('theBenchmark.p',fact_list_Osimps_I4_J) ).

fof(fact_listset_Osimps_I2_J,axiom,
    ! [V_As_2,V_A_2,T_b] : c_List_Olistset(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_As_2)) = c_List_Oset__Cons(T_b,V_A_2,c_List_Olistset(T_b,V_As_2)),
    file('theBenchmark.p',fact_listset_Osimps_I2_J) ).

fof(fact_zip__Cons,axiom,
    ! [V_ys_2,V_y_2,V_xs_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(T_b,T_c)),T_b,c_List_Olist_ONil(tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_b,T_c)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_b,T_c)))),T_b),c_COMBB(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c))),T_b),c_List_Olist_OCons(tc_prod(T_b,T_c))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_prod(T_b,T_c)),c_Product__Type_OPair(T_b,T_c)),V_y_2)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c))),c_List_Ozip(T_b,T_c)),V_ys_2))),V_xs_2),
    file('theBenchmark.p',fact_zip__Cons) ).

fof(fact_sorted__list__of__set__remove,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => c_List_Olinorder__class_Osorted__list__of__set(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = c_List_Oremove1(T_b,V_x_2,c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2)) ) ),
    file('theBenchmark.p',fact_sorted__list__of__set__remove) ).

fof(fact_upto_Opinduct,axiom,
    ! [V_P_2,V_a1_2,V_a0_2] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2)))
     => ( ! [B_i,B_j] :
            ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_i),B_j)))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_i),B_j))
               => hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_i),c_Groups_Oone__class_Oone(tc_Int_Oint))),B_j)) )
             => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) )
       => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ),
    file('theBenchmark.p',fact_upto_Opinduct) ).

fof(fact_sorted__list__of__set__empty,axiom,
    ! [T_b] :
      ( class_Orderings_Olinorder(T_b)
     => c_List_Olinorder__class_Osorted__list__of__set(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_List_Olist_ONil(T_b) ),
    file('theBenchmark.p',fact_sorted__list__of__set__empty) ).

fof(fact_anamorph_Osimps,axiom,
    ! [V_x_2,V_f_2,T_b,T_c,V_k_2] :
      ( ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => hAPP(hAPP(c_Lazy__Sequence_Oanamorph(T_c,T_b,V_f_2),V_k_2),V_x_2) = c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(T_b),T_c),tc_prod(T_b,T_c),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),T_c),c_List_Olist_ONil(T_b)),V_x_2),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_prod(tc_List_Olist(T_b),T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c)),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(T_b),T_c),tc_prod(tc_List_Olist(T_b),T_c)),tc_fun(tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c)),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c))),T_b),c_COMBB(tc_prod(tc_List_Olist(T_b),T_c),tc_prod(tc_List_Olist(T_b),T_c),T_c)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c))),tc_fun(tc_prod(tc_List_Olist(T_b),T_c),tc_prod(tc_List_Olist(T_b),T_c)),T_b),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),T_c,tc_prod(tc_List_Olist(T_b),T_c))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c))),T_b),hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c)),tc_List_Olist(T_b)),c_Product__Type_OPair(tc_List_Olist(T_b),T_c))),c_List_Olist_OCons(T_b))))),hAPP(c_Lazy__Sequence_Oanamorph(T_c,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_k_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))))),hAPP(V_f_2,V_x_2)) )
      & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => hAPP(hAPP(c_Lazy__Sequence_Oanamorph(T_c,T_b,V_f_2),V_k_2),V_x_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),T_c),c_List_Olist_ONil(T_b)),V_x_2) ) ),
    file('theBenchmark.p',fact_anamorph_Osimps) ).

fof(fact_sublist__Cons,axiom,
    ! [V_A_2,V_l_2,V_x_2,T_b] : c_List_Osublist(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_l_2),V_A_2) = hAPP(hAPP(c_List_Oappend(T_b),hAPP(hAPP(hAPP(c_If(tc_List_Olist(T_b)),hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))),c_List_Olist_ONil(T_b))),c_List_Osublist(T_b,V_l_2,hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),V_A_2)))),
    file('theBenchmark.p',fact_sublist__Cons) ).

fof(fact_append1__eq__conv,axiom,
    ! [V_y_2,V_ys_2,V_x_2,V_xs_2,T_b] :
      ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))) = hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),c_List_Olist_ONil(T_b)))
    <=> ( V_x_2 = V_y_2
        & V_xs_2 = V_ys_2 ) ),
    file('theBenchmark.p',fact_append1__eq__conv) ).

fof(fact_Cons__eq__append__conv,axiom,
    ! [V_zs_2,V_ys_2,V_xs_2,V_x_2,T_b] :
      ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) = hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_zs_2)
    <=> ( ? [B_ys_H] :
            ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2)
            & hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H) = V_ys_2 )
        | ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) = V_zs_2
          & V_ys_2 = c_List_Olist_ONil(T_b) ) ) ),
    file('theBenchmark.p',fact_Cons__eq__append__conv) ).

fof(fact_append__eq__Cons__conv,axiom,
    ! [V_xs_2,V_x_2,V_zs_2,V_ys_2,T_b] :
      ( hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_zs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)
    <=> ( ? [B_ys_H] :
            ( hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2) = V_xs_2
            & V_ys_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H) )
        | ( V_zs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)
          & V_ys_2 = c_List_Olist_ONil(T_b) ) ) ),
    file('theBenchmark.p',fact_append__eq__Cons__conv) ).

fof(fact_Cons__eq__appendI,axiom,
    ! [V_zs,V_xs,V_ys,V_xs1,V_x,T_a] :
      ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs1) = V_ys
     => ( V_xs = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_zs)
       => hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),V_ys),V_zs) ) ),
    file('theBenchmark.p',fact_Cons__eq__appendI) ).

fof(fact_append__Cons,axiom,
    ! [V_ys,V_xs,V_x,T_a] : hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_ys) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),
    file('theBenchmark.p',fact_append__Cons) ).

fof(fact_append__in__lists__conv,axiom,
    ! [V_A_2,V_ys_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)),c_List_Olists(T_b,V_A_2)))
    <=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_ys_2),c_List_Olists(T_b,V_A_2)))
        & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2))) ) ),
    file('theBenchmark.p',fact_append__in__lists__conv) ).

fof(fact_append__assoc,axiom,
    ! [V_zs,V_ys,V_xs,T_a] : hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_zs) = hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Oappend(T_a),V_ys),V_zs)),
    file('theBenchmark.p',fact_append__assoc) ).

fof(fact_append__eq__append__conv2,axiom,
    ! [V_tsa_2,V_zs_2,V_ys_2,V_xs_2,T_b] :
      ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),V_tsa_2)
    <=> ? [B_us] :
          ( ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),V_tsa_2)
            & hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),B_us) = V_zs_2 )
          | ( hAPP(hAPP(c_List_Oappend(T_b),B_us),V_ys_2) = V_tsa_2
            & V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),B_us) ) ) ),
    file('theBenchmark.p',fact_append__eq__append__conv2) ).

fof(fact_same__append__eq,axiom,
    ! [V_zs_2,V_ys_2,V_xs_2,T_b] :
      ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_zs_2)
    <=> V_ys_2 = V_zs_2 ),
    file('theBenchmark.p',fact_same__append__eq) ).

fof(fact_append__same__eq,axiom,
    ! [V_zs_2,V_xs_2,V_ys_2,T_b] :
      ( hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_xs_2) = hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),V_xs_2)
    <=> V_ys_2 = V_zs_2 ),
    file('theBenchmark.p',fact_append__same__eq) ).

fof(fact_append__eq__appendI,axiom,
    ! [V_us,V_ys,V_zs,V_xs1,V_xs,T_a] :
      ( hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_xs1) = V_zs
     => ( V_ys = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_us)
       => hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys) = hAPP(hAPP(c_List_Oappend(T_a),V_zs),V_us) ) ),
    file('theBenchmark.p',fact_append__eq__appendI) ).

fof(fact_listsum__append,axiom,
    ! [V_ys,V_xs,T_a] :
      ( class_Groups_Omonoid__add(T_a)
     => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs)),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_ys)) ),
    file('theBenchmark.p',fact_listsum__append) ).

fof(fact_length__append,axiom,
    ! [V_ys,V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys)),
    file('theBenchmark.p',fact_length__append) ).

fof(fact_zip__append,axiom,
    ! [V_vs,V_ys,V_us,T_b,V_xs,T_a] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_us)
     => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_vs)
       => hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),hAPP(hAPP(c_List_Oappend(T_b),V_us),V_vs)) = hAPP(hAPP(c_List_Oappend(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_us)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_ys),V_vs)) ) ),
    file('theBenchmark.p',fact_zip__append) ).

fof(fact_set__append,axiom,
    ! [V_ys_2,V_xs_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_ys_2)),
    file('theBenchmark.p',fact_set__append) ).

fof(fact_eq__Nil__appendI,axiom,
    ! [T_a,V_ys,V_xs] :
      ( V_xs = V_ys
     => V_xs = hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) ),
    file('theBenchmark.p',fact_eq__Nil__appendI) ).

fof(fact_append__self__conv2,axiom,
    ! [V_ys_2,V_xs_2,T_b] :
      ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_ys_2
    <=> V_xs_2 = c_List_Olist_ONil(T_b) ),
    file('theBenchmark.p',fact_append__self__conv2) ).

fof(fact_append__self__conv,axiom,
    ! [V_ys_2,V_xs_2,T_b] :
      ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_xs_2
    <=> V_ys_2 = c_List_Olist_ONil(T_b) ),
    file('theBenchmark.p',fact_append__self__conv) ).

fof(fact_append__is__Nil__conv,axiom,
    ! [V_ys_2,V_xs_2,T_b] :
      ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = c_List_Olist_ONil(T_b)
    <=> ( V_ys_2 = c_List_Olist_ONil(T_b)
        & V_xs_2 = c_List_Olist_ONil(T_b) ) ),
    file('theBenchmark.p',fact_append__is__Nil__conv) ).

fof(fact_self__append__conv2,axiom,
    ! [V_xs_2,T_b,V_ys_2] :
      ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
    <=> V_xs_2 = c_List_Olist_ONil(T_b) ),
    file('theBenchmark.p',fact_self__append__conv2) ).

fof(fact_self__append__conv,axiom,
    ! [V_ys_2,T_b,V_xs_2] :
      ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
    <=> V_ys_2 = c_List_Olist_ONil(T_b) ),
    file('theBenchmark.p',fact_self__append__conv) ).

fof(fact_append__Nil2,axiom,
    ! [V_xs,T_a] : hAPP(hAPP(c_List_Oappend(T_a),V_xs),c_List_Olist_ONil(T_a)) = V_xs,
    file('theBenchmark.p',fact_append__Nil2) ).

fof(fact_Nil__is__append__conv,axiom,
    ! [V_ys_2,V_xs_2,T_b] :
      ( c_List_Olist_ONil(T_b) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
    <=> ( V_ys_2 = c_List_Olist_ONil(T_b)
        & V_xs_2 = c_List_Olist_ONil(T_b) ) ),
    file('theBenchmark.p',fact_Nil__is__append__conv) ).

fof(fact_append__Nil,axiom,
    ! [V_ys,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) = V_ys,
    file('theBenchmark.p',fact_append__Nil) ).

fof(fact_butlast__append,axiom,
    ! [V_xs,T_a,V_ys] :
      ( ( V_ys != c_List_Olist_ONil(T_a)
       => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),V_xs),c_List_Obutlast(T_a,V_ys)) )
      & ( V_ys = c_List_Olist_ONil(T_a)
       => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Obutlast(T_a,V_xs) ) ),
    file('theBenchmark.p',fact_butlast__append) ).

fof(fact_nth__append__length,axiom,
    ! [V_ys,V_x,V_xs,T_a] : hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)) = V_x,
    file('theBenchmark.p',fact_nth__append__length) ).

fof(fact_nth__append__length__plus,axiom,
    ! [V_n,V_ys,V_xs,T_a] : hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n)) = hAPP(hAPP(c_List_Onth(T_a),V_ys),V_n),
    file('theBenchmark.p',fact_nth__append__length__plus) ).

fof(fact_take__append,axiom,
    ! [V_ys,V_xs,V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_ys)),
    file('theBenchmark.p',fact_take__append) ).

fof(fact_list__update__append1,axiom,
    ! [V_x,V_ys,V_xs,T_a,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
     => hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_i),V_x) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_ys) ),
    file('theBenchmark.p',fact_list__update__append1) ).

fof(fact_list__update__length,axiom,
    ! [V_y,V_ys,V_x,V_xs,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_y) = hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys)),
    file('theBenchmark.p',fact_list__update__length) ).

fof(fact_remove1__append,axiom,
    ! [V_ys_2,V_xs_2,V_x_2,T_b] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
       => c_List_Oremove1(T_b,V_x_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),c_List_Oremove1(T_b,V_x_2,V_ys_2)) )
      & ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
       => c_List_Oremove1(T_b,V_x_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),c_List_Oremove1(T_b,V_x_2,V_xs_2)),V_ys_2) ) ),
    file('theBenchmark.p',fact_remove1__append) ).

fof(fact_in__set__butlast__appendI,axiom,
    ! [V_ys_2,V_xs_2,V_x_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_ys_2))))
        | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_xs_2)))) )
     => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))))) ),
    file('theBenchmark.p',fact_in__set__butlast__appendI) ).

fof(fact_butlast__snoc,axiom,
    ! [V_x,V_xs,T_a] : c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a)))) = V_xs,
    file('theBenchmark.p',fact_butlast__snoc) ).

fof(fact_append__listrel1I,axiom,
    ! [V_vs_2,V_us_2,V_r_2,V_ys_2,V_xs_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_us_2),V_vs_2)),c_List_Olistrel1(T_b,V_r_2)))
          & V_xs_2 = V_ys_2 )
        | ( V_us_2 = V_vs_2
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) ) )
     => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_us_2)),hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_vs_2))),c_List_Olistrel1(T_b,V_r_2))) ),
    file('theBenchmark.p',fact_append__listrel1I) ).

fof(fact_lexord__append__leftI,axiom,
    ! [V_x_2,V_r_2,V_v_2,V_u_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_u_2),V_v_2)),c_List_Olexord(T_b,V_r_2)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_u_2)),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_v_2))),c_List_Olexord(T_b,V_r_2))) ),
    file('theBenchmark.p',fact_lexord__append__leftI) ).

fof(fact_distinct__append,axiom,
    ! [V_ys_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)))
    <=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_ys_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
        & hBOOL(hAPP(c_List_Odistinct(T_b),V_ys_2))
        & hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ),
    file('theBenchmark.p',fact_distinct__append) ).

fof(fact_nth__append,axiom,
    ! [V_ys,V_xs,T_a,V_n] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
       => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_n) = hAPP(hAPP(c_List_Onth(T_a),V_ys),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
       => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_n) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) ) ),
    file('theBenchmark.p',fact_nth__append) ).

fof(fact_list__update__append,axiom,
    ! [V_x,V_ys,V_xs,T_a,V_n] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
       => hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_n),V_x) = hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist__update(T_a,V_ys),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_x)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
       => hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_n),V_x) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_n),V_x)),V_ys) ) ),
    file('theBenchmark.p',fact_list__update__append) ).

fof(fact_sublist__append,axiom,
    ! [V_A_2,V_l_H_2,V_l_2,T_b] : c_List_Osublist(T_b,hAPP(hAPP(c_List_Oappend(T_b),V_l_2),V_l_H_2),V_A_2) = hAPP(hAPP(c_List_Oappend(T_b),c_List_Osublist(T_b,V_l_2,V_A_2)),c_List_Osublist(T_b,V_l_H_2,hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_l_2)))),V_A_2)))),
    file('theBenchmark.p',fact_sublist__append) ).

fof(fact_listrel1I,axiom,
    ! [V_ys_2,V_vs_2,V_us_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
     => ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_us_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_vs_2))
       => ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),V_us_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_vs_2))
         => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) ) ) ),
    file('theBenchmark.p',fact_listrel1I) ).

fof(fact_lexord__append__left__rightI,axiom,
    ! [V_y_2,V_x_2,V_u_2,V_r_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_u_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_x_2))),hAPP(hAPP(c_List_Oappend(T_b),V_u_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_b_2),V_y_2)))),c_List_Olexord(T_b,V_r_2))) ),
    file('theBenchmark.p',fact_lexord__append__left__rightI) ).

fof(fact_take__Suc__conv__app__nth,axiom,
    ! [V_xs,T_a,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
     => hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_i)),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)),c_List_Olist_ONil(T_a))) ),
    file('theBenchmark.p',fact_take__Suc__conv__app__nth) ).

fof(fact_snoc__listrel1__snoc__iff,axiom,
    ! [V_r_2,V_y_2,V_ys_2,V_x_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)))),hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),c_List_Olist_ONil(T_b))))),c_List_Olistrel1(T_b,V_r_2)))
    <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
          & V_xs_2 = V_ys_2 )
        | ( V_x_2 = V_y_2
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) ) ) ),
    file('theBenchmark.p',fact_snoc__listrel1__snoc__iff) ).

fof(fact_listrel1E,axiom,
    ! [V_r_2,V_ys_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
     => ~ ! [B_x,B_y] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_r_2))
           => ! [B_us,B_vs] :
                ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_vs))
               => V_ys_2 != hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),B_y),B_vs)) ) ) ),
    file('theBenchmark.p',fact_listrel1E) ).

fof(fact_lexord__append__leftD,axiom,
    ! [V_r_2,V_v_2,V_u_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_u_2)),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_v_2))),c_List_Olexord(T_b,V_r_2)))
     => ( ! [B_a] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_a),B_a)),V_r_2))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_u_2),V_v_2)),c_List_Olexord(T_b,V_r_2))) ) ),
    file('theBenchmark.p',fact_lexord__append__leftD) ).

fof(fact_rotate1__def,axiom,
    ! [V_xs_2,T_b] : hAPP(c_List_Orotate1(T_b),V_xs_2) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Oappend(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b)))),V_xs_2),
    file('theBenchmark.p',fact_rotate1__def) ).

fof(fact_upd__conv__take__nth__drop,axiom,
    ! [V_a,V_xs,T_a,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
     => hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_a) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_i)),V_xs))) ),
    file('theBenchmark.p',fact_upd__conv__take__nth__drop) ).

fof(fact_append__take__drop__id,axiom,
    ! [V_xs,V_n,T_a] : hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = V_xs,
    file('theBenchmark.p',fact_append__take__drop__id) ).

fof(fact_drop__Suc__Cons,axiom,
    ! [V_xs,V_x,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_n)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs),
    file('theBenchmark.p',fact_drop__Suc__Cons) ).

fof(fact_drop__1__Cons,axiom,
    ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Odrop(T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_xs,
    file('theBenchmark.p',fact_drop__1__Cons) ).

fof(fact_nth__via__drop,axiom,
    ! [V_ys,V_y,V_xs,V_n,T_a] :
      ( hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys)
     => hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) = V_y ),
    file('theBenchmark.p',fact_nth__via__drop) ).

fof(fact_distinct1__rotate,axiom,
    ! [V_xs_2,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate1(T_b),V_xs_2)))
    <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ),
    file('theBenchmark.p',fact_distinct1__rotate) ).

fof(fact_distinct__drop,axiom,
    ! [V_i,V_xs,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
     => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs))) ),
    file('theBenchmark.p',fact_distinct__drop) ).

fof(fact_drop__butlast,axiom,
    ! [V_xs,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),c_List_Obutlast(T_a,V_xs)) = c_List_Obutlast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)),
    file('theBenchmark.p',fact_drop__butlast) ).

fof(fact_butlast__drop,axiom,
    ! [V_xs,V_n,T_a] : c_List_Obutlast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),V_n),c_List_Obutlast(T_a,V_xs)),
    file('theBenchmark.p',fact_butlast__drop) ).

fof(fact_take__drop,axiom,
    ! [V_xs,V_m,V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(hAPP(c_List_Odrop(T_a),V_m),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),V_m),hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),V_xs)),
    file('theBenchmark.p',fact_take__drop) ).

fof(fact_drop__take,axiom,
    ! [V_xs,V_m,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(hAPP(c_List_Otake(T_a),V_m),V_xs)) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)),
    file('theBenchmark.p',fact_drop__take) ).

fof(fact_drop__drop,axiom,
    ! [V_xs,V_m,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(hAPP(c_List_Odrop(T_a),V_m),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),V_xs),
    file('theBenchmark.p',fact_drop__drop) ).

fof(fact_drop__0,axiom,
    ! [V_xs,T_a] : hAPP(hAPP(c_List_Odrop(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_xs) = V_xs,
    file('theBenchmark.p',fact_drop__0) ).

fof(fact_drop__zip,axiom,
    ! [V_ys,V_xs,V_n,T_b,T_a] : hAPP(hAPP(c_List_Odrop(tc_prod(T_a,T_b)),V_n),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)) = hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Odrop(T_b),V_n),V_ys)),
    file('theBenchmark.p',fact_drop__zip) ).

fof(fact_length__drop,axiom,
    ! [V_xs,V_n,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n),
    file('theBenchmark.p',fact_length__drop) ).

fof(fact_length__rotate1,axiom,
    ! [V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Orotate1(T_a),V_xs)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs),
    file('theBenchmark.p',fact_length__rotate1) ).

fof(fact_set__rotate1,axiom,
    ! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_Orotate1(T_b),V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2),
    file('theBenchmark.p',fact_set__rotate1) ).

fof(fact_in__set__dropD,axiom,
    ! [V_xs_2,V_n_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2))))
     => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ),
    file('theBenchmark.p',fact_in__set__dropD) ).

fof(fact_set__drop__subset,axiom,
    ! [V_xs_2,V_n_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2))),
    file('theBenchmark.p',fact_set__drop__subset) ).

fof(fact_rotate1__is__Nil__conv,axiom,
    ! [V_xs_2,T_b] :
      ( hAPP(c_List_Orotate1(T_b),V_xs_2) = c_List_Olist_ONil(T_b)
    <=> V_xs_2 = c_List_Olist_ONil(T_b) ),
    file('theBenchmark.p',fact_rotate1__is__Nil__conv) ).

fof(fact_drop__Nil,axiom,
    ! [V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a),
    file('theBenchmark.p',fact_drop__Nil) ).

fof(fact_set__drop__subset__set__drop,axiom,
    ! [V_xs_2,T_b,V_m_2,V_n_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Odrop(T_b),V_m_2),V_xs_2))),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2)))) ),
    file('theBenchmark.p',fact_set__drop__subset__set__drop) ).

fof(fact_drop__all,axiom,
    ! [V_n,V_xs,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n))
     => hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = c_List_Olist_ONil(T_a) ),
    file('theBenchmark.p',fact_drop__all) ).

fof(fact_drop__eq__Nil,axiom,
    ! [V_xs_2,V_n_2,T_b] :
      ( hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2) = c_List_Olist_ONil(T_b)
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),V_n_2)) ),
    file('theBenchmark.p',fact_drop__eq__Nil) ).

fof(fact_drop__append,axiom,
    ! [V_ys,V_xs,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Odrop(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_ys)),
    file('theBenchmark.p',fact_drop__append) ).

fof(fact_append__eq__conv__conj,axiom,
    ! [V_zs_2,V_ys_2,V_xs_2,T_b] :
      ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_zs_2
    <=> ( V_ys_2 = hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),V_zs_2)
        & V_xs_2 = hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),V_zs_2) ) ),
    file('theBenchmark.p',fact_append__eq__conv__conj) ).

fof(fact_drop__Cons,axiom,
    ! [V_xs_2,V_x_2,V_n_2,T_b] : hAPP(hAPP(c_List_Odrop(T_b),V_n_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_Nat_Onat_Onat__case(tc_List_Olist(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Odrop(T_b)),V_xs_2),V_n_2),
    file('theBenchmark.p',fact_drop__Cons) ).

fof(fact_drop__Cons_H,axiom,
    ! [V_xs,V_x,T_a,V_n] :
      ( ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs) )
      & ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) ) ),
    file('theBenchmark.p',fact_drop__Cons_H) ).

fof(fact_nth__drop,axiom,
    ! [V_xs,T_a,V_i,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_i)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
     => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)),V_i) = hAPP(hAPP(c_List_Onth(T_a),V_xs),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_i)) ),
    file('theBenchmark.p',fact_nth__drop) ).

fof(fact_append__eq__append__conv__if,axiom,
    ! [V_ys_092_060_094isub_0622_2,V_ys_092_060_094isub_0621_2,V_xs_092_060_094isub_0622_2,V_xs_092_060_094isub_0621_2,T_b] :
      ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_092_060_094isub_0621_2),V_xs_092_060_094isub_0622_2) = hAPP(hAPP(c_List_Oappend(T_b),V_ys_092_060_094isub_0621_2),V_ys_092_060_094isub_0622_2)
    <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_092_060_094isub_0621_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_092_060_094isub_0621_2)))
         => ( hAPP(hAPP(c_List_Oappend(T_b),hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_092_060_094isub_0621_2)),V_xs_092_060_094isub_0621_2)),V_xs_092_060_094isub_0622_2) = V_ys_092_060_094isub_0622_2
            & hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_092_060_094isub_0621_2)),V_xs_092_060_094isub_0621_2) = V_ys_092_060_094isub_0621_2 ) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_092_060_094isub_0621_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_092_060_094isub_0621_2)))
         => ( V_xs_092_060_094isub_0622_2 = hAPP(hAPP(c_List_Oappend(T_b),hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_092_060_094isub_0621_2)),V_ys_092_060_094isub_0621_2)),V_ys_092_060_094isub_0622_2)
            & V_xs_092_060_094isub_0621_2 = hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_092_060_094isub_0621_2)),V_ys_092_060_094isub_0621_2) ) ) ) ),
    file('theBenchmark.p',fact_append__eq__append__conv__if) ).

fof(fact_nth__drop_H,axiom,
    ! [V_xs,T_a,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
     => hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_i)),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs) ),
    file('theBenchmark.p',fact_nth__drop_H) ).

fof(fact_rotate__simps,axiom,
    ! [V_xs,V_x,T_b,T_a] :
      ( hAPP(c_List_Orotate1(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x),V_xs)) = hAPP(hAPP(c_List_Oappend(T_b),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x),c_List_Olist_ONil(T_b)))
      & hAPP(c_List_Orotate1(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ),
    file('theBenchmark.p',fact_rotate__simps) ).

fof(fact_drop__Cons__number__of,axiom,
    ! [V_xs,V_x,T_a,V_v] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) ) ),
    file('theBenchmark.p',fact_drop__Cons__number__of) ).

fof(fact_take__add,axiom,
    ! [V_xs,T_a,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
     => hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)),hAPP(hAPP(c_List_Otake(T_a),V_j),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs))) ),
    file('theBenchmark.p',fact_take__add) ).

fof(fact_rotate1__length01,axiom,
    ! [V_xs,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
     => hAPP(c_List_Orotate1(T_a),V_xs) = V_xs ),
    file('theBenchmark.p',fact_rotate1__length01) ).

fof(fact_zip__append2,axiom,
    ! [V_zs,V_ys,V_xs,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),hAPP(hAPP(c_List_Oappend(T_b),V_ys),V_zs)) = hAPP(hAPP(c_List_Oappend(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys)),V_xs)),V_ys)),hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys)),V_xs)),V_zs)),
    file('theBenchmark.p',fact_zip__append2) ).

fof(fact_zip__append1,axiom,
    ! [V_zs,V_ys,V_xs,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_zs) = hAPP(hAPP(c_List_Oappend(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_zs))),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_ys),hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_zs))),
    file('theBenchmark.p',fact_zip__append1) ).

fof(fact_id__take__nth__drop,axiom,
    ! [V_xs,T_a,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
     => V_xs = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_i)),V_xs))) ),
    file('theBenchmark.p',fact_id__take__nth__drop) ).

fof(fact_take__hd__drop,axiom,
    ! [V_xs,T_a,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
     => hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs))),c_List_Olist_ONil(T_a))) = hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_n)),V_xs) ),
    file('theBenchmark.p',fact_take__hd__drop) ).

fof(fact_hd__drop__conv__nth,axiom,
    ! [V_n,T_a,V_xs] :
      ( V_xs != c_List_Olist_ONil(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
       => hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) ) ),
    file('theBenchmark.p',fact_hd__drop__conv__nth) ).

fof(fact_hd_Osimps,axiom,
    ! [V_xs,V_x,T_a] : hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x,
    file('theBenchmark.p',fact_hd_Osimps) ).

fof(fact_hd__append,axiom,
    ! [V_ys,T_a,V_xs] :
      ( ( V_xs != c_List_Olist_ONil(T_a)
       => hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(c_List_Ohd(T_a),V_xs) )
      & ( V_xs = c_List_Olist_ONil(T_a)
       => hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(c_List_Ohd(T_a),V_ys) ) ),
    file('theBenchmark.p',fact_hd__append) ).

fof(fact_hd__append2,axiom,
    ! [V_ys,T_a,V_xs] :
      ( V_xs != c_List_Olist_ONil(T_a)
     => hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(c_List_Ohd(T_a),V_xs) ),
    file('theBenchmark.p',fact_hd__append2) ).

fof(fact_hd__in__set,axiom,
    ! [T_b,V_xs_2] :
      ( V_xs_2 != c_List_Olist_ONil(T_b)
     => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_List_Ohd(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_xs_2))) ),
    file('theBenchmark.p',fact_hd__in__set) ).

fof(fact_hd__conv__nth,axiom,
    ! [T_a,V_xs] :
      ( V_xs != c_List_Olist_ONil(T_a)
     => hAPP(c_List_Ohd(T_a),V_xs) = hAPP(hAPP(c_List_Onth(T_a),V_xs),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    file('theBenchmark.p',fact_hd__conv__nth) ).

fof(fact_rotate1__hd__tl,axiom,
    ! [T_a,V_xs] :
      ( V_xs != c_List_Olist_ONil(T_a)
     => hAPP(c_List_Orotate1(T_a),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Otl(T_a),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(c_List_Ohd(T_a),V_xs)),c_List_Olist_ONil(T_a))) ),
    file('theBenchmark.p',fact_rotate1__hd__tl) ).

fof(fact_hd__rotate__conv__nth,axiom,
    ! [V_n,T_a,V_xs] :
      ( V_xs != c_List_Olist_ONil(T_a)
     => hAPP(c_List_Ohd(T_a),hAPP(c_List_Orotate(T_a,V_n),V_xs)) = hAPP(hAPP(c_List_Onth(T_a),V_xs),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) ),
    file('theBenchmark.p',fact_hd__rotate__conv__nth) ).

fof(fact_tl__drop,axiom,
    ! [V_xs,V_n,T_a] : hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs)),
    file('theBenchmark.p',fact_tl__drop) ).

fof(fact_drop__tl,axiom,
    ! [V_xs,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs)) = hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)),
    file('theBenchmark.p',fact_drop__tl) ).

fof(fact_tl_Osimps_I2_J,axiom,
    ! [V_xs,V_x,T_a] : hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_xs,
    file('theBenchmark.p',fact_tl_Osimps_I2_J) ).

fof(fact_distinct__rotate,axiom,
    ! [V_xs_2,V_n_2,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2)))
    <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ),
    file('theBenchmark.p',fact_distinct__rotate) ).

fof(fact_distinct__tl,axiom,
    ! [V_xs,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
     => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Otl(T_a),V_xs))) ),
    file('theBenchmark.p',fact_distinct__tl) ).

fof(fact_rotate0,axiom,
    ! [T_b] : c_List_Orotate(T_b,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(T_b)),
    file('theBenchmark.p',fact_rotate0) ).

fof(fact_rotate__rotate,axiom,
    ! [V_xs,V_n,V_m,T_a] : hAPP(c_List_Orotate(T_a,V_m),hAPP(c_List_Orotate(T_a,V_n),V_xs)) = hAPP(c_List_Orotate(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_xs),
    file('theBenchmark.p',fact_rotate__rotate) ).

fof(fact_rotate__add,axiom,
    ! [V_n_2,V_m_2,T_b] : c_List_Orotate(T_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)) = hAPP(c_Fun_Ocomp(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Orotate(T_b,V_m_2)),c_List_Orotate(T_b,V_n_2)),
    file('theBenchmark.p',fact_rotate__add) ).

fof(fact_length__rotate,axiom,
    ! [V_xs,V_n,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Orotate(T_a,V_n),V_xs)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs),
    file('theBenchmark.p',fact_length__rotate) ).

fof(fact_set__rotate,axiom,
    ! [V_xs_2,V_n_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2),
    file('theBenchmark.p',fact_set__rotate) ).

fof(fact_rotate__is__Nil__conv,axiom,
    ! [V_xs_2,V_n_2,T_b] :
      ( hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2) = c_List_Olist_ONil(T_b)
    <=> V_xs_2 = c_List_Olist_ONil(T_b) ),
    file('theBenchmark.p',fact_rotate__is__Nil__conv) ).

fof(fact_tl_Osimps_I1_J,axiom,
    ! [T_a] : hAPP(c_List_Otl(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a),
    file('theBenchmark.p',fact_tl_Osimps_I1_J) ).

fof(fact_rotate1__rotate__swap,axiom,
    ! [V_xs,V_n,T_a] : hAPP(c_List_Orotate1(T_a),hAPP(c_List_Orotate(T_a,V_n),V_xs)) = hAPP(c_List_Orotate(T_a,V_n),hAPP(c_List_Orotate1(T_a),V_xs)),
    file('theBenchmark.p',fact_rotate1__rotate__swap) ).

fof(fact_rotate__def,axiom,
    ! [V_n_2,T_b] : c_List_Orotate(T_b,V_n_2) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_n_2),c_List_Orotate1(T_b)),
    file('theBenchmark.p',fact_rotate__def) ).

fof(fact_tl__append2,axiom,
    ! [V_ys,T_a,V_xs] :
      ( V_xs != c_List_Olist_ONil(T_a)
     => hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Otl(T_a),V_xs)),V_ys) ),
    file('theBenchmark.p',fact_tl__append2) ).

fof(fact_take__tl,axiom,
    ! [V_xs,V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs)) = hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_n)),V_xs)),
    file('theBenchmark.p',fact_take__tl) ).

fof(fact_rotate__conv__mod,axiom,
    ! [V_xs,V_n,T_a] : hAPP(c_List_Orotate(T_a,V_n),V_xs) = hAPP(c_List_Orotate(T_a,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_xs),
    file('theBenchmark.p',fact_rotate__conv__mod) ).

fof(fact_drop__Suc,axiom,
    ! [V_xs,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_n)),V_xs) = hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs)),
    file('theBenchmark.p',fact_drop__Suc) ).

fof(fact_rotate__Suc,axiom,
    ! [V_xs,V_n,T_a] : hAPP(c_List_Orotate(T_a,hAPP(c_Nat_OSuc,V_n)),V_xs) = hAPP(c_List_Orotate1(T_a),hAPP(c_List_Orotate(T_a,V_n),V_xs)),
    file('theBenchmark.p',fact_rotate__Suc) ).

fof(fact_tl__append,axiom,
    ! [V_ys_2,V_xs_2,T_b] : hAPP(c_List_Otl(T_b),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,hAPP(c_List_Otl(T_b),V_ys_2),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Oappend(T_b)),V_ys_2))),V_xs_2),
    file('theBenchmark.p',fact_tl__append) ).

fof(fact_rotate__id,axiom,
    ! [V_xs,T_a,V_n] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
     => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ),
    file('theBenchmark.p',fact_rotate__id) ).

fof(fact_rotate__length01,axiom,
    ! [V_n,V_xs,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
     => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ),
    file('theBenchmark.p',fact_rotate__length01) ).

fof(fact_length__tl,axiom,
    ! [V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Otl(T_a),V_xs)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    file('theBenchmark.p',fact_length__tl) ).

fof(fact_tl__take,axiom,
    ! [V_xs,V_n,T_a] : hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_List_Otl(T_a),V_xs)),
    file('theBenchmark.p',fact_tl__take) ).

fof(fact_take__Suc,axiom,
    ! [V_n,T_a,V_xs] :
      ( V_xs != c_List_Olist_ONil(T_a)
     => hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_n)),V_xs) = hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(c_List_Ohd(T_a),V_xs)),hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs))) ),
    file('theBenchmark.p',fact_take__Suc) ).

fof(fact_rotate__drop__take,axiom,
    ! [V_xs,V_n,T_a] : hAPP(c_List_Orotate(T_a,V_n),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Odrop(T_a),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_xs)),hAPP(hAPP(c_List_Otake(T_a),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_xs)),
    file('theBenchmark.p',fact_rotate__drop__take) ).

fof(fact_fold1__set,axiom,
    ! [V_xs_2,T_b] :
      ( class_Lattices_Oab__semigroup__idem__mult(T_b)
     => ( V_xs_2 != c_List_Olist_ONil(T_b)
       => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),hAPP(c_List_Ohd(T_b),V_xs_2)),hAPP(c_List_Otl(T_b),V_xs_2)) ) ),
    file('theBenchmark.p',fact_fold1__set) ).

fof(fact_lexord__append__rightI,axiom,
    ! [V_r_2,V_x_2,T_b,V_y_2] :
      ( ? [B_b,B_z] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_b),B_z)
     => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_y_2))),c_List_Olexord(T_b,V_r_2))) ),
    file('theBenchmark.p',fact_lexord__append__rightI) ).

fof(fact_foldl__Nil,axiom,
    ! [V_a_2,V_f_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),c_List_Olist_ONil(T_c)) = V_a_2,
    file('theBenchmark.p',fact_foldl__Nil) ).

fof(fact_start__le__sum,axiom,
    ! [V_ns_2,V_n_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_ns_2))) ),
    file('theBenchmark.p',fact_start__le__sum) ).

fof(fact_foldl__assoc,axiom,
    ! [V_zs_2,V_y_2,V_x_2,T_b] :
      ( class_Groups_Osemigroup__add(T_b)
     => hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_y_2)),V_zs_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_y_2),V_zs_2)) ),
    file('theBenchmark.p',fact_foldl__assoc) ).

fof(fact_foldl__absorb0,axiom,
    ! [V_zs_2,V_x_2,T_b] :
      ( class_Groups_Omonoid__add(T_b)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_zs_2)) = hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_zs_2) ),
    file('theBenchmark.p',fact_foldl__absorb0) ).

fof(fact_foldl__Cons,axiom,
    ! [V_xs_2,V_x_2,V_a_2,V_f_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,hAPP(hAPP(V_f_2,V_a_2),V_x_2)),V_xs_2),
    file('theBenchmark.p',fact_foldl__Cons) ).

fof(fact_foldl__append,axiom,
    ! [V_ys_2,V_xs_2,V_a_2,V_f_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2)) = hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),V_xs_2)),V_ys_2),
    file('theBenchmark.p',fact_foldl__append) ).

fof(fact_listsum__foldl,axiom,
    ! [T_b] :
      ( class_Groups_Omonoid__add(T_b)
     => c_List_Omonoid__add__class_Olistsum(T_b) = c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),c_Groups_Ozero__class_Ozero(T_b)) ),
    file('theBenchmark.p',fact_listsum__foldl) ).

fof(fact_sum__eq__0__conv,axiom,
    ! [V_ns_2,V_m_2] :
      ( hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_ns_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
           => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_sum__eq__0__conv) ).

fof(fact_fun__left__comm__idem_Ofold__set,axiom,
    ! [V_xs_2,V_y_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
     => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_c,T_b,hAPP(c_COMBC(T_b,T_c,T_c),V_f_2),V_y_2),V_xs_2) ),
    file('theBenchmark.p',fact_fun__left__comm__idem_Ofold__set) ).

fof(fact_Sup__set__fold,axiom,
    ! [V_xs_2,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Orderings_Obot__class_Obot(T_b)),V_xs_2) ),
    file('theBenchmark.p',fact_Sup__set__fold) ).

fof(fact_Inf__set__fold,axiom,
    ! [V_xs_2,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Orderings_Otop__class_Otop(T_b)),V_xs_2) ),
    file('theBenchmark.p',fact_Inf__set__fold) ).

fof(fact_Sup__fin__set__fold,axiom,
    ! [V_xs_2,V_x_2,T_b] :
      ( class_Lattices_Olattice(T_b)
     => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_xs_2) ),
    file('theBenchmark.p',fact_Sup__fin__set__fold) ).

fof(fact_Inf__fin__set__fold,axiom,
    ! [V_xs_2,V_x_2,T_b] :
      ( class_Lattices_Olattice(T_b)
     => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_xs_2) ),
    file('theBenchmark.p',fact_Inf__fin__set__fold) ).

fof(fact_Min__fin__set__fold,axiom,
    ! [V_xs_2,V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Orderings_Oord__class_Omin(T_b),V_x_2),V_xs_2) ),
    file('theBenchmark.p',fact_Min__fin__set__fold) ).

fof(fact_Max__fin__set__fold,axiom,
    ! [V_xs_2,V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_x_2),V_xs_2) ),
    file('theBenchmark.p',fact_Max__fin__set__fold) ).

fof(fact_min__max_OInf__fin__set__fold,axiom,
    ! [V_xs_2,V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Orderings_Oord__class_Omin(T_b),V_x_2),V_xs_2) ),
    file('theBenchmark.p',fact_min__max_OInf__fin__set__fold) ).

fof(fact_min__max_OSup__fin__set__fold,axiom,
    ! [V_xs_2,V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_x_2),V_xs_2) ),
    file('theBenchmark.p',fact_min__max_OSup__fin__set__fold) ).

fof(fact_SUPR__set__fold,axiom,
    ! [V_f_2,V_xs_2,T_c,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),hAPP(c_List_Oset(T_c),V_xs_2)),V_f_2) = hAPP(c_List_Ofoldl(T_b,T_c,hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_f_2)),c_Orderings_Obot__class_Obot(T_b)),V_xs_2) ),
    file('theBenchmark.p',fact_SUPR__set__fold) ).

fof(fact_INFI__set__fold,axiom,
    ! [V_f_2,V_xs_2,T_c,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),hAPP(c_List_Oset(T_c),V_xs_2)),V_f_2) = hAPP(c_List_Ofoldl(T_b,T_c,hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_f_2)),c_Orderings_Otop__class_Otop(T_b)),V_xs_2) ),
    file('theBenchmark.p',fact_INFI__set__fold) ).

fof(fact_elem__le__sum,axiom,
    ! [V_ns_2,V_n_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_n_2),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_ns_2))) ),
    file('theBenchmark.p',fact_elem__le__sum) ).

fof(fact_sorted__list__of__set__insert,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => c_List_Olinorder__class_Osorted__list__of__set(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),c_List_Olinorder__class_Osorted__list__of__set(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ),
    file('theBenchmark.p',fact_sorted__list__of__set__insert) ).

fof(fact_lexord__Nil__left,axiom,
    ! [V_r_2,V_y_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_y_2)),c_List_Olexord(T_b,V_r_2)))
    <=> ? [B_a,B_x] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_x) ),
    file('theBenchmark.p',fact_lexord__Nil__left) ).

fof(fact_insort__key_Osimps_I1_J,axiom,
    ! [V_x_2,V_f_2,T_b,T_c] :
      ( class_Orderings_Olinorder(T_c)
     => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),c_List_Olist_ONil(T_b)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ),
    file('theBenchmark.p',fact_insort__key_Osimps_I1_J) ).

fof(fact_insort__key_Osimps_I2_J,axiom,
    ! [V_ys_2,T_c,V_y_2,V_x_2,V_f_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
         => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)) = hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_ys_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
         => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)) = hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)) ) ) ),
    file('theBenchmark.p',fact_insort__key_Osimps_I2_J) ).

fof(fact_set__insort,axiom,
    ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
      ( class_Orderings_Olinorder(T_c)
     => hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)) ),
    file('theBenchmark.p',fact_set__insort) ).

fof(fact_length__insort,axiom,
    ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
      ( class_Orderings_Olinorder(T_c)
     => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),V_xs_2)) = hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)) ),
    file('theBenchmark.p',fact_length__insort) ).

fof(fact_insort__left__comm,axiom,
    ! [V_xs_2,V_y_2,V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_y_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),V_xs_2)) ),
    file('theBenchmark.p',fact_insort__left__comm) ).

fof(fact_fun__left__comm__insort,axiom,
    ! [T_b] :
      ( class_Orderings_Olinorder(T_b)
     => c_Finite__Set_Ofun__left__comm(T_b,tc_List_Olist(T_b),c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b))) ),
    file('theBenchmark.p',fact_fun__left__comm__insort) ).

fof(fact_insort__key__left__comm,axiom,
    ! [V_xs_2,T_c,V_y_2,V_x_2,V_f_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2)
       => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_y_2),V_xs_2)) ) ),
    file('theBenchmark.p',fact_insort__key__left__comm) ).

fof(fact_remove1__insort,axiom,
    ! [V_xs_2,V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => c_List_Oremove1(T_b,V_x_2,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),V_xs_2)) = V_xs_2 ),
    file('theBenchmark.p',fact_remove1__insort) ).

fof(fact_insort__not__Nil,axiom,
    ! [V_xs_2,V_a_2,V_f_2,T_b,T_c] :
      ( class_Orderings_Olinorder(T_c)
     => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_a_2),V_xs_2) != c_List_Olist_ONil(T_b) ),
    file('theBenchmark.p',fact_insort__not__Nil) ).

fof(fact_distinct__insort,axiom,
    ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
      ( class_Orderings_Olinorder(T_c)
     => ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),V_xs_2)))
      <=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
          & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ),
    file('theBenchmark.p',fact_distinct__insort) ).

fof(fact_insort__insert__insort__key,axiom,
    ! [V_xs_2,T_c,V_x_2,V_f_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_List_Oset(T_c),V_xs_2))))
       => c_List_Olinorder__class_Oinsort__insert__key(T_c,T_b,V_f_2,V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_xs_2) ) ),
    file('theBenchmark.p',fact_insort__insert__insort__key) ).

fof(fact_insort__insert__insort,axiom,
    ! [V_xs_2,V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
       => c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),V_xs_2) ) ),
    file('theBenchmark.p',fact_insort__insert__insort) ).

fof(fact_distinct__insort__insert,axiom,
    ! [V_x_2,V_f_2,V_xs_2,T_b,T_c] :
      ( class_Orderings_Olinorder(T_c)
     => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
       => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Oinsort__insert__key(T_b,T_c,V_f_2,V_x_2,V_xs_2))) ) ),
    file('theBenchmark.p',fact_distinct__insort__insert) ).

fof(fact_insort__insert__triv,axiom,
    ! [V_xs_2,V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
       => c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2) = V_xs_2 ) ),
    file('theBenchmark.p',fact_insort__insert__triv) ).

fof(fact_set__insort__insert,axiom,
    ! [V_xs_2,V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => hAPP(c_List_Oset(T_b),c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)) ),
    file('theBenchmark.p',fact_set__insort__insert) ).

fof(fact_insort__insert__key__triv,axiom,
    ! [V_xs_2,T_c,V_x_2,V_f_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_List_Oset(T_c),V_xs_2))))
       => c_List_Olinorder__class_Oinsort__insert__key(T_c,T_b,V_f_2,V_x_2,V_xs_2) = V_xs_2 ) ),
    file('theBenchmark.p',fact_insort__insert__key__triv) ).

fof(fact_last__list__update,axiom,
    ! [V_x,V_k,T_a,V_xs] :
      ( V_xs != c_List_Olist_ONil(T_a)
     => ( ( V_k != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
         => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = c_List_Olast(T_a,V_xs) )
        & ( V_k = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
         => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = V_x ) ) ),
    file('theBenchmark.p',fact_last__list__update) ).

fof(fact_last__conv__nth,axiom,
    ! [T_a,V_xs] :
      ( V_xs != c_List_Olist_ONil(T_a)
     => c_List_Olast(T_a,V_xs) = hAPP(hAPP(c_List_Onth(T_a),V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    file('theBenchmark.p',fact_last__conv__nth) ).

fof(fact_last__ConsL,axiom,
    ! [V_x,T_a,V_xs] :
      ( V_xs = c_List_Olist_ONil(T_a)
     => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ),
    file('theBenchmark.p',fact_last__ConsL) ).

fof(fact_last__ConsR,axiom,
    ! [V_x,T_a,V_xs] :
      ( V_xs != c_List_Olist_ONil(T_a)
     => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ),
    file('theBenchmark.p',fact_last__ConsR) ).

fof(fact_last_Osimps,axiom,
    ! [V_x,T_a,V_xs] :
      ( ( V_xs != c_List_Olist_ONil(T_a)
       => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) )
      & ( V_xs = c_List_Olist_ONil(T_a)
       => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ) ),
    file('theBenchmark.p',fact_last_Osimps) ).

fof(fact_last__appendL,axiom,
    ! [V_xs,T_a,V_ys] :
      ( V_ys = c_List_Olist_ONil(T_a)
     => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ),
    file('theBenchmark.p',fact_last__appendL) ).

fof(fact_last__appendR,axiom,
    ! [V_xs,T_a,V_ys] :
      ( V_ys != c_List_Olist_ONil(T_a)
     => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ),
    file('theBenchmark.p',fact_last__appendR) ).

fof(fact_last__append,axiom,
    ! [V_xs,T_a,V_ys] :
      ( ( V_ys != c_List_Olist_ONil(T_a)
       => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) )
      & ( V_ys = c_List_Olist_ONil(T_a)
       => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ) ),
    file('theBenchmark.p',fact_last__append) ).

fof(fact_last__in__set,axiom,
    ! [T_b,V_as_2] :
      ( V_as_2 != c_List_Olist_ONil(T_b)
     => hBOOL(hAPP(hAPP(c_member(T_b),c_List_Olast(T_b,V_as_2)),hAPP(c_List_Oset(T_b),V_as_2))) ),
    file('theBenchmark.p',fact_last__in__set) ).

fof(fact_last__snoc,axiom,
    ! [V_x,V_xs,T_a] : c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a)))) = V_x,
    file('theBenchmark.p',fact_last__snoc) ).

fof(fact_last__drop,axiom,
    ! [V_xs,T_a,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
     => c_List_Olast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = c_List_Olast(T_a,V_xs) ),
    file('theBenchmark.p',fact_last__drop) ).

fof(fact_snoc__eq__iff__butlast,axiom,
    ! [V_ys_2,V_x_2,V_xs_2,T_b] :
      ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))) = V_ys_2
    <=> ( c_List_Olast(T_b,V_ys_2) = V_x_2
        & c_List_Obutlast(T_b,V_ys_2) = V_xs_2
        & V_ys_2 != c_List_Olist_ONil(T_b) ) ),
    file('theBenchmark.p',fact_snoc__eq__iff__butlast) ).

fof(fact_append__butlast__last__id,axiom,
    ! [T_a,V_xs] :
      ( V_xs != c_List_Olist_ONil(T_a)
     => hAPP(hAPP(c_List_Oappend(T_a),c_List_Obutlast(T_a,V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),c_List_Olast(T_a,V_xs)),c_List_Olist_ONil(T_a))) = V_xs ),
    file('theBenchmark.p',fact_append__butlast__last__id) ).

fof(fact_lists_Osimps,axiom,
    ! [V_A_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_a_2),c_List_Olists(T_b,V_A_2)))
    <=> ( ? [B_a,B_l] :
            ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_l),c_List_Olists(T_b,V_A_2)))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
            & V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_l) )
        | V_a_2 = c_List_Olist_ONil(T_b) ) ),
    file('theBenchmark.p',fact_lists_Osimps) ).

fof(fact_select__weigth__select,axiom,
    ! [T_b,V_xs_2] :
      ( V_xs_2 != c_List_Olist_ONil(T_b)
     => c_Random_Oselect__weight(T_b,hAPP(hAPP(c_List_Omap(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,T_b)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_b),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),V_xs_2)) = c_Random_Oselect(T_b,V_xs_2) ),
    file('theBenchmark.p',fact_select__weigth__select) ).

fof(fact_inj__mapI,axiom,
    ! [V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
     => c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_c),hAPP(c_List_Omap(T_b,T_c),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))) ),
    file('theBenchmark.p',fact_inj__mapI) ).

fof(fact_last__map,axiom,
    ! [V_f_2,T_c,T_b,V_xs_2] :
      ( V_xs_2 != c_List_Olist_ONil(T_b)
     => c_List_Olast(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) = hAPP(V_f_2,c_List_Olast(T_b,V_xs_2)) ),
    file('theBenchmark.p',fact_last__map) ).

fof(fact_foldl__map,axiom,
    ! [V_xs_2,V_f_2,T_d,V_a_2,V_g_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_g_2,V_a_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_d,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_d,T_c),tc_fun(T_d,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_b),tc_fun(tc_fun(T_d,T_c),tc_fun(T_d,T_b)),T_b),c_COMBB(T_c,T_b,T_d)),V_g_2)),V_f_2),V_a_2),V_xs_2),
    file('theBenchmark.p',fact_foldl__map) ).

fof(fact_map__tl,axiom,
    ! [V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Otl(T_c),V_xs_2)) = hAPP(c_List_Otl(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)),
    file('theBenchmark.p',fact_map__tl) ).

fof(fact_rotate__map,axiom,
    ! [V_xs_2,V_f_2,T_c,V_n_2,T_b] : hAPP(c_List_Orotate(T_b,V_n_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Orotate(T_c,V_n_2),V_xs_2)),
    file('theBenchmark.p',fact_rotate__map) ).

fof(fact_zip__same__conv__map,axiom,
    ! [V_xs_2,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,tc_prod(T_b,T_b)),hAPP(hAPP(c_COMBS(T_b,T_b,tc_prod(T_b,T_b)),c_Product__Type_OPair(T_b,T_b)),c_COMBI(T_b))),V_xs_2),
    file('theBenchmark.p',fact_zip__same__conv__map) ).

fof(fact_zip__map__map,axiom,
    ! [V_ys_2,V_g_2,T_e,V_xs_2,V_f_2,T_d,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Omap(T_d,T_b),V_f_2),V_xs_2)),hAPP(hAPP(c_List_Omap(T_e,T_c),V_g_2),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_d,T_e),tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_e,T_c),tc_fun(T_e,tc_prod(T_b,T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(tc_fun(T_e,T_c),tc_fun(T_e,tc_prod(T_b,T_c))),T_d),c_COMBB(T_c,tc_prod(T_b,T_c),T_e)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_prod(T_b,T_c)),T_d),c_Product__Type_OPair(T_b,T_c)),V_f_2))),V_g_2))),hAPP(hAPP(c_List_Ozip(T_d,T_e),V_xs_2),V_ys_2)),
    file('theBenchmark.p',fact_zip__map__map) ).

fof(fact_zip__map1,axiom,
    ! [V_ys_2,V_xs_2,V_f_2,T_d,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Omap(T_d,T_b),V_f_2),V_xs_2)),V_ys_2) = hAPP(hAPP(c_List_Omap(tc_prod(T_d,T_c),tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_c,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_prod(T_b,T_c)),T_d),c_Product__Type_OPair(T_b,T_c)),V_f_2))),hAPP(hAPP(c_List_Ozip(T_d,T_c),V_xs_2),V_ys_2)),
    file('theBenchmark.p',fact_zip__map1) ).

fof(fact_map__zip__map,axiom,
    ! [V_ys_2,V_xs_2,V_g_2,T_e,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_d),T_b),V_f_2),hAPP(hAPP(c_List_Ozip(T_c,T_d),hAPP(hAPP(c_List_Omap(T_e,T_c),V_g_2),V_xs_2)),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_e,T_d),T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_e,T_d,T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,T_b),T_e),hAPP(c_COMBB(tc_prod(T_c,T_d),T_b,T_d),V_f_2)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_d,tc_prod(T_c,T_d)),T_e),c_Product__Type_OPair(T_c,T_d)),V_g_2)))),hAPP(hAPP(c_List_Ozip(T_e,T_d),V_xs_2),V_ys_2)),
    file('theBenchmark.p',fact_map__zip__map) ).

fof(fact_map__zip__map2,axiom,
    ! [V_ys_2,V_g_2,T_e,V_xs_2,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_d),T_b),V_f_2),hAPP(hAPP(c_List_Ozip(T_c,T_d),V_xs_2),hAPP(hAPP(c_List_Omap(T_e,T_d),V_g_2),V_ys_2))) = hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_e),T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_e,T_b),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_prod(T_c,T_d)),tc_fun(T_e,T_b),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),T_b,T_e),V_f_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_e,T_d),tc_fun(T_e,tc_prod(T_c,T_d))),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(tc_fun(T_e,T_d),tc_fun(T_e,tc_prod(T_c,T_d))),T_c),c_COMBB(T_d,tc_prod(T_c,T_d),T_e)),c_Product__Type_OPair(T_c,T_d))),V_g_2)))),hAPP(hAPP(c_List_Ozip(T_c,T_e),V_xs_2),V_ys_2)),
    file('theBenchmark.p',fact_map__zip__map2) ).

fof(fact_zip__map2,axiom,
    ! [V_ys_2,V_f_2,T_d,V_xs_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_d),tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_d,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_d,T_c),tc_fun(T_d,tc_prod(T_b,T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(tc_fun(T_d,T_c),tc_fun(T_d,tc_prod(T_b,T_c))),T_b),c_COMBB(T_c,tc_prod(T_b,T_c),T_d)),c_Product__Type_OPair(T_b,T_c))),V_f_2))),hAPP(hAPP(c_List_Ozip(T_b,T_d),V_xs_2),V_ys_2)),
    file('theBenchmark.p',fact_zip__map2) ).

fof(fact_Nil__is__map__conv,axiom,
    ! [V_xs_2,V_f_2,T_c,T_b] :
      ( c_List_Olist_ONil(T_b) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)
    <=> V_xs_2 = c_List_Olist_ONil(T_c) ),
    file('theBenchmark.p',fact_Nil__is__map__conv) ).

fof(fact_map_Osimps_I1_J,axiom,
    ! [V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Olist_ONil(T_c)) = c_List_Olist_ONil(T_b),
    file('theBenchmark.p',fact_map_Osimps_I1_J) ).

fof(fact_map__is__Nil__conv,axiom,
    ! [V_xs_2,V_f_2,T_b,T_c] :
      ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = c_List_Olist_ONil(T_b)
    <=> V_xs_2 = c_List_Olist_ONil(T_c) ),
    file('theBenchmark.p',fact_map__is__Nil__conv) ).

fof(fact_map__update,axiom,
    ! [V_y_2,V_k_2,V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Olist__update(T_c,V_xs_2),V_k_2),V_y_2)) = hAPP(hAPP(c_List_Olist__update(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)),V_k_2),hAPP(V_f_2,V_y_2)),
    file('theBenchmark.p',fact_map__update) ).

fof(fact_map__eq__conv,axiom,
    ! [V_g_2,V_xs_2,V_f_2,T_b,T_c] :
      ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_xs_2)
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2)))
         => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ),
    file('theBenchmark.p',fact_map__eq__conv) ).

fof(fact_map__eq__imp__length__eq,axiom,
    ! [V_ys_2,V_g_2,T_d,V_xs_2,V_f_2,T_b,T_c] :
      ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_d,T_b),V_g_2),V_ys_2)
     => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_d)),V_ys_2) ),
    file('theBenchmark.p',fact_map__eq__imp__length__eq) ).

fof(fact_length__map,axiom,
    ! [V_xs_2,V_f_2,T_c,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2),
    file('theBenchmark.p',fact_length__map) ).

fof(fact_listsum__subtractf,axiom,
    ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
      ( class_Groups_Oab__group__add(T_b)
     => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Ominus__class_Ominus(T_b)),V_f_2)),V_g_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_xs_2))) ),
    file('theBenchmark.p',fact_listsum__subtractf) ).

fof(fact_listsum__0,axiom,
    ! [V_xs_2,T_c,T_b] :
      ( class_Groups_Omonoid__add(T_b)
     => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(c_COMBK(T_b,T_c),c_Groups_Ozero__class_Ozero(T_b))),V_xs_2)) = c_Groups_Ozero__class_Ozero(T_b) ),
    file('theBenchmark.p',fact_listsum__0) ).

fof(fact_listsum__const__mult,axiom,
    ! [V_xs_2,V_f_2,V_c_2,T_c,T_b] :
      ( class_Rings_Osemiring__0(T_b)
     => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2)),V_f_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) ),
    file('theBenchmark.p',fact_listsum__const__mult) ).

fof(fact_listsum__mult__const,axiom,
    ! [V_xs_2,V_c_2,V_f_2,T_c,T_b] :
      ( class_Rings_Osemiring__0(T_b)
     => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Otimes__class_Otimes(T_b)),V_f_2)),V_c_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))),V_c_2) ),
    file('theBenchmark.p',fact_listsum__mult__const) ).

fof(fact_listsum__addf,axiom,
    ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Oplus__class_Oplus(T_b)),V_f_2)),V_g_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_xs_2))) ),
    file('theBenchmark.p',fact_listsum__addf) ).

fof(fact_inj__map__eq__map,axiom,
    ! [V_ys_2,V_xs_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
     => ( hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2)
      <=> V_xs_2 = V_ys_2 ) ),
    file('theBenchmark.p',fact_inj__map__eq__map) ).

fof(fact_map__injective,axiom,
    ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
      ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_ys_2)
     => ( c_Fun_Oinj__on(T_c,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
       => V_xs_2 = V_ys_2 ) ),
    file('theBenchmark.p',fact_map__injective) ).

fof(fact_map__ident,axiom,
    ! [V_xs_2,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_b),c_COMBI(T_b)),V_xs_2) = V_xs_2,
    file('theBenchmark.p',fact_map__ident) ).

fof(fact_take__map,axiom,
    ! [V_xs_2,V_f_2,T_c,V_n_2,T_b] : hAPP(hAPP(c_List_Otake(T_b),V_n_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Otake(T_c),V_n_2),V_xs_2)),
    file('theBenchmark.p',fact_take__map) ).

fof(fact_map__butlast,axiom,
    ! [V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Obutlast(T_c,V_xs_2)) = c_List_Obutlast(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)),
    file('theBenchmark.p',fact_map__butlast) ).

fof(fact_set__map,axiom,
    ! [V_xs_2,V_f_2,T_c,T_b] : hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_List_Oset(T_c),V_xs_2)),
    file('theBenchmark.p',fact_set__map) ).

fof(fact_map_Osimps_I2_J,axiom,
    ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),hAPP(V_f_2,V_x_2)),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)),
    file('theBenchmark.p',fact_map_Osimps_I2_J) ).

fof(fact_map__append,axiom,
    ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_ys_2)),
    file('theBenchmark.p',fact_map__append) ).

fof(fact_hd__map,axiom,
    ! [V_f_2,T_c,T_b,V_xs_2] :
      ( V_xs_2 != c_List_Olist_ONil(T_b)
     => hAPP(c_List_Ohd(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) = hAPP(V_f_2,hAPP(c_List_Ohd(T_b),V_xs_2)) ),
    file('theBenchmark.p',fact_hd__map) ).

fof(fact_drop__map,axiom,
    ! [V_xs_2,V_f_2,T_c,V_n_2,T_b] : hAPP(hAPP(c_List_Odrop(T_b),V_n_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Odrop(T_c),V_n_2),V_xs_2)),
    file('theBenchmark.p',fact_drop__map) ).

fof(fact_List_Omap_Oidentity,axiom,
    ! [T_b] : hAPP(c_List_Omap(T_b,T_b),c_COMBI(T_b)) = c_Fun_Oid(tc_List_Olist(T_b)),
    file('theBenchmark.p',fact_List_Omap_Oidentity) ).

fof(fact_List_Omap_Oid,axiom,
    ! [T_b] : hAPP(c_List_Omap(T_b,T_b),c_Fun_Oid(T_b)) = c_Fun_Oid(tc_List_Olist(T_b)),
    file('theBenchmark.p',fact_List_Omap_Oid) ).

fof(fact_map__map,axiom,
    ! [V_xs_2,V_g_2,T_d,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_g_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_d,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2)),V_xs_2),
    file('theBenchmark.p',fact_map__map) ).

fof(fact_List_Omap_Ocompositionality,axiom,
    ! [V_list_2,V_g_2,T_d,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_g_2),V_list_2)) = hAPP(hAPP(c_List_Omap(T_d,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2)),V_list_2),
    file('theBenchmark.p',fact_List_Omap_Ocompositionality) ).

fof(fact_map__comp__map,axiom,
    ! [V_g_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(tc_List_Olist(T_d),tc_List_Olist(T_c),tc_List_Olist(T_b),hAPP(c_List_Omap(T_d,T_c),V_f_2)),hAPP(c_List_Omap(T_b,T_d),V_g_2)) = hAPP(c_List_Omap(T_b,T_c),hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),V_g_2)),
    file('theBenchmark.p',fact_map__comp__map) ).

fof(fact_List_Omap_Ocomp,axiom,
    ! [V_g_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(tc_List_Olist(T_d),tc_List_Olist(T_c),tc_List_Olist(T_b),hAPP(c_List_Omap(T_d,T_c),V_f_2)),hAPP(c_List_Omap(T_b,T_d),V_g_2)) = hAPP(c_List_Omap(T_b,T_c),hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),V_g_2)),
    file('theBenchmark.p',fact_List_Omap_Ocomp) ).

fof(fact_list__size__map,axiom,
    ! [V_xs_2,V_g_2,T_c,V_f_2,T_b] : c_List_Olist_Olist__size(T_b,V_f_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_xs_2)) = c_List_Olist_Olist__size(T_c,hAPP(c_Fun_Ocomp(T_b,tc_Nat_Onat,T_c,V_f_2),V_g_2),V_xs_2),
    file('theBenchmark.p',fact_list__size__map) ).

fof(fact_map__inj__on,axiom,
    ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
      ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_ys_2)
     => ( c_Fun_Oinj__on(T_c,T_b,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_List_Oset(T_c),V_xs_2)),hAPP(c_List_Oset(T_c),V_ys_2)))
       => V_xs_2 = V_ys_2 ) ),
    file('theBenchmark.p',fact_map__inj__on) ).

fof(fact_inj__on__map__eq__map,axiom,
    ! [V_ys_2,V_xs_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_ys_2)))
     => ( hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2)
      <=> V_xs_2 = V_ys_2 ) ),
    file('theBenchmark.p',fact_inj__on__map__eq__map) ).

fof(fact_nth__map,axiom,
    ! [V_f_2,T_c,V_xs_2,T_b,V_n_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
     => hAPP(hAPP(c_List_Onth(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)),V_n_2) = hAPP(V_f_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2)) ),
    file('theBenchmark.p',fact_nth__map) ).

fof(fact_map__fun__upd,axiom,
    ! [V_v_2,V_f_2,T_c,V_xs_2,V_y_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2)))
     => hAPP(hAPP(c_List_Omap(T_b,T_c),c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_y_2,V_v_2)),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2) ),
    file('theBenchmark.p',fact_map__fun__upd) ).

fof(fact_distinct__map,axiom,
    ! [V_xs_2,V_f_2,T_c,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)))
    <=> ( c_Fun_Oinj__on(T_c,T_b,V_f_2,hAPP(c_List_Oset(T_c),V_xs_2))
        & hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2)) ) ),
    file('theBenchmark.p',fact_distinct__map) ).

fof(fact_listsum__abs,axiom,
    ! [V_xs_2,T_b] :
      ( class_Groups_Oordered__ab__group__add__abs(T_b)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_b,T_b),c_Groups_Oabs__class_Oabs(T_b)),V_xs_2)))) ),
    file('theBenchmark.p',fact_listsum__abs) ).

fof(fact_uminus__listsum__map,axiom,
    ! [V_xs_2,V_f_2,T_c,T_b] :
      ( class_Groups_Oab__group__add(T_b)
     => hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(c_Fun_Ocomp(T_b,T_b,T_c,c_Groups_Ouminus__class_Ouminus(T_b)),V_f_2)),V_xs_2)) ),
    file('theBenchmark.p',fact_uminus__listsum__map) ).

fof(fact_inj__on__mapI,axiom,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),c_List_Oset(T_b)),V_A_2)))
     => c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_c),hAPP(c_List_Omap(T_b,T_c),V_f_2),V_A_2) ),
    file('theBenchmark.p',fact_inj__on__mapI) ).

fof(fact_inj__mapD,axiom,
    ! [V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_c),hAPP(c_List_Omap(T_b,T_c),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))
     => c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
    file('theBenchmark.p',fact_inj__mapD) ).

fof(fact_inj__map,axiom,
    ! [V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_c),hAPP(c_List_Omap(T_b,T_c),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))
    <=> c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
    file('theBenchmark.p',fact_inj__map) ).

fof(fact_listsum__distinct__conv__setsum__set,axiom,
    ! [V_f_2,V_xs_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__add(T_c)
     => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
       => hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(c_List_Oset(T_b),V_xs_2)) ) ),
    file('theBenchmark.p',fact_listsum__distinct__conv__setsum__set) ).

fof(fact_listsum__triv,axiom,
    ! [V_xs_2,V_r_2,T_c,T_b] :
      ( class_Rings_Osemiring__1(T_b)
     => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(c_COMBK(T_b,T_c),V_r_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2))),V_r_2) ),
    file('theBenchmark.p',fact_listsum__triv) ).

fof(fact_listsum__map__remove1,axiom,
    ! [V_f_2,V_xs_2,V_x_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__add(T_c)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
       => hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_f_2,V_x_2)),hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),c_List_Oremove1(T_b,V_x_2,V_xs_2)))) ) ),
    file('theBenchmark.p',fact_listsum__map__remove1) ).

fof(fact_Nitpick_Osetsum_H__def,axiom,
    ! [V_f_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__add(T_c)
     => ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
         => c_Nitpick_Osetsum_H(T_b,T_c,V_f_2,V_A_2) = c_Groups_Ozero__class_Ozero(T_c) )
        & ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
         => c_Nitpick_Osetsum_H(T_b,T_c,V_f_2,V_A_2) = hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),c_Hilbert__Choice_OEps(tc_List_Olist(T_b),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_List_Oset(T_b))),V_A_2))),c_List_Odistinct(T_b))))) ) ) ),
    file('theBenchmark.p',fact_Nitpick_Osetsum_H__def) ).

fof(fact_pick__same,axiom,
    ! [V_xs_2,T_b,V_l_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_l_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
     => hAPP(c_Random_Opick(T_b,hAPP(hAPP(c_List_Omap(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,T_b)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_b),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),V_xs_2)),hAPP(c_Code__Numeral_Oof__nat,V_l_2)) = hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_l_2) ),
    file('theBenchmark.p',fact_pick__same) ).

fof(fact_zero__code__numeral__def,axiom,
    c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('theBenchmark.p',fact_zero__code__numeral__def) ).

fof(fact_Code__Numeral_Oof__nat__inject,axiom,
    ! [V_m_2,V_n_2] :
      ( hAPP(c_Code__Numeral_Oof__nat,V_n_2) = hAPP(c_Code__Numeral_Oof__nat,V_m_2)
    <=> V_n_2 = V_m_2 ),
    file('theBenchmark.p',fact_Code__Numeral_Oof__nat__inject) ).

fof(fact_times__code__numeral__code,axiom,
    ! [V_m,V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,V_n)),hAPP(c_Code__Numeral_Oof__nat,V_m)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m)),
    file('theBenchmark.p',fact_times__code__numeral__code) ).

fof(fact_Code__Numeral_Oof__nat__code,axiom,
    c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',fact_Code__Numeral_Oof__nat__code) ).

fof(fact_one__code__numeral__def,axiom,
    c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    file('theBenchmark.p',fact_one__code__numeral__def) ).

fof(fact_less__code__numeral__code,axiom,
    ! [V_m_2,V_n_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,V_n_2)),hAPP(c_Code__Numeral_Oof__nat,V_m_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ),
    file('theBenchmark.p',fact_less__code__numeral__code) ).

fof(fact_code__numeral_Oof__nat__inject,axiom,
    ! [V_y_2,V_x_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
     => ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
       => ( hAPP(c_Code__Numeral_Oof__nat,V_x_2) = hAPP(c_Code__Numeral_Oof__nat,V_y_2)
        <=> V_x_2 = V_y_2 ) ) ),
    file('theBenchmark.p',fact_code__numeral_Oof__nat__inject) ).

fof(fact_map__fst__zip,axiom,
    ! [V_ys_2,T_c,V_xs_2,T_b] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)
     => hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) = V_xs_2 ),
    file('theBenchmark.p',fact_map__fst__zip) ).

fof(fact_map__snd__zip,axiom,
    ! [V_ys_2,T_c,V_xs_2,T_b] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)
     => hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_c),c_Product__Type_Osnd(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) = V_ys_2 ),
    file('theBenchmark.p',fact_map__snd__zip) ).

fof(fact_number__of__code__numeral__def,axiom,
    c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral,tc_Int_Oint,c_Code__Numeral_Oof__nat),c_Int_Onat),
    file('theBenchmark.p',fact_number__of__code__numeral__def) ).

fof(fact_zip__map__fst__snd,axiom,
    ! [V_zs_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_zs_2)),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_c),c_Product__Type_Osnd(T_b,T_c)),V_zs_2)) = V_zs_2,
    file('theBenchmark.p',fact_zip__map__fst__snd) ).

fof(fact_plus__code__numeral__code,axiom,
    ! [V_m,V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,V_n)),hAPP(c_Code__Numeral_Oof__nat,V_m)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),
    file('theBenchmark.p',fact_plus__code__numeral__code) ).

fof(fact_less__eq__code__numeral__code,axiom,
    ! [V_m_2,V_n_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,V_n_2)),hAPP(c_Code__Numeral_Oof__nat,V_m_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ),
    file('theBenchmark.p',fact_less__eq__code__numeral__code) ).

fof(fact_subtract__code__numeral__code,axiom,
    ! [V_m,V_n] : hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,hAPP(c_Code__Numeral_Oof__nat,V_n)),hAPP(c_Code__Numeral_Oof__nat,V_m)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m)),
    file('theBenchmark.p',fact_subtract__code__numeral__code) ).

fof(fact_pick__member,axiom,
    ! [V_xs_2,T_b,V_i_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i_2),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2))))
     => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Random_Opick(T_b,V_xs_2),V_i_2)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),T_b),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2)))) ),
    file('theBenchmark.p',fact_pick__member) ).

fof(fact_zip__eq__conv,axiom,
    ! [V_zs_2,V_ys_2,T_c,V_xs_2,T_b] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)
     => ( hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2) = V_zs_2
      <=> ( hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_c),c_Product__Type_Osnd(T_b,T_c)),V_zs_2) = V_ys_2
          & hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_zs_2) = V_xs_2 ) ) ),
    file('theBenchmark.p',fact_zip__eq__conv) ).

fof(fact_list__size__conv__listsum,axiom,
    ! [V_xs_2,V_f_2,T_b] : c_List_Olist_Olist__size(T_b,V_f_2,V_xs_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(T_b,tc_Nat_Onat),V_f_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),
    file('theBenchmark.p',fact_list__size__conv__listsum) ).

fof(fact_code__numeral__not__eq__zero,axiom,
    ! [V_i_2] :
      ( V_i_2 != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),V_i_2)) ),
    file('theBenchmark.p',fact_code__numeral__not__eq__zero) ).

fof(fact_setsum__set__upto__conv__listsum__int,axiom,
    ! [V_j_2,V_i_2,V_f_2,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),V_f_2),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_i_2,V_j_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(tc_Int_Oint,T_b),V_f_2),c_List_Oupto(V_i_2,V_j_2))) ),
    file('theBenchmark.p',fact_setsum__set__upto__conv__listsum__int) ).

fof(fact_interv__listsum__conv__setsum__set__int,axiom,
    ! [V_l_2,V_k_2,V_f_2,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(tc_Int_Oint,T_b),V_f_2),c_List_Oupto(V_k_2,V_l_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),V_f_2),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_k_2,V_l_2))) ),
    file('theBenchmark.p',fact_interv__listsum__conv__setsum__set__int) ).

fof(fact_select__weight__member,axiom,
    ! [V_s_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2))))
     => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Product__Type_Ofst(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect__weight(T_b,V_xs_2),V_s_2))),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),T_b),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2)))) ),
    file('theBenchmark.p',fact_select__weight__member) ).

fof(fact_select__weight__def,axiom,
    ! [V_xs_2,T_b] : c_Random_Oselect__weight(T_b,V_xs_2) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Orange(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Opick(T_b,V_xs_2))),
    file('theBenchmark.p',fact_select__weight__def) ).

fof(fact_select__def,axiom,
    ! [V_xs_2,T_b] : c_Random_Oselect(T_b,V_xs_2) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Orange(hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Code__Numeral_Ocode__numeral),hAPP(c_List_Onth(T_b),V_xs_2)),c_Code__Numeral_Onat__of))),
    file('theBenchmark.p',fact_select__def) ).

fof(fact_listsum__mono,axiom,
    ! [V_g_2,V_f_2,V_xs_2,T_b,T_c] :
      ( ( class_Groups_Oordered__ab__semigroup__add(T_c)
        & class_Groups_Omonoid__add(T_c) )
     => ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_g_2),V_xs_2)))) ) ),
    file('theBenchmark.p',fact_listsum__mono) ).

fof(fact_nat__of__of__nat,axiom,
    ! [V_n] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_n)) = V_n,
    file('theBenchmark.p',fact_nat__of__of__nat) ).

fof(fact_of__nat__nat__of,axiom,
    ! [V_k] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_k)) = V_k,
    file('theBenchmark.p',fact_of__nat__nat__of) ).

fof(fact_nat__of__inverse,axiom,
    ! [V_x] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_x)) = V_x,
    file('theBenchmark.p',fact_nat__of__inverse) ).

fof(fact_times__code__numeral__def,axiom,
    ! [V_m,V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),V_n),V_m) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n)),hAPP(c_Code__Numeral_Onat__of,V_m))),
    file('theBenchmark.p',fact_times__code__numeral__def) ).

fof(fact_code__numeral_Onat__of__inject,axiom,
    ! [V_y_2,V_x_2] :
      ( hAPP(c_Code__Numeral_Onat__of,V_x_2) = hAPP(c_Code__Numeral_Onat__of,V_y_2)
    <=> V_x_2 = V_y_2 ),
    file('theBenchmark.p',fact_code__numeral_Onat__of__inject) ).

fof(fact_Code__Numeral_Onat__of__inject,axiom,
    ! [V_l_2,V_k_2] :
      ( hAPP(c_Code__Numeral_Onat__of,V_k_2) = hAPP(c_Code__Numeral_Onat__of,V_l_2)
    <=> V_k_2 = V_l_2 ),
    file('theBenchmark.p',fact_Code__Numeral_Onat__of__inject) ).

fof(fact_type__definition__code__numeral,axiom,
    c_Typedef_Otype__definition(tc_Code__Numeral_Ocode__numeral,tc_Nat_Onat,c_Code__Numeral_Onat__of,c_Code__Numeral_Oof__nat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    file('theBenchmark.p',fact_type__definition__code__numeral) ).

fof(fact_less__code__numeral__def,axiom,
    ! [V_m_2,V_n_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n_2)),hAPP(c_Code__Numeral_Onat__of,V_m_2))) ),
    file('theBenchmark.p',fact_less__code__numeral__def) ).

fof(fact_nat__of,axiom,
    ! [V_x_2] : hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_x_2)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    file('theBenchmark.p',fact_nat__of) ).

fof(fact_nat__of__number,axiom,
    ! [V_k] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),V_k)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_k),
    file('theBenchmark.p',fact_nat__of__number) ).

fof(fact_int__of__def,axiom,
    c_Code__Numeral_Oint__of = hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Int_Oint,tc_Code__Numeral_Ocode__numeral,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_Code__Numeral_Onat__of),
    file('theBenchmark.p',fact_int__of__def) ).

fof(fact_less__eq__code__numeral__def,axiom,
    ! [V_m_2,V_n_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n_2)),hAPP(c_Code__Numeral_Onat__of,V_m_2))) ),
    file('theBenchmark.p',fact_less__eq__code__numeral__def) ).

fof(fact_nat__of__code,axiom,
    ! [V_i] : hAPP(c_Code__Numeral_Onat__of,V_i) = c_Code__Numeral_Onat__of__aux(V_i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('theBenchmark.p',fact_nat__of__code) ).

fof(fact_nat__of__aux__def,axiom,
    ! [V_n,V_i] : c_Code__Numeral_Onat__of__aux(V_i,V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_i)),V_n),
    file('theBenchmark.p',fact_nat__of__aux__def) ).

fof(fact_Suc__code__numeral__def,axiom,
    ! [V_k] : c_Code__Numeral_OSuc__code__numeral(V_k) = hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,V_k))),
    file('theBenchmark.p',fact_Suc__code__numeral__def) ).

fof(fact_minus__code__numeral__def,axiom,
    ! [V_m,V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_n),V_m) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n)),hAPP(c_Code__Numeral_Onat__of,V_m))),
    file('theBenchmark.p',fact_minus__code__numeral__def) ).

fof(fact_of__nat__inverse,axiom,
    ! [V_y_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
     => hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_y_2)) = V_y_2 ),
    file('theBenchmark.p',fact_of__nat__inverse) ).

fof(fact_plus__code__numeral__def,axiom,
    ! [V_m,V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),V_n),V_m) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n)),hAPP(c_Code__Numeral_Onat__of,V_m))),
    file('theBenchmark.p',fact_plus__code__numeral__def) ).

fof(fact_div__code__numeral__def,axiom,
    ! [V_m,V_n] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_n),V_m) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n)),hAPP(c_Code__Numeral_Onat__of,V_m))),
    file('theBenchmark.p',fact_div__code__numeral__def) ).

fof(fact_mod__code__numeral__def,axiom,
    ! [V_m,V_n] : c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,V_n,V_m) = hAPP(c_Code__Numeral_Oof__nat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Code__Numeral_Onat__of,V_n),hAPP(c_Code__Numeral_Onat__of,V_m))),
    file('theBenchmark.p',fact_mod__code__numeral__def) ).

fof(fact_code__numeral__decr,axiom,
    ! [V_k] :
      ( V_k != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_k)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Code__Numeral_Onat__of,V_k))) ),
    file('theBenchmark.p',fact_code__numeral__decr) ).

fof(fact_New__DSequence_Opos__not__seq__def,axiom,
    ! [V_i_2,V_xq_2] : hAPP(c_New__DSequence_Opos__not__seq(V_xq_2),V_i_2) = c_Lazy__Sequence_Ohb__not__seq(hAPP(V_xq_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_i_2))),
    file('theBenchmark.p',fact_New__DSequence_Opos__not__seq__def) ).

fof(fact_partition__set,axiom,
    ! [V_no_2,V_yes_2,V_xs_2,V_P_2,T_b] :
      ( c_List_Opartition(T_b,V_P_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_yes_2),V_no_2)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_yes_2)),hAPP(c_List_Oset(T_b),V_no_2)) = hAPP(c_List_Oset(T_b),V_xs_2) ),
    file('theBenchmark.p',fact_partition__set) ).

fof(fact_partition__P,axiom,
    ! [V_no_2,V_yes_2,V_xs_2,V_P_2,T_b] :
      ( c_List_Opartition(T_b,V_P_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_yes_2),V_no_2)
     => ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_no_2)))
           => ~ hBOOL(hAPP(V_P_2,B_x)) )
        & ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_yes_2)))
           => hBOOL(hAPP(V_P_2,B_x)) ) ) ),
    file('theBenchmark.p',fact_partition__P) ).

fof(fact_partition_Osimps_I1_J,axiom,
    ! [V_P_2,T_b] : c_List_Opartition(T_b,V_P_2,c_List_Olist_ONil(T_b)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_List_Olist_ONil(T_b)),
    file('theBenchmark.p',fact_partition_Osimps_I1_J) ).

fof(fact_partition_Osimps_I2_J,axiom,
    ! [V_xs_2,V_x_2,V_P_2,T_b] : c_List_Opartition(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_fun(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_List_Olist(T_b)),c_COMBS(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_List_Olist(T_b)),hAPP(c_If(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(V_P_2,V_x_2)))),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_List_Olist(T_b)),c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(c_List_Olist_OCons(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_List_Olist(T_b)),c_COMBB(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_List_Olist(T_b))),c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(c_List_Olist_OCons(T_b),V_x_2)))),c_List_Opartition(T_b,V_P_2,V_xs_2)),
    file('theBenchmark.p',fact_partition_Osimps_I2_J) ).

fof(fact_lists__Int__eq,axiom,
    ! [V_B_2,V_A_2,T_b] : c_List_Olistsp(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(T_b))),c_List_Olists(T_b,V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(T_b))),c_List_Olists(T_b,V_B_2))),
    file('theBenchmark.p',fact_lists__Int__eq) ).

fof(fact_lists__IntI,axiom,
    ! [V_B_2,V_A_2,V_l_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_l_2),c_List_Olists(T_b,V_A_2)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_l_2),c_List_Olists(T_b,V_B_2)))
       => hBOOL(hAPP(c_List_Olistsp(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_l_2)) ) ),
    file('theBenchmark.p',fact_lists__IntI) ).

fof(fact_listsp_ONil,axiom,
    ! [V_A_2,T_b] : hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),c_List_Olist_ONil(T_b))),
    file('theBenchmark.p',fact_listsp_ONil) ).

fof(fact_listsp_Oequations_I1_J,axiom,
    ! [V_A_2,T_b] : hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),c_List_Olist_ONil(T_b))),
    file('theBenchmark.p',fact_listsp_Oequations_I1_J) ).

fof(fact_in__listsp__conv__set,axiom,
    ! [V_xs_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_xs_2))
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
         => hBOOL(hAPP(V_A_2,B_x)) ) ),
    file('theBenchmark.p',fact_in__listsp__conv__set) ).

fof(fact_listsp__conj__eq,axiom,
    ! [V_x_2,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_List_Olistsp(T_b,hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_A_2)),V_B_2)),V_x_2))
    <=> ( hBOOL(hAPP(c_List_Olistsp(T_b,V_B_2),V_x_2))
        & hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_x_2)) ) ),
    file('theBenchmark.p',fact_listsp__conj__eq) ).

fof(fact_listsp__infI,axiom,
    ! [V_B_2,V_l_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_l_2))
     => ( hBOOL(hAPP(c_List_Olistsp(T_b,V_B_2),V_l_2))
       => hBOOL(hAPP(c_List_Olistsp(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_l_2)) ) ),
    file('theBenchmark.p',fact_listsp__infI) ).

fof(fact_listsp__inf__eq,axiom,
    ! [V_B_2,V_A_2,T_b] : c_List_Olistsp(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),c_List_Olistsp(T_b,V_A_2)),c_List_Olistsp(T_b,V_B_2)),
    file('theBenchmark.p',fact_listsp__inf__eq) ).

fof(fact_listsp_Oequations_I2_J,axiom,
    ! [V_a2_2,V_a1_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a1_2),V_a2_2)))
    <=> ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_a2_2))
        & hBOOL(hAPP(V_A_2,V_a1_2)) ) ),
    file('theBenchmark.p',fact_listsp_Oequations_I2_J) ).

fof(fact_append__in__listsp__conv,axiom,
    ! [V_ys_2,V_xs_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)))
    <=> ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_ys_2))
        & hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_xs_2)) ) ),
    file('theBenchmark.p',fact_append__in__listsp__conv) ).

fof(fact_listsp__mono,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),c_List_Olistsp(T_b,V_A_2)),c_List_Olistsp(T_b,V_B_2))) ),
    file('theBenchmark.p',fact_listsp__mono) ).

fof(fact_listsp__lists__eq,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_List_Olistsp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)),V_x_2))
    <=> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_x_2),c_List_Olists(T_b,V_A_2))) ),
    file('theBenchmark.p',fact_listsp__lists__eq) ).

fof(fact_product_Osimps_I2_J,axiom,
    ! [V_ys_2,V_xs_2,V_x_2,T_c,T_b] : c_Enum_Oproduct(T_b,T_c,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Omap(T_c,tc_prod(T_b,T_c)),hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2)),V_ys_2)),c_Enum_Oproduct(T_b,T_c,V_xs_2,V_ys_2)),
    file('theBenchmark.p',fact_product_Osimps_I2_J) ).

fof(fact_list__all2__def,axiom,
    ! [V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
      ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
    <=> ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),B_x),hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))))
           => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_P_2),B_x)) )
        & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2) ) ),
    file('theBenchmark.p',fact_list__all2__def) ).

fof(fact_list__all2__map1,axiom,
    ! [V_bs_2,V_as_2,V_f_2,T_d,V_P_2,T_c,T_b] :
      ( c_List_Olist__all2(T_b,T_c,V_P_2,hAPP(hAPP(c_List_Omap(T_d,T_b),V_f_2),V_as_2),V_bs_2)
    <=> c_List_Olist__all2(T_d,T_c,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),V_P_2),V_f_2),V_as_2,V_bs_2) ),
    file('theBenchmark.p',fact_list__all2__map1) ).

fof(fact_list__all2__map2,axiom,
    ! [V_bs_2,V_f_2,T_d,V_as_2,V_P_2,T_c,T_b] :
      ( c_List_Olist__all2(T_b,T_c,V_P_2,V_as_2,hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_bs_2))
    <=> c_List_Olist__all2(T_b,T_d,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_d,T_c),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_d,T_c),tc_fun(T_d,tc_HOL_Obool)),T_b),c_COMBB(T_c,tc_HOL_Obool,T_d)),V_P_2)),V_f_2),V_as_2,V_bs_2) ),
    file('theBenchmark.p',fact_list__all2__map2) ).

fof(fact_list__all2__dropI,axiom,
    ! [V_n_2,V_bs_2,V_as_2,V_P_2,T_c,T_b] :
      ( c_List_Olist__all2(T_b,T_c,V_P_2,V_as_2,V_bs_2)
     => c_List_Olist__all2(T_b,T_c,V_P_2,hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_as_2),hAPP(hAPP(c_List_Odrop(T_c),V_n_2),V_bs_2)) ),
    file('theBenchmark.p',fact_list__all2__dropI) ).

fof(fact_list__all2__appendI,axiom,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,V_P_2,T_c,T_b] :
      ( c_List_Olist__all2(T_b,T_c,V_P_2,V_a_2,V_b_2)
     => ( c_List_Olist__all2(T_b,T_c,V_P_2,V_c_2,V_d_2)
       => c_List_Olist__all2(T_b,T_c,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_a_2),V_c_2),hAPP(hAPP(c_List_Oappend(T_c),V_b_2),V_d_2)) ) ),
    file('theBenchmark.p',fact_list__all2__appendI) ).

fof(fact_list__all2__append,axiom,
    ! [V_vs_2,V_us_2,V_P_2,V_ys_2,T_c,V_xs_2,T_b] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)
     => ( c_List_Olist__all2(T_b,T_c,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_us_2),hAPP(hAPP(c_List_Oappend(T_c),V_ys_2),V_vs_2))
      <=> ( c_List_Olist__all2(T_b,T_c,V_P_2,V_us_2,V_vs_2)
          & c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2) ) ) ),
    file('theBenchmark.p',fact_list__all2__append) ).

fof(fact_list__all2__Cons,axiom,
    ! [V_ys_2,V_y_2,V_xs_2,V_x_2,V_P_2,T_c,T_b] :
      ( c_List_Olist__all2(T_b,T_c,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2))
    <=> ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
        & hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2)) ) ),
    file('theBenchmark.p',fact_list__all2__Cons) ).

fof(fact_list__all2__takeI,axiom,
    ! [V_n_2,V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
      ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
     => c_List_Olist__all2(T_b,T_c,V_P_2,hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2),hAPP(hAPP(c_List_Otake(T_c),V_n_2),V_ys_2)) ),
    file('theBenchmark.p',fact_list__all2__takeI) ).

fof(fact_list__all2__eq,axiom,
    ! [T_b,V_ys_2,V_xs_2] :
      ( V_xs_2 = V_ys_2
    <=> c_List_Olist__all2(T_b,T_b,c_fequal,V_xs_2,V_ys_2) ),
    file('theBenchmark.p',fact_list__all2__eq) ).

fof(fact_list__all2__lengthD,axiom,
    ! [V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
      ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
     => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2) ),
    file('theBenchmark.p',fact_list__all2__lengthD) ).

fof(fact_list__all2__Nil2,axiom,
    ! [V_xs_2,V_P_2,T_c,T_b] :
      ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,c_List_Olist_ONil(T_c))
    <=> V_xs_2 = c_List_Olist_ONil(T_b) ),
    file('theBenchmark.p',fact_list__all2__Nil2) ).

fof(fact_list__all2__Nil,axiom,
    ! [V_ys_2,V_P_2,T_c,T_b] :
      ( c_List_Olist__all2(T_b,T_c,V_P_2,c_List_Olist_ONil(T_b),V_ys_2)
    <=> V_ys_2 = c_List_Olist_ONil(T_c) ),
    file('theBenchmark.p',fact_list__all2__Nil) ).

fof(fact_product_Osimps_I1_J,axiom,
    ! [V_uu,T_b,T_a] : c_Enum_Oproduct(T_a,T_b,c_List_Olist_ONil(T_a),V_uu) = c_List_Olist_ONil(tc_prod(T_a,T_b)),
    file('theBenchmark.p',fact_product_Osimps_I1_J) ).

fof(fact_list__all2__conv__all__nth,axiom,
    ! [V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
      ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
    <=> ( ! [B_i] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
           => hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i)),hAPP(hAPP(c_List_Onth(T_c),V_ys_2),B_i))) )
        & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2) ) ),
    file('theBenchmark.p',fact_list__all2__conv__all__nth) ).

fof(fact_list__all2__nthD,axiom,
    ! [V_p_2,V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
      ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_p_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
       => hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_p_2)),hAPP(hAPP(c_List_Onth(T_c),V_ys_2),V_p_2))) ) ),
    file('theBenchmark.p',fact_list__all2__nthD) ).

fof(fact_list__all2__nthD2,axiom,
    ! [V_p_2,V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
      ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_p_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)))
       => hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_p_2)),hAPP(hAPP(c_List_Onth(T_c),V_ys_2),V_p_2))) ) ),
    file('theBenchmark.p',fact_list__all2__nthD2) ).

fof(fact_list__all2__update__cong,axiom,
    ! [V_y_2,V_x_2,V_ys_2,V_P_2,T_c,V_xs_2,T_b,V_i_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
     => ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
       => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
         => c_List_Olist__all2(T_b,T_c,V_P_2,hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2),hAPP(hAPP(c_List_Olist__update(T_c,V_ys_2),V_i_2),V_y_2)) ) ) ),
    file('theBenchmark.p',fact_list__all2__update__cong) ).

fof(fact_list__all2__update__cong2,axiom,
    ! [V_i_2,V_y_2,V_x_2,V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
      ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
     => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)))
         => c_List_Olist__all2(T_b,T_c,V_P_2,hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2),hAPP(hAPP(c_List_Olist__update(T_c,V_ys_2),V_i_2),V_y_2)) ) ) ),
    file('theBenchmark.p',fact_list__all2__update__cong2) ).

fof(fact_distinct__product,axiom,
    ! [V_ys,T_b,V_xs,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
     => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_ys))
       => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),c_Enum_Oproduct(T_a,T_b,V_xs,V_ys))) ) ),
    file('theBenchmark.p',fact_distinct__product) ).

fof(fact_product__list__set,axiom,
    ! [V_ys_2,V_xs_2,T_c,T_b] : hAPP(c_List_Oset(tc_prod(T_b,T_c)),c_Enum_Oproduct(T_b,T_c,V_xs_2,V_ys_2)) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_List_Oset(T_c),V_ys_2))),
    file('theBenchmark.p',fact_product__list__set) ).

fof(fact_sublists__powset,axiom,
    ! [V_xs_2,T_b] : hAPP(c_Set_Oimage(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),c_List_Oset(T_b)),hAPP(c_List_Oset(tc_List_Olist(T_b)),c_Enum_Osublists(T_b,V_xs_2))) = hAPP(c_Set_OPow(T_b),hAPP(c_List_Oset(T_b),V_xs_2)),
    file('theBenchmark.p',fact_sublists__powset) ).

fof(fact_length__sublists,axiom,
    ! [V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_Enum_Osublists(T_a,V_xs)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),
    file('theBenchmark.p',fact_length__sublists) ).

fof(fact_sublists_Osimps_I1_J,axiom,
    ! [T_a] : c_Enum_Osublists(T_a,c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_List_Olist_ONil(tc_List_Olist(T_a))),
    file('theBenchmark.p',fact_sublists_Osimps_I1_J) ).

fof(fact_sublists_Osimps_I2_J,axiom,
    ! [V_xs_2,V_x_2,T_b] : c_Enum_Osublists(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),c_Enum_Osublists(T_b,V_xs_2)),hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(T_b)),tc_fun(tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),tc_List_Olist(tc_List_Olist(T_b))),c_List_Oappend(tc_List_Olist(T_b))),hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(c_List_Olist_OCons(T_b),V_x_2)))),c_COMBI(tc_List_Olist(tc_List_Olist(T_b))))),
    file('theBenchmark.p',fact_sublists_Osimps_I2_J) ).

fof(fact_distinct__set__sublists,axiom,
    ! [V_xs_2,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
     => hBOOL(hAPP(c_List_Odistinct(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool)),c_List_Oset(T_b)),c_Enum_Osublists(T_b,V_xs_2)))) ),
    file('theBenchmark.p',fact_distinct__set__sublists) ).

fof(fact_set__n__lists,axiom,
    ! [V_xs_2,V_n_2,T_b] : hAPP(c_List_Oset(tc_List_Olist(T_b)),c_Enum_On__lists(T_b,V_n_2,V_xs_2)) = hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_n_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),c_List_Oset(T_b))),hAPP(c_List_Oset(T_b),V_xs_2)))),
    file('theBenchmark.p',fact_set__n__lists) ).

fof(fact_enum__the__def,axiom,
    ! [V_P_2,T_b] : c_Enum_Oenum__the(T_b,V_P_2) = c_HOL_OThe(T_b,V_P_2),
    file('theBenchmark.p',fact_enum__the__def) ).

fof(fact_distinct__n__lists,axiom,
    ! [V_n,V_xs,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
     => hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n,V_xs))) ),
    file('theBenchmark.p',fact_distinct__n__lists) ).

fof(fact_n__lists_Osimps_I1_J,axiom,
    ! [V_xs,T_a] : c_Enum_On__lists(T_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_xs) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_List_Olist_ONil(tc_List_Olist(T_a))),
    file('theBenchmark.p',fact_n__lists_Osimps_I1_J) ).

fof(fact_n__lists__Nil,axiom,
    ! [T_a,V_n] :
      ( ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => c_Enum_On__lists(T_a,V_n,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(tc_List_Olist(T_a)) )
      & ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => c_Enum_On__lists(T_a,V_n,c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_List_Olist_ONil(tc_List_Olist(T_a))) ) ),
    file('theBenchmark.p',fact_n__lists__Nil) ).

fof(fact_length__n__lists,axiom,
    ! [V_xs,V_n,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_Enum_On__lists(T_a,V_n,V_xs)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n),
    file('theBenchmark.p',fact_length__n__lists) ).

fof(fact_length__n__lists__elem,axiom,
    ! [V_xs_2,V_n_2,V_ys_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_ys_2),hAPP(c_List_Oset(tc_List_Olist(T_b)),c_Enum_On__lists(T_b,V_n_2,V_xs_2))))
     => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = V_n_2 ),
    file('theBenchmark.p',fact_length__n__lists__elem) ).

fof(fact_list__all2I,axiom,
    ! [V_P_2,V_b_2,V_a_2,T_c,T_b] :
      ( ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),B_x),hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_a_2),V_b_2))))
         => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_P_2),B_x)) )
     => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_a_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_b_2)
       => c_List_Olist__all2(T_b,T_c,V_P_2,V_a_2,V_b_2) ) ),
    file('theBenchmark.p',fact_list__all2I) ).

fof(fact_all__nth__imp__all__set,axiom,
    ! [V_x_2,V_P_2,V_xs_2,T_b] :
      ( ! [B_i] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
         => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) )
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
       => hBOOL(hAPP(V_P_2,V_x_2)) ) ),
    file('theBenchmark.p',fact_all__nth__imp__all__set) ).

fof(fact_fun__left__comm_Ofold__set__remdups,axiom,
    ! [V_xs_2,V_y_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
     => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_c,T_b,hAPP(c_COMBC(T_b,T_c,T_c),V_f_2),V_y_2),c_List_Oremdups(T_b,V_xs_2)) ),
    file('theBenchmark.p',fact_fun__left__comm_Ofold__set__remdups) ).

fof(fact_map__removeAll__inj__on,axiom,
    ! [V_xs_2,V_x_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
     => hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),hAPP(c_List_OremoveAll(T_b,V_x_2),V_xs_2)) = hAPP(c_List_OremoveAll(T_c,hAPP(V_f_2,V_x_2)),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) ),
    file('theBenchmark.p',fact_map__removeAll__inj__on) ).

fof(fact_distinct__remdups,axiom,
    ! [V_xs,T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremdups(T_a,V_xs))),
    file('theBenchmark.p',fact_distinct__remdups) ).

fof(fact_length__remdups__leq,axiom,
    ! [V_xs,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oremdups(T_a,V_xs))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),
    file('theBenchmark.p',fact_length__remdups__leq) ).

fof(fact_remdups__id__iff__distinct,axiom,
    ! [V_xs_2,T_b] :
      ( c_List_Oremdups(T_b,V_xs_2) = V_xs_2
    <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ),
    file('theBenchmark.p',fact_remdups__id__iff__distinct) ).

fof(fact_distinct__removeAll,axiom,
    ! [V_x,V_xs,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
     => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_OremoveAll(T_a,V_x),V_xs))) ),
    file('theBenchmark.p',fact_distinct__removeAll) ).

fof(fact_distinct__remdups__id,axiom,
    ! [V_xs,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
     => c_List_Oremdups(T_a,V_xs) = V_xs ),
    file('theBenchmark.p',fact_distinct__remdups__id) ).

fof(fact_set__remdups,axiom,
    ! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),c_List_Oremdups(T_b,V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2),
    file('theBenchmark.p',fact_set__remdups) ).

fof(fact_length__remdups__eq,axiom,
    ! [V_xs_2,T_b] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremdups(T_b,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)
    <=> c_List_Oremdups(T_b,V_xs_2) = V_xs_2 ),
    file('theBenchmark.p',fact_length__remdups__eq) ).

fof(fact_remdups__remdups,axiom,
    ! [V_xs,T_a] : c_List_Oremdups(T_a,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,V_xs),
    file('theBenchmark.p',fact_remdups__remdups) ).

fof(fact_remdups_Osimps_I1_J,axiom,
    ! [T_a] : c_List_Oremdups(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a),
    file('theBenchmark.p',fact_remdups_Osimps_I1_J) ).

fof(fact_remdups__eq__nil__right__iff,axiom,
    ! [V_x_2,T_b] :
      ( c_List_Olist_ONil(T_b) = c_List_Oremdups(T_b,V_x_2)
    <=> V_x_2 = c_List_Olist_ONil(T_b) ),
    file('theBenchmark.p',fact_remdups__eq__nil__right__iff) ).

fof(fact_removeAll_Osimps_I1_J,axiom,
    ! [V_x,T_a] : hAPP(c_List_OremoveAll(T_a,V_x),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a),
    file('theBenchmark.p',fact_removeAll_Osimps_I1_J) ).

fof(fact_remdups__eq__nil__iff,axiom,
    ! [V_x_2,T_b] :
      ( c_List_Oremdups(T_b,V_x_2) = c_List_Olist_ONil(T_b)
    <=> V_x_2 = c_List_Olist_ONil(T_b) ),
    file('theBenchmark.p',fact_remdups__eq__nil__iff) ).

fof(fact_removeAll_Osimps_I2_J,axiom,
    ! [V_xs,T_a,V_y,V_x] :
      ( ( V_x != V_y
       => hAPP(c_List_OremoveAll(T_a,V_x),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),hAPP(c_List_OremoveAll(T_a,V_x),V_xs)) )
      & ( V_x = V_y
       => hAPP(c_List_OremoveAll(T_a,V_x),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = hAPP(c_List_OremoveAll(T_a,V_x),V_xs) ) ),
    file('theBenchmark.p',fact_removeAll_Osimps_I2_J) ).

fof(fact_removeAll__append,axiom,
    ! [V_ys,V_xs,V_x,T_a] : hAPP(c_List_OremoveAll(T_a,V_x),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_OremoveAll(T_a,V_x),V_xs)),hAPP(c_List_OremoveAll(T_a,V_x),V_ys)),
    file('theBenchmark.p',fact_removeAll__append) ).

fof(fact_remdups__map__remdups,axiom,
    ! [V_xs_2,V_f_2,T_c,T_b] : c_List_Oremdups(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Oremdups(T_c,V_xs_2))) = c_List_Oremdups(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)),
    file('theBenchmark.p',fact_remdups__map__remdups) ).

fof(fact_remove1__remdups,axiom,
    ! [V_x,V_xs,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
     => c_List_Oremove1(T_a,V_x,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,c_List_Oremove1(T_a,V_x,V_xs)) ),
    file('theBenchmark.p',fact_remove1__remdups) ).

fof(fact_removeAll__id,axiom,
    ! [V_xs_2,V_x_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
     => hAPP(c_List_OremoveAll(T_b,V_x_2),V_xs_2) = V_xs_2 ),
    file('theBenchmark.p',fact_removeAll__id) ).

fof(fact_distinct__remove1__removeAll,axiom,
    ! [V_x,V_xs,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
     => c_List_Oremove1(T_a,V_x,V_xs) = hAPP(c_List_OremoveAll(T_a,V_x),V_xs) ),
    file('theBenchmark.p',fact_distinct__remove1__removeAll) ).

fof(fact_remdups_Osimps_I2_J,axiom,
    ! [V_xs_2,V_x_2,T_b] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
       => c_List_Oremdups(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Oremdups(T_b,V_xs_2)) )
      & ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
       => c_List_Oremdups(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_List_Oremdups(T_b,V_xs_2) ) ),
    file('theBenchmark.p',fact_remdups_Osimps_I2_J) ).

fof(fact_length__remdups__card__conv,axiom,
    ! [V_xs_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremdups(T_b,V_xs_2)) = hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_List_Oset(T_b),V_xs_2)),
    file('theBenchmark.p',fact_length__remdups__card__conv) ).

fof(fact_map__removeAll__inj,axiom,
    ! [V_xs_2,V_x_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
     => hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),hAPP(c_List_OremoveAll(T_b,V_x_2),V_xs_2)) = hAPP(c_List_OremoveAll(T_c,hAPP(V_f_2,V_x_2)),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) ),
    file('theBenchmark.p',fact_map__removeAll__inj) ).

fof(fact_set__removeAll,axiom,
    ! [V_xs_2,V_x_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_OremoveAll(T_b,V_x_2),V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),
    file('theBenchmark.p',fact_set__removeAll) ).

fof(fact_length__remdups__concat,axiom,
    ! [V_xss_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremdups(T_b,c_List_Oconcat(T_b,V_xss_2))) = hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2)),c_List_Oset(T_b))),
    file('theBenchmark.p',fact_length__remdups__concat) ).

fof(fact_sorted__list__of__set__sort__remdups,axiom,
    ! [V_xs_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => c_List_Olinorder__class_Osorted__list__of__set(T_b,hAPP(c_List_Oset(T_b),V_xs_2)) = c_List_Olinorder__class_Osort__key(T_b,T_b,c_COMBI(T_b),c_List_Oremdups(T_b,V_xs_2)) ),
    file('theBenchmark.p',fact_sorted__list__of__set__sort__remdups) ).

fof(fact_sort__key__simps_I1_J,axiom,
    ! [V_f_2,T_b,T_c] :
      ( class_Orderings_Olinorder(T_c)
     => c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b) ),
    file('theBenchmark.p',fact_sort__key__simps_I1_J) ).

fof(fact_foldl__conv__concat,axiom,
    ! [V_xss_2,V_xs_2,T_b] : hAPP(c_List_Ofoldl(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Oappend(T_b),V_xs_2),V_xss_2) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),c_List_Oconcat(T_b,V_xss_2)),
    file('theBenchmark.p',fact_foldl__conv__concat) ).

fof(fact_concat__conv__foldl,axiom,
    ! [V_xss_2,T_b] : c_List_Oconcat(T_b,V_xss_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Oappend(T_b),c_List_Olist_ONil(T_b)),V_xss_2),
    file('theBenchmark.p',fact_concat__conv__foldl) ).

fof(fact_length__sort,axiom,
    ! [V_xs_2,V_f_2,T_b,T_c] :
      ( class_Orderings_Olinorder(T_c)
     => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) ),
    file('theBenchmark.p',fact_length__sort) ).

fof(fact_set__sort,axiom,
    ! [V_xs_2,V_f_2,T_b,T_c] :
      ( class_Orderings_Olinorder(T_c)
     => hAPP(c_List_Oset(T_b),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2) ),
    file('theBenchmark.p',fact_set__sort) ).

fof(fact_distinct__sort,axiom,
    ! [V_xs_2,V_f_2,T_b,T_c] :
      ( class_Orderings_Olinorder(T_c)
     => ( hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2)))
      <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ),
    file('theBenchmark.p',fact_distinct__sort) ).

fof(fact_concat_Osimps_I1_J,axiom,
    ! [T_a] : c_List_Oconcat(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(T_a),
    file('theBenchmark.p',fact_concat_Osimps_I1_J) ).

fof(fact_concat_Osimps_I2_J,axiom,
    ! [V_xs,V_x,T_a] : c_List_Oconcat(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),V_x),V_xs)) = hAPP(hAPP(c_List_Oappend(T_a),V_x),c_List_Oconcat(T_a,V_xs)),
    file('theBenchmark.p',fact_concat_Osimps_I2_J) ).

fof(fact_Nil__eq__concat__conv,axiom,
    ! [V_xss_2,T_b] :
      ( c_List_Olist_ONil(T_b) = c_List_Oconcat(T_b,V_xss_2)
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2)))
         => B_x = c_List_Olist_ONil(T_b) ) ),
    file('theBenchmark.p',fact_Nil__eq__concat__conv) ).

fof(fact_concat__eq__Nil__conv,axiom,
    ! [V_xss_2,T_b] :
      ( c_List_Oconcat(T_b,V_xss_2) = c_List_Olist_ONil(T_b)
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2)))
         => B_x = c_List_Olist_ONil(T_b) ) ),
    file('theBenchmark.p',fact_concat__eq__Nil__conv) ).

fof(fact_map__concat,axiom,
    ! [V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Oconcat(T_c,V_xs_2)) = c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_List_Olist(T_b)),hAPP(c_List_Omap(T_c,T_b),V_f_2)),V_xs_2)),
    file('theBenchmark.p',fact_map__concat) ).

fof(fact_length__concat,axiom,
    ! [V_xss_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oconcat(T_b,V_xss_2)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xss_2)),
    file('theBenchmark.p',fact_length__concat) ).

fof(fact_set__concat,axiom,
    ! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),c_List_Oconcat(T_b,V_xs_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)),c_List_Oset(T_b)),
    file('theBenchmark.p',fact_set__concat) ).

fof(fact_sort__key__simps_I2_J,axiom,
    ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
      ( class_Orderings_Olinorder(T_c)
     => c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2)) ),
    file('theBenchmark.p',fact_sort__key__simps_I2_J) ).

fof(fact_concat__append,axiom,
    ! [V_ys,V_xs,T_a] : c_List_Oconcat(T_a,hAPP(hAPP(c_List_Oappend(tc_List_Olist(T_a)),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),c_List_Oconcat(T_a,V_xs)),c_List_Oconcat(T_a,V_ys)),
    file('theBenchmark.p',fact_concat__append) ).

fof(fact_sort__foldl__insort,axiom,
    ! [V_xs_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => c_List_Olinorder__class_Osort__key(T_b,T_b,c_COMBI(T_b),V_xs_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_b),T_b,hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b))),c_List_Olist_ONil(T_b)),V_xs_2) ),
    file('theBenchmark.p',fact_sort__foldl__insort) ).

fof(fact_concat__eq__concat__iff,axiom,
    ! [V_ys_2,V_xs_2,T_b] :
      ( ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),B_x),hAPP(c_List_Oset(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2))))
         => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),B_x)) )
     => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_ys_2)
       => ( c_List_Oconcat(T_b,V_xs_2) = c_List_Oconcat(T_b,V_ys_2)
        <=> V_xs_2 = V_ys_2 ) ) ),
    file('theBenchmark.p',fact_concat__eq__concat__iff) ).

fof(fact_concat__injective,axiom,
    ! [V_ys_2,V_xs_2,T_b] :
      ( c_List_Oconcat(T_b,V_xs_2) = c_List_Oconcat(T_b,V_ys_2)
     => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_ys_2)
       => ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),B_x),hAPP(c_List_Oset(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2))))
             => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),B_x)) )
         => V_xs_2 = V_ys_2 ) ) ),
    file('theBenchmark.p',fact_concat__injective) ).

fof(fact_concat__map__singleton,axiom,
    ! [V_xs_2,V_f_2,T_c,T_b] : c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(T_c,tc_List_Olist(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_c),c_List_Olist_OCons(T_b)),V_f_2)),c_List_Olist_ONil(T_b))),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2),
    file('theBenchmark.p',fact_concat__map__singleton) ).

fof(fact_n__lists_Osimps_I2_J,axiom,
    ! [V_xs_2,V_n_2,T_b] : c_Enum_On__lists(T_b,hAPP(c_Nat_OSuc,V_n_2),V_xs_2) = c_List_Oconcat(tc_List_Olist(T_b),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),tc_List_Olist(T_b)),c_List_Omap(T_b,tc_List_Olist(T_b))),hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)))),V_xs_2)),c_Enum_On__lists(T_b,V_n_2,V_xs_2))),
    file('theBenchmark.p',fact_n__lists_Osimps_I2_J) ).

fof(fact_transpose_Osimps_I3_J,axiom,
    ! [V_xss_2,V_xs_2,V_x_2,T_b] : c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_xss_2)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),c_COMBK(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b))))),V_xss_2)))),c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),V_xs_2),c_List_Oconcat(tc_List_Olist(T_b),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_b)),T_b,c_List_Olist_ONil(tc_List_Olist(T_b)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_OCons(tc_List_Olist(T_b))),c_List_Olist_ONil(tc_List_Olist(T_b)))))),V_xss_2))))),
    file('theBenchmark.p',fact_transpose_Osimps_I3_J) ).

fof(fact_transpose__aux__filter__head,axiom,
    ! [V_xss_2,T_b] : c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),c_COMBK(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b))))),V_xss_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),T_b),c_List_Ohd(T_b)),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_b)))),V_xss_2)),
    file('theBenchmark.p',fact_transpose__aux__filter__head) ).

fof(fact_filter__concat,axiom,
    ! [V_xs_2,V_p_2,T_b] : hAPP(c_List_Ofilter(T_b,V_p_2),c_List_Oconcat(T_b,V_xs_2)) = c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Ofilter(T_b,V_p_2)),V_xs_2)),
    file('theBenchmark.p',fact_filter__concat) ).

fof(fact_filter__sort,axiom,
    ! [V_xs_2,V_f_2,V_P_2,T_b,T_c] :
      ( class_Orderings_Olinorder(T_c)
     => hAPP(c_List_Ofilter(T_b,V_P_2),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2)) = c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) ),
    file('theBenchmark.p',fact_filter__sort) ).

fof(fact_distinct__filter,axiom,
    ! [V_P_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
     => hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2))) ),
    file('theBenchmark.p',fact_distinct__filter) ).

fof(fact_filter__is__subset,axiom,
    ! [V_xs_2,V_P_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2))),
    file('theBenchmark.p',fact_filter__is__subset) ).

fof(fact_filter__id__conv,axiom,
    ! [V_xs_2,V_P_2,T_b] :
      ( hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) = V_xs_2
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
         => hBOOL(hAPP(V_P_2,B_x)) ) ),
    file('theBenchmark.p',fact_filter__id__conv) ).

fof(fact_sum__length__filter__compl,axiom,
    ! [V_xs_2,V_P_2,T_b] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_P_2)),V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2),
    file('theBenchmark.p',fact_sum__length__filter__compl) ).

fof(fact_length__filter__le,axiom,
    ! [V_xs_2,V_P_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))),
    file('theBenchmark.p',fact_length__filter__le) ).

fof(fact_filter__filter,axiom,
    ! [V_xs_2,V_Q_2,V_P_2,T_b] : hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(c_List_Ofilter(T_b,V_Q_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Q_2)),V_P_2)),V_xs_2),
    file('theBenchmark.p',fact_filter__filter) ).

fof(fact_remove1__filter__not,axiom,
    ! [V_xs_2,T_b,V_x_2,V_P_2] :
      ( ~ hBOOL(hAPP(V_P_2,V_x_2))
     => c_List_Oremove1(T_b,V_x_2,hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) ),
    file('theBenchmark.p',fact_remove1__filter__not) ).

fof(fact_filter__remove1,axiom,
    ! [V_xs_2,V_x_2,V_Q_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Q_2),c_List_Oremove1(T_b,V_x_2,V_xs_2)) = c_List_Oremove1(T_b,V_x_2,hAPP(c_List_Ofilter(T_b,V_Q_2),V_xs_2)),
    file('theBenchmark.p',fact_filter__remove1) ).

fof(fact_filter__insort__triv,axiom,
    ! [V_xs_2,V_f_2,T_b,V_x_2,V_P_2,T_c] :
      ( class_Orderings_Olinorder(T_c)
     => ( ~ hBOOL(hAPP(V_P_2,V_x_2))
       => hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) ) ),
    file('theBenchmark.p',fact_filter__insort__triv) ).

fof(fact_partition__filter1,axiom,
    ! [V_xs_2,V_P_2,T_b] : hAPP(c_Product__Type_Ofst(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Opartition(T_b,V_P_2,V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2),
    file('theBenchmark.p',fact_partition__filter1) ).

fof(fact_partition__filter2,axiom,
    ! [V_xs_2,V_P_2,T_b] : hAPP(c_Product__Type_Osnd(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Opartition(T_b,V_P_2,V_xs_2)) = hAPP(c_List_Ofilter(T_b,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,T_b,c_fNot),V_P_2)),V_xs_2),
    file('theBenchmark.p',fact_partition__filter2) ).

fof(fact_partition__filter__conv,axiom,
    ! [V_xs_2,V_f_2,T_b] : c_List_Opartition(T_b,V_f_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_f_2),V_xs_2)),hAPP(c_List_Ofilter(T_b,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,T_b,c_fNot),V_f_2)),V_xs_2)),
    file('theBenchmark.p',fact_partition__filter__conv) ).

fof(fact_filter__map,axiom,
    ! [V_xs_2,V_f_2,T_c,V_P_2,T_b] : hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Ofilter(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_P_2),V_f_2)),V_xs_2)),
    file('theBenchmark.p',fact_filter__map) ).

fof(fact_transpose_Osimps_I1_J,axiom,
    ! [T_a] : c_List_Otranspose(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(tc_List_Olist(T_a)),
    file('theBenchmark.p',fact_transpose_Osimps_I1_J) ).

fof(fact_filter_Osimps_I1_J,axiom,
    ! [V_P_2,T_b] : hAPP(c_List_Ofilter(T_b,V_P_2),c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b),
    file('theBenchmark.p',fact_filter_Osimps_I1_J) ).

fof(fact_filter_Osimps_I2_J,axiom,
    ! [V_xs_2,T_b,V_x_2,V_P_2] :
      ( ( ~ hBOOL(hAPP(V_P_2,V_x_2))
       => hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) )
      & ( hBOOL(hAPP(V_P_2,V_x_2))
       => hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) ) ),
    file('theBenchmark.p',fact_filter_Osimps_I2_J) ).

fof(fact_filter__append,axiom,
    ! [V_ys_2,V_xs_2,V_P_2,T_b] : hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)),hAPP(c_List_Ofilter(T_b,V_P_2),V_ys_2)),
    file('theBenchmark.p',fact_filter__append) ).

fof(fact_filter__empty__conv,axiom,
    ! [V_xs_2,V_P_2,T_b] :
      ( hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) = c_List_Olist_ONil(T_b)
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
         => ~ hBOOL(hAPP(V_P_2,B_x)) ) ),
    file('theBenchmark.p',fact_filter__empty__conv) ).

fof(fact_length__filter__map,axiom,
    ! [V_xs_2,V_f_2,T_c,V_P_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),hAPP(c_List_Ofilter(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_P_2),V_f_2)),V_xs_2)),
    file('theBenchmark.p',fact_length__filter__map) ).

fof(fact_removeAll__filter__not,axiom,
    ! [V_xs_2,T_b,V_x_2,V_P_2] :
      ( ~ hBOOL(hAPP(V_P_2,V_x_2))
     => hAPP(c_List_OremoveAll(T_b,V_x_2),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) ),
    file('theBenchmark.p',fact_removeAll__filter__not) ).

fof(fact_remdups__filter,axiom,
    ! [V_xs_2,V_P_2,T_b] : c_List_Oremdups(T_b,hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_P_2),c_List_Oremdups(T_b,V_xs_2)),
    file('theBenchmark.p',fact_remdups__filter) ).

fof(fact_removeAll__filter__not__eq,axiom,
    ! [V_x_2,T_b] : c_List_OremoveAll(T_b,V_x_2) = c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(c_fequal,V_x_2))),
    file('theBenchmark.p',fact_removeAll__filter__not__eq) ).

fof(fact_transpose_Osimps_I2_J,axiom,
    ! [V_xss,T_a] : c_List_Otranspose(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),V_xss)) = c_List_Otranspose(T_a,V_xss),
    file('theBenchmark.p',fact_transpose_Osimps_I2_J) ).

fof(fact_nth__transpose,axiom,
    ! [V_xs_2,T_b,V_i_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2))))
     => hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),c_List_Otranspose(T_b,V_xs_2)),V_i_2) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,T_b),c_List_Onth(T_b)),V_i_2)),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_xs_2)) ),
    file('theBenchmark.p',fact_nth__transpose) ).

fof(fact_transpose__map__map,axiom,
    ! [V_xs_2,V_f_2,T_c,T_b] : c_List_Otranspose(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_List_Olist(T_b)),hAPP(c_List_Omap(T_c,T_b),V_f_2)),V_xs_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_List_Olist(T_b)),hAPP(c_List_Omap(T_c,T_b),V_f_2)),c_List_Otranspose(T_c,V_xs_2)),
    file('theBenchmark.p',fact_transpose__map__map) ).

fof(fact_set__filter,axiom,
    ! [V_xs_2,V_P_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),hAPP(c_List_Oset(T_b),V_xs_2)))),V_P_2)),
    file('theBenchmark.p',fact_set__filter) ).

fof(fact_length__filter__less,axiom,
    ! [V_P_2,V_xs_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
     => ( ~ hBOOL(hAPP(V_P_2,V_x_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ) ),
    file('theBenchmark.p',fact_length__filter__less) ).

fof(fact_set__minus__filter__out,axiom,
    ! [V_y_2,V_xs_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_List_Oset(T_b),hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_y_2))),V_xs_2)),
    file('theBenchmark.p',fact_set__minus__filter__out) ).

fof(fact_filter__in__sublist,axiom,
    ! [V_s_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
     => hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_s_2)))),V_xs_2) = c_List_Osublist(T_b,V_xs_2,V_s_2) ),
    file('theBenchmark.p',fact_filter__in__sublist) ).

fof(fact_transpose__empty,axiom,
    ! [V_xs_2,T_b] :
      ( c_List_Otranspose(T_b,V_xs_2) = c_List_Olist_ONil(tc_List_Olist(T_b))
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
         => B_x = c_List_Olist_ONil(T_b) ) ),
    file('theBenchmark.p',fact_transpose__empty) ).

fof(fact_length__filter__conv__card,axiom,
    ! [V_xs_2,V_p_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_p_2),V_xs_2)) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,tc_Nat_Onat),V_p_2),hAPP(c_List_Onth(T_b),V_xs_2))))),
    file('theBenchmark.p',fact_length__filter__conv__card) ).

fof(fact_transpose__aux__filter__tail,axiom,
    ! [V_xss_2,T_b] : c_List_Oconcat(tc_List_Olist(T_b),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_b)),T_b,c_List_Olist_ONil(tc_List_Olist(T_b)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_OCons(tc_List_Olist(T_b))),c_List_Olist_ONil(tc_List_Olist(T_b)))))),V_xss_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Otl(T_b)),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_b)))),V_xss_2)),
    file('theBenchmark.p',fact_transpose__aux__filter__tail) ).

fof(fact_transpose_Opsimps_I3_J,axiom,
    ! [V_xss_2,V_xs_2,V_x_2,T_b] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_b)),c_List_Otranspose__rel(T_b)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_xss_2)))
     => c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_xss_2)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),c_COMBK(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b))))),V_xss_2)))),c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),V_xs_2),c_List_Oconcat(tc_List_Olist(T_b),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_b)),T_b,c_List_Olist_ONil(tc_List_Olist(T_b)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_OCons(tc_List_Olist(T_b))),c_List_Olist_ONil(tc_List_Olist(T_b)))))),V_xss_2))))) ),
    file('theBenchmark.p',fact_transpose_Opsimps_I3_J) ).

fof(fact_transpose_Opsimps_I2_J,axiom,
    ! [V_xss_2,T_b] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_b)),c_List_Otranspose__rel(T_b)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_xss_2)))
     => c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_xss_2)) = c_List_Otranspose(T_b,V_xss_2) ),
    file('theBenchmark.p',fact_transpose_Opsimps_I2_J) ).

fof(fact_sublist__shift__lemma__Suc,axiom,
    ! [V_is_2,V_xs_2,V_P_2,T_b] : hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(T_b,tc_Nat_Onat)),V_P_2),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_prod(T_b,tc_Nat_Onat)),c_Nat_OSuc),c_Product__Type_Osnd(T_b,tc_Nat_Onat)))),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),V_is_2))) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(T_b,tc_Nat_Onat)),V_P_2),c_Product__Type_Osnd(T_b,tc_Nat_Onat))),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),V_is_2)))),
    file('theBenchmark.p',fact_sublist__shift__lemma__Suc) ).

fof(fact_select__weigth__drop__zero,axiom,
    ! [V_xs_2,T_b] : c_Random_Oselect__weight(T_b,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),V_xs_2)) = c_Random_Oselect__weight(T_b,V_xs_2),
    file('theBenchmark.p',fact_select__weigth__drop__zero) ).

fof(fact_pick__drop__zero,axiom,
    ! [V_xs_2,T_b] : c_Random_Opick(T_b,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),V_xs_2)) = c_Random_Opick(T_b,V_xs_2),
    file('theBenchmark.p',fact_pick__drop__zero) ).

fof(fact_transpose_Opsimps_I1_J,axiom,
    ! [T_b] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_b)),c_List_Otranspose__rel(T_b)),c_List_Olist_ONil(tc_List_Olist(T_b))))
     => c_List_Otranspose(T_b,c_List_Olist_ONil(tc_List_Olist(T_b))) = c_List_Olist_ONil(tc_List_Olist(T_b)) ),
    file('theBenchmark.p',fact_transpose_Opsimps_I1_J) ).

fof(fact_transpose__max__length,axiom,
    ! [V_xs_2,T_b] : c_List_Ofoldr(tc_List_Olist(T_b),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_b)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_b)))),V_xs_2)),
    file('theBenchmark.p',fact_transpose__max__length) ).

fof(fact_transpose__aux__max,axiom,
    ! [V_xss_2,T_c,V_xs_2,T_b] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))),c_List_Ofoldr(tc_List_Olist(T_c),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_c)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_c))),V_xss_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),c_List_Ofoldr(tc_List_Olist(T_c),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_c)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_c)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_c)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_List_Ofilter(tc_List_Olist(T_c),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_c)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_List_Olist(T_c),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_c)))),V_xss_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
    file('theBenchmark.p',fact_transpose__aux__max) ).

fof(fact_foldr_Osimps_I1_J,axiom,
    ! [V_a_2,V_f_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_f_2,c_List_Olist_ONil(T_c),V_a_2) = V_a_2,
    file('theBenchmark.p',fact_foldr_Osimps_I1_J) ).

fof(fact_foldr_Osimps_I2_J,axiom,
    ! [V_a_2,V_xs_2,V_x_2,V_f_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2),V_a_2) = hAPP(hAPP(V_f_2,V_x_2),c_List_Ofoldr(T_c,T_b,V_f_2,V_xs_2,V_a_2)),
    file('theBenchmark.p',fact_foldr_Osimps_I2_J) ).

fof(fact_foldr__append,axiom,
    ! [V_a_2,V_ys_2,V_xs_2,V_f_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_f_2,hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2),V_a_2) = c_List_Ofoldr(T_c,T_b,V_f_2,V_xs_2,c_List_Ofoldr(T_c,T_b,V_f_2,V_ys_2,V_a_2)),
    file('theBenchmark.p',fact_foldr__append) ).

fof(fact_foldr__conv__foldl,axiom,
    ! [V_a_2,V_xs_2,T_b] :
      ( class_Groups_Oab__semigroup__add(T_b)
     => c_List_Ofoldr(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_xs_2,V_a_2) = hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_xs_2) ),
    file('theBenchmark.p',fact_foldr__conv__foldl) ).

fof(fact_foldr__map,axiom,
    ! [V_a_2,V_xs_2,V_f_2,T_d,V_g_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_g_2,hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2),V_a_2) = c_List_Ofoldr(T_d,T_b,hAPP(c_Fun_Ocomp(T_c,tc_fun(T_b,T_b),T_d,V_g_2),V_f_2),V_xs_2,V_a_2),
    file('theBenchmark.p',fact_foldr__map) ).

fof(fact_foldl__foldr1__lemma,axiom,
    ! [V_xs_2,V_a_2,T_b] :
      ( class_Groups_Omonoid__add(T_b)
     => hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_xs_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),c_List_Ofoldr(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_xs_2,c_Groups_Ozero__class_Ozero(T_b))) ),
    file('theBenchmark.p',fact_foldl__foldr1__lemma) ).

fof(fact_foldl__foldr1,axiom,
    ! [V_xs_2,T_b] :
      ( class_Groups_Omonoid__add(T_b)
     => hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_xs_2) = c_List_Ofoldr(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_xs_2,c_Groups_Ozero__class_Ozero(T_b)) ),
    file('theBenchmark.p',fact_foldl__foldr1) ).

fof(fact_length__transpose,axiom,
    ! [V_xs_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2)) = c_List_Ofoldr(tc_List_Olist(T_b),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_b)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('theBenchmark.p',fact_length__transpose) ).

fof(fact_sublist__def,axiom,
    ! [V_A_2,V_xs_2,T_b] : c_List_Osublist(T_b,V_xs_2,V_A_2) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_b,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(T_b,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(T_b,tc_Nat_Onat))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))))),
    file('theBenchmark.p',fact_sublist__def) ).

fof(fact_sublist__shift__lemma,axiom,
    ! [V_i_2,V_xs_2,V_A_2,T_b] : hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_b,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(T_b,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(T_b,tc_Nat_Onat))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),c_List_Oupt(V_i_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))))) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_b,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(T_b,tc_Nat_Onat)),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(T_b,tc_Nat_Onat),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_prod(T_b,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Product__Type_Osnd(T_b,tc_Nat_Onat))),V_i_2))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))))),
    file('theBenchmark.p',fact_sublist__shift__lemma) ).

fof(fact_set__upt,axiom,
    ! [V_j_2,V_i_2] : hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_i_2,V_j_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2),
    file('theBenchmark.p',fact_set__upt) ).

fof(fact_atLeastLessThan__upt,axiom,
    ! [V_j_2,V_i_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_i_2,V_j_2)),
    file('theBenchmark.p',fact_atLeastLessThan__upt) ).

fof(fact_upt__Suc,axiom,
    ! [V_j,V_i] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
       => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = c_List_Olist_ONil(tc_Nat_Onat) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
       => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(V_i,V_j)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_j),c_List_Olist_ONil(tc_Nat_Onat))) ) ),
    file('theBenchmark.p',fact_upt__Suc) ).

fof(fact_upt__Suc__append,axiom,
    ! [V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
     => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(V_i,V_j)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_j),c_List_Olist_ONil(tc_Nat_Onat))) ),
    file('theBenchmark.p',fact_upt__Suc__append) ).

fof(fact_upt__add__eq__append,axiom,
    ! [V_k,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
     => c_List_Oupt(V_i,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(V_i,V_j)),c_List_Oupt(V_j,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k))) ),
    file('theBenchmark.p',fact_upt__add__eq__append) ).

fof(fact_upt__rec,axiom,
    ! [V_j,V_i] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
       => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
       => c_List_Oupt(V_i,V_j) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_i),c_List_Oupt(hAPP(c_Nat_OSuc,V_i),V_j)) ) ),
    file('theBenchmark.p',fact_upt__rec) ).

fof(fact_upt__conv__Cons,axiom,
    ! [V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
     => c_List_Oupt(V_i,V_j) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_i),c_List_Oupt(hAPP(c_Nat_OSuc,V_i),V_j)) ),
    file('theBenchmark.p',fact_upt__conv__Cons) ).

fof(fact_upt__conv__Nil,axiom,
    ! [V_i,V_j] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i))
     => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ),
    file('theBenchmark.p',fact_upt__conv__Nil) ).

fof(fact_upt__eq__Nil__conv,axiom,
    ! [V_j_2,V_i_2] :
      ( c_List_Oupt(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Nat_Onat)
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
        | V_j_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_upt__eq__Nil__conv) ).

fof(fact_upt__0,axiom,
    ! [V_i] : c_List_Oupt(V_i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat),
    file('theBenchmark.p',fact_upt__0) ).

fof(fact_take__upt,axiom,
    ! [V_n,V_m,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m)),V_n))
     => hAPP(hAPP(c_List_Otake(tc_Nat_Onat),V_m),c_List_Oupt(V_i,V_n)) = c_List_Oupt(V_i,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m)) ),
    file('theBenchmark.p',fact_take__upt) ).

fof(fact_sorted__list__of__set__range,axiom,
    ! [V_n_2,V_m_2] : c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)) = c_List_Oupt(V_m_2,V_n_2),
    file('theBenchmark.p',fact_sorted__list__of__set__range) ).

fof(fact_hd__upt,axiom,
    ! [V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
     => hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(V_i,V_j)) = V_i ),
    file('theBenchmark.p',fact_hd__upt) ).

fof(fact_drop__upt,axiom,
    ! [V_j,V_i,V_m] : hAPP(hAPP(c_List_Odrop(tc_Nat_Onat),V_m),c_List_Oupt(V_i,V_j)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m),V_j),
    file('theBenchmark.p',fact_drop__upt) ).

fof(fact_distinct__upt,axiom,
    ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(V_i,V_j))),
    file('theBenchmark.p',fact_distinct__upt) ).

fof(fact_length__upt,axiom,
    ! [V_j,V_i] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),c_List_Oupt(V_i,V_j)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_i),
    file('theBenchmark.p',fact_length__upt) ).

fof(fact_upt__rec__number__of,axiom,
    ! [V_n,V_m] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n)))
       => c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n)) = c_List_Olist_ONil(tc_Nat_Onat) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n)))
       => c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m)),c_List_Oupt(hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n))) ) ),
    file('theBenchmark.p',fact_upt__rec__number__of) ).

fof(fact_upt__eq__Cons__conv,axiom,
    ! [V_xs_2,V_x_2,V_j_2,V_i_2] :
      ( c_List_Oupt(V_i_2,V_j_2) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_x_2),V_xs_2)
    <=> ( c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_j_2) = V_xs_2
        & V_i_2 = V_x_2
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_j_2)) ) ),
    file('theBenchmark.p',fact_upt__eq__Cons__conv) ).

fof(fact_last__upt,axiom,
    ! [V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
     => c_List_Olast(tc_Nat_Onat,c_List_Oupt(V_i,V_j)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    file('theBenchmark.p',fact_last__upt) ).

fof(fact_map__Suc__upt,axiom,
    ! [V_n_2,V_m_2] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),c_List_Oupt(V_m_2,V_n_2)) = c_List_Oupt(hAPP(c_Nat_OSuc,V_m_2),hAPP(c_Nat_OSuc,V_n_2)),
    file('theBenchmark.p',fact_map__Suc__upt) ).

fof(fact_atLeastAtMost__upt,axiom,
    ! [V_m_2,V_n_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_n_2,V_m_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_n_2,hAPP(c_Nat_OSuc,V_m_2))),
    file('theBenchmark.p',fact_atLeastAtMost__upt) ).

fof(fact_atLeast__upt,axiom,
    ! [V_n_2] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)),
    file('theBenchmark.p',fact_atLeast__upt) ).

fof(fact_nth__upt,axiom,
    ! [V_j,V_k,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),V_j))
     => hAPP(hAPP(c_List_Onth(tc_Nat_Onat),c_List_Oupt(V_i,V_j)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k) ),
    file('theBenchmark.p',fact_nth__upt) ).

fof(fact_greaterThanAtMost__upt,axiom,
    ! [V_m_2,V_n_2] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_n_2,V_m_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,V_n_2),hAPP(c_Nat_OSuc,V_m_2))),
    file('theBenchmark.p',fact_greaterThanAtMost__upt) ).

fof(fact_greaterThanLessThan__upt,axiom,
    ! [V_m_2,V_n_2] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,V_n_2,V_m_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,V_n_2),V_m_2)),
    file('theBenchmark.p',fact_greaterThanLessThan__upt) ).

fof(fact_atMost__upto,axiom,
    ! [V_n_2] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2))),
    file('theBenchmark.p',fact_atMost__upto) ).

fof(fact_map__nth,axiom,
    ! [V_xs_2,T_b] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),hAPP(c_List_Onth(T_b),V_xs_2)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) = V_xs_2,
    file('theBenchmark.p',fact_map__nth) ).

fof(fact_setsum__set__upt__conv__listsum__nat,axiom,
    ! [V_n_2,V_m_2,V_f_2,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_m_2,V_n_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),V_f_2),c_List_Oupt(V_m_2,V_n_2))) ),
    file('theBenchmark.p',fact_setsum__set__upt__conv__listsum__nat) ).

fof(fact_interv__listsum__conv__setsum__set__nat,axiom,
    ! [V_n_2,V_m_2,V_f_2,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),V_f_2),c_List_Oupt(V_m_2,V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_m_2,V_n_2))) ),
    file('theBenchmark.p',fact_interv__listsum__conv__setsum__set__nat) ).

fof(fact_nth__map__upt,axiom,
    ! [V_f_2,T_b,V_m_2,V_n_2,V_i_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_m_2)))
     => hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),V_f_2),c_List_Oupt(V_m_2,V_n_2))),V_i_2) = hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_i_2)) ),
    file('theBenchmark.p',fact_nth__map__upt) ).

fof(fact_transpose__rectangle,axiom,
    ! [V_n_2,T_b,V_xs_2] :
      ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_b))
       => V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
     => ( ! [B_i] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2)))
           => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),B_i)) = V_n_2 )
       => c_List_Otranspose(T_b,V_xs_2) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(T_b)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(T_b)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,T_b)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_Nat_Onat,T_b),tc_Nat_Onat),c_List_Onth(T_b)),hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)) ) ),
    file('theBenchmark.p',fact_transpose__rectangle) ).

fof(fact_insort__key__remove1,axiom,
    ! [V_f_2,V_xs_2,V_a_2,T_b,T_c] :
      ( class_Orderings_Olinorder(T_c)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2)))
       => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))
         => ( hAPP(c_List_Ohd(T_b),hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(T_c,tc_HOL_Obool,T_b),hAPP(c_fequal,hAPP(V_f_2,V_a_2))),V_f_2)),V_xs_2)) = V_a_2
           => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_a_2),c_List_Oremove1(T_b,V_a_2,V_xs_2)) = V_xs_2 ) ) ) ),
    file('theBenchmark.p',fact_insort__key__remove1) ).

fof(fact_sorted_ONil,axiom,
    ! [T_a] :
      ( class_Orderings_Olinorder(T_a)
     => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ),
    file('theBenchmark.p',fact_sorted_ONil) ).

fof(fact_sorted__single,axiom,
    ! [V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))) ),
    file('theBenchmark.p',fact_sorted__single) ).

fof(fact_sorted__upt,axiom,
    ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(V_i,V_j)),
    file('theBenchmark.p',fact_sorted__upt) ).

fof(fact_sorted__sort,axiom,
    ! [V_xs_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Osort__key(T_b,T_b,c_COMBI(T_b),V_xs_2)) ),
    file('theBenchmark.p',fact_sorted__sort) ).

fof(fact_sorted__insort__insert,axiom,
    ! [V_x_2,V_xs_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
       => c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2)) ) ),
    file('theBenchmark.p',fact_sorted__insort__insert) ).

fof(fact_sorted__drop,axiom,
    ! [V_n,V_xs,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
       => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) ) ),
    file('theBenchmark.p',fact_sorted__drop) ).

fof(fact_sorted__upto,axiom,
    ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(V_i,V_j)),
    file('theBenchmark.p',fact_sorted__upto) ).

fof(fact_sorted__take,axiom,
    ! [V_n,V_xs,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
       => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) ) ),
    file('theBenchmark.p',fact_sorted__take) ).

fof(fact_sorted__remove1,axiom,
    ! [V_a,V_xs,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
       => c_List_Olinorder__class_Osorted(T_a,c_List_Oremove1(T_a,V_a,V_xs)) ) ),
    file('theBenchmark.p',fact_sorted__remove1) ).

fof(fact_sorted__tl,axiom,
    ! [V_xs,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
       => c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Otl(T_a),V_xs)) ) ),
    file('theBenchmark.p',fact_sorted__tl) ).

fof(fact_sorted__insort,axiom,
    ! [V_xs_2,V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),V_xs_2))
      <=> c_List_Olinorder__class_Osorted(T_b,V_xs_2) ) ),
    file('theBenchmark.p',fact_sorted__insort) ).

fof(fact_sorted__butlast,axiom,
    ! [V_xs,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( V_xs != c_List_Olist_ONil(T_a)
       => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
         => c_List_Olinorder__class_Osorted(T_a,c_List_Obutlast(T_a,V_xs)) ) ) ),
    file('theBenchmark.p',fact_sorted__butlast) ).

fof(fact_sorted_Oequations_I1_J,axiom,
    ! [T_a] :
      ( class_Orderings_Olinorder(T_a)
     => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ),
    file('theBenchmark.p',fact_sorted_Oequations_I1_J) ).

fof(fact_sorted__many,axiom,
    ! [V_zs,V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
       => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_zs))
         => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_zs))) ) ) ),
    file('theBenchmark.p',fact_sorted__many) ).

fof(fact_sorted__many__eq,axiom,
    ! [V_zs_2,V_y_2,V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_zs_2)))
      <=> ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_zs_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ),
    file('theBenchmark.p',fact_sorted__many__eq) ).

fof(fact_sorted__remdups,axiom,
    ! [V_l,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( c_List_Olinorder__class_Osorted(T_a,V_l)
       => c_List_Olinorder__class_Osorted(T_a,c_List_Oremdups(T_a,V_l)) ) ),
    file('theBenchmark.p',fact_sorted__remdups) ).

fof(fact_sorted__distinct__set__unique,axiom,
    ! [V_ys_2,V_xs_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
       => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
         => ( c_List_Olinorder__class_Osorted(T_b,V_ys_2)
           => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_ys_2))
             => ( hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_List_Oset(T_b),V_ys_2)
               => V_xs_2 = V_ys_2 ) ) ) ) ) ),
    file('theBenchmark.p',fact_sorted__distinct__set__unique) ).

fof(fact_sorted__sort__key,axiom,
    ! [V_xs_2,V_f_2,T_c,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Olinorder__class_Osort__key(T_c,T_b,V_f_2,V_xs_2))) ),
    file('theBenchmark.p',fact_sorted__sort__key) ).

fof(fact_sorted__insort__insert__key,axiom,
    ! [V_x_2,V_xs_2,V_f_2,T_c,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
       => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Olinorder__class_Oinsort__insert__key(T_c,T_b,V_f_2,V_x_2,V_xs_2))) ) ),
    file('theBenchmark.p',fact_sorted__insort__insert__key) ).

fof(fact_sorted__map__remove1,axiom,
    ! [V_x_2,V_xs_2,V_f_2,T_c,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
       => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Oremove1(T_c,V_x_2,V_xs_2))) ) ),
    file('theBenchmark.p',fact_sorted__map__remove1) ).

fof(fact_sorted__insort__key,axiom,
    ! [V_xs_2,V_x_2,V_f_2,T_c,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_xs_2)))
      <=> c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) ) ),
    file('theBenchmark.p',fact_sorted__insort__key) ).

fof(fact_sorted__filter,axiom,
    ! [V_P_2,V_xs_2,V_f_2,T_c,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
       => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Ofilter(T_c,V_P_2),V_xs_2))) ) ),
    file('theBenchmark.p',fact_sorted__filter) ).

fof(fact_sorted__map__same,axiom,
    ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Ofilter(T_c,hAPP(hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_c),c_fequal),V_f_2)),hAPP(V_g_2,V_xs_2))),V_xs_2))) ),
    file('theBenchmark.p',fact_sorted__map__same) ).

fof(fact_sorted__same,axiom,
    ! [V_xs_2,V_g_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => c_List_Olinorder__class_Osorted(T_b,hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),hAPP(V_g_2,V_xs_2))),V_xs_2)) ),
    file('theBenchmark.p',fact_sorted__same) ).

fof(fact_sorted__Cons,axiom,
    ! [V_xs_2,V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
      <=> ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) )
          & c_List_Olinorder__class_Osorted(T_b,V_xs_2) ) ) ),
    file('theBenchmark.p',fact_sorted__Cons) ).

fof(fact_sorted__append,axiom,
    ! [V_ys_2,V_xs_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))
      <=> ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
             => ! [B_xa] :
                  ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(c_List_Oset(T_b),V_ys_2)))
                 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),B_xa)) ) )
          & c_List_Olinorder__class_Osorted(T_b,V_ys_2)
          & c_List_Olinorder__class_Osorted(T_b,V_xs_2) ) ) ),
    file('theBenchmark.p',fact_sorted__append) ).

fof(fact_filter__insort,axiom,
    ! [V_x_2,V_P_2,V_xs_2,V_f_2,T_c,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
       => ( hBOOL(hAPP(V_P_2,V_x_2))
         => hAPP(c_List_Ofilter(T_c,V_P_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),hAPP(c_List_Ofilter(T_c,V_P_2),V_xs_2)) ) ) ),
    file('theBenchmark.p',fact_filter__insort) ).

fof(fact_sorted_Oequations_I2_J,axiom,
    ! [V_a1_2,V_a2_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a2_2),V_a1_2))
      <=> ( c_List_Olinorder__class_Osorted(T_b,V_a1_2)
          & ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_a1_2)))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a2_2),B_x)) ) ) ) ),
    file('theBenchmark.p',fact_sorted_Oequations_I2_J) ).

fof(fact_sorted__list__of__set,axiom,
    ! [V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2)))
          & c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2))
          & hAPP(c_List_Oset(T_b),c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2)) = V_A_2 ) ) ),
    file('theBenchmark.p',fact_sorted__list__of__set) ).

fof(fact_insort__remove1,axiom,
    ! [V_xs_2,V_a_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2)))
       => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
         => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_a_2),c_List_Oremove1(T_b,V_a_2,V_xs_2)) = V_xs_2 ) ) ),
    file('theBenchmark.p',fact_insort__remove1) ).

fof(fact_sorted__equals__nth__mono,axiom,
    ! [V_xs_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
      <=> ! [B_j] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
           => ! [B_i] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i)),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_j))) ) ) ) ),
    file('theBenchmark.p',fact_sorted__equals__nth__mono) ).

fof(fact_sorted__nth__mono,axiom,
    ! [V_j,V_i,V_xs,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_j))) ) ) ) ),
    file('theBenchmark.p',fact_sorted__nth__mono) ).

fof(fact_map__sorted__distinct__set__unique,axiom,
    ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
      ( class_Orderings_Olinorder(T_c)
     => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_ys_2)))
       => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))
         => ( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)))
           => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2))
             => ( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2)))
               => ( hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_List_Oset(T_b),V_ys_2)
                 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ),
    file('theBenchmark.p',fact_map__sorted__distinct__set__unique) ).

fof(fact_transpose__column,axiom,
    ! [V_i_2,V_xs_2,T_b] :
      ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2)))
       => hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,T_b),c_List_Onth(T_b)),V_i_2)),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),c_List_Otranspose(T_b,V_xs_2))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),V_i_2) ) ),
    file('theBenchmark.p',fact_transpose__column) ).

fof(fact_nth__nth__transpose__sorted,axiom,
    ! [V_j_2,V_i_2,V_xs_2,T_b] :
      ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2))))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_xs_2))))
         => hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),c_List_Otranspose(T_b,V_xs_2)),V_i_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),V_j_2)),V_i_2) ) ) ),
    file('theBenchmark.p',fact_nth__nth__transpose__sorted) ).

fof(fact_inj__on__rev,axiom,
    ! [V_A_2,T_b] : c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Orev(T_b),V_A_2),
    file('theBenchmark.p',fact_inj__on__rev) ).

fof(fact_distinct__rev,axiom,
    ! [V_xs_2,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orev(T_b),V_xs_2)))
    <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ),
    file('theBenchmark.p',fact_distinct__rev) ).

fof(fact_rev_Osimps_I1_J,axiom,
    ! [T_a] : hAPP(c_List_Orev(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a),
    file('theBenchmark.p',fact_rev_Osimps_I1_J) ).

fof(fact_Nil__is__rev__conv,axiom,
    ! [V_xs_2,T_b] :
      ( c_List_Olist_ONil(T_b) = hAPP(c_List_Orev(T_b),V_xs_2)
    <=> V_xs_2 = c_List_Olist_ONil(T_b) ),
    file('theBenchmark.p',fact_Nil__is__rev__conv) ).

fof(fact_rev__is__Nil__conv,axiom,
    ! [V_xs_2,T_b] :
      ( hAPP(c_List_Orev(T_b),V_xs_2) = c_List_Olist_ONil(T_b)
    <=> V_xs_2 = c_List_Olist_ONil(T_b) ),
    file('theBenchmark.p',fact_rev__is__Nil__conv) ).

fof(fact_rev__singleton__conv,axiom,
    ! [V_x_2,V_xs_2,T_b] :
      ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))
    <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ),
    file('theBenchmark.p',fact_rev__singleton__conv) ).

fof(fact_singleton__rev__conv,axiom,
    ! [V_xs_2,V_x_2,T_b] :
      ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) = hAPP(c_List_Orev(T_b),V_xs_2)
    <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ),
    file('theBenchmark.p',fact_singleton__rev__conv) ).

fof(fact_rev__append,axiom,
    ! [V_ys,V_xs,T_a] : hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Orev(T_a),V_ys)),hAPP(c_List_Orev(T_a),V_xs)),
    file('theBenchmark.p',fact_rev__append) ).

fof(fact_rev__concat,axiom,
    ! [V_xs_2,T_b] : hAPP(c_List_Orev(T_b),c_List_Oconcat(T_b,V_xs_2)) = c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Orev(T_b)),hAPP(c_List_Orev(tc_List_Olist(T_b)),V_xs_2))),
    file('theBenchmark.p',fact_rev__concat) ).

fof(fact_rev__map,axiom,
    ! [V_xs_2,V_f_2,T_c,T_b] : hAPP(c_List_Orev(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Orev(T_c),V_xs_2)),
    file('theBenchmark.p',fact_rev__map) ).

fof(fact_rev__filter,axiom,
    ! [V_xs_2,V_P_2,T_b] : hAPP(c_List_Orev(T_b),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(c_List_Orev(T_b),V_xs_2)),
    file('theBenchmark.p',fact_rev__filter) ).

fof(fact_zip__rev,axiom,
    ! [V_ys,T_b,V_xs,T_a] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys)
     => hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(c_List_Orev(T_a),V_xs)),hAPP(c_List_Orev(T_b),V_ys)) = hAPP(c_List_Orev(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)) ),
    file('theBenchmark.p',fact_zip__rev) ).

fof(fact_set__rev,axiom,
    ! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_Orev(T_b),V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2),
    file('theBenchmark.p',fact_set__rev) ).

fof(fact_list__all2__rev1,axiom,
    ! [V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
      ( c_List_Olist__all2(T_b,T_c,V_P_2,hAPP(c_List_Orev(T_b),V_xs_2),V_ys_2)
    <=> c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,hAPP(c_List_Orev(T_c),V_ys_2)) ),
    file('theBenchmark.p',fact_list__all2__rev1) ).

fof(fact_list__all2__rev,axiom,
    ! [V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
      ( c_List_Olist__all2(T_b,T_c,V_P_2,hAPP(c_List_Orev(T_b),V_xs_2),hAPP(c_List_Orev(T_c),V_ys_2))
    <=> c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2) ),
    file('theBenchmark.p',fact_list__all2__rev) ).

fof(fact_rev__is__rev__conv,axiom,
    ! [V_ys_2,V_xs_2,T_b] :
      ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(c_List_Orev(T_b),V_ys_2)
    <=> V_xs_2 = V_ys_2 ),
    file('theBenchmark.p',fact_rev__is__rev__conv) ).

fof(fact_rev__swap,axiom,
    ! [V_ys_2,V_xs_2,T_b] :
      ( hAPP(c_List_Orev(T_b),V_xs_2) = V_ys_2
    <=> V_xs_2 = hAPP(c_List_Orev(T_b),V_ys_2) ),
    file('theBenchmark.p',fact_rev__swap) ).

fof(fact_rev__rev__ident,axiom,
    ! [V_xs,T_a] : hAPP(c_List_Orev(T_a),hAPP(c_List_Orev(T_a),V_xs)) = V_xs,
    file('theBenchmark.p',fact_rev__rev__ident) ).

fof(fact_listsum__rev,axiom,
    ! [V_xs,T_a] :
      ( class_Groups_Ocomm__monoid__add(T_a)
     => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs) ),
    file('theBenchmark.p',fact_listsum__rev) ).

fof(fact_length__rev,axiom,
    ! [V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs),
    file('theBenchmark.p',fact_length__rev) ).

fof(fact_foldr__foldl,axiom,
    ! [V_a_2,V_xs_2,V_f_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_f_2,V_xs_2,V_a_2) = hAPP(c_List_Ofoldl(T_b,T_c,hAPP(c_COMBC(T_c,T_b,T_b),V_f_2),V_a_2),hAPP(c_List_Orev(T_c),V_xs_2)),
    file('theBenchmark.p',fact_foldr__foldl) ).

fof(fact_foldl__foldr,axiom,
    ! [V_xs_2,V_a_2,V_f_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),V_xs_2) = c_List_Ofoldr(T_c,T_b,hAPP(c_COMBC(T_b,T_c,T_b),V_f_2),hAPP(c_List_Orev(T_c),V_xs_2),V_a_2),
    file('theBenchmark.p',fact_foldl__foldr) ).

fof(fact_rev_Osimps_I2_J,axiom,
    ! [V_xs,V_x,T_a] : hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Orev(T_a),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))),
    file('theBenchmark.p',fact_rev_Osimps_I2_J) ).

fof(fact_rev__eq__Cons__iff,axiom,
    ! [V_ys_2,V_y_2,V_xs_2,T_b] :
      ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)
    <=> V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),hAPP(c_List_Orev(T_b),V_ys_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),c_List_Olist_ONil(T_b))) ),
    file('theBenchmark.p',fact_rev__eq__Cons__iff) ).

fof(fact_last__rev,axiom,
    ! [T_a,V_xs] :
      ( V_xs != c_List_Olist_ONil(T_a)
     => c_List_Olast(T_a,hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Ohd(T_a),V_xs) ),
    file('theBenchmark.p',fact_last__rev) ).

fof(fact_hd__rev,axiom,
    ! [T_a,V_xs] :
      ( V_xs != c_List_Olist_ONil(T_a)
     => hAPP(c_List_Ohd(T_a),hAPP(c_List_Orev(T_a),V_xs)) = c_List_Olast(T_a,V_xs) ),
    file('theBenchmark.p',fact_hd__rev) ).

fof(fact_sorted__transpose,axiom,
    ! [V_xs_2,T_b] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2)))),
    file('theBenchmark.p',fact_sorted__transpose) ).

fof(fact_rev__foldl__cons,axiom,
    ! [V_xs_2,T_b] : hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_b),T_b,hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b)),V_xs_2),
    file('theBenchmark.p',fact_rev__foldl__cons) ).

fof(fact_rev__drop,axiom,
    ! [V_xs,V_i,T_a] : hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs)) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_i)),hAPP(c_List_Orev(T_a),V_xs)),
    file('theBenchmark.p',fact_rev__drop) ).

fof(fact_rev__take,axiom,
    ! [V_xs,V_i,T_a] : hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_i)),hAPP(c_List_Orev(T_a),V_xs)),
    file('theBenchmark.p',fact_rev__take) ).

fof(fact_rotate__rev,axiom,
    ! [V_xs,V_n,T_a] : hAPP(c_List_Orotate(T_a,V_n),hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Orev(T_a),hAPP(c_List_Orotate(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))),V_xs)),
    file('theBenchmark.p',fact_rotate__rev) ).

fof(fact_rev__nth,axiom,
    ! [V_xs,T_a,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
     => hAPP(hAPP(c_List_Onth(T_a),hAPP(c_List_Orev(T_a),V_xs)),V_n) = hAPP(hAPP(c_List_Onth(T_a),V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_OSuc,V_n))) ),
    file('theBenchmark.p',fact_rev__nth) ).

fof(fact_rev__update,axiom,
    ! [V_y,V_xs,T_a,V_k] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
     => hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_y)) = hAPP(hAPP(c_List_Olist__update(T_a,hAPP(c_List_Orev(T_a),V_xs)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_k)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_y) ),
    file('theBenchmark.p',fact_rev__update) ).

fof(fact_sorted__rev__nth__mono,axiom,
    ! [V_j,V_i,V_xs,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),V_xs))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_j)),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i))) ) ) ) ),
    file('theBenchmark.p',fact_sorted__rev__nth__mono) ).

fof(fact_foldr__max__sorted,axiom,
    ! [V_y_2,V_xs_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( c_List_Olinorder__class_Osorted(T_b,hAPP(c_List_Orev(T_b),V_xs_2))
       => ( ( V_xs_2 != c_List_Olist_ONil(T_b)
           => c_List_Ofoldr(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_xs_2,V_y_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_y_2) )
          & ( V_xs_2 = c_List_Olist_ONil(T_b)
           => c_List_Ofoldr(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_xs_2,V_y_2) = V_y_2 ) ) ) ),
    file('theBenchmark.p',fact_foldr__max__sorted) ).

fof(fact_length__transpose__sorted,axiom,
    ! [V_xs_2,T_b] :
      ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2)))
     => ( ( V_xs_2 != c_List_Olist_ONil(tc_List_Olist(T_b))
         => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
        & ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_b))
         => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
    file('theBenchmark.p',fact_length__transpose__sorted) ).

fof(fact_transpose__column__length,axiom,
    ! [V_i_2,V_xs_2,T_b] :
      ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2)))
       => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),c_List_Otranspose(T_b,V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),V_i_2)) ) ),
    file('theBenchmark.p',fact_transpose__column__length) ).

fof(fact_transpose__transpose,axiom,
    ! [V_xs_2,T_b] :
      ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2)))
     => c_List_Otranspose(T_b,c_List_Otranspose(T_b,V_xs_2)) = c_List_OtakeWhile(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_b))),V_xs_2) ),
    file('theBenchmark.p',fact_transpose__transpose) ).

fof(fact_transfer__nat__int__list__functions_I2_J,axiom,
    c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)),
    file('theBenchmark.p',fact_transfer__nat__int__list__functions_I2_J) ).

fof(fact_sorted__takeWhile,axiom,
    ! [V_P_2,V_xs_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
       => c_List_Olinorder__class_Osorted(T_b,c_List_OtakeWhile(T_b,V_P_2,V_xs_2)) ) ),
    file('theBenchmark.p',fact_sorted__takeWhile) ).

fof(fact_length__takeWhile__le,axiom,
    ! [V_xs_2,V_P_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))),
    file('theBenchmark.p',fact_length__takeWhile__le) ).

fof(fact_takeWhile__eq__all__conv,axiom,
    ! [V_xs_2,V_P_2,T_b] :
      ( c_List_OtakeWhile(T_b,V_P_2,V_xs_2) = V_xs_2
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
         => hBOOL(hAPP(V_P_2,B_x)) ) ),
    file('theBenchmark.p',fact_takeWhile__eq__all__conv) ).

fof(fact_set__takeWhileD,axiom,
    ! [V_xs_2,V_P_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))))
     => ( hBOOL(hAPP(V_P_2,V_x_2))
        & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ),
    file('theBenchmark.p',fact_set__takeWhileD) ).

fof(fact_zip__takeWhile__snd,axiom,
    ! [V_ys_2,V_P_2,V_xs_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),c_List_OtakeWhile(T_c,V_P_2,V_ys_2)) = c_List_OtakeWhile(tc_prod(T_b,T_c),hAPP(c_Fun_Ocomp(T_c,tc_HOL_Obool,tc_prod(T_b,T_c),V_P_2),c_Product__Type_Osnd(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)),
    file('theBenchmark.p',fact_zip__takeWhile__snd) ).

fof(fact_zip__takeWhile__fst,axiom,
    ! [V_ys_2,V_xs_2,V_P_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),c_List_OtakeWhile(T_b,V_P_2,V_xs_2)),V_ys_2) = c_List_OtakeWhile(tc_prod(T_b,T_c),hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,tc_prod(T_b,T_c),V_P_2),c_Product__Type_Ofst(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)),
    file('theBenchmark.p',fact_zip__takeWhile__fst) ).

fof(fact_takeWhile__map,axiom,
    ! [V_xs_2,V_f_2,T_c,V_P_2,T_b] : c_List_OtakeWhile(T_b,V_P_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_OtakeWhile(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_P_2),V_f_2),V_xs_2)),
    file('theBenchmark.p',fact_takeWhile__map) ).

fof(fact_takeWhile__tail,axiom,
    ! [V_l_2,V_xs_2,T_b,V_x_2,V_P_2] :
      ( ~ hBOOL(hAPP(V_P_2,V_x_2))
     => c_List_OtakeWhile(T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_l_2))) = c_List_OtakeWhile(T_b,V_P_2,V_xs_2) ),
    file('theBenchmark.p',fact_takeWhile__tail) ).

fof(fact_takeWhile_Osimps_I2_J,axiom,
    ! [V_xs_2,T_b,V_x_2,V_P_2] :
      ( ( ~ hBOOL(hAPP(V_P_2,V_x_2))
       => c_List_OtakeWhile(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_List_Olist_ONil(T_b) )
      & ( hBOOL(hAPP(V_P_2,V_x_2))
       => c_List_OtakeWhile(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_OtakeWhile(T_b,V_P_2,V_xs_2)) ) ),
    file('theBenchmark.p',fact_takeWhile_Osimps_I2_J) ).

fof(fact_takeWhile_Osimps_I1_J,axiom,
    ! [V_P_2,T_b] : c_List_OtakeWhile(T_b,V_P_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b),
    file('theBenchmark.p',fact_takeWhile_Osimps_I1_J) ).

fof(fact_takeWhile__eq__take,axiom,
    ! [V_xs_2,V_P_2,T_b] : c_List_OtakeWhile(T_b,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))),V_xs_2),
    file('theBenchmark.p',fact_takeWhile__eq__take) ).

fof(fact_distinct__takeWhile,axiom,
    ! [V_P_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
     => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))) ),
    file('theBenchmark.p',fact_distinct__takeWhile) ).

fof(fact_return__list__def,axiom,
    ! [V_l_2] : c_List_Oreturn__list(V_l_2) = hAPP(hAPP(c_List_Omap(tc_Int_Oint,tc_Nat_Onat),c_Int_Onat),V_l_2),
    file('theBenchmark.p',fact_return__list__def) ).

fof(fact_takeWhile__append1,axiom,
    ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
     => ( ~ hBOOL(hAPP(V_P_2,V_x_2))
       => c_List_OtakeWhile(T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = c_List_OtakeWhile(T_b,V_P_2,V_xs_2) ) ),
    file('theBenchmark.p',fact_takeWhile__append1) ).

fof(fact_takeWhile__nth,axiom,
    ! [V_xs_2,V_P_2,T_b,V_j_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))))
     => hAPP(hAPP(c_List_Onth(T_b),c_List_OtakeWhile(T_b,V_P_2,V_xs_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_j_2) ),
    file('theBenchmark.p',fact_takeWhile__nth) ).

fof(fact_nth__length__takeWhile,axiom,
    ! [V_xs_2,V_P_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
     => ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))))) ),
    file('theBenchmark.p',fact_nth__length__takeWhile) ).

fof(fact_takeWhile__not__last,axiom,
    ! [T_b,V_xs_2] :
      ( V_xs_2 != c_List_Olist_ONil(T_b)
     => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
       => c_List_OtakeWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),c_List_Olast(T_b,V_xs_2))),V_xs_2) = c_List_Obutlast(T_b,V_xs_2) ) ),
    file('theBenchmark.p',fact_takeWhile__not__last) ).

fof(fact_filter__equals__takeWhile__sorted__rev,axiom,
    ! [V_t_2,V_xs_2,V_f_2,T_c,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( c_List_Olinorder__class_Osorted(T_b,hAPP(c_List_Orev(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)))
       => hAPP(c_List_Ofilter(T_c,hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,T_c),hAPP(c_Orderings_Oord__class_Oless(T_b),V_t_2)),V_f_2)),V_xs_2) = c_List_OtakeWhile(T_c,hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,T_c),hAPP(c_Orderings_Oord__class_Oless(T_b),V_t_2)),V_f_2),V_xs_2) ) ),
    file('theBenchmark.p',fact_filter__equals__takeWhile__sorted__rev) ).

fof(fact_transfer__nat__int__list__return__embed,axiom,
    ! [V_l] :
      ( c_List_Onat__list(V_l)
     => c_List_Oembed__list(c_List_Oreturn__list(V_l)) = V_l ),
    file('theBenchmark.p',fact_transfer__nat__int__list__return__embed) ).

fof(fact_transfer__nat__int__list__functions_I1_J,axiom,
    ! [V_m,V_l] : hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),V_l),V_m) = c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint),c_List_Oembed__list(V_l)),c_List_Oembed__list(V_m))),
    file('theBenchmark.p',fact_transfer__nat__int__list__functions_I1_J) ).

fof(fact_embed__list__def,axiom,
    ! [V_l_2] : c_List_Oembed__list(V_l_2) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_l_2),
    file('theBenchmark.p',fact_embed__list__def) ).

fof(fact_takeWhile__neq__rev,axiom,
    ! [V_x_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
       => c_List_OtakeWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)),hAPP(c_List_Orev(T_b),V_xs_2)) = hAPP(c_List_Orev(T_b),hAPP(c_List_Otl(T_b),c_List_OdropWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)),V_xs_2))) ) ),
    file('theBenchmark.p',fact_takeWhile__neq__rev) ).

fof(fact_dropWhile__neq__rev,axiom,
    ! [V_x_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
       => c_List_OdropWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)),hAPP(c_List_Orev(T_b),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),hAPP(c_List_Orev(T_b),c_List_OtakeWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)),V_xs_2))) ) ),
    file('theBenchmark.p',fact_dropWhile__neq__rev) ).

fof(fact_takeWhile__dropWhile__id,axiom,
    ! [V_xs_2,V_P_2,T_b] : hAPP(hAPP(c_List_Oappend(T_b),c_List_OtakeWhile(T_b,V_P_2,V_xs_2)),c_List_OdropWhile(T_b,V_P_2,V_xs_2)) = V_xs_2,
    file('theBenchmark.p',fact_takeWhile__dropWhile__id) ).

fof(fact_sorted__dropWhile,axiom,
    ! [V_P_2,V_xs_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
       => c_List_Olinorder__class_Osorted(T_b,c_List_OdropWhile(T_b,V_P_2,V_xs_2)) ) ),
    file('theBenchmark.p',fact_sorted__dropWhile) ).

fof(fact_length__dropWhile__le,axiom,
    ! [V_xs_2,V_P_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OdropWhile(T_b,V_P_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))),
    file('theBenchmark.p',fact_length__dropWhile__le) ).

fof(fact_dropWhile__eq__Nil__conv,axiom,
    ! [V_xs_2,V_P_2,T_b] :
      ( c_List_OdropWhile(T_b,V_P_2,V_xs_2) = c_List_Olist_ONil(T_b)
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
         => hBOOL(hAPP(V_P_2,B_x)) ) ),
    file('theBenchmark.p',fact_dropWhile__eq__Nil__conv) ).

fof(fact_dropWhile_Osimps_I2_J,axiom,
    ! [V_xs_2,T_b,V_x_2,V_P_2] :
      ( ( ~ hBOOL(hAPP(V_P_2,V_x_2))
       => c_List_OdropWhile(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) )
      & ( hBOOL(hAPP(V_P_2,V_x_2))
       => c_List_OdropWhile(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_List_OdropWhile(T_b,V_P_2,V_xs_2) ) ),
    file('theBenchmark.p',fact_dropWhile_Osimps_I2_J) ).

fof(fact_dropWhile_Osimps_I1_J,axiom,
    ! [V_P_2,T_b] : c_List_OdropWhile(T_b,V_P_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b),
    file('theBenchmark.p',fact_dropWhile_Osimps_I1_J) ).

fof(fact_distinct__dropWhile,axiom,
    ! [V_P_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
     => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_OdropWhile(T_b,V_P_2,V_xs_2))) ),
    file('theBenchmark.p',fact_distinct__dropWhile) ).

fof(fact_hd__dropWhile,axiom,
    ! [V_xs_2,V_P_2,T_b] :
      ( c_List_OdropWhile(T_b,V_P_2,V_xs_2) != c_List_Olist_ONil(T_b)
     => ~ hBOOL(hAPP(V_P_2,hAPP(c_List_Ohd(T_b),c_List_OdropWhile(T_b,V_P_2,V_xs_2)))) ),
    file('theBenchmark.p',fact_hd__dropWhile) ).

fof(fact_dropWhile__map,axiom,
    ! [V_xs_2,V_f_2,T_c,V_P_2,T_b] : c_List_OdropWhile(T_b,V_P_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_OdropWhile(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_P_2),V_f_2),V_xs_2)),
    file('theBenchmark.p',fact_dropWhile__map) ).

fof(fact_dropWhile__append1,axiom,
    ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
     => ( ~ hBOOL(hAPP(V_P_2,V_x_2))
       => c_List_OdropWhile(T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),c_List_OdropWhile(T_b,V_P_2,V_xs_2)),V_ys_2) ) ),
    file('theBenchmark.p',fact_dropWhile__append1) ).

fof(fact_dropWhile__eq__Cons__conv,axiom,
    ! [V_ys_2,V_y_2,V_xs_2,V_P_2,T_b] :
      ( c_List_OdropWhile(T_b,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)
    <=> ( ~ hBOOL(hAPP(V_P_2,V_y_2))
        & V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),c_List_OtakeWhile(T_b,V_P_2,V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)) ) ),
    file('theBenchmark.p',fact_dropWhile__eq__Cons__conv) ).

fof(fact_dropWhile__eq__drop,axiom,
    ! [V_xs_2,V_P_2,T_b] : c_List_OdropWhile(T_b,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))),V_xs_2),
    file('theBenchmark.p',fact_dropWhile__eq__drop) ).

fof(fact_dropWhile__nth,axiom,
    ! [V_xs_2,V_P_2,T_b,V_j_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OdropWhile(T_b,V_P_2,V_xs_2))))
     => hAPP(hAPP(c_List_Onth(T_b),c_List_OdropWhile(T_b,V_P_2,V_xs_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_b),V_xs_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_P_2,V_xs_2)))) ),
    file('theBenchmark.p',fact_dropWhile__nth) ).

fof(fact_listsum__map__filter,axiom,
    ! [V_f_2,V_P_2,V_xs_2,T_b,T_c] :
      ( class_Groups_Omonoid__add(T_c)
     => ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
           => ( ~ hBOOL(hAPP(V_P_2,B_x))
             => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) )
       => hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) ) ),
    file('theBenchmark.p',fact_listsum__map__filter) ).

fof(fact_sorted__nth__monoI,axiom,
    ! [V_xs,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( ! [B_i,B_j] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),B_i)),hAPP(hAPP(c_List_Onth(T_a),V_xs),B_j))) ) )
       => c_List_Olinorder__class_Osorted(T_a,V_xs) ) ),
    file('theBenchmark.p',fact_sorted__nth__monoI) ).

fof(fact_takeWhile__eq__filter,axiom,
    ! [V_xs_2,V_P_2,T_b] :
      ( ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),c_List_OdropWhile(T_b,V_P_2,V_xs_2))))
         => ~ hBOOL(hAPP(V_P_2,B_x)) )
     => c_List_OtakeWhile(T_b,V_P_2,V_xs_2) = hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) ),
    file('theBenchmark.p',fact_takeWhile__eq__filter) ).

fof(fact_takeWhile__eq__take__P__nth,axiom,
    ! [V_P_2,V_xs_2,T_b,V_n_2] :
      ( ! [B_i] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
           => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) ) )
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
         => ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2))) )
       => c_List_OtakeWhile(T_b,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2) ) ),
    file('theBenchmark.p',fact_takeWhile__eq__take__P__nth) ).

fof(fact_length__takeWhile__less__P__nth,axiom,
    ! [V_xs_2,T_b,V_P_2,V_j_2] :
      ( ! [B_i] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_j_2))
         => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_P_2,V_xs_2)))) ) ),
    file('theBenchmark.p',fact_length__takeWhile__less__P__nth) ).

fof(fact_sorted_Osimps,axiom,
    ! [V_a_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( c_List_Olinorder__class_Osorted(T_b,V_a_2)
      <=> ( ? [B_xs,B_x] :
              ( c_List_Olinorder__class_Osorted(T_b,B_xs)
              & ! [B_xa] :
                  ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(c_List_Oset(T_b),B_xs)))
                 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),B_xa)) )
              & V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_xs) )
          | V_a_2 = c_List_Olist_ONil(T_b) ) ) ),
    file('theBenchmark.p',fact_sorted_Osimps) ).

fof(fact_not__in__set__insert,axiom,
    ! [V_xs_2,V_x_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
     => c_List_Oinsert(T_b,V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) ),
    file('theBenchmark.p',fact_not__in__set__insert) ).

fof(fact_List_Oinsert__def,axiom,
    ! [V_xs_2,V_x_2,T_b] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
       => c_List_Oinsert(T_b,V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) )
      & ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
       => c_List_Oinsert(T_b,V_x_2,V_xs_2) = V_xs_2 ) ),
    file('theBenchmark.p',fact_List_Oinsert__def) ).

fof(fact_insert__remdups,axiom,
    ! [V_xs,V_x,T_a] : c_List_Oinsert(T_a,V_x,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,c_List_Oinsert(T_a,V_x,V_xs)),
    file('theBenchmark.p',fact_insert__remdups) ).

fof(fact_distinct__insert,axiom,
    ! [V_x,V_xs,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
     => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oinsert(T_a,V_x,V_xs))) ),
    file('theBenchmark.p',fact_distinct__insert) ).

fof(fact_in__set__insert,axiom,
    ! [V_xs_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
     => c_List_Oinsert(T_b,V_x_2,V_xs_2) = V_xs_2 ),
    file('theBenchmark.p',fact_in__set__insert) ).

fof(fact_List_Oset__insert,axiom,
    ! [V_xs_2,V_x_2,T_b] : hAPP(c_List_Oset(T_b),c_List_Oinsert(T_b,V_x_2,V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)),
    file('theBenchmark.p',fact_List_Oset__insert) ).

fof(fact_insert__Nil,axiom,
    ! [V_x,T_a] : c_List_Oinsert(T_a,V_x,c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a)),
    file('theBenchmark.p',fact_insert__Nil) ).

fof(fact_concat__map__maps,axiom,
    ! [V_xs_2,V_f_2,T_c,T_b] : c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(T_c,tc_List_Olist(T_b)),V_f_2),V_xs_2)) = c_List_Omaps(T_c,T_b,V_f_2,V_xs_2),
    file('theBenchmark.p',fact_concat__map__maps) ).

fof(fact_maps__def,axiom,
    ! [V_xs_2,V_f_2,T_b,T_c] : c_List_Omaps(T_c,T_b,V_f_2,V_xs_2) = c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(T_c,tc_List_Olist(T_b)),V_f_2),V_xs_2)),
    file('theBenchmark.p',fact_maps__def) ).

fof(fact_maps__simps_I2_J,axiom,
    ! [V_f_2,T_b,T_c] : c_List_Omaps(T_c,T_b,V_f_2,c_List_Olist_ONil(T_c)) = c_List_Olist_ONil(T_b),
    file('theBenchmark.p',fact_maps__simps_I2_J) ).

fof(fact_maps__simps_I1_J,axiom,
    ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] : c_List_Omaps(T_c,T_b,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Oappend(T_b),hAPP(V_f_2,V_x_2)),c_List_Omaps(T_c,T_b,V_f_2,V_xs_2)),
    file('theBenchmark.p',fact_maps__simps_I1_J) ).

fof(fact_distinct__concat,axiom,
    ! [V_xs_2,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_b)),V_xs_2))
     => ( ! [B_ys] :
            ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
           => hBOOL(hAPP(c_List_Odistinct(T_b),B_ys)) )
       => ( ! [B_ys] :
              ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
             => ! [B_zs] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_zs),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
                 => ( B_ys != B_zs
                   => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),B_ys)),hAPP(c_List_Oset(T_b),B_zs)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) )
         => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Oconcat(T_b,V_xs_2))) ) ) ),
    file('theBenchmark.p',fact_distinct__concat) ).

fof(fact_measures__lesseq,axiom,
    ! [V_fs_2,T_b,V_y_2,V_x_2,V_f_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_List_Omeasures(T_b,V_fs_2)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_List_Omeasures(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_b,tc_Nat_Onat)),V_f_2),V_fs_2)))) ) ),
    file('theBenchmark.p',fact_measures__lesseq) ).

fof(fact_wf__measures,axiom,
    ! [V_fs_2,T_b] : c_Wellfounded_Owf(T_b,c_List_Omeasures(T_b,V_fs_2)),
    file('theBenchmark.p',fact_wf__measures) ).

fof(fact_in__measures_I1_J,axiom,
    ! [V_y_2,V_x_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_List_Omeasures(T_b,c_List_Olist_ONil(tc_fun(T_b,tc_Nat_Onat))))),
    file('theBenchmark.p',fact_in__measures_I1_J) ).

fof(fact_measures__def,axiom,
    ! [V_fs_2,T_b] : c_List_Omeasures(T_b,V_fs_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_List_Olist(tc_Nat_Onat),T_b),c_List_Olex(tc_Nat_Onat,c_Wellfounded_Oless__than)),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(tc_fun(T_b,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_Nat_Onat),tc_Nat_Onat),tc_fun(tc_List_Olist(tc_fun(T_b,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),T_b),c_List_Omap(tc_fun(T_b,tc_Nat_Onat),tc_Nat_Onat)),hAPP(c_COMBC(tc_fun(T_b,tc_Nat_Onat),T_b,tc_Nat_Onat),c_COMBI(tc_fun(T_b,tc_Nat_Onat))))),V_fs_2)),
    file('theBenchmark.p',fact_measures__def) ).

fof(fact_measures__less,axiom,
    ! [V_fs_2,T_b,V_y_2,V_x_2,V_f_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_List_Omeasures(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_b,tc_Nat_Onat)),V_f_2),V_fs_2)))) ),
    file('theBenchmark.p',fact_measures__less) ).

fof(fact_in__measures_I2_J,axiom,
    ! [V_fs_2,V_f_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_List_Omeasures(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_b,tc_Nat_Onat)),V_f_2),V_fs_2))))
    <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_List_Omeasures(T_b,V_fs_2)))
          & hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) )
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) ) ),
    file('theBenchmark.p',fact_in__measures_I2_J) ).

fof(fact_foldl__apply,axiom,
    ! [V_s_2,V_g_2,V_h_2,V_f_2,T_c,T_d,V_xs_2,T_b] :
      ( ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
         => hAPP(c_Fun_Ocomp(T_d,T_d,T_c,hAPP(V_f_2,B_x)),V_h_2) = hAPP(c_Fun_Ocomp(T_c,T_d,T_c,V_h_2),hAPP(V_g_2,B_x)) )
     => hAPP(c_List_Ofoldl(T_d,T_b,hAPP(c_COMBC(T_b,T_d,T_d),V_f_2),hAPP(V_h_2,V_s_2)),V_xs_2) = hAPP(V_h_2,hAPP(c_List_Ofoldl(T_c,T_b,hAPP(c_COMBC(T_b,T_c,T_c),V_g_2),V_s_2),V_xs_2)) ),
    file('theBenchmark.p',fact_foldl__apply) ).

fof(fact_order__fun_I2_J,axiom,
    ! [V_g_2,V_f_2,T_b,T_c] :
      ( ( class_Enum_Oenum(T_b)
        & class_Orderings_Oorder(T_c) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,T_c)),V_f_2),V_g_2))
      <=> ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBS(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),V_g_2))))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) ) ) ),
    file('theBenchmark.p',fact_order__fun_I2_J) ).

fof(fact_enum__ex__prod__def,axiom,
    ! [V_P_2,T_b,T_c] :
      ( ( class_Enum_Oenum(T_b)
        & class_Enum_Oenum(T_c) )
     => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(T_b,T_c)),V_P_2))
      <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_Enum_Oenum__class_Oenum__ex(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,T_c),V_P_2)),c_Product__Type_OPair(T_b,T_c))))) ) ),
    file('theBenchmark.p',fact_enum__ex__prod__def) ).

fof(fact_exists__code,axiom,
    ! [V_P_2,T_b] :
      ( class_Enum_Oenum(T_b)
     => ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
      <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),V_P_2)) ) ),
    file('theBenchmark.p',fact_exists__code) ).

fof(fact_enum__ex,axiom,
    ! [V_P_2,T_b] :
      ( class_Enum_Oenum(T_b)
     => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),V_P_2))
      <=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ),
    file('theBenchmark.p',fact_enum__ex) ).

fof(fact_zip__obtain__same__length,axiom,
    ! [V_P_2,V_ys_2,T_c,V_xs_2,T_b] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Otake(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2))),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),hAPP(hAPP(c_List_Otake(T_c),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2))),V_ys_2))
       => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Otake(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2))),V_xs_2)),hAPP(hAPP(c_List_Otake(T_c),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2))),V_ys_2)))) )
     => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))) ),
    file('theBenchmark.p',fact_zip__obtain__same__length) ).

fof(fact_pos__not__random__dseq__def,axiom,
    ! [V_seed_2,V_size_2,V_nrandom_2,V_R_2] : c_New__Random__Sequence_Opos__not__random__dseq(V_R_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__not__seq(hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2)),
    file('theBenchmark.p',fact_pos__not__random__dseq__def) ).

fof(fact_dropWhile__append2,axiom,
    ! [V_ys_2,V_P_2,V_xs_2,T_b] :
      ( ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
         => hBOOL(hAPP(V_P_2,B_x)) )
     => c_List_OdropWhile(T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = c_List_OdropWhile(T_b,V_P_2,V_ys_2) ),
    file('theBenchmark.p',fact_dropWhile__append2) ).

fof(fact_list__all2__all__nthI,axiom,
    ! [V_P_2,V_b_2,T_c,V_a_2,T_b] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_a_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_b_2)
     => ( ! [B_n] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_a_2)))
           => hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_a_2),B_n)),hAPP(hAPP(c_List_Onth(T_c),V_b_2),B_n))) )
       => c_List_Olist__all2(T_b,T_c,V_P_2,V_a_2,V_b_2) ) ),
    file('theBenchmark.p',fact_list__all2__all__nthI) ).

fof(fact_finite__sorted__distinct__unique,axiom,
    ! [V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ? [B_x] :
            ( ! [B_y] :
                ( ( hBOOL(hAPP(c_List_Odistinct(T_b),B_y))
                  & c_List_Olinorder__class_Osorted(T_b,B_y)
                  & hAPP(c_List_Oset(T_b),B_y) = V_A_2 )
               => B_y = B_x )
            & hBOOL(hAPP(c_List_Odistinct(T_b),B_x))
            & c_List_Olinorder__class_Osorted(T_b,B_x)
            & hAPP(c_List_Oset(T_b),B_x) = V_A_2 ) ) ),
    file('theBenchmark.p',fact_finite__sorted__distinct__unique) ).

fof(fact_takeWhile__append2,axiom,
    ! [V_ys_2,V_P_2,V_xs_2,T_b] :
      ( ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
         => hBOOL(hAPP(V_P_2,B_x)) )
     => c_List_OtakeWhile(T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),c_List_OtakeWhile(T_b,V_P_2,V_ys_2)) ),
    file('theBenchmark.p',fact_takeWhile__append2) ).

fof(fact_insort__is__Cons,axiom,
    ! [V_a_2,V_f_2,V_xs_2,T_b,T_c] :
      ( class_Orderings_Olinorder(T_c)
     => ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_a_2)),hAPP(V_f_2,B_x))) )
       => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_a_2),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_xs_2) ) ),
    file('theBenchmark.p',fact_insort__is__Cons) ).

fof(fact_filter__eq__Cons__iff,axiom,
    ! [V_xs_2,V_x_2,V_ys_2,V_P_2,T_b] :
      ( hAPP(c_List_Ofilter(T_b,V_P_2),V_ys_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)
    <=> ? [B_us,B_vs] :
          ( V_xs_2 = hAPP(c_List_Ofilter(T_b,V_P_2),B_vs)
          & hBOOL(hAPP(V_P_2,V_x_2))
          & ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),B_us)))
             => ~ hBOOL(hAPP(V_P_2,B_x)) )
          & V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_vs)) ) ),
    file('theBenchmark.p',fact_filter__eq__Cons__iff) ).

fof(fact_Cons__eq__filter__iff,axiom,
    ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_b] :
      ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) = hAPP(c_List_Ofilter(T_b,V_P_2),V_ys_2)
    <=> ? [B_us,B_vs] :
          ( V_xs_2 = hAPP(c_List_Ofilter(T_b,V_P_2),B_vs)
          & hBOOL(hAPP(V_P_2,V_x_2))
          & ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),B_us)))
             => ~ hBOOL(hAPP(V_P_2,B_x)) )
          & V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_vs)) ) ),
    file('theBenchmark.p',fact_Cons__eq__filter__iff) ).

fof(fact_order__fun_I1_J,axiom,
    ! [V_g_2,V_f_2,T_b,T_c] :
      ( ( class_Enum_Oenum(T_b)
        & class_Orderings_Oorder(T_c) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
      <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),hAPP(hAPP(c_COMBS(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_Orderings_Oord__class_Oless__eq(T_c)),V_f_2)),V_g_2))) ) ),
    file('theBenchmark.p',fact_order__fun_I1_J) ).

fof(fact_enum__all,axiom,
    ! [V_P_2,T_b] :
      ( class_Enum_Oenum(T_b)
     => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),V_P_2))
      <=> ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ),
    file('theBenchmark.p',fact_enum__all) ).

fof(fact_all__code,axiom,
    ! [V_P_2,T_b] :
      ( class_Enum_Oenum(T_b)
     => ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
      <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),V_P_2)) ) ),
    file('theBenchmark.p',fact_all__code) ).

fof(fact_enum__all__prod__def,axiom,
    ! [V_P_2,T_b,T_c] :
      ( ( class_Enum_Oenum(T_b)
        & class_Enum_Oenum(T_c) )
     => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(T_b,T_c)),V_P_2))
      <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_Enum_Oenum__class_Oenum__all(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,T_c),V_P_2)),c_Product__Type_OPair(T_b,T_c))))) ) ),
    file('theBenchmark.p',fact_enum__all__prod__def) ).

fof(fact_list__ball__nth,axiom,
    ! [V_P_2,V_xs_2,T_b,V_n_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
     => ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
           => hBOOL(hAPP(V_P_2,B_x)) )
       => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2))) ) ),
    file('theBenchmark.p',fact_list__ball__nth) ).

fof(fact_sorted_OCons,axiom,
    ! [V_x_2,V_xs_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) )
       => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
         => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) ) ) ),
    file('theBenchmark.p',fact_sorted_OCons) ).

fof(fact_list__ex__length,axiom,
    ! [V_xs_2,V_P_2,T_b] :
      ( c_List_Olist__ex(T_b,V_P_2,V_xs_2)
    <=> ? [B_n] :
          ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ) ),
    file('theBenchmark.p',fact_list__ex__length) ).

fof(fact_in__set__conv__decomp__first,axiom,
    ! [V_xs_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
    <=> ? [B_ys] :
          ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),B_ys)))
          & ? [B_zs] : V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_zs)) ) ),
    file('theBenchmark.p',fact_in__set__conv__decomp__first) ).

fof(fact_list__ex__simps_I2_J,axiom,
    ! [V_P_2,T_b] : ~ c_List_Olist__ex(T_b,V_P_2,c_List_Olist_ONil(T_b)),
    file('theBenchmark.p',fact_list__ex__simps_I2_J) ).

fof(fact_list__ex__append,axiom,
    ! [V_ys_2,V_xs_2,V_P_2,T_b] :
      ( c_List_Olist__ex(T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))
    <=> ( c_List_Olist__ex(T_b,V_P_2,V_ys_2)
        | c_List_Olist__ex(T_b,V_P_2,V_xs_2) ) ),
    file('theBenchmark.p',fact_list__ex__append) ).

fof(fact_list__ex__iff,axiom,
    ! [V_xs_2,V_P_2,T_b] :
      ( c_List_Olist__ex(T_b,V_P_2,V_xs_2)
    <=> ? [B_x] :
          ( hBOOL(hAPP(V_P_2,B_x))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) ) ),
    file('theBenchmark.p',fact_list__ex__iff) ).

fof(fact_list__ex__rev,axiom,
    ! [V_xs_2,V_P_2,T_b] :
      ( c_List_Olist__ex(T_b,V_P_2,hAPP(c_List_Orev(T_b),V_xs_2))
    <=> c_List_Olist__ex(T_b,V_P_2,V_xs_2) ),
    file('theBenchmark.p',fact_list__ex__rev) ).

fof(fact_list__ex__simps_I1_J,axiom,
    ! [V_xs_2,V_x_2,V_P_2,T_b] :
      ( c_List_Olist__ex(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
    <=> ( c_List_Olist__ex(T_b,V_P_2,V_xs_2)
        | hBOOL(hAPP(V_P_2,V_x_2)) ) ),
    file('theBenchmark.p',fact_list__ex__simps_I1_J) ).

fof(fact_in__set__conv__decomp,axiom,
    ! [V_xs_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
    <=> ? [B_ys,B_zs] : V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_zs)) ),
    file('theBenchmark.p',fact_in__set__conv__decomp) ).

fof(fact_in__set__conv__decomp__last,axiom,
    ! [V_xs_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
    <=> ? [B_ys,B_zs] :
          ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),B_zs)))
          & V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_zs)) ) ),
    file('theBenchmark.p',fact_in__set__conv__decomp__last) ).

fof(fact_list__all__length,axiom,
    ! [V_xs_2,V_P_2,T_b] :
      ( c_List_Olist__all(T_b,V_P_2,V_xs_2)
    <=> ! [B_n] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
         => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n))) ) ),
    file('theBenchmark.p',fact_list__all__length) ).

fof(fact_measure__function__int,axiom,
    c_FunDef_Ois__measure(tc_Int_Oint,hAPP(c_Fun_Ocomp(tc_Int_Oint,tc_Nat_Onat,tc_Int_Oint,c_Int_Onat),c_Groups_Oabs__class_Oabs(tc_Int_Oint))),
    file('theBenchmark.p',fact_measure__function__int) ).

fof(fact_list__all__simps_I2_J,axiom,
    ! [V_P_2,T_b] : c_List_Olist__all(T_b,V_P_2,c_List_Olist_ONil(T_b)),
    file('theBenchmark.p',fact_list__all__simps_I2_J) ).

fof(fact_list__all__append,axiom,
    ! [V_ys_2,V_xs_2,V_P_2,T_b] :
      ( c_List_Olist__all(T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))
    <=> ( c_List_Olist__all(T_b,V_P_2,V_ys_2)
        & c_List_Olist__all(T_b,V_P_2,V_xs_2) ) ),
    file('theBenchmark.p',fact_list__all__append) ).

fof(fact_measure__size,axiom,
    ! [T_b] :
      ( class_Nat_Osize(T_b)
     => c_FunDef_Ois__measure(T_b,c_Nat_Osize__class_Osize(T_b)) ),
    file('theBenchmark.p',fact_measure__size) ).

fof(fact_is__measure_Ointros,axiom,
    ! [V_f_2,T_b] : c_FunDef_Ois__measure(T_b,V_f_2),
    file('theBenchmark.p',fact_is__measure_Ointros) ).

fof(fact_is__measure_Oequations,axiom,
    ! [V_a_2,T_b] : c_FunDef_Ois__measure(T_b,V_a_2),
    file('theBenchmark.p',fact_is__measure_Oequations) ).

fof(fact_is__measure_Osimps,axiom,
    ! [V_a_2,T_b] : c_FunDef_Ois__measure(T_b,V_a_2),
    file('theBenchmark.p',fact_is__measure_Osimps) ).

fof(fact_list__all__iff,axiom,
    ! [V_xs_2,V_P_2,T_b] :
      ( c_List_Olist__all(T_b,V_P_2,V_xs_2)
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
         => hBOOL(hAPP(V_P_2,B_x)) ) ),
    file('theBenchmark.p',fact_list__all__iff) ).

fof(fact_measure__fst,axiom,
    ! [T_c,V_f_2,T_b] :
      ( c_FunDef_Ois__measure(T_b,V_f_2)
     => c_FunDef_Ois__measure(tc_prod(T_b,T_c),hAPP(hAPP(c_COMBB(T_b,tc_Nat_Onat,tc_prod(T_b,T_c)),V_f_2),c_Product__Type_Ofst(T_b,T_c))) ),
    file('theBenchmark.p',fact_measure__fst) ).

fof(fact_measure__snd,axiom,
    ! [T_c,V_f_2,T_b] :
      ( c_FunDef_Ois__measure(T_b,V_f_2)
     => c_FunDef_Ois__measure(tc_prod(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,tc_Nat_Onat,tc_prod(T_c,T_b)),V_f_2),c_Product__Type_Osnd(T_c,T_b))) ),
    file('theBenchmark.p',fact_measure__snd) ).

fof(fact_list__all__rev,axiom,
    ! [V_xs_2,V_P_2,T_b] :
      ( c_List_Olist__all(T_b,V_P_2,hAPP(c_List_Orev(T_b),V_xs_2))
    <=> c_List_Olist__all(T_b,V_P_2,V_xs_2) ),
    file('theBenchmark.p',fact_list__all__rev) ).

fof(fact_list__all__simps_I1_J,axiom,
    ! [V_xs_2,V_x_2,V_P_2,T_b] :
      ( c_List_Olist__all(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
    <=> ( c_List_Olist__all(T_b,V_P_2,V_xs_2)
        & hBOOL(hAPP(V_P_2,V_x_2)) ) ),
    file('theBenchmark.p',fact_list__all__simps_I1_J) ).

fof(fact_Ball__set__list__all,axiom,
    ! [V_P_2,V_xs_2,T_b] :
      ( ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
         => hBOOL(hAPP(V_P_2,B_x)) )
    <=> c_List_Olist__all(T_b,V_P_2,V_xs_2) ),
    file('theBenchmark.p',fact_Ball__set__list__all) ).

fof(fact_list__all__iff__raw,axiom,
    ! [V_xs_2,V_P_2,T_b] :
      ( c_List_Olist__all(T_b,V_P_2,V_xs_2)
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
         => hBOOL(hAPP(V_P_2,B_x)) ) ),
    file('theBenchmark.p',fact_list__all__iff__raw) ).

fof(fact_list__ex1__simps_I2_J,axiom,
    ! [V_xs_2,V_x_2,V_P_2,T_b] :
      ( c_List_Olist__ex1(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
    <=> ( ( ~ hBOOL(hAPP(V_P_2,V_x_2))
         => c_List_Olist__ex1(T_b,V_P_2,V_xs_2) )
        & ( hBOOL(hAPP(V_P_2,V_x_2))
         => c_List_Olist__all(T_b,hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_P_2))),hAPP(c_fequal,V_x_2)),V_xs_2) ) ) ),
    file('theBenchmark.p',fact_list__ex1__simps_I2_J) ).

fof(fact_transfer__morphism__int__nat,axiom,
    c_Nat__Transfer_Otransfer__morphism(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_COMBK(tc_HOL_Obool,tc_Nat_Onat),c_fTrue)),
    file('theBenchmark.p',fact_transfer__morphism__int__nat) ).

fof(fact_list__ex1__simps_I1_J,axiom,
    ! [V_P_2,T_b] : ~ c_List_Olist__ex1(T_b,V_P_2,c_List_Olist_ONil(T_b)),
    file('theBenchmark.p',fact_list__ex1__simps_I1_J) ).

fof(fact_bool_Osize_I4_J,axiom,
    hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_bool_Osize_I4_J) ).

fof(fact_bool_Osize_I3_J,axiom,
    hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_bool_Osize_I3_J) ).

fof(fact_list__ex1__iff,axiom,
    ! [V_xs_2,V_P_2,T_b] :
      ( c_List_Olist__ex1(T_b,V_P_2,V_xs_2)
    <=> ? [B_x] :
          ( ! [B_y] :
              ( ( hBOOL(hAPP(V_P_2,B_y))
                & hBOOL(hAPP(hAPP(c_member(T_b),B_y),hAPP(c_List_Oset(T_b),V_xs_2))) )
             => B_y = B_x )
          & hBOOL(hAPP(V_P_2,B_x))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) ) ),
    file('theBenchmark.p',fact_list__ex1__iff) ).

fof(fact_New__DSequence_Opos__decr__bind__def,axiom,
    ! [V_f_2,V_x_2,T_b,T_c,V_i_2] :
      ( ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => hAPP(c_New__DSequence_Opos__decr__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = hAPP(c_Lazy__Sequence_Obind(T_c,T_b,hAPP(V_x_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_i_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b)),V_f_2),V_i_2)) )
      & ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => hAPP(c_New__DSequence_Opos__decr__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Oempty(T_b) ) ),
    file('theBenchmark.p',fact_New__DSequence_Opos__decr__bind__def) ).

fof(fact_New__DSequence_Oneg__decr__bind__def,axiom,
    ! [V_f_2,V_x_2,T_b,T_c,V_i_2] :
      ( ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => hAPP(c_New__DSequence_Oneg__decr__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohb__bind(T_c,T_b,hAPP(V_x_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_i_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b))),V_f_2),V_i_2)) )
      & ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => hAPP(c_New__DSequence_Oneg__decr__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohit__bound(T_b) ) ),
    file('theBenchmark.p',fact_New__DSequence_Oneg__decr__bind__def) ).

fof(fact_New__Random__Sequence_Oneg__decr__bind__def,axiom,
    ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_b,T_c] : c_New__Random__Sequence_Oneg__decr__bind(T_c,T_b,V_R_2,V_f_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Oneg__decr__bind(T_c,T_b,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_c,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b))))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)),
    file('theBenchmark.p',fact_New__Random__Sequence_Oneg__decr__bind__def) ).

fof(fact_New__Random__Sequence_Opos__decr__bind__def,axiom,
    ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_b,T_c] : c_New__Random__Sequence_Opos__decr__bind(T_c,T_b,V_R_2,V_f_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__decr__bind(T_c,T_b,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_c,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b)))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)),
    file('theBenchmark.p',fact_New__Random__Sequence_Opos__decr__bind__def) ).

fof(fact_New__DSequence_Oneg__bind__def,axiom,
    ! [V_i_2,V_f_2,V_x_2,T_b,T_c] : hAPP(c_New__DSequence_Oneg__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohb__bind(T_c,T_b,hAPP(V_x_2,V_i_2),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b))),V_f_2),V_i_2)),
    file('theBenchmark.p',fact_New__DSequence_Oneg__bind__def) ).

fof(fact_New__DSequence_Opos__empty__def,axiom,
    ! [V_i_1,T_a] : hAPP(c_New__DSequence_Opos__empty(T_a),V_i_1) = c_Lazy__Sequence_Oempty(T_a),
    file('theBenchmark.p',fact_New__DSequence_Opos__empty__def) ).

fof(fact_pos__empty__def,axiom,
    ! [V_seed_2,V_size_2,V_nrandom_2,T_b] : c_New__Random__Sequence_Opos__empty(T_b,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__empty(T_b),
    file('theBenchmark.p',fact_pos__empty__def) ).

fof(fact_neg__bind__def,axiom,
    ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_b,T_c] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(T_c,T_b,V_R_2,V_f_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Oneg__bind(T_c,T_b,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_c,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b))))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)),
    file('theBenchmark.p',fact_neg__bind__def) ).

fof(fact_New__DSequence_Opos__bind__def,axiom,
    ! [V_i_2,V_f_2,V_x_2,T_b,T_c] : hAPP(c_New__DSequence_Opos__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = hAPP(c_Lazy__Sequence_Obind(T_c,T_b,hAPP(V_x_2,V_i_2)),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b)),V_f_2),V_i_2)),
    file('theBenchmark.p',fact_New__DSequence_Opos__bind__def) ).

fof(fact_neg__map__def,axiom,
    ! [V_P_2,V_f_2,T_b,T_c] : c_New__Random__Sequence_Oneg__map(T_c,T_b,V_f_2,V_P_2) = c_New__Random__Sequence_Oneg__bind(T_c,T_b,V_P_2,hAPP(c_Fun_Ocomp(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)))))),T_c,c_New__Random__Sequence_Oneg__single(T_b)),V_f_2)),
    file('theBenchmark.p',fact_neg__map__def) ).

fof(fact_neg__single__def,axiom,
    ! [V_seed_2,V_size_2,V_nrandom_2,V_x_2,T_b] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(T_b),V_x_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Oneg__single(T_b,V_x_2),
    file('theBenchmark.p',fact_neg__single__def) ).

fof(fact_pos__bind__def,axiom,
    ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_b,T_c] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(T_c,T_b,V_R_2,V_f_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Opos__bind(T_c,T_b,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_c,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b)))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)),
    file('theBenchmark.p',fact_pos__bind__def) ).

fof(fact_New__DSequence_Oneg__single__def,axiom,
    ! [V_i_1,V_x,T_a] : hAPP(c_New__DSequence_Oneg__single(T_a,V_x),V_i_1) = c_Lazy__Sequence_Ohb__single(T_a,V_x),
    file('theBenchmark.p',fact_New__DSequence_Oneg__single__def) ).

fof(fact_pos__map__def,axiom,
    ! [V_P_2,V_f_2,T_b,T_c] : c_New__Random__Sequence_Opos__map(T_c,T_b,V_f_2,V_P_2) = c_New__Random__Sequence_Opos__bind(T_c,T_b,V_P_2,hAPP(c_Fun_Ocomp(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))))),T_c,c_New__Random__Sequence_Opos__single(T_b)),V_f_2)),
    file('theBenchmark.p',fact_pos__map__def) ).

fof(fact_pos__single__def,axiom,
    ! [V_seed_2,V_size_2,V_nrandom_2,V_x_2,T_b] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(T_b),V_x_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Opos__single(T_b,V_x_2),
    file('theBenchmark.p',fact_pos__single__def) ).

fof(fact_length__splice,axiom,
    ! [V_ys,V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Osplice(T_a,V_xs,V_ys)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys)),
    file('theBenchmark.p',fact_length__splice) ).

fof(fact_splice_Osimps_I3_J,axiom,
    ! [V_ys,V_y,V_xs,V_x,T_a] : c_List_Osplice(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),c_List_Osplice(T_a,V_xs,V_ys))),
    file('theBenchmark.p',fact_splice_Osimps_I3_J) ).

fof(fact_splice__Nil2,axiom,
    ! [V_xs,T_a] : c_List_Osplice(T_a,V_xs,c_List_Olist_ONil(T_a)) = V_xs,
    file('theBenchmark.p',fact_splice__Nil2) ).

fof(fact_splice_Osimps_I1_J,axiom,
    ! [V_ys,T_a] : c_List_Osplice(T_a,c_List_Olist_ONil(T_a),V_ys) = V_ys,
    file('theBenchmark.p',fact_splice_Osimps_I1_J) ).

fof(fact_splice_Osimps_I2_J,axiom,
    ! [V_va,V_v,T_a] : c_List_Osplice(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_v),V_va),c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_v),V_va),
    file('theBenchmark.p',fact_splice_Osimps_I2_J) ).

fof(fact_New__DSequence_Opos__single__def,axiom,
    ! [V_i_1,V_x,T_a] : hAPP(c_New__DSequence_Opos__single(T_a,V_x),V_i_1) = hAPP(c_Lazy__Sequence_Osingle(T_a),V_x),
    file('theBenchmark.p',fact_New__DSequence_Opos__single__def) ).

fof(fact_acyclicP__converse,axiom,
    ! [V_r_2,T_b] :
      ( c_Wellfounded_Oacyclic(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),c_Predicate_Oconversep(T_b,T_b,V_r_2))))
    <=> c_Wellfounded_Oacyclic(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))) ),
    file('theBenchmark.p',fact_acyclicP__converse) ).

fof(fact_converse__meet,axiom,
    ! [V_s_2,V_r_2,T_b,T_c] : c_Predicate_Oconversep(T_c,T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool))),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),c_Predicate_Oconversep(T_c,T_b,V_r_2)),c_Predicate_Oconversep(T_c,T_b,V_s_2)),
    file('theBenchmark.p',fact_converse__meet) ).

fof(fact_conversep__noteq,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_b,hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot)),c_fequal)),V_x_2),V_y_2))
    <=> V_x_2 != V_y_2 ),
    file('theBenchmark.p',fact_conversep__noteq) ).

fof(fact_conversep__eq,axiom,
    ! [T_b] : c_Predicate_Oconversep(T_b,T_b,c_fequal) = c_fequal,
    file('theBenchmark.p',fact_conversep__eq) ).

fof(fact_conversep__conversep,axiom,
    ! [V_r_2,T_b,T_c] : c_Predicate_Oconversep(T_c,T_b,c_Predicate_Oconversep(T_b,T_c,V_r_2)) = V_r_2,
    file('theBenchmark.p',fact_conversep__conversep) ).

fof(fact_conversep__iff,axiom,
    ! [V_b_2,V_a_2,V_r_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a_2),V_b_2))
    <=> hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2)) ),
    file('theBenchmark.p',fact_conversep__iff) ).

fof(fact_conversep_Oequations,axiom,
    ! [V_a1_2,V_a2_2,V_r_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a2_2),V_a1_2))
    <=> hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2)) ),
    file('theBenchmark.p',fact_conversep_Oequations) ).

fof(fact_conversep_Ointros,axiom,
    ! [T_c,T_b,V_b_2,V_a_2,V_r_2] :
      ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
     => hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_b_2),V_a_2)) ),
    file('theBenchmark.p',fact_conversep_Ointros) ).

fof(fact_conversepD,axiom,
    ! [V_b_2,V_a_2,V_r_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a_2),V_b_2))
     => hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2)) ),
    file('theBenchmark.p',fact_conversepD) ).

fof(fact_converse__pred__comp,axiom,
    ! [V_s_2,V_r_2,T_d,T_b,T_c] : c_Predicate_Oconversep(T_c,T_b,c_Predicate_Opred__comp(T_c,T_d,T_b,V_r_2,V_s_2)) = c_Predicate_Opred__comp(T_b,T_d,T_c,c_Predicate_Oconversep(T_d,T_b,V_s_2),c_Predicate_Oconversep(T_c,T_d,V_r_2)),
    file('theBenchmark.p',fact_converse__pred__comp) ).

fof(fact_converse__join,axiom,
    ! [V_s_2,V_r_2,T_b,T_c] : c_Predicate_Oconversep(T_c,T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool))),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),c_Predicate_Oconversep(T_c,T_b,V_r_2)),c_Predicate_Oconversep(T_c,T_b,V_s_2)),
    file('theBenchmark.p',fact_converse__join) ).

fof(fact_conversep__converse__eq,axiom,
    ! [V_y_2,V_x_2,V_r_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_r_2)),V_x_2),V_y_2))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2))) ),
    file('theBenchmark.p',fact_conversep__converse__eq) ).

fof(fact_,axiom,
    ! [V_s2_2,V_s1_2,T_c,T_b] : c_Lazy__Sequence_Oproduct(T_b,T_c,V_s1_2,V_s2_2) = hAPP(c_Lazy__Sequence_Obind(T_b,tc_prod(T_b,T_c),V_s1_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_b,T_c))),tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_b,T_c)),T_b),c_Lazy__Sequence_Obind(T_c,tc_prod(T_b,T_c),V_s2_2)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_b,T_c))),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_b,T_c)),T_c),c_Lazy__Sequence_Osingle(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),
    file('theBenchmark.p',fact_) ).

fof(fact_tl__replicate,axiom,
    ! [V_x,T_a,V_n] :
      ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
     => hAPP(c_List_Otl(T_a),c_List_Oreplicate(T_a,V_n,V_x)) = c_List_Oreplicate(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_x) ),
    file('theBenchmark.p',fact_tl__replicate) ).

fof(fact_replicate__length__filter,axiom,
    ! [V_xs_2,V_x_2,T_b] : c_List_Oreplicate(T_b,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,hAPP(c_fequal,V_x_2)),V_xs_2)),V_x_2) = hAPP(c_List_Ofilter(T_b,hAPP(c_fequal,V_x_2)),V_xs_2),
    file('theBenchmark.p',fact_replicate__length__filter) ).

fof(fact_length__replicate,axiom,
    ! [V_x,V_n,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oreplicate(T_a,V_n,V_x)) = V_n,
    file('theBenchmark.p',fact_length__replicate) ).

fof(fact_map__replicate__const,axiom,
    ! [V_lst_2,V_k_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(c_COMBK(T_b,T_c),V_k_2)),V_lst_2) = c_List_Oreplicate(T_b,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_lst_2),V_k_2),
    file('theBenchmark.p',fact_map__replicate__const) ).

fof(fact_replicate__app__Cons__same,axiom,
    ! [V_xs,V_x,V_n,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_n,V_x)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_n,V_x)),V_xs)),
    file('theBenchmark.p',fact_replicate__app__Cons__same) ).

fof(fact_replicate__Suc,axiom,
    ! [V_x,V_n,T_a] : c_List_Oreplicate(T_a,hAPP(c_Nat_OSuc,V_n),V_x) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Oreplicate(T_a,V_n,V_x)),
    file('theBenchmark.p',fact_replicate__Suc) ).

fof(fact_rev__replicate,axiom,
    ! [V_x,V_n,T_a] : hAPP(c_List_Orev(T_a),c_List_Oreplicate(T_a,V_n,V_x)) = c_List_Oreplicate(T_a,V_n,V_x),
    file('theBenchmark.p',fact_rev__replicate) ).

fof(fact_take__replicate,axiom,
    ! [V_x,V_k,V_i,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_i),c_List_Oreplicate(T_a,V_k,V_x)) = c_List_Oreplicate(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_i),V_k),V_x),
    file('theBenchmark.p',fact_take__replicate) ).

fof(fact_drop__replicate,axiom,
    ! [V_x,V_k,V_i,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_i),c_List_Oreplicate(T_a,V_k,V_x)) = c_List_Oreplicate(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_k),V_i),V_x),
    file('theBenchmark.p',fact_drop__replicate) ).

fof(fact_hd__replicate,axiom,
    ! [V_x,T_a,V_n] :
      ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
     => hAPP(c_List_Ohd(T_a),c_List_Oreplicate(T_a,V_n,V_x)) = V_x ),
    file('theBenchmark.p',fact_hd__replicate) ).

fof(fact_last__replicate,axiom,
    ! [V_x,T_a,V_n] :
      ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
     => c_List_Olast(T_a,c_List_Oreplicate(T_a,V_n,V_x)) = V_x ),
    file('theBenchmark.p',fact_last__replicate) ).

fof(fact_zip__replicate,axiom,
    ! [V_y,V_j,V_x,V_i,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),c_List_Oreplicate(T_a,V_i,V_x)),c_List_Oreplicate(T_b,V_j,V_y)) = c_List_Oreplicate(tc_prod(T_a,T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_i),V_j),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x),V_y)),
    file('theBenchmark.p',fact_zip__replicate) ).

fof(fact_Bex__set__replicate,axiom,
    ! [V_P_2,V_a_2,V_n_2,T_b] :
      ( ? [B_x] :
          ( hBOOL(hAPP(V_P_2,B_x))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_n_2,V_a_2)))) )
    <=> ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        & hBOOL(hAPP(V_P_2,V_a_2)) ) ),
    file('theBenchmark.p',fact_Bex__set__replicate) ).

fof(fact_Ball__set__replicate,axiom,
    ! [V_P_2,V_a_2,V_n_2,T_b] :
      ( ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_n_2,V_a_2))))
         => hBOOL(hAPP(V_P_2,B_x)) )
    <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(V_P_2,V_a_2)) ) ),
    file('theBenchmark.p',fact_Ball__set__replicate) ).

fof(fact_replicate__eq__replicate,axiom,
    ! [V_y_2,V_n_2,V_x_2,V_m_2,T_b] :
      ( c_List_Oreplicate(T_b,V_m_2,V_x_2) = c_List_Oreplicate(T_b,V_n_2,V_y_2)
    <=> ( ( V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => V_x_2 = V_y_2 )
        & V_m_2 = V_n_2 ) ),
    file('theBenchmark.p',fact_replicate__eq__replicate) ).

fof(fact_nth__replicate,axiom,
    ! [V_x,T_a,V_n,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n))
     => hAPP(hAPP(c_List_Onth(T_a),c_List_Oreplicate(T_a,V_n,V_x)),V_i) = V_x ),
    file('theBenchmark.p',fact_nth__replicate) ).

fof(fact_replicate__add,axiom,
    ! [V_x,V_m,V_n,T_a] : c_List_Oreplicate(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m),V_x) = hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_n,V_x)),c_List_Oreplicate(T_a,V_m,V_x)),
    file('theBenchmark.p',fact_replicate__add) ).

fof(fact_append__replicate__commute,axiom,
    ! [V_k,V_x,V_n,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_n,V_x)),c_List_Oreplicate(T_a,V_k,V_x)) = hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_k,V_x)),c_List_Oreplicate(T_a,V_n,V_x)),
    file('theBenchmark.p',fact_append__replicate__commute) ).

fof(fact_filter__replicate,axiom,
    ! [V_n_2,T_b,V_x_2,V_P_2] :
      ( ( ~ hBOOL(hAPP(V_P_2,V_x_2))
       => hAPP(c_List_Ofilter(T_b,V_P_2),c_List_Oreplicate(T_b,V_n_2,V_x_2)) = c_List_Olist_ONil(T_b) )
      & ( hBOOL(hAPP(V_P_2,V_x_2))
       => hAPP(c_List_Ofilter(T_b,V_P_2),c_List_Oreplicate(T_b,V_n_2,V_x_2)) = c_List_Oreplicate(T_b,V_n_2,V_x_2) ) ),
    file('theBenchmark.p',fact_filter__replicate) ).

fof(fact_concat__replicate__trivial,axiom,
    ! [V_i,T_a] : c_List_Oconcat(T_a,c_List_Oreplicate(tc_List_Olist(T_a),V_i,c_List_Olist_ONil(T_a))) = c_List_Olist_ONil(T_a),
    file('theBenchmark.p',fact_concat__replicate__trivial) ).

fof(fact_replicate__0,axiom,
    ! [V_x,T_a] : c_List_Oreplicate(T_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x) = c_List_Olist_ONil(T_a),
    file('theBenchmark.p',fact_replicate__0) ).

fof(fact_empty__replicate,axiom,
    ! [V_x_2,V_n_2,T_b] :
      ( c_List_Olist_ONil(T_b) = c_List_Oreplicate(T_b,V_n_2,V_x_2)
    <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('theBenchmark.p',fact_empty__replicate) ).

fof(fact_replicate__empty,axiom,
    ! [V_x_2,V_n_2,T_b] :
      ( c_List_Oreplicate(T_b,V_n_2,V_x_2) = c_List_Olist_ONil(T_b)
    <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('theBenchmark.p',fact_replicate__empty) ).

fof(fact_map__replicate,axiom,
    ! [V_x_2,V_n_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Oreplicate(T_c,V_n_2,V_x_2)) = c_List_Oreplicate(T_b,V_n_2,hAPP(V_f_2,V_x_2)),
    file('theBenchmark.p',fact_map__replicate) ).

fof(fact_in__set__replicate,axiom,
    ! [V_y_2,V_n_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_n_2,V_y_2))))
    <=> ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        & V_x_2 = V_y_2 ) ),
    file('theBenchmark.p',fact_in__set__replicate) ).

fof(fact_replicate__append__same,axiom,
    ! [V_x,V_i,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_i,V_x)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Oreplicate(T_a,V_i,V_x)),
    file('theBenchmark.p',fact_replicate__append__same) ).

fof(fact_map__replicate__trivial,axiom,
    ! [V_i_2,V_x_2,T_b] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),hAPP(c_COMBK(T_b,tc_Nat_Onat),V_x_2)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i_2)) = c_List_Oreplicate(T_b,V_i_2,V_x_2),
    file('theBenchmark.p',fact_map__replicate__trivial) ).

fof(fact_set__replicate__conv__if,axiom,
    ! [V_x_2,T_b,V_n_2] :
      ( ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_n_2,V_x_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) )
      & ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_n_2,V_x_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_set__replicate__conv__if) ).

fof(fact_set__replicate,axiom,
    ! [V_x_2,T_b,V_n_2] :
      ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
     => hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_n_2,V_x_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ),
    file('theBenchmark.p',fact_set__replicate) ).

fof(fact_set__replicate__Suc,axiom,
    ! [V_x_2,V_n_2,T_b] : hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,hAPP(c_Nat_OSuc,V_n_2),V_x_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),
    file('theBenchmark.p',fact_set__replicate__Suc) ).

fof(fact_small__lazy__list_Osimps,axiom,
    ! [V_d_2,T_b] :
      ( class_Lazy__Sequence_Osmall__lazy(T_b)
     => c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(T_b),V_d_2) = c_Lazy__Sequence_Oappend(tc_List_Olist(T_b),hAPP(c_Lazy__Sequence_Osingle(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),hAPP(hAPP(hAPP(c_If(tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_b))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)),hAPP(c_Lazy__Sequence_Obind(tc_prod(T_b,tc_List_Olist(T_b)),tc_List_Olist(T_b),c_Lazy__Sequence_Oproduct(T_b,tc_List_Olist(T_b),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_d_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_d_2),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_List_Olist(T_b),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_b))),T_b),hAPP(c_COMBB(tc_List_Olist(T_b),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_b)),tc_List_Olist(T_b)),c_Lazy__Sequence_Osingle(tc_List_Olist(T_b)))),c_List_Olist_OCons(T_b))))),c_Lazy__Sequence_Oempty(tc_List_Olist(T_b)))) ),
    file('theBenchmark.p',fact_small__lazy__list_Osimps) ).

fof(fact_eq__comp__r,axiom,
    ! [V_R_2,T_b] : c_Predicate_Opred__comp(T_b,T_b,T_b,c_fequal,c_Predicate_Opred__comp(T_b,T_b,T_b,V_R_2,c_fequal)) = V_R_2,
    file('theBenchmark.p',fact_eq__comp__r) ).

fof(fact_small__lazy__prod__def,axiom,
    ! [V_d,T_b,T_a] :
      ( ( class_Lazy__Sequence_Osmall__lazy(T_b)
        & class_Lazy__Sequence_Osmall__lazy(T_a) )
     => c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_prod(T_a,T_b),V_d) = c_Lazy__Sequence_Oproduct(T_a,T_b,c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(T_a,V_d),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(T_b,V_d)) ),
    file('theBenchmark.p',fact_small__lazy__prod__def) ).

fof(fact_New__DSequence_Opos__union__def,axiom,
    ! [V_i_2,V_yq_2,V_xq_2,T_b] : hAPP(c_New__DSequence_Opos__union(T_b,V_xq_2,V_yq_2),V_i_2) = c_Lazy__Sequence_Oappend(T_b,hAPP(V_xq_2,V_i_2),hAPP(V_yq_2,V_i_2)),
    file('theBenchmark.p',fact_New__DSequence_Opos__union__def) ).

fof(fact_lazy__sequence_Osize_I4_J,axiom,
    ! [V_lazy__sequence,V_a,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_a)),c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_a,V_lazy__sequence)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_a)),V_lazy__sequence)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('theBenchmark.p',fact_lazy__sequence_Osize_I4_J) ).

fof(fact__01,axiom,
    ! [V_yq,V_xq,V_x,T_a] : c_Lazy__Sequence_Oappend(T_a,c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_x,V_xq),V_yq) = c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_x,c_Lazy__Sequence_Oappend(T_a,V_xq,V_yq)),
    file('theBenchmark.p',fact__01) ).

fof(fact_lazy__sequence_Oinject,axiom,
    ! [V_lazy__sequence_H_2,V_a_H_2,V_lazy__sequence_2,V_a_2,T_b] :
      ( c_Lazy__Sequence_Olazy__sequence_OInsert(T_b,V_a_2,V_lazy__sequence_2) = c_Lazy__Sequence_Olazy__sequence_OInsert(T_b,V_a_H_2,V_lazy__sequence_H_2)
    <=> ( V_lazy__sequence_2 = V_lazy__sequence_H_2
        & V_a_2 = V_a_H_2 ) ),
    file('theBenchmark.p',fact_lazy__sequence_Oinject) ).

fof(fact_pos__union__def,axiom,
    ! [V_seed_2,V_size_2,V_nrandom_2,V_R2_2,V_R1_2,T_b] : c_New__Random__Sequence_Opos__union(T_b,V_R1_2,V_R2_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__union(T_b,hAPP(hAPP(hAPP(V_R1_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(hAPP(V_R2_2,V_nrandom_2),V_size_2),V_seed_2)),
    file('theBenchmark.p',fact_pos__union__def) ).

fof(fact_lazy__sequence_Osize_I2_J,axiom,
    ! [V_lazy__sequence_2,V_a_2,V_fa_2,T_b] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_b,V_fa_2),c_Lazy__Sequence_Olazy__sequence_OInsert(T_b,V_a_2,V_lazy__sequence_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_fa_2,V_a_2)),hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_b,V_fa_2),V_lazy__sequence_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('theBenchmark.p',fact_lazy__sequence_Osize_I2_J) ).

fof(fact_small__lazy_H_Osimps,axiom,
    ! [V_i,V_d] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d),V_i))
       => c_Lazy__Sequence_Osmall__lazy_H(V_d,V_i) = c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),V_i),c_Lazy__Sequence_Osmall__lazy_H(V_d,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i),c_Groups_Oone__class_Oone(tc_Int_Oint)))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d),V_i))
       => c_Lazy__Sequence_Osmall__lazy_H(V_d,V_i) = c_Lazy__Sequence_Oempty(tc_Int_Oint) ) ),
    file('theBenchmark.p',fact_small__lazy_H_Osimps) ).

fof(fact_small__lazy_H_Opsimps,axiom,
    ! [V_i_2,V_d_2] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_d_2),V_i_2)))
     => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
         => c_Lazy__Sequence_Osmall__lazy_H(V_d_2,V_i_2) = c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),V_i_2),c_Lazy__Sequence_Osmall__lazy_H(V_d_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
         => c_Lazy__Sequence_Osmall__lazy_H(V_d_2,V_i_2) = c_Lazy__Sequence_Oempty(tc_Int_Oint) ) ) ),
    file('theBenchmark.p',fact_small__lazy_H_Opsimps) ).

fof(fact_small__lazy__int__def,axiom,
    ! [V_d] : c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_Int_Oint,V_d) = c_Lazy__Sequence_Osmall__lazy_H(V_d,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_d)),
    file('theBenchmark.p',fact_small__lazy__int__def) ).

fof(fact_small__lazy_H_Opinduct,axiom,
    ! [V_P_2,V_a1_2,V_a0_2] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2)))
     => ( ! [B_d,B_i] :
            ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_d),B_i)))
           => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_d),B_i))
               => hBOOL(hAPP(hAPP(V_P_2,B_d),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_i),c_Groups_Oone__class_Oone(tc_Int_Oint)))) )
             => hBOOL(hAPP(hAPP(V_P_2,B_d),B_i)) ) )
       => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ),
    file('theBenchmark.p',fact_small__lazy_H_Opinduct) ).

fof(fact_size__code,axiom,
    ! [V_xq_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_b)),V_xq_2) = c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(T_b,tc_Lazy__Sequence_Olazy__sequence(T_b)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),T_b),hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(T_b)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_b)))),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(c_Lazy__Sequence_Oyield(T_b),V_xq_2)),
    file('theBenchmark.p',fact_size__code) ).

fof(fact_lazy__sequence__size__code,axiom,
    ! [V_xq_2,V_s_2,T_b] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_b,V_s_2),V_xq_2) = c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(T_b,tc_Lazy__Sequence_Olazy__sequence(T_b)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),hAPP(hAPP(c_COMBC(T_b,tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat)),T_b),c_COMBC(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),T_b),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(T_b)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat)),T_b),c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Lazy__Sequence_Olazy__sequence(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),T_b),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_s_2))),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_b,V_s_2))))),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Lazy__Sequence_Oyield(T_b),V_xq_2)),
    file('theBenchmark.p',fact_lazy__sequence__size__code) ).

fof(fact_seq__case,axiom,
    ! [V_xq_2,V_g_2,V_f_2,T_c,T_b] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(T_b,T_c,V_f_2,V_g_2,V_xq_2) = c_Option_Ooption_Ooption__case(T_b,tc_prod(T_c,tc_Lazy__Sequence_Olazy__sequence(T_c)),V_f_2,hAPP(c_Product__Type_Oprod_Oprod__case(T_c,tc_Lazy__Sequence_Olazy__sequence(T_c),T_b),V_g_2),hAPP(c_Lazy__Sequence_Oyield(T_c),V_xq_2)),
    file('theBenchmark.p',fact_seq__case) ).

fof(fact_yieldn__def,axiom,
    ! [T_b] : c_Lazy__Sequence_Oyieldn(T_b) = c_Lazy__Sequence_Oanamorph(tc_Lazy__Sequence_Olazy__sequence(T_b),T_b,c_Lazy__Sequence_Oyield(T_b)),
    file('theBenchmark.p',fact_yieldn__def) ).

fof(fact_lazy__sequence_Osimps_I5_J,axiom,
    ! [V_lazy__sequence_2,V_a_2,V_f2_2,V_f1_2,T_c,T_b] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(T_b,T_c,V_f1_2,V_f2_2,c_Lazy__Sequence_Olazy__sequence_OInsert(T_c,V_a_2,V_lazy__sequence_2)) = hAPP(hAPP(V_f2_2,V_a_2),V_lazy__sequence_2),
    file('theBenchmark.p',fact_lazy__sequence_Osimps_I5_J) ).

fof(fact_refl__on__INTER,axiom,
    ! [V_r_2,V_A_2,T_c,V_S_2,T_b] :
      ( ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
         => c_Relation_Orefl__on(T_c,hAPP(V_A_2,B_x),hAPP(V_r_2,B_x)) )
     => c_Relation_Orefl__on(T_c,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_S_2),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_S_2),V_r_2)) ),
    file('theBenchmark.p',fact_refl__on__INTER) ).

fof(fact_in__set__member,axiom,
    ! [V_xs_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
    <=> hBOOL(hAPP(hAPP(c_List_Omember(T_b),V_xs_2),V_x_2)) ),
    file('theBenchmark.p',fact_in__set__member) ).

fof(fact_member__rec_I2_J,axiom,
    ! [V_y,T_a] : ~ hBOOL(hAPP(hAPP(c_List_Omember(T_a),c_List_Olist_ONil(T_a)),V_y)),
    file('theBenchmark.p',fact_member__rec_I2_J) ).

fof(fact_member__set,axiom,
    ! [T_b] : c_List_Omember(T_b) = c_List_Oset(T_b),
    file('theBenchmark.p',fact_member__set) ).

fof(fact_member__rec_I1_J,axiom,
    ! [V_y_2,V_xs_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_List_Omember(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_y_2))
    <=> ( hBOOL(hAPP(hAPP(c_List_Omember(T_b),V_xs_2),V_y_2))
        | V_x_2 = V_y_2 ) ),
    file('theBenchmark.p',fact_member__rec_I1_J) ).

fof(fact_List_Omember__def,axiom,
    ! [V_x_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_List_Omember(T_b),V_xs_2),V_x_2))
    <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ),
    file('theBenchmark.p',fact_List_Omember__def) ).

fof(fact_list__ex1__iff__raw,axiom,
    ! [V_xs_2,V_P_2,T_b] :
      ( c_List_Olist__ex1(T_b,V_P_2,V_xs_2)
    <=> ? [B_x] :
          ( ! [B_y] :
              ( ( hBOOL(hAPP(V_P_2,B_y))
                & hBOOL(hAPP(hAPP(c_member(T_b),B_y),hAPP(c_List_Oset(T_b),V_xs_2))) )
             => B_y = B_x )
          & hBOOL(hAPP(V_P_2,B_x))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) ) ),
    file('theBenchmark.p',fact_list__ex1__iff__raw) ).

fof(fact_setsum__UNION__zero,axiom,
    ! [V_f_2,V_S_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__add(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_S_2))
       => ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_S_2))
             => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_x)) )
         => ( ! [B_T1] :
                ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_T1),V_S_2))
               => ! [B_T2] :
                    ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_T2),V_S_2))
                   => ( B_T1 != B_T2
                     => ! [B_x] :
                          ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_T1))
                         => ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_T2))
                           => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2)),V_S_2) ) ) ) ),
    file('theBenchmark.p',fact_setsum__UNION__zero) ).

fof(fact_THE__default__def,axiom,
    ! [V_d_2,T_b,V_P_2] :
      ( ( ~ ? [B_x] :
              ( ! [B_y] :
                  ( hBOOL(hAPP(V_P_2,B_y))
                 => B_y = B_x )
              & hBOOL(hAPP(V_P_2,B_x)) )
       => c_FunDef_OTHE__default(T_b,V_d_2,V_P_2) = V_d_2 )
      & ( ? [B_x] :
            ( ! [B_y] :
                ( hBOOL(hAPP(V_P_2,B_y))
               => B_y = B_x )
            & hBOOL(hAPP(V_P_2,B_x)) )
       => c_FunDef_OTHE__default(T_b,V_d_2,V_P_2) = c_HOL_OThe(T_b,V_P_2) ) ),
    file('theBenchmark.p',fact_THE__default__def) ).

fof(fact_INF2__I,axiom,
    ! [T_d,T_c,V_c_2,V_b_2,V_B_2,V_A_2,T_b] :
      ( ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
         => hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) )
     => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) ),
    file('theBenchmark.p',fact_INF2__I) ).

fof(fact_SUP2__E,axiom,
    ! [V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2))
     => ~ ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
           => ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) ) ),
    file('theBenchmark.p',fact_SUP2__E) ).

fof(fact_finite__maxlen,axiom,
    ! [V_M_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_b)),V_M_2))
     => ? [B_n] :
        ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),V_M_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),B_x)),B_n)) ) ),
    file('theBenchmark.p',fact_finite__maxlen) ).

fof(fact_lazy__sequence_Osize_I3_J,axiom,
    ! [T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_a)),c_Lazy__Sequence_Olazy__sequence_OEmpty(T_a)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_lazy__sequence_Osize_I3_J) ).

fof(fact_lazy__sequence_Osize_I1_J,axiom,
    ! [V_fa_2,T_b] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_b,V_fa_2),c_Lazy__Sequence_Olazy__sequence_OEmpty(T_b)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_lazy__sequence_Osize_I1_J) ).

fof(fact__02,axiom,
    ! [V_yq,T_a] : c_Lazy__Sequence_Oappend(T_a,c_Lazy__Sequence_Olazy__sequence_OEmpty(T_a),V_yq) = V_yq,
    file('theBenchmark.p',fact__02) ).

fof(fact_lazy__sequence_Osimps_I3_J,axiom,
    ! [V_lazy__sequence_H,V_a_H,T_a] : c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_a_H,V_lazy__sequence_H) != c_Lazy__Sequence_Olazy__sequence_OEmpty(T_a),
    file('theBenchmark.p',fact_lazy__sequence_Osimps_I3_J) ).

fof(fact_lazy__sequence_Osimps_I2_J,axiom,
    ! [V_lazy__sequence_H,V_a_H,T_a] : c_Lazy__Sequence_Olazy__sequence_OEmpty(T_a) != c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_a_H,V_lazy__sequence_H),
    file('theBenchmark.p',fact_lazy__sequence_Osimps_I2_J) ).

fof(fact_lazy__sequence_Osimps_I4_J,axiom,
    ! [V_f2_2,V_f1_2,T_c,T_b] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(T_b,T_c,V_f1_2,V_f2_2,c_Lazy__Sequence_Olazy__sequence_OEmpty(T_c)) = V_f1_2,
    file('theBenchmark.p',fact_lazy__sequence_Osimps_I4_J) ).

fof(fact_list__all__iff__all__interval__int,axiom,
    ! [V_j_2,V_i_2,V_P_2] :
      ( c_List_Olist__all(tc_Int_Oint,V_P_2,c_List_Oupto(V_i_2,V_j_2))
    <=> c_List_Oall__interval__int(V_P_2,V_i_2,V_j_2) ),
    file('theBenchmark.p',fact_list__all__iff__all__interval__int) ).

fof(fact_list__ex__iff__not__all__inverval__int,axiom,
    ! [V_j_2,V_i_2,V_P_2] :
      ( c_List_Olist__ex(tc_Int_Oint,V_P_2,c_List_Oupto(V_i_2,V_j_2))
    <=> ~ c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint,c_fNot),V_P_2),V_i_2,V_j_2) ),
    file('theBenchmark.p',fact_list__ex__iff__not__all__inverval__int) ).

fof(fact_all__interval__int__def,axiom,
    ! [V_j_2,V_i_2,V_P_2] :
      ( c_List_Oall__interval__int(V_P_2,V_i_2,V_j_2)
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2)))
         => hBOOL(hAPP(V_P_2,B_x)) ) ),
    file('theBenchmark.p',fact_all__interval__int__def) ).

fof(fact_code__numeral_Orecs_I2_J,axiom,
    ! [V_code__numeral_2,V_f2_2,V_f1_2,T_b] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(T_b,V_f1_2,V_f2_2,c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2)) = hAPP(hAPP(V_f2_2,V_code__numeral_2),c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(T_b,V_f1_2,V_f2_2,V_code__numeral_2)),
    file('theBenchmark.p',fact_code__numeral_Orecs_I2_J) ).

fof(fact_Random_Osimps,axiom,
    ! [V_size_2,V_g_2,T_b,V_nrandom_2] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_nrandom_2),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))
       => c_Random__Sequence_ORandom(T_b,V_g_2,V_nrandom_2,V_size_2) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm)),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(V_g_2,V_size_2)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random__Sequence_ORandom(T_b,V_g_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_nrandom_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),V_size_2))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b))))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b))))),c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b))))),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Ounion(T_b)),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Osingle(T_b)),c_Product__Type_Ofst(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))))))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_nrandom_2),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))
       => c_Random__Sequence_ORandom(T_b,V_g_2,V_nrandom_2,V_size_2) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(T_b)) ) ),
    file('theBenchmark.p',fact_Random_Osimps) ).

fof(fact_code__numeral_Orecs_I1_J,axiom,
    ! [V_f2_2,V_f1_2,T_b] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(T_b,V_f1_2,V_f2_2,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = V_f1_2,
    file('theBenchmark.p',fact_code__numeral_Orecs_I1_J) ).

fof(fact_Random__Sequence_Oempty__def,axiom,
    ! [V_size_2,V_nrandom_2,T_b] : c_Random__Sequence_Oempty(T_b,V_nrandom_2,V_size_2) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(T_b)),
    file('theBenchmark.p',fact_Random__Sequence_Oempty__def) ).

fof(fact_Random__Sequence_Osingle__def,axiom,
    ! [V_size_2,V_nrandom_2,V_x_2,T_b] : hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(T_b),V_x_2),V_nrandom_2),V_size_2) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_DSequence_Osingle(T_b),V_x_2)),
    file('theBenchmark.p',fact_Random__Sequence_Osingle__def) ).

fof(fact_Random__Sequence_Omap__def,axiom,
    ! [V_P_2,V_f_2,T_b,T_c] : c_Random__Sequence_Omap(T_c,T_b,V_f_2,V_P_2) = c_Random__Sequence_Obind(T_c,T_b,V_P_2,hAPP(c_Fun_Ocomp(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))))),T_c,c_Random__Sequence_Osingle(T_b)),V_f_2)),
    file('theBenchmark.p',fact_Random__Sequence_Omap__def) ).

fof(fact_exE__realizer,axiom,
    ! [T_d,V_f_2,V_Q_2,V_p_2,T_b,T_c,V_P_2] :
      ( hBOOL(hAPP(hAPP(V_P_2,hAPP(c_Product__Type_Osnd(T_c,T_b),V_p_2)),hAPP(c_Product__Type_Ofst(T_c,T_b),V_p_2)))
     => ( ! [B_x,B_y] :
            ( hBOOL(hAPP(hAPP(V_P_2,B_y),B_x))
           => hBOOL(hAPP(V_Q_2,hAPP(hAPP(V_f_2,B_x),B_y))) )
       => hBOOL(hAPP(V_Q_2,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,T_d),V_f_2),V_p_2))) ) ),
    file('theBenchmark.p',fact_exE__realizer) ).

fof(fact_Image__Collect__split,axiom,
    ! [V_A_2,V_P_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,hAPP(c_Set_OCollect(tc_prod(T_c,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,tc_HOL_Obool),V_P_2))),V_A_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)))),hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),V_P_2)))),
    file('theBenchmark.p',fact_Image__Collect__split) ).

fof(fact_lexord__trans,axiom,
    ! [V_z_2,V_r_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_y_2),V_z_2)),c_List_Olexord(T_b,V_r_2)))
       => ( c_Relation_Otrans(T_b,V_r_2)
         => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_z_2)),c_List_Olexord(T_b,V_r_2))) ) ) ),
    file('theBenchmark.p',fact_lexord__trans) ).

fof(fact_trans__less__than,axiom,
    c_Relation_Otrans(tc_Nat_Onat,c_Wellfounded_Oless__than),
    file('theBenchmark.p',fact_trans__less__than) ).

fof(fact_trans__lex__prod,axiom,
    ! [V_R2_2,T_c,V_R1_2,T_b] :
      ( c_Relation_Otrans(T_b,V_R1_2)
     => ( c_Relation_Otrans(T_c,V_R2_2)
       => c_Relation_Otrans(tc_prod(T_b,T_c),c_Wellfounded_Olex__prod(T_b,T_c,V_R1_2,V_R2_2)) ) ),
    file('theBenchmark.p',fact_trans__lex__prod) ).

fof(fact_transD,axiom,
    ! [V_c_2,V_b_2,V_a_2,V_r_2,T_b] :
      ( c_Relation_Otrans(T_b,V_r_2)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
       => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),V_r_2))
         => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),V_r_2)) ) ) ),
    file('theBenchmark.p',fact_transD) ).

fof(fact_trans__def,axiom,
    ! [V_r_2,T_b] :
      ( c_Relation_Otrans(T_b,V_r_2)
    <=> ! [B_x,B_y] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_r_2))
         => ! [B_z] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_z)),V_r_2))
             => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_z)),V_r_2)) ) ) ),
    file('theBenchmark.p',fact_trans__def) ).

fof(fact_trans__rtrancl,axiom,
    ! [V_r_2,T_b] : c_Relation_Otrans(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)),
    file('theBenchmark.p',fact_trans__rtrancl) ).

fof(fact_trans__Id,axiom,
    ! [T_b] : c_Relation_Otrans(T_b,c_Relation_OId(T_b)),
    file('theBenchmark.p',fact_trans__Id) ).

fof(fact_trans__trancl,axiom,
    ! [V_r_2,T_b] : c_Relation_Otrans(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)),
    file('theBenchmark.p',fact_trans__trancl) ).

fof(fact_trancl__id,axiom,
    ! [V_r_2,T_b] :
      ( c_Relation_Otrans(T_b,V_r_2)
     => c_Transitive__Closure_Otrancl(T_b,V_r_2) = V_r_2 ),
    file('theBenchmark.p',fact_trancl__id) ).

fof(fact_trans__Id__on,axiom,
    ! [V_A_2,T_b] : c_Relation_Otrans(T_b,c_Relation_OId__on(T_b,V_A_2)),
    file('theBenchmark.p',fact_trans__Id__on) ).

fof(fact_trans__finite__psubset,axiom,
    ! [T_b] : c_Relation_Otrans(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_b)),
    file('theBenchmark.p',fact_trans__finite__psubset) ).

fof(fact_lexord__transI,axiom,
    ! [V_r_2,T_b] :
      ( c_Relation_Otrans(T_b,V_r_2)
     => c_Relation_Otrans(tc_List_Olist(T_b),c_List_Olexord(T_b,V_r_2)) ),
    file('theBenchmark.p',fact_lexord__transI) ).

fof(fact_listrel__trans,axiom,
    ! [V_r_2,T_b] :
      ( c_Relation_Otrans(T_b,V_r_2)
     => c_Relation_Otrans(tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)) ),
    file('theBenchmark.p',fact_listrel__trans) ).

fof(fact_bex__empty,axiom,
    ! [V_P_2,T_b] :
      ~ ? [B_x] :
          ( hBOOL(hAPP(V_P_2,B_x))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ),
    file('theBenchmark.p',fact_bex__empty) ).

fof(fact_trans__converse,axiom,
    ! [V_r_2,T_b] :
      ( c_Relation_Otrans(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
    <=> c_Relation_Otrans(T_b,V_r_2) ),
    file('theBenchmark.p',fact_trans__converse) ).

fof(fact_finite__Collect__bex,axiom,
    ! [V_Q_2,T_c,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),V_Q_2)))))
      <=> ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
           => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),V_Q_2),B_x)))) ) ) ),
    file('theBenchmark.p',fact_finite__Collect__bex) ).

fof(fact_bex__UNIV,axiom,
    ! [V_P_2,T_b] :
      ( ? [B_x] :
          ( hBOOL(hAPP(V_P_2,B_x))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) )
    <=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ),
    file('theBenchmark.p',fact_bex__UNIV) ).

fof(fact_trans__Int,axiom,
    ! [V_s_2,V_r_2,T_b] :
      ( c_Relation_Otrans(T_b,V_r_2)
     => ( c_Relation_Otrans(T_b,V_s_2)
       => c_Relation_Otrans(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ) ),
    file('theBenchmark.p',fact_trans__Int) ).

fof(fact_SUPR__bool__eq,axiom,
    ! [T_b] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_HOL_Obool) = c_Set_OBex(T_b),
    file('theBenchmark.p',fact_SUPR__bool__eq) ).

fof(fact_trans__O__subset,axiom,
    ! [V_r_2,T_b] :
      ( c_Relation_Otrans(T_b,V_r_2)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_r_2),V_r_2)),V_r_2)) ),
    file('theBenchmark.p',fact_trans__O__subset) ).

fof(fact_trans__reflclI,axiom,
    ! [V_r_2,T_b] :
      ( c_Relation_Otrans(T_b,V_r_2)
     => c_Relation_Otrans(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))) ),
    file('theBenchmark.p',fact_trans__reflclI) ).

fof(fact_trans__inv__image,axiom,
    ! [V_f_2,T_c,V_r_2,T_b] :
      ( c_Relation_Otrans(T_b,V_r_2)
     => c_Relation_Otrans(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2)) ),
    file('theBenchmark.p',fact_trans__inv__image) ).

fof(fact_Union__eq,axiom,
    ! [V_A_2,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_b,tc_HOL_Obool))),V_A_2)))),c_member(T_b)))),
    file('theBenchmark.p',fact_Union__eq) ).

fof(fact_Bex__set__list__ex,axiom,
    ! [V_P_2,V_xs_2,T_b] :
      ( ? [B_x] :
          ( hBOOL(hAPP(V_P_2,B_x))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) )
    <=> c_List_Olist__ex(T_b,V_P_2,V_xs_2) ),
    file('theBenchmark.p',fact_Bex__set__list__ex) ).

fof(fact_list__ex__iff__raw,axiom,
    ! [V_xs_2,V_P_2,T_b] :
      ( c_List_Olist__ex(T_b,V_P_2,V_xs_2)
    <=> ? [B_x] :
          ( hBOOL(hAPP(V_P_2,B_x))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) ) ),
    file('theBenchmark.p',fact_list__ex__iff__raw) ).

fof(fact_UN__eq,axiom,
    ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_OCollect(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c)),c_fequal)),V_B_2))))),
    file('theBenchmark.p',fact_UN__eq) ).

fof(fact_INT__eq,axiom,
    ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_OCollect(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c)),c_fequal)),V_B_2))))),
    file('theBenchmark.p',fact_INT__eq) ).

fof(fact_Sup__fun__def,axiom,
    ! [V_x_2,V_A_2,T_c,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,T_b),V_A_2),V_x_2) = c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_fun(T_c,T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_fun(T_c,T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_c,T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_c,T_b))),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_fun(T_c,T_b))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),T_c,T_b),c_COMBI(tc_fun(T_c,T_b))),V_x_2)))))) ),
    file('theBenchmark.p',fact_Sup__fun__def) ).

fof(fact_Sup__apply,axiom,
    ! [V_x_2,V_A_2,T_c,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,T_b),V_A_2),V_x_2) = c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_fun(T_c,T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_fun(T_c,T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_c,T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_c,T_b))),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_fun(T_c,T_b))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),T_c,T_b),c_COMBI(tc_fun(T_c,T_b))),V_x_2)))))) ),
    file('theBenchmark.p',fact_Sup__apply) ).

fof(fact_Inf__fun__def,axiom,
    ! [V_x_2,V_A_2,T_c,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,T_b),V_A_2),V_x_2) = c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_fun(T_c,T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_fun(T_c,T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_c,T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_c,T_b))),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_fun(T_c,T_b))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),T_c,T_b),c_COMBI(tc_fun(T_c,T_b))),V_x_2)))))) ),
    file('theBenchmark.p',fact_Inf__fun__def) ).

fof(fact_Inf__apply,axiom,
    ! [V_x_2,V_A_2,T_c,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,T_b),V_A_2),V_x_2) = c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_fun(T_c,T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_fun(T_c,T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_c,T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_c,T_b))),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_fun(T_c,T_b))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),T_c,T_b),c_COMBI(tc_fun(T_c,T_b))),V_x_2)))))) ),
    file('theBenchmark.p',fact_Inf__apply) ).

fof(fact_max__extp_Ointros,axiom,
    ! [V_R_2,V_Y_2,V_X_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Y_2))
       => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_X_2))
               => ? [B_xa] :
                    ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa))
                    & hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_Y_2)) ) )
           => c_Wellfounded_Omax__extp(T_b,V_R_2,V_X_2,V_Y_2) ) ) ) ),
    file('theBenchmark.p',fact_max__extp_Ointros) ).

fof(fact_transp__def,axiom,
    ! [V_r_2,T_b] :
      ( c_Predicate_Otransp(T_b,V_r_2)
    <=> c_Relation_Otrans(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))) ),
    file('theBenchmark.p',fact_transp__def) ).

fof(fact_transpE,axiom,
    ! [V_z_2,V_y_2,V_x_2,V_r_2,T_b] :
      ( c_Predicate_Otransp(T_b,V_r_2)
     => ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2))
       => ( hBOOL(hAPP(hAPP(V_r_2,V_y_2),V_z_2))
         => hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_z_2)) ) ) ),
    file('theBenchmark.p',fact_transpE) ).

fof(fact_equivp__reflp__symp__transp,axiom,
    ! [V_R_2,T_b] :
      ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
    <=> ( c_Predicate_Otransp(T_b,V_R_2)
        & c_Predicate_Osymp(T_b,V_R_2)
        & c_Predicate_Oreflp(T_b,V_R_2) ) ),
    file('theBenchmark.p',fact_equivp__reflp__symp__transp) ).

fof(fact_equivpI,axiom,
    ! [V_R_2,T_b] :
      ( c_Predicate_Oreflp(T_b,V_R_2)
     => ( c_Predicate_Osymp(T_b,V_R_2)
       => ( c_Predicate_Otransp(T_b,V_R_2)
         => c_Equiv__Relations_Oequivp(T_b,V_R_2) ) ) ),
    file('theBenchmark.p',fact_equivpI) ).

fof(fact_sympE,axiom,
    ! [V_y_2,V_x_2,V_r_2,T_b] :
      ( c_Predicate_Osymp(T_b,V_r_2)
     => ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2))
       => hBOOL(hAPP(hAPP(V_r_2,V_y_2),V_x_2)) ) ),
    file('theBenchmark.p',fact_sympE) ).

fof(fact_equivpE,axiom,
    ! [V_R_2,T_b] :
      ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
     => ~ ( c_Predicate_Oreflp(T_b,V_R_2)
         => ( c_Predicate_Osymp(T_b,V_R_2)
           => ~ c_Predicate_Otransp(T_b,V_R_2) ) ) ),
    file('theBenchmark.p',fact_equivpE) ).

fof(fact_max__extp_Osimps,axiom,
    ! [V_a2_2,V_a1_2,V_R_2,T_b] :
      ( c_Wellfounded_Omax__extp(T_b,V_R_2,V_a1_2,V_a2_2)
    <=> ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2))
           => ? [B_xa] :
                ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa))
                & hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2)) ) )
        & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2)) ) ),
    file('theBenchmark.p',fact_max__extp_Osimps) ).

fof(fact_trans__diff__Id,axiom,
    ! [V_r_2,T_b] :
      ( c_Relation_Otrans(T_b,V_r_2)
     => ( c_Relation_Oantisym(T_b,V_r_2)
       => c_Relation_Otrans(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))) ) ),
    file('theBenchmark.p',fact_trans__diff__Id) ).

fof(fact_antisym__Id__on,axiom,
    ! [V_A_2,T_b] : c_Relation_Oantisym(T_b,c_Relation_OId__on(T_b,V_A_2)),
    file('theBenchmark.p',fact_antisym__Id__on) ).

fof(fact_antisym__converse,axiom,
    ! [V_r_2,T_b] :
      ( c_Relation_Oantisym(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
    <=> c_Relation_Oantisym(T_b,V_r_2) ),
    file('theBenchmark.p',fact_antisym__converse) ).

fof(fact_antisym__empty,axiom,
    ! [T_b] : c_Relation_Oantisym(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))),
    file('theBenchmark.p',fact_antisym__empty) ).

fof(fact_antisym__Id,axiom,
    ! [T_b] : c_Relation_Oantisym(T_b,c_Relation_OId(T_b)),
    file('theBenchmark.p',fact_antisym__Id) ).

fof(fact_antisym__subset,axiom,
    ! [V_s_2,V_r_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
     => ( c_Relation_Oantisym(T_b,V_s_2)
       => c_Relation_Oantisym(T_b,V_r_2) ) ),
    file('theBenchmark.p',fact_antisym__subset) ).

fof(fact_antisym__def,axiom,
    ! [V_r_2,T_b] :
      ( c_Relation_Oantisym(T_b,V_r_2)
    <=> ! [B_x,B_y] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_r_2))
         => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_x)),V_r_2))
           => B_x = B_y ) ) ),
    file('theBenchmark.p',fact_antisym__def) ).

fof(fact_antisymD,axiom,
    ! [V_b_2,V_a_2,V_r_2,T_b] :
      ( c_Relation_Oantisym(T_b,V_r_2)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
       => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_a_2)),V_r_2))
         => V_a_2 = V_b_2 ) ) ),
    file('theBenchmark.p',fact_antisymD) ).

fof(fact_antisym__reflcl,axiom,
    ! [V_r_2,T_b] :
      ( c_Relation_Oantisym(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b)))
    <=> c_Relation_Oantisym(T_b,V_r_2) ),
    file('theBenchmark.p',fact_antisym__reflcl) ).

fof(fact_acyclic__impl__antisym__rtrancl,axiom,
    ! [V_r_2,T_b] :
      ( c_Wellfounded_Oacyclic(T_b,V_r_2)
     => c_Relation_Oantisym(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) ),
    file('theBenchmark.p',fact_acyclic__impl__antisym__rtrancl) ).

fof(fact_fun__lub__def,axiom,
    ! [V_x_2,V_A_2,V_L_2,T_d,T_b,T_c] : c_Partial__Function_Ofun__lub(T_c,T_b,T_d,V_L_2,V_A_2,V_x_2) = hAPP(V_L_2,hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(tc_fun(T_d,T_c))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool),tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool),T_c),hAPP(c_COMBS(tc_fun(T_d,T_c),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_d,T_c)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_d,T_c),tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_d,T_c))),V_A_2)))),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_fun(T_d,T_c),T_c),tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_d,T_c),T_c),tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool)),T_c),c_COMBB(T_c,tc_HOL_Obool,tc_fun(T_d,T_c))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(T_d,T_c),T_d,T_c),c_COMBI(tc_fun(T_d,T_c))),V_x_2)))))),
    file('theBenchmark.p',fact_fun__lub__def) ).

fof(fact_sym__trans__comp__subset,axiom,
    ! [V_r_2,T_b] :
      ( c_Relation_Osym(T_b,V_r_2)
     => ( c_Relation_Otrans(T_b,V_r_2)
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),V_r_2)),V_r_2)) ) ),
    file('theBenchmark.p',fact_sym__trans__comp__subset) ).

fof(fact_symD,axiom,
    ! [V_b_2,V_a_2,V_r_2,T_b] :
      ( c_Relation_Osym(T_b,V_r_2)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_a_2)),V_r_2)) ) ),
    file('theBenchmark.p',fact_symD) ).

fof(fact_sym__def,axiom,
    ! [V_r_2,T_b] :
      ( c_Relation_Osym(T_b,V_r_2)
    <=> ! [B_x,B_y] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_r_2))
         => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_x)),V_r_2)) ) ),
    file('theBenchmark.p',fact_sym__def) ).

fof(fact_sym__rtrancl,axiom,
    ! [V_r_2,T_b] :
      ( c_Relation_Osym(T_b,V_r_2)
     => c_Relation_Osym(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) ),
    file('theBenchmark.p',fact_sym__rtrancl) ).

fof(fact_sym__Id,axiom,
    ! [T_b] : c_Relation_Osym(T_b,c_Relation_OId(T_b)),
    file('theBenchmark.p',fact_sym__Id) ).

fof(fact_sym__Un,axiom,
    ! [V_s_2,V_r_2,T_b] :
      ( c_Relation_Osym(T_b,V_r_2)
     => ( c_Relation_Osym(T_b,V_s_2)
       => c_Relation_Osym(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ) ),
    file('theBenchmark.p',fact_sym__Un) ).

fof(fact_sym__trancl,axiom,
    ! [V_r_2,T_b] :
      ( c_Relation_Osym(T_b,V_r_2)
     => c_Relation_Osym(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)) ),
    file('theBenchmark.p',fact_sym__trancl) ).

fof(fact_sym__Id__on,axiom,
    ! [V_A_2,T_b] : c_Relation_Osym(T_b,c_Relation_OId__on(T_b,V_A_2)),
    file('theBenchmark.p',fact_sym__Id__on) ).

fof(fact_listrel__sym,axiom,
    ! [V_r_2,T_b] :
      ( c_Relation_Osym(T_b,V_r_2)
     => c_Relation_Osym(tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)) ),
    file('theBenchmark.p',fact_listrel__sym) ).

fof(fact_sym__converse,axiom,
    ! [V_r_2,T_b] :
      ( c_Relation_Osym(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
    <=> c_Relation_Osym(T_b,V_r_2) ),
    file('theBenchmark.p',fact_sym__converse) ).

fof(fact_sym__conv__converse__eq,axiom,
    ! [V_r_2,T_b] :
      ( c_Relation_Osym(T_b,V_r_2)
    <=> hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2) = V_r_2 ),
    file('theBenchmark.p',fact_sym__conv__converse__eq) ).

fof(fact_sym__Int,axiom,
    ! [V_s_2,V_r_2,T_b] :
      ( c_Relation_Osym(T_b,V_r_2)
     => ( c_Relation_Osym(T_b,V_s_2)
       => c_Relation_Osym(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ) ),
    file('theBenchmark.p',fact_sym__Int) ).

fof(fact_sym__Un__converse,axiom,
    ! [V_r_2,T_b] : c_Relation_Osym(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))),
    file('theBenchmark.p',fact_sym__Un__converse) ).

fof(fact_sym__inv__image,axiom,
    ! [V_f_2,T_c,V_r_2,T_b] :
      ( c_Relation_Osym(T_b,V_r_2)
     => c_Relation_Osym(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2)) ),
    file('theBenchmark.p',fact_sym__inv__image) ).

fof(fact_sym__Int__converse,axiom,
    ! [V_r_2,T_b] : c_Relation_Osym(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))),
    file('theBenchmark.p',fact_sym__Int__converse) ).

fof(fact_equivE,axiom,
    ! [V_r_2,V_A_2,T_b] :
      ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
     => ~ ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
         => ( c_Relation_Osym(T_b,V_r_2)
           => ~ c_Relation_Otrans(T_b,V_r_2) ) ) ),
    file('theBenchmark.p',fact_equivE) ).

fof(fact_equivI,axiom,
    ! [V_r_2,V_A_2,T_b] :
      ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
     => ( c_Relation_Osym(T_b,V_r_2)
       => ( c_Relation_Otrans(T_b,V_r_2)
         => c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ) ) ),
    file('theBenchmark.p',fact_equivI) ).

fof(fact_equiv__def,axiom,
    ! [V_r_2,V_A_2,T_b] :
      ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
    <=> ( c_Relation_Otrans(T_b,V_r_2)
        & c_Relation_Osym(T_b,V_r_2)
        & c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ) ),
    file('theBenchmark.p',fact_equiv__def) ).

fof(fact_symp__def,axiom,
    ! [V_r_2,T_b] :
      ( c_Predicate_Osymp(T_b,V_r_2)
    <=> c_Relation_Osym(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))) ),
    file('theBenchmark.p',fact_symp__def) ).

fof(fact_part__equivp__refl__symp__transp,axiom,
    ! [V_R_2,T_b] :
      ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
    <=> ( c_Predicate_Otransp(T_b,V_R_2)
        & c_Predicate_Osymp(T_b,V_R_2)
        & ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x)) ) ),
    file('theBenchmark.p',fact_part__equivp__refl__symp__transp) ).

fof(fact_part__equivpI,axiom,
    ! [T_b,V_R_2] :
      ( ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x))
     => ( c_Predicate_Osymp(T_b,V_R_2)
       => ( c_Predicate_Otransp(T_b,V_R_2)
         => c_Equiv__Relations_Opart__equivp(T_b,V_R_2) ) ) ),
    file('theBenchmark.p',fact_part__equivpI) ).

fof(fact_part__equivp__def,axiom,
    ! [V_R_2,T_b] :
      ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
    <=> ( ! [B_x,B_y] :
            ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_y))
          <=> ( hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y)
              & hBOOL(hAPP(hAPP(V_R_2,B_y),B_y))
              & hBOOL(hAPP(hAPP(V_R_2,B_x),B_x)) ) )
        & ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x)) ) ),
    file('theBenchmark.p',fact_part__equivp__def) ).

fof(fact_part__equivp__symp,axiom,
    ! [V_y_2,V_x_2,V_R_2,T_b] :
      ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
     => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
       => hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ),
    file('theBenchmark.p',fact_part__equivp__symp) ).

fof(fact_part__equivp__transp,axiom,
    ! [V_z_2,V_y_2,V_x_2,V_R_2,T_b] :
      ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
     => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
       => ( hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_z_2))
         => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_z_2)) ) ) ),
    file('theBenchmark.p',fact_part__equivp__transp) ).

fof(fact_equivp__implies__part__equivp,axiom,
    ! [V_R_2,T_b] :
      ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
     => c_Equiv__Relations_Opart__equivp(T_b,V_R_2) ),
    file('theBenchmark.p',fact_equivp__implies__part__equivp) ).

fof(fact_part__equivpE,axiom,
    ! [V_R_2,T_b] :
      ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
     => ~ ( ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x))
         => ( c_Predicate_Osymp(T_b,V_R_2)
           => ~ c_Predicate_Otransp(T_b,V_R_2) ) ) ),
    file('theBenchmark.p',fact_part__equivpE) ).

fof(fact_part__equivp__typedef,axiom,
    ! [V_R_2,T_b] :
      ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
     => ? [B_d] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_d),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBS(T_b,T_b,tc_HOL_Obool),V_R_2),c_COMBI(T_b))))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b)),c_fequal)),V_R_2))))) ),
    file('theBenchmark.p',fact_part__equivp__typedef) ).

fof(fact_inj__iff,axiom,
    ! [V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
    <=> hAPP(c_Fun_Ocomp(T_c,T_b,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)),V_f_2) = c_Fun_Oid(T_b) ),
    file('theBenchmark.p',fact_inj__iff) ).

fof(fact_inv__o__cancel,axiom,
    ! [V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
     => hAPP(c_Fun_Ocomp(T_c,T_b,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)),V_f_2) = c_Fun_Oid(T_b) ),
    file('theBenchmark.p',fact_inv__o__cancel) ).

fof(fact_inv__id,axiom,
    ! [T_b] : c_Hilbert__Choice_Oinv__into(T_b,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Fun_Oid(T_b)) = c_Fun_Oid(T_b),
    file('theBenchmark.p',fact_inv__id) ).

fof(fact_inv__f__eq,axiom,
    ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
     => ( hAPP(V_f_2,V_x_2) = V_y_2
       => hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),V_y_2) = V_x_2 ) ),
    file('theBenchmark.p',fact_inv__f__eq) ).

fof(fact_inv__f__f,axiom,
    ! [V_x_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
     => hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2 ),
    file('theBenchmark.p',fact_inv__f__f) ).

fof(fact_inv__into__f__f,axiom,
    ! [V_x_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
       => hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2 ) ),
    file('theBenchmark.p',fact_inv__into__f__f) ).

fof(fact_inv__into__f__eq,axiom,
    ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
       => ( hAPP(V_f_2,V_x_2) = V_y_2
         => hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ),
    file('theBenchmark.p',fact_inv__into__f__eq) ).

fof(fact_f__inv__into__f,axiom,
    ! [V_A_2,V_f_2,T_c,V_y_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
     => hAPP(V_f_2,hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_b,V_A_2,V_f_2),V_y_2)) = V_y_2 ),
    file('theBenchmark.p',fact_f__inv__into__f) ).

fof(fact_inv__into__into,axiom,
    ! [V_A_2,V_f_2,T_c,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
     => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_b,V_A_2,V_f_2),V_x_2)),V_A_2)) ),
    file('theBenchmark.p',fact_inv__into__into) ).

fof(fact_inv__into__injective,axiom,
    ! [V_y_2,V_x_2,V_f_2,V_A_2,T_c,T_b] :
      ( hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),V_x_2) = hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),V_y_2)
     => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
       => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
         => V_x_2 = V_y_2 ) ) ),
    file('theBenchmark.p',fact_inv__into__injective) ).

fof(fact_image__surj__f__inv__f,axiom,
    ! [V_A_2,V_f_2,T_b,T_c] :
      ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
     => hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Oimage(T_b,T_c,c_Hilbert__Choice_Oinv__into(T_c,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2)),V_A_2)) = V_A_2 ),
    file('theBenchmark.p',fact_image__surj__f__inv__f) ).

fof(fact_surj__f__inv__f,axiom,
    ! [V_y_2,V_f_2,T_b,T_c] :
      ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
     => hAPP(V_f_2,hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2),V_y_2)) = V_y_2 ),
    file('theBenchmark.p',fact_surj__f__inv__f) ).

fof(fact_surj__iff__all,axiom,
    ! [V_f_2,T_b,T_c] :
      ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
    <=> ! [B_x] : hAPP(V_f_2,hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2),B_x)) = B_x ),
    file('theBenchmark.p',fact_surj__iff__all) ).

fof(fact_image__inv__into__cancel,axiom,
    ! [V_B_H_2,V_A_H_2,V_A_2,V_f_2,T_b,T_c] :
      ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_A_H_2
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_H_2),V_A_H_2))
       => hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Oimage(T_b,T_c,c_Hilbert__Choice_Oinv__into(T_c,T_b,V_A_2,V_f_2)),V_B_H_2)) = V_B_H_2 ) ),
    file('theBenchmark.p',fact_image__inv__into__cancel) ).

fof(fact_inv__into__def,axiom,
    ! [V_x_2,V_f_2,V_A_2,T_c,T_b] : hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),V_x_2) = c_Hilbert__Choice_OEps(T_b,hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),V_x_2))),
    file('theBenchmark.p',fact_inv__into__def) ).

fof(fact_inv__def,axiom,
    ! [V_y_2,V_f_2,T_c,T_b] : hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),V_y_2) = c_Hilbert__Choice_OEps(T_b,hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),V_y_2)),
    file('theBenchmark.p',fact_inv__def) ).

fof(fact_o__inv__o__cancel,axiom,
    ! [V_g_2,T_d,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
     => hAPP(c_Fun_Ocomp(T_c,T_d,T_b,hAPP(c_Fun_Ocomp(T_b,T_d,T_c,V_g_2),c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2))),V_f_2) = V_g_2 ),
    file('theBenchmark.p',fact_o__inv__o__cancel) ).

fof(fact_surj__imp__inj__inv,axiom,
    ! [V_f_2,T_b,T_c] :
      ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
     => c_Fun_Oinj__on(T_b,T_c,c_Hilbert__Choice_Oinv__into(T_c,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
    file('theBenchmark.p',fact_surj__imp__inj__inv) ).

fof(fact_inv__image__comp,axiom,
    ! [V_X_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
     => hAPP(c_Set_Oimage(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_X_2)) = V_X_2 ),
    file('theBenchmark.p',fact_inv__image__comp) ).

fof(fact_image__inv__f__f,axiom,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
     => hAPP(c_Set_Oimage(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = V_A_2 ),
    file('theBenchmark.p',fact_image__inv__f__f) ).

fof(fact_inj__imp__surj__inv,axiom,
    ! [V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
     => hAPP(c_Set_Oimage(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_inj__imp__surj__inv) ).

fof(fact_inv__into__image__cancel,axiom,
    ! [V_S_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_A_2))
       => hAPP(c_Set_Oimage(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_S_2)) = V_S_2 ) ),
    file('theBenchmark.p',fact_inv__into__image__cancel) ).

fof(fact_inj__on__inv__into,axiom,
    ! [V_A_2,V_f_2,T_c,V_B_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
     => c_Fun_Oinj__on(T_b,T_c,c_Hilbert__Choice_Oinv__into(T_c,T_b,V_A_2,V_f_2),V_B_2) ),
    file('theBenchmark.p',fact_inj__on__inv__into) ).

fof(fact_inv__into__comp,axiom,
    ! [V_x_2,V_A_2,V_g_2,T_d,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2))
     => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,V_A_2)
       => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2))))
         => hAPP(c_Hilbert__Choice_Oinv__into(T_d,T_c,V_A_2,hAPP(c_Fun_Ocomp(T_b,T_c,T_d,V_f_2),V_g_2)),V_x_2) = hAPP(hAPP(c_Fun_Ocomp(T_b,T_d,T_c,c_Hilbert__Choice_Oinv__into(T_d,T_b,V_A_2,V_g_2)),c_Hilbert__Choice_Oinv__into(T_b,T_c,hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2),V_f_2)),V_x_2) ) ) ),
    file('theBenchmark.p',fact_inv__into__comp) ).

fof(fact_surj__iff,axiom,
    ! [V_f_2,T_b,T_c] :
      ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
    <=> hAPP(c_Fun_Ocomp(T_c,T_b,T_b,V_f_2),c_Hilbert__Choice_Oinv__into(T_c,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2)) = c_Fun_Oid(T_b) ),
    file('theBenchmark.p',fact_surj__iff) ).

fof(fact_inj__transfer,axiom,
    ! [V_x_2,V_P_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
     => ( ! [B_y] :
            ( hBOOL(hAPP(hAPP(c_member(T_c),B_y),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))))
           => hBOOL(hAPP(V_P_2,hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),B_y))) )
       => hBOOL(hAPP(V_P_2,V_x_2)) ) ),
    file('theBenchmark.p',fact_inj__transfer) ).

fof(fact_fold__image__UN__disjoint,axiom,
    ! [V_g_2,V_A_2,T_c,V_I_2,T_b,T_d] :
      ( class_Groups_Ocomm__monoid__mult(T_d)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_I_2))
       => ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2))
             => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_A_2,B_x))) )
         => ( ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2))
               => ! [B_xa] :
                    ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_I_2))
                   => ( B_x != B_xa
                     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_A_2,B_x)),hAPP(V_A_2,B_xa)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) )
           => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Otimes__class_Otimes(T_d)),V_g_2),c_Groups_Oone__class_Oone(T_d)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_b,c_Groups_Otimes__class_Otimes(T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),T_d,T_b),hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Otimes__class_Otimes(T_d)),V_g_2),c_Groups_Oone__class_Oone(T_d))),V_A_2)),c_Groups_Oone__class_Oone(T_d)),V_I_2) ) ) ) ),
    file('theBenchmark.p',fact_fold__image__UN__disjoint) ).

fof(fact_nat__of__induct,axiom,
    ! [V_P_2,V_y_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
     => ( ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Code__Numeral_Onat__of,B_x)))
       => hBOOL(hAPP(V_P_2,V_y_2)) ) ),
    file('theBenchmark.p',fact_nat__of__induct) ).

fof(fact_nat__of__cases,axiom,
    ! [V_y_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
     => ~ ! [B_x] : V_y_2 != hAPP(c_Code__Numeral_Onat__of,B_x) ),
    file('theBenchmark.p',fact_nat__of__cases) ).

fof(fact_of__nat__induct,axiom,
    ! [V_x_2,V_P_2] :
      ( ! [B_y] :
          ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_y),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
         => hBOOL(hAPP(V_P_2,hAPP(c_Code__Numeral_Oof__nat,B_y))) )
     => hBOOL(hAPP(V_P_2,V_x_2)) ),
    file('theBenchmark.p',fact_of__nat__induct) ).

fof(fact_of__nat__cases,axiom,
    ! [V_x_2] :
      ~ ! [B_y] :
          ( V_x_2 = hAPP(c_Code__Numeral_Oof__nat,B_y)
         => ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_y),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ),
    file('theBenchmark.p',fact_of__nat__cases) ).

fof(fact_lazy__sequence_Orecs_I1_J,axiom,
    ! [V_f2_2,V_f1_2,T_c,T_b] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(T_b,T_c,V_f1_2,V_f2_2,c_Lazy__Sequence_Olazy__sequence_OEmpty(T_c)) = V_f1_2,
    file('theBenchmark.p',fact_lazy__sequence_Orecs_I1_J) ).

fof(fact_Least__Suc2,axiom,
    ! [V_m_2,V_Q_2,V_n_2,V_P_2] :
      ( hBOOL(hAPP(V_P_2,V_n_2))
     => ( hBOOL(hAPP(V_Q_2,V_m_2))
       => ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
         => ( ! [B_k] :
                ( hBOOL(hAPP(V_P_2,hAPP(c_Nat_OSuc,B_k)))
              <=> hBOOL(hAPP(V_Q_2,B_k)) )
           => c_Orderings_Oord__class_OLeast(tc_Nat_Onat,V_P_2) = hAPP(c_Nat_OSuc,c_Orderings_Oord__class_OLeast(tc_Nat_Onat,V_Q_2)) ) ) ) ),
    file('theBenchmark.p',fact_Least__Suc2) ).

fof(fact_lazy__sequence_Orecs_I2_J,axiom,
    ! [V_lazy__sequence_2,V_a_2,V_f2_2,V_f1_2,T_c,T_b] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(T_b,T_c,V_f1_2,V_f2_2,c_Lazy__Sequence_Olazy__sequence_OInsert(T_c,V_a_2,V_lazy__sequence_2)) = hAPP(hAPP(hAPP(V_f2_2,V_a_2),V_lazy__sequence_2),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(T_b,T_c,V_f1_2,V_f2_2,V_lazy__sequence_2)),
    file('theBenchmark.p',fact_lazy__sequence_Orecs_I2_J) ).

fof(fact_beyond__def,axiom,
    ! [V_l,V_k] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
       => c_Quickcheck_Obeyond(V_k,V_l) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
       => c_Quickcheck_Obeyond(V_k,V_l) = V_l ) ),
    file('theBenchmark.p',fact_beyond__def) ).

fof(fact_bij__image__Collect__eq,axiom,
    ! [V_P_2,V_f_2,T_c,T_b] :
      ( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
     => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(c_Set_OCollect(T_b),V_P_2)) = hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,T_c),V_P_2),c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2))) ),
    file('theBenchmark.p',fact_bij__image__Collect__eq) ).

fof(fact_bij__betw__id,axiom,
    ! [V_A_2,T_b] : c_Fun_Obij__betw(T_b,T_b,c_Fun_Oid(T_b),V_A_2,V_A_2),
    file('theBenchmark.p',fact_bij__betw__id) ).

fof(fact_bij__betw__inv__into,axiom,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
     => c_Fun_Obij__betw(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),V_B_2,V_A_2) ),
    file('theBenchmark.p',fact_bij__betw__inv__into) ).

fof(fact_inv__into__inv__into__eq,axiom,
    ! [V_a_2,V_A_H_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
       => hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_b,V_A_H_2,c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2)),V_a_2) = hAPP(V_f_2,V_a_2) ) ),
    file('theBenchmark.p',fact_inv__into__inv__into__eq) ).

fof(fact_bij__imp__bij__inv,axiom,
    ! [V_f_2,T_c,T_b] :
      ( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
     => c_Fun_Obij__betw(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
    file('theBenchmark.p',fact_bij__imp__bij__inv) ).

fof(fact_inv__inv__eq,axiom,
    ! [V_f_2,T_c,T_b] :
      ( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
     => c_Hilbert__Choice_Oinv__into(T_c,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)) = V_f_2 ),
    file('theBenchmark.p',fact_inv__inv__eq) ).

fof(fact_o__inv__distrib,axiom,
    ! [V_g_2,T_d,V_f_2,T_c,T_b] :
      ( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
     => ( c_Fun_Obij__betw(T_d,T_b,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
       => c_Hilbert__Choice_Oinv__into(T_d,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Fun_Ocomp(T_b,T_c,T_d,V_f_2),V_g_2)) = hAPP(c_Fun_Ocomp(T_b,T_d,T_c,c_Hilbert__Choice_Oinv__into(T_d,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)),V_g_2)),c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)) ) ),
    file('theBenchmark.p',fact_o__inv__distrib) ).

fof(fact_bij__image__INT,axiom,
    ! [V_B_2,V_A_2,T_d,V_f_2,T_c,T_b] :
      ( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
     => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_d),c_Set_Oimage(T_b,T_c,V_f_2)),V_B_2)) ),
    file('theBenchmark.p',fact_bij__image__INT) ).

fof(fact_bij__betw__comp__iff2,axiom,
    ! [V_A_2,V_f_2,T_d,V_A_H_H_2,V_A_H_2,V_f_H_2,T_c,T_b] :
      ( c_Fun_Obij__betw(T_b,T_c,V_f_H_2,V_A_H_2,V_A_H_H_2)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_d,T_b,V_f_2),V_A_2)),V_A_H_2))
       => ( c_Fun_Obij__betw(T_d,T_b,V_f_2,V_A_2,V_A_H_2)
        <=> c_Fun_Obij__betw(T_d,T_c,hAPP(c_Fun_Ocomp(T_b,T_c,T_d,V_f_H_2),V_f_2),V_A_2,V_A_H_H_2) ) ) ),
    file('theBenchmark.p',fact_bij__betw__comp__iff2) ).

fof(fact_bij__betw__comp__iff,axiom,
    ! [V_A_H_H_2,V_f_H_2,T_d,V_A_H_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2)
     => ( c_Fun_Obij__betw(T_c,T_d,V_f_H_2,V_A_H_2,V_A_H_H_2)
      <=> c_Fun_Obij__betw(T_b,T_d,hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_f_H_2),V_f_2),V_A_2,V_A_H_H_2) ) ),
    file('theBenchmark.p',fact_bij__betw__comp__iff) ).

fof(fact_bij__betw__trans,axiom,
    ! [V_C_2,V_g_2,T_d,V_B_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
     => ( c_Fun_Obij__betw(T_c,T_d,V_g_2,V_B_2,V_C_2)
       => c_Fun_Obij__betw(T_b,T_d,hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_g_2),V_f_2),V_A_2,V_C_2) ) ),
    file('theBenchmark.p',fact_bij__betw__trans) ).

fof(fact_bij__comp,axiom,
    ! [V_g_2,T_d,V_f_2,T_c,T_b] :
      ( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
     => ( c_Fun_Obij__betw(T_c,T_d,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)))
       => c_Fun_Obij__betw(T_b,T_d,hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_g_2),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) ) ),
    file('theBenchmark.p',fact_bij__comp) ).

fof(fact_finite__vimage__iff,axiom,
    ! [V_F_2,V_h_2,T_c,T_b] :
      ( c_Fun_Obij__betw(T_b,T_c,V_h_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_c,V_h_2),V_F_2)))
      <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2)) ) ),
    file('theBenchmark.p',fact_finite__vimage__iff) ).

fof(fact_bij__image__Compl__eq,axiom,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
     => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) ),
    file('theBenchmark.p',fact_bij__image__Compl__eq) ).

fof(fact_bij__def,axiom,
    ! [V_f_2,T_c,T_b] :
      ( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
    <=> ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))
        & c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ),
    file('theBenchmark.p',fact_bij__def) ).

fof(fact_bijI,axiom,
    ! [V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
     => ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))
       => c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) ) ),
    file('theBenchmark.p',fact_bijI) ).

fof(fact_bij__betw__combine,axiom,
    ! [V_D_2,V_C_2,V_B_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
     => ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_C_2,V_D_2)
       => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_D_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
         => c_Fun_Obij__betw(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_D_2)) ) ) ),
    file('theBenchmark.p',fact_bij__betw__combine) ).

fof(fact_bij__betw__Disj__Un,axiom,
    ! [V_f_2,V_B_H_2,V_A_H_2,T_c,V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
     => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_H_2),V_B_H_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
       => ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2)
         => ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_B_2,V_B_H_2)
           => c_Fun_Obij__betw(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_H_2),V_B_H_2)) ) ) ) ),
    file('theBenchmark.p',fact_bij__betw__Disj__Un) ).

fof(fact_bij__betw__subset,axiom,
    ! [V_B_H_2,V_B_2,V_A_H_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
       => ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2) = V_B_H_2
         => c_Fun_Obij__betw(T_b,T_c,V_f_2,V_B_2,V_B_H_2) ) ) ),
    file('theBenchmark.p',fact_bij__betw__subset) ).

fof(fact_bij__is__surj,axiom,
    ! [V_f_2,T_c,T_b] :
      ( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
     => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_bij__is__surj) ).

fof(fact_bij__betw__imp__surj,axiom,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
     => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_bij__betw__imp__surj) ).

fof(fact_inj__on__imp__bij__betw,axiom,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
     => c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) ),
    file('theBenchmark.p',fact_inj__on__imp__bij__betw) ).

fof(fact_bij__betw__def,axiom,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
    <=> ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) = V_B_2
        & c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ),
    file('theBenchmark.p',fact_bij__betw__def) ).

fof(fact_bij__betw__imp__inj__on,axiom,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
     => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ),
    file('theBenchmark.p',fact_bij__betw__imp__inj__on) ).

fof(fact_bij__is__inj,axiom,
    ! [V_f_2,T_c,T_b] :
      ( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
     => c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
    file('theBenchmark.p',fact_bij__is__inj) ).

fof(fact_bij__betw__same__card,axiom,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
     => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2) ),
    file('theBenchmark.p',fact_bij__betw__same__card) ).

fof(fact_beyond__zero,axiom,
    ! [V_k] : c_Quickcheck_Obeyond(V_k,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',fact_beyond__zero) ).

fof(fact_bij__betw__the__inv__into,axiom,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
     => c_Fun_Obij__betw(T_c,T_b,c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_B_2,V_A_2) ),
    file('theBenchmark.p',fact_bij__betw__the__inv__into) ).

fof(fact_bij__betw__empty1,axiom,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_A_2)
     => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_bij__betw__empty1) ).

fof(fact_bij__betw__empty2,axiom,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))
     => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_bij__betw__empty2) ).

fof(fact_bij__betw__finite,axiom,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ),
    file('theBenchmark.p',fact_bij__betw__finite) ).

fof(fact_BIJ,axiom,
    ! [V_B_2,T_c,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
       => ( ? [B_f] : c_Fun_Obij__betw(T_b,T_c,B_f,V_A_2,V_B_2)
        <=> hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2) ) ) ),
    file('theBenchmark.p',fact_BIJ) ).

fof(fact_bij__betw__id__iff,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( c_Fun_Obij__betw(T_b,T_b,c_Fun_Oid(T_b),V_A_2,V_B_2)
    <=> V_A_2 = V_B_2 ),
    file('theBenchmark.p',fact_bij__betw__id__iff) ).

fof(fact_bij__id,axiom,
    ! [T_b] : c_Fun_Obij__betw(T_b,T_b,c_Fun_Oid(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),
    file('theBenchmark.p',fact_bij__id) ).

fof(fact_vimage__subset__eq,axiom,
    ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
      ( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)),V_A_2))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) ) ),
    file('theBenchmark.p',fact_vimage__subset__eq) ).

fof(fact_bij__vimage__eq__inv__image,axiom,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
     => hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2) = hAPP(c_Set_Oimage(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)),V_A_2) ),
    file('theBenchmark.p',fact_bij__vimage__eq__inv__image) ).

fof(fact_ex__bij__betw__nat__finite__1,axiom,
    ! [V_M_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_M_2))
     => ? [B_h] : c_Fun_Obij__betw(tc_Nat_Onat,T_b,B_h,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_M_2)),V_M_2) ),
    file('theBenchmark.p',fact_ex__bij__betw__nat__finite__1) ).

fof(fact_Cantor__Bernstein,axiom,
    ! [V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),V_B_2))
       => ( c_Fun_Oinj__on(T_c,T_b,V_g_2,V_B_2)
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_g_2),V_B_2)),V_A_2))
           => ? [B_h] : c_Fun_Obij__betw(T_b,T_c,B_h,V_A_2,V_B_2) ) ) ) ),
    file('theBenchmark.p',fact_Cantor__Bernstein) ).

fof(fact_ex__bij__betw__nat__finite,axiom,
    ! [V_M_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_M_2))
     => ? [B_h] : c_Fun_Obij__betw(tc_Nat_Onat,T_b,B_h,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),V_M_2)),V_M_2) ),
    file('theBenchmark.p',fact_ex__bij__betw__nat__finite) ).

fof(fact_ex__bij__betw__finite__nat,axiom,
    ! [V_M_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_M_2))
     => ? [B_h] : c_Fun_Obij__betw(T_b,tc_Nat_Onat,B_h,V_M_2,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),V_M_2))) ),
    file('theBenchmark.p',fact_ex__bij__betw__finite__nat) ).

fof(fact_curry__def,axiom,
    ! [V_y_2,V_x_2,V_c_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Ocurry(T_c,T_d,T_b,V_c_2),V_x_2),V_y_2) = hAPP(V_c_2,hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2)),
    file('theBenchmark.p',fact_curry__def) ).

fof(fact_refl__on__UNION,axiom,
    ! [V_r_2,V_A_2,T_c,V_S_2,T_b] :
      ( ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
         => c_Relation_Orefl__on(T_c,hAPP(V_A_2,B_x),hAPP(V_r_2,B_x)) )
     => c_Relation_Orefl__on(T_c,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_S_2),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_S_2),V_r_2)) ),
    file('theBenchmark.p',fact_refl__on__UNION) ).

fof(fact_curryI,axiom,
    ! [V_b_2,V_a_2,T_c,T_b,V_f_2] :
      ( hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)))
     => hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2)) ),
    file('theBenchmark.p',fact_curryI) ).

fof(fact_split__curry,axiom,
    ! [V_f_2,T_d,T_c,T_b] : hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),c_Product__Type_Ocurry(T_b,T_c,T_d,V_f_2)) = V_f_2,
    file('theBenchmark.p',fact_split__curry) ).

fof(fact_curry__split,axiom,
    ! [V_f_2,T_d,T_c,T_b] : c_Product__Type_Ocurry(T_b,T_c,T_d,hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_f_2)) = V_f_2,
    file('theBenchmark.p',fact_curry__split) ).

fof(fact_curry__conv,axiom,
    ! [V_b_2,V_a_2,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Ocurry(T_c,T_d,T_b,V_f_2),V_a_2),V_b_2) = hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)),
    file('theBenchmark.p',fact_curry__conv) ).

fof(fact_curryD,axiom,
    ! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2))
     => hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ),
    file('theBenchmark.p',fact_curryD) ).

fof(fact_curryE,axiom,
    ! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2))
     => hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ),
    file('theBenchmark.p',fact_curryE) ).

fof(fact_bex__reg__eqv,axiom,
    ! [V_P_2,V_R_2,T_b] :
      ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
     => ( ? [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Quotient_ORespects(T_b,V_R_2))) )
      <=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ),
    file('theBenchmark.p',fact_bex__reg__eqv) ).

fof(fact_wf__weak__decr__stable,axiom,
    ! [V_r_2,V_f_2,T_b] :
      ( ! [B_i] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_i))),hAPP(V_f_2,B_i))),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
     => ( c_Wellfounded_Owf(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2))
       => ? [B_i] :
          ! [B_k] : hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_i),B_k)) = hAPP(V_f_2,B_i) ) ),
    file('theBenchmark.p',fact_wf__weak__decr__stable) ).

fof(fact_Respects__def,axiom,
    ! [V_x_2,V_R_2,T_b] :
      ( hBOOL(hAPP(c_Quotient_ORespects(T_b,V_R_2),V_x_2))
    <=> hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ),
    file('theBenchmark.p',fact_Respects__def) ).

fof(fact_in__respects,axiom,
    ! [V_R_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Quotient_ORespects(T_b,V_R_2)))
    <=> hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ),
    file('theBenchmark.p',fact_in__respects) ).

fof(fact_bex__reg__right,axiom,
    ! [V_P_2,V_Q_2,V_R_2,T_b] :
      ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
     => ( ! [B_x] :
            ( hBOOL(hAPP(V_Q_2,B_x))
           => hBOOL(hAPP(V_P_2,B_x)) )
       => ( ? [B_x1] : hBOOL(hAPP(V_Q_2,B_x1))
         => ? [B_x] :
              ( hBOOL(hAPP(V_P_2,B_x))
              & hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Quotient_ORespects(T_b,V_R_2))) ) ) ) ),
    file('theBenchmark.p',fact_bex__reg__right) ).

fof(fact_babs__reg__eqv,axiom,
    ! [V_P_2,T_c,V_R_2,T_b] :
      ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
     => c_Quotient_OBabs(T_b,T_c,c_Quotient_ORespects(T_b,V_R_2),V_P_2) = V_P_2 ),
    file('theBenchmark.p',fact_babs__reg__eqv) ).

fof(fact_Babs__def,axiom,
    ! [V_m_2,T_c,V_p_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_p_2))
     => hAPP(c_Quotient_OBabs(T_b,T_c,V_p_2,V_m_2),V_x_2) = hAPP(V_m_2,V_x_2) ),
    file('theBenchmark.p',fact_Babs__def) ).

fof(fact_INT__anti__mono,axiom,
    ! [V_g_2,V_f_2,T_c,V_A_2,V_B_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
     => ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_f_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_g_2))) ) ),
    file('theBenchmark.p',fact_INT__anti__mono) ).

fof(fact_INT__greatest,axiom,
    ! [V_B_2,V_C_2,T_c,V_A_2,T_b] :
      ( ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(V_B_2,B_x))) )
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ),
    file('theBenchmark.p',fact_INT__greatest) ).

fof(fact_converse__rtranclE2,axiom,
    ! [V_r_2,V_zb_2,V_za_2,V_xb_2,V_xa_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_xa_2),V_xb_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_za_2),V_zb_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_b,T_c),V_r_2)))
     => ( hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_xa_2),V_xb_2) != hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_za_2),V_zb_2)
       => ~ ! [B_a,B_b] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_xa_2),V_xb_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b))),V_r_2))
             => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_za_2),V_zb_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_b,T_c),V_r_2))) ) ) ),
    file('theBenchmark.p',fact_converse__rtranclE2) ).

fof(fact_converse__rtrancl__induct2,axiom,
    ! [V_P_2,V_r_2,V_by_2,V_bx_2,V_ay_2,V_ax_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_ax_2),V_ay_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_bx_2),V_by_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_b,T_c),V_r_2)))
     => ( hBOOL(hAPP(hAPP(V_P_2,V_bx_2),V_by_2))
       => ( ! [B_a,B_b,B_aa,B_ba] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_aa),B_ba))),V_r_2))
             => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_aa),B_ba)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_bx_2),V_by_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_b,T_c),V_r_2)))
               => ( hBOOL(hAPP(hAPP(V_P_2,B_aa),B_ba))
                 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) ) )
         => hBOOL(hAPP(hAPP(V_P_2,V_ax_2),V_ay_2)) ) ) ),
    file('theBenchmark.p',fact_converse__rtrancl__induct2) ).

fof(fact_rtrancl__induct2,axiom,
    ! [V_P_2,V_r_2,V_by_2,V_bx_2,V_ay_2,V_ax_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_ax_2),V_ay_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_bx_2),V_by_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_b,T_c),V_r_2)))
     => ( hBOOL(hAPP(hAPP(V_P_2,V_ax_2),V_ay_2))
       => ( ! [B_a,B_b] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_ax_2),V_ay_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b))),c_Transitive__Closure_Ortrancl(tc_prod(T_b,T_c),V_r_2)))
             => ! [B_aa,B_ba] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_aa),B_ba))),V_r_2))
                 => ( hBOOL(hAPP(hAPP(V_P_2,B_a),B_b))
                   => hBOOL(hAPP(hAPP(V_P_2,B_aa),B_ba)) ) ) )
         => hBOOL(hAPP(hAPP(V_P_2,V_bx_2),V_by_2)) ) ) ),
    file('theBenchmark.p',fact_rtrancl__induct2) ).

fof(fact_congruentI,axiom,
    ! [T_c,V_f_2,V_r_2,T_b] :
      ( ! [B_y,B_z] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_z)),V_r_2))
         => hAPP(V_f_2,B_y) = hAPP(V_f_2,B_z) )
     => c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2) ),
    file('theBenchmark.p',fact_congruentI) ).

fof(fact_congruent2I_H,axiom,
    ! [T_d,V_f_2,V_r2_2,T_c,V_r1_2,T_b] :
      ( ! [B_y1,B_z1] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y1),B_z1)),V_r1_2))
         => ! [B_y2,B_z2] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_y2),B_z2)),V_r2_2))
             => hAPP(hAPP(V_f_2,B_y1),B_y2) = hAPP(hAPP(V_f_2,B_z1),B_z2) ) )
     => c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2) ),
    file('theBenchmark.p',fact_congruent2I_H) ).

fof(fact__03,axiom,
    ! [V_xqq,V_xq,T_a] : c_Lazy__Sequence_Oflat(T_a,c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Lazy__Sequence_Olazy__sequence(T_a),V_xq,V_xqq)) = c_Lazy__Sequence_Oappend(T_a,V_xq,c_Lazy__Sequence_Oflat(T_a,V_xqq)),
    file('theBenchmark.p',fact__03) ).

fof(fact__04,axiom,
    ! [T_a] : c_Lazy__Sequence_Oflat(T_a,c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Lazy__Sequence_Olazy__sequence(T_a))) = c_Lazy__Sequence_Olazy__sequence_OEmpty(T_a),
    file('theBenchmark.p',fact__04) ).

fof(fact__05,axiom,
    ! [V_f_2,V_xq_2,T_b,T_c] : hAPP(c_Lazy__Sequence_Obind(T_c,T_b,V_xq_2),V_f_2) = c_Lazy__Sequence_Oflat(T_b,c_Lazy__Sequence_Omap(T_c,tc_Lazy__Sequence_Olazy__sequence(T_b),V_f_2,V_xq_2)),
    file('theBenchmark.p',fact__05) ).

fof(fact_list__all__iff__all__interval__nat,axiom,
    ! [V_j_2,V_i_2,V_P_2] :
      ( c_List_Olist__all(tc_Nat_Onat,V_P_2,c_List_Oupt(V_i_2,V_j_2))
    <=> c_List_Oall__interval__nat(V_P_2,V_i_2,V_j_2) ),
    file('theBenchmark.p',fact_list__all__iff__all__interval__nat) ).

fof(fact__06,axiom,
    ! [V_xq_2,V_x_2,V_f_2,T_b,T_c] : c_Lazy__Sequence_Omap(T_c,T_b,V_f_2,c_Lazy__Sequence_Olazy__sequence_OInsert(T_c,V_x_2,V_xq_2)) = c_Lazy__Sequence_Olazy__sequence_OInsert(T_b,hAPP(V_f_2,V_x_2),c_Lazy__Sequence_Omap(T_c,T_b,V_f_2,V_xq_2)),
    file('theBenchmark.p',fact__06) ).

fof(fact__07,axiom,
    ! [V_f_2,T_b,T_c] : c_Lazy__Sequence_Omap(T_c,T_b,V_f_2,c_Lazy__Sequence_Olazy__sequence_OEmpty(T_c)) = c_Lazy__Sequence_Olazy__sequence_OEmpty(T_b),
    file('theBenchmark.p',fact__07) ).

fof(fact_all__interval__nat__def,axiom,
    ! [V_j_2,V_i_2,V_P_2] :
      ( c_List_Oall__interval__nat(V_P_2,V_i_2,V_j_2)
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2)))
         => hBOOL(hAPP(V_P_2,B_x)) ) ),
    file('theBenchmark.p',fact_all__interval__nat__def) ).

fof(fact_list__ex__iff__not__all__inverval__nat,axiom,
    ! [V_j_2,V_i_2,V_P_2] :
      ( c_List_Olist__ex(tc_Nat_Onat,V_P_2,c_List_Oupt(V_i_2,V_j_2))
    <=> ~ c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat,c_fNot),V_P_2),V_i_2,V_j_2) ),
    file('theBenchmark.p',fact_list__ex__iff__not__all__inverval__nat) ).

fof(fact_New__DSequence_Opos__map__def,axiom,
    ! [V_i_2,V_xq_2,V_f_2,T_b,T_c] : c_New__DSequence_Opos__map(T_c,T_b,V_f_2,V_xq_2,V_i_2) = c_Lazy__Sequence_Omap(T_c,T_b,V_f_2,hAPP(V_xq_2,V_i_2)),
    file('theBenchmark.p',fact_New__DSequence_Opos__map__def) ).

fof(fact_folding__image_Ocong,axiom,
    ! [V_h_2,V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
       => ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
             => hAPP(V_g_2,B_x) = hAPP(V_h_2,B_x) )
         => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = hAPP(hAPP(V_F_2,V_h_2),V_A_2) ) ) ),
    file('theBenchmark.p',fact_folding__image_Ocong) ).

fof(fact_power__dvd__imp__le,axiom,
    ! [V_n,V_m,V_i] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_i))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ),
    file('theBenchmark.p',fact_power__dvd__imp__le) ).

fof(fact_finite__nonempty__imp__fold1Set,axiom,
    ! [V_f_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => ? [B_x1] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,V_A_2),B_x1)) ) ),
    file('theBenchmark.p',fact_finite__nonempty__imp__fold1Set) ).

fof(fact_dvd_Oorder__refl,axiom,
    ! [V_x] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_x)),
    file('theBenchmark.p',fact_dvd_Oorder__refl) ).

fof(fact_dvd__0__right,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) ),
    file('theBenchmark.p',fact_dvd__0__right) ).

fof(fact_dvd__1__left,axiom,
    ! [V_k] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k)),
    file('theBenchmark.p',fact_dvd__1__left) ).

fof(fact_dvd__imp__le,axiom,
    ! [V_n,V_k] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ),
    file('theBenchmark.p',fact_dvd__imp__le) ).

fof(fact_dvd__eq__mod__eq__0__number__of,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( ( class_Int_Onumber(T_b)
        & class_Divides_Osemiring__div(T_b) )
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
      <=> c_Divides_Odiv__class_Omod(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)) = c_Groups_Ozero__class_Ozero(T_b) ) ),
    file('theBenchmark.p',fact_dvd__eq__mod__eq__0__number__of) ).

fof(fact_le__imp__power__dvd,axiom,
    ! [V_a,V_n,V_m,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
       => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ),
    file('theBenchmark.p',fact_le__imp__power__dvd) ).

fof(fact_dvd__power__le,axiom,
    ! [V_m,V_n,V_y,V_x,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
         => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_m))) ) ) ),
    file('theBenchmark.p',fact_dvd__power__le) ).

fof(fact_power__le__dvd,axiom,
    ! [V_m,V_b,V_n,V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_b))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
         => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),V_b)) ) ) ),
    file('theBenchmark.p',fact_power__le__dvd) ).

fof(fact_dvd_OatLeastatMost__subset__iff,axiom,
    ! [V_d_2,V_c_2,V_b_2,V_a_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2,V_d_2)))
    <=> ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_d_2))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2),V_a_2)) )
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) ) ),
    file('theBenchmark.p',fact_dvd_OatLeastatMost__subset__iff) ).

fof(fact_dvd__diffD,axiom,
    ! [V_n,V_m,V_k] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)))
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
         => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m)) ) ) ),
    file('theBenchmark.p',fact_dvd__diffD) ).

fof(fact_dvd__diffD1,axiom,
    ! [V_n,V_m,V_k] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)))
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
         => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n)) ) ) ),
    file('theBenchmark.p',fact_dvd__diffD1) ).

fof(fact_dvd_OlessThan__iff,axiom,
    ! [V_k_2,V_i_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_i_2),c_SetInterval_Oord_OlessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2)))
    <=> ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2)) ) ),
    file('theBenchmark.p',fact_dvd_OlessThan__iff) ).

fof(fact_dvd_OgreaterThan__iff,axiom,
    ! [V_k_2,V_i_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_i_2),c_SetInterval_Oord_OgreaterThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2)))
    <=> ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2)) ) ),
    file('theBenchmark.p',fact_dvd_OgreaterThan__iff) ).

fof(fact_dvd_OatLeast__iff,axiom,
    ! [V_k_2,V_i_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_i_2),c_SetInterval_Oord_OatLeast(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2)))
    <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2)) ),
    file('theBenchmark.p',fact_dvd_OatLeast__iff) ).

fof(fact_dvd_OatMost__iff,axiom,
    ! [V_k_2,V_i_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_i_2),c_SetInterval_Oord_OatMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2)))
    <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2)) ),
    file('theBenchmark.p',fact_dvd_OatMost__iff) ).

fof(fact_dvd__1__iff__1,axiom,
    ! [V_m_2] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
    <=> V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    file('theBenchmark.p',fact_dvd__1__iff__1) ).

fof(fact_nat__dvd__not__less,axiom,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
       => ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_n),V_m)) ) ),
    file('theBenchmark.p',fact_nat__dvd__not__less) ).

fof(fact_dvd__div__neg,axiom,
    ! [V_x,V_y,T_a] :
      ( class_Divides_Oring__div(T_a)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),V_y)) ) ),
    file('theBenchmark.p',fact_dvd__div__neg) ).

fof(fact_dvd__neg__div,axiom,
    ! [V_x,V_y,T_a] :
      ( class_Divides_Oring__div(T_a)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),V_y) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),V_y)) ) ),
    file('theBenchmark.p',fact_dvd__neg__div) ).

fof(fact_dvd__minus__iff,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Rings_Ocomm__ring__1(T_b)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)))
      <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),V_y_2)) ) ),
    file('theBenchmark.p',fact_dvd__minus__iff) ).

fof(fact_minus__dvd__iff,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Rings_Ocomm__ring__1(T_b)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)),V_y_2))
      <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),V_y_2)) ) ),
    file('theBenchmark.p',fact_minus__dvd__iff) ).

fof(fact_dvd__diff__nat,axiom,
    ! [V_n,V_m,V_k] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m))
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n))
       => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n))) ) ),
    file('theBenchmark.p',fact_dvd__diff__nat) ).

fof(fact_dvd__diff,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Rings_Ocomm__ring__1(T_a)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y))
       => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_z))
         => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_y),V_z))) ) ) ),
    file('theBenchmark.p',fact_dvd__diff) ).

fof(fact_div__power,axiom,
    ! [V_n,V_x,V_y,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
       => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),V_y)),V_n) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_n)) ) ),
    file('theBenchmark.p',fact_div__power) ).

fof(fact_dvd__imp__mod__0,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
       => c_Divides_Odiv__class_Omod(T_a,V_b,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ),
    file('theBenchmark.p',fact_dvd__imp__mod__0) ).

fof(fact_dvd__eq__mod__eq__0,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( class_Divides_Osemiring__div(T_b)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
      <=> c_Divides_Odiv__class_Omod(T_b,V_b_2,V_a_2) = c_Groups_Ozero__class_Ozero(T_b) ) ),
    file('theBenchmark.p',fact_dvd__eq__mod__eq__0) ).

fof(fact_dvd__mod__iff,axiom,
    ! [V_m_2,V_n_2,V_k_2,T_b] :
      ( class_Divides_Osemiring__div(T_b)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),V_n_2))
       => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),c_Divides_Odiv__class_Omod(T_b,V_m_2,V_n_2)))
        <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),V_m_2)) ) ) ),
    file('theBenchmark.p',fact_dvd__mod__iff) ).

fof(fact_mod__mod__cancel,axiom,
    ! [V_a,V_b,V_c,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_b))
       => c_Divides_Odiv__class_Omod(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,V_a,V_c) ) ),
    file('theBenchmark.p',fact_mod__mod__cancel) ).

fof(fact_dvd__mod,axiom,
    ! [V_n,V_m,V_k,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_m))
       => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_n))
         => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),c_Divides_Odiv__class_Omod(T_a,V_m,V_n))) ) ) ),
    file('theBenchmark.p',fact_dvd__mod) ).

fof(fact_dvd__mod__imp__dvd,axiom,
    ! [V_n,V_m,V_k,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),c_Divides_Odiv__class_Omod(T_a,V_m,V_n)))
       => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_n))
         => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_m)) ) ) ),
    file('theBenchmark.p',fact_dvd__mod__imp__dvd) ).

fof(fact_dvd__0__left,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
       => V_a = c_Groups_Ozero__class_Ozero(T_a) ) ),
    file('theBenchmark.p',fact_dvd__0__left) ).

fof(fact_div__dvd__div,axiom,
    ! [V_c_2,V_b_2,V_a_2,T_b] :
      ( class_Divides_Osemiring__div(T_b)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
       => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_c_2))
         => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_b_2),V_a_2)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_c_2),V_a_2)))
          <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_b_2),V_c_2)) ) ) ) ),
    file('theBenchmark.p',fact_div__dvd__div) ).

fof(fact_dvd__power__same,axiom,
    ! [V_n,V_y,V_x,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y))
       => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_n))) ) ),
    file('theBenchmark.p',fact_dvd__power__same) ).

fof(fact_dvd__trans,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
       => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_c))
         => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c)) ) ) ),
    file('theBenchmark.p',fact_dvd__trans) ).

fof(fact_dvd__refl,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_a)) ),
    file('theBenchmark.p',fact_dvd__refl) ).

fof(fact_dvd_Oless__asym,axiom,
    ! [V_y,V_x] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) )
     => ~ ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) ) ),
    file('theBenchmark.p',fact_dvd_Oless__asym) ).

fof(fact_dvd_Oless__trans,axiom,
    ! [V_z,V_y,V_x] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) )
     => ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_y))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z)) )
       => ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z)) ) ) ),
    file('theBenchmark.p',fact_dvd_Oless__trans) ).

fof(fact_dvd_Oless__asym_H,axiom,
    ! [V_b,V_a] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) )
     => ~ ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)) ) ),
    file('theBenchmark.p',fact_dvd_Oless__asym_H) ).

fof(fact_dvd_Oless__le__trans,axiom,
    ! [V_z,V_y,V_x] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) )
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))
       => ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z)) ) ) ),
    file('theBenchmark.p',fact_dvd_Oless__le__trans) ).

fof(fact_dvd_Oord__less__eq__trans,axiom,
    ! [V_c,V_b,V_a] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) )
     => ( V_b = V_c
       => ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_a))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)) ) ) ),
    file('theBenchmark.p',fact_dvd_Oord__less__eq__trans) ).

fof(fact_dvd_Oless__imp__not__eq2,axiom,
    ! [V_y,V_x] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) )
     => V_y != V_x ),
    file('theBenchmark.p',fact_dvd_Oless__imp__not__eq2) ).

fof(fact_dvd_Oless__imp__not__eq,axiom,
    ! [V_y,V_x] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) )
     => V_x != V_y ),
    file('theBenchmark.p',fact_dvd_Oless__imp__not__eq) ).

fof(fact_dvd_Oless__imp__not__less,axiom,
    ! [V_y,V_x] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) )
     => ~ ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) ) ),
    file('theBenchmark.p',fact_dvd_Oless__imp__not__less) ).

fof(fact_dvd_Oless__imp__le,axiom,
    ! [V_y,V_x] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) )
     => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ),
    file('theBenchmark.p',fact_dvd_Oless__imp__le) ).

fof(fact_dvd_Oless__not__sym,axiom,
    ! [V_y,V_x] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) )
     => ~ ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) ) ),
    file('theBenchmark.p',fact_dvd_Oless__not__sym) ).

fof(fact_dvd_Oless__imp__neq,axiom,
    ! [V_y,V_x] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) )
     => V_x != V_y ),
    file('theBenchmark.p',fact_dvd_Oless__imp__neq) ).

fof(fact_dvd_Ole__less__trans,axiom,
    ! [V_z,V_y,V_x] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
     => ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_y))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z)) )
       => ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z)) ) ) ),
    file('theBenchmark.p',fact_dvd_Ole__less__trans) ).

fof(fact_dvd_Oord__eq__less__trans,axiom,
    ! [V_c,V_b,V_a] :
      ( V_a = V_b
     => ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_b))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_c)) )
       => ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_a))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)) ) ) ),
    file('theBenchmark.p',fact_dvd_Oord__eq__less__trans) ).

fof(fact_dvd_Oorder__trans,axiom,
    ! [V_z,V_y,V_x] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))
       => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z)) ) ),
    file('theBenchmark.p',fact_dvd_Oorder__trans) ).

fof(fact_dvd_Oantisym,axiom,
    ! [V_y,V_x] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
       => V_x = V_y ) ),
    file('theBenchmark.p',fact_dvd_Oantisym) ).

fof(fact_dvd__antisym,axiom,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m),V_n))
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_n),V_m))
       => V_m = V_n ) ),
    file('theBenchmark.p',fact_dvd__antisym) ).

fof(fact_dvd_Oord__le__eq__trans,axiom,
    ! [V_c,V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
     => ( V_b = V_c
       => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)) ) ),
    file('theBenchmark.p',fact_dvd_Oord__le__eq__trans) ).

fof(fact_dvd_Oord__eq__le__trans,axiom,
    ! [V_c,V_b,V_a] :
      ( V_a = V_b
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_c))
       => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)) ) ),
    file('theBenchmark.p',fact_dvd_Oord__eq__le__trans) ).

fof(fact_dvd_Ole__neq__trans,axiom,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
     => ( V_a != V_b
       => ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) ) ) ),
    file('theBenchmark.p',fact_dvd_Ole__neq__trans) ).

fof(fact_dvd_Ole__imp__less__or__eq,axiom,
    ! [V_y,V_x] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
     => ( V_x = V_y
        | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ) ),
    file('theBenchmark.p',fact_dvd_Ole__imp__less__or__eq) ).

fof(arity_HOL__Obool__Lattices_Obounded__lattice,axiom,
    class_Lattices_Obounded__lattice(tc_HOL_Obool),
    file('theBenchmark.p',arity_HOL__Obool__Lattices_Obounded__lattice) ).

fof(arity_fun__Lattices_Obounded__lattice,axiom,
    ! [T_2,T_1] :
      ( class_Lattices_Obounded__lattice(T_1)
     => class_Lattices_Obounded__lattice(tc_fun(T_2,T_1)) ),
    file('theBenchmark.p',arity_fun__Lattices_Obounded__lattice) ).

fof(arity_fun__Complete__Lattice_Ocomplete__lattice,axiom,
    ! [T_2,T_1] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_1)
     => class_Complete__Lattice_Ocomplete__lattice(tc_fun(T_2,T_1)) ),
    file('theBenchmark.p',arity_fun__Complete__Lattice_Ocomplete__lattice) ).

fof(arity_fun__Lattices_Obounded__lattice__top,axiom,
    ! [T_2,T_1] :
      ( class_Lattices_Obounded__lattice(T_1)
     => class_Lattices_Obounded__lattice__top(tc_fun(T_2,T_1)) ),
    file('theBenchmark.p',arity_fun__Lattices_Obounded__lattice__top) ).

fof(arity_fun__Lattices_Obounded__lattice__bot,axiom,
    ! [T_2,T_1] :
      ( class_Lattices_Obounded__lattice(T_1)
     => class_Lattices_Obounded__lattice__bot(tc_fun(T_2,T_1)) ),
    file('theBenchmark.p',arity_fun__Lattices_Obounded__lattice__bot) ).

fof(arity_fun__Lattices_Osemilattice__sup,axiom,
    ! [T_2,T_1] :
      ( class_Lattices_Olattice(T_1)
     => class_Lattices_Osemilattice__sup(tc_fun(T_2,T_1)) ),
    file('theBenchmark.p',arity_fun__Lattices_Osemilattice__sup) ).

fof(arity_fun__Lattices_Osemilattice__inf,axiom,
    ! [T_2,T_1] :
      ( class_Lattices_Olattice(T_1)
     => class_Lattices_Osemilattice__inf(tc_fun(T_2,T_1)) ),
    file('theBenchmark.p',arity_fun__Lattices_Osemilattice__inf) ).

fof(arity_fun__Lattices_Odistrib__lattice,axiom,
    ! [T_2,T_1] :
      ( class_Lattices_Odistrib__lattice(T_1)
     => class_Lattices_Odistrib__lattice(tc_fun(T_2,T_1)) ),
    file('theBenchmark.p',arity_fun__Lattices_Odistrib__lattice) ).

fof(arity_fun__Lattices_Oboolean__algebra,axiom,
    ! [T_2,T_1] :
      ( class_Lattices_Oboolean__algebra(T_1)
     => class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)) ),
    file('theBenchmark.p',arity_fun__Lattices_Oboolean__algebra) ).

fof(arity_fun__Orderings_Opreorder,axiom,
    ! [T_2,T_1] :
      ( class_Orderings_Opreorder(T_1)
     => class_Orderings_Opreorder(tc_fun(T_2,T_1)) ),
    file('theBenchmark.p',arity_fun__Orderings_Opreorder) ).

fof(arity_fun__Finite__Set_Ofinite,axiom,
    ! [T_1,T_2] :
      ( ( class_Finite__Set_Ofinite(T_1)
        & class_Finite__Set_Ofinite(T_2) )
     => class_Finite__Set_Ofinite(tc_fun(T_2,T_1)) ),
    file('theBenchmark.p',arity_fun__Finite__Set_Ofinite) ).

fof(arity_fun__Lattices_Olattice,axiom,
    ! [T_2,T_1] :
      ( class_Lattices_Olattice(T_1)
     => class_Lattices_Olattice(tc_fun(T_2,T_1)) ),
    file('theBenchmark.p',arity_fun__Lattices_Olattice) ).

fof(arity_fun__Orderings_Oorder,axiom,
    ! [T_2,T_1] :
      ( class_Orderings_Oorder(T_1)
     => class_Orderings_Oorder(tc_fun(T_2,T_1)) ),
    file('theBenchmark.p',arity_fun__Orderings_Oorder) ).

fof(arity_fun__Orderings_Otop,axiom,
    ! [T_2,T_1] :
      ( class_Orderings_Otop(T_1)
     => class_Orderings_Otop(tc_fun(T_2,T_1)) ),
    file('theBenchmark.p',arity_fun__Orderings_Otop) ).

fof(arity_fun__Orderings_Oord,axiom,
    ! [T_2,T_1] :
      ( class_Orderings_Oord(T_1)
     => class_Orderings_Oord(tc_fun(T_2,T_1)) ),
    file('theBenchmark.p',arity_fun__Orderings_Oord) ).

fof(arity_fun__Orderings_Obot,axiom,
    ! [T_2,T_1] :
      ( class_Orderings_Obot(T_1)
     => class_Orderings_Obot(tc_fun(T_2,T_1)) ),
    file('theBenchmark.p',arity_fun__Orderings_Obot) ).

fof(arity_fun__Groups_Ouminus,axiom,
    ! [T_2,T_1] :
      ( class_Groups_Ouminus(T_1)
     => class_Groups_Ouminus(tc_fun(T_2,T_1)) ),
    file('theBenchmark.p',arity_fun__Groups_Ouminus) ).

fof(arity_fun__Groups_Ominus,axiom,
    ! [T_2,T_1] :
      ( class_Groups_Ominus(T_1)
     => class_Groups_Ominus(tc_fun(T_2,T_1)) ),
    file('theBenchmark.p',arity_fun__Groups_Ominus) ).

fof(arity_fun__Enum_Oenum,axiom,
    ! [T_1,T_2] :
      ( ( class_Enum_Oenum(T_1)
        & class_Enum_Oenum(T_2) )
     => class_Enum_Oenum(tc_fun(T_2,T_1)) ),
    file('theBenchmark.p',arity_fun__Enum_Oenum) ).

fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).

fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add) ).

fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le) ).

fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom,
    class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Olinordered__comm__semiring__strict) ).

fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom,
    class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1__strict) ).

fof(arity_Int__Oint__Groups_Olinordered__ab__semigroup__add,axiom,
    class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Groups_Olinordered__ab__semigroup__add) ).

fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom,
    class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__strict) ).

fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom,
    class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add) ).

fof(arity_Int__Oint__Groups_Oordered__ab__group__add__abs,axiom,
    class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__group__add__abs) ).

fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom,
    class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Groups_Oordered__comm__monoid__add) ).

fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom,
    class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Groups_Olinordered__ab__group__add) ).

fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom,
    class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Groups_Ocancel__ab__semigroup__add) ).

fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom,
    class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Oring__1__no__zero__divisors) ).

fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom,
    class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Oordered__cancel__semiring) ).

fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom,
    class_Rings_Olinordered__ring__strict(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring__strict) ).

fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom,
    class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Oring__no__zero__divisors) ).

fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom,
    class_Rings_Oordered__comm__semiring(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Oordered__comm__semiring) ).

fof(arity_Int__Oint__Rings_Olinordered__semiring__1,axiom,
    class_Rings_Olinordered__semiring__1(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1) ).

fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom,
    class_Groups_Oordered__ab__group__add(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__group__add) ).

fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom,
    class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Groups_Ocancel__semigroup__add) ).

fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom,
    class_Rings_Olinordered__semiring(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring) ).

fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom,
    class_Rings_Olinordered__semidom(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semidom) ).

fof(arity_Int__Oint__Lazy__Sequence_Osmall__lazy,axiom,
    class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Lazy__Sequence_Osmall__lazy) ).

fof(arity_Int__Oint__Lattices_Osemilattice__sup,axiom,
    class_Lattices_Osemilattice__sup(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Lattices_Osemilattice__sup) ).

fof(arity_Int__Oint__Lattices_Osemilattice__inf,axiom,
    class_Lattices_Osemilattice__inf(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Lattices_Osemilattice__inf) ).

fof(arity_Int__Oint__Lattices_Odistrib__lattice,axiom,
    class_Lattices_Odistrib__lattice(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Lattices_Odistrib__lattice) ).

fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom,
    class_Groups_Oab__semigroup__mult(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__mult) ).

fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom,
    class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__mult) ).

fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom,
    class_Groups_Oab__semigroup__add(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__add) ).

fof(arity_Int__Oint__Rings_Oordered__semiring,axiom,
    class_Rings_Oordered__semiring(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Oordered__semiring) ).

fof(arity_Int__Oint__Rings_Oordered__ring__abs,axiom,
    class_Rings_Oordered__ring__abs(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Oordered__ring__abs) ).

fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom,
    class_Rings_Ono__zero__divisors(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Ono__zero__divisors) ).

fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom,
    class_Groups_Ocomm__monoid__add(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__add) ).

fof(arity_Int__Oint__Rings_Olinordered__ring,axiom,
    class_Rings_Olinordered__ring(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring) ).

fof(arity_Int__Oint__Rings_Olinordered__idom,axiom,
    class_Rings_Olinordered__idom(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Olinordered__idom) ).

fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom,
    class_Rings_Ocomm__semiring__1(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring__1) ).

fof(arity_Int__Oint__Groups_Osemigroup__add,axiom,
    class_Groups_Osemigroup__add(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Groups_Osemigroup__add) ).

fof(arity_Int__Oint__Divides_Osemiring__div,axiom,
    class_Divides_Osemiring__div(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Divides_Osemiring__div) ).

fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom,
    class_Rings_Ocomm__semiring(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring) ).

fof(arity_Int__Oint__Nat_Osemiring__char__0,axiom,
    class_Nat_Osemiring__char__0(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Nat_Osemiring__char__0) ).

fof(arity_Int__Oint__Groups_Oab__group__add,axiom,
    class_Groups_Oab__group__add(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Groups_Oab__group__add) ).

fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom,
    class_Rings_Ozero__neq__one(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Ozero__neq__one) ).

fof(arity_Int__Oint__Rings_Oordered__ring,axiom,
    class_Rings_Oordered__ring(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Oordered__ring) ).

fof(arity_Int__Oint__Orderings_Opreorder,axiom,
    class_Orderings_Opreorder(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Orderings_Opreorder) ).

fof(arity_Int__Oint__Orderings_Olinorder,axiom,
    class_Orderings_Olinorder(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Orderings_Olinorder) ).

fof(arity_Int__Oint__Groups_Omonoid__mult,axiom,
    class_Groups_Omonoid__mult(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Groups_Omonoid__mult) ).

fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom,
    class_Rings_Ocomm__ring__1(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring__1) ).

fof(arity_Int__Oint__Groups_Omonoid__add,axiom,
    class_Groups_Omonoid__add(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Groups_Omonoid__add) ).

fof(arity_Int__Oint__Rings_Osemiring__1,axiom,
    class_Rings_Osemiring__1(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Osemiring__1) ).

fof(arity_Int__Oint__Rings_Osemiring__0,axiom,
    class_Rings_Osemiring__0(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Osemiring__0) ).

fof(arity_Int__Oint__Lattices_Olattice,axiom,
    class_Lattices_Olattice(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Lattices_Olattice) ).

fof(arity_Int__Oint__Groups_Ogroup__add,axiom,
    class_Groups_Ogroup__add(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Groups_Ogroup__add) ).

fof(arity_Int__Oint__Divides_Oring__div,axiom,
    class_Divides_Oring__div(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Divides_Oring__div) ).

fof(arity_Int__Oint__Rings_Omult__zero,axiom,
    class_Rings_Omult__zero(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Omult__zero) ).

fof(arity_Int__Oint__Orderings_Oorder,axiom,
    class_Orderings_Oorder(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Orderings_Oorder) ).

fof(arity_Int__Oint__Int_Oring__char__0,axiom,
    class_Int_Oring__char__0(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Int_Oring__char__0) ).

fof(arity_Int__Oint__Int_Onumber__ring,axiom,
    class_Int_Onumber__ring(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Int_Onumber__ring) ).

fof(arity_Int__Oint__Rings_Osemiring,axiom,
    class_Rings_Osemiring(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Osemiring) ).

fof(arity_Int__Oint__Orderings_Oord,axiom,
    class_Orderings_Oord(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Orderings_Oord) ).

fof(arity_Int__Oint__Groups_Ouminus,axiom,
    class_Groups_Ouminus(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Groups_Ouminus) ).

fof(arity_Int__Oint__Groups_Osgn__if,axiom,
    class_Groups_Osgn__if(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Groups_Osgn__if) ).

fof(arity_Int__Oint__Groups_Oabs__if,axiom,
    class_Groups_Oabs__if(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Groups_Oabs__if) ).

fof(arity_Int__Oint__Rings_Oring__1,axiom,
    class_Rings_Oring__1(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Oring__1) ).

fof(arity_Int__Oint__Groups_Ominus,axiom,
    class_Groups_Ominus(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Groups_Ominus) ).

fof(arity_Int__Oint__Power_Opower,axiom,
    class_Power_Opower(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Power_Opower) ).

fof(arity_Int__Oint__Groups_Ozero,axiom,
    class_Groups_Ozero(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Groups_Ozero) ).

fof(arity_Int__Oint__Rings_Oring,axiom,
    class_Rings_Oring(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Oring) ).

fof(arity_Int__Oint__Rings_Oidom,axiom,
    class_Rings_Oidom(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Oidom) ).

fof(arity_Int__Oint__Int_Onumber,axiom,
    class_Int_Onumber(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Int_Onumber) ).

fof(arity_Int__Oint__Groups_Oone,axiom,
    class_Groups_Oone(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Groups_Oone) ).

fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).

fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add) ).

fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le) ).

fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom,
    class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict) ).

fof(arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add,axiom,
    class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add) ).

fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom,
    class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring__strict) ).

fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom,
    class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add) ).

fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom,
    class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Groups_Oordered__comm__monoid__add) ).

fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom,
    class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add) ).

fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom,
    class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Rings_Oordered__cancel__semiring) ).

fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom,
    class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Rings_Oordered__comm__semiring) ).

fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom,
    class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__semigroup__add) ).

fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom,
    class_Rings_Olinordered__semiring(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring) ).

fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom,
    class_Rings_Olinordered__semidom(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semidom) ).

fof(arity_Nat__Onat__Lattices_Osemilattice__sup,axiom,
    class_Lattices_Osemilattice__sup(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Lattices_Osemilattice__sup) ).

fof(arity_Nat__Onat__Lattices_Osemilattice__inf,axiom,
    class_Lattices_Osemilattice__inf(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Lattices_Osemilattice__inf) ).

fof(arity_Nat__Onat__Lattices_Odistrib__lattice,axiom,
    class_Lattices_Odistrib__lattice(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Lattices_Odistrib__lattice) ).

fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom,
    class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__mult) ).

fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom,
    class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__mult) ).

fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom,
    class_Groups_Oab__semigroup__add(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__add) ).

fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom,
    class_Rings_Oordered__semiring(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Rings_Oordered__semiring) ).

fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom,
    class_Rings_Ono__zero__divisors(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Rings_Ono__zero__divisors) ).

fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom,
    class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__add) ).

fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom,
    class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__1) ).

fof(arity_Nat__Onat__Groups_Osemigroup__add,axiom,
    class_Groups_Osemigroup__add(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Groups_Osemigroup__add) ).

fof(arity_Nat__Onat__Divides_Osemiring__div,axiom,
    class_Divides_Osemiring__div(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Divides_Osemiring__div) ).

fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom,
    class_Rings_Ocomm__semiring(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring) ).

fof(arity_Nat__Onat__Orderings_Owellorder,axiom,
    class_Orderings_Owellorder(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Orderings_Owellorder) ).

fof(arity_Nat__Onat__Nat_Osemiring__char__0,axiom,
    class_Nat_Osemiring__char__0(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Nat_Osemiring__char__0) ).

fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom,
    class_Rings_Ozero__neq__one(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Rings_Ozero__neq__one) ).

fof(arity_Nat__Onat__Orderings_Opreorder,axiom,
    class_Orderings_Opreorder(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Orderings_Opreorder) ).

fof(arity_Nat__Onat__Orderings_Olinorder,axiom,
    class_Orderings_Olinorder(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder) ).

fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom,
    class_Groups_Omonoid__mult(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__mult) ).

fof(arity_Nat__Onat__Groups_Omonoid__add,axiom,
    class_Groups_Omonoid__add(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__add) ).

fof(arity_Nat__Onat__Rings_Osemiring__1,axiom,
    class_Rings_Osemiring__1(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__1) ).

fof(arity_Nat__Onat__Rings_Osemiring__0,axiom,
    class_Rings_Osemiring__0(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__0) ).

fof(arity_Nat__Onat__Lattices_Olattice,axiom,
    class_Lattices_Olattice(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Lattices_Olattice) ).

fof(arity_Nat__Onat__Rings_Omult__zero,axiom,
    class_Rings_Omult__zero(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Rings_Omult__zero) ).

fof(arity_Nat__Onat__Orderings_Oorder,axiom,
    class_Orderings_Oorder(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Orderings_Oorder) ).

fof(arity_Nat__Onat__Rings_Osemiring,axiom,
    class_Rings_Osemiring(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Rings_Osemiring) ).

fof(arity_Nat__Onat__Orderings_Oord,axiom,
    class_Orderings_Oord(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Orderings_Oord) ).

fof(arity_Nat__Onat__Orderings_Obot,axiom,
    class_Orderings_Obot(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Orderings_Obot) ).

fof(arity_Nat__Onat__Groups_Ominus,axiom,
    class_Groups_Ominus(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Groups_Ominus) ).

fof(arity_Nat__Onat__Power_Opower,axiom,
    class_Power_Opower(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Power_Opower) ).

fof(arity_Nat__Onat__Groups_Ozero,axiom,
    class_Groups_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Groups_Ozero) ).

fof(arity_Nat__Onat__Int_Onumber,axiom,
    class_Int_Onumber(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Int_Onumber) ).

fof(arity_Nat__Onat__Groups_Oone,axiom,
    class_Groups_Oone(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Groups_Oone) ).

fof(arity_Nat__Onat__Nat_Osize,axiom,
    class_Nat_Osize(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Nat_Osize) ).

fof(arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice,axiom,
    class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool),
    file('theBenchmark.p',arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice) ).

fof(arity_HOL__Obool__Lattices_Obounded__lattice__top,axiom,
    class_Lattices_Obounded__lattice__top(tc_HOL_Obool),
    file('theBenchmark.p',arity_HOL__Obool__Lattices_Obounded__lattice__top) ).

fof(arity_HOL__Obool__Lattices_Obounded__lattice__bot,axiom,
    class_Lattices_Obounded__lattice__bot(tc_HOL_Obool),
    file('theBenchmark.p',arity_HOL__Obool__Lattices_Obounded__lattice__bot) ).

fof(arity_HOL__Obool__Lattices_Osemilattice__sup,axiom,
    class_Lattices_Osemilattice__sup(tc_HOL_Obool),
    file('theBenchmark.p',arity_HOL__Obool__Lattices_Osemilattice__sup) ).

fof(arity_HOL__Obool__Lattices_Osemilattice__inf,axiom,
    class_Lattices_Osemilattice__inf(tc_HOL_Obool),
    file('theBenchmark.p',arity_HOL__Obool__Lattices_Osemilattice__inf) ).

fof(arity_HOL__Obool__Lattices_Odistrib__lattice,axiom,
    class_Lattices_Odistrib__lattice(tc_HOL_Obool),
    file('theBenchmark.p',arity_HOL__Obool__Lattices_Odistrib__lattice) ).

fof(arity_HOL__Obool__Lattices_Oboolean__algebra,axiom,
    class_Lattices_Oboolean__algebra(tc_HOL_Obool),
    file('theBenchmark.p',arity_HOL__Obool__Lattices_Oboolean__algebra) ).

fof(arity_HOL__Obool__Orderings_Opreorder,axiom,
    class_Orderings_Opreorder(tc_HOL_Obool),
    file('theBenchmark.p',arity_HOL__Obool__Orderings_Opreorder) ).

fof(arity_HOL__Obool__Finite__Set_Ofinite,axiom,
    class_Finite__Set_Ofinite(tc_HOL_Obool),
    file('theBenchmark.p',arity_HOL__Obool__Finite__Set_Ofinite) ).

fof(arity_HOL__Obool__Lattices_Olattice,axiom,
    class_Lattices_Olattice(tc_HOL_Obool),
    file('theBenchmark.p',arity_HOL__Obool__Lattices_Olattice) ).

fof(arity_HOL__Obool__Orderings_Oorder,axiom,
    class_Orderings_Oorder(tc_HOL_Obool),
    file('theBenchmark.p',arity_HOL__Obool__Orderings_Oorder) ).

fof(arity_HOL__Obool__Orderings_Otop,axiom,
    class_Orderings_Otop(tc_HOL_Obool),
    file('theBenchmark.p',arity_HOL__Obool__Orderings_Otop) ).

fof(arity_HOL__Obool__Orderings_Oord,axiom,
    class_Orderings_Oord(tc_HOL_Obool),
    file('theBenchmark.p',arity_HOL__Obool__Orderings_Oord) ).

fof(arity_HOL__Obool__Orderings_Obot,axiom,
    class_Orderings_Obot(tc_HOL_Obool),
    file('theBenchmark.p',arity_HOL__Obool__Orderings_Obot) ).

fof(arity_HOL__Obool__Groups_Ouminus,axiom,
    class_Groups_Ouminus(tc_HOL_Obool),
    file('theBenchmark.p',arity_HOL__Obool__Groups_Ouminus) ).

fof(arity_HOL__Obool__Groups_Ominus,axiom,
    class_Groups_Ominus(tc_HOL_Obool),
    file('theBenchmark.p',arity_HOL__Obool__Groups_Ominus) ).

fof(arity_HOL__Obool__Enum_Oenum,axiom,
    class_Enum_Oenum(tc_HOL_Obool),
    file('theBenchmark.p',arity_HOL__Obool__Enum_Oenum) ).

fof(arity_HOL__Obool__Nat_Osize,axiom,
    class_Nat_Osize(tc_HOL_Obool),
    file('theBenchmark.p',arity_HOL__Obool__Nat_Osize) ).

fof(arity_List__Olist__Lazy__Sequence_Osmall__lazy,axiom,
    ! [T_1] :
      ( class_Lazy__Sequence_Osmall__lazy(T_1)
     => class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(T_1)) ),
    file('theBenchmark.p',arity_List__Olist__Lazy__Sequence_Osmall__lazy) ).

fof(arity_List__Olist__Nat_Osize,axiom,
    ! [T_1] : class_Nat_Osize(tc_List_Olist(T_1)),
    file('theBenchmark.p',arity_List__Olist__Nat_Osize) ).

fof(arity_sum__Finite__Set_Ofinite,axiom,
    ! [T_1,T_2] :
      ( ( class_Finite__Set_Ofinite(T_1)
        & class_Finite__Set_Ofinite(T_2) )
     => class_Finite__Set_Ofinite(tc_sum(T_2,T_1)) ),
    file('theBenchmark.p',arity_sum__Finite__Set_Ofinite) ).

fof(arity_sum__Enum_Oenum,axiom,
    ! [T_1,T_2] :
      ( ( class_Enum_Oenum(T_1)
        & class_Enum_Oenum(T_2) )
     => class_Enum_Oenum(tc_sum(T_2,T_1)) ),
    file('theBenchmark.p',arity_sum__Enum_Oenum) ).

fof(arity_sum__Nat_Osize,axiom,
    ! [T_1,T_2] : class_Nat_Osize(tc_sum(T_2,T_1)),
    file('theBenchmark.p',arity_sum__Nat_Osize) ).

fof(arity_Option__Ooption__Finite__Set_Ofinite,axiom,
    ! [T_1] :
      ( class_Finite__Set_Ofinite(T_1)
     => class_Finite__Set_Ofinite(tc_Option_Ooption(T_1)) ),
    file('theBenchmark.p',arity_Option__Ooption__Finite__Set_Ofinite) ).

fof(arity_Option__Ooption__Enum_Oenum,axiom,
    ! [T_1] :
      ( class_Enum_Oenum(T_1)
     => class_Enum_Oenum(tc_Option_Ooption(T_1)) ),
    file('theBenchmark.p',arity_Option__Ooption__Enum_Oenum) ).

fof(arity_Option__Ooption__Nat_Osize,axiom,
    ! [T_1] : class_Nat_Osize(tc_Option_Ooption(T_1)),
    file('theBenchmark.p',arity_Option__Ooption__Nat_Osize) ).

fof(arity_Nitpick__Opair____box__Nat_Osize,axiom,
    ! [T_1,T_2] : class_Nat_Osize(tc_Nitpick_Opair__box(T_2,T_1)),
    file('theBenchmark.p',arity_Nitpick__Opair____box__Nat_Osize) ).

fof(arity_prod__Lazy__Sequence_Osmall__lazy,axiom,
    ! [T_1,T_2] :
      ( ( class_Lazy__Sequence_Osmall__lazy(T_1)
        & class_Lazy__Sequence_Osmall__lazy(T_2) )
     => class_Lazy__Sequence_Osmall__lazy(tc_prod(T_2,T_1)) ),
    file('theBenchmark.p',arity_prod__Lazy__Sequence_Osmall__lazy) ).

fof(arity_prod__Finite__Set_Ofinite,axiom,
    ! [T_1,T_2] :
      ( ( class_Finite__Set_Ofinite(T_1)
        & class_Finite__Set_Ofinite(T_2) )
     => class_Finite__Set_Ofinite(tc_prod(T_2,T_1)) ),
    file('theBenchmark.p',arity_prod__Finite__Set_Ofinite) ).

fof(arity_prod__Enum_Oenum,axiom,
    ! [T_1,T_2] :
      ( ( class_Enum_Oenum(T_1)
        & class_Enum_Oenum(T_2) )
     => class_Enum_Oenum(tc_prod(T_2,T_1)) ),
    file('theBenchmark.p',arity_prod__Enum_Oenum) ).

fof(arity_prod__Nat_Osize,axiom,
    ! [T_1,T_2] : class_Nat_Osize(tc_prod(T_2,T_1)),
    file('theBenchmark.p',arity_prod__Nat_Osize) ).

fof(arity_Product____Type__Ounit__Lazy__Sequence_Osmall__lazy,axiom,
    class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit),
    file('theBenchmark.p',arity_Product____Type__Ounit__Lazy__Sequence_Osmall__lazy) ).

fof(arity_Product____Type__Ounit__Finite__Set_Ofinite,axiom,
    class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
    file('theBenchmark.p',arity_Product____Type__Ounit__Finite__Set_Ofinite) ).

fof(arity_Product____Type__Ounit__Enum_Oenum,axiom,
    class_Enum_Oenum(tc_Product__Type_Ounit),
    file('theBenchmark.p',arity_Product____Type__Ounit__Enum_Oenum) ).

fof(arity_Product____Type__Ounit__Nat_Osize,axiom,
    class_Nat_Osize(tc_Product__Type_Ounit),
    file('theBenchmark.p',arity_Product____Type__Ounit__Nat_Osize) ).

fof(arity_Code____Evaluation__Oterm__Nat_Osize,axiom,
    class_Nat_Osize(tc_Code__Evaluation_Oterm),
    file('theBenchmark.p',arity_Code____Evaluation__Oterm__Nat_Osize) ).

fof(arity_Hoare____Mirabelle__Otriple__Nat_Osize,axiom,
    ! [T_1] : class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(T_1)),
    file('theBenchmark.p',arity_Hoare____Mirabelle__Otriple__Nat_Osize) ).

fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add,axiom,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add) ).

fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le) ).

fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict,axiom,
    class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict) ).

fof(arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add,axiom,
    class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add) ).

fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict,axiom,
    class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict) ).

fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add,axiom,
    class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add) ).

fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add,axiom,
    class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add) ).

fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add,axiom,
    class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add) ).

fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring,axiom,
    class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring) ).

fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring,axiom,
    class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring) ).

fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add,axiom,
    class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add) ).

fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring,axiom,
    class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring) ).

fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom,axiom,
    class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom) ).

fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult,axiom,
    class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult) ).

fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult,axiom,
    class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult) ).

fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add,axiom,
    class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add) ).

fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring,axiom,
    class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring) ).

fof(arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors,axiom,
    class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors) ).

fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add,axiom,
    class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add) ).

fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1,axiom,
    class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1) ).

fof(arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add,axiom,
    class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add) ).

fof(arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div,axiom,
    class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div) ).

fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring,axiom,
    class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring) ).

fof(arity_Code____Numeral__Ocode____numeral__Nat_Osemiring__char__0,axiom,
    class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Nat_Osemiring__char__0) ).

fof(arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one,axiom,
    class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one) ).

fof(arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder,axiom,
    class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder) ).

fof(arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder,axiom,
    class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder) ).

fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult,axiom,
    class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult) ).

fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add,axiom,
    class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add) ).

fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1,axiom,
    class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1) ).

fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0,axiom,
    class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0) ).

fof(arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero,axiom,
    class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero) ).

fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oorder,axiom,
    class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Orderings_Oorder) ).

fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring,axiom,
    class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Osemiring) ).

fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oord,axiom,
    class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Orderings_Oord) ).

fof(arity_Code____Numeral__Ocode____numeral__Groups_Ominus,axiom,
    class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Ominus) ).

fof(arity_Code____Numeral__Ocode____numeral__Power_Opower,axiom,
    class_Power_Opower(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Power_Opower) ).

fof(arity_Code____Numeral__Ocode____numeral__Groups_Ozero,axiom,
    class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Ozero) ).

fof(arity_Code____Numeral__Ocode____numeral__Int_Onumber,axiom,
    class_Int_Onumber(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Int_Onumber) ).

fof(arity_Code____Numeral__Ocode____numeral__Groups_Oone,axiom,
    class_Groups_Oone(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oone) ).

fof(arity_Code____Numeral__Ocode____numeral__Nat_Osize,axiom,
    class_Nat_Osize(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Nat_Osize) ).

fof(arity_Lazy____Sequence__Olazy____sequence__Nat_Osize,axiom,
    ! [T_1] : class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(T_1)),
    file('theBenchmark.p',arity_Lazy____Sequence__Olazy____sequence__Nat_Osize) ).

fof(help_c__COMBI__1,axiom,
    ! [V_P,T_a] : hAPP(c_COMBI(T_a),V_P) = V_P,
    file('theBenchmark.p',help_c__COMBI__1) ).

fof(help_c__COMBK__1,axiom,
    ! [V_Q,V_P,T_b,T_a] : hAPP(hAPP(c_COMBK(T_a,T_b),V_P),V_Q) = V_P,
    file('theBenchmark.p',help_c__COMBK__1) ).

fof(help_c__COMBB__1,axiom,
    ! [V_R_2,V_Q_2,V_P_2,T_d,T_b,T_c] : hAPP(hAPP(hAPP(c_COMBB(T_c,T_b,T_d),V_P_2),V_Q_2),V_R_2) = hAPP(V_P_2,hAPP(V_Q_2,V_R_2)),
    file('theBenchmark.p',help_c__COMBB__1) ).

fof(help_c__COMBC__1,axiom,
    ! [V_R_2,V_Q_2,V_P_2,T_b,T_d,T_c] : hAPP(hAPP(hAPP(c_COMBC(T_c,T_d,T_b),V_P_2),V_Q_2),V_R_2) = hAPP(hAPP(V_P_2,V_R_2),V_Q_2),
    file('theBenchmark.p',help_c__COMBC__1) ).

fof(help_c__COMBS__1,axiom,
    ! [V_R_2,V_Q_2,V_P_2,T_b,T_d,T_c] : hAPP(hAPP(hAPP(c_COMBS(T_c,T_d,T_b),V_P_2),V_Q_2),V_R_2) = hAPP(hAPP(V_P_2,V_R_2),hAPP(V_Q_2,V_R_2)),
    file('theBenchmark.p',help_c__COMBS__1) ).

fof(help_c__fequal__1,axiom,
    ! [V_y_2,V_x_2] :
      ( V_x_2 = V_y_2
      | ~ hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) ),
    file('theBenchmark.p',help_c__fequal__1) ).

fof(help_c__fequal__2,axiom,
    ! [V_y_2,V_x_2] :
      ( hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2))
      | V_x_2 != V_y_2 ),
    file('theBenchmark.p',help_c__fequal__2) ).

fof(help_c__fFalse__1,axiom,
    ~ hBOOL(c_fFalse),
    file('theBenchmark.p',help_c__fFalse__1) ).

fof(help_c__fTrue__1,axiom,
    hBOOL(c_fTrue),
    file('theBenchmark.p',help_c__fTrue__1) ).

fof(help_c__fNot__1,axiom,
    ! [V_P_2] :
      ( ~ hBOOL(V_P_2)
      | ~ hBOOL(hAPP(c_fNot,V_P_2)) ),
    file('theBenchmark.p',help_c__fNot__1) ).

fof(help_c__fNot__2,axiom,
    ! [V_P_2] :
      ( hBOOL(hAPP(c_fNot,V_P_2))
      | ~ ~ hBOOL(V_P_2) ),
    file('theBenchmark.p',help_c__fNot__2) ).

fof(help_c__fconj__1,axiom,
    ! [V_Q_2,V_P_2] :
      ( hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2))
      | ~ hBOOL(V_Q_2)
      | ~ hBOOL(V_P_2) ),
    file('theBenchmark.p',help_c__fconj__1) ).

fof(help_c__fconj__2,axiom,
    ! [V_Q_2,V_P_2] :
      ( hBOOL(V_P_2)
      | ~ hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2)) ),
    file('theBenchmark.p',help_c__fconj__2) ).

fof(help_c__fconj__3,axiom,
    ! [V_Q_2,V_P_2] :
      ( hBOOL(V_Q_2)
      | ~ hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2)) ),
    file('theBenchmark.p',help_c__fconj__3) ).

fof(help_c__fdisj__1,axiom,
    ! [V_Q_2,V_P_2] :
      ( hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2))
      | ~ hBOOL(V_P_2) ),
    file('theBenchmark.p',help_c__fdisj__1) ).

fof(help_c__fdisj__2,axiom,
    ! [V_P_2,V_Q_2] :
      ( hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2))
      | ~ hBOOL(V_Q_2) ),
    file('theBenchmark.p',help_c__fdisj__2) ).

fof(help_c__fdisj__3,axiom,
    ! [V_Q_2,V_P_2] :
      ( hBOOL(V_Q_2)
      | hBOOL(V_P_2)
      | ~ hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2)) ),
    file('theBenchmark.p',help_c__fdisj__3) ).

fof(help_c__fimplies__1,axiom,
    ! [V_Q_2,V_P_2] :
      ( hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2))
      | hBOOL(V_P_2) ),
    file('theBenchmark.p',help_c__fimplies__1) ).

fof(help_c__fimplies__2,axiom,
    ! [V_P_2,V_Q_2] :
      ( hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2))
      | ~ hBOOL(V_Q_2) ),
    file('theBenchmark.p',help_c__fimplies__2) ).

fof(help_c__fimplies__3,axiom,
    ! [V_Q_2,V_P_2] :
      ( hBOOL(V_Q_2)
      | ~ hBOOL(V_P_2)
      | ~ hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2)) ),
    file('theBenchmark.p',help_c__fimplies__3) ).

fof(conj_0,hypothesis,
    c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G_H,v_ts),
    file('theBenchmark.p',conj_0) ).

fof(conj_1,conjecture,
    ! [B_G] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_G_H),B_G))
     => c_Hoare__Mirabelle_Ohoare__derivs(t_a,B_G,v_ts) ),
    file('theBenchmark.p',conj_1) ).

fof(f_1_1,plain,
    ! [V_g_2,V_f_2] :
      ( V_f_2 = V_g_2
      | ? [B_x] : hAPP(V_f_2,B_x) != hAPP(V_g_2,B_x) ),
    inference(fof_nnf,[status(thm)],[fact_ext]) ).

fof(f_1_2,plain,
    ! [U_2,U_1] :
      ( U_1 = U_2
      | ? [U_0] : hAPP(U_1,U_0) != hAPP(U_2,U_0) ),
    inference(variable_rename,[status(thm)],[f_1_1]) ).

fof(f_1_3,plain,
    ! [U_2,U_1] :
      ( U_1 = U_2
      | hAPP(U_1,sK1(U_2,U_1)) != hAPP(U_2,sK1(U_2,U_1)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_0,sK1(U_2,U_1))],[f_1_2]) ).

cnf(f_1_4,plain,
    ( U_1 = U_2
    | hAPP(U_1,sK1(U_2,U_1)) != hAPP(U_2,sK1(U_2,U_1)) ),
    inference(clausify,[status(thm)],[f_1_3]) ).

fof(f_2_1,plain,
    ! [V_G_2,V_tsa_2,T_b] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_tsa_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_tsa_2),V_G_2)) ),
    inference(fof_nnf,[status(thm)],[fact_asm]) ).

fof(f_2_2,plain,
    ! [U_5,U_4,U_3] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_3,U_5,U_4)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(U_3),tc_HOL_Obool)),U_4),U_5)) ),
    inference(variable_rename,[status(thm)],[f_2_1]) ).

cnf(f_2_3,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_3,U_5,U_4)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(U_3),tc_HOL_Obool)),U_4),U_5)) ),
    inference(clausify,[status(thm)],[f_2_2]) ).

fof(f_3_1,plain,
    ! [V_tsa_2,V_ts_H_2,V_G_2,T_b] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_tsa_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_tsa_2),V_ts_H_2))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_ts_H_2) ),
    inference(fof_nnf,[status(thm)],[fact_weaken]) ).

fof(f_3_2,plain,
    ! [U_9,U_8,U_7,U_6] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_6,U_7,U_9)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(U_6),tc_HOL_Obool)),U_9),U_8))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_6,U_7,U_8) ),
    inference(variable_rename,[status(thm)],[f_3_1]) ).

cnf(f_3_3,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_6,U_7,U_9)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(U_6),tc_HOL_Obool)),U_9),U_8))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_6,U_7,U_8) ),
    inference(clausify,[status(thm)],[f_3_2]) ).

fof(f_4_1,plain,
    ! [V_G_2,V_tsa_2,V_G_Ha_2,T_b] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_tsa_2)
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_G_Ha_2)
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_Ha_2,V_tsa_2) ),
    inference(fof_nnf,[status(thm)],[fact_cut]) ).

fof(f_4_2,plain,
    ! [U_13,U_12,U_11,U_10] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_10,U_13,U_12)
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_10,U_13,U_11)
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_10,U_11,U_12) ),
    inference(variable_rename,[status(thm)],[f_4_1]) ).

cnf(f_4_3,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_10,U_13,U_12)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_10,U_13,U_11)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_10,U_11,U_12) ),
    inference(clausify,[status(thm)],[f_4_2]) ).

fof(f_5_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( V_A_2 = V_B_2
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_equalityI]) ).

fof(f_5_2,plain,
    ! [U_16,U_15,U_14] :
      ( U_15 = U_16
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14,tc_HOL_Obool)),U_16),U_15))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14,tc_HOL_Obool)),U_15),U_16)) ),
    inference(variable_rename,[status(thm)],[f_5_1]) ).

cnf(f_5_3,plain,
    ( U_15 = U_16
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14,tc_HOL_Obool)),U_16),U_15))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14,tc_HOL_Obool)),U_15),U_16)) ),
    inference(clausify,[status(thm)],[f_5_2]) ).

fof(f_6_1,plain,
    ! [V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_x))
      | ~ class_Orderings_Opreorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_order__refl]) ).

fof(f_6_2,plain,
    ! [U_18,U_17] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17),U_18),U_18))
      | ~ class_Orderings_Opreorder(U_17) ),
    inference(variable_rename,[status(thm)],[f_6_1]) ).

cnf(f_6_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17),U_18),U_18))
    | ~ class_Orderings_Opreorder(U_17) ),
    inference(clausify,[status(thm)],[f_6_2]) ).

fof(f_7_1,plain,
    ! [V_g_2,V_f_2,T_b,T_c] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
          | ? [B_x] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
        & ( ! [B_x] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) ) )
      | ~ class_Orderings_Oord(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_le__fun__def]) ).

fof(f_7_2,plain,
    ! [U_24,U_23,U_22,U_21] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_22,U_21)),U_23),U_24))
          | ? [U_20] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_21),hAPP(U_23,U_20)),hAPP(U_24,U_20))) )
        & ( ! [U_19] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_21),hAPP(U_23,U_19)),hAPP(U_24,U_19)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_22,U_21)),U_23),U_24)) ) )
      | ~ class_Orderings_Oord(U_21) ),
    inference(variable_rename,[status(thm)],[f_7_1]) ).

fof(f_7_3,plain,
    ! [U_24,U_23,U_22,U_21] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_22,U_21)),U_23),U_24))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_21),hAPP(U_23,sK2(U_24,U_23,U_22,U_21))),hAPP(U_24,sK2(U_24,U_23,U_22,U_21)))) )
        & ( ! [U_19] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_21),hAPP(U_23,U_19)),hAPP(U_24,U_19)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_22,U_21)),U_23),U_24)) ) )
      | ~ class_Orderings_Oord(U_21) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_20,sK2(U_24,U_23,U_22,U_21))],[f_7_2]) ).

cnf(f_7_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_21),hAPP(U_23,U_19)),hAPP(U_24,U_19)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_22,U_21)),U_23),U_24))
    | ~ class_Orderings_Oord(U_21) ),
    inference(clausify,[status(thm)],[f_7_3]) ).

cnf(f_7_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_22,U_21)),U_23),U_24))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_21),hAPP(U_23,sK2(U_24,U_23,U_22,U_21))),hAPP(U_24,sK2(U_24,U_23,U_22,U_21))))
    | ~ class_Orderings_Oord(U_21) ),
    inference(clausify,[status(thm)],[f_7_3]) ).

fof(f_8_1,plain,
    ! [V_x_2,V_g_2,V_f_2,T_b,T_c] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
      | ~ class_Orderings_Oord(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_le__funD]) ).

fof(f_8_2,plain,
    ! [U_29,U_28,U_27,U_26,U_25] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_25),hAPP(U_27,U_29)),hAPP(U_28,U_29)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_26,U_25)),U_27),U_28))
      | ~ class_Orderings_Oord(U_25) ),
    inference(variable_rename,[status(thm)],[f_8_1]) ).

cnf(f_8_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_25),hAPP(U_27,U_29)),hAPP(U_28,U_29)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_26,U_25)),U_27),U_28))
    | ~ class_Orderings_Oord(U_25) ),
    inference(clausify,[status(thm)],[f_8_2]) ).

fof(f_9_1,plain,
    ! [V_x_2,V_g_2,V_f_2,T_b,T_c] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
      | ~ class_Orderings_Oord(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_le__funE]) ).

fof(f_9_2,plain,
    ! [U_34,U_33,U_32,U_31,U_30] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_30),hAPP(U_32,U_34)),hAPP(U_33,U_34)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_31,U_30)),U_32),U_33))
      | ~ class_Orderings_Oord(U_30) ),
    inference(variable_rename,[status(thm)],[f_9_1]) ).

cnf(f_9_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_30),hAPP(U_32,U_34)),hAPP(U_33,U_34)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_31,U_30)),U_32),U_33))
    | ~ class_Orderings_Oord(U_30) ),
    inference(clausify,[status(thm)],[f_9_2]) ).

fof(f_10_1,plain,
    ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_subset__refl]) ).

fof(f_10_2,plain,
    ! [U_36,U_35] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_35,tc_HOL_Obool)),U_36),U_36)),
    inference(variable_rename,[status(thm)],[f_10_1]) ).

cnf(f_10_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_35,tc_HOL_Obool)),U_36),U_36)),
    inference(clausify,[status(thm)],[f_10_2]) ).

fof(f_11_1,plain,
    ! [T_b,V_B_2,V_A_2] :
      ( ( V_A_2 = V_B_2
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
        | V_A_2 != V_B_2 ) ),
    inference(fof_nnf,[status(thm)],[fact_set__eq__subset]) ).

fof(f_11_2,plain,
    ! [U_39,U_38,U_37] :
      ( ( U_37 = U_38
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_39,tc_HOL_Obool)),U_38),U_37))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_39,tc_HOL_Obool)),U_37),U_38)) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_39,tc_HOL_Obool)),U_38),U_37))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_39,tc_HOL_Obool)),U_37),U_38)) )
        | U_37 != U_38 ) ),
    inference(variable_rename,[status(thm)],[f_11_1]) ).

fof(f_11_3,plain,
    ( ! [U_45,U_43,U_41] :
        ( U_41 = U_43
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_45,tc_HOL_Obool)),U_43),U_41))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_45,tc_HOL_Obool)),U_41),U_43)) )
    & ! [U_44,U_42,U_40] :
        ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_44,tc_HOL_Obool)),U_42),U_40))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_44,tc_HOL_Obool)),U_40),U_42)) )
        | U_40 != U_42 ) ),
    inference(miniscope,[status(thm)],[f_11_2]) ).

cnf(f_11_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_44,tc_HOL_Obool)),U_40),U_42))
    | U_40 != U_42 ),
    inference(clausify,[status(thm)],[f_11_3]) ).

cnf(f_11_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_44,tc_HOL_Obool)),U_42),U_40))
    | U_40 != U_42 ),
    inference(clausify,[status(thm)],[f_11_3]) ).

cnf(f_11_6,plain,
    ( U_41 = U_43
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_45,tc_HOL_Obool)),U_43),U_41))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_45,tc_HOL_Obool)),U_41),U_43)) ),
    inference(clausify,[status(thm)],[f_11_3]) ).

fof(f_12_1,plain,
    ! [V_Q_2,T_b,V_x_2,V_P_2] :
      ( hBOOL(hAPP(V_Q_2,V_x_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_P_2),V_Q_2))
      | ~ hBOOL(hAPP(V_P_2,V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_rev__predicate1D]) ).

fof(f_12_2,plain,
    ! [U_49,U_48,U_47,U_46] :
      ( hBOOL(hAPP(U_49,U_47))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_48,tc_HOL_Obool)),U_46),U_49))
      | ~ hBOOL(hAPP(U_46,U_47)) ),
    inference(variable_rename,[status(thm)],[f_12_1]) ).

cnf(f_12_3,plain,
    ( hBOOL(hAPP(U_49,U_47))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_48,tc_HOL_Obool)),U_46),U_49))
    | ~ hBOOL(hAPP(U_46,U_47)) ),
    inference(clausify,[status(thm)],[f_12_2]) ).

fof(f_13_1,plain,
    ! [T_b,V_B_2,V_A_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
      | V_A_2 != V_B_2 ),
    inference(fof_nnf,[status(thm)],[fact_equalityD1]) ).

fof(f_13_2,plain,
    ! [U_52,U_51,U_50] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_52,tc_HOL_Obool)),U_50),U_51))
      | U_50 != U_51 ),
    inference(variable_rename,[status(thm)],[f_13_1]) ).

cnf(f_13_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_52,tc_HOL_Obool)),U_50),U_51))
    | U_50 != U_51 ),
    inference(clausify,[status(thm)],[f_13_2]) ).

fof(f_14_1,plain,
    ! [T_b,V_B_2,V_A_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
      | V_A_2 != V_B_2 ),
    inference(fof_nnf,[status(thm)],[fact_equalityD2]) ).

fof(f_14_2,plain,
    ! [U_55,U_54,U_53] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_55,tc_HOL_Obool)),U_54),U_53))
      | U_53 != U_54 ),
    inference(variable_rename,[status(thm)],[f_14_1]) ).

cnf(f_14_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_55,tc_HOL_Obool)),U_54),U_53))
    | U_53 != U_54 ),
    inference(clausify,[status(thm)],[f_14_2]) ).

fof(f_15_1,plain,
    ! [V_x_2,V_Q_2,V_P_2,T_b] :
      ( hBOOL(hAPP(V_Q_2,V_x_2))
      | ~ hBOOL(hAPP(V_P_2,V_x_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_P_2),V_Q_2)) ),
    inference(fof_nnf,[status(thm)],[fact_predicate1D]) ).

fof(f_15_2,plain,
    ! [U_59,U_58,U_57,U_56] :
      ( hBOOL(hAPP(U_58,U_59))
      | ~ hBOOL(hAPP(U_57,U_59))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_56,tc_HOL_Obool)),U_57),U_58)) ),
    inference(variable_rename,[status(thm)],[f_15_1]) ).

fof(f_15_3,plain,
    ! [U_59,U_58,U_57] :
      ( ! [U_56] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_56,tc_HOL_Obool)),U_57),U_58))
      | hBOOL(hAPP(U_58,U_59))
      | ~ hBOOL(hAPP(U_57,U_59)) ),
    inference(miniscope,[status(thm)],[f_15_2]) ).

cnf(f_15_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_56,tc_HOL_Obool)),U_57),U_58))
    | hBOOL(hAPP(U_58,U_59))
    | ~ hBOOL(hAPP(U_57,U_59)) ),
    inference(clausify,[status(thm)],[f_15_3]) ).

fof(f_16_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_subset__trans]) ).

fof(f_16_2,plain,
    ! [U_63,U_62,U_61,U_60] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_60,tc_HOL_Obool)),U_61),U_63))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_60,tc_HOL_Obool)),U_62),U_63))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_60,tc_HOL_Obool)),U_61),U_62)) ),
    inference(variable_rename,[status(thm)],[f_16_1]) ).

cnf(f_16_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_60,tc_HOL_Obool)),U_61),U_63))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_60,tc_HOL_Obool)),U_62),U_63))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_60,tc_HOL_Obool)),U_61),U_62)) ),
    inference(clausify,[status(thm)],[f_16_2]) ).

fof(f_17_1,plain,
    ! [V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_linorder__le__cases]) ).

fof(f_17_2,plain,
    ! [U_66,U_65,U_64] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_64),U_66),U_65))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_64),U_65),U_66))
      | ~ class_Orderings_Olinorder(U_64) ),
    inference(variable_rename,[status(thm)],[f_17_1]) ).

cnf(f_17_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_64),U_66),U_65))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_64),U_65),U_66))
    | ~ class_Orderings_Olinorder(U_64) ),
    inference(clausify,[status(thm)],[f_17_2]) ).

fof(f_18_1,plain,
    ! [V_z,V_x,V_y,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_xt1_I6_J]) ).

fof(f_18_2,plain,
    ! [U_70,U_69,U_68,U_67] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_67),U_70),U_69))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_67),U_70),U_68))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_67),U_68),U_69))
      | ~ class_Orderings_Oorder(U_67) ),
    inference(variable_rename,[status(thm)],[f_18_1]) ).

cnf(f_18_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_67),U_70),U_69))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_67),U_70),U_68))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_67),U_68),U_69))
    | ~ class_Orderings_Oorder(U_67) ),
    inference(clausify,[status(thm)],[f_18_2]) ).

fof(f_19_1,plain,
    ! [V_x,V_y,T_a] :
      ( V_x = V_y
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_xt1_I5_J]) ).

fof(f_19_2,plain,
    ! [U_73,U_72,U_71] :
      ( U_73 = U_72
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_71),U_73),U_72))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_71),U_72),U_73))
      | ~ class_Orderings_Oorder(U_71) ),
    inference(variable_rename,[status(thm)],[f_19_1]) ).

cnf(f_19_3,plain,
    ( U_73 = U_72
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_71),U_73),U_72))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_71),U_72),U_73))
    | ~ class_Orderings_Oorder(U_71) ),
    inference(clausify,[status(thm)],[f_19_2]) ).

fof(f_20_1,plain,
    ! [V_z,V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
      | ~ class_Orderings_Opreorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_order__trans]) ).

fof(f_20_2,plain,
    ! [U_77,U_76,U_75,U_74] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_74),U_75),U_77))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_74),U_76),U_77))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_74),U_75),U_76))
      | ~ class_Orderings_Opreorder(U_74) ),
    inference(variable_rename,[status(thm)],[f_20_1]) ).

cnf(f_20_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_74),U_75),U_77))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_74),U_76),U_77))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_74),U_75),U_76))
    | ~ class_Orderings_Opreorder(U_74) ),
    inference(clausify,[status(thm)],[f_20_2]) ).

fof(f_21_1,plain,
    ! [V_y,V_x,T_a] :
      ( V_x = V_y
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_order__antisym]) ).

fof(f_21_2,plain,
    ! [U_80,U_79,U_78] :
      ( U_79 = U_80
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_78),U_80),U_79))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_78),U_79),U_80))
      | ~ class_Orderings_Oorder(U_78) ),
    inference(variable_rename,[status(thm)],[f_21_1]) ).

cnf(f_21_3,plain,
    ( U_79 = U_80
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_78),U_80),U_79))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_78),U_79),U_80))
    | ~ class_Orderings_Oorder(U_78) ),
    inference(clausify,[status(thm)],[f_21_2]) ).

fof(f_22_1,plain,
    ! [V_c,V_a,V_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a))
      | V_b != V_c
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_xt1_I4_J]) ).

fof(f_22_2,plain,
    ! [U_84,U_83,U_82,U_81] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_81),U_84),U_83))
      | U_82 != U_84
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_81),U_82),U_83))
      | ~ class_Orderings_Oorder(U_81) ),
    inference(variable_rename,[status(thm)],[f_22_1]) ).

cnf(f_22_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_81),U_84),U_83))
    | U_82 != U_84
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_81),U_82),U_83))
    | ~ class_Orderings_Oorder(U_81) ),
    inference(clausify,[status(thm)],[f_22_2]) ).

fof(f_23_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
      | V_b != V_c
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
      | ~ class_Orderings_Oord(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_ord__le__eq__trans]) ).

fof(f_23_2,plain,
    ! [U_88,U_87,U_86,U_85] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_85),U_86),U_88))
      | U_87 != U_88
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_85),U_86),U_87))
      | ~ class_Orderings_Oord(U_85) ),
    inference(variable_rename,[status(thm)],[f_23_1]) ).

cnf(f_23_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_85),U_86),U_88))
    | U_87 != U_88
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_85),U_86),U_87))
    | ~ class_Orderings_Oord(U_85) ),
    inference(clausify,[status(thm)],[f_23_2]) ).

fof(f_24_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_b))
      | V_a != V_b
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_xt1_I3_J]) ).

fof(f_24_2,plain,
    ! [U_92,U_91,U_90,U_89] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_89),U_92),U_90))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_89),U_92),U_91))
      | U_90 != U_91
      | ~ class_Orderings_Oorder(U_89) ),
    inference(variable_rename,[status(thm)],[f_24_1]) ).

cnf(f_24_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_89),U_92),U_90))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_89),U_92),U_91))
    | U_90 != U_91
    | ~ class_Orderings_Oorder(U_89) ),
    inference(clausify,[status(thm)],[f_24_2]) ).

fof(f_25_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
      | V_a != V_b
      | ~ class_Orderings_Oord(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_ord__eq__le__trans]) ).

fof(f_25_2,plain,
    ! [U_96,U_95,U_94,U_93] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_93),U_94),U_96))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_93),U_95),U_96))
      | U_94 != U_95
      | ~ class_Orderings_Oord(U_93) ),
    inference(variable_rename,[status(thm)],[f_25_1]) ).

cnf(f_25_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_93),U_94),U_96))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_93),U_95),U_96))
    | U_94 != U_95
    | ~ class_Orderings_Oord(U_93) ),
    inference(clausify,[status(thm)],[f_25_2]) ).

fof(f_26_1,plain,
    ! [V_x_2,V_y_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
          | V_x_2 != V_y_2 )
        & ( V_x_2 = V_y_2
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_order__antisym__conv]) ).

fof(f_26_2,plain,
    ! [U_99,U_98,U_97] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_97),U_99),U_98))
          | U_99 != U_98 )
        & ( U_99 = U_98
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_97),U_99),U_98)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_97),U_98),U_99))
      | ~ class_Orderings_Oorder(U_97) ),
    inference(variable_rename,[status(thm)],[f_26_1]) ).

cnf(f_26_3,plain,
    ( U_99 = U_98
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_97),U_99),U_98))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_97),U_98),U_99))
    | ~ class_Orderings_Oorder(U_97) ),
    inference(clausify,[status(thm)],[f_26_2]) ).

cnf(f_26_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_97),U_99),U_98))
    | U_99 != U_98
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_97),U_98),U_99))
    | ~ class_Orderings_Oorder(U_97) ),
    inference(clausify,[status(thm)],[f_26_2]) ).

fof(f_27_1,plain,
    ! [V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
      | V_x != V_y
      | ~ class_Orderings_Opreorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_order__eq__refl]) ).

fof(f_27_2,plain,
    ! [U_102,U_101,U_100] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_100),U_101),U_102))
      | U_101 != U_102
      | ~ class_Orderings_Opreorder(U_100) ),
    inference(variable_rename,[status(thm)],[f_27_1]) ).

cnf(f_27_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_100),U_101),U_102))
    | U_101 != U_102
    | ~ class_Orderings_Opreorder(U_100) ),
    inference(clausify,[status(thm)],[f_27_2]) ).

fof(f_28_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( V_x_2 = V_y_2
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) )
          | V_x_2 != V_y_2 ) )
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_order__eq__iff]) ).

fof(f_28_2,plain,
    ! [U_105,U_104,U_103] :
      ( ( ( U_104 = U_105
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_103),U_105),U_104))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_103),U_104),U_105)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_103),U_105),U_104))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_103),U_104),U_105)) )
          | U_104 != U_105 ) )
      | ~ class_Orderings_Oorder(U_103) ),
    inference(variable_rename,[status(thm)],[f_28_1]) ).

cnf(f_28_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_103),U_104),U_105))
    | U_104 != U_105
    | ~ class_Orderings_Oorder(U_103) ),
    inference(clausify,[status(thm)],[f_28_2]) ).

cnf(f_28_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_103),U_105),U_104))
    | U_104 != U_105
    | ~ class_Orderings_Oorder(U_103) ),
    inference(clausify,[status(thm)],[f_28_2]) ).

cnf(f_28_5,plain,
    ( U_104 = U_105
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_103),U_105),U_104))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_103),U_104),U_105))
    | ~ class_Orderings_Oorder(U_103) ),
    inference(clausify,[status(thm)],[f_28_2]) ).

fof(f_29_1,plain,
    ! [V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_linorder__linear]) ).

fof(f_29_2,plain,
    ! [U_108,U_107,U_106] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_106),U_108),U_107))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_106),U_107),U_108))
      | ~ class_Orderings_Olinorder(U_106) ),
    inference(variable_rename,[status(thm)],[f_29_1]) ).

cnf(f_29_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_106),U_108),U_107))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_106),U_107),U_108))
    | ~ class_Orderings_Olinorder(U_106) ),
    inference(clausify,[status(thm)],[f_29_2]) ).

fof(f_30_1,plain,
    ! [T_b,V_B_2,V_A_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
      | V_A_2 != V_B_2 ),
    inference(fof_nnf,[status(thm)],[fact_equalityE]) ).

fof(f_30_2,plain,
    ! [U_111,U_110,U_109] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_111,tc_HOL_Obool)),U_110),U_109))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_111,tc_HOL_Obool)),U_109),U_110)) )
      | U_109 != U_110 ),
    inference(variable_rename,[status(thm)],[f_30_1]) ).

cnf(f_30_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_111,tc_HOL_Obool)),U_109),U_110))
    | U_109 != U_110 ),
    inference(clausify,[status(thm)],[f_30_2]) ).

cnf(f_30_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_111,tc_HOL_Obool)),U_110),U_109))
    | U_109 != U_110 ),
    inference(clausify,[status(thm)],[f_30_2]) ).

fof(f_31_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(T_b,V_A_2)),c_Predicate_OPowp(T_b,V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Powp__mono]) ).

fof(f_31_2,plain,
    ! [U_114,U_113,U_112] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_112,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(U_112,U_113)),c_Predicate_OPowp(U_112,U_114)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_112,tc_HOL_Obool)),U_113),U_114)) ),
    inference(variable_rename,[status(thm)],[f_31_1]) ).

cnf(f_31_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_112,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(U_112,U_113)),c_Predicate_OPowp(U_112,U_114)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_112,tc_HOL_Obool)),U_113),U_114)) ),
    inference(clausify,[status(thm)],[f_31_2]) ).

fof(f_32_1,plain,
    ! [T_b,V_g_2,V_f_2,T_c] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
      | ? [B_x] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x)))
      | ~ class_Orderings_Oord(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_le__funI]) ).

fof(f_32_2,plain,
    ! [U_119,U_118,U_117,U_116] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_119,U_116)),U_117),U_118))
      | ? [U_115] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_116),hAPP(U_117,U_115)),hAPP(U_118,U_115)))
      | ~ class_Orderings_Oord(U_116) ),
    inference(variable_rename,[status(thm)],[f_32_1]) ).

fof(f_32_3,plain,
    ! [U_119,U_118,U_117,U_116] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_119,U_116)),U_117),U_118))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_116),hAPP(U_117,sK3(U_119,U_118,U_117,U_116))),hAPP(U_118,sK3(U_119,U_118,U_117,U_116))))
      | ~ class_Orderings_Oord(U_116) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_115,sK3(U_119,U_118,U_117,U_116))],[f_32_2]) ).

cnf(f_32_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_119,U_116)),U_117),U_118))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_116),hAPP(U_117,sK3(U_119,U_118,U_117,U_116))),hAPP(U_118,sK3(U_119,U_118,U_117,U_116))))
    | ~ class_Orderings_Oord(U_116) ),
    inference(clausify,[status(thm)],[f_32_3]) ).

fof(f_33_1,plain,
    ! [V_y_2,V_x_2,V_f_2,T_b,T_c] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) ) )
      | ~ c_Orderings_Oorder__class_Ostrict__mono(T_b,T_c,V_f_2)
      | ~ class_Orderings_Olinorder(T_b)
      | ~ class_Orderings_Oorder(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_strict__mono__less__eq]) ).

fof(f_33_2,plain,
    ! [U_124,U_123,U_122,U_121,U_120] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_120),hAPP(U_122,U_123)),hAPP(U_122,U_124)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_121),U_123),U_124)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_121),U_123),U_124))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_120),hAPP(U_122,U_123)),hAPP(U_122,U_124))) ) )
      | ~ c_Orderings_Oorder__class_Ostrict__mono(U_121,U_120,U_122)
      | ~ class_Orderings_Olinorder(U_121)
      | ~ class_Orderings_Oorder(U_120) ),
    inference(variable_rename,[status(thm)],[f_33_1]) ).

cnf(f_33_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_121),U_123),U_124))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_120),hAPP(U_122,U_123)),hAPP(U_122,U_124)))
    | ~ c_Orderings_Oorder__class_Ostrict__mono(U_121,U_120,U_122)
    | ~ class_Orderings_Olinorder(U_121)
    | ~ class_Orderings_Oorder(U_120) ),
    inference(clausify,[status(thm)],[f_33_2]) ).

cnf(f_33_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_120),hAPP(U_122,U_123)),hAPP(U_122,U_124)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_121),U_123),U_124))
    | ~ c_Orderings_Oorder__class_Ostrict__mono(U_121,U_120,U_122)
    | ~ class_Orderings_Olinorder(U_121)
    | ~ class_Orderings_Oorder(U_120) ),
    inference(clausify,[status(thm)],[f_33_2]) ).

fof(f_34_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_y_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_y_2))) ) )
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_greaterThan__subset__iff]) ).

fof(f_34_2,plain,
    ! [U_127,U_126,U_125] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_125,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_125),U_126)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_125),U_127)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_125),U_127),U_126)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_125),U_127),U_126))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_125,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_125),U_126)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_125),U_127))) ) )
      | ~ class_Orderings_Olinorder(U_125) ),
    inference(variable_rename,[status(thm)],[f_34_1]) ).

cnf(f_34_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_125),U_127),U_126))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_125,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_125),U_126)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_125),U_127)))
    | ~ class_Orderings_Olinorder(U_125) ),
    inference(clausify,[status(thm)],[f_34_2]) ).

cnf(f_34_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_125,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_125),U_126)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_125),U_127)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_125),U_127),U_126))
    | ~ class_Orderings_Olinorder(U_125) ),
    inference(clausify,[status(thm)],[f_34_2]) ).

fof(f_35_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_y_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_y_2))) ) )
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_lessThan__subset__iff]) ).

fof(f_35_2,plain,
    ! [U_130,U_129,U_128] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_128,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_128),U_129)),hAPP(c_SetInterval_Oord__class_OlessThan(U_128),U_130)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_128),U_129),U_130)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_128),U_129),U_130))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_128,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_128),U_129)),hAPP(c_SetInterval_Oord__class_OlessThan(U_128),U_130))) ) )
      | ~ class_Orderings_Olinorder(U_128) ),
    inference(variable_rename,[status(thm)],[f_35_1]) ).

cnf(f_35_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_128),U_129),U_130))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_128,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_128),U_129)),hAPP(c_SetInterval_Oord__class_OlessThan(U_128),U_130)))
    | ~ class_Orderings_Olinorder(U_128) ),
    inference(clausify,[status(thm)],[f_35_2]) ).

cnf(f_35_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_128,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_128),U_129)),hAPP(c_SetInterval_Oord__class_OlessThan(U_128),U_130)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_128),U_129),U_130))
    | ~ class_Orderings_Olinorder(U_128) ),
    inference(clausify,[status(thm)],[f_35_2]) ).

fof(f_36_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_y_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_y_2))) ) )
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_atLeast__subset__iff]) ).

fof(f_36_2,plain,
    ! [U_133,U_132,U_131] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_131,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_131),U_132)),hAPP(c_SetInterval_Oord__class_OatLeast(U_131),U_133)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_131),U_133),U_132)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_131),U_133),U_132))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_131,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_131),U_132)),hAPP(c_SetInterval_Oord__class_OatLeast(U_131),U_133))) ) )
      | ~ class_Orderings_Oorder(U_131) ),
    inference(variable_rename,[status(thm)],[f_36_1]) ).

cnf(f_36_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_131),U_133),U_132))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_131,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_131),U_132)),hAPP(c_SetInterval_Oord__class_OatLeast(U_131),U_133)))
    | ~ class_Orderings_Oorder(U_131) ),
    inference(clausify,[status(thm)],[f_36_2]) ).

cnf(f_36_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_131,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_131),U_132)),hAPP(c_SetInterval_Oord__class_OatLeast(U_131),U_133)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_131),U_133),U_132))
    | ~ class_Orderings_Oorder(U_131) ),
    inference(clausify,[status(thm)],[f_36_2]) ).

fof(f_37_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_y_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_y_2))) ) )
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_atMost__subset__iff]) ).

fof(f_37_2,plain,
    ! [U_136,U_135,U_134] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_134,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_134),U_135)),hAPP(c_SetInterval_Oord__class_OatMost(U_134),U_136)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_134),U_135),U_136)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_134),U_135),U_136))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_134,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_134),U_135)),hAPP(c_SetInterval_Oord__class_OatMost(U_134),U_136))) ) )
      | ~ class_Orderings_Oorder(U_134) ),
    inference(variable_rename,[status(thm)],[f_37_1]) ).

cnf(f_37_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_134),U_135),U_136))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_134,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_134),U_135)),hAPP(c_SetInterval_Oord__class_OatMost(U_134),U_136)))
    | ~ class_Orderings_Oorder(U_134) ),
    inference(clausify,[status(thm)],[f_37_2]) ).

cnf(f_37_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_134,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_134),U_135)),hAPP(c_SetInterval_Oord__class_OatMost(U_134),U_136)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_134),U_135),U_136))
    | ~ class_Orderings_Oorder(U_134) ),
    inference(clausify,[status(thm)],[f_37_2]) ).

fof(f_38_1,plain,
    ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),V_f_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_B_2),V_f_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_SUP__subset]) ).

fof(f_38_2,plain,
    ! [U_141,U_140,U_139,U_138,U_137] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_137),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_138,U_137),U_139),U_141)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_138,U_137),U_140),U_141)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_138,tc_HOL_Obool)),U_139),U_140))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_137) ),
    inference(variable_rename,[status(thm)],[f_38_1]) ).

cnf(f_38_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_137),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_138,U_137),U_139),U_141)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_138,U_137),U_140),U_141)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_138,tc_HOL_Obool)),U_139),U_140))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_137) ),
    inference(clausify,[status(thm)],[f_38_2]) ).

fof(f_39_1,plain,
    ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_B_2),V_f_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),V_f_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_INF__subset]) ).

fof(f_39_2,plain,
    ! [U_146,U_145,U_144,U_143,U_142] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_142),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_143,U_142),U_145),U_146)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_143,U_142),U_144),U_146)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_143,tc_HOL_Obool)),U_144),U_145))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_142) ),
    inference(variable_rename,[status(thm)],[f_39_1]) ).

cnf(f_39_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_142),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_143,U_142),U_145),U_146)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_143,U_142),U_144),U_146)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_143,tc_HOL_Obool)),U_144),U_145))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_142) ),
    inference(clausify,[status(thm)],[f_39_2]) ).

fof(f_40_1,plain,
    ! [V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)))
      | ~ class_Orderings_Otop(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_top__greatest]) ).

fof(f_40_2,plain,
    ! [U_148,U_147] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_147),U_148),c_Orderings_Otop__class_Otop(U_147)))
      | ~ class_Orderings_Otop(U_147) ),
    inference(variable_rename,[status(thm)],[f_40_1]) ).

cnf(f_40_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_147),U_148),c_Orderings_Otop__class_Otop(U_147)))
    | ~ class_Orderings_Otop(U_147) ),
    inference(clausify,[status(thm)],[f_40_2]) ).

fof(f_41_1,plain,
    ! [V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x))
      | ~ class_Orderings_Obot(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_bot__least]) ).

fof(f_41_2,plain,
    ! [U_150,U_149] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_149),c_Orderings_Obot__class_Obot(U_149)),U_150))
      | ~ class_Orderings_Obot(U_149) ),
    inference(variable_rename,[status(thm)],[f_41_1]) ).

cnf(f_41_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_149),c_Orderings_Obot__class_Obot(U_149)),U_150))
    | ~ class_Orderings_Obot(U_149) ),
    inference(clausify,[status(thm)],[f_41_2]) ).

fof(f_42_1,plain,
    ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_empty__subsetI]) ).

fof(f_42_2,plain,
    ! [U_152,U_151] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_151,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_151,tc_HOL_Obool))),U_152)),
    inference(variable_rename,[status(thm)],[f_42_1]) ).

cnf(f_42_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_151,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_151,tc_HOL_Obool))),U_152)),
    inference(clausify,[status(thm)],[f_42_2]) ).

fof(f_43_1,plain,
    ! [T_b] : c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_UNIV__not__empty]) ).

fof(f_43_2,plain,
    ! [U_153] : c_Orderings_Otop__class_Otop(tc_fun(U_153,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(U_153,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_43_1]) ).

cnf(f_43_3,plain,
    c_Orderings_Otop__class_Otop(tc_fun(U_153,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(U_153,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_43_2]) ).

fof(f_44_1,plain,
    ! [V_x_2,T_c,T_b] :
      ( hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b)
      | ~ class_Orderings_Obot(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_bot__apply]) ).

fof(f_44_2,plain,
    ! [U_156,U_155,U_154] :
      ( hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_155,U_154)),U_156) = c_Orderings_Obot__class_Obot(U_154)
      | ~ class_Orderings_Obot(U_154) ),
    inference(variable_rename,[status(thm)],[f_44_1]) ).

cnf(f_44_3,plain,
    ( hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_155,U_154)),U_156) = c_Orderings_Obot__class_Obot(U_154)
    | ~ class_Orderings_Obot(U_154) ),
    inference(clausify,[status(thm)],[f_44_2]) ).

fof(f_45_1,plain,
    ! [V_x_2,T_c,T_b] :
      ( hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Otop__class_Otop(T_b)
      | ~ class_Orderings_Otop(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_top__apply]) ).

fof(f_45_2,plain,
    ! [U_159,U_158,U_157] :
      ( hAPP(c_Orderings_Otop__class_Otop(tc_fun(U_158,U_157)),U_159) = c_Orderings_Otop__class_Otop(U_157)
      | ~ class_Orderings_Otop(U_157) ),
    inference(variable_rename,[status(thm)],[f_45_1]) ).

cnf(f_45_3,plain,
    ( hAPP(c_Orderings_Otop__class_Otop(tc_fun(U_158,U_157)),U_159) = c_Orderings_Otop__class_Otop(U_157)
    | ~ class_Orderings_Otop(U_157) ),
    inference(clausify,[status(thm)],[f_45_2]) ).

fof(f_46_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_y_2)
          | V_x_2 != V_y_2 )
        & ( V_x_2 = V_y_2
          | hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2) != hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_y_2) ) )
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_greaterThan__eq__iff]) ).

fof(f_46_2,plain,
    ! [U_162,U_161,U_160] :
      ( ( ( hAPP(c_SetInterval_Oord__class_OgreaterThan(U_160),U_161) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_160),U_162)
          | U_161 != U_162 )
        & ( U_161 = U_162
          | hAPP(c_SetInterval_Oord__class_OgreaterThan(U_160),U_161) != hAPP(c_SetInterval_Oord__class_OgreaterThan(U_160),U_162) ) )
      | ~ class_Orderings_Olinorder(U_160) ),
    inference(variable_rename,[status(thm)],[f_46_1]) ).

cnf(f_46_3,plain,
    ( U_161 = U_162
    | hAPP(c_SetInterval_Oord__class_OgreaterThan(U_160),U_161) != hAPP(c_SetInterval_Oord__class_OgreaterThan(U_160),U_162)
    | ~ class_Orderings_Olinorder(U_160) ),
    inference(clausify,[status(thm)],[f_46_2]) ).

cnf(f_46_4,plain,
    ( hAPP(c_SetInterval_Oord__class_OgreaterThan(U_160),U_161) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_160),U_162)
    | U_161 != U_162
    | ~ class_Orderings_Olinorder(U_160) ),
    inference(clausify,[status(thm)],[f_46_2]) ).

fof(f_47_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_y_2)
          | V_x_2 != V_y_2 )
        & ( V_x_2 = V_y_2
          | hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2) != hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_y_2) ) )
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_lessThan__eq__iff]) ).

fof(f_47_2,plain,
    ! [U_165,U_164,U_163] :
      ( ( ( hAPP(c_SetInterval_Oord__class_OlessThan(U_163),U_164) = hAPP(c_SetInterval_Oord__class_OlessThan(U_163),U_165)
          | U_164 != U_165 )
        & ( U_164 = U_165
          | hAPP(c_SetInterval_Oord__class_OlessThan(U_163),U_164) != hAPP(c_SetInterval_Oord__class_OlessThan(U_163),U_165) ) )
      | ~ class_Orderings_Olinorder(U_163) ),
    inference(variable_rename,[status(thm)],[f_47_1]) ).

cnf(f_47_3,plain,
    ( U_164 = U_165
    | hAPP(c_SetInterval_Oord__class_OlessThan(U_163),U_164) != hAPP(c_SetInterval_Oord__class_OlessThan(U_163),U_165)
    | ~ class_Orderings_Olinorder(U_163) ),
    inference(clausify,[status(thm)],[f_47_2]) ).

cnf(f_47_4,plain,
    ( hAPP(c_SetInterval_Oord__class_OlessThan(U_163),U_164) = hAPP(c_SetInterval_Oord__class_OlessThan(U_163),U_165)
    | U_164 != U_165
    | ~ class_Orderings_Olinorder(U_163) ),
    inference(clausify,[status(thm)],[f_47_2]) ).

fof(f_48_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_y_2)
          | V_x_2 != V_y_2 )
        & ( V_x_2 = V_y_2
          | hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2) != hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_y_2) ) )
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_atLeast__eq__iff]) ).

fof(f_48_2,plain,
    ! [U_168,U_167,U_166] :
      ( ( ( hAPP(c_SetInterval_Oord__class_OatLeast(U_166),U_167) = hAPP(c_SetInterval_Oord__class_OatLeast(U_166),U_168)
          | U_167 != U_168 )
        & ( U_167 = U_168
          | hAPP(c_SetInterval_Oord__class_OatLeast(U_166),U_167) != hAPP(c_SetInterval_Oord__class_OatLeast(U_166),U_168) ) )
      | ~ class_Orderings_Olinorder(U_166) ),
    inference(variable_rename,[status(thm)],[f_48_1]) ).

cnf(f_48_3,plain,
    ( U_167 = U_168
    | hAPP(c_SetInterval_Oord__class_OatLeast(U_166),U_167) != hAPP(c_SetInterval_Oord__class_OatLeast(U_166),U_168)
    | ~ class_Orderings_Olinorder(U_166) ),
    inference(clausify,[status(thm)],[f_48_2]) ).

cnf(f_48_4,plain,
    ( hAPP(c_SetInterval_Oord__class_OatLeast(U_166),U_167) = hAPP(c_SetInterval_Oord__class_OatLeast(U_166),U_168)
    | U_167 != U_168
    | ~ class_Orderings_Olinorder(U_166) ),
    inference(clausify,[status(thm)],[f_48_2]) ).

fof(f_49_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_y_2)
          | V_x_2 != V_y_2 )
        & ( V_x_2 = V_y_2
          | hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2) != hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_y_2) ) )
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_atMost__eq__iff]) ).

fof(f_49_2,plain,
    ! [U_171,U_170,U_169] :
      ( ( ( hAPP(c_SetInterval_Oord__class_OatMost(U_169),U_170) = hAPP(c_SetInterval_Oord__class_OatMost(U_169),U_171)
          | U_170 != U_171 )
        & ( U_170 = U_171
          | hAPP(c_SetInterval_Oord__class_OatMost(U_169),U_170) != hAPP(c_SetInterval_Oord__class_OatMost(U_169),U_171) ) )
      | ~ class_Orderings_Olinorder(U_169) ),
    inference(variable_rename,[status(thm)],[f_49_1]) ).

cnf(f_49_3,plain,
    ( U_170 = U_171
    | hAPP(c_SetInterval_Oord__class_OatMost(U_169),U_170) != hAPP(c_SetInterval_Oord__class_OatMost(U_169),U_171)
    | ~ class_Orderings_Olinorder(U_169) ),
    inference(clausify,[status(thm)],[f_49_2]) ).

cnf(f_49_4,plain,
    ( hAPP(c_SetInterval_Oord__class_OatMost(U_169),U_170) = hAPP(c_SetInterval_Oord__class_OatMost(U_169),U_171)
    | U_170 != U_171
    | ~ class_Orderings_Olinorder(U_169) ),
    inference(clausify,[status(thm)],[f_49_2]) ).

fof(f_50_1,plain,
    ! [V_y_2,V_x_2,V_f_2,T_b,T_c] :
      ( ( ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
          | V_x_2 != V_y_2 )
        & ( V_x_2 = V_y_2
          | hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) ) )
      | ~ c_Orderings_Oorder__class_Ostrict__mono(T_b,T_c,V_f_2)
      | ~ class_Orderings_Olinorder(T_b)
      | ~ class_Orderings_Oorder(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_strict__mono__eq]) ).

fof(f_50_2,plain,
    ! [U_176,U_175,U_174,U_173,U_172] :
      ( ( ( hAPP(U_174,U_175) = hAPP(U_174,U_176)
          | U_175 != U_176 )
        & ( U_175 = U_176
          | hAPP(U_174,U_175) != hAPP(U_174,U_176) ) )
      | ~ c_Orderings_Oorder__class_Ostrict__mono(U_173,U_172,U_174)
      | ~ class_Orderings_Olinorder(U_173)
      | ~ class_Orderings_Oorder(U_172) ),
    inference(variable_rename,[status(thm)],[f_50_1]) ).

cnf(f_50_3,plain,
    ( U_175 = U_176
    | hAPP(U_174,U_175) != hAPP(U_174,U_176)
    | ~ c_Orderings_Oorder__class_Ostrict__mono(U_173,U_172,U_174)
    | ~ class_Orderings_Olinorder(U_173)
    | ~ class_Orderings_Oorder(U_172) ),
    inference(clausify,[status(thm)],[f_50_2]) ).

cnf(f_50_4,plain,
    ( hAPP(U_174,U_175) = hAPP(U_174,U_176)
    | U_175 != U_176
    | ~ c_Orderings_Oorder__class_Ostrict__mono(U_173,U_172,U_174)
    | ~ class_Orderings_Olinorder(U_173)
    | ~ class_Orderings_Oorder(U_172) ),
    inference(clausify,[status(thm)],[f_50_2]) ).

fof(f_51_1,plain,
    ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_subset__UNIV]) ).

fof(f_51_2,plain,
    ! [U_178,U_177] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_177,tc_HOL_Obool)),U_178),c_Orderings_Otop__class_Otop(tc_fun(U_177,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_51_1]) ).

cnf(f_51_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_177,tc_HOL_Obool)),U_178),c_Orderings_Otop__class_Otop(tc_fun(U_177,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_51_2]) ).

fof(f_52_1,plain,
    ! [V_A_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
        | V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
      & ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_subset__empty]) ).

fof(f_52_2,plain,
    ! [U_180,U_179] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_179,tc_HOL_Obool)),U_180),c_Orderings_Obot__class_Obot(tc_fun(U_179,tc_HOL_Obool))))
        | U_180 != c_Orderings_Obot__class_Obot(tc_fun(U_179,tc_HOL_Obool)) )
      & ( U_180 = c_Orderings_Obot__class_Obot(tc_fun(U_179,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_179,tc_HOL_Obool)),U_180),c_Orderings_Obot__class_Obot(tc_fun(U_179,tc_HOL_Obool)))) ) ),
    inference(variable_rename,[status(thm)],[f_52_1]) ).

fof(f_52_3,plain,
    ( ! [U_184,U_182] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_182,tc_HOL_Obool)),U_184),c_Orderings_Obot__class_Obot(tc_fun(U_182,tc_HOL_Obool))))
        | U_184 != c_Orderings_Obot__class_Obot(tc_fun(U_182,tc_HOL_Obool)) )
    & ! [U_183,U_181] :
        ( U_183 = c_Orderings_Obot__class_Obot(tc_fun(U_181,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_181,tc_HOL_Obool)),U_183),c_Orderings_Obot__class_Obot(tc_fun(U_181,tc_HOL_Obool)))) ) ),
    inference(miniscope,[status(thm)],[f_52_2]) ).

cnf(f_52_4,plain,
    ( U_183 = c_Orderings_Obot__class_Obot(tc_fun(U_181,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_181,tc_HOL_Obool)),U_183),c_Orderings_Obot__class_Obot(tc_fun(U_181,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_52_3]) ).

cnf(f_52_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_182,tc_HOL_Obool)),U_184),c_Orderings_Obot__class_Obot(tc_fun(U_182,tc_HOL_Obool))))
    | U_184 != c_Orderings_Obot__class_Obot(tc_fun(U_182,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_52_3]) ).

fof(f_53_1,plain,
    ! [V_G_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))),
    inference(fof_nnf,[status(thm)],[fact_empty]) ).

fof(f_53_2,plain,
    ! [U_186,U_185] : c_Hoare__Mirabelle_Ohoare__derivs(U_185,U_186,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_185),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_53_1]) ).

cnf(f_53_3,plain,
    c_Hoare__Mirabelle_Ohoare__derivs(U_185,U_186,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_185),tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_53_2]) ).

fof(f_54_1,plain,
    ! [V_a_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))),
    inference(fof_nnf,[status(thm)],[fact_hoare__derivs_Oequations_I1_J]) ).

fof(f_54_2,plain,
    ! [U_188,U_187] : c_Hoare__Mirabelle_Ohoare__derivs(U_187,U_188,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_187),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_54_1]) ).

cnf(f_54_3,plain,
    c_Hoare__Mirabelle_Ohoare__derivs(U_187,U_188,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_187),tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_54_2]) ).

fof(f_55_1,plain,
    ! [T_b] :
      ( c_Complete__Lattice_OInf__class_OInf(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(T_b)
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__empty]) ).

fof(f_55_2,plain,
    ! [U_189] :
      ( c_Complete__Lattice_OInf__class_OInf(U_189,c_Orderings_Obot__class_Obot(tc_fun(U_189,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(U_189)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_189) ),
    inference(variable_rename,[status(thm)],[f_55_1]) ).

cnf(f_55_3,plain,
    ( c_Complete__Lattice_OInf__class_OInf(U_189,c_Orderings_Obot__class_Obot(tc_fun(U_189,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(U_189)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_189) ),
    inference(clausify,[status(thm)],[f_55_2]) ).

fof(f_56_1,plain,
    ! [T_b] :
      ( c_Complete__Lattice_OSup__class_OSup(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(T_b)
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__empty]) ).

fof(f_56_2,plain,
    ! [U_190] :
      ( c_Complete__Lattice_OSup__class_OSup(U_190,c_Orderings_Obot__class_Obot(tc_fun(U_190,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(U_190)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_190) ),
    inference(variable_rename,[status(thm)],[f_56_1]) ).

cnf(f_56_3,plain,
    ( c_Complete__Lattice_OSup__class_OSup(U_190,c_Orderings_Obot__class_Obot(tc_fun(U_190,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(U_190)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_190) ),
    inference(clausify,[status(thm)],[f_56_2]) ).

fof(f_57_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)),hAPP(c_Set_OPow(T_b),V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Pow__mono]) ).

fof(f_57_2,plain,
    ! [U_193,U_192,U_191] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_191,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_191),U_192)),hAPP(c_Set_OPow(U_191),U_193)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_191,tc_HOL_Obool)),U_192),U_193)) ),
    inference(variable_rename,[status(thm)],[f_57_1]) ).

cnf(f_57_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_191,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_191),U_192)),hAPP(c_Set_OPow(U_191),U_193)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_191,tc_HOL_Obool)),U_192),U_193)) ),
    inference(clausify,[status(thm)],[f_57_2]) ).

fof(f_58_1,plain,
    ! [V_k_2,V_l_2,T_b] :
      ( c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_k_2))
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_greaterThanLessThan__empty]) ).

fof(f_58_2,plain,
    ! [U_196,U_195,U_194] :
      ( c_SetInterval_Oord__class_OgreaterThanLessThan(U_194,U_196,U_195) = c_Orderings_Obot__class_Obot(tc_fun(U_194,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_194),U_195),U_196))
      | ~ class_Orderings_Oorder(U_194) ),
    inference(variable_rename,[status(thm)],[f_58_1]) ).

cnf(f_58_3,plain,
    ( c_SetInterval_Oord__class_OgreaterThanLessThan(U_194,U_196,U_195) = c_Orderings_Obot__class_Obot(tc_fun(U_194,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_194),U_195),U_196))
    | ~ class_Orderings_Oorder(U_194) ),
    inference(clausify,[status(thm)],[f_58_2]) ).

fof(f_59_1,plain,
    ! [V_k_2,V_l_2,T_b] :
      ( c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_k_2))
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_greaterThanAtMost__empty]) ).

fof(f_59_2,plain,
    ! [U_199,U_198,U_197] :
      ( c_SetInterval_Oord__class_OgreaterThanAtMost(U_197,U_199,U_198) = c_Orderings_Obot__class_Obot(tc_fun(U_197,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_197),U_198),U_199))
      | ~ class_Orderings_Oorder(U_197) ),
    inference(variable_rename,[status(thm)],[f_59_1]) ).

cnf(f_59_3,plain,
    ( c_SetInterval_Oord__class_OgreaterThanAtMost(U_197,U_199,U_198) = c_Orderings_Obot__class_Obot(tc_fun(U_197,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_197),U_198),U_199))
    | ~ class_Orderings_Oorder(U_197) ),
    inference(clausify,[status(thm)],[f_59_2]) ).

fof(f_60_1,plain,
    ! [V_A_2,V_B_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_B_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Inter__anti__mono]) ).

fof(f_60_2,plain,
    ! [U_202,U_201,U_200] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_200,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_200,tc_HOL_Obool),U_202)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_200,tc_HOL_Obool),U_201)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_200,tc_HOL_Obool),tc_HOL_Obool)),U_201),U_202)) ),
    inference(variable_rename,[status(thm)],[f_60_1]) ).

cnf(f_60_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_200,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_200,tc_HOL_Obool),U_202)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_200,tc_HOL_Obool),U_201)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_200,tc_HOL_Obool),tc_HOL_Obool)),U_201),U_202)) ),
    inference(clausify,[status(thm)],[f_60_2]) ).

fof(f_61_1,plain,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2)) )
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__subset__iff]) ).

fof(f_61_2,plain,
    ! [U_207,U_206,U_205,U_204,U_203] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_203),U_205),U_207))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_203),U_206),U_204)) )
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_203),U_205),U_204))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_203,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_203,U_204),U_205)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_203,U_206),U_207)))
      | ~ class_Orderings_Olinorder(U_203) ),
    inference(variable_rename,[status(thm)],[f_61_1]) ).

cnf(f_61_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_203),U_206),U_204))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_203),U_205),U_204))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_203,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_203,U_204),U_205)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_203,U_206),U_207)))
    | ~ class_Orderings_Olinorder(U_203) ),
    inference(clausify,[status(thm)],[f_61_2]) ).

cnf(f_61_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_203),U_205),U_207))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_203),U_205),U_204))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_203,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_203,U_204),U_205)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_203,U_206),U_207)))
    | ~ class_Orderings_Olinorder(U_203) ),
    inference(clausify,[status(thm)],[f_61_2]) ).

fof(f_62_1,plain,
    ! [V_k_2,T_b] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2)
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Compl__greaterThan]) ).

fof(f_62_2,plain,
    ! [U_209,U_208] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_208,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_208),U_209)) = hAPP(c_SetInterval_Oord__class_OatMost(U_208),U_209)
      | ~ class_Orderings_Olinorder(U_208) ),
    inference(variable_rename,[status(thm)],[f_62_1]) ).

cnf(f_62_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_208,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_208),U_209)) = hAPP(c_SetInterval_Oord__class_OatMost(U_208),U_209)
    | ~ class_Orderings_Olinorder(U_208) ),
    inference(clausify,[status(thm)],[f_62_2]) ).

fof(f_63_1,plain,
    ! [V_k_2,T_b] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2)
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Compl__atMost]) ).

fof(f_63_2,plain,
    ! [U_211,U_210] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_210,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_210),U_211)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_210),U_211)
      | ~ class_Orderings_Olinorder(U_210) ),
    inference(variable_rename,[status(thm)],[f_63_1]) ).

cnf(f_63_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_210,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_210),U_211)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_210),U_211)
    | ~ class_Orderings_Olinorder(U_210) ),
    inference(clausify,[status(thm)],[f_63_2]) ).

fof(f_64_1,plain,
    ! [V_a_2,V_b_2,T_b] :
      ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2))
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__empty]) ).

fof(f_64_2,plain,
    ! [U_214,U_213,U_212] :
      ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_212,U_214),U_213) = c_Orderings_Obot__class_Obot(tc_fun(U_212,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_212),U_213),U_214))
      | ~ class_Orderings_Oorder(U_212) ),
    inference(variable_rename,[status(thm)],[f_64_1]) ).

cnf(f_64_3,plain,
    ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_212,U_214),U_213) = c_Orderings_Obot__class_Obot(tc_fun(U_212,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_212),U_213),U_214))
    | ~ class_Orderings_Oorder(U_212) ),
    inference(clausify,[status(thm)],[f_64_2]) ).

fof(f_65_1,plain,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2)) )
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2))) ) )
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_atLeastatMost__subset__iff]) ).

fof(f_65_2,plain,
    ! [U_219,U_218,U_217,U_216,U_215] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_215,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_215,U_216,U_217)),c_SetInterval_Oord__class_OatLeastAtMost(U_215,U_218,U_219)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_215),U_217),U_219))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_215),U_218),U_216)) )
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_215),U_216),U_217)) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_215),U_217),U_219))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_215),U_218),U_216)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_215),U_216),U_217))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_215,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_215,U_216,U_217)),c_SetInterval_Oord__class_OatLeastAtMost(U_215,U_218,U_219))) ) )
      | ~ class_Orderings_Oorder(U_215) ),
    inference(variable_rename,[status(thm)],[f_65_1]) ).

cnf(f_65_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_215),U_218),U_216))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_215),U_216),U_217))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_215,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_215,U_216,U_217)),c_SetInterval_Oord__class_OatLeastAtMost(U_215,U_218,U_219)))
    | ~ class_Orderings_Oorder(U_215) ),
    inference(clausify,[status(thm)],[f_65_2]) ).

cnf(f_65_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_215),U_217),U_219))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_215),U_216),U_217))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_215,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_215,U_216,U_217)),c_SetInterval_Oord__class_OatLeastAtMost(U_215,U_218,U_219)))
    | ~ class_Orderings_Oorder(U_215) ),
    inference(clausify,[status(thm)],[f_65_2]) ).

cnf(f_65_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_215),U_216),U_217))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_215,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_215,U_216,U_217)),c_SetInterval_Oord__class_OatLeastAtMost(U_215,U_218,U_219)))
    | ~ class_Orderings_Oorder(U_215) ),
    inference(clausify,[status(thm)],[f_65_2]) ).

cnf(f_65_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_215),U_217),U_219))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_215),U_218),U_216))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_215,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_215,U_216,U_217)),c_SetInterval_Oord__class_OatLeastAtMost(U_215,U_218,U_219)))
    | ~ class_Orderings_Oorder(U_215) ),
    inference(clausify,[status(thm)],[f_65_2]) ).

fof(f_66_1,plain,
    ! [V_k_2,T_b] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_k_2)
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Compl__lessThan]) ).

fof(f_66_2,plain,
    ! [U_221,U_220] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_220,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_220),U_221)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_220),U_221)
      | ~ class_Orderings_Olinorder(U_220) ),
    inference(variable_rename,[status(thm)],[f_66_1]) ).

cnf(f_66_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_220,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_220),U_221)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_220),U_221)
    | ~ class_Orderings_Olinorder(U_220) ),
    inference(clausify,[status(thm)],[f_66_2]) ).

fof(f_67_1,plain,
    ! [V_x_2,T_b] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_x_2)),
    inference(fof_nnf,[status(thm)],[fact_top1I]) ).

fof(f_67_2,plain,
    ! [U_223,U_222] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(U_222,tc_HOL_Obool)),U_223)),
    inference(variable_rename,[status(thm)],[f_67_1]) ).

cnf(f_67_3,plain,
    hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(U_222,tc_HOL_Obool)),U_223)),
    inference(clausify,[status(thm)],[f_67_2]) ).

fof(f_68_1,plain,
    ! [V_A_2,T_b] : hAPP(c_Set_OPow(T_b),V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Pow__not__empty]) ).

fof(f_68_2,plain,
    ! [U_225,U_224] : hAPP(c_Set_OPow(U_224),U_225) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_224,tc_HOL_Obool),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_68_1]) ).

cnf(f_68_3,plain,
    hAPP(c_Set_OPow(U_224),U_225) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_224,tc_HOL_Obool),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_68_2]) ).

fof(f_69_1,plain,
    ! [T_b] : hAPP(c_Set_OPow(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Pow__UNIV]) ).

fof(f_69_2,plain,
    ! [U_226] : hAPP(c_Set_OPow(U_226),c_Orderings_Otop__class_Otop(tc_fun(U_226,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_226,tc_HOL_Obool),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_69_1]) ).

cnf(f_69_3,plain,
    hAPP(c_Set_OPow(U_226),c_Orderings_Otop__class_Otop(tc_fun(U_226,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_226,tc_HOL_Obool),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_69_2]) ).

fof(f_70_1,plain,
    ! [V_A_2,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_OPow(T_b),V_A_2)) = V_A_2,
    inference(fof_nnf,[status(thm)],[fact_Union__Pow__eq]) ).

fof(f_70_2,plain,
    ! [U_228,U_227] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_227,tc_HOL_Obool),hAPP(c_Set_OPow(U_227),U_228)) = U_228,
    inference(variable_rename,[status(thm)],[f_70_1]) ).

cnf(f_70_3,plain,
    c_Complete__Lattice_OSup__class_OSup(tc_fun(U_227,tc_HOL_Obool),hAPP(c_Set_OPow(U_227),U_228)) = U_228,
    inference(clausify,[status(thm)],[f_70_2]) ).

fof(f_71_1,plain,
    ! [T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Union__UNIV]) ).

fof(f_71_2,plain,
    ! [U_229] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_229,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_229,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_229,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_71_1]) ).

cnf(f_71_3,plain,
    c_Complete__Lattice_OSup__class_OSup(tc_fun(U_229,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_229,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_229,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_71_2]) ).

fof(f_72_1,plain,
    ! [T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Inter__empty]) ).

fof(f_72_2,plain,
    ! [U_230] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_230,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_230,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_230,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_72_1]) ).

cnf(f_72_3,plain,
    c_Complete__Lattice_OInf__class_OInf(tc_fun(U_230,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_230,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_230,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_72_2]) ).

fof(f_73_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)
        | V_A_2 != V_B_2 )
      & ( V_A_2 = V_B_2
        | hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2) != hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_Compl__eq__Compl__iff]) ).

fof(f_73_2,plain,
    ! [U_233,U_232,U_231] :
      ( ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_231,tc_HOL_Obool)),U_232) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_231,tc_HOL_Obool)),U_233)
        | U_232 != U_233 )
      & ( U_232 = U_233
        | hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_231,tc_HOL_Obool)),U_232) != hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_231,tc_HOL_Obool)),U_233) ) ),
    inference(variable_rename,[status(thm)],[f_73_1]) ).

fof(f_73_3,plain,
    ( ! [U_239,U_237] :
        ( ! [U_235] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_235,tc_HOL_Obool)),U_237) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_235,tc_HOL_Obool)),U_239)
        | U_237 != U_239 )
    & ! [U_238,U_236] :
        ( ! [U_234] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_234,tc_HOL_Obool)),U_236) != hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_234,tc_HOL_Obool)),U_238)
        | U_236 = U_238 ) ),
    inference(miniscope,[status(thm)],[f_73_2]) ).

cnf(f_73_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_234,tc_HOL_Obool)),U_236) != hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_234,tc_HOL_Obool)),U_238)
    | U_236 = U_238 ),
    inference(clausify,[status(thm)],[f_73_3]) ).

cnf(f_73_5,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_235,tc_HOL_Obool)),U_237) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_235,tc_HOL_Obool)),U_239)
    | U_237 != U_239 ),
    inference(clausify,[status(thm)],[f_73_3]) ).

fof(f_74_1,plain,
    ! [V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = V_A_2,
    inference(fof_nnf,[status(thm)],[fact_double__complement]) ).

fof(f_74_2,plain,
    ! [U_241,U_240] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_240,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_240,tc_HOL_Obool)),U_241)) = U_241,
    inference(variable_rename,[status(thm)],[f_74_1]) ).

cnf(f_74_3,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_240,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_240,tc_HOL_Obool)),U_241)) = U_241,
    inference(clausify,[status(thm)],[f_74_2]) ).

fof(f_75_1,plain,
    ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)))),
    inference(fof_nnf,[status(thm)],[fact_subset__Pow__Union]) ).

fof(f_75_2,plain,
    ! [U_243,U_242] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_242,tc_HOL_Obool),tc_HOL_Obool)),U_243),hAPP(c_Set_OPow(U_242),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_242,tc_HOL_Obool),U_243)))),
    inference(variable_rename,[status(thm)],[f_75_1]) ).

cnf(f_75_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_242,tc_HOL_Obool),tc_HOL_Obool)),U_243),hAPP(c_Set_OPow(U_242),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_242,tc_HOL_Obool),U_243)))),
    inference(clausify,[status(thm)],[f_75_2]) ).

fof(f_76_1,plain,
    ! [T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Compl__UNIV__eq]) ).

fof(f_76_2,plain,
    ! [U_244] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_244,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_244,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_244,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_76_1]) ).

cnf(f_76_3,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_244,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_244,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_244,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_76_2]) ).

fof(f_77_1,plain,
    ! [T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Compl__empty__eq]) ).

fof(f_77_2,plain,
    ! [U_245] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_245,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_245,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_245,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_77_1]) ).

cnf(f_77_3,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_245,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_245,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_245,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_77_2]) ).

fof(f_78_1,plain,
    ! [T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Union__empty]) ).

fof(f_78_2,plain,
    ! [U_246] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_246,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_246,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_246,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_78_1]) ).

cnf(f_78_3,plain,
    c_Complete__Lattice_OSup__class_OSup(tc_fun(U_246,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_246,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_246,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_78_2]) ).

fof(f_79_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Compl__anti__mono]) ).

fof(f_79_2,plain,
    ! [U_249,U_248,U_247] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_247,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_247,tc_HOL_Obool)),U_249)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_247,tc_HOL_Obool)),U_248)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_247,tc_HOL_Obool)),U_248),U_249)) ),
    inference(variable_rename,[status(thm)],[f_79_1]) ).

cnf(f_79_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_247,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_247,tc_HOL_Obool)),U_249)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_247,tc_HOL_Obool)),U_248)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_247,tc_HOL_Obool)),U_248),U_249)) ),
    inference(clausify,[status(thm)],[f_79_2]) ).

fof(f_80_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_Compl__subset__Compl__iff]) ).

fof(f_80_2,plain,
    ! [U_252,U_251,U_250] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_250,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_250,tc_HOL_Obool)),U_251)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_250,tc_HOL_Obool)),U_252)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_250,tc_HOL_Obool)),U_252),U_251)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_250,tc_HOL_Obool)),U_252),U_251))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_250,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_250,tc_HOL_Obool)),U_251)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_250,tc_HOL_Obool)),U_252))) ) ),
    inference(variable_rename,[status(thm)],[f_80_1]) ).

fof(f_80_3,plain,
    ( ! [U_258,U_256,U_254] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_254,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_254,tc_HOL_Obool)),U_256)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_254,tc_HOL_Obool)),U_258)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_254,tc_HOL_Obool)),U_258),U_256)) )
    & ! [U_257,U_255,U_253] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_253,tc_HOL_Obool)),U_257),U_255))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_253,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_253,tc_HOL_Obool)),U_255)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_253,tc_HOL_Obool)),U_257))) ) ),
    inference(miniscope,[status(thm)],[f_80_2]) ).

cnf(f_80_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_253,tc_HOL_Obool)),U_257),U_255))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_253,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_253,tc_HOL_Obool)),U_255)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_253,tc_HOL_Obool)),U_257))) ),
    inference(clausify,[status(thm)],[f_80_3]) ).

cnf(f_80_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_254,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_254,tc_HOL_Obool)),U_256)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_254,tc_HOL_Obool)),U_258)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_254,tc_HOL_Obool)),U_258),U_256)) ),
    inference(clausify,[status(thm)],[f_80_3]) ).

fof(f_81_1,plain,
    ! [T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Inter__UNIV]) ).

fof(f_81_2,plain,
    ! [U_259] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_259,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_259,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_259,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_81_1]) ).

cnf(f_81_3,plain,
    c_Complete__Lattice_OInf__class_OInf(tc_fun(U_259,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_259,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_259,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_81_2]) ).

fof(f_82_1,plain,
    ! [V_b_2,V_A_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2)),V_b_2))
          | ? [B_x] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2))
              & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
        & ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2))
              | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2)),V_b_2)) ) )
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__le__iff]) ).

fof(f_82_2,plain,
    ! [U_264,U_263,U_262] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_262),c_Complete__Lattice_OSup__class_OSup(U_262,U_263)),U_264))
          | ? [U_261] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_262),U_261),U_264))
              & hBOOL(hAPP(hAPP(c_member(U_262),U_261),U_263)) ) )
        & ( ! [U_260] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_262),U_260),U_264))
              | ~ hBOOL(hAPP(hAPP(c_member(U_262),U_260),U_263)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_262),c_Complete__Lattice_OSup__class_OSup(U_262,U_263)),U_264)) ) )
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_262) ),
    inference(variable_rename,[status(thm)],[f_82_1]) ).

fof(f_82_3,plain,
    ! [U_264,U_263,U_262] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_262),c_Complete__Lattice_OSup__class_OSup(U_262,U_263)),U_264))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_262),sK4(U_264,U_263,U_262)),U_264))
            & hBOOL(hAPP(hAPP(c_member(U_262),sK4(U_264,U_263,U_262)),U_263)) ) )
        & ( ! [U_260] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_262),U_260),U_264))
              | ~ hBOOL(hAPP(hAPP(c_member(U_262),U_260),U_263)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_262),c_Complete__Lattice_OSup__class_OSup(U_262,U_263)),U_264)) ) )
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_262) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_261,sK4(U_264,U_263,U_262))],[f_82_2]) ).

cnf(f_82_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_262),U_260),U_264))
    | ~ hBOOL(hAPP(hAPP(c_member(U_262),U_260),U_263))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_262),c_Complete__Lattice_OSup__class_OSup(U_262,U_263)),U_264))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_262) ),
    inference(clausify,[status(thm)],[f_82_3]) ).

cnf(f_82_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_262),sK4(U_264,U_263,U_262)),U_263))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_262),c_Complete__Lattice_OSup__class_OSup(U_262,U_263)),U_264))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_262) ),
    inference(clausify,[status(thm)],[f_82_3]) ).

cnf(f_82_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_262),sK4(U_264,U_263,U_262)),U_264))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_262),c_Complete__Lattice_OSup__class_OSup(U_262,U_263)),U_264))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_262) ),
    inference(clausify,[status(thm)],[f_82_3]) ).

fof(f_83_1,plain,
    ! [V_A_2,V_b_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2)))
          | ? [B_x] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x))
              & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
        & ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x))
              | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2))) ) )
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_le__Inf__iff]) ).

fof(f_83_2,plain,
    ! [U_269,U_268,U_267] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_267),U_268),c_Complete__Lattice_OInf__class_OInf(U_267,U_269)))
          | ? [U_266] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_267),U_268),U_266))
              & hBOOL(hAPP(hAPP(c_member(U_267),U_266),U_269)) ) )
        & ( ! [U_265] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_267),U_268),U_265))
              | ~ hBOOL(hAPP(hAPP(c_member(U_267),U_265),U_269)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_267),U_268),c_Complete__Lattice_OInf__class_OInf(U_267,U_269))) ) )
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_267) ),
    inference(variable_rename,[status(thm)],[f_83_1]) ).

fof(f_83_3,plain,
    ! [U_269,U_268,U_267] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_267),U_268),c_Complete__Lattice_OInf__class_OInf(U_267,U_269)))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_267),U_268),sK5(U_269,U_268,U_267)))
            & hBOOL(hAPP(hAPP(c_member(U_267),sK5(U_269,U_268,U_267)),U_269)) ) )
        & ( ! [U_265] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_267),U_268),U_265))
              | ~ hBOOL(hAPP(hAPP(c_member(U_267),U_265),U_269)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_267),U_268),c_Complete__Lattice_OInf__class_OInf(U_267,U_269))) ) )
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_267) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_266,sK5(U_269,U_268,U_267))],[f_83_2]) ).

cnf(f_83_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_267),U_268),U_265))
    | ~ hBOOL(hAPP(hAPP(c_member(U_267),U_265),U_269))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_267),U_268),c_Complete__Lattice_OInf__class_OInf(U_267,U_269)))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_267) ),
    inference(clausify,[status(thm)],[f_83_3]) ).

cnf(f_83_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_267),sK5(U_269,U_268,U_267)),U_269))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_267),U_268),c_Complete__Lattice_OInf__class_OInf(U_267,U_269)))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_267) ),
    inference(clausify,[status(thm)],[f_83_3]) ).

cnf(f_83_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_267),U_268),sK5(U_269,U_268,U_267)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_267),U_268),c_Complete__Lattice_OInf__class_OInf(U_267,U_269)))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_267) ),
    inference(clausify,[status(thm)],[f_83_3]) ).

fof(f_84_1,plain,
    ! [T_b] :
      ( c_Complete__Lattice_OInf__class_OInf(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(T_b)
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__UNIV]) ).

fof(f_84_2,plain,
    ! [U_270] :
      ( c_Complete__Lattice_OInf__class_OInf(U_270,c_Orderings_Otop__class_Otop(tc_fun(U_270,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(U_270)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_270) ),
    inference(variable_rename,[status(thm)],[f_84_1]) ).

cnf(f_84_3,plain,
    ( c_Complete__Lattice_OInf__class_OInf(U_270,c_Orderings_Otop__class_Otop(tc_fun(U_270,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(U_270)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_270) ),
    inference(clausify,[status(thm)],[f_84_2]) ).

fof(f_85_1,plain,
    ! [T_b] :
      ( c_Complete__Lattice_OSup__class_OSup(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(T_b)
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__UNIV]) ).

fof(f_85_2,plain,
    ! [U_271] :
      ( c_Complete__Lattice_OSup__class_OSup(U_271,c_Orderings_Otop__class_Otop(tc_fun(U_271,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(U_271)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_271) ),
    inference(variable_rename,[status(thm)],[f_85_1]) ).

cnf(f_85_3,plain,
    ( c_Complete__Lattice_OSup__class_OSup(U_271,c_Orderings_Otop__class_Otop(tc_fun(U_271,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(U_271)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_271) ),
    inference(clausify,[status(thm)],[f_85_2]) ).

fof(f_86_1,plain,
    ! [V_A_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
        | V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
      & ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_subset__Compl__self__eq]) ).

fof(f_86_2,plain,
    ! [U_273,U_272] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_272,tc_HOL_Obool)),U_273),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_272,tc_HOL_Obool)),U_273)))
        | U_273 != c_Orderings_Obot__class_Obot(tc_fun(U_272,tc_HOL_Obool)) )
      & ( U_273 = c_Orderings_Obot__class_Obot(tc_fun(U_272,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_272,tc_HOL_Obool)),U_273),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_272,tc_HOL_Obool)),U_273))) ) ),
    inference(variable_rename,[status(thm)],[f_86_1]) ).

fof(f_86_3,plain,
    ( ! [U_277,U_275] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_275,tc_HOL_Obool)),U_277),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_275,tc_HOL_Obool)),U_277)))
        | U_277 != c_Orderings_Obot__class_Obot(tc_fun(U_275,tc_HOL_Obool)) )
    & ! [U_276,U_274] :
        ( U_276 = c_Orderings_Obot__class_Obot(tc_fun(U_274,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_274,tc_HOL_Obool)),U_276),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_274,tc_HOL_Obool)),U_276))) ) ),
    inference(miniscope,[status(thm)],[f_86_2]) ).

cnf(f_86_4,plain,
    ( U_276 = c_Orderings_Obot__class_Obot(tc_fun(U_274,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_274,tc_HOL_Obool)),U_276),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_274,tc_HOL_Obool)),U_276))) ),
    inference(clausify,[status(thm)],[f_86_3]) ).

cnf(f_86_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_275,tc_HOL_Obool)),U_277),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_275,tc_HOL_Obool)),U_277)))
    | U_277 != c_Orderings_Obot__class_Obot(tc_fun(U_275,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_86_3]) ).

fof(f_87_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Union__mono]) ).

fof(f_87_2,plain,
    ! [U_280,U_279,U_278] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_278,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_278,tc_HOL_Obool),U_279)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_278,tc_HOL_Obool),U_280)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_278,tc_HOL_Obool),tc_HOL_Obool)),U_279),U_280)) ),
    inference(variable_rename,[status(thm)],[f_87_1]) ).

cnf(f_87_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_278,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_278,tc_HOL_Obool),U_279)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_278,tc_HOL_Obool),U_280)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_278,tc_HOL_Obool),tc_HOL_Obool)),U_279),U_280)) ),
    inference(clausify,[status(thm)],[f_87_2]) ).

fof(f_88_1,plain,
    ! [V_b_2,V_a_2,T_b] :
      ( ( ( c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
          | c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) )
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_atLeastatMost__empty__iff]) ).

fof(f_88_2,plain,
    ! [U_283,U_282,U_281] :
      ( ( ( c_SetInterval_Oord__class_OatLeastAtMost(U_281,U_282,U_283) = c_Orderings_Obot__class_Obot(tc_fun(U_281,tc_HOL_Obool))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_281),U_282),U_283)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_281),U_282),U_283))
          | c_SetInterval_Oord__class_OatLeastAtMost(U_281,U_282,U_283) != c_Orderings_Obot__class_Obot(tc_fun(U_281,tc_HOL_Obool)) ) )
      | ~ class_Orderings_Oorder(U_281) ),
    inference(variable_rename,[status(thm)],[f_88_1]) ).

cnf(f_88_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_281),U_282),U_283))
    | c_SetInterval_Oord__class_OatLeastAtMost(U_281,U_282,U_283) != c_Orderings_Obot__class_Obot(tc_fun(U_281,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_281) ),
    inference(clausify,[status(thm)],[f_88_2]) ).

cnf(f_88_4,plain,
    ( c_SetInterval_Oord__class_OatLeastAtMost(U_281,U_282,U_283) = c_Orderings_Obot__class_Obot(tc_fun(U_281,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_281),U_282),U_283))
    | ~ class_Orderings_Oorder(U_281) ),
    inference(clausify,[status(thm)],[f_88_2]) ).

fof(f_89_1,plain,
    ! [V_b_2,V_a_2,T_b] :
      ( ( ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
          | c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) != c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) ) )
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_atLeastatMost__empty__iff2]) ).

fof(f_89_2,plain,
    ! [U_286,U_285,U_284] :
      ( ( ( c_Orderings_Obot__class_Obot(tc_fun(U_284,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(U_284,U_285,U_286)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_284),U_285),U_286)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_284),U_285),U_286))
          | c_Orderings_Obot__class_Obot(tc_fun(U_284,tc_HOL_Obool)) != c_SetInterval_Oord__class_OatLeastAtMost(U_284,U_285,U_286) ) )
      | ~ class_Orderings_Oorder(U_284) ),
    inference(variable_rename,[status(thm)],[f_89_1]) ).

cnf(f_89_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_284),U_285),U_286))
    | c_Orderings_Obot__class_Obot(tc_fun(U_284,tc_HOL_Obool)) != c_SetInterval_Oord__class_OatLeastAtMost(U_284,U_285,U_286)
    | ~ class_Orderings_Oorder(U_284) ),
    inference(clausify,[status(thm)],[f_89_2]) ).

cnf(f_89_4,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(U_284,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(U_284,U_285,U_286)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_284),U_285),U_286))
    | ~ class_Orderings_Oorder(U_284) ),
    inference(clausify,[status(thm)],[f_89_2]) ).

fof(f_90_1,plain,
    ! [V_k_2,T_b] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_k_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2)
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Compl__atLeast]) ).

fof(f_90_2,plain,
    ! [U_288,U_287] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_287,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_287),U_288)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_287),U_288)
      | ~ class_Orderings_Olinorder(U_287) ),
    inference(variable_rename,[status(thm)],[f_90_1]) ).

cnf(f_90_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_287,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_287),U_288)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_287),U_288)
    | ~ class_Orderings_Olinorder(U_287) ),
    inference(clausify,[status(thm)],[f_90_2]) ).

fof(f_91_1,plain,
    ! [T_a] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Otop__class_Otop(T_a)
      | ~ class_Lattices_Oboolean__algebra(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_compl__bot__eq]) ).

fof(f_91_2,plain,
    ! [U_289] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_289),c_Orderings_Obot__class_Obot(U_289)) = c_Orderings_Otop__class_Otop(U_289)
      | ~ class_Lattices_Oboolean__algebra(U_289) ),
    inference(variable_rename,[status(thm)],[f_91_1]) ).

cnf(f_91_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_289),c_Orderings_Obot__class_Obot(U_289)) = c_Orderings_Otop__class_Otop(U_289)
    | ~ class_Lattices_Oboolean__algebra(U_289) ),
    inference(clausify,[status(thm)],[f_91_2]) ).

fof(f_92_1,plain,
    ! [T_a] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Otop__class_Otop(T_a)) = c_Orderings_Obot__class_Obot(T_a)
      | ~ class_Lattices_Oboolean__algebra(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_compl__top__eq]) ).

fof(f_92_2,plain,
    ! [U_290] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_290),c_Orderings_Otop__class_Otop(U_290)) = c_Orderings_Obot__class_Obot(U_290)
      | ~ class_Lattices_Oboolean__algebra(U_290) ),
    inference(variable_rename,[status(thm)],[f_92_1]) ).

cnf(f_92_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_290),c_Orderings_Otop__class_Otop(U_290)) = c_Orderings_Obot__class_Obot(U_290)
    | ~ class_Lattices_Oboolean__algebra(U_290) ),
    inference(clausify,[status(thm)],[f_92_2]) ).

fof(f_93_1,plain,
    ! [V_x_2,V_A_2,T_c,T_b] :
      ( hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,T_b)),V_A_2),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(V_A_2,V_x_2))
      | ~ class_Groups_Ouminus(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_uminus__apply]) ).

fof(f_93_2,plain,
    ! [U_294,U_293,U_292,U_291] :
      ( hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_292,U_291)),U_293),U_294) = hAPP(c_Groups_Ouminus__class_Ouminus(U_291),hAPP(U_293,U_294))
      | ~ class_Groups_Ouminus(U_291) ),
    inference(variable_rename,[status(thm)],[f_93_1]) ).

cnf(f_93_3,plain,
    ( hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_292,U_291)),U_293),U_294) = hAPP(c_Groups_Ouminus__class_Ouminus(U_291),hAPP(U_293,U_294))
    | ~ class_Groups_Ouminus(U_291) ),
    inference(clausify,[status(thm)],[f_93_2]) ).

fof(f_94_1,plain,
    ! [V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
      | ~ class_Lattices_Oboolean__algebra(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_compl__mono]) ).

fof(f_94_2,plain,
    ! [U_297,U_296,U_295] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_295),hAPP(c_Groups_Ouminus__class_Ouminus(U_295),U_297)),hAPP(c_Groups_Ouminus__class_Ouminus(U_295),U_296)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_295),U_296),U_297))
      | ~ class_Lattices_Oboolean__algebra(U_295) ),
    inference(variable_rename,[status(thm)],[f_94_1]) ).

cnf(f_94_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_295),hAPP(c_Groups_Ouminus__class_Ouminus(U_295),U_297)),hAPP(c_Groups_Ouminus__class_Ouminus(U_295),U_296)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_295),U_296),U_297))
    | ~ class_Lattices_Oboolean__algebra(U_295) ),
    inference(clausify,[status(thm)],[f_94_2]) ).

fof(f_95_1,plain,
    ! [V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
      | ~ class_Groups_Oordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_le__imp__neg__le]) ).

fof(f_95_2,plain,
    ! [U_300,U_299,U_298] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_298),hAPP(c_Groups_Ouminus__class_Ouminus(U_298),U_300)),hAPP(c_Groups_Ouminus__class_Ouminus(U_298),U_299)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_298),U_299),U_300))
      | ~ class_Groups_Oordered__ab__group__add(U_298) ),
    inference(variable_rename,[status(thm)],[f_95_1]) ).

cnf(f_95_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_298),hAPP(c_Groups_Ouminus__class_Ouminus(U_298),U_300)),hAPP(c_Groups_Ouminus__class_Ouminus(U_298),U_299)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_298),U_299),U_300))
    | ~ class_Groups_Oordered__ab__group__add(U_298) ),
    inference(clausify,[status(thm)],[f_95_2]) ).

fof(f_96_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2))) ) )
      | ~ class_Lattices_Oboolean__algebra(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_compl__le__compl__iff]) ).

fof(f_96_2,plain,
    ! [U_303,U_302,U_301] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_301),hAPP(c_Groups_Ouminus__class_Ouminus(U_301),U_302)),hAPP(c_Groups_Ouminus__class_Ouminus(U_301),U_303)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_301),U_303),U_302)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_301),U_303),U_302))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_301),hAPP(c_Groups_Ouminus__class_Ouminus(U_301),U_302)),hAPP(c_Groups_Ouminus__class_Ouminus(U_301),U_303))) ) )
      | ~ class_Lattices_Oboolean__algebra(U_301) ),
    inference(variable_rename,[status(thm)],[f_96_1]) ).

cnf(f_96_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_301),U_303),U_302))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_301),hAPP(c_Groups_Ouminus__class_Ouminus(U_301),U_302)),hAPP(c_Groups_Ouminus__class_Ouminus(U_301),U_303)))
    | ~ class_Lattices_Oboolean__algebra(U_301) ),
    inference(clausify,[status(thm)],[f_96_2]) ).

cnf(f_96_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_301),hAPP(c_Groups_Ouminus__class_Ouminus(U_301),U_302)),hAPP(c_Groups_Ouminus__class_Ouminus(U_301),U_303)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_301),U_303),U_302))
    | ~ class_Lattices_Oboolean__algebra(U_301) ),
    inference(clausify,[status(thm)],[f_96_2]) ).

fof(f_97_1,plain,
    ! [V_a_2,V_b_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) ) )
      | ~ class_Groups_Oordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_neg__le__iff__le]) ).

fof(f_97_2,plain,
    ! [U_306,U_305,U_304] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_304),hAPP(c_Groups_Ouminus__class_Ouminus(U_304),U_305)),hAPP(c_Groups_Ouminus__class_Ouminus(U_304),U_306)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_304),U_306),U_305)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_304),U_306),U_305))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_304),hAPP(c_Groups_Ouminus__class_Ouminus(U_304),U_305)),hAPP(c_Groups_Ouminus__class_Ouminus(U_304),U_306))) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_304) ),
    inference(variable_rename,[status(thm)],[f_97_1]) ).

cnf(f_97_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_304),U_306),U_305))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_304),hAPP(c_Groups_Ouminus__class_Ouminus(U_304),U_305)),hAPP(c_Groups_Ouminus__class_Ouminus(U_304),U_306)))
    | ~ class_Groups_Oordered__ab__group__add(U_304) ),
    inference(clausify,[status(thm)],[f_97_2]) ).

cnf(f_97_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_304),hAPP(c_Groups_Ouminus__class_Ouminus(U_304),U_305)),hAPP(c_Groups_Ouminus__class_Ouminus(U_304),U_306)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_304),U_306),U_305))
    | ~ class_Groups_Oordered__ab__group__add(U_304) ),
    inference(clausify,[status(thm)],[f_97_2]) ).

fof(f_98_1,plain,
    ! [V_b_2,V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),V_a_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),V_a_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2)) ) )
      | ~ class_Groups_Oordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_minus__le__iff]) ).

fof(f_98_2,plain,
    ! [U_309,U_308,U_307] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_307),hAPP(c_Groups_Ouminus__class_Ouminus(U_307),U_308)),U_309))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_307),hAPP(c_Groups_Ouminus__class_Ouminus(U_307),U_309)),U_308)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_307),hAPP(c_Groups_Ouminus__class_Ouminus(U_307),U_309)),U_308))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_307),hAPP(c_Groups_Ouminus__class_Ouminus(U_307),U_308)),U_309)) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_307) ),
    inference(variable_rename,[status(thm)],[f_98_1]) ).

cnf(f_98_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_307),hAPP(c_Groups_Ouminus__class_Ouminus(U_307),U_309)),U_308))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_307),hAPP(c_Groups_Ouminus__class_Ouminus(U_307),U_308)),U_309))
    | ~ class_Groups_Oordered__ab__group__add(U_307) ),
    inference(clausify,[status(thm)],[f_98_2]) ).

cnf(f_98_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_307),hAPP(c_Groups_Ouminus__class_Ouminus(U_307),U_308)),U_309))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_307),hAPP(c_Groups_Ouminus__class_Ouminus(U_307),U_309)),U_308))
    | ~ class_Groups_Oordered__ab__group__add(U_307) ),
    inference(clausify,[status(thm)],[f_98_2]) ).

fof(f_99_1,plain,
    ! [V_b_2,V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2))) ) )
      | ~ class_Groups_Oordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_le__minus__iff]) ).

fof(f_99_2,plain,
    ! [U_312,U_311,U_310] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_310),U_311),hAPP(c_Groups_Ouminus__class_Ouminus(U_310),U_312)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_310),U_312),hAPP(c_Groups_Ouminus__class_Ouminus(U_310),U_311))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_310),U_312),hAPP(c_Groups_Ouminus__class_Ouminus(U_310),U_311)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_310),U_311),hAPP(c_Groups_Ouminus__class_Ouminus(U_310),U_312))) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_310) ),
    inference(variable_rename,[status(thm)],[f_99_1]) ).

cnf(f_99_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_310),U_312),hAPP(c_Groups_Ouminus__class_Ouminus(U_310),U_311)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_310),U_311),hAPP(c_Groups_Ouminus__class_Ouminus(U_310),U_312)))
    | ~ class_Groups_Oordered__ab__group__add(U_310) ),
    inference(clausify,[status(thm)],[f_99_2]) ).

cnf(f_99_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_310),U_311),hAPP(c_Groups_Ouminus__class_Ouminus(U_310),U_312)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_310),U_312),hAPP(c_Groups_Ouminus__class_Ouminus(U_310),U_311)))
    | ~ class_Groups_Oordered__ab__group__add(U_310) ),
    inference(clausify,[status(thm)],[f_99_2]) ).

fof(f_100_1,plain,
    ! [V_u_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_l_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I13_J]) ).

fof(f_100_2,plain,
    ! [U_315,U_314,U_313] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_313,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_313,U_314,U_315)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_313),U_315)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_313),U_314)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_313),U_314),U_315))
      | ~ class_Orderings_Olinorder(U_313) ),
    inference(variable_rename,[status(thm)],[f_100_1]) ).

cnf(f_100_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_313,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_313,U_314,U_315)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_313),U_315)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_313),U_314)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_313),U_314),U_315))
    | ~ class_Orderings_Olinorder(U_313) ),
    inference(clausify,[status(thm)],[f_100_2]) ).

fof(f_101_1,plain,
    ! [V_u_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_l_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_u_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I10_J]) ).

fof(f_101_2,plain,
    ! [U_318,U_317,U_316] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_316,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_316),U_317)),c_SetInterval_Oord__class_OatLeastAtMost(U_316,U_317,U_318)) = hAPP(c_SetInterval_Oord__class_OatMost(U_316),U_318)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_316),U_317),U_318))
      | ~ class_Orderings_Olinorder(U_316) ),
    inference(variable_rename,[status(thm)],[f_101_1]) ).

cnf(f_101_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_316,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_316),U_317)),c_SetInterval_Oord__class_OatLeastAtMost(U_316,U_317,U_318)) = hAPP(c_SetInterval_Oord__class_OatMost(U_316),U_318)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_316),U_317),U_318))
    | ~ class_Orderings_Olinorder(U_316) ),
    inference(clausify,[status(thm)],[f_101_2]) ).

fof(f_102_1,plain,
    ! [V_u_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I5_J]) ).

fof(f_102_2,plain,
    ! [U_321,U_320,U_319] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_319,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_319,U_320,U_321)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_319),U_321)) = c_Orderings_Obot__class_Obot(tc_fun(U_319,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_319) ),
    inference(variable_rename,[status(thm)],[f_102_1]) ).

cnf(f_102_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_319,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_319,U_320,U_321)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_319),U_321)) = c_Orderings_Obot__class_Obot(tc_fun(U_319,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_319) ),
    inference(clausify,[status(thm)],[f_102_2]) ).

fof(f_103_1,plain,
    ! [V_x_2,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(V_B_2,V_x_2))
      | hBOOL(hAPP(V_A_2,V_x_2))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_sup1E]) ).

fof(f_103_2,plain,
    ! [U_325,U_324,U_323,U_322] :
      ( hBOOL(hAPP(U_324,U_325))
      | hBOOL(hAPP(U_323,U_325))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_322,tc_HOL_Obool)),U_323),U_324),U_325)) ),
    inference(variable_rename,[status(thm)],[f_103_1]) ).

fof(f_103_3,plain,
    ! [U_325,U_324,U_323] :
      ( ! [U_322] : ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_322,tc_HOL_Obool)),U_323),U_324),U_325))
      | hBOOL(hAPP(U_324,U_325))
      | hBOOL(hAPP(U_323,U_325)) ),
    inference(miniscope,[status(thm)],[f_103_2]) ).

cnf(f_103_4,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_322,tc_HOL_Obool)),U_323),U_324),U_325))
    | hBOOL(hAPP(U_324,U_325))
    | hBOOL(hAPP(U_323,U_325)) ),
    inference(clausify,[status(thm)],[f_103_3]) ).

fof(f_104_1,plain,
    ! [T_b,V_A_2,V_x_2,V_B_2] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2))
      | ( ~ hBOOL(hAPP(V_A_2,V_x_2))
        & ~ hBOOL(hAPP(V_B_2,V_x_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_sup1CI]) ).

fof(f_104_2,plain,
    ! [U_329,U_328,U_327,U_326] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_329,tc_HOL_Obool)),U_328),U_326),U_327))
      | ( ~ hBOOL(hAPP(U_328,U_327))
        & ~ hBOOL(hAPP(U_326,U_327)) ) ),
    inference(variable_rename,[status(thm)],[f_104_1]) ).

cnf(f_104_3,plain,
    ( ~ hBOOL(hAPP(U_326,U_327))
    | hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_329,tc_HOL_Obool)),U_328),U_326),U_327)) ),
    inference(clausify,[status(thm)],[f_104_2]) ).

cnf(f_104_4,plain,
    ( ~ hBOOL(hAPP(U_328,U_327))
    | hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_329,tc_HOL_Obool)),U_328),U_326),U_327)) ),
    inference(clausify,[status(thm)],[f_104_2]) ).

fof(f_105_1,plain,
    ! [T_b,V_B_2,V_x_2,V_A_2] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2))
      | ~ hBOOL(hAPP(V_B_2,V_x_2))
      | ~ hBOOL(hAPP(V_A_2,V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_inf1I]) ).

fof(f_105_2,plain,
    ! [U_333,U_332,U_331,U_330] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_333,tc_HOL_Obool)),U_330),U_332),U_331))
      | ~ hBOOL(hAPP(U_332,U_331))
      | ~ hBOOL(hAPP(U_330,U_331)) ),
    inference(variable_rename,[status(thm)],[f_105_1]) ).

cnf(f_105_3,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_333,tc_HOL_Obool)),U_330),U_332),U_331))
    | ~ hBOOL(hAPP(U_332,U_331))
    | ~ hBOOL(hAPP(U_330,U_331)) ),
    inference(clausify,[status(thm)],[f_105_2]) ).

fof(f_106_1,plain,
    ! [V_x_2,V_B_2,V_A_2,T_b] :
      ( ( hBOOL(hAPP(V_B_2,V_x_2))
        & hBOOL(hAPP(V_A_2,V_x_2)) )
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_inf1E]) ).

fof(f_106_2,plain,
    ! [U_337,U_336,U_335,U_334] :
      ( ( hBOOL(hAPP(U_336,U_337))
        & hBOOL(hAPP(U_335,U_337)) )
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_334,tc_HOL_Obool)),U_335),U_336),U_337)) ),
    inference(variable_rename,[status(thm)],[f_106_1]) ).

fof(f_106_3,plain,
    ! [U_337,U_336,U_335] :
      ( ! [U_334] : ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_334,tc_HOL_Obool)),U_335),U_336),U_337))
      | ( hBOOL(hAPP(U_336,U_337))
        & hBOOL(hAPP(U_335,U_337)) ) ),
    inference(miniscope,[status(thm)],[f_106_2]) ).

cnf(f_106_4,plain,
    ( hBOOL(hAPP(U_335,U_337))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_334,tc_HOL_Obool)),U_335),U_336),U_337)) ),
    inference(clausify,[status(thm)],[f_106_3]) ).

cnf(f_106_5,plain,
    ( hBOOL(hAPP(U_336,U_337))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_334,tc_HOL_Obool)),U_335),U_336),U_337)) ),
    inference(clausify,[status(thm)],[f_106_3]) ).

fof(f_107_1,plain,
    ! [V_B_2,V_A_2,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_Union__Un__distrib]) ).

fof(f_107_2,plain,
    ! [U_340,U_339,U_338] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_338,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_338,tc_HOL_Obool),tc_HOL_Obool)),U_339),U_340)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_338,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_338,tc_HOL_Obool),U_339)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_338,tc_HOL_Obool),U_340)),
    inference(variable_rename,[status(thm)],[f_107_1]) ).

cnf(f_107_3,plain,
    c_Complete__Lattice_OSup__class_OSup(tc_fun(U_338,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_338,tc_HOL_Obool),tc_HOL_Obool)),U_339),U_340)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_338,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_338,tc_HOL_Obool),U_339)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_338,tc_HOL_Obool),U_340)),
    inference(clausify,[status(thm)],[f_107_2]) ).

fof(f_108_1,plain,
    ! [V_y,V_x,T_a] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y))
      | ~ class_Lattices_Oboolean__algebra(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_compl__inf]) ).

fof(f_108_2,plain,
    ! [U_343,U_342,U_341] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_341),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_341),U_342),U_343)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_341),hAPP(c_Groups_Ouminus__class_Ouminus(U_341),U_342)),hAPP(c_Groups_Ouminus__class_Ouminus(U_341),U_343))
      | ~ class_Lattices_Oboolean__algebra(U_341) ),
    inference(variable_rename,[status(thm)],[f_108_1]) ).

cnf(f_108_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_341),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_341),U_342),U_343)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_341),hAPP(c_Groups_Ouminus__class_Ouminus(U_341),U_342)),hAPP(c_Groups_Ouminus__class_Ouminus(U_341),U_343))
    | ~ class_Lattices_Oboolean__algebra(U_341) ),
    inference(clausify,[status(thm)],[f_108_2]) ).

fof(f_109_1,plain,
    ! [V_y,V_x,T_a] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y))
      | ~ class_Lattices_Oboolean__algebra(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_compl__sup]) ).

fof(f_109_2,plain,
    ! [U_346,U_345,U_344] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_344),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_344),U_345),U_346)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_344),hAPP(c_Groups_Ouminus__class_Ouminus(U_344),U_345)),hAPP(c_Groups_Ouminus__class_Ouminus(U_344),U_346))
      | ~ class_Lattices_Oboolean__algebra(U_344) ),
    inference(variable_rename,[status(thm)],[f_109_1]) ).

cnf(f_109_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_344),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_344),U_345),U_346)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_344),hAPP(c_Groups_Ouminus__class_Ouminus(U_344),U_345)),hAPP(c_Groups_Ouminus__class_Ouminus(U_344),U_346))
    | ~ class_Lattices_Oboolean__algebra(U_344) ),
    inference(clausify,[status(thm)],[f_109_2]) ).

fof(f_110_1,plain,
    ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_A_2) = V_A_2,
    inference(fof_nnf,[status(thm)],[fact_Int__absorb]) ).

fof(f_110_2,plain,
    ! [U_348,U_347] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_347,tc_HOL_Obool)),U_348),U_348) = U_348,
    inference(variable_rename,[status(thm)],[f_110_1]) ).

cnf(f_110_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_347,tc_HOL_Obool)),U_348),U_348) = U_348,
    inference(clausify,[status(thm)],[f_110_2]) ).

fof(f_111_1,plain,
    ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_A_2) = V_A_2,
    inference(fof_nnf,[status(thm)],[fact_Un__absorb]) ).

fof(f_111_2,plain,
    ! [U_350,U_349] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_349,tc_HOL_Obool)),U_350),U_350) = U_350,
    inference(variable_rename,[status(thm)],[f_111_1]) ).

cnf(f_111_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_349,tc_HOL_Obool)),U_350),U_350) = U_350,
    inference(clausify,[status(thm)],[f_111_2]) ).

fof(f_112_1,plain,
    ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2),
    inference(fof_nnf,[status(thm)],[fact_Int__commute]) ).

fof(f_112_2,plain,
    ! [U_353,U_352,U_351] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_351,tc_HOL_Obool)),U_352),U_353) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_351,tc_HOL_Obool)),U_353),U_352),
    inference(variable_rename,[status(thm)],[f_112_1]) ).

cnf(f_112_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_351,tc_HOL_Obool)),U_352),U_353) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_351,tc_HOL_Obool)),U_353),U_352),
    inference(clausify,[status(thm)],[f_112_2]) ).

fof(f_113_1,plain,
    ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2),
    inference(fof_nnf,[status(thm)],[fact_Un__commute]) ).

fof(f_113_2,plain,
    ! [U_356,U_355,U_354] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_354,tc_HOL_Obool)),U_355),U_356) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_354,tc_HOL_Obool)),U_356),U_355),
    inference(variable_rename,[status(thm)],[f_113_1]) ).

cnf(f_113_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_354,tc_HOL_Obool)),U_355),U_356) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_354,tc_HOL_Obool)),U_356),U_355),
    inference(clausify,[status(thm)],[f_113_2]) ).

fof(f_114_1,plain,
    ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),
    inference(fof_nnf,[status(thm)],[fact_Int__left__absorb]) ).

fof(f_114_2,plain,
    ! [U_359,U_358,U_357] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_357,tc_HOL_Obool)),U_358),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_357,tc_HOL_Obool)),U_358),U_359)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_357,tc_HOL_Obool)),U_358),U_359),
    inference(variable_rename,[status(thm)],[f_114_1]) ).

cnf(f_114_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_357,tc_HOL_Obool)),U_358),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_357,tc_HOL_Obool)),U_358),U_359)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_357,tc_HOL_Obool)),U_358),U_359),
    inference(clausify,[status(thm)],[f_114_2]) ).

fof(f_115_1,plain,
    ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),
    inference(fof_nnf,[status(thm)],[fact_Un__left__absorb]) ).

fof(f_115_2,plain,
    ! [U_362,U_361,U_360] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_360,tc_HOL_Obool)),U_361),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_360,tc_HOL_Obool)),U_361),U_362)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_360,tc_HOL_Obool)),U_361),U_362),
    inference(variable_rename,[status(thm)],[f_115_1]) ).

cnf(f_115_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_360,tc_HOL_Obool)),U_361),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_360,tc_HOL_Obool)),U_361),U_362)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_360,tc_HOL_Obool)),U_361),U_362),
    inference(clausify,[status(thm)],[f_115_2]) ).

fof(f_116_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),
    inference(fof_nnf,[status(thm)],[fact_Int__left__commute]) ).

fof(f_116_2,plain,
    ! [U_366,U_365,U_364,U_363] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_363,tc_HOL_Obool)),U_364),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_363,tc_HOL_Obool)),U_365),U_366)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_363,tc_HOL_Obool)),U_365),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_363,tc_HOL_Obool)),U_364),U_366)),
    inference(variable_rename,[status(thm)],[f_116_1]) ).

cnf(f_116_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_363,tc_HOL_Obool)),U_364),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_363,tc_HOL_Obool)),U_365),U_366)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_363,tc_HOL_Obool)),U_365),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_363,tc_HOL_Obool)),U_364),U_366)),
    inference(clausify,[status(thm)],[f_116_2]) ).

fof(f_117_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),
    inference(fof_nnf,[status(thm)],[fact_Un__left__commute]) ).

fof(f_117_2,plain,
    ! [U_370,U_369,U_368,U_367] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_367,tc_HOL_Obool)),U_368),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_367,tc_HOL_Obool)),U_369),U_370)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_367,tc_HOL_Obool)),U_369),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_367,tc_HOL_Obool)),U_368),U_370)),
    inference(variable_rename,[status(thm)],[f_117_1]) ).

cnf(f_117_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_367,tc_HOL_Obool)),U_368),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_367,tc_HOL_Obool)),U_369),U_370)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_367,tc_HOL_Obool)),U_369),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_367,tc_HOL_Obool)),U_368),U_370)),
    inference(clausify,[status(thm)],[f_117_2]) ).

fof(f_118_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),
    inference(fof_nnf,[status(thm)],[fact_Int__Un__distrib]) ).

fof(f_118_2,plain,
    ! [U_374,U_373,U_372,U_371] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_371,tc_HOL_Obool)),U_372),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_371,tc_HOL_Obool)),U_373),U_374)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_371,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_371,tc_HOL_Obool)),U_372),U_373)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_371,tc_HOL_Obool)),U_372),U_374)),
    inference(variable_rename,[status(thm)],[f_118_1]) ).

cnf(f_118_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_371,tc_HOL_Obool)),U_372),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_371,tc_HOL_Obool)),U_373),U_374)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_371,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_371,tc_HOL_Obool)),U_372),U_373)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_371,tc_HOL_Obool)),U_372),U_374)),
    inference(clausify,[status(thm)],[f_118_2]) ).

fof(f_119_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),
    inference(fof_nnf,[status(thm)],[fact_Un__Int__distrib]) ).

fof(f_119_2,plain,
    ! [U_378,U_377,U_376,U_375] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_375,tc_HOL_Obool)),U_376),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_375,tc_HOL_Obool)),U_377),U_378)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_375,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_375,tc_HOL_Obool)),U_376),U_377)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_375,tc_HOL_Obool)),U_376),U_378)),
    inference(variable_rename,[status(thm)],[f_119_1]) ).

cnf(f_119_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_375,tc_HOL_Obool)),U_376),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_375,tc_HOL_Obool)),U_377),U_378)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_375,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_375,tc_HOL_Obool)),U_376),U_377)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_375,tc_HOL_Obool)),U_376),U_378)),
    inference(clausify,[status(thm)],[f_119_2]) ).

fof(f_120_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)),
    inference(fof_nnf,[status(thm)],[fact_Int__assoc]) ).

fof(f_120_2,plain,
    ! [U_382,U_381,U_380,U_379] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_379,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_379,tc_HOL_Obool)),U_380),U_381)),U_382) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_379,tc_HOL_Obool)),U_380),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_379,tc_HOL_Obool)),U_381),U_382)),
    inference(variable_rename,[status(thm)],[f_120_1]) ).

cnf(f_120_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_379,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_379,tc_HOL_Obool)),U_380),U_381)),U_382) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_379,tc_HOL_Obool)),U_380),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_379,tc_HOL_Obool)),U_381),U_382)),
    inference(clausify,[status(thm)],[f_120_2]) ).

fof(f_121_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)),
    inference(fof_nnf,[status(thm)],[fact_Un__assoc]) ).

fof(f_121_2,plain,
    ! [U_386,U_385,U_384,U_383] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_383,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_383,tc_HOL_Obool)),U_384),U_385)),U_386) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_383,tc_HOL_Obool)),U_384),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_383,tc_HOL_Obool)),U_385),U_386)),
    inference(variable_rename,[status(thm)],[f_121_1]) ).

cnf(f_121_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_383,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_383,tc_HOL_Obool)),U_384),U_385)),U_386) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_383,tc_HOL_Obool)),U_384),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_383,tc_HOL_Obool)),U_385),U_386)),
    inference(clausify,[status(thm)],[f_121_2]) ).

fof(f_122_1,plain,
    ! [V_A_2,V_C_2,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_Int__Un__distrib2]) ).

fof(f_122_2,plain,
    ! [U_390,U_389,U_388,U_387] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_387,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_387,tc_HOL_Obool)),U_388),U_389)),U_390) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_387,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_387,tc_HOL_Obool)),U_388),U_390)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_387,tc_HOL_Obool)),U_389),U_390)),
    inference(variable_rename,[status(thm)],[f_122_1]) ).

cnf(f_122_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_387,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_387,tc_HOL_Obool)),U_388),U_389)),U_390) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_387,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_387,tc_HOL_Obool)),U_388),U_390)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_387,tc_HOL_Obool)),U_389),U_390)),
    inference(clausify,[status(thm)],[f_122_2]) ).

fof(f_123_1,plain,
    ! [V_A_2,V_C_2,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_Un__Int__distrib2]) ).

fof(f_123_2,plain,
    ! [U_394,U_393,U_392,U_391] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_391,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_391,tc_HOL_Obool)),U_392),U_393)),U_394) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_391,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_391,tc_HOL_Obool)),U_392),U_394)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_391,tc_HOL_Obool)),U_393),U_394)),
    inference(variable_rename,[status(thm)],[f_123_1]) ).

cnf(f_123_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_391,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_391,tc_HOL_Obool)),U_392),U_393)),U_394) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_391,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_391,tc_HOL_Obool)),U_392),U_394)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_391,tc_HOL_Obool)),U_393),U_394)),
    inference(clausify,[status(thm)],[f_123_2]) ).

fof(f_124_1,plain,
    ! [V_P_2,V_B_2,V_A_2,T_b] :
      ( ( ? [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) )
        | ( ! [B_x] :
              ( ~ hBOOL(hAPP(V_P_2,B_x))
              | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) )
          & ! [B_x] :
              ( ~ hBOOL(hAPP(V_P_2,B_x))
              | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) )
      & ( ? [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) )
        | ? [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
        | ! [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_bex__Un]) ).

fof(f_124_2,plain,
    ! [U_404,U_403,U_402,U_401] :
      ( ( ? [U_400] :
            ( hBOOL(hAPP(U_404,U_400))
            & hBOOL(hAPP(hAPP(c_member(U_401),U_400),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_401,tc_HOL_Obool)),U_402),U_403))) )
        | ( ! [U_399] :
              ( ~ hBOOL(hAPP(U_404,U_399))
              | ~ hBOOL(hAPP(hAPP(c_member(U_401),U_399),U_403)) )
          & ! [U_398] :
              ( ~ hBOOL(hAPP(U_404,U_398))
              | ~ hBOOL(hAPP(hAPP(c_member(U_401),U_398),U_402)) ) ) )
      & ( ? [U_397] :
            ( hBOOL(hAPP(U_404,U_397))
            & hBOOL(hAPP(hAPP(c_member(U_401),U_397),U_403)) )
        | ? [U_396] :
            ( hBOOL(hAPP(U_404,U_396))
            & hBOOL(hAPP(hAPP(c_member(U_401),U_396),U_402)) )
        | ! [U_395] :
            ( ~ hBOOL(hAPP(U_404,U_395))
            | ~ hBOOL(hAPP(hAPP(c_member(U_401),U_395),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_401,tc_HOL_Obool)),U_402),U_403))) ) ) ),
    inference(variable_rename,[status(thm)],[f_124_1]) ).

fof(f_124_3,plain,
    ( ! [U_412,U_410,U_408,U_406] :
        ( ? [U_400] :
            ( hBOOL(hAPP(U_412,U_400))
            & hBOOL(hAPP(hAPP(c_member(U_406),U_400),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_406,tc_HOL_Obool)),U_408),U_410))) )
        | ( ! [U_399] :
              ( ~ hBOOL(hAPP(U_412,U_399))
              | ~ hBOOL(hAPP(hAPP(c_member(U_406),U_399),U_410)) )
          & ! [U_398] :
              ( ~ hBOOL(hAPP(U_412,U_398))
              | ~ hBOOL(hAPP(hAPP(c_member(U_406),U_398),U_408)) ) ) )
    & ! [U_411,U_409,U_407,U_405] :
        ( ? [U_397] :
            ( hBOOL(hAPP(U_411,U_397))
            & hBOOL(hAPP(hAPP(c_member(U_405),U_397),U_409)) )
        | ? [U_396] :
            ( hBOOL(hAPP(U_411,U_396))
            & hBOOL(hAPP(hAPP(c_member(U_405),U_396),U_407)) )
        | ! [U_395] :
            ( ~ hBOOL(hAPP(U_411,U_395))
            | ~ hBOOL(hAPP(hAPP(c_member(U_405),U_395),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_405,tc_HOL_Obool)),U_407),U_409))) ) ) ),
    inference(miniscope,[status(thm)],[f_124_2]) ).

fof(f_124_4,plain,
    ( ! [U_412,U_410,U_408,U_406] :
        ( ? [U_400] :
            ( hBOOL(hAPP(U_412,U_400))
            & hBOOL(hAPP(hAPP(c_member(U_406),U_400),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_406,tc_HOL_Obool)),U_408),U_410))) )
        | ( ! [U_399] :
              ( ~ hBOOL(hAPP(U_412,U_399))
              | ~ hBOOL(hAPP(hAPP(c_member(U_406),U_399),U_410)) )
          & ! [U_398] :
              ( ~ hBOOL(hAPP(U_412,U_398))
              | ~ hBOOL(hAPP(hAPP(c_member(U_406),U_398),U_408)) ) ) )
    & ! [U_411,U_409,U_407,U_405] :
        ( ? [U_397] :
            ( hBOOL(hAPP(U_411,U_397))
            & hBOOL(hAPP(hAPP(c_member(U_405),U_397),U_409)) )
        | ( hBOOL(hAPP(U_411,sK6(U_411,U_409,U_407,U_405)))
          & hBOOL(hAPP(hAPP(c_member(U_405),sK6(U_411,U_409,U_407,U_405)),U_407)) )
        | ! [U_395] :
            ( ~ hBOOL(hAPP(U_411,U_395))
            | ~ hBOOL(hAPP(hAPP(c_member(U_405),U_395),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_405,tc_HOL_Obool)),U_407),U_409))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_396,sK6(U_411,U_409,U_407,U_405))],[f_124_3]) ).

fof(f_124_5,plain,
    ( ! [U_412,U_410,U_408,U_406] :
        ( ? [U_400] :
            ( hBOOL(hAPP(U_412,U_400))
            & hBOOL(hAPP(hAPP(c_member(U_406),U_400),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_406,tc_HOL_Obool)),U_408),U_410))) )
        | ( ! [U_399] :
              ( ~ hBOOL(hAPP(U_412,U_399))
              | ~ hBOOL(hAPP(hAPP(c_member(U_406),U_399),U_410)) )
          & ! [U_398] :
              ( ~ hBOOL(hAPP(U_412,U_398))
              | ~ hBOOL(hAPP(hAPP(c_member(U_406),U_398),U_408)) ) ) )
    & ! [U_411,U_409,U_407,U_405] :
        ( ( hBOOL(hAPP(U_411,sK7(U_411,U_409,U_407,U_405)))
          & hBOOL(hAPP(hAPP(c_member(U_405),sK7(U_411,U_409,U_407,U_405)),U_409)) )
        | ( hBOOL(hAPP(U_411,sK6(U_411,U_409,U_407,U_405)))
          & hBOOL(hAPP(hAPP(c_member(U_405),sK6(U_411,U_409,U_407,U_405)),U_407)) )
        | ! [U_395] :
            ( ~ hBOOL(hAPP(U_411,U_395))
            | ~ hBOOL(hAPP(hAPP(c_member(U_405),U_395),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_405,tc_HOL_Obool)),U_407),U_409))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_397,sK7(U_411,U_409,U_407,U_405))],[f_124_4]) ).

fof(f_124_6,plain,
    ( ! [U_412,U_410,U_408,U_406] :
        ( ( hBOOL(hAPP(U_412,sK8(U_412,U_410,U_408,U_406)))
          & hBOOL(hAPP(hAPP(c_member(U_406),sK8(U_412,U_410,U_408,U_406)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_406,tc_HOL_Obool)),U_408),U_410))) )
        | ( ! [U_399] :
              ( ~ hBOOL(hAPP(U_412,U_399))
              | ~ hBOOL(hAPP(hAPP(c_member(U_406),U_399),U_410)) )
          & ! [U_398] :
              ( ~ hBOOL(hAPP(U_412,U_398))
              | ~ hBOOL(hAPP(hAPP(c_member(U_406),U_398),U_408)) ) ) )
    & ! [U_411,U_409,U_407,U_405] :
        ( ( hBOOL(hAPP(U_411,sK7(U_411,U_409,U_407,U_405)))
          & hBOOL(hAPP(hAPP(c_member(U_405),sK7(U_411,U_409,U_407,U_405)),U_409)) )
        | ( hBOOL(hAPP(U_411,sK6(U_411,U_409,U_407,U_405)))
          & hBOOL(hAPP(hAPP(c_member(U_405),sK6(U_411,U_409,U_407,U_405)),U_407)) )
        | ! [U_395] :
            ( ~ hBOOL(hAPP(U_411,U_395))
            | ~ hBOOL(hAPP(hAPP(c_member(U_405),U_395),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_405,tc_HOL_Obool)),U_407),U_409))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_400,sK8(U_412,U_410,U_408,U_406))],[f_124_5]) ).

cnf(f_124_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_405),sK7(U_411,U_409,U_407,U_405)),U_409))
    | hBOOL(hAPP(hAPP(c_member(U_405),sK6(U_411,U_409,U_407,U_405)),U_407))
    | ~ hBOOL(hAPP(U_411,U_395))
    | ~ hBOOL(hAPP(hAPP(c_member(U_405),U_395),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_405,tc_HOL_Obool)),U_407),U_409))) ),
    inference(clausify,[status(thm)],[f_124_6]) ).

cnf(f_124_8,plain,
    ( hBOOL(hAPP(U_411,sK7(U_411,U_409,U_407,U_405)))
    | hBOOL(hAPP(hAPP(c_member(U_405),sK6(U_411,U_409,U_407,U_405)),U_407))
    | ~ hBOOL(hAPP(U_411,U_395))
    | ~ hBOOL(hAPP(hAPP(c_member(U_405),U_395),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_405,tc_HOL_Obool)),U_407),U_409))) ),
    inference(clausify,[status(thm)],[f_124_6]) ).

cnf(f_124_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_405),sK7(U_411,U_409,U_407,U_405)),U_409))
    | hBOOL(hAPP(U_411,sK6(U_411,U_409,U_407,U_405)))
    | ~ hBOOL(hAPP(U_411,U_395))
    | ~ hBOOL(hAPP(hAPP(c_member(U_405),U_395),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_405,tc_HOL_Obool)),U_407),U_409))) ),
    inference(clausify,[status(thm)],[f_124_6]) ).

cnf(f_124_10,plain,
    ( hBOOL(hAPP(U_411,sK7(U_411,U_409,U_407,U_405)))
    | hBOOL(hAPP(U_411,sK6(U_411,U_409,U_407,U_405)))
    | ~ hBOOL(hAPP(U_411,U_395))
    | ~ hBOOL(hAPP(hAPP(c_member(U_405),U_395),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_405,tc_HOL_Obool)),U_407),U_409))) ),
    inference(clausify,[status(thm)],[f_124_6]) ).

cnf(f_124_11,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_406),sK8(U_412,U_410,U_408,U_406)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_406,tc_HOL_Obool)),U_408),U_410)))
    | ~ hBOOL(hAPP(U_412,U_398))
    | ~ hBOOL(hAPP(hAPP(c_member(U_406),U_398),U_408)) ),
    inference(clausify,[status(thm)],[f_124_6]) ).

cnf(f_124_12,plain,
    ( hBOOL(hAPP(U_412,sK8(U_412,U_410,U_408,U_406)))
    | ~ hBOOL(hAPP(U_412,U_398))
    | ~ hBOOL(hAPP(hAPP(c_member(U_406),U_398),U_408)) ),
    inference(clausify,[status(thm)],[f_124_6]) ).

cnf(f_124_13,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_406),sK8(U_412,U_410,U_408,U_406)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_406,tc_HOL_Obool)),U_408),U_410)))
    | ~ hBOOL(hAPP(U_412,U_399))
    | ~ hBOOL(hAPP(hAPP(c_member(U_406),U_399),U_410)) ),
    inference(clausify,[status(thm)],[f_124_6]) ).

cnf(f_124_14,plain,
    ( hBOOL(hAPP(U_412,sK8(U_412,U_410,U_408,U_406)))
    | ~ hBOOL(hAPP(U_412,U_399))
    | ~ hBOOL(hAPP(hAPP(c_member(U_406),U_399),U_410)) ),
    inference(clausify,[status(thm)],[f_124_6]) ).

fof(f_125_1,plain,
    ! [V_P_2,V_B_2,V_A_2,T_b] :
      ( ( ! [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) )
        | ? [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) )
        | ? [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
      & ( ( ! [B_x] :
              ( hBOOL(hAPP(V_P_2,B_x))
              | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) )
          & ! [B_x] :
              ( hBOOL(hAPP(V_P_2,B_x))
              | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
        | ? [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_ball__Un]) ).

fof(f_125_2,plain,
    ! [U_422,U_421,U_420,U_419] :
      ( ( ! [U_418] :
            ( hBOOL(hAPP(U_422,U_418))
            | ~ hBOOL(hAPP(hAPP(c_member(U_419),U_418),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_419,tc_HOL_Obool)),U_420),U_421))) )
        | ? [U_417] :
            ( ~ hBOOL(hAPP(U_422,U_417))
            & hBOOL(hAPP(hAPP(c_member(U_419),U_417),U_421)) )
        | ? [U_416] :
            ( ~ hBOOL(hAPP(U_422,U_416))
            & hBOOL(hAPP(hAPP(c_member(U_419),U_416),U_420)) ) )
      & ( ( ! [U_415] :
              ( hBOOL(hAPP(U_422,U_415))
              | ~ hBOOL(hAPP(hAPP(c_member(U_419),U_415),U_421)) )
          & ! [U_414] :
              ( hBOOL(hAPP(U_422,U_414))
              | ~ hBOOL(hAPP(hAPP(c_member(U_419),U_414),U_420)) ) )
        | ? [U_413] :
            ( ~ hBOOL(hAPP(U_422,U_413))
            & hBOOL(hAPP(hAPP(c_member(U_419),U_413),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_419,tc_HOL_Obool)),U_420),U_421))) ) ) ),
    inference(variable_rename,[status(thm)],[f_125_1]) ).

fof(f_125_3,plain,
    ( ! [U_430,U_428,U_426,U_424] :
        ( ! [U_418] :
            ( hBOOL(hAPP(U_430,U_418))
            | ~ hBOOL(hAPP(hAPP(c_member(U_424),U_418),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_424,tc_HOL_Obool)),U_426),U_428))) )
        | ? [U_417] :
            ( ~ hBOOL(hAPP(U_430,U_417))
            & hBOOL(hAPP(hAPP(c_member(U_424),U_417),U_428)) )
        | ? [U_416] :
            ( ~ hBOOL(hAPP(U_430,U_416))
            & hBOOL(hAPP(hAPP(c_member(U_424),U_416),U_426)) ) )
    & ! [U_429,U_427,U_425,U_423] :
        ( ( ! [U_415] :
              ( hBOOL(hAPP(U_429,U_415))
              | ~ hBOOL(hAPP(hAPP(c_member(U_423),U_415),U_427)) )
          & ! [U_414] :
              ( hBOOL(hAPP(U_429,U_414))
              | ~ hBOOL(hAPP(hAPP(c_member(U_423),U_414),U_425)) ) )
        | ? [U_413] :
            ( ~ hBOOL(hAPP(U_429,U_413))
            & hBOOL(hAPP(hAPP(c_member(U_423),U_413),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_423,tc_HOL_Obool)),U_425),U_427))) ) ) ),
    inference(miniscope,[status(thm)],[f_125_2]) ).

fof(f_125_4,plain,
    ( ! [U_430,U_428,U_426,U_424] :
        ( ! [U_418] :
            ( hBOOL(hAPP(U_430,U_418))
            | ~ hBOOL(hAPP(hAPP(c_member(U_424),U_418),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_424,tc_HOL_Obool)),U_426),U_428))) )
        | ? [U_417] :
            ( ~ hBOOL(hAPP(U_430,U_417))
            & hBOOL(hAPP(hAPP(c_member(U_424),U_417),U_428)) )
        | ? [U_416] :
            ( ~ hBOOL(hAPP(U_430,U_416))
            & hBOOL(hAPP(hAPP(c_member(U_424),U_416),U_426)) ) )
    & ! [U_429,U_427,U_425,U_423] :
        ( ( ! [U_415] :
              ( hBOOL(hAPP(U_429,U_415))
              | ~ hBOOL(hAPP(hAPP(c_member(U_423),U_415),U_427)) )
          & ! [U_414] :
              ( hBOOL(hAPP(U_429,U_414))
              | ~ hBOOL(hAPP(hAPP(c_member(U_423),U_414),U_425)) ) )
        | ( ~ hBOOL(hAPP(U_429,sK9(U_429,U_427,U_425,U_423)))
          & hBOOL(hAPP(hAPP(c_member(U_423),sK9(U_429,U_427,U_425,U_423)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_423,tc_HOL_Obool)),U_425),U_427))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_413,sK9(U_429,U_427,U_425,U_423))],[f_125_3]) ).

fof(f_125_5,plain,
    ( ! [U_430,U_428,U_426,U_424] :
        ( ! [U_418] :
            ( hBOOL(hAPP(U_430,U_418))
            | ~ hBOOL(hAPP(hAPP(c_member(U_424),U_418),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_424,tc_HOL_Obool)),U_426),U_428))) )
        | ? [U_417] :
            ( ~ hBOOL(hAPP(U_430,U_417))
            & hBOOL(hAPP(hAPP(c_member(U_424),U_417),U_428)) )
        | ( ~ hBOOL(hAPP(U_430,sK10(U_430,U_428,U_426,U_424)))
          & hBOOL(hAPP(hAPP(c_member(U_424),sK10(U_430,U_428,U_426,U_424)),U_426)) ) )
    & ! [U_429,U_427,U_425,U_423] :
        ( ( ! [U_415] :
              ( hBOOL(hAPP(U_429,U_415))
              | ~ hBOOL(hAPP(hAPP(c_member(U_423),U_415),U_427)) )
          & ! [U_414] :
              ( hBOOL(hAPP(U_429,U_414))
              | ~ hBOOL(hAPP(hAPP(c_member(U_423),U_414),U_425)) ) )
        | ( ~ hBOOL(hAPP(U_429,sK9(U_429,U_427,U_425,U_423)))
          & hBOOL(hAPP(hAPP(c_member(U_423),sK9(U_429,U_427,U_425,U_423)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_423,tc_HOL_Obool)),U_425),U_427))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_416,sK10(U_430,U_428,U_426,U_424))],[f_125_4]) ).

fof(f_125_6,plain,
    ( ! [U_430,U_428,U_426,U_424] :
        ( ! [U_418] :
            ( hBOOL(hAPP(U_430,U_418))
            | ~ hBOOL(hAPP(hAPP(c_member(U_424),U_418),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_424,tc_HOL_Obool)),U_426),U_428))) )
        | ( ~ hBOOL(hAPP(U_430,sK11(U_430,U_428,U_426,U_424)))
          & hBOOL(hAPP(hAPP(c_member(U_424),sK11(U_430,U_428,U_426,U_424)),U_428)) )
        | ( ~ hBOOL(hAPP(U_430,sK10(U_430,U_428,U_426,U_424)))
          & hBOOL(hAPP(hAPP(c_member(U_424),sK10(U_430,U_428,U_426,U_424)),U_426)) ) )
    & ! [U_429,U_427,U_425,U_423] :
        ( ( ! [U_415] :
              ( hBOOL(hAPP(U_429,U_415))
              | ~ hBOOL(hAPP(hAPP(c_member(U_423),U_415),U_427)) )
          & ! [U_414] :
              ( hBOOL(hAPP(U_429,U_414))
              | ~ hBOOL(hAPP(hAPP(c_member(U_423),U_414),U_425)) ) )
        | ( ~ hBOOL(hAPP(U_429,sK9(U_429,U_427,U_425,U_423)))
          & hBOOL(hAPP(hAPP(c_member(U_423),sK9(U_429,U_427,U_425,U_423)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_423,tc_HOL_Obool)),U_425),U_427))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_417,sK11(U_430,U_428,U_426,U_424))],[f_125_5]) ).

cnf(f_125_7,plain,
    ( hBOOL(hAPP(U_429,U_414))
    | ~ hBOOL(hAPP(hAPP(c_member(U_423),U_414),U_425))
    | hBOOL(hAPP(hAPP(c_member(U_423),sK9(U_429,U_427,U_425,U_423)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_423,tc_HOL_Obool)),U_425),U_427))) ),
    inference(clausify,[status(thm)],[f_125_6]) ).

cnf(f_125_8,plain,
    ( hBOOL(hAPP(U_429,U_415))
    | ~ hBOOL(hAPP(hAPP(c_member(U_423),U_415),U_427))
    | hBOOL(hAPP(hAPP(c_member(U_423),sK9(U_429,U_427,U_425,U_423)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_423,tc_HOL_Obool)),U_425),U_427))) ),
    inference(clausify,[status(thm)],[f_125_6]) ).

cnf(f_125_9,plain,
    ( hBOOL(hAPP(U_429,U_414))
    | ~ hBOOL(hAPP(hAPP(c_member(U_423),U_414),U_425))
    | ~ hBOOL(hAPP(U_429,sK9(U_429,U_427,U_425,U_423))) ),
    inference(clausify,[status(thm)],[f_125_6]) ).

cnf(f_125_10,plain,
    ( hBOOL(hAPP(U_429,U_415))
    | ~ hBOOL(hAPP(hAPP(c_member(U_423),U_415),U_427))
    | ~ hBOOL(hAPP(U_429,sK9(U_429,U_427,U_425,U_423))) ),
    inference(clausify,[status(thm)],[f_125_6]) ).

cnf(f_125_11,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_424),sK11(U_430,U_428,U_426,U_424)),U_428))
    | hBOOL(hAPP(hAPP(c_member(U_424),sK10(U_430,U_428,U_426,U_424)),U_426))
    | hBOOL(hAPP(U_430,U_418))
    | ~ hBOOL(hAPP(hAPP(c_member(U_424),U_418),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_424,tc_HOL_Obool)),U_426),U_428))) ),
    inference(clausify,[status(thm)],[f_125_6]) ).

cnf(f_125_12,plain,
    ( ~ hBOOL(hAPP(U_430,sK11(U_430,U_428,U_426,U_424)))
    | hBOOL(hAPP(hAPP(c_member(U_424),sK10(U_430,U_428,U_426,U_424)),U_426))
    | hBOOL(hAPP(U_430,U_418))
    | ~ hBOOL(hAPP(hAPP(c_member(U_424),U_418),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_424,tc_HOL_Obool)),U_426),U_428))) ),
    inference(clausify,[status(thm)],[f_125_6]) ).

cnf(f_125_13,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_424),sK11(U_430,U_428,U_426,U_424)),U_428))
    | ~ hBOOL(hAPP(U_430,sK10(U_430,U_428,U_426,U_424)))
    | hBOOL(hAPP(U_430,U_418))
    | ~ hBOOL(hAPP(hAPP(c_member(U_424),U_418),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_424,tc_HOL_Obool)),U_426),U_428))) ),
    inference(clausify,[status(thm)],[f_125_6]) ).

cnf(f_125_14,plain,
    ( ~ hBOOL(hAPP(U_430,sK11(U_430,U_428,U_426,U_424)))
    | ~ hBOOL(hAPP(U_430,sK10(U_430,U_428,U_426,U_424)))
    | hBOOL(hAPP(U_430,U_418))
    | ~ hBOOL(hAPP(hAPP(c_member(U_424),U_418),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_424,tc_HOL_Obool)),U_426),U_428))) ),
    inference(clausify,[status(thm)],[f_125_6]) ).

fof(f_126_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_Un__Int__crazy]) ).

fof(f_126_2,plain,
    ! [U_434,U_433,U_432,U_431] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_431,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_431,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_431,tc_HOL_Obool)),U_432),U_433)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_431,tc_HOL_Obool)),U_433),U_434))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_431,tc_HOL_Obool)),U_434),U_432)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_431,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_431,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_431,tc_HOL_Obool)),U_432),U_433)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_431,tc_HOL_Obool)),U_433),U_434))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_431,tc_HOL_Obool)),U_434),U_432)),
    inference(variable_rename,[status(thm)],[f_126_1]) ).

cnf(f_126_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_431,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_431,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_431,tc_HOL_Obool)),U_432),U_433)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_431,tc_HOL_Obool)),U_433),U_434))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_431,tc_HOL_Obool)),U_434),U_432)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_431,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_431,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_431,tc_HOL_Obool)),U_432),U_433)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_431,tc_HOL_Obool)),U_433),U_434))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_431,tc_HOL_Obool)),U_434),U_432)),
    inference(clausify,[status(thm)],[f_126_2]) ).

fof(f_127_1,plain,
    ! [V_B_2,T_b,V_x_2,V_A_2] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2))
      | ~ hBOOL(hAPP(V_A_2,V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_sup1I1]) ).

fof(f_127_2,plain,
    ! [U_438,U_437,U_436,U_435] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_437,tc_HOL_Obool)),U_435),U_438),U_436))
      | ~ hBOOL(hAPP(U_435,U_436)) ),
    inference(variable_rename,[status(thm)],[f_127_1]) ).

cnf(f_127_3,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_437,tc_HOL_Obool)),U_435),U_438),U_436))
    | ~ hBOOL(hAPP(U_435,U_436)) ),
    inference(clausify,[status(thm)],[f_127_2]) ).

fof(f_128_1,plain,
    ! [V_A_2,T_b,V_x_2,V_B_2] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2))
      | ~ hBOOL(hAPP(V_B_2,V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_sup1I2]) ).

fof(f_128_2,plain,
    ! [U_442,U_441,U_440,U_439] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_441,tc_HOL_Obool)),U_442),U_439),U_440))
      | ~ hBOOL(hAPP(U_439,U_440)) ),
    inference(variable_rename,[status(thm)],[f_128_1]) ).

cnf(f_128_3,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_441,tc_HOL_Obool)),U_442),U_439),U_440))
    | ~ hBOOL(hAPP(U_439,U_440)) ),
    inference(clausify,[status(thm)],[f_128_2]) ).

fof(f_129_1,plain,
    ! [V_x_2,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(V_A_2,V_x_2))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_inf1D1]) ).

fof(f_129_2,plain,
    ! [U_446,U_445,U_444,U_443] :
      ( hBOOL(hAPP(U_444,U_446))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_443,tc_HOL_Obool)),U_444),U_445),U_446)) ),
    inference(variable_rename,[status(thm)],[f_129_1]) ).

fof(f_129_3,plain,
    ! [U_446,U_445,U_444] :
      ( ! [U_443] : ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_443,tc_HOL_Obool)),U_444),U_445),U_446))
      | hBOOL(hAPP(U_444,U_446)) ),
    inference(miniscope,[status(thm)],[f_129_2]) ).

cnf(f_129_4,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_443,tc_HOL_Obool)),U_444),U_445),U_446))
    | hBOOL(hAPP(U_444,U_446)) ),
    inference(clausify,[status(thm)],[f_129_3]) ).

fof(f_130_1,plain,
    ! [V_x_2,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(V_B_2,V_x_2))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_inf1D2]) ).

fof(f_130_2,plain,
    ! [U_450,U_449,U_448,U_447] :
      ( hBOOL(hAPP(U_449,U_450))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_447,tc_HOL_Obool)),U_448),U_449),U_450)) ),
    inference(variable_rename,[status(thm)],[f_130_1]) ).

fof(f_130_3,plain,
    ! [U_450,U_449] :
      ( ! [U_448,U_447] : ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_447,tc_HOL_Obool)),U_448),U_449),U_450))
      | hBOOL(hAPP(U_449,U_450)) ),
    inference(miniscope,[status(thm)],[f_130_2]) ).

cnf(f_130_4,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_447,tc_HOL_Obool)),U_448),U_449),U_450))
    | hBOOL(hAPP(U_449,U_450)) ),
    inference(clausify,[status(thm)],[f_130_3]) ).

fof(f_131_1,plain,
    ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
      ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,T_b)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sup__apply]) ).

fof(f_131_2,plain,
    ! [U_455,U_454,U_453,U_452,U_451] :
      ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_452,U_451)),U_453),U_454),U_455) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_451),hAPP(U_453,U_455)),hAPP(U_454,U_455))
      | ~ class_Lattices_Olattice(U_451) ),
    inference(variable_rename,[status(thm)],[f_131_1]) ).

cnf(f_131_3,plain,
    ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_452,U_451)),U_453),U_454),U_455) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_451),hAPP(U_453,U_455)),hAPP(U_454,U_455))
    | ~ class_Lattices_Olattice(U_451) ),
    inference(clausify,[status(thm)],[f_131_2]) ).

fof(f_132_1,plain,
    ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
      ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,T_b)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_inf__apply]) ).

fof(f_132_2,plain,
    ! [U_460,U_459,U_458,U_457,U_456] :
      ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_457,U_456)),U_458),U_459),U_460) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_456),hAPP(U_458,U_460)),hAPP(U_459,U_460))
      | ~ class_Lattices_Olattice(U_456) ),
    inference(variable_rename,[status(thm)],[f_132_1]) ).

cnf(f_132_3,plain,
    ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_457,U_456)),U_458),U_459),U_460) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_456),hAPP(U_458,U_460)),hAPP(U_459,U_460))
    | ~ class_Lattices_Olattice(U_456) ),
    inference(clausify,[status(thm)],[f_132_2]) ).

fof(f_133_1,plain,
    ! [V_x,V_z,V_y,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)),V_x) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_x)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_z),V_x))
      | ~ class_Lattices_Odistrib__lattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sup__inf__distrib2]) ).

fof(f_133_2,plain,
    ! [U_464,U_463,U_462,U_461] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_461),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_461),U_462),U_463)),U_464) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_461),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_461),U_462),U_464)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_461),U_463),U_464))
      | ~ class_Lattices_Odistrib__lattice(U_461) ),
    inference(variable_rename,[status(thm)],[f_133_1]) ).

cnf(f_133_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_461),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_461),U_462),U_463)),U_464) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_461),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_461),U_462),U_464)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_461),U_463),U_464))
    | ~ class_Lattices_Odistrib__lattice(U_461) ),
    inference(clausify,[status(thm)],[f_133_2]) ).

fof(f_134_1,plain,
    ! [V_x,V_z,V_y,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)),V_x) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_x)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_z),V_x))
      | ~ class_Lattices_Odistrib__lattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf__sup__distrib2]) ).

fof(f_134_2,plain,
    ! [U_468,U_467,U_466,U_465] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_465),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_465),U_466),U_467)),U_468) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_465),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_465),U_466),U_468)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_465),U_467),U_468))
      | ~ class_Lattices_Odistrib__lattice(U_465) ),
    inference(variable_rename,[status(thm)],[f_134_1]) ).

cnf(f_134_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_465),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_465),U_466),U_467)),U_468) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_465),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_465),U_466),U_468)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_465),U_467),U_468))
    | ~ class_Lattices_Odistrib__lattice(U_465) ),
    inference(clausify,[status(thm)],[f_134_2]) ).

fof(f_135_1,plain,
    ! [V_z,V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z))
      | ~ class_Lattices_Osemilattice__sup(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sup__assoc]) ).

fof(f_135_2,plain,
    ! [U_472,U_471,U_470,U_469] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_469),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_469),U_470),U_471)),U_472) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_469),U_470),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_469),U_471),U_472))
      | ~ class_Lattices_Osemilattice__sup(U_469) ),
    inference(variable_rename,[status(thm)],[f_135_1]) ).

cnf(f_135_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_469),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_469),U_470),U_471)),U_472) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_469),U_470),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_469),U_471),U_472))
    | ~ class_Lattices_Osemilattice__sup(U_469) ),
    inference(clausify,[status(thm)],[f_135_2]) ).

fof(f_136_1,plain,
    ! [V_z,V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z))
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I6_J]) ).

fof(f_136_2,plain,
    ! [U_476,U_475,U_474,U_473] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_473),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_473),U_474),U_475)),U_476) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_473),U_474),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_473),U_475),U_476))
      | ~ class_Lattices_Olattice(U_473) ),
    inference(variable_rename,[status(thm)],[f_136_1]) ).

cnf(f_136_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_473),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_473),U_474),U_475)),U_476) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_473),U_474),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_473),U_475),U_476))
    | ~ class_Lattices_Olattice(U_473) ),
    inference(clausify,[status(thm)],[f_136_2]) ).

fof(f_137_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b),V_c))
      | ~ class_Lattices_Osemilattice__sup(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sup_Oassoc]) ).

fof(f_137_2,plain,
    ! [U_480,U_479,U_478,U_477] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_477),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_477),U_478),U_479)),U_480) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_477),U_478),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_477),U_479),U_480))
      | ~ class_Lattices_Osemilattice__sup(U_477) ),
    inference(variable_rename,[status(thm)],[f_137_1]) ).

cnf(f_137_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_477),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_477),U_478),U_479)),U_480) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_477),U_478),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_477),U_479),U_480))
    | ~ class_Lattices_Osemilattice__sup(U_477) ),
    inference(clausify,[status(thm)],[f_137_2]) ).

fof(f_138_1,plain,
    ! [V_z,V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z))
      | ~ class_Lattices_Osemilattice__inf(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf__assoc]) ).

fof(f_138_2,plain,
    ! [U_484,U_483,U_482,U_481] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_481),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_481),U_482),U_483)),U_484) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_481),U_482),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_481),U_483),U_484))
      | ~ class_Lattices_Osemilattice__inf(U_481) ),
    inference(variable_rename,[status(thm)],[f_138_1]) ).

cnf(f_138_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_481),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_481),U_482),U_483)),U_484) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_481),U_482),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_481),U_483),U_484))
    | ~ class_Lattices_Osemilattice__inf(U_481) ),
    inference(clausify,[status(thm)],[f_138_2]) ).

fof(f_139_1,plain,
    ! [V_z,V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z))
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I2_J]) ).

fof(f_139_2,plain,
    ! [U_488,U_487,U_486,U_485] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_485),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_485),U_486),U_487)),U_488) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_485),U_486),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_485),U_487),U_488))
      | ~ class_Lattices_Olattice(U_485) ),
    inference(variable_rename,[status(thm)],[f_139_1]) ).

cnf(f_139_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_485),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_485),U_486),U_487)),U_488) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_485),U_486),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_485),U_487),U_488))
    | ~ class_Lattices_Olattice(U_485) ),
    inference(clausify,[status(thm)],[f_139_2]) ).

fof(f_140_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b),V_c))
      | ~ class_Lattices_Osemilattice__inf(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf_Oassoc]) ).

fof(f_140_2,plain,
    ! [U_492,U_491,U_490,U_489] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_489),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_489),U_490),U_491)),U_492) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_489),U_490),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_489),U_491),U_492))
      | ~ class_Lattices_Osemilattice__inf(U_489) ),
    inference(variable_rename,[status(thm)],[f_140_1]) ).

cnf(f_140_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_489),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_489),U_490),U_491)),U_492) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_489),U_490),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_489),U_491),U_492))
    | ~ class_Lattices_Osemilattice__inf(U_489) ),
    inference(clausify,[status(thm)],[f_140_2]) ).

fof(f_141_1,plain,
    ! [V_z,V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_z))
      | ~ class_Lattices_Odistrib__lattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sup__inf__distrib1]) ).

fof(f_141_2,plain,
    ! [U_496,U_495,U_494,U_493] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_493),U_494),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_493),U_495),U_496)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_493),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_493),U_494),U_495)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_493),U_494),U_496))
      | ~ class_Lattices_Odistrib__lattice(U_493) ),
    inference(variable_rename,[status(thm)],[f_141_1]) ).

cnf(f_141_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_493),U_494),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_493),U_495),U_496)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_493),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_493),U_494),U_495)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_493),U_494),U_496))
    | ~ class_Lattices_Odistrib__lattice(U_493) ),
    inference(clausify,[status(thm)],[f_141_2]) ).

fof(f_142_1,plain,
    ! [V_z,V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_z))
      | ~ class_Lattices_Odistrib__lattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf__sup__distrib1]) ).

fof(f_142_2,plain,
    ! [U_500,U_499,U_498,U_497] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_497),U_498),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_497),U_499),U_500)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_497),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_497),U_498),U_499)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_497),U_498),U_500))
      | ~ class_Lattices_Odistrib__lattice(U_497) ),
    inference(variable_rename,[status(thm)],[f_142_1]) ).

cnf(f_142_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_497),U_498),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_497),U_499),U_500)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_497),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_497),U_498),U_499)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_497),U_498),U_500))
    | ~ class_Lattices_Odistrib__lattice(U_497) ),
    inference(clausify,[status(thm)],[f_142_2]) ).

fof(f_143_1,plain,
    ! [V_z,V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_z))
      | ~ class_Lattices_Osemilattice__sup(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sup__left__commute]) ).

fof(f_143_2,plain,
    ! [U_504,U_503,U_502,U_501] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_501),U_502),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_501),U_503),U_504)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_501),U_503),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_501),U_502),U_504))
      | ~ class_Lattices_Osemilattice__sup(U_501) ),
    inference(variable_rename,[status(thm)],[f_143_1]) ).

cnf(f_143_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_501),U_502),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_501),U_503),U_504)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_501),U_503),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_501),U_502),U_504))
    | ~ class_Lattices_Osemilattice__sup(U_501) ),
    inference(clausify,[status(thm)],[f_143_2]) ).

fof(f_144_1,plain,
    ! [V_z,V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_z))
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I7_J]) ).

fof(f_144_2,plain,
    ! [U_508,U_507,U_506,U_505] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_505),U_506),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_505),U_507),U_508)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_505),U_507),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_505),U_506),U_508))
      | ~ class_Lattices_Olattice(U_505) ),
    inference(variable_rename,[status(thm)],[f_144_1]) ).

cnf(f_144_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_505),U_506),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_505),U_507),U_508)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_505),U_507),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_505),U_506),U_508))
    | ~ class_Lattices_Olattice(U_505) ),
    inference(clausify,[status(thm)],[f_144_2]) ).

fof(f_145_1,plain,
    ! [V_c,V_a,V_b,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_c)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b),V_c))
      | ~ class_Lattices_Osemilattice__sup(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sup_Oleft__commute]) ).

fof(f_145_2,plain,
    ! [U_512,U_511,U_510,U_509] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_509),U_510),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_509),U_511),U_512)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_509),U_511),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_509),U_510),U_512))
      | ~ class_Lattices_Osemilattice__sup(U_509) ),
    inference(variable_rename,[status(thm)],[f_145_1]) ).

cnf(f_145_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_509),U_510),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_509),U_511),U_512)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_509),U_511),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_509),U_510),U_512))
    | ~ class_Lattices_Osemilattice__sup(U_509) ),
    inference(clausify,[status(thm)],[f_145_2]) ).

fof(f_146_1,plain,
    ! [V_z,V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_z))
      | ~ class_Lattices_Osemilattice__inf(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf__left__commute]) ).

fof(f_146_2,plain,
    ! [U_516,U_515,U_514,U_513] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_513),U_514),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_513),U_515),U_516)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_513),U_515),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_513),U_514),U_516))
      | ~ class_Lattices_Osemilattice__inf(U_513) ),
    inference(variable_rename,[status(thm)],[f_146_1]) ).

cnf(f_146_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_513),U_514),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_513),U_515),U_516)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_513),U_515),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_513),U_514),U_516))
    | ~ class_Lattices_Osemilattice__inf(U_513) ),
    inference(clausify,[status(thm)],[f_146_2]) ).

fof(f_147_1,plain,
    ! [V_z,V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_z))
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I3_J]) ).

fof(f_147_2,plain,
    ! [U_520,U_519,U_518,U_517] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_517),U_518),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_517),U_519),U_520)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_517),U_519),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_517),U_518),U_520))
      | ~ class_Lattices_Olattice(U_517) ),
    inference(variable_rename,[status(thm)],[f_147_1]) ).

cnf(f_147_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_517),U_518),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_517),U_519),U_520)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_517),U_519),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_517),U_518),U_520))
    | ~ class_Lattices_Olattice(U_517) ),
    inference(clausify,[status(thm)],[f_147_2]) ).

fof(f_148_1,plain,
    ! [V_c,V_a,V_b,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_c)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b),V_c))
      | ~ class_Lattices_Osemilattice__inf(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf_Oleft__commute]) ).

fof(f_148_2,plain,
    ! [U_524,U_523,U_522,U_521] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_521),U_522),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_521),U_523),U_524)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_521),U_523),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_521),U_522),U_524))
      | ~ class_Lattices_Osemilattice__inf(U_521) ),
    inference(variable_rename,[status(thm)],[f_148_1]) ).

cnf(f_148_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_521),U_522),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_521),U_523),U_524)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_521),U_523),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_521),U_522),U_524))
    | ~ class_Lattices_Osemilattice__inf(U_521) ),
    inference(clausify,[status(thm)],[f_148_2]) ).

fof(f_149_1,plain,
    ! [V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)
      | ~ class_Lattices_Osemilattice__sup(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sup__left__idem]) ).

fof(f_149_2,plain,
    ! [U_527,U_526,U_525] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_525),U_526),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_525),U_526),U_527)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_525),U_526),U_527)
      | ~ class_Lattices_Osemilattice__sup(U_525) ),
    inference(variable_rename,[status(thm)],[f_149_1]) ).

cnf(f_149_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_525),U_526),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_525),U_526),U_527)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_525),U_526),U_527)
    | ~ class_Lattices_Osemilattice__sup(U_525) ),
    inference(clausify,[status(thm)],[f_149_2]) ).

fof(f_150_1,plain,
    ! [V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I8_J]) ).

fof(f_150_2,plain,
    ! [U_530,U_529,U_528] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_528),U_529),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_528),U_529),U_530)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_528),U_529),U_530)
      | ~ class_Lattices_Olattice(U_528) ),
    inference(variable_rename,[status(thm)],[f_150_1]) ).

cnf(f_150_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_528),U_529),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_528),U_529),U_530)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_528),U_529),U_530)
    | ~ class_Lattices_Olattice(U_528) ),
    inference(clausify,[status(thm)],[f_150_2]) ).

fof(f_151_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)
      | ~ class_Lattices_Osemilattice__sup(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sup_Oleft__idem]) ).

fof(f_151_2,plain,
    ! [U_533,U_532,U_531] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_531),U_532),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_531),U_532),U_533)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_531),U_532),U_533)
      | ~ class_Lattices_Osemilattice__sup(U_531) ),
    inference(variable_rename,[status(thm)],[f_151_1]) ).

cnf(f_151_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_531),U_532),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_531),U_532),U_533)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_531),U_532),U_533)
    | ~ class_Lattices_Osemilattice__sup(U_531) ),
    inference(clausify,[status(thm)],[f_151_2]) ).

fof(f_152_1,plain,
    ! [V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)
      | ~ class_Lattices_Osemilattice__inf(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf__left__idem]) ).

fof(f_152_2,plain,
    ! [U_536,U_535,U_534] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_534),U_535),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_534),U_535),U_536)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_534),U_535),U_536)
      | ~ class_Lattices_Osemilattice__inf(U_534) ),
    inference(variable_rename,[status(thm)],[f_152_1]) ).

cnf(f_152_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_534),U_535),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_534),U_535),U_536)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_534),U_535),U_536)
    | ~ class_Lattices_Osemilattice__inf(U_534) ),
    inference(clausify,[status(thm)],[f_152_2]) ).

fof(f_153_1,plain,
    ! [V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I4_J]) ).

fof(f_153_2,plain,
    ! [U_539,U_538,U_537] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_537),U_538),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_537),U_538),U_539)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_537),U_538),U_539)
      | ~ class_Lattices_Olattice(U_537) ),
    inference(variable_rename,[status(thm)],[f_153_1]) ).

cnf(f_153_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_537),U_538),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_537),U_538),U_539)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_537),U_538),U_539)
    | ~ class_Lattices_Olattice(U_537) ),
    inference(clausify,[status(thm)],[f_153_2]) ).

fof(f_154_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)
      | ~ class_Lattices_Osemilattice__inf(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf_Oleft__idem]) ).

fof(f_154_2,plain,
    ! [U_542,U_541,U_540] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_540),U_541),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_540),U_541),U_542)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_540),U_541),U_542)
      | ~ class_Lattices_Osemilattice__inf(U_540) ),
    inference(variable_rename,[status(thm)],[f_154_1]) ).

cnf(f_154_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_540),U_541),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_540),U_541),U_542)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_540),U_541),U_542)
    | ~ class_Lattices_Osemilattice__inf(U_540) ),
    inference(clausify,[status(thm)],[f_154_2]) ).

fof(f_155_1,plain,
    ! [V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)) = V_x
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sup__inf__absorb]) ).

fof(f_155_2,plain,
    ! [U_545,U_544,U_543] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_543),U_544),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_543),U_544),U_545)) = U_544
      | ~ class_Lattices_Olattice(U_543) ),
    inference(variable_rename,[status(thm)],[f_155_1]) ).

cnf(f_155_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_543),U_544),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_543),U_544),U_545)) = U_544
    | ~ class_Lattices_Olattice(U_543) ),
    inference(clausify,[status(thm)],[f_155_2]) ).

fof(f_156_1,plain,
    ! [V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)) = V_x
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf__sup__absorb]) ).

fof(f_156_2,plain,
    ! [U_548,U_547,U_546] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_546),U_547),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_546),U_547),U_548)) = U_547
      | ~ class_Lattices_Olattice(U_546) ),
    inference(variable_rename,[status(thm)],[f_156_1]) ).

cnf(f_156_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_546),U_547),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_546),U_547),U_548)) = U_547
    | ~ class_Lattices_Olattice(U_546) ),
    inference(clausify,[status(thm)],[f_156_2]) ).

fof(f_157_1,plain,
    ! [V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_x)
      | ~ class_Lattices_Osemilattice__sup(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sup__commute]) ).

fof(f_157_2,plain,
    ! [U_551,U_550,U_549] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_549),U_550),U_551) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_549),U_551),U_550)
      | ~ class_Lattices_Osemilattice__sup(U_549) ),
    inference(variable_rename,[status(thm)],[f_157_1]) ).

cnf(f_157_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_549),U_550),U_551) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_549),U_551),U_550)
    | ~ class_Lattices_Osemilattice__sup(U_549) ),
    inference(clausify,[status(thm)],[f_157_2]) ).

fof(f_158_1,plain,
    ! [V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_x)
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I5_J]) ).

fof(f_158_2,plain,
    ! [U_554,U_553,U_552] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_552),U_553),U_554) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_552),U_554),U_553)
      | ~ class_Lattices_Olattice(U_552) ),
    inference(variable_rename,[status(thm)],[f_158_1]) ).

cnf(f_158_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_552),U_553),U_554) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_552),U_554),U_553)
    | ~ class_Lattices_Olattice(U_552) ),
    inference(clausify,[status(thm)],[f_158_2]) ).

fof(f_159_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b),V_a)
      | ~ class_Lattices_Osemilattice__sup(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sup_Ocommute]) ).

fof(f_159_2,plain,
    ! [U_557,U_556,U_555] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_555),U_556),U_557) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_555),U_557),U_556)
      | ~ class_Lattices_Osemilattice__sup(U_555) ),
    inference(variable_rename,[status(thm)],[f_159_1]) ).

cnf(f_159_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_555),U_556),U_557) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_555),U_557),U_556)
    | ~ class_Lattices_Osemilattice__sup(U_555) ),
    inference(clausify,[status(thm)],[f_159_2]) ).

fof(f_160_1,plain,
    ! [V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_x)
      | ~ class_Lattices_Osemilattice__inf(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf__commute]) ).

fof(f_160_2,plain,
    ! [U_560,U_559,U_558] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_558),U_559),U_560) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_558),U_560),U_559)
      | ~ class_Lattices_Osemilattice__inf(U_558) ),
    inference(variable_rename,[status(thm)],[f_160_1]) ).

cnf(f_160_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_558),U_559),U_560) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_558),U_560),U_559)
    | ~ class_Lattices_Osemilattice__inf(U_558) ),
    inference(clausify,[status(thm)],[f_160_2]) ).

fof(f_161_1,plain,
    ! [V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_x)
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I1_J]) ).

fof(f_161_2,plain,
    ! [U_563,U_562,U_561] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_561),U_562),U_563) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_561),U_563),U_562)
      | ~ class_Lattices_Olattice(U_561) ),
    inference(variable_rename,[status(thm)],[f_161_1]) ).

cnf(f_161_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_561),U_562),U_563) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_561),U_563),U_562)
    | ~ class_Lattices_Olattice(U_561) ),
    inference(clausify,[status(thm)],[f_161_2]) ).

fof(f_162_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b),V_a)
      | ~ class_Lattices_Osemilattice__inf(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf_Ocommute]) ).

fof(f_162_2,plain,
    ! [U_566,U_565,U_564] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_564),U_565),U_566) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_564),U_566),U_565)
      | ~ class_Lattices_Osemilattice__inf(U_564) ),
    inference(variable_rename,[status(thm)],[f_162_1]) ).

cnf(f_162_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_564),U_565),U_566) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_564),U_566),U_565)
    | ~ class_Lattices_Osemilattice__inf(U_564) ),
    inference(clausify,[status(thm)],[f_162_2]) ).

fof(f_163_1,plain,
    ! [V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x
      | ~ class_Lattices_Osemilattice__sup(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sup__idem]) ).

fof(f_163_2,plain,
    ! [U_568,U_567] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_567),U_568),U_568) = U_568
      | ~ class_Lattices_Osemilattice__sup(U_567) ),
    inference(variable_rename,[status(thm)],[f_163_1]) ).

cnf(f_163_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_567),U_568),U_568) = U_568
    | ~ class_Lattices_Osemilattice__sup(U_567) ),
    inference(clausify,[status(thm)],[f_163_2]) ).

fof(f_164_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_a) = V_a
      | ~ class_Lattices_Osemilattice__sup(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sup_Oidem]) ).

fof(f_164_2,plain,
    ! [U_570,U_569] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_569),U_570),U_570) = U_570
      | ~ class_Lattices_Osemilattice__sup(U_569) ),
    inference(variable_rename,[status(thm)],[f_164_1]) ).

cnf(f_164_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_569),U_570),U_570) = U_570
    | ~ class_Lattices_Osemilattice__sup(U_569) ),
    inference(clausify,[status(thm)],[f_164_2]) ).

fof(f_165_1,plain,
    ! [V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x
      | ~ class_Lattices_Osemilattice__inf(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf__idem]) ).

fof(f_165_2,plain,
    ! [U_572,U_571] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_571),U_572),U_572) = U_572
      | ~ class_Lattices_Osemilattice__inf(U_571) ),
    inference(variable_rename,[status(thm)],[f_165_1]) ).

cnf(f_165_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_571),U_572),U_572) = U_572
    | ~ class_Lattices_Osemilattice__inf(U_571) ),
    inference(clausify,[status(thm)],[f_165_2]) ).

fof(f_166_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_a) = V_a
      | ~ class_Lattices_Osemilattice__inf(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf_Oidem]) ).

fof(f_166_2,plain,
    ! [U_574,U_573] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_573),U_574),U_574) = U_574
      | ~ class_Lattices_Osemilattice__inf(U_573) ),
    inference(variable_rename,[status(thm)],[f_166_1]) ).

cnf(f_166_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_573),U_574),U_574) = U_574
    | ~ class_Lattices_Osemilattice__inf(U_573) ),
    inference(clausify,[status(thm)],[f_166_2]) ).

fof(f_167_1,plain,
    ! [V_z,V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_z))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z))))
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_distrib__inf__le]) ).

fof(f_167_2,plain,
    ! [U_578,U_577,U_576,U_575] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_575),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_575),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_575),U_576),U_577)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_575),U_576),U_578))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_575),U_576),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_575),U_577),U_578))))
      | ~ class_Lattices_Olattice(U_575) ),
    inference(variable_rename,[status(thm)],[f_167_1]) ).

cnf(f_167_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_575),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_575),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_575),U_576),U_577)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_575),U_576),U_578))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_575),U_576),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_575),U_577),U_578))))
    | ~ class_Lattices_Olattice(U_575) ),
    inference(clausify,[status(thm)],[f_167_2]) ).

fof(f_168_1,plain,
    ! [V_z,V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_z))))
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_distrib__sup__le]) ).

fof(f_168_2,plain,
    ! [U_582,U_581,U_580,U_579] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_579),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_579),U_580),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_579),U_581),U_582))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_579),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_579),U_580),U_581)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_579),U_580),U_582))))
      | ~ class_Lattices_Olattice(U_579) ),
    inference(variable_rename,[status(thm)],[f_168_1]) ).

cnf(f_168_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_579),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_579),U_580),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_579),U_581),U_582))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_579),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_579),U_580),U_581)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_579),U_580),U_582))))
    | ~ class_Lattices_Olattice(U_579) ),
    inference(clausify,[status(thm)],[f_168_2]) ).

fof(f_169_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_b] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Un__Int__assoc__eq]) ).

fof(f_169_2,plain,
    ! [U_586,U_585,U_584,U_583] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_583,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_583,tc_HOL_Obool)),U_584),U_585)),U_586) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_583,tc_HOL_Obool)),U_584),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_583,tc_HOL_Obool)),U_585),U_586))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_583,tc_HOL_Obool)),U_586),U_584)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_583,tc_HOL_Obool)),U_586),U_584))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_583,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_583,tc_HOL_Obool)),U_584),U_585)),U_586) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_583,tc_HOL_Obool)),U_584),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_583,tc_HOL_Obool)),U_585),U_586)) ) ),
    inference(variable_rename,[status(thm)],[f_169_1]) ).

fof(f_169_3,plain,
    ( ! [U_594,U_592,U_590,U_588] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_588,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_588,tc_HOL_Obool)),U_590),U_592)),U_594) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_588,tc_HOL_Obool)),U_590),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_588,tc_HOL_Obool)),U_592),U_594))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_588,tc_HOL_Obool)),U_594),U_590)) )
    & ! [U_593,U_591,U_589,U_587] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_587,tc_HOL_Obool)),U_593),U_589))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_587,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_587,tc_HOL_Obool)),U_589),U_591)),U_593) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_587,tc_HOL_Obool)),U_589),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_587,tc_HOL_Obool)),U_591),U_593)) ) ),
    inference(miniscope,[status(thm)],[f_169_2]) ).

cnf(f_169_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_587,tc_HOL_Obool)),U_593),U_589))
    | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_587,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_587,tc_HOL_Obool)),U_589),U_591)),U_593) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_587,tc_HOL_Obool)),U_589),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_587,tc_HOL_Obool)),U_591),U_593)) ),
    inference(clausify,[status(thm)],[f_169_3]) ).

cnf(f_169_5,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_588,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_588,tc_HOL_Obool)),U_590),U_592)),U_594) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_588,tc_HOL_Obool)),U_590),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_588,tc_HOL_Obool)),U_592),U_594))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_588,tc_HOL_Obool)),U_594),U_590)) ),
    inference(clausify,[status(thm)],[f_169_3]) ).

fof(f_170_1,plain,
    ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)))),
    inference(fof_nnf,[status(thm)],[fact_Union__Int__subset]) ).

fof(f_170_2,plain,
    ! [U_597,U_596,U_595] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_595,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_595,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_595,tc_HOL_Obool),tc_HOL_Obool)),U_596),U_597))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_595,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_595,tc_HOL_Obool),U_596)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_595,tc_HOL_Obool),U_597)))),
    inference(variable_rename,[status(thm)],[f_170_1]) ).

cnf(f_170_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_595,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_595,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_595,tc_HOL_Obool),tc_HOL_Obool)),U_596),U_597))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_595,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_595,tc_HOL_Obool),U_596)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_595,tc_HOL_Obool),U_597)))),
    inference(clausify,[status(thm)],[f_170_2]) ).

fof(f_171_1,plain,
    ! [V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)))
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf__sup__ord_I3_J]) ).

fof(f_171_2,plain,
    ! [U_600,U_599,U_598] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_598),U_599),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_598),U_599),U_600)))
      | ~ class_Lattices_Olattice(U_598) ),
    inference(variable_rename,[status(thm)],[f_171_1]) ).

cnf(f_171_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_598),U_599),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_598),U_599),U_600)))
    | ~ class_Lattices_Olattice(U_598) ),
    inference(clausify,[status(thm)],[f_171_2]) ).

fof(f_172_1,plain,
    ! [V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)))
      | ~ class_Lattices_Osemilattice__sup(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sup__ge1]) ).

fof(f_172_2,plain,
    ! [U_603,U_602,U_601] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_601),U_602),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_601),U_602),U_603)))
      | ~ class_Lattices_Osemilattice__sup(U_601) ),
    inference(variable_rename,[status(thm)],[f_172_1]) ).

cnf(f_172_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_601),U_602),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_601),U_602),U_603)))
    | ~ class_Lattices_Osemilattice__sup(U_601) ),
    inference(clausify,[status(thm)],[f_172_2]) ).

fof(f_173_1,plain,
    ! [V_x,V_y,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)))
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf__sup__ord_I4_J]) ).

fof(f_173_2,plain,
    ! [U_606,U_605,U_604] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_604),U_605),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_604),U_606),U_605)))
      | ~ class_Lattices_Olattice(U_604) ),
    inference(variable_rename,[status(thm)],[f_173_1]) ).

cnf(f_173_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_604),U_605),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_604),U_606),U_605)))
    | ~ class_Lattices_Olattice(U_604) ),
    inference(clausify,[status(thm)],[f_173_2]) ).

fof(f_174_1,plain,
    ! [V_x,V_y,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)))
      | ~ class_Lattices_Osemilattice__sup(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sup__ge2]) ).

fof(f_174_2,plain,
    ! [U_609,U_608,U_607] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_607),U_608),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_607),U_609),U_608)))
      | ~ class_Lattices_Osemilattice__sup(U_607) ),
    inference(variable_rename,[status(thm)],[f_174_1]) ).

cnf(f_174_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_607),U_608),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_607),U_609),U_608)))
    | ~ class_Lattices_Osemilattice__sup(U_607) ),
    inference(clausify,[status(thm)],[f_174_2]) ).

fof(f_175_1,plain,
    ! [V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_x))
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf__sup__ord_I1_J]) ).

fof(f_175_2,plain,
    ! [U_612,U_611,U_610] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_610),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_610),U_611),U_612)),U_611))
      | ~ class_Lattices_Olattice(U_610) ),
    inference(variable_rename,[status(thm)],[f_175_1]) ).

cnf(f_175_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_610),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_610),U_611),U_612)),U_611))
    | ~ class_Lattices_Olattice(U_610) ),
    inference(clausify,[status(thm)],[f_175_2]) ).

fof(f_176_1,plain,
    ! [V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_x))
      | ~ class_Lattices_Osemilattice__inf(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf__le1]) ).

fof(f_176_2,plain,
    ! [U_615,U_614,U_613] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_613),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_613),U_614),U_615)),U_614))
      | ~ class_Lattices_Osemilattice__inf(U_613) ),
    inference(variable_rename,[status(thm)],[f_176_1]) ).

cnf(f_176_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_613),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_613),U_614),U_615)),U_614))
    | ~ class_Lattices_Osemilattice__inf(U_613) ),
    inference(clausify,[status(thm)],[f_176_2]) ).

fof(f_177_1,plain,
    ! [V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_y))
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf__sup__ord_I2_J]) ).

fof(f_177_2,plain,
    ! [U_618,U_617,U_616] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_616),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_616),U_617),U_618)),U_618))
      | ~ class_Lattices_Olattice(U_616) ),
    inference(variable_rename,[status(thm)],[f_177_1]) ).

cnf(f_177_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_616),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_616),U_617),U_618)),U_618))
    | ~ class_Lattices_Olattice(U_616) ),
    inference(clausify,[status(thm)],[f_177_2]) ).

fof(f_178_1,plain,
    ! [V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_y))
      | ~ class_Lattices_Osemilattice__inf(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf__le2]) ).

fof(f_178_2,plain,
    ! [U_621,U_620,U_619] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_619),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_619),U_620),U_621)),U_621))
      | ~ class_Lattices_Osemilattice__inf(U_619) ),
    inference(variable_rename,[status(thm)],[f_178_1]) ).

cnf(f_178_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_619),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_619),U_620),U_621)),U_621))
    | ~ class_Lattices_Osemilattice__inf(U_619) ),
    inference(clausify,[status(thm)],[f_178_2]) ).

fof(f_179_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
          | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) != V_x_2 )
        & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) = V_x_2
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) )
      | ~ class_Lattices_Osemilattice__inf(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_le__iff__inf]) ).

fof(f_179_2,plain,
    ! [U_624,U_623,U_622] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_622),U_623),U_624))
          | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_622),U_623),U_624) != U_623 )
        & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_622),U_623),U_624) = U_623
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_622),U_623),U_624)) ) )
      | ~ class_Lattices_Osemilattice__inf(U_622) ),
    inference(variable_rename,[status(thm)],[f_179_1]) ).

cnf(f_179_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_622),U_623),U_624) = U_623
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_622),U_623),U_624))
    | ~ class_Lattices_Osemilattice__inf(U_622) ),
    inference(clausify,[status(thm)],[f_179_2]) ).

cnf(f_179_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_622),U_623),U_624))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_622),U_623),U_624) != U_623
    | ~ class_Lattices_Osemilattice__inf(U_622) ),
    inference(clausify,[status(thm)],[f_179_2]) ).

fof(f_180_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
          | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) != V_y_2 )
        & ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) = V_y_2
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) )
      | ~ class_Lattices_Osemilattice__sup(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_le__iff__sup]) ).

fof(f_180_2,plain,
    ! [U_627,U_626,U_625] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_625),U_626),U_627))
          | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_625),U_626),U_627) != U_627 )
        & ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_625),U_626),U_627) = U_627
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_625),U_626),U_627)) ) )
      | ~ class_Lattices_Osemilattice__sup(U_625) ),
    inference(variable_rename,[status(thm)],[f_180_1]) ).

cnf(f_180_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_625),U_626),U_627) = U_627
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_625),U_626),U_627))
    | ~ class_Lattices_Osemilattice__sup(U_625) ),
    inference(clausify,[status(thm)],[f_180_2]) ).

cnf(f_180_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_625),U_626),U_627))
    | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_625),U_626),U_627) != U_627
    | ~ class_Lattices_Osemilattice__sup(U_625) ),
    inference(clausify,[status(thm)],[f_180_2]) ).

fof(f_181_1,plain,
    ! [V_z_2,V_y_2,V_x_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_y_2),V_z_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_y_2),V_z_2))) ) )
      | ~ class_Lattices_Osemilattice__inf(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_le__inf__iff]) ).

fof(f_181_2,plain,
    ! [U_631,U_630,U_629,U_628] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_628),U_629),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_628),U_630),U_631)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_628),U_629),U_631))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_628),U_629),U_630)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_628),U_629),U_631))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_628),U_629),U_630)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_628),U_629),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_628),U_630),U_631))) ) )
      | ~ class_Lattices_Osemilattice__inf(U_628) ),
    inference(variable_rename,[status(thm)],[f_181_1]) ).

cnf(f_181_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_628),U_629),U_630))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_628),U_629),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_628),U_630),U_631)))
    | ~ class_Lattices_Osemilattice__inf(U_628) ),
    inference(clausify,[status(thm)],[f_181_2]) ).

cnf(f_181_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_628),U_629),U_631))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_628),U_629),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_628),U_630),U_631)))
    | ~ class_Lattices_Osemilattice__inf(U_628) ),
    inference(clausify,[status(thm)],[f_181_2]) ).

cnf(f_181_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_628),U_629),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_628),U_630),U_631)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_628),U_629),U_631))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_628),U_629),U_630))
    | ~ class_Lattices_Osemilattice__inf(U_628) ),
    inference(clausify,[status(thm)],[f_181_2]) ).

fof(f_182_1,plain,
    ! [V_z_2,V_y_2,V_x_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2)),V_z_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2)),V_z_2)) ) )
      | ~ class_Lattices_Osemilattice__sup(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_le__sup__iff]) ).

fof(f_182_2,plain,
    ! [U_635,U_634,U_633,U_632] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_632),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_632),U_633),U_634)),U_635))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_632),U_634),U_635))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_632),U_633),U_635)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_632),U_634),U_635))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_632),U_633),U_635)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_632),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_632),U_633),U_634)),U_635)) ) )
      | ~ class_Lattices_Osemilattice__sup(U_632) ),
    inference(variable_rename,[status(thm)],[f_182_1]) ).

cnf(f_182_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_632),U_633),U_635))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_632),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_632),U_633),U_634)),U_635))
    | ~ class_Lattices_Osemilattice__sup(U_632) ),
    inference(clausify,[status(thm)],[f_182_2]) ).

cnf(f_182_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_632),U_634),U_635))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_632),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_632),U_633),U_634)),U_635))
    | ~ class_Lattices_Osemilattice__sup(U_632) ),
    inference(clausify,[status(thm)],[f_182_2]) ).

cnf(f_182_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_632),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_632),U_633),U_634)),U_635))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_632),U_634),U_635))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_632),U_633),U_635))
    | ~ class_Lattices_Osemilattice__sup(U_632) ),
    inference(clausify,[status(thm)],[f_182_2]) ).

fof(f_183_1,plain,
    ! [V_b,V_a,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
      | ~ class_Lattices_Osemilattice__sup(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_le__supI1]) ).

fof(f_183_2,plain,
    ! [U_639,U_638,U_637,U_636] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_636),U_637),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_636),U_638),U_639)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_636),U_637),U_638))
      | ~ class_Lattices_Osemilattice__sup(U_636) ),
    inference(variable_rename,[status(thm)],[f_183_1]) ).

cnf(f_183_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_636),U_637),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_636),U_638),U_639)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_636),U_637),U_638))
    | ~ class_Lattices_Osemilattice__sup(U_636) ),
    inference(clausify,[status(thm)],[f_183_2]) ).

fof(f_184_1,plain,
    ! [V_a,V_b,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
      | ~ class_Lattices_Osemilattice__sup(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_le__supI2]) ).

fof(f_184_2,plain,
    ! [U_643,U_642,U_641,U_640] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_640),U_641),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_640),U_643),U_642)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_640),U_641),U_642))
      | ~ class_Lattices_Osemilattice__sup(U_640) ),
    inference(variable_rename,[status(thm)],[f_184_1]) ).

cnf(f_184_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_640),U_641),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_640),U_643),U_642)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_640),U_641),U_642))
    | ~ class_Lattices_Osemilattice__sup(U_640) ),
    inference(clausify,[status(thm)],[f_184_2]) ).

fof(f_185_1,plain,
    ! [V_b,V_x,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
      | ~ class_Lattices_Osemilattice__inf(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_le__infI1]) ).

fof(f_185_2,plain,
    ! [U_647,U_646,U_645,U_644] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_644),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_644),U_645),U_647)),U_646))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_644),U_645),U_646))
      | ~ class_Lattices_Osemilattice__inf(U_644) ),
    inference(variable_rename,[status(thm)],[f_185_1]) ).

cnf(f_185_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_644),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_644),U_645),U_647)),U_646))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_644),U_645),U_646))
    | ~ class_Lattices_Osemilattice__inf(U_644) ),
    inference(clausify,[status(thm)],[f_185_2]) ).

fof(f_186_1,plain,
    ! [V_a,V_x,V_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
      | ~ class_Lattices_Osemilattice__inf(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_le__infI2]) ).

fof(f_186_2,plain,
    ! [U_651,U_650,U_649,U_648] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_648),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_648),U_651),U_649)),U_650))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_648),U_649),U_650))
      | ~ class_Lattices_Osemilattice__inf(U_648) ),
    inference(variable_rename,[status(thm)],[f_186_1]) ).

cnf(f_186_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_648),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_648),U_651),U_649)),U_650))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_648),U_649),U_650))
    | ~ class_Lattices_Osemilattice__inf(U_648) ),
    inference(clausify,[status(thm)],[f_186_2]) ).

fof(f_187_1,plain,
    ! [V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_x
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
      | ~ class_Lattices_Osemilattice__inf(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf__absorb1]) ).

fof(f_187_2,plain,
    ! [U_654,U_653,U_652] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_652),U_653),U_654) = U_653
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_652),U_653),U_654))
      | ~ class_Lattices_Osemilattice__inf(U_652) ),
    inference(variable_rename,[status(thm)],[f_187_1]) ).

cnf(f_187_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_652),U_653),U_654) = U_653
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_652),U_653),U_654))
    | ~ class_Lattices_Osemilattice__inf(U_652) ),
    inference(clausify,[status(thm)],[f_187_2]) ).

fof(f_188_1,plain,
    ! [V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_y
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
      | ~ class_Lattices_Osemilattice__sup(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sup__absorb2]) ).

fof(f_188_2,plain,
    ! [U_657,U_656,U_655] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_655),U_656),U_657) = U_657
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_655),U_656),U_657))
      | ~ class_Lattices_Osemilattice__sup(U_655) ),
    inference(variable_rename,[status(thm)],[f_188_1]) ).

cnf(f_188_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_655),U_656),U_657) = U_657
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_655),U_656),U_657))
    | ~ class_Lattices_Osemilattice__sup(U_655) ),
    inference(clausify,[status(thm)],[f_188_2]) ).

fof(f_189_1,plain,
    ! [V_x,V_y,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_y
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
      | ~ class_Lattices_Osemilattice__inf(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf__absorb2]) ).

fof(f_189_2,plain,
    ! [U_660,U_659,U_658] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_658),U_660),U_659) = U_659
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_658),U_659),U_660))
      | ~ class_Lattices_Osemilattice__inf(U_658) ),
    inference(variable_rename,[status(thm)],[f_189_1]) ).

cnf(f_189_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_658),U_660),U_659) = U_659
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_658),U_659),U_660))
    | ~ class_Lattices_Osemilattice__inf(U_658) ),
    inference(clausify,[status(thm)],[f_189_2]) ).

fof(f_190_1,plain,
    ! [V_x,V_y,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_x
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
      | ~ class_Lattices_Osemilattice__sup(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sup__absorb1]) ).

fof(f_190_2,plain,
    ! [U_663,U_662,U_661] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_661),U_663),U_662) = U_663
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_661),U_662),U_663))
      | ~ class_Lattices_Osemilattice__sup(U_661) ),
    inference(variable_rename,[status(thm)],[f_190_1]) ).

cnf(f_190_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_661),U_663),U_662) = U_663
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_661),U_662),U_663))
    | ~ class_Lattices_Osemilattice__sup(U_661) ),
    inference(clausify,[status(thm)],[f_190_2]) ).

fof(f_191_1,plain,
    ! [V_b,V_a,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
      | ~ class_Lattices_Osemilattice__inf(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_le__infI]) ).

fof(f_191_2,plain,
    ! [U_667,U_666,U_665,U_664] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_664),U_665),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_664),U_666),U_667)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_664),U_665),U_667))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_664),U_665),U_666))
      | ~ class_Lattices_Osemilattice__inf(U_664) ),
    inference(variable_rename,[status(thm)],[f_191_1]) ).

cnf(f_191_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_664),U_665),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_664),U_666),U_667)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_664),U_665),U_667))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_664),U_665),U_666))
    | ~ class_Lattices_Osemilattice__inf(U_664) ),
    inference(clausify,[status(thm)],[f_191_2]) ).

fof(f_192_1,plain,
    ! [V_z,V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
      | ~ class_Lattices_Osemilattice__inf(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf__greatest]) ).

fof(f_192_2,plain,
    ! [U_671,U_670,U_669,U_668] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_668),U_669),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_668),U_670),U_671)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_668),U_669),U_671))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_668),U_669),U_670))
      | ~ class_Lattices_Osemilattice__inf(U_668) ),
    inference(variable_rename,[status(thm)],[f_192_1]) ).

cnf(f_192_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_668),U_669),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_668),U_670),U_671)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_668),U_669),U_671))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_668),U_669),U_670))
    | ~ class_Lattices_Osemilattice__inf(U_668) ),
    inference(clausify,[status(thm)],[f_192_2]) ).

fof(f_193_1,plain,
    ! [V_b,V_x,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
      | ~ class_Lattices_Osemilattice__sup(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_le__supI]) ).

fof(f_193_2,plain,
    ! [U_675,U_674,U_673,U_672] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_672),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_672),U_673),U_675)),U_674))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_672),U_675),U_674))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_672),U_673),U_674))
      | ~ class_Lattices_Osemilattice__sup(U_672) ),
    inference(variable_rename,[status(thm)],[f_193_1]) ).

cnf(f_193_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_672),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_672),U_673),U_675)),U_674))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_672),U_675),U_674))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_672),U_673),U_674))
    | ~ class_Lattices_Osemilattice__sup(U_672) ),
    inference(clausify,[status(thm)],[f_193_2]) ).

fof(f_194_1,plain,
    ! [V_z,V_x,V_y,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
      | ~ class_Lattices_Osemilattice__sup(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sup__least]) ).

fof(f_194_2,plain,
    ! [U_679,U_678,U_677,U_676] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_676),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_676),U_677),U_679)),U_678))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_676),U_679),U_678))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_676),U_677),U_678))
      | ~ class_Lattices_Osemilattice__sup(U_676) ),
    inference(variable_rename,[status(thm)],[f_194_1]) ).

cnf(f_194_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_676),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_676),U_677),U_679)),U_678))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_676),U_679),U_678))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_676),U_677),U_678))
    | ~ class_Lattices_Osemilattice__sup(U_676) ),
    inference(clausify,[status(thm)],[f_194_2]) ).

fof(f_195_1,plain,
    ! [V_d,V_b,V_c,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_c),V_d)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
      | ~ class_Lattices_Osemilattice__inf(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf__mono]) ).

fof(f_195_2,plain,
    ! [U_684,U_683,U_682,U_681,U_680] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_680),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_680),U_681),U_683)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_680),U_682),U_684)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_680),U_683),U_684))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_680),U_681),U_682))
      | ~ class_Lattices_Osemilattice__inf(U_680) ),
    inference(variable_rename,[status(thm)],[f_195_1]) ).

cnf(f_195_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_680),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_680),U_681),U_683)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_680),U_682),U_684)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_680),U_683),U_684))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_680),U_681),U_682))
    | ~ class_Lattices_Osemilattice__inf(U_680) ),
    inference(clausify,[status(thm)],[f_195_2]) ).

fof(f_196_1,plain,
    ! [V_d,V_b,V_c,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_c),V_d)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
      | ~ class_Lattices_Osemilattice__sup(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sup__mono]) ).

fof(f_196_2,plain,
    ! [U_689,U_688,U_687,U_686,U_685] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_685),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_685),U_686),U_688)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_685),U_687),U_689)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_685),U_688),U_689))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_685),U_686),U_687))
      | ~ class_Lattices_Osemilattice__sup(U_685) ),
    inference(variable_rename,[status(thm)],[f_196_1]) ).

cnf(f_196_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_685),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_685),U_686),U_688)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_685),U_687),U_689)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_685),U_688),U_689))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_685),U_686),U_687))
    | ~ class_Lattices_Osemilattice__sup(U_685) ),
    inference(clausify,[status(thm)],[f_196_2]) ).

fof(f_197_1,plain,
    ! [V_b,V_a,V_x,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)))
      | ~ class_Lattices_Osemilattice__inf(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_le__infE]) ).

fof(f_197_2,plain,
    ! [U_693,U_692,U_691,U_690] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_690),U_691),U_693))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_690),U_691),U_692)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_690),U_691),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_690),U_692),U_693)))
      | ~ class_Lattices_Osemilattice__inf(U_690) ),
    inference(variable_rename,[status(thm)],[f_197_1]) ).

cnf(f_197_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_690),U_691),U_692))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_690),U_691),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_690),U_692),U_693)))
    | ~ class_Lattices_Osemilattice__inf(U_690) ),
    inference(clausify,[status(thm)],[f_197_2]) ).

cnf(f_197_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_690),U_691),U_693))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_690),U_691),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_690),U_692),U_693)))
    | ~ class_Lattices_Osemilattice__inf(U_690) ),
    inference(clausify,[status(thm)],[f_197_2]) ).

fof(f_198_1,plain,
    ! [V_x,V_b,V_a,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)),V_x))
      | ~ class_Lattices_Osemilattice__sup(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_le__supE]) ).

fof(f_198_2,plain,
    ! [U_697,U_696,U_695,U_694] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_694),U_696),U_697))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_694),U_695),U_697)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_694),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_694),U_695),U_696)),U_697))
      | ~ class_Lattices_Osemilattice__sup(U_694) ),
    inference(variable_rename,[status(thm)],[f_198_1]) ).

cnf(f_198_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_694),U_695),U_697))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_694),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_694),U_695),U_696)),U_697))
    | ~ class_Lattices_Osemilattice__sup(U_694) ),
    inference(clausify,[status(thm)],[f_198_2]) ).

cnf(f_198_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_694),U_696),U_697))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_694),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_694),U_695),U_696)),U_697))
    | ~ class_Lattices_Osemilattice__sup(U_694) ),
    inference(clausify,[status(thm)],[f_198_2]) ).

fof(f_199_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) = c_Orderings_Obot__class_Obot(T_b)
          | V_y_2 != c_Orderings_Obot__class_Obot(T_b)
          | V_x_2 != c_Orderings_Obot__class_Obot(T_b) )
        & ( ( V_y_2 = c_Orderings_Obot__class_Obot(T_b)
            & V_x_2 = c_Orderings_Obot__class_Obot(T_b) )
          | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) != c_Orderings_Obot__class_Obot(T_b) ) )
      | ~ class_Lattices_Obounded__lattice__bot(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sup__eq__bot__iff]) ).

fof(f_199_2,plain,
    ! [U_700,U_699,U_698] :
      ( ( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_698),U_699),U_700) = c_Orderings_Obot__class_Obot(U_698)
          | U_700 != c_Orderings_Obot__class_Obot(U_698)
          | U_699 != c_Orderings_Obot__class_Obot(U_698) )
        & ( ( U_700 = c_Orderings_Obot__class_Obot(U_698)
            & U_699 = c_Orderings_Obot__class_Obot(U_698) )
          | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_698),U_699),U_700) != c_Orderings_Obot__class_Obot(U_698) ) )
      | ~ class_Lattices_Obounded__lattice__bot(U_698) ),
    inference(variable_rename,[status(thm)],[f_199_1]) ).

cnf(f_199_3,plain,
    ( U_699 = c_Orderings_Obot__class_Obot(U_698)
    | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_698),U_699),U_700) != c_Orderings_Obot__class_Obot(U_698)
    | ~ class_Lattices_Obounded__lattice__bot(U_698) ),
    inference(clausify,[status(thm)],[f_199_2]) ).

cnf(f_199_4,plain,
    ( U_700 = c_Orderings_Obot__class_Obot(U_698)
    | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_698),U_699),U_700) != c_Orderings_Obot__class_Obot(U_698)
    | ~ class_Lattices_Obounded__lattice__bot(U_698) ),
    inference(clausify,[status(thm)],[f_199_2]) ).

cnf(f_199_5,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_698),U_699),U_700) = c_Orderings_Obot__class_Obot(U_698)
    | U_700 != c_Orderings_Obot__class_Obot(U_698)
    | U_699 != c_Orderings_Obot__class_Obot(U_698)
    | ~ class_Lattices_Obounded__lattice__bot(U_698) ),
    inference(clausify,[status(thm)],[f_199_2]) ).

fof(f_200_1,plain,
    ! [V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)) = V_x
      | ~ class_Lattices_Obounded__lattice__bot(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sup__bot__right]) ).

fof(f_200_2,plain,
    ! [U_702,U_701] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_701),U_702),c_Orderings_Obot__class_Obot(U_701)) = U_702
      | ~ class_Lattices_Obounded__lattice__bot(U_701) ),
    inference(variable_rename,[status(thm)],[f_200_1]) ).

cnf(f_200_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_701),U_702),c_Orderings_Obot__class_Obot(U_701)) = U_702
    | ~ class_Lattices_Obounded__lattice__bot(U_701) ),
    inference(clausify,[status(thm)],[f_200_2]) ).

fof(f_201_1,plain,
    ! [V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Obot__class_Obot(T_a)
      | ~ class_Lattices_Obounded__lattice__bot(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf__bot__right]) ).

fof(f_201_2,plain,
    ! [U_704,U_703] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_703),U_704),c_Orderings_Obot__class_Obot(U_703)) = c_Orderings_Obot__class_Obot(U_703)
      | ~ class_Lattices_Obounded__lattice__bot(U_703) ),
    inference(variable_rename,[status(thm)],[f_201_1]) ).

cnf(f_201_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_703),U_704),c_Orderings_Obot__class_Obot(U_703)) = c_Orderings_Obot__class_Obot(U_703)
    | ~ class_Lattices_Obounded__lattice__bot(U_703) ),
    inference(clausify,[status(thm)],[f_201_2]) ).

fof(f_202_1,plain,
    ! [V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = V_x
      | ~ class_Lattices_Obounded__lattice__bot(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sup__bot__left]) ).

fof(f_202_2,plain,
    ! [U_706,U_705] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_705),c_Orderings_Obot__class_Obot(U_705)),U_706) = U_706
      | ~ class_Lattices_Obounded__lattice__bot(U_705) ),
    inference(variable_rename,[status(thm)],[f_202_1]) ).

cnf(f_202_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_705),c_Orderings_Obot__class_Obot(U_705)),U_706) = U_706
    | ~ class_Lattices_Obounded__lattice__bot(U_705) ),
    inference(clausify,[status(thm)],[f_202_2]) ).

fof(f_203_1,plain,
    ! [V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = c_Orderings_Obot__class_Obot(T_a)
      | ~ class_Lattices_Obounded__lattice__bot(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf__bot__left]) ).

fof(f_203_2,plain,
    ! [U_708,U_707] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_707),c_Orderings_Obot__class_Obot(U_707)),U_708) = c_Orderings_Obot__class_Obot(U_707)
      | ~ class_Lattices_Obounded__lattice__bot(U_707) ),
    inference(variable_rename,[status(thm)],[f_203_1]) ).

cnf(f_203_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_707),c_Orderings_Obot__class_Obot(U_707)),U_708) = c_Orderings_Obot__class_Obot(U_707)
    | ~ class_Lattices_Obounded__lattice__bot(U_707) ),
    inference(clausify,[status(thm)],[f_203_2]) ).

fof(f_204_1,plain,
    ! [V_B_2,V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_Compl__Int]) ).

fof(f_204_2,plain,
    ! [U_711,U_710,U_709] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_709,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_709,tc_HOL_Obool)),U_710),U_711)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_709,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_709,tc_HOL_Obool)),U_710)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_709,tc_HOL_Obool)),U_711)),
    inference(variable_rename,[status(thm)],[f_204_1]) ).

cnf(f_204_3,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_709,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_709,tc_HOL_Obool)),U_710),U_711)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_709,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_709,tc_HOL_Obool)),U_710)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_709,tc_HOL_Obool)),U_711)),
    inference(clausify,[status(thm)],[f_204_2]) ).

fof(f_205_1,plain,
    ! [V_B_2,V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_Compl__Un]) ).

fof(f_205_2,plain,
    ! [U_714,U_713,U_712] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_712,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_712,tc_HOL_Obool)),U_713),U_714)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_712,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_712,tc_HOL_Obool)),U_713)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_712,tc_HOL_Obool)),U_714)),
    inference(variable_rename,[status(thm)],[f_205_1]) ).

cnf(f_205_3,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_712,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_712,tc_HOL_Obool)),U_713),U_714)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_712,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_712,tc_HOL_Obool)),U_713)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_712,tc_HOL_Obool)),U_714)),
    inference(clausify,[status(thm)],[f_205_2]) ).

fof(f_206_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) = c_Orderings_Otop__class_Otop(T_b)
          | V_y_2 != c_Orderings_Otop__class_Otop(T_b)
          | V_x_2 != c_Orderings_Otop__class_Otop(T_b) )
        & ( ( V_y_2 = c_Orderings_Otop__class_Otop(T_b)
            & V_x_2 = c_Orderings_Otop__class_Otop(T_b) )
          | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) != c_Orderings_Otop__class_Otop(T_b) ) )
      | ~ class_Lattices_Obounded__lattice__top(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_inf__eq__top__iff]) ).

fof(f_206_2,plain,
    ! [U_717,U_716,U_715] :
      ( ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_715),U_716),U_717) = c_Orderings_Otop__class_Otop(U_715)
          | U_717 != c_Orderings_Otop__class_Otop(U_715)
          | U_716 != c_Orderings_Otop__class_Otop(U_715) )
        & ( ( U_717 = c_Orderings_Otop__class_Otop(U_715)
            & U_716 = c_Orderings_Otop__class_Otop(U_715) )
          | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_715),U_716),U_717) != c_Orderings_Otop__class_Otop(U_715) ) )
      | ~ class_Lattices_Obounded__lattice__top(U_715) ),
    inference(variable_rename,[status(thm)],[f_206_1]) ).

cnf(f_206_3,plain,
    ( U_716 = c_Orderings_Otop__class_Otop(U_715)
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_715),U_716),U_717) != c_Orderings_Otop__class_Otop(U_715)
    | ~ class_Lattices_Obounded__lattice__top(U_715) ),
    inference(clausify,[status(thm)],[f_206_2]) ).

cnf(f_206_4,plain,
    ( U_717 = c_Orderings_Otop__class_Otop(U_715)
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_715),U_716),U_717) != c_Orderings_Otop__class_Otop(U_715)
    | ~ class_Lattices_Obounded__lattice__top(U_715) ),
    inference(clausify,[status(thm)],[f_206_2]) ).

cnf(f_206_5,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_715),U_716),U_717) = c_Orderings_Otop__class_Otop(U_715)
    | U_717 != c_Orderings_Otop__class_Otop(U_715)
    | U_716 != c_Orderings_Otop__class_Otop(U_715)
    | ~ class_Lattices_Obounded__lattice__top(U_715) ),
    inference(clausify,[status(thm)],[f_206_2]) ).

fof(f_207_1,plain,
    ! [V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)) = V_x
      | ~ class_Lattices_Obounded__lattice__top(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf__top__right]) ).

fof(f_207_2,plain,
    ! [U_719,U_718] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_718),U_719),c_Orderings_Otop__class_Otop(U_718)) = U_719
      | ~ class_Lattices_Obounded__lattice__top(U_718) ),
    inference(variable_rename,[status(thm)],[f_207_1]) ).

cnf(f_207_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_718),U_719),c_Orderings_Otop__class_Otop(U_718)) = U_719
    | ~ class_Lattices_Obounded__lattice__top(U_718) ),
    inference(clausify,[status(thm)],[f_207_2]) ).

fof(f_208_1,plain,
    ! [V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)) = c_Orderings_Otop__class_Otop(T_a)
      | ~ class_Lattices_Obounded__lattice__top(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sup__top__right]) ).

fof(f_208_2,plain,
    ! [U_721,U_720] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_720),U_721),c_Orderings_Otop__class_Otop(U_720)) = c_Orderings_Otop__class_Otop(U_720)
      | ~ class_Lattices_Obounded__lattice__top(U_720) ),
    inference(variable_rename,[status(thm)],[f_208_1]) ).

cnf(f_208_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_720),U_721),c_Orderings_Otop__class_Otop(U_720)) = c_Orderings_Otop__class_Otop(U_720)
    | ~ class_Lattices_Obounded__lattice__top(U_720) ),
    inference(clausify,[status(thm)],[f_208_2]) ).

fof(f_209_1,plain,
    ! [V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Otop__class_Otop(T_a)),V_x) = V_x
      | ~ class_Lattices_Obounded__lattice__top(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf__top__left]) ).

fof(f_209_2,plain,
    ! [U_723,U_722] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_722),c_Orderings_Otop__class_Otop(U_722)),U_723) = U_723
      | ~ class_Lattices_Obounded__lattice__top(U_722) ),
    inference(variable_rename,[status(thm)],[f_209_1]) ).

cnf(f_209_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_722),c_Orderings_Otop__class_Otop(U_722)),U_723) = U_723
    | ~ class_Lattices_Obounded__lattice__top(U_722) ),
    inference(clausify,[status(thm)],[f_209_2]) ).

fof(f_210_1,plain,
    ! [V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Orderings_Otop__class_Otop(T_a)),V_x) = c_Orderings_Otop__class_Otop(T_a)
      | ~ class_Lattices_Obounded__lattice__top(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sup__top__left]) ).

fof(f_210_2,plain,
    ! [U_725,U_724] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_724),c_Orderings_Otop__class_Otop(U_724)),U_725) = c_Orderings_Otop__class_Otop(U_724)
      | ~ class_Lattices_Obounded__lattice__top(U_724) ),
    inference(variable_rename,[status(thm)],[f_210_1]) ).

cnf(f_210_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_724),c_Orderings_Otop__class_Otop(U_724)),U_725) = c_Orderings_Otop__class_Otop(U_724)
    | ~ class_Lattices_Obounded__lattice__top(U_724) ),
    inference(clausify,[status(thm)],[f_210_2]) ).

fof(f_211_1,plain,
    ! [V_B_2,V_A_2,T_b] : hAPP(c_Set_OPow(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)),hAPP(c_Set_OPow(T_b),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_Pow__Int__eq]) ).

fof(f_211_2,plain,
    ! [U_728,U_727,U_726] : hAPP(c_Set_OPow(U_726),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_726,tc_HOL_Obool)),U_727),U_728)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_726,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_726),U_727)),hAPP(c_Set_OPow(U_726),U_728)),
    inference(variable_rename,[status(thm)],[f_211_1]) ).

cnf(f_211_3,plain,
    hAPP(c_Set_OPow(U_726),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_726,tc_HOL_Obool)),U_727),U_728)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_726,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_726),U_727)),hAPP(c_Set_OPow(U_726),U_728)),
    inference(clausify,[status(thm)],[f_211_2]) ).

fof(f_212_1,plain,
    ! [V_B_2,V_A_2,T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_Inter__Un__distrib]) ).

fof(f_212_2,plain,
    ! [U_731,U_730,U_729] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_729,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_729,tc_HOL_Obool),tc_HOL_Obool)),U_730),U_731)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_729,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_729,tc_HOL_Obool),U_730)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_729,tc_HOL_Obool),U_731)),
    inference(variable_rename,[status(thm)],[f_212_1]) ).

cnf(f_212_3,plain,
    c_Complete__Lattice_OInf__class_OInf(tc_fun(U_729,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_729,tc_HOL_Obool),tc_HOL_Obool)),U_730),U_731)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_729,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_729,tc_HOL_Obool),U_730)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_729,tc_HOL_Obool),U_731)),
    inference(clausify,[status(thm)],[f_212_2]) ).

fof(f_213_1,plain,
    ! [V_y,V_x,T_a] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) = V_y
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) != c_Orderings_Otop__class_Otop(T_a)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) != c_Orderings_Obot__class_Obot(T_a)
      | ~ class_Lattices_Oboolean__algebra(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_compl__unique]) ).

fof(f_213_2,plain,
    ! [U_734,U_733,U_732] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_732),U_733) = U_734
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_732),U_733),U_734) != c_Orderings_Otop__class_Otop(U_732)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_732),U_733),U_734) != c_Orderings_Obot__class_Obot(U_732)
      | ~ class_Lattices_Oboolean__algebra(U_732) ),
    inference(variable_rename,[status(thm)],[f_213_1]) ).

cnf(f_213_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_732),U_733) = U_734
    | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_732),U_733),U_734) != c_Orderings_Otop__class_Otop(U_732)
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_732),U_733),U_734) != c_Orderings_Obot__class_Obot(U_732)
    | ~ class_Lattices_Oboolean__algebra(U_732) ),
    inference(clausify,[status(thm)],[f_213_2]) ).

fof(f_214_1,plain,
    ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2))),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)))),
    inference(fof_nnf,[status(thm)],[fact_Inter__Un__subset]) ).

fof(f_214_2,plain,
    ! [U_737,U_736,U_735] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_735,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_735,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_735,tc_HOL_Obool),U_736)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_735,tc_HOL_Obool),U_737))),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_735,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_735,tc_HOL_Obool),tc_HOL_Obool)),U_736),U_737)))),
    inference(variable_rename,[status(thm)],[f_214_1]) ).

cnf(f_214_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_735,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_735,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_735,tc_HOL_Obool),U_736)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_735,tc_HOL_Obool),U_737))),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_735,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_735,tc_HOL_Obool),tc_HOL_Obool)),U_736),U_737)))),
    inference(clausify,[status(thm)],[f_214_2]) ).

fof(f_215_1,plain,
    ! [V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = V_B_2,
    inference(fof_nnf,[status(thm)],[fact_Un__empty__left]) ).

fof(f_215_2,plain,
    ! [U_739,U_738] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_738,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_738,tc_HOL_Obool))),U_739) = U_739,
    inference(variable_rename,[status(thm)],[f_215_1]) ).

cnf(f_215_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_738,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_738,tc_HOL_Obool))),U_739) = U_739,
    inference(clausify,[status(thm)],[f_215_2]) ).

fof(f_216_1,plain,
    ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_A_2,
    inference(fof_nnf,[status(thm)],[fact_Un__empty__right]) ).

fof(f_216_2,plain,
    ! [U_741,U_740] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_740,tc_HOL_Obool)),U_741),c_Orderings_Obot__class_Obot(tc_fun(U_740,tc_HOL_Obool))) = U_741,
    inference(variable_rename,[status(thm)],[f_216_1]) ).

cnf(f_216_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_740,tc_HOL_Obool)),U_741),c_Orderings_Obot__class_Obot(tc_fun(U_740,tc_HOL_Obool))) = U_741,
    inference(clausify,[status(thm)],[f_216_2]) ).

fof(f_217_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
        | V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
        | V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
      & ( ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
          & V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Un__empty]) ).

fof(f_217_2,plain,
    ! [U_744,U_743,U_742] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_742,tc_HOL_Obool)),U_743),U_744) = c_Orderings_Obot__class_Obot(tc_fun(U_742,tc_HOL_Obool))
        | U_744 != c_Orderings_Obot__class_Obot(tc_fun(U_742,tc_HOL_Obool))
        | U_743 != c_Orderings_Obot__class_Obot(tc_fun(U_742,tc_HOL_Obool)) )
      & ( ( U_744 = c_Orderings_Obot__class_Obot(tc_fun(U_742,tc_HOL_Obool))
          & U_743 = c_Orderings_Obot__class_Obot(tc_fun(U_742,tc_HOL_Obool)) )
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_742,tc_HOL_Obool)),U_743),U_744) != c_Orderings_Obot__class_Obot(tc_fun(U_742,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_217_1]) ).

fof(f_217_3,plain,
    ( ! [U_750,U_748,U_746] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_746,tc_HOL_Obool)),U_748),U_750) = c_Orderings_Obot__class_Obot(tc_fun(U_746,tc_HOL_Obool))
        | U_750 != c_Orderings_Obot__class_Obot(tc_fun(U_746,tc_HOL_Obool))
        | U_748 != c_Orderings_Obot__class_Obot(tc_fun(U_746,tc_HOL_Obool)) )
    & ! [U_749,U_747,U_745] :
        ( ( U_749 = c_Orderings_Obot__class_Obot(tc_fun(U_745,tc_HOL_Obool))
          & U_747 = c_Orderings_Obot__class_Obot(tc_fun(U_745,tc_HOL_Obool)) )
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_745,tc_HOL_Obool)),U_747),U_749) != c_Orderings_Obot__class_Obot(tc_fun(U_745,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_217_2]) ).

cnf(f_217_4,plain,
    ( U_747 = c_Orderings_Obot__class_Obot(tc_fun(U_745,tc_HOL_Obool))
    | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_745,tc_HOL_Obool)),U_747),U_749) != c_Orderings_Obot__class_Obot(tc_fun(U_745,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_217_3]) ).

cnf(f_217_5,plain,
    ( U_749 = c_Orderings_Obot__class_Obot(tc_fun(U_745,tc_HOL_Obool))
    | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_745,tc_HOL_Obool)),U_747),U_749) != c_Orderings_Obot__class_Obot(tc_fun(U_745,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_217_3]) ).

cnf(f_217_6,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_746,tc_HOL_Obool)),U_748),U_750) = c_Orderings_Obot__class_Obot(tc_fun(U_746,tc_HOL_Obool))
    | U_750 != c_Orderings_Obot__class_Obot(tc_fun(U_746,tc_HOL_Obool))
    | U_748 != c_Orderings_Obot__class_Obot(tc_fun(U_746,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_217_3]) ).

fof(f_218_1,plain,
    ! [V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Int__empty__left]) ).

fof(f_218_2,plain,
    ! [U_752,U_751] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_751,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_751,tc_HOL_Obool))),U_752) = c_Orderings_Obot__class_Obot(tc_fun(U_751,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_218_1]) ).

cnf(f_218_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_751,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_751,tc_HOL_Obool))),U_752) = c_Orderings_Obot__class_Obot(tc_fun(U_751,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_218_2]) ).

fof(f_219_1,plain,
    ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Int__empty__right]) ).

fof(f_219_2,plain,
    ! [U_754,U_753] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_753,tc_HOL_Obool)),U_754),c_Orderings_Obot__class_Obot(tc_fun(U_753,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_753,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_219_1]) ).

cnf(f_219_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_753,tc_HOL_Obool)),U_754),c_Orderings_Obot__class_Obot(tc_fun(U_753,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_753,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_219_2]) ).

fof(f_220_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
        | ? [B_x] :
            ( ? [B_xa] :
                ( B_x = B_xa
                & hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_B_2)) )
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
      & ( ! [B_x] :
            ( ! [B_xa] :
                ( B_x != B_xa
                | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_B_2)) )
            | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_disjoint__iff__not__equal]) ).

fof(f_220_2,plain,
    ! [U_761,U_760,U_759] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_759,tc_HOL_Obool)),U_760),U_761) = c_Orderings_Obot__class_Obot(tc_fun(U_759,tc_HOL_Obool))
        | ? [U_758] :
            ( ? [U_757] :
                ( U_758 = U_757
                & hBOOL(hAPP(hAPP(c_member(U_759),U_757),U_761)) )
            & hBOOL(hAPP(hAPP(c_member(U_759),U_758),U_760)) ) )
      & ( ! [U_756] :
            ( ! [U_755] :
                ( U_756 != U_755
                | ~ hBOOL(hAPP(hAPP(c_member(U_759),U_755),U_761)) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_759),U_756),U_760)) )
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_759,tc_HOL_Obool)),U_760),U_761) != c_Orderings_Obot__class_Obot(tc_fun(U_759,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_220_1]) ).

fof(f_220_3,plain,
    ( ! [U_767,U_765,U_763] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_763,tc_HOL_Obool)),U_765),U_767) = c_Orderings_Obot__class_Obot(tc_fun(U_763,tc_HOL_Obool))
        | ? [U_758] :
            ( ? [U_757] :
                ( U_758 = U_757
                & hBOOL(hAPP(hAPP(c_member(U_763),U_757),U_767)) )
            & hBOOL(hAPP(hAPP(c_member(U_763),U_758),U_765)) ) )
    & ! [U_766,U_764,U_762] :
        ( ! [U_756] :
            ( ! [U_755] :
                ( U_756 != U_755
                | ~ hBOOL(hAPP(hAPP(c_member(U_762),U_755),U_766)) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_762),U_756),U_764)) )
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_762,tc_HOL_Obool)),U_764),U_766) != c_Orderings_Obot__class_Obot(tc_fun(U_762,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_220_2]) ).

fof(f_220_4,plain,
    ( ! [U_767,U_765,U_763] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_763,tc_HOL_Obool)),U_765),U_767) = c_Orderings_Obot__class_Obot(tc_fun(U_763,tc_HOL_Obool))
        | ( ? [U_757] :
              ( sK12(U_767,U_765,U_763) = U_757
              & hBOOL(hAPP(hAPP(c_member(U_763),U_757),U_767)) )
          & hBOOL(hAPP(hAPP(c_member(U_763),sK12(U_767,U_765,U_763)),U_765)) ) )
    & ! [U_766,U_764,U_762] :
        ( ! [U_756] :
            ( ! [U_755] :
                ( U_756 != U_755
                | ~ hBOOL(hAPP(hAPP(c_member(U_762),U_755),U_766)) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_762),U_756),U_764)) )
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_762,tc_HOL_Obool)),U_764),U_766) != c_Orderings_Obot__class_Obot(tc_fun(U_762,tc_HOL_Obool)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_758,sK12(U_767,U_765,U_763))],[f_220_3]) ).

fof(f_220_5,plain,
    ( ! [U_767,U_765,U_763] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_763,tc_HOL_Obool)),U_765),U_767) = c_Orderings_Obot__class_Obot(tc_fun(U_763,tc_HOL_Obool))
        | ( sK12(U_767,U_765,U_763) = sK13(U_767,U_765,U_763)
          & hBOOL(hAPP(hAPP(c_member(U_763),sK13(U_767,U_765,U_763)),U_767))
          & hBOOL(hAPP(hAPP(c_member(U_763),sK12(U_767,U_765,U_763)),U_765)) ) )
    & ! [U_766,U_764,U_762] :
        ( ! [U_756] :
            ( ! [U_755] :
                ( U_756 != U_755
                | ~ hBOOL(hAPP(hAPP(c_member(U_762),U_755),U_766)) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_762),U_756),U_764)) )
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_762,tc_HOL_Obool)),U_764),U_766) != c_Orderings_Obot__class_Obot(tc_fun(U_762,tc_HOL_Obool)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_757,sK13(U_767,U_765,U_763))],[f_220_4]) ).

cnf(f_220_6,plain,
    ( U_756 != U_755
    | ~ hBOOL(hAPP(hAPP(c_member(U_762),U_755),U_766))
    | ~ hBOOL(hAPP(hAPP(c_member(U_762),U_756),U_764))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_762,tc_HOL_Obool)),U_764),U_766) != c_Orderings_Obot__class_Obot(tc_fun(U_762,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_220_5]) ).

cnf(f_220_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_763),sK12(U_767,U_765,U_763)),U_765))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_763,tc_HOL_Obool)),U_765),U_767) = c_Orderings_Obot__class_Obot(tc_fun(U_763,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_220_5]) ).

cnf(f_220_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_763),sK13(U_767,U_765,U_763)),U_767))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_763,tc_HOL_Obool)),U_765),U_767) = c_Orderings_Obot__class_Obot(tc_fun(U_763,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_220_5]) ).

cnf(f_220_9,plain,
    ( sK12(U_767,U_765,U_763) = sK13(U_767,U_765,U_763)
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_763,tc_HOL_Obool)),U_765),U_767) = c_Orderings_Obot__class_Obot(tc_fun(U_763,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_220_5]) ).

fof(f_221_1,plain,
    ! [V_A_2,V_C_2,T_b] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
        | ? [B_x] :
            ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),B_x),V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_C_2)) ) )
      & ( ! [B_x] :
            ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),B_x),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_C_2)) )
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2)),V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Union__disjoint]) ).

fof(f_221_2,plain,
    ! [U_772,U_771,U_770] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_770,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_770,tc_HOL_Obool),U_771)),U_772) = c_Orderings_Obot__class_Obot(tc_fun(U_770,tc_HOL_Obool))
        | ? [U_769] :
            ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_770,tc_HOL_Obool)),U_769),U_772) != c_Orderings_Obot__class_Obot(tc_fun(U_770,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(tc_fun(U_770,tc_HOL_Obool)),U_769),U_771)) ) )
      & ( ! [U_768] :
            ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_770,tc_HOL_Obool)),U_768),U_772) = c_Orderings_Obot__class_Obot(tc_fun(U_770,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_770,tc_HOL_Obool)),U_768),U_771)) )
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_770,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_770,tc_HOL_Obool),U_771)),U_772) != c_Orderings_Obot__class_Obot(tc_fun(U_770,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_221_1]) ).

fof(f_221_3,plain,
    ( ! [U_778,U_776,U_774] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_774,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_774,tc_HOL_Obool),U_776)),U_778) = c_Orderings_Obot__class_Obot(tc_fun(U_774,tc_HOL_Obool))
        | ? [U_769] :
            ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_774,tc_HOL_Obool)),U_769),U_778) != c_Orderings_Obot__class_Obot(tc_fun(U_774,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(tc_fun(U_774,tc_HOL_Obool)),U_769),U_776)) ) )
    & ! [U_777,U_775,U_773] :
        ( ! [U_768] :
            ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_773,tc_HOL_Obool)),U_768),U_777) = c_Orderings_Obot__class_Obot(tc_fun(U_773,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_773,tc_HOL_Obool)),U_768),U_775)) )
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_773,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_773,tc_HOL_Obool),U_775)),U_777) != c_Orderings_Obot__class_Obot(tc_fun(U_773,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_221_2]) ).

fof(f_221_4,plain,
    ( ! [U_778,U_776,U_774] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_774,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_774,tc_HOL_Obool),U_776)),U_778) = c_Orderings_Obot__class_Obot(tc_fun(U_774,tc_HOL_Obool))
        | ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_774,tc_HOL_Obool)),sK14(U_778,U_776,U_774)),U_778) != c_Orderings_Obot__class_Obot(tc_fun(U_774,tc_HOL_Obool))
          & hBOOL(hAPP(hAPP(c_member(tc_fun(U_774,tc_HOL_Obool)),sK14(U_778,U_776,U_774)),U_776)) ) )
    & ! [U_777,U_775,U_773] :
        ( ! [U_768] :
            ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_773,tc_HOL_Obool)),U_768),U_777) = c_Orderings_Obot__class_Obot(tc_fun(U_773,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_773,tc_HOL_Obool)),U_768),U_775)) )
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_773,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_773,tc_HOL_Obool),U_775)),U_777) != c_Orderings_Obot__class_Obot(tc_fun(U_773,tc_HOL_Obool)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_769,sK14(U_778,U_776,U_774))],[f_221_3]) ).

cnf(f_221_5,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_773,tc_HOL_Obool)),U_768),U_777) = c_Orderings_Obot__class_Obot(tc_fun(U_773,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_773,tc_HOL_Obool)),U_768),U_775))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_773,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_773,tc_HOL_Obool),U_775)),U_777) != c_Orderings_Obot__class_Obot(tc_fun(U_773,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_221_4]) ).

cnf(f_221_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_774,tc_HOL_Obool)),sK14(U_778,U_776,U_774)),U_776))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_774,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_774,tc_HOL_Obool),U_776)),U_778) = c_Orderings_Obot__class_Obot(tc_fun(U_774,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_221_4]) ).

cnf(f_221_7,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_774,tc_HOL_Obool)),sK14(U_778,U_776,U_774)),U_778) != c_Orderings_Obot__class_Obot(tc_fun(U_774,tc_HOL_Obool))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_774,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_774,tc_HOL_Obool),U_776)),U_778) = c_Orderings_Obot__class_Obot(tc_fun(U_774,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_221_4]) ).

fof(f_222_1,plain,
    ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),
    inference(fof_nnf,[status(thm)],[fact_Un__upper1]) ).

fof(f_222_2,plain,
    ! [U_781,U_780,U_779] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_779,tc_HOL_Obool)),U_780),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_779,tc_HOL_Obool)),U_780),U_781))),
    inference(variable_rename,[status(thm)],[f_222_1]) ).

cnf(f_222_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_779,tc_HOL_Obool)),U_780),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_779,tc_HOL_Obool)),U_780),U_781))),
    inference(clausify,[status(thm)],[f_222_2]) ).

fof(f_223_1,plain,
    ! [V_A_2,V_B_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),
    inference(fof_nnf,[status(thm)],[fact_Un__upper2]) ).

fof(f_223_2,plain,
    ! [U_784,U_783,U_782] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_782,tc_HOL_Obool)),U_783),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_782,tc_HOL_Obool)),U_784),U_783))),
    inference(variable_rename,[status(thm)],[f_223_1]) ).

cnf(f_223_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_782,tc_HOL_Obool)),U_783),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_782,tc_HOL_Obool)),U_784),U_783))),
    inference(clausify,[status(thm)],[f_223_2]) ).

fof(f_224_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != V_B_2 )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_subset__Un__eq]) ).

fof(f_224_2,plain,
    ! [U_787,U_786,U_785] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_785,tc_HOL_Obool)),U_786),U_787))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_785,tc_HOL_Obool)),U_786),U_787) != U_787 )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_785,tc_HOL_Obool)),U_786),U_787) = U_787
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_785,tc_HOL_Obool)),U_786),U_787)) ) ),
    inference(variable_rename,[status(thm)],[f_224_1]) ).

fof(f_224_3,plain,
    ( ! [U_793,U_791,U_789] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_789,tc_HOL_Obool)),U_791),U_793))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_789,tc_HOL_Obool)),U_791),U_793) != U_793 )
    & ! [U_792,U_790,U_788] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_788,tc_HOL_Obool)),U_790),U_792) = U_792
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_788,tc_HOL_Obool)),U_790),U_792)) ) ),
    inference(miniscope,[status(thm)],[f_224_2]) ).

cnf(f_224_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_788,tc_HOL_Obool)),U_790),U_792) = U_792
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_788,tc_HOL_Obool)),U_790),U_792)) ),
    inference(clausify,[status(thm)],[f_224_3]) ).

cnf(f_224_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_789,tc_HOL_Obool)),U_791),U_793))
    | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_789,tc_HOL_Obool)),U_791),U_793) != U_793 ),
    inference(clausify,[status(thm)],[f_224_3]) ).

fof(f_225_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Un__absorb1]) ).

fof(f_225_2,plain,
    ! [U_796,U_795,U_794] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_794,tc_HOL_Obool)),U_795),U_796) = U_796
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_794,tc_HOL_Obool)),U_795),U_796)) ),
    inference(variable_rename,[status(thm)],[f_225_1]) ).

cnf(f_225_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_794,tc_HOL_Obool)),U_795),U_796) = U_796
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_794,tc_HOL_Obool)),U_795),U_796)) ),
    inference(clausify,[status(thm)],[f_225_2]) ).

fof(f_226_1,plain,
    ! [V_A_2,V_B_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Un__absorb2]) ).

fof(f_226_2,plain,
    ! [U_799,U_798,U_797] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_797,tc_HOL_Obool)),U_799),U_798) = U_799
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_797,tc_HOL_Obool)),U_798),U_799)) ),
    inference(variable_rename,[status(thm)],[f_226_1]) ).

cnf(f_226_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_797,tc_HOL_Obool)),U_799),U_798) = U_799
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_797,tc_HOL_Obool)),U_798),U_799)) ),
    inference(clausify,[status(thm)],[f_226_2]) ).

fof(f_227_1,plain,
    ! [V_B_2,V_C_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Un__least]) ).

fof(f_227_2,plain,
    ! [U_803,U_802,U_801,U_800] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_800,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_800,tc_HOL_Obool)),U_801),U_803)),U_802))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_800,tc_HOL_Obool)),U_803),U_802))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_800,tc_HOL_Obool)),U_801),U_802)) ),
    inference(variable_rename,[status(thm)],[f_227_1]) ).

cnf(f_227_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_800,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_800,tc_HOL_Obool)),U_801),U_803)),U_802))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_800,tc_HOL_Obool)),U_803),U_802))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_800,tc_HOL_Obool)),U_801),U_802)) ),
    inference(clausify,[status(thm)],[f_227_2]) ).

fof(f_228_1,plain,
    ! [V_D_2,V_B_2,V_C_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Un__mono]) ).

fof(f_228_2,plain,
    ! [U_808,U_807,U_806,U_805,U_804] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_804,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_804,tc_HOL_Obool)),U_805),U_807)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_804,tc_HOL_Obool)),U_806),U_808)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_804,tc_HOL_Obool)),U_807),U_808))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_804,tc_HOL_Obool)),U_805),U_806)) ),
    inference(variable_rename,[status(thm)],[f_228_1]) ).

cnf(f_228_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_804,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_804,tc_HOL_Obool)),U_805),U_807)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_804,tc_HOL_Obool)),U_806),U_808)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_804,tc_HOL_Obool)),U_807),U_808))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_804,tc_HOL_Obool)),U_805),U_806)) ),
    inference(clausify,[status(thm)],[f_228_2]) ).

fof(f_229_1,plain,
    ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Un__UNIV__right]) ).

fof(f_229_2,plain,
    ! [U_810,U_809] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_809,tc_HOL_Obool)),U_810),c_Orderings_Otop__class_Otop(tc_fun(U_809,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_809,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_229_1]) ).

cnf(f_229_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_809,tc_HOL_Obool)),U_810),c_Orderings_Otop__class_Otop(tc_fun(U_809,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_809,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_229_2]) ).

fof(f_230_1,plain,
    ! [V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Un__UNIV__left]) ).

fof(f_230_2,plain,
    ! [U_812,U_811] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_811,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_811,tc_HOL_Obool))),U_812) = c_Orderings_Otop__class_Otop(tc_fun(U_811,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_230_1]) ).

cnf(f_230_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_811,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_811,tc_HOL_Obool))),U_812) = c_Orderings_Otop__class_Otop(tc_fun(U_811,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_230_2]) ).

fof(f_231_1,plain,
    ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_Int__lower1]) ).

fof(f_231_2,plain,
    ! [U_815,U_814,U_813] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_813,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_813,tc_HOL_Obool)),U_814),U_815)),U_814)),
    inference(variable_rename,[status(thm)],[f_231_1]) ).

cnf(f_231_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_813,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_813,tc_HOL_Obool)),U_814),U_815)),U_814)),
    inference(clausify,[status(thm)],[f_231_2]) ).

fof(f_232_1,plain,
    ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_Int__lower2]) ).

fof(f_232_2,plain,
    ! [U_818,U_817,U_816] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_816,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_816,tc_HOL_Obool)),U_817),U_818)),U_818)),
    inference(variable_rename,[status(thm)],[f_232_1]) ).

cnf(f_232_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_816,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_816,tc_HOL_Obool)),U_817),U_818)),U_818)),
    inference(clausify,[status(thm)],[f_232_2]) ).

fof(f_233_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Int__absorb2]) ).

fof(f_233_2,plain,
    ! [U_821,U_820,U_819] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_819,tc_HOL_Obool)),U_820),U_821) = U_820
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_819,tc_HOL_Obool)),U_820),U_821)) ),
    inference(variable_rename,[status(thm)],[f_233_1]) ).

cnf(f_233_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_819,tc_HOL_Obool)),U_820),U_821) = U_820
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_819,tc_HOL_Obool)),U_820),U_821)) ),
    inference(clausify,[status(thm)],[f_233_2]) ).

fof(f_234_1,plain,
    ! [V_A_2,V_B_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Int__absorb1]) ).

fof(f_234_2,plain,
    ! [U_824,U_823,U_822] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_822,tc_HOL_Obool)),U_824),U_823) = U_823
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_822,tc_HOL_Obool)),U_823),U_824)) ),
    inference(variable_rename,[status(thm)],[f_234_1]) ).

cnf(f_234_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_822,tc_HOL_Obool)),U_824),U_823) = U_823
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_822,tc_HOL_Obool)),U_823),U_824)) ),
    inference(clausify,[status(thm)],[f_234_2]) ).

fof(f_235_1,plain,
    ! [V_B_2,V_A_2,V_C_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Int__greatest]) ).

fof(f_235_2,plain,
    ! [U_828,U_827,U_826,U_825] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_825,tc_HOL_Obool)),U_826),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_825,tc_HOL_Obool)),U_827),U_828)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_825,tc_HOL_Obool)),U_826),U_828))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_825,tc_HOL_Obool)),U_826),U_827)) ),
    inference(variable_rename,[status(thm)],[f_235_1]) ).

cnf(f_235_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_825,tc_HOL_Obool)),U_826),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_825,tc_HOL_Obool)),U_827),U_828)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_825,tc_HOL_Obool)),U_826),U_828))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_825,tc_HOL_Obool)),U_826),U_827)) ),
    inference(clausify,[status(thm)],[f_235_2]) ).

fof(f_236_1,plain,
    ! [V_D_2,V_B_2,V_C_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Int__mono]) ).

fof(f_236_2,plain,
    ! [U_833,U_832,U_831,U_830,U_829] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_829,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_829,tc_HOL_Obool)),U_830),U_832)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_829,tc_HOL_Obool)),U_831),U_833)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_829,tc_HOL_Obool)),U_832),U_833))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_829,tc_HOL_Obool)),U_830),U_831)) ),
    inference(variable_rename,[status(thm)],[f_236_1]) ).

cnf(f_236_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_829,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_829,tc_HOL_Obool)),U_830),U_832)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_829,tc_HOL_Obool)),U_831),U_833)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_829,tc_HOL_Obool)),U_832),U_833))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_829,tc_HOL_Obool)),U_830),U_831)) ),
    inference(clausify,[status(thm)],[f_236_2]) ).

fof(f_237_1,plain,
    ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = V_A_2,
    inference(fof_nnf,[status(thm)],[fact_Int__UNIV__right]) ).

fof(f_237_2,plain,
    ! [U_835,U_834] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_834,tc_HOL_Obool)),U_835),c_Orderings_Otop__class_Otop(tc_fun(U_834,tc_HOL_Obool))) = U_835,
    inference(variable_rename,[status(thm)],[f_237_1]) ).

cnf(f_237_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_834,tc_HOL_Obool)),U_835),c_Orderings_Otop__class_Otop(tc_fun(U_834,tc_HOL_Obool))) = U_835,
    inference(clausify,[status(thm)],[f_237_2]) ).

fof(f_238_1,plain,
    ! [V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = V_B_2,
    inference(fof_nnf,[status(thm)],[fact_Int__UNIV__left]) ).

fof(f_238_2,plain,
    ! [U_837,U_836] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_836,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_836,tc_HOL_Obool))),U_837) = U_837,
    inference(variable_rename,[status(thm)],[f_238_1]) ).

cnf(f_238_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_836,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_836,tc_HOL_Obool))),U_837) = U_837,
    inference(clausify,[status(thm)],[f_238_2]) ).

fof(f_239_1,plain,
    ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)),hAPP(c_Set_OPow(T_b),V_B_2))),hAPP(c_Set_OPow(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))),
    inference(fof_nnf,[status(thm)],[fact_Un__Pow__subset]) ).

fof(f_239_2,plain,
    ! [U_840,U_839,U_838] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_838,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_838,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_838),U_839)),hAPP(c_Set_OPow(U_838),U_840))),hAPP(c_Set_OPow(U_838),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_838,tc_HOL_Obool)),U_839),U_840)))),
    inference(variable_rename,[status(thm)],[f_239_1]) ).

cnf(f_239_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_838,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_838,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_838),U_839)),hAPP(c_Set_OPow(U_838),U_840))),hAPP(c_Set_OPow(U_838),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_838,tc_HOL_Obool)),U_839),U_840)))),
    inference(clausify,[status(thm)],[f_239_2]) ).

fof(f_240_1,plain,
    ! [V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = c_Orderings_Obot__class_Obot(T_a)
      | ~ class_Lattices_Oboolean__algebra(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf__compl__bot]) ).

fof(f_240_2,plain,
    ! [U_842,U_841] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_841),U_842),hAPP(c_Groups_Ouminus__class_Ouminus(U_841),U_842)) = c_Orderings_Obot__class_Obot(U_841)
      | ~ class_Lattices_Oboolean__algebra(U_841) ),
    inference(variable_rename,[status(thm)],[f_240_1]) ).

cnf(f_240_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_841),U_842),hAPP(c_Groups_Ouminus__class_Ouminus(U_841),U_842)) = c_Orderings_Obot__class_Obot(U_841)
    | ~ class_Lattices_Oboolean__algebra(U_841) ),
    inference(clausify,[status(thm)],[f_240_2]) ).

fof(f_241_1,plain,
    ! [V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),V_x) = c_Orderings_Obot__class_Obot(T_a)
      | ~ class_Lattices_Oboolean__algebra(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_compl__inf__bot]) ).

fof(f_241_2,plain,
    ! [U_844,U_843] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_843),hAPP(c_Groups_Ouminus__class_Ouminus(U_843),U_844)),U_844) = c_Orderings_Obot__class_Obot(U_843)
      | ~ class_Lattices_Oboolean__algebra(U_843) ),
    inference(variable_rename,[status(thm)],[f_241_1]) ).

cnf(f_241_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_843),hAPP(c_Groups_Ouminus__class_Ouminus(U_843),U_844)),U_844) = c_Orderings_Obot__class_Obot(U_843)
    | ~ class_Lattices_Oboolean__algebra(U_843) ),
    inference(clausify,[status(thm)],[f_241_2]) ).

fof(f_242_1,plain,
    ! [V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = c_Orderings_Otop__class_Otop(T_a)
      | ~ class_Lattices_Oboolean__algebra(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sup__compl__top]) ).

fof(f_242_2,plain,
    ! [U_846,U_845] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_845),U_846),hAPP(c_Groups_Ouminus__class_Ouminus(U_845),U_846)) = c_Orderings_Otop__class_Otop(U_845)
      | ~ class_Lattices_Oboolean__algebra(U_845) ),
    inference(variable_rename,[status(thm)],[f_242_1]) ).

cnf(f_242_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_845),U_846),hAPP(c_Groups_Ouminus__class_Ouminus(U_845),U_846)) = c_Orderings_Otop__class_Otop(U_845)
    | ~ class_Lattices_Oboolean__algebra(U_845) ),
    inference(clausify,[status(thm)],[f_242_2]) ).

fof(f_243_1,plain,
    ! [V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),V_x) = c_Orderings_Otop__class_Otop(T_a)
      | ~ class_Lattices_Oboolean__algebra(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_compl__sup__top]) ).

fof(f_243_2,plain,
    ! [U_848,U_847] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_847),hAPP(c_Groups_Ouminus__class_Ouminus(U_847),U_848)),U_848) = c_Orderings_Otop__class_Otop(U_847)
      | ~ class_Lattices_Oboolean__algebra(U_847) ),
    inference(variable_rename,[status(thm)],[f_243_1]) ).

cnf(f_243_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_847),hAPP(c_Groups_Ouminus__class_Ouminus(U_847),U_848)),U_848) = c_Orderings_Otop__class_Otop(U_847)
    | ~ class_Lattices_Oboolean__algebra(U_847) ),
    inference(clausify,[status(thm)],[f_243_2]) ).

fof(f_244_1,plain,
    ! [V_u_2,V_m_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_m_2),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I17_J]) ).

fof(f_244_2,plain,
    ! [U_852,U_851,U_850,U_849] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_849,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_849,U_850),U_851)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_849,U_851),U_852)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_849,U_850),U_852)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_849),U_851),U_852))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_849),U_850),U_851))
      | ~ class_Orderings_Olinorder(U_849) ),
    inference(variable_rename,[status(thm)],[f_244_1]) ).

cnf(f_244_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_849,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_849,U_850),U_851)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_849,U_851),U_852)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_849,U_850),U_852)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_849),U_851),U_852))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_849),U_850),U_851))
    | ~ class_Orderings_Olinorder(U_849) ),
    inference(clausify,[status(thm)],[f_244_2]) ).

fof(f_245_1,plain,
    ! [V_u_2,V_m_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_m_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I11_J]) ).

fof(f_245_2,plain,
    ! [U_856,U_855,U_854,U_853] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_853,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_853,U_854),U_855)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_853,U_855),U_856)) = c_Orderings_Obot__class_Obot(tc_fun(U_853,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_853) ),
    inference(variable_rename,[status(thm)],[f_245_1]) ).

cnf(f_245_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_853,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_853,U_854),U_855)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_853,U_855),U_856)) = c_Orderings_Obot__class_Obot(tc_fun(U_853,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_853) ),
    inference(clausify,[status(thm)],[f_245_2]) ).

fof(f_246_1,plain,
    ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Compl__disjoint]) ).

fof(f_246_2,plain,
    ! [U_858,U_857] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_857,tc_HOL_Obool)),U_858),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_857,tc_HOL_Obool)),U_858)) = c_Orderings_Obot__class_Obot(tc_fun(U_857,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_246_1]) ).

cnf(f_246_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_857,tc_HOL_Obool)),U_858),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_857,tc_HOL_Obool)),U_858)) = c_Orderings_Obot__class_Obot(tc_fun(U_857,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_246_2]) ).

fof(f_247_1,plain,
    ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Compl__disjoint2]) ).

fof(f_247_2,plain,
    ! [U_860,U_859] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_859,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_859,tc_HOL_Obool)),U_860)),U_860) = c_Orderings_Obot__class_Obot(tc_fun(U_859,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_247_1]) ).

cnf(f_247_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_859,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_859,tc_HOL_Obool)),U_860)),U_860) = c_Orderings_Obot__class_Obot(tc_fun(U_859,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_247_2]) ).

fof(f_248_1,plain,
    ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Compl__partition2]) ).

fof(f_248_2,plain,
    ! [U_862,U_861] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_861,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_861,tc_HOL_Obool)),U_862)),U_862) = c_Orderings_Otop__class_Otop(tc_fun(U_861,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_248_1]) ).

cnf(f_248_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_861,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_861,tc_HOL_Obool)),U_862)),U_862) = c_Orderings_Otop__class_Otop(tc_fun(U_861,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_248_2]) ).

fof(f_249_1,plain,
    ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Compl__partition]) ).

fof(f_249_2,plain,
    ! [U_864,U_863] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_863,tc_HOL_Obool)),U_864),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_863,tc_HOL_Obool)),U_864)) = c_Orderings_Otop__class_Otop(tc_fun(U_863,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_249_1]) ).

cnf(f_249_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_863,tc_HOL_Obool)),U_864),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_863,tc_HOL_Obool)),U_864)) = c_Orderings_Otop__class_Otop(tc_fun(U_863,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_249_2]) ).

fof(f_250_1,plain,
    ! [V_u_2,V_m_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I20_J]) ).

fof(f_250_2,plain,
    ! [U_868,U_867,U_866,U_865] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_865,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_865,U_866,U_867)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_865,U_867,U_868)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_865,U_866,U_868)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_865),U_867),U_868))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_865),U_866),U_867))
      | ~ class_Orderings_Olinorder(U_865) ),
    inference(variable_rename,[status(thm)],[f_250_1]) ).

cnf(f_250_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_865,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_865,U_866,U_867)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_865,U_867,U_868)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_865,U_866,U_868)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_865),U_867),U_868))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_865),U_866),U_867))
    | ~ class_Orderings_Olinorder(U_865) ),
    inference(clausify,[status(thm)],[f_250_2]) ).

fof(f_251_1,plain,
    ! [V_u_2,V_m_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I14_J]) ).

fof(f_251_2,plain,
    ! [U_872,U_871,U_870,U_869] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_869,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_869,U_870,U_871)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_869,U_871,U_872)) = c_Orderings_Obot__class_Obot(tc_fun(U_869,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_869) ),
    inference(variable_rename,[status(thm)],[f_251_1]) ).

cnf(f_251_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_869,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_869,U_870,U_871)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_869,U_871,U_872)) = c_Orderings_Obot__class_Obot(tc_fun(U_869,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_869) ),
    inference(clausify,[status(thm)],[f_251_2]) ).

fof(f_252_1,plain,
    ! [V_u_2,V_m_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I21_J]) ).

fof(f_252_2,plain,
    ! [U_876,U_875,U_874,U_873] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_873,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_873,U_874),U_875)),c_SetInterval_Oord__class_OatLeastAtMost(U_873,U_875,U_876)) = c_SetInterval_Oord__class_OatLeastAtMost(U_873,U_874,U_876)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_873),U_875),U_876))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_873),U_874),U_875))
      | ~ class_Orderings_Olinorder(U_873) ),
    inference(variable_rename,[status(thm)],[f_252_1]) ).

cnf(f_252_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_873,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_873,U_874),U_875)),c_SetInterval_Oord__class_OatLeastAtMost(U_873,U_875,U_876)) = c_SetInterval_Oord__class_OatLeastAtMost(U_873,U_874,U_876)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_873),U_875),U_876))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_873),U_874),U_875))
    | ~ class_Orderings_Olinorder(U_873) ),
    inference(clausify,[status(thm)],[f_252_2]) ).

fof(f_253_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_disjoint__eq__subset__Compl]) ).

fof(f_253_2,plain,
    ! [U_879,U_878,U_877] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_877,tc_HOL_Obool)),U_878),U_879) = c_Orderings_Obot__class_Obot(tc_fun(U_877,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_877,tc_HOL_Obool)),U_878),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_877,tc_HOL_Obool)),U_879))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_877,tc_HOL_Obool)),U_878),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_877,tc_HOL_Obool)),U_879)))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_877,tc_HOL_Obool)),U_878),U_879) != c_Orderings_Obot__class_Obot(tc_fun(U_877,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_253_1]) ).

fof(f_253_3,plain,
    ( ! [U_885,U_883,U_881] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_881,tc_HOL_Obool)),U_883),U_885) = c_Orderings_Obot__class_Obot(tc_fun(U_881,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_881,tc_HOL_Obool)),U_883),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_881,tc_HOL_Obool)),U_885))) )
    & ! [U_884,U_882,U_880] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_880,tc_HOL_Obool)),U_882),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_880,tc_HOL_Obool)),U_884)))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_880,tc_HOL_Obool)),U_882),U_884) != c_Orderings_Obot__class_Obot(tc_fun(U_880,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_253_2]) ).

cnf(f_253_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_880,tc_HOL_Obool)),U_882),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_880,tc_HOL_Obool)),U_884)))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_880,tc_HOL_Obool)),U_882),U_884) != c_Orderings_Obot__class_Obot(tc_fun(U_880,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_253_3]) ).

cnf(f_253_5,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_881,tc_HOL_Obool)),U_883),U_885) = c_Orderings_Obot__class_Obot(tc_fun(U_881,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_881,tc_HOL_Obool)),U_883),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_881,tc_HOL_Obool)),U_885))) ),
    inference(clausify,[status(thm)],[f_253_3]) ).

fof(f_254_1,plain,
    ! [V_u_2,V_m_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I15_J]) ).

fof(f_254_2,plain,
    ! [U_889,U_888,U_887,U_886] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_886,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_886,U_887),U_888)),c_SetInterval_Oord__class_OatLeastAtMost(U_886,U_888,U_889)) = c_Orderings_Obot__class_Obot(tc_fun(U_886,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_886) ),
    inference(variable_rename,[status(thm)],[f_254_1]) ).

cnf(f_254_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_886,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_886,U_887),U_888)),c_SetInterval_Oord__class_OatLeastAtMost(U_886,U_888,U_889)) = c_Orderings_Obot__class_Obot(tc_fun(U_886,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_886) ),
    inference(clausify,[status(thm)],[f_254_2]) ).

fof(f_255_1,plain,
    ! [V_u_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_l_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_u_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I8_J]) ).

fof(f_255_2,plain,
    ! [U_892,U_891,U_890] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_890,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_890),U_891)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_890,U_891),U_892)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_890),U_892)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_890),U_891),U_892))
      | ~ class_Orderings_Olinorder(U_890) ),
    inference(variable_rename,[status(thm)],[f_255_1]) ).

cnf(f_255_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_890,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_890),U_891)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_890,U_891),U_892)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_890),U_892)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_890),U_891),U_892))
    | ~ class_Orderings_Olinorder(U_890) ),
    inference(clausify,[status(thm)],[f_255_2]) ).

fof(f_256_1,plain,
    ! [V_u_2,V_m_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I22_J]) ).

fof(f_256_2,plain,
    ! [U_896,U_895,U_894,U_893] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_893,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_893,U_894,U_895)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_893,U_895,U_896)) = c_SetInterval_Oord__class_OatLeastAtMost(U_893,U_894,U_896)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_893),U_895),U_896))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_893),U_894),U_895))
      | ~ class_Orderings_Olinorder(U_893) ),
    inference(variable_rename,[status(thm)],[f_256_1]) ).

cnf(f_256_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_893,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_893,U_894,U_895)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_893,U_895,U_896)) = c_SetInterval_Oord__class_OatLeastAtMost(U_893,U_894,U_896)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_893),U_895),U_896))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_893),U_894),U_895))
    | ~ class_Orderings_Olinorder(U_893) ),
    inference(clausify,[status(thm)],[f_256_2]) ).

fof(f_257_1,plain,
    ! [V_u_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_l_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I4_J]) ).

fof(f_257_2,plain,
    ! [U_899,U_898,U_897] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_897,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_897),U_898)),c_SetInterval_Oord__class_OatLeastAtMost(U_897,U_898,U_899)) = c_Orderings_Obot__class_Obot(tc_fun(U_897,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_897) ),
    inference(variable_rename,[status(thm)],[f_257_1]) ).

cnf(f_257_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_897,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_897),U_898)),c_SetInterval_Oord__class_OatLeastAtMost(U_897,U_898,U_899)) = c_Orderings_Obot__class_Obot(tc_fun(U_897,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_897) ),
    inference(clausify,[status(thm)],[f_257_2]) ).

fof(f_258_1,plain,
    ! [V_u_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_l_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I2_J]) ).

fof(f_258_2,plain,
    ! [U_902,U_901,U_900] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_900,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_900),U_901)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_900,U_901),U_902)) = c_Orderings_Obot__class_Obot(tc_fun(U_900,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_900) ),
    inference(variable_rename,[status(thm)],[f_258_1]) ).

cnf(f_258_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_900,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_900),U_901)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_900,U_901),U_902)) = c_Orderings_Obot__class_Obot(tc_fun(U_900,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_900) ),
    inference(clausify,[status(thm)],[f_258_2]) ).

fof(f_259_1,plain,
    ! [V_u_2,V_m_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I16_J]) ).

fof(f_259_2,plain,
    ! [U_906,U_905,U_904,U_903] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_903,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_903,U_904,U_905)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_903,U_905,U_906)) = c_Orderings_Obot__class_Obot(tc_fun(U_903,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_903) ),
    inference(variable_rename,[status(thm)],[f_259_1]) ).

cnf(f_259_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_903,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_903,U_904,U_905)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_903,U_905,U_906)) = c_Orderings_Obot__class_Obot(tc_fun(U_903,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_903) ),
    inference(clausify,[status(thm)],[f_259_2]) ).

fof(f_260_1,plain,
    ! [V_u_2,V_m_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I12_J]) ).

fof(f_260_2,plain,
    ! [U_910,U_909,U_908,U_907] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_907,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_907,U_908,U_909)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_907,U_909,U_910)) = c_Orderings_Obot__class_Obot(tc_fun(U_907,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_907) ),
    inference(variable_rename,[status(thm)],[f_260_1]) ).

cnf(f_260_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_907,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_907,U_908,U_909)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_907,U_909,U_910)) = c_Orderings_Obot__class_Obot(tc_fun(U_907,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_907) ),
    inference(clausify,[status(thm)],[f_260_2]) ).

fof(f_261_1,plain,
    ! [V_u_2,V_m_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I13_J]) ).

fof(f_261_2,plain,
    ! [U_914,U_913,U_912,U_911] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_911,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_911,U_912,U_913)),c_SetInterval_Oord__class_OatLeastAtMost(U_911,U_913,U_914)) = c_Orderings_Obot__class_Obot(tc_fun(U_911,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_911) ),
    inference(variable_rename,[status(thm)],[f_261_1]) ).

cnf(f_261_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_911,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_911,U_912,U_913)),c_SetInterval_Oord__class_OatLeastAtMost(U_911,U_913,U_914)) = c_Orderings_Obot__class_Obot(tc_fun(U_911,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_911) ),
    inference(clausify,[status(thm)],[f_261_2]) ).

fof(f_262_1,plain,
    ! [V_u_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_l_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I14_J]) ).

fof(f_262_2,plain,
    ! [U_917,U_916,U_915] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_915,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_915,U_916),U_917)),hAPP(c_SetInterval_Oord__class_OatLeast(U_915),U_917)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_915),U_916)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_915),U_916),U_917))
      | ~ class_Orderings_Olinorder(U_915) ),
    inference(variable_rename,[status(thm)],[f_262_1]) ).

cnf(f_262_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_915,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_915,U_916),U_917)),hAPP(c_SetInterval_Oord__class_OatLeast(U_915),U_917)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_915),U_916)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_915),U_916),U_917))
    | ~ class_Orderings_Olinorder(U_915) ),
    inference(clausify,[status(thm)],[f_262_2]) ).

fof(f_263_1,plain,
    ! [V_u_2,V_m_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_m_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I9_J]) ).

fof(f_263_2,plain,
    ! [U_921,U_920,U_919,U_918] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_918,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_918,U_919,U_920)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_918,U_920),U_921)) = c_Orderings_Obot__class_Obot(tc_fun(U_918,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_918) ),
    inference(variable_rename,[status(thm)],[f_263_1]) ).

cnf(f_263_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_918,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_918,U_919,U_920)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_918,U_920),U_921)) = c_Orderings_Obot__class_Obot(tc_fun(U_918,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_918) ),
    inference(clausify,[status(thm)],[f_263_2]) ).

fof(f_264_1,plain,
    ! [V_u_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I8_J]) ).

fof(f_264_2,plain,
    ! [U_924,U_923,U_922] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_922,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_922,U_923),U_924)),hAPP(c_SetInterval_Oord__class_OatLeast(U_922),U_924)) = c_Orderings_Obot__class_Obot(tc_fun(U_922,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_922) ),
    inference(variable_rename,[status(thm)],[f_264_1]) ).

cnf(f_264_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_922,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_922,U_923),U_924)),hAPP(c_SetInterval_Oord__class_OatLeast(U_922),U_924)) = c_Orderings_Obot__class_Obot(tc_fun(U_922,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_922) ),
    inference(clausify,[status(thm)],[f_264_2]) ).

fof(f_265_1,plain,
    ! [V_u_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I7_J]) ).

fof(f_265_2,plain,
    ! [U_927,U_926,U_925] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_925,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_925,U_926,U_927)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_925),U_927)) = c_Orderings_Obot__class_Obot(tc_fun(U_925,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_925) ),
    inference(variable_rename,[status(thm)],[f_265_1]) ).

cnf(f_265_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_925,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_925,U_926,U_927)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_925),U_927)) = c_Orderings_Obot__class_Obot(tc_fun(U_925,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_925) ),
    inference(clausify,[status(thm)],[f_265_2]) ).

fof(f_266_1,plain,
    ! [V_u_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_l_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_u_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I9_J]) ).

fof(f_266_2,plain,
    ! [U_930,U_929,U_928] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_928,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_928),U_929)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_928,U_929,U_930)) = hAPP(c_SetInterval_Oord__class_OatMost(U_928),U_930)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_928),U_929),U_930))
      | ~ class_Orderings_Olinorder(U_928) ),
    inference(variable_rename,[status(thm)],[f_266_1]) ).

cnf(f_266_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_928,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_928),U_929)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_928,U_929,U_930)) = hAPP(c_SetInterval_Oord__class_OatMost(U_928),U_930)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_928),U_929),U_930))
    | ~ class_Orderings_Olinorder(U_928) ),
    inference(clausify,[status(thm)],[f_266_2]) ).

fof(f_267_1,plain,
    ! [V_u_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_l_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I3_J]) ).

fof(f_267_2,plain,
    ! [U_933,U_932,U_931] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_931,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_931),U_932)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_931,U_932,U_933)) = c_Orderings_Obot__class_Obot(tc_fun(U_931,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_931) ),
    inference(variable_rename,[status(thm)],[f_267_1]) ).

cnf(f_267_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_931,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_931),U_932)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_931,U_932,U_933)) = c_Orderings_Obot__class_Obot(tc_fun(U_931,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_931) ),
    inference(clausify,[status(thm)],[f_267_2]) ).

fof(f_268_1,plain,
    ! [V_u_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_l_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I1_J]) ).

fof(f_268_2,plain,
    ! [U_936,U_935,U_934] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_934,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_934),U_935)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_934,U_935,U_936)) = c_Orderings_Obot__class_Obot(tc_fun(U_934,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_934) ),
    inference(variable_rename,[status(thm)],[f_268_1]) ).

cnf(f_268_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_934,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_934),U_935)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_934,U_935,U_936)) = c_Orderings_Obot__class_Obot(tc_fun(U_934,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_934) ),
    inference(clausify,[status(thm)],[f_268_2]) ).

fof(f_269_1,plain,
    ! [V_u_2,V_m_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I10_J]) ).

fof(f_269_2,plain,
    ! [U_940,U_939,U_938,U_937] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_937,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_937,U_938,U_939)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_937,U_939,U_940)) = c_Orderings_Obot__class_Obot(tc_fun(U_937,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_937) ),
    inference(variable_rename,[status(thm)],[f_269_1]) ).

cnf(f_269_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_937,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_937,U_938,U_939)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_937,U_939,U_940)) = c_Orderings_Obot__class_Obot(tc_fun(U_937,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_937) ),
    inference(clausify,[status(thm)],[f_269_2]) ).

fof(f_270_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)
          | V_x_2 != V_y_2 )
        & ( V_x_2 = V_y_2
          | hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2) != hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2) ) )
      | ~ class_Lattices_Oboolean__algebra(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_compl__eq__compl__iff]) ).

fof(f_270_2,plain,
    ! [U_943,U_942,U_941] :
      ( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(U_941),U_942) = hAPP(c_Groups_Ouminus__class_Ouminus(U_941),U_943)
          | U_942 != U_943 )
        & ( U_942 = U_943
          | hAPP(c_Groups_Ouminus__class_Ouminus(U_941),U_942) != hAPP(c_Groups_Ouminus__class_Ouminus(U_941),U_943) ) )
      | ~ class_Lattices_Oboolean__algebra(U_941) ),
    inference(variable_rename,[status(thm)],[f_270_1]) ).

cnf(f_270_3,plain,
    ( U_942 = U_943
    | hAPP(c_Groups_Ouminus__class_Ouminus(U_941),U_942) != hAPP(c_Groups_Ouminus__class_Ouminus(U_941),U_943)
    | ~ class_Lattices_Oboolean__algebra(U_941) ),
    inference(clausify,[status(thm)],[f_270_2]) ).

cnf(f_270_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_941),U_942) = hAPP(c_Groups_Ouminus__class_Ouminus(U_941),U_943)
    | U_942 != U_943
    | ~ class_Lattices_Oboolean__algebra(U_941) ),
    inference(clausify,[status(thm)],[f_270_2]) ).

fof(f_271_1,plain,
    ! [V_b_2,V_a_2,T_b] :
      ( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
          | V_a_2 != V_b_2 )
        & ( V_a_2 = V_b_2
          | hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) != hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) ) )
      | ~ class_Groups_Ogroup__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_neg__equal__iff__equal]) ).

fof(f_271_2,plain,
    ! [U_946,U_945,U_944] :
      ( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(U_944),U_945) = hAPP(c_Groups_Ouminus__class_Ouminus(U_944),U_946)
          | U_945 != U_946 )
        & ( U_945 = U_946
          | hAPP(c_Groups_Ouminus__class_Ouminus(U_944),U_945) != hAPP(c_Groups_Ouminus__class_Ouminus(U_944),U_946) ) )
      | ~ class_Groups_Ogroup__add(U_944) ),
    inference(variable_rename,[status(thm)],[f_271_1]) ).

cnf(f_271_3,plain,
    ( U_945 = U_946
    | hAPP(c_Groups_Ouminus__class_Ouminus(U_944),U_945) != hAPP(c_Groups_Ouminus__class_Ouminus(U_944),U_946)
    | ~ class_Groups_Ogroup__add(U_944) ),
    inference(clausify,[status(thm)],[f_271_2]) ).

cnf(f_271_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_944),U_945) = hAPP(c_Groups_Ouminus__class_Ouminus(U_944),U_946)
    | U_945 != U_946
    | ~ class_Groups_Ogroup__add(U_944) ),
    inference(clausify,[status(thm)],[f_271_2]) ).

fof(f_272_1,plain,
    ! [V_b_2,V_a_2,T_b] :
      ( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = V_b_2
          | hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) != V_a_2 )
        & ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) = V_a_2
          | hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) != V_b_2 ) )
      | ~ class_Groups_Ogroup__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_minus__equation__iff]) ).

fof(f_272_2,plain,
    ! [U_949,U_948,U_947] :
      ( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(U_947),U_948) = U_949
          | hAPP(c_Groups_Ouminus__class_Ouminus(U_947),U_949) != U_948 )
        & ( hAPP(c_Groups_Ouminus__class_Ouminus(U_947),U_949) = U_948
          | hAPP(c_Groups_Ouminus__class_Ouminus(U_947),U_948) != U_949 ) )
      | ~ class_Groups_Ogroup__add(U_947) ),
    inference(variable_rename,[status(thm)],[f_272_1]) ).

cnf(f_272_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_947),U_949) = U_948
    | hAPP(c_Groups_Ouminus__class_Ouminus(U_947),U_948) != U_949
    | ~ class_Groups_Ogroup__add(U_947) ),
    inference(clausify,[status(thm)],[f_272_2]) ).

cnf(f_272_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_947),U_948) = U_949
    | hAPP(c_Groups_Ouminus__class_Ouminus(U_947),U_949) != U_948
    | ~ class_Groups_Ogroup__add(U_947) ),
    inference(clausify,[status(thm)],[f_272_2]) ).

fof(f_273_1,plain,
    ! [V_b_2,V_a_2,T_b] :
      ( ( ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
          | V_b_2 != hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) )
        & ( V_b_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)
          | V_a_2 != hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) ) )
      | ~ class_Groups_Ogroup__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_equation__minus__iff]) ).

fof(f_273_2,plain,
    ! [U_952,U_951,U_950] :
      ( ( ( U_951 = hAPP(c_Groups_Ouminus__class_Ouminus(U_950),U_952)
          | U_952 != hAPP(c_Groups_Ouminus__class_Ouminus(U_950),U_951) )
        & ( U_952 = hAPP(c_Groups_Ouminus__class_Ouminus(U_950),U_951)
          | U_951 != hAPP(c_Groups_Ouminus__class_Ouminus(U_950),U_952) ) )
      | ~ class_Groups_Ogroup__add(U_950) ),
    inference(variable_rename,[status(thm)],[f_273_1]) ).

cnf(f_273_3,plain,
    ( U_952 = hAPP(c_Groups_Ouminus__class_Ouminus(U_950),U_951)
    | U_951 != hAPP(c_Groups_Ouminus__class_Ouminus(U_950),U_952)
    | ~ class_Groups_Ogroup__add(U_950) ),
    inference(clausify,[status(thm)],[f_273_2]) ).

cnf(f_273_4,plain,
    ( U_951 = hAPP(c_Groups_Ouminus__class_Ouminus(U_950),U_952)
    | U_952 != hAPP(c_Groups_Ouminus__class_Ouminus(U_950),U_951)
    | ~ class_Groups_Ogroup__add(U_950) ),
    inference(clausify,[status(thm)],[f_273_2]) ).

fof(f_274_1,plain,
    ! [V_x,T_a] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = V_x
      | ~ class_Lattices_Oboolean__algebra(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_double__compl]) ).

fof(f_274_2,plain,
    ! [U_954,U_953] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_953),hAPP(c_Groups_Ouminus__class_Ouminus(U_953),U_954)) = U_954
      | ~ class_Lattices_Oboolean__algebra(U_953) ),
    inference(variable_rename,[status(thm)],[f_274_1]) ).

cnf(f_274_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_953),hAPP(c_Groups_Ouminus__class_Ouminus(U_953),U_954)) = U_954
    | ~ class_Lattices_Oboolean__algebra(U_953) ),
    inference(clausify,[status(thm)],[f_274_2]) ).

fof(f_275_1,plain,
    ! [V_a,T_a] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = V_a
      | ~ class_Groups_Ogroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_minus__minus]) ).

fof(f_275_2,plain,
    ! [U_956,U_955] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_955),hAPP(c_Groups_Ouminus__class_Ouminus(U_955),U_956)) = U_956
      | ~ class_Groups_Ogroup__add(U_955) ),
    inference(variable_rename,[status(thm)],[f_275_1]) ).

cnf(f_275_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_955),hAPP(c_Groups_Ouminus__class_Ouminus(U_955),U_956)) = U_956
    | ~ class_Groups_Ogroup__add(U_955) ),
    inference(clausify,[status(thm)],[f_275_2]) ).

fof(f_276_1,plain,
    ! [V_u_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_u_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_l_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I11_J]) ).

fof(f_276_2,plain,
    ! [U_959,U_958,U_957] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_957,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_957,U_958,U_959)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_957),U_959)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_957),U_958)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_957),U_958),U_959))
      | ~ class_Orderings_Olinorder(U_957) ),
    inference(variable_rename,[status(thm)],[f_276_1]) ).

cnf(f_276_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_957,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_957,U_958,U_959)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_957),U_959)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_957),U_958)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_957),U_958),U_959))
    | ~ class_Orderings_Olinorder(U_957) ),
    inference(clausify,[status(thm)],[f_276_2]) ).

fof(f_277_1,plain,
    ! [V_u_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I6_J]) ).

fof(f_277_2,plain,
    ! [U_962,U_961,U_960] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_960,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_960,U_961,U_962)),hAPP(c_SetInterval_Oord__class_OatLeast(U_960),U_962)) = c_Orderings_Obot__class_Obot(tc_fun(U_960,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_960) ),
    inference(variable_rename,[status(thm)],[f_277_1]) ).

cnf(f_277_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_960,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_960,U_961,U_962)),hAPP(c_SetInterval_Oord__class_OatLeast(U_960),U_962)) = c_Orderings_Obot__class_Obot(tc_fun(U_960,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_960) ),
    inference(clausify,[status(thm)],[f_277_2]) ).

fof(f_278_1,plain,
    ! [V_u_2,V_m_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_m_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I19_J]) ).

fof(f_278_2,plain,
    ! [U_966,U_965,U_964,U_963] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_963,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_963,U_964,U_965)),c_SetInterval_Oord__class_OatLeastAtMost(U_963,U_965,U_966)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_963,U_964,U_966)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_963),U_965),U_966))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_963),U_964),U_965))
      | ~ class_Orderings_Olinorder(U_963) ),
    inference(variable_rename,[status(thm)],[f_278_1]) ).

cnf(f_278_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_963,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_963,U_964,U_965)),c_SetInterval_Oord__class_OatLeastAtMost(U_963,U_965,U_966)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_963,U_964,U_966)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_963),U_965),U_966))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_963),U_964),U_965))
    | ~ class_Orderings_Olinorder(U_963) ),
    inference(clausify,[status(thm)],[f_278_2]) ).

fof(f_279_1,plain,
    ! [V_u_2,V_m_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_m_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_u_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I18_J]) ).

fof(f_279_2,plain,
    ! [U_970,U_969,U_968,U_967] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_967,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_967,U_968,U_969)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_967,U_969,U_970)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_967,U_968),U_970)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_967),U_969),U_970))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_967),U_968),U_969))
      | ~ class_Orderings_Olinorder(U_967) ),
    inference(variable_rename,[status(thm)],[f_279_1]) ).

cnf(f_279_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_967,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_967,U_968,U_969)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_967,U_969,U_970)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_967,U_968),U_970)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_967),U_969),U_970))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_967),U_968),U_969))
    | ~ class_Orderings_Olinorder(U_967) ),
    inference(clausify,[status(thm)],[f_279_2]) ).

fof(f_280_1,plain,
    ! [V_u_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I5_J]) ).

fof(f_280_2,plain,
    ! [U_973,U_972,U_971] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_971,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_971),U_972),c_Orderings_Obot__class_Obot(tc_fun(U_971,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(U_971,U_972,U_973)) = c_SetInterval_Oord__class_OatLeastAtMost(U_971,U_972,U_973)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_971),U_972),U_973))
      | ~ class_Orderings_Olinorder(U_971) ),
    inference(variable_rename,[status(thm)],[f_280_1]) ).

cnf(f_280_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_971,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_971),U_972),c_Orderings_Obot__class_Obot(tc_fun(U_971,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(U_971,U_972,U_973)) = c_SetInterval_Oord__class_OatLeastAtMost(U_971,U_972,U_973)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_971),U_972),U_973))
    | ~ class_Orderings_Olinorder(U_971) ),
    inference(clausify,[status(thm)],[f_280_2]) ).

fof(f_281_1,plain,
    ! [V_u_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I6_J]) ).

fof(f_281_2,plain,
    ! [U_976,U_975,U_974] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_974,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_974,U_975),U_976)),hAPP(hAPP(c_Set_Oinsert(U_974),U_976),c_Orderings_Obot__class_Obot(tc_fun(U_974,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(U_974,U_975,U_976)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_974),U_975),U_976))
      | ~ class_Orderings_Olinorder(U_974) ),
    inference(variable_rename,[status(thm)],[f_281_1]) ).

cnf(f_281_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_974,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_974,U_975),U_976)),hAPP(hAPP(c_Set_Oinsert(U_974),U_976),c_Orderings_Obot__class_Obot(tc_fun(U_974,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(U_974,U_975,U_976)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_974),U_975),U_976))
    | ~ class_Orderings_Olinorder(U_974) ),
    inference(clausify,[status(thm)],[f_281_2]) ).

fof(f_282_1,plain,
    ! [V_u_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_u_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_l_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I12_J]) ).

fof(f_282_2,plain,
    ! [U_979,U_978,U_977] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_977,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_977,U_978,U_979)),hAPP(c_SetInterval_Oord__class_OatLeast(U_977),U_979)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_977),U_978)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_977),U_978),U_979))
      | ~ class_Orderings_Olinorder(U_977) ),
    inference(variable_rename,[status(thm)],[f_282_1]) ).

cnf(f_282_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_977,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_977,U_978,U_979)),hAPP(c_SetInterval_Oord__class_OatLeast(U_977),U_979)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_977),U_978)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_977),U_978),U_979))
    | ~ class_Orderings_Olinorder(U_977) ),
    inference(clausify,[status(thm)],[f_282_2]) ).

fof(f_283_1,plain,
    ! [V_u_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_l_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_u_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I7_J]) ).

fof(f_283_2,plain,
    ! [U_982,U_981,U_980] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_980,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_980),U_981)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_980,U_981,U_982)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_980),U_982)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_980),U_981),U_982))
      | ~ class_Orderings_Olinorder(U_980) ),
    inference(variable_rename,[status(thm)],[f_283_1]) ).

cnf(f_283_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_980,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_980),U_981)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_980,U_981,U_982)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_980),U_982)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_980),U_981),U_982))
    | ~ class_Orderings_Olinorder(U_980) ),
    inference(clausify,[status(thm)],[f_283_2]) ).

fof(f_284_1,plain,
    ! [V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_l_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_l_2)
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I1_J]) ).

fof(f_284_2,plain,
    ! [U_984,U_983] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_983,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_983),U_984),c_Orderings_Obot__class_Obot(tc_fun(U_983,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_983),U_984)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_983),U_984)
      | ~ class_Orderings_Olinorder(U_983) ),
    inference(variable_rename,[status(thm)],[f_284_1]) ).

cnf(f_284_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_983,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_983),U_984),c_Orderings_Obot__class_Obot(tc_fun(U_983,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_983),U_984)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_983),U_984)
    | ~ class_Orderings_Olinorder(U_983) ),
    inference(clausify,[status(thm)],[f_284_2]) ).

fof(f_285_1,plain,
    ! [V_u_2,V_m_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_u_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I16_J]) ).

fof(f_285_2,plain,
    ! [U_988,U_987,U_986,U_985] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_985,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_985,U_986,U_987)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_985,U_987,U_988)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_985,U_986,U_988)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_985),U_987),U_988))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_985),U_986),U_987))
      | ~ class_Orderings_Olinorder(U_985) ),
    inference(variable_rename,[status(thm)],[f_285_1]) ).

cnf(f_285_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_985,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_985,U_986,U_987)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_985,U_987,U_988)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_985,U_986,U_988)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_985),U_987),U_988))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_985),U_986),U_987))
    | ~ class_Orderings_Olinorder(U_985) ),
    inference(clausify,[status(thm)],[f_285_2]) ).

fof(f_286_1,plain,
    ! [V_n_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_n_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_n_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_n_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_atMost__Int__atLeast]) ).

fof(f_286_2,plain,
    ! [U_990,U_989] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_989,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_989),U_990)),hAPP(c_SetInterval_Oord__class_OatLeast(U_989),U_990)) = hAPP(hAPP(c_Set_Oinsert(U_989),U_990),c_Orderings_Obot__class_Obot(tc_fun(U_989,tc_HOL_Obool)))
      | ~ class_Orderings_Oorder(U_989) ),
    inference(variable_rename,[status(thm)],[f_286_1]) ).

cnf(f_286_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_989,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_989),U_990)),hAPP(c_SetInterval_Oord__class_OatLeast(U_989),U_990)) = hAPP(hAPP(c_Set_Oinsert(U_989),U_990),c_Orderings_Obot__class_Obot(tc_fun(U_989,tc_HOL_Obool)))
    | ~ class_Orderings_Oorder(U_989) ),
    inference(clausify,[status(thm)],[f_286_2]) ).

fof(f_287_1,plain,
    ! [V_u_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_u_2)
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I2_J]) ).

fof(f_287_2,plain,
    ! [U_992,U_991] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_991,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_991),U_992)),hAPP(hAPP(c_Set_Oinsert(U_991),U_992),c_Orderings_Obot__class_Obot(tc_fun(U_991,tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(U_991),U_992)
      | ~ class_Orderings_Olinorder(U_991) ),
    inference(variable_rename,[status(thm)],[f_287_1]) ).

cnf(f_287_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_991,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_991),U_992)),hAPP(hAPP(c_Set_Oinsert(U_991),U_992),c_Orderings_Obot__class_Obot(tc_fun(U_991,tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(U_991),U_992)
    | ~ class_Orderings_Olinorder(U_991) ),
    inference(clausify,[status(thm)],[f_287_2]) ).

fof(f_288_1,plain,
    ! [V_u_2,V_m_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_m_2),V_u_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_m_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I15_J]) ).

fof(f_288_2,plain,
    ! [U_996,U_995,U_994,U_993] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_993,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_993,U_994,U_995)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_993,U_995),U_996)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_993,U_994,U_996)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_993),U_995),U_996))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_993),U_994),U_995))
      | ~ class_Orderings_Olinorder(U_993) ),
    inference(variable_rename,[status(thm)],[f_288_1]) ).

cnf(f_288_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_993,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_993,U_994,U_995)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_993,U_995),U_996)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_993,U_994,U_996)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_993),U_995),U_996))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_993),U_994),U_995))
    | ~ class_Orderings_Olinorder(U_993) ),
    inference(clausify,[status(thm)],[f_288_2]) ).

fof(f_289_1,plain,
    ! [V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
      | V_x = V_y
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_linorder__cases]) ).

fof(f_289_2,plain,
    ! [U_999,U_998,U_997] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_997),U_999),U_998))
      | U_998 = U_999
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_997),U_998),U_999))
      | ~ class_Orderings_Olinorder(U_997) ),
    inference(variable_rename,[status(thm)],[f_289_1]) ).

cnf(f_289_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_997),U_999),U_998))
    | U_998 = U_999
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_997),U_998),U_999))
    | ~ class_Orderings_Olinorder(U_997) ),
    inference(clausify,[status(thm)],[f_289_2]) ).

fof(f_290_1,plain,
    ! [V_y,V_x,T_a] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
      | ~ class_Orderings_Opreorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_order__less__asym]) ).

fof(f_290_2,plain,
    ! [U_1002,U_1001,U_1000] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1000),U_1002),U_1001))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1000),U_1001),U_1002))
      | ~ class_Orderings_Opreorder(U_1000) ),
    inference(variable_rename,[status(thm)],[f_290_1]) ).

cnf(f_290_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1000),U_1002),U_1001))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1000),U_1001),U_1002))
    | ~ class_Orderings_Opreorder(U_1000) ),
    inference(clausify,[status(thm)],[f_290_2]) ).

fof(f_291_1,plain,
    ! [V_z,V_x,V_y,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_xt1_I10_J]) ).

fof(f_291_2,plain,
    ! [U_1006,U_1005,U_1004,U_1003] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1003),U_1006),U_1005))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1003),U_1006),U_1004))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1003),U_1004),U_1005))
      | ~ class_Orderings_Oorder(U_1003) ),
    inference(variable_rename,[status(thm)],[f_291_1]) ).

cnf(f_291_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1003),U_1006),U_1005))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1003),U_1006),U_1004))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1003),U_1004),U_1005))
    | ~ class_Orderings_Oorder(U_1003) ),
    inference(clausify,[status(thm)],[f_291_2]) ).

fof(f_292_1,plain,
    ! [V_z,V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
      | ~ class_Orderings_Opreorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_order__less__trans]) ).

fof(f_292_2,plain,
    ! [U_1010,U_1009,U_1008,U_1007] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1007),U_1008),U_1010))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1007),U_1009),U_1010))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1007),U_1008),U_1009))
      | ~ class_Orderings_Opreorder(U_1007) ),
    inference(variable_rename,[status(thm)],[f_292_1]) ).

cnf(f_292_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1007),U_1008),U_1010))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1007),U_1009),U_1010))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1007),U_1008),U_1009))
    | ~ class_Orderings_Opreorder(U_1007) ),
    inference(clausify,[status(thm)],[f_292_2]) ).

fof(f_293_1,plain,
    ! [V_c,V_a,V_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a))
      | V_b != V_c
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_xt1_I2_J]) ).

fof(f_293_2,plain,
    ! [U_1014,U_1013,U_1012,U_1011] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1011),U_1014),U_1013))
      | U_1012 != U_1014
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1011),U_1012),U_1013))
      | ~ class_Orderings_Oorder(U_1011) ),
    inference(variable_rename,[status(thm)],[f_293_1]) ).

cnf(f_293_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1011),U_1014),U_1013))
    | U_1012 != U_1014
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1011),U_1012),U_1013))
    | ~ class_Orderings_Oorder(U_1011) ),
    inference(clausify,[status(thm)],[f_293_2]) ).

fof(f_294_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c))
      | V_b != V_c
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
      | ~ class_Orderings_Oord(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_ord__less__eq__trans]) ).

fof(f_294_2,plain,
    ! [U_1018,U_1017,U_1016,U_1015] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1015),U_1016),U_1018))
      | U_1017 != U_1018
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1015),U_1016),U_1017))
      | ~ class_Orderings_Oord(U_1015) ),
    inference(variable_rename,[status(thm)],[f_294_1]) ).

cnf(f_294_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1015),U_1016),U_1018))
    | U_1017 != U_1018
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1015),U_1016),U_1017))
    | ~ class_Orderings_Oord(U_1015) ),
    inference(clausify,[status(thm)],[f_294_2]) ).

fof(f_295_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_b))
      | V_a != V_b
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_xt1_I1_J]) ).

fof(f_295_2,plain,
    ! [U_1022,U_1021,U_1020,U_1019] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1019),U_1022),U_1020))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1019),U_1022),U_1021))
      | U_1020 != U_1021
      | ~ class_Orderings_Oorder(U_1019) ),
    inference(variable_rename,[status(thm)],[f_295_1]) ).

cnf(f_295_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1019),U_1022),U_1020))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1019),U_1022),U_1021))
    | U_1020 != U_1021
    | ~ class_Orderings_Oorder(U_1019) ),
    inference(clausify,[status(thm)],[f_295_2]) ).

fof(f_296_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
      | V_a != V_b
      | ~ class_Orderings_Oord(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_ord__eq__less__trans]) ).

fof(f_296_2,plain,
    ! [U_1026,U_1025,U_1024,U_1023] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1023),U_1024),U_1026))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1023),U_1025),U_1026))
      | U_1024 != U_1025
      | ~ class_Orderings_Oord(U_1023) ),
    inference(variable_rename,[status(thm)],[f_296_1]) ).

cnf(f_296_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1023),U_1024),U_1026))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1023),U_1025),U_1026))
    | U_1024 != U_1025
    | ~ class_Orderings_Oord(U_1023) ),
    inference(clausify,[status(thm)],[f_296_2]) ).

fof(f_297_1,plain,
    ! [V_a,V_b,T_a] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_xt1_I9_J]) ).

fof(f_297_2,plain,
    ! [U_1029,U_1028,U_1027] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1027),U_1029),U_1028))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1027),U_1028),U_1029))
      | ~ class_Orderings_Oorder(U_1027) ),
    inference(variable_rename,[status(thm)],[f_297_1]) ).

cnf(f_297_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1027),U_1029),U_1028))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1027),U_1028),U_1029))
    | ~ class_Orderings_Oorder(U_1027) ),
    inference(clausify,[status(thm)],[f_297_2]) ).

fof(f_298_1,plain,
    ! [V_b,V_a,T_a] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
      | ~ class_Orderings_Opreorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_order__less__asym_H]) ).

fof(f_298_2,plain,
    ! [U_1032,U_1031,U_1030] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1030),U_1032),U_1031))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1030),U_1031),U_1032))
      | ~ class_Orderings_Opreorder(U_1030) ),
    inference(variable_rename,[status(thm)],[f_298_1]) ).

cnf(f_298_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1030),U_1032),U_1031))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1030),U_1031),U_1032))
    | ~ class_Orderings_Opreorder(U_1030) ),
    inference(clausify,[status(thm)],[f_298_2]) ).

fof(f_299_1,plain,
    ! [V_y,V_x,T_a] :
      ( V_y != V_x
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__eq2]) ).

fof(f_299_2,plain,
    ! [U_1035,U_1034,U_1033] :
      ( U_1035 != U_1034
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1033),U_1034),U_1035))
      | ~ class_Orderings_Oorder(U_1033) ),
    inference(variable_rename,[status(thm)],[f_299_1]) ).

cnf(f_299_3,plain,
    ( U_1035 != U_1034
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1033),U_1034),U_1035))
    | ~ class_Orderings_Oorder(U_1033) ),
    inference(clausify,[status(thm)],[f_299_2]) ).

fof(f_300_1,plain,
    ! [V_y,V_x,T_a] :
      ( V_x != V_y
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__eq]) ).

fof(f_300_2,plain,
    ! [U_1038,U_1037,U_1036] :
      ( U_1037 != U_1038
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1036),U_1037),U_1038))
      | ~ class_Orderings_Oorder(U_1036) ),
    inference(variable_rename,[status(thm)],[f_300_1]) ).

cnf(f_300_3,plain,
    ( U_1037 != U_1038
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1036),U_1037),U_1038))
    | ~ class_Orderings_Oorder(U_1036) ),
    inference(clausify,[status(thm)],[f_300_2]) ).

fof(f_301_1,plain,
    ! [V_y,V_x,T_a] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
      | ~ class_Orderings_Opreorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__less]) ).

fof(f_301_2,plain,
    ! [U_1041,U_1040,U_1039] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1039),U_1041),U_1040))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1039),U_1040),U_1041))
      | ~ class_Orderings_Opreorder(U_1039) ),
    inference(variable_rename,[status(thm)],[f_301_1]) ).

cnf(f_301_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1039),U_1041),U_1040))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1039),U_1040),U_1041))
    | ~ class_Orderings_Opreorder(U_1039) ),
    inference(clausify,[status(thm)],[f_301_2]) ).

fof(f_302_1,plain,
    ! [V_y,V_x,T_a] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
      | ~ class_Orderings_Opreorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_order__less__not__sym]) ).

fof(f_302_2,plain,
    ! [U_1044,U_1043,U_1042] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1042),U_1044),U_1043))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1042),U_1043),U_1044))
      | ~ class_Orderings_Opreorder(U_1042) ),
    inference(variable_rename,[status(thm)],[f_302_1]) ).

cnf(f_302_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1042),U_1044),U_1043))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1042),U_1043),U_1044))
    | ~ class_Orderings_Opreorder(U_1042) ),
    inference(clausify,[status(thm)],[f_302_2]) ).

fof(f_303_1,plain,
    ! [V_y,V_x,T_a] :
      ( V_x != V_y
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_less__imp__neq]) ).

fof(f_303_2,plain,
    ! [U_1047,U_1046,U_1045] :
      ( U_1046 != U_1047
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1045),U_1046),U_1047))
      | ~ class_Orderings_Oorder(U_1045) ),
    inference(variable_rename,[status(thm)],[f_303_1]) ).

cnf(f_303_3,plain,
    ( U_1046 != U_1047
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1045),U_1046),U_1047))
    | ~ class_Orderings_Oorder(U_1045) ),
    inference(clausify,[status(thm)],[f_303_2]) ).

fof(f_304_1,plain,
    ! [V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
      | V_x = V_y
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_linorder__neqE]) ).

fof(f_304_2,plain,
    ! [U_1050,U_1049,U_1048] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1048),U_1050),U_1049))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1048),U_1049),U_1050))
      | U_1049 = U_1050
      | ~ class_Orderings_Olinorder(U_1048) ),
    inference(variable_rename,[status(thm)],[f_304_1]) ).

cnf(f_304_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1048),U_1050),U_1049))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1048),U_1049),U_1050))
    | U_1049 = U_1050
    | ~ class_Orderings_Olinorder(U_1048) ),
    inference(clausify,[status(thm)],[f_304_2]) ).

fof(f_305_1,plain,
    ! [V_x_2,V_y_2,T_b] :
      ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
          | V_x_2 != V_y_2 )
        & ( V_x_2 = V_y_2
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) ) )
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_linorder__antisym__conv3]) ).

fof(f_305_2,plain,
    ! [U_1053,U_1052,U_1051] :
      ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1051),U_1053),U_1052))
          | U_1053 != U_1052 )
        & ( U_1053 = U_1052
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1051),U_1053),U_1052)) ) )
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1051),U_1052),U_1053))
      | ~ class_Orderings_Olinorder(U_1051) ),
    inference(variable_rename,[status(thm)],[f_305_1]) ).

cnf(f_305_3,plain,
    ( U_1053 = U_1052
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1051),U_1053),U_1052))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1051),U_1052),U_1053))
    | ~ class_Orderings_Olinorder(U_1051) ),
    inference(clausify,[status(thm)],[f_305_2]) ).

cnf(f_305_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1051),U_1053),U_1052))
    | U_1053 != U_1052
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1051),U_1052),U_1053))
    | ~ class_Orderings_Olinorder(U_1051) ),
    inference(clausify,[status(thm)],[f_305_2]) ).

fof(f_306_1,plain,
    ! [V_x_2,V_A_2,V_y_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),V_A_2),V_x_2))
        | ( ~ hBOOL(hAPP(V_A_2,V_x_2))
          & V_y_2 != V_x_2 ) )
      & ( hBOOL(hAPP(V_A_2,V_x_2))
        | V_y_2 = V_x_2
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),V_A_2),V_x_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_insert__code]) ).

fof(f_306_2,plain,
    ! [U_1057,U_1056,U_1055,U_1054] :
      ( ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_1054),U_1055),U_1056),U_1057))
        | ( ~ hBOOL(hAPP(U_1056,U_1057))
          & U_1055 != U_1057 ) )
      & ( hBOOL(hAPP(U_1056,U_1057))
        | U_1055 = U_1057
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_1054),U_1055),U_1056),U_1057)) ) ),
    inference(variable_rename,[status(thm)],[f_306_1]) ).

fof(f_306_3,plain,
    ( ! [U_1065,U_1063,U_1061] :
        ( ! [U_1059] : hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_1059),U_1061),U_1063),U_1065))
        | ( ~ hBOOL(hAPP(U_1063,U_1065))
          & U_1061 != U_1065 ) )
    & ! [U_1064,U_1062,U_1060] :
        ( ! [U_1058] : ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_1058),U_1060),U_1062),U_1064))
        | hBOOL(hAPP(U_1062,U_1064))
        | U_1060 = U_1064 ) ),
    inference(miniscope,[status(thm)],[f_306_2]) ).

cnf(f_306_4,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_1058),U_1060),U_1062),U_1064))
    | hBOOL(hAPP(U_1062,U_1064))
    | U_1060 = U_1064 ),
    inference(clausify,[status(thm)],[f_306_3]) ).

cnf(f_306_5,plain,
    ( U_1061 != U_1065
    | hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_1059),U_1061),U_1063),U_1065)) ),
    inference(clausify,[status(thm)],[f_306_3]) ).

cnf(f_306_6,plain,
    ( ~ hBOOL(hAPP(U_1063,U_1065))
    | hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_1059),U_1061),U_1063),U_1065)) ),
    inference(clausify,[status(thm)],[f_306_3]) ).

fof(f_307_1,plain,
    ! [V_A_2,V_y_2,V_x_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),V_A_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_insert__commute]) ).

fof(f_307_2,plain,
    ! [U_1069,U_1068,U_1067,U_1066] : hAPP(hAPP(c_Set_Oinsert(U_1066),U_1067),hAPP(hAPP(c_Set_Oinsert(U_1066),U_1068),U_1069)) = hAPP(hAPP(c_Set_Oinsert(U_1066),U_1068),hAPP(hAPP(c_Set_Oinsert(U_1066),U_1067),U_1069)),
    inference(variable_rename,[status(thm)],[f_307_1]) ).

cnf(f_307_3,plain,
    hAPP(hAPP(c_Set_Oinsert(U_1066),U_1067),hAPP(hAPP(c_Set_Oinsert(U_1066),U_1068),U_1069)) = hAPP(hAPP(c_Set_Oinsert(U_1066),U_1068),hAPP(hAPP(c_Set_Oinsert(U_1066),U_1067),U_1069)),
    inference(clausify,[status(thm)],[f_307_2]) ).

fof(f_308_1,plain,
    ! [V_A_2,V_x_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2),
    inference(fof_nnf,[status(thm)],[fact_insert__absorb2]) ).

fof(f_308_2,plain,
    ! [U_1072,U_1071,U_1070] : hAPP(hAPP(c_Set_Oinsert(U_1070),U_1071),hAPP(hAPP(c_Set_Oinsert(U_1070),U_1071),U_1072)) = hAPP(hAPP(c_Set_Oinsert(U_1070),U_1071),U_1072),
    inference(variable_rename,[status(thm)],[f_308_1]) ).

cnf(f_308_3,plain,
    hAPP(hAPP(c_Set_Oinsert(U_1070),U_1071),hAPP(hAPP(c_Set_Oinsert(U_1070),U_1071),U_1072)) = hAPP(hAPP(c_Set_Oinsert(U_1070),U_1071),U_1072),
    inference(clausify,[status(thm)],[f_308_2]) ).

fof(f_309_1,plain,
    ! [V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
      | V_x = V_y
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_linorder__less__linear]) ).

fof(f_309_2,plain,
    ! [U_1075,U_1074,U_1073] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1073),U_1075),U_1074))
      | U_1074 = U_1075
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1073),U_1074),U_1075))
      | ~ class_Orderings_Olinorder(U_1073) ),
    inference(variable_rename,[status(thm)],[f_309_1]) ).

cnf(f_309_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1073),U_1075),U_1074))
    | U_1074 = U_1075
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1073),U_1074),U_1075))
    | ~ class_Orderings_Olinorder(U_1073) ),
    inference(clausify,[status(thm)],[f_309_2]) ).

fof(f_310_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
          | ( V_x_2 != V_y_2
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) ) )
        & ( V_x_2 = V_y_2
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) ) )
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_not__less__iff__gr__or__eq]) ).

fof(f_310_2,plain,
    ! [U_1078,U_1077,U_1076] :
      ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1076),U_1077),U_1078))
          | ( U_1077 != U_1078
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1076),U_1078),U_1077)) ) )
        & ( U_1077 = U_1078
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1076),U_1078),U_1077))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1076),U_1077),U_1078)) ) )
      | ~ class_Orderings_Olinorder(U_1076) ),
    inference(variable_rename,[status(thm)],[f_310_1]) ).

cnf(f_310_3,plain,
    ( U_1077 = U_1078
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1076),U_1078),U_1077))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1076),U_1077),U_1078))
    | ~ class_Orderings_Olinorder(U_1076) ),
    inference(clausify,[status(thm)],[f_310_2]) ).

cnf(f_310_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1076),U_1078),U_1077))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1076),U_1077),U_1078))
    | ~ class_Orderings_Olinorder(U_1076) ),
    inference(clausify,[status(thm)],[f_310_2]) ).

cnf(f_310_5,plain,
    ( U_1077 != U_1078
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1076),U_1077),U_1078))
    | ~ class_Orderings_Olinorder(U_1076) ),
    inference(clausify,[status(thm)],[f_310_2]) ).

fof(f_311_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( V_x_2 != V_y_2
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2))
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) ) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
          | V_x_2 = V_y_2 ) )
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_linorder__neq__iff]) ).

fof(f_311_2,plain,
    ! [U_1081,U_1080,U_1079] :
      ( ( ( U_1080 != U_1081
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1079),U_1081),U_1080))
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1079),U_1080),U_1081)) ) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1079),U_1081),U_1080))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1079),U_1080),U_1081))
          | U_1080 = U_1081 ) )
      | ~ class_Orderings_Olinorder(U_1079) ),
    inference(variable_rename,[status(thm)],[f_311_1]) ).

cnf(f_311_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1079),U_1081),U_1080))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1079),U_1080),U_1081))
    | U_1080 = U_1081
    | ~ class_Orderings_Olinorder(U_1079) ),
    inference(clausify,[status(thm)],[f_311_2]) ).

cnf(f_311_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1079),U_1080),U_1081))
    | U_1080 != U_1081
    | ~ class_Orderings_Olinorder(U_1079) ),
    inference(clausify,[status(thm)],[f_311_2]) ).

cnf(f_311_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1079),U_1081),U_1080))
    | U_1080 != U_1081
    | ~ class_Orderings_Olinorder(U_1079) ),
    inference(clausify,[status(thm)],[f_311_2]) ).

fof(f_312_1,plain,
    ! [V_x,T_a] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_x))
      | ~ class_Orderings_Opreorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_order__less__irrefl]) ).

fof(f_312_2,plain,
    ! [U_1083,U_1082] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1082),U_1083),U_1083))
      | ~ class_Orderings_Opreorder(U_1082) ),
    inference(variable_rename,[status(thm)],[f_312_1]) ).

cnf(f_312_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1082),U_1083),U_1083))
    | ~ class_Orderings_Opreorder(U_1082) ),
    inference(clausify,[status(thm)],[f_312_2]) ).

fof(f_313_1,plain,
    ! [V_n_2,V_m_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_m_2)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_n_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_n_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_n_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_m_2)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_n_2))) ) )
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_lessThan__strict__subset__iff]) ).

fof(f_313_2,plain,
    ! [U_1086,U_1085,U_1084] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1084,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_1084),U_1085)),hAPP(c_SetInterval_Oord__class_OlessThan(U_1084),U_1086)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1084),U_1085),U_1086)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1084),U_1085),U_1086))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1084,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_1084),U_1085)),hAPP(c_SetInterval_Oord__class_OlessThan(U_1084),U_1086))) ) )
      | ~ class_Orderings_Olinorder(U_1084) ),
    inference(variable_rename,[status(thm)],[f_313_1]) ).

cnf(f_313_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1084),U_1085),U_1086))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1084,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_1084),U_1085)),hAPP(c_SetInterval_Oord__class_OlessThan(U_1084),U_1086)))
    | ~ class_Orderings_Olinorder(U_1084) ),
    inference(clausify,[status(thm)],[f_313_2]) ).

cnf(f_313_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1084,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_1084),U_1085)),hAPP(c_SetInterval_Oord__class_OlessThan(U_1084),U_1086)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1084),U_1085),U_1086))
    | ~ class_Orderings_Olinorder(U_1084) ),
    inference(clausify,[status(thm)],[f_313_2]) ).

fof(f_314_1,plain,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_d_2))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_d_2))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_a_2)) )
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2)) )
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_d_2))
            & ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_d_2))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_a_2)) )
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2)) )
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2))) ) )
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_atLeastatMost__psubset__iff]) ).

fof(f_314_2,plain,
    ! [U_1091,U_1090,U_1089,U_1088,U_1087] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1087,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_1087,U_1088,U_1089)),c_SetInterval_Oord__class_OatLeastAtMost(U_1087,U_1090,U_1091)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1087),U_1090),U_1091))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1087),U_1089),U_1091))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1087),U_1090),U_1088)) )
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1087),U_1089),U_1091))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1087),U_1090),U_1088)) )
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1087),U_1088),U_1089)) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1087),U_1090),U_1091))
            & ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1087),U_1089),U_1091))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1087),U_1090),U_1088)) )
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1087),U_1089),U_1091))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1087),U_1090),U_1088)) )
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1087),U_1088),U_1089)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1087,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_1087,U_1088,U_1089)),c_SetInterval_Oord__class_OatLeastAtMost(U_1087,U_1090,U_1091))) ) )
      | ~ class_Orderings_Oorder(U_1087) ),
    inference(variable_rename,[status(thm)],[f_314_1]) ).

cnf(f_314_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1087),U_1090),U_1088))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1087),U_1088),U_1089))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1087,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_1087,U_1088,U_1089)),c_SetInterval_Oord__class_OatLeastAtMost(U_1087,U_1090,U_1091)))
    | ~ class_Orderings_Oorder(U_1087) ),
    inference(clausify,[status(thm)],[f_314_2]) ).

cnf(f_314_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1087),U_1089),U_1091))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1087),U_1088),U_1089))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1087,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_1087,U_1088,U_1089)),c_SetInterval_Oord__class_OatLeastAtMost(U_1087,U_1090,U_1091)))
    | ~ class_Orderings_Oorder(U_1087) ),
    inference(clausify,[status(thm)],[f_314_2]) ).

cnf(f_314_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1087),U_1089),U_1091))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1087),U_1090),U_1088))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1087),U_1088),U_1089))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1087,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_1087,U_1088,U_1089)),c_SetInterval_Oord__class_OatLeastAtMost(U_1087,U_1090,U_1091)))
    | ~ class_Orderings_Oorder(U_1087) ),
    inference(clausify,[status(thm)],[f_314_2]) ).

cnf(f_314_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1087),U_1090),U_1091))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1087,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_1087,U_1088,U_1089)),c_SetInterval_Oord__class_OatLeastAtMost(U_1087,U_1090,U_1091)))
    | ~ class_Orderings_Oorder(U_1087) ),
    inference(clausify,[status(thm)],[f_314_2]) ).

cnf(f_314_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1087),U_1088),U_1089))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1087),U_1090),U_1091))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1087,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_1087,U_1088,U_1089)),c_SetInterval_Oord__class_OatLeastAtMost(U_1087,U_1090,U_1091)))
    | ~ class_Orderings_Oorder(U_1087) ),
    inference(clausify,[status(thm)],[f_314_2]) ).

cnf(f_314_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1087),U_1090),U_1088))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1087),U_1089),U_1091))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1087),U_1090),U_1088))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1087),U_1090),U_1091))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1087,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_1087,U_1088,U_1089)),c_SetInterval_Oord__class_OatLeastAtMost(U_1087,U_1090,U_1091)))
    | ~ class_Orderings_Oorder(U_1087) ),
    inference(clausify,[status(thm)],[f_314_2]) ).

cnf(f_314_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1087),U_1089),U_1091))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1087),U_1089),U_1091))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1087),U_1090),U_1088))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1087),U_1090),U_1091))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1087,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_1087,U_1088,U_1089)),c_SetInterval_Oord__class_OatLeastAtMost(U_1087,U_1090,U_1091)))
    | ~ class_Orderings_Oorder(U_1087) ),
    inference(clausify,[status(thm)],[f_314_2]) ).

fof(f_315_1,plain,
    ! [V_g_2,V_f_2,T_b,T_c] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,T_c)),V_f_2),V_g_2))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_g_2),V_f_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) )
        & ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_g_2),V_f_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,T_c)),V_f_2),V_g_2)) ) )
      | ~ class_Orderings_Oord(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_less__fun__def]) ).

fof(f_315_2,plain,
    ! [U_1095,U_1094,U_1093,U_1092] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1093,U_1092)),U_1094),U_1095))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1093,U_1092)),U_1095),U_1094))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1093,U_1092)),U_1094),U_1095)) )
        & ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1093,U_1092)),U_1095),U_1094))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1093,U_1092)),U_1094),U_1095)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1093,U_1092)),U_1094),U_1095)) ) )
      | ~ class_Orderings_Oord(U_1092) ),
    inference(variable_rename,[status(thm)],[f_315_1]) ).

cnf(f_315_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1093,U_1092)),U_1094),U_1095))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1093,U_1092)),U_1094),U_1095))
    | ~ class_Orderings_Oord(U_1092) ),
    inference(clausify,[status(thm)],[f_315_2]) ).

cnf(f_315_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1093,U_1092)),U_1095),U_1094))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1093,U_1092)),U_1094),U_1095))
    | ~ class_Orderings_Oord(U_1092) ),
    inference(clausify,[status(thm)],[f_315_2]) ).

cnf(f_315_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1093,U_1092)),U_1094),U_1095))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1093,U_1092)),U_1095),U_1094))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1093,U_1092)),U_1094),U_1095))
    | ~ class_Orderings_Oord(U_1092) ),
    inference(clausify,[status(thm)],[f_315_2]) ).

fof(f_316_1,plain,
    ! [V_z,V_x,V_y,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_xt1_I8_J]) ).

fof(f_316_2,plain,
    ! [U_1099,U_1098,U_1097,U_1096] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1096),U_1099),U_1098))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1096),U_1099),U_1097))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1096),U_1097),U_1098))
      | ~ class_Orderings_Oorder(U_1096) ),
    inference(variable_rename,[status(thm)],[f_316_1]) ).

cnf(f_316_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1096),U_1099),U_1098))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1096),U_1099),U_1097))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1096),U_1097),U_1098))
    | ~ class_Orderings_Oorder(U_1096) ),
    inference(clausify,[status(thm)],[f_316_2]) ).

fof(f_317_1,plain,
    ! [V_z,V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
      | ~ class_Orderings_Opreorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_order__le__less__trans]) ).

fof(f_317_2,plain,
    ! [U_1103,U_1102,U_1101,U_1100] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1100),U_1101),U_1103))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1100),U_1102),U_1103))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1100),U_1101),U_1102))
      | ~ class_Orderings_Opreorder(U_1100) ),
    inference(variable_rename,[status(thm)],[f_317_1]) ).

cnf(f_317_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1100),U_1101),U_1103))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1100),U_1102),U_1103))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1100),U_1101),U_1102))
    | ~ class_Orderings_Opreorder(U_1100) ),
    inference(clausify,[status(thm)],[f_317_2]) ).

fof(f_318_1,plain,
    ! [V_z,V_x,V_y,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_xt1_I7_J]) ).

fof(f_318_2,plain,
    ! [U_1107,U_1106,U_1105,U_1104] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1104),U_1107),U_1106))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1104),U_1107),U_1105))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1104),U_1105),U_1106))
      | ~ class_Orderings_Oorder(U_1104) ),
    inference(variable_rename,[status(thm)],[f_318_1]) ).

cnf(f_318_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1104),U_1107),U_1106))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1104),U_1107),U_1105))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1104),U_1105),U_1106))
    | ~ class_Orderings_Oorder(U_1104) ),
    inference(clausify,[status(thm)],[f_318_2]) ).

fof(f_319_1,plain,
    ! [V_z,V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
      | ~ class_Orderings_Opreorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_order__less__le__trans]) ).

fof(f_319_2,plain,
    ! [U_1111,U_1110,U_1109,U_1108] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1108),U_1109),U_1111))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1108),U_1110),U_1111))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1108),U_1109),U_1110))
      | ~ class_Orderings_Opreorder(U_1108) ),
    inference(variable_rename,[status(thm)],[f_319_1]) ).

cnf(f_319_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1108),U_1109),U_1111))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1108),U_1110),U_1111))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1108),U_1109),U_1110))
    | ~ class_Orderings_Opreorder(U_1108) ),
    inference(clausify,[status(thm)],[f_319_2]) ).

fof(f_320_1,plain,
    ! [V_a,V_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
      | V_a = V_b
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_xt1_I11_J]) ).

fof(f_320_2,plain,
    ! [U_1114,U_1113,U_1112] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1112),U_1113),U_1114))
      | U_1114 = U_1113
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1112),U_1113),U_1114))
      | ~ class_Orderings_Oorder(U_1112) ),
    inference(variable_rename,[status(thm)],[f_320_1]) ).

cnf(f_320_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1112),U_1113),U_1114))
    | U_1114 = U_1113
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1112),U_1113),U_1114))
    | ~ class_Orderings_Oorder(U_1112) ),
    inference(clausify,[status(thm)],[f_320_2]) ).

fof(f_321_1,plain,
    ! [V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
      | V_a = V_b
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_order__le__neq__trans]) ).

fof(f_321_2,plain,
    ! [U_1117,U_1116,U_1115] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1115),U_1116),U_1117))
      | U_1116 = U_1117
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1115),U_1116),U_1117))
      | ~ class_Orderings_Oorder(U_1115) ),
    inference(variable_rename,[status(thm)],[f_321_1]) ).

cnf(f_321_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1115),U_1116),U_1117))
    | U_1116 = U_1117
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1115),U_1116),U_1117))
    | ~ class_Orderings_Oorder(U_1115) ),
    inference(clausify,[status(thm)],[f_321_2]) ).

fof(f_322_1,plain,
    ! [V_y,V_x,T_a] :
      ( V_x = V_y
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_order__le__imp__less__or__eq]) ).

fof(f_322_2,plain,
    ! [U_1120,U_1119,U_1118] :
      ( U_1119 = U_1120
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1118),U_1119),U_1120))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1118),U_1119),U_1120))
      | ~ class_Orderings_Oorder(U_1118) ),
    inference(variable_rename,[status(thm)],[f_322_1]) ).

cnf(f_322_3,plain,
    ( U_1119 = U_1120
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1118),U_1119),U_1120))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1118),U_1119),U_1120))
    | ~ class_Orderings_Oorder(U_1118) ),
    inference(clausify,[status(thm)],[f_322_2]) ).

fof(f_323_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
          | V_x_2 != V_y_2 )
        & ( V_x_2 = V_y_2
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_linorder__antisym__conv2]) ).

fof(f_323_2,plain,
    ! [U_1123,U_1122,U_1121] :
      ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1121),U_1122),U_1123))
          | U_1122 != U_1123 )
        & ( U_1122 = U_1123
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1121),U_1122),U_1123)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1121),U_1122),U_1123))
      | ~ class_Orderings_Olinorder(U_1121) ),
    inference(variable_rename,[status(thm)],[f_323_1]) ).

cnf(f_323_3,plain,
    ( U_1122 = U_1123
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1121),U_1122),U_1123))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1121),U_1122),U_1123))
    | ~ class_Orderings_Olinorder(U_1121) ),
    inference(clausify,[status(thm)],[f_323_2]) ).

cnf(f_323_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1121),U_1122),U_1123))
    | U_1122 != U_1123
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1121),U_1122),U_1123))
    | ~ class_Orderings_Olinorder(U_1121) ),
    inference(clausify,[status(thm)],[f_323_2]) ).

fof(f_324_1,plain,
    ! [V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
      | ~ class_Orderings_Opreorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_order__less__imp__le]) ).

fof(f_324_2,plain,
    ! [U_1126,U_1125,U_1124] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1124),U_1125),U_1126))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1124),U_1125),U_1126))
      | ~ class_Orderings_Opreorder(U_1124) ),
    inference(variable_rename,[status(thm)],[f_324_1]) ).

cnf(f_324_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1124),U_1125),U_1126))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1124),U_1125),U_1126))
    | ~ class_Orderings_Opreorder(U_1124) ),
    inference(clausify,[status(thm)],[f_324_2]) ).

fof(f_325_1,plain,
    ! [V_x,V_y,T_a] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_leD]) ).

fof(f_325_2,plain,
    ! [U_1129,U_1128,U_1127] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1127),U_1129),U_1128))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1127),U_1128),U_1129))
      | ~ class_Orderings_Olinorder(U_1127) ),
    inference(variable_rename,[status(thm)],[f_325_1]) ).

cnf(f_325_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1127),U_1129),U_1128))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1127),U_1128),U_1129))
    | ~ class_Orderings_Olinorder(U_1127) ),
    inference(clausify,[status(thm)],[f_325_2]) ).

fof(f_326_1,plain,
    ! [V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
      | V_a = V_b
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_xt1_I12_J]) ).

fof(f_326_2,plain,
    ! [U_1132,U_1131,U_1130] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1130),U_1132),U_1131))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1130),U_1132),U_1131))
      | U_1131 = U_1132
      | ~ class_Orderings_Oorder(U_1130) ),
    inference(variable_rename,[status(thm)],[f_326_1]) ).

cnf(f_326_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1130),U_1132),U_1131))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1130),U_1132),U_1131))
    | U_1131 = U_1132
    | ~ class_Orderings_Oorder(U_1130) ),
    inference(clausify,[status(thm)],[f_326_2]) ).

fof(f_327_1,plain,
    ! [V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
      | V_a = V_b
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_order__neq__le__trans]) ).

fof(f_327_2,plain,
    ! [U_1135,U_1134,U_1133] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1133),U_1134),U_1135))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1133),U_1134),U_1135))
      | U_1134 = U_1135
      | ~ class_Orderings_Oorder(U_1133) ),
    inference(variable_rename,[status(thm)],[f_327_1]) ).

cnf(f_327_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1133),U_1134),U_1135))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1133),U_1134),U_1135))
    | U_1134 = U_1135
    | ~ class_Orderings_Oorder(U_1133) ),
    inference(clausify,[status(thm)],[f_327_2]) ).

fof(f_328_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
          | V_x_2 != V_y_2 )
        & ( V_x_2 = V_y_2
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) )
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_linorder__antisym__conv1]) ).

fof(f_328_2,plain,
    ! [U_1138,U_1137,U_1136] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1136),U_1137),U_1138))
          | U_1137 != U_1138 )
        & ( U_1137 = U_1138
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1136),U_1137),U_1138)) ) )
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1136),U_1137),U_1138))
      | ~ class_Orderings_Olinorder(U_1136) ),
    inference(variable_rename,[status(thm)],[f_328_1]) ).

cnf(f_328_3,plain,
    ( U_1137 = U_1138
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1136),U_1137),U_1138))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1136),U_1137),U_1138))
    | ~ class_Orderings_Olinorder(U_1136) ),
    inference(clausify,[status(thm)],[f_328_2]) ).

cnf(f_328_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1136),U_1137),U_1138))
    | U_1137 != U_1138
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1136),U_1137),U_1138))
    | ~ class_Orderings_Olinorder(U_1136) ),
    inference(clausify,[status(thm)],[f_328_2]) ).

fof(f_329_1,plain,
    ! [V_x,V_y,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_not__leE]) ).

fof(f_329_2,plain,
    ! [U_1141,U_1140,U_1139] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1139),U_1141),U_1140))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1139),U_1140),U_1141))
      | ~ class_Orderings_Olinorder(U_1139) ),
    inference(variable_rename,[status(thm)],[f_329_1]) ).

cnf(f_329_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1139),U_1141),U_1140))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1139),U_1140),U_1141))
    | ~ class_Orderings_Olinorder(U_1139) ),
    inference(clausify,[status(thm)],[f_329_2]) ).

fof(f_330_1,plain,
    ! [V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_leI]) ).

fof(f_330_2,plain,
    ! [U_1144,U_1143,U_1142] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1142),U_1144),U_1143))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1142),U_1143),U_1144))
      | ~ class_Orderings_Olinorder(U_1142) ),
    inference(variable_rename,[status(thm)],[f_330_1]) ).

cnf(f_330_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1142),U_1144),U_1143))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1142),U_1143),U_1144))
    | ~ class_Orderings_Olinorder(U_1142) ),
    inference(clausify,[status(thm)],[f_330_2]) ).

fof(f_331_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
          | ( V_x_2 != V_y_2
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) ) )
        & ( V_x_2 = V_y_2
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) )
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_order__le__less]) ).

fof(f_331_2,plain,
    ! [U_1147,U_1146,U_1145] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1145),U_1146),U_1147))
          | ( U_1146 != U_1147
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1145),U_1146),U_1147)) ) )
        & ( U_1146 = U_1147
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1145),U_1146),U_1147))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1145),U_1146),U_1147)) ) )
      | ~ class_Orderings_Oorder(U_1145) ),
    inference(variable_rename,[status(thm)],[f_331_1]) ).

cnf(f_331_3,plain,
    ( U_1146 = U_1147
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1145),U_1146),U_1147))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1145),U_1146),U_1147))
    | ~ class_Orderings_Oorder(U_1145) ),
    inference(clausify,[status(thm)],[f_331_2]) ).

cnf(f_331_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1145),U_1146),U_1147))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1145),U_1146),U_1147))
    | ~ class_Orderings_Oorder(U_1145) ),
    inference(clausify,[status(thm)],[f_331_2]) ).

cnf(f_331_5,plain,
    ( U_1146 != U_1147
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1145),U_1146),U_1147))
    | ~ class_Orderings_Oorder(U_1145) ),
    inference(clausify,[status(thm)],[f_331_2]) ).

fof(f_332_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) )
        & ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) ) )
      | ~ class_Orderings_Opreorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_less__le__not__le]) ).

fof(f_332_2,plain,
    ! [U_1150,U_1149,U_1148] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1148),U_1149),U_1150))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1148),U_1150),U_1149))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1148),U_1149),U_1150)) )
        & ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1148),U_1150),U_1149))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1148),U_1149),U_1150)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1148),U_1149),U_1150)) ) )
      | ~ class_Orderings_Opreorder(U_1148) ),
    inference(variable_rename,[status(thm)],[f_332_1]) ).

cnf(f_332_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1148),U_1149),U_1150))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1148),U_1149),U_1150))
    | ~ class_Orderings_Opreorder(U_1148) ),
    inference(clausify,[status(thm)],[f_332_2]) ).

cnf(f_332_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1148),U_1150),U_1149))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1148),U_1149),U_1150))
    | ~ class_Orderings_Opreorder(U_1148) ),
    inference(clausify,[status(thm)],[f_332_2]) ).

cnf(f_332_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1148),U_1149),U_1150))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1148),U_1150),U_1149))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1148),U_1149),U_1150))
    | ~ class_Orderings_Opreorder(U_1148) ),
    inference(clausify,[status(thm)],[f_332_2]) ).

fof(f_333_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
          | V_x_2 = V_y_2
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) )
        & ( ( V_x_2 != V_y_2
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) ) )
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_order__less__le]) ).

fof(f_333_2,plain,
    ! [U_1153,U_1152,U_1151] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1151),U_1152),U_1153))
          | U_1152 = U_1153
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1151),U_1152),U_1153)) )
        & ( ( U_1152 != U_1153
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1151),U_1152),U_1153)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1151),U_1152),U_1153)) ) )
      | ~ class_Orderings_Oorder(U_1151) ),
    inference(variable_rename,[status(thm)],[f_333_1]) ).

cnf(f_333_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1151),U_1152),U_1153))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1151),U_1152),U_1153))
    | ~ class_Orderings_Oorder(U_1151) ),
    inference(clausify,[status(thm)],[f_333_2]) ).

cnf(f_333_4,plain,
    ( U_1152 != U_1153
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1151),U_1152),U_1153))
    | ~ class_Orderings_Oorder(U_1151) ),
    inference(clausify,[status(thm)],[f_333_2]) ).

cnf(f_333_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1151),U_1152),U_1153))
    | U_1152 = U_1153
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1151),U_1152),U_1153))
    | ~ class_Orderings_Oorder(U_1151) ),
    inference(clausify,[status(thm)],[f_333_2]) ).

fof(f_334_1,plain,
    ! [V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_linorder__le__less__linear]) ).

fof(f_334_2,plain,
    ! [U_1156,U_1155,U_1154] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1154),U_1156),U_1155))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1154),U_1155),U_1156))
      | ~ class_Orderings_Olinorder(U_1154) ),
    inference(variable_rename,[status(thm)],[f_334_1]) ).

cnf(f_334_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1154),U_1156),U_1155))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1154),U_1155),U_1156))
    | ~ class_Orderings_Olinorder(U_1154) ),
    inference(clausify,[status(thm)],[f_334_2]) ).

fof(f_335_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) )
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_linorder__not__le]) ).

fof(f_335_2,plain,
    ! [U_1159,U_1158,U_1157] :
      ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1157),U_1158),U_1159))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1157),U_1159),U_1158)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1157),U_1159),U_1158))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1157),U_1158),U_1159)) ) )
      | ~ class_Orderings_Olinorder(U_1157) ),
    inference(variable_rename,[status(thm)],[f_335_1]) ).

cnf(f_335_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1157),U_1159),U_1158))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1157),U_1158),U_1159))
    | ~ class_Orderings_Olinorder(U_1157) ),
    inference(clausify,[status(thm)],[f_335_2]) ).

cnf(f_335_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1157),U_1158),U_1159))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1157),U_1159),U_1158))
    | ~ class_Orderings_Olinorder(U_1157) ),
    inference(clausify,[status(thm)],[f_335_2]) ).

fof(f_336_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) ) )
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_linorder__not__less]) ).

fof(f_336_2,plain,
    ! [U_1162,U_1161,U_1160] :
      ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1160),U_1161),U_1162))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1160),U_1162),U_1161)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1160),U_1162),U_1161))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1160),U_1161),U_1162)) ) )
      | ~ class_Orderings_Olinorder(U_1160) ),
    inference(variable_rename,[status(thm)],[f_336_1]) ).

cnf(f_336_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1160),U_1162),U_1161))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1160),U_1161),U_1162))
    | ~ class_Orderings_Olinorder(U_1160) ),
    inference(clausify,[status(thm)],[f_336_2]) ).

cnf(f_336_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1160),U_1161),U_1162))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1160),U_1162),U_1161))
    | ~ class_Orderings_Olinorder(U_1160) ),
    inference(clausify,[status(thm)],[f_336_2]) ).

fof(f_337_1,plain,
    ! [V_b_2,V_a_2,T_b] :
      ( V_a_2 = V_b_2
      | hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) != hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_singleton__inject]) ).

fof(f_337_2,plain,
    ! [U_1165,U_1164,U_1163] :
      ( U_1164 = U_1165
      | hAPP(hAPP(c_Set_Oinsert(U_1163),U_1164),c_Orderings_Obot__class_Obot(tc_fun(U_1163,tc_HOL_Obool))) != hAPP(hAPP(c_Set_Oinsert(U_1163),U_1165),c_Orderings_Obot__class_Obot(tc_fun(U_1163,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_337_1]) ).

fof(f_337_3,plain,
    ! [U_1165,U_1164] :
      ( ! [U_1163] : hAPP(hAPP(c_Set_Oinsert(U_1163),U_1164),c_Orderings_Obot__class_Obot(tc_fun(U_1163,tc_HOL_Obool))) != hAPP(hAPP(c_Set_Oinsert(U_1163),U_1165),c_Orderings_Obot__class_Obot(tc_fun(U_1163,tc_HOL_Obool)))
      | U_1164 = U_1165 ),
    inference(miniscope,[status(thm)],[f_337_2]) ).

cnf(f_337_4,plain,
    ( hAPP(hAPP(c_Set_Oinsert(U_1163),U_1164),c_Orderings_Obot__class_Obot(tc_fun(U_1163,tc_HOL_Obool))) != hAPP(hAPP(c_Set_Oinsert(U_1163),U_1165),c_Orderings_Obot__class_Obot(tc_fun(U_1163,tc_HOL_Obool)))
    | U_1164 = U_1165 ),
    inference(clausify,[status(thm)],[f_337_3]) ).

fof(f_338_1,plain,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
      ( ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(T_b),V_c_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_d_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
        | ( ( V_b_2 != V_c_2
            | V_a_2 != V_d_2 )
          & ( V_b_2 != V_d_2
            | V_a_2 != V_c_2 ) ) )
      & ( ( V_b_2 = V_c_2
          & V_a_2 = V_d_2 )
        | ( V_b_2 = V_d_2
          & V_a_2 = V_c_2 )
        | hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(T_b),V_c_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_d_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_doubleton__eq__iff]) ).

fof(f_338_2,plain,
    ! [U_1170,U_1169,U_1168,U_1167,U_1166] :
      ( ( hAPP(hAPP(c_Set_Oinsert(U_1166),U_1167),hAPP(hAPP(c_Set_Oinsert(U_1166),U_1168),c_Orderings_Obot__class_Obot(tc_fun(U_1166,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(U_1166),U_1169),hAPP(hAPP(c_Set_Oinsert(U_1166),U_1170),c_Orderings_Obot__class_Obot(tc_fun(U_1166,tc_HOL_Obool))))
        | ( ( U_1168 != U_1169
            | U_1167 != U_1170 )
          & ( U_1168 != U_1170
            | U_1167 != U_1169 ) ) )
      & ( ( U_1168 = U_1169
          & U_1167 = U_1170 )
        | ( U_1168 = U_1170
          & U_1167 = U_1169 )
        | hAPP(hAPP(c_Set_Oinsert(U_1166),U_1167),hAPP(hAPP(c_Set_Oinsert(U_1166),U_1168),c_Orderings_Obot__class_Obot(tc_fun(U_1166,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(U_1166),U_1169),hAPP(hAPP(c_Set_Oinsert(U_1166),U_1170),c_Orderings_Obot__class_Obot(tc_fun(U_1166,tc_HOL_Obool)))) ) ),
    inference(variable_rename,[status(thm)],[f_338_1]) ).

fof(f_338_3,plain,
    ( ! [U_1180,U_1178,U_1176,U_1174] :
        ( ! [U_1172] : hAPP(hAPP(c_Set_Oinsert(U_1172),U_1174),hAPP(hAPP(c_Set_Oinsert(U_1172),U_1176),c_Orderings_Obot__class_Obot(tc_fun(U_1172,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(U_1172),U_1178),hAPP(hAPP(c_Set_Oinsert(U_1172),U_1180),c_Orderings_Obot__class_Obot(tc_fun(U_1172,tc_HOL_Obool))))
        | ( ( U_1176 != U_1178
            | U_1174 != U_1180 )
          & ( U_1176 != U_1180
            | U_1174 != U_1178 ) ) )
    & ! [U_1179,U_1177,U_1175,U_1173] :
        ( ! [U_1171] : hAPP(hAPP(c_Set_Oinsert(U_1171),U_1173),hAPP(hAPP(c_Set_Oinsert(U_1171),U_1175),c_Orderings_Obot__class_Obot(tc_fun(U_1171,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(U_1171),U_1177),hAPP(hAPP(c_Set_Oinsert(U_1171),U_1179),c_Orderings_Obot__class_Obot(tc_fun(U_1171,tc_HOL_Obool))))
        | ( U_1175 = U_1177
          & U_1173 = U_1179 )
        | ( U_1175 = U_1179
          & U_1173 = U_1177 ) ) ),
    inference(miniscope,[status(thm)],[f_338_2]) ).

cnf(f_338_4,plain,
    ( U_1173 = U_1179
    | U_1173 = U_1177
    | hAPP(hAPP(c_Set_Oinsert(U_1171),U_1173),hAPP(hAPP(c_Set_Oinsert(U_1171),U_1175),c_Orderings_Obot__class_Obot(tc_fun(U_1171,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(U_1171),U_1177),hAPP(hAPP(c_Set_Oinsert(U_1171),U_1179),c_Orderings_Obot__class_Obot(tc_fun(U_1171,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_338_3]) ).

cnf(f_338_5,plain,
    ( U_1175 = U_1177
    | U_1173 = U_1177
    | hAPP(hAPP(c_Set_Oinsert(U_1171),U_1173),hAPP(hAPP(c_Set_Oinsert(U_1171),U_1175),c_Orderings_Obot__class_Obot(tc_fun(U_1171,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(U_1171),U_1177),hAPP(hAPP(c_Set_Oinsert(U_1171),U_1179),c_Orderings_Obot__class_Obot(tc_fun(U_1171,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_338_3]) ).

cnf(f_338_6,plain,
    ( U_1173 = U_1179
    | U_1175 = U_1179
    | hAPP(hAPP(c_Set_Oinsert(U_1171),U_1173),hAPP(hAPP(c_Set_Oinsert(U_1171),U_1175),c_Orderings_Obot__class_Obot(tc_fun(U_1171,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(U_1171),U_1177),hAPP(hAPP(c_Set_Oinsert(U_1171),U_1179),c_Orderings_Obot__class_Obot(tc_fun(U_1171,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_338_3]) ).

cnf(f_338_7,plain,
    ( U_1175 = U_1177
    | U_1175 = U_1179
    | hAPP(hAPP(c_Set_Oinsert(U_1171),U_1173),hAPP(hAPP(c_Set_Oinsert(U_1171),U_1175),c_Orderings_Obot__class_Obot(tc_fun(U_1171,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(U_1171),U_1177),hAPP(hAPP(c_Set_Oinsert(U_1171),U_1179),c_Orderings_Obot__class_Obot(tc_fun(U_1171,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_338_3]) ).

cnf(f_338_8,plain,
    ( U_1176 != U_1180
    | U_1174 != U_1178
    | hAPP(hAPP(c_Set_Oinsert(U_1172),U_1174),hAPP(hAPP(c_Set_Oinsert(U_1172),U_1176),c_Orderings_Obot__class_Obot(tc_fun(U_1172,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(U_1172),U_1178),hAPP(hAPP(c_Set_Oinsert(U_1172),U_1180),c_Orderings_Obot__class_Obot(tc_fun(U_1172,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_338_3]) ).

cnf(f_338_9,plain,
    ( U_1176 != U_1178
    | U_1174 != U_1180
    | hAPP(hAPP(c_Set_Oinsert(U_1172),U_1174),hAPP(hAPP(c_Set_Oinsert(U_1172),U_1176),c_Orderings_Obot__class_Obot(tc_fun(U_1172,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(U_1172),U_1178),hAPP(hAPP(c_Set_Oinsert(U_1172),U_1180),c_Orderings_Obot__class_Obot(tc_fun(U_1172,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_338_3]) ).

fof(f_339_1,plain,
    ! [V_A_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_insert__not__empty]) ).

fof(f_339_2,plain,
    ! [U_1183,U_1182,U_1181] : hAPP(hAPP(c_Set_Oinsert(U_1181),U_1182),U_1183) != c_Orderings_Obot__class_Obot(tc_fun(U_1181,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_339_1]) ).

cnf(f_339_3,plain,
    hAPP(hAPP(c_Set_Oinsert(U_1181),U_1182),U_1183) != c_Orderings_Obot__class_Obot(tc_fun(U_1181,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_339_2]) ).

fof(f_340_1,plain,
    ! [V_A_2,V_a_2,T_b] : c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2),
    inference(fof_nnf,[status(thm)],[fact_empty__not__insert]) ).

fof(f_340_2,plain,
    ! [U_1186,U_1185,U_1184] : c_Orderings_Obot__class_Obot(tc_fun(U_1184,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(U_1184),U_1185),U_1186),
    inference(variable_rename,[status(thm)],[f_340_1]) ).

cnf(f_340_3,plain,
    c_Orderings_Obot__class_Obot(tc_fun(U_1184,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(U_1184),U_1185),U_1186),
    inference(clausify,[status(thm)],[f_340_2]) ).

fof(f_341_1,plain,
    ! [V_a_2,V_D_2,V_C_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_C_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_D_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2)) ),
    inference(fof_nnf,[status(thm)],[fact_insert__mono]) ).

fof(f_341_2,plain,
    ! [U_1190,U_1189,U_1188,U_1187] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1187,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1187),U_1190),U_1188)),hAPP(hAPP(c_Set_Oinsert(U_1187),U_1190),U_1189)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1187,tc_HOL_Obool)),U_1188),U_1189)) ),
    inference(variable_rename,[status(thm)],[f_341_1]) ).

cnf(f_341_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1187,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1187),U_1190),U_1188)),hAPP(hAPP(c_Set_Oinsert(U_1187),U_1190),U_1189)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1187,tc_HOL_Obool)),U_1188),U_1189)) ),
    inference(clausify,[status(thm)],[f_341_2]) ).

fof(f_342_1,plain,
    ! [V_b_2,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_subset__insertI2]) ).

fof(f_342_2,plain,
    ! [U_1194,U_1193,U_1192,U_1191] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1191,tc_HOL_Obool)),U_1192),hAPP(hAPP(c_Set_Oinsert(U_1191),U_1194),U_1193)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1191,tc_HOL_Obool)),U_1192),U_1193)) ),
    inference(variable_rename,[status(thm)],[f_342_1]) ).

cnf(f_342_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1191,tc_HOL_Obool)),U_1192),hAPP(hAPP(c_Set_Oinsert(U_1191),U_1194),U_1193)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1191,tc_HOL_Obool)),U_1192),U_1193)) ),
    inference(clausify,[status(thm)],[f_342_2]) ).

fof(f_343_1,plain,
    ! [V_a_2,V_B_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2))),
    inference(fof_nnf,[status(thm)],[fact_subset__insertI]) ).

fof(f_343_2,plain,
    ! [U_1197,U_1196,U_1195] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1195,tc_HOL_Obool)),U_1196),hAPP(hAPP(c_Set_Oinsert(U_1195),U_1197),U_1196))),
    inference(variable_rename,[status(thm)],[f_343_1]) ).

cnf(f_343_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1195,tc_HOL_Obool)),U_1196),hAPP(hAPP(c_Set_Oinsert(U_1195),U_1197),U_1196))),
    inference(clausify,[status(thm)],[f_343_2]) ).

fof(f_344_1,plain,
    ! [V_A_2,T_b] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_not__psubset__empty]) ).

fof(f_344_2,plain,
    ! [U_1199,U_1198] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1198,tc_HOL_Obool)),U_1199),c_Orderings_Obot__class_Obot(tc_fun(U_1198,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_344_1]) ).

cnf(f_344_3,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1198,tc_HOL_Obool)),U_1199),c_Orderings_Obot__class_Obot(tc_fun(U_1198,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_344_2]) ).

fof(f_345_1,plain,
    ! [V_C_2,V_B_2,V_a_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)),
    inference(fof_nnf,[status(thm)],[fact_Un__insert__left]) ).

fof(f_345_2,plain,
    ! [U_1203,U_1202,U_1201,U_1200] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1200,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1200),U_1201),U_1202)),U_1203) = hAPP(hAPP(c_Set_Oinsert(U_1200),U_1201),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1200,tc_HOL_Obool)),U_1202),U_1203)),
    inference(variable_rename,[status(thm)],[f_345_1]) ).

cnf(f_345_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1200,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1200),U_1201),U_1202)),U_1203) = hAPP(hAPP(c_Set_Oinsert(U_1200),U_1201),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1200,tc_HOL_Obool)),U_1202),U_1203)),
    inference(clausify,[status(thm)],[f_345_2]) ).

fof(f_346_1,plain,
    ! [V_B_2,V_a_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_Un__insert__right]) ).

fof(f_346_2,plain,
    ! [U_1207,U_1206,U_1205,U_1204] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1204,tc_HOL_Obool)),U_1205),hAPP(hAPP(c_Set_Oinsert(U_1204),U_1206),U_1207)) = hAPP(hAPP(c_Set_Oinsert(U_1204),U_1206),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1204,tc_HOL_Obool)),U_1205),U_1207)),
    inference(variable_rename,[status(thm)],[f_346_1]) ).

cnf(f_346_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1204,tc_HOL_Obool)),U_1205),hAPP(hAPP(c_Set_Oinsert(U_1204),U_1206),U_1207)) = hAPP(hAPP(c_Set_Oinsert(U_1204),U_1206),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1204,tc_HOL_Obool)),U_1205),U_1207)),
    inference(clausify,[status(thm)],[f_346_2]) ).

fof(f_347_1,plain,
    ! [V_B_2,V_A_2,V_a_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_insert__inter__insert]) ).

fof(f_347_2,plain,
    ! [U_1211,U_1210,U_1209,U_1208] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1208,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1208),U_1209),U_1210)),hAPP(hAPP(c_Set_Oinsert(U_1208),U_1209),U_1211)) = hAPP(hAPP(c_Set_Oinsert(U_1208),U_1209),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1208,tc_HOL_Obool)),U_1210),U_1211)),
    inference(variable_rename,[status(thm)],[f_347_1]) ).

cnf(f_347_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1208,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1208),U_1209),U_1210)),hAPP(hAPP(c_Set_Oinsert(U_1208),U_1209),U_1211)) = hAPP(hAPP(c_Set_Oinsert(U_1208),U_1209),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1208,tc_HOL_Obool)),U_1210),U_1211)),
    inference(clausify,[status(thm)],[f_347_2]) ).

fof(f_348_1,plain,
    ! [V_b,V_a,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
      | ~ class_Lattices_Osemilattice__sup(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_less__supI1]) ).

fof(f_348_2,plain,
    ! [U_1215,U_1214,U_1213,U_1212] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1212),U_1213),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1212),U_1214),U_1215)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1212),U_1213),U_1214))
      | ~ class_Lattices_Osemilattice__sup(U_1212) ),
    inference(variable_rename,[status(thm)],[f_348_1]) ).

cnf(f_348_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1212),U_1213),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1212),U_1214),U_1215)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1212),U_1213),U_1214))
    | ~ class_Lattices_Osemilattice__sup(U_1212) ),
    inference(clausify,[status(thm)],[f_348_2]) ).

fof(f_349_1,plain,
    ! [V_a,V_b,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b))
      | ~ class_Lattices_Osemilattice__sup(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_less__supI2]) ).

fof(f_349_2,plain,
    ! [U_1219,U_1218,U_1217,U_1216] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1216),U_1217),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1216),U_1219),U_1218)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1216),U_1217),U_1218))
      | ~ class_Lattices_Osemilattice__sup(U_1216) ),
    inference(variable_rename,[status(thm)],[f_349_1]) ).

cnf(f_349_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1216),U_1217),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1216),U_1219),U_1218)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1216),U_1217),U_1218))
    | ~ class_Lattices_Osemilattice__sup(U_1216) ),
    inference(clausify,[status(thm)],[f_349_2]) ).

fof(f_350_1,plain,
    ! [V_b,V_x,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x))
      | ~ class_Lattices_Osemilattice__inf(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_less__infI1]) ).

fof(f_350_2,plain,
    ! [U_1223,U_1222,U_1221,U_1220] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1220),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1220),U_1221),U_1223)),U_1222))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1220),U_1221),U_1222))
      | ~ class_Lattices_Osemilattice__inf(U_1220) ),
    inference(variable_rename,[status(thm)],[f_350_1]) ).

cnf(f_350_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1220),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1220),U_1221),U_1223)),U_1222))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1220),U_1221),U_1222))
    | ~ class_Lattices_Osemilattice__inf(U_1220) ),
    inference(clausify,[status(thm)],[f_350_2]) ).

fof(f_351_1,plain,
    ! [V_a,V_x,V_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x))
      | ~ class_Lattices_Osemilattice__inf(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_less__infI2]) ).

fof(f_351_2,plain,
    ! [U_1227,U_1226,U_1225,U_1224] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1224),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1224),U_1227),U_1225)),U_1226))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1224),U_1225),U_1226))
      | ~ class_Lattices_Osemilattice__inf(U_1224) ),
    inference(variable_rename,[status(thm)],[f_351_1]) ).

cnf(f_351_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1224),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1224),U_1227),U_1225)),U_1226))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1224),U_1225),U_1226))
    | ~ class_Lattices_Osemilattice__inf(U_1224) ),
    inference(clausify,[status(thm)],[f_351_2]) ).

fof(f_352_1,plain,
    ! [V_b_2,V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2))) ) )
      | ~ class_Groups_Oordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_less__minus__iff]) ).

fof(f_352_2,plain,
    ! [U_1230,U_1229,U_1228] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1228),U_1229),hAPP(c_Groups_Ouminus__class_Ouminus(U_1228),U_1230)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1228),U_1230),hAPP(c_Groups_Ouminus__class_Ouminus(U_1228),U_1229))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1228),U_1230),hAPP(c_Groups_Ouminus__class_Ouminus(U_1228),U_1229)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1228),U_1229),hAPP(c_Groups_Ouminus__class_Ouminus(U_1228),U_1230))) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_1228) ),
    inference(variable_rename,[status(thm)],[f_352_1]) ).

cnf(f_352_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1228),U_1230),hAPP(c_Groups_Ouminus__class_Ouminus(U_1228),U_1229)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1228),U_1229),hAPP(c_Groups_Ouminus__class_Ouminus(U_1228),U_1230)))
    | ~ class_Groups_Oordered__ab__group__add(U_1228) ),
    inference(clausify,[status(thm)],[f_352_2]) ).

cnf(f_352_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1228),U_1229),hAPP(c_Groups_Ouminus__class_Ouminus(U_1228),U_1230)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1228),U_1230),hAPP(c_Groups_Ouminus__class_Ouminus(U_1228),U_1229)))
    | ~ class_Groups_Oordered__ab__group__add(U_1228) ),
    inference(clausify,[status(thm)],[f_352_2]) ).

fof(f_353_1,plain,
    ! [V_b_2,V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),V_a_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),V_a_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2)) ) )
      | ~ class_Groups_Oordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_minus__less__iff]) ).

fof(f_353_2,plain,
    ! [U_1233,U_1232,U_1231] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1231),hAPP(c_Groups_Ouminus__class_Ouminus(U_1231),U_1232)),U_1233))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1231),hAPP(c_Groups_Ouminus__class_Ouminus(U_1231),U_1233)),U_1232)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1231),hAPP(c_Groups_Ouminus__class_Ouminus(U_1231),U_1233)),U_1232))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1231),hAPP(c_Groups_Ouminus__class_Ouminus(U_1231),U_1232)),U_1233)) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_1231) ),
    inference(variable_rename,[status(thm)],[f_353_1]) ).

cnf(f_353_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1231),hAPP(c_Groups_Ouminus__class_Ouminus(U_1231),U_1233)),U_1232))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1231),hAPP(c_Groups_Ouminus__class_Ouminus(U_1231),U_1232)),U_1233))
    | ~ class_Groups_Oordered__ab__group__add(U_1231) ),
    inference(clausify,[status(thm)],[f_353_2]) ).

cnf(f_353_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1231),hAPP(c_Groups_Ouminus__class_Ouminus(U_1231),U_1232)),U_1233))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1231),hAPP(c_Groups_Ouminus__class_Ouminus(U_1231),U_1233)),U_1232))
    | ~ class_Groups_Oordered__ab__group__add(U_1231) ),
    inference(clausify,[status(thm)],[f_353_2]) ).

fof(f_354_1,plain,
    ! [V_a_2,V_b_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) ) )
      | ~ class_Groups_Oordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_neg__less__iff__less]) ).

fof(f_354_2,plain,
    ! [U_1236,U_1235,U_1234] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1234),hAPP(c_Groups_Ouminus__class_Ouminus(U_1234),U_1235)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1234),U_1236)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1234),U_1236),U_1235)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1234),U_1236),U_1235))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1234),hAPP(c_Groups_Ouminus__class_Ouminus(U_1234),U_1235)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1234),U_1236))) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_1234) ),
    inference(variable_rename,[status(thm)],[f_354_1]) ).

cnf(f_354_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1234),U_1236),U_1235))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1234),hAPP(c_Groups_Ouminus__class_Ouminus(U_1234),U_1235)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1234),U_1236)))
    | ~ class_Groups_Oordered__ab__group__add(U_1234) ),
    inference(clausify,[status(thm)],[f_354_2]) ).

cnf(f_354_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1234),hAPP(c_Groups_Ouminus__class_Ouminus(U_1234),U_1235)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1234),U_1236)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1234),U_1236),U_1235))
    | ~ class_Groups_Oordered__ab__group__add(U_1234) ),
    inference(clausify,[status(thm)],[f_354_2]) ).

fof(f_355_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_subset__psubset__trans]) ).

fof(f_355_2,plain,
    ! [U_1240,U_1239,U_1238,U_1237] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1237,tc_HOL_Obool)),U_1238),U_1240))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1237,tc_HOL_Obool)),U_1239),U_1240))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1237,tc_HOL_Obool)),U_1238),U_1239)) ),
    inference(variable_rename,[status(thm)],[f_355_1]) ).

cnf(f_355_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1237,tc_HOL_Obool)),U_1238),U_1240))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1237,tc_HOL_Obool)),U_1239),U_1240))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1237,tc_HOL_Obool)),U_1238),U_1239)) ),
    inference(clausify,[status(thm)],[f_355_2]) ).

fof(f_356_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_psubset__subset__trans]) ).

fof(f_356_2,plain,
    ! [U_1244,U_1243,U_1242,U_1241] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1241,tc_HOL_Obool)),U_1242),U_1244))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1241,tc_HOL_Obool)),U_1243),U_1244))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1241,tc_HOL_Obool)),U_1242),U_1243)) ),
    inference(variable_rename,[status(thm)],[f_356_1]) ).

cnf(f_356_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1241,tc_HOL_Obool)),U_1242),U_1244))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1241,tc_HOL_Obool)),U_1243),U_1244))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1241,tc_HOL_Obool)),U_1242),U_1243)) ),
    inference(clausify,[status(thm)],[f_356_2]) ).

fof(f_357_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_psubset__imp__subset]) ).

fof(f_357_2,plain,
    ! [U_1247,U_1246,U_1245] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1245,tc_HOL_Obool)),U_1246),U_1247))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1245,tc_HOL_Obool)),U_1246),U_1247)) ),
    inference(variable_rename,[status(thm)],[f_357_1]) ).

cnf(f_357_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1245,tc_HOL_Obool)),U_1246),U_1247))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1245,tc_HOL_Obool)),U_1246),U_1247)) ),
    inference(clausify,[status(thm)],[f_357_2]) ).

fof(f_358_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
        | ( V_A_2 != V_B_2
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) )
      & ( V_A_2 = V_B_2
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_subset__iff__psubset__eq]) ).

fof(f_358_2,plain,
    ! [U_1250,U_1249,U_1248] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1248,tc_HOL_Obool)),U_1249),U_1250))
        | ( U_1249 != U_1250
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1248,tc_HOL_Obool)),U_1249),U_1250)) ) )
      & ( U_1249 = U_1250
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1248,tc_HOL_Obool)),U_1249),U_1250))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1248,tc_HOL_Obool)),U_1249),U_1250)) ) ),
    inference(variable_rename,[status(thm)],[f_358_1]) ).

fof(f_358_3,plain,
    ( ! [U_1256,U_1254,U_1252] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1252,tc_HOL_Obool)),U_1254),U_1256))
        | ( U_1254 != U_1256
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1252,tc_HOL_Obool)),U_1254),U_1256)) ) )
    & ! [U_1255,U_1253,U_1251] :
        ( U_1253 = U_1255
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1251,tc_HOL_Obool)),U_1253),U_1255))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1251,tc_HOL_Obool)),U_1253),U_1255)) ) ),
    inference(miniscope,[status(thm)],[f_358_2]) ).

cnf(f_358_4,plain,
    ( U_1253 = U_1255
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1251,tc_HOL_Obool)),U_1253),U_1255))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1251,tc_HOL_Obool)),U_1253),U_1255)) ),
    inference(clausify,[status(thm)],[f_358_3]) ).

cnf(f_358_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1252,tc_HOL_Obool)),U_1254),U_1256))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1252,tc_HOL_Obool)),U_1254),U_1256)) ),
    inference(clausify,[status(thm)],[f_358_3]) ).

cnf(f_358_6,plain,
    ( U_1254 != U_1256
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1252,tc_HOL_Obool)),U_1254),U_1256)) ),
    inference(clausify,[status(thm)],[f_358_3]) ).

fof(f_359_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
        | V_A_2 = V_B_2
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
      & ( ( V_A_2 != V_B_2
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_psubset__eq]) ).

fof(f_359_2,plain,
    ! [U_1259,U_1258,U_1257] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1257,tc_HOL_Obool)),U_1258),U_1259))
        | U_1258 = U_1259
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1257,tc_HOL_Obool)),U_1258),U_1259)) )
      & ( ( U_1258 != U_1259
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1257,tc_HOL_Obool)),U_1258),U_1259)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1257,tc_HOL_Obool)),U_1258),U_1259)) ) ),
    inference(variable_rename,[status(thm)],[f_359_1]) ).

fof(f_359_3,plain,
    ( ! [U_1265,U_1263,U_1261] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1261,tc_HOL_Obool)),U_1263),U_1265))
        | U_1263 = U_1265
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1261,tc_HOL_Obool)),U_1263),U_1265)) )
    & ! [U_1264,U_1262,U_1260] :
        ( ( U_1262 != U_1264
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1260,tc_HOL_Obool)),U_1262),U_1264)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1260,tc_HOL_Obool)),U_1262),U_1264)) ) ),
    inference(miniscope,[status(thm)],[f_359_2]) ).

cnf(f_359_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1260,tc_HOL_Obool)),U_1262),U_1264))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1260,tc_HOL_Obool)),U_1262),U_1264)) ),
    inference(clausify,[status(thm)],[f_359_3]) ).

cnf(f_359_5,plain,
    ( U_1262 != U_1264
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1260,tc_HOL_Obool)),U_1262),U_1264)) ),
    inference(clausify,[status(thm)],[f_359_3]) ).

cnf(f_359_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1261,tc_HOL_Obool)),U_1263),U_1265))
    | U_1263 = U_1265
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1261,tc_HOL_Obool)),U_1263),U_1265)) ),
    inference(clausify,[status(thm)],[f_359_3]) ).

fof(f_360_1,plain,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
      ( V_b_2 = V_d_2
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
      | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__inj_I2_J]) ).

fof(f_360_2,plain,
    ! [U_1270,U_1269,U_1268,U_1267,U_1266] :
      ( U_1268 = U_1270
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1266),U_1269),U_1270))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1266),U_1267),U_1268))
      | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1266,U_1267),U_1268) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1266,U_1269),U_1270)
      | ~ class_Orderings_Olinorder(U_1266) ),
    inference(variable_rename,[status(thm)],[f_360_1]) ).

cnf(f_360_3,plain,
    ( U_1268 = U_1270
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1266),U_1269),U_1270))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1266),U_1267),U_1268))
    | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1266,U_1267),U_1268) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1266,U_1269),U_1270)
    | ~ class_Orderings_Olinorder(U_1266) ),
    inference(clausify,[status(thm)],[f_360_2]) ).

fof(f_361_1,plain,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
      ( V_a_2 = V_c_2
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
      | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__inj_I1_J]) ).

fof(f_361_2,plain,
    ! [U_1275,U_1274,U_1273,U_1272,U_1271] :
      ( U_1272 = U_1274
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1271),U_1274),U_1275))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1271),U_1272),U_1273))
      | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1271,U_1272),U_1273) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1271,U_1274),U_1275)
      | ~ class_Orderings_Olinorder(U_1271) ),
    inference(variable_rename,[status(thm)],[f_361_1]) ).

cnf(f_361_3,plain,
    ( U_1272 = U_1274
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1271),U_1274),U_1275))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1271),U_1272),U_1273))
    | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1271,U_1272),U_1273) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1271,U_1274),U_1275)
    | ~ class_Orderings_Olinorder(U_1271) ),
    inference(clausify,[status(thm)],[f_361_2]) ).

fof(f_362_1,plain,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
      ( ( ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)
          | V_b_2 != V_d_2
          | V_a_2 != V_c_2 )
        & ( ( V_b_2 = V_d_2
            & V_a_2 = V_c_2 )
          | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__eq__iff]) ).

fof(f_362_2,plain,
    ! [U_1280,U_1279,U_1278,U_1277,U_1276] :
      ( ( ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1276,U_1277),U_1278) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1276,U_1279),U_1280)
          | U_1278 != U_1280
          | U_1277 != U_1279 )
        & ( ( U_1278 = U_1280
            & U_1277 = U_1279 )
          | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1276,U_1277),U_1278) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1276,U_1279),U_1280) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1276),U_1279),U_1280))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1276),U_1277),U_1278))
      | ~ class_Orderings_Olinorder(U_1276) ),
    inference(variable_rename,[status(thm)],[f_362_1]) ).

cnf(f_362_3,plain,
    ( U_1277 = U_1279
    | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1276,U_1277),U_1278) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1276,U_1279),U_1280)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1276),U_1279),U_1280))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1276),U_1277),U_1278))
    | ~ class_Orderings_Olinorder(U_1276) ),
    inference(clausify,[status(thm)],[f_362_2]) ).

cnf(f_362_4,plain,
    ( U_1278 = U_1280
    | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1276,U_1277),U_1278) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1276,U_1279),U_1280)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1276),U_1279),U_1280))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1276),U_1277),U_1278))
    | ~ class_Orderings_Olinorder(U_1276) ),
    inference(clausify,[status(thm)],[f_362_2]) ).

cnf(f_362_5,plain,
    ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1276,U_1277),U_1278) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1276,U_1279),U_1280)
    | U_1278 != U_1280
    | U_1277 != U_1279
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1276),U_1279),U_1280))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1276),U_1277),U_1278))
    | ~ class_Orderings_Olinorder(U_1276) ),
    inference(clausify,[status(thm)],[f_362_2]) ).

fof(f_363_1,plain,
    ! [V_S_2,V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_S_2)))
          | ! [B_x] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),B_x))
              | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) ) )
        & ( ? [B_x] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),B_x))
              & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_S_2))) ) )
      | ~ class_Orderings_Olinorder(T_b)
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_less__Sup__iff]) ).

fof(f_363_2,plain,
    ! [U_1285,U_1284,U_1283] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1283),U_1284),c_Complete__Lattice_OSup__class_OSup(U_1283,U_1285)))
          | ! [U_1282] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1283),U_1284),U_1282))
              | ~ hBOOL(hAPP(hAPP(c_member(U_1283),U_1282),U_1285)) ) )
        & ( ? [U_1281] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1283),U_1284),U_1281))
              & hBOOL(hAPP(hAPP(c_member(U_1283),U_1281),U_1285)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1283),U_1284),c_Complete__Lattice_OSup__class_OSup(U_1283,U_1285))) ) )
      | ~ class_Orderings_Olinorder(U_1283)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_1283) ),
    inference(variable_rename,[status(thm)],[f_363_1]) ).

fof(f_363_3,plain,
    ! [U_1285,U_1284,U_1283] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1283),U_1284),c_Complete__Lattice_OSup__class_OSup(U_1283,U_1285)))
          | ! [U_1282] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1283),U_1284),U_1282))
              | ~ hBOOL(hAPP(hAPP(c_member(U_1283),U_1282),U_1285)) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1283),U_1284),sK15(U_1285,U_1284,U_1283)))
            & hBOOL(hAPP(hAPP(c_member(U_1283),sK15(U_1285,U_1284,U_1283)),U_1285)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1283),U_1284),c_Complete__Lattice_OSup__class_OSup(U_1283,U_1285))) ) )
      | ~ class_Orderings_Olinorder(U_1283)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_1283) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_1281,sK15(U_1285,U_1284,U_1283))],[f_363_2]) ).

cnf(f_363_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_1283),sK15(U_1285,U_1284,U_1283)),U_1285))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1283),U_1284),c_Complete__Lattice_OSup__class_OSup(U_1283,U_1285)))
    | ~ class_Orderings_Olinorder(U_1283)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_1283) ),
    inference(clausify,[status(thm)],[f_363_3]) ).

cnf(f_363_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1283),U_1284),sK15(U_1285,U_1284,U_1283)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1283),U_1284),c_Complete__Lattice_OSup__class_OSup(U_1283,U_1285)))
    | ~ class_Orderings_Olinorder(U_1283)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_1283) ),
    inference(clausify,[status(thm)],[f_363_3]) ).

cnf(f_363_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1283),U_1284),c_Complete__Lattice_OSup__class_OSup(U_1283,U_1285)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1283),U_1284),U_1282))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1283),U_1282),U_1285))
    | ~ class_Orderings_Olinorder(U_1283)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_1283) ),
    inference(clausify,[status(thm)],[f_363_3]) ).

fof(f_364_1,plain,
    ! [V_a_2,V_S_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Complete__Lattice_OInf__class_OInf(T_b,V_S_2)),V_a_2))
          | ! [B_x] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_a_2))
              | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) ) )
        & ( ? [B_x] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_a_2))
              & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Complete__Lattice_OInf__class_OInf(T_b,V_S_2)),V_a_2)) ) )
      | ~ class_Orderings_Olinorder(T_b)
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__less__iff]) ).

fof(f_364_2,plain,
    ! [U_1290,U_1289,U_1288] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1288),c_Complete__Lattice_OInf__class_OInf(U_1288,U_1289)),U_1290))
          | ! [U_1287] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1288),U_1287),U_1290))
              | ~ hBOOL(hAPP(hAPP(c_member(U_1288),U_1287),U_1289)) ) )
        & ( ? [U_1286] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1288),U_1286),U_1290))
              & hBOOL(hAPP(hAPP(c_member(U_1288),U_1286),U_1289)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1288),c_Complete__Lattice_OInf__class_OInf(U_1288,U_1289)),U_1290)) ) )
      | ~ class_Orderings_Olinorder(U_1288)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_1288) ),
    inference(variable_rename,[status(thm)],[f_364_1]) ).

fof(f_364_3,plain,
    ! [U_1290,U_1289,U_1288] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1288),c_Complete__Lattice_OInf__class_OInf(U_1288,U_1289)),U_1290))
          | ! [U_1287] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1288),U_1287),U_1290))
              | ~ hBOOL(hAPP(hAPP(c_member(U_1288),U_1287),U_1289)) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1288),sK16(U_1290,U_1289,U_1288)),U_1290))
            & hBOOL(hAPP(hAPP(c_member(U_1288),sK16(U_1290,U_1289,U_1288)),U_1289)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1288),c_Complete__Lattice_OInf__class_OInf(U_1288,U_1289)),U_1290)) ) )
      | ~ class_Orderings_Olinorder(U_1288)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_1288) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_1286,sK16(U_1290,U_1289,U_1288))],[f_364_2]) ).

cnf(f_364_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_1288),sK16(U_1290,U_1289,U_1288)),U_1289))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1288),c_Complete__Lattice_OInf__class_OInf(U_1288,U_1289)),U_1290))
    | ~ class_Orderings_Olinorder(U_1288)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_1288) ),
    inference(clausify,[status(thm)],[f_364_3]) ).

cnf(f_364_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1288),sK16(U_1290,U_1289,U_1288)),U_1290))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1288),c_Complete__Lattice_OInf__class_OInf(U_1288,U_1289)),U_1290))
    | ~ class_Orderings_Olinorder(U_1288)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_1288) ),
    inference(clausify,[status(thm)],[f_364_3]) ).

cnf(f_364_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1288),c_Complete__Lattice_OInf__class_OInf(U_1288,U_1289)),U_1290))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1288),U_1287),U_1290))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1288),U_1287),U_1289))
    | ~ class_Orderings_Olinorder(U_1288)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_1288) ),
    inference(clausify,[status(thm)],[f_364_3]) ).

fof(f_365_1,plain,
    ! [V_y_2,V_x_2,V_f_2,T_b,T_c] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
      | ~ c_Orderings_Oorder__class_Ostrict__mono(T_b,T_c,V_f_2)
      | ~ class_Orderings_Oorder(T_b)
      | ~ class_Orderings_Oorder(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_strict__monoD]) ).

fof(f_365_2,plain,
    ! [U_1295,U_1294,U_1293,U_1292,U_1291] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1291),hAPP(U_1293,U_1294)),hAPP(U_1293,U_1295)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1292),U_1294),U_1295))
      | ~ c_Orderings_Oorder__class_Ostrict__mono(U_1292,U_1291,U_1293)
      | ~ class_Orderings_Oorder(U_1292)
      | ~ class_Orderings_Oorder(U_1291) ),
    inference(variable_rename,[status(thm)],[f_365_1]) ).

cnf(f_365_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1291),hAPP(U_1293,U_1294)),hAPP(U_1293,U_1295)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1292),U_1294),U_1295))
    | ~ c_Orderings_Oorder__class_Ostrict__mono(U_1292,U_1291,U_1293)
    | ~ class_Orderings_Oorder(U_1292)
    | ~ class_Orderings_Oorder(U_1291) ),
    inference(clausify,[status(thm)],[f_365_2]) ).

fof(f_366_1,plain,
    ! [V_y_2,V_x_2,V_f_2,T_b,T_c] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) ) )
      | ~ c_Orderings_Oorder__class_Ostrict__mono(T_b,T_c,V_f_2)
      | ~ class_Orderings_Olinorder(T_b)
      | ~ class_Orderings_Oorder(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_strict__mono__less]) ).

fof(f_366_2,plain,
    ! [U_1300,U_1299,U_1298,U_1297,U_1296] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1296),hAPP(U_1298,U_1299)),hAPP(U_1298,U_1300)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1297),U_1299),U_1300)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1297),U_1299),U_1300))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1296),hAPP(U_1298,U_1299)),hAPP(U_1298,U_1300))) ) )
      | ~ c_Orderings_Oorder__class_Ostrict__mono(U_1297,U_1296,U_1298)
      | ~ class_Orderings_Olinorder(U_1297)
      | ~ class_Orderings_Oorder(U_1296) ),
    inference(variable_rename,[status(thm)],[f_366_1]) ).

cnf(f_366_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1297),U_1299),U_1300))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1296),hAPP(U_1298,U_1299)),hAPP(U_1298,U_1300)))
    | ~ c_Orderings_Oorder__class_Ostrict__mono(U_1297,U_1296,U_1298)
    | ~ class_Orderings_Olinorder(U_1297)
    | ~ class_Orderings_Oorder(U_1296) ),
    inference(clausify,[status(thm)],[f_366_2]) ).

cnf(f_366_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1296),hAPP(U_1298,U_1299)),hAPP(U_1298,U_1300)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1297),U_1299),U_1300))
    | ~ c_Orderings_Oorder__class_Ostrict__mono(U_1297,U_1296,U_1298)
    | ~ class_Orderings_Olinorder(U_1297)
    | ~ class_Orderings_Oorder(U_1296) ),
    inference(clausify,[status(thm)],[f_366_2]) ).

fof(f_367_1,plain,
    ! [V_u_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I3_J]) ).

fof(f_367_2,plain,
    ! [U_1303,U_1302,U_1301] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1301,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1301),U_1302),c_Orderings_Obot__class_Obot(tc_fun(U_1301,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1301,U_1302,U_1303)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1301,U_1302),U_1303)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1301),U_1302),U_1303))
      | ~ class_Orderings_Olinorder(U_1301) ),
    inference(variable_rename,[status(thm)],[f_367_1]) ).

cnf(f_367_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1301,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1301),U_1302),c_Orderings_Obot__class_Obot(tc_fun(U_1301,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1301,U_1302,U_1303)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1301,U_1302),U_1303)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1301),U_1302),U_1303))
    | ~ class_Orderings_Olinorder(U_1301) ),
    inference(clausify,[status(thm)],[f_367_2]) ).

fof(f_368_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) ),
    inference(fof_nnf,[status(thm)],[fact_subset__singletonD]) ).

fof(f_368_2,plain,
    ! [U_1306,U_1305,U_1304] :
      ( U_1305 = hAPP(hAPP(c_Set_Oinsert(U_1304),U_1306),c_Orderings_Obot__class_Obot(tc_fun(U_1304,tc_HOL_Obool)))
      | U_1305 = c_Orderings_Obot__class_Obot(tc_fun(U_1304,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1304,tc_HOL_Obool)),U_1305),hAPP(hAPP(c_Set_Oinsert(U_1304),U_1306),c_Orderings_Obot__class_Obot(tc_fun(U_1304,tc_HOL_Obool))))) ),
    inference(variable_rename,[status(thm)],[f_368_1]) ).

cnf(f_368_3,plain,
    ( U_1305 = hAPP(hAPP(c_Set_Oinsert(U_1304),U_1306),c_Orderings_Obot__class_Obot(tc_fun(U_1304,tc_HOL_Obool)))
    | U_1305 = c_Orderings_Obot__class_Obot(tc_fun(U_1304,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1304,tc_HOL_Obool)),U_1305),hAPP(hAPP(c_Set_Oinsert(U_1304),U_1306),c_Orderings_Obot__class_Obot(tc_fun(U_1304,tc_HOL_Obool))))) ),
    inference(clausify,[status(thm)],[f_368_2]) ).

fof(f_369_1,plain,
    ! [V_A_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_A_2),
    inference(fof_nnf,[status(thm)],[fact_insert__is__Un]) ).

fof(f_369_2,plain,
    ! [U_1309,U_1308,U_1307] : hAPP(hAPP(c_Set_Oinsert(U_1307),U_1308),U_1309) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1307,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1307),U_1308),c_Orderings_Obot__class_Obot(tc_fun(U_1307,tc_HOL_Obool)))),U_1309),
    inference(variable_rename,[status(thm)],[f_369_1]) ).

cnf(f_369_3,plain,
    hAPP(hAPP(c_Set_Oinsert(U_1307),U_1308),U_1309) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1307,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1307),U_1308),c_Orderings_Obot__class_Obot(tc_fun(U_1307,tc_HOL_Obool)))),U_1309),
    inference(clausify,[status(thm)],[f_369_2]) ).

fof(f_370_1,plain,
    ! [V_u_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I4_J]) ).

fof(f_370_2,plain,
    ! [U_1312,U_1311,U_1310] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1310,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1310,U_1311,U_1312)),hAPP(hAPP(c_Set_Oinsert(U_1310),U_1312),c_Orderings_Obot__class_Obot(tc_fun(U_1310,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_1310,U_1311,U_1312)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1310),U_1311),U_1312))
      | ~ class_Orderings_Olinorder(U_1310) ),
    inference(variable_rename,[status(thm)],[f_370_1]) ).

cnf(f_370_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1310,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1310,U_1311,U_1312)),hAPP(hAPP(c_Set_Oinsert(U_1310),U_1312),c_Orderings_Obot__class_Obot(tc_fun(U_1310,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_1310,U_1311,U_1312)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1310),U_1311),U_1312))
    | ~ class_Orderings_Olinorder(U_1310) ),
    inference(clausify,[status(thm)],[f_370_2]) ).

fof(f_371_1,plain,
    ! [V_a_2,T_b] :
      ( c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_a_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_atLeastAtMost__singleton]) ).

fof(f_371_2,plain,
    ! [U_1314,U_1313] :
      ( c_SetInterval_Oord__class_OatLeastAtMost(U_1313,U_1314,U_1314) = hAPP(hAPP(c_Set_Oinsert(U_1313),U_1314),c_Orderings_Obot__class_Obot(tc_fun(U_1313,tc_HOL_Obool)))
      | ~ class_Orderings_Oorder(U_1313) ),
    inference(variable_rename,[status(thm)],[f_371_1]) ).

cnf(f_371_3,plain,
    ( c_SetInterval_Oord__class_OatLeastAtMost(U_1313,U_1314,U_1314) = hAPP(hAPP(c_Set_Oinsert(U_1313),U_1314),c_Orderings_Obot__class_Obot(tc_fun(U_1313,tc_HOL_Obool)))
    | ~ class_Orderings_Oorder(U_1313) ),
    inference(clausify,[status(thm)],[f_371_2]) ).

fof(f_372_1,plain,
    ! [V_c_2,V_b_2,V_a_2,T_b] :
      ( ( ( c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))
          | V_b_2 != V_c_2
          | V_a_2 != V_b_2 )
        & ( ( V_b_2 = V_c_2
            & V_a_2 = V_b_2 )
          | c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) != hAPP(hAPP(c_Set_Oinsert(T_b),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) )
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_atLeastAtMost__singleton__iff]) ).

fof(f_372_2,plain,
    ! [U_1318,U_1317,U_1316,U_1315] :
      ( ( ( c_SetInterval_Oord__class_OatLeastAtMost(U_1315,U_1316,U_1317) = hAPP(hAPP(c_Set_Oinsert(U_1315),U_1318),c_Orderings_Obot__class_Obot(tc_fun(U_1315,tc_HOL_Obool)))
          | U_1317 != U_1318
          | U_1316 != U_1317 )
        & ( ( U_1317 = U_1318
            & U_1316 = U_1317 )
          | c_SetInterval_Oord__class_OatLeastAtMost(U_1315,U_1316,U_1317) != hAPP(hAPP(c_Set_Oinsert(U_1315),U_1318),c_Orderings_Obot__class_Obot(tc_fun(U_1315,tc_HOL_Obool))) ) )
      | ~ class_Orderings_Oorder(U_1315) ),
    inference(variable_rename,[status(thm)],[f_372_1]) ).

cnf(f_372_3,plain,
    ( U_1316 = U_1317
    | c_SetInterval_Oord__class_OatLeastAtMost(U_1315,U_1316,U_1317) != hAPP(hAPP(c_Set_Oinsert(U_1315),U_1318),c_Orderings_Obot__class_Obot(tc_fun(U_1315,tc_HOL_Obool)))
    | ~ class_Orderings_Oorder(U_1315) ),
    inference(clausify,[status(thm)],[f_372_2]) ).

cnf(f_372_4,plain,
    ( U_1317 = U_1318
    | c_SetInterval_Oord__class_OatLeastAtMost(U_1315,U_1316,U_1317) != hAPP(hAPP(c_Set_Oinsert(U_1315),U_1318),c_Orderings_Obot__class_Obot(tc_fun(U_1315,tc_HOL_Obool)))
    | ~ class_Orderings_Oorder(U_1315) ),
    inference(clausify,[status(thm)],[f_372_2]) ).

cnf(f_372_5,plain,
    ( c_SetInterval_Oord__class_OatLeastAtMost(U_1315,U_1316,U_1317) = hAPP(hAPP(c_Set_Oinsert(U_1315),U_1318),c_Orderings_Obot__class_Obot(tc_fun(U_1315,tc_HOL_Obool)))
    | U_1317 != U_1318
    | U_1316 != U_1317
    | ~ class_Orderings_Oorder(U_1315) ),
    inference(clausify,[status(thm)],[f_372_2]) ).

fof(f_373_1,plain,
    ! [V_b_2,V_a_2,T_b] :
      ( c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))
      | V_a_2 != V_b_2
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_atLeastAtMost__singleton_H]) ).

fof(f_373_2,plain,
    ! [U_1321,U_1320,U_1319] :
      ( c_SetInterval_Oord__class_OatLeastAtMost(U_1319,U_1320,U_1321) = hAPP(hAPP(c_Set_Oinsert(U_1319),U_1320),c_Orderings_Obot__class_Obot(tc_fun(U_1319,tc_HOL_Obool)))
      | U_1320 != U_1321
      | ~ class_Orderings_Oorder(U_1319) ),
    inference(variable_rename,[status(thm)],[f_373_1]) ).

cnf(f_373_3,plain,
    ( c_SetInterval_Oord__class_OatLeastAtMost(U_1319,U_1320,U_1321) = hAPP(hAPP(c_Set_Oinsert(U_1319),U_1320),c_Orderings_Obot__class_Obot(tc_fun(U_1319,tc_HOL_Obool)))
    | U_1320 != U_1321
    | ~ class_Orderings_Oorder(U_1319) ),
    inference(clausify,[status(thm)],[f_373_2]) ).

fof(f_374_1,plain,
    ! [V_a_2,T_b] :
      ( c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_a_2
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__singleton]) ).

fof(f_374_2,plain,
    ! [U_1323,U_1322] :
      ( c_Complete__Lattice_OSup__class_OSup(U_1322,hAPP(hAPP(c_Set_Oinsert(U_1322),U_1323),c_Orderings_Obot__class_Obot(tc_fun(U_1322,tc_HOL_Obool)))) = U_1323
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_1322) ),
    inference(variable_rename,[status(thm)],[f_374_1]) ).

cnf(f_374_3,plain,
    ( c_Complete__Lattice_OSup__class_OSup(U_1322,hAPP(hAPP(c_Set_Oinsert(U_1322),U_1323),c_Orderings_Obot__class_Obot(tc_fun(U_1322,tc_HOL_Obool)))) = U_1323
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_1322) ),
    inference(clausify,[status(thm)],[f_374_2]) ).

fof(f_375_1,plain,
    ! [V_A_2,V_a_2,T_b] :
      ( c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__insert]) ).

fof(f_375_2,plain,
    ! [U_1326,U_1325,U_1324] :
      ( c_Complete__Lattice_OSup__class_OSup(U_1324,hAPP(hAPP(c_Set_Oinsert(U_1324),U_1325),U_1326)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1324),U_1325),c_Complete__Lattice_OSup__class_OSup(U_1324,U_1326))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_1324) ),
    inference(variable_rename,[status(thm)],[f_375_1]) ).

cnf(f_375_3,plain,
    ( c_Complete__Lattice_OSup__class_OSup(U_1324,hAPP(hAPP(c_Set_Oinsert(U_1324),U_1325),U_1326)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1324),U_1325),c_Complete__Lattice_OSup__class_OSup(U_1324,U_1326))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_1324) ),
    inference(clausify,[status(thm)],[f_375_2]) ).

fof(f_376_1,plain,
    ! [V_a_2,V_b_2,T_b] :
      ( c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2))
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_atLeastatMost__empty]) ).

fof(f_376_2,plain,
    ! [U_1329,U_1328,U_1327] :
      ( c_SetInterval_Oord__class_OatLeastAtMost(U_1327,U_1329,U_1328) = c_Orderings_Obot__class_Obot(tc_fun(U_1327,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1327),U_1328),U_1329))
      | ~ class_Orderings_Oorder(U_1327) ),
    inference(variable_rename,[status(thm)],[f_376_1]) ).

cnf(f_376_3,plain,
    ( c_SetInterval_Oord__class_OatLeastAtMost(U_1327,U_1329,U_1328) = c_Orderings_Obot__class_Obot(tc_fun(U_1327,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1327),U_1328),U_1329))
    | ~ class_Orderings_Oorder(U_1327) ),
    inference(clausify,[status(thm)],[f_376_2]) ).

fof(f_377_1,plain,
    ! [V_b_2,V_a_2,T_b] :
      ( ( ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
          | c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) ) )
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__empty__iff2]) ).

fof(f_377_2,plain,
    ! [U_1332,U_1331,U_1330] :
      ( ( ( c_Orderings_Obot__class_Obot(tc_fun(U_1330,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1330,U_1331),U_1332)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1330),U_1331),U_1332)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1330),U_1331),U_1332))
          | c_Orderings_Obot__class_Obot(tc_fun(U_1330,tc_HOL_Obool)) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1330,U_1331),U_1332) ) )
      | ~ class_Orderings_Oorder(U_1330) ),
    inference(variable_rename,[status(thm)],[f_377_1]) ).

cnf(f_377_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1330),U_1331),U_1332))
    | c_Orderings_Obot__class_Obot(tc_fun(U_1330,tc_HOL_Obool)) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1330,U_1331),U_1332)
    | ~ class_Orderings_Oorder(U_1330) ),
    inference(clausify,[status(thm)],[f_377_2]) ).

cnf(f_377_4,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(U_1330,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1330,U_1331),U_1332)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1330),U_1331),U_1332))
    | ~ class_Orderings_Oorder(U_1330) ),
    inference(clausify,[status(thm)],[f_377_2]) ).

fof(f_378_1,plain,
    ! [V_b_2,V_a_2,T_b] :
      ( ( ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
          | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) )
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__empty__iff]) ).

fof(f_378_2,plain,
    ! [U_1335,U_1334,U_1333] :
      ( ( ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1333,U_1334),U_1335) = c_Orderings_Obot__class_Obot(tc_fun(U_1333,tc_HOL_Obool))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1333),U_1334),U_1335)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1333),U_1334),U_1335))
          | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1333,U_1334),U_1335) != c_Orderings_Obot__class_Obot(tc_fun(U_1333,tc_HOL_Obool)) ) )
      | ~ class_Orderings_Oorder(U_1333) ),
    inference(variable_rename,[status(thm)],[f_378_1]) ).

cnf(f_378_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1333),U_1334),U_1335))
    | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1333,U_1334),U_1335) != c_Orderings_Obot__class_Obot(tc_fun(U_1333,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_1333) ),
    inference(clausify,[status(thm)],[f_378_2]) ).

cnf(f_378_4,plain,
    ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1333,U_1334),U_1335) = c_Orderings_Obot__class_Obot(tc_fun(U_1333,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1333),U_1334),U_1335))
    | ~ class_Orderings_Oorder(U_1333) ),
    inference(clausify,[status(thm)],[f_378_2]) ).

fof(f_379_1,plain,
    ! [V_a_2,T_b] :
      ( c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_a_2
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__singleton]) ).

fof(f_379_2,plain,
    ! [U_1337,U_1336] :
      ( c_Complete__Lattice_OInf__class_OInf(U_1336,hAPP(hAPP(c_Set_Oinsert(U_1336),U_1337),c_Orderings_Obot__class_Obot(tc_fun(U_1336,tc_HOL_Obool)))) = U_1337
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_1336) ),
    inference(variable_rename,[status(thm)],[f_379_1]) ).

cnf(f_379_3,plain,
    ( c_Complete__Lattice_OInf__class_OInf(U_1336,hAPP(hAPP(c_Set_Oinsert(U_1336),U_1337),c_Orderings_Obot__class_Obot(tc_fun(U_1336,tc_HOL_Obool)))) = U_1337
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_1336) ),
    inference(clausify,[status(thm)],[f_379_2]) ).

fof(f_380_1,plain,
    ! [V_A_2,V_a_2,T_b] :
      ( c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__insert]) ).

fof(f_380_2,plain,
    ! [U_1340,U_1339,U_1338] :
      ( c_Complete__Lattice_OInf__class_OInf(U_1338,hAPP(hAPP(c_Set_Oinsert(U_1338),U_1339),U_1340)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1338),U_1339),c_Complete__Lattice_OInf__class_OInf(U_1338,U_1340))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_1338) ),
    inference(variable_rename,[status(thm)],[f_380_1]) ).

cnf(f_380_3,plain,
    ( c_Complete__Lattice_OInf__class_OInf(U_1338,hAPP(hAPP(c_Set_Oinsert(U_1338),U_1339),U_1340)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1338),U_1339),c_Complete__Lattice_OInf__class_OInf(U_1338,U_1340))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_1338) ),
    inference(clausify,[status(thm)],[f_380_2]) ).

fof(f_381_1,plain,
    ! [V_B_2,V_a_2,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_a_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_Union__insert]) ).

fof(f_381_2,plain,
    ! [U_1343,U_1342,U_1341] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1341,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_1341,tc_HOL_Obool)),U_1342),U_1343)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1341,tc_HOL_Obool)),U_1342),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1341,tc_HOL_Obool),U_1343)),
    inference(variable_rename,[status(thm)],[f_381_1]) ).

cnf(f_381_3,plain,
    c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1341,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_1341,tc_HOL_Obool)),U_1342),U_1343)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1341,tc_HOL_Obool)),U_1342),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1341,tc_HOL_Obool),U_1343)),
    inference(clausify,[status(thm)],[f_381_2]) ).

fof(f_382_1,plain,
    ! [V_l_2,V_k_2,T_b] :
      ( ( ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_k_2,V_l_2)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2))
          | c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) != c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_k_2,V_l_2) ) )
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_greaterThanAtMost__empty__iff2]) ).

fof(f_382_2,plain,
    ! [U_1346,U_1345,U_1344] :
      ( ( ( c_Orderings_Obot__class_Obot(tc_fun(U_1344,tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_1344,U_1345,U_1346)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1344),U_1345),U_1346)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1344),U_1345),U_1346))
          | c_Orderings_Obot__class_Obot(tc_fun(U_1344,tc_HOL_Obool)) != c_SetInterval_Oord__class_OgreaterThanAtMost(U_1344,U_1345,U_1346) ) )
      | ~ class_Orderings_Oorder(U_1344) ),
    inference(variable_rename,[status(thm)],[f_382_1]) ).

cnf(f_382_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1344),U_1345),U_1346))
    | c_Orderings_Obot__class_Obot(tc_fun(U_1344,tc_HOL_Obool)) != c_SetInterval_Oord__class_OgreaterThanAtMost(U_1344,U_1345,U_1346)
    | ~ class_Orderings_Oorder(U_1344) ),
    inference(clausify,[status(thm)],[f_382_2]) ).

cnf(f_382_4,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(U_1344,tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_1344,U_1345,U_1346)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1344),U_1345),U_1346))
    | ~ class_Orderings_Oorder(U_1344) ),
    inference(clausify,[status(thm)],[f_382_2]) ).

fof(f_383_1,plain,
    ! [V_l_2,V_k_2,T_b] :
      ( ( ( c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2))
          | c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_k_2,V_l_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) )
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_greaterThanAtMost__empty__iff]) ).

fof(f_383_2,plain,
    ! [U_1349,U_1348,U_1347] :
      ( ( ( c_SetInterval_Oord__class_OgreaterThanAtMost(U_1347,U_1348,U_1349) = c_Orderings_Obot__class_Obot(tc_fun(U_1347,tc_HOL_Obool))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1347),U_1348),U_1349)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1347),U_1348),U_1349))
          | c_SetInterval_Oord__class_OgreaterThanAtMost(U_1347,U_1348,U_1349) != c_Orderings_Obot__class_Obot(tc_fun(U_1347,tc_HOL_Obool)) ) )
      | ~ class_Orderings_Oorder(U_1347) ),
    inference(variable_rename,[status(thm)],[f_383_1]) ).

cnf(f_383_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1347),U_1348),U_1349))
    | c_SetInterval_Oord__class_OgreaterThanAtMost(U_1347,U_1348,U_1349) != c_Orderings_Obot__class_Obot(tc_fun(U_1347,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_1347) ),
    inference(clausify,[status(thm)],[f_383_2]) ).

cnf(f_383_4,plain,
    ( c_SetInterval_Oord__class_OgreaterThanAtMost(U_1347,U_1348,U_1349) = c_Orderings_Obot__class_Obot(tc_fun(U_1347,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1347),U_1348),U_1349))
    | ~ class_Orderings_Oorder(U_1347) ),
    inference(clausify,[status(thm)],[f_383_2]) ).

fof(f_384_1,plain,
    ! [V_B_2,V_a_2,T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_a_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_Inter__insert]) ).

fof(f_384_2,plain,
    ! [U_1352,U_1351,U_1350] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_1350,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_1350,tc_HOL_Obool)),U_1351),U_1352)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1350,tc_HOL_Obool)),U_1351),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_1350,tc_HOL_Obool),U_1352)),
    inference(variable_rename,[status(thm)],[f_384_1]) ).

cnf(f_384_3,plain,
    c_Complete__Lattice_OInf__class_OInf(tc_fun(U_1350,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_1350,tc_HOL_Obool)),U_1351),U_1352)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1350,tc_HOL_Obool)),U_1351),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_1350,tc_HOL_Obool),U_1352)),
    inference(clausify,[status(thm)],[f_384_2]) ).

fof(f_385_1,plain,
    ! [V_tsa_2,V_t_2,V_G_2,T_b] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),V_t_2),V_tsa_2))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_tsa_2)
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),V_t_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ),
    inference(fof_nnf,[status(thm)],[fact_hoare__derivs_Oinsert]) ).

fof(f_385_2,plain,
    ! [U_1356,U_1355,U_1354,U_1353] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_1353,U_1354,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_1353)),U_1355),U_1356))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_1353,U_1354,U_1356)
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_1353,U_1354,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_1353)),U_1355),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_1353),tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_385_1]) ).

cnf(f_385_3,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_1353,U_1354,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_1353)),U_1355),U_1356))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_1353,U_1354,U_1356)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_1353,U_1354,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_1353)),U_1355),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_1353),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_385_2]) ).

fof(f_386_1,plain,
    ! [V_b_2,V_a_2,T_b] :
      ( c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),V_b_2)
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__binary]) ).

fof(f_386_2,plain,
    ! [U_1359,U_1358,U_1357] :
      ( c_Complete__Lattice_OSup__class_OSup(U_1357,hAPP(hAPP(c_Set_Oinsert(U_1357),U_1358),hAPP(hAPP(c_Set_Oinsert(U_1357),U_1359),c_Orderings_Obot__class_Obot(tc_fun(U_1357,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1357),U_1358),U_1359)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_1357) ),
    inference(variable_rename,[status(thm)],[f_386_1]) ).

cnf(f_386_3,plain,
    ( c_Complete__Lattice_OSup__class_OSup(U_1357,hAPP(hAPP(c_Set_Oinsert(U_1357),U_1358),hAPP(hAPP(c_Set_Oinsert(U_1357),U_1359),c_Orderings_Obot__class_Obot(tc_fun(U_1357,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1357),U_1358),U_1359)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_1357) ),
    inference(clausify,[status(thm)],[f_386_2]) ).

fof(f_387_1,plain,
    ! [V_b_2,V_a_2,T_b] :
      ( c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),V_b_2)
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__binary]) ).

fof(f_387_2,plain,
    ! [U_1362,U_1361,U_1360] :
      ( c_Complete__Lattice_OInf__class_OInf(U_1360,hAPP(hAPP(c_Set_Oinsert(U_1360),U_1361),hAPP(hAPP(c_Set_Oinsert(U_1360),U_1362),c_Orderings_Obot__class_Obot(tc_fun(U_1360,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1360),U_1361),U_1362)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_1360) ),
    inference(variable_rename,[status(thm)],[f_387_1]) ).

cnf(f_387_3,plain,
    ( c_Complete__Lattice_OInf__class_OInf(U_1360,hAPP(hAPP(c_Set_Oinsert(U_1360),U_1361),hAPP(hAPP(c_Set_Oinsert(U_1360),U_1362),c_Orderings_Obot__class_Obot(tc_fun(U_1360,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1360),U_1361),U_1362)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_1360) ),
    inference(clausify,[status(thm)],[f_387_2]) ).

fof(f_388_1,plain,
    ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_B_2),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))))),
    inference(fof_nnf,[status(thm)],[fact_Un__eq__Union]) ).

fof(f_388_2,plain,
    ! [U_1365,U_1364,U_1363] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1363,tc_HOL_Obool)),U_1364),U_1365) = c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1363,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_1363,tc_HOL_Obool)),U_1364),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_1363,tc_HOL_Obool)),U_1365),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_1363,tc_HOL_Obool),tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_388_1]) ).

cnf(f_388_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1363,tc_HOL_Obool)),U_1364),U_1365) = c_Complete__Lattice_OSup__class_OSup(tc_fun(U_1363,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_1363,tc_HOL_Obool)),U_1364),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_1363,tc_HOL_Obool)),U_1365),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_1363,tc_HOL_Obool),tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_388_2]) ).

fof(f_389_1,plain,
    ! [T_b] : hAPP(c_Set_OPow(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))),
    inference(fof_nnf,[status(thm)],[fact_Pow__empty]) ).

fof(f_389_2,plain,
    ! [U_1366] : hAPP(c_Set_OPow(U_1366),c_Orderings_Obot__class_Obot(tc_fun(U_1366,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(U_1366,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_1366,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_1366,tc_HOL_Obool),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_389_1]) ).

cnf(f_389_3,plain,
    hAPP(c_Set_OPow(U_1366),c_Orderings_Obot__class_Obot(tc_fun(U_1366,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(U_1366,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_1366,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_1366,tc_HOL_Obool),tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_389_2]) ).

fof(f_390_1,plain,
    ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_B_2),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))))),
    inference(fof_nnf,[status(thm)],[fact_Int__eq__Inter]) ).

fof(f_390_2,plain,
    ! [U_1369,U_1368,U_1367] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1367,tc_HOL_Obool)),U_1368),U_1369) = c_Complete__Lattice_OInf__class_OInf(tc_fun(U_1367,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_1367,tc_HOL_Obool)),U_1368),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_1367,tc_HOL_Obool)),U_1369),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_1367,tc_HOL_Obool),tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_390_1]) ).

cnf(f_390_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1367,tc_HOL_Obool)),U_1368),U_1369) = c_Complete__Lattice_OInf__class_OInf(tc_fun(U_1367,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_1367,tc_HOL_Obool)),U_1368),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_1367,tc_HOL_Obool)),U_1369),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_1367,tc_HOL_Obool),tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_390_2]) ).

fof(f_391_1,plain,
    ! [V_x_2,T_b] : c_Set_Othe__elem(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2,
    inference(fof_nnf,[status(thm)],[fact_the__elem__eq]) ).

fof(f_391_2,plain,
    ! [U_1371,U_1370] : c_Set_Othe__elem(U_1370,hAPP(hAPP(c_Set_Oinsert(U_1370),U_1371),c_Orderings_Obot__class_Obot(tc_fun(U_1370,tc_HOL_Obool)))) = U_1371,
    inference(variable_rename,[status(thm)],[f_391_1]) ).

cnf(f_391_3,plain,
    c_Set_Othe__elem(U_1370,hAPP(hAPP(c_Set_Oinsert(U_1370),U_1371),c_Orderings_Obot__class_Obot(tc_fun(U_1370,tc_HOL_Obool)))) = U_1371,
    inference(clausify,[status(thm)],[f_391_2]) ).

fof(f_392_1,plain,
    ! [V_A_2,V_a_2,T_b] : hAPP(c_Set_OPow(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)),hAPP(c_Set_Oimage(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oinsert(T_b),V_a_2)),hAPP(c_Set_OPow(T_b),V_A_2))),
    inference(fof_nnf,[status(thm)],[fact_Pow__insert]) ).

fof(f_392_2,plain,
    ! [U_1374,U_1373,U_1372] : hAPP(c_Set_OPow(U_1372),hAPP(hAPP(c_Set_Oinsert(U_1372),U_1373),U_1374)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_1372,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_1372),U_1374)),hAPP(c_Set_Oimage(tc_fun(U_1372,tc_HOL_Obool),tc_fun(U_1372,tc_HOL_Obool),hAPP(c_Set_Oinsert(U_1372),U_1373)),hAPP(c_Set_OPow(U_1372),U_1374))),
    inference(variable_rename,[status(thm)],[f_392_1]) ).

cnf(f_392_3,plain,
    hAPP(c_Set_OPow(U_1372),hAPP(hAPP(c_Set_Oinsert(U_1372),U_1373),U_1374)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_1372,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_1372),U_1374)),hAPP(c_Set_Oimage(tc_fun(U_1372,tc_HOL_Obool),tc_fun(U_1372,tc_HOL_Obool),hAPP(c_Set_Oinsert(U_1372),U_1373)),hAPP(c_Set_OPow(U_1372),U_1374))),
    inference(clausify,[status(thm)],[f_392_2]) ).

fof(f_393_1,plain,
    ! [V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oidem]) ).

fof(f_393_2,plain,
    ! [U_1376,U_1375] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1375),U_1376),U_1376) = U_1376
      | ~ class_Lattices_Olattice(U_1375) ),
    inference(variable_rename,[status(thm)],[f_393_1]) ).

cnf(f_393_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1375),U_1376),U_1376) = U_1376
    | ~ class_Lattices_Olattice(U_1375) ),
    inference(clausify,[status(thm)],[f_393_2]) ).

fof(f_394_1,plain,
    ! [V_x,T_a] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x
      | ~ class_Lattices_Olattice(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oidem]) ).

fof(f_394_2,plain,
    ! [U_1378,U_1377] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1377),U_1378),U_1378) = U_1378
      | ~ class_Lattices_Olattice(U_1377) ),
    inference(variable_rename,[status(thm)],[f_394_1]) ).

cnf(f_394_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1377),U_1378),U_1378) = U_1378
    | ~ class_Lattices_Olattice(U_1377) ),
    inference(clausify,[status(thm)],[f_394_2]) ).

fof(f_395_1,plain,
    ! [V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
      | V_x = V_y
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_linorder__neqE__linordered__idom]) ).

fof(f_395_2,plain,
    ! [U_1381,U_1380,U_1379] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1379),U_1381),U_1380))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1379),U_1380),U_1381))
      | U_1380 = U_1381
      | ~ class_Rings_Olinordered__idom(U_1379) ),
    inference(variable_rename,[status(thm)],[f_395_1]) ).

cnf(f_395_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1379),U_1381),U_1380))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1379),U_1380),U_1381))
    | U_1380 = U_1381
    | ~ class_Rings_Olinordered__idom(U_1379) ),
    inference(clausify,[status(thm)],[f_395_2]) ).

fof(f_396_1,plain,
    ! [V_c_2,V_b_2,V_a_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_c_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),V_b_2)
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Int__atLeastAtMostL2]) ).

fof(f_396_2,plain,
    ! [U_1385,U_1384,U_1383,U_1382] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1382,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_1382,U_1383,U_1384)),hAPP(c_SetInterval_Oord__class_OatLeast(U_1382),U_1385)) = c_SetInterval_Oord__class_OatLeastAtMost(U_1382,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1382),U_1383),U_1385),U_1384)
      | ~ class_Orderings_Olinorder(U_1382) ),
    inference(variable_rename,[status(thm)],[f_396_1]) ).

cnf(f_396_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1382,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_1382,U_1383,U_1384)),hAPP(c_SetInterval_Oord__class_OatLeast(U_1382),U_1385)) = c_SetInterval_Oord__class_OatLeastAtMost(U_1382,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1382),U_1383),U_1385),U_1384)
    | ~ class_Orderings_Olinorder(U_1382) ),
    inference(clausify,[status(thm)],[f_396_2]) ).

fof(f_397_1,plain,
    ! [V_d_2,V_c_2,V_a_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_a_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),V_d_2)
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Int__atLeastAtMostR2]) ).

fof(f_397_2,plain,
    ! [U_1389,U_1388,U_1387,U_1386] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1386,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_1386),U_1387)),c_SetInterval_Oord__class_OatLeastAtMost(U_1386,U_1388,U_1389)) = c_SetInterval_Oord__class_OatLeastAtMost(U_1386,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1386),U_1387),U_1388),U_1389)
      | ~ class_Orderings_Olinorder(U_1386) ),
    inference(variable_rename,[status(thm)],[f_397_1]) ).

cnf(f_397_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1386,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_1386),U_1387)),c_SetInterval_Oord__class_OatLeastAtMost(U_1386,U_1388,U_1389)) = c_SetInterval_Oord__class_OatLeastAtMost(U_1386,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1386),U_1387),U_1388),U_1389)
    | ~ class_Orderings_Olinorder(U_1386) ),
    inference(clausify,[status(thm)],[f_397_2]) ).

fof(f_398_1,plain,
    ! [V_x_2,T_b] :
      ( hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2))
      | ~ class_Groups_Oordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_image__uminus__atMost]) ).

fof(f_398_2,plain,
    ! [U_1391,U_1390] :
      ( hAPP(c_Set_Oimage(U_1390,U_1390,c_Groups_Ouminus__class_Ouminus(U_1390)),hAPP(c_SetInterval_Oord__class_OatMost(U_1390),U_1391)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_1390),hAPP(c_Groups_Ouminus__class_Ouminus(U_1390),U_1391))
      | ~ class_Groups_Oordered__ab__group__add(U_1390) ),
    inference(variable_rename,[status(thm)],[f_398_1]) ).

cnf(f_398_3,plain,
    ( hAPP(c_Set_Oimage(U_1390,U_1390,c_Groups_Ouminus__class_Ouminus(U_1390)),hAPP(c_SetInterval_Oord__class_OatMost(U_1390),U_1391)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_1390),hAPP(c_Groups_Ouminus__class_Ouminus(U_1390),U_1391))
    | ~ class_Groups_Oordered__ab__group__add(U_1390) ),
    inference(clausify,[status(thm)],[f_398_2]) ).

fof(f_399_1,plain,
    ! [V_x_2,T_b] :
      ( hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2))
      | ~ class_Groups_Oordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_image__uminus__atLeast]) ).

fof(f_399_2,plain,
    ! [U_1393,U_1392] :
      ( hAPP(c_Set_Oimage(U_1392,U_1392,c_Groups_Ouminus__class_Ouminus(U_1392)),hAPP(c_SetInterval_Oord__class_OatLeast(U_1392),U_1393)) = hAPP(c_SetInterval_Oord__class_OatMost(U_1392),hAPP(c_Groups_Ouminus__class_Ouminus(U_1392),U_1393))
      | ~ class_Groups_Oordered__ab__group__add(U_1392) ),
    inference(variable_rename,[status(thm)],[f_399_1]) ).

cnf(f_399_3,plain,
    ( hAPP(c_Set_Oimage(U_1392,U_1392,c_Groups_Ouminus__class_Ouminus(U_1392)),hAPP(c_SetInterval_Oord__class_OatLeast(U_1392),U_1393)) = hAPP(c_SetInterval_Oord__class_OatMost(U_1392),hAPP(c_Groups_Ouminus__class_Ouminus(U_1392),U_1393))
    | ~ class_Groups_Oordered__ab__group__add(U_1392) ),
    inference(clausify,[status(thm)],[f_399_2]) ).

fof(f_400_1,plain,
    ! [V_x_2,T_b] :
      ( hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2))
      | ~ class_Groups_Oordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_image__uminus__lessThan]) ).

fof(f_400_2,plain,
    ! [U_1395,U_1394] :
      ( hAPP(c_Set_Oimage(U_1394,U_1394,c_Groups_Ouminus__class_Ouminus(U_1394)),hAPP(c_SetInterval_Oord__class_OlessThan(U_1394),U_1395)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_1394),hAPP(c_Groups_Ouminus__class_Ouminus(U_1394),U_1395))
      | ~ class_Groups_Oordered__ab__group__add(U_1394) ),
    inference(variable_rename,[status(thm)],[f_400_1]) ).

cnf(f_400_3,plain,
    ( hAPP(c_Set_Oimage(U_1394,U_1394,c_Groups_Ouminus__class_Ouminus(U_1394)),hAPP(c_SetInterval_Oord__class_OlessThan(U_1394),U_1395)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_1394),hAPP(c_Groups_Ouminus__class_Ouminus(U_1394),U_1395))
    | ~ class_Groups_Oordered__ab__group__add(U_1394) ),
    inference(clausify,[status(thm)],[f_400_2]) ).

fof(f_401_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_psubset__trans]) ).

fof(f_401_2,plain,
    ! [U_1399,U_1398,U_1397,U_1396] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1396,tc_HOL_Obool)),U_1397),U_1399))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1396,tc_HOL_Obool)),U_1398),U_1399))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1396,tc_HOL_Obool)),U_1397),U_1398)) ),
    inference(variable_rename,[status(thm)],[f_401_1]) ).

cnf(f_401_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1396,tc_HOL_Obool)),U_1397),U_1399))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1396,tc_HOL_Obool)),U_1398),U_1399))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1396,tc_HOL_Obool)),U_1397),U_1398)) ),
    inference(clausify,[status(thm)],[f_401_2]) ).

fof(f_402_1,plain,
    ! [V_x,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_x) = V_x
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Max_Oidem]) ).

fof(f_402_2,plain,
    ! [U_1401,U_1400] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1400),U_1401),U_1401) = U_1401
      | ~ class_Orderings_Olinorder(U_1400) ),
    inference(variable_rename,[status(thm)],[f_402_1]) ).

cnf(f_402_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1400),U_1401),U_1401) = U_1401
    | ~ class_Orderings_Olinorder(U_1400) ),
    inference(clausify,[status(thm)],[f_402_2]) ).

fof(f_403_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_a) = V_a
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Osup_Oidem]) ).

fof(f_403_2,plain,
    ! [U_1403,U_1402] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1402),U_1403),U_1403) = U_1403
      | ~ class_Orderings_Olinorder(U_1402) ),
    inference(variable_rename,[status(thm)],[f_403_1]) ).

cnf(f_403_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1402),U_1403),U_1403) = U_1403
    | ~ class_Orderings_Olinorder(U_1402) ),
    inference(clausify,[status(thm)],[f_403_2]) ).

fof(f_404_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b),V_a)
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Osup_Ocommute]) ).

fof(f_404_2,plain,
    ! [U_1406,U_1405,U_1404] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1404),U_1405),U_1406) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1404),U_1406),U_1405)
      | ~ class_Orderings_Olinorder(U_1404) ),
    inference(variable_rename,[status(thm)],[f_404_1]) ).

cnf(f_404_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1404),U_1405),U_1406) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1404),U_1406),U_1405)
    | ~ class_Orderings_Olinorder(U_1404) ),
    inference(clausify,[status(thm)],[f_404_2]) ).

fof(f_405_1,plain,
    ! [V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_x)
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Osup__commute]) ).

fof(f_405_2,plain,
    ! [U_1409,U_1408,U_1407] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1407),U_1408),U_1409) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1407),U_1409),U_1408)
      | ~ class_Orderings_Olinorder(U_1407) ),
    inference(variable_rename,[status(thm)],[f_405_1]) ).

cnf(f_405_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1407),U_1408),U_1409) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1407),U_1409),U_1408)
    | ~ class_Orderings_Olinorder(U_1407) ),
    inference(clausify,[status(thm)],[f_405_2]) ).

fof(f_406_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Osup_Oleft__idem]) ).

fof(f_406_2,plain,
    ! [U_1412,U_1411,U_1410] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1410),U_1411),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1410),U_1411),U_1412)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1410),U_1411),U_1412)
      | ~ class_Orderings_Olinorder(U_1410) ),
    inference(variable_rename,[status(thm)],[f_406_1]) ).

cnf(f_406_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1410),U_1411),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1410),U_1411),U_1412)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1410),U_1411),U_1412)
    | ~ class_Orderings_Olinorder(U_1410) ),
    inference(clausify,[status(thm)],[f_406_2]) ).

fof(f_407_1,plain,
    ! [V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Osup__left__idem]) ).

fof(f_407_2,plain,
    ! [U_1415,U_1414,U_1413] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1413),U_1414),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1413),U_1414),U_1415)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1413),U_1414),U_1415)
      | ~ class_Orderings_Olinorder(U_1413) ),
    inference(variable_rename,[status(thm)],[f_407_1]) ).

cnf(f_407_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1413),U_1414),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1413),U_1414),U_1415)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1413),U_1414),U_1415)
    | ~ class_Orderings_Olinorder(U_1413) ),
    inference(clausify,[status(thm)],[f_407_2]) ).

fof(f_408_1,plain,
    ! [V_c,V_a,V_b,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_c)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b),V_c))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Osup_Oleft__commute]) ).

fof(f_408_2,plain,
    ! [U_1419,U_1418,U_1417,U_1416] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1416),U_1417),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1416),U_1418),U_1419)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1416),U_1418),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1416),U_1417),U_1419))
      | ~ class_Orderings_Olinorder(U_1416) ),
    inference(variable_rename,[status(thm)],[f_408_1]) ).

cnf(f_408_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1416),U_1417),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1416),U_1418),U_1419)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1416),U_1418),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1416),U_1417),U_1419))
    | ~ class_Orderings_Olinorder(U_1416) ),
    inference(clausify,[status(thm)],[f_408_2]) ).

fof(f_409_1,plain,
    ! [V_z,V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_z))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Osup__left__commute]) ).

fof(f_409_2,plain,
    ! [U_1423,U_1422,U_1421,U_1420] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1420),U_1421),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1420),U_1422),U_1423)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1420),U_1422),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1420),U_1421),U_1423))
      | ~ class_Orderings_Olinorder(U_1420) ),
    inference(variable_rename,[status(thm)],[f_409_1]) ).

cnf(f_409_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1420),U_1421),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1420),U_1422),U_1423)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1420),U_1422),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1420),U_1421),U_1423))
    | ~ class_Orderings_Olinorder(U_1420) ),
    inference(clausify,[status(thm)],[f_409_2]) ).

fof(f_410_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b),V_c))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Osup_Oassoc]) ).

fof(f_410_2,plain,
    ! [U_1427,U_1426,U_1425,U_1424] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1424),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1424),U_1425),U_1426)),U_1427) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1424),U_1425),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1424),U_1426),U_1427))
      | ~ class_Orderings_Olinorder(U_1424) ),
    inference(variable_rename,[status(thm)],[f_410_1]) ).

cnf(f_410_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1424),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1424),U_1425),U_1426)),U_1427) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1424),U_1425),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1424),U_1426),U_1427))
    | ~ class_Orderings_Olinorder(U_1424) ),
    inference(clausify,[status(thm)],[f_410_2]) ).

fof(f_411_1,plain,
    ! [V_z,V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Osup__assoc]) ).

fof(f_411_2,plain,
    ! [U_1431,U_1430,U_1429,U_1428] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1428),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1428),U_1429),U_1430)),U_1431) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1428),U_1429),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1428),U_1430),U_1431))
      | ~ class_Orderings_Olinorder(U_1428) ),
    inference(variable_rename,[status(thm)],[f_411_1]) ).

cnf(f_411_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1428),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1428),U_1429),U_1430)),U_1431) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1428),U_1429),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1428),U_1430),U_1431))
    | ~ class_Orderings_Olinorder(U_1428) ),
    inference(clausify,[status(thm)],[f_411_2]) ).

fof(f_412_1,plain,
    ! [V_B_2,V_A_2,V_f_2,T_b,T_c] :
      ( hAPP(c_Set_Oimage(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_c,T_b,V_f_2)),hAPP(c_Set_OPow(T_c),V_A_2)) = hAPP(c_Set_OPow(T_b),V_B_2)
      | hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) != V_B_2 ),
    inference(fof_nnf,[status(thm)],[fact_image__Pow__surj]) ).

fof(f_412_2,plain,
    ! [U_1436,U_1435,U_1434,U_1433,U_1432] :
      ( hAPP(c_Set_Oimage(tc_fun(U_1432,tc_HOL_Obool),tc_fun(U_1433,tc_HOL_Obool),c_Set_Oimage(U_1432,U_1433,U_1434)),hAPP(c_Set_OPow(U_1432),U_1435)) = hAPP(c_Set_OPow(U_1433),U_1436)
      | hAPP(c_Set_Oimage(U_1432,U_1433,U_1434),U_1435) != U_1436 ),
    inference(variable_rename,[status(thm)],[f_412_1]) ).

cnf(f_412_3,plain,
    ( hAPP(c_Set_Oimage(tc_fun(U_1432,tc_HOL_Obool),tc_fun(U_1433,tc_HOL_Obool),c_Set_Oimage(U_1432,U_1433,U_1434)),hAPP(c_Set_OPow(U_1432),U_1435)) = hAPP(c_Set_OPow(U_1433),U_1436)
    | hAPP(c_Set_Oimage(U_1432,U_1433,U_1434),U_1435) != U_1436 ),
    inference(clausify,[status(thm)],[f_412_2]) ).

fof(f_413_1,plain,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)
        | V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
      & ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
        | c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) != hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_empty__is__image]) ).

fof(f_413_2,plain,
    ! [U_1440,U_1439,U_1438,U_1437] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(U_1437,tc_HOL_Obool)) = hAPP(c_Set_Oimage(U_1438,U_1437,U_1439),U_1440)
        | U_1440 != c_Orderings_Obot__class_Obot(tc_fun(U_1438,tc_HOL_Obool)) )
      & ( U_1440 = c_Orderings_Obot__class_Obot(tc_fun(U_1438,tc_HOL_Obool))
        | c_Orderings_Obot__class_Obot(tc_fun(U_1437,tc_HOL_Obool)) != hAPP(c_Set_Oimage(U_1438,U_1437,U_1439),U_1440) ) ),
    inference(variable_rename,[status(thm)],[f_413_1]) ).

fof(f_413_3,plain,
    ( ! [U_1448,U_1446,U_1444] :
        ( ! [U_1442] : c_Orderings_Obot__class_Obot(tc_fun(U_1442,tc_HOL_Obool)) = hAPP(c_Set_Oimage(U_1444,U_1442,U_1446),U_1448)
        | U_1448 != c_Orderings_Obot__class_Obot(tc_fun(U_1444,tc_HOL_Obool)) )
    & ! [U_1447,U_1445,U_1443] :
        ( ! [U_1441] : c_Orderings_Obot__class_Obot(tc_fun(U_1441,tc_HOL_Obool)) != hAPP(c_Set_Oimage(U_1443,U_1441,U_1445),U_1447)
        | U_1447 = c_Orderings_Obot__class_Obot(tc_fun(U_1443,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_413_2]) ).

cnf(f_413_4,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(U_1441,tc_HOL_Obool)) != hAPP(c_Set_Oimage(U_1443,U_1441,U_1445),U_1447)
    | U_1447 = c_Orderings_Obot__class_Obot(tc_fun(U_1443,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_413_3]) ).

cnf(f_413_5,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(U_1442,tc_HOL_Obool)) = hAPP(c_Set_Oimage(U_1444,U_1442,U_1446),U_1448)
    | U_1448 != c_Orderings_Obot__class_Obot(tc_fun(U_1444,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_413_3]) ).

fof(f_414_1,plain,
    ! [V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_image__empty]) ).

fof(f_414_2,plain,
    ! [U_1451,U_1450,U_1449] : hAPP(c_Set_Oimage(U_1449,U_1450,U_1451),c_Orderings_Obot__class_Obot(tc_fun(U_1449,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_1450,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_414_1]) ).

cnf(f_414_3,plain,
    hAPP(c_Set_Oimage(U_1449,U_1450,U_1451),c_Orderings_Obot__class_Obot(tc_fun(U_1449,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_1450,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_414_2]) ).

fof(f_415_1,plain,
    ! [V_A_2,V_f_2,T_b,T_c] :
      ( ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
        | V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
      & ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
        | hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_image__is__empty]) ).

fof(f_415_2,plain,
    ! [U_1455,U_1454,U_1453,U_1452] :
      ( ( hAPP(c_Set_Oimage(U_1452,U_1453,U_1454),U_1455) = c_Orderings_Obot__class_Obot(tc_fun(U_1453,tc_HOL_Obool))
        | U_1455 != c_Orderings_Obot__class_Obot(tc_fun(U_1452,tc_HOL_Obool)) )
      & ( U_1455 = c_Orderings_Obot__class_Obot(tc_fun(U_1452,tc_HOL_Obool))
        | hAPP(c_Set_Oimage(U_1452,U_1453,U_1454),U_1455) != c_Orderings_Obot__class_Obot(tc_fun(U_1453,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_415_1]) ).

fof(f_415_3,plain,
    ( ! [U_1463,U_1461,U_1459,U_1457] :
        ( hAPP(c_Set_Oimage(U_1457,U_1459,U_1461),U_1463) = c_Orderings_Obot__class_Obot(tc_fun(U_1459,tc_HOL_Obool))
        | U_1463 != c_Orderings_Obot__class_Obot(tc_fun(U_1457,tc_HOL_Obool)) )
    & ! [U_1462,U_1460,U_1458,U_1456] :
        ( U_1462 = c_Orderings_Obot__class_Obot(tc_fun(U_1456,tc_HOL_Obool))
        | hAPP(c_Set_Oimage(U_1456,U_1458,U_1460),U_1462) != c_Orderings_Obot__class_Obot(tc_fun(U_1458,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_415_2]) ).

cnf(f_415_4,plain,
    ( U_1462 = c_Orderings_Obot__class_Obot(tc_fun(U_1456,tc_HOL_Obool))
    | hAPP(c_Set_Oimage(U_1456,U_1458,U_1460),U_1462) != c_Orderings_Obot__class_Obot(tc_fun(U_1458,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_415_3]) ).

cnf(f_415_5,plain,
    ( hAPP(c_Set_Oimage(U_1457,U_1459,U_1461),U_1463) = c_Orderings_Obot__class_Obot(tc_fun(U_1459,tc_HOL_Obool))
    | U_1463 != c_Orderings_Obot__class_Obot(tc_fun(U_1457,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_415_3]) ).

fof(f_416_1,plain,
    ! [V_B_2,V_a_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_image__insert]) ).

fof(f_416_2,plain,
    ! [U_1468,U_1467,U_1466,U_1465,U_1464] : hAPP(c_Set_Oimage(U_1464,U_1465,U_1466),hAPP(hAPP(c_Set_Oinsert(U_1464),U_1467),U_1468)) = hAPP(hAPP(c_Set_Oinsert(U_1465),hAPP(U_1466,U_1467)),hAPP(c_Set_Oimage(U_1464,U_1465,U_1466),U_1468)),
    inference(variable_rename,[status(thm)],[f_416_1]) ).

cnf(f_416_3,plain,
    hAPP(c_Set_Oimage(U_1464,U_1465,U_1466),hAPP(hAPP(c_Set_Oinsert(U_1464),U_1467),U_1468)) = hAPP(hAPP(c_Set_Oinsert(U_1465),hAPP(U_1466,U_1467)),hAPP(c_Set_Oimage(U_1464,U_1465,U_1466),U_1468)),
    inference(clausify,[status(thm)],[f_416_2]) ).

fof(f_417_1,plain,
    ! [V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_le__maxI1]) ).

fof(f_417_2,plain,
    ! [U_1471,U_1470,U_1469] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1469),U_1470),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1469),U_1470),U_1471)))
      | ~ class_Orderings_Olinorder(U_1469) ),
    inference(variable_rename,[status(thm)],[f_417_1]) ).

cnf(f_417_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1469),U_1470),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1469),U_1470),U_1471)))
    | ~ class_Orderings_Olinorder(U_1469) ),
    inference(clausify,[status(thm)],[f_417_2]) ).

fof(f_418_1,plain,
    ! [V_x,V_y,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_le__maxI2]) ).

fof(f_418_2,plain,
    ! [U_1474,U_1473,U_1472] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1472),U_1473),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1472),U_1474),U_1473)))
      | ~ class_Orderings_Olinorder(U_1472) ),
    inference(variable_rename,[status(thm)],[f_418_1]) ).

cnf(f_418_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1472),U_1473),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1472),U_1474),U_1473)))
    | ~ class_Orderings_Olinorder(U_1472) ),
    inference(clausify,[status(thm)],[f_418_2]) ).

fof(f_419_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
          | hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2) != V_y_2 )
        & ( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2) = V_y_2
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) )
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Ole__iff__sup]) ).

fof(f_419_2,plain,
    ! [U_1477,U_1476,U_1475] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1475),U_1476),U_1477))
          | hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1475),U_1476),U_1477) != U_1477 )
        & ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1475),U_1476),U_1477) = U_1477
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1475),U_1476),U_1477)) ) )
      | ~ class_Orderings_Olinorder(U_1475) ),
    inference(variable_rename,[status(thm)],[f_419_1]) ).

cnf(f_419_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1475),U_1476),U_1477) = U_1477
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1475),U_1476),U_1477))
    | ~ class_Orderings_Olinorder(U_1475) ),
    inference(clausify,[status(thm)],[f_419_2]) ).

cnf(f_419_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1475),U_1476),U_1477))
    | hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1475),U_1476),U_1477) != U_1477
    | ~ class_Orderings_Olinorder(U_1475) ),
    inference(clausify,[status(thm)],[f_419_2]) ).

fof(f_420_1,plain,
    ! [V_z_2,V_y_2,V_x_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2)),V_z_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2)),V_z_2)) ) )
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Ole__sup__iff]) ).

fof(f_420_2,plain,
    ! [U_1481,U_1480,U_1479,U_1478] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1478),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1478),U_1479),U_1480)),U_1481))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1478),U_1480),U_1481))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1478),U_1479),U_1481)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1478),U_1480),U_1481))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1478),U_1479),U_1481)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1478),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1478),U_1479),U_1480)),U_1481)) ) )
      | ~ class_Orderings_Olinorder(U_1478) ),
    inference(variable_rename,[status(thm)],[f_420_1]) ).

cnf(f_420_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1478),U_1479),U_1481))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1478),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1478),U_1479),U_1480)),U_1481))
    | ~ class_Orderings_Olinorder(U_1478) ),
    inference(clausify,[status(thm)],[f_420_2]) ).

cnf(f_420_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1478),U_1480),U_1481))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1478),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1478),U_1479),U_1480)),U_1481))
    | ~ class_Orderings_Olinorder(U_1478) ),
    inference(clausify,[status(thm)],[f_420_2]) ).

cnf(f_420_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1478),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1478),U_1479),U_1480)),U_1481))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1478),U_1480),U_1481))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1478),U_1479),U_1481))
    | ~ class_Orderings_Olinorder(U_1478) ),
    inference(clausify,[status(thm)],[f_420_2]) ).

fof(f_421_1,plain,
    ! [V_b,V_a,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Ole__supI1]) ).

fof(f_421_2,plain,
    ! [U_1485,U_1484,U_1483,U_1482] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1482),U_1483),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1482),U_1484),U_1485)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1482),U_1483),U_1484))
      | ~ class_Orderings_Olinorder(U_1482) ),
    inference(variable_rename,[status(thm)],[f_421_1]) ).

cnf(f_421_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1482),U_1483),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1482),U_1484),U_1485)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1482),U_1483),U_1484))
    | ~ class_Orderings_Olinorder(U_1482) ),
    inference(clausify,[status(thm)],[f_421_2]) ).

fof(f_422_1,plain,
    ! [V_a,V_b,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Ole__supI2]) ).

fof(f_422_2,plain,
    ! [U_1489,U_1488,U_1487,U_1486] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1486),U_1487),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1486),U_1489),U_1488)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1486),U_1487),U_1488))
      | ~ class_Orderings_Olinorder(U_1486) ),
    inference(variable_rename,[status(thm)],[f_422_1]) ).

cnf(f_422_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1486),U_1487),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1486),U_1489),U_1488)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1486),U_1487),U_1488))
    | ~ class_Orderings_Olinorder(U_1486) ),
    inference(clausify,[status(thm)],[f_422_2]) ).

fof(f_423_1,plain,
    ! [V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_y
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Osup__absorb2]) ).

fof(f_423_2,plain,
    ! [U_1492,U_1491,U_1490] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1490),U_1491),U_1492) = U_1492
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1490),U_1491),U_1492))
      | ~ class_Orderings_Olinorder(U_1490) ),
    inference(variable_rename,[status(thm)],[f_423_1]) ).

cnf(f_423_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1490),U_1491),U_1492) = U_1492
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1490),U_1491),U_1492))
    | ~ class_Orderings_Olinorder(U_1490) ),
    inference(clausify,[status(thm)],[f_423_2]) ).

fof(f_424_1,plain,
    ! [V_x,V_y,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_x
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Osup__absorb1]) ).

fof(f_424_2,plain,
    ! [U_1495,U_1494,U_1493] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1493),U_1495),U_1494) = U_1495
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1493),U_1494),U_1495))
      | ~ class_Orderings_Olinorder(U_1493) ),
    inference(variable_rename,[status(thm)],[f_424_1]) ).

cnf(f_424_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1493),U_1495),U_1494) = U_1495
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1493),U_1494),U_1495))
    | ~ class_Orderings_Olinorder(U_1493) ),
    inference(clausify,[status(thm)],[f_424_2]) ).

fof(f_425_1,plain,
    ! [V_b,V_x,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Ole__supI]) ).

fof(f_425_2,plain,
    ! [U_1499,U_1498,U_1497,U_1496] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1496),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1496),U_1497),U_1499)),U_1498))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1496),U_1499),U_1498))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1496),U_1497),U_1498))
      | ~ class_Orderings_Olinorder(U_1496) ),
    inference(variable_rename,[status(thm)],[f_425_1]) ).

cnf(f_425_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1496),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1496),U_1497),U_1499)),U_1498))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1496),U_1499),U_1498))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1496),U_1497),U_1498))
    | ~ class_Orderings_Olinorder(U_1496) ),
    inference(clausify,[status(thm)],[f_425_2]) ).

fof(f_426_1,plain,
    ! [V_z,V_x,V_y,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Osup__least]) ).

fof(f_426_2,plain,
    ! [U_1503,U_1502,U_1501,U_1500] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1500),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1500),U_1501),U_1503)),U_1502))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1500),U_1503),U_1502))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1500),U_1501),U_1502))
      | ~ class_Orderings_Olinorder(U_1500) ),
    inference(variable_rename,[status(thm)],[f_426_1]) ).

cnf(f_426_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1500),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1500),U_1501),U_1503)),U_1502))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1500),U_1503),U_1502))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1500),U_1501),U_1502))
    | ~ class_Orderings_Olinorder(U_1500) ),
    inference(clausify,[status(thm)],[f_426_2]) ).

fof(f_427_1,plain,
    ! [V_d,V_b,V_c,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_c),V_d)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Osup__mono]) ).

fof(f_427_2,plain,
    ! [U_1508,U_1507,U_1506,U_1505,U_1504] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1504),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1504),U_1505),U_1507)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1504),U_1506),U_1508)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1504),U_1507),U_1508))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1504),U_1505),U_1506))
      | ~ class_Orderings_Olinorder(U_1504) ),
    inference(variable_rename,[status(thm)],[f_427_1]) ).

cnf(f_427_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1504),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1504),U_1505),U_1507)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1504),U_1506),U_1508)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1504),U_1507),U_1508))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1504),U_1505),U_1506))
    | ~ class_Orderings_Olinorder(U_1504) ),
    inference(clausify,[status(thm)],[f_427_2]) ).

fof(f_428_1,plain,
    ! [V_x,V_b,V_a,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)),V_x))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Ole__supE]) ).

fof(f_428_2,plain,
    ! [U_1512,U_1511,U_1510,U_1509] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1509),U_1511),U_1512))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1509),U_1510),U_1512)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1509),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1509),U_1510),U_1511)),U_1512))
      | ~ class_Orderings_Olinorder(U_1509) ),
    inference(variable_rename,[status(thm)],[f_428_1]) ).

cnf(f_428_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1509),U_1510),U_1512))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1509),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1509),U_1510),U_1511)),U_1512))
    | ~ class_Orderings_Olinorder(U_1509) ),
    inference(clausify,[status(thm)],[f_428_2]) ).

cnf(f_428_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1509),U_1511),U_1512))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1509),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1509),U_1510),U_1511)),U_1512))
    | ~ class_Orderings_Olinorder(U_1509) ),
    inference(clausify,[status(thm)],[f_428_2]) ).

fof(f_429_1,plain,
    ! [V_y_2,V_x_2,V_z_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2)))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_y_2))
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_x_2)) ) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_y_2))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_x_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2))) ) )
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_le__max__iff__disj]) ).

fof(f_429_2,plain,
    ! [U_1516,U_1515,U_1514,U_1513] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1513),U_1514),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1513),U_1515),U_1516)))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1513),U_1514),U_1516))
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1513),U_1514),U_1515)) ) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1513),U_1514),U_1516))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1513),U_1514),U_1515))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1513),U_1514),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1513),U_1515),U_1516))) ) )
      | ~ class_Orderings_Olinorder(U_1513) ),
    inference(variable_rename,[status(thm)],[f_429_1]) ).

cnf(f_429_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1513),U_1514),U_1516))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1513),U_1514),U_1515))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1513),U_1514),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1513),U_1515),U_1516)))
    | ~ class_Orderings_Olinorder(U_1513) ),
    inference(clausify,[status(thm)],[f_429_2]) ).

cnf(f_429_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1513),U_1514),U_1515))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1513),U_1514),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1513),U_1515),U_1516)))
    | ~ class_Orderings_Olinorder(U_1513) ),
    inference(clausify,[status(thm)],[f_429_2]) ).

cnf(f_429_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1513),U_1514),U_1516))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1513),U_1514),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1513),U_1515),U_1516)))
    | ~ class_Orderings_Olinorder(U_1513) ),
    inference(clausify,[status(thm)],[f_429_2]) ).

fof(f_430_1,plain,
    ! [V_y_2,V_x_2,V_z_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2)))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2))
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2)) ) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2))) ) )
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_less__max__iff__disj]) ).

fof(f_430_2,plain,
    ! [U_1520,U_1519,U_1518,U_1517] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1517),U_1518),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1517),U_1519),U_1520)))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1517),U_1518),U_1520))
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1517),U_1518),U_1519)) ) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1517),U_1518),U_1520))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1517),U_1518),U_1519))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1517),U_1518),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1517),U_1519),U_1520))) ) )
      | ~ class_Orderings_Olinorder(U_1517) ),
    inference(variable_rename,[status(thm)],[f_430_1]) ).

cnf(f_430_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1517),U_1518),U_1520))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1517),U_1518),U_1519))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1517),U_1518),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1517),U_1519),U_1520)))
    | ~ class_Orderings_Olinorder(U_1517) ),
    inference(clausify,[status(thm)],[f_430_2]) ).

cnf(f_430_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1517),U_1518),U_1519))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1517),U_1518),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1517),U_1519),U_1520)))
    | ~ class_Orderings_Olinorder(U_1517) ),
    inference(clausify,[status(thm)],[f_430_2]) ).

cnf(f_430_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1517),U_1518),U_1520))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1517),U_1518),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1517),U_1519),U_1520)))
    | ~ class_Orderings_Olinorder(U_1517) ),
    inference(clausify,[status(thm)],[f_430_2]) ).

fof(f_431_1,plain,
    ! [V_z_2,V_y_2,V_x_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2)),V_z_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2)),V_z_2)) ) )
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_max__less__iff__conj]) ).

fof(f_431_2,plain,
    ! [U_1524,U_1523,U_1522,U_1521] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1521),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1521),U_1522),U_1523)),U_1524))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1521),U_1523),U_1524))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1521),U_1522),U_1524)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1521),U_1523),U_1524))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1521),U_1522),U_1524)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1521),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1521),U_1522),U_1523)),U_1524)) ) )
      | ~ class_Orderings_Olinorder(U_1521) ),
    inference(variable_rename,[status(thm)],[f_431_1]) ).

cnf(f_431_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1521),U_1522),U_1524))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1521),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1521),U_1522),U_1523)),U_1524))
    | ~ class_Orderings_Olinorder(U_1521) ),
    inference(clausify,[status(thm)],[f_431_2]) ).

cnf(f_431_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1521),U_1523),U_1524))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1521),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1521),U_1522),U_1523)),U_1524))
    | ~ class_Orderings_Olinorder(U_1521) ),
    inference(clausify,[status(thm)],[f_431_2]) ).

cnf(f_431_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1521),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1521),U_1522),U_1523)),U_1524))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1521),U_1523),U_1524))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1521),U_1522),U_1524))
    | ~ class_Orderings_Olinorder(U_1521) ),
    inference(clausify,[status(thm)],[f_431_2]) ).

fof(f_432_1,plain,
    ! [V_b,V_a,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Oless__supI1]) ).

fof(f_432_2,plain,
    ! [U_1528,U_1527,U_1526,U_1525] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1525),U_1526),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1525),U_1527),U_1528)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1525),U_1526),U_1527))
      | ~ class_Orderings_Olinorder(U_1525) ),
    inference(variable_rename,[status(thm)],[f_432_1]) ).

cnf(f_432_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1525),U_1526),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1525),U_1527),U_1528)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1525),U_1526),U_1527))
    | ~ class_Orderings_Olinorder(U_1525) ),
    inference(clausify,[status(thm)],[f_432_2]) ).

fof(f_433_1,plain,
    ! [V_a,V_b,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Oless__supI2]) ).

fof(f_433_2,plain,
    ! [U_1532,U_1531,U_1530,U_1529] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1529),U_1530),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1529),U_1532),U_1531)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1529),U_1530),U_1531))
      | ~ class_Orderings_Olinorder(U_1529) ),
    inference(variable_rename,[status(thm)],[f_433_1]) ).

cnf(f_433_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1529),U_1530),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1529),U_1532),U_1531)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1529),U_1530),U_1531))
    | ~ class_Orderings_Olinorder(U_1529) ),
    inference(clausify,[status(thm)],[f_433_2]) ).

fof(f_434_1,plain,
    ! [V_A_2,V_f_2,T_c,V_B_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
        | ! [B_AA] :
            ( V_B_2 != hAPP(c_Set_Oimage(T_c,T_b,V_f_2),B_AA)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),B_AA),V_A_2)) ) )
      & ( ? [B_AA] :
            ( V_B_2 = hAPP(c_Set_Oimage(T_c,T_b,V_f_2),B_AA)
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),B_AA),V_A_2)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_subset__image__iff]) ).

fof(f_434_2,plain,
    ! [U_1539,U_1538,U_1537,U_1536,U_1535] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1535,tc_HOL_Obool)),U_1536),hAPP(c_Set_Oimage(U_1537,U_1535,U_1538),U_1539)))
        | ! [U_1534] :
            ( U_1536 != hAPP(c_Set_Oimage(U_1537,U_1535,U_1538),U_1534)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1537,tc_HOL_Obool)),U_1534),U_1539)) ) )
      & ( ? [U_1533] :
            ( U_1536 = hAPP(c_Set_Oimage(U_1537,U_1535,U_1538),U_1533)
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1537,tc_HOL_Obool)),U_1533),U_1539)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1535,tc_HOL_Obool)),U_1536),hAPP(c_Set_Oimage(U_1537,U_1535,U_1538),U_1539))) ) ),
    inference(variable_rename,[status(thm)],[f_434_1]) ).

fof(f_434_3,plain,
    ( ! [U_1549,U_1547,U_1545,U_1543,U_1541] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1541,tc_HOL_Obool)),U_1543),hAPP(c_Set_Oimage(U_1545,U_1541,U_1547),U_1549)))
        | ! [U_1534] :
            ( U_1543 != hAPP(c_Set_Oimage(U_1545,U_1541,U_1547),U_1534)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1545,tc_HOL_Obool)),U_1534),U_1549)) ) )
    & ! [U_1548,U_1546,U_1544,U_1542,U_1540] :
        ( ? [U_1533] :
            ( U_1542 = hAPP(c_Set_Oimage(U_1544,U_1540,U_1546),U_1533)
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1544,tc_HOL_Obool)),U_1533),U_1548)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1540,tc_HOL_Obool)),U_1542),hAPP(c_Set_Oimage(U_1544,U_1540,U_1546),U_1548))) ) ),
    inference(miniscope,[status(thm)],[f_434_2]) ).

fof(f_434_4,plain,
    ( ! [U_1549,U_1547,U_1545,U_1543,U_1541] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1541,tc_HOL_Obool)),U_1543),hAPP(c_Set_Oimage(U_1545,U_1541,U_1547),U_1549)))
        | ! [U_1534] :
            ( U_1543 != hAPP(c_Set_Oimage(U_1545,U_1541,U_1547),U_1534)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1545,tc_HOL_Obool)),U_1534),U_1549)) ) )
    & ! [U_1548,U_1546,U_1544,U_1542,U_1540] :
        ( ( U_1542 = hAPP(c_Set_Oimage(U_1544,U_1540,U_1546),sK17(U_1548,U_1546,U_1544,U_1542,U_1540))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1544,tc_HOL_Obool)),sK17(U_1548,U_1546,U_1544,U_1542,U_1540)),U_1548)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1540,tc_HOL_Obool)),U_1542),hAPP(c_Set_Oimage(U_1544,U_1540,U_1546),U_1548))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_1533,sK17(U_1548,U_1546,U_1544,U_1542,U_1540))],[f_434_3]) ).

cnf(f_434_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1544,tc_HOL_Obool)),sK17(U_1548,U_1546,U_1544,U_1542,U_1540)),U_1548))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1540,tc_HOL_Obool)),U_1542),hAPP(c_Set_Oimage(U_1544,U_1540,U_1546),U_1548))) ),
    inference(clausify,[status(thm)],[f_434_4]) ).

cnf(f_434_6,plain,
    ( U_1542 = hAPP(c_Set_Oimage(U_1544,U_1540,U_1546),sK17(U_1548,U_1546,U_1544,U_1542,U_1540))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1540,tc_HOL_Obool)),U_1542),hAPP(c_Set_Oimage(U_1544,U_1540,U_1546),U_1548))) ),
    inference(clausify,[status(thm)],[f_434_4]) ).

cnf(f_434_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1541,tc_HOL_Obool)),U_1543),hAPP(c_Set_Oimage(U_1545,U_1541,U_1547),U_1549)))
    | U_1543 != hAPP(c_Set_Oimage(U_1545,U_1541,U_1547),U_1534)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1545,tc_HOL_Obool)),U_1534),U_1549)) ),
    inference(clausify,[status(thm)],[f_434_4]) ).

fof(f_435_1,plain,
    ! [V_f_2,T_c,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_image__mono]) ).

fof(f_435_2,plain,
    ! [U_1554,U_1553,U_1552,U_1551,U_1550] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1553,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_1550,U_1553,U_1554),U_1551)),hAPP(c_Set_Oimage(U_1550,U_1553,U_1554),U_1552)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1550,tc_HOL_Obool)),U_1551),U_1552)) ),
    inference(variable_rename,[status(thm)],[f_435_1]) ).

cnf(f_435_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1553,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_1550,U_1553,U_1554),U_1551)),hAPP(c_Set_Oimage(U_1550,U_1553,U_1554),U_1552)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1550,tc_HOL_Obool)),U_1551),U_1552)) ),
    inference(clausify,[status(thm)],[f_435_2]) ).

fof(f_436_1,plain,
    ! [V_B_2,V_A_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_image__Un]) ).

fof(f_436_2,plain,
    ! [U_1559,U_1558,U_1557,U_1556,U_1555] : hAPP(c_Set_Oimage(U_1555,U_1556,U_1557),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1555,tc_HOL_Obool)),U_1558),U_1559)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1556,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_1555,U_1556,U_1557),U_1558)),hAPP(c_Set_Oimage(U_1555,U_1556,U_1557),U_1559)),
    inference(variable_rename,[status(thm)],[f_436_1]) ).

cnf(f_436_3,plain,
    hAPP(c_Set_Oimage(U_1555,U_1556,U_1557),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1555,tc_HOL_Obool)),U_1558),U_1559)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1556,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_1555,U_1556,U_1557),U_1558)),hAPP(c_Set_Oimage(U_1555,U_1556,U_1557),U_1559)),
    inference(clausify,[status(thm)],[f_436_2]) ).

fof(f_437_1,plain,
    ! [T_b] :
      ( c_Lattices_Osemilattice__sup__class_Osup(T_b) = c_Orderings_Oord__class_Omax(T_b)
      | ~ class_Orderings_Olinorder(T_b)
      | ~ class_Lattices_Osemilattice__sup(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sup__max]) ).

fof(f_437_2,plain,
    ! [U_1560] :
      ( c_Lattices_Osemilattice__sup__class_Osup(U_1560) = c_Orderings_Oord__class_Omax(U_1560)
      | ~ class_Orderings_Olinorder(U_1560)
      | ~ class_Lattices_Osemilattice__sup(U_1560) ),
    inference(variable_rename,[status(thm)],[f_437_1]) ).

cnf(f_437_3,plain,
    ( c_Lattices_Osemilattice__sup__class_Osup(U_1560) = c_Orderings_Oord__class_Omax(U_1560)
    | ~ class_Orderings_Olinorder(U_1560)
    | ~ class_Lattices_Osemilattice__sup(U_1560) ),
    inference(clausify,[status(thm)],[f_437_2]) ).

fof(f_438_1,plain,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_c,T_b,V_f_2)),hAPP(c_Set_OPow(T_c),V_A_2))),hAPP(c_Set_OPow(T_b),V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_image__Pow__mono]) ).

fof(f_438_2,plain,
    ! [U_1565,U_1564,U_1563,U_1562,U_1561] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_1561,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_fun(U_1562,tc_HOL_Obool),tc_fun(U_1561,tc_HOL_Obool),c_Set_Oimage(U_1562,U_1561,U_1563)),hAPP(c_Set_OPow(U_1562),U_1564))),hAPP(c_Set_OPow(U_1561),U_1565)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1561,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_1562,U_1561,U_1563),U_1564)),U_1565)) ),
    inference(variable_rename,[status(thm)],[f_438_1]) ).

cnf(f_438_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_1561,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_fun(U_1562,tc_HOL_Obool),tc_fun(U_1561,tc_HOL_Obool),c_Set_Oimage(U_1562,U_1561,U_1563)),hAPP(c_Set_OPow(U_1562),U_1564))),hAPP(c_Set_OPow(U_1561),U_1565)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1561,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_1562,U_1561,U_1563),U_1564)),U_1565)) ),
    inference(clausify,[status(thm)],[f_438_2]) ).

fof(f_439_1,plain,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_B_2)))),
    inference(fof_nnf,[status(thm)],[fact_image__Int__subset]) ).

fof(f_439_2,plain,
    ! [U_1570,U_1569,U_1568,U_1567,U_1566] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1566,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_1567,U_1566,U_1568),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1567,tc_HOL_Obool)),U_1569),U_1570))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1566,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_1567,U_1566,U_1568),U_1569)),hAPP(c_Set_Oimage(U_1567,U_1566,U_1568),U_1570)))),
    inference(variable_rename,[status(thm)],[f_439_1]) ).

cnf(f_439_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1566,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_1567,U_1566,U_1568),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1567,tc_HOL_Obool)),U_1569),U_1570))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1566,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_1567,U_1566,U_1568),U_1569)),hAPP(c_Set_Oimage(U_1567,U_1566,U_1568),U_1570)))),
    inference(clausify,[status(thm)],[f_439_2]) ).

fof(f_440_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_x_2,V_y_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2))
      | ~ class_Groups_Oordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_image__uminus__atLeastAtMost]) ).

fof(f_440_2,plain,
    ! [U_1573,U_1572,U_1571] :
      ( hAPP(c_Set_Oimage(U_1571,U_1571,c_Groups_Ouminus__class_Ouminus(U_1571)),c_SetInterval_Oord__class_OatLeastAtMost(U_1571,U_1572,U_1573)) = c_SetInterval_Oord__class_OatLeastAtMost(U_1571,hAPP(c_Groups_Ouminus__class_Ouminus(U_1571),U_1573),hAPP(c_Groups_Ouminus__class_Ouminus(U_1571),U_1572))
      | ~ class_Groups_Oordered__ab__group__add(U_1571) ),
    inference(variable_rename,[status(thm)],[f_440_1]) ).

cnf(f_440_3,plain,
    ( hAPP(c_Set_Oimage(U_1571,U_1571,c_Groups_Ouminus__class_Ouminus(U_1571)),c_SetInterval_Oord__class_OatLeastAtMost(U_1571,U_1572,U_1573)) = c_SetInterval_Oord__class_OatLeastAtMost(U_1571,hAPP(c_Groups_Ouminus__class_Ouminus(U_1571),U_1573),hAPP(c_Groups_Ouminus__class_Ouminus(U_1571),U_1572))
    | ~ class_Groups_Oordered__ab__group__add(U_1571) ),
    inference(clausify,[status(thm)],[f_440_2]) ).

fof(f_441_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_x_2,V_y_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2))
      | ~ class_Groups_Oordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_image__uminus__greaterThanLessThan]) ).

fof(f_441_2,plain,
    ! [U_1576,U_1575,U_1574] :
      ( hAPP(c_Set_Oimage(U_1574,U_1574,c_Groups_Ouminus__class_Ouminus(U_1574)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1574,U_1575,U_1576)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_1574,hAPP(c_Groups_Ouminus__class_Ouminus(U_1574),U_1576),hAPP(c_Groups_Ouminus__class_Ouminus(U_1574),U_1575))
      | ~ class_Groups_Oordered__ab__group__add(U_1574) ),
    inference(variable_rename,[status(thm)],[f_441_1]) ).

cnf(f_441_3,plain,
    ( hAPP(c_Set_Oimage(U_1574,U_1574,c_Groups_Ouminus__class_Ouminus(U_1574)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1574,U_1575,U_1576)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_1574,hAPP(c_Groups_Ouminus__class_Ouminus(U_1574),U_1576),hAPP(c_Groups_Ouminus__class_Ouminus(U_1574),U_1575))
    | ~ class_Groups_Oordered__ab__group__add(U_1574) ),
    inference(clausify,[status(thm)],[f_441_2]) ).

fof(f_442_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_x_2),V_y_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2))
      | ~ class_Groups_Oordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_image__uminus__atLeastLessThan]) ).

fof(f_442_2,plain,
    ! [U_1579,U_1578,U_1577] :
      ( hAPP(c_Set_Oimage(U_1577,U_1577,c_Groups_Ouminus__class_Ouminus(U_1577)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1577,U_1578),U_1579)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_1577,hAPP(c_Groups_Ouminus__class_Ouminus(U_1577),U_1579),hAPP(c_Groups_Ouminus__class_Ouminus(U_1577),U_1578))
      | ~ class_Groups_Oordered__ab__group__add(U_1577) ),
    inference(variable_rename,[status(thm)],[f_442_1]) ).

cnf(f_442_3,plain,
    ( hAPP(c_Set_Oimage(U_1577,U_1577,c_Groups_Ouminus__class_Ouminus(U_1577)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1577,U_1578),U_1579)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_1577,hAPP(c_Groups_Ouminus__class_Ouminus(U_1577),U_1579),hAPP(c_Groups_Ouminus__class_Ouminus(U_1577),U_1578))
    | ~ class_Groups_Oordered__ab__group__add(U_1577) ),
    inference(clausify,[status(thm)],[f_442_2]) ).

fof(f_443_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_x_2,V_y_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2))
      | ~ class_Groups_Oordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_image__uminus__greaterThanAtMost]) ).

fof(f_443_2,plain,
    ! [U_1582,U_1581,U_1580] :
      ( hAPP(c_Set_Oimage(U_1580,U_1580,c_Groups_Ouminus__class_Ouminus(U_1580)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_1580,U_1581,U_1582)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1580,hAPP(c_Groups_Ouminus__class_Ouminus(U_1580),U_1582)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1580),U_1581))
      | ~ class_Groups_Oordered__ab__group__add(U_1580) ),
    inference(variable_rename,[status(thm)],[f_443_1]) ).

cnf(f_443_3,plain,
    ( hAPP(c_Set_Oimage(U_1580,U_1580,c_Groups_Ouminus__class_Ouminus(U_1580)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_1580,U_1581,U_1582)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1580,hAPP(c_Groups_Ouminus__class_Ouminus(U_1580),U_1582)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1580),U_1581))
    | ~ class_Groups_Oordered__ab__group__add(U_1580) ),
    inference(clausify,[status(thm)],[f_443_2]) ).

fof(f_444_1,plain,
    ! [V_x_2,T_b] :
      ( hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2))
      | ~ class_Groups_Oordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_image__uminus__greaterThan]) ).

fof(f_444_2,plain,
    ! [U_1584,U_1583] :
      ( hAPP(c_Set_Oimage(U_1583,U_1583,c_Groups_Ouminus__class_Ouminus(U_1583)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_1583),U_1584)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_1583),hAPP(c_Groups_Ouminus__class_Ouminus(U_1583),U_1584))
      | ~ class_Groups_Oordered__ab__group__add(U_1583) ),
    inference(variable_rename,[status(thm)],[f_444_1]) ).

cnf(f_444_3,plain,
    ( hAPP(c_Set_Oimage(U_1583,U_1583,c_Groups_Ouminus__class_Ouminus(U_1583)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_1583),U_1584)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_1583),hAPP(c_Groups_Ouminus__class_Ouminus(U_1583),U_1584))
    | ~ class_Groups_Oordered__ab__group__add(U_1583) ),
    inference(clausify,[status(thm)],[f_444_2]) ).

fof(f_445_1,plain,
    ! [V_A_2,V_f_2,T_b,T_c] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2))))
      | hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ),
    inference(fof_nnf,[status(thm)],[fact_surj__Compl__image__subset]) ).

fof(f_445_2,plain,
    ! [U_1588,U_1587,U_1586,U_1585] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1586,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1586,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_1585,U_1586,U_1587),U_1588))),hAPP(c_Set_Oimage(U_1585,U_1586,U_1587),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1585,tc_HOL_Obool)),U_1588))))
      | hAPP(c_Set_Oimage(U_1585,U_1586,U_1587),c_Orderings_Otop__class_Otop(tc_fun(U_1585,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_1586,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_445_1]) ).

cnf(f_445_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1586,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1586,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_1585,U_1586,U_1587),U_1588))),hAPP(c_Set_Oimage(U_1585,U_1586,U_1587),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1585,tc_HOL_Obool)),U_1588))))
    | hAPP(c_Set_Oimage(U_1585,U_1586,U_1587),c_Orderings_Otop__class_Otop(tc_fun(U_1585,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_1586,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_445_2]) ).

fof(f_446_1,plain,
    ! [V_A_2,T_b,B_f] : hAPP(c_Set_Oimage(T_b,tc_fun(T_b,tc_HOL_Obool),B_f),V_A_2) != hAPP(c_Set_OPow(T_b),V_A_2),
    inference(fof_nnf,[status(thm)],[fact_Cantors__paradox]) ).

fof(f_446_2,plain,
    ! [U_1591,U_1590,U_1589] : hAPP(c_Set_Oimage(U_1590,tc_fun(U_1590,tc_HOL_Obool),U_1589),U_1591) != hAPP(c_Set_OPow(U_1590),U_1591),
    inference(variable_rename,[status(thm)],[f_446_1]) ).

cnf(f_446_3,plain,
    hAPP(c_Set_Oimage(U_1590,tc_fun(U_1590,tc_HOL_Obool),U_1589),U_1591) != hAPP(c_Set_OPow(U_1590),U_1591),
    inference(clausify,[status(thm)],[f_446_2]) ).

fof(f_447_1,plain,
    ! [T_b] :
      ( c_Orderings_Oord__class_Omax(T_b) = c_Orderings_Oord_Omax(T_b,c_Orderings_Oord__class_Oless__eq(T_b))
      | ~ class_Orderings_Oord(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_max__ord__max]) ).

fof(f_447_2,plain,
    ! [U_1592] :
      ( c_Orderings_Oord__class_Omax(U_1592) = c_Orderings_Oord_Omax(U_1592,c_Orderings_Oord__class_Oless__eq(U_1592))
      | ~ class_Orderings_Oord(U_1592) ),
    inference(variable_rename,[status(thm)],[f_447_1]) ).

cnf(f_447_3,plain,
    ( c_Orderings_Oord__class_Omax(U_1592) = c_Orderings_Oord_Omax(U_1592,c_Orderings_Oord__class_Oless__eq(U_1592))
    | ~ class_Orderings_Oord(U_1592) ),
    inference(clausify,[status(thm)],[f_447_2]) ).

fof(f_448_1,plain,
    ! [V_B_2,V_A_2,V_f_2,T_b,T_c] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),hAPP(V_f_2,V_A_2)),hAPP(V_f_2,V_B_2))),hAPP(V_f_2,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_A_2),V_B_2))))
      | ~ c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
      | ~ class_Orderings_Olinorder(T_b)
      | ~ class_Lattices_Osemilattice__sup(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Omono__sup]) ).

fof(f_448_2,plain,
    ! [U_1597,U_1596,U_1595,U_1594,U_1593] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1593),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1593),hAPP(U_1595,U_1596)),hAPP(U_1595,U_1597))),hAPP(U_1595,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1594),U_1596),U_1597))))
      | ~ c_Orderings_Oorder__class_Omono(U_1594,U_1593,U_1595)
      | ~ class_Orderings_Olinorder(U_1594)
      | ~ class_Lattices_Osemilattice__sup(U_1593) ),
    inference(variable_rename,[status(thm)],[f_448_1]) ).

cnf(f_448_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1593),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1593),hAPP(U_1595,U_1596)),hAPP(U_1595,U_1597))),hAPP(U_1595,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1594),U_1596),U_1597))))
    | ~ c_Orderings_Oorder__class_Omono(U_1594,U_1593,U_1595)
    | ~ class_Orderings_Olinorder(U_1594)
    | ~ class_Lattices_Osemilattice__sup(U_1593) ),
    inference(clausify,[status(thm)],[f_448_2]) ).

fof(f_449_1,plain,
    ! [V_x_2,T_b] :
      ( c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Osingleton]) ).

fof(f_449_2,plain,
    ! [U_1599,U_1598] :
      ( c_Big__Operators_Olattice_OSup__fin(U_1598,c_Orderings_Oord__class_Omax(U_1598),hAPP(hAPP(c_Set_Oinsert(U_1598),U_1599),c_Orderings_Obot__class_Obot(tc_fun(U_1598,tc_HOL_Obool)))) = U_1599
      | ~ class_Orderings_Olinorder(U_1598) ),
    inference(variable_rename,[status(thm)],[f_449_1]) ).

cnf(f_449_3,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_1598,c_Orderings_Oord__class_Omax(U_1598),hAPP(hAPP(c_Set_Oinsert(U_1598),U_1599),c_Orderings_Obot__class_Obot(tc_fun(U_1598,tc_HOL_Obool)))) = U_1599
    | ~ class_Orderings_Olinorder(U_1598) ),
    inference(clausify,[status(thm)],[f_449_2]) ).

fof(f_450_1,plain,
    ! [V_d_2,V_c_2,V_b_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Int__atLeastAtMostR1]) ).

fof(f_450_2,plain,
    ! [U_1603,U_1602,U_1601,U_1600] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1600,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_1600),U_1601)),c_SetInterval_Oord__class_OatLeastAtMost(U_1600,U_1602,U_1603)) = c_SetInterval_Oord__class_OatLeastAtMost(U_1600,U_1602,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1600),U_1601),U_1603))
      | ~ class_Orderings_Olinorder(U_1600) ),
    inference(variable_rename,[status(thm)],[f_450_1]) ).

cnf(f_450_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1600,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_1600),U_1601)),c_SetInterval_Oord__class_OatLeastAtMost(U_1600,U_1602,U_1603)) = c_SetInterval_Oord__class_OatLeastAtMost(U_1600,U_1602,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1600),U_1601),U_1603))
    | ~ class_Orderings_Olinorder(U_1600) ),
    inference(clausify,[status(thm)],[f_450_2]) ).

fof(f_451_1,plain,
    ! [V_d_2,V_b_2,V_a_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Int__atLeastAtMostL1]) ).

fof(f_451_2,plain,
    ! [U_1607,U_1606,U_1605,U_1604] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1604,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_1604,U_1605,U_1606)),hAPP(c_SetInterval_Oord__class_OatMost(U_1604),U_1607)) = c_SetInterval_Oord__class_OatLeastAtMost(U_1604,U_1605,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1604),U_1606),U_1607))
      | ~ class_Orderings_Olinorder(U_1604) ),
    inference(variable_rename,[status(thm)],[f_451_1]) ).

cnf(f_451_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1604,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_1604,U_1605,U_1606)),hAPP(c_SetInterval_Oord__class_OatMost(U_1604),U_1607)) = c_SetInterval_Oord__class_OatLeastAtMost(U_1604,U_1605,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1604),U_1606),U_1607))
    | ~ class_Orderings_Olinorder(U_1604) ),
    inference(clausify,[status(thm)],[f_451_2]) ).

fof(f_452_1,plain,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Int__greaterThanLessThan]) ).

fof(f_452_2,plain,
    ! [U_1612,U_1611,U_1610,U_1609,U_1608] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1608,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1608,U_1609,U_1610)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1608,U_1611,U_1612)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_1608,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1608),U_1609),U_1611),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1608),U_1610),U_1612))
      | ~ class_Orderings_Olinorder(U_1608) ),
    inference(variable_rename,[status(thm)],[f_452_1]) ).

cnf(f_452_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1608,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1608,U_1609,U_1610)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_1608,U_1611,U_1612)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_1608,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1608),U_1609),U_1611),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1608),U_1610),U_1612))
    | ~ class_Orderings_Olinorder(U_1608) ),
    inference(clausify,[status(thm)],[f_452_2]) ).

fof(f_453_1,plain,
    ! [V_f_2,T_b,T_c] :
      ( c_Orderings_Oorder__class_Ostrict__mono(T_b,T_c,V_f_2)
      | ? [B_x,B_y] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(V_f_2,B_x)),hAPP(V_f_2,B_y)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),B_y)) )
      | ~ class_Orderings_Oorder(T_b)
      | ~ class_Orderings_Oorder(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_strict__monoI]) ).

fof(f_453_2,plain,
    ! [U_1617,U_1616,U_1615] :
      ( c_Orderings_Oorder__class_Ostrict__mono(U_1616,U_1615,U_1617)
      | ? [U_1614,U_1613] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1615),hAPP(U_1617,U_1614)),hAPP(U_1617,U_1613)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1616),U_1614),U_1613)) )
      | ~ class_Orderings_Oorder(U_1616)
      | ~ class_Orderings_Oorder(U_1615) ),
    inference(variable_rename,[status(thm)],[f_453_1]) ).

fof(f_453_3,plain,
    ! [U_1617,U_1616,U_1615] :
      ( c_Orderings_Oorder__class_Ostrict__mono(U_1616,U_1615,U_1617)
      | ? [U_1613] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1615),hAPP(U_1617,sK18(U_1617,U_1616,U_1615))),hAPP(U_1617,U_1613)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1616),sK18(U_1617,U_1616,U_1615)),U_1613)) )
      | ~ class_Orderings_Oorder(U_1616)
      | ~ class_Orderings_Oorder(U_1615) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_1614,sK18(U_1617,U_1616,U_1615))],[f_453_2]) ).

fof(f_453_4,plain,
    ! [U_1617,U_1616,U_1615] :
      ( c_Orderings_Oorder__class_Ostrict__mono(U_1616,U_1615,U_1617)
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1615),hAPP(U_1617,sK18(U_1617,U_1616,U_1615))),hAPP(U_1617,sK19(U_1617,U_1616,U_1615))))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1616),sK18(U_1617,U_1616,U_1615)),sK19(U_1617,U_1616,U_1615))) )
      | ~ class_Orderings_Oorder(U_1616)
      | ~ class_Orderings_Oorder(U_1615) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_1613,sK19(U_1617,U_1616,U_1615))],[f_453_3]) ).

cnf(f_453_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1616),sK18(U_1617,U_1616,U_1615)),sK19(U_1617,U_1616,U_1615)))
    | c_Orderings_Oorder__class_Ostrict__mono(U_1616,U_1615,U_1617)
    | ~ class_Orderings_Oorder(U_1616)
    | ~ class_Orderings_Oorder(U_1615) ),
    inference(clausify,[status(thm)],[f_453_4]) ).

cnf(f_453_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1615),hAPP(U_1617,sK18(U_1617,U_1616,U_1615))),hAPP(U_1617,sK19(U_1617,U_1616,U_1615))))
    | c_Orderings_Oorder__class_Ostrict__mono(U_1616,U_1615,U_1617)
    | ~ class_Orderings_Oorder(U_1616)
    | ~ class_Orderings_Oorder(U_1615) ),
    inference(clausify,[status(thm)],[f_453_4]) ).

fof(f_454_1,plain,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Int__greaterThanAtMost]) ).

fof(f_454_2,plain,
    ! [U_1622,U_1621,U_1620,U_1619,U_1618] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1618,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_1618,U_1619,U_1620)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_1618,U_1621,U_1622)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_1618,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1618),U_1619),U_1621),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1618),U_1620),U_1622))
      | ~ class_Orderings_Olinorder(U_1618) ),
    inference(variable_rename,[status(thm)],[f_454_1]) ).

cnf(f_454_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1618,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_1618,U_1619,U_1620)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_1618,U_1621,U_1622)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_1618,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1618),U_1619),U_1621),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1618),U_1620),U_1622))
    | ~ class_Orderings_Olinorder(U_1618) ),
    inference(clausify,[status(thm)],[f_454_2]) ).

fof(f_455_1,plain,
    ! [V_x,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_x) = V_x
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Min_Oidem]) ).

fof(f_455_2,plain,
    ! [U_1624,U_1623] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1623),U_1624),U_1624) = U_1624
      | ~ class_Orderings_Olinorder(U_1623) ),
    inference(variable_rename,[status(thm)],[f_455_1]) ).

cnf(f_455_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1623),U_1624),U_1624) = U_1624
    | ~ class_Orderings_Olinorder(U_1623) ),
    inference(clausify,[status(thm)],[f_455_2]) ).

fof(f_456_1,plain,
    ! [V_z,V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__assoc]) ).

fof(f_456_2,plain,
    ! [U_1628,U_1627,U_1626,U_1625] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1625),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1625),U_1626),U_1627)),U_1628) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1625),U_1626),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1625),U_1627),U_1628))
      | ~ class_Orderings_Olinorder(U_1625) ),
    inference(variable_rename,[status(thm)],[f_456_1]) ).

cnf(f_456_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1625),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1625),U_1626),U_1627)),U_1628) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1625),U_1626),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1625),U_1627),U_1628))
    | ~ class_Orderings_Olinorder(U_1625) ),
    inference(clausify,[status(thm)],[f_456_2]) ).

fof(f_457_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b),V_c))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Oinf_Oassoc]) ).

fof(f_457_2,plain,
    ! [U_1632,U_1631,U_1630,U_1629] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1629),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1629),U_1630),U_1631)),U_1632) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1629),U_1630),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1629),U_1631),U_1632))
      | ~ class_Orderings_Olinorder(U_1629) ),
    inference(variable_rename,[status(thm)],[f_457_1]) ).

cnf(f_457_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1629),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1629),U_1630),U_1631)),U_1632) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1629),U_1630),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1629),U_1631),U_1632))
    | ~ class_Orderings_Olinorder(U_1629) ),
    inference(clausify,[status(thm)],[f_457_2]) ).

fof(f_458_1,plain,
    ! [V_z,V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_z))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__left__commute]) ).

fof(f_458_2,plain,
    ! [U_1636,U_1635,U_1634,U_1633] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1633),U_1634),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1633),U_1635),U_1636)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1633),U_1635),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1633),U_1634),U_1636))
      | ~ class_Orderings_Olinorder(U_1633) ),
    inference(variable_rename,[status(thm)],[f_458_1]) ).

cnf(f_458_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1633),U_1634),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1633),U_1635),U_1636)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1633),U_1635),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1633),U_1634),U_1636))
    | ~ class_Orderings_Olinorder(U_1633) ),
    inference(clausify,[status(thm)],[f_458_2]) ).

fof(f_459_1,plain,
    ! [V_c,V_a,V_b,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_c)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b),V_c))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Oinf_Oleft__commute]) ).

fof(f_459_2,plain,
    ! [U_1640,U_1639,U_1638,U_1637] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1637),U_1638),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1637),U_1639),U_1640)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1637),U_1639),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1637),U_1638),U_1640))
      | ~ class_Orderings_Olinorder(U_1637) ),
    inference(variable_rename,[status(thm)],[f_459_1]) ).

cnf(f_459_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1637),U_1638),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1637),U_1639),U_1640)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1637),U_1639),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1637),U_1638),U_1640))
    | ~ class_Orderings_Olinorder(U_1637) ),
    inference(clausify,[status(thm)],[f_459_2]) ).

fof(f_460_1,plain,
    ! [V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__left__idem]) ).

fof(f_460_2,plain,
    ! [U_1643,U_1642,U_1641] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1641),U_1642),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1641),U_1642),U_1643)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1641),U_1642),U_1643)
      | ~ class_Orderings_Olinorder(U_1641) ),
    inference(variable_rename,[status(thm)],[f_460_1]) ).

cnf(f_460_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1641),U_1642),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1641),U_1642),U_1643)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1641),U_1642),U_1643)
    | ~ class_Orderings_Olinorder(U_1641) ),
    inference(clausify,[status(thm)],[f_460_2]) ).

fof(f_461_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Oinf_Oleft__idem]) ).

fof(f_461_2,plain,
    ! [U_1646,U_1645,U_1644] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1644),U_1645),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1644),U_1645),U_1646)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1644),U_1645),U_1646)
      | ~ class_Orderings_Olinorder(U_1644) ),
    inference(variable_rename,[status(thm)],[f_461_1]) ).

cnf(f_461_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1644),U_1645),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1644),U_1645),U_1646)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1644),U_1645),U_1646)
    | ~ class_Orderings_Olinorder(U_1644) ),
    inference(clausify,[status(thm)],[f_461_2]) ).

fof(f_462_1,plain,
    ! [V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_x)
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__commute]) ).

fof(f_462_2,plain,
    ! [U_1649,U_1648,U_1647] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1647),U_1648),U_1649) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1647),U_1649),U_1648)
      | ~ class_Orderings_Olinorder(U_1647) ),
    inference(variable_rename,[status(thm)],[f_462_1]) ).

cnf(f_462_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1647),U_1648),U_1649) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1647),U_1649),U_1648)
    | ~ class_Orderings_Olinorder(U_1647) ),
    inference(clausify,[status(thm)],[f_462_2]) ).

fof(f_463_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b),V_a)
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Oinf_Ocommute]) ).

fof(f_463_2,plain,
    ! [U_1652,U_1651,U_1650] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1650),U_1651),U_1652) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1650),U_1652),U_1651)
      | ~ class_Orderings_Olinorder(U_1650) ),
    inference(variable_rename,[status(thm)],[f_463_1]) ).

cnf(f_463_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1650),U_1651),U_1652) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1650),U_1652),U_1651)
    | ~ class_Orderings_Olinorder(U_1650) ),
    inference(clausify,[status(thm)],[f_463_2]) ).

fof(f_464_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_a) = V_a
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Oinf_Oidem]) ).

fof(f_464_2,plain,
    ! [U_1654,U_1653] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1653),U_1654),U_1654) = U_1654
      | ~ class_Orderings_Olinorder(U_1653) ),
    inference(variable_rename,[status(thm)],[f_464_1]) ).

cnf(f_464_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1653),U_1654),U_1654) = U_1654
    | ~ class_Orderings_Olinorder(U_1653) ),
    inference(clausify,[status(thm)],[f_464_2]) ).

fof(f_465_1,plain,
    ! [V_n_2,V_m_2,V_f_2,T_b,T_c] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),hAPP(V_f_2,V_m_2)),hAPP(V_f_2,V_n_2)) = hAPP(V_f_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_m_2),V_n_2))
      | ~ c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
      | ~ class_Orderings_Olinorder(T_b)
      | ~ class_Orderings_Olinorder(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_min__of__mono]) ).

fof(f_465_2,plain,
    ! [U_1659,U_1658,U_1657,U_1656,U_1655] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1655),hAPP(U_1657,U_1658)),hAPP(U_1657,U_1659)) = hAPP(U_1657,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1656),U_1658),U_1659))
      | ~ c_Orderings_Oorder__class_Omono(U_1656,U_1655,U_1657)
      | ~ class_Orderings_Olinorder(U_1656)
      | ~ class_Orderings_Olinorder(U_1655) ),
    inference(variable_rename,[status(thm)],[f_465_1]) ).

cnf(f_465_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1655),hAPP(U_1657,U_1658)),hAPP(U_1657,U_1659)) = hAPP(U_1657,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1656),U_1658),U_1659))
    | ~ c_Orderings_Oorder__class_Omono(U_1656,U_1655,U_1657)
    | ~ class_Orderings_Olinorder(U_1656)
    | ~ class_Orderings_Olinorder(U_1655) ),
    inference(clausify,[status(thm)],[f_465_2]) ).

fof(f_466_1,plain,
    ! [V_z_2,V_y_2,V_x_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2)),V_z_2))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2))
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) ) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2)),V_z_2)) ) )
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__le__iff__disj]) ).

fof(f_466_2,plain,
    ! [U_1663,U_1662,U_1661,U_1660] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1660),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1660),U_1661),U_1662)),U_1663))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1660),U_1662),U_1663))
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1660),U_1661),U_1663)) ) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1660),U_1662),U_1663))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1660),U_1661),U_1663))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1660),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1660),U_1661),U_1662)),U_1663)) ) )
      | ~ class_Orderings_Olinorder(U_1660) ),
    inference(variable_rename,[status(thm)],[f_466_1]) ).

cnf(f_466_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1660),U_1662),U_1663))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1660),U_1661),U_1663))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1660),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1660),U_1661),U_1662)),U_1663))
    | ~ class_Orderings_Olinorder(U_1660) ),
    inference(clausify,[status(thm)],[f_466_2]) ).

cnf(f_466_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1660),U_1661),U_1663))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1660),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1660),U_1661),U_1662)),U_1663))
    | ~ class_Orderings_Olinorder(U_1660) ),
    inference(clausify,[status(thm)],[f_466_2]) ).

cnf(f_466_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1660),U_1662),U_1663))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1660),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1660),U_1661),U_1662)),U_1663))
    | ~ class_Orderings_Olinorder(U_1660) ),
    inference(clausify,[status(thm)],[f_466_2]) ).

fof(f_467_1,plain,
    ! [V_b,V_a,V_x,T_a] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Ole__infE]) ).

fof(f_467_2,plain,
    ! [U_1667,U_1666,U_1665,U_1664] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1664),U_1665),U_1667))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1664),U_1665),U_1666)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1664),U_1665),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1664),U_1666),U_1667)))
      | ~ class_Orderings_Olinorder(U_1664) ),
    inference(variable_rename,[status(thm)],[f_467_1]) ).

cnf(f_467_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1664),U_1665),U_1666))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1664),U_1665),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1664),U_1666),U_1667)))
    | ~ class_Orderings_Olinorder(U_1664) ),
    inference(clausify,[status(thm)],[f_467_2]) ).

cnf(f_467_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1664),U_1665),U_1667))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1664),U_1665),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1664),U_1666),U_1667)))
    | ~ class_Orderings_Olinorder(U_1664) ),
    inference(clausify,[status(thm)],[f_467_2]) ).

fof(f_468_1,plain,
    ! [V_d,V_b,V_c,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_c),V_d)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__mono]) ).

fof(f_468_2,plain,
    ! [U_1672,U_1671,U_1670,U_1669,U_1668] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1668),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1668),U_1669),U_1671)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1668),U_1670),U_1672)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1668),U_1671),U_1672))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1668),U_1669),U_1670))
      | ~ class_Orderings_Olinorder(U_1668) ),
    inference(variable_rename,[status(thm)],[f_468_1]) ).

cnf(f_468_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1668),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1668),U_1669),U_1671)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1668),U_1670),U_1672)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1668),U_1671),U_1672))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1668),U_1669),U_1670))
    | ~ class_Orderings_Olinorder(U_1668) ),
    inference(clausify,[status(thm)],[f_468_2]) ).

fof(f_469_1,plain,
    ! [V_z,V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__greatest]) ).

fof(f_469_2,plain,
    ! [U_1676,U_1675,U_1674,U_1673] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1673),U_1674),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1673),U_1675),U_1676)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1673),U_1674),U_1676))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1673),U_1674),U_1675))
      | ~ class_Orderings_Olinorder(U_1673) ),
    inference(variable_rename,[status(thm)],[f_469_1]) ).

cnf(f_469_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1673),U_1674),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1673),U_1675),U_1676)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1673),U_1674),U_1676))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1673),U_1674),U_1675))
    | ~ class_Orderings_Olinorder(U_1673) ),
    inference(clausify,[status(thm)],[f_469_2]) ).

fof(f_470_1,plain,
    ! [V_b,V_a,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Ole__infI]) ).

fof(f_470_2,plain,
    ! [U_1680,U_1679,U_1678,U_1677] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1677),U_1678),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1677),U_1679),U_1680)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1677),U_1678),U_1680))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1677),U_1678),U_1679))
      | ~ class_Orderings_Olinorder(U_1677) ),
    inference(variable_rename,[status(thm)],[f_470_1]) ).

cnf(f_470_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1677),U_1678),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1677),U_1679),U_1680)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1677),U_1678),U_1680))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1677),U_1678),U_1679))
    | ~ class_Orderings_Olinorder(U_1677) ),
    inference(clausify,[status(thm)],[f_470_2]) ).

fof(f_471_1,plain,
    ! [V_x,V_y,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_y
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__absorb2]) ).

fof(f_471_2,plain,
    ! [U_1683,U_1682,U_1681] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1681),U_1683),U_1682) = U_1682
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1681),U_1682),U_1683))
      | ~ class_Orderings_Olinorder(U_1681) ),
    inference(variable_rename,[status(thm)],[f_471_1]) ).

cnf(f_471_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1681),U_1683),U_1682) = U_1682
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1681),U_1682),U_1683))
    | ~ class_Orderings_Olinorder(U_1681) ),
    inference(clausify,[status(thm)],[f_471_2]) ).

fof(f_472_1,plain,
    ! [V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_x
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__absorb1]) ).

fof(f_472_2,plain,
    ! [U_1686,U_1685,U_1684] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1684),U_1685),U_1686) = U_1685
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1684),U_1685),U_1686))
      | ~ class_Orderings_Olinorder(U_1684) ),
    inference(variable_rename,[status(thm)],[f_472_1]) ).

cnf(f_472_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1684),U_1685),U_1686) = U_1685
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1684),U_1685),U_1686))
    | ~ class_Orderings_Olinorder(U_1684) ),
    inference(clausify,[status(thm)],[f_472_2]) ).

fof(f_473_1,plain,
    ! [V_a,V_x,V_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Ole__infI2]) ).

fof(f_473_2,plain,
    ! [U_1690,U_1689,U_1688,U_1687] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1687),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1687),U_1690),U_1688)),U_1689))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1687),U_1688),U_1689))
      | ~ class_Orderings_Olinorder(U_1687) ),
    inference(variable_rename,[status(thm)],[f_473_1]) ).

cnf(f_473_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1687),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1687),U_1690),U_1688)),U_1689))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1687),U_1688),U_1689))
    | ~ class_Orderings_Olinorder(U_1687) ),
    inference(clausify,[status(thm)],[f_473_2]) ).

fof(f_474_1,plain,
    ! [V_b,V_x,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Ole__infI1]) ).

fof(f_474_2,plain,
    ! [U_1694,U_1693,U_1692,U_1691] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1691),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1691),U_1692),U_1694)),U_1693))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1691),U_1692),U_1693))
      | ~ class_Orderings_Olinorder(U_1691) ),
    inference(variable_rename,[status(thm)],[f_474_1]) ).

cnf(f_474_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1691),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1691),U_1692),U_1694)),U_1693))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1691),U_1692),U_1693))
    | ~ class_Orderings_Olinorder(U_1691) ),
    inference(clausify,[status(thm)],[f_474_2]) ).

fof(f_475_1,plain,
    ! [V_z_2,V_y_2,V_x_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_y_2),V_z_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_y_2),V_z_2))) ) )
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Ole__inf__iff]) ).

fof(f_475_2,plain,
    ! [U_1698,U_1697,U_1696,U_1695] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1695),U_1696),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1695),U_1697),U_1698)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1695),U_1696),U_1698))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1695),U_1696),U_1697)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1695),U_1696),U_1698))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1695),U_1696),U_1697)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1695),U_1696),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1695),U_1697),U_1698))) ) )
      | ~ class_Orderings_Olinorder(U_1695) ),
    inference(variable_rename,[status(thm)],[f_475_1]) ).

cnf(f_475_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1695),U_1696),U_1697))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1695),U_1696),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1695),U_1697),U_1698)))
    | ~ class_Orderings_Olinorder(U_1695) ),
    inference(clausify,[status(thm)],[f_475_2]) ).

cnf(f_475_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1695),U_1696),U_1698))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1695),U_1696),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1695),U_1697),U_1698)))
    | ~ class_Orderings_Olinorder(U_1695) ),
    inference(clausify,[status(thm)],[f_475_2]) ).

cnf(f_475_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1695),U_1696),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1695),U_1697),U_1698)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1695),U_1696),U_1698))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1695),U_1696),U_1697))
    | ~ class_Orderings_Olinorder(U_1695) ),
    inference(clausify,[status(thm)],[f_475_2]) ).

fof(f_476_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
          | hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2) != V_x_2 )
        & ( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2) = V_x_2
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) )
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Ole__iff__inf]) ).

fof(f_476_2,plain,
    ! [U_1701,U_1700,U_1699] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1699),U_1700),U_1701))
          | hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1699),U_1700),U_1701) != U_1700 )
        & ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1699),U_1700),U_1701) = U_1700
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1699),U_1700),U_1701)) ) )
      | ~ class_Orderings_Olinorder(U_1699) ),
    inference(variable_rename,[status(thm)],[f_476_1]) ).

cnf(f_476_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1699),U_1700),U_1701) = U_1700
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1699),U_1700),U_1701))
    | ~ class_Orderings_Olinorder(U_1699) ),
    inference(clausify,[status(thm)],[f_476_2]) ).

cnf(f_476_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1699),U_1700),U_1701))
    | hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1699),U_1700),U_1701) != U_1700
    | ~ class_Orderings_Olinorder(U_1699) ),
    inference(clausify,[status(thm)],[f_476_2]) ).

fof(f_477_1,plain,
    ! [V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_y))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__le2]) ).

fof(f_477_2,plain,
    ! [U_1704,U_1703,U_1702] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1702),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1702),U_1703),U_1704)),U_1704))
      | ~ class_Orderings_Olinorder(U_1702) ),
    inference(variable_rename,[status(thm)],[f_477_1]) ).

cnf(f_477_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1702),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1702),U_1703),U_1704)),U_1704))
    | ~ class_Orderings_Olinorder(U_1702) ),
    inference(clausify,[status(thm)],[f_477_2]) ).

fof(f_478_1,plain,
    ! [V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_x))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__le1]) ).

fof(f_478_2,plain,
    ! [U_1707,U_1706,U_1705] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1705),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1705),U_1706),U_1707)),U_1706))
      | ~ class_Orderings_Olinorder(U_1705) ),
    inference(variable_rename,[status(thm)],[f_478_1]) ).

cnf(f_478_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1705),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1705),U_1706),U_1707)),U_1706))
    | ~ class_Orderings_Olinorder(U_1705) ),
    inference(clausify,[status(thm)],[f_478_2]) ).

fof(f_479_1,plain,
    ! [V_a,V_x,V_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Oless__infI2]) ).

fof(f_479_2,plain,
    ! [U_1711,U_1710,U_1709,U_1708] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1708),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1708),U_1711),U_1709)),U_1710))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1708),U_1709),U_1710))
      | ~ class_Orderings_Olinorder(U_1708) ),
    inference(variable_rename,[status(thm)],[f_479_1]) ).

cnf(f_479_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1708),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1708),U_1711),U_1709)),U_1710))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1708),U_1709),U_1710))
    | ~ class_Orderings_Olinorder(U_1708) ),
    inference(clausify,[status(thm)],[f_479_2]) ).

fof(f_480_1,plain,
    ! [V_b,V_x,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Oless__infI1]) ).

fof(f_480_2,plain,
    ! [U_1715,U_1714,U_1713,U_1712] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1712),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1712),U_1713),U_1715)),U_1714))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1712),U_1713),U_1714))
      | ~ class_Orderings_Olinorder(U_1712) ),
    inference(variable_rename,[status(thm)],[f_480_1]) ).

cnf(f_480_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1712),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1712),U_1713),U_1715)),U_1714))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1712),U_1713),U_1714))
    | ~ class_Orderings_Olinorder(U_1712) ),
    inference(clausify,[status(thm)],[f_480_2]) ).

fof(f_481_1,plain,
    ! [V_z_2,V_y_2,V_x_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2)),V_z_2))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2))
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2)) ) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2)),V_z_2)) ) )
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__less__iff__disj]) ).

fof(f_481_2,plain,
    ! [U_1719,U_1718,U_1717,U_1716] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1716),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1716),U_1717),U_1718)),U_1719))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1716),U_1718),U_1719))
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1716),U_1717),U_1719)) ) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1716),U_1718),U_1719))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1716),U_1717),U_1719))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1716),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1716),U_1717),U_1718)),U_1719)) ) )
      | ~ class_Orderings_Olinorder(U_1716) ),
    inference(variable_rename,[status(thm)],[f_481_1]) ).

cnf(f_481_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1716),U_1718),U_1719))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1716),U_1717),U_1719))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1716),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1716),U_1717),U_1718)),U_1719))
    | ~ class_Orderings_Olinorder(U_1716) ),
    inference(clausify,[status(thm)],[f_481_2]) ).

cnf(f_481_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1716),U_1717),U_1719))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1716),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1716),U_1717),U_1718)),U_1719))
    | ~ class_Orderings_Olinorder(U_1716) ),
    inference(clausify,[status(thm)],[f_481_2]) ).

cnf(f_481_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1716),U_1718),U_1719))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1716),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1716),U_1717),U_1718)),U_1719))
    | ~ class_Orderings_Olinorder(U_1716) ),
    inference(clausify,[status(thm)],[f_481_2]) ).

fof(f_482_1,plain,
    ! [V_y_2,V_x_2,V_z_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2))) ) )
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__less__iff__conj]) ).

fof(f_482_2,plain,
    ! [U_1723,U_1722,U_1721,U_1720] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1720),U_1721),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1720),U_1722),U_1723)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1720),U_1721),U_1723))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1720),U_1721),U_1722)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1720),U_1721),U_1723))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1720),U_1721),U_1722)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1720),U_1721),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1720),U_1722),U_1723))) ) )
      | ~ class_Orderings_Olinorder(U_1720) ),
    inference(variable_rename,[status(thm)],[f_482_1]) ).

cnf(f_482_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1720),U_1721),U_1722))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1720),U_1721),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1720),U_1722),U_1723)))
    | ~ class_Orderings_Olinorder(U_1720) ),
    inference(clausify,[status(thm)],[f_482_2]) ).

cnf(f_482_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1720),U_1721),U_1723))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1720),U_1721),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1720),U_1722),U_1723)))
    | ~ class_Orderings_Olinorder(U_1720) ),
    inference(clausify,[status(thm)],[f_482_2]) ).

cnf(f_482_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1720),U_1721),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1720),U_1722),U_1723)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1720),U_1721),U_1723))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1720),U_1721),U_1722))
    | ~ class_Orderings_Olinorder(U_1720) ),
    inference(clausify,[status(thm)],[f_482_2]) ).

fof(f_483_1,plain,
    ! [V_B_2,V_A_2,V_f_2,T_b,T_c] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),hAPP(V_f_2,V_A_2)),hAPP(V_f_2,V_B_2))))
      | ~ c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
      | ~ class_Orderings_Olinorder(T_b)
      | ~ class_Lattices_Osemilattice__inf(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Omono__inf]) ).

fof(f_483_2,plain,
    ! [U_1728,U_1727,U_1726,U_1725,U_1724] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1724),hAPP(U_1726,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1725),U_1727),U_1728))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1724),hAPP(U_1726,U_1727)),hAPP(U_1726,U_1728))))
      | ~ c_Orderings_Oorder__class_Omono(U_1725,U_1724,U_1726)
      | ~ class_Orderings_Olinorder(U_1725)
      | ~ class_Lattices_Osemilattice__inf(U_1724) ),
    inference(variable_rename,[status(thm)],[f_483_1]) ).

cnf(f_483_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1724),hAPP(U_1726,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1725),U_1727),U_1728))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1724),hAPP(U_1726,U_1727)),hAPP(U_1726,U_1728))))
    | ~ c_Orderings_Oorder__class_Omono(U_1725,U_1724,U_1726)
    | ~ class_Orderings_Olinorder(U_1725)
    | ~ class_Lattices_Osemilattice__inf(U_1724) ),
    inference(clausify,[status(thm)],[f_483_2]) ).

fof(f_484_1,plain,
    ! [T_b] :
      ( c_Lattices_Osemilattice__inf__class_Oinf(T_b) = c_Orderings_Oord__class_Omin(T_b)
      | ~ class_Orderings_Olinorder(T_b)
      | ~ class_Lattices_Osemilattice__inf(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_inf__min]) ).

fof(f_484_2,plain,
    ! [U_1729] :
      ( c_Lattices_Osemilattice__inf__class_Oinf(U_1729) = c_Orderings_Oord__class_Omin(U_1729)
      | ~ class_Orderings_Olinorder(U_1729)
      | ~ class_Lattices_Osemilattice__inf(U_1729) ),
    inference(variable_rename,[status(thm)],[f_484_1]) ).

cnf(f_484_3,plain,
    ( c_Lattices_Osemilattice__inf__class_Oinf(U_1729) = c_Orderings_Oord__class_Omin(U_1729)
    | ~ class_Orderings_Olinorder(U_1729)
    | ~ class_Lattices_Osemilattice__inf(U_1729) ),
    inference(clausify,[status(thm)],[f_484_2]) ).

fof(f_485_1,plain,
    ! [V_x,V_z,V_y,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)),V_x) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_x)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_z),V_x))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__sup__distrib2]) ).

fof(f_485_2,plain,
    ! [U_1733,U_1732,U_1731,U_1730] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1730),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1730),U_1731),U_1732)),U_1733) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1730),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1730),U_1731),U_1733)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1730),U_1732),U_1733))
      | ~ class_Orderings_Olinorder(U_1730) ),
    inference(variable_rename,[status(thm)],[f_485_1]) ).

cnf(f_485_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1730),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1730),U_1731),U_1732)),U_1733) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1730),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1730),U_1731),U_1733)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1730),U_1732),U_1733))
    | ~ class_Orderings_Olinorder(U_1730) ),
    inference(clausify,[status(thm)],[f_485_2]) ).

fof(f_486_1,plain,
    ! [V_x,V_z,V_y,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z)),V_x) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_x)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_z),V_x))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Osup__inf__distrib2]) ).

fof(f_486_2,plain,
    ! [U_1737,U_1736,U_1735,U_1734] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1734),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1734),U_1735),U_1736)),U_1737) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1734),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1734),U_1735),U_1737)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1734),U_1736),U_1737))
      | ~ class_Orderings_Olinorder(U_1734) ),
    inference(variable_rename,[status(thm)],[f_486_1]) ).

cnf(f_486_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1734),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1734),U_1735),U_1736)),U_1737) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1734),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1734),U_1735),U_1737)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1734),U_1736),U_1737))
    | ~ class_Orderings_Olinorder(U_1734) ),
    inference(clausify,[status(thm)],[f_486_2]) ).

fof(f_487_1,plain,
    ! [V_z,V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_z))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__sup__distrib1]) ).

fof(f_487_2,plain,
    ! [U_1741,U_1740,U_1739,U_1738] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1738),U_1739),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1738),U_1740),U_1741)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1738),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1738),U_1739),U_1740)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1738),U_1739),U_1741))
      | ~ class_Orderings_Olinorder(U_1738) ),
    inference(variable_rename,[status(thm)],[f_487_1]) ).

cnf(f_487_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1738),U_1739),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1738),U_1740),U_1741)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1738),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1738),U_1739),U_1740)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1738),U_1739),U_1741))
    | ~ class_Orderings_Olinorder(U_1738) ),
    inference(clausify,[status(thm)],[f_487_2]) ).

fof(f_488_1,plain,
    ! [V_z,V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_z))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Osup__inf__distrib1]) ).

fof(f_488_2,plain,
    ! [U_1745,U_1744,U_1743,U_1742] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1742),U_1743),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1742),U_1744),U_1745)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1742),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1742),U_1743),U_1744)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1742),U_1743),U_1745))
      | ~ class_Orderings_Olinorder(U_1742) ),
    inference(variable_rename,[status(thm)],[f_488_1]) ).

cnf(f_488_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1742),U_1743),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1742),U_1744),U_1745)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1742),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1742),U_1743),U_1744)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1742),U_1743),U_1745))
    | ~ class_Orderings_Olinorder(U_1742) ),
    inference(clausify,[status(thm)],[f_488_2]) ).

fof(f_489_1,plain,
    ! [V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)) = V_x
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__sup__absorb]) ).

fof(f_489_2,plain,
    ! [U_1748,U_1747,U_1746] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1746),U_1747),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1746),U_1747),U_1748)) = U_1747
      | ~ class_Orderings_Olinorder(U_1746) ),
    inference(variable_rename,[status(thm)],[f_489_1]) ).

cnf(f_489_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1746),U_1747),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1746),U_1747),U_1748)) = U_1747
    | ~ class_Orderings_Olinorder(U_1746) ),
    inference(clausify,[status(thm)],[f_489_2]) ).

fof(f_490_1,plain,
    ! [V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)) = V_x
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Osup__inf__absorb]) ).

fof(f_490_2,plain,
    ! [U_1751,U_1750,U_1749] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1749),U_1750),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1749),U_1750),U_1751)) = U_1750
      | ~ class_Orderings_Olinorder(U_1749) ),
    inference(variable_rename,[status(thm)],[f_490_1]) ).

cnf(f_490_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1749),U_1750),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1749),U_1750),U_1751)) = U_1750
    | ~ class_Orderings_Olinorder(U_1749) ),
    inference(clausify,[status(thm)],[f_490_2]) ).

fof(f_491_1,plain,
    ! [V_y_2,V_x_2,V_f_2,T_b,T_c] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
      | ~ c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
      | ~ class_Orderings_Oorder(T_b)
      | ~ class_Orderings_Oorder(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_monoD]) ).

fof(f_491_2,plain,
    ! [U_1756,U_1755,U_1754,U_1753,U_1752] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1752),hAPP(U_1754,U_1755)),hAPP(U_1754,U_1756)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1753),U_1755),U_1756))
      | ~ c_Orderings_Oorder__class_Omono(U_1753,U_1752,U_1754)
      | ~ class_Orderings_Oorder(U_1753)
      | ~ class_Orderings_Oorder(U_1752) ),
    inference(variable_rename,[status(thm)],[f_491_1]) ).

cnf(f_491_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1752),hAPP(U_1754,U_1755)),hAPP(U_1754,U_1756)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1753),U_1755),U_1756))
    | ~ c_Orderings_Oorder__class_Omono(U_1753,U_1752,U_1754)
    | ~ class_Orderings_Oorder(U_1753)
    | ~ class_Orderings_Oorder(U_1752) ),
    inference(clausify,[status(thm)],[f_491_2]) ).

fof(f_492_1,plain,
    ! [V_n_2,V_m_2,V_f_2,T_b,T_c] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),hAPP(V_f_2,V_m_2)),hAPP(V_f_2,V_n_2)) = hAPP(V_f_2,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_m_2),V_n_2))
      | ~ c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
      | ~ class_Orderings_Olinorder(T_b)
      | ~ class_Orderings_Olinorder(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_max__of__mono]) ).

fof(f_492_2,plain,
    ! [U_1761,U_1760,U_1759,U_1758,U_1757] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1757),hAPP(U_1759,U_1760)),hAPP(U_1759,U_1761)) = hAPP(U_1759,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1758),U_1760),U_1761))
      | ~ c_Orderings_Oorder__class_Omono(U_1758,U_1757,U_1759)
      | ~ class_Orderings_Olinorder(U_1758)
      | ~ class_Orderings_Olinorder(U_1757) ),
    inference(variable_rename,[status(thm)],[f_492_1]) ).

cnf(f_492_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1757),hAPP(U_1759,U_1760)),hAPP(U_1759,U_1761)) = hAPP(U_1759,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1758),U_1760),U_1761))
    | ~ c_Orderings_Oorder__class_Omono(U_1758,U_1757,U_1759)
    | ~ class_Orderings_Olinorder(U_1758)
    | ~ class_Orderings_Olinorder(U_1757) ),
    inference(clausify,[status(thm)],[f_492_2]) ).

fof(f_493_1,plain,
    ! [V_z,V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_z))),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z))))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Odistrib__inf__le]) ).

fof(f_493_2,plain,
    ! [U_1765,U_1764,U_1763,U_1762] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1762),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1762),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1762),U_1763),U_1764)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1762),U_1763),U_1765))),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1762),U_1763),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1762),U_1764),U_1765))))
      | ~ class_Orderings_Olinorder(U_1762) ),
    inference(variable_rename,[status(thm)],[f_493_1]) ).

cnf(f_493_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1762),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1762),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1762),U_1763),U_1764)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1762),U_1763),U_1765))),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1762),U_1763),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1762),U_1764),U_1765))))
    | ~ class_Orderings_Olinorder(U_1762) ),
    inference(clausify,[status(thm)],[f_493_2]) ).

fof(f_494_1,plain,
    ! [V_z,V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z))),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_z))))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Odistrib__sup__le]) ).

fof(f_494_2,plain,
    ! [U_1769,U_1768,U_1767,U_1766] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1766),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1766),U_1767),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1766),U_1768),U_1769))),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1766),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1766),U_1767),U_1768)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1766),U_1767),U_1769))))
      | ~ class_Orderings_Olinorder(U_1766) ),
    inference(variable_rename,[status(thm)],[f_494_1]) ).

cnf(f_494_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1766),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1766),U_1767),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1766),U_1768),U_1769))),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1766),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1766),U_1767),U_1768)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1766),U_1767),U_1769))))
    | ~ class_Orderings_Olinorder(U_1766) ),
    inference(clausify,[status(thm)],[f_494_2]) ).

fof(f_495_1,plain,
    ! [V_y,V_x,T_a] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y))
      | ~ class_Groups_Olinordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_minus__max__eq__min]) ).

fof(f_495_2,plain,
    ! [U_1772,U_1771,U_1770] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1770),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1770),U_1771),U_1772)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1770),hAPP(c_Groups_Ouminus__class_Ouminus(U_1770),U_1771)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1770),U_1772))
      | ~ class_Groups_Olinordered__ab__group__add(U_1770) ),
    inference(variable_rename,[status(thm)],[f_495_1]) ).

cnf(f_495_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1770),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1770),U_1771),U_1772)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1770),hAPP(c_Groups_Ouminus__class_Ouminus(U_1770),U_1771)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1770),U_1772))
    | ~ class_Groups_Olinordered__ab__group__add(U_1770) ),
    inference(clausify,[status(thm)],[f_495_2]) ).

fof(f_496_1,plain,
    ! [V_y,V_x,T_a] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y))
      | ~ class_Groups_Olinordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_minus__min__eq__max]) ).

fof(f_496_2,plain,
    ! [U_1775,U_1774,U_1773] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1773),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1773),U_1774),U_1775)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1773),hAPP(c_Groups_Ouminus__class_Ouminus(U_1773),U_1774)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1773),U_1775))
      | ~ class_Groups_Olinordered__ab__group__add(U_1773) ),
    inference(variable_rename,[status(thm)],[f_496_1]) ).

cnf(f_496_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1773),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1773),U_1774),U_1775)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1773),hAPP(c_Groups_Ouminus__class_Ouminus(U_1773),U_1774)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1773),U_1775))
    | ~ class_Groups_Olinordered__ab__group__add(U_1773) ),
    inference(clausify,[status(thm)],[f_496_2]) ).

fof(f_497_1,plain,
    ! [V_f_2,T_b,T_c] :
      ( c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
      | ~ c_Orderings_Oorder__class_Ostrict__mono(T_b,T_c,V_f_2)
      | ~ class_Orderings_Oorder(T_b)
      | ~ class_Orderings_Oorder(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_strict__mono__mono]) ).

fof(f_497_2,plain,
    ! [U_1778,U_1777,U_1776] :
      ( c_Orderings_Oorder__class_Omono(U_1777,U_1776,U_1778)
      | ~ c_Orderings_Oorder__class_Ostrict__mono(U_1777,U_1776,U_1778)
      | ~ class_Orderings_Oorder(U_1777)
      | ~ class_Orderings_Oorder(U_1776) ),
    inference(variable_rename,[status(thm)],[f_497_1]) ).

cnf(f_497_3,plain,
    ( c_Orderings_Oorder__class_Omono(U_1777,U_1776,U_1778)
    | ~ c_Orderings_Oorder__class_Ostrict__mono(U_1777,U_1776,U_1778)
    | ~ class_Orderings_Oorder(U_1777)
    | ~ class_Orderings_Oorder(U_1776) ),
    inference(clausify,[status(thm)],[f_497_2]) ).

fof(f_498_1,plain,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_f_2,V_A_2)),hAPP(V_f_2,V_B_2))),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))))
      | ~ c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_mono__Un]) ).

fof(f_498_2,plain,
    ! [U_1783,U_1782,U_1781,U_1780,U_1779] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1780,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1780,tc_HOL_Obool)),hAPP(U_1781,U_1782)),hAPP(U_1781,U_1783))),hAPP(U_1781,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1779,tc_HOL_Obool)),U_1782),U_1783))))
      | ~ c_Orderings_Oorder__class_Omono(tc_fun(U_1779,tc_HOL_Obool),tc_fun(U_1780,tc_HOL_Obool),U_1781) ),
    inference(variable_rename,[status(thm)],[f_498_1]) ).

cnf(f_498_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1780,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1780,tc_HOL_Obool)),hAPP(U_1781,U_1782)),hAPP(U_1781,U_1783))),hAPP(U_1781,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1779,tc_HOL_Obool)),U_1782),U_1783))))
    | ~ c_Orderings_Oorder__class_Omono(tc_fun(U_1779,tc_HOL_Obool),tc_fun(U_1780,tc_HOL_Obool),U_1781) ),
    inference(clausify,[status(thm)],[f_498_2]) ).

fof(f_499_1,plain,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_f_2,V_A_2)),hAPP(V_f_2,V_B_2))))
      | ~ c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_mono__Int]) ).

fof(f_499_2,plain,
    ! [U_1788,U_1787,U_1786,U_1785,U_1784] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1785,tc_HOL_Obool)),hAPP(U_1786,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1784,tc_HOL_Obool)),U_1787),U_1788))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1785,tc_HOL_Obool)),hAPP(U_1786,U_1787)),hAPP(U_1786,U_1788))))
      | ~ c_Orderings_Oorder__class_Omono(tc_fun(U_1784,tc_HOL_Obool),tc_fun(U_1785,tc_HOL_Obool),U_1786) ),
    inference(variable_rename,[status(thm)],[f_499_1]) ).

cnf(f_499_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1785,tc_HOL_Obool)),hAPP(U_1786,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1784,tc_HOL_Obool)),U_1787),U_1788))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1785,tc_HOL_Obool)),hAPP(U_1786,U_1787)),hAPP(U_1786,U_1788))))
    | ~ c_Orderings_Oorder__class_Omono(tc_fun(U_1784,tc_HOL_Obool),tc_fun(U_1785,tc_HOL_Obool),U_1786) ),
    inference(clausify,[status(thm)],[f_499_2]) ).

fof(f_500_1,plain,
    ! [V_B_2,V_A_2,V_f_2,T_b,T_c] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),hAPP(V_f_2,V_A_2)),hAPP(V_f_2,V_B_2))),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_A_2),V_B_2))))
      | ~ c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
      | ~ class_Lattices_Osemilattice__sup(T_b)
      | ~ class_Lattices_Osemilattice__sup(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_mono__sup]) ).

fof(f_500_2,plain,
    ! [U_1793,U_1792,U_1791,U_1790,U_1789] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1789),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1789),hAPP(U_1791,U_1792)),hAPP(U_1791,U_1793))),hAPP(U_1791,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1790),U_1792),U_1793))))
      | ~ c_Orderings_Oorder__class_Omono(U_1790,U_1789,U_1791)
      | ~ class_Lattices_Osemilattice__sup(U_1790)
      | ~ class_Lattices_Osemilattice__sup(U_1789) ),
    inference(variable_rename,[status(thm)],[f_500_1]) ).

cnf(f_500_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1789),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1789),hAPP(U_1791,U_1792)),hAPP(U_1791,U_1793))),hAPP(U_1791,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_1790),U_1792),U_1793))))
    | ~ c_Orderings_Oorder__class_Omono(U_1790,U_1789,U_1791)
    | ~ class_Lattices_Osemilattice__sup(U_1790)
    | ~ class_Lattices_Osemilattice__sup(U_1789) ),
    inference(clausify,[status(thm)],[f_500_2]) ).

fof(f_501_1,plain,
    ! [V_B_2,V_A_2,V_f_2,T_b,T_c] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),hAPP(V_f_2,V_A_2)),hAPP(V_f_2,V_B_2))))
      | ~ c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
      | ~ class_Lattices_Osemilattice__inf(T_b)
      | ~ class_Lattices_Osemilattice__inf(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_mono__inf]) ).

fof(f_501_2,plain,
    ! [U_1798,U_1797,U_1796,U_1795,U_1794] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1794),hAPP(U_1796,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1795),U_1797),U_1798))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1794),hAPP(U_1796,U_1797)),hAPP(U_1796,U_1798))))
      | ~ c_Orderings_Oorder__class_Omono(U_1795,U_1794,U_1796)
      | ~ class_Lattices_Osemilattice__inf(U_1795)
      | ~ class_Lattices_Osemilattice__inf(U_1794) ),
    inference(variable_rename,[status(thm)],[f_501_1]) ).

cnf(f_501_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1794),hAPP(U_1796,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1795),U_1797),U_1798))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_1794),hAPP(U_1796,U_1797)),hAPP(U_1796,U_1798))))
    | ~ c_Orderings_Oorder__class_Omono(U_1795,U_1794,U_1796)
    | ~ class_Lattices_Osemilattice__inf(U_1795)
    | ~ class_Lattices_Osemilattice__inf(U_1794) ),
    inference(clausify,[status(thm)],[f_501_2]) ).

fof(f_502_1,plain,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Int__atLeastAtMost]) ).

fof(f_502_2,plain,
    ! [U_1803,U_1802,U_1801,U_1800,U_1799] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1799,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_1799,U_1800,U_1801)),c_SetInterval_Oord__class_OatLeastAtMost(U_1799,U_1802,U_1803)) = c_SetInterval_Oord__class_OatLeastAtMost(U_1799,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1799),U_1800),U_1802),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1799),U_1801),U_1803))
      | ~ class_Orderings_Olinorder(U_1799) ),
    inference(variable_rename,[status(thm)],[f_502_1]) ).

cnf(f_502_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1799,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_1799,U_1800,U_1801)),c_SetInterval_Oord__class_OatLeastAtMost(U_1799,U_1802,U_1803)) = c_SetInterval_Oord__class_OatLeastAtMost(U_1799,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1799),U_1800),U_1802),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1799),U_1801),U_1803))
    | ~ class_Orderings_Olinorder(U_1799) ),
    inference(clausify,[status(thm)],[f_502_2]) ).

fof(f_503_1,plain,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Int__atLeastLessThan]) ).

fof(f_503_2,plain,
    ! [U_1808,U_1807,U_1806,U_1805,U_1804] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1804,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1804,U_1805),U_1806)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1804,U_1807),U_1808)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1804,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1804),U_1805),U_1807)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1804),U_1806),U_1808))
      | ~ class_Orderings_Olinorder(U_1804) ),
    inference(variable_rename,[status(thm)],[f_503_1]) ).

cnf(f_503_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1804,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1804,U_1805),U_1806)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1804,U_1807),U_1808)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_1804,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1804),U_1805),U_1807)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1804),U_1806),U_1808))
    | ~ class_Orderings_Olinorder(U_1804) ),
    inference(clausify,[status(thm)],[f_503_2]) ).

fof(f_504_1,plain,
    ! [T_b] :
      ( c_Orderings_Oord__class_Omin(T_b) = c_Orderings_Oord_Omin(T_b,c_Orderings_Oord__class_Oless__eq(T_b))
      | ~ class_Orderings_Oord(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__ord__min]) ).

fof(f_504_2,plain,
    ! [U_1809] :
      ( c_Orderings_Oord__class_Omin(U_1809) = c_Orderings_Oord_Omin(U_1809,c_Orderings_Oord__class_Oless__eq(U_1809))
      | ~ class_Orderings_Oord(U_1809) ),
    inference(variable_rename,[status(thm)],[f_504_1]) ).

cnf(f_504_3,plain,
    ( c_Orderings_Oord__class_Omin(U_1809) = c_Orderings_Oord_Omin(U_1809,c_Orderings_Oord__class_Oless__eq(U_1809))
    | ~ class_Orderings_Oord(U_1809) ),
    inference(clausify,[status(thm)],[f_504_2]) ).

fof(f_505_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Ounion__inter]) ).

fof(f_505_2,plain,
    ! [U_1812,U_1811,U_1810] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1810),c_Big__Operators_Olattice_OSup__fin(U_1810,c_Orderings_Oord__class_Omax(U_1810),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1810,tc_HOL_Obool)),U_1811),U_1812))),c_Big__Operators_Olattice_OSup__fin(U_1810,c_Orderings_Oord__class_Omax(U_1810),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1810,tc_HOL_Obool)),U_1811),U_1812))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1810),c_Big__Operators_Olattice_OSup__fin(U_1810,c_Orderings_Oord__class_Omax(U_1810),U_1811)),c_Big__Operators_Olattice_OSup__fin(U_1810,c_Orderings_Oord__class_Omax(U_1810),U_1812))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1810,tc_HOL_Obool)),U_1811),U_1812) = c_Orderings_Obot__class_Obot(tc_fun(U_1810,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1810),U_1812))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1810),U_1811))
      | ~ class_Orderings_Olinorder(U_1810) ),
    inference(variable_rename,[status(thm)],[f_505_1]) ).

cnf(f_505_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1810),c_Big__Operators_Olattice_OSup__fin(U_1810,c_Orderings_Oord__class_Omax(U_1810),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1810,tc_HOL_Obool)),U_1811),U_1812))),c_Big__Operators_Olattice_OSup__fin(U_1810,c_Orderings_Oord__class_Omax(U_1810),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1810,tc_HOL_Obool)),U_1811),U_1812))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1810),c_Big__Operators_Olattice_OSup__fin(U_1810,c_Orderings_Oord__class_Omax(U_1810),U_1811)),c_Big__Operators_Olattice_OSup__fin(U_1810,c_Orderings_Oord__class_Omax(U_1810),U_1812))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1810,tc_HOL_Obool)),U_1811),U_1812) = c_Orderings_Obot__class_Obot(tc_fun(U_1810,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1810),U_1812))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1810),U_1811))
    | ~ class_Orderings_Olinorder(U_1810) ),
    inference(clausify,[status(thm)],[f_505_2]) ).

fof(f_506_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Ounion__disjoint]) ).

fof(f_506_2,plain,
    ! [U_1815,U_1814,U_1813] :
      ( c_Big__Operators_Olattice_OSup__fin(U_1813,c_Orderings_Oord__class_Omax(U_1813),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1813,tc_HOL_Obool)),U_1814),U_1815)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1813),c_Big__Operators_Olattice_OSup__fin(U_1813,c_Orderings_Oord__class_Omax(U_1813),U_1814)),c_Big__Operators_Olattice_OSup__fin(U_1813,c_Orderings_Oord__class_Omax(U_1813),U_1815))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1813,tc_HOL_Obool)),U_1814),U_1815) != c_Orderings_Obot__class_Obot(tc_fun(U_1813,tc_HOL_Obool))
      | U_1815 = c_Orderings_Obot__class_Obot(tc_fun(U_1813,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1813),U_1815))
      | U_1814 = c_Orderings_Obot__class_Obot(tc_fun(U_1813,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1813),U_1814))
      | ~ class_Orderings_Olinorder(U_1813) ),
    inference(variable_rename,[status(thm)],[f_506_1]) ).

cnf(f_506_3,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_1813,c_Orderings_Oord__class_Omax(U_1813),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1813,tc_HOL_Obool)),U_1814),U_1815)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1813),c_Big__Operators_Olattice_OSup__fin(U_1813,c_Orderings_Oord__class_Omax(U_1813),U_1814)),c_Big__Operators_Olattice_OSup__fin(U_1813,c_Orderings_Oord__class_Omax(U_1813),U_1815))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1813,tc_HOL_Obool)),U_1814),U_1815) != c_Orderings_Obot__class_Obot(tc_fun(U_1813,tc_HOL_Obool))
    | U_1815 = c_Orderings_Obot__class_Obot(tc_fun(U_1813,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1813),U_1815))
    | U_1814 = c_Orderings_Obot__class_Obot(tc_fun(U_1813,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1813),U_1814))
    | ~ class_Orderings_Olinorder(U_1813) ),
    inference(clausify,[status(thm)],[f_506_2]) ).

fof(f_507_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Ounion__idem]) ).

fof(f_507_2,plain,
    ! [U_1818,U_1817,U_1816] :
      ( c_Big__Operators_Olattice_OSup__fin(U_1816,c_Orderings_Oord__class_Omax(U_1816),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1816,tc_HOL_Obool)),U_1817),U_1818)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1816),c_Big__Operators_Olattice_OSup__fin(U_1816,c_Orderings_Oord__class_Omax(U_1816),U_1817)),c_Big__Operators_Olattice_OSup__fin(U_1816,c_Orderings_Oord__class_Omax(U_1816),U_1818))
      | U_1818 = c_Orderings_Obot__class_Obot(tc_fun(U_1816,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1816),U_1818))
      | U_1817 = c_Orderings_Obot__class_Obot(tc_fun(U_1816,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1816),U_1817))
      | ~ class_Orderings_Olinorder(U_1816) ),
    inference(variable_rename,[status(thm)],[f_507_1]) ).

cnf(f_507_3,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_1816,c_Orderings_Oord__class_Omax(U_1816),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1816,tc_HOL_Obool)),U_1817),U_1818)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1816),c_Big__Operators_Olattice_OSup__fin(U_1816,c_Orderings_Oord__class_Omax(U_1816),U_1817)),c_Big__Operators_Olattice_OSup__fin(U_1816,c_Orderings_Oord__class_Omax(U_1816),U_1818))
    | U_1818 = c_Orderings_Obot__class_Obot(tc_fun(U_1816,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1816),U_1818))
    | U_1817 = c_Orderings_Obot__class_Obot(tc_fun(U_1816,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1816),U_1817))
    | ~ class_Orderings_Olinorder(U_1816) ),
    inference(clausify,[status(thm)],[f_507_2]) ).

fof(f_508_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Osubset__idem]) ).

fof(f_508_2,plain,
    ! [U_1821,U_1820,U_1819] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1819),c_Big__Operators_Olattice_OSup__fin(U_1819,c_Orderings_Oord__class_Omax(U_1819),U_1821)),c_Big__Operators_Olattice_OSup__fin(U_1819,c_Orderings_Oord__class_Omax(U_1819),U_1820)) = c_Big__Operators_Olattice_OSup__fin(U_1819,c_Orderings_Oord__class_Omax(U_1819),U_1820)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1819,tc_HOL_Obool)),U_1821),U_1820))
      | U_1821 = c_Orderings_Obot__class_Obot(tc_fun(U_1819,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1819),U_1820))
      | ~ class_Orderings_Olinorder(U_1819) ),
    inference(variable_rename,[status(thm)],[f_508_1]) ).

cnf(f_508_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1819),c_Big__Operators_Olattice_OSup__fin(U_1819,c_Orderings_Oord__class_Omax(U_1819),U_1821)),c_Big__Operators_Olattice_OSup__fin(U_1819,c_Orderings_Oord__class_Omax(U_1819),U_1820)) = c_Big__Operators_Olattice_OSup__fin(U_1819,c_Orderings_Oord__class_Omax(U_1819),U_1820)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1819,tc_HOL_Obool)),U_1821),U_1820))
    | U_1821 = c_Orderings_Obot__class_Obot(tc_fun(U_1819,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1819),U_1820))
    | ~ class_Orderings_Olinorder(U_1819) ),
    inference(clausify,[status(thm)],[f_508_2]) ).

fof(f_509_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oinsert__idem]) ).

fof(f_509_2,plain,
    ! [U_1824,U_1823,U_1822] :
      ( c_Big__Operators_Olattice_OSup__fin(U_1822,c_Orderings_Oord__class_Omax(U_1822),hAPP(hAPP(c_Set_Oinsert(U_1822),U_1824),U_1823)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1822),U_1824),c_Big__Operators_Olattice_OSup__fin(U_1822,c_Orderings_Oord__class_Omax(U_1822),U_1823))
      | U_1823 = c_Orderings_Obot__class_Obot(tc_fun(U_1822,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1822),U_1823))
      | ~ class_Orderings_Olinorder(U_1822) ),
    inference(variable_rename,[status(thm)],[f_509_1]) ).

cnf(f_509_3,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_1822,c_Orderings_Oord__class_Omax(U_1822),hAPP(hAPP(c_Set_Oinsert(U_1822),U_1824),U_1823)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1822),U_1824),c_Big__Operators_Olattice_OSup__fin(U_1822,c_Orderings_Oord__class_Omax(U_1822),U_1823))
    | U_1823 = c_Orderings_Obot__class_Obot(tc_fun(U_1822,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1822),U_1823))
    | ~ class_Orderings_Olinorder(U_1822) ),
    inference(clausify,[status(thm)],[f_509_2]) ).

fof(f_510_1,plain,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))))
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_inj__image__Compl__subset]) ).

fof(f_510_2,plain,
    ! [U_1828,U_1827,U_1826,U_1825] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1826,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_1825,U_1826,U_1827),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1825,tc_HOL_Obool)),U_1828))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1826,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_1825,U_1826,U_1827),U_1828))))
      | ~ c_Fun_Oinj__on(U_1825,U_1826,U_1827,c_Orderings_Otop__class_Otop(tc_fun(U_1825,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_510_1]) ).

cnf(f_510_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1826,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_1825,U_1826,U_1827),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1825,tc_HOL_Obool)),U_1828))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1826,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_1825,U_1826,U_1827),U_1828))))
    | ~ c_Fun_Oinj__on(U_1825,U_1826,U_1827,c_Orderings_Otop__class_Otop(tc_fun(U_1825,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_510_2]) ).

fof(f_511_1,plain,
    ! [V_x_2,T_b] :
      ( c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Osingleton]) ).

fof(f_511_2,plain,
    ! [U_1830,U_1829] :
      ( c_Big__Operators_Olattice_OInf__fin(U_1829,c_Orderings_Oord__class_Omin(U_1829),hAPP(hAPP(c_Set_Oinsert(U_1829),U_1830),c_Orderings_Obot__class_Obot(tc_fun(U_1829,tc_HOL_Obool)))) = U_1830
      | ~ class_Orderings_Olinorder(U_1829) ),
    inference(variable_rename,[status(thm)],[f_511_1]) ).

cnf(f_511_3,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_1829,c_Orderings_Oord__class_Omin(U_1829),hAPP(hAPP(c_Set_Oinsert(U_1829),U_1830),c_Orderings_Obot__class_Obot(tc_fun(U_1829,tc_HOL_Obool)))) = U_1830
    | ~ class_Orderings_Olinorder(U_1829) ),
    inference(clausify,[status(thm)],[f_511_2]) ).

fof(f_512_1,plain,
    ! [V_k_2,T_b] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_k_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_k_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_single__Diff__lessThan]) ).

fof(f_512_2,plain,
    ! [U_1832,U_1831] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1831,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1831),U_1832),c_Orderings_Obot__class_Obot(tc_fun(U_1831,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(U_1831),U_1832)) = hAPP(hAPP(c_Set_Oinsert(U_1831),U_1832),c_Orderings_Obot__class_Obot(tc_fun(U_1831,tc_HOL_Obool)))
      | ~ class_Orderings_Oorder(U_1831) ),
    inference(variable_rename,[status(thm)],[f_512_1]) ).

cnf(f_512_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1831,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_1831),U_1832),c_Orderings_Obot__class_Obot(tc_fun(U_1831,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(U_1831),U_1832)) = hAPP(hAPP(c_Set_Oinsert(U_1831),U_1832),c_Orderings_Obot__class_Obot(tc_fun(U_1831,tc_HOL_Obool)))
    | ~ class_Orderings_Oorder(U_1831) ),
    inference(clausify,[status(thm)],[f_512_2]) ).

fof(f_513_1,plain,
    ! [V_g_2,V_f_2,T_c,T_b] : c_Fun_Ooverride__on(T_b,T_c,V_f_2,V_g_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_f_2,
    inference(fof_nnf,[status(thm)],[fact_override__on__emptyset]) ).

fof(f_513_2,plain,
    ! [U_1836,U_1835,U_1834,U_1833] : c_Fun_Ooverride__on(U_1833,U_1834,U_1835,U_1836,c_Orderings_Obot__class_Obot(tc_fun(U_1833,tc_HOL_Obool))) = U_1835,
    inference(variable_rename,[status(thm)],[f_513_1]) ).

cnf(f_513_3,plain,
    c_Fun_Ooverride__on(U_1833,U_1834,U_1835,U_1836,c_Orderings_Obot__class_Obot(tc_fun(U_1833,tc_HOL_Obool))) = U_1835,
    inference(clausify,[status(thm)],[f_513_2]) ).

fof(f_514_1,plain,
    ! [V_f_2,T_c,T_b] : c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),
    inference(fof_nnf,[status(thm)],[fact_inj__on__empty]) ).

fof(f_514_2,plain,
    ! [U_1839,U_1838,U_1837] : c_Fun_Oinj__on(U_1837,U_1838,U_1839,c_Orderings_Obot__class_Obot(tc_fun(U_1837,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_514_1]) ).

cnf(f_514_3,plain,
    c_Fun_Oinj__on(U_1837,U_1838,U_1839,c_Orderings_Obot__class_Obot(tc_fun(U_1837,tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_514_2]) ).

fof(f_515_1,plain,
    ! [V_A_2,T_b] :
      ( c_Fun_Oinj__on(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b),V_A_2)
      | ~ class_Groups_Oordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_inj__uminus]) ).

fof(f_515_2,plain,
    ! [U_1841,U_1840] :
      ( c_Fun_Oinj__on(U_1840,U_1840,c_Groups_Ouminus__class_Ouminus(U_1840),U_1841)
      | ~ class_Groups_Oordered__ab__group__add(U_1840) ),
    inference(variable_rename,[status(thm)],[f_515_1]) ).

cnf(f_515_3,plain,
    ( c_Fun_Oinj__on(U_1840,U_1840,c_Groups_Ouminus__class_Ouminus(U_1840),U_1841)
    | ~ class_Groups_Oordered__ab__group__add(U_1840) ),
    inference(clausify,[status(thm)],[f_515_2]) ).

fof(f_516_1,plain,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
        | ? [B_x] :
            ( ? [B_xa] :
                ( B_x != B_xa
                & hAPP(V_f_2,B_x) = hAPP(V_f_2,B_xa)
                & hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2)) )
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
      & ( ! [B_x] :
            ( ! [B_xa] :
                ( B_x = B_xa
                | hAPP(V_f_2,B_x) != hAPP(V_f_2,B_xa)
                | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2)) )
            | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
        | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_inj__on__def]) ).

fof(f_516_2,plain,
    ! [U_1849,U_1848,U_1847,U_1846] :
      ( ( c_Fun_Oinj__on(U_1846,U_1847,U_1848,U_1849)
        | ? [U_1845] :
            ( ? [U_1844] :
                ( U_1845 != U_1844
                & hAPP(U_1848,U_1845) = hAPP(U_1848,U_1844)
                & hBOOL(hAPP(hAPP(c_member(U_1846),U_1844),U_1849)) )
            & hBOOL(hAPP(hAPP(c_member(U_1846),U_1845),U_1849)) ) )
      & ( ! [U_1843] :
            ( ! [U_1842] :
                ( U_1843 = U_1842
                | hAPP(U_1848,U_1843) != hAPP(U_1848,U_1842)
                | ~ hBOOL(hAPP(hAPP(c_member(U_1846),U_1842),U_1849)) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_1846),U_1843),U_1849)) )
        | ~ c_Fun_Oinj__on(U_1846,U_1847,U_1848,U_1849) ) ),
    inference(variable_rename,[status(thm)],[f_516_1]) ).

fof(f_516_3,plain,
    ( ! [U_1857,U_1855,U_1853,U_1851] :
        ( c_Fun_Oinj__on(U_1851,U_1853,U_1855,U_1857)
        | ? [U_1845] :
            ( ? [U_1844] :
                ( U_1845 != U_1844
                & hAPP(U_1855,U_1845) = hAPP(U_1855,U_1844)
                & hBOOL(hAPP(hAPP(c_member(U_1851),U_1844),U_1857)) )
            & hBOOL(hAPP(hAPP(c_member(U_1851),U_1845),U_1857)) ) )
    & ! [U_1856,U_1854,U_1852,U_1850] :
        ( ! [U_1843] :
            ( ! [U_1842] :
                ( U_1843 = U_1842
                | hAPP(U_1854,U_1843) != hAPP(U_1854,U_1842)
                | ~ hBOOL(hAPP(hAPP(c_member(U_1850),U_1842),U_1856)) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_1850),U_1843),U_1856)) )
        | ~ c_Fun_Oinj__on(U_1850,U_1852,U_1854,U_1856) ) ),
    inference(miniscope,[status(thm)],[f_516_2]) ).

fof(f_516_4,plain,
    ( ! [U_1857,U_1855,U_1853,U_1851] :
        ( c_Fun_Oinj__on(U_1851,U_1853,U_1855,U_1857)
        | ( ? [U_1844] :
              ( sK20(U_1857,U_1855,U_1853,U_1851) != U_1844
              & hAPP(U_1855,sK20(U_1857,U_1855,U_1853,U_1851)) = hAPP(U_1855,U_1844)
              & hBOOL(hAPP(hAPP(c_member(U_1851),U_1844),U_1857)) )
          & hBOOL(hAPP(hAPP(c_member(U_1851),sK20(U_1857,U_1855,U_1853,U_1851)),U_1857)) ) )
    & ! [U_1856,U_1854,U_1852,U_1850] :
        ( ! [U_1843] :
            ( ! [U_1842] :
                ( U_1843 = U_1842
                | hAPP(U_1854,U_1843) != hAPP(U_1854,U_1842)
                | ~ hBOOL(hAPP(hAPP(c_member(U_1850),U_1842),U_1856)) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_1850),U_1843),U_1856)) )
        | ~ c_Fun_Oinj__on(U_1850,U_1852,U_1854,U_1856) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_1845,sK20(U_1857,U_1855,U_1853,U_1851))],[f_516_3]) ).

fof(f_516_5,plain,
    ( ! [U_1857,U_1855,U_1853,U_1851] :
        ( c_Fun_Oinj__on(U_1851,U_1853,U_1855,U_1857)
        | ( sK20(U_1857,U_1855,U_1853,U_1851) != sK21(U_1857,U_1855,U_1853,U_1851)
          & hAPP(U_1855,sK20(U_1857,U_1855,U_1853,U_1851)) = hAPP(U_1855,sK21(U_1857,U_1855,U_1853,U_1851))
          & hBOOL(hAPP(hAPP(c_member(U_1851),sK21(U_1857,U_1855,U_1853,U_1851)),U_1857))
          & hBOOL(hAPP(hAPP(c_member(U_1851),sK20(U_1857,U_1855,U_1853,U_1851)),U_1857)) ) )
    & ! [U_1856,U_1854,U_1852,U_1850] :
        ( ! [U_1843] :
            ( ! [U_1842] :
                ( U_1843 = U_1842
                | hAPP(U_1854,U_1843) != hAPP(U_1854,U_1842)
                | ~ hBOOL(hAPP(hAPP(c_member(U_1850),U_1842),U_1856)) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_1850),U_1843),U_1856)) )
        | ~ c_Fun_Oinj__on(U_1850,U_1852,U_1854,U_1856) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_1844,sK21(U_1857,U_1855,U_1853,U_1851))],[f_516_4]) ).

cnf(f_516_6,plain,
    ( U_1843 = U_1842
    | hAPP(U_1854,U_1843) != hAPP(U_1854,U_1842)
    | ~ hBOOL(hAPP(hAPP(c_member(U_1850),U_1842),U_1856))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1850),U_1843),U_1856))
    | ~ c_Fun_Oinj__on(U_1850,U_1852,U_1854,U_1856) ),
    inference(clausify,[status(thm)],[f_516_5]) ).

cnf(f_516_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_1851),sK20(U_1857,U_1855,U_1853,U_1851)),U_1857))
    | c_Fun_Oinj__on(U_1851,U_1853,U_1855,U_1857) ),
    inference(clausify,[status(thm)],[f_516_5]) ).

cnf(f_516_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_1851),sK21(U_1857,U_1855,U_1853,U_1851)),U_1857))
    | c_Fun_Oinj__on(U_1851,U_1853,U_1855,U_1857) ),
    inference(clausify,[status(thm)],[f_516_5]) ).

cnf(f_516_9,plain,
    ( hAPP(U_1855,sK20(U_1857,U_1855,U_1853,U_1851)) = hAPP(U_1855,sK21(U_1857,U_1855,U_1853,U_1851))
    | c_Fun_Oinj__on(U_1851,U_1853,U_1855,U_1857) ),
    inference(clausify,[status(thm)],[f_516_5]) ).

cnf(f_516_10,plain,
    ( sK20(U_1857,U_1855,U_1853,U_1851) != sK21(U_1857,U_1855,U_1853,U_1851)
    | c_Fun_Oinj__on(U_1851,U_1853,U_1855,U_1857) ),
    inference(clausify,[status(thm)],[f_516_5]) ).

fof(f_517_1,plain,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_inj__on__diff]) ).

fof(f_517_2,plain,
    ! [U_1862,U_1861,U_1860,U_1859,U_1858] :
      ( c_Fun_Oinj__on(U_1858,U_1859,U_1860,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1858,tc_HOL_Obool)),U_1861),U_1862))
      | ~ c_Fun_Oinj__on(U_1858,U_1859,U_1860,U_1861) ),
    inference(variable_rename,[status(thm)],[f_517_1]) ).

cnf(f_517_3,plain,
    ( c_Fun_Oinj__on(U_1858,U_1859,U_1860,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1858,tc_HOL_Obool)),U_1861),U_1862))
    | ~ c_Fun_Oinj__on(U_1858,U_1859,U_1860,U_1861) ),
    inference(clausify,[status(thm)],[f_517_2]) ).

fof(f_518_1,plain,
    ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),
    inference(fof_nnf,[status(thm)],[fact_Diff__idemp]) ).

fof(f_518_2,plain,
    ! [U_1865,U_1864,U_1863] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1863,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1863,tc_HOL_Obool)),U_1864),U_1865)),U_1865) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1863,tc_HOL_Obool)),U_1864),U_1865),
    inference(variable_rename,[status(thm)],[f_518_1]) ).

cnf(f_518_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1863,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1863,tc_HOL_Obool)),U_1864),U_1865)),U_1865) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1863,tc_HOL_Obool)),U_1864),U_1865),
    inference(clausify,[status(thm)],[f_518_2]) ).

fof(f_519_1,plain,
    ! [V_x_2,V_B_2,V_A_2,T_c,T_b] :
      ( hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,T_b)),V_A_2),V_B_2),V_x_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(V_A_2,V_x_2)),hAPP(V_B_2,V_x_2))
      | ~ class_Groups_Ominus(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_minus__apply]) ).

fof(f_519_2,plain,
    ! [U_1870,U_1869,U_1868,U_1867,U_1866] :
      ( hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1867,U_1866)),U_1868),U_1869),U_1870) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1866),hAPP(U_1868,U_1870)),hAPP(U_1869,U_1870))
      | ~ class_Groups_Ominus(U_1866) ),
    inference(variable_rename,[status(thm)],[f_519_1]) ).

cnf(f_519_3,plain,
    ( hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1867,U_1866)),U_1868),U_1869),U_1870) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1866),hAPP(U_1868,U_1870)),hAPP(U_1869,U_1870))
    | ~ class_Groups_Ominus(U_1866) ),
    inference(clausify,[status(thm)],[f_519_2]) ).

fof(f_520_1,plain,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
      ( ( ( V_a_2 = V_b_2
          | V_c_2 != V_d_2 )
        & ( V_c_2 = V_d_2
          | V_a_2 != V_b_2 ) )
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_c_2),V_d_2)
      | ~ class_Groups_Oab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__eq]) ).

fof(f_520_2,plain,
    ! [U_1875,U_1874,U_1873,U_1872,U_1871] :
      ( ( ( U_1872 = U_1873
          | U_1874 != U_1875 )
        & ( U_1874 = U_1875
          | U_1872 != U_1873 ) )
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1871),U_1872),U_1873) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1871),U_1874),U_1875)
      | ~ class_Groups_Oab__group__add(U_1871) ),
    inference(variable_rename,[status(thm)],[f_520_1]) ).

cnf(f_520_3,plain,
    ( U_1874 = U_1875
    | U_1872 != U_1873
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1871),U_1872),U_1873) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1871),U_1874),U_1875)
    | ~ class_Groups_Oab__group__add(U_1871) ),
    inference(clausify,[status(thm)],[f_520_2]) ).

cnf(f_520_4,plain,
    ( U_1872 = U_1873
    | U_1874 != U_1875
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1871),U_1872),U_1873) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1871),U_1874),U_1875)
    | ~ class_Groups_Oab__group__add(U_1871) ),
    inference(clausify,[status(thm)],[f_520_2]) ).

fof(f_521_1,plain,
    ! [V_B_2,V_A_2,V_C_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2) ),
    inference(fof_nnf,[status(thm)],[fact_inj__on__image__set__diff]) ).

fof(f_521_2,plain,
    ! [U_1881,U_1880,U_1879,U_1878,U_1877,U_1876] :
      ( hAPP(c_Set_Oimage(U_1876,U_1877,U_1878),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1876,tc_HOL_Obool)),U_1880),U_1881)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1877,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_1876,U_1877,U_1878),U_1880)),hAPP(c_Set_Oimage(U_1876,U_1877,U_1878),U_1881))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1876,tc_HOL_Obool)),U_1881),U_1879))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1876,tc_HOL_Obool)),U_1880),U_1879))
      | ~ c_Fun_Oinj__on(U_1876,U_1877,U_1878,U_1879) ),
    inference(variable_rename,[status(thm)],[f_521_1]) ).

cnf(f_521_3,plain,
    ( hAPP(c_Set_Oimage(U_1876,U_1877,U_1878),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1876,tc_HOL_Obool)),U_1880),U_1881)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1877,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_1876,U_1877,U_1878),U_1880)),hAPP(c_Set_Oimage(U_1876,U_1877,U_1878),U_1881))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1876,tc_HOL_Obool)),U_1881),U_1879))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1876,tc_HOL_Obool)),U_1880),U_1879))
    | ~ c_Fun_Oinj__on(U_1876,U_1877,U_1878,U_1879) ),
    inference(clausify,[status(thm)],[f_521_2]) ).

fof(f_522_1,plain,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2))
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_image__set__diff]) ).

fof(f_522_2,plain,
    ! [U_1886,U_1885,U_1884,U_1883,U_1882] :
      ( hAPP(c_Set_Oimage(U_1882,U_1883,U_1884),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1882,tc_HOL_Obool)),U_1885),U_1886)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1883,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_1882,U_1883,U_1884),U_1885)),hAPP(c_Set_Oimage(U_1882,U_1883,U_1884),U_1886))
      | ~ c_Fun_Oinj__on(U_1882,U_1883,U_1884,c_Orderings_Otop__class_Otop(tc_fun(U_1882,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_522_1]) ).

cnf(f_522_3,plain,
    ( hAPP(c_Set_Oimage(U_1882,U_1883,U_1884),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1882,tc_HOL_Obool)),U_1885),U_1886)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1883,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_1882,U_1883,U_1884),U_1885)),hAPP(c_Set_Oimage(U_1882,U_1883,U_1884),U_1886))
    | ~ c_Fun_Oinj__on(U_1882,U_1883,U_1884,c_Orderings_Otop__class_Otop(tc_fun(U_1882,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_522_2]) ).

fof(f_523_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( ( ( c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oinsert__remove]) ).

fof(f_523_2,plain,
    ! [U_1889,U_1888,U_1887] :
      ( ( ( c_Big__Operators_Olattice_OInf__fin(U_1887,c_Orderings_Oord__class_Omin(U_1887),hAPP(hAPP(c_Set_Oinsert(U_1887),U_1889),U_1888)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1887),U_1889),c_Big__Operators_Olattice_OInf__fin(U_1887,c_Orderings_Oord__class_Omin(U_1887),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1887,tc_HOL_Obool)),U_1888),hAPP(hAPP(c_Set_Oinsert(U_1887),U_1889),c_Orderings_Obot__class_Obot(tc_fun(U_1887,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1887,tc_HOL_Obool)),U_1888),hAPP(hAPP(c_Set_Oinsert(U_1887),U_1889),c_Orderings_Obot__class_Obot(tc_fun(U_1887,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_1887,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olattice_OInf__fin(U_1887,c_Orderings_Oord__class_Omin(U_1887),hAPP(hAPP(c_Set_Oinsert(U_1887),U_1889),U_1888)) = U_1889
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1887,tc_HOL_Obool)),U_1888),hAPP(hAPP(c_Set_Oinsert(U_1887),U_1889),c_Orderings_Obot__class_Obot(tc_fun(U_1887,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_1887,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1887),U_1888))
      | ~ class_Orderings_Olinorder(U_1887) ),
    inference(variable_rename,[status(thm)],[f_523_1]) ).

cnf(f_523_3,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_1887,c_Orderings_Oord__class_Omin(U_1887),hAPP(hAPP(c_Set_Oinsert(U_1887),U_1889),U_1888)) = U_1889
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1887,tc_HOL_Obool)),U_1888),hAPP(hAPP(c_Set_Oinsert(U_1887),U_1889),c_Orderings_Obot__class_Obot(tc_fun(U_1887,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_1887,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1887),U_1888))
    | ~ class_Orderings_Olinorder(U_1887) ),
    inference(clausify,[status(thm)],[f_523_2]) ).

cnf(f_523_4,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_1887,c_Orderings_Oord__class_Omin(U_1887),hAPP(hAPP(c_Set_Oinsert(U_1887),U_1889),U_1888)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1887),U_1889),c_Big__Operators_Olattice_OInf__fin(U_1887,c_Orderings_Oord__class_Omin(U_1887),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1887,tc_HOL_Obool)),U_1888),hAPP(hAPP(c_Set_Oinsert(U_1887),U_1889),c_Orderings_Obot__class_Obot(tc_fun(U_1887,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1887,tc_HOL_Obool)),U_1888),hAPP(hAPP(c_Set_Oinsert(U_1887),U_1889),c_Orderings_Obot__class_Obot(tc_fun(U_1887,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_1887,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1887),U_1888))
    | ~ class_Orderings_Olinorder(U_1887) ),
    inference(clausify,[status(thm)],[f_523_2]) ).

fof(f_524_1,plain,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_d_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_d_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) )
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_c_2),V_d_2)
      | ~ class_Groups_Oordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__less__eq]) ).

fof(f_524_2,plain,
    ! [U_1894,U_1893,U_1892,U_1891,U_1890] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1890),U_1891),U_1892))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1890),U_1893),U_1894)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1890),U_1893),U_1894))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1890),U_1891),U_1892)) ) )
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1890),U_1891),U_1892) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1890),U_1893),U_1894)
      | ~ class_Groups_Oordered__ab__group__add(U_1890) ),
    inference(variable_rename,[status(thm)],[f_524_1]) ).

cnf(f_524_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1890),U_1893),U_1894))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1890),U_1891),U_1892))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1890),U_1891),U_1892) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1890),U_1893),U_1894)
    | ~ class_Groups_Oordered__ab__group__add(U_1890) ),
    inference(clausify,[status(thm)],[f_524_2]) ).

cnf(f_524_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1890),U_1891),U_1892))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1890),U_1893),U_1894))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1890),U_1891),U_1892) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1890),U_1893),U_1894)
    | ~ class_Groups_Oordered__ab__group__add(U_1890) ),
    inference(clausify,[status(thm)],[f_524_2]) ).

fof(f_525_1,plain,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) )
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_c_2),V_d_2)
      | ~ class_Groups_Oordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__less]) ).

fof(f_525_2,plain,
    ! [U_1899,U_1898,U_1897,U_1896,U_1895] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1895),U_1896),U_1897))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1895),U_1898),U_1899)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1895),U_1898),U_1899))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1895),U_1896),U_1897)) ) )
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1895),U_1896),U_1897) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1895),U_1898),U_1899)
      | ~ class_Groups_Oordered__ab__group__add(U_1895) ),
    inference(variable_rename,[status(thm)],[f_525_1]) ).

cnf(f_525_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1895),U_1898),U_1899))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1895),U_1896),U_1897))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1895),U_1896),U_1897) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1895),U_1898),U_1899)
    | ~ class_Groups_Oordered__ab__group__add(U_1895) ),
    inference(clausify,[status(thm)],[f_525_2]) ).

cnf(f_525_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1895),U_1896),U_1897))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1895),U_1898),U_1899))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1895),U_1896),U_1897) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1895),U_1898),U_1899)
    | ~ class_Groups_Oordered__ab__group__add(U_1895) ),
    inference(clausify,[status(thm)],[f_525_2]) ).

fof(f_526_1,plain,
    ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) ),
    inference(fof_nnf,[status(thm)],[fact_subset__inj__on]) ).

fof(f_526_2,plain,
    ! [U_1904,U_1903,U_1902,U_1901,U_1900] :
      ( c_Fun_Oinj__on(U_1900,U_1901,U_1902,U_1904)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1900,tc_HOL_Obool)),U_1904),U_1903))
      | ~ c_Fun_Oinj__on(U_1900,U_1901,U_1902,U_1903) ),
    inference(variable_rename,[status(thm)],[f_526_1]) ).

cnf(f_526_3,plain,
    ( c_Fun_Oinj__on(U_1900,U_1901,U_1902,U_1904)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1900,tc_HOL_Obool)),U_1904),U_1903))
    | ~ c_Fun_Oinj__on(U_1900,U_1901,U_1902,U_1903) ),
    inference(clausify,[status(thm)],[f_526_2]) ).

fof(f_527_1,plain,
    ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
      ( ( ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
          | V_x_2 != V_y_2 )
        & ( V_x_2 = V_y_2
          | hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) ) )
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_inj__eq]) ).

fof(f_527_2,plain,
    ! [U_1909,U_1908,U_1907,U_1906,U_1905] :
      ( ( ( hAPP(U_1907,U_1908) = hAPP(U_1907,U_1909)
          | U_1908 != U_1909 )
        & ( U_1908 = U_1909
          | hAPP(U_1907,U_1908) != hAPP(U_1907,U_1909) ) )
      | ~ c_Fun_Oinj__on(U_1905,U_1906,U_1907,c_Orderings_Otop__class_Otop(tc_fun(U_1905,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_527_1]) ).

fof(f_527_3,plain,
    ! [U_1909,U_1908,U_1907] :
      ( ! [U_1906,U_1905] : ~ c_Fun_Oinj__on(U_1905,U_1906,U_1907,c_Orderings_Otop__class_Otop(tc_fun(U_1905,tc_HOL_Obool)))
      | ( ( hAPP(U_1907,U_1908) = hAPP(U_1907,U_1909)
          | U_1908 != U_1909 )
        & ( U_1908 = U_1909
          | hAPP(U_1907,U_1908) != hAPP(U_1907,U_1909) ) ) ),
    inference(miniscope,[status(thm)],[f_527_2]) ).

cnf(f_527_4,plain,
    ( U_1908 = U_1909
    | hAPP(U_1907,U_1908) != hAPP(U_1907,U_1909)
    | ~ c_Fun_Oinj__on(U_1905,U_1906,U_1907,c_Orderings_Otop__class_Otop(tc_fun(U_1905,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_527_3]) ).

cnf(f_527_5,plain,
    ( hAPP(U_1907,U_1908) = hAPP(U_1907,U_1909)
    | U_1908 != U_1909
    | ~ c_Fun_Oinj__on(U_1905,U_1906,U_1907,c_Orderings_Otop__class_Otop(tc_fun(U_1905,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_527_3]) ).

fof(f_528_1,plain,
    ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
      ( V_x_2 = V_y_2
      | hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2)
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_injD]) ).

fof(f_528_2,plain,
    ! [U_1914,U_1913,U_1912,U_1911,U_1910] :
      ( U_1913 = U_1914
      | hAPP(U_1912,U_1913) != hAPP(U_1912,U_1914)
      | ~ c_Fun_Oinj__on(U_1910,U_1911,U_1912,c_Orderings_Otop__class_Otop(tc_fun(U_1910,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_528_1]) ).

fof(f_528_3,plain,
    ! [U_1914,U_1913,U_1912] :
      ( ! [U_1911,U_1910] : ~ c_Fun_Oinj__on(U_1910,U_1911,U_1912,c_Orderings_Otop__class_Otop(tc_fun(U_1910,tc_HOL_Obool)))
      | U_1913 = U_1914
      | hAPP(U_1912,U_1913) != hAPP(U_1912,U_1914) ),
    inference(miniscope,[status(thm)],[f_528_2]) ).

cnf(f_528_4,plain,
    ( ~ c_Fun_Oinj__on(U_1910,U_1911,U_1912,c_Orderings_Otop__class_Otop(tc_fun(U_1910,tc_HOL_Obool)))
    | U_1913 = U_1914
    | hAPP(U_1912,U_1913) != hAPP(U_1912,U_1914) ),
    inference(clausify,[status(thm)],[f_528_3]) ).

fof(f_529_1,plain,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_inj__on__Int]) ).

fof(f_529_2,plain,
    ! [U_1919,U_1918,U_1917,U_1916,U_1915] :
      ( c_Fun_Oinj__on(U_1915,U_1916,U_1917,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1915,tc_HOL_Obool)),U_1918),U_1919))
      | ~ c_Fun_Oinj__on(U_1915,U_1916,U_1917,U_1919)
      | ~ c_Fun_Oinj__on(U_1915,U_1916,U_1917,U_1918) ),
    inference(variable_rename,[status(thm)],[f_529_1]) ).

cnf(f_529_3,plain,
    ( c_Fun_Oinj__on(U_1915,U_1916,U_1917,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1915,tc_HOL_Obool)),U_1918),U_1919))
    | ~ c_Fun_Oinj__on(U_1915,U_1916,U_1917,U_1919)
    | ~ c_Fun_Oinj__on(U_1915,U_1916,U_1917,U_1918) ),
    inference(clausify,[status(thm)],[f_529_2]) ).

fof(f_530_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_a)
      | ~ class_Groups_Oab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_minus__diff__eq]) ).

fof(f_530_2,plain,
    ! [U_1922,U_1921,U_1920] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1920),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1920),U_1921),U_1922)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1920),U_1922),U_1921)
      | ~ class_Groups_Oab__group__add(U_1920) ),
    inference(variable_rename,[status(thm)],[f_530_1]) ).

cnf(f_530_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1920),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1920),U_1921),U_1922)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1920),U_1922),U_1921)
    | ~ class_Groups_Oab__group__add(U_1920) ),
    inference(clausify,[status(thm)],[f_530_2]) ).

fof(f_531_1,plain,
    ! [V_z,V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_y),V_z))
      | ~ class_Groups_Oordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__diff__distrib__left]) ).

fof(f_531_2,plain,
    ! [U_1926,U_1925,U_1924,U_1923] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1923),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1923),U_1924),U_1925)),U_1926) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1923),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1923),U_1924),U_1926)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1923),U_1925),U_1926))
      | ~ class_Groups_Oordered__ab__group__add(U_1923) ),
    inference(variable_rename,[status(thm)],[f_531_1]) ).

cnf(f_531_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1923),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1923),U_1924),U_1925)),U_1926) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1923),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1923),U_1924),U_1926)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1923),U_1925),U_1926))
    | ~ class_Groups_Oordered__ab__group__add(U_1923) ),
    inference(clausify,[status(thm)],[f_531_2]) ).

fof(f_532_1,plain,
    ! [V_z,V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_y),V_z))
      | ~ class_Groups_Oordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_max__diff__distrib__left]) ).

fof(f_532_2,plain,
    ! [U_1930,U_1929,U_1928,U_1927] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1927),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1927),U_1928),U_1929)),U_1930) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1927),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1927),U_1928),U_1930)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1927),U_1929),U_1930))
      | ~ class_Groups_Oordered__ab__group__add(U_1927) ),
    inference(variable_rename,[status(thm)],[f_532_1]) ).

cnf(f_532_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1927),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1927),U_1928),U_1929)),U_1930) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_1927),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1927),U_1928),U_1930)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1927),U_1929),U_1930))
    | ~ class_Groups_Oordered__ab__group__add(U_1927) ),
    inference(clausify,[status(thm)],[f_532_2]) ).

fof(f_533_1,plain,
    ! [V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_empty__Diff]) ).

fof(f_533_2,plain,
    ! [U_1932,U_1931] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1931,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_1931,tc_HOL_Obool))),U_1932) = c_Orderings_Obot__class_Obot(tc_fun(U_1931,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_533_1]) ).

cnf(f_533_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1931,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_1931,tc_HOL_Obool))),U_1932) = c_Orderings_Obot__class_Obot(tc_fun(U_1931,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_533_2]) ).

fof(f_534_1,plain,
    ! [V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_A_2,
    inference(fof_nnf,[status(thm)],[fact_Diff__empty]) ).

fof(f_534_2,plain,
    ! [U_1934,U_1933] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1933,tc_HOL_Obool)),U_1934),c_Orderings_Obot__class_Obot(tc_fun(U_1933,tc_HOL_Obool))) = U_1934,
    inference(variable_rename,[status(thm)],[f_534_1]) ).

cnf(f_534_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1933,tc_HOL_Obool)),U_1934),c_Orderings_Obot__class_Obot(tc_fun(U_1933,tc_HOL_Obool))) = U_1934,
    inference(clausify,[status(thm)],[f_534_2]) ).

fof(f_535_1,plain,
    ! [V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Diff__cancel]) ).

fof(f_535_2,plain,
    ! [U_1936,U_1935] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1935,tc_HOL_Obool)),U_1936),U_1936) = c_Orderings_Obot__class_Obot(tc_fun(U_1935,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_535_1]) ).

cnf(f_535_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1935,tc_HOL_Obool)),U_1936),U_1936) = c_Orderings_Obot__class_Obot(tc_fun(U_1935,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_535_2]) ).

fof(f_536_1,plain,
    ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_Diff__subset]) ).

fof(f_536_2,plain,
    ! [U_1939,U_1938,U_1937] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1937,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1937,tc_HOL_Obool)),U_1938),U_1939)),U_1938)),
    inference(variable_rename,[status(thm)],[f_536_1]) ).

cnf(f_536_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1937,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1937,tc_HOL_Obool)),U_1938),U_1939)),U_1938)),
    inference(clausify,[status(thm)],[f_536_2]) ).

fof(f_537_1,plain,
    ! [V_B_2,V_D_2,V_C_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_D_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Diff__mono]) ).

fof(f_537_2,plain,
    ! [U_1944,U_1943,U_1942,U_1941,U_1940] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1940,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1940,tc_HOL_Obool)),U_1941),U_1944)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1940,tc_HOL_Obool)),U_1942),U_1943)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1940,tc_HOL_Obool)),U_1943),U_1944))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1940,tc_HOL_Obool)),U_1941),U_1942)) ),
    inference(variable_rename,[status(thm)],[f_537_1]) ).

cnf(f_537_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1940,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1940,tc_HOL_Obool)),U_1941),U_1944)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1940,tc_HOL_Obool)),U_1942),U_1943)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1940,tc_HOL_Obool)),U_1943),U_1944))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1940,tc_HOL_Obool)),U_1941),U_1942)) ),
    inference(clausify,[status(thm)],[f_537_2]) ).

fof(f_538_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) = V_A_2
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_double__diff]) ).

fof(f_538_2,plain,
    ! [U_1948,U_1947,U_1946,U_1945] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1945,tc_HOL_Obool)),U_1947),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1945,tc_HOL_Obool)),U_1948),U_1946)) = U_1946
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1945,tc_HOL_Obool)),U_1947),U_1948))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1945,tc_HOL_Obool)),U_1946),U_1947)) ),
    inference(variable_rename,[status(thm)],[f_538_1]) ).

cnf(f_538_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1945,tc_HOL_Obool)),U_1947),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1945,tc_HOL_Obool)),U_1948),U_1946)) = U_1946
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1945,tc_HOL_Obool)),U_1947),U_1948))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1945,tc_HOL_Obool)),U_1946),U_1947)) ),
    inference(clausify,[status(thm)],[f_538_2]) ).

fof(f_539_1,plain,
    ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),
    inference(fof_nnf,[status(thm)],[fact_Un__Diff__cancel]) ).

fof(f_539_2,plain,
    ! [U_1951,U_1950,U_1949] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1949,tc_HOL_Obool)),U_1950),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1949,tc_HOL_Obool)),U_1951),U_1950)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1949,tc_HOL_Obool)),U_1950),U_1951),
    inference(variable_rename,[status(thm)],[f_539_1]) ).

cnf(f_539_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1949,tc_HOL_Obool)),U_1950),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1949,tc_HOL_Obool)),U_1951),U_1950)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1949,tc_HOL_Obool)),U_1950),U_1951),
    inference(clausify,[status(thm)],[f_539_2]) ).

fof(f_540_1,plain,
    ! [V_A_2,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2),
    inference(fof_nnf,[status(thm)],[fact_Un__Diff__cancel2]) ).

fof(f_540_2,plain,
    ! [U_1954,U_1953,U_1952] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1952,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1952,tc_HOL_Obool)),U_1953),U_1954)),U_1954) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1952,tc_HOL_Obool)),U_1953),U_1954),
    inference(variable_rename,[status(thm)],[f_540_1]) ).

cnf(f_540_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1952,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1952,tc_HOL_Obool)),U_1953),U_1954)),U_1954) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1952,tc_HOL_Obool)),U_1953),U_1954),
    inference(clausify,[status(thm)],[f_540_2]) ).

fof(f_541_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)),
    inference(fof_nnf,[status(thm)],[fact_Un__Diff]) ).

fof(f_541_2,plain,
    ! [U_1958,U_1957,U_1956,U_1955] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1955,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1955,tc_HOL_Obool)),U_1956),U_1957)),U_1958) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1955,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1955,tc_HOL_Obool)),U_1956),U_1958)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1955,tc_HOL_Obool)),U_1957),U_1958)),
    inference(variable_rename,[status(thm)],[f_541_1]) ).

cnf(f_541_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1955,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1955,tc_HOL_Obool)),U_1956),U_1957)),U_1958) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1955,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1955,tc_HOL_Obool)),U_1956),U_1958)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1955,tc_HOL_Obool)),U_1957),U_1958)),
    inference(clausify,[status(thm)],[f_541_2]) ).

fof(f_542_1,plain,
    ! [V_B_2,V_A_2,V_C_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_Diff__Int__distrib]) ).

fof(f_542_2,plain,
    ! [U_1962,U_1961,U_1960,U_1959] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1959,tc_HOL_Obool)),U_1960),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1959,tc_HOL_Obool)),U_1961),U_1962)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1959,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1959,tc_HOL_Obool)),U_1960),U_1961)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1959,tc_HOL_Obool)),U_1960),U_1962)),
    inference(variable_rename,[status(thm)],[f_542_1]) ).

cnf(f_542_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1959,tc_HOL_Obool)),U_1960),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1959,tc_HOL_Obool)),U_1961),U_1962)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1959,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1959,tc_HOL_Obool)),U_1960),U_1961)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1959,tc_HOL_Obool)),U_1960),U_1962)),
    inference(clausify,[status(thm)],[f_542_2]) ).

fof(f_543_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)),
    inference(fof_nnf,[status(thm)],[fact_Int__Diff]) ).

fof(f_543_2,plain,
    ! [U_1966,U_1965,U_1964,U_1963] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1963,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1963,tc_HOL_Obool)),U_1964),U_1965)),U_1966) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1963,tc_HOL_Obool)),U_1964),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1963,tc_HOL_Obool)),U_1965),U_1966)),
    inference(variable_rename,[status(thm)],[f_543_1]) ).

cnf(f_543_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1963,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1963,tc_HOL_Obool)),U_1964),U_1965)),U_1966) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1963,tc_HOL_Obool)),U_1964),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1963,tc_HOL_Obool)),U_1965),U_1966)),
    inference(clausify,[status(thm)],[f_543_2]) ).

fof(f_544_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)),
    inference(fof_nnf,[status(thm)],[fact_Diff__Int__distrib2]) ).

fof(f_544_2,plain,
    ! [U_1970,U_1969,U_1968,U_1967] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1967,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1967,tc_HOL_Obool)),U_1968),U_1969)),U_1970) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1967,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1967,tc_HOL_Obool)),U_1968),U_1970)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1967,tc_HOL_Obool)),U_1969),U_1970)),
    inference(variable_rename,[status(thm)],[f_544_1]) ).

cnf(f_544_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1967,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1967,tc_HOL_Obool)),U_1968),U_1969)),U_1970) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1967,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1967,tc_HOL_Obool)),U_1968),U_1970)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1967,tc_HOL_Obool)),U_1969),U_1970)),
    inference(clausify,[status(thm)],[f_544_2]) ).

fof(f_545_1,plain,
    ! [V_B_2,V_C_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),V_B_2),
    inference(fof_nnf,[status(thm)],[fact_Diff__Int2]) ).

fof(f_545_2,plain,
    ! [U_1974,U_1973,U_1972,U_1971] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1971,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1971,tc_HOL_Obool)),U_1972),U_1973)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1971,tc_HOL_Obool)),U_1974),U_1973)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1971,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1971,tc_HOL_Obool)),U_1972),U_1973)),U_1974),
    inference(variable_rename,[status(thm)],[f_545_1]) ).

cnf(f_545_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1971,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1971,tc_HOL_Obool)),U_1972),U_1973)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1971,tc_HOL_Obool)),U_1974),U_1973)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1971,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1971,tc_HOL_Obool)),U_1972),U_1973)),U_1974),
    inference(clausify,[status(thm)],[f_545_2]) ).

fof(f_546_1,plain,
    ! [V_A_2,V_f_2,T_b,T_c] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
      | ~ c_Orderings_Oorder__class_Ostrict__mono(T_b,T_c,V_f_2)
      | ~ class_Orderings_Olinorder(T_b)
      | ~ class_Orderings_Oorder(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_strict__mono__imp__inj__on]) ).

fof(f_546_2,plain,
    ! [U_1978,U_1977,U_1976,U_1975] :
      ( c_Fun_Oinj__on(U_1976,U_1975,U_1977,U_1978)
      | ~ c_Orderings_Oorder__class_Ostrict__mono(U_1976,U_1975,U_1977)
      | ~ class_Orderings_Olinorder(U_1976)
      | ~ class_Orderings_Oorder(U_1975) ),
    inference(variable_rename,[status(thm)],[f_546_1]) ).

cnf(f_546_3,plain,
    ( c_Fun_Oinj__on(U_1976,U_1975,U_1977,U_1978)
    | ~ c_Orderings_Oorder__class_Ostrict__mono(U_1976,U_1975,U_1977)
    | ~ class_Orderings_Olinorder(U_1976)
    | ~ class_Orderings_Oorder(U_1975) ),
    inference(clausify,[status(thm)],[f_546_2]) ).

fof(f_547_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oinsert__idem]) ).

fof(f_547_2,plain,
    ! [U_1981,U_1980,U_1979] :
      ( c_Big__Operators_Olattice_OInf__fin(U_1979,c_Orderings_Oord__class_Omin(U_1979),hAPP(hAPP(c_Set_Oinsert(U_1979),U_1981),U_1980)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1979),U_1981),c_Big__Operators_Olattice_OInf__fin(U_1979,c_Orderings_Oord__class_Omin(U_1979),U_1980))
      | U_1980 = c_Orderings_Obot__class_Obot(tc_fun(U_1979,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1979),U_1980))
      | ~ class_Orderings_Olinorder(U_1979) ),
    inference(variable_rename,[status(thm)],[f_547_1]) ).

cnf(f_547_3,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_1979,c_Orderings_Oord__class_Omin(U_1979),hAPP(hAPP(c_Set_Oinsert(U_1979),U_1981),U_1980)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1979),U_1981),c_Big__Operators_Olattice_OInf__fin(U_1979,c_Orderings_Oord__class_Omin(U_1979),U_1980))
    | U_1980 = c_Orderings_Obot__class_Obot(tc_fun(U_1979,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1979),U_1980))
    | ~ class_Orderings_Olinorder(U_1979) ),
    inference(clausify,[status(thm)],[f_547_2]) ).

fof(f_548_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Osubset__idem]) ).

fof(f_548_2,plain,
    ! [U_1984,U_1983,U_1982] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1982),c_Big__Operators_Olattice_OInf__fin(U_1982,c_Orderings_Oord__class_Omin(U_1982),U_1984)),c_Big__Operators_Olattice_OInf__fin(U_1982,c_Orderings_Oord__class_Omin(U_1982),U_1983)) = c_Big__Operators_Olattice_OInf__fin(U_1982,c_Orderings_Oord__class_Omin(U_1982),U_1983)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1982,tc_HOL_Obool)),U_1984),U_1983))
      | U_1984 = c_Orderings_Obot__class_Obot(tc_fun(U_1982,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1982),U_1983))
      | ~ class_Orderings_Olinorder(U_1982) ),
    inference(variable_rename,[status(thm)],[f_548_1]) ).

cnf(f_548_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1982),c_Big__Operators_Olattice_OInf__fin(U_1982,c_Orderings_Oord__class_Omin(U_1982),U_1984)),c_Big__Operators_Olattice_OInf__fin(U_1982,c_Orderings_Oord__class_Omin(U_1982),U_1983)) = c_Big__Operators_Olattice_OInf__fin(U_1982,c_Orderings_Oord__class_Omin(U_1982),U_1983)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1982,tc_HOL_Obool)),U_1984),U_1983))
    | U_1984 = c_Orderings_Obot__class_Obot(tc_fun(U_1982,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1982),U_1983))
    | ~ class_Orderings_Olinorder(U_1982) ),
    inference(clausify,[status(thm)],[f_548_2]) ).

fof(f_549_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Ounion__idem]) ).

fof(f_549_2,plain,
    ! [U_1987,U_1986,U_1985] :
      ( c_Big__Operators_Olattice_OInf__fin(U_1985,c_Orderings_Oord__class_Omin(U_1985),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1985,tc_HOL_Obool)),U_1986),U_1987)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1985),c_Big__Operators_Olattice_OInf__fin(U_1985,c_Orderings_Oord__class_Omin(U_1985),U_1986)),c_Big__Operators_Olattice_OInf__fin(U_1985,c_Orderings_Oord__class_Omin(U_1985),U_1987))
      | U_1987 = c_Orderings_Obot__class_Obot(tc_fun(U_1985,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1985),U_1987))
      | U_1986 = c_Orderings_Obot__class_Obot(tc_fun(U_1985,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1985),U_1986))
      | ~ class_Orderings_Olinorder(U_1985) ),
    inference(variable_rename,[status(thm)],[f_549_1]) ).

cnf(f_549_3,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_1985,c_Orderings_Oord__class_Omin(U_1985),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1985,tc_HOL_Obool)),U_1986),U_1987)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_1985),c_Big__Operators_Olattice_OInf__fin(U_1985,c_Orderings_Oord__class_Omin(U_1985),U_1986)),c_Big__Operators_Olattice_OInf__fin(U_1985,c_Orderings_Oord__class_Omin(U_1985),U_1987))
    | U_1987 = c_Orderings_Obot__class_Obot(tc_fun(U_1985,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1985),U_1987))
    | U_1986 = c_Orderings_Obot__class_Obot(tc_fun(U_1985,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_1985),U_1986))
    | ~ class_Orderings_Olinorder(U_1985) ),
    inference(clausify,[status(thm)],[f_549_2]) ).

fof(f_550_1,plain,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
      ( ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))) != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
        | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
        | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) )
      & ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
          & c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
          & c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) )
        | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_inj__on__Un]) ).

fof(f_550_2,plain,
    ! [U_1992,U_1991,U_1990,U_1989,U_1988] :
      ( ( c_Fun_Oinj__on(U_1988,U_1989,U_1990,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1988,tc_HOL_Obool)),U_1991),U_1992))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1989,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_1988,U_1989,U_1990),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1988,tc_HOL_Obool)),U_1991),U_1992))),hAPP(c_Set_Oimage(U_1988,U_1989,U_1990),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1988,tc_HOL_Obool)),U_1992),U_1991))) != c_Orderings_Obot__class_Obot(tc_fun(U_1989,tc_HOL_Obool))
        | ~ c_Fun_Oinj__on(U_1988,U_1989,U_1990,U_1992)
        | ~ c_Fun_Oinj__on(U_1988,U_1989,U_1990,U_1991) )
      & ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1989,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_1988,U_1989,U_1990),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1988,tc_HOL_Obool)),U_1991),U_1992))),hAPP(c_Set_Oimage(U_1988,U_1989,U_1990),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1988,tc_HOL_Obool)),U_1992),U_1991))) = c_Orderings_Obot__class_Obot(tc_fun(U_1989,tc_HOL_Obool))
          & c_Fun_Oinj__on(U_1988,U_1989,U_1990,U_1992)
          & c_Fun_Oinj__on(U_1988,U_1989,U_1990,U_1991) )
        | ~ c_Fun_Oinj__on(U_1988,U_1989,U_1990,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1988,tc_HOL_Obool)),U_1991),U_1992)) ) ),
    inference(variable_rename,[status(thm)],[f_550_1]) ).

fof(f_550_3,plain,
    ( ! [U_2002,U_2000,U_1998,U_1996,U_1994] :
        ( c_Fun_Oinj__on(U_1994,U_1996,U_1998,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1994,tc_HOL_Obool)),U_2000),U_2002))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1996,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_1994,U_1996,U_1998),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1994,tc_HOL_Obool)),U_2000),U_2002))),hAPP(c_Set_Oimage(U_1994,U_1996,U_1998),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1994,tc_HOL_Obool)),U_2002),U_2000))) != c_Orderings_Obot__class_Obot(tc_fun(U_1996,tc_HOL_Obool))
        | ~ c_Fun_Oinj__on(U_1994,U_1996,U_1998,U_2002)
        | ~ c_Fun_Oinj__on(U_1994,U_1996,U_1998,U_2000) )
    & ! [U_2001,U_1999,U_1997,U_1995,U_1993] :
        ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1995,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_1993,U_1995,U_1997),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1993,tc_HOL_Obool)),U_1999),U_2001))),hAPP(c_Set_Oimage(U_1993,U_1995,U_1997),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1993,tc_HOL_Obool)),U_2001),U_1999))) = c_Orderings_Obot__class_Obot(tc_fun(U_1995,tc_HOL_Obool))
          & c_Fun_Oinj__on(U_1993,U_1995,U_1997,U_2001)
          & c_Fun_Oinj__on(U_1993,U_1995,U_1997,U_1999) )
        | ~ c_Fun_Oinj__on(U_1993,U_1995,U_1997,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1993,tc_HOL_Obool)),U_1999),U_2001)) ) ),
    inference(miniscope,[status(thm)],[f_550_2]) ).

cnf(f_550_4,plain,
    ( c_Fun_Oinj__on(U_1993,U_1995,U_1997,U_1999)
    | ~ c_Fun_Oinj__on(U_1993,U_1995,U_1997,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1993,tc_HOL_Obool)),U_1999),U_2001)) ),
    inference(clausify,[status(thm)],[f_550_3]) ).

cnf(f_550_5,plain,
    ( c_Fun_Oinj__on(U_1993,U_1995,U_1997,U_2001)
    | ~ c_Fun_Oinj__on(U_1993,U_1995,U_1997,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1993,tc_HOL_Obool)),U_1999),U_2001)) ),
    inference(clausify,[status(thm)],[f_550_3]) ).

cnf(f_550_6,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1995,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_1993,U_1995,U_1997),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1993,tc_HOL_Obool)),U_1999),U_2001))),hAPP(c_Set_Oimage(U_1993,U_1995,U_1997),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1993,tc_HOL_Obool)),U_2001),U_1999))) = c_Orderings_Obot__class_Obot(tc_fun(U_1995,tc_HOL_Obool))
    | ~ c_Fun_Oinj__on(U_1993,U_1995,U_1997,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1993,tc_HOL_Obool)),U_1999),U_2001)) ),
    inference(clausify,[status(thm)],[f_550_3]) ).

cnf(f_550_7,plain,
    ( c_Fun_Oinj__on(U_1994,U_1996,U_1998,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_1994,tc_HOL_Obool)),U_2000),U_2002))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_1996,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_1994,U_1996,U_1998),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1994,tc_HOL_Obool)),U_2000),U_2002))),hAPP(c_Set_Oimage(U_1994,U_1996,U_1998),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_1994,tc_HOL_Obool)),U_2002),U_2000))) != c_Orderings_Obot__class_Obot(tc_fun(U_1996,tc_HOL_Obool))
    | ~ c_Fun_Oinj__on(U_1994,U_1996,U_1998,U_2002)
    | ~ c_Fun_Oinj__on(U_1994,U_1996,U_1998,U_2000) ),
    inference(clausify,[status(thm)],[f_550_3]) ).

fof(f_551_1,plain,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
      ( ( ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)
          | V_A_2 != V_B_2 )
        & ( V_A_2 = V_B_2
          | hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) != hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2) ) )
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_inj__image__eq__iff]) ).

fof(f_551_2,plain,
    ! [U_2007,U_2006,U_2005,U_2004,U_2003] :
      ( ( ( hAPP(c_Set_Oimage(U_2003,U_2004,U_2005),U_2006) = hAPP(c_Set_Oimage(U_2003,U_2004,U_2005),U_2007)
          | U_2006 != U_2007 )
        & ( U_2006 = U_2007
          | hAPP(c_Set_Oimage(U_2003,U_2004,U_2005),U_2006) != hAPP(c_Set_Oimage(U_2003,U_2004,U_2005),U_2007) ) )
      | ~ c_Fun_Oinj__on(U_2003,U_2004,U_2005,c_Orderings_Otop__class_Otop(tc_fun(U_2003,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_551_1]) ).

cnf(f_551_3,plain,
    ( U_2006 = U_2007
    | hAPP(c_Set_Oimage(U_2003,U_2004,U_2005),U_2006) != hAPP(c_Set_Oimage(U_2003,U_2004,U_2005),U_2007)
    | ~ c_Fun_Oinj__on(U_2003,U_2004,U_2005,c_Orderings_Otop__class_Otop(tc_fun(U_2003,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_551_2]) ).

cnf(f_551_4,plain,
    ( hAPP(c_Set_Oimage(U_2003,U_2004,U_2005),U_2006) = hAPP(c_Set_Oimage(U_2003,U_2004,U_2005),U_2007)
    | U_2006 != U_2007
    | ~ c_Fun_Oinj__on(U_2003,U_2004,U_2005,c_Orderings_Otop__class_Otop(tc_fun(U_2003,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_551_2]) ).

fof(f_552_1,plain,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
      ( ( ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)
          | V_A_2 != V_B_2 )
        & ( V_A_2 = V_B_2
          | hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) != hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2) ) )
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_inj__on__Un__image__eq__iff]) ).

fof(f_552_2,plain,
    ! [U_2012,U_2011,U_2010,U_2009,U_2008] :
      ( ( ( hAPP(c_Set_Oimage(U_2008,U_2009,U_2010),U_2011) = hAPP(c_Set_Oimage(U_2008,U_2009,U_2010),U_2012)
          | U_2011 != U_2012 )
        & ( U_2011 = U_2012
          | hAPP(c_Set_Oimage(U_2008,U_2009,U_2010),U_2011) != hAPP(c_Set_Oimage(U_2008,U_2009,U_2010),U_2012) ) )
      | ~ c_Fun_Oinj__on(U_2008,U_2009,U_2010,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2008,tc_HOL_Obool)),U_2011),U_2012)) ),
    inference(variable_rename,[status(thm)],[f_552_1]) ).

cnf(f_552_3,plain,
    ( U_2011 = U_2012
    | hAPP(c_Set_Oimage(U_2008,U_2009,U_2010),U_2011) != hAPP(c_Set_Oimage(U_2008,U_2009,U_2010),U_2012)
    | ~ c_Fun_Oinj__on(U_2008,U_2009,U_2010,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2008,tc_HOL_Obool)),U_2011),U_2012)) ),
    inference(clausify,[status(thm)],[f_552_2]) ).

cnf(f_552_4,plain,
    ( hAPP(c_Set_Oimage(U_2008,U_2009,U_2010),U_2011) = hAPP(c_Set_Oimage(U_2008,U_2009,U_2010),U_2012)
    | U_2011 != U_2012
    | ~ c_Fun_Oinj__on(U_2008,U_2009,U_2010,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2008,tc_HOL_Obool)),U_2011),U_2012)) ),
    inference(clausify,[status(thm)],[f_552_2]) ).

fof(f_553_1,plain,
    ! [V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y))
      | ~ class_Lattices_Oboolean__algebra(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_diff__eq]) ).

fof(f_553_2,plain,
    ! [U_2015,U_2014,U_2013] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2013),U_2014),U_2015) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2013),U_2014),hAPP(c_Groups_Ouminus__class_Ouminus(U_2013),U_2015))
      | ~ class_Lattices_Oboolean__algebra(U_2013) ),
    inference(variable_rename,[status(thm)],[f_553_1]) ).

cnf(f_553_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2013),U_2014),U_2015) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2013),U_2014),hAPP(c_Groups_Ouminus__class_Ouminus(U_2013),U_2015))
    | ~ class_Lattices_Oboolean__algebra(U_2013) ),
    inference(clausify,[status(thm)],[f_553_2]) ).

fof(f_554_1,plain,
    ! [V_B_2,V_a_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_Diff__insert]) ).

fof(f_554_2,plain,
    ! [U_2019,U_2018,U_2017,U_2016] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2016,tc_HOL_Obool)),U_2017),hAPP(hAPP(c_Set_Oinsert(U_2016),U_2018),U_2019)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2016,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2016,tc_HOL_Obool)),U_2017),U_2019)),hAPP(hAPP(c_Set_Oinsert(U_2016),U_2018),c_Orderings_Obot__class_Obot(tc_fun(U_2016,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_554_1]) ).

cnf(f_554_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2016,tc_HOL_Obool)),U_2017),hAPP(hAPP(c_Set_Oinsert(U_2016),U_2018),U_2019)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2016,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2016,tc_HOL_Obool)),U_2017),U_2019)),hAPP(hAPP(c_Set_Oinsert(U_2016),U_2018),c_Orderings_Obot__class_Obot(tc_fun(U_2016,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_554_2]) ).

fof(f_555_1,plain,
    ! [V_B_2,V_a_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_B_2),
    inference(fof_nnf,[status(thm)],[fact_Diff__insert2]) ).

fof(f_555_2,plain,
    ! [U_2023,U_2022,U_2021,U_2020] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2020,tc_HOL_Obool)),U_2021),hAPP(hAPP(c_Set_Oinsert(U_2020),U_2022),U_2023)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2020,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2020,tc_HOL_Obool)),U_2021),hAPP(hAPP(c_Set_Oinsert(U_2020),U_2022),c_Orderings_Obot__class_Obot(tc_fun(U_2020,tc_HOL_Obool))))),U_2023),
    inference(variable_rename,[status(thm)],[f_555_1]) ).

cnf(f_555_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2020,tc_HOL_Obool)),U_2021),hAPP(hAPP(c_Set_Oinsert(U_2020),U_2022),U_2023)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2020,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2020,tc_HOL_Obool)),U_2021),hAPP(hAPP(c_Set_Oinsert(U_2020),U_2022),c_Orderings_Obot__class_Obot(tc_fun(U_2020,tc_HOL_Obool))))),U_2023),
    inference(clausify,[status(thm)],[f_555_2]) ).

fof(f_556_1,plain,
    ! [V_A_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2),
    inference(fof_nnf,[status(thm)],[fact_insert__Diff__single]) ).

fof(f_556_2,plain,
    ! [U_2026,U_2025,U_2024] : hAPP(hAPP(c_Set_Oinsert(U_2024),U_2025),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2024,tc_HOL_Obool)),U_2026),hAPP(hAPP(c_Set_Oinsert(U_2024),U_2025),c_Orderings_Obot__class_Obot(tc_fun(U_2024,tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(U_2024),U_2025),U_2026),
    inference(variable_rename,[status(thm)],[f_556_1]) ).

cnf(f_556_3,plain,
    hAPP(hAPP(c_Set_Oinsert(U_2024),U_2025),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2024,tc_HOL_Obool)),U_2026),hAPP(hAPP(c_Set_Oinsert(U_2024),U_2025),c_Orderings_Obot__class_Obot(tc_fun(U_2024,tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(U_2024),U_2025),U_2026),
    inference(clausify,[status(thm)],[f_556_2]) ).

fof(f_557_1,plain,
    ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) ),
    inference(fof_nnf,[status(thm)],[fact_inj__on__strict__subset]) ).

fof(f_557_2,plain,
    ! [U_2031,U_2030,U_2029,U_2028,U_2027] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2028,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2027,U_2028,U_2029),U_2031)),hAPP(c_Set_Oimage(U_2027,U_2028,U_2029),U_2030)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2027,tc_HOL_Obool)),U_2031),U_2030))
      | ~ c_Fun_Oinj__on(U_2027,U_2028,U_2029,U_2030) ),
    inference(variable_rename,[status(thm)],[f_557_1]) ).

cnf(f_557_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2028,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2027,U_2028,U_2029),U_2031)),hAPP(c_Set_Oimage(U_2027,U_2028,U_2029),U_2030)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2027,tc_HOL_Obool)),U_2031),U_2030))
    | ~ c_Fun_Oinj__on(U_2027,U_2028,U_2029,U_2030) ),
    inference(clausify,[status(thm)],[f_557_2]) ).

fof(f_558_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( ( ( c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oinsert__remove]) ).

fof(f_558_2,plain,
    ! [U_2034,U_2033,U_2032] :
      ( ( ( c_Big__Operators_Olattice_OSup__fin(U_2032,c_Orderings_Oord__class_Omax(U_2032),hAPP(hAPP(c_Set_Oinsert(U_2032),U_2034),U_2033)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2032),U_2034),c_Big__Operators_Olattice_OSup__fin(U_2032,c_Orderings_Oord__class_Omax(U_2032),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2032,tc_HOL_Obool)),U_2033),hAPP(hAPP(c_Set_Oinsert(U_2032),U_2034),c_Orderings_Obot__class_Obot(tc_fun(U_2032,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2032,tc_HOL_Obool)),U_2033),hAPP(hAPP(c_Set_Oinsert(U_2032),U_2034),c_Orderings_Obot__class_Obot(tc_fun(U_2032,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_2032,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olattice_OSup__fin(U_2032,c_Orderings_Oord__class_Omax(U_2032),hAPP(hAPP(c_Set_Oinsert(U_2032),U_2034),U_2033)) = U_2034
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2032,tc_HOL_Obool)),U_2033),hAPP(hAPP(c_Set_Oinsert(U_2032),U_2034),c_Orderings_Obot__class_Obot(tc_fun(U_2032,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_2032,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2032),U_2033))
      | ~ class_Orderings_Olinorder(U_2032) ),
    inference(variable_rename,[status(thm)],[f_558_1]) ).

cnf(f_558_3,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_2032,c_Orderings_Oord__class_Omax(U_2032),hAPP(hAPP(c_Set_Oinsert(U_2032),U_2034),U_2033)) = U_2034
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2032,tc_HOL_Obool)),U_2033),hAPP(hAPP(c_Set_Oinsert(U_2032),U_2034),c_Orderings_Obot__class_Obot(tc_fun(U_2032,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_2032,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2032),U_2033))
    | ~ class_Orderings_Olinorder(U_2032) ),
    inference(clausify,[status(thm)],[f_558_2]) ).

cnf(f_558_4,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_2032,c_Orderings_Oord__class_Omax(U_2032),hAPP(hAPP(c_Set_Oinsert(U_2032),U_2034),U_2033)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2032),U_2034),c_Big__Operators_Olattice_OSup__fin(U_2032,c_Orderings_Oord__class_Omax(U_2032),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2032,tc_HOL_Obool)),U_2033),hAPP(hAPP(c_Set_Oinsert(U_2032),U_2034),c_Orderings_Obot__class_Obot(tc_fun(U_2032,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2032,tc_HOL_Obool)),U_2033),hAPP(hAPP(c_Set_Oinsert(U_2032),U_2034),c_Orderings_Obot__class_Obot(tc_fun(U_2032,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_2032,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2032),U_2033))
    | ~ class_Orderings_Olinorder(U_2032) ),
    inference(clausify,[status(thm)],[f_558_2]) ).

fof(f_559_1,plain,
    ! [V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Diff__UNIV]) ).

fof(f_559_2,plain,
    ! [U_2036,U_2035] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2035,tc_HOL_Obool)),U_2036),c_Orderings_Otop__class_Otop(tc_fun(U_2035,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_2035,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_559_1]) ).

cnf(f_559_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2035,tc_HOL_Obool)),U_2036),c_Orderings_Otop__class_Otop(tc_fun(U_2035,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_2035,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_559_2]) ).

fof(f_560_1,plain,
    ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Diff__disjoint]) ).

fof(f_560_2,plain,
    ! [U_2039,U_2038,U_2037] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2037,tc_HOL_Obool)),U_2038),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2037,tc_HOL_Obool)),U_2039),U_2038)) = c_Orderings_Obot__class_Obot(tc_fun(U_2037,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_560_1]) ).

cnf(f_560_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2037,tc_HOL_Obool)),U_2038),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2037,tc_HOL_Obool)),U_2039),U_2038)) = c_Orderings_Obot__class_Obot(tc_fun(U_2037,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_560_2]) ).

fof(f_561_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
    inference(fof_nnf,[status(thm)],[fact_Diff__triv]) ).

fof(f_561_2,plain,
    ! [U_2042,U_2041,U_2040] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2040,tc_HOL_Obool)),U_2041),U_2042) = U_2041
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2040,tc_HOL_Obool)),U_2041),U_2042) != c_Orderings_Obot__class_Obot(tc_fun(U_2040,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_561_1]) ).

cnf(f_561_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2040,tc_HOL_Obool)),U_2041),U_2042) = U_2041
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2040,tc_HOL_Obool)),U_2041),U_2042) != c_Orderings_Obot__class_Obot(tc_fun(U_2040,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_561_2]) ).

fof(f_562_1,plain,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_B_2))),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))),
    inference(fof_nnf,[status(thm)],[fact_image__diff__subset]) ).

fof(f_562_2,plain,
    ! [U_2047,U_2046,U_2045,U_2044,U_2043] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2043,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2043,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2044,U_2043,U_2045),U_2046)),hAPP(c_Set_Oimage(U_2044,U_2043,U_2045),U_2047))),hAPP(c_Set_Oimage(U_2044,U_2043,U_2045),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2044,tc_HOL_Obool)),U_2046),U_2047)))),
    inference(variable_rename,[status(thm)],[f_562_1]) ).

cnf(f_562_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2043,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2043,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2044,U_2043,U_2045),U_2046)),hAPP(c_Set_Oimage(U_2044,U_2043,U_2045),U_2047))),hAPP(c_Set_Oimage(U_2044,U_2043,U_2045),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2044,tc_HOL_Obool)),U_2046),U_2047)))),
    inference(clausify,[status(thm)],[f_562_2]) ).

fof(f_563_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) = V_B_2
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Diff__partition]) ).

fof(f_563_2,plain,
    ! [U_2050,U_2049,U_2048] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2048,tc_HOL_Obool)),U_2049),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2048,tc_HOL_Obool)),U_2050),U_2049)) = U_2050
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2048,tc_HOL_Obool)),U_2049),U_2050)) ),
    inference(variable_rename,[status(thm)],[f_563_1]) ).

cnf(f_563_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2048,tc_HOL_Obool)),U_2049),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2048,tc_HOL_Obool)),U_2050),U_2049)) = U_2050
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2048,tc_HOL_Obool)),U_2049),U_2050)) ),
    inference(clausify,[status(thm)],[f_563_2]) ).

fof(f_564_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Diff__subset__conv]) ).

fof(f_564_2,plain,
    ! [U_2054,U_2053,U_2052,U_2051] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2051,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2051,tc_HOL_Obool)),U_2052),U_2053)),U_2054))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2051,tc_HOL_Obool)),U_2052),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2051,tc_HOL_Obool)),U_2053),U_2054))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2051,tc_HOL_Obool)),U_2052),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2051,tc_HOL_Obool)),U_2053),U_2054)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2051,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2051,tc_HOL_Obool)),U_2052),U_2053)),U_2054)) ) ),
    inference(variable_rename,[status(thm)],[f_564_1]) ).

fof(f_564_3,plain,
    ( ! [U_2062,U_2060,U_2058,U_2056] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2056,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2056,tc_HOL_Obool)),U_2058),U_2060)),U_2062))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2056,tc_HOL_Obool)),U_2058),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2056,tc_HOL_Obool)),U_2060),U_2062))) )
    & ! [U_2061,U_2059,U_2057,U_2055] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2055,tc_HOL_Obool)),U_2057),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2055,tc_HOL_Obool)),U_2059),U_2061)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2055,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2055,tc_HOL_Obool)),U_2057),U_2059)),U_2061)) ) ),
    inference(miniscope,[status(thm)],[f_564_2]) ).

cnf(f_564_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2055,tc_HOL_Obool)),U_2057),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2055,tc_HOL_Obool)),U_2059),U_2061)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2055,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2055,tc_HOL_Obool)),U_2057),U_2059)),U_2061)) ),
    inference(clausify,[status(thm)],[f_564_3]) ).

cnf(f_564_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2056,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2056,tc_HOL_Obool)),U_2058),U_2060)),U_2062))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2056,tc_HOL_Obool)),U_2058),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2056,tc_HOL_Obool)),U_2060),U_2062))) ),
    inference(clausify,[status(thm)],[f_564_3]) ).

fof(f_565_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),
    inference(fof_nnf,[status(thm)],[fact_Diff__Int]) ).

fof(f_565_2,plain,
    ! [U_2066,U_2065,U_2064,U_2063] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2063,tc_HOL_Obool)),U_2064),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2063,tc_HOL_Obool)),U_2065),U_2066)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2063,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2063,tc_HOL_Obool)),U_2064),U_2065)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2063,tc_HOL_Obool)),U_2064),U_2066)),
    inference(variable_rename,[status(thm)],[f_565_1]) ).

cnf(f_565_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2063,tc_HOL_Obool)),U_2064),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2063,tc_HOL_Obool)),U_2065),U_2066)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2063,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2063,tc_HOL_Obool)),U_2064),U_2065)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2063,tc_HOL_Obool)),U_2064),U_2066)),
    inference(clausify,[status(thm)],[f_565_2]) ).

fof(f_566_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),
    inference(fof_nnf,[status(thm)],[fact_Diff__Un]) ).

fof(f_566_2,plain,
    ! [U_2070,U_2069,U_2068,U_2067] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2067,tc_HOL_Obool)),U_2068),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2067,tc_HOL_Obool)),U_2069),U_2070)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2067,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2067,tc_HOL_Obool)),U_2068),U_2069)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2067,tc_HOL_Obool)),U_2068),U_2070)),
    inference(variable_rename,[status(thm)],[f_566_1]) ).

cnf(f_566_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2067,tc_HOL_Obool)),U_2068),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2067,tc_HOL_Obool)),U_2069),U_2070)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2067,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2067,tc_HOL_Obool)),U_2068),U_2069)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2067,tc_HOL_Obool)),U_2068),U_2070)),
    inference(clausify,[status(thm)],[f_566_2]) ).

fof(f_567_1,plain,
    ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = V_A_2,
    inference(fof_nnf,[status(thm)],[fact_Un__Diff__Int]) ).

fof(f_567_2,plain,
    ! [U_2073,U_2072,U_2071] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2071,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2071,tc_HOL_Obool)),U_2072),U_2073)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2071,tc_HOL_Obool)),U_2072),U_2073)) = U_2072,
    inference(variable_rename,[status(thm)],[f_567_1]) ).

cnf(f_567_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2071,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2071,tc_HOL_Obool)),U_2072),U_2073)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2071,tc_HOL_Obool)),U_2072),U_2073)) = U_2072,
    inference(clausify,[status(thm)],[f_567_2]) ).

fof(f_568_1,plain,
    ! [V_m_2,V_n_2,V_i_2,T_b] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_i_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_i_2),V_n_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_n_2),V_m_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_n_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_ivl__diff]) ).

fof(f_568_2,plain,
    ! [U_2077,U_2076,U_2075,U_2074] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2074,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2074,U_2075),U_2077)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2074,U_2075),U_2076)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2074,U_2076),U_2077)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2074),U_2075),U_2076))
      | ~ class_Orderings_Olinorder(U_2074) ),
    inference(variable_rename,[status(thm)],[f_568_1]) ).

cnf(f_568_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2074,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2074,U_2075),U_2077)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2074,U_2075),U_2076)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_2074,U_2076),U_2077)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2074),U_2075),U_2076))
    | ~ class_Orderings_Olinorder(U_2074) ),
    inference(clausify,[status(thm)],[f_568_2]) ).

fof(f_569_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Ounion__disjoint]) ).

fof(f_569_2,plain,
    ! [U_2080,U_2079,U_2078] :
      ( c_Big__Operators_Olattice_OInf__fin(U_2078,c_Orderings_Oord__class_Omin(U_2078),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2078,tc_HOL_Obool)),U_2079),U_2080)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2078),c_Big__Operators_Olattice_OInf__fin(U_2078,c_Orderings_Oord__class_Omin(U_2078),U_2079)),c_Big__Operators_Olattice_OInf__fin(U_2078,c_Orderings_Oord__class_Omin(U_2078),U_2080))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2078,tc_HOL_Obool)),U_2079),U_2080) != c_Orderings_Obot__class_Obot(tc_fun(U_2078,tc_HOL_Obool))
      | U_2080 = c_Orderings_Obot__class_Obot(tc_fun(U_2078,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2078),U_2080))
      | U_2079 = c_Orderings_Obot__class_Obot(tc_fun(U_2078,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2078),U_2079))
      | ~ class_Orderings_Olinorder(U_2078) ),
    inference(variable_rename,[status(thm)],[f_569_1]) ).

cnf(f_569_3,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_2078,c_Orderings_Oord__class_Omin(U_2078),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2078,tc_HOL_Obool)),U_2079),U_2080)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2078),c_Big__Operators_Olattice_OInf__fin(U_2078,c_Orderings_Oord__class_Omin(U_2078),U_2079)),c_Big__Operators_Olattice_OInf__fin(U_2078,c_Orderings_Oord__class_Omin(U_2078),U_2080))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2078,tc_HOL_Obool)),U_2079),U_2080) != c_Orderings_Obot__class_Obot(tc_fun(U_2078,tc_HOL_Obool))
    | U_2080 = c_Orderings_Obot__class_Obot(tc_fun(U_2078,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2078),U_2080))
    | U_2079 = c_Orderings_Obot__class_Obot(tc_fun(U_2078,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2078),U_2079))
    | ~ class_Orderings_Olinorder(U_2078) ),
    inference(clausify,[status(thm)],[f_569_2]) ).

fof(f_570_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Ounion__inter]) ).

fof(f_570_2,plain,
    ! [U_2083,U_2082,U_2081] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2081),c_Big__Operators_Olattice_OInf__fin(U_2081,c_Orderings_Oord__class_Omin(U_2081),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2081,tc_HOL_Obool)),U_2082),U_2083))),c_Big__Operators_Olattice_OInf__fin(U_2081,c_Orderings_Oord__class_Omin(U_2081),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2081,tc_HOL_Obool)),U_2082),U_2083))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2081),c_Big__Operators_Olattice_OInf__fin(U_2081,c_Orderings_Oord__class_Omin(U_2081),U_2082)),c_Big__Operators_Olattice_OInf__fin(U_2081,c_Orderings_Oord__class_Omin(U_2081),U_2083))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2081,tc_HOL_Obool)),U_2082),U_2083) = c_Orderings_Obot__class_Obot(tc_fun(U_2081,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2081),U_2083))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2081),U_2082))
      | ~ class_Orderings_Olinorder(U_2081) ),
    inference(variable_rename,[status(thm)],[f_570_1]) ).

cnf(f_570_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2081),c_Big__Operators_Olattice_OInf__fin(U_2081,c_Orderings_Oord__class_Omin(U_2081),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2081,tc_HOL_Obool)),U_2082),U_2083))),c_Big__Operators_Olattice_OInf__fin(U_2081,c_Orderings_Oord__class_Omin(U_2081),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2081,tc_HOL_Obool)),U_2082),U_2083))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2081),c_Big__Operators_Olattice_OInf__fin(U_2081,c_Orderings_Oord__class_Omin(U_2081),U_2082)),c_Big__Operators_Olattice_OInf__fin(U_2081,c_Orderings_Oord__class_Omin(U_2081),U_2083))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2081,tc_HOL_Obool)),U_2082),U_2083) = c_Orderings_Obot__class_Obot(tc_fun(U_2081,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2081),U_2083))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2081),U_2082))
    | ~ class_Orderings_Olinorder(U_2081) ),
    inference(clausify,[status(thm)],[f_570_2]) ).

fof(f_571_1,plain,
    ! [V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_A_2),
    inference(fof_nnf,[status(thm)],[fact_Compl__eq__Diff__UNIV]) ).

fof(f_571_2,plain,
    ! [U_2085,U_2084] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2084,tc_HOL_Obool)),U_2085) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2084,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_2084,tc_HOL_Obool))),U_2085),
    inference(variable_rename,[status(thm)],[f_571_1]) ).

cnf(f_571_3,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2084,tc_HOL_Obool)),U_2085) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2084,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_2084,tc_HOL_Obool))),U_2085),
    inference(clausify,[status(thm)],[f_571_2]) ).

fof(f_572_1,plain,
    ! [V_B_2,V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2),
    inference(fof_nnf,[status(thm)],[fact_Compl__Diff__eq]) ).

fof(f_572_2,plain,
    ! [U_2088,U_2087,U_2086] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2086,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2086,tc_HOL_Obool)),U_2087),U_2088)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2086,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2086,tc_HOL_Obool)),U_2087)),U_2088),
    inference(variable_rename,[status(thm)],[f_572_1]) ).

cnf(f_572_3,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2086,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2086,tc_HOL_Obool)),U_2087),U_2088)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2086,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2086,tc_HOL_Obool)),U_2087)),U_2088),
    inference(clausify,[status(thm)],[f_572_2]) ).

fof(f_573_1,plain,
    ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_Diff__eq]) ).

fof(f_573_2,plain,
    ! [U_2091,U_2090,U_2089] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2089,tc_HOL_Obool)),U_2090),U_2091) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2089,tc_HOL_Obool)),U_2090),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2089,tc_HOL_Obool)),U_2091)),
    inference(variable_rename,[status(thm)],[f_573_1]) ).

cnf(f_573_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2089,tc_HOL_Obool)),U_2090),U_2091) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2089,tc_HOL_Obool)),U_2090),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2089,tc_HOL_Obool)),U_2091)),
    inference(clausify,[status(thm)],[f_573_2]) ).

fof(f_574_1,plain,
    ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),
    inference(fof_nnf,[status(thm)],[fact_Diff__Compl]) ).

fof(f_574_2,plain,
    ! [U_2094,U_2093,U_2092] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2092,tc_HOL_Obool)),U_2093),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2092,tc_HOL_Obool)),U_2094)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2092,tc_HOL_Obool)),U_2093),U_2094),
    inference(variable_rename,[status(thm)],[f_574_1]) ).

cnf(f_574_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2092,tc_HOL_Obool)),U_2093),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2092,tc_HOL_Obool)),U_2094)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2092,tc_HOL_Obool)),U_2093),U_2094),
    inference(clausify,[status(thm)],[f_574_2]) ).

fof(f_575_1,plain,
    ! [V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OInf__le__Sup]) ).

fof(f_575_2,plain,
    ! [U_2096,U_2095] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2095),c_Big__Operators_Olattice_OInf__fin(U_2095,c_Orderings_Oord__class_Omin(U_2095),U_2096)),c_Big__Operators_Olattice_OSup__fin(U_2095,c_Orderings_Oord__class_Omax(U_2095),U_2096)))
      | U_2096 = c_Orderings_Obot__class_Obot(tc_fun(U_2095,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2095),U_2096))
      | ~ class_Orderings_Olinorder(U_2095) ),
    inference(variable_rename,[status(thm)],[f_575_1]) ).

cnf(f_575_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2095),c_Big__Operators_Olattice_OInf__fin(U_2095,c_Orderings_Oord__class_Omin(U_2095),U_2096)),c_Big__Operators_Olattice_OSup__fin(U_2095,c_Orderings_Oord__class_Omax(U_2095),U_2096)))
    | U_2096 = c_Orderings_Obot__class_Obot(tc_fun(U_2095,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2095),U_2096))
    | ~ class_Orderings_Olinorder(U_2095) ),
    inference(clausify,[status(thm)],[f_575_2]) ).

fof(f_576_1,plain,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2))) ) )
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_inj__image__subset__iff]) ).

fof(f_576_2,plain,
    ! [U_2101,U_2100,U_2099,U_2098,U_2097] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2098,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2097,U_2098,U_2099),U_2100)),hAPP(c_Set_Oimage(U_2097,U_2098,U_2099),U_2101)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2097,tc_HOL_Obool)),U_2100),U_2101)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2097,tc_HOL_Obool)),U_2100),U_2101))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2098,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2097,U_2098,U_2099),U_2100)),hAPP(c_Set_Oimage(U_2097,U_2098,U_2099),U_2101))) ) )
      | ~ c_Fun_Oinj__on(U_2097,U_2098,U_2099,c_Orderings_Otop__class_Otop(tc_fun(U_2097,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_576_1]) ).

cnf(f_576_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2097,tc_HOL_Obool)),U_2100),U_2101))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2098,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2097,U_2098,U_2099),U_2100)),hAPP(c_Set_Oimage(U_2097,U_2098,U_2099),U_2101)))
    | ~ c_Fun_Oinj__on(U_2097,U_2098,U_2099,c_Orderings_Otop__class_Otop(tc_fun(U_2097,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_576_2]) ).

cnf(f_576_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2098,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2097,U_2098,U_2099),U_2100)),hAPP(c_Set_Oimage(U_2097,U_2098,U_2099),U_2101)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2097,tc_HOL_Obool)),U_2100),U_2101))
    | ~ c_Fun_Oinj__on(U_2097,U_2098,U_2099,c_Orderings_Otop__class_Otop(tc_fun(U_2097,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_576_2]) ).

fof(f_577_1,plain,
    ! [V_B_2,V_A_2,V_C_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2) ),
    inference(fof_nnf,[status(thm)],[fact_inj__on__image__Int]) ).

fof(f_577_2,plain,
    ! [U_2107,U_2106,U_2105,U_2104,U_2103,U_2102] :
      ( hAPP(c_Set_Oimage(U_2102,U_2103,U_2104),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2102,tc_HOL_Obool)),U_2106),U_2107)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2103,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2102,U_2103,U_2104),U_2106)),hAPP(c_Set_Oimage(U_2102,U_2103,U_2104),U_2107))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2102,tc_HOL_Obool)),U_2107),U_2105))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2102,tc_HOL_Obool)),U_2106),U_2105))
      | ~ c_Fun_Oinj__on(U_2102,U_2103,U_2104,U_2105) ),
    inference(variable_rename,[status(thm)],[f_577_1]) ).

cnf(f_577_3,plain,
    ( hAPP(c_Set_Oimage(U_2102,U_2103,U_2104),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2102,tc_HOL_Obool)),U_2106),U_2107)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2103,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2102,U_2103,U_2104),U_2106)),hAPP(c_Set_Oimage(U_2102,U_2103,U_2104),U_2107))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2102,tc_HOL_Obool)),U_2107),U_2105))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2102,tc_HOL_Obool)),U_2106),U_2105))
    | ~ c_Fun_Oinj__on(U_2102,U_2103,U_2104,U_2105) ),
    inference(clausify,[status(thm)],[f_577_2]) ).

fof(f_578_1,plain,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2))
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_image__Int]) ).

fof(f_578_2,plain,
    ! [U_2112,U_2111,U_2110,U_2109,U_2108] :
      ( hAPP(c_Set_Oimage(U_2108,U_2109,U_2110),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2108,tc_HOL_Obool)),U_2111),U_2112)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2109,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2108,U_2109,U_2110),U_2111)),hAPP(c_Set_Oimage(U_2108,U_2109,U_2110),U_2112))
      | ~ c_Fun_Oinj__on(U_2108,U_2109,U_2110,c_Orderings_Otop__class_Otop(tc_fun(U_2108,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_578_1]) ).

cnf(f_578_3,plain,
    ( hAPP(c_Set_Oimage(U_2108,U_2109,U_2110),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2108,tc_HOL_Obool)),U_2111),U_2112)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2109,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2108,U_2109,U_2110),U_2111)),hAPP(c_Set_Oimage(U_2108,U_2109,U_2110),U_2112))
    | ~ c_Fun_Oinj__on(U_2108,U_2109,U_2110,c_Orderings_Otop__class_Otop(tc_fun(U_2108,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_578_2]) ).

fof(f_579_1,plain,
    ! [V_M_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_M_2)))
      | ! [B_x] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_x))
          | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_M_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_finite__Inter]) ).

fof(f_579_2,plain,
    ! [U_2115,U_2114] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2114),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_2114,tc_HOL_Obool),U_2115)))
      | ! [U_2113] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2114),U_2113))
          | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_2114,tc_HOL_Obool)),U_2113),U_2115)) ) ),
    inference(variable_rename,[status(thm)],[f_579_1]) ).

cnf(f_579_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2114),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_2114,tc_HOL_Obool),U_2115)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2114),U_2113))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_2114,tc_HOL_Obool)),U_2113),U_2115)) ),
    inference(clausify,[status(thm)],[f_579_2]) ).

fof(f_580_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__Diff]) ).

fof(f_580_2,plain,
    ! [U_2118,U_2117,U_2116] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2116),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2116,tc_HOL_Obool)),U_2117),U_2118)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2116),U_2117)) ),
    inference(variable_rename,[status(thm)],[f_580_1]) ).

cnf(f_580_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2116),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2116,tc_HOL_Obool)),U_2117),U_2118)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2116),U_2117)) ),
    inference(clausify,[status(thm)],[f_580_2]) ).

fof(f_581_1,plain,
    ! [V_G_2,V_F_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_G_2)))
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_G_2))
        & ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_finite__Int]) ).

fof(f_581_2,plain,
    ! [U_2121,U_2120,U_2119] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2119),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2119,tc_HOL_Obool)),U_2120),U_2121)))
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2119),U_2121))
        & ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2119),U_2120)) ) ),
    inference(variable_rename,[status(thm)],[f_581_1]) ).

cnf(f_581_3,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2119),U_2120))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_2119),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2119,tc_HOL_Obool)),U_2120),U_2121))) ),
    inference(clausify,[status(thm)],[f_581_2]) ).

cnf(f_581_4,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2119),U_2121))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_2119),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2119,tc_HOL_Obool)),U_2120),U_2121))) ),
    inference(clausify,[status(thm)],[f_581_2]) ).

fof(f_582_1,plain,
    ! [V_h_2,T_c,V_F_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_h_2),V_F_2)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__imageI]) ).

fof(f_582_2,plain,
    ! [U_2125,U_2124,U_2123,U_2122] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2124),hAPP(c_Set_Oimage(U_2122,U_2124,U_2125),U_2123)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2122),U_2123)) ),
    inference(variable_rename,[status(thm)],[f_582_1]) ).

cnf(f_582_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2124),hAPP(c_Set_Oimage(U_2122,U_2124,U_2125),U_2123)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2122),U_2123)) ),
    inference(clausify,[status(thm)],[f_582_2]) ).

fof(f_583_1,plain,
    ! [V_a_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite_OinsertI]) ).

fof(f_583_2,plain,
    ! [U_2128,U_2127,U_2126] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2126),hAPP(hAPP(c_Set_Oinsert(U_2126),U_2128),U_2127)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2126),U_2127)) ),
    inference(variable_rename,[status(thm)],[f_583_1]) ).

cnf(f_583_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2126),hAPP(hAPP(c_Set_Oinsert(U_2126),U_2128),U_2127)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2126),U_2127)) ),
    inference(clausify,[status(thm)],[f_583_2]) ).

fof(f_584_1,plain,
    ! [T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_finite_OemptyI]) ).

fof(f_584_2,plain,
    ! [U_2129] : hBOOL(hAPP(c_Finite__Set_Ofinite(U_2129),c_Orderings_Obot__class_Obot(tc_fun(U_2129,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_584_1]) ).

cnf(f_584_3,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(U_2129),c_Orderings_Obot__class_Obot(tc_fun(U_2129,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_584_2]) ).

fof(f_585_1,plain,
    ! [V_f_2,T_b] :
      ( hAPP(c_Set_Oimage(T_b,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
      | ~ c_Fun_Oinj__on(T_b,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ),
    inference(fof_nnf,[status(thm)],[fact_finite__UNIV__inj__surj]) ).

fof(f_585_2,plain,
    ! [U_2131,U_2130] :
      ( hAPP(c_Set_Oimage(U_2130,U_2130,U_2131),c_Orderings_Otop__class_Otop(tc_fun(U_2130,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_2130,tc_HOL_Obool))
      | ~ c_Fun_Oinj__on(U_2130,U_2130,U_2131,c_Orderings_Otop__class_Otop(tc_fun(U_2130,tc_HOL_Obool)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2130),c_Orderings_Otop__class_Otop(tc_fun(U_2130,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_585_1]) ).

cnf(f_585_3,plain,
    ( hAPP(c_Set_Oimage(U_2130,U_2130,U_2131),c_Orderings_Otop__class_Otop(tc_fun(U_2130,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_2130,tc_HOL_Obool))
    | ~ c_Fun_Oinj__on(U_2130,U_2130,U_2131,c_Orderings_Otop__class_Otop(tc_fun(U_2130,tc_HOL_Obool)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2130),c_Orderings_Otop__class_Otop(tc_fun(U_2130,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_585_2]) ).

fof(f_586_1,plain,
    ! [V_f_2,T_b] :
      ( c_Fun_Oinj__on(T_b,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
      | hAPP(c_Set_Oimage(T_b,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ),
    inference(fof_nnf,[status(thm)],[fact_finite__UNIV__surj__inj]) ).

fof(f_586_2,plain,
    ! [U_2133,U_2132] :
      ( c_Fun_Oinj__on(U_2132,U_2132,U_2133,c_Orderings_Otop__class_Otop(tc_fun(U_2132,tc_HOL_Obool)))
      | hAPP(c_Set_Oimage(U_2132,U_2132,U_2133),c_Orderings_Otop__class_Otop(tc_fun(U_2132,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_2132,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2132),c_Orderings_Otop__class_Otop(tc_fun(U_2132,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_586_1]) ).

cnf(f_586_3,plain,
    ( c_Fun_Oinj__on(U_2132,U_2132,U_2133,c_Orderings_Otop__class_Otop(tc_fun(U_2132,tc_HOL_Obool)))
    | hAPP(c_Set_Oimage(U_2132,U_2132,U_2133),c_Orderings_Otop__class_Otop(tc_fun(U_2132,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_2132,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2132),c_Orderings_Otop__class_Otop(tc_fun(U_2132,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_586_2]) ).

fof(f_587_1,plain,
    ! [V_f_2,V_A_2,T_b] :
      ( hAPP(c_Set_Oimage(T_b,T_b,V_f_2),V_A_2) = V_A_2
      | ~ c_Fun_Oinj__on(T_b,T_b,V_f_2,V_A_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_b,V_f_2),V_A_2)),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_endo__inj__surj]) ).

fof(f_587_2,plain,
    ! [U_2136,U_2135,U_2134] :
      ( hAPP(c_Set_Oimage(U_2134,U_2134,U_2136),U_2135) = U_2135
      | ~ c_Fun_Oinj__on(U_2134,U_2134,U_2136,U_2135)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2134,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2134,U_2134,U_2136),U_2135)),U_2135))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2134),U_2135)) ),
    inference(variable_rename,[status(thm)],[f_587_1]) ).

cnf(f_587_3,plain,
    ( hAPP(c_Set_Oimage(U_2134,U_2134,U_2136),U_2135) = U_2135
    | ~ c_Fun_Oinj__on(U_2134,U_2134,U_2136,U_2135)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2134,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2134,U_2134,U_2136),U_2135)),U_2135))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2134),U_2135)) ),
    inference(clausify,[status(thm)],[f_587_2]) ).

fof(f_588_1,plain,
    ! [V_B_2,T_c,V_A_2,T_b] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))
          | ? [B_x] :
              ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x)))
              & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
        & ( ! [B_x] :
              ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x)))
              | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__UN]) ).

fof(f_588_2,plain,
    ! [U_2142,U_2141,U_2140,U_2139] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2141),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2139,tc_fun(U_2141,tc_HOL_Obool)),U_2140),U_2142)))
          | ? [U_2138] :
              ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2141),hAPP(U_2142,U_2138)))
              & hBOOL(hAPP(hAPP(c_member(U_2139),U_2138),U_2140)) ) )
        & ( ! [U_2137] :
              ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2141),hAPP(U_2142,U_2137)))
              | ~ hBOOL(hAPP(hAPP(c_member(U_2139),U_2137),U_2140)) )
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2141),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2139,tc_fun(U_2141,tc_HOL_Obool)),U_2140),U_2142))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2139),U_2140)) ),
    inference(variable_rename,[status(thm)],[f_588_1]) ).

fof(f_588_3,plain,
    ! [U_2142,U_2141,U_2140,U_2139] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2141),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2139,tc_fun(U_2141,tc_HOL_Obool)),U_2140),U_2142)))
          | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2141),hAPP(U_2142,sK22(U_2142,U_2141,U_2140,U_2139))))
            & hBOOL(hAPP(hAPP(c_member(U_2139),sK22(U_2142,U_2141,U_2140,U_2139)),U_2140)) ) )
        & ( ! [U_2137] :
              ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2141),hAPP(U_2142,U_2137)))
              | ~ hBOOL(hAPP(hAPP(c_member(U_2139),U_2137),U_2140)) )
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2141),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2139,tc_fun(U_2141,tc_HOL_Obool)),U_2140),U_2142))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2139),U_2140)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_2138,sK22(U_2142,U_2141,U_2140,U_2139))],[f_588_2]) ).

cnf(f_588_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2141),hAPP(U_2142,U_2137)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2139),U_2137),U_2140))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2141),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2139,tc_fun(U_2141,tc_HOL_Obool)),U_2140),U_2142)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2139),U_2140)) ),
    inference(clausify,[status(thm)],[f_588_3]) ).

cnf(f_588_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2139),sK22(U_2142,U_2141,U_2140,U_2139)),U_2140))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_2141),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2139,tc_fun(U_2141,tc_HOL_Obool)),U_2140),U_2142)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2139),U_2140)) ),
    inference(clausify,[status(thm)],[f_588_3]) ).

cnf(f_588_6,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2141),hAPP(U_2142,sK22(U_2142,U_2141,U_2140,U_2139))))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_2141),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2139,tc_fun(U_2141,tc_HOL_Obool)),U_2140),U_2142)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2139),U_2140)) ),
    inference(clausify,[status(thm)],[f_588_3]) ).

fof(f_589_1,plain,
    ! [V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Finite__Set_Ofinite(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_finite]) ).

fof(f_589_2,plain,
    ! [U_2144,U_2143] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2143),U_2144))
      | ~ class_Finite__Set_Ofinite(U_2143) ),
    inference(variable_rename,[status(thm)],[f_589_1]) ).

cnf(f_589_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2143),U_2144))
    | ~ class_Finite__Set_Ofinite(U_2143) ),
    inference(clausify,[status(thm)],[f_589_2]) ).

fof(f_590_1,plain,
    ! [V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Finite__Set_Ofinite(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_finite__code]) ).

fof(f_590_2,plain,
    ! [U_2146,U_2145] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2145),U_2146))
      | ~ class_Finite__Set_Ofinite(U_2145) ),
    inference(variable_rename,[status(thm)],[f_590_1]) ).

cnf(f_590_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2145),U_2146))
    | ~ class_Finite__Set_Ofinite(U_2145) ),
    inference(clausify,[status(thm)],[f_590_2]) ).

fof(f_591_1,plain,
    ! [T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_finite_Oequations_I1_J]) ).

fof(f_591_2,plain,
    ! [U_2147] : hBOOL(hAPP(c_Finite__Set_Ofinite(U_2147),c_Orderings_Obot__class_Obot(tc_fun(U_2147,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_591_1]) ).

cnf(f_591_3,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(U_2147),c_Orderings_Obot__class_Obot(tc_fun(U_2147,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_591_2]) ).

fof(f_592_1,plain,
    ! [V_A_2,V_a_2,T_b] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_finite__insert]) ).

fof(f_592_2,plain,
    ! [U_2150,U_2149,U_2148] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2148),hAPP(hAPP(c_Set_Oinsert(U_2148),U_2149),U_2150)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2148),U_2150)) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2148),U_2150))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2148),hAPP(hAPP(c_Set_Oinsert(U_2148),U_2149),U_2150))) ) ),
    inference(variable_rename,[status(thm)],[f_592_1]) ).

fof(f_592_3,plain,
    ( ! [U_2156,U_2154,U_2152] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2152),hAPP(hAPP(c_Set_Oinsert(U_2152),U_2154),U_2156)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2152),U_2156)) )
    & ! [U_2155,U_2153,U_2151] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2151),U_2155))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2151),hAPP(hAPP(c_Set_Oinsert(U_2151),U_2153),U_2155))) ) ),
    inference(miniscope,[status(thm)],[f_592_2]) ).

cnf(f_592_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2151),U_2155))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2151),hAPP(hAPP(c_Set_Oinsert(U_2151),U_2153),U_2155))) ),
    inference(clausify,[status(thm)],[f_592_3]) ).

cnf(f_592_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2152),hAPP(hAPP(c_Set_Oinsert(U_2152),U_2154),U_2156)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2152),U_2156)) ),
    inference(clausify,[status(thm)],[f_592_3]) ).

fof(f_593_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__subset]) ).

fof(f_593_2,plain,
    ! [U_2159,U_2158,U_2157] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2157),U_2158))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2157),U_2159))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2157,tc_HOL_Obool)),U_2158),U_2159)) ),
    inference(variable_rename,[status(thm)],[f_593_1]) ).

cnf(f_593_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2157),U_2158))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2157),U_2159))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2157,tc_HOL_Obool)),U_2158),U_2159)) ),
    inference(clausify,[status(thm)],[f_593_2]) ).

fof(f_594_1,plain,
    ! [V_A_2,V_B_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_rev__finite__subset]) ).

fof(f_594_2,plain,
    ! [U_2162,U_2161,U_2160] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2160),U_2162))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2160,tc_HOL_Obool)),U_2162),U_2161))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2160),U_2161)) ),
    inference(variable_rename,[status(thm)],[f_594_1]) ).

cnf(f_594_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2160),U_2162))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2160,tc_HOL_Obool)),U_2162),U_2161))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2160),U_2161)) ),
    inference(clausify,[status(thm)],[f_594_2]) ).

fof(f_595_1,plain,
    ! [T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
      | ~ class_Finite__Set_Ofinite(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_finite__UNIV]) ).

fof(f_595_2,plain,
    ! [U_2163] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2163),c_Orderings_Otop__class_Otop(tc_fun(U_2163,tc_HOL_Obool))))
      | ~ class_Finite__Set_Ofinite(U_2163) ),
    inference(variable_rename,[status(thm)],[f_595_1]) ).

cnf(f_595_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2163),c_Orderings_Otop__class_Otop(tc_fun(U_2163,tc_HOL_Obool))))
    | ~ class_Finite__Set_Ofinite(U_2163) ),
    inference(clausify,[status(thm)],[f_595_2]) ).

fof(f_596_1,plain,
    ! [T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ),
    inference(fof_nnf,[status(thm)],[fact_finite__Prod__UNIV]) ).

fof(f_596_2,plain,
    ! [U_2165,U_2164] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_2164,U_2165)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_2164,U_2165),tc_HOL_Obool))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2165),c_Orderings_Otop__class_Otop(tc_fun(U_2165,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2164),c_Orderings_Otop__class_Otop(tc_fun(U_2164,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_596_1]) ).

cnf(f_596_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_2164,U_2165)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_2164,U_2165),tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2165),c_Orderings_Otop__class_Otop(tc_fun(U_2165,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2164),c_Orderings_Otop__class_Otop(tc_fun(U_2164,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_596_2]) ).

fof(f_597_1,plain,
    ! [T_c,T_b] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(T_b,T_c),tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) )
      & ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(T_b,T_c),tc_HOL_Obool)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_finite__Plus__UNIV__iff]) ).

fof(f_597_2,plain,
    ! [U_2167,U_2166] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_2166,U_2167)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_2166,U_2167),tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2167),c_Orderings_Otop__class_Otop(tc_fun(U_2167,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2166),c_Orderings_Otop__class_Otop(tc_fun(U_2166,tc_HOL_Obool)))) )
      & ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2167),c_Orderings_Otop__class_Otop(tc_fun(U_2167,tc_HOL_Obool))))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_2166),c_Orderings_Otop__class_Otop(tc_fun(U_2166,tc_HOL_Obool)))) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_2166,U_2167)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_2166,U_2167),tc_HOL_Obool)))) ) ),
    inference(variable_rename,[status(thm)],[f_597_1]) ).

fof(f_597_3,plain,
    ( ! [U_2171,U_2169] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_2169,U_2171)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_2169,U_2171),tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2171),c_Orderings_Otop__class_Otop(tc_fun(U_2171,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2169),c_Orderings_Otop__class_Otop(tc_fun(U_2169,tc_HOL_Obool)))) )
    & ! [U_2170,U_2168] :
        ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2170),c_Orderings_Otop__class_Otop(tc_fun(U_2170,tc_HOL_Obool))))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_2168),c_Orderings_Otop__class_Otop(tc_fun(U_2168,tc_HOL_Obool)))) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_2168,U_2170)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_2168,U_2170),tc_HOL_Obool)))) ) ),
    inference(miniscope,[status(thm)],[f_597_2]) ).

cnf(f_597_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2168),c_Orderings_Otop__class_Otop(tc_fun(U_2168,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_2168,U_2170)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_2168,U_2170),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_597_3]) ).

cnf(f_597_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2170),c_Orderings_Otop__class_Otop(tc_fun(U_2170,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_2168,U_2170)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_2168,U_2170),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_597_3]) ).

cnf(f_597_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_2169,U_2171)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_2169,U_2171),tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2171),c_Orderings_Otop__class_Otop(tc_fun(U_2171,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2169),c_Orderings_Otop__class_Otop(tc_fun(U_2169,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_597_3]) ).

fof(f_598_1,plain,
    ! [T_b] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_b)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(T_b),tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_b)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(T_b),tc_HOL_Obool)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_finite__option__UNIV]) ).

fof(f_598_2,plain,
    ! [U_2172] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_2172)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_2172),tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2172),c_Orderings_Otop__class_Otop(tc_fun(U_2172,tc_HOL_Obool)))) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2172),c_Orderings_Otop__class_Otop(tc_fun(U_2172,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_2172)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_2172),tc_HOL_Obool)))) ) ),
    inference(variable_rename,[status(thm)],[f_598_1]) ).

fof(f_598_3,plain,
    ( ! [U_2174] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_2174)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_2174),tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2174),c_Orderings_Otop__class_Otop(tc_fun(U_2174,tc_HOL_Obool)))) )
    & ! [U_2173] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2173),c_Orderings_Otop__class_Otop(tc_fun(U_2173,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_2173)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_2173),tc_HOL_Obool)))) ) ),
    inference(miniscope,[status(thm)],[f_598_2]) ).

cnf(f_598_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2173),c_Orderings_Otop__class_Otop(tc_fun(U_2173,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_2173)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_2173),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_598_3]) ).

cnf(f_598_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_2174)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_2174),tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2174),c_Orderings_Otop__class_Otop(tc_fun(U_2174,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_598_3]) ).

fof(f_599_1,plain,
    ! [V_G_2,V_F_2,T_b] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_G_2)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_G_2))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) )
      & ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_G_2))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_G_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_finite__Un]) ).

fof(f_599_2,plain,
    ! [U_2177,U_2176,U_2175] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2175),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2175,tc_HOL_Obool)),U_2176),U_2177)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2175),U_2177))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2175),U_2176)) )
      & ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2175),U_2177))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_2175),U_2176)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2175),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2175,tc_HOL_Obool)),U_2176),U_2177))) ) ),
    inference(variable_rename,[status(thm)],[f_599_1]) ).

fof(f_599_3,plain,
    ( ! [U_2183,U_2181,U_2179] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2179),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2179,tc_HOL_Obool)),U_2181),U_2183)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2179),U_2183))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2179),U_2181)) )
    & ! [U_2182,U_2180,U_2178] :
        ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2178),U_2182))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_2178),U_2180)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2178),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2178,tc_HOL_Obool)),U_2180),U_2182))) ) ),
    inference(miniscope,[status(thm)],[f_599_2]) ).

cnf(f_599_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2178),U_2180))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2178),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2178,tc_HOL_Obool)),U_2180),U_2182))) ),
    inference(clausify,[status(thm)],[f_599_3]) ).

cnf(f_599_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2178),U_2182))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2178),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2178,tc_HOL_Obool)),U_2180),U_2182))) ),
    inference(clausify,[status(thm)],[f_599_3]) ).

cnf(f_599_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2179),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2179,tc_HOL_Obool)),U_2181),U_2183)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2179),U_2183))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2179),U_2181)) ),
    inference(clausify,[status(thm)],[f_599_3]) ).

fof(f_600_1,plain,
    ! [V_G_2,V_F_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_G_2)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_G_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__UnI]) ).

fof(f_600_2,plain,
    ! [U_2186,U_2185,U_2184] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2184),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2184,tc_HOL_Obool)),U_2185),U_2186)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2184),U_2186))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2184),U_2185)) ),
    inference(variable_rename,[status(thm)],[f_600_1]) ).

cnf(f_600_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2184),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2184,tc_HOL_Obool)),U_2185),U_2186)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2184),U_2186))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2184),U_2185)) ),
    inference(clausify,[status(thm)],[f_600_2]) ).

fof(f_601_1,plain,
    ! [V_A_2,V_B_2,T_b] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) )
        & ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__Diff2]) ).

fof(f_601_2,plain,
    ! [U_2189,U_2188,U_2187] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2187),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2187,tc_HOL_Obool)),U_2189),U_2188)))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2187),U_2189)) )
        & ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2187),U_2189))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2187),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2187,tc_HOL_Obool)),U_2189),U_2188))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2187),U_2188)) ),
    inference(variable_rename,[status(thm)],[f_601_1]) ).

cnf(f_601_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2187),U_2189))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2187),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2187,tc_HOL_Obool)),U_2189),U_2188)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2187),U_2188)) ),
    inference(clausify,[status(thm)],[f_601_2]) ).

cnf(f_601_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2187),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2187,tc_HOL_Obool)),U_2189),U_2188)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2187),U_2189))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2187),U_2188)) ),
    inference(clausify,[status(thm)],[f_601_2]) ).

fof(f_602_1,plain,
    ! [V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2))) ),
    inference(fof_nnf,[status(thm)],[fact_finite__UnionD]) ).

fof(f_602_2,plain,
    ! [U_2191,U_2190] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_2190,tc_HOL_Obool)),U_2191))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2190),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2190,tc_HOL_Obool),U_2191))) ),
    inference(variable_rename,[status(thm)],[f_602_1]) ).

cnf(f_602_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_2190,tc_HOL_Obool)),U_2191))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2190),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2190,tc_HOL_Obool),U_2191))) ),
    inference(clausify,[status(thm)],[f_602_2]) ).

fof(f_603_1,plain,
    ! [V_A_2,T_b] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_finite__Pow__iff]) ).

fof(f_603_2,plain,
    ! [U_2193,U_2192] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_2192,tc_HOL_Obool)),hAPP(c_Set_OPow(U_2192),U_2193)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2192),U_2193)) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2192),U_2193))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_2192,tc_HOL_Obool)),hAPP(c_Set_OPow(U_2192),U_2193))) ) ),
    inference(variable_rename,[status(thm)],[f_603_1]) ).

fof(f_603_3,plain,
    ( ! [U_2197,U_2195] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_2195,tc_HOL_Obool)),hAPP(c_Set_OPow(U_2195),U_2197)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2195),U_2197)) )
    & ! [U_2196,U_2194] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2194),U_2196))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_2194,tc_HOL_Obool)),hAPP(c_Set_OPow(U_2194),U_2196))) ) ),
    inference(miniscope,[status(thm)],[f_603_2]) ).

cnf(f_603_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2194),U_2196))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_2194,tc_HOL_Obool)),hAPP(c_Set_OPow(U_2194),U_2196))) ),
    inference(clausify,[status(thm)],[f_603_3]) ).

cnf(f_603_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_2195,tc_HOL_Obool)),hAPP(c_Set_OPow(U_2195),U_2197)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2195),U_2197)) ),
    inference(clausify,[status(thm)],[f_603_3]) ).

fof(f_604_1,plain,
    ! [V_f_2,V_B_2,T_c,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__surj]) ).

fof(f_604_2,plain,
    ! [U_2202,U_2201,U_2200,U_2199,U_2198] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2200),U_2201))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2200,tc_HOL_Obool)),U_2201),hAPP(c_Set_Oimage(U_2198,U_2200,U_2202),U_2199)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2198),U_2199)) ),
    inference(variable_rename,[status(thm)],[f_604_1]) ).

cnf(f_604_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2200),U_2201))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2200,tc_HOL_Obool)),U_2201),hAPP(c_Set_Oimage(U_2198,U_2200,U_2202),U_2199)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2198),U_2199)) ),
    inference(clausify,[status(thm)],[f_604_2]) ).

fof(f_605_1,plain,
    ! [V_B_2,V_a_2,V_A_2,T_b] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_finite__Diff__insert]) ).

fof(f_605_2,plain,
    ! [U_2206,U_2205,U_2204,U_2203] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2203),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2203,tc_HOL_Obool)),U_2204),hAPP(hAPP(c_Set_Oinsert(U_2203),U_2205),U_2206))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2203),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2203,tc_HOL_Obool)),U_2204),U_2206))) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2203),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2203,tc_HOL_Obool)),U_2204),U_2206)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2203),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2203,tc_HOL_Obool)),U_2204),hAPP(hAPP(c_Set_Oinsert(U_2203),U_2205),U_2206)))) ) ),
    inference(variable_rename,[status(thm)],[f_605_1]) ).

fof(f_605_3,plain,
    ( ! [U_2214,U_2212,U_2210,U_2208] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2208),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2208,tc_HOL_Obool)),U_2210),hAPP(hAPP(c_Set_Oinsert(U_2208),U_2212),U_2214))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2208),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2208,tc_HOL_Obool)),U_2210),U_2214))) )
    & ! [U_2213,U_2211,U_2209,U_2207] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2207),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2207,tc_HOL_Obool)),U_2209),U_2213)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2207),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2207,tc_HOL_Obool)),U_2209),hAPP(hAPP(c_Set_Oinsert(U_2207),U_2211),U_2213)))) ) ),
    inference(miniscope,[status(thm)],[f_605_2]) ).

cnf(f_605_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2207),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2207,tc_HOL_Obool)),U_2209),U_2213)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2207),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2207,tc_HOL_Obool)),U_2209),hAPP(hAPP(c_Set_Oinsert(U_2207),U_2211),U_2213)))) ),
    inference(clausify,[status(thm)],[f_605_3]) ).

cnf(f_605_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2208),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2208,tc_HOL_Obool)),U_2210),hAPP(hAPP(c_Set_Oinsert(U_2208),U_2212),U_2214))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2208),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2208,tc_HOL_Obool)),U_2210),U_2214))) ),
    inference(clausify,[status(thm)],[f_605_3]) ).

fof(f_606_1,plain,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
      | ~ c_Fun_Oinj__on(T_c,T_b,V_f_2,V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) ),
    inference(fof_nnf,[status(thm)],[fact_finite__imageD]) ).

fof(f_606_2,plain,
    ! [U_2218,U_2217,U_2216,U_2215] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2216),U_2218))
      | ~ c_Fun_Oinj__on(U_2216,U_2215,U_2217,U_2218)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2215),hAPP(c_Set_Oimage(U_2216,U_2215,U_2217),U_2218))) ),
    inference(variable_rename,[status(thm)],[f_606_1]) ).

cnf(f_606_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2216),U_2218))
    | ~ c_Fun_Oinj__on(U_2216,U_2215,U_2217,U_2218)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2215),hAPP(c_Set_Oimage(U_2216,U_2215,U_2217),U_2218))) ),
    inference(clausify,[status(thm)],[f_606_2]) ).

fof(f_607_1,plain,
    ! [V_A_2,T_b] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) )
        & ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__compl]) ).

fof(f_607_2,plain,
    ! [U_2220,U_2219] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2219),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2219,tc_HOL_Obool)),U_2220)))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2219),c_Orderings_Otop__class_Otop(tc_fun(U_2219,tc_HOL_Obool)))) )
        & ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2219),c_Orderings_Otop__class_Otop(tc_fun(U_2219,tc_HOL_Obool))))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2219),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2219,tc_HOL_Obool)),U_2220))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2219),U_2220)) ),
    inference(variable_rename,[status(thm)],[f_607_1]) ).

cnf(f_607_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2219),c_Orderings_Otop__class_Otop(tc_fun(U_2219,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2219),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2219,tc_HOL_Obool)),U_2220)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2219),U_2220)) ),
    inference(clausify,[status(thm)],[f_607_2]) ).

cnf(f_607_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2219),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2219,tc_HOL_Obool)),U_2220)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2219),c_Orderings_Otop__class_Otop(tc_fun(U_2219,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2219),U_2220)) ),
    inference(clausify,[status(thm)],[f_607_2]) ).

fof(f_608_1,plain,
    ! [T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,T_c),tc_HOL_Obool)))) ),
    inference(fof_nnf,[status(thm)],[fact_finite__fun__UNIVD2]) ).

fof(f_608_2,plain,
    ! [U_2222,U_2221] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2222),c_Orderings_Otop__class_Otop(tc_fun(U_2222,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_2221,U_2222)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_2221,U_2222),tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_608_1]) ).

fof(f_608_3,plain,
    ! [U_2222] :
      ( ! [U_2221] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_2221,U_2222)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_2221,U_2222),tc_HOL_Obool))))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_2222),c_Orderings_Otop__class_Otop(tc_fun(U_2222,tc_HOL_Obool)))) ),
    inference(miniscope,[status(thm)],[f_608_2]) ).

cnf(f_608_4,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_2221,U_2222)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_2221,U_2222),tc_HOL_Obool))))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_2222),c_Orderings_Otop__class_Otop(tc_fun(U_2222,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_608_3]) ).

fof(f_609_1,plain,
    ! [V_f_2,V_A_2,T_b] :
      ( c_Fun_Oinj__on(T_b,T_b,V_f_2,V_A_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_Oimage(T_b,T_b,V_f_2),V_A_2)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__surj__inj]) ).

fof(f_609_2,plain,
    ! [U_2225,U_2224,U_2223] :
      ( c_Fun_Oinj__on(U_2223,U_2223,U_2225,U_2224)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2223,tc_HOL_Obool)),U_2224),hAPP(c_Set_Oimage(U_2223,U_2223,U_2225),U_2224)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2223),U_2224)) ),
    inference(variable_rename,[status(thm)],[f_609_1]) ).

cnf(f_609_3,plain,
    ( c_Fun_Oinj__on(U_2223,U_2223,U_2225,U_2224)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2223,tc_HOL_Obool)),U_2224),hAPP(c_Set_Oimage(U_2223,U_2223,U_2225),U_2224)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2223),U_2224)) ),
    inference(clausify,[status(thm)],[f_609_2]) ).

fof(f_610_1,plain,
    ! [V_A_H_2,T_c,T_b,V_A_2] :
      ( ( ( ? [B_f] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,B_f),V_A_2)),V_A_H_2))
              & c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2) )
          | ! [B_g] : hAPP(c_Set_Oimage(T_c,T_b,B_g),V_A_H_2) != V_A_2 )
        & ( ? [B_g] : hAPP(c_Set_Oimage(T_c,T_b,B_g),V_A_H_2) = V_A_2
          | ! [B_f] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,B_f),V_A_2)),V_A_H_2))
              | ~ c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2) ) ) )
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
    inference(fof_nnf,[status(thm)],[fact_inj__on__iff__surj]) ).

fof(f_610_2,plain,
    ! [U_2233,U_2232,U_2231,U_2230] :
      ( ( ( ? [U_2229] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2232,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2231,U_2232,U_2229),U_2230)),U_2233))
              & c_Fun_Oinj__on(U_2231,U_2232,U_2229,U_2230) )
          | ! [U_2228] : hAPP(c_Set_Oimage(U_2232,U_2231,U_2228),U_2233) != U_2230 )
        & ( ? [U_2227] : hAPP(c_Set_Oimage(U_2232,U_2231,U_2227),U_2233) = U_2230
          | ! [U_2226] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2232,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2231,U_2232,U_2226),U_2230)),U_2233))
              | ~ c_Fun_Oinj__on(U_2231,U_2232,U_2226,U_2230) ) ) )
      | U_2230 = c_Orderings_Obot__class_Obot(tc_fun(U_2231,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_610_1]) ).

fof(f_610_3,plain,
    ! [U_2233,U_2232,U_2231,U_2230] :
      ( ( ( ? [U_2229] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2232,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2231,U_2232,U_2229),U_2230)),U_2233))
              & c_Fun_Oinj__on(U_2231,U_2232,U_2229,U_2230) )
          | ! [U_2228] : hAPP(c_Set_Oimage(U_2232,U_2231,U_2228),U_2233) != U_2230 )
        & ( hAPP(c_Set_Oimage(U_2232,U_2231,sK23(U_2233,U_2232,U_2231,U_2230)),U_2233) = U_2230
          | ! [U_2226] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2232,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2231,U_2232,U_2226),U_2230)),U_2233))
              | ~ c_Fun_Oinj__on(U_2231,U_2232,U_2226,U_2230) ) ) )
      | U_2230 = c_Orderings_Obot__class_Obot(tc_fun(U_2231,tc_HOL_Obool)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(U_2227,sK23(U_2233,U_2232,U_2231,U_2230))],[f_610_2]) ).

fof(f_610_4,plain,
    ! [U_2233,U_2232,U_2231,U_2230] :
      ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2232,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2231,U_2232,sK24(U_2233,U_2232,U_2231,U_2230)),U_2230)),U_2233))
            & c_Fun_Oinj__on(U_2231,U_2232,sK24(U_2233,U_2232,U_2231,U_2230),U_2230) )
          | ! [U_2228] : hAPP(c_Set_Oimage(U_2232,U_2231,U_2228),U_2233) != U_2230 )
        & ( hAPP(c_Set_Oimage(U_2232,U_2231,sK23(U_2233,U_2232,U_2231,U_2230)),U_2233) = U_2230
          | ! [U_2226] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2232,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2231,U_2232,U_2226),U_2230)),U_2233))
              | ~ c_Fun_Oinj__on(U_2231,U_2232,U_2226,U_2230) ) ) )
      | U_2230 = c_Orderings_Obot__class_Obot(tc_fun(U_2231,tc_HOL_Obool)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(U_2229,sK24(U_2233,U_2232,U_2231,U_2230))],[f_610_3]) ).

cnf(f_610_5,plain,
    ( hAPP(c_Set_Oimage(U_2232,U_2231,sK23(U_2233,U_2232,U_2231,U_2230)),U_2233) = U_2230
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2232,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2231,U_2232,U_2226),U_2230)),U_2233))
    | ~ c_Fun_Oinj__on(U_2231,U_2232,U_2226,U_2230)
    | U_2230 = c_Orderings_Obot__class_Obot(tc_fun(U_2231,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_610_4]) ).

cnf(f_610_6,plain,
    ( c_Fun_Oinj__on(U_2231,U_2232,sK24(U_2233,U_2232,U_2231,U_2230),U_2230)
    | hAPP(c_Set_Oimage(U_2232,U_2231,U_2228),U_2233) != U_2230
    | U_2230 = c_Orderings_Obot__class_Obot(tc_fun(U_2231,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_610_4]) ).

cnf(f_610_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2232,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_2231,U_2232,sK24(U_2233,U_2232,U_2231,U_2230)),U_2230)),U_2233))
    | hAPP(c_Set_Oimage(U_2232,U_2231,U_2228),U_2233) != U_2230
    | U_2230 = c_Orderings_Obot__class_Obot(tc_fun(U_2231,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_610_4]) ).

fof(f_611_1,plain,
    ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
      ( hAPP(hAPP(V_f_2,hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__one_Ounion__inter]) ).

fof(f_611_2,plain,
    ! [U_2238,U_2237,U_2236,U_2235,U_2234] :
      ( hAPP(hAPP(U_2235,hAPP(U_2236,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2234,tc_HOL_Obool)),U_2237),U_2238))),hAPP(U_2236,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2234,tc_HOL_Obool)),U_2237),U_2238))) = hAPP(hAPP(U_2235,hAPP(U_2236,U_2237)),hAPP(U_2236,U_2238))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2234,tc_HOL_Obool)),U_2237),U_2238) = c_Orderings_Obot__class_Obot(tc_fun(U_2234,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2234),U_2238))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2234),U_2237))
      | ~ c_Finite__Set_Ofolding__one(U_2234,U_2235,U_2236) ),
    inference(variable_rename,[status(thm)],[f_611_1]) ).

cnf(f_611_3,plain,
    ( hAPP(hAPP(U_2235,hAPP(U_2236,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2234,tc_HOL_Obool)),U_2237),U_2238))),hAPP(U_2236,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2234,tc_HOL_Obool)),U_2237),U_2238))) = hAPP(hAPP(U_2235,hAPP(U_2236,U_2237)),hAPP(U_2236,U_2238))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2234,tc_HOL_Obool)),U_2237),U_2238) = c_Orderings_Obot__class_Obot(tc_fun(U_2234,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2234),U_2238))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2234),U_2237))
    | ~ c_Finite__Set_Ofolding__one(U_2234,U_2235,U_2236) ),
    inference(clausify,[status(thm)],[f_611_2]) ).

fof(f_612_1,plain,
    ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
      ( hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__one_Ounion__disjoint]) ).

fof(f_612_2,plain,
    ! [U_2243,U_2242,U_2241,U_2240,U_2239] :
      ( hAPP(U_2241,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2239,tc_HOL_Obool)),U_2242),U_2243)) = hAPP(hAPP(U_2240,hAPP(U_2241,U_2242)),hAPP(U_2241,U_2243))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2239,tc_HOL_Obool)),U_2242),U_2243) != c_Orderings_Obot__class_Obot(tc_fun(U_2239,tc_HOL_Obool))
      | U_2243 = c_Orderings_Obot__class_Obot(tc_fun(U_2239,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2239),U_2243))
      | U_2242 = c_Orderings_Obot__class_Obot(tc_fun(U_2239,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2239),U_2242))
      | ~ c_Finite__Set_Ofolding__one(U_2239,U_2240,U_2241) ),
    inference(variable_rename,[status(thm)],[f_612_1]) ).

cnf(f_612_3,plain,
    ( hAPP(U_2241,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2239,tc_HOL_Obool)),U_2242),U_2243)) = hAPP(hAPP(U_2240,hAPP(U_2241,U_2242)),hAPP(U_2241,U_2243))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2239,tc_HOL_Obool)),U_2242),U_2243) != c_Orderings_Obot__class_Obot(tc_fun(U_2239,tc_HOL_Obool))
    | U_2243 = c_Orderings_Obot__class_Obot(tc_fun(U_2239,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2239),U_2243))
    | U_2242 = c_Orderings_Obot__class_Obot(tc_fun(U_2239,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2239),U_2242))
    | ~ c_Finite__Set_Ofolding__one(U_2239,U_2240,U_2241) ),
    inference(clausify,[status(thm)],[f_612_2]) ).

fof(f_613_1,plain,
    ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
      ( hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
      | ~ c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Ounion__disjoint]) ).

fof(f_613_2,plain,
    ! [U_2251,U_2250,U_2249,U_2248,U_2247,U_2246,U_2245,U_2244] :
      ( hAPP(U_2249,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2245,tc_HOL_Obool)),U_2250),U_2251)) = hAPP(hAPP(U_2246,hAPP(U_2249,U_2250)),hAPP(U_2249,U_2251))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2245,tc_HOL_Obool)),U_2250),U_2251) != c_Orderings_Obot__class_Obot(tc_fun(U_2245,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2245),U_2251))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2245),U_2250))
      | ~ c_Finite__Set_Ofolding__image__simple(U_2244,U_2245,U_2246,U_2247,U_2248,U_2249) ),
    inference(variable_rename,[status(thm)],[f_613_1]) ).

fof(f_613_3,plain,
    ! [U_2251,U_2250,U_2249,U_2248,U_2247,U_2246,U_2245] :
      ( ! [U_2244] : ~ c_Finite__Set_Ofolding__image__simple(U_2244,U_2245,U_2246,U_2247,U_2248,U_2249)
      | hAPP(U_2249,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2245,tc_HOL_Obool)),U_2250),U_2251)) = hAPP(hAPP(U_2246,hAPP(U_2249,U_2250)),hAPP(U_2249,U_2251))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2245,tc_HOL_Obool)),U_2250),U_2251) != c_Orderings_Obot__class_Obot(tc_fun(U_2245,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2245),U_2251))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2245),U_2250)) ),
    inference(miniscope,[status(thm)],[f_613_2]) ).

cnf(f_613_4,plain,
    ( ~ c_Finite__Set_Ofolding__image__simple(U_2244,U_2245,U_2246,U_2247,U_2248,U_2249)
    | hAPP(U_2249,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2245,tc_HOL_Obool)),U_2250),U_2251)) = hAPP(hAPP(U_2246,hAPP(U_2249,U_2250)),hAPP(U_2249,U_2251))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2245,tc_HOL_Obool)),U_2250),U_2251) != c_Orderings_Obot__class_Obot(tc_fun(U_2245,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2245),U_2251))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2245),U_2250)) ),
    inference(clausify,[status(thm)],[f_613_3]) ).

fof(f_614_1,plain,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
      ( ( ( hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
        & ( hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__one_Oinsert__remove]) ).

fof(f_614_2,plain,
    ! [U_2256,U_2255,U_2254,U_2253,U_2252] :
      ( ( ( hAPP(U_2254,hAPP(hAPP(c_Set_Oinsert(U_2252),U_2256),U_2255)) = hAPP(hAPP(U_2253,U_2256),hAPP(U_2254,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2252,tc_HOL_Obool)),U_2255),hAPP(hAPP(c_Set_Oinsert(U_2252),U_2256),c_Orderings_Obot__class_Obot(tc_fun(U_2252,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2252,tc_HOL_Obool)),U_2255),hAPP(hAPP(c_Set_Oinsert(U_2252),U_2256),c_Orderings_Obot__class_Obot(tc_fun(U_2252,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_2252,tc_HOL_Obool)) )
        & ( hAPP(U_2254,hAPP(hAPP(c_Set_Oinsert(U_2252),U_2256),U_2255)) = U_2256
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2252,tc_HOL_Obool)),U_2255),hAPP(hAPP(c_Set_Oinsert(U_2252),U_2256),c_Orderings_Obot__class_Obot(tc_fun(U_2252,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_2252,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2252),U_2255))
      | ~ c_Finite__Set_Ofolding__one(U_2252,U_2253,U_2254) ),
    inference(variable_rename,[status(thm)],[f_614_1]) ).

cnf(f_614_3,plain,
    ( hAPP(U_2254,hAPP(hAPP(c_Set_Oinsert(U_2252),U_2256),U_2255)) = U_2256
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2252,tc_HOL_Obool)),U_2255),hAPP(hAPP(c_Set_Oinsert(U_2252),U_2256),c_Orderings_Obot__class_Obot(tc_fun(U_2252,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_2252,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2252),U_2255))
    | ~ c_Finite__Set_Ofolding__one(U_2252,U_2253,U_2254) ),
    inference(clausify,[status(thm)],[f_614_2]) ).

cnf(f_614_4,plain,
    ( hAPP(U_2254,hAPP(hAPP(c_Set_Oinsert(U_2252),U_2256),U_2255)) = hAPP(hAPP(U_2253,U_2256),hAPP(U_2254,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2252,tc_HOL_Obool)),U_2255),hAPP(hAPP(c_Set_Oinsert(U_2252),U_2256),c_Orderings_Obot__class_Obot(tc_fun(U_2252,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2252,tc_HOL_Obool)),U_2255),hAPP(hAPP(c_Set_Oinsert(U_2252),U_2256),c_Orderings_Obot__class_Obot(tc_fun(U_2252,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_2252,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2252),U_2255))
    | ~ c_Finite__Set_Ofolding__one(U_2252,U_2253,U_2254) ),
    inference(clausify,[status(thm)],[f_614_2]) ).

fof(f_615_1,plain,
    ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
      ( hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
      | ~ c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Oinsert__remove]) ).

fof(f_615_2,plain,
    ! [U_2264,U_2263,U_2262,U_2261,U_2260,U_2259,U_2258,U_2257] :
      ( hAPP(U_2262,hAPP(hAPP(c_Set_Oinsert(U_2258),U_2264),U_2263)) = hAPP(hAPP(U_2259,hAPP(U_2261,U_2264)),hAPP(U_2262,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2258,tc_HOL_Obool)),U_2263),hAPP(hAPP(c_Set_Oinsert(U_2258),U_2264),c_Orderings_Obot__class_Obot(tc_fun(U_2258,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2258),U_2263))
      | ~ c_Finite__Set_Ofolding__image__simple(U_2257,U_2258,U_2259,U_2260,U_2261,U_2262) ),
    inference(variable_rename,[status(thm)],[f_615_1]) ).

fof(f_615_3,plain,
    ! [U_2264,U_2263,U_2262,U_2261,U_2260,U_2259,U_2258] :
      ( ! [U_2257] : ~ c_Finite__Set_Ofolding__image__simple(U_2257,U_2258,U_2259,U_2260,U_2261,U_2262)
      | hAPP(U_2262,hAPP(hAPP(c_Set_Oinsert(U_2258),U_2264),U_2263)) = hAPP(hAPP(U_2259,hAPP(U_2261,U_2264)),hAPP(U_2262,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2258,tc_HOL_Obool)),U_2263),hAPP(hAPP(c_Set_Oinsert(U_2258),U_2264),c_Orderings_Obot__class_Obot(tc_fun(U_2258,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2258),U_2263)) ),
    inference(miniscope,[status(thm)],[f_615_2]) ).

cnf(f_615_4,plain,
    ( ~ c_Finite__Set_Ofolding__image__simple(U_2257,U_2258,U_2259,U_2260,U_2261,U_2262)
    | hAPP(U_2262,hAPP(hAPP(c_Set_Oinsert(U_2258),U_2264),U_2263)) = hAPP(hAPP(U_2259,hAPP(U_2261,U_2264)),hAPP(U_2262,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2258,tc_HOL_Obool)),U_2263),hAPP(hAPP(c_Set_Oinsert(U_2258),U_2264),c_Orderings_Obot__class_Obot(tc_fun(U_2258,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2258),U_2263)) ),
    inference(clausify,[status(thm)],[f_615_3]) ).

fof(f_616_1,plain,
    ! [V_N_2,V_h_2,T_b] :
      ( hAPP(V_h_2,c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_N_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2))
      | V_N_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
      | ? [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),B_x),B_y)) != hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Ohom__commute]) ).

fof(f_616_2,plain,
    ! [U_2269,U_2268,U_2267] :
      ( hAPP(U_2268,c_Big__Operators_Olattice_OSup__fin(U_2267,c_Orderings_Oord__class_Omax(U_2267),U_2269)) = c_Big__Operators_Olattice_OSup__fin(U_2267,c_Orderings_Oord__class_Omax(U_2267),hAPP(c_Set_Oimage(U_2267,U_2267,U_2268),U_2269))
      | U_2269 = c_Orderings_Obot__class_Obot(tc_fun(U_2267,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2267),U_2269))
      | ? [U_2266,U_2265] : hAPP(U_2268,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2267),U_2266),U_2265)) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2267),hAPP(U_2268,U_2266)),hAPP(U_2268,U_2265))
      | ~ class_Orderings_Olinorder(U_2267) ),
    inference(variable_rename,[status(thm)],[f_616_1]) ).

fof(f_616_3,plain,
    ! [U_2269,U_2268,U_2267] :
      ( hAPP(U_2268,c_Big__Operators_Olattice_OSup__fin(U_2267,c_Orderings_Oord__class_Omax(U_2267),U_2269)) = c_Big__Operators_Olattice_OSup__fin(U_2267,c_Orderings_Oord__class_Omax(U_2267),hAPP(c_Set_Oimage(U_2267,U_2267,U_2268),U_2269))
      | U_2269 = c_Orderings_Obot__class_Obot(tc_fun(U_2267,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2267),U_2269))
      | ? [U_2265] : hAPP(U_2268,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2267),sK25(U_2269,U_2268,U_2267)),U_2265)) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2267),hAPP(U_2268,sK25(U_2269,U_2268,U_2267))),hAPP(U_2268,U_2265))
      | ~ class_Orderings_Olinorder(U_2267) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(U_2266,sK25(U_2269,U_2268,U_2267))],[f_616_2]) ).

fof(f_616_4,plain,
    ! [U_2269,U_2268,U_2267] :
      ( hAPP(U_2268,c_Big__Operators_Olattice_OSup__fin(U_2267,c_Orderings_Oord__class_Omax(U_2267),U_2269)) = c_Big__Operators_Olattice_OSup__fin(U_2267,c_Orderings_Oord__class_Omax(U_2267),hAPP(c_Set_Oimage(U_2267,U_2267,U_2268),U_2269))
      | U_2269 = c_Orderings_Obot__class_Obot(tc_fun(U_2267,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2267),U_2269))
      | hAPP(U_2268,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2267),sK25(U_2269,U_2268,U_2267)),sK26(U_2269,U_2268,U_2267))) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2267),hAPP(U_2268,sK25(U_2269,U_2268,U_2267))),hAPP(U_2268,sK26(U_2269,U_2268,U_2267)))
      | ~ class_Orderings_Olinorder(U_2267) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(U_2265,sK26(U_2269,U_2268,U_2267))],[f_616_3]) ).

cnf(f_616_5,plain,
    ( hAPP(U_2268,c_Big__Operators_Olattice_OSup__fin(U_2267,c_Orderings_Oord__class_Omax(U_2267),U_2269)) = c_Big__Operators_Olattice_OSup__fin(U_2267,c_Orderings_Oord__class_Omax(U_2267),hAPP(c_Set_Oimage(U_2267,U_2267,U_2268),U_2269))
    | U_2269 = c_Orderings_Obot__class_Obot(tc_fun(U_2267,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2267),U_2269))
    | hAPP(U_2268,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2267),sK25(U_2269,U_2268,U_2267)),sK26(U_2269,U_2268,U_2267))) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2267),hAPP(U_2268,sK25(U_2269,U_2268,U_2267))),hAPP(U_2268,sK26(U_2269,U_2268,U_2267)))
    | ~ class_Orderings_Olinorder(U_2267) ),
    inference(clausify,[status(thm)],[f_616_4]) ).

fof(f_617_1,plain,
    ! [V_N_2,V_h_2,T_b] :
      ( hAPP(V_h_2,c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_N_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2))
      | V_N_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
      | ? [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),B_x),B_y)) != hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Ohom__commute]) ).

fof(f_617_2,plain,
    ! [U_2274,U_2273,U_2272] :
      ( hAPP(U_2273,c_Big__Operators_Olattice_OInf__fin(U_2272,c_Orderings_Oord__class_Omin(U_2272),U_2274)) = c_Big__Operators_Olattice_OInf__fin(U_2272,c_Orderings_Oord__class_Omin(U_2272),hAPP(c_Set_Oimage(U_2272,U_2272,U_2273),U_2274))
      | U_2274 = c_Orderings_Obot__class_Obot(tc_fun(U_2272,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2272),U_2274))
      | ? [U_2271,U_2270] : hAPP(U_2273,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2272),U_2271),U_2270)) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2272),hAPP(U_2273,U_2271)),hAPP(U_2273,U_2270))
      | ~ class_Orderings_Olinorder(U_2272) ),
    inference(variable_rename,[status(thm)],[f_617_1]) ).

fof(f_617_3,plain,
    ! [U_2274,U_2273,U_2272] :
      ( hAPP(U_2273,c_Big__Operators_Olattice_OInf__fin(U_2272,c_Orderings_Oord__class_Omin(U_2272),U_2274)) = c_Big__Operators_Olattice_OInf__fin(U_2272,c_Orderings_Oord__class_Omin(U_2272),hAPP(c_Set_Oimage(U_2272,U_2272,U_2273),U_2274))
      | U_2274 = c_Orderings_Obot__class_Obot(tc_fun(U_2272,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2272),U_2274))
      | ? [U_2270] : hAPP(U_2273,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2272),sK27(U_2274,U_2273,U_2272)),U_2270)) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2272),hAPP(U_2273,sK27(U_2274,U_2273,U_2272))),hAPP(U_2273,U_2270))
      | ~ class_Orderings_Olinorder(U_2272) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(U_2271,sK27(U_2274,U_2273,U_2272))],[f_617_2]) ).

fof(f_617_4,plain,
    ! [U_2274,U_2273,U_2272] :
      ( hAPP(U_2273,c_Big__Operators_Olattice_OInf__fin(U_2272,c_Orderings_Oord__class_Omin(U_2272),U_2274)) = c_Big__Operators_Olattice_OInf__fin(U_2272,c_Orderings_Oord__class_Omin(U_2272),hAPP(c_Set_Oimage(U_2272,U_2272,U_2273),U_2274))
      | U_2274 = c_Orderings_Obot__class_Obot(tc_fun(U_2272,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2272),U_2274))
      | hAPP(U_2273,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2272),sK27(U_2274,U_2273,U_2272)),sK28(U_2274,U_2273,U_2272))) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2272),hAPP(U_2273,sK27(U_2274,U_2273,U_2272))),hAPP(U_2273,sK28(U_2274,U_2273,U_2272)))
      | ~ class_Orderings_Olinorder(U_2272) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(U_2270,sK28(U_2274,U_2273,U_2272))],[f_617_3]) ).

cnf(f_617_5,plain,
    ( hAPP(U_2273,c_Big__Operators_Olattice_OInf__fin(U_2272,c_Orderings_Oord__class_Omin(U_2272),U_2274)) = c_Big__Operators_Olattice_OInf__fin(U_2272,c_Orderings_Oord__class_Omin(U_2272),hAPP(c_Set_Oimage(U_2272,U_2272,U_2273),U_2274))
    | U_2274 = c_Orderings_Obot__class_Obot(tc_fun(U_2272,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2272),U_2274))
    | hAPP(U_2273,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2272),sK27(U_2274,U_2273,U_2272)),sK28(U_2274,U_2273,U_2272))) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2272),hAPP(U_2273,sK27(U_2274,U_2273,U_2272))),hAPP(U_2273,sK28(U_2274,U_2273,U_2272)))
    | ~ class_Orderings_Olinorder(U_2272) ),
    inference(clausify,[status(thm)],[f_617_4]) ).

fof(f_618_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( ( ( c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) = V_x_2
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oremove]) ).

fof(f_618_2,plain,
    ! [U_2277,U_2276,U_2275] :
      ( ( ( c_Big__Operators_Olattice_OSup__fin(U_2275,c_Orderings_Oord__class_Omax(U_2275),U_2276) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2275),U_2277),c_Big__Operators_Olattice_OSup__fin(U_2275,c_Orderings_Oord__class_Omax(U_2275),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2275,tc_HOL_Obool)),U_2276),hAPP(hAPP(c_Set_Oinsert(U_2275),U_2277),c_Orderings_Obot__class_Obot(tc_fun(U_2275,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2275,tc_HOL_Obool)),U_2276),hAPP(hAPP(c_Set_Oinsert(U_2275),U_2277),c_Orderings_Obot__class_Obot(tc_fun(U_2275,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_2275,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olattice_OSup__fin(U_2275,c_Orderings_Oord__class_Omax(U_2275),U_2276) = U_2277
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2275,tc_HOL_Obool)),U_2276),hAPP(hAPP(c_Set_Oinsert(U_2275),U_2277),c_Orderings_Obot__class_Obot(tc_fun(U_2275,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_2275,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_2275),U_2277),U_2276))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2275),U_2276))
      | ~ class_Orderings_Olinorder(U_2275) ),
    inference(variable_rename,[status(thm)],[f_618_1]) ).

cnf(f_618_3,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_2275,c_Orderings_Oord__class_Omax(U_2275),U_2276) = U_2277
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2275,tc_HOL_Obool)),U_2276),hAPP(hAPP(c_Set_Oinsert(U_2275),U_2277),c_Orderings_Obot__class_Obot(tc_fun(U_2275,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_2275,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2275),U_2277),U_2276))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2275),U_2276))
    | ~ class_Orderings_Olinorder(U_2275) ),
    inference(clausify,[status(thm)],[f_618_2]) ).

cnf(f_618_4,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_2275,c_Orderings_Oord__class_Omax(U_2275),U_2276) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2275),U_2277),c_Big__Operators_Olattice_OSup__fin(U_2275,c_Orderings_Oord__class_Omax(U_2275),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2275,tc_HOL_Obool)),U_2276),hAPP(hAPP(c_Set_Oinsert(U_2275),U_2277),c_Orderings_Obot__class_Obot(tc_fun(U_2275,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2275,tc_HOL_Obool)),U_2276),hAPP(hAPP(c_Set_Oinsert(U_2275),U_2277),c_Orderings_Obot__class_Obot(tc_fun(U_2275,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_2275,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2275),U_2277),U_2276))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2275),U_2276))
    | ~ class_Orderings_Olinorder(U_2275) ),
    inference(clausify,[status(thm)],[f_618_2]) ).

fof(f_619_1,plain,
    ! [V_c_2,T_b,V_B_2,V_A_2] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
        & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) )
      | ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
        & hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) )
      | V_A_2 != V_B_2 ),
    inference(fof_nnf,[status(thm)],[fact_equalityCE]) ).

fof(f_619_2,plain,
    ! [U_2281,U_2280,U_2279,U_2278] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(U_2280),U_2281),U_2279))
        & ~ hBOOL(hAPP(hAPP(c_member(U_2280),U_2281),U_2278)) )
      | ( hBOOL(hAPP(hAPP(c_member(U_2280),U_2281),U_2279))
        & hBOOL(hAPP(hAPP(c_member(U_2280),U_2281),U_2278)) )
      | U_2278 != U_2279 ),
    inference(variable_rename,[status(thm)],[f_619_1]) ).

cnf(f_619_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_2280),U_2281),U_2278))
    | hBOOL(hAPP(hAPP(c_member(U_2280),U_2281),U_2278))
    | U_2278 != U_2279 ),
    inference(clausify,[status(thm)],[f_619_2]) ).

cnf(f_619_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_2280),U_2281),U_2279))
    | hBOOL(hAPP(hAPP(c_member(U_2280),U_2281),U_2278))
    | U_2278 != U_2279 ),
    inference(clausify,[status(thm)],[f_619_2]) ).

cnf(f_619_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_2280),U_2281),U_2278))
    | hBOOL(hAPP(hAPP(c_member(U_2280),U_2281),U_2279))
    | U_2278 != U_2279 ),
    inference(clausify,[status(thm)],[f_619_2]) ).

cnf(f_619_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_2280),U_2281),U_2279))
    | hBOOL(hAPP(hAPP(c_member(U_2280),U_2281),U_2279))
    | U_2278 != U_2279 ),
    inference(clausify,[status(thm)],[f_619_2]) ).

fof(f_620_1,plain,
    ! [V_a_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_emptyE]) ).

fof(f_620_2,plain,
    ! [U_2283,U_2282] : ~ hBOOL(hAPP(hAPP(c_member(U_2282),U_2283),c_Orderings_Obot__class_Obot(tc_fun(U_2282,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_620_1]) ).

cnf(f_620_3,plain,
    ~ hBOOL(hAPP(hAPP(c_member(U_2282),U_2283),c_Orderings_Obot__class_Obot(tc_fun(U_2282,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_620_2]) ).

fof(f_621_1,plain,
    ! [V_A_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | V_a_2 = V_b_2
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2))) ),
    inference(fof_nnf,[status(thm)],[fact_insertE]) ).

fof(f_621_2,plain,
    ! [U_2287,U_2286,U_2285,U_2284] :
      ( hBOOL(hAPP(hAPP(c_member(U_2284),U_2285),U_2287))
      | U_2285 = U_2286
      | ~ hBOOL(hAPP(hAPP(c_member(U_2284),U_2285),hAPP(hAPP(c_Set_Oinsert(U_2284),U_2286),U_2287))) ),
    inference(variable_rename,[status(thm)],[f_621_1]) ).

cnf(f_621_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2284),U_2285),U_2287))
    | U_2285 = U_2286
    | ~ hBOOL(hAPP(hAPP(c_member(U_2284),U_2285),hAPP(hAPP(c_Set_Oinsert(U_2284),U_2286),U_2287))) ),
    inference(clausify,[status(thm)],[f_621_2]) ).

fof(f_622_1,plain,
    ! [V_b_2,V_B_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2)))
      | ( V_a_2 != V_b_2
        & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_insertCI]) ).

fof(f_622_2,plain,
    ! [U_2291,U_2290,U_2289,U_2288] :
      ( hBOOL(hAPP(hAPP(c_member(U_2288),U_2289),hAPP(hAPP(c_Set_Oinsert(U_2288),U_2291),U_2290)))
      | ( U_2289 != U_2291
        & ~ hBOOL(hAPP(hAPP(c_member(U_2288),U_2289),U_2290)) ) ),
    inference(variable_rename,[status(thm)],[f_622_1]) ).

cnf(f_622_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_2288),U_2289),U_2290))
    | hBOOL(hAPP(hAPP(c_member(U_2288),U_2289),hAPP(hAPP(c_Set_Oinsert(U_2288),U_2291),U_2290))) ),
    inference(clausify,[status(thm)],[f_622_2]) ).

cnf(f_622_4,plain,
    ( U_2289 != U_2291
    | hBOOL(hAPP(hAPP(c_member(U_2288),U_2289),hAPP(hAPP(c_Set_Oinsert(U_2288),U_2291),U_2290))) ),
    inference(clausify,[status(thm)],[f_622_2]) ).

fof(f_623_1,plain,
    ! [V_c_2,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_subsetD]) ).

fof(f_623_2,plain,
    ! [U_2295,U_2294,U_2293,U_2292] :
      ( hBOOL(hAPP(hAPP(c_member(U_2292),U_2295),U_2294))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2292),U_2295),U_2293))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2292,tc_HOL_Obool)),U_2293),U_2294)) ),
    inference(variable_rename,[status(thm)],[f_623_1]) ).

cnf(f_623_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2292),U_2295),U_2294))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2292),U_2295),U_2293))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2292,tc_HOL_Obool)),U_2293),U_2294)) ),
    inference(clausify,[status(thm)],[f_623_2]) ).

fof(f_624_1,plain,
    ! [V_x_2,T_b] : hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_UNIV__I]) ).

fof(f_624_2,plain,
    ! [U_2297,U_2296] : hBOOL(hAPP(hAPP(c_member(U_2296),U_2297),c_Orderings_Otop__class_Otop(tc_fun(U_2296,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_624_1]) ).

cnf(f_624_3,plain,
    hBOOL(hAPP(hAPP(c_member(U_2296),U_2297),c_Orderings_Otop__class_Otop(tc_fun(U_2296,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_624_2]) ).

fof(f_625_1,plain,
    ! [T_b,V_A_2,T_c,V_x_2,V_f_2,V_b_2] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
      | V_b_2 != hAPP(V_f_2,V_x_2) ),
    inference(fof_nnf,[status(thm)],[fact_image__eqI]) ).

fof(f_625_2,plain,
    ! [U_2303,U_2302,U_2301,U_2300,U_2299,U_2298] :
      ( hBOOL(hAPP(hAPP(c_member(U_2303),U_2298),hAPP(c_Set_Oimage(U_2301,U_2303,U_2299),U_2302)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2301),U_2300),U_2302))
      | U_2298 != hAPP(U_2299,U_2300) ),
    inference(variable_rename,[status(thm)],[f_625_1]) ).

cnf(f_625_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2303),U_2298),hAPP(c_Set_Oimage(U_2301,U_2303,U_2299),U_2302)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2301),U_2300),U_2302))
    | U_2298 != hAPP(U_2299,U_2300) ),
    inference(clausify,[status(thm)],[f_625_2]) ).

fof(f_626_1,plain,
    ! [V_B_2,V_A_2,V_c_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
      | hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ),
    inference(fof_nnf,[status(thm)],[fact_UnE]) ).

fof(f_626_2,plain,
    ! [U_2307,U_2306,U_2305,U_2304] :
      ( hBOOL(hAPP(hAPP(c_member(U_2304),U_2305),U_2307))
      | hBOOL(hAPP(hAPP(c_member(U_2304),U_2305),U_2306))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2304),U_2305),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2304,tc_HOL_Obool)),U_2306),U_2307))) ),
    inference(variable_rename,[status(thm)],[f_626_1]) ).

cnf(f_626_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2304),U_2305),U_2307))
    | hBOOL(hAPP(hAPP(c_member(U_2304),U_2305),U_2306))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2304),U_2305),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2304,tc_HOL_Obool)),U_2306),U_2307))) ),
    inference(clausify,[status(thm)],[f_626_2]) ).

fof(f_627_1,plain,
    ! [V_A_2,V_B_2,V_c_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
      | ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
        & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_UnCI]) ).

fof(f_627_2,plain,
    ! [U_2311,U_2310,U_2309,U_2308] :
      ( hBOOL(hAPP(hAPP(c_member(U_2308),U_2309),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2308,tc_HOL_Obool)),U_2311),U_2310)))
      | ( ~ hBOOL(hAPP(hAPP(c_member(U_2308),U_2309),U_2311))
        & ~ hBOOL(hAPP(hAPP(c_member(U_2308),U_2309),U_2310)) ) ),
    inference(variable_rename,[status(thm)],[f_627_1]) ).

cnf(f_627_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_2308),U_2309),U_2310))
    | hBOOL(hAPP(hAPP(c_member(U_2308),U_2309),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2308,tc_HOL_Obool)),U_2311),U_2310))) ),
    inference(clausify,[status(thm)],[f_627_2]) ).

cnf(f_627_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_2308),U_2309),U_2311))
    | hBOOL(hAPP(hAPP(c_member(U_2308),U_2309),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2308,tc_HOL_Obool)),U_2311),U_2310))) ),
    inference(clausify,[status(thm)],[f_627_2]) ).

fof(f_628_1,plain,
    ! [V_B_2,V_A_2,V_c_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_IntI]) ).

fof(f_628_2,plain,
    ! [U_2315,U_2314,U_2313,U_2312] :
      ( hBOOL(hAPP(hAPP(c_member(U_2312),U_2313),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2312,tc_HOL_Obool)),U_2314),U_2315)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2312),U_2313),U_2315))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2312),U_2313),U_2314)) ),
    inference(variable_rename,[status(thm)],[f_628_1]) ).

cnf(f_628_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2312),U_2313),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2312,tc_HOL_Obool)),U_2314),U_2315)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2312),U_2313),U_2315))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2312),U_2313),U_2314)) ),
    inference(clausify,[status(thm)],[f_628_2]) ).

fof(f_629_1,plain,
    ! [V_B_2,V_A_2,V_c_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
        & hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) )
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ),
    inference(fof_nnf,[status(thm)],[fact_IntE]) ).

fof(f_629_2,plain,
    ! [U_2319,U_2318,U_2317,U_2316] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_2316),U_2317),U_2319))
        & hBOOL(hAPP(hAPP(c_member(U_2316),U_2317),U_2318)) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_2316),U_2317),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2316,tc_HOL_Obool)),U_2318),U_2319))) ),
    inference(variable_rename,[status(thm)],[f_629_1]) ).

cnf(f_629_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2316),U_2317),U_2318))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2316),U_2317),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2316,tc_HOL_Obool)),U_2318),U_2319))) ),
    inference(clausify,[status(thm)],[f_629_2]) ).

cnf(f_629_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2316),U_2317),U_2319))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2316),U_2317),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2316,tc_HOL_Obool)),U_2318),U_2319))) ),
    inference(clausify,[status(thm)],[f_629_2]) ).

fof(f_630_1,plain,
    ! [V_B_2,V_A_2,V_c_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
      | hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_DiffI]) ).

fof(f_630_2,plain,
    ! [U_2323,U_2322,U_2321,U_2320] :
      ( hBOOL(hAPP(hAPP(c_member(U_2320),U_2321),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2320,tc_HOL_Obool)),U_2322),U_2323)))
      | hBOOL(hAPP(hAPP(c_member(U_2320),U_2321),U_2323))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2320),U_2321),U_2322)) ),
    inference(variable_rename,[status(thm)],[f_630_1]) ).

cnf(f_630_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2320),U_2321),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2320,tc_HOL_Obool)),U_2322),U_2323)))
    | hBOOL(hAPP(hAPP(c_member(U_2320),U_2321),U_2323))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2320),U_2321),U_2322)) ),
    inference(clausify,[status(thm)],[f_630_2]) ).

fof(f_631_1,plain,
    ! [V_B_2,V_A_2,V_c_2,T_b] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
        & hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) )
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ),
    inference(fof_nnf,[status(thm)],[fact_DiffE]) ).

fof(f_631_2,plain,
    ! [U_2327,U_2326,U_2325,U_2324] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(U_2324),U_2325),U_2327))
        & hBOOL(hAPP(hAPP(c_member(U_2324),U_2325),U_2326)) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_2324),U_2325),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2324,tc_HOL_Obool)),U_2326),U_2327))) ),
    inference(variable_rename,[status(thm)],[f_631_1]) ).

cnf(f_631_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2324),U_2325),U_2326))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2324),U_2325),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2324,tc_HOL_Obool)),U_2326),U_2327))) ),
    inference(clausify,[status(thm)],[f_631_2]) ).

cnf(f_631_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_2324),U_2325),U_2327))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2324),U_2325),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2324,tc_HOL_Obool)),U_2326),U_2327))) ),
    inference(clausify,[status(thm)],[f_631_2]) ).

fof(f_632_1,plain,
    ! [V_A_2,V_c_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
      | hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_ComplI]) ).

fof(f_632_2,plain,
    ! [U_2330,U_2329,U_2328] :
      ( hBOOL(hAPP(hAPP(c_member(U_2328),U_2329),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2328,tc_HOL_Obool)),U_2330)))
      | hBOOL(hAPP(hAPP(c_member(U_2328),U_2329),U_2330)) ),
    inference(variable_rename,[status(thm)],[f_632_1]) ).

cnf(f_632_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2328),U_2329),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2328,tc_HOL_Obool)),U_2330)))
    | hBOOL(hAPP(hAPP(c_member(U_2328),U_2329),U_2330)) ),
    inference(clausify,[status(thm)],[f_632_2]) ).

fof(f_633_1,plain,
    ! [V_A_2,V_C_2,V_X_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2)) ),
    inference(fof_nnf,[status(thm)],[fact_UnionI]) ).

fof(f_633_2,plain,
    ! [U_2334,U_2333,U_2332,U_2331] :
      ( hBOOL(hAPP(hAPP(c_member(U_2331),U_2334),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2331,tc_HOL_Obool),U_2333)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2331),U_2334),U_2332))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_2331,tc_HOL_Obool)),U_2332),U_2333)) ),
    inference(variable_rename,[status(thm)],[f_633_1]) ).

cnf(f_633_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2331),U_2334),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2331,tc_HOL_Obool),U_2333)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2331),U_2334),U_2332))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_2331,tc_HOL_Obool)),U_2332),U_2333)) ),
    inference(clausify,[status(thm)],[f_633_2]) ).

fof(f_634_1,plain,
    ! [V_X_2,V_C_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_C_2))) ),
    inference(fof_nnf,[status(thm)],[fact_InterD]) ).

fof(f_634_2,plain,
    ! [U_2338,U_2337,U_2336,U_2335] :
      ( hBOOL(hAPP(hAPP(c_member(U_2335),U_2336),U_2338))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_2335,tc_HOL_Obool)),U_2338),U_2337))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2335),U_2336),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_2335,tc_HOL_Obool),U_2337))) ),
    inference(variable_rename,[status(thm)],[f_634_1]) ).

cnf(f_634_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2335),U_2336),U_2338))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_2335,tc_HOL_Obool)),U_2338),U_2337))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2335),U_2336),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_2335,tc_HOL_Obool),U_2337))) ),
    inference(clausify,[status(thm)],[f_634_2]) ).

fof(f_635_1,plain,
    ! [V_X_2,V_C_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_C_2))) ),
    inference(fof_nnf,[status(thm)],[fact_InterE]) ).

fof(f_635_2,plain,
    ! [U_2342,U_2341,U_2340,U_2339] :
      ( hBOOL(hAPP(hAPP(c_member(U_2339),U_2340),U_2342))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_2339,tc_HOL_Obool)),U_2342),U_2341))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2339),U_2340),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_2339,tc_HOL_Obool),U_2341))) ),
    inference(variable_rename,[status(thm)],[f_635_1]) ).

cnf(f_635_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2339),U_2340),U_2342))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_2339,tc_HOL_Obool)),U_2342),U_2341))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2339),U_2340),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_2339,tc_HOL_Obool),U_2341))) ),
    inference(clausify,[status(thm)],[f_635_2]) ).

fof(f_636_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_PowI]) ).

fof(f_636_2,plain,
    ! [U_2345,U_2344,U_2343] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_2343,tc_HOL_Obool)),U_2344),hAPP(c_Set_OPow(U_2343),U_2345)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2343,tc_HOL_Obool)),U_2344),U_2345)) ),
    inference(variable_rename,[status(thm)],[f_636_1]) ).

cnf(f_636_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_2343,tc_HOL_Obool)),U_2344),hAPP(c_Set_OPow(U_2343),U_2345)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2343,tc_HOL_Obool)),U_2344),U_2345)) ),
    inference(clausify,[status(thm)],[f_636_2]) ).

fof(f_637_1,plain,
    ! [V_A_2,V_x_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
        | ~ hBOOL(hAPP(V_A_2,V_x_2)) )
      & ( hBOOL(hAPP(V_A_2,V_x_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_mem__def]) ).

fof(f_637_2,plain,
    ! [U_2348,U_2347,U_2346] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_2346),U_2347),U_2348))
        | ~ hBOOL(hAPP(U_2348,U_2347)) )
      & ( hBOOL(hAPP(U_2348,U_2347))
        | ~ hBOOL(hAPP(hAPP(c_member(U_2346),U_2347),U_2348)) ) ),
    inference(variable_rename,[status(thm)],[f_637_1]) ).

fof(f_637_3,plain,
    ( ! [U_2354,U_2352] :
        ( ! [U_2350] : hBOOL(hAPP(hAPP(c_member(U_2350),U_2352),U_2354))
        | ~ hBOOL(hAPP(U_2354,U_2352)) )
    & ! [U_2353,U_2351] :
        ( ! [U_2349] : ~ hBOOL(hAPP(hAPP(c_member(U_2349),U_2351),U_2353))
        | hBOOL(hAPP(U_2353,U_2351)) ) ),
    inference(miniscope,[status(thm)],[f_637_2]) ).

cnf(f_637_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_2349),U_2351),U_2353))
    | hBOOL(hAPP(U_2353,U_2351)) ),
    inference(clausify,[status(thm)],[f_637_3]) ).

cnf(f_637_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2350),U_2352),U_2354))
    | ~ hBOOL(hAPP(U_2354,U_2352)) ),
    inference(clausify,[status(thm)],[f_637_3]) ).

fof(f_638_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_fequal,V_y_2)))
        | V_x_2 != V_y_2 )
      & ( V_x_2 = V_y_2
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_fequal,V_y_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_eq__mem]) ).

fof(f_638_2,plain,
    ! [U_2357,U_2356,U_2355] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_2355),U_2356),hAPP(c_fequal,U_2357)))
        | U_2356 != U_2357 )
      & ( U_2356 = U_2357
        | ~ hBOOL(hAPP(hAPP(c_member(U_2355),U_2356),hAPP(c_fequal,U_2357))) ) ),
    inference(variable_rename,[status(thm)],[f_638_1]) ).

fof(f_638_3,plain,
    ( ! [U_2363,U_2361] :
        ( ! [U_2359] : hBOOL(hAPP(hAPP(c_member(U_2359),U_2361),hAPP(c_fequal,U_2363)))
        | U_2361 != U_2363 )
    & ! [U_2362,U_2360] :
        ( ! [U_2358] : ~ hBOOL(hAPP(hAPP(c_member(U_2358),U_2360),hAPP(c_fequal,U_2362)))
        | U_2360 = U_2362 ) ),
    inference(miniscope,[status(thm)],[f_638_2]) ).

cnf(f_638_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_2358),U_2360),hAPP(c_fequal,U_2362)))
    | U_2360 = U_2362 ),
    inference(clausify,[status(thm)],[f_638_3]) ).

cnf(f_638_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2359),U_2361),hAPP(c_fequal,U_2363)))
    | U_2361 != U_2363 ),
    inference(clausify,[status(thm)],[f_638_3]) ).

fof(f_639_1,plain,
    ! [V_x_2,T_b,V_B_2,V_A_2] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
          | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) )
        & ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
          | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) )
      | V_A_2 != V_B_2 ),
    inference(fof_nnf,[status(thm)],[fact_eqset__imp__iff]) ).

fof(f_639_2,plain,
    ! [U_2367,U_2366,U_2365,U_2364] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(U_2366),U_2367),U_2364))
          | ~ hBOOL(hAPP(hAPP(c_member(U_2366),U_2367),U_2365)) )
        & ( hBOOL(hAPP(hAPP(c_member(U_2366),U_2367),U_2365))
          | ~ hBOOL(hAPP(hAPP(c_member(U_2366),U_2367),U_2364)) ) )
      | U_2364 != U_2365 ),
    inference(variable_rename,[status(thm)],[f_639_1]) ).

cnf(f_639_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2366),U_2367),U_2365))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2366),U_2367),U_2364))
    | U_2364 != U_2365 ),
    inference(clausify,[status(thm)],[f_639_2]) ).

cnf(f_639_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2366),U_2367),U_2364))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2366),U_2367),U_2365))
    | U_2364 != U_2365 ),
    inference(clausify,[status(thm)],[f_639_2]) ).

fof(f_640_1,plain,
    ! [V_A_2,T_b,V_y_2,V_x_2] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
          | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) )
        & ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
          | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) )
      | V_x_2 != V_y_2 ),
    inference(fof_nnf,[status(thm)],[fact_eqelem__imp__iff]) ).

fof(f_640_2,plain,
    ! [U_2371,U_2370,U_2369,U_2368] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(U_2370),U_2368),U_2371))
          | ~ hBOOL(hAPP(hAPP(c_member(U_2370),U_2369),U_2371)) )
        & ( hBOOL(hAPP(hAPP(c_member(U_2370),U_2369),U_2371))
          | ~ hBOOL(hAPP(hAPP(c_member(U_2370),U_2368),U_2371)) ) )
      | U_2368 != U_2369 ),
    inference(variable_rename,[status(thm)],[f_640_1]) ).

cnf(f_640_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2370),U_2369),U_2371))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2370),U_2368),U_2371))
    | U_2368 != U_2369 ),
    inference(clausify,[status(thm)],[f_640_2]) ).

cnf(f_640_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2370),U_2368),U_2371))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2370),U_2369),U_2371))
    | U_2368 != U_2369 ),
    inference(clausify,[status(thm)],[f_640_2]) ).

fof(f_641_1,plain,
    ! [V_A_2,T_b,V_b_2,V_a_2] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
      | V_a_2 != V_b_2 ),
    inference(fof_nnf,[status(thm)],[fact_eq__mem__trans]) ).

fof(f_641_2,plain,
    ! [U_2375,U_2374,U_2373,U_2372] :
      ( hBOOL(hAPP(hAPP(c_member(U_2374),U_2372),U_2375))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2374),U_2373),U_2375))
      | U_2372 != U_2373 ),
    inference(variable_rename,[status(thm)],[f_641_1]) ).

cnf(f_641_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2374),U_2372),U_2375))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2374),U_2373),U_2375))
    | U_2372 != U_2373 ),
    inference(clausify,[status(thm)],[f_641_2]) ).

fof(f_642_1,plain,
    ! [V_P_2,V_B_2,V_A_2,T_c,T_b] :
      ( ( ! [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) )
        | ? [B_x] :
            ( ? [B_xa] :
                ( ~ hBOOL(hAPP(V_P_2,B_xa))
                & hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(V_B_2,B_x))) )
            & hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) )
      & ( ! [B_x] :
            ( ! [B_xa] :
                ( hBOOL(hAPP(V_P_2,B_xa))
                | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(V_B_2,B_x))) )
            | ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
        | ? [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_ball__UN]) ).

fof(f_642_2,plain,
    ! [U_2386,U_2385,U_2384,U_2383,U_2382] :
      ( ( ! [U_2381] :
            ( hBOOL(hAPP(U_2386,U_2381))
            | ~ hBOOL(hAPP(hAPP(c_member(U_2382),U_2381),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2383,tc_fun(U_2382,tc_HOL_Obool)),U_2384),U_2385))) )
        | ? [U_2380] :
            ( ? [U_2379] :
                ( ~ hBOOL(hAPP(U_2386,U_2379))
                & hBOOL(hAPP(hAPP(c_member(U_2382),U_2379),hAPP(U_2385,U_2380))) )
            & hBOOL(hAPP(hAPP(c_member(U_2383),U_2380),U_2384)) ) )
      & ( ! [U_2378] :
            ( ! [U_2377] :
                ( hBOOL(hAPP(U_2386,U_2377))
                | ~ hBOOL(hAPP(hAPP(c_member(U_2382),U_2377),hAPP(U_2385,U_2378))) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_2383),U_2378),U_2384)) )
        | ? [U_2376] :
            ( ~ hBOOL(hAPP(U_2386,U_2376))
            & hBOOL(hAPP(hAPP(c_member(U_2382),U_2376),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2383,tc_fun(U_2382,tc_HOL_Obool)),U_2384),U_2385))) ) ) ),
    inference(variable_rename,[status(thm)],[f_642_1]) ).

fof(f_642_3,plain,
    ( ! [U_2396,U_2394,U_2392,U_2390,U_2388] :
        ( ! [U_2381] :
            ( hBOOL(hAPP(U_2396,U_2381))
            | ~ hBOOL(hAPP(hAPP(c_member(U_2388),U_2381),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2390,tc_fun(U_2388,tc_HOL_Obool)),U_2392),U_2394))) )
        | ? [U_2380] :
            ( ? [U_2379] :
                ( ~ hBOOL(hAPP(U_2396,U_2379))
                & hBOOL(hAPP(hAPP(c_member(U_2388),U_2379),hAPP(U_2394,U_2380))) )
            & hBOOL(hAPP(hAPP(c_member(U_2390),U_2380),U_2392)) ) )
    & ! [U_2395,U_2393,U_2391,U_2389,U_2387] :
        ( ! [U_2378] :
            ( ! [U_2377] :
                ( hBOOL(hAPP(U_2395,U_2377))
                | ~ hBOOL(hAPP(hAPP(c_member(U_2387),U_2377),hAPP(U_2393,U_2378))) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_2389),U_2378),U_2391)) )
        | ? [U_2376] :
            ( ~ hBOOL(hAPP(U_2395,U_2376))
            & hBOOL(hAPP(hAPP(c_member(U_2387),U_2376),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2389,tc_fun(U_2387,tc_HOL_Obool)),U_2391),U_2393))) ) ) ),
    inference(miniscope,[status(thm)],[f_642_2]) ).

fof(f_642_4,plain,
    ( ! [U_2396,U_2394,U_2392,U_2390,U_2388] :
        ( ! [U_2381] :
            ( hBOOL(hAPP(U_2396,U_2381))
            | ~ hBOOL(hAPP(hAPP(c_member(U_2388),U_2381),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2390,tc_fun(U_2388,tc_HOL_Obool)),U_2392),U_2394))) )
        | ? [U_2380] :
            ( ? [U_2379] :
                ( ~ hBOOL(hAPP(U_2396,U_2379))
                & hBOOL(hAPP(hAPP(c_member(U_2388),U_2379),hAPP(U_2394,U_2380))) )
            & hBOOL(hAPP(hAPP(c_member(U_2390),U_2380),U_2392)) ) )
    & ! [U_2395,U_2393,U_2391,U_2389,U_2387] :
        ( ! [U_2378] :
            ( ! [U_2377] :
                ( hBOOL(hAPP(U_2395,U_2377))
                | ~ hBOOL(hAPP(hAPP(c_member(U_2387),U_2377),hAPP(U_2393,U_2378))) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_2389),U_2378),U_2391)) )
        | ( ~ hBOOL(hAPP(U_2395,sK29(U_2395,U_2393,U_2391,U_2389,U_2387)))
          & hBOOL(hAPP(hAPP(c_member(U_2387),sK29(U_2395,U_2393,U_2391,U_2389,U_2387)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2389,tc_fun(U_2387,tc_HOL_Obool)),U_2391),U_2393))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(U_2376,sK29(U_2395,U_2393,U_2391,U_2389,U_2387))],[f_642_3]) ).

fof(f_642_5,plain,
    ( ! [U_2396,U_2394,U_2392,U_2390,U_2388] :
        ( ! [U_2381] :
            ( hBOOL(hAPP(U_2396,U_2381))
            | ~ hBOOL(hAPP(hAPP(c_member(U_2388),U_2381),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2390,tc_fun(U_2388,tc_HOL_Obool)),U_2392),U_2394))) )
        | ( ? [U_2379] :
              ( ~ hBOOL(hAPP(U_2396,U_2379))
              & hBOOL(hAPP(hAPP(c_member(U_2388),U_2379),hAPP(U_2394,sK30(U_2396,U_2394,U_2392,U_2390,U_2388)))) )
          & hBOOL(hAPP(hAPP(c_member(U_2390),sK30(U_2396,U_2394,U_2392,U_2390,U_2388)),U_2392)) ) )
    & ! [U_2395,U_2393,U_2391,U_2389,U_2387] :
        ( ! [U_2378] :
            ( ! [U_2377] :
                ( hBOOL(hAPP(U_2395,U_2377))
                | ~ hBOOL(hAPP(hAPP(c_member(U_2387),U_2377),hAPP(U_2393,U_2378))) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_2389),U_2378),U_2391)) )
        | ( ~ hBOOL(hAPP(U_2395,sK29(U_2395,U_2393,U_2391,U_2389,U_2387)))
          & hBOOL(hAPP(hAPP(c_member(U_2387),sK29(U_2395,U_2393,U_2391,U_2389,U_2387)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2389,tc_fun(U_2387,tc_HOL_Obool)),U_2391),U_2393))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK30]),skolemize(U_2380,sK30(U_2396,U_2394,U_2392,U_2390,U_2388))],[f_642_4]) ).

fof(f_642_6,plain,
    ( ! [U_2396,U_2394,U_2392,U_2390,U_2388] :
        ( ! [U_2381] :
            ( hBOOL(hAPP(U_2396,U_2381))
            | ~ hBOOL(hAPP(hAPP(c_member(U_2388),U_2381),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2390,tc_fun(U_2388,tc_HOL_Obool)),U_2392),U_2394))) )
        | ( ~ hBOOL(hAPP(U_2396,sK31(U_2396,U_2394,U_2392,U_2390,U_2388)))
          & hBOOL(hAPP(hAPP(c_member(U_2388),sK31(U_2396,U_2394,U_2392,U_2390,U_2388)),hAPP(U_2394,sK30(U_2396,U_2394,U_2392,U_2390,U_2388))))
          & hBOOL(hAPP(hAPP(c_member(U_2390),sK30(U_2396,U_2394,U_2392,U_2390,U_2388)),U_2392)) ) )
    & ! [U_2395,U_2393,U_2391,U_2389,U_2387] :
        ( ! [U_2378] :
            ( ! [U_2377] :
                ( hBOOL(hAPP(U_2395,U_2377))
                | ~ hBOOL(hAPP(hAPP(c_member(U_2387),U_2377),hAPP(U_2393,U_2378))) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_2389),U_2378),U_2391)) )
        | ( ~ hBOOL(hAPP(U_2395,sK29(U_2395,U_2393,U_2391,U_2389,U_2387)))
          & hBOOL(hAPP(hAPP(c_member(U_2387),sK29(U_2395,U_2393,U_2391,U_2389,U_2387)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2389,tc_fun(U_2387,tc_HOL_Obool)),U_2391),U_2393))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK31]),skolemize(U_2379,sK31(U_2396,U_2394,U_2392,U_2390,U_2388))],[f_642_5]) ).

cnf(f_642_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2387),sK29(U_2395,U_2393,U_2391,U_2389,U_2387)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2389,tc_fun(U_2387,tc_HOL_Obool)),U_2391),U_2393)))
    | hBOOL(hAPP(U_2395,U_2377))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2387),U_2377),hAPP(U_2393,U_2378)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2389),U_2378),U_2391)) ),
    inference(clausify,[status(thm)],[f_642_6]) ).

cnf(f_642_8,plain,
    ( ~ hBOOL(hAPP(U_2395,sK29(U_2395,U_2393,U_2391,U_2389,U_2387)))
    | hBOOL(hAPP(U_2395,U_2377))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2387),U_2377),hAPP(U_2393,U_2378)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2389),U_2378),U_2391)) ),
    inference(clausify,[status(thm)],[f_642_6]) ).

cnf(f_642_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2390),sK30(U_2396,U_2394,U_2392,U_2390,U_2388)),U_2392))
    | hBOOL(hAPP(U_2396,U_2381))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2388),U_2381),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2390,tc_fun(U_2388,tc_HOL_Obool)),U_2392),U_2394))) ),
    inference(clausify,[status(thm)],[f_642_6]) ).

cnf(f_642_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2388),sK31(U_2396,U_2394,U_2392,U_2390,U_2388)),hAPP(U_2394,sK30(U_2396,U_2394,U_2392,U_2390,U_2388))))
    | hBOOL(hAPP(U_2396,U_2381))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2388),U_2381),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2390,tc_fun(U_2388,tc_HOL_Obool)),U_2392),U_2394))) ),
    inference(clausify,[status(thm)],[f_642_6]) ).

cnf(f_642_11,plain,
    ( ~ hBOOL(hAPP(U_2396,sK31(U_2396,U_2394,U_2392,U_2390,U_2388)))
    | hBOOL(hAPP(U_2396,U_2381))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2388),U_2381),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_2390,tc_fun(U_2388,tc_HOL_Obool)),U_2392),U_2394))) ),
    inference(clausify,[status(thm)],[f_642_6]) ).

fof(f_643_1,plain,
    ! [V_A_2,T_b] :
      ( ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
        | V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
      & ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
        | ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_all__not__in__conv]) ).

fof(f_643_2,plain,
    ! [U_2400,U_2399] :
      ( ( ! [U_2398] : ~ hBOOL(hAPP(hAPP(c_member(U_2399),U_2398),U_2400))
        | U_2400 != c_Orderings_Obot__class_Obot(tc_fun(U_2399,tc_HOL_Obool)) )
      & ( U_2400 = c_Orderings_Obot__class_Obot(tc_fun(U_2399,tc_HOL_Obool))
        | ? [U_2397] : hBOOL(hAPP(hAPP(c_member(U_2399),U_2397),U_2400)) ) ),
    inference(variable_rename,[status(thm)],[f_643_1]) ).

fof(f_643_3,plain,
    ( ! [U_2404,U_2402] :
        ( ! [U_2398] : ~ hBOOL(hAPP(hAPP(c_member(U_2402),U_2398),U_2404))
        | U_2404 != c_Orderings_Obot__class_Obot(tc_fun(U_2402,tc_HOL_Obool)) )
    & ! [U_2403,U_2401] :
        ( U_2403 = c_Orderings_Obot__class_Obot(tc_fun(U_2401,tc_HOL_Obool))
        | ? [U_2397] : hBOOL(hAPP(hAPP(c_member(U_2401),U_2397),U_2403)) ) ),
    inference(miniscope,[status(thm)],[f_643_2]) ).

fof(f_643_4,plain,
    ( ! [U_2404,U_2402] :
        ( ! [U_2398] : ~ hBOOL(hAPP(hAPP(c_member(U_2402),U_2398),U_2404))
        | U_2404 != c_Orderings_Obot__class_Obot(tc_fun(U_2402,tc_HOL_Obool)) )
    & ! [U_2403,U_2401] :
        ( U_2403 = c_Orderings_Obot__class_Obot(tc_fun(U_2401,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_member(U_2401),sK32(U_2403,U_2401)),U_2403)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK32]),skolemize(U_2397,sK32(U_2403,U_2401))],[f_643_3]) ).

cnf(f_643_5,plain,
    ( U_2403 = c_Orderings_Obot__class_Obot(tc_fun(U_2401,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(U_2401),sK32(U_2403,U_2401)),U_2403)) ),
    inference(clausify,[status(thm)],[f_643_4]) ).

cnf(f_643_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_2402),U_2398),U_2404))
    | U_2404 != c_Orderings_Obot__class_Obot(tc_fun(U_2402,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_643_4]) ).

fof(f_644_1,plain,
    ! [V_A_2,T_b] :
      ( ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
        | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
      & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
        | ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_ex__in__conv]) ).

fof(f_644_2,plain,
    ! [U_2408,U_2407] :
      ( ( ? [U_2406] : hBOOL(hAPP(hAPP(c_member(U_2407),U_2406),U_2408))
        | U_2408 = c_Orderings_Obot__class_Obot(tc_fun(U_2407,tc_HOL_Obool)) )
      & ( U_2408 != c_Orderings_Obot__class_Obot(tc_fun(U_2407,tc_HOL_Obool))
        | ! [U_2405] : ~ hBOOL(hAPP(hAPP(c_member(U_2407),U_2405),U_2408)) ) ),
    inference(variable_rename,[status(thm)],[f_644_1]) ).

fof(f_644_3,plain,
    ( ! [U_2412,U_2410] :
        ( ? [U_2406] : hBOOL(hAPP(hAPP(c_member(U_2410),U_2406),U_2412))
        | U_2412 = c_Orderings_Obot__class_Obot(tc_fun(U_2410,tc_HOL_Obool)) )
    & ! [U_2411,U_2409] :
        ( U_2411 != c_Orderings_Obot__class_Obot(tc_fun(U_2409,tc_HOL_Obool))
        | ! [U_2405] : ~ hBOOL(hAPP(hAPP(c_member(U_2409),U_2405),U_2411)) ) ),
    inference(miniscope,[status(thm)],[f_644_2]) ).

fof(f_644_4,plain,
    ( ! [U_2412,U_2410] :
        ( hBOOL(hAPP(hAPP(c_member(U_2410),sK33(U_2412,U_2410)),U_2412))
        | U_2412 = c_Orderings_Obot__class_Obot(tc_fun(U_2410,tc_HOL_Obool)) )
    & ! [U_2411,U_2409] :
        ( U_2411 != c_Orderings_Obot__class_Obot(tc_fun(U_2409,tc_HOL_Obool))
        | ! [U_2405] : ~ hBOOL(hAPP(hAPP(c_member(U_2409),U_2405),U_2411)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK33]),skolemize(U_2406,sK33(U_2412,U_2410))],[f_644_3]) ).

cnf(f_644_5,plain,
    ( U_2411 != c_Orderings_Obot__class_Obot(tc_fun(U_2409,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2409),U_2405),U_2411)) ),
    inference(clausify,[status(thm)],[f_644_4]) ).

cnf(f_644_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2410),sK33(U_2412,U_2410)),U_2412))
    | U_2412 = c_Orderings_Obot__class_Obot(tc_fun(U_2410,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_644_4]) ).

fof(f_645_1,plain,
    ! [V_c_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_empty__iff]) ).

fof(f_645_2,plain,
    ! [U_2414,U_2413] : ~ hBOOL(hAPP(hAPP(c_member(U_2413),U_2414),c_Orderings_Obot__class_Obot(tc_fun(U_2413,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_645_1]) ).

cnf(f_645_3,plain,
    ~ hBOOL(hAPP(hAPP(c_member(U_2413),U_2414),c_Orderings_Obot__class_Obot(tc_fun(U_2413,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_645_2]) ).

fof(f_646_1,plain,
    ! [V_a_2,T_b,V_A_2] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
    inference(fof_nnf,[status(thm)],[fact_equals0D]) ).

fof(f_646_2,plain,
    ! [U_2417,U_2416,U_2415] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_2416),U_2417),U_2415))
      | U_2415 != c_Orderings_Obot__class_Obot(tc_fun(U_2416,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_646_1]) ).

cnf(f_646_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_2416),U_2417),U_2415))
    | U_2415 != c_Orderings_Obot__class_Obot(tc_fun(U_2416,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_646_2]) ).

fof(f_647_1,plain,
    ! [V_B_2,V_a_2,T_b] : hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2))),
    inference(fof_nnf,[status(thm)],[fact_insertI1]) ).

fof(f_647_2,plain,
    ! [U_2420,U_2419,U_2418] : hBOOL(hAPP(hAPP(c_member(U_2418),U_2419),hAPP(hAPP(c_Set_Oinsert(U_2418),U_2419),U_2420))),
    inference(variable_rename,[status(thm)],[f_647_1]) ).

cnf(f_647_3,plain,
    hBOOL(hAPP(hAPP(c_member(U_2418),U_2419),hAPP(hAPP(c_Set_Oinsert(U_2418),U_2419),U_2420))),
    inference(clausify,[status(thm)],[f_647_2]) ).

fof(f_648_1,plain,
    ! [V_A_2,V_b_2,V_a_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2)))
        | ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
          & V_a_2 != V_b_2 ) )
      & ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
        | V_a_2 = V_b_2
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_insert__iff]) ).

fof(f_648_2,plain,
    ! [U_2424,U_2423,U_2422,U_2421] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_2421),U_2422),hAPP(hAPP(c_Set_Oinsert(U_2421),U_2423),U_2424)))
        | ( ~ hBOOL(hAPP(hAPP(c_member(U_2421),U_2422),U_2424))
          & U_2422 != U_2423 ) )
      & ( hBOOL(hAPP(hAPP(c_member(U_2421),U_2422),U_2424))
        | U_2422 = U_2423
        | ~ hBOOL(hAPP(hAPP(c_member(U_2421),U_2422),hAPP(hAPP(c_Set_Oinsert(U_2421),U_2423),U_2424))) ) ),
    inference(variable_rename,[status(thm)],[f_648_1]) ).

fof(f_648_3,plain,
    ( ! [U_2432,U_2430,U_2428,U_2426] :
        ( hBOOL(hAPP(hAPP(c_member(U_2426),U_2428),hAPP(hAPP(c_Set_Oinsert(U_2426),U_2430),U_2432)))
        | ( ~ hBOOL(hAPP(hAPP(c_member(U_2426),U_2428),U_2432))
          & U_2428 != U_2430 ) )
    & ! [U_2431,U_2429,U_2427,U_2425] :
        ( hBOOL(hAPP(hAPP(c_member(U_2425),U_2427),U_2431))
        | U_2427 = U_2429
        | ~ hBOOL(hAPP(hAPP(c_member(U_2425),U_2427),hAPP(hAPP(c_Set_Oinsert(U_2425),U_2429),U_2431))) ) ),
    inference(miniscope,[status(thm)],[f_648_2]) ).

cnf(f_648_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2425),U_2427),U_2431))
    | U_2427 = U_2429
    | ~ hBOOL(hAPP(hAPP(c_member(U_2425),U_2427),hAPP(hAPP(c_Set_Oinsert(U_2425),U_2429),U_2431))) ),
    inference(clausify,[status(thm)],[f_648_3]) ).

cnf(f_648_5,plain,
    ( U_2428 != U_2430
    | hBOOL(hAPP(hAPP(c_member(U_2426),U_2428),hAPP(hAPP(c_Set_Oinsert(U_2426),U_2430),U_2432))) ),
    inference(clausify,[status(thm)],[f_648_3]) ).

cnf(f_648_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_2426),U_2428),U_2432))
    | hBOOL(hAPP(hAPP(c_member(U_2426),U_2428),hAPP(hAPP(c_Set_Oinsert(U_2426),U_2430),U_2432))) ),
    inference(clausify,[status(thm)],[f_648_3]) ).

fof(f_649_1,plain,
    ! [V_B_2,V_A_2,V_x_2,T_b] :
      ( ( ( hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2)
          | V_A_2 != V_B_2 )
        & ( V_A_2 = V_B_2
          | hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2) != hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2) ) )
      | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
      | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_insert__ident]) ).

fof(f_649_2,plain,
    ! [U_2436,U_2435,U_2434,U_2433] :
      ( ( ( hAPP(hAPP(c_Set_Oinsert(U_2433),U_2434),U_2435) = hAPP(hAPP(c_Set_Oinsert(U_2433),U_2434),U_2436)
          | U_2435 != U_2436 )
        & ( U_2435 = U_2436
          | hAPP(hAPP(c_Set_Oinsert(U_2433),U_2434),U_2435) != hAPP(hAPP(c_Set_Oinsert(U_2433),U_2434),U_2436) ) )
      | hBOOL(hAPP(hAPP(c_member(U_2433),U_2434),U_2436))
      | hBOOL(hAPP(hAPP(c_member(U_2433),U_2434),U_2435)) ),
    inference(variable_rename,[status(thm)],[f_649_1]) ).

cnf(f_649_3,plain,
    ( U_2435 = U_2436
    | hAPP(hAPP(c_Set_Oinsert(U_2433),U_2434),U_2435) != hAPP(hAPP(c_Set_Oinsert(U_2433),U_2434),U_2436)
    | hBOOL(hAPP(hAPP(c_member(U_2433),U_2434),U_2436))
    | hBOOL(hAPP(hAPP(c_member(U_2433),U_2434),U_2435)) ),
    inference(clausify,[status(thm)],[f_649_2]) ).

cnf(f_649_4,plain,
    ( hAPP(hAPP(c_Set_Oinsert(U_2433),U_2434),U_2435) = hAPP(hAPP(c_Set_Oinsert(U_2433),U_2434),U_2436)
    | U_2435 != U_2436
    | hBOOL(hAPP(hAPP(c_member(U_2433),U_2434),U_2436))
    | hBOOL(hAPP(hAPP(c_member(U_2433),U_2434),U_2435)) ),
    inference(clausify,[status(thm)],[f_649_2]) ).

fof(f_650_1,plain,
    ! [V_b_2,V_B_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_insertI2]) ).

fof(f_650_2,plain,
    ! [U_2440,U_2439,U_2438,U_2437] :
      ( hBOOL(hAPP(hAPP(c_member(U_2437),U_2438),hAPP(hAPP(c_Set_Oinsert(U_2437),U_2440),U_2439)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2437),U_2438),U_2439)) ),
    inference(variable_rename,[status(thm)],[f_650_1]) ).

cnf(f_650_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2437),U_2438),hAPP(hAPP(c_Set_Oinsert(U_2437),U_2440),U_2439)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2437),U_2438),U_2439)) ),
    inference(clausify,[status(thm)],[f_650_2]) ).

fof(f_651_1,plain,
    ! [V_A_2,V_a_2,T_b] :
      ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) = V_A_2
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_insert__absorb]) ).

fof(f_651_2,plain,
    ! [U_2443,U_2442,U_2441] :
      ( hAPP(hAPP(c_Set_Oinsert(U_2441),U_2442),U_2443) = U_2443
      | ~ hBOOL(hAPP(hAPP(c_member(U_2441),U_2442),U_2443)) ),
    inference(variable_rename,[status(thm)],[f_651_1]) ).

cnf(f_651_3,plain,
    ( hAPP(hAPP(c_Set_Oinsert(U_2441),U_2442),U_2443) = U_2443
    | ~ hBOOL(hAPP(hAPP(c_member(U_2441),U_2442),U_2443)) ),
    inference(clausify,[status(thm)],[f_651_2]) ).

fof(f_652_1,plain,
    ! [V_x_2,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_in__mono]) ).

fof(f_652_2,plain,
    ! [U_2447,U_2446,U_2445,U_2444] :
      ( hBOOL(hAPP(hAPP(c_member(U_2444),U_2447),U_2446))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2444),U_2447),U_2445))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2444,tc_HOL_Obool)),U_2445),U_2446)) ),
    inference(variable_rename,[status(thm)],[f_652_1]) ).

cnf(f_652_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2444),U_2447),U_2446))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2444),U_2447),U_2445))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2444,tc_HOL_Obool)),U_2445),U_2446)) ),
    inference(clausify,[status(thm)],[f_652_2]) ).

fof(f_653_1,plain,
    ! [V_B_2,V_A_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_set__rev__mp]) ).

fof(f_653_2,plain,
    ! [U_2451,U_2450,U_2449,U_2448] :
      ( hBOOL(hAPP(hAPP(c_member(U_2448),U_2449),U_2451))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2448,tc_HOL_Obool)),U_2450),U_2451))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2448),U_2449),U_2450)) ),
    inference(variable_rename,[status(thm)],[f_653_1]) ).

cnf(f_653_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2448),U_2449),U_2451))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2448,tc_HOL_Obool)),U_2450),U_2451))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2448),U_2449),U_2450)) ),
    inference(clausify,[status(thm)],[f_653_2]) ).

fof(f_654_1,plain,
    ! [V_x_2,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_set__mp]) ).

fof(f_654_2,plain,
    ! [U_2455,U_2454,U_2453,U_2452] :
      ( hBOOL(hAPP(hAPP(c_member(U_2452),U_2455),U_2454))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2452),U_2455),U_2453))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2452,tc_HOL_Obool)),U_2453),U_2454)) ),
    inference(variable_rename,[status(thm)],[f_654_1]) ).

cnf(f_654_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2452),U_2455),U_2454))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2452),U_2455),U_2453))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2452,tc_HOL_Obool)),U_2453),U_2454)) ),
    inference(clausify,[status(thm)],[f_654_2]) ).

fof(f_655_1,plain,
    ! [V_A_2,V_f_2,T_c,V_z_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
        | ! [B_x] :
            ( V_z_2 != hAPP(V_f_2,B_x)
            | ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) )
      & ( ? [B_x] :
            ( V_z_2 = hAPP(V_f_2,B_x)
            & hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_image__iff]) ).

fof(f_655_2,plain,
    ! [U_2462,U_2461,U_2460,U_2459,U_2458] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_2458),U_2459),hAPP(c_Set_Oimage(U_2460,U_2458,U_2461),U_2462)))
        | ! [U_2457] :
            ( U_2459 != hAPP(U_2461,U_2457)
            | ~ hBOOL(hAPP(hAPP(c_member(U_2460),U_2457),U_2462)) ) )
      & ( ? [U_2456] :
            ( U_2459 = hAPP(U_2461,U_2456)
            & hBOOL(hAPP(hAPP(c_member(U_2460),U_2456),U_2462)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_2458),U_2459),hAPP(c_Set_Oimage(U_2460,U_2458,U_2461),U_2462))) ) ),
    inference(variable_rename,[status(thm)],[f_655_1]) ).

fof(f_655_3,plain,
    ( ! [U_2472,U_2470,U_2468,U_2466] :
        ( ! [U_2464] : hBOOL(hAPP(hAPP(c_member(U_2464),U_2466),hAPP(c_Set_Oimage(U_2468,U_2464,U_2470),U_2472)))
        | ! [U_2457] :
            ( U_2466 != hAPP(U_2470,U_2457)
            | ~ hBOOL(hAPP(hAPP(c_member(U_2468),U_2457),U_2472)) ) )
    & ! [U_2471,U_2469,U_2467,U_2465] :
        ( ! [U_2463] : ~ hBOOL(hAPP(hAPP(c_member(U_2463),U_2465),hAPP(c_Set_Oimage(U_2467,U_2463,U_2469),U_2471)))
        | ? [U_2456] :
            ( U_2465 = hAPP(U_2469,U_2456)
            & hBOOL(hAPP(hAPP(c_member(U_2467),U_2456),U_2471)) ) ) ),
    inference(miniscope,[status(thm)],[f_655_2]) ).

fof(f_655_4,plain,
    ( ! [U_2472,U_2470,U_2468,U_2466] :
        ( ! [U_2464] : hBOOL(hAPP(hAPP(c_member(U_2464),U_2466),hAPP(c_Set_Oimage(U_2468,U_2464,U_2470),U_2472)))
        | ! [U_2457] :
            ( U_2466 != hAPP(U_2470,U_2457)
            | ~ hBOOL(hAPP(hAPP(c_member(U_2468),U_2457),U_2472)) ) )
    & ! [U_2471,U_2469,U_2467,U_2465] :
        ( ! [U_2463] : ~ hBOOL(hAPP(hAPP(c_member(U_2463),U_2465),hAPP(c_Set_Oimage(U_2467,U_2463,U_2469),U_2471)))
        | ( U_2465 = hAPP(U_2469,sK34(U_2471,U_2469,U_2467,U_2465))
          & hBOOL(hAPP(hAPP(c_member(U_2467),sK34(U_2471,U_2469,U_2467,U_2465)),U_2471)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK34]),skolemize(U_2456,sK34(U_2471,U_2469,U_2467,U_2465))],[f_655_3]) ).

cnf(f_655_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2467),sK34(U_2471,U_2469,U_2467,U_2465)),U_2471))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2463),U_2465),hAPP(c_Set_Oimage(U_2467,U_2463,U_2469),U_2471))) ),
    inference(clausify,[status(thm)],[f_655_4]) ).

cnf(f_655_6,plain,
    ( U_2465 = hAPP(U_2469,sK34(U_2471,U_2469,U_2467,U_2465))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2463),U_2465),hAPP(c_Set_Oimage(U_2467,U_2463,U_2469),U_2471))) ),
    inference(clausify,[status(thm)],[f_655_4]) ).

cnf(f_655_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2464),U_2466),hAPP(c_Set_Oimage(U_2468,U_2464,U_2470),U_2472)))
    | U_2466 != hAPP(U_2470,U_2457)
    | ~ hBOOL(hAPP(hAPP(c_member(U_2468),U_2457),U_2472)) ),
    inference(clausify,[status(thm)],[f_655_4]) ).

fof(f_656_1,plain,
    ! [V_f_2,T_c,V_A_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_imageI]) ).

fof(f_656_2,plain,
    ! [U_2477,U_2476,U_2475,U_2474,U_2473] :
      ( hBOOL(hAPP(hAPP(c_member(U_2476),hAPP(U_2477,U_2474)),hAPP(c_Set_Oimage(U_2473,U_2476,U_2477),U_2475)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2473),U_2474),U_2475)) ),
    inference(variable_rename,[status(thm)],[f_656_1]) ).

cnf(f_656_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2476),hAPP(U_2477,U_2474)),hAPP(c_Set_Oimage(U_2473,U_2476,U_2477),U_2475)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2473),U_2474),U_2475)) ),
    inference(clausify,[status(thm)],[f_656_2]) ).

fof(f_657_1,plain,
    ! [T_c,V_f_2,V_b_2,V_A_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
      | V_b_2 != hAPP(V_f_2,V_x_2)
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_rev__image__eqI]) ).

fof(f_657_2,plain,
    ! [U_2483,U_2482,U_2481,U_2480,U_2479,U_2478] :
      ( hBOOL(hAPP(hAPP(c_member(U_2483),U_2481),hAPP(c_Set_Oimage(U_2478,U_2483,U_2482),U_2480)))
      | U_2481 != hAPP(U_2482,U_2479)
      | ~ hBOOL(hAPP(hAPP(c_member(U_2478),U_2479),U_2480)) ),
    inference(variable_rename,[status(thm)],[f_657_1]) ).

cnf(f_657_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2483),U_2481),hAPP(c_Set_Oimage(U_2478,U_2483,U_2482),U_2480)))
    | U_2481 != hAPP(U_2482,U_2479)
    | ~ hBOOL(hAPP(hAPP(c_member(U_2478),U_2479),U_2480)) ),
    inference(clausify,[status(thm)],[f_657_2]) ).

fof(f_658_1,plain,
    ! [V_B_2,V_A_2,V_c_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
        | ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
          & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) )
      & ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
        | hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_Un__iff]) ).

fof(f_658_2,plain,
    ! [U_2487,U_2486,U_2485,U_2484] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_2484),U_2485),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2484,tc_HOL_Obool)),U_2486),U_2487)))
        | ( ~ hBOOL(hAPP(hAPP(c_member(U_2484),U_2485),U_2487))
          & ~ hBOOL(hAPP(hAPP(c_member(U_2484),U_2485),U_2486)) ) )
      & ( hBOOL(hAPP(hAPP(c_member(U_2484),U_2485),U_2487))
        | hBOOL(hAPP(hAPP(c_member(U_2484),U_2485),U_2486))
        | ~ hBOOL(hAPP(hAPP(c_member(U_2484),U_2485),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2484,tc_HOL_Obool)),U_2486),U_2487))) ) ),
    inference(variable_rename,[status(thm)],[f_658_1]) ).

fof(f_658_3,plain,
    ( ! [U_2495,U_2493,U_2491,U_2489] :
        ( hBOOL(hAPP(hAPP(c_member(U_2489),U_2491),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2489,tc_HOL_Obool)),U_2493),U_2495)))
        | ( ~ hBOOL(hAPP(hAPP(c_member(U_2489),U_2491),U_2495))
          & ~ hBOOL(hAPP(hAPP(c_member(U_2489),U_2491),U_2493)) ) )
    & ! [U_2494,U_2492,U_2490,U_2488] :
        ( hBOOL(hAPP(hAPP(c_member(U_2488),U_2490),U_2494))
        | hBOOL(hAPP(hAPP(c_member(U_2488),U_2490),U_2492))
        | ~ hBOOL(hAPP(hAPP(c_member(U_2488),U_2490),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2488,tc_HOL_Obool)),U_2492),U_2494))) ) ),
    inference(miniscope,[status(thm)],[f_658_2]) ).

cnf(f_658_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2488),U_2490),U_2494))
    | hBOOL(hAPP(hAPP(c_member(U_2488),U_2490),U_2492))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2488),U_2490),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2488,tc_HOL_Obool)),U_2492),U_2494))) ),
    inference(clausify,[status(thm)],[f_658_3]) ).

cnf(f_658_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_2489),U_2491),U_2493))
    | hBOOL(hAPP(hAPP(c_member(U_2489),U_2491),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2489,tc_HOL_Obool)),U_2493),U_2495))) ),
    inference(clausify,[status(thm)],[f_658_3]) ).

cnf(f_658_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_2489),U_2491),U_2495))
    | hBOOL(hAPP(hAPP(c_member(U_2489),U_2491),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2489,tc_HOL_Obool)),U_2493),U_2495))) ),
    inference(clausify,[status(thm)],[f_658_3]) ).

fof(f_659_1,plain,
    ! [V_B_2,V_A_2,V_c_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_UnI1]) ).

fof(f_659_2,plain,
    ! [U_2499,U_2498,U_2497,U_2496] :
      ( hBOOL(hAPP(hAPP(c_member(U_2496),U_2497),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2496,tc_HOL_Obool)),U_2498),U_2499)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2496),U_2497),U_2498)) ),
    inference(variable_rename,[status(thm)],[f_659_1]) ).

cnf(f_659_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2496),U_2497),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2496,tc_HOL_Obool)),U_2498),U_2499)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2496),U_2497),U_2498)) ),
    inference(clausify,[status(thm)],[f_659_2]) ).

fof(f_660_1,plain,
    ! [V_A_2,V_B_2,V_c_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_UnI2]) ).

fof(f_660_2,plain,
    ! [U_2503,U_2502,U_2501,U_2500] :
      ( hBOOL(hAPP(hAPP(c_member(U_2500),U_2501),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2500,tc_HOL_Obool)),U_2503),U_2502)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2500),U_2501),U_2502)) ),
    inference(variable_rename,[status(thm)],[f_660_1]) ).

cnf(f_660_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2500),U_2501),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2500,tc_HOL_Obool)),U_2503),U_2502)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2500),U_2501),U_2502)) ),
    inference(clausify,[status(thm)],[f_660_2]) ).

fof(f_661_1,plain,
    ! [V_B_2,V_A_2,V_c_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) )
      & ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
          & hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) )
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_Int__iff]) ).

fof(f_661_2,plain,
    ! [U_2507,U_2506,U_2505,U_2504] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_2504),U_2505),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2504,tc_HOL_Obool)),U_2506),U_2507)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_2504),U_2505),U_2507))
        | ~ hBOOL(hAPP(hAPP(c_member(U_2504),U_2505),U_2506)) )
      & ( ( hBOOL(hAPP(hAPP(c_member(U_2504),U_2505),U_2507))
          & hBOOL(hAPP(hAPP(c_member(U_2504),U_2505),U_2506)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_2504),U_2505),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2504,tc_HOL_Obool)),U_2506),U_2507))) ) ),
    inference(variable_rename,[status(thm)],[f_661_1]) ).

fof(f_661_3,plain,
    ( ! [U_2515,U_2513,U_2511,U_2509] :
        ( hBOOL(hAPP(hAPP(c_member(U_2509),U_2511),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2509,tc_HOL_Obool)),U_2513),U_2515)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_2509),U_2511),U_2515))
        | ~ hBOOL(hAPP(hAPP(c_member(U_2509),U_2511),U_2513)) )
    & ! [U_2514,U_2512,U_2510,U_2508] :
        ( ( hBOOL(hAPP(hAPP(c_member(U_2508),U_2510),U_2514))
          & hBOOL(hAPP(hAPP(c_member(U_2508),U_2510),U_2512)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_2508),U_2510),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2508,tc_HOL_Obool)),U_2512),U_2514))) ) ),
    inference(miniscope,[status(thm)],[f_661_2]) ).

cnf(f_661_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2508),U_2510),U_2512))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2508),U_2510),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2508,tc_HOL_Obool)),U_2512),U_2514))) ),
    inference(clausify,[status(thm)],[f_661_3]) ).

cnf(f_661_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2508),U_2510),U_2514))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2508),U_2510),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2508,tc_HOL_Obool)),U_2512),U_2514))) ),
    inference(clausify,[status(thm)],[f_661_3]) ).

cnf(f_661_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2509),U_2511),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2509,tc_HOL_Obool)),U_2513),U_2515)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2509),U_2511),U_2515))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2509),U_2511),U_2513)) ),
    inference(clausify,[status(thm)],[f_661_3]) ).

fof(f_662_1,plain,
    ! [V_B_2,V_A_2,V_c_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ),
    inference(fof_nnf,[status(thm)],[fact_IntD1]) ).

fof(f_662_2,plain,
    ! [U_2519,U_2518,U_2517,U_2516] :
      ( hBOOL(hAPP(hAPP(c_member(U_2516),U_2517),U_2518))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2516),U_2517),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2516,tc_HOL_Obool)),U_2518),U_2519))) ),
    inference(variable_rename,[status(thm)],[f_662_1]) ).

cnf(f_662_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2516),U_2517),U_2518))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2516),U_2517),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2516,tc_HOL_Obool)),U_2518),U_2519))) ),
    inference(clausify,[status(thm)],[f_662_2]) ).

fof(f_663_1,plain,
    ! [V_B_2,V_A_2,V_c_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ),
    inference(fof_nnf,[status(thm)],[fact_IntD2]) ).

fof(f_663_2,plain,
    ! [U_2523,U_2522,U_2521,U_2520] :
      ( hBOOL(hAPP(hAPP(c_member(U_2520),U_2521),U_2523))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2520),U_2521),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2520,tc_HOL_Obool)),U_2522),U_2523))) ),
    inference(variable_rename,[status(thm)],[f_663_1]) ).

cnf(f_663_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2520),U_2521),U_2523))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2520),U_2521),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2520,tc_HOL_Obool)),U_2522),U_2523))) ),
    inference(clausify,[status(thm)],[f_663_2]) ).

fof(f_664_1,plain,
    ! [V_B_2,V_A_2,V_c_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
        | hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) )
      & ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
          & hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) )
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_Diff__iff]) ).

fof(f_664_2,plain,
    ! [U_2527,U_2526,U_2525,U_2524] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_2524),U_2525),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2524,tc_HOL_Obool)),U_2526),U_2527)))
        | hBOOL(hAPP(hAPP(c_member(U_2524),U_2525),U_2527))
        | ~ hBOOL(hAPP(hAPP(c_member(U_2524),U_2525),U_2526)) )
      & ( ( ~ hBOOL(hAPP(hAPP(c_member(U_2524),U_2525),U_2527))
          & hBOOL(hAPP(hAPP(c_member(U_2524),U_2525),U_2526)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_2524),U_2525),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2524,tc_HOL_Obool)),U_2526),U_2527))) ) ),
    inference(variable_rename,[status(thm)],[f_664_1]) ).

fof(f_664_3,plain,
    ( ! [U_2535,U_2533,U_2531,U_2529] :
        ( hBOOL(hAPP(hAPP(c_member(U_2529),U_2531),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2529,tc_HOL_Obool)),U_2533),U_2535)))
        | hBOOL(hAPP(hAPP(c_member(U_2529),U_2531),U_2535))
        | ~ hBOOL(hAPP(hAPP(c_member(U_2529),U_2531),U_2533)) )
    & ! [U_2534,U_2532,U_2530,U_2528] :
        ( ( ~ hBOOL(hAPP(hAPP(c_member(U_2528),U_2530),U_2534))
          & hBOOL(hAPP(hAPP(c_member(U_2528),U_2530),U_2532)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_2528),U_2530),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2528,tc_HOL_Obool)),U_2532),U_2534))) ) ),
    inference(miniscope,[status(thm)],[f_664_2]) ).

cnf(f_664_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2528),U_2530),U_2532))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2528),U_2530),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2528,tc_HOL_Obool)),U_2532),U_2534))) ),
    inference(clausify,[status(thm)],[f_664_3]) ).

cnf(f_664_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_2528),U_2530),U_2534))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2528),U_2530),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2528,tc_HOL_Obool)),U_2532),U_2534))) ),
    inference(clausify,[status(thm)],[f_664_3]) ).

cnf(f_664_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2529),U_2531),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2529,tc_HOL_Obool)),U_2533),U_2535)))
    | hBOOL(hAPP(hAPP(c_member(U_2529),U_2531),U_2535))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2529),U_2531),U_2533)) ),
    inference(clausify,[status(thm)],[f_664_3]) ).

fof(f_665_1,plain,
    ! [V_B_2,V_A_2,V_c_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ),
    inference(fof_nnf,[status(thm)],[fact_DiffD1]) ).

fof(f_665_2,plain,
    ! [U_2539,U_2538,U_2537,U_2536] :
      ( hBOOL(hAPP(hAPP(c_member(U_2536),U_2537),U_2538))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2536),U_2537),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2536,tc_HOL_Obool)),U_2538),U_2539))) ),
    inference(variable_rename,[status(thm)],[f_665_1]) ).

cnf(f_665_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2536),U_2537),U_2538))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2536),U_2537),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2536,tc_HOL_Obool)),U_2538),U_2539))) ),
    inference(clausify,[status(thm)],[f_665_2]) ).

fof(f_666_1,plain,
    ! [V_B_2,V_A_2,V_c_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ),
    inference(fof_nnf,[status(thm)],[fact_DiffD2]) ).

fof(f_666_2,plain,
    ! [U_2543,U_2542,U_2541,U_2540] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_2540),U_2541),U_2543))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2540),U_2541),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2540,tc_HOL_Obool)),U_2542),U_2543))) ),
    inference(variable_rename,[status(thm)],[f_666_1]) ).

cnf(f_666_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_2540),U_2541),U_2543))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2540),U_2541),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2540,tc_HOL_Obool)),U_2542),U_2543))) ),
    inference(clausify,[status(thm)],[f_666_2]) ).

fof(f_667_1,plain,
    ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
      ( hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2)
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | V_x_2 = V_y_2
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_inj__on__contraD]) ).

fof(f_667_2,plain,
    ! [U_2549,U_2548,U_2547,U_2546,U_2545,U_2544] :
      ( hAPP(U_2546,U_2548) != hAPP(U_2546,U_2549)
      | ~ hBOOL(hAPP(hAPP(c_member(U_2544),U_2549),U_2547))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2544),U_2548),U_2547))
      | U_2548 = U_2549
      | ~ c_Fun_Oinj__on(U_2544,U_2545,U_2546,U_2547) ),
    inference(variable_rename,[status(thm)],[f_667_1]) ).

cnf(f_667_3,plain,
    ( hAPP(U_2546,U_2548) != hAPP(U_2546,U_2549)
    | ~ hBOOL(hAPP(hAPP(c_member(U_2544),U_2549),U_2547))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2544),U_2548),U_2547))
    | U_2548 = U_2549
    | ~ c_Fun_Oinj__on(U_2544,U_2545,U_2546,U_2547) ),
    inference(clausify,[status(thm)],[f_667_2]) ).

fof(f_668_1,plain,
    ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
      ( ( ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
          | V_x_2 != V_y_2 )
        & ( V_x_2 = V_y_2
          | hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_inj__on__iff]) ).

fof(f_668_2,plain,
    ! [U_2555,U_2554,U_2553,U_2552,U_2551,U_2550] :
      ( ( ( hAPP(U_2552,U_2554) = hAPP(U_2552,U_2555)
          | U_2554 != U_2555 )
        & ( U_2554 = U_2555
          | hAPP(U_2552,U_2554) != hAPP(U_2552,U_2555) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_2550),U_2555),U_2553))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2550),U_2554),U_2553))
      | ~ c_Fun_Oinj__on(U_2550,U_2551,U_2552,U_2553) ),
    inference(variable_rename,[status(thm)],[f_668_1]) ).

cnf(f_668_3,plain,
    ( U_2554 = U_2555
    | hAPP(U_2552,U_2554) != hAPP(U_2552,U_2555)
    | ~ hBOOL(hAPP(hAPP(c_member(U_2550),U_2555),U_2553))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2550),U_2554),U_2553))
    | ~ c_Fun_Oinj__on(U_2550,U_2551,U_2552,U_2553) ),
    inference(clausify,[status(thm)],[f_668_2]) ).

cnf(f_668_4,plain,
    ( hAPP(U_2552,U_2554) = hAPP(U_2552,U_2555)
    | U_2554 != U_2555
    | ~ hBOOL(hAPP(hAPP(c_member(U_2550),U_2555),U_2553))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2550),U_2554),U_2553))
    | ~ c_Fun_Oinj__on(U_2550,U_2551,U_2552,U_2553) ),
    inference(clausify,[status(thm)],[f_668_2]) ).

fof(f_669_1,plain,
    ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
      ( V_x_2 = V_y_2
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2)
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_inj__onD]) ).

fof(f_669_2,plain,
    ! [U_2561,U_2560,U_2559,U_2558,U_2557,U_2556] :
      ( U_2560 = U_2561
      | ~ hBOOL(hAPP(hAPP(c_member(U_2556),U_2561),U_2559))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2556),U_2560),U_2559))
      | hAPP(U_2558,U_2560) != hAPP(U_2558,U_2561)
      | ~ c_Fun_Oinj__on(U_2556,U_2557,U_2558,U_2559) ),
    inference(variable_rename,[status(thm)],[f_669_1]) ).

cnf(f_669_3,plain,
    ( U_2560 = U_2561
    | ~ hBOOL(hAPP(hAPP(c_member(U_2556),U_2561),U_2559))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2556),U_2560),U_2559))
    | hAPP(U_2558,U_2560) != hAPP(U_2558,U_2561)
    | ~ c_Fun_Oinj__on(U_2556,U_2557,U_2558,U_2559) ),
    inference(clausify,[status(thm)],[f_669_2]) ).

fof(f_670_1,plain,
    ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
      ( hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,V_A_2))
      | hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
      | ~ c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Oinsert]) ).

fof(f_670_2,plain,
    ! [U_2569,U_2568,U_2567,U_2566,U_2565,U_2564,U_2563,U_2562] :
      ( hAPP(U_2567,hAPP(hAPP(c_Set_Oinsert(U_2563),U_2569),U_2568)) = hAPP(hAPP(U_2564,hAPP(U_2566,U_2569)),hAPP(U_2567,U_2568))
      | hBOOL(hAPP(hAPP(c_member(U_2563),U_2569),U_2568))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2563),U_2568))
      | ~ c_Finite__Set_Ofolding__image__simple(U_2562,U_2563,U_2564,U_2565,U_2566,U_2567) ),
    inference(variable_rename,[status(thm)],[f_670_1]) ).

fof(f_670_3,plain,
    ! [U_2569,U_2568,U_2567,U_2566,U_2565,U_2564,U_2563] :
      ( ! [U_2562] : ~ c_Finite__Set_Ofolding__image__simple(U_2562,U_2563,U_2564,U_2565,U_2566,U_2567)
      | hAPP(U_2567,hAPP(hAPP(c_Set_Oinsert(U_2563),U_2569),U_2568)) = hAPP(hAPP(U_2564,hAPP(U_2566,U_2569)),hAPP(U_2567,U_2568))
      | hBOOL(hAPP(hAPP(c_member(U_2563),U_2569),U_2568))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2563),U_2568)) ),
    inference(miniscope,[status(thm)],[f_670_2]) ).

cnf(f_670_4,plain,
    ( ~ c_Finite__Set_Ofolding__image__simple(U_2562,U_2563,U_2564,U_2565,U_2566,U_2567)
    | hAPP(U_2567,hAPP(hAPP(c_Set_Oinsert(U_2563),U_2569),U_2568)) = hAPP(hAPP(U_2564,hAPP(U_2566,U_2569)),hAPP(U_2567,U_2568))
    | hBOOL(hAPP(hAPP(c_member(U_2563),U_2569),U_2568))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2563),U_2568)) ),
    inference(clausify,[status(thm)],[f_670_3]) ).

fof(f_671_1,plain,
    ! [V_A_2,V_c_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
        | hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_Compl__iff]) ).

fof(f_671_2,plain,
    ! [U_2572,U_2571,U_2570] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_2570),U_2571),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2570,tc_HOL_Obool)),U_2572)))
        | hBOOL(hAPP(hAPP(c_member(U_2570),U_2571),U_2572)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(U_2570),U_2571),U_2572))
        | ~ hBOOL(hAPP(hAPP(c_member(U_2570),U_2571),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2570,tc_HOL_Obool)),U_2572))) ) ),
    inference(variable_rename,[status(thm)],[f_671_1]) ).

fof(f_671_3,plain,
    ( ! [U_2578,U_2576,U_2574] :
        ( hBOOL(hAPP(hAPP(c_member(U_2574),U_2576),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2574,tc_HOL_Obool)),U_2578)))
        | hBOOL(hAPP(hAPP(c_member(U_2574),U_2576),U_2578)) )
    & ! [U_2577,U_2575,U_2573] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_2573),U_2575),U_2577))
        | ~ hBOOL(hAPP(hAPP(c_member(U_2573),U_2575),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2573,tc_HOL_Obool)),U_2577))) ) ),
    inference(miniscope,[status(thm)],[f_671_2]) ).

cnf(f_671_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_2573),U_2575),U_2577))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2573),U_2575),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2573,tc_HOL_Obool)),U_2577))) ),
    inference(clausify,[status(thm)],[f_671_3]) ).

cnf(f_671_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2574),U_2576),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2574,tc_HOL_Obool)),U_2578)))
    | hBOOL(hAPP(hAPP(c_member(U_2574),U_2576),U_2578)) ),
    inference(clausify,[status(thm)],[f_671_3]) ).

fof(f_672_1,plain,
    ! [V_A_2,V_c_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) ),
    inference(fof_nnf,[status(thm)],[fact_ComplD]) ).

fof(f_672_2,plain,
    ! [U_2581,U_2580,U_2579] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_2579),U_2580),U_2581))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2579),U_2580),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2579,tc_HOL_Obool)),U_2581))) ),
    inference(variable_rename,[status(thm)],[f_672_1]) ).

cnf(f_672_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_2579),U_2580),U_2581))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2579),U_2580),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2579,tc_HOL_Obool)),U_2581))) ),
    inference(clausify,[status(thm)],[f_672_2]) ).

fof(f_673_1,plain,
    ! [V_A_2,V_c_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) ),
    inference(fof_nnf,[status(thm)],[fact_ComplE]) ).

fof(f_673_2,plain,
    ! [U_2584,U_2583,U_2582] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_2582),U_2583),U_2584))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2582),U_2583),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2582,tc_HOL_Obool)),U_2584))) ),
    inference(variable_rename,[status(thm)],[f_673_1]) ).

cnf(f_673_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_2582),U_2583),U_2584))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2582),U_2583),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2582,tc_HOL_Obool)),U_2584))) ),
    inference(clausify,[status(thm)],[f_673_2]) ).

fof(f_674_1,plain,
    ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_A_2))),
    inference(fof_nnf,[status(thm)],[fact_Pow__top]) ).

fof(f_674_2,plain,
    ! [U_2586,U_2585] : hBOOL(hAPP(hAPP(c_member(tc_fun(U_2585,tc_HOL_Obool)),U_2586),hAPP(c_Set_OPow(U_2585),U_2586))),
    inference(variable_rename,[status(thm)],[f_674_1]) ).

cnf(f_674_3,plain,
    hBOOL(hAPP(hAPP(c_member(tc_fun(U_2585,tc_HOL_Obool)),U_2586),hAPP(c_Set_OPow(U_2585),U_2586))),
    inference(clausify,[status(thm)],[f_674_2]) ).

fof(f_675_1,plain,
    ! [V_c_2,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_psubsetD]) ).

fof(f_675_2,plain,
    ! [U_2590,U_2589,U_2588,U_2587] :
      ( hBOOL(hAPP(hAPP(c_member(U_2587),U_2590),U_2589))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2587),U_2590),U_2588))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2587,tc_HOL_Obool)),U_2588),U_2589)) ),
    inference(variable_rename,[status(thm)],[f_675_1]) ).

cnf(f_675_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2587),U_2590),U_2589))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2587),U_2590),U_2588))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2587,tc_HOL_Obool)),U_2588),U_2589)) ),
    inference(clausify,[status(thm)],[f_675_2]) ).

fof(f_676_1,plain,
    ! [V_g_2,V_f_2,T_c,V_A_2,V_a_2,T_b] :
      ( hAPP(c_Fun_Ooverride__on(T_b,T_c,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_f_2,V_a_2)
      | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_override__on__apply__notin]) ).

fof(f_676_2,plain,
    ! [U_2596,U_2595,U_2594,U_2593,U_2592,U_2591] :
      ( hAPP(c_Fun_Ooverride__on(U_2591,U_2594,U_2595,U_2596,U_2593),U_2592) = hAPP(U_2595,U_2592)
      | hBOOL(hAPP(hAPP(c_member(U_2591),U_2592),U_2593)) ),
    inference(variable_rename,[status(thm)],[f_676_1]) ).

cnf(f_676_3,plain,
    ( hAPP(c_Fun_Ooverride__on(U_2591,U_2594,U_2595,U_2596,U_2593),U_2592) = hAPP(U_2595,U_2592)
    | hBOOL(hAPP(hAPP(c_member(U_2591),U_2592),U_2593)) ),
    inference(clausify,[status(thm)],[f_676_2]) ).

fof(f_677_1,plain,
    ! [V_g_2,V_f_2,T_c,V_A_2,V_a_2,T_b] :
      ( hAPP(c_Fun_Ooverride__on(T_b,T_c,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_g_2,V_a_2)
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_override__on__apply__in]) ).

fof(f_677_2,plain,
    ! [U_2602,U_2601,U_2600,U_2599,U_2598,U_2597] :
      ( hAPP(c_Fun_Ooverride__on(U_2597,U_2600,U_2601,U_2602,U_2599),U_2598) = hAPP(U_2602,U_2598)
      | ~ hBOOL(hAPP(hAPP(c_member(U_2597),U_2598),U_2599)) ),
    inference(variable_rename,[status(thm)],[f_677_1]) ).

cnf(f_677_3,plain,
    ( hAPP(c_Fun_Ooverride__on(U_2597,U_2600,U_2601,U_2602,U_2599),U_2598) = hAPP(U_2602,U_2598)
    | ~ hBOOL(hAPP(hAPP(c_member(U_2597),U_2598),U_2599)) ),
    inference(clausify,[status(thm)],[f_677_2]) ).

fof(f_678_1,plain,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
      ( hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__one_Oinsert]) ).

fof(f_678_2,plain,
    ! [U_2607,U_2606,U_2605,U_2604,U_2603] :
      ( hAPP(U_2605,hAPP(hAPP(c_Set_Oinsert(U_2603),U_2607),U_2606)) = hAPP(hAPP(U_2604,U_2607),hAPP(U_2605,U_2606))
      | U_2606 = c_Orderings_Obot__class_Obot(tc_fun(U_2603,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(U_2603),U_2607),U_2606))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2603),U_2606))
      | ~ c_Finite__Set_Ofolding__one(U_2603,U_2604,U_2605) ),
    inference(variable_rename,[status(thm)],[f_678_1]) ).

cnf(f_678_3,plain,
    ( hAPP(U_2605,hAPP(hAPP(c_Set_Oinsert(U_2603),U_2607),U_2606)) = hAPP(hAPP(U_2604,U_2607),hAPP(U_2605,U_2606))
    | U_2606 = c_Orderings_Obot__class_Obot(tc_fun(U_2603,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(U_2603),U_2607),U_2606))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2603),U_2606))
    | ~ c_Finite__Set_Ofolding__one(U_2603,U_2604,U_2605) ),
    inference(clausify,[status(thm)],[f_678_2]) ).

fof(f_679_1,plain,
    ! [V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
      ( hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_z_2
      | ~ c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Oempty]) ).

fof(f_679_2,plain,
    ! [U_2613,U_2612,U_2611,U_2610,U_2609,U_2608] :
      ( hAPP(U_2613,c_Orderings_Obot__class_Obot(tc_fun(U_2609,tc_HOL_Obool))) = U_2611
      | ~ c_Finite__Set_Ofolding__image__simple(U_2608,U_2609,U_2610,U_2611,U_2612,U_2613) ),
    inference(variable_rename,[status(thm)],[f_679_1]) ).

fof(f_679_3,plain,
    ! [U_2613,U_2612,U_2611,U_2610,U_2609] :
      ( ! [U_2608] : ~ c_Finite__Set_Ofolding__image__simple(U_2608,U_2609,U_2610,U_2611,U_2612,U_2613)
      | hAPP(U_2613,c_Orderings_Obot__class_Obot(tc_fun(U_2609,tc_HOL_Obool))) = U_2611 ),
    inference(miniscope,[status(thm)],[f_679_2]) ).

cnf(f_679_4,plain,
    ( ~ c_Finite__Set_Ofolding__image__simple(U_2608,U_2609,U_2610,U_2611,U_2612,U_2613)
    | hAPP(U_2613,c_Orderings_Obot__class_Obot(tc_fun(U_2609,tc_HOL_Obool))) = U_2611 ),
    inference(clausify,[status(thm)],[f_679_3]) ).

fof(f_680_1,plain,
    ! [V_a_2,V_b_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))
        | V_b_2 != V_a_2 )
      & ( V_b_2 = V_a_2
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) ) ),
    inference(fof_nnf,[status(thm)],[fact_singleton__iff]) ).

fof(f_680_2,plain,
    ! [U_2616,U_2615,U_2614] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_2614),U_2615),hAPP(hAPP(c_Set_Oinsert(U_2614),U_2616),c_Orderings_Obot__class_Obot(tc_fun(U_2614,tc_HOL_Obool)))))
        | U_2615 != U_2616 )
      & ( U_2615 = U_2616
        | ~ hBOOL(hAPP(hAPP(c_member(U_2614),U_2615),hAPP(hAPP(c_Set_Oinsert(U_2614),U_2616),c_Orderings_Obot__class_Obot(tc_fun(U_2614,tc_HOL_Obool))))) ) ),
    inference(variable_rename,[status(thm)],[f_680_1]) ).

fof(f_680_3,plain,
    ( ! [U_2622,U_2620] :
        ( ! [U_2618] : hBOOL(hAPP(hAPP(c_member(U_2618),U_2620),hAPP(hAPP(c_Set_Oinsert(U_2618),U_2622),c_Orderings_Obot__class_Obot(tc_fun(U_2618,tc_HOL_Obool)))))
        | U_2620 != U_2622 )
    & ! [U_2621,U_2619] :
        ( ! [U_2617] : ~ hBOOL(hAPP(hAPP(c_member(U_2617),U_2619),hAPP(hAPP(c_Set_Oinsert(U_2617),U_2621),c_Orderings_Obot__class_Obot(tc_fun(U_2617,tc_HOL_Obool)))))
        | U_2619 = U_2621 ) ),
    inference(miniscope,[status(thm)],[f_680_2]) ).

cnf(f_680_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_2617),U_2619),hAPP(hAPP(c_Set_Oinsert(U_2617),U_2621),c_Orderings_Obot__class_Obot(tc_fun(U_2617,tc_HOL_Obool)))))
    | U_2619 = U_2621 ),
    inference(clausify,[status(thm)],[f_680_3]) ).

cnf(f_680_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2618),U_2620),hAPP(hAPP(c_Set_Oinsert(U_2618),U_2622),c_Orderings_Obot__class_Obot(tc_fun(U_2618,tc_HOL_Obool)))))
    | U_2620 != U_2622 ),
    inference(clausify,[status(thm)],[f_680_3]) ).

fof(f_681_1,plain,
    ! [V_a_2,V_b_2,T_b] :
      ( V_b_2 = V_a_2
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) ),
    inference(fof_nnf,[status(thm)],[fact_singletonE]) ).

fof(f_681_2,plain,
    ! [U_2625,U_2624,U_2623] :
      ( U_2624 = U_2625
      | ~ hBOOL(hAPP(hAPP(c_member(U_2623),U_2624),hAPP(hAPP(c_Set_Oinsert(U_2623),U_2625),c_Orderings_Obot__class_Obot(tc_fun(U_2623,tc_HOL_Obool))))) ),
    inference(variable_rename,[status(thm)],[f_681_1]) ).

fof(f_681_3,plain,
    ! [U_2625,U_2624] :
      ( ! [U_2623] : ~ hBOOL(hAPP(hAPP(c_member(U_2623),U_2624),hAPP(hAPP(c_Set_Oinsert(U_2623),U_2625),c_Orderings_Obot__class_Obot(tc_fun(U_2623,tc_HOL_Obool)))))
      | U_2624 = U_2625 ),
    inference(miniscope,[status(thm)],[f_681_2]) ).

cnf(f_681_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_2623),U_2624),hAPP(hAPP(c_Set_Oinsert(U_2623),U_2625),c_Orderings_Obot__class_Obot(tc_fun(U_2623,tc_HOL_Obool)))))
    | U_2624 = U_2625 ),
    inference(clausify,[status(thm)],[f_681_3]) ).

fof(f_682_1,plain,
    ! [V_B_2,V_A_2,V_x_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2))) ) )
      | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_subset__insert]) ).

fof(f_682_2,plain,
    ! [U_2629,U_2628,U_2627,U_2626] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2626,tc_HOL_Obool)),U_2628),hAPP(hAPP(c_Set_Oinsert(U_2626),U_2627),U_2629)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2626,tc_HOL_Obool)),U_2628),U_2629)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2626,tc_HOL_Obool)),U_2628),U_2629))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2626,tc_HOL_Obool)),U_2628),hAPP(hAPP(c_Set_Oinsert(U_2626),U_2627),U_2629))) ) )
      | hBOOL(hAPP(hAPP(c_member(U_2626),U_2627),U_2628)) ),
    inference(variable_rename,[status(thm)],[f_682_1]) ).

cnf(f_682_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2626,tc_HOL_Obool)),U_2628),U_2629))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2626,tc_HOL_Obool)),U_2628),hAPP(hAPP(c_Set_Oinsert(U_2626),U_2627),U_2629)))
    | hBOOL(hAPP(hAPP(c_member(U_2626),U_2627),U_2628)) ),
    inference(clausify,[status(thm)],[f_682_2]) ).

cnf(f_682_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2626,tc_HOL_Obool)),U_2628),hAPP(hAPP(c_Set_Oinsert(U_2626),U_2627),U_2629)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2626,tc_HOL_Obool)),U_2628),U_2629))
    | hBOOL(hAPP(hAPP(c_member(U_2626),U_2627),U_2628)) ),
    inference(clausify,[status(thm)],[f_682_2]) ).

fof(f_683_1,plain,
    ! [V_B_2,V_A_2,V_x_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
          & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_insert__subset]) ).

fof(f_683_2,plain,
    ! [U_2633,U_2632,U_2631,U_2630] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2630,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_2630),U_2631),U_2632)),U_2633))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2630,tc_HOL_Obool)),U_2632),U_2633))
        | ~ hBOOL(hAPP(hAPP(c_member(U_2630),U_2631),U_2633)) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2630,tc_HOL_Obool)),U_2632),U_2633))
          & hBOOL(hAPP(hAPP(c_member(U_2630),U_2631),U_2633)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2630,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_2630),U_2631),U_2632)),U_2633)) ) ),
    inference(variable_rename,[status(thm)],[f_683_1]) ).

fof(f_683_3,plain,
    ( ! [U_2641,U_2639,U_2637,U_2635] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2635,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_2635),U_2637),U_2639)),U_2641))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2635,tc_HOL_Obool)),U_2639),U_2641))
        | ~ hBOOL(hAPP(hAPP(c_member(U_2635),U_2637),U_2641)) )
    & ! [U_2640,U_2638,U_2636,U_2634] :
        ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2634,tc_HOL_Obool)),U_2638),U_2640))
          & hBOOL(hAPP(hAPP(c_member(U_2634),U_2636),U_2640)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2634,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_2634),U_2636),U_2638)),U_2640)) ) ),
    inference(miniscope,[status(thm)],[f_683_2]) ).

cnf(f_683_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2634),U_2636),U_2640))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2634,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_2634),U_2636),U_2638)),U_2640)) ),
    inference(clausify,[status(thm)],[f_683_3]) ).

cnf(f_683_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2634,tc_HOL_Obool)),U_2638),U_2640))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2634,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_2634),U_2636),U_2638)),U_2640)) ),
    inference(clausify,[status(thm)],[f_683_3]) ).

cnf(f_683_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2635,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_2635),U_2637),U_2639)),U_2641))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2635,tc_HOL_Obool)),U_2639),U_2641))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2635),U_2637),U_2641)) ),
    inference(clausify,[status(thm)],[f_683_3]) ).

fof(f_684_1,plain,
    ! [V_f_2,T_c,V_A_2,V_x_2,T_b] :
      ( hAPP(hAPP(c_Set_Oinsert(T_c),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_insert__image]) ).

fof(f_684_2,plain,
    ! [U_2646,U_2645,U_2644,U_2643,U_2642] :
      ( hAPP(hAPP(c_Set_Oinsert(U_2645),hAPP(U_2646,U_2643)),hAPP(c_Set_Oimage(U_2642,U_2645,U_2646),U_2644)) = hAPP(c_Set_Oimage(U_2642,U_2645,U_2646),U_2644)
      | ~ hBOOL(hAPP(hAPP(c_member(U_2642),U_2643),U_2644)) ),
    inference(variable_rename,[status(thm)],[f_684_1]) ).

cnf(f_684_3,plain,
    ( hAPP(hAPP(c_Set_Oinsert(U_2645),hAPP(U_2646,U_2643)),hAPP(c_Set_Oimage(U_2642,U_2645,U_2646),U_2644)) = hAPP(c_Set_Oimage(U_2642,U_2645,U_2646),U_2644)
    | ~ hBOOL(hAPP(hAPP(c_member(U_2642),U_2643),U_2644)) ),
    inference(clausify,[status(thm)],[f_684_2]) ).

fof(f_685_1,plain,
    ! [V_B_2,V_A_2,V_a_2,T_b] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)
        | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Int__insert__right]) ).

fof(f_685_2,plain,
    ! [U_2650,U_2649,U_2648,U_2647] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2647,tc_HOL_Obool)),U_2649),hAPP(hAPP(c_Set_Oinsert(U_2647),U_2648),U_2650)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2647,tc_HOL_Obool)),U_2649),U_2650)
        | hBOOL(hAPP(hAPP(c_member(U_2647),U_2648),U_2649)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2647,tc_HOL_Obool)),U_2649),hAPP(hAPP(c_Set_Oinsert(U_2647),U_2648),U_2650)) = hAPP(hAPP(c_Set_Oinsert(U_2647),U_2648),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2647,tc_HOL_Obool)),U_2649),U_2650))
        | ~ hBOOL(hAPP(hAPP(c_member(U_2647),U_2648),U_2649)) ) ),
    inference(variable_rename,[status(thm)],[f_685_1]) ).

fof(f_685_3,plain,
    ( ! [U_2658,U_2656,U_2654,U_2652] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2652,tc_HOL_Obool)),U_2656),hAPP(hAPP(c_Set_Oinsert(U_2652),U_2654),U_2658)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2652,tc_HOL_Obool)),U_2656),U_2658)
        | hBOOL(hAPP(hAPP(c_member(U_2652),U_2654),U_2656)) )
    & ! [U_2657,U_2655,U_2653,U_2651] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2651,tc_HOL_Obool)),U_2655),hAPP(hAPP(c_Set_Oinsert(U_2651),U_2653),U_2657)) = hAPP(hAPP(c_Set_Oinsert(U_2651),U_2653),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2651,tc_HOL_Obool)),U_2655),U_2657))
        | ~ hBOOL(hAPP(hAPP(c_member(U_2651),U_2653),U_2655)) ) ),
    inference(miniscope,[status(thm)],[f_685_2]) ).

cnf(f_685_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2651,tc_HOL_Obool)),U_2655),hAPP(hAPP(c_Set_Oinsert(U_2651),U_2653),U_2657)) = hAPP(hAPP(c_Set_Oinsert(U_2651),U_2653),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2651,tc_HOL_Obool)),U_2655),U_2657))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2651),U_2653),U_2655)) ),
    inference(clausify,[status(thm)],[f_685_3]) ).

cnf(f_685_5,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2652,tc_HOL_Obool)),U_2656),hAPP(hAPP(c_Set_Oinsert(U_2652),U_2654),U_2658)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2652,tc_HOL_Obool)),U_2656),U_2658)
    | hBOOL(hAPP(hAPP(c_member(U_2652),U_2654),U_2656)) ),
    inference(clausify,[status(thm)],[f_685_3]) ).

fof(f_686_1,plain,
    ! [V_B_2,V_C_2,V_a_2,T_b] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)
        | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Int__insert__left]) ).

fof(f_686_2,plain,
    ! [U_2662,U_2661,U_2660,U_2659] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2659,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_2659),U_2660),U_2662)),U_2661) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2659,tc_HOL_Obool)),U_2662),U_2661)
        | hBOOL(hAPP(hAPP(c_member(U_2659),U_2660),U_2661)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2659,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_2659),U_2660),U_2662)),U_2661) = hAPP(hAPP(c_Set_Oinsert(U_2659),U_2660),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2659,tc_HOL_Obool)),U_2662),U_2661))
        | ~ hBOOL(hAPP(hAPP(c_member(U_2659),U_2660),U_2661)) ) ),
    inference(variable_rename,[status(thm)],[f_686_1]) ).

fof(f_686_3,plain,
    ( ! [U_2670,U_2668,U_2666,U_2664] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2664,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_2664),U_2666),U_2670)),U_2668) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2664,tc_HOL_Obool)),U_2670),U_2668)
        | hBOOL(hAPP(hAPP(c_member(U_2664),U_2666),U_2668)) )
    & ! [U_2669,U_2667,U_2665,U_2663] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2663,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_2663),U_2665),U_2669)),U_2667) = hAPP(hAPP(c_Set_Oinsert(U_2663),U_2665),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2663,tc_HOL_Obool)),U_2669),U_2667))
        | ~ hBOOL(hAPP(hAPP(c_member(U_2663),U_2665),U_2667)) ) ),
    inference(miniscope,[status(thm)],[f_686_2]) ).

cnf(f_686_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2663,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_2663),U_2665),U_2669)),U_2667) = hAPP(hAPP(c_Set_Oinsert(U_2663),U_2665),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2663,tc_HOL_Obool)),U_2669),U_2667))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2663),U_2665),U_2667)) ),
    inference(clausify,[status(thm)],[f_686_3]) ).

cnf(f_686_5,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2664,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_2664),U_2666),U_2670)),U_2668) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2664,tc_HOL_Obool)),U_2670),U_2668)
    | hBOOL(hAPP(hAPP(c_member(U_2664),U_2666),U_2668)) ),
    inference(clausify,[status(thm)],[f_686_3]) ).

fof(f_687_1,plain,
    ! [V_B_2,V_A_2,V_a_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)
      | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Int__insert__right__if0]) ).

fof(f_687_2,plain,
    ! [U_2674,U_2673,U_2672,U_2671] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2671,tc_HOL_Obool)),U_2673),hAPP(hAPP(c_Set_Oinsert(U_2671),U_2672),U_2674)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2671,tc_HOL_Obool)),U_2673),U_2674)
      | hBOOL(hAPP(hAPP(c_member(U_2671),U_2672),U_2673)) ),
    inference(variable_rename,[status(thm)],[f_687_1]) ).

cnf(f_687_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2671,tc_HOL_Obool)),U_2673),hAPP(hAPP(c_Set_Oinsert(U_2671),U_2672),U_2674)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2671,tc_HOL_Obool)),U_2673),U_2674)
    | hBOOL(hAPP(hAPP(c_member(U_2671),U_2672),U_2673)) ),
    inference(clausify,[status(thm)],[f_687_2]) ).

fof(f_688_1,plain,
    ! [V_B_2,V_C_2,V_a_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)
      | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Int__insert__left__if0]) ).

fof(f_688_2,plain,
    ! [U_2678,U_2677,U_2676,U_2675] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2675,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_2675),U_2676),U_2678)),U_2677) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2675,tc_HOL_Obool)),U_2678),U_2677)
      | hBOOL(hAPP(hAPP(c_member(U_2675),U_2676),U_2677)) ),
    inference(variable_rename,[status(thm)],[f_688_1]) ).

cnf(f_688_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2675,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_2675),U_2676),U_2678)),U_2677) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2675,tc_HOL_Obool)),U_2678),U_2677)
    | hBOOL(hAPP(hAPP(c_member(U_2675),U_2676),U_2677)) ),
    inference(clausify,[status(thm)],[f_688_2]) ).

fof(f_689_1,plain,
    ! [V_B_2,V_A_2,V_a_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Int__insert__right__if1]) ).

fof(f_689_2,plain,
    ! [U_2682,U_2681,U_2680,U_2679] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2679,tc_HOL_Obool)),U_2681),hAPP(hAPP(c_Set_Oinsert(U_2679),U_2680),U_2682)) = hAPP(hAPP(c_Set_Oinsert(U_2679),U_2680),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2679,tc_HOL_Obool)),U_2681),U_2682))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2679),U_2680),U_2681)) ),
    inference(variable_rename,[status(thm)],[f_689_1]) ).

cnf(f_689_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2679,tc_HOL_Obool)),U_2681),hAPP(hAPP(c_Set_Oinsert(U_2679),U_2680),U_2682)) = hAPP(hAPP(c_Set_Oinsert(U_2679),U_2680),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2679,tc_HOL_Obool)),U_2681),U_2682))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2679),U_2680),U_2681)) ),
    inference(clausify,[status(thm)],[f_689_2]) ).

fof(f_690_1,plain,
    ! [V_B_2,V_C_2,V_a_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Int__insert__left__if1]) ).

fof(f_690_2,plain,
    ! [U_2686,U_2685,U_2684,U_2683] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2683,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_2683),U_2684),U_2686)),U_2685) = hAPP(hAPP(c_Set_Oinsert(U_2683),U_2684),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2683,tc_HOL_Obool)),U_2686),U_2685))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2683),U_2684),U_2685)) ),
    inference(variable_rename,[status(thm)],[f_690_1]) ).

cnf(f_690_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2683,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_2683),U_2684),U_2686)),U_2685) = hAPP(hAPP(c_Set_Oinsert(U_2683),U_2684),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2683,tc_HOL_Obool)),U_2686),U_2685))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2683),U_2684),U_2685)) ),
    inference(clausify,[status(thm)],[f_690_2]) ).

fof(f_691_1,plain,
    ! [T_c,T_b,V_x_2,V_f_2,V_b_2] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))))
      | V_b_2 != hAPP(V_f_2,V_x_2) ),
    inference(fof_nnf,[status(thm)],[fact_range__eqI]) ).

fof(f_691_2,plain,
    ! [U_2691,U_2690,U_2689,U_2688,U_2687] :
      ( hBOOL(hAPP(hAPP(c_member(U_2690),U_2687),hAPP(c_Set_Oimage(U_2691,U_2690,U_2688),c_Orderings_Otop__class_Otop(tc_fun(U_2691,tc_HOL_Obool)))))
      | U_2687 != hAPP(U_2688,U_2689) ),
    inference(variable_rename,[status(thm)],[f_691_1]) ).

cnf(f_691_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2690),U_2687),hAPP(c_Set_Oimage(U_2691,U_2690,U_2688),c_Orderings_Otop__class_Otop(tc_fun(U_2691,tc_HOL_Obool)))))
    | U_2687 != hAPP(U_2688,U_2689) ),
    inference(clausify,[status(thm)],[f_691_2]) ).

fof(f_692_1,plain,
    ! [T_c,V_x_2,V_f_2,T_b] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))),
    inference(fof_nnf,[status(thm)],[fact_rangeI]) ).

fof(f_692_2,plain,
    ! [U_2695,U_2694,U_2693,U_2692] : hBOOL(hAPP(hAPP(c_member(U_2692),hAPP(U_2693,U_2694)),hAPP(c_Set_Oimage(U_2695,U_2692,U_2693),c_Orderings_Otop__class_Otop(tc_fun(U_2695,tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_692_1]) ).

cnf(f_692_3,plain,
    hBOOL(hAPP(hAPP(c_member(U_2692),hAPP(U_2693,U_2694)),hAPP(c_Set_Oimage(U_2695,U_2692,U_2693),c_Orderings_Otop__class_Otop(tc_fun(U_2695,tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_692_2]) ).

fof(f_693_1,plain,
    ! [V_A_2,V_B_2,V_x_2,T_b] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_insert__Diff1]) ).

fof(f_693_2,plain,
    ! [U_2699,U_2698,U_2697,U_2696] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2696,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_2696),U_2697),U_2699)),U_2698) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2696,tc_HOL_Obool)),U_2699),U_2698)
      | ~ hBOOL(hAPP(hAPP(c_member(U_2696),U_2697),U_2698)) ),
    inference(variable_rename,[status(thm)],[f_693_1]) ).

cnf(f_693_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2696,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_2696),U_2697),U_2699)),U_2698) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2696,tc_HOL_Obool)),U_2699),U_2698)
    | ~ hBOOL(hAPP(hAPP(c_member(U_2696),U_2697),U_2698)) ),
    inference(clausify,[status(thm)],[f_693_2]) ).

fof(f_694_1,plain,
    ! [V_A_2,V_B_2,V_x_2,T_b] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
        | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_insert__Diff__if]) ).

fof(f_694_2,plain,
    ! [U_2703,U_2702,U_2701,U_2700] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2700,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_2700),U_2701),U_2703)),U_2702) = hAPP(hAPP(c_Set_Oinsert(U_2700),U_2701),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2700,tc_HOL_Obool)),U_2703),U_2702))
        | hBOOL(hAPP(hAPP(c_member(U_2700),U_2701),U_2702)) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2700,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_2700),U_2701),U_2703)),U_2702) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2700,tc_HOL_Obool)),U_2703),U_2702)
        | ~ hBOOL(hAPP(hAPP(c_member(U_2700),U_2701),U_2702)) ) ),
    inference(variable_rename,[status(thm)],[f_694_1]) ).

fof(f_694_3,plain,
    ( ! [U_2711,U_2709,U_2707,U_2705] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2705,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_2705),U_2707),U_2711)),U_2709) = hAPP(hAPP(c_Set_Oinsert(U_2705),U_2707),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2705,tc_HOL_Obool)),U_2711),U_2709))
        | hBOOL(hAPP(hAPP(c_member(U_2705),U_2707),U_2709)) )
    & ! [U_2710,U_2708,U_2706,U_2704] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2704,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_2704),U_2706),U_2710)),U_2708) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2704,tc_HOL_Obool)),U_2710),U_2708)
        | ~ hBOOL(hAPP(hAPP(c_member(U_2704),U_2706),U_2708)) ) ),
    inference(miniscope,[status(thm)],[f_694_2]) ).

cnf(f_694_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2704,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_2704),U_2706),U_2710)),U_2708) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2704,tc_HOL_Obool)),U_2710),U_2708)
    | ~ hBOOL(hAPP(hAPP(c_member(U_2704),U_2706),U_2708)) ),
    inference(clausify,[status(thm)],[f_694_3]) ).

cnf(f_694_5,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2705,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_2705),U_2707),U_2711)),U_2709) = hAPP(hAPP(c_Set_Oinsert(U_2705),U_2707),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2705,tc_HOL_Obool)),U_2711),U_2709))
    | hBOOL(hAPP(hAPP(c_member(U_2705),U_2707),U_2709)) ),
    inference(clausify,[status(thm)],[f_694_3]) ).

fof(f_695_1,plain,
    ! [V_A_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__upper]) ).

fof(f_695_2,plain,
    ! [U_2714,U_2713,U_2712] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2712),U_2713),c_Complete__Lattice_OSup__class_OSup(U_2712,U_2714)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2712),U_2713),U_2714))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_2712) ),
    inference(variable_rename,[status(thm)],[f_695_1]) ).

cnf(f_695_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2712),U_2713),c_Complete__Lattice_OSup__class_OSup(U_2712,U_2714)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2712),U_2713),U_2714))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_2712) ),
    inference(clausify,[status(thm)],[f_695_2]) ).

fof(f_696_1,plain,
    ! [V_A_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2)),V_x_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__lower]) ).

fof(f_696_2,plain,
    ! [U_2717,U_2716,U_2715] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2715),c_Complete__Lattice_OInf__class_OInf(U_2715,U_2717)),U_2716))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2715),U_2716),U_2717))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_2715) ),
    inference(variable_rename,[status(thm)],[f_696_1]) ).

cnf(f_696_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2715),c_Complete__Lattice_OInf__class_OInf(U_2715,U_2717)),U_2716))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2715),U_2716),U_2717))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_2715) ),
    inference(clausify,[status(thm)],[f_696_2]) ).

fof(f_697_1,plain,
    ! [V_k_2,V_i_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_i_2),V_k_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_i_2),V_k_2))
          | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2))) ) )
      | ~ class_Orderings_Oord(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_lessThan__iff]) ).

fof(f_697_2,plain,
    ! [U_2720,U_2719,U_2718] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(U_2718),U_2719),hAPP(c_SetInterval_Oord__class_OlessThan(U_2718),U_2720)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2718),U_2719),U_2720)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2718),U_2719),U_2720))
          | ~ hBOOL(hAPP(hAPP(c_member(U_2718),U_2719),hAPP(c_SetInterval_Oord__class_OlessThan(U_2718),U_2720))) ) )
      | ~ class_Orderings_Oord(U_2718) ),
    inference(variable_rename,[status(thm)],[f_697_1]) ).

cnf(f_697_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2718),U_2719),U_2720))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2718),U_2719),hAPP(c_SetInterval_Oord__class_OlessThan(U_2718),U_2720)))
    | ~ class_Orderings_Oord(U_2718) ),
    inference(clausify,[status(thm)],[f_697_2]) ).

cnf(f_697_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2718),U_2719),hAPP(c_SetInterval_Oord__class_OlessThan(U_2718),U_2720)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2718),U_2719),U_2720))
    | ~ class_Orderings_Oord(U_2718) ),
    inference(clausify,[status(thm)],[f_697_2]) ).

fof(f_698_1,plain,
    ! [V_k_2,V_i_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_k_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_k_2))
          | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2))) ) )
      | ~ class_Orderings_Oord(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_atMost__iff]) ).

fof(f_698_2,plain,
    ! [U_2723,U_2722,U_2721] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(U_2721),U_2722),hAPP(c_SetInterval_Oord__class_OatMost(U_2721),U_2723)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2721),U_2722),U_2723)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2721),U_2722),U_2723))
          | ~ hBOOL(hAPP(hAPP(c_member(U_2721),U_2722),hAPP(c_SetInterval_Oord__class_OatMost(U_2721),U_2723))) ) )
      | ~ class_Orderings_Oord(U_2721) ),
    inference(variable_rename,[status(thm)],[f_698_1]) ).

cnf(f_698_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2721),U_2722),U_2723))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2721),U_2722),hAPP(c_SetInterval_Oord__class_OatMost(U_2721),U_2723)))
    | ~ class_Orderings_Oord(U_2721) ),
    inference(clausify,[status(thm)],[f_698_2]) ).

cnf(f_698_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2721),U_2722),hAPP(c_SetInterval_Oord__class_OatMost(U_2721),U_2723)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2721),U_2722),U_2723))
    | ~ class_Orderings_Oord(U_2721) ),
    inference(clausify,[status(thm)],[f_698_2]) ).

fof(f_699_1,plain,
    ! [V_A_2,V_B_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Union__upper]) ).

fof(f_699_2,plain,
    ! [U_2726,U_2725,U_2724] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2724,tc_HOL_Obool)),U_2725),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2724,tc_HOL_Obool),U_2726)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_2724,tc_HOL_Obool)),U_2725),U_2726)) ),
    inference(variable_rename,[status(thm)],[f_699_1]) ).

cnf(f_699_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2724,tc_HOL_Obool)),U_2725),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2724,tc_HOL_Obool),U_2726)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_2724,tc_HOL_Obool)),U_2725),U_2726)) ),
    inference(clausify,[status(thm)],[f_699_2]) ).

fof(f_700_1,plain,
    ! [V_B_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),hAPP(c_Set_OPow(T_b),V_B_2))),
    inference(fof_nnf,[status(thm)],[fact_Pow__bottom]) ).

fof(f_700_2,plain,
    ! [U_2728,U_2727] : hBOOL(hAPP(hAPP(c_member(tc_fun(U_2727,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_2727,tc_HOL_Obool))),hAPP(c_Set_OPow(U_2727),U_2728))),
    inference(variable_rename,[status(thm)],[f_700_1]) ).

cnf(f_700_3,plain,
    hBOOL(hAPP(hAPP(c_member(tc_fun(U_2727,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_2727,tc_HOL_Obool))),hAPP(c_Set_OPow(U_2727),U_2728))),
    inference(clausify,[status(thm)],[f_700_2]) ).

fof(f_701_1,plain,
    ! [V_k_2,V_i_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_k_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_k_2),V_i_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_k_2),V_i_2))
          | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_k_2))) ) )
      | ~ class_Orderings_Oord(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_atLeast__iff]) ).

fof(f_701_2,plain,
    ! [U_2731,U_2730,U_2729] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(U_2729),U_2730),hAPP(c_SetInterval_Oord__class_OatLeast(U_2729),U_2731)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2729),U_2731),U_2730)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2729),U_2731),U_2730))
          | ~ hBOOL(hAPP(hAPP(c_member(U_2729),U_2730),hAPP(c_SetInterval_Oord__class_OatLeast(U_2729),U_2731))) ) )
      | ~ class_Orderings_Oord(U_2729) ),
    inference(variable_rename,[status(thm)],[f_701_1]) ).

cnf(f_701_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2729),U_2731),U_2730))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2729),U_2730),hAPP(c_SetInterval_Oord__class_OatLeast(U_2729),U_2731)))
    | ~ class_Orderings_Oord(U_2729) ),
    inference(clausify,[status(thm)],[f_701_2]) ).

cnf(f_701_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2729),U_2730),hAPP(c_SetInterval_Oord__class_OatLeast(U_2729),U_2731)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2729),U_2731),U_2730))
    | ~ class_Orderings_Oord(U_2729) ),
    inference(clausify,[status(thm)],[f_701_2]) ).

fof(f_702_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2))) ),
    inference(fof_nnf,[status(thm)],[fact_PowD]) ).

fof(f_702_2,plain,
    ! [U_2734,U_2733,U_2732] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2732,tc_HOL_Obool)),U_2733),U_2734))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_2732,tc_HOL_Obool)),U_2733),hAPP(c_Set_OPow(U_2732),U_2734))) ),
    inference(variable_rename,[status(thm)],[f_702_1]) ).

cnf(f_702_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2732,tc_HOL_Obool)),U_2733),U_2734))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_2732,tc_HOL_Obool)),U_2733),hAPP(c_Set_OPow(U_2732),U_2734))) ),
    inference(clausify,[status(thm)],[f_702_2]) ).

fof(f_703_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_Pow__iff]) ).

fof(f_703_2,plain,
    ! [U_2737,U_2736,U_2735] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_2735,tc_HOL_Obool)),U_2736),hAPP(c_Set_OPow(U_2735),U_2737)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2735,tc_HOL_Obool)),U_2736),U_2737)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2735,tc_HOL_Obool)),U_2736),U_2737))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_2735,tc_HOL_Obool)),U_2736),hAPP(c_Set_OPow(U_2735),U_2737))) ) ),
    inference(variable_rename,[status(thm)],[f_703_1]) ).

fof(f_703_3,plain,
    ( ! [U_2743,U_2741,U_2739] :
        ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_2739,tc_HOL_Obool)),U_2741),hAPP(c_Set_OPow(U_2739),U_2743)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2739,tc_HOL_Obool)),U_2741),U_2743)) )
    & ! [U_2742,U_2740,U_2738] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2738,tc_HOL_Obool)),U_2740),U_2742))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_2738,tc_HOL_Obool)),U_2740),hAPP(c_Set_OPow(U_2738),U_2742))) ) ),
    inference(miniscope,[status(thm)],[f_703_2]) ).

cnf(f_703_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2738,tc_HOL_Obool)),U_2740),U_2742))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_2738,tc_HOL_Obool)),U_2740),hAPP(c_Set_OPow(U_2738),U_2742))) ),
    inference(clausify,[status(thm)],[f_703_3]) ).

cnf(f_703_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_2739,tc_HOL_Obool)),U_2741),hAPP(c_Set_OPow(U_2739),U_2743)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2739,tc_HOL_Obool)),U_2741),U_2743)) ),
    inference(clausify,[status(thm)],[f_703_3]) ).

fof(f_704_1,plain,
    ! [V_k_2,V_i_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_i_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_i_2))
          | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2))) ) )
      | ~ class_Orderings_Oord(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_greaterThan__iff]) ).

fof(f_704_2,plain,
    ! [U_2746,U_2745,U_2744] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(U_2744),U_2745),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_2744),U_2746)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2744),U_2746),U_2745)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2744),U_2746),U_2745))
          | ~ hBOOL(hAPP(hAPP(c_member(U_2744),U_2745),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_2744),U_2746))) ) )
      | ~ class_Orderings_Oord(U_2744) ),
    inference(variable_rename,[status(thm)],[f_704_1]) ).

cnf(f_704_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2744),U_2746),U_2745))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2744),U_2745),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_2744),U_2746)))
    | ~ class_Orderings_Oord(U_2744) ),
    inference(clausify,[status(thm)],[f_704_2]) ).

cnf(f_704_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2744),U_2745),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_2744),U_2746)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2744),U_2746),U_2745))
    | ~ class_Orderings_Oord(U_2744) ),
    inference(clausify,[status(thm)],[f_704_2]) ).

fof(f_705_1,plain,
    ! [V_A_2,V_B_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Inter__lower]) ).

fof(f_705_2,plain,
    ! [U_2749,U_2748,U_2747] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2747,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_2747,tc_HOL_Obool),U_2749)),U_2748))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_2747,tc_HOL_Obool)),U_2748),U_2749)) ),
    inference(variable_rename,[status(thm)],[f_705_1]) ).

cnf(f_705_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2747,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_2747,tc_HOL_Obool),U_2749)),U_2748))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_2747,tc_HOL_Obool)),U_2748),U_2749)) ),
    inference(clausify,[status(thm)],[f_705_2]) ).

fof(f_706_1,plain,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
      ( ( ( hAPP(V_F_2,V_A_2) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
        & ( hAPP(V_F_2,V_A_2) = V_x_2
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__one_Oremove]) ).

fof(f_706_2,plain,
    ! [U_2754,U_2753,U_2752,U_2751,U_2750] :
      ( ( ( hAPP(U_2752,U_2753) = hAPP(hAPP(U_2751,U_2754),hAPP(U_2752,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2750,tc_HOL_Obool)),U_2753),hAPP(hAPP(c_Set_Oinsert(U_2750),U_2754),c_Orderings_Obot__class_Obot(tc_fun(U_2750,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2750,tc_HOL_Obool)),U_2753),hAPP(hAPP(c_Set_Oinsert(U_2750),U_2754),c_Orderings_Obot__class_Obot(tc_fun(U_2750,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_2750,tc_HOL_Obool)) )
        & ( hAPP(U_2752,U_2753) = U_2754
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2750,tc_HOL_Obool)),U_2753),hAPP(hAPP(c_Set_Oinsert(U_2750),U_2754),c_Orderings_Obot__class_Obot(tc_fun(U_2750,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_2750,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_2750),U_2754),U_2753))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2750),U_2753))
      | ~ c_Finite__Set_Ofolding__one(U_2750,U_2751,U_2752) ),
    inference(variable_rename,[status(thm)],[f_706_1]) ).

cnf(f_706_3,plain,
    ( hAPP(U_2752,U_2753) = U_2754
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2750,tc_HOL_Obool)),U_2753),hAPP(hAPP(c_Set_Oinsert(U_2750),U_2754),c_Orderings_Obot__class_Obot(tc_fun(U_2750,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_2750,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2750),U_2754),U_2753))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2750),U_2753))
    | ~ c_Finite__Set_Ofolding__one(U_2750,U_2751,U_2752) ),
    inference(clausify,[status(thm)],[f_706_2]) ).

cnf(f_706_4,plain,
    ( hAPP(U_2752,U_2753) = hAPP(hAPP(U_2751,U_2754),hAPP(U_2752,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2750,tc_HOL_Obool)),U_2753),hAPP(hAPP(c_Set_Oinsert(U_2750),U_2754),c_Orderings_Obot__class_Obot(tc_fun(U_2750,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2750,tc_HOL_Obool)),U_2753),hAPP(hAPP(c_Set_Oinsert(U_2750),U_2754),c_Orderings_Obot__class_Obot(tc_fun(U_2750,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_2750,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2750),U_2754),U_2753))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2750),U_2753))
    | ~ c_Finite__Set_Ofolding__one(U_2750,U_2751,U_2752) ),
    inference(clausify,[status(thm)],[f_706_2]) ).

fof(f_707_1,plain,
    ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
      ( hAPP(V_F_2,V_A_2) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
      | ~ c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Oremove]) ).

fof(f_707_2,plain,
    ! [U_2762,U_2761,U_2760,U_2759,U_2758,U_2757,U_2756,U_2755] :
      ( hAPP(U_2760,U_2761) = hAPP(hAPP(U_2757,hAPP(U_2759,U_2762)),hAPP(U_2760,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2756,tc_HOL_Obool)),U_2761),hAPP(hAPP(c_Set_Oinsert(U_2756),U_2762),c_Orderings_Obot__class_Obot(tc_fun(U_2756,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2756),U_2762),U_2761))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2756),U_2761))
      | ~ c_Finite__Set_Ofolding__image__simple(U_2755,U_2756,U_2757,U_2758,U_2759,U_2760) ),
    inference(variable_rename,[status(thm)],[f_707_1]) ).

fof(f_707_3,plain,
    ! [U_2762,U_2761,U_2760,U_2759,U_2758,U_2757,U_2756] :
      ( ! [U_2755] : ~ c_Finite__Set_Ofolding__image__simple(U_2755,U_2756,U_2757,U_2758,U_2759,U_2760)
      | hAPP(U_2760,U_2761) = hAPP(hAPP(U_2757,hAPP(U_2759,U_2762)),hAPP(U_2760,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2756,tc_HOL_Obool)),U_2761),hAPP(hAPP(c_Set_Oinsert(U_2756),U_2762),c_Orderings_Obot__class_Obot(tc_fun(U_2756,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2756),U_2762),U_2761))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2756),U_2761)) ),
    inference(miniscope,[status(thm)],[f_707_2]) ).

cnf(f_707_4,plain,
    ( ~ c_Finite__Set_Ofolding__image__simple(U_2755,U_2756,U_2757,U_2758,U_2759,U_2760)
    | hAPP(U_2760,U_2761) = hAPP(hAPP(U_2757,hAPP(U_2759,U_2762)),hAPP(U_2760,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2756,tc_HOL_Obool)),U_2761),hAPP(hAPP(c_Set_Oinsert(U_2756),U_2762),c_Orderings_Obot__class_Obot(tc_fun(U_2756,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2756),U_2762),U_2761))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2756),U_2761)) ),
    inference(clausify,[status(thm)],[f_707_3]) ).

fof(f_708_1,plain,
    ! [V_A_2,V_a_2,T_b] :
      ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = V_A_2
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_insert__Diff]) ).

fof(f_708_2,plain,
    ! [U_2765,U_2764,U_2763] :
      ( hAPP(hAPP(c_Set_Oinsert(U_2763),U_2764),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2763,tc_HOL_Obool)),U_2765),hAPP(hAPP(c_Set_Oinsert(U_2763),U_2764),c_Orderings_Obot__class_Obot(tc_fun(U_2763,tc_HOL_Obool))))) = U_2765
      | ~ hBOOL(hAPP(hAPP(c_member(U_2763),U_2764),U_2765)) ),
    inference(variable_rename,[status(thm)],[f_708_1]) ).

cnf(f_708_3,plain,
    ( hAPP(hAPP(c_Set_Oinsert(U_2763),U_2764),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2763,tc_HOL_Obool)),U_2765),hAPP(hAPP(c_Set_Oinsert(U_2763),U_2764),c_Orderings_Obot__class_Obot(tc_fun(U_2763,tc_HOL_Obool))))) = U_2765
    | ~ hBOOL(hAPP(hAPP(c_member(U_2763),U_2764),U_2765)) ),
    inference(clausify,[status(thm)],[f_708_2]) ).

fof(f_709_1,plain,
    ! [V_A_2,V_x_2,T_b] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_A_2
      | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Diff__insert__absorb]) ).

fof(f_709_2,plain,
    ! [U_2768,U_2767,U_2766] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2766,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_2766),U_2767),U_2768)),hAPP(hAPP(c_Set_Oinsert(U_2766),U_2767),c_Orderings_Obot__class_Obot(tc_fun(U_2766,tc_HOL_Obool)))) = U_2768
      | hBOOL(hAPP(hAPP(c_member(U_2766),U_2767),U_2768)) ),
    inference(variable_rename,[status(thm)],[f_709_1]) ).

cnf(f_709_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2766,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_2766),U_2767),U_2768)),hAPP(hAPP(c_Set_Oinsert(U_2766),U_2767),c_Orderings_Obot__class_Obot(tc_fun(U_2766,tc_HOL_Obool)))) = U_2768
    | hBOOL(hAPP(hAPP(c_member(U_2766),U_2767),U_2768)) ),
    inference(clausify,[status(thm)],[f_709_2]) ).

fof(f_710_1,plain,
    ! [V_b_2,V_f_2,T_c,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))))
          | ! [B_x] :
              ( ? [B_y] :
                  ( B_y != B_x
                  & V_b_2 = hAPP(V_f_2,B_y) )
              | V_b_2 != hAPP(V_f_2,B_x) ) )
        & ( ? [B_x] :
              ( ! [B_y] :
                  ( B_y = B_x
                  | V_b_2 != hAPP(V_f_2,B_y) )
              & V_b_2 = hAPP(V_f_2,B_x) )
          | ~ hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) ) )
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_range__ex1__eq]) ).

fof(f_710_2,plain,
    ! [U_2776,U_2775,U_2774,U_2773] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(U_2774),U_2776),hAPP(c_Set_Oimage(U_2773,U_2774,U_2775),c_Orderings_Otop__class_Otop(tc_fun(U_2773,tc_HOL_Obool)))))
          | ! [U_2772] :
              ( ? [U_2771] :
                  ( U_2771 != U_2772
                  & U_2776 = hAPP(U_2775,U_2771) )
              | U_2776 != hAPP(U_2775,U_2772) ) )
        & ( ? [U_2770] :
              ( ! [U_2769] :
                  ( U_2769 = U_2770
                  | U_2776 != hAPP(U_2775,U_2769) )
              & U_2776 = hAPP(U_2775,U_2770) )
          | ~ hBOOL(hAPP(hAPP(c_member(U_2774),U_2776),hAPP(c_Set_Oimage(U_2773,U_2774,U_2775),c_Orderings_Otop__class_Otop(tc_fun(U_2773,tc_HOL_Obool))))) ) )
      | ~ c_Fun_Oinj__on(U_2773,U_2774,U_2775,c_Orderings_Otop__class_Otop(tc_fun(U_2773,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_710_1]) ).

fof(f_710_3,plain,
    ! [U_2776,U_2775,U_2774,U_2773] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(U_2774),U_2776),hAPP(c_Set_Oimage(U_2773,U_2774,U_2775),c_Orderings_Otop__class_Otop(tc_fun(U_2773,tc_HOL_Obool)))))
          | ! [U_2772] :
              ( ? [U_2771] :
                  ( U_2771 != U_2772
                  & U_2776 = hAPP(U_2775,U_2771) )
              | U_2776 != hAPP(U_2775,U_2772) ) )
        & ( ( ! [U_2769] :
                ( U_2769 = sK35(U_2776,U_2775,U_2774,U_2773)
                | U_2776 != hAPP(U_2775,U_2769) )
            & U_2776 = hAPP(U_2775,sK35(U_2776,U_2775,U_2774,U_2773)) )
          | ~ hBOOL(hAPP(hAPP(c_member(U_2774),U_2776),hAPP(c_Set_Oimage(U_2773,U_2774,U_2775),c_Orderings_Otop__class_Otop(tc_fun(U_2773,tc_HOL_Obool))))) ) )
      | ~ c_Fun_Oinj__on(U_2773,U_2774,U_2775,c_Orderings_Otop__class_Otop(tc_fun(U_2773,tc_HOL_Obool))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK35]),skolemize(U_2770,sK35(U_2776,U_2775,U_2774,U_2773))],[f_710_2]) ).

fof(f_710_4,plain,
    ! [U_2776,U_2775,U_2774,U_2773] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(U_2774),U_2776),hAPP(c_Set_Oimage(U_2773,U_2774,U_2775),c_Orderings_Otop__class_Otop(tc_fun(U_2773,tc_HOL_Obool)))))
          | ! [U_2772] :
              ( ( sK36(U_2776,U_2775,U_2774,U_2773,U_2772) != U_2772
                & U_2776 = hAPP(U_2775,sK36(U_2776,U_2775,U_2774,U_2773,U_2772)) )
              | U_2776 != hAPP(U_2775,U_2772) ) )
        & ( ( ! [U_2769] :
                ( U_2769 = sK35(U_2776,U_2775,U_2774,U_2773)
                | U_2776 != hAPP(U_2775,U_2769) )
            & U_2776 = hAPP(U_2775,sK35(U_2776,U_2775,U_2774,U_2773)) )
          | ~ hBOOL(hAPP(hAPP(c_member(U_2774),U_2776),hAPP(c_Set_Oimage(U_2773,U_2774,U_2775),c_Orderings_Otop__class_Otop(tc_fun(U_2773,tc_HOL_Obool))))) ) )
      | ~ c_Fun_Oinj__on(U_2773,U_2774,U_2775,c_Orderings_Otop__class_Otop(tc_fun(U_2773,tc_HOL_Obool))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK36]),skolemize(U_2771,sK36(U_2776,U_2775,U_2774,U_2773,U_2772))],[f_710_3]) ).

cnf(f_710_5,plain,
    ( U_2776 = hAPP(U_2775,sK35(U_2776,U_2775,U_2774,U_2773))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2774),U_2776),hAPP(c_Set_Oimage(U_2773,U_2774,U_2775),c_Orderings_Otop__class_Otop(tc_fun(U_2773,tc_HOL_Obool)))))
    | ~ c_Fun_Oinj__on(U_2773,U_2774,U_2775,c_Orderings_Otop__class_Otop(tc_fun(U_2773,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_710_4]) ).

cnf(f_710_6,plain,
    ( U_2769 = sK35(U_2776,U_2775,U_2774,U_2773)
    | U_2776 != hAPP(U_2775,U_2769)
    | ~ hBOOL(hAPP(hAPP(c_member(U_2774),U_2776),hAPP(c_Set_Oimage(U_2773,U_2774,U_2775),c_Orderings_Otop__class_Otop(tc_fun(U_2773,tc_HOL_Obool)))))
    | ~ c_Fun_Oinj__on(U_2773,U_2774,U_2775,c_Orderings_Otop__class_Otop(tc_fun(U_2773,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_710_4]) ).

cnf(f_710_7,plain,
    ( U_2776 = hAPP(U_2775,sK36(U_2776,U_2775,U_2774,U_2773,U_2772))
    | U_2776 != hAPP(U_2775,U_2772)
    | hBOOL(hAPP(hAPP(c_member(U_2774),U_2776),hAPP(c_Set_Oimage(U_2773,U_2774,U_2775),c_Orderings_Otop__class_Otop(tc_fun(U_2773,tc_HOL_Obool)))))
    | ~ c_Fun_Oinj__on(U_2773,U_2774,U_2775,c_Orderings_Otop__class_Otop(tc_fun(U_2773,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_710_4]) ).

cnf(f_710_8,plain,
    ( sK36(U_2776,U_2775,U_2774,U_2773,U_2772) != U_2772
    | U_2776 != hAPP(U_2775,U_2772)
    | hBOOL(hAPP(hAPP(c_member(U_2774),U_2776),hAPP(c_Set_Oimage(U_2773,U_2774,U_2775),c_Orderings_Otop__class_Otop(tc_fun(U_2773,tc_HOL_Obool)))))
    | ~ c_Fun_Oinj__on(U_2773,U_2774,U_2775,c_Orderings_Otop__class_Otop(tc_fun(U_2773,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_710_4]) ).

fof(f_711_1,plain,
    ! [V_A_2,V_a_2,V_f_2,T_c,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
          | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) )
        & ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
          | ~ hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) ) )
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_inj__image__mem__iff]) ).

fof(f_711_2,plain,
    ! [U_2781,U_2780,U_2779,U_2778,U_2777] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(U_2778),hAPP(U_2779,U_2780)),hAPP(c_Set_Oimage(U_2777,U_2778,U_2779),U_2781)))
          | ~ hBOOL(hAPP(hAPP(c_member(U_2777),U_2780),U_2781)) )
        & ( hBOOL(hAPP(hAPP(c_member(U_2777),U_2780),U_2781))
          | ~ hBOOL(hAPP(hAPP(c_member(U_2778),hAPP(U_2779,U_2780)),hAPP(c_Set_Oimage(U_2777,U_2778,U_2779),U_2781))) ) )
      | ~ c_Fun_Oinj__on(U_2777,U_2778,U_2779,c_Orderings_Otop__class_Otop(tc_fun(U_2777,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_711_1]) ).

cnf(f_711_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2777),U_2780),U_2781))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2778),hAPP(U_2779,U_2780)),hAPP(c_Set_Oimage(U_2777,U_2778,U_2779),U_2781)))
    | ~ c_Fun_Oinj__on(U_2777,U_2778,U_2779,c_Orderings_Otop__class_Otop(tc_fun(U_2777,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_711_2]) ).

cnf(f_711_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2778),hAPP(U_2779,U_2780)),hAPP(c_Set_Oimage(U_2777,U_2778,U_2779),U_2781)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2777),U_2780),U_2781))
    | ~ c_Fun_Oinj__on(U_2777,U_2778,U_2779,c_Orderings_Otop__class_Otop(tc_fun(U_2777,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_711_2]) ).

fof(f_712_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oin__idem]) ).

fof(f_712_2,plain,
    ! [U_2784,U_2783,U_2782] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2782),U_2784),c_Big__Operators_Olattice_OInf__fin(U_2782,c_Orderings_Oord__class_Omin(U_2782),U_2783)) = c_Big__Operators_Olattice_OInf__fin(U_2782,c_Orderings_Oord__class_Omin(U_2782),U_2783)
      | ~ hBOOL(hAPP(hAPP(c_member(U_2782),U_2784),U_2783))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2782),U_2783))
      | ~ class_Orderings_Olinorder(U_2782) ),
    inference(variable_rename,[status(thm)],[f_712_1]) ).

cnf(f_712_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2782),U_2784),c_Big__Operators_Olattice_OInf__fin(U_2782,c_Orderings_Oord__class_Omin(U_2782),U_2783)) = c_Big__Operators_Olattice_OInf__fin(U_2782,c_Orderings_Oord__class_Omin(U_2782),U_2783)
    | ~ hBOOL(hAPP(hAPP(c_member(U_2782),U_2784),U_2783))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2782),U_2783))
    | ~ class_Orderings_Olinorder(U_2782) ),
    inference(clausify,[status(thm)],[f_712_2]) ).

fof(f_713_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oin__idem]) ).

fof(f_713_2,plain,
    ! [U_2787,U_2786,U_2785] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2785),U_2787),c_Big__Operators_Olattice_OSup__fin(U_2785,c_Orderings_Oord__class_Omax(U_2785),U_2786)) = c_Big__Operators_Olattice_OSup__fin(U_2785,c_Orderings_Oord__class_Omax(U_2785),U_2786)
      | ~ hBOOL(hAPP(hAPP(c_member(U_2785),U_2787),U_2786))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2785),U_2786))
      | ~ class_Orderings_Olinorder(U_2785) ),
    inference(variable_rename,[status(thm)],[f_713_1]) ).

cnf(f_713_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2785),U_2787),c_Big__Operators_Olattice_OSup__fin(U_2785,c_Orderings_Oord__class_Omax(U_2785),U_2786)) = c_Big__Operators_Olattice_OSup__fin(U_2785,c_Orderings_Oord__class_Omax(U_2785),U_2786)
    | ~ hBOOL(hAPP(hAPP(c_member(U_2785),U_2787),U_2786))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2785),U_2786))
    | ~ class_Orderings_Olinorder(U_2785) ),
    inference(clausify,[status(thm)],[f_713_2]) ).

fof(f_714_1,plain,
    ! [V_x_2,V_F_2,V_f_2,T_b] :
      ( hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2
      | ~ c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__one_Osingleton]) ).

fof(f_714_2,plain,
    ! [U_2791,U_2790,U_2789,U_2788] :
      ( hAPP(U_2790,hAPP(hAPP(c_Set_Oinsert(U_2788),U_2791),c_Orderings_Obot__class_Obot(tc_fun(U_2788,tc_HOL_Obool)))) = U_2791
      | ~ c_Finite__Set_Ofolding__one(U_2788,U_2789,U_2790) ),
    inference(variable_rename,[status(thm)],[f_714_1]) ).

cnf(f_714_3,plain,
    ( hAPP(U_2790,hAPP(hAPP(c_Set_Oinsert(U_2788),U_2791),c_Orderings_Obot__class_Obot(tc_fun(U_2788,tc_HOL_Obool)))) = U_2791
    | ~ c_Finite__Set_Ofolding__one(U_2788,U_2789,U_2790) ),
    inference(clausify,[status(thm)],[f_714_2]) ).

fof(f_715_1,plain,
    ! [V_B_2,V_x_2,V_A_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
          & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) )
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_B_2))
          & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) )
      & ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
            | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_B_2))
            | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_subset__insert__iff]) ).

fof(f_715_2,plain,
    ! [U_2795,U_2794,U_2793,U_2792] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2792,tc_HOL_Obool)),U_2793),hAPP(hAPP(c_Set_Oinsert(U_2792),U_2794),U_2795)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2792,tc_HOL_Obool)),U_2793),U_2795))
          & ~ hBOOL(hAPP(hAPP(c_member(U_2792),U_2794),U_2793)) )
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2792,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2792,tc_HOL_Obool)),U_2793),hAPP(hAPP(c_Set_Oinsert(U_2792),U_2794),c_Orderings_Obot__class_Obot(tc_fun(U_2792,tc_HOL_Obool))))),U_2795))
          & hBOOL(hAPP(hAPP(c_member(U_2792),U_2794),U_2793)) ) )
      & ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2792,tc_HOL_Obool)),U_2793),U_2795))
            | hBOOL(hAPP(hAPP(c_member(U_2792),U_2794),U_2793)) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2792,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2792,tc_HOL_Obool)),U_2793),hAPP(hAPP(c_Set_Oinsert(U_2792),U_2794),c_Orderings_Obot__class_Obot(tc_fun(U_2792,tc_HOL_Obool))))),U_2795))
            | ~ hBOOL(hAPP(hAPP(c_member(U_2792),U_2794),U_2793)) ) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2792,tc_HOL_Obool)),U_2793),hAPP(hAPP(c_Set_Oinsert(U_2792),U_2794),U_2795))) ) ),
    inference(variable_rename,[status(thm)],[f_715_1]) ).

fof(f_715_3,plain,
    ( ! [U_2803,U_2801,U_2799,U_2797] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2797,tc_HOL_Obool)),U_2799),hAPP(hAPP(c_Set_Oinsert(U_2797),U_2801),U_2803)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2797,tc_HOL_Obool)),U_2799),U_2803))
          & ~ hBOOL(hAPP(hAPP(c_member(U_2797),U_2801),U_2799)) )
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2797,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2797,tc_HOL_Obool)),U_2799),hAPP(hAPP(c_Set_Oinsert(U_2797),U_2801),c_Orderings_Obot__class_Obot(tc_fun(U_2797,tc_HOL_Obool))))),U_2803))
          & hBOOL(hAPP(hAPP(c_member(U_2797),U_2801),U_2799)) ) )
    & ! [U_2802,U_2800,U_2798,U_2796] :
        ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2796,tc_HOL_Obool)),U_2798),U_2802))
            | hBOOL(hAPP(hAPP(c_member(U_2796),U_2800),U_2798)) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2796,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2796,tc_HOL_Obool)),U_2798),hAPP(hAPP(c_Set_Oinsert(U_2796),U_2800),c_Orderings_Obot__class_Obot(tc_fun(U_2796,tc_HOL_Obool))))),U_2802))
            | ~ hBOOL(hAPP(hAPP(c_member(U_2796),U_2800),U_2798)) ) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2796,tc_HOL_Obool)),U_2798),hAPP(hAPP(c_Set_Oinsert(U_2796),U_2800),U_2802))) ) ),
    inference(miniscope,[status(thm)],[f_715_2]) ).

cnf(f_715_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2796,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2796,tc_HOL_Obool)),U_2798),hAPP(hAPP(c_Set_Oinsert(U_2796),U_2800),c_Orderings_Obot__class_Obot(tc_fun(U_2796,tc_HOL_Obool))))),U_2802))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2796),U_2800),U_2798))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2796,tc_HOL_Obool)),U_2798),hAPP(hAPP(c_Set_Oinsert(U_2796),U_2800),U_2802))) ),
    inference(clausify,[status(thm)],[f_715_3]) ).

cnf(f_715_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2796,tc_HOL_Obool)),U_2798),U_2802))
    | hBOOL(hAPP(hAPP(c_member(U_2796),U_2800),U_2798))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2796,tc_HOL_Obool)),U_2798),hAPP(hAPP(c_Set_Oinsert(U_2796),U_2800),U_2802))) ),
    inference(clausify,[status(thm)],[f_715_3]) ).

cnf(f_715_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_2797),U_2801),U_2799))
    | hBOOL(hAPP(hAPP(c_member(U_2797),U_2801),U_2799))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2797,tc_HOL_Obool)),U_2799),hAPP(hAPP(c_Set_Oinsert(U_2797),U_2801),U_2803))) ),
    inference(clausify,[status(thm)],[f_715_3]) ).

cnf(f_715_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2797,tc_HOL_Obool)),U_2799),U_2803))
    | hBOOL(hAPP(hAPP(c_member(U_2797),U_2801),U_2799))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2797,tc_HOL_Obool)),U_2799),hAPP(hAPP(c_Set_Oinsert(U_2797),U_2801),U_2803))) ),
    inference(clausify,[status(thm)],[f_715_3]) ).

cnf(f_715_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_2797),U_2801),U_2799))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2797,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2797,tc_HOL_Obool)),U_2799),hAPP(hAPP(c_Set_Oinsert(U_2797),U_2801),c_Orderings_Obot__class_Obot(tc_fun(U_2797,tc_HOL_Obool))))),U_2803))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2797,tc_HOL_Obool)),U_2799),hAPP(hAPP(c_Set_Oinsert(U_2797),U_2801),U_2803))) ),
    inference(clausify,[status(thm)],[f_715_3]) ).

cnf(f_715_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2797,tc_HOL_Obool)),U_2799),U_2803))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2797,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2797,tc_HOL_Obool)),U_2799),hAPP(hAPP(c_Set_Oinsert(U_2797),U_2801),c_Orderings_Obot__class_Obot(tc_fun(U_2797,tc_HOL_Obool))))),U_2803))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2797,tc_HOL_Obool)),U_2799),hAPP(hAPP(c_Set_Oinsert(U_2797),U_2801),U_2803))) ),
    inference(clausify,[status(thm)],[f_715_3]) ).

fof(f_716_1,plain,
    ! [V_B_2,V_x_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_diff__single__insert]) ).

fof(f_716_2,plain,
    ! [U_2807,U_2806,U_2805,U_2804] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2804,tc_HOL_Obool)),U_2805),hAPP(hAPP(c_Set_Oinsert(U_2804),U_2806),U_2807)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2804),U_2806),U_2805))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2804,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2804,tc_HOL_Obool)),U_2805),hAPP(hAPP(c_Set_Oinsert(U_2804),U_2806),c_Orderings_Obot__class_Obot(tc_fun(U_2804,tc_HOL_Obool))))),U_2807)) ),
    inference(variable_rename,[status(thm)],[f_716_1]) ).

cnf(f_716_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2804,tc_HOL_Obool)),U_2805),hAPP(hAPP(c_Set_Oinsert(U_2804),U_2806),U_2807)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2804),U_2806),U_2805))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2804,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2804,tc_HOL_Obool)),U_2805),hAPP(hAPP(c_Set_Oinsert(U_2804),U_2806),c_Orderings_Obot__class_Obot(tc_fun(U_2804,tc_HOL_Obool))))),U_2807)) ),
    inference(clausify,[status(thm)],[f_716_2]) ).

fof(f_717_1,plain,
    ! [V_a_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) = V_a_2
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Osup__Inf__absorb]) ).

fof(f_717_2,plain,
    ! [U_2810,U_2809,U_2808] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2808),U_2810),c_Big__Operators_Olattice_OInf__fin(U_2808,c_Orderings_Oord__class_Omin(U_2808),U_2809)) = U_2810
      | ~ hBOOL(hAPP(hAPP(c_member(U_2808),U_2810),U_2809))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2808),U_2809))
      | ~ class_Orderings_Olinorder(U_2808) ),
    inference(variable_rename,[status(thm)],[f_717_1]) ).

cnf(f_717_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2808),U_2810),c_Big__Operators_Olattice_OInf__fin(U_2808,c_Orderings_Oord__class_Omin(U_2808),U_2809)) = U_2810
    | ~ hBOOL(hAPP(hAPP(c_member(U_2808),U_2810),U_2809))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2808),U_2809))
    | ~ class_Orderings_Olinorder(U_2808) ),
    inference(clausify,[status(thm)],[f_717_2]) ).

fof(f_718_1,plain,
    ! [V_a_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_a_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) = V_a_2
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__Sup__absorb]) ).

fof(f_718_2,plain,
    ! [U_2813,U_2812,U_2811] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2811),U_2813),c_Big__Operators_Olattice_OSup__fin(U_2811,c_Orderings_Oord__class_Omax(U_2811),U_2812)) = U_2813
      | ~ hBOOL(hAPP(hAPP(c_member(U_2811),U_2813),U_2812))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2811),U_2812))
      | ~ class_Orderings_Olinorder(U_2811) ),
    inference(variable_rename,[status(thm)],[f_718_1]) ).

cnf(f_718_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2811),U_2813),c_Big__Operators_Olattice_OSup__fin(U_2811,c_Orderings_Oord__class_Omax(U_2811),U_2812)) = U_2813
    | ~ hBOOL(hAPP(hAPP(c_member(U_2811),U_2813),U_2812))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2811),U_2812))
    | ~ class_Orderings_Olinorder(U_2811) ),
    inference(clausify,[status(thm)],[f_718_2]) ).

fof(f_719_1,plain,
    ! [V_A_2,V_a_2,V_f_2,T_c,T_b] :
      ( ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2))
        | hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))))
        | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) )
      & ( ( ~ hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))))
          & c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) )
        | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_inj__on__insert]) ).

fof(f_719_2,plain,
    ! [U_2818,U_2817,U_2816,U_2815,U_2814] :
      ( ( c_Fun_Oinj__on(U_2814,U_2815,U_2816,hAPP(hAPP(c_Set_Oinsert(U_2814),U_2817),U_2818))
        | hBOOL(hAPP(hAPP(c_member(U_2815),hAPP(U_2816,U_2817)),hAPP(c_Set_Oimage(U_2814,U_2815,U_2816),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2814,tc_HOL_Obool)),U_2818),hAPP(hAPP(c_Set_Oinsert(U_2814),U_2817),c_Orderings_Obot__class_Obot(tc_fun(U_2814,tc_HOL_Obool)))))))
        | ~ c_Fun_Oinj__on(U_2814,U_2815,U_2816,U_2818) )
      & ( ( ~ hBOOL(hAPP(hAPP(c_member(U_2815),hAPP(U_2816,U_2817)),hAPP(c_Set_Oimage(U_2814,U_2815,U_2816),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2814,tc_HOL_Obool)),U_2818),hAPP(hAPP(c_Set_Oinsert(U_2814),U_2817),c_Orderings_Obot__class_Obot(tc_fun(U_2814,tc_HOL_Obool)))))))
          & c_Fun_Oinj__on(U_2814,U_2815,U_2816,U_2818) )
        | ~ c_Fun_Oinj__on(U_2814,U_2815,U_2816,hAPP(hAPP(c_Set_Oinsert(U_2814),U_2817),U_2818)) ) ),
    inference(variable_rename,[status(thm)],[f_719_1]) ).

fof(f_719_3,plain,
    ( ! [U_2828,U_2826,U_2824,U_2822,U_2820] :
        ( c_Fun_Oinj__on(U_2820,U_2822,U_2824,hAPP(hAPP(c_Set_Oinsert(U_2820),U_2826),U_2828))
        | hBOOL(hAPP(hAPP(c_member(U_2822),hAPP(U_2824,U_2826)),hAPP(c_Set_Oimage(U_2820,U_2822,U_2824),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2820,tc_HOL_Obool)),U_2828),hAPP(hAPP(c_Set_Oinsert(U_2820),U_2826),c_Orderings_Obot__class_Obot(tc_fun(U_2820,tc_HOL_Obool)))))))
        | ~ c_Fun_Oinj__on(U_2820,U_2822,U_2824,U_2828) )
    & ! [U_2827,U_2825,U_2823,U_2821,U_2819] :
        ( ( ~ hBOOL(hAPP(hAPP(c_member(U_2821),hAPP(U_2823,U_2825)),hAPP(c_Set_Oimage(U_2819,U_2821,U_2823),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2819,tc_HOL_Obool)),U_2827),hAPP(hAPP(c_Set_Oinsert(U_2819),U_2825),c_Orderings_Obot__class_Obot(tc_fun(U_2819,tc_HOL_Obool)))))))
          & c_Fun_Oinj__on(U_2819,U_2821,U_2823,U_2827) )
        | ~ c_Fun_Oinj__on(U_2819,U_2821,U_2823,hAPP(hAPP(c_Set_Oinsert(U_2819),U_2825),U_2827)) ) ),
    inference(miniscope,[status(thm)],[f_719_2]) ).

cnf(f_719_4,plain,
    ( c_Fun_Oinj__on(U_2819,U_2821,U_2823,U_2827)
    | ~ c_Fun_Oinj__on(U_2819,U_2821,U_2823,hAPP(hAPP(c_Set_Oinsert(U_2819),U_2825),U_2827)) ),
    inference(clausify,[status(thm)],[f_719_3]) ).

cnf(f_719_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_2821),hAPP(U_2823,U_2825)),hAPP(c_Set_Oimage(U_2819,U_2821,U_2823),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2819,tc_HOL_Obool)),U_2827),hAPP(hAPP(c_Set_Oinsert(U_2819),U_2825),c_Orderings_Obot__class_Obot(tc_fun(U_2819,tc_HOL_Obool)))))))
    | ~ c_Fun_Oinj__on(U_2819,U_2821,U_2823,hAPP(hAPP(c_Set_Oinsert(U_2819),U_2825),U_2827)) ),
    inference(clausify,[status(thm)],[f_719_3]) ).

cnf(f_719_6,plain,
    ( c_Fun_Oinj__on(U_2820,U_2822,U_2824,hAPP(hAPP(c_Set_Oinsert(U_2820),U_2826),U_2828))
    | hBOOL(hAPP(hAPP(c_member(U_2822),hAPP(U_2824,U_2826)),hAPP(c_Set_Oimage(U_2820,U_2822,U_2824),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2820,tc_HOL_Obool)),U_2828),hAPP(hAPP(c_Set_Oinsert(U_2820),U_2826),c_Orderings_Obot__class_Obot(tc_fun(U_2820,tc_HOL_Obool)))))))
    | ~ c_Fun_Oinj__on(U_2820,U_2822,U_2824,U_2828) ),
    inference(clausify,[status(thm)],[f_719_3]) ).

fof(f_720_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oinsert]) ).

fof(f_720_2,plain,
    ! [U_2831,U_2830,U_2829] :
      ( c_Big__Operators_Olattice_OInf__fin(U_2829,c_Orderings_Oord__class_Omin(U_2829),hAPP(hAPP(c_Set_Oinsert(U_2829),U_2831),U_2830)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2829),U_2831),c_Big__Operators_Olattice_OInf__fin(U_2829,c_Orderings_Oord__class_Omin(U_2829),U_2830))
      | U_2830 = c_Orderings_Obot__class_Obot(tc_fun(U_2829,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(U_2829),U_2831),U_2830))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2829),U_2830))
      | ~ class_Orderings_Olinorder(U_2829) ),
    inference(variable_rename,[status(thm)],[f_720_1]) ).

cnf(f_720_3,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_2829,c_Orderings_Oord__class_Omin(U_2829),hAPP(hAPP(c_Set_Oinsert(U_2829),U_2831),U_2830)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2829),U_2831),c_Big__Operators_Olattice_OInf__fin(U_2829,c_Orderings_Oord__class_Omin(U_2829),U_2830))
    | U_2830 = c_Orderings_Obot__class_Obot(tc_fun(U_2829,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(U_2829),U_2831),U_2830))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2829),U_2830))
    | ~ class_Orderings_Olinorder(U_2829) ),
    inference(clausify,[status(thm)],[f_720_2]) ).

fof(f_721_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oinsert]) ).

fof(f_721_2,plain,
    ! [U_2834,U_2833,U_2832] :
      ( c_Big__Operators_Olattice_OSup__fin(U_2832,c_Orderings_Oord__class_Omax(U_2832),hAPP(hAPP(c_Set_Oinsert(U_2832),U_2834),U_2833)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2832),U_2834),c_Big__Operators_Olattice_OSup__fin(U_2832,c_Orderings_Oord__class_Omax(U_2832),U_2833))
      | U_2833 = c_Orderings_Obot__class_Obot(tc_fun(U_2832,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(U_2832),U_2834),U_2833))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2832),U_2833))
      | ~ class_Orderings_Olinorder(U_2832) ),
    inference(variable_rename,[status(thm)],[f_721_1]) ).

cnf(f_721_3,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_2832,c_Orderings_Oord__class_Omax(U_2832),hAPP(hAPP(c_Set_Oinsert(U_2832),U_2834),U_2833)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2832),U_2834),c_Big__Operators_Olattice_OSup__fin(U_2832,c_Orderings_Oord__class_Omax(U_2832),U_2833))
    | U_2833 = c_Orderings_Obot__class_Obot(tc_fun(U_2832,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(U_2832),U_2834),U_2833))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2832),U_2833))
    | ~ class_Orderings_Olinorder(U_2832) ),
    inference(clausify,[status(thm)],[f_721_2]) ).

fof(f_722_1,plain,
    ! [V_B_2,V_x_2,V_A_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2)))
        | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
              & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) )
            | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_B_2))
              & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) )
          & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) )
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
          & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) )
      & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
                | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) )
              & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_B_2))
                | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) )
            | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
            | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_psubset__insert__iff]) ).

fof(f_722_2,plain,
    ! [U_2838,U_2837,U_2836,U_2835] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2835,tc_HOL_Obool)),U_2836),hAPP(hAPP(c_Set_Oinsert(U_2835),U_2837),U_2838)))
        | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2835,tc_HOL_Obool)),U_2836),U_2838))
              & ~ hBOOL(hAPP(hAPP(c_member(U_2835),U_2837),U_2836)) )
            | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2835,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2835,tc_HOL_Obool)),U_2836),hAPP(hAPP(c_Set_Oinsert(U_2835),U_2837),c_Orderings_Obot__class_Obot(tc_fun(U_2835,tc_HOL_Obool))))),U_2838))
              & hBOOL(hAPP(hAPP(c_member(U_2835),U_2837),U_2836)) ) )
          & ~ hBOOL(hAPP(hAPP(c_member(U_2835),U_2837),U_2838)) )
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2835,tc_HOL_Obool)),U_2836),U_2838))
          & hBOOL(hAPP(hAPP(c_member(U_2835),U_2837),U_2838)) ) )
      & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2835,tc_HOL_Obool)),U_2836),U_2838))
                | hBOOL(hAPP(hAPP(c_member(U_2835),U_2837),U_2836)) )
              & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2835,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2835,tc_HOL_Obool)),U_2836),hAPP(hAPP(c_Set_Oinsert(U_2835),U_2837),c_Orderings_Obot__class_Obot(tc_fun(U_2835,tc_HOL_Obool))))),U_2838))
                | ~ hBOOL(hAPP(hAPP(c_member(U_2835),U_2837),U_2836)) ) )
            | hBOOL(hAPP(hAPP(c_member(U_2835),U_2837),U_2838)) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2835,tc_HOL_Obool)),U_2836),U_2838))
            | ~ hBOOL(hAPP(hAPP(c_member(U_2835),U_2837),U_2838)) ) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2835,tc_HOL_Obool)),U_2836),hAPP(hAPP(c_Set_Oinsert(U_2835),U_2837),U_2838))) ) ),
    inference(variable_rename,[status(thm)],[f_722_1]) ).

fof(f_722_3,plain,
    ( ! [U_2846,U_2844,U_2842,U_2840] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2840,tc_HOL_Obool)),U_2842),hAPP(hAPP(c_Set_Oinsert(U_2840),U_2844),U_2846)))
        | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2840,tc_HOL_Obool)),U_2842),U_2846))
              & ~ hBOOL(hAPP(hAPP(c_member(U_2840),U_2844),U_2842)) )
            | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2840,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2840,tc_HOL_Obool)),U_2842),hAPP(hAPP(c_Set_Oinsert(U_2840),U_2844),c_Orderings_Obot__class_Obot(tc_fun(U_2840,tc_HOL_Obool))))),U_2846))
              & hBOOL(hAPP(hAPP(c_member(U_2840),U_2844),U_2842)) ) )
          & ~ hBOOL(hAPP(hAPP(c_member(U_2840),U_2844),U_2846)) )
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2840,tc_HOL_Obool)),U_2842),U_2846))
          & hBOOL(hAPP(hAPP(c_member(U_2840),U_2844),U_2846)) ) )
    & ! [U_2845,U_2843,U_2841,U_2839] :
        ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2839,tc_HOL_Obool)),U_2841),U_2845))
                | hBOOL(hAPP(hAPP(c_member(U_2839),U_2843),U_2841)) )
              & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2839,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2839,tc_HOL_Obool)),U_2841),hAPP(hAPP(c_Set_Oinsert(U_2839),U_2843),c_Orderings_Obot__class_Obot(tc_fun(U_2839,tc_HOL_Obool))))),U_2845))
                | ~ hBOOL(hAPP(hAPP(c_member(U_2839),U_2843),U_2841)) ) )
            | hBOOL(hAPP(hAPP(c_member(U_2839),U_2843),U_2845)) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2839,tc_HOL_Obool)),U_2841),U_2845))
            | ~ hBOOL(hAPP(hAPP(c_member(U_2839),U_2843),U_2845)) ) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2839,tc_HOL_Obool)),U_2841),hAPP(hAPP(c_Set_Oinsert(U_2839),U_2843),U_2845))) ) ),
    inference(miniscope,[status(thm)],[f_722_2]) ).

cnf(f_722_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2839,tc_HOL_Obool)),U_2841),U_2845))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2839),U_2843),U_2845))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2839,tc_HOL_Obool)),U_2841),hAPP(hAPP(c_Set_Oinsert(U_2839),U_2843),U_2845))) ),
    inference(clausify,[status(thm)],[f_722_3]) ).

cnf(f_722_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2839,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2839,tc_HOL_Obool)),U_2841),hAPP(hAPP(c_Set_Oinsert(U_2839),U_2843),c_Orderings_Obot__class_Obot(tc_fun(U_2839,tc_HOL_Obool))))),U_2845))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2839),U_2843),U_2841))
    | hBOOL(hAPP(hAPP(c_member(U_2839),U_2843),U_2845))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2839,tc_HOL_Obool)),U_2841),hAPP(hAPP(c_Set_Oinsert(U_2839),U_2843),U_2845))) ),
    inference(clausify,[status(thm)],[f_722_3]) ).

cnf(f_722_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2839,tc_HOL_Obool)),U_2841),U_2845))
    | hBOOL(hAPP(hAPP(c_member(U_2839),U_2843),U_2841))
    | hBOOL(hAPP(hAPP(c_member(U_2839),U_2843),U_2845))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2839,tc_HOL_Obool)),U_2841),hAPP(hAPP(c_Set_Oinsert(U_2839),U_2843),U_2845))) ),
    inference(clausify,[status(thm)],[f_722_3]) ).

cnf(f_722_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_2840),U_2844),U_2846))
    | hBOOL(hAPP(hAPP(c_member(U_2840),U_2844),U_2846))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2840,tc_HOL_Obool)),U_2842),hAPP(hAPP(c_Set_Oinsert(U_2840),U_2844),U_2846))) ),
    inference(clausify,[status(thm)],[f_722_3]) ).

cnf(f_722_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_2840),U_2844),U_2842))
    | hBOOL(hAPP(hAPP(c_member(U_2840),U_2844),U_2842))
    | hBOOL(hAPP(hAPP(c_member(U_2840),U_2844),U_2846))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2840,tc_HOL_Obool)),U_2842),hAPP(hAPP(c_Set_Oinsert(U_2840),U_2844),U_2846))) ),
    inference(clausify,[status(thm)],[f_722_3]) ).

cnf(f_722_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2840,tc_HOL_Obool)),U_2842),U_2846))
    | hBOOL(hAPP(hAPP(c_member(U_2840),U_2844),U_2842))
    | hBOOL(hAPP(hAPP(c_member(U_2840),U_2844),U_2846))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2840,tc_HOL_Obool)),U_2842),hAPP(hAPP(c_Set_Oinsert(U_2840),U_2844),U_2846))) ),
    inference(clausify,[status(thm)],[f_722_3]) ).

cnf(f_722_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_2840),U_2844),U_2842))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2840,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2840,tc_HOL_Obool)),U_2842),hAPP(hAPP(c_Set_Oinsert(U_2840),U_2844),c_Orderings_Obot__class_Obot(tc_fun(U_2840,tc_HOL_Obool))))),U_2846))
    | hBOOL(hAPP(hAPP(c_member(U_2840),U_2844),U_2846))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2840,tc_HOL_Obool)),U_2842),hAPP(hAPP(c_Set_Oinsert(U_2840),U_2844),U_2846))) ),
    inference(clausify,[status(thm)],[f_722_3]) ).

cnf(f_722_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2840,tc_HOL_Obool)),U_2842),U_2846))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2840,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2840,tc_HOL_Obool)),U_2842),hAPP(hAPP(c_Set_Oinsert(U_2840),U_2844),c_Orderings_Obot__class_Obot(tc_fun(U_2840,tc_HOL_Obool))))),U_2846))
    | hBOOL(hAPP(hAPP(c_member(U_2840),U_2844),U_2846))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2840,tc_HOL_Obool)),U_2842),hAPP(hAPP(c_Set_Oinsert(U_2840),U_2844),U_2846))) ),
    inference(clausify,[status(thm)],[f_722_3]) ).

cnf(f_722_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_2840),U_2844),U_2846))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2840,tc_HOL_Obool)),U_2842),U_2846))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2840,tc_HOL_Obool)),U_2842),hAPP(hAPP(c_Set_Oinsert(U_2840),U_2844),U_2846))) ),
    inference(clausify,[status(thm)],[f_722_3]) ).

cnf(f_722_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_2840),U_2844),U_2842))
    | hBOOL(hAPP(hAPP(c_member(U_2840),U_2844),U_2842))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2840,tc_HOL_Obool)),U_2842),U_2846))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2840,tc_HOL_Obool)),U_2842),hAPP(hAPP(c_Set_Oinsert(U_2840),U_2844),U_2846))) ),
    inference(clausify,[status(thm)],[f_722_3]) ).

cnf(f_722_14,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2840,tc_HOL_Obool)),U_2842),U_2846))
    | hBOOL(hAPP(hAPP(c_member(U_2840),U_2844),U_2842))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2840,tc_HOL_Obool)),U_2842),U_2846))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2840,tc_HOL_Obool)),U_2842),hAPP(hAPP(c_Set_Oinsert(U_2840),U_2844),U_2846))) ),
    inference(clausify,[status(thm)],[f_722_3]) ).

cnf(f_722_15,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_2840),U_2844),U_2842))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2840,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2840,tc_HOL_Obool)),U_2842),hAPP(hAPP(c_Set_Oinsert(U_2840),U_2844),c_Orderings_Obot__class_Obot(tc_fun(U_2840,tc_HOL_Obool))))),U_2846))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2840,tc_HOL_Obool)),U_2842),U_2846))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2840,tc_HOL_Obool)),U_2842),hAPP(hAPP(c_Set_Oinsert(U_2840),U_2844),U_2846))) ),
    inference(clausify,[status(thm)],[f_722_3]) ).

cnf(f_722_16,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2840,tc_HOL_Obool)),U_2842),U_2846))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2840,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2840,tc_HOL_Obool)),U_2842),hAPP(hAPP(c_Set_Oinsert(U_2840),U_2844),c_Orderings_Obot__class_Obot(tc_fun(U_2840,tc_HOL_Obool))))),U_2846))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2840,tc_HOL_Obool)),U_2842),U_2846))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_2840,tc_HOL_Obool)),U_2842),hAPP(hAPP(c_Set_Oinsert(U_2840),U_2844),U_2846))) ),
    inference(clausify,[status(thm)],[f_722_3]) ).

fof(f_723_1,plain,
    ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
      ( hAPP(hAPP(V_f_2,hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
      | ~ c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Ounion__inter]) ).

fof(f_723_2,plain,
    ! [U_2854,U_2853,U_2852,U_2851,U_2850,U_2849,U_2848,U_2847] :
      ( hAPP(hAPP(U_2849,hAPP(U_2852,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2848,tc_HOL_Obool)),U_2853),U_2854))),hAPP(U_2852,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2848,tc_HOL_Obool)),U_2853),U_2854))) = hAPP(hAPP(U_2849,hAPP(U_2852,U_2853)),hAPP(U_2852,U_2854))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2848),U_2854))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2848),U_2853))
      | ~ c_Finite__Set_Ofolding__image__simple(U_2847,U_2848,U_2849,U_2850,U_2851,U_2852) ),
    inference(variable_rename,[status(thm)],[f_723_1]) ).

fof(f_723_3,plain,
    ! [U_2854,U_2853,U_2852,U_2851,U_2850,U_2849,U_2848] :
      ( ! [U_2847] : ~ c_Finite__Set_Ofolding__image__simple(U_2847,U_2848,U_2849,U_2850,U_2851,U_2852)
      | hAPP(hAPP(U_2849,hAPP(U_2852,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2848,tc_HOL_Obool)),U_2853),U_2854))),hAPP(U_2852,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2848,tc_HOL_Obool)),U_2853),U_2854))) = hAPP(hAPP(U_2849,hAPP(U_2852,U_2853)),hAPP(U_2852,U_2854))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2848),U_2854))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2848),U_2853)) ),
    inference(miniscope,[status(thm)],[f_723_2]) ).

cnf(f_723_4,plain,
    ( ~ c_Finite__Set_Ofolding__image__simple(U_2847,U_2848,U_2849,U_2850,U_2851,U_2852)
    | hAPP(hAPP(U_2849,hAPP(U_2852,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_2848,tc_HOL_Obool)),U_2853),U_2854))),hAPP(U_2852,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2848,tc_HOL_Obool)),U_2853),U_2854))) = hAPP(hAPP(U_2849,hAPP(U_2852,U_2853)),hAPP(U_2852,U_2854))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2848),U_2854))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2848),U_2853)) ),
    inference(clausify,[status(thm)],[f_723_3]) ).

fof(f_724_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( ( ( c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) = V_x_2
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oremove]) ).

fof(f_724_2,plain,
    ! [U_2857,U_2856,U_2855] :
      ( ( ( c_Big__Operators_Olattice_OInf__fin(U_2855,c_Orderings_Oord__class_Omin(U_2855),U_2856) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2855),U_2857),c_Big__Operators_Olattice_OInf__fin(U_2855,c_Orderings_Oord__class_Omin(U_2855),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2855,tc_HOL_Obool)),U_2856),hAPP(hAPP(c_Set_Oinsert(U_2855),U_2857),c_Orderings_Obot__class_Obot(tc_fun(U_2855,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2855,tc_HOL_Obool)),U_2856),hAPP(hAPP(c_Set_Oinsert(U_2855),U_2857),c_Orderings_Obot__class_Obot(tc_fun(U_2855,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_2855,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olattice_OInf__fin(U_2855,c_Orderings_Oord__class_Omin(U_2855),U_2856) = U_2857
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2855,tc_HOL_Obool)),U_2856),hAPP(hAPP(c_Set_Oinsert(U_2855),U_2857),c_Orderings_Obot__class_Obot(tc_fun(U_2855,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_2855,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_2855),U_2857),U_2856))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2855),U_2856))
      | ~ class_Orderings_Olinorder(U_2855) ),
    inference(variable_rename,[status(thm)],[f_724_1]) ).

cnf(f_724_3,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_2855,c_Orderings_Oord__class_Omin(U_2855),U_2856) = U_2857
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2855,tc_HOL_Obool)),U_2856),hAPP(hAPP(c_Set_Oinsert(U_2855),U_2857),c_Orderings_Obot__class_Obot(tc_fun(U_2855,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_2855,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2855),U_2857),U_2856))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2855),U_2856))
    | ~ class_Orderings_Olinorder(U_2855) ),
    inference(clausify,[status(thm)],[f_724_2]) ).

cnf(f_724_4,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_2855,c_Orderings_Oord__class_Omin(U_2855),U_2856) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2855),U_2857),c_Big__Operators_Olattice_OInf__fin(U_2855,c_Orderings_Oord__class_Omin(U_2855),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2855,tc_HOL_Obool)),U_2856),hAPP(hAPP(c_Set_Oinsert(U_2855),U_2857),c_Orderings_Obot__class_Obot(tc_fun(U_2855,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2855,tc_HOL_Obool)),U_2856),hAPP(hAPP(c_Set_Oinsert(U_2855),U_2857),c_Orderings_Obot__class_Obot(tc_fun(U_2855,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_2855,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2855),U_2857),U_2856))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2855),U_2856))
    | ~ class_Orderings_Olinorder(U_2855) ),
    inference(clausify,[status(thm)],[f_724_2]) ).

fof(f_725_1,plain,
    ! [V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),V_A_2))
      | ? [B_x,B_y] : ~ hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oclosed]) ).

fof(f_725_2,plain,
    ! [U_2861,U_2860] :
      ( hBOOL(hAPP(hAPP(c_member(U_2860),c_Big__Operators_Olattice_OSup__fin(U_2860,c_Orderings_Oord__class_Omax(U_2860),U_2861)),U_2861))
      | ? [U_2859,U_2858] : ~ hBOOL(hAPP(hAPP(c_member(U_2860),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2860),U_2859),U_2858)),hAPP(hAPP(c_Set_Oinsert(U_2860),U_2859),hAPP(hAPP(c_Set_Oinsert(U_2860),U_2858),c_Orderings_Obot__class_Obot(tc_fun(U_2860,tc_HOL_Obool))))))
      | U_2861 = c_Orderings_Obot__class_Obot(tc_fun(U_2860,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2860),U_2861))
      | ~ class_Orderings_Olinorder(U_2860) ),
    inference(variable_rename,[status(thm)],[f_725_1]) ).

fof(f_725_3,plain,
    ! [U_2861,U_2860] :
      ( hBOOL(hAPP(hAPP(c_member(U_2860),c_Big__Operators_Olattice_OSup__fin(U_2860,c_Orderings_Oord__class_Omax(U_2860),U_2861)),U_2861))
      | ? [U_2858] : ~ hBOOL(hAPP(hAPP(c_member(U_2860),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2860),sK37(U_2861,U_2860)),U_2858)),hAPP(hAPP(c_Set_Oinsert(U_2860),sK37(U_2861,U_2860)),hAPP(hAPP(c_Set_Oinsert(U_2860),U_2858),c_Orderings_Obot__class_Obot(tc_fun(U_2860,tc_HOL_Obool))))))
      | U_2861 = c_Orderings_Obot__class_Obot(tc_fun(U_2860,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2860),U_2861))
      | ~ class_Orderings_Olinorder(U_2860) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK37]),skolemize(U_2859,sK37(U_2861,U_2860))],[f_725_2]) ).

fof(f_725_4,plain,
    ! [U_2861,U_2860] :
      ( hBOOL(hAPP(hAPP(c_member(U_2860),c_Big__Operators_Olattice_OSup__fin(U_2860,c_Orderings_Oord__class_Omax(U_2860),U_2861)),U_2861))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2860),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2860),sK37(U_2861,U_2860)),sK38(U_2861,U_2860))),hAPP(hAPP(c_Set_Oinsert(U_2860),sK37(U_2861,U_2860)),hAPP(hAPP(c_Set_Oinsert(U_2860),sK38(U_2861,U_2860)),c_Orderings_Obot__class_Obot(tc_fun(U_2860,tc_HOL_Obool))))))
      | U_2861 = c_Orderings_Obot__class_Obot(tc_fun(U_2860,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2860),U_2861))
      | ~ class_Orderings_Olinorder(U_2860) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK38]),skolemize(U_2858,sK38(U_2861,U_2860))],[f_725_3]) ).

cnf(f_725_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2860),c_Big__Operators_Olattice_OSup__fin(U_2860,c_Orderings_Oord__class_Omax(U_2860),U_2861)),U_2861))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2860),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2860),sK37(U_2861,U_2860)),sK38(U_2861,U_2860))),hAPP(hAPP(c_Set_Oinsert(U_2860),sK37(U_2861,U_2860)),hAPP(hAPP(c_Set_Oinsert(U_2860),sK38(U_2861,U_2860)),c_Orderings_Obot__class_Obot(tc_fun(U_2860,tc_HOL_Obool))))))
    | U_2861 = c_Orderings_Obot__class_Obot(tc_fun(U_2860,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2860),U_2861))
    | ~ class_Orderings_Olinorder(U_2860) ),
    inference(clausify,[status(thm)],[f_725_4]) ).

fof(f_726_1,plain,
    ! [V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),V_A_2))
      | ? [B_x,B_y] : ~ hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oclosed]) ).

fof(f_726_2,plain,
    ! [U_2865,U_2864] :
      ( hBOOL(hAPP(hAPP(c_member(U_2864),c_Big__Operators_Olattice_OInf__fin(U_2864,c_Orderings_Oord__class_Omin(U_2864),U_2865)),U_2865))
      | ? [U_2863,U_2862] : ~ hBOOL(hAPP(hAPP(c_member(U_2864),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2864),U_2863),U_2862)),hAPP(hAPP(c_Set_Oinsert(U_2864),U_2863),hAPP(hAPP(c_Set_Oinsert(U_2864),U_2862),c_Orderings_Obot__class_Obot(tc_fun(U_2864,tc_HOL_Obool))))))
      | U_2865 = c_Orderings_Obot__class_Obot(tc_fun(U_2864,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2864),U_2865))
      | ~ class_Orderings_Olinorder(U_2864) ),
    inference(variable_rename,[status(thm)],[f_726_1]) ).

fof(f_726_3,plain,
    ! [U_2865,U_2864] :
      ( hBOOL(hAPP(hAPP(c_member(U_2864),c_Big__Operators_Olattice_OInf__fin(U_2864,c_Orderings_Oord__class_Omin(U_2864),U_2865)),U_2865))
      | ? [U_2862] : ~ hBOOL(hAPP(hAPP(c_member(U_2864),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2864),sK39(U_2865,U_2864)),U_2862)),hAPP(hAPP(c_Set_Oinsert(U_2864),sK39(U_2865,U_2864)),hAPP(hAPP(c_Set_Oinsert(U_2864),U_2862),c_Orderings_Obot__class_Obot(tc_fun(U_2864,tc_HOL_Obool))))))
      | U_2865 = c_Orderings_Obot__class_Obot(tc_fun(U_2864,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2864),U_2865))
      | ~ class_Orderings_Olinorder(U_2864) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK39]),skolemize(U_2863,sK39(U_2865,U_2864))],[f_726_2]) ).

fof(f_726_4,plain,
    ! [U_2865,U_2864] :
      ( hBOOL(hAPP(hAPP(c_member(U_2864),c_Big__Operators_Olattice_OInf__fin(U_2864,c_Orderings_Oord__class_Omin(U_2864),U_2865)),U_2865))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2864),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2864),sK39(U_2865,U_2864)),sK40(U_2865,U_2864))),hAPP(hAPP(c_Set_Oinsert(U_2864),sK39(U_2865,U_2864)),hAPP(hAPP(c_Set_Oinsert(U_2864),sK40(U_2865,U_2864)),c_Orderings_Obot__class_Obot(tc_fun(U_2864,tc_HOL_Obool))))))
      | U_2865 = c_Orderings_Obot__class_Obot(tc_fun(U_2864,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2864),U_2865))
      | ~ class_Orderings_Olinorder(U_2864) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK40]),skolemize(U_2862,sK40(U_2865,U_2864))],[f_726_3]) ).

cnf(f_726_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2864),c_Big__Operators_Olattice_OInf__fin(U_2864,c_Orderings_Oord__class_Omin(U_2864),U_2865)),U_2865))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2864),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2864),sK39(U_2865,U_2864)),sK40(U_2865,U_2864))),hAPP(hAPP(c_Set_Oinsert(U_2864),sK39(U_2865,U_2864)),hAPP(hAPP(c_Set_Oinsert(U_2864),sK40(U_2865,U_2864)),c_Orderings_Obot__class_Obot(tc_fun(U_2864,tc_HOL_Obool))))))
    | U_2865 = c_Orderings_Obot__class_Obot(tc_fun(U_2864,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2864),U_2865))
    | ~ class_Orderings_Olinorder(U_2864) ),
    inference(clausify,[status(thm)],[f_726_4]) ).

fof(f_727_1,plain,
    ! [V_k_2,V_less__eq_2,V_i_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatMost(T_b,V_less__eq_2,V_k_2)))
        | ~ hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_k_2)) )
      & ( hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_k_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatMost(T_b,V_less__eq_2,V_k_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_ord_OatMost__iff]) ).

fof(f_727_2,plain,
    ! [U_2869,U_2868,U_2867,U_2866] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_2866),U_2867),c_SetInterval_Oord_OatMost(U_2866,U_2868,U_2869)))
        | ~ hBOOL(hAPP(hAPP(U_2868,U_2867),U_2869)) )
      & ( hBOOL(hAPP(hAPP(U_2868,U_2867),U_2869))
        | ~ hBOOL(hAPP(hAPP(c_member(U_2866),U_2867),c_SetInterval_Oord_OatMost(U_2866,U_2868,U_2869))) ) ),
    inference(variable_rename,[status(thm)],[f_727_1]) ).

fof(f_727_3,plain,
    ( ! [U_2877,U_2875,U_2873] :
        ( ! [U_2871] : hBOOL(hAPP(hAPP(c_member(U_2871),U_2873),c_SetInterval_Oord_OatMost(U_2871,U_2875,U_2877)))
        | ~ hBOOL(hAPP(hAPP(U_2875,U_2873),U_2877)) )
    & ! [U_2876,U_2874,U_2872] :
        ( ! [U_2870] : ~ hBOOL(hAPP(hAPP(c_member(U_2870),U_2872),c_SetInterval_Oord_OatMost(U_2870,U_2874,U_2876)))
        | hBOOL(hAPP(hAPP(U_2874,U_2872),U_2876)) ) ),
    inference(miniscope,[status(thm)],[f_727_2]) ).

cnf(f_727_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_2870),U_2872),c_SetInterval_Oord_OatMost(U_2870,U_2874,U_2876)))
    | hBOOL(hAPP(hAPP(U_2874,U_2872),U_2876)) ),
    inference(clausify,[status(thm)],[f_727_3]) ).

cnf(f_727_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2871),U_2873),c_SetInterval_Oord_OatMost(U_2871,U_2875,U_2877)))
    | ~ hBOOL(hAPP(hAPP(U_2875,U_2873),U_2877)) ),
    inference(clausify,[status(thm)],[f_727_3]) ).

fof(f_728_1,plain,
    ! [V_k_2,V_less__eq_2,V_i_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeast(T_b,V_less__eq_2,V_k_2)))
        | ~ hBOOL(hAPP(hAPP(V_less__eq_2,V_k_2),V_i_2)) )
      & ( hBOOL(hAPP(hAPP(V_less__eq_2,V_k_2),V_i_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeast(T_b,V_less__eq_2,V_k_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_ord_OatLeast__iff]) ).

fof(f_728_2,plain,
    ! [U_2881,U_2880,U_2879,U_2878] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_2878),U_2879),c_SetInterval_Oord_OatLeast(U_2878,U_2880,U_2881)))
        | ~ hBOOL(hAPP(hAPP(U_2880,U_2881),U_2879)) )
      & ( hBOOL(hAPP(hAPP(U_2880,U_2881),U_2879))
        | ~ hBOOL(hAPP(hAPP(c_member(U_2878),U_2879),c_SetInterval_Oord_OatLeast(U_2878,U_2880,U_2881))) ) ),
    inference(variable_rename,[status(thm)],[f_728_1]) ).

fof(f_728_3,plain,
    ( ! [U_2889,U_2887,U_2885] :
        ( ! [U_2883] : hBOOL(hAPP(hAPP(c_member(U_2883),U_2885),c_SetInterval_Oord_OatLeast(U_2883,U_2887,U_2889)))
        | ~ hBOOL(hAPP(hAPP(U_2887,U_2889),U_2885)) )
    & ! [U_2888,U_2886,U_2884] :
        ( ! [U_2882] : ~ hBOOL(hAPP(hAPP(c_member(U_2882),U_2884),c_SetInterval_Oord_OatLeast(U_2882,U_2886,U_2888)))
        | hBOOL(hAPP(hAPP(U_2886,U_2888),U_2884)) ) ),
    inference(miniscope,[status(thm)],[f_728_2]) ).

cnf(f_728_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_2882),U_2884),c_SetInterval_Oord_OatLeast(U_2882,U_2886,U_2888)))
    | hBOOL(hAPP(hAPP(U_2886,U_2888),U_2884)) ),
    inference(clausify,[status(thm)],[f_728_3]) ).

cnf(f_728_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2883),U_2885),c_SetInterval_Oord_OatLeast(U_2883,U_2887,U_2889)))
    | ~ hBOOL(hAPP(hAPP(U_2887,U_2889),U_2885)) ),
    inference(clausify,[status(thm)],[f_728_3]) ).

fof(f_729_1,plain,
    ! [V_k_2,V_less_2,V_i_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OlessThan(T_b,V_less_2,V_k_2)))
        | ~ hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_k_2)) )
      & ( hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_k_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OlessThan(T_b,V_less_2,V_k_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_ord_OlessThan__iff]) ).

fof(f_729_2,plain,
    ! [U_2893,U_2892,U_2891,U_2890] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_2890),U_2891),c_SetInterval_Oord_OlessThan(U_2890,U_2892,U_2893)))
        | ~ hBOOL(hAPP(hAPP(U_2892,U_2891),U_2893)) )
      & ( hBOOL(hAPP(hAPP(U_2892,U_2891),U_2893))
        | ~ hBOOL(hAPP(hAPP(c_member(U_2890),U_2891),c_SetInterval_Oord_OlessThan(U_2890,U_2892,U_2893))) ) ),
    inference(variable_rename,[status(thm)],[f_729_1]) ).

fof(f_729_3,plain,
    ( ! [U_2901,U_2899,U_2897] :
        ( ! [U_2895] : hBOOL(hAPP(hAPP(c_member(U_2895),U_2897),c_SetInterval_Oord_OlessThan(U_2895,U_2899,U_2901)))
        | ~ hBOOL(hAPP(hAPP(U_2899,U_2897),U_2901)) )
    & ! [U_2900,U_2898,U_2896] :
        ( ! [U_2894] : ~ hBOOL(hAPP(hAPP(c_member(U_2894),U_2896),c_SetInterval_Oord_OlessThan(U_2894,U_2898,U_2900)))
        | hBOOL(hAPP(hAPP(U_2898,U_2896),U_2900)) ) ),
    inference(miniscope,[status(thm)],[f_729_2]) ).

cnf(f_729_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_2894),U_2896),c_SetInterval_Oord_OlessThan(U_2894,U_2898,U_2900)))
    | hBOOL(hAPP(hAPP(U_2898,U_2896),U_2900)) ),
    inference(clausify,[status(thm)],[f_729_3]) ).

cnf(f_729_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2895),U_2897),c_SetInterval_Oord_OlessThan(U_2895,U_2899,U_2901)))
    | ~ hBOOL(hAPP(hAPP(U_2899,U_2897),U_2901)) ),
    inference(clausify,[status(thm)],[f_729_3]) ).

fof(f_730_1,plain,
    ! [V_k_2,V_less_2,V_i_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThan(T_b,V_less_2,V_k_2)))
        | ~ hBOOL(hAPP(hAPP(V_less_2,V_k_2),V_i_2)) )
      & ( hBOOL(hAPP(hAPP(V_less_2,V_k_2),V_i_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThan(T_b,V_less_2,V_k_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_ord_OgreaterThan__iff]) ).

fof(f_730_2,plain,
    ! [U_2905,U_2904,U_2903,U_2902] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_2902),U_2903),c_SetInterval_Oord_OgreaterThan(U_2902,U_2904,U_2905)))
        | ~ hBOOL(hAPP(hAPP(U_2904,U_2905),U_2903)) )
      & ( hBOOL(hAPP(hAPP(U_2904,U_2905),U_2903))
        | ~ hBOOL(hAPP(hAPP(c_member(U_2902),U_2903),c_SetInterval_Oord_OgreaterThan(U_2902,U_2904,U_2905))) ) ),
    inference(variable_rename,[status(thm)],[f_730_1]) ).

fof(f_730_3,plain,
    ( ! [U_2913,U_2911,U_2909] :
        ( ! [U_2907] : hBOOL(hAPP(hAPP(c_member(U_2907),U_2909),c_SetInterval_Oord_OgreaterThan(U_2907,U_2911,U_2913)))
        | ~ hBOOL(hAPP(hAPP(U_2911,U_2913),U_2909)) )
    & ! [U_2912,U_2910,U_2908] :
        ( ! [U_2906] : ~ hBOOL(hAPP(hAPP(c_member(U_2906),U_2908),c_SetInterval_Oord_OgreaterThan(U_2906,U_2910,U_2912)))
        | hBOOL(hAPP(hAPP(U_2910,U_2912),U_2908)) ) ),
    inference(miniscope,[status(thm)],[f_730_2]) ).

cnf(f_730_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_2906),U_2908),c_SetInterval_Oord_OgreaterThan(U_2906,U_2910,U_2912)))
    | hBOOL(hAPP(hAPP(U_2910,U_2912),U_2908)) ),
    inference(clausify,[status(thm)],[f_730_3]) ).

cnf(f_730_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2907),U_2909),c_SetInterval_Oord_OgreaterThan(U_2907,U_2911,U_2913)))
    | ~ hBOOL(hAPP(hAPP(U_2911,U_2913),U_2909)) ),
    inference(clausify,[status(thm)],[f_730_3]) ).

fof(f_731_1,plain,
    ! [V_u_2,V_l_2,V_less__eq_2,V_i_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeastAtMost(T_b,V_less__eq_2,V_l_2,V_u_2)))
        | ~ hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2))
        | ~ hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2)) )
      & ( ( hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2))
          & hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2)) )
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeastAtMost(T_b,V_less__eq_2,V_l_2,V_u_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_ord_OatLeastAtMost__iff]) ).

fof(f_731_2,plain,
    ! [U_2918,U_2917,U_2916,U_2915,U_2914] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_2914),U_2915),c_SetInterval_Oord_OatLeastAtMost(U_2914,U_2916,U_2917,U_2918)))
        | ~ hBOOL(hAPP(hAPP(U_2916,U_2915),U_2918))
        | ~ hBOOL(hAPP(hAPP(U_2916,U_2917),U_2915)) )
      & ( ( hBOOL(hAPP(hAPP(U_2916,U_2915),U_2918))
          & hBOOL(hAPP(hAPP(U_2916,U_2917),U_2915)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_2914),U_2915),c_SetInterval_Oord_OatLeastAtMost(U_2914,U_2916,U_2917,U_2918))) ) ),
    inference(variable_rename,[status(thm)],[f_731_1]) ).

fof(f_731_3,plain,
    ( ! [U_2928,U_2926,U_2924,U_2922] :
        ( ! [U_2920] : hBOOL(hAPP(hAPP(c_member(U_2920),U_2922),c_SetInterval_Oord_OatLeastAtMost(U_2920,U_2924,U_2926,U_2928)))
        | ~ hBOOL(hAPP(hAPP(U_2924,U_2922),U_2928))
        | ~ hBOOL(hAPP(hAPP(U_2924,U_2926),U_2922)) )
    & ! [U_2927,U_2925,U_2923,U_2921] :
        ( ! [U_2919] : ~ hBOOL(hAPP(hAPP(c_member(U_2919),U_2921),c_SetInterval_Oord_OatLeastAtMost(U_2919,U_2923,U_2925,U_2927)))
        | ( hBOOL(hAPP(hAPP(U_2923,U_2921),U_2927))
          & hBOOL(hAPP(hAPP(U_2923,U_2925),U_2921)) ) ) ),
    inference(miniscope,[status(thm)],[f_731_2]) ).

cnf(f_731_4,plain,
    ( hBOOL(hAPP(hAPP(U_2923,U_2925),U_2921))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2919),U_2921),c_SetInterval_Oord_OatLeastAtMost(U_2919,U_2923,U_2925,U_2927))) ),
    inference(clausify,[status(thm)],[f_731_3]) ).

cnf(f_731_5,plain,
    ( hBOOL(hAPP(hAPP(U_2923,U_2921),U_2927))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2919),U_2921),c_SetInterval_Oord_OatLeastAtMost(U_2919,U_2923,U_2925,U_2927))) ),
    inference(clausify,[status(thm)],[f_731_3]) ).

cnf(f_731_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2920),U_2922),c_SetInterval_Oord_OatLeastAtMost(U_2920,U_2924,U_2926,U_2928)))
    | ~ hBOOL(hAPP(hAPP(U_2924,U_2922),U_2928))
    | ~ hBOOL(hAPP(hAPP(U_2924,U_2926),U_2922)) ),
    inference(clausify,[status(thm)],[f_731_3]) ).

fof(f_732_1,plain,
    ! [V_u_2,V_l_2,V_less_2,V_i_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThanLessThan(T_b,V_less_2,V_l_2,V_u_2)))
        | ~ hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2))
        | ~ hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)) )
      & ( ( hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2))
          & hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)) )
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThanLessThan(T_b,V_less_2,V_l_2,V_u_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_ord_OgreaterThanLessThan__iff]) ).

fof(f_732_2,plain,
    ! [U_2933,U_2932,U_2931,U_2930,U_2929] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_2929),U_2930),c_SetInterval_Oord_OgreaterThanLessThan(U_2929,U_2931,U_2932,U_2933)))
        | ~ hBOOL(hAPP(hAPP(U_2931,U_2930),U_2933))
        | ~ hBOOL(hAPP(hAPP(U_2931,U_2932),U_2930)) )
      & ( ( hBOOL(hAPP(hAPP(U_2931,U_2930),U_2933))
          & hBOOL(hAPP(hAPP(U_2931,U_2932),U_2930)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_2929),U_2930),c_SetInterval_Oord_OgreaterThanLessThan(U_2929,U_2931,U_2932,U_2933))) ) ),
    inference(variable_rename,[status(thm)],[f_732_1]) ).

fof(f_732_3,plain,
    ( ! [U_2943,U_2941,U_2939,U_2937] :
        ( ! [U_2935] : hBOOL(hAPP(hAPP(c_member(U_2935),U_2937),c_SetInterval_Oord_OgreaterThanLessThan(U_2935,U_2939,U_2941,U_2943)))
        | ~ hBOOL(hAPP(hAPP(U_2939,U_2937),U_2943))
        | ~ hBOOL(hAPP(hAPP(U_2939,U_2941),U_2937)) )
    & ! [U_2942,U_2940,U_2938,U_2936] :
        ( ! [U_2934] : ~ hBOOL(hAPP(hAPP(c_member(U_2934),U_2936),c_SetInterval_Oord_OgreaterThanLessThan(U_2934,U_2938,U_2940,U_2942)))
        | ( hBOOL(hAPP(hAPP(U_2938,U_2936),U_2942))
          & hBOOL(hAPP(hAPP(U_2938,U_2940),U_2936)) ) ) ),
    inference(miniscope,[status(thm)],[f_732_2]) ).

cnf(f_732_4,plain,
    ( hBOOL(hAPP(hAPP(U_2938,U_2940),U_2936))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2934),U_2936),c_SetInterval_Oord_OgreaterThanLessThan(U_2934,U_2938,U_2940,U_2942))) ),
    inference(clausify,[status(thm)],[f_732_3]) ).

cnf(f_732_5,plain,
    ( hBOOL(hAPP(hAPP(U_2938,U_2936),U_2942))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2934),U_2936),c_SetInterval_Oord_OgreaterThanLessThan(U_2934,U_2938,U_2940,U_2942))) ),
    inference(clausify,[status(thm)],[f_732_3]) ).

cnf(f_732_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2935),U_2937),c_SetInterval_Oord_OgreaterThanLessThan(U_2935,U_2939,U_2941,U_2943)))
    | ~ hBOOL(hAPP(hAPP(U_2939,U_2937),U_2943))
    | ~ hBOOL(hAPP(hAPP(U_2939,U_2941),U_2937)) ),
    inference(clausify,[status(thm)],[f_732_3]) ).

fof(f_733_1,plain,
    ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeastLessThan(T_b,V_less__eq_2,V_less_2,V_l_2,V_u_2)))
        | ~ hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2))
        | ~ hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2)) )
      & ( ( hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2))
          & hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2)) )
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeastLessThan(T_b,V_less__eq_2,V_less_2,V_l_2,V_u_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_ord_OatLeastLessThan__iff]) ).

fof(f_733_2,plain,
    ! [U_2949,U_2948,U_2947,U_2946,U_2945,U_2944] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_2944),U_2945),c_SetInterval_Oord_OatLeastLessThan(U_2944,U_2946,U_2947,U_2948,U_2949)))
        | ~ hBOOL(hAPP(hAPP(U_2947,U_2945),U_2949))
        | ~ hBOOL(hAPP(hAPP(U_2946,U_2948),U_2945)) )
      & ( ( hBOOL(hAPP(hAPP(U_2947,U_2945),U_2949))
          & hBOOL(hAPP(hAPP(U_2946,U_2948),U_2945)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_2944),U_2945),c_SetInterval_Oord_OatLeastLessThan(U_2944,U_2946,U_2947,U_2948,U_2949))) ) ),
    inference(variable_rename,[status(thm)],[f_733_1]) ).

fof(f_733_3,plain,
    ( ! [U_2961,U_2959,U_2957,U_2955,U_2953] :
        ( ! [U_2951] : hBOOL(hAPP(hAPP(c_member(U_2951),U_2953),c_SetInterval_Oord_OatLeastLessThan(U_2951,U_2955,U_2957,U_2959,U_2961)))
        | ~ hBOOL(hAPP(hAPP(U_2957,U_2953),U_2961))
        | ~ hBOOL(hAPP(hAPP(U_2955,U_2959),U_2953)) )
    & ! [U_2960,U_2958,U_2956,U_2954,U_2952] :
        ( ! [U_2950] : ~ hBOOL(hAPP(hAPP(c_member(U_2950),U_2952),c_SetInterval_Oord_OatLeastLessThan(U_2950,U_2954,U_2956,U_2958,U_2960)))
        | ( hBOOL(hAPP(hAPP(U_2956,U_2952),U_2960))
          & hBOOL(hAPP(hAPP(U_2954,U_2958),U_2952)) ) ) ),
    inference(miniscope,[status(thm)],[f_733_2]) ).

cnf(f_733_4,plain,
    ( hBOOL(hAPP(hAPP(U_2954,U_2958),U_2952))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2950),U_2952),c_SetInterval_Oord_OatLeastLessThan(U_2950,U_2954,U_2956,U_2958,U_2960))) ),
    inference(clausify,[status(thm)],[f_733_3]) ).

cnf(f_733_5,plain,
    ( hBOOL(hAPP(hAPP(U_2956,U_2952),U_2960))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2950),U_2952),c_SetInterval_Oord_OatLeastLessThan(U_2950,U_2954,U_2956,U_2958,U_2960))) ),
    inference(clausify,[status(thm)],[f_733_3]) ).

cnf(f_733_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2951),U_2953),c_SetInterval_Oord_OatLeastLessThan(U_2951,U_2955,U_2957,U_2959,U_2961)))
    | ~ hBOOL(hAPP(hAPP(U_2957,U_2953),U_2961))
    | ~ hBOOL(hAPP(hAPP(U_2955,U_2959),U_2953)) ),
    inference(clausify,[status(thm)],[f_733_3]) ).

fof(f_734_1,plain,
    ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThanAtMost(T_b,V_less__eq_2,V_less_2,V_l_2,V_u_2)))
        | ~ hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2))
        | ~ hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)) )
      & ( ( hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2))
          & hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)) )
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThanAtMost(T_b,V_less__eq_2,V_less_2,V_l_2,V_u_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_ord_OgreaterThanAtMost__iff]) ).

fof(f_734_2,plain,
    ! [U_2967,U_2966,U_2965,U_2964,U_2963,U_2962] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_2962),U_2963),c_SetInterval_Oord_OgreaterThanAtMost(U_2962,U_2964,U_2965,U_2966,U_2967)))
        | ~ hBOOL(hAPP(hAPP(U_2964,U_2963),U_2967))
        | ~ hBOOL(hAPP(hAPP(U_2965,U_2966),U_2963)) )
      & ( ( hBOOL(hAPP(hAPP(U_2964,U_2963),U_2967))
          & hBOOL(hAPP(hAPP(U_2965,U_2966),U_2963)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_2962),U_2963),c_SetInterval_Oord_OgreaterThanAtMost(U_2962,U_2964,U_2965,U_2966,U_2967))) ) ),
    inference(variable_rename,[status(thm)],[f_734_1]) ).

fof(f_734_3,plain,
    ( ! [U_2979,U_2977,U_2975,U_2973,U_2971] :
        ( ! [U_2969] : hBOOL(hAPP(hAPP(c_member(U_2969),U_2971),c_SetInterval_Oord_OgreaterThanAtMost(U_2969,U_2973,U_2975,U_2977,U_2979)))
        | ~ hBOOL(hAPP(hAPP(U_2973,U_2971),U_2979))
        | ~ hBOOL(hAPP(hAPP(U_2975,U_2977),U_2971)) )
    & ! [U_2978,U_2976,U_2974,U_2972,U_2970] :
        ( ! [U_2968] : ~ hBOOL(hAPP(hAPP(c_member(U_2968),U_2970),c_SetInterval_Oord_OgreaterThanAtMost(U_2968,U_2972,U_2974,U_2976,U_2978)))
        | ( hBOOL(hAPP(hAPP(U_2972,U_2970),U_2978))
          & hBOOL(hAPP(hAPP(U_2974,U_2976),U_2970)) ) ) ),
    inference(miniscope,[status(thm)],[f_734_2]) ).

cnf(f_734_4,plain,
    ( hBOOL(hAPP(hAPP(U_2974,U_2976),U_2970))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2968),U_2970),c_SetInterval_Oord_OgreaterThanAtMost(U_2968,U_2972,U_2974,U_2976,U_2978))) ),
    inference(clausify,[status(thm)],[f_734_3]) ).

cnf(f_734_5,plain,
    ( hBOOL(hAPP(hAPP(U_2972,U_2970),U_2978))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2968),U_2970),c_SetInterval_Oord_OgreaterThanAtMost(U_2968,U_2972,U_2974,U_2976,U_2978))) ),
    inference(clausify,[status(thm)],[f_734_3]) ).

cnf(f_734_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2969),U_2971),c_SetInterval_Oord_OgreaterThanAtMost(U_2969,U_2973,U_2975,U_2977,U_2979)))
    | ~ hBOOL(hAPP(hAPP(U_2973,U_2971),U_2979))
    | ~ hBOOL(hAPP(hAPP(U_2975,U_2977),U_2971)) ),
    inference(clausify,[status(thm)],[f_734_3]) ).

fof(f_735_1,plain,
    ! [V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)))
      | ? [B_M] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_M))
          & hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_M),V_A_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__Union]) ).

fof(f_735_2,plain,
    ! [U_2982,U_2981] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2981),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2981,tc_HOL_Obool),U_2982)))
      | ? [U_2980] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2981),U_2980))
          & hBOOL(hAPP(hAPP(c_member(tc_fun(U_2981,tc_HOL_Obool)),U_2980),U_2982)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_2981,tc_HOL_Obool)),U_2982)) ),
    inference(variable_rename,[status(thm)],[f_735_1]) ).

fof(f_735_3,plain,
    ! [U_2982,U_2981] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_2981),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2981,tc_HOL_Obool),U_2982)))
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2981),sK41(U_2982,U_2981)))
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_2981,tc_HOL_Obool)),sK41(U_2982,U_2981)),U_2982)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_2981,tc_HOL_Obool)),U_2982)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK41]),skolemize(U_2980,sK41(U_2982,U_2981))],[f_735_2]) ).

cnf(f_735_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_2981,tc_HOL_Obool)),sK41(U_2982,U_2981)),U_2982))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_2981),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2981,tc_HOL_Obool),U_2982)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_2981,tc_HOL_Obool)),U_2982)) ),
    inference(clausify,[status(thm)],[f_735_3]) ).

cnf(f_735_5,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2981),sK41(U_2982,U_2981)))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_2981),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2981,tc_HOL_Obool),U_2982)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_2981,tc_HOL_Obool)),U_2982)) ),
    inference(clausify,[status(thm)],[f_735_3]) ).

fof(f_736_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( ( ( c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = V_x_2
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oremove]) ).

fof(f_736_2,plain,
    ! [U_2985,U_2984,U_2983] :
      ( ( ( c_Big__Operators_Olattice__class_OInf__fin(U_2983,U_2984) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2983),U_2985),c_Big__Operators_Olattice__class_OInf__fin(U_2983,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2983,tc_HOL_Obool)),U_2984),hAPP(hAPP(c_Set_Oinsert(U_2983),U_2985),c_Orderings_Obot__class_Obot(tc_fun(U_2983,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2983,tc_HOL_Obool)),U_2984),hAPP(hAPP(c_Set_Oinsert(U_2983),U_2985),c_Orderings_Obot__class_Obot(tc_fun(U_2983,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_2983,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olattice__class_OInf__fin(U_2983,U_2984) = U_2985
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2983,tc_HOL_Obool)),U_2984),hAPP(hAPP(c_Set_Oinsert(U_2983),U_2985),c_Orderings_Obot__class_Obot(tc_fun(U_2983,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_2983,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_2983),U_2985),U_2984))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2983),U_2984))
      | ~ class_Lattices_Olattice(U_2983) ),
    inference(variable_rename,[status(thm)],[f_736_1]) ).

cnf(f_736_3,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_2983,U_2984) = U_2985
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2983,tc_HOL_Obool)),U_2984),hAPP(hAPP(c_Set_Oinsert(U_2983),U_2985),c_Orderings_Obot__class_Obot(tc_fun(U_2983,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_2983,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2983),U_2985),U_2984))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2983),U_2984))
    | ~ class_Lattices_Olattice(U_2983) ),
    inference(clausify,[status(thm)],[f_736_2]) ).

cnf(f_736_4,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_2983,U_2984) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_2983),U_2985),c_Big__Operators_Olattice__class_OInf__fin(U_2983,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2983,tc_HOL_Obool)),U_2984),hAPP(hAPP(c_Set_Oinsert(U_2983),U_2985),c_Orderings_Obot__class_Obot(tc_fun(U_2983,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2983,tc_HOL_Obool)),U_2984),hAPP(hAPP(c_Set_Oinsert(U_2983),U_2985),c_Orderings_Obot__class_Obot(tc_fun(U_2983,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_2983,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2983),U_2985),U_2984))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2983),U_2984))
    | ~ class_Lattices_Olattice(U_2983) ),
    inference(clausify,[status(thm)],[f_736_2]) ).

fof(f_737_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( ( ( c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = V_x_2
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oremove]) ).

fof(f_737_2,plain,
    ! [U_2988,U_2987,U_2986] :
      ( ( ( c_Big__Operators_Olattice__class_OSup__fin(U_2986,U_2987) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2986),U_2988),c_Big__Operators_Olattice__class_OSup__fin(U_2986,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2986,tc_HOL_Obool)),U_2987),hAPP(hAPP(c_Set_Oinsert(U_2986),U_2988),c_Orderings_Obot__class_Obot(tc_fun(U_2986,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2986,tc_HOL_Obool)),U_2987),hAPP(hAPP(c_Set_Oinsert(U_2986),U_2988),c_Orderings_Obot__class_Obot(tc_fun(U_2986,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_2986,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olattice__class_OSup__fin(U_2986,U_2987) = U_2988
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2986,tc_HOL_Obool)),U_2987),hAPP(hAPP(c_Set_Oinsert(U_2986),U_2988),c_Orderings_Obot__class_Obot(tc_fun(U_2986,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_2986,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_2986),U_2988),U_2987))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2986),U_2987))
      | ~ class_Lattices_Olattice(U_2986) ),
    inference(variable_rename,[status(thm)],[f_737_1]) ).

cnf(f_737_3,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_2986,U_2987) = U_2988
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2986,tc_HOL_Obool)),U_2987),hAPP(hAPP(c_Set_Oinsert(U_2986),U_2988),c_Orderings_Obot__class_Obot(tc_fun(U_2986,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_2986,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2986),U_2988),U_2987))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2986),U_2987))
    | ~ class_Lattices_Olattice(U_2986) ),
    inference(clausify,[status(thm)],[f_737_2]) ).

cnf(f_737_4,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_2986,U_2987) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_2986),U_2988),c_Big__Operators_Olattice__class_OSup__fin(U_2986,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2986,tc_HOL_Obool)),U_2987),hAPP(hAPP(c_Set_Oinsert(U_2986),U_2988),c_Orderings_Obot__class_Obot(tc_fun(U_2986,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2986,tc_HOL_Obool)),U_2987),hAPP(hAPP(c_Set_Oinsert(U_2986),U_2988),c_Orderings_Obot__class_Obot(tc_fun(U_2986,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_2986,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2986),U_2988),U_2987))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2986),U_2987))
    | ~ class_Lattices_Olattice(U_2986) ),
    inference(clausify,[status(thm)],[f_737_2]) ).

fof(f_738_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( ( ( c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = V_x_2
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Max_Oremove]) ).

fof(f_738_2,plain,
    ! [U_2991,U_2990,U_2989] :
      ( ( ( c_Big__Operators_Olinorder__class_OMax(U_2989,U_2990) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2989),U_2991),c_Big__Operators_Olinorder__class_OMax(U_2989,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2989,tc_HOL_Obool)),U_2990),hAPP(hAPP(c_Set_Oinsert(U_2989),U_2991),c_Orderings_Obot__class_Obot(tc_fun(U_2989,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2989,tc_HOL_Obool)),U_2990),hAPP(hAPP(c_Set_Oinsert(U_2989),U_2991),c_Orderings_Obot__class_Obot(tc_fun(U_2989,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_2989,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olinorder__class_OMax(U_2989,U_2990) = U_2991
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2989,tc_HOL_Obool)),U_2990),hAPP(hAPP(c_Set_Oinsert(U_2989),U_2991),c_Orderings_Obot__class_Obot(tc_fun(U_2989,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_2989,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_2989),U_2991),U_2990))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2989),U_2990))
      | ~ class_Orderings_Olinorder(U_2989) ),
    inference(variable_rename,[status(thm)],[f_738_1]) ).

cnf(f_738_3,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_2989,U_2990) = U_2991
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2989,tc_HOL_Obool)),U_2990),hAPP(hAPP(c_Set_Oinsert(U_2989),U_2991),c_Orderings_Obot__class_Obot(tc_fun(U_2989,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_2989,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2989),U_2991),U_2990))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2989),U_2990))
    | ~ class_Orderings_Olinorder(U_2989) ),
    inference(clausify,[status(thm)],[f_738_2]) ).

cnf(f_738_4,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_2989,U_2990) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_2989),U_2991),c_Big__Operators_Olinorder__class_OMax(U_2989,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2989,tc_HOL_Obool)),U_2990),hAPP(hAPP(c_Set_Oinsert(U_2989),U_2991),c_Orderings_Obot__class_Obot(tc_fun(U_2989,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2989,tc_HOL_Obool)),U_2990),hAPP(hAPP(c_Set_Oinsert(U_2989),U_2991),c_Orderings_Obot__class_Obot(tc_fun(U_2989,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_2989,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2989),U_2991),U_2990))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2989),U_2990))
    | ~ class_Orderings_Olinorder(U_2989) ),
    inference(clausify,[status(thm)],[f_738_2]) ).

fof(f_739_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( ( ( c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = V_x_2
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Min_Oremove]) ).

fof(f_739_2,plain,
    ! [U_2994,U_2993,U_2992] :
      ( ( ( c_Big__Operators_Olinorder__class_OMin(U_2992,U_2993) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2992),U_2994),c_Big__Operators_Olinorder__class_OMin(U_2992,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2992,tc_HOL_Obool)),U_2993),hAPP(hAPP(c_Set_Oinsert(U_2992),U_2994),c_Orderings_Obot__class_Obot(tc_fun(U_2992,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2992,tc_HOL_Obool)),U_2993),hAPP(hAPP(c_Set_Oinsert(U_2992),U_2994),c_Orderings_Obot__class_Obot(tc_fun(U_2992,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_2992,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olinorder__class_OMin(U_2992,U_2993) = U_2994
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2992,tc_HOL_Obool)),U_2993),hAPP(hAPP(c_Set_Oinsert(U_2992),U_2994),c_Orderings_Obot__class_Obot(tc_fun(U_2992,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_2992,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_2992),U_2994),U_2993))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2992),U_2993))
      | ~ class_Orderings_Olinorder(U_2992) ),
    inference(variable_rename,[status(thm)],[f_739_1]) ).

cnf(f_739_3,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_2992,U_2993) = U_2994
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2992,tc_HOL_Obool)),U_2993),hAPP(hAPP(c_Set_Oinsert(U_2992),U_2994),c_Orderings_Obot__class_Obot(tc_fun(U_2992,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_2992,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2992),U_2994),U_2993))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2992),U_2993))
    | ~ class_Orderings_Olinorder(U_2992) ),
    inference(clausify,[status(thm)],[f_739_2]) ).

cnf(f_739_4,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_2992,U_2993) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_2992),U_2994),c_Big__Operators_Olinorder__class_OMin(U_2992,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2992,tc_HOL_Obool)),U_2993),hAPP(hAPP(c_Set_Oinsert(U_2992),U_2994),c_Orderings_Obot__class_Obot(tc_fun(U_2992,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2992,tc_HOL_Obool)),U_2993),hAPP(hAPP(c_Set_Oinsert(U_2992),U_2994),c_Orderings_Obot__class_Obot(tc_fun(U_2992,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_2992,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2992),U_2994),U_2993))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_2992),U_2993))
    | ~ class_Orderings_Olinorder(U_2992) ),
    inference(clausify,[status(thm)],[f_739_2]) ).

fof(f_740_1,plain,
    ! [V_x_2,T_b] : hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_iso__tuple__UNIV__I]) ).

fof(f_740_2,plain,
    ! [U_2996,U_2995] : hBOOL(hAPP(hAPP(c_member(U_2995),U_2996),c_Orderings_Otop__class_Otop(tc_fun(U_2995,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_740_1]) ).

cnf(f_740_3,plain,
    hBOOL(hAPP(hAPP(c_member(U_2995),U_2996),c_Orderings_Otop__class_Otop(tc_fun(U_2995,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_740_2]) ).

fof(f_741_1,plain,
    ! [V_F_2,V_x_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_x_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_F_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ? [B_x] :
          ( ? [B_xa] :
              ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),B_x),B_xa) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
              & B_x != B_xa
              & hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_xa),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_F_2))) )
          & hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_F_2))) )
      | hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_F_2)) ),
    inference(fof_nnf,[status(thm)],[fact_insert__partition]) ).

fof(f_741_2,plain,
    ! [U_3001,U_3000,U_2999] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2999,tc_HOL_Obool)),U_3000),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2999,tc_HOL_Obool),U_3001)) = c_Orderings_Obot__class_Obot(tc_fun(U_2999,tc_HOL_Obool))
      | ? [U_2998] :
          ( ? [U_2997] :
              ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2999,tc_HOL_Obool)),U_2998),U_2997) != c_Orderings_Obot__class_Obot(tc_fun(U_2999,tc_HOL_Obool))
              & U_2998 != U_2997
              & hBOOL(hAPP(hAPP(c_member(tc_fun(U_2999,tc_HOL_Obool)),U_2997),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_2999,tc_HOL_Obool)),U_3000),U_3001))) )
          & hBOOL(hAPP(hAPP(c_member(tc_fun(U_2999,tc_HOL_Obool)),U_2998),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_2999,tc_HOL_Obool)),U_3000),U_3001))) )
      | hBOOL(hAPP(hAPP(c_member(tc_fun(U_2999,tc_HOL_Obool)),U_3000),U_3001)) ),
    inference(variable_rename,[status(thm)],[f_741_1]) ).

fof(f_741_3,plain,
    ! [U_3001,U_3000,U_2999] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2999,tc_HOL_Obool)),U_3000),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2999,tc_HOL_Obool),U_3001)) = c_Orderings_Obot__class_Obot(tc_fun(U_2999,tc_HOL_Obool))
      | ( ? [U_2997] :
            ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2999,tc_HOL_Obool)),sK42(U_3001,U_3000,U_2999)),U_2997) != c_Orderings_Obot__class_Obot(tc_fun(U_2999,tc_HOL_Obool))
            & sK42(U_3001,U_3000,U_2999) != U_2997
            & hBOOL(hAPP(hAPP(c_member(tc_fun(U_2999,tc_HOL_Obool)),U_2997),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_2999,tc_HOL_Obool)),U_3000),U_3001))) )
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_2999,tc_HOL_Obool)),sK42(U_3001,U_3000,U_2999)),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_2999,tc_HOL_Obool)),U_3000),U_3001))) )
      | hBOOL(hAPP(hAPP(c_member(tc_fun(U_2999,tc_HOL_Obool)),U_3000),U_3001)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK42]),skolemize(U_2998,sK42(U_3001,U_3000,U_2999))],[f_741_2]) ).

fof(f_741_4,plain,
    ! [U_3001,U_3000,U_2999] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2999,tc_HOL_Obool)),U_3000),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2999,tc_HOL_Obool),U_3001)) = c_Orderings_Obot__class_Obot(tc_fun(U_2999,tc_HOL_Obool))
      | ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2999,tc_HOL_Obool)),sK42(U_3001,U_3000,U_2999)),sK43(U_3001,U_3000,U_2999)) != c_Orderings_Obot__class_Obot(tc_fun(U_2999,tc_HOL_Obool))
        & sK42(U_3001,U_3000,U_2999) != sK43(U_3001,U_3000,U_2999)
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_2999,tc_HOL_Obool)),sK43(U_3001,U_3000,U_2999)),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_2999,tc_HOL_Obool)),U_3000),U_3001)))
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_2999,tc_HOL_Obool)),sK42(U_3001,U_3000,U_2999)),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_2999,tc_HOL_Obool)),U_3000),U_3001))) )
      | hBOOL(hAPP(hAPP(c_member(tc_fun(U_2999,tc_HOL_Obool)),U_3000),U_3001)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK43]),skolemize(U_2997,sK43(U_3001,U_3000,U_2999))],[f_741_3]) ).

cnf(f_741_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_2999,tc_HOL_Obool)),sK42(U_3001,U_3000,U_2999)),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_2999,tc_HOL_Obool)),U_3000),U_3001)))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2999,tc_HOL_Obool)),U_3000),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2999,tc_HOL_Obool),U_3001)) = c_Orderings_Obot__class_Obot(tc_fun(U_2999,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(tc_fun(U_2999,tc_HOL_Obool)),U_3000),U_3001)) ),
    inference(clausify,[status(thm)],[f_741_4]) ).

cnf(f_741_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_2999,tc_HOL_Obool)),sK43(U_3001,U_3000,U_2999)),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_2999,tc_HOL_Obool)),U_3000),U_3001)))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2999,tc_HOL_Obool)),U_3000),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2999,tc_HOL_Obool),U_3001)) = c_Orderings_Obot__class_Obot(tc_fun(U_2999,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(tc_fun(U_2999,tc_HOL_Obool)),U_3000),U_3001)) ),
    inference(clausify,[status(thm)],[f_741_4]) ).

cnf(f_741_7,plain,
    ( sK42(U_3001,U_3000,U_2999) != sK43(U_3001,U_3000,U_2999)
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2999,tc_HOL_Obool)),U_3000),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2999,tc_HOL_Obool),U_3001)) = c_Orderings_Obot__class_Obot(tc_fun(U_2999,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(tc_fun(U_2999,tc_HOL_Obool)),U_3000),U_3001)) ),
    inference(clausify,[status(thm)],[f_741_4]) ).

cnf(f_741_8,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2999,tc_HOL_Obool)),sK42(U_3001,U_3000,U_2999)),sK43(U_3001,U_3000,U_2999)) != c_Orderings_Obot__class_Obot(tc_fun(U_2999,tc_HOL_Obool))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_2999,tc_HOL_Obool)),U_3000),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_2999,tc_HOL_Obool),U_3001)) = c_Orderings_Obot__class_Obot(tc_fun(U_2999,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(tc_fun(U_2999,tc_HOL_Obool)),U_3000),U_3001)) ),
    inference(clausify,[status(thm)],[f_741_4]) ).

fof(f_742_1,plain,
    ! [V_A_2,V_F_2,V_f_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_F_2,V_A_2)),V_A_2))
      | ? [B_x,B_y] : ~ hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(V_f_2,B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__one_Oclosed]) ).

fof(f_742_2,plain,
    ! [U_3007,U_3006,U_3005,U_3004] :
      ( hBOOL(hAPP(hAPP(c_member(U_3004),hAPP(U_3006,U_3007)),U_3007))
      | ? [U_3003,U_3002] : ~ hBOOL(hAPP(hAPP(c_member(U_3004),hAPP(hAPP(U_3005,U_3003),U_3002)),hAPP(hAPP(c_Set_Oinsert(U_3004),U_3003),hAPP(hAPP(c_Set_Oinsert(U_3004),U_3002),c_Orderings_Obot__class_Obot(tc_fun(U_3004,tc_HOL_Obool))))))
      | U_3007 = c_Orderings_Obot__class_Obot(tc_fun(U_3004,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3004),U_3007))
      | ~ c_Finite__Set_Ofolding__one(U_3004,U_3005,U_3006) ),
    inference(variable_rename,[status(thm)],[f_742_1]) ).

fof(f_742_3,plain,
    ! [U_3007,U_3006,U_3005,U_3004] :
      ( hBOOL(hAPP(hAPP(c_member(U_3004),hAPP(U_3006,U_3007)),U_3007))
      | ? [U_3002] : ~ hBOOL(hAPP(hAPP(c_member(U_3004),hAPP(hAPP(U_3005,sK44(U_3007,U_3006,U_3005,U_3004)),U_3002)),hAPP(hAPP(c_Set_Oinsert(U_3004),sK44(U_3007,U_3006,U_3005,U_3004)),hAPP(hAPP(c_Set_Oinsert(U_3004),U_3002),c_Orderings_Obot__class_Obot(tc_fun(U_3004,tc_HOL_Obool))))))
      | U_3007 = c_Orderings_Obot__class_Obot(tc_fun(U_3004,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3004),U_3007))
      | ~ c_Finite__Set_Ofolding__one(U_3004,U_3005,U_3006) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK44]),skolemize(U_3003,sK44(U_3007,U_3006,U_3005,U_3004))],[f_742_2]) ).

fof(f_742_4,plain,
    ! [U_3007,U_3006,U_3005,U_3004] :
      ( hBOOL(hAPP(hAPP(c_member(U_3004),hAPP(U_3006,U_3007)),U_3007))
      | ~ hBOOL(hAPP(hAPP(c_member(U_3004),hAPP(hAPP(U_3005,sK44(U_3007,U_3006,U_3005,U_3004)),sK45(U_3007,U_3006,U_3005,U_3004))),hAPP(hAPP(c_Set_Oinsert(U_3004),sK44(U_3007,U_3006,U_3005,U_3004)),hAPP(hAPP(c_Set_Oinsert(U_3004),sK45(U_3007,U_3006,U_3005,U_3004)),c_Orderings_Obot__class_Obot(tc_fun(U_3004,tc_HOL_Obool))))))
      | U_3007 = c_Orderings_Obot__class_Obot(tc_fun(U_3004,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3004),U_3007))
      | ~ c_Finite__Set_Ofolding__one(U_3004,U_3005,U_3006) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK45]),skolemize(U_3002,sK45(U_3007,U_3006,U_3005,U_3004))],[f_742_3]) ).

cnf(f_742_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_3004),hAPP(U_3006,U_3007)),U_3007))
    | ~ hBOOL(hAPP(hAPP(c_member(U_3004),hAPP(hAPP(U_3005,sK44(U_3007,U_3006,U_3005,U_3004)),sK45(U_3007,U_3006,U_3005,U_3004))),hAPP(hAPP(c_Set_Oinsert(U_3004),sK44(U_3007,U_3006,U_3005,U_3004)),hAPP(hAPP(c_Set_Oinsert(U_3004),sK45(U_3007,U_3006,U_3005,U_3004)),c_Orderings_Obot__class_Obot(tc_fun(U_3004,tc_HOL_Obool))))))
    | U_3007 = c_Orderings_Obot__class_Obot(tc_fun(U_3004,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3004),U_3007))
    | ~ c_Finite__Set_Ofolding__one(U_3004,U_3005,U_3006) ),
    inference(clausify,[status(thm)],[f_742_4]) ).

fof(f_743_1,plain,
    ! [V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__le__Sup]) ).

fof(f_743_2,plain,
    ! [U_3009,U_3008] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3008),c_Big__Operators_Olattice__class_OInf__fin(U_3008,U_3009)),c_Big__Operators_Olattice__class_OSup__fin(U_3008,U_3009)))
      | U_3009 = c_Orderings_Obot__class_Obot(tc_fun(U_3008,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3008),U_3009))
      | ~ class_Lattices_Olattice(U_3008) ),
    inference(variable_rename,[status(thm)],[f_743_1]) ).

cnf(f_743_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3008),c_Big__Operators_Olattice__class_OInf__fin(U_3008,U_3009)),c_Big__Operators_Olattice__class_OSup__fin(U_3008,U_3009)))
    | U_3009 = c_Orderings_Obot__class_Obot(tc_fun(U_3008,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3008),U_3009))
    | ~ class_Lattices_Olattice(U_3008) ),
    inference(clausify,[status(thm)],[f_743_2]) ).

fof(f_744_1,plain,
    ! [V_S_2,T_b] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_S_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),V_S_2))
      | V_S_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
      | ~ class_Groups_Olinordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_minus__Max__eq__Min]) ).

fof(f_744_2,plain,
    ! [U_3011,U_3010] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_3010),c_Big__Operators_Olinorder__class_OMax(U_3010,U_3011)) = c_Big__Operators_Olinorder__class_OMin(U_3010,hAPP(c_Set_Oimage(U_3010,U_3010,c_Groups_Ouminus__class_Ouminus(U_3010)),U_3011))
      | U_3011 = c_Orderings_Obot__class_Obot(tc_fun(U_3010,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3010),U_3011))
      | ~ class_Groups_Olinordered__ab__group__add(U_3010) ),
    inference(variable_rename,[status(thm)],[f_744_1]) ).

cnf(f_744_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_3010),c_Big__Operators_Olinorder__class_OMax(U_3010,U_3011)) = c_Big__Operators_Olinorder__class_OMin(U_3010,hAPP(c_Set_Oimage(U_3010,U_3010,c_Groups_Ouminus__class_Ouminus(U_3010)),U_3011))
    | U_3011 = c_Orderings_Obot__class_Obot(tc_fun(U_3010,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3010),U_3011))
    | ~ class_Groups_Olinordered__ab__group__add(U_3010) ),
    inference(clausify,[status(thm)],[f_744_2]) ).

fof(f_745_1,plain,
    ! [V_S_2,T_b] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_S_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),V_S_2))
      | V_S_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
      | ~ class_Groups_Olinordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_minus__Min__eq__Max]) ).

fof(f_745_2,plain,
    ! [U_3013,U_3012] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_3012),c_Big__Operators_Olinorder__class_OMin(U_3012,U_3013)) = c_Big__Operators_Olinorder__class_OMax(U_3012,hAPP(c_Set_Oimage(U_3012,U_3012,c_Groups_Ouminus__class_Ouminus(U_3012)),U_3013))
      | U_3013 = c_Orderings_Obot__class_Obot(tc_fun(U_3012,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3012),U_3013))
      | ~ class_Groups_Olinordered__ab__group__add(U_3012) ),
    inference(variable_rename,[status(thm)],[f_745_1]) ).

cnf(f_745_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_3012),c_Big__Operators_Olinorder__class_OMin(U_3012,U_3013)) = c_Big__Operators_Olinorder__class_OMax(U_3012,hAPP(c_Set_Oimage(U_3012,U_3012,c_Groups_Ouminus__class_Ouminus(U_3012)),U_3013))
    | U_3013 = c_Orderings_Obot__class_Obot(tc_fun(U_3012,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3012),U_3013))
    | ~ class_Groups_Olinordered__ab__group__add(U_3012) ),
    inference(clausify,[status(thm)],[f_745_2]) ).

fof(f_746_1,plain,
    ! [V_x_2,T_b] :
      ( c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Max_Osingleton]) ).

fof(f_746_2,plain,
    ! [U_3015,U_3014] :
      ( c_Big__Operators_Olinorder__class_OMax(U_3014,hAPP(hAPP(c_Set_Oinsert(U_3014),U_3015),c_Orderings_Obot__class_Obot(tc_fun(U_3014,tc_HOL_Obool)))) = U_3015
      | ~ class_Orderings_Olinorder(U_3014) ),
    inference(variable_rename,[status(thm)],[f_746_1]) ).

cnf(f_746_3,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_3014,hAPP(hAPP(c_Set_Oinsert(U_3014),U_3015),c_Orderings_Obot__class_Obot(tc_fun(U_3014,tc_HOL_Obool)))) = U_3015
    | ~ class_Orderings_Olinorder(U_3014) ),
    inference(clausify,[status(thm)],[f_746_2]) ).

fof(f_747_1,plain,
    ! [V_x_2,T_b] :
      ( c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Min_Osingleton]) ).

fof(f_747_2,plain,
    ! [U_3017,U_3016] :
      ( c_Big__Operators_Olinorder__class_OMin(U_3016,hAPP(hAPP(c_Set_Oinsert(U_3016),U_3017),c_Orderings_Obot__class_Obot(tc_fun(U_3016,tc_HOL_Obool)))) = U_3017
      | ~ class_Orderings_Olinorder(U_3016) ),
    inference(variable_rename,[status(thm)],[f_747_1]) ).

cnf(f_747_3,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_3016,hAPP(hAPP(c_Set_Oinsert(U_3016),U_3017),c_Orderings_Obot__class_Obot(tc_fun(U_3016,tc_HOL_Obool)))) = U_3017
    | ~ class_Orderings_Olinorder(U_3016) ),
    inference(clausify,[status(thm)],[f_747_2]) ).

fof(f_748_1,plain,
    ! [V_x_2,T_b] :
      ( c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__fin_Osingleton]) ).

fof(f_748_2,plain,
    ! [U_3019,U_3018] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_3018,hAPP(hAPP(c_Set_Oinsert(U_3018),U_3019),c_Orderings_Obot__class_Obot(tc_fun(U_3018,tc_HOL_Obool)))) = U_3019
      | ~ class_Lattices_Olattice(U_3018) ),
    inference(variable_rename,[status(thm)],[f_748_1]) ).

cnf(f_748_3,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_3018,hAPP(hAPP(c_Set_Oinsert(U_3018),U_3019),c_Orderings_Obot__class_Obot(tc_fun(U_3018,tc_HOL_Obool)))) = U_3019
    | ~ class_Lattices_Olattice(U_3018) ),
    inference(clausify,[status(thm)],[f_748_2]) ).

fof(f_749_1,plain,
    ! [V_x_2,T_b] :
      ( c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__fin_Osingleton]) ).

fof(f_749_2,plain,
    ! [U_3021,U_3020] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_3020,hAPP(hAPP(c_Set_Oinsert(U_3020),U_3021),c_Orderings_Obot__class_Obot(tc_fun(U_3020,tc_HOL_Obool)))) = U_3021
      | ~ class_Lattices_Olattice(U_3020) ),
    inference(variable_rename,[status(thm)],[f_749_1]) ).

cnf(f_749_3,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_3020,hAPP(hAPP(c_Set_Oinsert(U_3020),U_3021),c_Orderings_Obot__class_Obot(tc_fun(U_3020,tc_HOL_Obool)))) = U_3021
    | ~ class_Lattices_Olattice(U_3020) ),
    inference(clausify,[status(thm)],[f_749_2]) ).

fof(f_750_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Max__ge]) ).

fof(f_750_2,plain,
    ! [U_3024,U_3023,U_3022] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3022),U_3024),c_Big__Operators_Olinorder__class_OMax(U_3022,U_3023)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_3022),U_3024),U_3023))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3022),U_3023))
      | ~ class_Orderings_Olinorder(U_3022) ),
    inference(variable_rename,[status(thm)],[f_750_1]) ).

cnf(f_750_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3022),U_3024),c_Big__Operators_Olinorder__class_OMax(U_3022,U_3023)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_3022),U_3024),U_3023))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3022),U_3023))
    | ~ class_Orderings_Olinorder(U_3022) ),
    inference(clausify,[status(thm)],[f_750_2]) ).

fof(f_751_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_x_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Min__le]) ).

fof(f_751_2,plain,
    ! [U_3027,U_3026,U_3025] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3025),c_Big__Operators_Olinorder__class_OMin(U_3025,U_3026)),U_3027))
      | ~ hBOOL(hAPP(hAPP(c_member(U_3025),U_3027),U_3026))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3025),U_3026))
      | ~ class_Orderings_Olinorder(U_3025) ),
    inference(variable_rename,[status(thm)],[f_751_1]) ).

cnf(f_751_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3025),c_Big__Operators_Olinorder__class_OMin(U_3025,U_3026)),U_3027))
    | ~ hBOOL(hAPP(hAPP(c_member(U_3025),U_3027),U_3026))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3025),U_3026))
    | ~ class_Orderings_Olinorder(U_3025) ),
    inference(clausify,[status(thm)],[f_751_2]) ).

fof(f_752_1,plain,
    ! [V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_A_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Min__in]) ).

fof(f_752_2,plain,
    ! [U_3029,U_3028] :
      ( hBOOL(hAPP(hAPP(c_member(U_3028),c_Big__Operators_Olinorder__class_OMin(U_3028,U_3029)),U_3029))
      | U_3029 = c_Orderings_Obot__class_Obot(tc_fun(U_3028,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3028),U_3029))
      | ~ class_Orderings_Olinorder(U_3028) ),
    inference(variable_rename,[status(thm)],[f_752_1]) ).

cnf(f_752_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_3028),c_Big__Operators_Olinorder__class_OMin(U_3028,U_3029)),U_3029))
    | U_3029 = c_Orderings_Obot__class_Obot(tc_fun(U_3028,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3028),U_3029))
    | ~ class_Orderings_Olinorder(U_3028) ),
    inference(clausify,[status(thm)],[f_752_2]) ).

fof(f_753_1,plain,
    ! [V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),V_A_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Max__in]) ).

fof(f_753_2,plain,
    ! [U_3031,U_3030] :
      ( hBOOL(hAPP(hAPP(c_member(U_3030),c_Big__Operators_Olinorder__class_OMax(U_3030,U_3031)),U_3031))
      | U_3031 = c_Orderings_Obot__class_Obot(tc_fun(U_3030,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3030),U_3031))
      | ~ class_Orderings_Olinorder(U_3030) ),
    inference(variable_rename,[status(thm)],[f_753_1]) ).

cnf(f_753_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_3030),c_Big__Operators_Olinorder__class_OMax(U_3030,U_3031)),U_3031))
    | U_3031 = c_Orderings_Obot__class_Obot(tc_fun(U_3030,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3030),U_3031))
    | ~ class_Orderings_Olinorder(U_3030) ),
    inference(clausify,[status(thm)],[f_753_2]) ).

fof(f_754_1,plain,
    ! [V_a_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) = V_a_2
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sup__Inf__absorb]) ).

fof(f_754_2,plain,
    ! [U_3034,U_3033,U_3032] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3032),U_3034),c_Big__Operators_Olattice__class_OInf__fin(U_3032,U_3033)) = U_3034
      | ~ hBOOL(hAPP(hAPP(c_member(U_3032),U_3034),U_3033))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3032),U_3033))
      | ~ class_Lattices_Olattice(U_3032) ),
    inference(variable_rename,[status(thm)],[f_754_1]) ).

cnf(f_754_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3032),U_3034),c_Big__Operators_Olattice__class_OInf__fin(U_3032,U_3033)) = U_3034
    | ~ hBOOL(hAPP(hAPP(c_member(U_3032),U_3034),U_3033))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3032),U_3033))
    | ~ class_Lattices_Olattice(U_3032) ),
    inference(clausify,[status(thm)],[f_754_2]) ).

fof(f_755_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oin__idem]) ).

fof(f_755_2,plain,
    ! [U_3037,U_3036,U_3035] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3035),U_3037),c_Big__Operators_Olattice__class_OSup__fin(U_3035,U_3036)) = c_Big__Operators_Olattice__class_OSup__fin(U_3035,U_3036)
      | ~ hBOOL(hAPP(hAPP(c_member(U_3035),U_3037),U_3036))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3035),U_3036))
      | ~ class_Lattices_Olattice(U_3035) ),
    inference(variable_rename,[status(thm)],[f_755_1]) ).

cnf(f_755_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3035),U_3037),c_Big__Operators_Olattice__class_OSup__fin(U_3035,U_3036)) = c_Big__Operators_Olattice__class_OSup__fin(U_3035,U_3036)
    | ~ hBOOL(hAPP(hAPP(c_member(U_3035),U_3037),U_3036))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3035),U_3036))
    | ~ class_Lattices_Olattice(U_3035) ),
    inference(clausify,[status(thm)],[f_755_2]) ).

fof(f_756_1,plain,
    ! [V_a_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) = V_a_2
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_inf__Sup__absorb]) ).

fof(f_756_2,plain,
    ! [U_3040,U_3039,U_3038] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_3038),U_3040),c_Big__Operators_Olattice__class_OSup__fin(U_3038,U_3039)) = U_3040
      | ~ hBOOL(hAPP(hAPP(c_member(U_3038),U_3040),U_3039))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3038),U_3039))
      | ~ class_Lattices_Olattice(U_3038) ),
    inference(variable_rename,[status(thm)],[f_756_1]) ).

cnf(f_756_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_3038),U_3040),c_Big__Operators_Olattice__class_OSup__fin(U_3038,U_3039)) = U_3040
    | ~ hBOOL(hAPP(hAPP(c_member(U_3038),U_3040),U_3039))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3038),U_3039))
    | ~ class_Lattices_Olattice(U_3038) ),
    inference(clausify,[status(thm)],[f_756_2]) ).

fof(f_757_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oin__idem]) ).

fof(f_757_2,plain,
    ! [U_3043,U_3042,U_3041] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_3041),U_3043),c_Big__Operators_Olattice__class_OInf__fin(U_3041,U_3042)) = c_Big__Operators_Olattice__class_OInf__fin(U_3041,U_3042)
      | ~ hBOOL(hAPP(hAPP(c_member(U_3041),U_3043),U_3042))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3041),U_3042))
      | ~ class_Lattices_Olattice(U_3041) ),
    inference(variable_rename,[status(thm)],[f_757_1]) ).

cnf(f_757_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_3041),U_3043),c_Big__Operators_Olattice__class_OInf__fin(U_3041,U_3042)) = c_Big__Operators_Olattice__class_OInf__fin(U_3041,U_3042)
    | ~ hBOOL(hAPP(hAPP(c_member(U_3041),U_3043),U_3042))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3041),U_3042))
    | ~ class_Lattices_Olattice(U_3041) ),
    inference(clausify,[status(thm)],[f_757_2]) ).

fof(f_758_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Min_Oin__idem]) ).

fof(f_758_2,plain,
    ! [U_3046,U_3045,U_3044] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_3044),U_3046),c_Big__Operators_Olinorder__class_OMin(U_3044,U_3045)) = c_Big__Operators_Olinorder__class_OMin(U_3044,U_3045)
      | ~ hBOOL(hAPP(hAPP(c_member(U_3044),U_3046),U_3045))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3044),U_3045))
      | ~ class_Orderings_Olinorder(U_3044) ),
    inference(variable_rename,[status(thm)],[f_758_1]) ).

cnf(f_758_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_3044),U_3046),c_Big__Operators_Olinorder__class_OMin(U_3044,U_3045)) = c_Big__Operators_Olinorder__class_OMin(U_3044,U_3045)
    | ~ hBOOL(hAPP(hAPP(c_member(U_3044),U_3046),U_3045))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3044),U_3045))
    | ~ class_Orderings_Olinorder(U_3044) ),
    inference(clausify,[status(thm)],[f_758_2]) ).

fof(f_759_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Max_Oin__idem]) ).

fof(f_759_2,plain,
    ! [U_3049,U_3048,U_3047] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_3047),U_3049),c_Big__Operators_Olinorder__class_OMax(U_3047,U_3048)) = c_Big__Operators_Olinorder__class_OMax(U_3047,U_3048)
      | ~ hBOOL(hAPP(hAPP(c_member(U_3047),U_3049),U_3048))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3047),U_3048))
      | ~ class_Orderings_Olinorder(U_3047) ),
    inference(variable_rename,[status(thm)],[f_759_1]) ).

cnf(f_759_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_3047),U_3049),c_Big__Operators_Olinorder__class_OMax(U_3047,U_3048)) = c_Big__Operators_Olinorder__class_OMax(U_3047,U_3048)
    | ~ hBOOL(hAPP(hAPP(c_member(U_3047),U_3049),U_3048))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3047),U_3048))
    | ~ class_Orderings_Olinorder(U_3047) ),
    inference(clausify,[status(thm)],[f_759_2]) ).

fof(f_760_1,plain,
    ! [V_A_2,T_b] :
      ( c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2)
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__fin__Sup]) ).

fof(f_760_2,plain,
    ! [U_3051,U_3050] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_3050,U_3051) = c_Complete__Lattice_OSup__class_OSup(U_3050,U_3051)
      | U_3051 = c_Orderings_Obot__class_Obot(tc_fun(U_3050,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3050),U_3051))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_3050) ),
    inference(variable_rename,[status(thm)],[f_760_1]) ).

cnf(f_760_3,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_3050,U_3051) = c_Complete__Lattice_OSup__class_OSup(U_3050,U_3051)
    | U_3051 = c_Orderings_Obot__class_Obot(tc_fun(U_3050,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3050),U_3051))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_3050) ),
    inference(clausify,[status(thm)],[f_760_2]) ).

fof(f_761_1,plain,
    ! [V_A_2,T_b] :
      ( c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2)
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__fin__Inf]) ).

fof(f_761_2,plain,
    ! [U_3053,U_3052] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_3052,U_3053) = c_Complete__Lattice_OInf__class_OInf(U_3052,U_3053)
      | U_3053 = c_Orderings_Obot__class_Obot(tc_fun(U_3052,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3052),U_3053))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_3052) ),
    inference(variable_rename,[status(thm)],[f_761_1]) ).

cnf(f_761_3,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_3052,U_3053) = c_Complete__Lattice_OInf__class_OInf(U_3052,U_3053)
    | U_3053 = c_Orderings_Obot__class_Obot(tc_fun(U_3052,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3052),U_3053))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_3052) ),
    inference(clausify,[status(thm)],[f_761_2]) ).

fof(f_762_1,plain,
    ! [V_N_2,V_M_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_M_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_N_2)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
      | V_M_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_M_2),V_N_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Max__mono]) ).

fof(f_762_2,plain,
    ! [U_3056,U_3055,U_3054] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3054),c_Big__Operators_Olinorder__class_OMax(U_3054,U_3055)),c_Big__Operators_Olinorder__class_OMax(U_3054,U_3056)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3054),U_3056))
      | U_3055 = c_Orderings_Obot__class_Obot(tc_fun(U_3054,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3054,tc_HOL_Obool)),U_3055),U_3056))
      | ~ class_Orderings_Olinorder(U_3054) ),
    inference(variable_rename,[status(thm)],[f_762_1]) ).

cnf(f_762_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3054),c_Big__Operators_Olinorder__class_OMax(U_3054,U_3055)),c_Big__Operators_Olinorder__class_OMax(U_3054,U_3056)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3054),U_3056))
    | U_3055 = c_Orderings_Obot__class_Obot(tc_fun(U_3054,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3054,tc_HOL_Obool)),U_3055),U_3056))
    | ~ class_Orderings_Olinorder(U_3054) ),
    inference(clausify,[status(thm)],[f_762_2]) ).

fof(f_763_1,plain,
    ! [V_N_2,V_M_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_N_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_M_2)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
      | V_M_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_M_2),V_N_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Min__antimono]) ).

fof(f_763_2,plain,
    ! [U_3059,U_3058,U_3057] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3057),c_Big__Operators_Olinorder__class_OMin(U_3057,U_3059)),c_Big__Operators_Olinorder__class_OMin(U_3057,U_3058)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3057),U_3059))
      | U_3058 = c_Orderings_Obot__class_Obot(tc_fun(U_3057,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3057,tc_HOL_Obool)),U_3058),U_3059))
      | ~ class_Orderings_Olinorder(U_3057) ),
    inference(variable_rename,[status(thm)],[f_763_1]) ).

cnf(f_763_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3057),c_Big__Operators_Olinorder__class_OMin(U_3057,U_3059)),c_Big__Operators_Olinorder__class_OMin(U_3057,U_3058)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3057),U_3059))
    | U_3058 = c_Orderings_Obot__class_Obot(tc_fun(U_3057,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3057,tc_HOL_Obool)),U_3058),U_3059))
    | ~ class_Orderings_Olinorder(U_3057) ),
    inference(clausify,[status(thm)],[f_763_2]) ).

fof(f_764_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oinsert__idem]) ).

fof(f_764_2,plain,
    ! [U_3062,U_3061,U_3060] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_3060,hAPP(hAPP(c_Set_Oinsert(U_3060),U_3062),U_3061)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3060),U_3062),c_Big__Operators_Olattice__class_OSup__fin(U_3060,U_3061))
      | U_3061 = c_Orderings_Obot__class_Obot(tc_fun(U_3060,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3060),U_3061))
      | ~ class_Lattices_Olattice(U_3060) ),
    inference(variable_rename,[status(thm)],[f_764_1]) ).

cnf(f_764_3,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_3060,hAPP(hAPP(c_Set_Oinsert(U_3060),U_3062),U_3061)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3060),U_3062),c_Big__Operators_Olattice__class_OSup__fin(U_3060,U_3061))
    | U_3061 = c_Orderings_Obot__class_Obot(tc_fun(U_3060,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3060),U_3061))
    | ~ class_Lattices_Olattice(U_3060) ),
    inference(clausify,[status(thm)],[f_764_2]) ).

fof(f_765_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oinsert__idem]) ).

fof(f_765_2,plain,
    ! [U_3065,U_3064,U_3063] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_3063,hAPP(hAPP(c_Set_Oinsert(U_3063),U_3065),U_3064)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_3063),U_3065),c_Big__Operators_Olattice__class_OInf__fin(U_3063,U_3064))
      | U_3064 = c_Orderings_Obot__class_Obot(tc_fun(U_3063,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3063),U_3064))
      | ~ class_Lattices_Olattice(U_3063) ),
    inference(variable_rename,[status(thm)],[f_765_1]) ).

cnf(f_765_3,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_3063,hAPP(hAPP(c_Set_Oinsert(U_3063),U_3065),U_3064)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_3063),U_3065),c_Big__Operators_Olattice__class_OInf__fin(U_3063,U_3064))
    | U_3064 = c_Orderings_Obot__class_Obot(tc_fun(U_3063,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3063),U_3064))
    | ~ class_Lattices_Olattice(U_3063) ),
    inference(clausify,[status(thm)],[f_765_2]) ).

fof(f_766_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Min__insert]) ).

fof(f_766_2,plain,
    ! [U_3068,U_3067,U_3066] :
      ( c_Big__Operators_Olinorder__class_OMin(U_3066,hAPP(hAPP(c_Set_Oinsert(U_3066),U_3068),U_3067)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_3066),U_3068),c_Big__Operators_Olinorder__class_OMin(U_3066,U_3067))
      | U_3067 = c_Orderings_Obot__class_Obot(tc_fun(U_3066,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3066),U_3067))
      | ~ class_Orderings_Olinorder(U_3066) ),
    inference(variable_rename,[status(thm)],[f_766_1]) ).

cnf(f_766_3,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_3066,hAPP(hAPP(c_Set_Oinsert(U_3066),U_3068),U_3067)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_3066),U_3068),c_Big__Operators_Olinorder__class_OMin(U_3066,U_3067))
    | U_3067 = c_Orderings_Obot__class_Obot(tc_fun(U_3066,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3066),U_3067))
    | ~ class_Orderings_Olinorder(U_3066) ),
    inference(clausify,[status(thm)],[f_766_2]) ).

fof(f_767_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__fin_Osubset__idem]) ).

fof(f_767_2,plain,
    ! [U_3071,U_3070,U_3069] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3069),c_Big__Operators_Olattice__class_OSup__fin(U_3069,U_3071)),c_Big__Operators_Olattice__class_OSup__fin(U_3069,U_3070)) = c_Big__Operators_Olattice__class_OSup__fin(U_3069,U_3070)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3069,tc_HOL_Obool)),U_3071),U_3070))
      | U_3071 = c_Orderings_Obot__class_Obot(tc_fun(U_3069,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3069),U_3070))
      | ~ class_Lattices_Olattice(U_3069) ),
    inference(variable_rename,[status(thm)],[f_767_1]) ).

cnf(f_767_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3069),c_Big__Operators_Olattice__class_OSup__fin(U_3069,U_3071)),c_Big__Operators_Olattice__class_OSup__fin(U_3069,U_3070)) = c_Big__Operators_Olattice__class_OSup__fin(U_3069,U_3070)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3069,tc_HOL_Obool)),U_3071),U_3070))
    | U_3071 = c_Orderings_Obot__class_Obot(tc_fun(U_3069,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3069),U_3070))
    | ~ class_Lattices_Olattice(U_3069) ),
    inference(clausify,[status(thm)],[f_767_2]) ).

fof(f_768_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Max__insert]) ).

fof(f_768_2,plain,
    ! [U_3074,U_3073,U_3072] :
      ( c_Big__Operators_Olinorder__class_OMax(U_3072,hAPP(hAPP(c_Set_Oinsert(U_3072),U_3074),U_3073)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_3072),U_3074),c_Big__Operators_Olinorder__class_OMax(U_3072,U_3073))
      | U_3073 = c_Orderings_Obot__class_Obot(tc_fun(U_3072,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3072),U_3073))
      | ~ class_Orderings_Olinorder(U_3072) ),
    inference(variable_rename,[status(thm)],[f_768_1]) ).

cnf(f_768_3,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_3072,hAPP(hAPP(c_Set_Oinsert(U_3072),U_3074),U_3073)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_3072),U_3074),c_Big__Operators_Olinorder__class_OMax(U_3072,U_3073))
    | U_3073 = c_Orderings_Obot__class_Obot(tc_fun(U_3072,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3072),U_3073))
    | ~ class_Orderings_Olinorder(U_3072) ),
    inference(clausify,[status(thm)],[f_768_2]) ).

fof(f_769_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__fin_Osubset__idem]) ).

fof(f_769_2,plain,
    ! [U_3077,U_3076,U_3075] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_3075),c_Big__Operators_Olattice__class_OInf__fin(U_3075,U_3077)),c_Big__Operators_Olattice__class_OInf__fin(U_3075,U_3076)) = c_Big__Operators_Olattice__class_OInf__fin(U_3075,U_3076)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3075,tc_HOL_Obool)),U_3077),U_3076))
      | U_3077 = c_Orderings_Obot__class_Obot(tc_fun(U_3075,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3075),U_3076))
      | ~ class_Lattices_Olattice(U_3075) ),
    inference(variable_rename,[status(thm)],[f_769_1]) ).

cnf(f_769_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_3075),c_Big__Operators_Olattice__class_OInf__fin(U_3075,U_3077)),c_Big__Operators_Olattice__class_OInf__fin(U_3075,U_3076)) = c_Big__Operators_Olattice__class_OInf__fin(U_3075,U_3076)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3075,tc_HOL_Obool)),U_3077),U_3076))
    | U_3077 = c_Orderings_Obot__class_Obot(tc_fun(U_3075,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3075),U_3076))
    | ~ class_Lattices_Olattice(U_3075) ),
    inference(clausify,[status(thm)],[f_769_2]) ).

fof(f_770_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_B_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Min_Osubset__idem]) ).

fof(f_770_2,plain,
    ! [U_3080,U_3079,U_3078] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_3078),c_Big__Operators_Olinorder__class_OMin(U_3078,U_3080)),c_Big__Operators_Olinorder__class_OMin(U_3078,U_3079)) = c_Big__Operators_Olinorder__class_OMin(U_3078,U_3079)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3078,tc_HOL_Obool)),U_3080),U_3079))
      | U_3080 = c_Orderings_Obot__class_Obot(tc_fun(U_3078,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3078),U_3079))
      | ~ class_Orderings_Olinorder(U_3078) ),
    inference(variable_rename,[status(thm)],[f_770_1]) ).

cnf(f_770_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_3078),c_Big__Operators_Olinorder__class_OMin(U_3078,U_3080)),c_Big__Operators_Olinorder__class_OMin(U_3078,U_3079)) = c_Big__Operators_Olinorder__class_OMin(U_3078,U_3079)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3078,tc_HOL_Obool)),U_3080),U_3079))
    | U_3080 = c_Orderings_Obot__class_Obot(tc_fun(U_3078,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3078),U_3079))
    | ~ class_Orderings_Olinorder(U_3078) ),
    inference(clausify,[status(thm)],[f_770_2]) ).

fof(f_771_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__fin_Ounion__idem]) ).

fof(f_771_2,plain,
    ! [U_3083,U_3082,U_3081] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_3081,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3081,tc_HOL_Obool)),U_3082),U_3083)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3081),c_Big__Operators_Olattice__class_OSup__fin(U_3081,U_3082)),c_Big__Operators_Olattice__class_OSup__fin(U_3081,U_3083))
      | U_3083 = c_Orderings_Obot__class_Obot(tc_fun(U_3081,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3081),U_3083))
      | U_3082 = c_Orderings_Obot__class_Obot(tc_fun(U_3081,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3081),U_3082))
      | ~ class_Lattices_Olattice(U_3081) ),
    inference(variable_rename,[status(thm)],[f_771_1]) ).

cnf(f_771_3,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_3081,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3081,tc_HOL_Obool)),U_3082),U_3083)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3081),c_Big__Operators_Olattice__class_OSup__fin(U_3081,U_3082)),c_Big__Operators_Olattice__class_OSup__fin(U_3081,U_3083))
    | U_3083 = c_Orderings_Obot__class_Obot(tc_fun(U_3081,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3081),U_3083))
    | U_3082 = c_Orderings_Obot__class_Obot(tc_fun(U_3081,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3081),U_3082))
    | ~ class_Lattices_Olattice(U_3081) ),
    inference(clausify,[status(thm)],[f_771_2]) ).

fof(f_772_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_B_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Max_Osubset__idem]) ).

fof(f_772_2,plain,
    ! [U_3086,U_3085,U_3084] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_3084),c_Big__Operators_Olinorder__class_OMax(U_3084,U_3086)),c_Big__Operators_Olinorder__class_OMax(U_3084,U_3085)) = c_Big__Operators_Olinorder__class_OMax(U_3084,U_3085)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3084,tc_HOL_Obool)),U_3086),U_3085))
      | U_3086 = c_Orderings_Obot__class_Obot(tc_fun(U_3084,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3084),U_3085))
      | ~ class_Orderings_Olinorder(U_3084) ),
    inference(variable_rename,[status(thm)],[f_772_1]) ).

cnf(f_772_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_3084),c_Big__Operators_Olinorder__class_OMax(U_3084,U_3086)),c_Big__Operators_Olinorder__class_OMax(U_3084,U_3085)) = c_Big__Operators_Olinorder__class_OMax(U_3084,U_3085)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3084,tc_HOL_Obool)),U_3086),U_3085))
    | U_3086 = c_Orderings_Obot__class_Obot(tc_fun(U_3084,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3084),U_3085))
    | ~ class_Orderings_Olinorder(U_3084) ),
    inference(clausify,[status(thm)],[f_772_2]) ).

fof(f_773_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__fin_Ounion__idem]) ).

fof(f_773_2,plain,
    ! [U_3089,U_3088,U_3087] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_3087,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3087,tc_HOL_Obool)),U_3088),U_3089)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_3087),c_Big__Operators_Olattice__class_OInf__fin(U_3087,U_3088)),c_Big__Operators_Olattice__class_OInf__fin(U_3087,U_3089))
      | U_3089 = c_Orderings_Obot__class_Obot(tc_fun(U_3087,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3087),U_3089))
      | U_3088 = c_Orderings_Obot__class_Obot(tc_fun(U_3087,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3087),U_3088))
      | ~ class_Lattices_Olattice(U_3087) ),
    inference(variable_rename,[status(thm)],[f_773_1]) ).

cnf(f_773_3,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_3087,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3087,tc_HOL_Obool)),U_3088),U_3089)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_3087),c_Big__Operators_Olattice__class_OInf__fin(U_3087,U_3088)),c_Big__Operators_Olattice__class_OInf__fin(U_3087,U_3089))
    | U_3089 = c_Orderings_Obot__class_Obot(tc_fun(U_3087,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3087),U_3089))
    | U_3088 = c_Orderings_Obot__class_Obot(tc_fun(U_3087,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3087),U_3088))
    | ~ class_Lattices_Olattice(U_3087) ),
    inference(clausify,[status(thm)],[f_773_2]) ).

fof(f_774_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_B_2))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Min__Un]) ).

fof(f_774_2,plain,
    ! [U_3092,U_3091,U_3090] :
      ( c_Big__Operators_Olinorder__class_OMin(U_3090,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3090,tc_HOL_Obool)),U_3091),U_3092)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_3090),c_Big__Operators_Olinorder__class_OMin(U_3090,U_3091)),c_Big__Operators_Olinorder__class_OMin(U_3090,U_3092))
      | U_3092 = c_Orderings_Obot__class_Obot(tc_fun(U_3090,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3090),U_3092))
      | U_3091 = c_Orderings_Obot__class_Obot(tc_fun(U_3090,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3090),U_3091))
      | ~ class_Orderings_Olinorder(U_3090) ),
    inference(variable_rename,[status(thm)],[f_774_1]) ).

cnf(f_774_3,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_3090,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3090,tc_HOL_Obool)),U_3091),U_3092)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_3090),c_Big__Operators_Olinorder__class_OMin(U_3090,U_3091)),c_Big__Operators_Olinorder__class_OMin(U_3090,U_3092))
    | U_3092 = c_Orderings_Obot__class_Obot(tc_fun(U_3090,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3090),U_3092))
    | U_3091 = c_Orderings_Obot__class_Obot(tc_fun(U_3090,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3090),U_3091))
    | ~ class_Orderings_Olinorder(U_3090) ),
    inference(clausify,[status(thm)],[f_774_2]) ).

fof(f_775_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_B_2))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Max__Un]) ).

fof(f_775_2,plain,
    ! [U_3095,U_3094,U_3093] :
      ( c_Big__Operators_Olinorder__class_OMax(U_3093,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3093,tc_HOL_Obool)),U_3094),U_3095)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_3093),c_Big__Operators_Olinorder__class_OMax(U_3093,U_3094)),c_Big__Operators_Olinorder__class_OMax(U_3093,U_3095))
      | U_3095 = c_Orderings_Obot__class_Obot(tc_fun(U_3093,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3093),U_3095))
      | U_3094 = c_Orderings_Obot__class_Obot(tc_fun(U_3093,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3093),U_3094))
      | ~ class_Orderings_Olinorder(U_3093) ),
    inference(variable_rename,[status(thm)],[f_775_1]) ).

cnf(f_775_3,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_3093,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3093,tc_HOL_Obool)),U_3094),U_3095)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_3093),c_Big__Operators_Olinorder__class_OMax(U_3093,U_3094)),c_Big__Operators_Olinorder__class_OMax(U_3093,U_3095))
    | U_3095 = c_Orderings_Obot__class_Obot(tc_fun(U_3093,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3093),U_3095))
    | U_3094 = c_Orderings_Obot__class_Obot(tc_fun(U_3093,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3093),U_3094))
    | ~ class_Orderings_Olinorder(U_3093) ),
    inference(clausify,[status(thm)],[f_775_2]) ).

fof(f_776_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oinsert]) ).

fof(f_776_2,plain,
    ! [U_3098,U_3097,U_3096] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_3096,hAPP(hAPP(c_Set_Oinsert(U_3096),U_3098),U_3097)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3096),U_3098),c_Big__Operators_Olattice__class_OSup__fin(U_3096,U_3097))
      | U_3097 = c_Orderings_Obot__class_Obot(tc_fun(U_3096,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(U_3096),U_3098),U_3097))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3096),U_3097))
      | ~ class_Lattices_Olattice(U_3096) ),
    inference(variable_rename,[status(thm)],[f_776_1]) ).

cnf(f_776_3,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_3096,hAPP(hAPP(c_Set_Oinsert(U_3096),U_3098),U_3097)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3096),U_3098),c_Big__Operators_Olattice__class_OSup__fin(U_3096,U_3097))
    | U_3097 = c_Orderings_Obot__class_Obot(tc_fun(U_3096,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(U_3096),U_3098),U_3097))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3096),U_3097))
    | ~ class_Lattices_Olattice(U_3096) ),
    inference(clausify,[status(thm)],[f_776_2]) ).

fof(f_777_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oinsert]) ).

fof(f_777_2,plain,
    ! [U_3101,U_3100,U_3099] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_3099,hAPP(hAPP(c_Set_Oinsert(U_3099),U_3101),U_3100)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_3099),U_3101),c_Big__Operators_Olattice__class_OInf__fin(U_3099,U_3100))
      | U_3100 = c_Orderings_Obot__class_Obot(tc_fun(U_3099,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(U_3099),U_3101),U_3100))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3099),U_3100))
      | ~ class_Lattices_Olattice(U_3099) ),
    inference(variable_rename,[status(thm)],[f_777_1]) ).

cnf(f_777_3,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_3099,hAPP(hAPP(c_Set_Oinsert(U_3099),U_3101),U_3100)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_3099),U_3101),c_Big__Operators_Olattice__class_OInf__fin(U_3099,U_3100))
    | U_3100 = c_Orderings_Obot__class_Obot(tc_fun(U_3099,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(U_3099),U_3101),U_3100))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3099),U_3100))
    | ~ class_Lattices_Olattice(U_3099) ),
    inference(clausify,[status(thm)],[f_777_2]) ).

fof(f_778_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Min_Oinsert]) ).

fof(f_778_2,plain,
    ! [U_3104,U_3103,U_3102] :
      ( c_Big__Operators_Olinorder__class_OMin(U_3102,hAPP(hAPP(c_Set_Oinsert(U_3102),U_3104),U_3103)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_3102),U_3104),c_Big__Operators_Olinorder__class_OMin(U_3102,U_3103))
      | U_3103 = c_Orderings_Obot__class_Obot(tc_fun(U_3102,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(U_3102),U_3104),U_3103))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3102),U_3103))
      | ~ class_Orderings_Olinorder(U_3102) ),
    inference(variable_rename,[status(thm)],[f_778_1]) ).

cnf(f_778_3,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_3102,hAPP(hAPP(c_Set_Oinsert(U_3102),U_3104),U_3103)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_3102),U_3104),c_Big__Operators_Olinorder__class_OMin(U_3102,U_3103))
    | U_3103 = c_Orderings_Obot__class_Obot(tc_fun(U_3102,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(U_3102),U_3104),U_3103))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3102),U_3103))
    | ~ class_Orderings_Olinorder(U_3102) ),
    inference(clausify,[status(thm)],[f_778_2]) ).

fof(f_779_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Max_Oinsert]) ).

fof(f_779_2,plain,
    ! [U_3107,U_3106,U_3105] :
      ( c_Big__Operators_Olinorder__class_OMax(U_3105,hAPP(hAPP(c_Set_Oinsert(U_3105),U_3107),U_3106)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_3105),U_3107),c_Big__Operators_Olinorder__class_OMax(U_3105,U_3106))
      | U_3106 = c_Orderings_Obot__class_Obot(tc_fun(U_3105,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(U_3105),U_3107),U_3106))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3105),U_3106))
      | ~ class_Orderings_Olinorder(U_3105) ),
    inference(variable_rename,[status(thm)],[f_779_1]) ).

cnf(f_779_3,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_3105,hAPP(hAPP(c_Set_Oinsert(U_3105),U_3107),U_3106)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_3105),U_3107),c_Big__Operators_Olinorder__class_OMax(U_3105,U_3106))
    | U_3106 = c_Orderings_Obot__class_Obot(tc_fun(U_3105,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(U_3105),U_3107),U_3106))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3105),U_3106))
    | ~ class_Orderings_Olinorder(U_3105) ),
    inference(clausify,[status(thm)],[f_779_2]) ).

fof(f_780_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( ( ( c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oinsert__remove]) ).

fof(f_780_2,plain,
    ! [U_3110,U_3109,U_3108] :
      ( ( ( c_Big__Operators_Olattice__class_OSup__fin(U_3108,hAPP(hAPP(c_Set_Oinsert(U_3108),U_3110),U_3109)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3108),U_3110),c_Big__Operators_Olattice__class_OSup__fin(U_3108,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3108,tc_HOL_Obool)),U_3109),hAPP(hAPP(c_Set_Oinsert(U_3108),U_3110),c_Orderings_Obot__class_Obot(tc_fun(U_3108,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3108,tc_HOL_Obool)),U_3109),hAPP(hAPP(c_Set_Oinsert(U_3108),U_3110),c_Orderings_Obot__class_Obot(tc_fun(U_3108,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_3108,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olattice__class_OSup__fin(U_3108,hAPP(hAPP(c_Set_Oinsert(U_3108),U_3110),U_3109)) = U_3110
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3108,tc_HOL_Obool)),U_3109),hAPP(hAPP(c_Set_Oinsert(U_3108),U_3110),c_Orderings_Obot__class_Obot(tc_fun(U_3108,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_3108,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3108),U_3109))
      | ~ class_Lattices_Olattice(U_3108) ),
    inference(variable_rename,[status(thm)],[f_780_1]) ).

cnf(f_780_3,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_3108,hAPP(hAPP(c_Set_Oinsert(U_3108),U_3110),U_3109)) = U_3110
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3108,tc_HOL_Obool)),U_3109),hAPP(hAPP(c_Set_Oinsert(U_3108),U_3110),c_Orderings_Obot__class_Obot(tc_fun(U_3108,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_3108,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3108),U_3109))
    | ~ class_Lattices_Olattice(U_3108) ),
    inference(clausify,[status(thm)],[f_780_2]) ).

cnf(f_780_4,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_3108,hAPP(hAPP(c_Set_Oinsert(U_3108),U_3110),U_3109)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3108),U_3110),c_Big__Operators_Olattice__class_OSup__fin(U_3108,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3108,tc_HOL_Obool)),U_3109),hAPP(hAPP(c_Set_Oinsert(U_3108),U_3110),c_Orderings_Obot__class_Obot(tc_fun(U_3108,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3108,tc_HOL_Obool)),U_3109),hAPP(hAPP(c_Set_Oinsert(U_3108),U_3110),c_Orderings_Obot__class_Obot(tc_fun(U_3108,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_3108,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3108),U_3109))
    | ~ class_Lattices_Olattice(U_3108) ),
    inference(clausify,[status(thm)],[f_780_2]) ).

fof(f_781_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( ( ( c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oinsert__remove]) ).

fof(f_781_2,plain,
    ! [U_3113,U_3112,U_3111] :
      ( ( ( c_Big__Operators_Olattice__class_OInf__fin(U_3111,hAPP(hAPP(c_Set_Oinsert(U_3111),U_3113),U_3112)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_3111),U_3113),c_Big__Operators_Olattice__class_OInf__fin(U_3111,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3111,tc_HOL_Obool)),U_3112),hAPP(hAPP(c_Set_Oinsert(U_3111),U_3113),c_Orderings_Obot__class_Obot(tc_fun(U_3111,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3111,tc_HOL_Obool)),U_3112),hAPP(hAPP(c_Set_Oinsert(U_3111),U_3113),c_Orderings_Obot__class_Obot(tc_fun(U_3111,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_3111,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olattice__class_OInf__fin(U_3111,hAPP(hAPP(c_Set_Oinsert(U_3111),U_3113),U_3112)) = U_3113
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3111,tc_HOL_Obool)),U_3112),hAPP(hAPP(c_Set_Oinsert(U_3111),U_3113),c_Orderings_Obot__class_Obot(tc_fun(U_3111,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_3111,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3111),U_3112))
      | ~ class_Lattices_Olattice(U_3111) ),
    inference(variable_rename,[status(thm)],[f_781_1]) ).

cnf(f_781_3,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_3111,hAPP(hAPP(c_Set_Oinsert(U_3111),U_3113),U_3112)) = U_3113
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3111,tc_HOL_Obool)),U_3112),hAPP(hAPP(c_Set_Oinsert(U_3111),U_3113),c_Orderings_Obot__class_Obot(tc_fun(U_3111,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_3111,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3111),U_3112))
    | ~ class_Lattices_Olattice(U_3111) ),
    inference(clausify,[status(thm)],[f_781_2]) ).

cnf(f_781_4,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_3111,hAPP(hAPP(c_Set_Oinsert(U_3111),U_3113),U_3112)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_3111),U_3113),c_Big__Operators_Olattice__class_OInf__fin(U_3111,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3111,tc_HOL_Obool)),U_3112),hAPP(hAPP(c_Set_Oinsert(U_3111),U_3113),c_Orderings_Obot__class_Obot(tc_fun(U_3111,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3111,tc_HOL_Obool)),U_3112),hAPP(hAPP(c_Set_Oinsert(U_3111),U_3113),c_Orderings_Obot__class_Obot(tc_fun(U_3111,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_3111,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3111),U_3112))
    | ~ class_Lattices_Olattice(U_3111) ),
    inference(clausify,[status(thm)],[f_781_2]) ).

fof(f_782_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( ( ( c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Min_Oinsert__remove]) ).

fof(f_782_2,plain,
    ! [U_3116,U_3115,U_3114] :
      ( ( ( c_Big__Operators_Olinorder__class_OMin(U_3114,hAPP(hAPP(c_Set_Oinsert(U_3114),U_3116),U_3115)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_3114),U_3116),c_Big__Operators_Olinorder__class_OMin(U_3114,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3114,tc_HOL_Obool)),U_3115),hAPP(hAPP(c_Set_Oinsert(U_3114),U_3116),c_Orderings_Obot__class_Obot(tc_fun(U_3114,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3114,tc_HOL_Obool)),U_3115),hAPP(hAPP(c_Set_Oinsert(U_3114),U_3116),c_Orderings_Obot__class_Obot(tc_fun(U_3114,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_3114,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olinorder__class_OMin(U_3114,hAPP(hAPP(c_Set_Oinsert(U_3114),U_3116),U_3115)) = U_3116
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3114,tc_HOL_Obool)),U_3115),hAPP(hAPP(c_Set_Oinsert(U_3114),U_3116),c_Orderings_Obot__class_Obot(tc_fun(U_3114,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_3114,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3114),U_3115))
      | ~ class_Orderings_Olinorder(U_3114) ),
    inference(variable_rename,[status(thm)],[f_782_1]) ).

cnf(f_782_3,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_3114,hAPP(hAPP(c_Set_Oinsert(U_3114),U_3116),U_3115)) = U_3116
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3114,tc_HOL_Obool)),U_3115),hAPP(hAPP(c_Set_Oinsert(U_3114),U_3116),c_Orderings_Obot__class_Obot(tc_fun(U_3114,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_3114,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3114),U_3115))
    | ~ class_Orderings_Olinorder(U_3114) ),
    inference(clausify,[status(thm)],[f_782_2]) ).

cnf(f_782_4,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_3114,hAPP(hAPP(c_Set_Oinsert(U_3114),U_3116),U_3115)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_3114),U_3116),c_Big__Operators_Olinorder__class_OMin(U_3114,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3114,tc_HOL_Obool)),U_3115),hAPP(hAPP(c_Set_Oinsert(U_3114),U_3116),c_Orderings_Obot__class_Obot(tc_fun(U_3114,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3114,tc_HOL_Obool)),U_3115),hAPP(hAPP(c_Set_Oinsert(U_3114),U_3116),c_Orderings_Obot__class_Obot(tc_fun(U_3114,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_3114,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3114),U_3115))
    | ~ class_Orderings_Olinorder(U_3114) ),
    inference(clausify,[status(thm)],[f_782_2]) ).

fof(f_783_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__fin_Ounion__disjoint]) ).

fof(f_783_2,plain,
    ! [U_3119,U_3118,U_3117] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_3117,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3117,tc_HOL_Obool)),U_3118),U_3119)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3117),c_Big__Operators_Olattice__class_OSup__fin(U_3117,U_3118)),c_Big__Operators_Olattice__class_OSup__fin(U_3117,U_3119))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3117,tc_HOL_Obool)),U_3118),U_3119) != c_Orderings_Obot__class_Obot(tc_fun(U_3117,tc_HOL_Obool))
      | U_3119 = c_Orderings_Obot__class_Obot(tc_fun(U_3117,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3117),U_3119))
      | U_3118 = c_Orderings_Obot__class_Obot(tc_fun(U_3117,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3117),U_3118))
      | ~ class_Lattices_Olattice(U_3117) ),
    inference(variable_rename,[status(thm)],[f_783_1]) ).

cnf(f_783_3,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_3117,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3117,tc_HOL_Obool)),U_3118),U_3119)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3117),c_Big__Operators_Olattice__class_OSup__fin(U_3117,U_3118)),c_Big__Operators_Olattice__class_OSup__fin(U_3117,U_3119))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3117,tc_HOL_Obool)),U_3118),U_3119) != c_Orderings_Obot__class_Obot(tc_fun(U_3117,tc_HOL_Obool))
    | U_3119 = c_Orderings_Obot__class_Obot(tc_fun(U_3117,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3117),U_3119))
    | U_3118 = c_Orderings_Obot__class_Obot(tc_fun(U_3117,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3117),U_3118))
    | ~ class_Lattices_Olattice(U_3117) ),
    inference(clausify,[status(thm)],[f_783_2]) ).

fof(f_784_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__fin_Ounion__inter]) ).

fof(f_784_2,plain,
    ! [U_3122,U_3121,U_3120] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3120),c_Big__Operators_Olattice__class_OSup__fin(U_3120,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3120,tc_HOL_Obool)),U_3121),U_3122))),c_Big__Operators_Olattice__class_OSup__fin(U_3120,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3120,tc_HOL_Obool)),U_3121),U_3122))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3120),c_Big__Operators_Olattice__class_OSup__fin(U_3120,U_3121)),c_Big__Operators_Olattice__class_OSup__fin(U_3120,U_3122))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3120,tc_HOL_Obool)),U_3121),U_3122) = c_Orderings_Obot__class_Obot(tc_fun(U_3120,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3120),U_3122))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3120),U_3121))
      | ~ class_Lattices_Olattice(U_3120) ),
    inference(variable_rename,[status(thm)],[f_784_1]) ).

cnf(f_784_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3120),c_Big__Operators_Olattice__class_OSup__fin(U_3120,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3120,tc_HOL_Obool)),U_3121),U_3122))),c_Big__Operators_Olattice__class_OSup__fin(U_3120,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3120,tc_HOL_Obool)),U_3121),U_3122))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3120),c_Big__Operators_Olattice__class_OSup__fin(U_3120,U_3121)),c_Big__Operators_Olattice__class_OSup__fin(U_3120,U_3122))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3120,tc_HOL_Obool)),U_3121),U_3122) = c_Orderings_Obot__class_Obot(tc_fun(U_3120,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3120),U_3122))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3120),U_3121))
    | ~ class_Lattices_Olattice(U_3120) ),
    inference(clausify,[status(thm)],[f_784_2]) ).

fof(f_785_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( ( ( c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Max_Oinsert__remove]) ).

fof(f_785_2,plain,
    ! [U_3125,U_3124,U_3123] :
      ( ( ( c_Big__Operators_Olinorder__class_OMax(U_3123,hAPP(hAPP(c_Set_Oinsert(U_3123),U_3125),U_3124)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_3123),U_3125),c_Big__Operators_Olinorder__class_OMax(U_3123,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3123,tc_HOL_Obool)),U_3124),hAPP(hAPP(c_Set_Oinsert(U_3123),U_3125),c_Orderings_Obot__class_Obot(tc_fun(U_3123,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3123,tc_HOL_Obool)),U_3124),hAPP(hAPP(c_Set_Oinsert(U_3123),U_3125),c_Orderings_Obot__class_Obot(tc_fun(U_3123,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_3123,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olinorder__class_OMax(U_3123,hAPP(hAPP(c_Set_Oinsert(U_3123),U_3125),U_3124)) = U_3125
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3123,tc_HOL_Obool)),U_3124),hAPP(hAPP(c_Set_Oinsert(U_3123),U_3125),c_Orderings_Obot__class_Obot(tc_fun(U_3123,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_3123,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3123),U_3124))
      | ~ class_Orderings_Olinorder(U_3123) ),
    inference(variable_rename,[status(thm)],[f_785_1]) ).

cnf(f_785_3,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_3123,hAPP(hAPP(c_Set_Oinsert(U_3123),U_3125),U_3124)) = U_3125
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3123,tc_HOL_Obool)),U_3124),hAPP(hAPP(c_Set_Oinsert(U_3123),U_3125),c_Orderings_Obot__class_Obot(tc_fun(U_3123,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_3123,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3123),U_3124))
    | ~ class_Orderings_Olinorder(U_3123) ),
    inference(clausify,[status(thm)],[f_785_2]) ).

cnf(f_785_4,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_3123,hAPP(hAPP(c_Set_Oinsert(U_3123),U_3125),U_3124)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_3123),U_3125),c_Big__Operators_Olinorder__class_OMax(U_3123,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3123,tc_HOL_Obool)),U_3124),hAPP(hAPP(c_Set_Oinsert(U_3123),U_3125),c_Orderings_Obot__class_Obot(tc_fun(U_3123,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3123,tc_HOL_Obool)),U_3124),hAPP(hAPP(c_Set_Oinsert(U_3123),U_3125),c_Orderings_Obot__class_Obot(tc_fun(U_3123,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_3123,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3123),U_3124))
    | ~ class_Orderings_Olinorder(U_3123) ),
    inference(clausify,[status(thm)],[f_785_2]) ).

fof(f_786_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__fin_Ounion__disjoint]) ).

fof(f_786_2,plain,
    ! [U_3128,U_3127,U_3126] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_3126,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3126,tc_HOL_Obool)),U_3127),U_3128)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_3126),c_Big__Operators_Olattice__class_OInf__fin(U_3126,U_3127)),c_Big__Operators_Olattice__class_OInf__fin(U_3126,U_3128))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3126,tc_HOL_Obool)),U_3127),U_3128) != c_Orderings_Obot__class_Obot(tc_fun(U_3126,tc_HOL_Obool))
      | U_3128 = c_Orderings_Obot__class_Obot(tc_fun(U_3126,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3126),U_3128))
      | U_3127 = c_Orderings_Obot__class_Obot(tc_fun(U_3126,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3126),U_3127))
      | ~ class_Lattices_Olattice(U_3126) ),
    inference(variable_rename,[status(thm)],[f_786_1]) ).

cnf(f_786_3,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_3126,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3126,tc_HOL_Obool)),U_3127),U_3128)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_3126),c_Big__Operators_Olattice__class_OInf__fin(U_3126,U_3127)),c_Big__Operators_Olattice__class_OInf__fin(U_3126,U_3128))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3126,tc_HOL_Obool)),U_3127),U_3128) != c_Orderings_Obot__class_Obot(tc_fun(U_3126,tc_HOL_Obool))
    | U_3128 = c_Orderings_Obot__class_Obot(tc_fun(U_3126,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3126),U_3128))
    | U_3127 = c_Orderings_Obot__class_Obot(tc_fun(U_3126,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3126),U_3127))
    | ~ class_Lattices_Olattice(U_3126) ),
    inference(clausify,[status(thm)],[f_786_2]) ).

fof(f_787_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__fin_Ounion__inter]) ).

fof(f_787_2,plain,
    ! [U_3131,U_3130,U_3129] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_3129),c_Big__Operators_Olattice__class_OInf__fin(U_3129,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3129,tc_HOL_Obool)),U_3130),U_3131))),c_Big__Operators_Olattice__class_OInf__fin(U_3129,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3129,tc_HOL_Obool)),U_3130),U_3131))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_3129),c_Big__Operators_Olattice__class_OInf__fin(U_3129,U_3130)),c_Big__Operators_Olattice__class_OInf__fin(U_3129,U_3131))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3129,tc_HOL_Obool)),U_3130),U_3131) = c_Orderings_Obot__class_Obot(tc_fun(U_3129,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3129),U_3131))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3129),U_3130))
      | ~ class_Lattices_Olattice(U_3129) ),
    inference(variable_rename,[status(thm)],[f_787_1]) ).

cnf(f_787_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_3129),c_Big__Operators_Olattice__class_OInf__fin(U_3129,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3129,tc_HOL_Obool)),U_3130),U_3131))),c_Big__Operators_Olattice__class_OInf__fin(U_3129,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3129,tc_HOL_Obool)),U_3130),U_3131))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_3129),c_Big__Operators_Olattice__class_OInf__fin(U_3129,U_3130)),c_Big__Operators_Olattice__class_OInf__fin(U_3129,U_3131))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3129,tc_HOL_Obool)),U_3130),U_3131) = c_Orderings_Obot__class_Obot(tc_fun(U_3129,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3129),U_3131))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3129),U_3130))
    | ~ class_Lattices_Olattice(U_3129) ),
    inference(clausify,[status(thm)],[f_787_2]) ).

fof(f_788_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_B_2))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Min_Ounion__disjoint]) ).

fof(f_788_2,plain,
    ! [U_3134,U_3133,U_3132] :
      ( c_Big__Operators_Olinorder__class_OMin(U_3132,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3132,tc_HOL_Obool)),U_3133),U_3134)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_3132),c_Big__Operators_Olinorder__class_OMin(U_3132,U_3133)),c_Big__Operators_Olinorder__class_OMin(U_3132,U_3134))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3132,tc_HOL_Obool)),U_3133),U_3134) != c_Orderings_Obot__class_Obot(tc_fun(U_3132,tc_HOL_Obool))
      | U_3134 = c_Orderings_Obot__class_Obot(tc_fun(U_3132,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3132),U_3134))
      | U_3133 = c_Orderings_Obot__class_Obot(tc_fun(U_3132,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3132),U_3133))
      | ~ class_Orderings_Olinorder(U_3132) ),
    inference(variable_rename,[status(thm)],[f_788_1]) ).

cnf(f_788_3,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_3132,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3132,tc_HOL_Obool)),U_3133),U_3134)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_3132),c_Big__Operators_Olinorder__class_OMin(U_3132,U_3133)),c_Big__Operators_Olinorder__class_OMin(U_3132,U_3134))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3132,tc_HOL_Obool)),U_3133),U_3134) != c_Orderings_Obot__class_Obot(tc_fun(U_3132,tc_HOL_Obool))
    | U_3134 = c_Orderings_Obot__class_Obot(tc_fun(U_3132,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3132),U_3134))
    | U_3133 = c_Orderings_Obot__class_Obot(tc_fun(U_3132,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3132),U_3133))
    | ~ class_Orderings_Olinorder(U_3132) ),
    inference(clausify,[status(thm)],[f_788_2]) ).

fof(f_789_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_B_2))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Min_Ounion__inter]) ).

fof(f_789_2,plain,
    ! [U_3137,U_3136,U_3135] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_3135),c_Big__Operators_Olinorder__class_OMin(U_3135,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3135,tc_HOL_Obool)),U_3136),U_3137))),c_Big__Operators_Olinorder__class_OMin(U_3135,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3135,tc_HOL_Obool)),U_3136),U_3137))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_3135),c_Big__Operators_Olinorder__class_OMin(U_3135,U_3136)),c_Big__Operators_Olinorder__class_OMin(U_3135,U_3137))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3135,tc_HOL_Obool)),U_3136),U_3137) = c_Orderings_Obot__class_Obot(tc_fun(U_3135,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3135),U_3137))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3135),U_3136))
      | ~ class_Orderings_Olinorder(U_3135) ),
    inference(variable_rename,[status(thm)],[f_789_1]) ).

cnf(f_789_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_3135),c_Big__Operators_Olinorder__class_OMin(U_3135,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3135,tc_HOL_Obool)),U_3136),U_3137))),c_Big__Operators_Olinorder__class_OMin(U_3135,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3135,tc_HOL_Obool)),U_3136),U_3137))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_3135),c_Big__Operators_Olinorder__class_OMin(U_3135,U_3136)),c_Big__Operators_Olinorder__class_OMin(U_3135,U_3137))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3135,tc_HOL_Obool)),U_3136),U_3137) = c_Orderings_Obot__class_Obot(tc_fun(U_3135,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3135),U_3137))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3135),U_3136))
    | ~ class_Orderings_Olinorder(U_3135) ),
    inference(clausify,[status(thm)],[f_789_2]) ).

fof(f_790_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_B_2))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Max_Ounion__disjoint]) ).

fof(f_790_2,plain,
    ! [U_3140,U_3139,U_3138] :
      ( c_Big__Operators_Olinorder__class_OMax(U_3138,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3138,tc_HOL_Obool)),U_3139),U_3140)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_3138),c_Big__Operators_Olinorder__class_OMax(U_3138,U_3139)),c_Big__Operators_Olinorder__class_OMax(U_3138,U_3140))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3138,tc_HOL_Obool)),U_3139),U_3140) != c_Orderings_Obot__class_Obot(tc_fun(U_3138,tc_HOL_Obool))
      | U_3140 = c_Orderings_Obot__class_Obot(tc_fun(U_3138,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3138),U_3140))
      | U_3139 = c_Orderings_Obot__class_Obot(tc_fun(U_3138,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3138),U_3139))
      | ~ class_Orderings_Olinorder(U_3138) ),
    inference(variable_rename,[status(thm)],[f_790_1]) ).

cnf(f_790_3,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_3138,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3138,tc_HOL_Obool)),U_3139),U_3140)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_3138),c_Big__Operators_Olinorder__class_OMax(U_3138,U_3139)),c_Big__Operators_Olinorder__class_OMax(U_3138,U_3140))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3138,tc_HOL_Obool)),U_3139),U_3140) != c_Orderings_Obot__class_Obot(tc_fun(U_3138,tc_HOL_Obool))
    | U_3140 = c_Orderings_Obot__class_Obot(tc_fun(U_3138,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3138),U_3140))
    | U_3139 = c_Orderings_Obot__class_Obot(tc_fun(U_3138,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3138),U_3139))
    | ~ class_Orderings_Olinorder(U_3138) ),
    inference(clausify,[status(thm)],[f_790_2]) ).

fof(f_791_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_B_2))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Max_Ounion__inter]) ).

fof(f_791_2,plain,
    ! [U_3143,U_3142,U_3141] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_3141),c_Big__Operators_Olinorder__class_OMax(U_3141,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3141,tc_HOL_Obool)),U_3142),U_3143))),c_Big__Operators_Olinorder__class_OMax(U_3141,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3141,tc_HOL_Obool)),U_3142),U_3143))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_3141),c_Big__Operators_Olinorder__class_OMax(U_3141,U_3142)),c_Big__Operators_Olinorder__class_OMax(U_3141,U_3143))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3141,tc_HOL_Obool)),U_3142),U_3143) = c_Orderings_Obot__class_Obot(tc_fun(U_3141,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3141),U_3143))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3141),U_3142))
      | ~ class_Orderings_Olinorder(U_3141) ),
    inference(variable_rename,[status(thm)],[f_791_1]) ).

cnf(f_791_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_3141),c_Big__Operators_Olinorder__class_OMax(U_3141,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3141,tc_HOL_Obool)),U_3142),U_3143))),c_Big__Operators_Olinorder__class_OMax(U_3141,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3141,tc_HOL_Obool)),U_3142),U_3143))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_3141),c_Big__Operators_Olinorder__class_OMax(U_3141,U_3142)),c_Big__Operators_Olinorder__class_OMax(U_3141,U_3143))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3141,tc_HOL_Obool)),U_3142),U_3143) = c_Orderings_Obot__class_Obot(tc_fun(U_3141,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3141),U_3143))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3141),U_3142))
    | ~ class_Orderings_Olinorder(U_3141) ),
    inference(clausify,[status(thm)],[f_791_2]) ).

fof(f_792_1,plain,
    ! [V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),V_A_2))
      | ? [B_x,B_y] : ~ hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Max_Oclosed]) ).

fof(f_792_2,plain,
    ! [U_3147,U_3146] :
      ( hBOOL(hAPP(hAPP(c_member(U_3146),c_Big__Operators_Olinorder__class_OMax(U_3146,U_3147)),U_3147))
      | ? [U_3145,U_3144] : ~ hBOOL(hAPP(hAPP(c_member(U_3146),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_3146),U_3145),U_3144)),hAPP(hAPP(c_Set_Oinsert(U_3146),U_3145),hAPP(hAPP(c_Set_Oinsert(U_3146),U_3144),c_Orderings_Obot__class_Obot(tc_fun(U_3146,tc_HOL_Obool))))))
      | U_3147 = c_Orderings_Obot__class_Obot(tc_fun(U_3146,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3146),U_3147))
      | ~ class_Orderings_Olinorder(U_3146) ),
    inference(variable_rename,[status(thm)],[f_792_1]) ).

fof(f_792_3,plain,
    ! [U_3147,U_3146] :
      ( hBOOL(hAPP(hAPP(c_member(U_3146),c_Big__Operators_Olinorder__class_OMax(U_3146,U_3147)),U_3147))
      | ? [U_3144] : ~ hBOOL(hAPP(hAPP(c_member(U_3146),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_3146),sK46(U_3147,U_3146)),U_3144)),hAPP(hAPP(c_Set_Oinsert(U_3146),sK46(U_3147,U_3146)),hAPP(hAPP(c_Set_Oinsert(U_3146),U_3144),c_Orderings_Obot__class_Obot(tc_fun(U_3146,tc_HOL_Obool))))))
      | U_3147 = c_Orderings_Obot__class_Obot(tc_fun(U_3146,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3146),U_3147))
      | ~ class_Orderings_Olinorder(U_3146) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK46]),skolemize(U_3145,sK46(U_3147,U_3146))],[f_792_2]) ).

fof(f_792_4,plain,
    ! [U_3147,U_3146] :
      ( hBOOL(hAPP(hAPP(c_member(U_3146),c_Big__Operators_Olinorder__class_OMax(U_3146,U_3147)),U_3147))
      | ~ hBOOL(hAPP(hAPP(c_member(U_3146),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_3146),sK46(U_3147,U_3146)),sK47(U_3147,U_3146))),hAPP(hAPP(c_Set_Oinsert(U_3146),sK46(U_3147,U_3146)),hAPP(hAPP(c_Set_Oinsert(U_3146),sK47(U_3147,U_3146)),c_Orderings_Obot__class_Obot(tc_fun(U_3146,tc_HOL_Obool))))))
      | U_3147 = c_Orderings_Obot__class_Obot(tc_fun(U_3146,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3146),U_3147))
      | ~ class_Orderings_Olinorder(U_3146) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK47]),skolemize(U_3144,sK47(U_3147,U_3146))],[f_792_3]) ).

cnf(f_792_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_3146),c_Big__Operators_Olinorder__class_OMax(U_3146,U_3147)),U_3147))
    | ~ hBOOL(hAPP(hAPP(c_member(U_3146),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_3146),sK46(U_3147,U_3146)),sK47(U_3147,U_3146))),hAPP(hAPP(c_Set_Oinsert(U_3146),sK46(U_3147,U_3146)),hAPP(hAPP(c_Set_Oinsert(U_3146),sK47(U_3147,U_3146)),c_Orderings_Obot__class_Obot(tc_fun(U_3146,tc_HOL_Obool))))))
    | U_3147 = c_Orderings_Obot__class_Obot(tc_fun(U_3146,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3146),U_3147))
    | ~ class_Orderings_Olinorder(U_3146) ),
    inference(clausify,[status(thm)],[f_792_4]) ).

fof(f_793_1,plain,
    ! [V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_A_2))
      | ? [B_x,B_y] : ~ hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Min_Oclosed]) ).

fof(f_793_2,plain,
    ! [U_3151,U_3150] :
      ( hBOOL(hAPP(hAPP(c_member(U_3150),c_Big__Operators_Olinorder__class_OMin(U_3150,U_3151)),U_3151))
      | ? [U_3149,U_3148] : ~ hBOOL(hAPP(hAPP(c_member(U_3150),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_3150),U_3149),U_3148)),hAPP(hAPP(c_Set_Oinsert(U_3150),U_3149),hAPP(hAPP(c_Set_Oinsert(U_3150),U_3148),c_Orderings_Obot__class_Obot(tc_fun(U_3150,tc_HOL_Obool))))))
      | U_3151 = c_Orderings_Obot__class_Obot(tc_fun(U_3150,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3150),U_3151))
      | ~ class_Orderings_Olinorder(U_3150) ),
    inference(variable_rename,[status(thm)],[f_793_1]) ).

fof(f_793_3,plain,
    ! [U_3151,U_3150] :
      ( hBOOL(hAPP(hAPP(c_member(U_3150),c_Big__Operators_Olinorder__class_OMin(U_3150,U_3151)),U_3151))
      | ? [U_3148] : ~ hBOOL(hAPP(hAPP(c_member(U_3150),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_3150),sK48(U_3151,U_3150)),U_3148)),hAPP(hAPP(c_Set_Oinsert(U_3150),sK48(U_3151,U_3150)),hAPP(hAPP(c_Set_Oinsert(U_3150),U_3148),c_Orderings_Obot__class_Obot(tc_fun(U_3150,tc_HOL_Obool))))))
      | U_3151 = c_Orderings_Obot__class_Obot(tc_fun(U_3150,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3150),U_3151))
      | ~ class_Orderings_Olinorder(U_3150) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK48]),skolemize(U_3149,sK48(U_3151,U_3150))],[f_793_2]) ).

fof(f_793_4,plain,
    ! [U_3151,U_3150] :
      ( hBOOL(hAPP(hAPP(c_member(U_3150),c_Big__Operators_Olinorder__class_OMin(U_3150,U_3151)),U_3151))
      | ~ hBOOL(hAPP(hAPP(c_member(U_3150),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_3150),sK48(U_3151,U_3150)),sK49(U_3151,U_3150))),hAPP(hAPP(c_Set_Oinsert(U_3150),sK48(U_3151,U_3150)),hAPP(hAPP(c_Set_Oinsert(U_3150),sK49(U_3151,U_3150)),c_Orderings_Obot__class_Obot(tc_fun(U_3150,tc_HOL_Obool))))))
      | U_3151 = c_Orderings_Obot__class_Obot(tc_fun(U_3150,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3150),U_3151))
      | ~ class_Orderings_Olinorder(U_3150) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK49]),skolemize(U_3148,sK49(U_3151,U_3150))],[f_793_3]) ).

cnf(f_793_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_3150),c_Big__Operators_Olinorder__class_OMin(U_3150,U_3151)),U_3151))
    | ~ hBOOL(hAPP(hAPP(c_member(U_3150),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_3150),sK48(U_3151,U_3150)),sK49(U_3151,U_3150))),hAPP(hAPP(c_Set_Oinsert(U_3150),sK48(U_3151,U_3150)),hAPP(hAPP(c_Set_Oinsert(U_3150),sK49(U_3151,U_3150)),c_Orderings_Obot__class_Obot(tc_fun(U_3150,tc_HOL_Obool))))))
    | U_3151 = c_Orderings_Obot__class_Obot(tc_fun(U_3150,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3150),U_3151))
    | ~ class_Orderings_Olinorder(U_3150) ),
    inference(clausify,[status(thm)],[f_793_4]) ).

fof(f_794_1,plain,
    ! [V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),V_A_2))
      | ? [B_x,B_y] : ~ hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oclosed]) ).

fof(f_794_2,plain,
    ! [U_3155,U_3154] :
      ( hBOOL(hAPP(hAPP(c_member(U_3154),c_Big__Operators_Olattice__class_OInf__fin(U_3154,U_3155)),U_3155))
      | ? [U_3153,U_3152] : ~ hBOOL(hAPP(hAPP(c_member(U_3154),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_3154),U_3153),U_3152)),hAPP(hAPP(c_Set_Oinsert(U_3154),U_3153),hAPP(hAPP(c_Set_Oinsert(U_3154),U_3152),c_Orderings_Obot__class_Obot(tc_fun(U_3154,tc_HOL_Obool))))))
      | U_3155 = c_Orderings_Obot__class_Obot(tc_fun(U_3154,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3154),U_3155))
      | ~ class_Lattices_Olattice(U_3154) ),
    inference(variable_rename,[status(thm)],[f_794_1]) ).

fof(f_794_3,plain,
    ! [U_3155,U_3154] :
      ( hBOOL(hAPP(hAPP(c_member(U_3154),c_Big__Operators_Olattice__class_OInf__fin(U_3154,U_3155)),U_3155))
      | ? [U_3152] : ~ hBOOL(hAPP(hAPP(c_member(U_3154),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_3154),sK50(U_3155,U_3154)),U_3152)),hAPP(hAPP(c_Set_Oinsert(U_3154),sK50(U_3155,U_3154)),hAPP(hAPP(c_Set_Oinsert(U_3154),U_3152),c_Orderings_Obot__class_Obot(tc_fun(U_3154,tc_HOL_Obool))))))
      | U_3155 = c_Orderings_Obot__class_Obot(tc_fun(U_3154,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3154),U_3155))
      | ~ class_Lattices_Olattice(U_3154) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK50]),skolemize(U_3153,sK50(U_3155,U_3154))],[f_794_2]) ).

fof(f_794_4,plain,
    ! [U_3155,U_3154] :
      ( hBOOL(hAPP(hAPP(c_member(U_3154),c_Big__Operators_Olattice__class_OInf__fin(U_3154,U_3155)),U_3155))
      | ~ hBOOL(hAPP(hAPP(c_member(U_3154),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_3154),sK50(U_3155,U_3154)),sK51(U_3155,U_3154))),hAPP(hAPP(c_Set_Oinsert(U_3154),sK50(U_3155,U_3154)),hAPP(hAPP(c_Set_Oinsert(U_3154),sK51(U_3155,U_3154)),c_Orderings_Obot__class_Obot(tc_fun(U_3154,tc_HOL_Obool))))))
      | U_3155 = c_Orderings_Obot__class_Obot(tc_fun(U_3154,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3154),U_3155))
      | ~ class_Lattices_Olattice(U_3154) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK51]),skolemize(U_3152,sK51(U_3155,U_3154))],[f_794_3]) ).

cnf(f_794_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_3154),c_Big__Operators_Olattice__class_OInf__fin(U_3154,U_3155)),U_3155))
    | ~ hBOOL(hAPP(hAPP(c_member(U_3154),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_3154),sK50(U_3155,U_3154)),sK51(U_3155,U_3154))),hAPP(hAPP(c_Set_Oinsert(U_3154),sK50(U_3155,U_3154)),hAPP(hAPP(c_Set_Oinsert(U_3154),sK51(U_3155,U_3154)),c_Orderings_Obot__class_Obot(tc_fun(U_3154,tc_HOL_Obool))))))
    | U_3155 = c_Orderings_Obot__class_Obot(tc_fun(U_3154,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3154),U_3155))
    | ~ class_Lattices_Olattice(U_3154) ),
    inference(clausify,[status(thm)],[f_794_4]) ).

fof(f_795_1,plain,
    ! [V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),V_A_2))
      | ? [B_x,B_y] : ~ hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oclosed]) ).

fof(f_795_2,plain,
    ! [U_3159,U_3158] :
      ( hBOOL(hAPP(hAPP(c_member(U_3158),c_Big__Operators_Olattice__class_OSup__fin(U_3158,U_3159)),U_3159))
      | ? [U_3157,U_3156] : ~ hBOOL(hAPP(hAPP(c_member(U_3158),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3158),U_3157),U_3156)),hAPP(hAPP(c_Set_Oinsert(U_3158),U_3157),hAPP(hAPP(c_Set_Oinsert(U_3158),U_3156),c_Orderings_Obot__class_Obot(tc_fun(U_3158,tc_HOL_Obool))))))
      | U_3159 = c_Orderings_Obot__class_Obot(tc_fun(U_3158,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3158),U_3159))
      | ~ class_Lattices_Olattice(U_3158) ),
    inference(variable_rename,[status(thm)],[f_795_1]) ).

fof(f_795_3,plain,
    ! [U_3159,U_3158] :
      ( hBOOL(hAPP(hAPP(c_member(U_3158),c_Big__Operators_Olattice__class_OSup__fin(U_3158,U_3159)),U_3159))
      | ? [U_3156] : ~ hBOOL(hAPP(hAPP(c_member(U_3158),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3158),sK52(U_3159,U_3158)),U_3156)),hAPP(hAPP(c_Set_Oinsert(U_3158),sK52(U_3159,U_3158)),hAPP(hAPP(c_Set_Oinsert(U_3158),U_3156),c_Orderings_Obot__class_Obot(tc_fun(U_3158,tc_HOL_Obool))))))
      | U_3159 = c_Orderings_Obot__class_Obot(tc_fun(U_3158,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3158),U_3159))
      | ~ class_Lattices_Olattice(U_3158) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK52]),skolemize(U_3157,sK52(U_3159,U_3158))],[f_795_2]) ).

fof(f_795_4,plain,
    ! [U_3159,U_3158] :
      ( hBOOL(hAPP(hAPP(c_member(U_3158),c_Big__Operators_Olattice__class_OSup__fin(U_3158,U_3159)),U_3159))
      | ~ hBOOL(hAPP(hAPP(c_member(U_3158),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3158),sK52(U_3159,U_3158)),sK53(U_3159,U_3158))),hAPP(hAPP(c_Set_Oinsert(U_3158),sK52(U_3159,U_3158)),hAPP(hAPP(c_Set_Oinsert(U_3158),sK53(U_3159,U_3158)),c_Orderings_Obot__class_Obot(tc_fun(U_3158,tc_HOL_Obool))))))
      | U_3159 = c_Orderings_Obot__class_Obot(tc_fun(U_3158,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3158),U_3159))
      | ~ class_Lattices_Olattice(U_3158) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK53]),skolemize(U_3156,sK53(U_3159,U_3158))],[f_795_3]) ).

cnf(f_795_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_3158),c_Big__Operators_Olattice__class_OSup__fin(U_3158,U_3159)),U_3159))
    | ~ hBOOL(hAPP(hAPP(c_member(U_3158),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3158),sK52(U_3159,U_3158)),sK53(U_3159,U_3158))),hAPP(hAPP(c_Set_Oinsert(U_3158),sK52(U_3159,U_3158)),hAPP(hAPP(c_Set_Oinsert(U_3158),sK53(U_3159,U_3158)),c_Orderings_Obot__class_Obot(tc_fun(U_3158,tc_HOL_Obool))))))
    | U_3159 = c_Orderings_Obot__class_Obot(tc_fun(U_3158,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3158),U_3159))
    | ~ class_Lattices_Olattice(U_3158) ),
    inference(clausify,[status(thm)],[f_795_4]) ).

fof(f_796_1,plain,
    ! [V_y_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
      ( ( hAPP(c_Set_Oimage(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2)),V_A_2) = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
        | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) )
      & ( hAPP(c_Set_Oimage(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_fun__upd__image]) ).

fof(f_796_2,plain,
    ! [U_3165,U_3164,U_3163,U_3162,U_3161,U_3160] :
      ( ( hAPP(c_Set_Oimage(U_3160,U_3163,c_Fun_Ofun__upd(U_3160,U_3163,U_3164,U_3161,U_3165)),U_3162) = hAPP(c_Set_Oimage(U_3160,U_3163,U_3164),U_3162)
        | hBOOL(hAPP(hAPP(c_member(U_3160),U_3161),U_3162)) )
      & ( hAPP(c_Set_Oimage(U_3160,U_3163,c_Fun_Ofun__upd(U_3160,U_3163,U_3164,U_3161,U_3165)),U_3162) = hAPP(hAPP(c_Set_Oinsert(U_3163),U_3165),hAPP(c_Set_Oimage(U_3160,U_3163,U_3164),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3160,tc_HOL_Obool)),U_3162),hAPP(hAPP(c_Set_Oinsert(U_3160),U_3161),c_Orderings_Obot__class_Obot(tc_fun(U_3160,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(hAPP(c_member(U_3160),U_3161),U_3162)) ) ),
    inference(variable_rename,[status(thm)],[f_796_1]) ).

fof(f_796_3,plain,
    ( ! [U_3177,U_3175,U_3173,U_3171,U_3169,U_3167] :
        ( hAPP(c_Set_Oimage(U_3167,U_3173,c_Fun_Ofun__upd(U_3167,U_3173,U_3175,U_3169,U_3177)),U_3171) = hAPP(c_Set_Oimage(U_3167,U_3173,U_3175),U_3171)
        | hBOOL(hAPP(hAPP(c_member(U_3167),U_3169),U_3171)) )
    & ! [U_3176,U_3174,U_3172,U_3170,U_3168,U_3166] :
        ( hAPP(c_Set_Oimage(U_3166,U_3172,c_Fun_Ofun__upd(U_3166,U_3172,U_3174,U_3168,U_3176)),U_3170) = hAPP(hAPP(c_Set_Oinsert(U_3172),U_3176),hAPP(c_Set_Oimage(U_3166,U_3172,U_3174),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3166,tc_HOL_Obool)),U_3170),hAPP(hAPP(c_Set_Oinsert(U_3166),U_3168),c_Orderings_Obot__class_Obot(tc_fun(U_3166,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(hAPP(c_member(U_3166),U_3168),U_3170)) ) ),
    inference(miniscope,[status(thm)],[f_796_2]) ).

cnf(f_796_4,plain,
    ( hAPP(c_Set_Oimage(U_3166,U_3172,c_Fun_Ofun__upd(U_3166,U_3172,U_3174,U_3168,U_3176)),U_3170) = hAPP(hAPP(c_Set_Oinsert(U_3172),U_3176),hAPP(c_Set_Oimage(U_3166,U_3172,U_3174),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3166,tc_HOL_Obool)),U_3170),hAPP(hAPP(c_Set_Oinsert(U_3166),U_3168),c_Orderings_Obot__class_Obot(tc_fun(U_3166,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_3166),U_3168),U_3170)) ),
    inference(clausify,[status(thm)],[f_796_3]) ).

cnf(f_796_5,plain,
    ( hAPP(c_Set_Oimage(U_3167,U_3173,c_Fun_Ofun__upd(U_3167,U_3173,U_3175,U_3169,U_3177)),U_3171) = hAPP(c_Set_Oimage(U_3167,U_3173,U_3175),U_3171)
    | hBOOL(hAPP(hAPP(c_member(U_3167),U_3169),U_3171)) ),
    inference(clausify,[status(thm)],[f_796_3]) ).

fof(f_797_1,plain,
    ! [V_B_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_x_2)),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_the__inv__into__into]) ).

fof(f_797_2,plain,
    ! [U_3183,U_3182,U_3181,U_3180,U_3179,U_3178] :
      ( hBOOL(hAPP(hAPP(c_member(U_3178),hAPP(c_Fun_Othe__inv__into(U_3178,U_3179,U_3181,U_3180),U_3182)),U_3183))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3178,tc_HOL_Obool)),U_3181),U_3183))
      | ~ hBOOL(hAPP(hAPP(c_member(U_3179),U_3182),hAPP(c_Set_Oimage(U_3178,U_3179,U_3180),U_3181)))
      | ~ c_Fun_Oinj__on(U_3178,U_3179,U_3180,U_3181) ),
    inference(variable_rename,[status(thm)],[f_797_1]) ).

cnf(f_797_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_3178),hAPP(c_Fun_Othe__inv__into(U_3178,U_3179,U_3181,U_3180),U_3182)),U_3183))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3178,tc_HOL_Obool)),U_3181),U_3183))
    | ~ hBOOL(hAPP(hAPP(c_member(U_3179),U_3182),hAPP(c_Set_Oimage(U_3178,U_3179,U_3180),U_3181)))
    | ~ c_Fun_Oinj__on(U_3178,U_3179,U_3180,U_3181) ),
    inference(clausify,[status(thm)],[f_797_2]) ).

fof(f_798_1,plain,
    ! [V_N_2,V_h_2,T_b] :
      ( hAPP(V_h_2,c_Big__Operators_Olinorder__class_OMax(T_b,V_N_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2))
      | V_N_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
      | ? [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),B_x),B_y)) != hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Max_Ohom__commute]) ).

fof(f_798_2,plain,
    ! [U_3188,U_3187,U_3186] :
      ( hAPP(U_3187,c_Big__Operators_Olinorder__class_OMax(U_3186,U_3188)) = c_Big__Operators_Olinorder__class_OMax(U_3186,hAPP(c_Set_Oimage(U_3186,U_3186,U_3187),U_3188))
      | U_3188 = c_Orderings_Obot__class_Obot(tc_fun(U_3186,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3186),U_3188))
      | ? [U_3185,U_3184] : hAPP(U_3187,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_3186),U_3185),U_3184)) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_3186),hAPP(U_3187,U_3185)),hAPP(U_3187,U_3184))
      | ~ class_Orderings_Olinorder(U_3186) ),
    inference(variable_rename,[status(thm)],[f_798_1]) ).

fof(f_798_3,plain,
    ! [U_3188,U_3187,U_3186] :
      ( hAPP(U_3187,c_Big__Operators_Olinorder__class_OMax(U_3186,U_3188)) = c_Big__Operators_Olinorder__class_OMax(U_3186,hAPP(c_Set_Oimage(U_3186,U_3186,U_3187),U_3188))
      | U_3188 = c_Orderings_Obot__class_Obot(tc_fun(U_3186,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3186),U_3188))
      | ? [U_3184] : hAPP(U_3187,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_3186),sK54(U_3188,U_3187,U_3186)),U_3184)) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_3186),hAPP(U_3187,sK54(U_3188,U_3187,U_3186))),hAPP(U_3187,U_3184))
      | ~ class_Orderings_Olinorder(U_3186) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK54]),skolemize(U_3185,sK54(U_3188,U_3187,U_3186))],[f_798_2]) ).

fof(f_798_4,plain,
    ! [U_3188,U_3187,U_3186] :
      ( hAPP(U_3187,c_Big__Operators_Olinorder__class_OMax(U_3186,U_3188)) = c_Big__Operators_Olinorder__class_OMax(U_3186,hAPP(c_Set_Oimage(U_3186,U_3186,U_3187),U_3188))
      | U_3188 = c_Orderings_Obot__class_Obot(tc_fun(U_3186,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3186),U_3188))
      | hAPP(U_3187,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_3186),sK54(U_3188,U_3187,U_3186)),sK55(U_3188,U_3187,U_3186))) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_3186),hAPP(U_3187,sK54(U_3188,U_3187,U_3186))),hAPP(U_3187,sK55(U_3188,U_3187,U_3186)))
      | ~ class_Orderings_Olinorder(U_3186) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK55]),skolemize(U_3184,sK55(U_3188,U_3187,U_3186))],[f_798_3]) ).

cnf(f_798_5,plain,
    ( hAPP(U_3187,c_Big__Operators_Olinorder__class_OMax(U_3186,U_3188)) = c_Big__Operators_Olinorder__class_OMax(U_3186,hAPP(c_Set_Oimage(U_3186,U_3186,U_3187),U_3188))
    | U_3188 = c_Orderings_Obot__class_Obot(tc_fun(U_3186,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3186),U_3188))
    | hAPP(U_3187,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_3186),sK54(U_3188,U_3187,U_3186)),sK55(U_3188,U_3187,U_3186))) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_3186),hAPP(U_3187,sK54(U_3188,U_3187,U_3186))),hAPP(U_3187,sK55(U_3188,U_3187,U_3186)))
    | ~ class_Orderings_Olinorder(U_3186) ),
    inference(clausify,[status(thm)],[f_798_4]) ).

fof(f_799_1,plain,
    ! [V_N_2,V_h_2,T_b] :
      ( hAPP(V_h_2,c_Big__Operators_Olinorder__class_OMin(T_b,V_N_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2))
      | V_N_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
      | ? [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),B_x),B_y)) != hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Min_Ohom__commute]) ).

fof(f_799_2,plain,
    ! [U_3193,U_3192,U_3191] :
      ( hAPP(U_3192,c_Big__Operators_Olinorder__class_OMin(U_3191,U_3193)) = c_Big__Operators_Olinorder__class_OMin(U_3191,hAPP(c_Set_Oimage(U_3191,U_3191,U_3192),U_3193))
      | U_3193 = c_Orderings_Obot__class_Obot(tc_fun(U_3191,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3191),U_3193))
      | ? [U_3190,U_3189] : hAPP(U_3192,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_3191),U_3190),U_3189)) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_3191),hAPP(U_3192,U_3190)),hAPP(U_3192,U_3189))
      | ~ class_Orderings_Olinorder(U_3191) ),
    inference(variable_rename,[status(thm)],[f_799_1]) ).

fof(f_799_3,plain,
    ! [U_3193,U_3192,U_3191] :
      ( hAPP(U_3192,c_Big__Operators_Olinorder__class_OMin(U_3191,U_3193)) = c_Big__Operators_Olinorder__class_OMin(U_3191,hAPP(c_Set_Oimage(U_3191,U_3191,U_3192),U_3193))
      | U_3193 = c_Orderings_Obot__class_Obot(tc_fun(U_3191,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3191),U_3193))
      | ? [U_3189] : hAPP(U_3192,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_3191),sK56(U_3193,U_3192,U_3191)),U_3189)) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_3191),hAPP(U_3192,sK56(U_3193,U_3192,U_3191))),hAPP(U_3192,U_3189))
      | ~ class_Orderings_Olinorder(U_3191) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK56]),skolemize(U_3190,sK56(U_3193,U_3192,U_3191))],[f_799_2]) ).

fof(f_799_4,plain,
    ! [U_3193,U_3192,U_3191] :
      ( hAPP(U_3192,c_Big__Operators_Olinorder__class_OMin(U_3191,U_3193)) = c_Big__Operators_Olinorder__class_OMin(U_3191,hAPP(c_Set_Oimage(U_3191,U_3191,U_3192),U_3193))
      | U_3193 = c_Orderings_Obot__class_Obot(tc_fun(U_3191,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3191),U_3193))
      | hAPP(U_3192,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_3191),sK56(U_3193,U_3192,U_3191)),sK57(U_3193,U_3192,U_3191))) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_3191),hAPP(U_3192,sK56(U_3193,U_3192,U_3191))),hAPP(U_3192,sK57(U_3193,U_3192,U_3191)))
      | ~ class_Orderings_Olinorder(U_3191) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK57]),skolemize(U_3189,sK57(U_3193,U_3192,U_3191))],[f_799_3]) ).

cnf(f_799_5,plain,
    ( hAPP(U_3192,c_Big__Operators_Olinorder__class_OMin(U_3191,U_3193)) = c_Big__Operators_Olinorder__class_OMin(U_3191,hAPP(c_Set_Oimage(U_3191,U_3191,U_3192),U_3193))
    | U_3193 = c_Orderings_Obot__class_Obot(tc_fun(U_3191,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3191),U_3193))
    | hAPP(U_3192,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_3191),sK56(U_3193,U_3192,U_3191)),sK57(U_3193,U_3192,U_3191))) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_3191),hAPP(U_3192,sK56(U_3193,U_3192,U_3191))),hAPP(U_3192,sK57(U_3193,U_3192,U_3191)))
    | ~ class_Orderings_Olinorder(U_3191) ),
    inference(clausify,[status(thm)],[f_799_4]) ).

fof(f_800_1,plain,
    ! [V_x_2,V_f_2,T_c,T_b] : c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,hAPP(V_f_2,V_x_2)) = V_f_2,
    inference(fof_nnf,[status(thm)],[fact_fun__upd__triv]) ).

fof(f_800_2,plain,
    ! [U_3197,U_3196,U_3195,U_3194] : c_Fun_Ofun__upd(U_3194,U_3195,U_3196,U_3197,hAPP(U_3196,U_3197)) = U_3196,
    inference(variable_rename,[status(thm)],[f_800_1]) ).

cnf(f_800_3,plain,
    c_Fun_Ofun__upd(U_3194,U_3195,U_3196,U_3197,hAPP(U_3196,U_3197)) = U_3196,
    inference(clausify,[status(thm)],[f_800_2]) ).

fof(f_801_1,plain,
    ! [T_b,T_c,V_y_2,V_x_2,V_f_2] :
      ( c_Fun_Ofun__upd(T_c,T_b,V_f_2,V_x_2,V_y_2) = V_f_2
      | hAPP(V_f_2,V_x_2) != V_y_2 ),
    inference(fof_nnf,[status(thm)],[fact_fun__upd__idem]) ).

fof(f_801_2,plain,
    ! [U_3202,U_3201,U_3200,U_3199,U_3198] :
      ( c_Fun_Ofun__upd(U_3201,U_3202,U_3198,U_3199,U_3200) = U_3198
      | hAPP(U_3198,U_3199) != U_3200 ),
    inference(variable_rename,[status(thm)],[f_801_1]) ).

cnf(f_801_3,plain,
    ( c_Fun_Ofun__upd(U_3201,U_3202,U_3198,U_3199,U_3200) = U_3198
    | hAPP(U_3198,U_3199) != U_3200 ),
    inference(clausify,[status(thm)],[f_801_2]) ).

fof(f_802_1,plain,
    ! [V_y_2,V_f_2,T_c,T_b,V_x_2,V_z_2] :
      ( hAPP(c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2),V_z_2) = hAPP(V_f_2,V_z_2)
      | V_z_2 = V_x_2 ),
    inference(fof_nnf,[status(thm)],[fact_fun__upd__other]) ).

fof(f_802_2,plain,
    ! [U_3208,U_3207,U_3206,U_3205,U_3204,U_3203] :
      ( hAPP(c_Fun_Ofun__upd(U_3205,U_3206,U_3207,U_3204,U_3208),U_3203) = hAPP(U_3207,U_3203)
      | U_3203 = U_3204 ),
    inference(variable_rename,[status(thm)],[f_802_1]) ).

cnf(f_802_3,plain,
    ( hAPP(c_Fun_Ofun__upd(U_3205,U_3206,U_3207,U_3204,U_3208),U_3203) = hAPP(U_3207,U_3203)
    | U_3203 = U_3204 ),
    inference(clausify,[status(thm)],[f_802_2]) ).

fof(f_803_1,plain,
    ! [V_d_2,V_b_2,V_m_2,T_c,T_b,V_c_2,V_a_2] :
      ( c_Fun_Ofun__upd(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_m_2,V_a_2,V_b_2),V_c_2,V_d_2) = c_Fun_Ofun__upd(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_m_2,V_c_2,V_d_2),V_a_2,V_b_2)
      | V_a_2 = V_c_2 ),
    inference(fof_nnf,[status(thm)],[fact_fun__upd__twist]) ).

fof(f_803_2,plain,
    ! [U_3215,U_3214,U_3213,U_3212,U_3211,U_3210,U_3209] :
      ( c_Fun_Ofun__upd(U_3211,U_3212,c_Fun_Ofun__upd(U_3211,U_3212,U_3213,U_3209,U_3214),U_3210,U_3215) = c_Fun_Ofun__upd(U_3211,U_3212,c_Fun_Ofun__upd(U_3211,U_3212,U_3213,U_3210,U_3215),U_3209,U_3214)
      | U_3209 = U_3210 ),
    inference(variable_rename,[status(thm)],[f_803_1]) ).

cnf(f_803_3,plain,
    ( c_Fun_Ofun__upd(U_3211,U_3212,c_Fun_Ofun__upd(U_3211,U_3212,U_3213,U_3209,U_3214),U_3210,U_3215) = c_Fun_Ofun__upd(U_3211,U_3212,c_Fun_Ofun__upd(U_3211,U_3212,U_3213,U_3210,U_3215),U_3209,U_3214)
    | U_3209 = U_3210 ),
    inference(clausify,[status(thm)],[f_803_2]) ).

fof(f_804_1,plain,
    ! [V_y_2,V_f_2,T_c,T_b,V_x_2,V_z_2] :
      ( ( hAPP(c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2),V_z_2) = hAPP(V_f_2,V_z_2)
        | V_z_2 = V_x_2 )
      & ( hAPP(c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2),V_z_2) = V_y_2
        | V_z_2 != V_x_2 ) ),
    inference(fof_nnf,[status(thm)],[fact_fun__upd__apply]) ).

fof(f_804_2,plain,
    ! [U_3221,U_3220,U_3219,U_3218,U_3217,U_3216] :
      ( ( hAPP(c_Fun_Ofun__upd(U_3218,U_3219,U_3220,U_3217,U_3221),U_3216) = hAPP(U_3220,U_3216)
        | U_3216 = U_3217 )
      & ( hAPP(c_Fun_Ofun__upd(U_3218,U_3219,U_3220,U_3217,U_3221),U_3216) = U_3221
        | U_3216 != U_3217 ) ),
    inference(variable_rename,[status(thm)],[f_804_1]) ).

fof(f_804_3,plain,
    ( ! [U_3233,U_3231,U_3229,U_3227,U_3225,U_3223] :
        ( hAPP(c_Fun_Ofun__upd(U_3227,U_3229,U_3231,U_3225,U_3233),U_3223) = hAPP(U_3231,U_3223)
        | U_3223 = U_3225 )
    & ! [U_3232,U_3230,U_3228,U_3226,U_3224,U_3222] :
        ( hAPP(c_Fun_Ofun__upd(U_3226,U_3228,U_3230,U_3224,U_3232),U_3222) = U_3232
        | U_3222 != U_3224 ) ),
    inference(miniscope,[status(thm)],[f_804_2]) ).

cnf(f_804_4,plain,
    ( hAPP(c_Fun_Ofun__upd(U_3226,U_3228,U_3230,U_3224,U_3232),U_3222) = U_3232
    | U_3222 != U_3224 ),
    inference(clausify,[status(thm)],[f_804_3]) ).

cnf(f_804_5,plain,
    ( hAPP(c_Fun_Ofun__upd(U_3227,U_3229,U_3231,U_3225,U_3233),U_3223) = hAPP(U_3231,U_3223)
    | U_3223 = U_3225 ),
    inference(clausify,[status(thm)],[f_804_3]) ).

fof(f_805_1,plain,
    ! [V_y_2,V_x_2,V_f_2,T_b,T_c] : hAPP(c_Fun_Ofun__upd(T_c,T_b,V_f_2,V_x_2,V_y_2),V_x_2) = V_y_2,
    inference(fof_nnf,[status(thm)],[fact_fun__upd__same]) ).

fof(f_805_2,plain,
    ! [U_3238,U_3237,U_3236,U_3235,U_3234] : hAPP(c_Fun_Ofun__upd(U_3234,U_3235,U_3236,U_3237,U_3238),U_3237) = U_3238,
    inference(variable_rename,[status(thm)],[f_805_1]) ).

cnf(f_805_3,plain,
    hAPP(c_Fun_Ofun__upd(U_3234,U_3235,U_3236,U_3237,U_3238),U_3237) = U_3238,
    inference(clausify,[status(thm)],[f_805_2]) ).

fof(f_806_1,plain,
    ! [V_z_2,V_y_2,V_x_2,V_f_2,T_c,T_b] : c_Fun_Ofun__upd(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2),V_x_2,V_z_2) = c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_z_2),
    inference(fof_nnf,[status(thm)],[fact_fun__upd__upd]) ).

fof(f_806_2,plain,
    ! [U_3244,U_3243,U_3242,U_3241,U_3240,U_3239] : c_Fun_Ofun__upd(U_3239,U_3240,c_Fun_Ofun__upd(U_3239,U_3240,U_3241,U_3242,U_3243),U_3242,U_3244) = c_Fun_Ofun__upd(U_3239,U_3240,U_3241,U_3242,U_3244),
    inference(variable_rename,[status(thm)],[f_806_1]) ).

cnf(f_806_3,plain,
    c_Fun_Ofun__upd(U_3239,U_3240,c_Fun_Ofun__upd(U_3239,U_3240,U_3241,U_3242,U_3243),U_3242,U_3244) = c_Fun_Ofun__upd(U_3239,U_3240,U_3241,U_3242,U_3244),
    inference(clausify,[status(thm)],[f_806_2]) ).

fof(f_807_1,plain,
    ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
      ( ( c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2) = V_f_2
        | hAPP(V_f_2,V_x_2) != V_y_2 )
      & ( hAPP(V_f_2,V_x_2) = V_y_2
        | c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2) != V_f_2 ) ),
    inference(fof_nnf,[status(thm)],[fact_fun__upd__idem__iff]) ).

fof(f_807_2,plain,
    ! [U_3249,U_3248,U_3247,U_3246,U_3245] :
      ( ( c_Fun_Ofun__upd(U_3245,U_3246,U_3247,U_3248,U_3249) = U_3247
        | hAPP(U_3247,U_3248) != U_3249 )
      & ( hAPP(U_3247,U_3248) = U_3249
        | c_Fun_Ofun__upd(U_3245,U_3246,U_3247,U_3248,U_3249) != U_3247 ) ),
    inference(variable_rename,[status(thm)],[f_807_1]) ).

fof(f_807_3,plain,
    ( ! [U_3259,U_3257,U_3255] :
        ( ! [U_3253,U_3251] : c_Fun_Ofun__upd(U_3251,U_3253,U_3255,U_3257,U_3259) = U_3255
        | hAPP(U_3255,U_3257) != U_3259 )
    & ! [U_3258,U_3256,U_3254] :
        ( ! [U_3252,U_3250] : c_Fun_Ofun__upd(U_3250,U_3252,U_3254,U_3256,U_3258) != U_3254
        | hAPP(U_3254,U_3256) = U_3258 ) ),
    inference(miniscope,[status(thm)],[f_807_2]) ).

cnf(f_807_4,plain,
    ( c_Fun_Ofun__upd(U_3250,U_3252,U_3254,U_3256,U_3258) != U_3254
    | hAPP(U_3254,U_3256) = U_3258 ),
    inference(clausify,[status(thm)],[f_807_3]) ).

cnf(f_807_5,plain,
    ( c_Fun_Ofun__upd(U_3251,U_3253,U_3255,U_3257,U_3259) = U_3255
    | hAPP(U_3255,U_3257) != U_3259 ),
    inference(clausify,[status(thm)],[f_807_3]) ).

fof(f_808_1,plain,
    ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_y_2) = V_x_2
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | hAPP(V_f_2,V_x_2) != V_y_2
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_the__inv__into__f__eq]) ).

fof(f_808_2,plain,
    ! [U_3265,U_3264,U_3263,U_3262,U_3261,U_3260] :
      ( hAPP(c_Fun_Othe__inv__into(U_3260,U_3261,U_3263,U_3262),U_3265) = U_3264
      | ~ hBOOL(hAPP(hAPP(c_member(U_3260),U_3264),U_3263))
      | hAPP(U_3262,U_3264) != U_3265
      | ~ c_Fun_Oinj__on(U_3260,U_3261,U_3262,U_3263) ),
    inference(variable_rename,[status(thm)],[f_808_1]) ).

cnf(f_808_3,plain,
    ( hAPP(c_Fun_Othe__inv__into(U_3260,U_3261,U_3263,U_3262),U_3265) = U_3264
    | ~ hBOOL(hAPP(hAPP(c_member(U_3260),U_3264),U_3263))
    | hAPP(U_3262,U_3264) != U_3265
    | ~ c_Fun_Oinj__on(U_3260,U_3261,U_3262,U_3263) ),
    inference(clausify,[status(thm)],[f_808_2]) ).

fof(f_809_1,plain,
    ! [V_x_2,V_A_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_the__inv__into__f__f]) ).

fof(f_809_2,plain,
    ! [U_3270,U_3269,U_3268,U_3267,U_3266] :
      ( hAPP(c_Fun_Othe__inv__into(U_3266,U_3267,U_3269,U_3268),hAPP(U_3268,U_3270)) = U_3270
      | ~ hBOOL(hAPP(hAPP(c_member(U_3266),U_3270),U_3269))
      | ~ c_Fun_Oinj__on(U_3266,U_3267,U_3268,U_3269) ),
    inference(variable_rename,[status(thm)],[f_809_1]) ).

cnf(f_809_3,plain,
    ( hAPP(c_Fun_Othe__inv__into(U_3266,U_3267,U_3269,U_3268),hAPP(U_3268,U_3270)) = U_3270
    | ~ hBOOL(hAPP(hAPP(c_member(U_3266),U_3270),U_3269))
    | ~ c_Fun_Oinj__on(U_3266,U_3267,U_3268,U_3269) ),
    inference(clausify,[status(thm)],[f_809_2]) ).

fof(f_810_1,plain,
    ! [V_x_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Fun_Othe__inv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_the__inv__f__f]) ).

fof(f_810_2,plain,
    ! [U_3274,U_3273,U_3272,U_3271] :
      ( hAPP(c_Fun_Othe__inv__into(U_3271,U_3272,c_Orderings_Otop__class_Otop(tc_fun(U_3271,tc_HOL_Obool)),U_3273),hAPP(U_3273,U_3274)) = U_3274
      | ~ c_Fun_Oinj__on(U_3271,U_3272,U_3273,c_Orderings_Otop__class_Otop(tc_fun(U_3271,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_810_1]) ).

cnf(f_810_3,plain,
    ( hAPP(c_Fun_Othe__inv__into(U_3271,U_3272,c_Orderings_Otop__class_Otop(tc_fun(U_3271,tc_HOL_Obool)),U_3273),hAPP(U_3273,U_3274)) = U_3274
    | ~ c_Fun_Oinj__on(U_3271,U_3272,U_3273,c_Orderings_Otop__class_Otop(tc_fun(U_3271,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_810_2]) ).

fof(f_811_1,plain,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Set_Oimage(T_c,T_b,c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = V_A_2
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_the__inv__into__onto]) ).

fof(f_811_2,plain,
    ! [U_3278,U_3277,U_3276,U_3275] :
      ( hAPP(c_Set_Oimage(U_3276,U_3275,c_Fun_Othe__inv__into(U_3275,U_3276,U_3278,U_3277)),hAPP(c_Set_Oimage(U_3275,U_3276,U_3277),U_3278)) = U_3278
      | ~ c_Fun_Oinj__on(U_3275,U_3276,U_3277,U_3278) ),
    inference(variable_rename,[status(thm)],[f_811_1]) ).

cnf(f_811_3,plain,
    ( hAPP(c_Set_Oimage(U_3276,U_3275,c_Fun_Othe__inv__into(U_3275,U_3276,U_3278,U_3277)),hAPP(c_Set_Oimage(U_3275,U_3276,U_3277),U_3278)) = U_3278
    | ~ c_Fun_Oinj__on(U_3275,U_3276,U_3277,U_3278) ),
    inference(clausify,[status(thm)],[f_811_2]) ).

fof(f_812_1,plain,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_c,T_b,c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_inj__on__the__inv__into]) ).

fof(f_812_2,plain,
    ! [U_3282,U_3281,U_3280,U_3279] :
      ( c_Fun_Oinj__on(U_3280,U_3279,c_Fun_Othe__inv__into(U_3279,U_3280,U_3282,U_3281),hAPP(c_Set_Oimage(U_3279,U_3280,U_3281),U_3282))
      | ~ c_Fun_Oinj__on(U_3279,U_3280,U_3281,U_3282) ),
    inference(variable_rename,[status(thm)],[f_812_1]) ).

cnf(f_812_3,plain,
    ( c_Fun_Oinj__on(U_3280,U_3279,c_Fun_Othe__inv__into(U_3279,U_3280,U_3282,U_3281),hAPP(c_Set_Oimage(U_3279,U_3280,U_3281),U_3282))
    | ~ c_Fun_Oinj__on(U_3279,U_3280,U_3281,U_3282) ),
    inference(clausify,[status(thm)],[f_812_2]) ).

fof(f_813_1,plain,
    ! [V_x_2,V_y_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2),V_A_2)
      | hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_inj__on__fun__updI]) ).

fof(f_813_2,plain,
    ! [U_3288,U_3287,U_3286,U_3285,U_3284,U_3283] :
      ( c_Fun_Oinj__on(U_3283,U_3284,c_Fun_Ofun__upd(U_3283,U_3284,U_3285,U_3288,U_3287),U_3286)
      | hBOOL(hAPP(hAPP(c_member(U_3284),U_3287),hAPP(c_Set_Oimage(U_3283,U_3284,U_3285),U_3286)))
      | ~ c_Fun_Oinj__on(U_3283,U_3284,U_3285,U_3286) ),
    inference(variable_rename,[status(thm)],[f_813_1]) ).

cnf(f_813_3,plain,
    ( c_Fun_Oinj__on(U_3283,U_3284,c_Fun_Ofun__upd(U_3283,U_3284,U_3285,U_3288,U_3287),U_3286)
    | hBOOL(hAPP(hAPP(c_member(U_3284),U_3287),hAPP(c_Set_Oimage(U_3283,U_3284,U_3285),U_3286)))
    | ~ c_Fun_Oinj__on(U_3283,U_3284,U_3285,U_3286) ),
    inference(clausify,[status(thm)],[f_813_2]) ).

fof(f_814_1,plain,
    ! [V_y_2,V_A_2,V_f_2,T_c,T_b] :
      ( hAPP(V_f_2,hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_y_2)) = V_y_2
      | ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_f__the__inv__into__f]) ).

fof(f_814_2,plain,
    ! [U_3293,U_3292,U_3291,U_3290,U_3289] :
      ( hAPP(U_3291,hAPP(c_Fun_Othe__inv__into(U_3289,U_3290,U_3292,U_3291),U_3293)) = U_3293
      | ~ hBOOL(hAPP(hAPP(c_member(U_3290),U_3293),hAPP(c_Set_Oimage(U_3289,U_3290,U_3291),U_3292)))
      | ~ c_Fun_Oinj__on(U_3289,U_3290,U_3291,U_3292) ),
    inference(variable_rename,[status(thm)],[f_814_1]) ).

cnf(f_814_3,plain,
    ( hAPP(U_3291,hAPP(c_Fun_Othe__inv__into(U_3289,U_3290,U_3292,U_3291),U_3293)) = U_3293
    | ~ hBOOL(hAPP(hAPP(c_member(U_3290),U_3293),hAPP(c_Set_Oimage(U_3289,U_3290,U_3291),U_3292)))
    | ~ c_Fun_Oinj__on(U_3289,U_3290,U_3291,U_3292) ),
    inference(clausify,[status(thm)],[f_814_2]) ).

fof(f_815_1,plain,
    ! [V_N_2,V_h_2,T_b] :
      ( hAPP(V_h_2,c_Big__Operators_Olattice__class_OInf__fin(T_b,V_N_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2))
      | V_N_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
      | ? [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),B_x),B_y)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__fin_Ohom__commute]) ).

fof(f_815_2,plain,
    ! [U_3298,U_3297,U_3296] :
      ( hAPP(U_3297,c_Big__Operators_Olattice__class_OInf__fin(U_3296,U_3298)) = c_Big__Operators_Olattice__class_OInf__fin(U_3296,hAPP(c_Set_Oimage(U_3296,U_3296,U_3297),U_3298))
      | U_3298 = c_Orderings_Obot__class_Obot(tc_fun(U_3296,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3296),U_3298))
      | ? [U_3295,U_3294] : hAPP(U_3297,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_3296),U_3295),U_3294)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_3296),hAPP(U_3297,U_3295)),hAPP(U_3297,U_3294))
      | ~ class_Lattices_Olattice(U_3296) ),
    inference(variable_rename,[status(thm)],[f_815_1]) ).

fof(f_815_3,plain,
    ! [U_3298,U_3297,U_3296] :
      ( hAPP(U_3297,c_Big__Operators_Olattice__class_OInf__fin(U_3296,U_3298)) = c_Big__Operators_Olattice__class_OInf__fin(U_3296,hAPP(c_Set_Oimage(U_3296,U_3296,U_3297),U_3298))
      | U_3298 = c_Orderings_Obot__class_Obot(tc_fun(U_3296,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3296),U_3298))
      | ? [U_3294] : hAPP(U_3297,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_3296),sK58(U_3298,U_3297,U_3296)),U_3294)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_3296),hAPP(U_3297,sK58(U_3298,U_3297,U_3296))),hAPP(U_3297,U_3294))
      | ~ class_Lattices_Olattice(U_3296) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK58]),skolemize(U_3295,sK58(U_3298,U_3297,U_3296))],[f_815_2]) ).

fof(f_815_4,plain,
    ! [U_3298,U_3297,U_3296] :
      ( hAPP(U_3297,c_Big__Operators_Olattice__class_OInf__fin(U_3296,U_3298)) = c_Big__Operators_Olattice__class_OInf__fin(U_3296,hAPP(c_Set_Oimage(U_3296,U_3296,U_3297),U_3298))
      | U_3298 = c_Orderings_Obot__class_Obot(tc_fun(U_3296,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3296),U_3298))
      | hAPP(U_3297,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_3296),sK58(U_3298,U_3297,U_3296)),sK59(U_3298,U_3297,U_3296))) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_3296),hAPP(U_3297,sK58(U_3298,U_3297,U_3296))),hAPP(U_3297,sK59(U_3298,U_3297,U_3296)))
      | ~ class_Lattices_Olattice(U_3296) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK59]),skolemize(U_3294,sK59(U_3298,U_3297,U_3296))],[f_815_3]) ).

cnf(f_815_5,plain,
    ( hAPP(U_3297,c_Big__Operators_Olattice__class_OInf__fin(U_3296,U_3298)) = c_Big__Operators_Olattice__class_OInf__fin(U_3296,hAPP(c_Set_Oimage(U_3296,U_3296,U_3297),U_3298))
    | U_3298 = c_Orderings_Obot__class_Obot(tc_fun(U_3296,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3296),U_3298))
    | hAPP(U_3297,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_3296),sK58(U_3298,U_3297,U_3296)),sK59(U_3298,U_3297,U_3296))) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_3296),hAPP(U_3297,sK58(U_3298,U_3297,U_3296))),hAPP(U_3297,sK59(U_3298,U_3297,U_3296)))
    | ~ class_Lattices_Olattice(U_3296) ),
    inference(clausify,[status(thm)],[f_815_4]) ).

fof(f_816_1,plain,
    ! [V_N_2,V_h_2,T_b] :
      ( hAPP(V_h_2,c_Big__Operators_Olattice__class_OSup__fin(T_b,V_N_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2))
      | V_N_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
      | ? [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),B_x),B_y)) != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__fin_Ohom__commute]) ).

fof(f_816_2,plain,
    ! [U_3303,U_3302,U_3301] :
      ( hAPP(U_3302,c_Big__Operators_Olattice__class_OSup__fin(U_3301,U_3303)) = c_Big__Operators_Olattice__class_OSup__fin(U_3301,hAPP(c_Set_Oimage(U_3301,U_3301,U_3302),U_3303))
      | U_3303 = c_Orderings_Obot__class_Obot(tc_fun(U_3301,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3301),U_3303))
      | ? [U_3300,U_3299] : hAPP(U_3302,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3301),U_3300),U_3299)) != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3301),hAPP(U_3302,U_3300)),hAPP(U_3302,U_3299))
      | ~ class_Lattices_Olattice(U_3301) ),
    inference(variable_rename,[status(thm)],[f_816_1]) ).

fof(f_816_3,plain,
    ! [U_3303,U_3302,U_3301] :
      ( hAPP(U_3302,c_Big__Operators_Olattice__class_OSup__fin(U_3301,U_3303)) = c_Big__Operators_Olattice__class_OSup__fin(U_3301,hAPP(c_Set_Oimage(U_3301,U_3301,U_3302),U_3303))
      | U_3303 = c_Orderings_Obot__class_Obot(tc_fun(U_3301,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3301),U_3303))
      | ? [U_3299] : hAPP(U_3302,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3301),sK60(U_3303,U_3302,U_3301)),U_3299)) != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3301),hAPP(U_3302,sK60(U_3303,U_3302,U_3301))),hAPP(U_3302,U_3299))
      | ~ class_Lattices_Olattice(U_3301) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK60]),skolemize(U_3300,sK60(U_3303,U_3302,U_3301))],[f_816_2]) ).

fof(f_816_4,plain,
    ! [U_3303,U_3302,U_3301] :
      ( hAPP(U_3302,c_Big__Operators_Olattice__class_OSup__fin(U_3301,U_3303)) = c_Big__Operators_Olattice__class_OSup__fin(U_3301,hAPP(c_Set_Oimage(U_3301,U_3301,U_3302),U_3303))
      | U_3303 = c_Orderings_Obot__class_Obot(tc_fun(U_3301,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3301),U_3303))
      | hAPP(U_3302,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3301),sK60(U_3303,U_3302,U_3301)),sK61(U_3303,U_3302,U_3301))) != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3301),hAPP(U_3302,sK60(U_3303,U_3302,U_3301))),hAPP(U_3302,sK61(U_3303,U_3302,U_3301)))
      | ~ class_Lattices_Olattice(U_3301) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK61]),skolemize(U_3299,sK61(U_3303,U_3302,U_3301))],[f_816_3]) ).

cnf(f_816_5,plain,
    ( hAPP(U_3302,c_Big__Operators_Olattice__class_OSup__fin(U_3301,U_3303)) = c_Big__Operators_Olattice__class_OSup__fin(U_3301,hAPP(c_Set_Oimage(U_3301,U_3301,U_3302),U_3303))
    | U_3303 = c_Orderings_Obot__class_Obot(tc_fun(U_3301,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3301),U_3303))
    | hAPP(U_3302,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3301),sK60(U_3303,U_3302,U_3301)),sK61(U_3303,U_3302,U_3301))) != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_3301),hAPP(U_3302,sK60(U_3303,U_3302,U_3301))),hAPP(U_3302,sK61(U_3303,U_3302,U_3301)))
    | ~ class_Lattices_Olattice(U_3301) ),
    inference(clausify,[status(thm)],[f_816_4]) ).

fof(f_817_1,plain,
    ! [V_P_2,V_A_2,T_b] :
      ( hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
      | ? [B_a,B_A] :
          ( ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),B_A),hAPP(hAPP(c_Set_Oinsert(T_b),B_a),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
          & hBOOL(hAPP(V_P_2,B_A))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_A)) )
      | ~ hBOOL(hAPP(V_P_2,V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__empty__induct]) ).

fof(f_817_2,plain,
    ! [U_3308,U_3307,U_3306] :
      ( hBOOL(hAPP(U_3308,c_Orderings_Obot__class_Obot(tc_fun(U_3306,tc_HOL_Obool))))
      | ? [U_3305,U_3304] :
          ( ~ hBOOL(hAPP(U_3308,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3306,tc_HOL_Obool)),U_3304),hAPP(hAPP(c_Set_Oinsert(U_3306),U_3305),c_Orderings_Obot__class_Obot(tc_fun(U_3306,tc_HOL_Obool))))))
          & hBOOL(hAPP(U_3308,U_3304))
          & hBOOL(hAPP(hAPP(c_member(U_3306),U_3305),U_3304))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_3306),U_3304)) )
      | ~ hBOOL(hAPP(U_3308,U_3307))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3306),U_3307)) ),
    inference(variable_rename,[status(thm)],[f_817_1]) ).

fof(f_817_3,plain,
    ! [U_3308,U_3307,U_3306] :
      ( hBOOL(hAPP(U_3308,c_Orderings_Obot__class_Obot(tc_fun(U_3306,tc_HOL_Obool))))
      | ? [U_3304] :
          ( ~ hBOOL(hAPP(U_3308,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3306,tc_HOL_Obool)),U_3304),hAPP(hAPP(c_Set_Oinsert(U_3306),sK62(U_3308,U_3307,U_3306)),c_Orderings_Obot__class_Obot(tc_fun(U_3306,tc_HOL_Obool))))))
          & hBOOL(hAPP(U_3308,U_3304))
          & hBOOL(hAPP(hAPP(c_member(U_3306),sK62(U_3308,U_3307,U_3306)),U_3304))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_3306),U_3304)) )
      | ~ hBOOL(hAPP(U_3308,U_3307))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3306),U_3307)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK62]),skolemize(U_3305,sK62(U_3308,U_3307,U_3306))],[f_817_2]) ).

fof(f_817_4,plain,
    ! [U_3308,U_3307,U_3306] :
      ( hBOOL(hAPP(U_3308,c_Orderings_Obot__class_Obot(tc_fun(U_3306,tc_HOL_Obool))))
      | ( ~ hBOOL(hAPP(U_3308,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3306,tc_HOL_Obool)),sK63(U_3308,U_3307,U_3306)),hAPP(hAPP(c_Set_Oinsert(U_3306),sK62(U_3308,U_3307,U_3306)),c_Orderings_Obot__class_Obot(tc_fun(U_3306,tc_HOL_Obool))))))
        & hBOOL(hAPP(U_3308,sK63(U_3308,U_3307,U_3306)))
        & hBOOL(hAPP(hAPP(c_member(U_3306),sK62(U_3308,U_3307,U_3306)),sK63(U_3308,U_3307,U_3306)))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(U_3306),sK63(U_3308,U_3307,U_3306))) )
      | ~ hBOOL(hAPP(U_3308,U_3307))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3306),U_3307)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK63]),skolemize(U_3304,sK63(U_3308,U_3307,U_3306))],[f_817_3]) ).

cnf(f_817_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3306),sK63(U_3308,U_3307,U_3306)))
    | hBOOL(hAPP(U_3308,c_Orderings_Obot__class_Obot(tc_fun(U_3306,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(U_3308,U_3307))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3306),U_3307)) ),
    inference(clausify,[status(thm)],[f_817_4]) ).

cnf(f_817_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_3306),sK62(U_3308,U_3307,U_3306)),sK63(U_3308,U_3307,U_3306)))
    | hBOOL(hAPP(U_3308,c_Orderings_Obot__class_Obot(tc_fun(U_3306,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(U_3308,U_3307))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3306),U_3307)) ),
    inference(clausify,[status(thm)],[f_817_4]) ).

cnf(f_817_7,plain,
    ( hBOOL(hAPP(U_3308,sK63(U_3308,U_3307,U_3306)))
    | hBOOL(hAPP(U_3308,c_Orderings_Obot__class_Obot(tc_fun(U_3306,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(U_3308,U_3307))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3306),U_3307)) ),
    inference(clausify,[status(thm)],[f_817_4]) ).

cnf(f_817_8,plain,
    ( ~ hBOOL(hAPP(U_3308,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3306,tc_HOL_Obool)),sK63(U_3308,U_3307,U_3306)),hAPP(hAPP(c_Set_Oinsert(U_3306),sK62(U_3308,U_3307,U_3306)),c_Orderings_Obot__class_Obot(tc_fun(U_3306,tc_HOL_Obool))))))
    | hBOOL(hAPP(U_3308,c_Orderings_Obot__class_Obot(tc_fun(U_3306,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(U_3308,U_3307))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3306),U_3307)) ),
    inference(clausify,[status(thm)],[f_817_4]) ).

fof(f_818_1,plain,
    ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
      ( hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Ounion__idem]) ).

fof(f_818_2,plain,
    ! [U_3313,U_3312,U_3311,U_3310,U_3309] :
      ( hAPP(U_3311,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3309,tc_HOL_Obool)),U_3312),U_3313)) = hAPP(hAPP(U_3310,hAPP(U_3311,U_3312)),hAPP(U_3311,U_3313))
      | U_3313 = c_Orderings_Obot__class_Obot(tc_fun(U_3309,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3309),U_3313))
      | U_3312 = c_Orderings_Obot__class_Obot(tc_fun(U_3309,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3309),U_3312))
      | ~ c_Finite__Set_Ofolding__one__idem(U_3309,U_3310,U_3311) ),
    inference(variable_rename,[status(thm)],[f_818_1]) ).

cnf(f_818_3,plain,
    ( hAPP(U_3311,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3309,tc_HOL_Obool)),U_3312),U_3313)) = hAPP(hAPP(U_3310,hAPP(U_3311,U_3312)),hAPP(U_3311,U_3313))
    | U_3313 = c_Orderings_Obot__class_Obot(tc_fun(U_3309,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3309),U_3313))
    | U_3312 = c_Orderings_Obot__class_Obot(tc_fun(U_3309,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3309),U_3312))
    | ~ c_Finite__Set_Ofolding__one__idem(U_3309,U_3310,U_3311) ),
    inference(clausify,[status(thm)],[f_818_2]) ).

fof(f_819_1,plain,
    ! [V_P_2,V_A_2,V_F_2,T_b] :
      ( hBOOL(hAPP(V_P_2,V_F_2))
      | ? [B_a,B_F] :
          ( ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_F)))
          & hBOOL(hAPP(V_P_2,B_F))
          & ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_F))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_F)) )
      | ~ hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__subset__induct]) ).

fof(f_819_2,plain,
    ! [U_3319,U_3318,U_3317,U_3316] :
      ( hBOOL(hAPP(U_3319,U_3317))
      | ? [U_3315,U_3314] :
          ( ~ hBOOL(hAPP(U_3319,hAPP(hAPP(c_Set_Oinsert(U_3316),U_3315),U_3314)))
          & hBOOL(hAPP(U_3319,U_3314))
          & ~ hBOOL(hAPP(hAPP(c_member(U_3316),U_3315),U_3314))
          & hBOOL(hAPP(hAPP(c_member(U_3316),U_3315),U_3318))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_3316),U_3314)) )
      | ~ hBOOL(hAPP(U_3319,c_Orderings_Obot__class_Obot(tc_fun(U_3316,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3316,tc_HOL_Obool)),U_3317),U_3318))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3316),U_3317)) ),
    inference(variable_rename,[status(thm)],[f_819_1]) ).

fof(f_819_3,plain,
    ! [U_3319,U_3318,U_3317,U_3316] :
      ( hBOOL(hAPP(U_3319,U_3317))
      | ? [U_3314] :
          ( ~ hBOOL(hAPP(U_3319,hAPP(hAPP(c_Set_Oinsert(U_3316),sK64(U_3319,U_3318,U_3317,U_3316)),U_3314)))
          & hBOOL(hAPP(U_3319,U_3314))
          & ~ hBOOL(hAPP(hAPP(c_member(U_3316),sK64(U_3319,U_3318,U_3317,U_3316)),U_3314))
          & hBOOL(hAPP(hAPP(c_member(U_3316),sK64(U_3319,U_3318,U_3317,U_3316)),U_3318))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_3316),U_3314)) )
      | ~ hBOOL(hAPP(U_3319,c_Orderings_Obot__class_Obot(tc_fun(U_3316,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3316,tc_HOL_Obool)),U_3317),U_3318))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3316),U_3317)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK64]),skolemize(U_3315,sK64(U_3319,U_3318,U_3317,U_3316))],[f_819_2]) ).

fof(f_819_4,plain,
    ! [U_3319,U_3318,U_3317,U_3316] :
      ( hBOOL(hAPP(U_3319,U_3317))
      | ( ~ hBOOL(hAPP(U_3319,hAPP(hAPP(c_Set_Oinsert(U_3316),sK64(U_3319,U_3318,U_3317,U_3316)),sK65(U_3319,U_3318,U_3317,U_3316))))
        & hBOOL(hAPP(U_3319,sK65(U_3319,U_3318,U_3317,U_3316)))
        & ~ hBOOL(hAPP(hAPP(c_member(U_3316),sK64(U_3319,U_3318,U_3317,U_3316)),sK65(U_3319,U_3318,U_3317,U_3316)))
        & hBOOL(hAPP(hAPP(c_member(U_3316),sK64(U_3319,U_3318,U_3317,U_3316)),U_3318))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(U_3316),sK65(U_3319,U_3318,U_3317,U_3316))) )
      | ~ hBOOL(hAPP(U_3319,c_Orderings_Obot__class_Obot(tc_fun(U_3316,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3316,tc_HOL_Obool)),U_3317),U_3318))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3316),U_3317)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK65]),skolemize(U_3314,sK65(U_3319,U_3318,U_3317,U_3316))],[f_819_3]) ).

cnf(f_819_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_3316),sK65(U_3319,U_3318,U_3317,U_3316)))
    | hBOOL(hAPP(U_3319,U_3317))
    | ~ hBOOL(hAPP(U_3319,c_Orderings_Obot__class_Obot(tc_fun(U_3316,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3316,tc_HOL_Obool)),U_3317),U_3318))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3316),U_3317)) ),
    inference(clausify,[status(thm)],[f_819_4]) ).

cnf(f_819_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_3316),sK64(U_3319,U_3318,U_3317,U_3316)),U_3318))
    | hBOOL(hAPP(U_3319,U_3317))
    | ~ hBOOL(hAPP(U_3319,c_Orderings_Obot__class_Obot(tc_fun(U_3316,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3316,tc_HOL_Obool)),U_3317),U_3318))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3316),U_3317)) ),
    inference(clausify,[status(thm)],[f_819_4]) ).

cnf(f_819_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_3316),sK64(U_3319,U_3318,U_3317,U_3316)),sK65(U_3319,U_3318,U_3317,U_3316)))
    | hBOOL(hAPP(U_3319,U_3317))
    | ~ hBOOL(hAPP(U_3319,c_Orderings_Obot__class_Obot(tc_fun(U_3316,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3316,tc_HOL_Obool)),U_3317),U_3318))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3316),U_3317)) ),
    inference(clausify,[status(thm)],[f_819_4]) ).

cnf(f_819_8,plain,
    ( hBOOL(hAPP(U_3319,sK65(U_3319,U_3318,U_3317,U_3316)))
    | hBOOL(hAPP(U_3319,U_3317))
    | ~ hBOOL(hAPP(U_3319,c_Orderings_Obot__class_Obot(tc_fun(U_3316,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3316,tc_HOL_Obool)),U_3317),U_3318))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3316),U_3317)) ),
    inference(clausify,[status(thm)],[f_819_4]) ).

cnf(f_819_9,plain,
    ( ~ hBOOL(hAPP(U_3319,hAPP(hAPP(c_Set_Oinsert(U_3316),sK64(U_3319,U_3318,U_3317,U_3316)),sK65(U_3319,U_3318,U_3317,U_3316))))
    | hBOOL(hAPP(U_3319,U_3317))
    | ~ hBOOL(hAPP(U_3319,c_Orderings_Obot__class_Obot(tc_fun(U_3316,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3316,tc_HOL_Obool)),U_3317),U_3318))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3316),U_3317)) ),
    inference(clausify,[status(thm)],[f_819_4]) ).

fof(f_820_1,plain,
    ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
      ( hAPP(hAPP(V_f_2,hAPP(V_F_2,V_B_2)),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Osubset__idem]) ).

fof(f_820_2,plain,
    ! [U_3324,U_3323,U_3322,U_3321,U_3320] :
      ( hAPP(hAPP(U_3321,hAPP(U_3322,U_3324)),hAPP(U_3322,U_3323)) = hAPP(U_3322,U_3323)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3320,tc_HOL_Obool)),U_3324),U_3323))
      | U_3324 = c_Orderings_Obot__class_Obot(tc_fun(U_3320,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3320),U_3323))
      | ~ c_Finite__Set_Ofolding__one__idem(U_3320,U_3321,U_3322) ),
    inference(variable_rename,[status(thm)],[f_820_1]) ).

cnf(f_820_3,plain,
    ( hAPP(hAPP(U_3321,hAPP(U_3322,U_3324)),hAPP(U_3322,U_3323)) = hAPP(U_3322,U_3323)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3320,tc_HOL_Obool)),U_3324),U_3323))
    | U_3324 = c_Orderings_Obot__class_Obot(tc_fun(U_3320,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3320),U_3323))
    | ~ c_Finite__Set_Ofolding__one__idem(U_3320,U_3321,U_3322) ),
    inference(clausify,[status(thm)],[f_820_2]) ).

fof(f_821_1,plain,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
      ( hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Oinsert__idem]) ).

fof(f_821_2,plain,
    ! [U_3329,U_3328,U_3327,U_3326,U_3325] :
      ( hAPP(U_3327,hAPP(hAPP(c_Set_Oinsert(U_3325),U_3329),U_3328)) = hAPP(hAPP(U_3326,U_3329),hAPP(U_3327,U_3328))
      | U_3328 = c_Orderings_Obot__class_Obot(tc_fun(U_3325,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3325),U_3328))
      | ~ c_Finite__Set_Ofolding__one__idem(U_3325,U_3326,U_3327) ),
    inference(variable_rename,[status(thm)],[f_821_1]) ).

cnf(f_821_3,plain,
    ( hAPP(U_3327,hAPP(hAPP(c_Set_Oinsert(U_3325),U_3329),U_3328)) = hAPP(hAPP(U_3326,U_3329),hAPP(U_3327,U_3328))
    | U_3328 = c_Orderings_Obot__class_Obot(tc_fun(U_3325,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3325),U_3328))
    | ~ c_Finite__Set_Ofolding__one__idem(U_3325,U_3326,U_3327) ),
    inference(clausify,[status(thm)],[f_821_2]) ).

fof(f_822_1,plain,
    ! [V_f_2,T_c,T_b,V_S_2] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_S_2))
      | ? [B_A] :
          ( ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,B_A)
          & hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_A),V_S_2)) )
      | V_S_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)) ),
    inference(fof_nnf,[status(thm)],[fact_inj__on__Inter]) ).

fof(f_822_2,plain,
    ! [U_3334,U_3333,U_3332,U_3331] :
      ( c_Fun_Oinj__on(U_3332,U_3333,U_3334,c_Complete__Lattice_OInf__class_OInf(tc_fun(U_3332,tc_HOL_Obool),U_3331))
      | ? [U_3330] :
          ( ~ c_Fun_Oinj__on(U_3332,U_3333,U_3334,U_3330)
          & hBOOL(hAPP(hAPP(c_member(tc_fun(U_3332,tc_HOL_Obool)),U_3330),U_3331)) )
      | U_3331 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_3332,tc_HOL_Obool),tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_822_1]) ).

fof(f_822_3,plain,
    ! [U_3334,U_3333,U_3332,U_3331] :
      ( c_Fun_Oinj__on(U_3332,U_3333,U_3334,c_Complete__Lattice_OInf__class_OInf(tc_fun(U_3332,tc_HOL_Obool),U_3331))
      | ( ~ c_Fun_Oinj__on(U_3332,U_3333,U_3334,sK66(U_3334,U_3333,U_3332,U_3331))
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_3332,tc_HOL_Obool)),sK66(U_3334,U_3333,U_3332,U_3331)),U_3331)) )
      | U_3331 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_3332,tc_HOL_Obool),tc_HOL_Obool)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK66]),skolemize(U_3330,sK66(U_3334,U_3333,U_3332,U_3331))],[f_822_2]) ).

cnf(f_822_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_3332,tc_HOL_Obool)),sK66(U_3334,U_3333,U_3332,U_3331)),U_3331))
    | c_Fun_Oinj__on(U_3332,U_3333,U_3334,c_Complete__Lattice_OInf__class_OInf(tc_fun(U_3332,tc_HOL_Obool),U_3331))
    | U_3331 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_3332,tc_HOL_Obool),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_822_3]) ).

cnf(f_822_5,plain,
    ( ~ c_Fun_Oinj__on(U_3332,U_3333,U_3334,sK66(U_3334,U_3333,U_3332,U_3331))
    | c_Fun_Oinj__on(U_3332,U_3333,U_3334,c_Complete__Lattice_OInf__class_OInf(tc_fun(U_3332,tc_HOL_Obool),U_3331))
    | U_3331 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_3332,tc_HOL_Obool),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_822_3]) ).

fof(f_823_1,plain,
    ! [V_x_2,V_F_2,V_f_2,T_b] :
      ( hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2
      | ~ c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Oidem]) ).

fof(f_823_2,plain,
    ! [U_3338,U_3337,U_3336,U_3335] :
      ( hAPP(hAPP(U_3336,U_3338),U_3338) = U_3338
      | ~ c_Finite__Set_Ofolding__one__idem(U_3335,U_3336,U_3337) ),
    inference(variable_rename,[status(thm)],[f_823_1]) ).

fof(f_823_3,plain,
    ! [U_3338,U_3337,U_3336] :
      ( ! [U_3335] : ~ c_Finite__Set_Ofolding__one__idem(U_3335,U_3336,U_3337)
      | hAPP(hAPP(U_3336,U_3338),U_3338) = U_3338 ),
    inference(miniscope,[status(thm)],[f_823_2]) ).

cnf(f_823_4,plain,
    ( ~ c_Finite__Set_Ofolding__one__idem(U_3335,U_3336,U_3337)
    | hAPP(hAPP(U_3336,U_3338),U_3338) = U_3338 ),
    inference(clausify,[status(thm)],[f_823_3]) ).

fof(f_824_1,plain,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
      ( hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2)
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Oin__idem]) ).

fof(f_824_2,plain,
    ! [U_3343,U_3342,U_3341,U_3340,U_3339] :
      ( hAPP(hAPP(U_3340,U_3343),hAPP(U_3341,U_3342)) = hAPP(U_3341,U_3342)
      | ~ hBOOL(hAPP(hAPP(c_member(U_3339),U_3343),U_3342))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3339),U_3342))
      | ~ c_Finite__Set_Ofolding__one__idem(U_3339,U_3340,U_3341) ),
    inference(variable_rename,[status(thm)],[f_824_1]) ).

cnf(f_824_3,plain,
    ( hAPP(hAPP(U_3340,U_3343),hAPP(U_3341,U_3342)) = hAPP(U_3341,U_3342)
    | ~ hBOOL(hAPP(hAPP(c_member(U_3339),U_3343),U_3342))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3339),U_3342))
    | ~ c_Finite__Set_Ofolding__one__idem(U_3339,U_3340,U_3341) ),
    inference(clausify,[status(thm)],[f_824_2]) ).

fof(f_825_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),V_B_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))
      | ? [B_X] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_X),V_B_2))
          & hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Inter__subset]) ).

fof(f_825_2,plain,
    ! [U_3347,U_3346,U_3345] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3345,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_3345,tc_HOL_Obool),U_3346)),U_3347))
      | U_3346 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_3345,tc_HOL_Obool),tc_HOL_Obool))
      | ? [U_3344] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3345,tc_HOL_Obool)),U_3344),U_3347))
          & hBOOL(hAPP(hAPP(c_member(tc_fun(U_3345,tc_HOL_Obool)),U_3344),U_3346)) ) ),
    inference(variable_rename,[status(thm)],[f_825_1]) ).

fof(f_825_3,plain,
    ! [U_3347,U_3346,U_3345] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3345,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_3345,tc_HOL_Obool),U_3346)),U_3347))
      | U_3346 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_3345,tc_HOL_Obool),tc_HOL_Obool))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3345,tc_HOL_Obool)),sK67(U_3347,U_3346,U_3345)),U_3347))
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_3345,tc_HOL_Obool)),sK67(U_3347,U_3346,U_3345)),U_3346)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK67]),skolemize(U_3344,sK67(U_3347,U_3346,U_3345))],[f_825_2]) ).

cnf(f_825_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_3345,tc_HOL_Obool)),sK67(U_3347,U_3346,U_3345)),U_3346))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3345,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_3345,tc_HOL_Obool),U_3346)),U_3347))
    | U_3346 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_3345,tc_HOL_Obool),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_825_3]) ).

cnf(f_825_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3345,tc_HOL_Obool)),sK67(U_3347,U_3346,U_3345)),U_3347))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3345,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_3345,tc_HOL_Obool),U_3346)),U_3347))
    | U_3346 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_3345,tc_HOL_Obool),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_825_3]) ).

fof(f_826_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_B_2)),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_fold1__antimono]) ).

fof(f_826_2,plain,
    ! [U_3350,U_3349,U_3348] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3348),hAPP(c_Finite__Set_Ofold1(U_3348,c_Orderings_Oord__class_Omin(U_3348)),U_3350)),hAPP(c_Finite__Set_Ofold1(U_3348,c_Orderings_Oord__class_Omin(U_3348)),U_3349)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3348),U_3350))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3348,tc_HOL_Obool)),U_3349),U_3350))
      | U_3349 = c_Orderings_Obot__class_Obot(tc_fun(U_3348,tc_HOL_Obool))
      | ~ class_Orderings_Olinorder(U_3348) ),
    inference(variable_rename,[status(thm)],[f_826_1]) ).

cnf(f_826_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3348),hAPP(c_Finite__Set_Ofold1(U_3348,c_Orderings_Oord__class_Omin(U_3348)),U_3350)),hAPP(c_Finite__Set_Ofold1(U_3348,c_Orderings_Oord__class_Omin(U_3348)),U_3349)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3348),U_3350))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3348,tc_HOL_Obool)),U_3349),U_3350))
    | U_3349 = c_Orderings_Obot__class_Obot(tc_fun(U_3348,tc_HOL_Obool))
    | ~ class_Orderings_Olinorder(U_3348) ),
    inference(clausify,[status(thm)],[f_826_2]) ).

fof(f_827_1,plain,
    ! [V_N_2,V_h_2,V_F_2,V_f_2,T_b] :
      ( hAPP(V_h_2,hAPP(V_F_2,V_N_2)) = hAPP(V_F_2,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2))
      | V_N_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
      | ? [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(V_f_2,B_x),B_y)) != hAPP(hAPP(V_f_2,hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
      | ~ c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Ohom__commute]) ).

fof(f_827_2,plain,
    ! [U_3357,U_3356,U_3355,U_3354,U_3353] :
      ( hAPP(U_3356,hAPP(U_3355,U_3357)) = hAPP(U_3355,hAPP(c_Set_Oimage(U_3353,U_3353,U_3356),U_3357))
      | U_3357 = c_Orderings_Obot__class_Obot(tc_fun(U_3353,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3353),U_3357))
      | ? [U_3352,U_3351] : hAPP(U_3356,hAPP(hAPP(U_3354,U_3352),U_3351)) != hAPP(hAPP(U_3354,hAPP(U_3356,U_3352)),hAPP(U_3356,U_3351))
      | ~ c_Finite__Set_Ofolding__one__idem(U_3353,U_3354,U_3355) ),
    inference(variable_rename,[status(thm)],[f_827_1]) ).

fof(f_827_3,plain,
    ! [U_3357,U_3356,U_3355,U_3354,U_3353] :
      ( hAPP(U_3356,hAPP(U_3355,U_3357)) = hAPP(U_3355,hAPP(c_Set_Oimage(U_3353,U_3353,U_3356),U_3357))
      | U_3357 = c_Orderings_Obot__class_Obot(tc_fun(U_3353,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3353),U_3357))
      | ? [U_3351] : hAPP(U_3356,hAPP(hAPP(U_3354,sK68(U_3357,U_3356,U_3355,U_3354,U_3353)),U_3351)) != hAPP(hAPP(U_3354,hAPP(U_3356,sK68(U_3357,U_3356,U_3355,U_3354,U_3353))),hAPP(U_3356,U_3351))
      | ~ c_Finite__Set_Ofolding__one__idem(U_3353,U_3354,U_3355) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK68]),skolemize(U_3352,sK68(U_3357,U_3356,U_3355,U_3354,U_3353))],[f_827_2]) ).

fof(f_827_4,plain,
    ! [U_3357,U_3356,U_3355,U_3354,U_3353] :
      ( hAPP(U_3356,hAPP(U_3355,U_3357)) = hAPP(U_3355,hAPP(c_Set_Oimage(U_3353,U_3353,U_3356),U_3357))
      | U_3357 = c_Orderings_Obot__class_Obot(tc_fun(U_3353,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3353),U_3357))
      | hAPP(U_3356,hAPP(hAPP(U_3354,sK68(U_3357,U_3356,U_3355,U_3354,U_3353)),sK69(U_3357,U_3356,U_3355,U_3354,U_3353))) != hAPP(hAPP(U_3354,hAPP(U_3356,sK68(U_3357,U_3356,U_3355,U_3354,U_3353))),hAPP(U_3356,sK69(U_3357,U_3356,U_3355,U_3354,U_3353)))
      | ~ c_Finite__Set_Ofolding__one__idem(U_3353,U_3354,U_3355) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK69]),skolemize(U_3351,sK69(U_3357,U_3356,U_3355,U_3354,U_3353))],[f_827_3]) ).

cnf(f_827_5,plain,
    ( hAPP(U_3356,hAPP(U_3355,U_3357)) = hAPP(U_3355,hAPP(c_Set_Oimage(U_3353,U_3353,U_3356),U_3357))
    | U_3357 = c_Orderings_Obot__class_Obot(tc_fun(U_3353,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3353),U_3357))
    | hAPP(U_3356,hAPP(hAPP(U_3354,sK68(U_3357,U_3356,U_3355,U_3354,U_3353)),sK69(U_3357,U_3356,U_3355,U_3354,U_3353))) != hAPP(hAPP(U_3354,hAPP(U_3356,sK68(U_3357,U_3356,U_3355,U_3354,U_3353))),hAPP(U_3356,sK69(U_3357,U_3356,U_3355,U_3354,U_3353)))
    | ~ c_Finite__Set_Ofolding__one__idem(U_3353,U_3354,U_3355) ),
    inference(clausify,[status(thm)],[f_827_4]) ).

fof(f_828_1,plain,
    ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
      ( hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2))
      | ? [B_x] :
          ( hAPP(V_g_2,B_x) != V_z_2
          & hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
      | ~ c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Ounion__inter__neutral]) ).

fof(f_828_2,plain,
    ! [U_3366,U_3365,U_3364,U_3363,U_3362,U_3361,U_3360,U_3359] :
      ( hAPP(U_3364,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3360,tc_HOL_Obool)),U_3365),U_3366)) = hAPP(hAPP(U_3361,hAPP(U_3364,U_3365)),hAPP(U_3364,U_3366))
      | ? [U_3358] :
          ( hAPP(U_3363,U_3358) != U_3362
          & hBOOL(hAPP(hAPP(c_member(U_3360),U_3358),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3360,tc_HOL_Obool)),U_3365),U_3366))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3360),U_3366))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3360),U_3365))
      | ~ c_Finite__Set_Ofolding__image__simple(U_3359,U_3360,U_3361,U_3362,U_3363,U_3364) ),
    inference(variable_rename,[status(thm)],[f_828_1]) ).

fof(f_828_3,plain,
    ! [U_3366,U_3365,U_3364,U_3363,U_3362,U_3361,U_3360] :
      ( ! [U_3359] : ~ c_Finite__Set_Ofolding__image__simple(U_3359,U_3360,U_3361,U_3362,U_3363,U_3364)
      | hAPP(U_3364,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3360,tc_HOL_Obool)),U_3365),U_3366)) = hAPP(hAPP(U_3361,hAPP(U_3364,U_3365)),hAPP(U_3364,U_3366))
      | ? [U_3358] :
          ( hAPP(U_3363,U_3358) != U_3362
          & hBOOL(hAPP(hAPP(c_member(U_3360),U_3358),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3360,tc_HOL_Obool)),U_3365),U_3366))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3360),U_3366))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3360),U_3365)) ),
    inference(miniscope,[status(thm)],[f_828_2]) ).

fof(f_828_4,plain,
    ! [U_3366,U_3365,U_3364,U_3363,U_3362,U_3361,U_3360] :
      ( ! [U_3359] : ~ c_Finite__Set_Ofolding__image__simple(U_3359,U_3360,U_3361,U_3362,U_3363,U_3364)
      | hAPP(U_3364,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3360,tc_HOL_Obool)),U_3365),U_3366)) = hAPP(hAPP(U_3361,hAPP(U_3364,U_3365)),hAPP(U_3364,U_3366))
      | ( hAPP(U_3363,sK70(U_3366,U_3365,U_3364,U_3363,U_3362,U_3361,U_3360)) != U_3362
        & hBOOL(hAPP(hAPP(c_member(U_3360),sK70(U_3366,U_3365,U_3364,U_3363,U_3362,U_3361,U_3360)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3360,tc_HOL_Obool)),U_3365),U_3366))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3360),U_3366))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3360),U_3365)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK70]),skolemize(U_3358,sK70(U_3366,U_3365,U_3364,U_3363,U_3362,U_3361,U_3360))],[f_828_3]) ).

cnf(f_828_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_3360),sK70(U_3366,U_3365,U_3364,U_3363,U_3362,U_3361,U_3360)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3360,tc_HOL_Obool)),U_3365),U_3366)))
    | hAPP(U_3364,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3360,tc_HOL_Obool)),U_3365),U_3366)) = hAPP(hAPP(U_3361,hAPP(U_3364,U_3365)),hAPP(U_3364,U_3366))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3360),U_3366))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3360),U_3365))
    | ~ c_Finite__Set_Ofolding__image__simple(U_3359,U_3360,U_3361,U_3362,U_3363,U_3364) ),
    inference(clausify,[status(thm)],[f_828_4]) ).

cnf(f_828_6,plain,
    ( hAPP(U_3363,sK70(U_3366,U_3365,U_3364,U_3363,U_3362,U_3361,U_3360)) != U_3362
    | hAPP(U_3364,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3360,tc_HOL_Obool)),U_3365),U_3366)) = hAPP(hAPP(U_3361,hAPP(U_3364,U_3365)),hAPP(U_3364,U_3366))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3360),U_3366))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3360),U_3365))
    | ~ c_Finite__Set_Ofolding__image__simple(U_3359,U_3360,U_3361,U_3362,U_3363,U_3364) ),
    inference(clausify,[status(thm)],[f_828_4]) ).

fof(f_829_1,plain,
    ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)
          | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2))
          | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Oab__group__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__diff1]) ).

fof(f_829_2,plain,
    ! [U_3371,U_3370,U_3369,U_3368,U_3367] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3368,U_3367),U_3371),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3368,tc_HOL_Obool)),U_3369),hAPP(hAPP(c_Set_Oinsert(U_3368),U_3370),c_Orderings_Obot__class_Obot(tc_fun(U_3368,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3368,U_3367),U_3371),U_3369)
          | hBOOL(hAPP(hAPP(c_member(U_3368),U_3370),U_3369)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3368,U_3367),U_3371),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3368,tc_HOL_Obool)),U_3369),hAPP(hAPP(c_Set_Oinsert(U_3368),U_3370),c_Orderings_Obot__class_Obot(tc_fun(U_3368,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3367),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3368,U_3367),U_3371),U_3369)),hAPP(U_3371,U_3370))
          | ~ hBOOL(hAPP(hAPP(c_member(U_3368),U_3370),U_3369)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3368),U_3369))
      | ~ class_Groups_Oab__group__add(U_3367) ),
    inference(variable_rename,[status(thm)],[f_829_1]) ).

cnf(f_829_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3368,U_3367),U_3371),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3368,tc_HOL_Obool)),U_3369),hAPP(hAPP(c_Set_Oinsert(U_3368),U_3370),c_Orderings_Obot__class_Obot(tc_fun(U_3368,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3367),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3368,U_3367),U_3371),U_3369)),hAPP(U_3371,U_3370))
    | ~ hBOOL(hAPP(hAPP(c_member(U_3368),U_3370),U_3369))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3368),U_3369))
    | ~ class_Groups_Oab__group__add(U_3367) ),
    inference(clausify,[status(thm)],[f_829_2]) ).

cnf(f_829_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3368,U_3367),U_3371),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3368,tc_HOL_Obool)),U_3369),hAPP(hAPP(c_Set_Oinsert(U_3368),U_3370),c_Orderings_Obot__class_Obot(tc_fun(U_3368,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3368,U_3367),U_3371),U_3369)
    | hBOOL(hAPP(hAPP(c_member(U_3368),U_3370),U_3369))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3368),U_3369))
    | ~ class_Groups_Oab__group__add(U_3367) ),
    inference(clausify,[status(thm)],[f_829_2]) ).

fof(f_830_1,plain,
    ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Rings_Oring(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__diff1__ring]) ).

fof(f_830_2,plain,
    ! [U_3376,U_3375,U_3374,U_3373,U_3372] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3373,U_3372),U_3376),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3373,tc_HOL_Obool)),U_3374),hAPP(hAPP(c_Set_Oinsert(U_3373),U_3375),c_Orderings_Obot__class_Obot(tc_fun(U_3373,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3372),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3373,U_3372),U_3376),U_3374)),hAPP(U_3376,U_3375))
      | ~ hBOOL(hAPP(hAPP(c_member(U_3373),U_3375),U_3374))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3373),U_3374))
      | ~ class_Rings_Oring(U_3372) ),
    inference(variable_rename,[status(thm)],[f_830_1]) ).

cnf(f_830_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3373,U_3372),U_3376),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3373,tc_HOL_Obool)),U_3374),hAPP(hAPP(c_Set_Oinsert(U_3373),U_3375),c_Orderings_Obot__class_Obot(tc_fun(U_3373,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3372),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3373,U_3372),U_3376),U_3374)),hAPP(U_3376,U_3375))
    | ~ hBOOL(hAPP(hAPP(c_member(U_3373),U_3375),U_3374))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3373),U_3374))
    | ~ class_Rings_Oring(U_3372) ),
    inference(clausify,[status(thm)],[f_830_2]) ).

fof(f_831_1,plain,
    ! [V_A_2,V_C_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_C_2)))
      | ? [B_X] :
          ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),B_X))
          & hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_InterI]) ).

fof(f_831_2,plain,
    ! [U_3380,U_3379,U_3378] :
      ( hBOOL(hAPP(hAPP(c_member(U_3378),U_3380),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_3378,tc_HOL_Obool),U_3379)))
      | ? [U_3377] :
          ( ~ hBOOL(hAPP(hAPP(c_member(U_3378),U_3380),U_3377))
          & hBOOL(hAPP(hAPP(c_member(tc_fun(U_3378,tc_HOL_Obool)),U_3377),U_3379)) ) ),
    inference(variable_rename,[status(thm)],[f_831_1]) ).

fof(f_831_3,plain,
    ! [U_3380,U_3379,U_3378] :
      ( hBOOL(hAPP(hAPP(c_member(U_3378),U_3380),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_3378,tc_HOL_Obool),U_3379)))
      | ( ~ hBOOL(hAPP(hAPP(c_member(U_3378),U_3380),sK71(U_3380,U_3379,U_3378)))
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_3378,tc_HOL_Obool)),sK71(U_3380,U_3379,U_3378)),U_3379)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK71]),skolemize(U_3377,sK71(U_3380,U_3379,U_3378))],[f_831_2]) ).

cnf(f_831_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_3378,tc_HOL_Obool)),sK71(U_3380,U_3379,U_3378)),U_3379))
    | hBOOL(hAPP(hAPP(c_member(U_3378),U_3380),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_3378,tc_HOL_Obool),U_3379))) ),
    inference(clausify,[status(thm)],[f_831_3]) ).

cnf(f_831_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_3378),U_3380),sK71(U_3380,U_3379,U_3378)))
    | hBOOL(hAPP(hAPP(c_member(U_3378),U_3380),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_3378,tc_HOL_Obool),U_3379))) ),
    inference(clausify,[status(thm)],[f_831_3]) ).

fof(f_832_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = V_x_2
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ? [B_y] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_y))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Min__eqI]) ).

fof(f_832_2,plain,
    ! [U_3384,U_3383,U_3382] :
      ( c_Big__Operators_Olinorder__class_OMin(U_3382,U_3383) = U_3384
      | ~ hBOOL(hAPP(hAPP(c_member(U_3382),U_3384),U_3383))
      | ? [U_3381] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3382),U_3384),U_3381))
          & hBOOL(hAPP(hAPP(c_member(U_3382),U_3381),U_3383)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3382),U_3383))
      | ~ class_Orderings_Olinorder(U_3382) ),
    inference(variable_rename,[status(thm)],[f_832_1]) ).

fof(f_832_3,plain,
    ! [U_3384,U_3383,U_3382] :
      ( c_Big__Operators_Olinorder__class_OMin(U_3382,U_3383) = U_3384
      | ~ hBOOL(hAPP(hAPP(c_member(U_3382),U_3384),U_3383))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3382),U_3384),sK72(U_3384,U_3383,U_3382)))
        & hBOOL(hAPP(hAPP(c_member(U_3382),sK72(U_3384,U_3383,U_3382)),U_3383)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3382),U_3383))
      | ~ class_Orderings_Olinorder(U_3382) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK72]),skolemize(U_3381,sK72(U_3384,U_3383,U_3382))],[f_832_2]) ).

cnf(f_832_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_3382),sK72(U_3384,U_3383,U_3382)),U_3383))
    | c_Big__Operators_Olinorder__class_OMin(U_3382,U_3383) = U_3384
    | ~ hBOOL(hAPP(hAPP(c_member(U_3382),U_3384),U_3383))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3382),U_3383))
    | ~ class_Orderings_Olinorder(U_3382) ),
    inference(clausify,[status(thm)],[f_832_3]) ).

cnf(f_832_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3382),U_3384),sK72(U_3384,U_3383,U_3382)))
    | c_Big__Operators_Olinorder__class_OMin(U_3382,U_3383) = U_3384
    | ~ hBOOL(hAPP(hAPP(c_member(U_3382),U_3384),U_3383))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3382),U_3383))
    | ~ class_Orderings_Olinorder(U_3382) ),
    inference(clausify,[status(thm)],[f_832_3]) ).

fof(f_833_1,plain,
    ! [V_f_2,V_p_2,V_n_2,V_m_2,T_b] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_p_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_n_2),V_p_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
      | ~ class_Groups_Oab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__diff__nat__ivl]) ).

fof(f_833_2,plain,
    ! [U_3389,U_3388,U_3387,U_3386,U_3385] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3385),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_3385),U_3389),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_3386),U_3388))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_3385),U_3389),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_3386),U_3387))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_3385),U_3389),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_3387),U_3388))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3387),U_3388))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3386),U_3387))
      | ~ class_Groups_Oab__group__add(U_3385) ),
    inference(variable_rename,[status(thm)],[f_833_1]) ).

cnf(f_833_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3385),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_3385),U_3389),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_3386),U_3388))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_3385),U_3389),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_3386),U_3387))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_3385),U_3389),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_3387),U_3388))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3387),U_3388))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3386),U_3387))
    | ~ class_Groups_Oab__group__add(U_3385) ),
    inference(clausify,[status(thm)],[f_833_2]) ).

fof(f_834_1,plain,
    ! [V_a_2,V_f_2,T_b,V_g_2] :
      ( hAPP(V_g_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_a_2
      | V_g_2 != c_Finite__Set_Ofold1(T_b,V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_fold1__singleton__def]) ).

fof(f_834_2,plain,
    ! [U_3393,U_3392,U_3391,U_3390] :
      ( hAPP(U_3390,hAPP(hAPP(c_Set_Oinsert(U_3391),U_3393),c_Orderings_Obot__class_Obot(tc_fun(U_3391,tc_HOL_Obool)))) = U_3393
      | U_3390 != c_Finite__Set_Ofold1(U_3391,U_3392) ),
    inference(variable_rename,[status(thm)],[f_834_1]) ).

cnf(f_834_3,plain,
    ( hAPP(U_3390,hAPP(hAPP(c_Set_Oinsert(U_3391),U_3393),c_Orderings_Obot__class_Obot(tc_fun(U_3391,tc_HOL_Obool)))) = U_3393
    | U_3390 != c_Finite__Set_Ofold1(U_3391,U_3392) ),
    inference(clausify,[status(thm)],[f_834_2]) ).

fof(f_835_1,plain,
    ! [V_a_2,V_f_2,T_b] : hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_a_2,
    inference(fof_nnf,[status(thm)],[fact_fold1__singleton]) ).

fof(f_835_2,plain,
    ! [U_3396,U_3395,U_3394] : hAPP(c_Finite__Set_Ofold1(U_3394,U_3395),hAPP(hAPP(c_Set_Oinsert(U_3394),U_3396),c_Orderings_Obot__class_Obot(tc_fun(U_3394,tc_HOL_Obool)))) = U_3396,
    inference(variable_rename,[status(thm)],[f_835_1]) ).

cnf(f_835_3,plain,
    hAPP(c_Finite__Set_Ofold1(U_3394,U_3395),hAPP(hAPP(c_Set_Oinsert(U_3394),U_3396),c_Orderings_Obot__class_Obot(tc_fun(U_3394,tc_HOL_Obool)))) = U_3396,
    inference(clausify,[status(thm)],[f_835_2]) ).

fof(f_836_1,plain,
    ! [V_f_2,V_A_2,V_B_2,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__diff__nat]) ).

fof(f_836_2,plain,
    ! [U_3400,U_3399,U_3398,U_3397] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3397,tc_Nat_Onat),U_3400),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3397,tc_HOL_Obool)),U_3399),U_3398)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3397,tc_Nat_Onat),U_3400),U_3399)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3397,tc_Nat_Onat),U_3400),U_3398))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3397,tc_HOL_Obool)),U_3398),U_3399))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3397),U_3398)) ),
    inference(variable_rename,[status(thm)],[f_836_1]) ).

cnf(f_836_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3397,tc_Nat_Onat),U_3400),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3397,tc_HOL_Obool)),U_3399),U_3398)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3397,tc_Nat_Onat),U_3400),U_3399)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3397,tc_Nat_Onat),U_3400),U_3398))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3397,tc_HOL_Obool)),U_3398),U_3399))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3397),U_3398)) ),
    inference(clausify,[status(thm)],[f_836_2]) ).

fof(f_837_1,plain,
    ! [V_A_2,V_F_2,V_f_2,T_b] :
      ( hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__one_Oeq__fold]) ).

fof(f_837_2,plain,
    ! [U_3404,U_3403,U_3402,U_3401] :
      ( hAPP(U_3403,U_3404) = hAPP(c_Finite__Set_Ofold1(U_3401,U_3402),U_3404)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3401),U_3404))
      | ~ c_Finite__Set_Ofolding__one(U_3401,U_3402,U_3403) ),
    inference(variable_rename,[status(thm)],[f_837_1]) ).

cnf(f_837_3,plain,
    ( hAPP(U_3403,U_3404) = hAPP(c_Finite__Set_Ofold1(U_3401,U_3402),U_3404)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3401),U_3404))
    | ~ c_Finite__Set_Ofolding__one(U_3401,U_3402,U_3403) ),
    inference(clausify,[status(thm)],[f_837_2]) ).

fof(f_838_1,plain,
    ! [V_A_2,T_b] :
      ( c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__fin_OF__eq]) ).

fof(f_838_2,plain,
    ! [U_3406,U_3405] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_3405,U_3406) = hAPP(c_Finite__Set_Ofold1(U_3405,c_Lattices_Osemilattice__sup__class_Osup(U_3405)),U_3406)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3405),U_3406))
      | ~ class_Lattices_Olattice(U_3405) ),
    inference(variable_rename,[status(thm)],[f_838_1]) ).

cnf(f_838_3,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_3405,U_3406) = hAPP(c_Finite__Set_Ofold1(U_3405,c_Lattices_Osemilattice__sup__class_Osup(U_3405)),U_3406)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3405),U_3406))
    | ~ class_Lattices_Olattice(U_3405) ),
    inference(clausify,[status(thm)],[f_838_2]) ).

fof(f_839_1,plain,
    ! [V_A_2,T_b] :
      ( c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__fin_OF__eq]) ).

fof(f_839_2,plain,
    ! [U_3408,U_3407] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_3407,U_3408) = hAPP(c_Finite__Set_Ofold1(U_3407,c_Lattices_Osemilattice__inf__class_Oinf(U_3407)),U_3408)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3407),U_3408))
      | ~ class_Lattices_Olattice(U_3407) ),
    inference(variable_rename,[status(thm)],[f_839_1]) ).

cnf(f_839_3,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_3407,U_3408) = hAPP(c_Finite__Set_Ofold1(U_3407,c_Lattices_Osemilattice__inf__class_Oinf(U_3407)),U_3408)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3407),U_3408))
    | ~ class_Lattices_Olattice(U_3407) ),
    inference(clausify,[status(thm)],[f_839_2]) ).

fof(f_840_1,plain,
    ! [V_f_2,V_A_2,V_a_2,T_b] :
      ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2)
        | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) )
      & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__diff1__nat]) ).

fof(f_840_2,plain,
    ! [U_3412,U_3411,U_3410,U_3409] :
      ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3409,tc_Nat_Onat),U_3412),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3409,tc_HOL_Obool)),U_3411),hAPP(hAPP(c_Set_Oinsert(U_3409),U_3410),c_Orderings_Obot__class_Obot(tc_fun(U_3409,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3409,tc_Nat_Onat),U_3412),U_3411)
        | hBOOL(hAPP(hAPP(c_member(U_3409),U_3410),U_3411)) )
      & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3409,tc_Nat_Onat),U_3412),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3409,tc_HOL_Obool)),U_3411),hAPP(hAPP(c_Set_Oinsert(U_3409),U_3410),c_Orderings_Obot__class_Obot(tc_fun(U_3409,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3409,tc_Nat_Onat),U_3412),U_3411)),hAPP(U_3412,U_3410))
        | ~ hBOOL(hAPP(hAPP(c_member(U_3409),U_3410),U_3411)) ) ),
    inference(variable_rename,[status(thm)],[f_840_1]) ).

fof(f_840_3,plain,
    ( ! [U_3420,U_3418,U_3416,U_3414] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3414,tc_Nat_Onat),U_3420),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3414,tc_HOL_Obool)),U_3418),hAPP(hAPP(c_Set_Oinsert(U_3414),U_3416),c_Orderings_Obot__class_Obot(tc_fun(U_3414,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3414,tc_Nat_Onat),U_3420),U_3418)
        | hBOOL(hAPP(hAPP(c_member(U_3414),U_3416),U_3418)) )
    & ! [U_3419,U_3417,U_3415,U_3413] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3413,tc_Nat_Onat),U_3419),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3413,tc_HOL_Obool)),U_3417),hAPP(hAPP(c_Set_Oinsert(U_3413),U_3415),c_Orderings_Obot__class_Obot(tc_fun(U_3413,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3413,tc_Nat_Onat),U_3419),U_3417)),hAPP(U_3419,U_3415))
        | ~ hBOOL(hAPP(hAPP(c_member(U_3413),U_3415),U_3417)) ) ),
    inference(miniscope,[status(thm)],[f_840_2]) ).

cnf(f_840_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3413,tc_Nat_Onat),U_3419),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3413,tc_HOL_Obool)),U_3417),hAPP(hAPP(c_Set_Oinsert(U_3413),U_3415),c_Orderings_Obot__class_Obot(tc_fun(U_3413,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3413,tc_Nat_Onat),U_3419),U_3417)),hAPP(U_3419,U_3415))
    | ~ hBOOL(hAPP(hAPP(c_member(U_3413),U_3415),U_3417)) ),
    inference(clausify,[status(thm)],[f_840_3]) ).

cnf(f_840_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3414,tc_Nat_Onat),U_3420),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3414,tc_HOL_Obool)),U_3418),hAPP(hAPP(c_Set_Oinsert(U_3414),U_3416),c_Orderings_Obot__class_Obot(tc_fun(U_3414,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3414,tc_Nat_Onat),U_3420),U_3418)
    | hBOOL(hAPP(hAPP(c_member(U_3414),U_3416),U_3418)) ),
    inference(clausify,[status(thm)],[f_840_3]) ).

fof(f_841_1,plain,
    ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Oab__group__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__diff]) ).

fof(f_841_2,plain,
    ! [U_3425,U_3424,U_3423,U_3422,U_3421] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3422,U_3421),U_3425),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3422,tc_HOL_Obool)),U_3423),U_3424)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3421),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3422,U_3421),U_3425),U_3423)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3422,U_3421),U_3425),U_3424))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3422,tc_HOL_Obool)),U_3424),U_3423))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3422),U_3423))
      | ~ class_Groups_Oab__group__add(U_3421) ),
    inference(variable_rename,[status(thm)],[f_841_1]) ).

cnf(f_841_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3422,U_3421),U_3425),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3422,tc_HOL_Obool)),U_3423),U_3424)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3421),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3422,U_3421),U_3425),U_3423)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3422,U_3421),U_3425),U_3424))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_3422,tc_HOL_Obool)),U_3424),U_3423))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3422),U_3423))
    | ~ class_Groups_Oab__group__add(U_3421) ),
    inference(clausify,[status(thm)],[f_841_2]) ).

fof(f_842_1,plain,
    ! [V_A_2,T_b] :
      ( c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Min_OF__eq]) ).

fof(f_842_2,plain,
    ! [U_3427,U_3426] :
      ( c_Big__Operators_Olinorder__class_OMin(U_3426,U_3427) = hAPP(c_Finite__Set_Ofold1(U_3426,c_Orderings_Oord__class_Omin(U_3426)),U_3427)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3426),U_3427))
      | ~ class_Orderings_Olinorder(U_3426) ),
    inference(variable_rename,[status(thm)],[f_842_1]) ).

cnf(f_842_3,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_3426,U_3427) = hAPP(c_Finite__Set_Ofold1(U_3426,c_Orderings_Oord__class_Omin(U_3426)),U_3427)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3426),U_3427))
    | ~ class_Orderings_Olinorder(U_3426) ),
    inference(clausify,[status(thm)],[f_842_2]) ).

fof(f_843_1,plain,
    ! [V_A_2,T_b] :
      ( c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omax(T_b)),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Max_OF__eq]) ).

fof(f_843_2,plain,
    ! [U_3429,U_3428] :
      ( c_Big__Operators_Olinorder__class_OMax(U_3428,U_3429) = hAPP(c_Finite__Set_Ofold1(U_3428,c_Orderings_Oord__class_Omax(U_3428)),U_3429)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3428),U_3429))
      | ~ class_Orderings_Olinorder(U_3428) ),
    inference(variable_rename,[status(thm)],[f_843_1]) ).

cnf(f_843_3,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_3428,U_3429) = hAPP(c_Finite__Set_Ofold1(U_3428,c_Orderings_Oord__class_Omax(U_3428)),U_3429)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3428),U_3429))
    | ~ class_Orderings_Olinorder(U_3428) ),
    inference(clausify,[status(thm)],[f_843_2]) ).

fof(f_844_1,plain,
    ! [V_A_2,T_b] :
      ( c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_OF__eq]) ).

fof(f_844_2,plain,
    ! [U_3431,U_3430] :
      ( c_Big__Operators_Olattice_OInf__fin(U_3430,c_Orderings_Oord__class_Omin(U_3430),U_3431) = hAPP(c_Finite__Set_Ofold1(U_3430,c_Orderings_Oord__class_Omin(U_3430)),U_3431)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3430),U_3431))
      | ~ class_Orderings_Olinorder(U_3430) ),
    inference(variable_rename,[status(thm)],[f_844_1]) ).

cnf(f_844_3,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_3430,c_Orderings_Oord__class_Omin(U_3430),U_3431) = hAPP(c_Finite__Set_Ofold1(U_3430,c_Orderings_Oord__class_Omin(U_3430)),U_3431)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3430),U_3431))
    | ~ class_Orderings_Olinorder(U_3430) ),
    inference(clausify,[status(thm)],[f_844_2]) ).

fof(f_845_1,plain,
    ! [V_A_2,T_b] :
      ( c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omax(T_b)),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_OF__eq]) ).

fof(f_845_2,plain,
    ! [U_3433,U_3432] :
      ( c_Big__Operators_Olattice_OSup__fin(U_3432,c_Orderings_Oord__class_Omax(U_3432),U_3433) = hAPP(c_Finite__Set_Ofold1(U_3432,c_Orderings_Oord__class_Omax(U_3432)),U_3433)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3432),U_3433))
      | ~ class_Orderings_Olinorder(U_3432) ),
    inference(variable_rename,[status(thm)],[f_845_1]) ).

cnf(f_845_3,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_3432,c_Orderings_Oord__class_Omax(U_3432),U_3433) = hAPP(c_Finite__Set_Ofold1(U_3432,c_Orderings_Oord__class_Omax(U_3432)),U_3433)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3432),U_3433))
    | ~ class_Orderings_Olinorder(U_3432) ),
    inference(clausify,[status(thm)],[f_845_2]) ).

fof(f_846_1,plain,
    ! [V_a_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_A_2)),V_a_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Osemilattice__inf(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_fold1__belowI]) ).

fof(f_846_2,plain,
    ! [U_3436,U_3435,U_3434] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3434),hAPP(c_Finite__Set_Ofold1(U_3434,c_Lattices_Osemilattice__inf__class_Oinf(U_3434)),U_3435)),U_3436))
      | ~ hBOOL(hAPP(hAPP(c_member(U_3434),U_3436),U_3435))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3434),U_3435))
      | ~ class_Lattices_Osemilattice__inf(U_3434) ),
    inference(variable_rename,[status(thm)],[f_846_1]) ).

cnf(f_846_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3434),hAPP(c_Finite__Set_Ofold1(U_3434,c_Lattices_Osemilattice__inf__class_Oinf(U_3434)),U_3435)),U_3436))
    | ~ hBOOL(hAPP(hAPP(c_member(U_3434),U_3436),U_3435))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3434),U_3435))
    | ~ class_Lattices_Osemilattice__inf(U_3434) ),
    inference(clausify,[status(thm)],[f_846_2]) ).

fof(f_847_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_A_2)))
          | ? [B_x] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x))
              & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
        & ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x))
              | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_A_2))) ) )
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Osemilattice__inf(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_below__fold1__iff]) ).

fof(f_847_2,plain,
    ! [U_3441,U_3440,U_3439] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3439),U_3441),hAPP(c_Finite__Set_Ofold1(U_3439,c_Lattices_Osemilattice__inf__class_Oinf(U_3439)),U_3440)))
          | ? [U_3438] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3439),U_3441),U_3438))
              & hBOOL(hAPP(hAPP(c_member(U_3439),U_3438),U_3440)) ) )
        & ( ! [U_3437] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3439),U_3441),U_3437))
              | ~ hBOOL(hAPP(hAPP(c_member(U_3439),U_3437),U_3440)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3439),U_3441),hAPP(c_Finite__Set_Ofold1(U_3439,c_Lattices_Osemilattice__inf__class_Oinf(U_3439)),U_3440))) ) )
      | U_3440 = c_Orderings_Obot__class_Obot(tc_fun(U_3439,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3439),U_3440))
      | ~ class_Lattices_Osemilattice__inf(U_3439) ),
    inference(variable_rename,[status(thm)],[f_847_1]) ).

fof(f_847_3,plain,
    ! [U_3441,U_3440,U_3439] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3439),U_3441),hAPP(c_Finite__Set_Ofold1(U_3439,c_Lattices_Osemilattice__inf__class_Oinf(U_3439)),U_3440)))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3439),U_3441),sK73(U_3441,U_3440,U_3439)))
            & hBOOL(hAPP(hAPP(c_member(U_3439),sK73(U_3441,U_3440,U_3439)),U_3440)) ) )
        & ( ! [U_3437] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3439),U_3441),U_3437))
              | ~ hBOOL(hAPP(hAPP(c_member(U_3439),U_3437),U_3440)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3439),U_3441),hAPP(c_Finite__Set_Ofold1(U_3439,c_Lattices_Osemilattice__inf__class_Oinf(U_3439)),U_3440))) ) )
      | U_3440 = c_Orderings_Obot__class_Obot(tc_fun(U_3439,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3439),U_3440))
      | ~ class_Lattices_Osemilattice__inf(U_3439) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK73]),skolemize(U_3438,sK73(U_3441,U_3440,U_3439))],[f_847_2]) ).

cnf(f_847_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3439),U_3441),U_3437))
    | ~ hBOOL(hAPP(hAPP(c_member(U_3439),U_3437),U_3440))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3439),U_3441),hAPP(c_Finite__Set_Ofold1(U_3439,c_Lattices_Osemilattice__inf__class_Oinf(U_3439)),U_3440)))
    | U_3440 = c_Orderings_Obot__class_Obot(tc_fun(U_3439,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3439),U_3440))
    | ~ class_Lattices_Osemilattice__inf(U_3439) ),
    inference(clausify,[status(thm)],[f_847_3]) ).

cnf(f_847_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_3439),sK73(U_3441,U_3440,U_3439)),U_3440))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3439),U_3441),hAPP(c_Finite__Set_Ofold1(U_3439,c_Lattices_Osemilattice__inf__class_Oinf(U_3439)),U_3440)))
    | U_3440 = c_Orderings_Obot__class_Obot(tc_fun(U_3439,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3439),U_3440))
    | ~ class_Lattices_Osemilattice__inf(U_3439) ),
    inference(clausify,[status(thm)],[f_847_3]) ).

cnf(f_847_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3439),U_3441),sK73(U_3441,U_3440,U_3439)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3439),U_3441),hAPP(c_Finite__Set_Ofold1(U_3439,c_Lattices_Osemilattice__inf__class_Oinf(U_3439)),U_3440)))
    | U_3440 = c_Orderings_Obot__class_Obot(tc_fun(U_3439,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3439),U_3440))
    | ~ class_Lattices_Osemilattice__inf(U_3439) ),
    inference(clausify,[status(thm)],[f_847_3]) ).

fof(f_848_1,plain,
    ! [V_a_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)),V_a_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Ofold1__belowI]) ).

fof(f_848_2,plain,
    ! [U_3444,U_3443,U_3442] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3442),hAPP(c_Finite__Set_Ofold1(U_3442,c_Orderings_Oord__class_Omin(U_3442)),U_3443)),U_3444))
      | ~ hBOOL(hAPP(hAPP(c_member(U_3442),U_3444),U_3443))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3442),U_3443))
      | ~ class_Orderings_Olinorder(U_3442) ),
    inference(variable_rename,[status(thm)],[f_848_1]) ).

cnf(f_848_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3442),hAPP(c_Finite__Set_Ofold1(U_3442,c_Orderings_Oord__class_Omin(U_3442)),U_3443)),U_3444))
    | ~ hBOOL(hAPP(hAPP(c_member(U_3442),U_3444),U_3443))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3442),U_3443))
    | ~ class_Orderings_Olinorder(U_3442) ),
    inference(clausify,[status(thm)],[f_848_2]) ).

fof(f_849_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)))
          | ? [B_x] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x))
              & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
        & ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x))
              | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2))) ) )
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Obelow__fold1__iff]) ).

fof(f_849_2,plain,
    ! [U_3449,U_3448,U_3447] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3447),U_3449),hAPP(c_Finite__Set_Ofold1(U_3447,c_Orderings_Oord__class_Omin(U_3447)),U_3448)))
          | ? [U_3446] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3447),U_3449),U_3446))
              & hBOOL(hAPP(hAPP(c_member(U_3447),U_3446),U_3448)) ) )
        & ( ! [U_3445] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3447),U_3449),U_3445))
              | ~ hBOOL(hAPP(hAPP(c_member(U_3447),U_3445),U_3448)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3447),U_3449),hAPP(c_Finite__Set_Ofold1(U_3447,c_Orderings_Oord__class_Omin(U_3447)),U_3448))) ) )
      | U_3448 = c_Orderings_Obot__class_Obot(tc_fun(U_3447,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3447),U_3448))
      | ~ class_Orderings_Olinorder(U_3447) ),
    inference(variable_rename,[status(thm)],[f_849_1]) ).

fof(f_849_3,plain,
    ! [U_3449,U_3448,U_3447] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3447),U_3449),hAPP(c_Finite__Set_Ofold1(U_3447,c_Orderings_Oord__class_Omin(U_3447)),U_3448)))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3447),U_3449),sK74(U_3449,U_3448,U_3447)))
            & hBOOL(hAPP(hAPP(c_member(U_3447),sK74(U_3449,U_3448,U_3447)),U_3448)) ) )
        & ( ! [U_3445] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3447),U_3449),U_3445))
              | ~ hBOOL(hAPP(hAPP(c_member(U_3447),U_3445),U_3448)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3447),U_3449),hAPP(c_Finite__Set_Ofold1(U_3447,c_Orderings_Oord__class_Omin(U_3447)),U_3448))) ) )
      | U_3448 = c_Orderings_Obot__class_Obot(tc_fun(U_3447,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3447),U_3448))
      | ~ class_Orderings_Olinorder(U_3447) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK74]),skolemize(U_3446,sK74(U_3449,U_3448,U_3447))],[f_849_2]) ).

cnf(f_849_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3447),U_3449),U_3445))
    | ~ hBOOL(hAPP(hAPP(c_member(U_3447),U_3445),U_3448))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3447),U_3449),hAPP(c_Finite__Set_Ofold1(U_3447,c_Orderings_Oord__class_Omin(U_3447)),U_3448)))
    | U_3448 = c_Orderings_Obot__class_Obot(tc_fun(U_3447,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3447),U_3448))
    | ~ class_Orderings_Olinorder(U_3447) ),
    inference(clausify,[status(thm)],[f_849_3]) ).

cnf(f_849_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_3447),sK74(U_3449,U_3448,U_3447)),U_3448))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3447),U_3449),hAPP(c_Finite__Set_Ofold1(U_3447,c_Orderings_Oord__class_Omin(U_3447)),U_3448)))
    | U_3448 = c_Orderings_Obot__class_Obot(tc_fun(U_3447,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3447),U_3448))
    | ~ class_Orderings_Olinorder(U_3447) ),
    inference(clausify,[status(thm)],[f_849_3]) ).

cnf(f_849_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3447),U_3449),sK74(U_3449,U_3448,U_3447)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3447),U_3449),hAPP(c_Finite__Set_Ofold1(U_3447,c_Orderings_Oord__class_Omin(U_3447)),U_3448)))
    | U_3448 = c_Orderings_Obot__class_Obot(tc_fun(U_3447,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3447),U_3448))
    | ~ class_Orderings_Olinorder(U_3447) ),
    inference(clausify,[status(thm)],[f_849_3]) ).

fof(f_850_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)),V_x_2))
          | ! [B_x] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_x_2))
              | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
        & ( ? [B_x] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_x_2))
              & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)),V_x_2)) ) )
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_fold1__below__iff]) ).

fof(f_850_2,plain,
    ! [U_3454,U_3453,U_3452] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3452),hAPP(c_Finite__Set_Ofold1(U_3452,c_Orderings_Oord__class_Omin(U_3452)),U_3453)),U_3454))
          | ! [U_3451] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3452),U_3451),U_3454))
              | ~ hBOOL(hAPP(hAPP(c_member(U_3452),U_3451),U_3453)) ) )
        & ( ? [U_3450] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3452),U_3450),U_3454))
              & hBOOL(hAPP(hAPP(c_member(U_3452),U_3450),U_3453)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3452),hAPP(c_Finite__Set_Ofold1(U_3452,c_Orderings_Oord__class_Omin(U_3452)),U_3453)),U_3454)) ) )
      | U_3453 = c_Orderings_Obot__class_Obot(tc_fun(U_3452,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3452),U_3453))
      | ~ class_Orderings_Olinorder(U_3452) ),
    inference(variable_rename,[status(thm)],[f_850_1]) ).

fof(f_850_3,plain,
    ! [U_3454,U_3453,U_3452] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3452),hAPP(c_Finite__Set_Ofold1(U_3452,c_Orderings_Oord__class_Omin(U_3452)),U_3453)),U_3454))
          | ! [U_3451] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3452),U_3451),U_3454))
              | ~ hBOOL(hAPP(hAPP(c_member(U_3452),U_3451),U_3453)) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3452),sK75(U_3454,U_3453,U_3452)),U_3454))
            & hBOOL(hAPP(hAPP(c_member(U_3452),sK75(U_3454,U_3453,U_3452)),U_3453)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3452),hAPP(c_Finite__Set_Ofold1(U_3452,c_Orderings_Oord__class_Omin(U_3452)),U_3453)),U_3454)) ) )
      | U_3453 = c_Orderings_Obot__class_Obot(tc_fun(U_3452,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3452),U_3453))
      | ~ class_Orderings_Olinorder(U_3452) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK75]),skolemize(U_3450,sK75(U_3454,U_3453,U_3452))],[f_850_2]) ).

cnf(f_850_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_3452),sK75(U_3454,U_3453,U_3452)),U_3453))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3452),hAPP(c_Finite__Set_Ofold1(U_3452,c_Orderings_Oord__class_Omin(U_3452)),U_3453)),U_3454))
    | U_3453 = c_Orderings_Obot__class_Obot(tc_fun(U_3452,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3452),U_3453))
    | ~ class_Orderings_Olinorder(U_3452) ),
    inference(clausify,[status(thm)],[f_850_3]) ).

cnf(f_850_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3452),sK75(U_3454,U_3453,U_3452)),U_3454))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3452),hAPP(c_Finite__Set_Ofold1(U_3452,c_Orderings_Oord__class_Omin(U_3452)),U_3453)),U_3454))
    | U_3453 = c_Orderings_Obot__class_Obot(tc_fun(U_3452,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3452),U_3453))
    | ~ class_Orderings_Olinorder(U_3452) ),
    inference(clausify,[status(thm)],[f_850_3]) ).

cnf(f_850_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3452),hAPP(c_Finite__Set_Ofold1(U_3452,c_Orderings_Oord__class_Omin(U_3452)),U_3453)),U_3454))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3452),U_3451),U_3454))
    | ~ hBOOL(hAPP(hAPP(c_member(U_3452),U_3451),U_3453))
    | U_3453 = c_Orderings_Obot__class_Obot(tc_fun(U_3452,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3452),U_3453))
    | ~ class_Orderings_Olinorder(U_3452) ),
    inference(clausify,[status(thm)],[f_850_3]) ).

fof(f_851_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)))
          | ? [B_x] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),B_x))
              & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
        & ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),B_x))
              | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2))) ) )
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_strict__below__fold1__iff]) ).

fof(f_851_2,plain,
    ! [U_3459,U_3458,U_3457] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3457),U_3459),hAPP(c_Finite__Set_Ofold1(U_3457,c_Orderings_Oord__class_Omin(U_3457)),U_3458)))
          | ? [U_3456] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3457),U_3459),U_3456))
              & hBOOL(hAPP(hAPP(c_member(U_3457),U_3456),U_3458)) ) )
        & ( ! [U_3455] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3457),U_3459),U_3455))
              | ~ hBOOL(hAPP(hAPP(c_member(U_3457),U_3455),U_3458)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3457),U_3459),hAPP(c_Finite__Set_Ofold1(U_3457,c_Orderings_Oord__class_Omin(U_3457)),U_3458))) ) )
      | U_3458 = c_Orderings_Obot__class_Obot(tc_fun(U_3457,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3457),U_3458))
      | ~ class_Orderings_Olinorder(U_3457) ),
    inference(variable_rename,[status(thm)],[f_851_1]) ).

fof(f_851_3,plain,
    ! [U_3459,U_3458,U_3457] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3457),U_3459),hAPP(c_Finite__Set_Ofold1(U_3457,c_Orderings_Oord__class_Omin(U_3457)),U_3458)))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3457),U_3459),sK76(U_3459,U_3458,U_3457)))
            & hBOOL(hAPP(hAPP(c_member(U_3457),sK76(U_3459,U_3458,U_3457)),U_3458)) ) )
        & ( ! [U_3455] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3457),U_3459),U_3455))
              | ~ hBOOL(hAPP(hAPP(c_member(U_3457),U_3455),U_3458)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3457),U_3459),hAPP(c_Finite__Set_Ofold1(U_3457,c_Orderings_Oord__class_Omin(U_3457)),U_3458))) ) )
      | U_3458 = c_Orderings_Obot__class_Obot(tc_fun(U_3457,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3457),U_3458))
      | ~ class_Orderings_Olinorder(U_3457) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK76]),skolemize(U_3456,sK76(U_3459,U_3458,U_3457))],[f_851_2]) ).

cnf(f_851_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3457),U_3459),U_3455))
    | ~ hBOOL(hAPP(hAPP(c_member(U_3457),U_3455),U_3458))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3457),U_3459),hAPP(c_Finite__Set_Ofold1(U_3457,c_Orderings_Oord__class_Omin(U_3457)),U_3458)))
    | U_3458 = c_Orderings_Obot__class_Obot(tc_fun(U_3457,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3457),U_3458))
    | ~ class_Orderings_Olinorder(U_3457) ),
    inference(clausify,[status(thm)],[f_851_3]) ).

cnf(f_851_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_3457),sK76(U_3459,U_3458,U_3457)),U_3458))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3457),U_3459),hAPP(c_Finite__Set_Ofold1(U_3457,c_Orderings_Oord__class_Omin(U_3457)),U_3458)))
    | U_3458 = c_Orderings_Obot__class_Obot(tc_fun(U_3457,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3457),U_3458))
    | ~ class_Orderings_Olinorder(U_3457) ),
    inference(clausify,[status(thm)],[f_851_3]) ).

cnf(f_851_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3457),U_3459),sK76(U_3459,U_3458,U_3457)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3457),U_3459),hAPP(c_Finite__Set_Ofold1(U_3457,c_Orderings_Oord__class_Omin(U_3457)),U_3458)))
    | U_3458 = c_Orderings_Obot__class_Obot(tc_fun(U_3457,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3457),U_3458))
    | ~ class_Orderings_Olinorder(U_3457) ),
    inference(clausify,[status(thm)],[f_851_3]) ).

fof(f_852_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)),V_x_2))
          | ! [B_x] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_x_2))
              | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
        & ( ? [B_x] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_x_2))
              & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)),V_x_2)) ) )
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_fold1__strict__below__iff]) ).

fof(f_852_2,plain,
    ! [U_3464,U_3463,U_3462] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3462),hAPP(c_Finite__Set_Ofold1(U_3462,c_Orderings_Oord__class_Omin(U_3462)),U_3463)),U_3464))
          | ! [U_3461] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3462),U_3461),U_3464))
              | ~ hBOOL(hAPP(hAPP(c_member(U_3462),U_3461),U_3463)) ) )
        & ( ? [U_3460] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3462),U_3460),U_3464))
              & hBOOL(hAPP(hAPP(c_member(U_3462),U_3460),U_3463)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3462),hAPP(c_Finite__Set_Ofold1(U_3462,c_Orderings_Oord__class_Omin(U_3462)),U_3463)),U_3464)) ) )
      | U_3463 = c_Orderings_Obot__class_Obot(tc_fun(U_3462,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3462),U_3463))
      | ~ class_Orderings_Olinorder(U_3462) ),
    inference(variable_rename,[status(thm)],[f_852_1]) ).

fof(f_852_3,plain,
    ! [U_3464,U_3463,U_3462] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3462),hAPP(c_Finite__Set_Ofold1(U_3462,c_Orderings_Oord__class_Omin(U_3462)),U_3463)),U_3464))
          | ! [U_3461] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3462),U_3461),U_3464))
              | ~ hBOOL(hAPP(hAPP(c_member(U_3462),U_3461),U_3463)) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3462),sK77(U_3464,U_3463,U_3462)),U_3464))
            & hBOOL(hAPP(hAPP(c_member(U_3462),sK77(U_3464,U_3463,U_3462)),U_3463)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3462),hAPP(c_Finite__Set_Ofold1(U_3462,c_Orderings_Oord__class_Omin(U_3462)),U_3463)),U_3464)) ) )
      | U_3463 = c_Orderings_Obot__class_Obot(tc_fun(U_3462,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3462),U_3463))
      | ~ class_Orderings_Olinorder(U_3462) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK77]),skolemize(U_3460,sK77(U_3464,U_3463,U_3462))],[f_852_2]) ).

cnf(f_852_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_3462),sK77(U_3464,U_3463,U_3462)),U_3463))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3462),hAPP(c_Finite__Set_Ofold1(U_3462,c_Orderings_Oord__class_Omin(U_3462)),U_3463)),U_3464))
    | U_3463 = c_Orderings_Obot__class_Obot(tc_fun(U_3462,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3462),U_3463))
    | ~ class_Orderings_Olinorder(U_3462) ),
    inference(clausify,[status(thm)],[f_852_3]) ).

cnf(f_852_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3462),sK77(U_3464,U_3463,U_3462)),U_3464))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3462),hAPP(c_Finite__Set_Ofold1(U_3462,c_Orderings_Oord__class_Omin(U_3462)),U_3463)),U_3464))
    | U_3463 = c_Orderings_Obot__class_Obot(tc_fun(U_3462,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3462),U_3463))
    | ~ class_Orderings_Olinorder(U_3462) ),
    inference(clausify,[status(thm)],[f_852_3]) ).

cnf(f_852_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3462),hAPP(c_Finite__Set_Ofold1(U_3462,c_Orderings_Oord__class_Omin(U_3462)),U_3463)),U_3464))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3462),U_3461),U_3464))
    | ~ hBOOL(hAPP(hAPP(c_member(U_3462),U_3461),U_3463))
    | U_3463 = c_Orderings_Obot__class_Obot(tc_fun(U_3462,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3462),U_3463))
    | ~ class_Orderings_Olinorder(U_3462) ),
    inference(clausify,[status(thm)],[f_852_3]) ).

fof(f_853_1,plain,
    ! [V_A_2,V_F_2,V_f_2,T_b] :
      ( hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Big__Operators_Osemilattice__big(T_b,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_semilattice__big_OF__eq]) ).

fof(f_853_2,plain,
    ! [U_3468,U_3467,U_3466,U_3465] :
      ( hAPP(U_3467,U_3468) = hAPP(c_Finite__Set_Ofold1(U_3465,U_3466),U_3468)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3465),U_3468))
      | ~ c_Big__Operators_Osemilattice__big(U_3465,U_3466,U_3467) ),
    inference(variable_rename,[status(thm)],[f_853_1]) ).

cnf(f_853_3,plain,
    ( hAPP(U_3467,U_3468) = hAPP(c_Finite__Set_Ofold1(U_3465,U_3466),U_3468)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3465),U_3468))
    | ~ c_Big__Operators_Osemilattice__big(U_3465,U_3466,U_3467) ),
    inference(clausify,[status(thm)],[f_853_2]) ).

fof(f_854_1,plain,
    ! [V_g_2,V_f_2,V_A_2,T_b,T_c] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x)))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(T_c)
      | ~ class_Groups_Ocomm__monoid__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__strict__mono]) ).

fof(f_854_2,plain,
    ! [U_3474,U_3473,U_3472,U_3471,U_3470] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3470),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3471,U_3470),U_3473),U_3472)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3471,U_3470),U_3474),U_3472)))
      | ? [U_3469] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3470),hAPP(U_3473,U_3469)),hAPP(U_3474,U_3469)))
          & hBOOL(hAPP(hAPP(c_member(U_3471),U_3469),U_3472)) )
      | U_3472 = c_Orderings_Obot__class_Obot(tc_fun(U_3471,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3471),U_3472))
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_3470)
      | ~ class_Groups_Ocomm__monoid__add(U_3470) ),
    inference(variable_rename,[status(thm)],[f_854_1]) ).

fof(f_854_3,plain,
    ! [U_3474,U_3473,U_3472,U_3471,U_3470] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3470),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3471,U_3470),U_3473),U_3472)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3471,U_3470),U_3474),U_3472)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3470),hAPP(U_3473,sK78(U_3474,U_3473,U_3472,U_3471,U_3470))),hAPP(U_3474,sK78(U_3474,U_3473,U_3472,U_3471,U_3470))))
        & hBOOL(hAPP(hAPP(c_member(U_3471),sK78(U_3474,U_3473,U_3472,U_3471,U_3470)),U_3472)) )
      | U_3472 = c_Orderings_Obot__class_Obot(tc_fun(U_3471,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3471),U_3472))
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_3470)
      | ~ class_Groups_Ocomm__monoid__add(U_3470) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK78]),skolemize(U_3469,sK78(U_3474,U_3473,U_3472,U_3471,U_3470))],[f_854_2]) ).

cnf(f_854_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_3471),sK78(U_3474,U_3473,U_3472,U_3471,U_3470)),U_3472))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3470),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3471,U_3470),U_3473),U_3472)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3471,U_3470),U_3474),U_3472)))
    | U_3472 = c_Orderings_Obot__class_Obot(tc_fun(U_3471,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3471),U_3472))
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_3470)
    | ~ class_Groups_Ocomm__monoid__add(U_3470) ),
    inference(clausify,[status(thm)],[f_854_3]) ).

cnf(f_854_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3470),hAPP(U_3473,sK78(U_3474,U_3473,U_3472,U_3471,U_3470))),hAPP(U_3474,sK78(U_3474,U_3473,U_3472,U_3471,U_3470))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3470),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3471,U_3470),U_3473),U_3472)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3471,U_3470),U_3474),U_3472)))
    | U_3472 = c_Orderings_Obot__class_Obot(tc_fun(U_3471,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3471),U_3472))
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_3470)
    | ~ class_Groups_Ocomm__monoid__add(U_3470) ),
    inference(clausify,[status(thm)],[f_854_3]) ).

fof(f_855_1,plain,
    ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Ocomm__monoid__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum_Oremove]) ).

fof(f_855_2,plain,
    ! [U_3479,U_3478,U_3477,U_3476,U_3475] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3476,U_3475),U_3479),U_3477) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3475),hAPP(U_3479,U_3478)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3476,U_3475),U_3479),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3476,tc_HOL_Obool)),U_3477),hAPP(hAPP(c_Set_Oinsert(U_3476),U_3478),c_Orderings_Obot__class_Obot(tc_fun(U_3476,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_3476),U_3478),U_3477))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3476),U_3477))
      | ~ class_Groups_Ocomm__monoid__add(U_3475) ),
    inference(variable_rename,[status(thm)],[f_855_1]) ).

cnf(f_855_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3476,U_3475),U_3479),U_3477) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3475),hAPP(U_3479,U_3478)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3476,U_3475),U_3479),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3476,tc_HOL_Obool)),U_3477),hAPP(hAPP(c_Set_Oinsert(U_3476),U_3478),c_Orderings_Obot__class_Obot(tc_fun(U_3476,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_3476),U_3478),U_3477))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3476),U_3477))
    | ~ class_Groups_Ocomm__monoid__add(U_3475) ),
    inference(clausify,[status(thm)],[f_855_2]) ).

fof(f_856_1,plain,
    ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Ocomm__monoid__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__diff1_H]) ).

fof(f_856_2,plain,
    ! [U_3484,U_3483,U_3482,U_3481,U_3480] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3481,U_3480),U_3484),U_3482) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3480),hAPP(U_3484,U_3483)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3481,U_3480),U_3484),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3481,tc_HOL_Obool)),U_3482),hAPP(hAPP(c_Set_Oinsert(U_3481),U_3483),c_Orderings_Obot__class_Obot(tc_fun(U_3481,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_3481),U_3483),U_3482))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3481),U_3482))
      | ~ class_Groups_Ocomm__monoid__add(U_3480) ),
    inference(variable_rename,[status(thm)],[f_856_1]) ).

cnf(f_856_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3481,U_3480),U_3484),U_3482) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3480),hAPP(U_3484,U_3483)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3481,U_3480),U_3484),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3481,tc_HOL_Obool)),U_3482),hAPP(hAPP(c_Set_Oinsert(U_3481),U_3483),c_Orderings_Obot__class_Obot(tc_fun(U_3481,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_3481),U_3483),U_3482))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3481),U_3482))
    | ~ class_Groups_Ocomm__monoid__add(U_3480) ),
    inference(clausify,[status(thm)],[f_856_2]) ).

fof(f_857_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2)),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_B_2))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Oab__semigroup__mult(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_fold1__Un]) ).

fof(f_857_2,plain,
    ! [U_3487,U_3486,U_3485] :
      ( hAPP(c_Finite__Set_Ofold1(U_3485,c_Groups_Otimes__class_Otimes(U_3485)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3485,tc_HOL_Obool)),U_3486),U_3487)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3485),hAPP(c_Finite__Set_Ofold1(U_3485,c_Groups_Otimes__class_Otimes(U_3485)),U_3486)),hAPP(c_Finite__Set_Ofold1(U_3485,c_Groups_Otimes__class_Otimes(U_3485)),U_3487))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3485,tc_HOL_Obool)),U_3486),U_3487) != c_Orderings_Obot__class_Obot(tc_fun(U_3485,tc_HOL_Obool))
      | U_3487 = c_Orderings_Obot__class_Obot(tc_fun(U_3485,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3485),U_3487))
      | U_3486 = c_Orderings_Obot__class_Obot(tc_fun(U_3485,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3485),U_3486))
      | ~ class_Groups_Oab__semigroup__mult(U_3485) ),
    inference(variable_rename,[status(thm)],[f_857_1]) ).

cnf(f_857_3,plain,
    ( hAPP(c_Finite__Set_Ofold1(U_3485,c_Groups_Otimes__class_Otimes(U_3485)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3485,tc_HOL_Obool)),U_3486),U_3487)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3485),hAPP(c_Finite__Set_Ofold1(U_3485,c_Groups_Otimes__class_Otimes(U_3485)),U_3486)),hAPP(c_Finite__Set_Ofold1(U_3485,c_Groups_Otimes__class_Otimes(U_3485)),U_3487))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3485,tc_HOL_Obool)),U_3486),U_3487) != c_Orderings_Obot__class_Obot(tc_fun(U_3485,tc_HOL_Obool))
    | U_3487 = c_Orderings_Obot__class_Obot(tc_fun(U_3485,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3485),U_3487))
    | U_3486 = c_Orderings_Obot__class_Obot(tc_fun(U_3485,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3485),U_3486))
    | ~ class_Groups_Oab__semigroup__mult(U_3485) ),
    inference(clausify,[status(thm)],[f_857_2]) ).

fof(f_858_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2))
      | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ class_Groups_Oab__semigroup__mult(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_fold1__insert]) ).

fof(f_858_2,plain,
    ! [U_3490,U_3489,U_3488] :
      ( hAPP(c_Finite__Set_Ofold1(U_3488,c_Groups_Otimes__class_Otimes(U_3488)),hAPP(hAPP(c_Set_Oinsert(U_3488),U_3490),U_3489)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3488),U_3490),hAPP(c_Finite__Set_Ofold1(U_3488,c_Groups_Otimes__class_Otimes(U_3488)),U_3489))
      | hBOOL(hAPP(hAPP(c_member(U_3488),U_3490),U_3489))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3488),U_3489))
      | U_3489 = c_Orderings_Obot__class_Obot(tc_fun(U_3488,tc_HOL_Obool))
      | ~ class_Groups_Oab__semigroup__mult(U_3488) ),
    inference(variable_rename,[status(thm)],[f_858_1]) ).

cnf(f_858_3,plain,
    ( hAPP(c_Finite__Set_Ofold1(U_3488,c_Groups_Otimes__class_Otimes(U_3488)),hAPP(hAPP(c_Set_Oinsert(U_3488),U_3490),U_3489)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3488),U_3490),hAPP(c_Finite__Set_Ofold1(U_3488,c_Groups_Otimes__class_Otimes(U_3488)),U_3489))
    | hBOOL(hAPP(hAPP(c_member(U_3488),U_3490),U_3489))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3488),U_3489))
    | U_3489 = c_Orderings_Obot__class_Obot(tc_fun(U_3488,tc_HOL_Obool))
    | ~ class_Groups_Oab__semigroup__mult(U_3488) ),
    inference(clausify,[status(thm)],[f_858_2]) ).

fof(f_859_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = V_x_2
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ? [B_y] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_y),V_x_2))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Max__eqI]) ).

fof(f_859_2,plain,
    ! [U_3494,U_3493,U_3492] :
      ( c_Big__Operators_Olinorder__class_OMax(U_3492,U_3493) = U_3494
      | ~ hBOOL(hAPP(hAPP(c_member(U_3492),U_3494),U_3493))
      | ? [U_3491] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3492),U_3491),U_3494))
          & hBOOL(hAPP(hAPP(c_member(U_3492),U_3491),U_3493)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3492),U_3493))
      | ~ class_Orderings_Olinorder(U_3492) ),
    inference(variable_rename,[status(thm)],[f_859_1]) ).

fof(f_859_3,plain,
    ! [U_3494,U_3493,U_3492] :
      ( c_Big__Operators_Olinorder__class_OMax(U_3492,U_3493) = U_3494
      | ~ hBOOL(hAPP(hAPP(c_member(U_3492),U_3494),U_3493))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3492),sK79(U_3494,U_3493,U_3492)),U_3494))
        & hBOOL(hAPP(hAPP(c_member(U_3492),sK79(U_3494,U_3493,U_3492)),U_3493)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3492),U_3493))
      | ~ class_Orderings_Olinorder(U_3492) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK79]),skolemize(U_3491,sK79(U_3494,U_3493,U_3492))],[f_859_2]) ).

cnf(f_859_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_3492),sK79(U_3494,U_3493,U_3492)),U_3493))
    | c_Big__Operators_Olinorder__class_OMax(U_3492,U_3493) = U_3494
    | ~ hBOOL(hAPP(hAPP(c_member(U_3492),U_3494),U_3493))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3492),U_3493))
    | ~ class_Orderings_Olinorder(U_3492) ),
    inference(clausify,[status(thm)],[f_859_3]) ).

cnf(f_859_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3492),sK79(U_3494,U_3493,U_3492)),U_3494))
    | c_Big__Operators_Olinorder__class_OMax(U_3492,U_3493) = U_3494
    | ~ hBOOL(hAPP(hAPP(c_member(U_3492),U_3494),U_3493))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3492),U_3493))
    | ~ class_Orderings_Olinorder(U_3492) ),
    inference(clausify,[status(thm)],[f_859_3]) ).

fof(f_860_1,plain,
    ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),V_g_2),V_A_2)
      | ? [B_a] :
          ( hAPP(V_g_2,B_a) != hAPP(V_h_2,hAPP(V_f_2,B_a))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2)) )
      | V_B_2 != hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
      | ~ class_Groups_Ocomm__monoid__add(T_d) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__reindex__cong]) ).

fof(f_860_2,plain,
    ! [U_3503,U_3502,U_3501,U_3500,U_3499,U_3498,U_3497,U_3496] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3498,U_3496),U_3503),U_3501) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3497,U_3496),U_3502),U_3500)
      | ? [U_3495] :
          ( hAPP(U_3502,U_3495) != hAPP(U_3503,hAPP(U_3499,U_3495))
          & hBOOL(hAPP(hAPP(c_member(U_3497),U_3495),U_3500)) )
      | U_3501 != hAPP(c_Set_Oimage(U_3497,U_3498,U_3499),U_3500)
      | ~ c_Fun_Oinj__on(U_3497,U_3498,U_3499,U_3500)
      | ~ class_Groups_Ocomm__monoid__add(U_3496) ),
    inference(variable_rename,[status(thm)],[f_860_1]) ).

fof(f_860_3,plain,
    ! [U_3503,U_3502,U_3501,U_3500,U_3499,U_3498,U_3497,U_3496] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3498,U_3496),U_3503),U_3501) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3497,U_3496),U_3502),U_3500)
      | ( hAPP(U_3502,sK80(U_3503,U_3502,U_3501,U_3500,U_3499,U_3498,U_3497,U_3496)) != hAPP(U_3503,hAPP(U_3499,sK80(U_3503,U_3502,U_3501,U_3500,U_3499,U_3498,U_3497,U_3496)))
        & hBOOL(hAPP(hAPP(c_member(U_3497),sK80(U_3503,U_3502,U_3501,U_3500,U_3499,U_3498,U_3497,U_3496)),U_3500)) )
      | U_3501 != hAPP(c_Set_Oimage(U_3497,U_3498,U_3499),U_3500)
      | ~ c_Fun_Oinj__on(U_3497,U_3498,U_3499,U_3500)
      | ~ class_Groups_Ocomm__monoid__add(U_3496) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK80]),skolemize(U_3495,sK80(U_3503,U_3502,U_3501,U_3500,U_3499,U_3498,U_3497,U_3496))],[f_860_2]) ).

cnf(f_860_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_3497),sK80(U_3503,U_3502,U_3501,U_3500,U_3499,U_3498,U_3497,U_3496)),U_3500))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3498,U_3496),U_3503),U_3501) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3497,U_3496),U_3502),U_3500)
    | U_3501 != hAPP(c_Set_Oimage(U_3497,U_3498,U_3499),U_3500)
    | ~ c_Fun_Oinj__on(U_3497,U_3498,U_3499,U_3500)
    | ~ class_Groups_Ocomm__monoid__add(U_3496) ),
    inference(clausify,[status(thm)],[f_860_3]) ).

cnf(f_860_5,plain,
    ( hAPP(U_3502,sK80(U_3503,U_3502,U_3501,U_3500,U_3499,U_3498,U_3497,U_3496)) != hAPP(U_3503,hAPP(U_3499,sK80(U_3503,U_3502,U_3501,U_3500,U_3499,U_3498,U_3497,U_3496)))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3498,U_3496),U_3503),U_3501) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3497,U_3496),U_3502),U_3500)
    | U_3501 != hAPP(c_Set_Oimage(U_3497,U_3498,U_3499),U_3500)
    | ~ c_Fun_Oinj__on(U_3497,U_3498,U_3499,U_3500)
    | ~ class_Groups_Ocomm__monoid__add(U_3496) ),
    inference(clausify,[status(thm)],[f_860_3]) ).

fof(f_861_1,plain,
    ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_l_2),V_u_2))),
    inference(fof_nnf,[status(thm)],[fact_finite__atLeastLessThan]) ).

fof(f_861_2,plain,
    ! [U_3505,U_3504] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_3504),U_3505))),
    inference(variable_rename,[status(thm)],[f_861_1]) ).

cnf(f_861_3,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_3504),U_3505))),
    inference(clausify,[status(thm)],[f_861_2]) ).

fof(f_862_1,plain,
    ! [V_f_2,V_p_2,V_n_2,V_m_2,T_b] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_n_2),V_p_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_p_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__add__nat__ivl]) ).

fof(f_862_2,plain,
    ! [U_3510,U_3509,U_3508,U_3507,U_3506] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3506),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_3506),U_3510),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_3507),U_3508))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_3506),U_3510),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_3508),U_3509))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_3506),U_3510),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_3507),U_3509))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3508),U_3509))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3507),U_3508))
      | ~ class_Groups_Ocomm__monoid__add(U_3506) ),
    inference(variable_rename,[status(thm)],[f_862_1]) ).

cnf(f_862_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3506),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_3506),U_3510),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_3507),U_3508))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_3506),U_3510),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_3508),U_3509))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_3506),U_3510),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_3507),U_3509))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3508),U_3509))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3507),U_3508))
    | ~ class_Groups_Ocomm__monoid__add(U_3506) ),
    inference(clausify,[status(thm)],[f_862_2]) ).

fof(f_863_1,plain,
    ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)
          | V_c_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2) )
        & ( V_c_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2)
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2) ) )
      | ~ class_Rings_Oring(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_eq__add__iff2]) ).

fof(f_863_2,plain,
    ! [U_3516,U_3515,U_3514,U_3513,U_3512,U_3511] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3511),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3511),U_3512),U_3513)),U_3514) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3511),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3511),U_3515),U_3513)),U_3516)
          | U_3514 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3511),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3511),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3511),U_3515),U_3512)),U_3513)),U_3516) )
        & ( U_3514 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3511),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3511),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3511),U_3515),U_3512)),U_3513)),U_3516)
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3511),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3511),U_3512),U_3513)),U_3514) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3511),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3511),U_3515),U_3513)),U_3516) ) )
      | ~ class_Rings_Oring(U_3511) ),
    inference(variable_rename,[status(thm)],[f_863_1]) ).

cnf(f_863_3,plain,
    ( U_3514 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3511),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3511),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3511),U_3515),U_3512)),U_3513)),U_3516)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3511),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3511),U_3512),U_3513)),U_3514) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3511),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3511),U_3515),U_3513)),U_3516)
    | ~ class_Rings_Oring(U_3511) ),
    inference(clausify,[status(thm)],[f_863_2]) ).

cnf(f_863_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3511),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3511),U_3512),U_3513)),U_3514) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3511),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3511),U_3515),U_3513)),U_3516)
    | U_3514 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3511),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3511),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3511),U_3515),U_3512)),U_3513)),U_3516)
    | ~ class_Rings_Oring(U_3511) ),
    inference(clausify,[status(thm)],[f_863_2]) ).

fof(f_864_1,plain,
    ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_c_2) != V_d_2 )
        & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_c_2) = V_d_2
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2) ) )
      | ~ class_Rings_Oring(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_eq__add__iff1]) ).

fof(f_864_2,plain,
    ! [U_3522,U_3521,U_3520,U_3519,U_3518,U_3517] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3517),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3517),U_3518),U_3519)),U_3520) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3517),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3517),U_3521),U_3519)),U_3522)
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3517),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3517),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3517),U_3518),U_3521)),U_3519)),U_3520) != U_3522 )
        & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3517),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3517),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3517),U_3518),U_3521)),U_3519)),U_3520) = U_3522
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3517),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3517),U_3518),U_3519)),U_3520) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3517),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3517),U_3521),U_3519)),U_3522) ) )
      | ~ class_Rings_Oring(U_3517) ),
    inference(variable_rename,[status(thm)],[f_864_1]) ).

cnf(f_864_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3517),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3517),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3517),U_3518),U_3521)),U_3519)),U_3520) = U_3522
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3517),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3517),U_3518),U_3519)),U_3520) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3517),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3517),U_3521),U_3519)),U_3522)
    | ~ class_Rings_Oring(U_3517) ),
    inference(clausify,[status(thm)],[f_864_2]) ).

cnf(f_864_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3517),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3517),U_3518),U_3519)),U_3520) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3517),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3517),U_3521),U_3519)),U_3522)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3517),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3517),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3517),U_3518),U_3521)),U_3519)),U_3520) != U_3522
    | ~ class_Rings_Oring(U_3517) ),
    inference(clausify,[status(thm)],[f_864_2]) ).

fof(f_865_1,plain,
    ! [V_k_2,V_j_2,V_i_2] :
      ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),V_k_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_j_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),V_k_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) ),
    inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__add__Un]) ).

fof(f_865_2,plain,
    ! [U_3525,U_3524,U_3523] :
      ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_3523),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3524),U_3525)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_3523),U_3524)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_3524),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3524),U_3525)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3523),U_3524)) ),
    inference(variable_rename,[status(thm)],[f_865_1]) ).

cnf(f_865_3,plain,
    ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_3523),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3524),U_3525)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_3523),U_3524)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_3524),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3524),U_3525)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3523),U_3524)) ),
    inference(clausify,[status(thm)],[f_865_2]) ).

fof(f_866_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) = V_a
      | ~ class_Lattices_Oab__semigroup__idem__mult(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_times_Oidem]) ).

fof(f_866_2,plain,
    ! [U_3527,U_3526] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3526),U_3527),U_3527) = U_3527
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_3526) ),
    inference(variable_rename,[status(thm)],[f_866_1]) ).

cnf(f_866_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3526),U_3527),U_3527) = U_3527
    | ~ class_Lattices_Oab__semigroup__idem__mult(U_3526) ),
    inference(clausify,[status(thm)],[f_866_2]) ).

fof(f_867_1,plain,
    ! [V_x,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = V_x
      | ~ class_Lattices_Oab__semigroup__idem__mult(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__idem]) ).

fof(f_867_2,plain,
    ! [U_3529,U_3528] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3528),U_3529),U_3529) = U_3529
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_3528) ),
    inference(variable_rename,[status(thm)],[f_867_1]) ).

cnf(f_867_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3528),U_3529),U_3529) = U_3529
    | ~ class_Lattices_Oab__semigroup__idem__mult(U_3528) ),
    inference(clausify,[status(thm)],[f_867_2]) ).

fof(f_868_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)
      | ~ class_Lattices_Oab__semigroup__idem__mult(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__left__idem]) ).

fof(f_868_2,plain,
    ! [U_3532,U_3531,U_3530] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3530),U_3531),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3530),U_3531),U_3532)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3530),U_3531),U_3532)
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_3530) ),
    inference(variable_rename,[status(thm)],[f_868_1]) ).

cnf(f_868_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3530),U_3531),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3530),U_3531),U_3532)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3530),U_3531),U_3532)
    | ~ class_Lattices_Oab__semigroup__idem__mult(U_3530) ),
    inference(clausify,[status(thm)],[f_868_2]) ).

fof(f_869_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))
      | ~ class_Groups_Oab__semigroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_ab__semigroup__add__class_Oadd__ac_I1_J]) ).

fof(f_869_2,plain,
    ! [U_3536,U_3535,U_3534,U_3533] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3533),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3533),U_3534),U_3535)),U_3536) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3533),U_3534),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3533),U_3535),U_3536))
      | ~ class_Groups_Oab__semigroup__add(U_3533) ),
    inference(variable_rename,[status(thm)],[f_869_1]) ).

cnf(f_869_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3533),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3533),U_3534),U_3535)),U_3536) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3533),U_3534),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3533),U_3535),U_3536))
    | ~ class_Groups_Oab__semigroup__add(U_3533) ),
    inference(clausify,[status(thm)],[f_869_2]) ).

fof(f_870_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))
      | ~ class_Groups_Oab__semigroup__mult(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_ab__semigroup__mult__class_Omult__ac_I1_J]) ).

fof(f_870_2,plain,
    ! [U_3540,U_3539,U_3538,U_3537] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3537),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3537),U_3538),U_3539)),U_3540) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3537),U_3538),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3537),U_3539),U_3540))
      | ~ class_Groups_Oab__semigroup__mult(U_3537) ),
    inference(variable_rename,[status(thm)],[f_870_1]) ).

cnf(f_870_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3537),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3537),U_3538),U_3539)),U_3540) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3537),U_3538),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3537),U_3539),U_3540))
    | ~ class_Groups_Oab__semigroup__mult(U_3537) ),
    inference(clausify,[status(thm)],[f_870_2]) ).

fof(f_871_1,plain,
    ! [V_c_2,V_b_2,V_a_2,T_b] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_c_2)
          | V_b_2 != V_c_2 )
        & ( V_b_2 = V_c_2
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_c_2) ) )
      | ~ class_Groups_Ocancel__semigroup__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_add__left__cancel]) ).

fof(f_871_2,plain,
    ! [U_3544,U_3543,U_3542,U_3541] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3541),U_3542),U_3543) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3541),U_3542),U_3544)
          | U_3543 != U_3544 )
        & ( U_3543 = U_3544
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3541),U_3542),U_3543) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3541),U_3542),U_3544) ) )
      | ~ class_Groups_Ocancel__semigroup__add(U_3541) ),
    inference(variable_rename,[status(thm)],[f_871_1]) ).

cnf(f_871_3,plain,
    ( U_3543 = U_3544
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3541),U_3542),U_3543) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3541),U_3542),U_3544)
    | ~ class_Groups_Ocancel__semigroup__add(U_3541) ),
    inference(clausify,[status(thm)],[f_871_2]) ).

cnf(f_871_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3541),U_3542),U_3543) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3541),U_3542),U_3544)
    | U_3543 != U_3544
    | ~ class_Groups_Ocancel__semigroup__add(U_3541) ),
    inference(clausify,[status(thm)],[f_871_2]) ).

fof(f_872_1,plain,
    ! [V_c_2,V_a_2,V_b_2,T_b] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_a_2)
          | V_b_2 != V_c_2 )
        & ( V_b_2 = V_c_2
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_a_2) ) )
      | ~ class_Groups_Ocancel__semigroup__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_add__right__cancel]) ).

fof(f_872_2,plain,
    ! [U_3548,U_3547,U_3546,U_3545] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3545),U_3546),U_3547) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3545),U_3548),U_3547)
          | U_3546 != U_3548 )
        & ( U_3546 = U_3548
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3545),U_3546),U_3547) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3545),U_3548),U_3547) ) )
      | ~ class_Groups_Ocancel__semigroup__add(U_3545) ),
    inference(variable_rename,[status(thm)],[f_872_1]) ).

cnf(f_872_3,plain,
    ( U_3546 = U_3548
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3545),U_3546),U_3547) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3545),U_3548),U_3547)
    | ~ class_Groups_Ocancel__semigroup__add(U_3545) ),
    inference(clausify,[status(thm)],[f_872_2]) ).

cnf(f_872_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3545),U_3546),U_3547) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3545),U_3548),U_3547)
    | U_3546 != U_3548
    | ~ class_Groups_Ocancel__semigroup__add(U_3545) ),
    inference(clausify,[status(thm)],[f_872_2]) ).

fof(f_873_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( V_b = V_c
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)
      | ~ class_Groups_Ocancel__semigroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__left__imp__eq]) ).

fof(f_873_2,plain,
    ! [U_3552,U_3551,U_3550,U_3549] :
      ( U_3551 = U_3552
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3549),U_3550),U_3551) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3549),U_3550),U_3552)
      | ~ class_Groups_Ocancel__semigroup__add(U_3549) ),
    inference(variable_rename,[status(thm)],[f_873_1]) ).

cnf(f_873_3,plain,
    ( U_3551 = U_3552
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3549),U_3550),U_3551) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3549),U_3550),U_3552)
    | ~ class_Groups_Ocancel__semigroup__add(U_3549) ),
    inference(clausify,[status(thm)],[f_873_2]) ).

fof(f_874_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( V_b = V_c
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)
      | ~ class_Groups_Ocancel__ab__semigroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__imp__eq]) ).

fof(f_874_2,plain,
    ! [U_3556,U_3555,U_3554,U_3553] :
      ( U_3555 = U_3556
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3553),U_3554),U_3555) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3553),U_3554),U_3556)
      | ~ class_Groups_Ocancel__ab__semigroup__add(U_3553) ),
    inference(variable_rename,[status(thm)],[f_874_1]) ).

cnf(f_874_3,plain,
    ( U_3555 = U_3556
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3553),U_3554),U_3555) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3553),U_3554),U_3556)
    | ~ class_Groups_Ocancel__ab__semigroup__add(U_3553) ),
    inference(clausify,[status(thm)],[f_874_2]) ).

fof(f_875_1,plain,
    ! [V_c,V_a,V_b,T_a] :
      ( V_b = V_c
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)
      | ~ class_Groups_Ocancel__semigroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__right__imp__eq]) ).

fof(f_875_2,plain,
    ! [U_3560,U_3559,U_3558,U_3557] :
      ( U_3558 = U_3560
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3557),U_3558),U_3559) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3557),U_3560),U_3559)
      | ~ class_Groups_Ocancel__semigroup__add(U_3557) ),
    inference(variable_rename,[status(thm)],[f_875_1]) ).

cnf(f_875_3,plain,
    ( U_3558 = U_3560
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3557),U_3558),U_3559) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3557),U_3560),U_3559)
    | ~ class_Groups_Ocancel__semigroup__add(U_3557) ),
    inference(clausify,[status(thm)],[f_875_2]) ).

fof(f_876_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))
      | ~ class_Rings_Ocomm__semiring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__class_Odistrib]) ).

fof(f_876_2,plain,
    ! [U_3564,U_3563,U_3562,U_3561] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3561),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3561),U_3562),U_3563)),U_3564) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3561),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3561),U_3562),U_3564)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3561),U_3563),U_3564))
      | ~ class_Rings_Ocomm__semiring(U_3561) ),
    inference(variable_rename,[status(thm)],[f_876_1]) ).

cnf(f_876_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3561),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3561),U_3562),U_3563)),U_3564) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3561),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3561),U_3562),U_3564)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3561),U_3563),U_3564))
    | ~ class_Rings_Ocomm__semiring(U_3561) ),
    inference(clausify,[status(thm)],[f_876_2]) ).

fof(f_877_1,plain,
    ! [V_c,V_b,V_e,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_e)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_e)),V_c)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_e)),V_c)
      | ~ class_Rings_Osemiring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_combine__common__factor]) ).

fof(f_877_2,plain,
    ! [U_3569,U_3568,U_3567,U_3566,U_3565] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3565),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3565),U_3566),U_3567)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3565),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3565),U_3568),U_3567)),U_3569)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3565),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3565),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3565),U_3566),U_3568)),U_3567)),U_3569)
      | ~ class_Rings_Osemiring(U_3565) ),
    inference(variable_rename,[status(thm)],[f_877_1]) ).

cnf(f_877_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3565),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3565),U_3566),U_3567)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3565),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3565),U_3568),U_3567)),U_3569)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3565),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3565),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3565),U_3566),U_3568)),U_3567)),U_3569)
    | ~ class_Rings_Osemiring(U_3565) ),
    inference(clausify,[status(thm)],[f_877_2]) ).

fof(f_878_1,plain,
    ! [V_N_2] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2))
        | ! [B_m] :
          ? [B_x] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_x),B_m))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) ) )
      & ( ? [B_m] :
          ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_x),B_m))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_finite__nat__set__iff__bounded__le]) ).

fof(f_878_2,plain,
    ! [U_3574] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3574))
        | ! [U_3573] :
          ? [U_3572] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3572),U_3573))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_3572),U_3574)) ) )
      & ( ? [U_3571] :
          ! [U_3570] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3570),U_3571))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_3570),U_3574)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3574)) ) ),
    inference(variable_rename,[status(thm)],[f_878_1]) ).

fof(f_878_3,plain,
    ( ! [U_3576] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3576))
        | ! [U_3573] :
          ? [U_3572] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3572),U_3573))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_3572),U_3576)) ) )
    & ! [U_3575] :
        ( ? [U_3571] :
          ! [U_3570] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3570),U_3571))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_3570),U_3575)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3575)) ) ),
    inference(miniscope,[status(thm)],[f_878_2]) ).

fof(f_878_4,plain,
    ( ! [U_3576] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3576))
        | ! [U_3573] :
          ? [U_3572] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3572),U_3573))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_3572),U_3576)) ) )
    & ! [U_3575] :
        ( ! [U_3570] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3570),sK81(U_3575)))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_3570),U_3575)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3575)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK81]),skolemize(U_3571,sK81(U_3575))],[f_878_3]) ).

fof(f_878_5,plain,
    ( ! [U_3576] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3576))
        | ! [U_3573] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK82(U_3576,U_3573)),U_3573))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK82(U_3576,U_3573)),U_3576)) ) )
    & ! [U_3575] :
        ( ! [U_3570] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3570),sK81(U_3575)))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_3570),U_3575)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3575)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK82]),skolemize(U_3572,sK82(U_3576,U_3573))],[f_878_4]) ).

cnf(f_878_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3570),sK81(U_3575)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_3570),U_3575))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3575)) ),
    inference(clausify,[status(thm)],[f_878_5]) ).

cnf(f_878_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK82(U_3576,U_3573)),U_3576))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3576)) ),
    inference(clausify,[status(thm)],[f_878_5]) ).

cnf(f_878_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK82(U_3576,U_3573)),U_3573))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3576)) ),
    inference(clausify,[status(thm)],[f_878_5]) ).

fof(f_879_1,plain,
    ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2))) ) )
      | ~ class_Rings_Oordered__ring(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_le__add__iff2]) ).

fof(f_879_2,plain,
    ! [U_3582,U_3581,U_3580,U_3579,U_3578,U_3577] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3577),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3577),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3577),U_3578),U_3579)),U_3580)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3577),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3577),U_3581),U_3579)),U_3582)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3577),U_3580),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3577),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3577),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3577),U_3581),U_3578)),U_3579)),U_3582))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3577),U_3580),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3577),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3577),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3577),U_3581),U_3578)),U_3579)),U_3582)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3577),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3577),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3577),U_3578),U_3579)),U_3580)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3577),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3577),U_3581),U_3579)),U_3582))) ) )
      | ~ class_Rings_Oordered__ring(U_3577) ),
    inference(variable_rename,[status(thm)],[f_879_1]) ).

cnf(f_879_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3577),U_3580),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3577),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3577),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3577),U_3581),U_3578)),U_3579)),U_3582)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3577),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3577),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3577),U_3578),U_3579)),U_3580)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3577),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3577),U_3581),U_3579)),U_3582)))
    | ~ class_Rings_Oordered__ring(U_3577) ),
    inference(clausify,[status(thm)],[f_879_2]) ).

cnf(f_879_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3577),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3577),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3577),U_3578),U_3579)),U_3580)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3577),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3577),U_3581),U_3579)),U_3582)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3577),U_3580),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3577),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3577),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3577),U_3581),U_3578)),U_3579)),U_3582)))
    | ~ class_Rings_Oordered__ring(U_3577) ),
    inference(clausify,[status(thm)],[f_879_2]) ).

fof(f_880_1,plain,
    ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_c_2)),V_d_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_c_2)),V_d_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2))) ) )
      | ~ class_Rings_Oordered__ring(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_le__add__iff1]) ).

fof(f_880_2,plain,
    ! [U_3588,U_3587,U_3586,U_3585,U_3584,U_3583] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3583),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3583),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3583),U_3584),U_3585)),U_3586)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3583),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3583),U_3587),U_3585)),U_3588)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3583),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3583),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3583),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3583),U_3584),U_3587)),U_3585)),U_3586)),U_3588)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3583),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3583),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3583),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3583),U_3584),U_3587)),U_3585)),U_3586)),U_3588))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3583),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3583),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3583),U_3584),U_3585)),U_3586)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3583),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3583),U_3587),U_3585)),U_3588))) ) )
      | ~ class_Rings_Oordered__ring(U_3583) ),
    inference(variable_rename,[status(thm)],[f_880_1]) ).

cnf(f_880_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3583),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3583),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3583),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3583),U_3584),U_3587)),U_3585)),U_3586)),U_3588))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3583),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3583),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3583),U_3584),U_3585)),U_3586)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3583),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3583),U_3587),U_3585)),U_3588)))
    | ~ class_Rings_Oordered__ring(U_3583) ),
    inference(clausify,[status(thm)],[f_880_2]) ).

cnf(f_880_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3583),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3583),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3583),U_3584),U_3585)),U_3586)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3583),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3583),U_3587),U_3585)),U_3588)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3583),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3583),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3583),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3583),U_3584),U_3587)),U_3585)),U_3586)),U_3588))
    | ~ class_Rings_Oordered__ring(U_3583) ),
    inference(clausify,[status(thm)],[f_880_2]) ).

fof(f_881_1,plain,
    ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_c_2)),V_d_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_c_2)),V_d_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2))) ) )
      | ~ class_Rings_Oordered__ring(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_less__add__iff1]) ).

fof(f_881_2,plain,
    ! [U_3594,U_3593,U_3592,U_3591,U_3590,U_3589] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3589),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3589),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3589),U_3590),U_3591)),U_3592)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3589),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3589),U_3593),U_3591)),U_3594)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3589),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3589),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3589),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3589),U_3590),U_3593)),U_3591)),U_3592)),U_3594)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3589),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3589),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3589),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3589),U_3590),U_3593)),U_3591)),U_3592)),U_3594))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3589),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3589),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3589),U_3590),U_3591)),U_3592)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3589),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3589),U_3593),U_3591)),U_3594))) ) )
      | ~ class_Rings_Oordered__ring(U_3589) ),
    inference(variable_rename,[status(thm)],[f_881_1]) ).

cnf(f_881_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3589),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3589),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3589),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3589),U_3590),U_3593)),U_3591)),U_3592)),U_3594))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3589),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3589),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3589),U_3590),U_3591)),U_3592)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3589),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3589),U_3593),U_3591)),U_3594)))
    | ~ class_Rings_Oordered__ring(U_3589) ),
    inference(clausify,[status(thm)],[f_881_2]) ).

cnf(f_881_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3589),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3589),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3589),U_3590),U_3591)),U_3592)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3589),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3589),U_3593),U_3591)),U_3594)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3589),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3589),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3589),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3589),U_3590),U_3593)),U_3591)),U_3592)),U_3594))
    | ~ class_Rings_Oordered__ring(U_3589) ),
    inference(clausify,[status(thm)],[f_881_2]) ).

fof(f_882_1,plain,
    ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2))) ) )
      | ~ class_Rings_Oordered__ring(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_less__add__iff2]) ).

fof(f_882_2,plain,
    ! [U_3600,U_3599,U_3598,U_3597,U_3596,U_3595] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3595),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3595),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3595),U_3596),U_3597)),U_3598)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3595),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3595),U_3599),U_3597)),U_3600)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3595),U_3598),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3595),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3595),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3595),U_3599),U_3596)),U_3597)),U_3600))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3595),U_3598),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3595),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3595),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3595),U_3599),U_3596)),U_3597)),U_3600)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3595),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3595),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3595),U_3596),U_3597)),U_3598)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3595),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3595),U_3599),U_3597)),U_3600))) ) )
      | ~ class_Rings_Oordered__ring(U_3595) ),
    inference(variable_rename,[status(thm)],[f_882_1]) ).

cnf(f_882_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3595),U_3598),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3595),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3595),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3595),U_3599),U_3596)),U_3597)),U_3600)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3595),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3595),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3595),U_3596),U_3597)),U_3598)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3595),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3595),U_3599),U_3597)),U_3600)))
    | ~ class_Rings_Oordered__ring(U_3595) ),
    inference(clausify,[status(thm)],[f_882_2]) ).

cnf(f_882_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3595),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3595),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3595),U_3596),U_3597)),U_3598)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3595),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3595),U_3599),U_3597)),U_3600)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3595),U_3598),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3595),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3595),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3595),U_3599),U_3596)),U_3597)),U_3600)))
    | ~ class_Rings_Oordered__ring(U_3595) ),
    inference(clausify,[status(thm)],[f_882_2]) ).

fof(f_883_1,plain,
    ! [V_b_2,V_c_2,V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_c_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_c_2))) ) )
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_add__le__cancel__right]) ).

fof(f_883_2,plain,
    ! [U_3604,U_3603,U_3602,U_3601] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3601),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3601),U_3602),U_3603)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3601),U_3604),U_3603)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3601),U_3602),U_3604)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3601),U_3602),U_3604))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3601),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3601),U_3602),U_3603)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3601),U_3604),U_3603))) ) )
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_3601) ),
    inference(variable_rename,[status(thm)],[f_883_1]) ).

cnf(f_883_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3601),U_3602),U_3604))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3601),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3601),U_3602),U_3603)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3601),U_3604),U_3603)))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_3601) ),
    inference(clausify,[status(thm)],[f_883_2]) ).

cnf(f_883_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3601),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3601),U_3602),U_3603)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3601),U_3604),U_3603)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3601),U_3602),U_3604))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_3601) ),
    inference(clausify,[status(thm)],[f_883_2]) ).

fof(f_884_1,plain,
    ! [V_b_2,V_a_2,V_c_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_b_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_b_2))) ) )
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_add__le__cancel__left]) ).

fof(f_884_2,plain,
    ! [U_3608,U_3607,U_3606,U_3605] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3605),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3605),U_3606),U_3607)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3605),U_3606),U_3608)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3605),U_3607),U_3608)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3605),U_3607),U_3608))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3605),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3605),U_3606),U_3607)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3605),U_3606),U_3608))) ) )
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_3605) ),
    inference(variable_rename,[status(thm)],[f_884_1]) ).

cnf(f_884_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3605),U_3607),U_3608))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3605),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3605),U_3606),U_3607)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3605),U_3606),U_3608)))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_3605) ),
    inference(clausify,[status(thm)],[f_884_2]) ).

cnf(f_884_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3605),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3605),U_3606),U_3607)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3605),U_3606),U_3608)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3605),U_3607),U_3608))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_3605) ),
    inference(clausify,[status(thm)],[f_884_2]) ).

fof(f_885_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
      | ~ class_Groups_Oordered__ab__semigroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__right__mono]) ).

fof(f_885_2,plain,
    ! [U_3612,U_3611,U_3610,U_3609] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3609),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3609),U_3610),U_3612)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3609),U_3611),U_3612)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3609),U_3610),U_3611))
      | ~ class_Groups_Oordered__ab__semigroup__add(U_3609) ),
    inference(variable_rename,[status(thm)],[f_885_1]) ).

cnf(f_885_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3609),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3609),U_3610),U_3612)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3609),U_3611),U_3612)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3609),U_3610),U_3611))
    | ~ class_Groups_Oordered__ab__semigroup__add(U_3609) ),
    inference(clausify,[status(thm)],[f_885_2]) ).

fof(f_886_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
      | ~ class_Groups_Oordered__ab__semigroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__left__mono]) ).

fof(f_886_2,plain,
    ! [U_3616,U_3615,U_3614,U_3613] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3613),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3613),U_3616),U_3614)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3613),U_3616),U_3615)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3613),U_3614),U_3615))
      | ~ class_Groups_Oordered__ab__semigroup__add(U_3613) ),
    inference(variable_rename,[status(thm)],[f_886_1]) ).

cnf(f_886_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3613),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3613),U_3616),U_3614)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3613),U_3616),U_3615)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3613),U_3614),U_3615))
    | ~ class_Groups_Oordered__ab__semigroup__add(U_3613) ),
    inference(clausify,[status(thm)],[f_886_2]) ).

fof(f_887_1,plain,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
      | ~ class_Groups_Oordered__ab__semigroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__mono]) ).

fof(f_887_2,plain,
    ! [U_3621,U_3620,U_3619,U_3618,U_3617] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3617),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3617),U_3618),U_3620)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3617),U_3619),U_3621)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3617),U_3620),U_3621))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3617),U_3618),U_3619))
      | ~ class_Groups_Oordered__ab__semigroup__add(U_3617) ),
    inference(variable_rename,[status(thm)],[f_887_1]) ).

cnf(f_887_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3617),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3617),U_3618),U_3620)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3617),U_3619),U_3621)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3617),U_3620),U_3621))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3617),U_3618),U_3619))
    | ~ class_Groups_Oordered__ab__semigroup__add(U_3617) ),
    inference(clausify,[status(thm)],[f_887_2]) ).

fof(f_888_1,plain,
    ! [V_b,V_c,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__le__imp__le__right]) ).

fof(f_888_2,plain,
    ! [U_3625,U_3624,U_3623,U_3622] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3622),U_3623),U_3625))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3622),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3622),U_3623),U_3624)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3622),U_3625),U_3624)))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_3622) ),
    inference(variable_rename,[status(thm)],[f_888_1]) ).

cnf(f_888_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3622),U_3623),U_3625))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3622),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3622),U_3623),U_3624)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3622),U_3625),U_3624)))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_3622) ),
    inference(clausify,[status(thm)],[f_888_2]) ).

fof(f_889_1,plain,
    ! [V_b,V_a,V_c,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b)))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__le__imp__le__left]) ).

fof(f_889_2,plain,
    ! [U_3629,U_3628,U_3627,U_3626] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3626),U_3628),U_3629))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3626),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3626),U_3627),U_3628)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3626),U_3627),U_3629)))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_3626) ),
    inference(variable_rename,[status(thm)],[f_889_1]) ).

cnf(f_889_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3626),U_3628),U_3629))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3626),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3626),U_3627),U_3628)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3626),U_3627),U_3629)))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_3626) ),
    inference(clausify,[status(thm)],[f_889_2]) ).

fof(f_890_1,plain,
    ! [V_b_2,V_c_2,V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_c_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_c_2))) ) )
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_add__less__cancel__right]) ).

fof(f_890_2,plain,
    ! [U_3633,U_3632,U_3631,U_3630] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3630),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3630),U_3631),U_3632)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3630),U_3633),U_3632)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3630),U_3631),U_3633)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3630),U_3631),U_3633))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3630),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3630),U_3631),U_3632)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3630),U_3633),U_3632))) ) )
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_3630) ),
    inference(variable_rename,[status(thm)],[f_890_1]) ).

cnf(f_890_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3630),U_3631),U_3633))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3630),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3630),U_3631),U_3632)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3630),U_3633),U_3632)))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_3630) ),
    inference(clausify,[status(thm)],[f_890_2]) ).

cnf(f_890_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3630),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3630),U_3631),U_3632)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3630),U_3633),U_3632)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3630),U_3631),U_3633))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_3630) ),
    inference(clausify,[status(thm)],[f_890_2]) ).

fof(f_891_1,plain,
    ! [V_b_2,V_a_2,V_c_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_b_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_b_2))) ) )
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_add__less__cancel__left]) ).

fof(f_891_2,plain,
    ! [U_3637,U_3636,U_3635,U_3634] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3634),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3634),U_3635),U_3636)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3634),U_3635),U_3637)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3634),U_3636),U_3637)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3634),U_3636),U_3637))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3634),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3634),U_3635),U_3636)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3634),U_3635),U_3637))) ) )
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_3634) ),
    inference(variable_rename,[status(thm)],[f_891_1]) ).

cnf(f_891_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3634),U_3636),U_3637))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3634),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3634),U_3635),U_3636)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3634),U_3635),U_3637)))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_3634) ),
    inference(clausify,[status(thm)],[f_891_2]) ).

cnf(f_891_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3634),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3634),U_3635),U_3636)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3634),U_3635),U_3637)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3634),U_3636),U_3637))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_3634) ),
    inference(clausify,[status(thm)],[f_891_2]) ).

fof(f_892_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__strict__right__mono]) ).

fof(f_892_2,plain,
    ! [U_3641,U_3640,U_3639,U_3638] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3638),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3638),U_3639),U_3641)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3638),U_3640),U_3641)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3638),U_3639),U_3640))
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_3638) ),
    inference(variable_rename,[status(thm)],[f_892_1]) ).

cnf(f_892_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3638),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3638),U_3639),U_3641)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3638),U_3640),U_3641)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3638),U_3639),U_3640))
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_3638) ),
    inference(clausify,[status(thm)],[f_892_2]) ).

fof(f_893_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__strict__left__mono]) ).

fof(f_893_2,plain,
    ! [U_3645,U_3644,U_3643,U_3642] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3642),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3642),U_3645),U_3643)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3642),U_3645),U_3644)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3642),U_3643),U_3644))
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_3642) ),
    inference(variable_rename,[status(thm)],[f_893_1]) ).

cnf(f_893_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3642),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3642),U_3645),U_3643)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3642),U_3645),U_3644)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3642),U_3643),U_3644))
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_3642) ),
    inference(clausify,[status(thm)],[f_893_2]) ).

fof(f_894_1,plain,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__strict__mono]) ).

fof(f_894_2,plain,
    ! [U_3650,U_3649,U_3648,U_3647,U_3646] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3646),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3646),U_3647),U_3649)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3646),U_3648),U_3650)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3646),U_3649),U_3650))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3646),U_3647),U_3648))
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_3646) ),
    inference(variable_rename,[status(thm)],[f_894_1]) ).

cnf(f_894_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3646),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3646),U_3647),U_3649)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3646),U_3648),U_3650)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3646),U_3649),U_3650))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3646),U_3647),U_3648))
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_3646) ),
    inference(clausify,[status(thm)],[f_894_2]) ).

fof(f_895_1,plain,
    ! [V_b,V_c,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__less__imp__less__right]) ).

fof(f_895_2,plain,
    ! [U_3654,U_3653,U_3652,U_3651] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3651),U_3652),U_3654))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3651),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3651),U_3652),U_3653)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3651),U_3654),U_3653)))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_3651) ),
    inference(variable_rename,[status(thm)],[f_895_1]) ).

cnf(f_895_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3651),U_3652),U_3654))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3651),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3651),U_3652),U_3653)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3651),U_3654),U_3653)))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_3651) ),
    inference(clausify,[status(thm)],[f_895_2]) ).

fof(f_896_1,plain,
    ! [V_b,V_a,V_c,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b)))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__less__imp__less__left]) ).

fof(f_896_2,plain,
    ! [U_3658,U_3657,U_3656,U_3655] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3655),U_3657),U_3658))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3655),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3655),U_3656),U_3657)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3655),U_3656),U_3658)))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_3655) ),
    inference(variable_rename,[status(thm)],[f_896_1]) ).

cnf(f_896_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3655),U_3657),U_3658))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3655),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3655),U_3656),U_3657)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3655),U_3656),U_3658)))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_3655) ),
    inference(clausify,[status(thm)],[f_896_2]) ).

fof(f_897_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)),V_b) = V_a
      | ~ class_Groups_Ogroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_diff__add__cancel]) ).

fof(f_897_2,plain,
    ! [U_3661,U_3660,U_3659] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3659),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3659),U_3660),U_3661)),U_3661) = U_3660
      | ~ class_Groups_Ogroup__add(U_3659) ),
    inference(variable_rename,[status(thm)],[f_897_1]) ).

cnf(f_897_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3659),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3659),U_3660),U_3661)),U_3661) = U_3660
    | ~ class_Groups_Ogroup__add(U_3659) ),
    inference(clausify,[status(thm)],[f_897_2]) ).

fof(f_898_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_b) = V_a
      | ~ class_Groups_Ogroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__diff__cancel]) ).

fof(f_898_2,plain,
    ! [U_3664,U_3663,U_3662] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3662),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3662),U_3663),U_3664)),U_3664) = U_3663
      | ~ class_Groups_Ogroup__add(U_3662) ),
    inference(variable_rename,[status(thm)],[f_898_1]) ).

cnf(f_898_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3662),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3662),U_3663),U_3664)),U_3664) = U_3663
    | ~ class_Groups_Ogroup__add(U_3662) ),
    inference(clausify,[status(thm)],[f_898_2]) ).

fof(f_899_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)) = V_b
      | ~ class_Groups_Ogroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_minus__add__cancel]) ).

fof(f_899_2,plain,
    ! [U_3667,U_3666,U_3665] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3665),hAPP(c_Groups_Ouminus__class_Ouminus(U_3665),U_3666)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3665),U_3666),U_3667)) = U_3667
      | ~ class_Groups_Ogroup__add(U_3665) ),
    inference(variable_rename,[status(thm)],[f_899_1]) ).

cnf(f_899_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3665),hAPP(c_Groups_Ouminus__class_Ouminus(U_3665),U_3666)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3665),U_3666),U_3667)) = U_3667
    | ~ class_Groups_Ogroup__add(U_3665) ),
    inference(clausify,[status(thm)],[f_899_2]) ).

fof(f_900_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) = V_b
      | ~ class_Groups_Ogroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__minus__cancel]) ).

fof(f_900_2,plain,
    ! [U_3670,U_3669,U_3668] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3668),U_3669),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3668),hAPP(c_Groups_Ouminus__class_Ouminus(U_3668),U_3669)),U_3670)) = U_3670
      | ~ class_Groups_Ogroup__add(U_3668) ),
    inference(variable_rename,[status(thm)],[f_900_1]) ).

cnf(f_900_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3668),U_3669),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3668),hAPP(c_Groups_Ouminus__class_Ouminus(U_3668),U_3669)),U_3670)) = U_3670
    | ~ class_Groups_Ogroup__add(U_3668) ),
    inference(clausify,[status(thm)],[f_900_2]) ).

fof(f_901_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a))
      | ~ class_Groups_Ogroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_minus__add]) ).

fof(f_901_2,plain,
    ! [U_3673,U_3672,U_3671] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_3671),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3671),U_3672),U_3673)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3671),hAPP(c_Groups_Ouminus__class_Ouminus(U_3671),U_3673)),hAPP(c_Groups_Ouminus__class_Ouminus(U_3671),U_3672))
      | ~ class_Groups_Ogroup__add(U_3671) ),
    inference(variable_rename,[status(thm)],[f_901_1]) ).

cnf(f_901_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_3671),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3671),U_3672),U_3673)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3671),hAPP(c_Groups_Ouminus__class_Ouminus(U_3671),U_3673)),hAPP(c_Groups_Ouminus__class_Ouminus(U_3671),U_3672))
    | ~ class_Groups_Ogroup__add(U_3671) ),
    inference(clausify,[status(thm)],[f_901_2]) ).

fof(f_902_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b))
      | ~ class_Groups_Oab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_minus__add__distrib]) ).

fof(f_902_2,plain,
    ! [U_3676,U_3675,U_3674] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_3674),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3674),U_3675),U_3676)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3674),hAPP(c_Groups_Ouminus__class_Ouminus(U_3674),U_3675)),hAPP(c_Groups_Ouminus__class_Ouminus(U_3674),U_3676))
      | ~ class_Groups_Oab__group__add(U_3674) ),
    inference(variable_rename,[status(thm)],[f_902_1]) ).

cnf(f_902_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_3674),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3674),U_3675),U_3676)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3674),hAPP(c_Groups_Ouminus__class_Ouminus(U_3674),U_3675)),hAPP(c_Groups_Ouminus__class_Ouminus(U_3674),U_3676))
    | ~ class_Groups_Oab__group__add(U_3674) ),
    inference(clausify,[status(thm)],[f_902_2]) ).

fof(f_903_1,plain,
    ! [V_b_2,V_a_2,T_b] :
      ( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_a_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_b_2)
          | ( V_a_2 != hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
            & V_a_2 != V_b_2 ) )
        & ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
          | V_a_2 = V_b_2
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_a_2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_b_2) ) )
      | ~ class_Rings_Oidom(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_square__eq__iff]) ).

fof(f_903_2,plain,
    ! [U_3679,U_3678,U_3677] :
      ( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3677),U_3678),U_3678) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3677),U_3679),U_3679)
          | ( U_3678 != hAPP(c_Groups_Ouminus__class_Ouminus(U_3677),U_3679)
            & U_3678 != U_3679 ) )
        & ( U_3678 = hAPP(c_Groups_Ouminus__class_Ouminus(U_3677),U_3679)
          | U_3678 = U_3679
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3677),U_3678),U_3678) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3677),U_3679),U_3679) ) )
      | ~ class_Rings_Oidom(U_3677) ),
    inference(variable_rename,[status(thm)],[f_903_1]) ).

cnf(f_903_3,plain,
    ( U_3678 = hAPP(c_Groups_Ouminus__class_Ouminus(U_3677),U_3679)
    | U_3678 = U_3679
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3677),U_3678),U_3678) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3677),U_3679),U_3679)
    | ~ class_Rings_Oidom(U_3677) ),
    inference(clausify,[status(thm)],[f_903_2]) ).

cnf(f_903_4,plain,
    ( U_3678 != U_3679
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3677),U_3678),U_3678) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3677),U_3679),U_3679)
    | ~ class_Rings_Oidom(U_3677) ),
    inference(clausify,[status(thm)],[f_903_2]) ).

cnf(f_903_5,plain,
    ( U_3678 != hAPP(c_Groups_Ouminus__class_Ouminus(U_3677),U_3679)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3677),U_3678),U_3678) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3677),U_3679),U_3679)
    | ~ class_Rings_Oidom(U_3677) ),
    inference(clausify,[status(thm)],[f_903_2]) ).

fof(f_904_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)
      | ~ class_Rings_Oring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_minus__mult__minus]) ).

fof(f_904_2,plain,
    ! [U_3682,U_3681,U_3680] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3680),hAPP(c_Groups_Ouminus__class_Ouminus(U_3680),U_3681)),hAPP(c_Groups_Ouminus__class_Ouminus(U_3680),U_3682)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3680),U_3681),U_3682)
      | ~ class_Rings_Oring(U_3680) ),
    inference(variable_rename,[status(thm)],[f_904_1]) ).

cnf(f_904_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3680),hAPP(c_Groups_Ouminus__class_Ouminus(U_3680),U_3681)),hAPP(c_Groups_Ouminus__class_Ouminus(U_3680),U_3682)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3680),U_3681),U_3682)
    | ~ class_Rings_Oring(U_3680) ),
    inference(clausify,[status(thm)],[f_904_2]) ).

fof(f_905_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b))
      | ~ class_Rings_Oring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_minus__mult__commute]) ).

fof(f_905_2,plain,
    ! [U_3685,U_3684,U_3683] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3683),hAPP(c_Groups_Ouminus__class_Ouminus(U_3683),U_3684)),U_3685) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3683),U_3684),hAPP(c_Groups_Ouminus__class_Ouminus(U_3683),U_3685))
      | ~ class_Rings_Oring(U_3683) ),
    inference(variable_rename,[status(thm)],[f_905_1]) ).

cnf(f_905_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3683),hAPP(c_Groups_Ouminus__class_Ouminus(U_3683),U_3684)),U_3685) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3683),U_3684),hAPP(c_Groups_Ouminus__class_Ouminus(U_3683),U_3685))
    | ~ class_Rings_Oring(U_3683) ),
    inference(clausify,[status(thm)],[f_905_2]) ).

fof(f_906_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)
      | ~ class_Rings_Oring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_minus__mult__left]) ).

fof(f_906_2,plain,
    ! [U_3688,U_3687,U_3686] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_3686),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3686),U_3687),U_3688)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3686),hAPP(c_Groups_Ouminus__class_Ouminus(U_3686),U_3687)),U_3688)
      | ~ class_Rings_Oring(U_3686) ),
    inference(variable_rename,[status(thm)],[f_906_1]) ).

cnf(f_906_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_3686),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3686),U_3687),U_3688)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3686),hAPP(c_Groups_Ouminus__class_Ouminus(U_3686),U_3687)),U_3688)
    | ~ class_Rings_Oring(U_3686) ),
    inference(clausify,[status(thm)],[f_906_2]) ).

fof(f_907_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b))
      | ~ class_Rings_Oring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_minus__mult__right]) ).

fof(f_907_2,plain,
    ! [U_3691,U_3690,U_3689] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_3689),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3689),U_3690),U_3691)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3689),U_3690),hAPP(c_Groups_Ouminus__class_Ouminus(U_3689),U_3691))
      | ~ class_Rings_Oring(U_3689) ),
    inference(variable_rename,[status(thm)],[f_907_1]) ).

cnf(f_907_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_3689),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3689),U_3690),U_3691)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3689),U_3690),hAPP(c_Groups_Ouminus__class_Ouminus(U_3689),U_3691))
    | ~ class_Rings_Oring(U_3689) ),
    inference(clausify,[status(thm)],[f_907_2]) ).

fof(f_908_1,plain,
    ! [V_z,V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),V_z))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__add__distrib__left]) ).

fof(f_908_2,plain,
    ! [U_3695,U_3694,U_3693,U_3692] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3692),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_3692),U_3693),U_3694)),U_3695) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_3692),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3692),U_3693),U_3695)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3692),U_3694),U_3695))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_3692) ),
    inference(variable_rename,[status(thm)],[f_908_1]) ).

cnf(f_908_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3692),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_3692),U_3693),U_3694)),U_3695) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_3692),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3692),U_3693),U_3695)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3692),U_3694),U_3695))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_3692) ),
    inference(clausify,[status(thm)],[f_908_2]) ).

fof(f_909_1,plain,
    ! [V_z,V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),V_z))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_max__add__distrib__left]) ).

fof(f_909_2,plain,
    ! [U_3699,U_3698,U_3697,U_3696] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3696),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_3696),U_3697),U_3698)),U_3699) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_3696),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3696),U_3697),U_3699)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3696),U_3698),U_3699))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_3696) ),
    inference(variable_rename,[status(thm)],[f_909_1]) ).

cnf(f_909_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3696),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_3696),U_3697),U_3698)),U_3699) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_3696),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3696),U_3697),U_3699)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3696),U_3698),U_3699))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_3696) ),
    inference(clausify,[status(thm)],[f_909_2]) ).

fof(f_910_1,plain,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__le__less__mono]) ).

fof(f_910_2,plain,
    ! [U_3704,U_3703,U_3702,U_3701,U_3700] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3700),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3700),U_3701),U_3703)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3700),U_3702),U_3704)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3700),U_3703),U_3704))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3700),U_3701),U_3702))
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_3700) ),
    inference(variable_rename,[status(thm)],[f_910_1]) ).

cnf(f_910_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3700),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3700),U_3701),U_3703)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3700),U_3702),U_3704)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3700),U_3703),U_3704))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3700),U_3701),U_3702))
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_3700) ),
    inference(clausify,[status(thm)],[f_910_2]) ).

fof(f_911_1,plain,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__less__le__mono]) ).

fof(f_911_2,plain,
    ! [U_3709,U_3708,U_3707,U_3706,U_3705] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3705),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3705),U_3706),U_3708)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3705),U_3707),U_3709)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3705),U_3708),U_3709))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3705),U_3706),U_3707))
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_3705) ),
    inference(variable_rename,[status(thm)],[f_911_1]) ).

cnf(f_911_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3705),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3705),U_3706),U_3708)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3705),U_3707),U_3709)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3705),U_3708),U_3709))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3705),U_3706),U_3707))
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_3705) ),
    inference(clausify,[status(thm)],[f_911_2]) ).

fof(f_912_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)
      | ~ class_Groups_Ogroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_diff__minus__eq__add]) ).

fof(f_912_2,plain,
    ! [U_3712,U_3711,U_3710] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3710),U_3711),hAPP(c_Groups_Ouminus__class_Ouminus(U_3710),U_3712)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3710),U_3711),U_3712)
      | ~ class_Groups_Ogroup__add(U_3710) ),
    inference(variable_rename,[status(thm)],[f_912_1]) ).

cnf(f_912_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3710),U_3711),hAPP(c_Groups_Ouminus__class_Ouminus(U_3710),U_3712)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3710),U_3711),U_3712)
    | ~ class_Groups_Ogroup__add(U_3710) ),
    inference(clausify,[status(thm)],[f_912_2]) ).

fof(f_913_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b))
      | ~ class_Groups_Oab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_ab__diff__minus]) ).

fof(f_913_2,plain,
    ! [U_3715,U_3714,U_3713] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3713),U_3714),U_3715) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3713),U_3714),hAPP(c_Groups_Ouminus__class_Ouminus(U_3713),U_3715))
      | ~ class_Groups_Oab__group__add(U_3713) ),
    inference(variable_rename,[status(thm)],[f_913_1]) ).

cnf(f_913_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3713),U_3714),U_3715) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3713),U_3714),hAPP(c_Groups_Ouminus__class_Ouminus(U_3713),U_3715))
    | ~ class_Groups_Oab__group__add(U_3713) ),
    inference(clausify,[status(thm)],[f_913_2]) ).

fof(f_914_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b))
      | ~ class_Groups_Ogroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_diff__def]) ).

fof(f_914_2,plain,
    ! [U_3718,U_3717,U_3716] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3716),U_3717),U_3718) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3716),U_3717),hAPP(c_Groups_Ouminus__class_Ouminus(U_3716),U_3718))
      | ~ class_Groups_Ogroup__add(U_3716) ),
    inference(variable_rename,[status(thm)],[f_914_1]) ).

cnf(f_914_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3716),U_3717),U_3718) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3716),U_3717),hAPP(c_Groups_Ouminus__class_Ouminus(U_3716),U_3718))
    | ~ class_Groups_Ogroup__add(U_3716) ),
    inference(clausify,[status(thm)],[f_914_2]) ).

fof(f_915_1,plain,
    ! [V_f_2,V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__Un__nat]) ).

fof(f_915_2,plain,
    ! [U_3722,U_3721,U_3720,U_3719] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3719,tc_Nat_Onat),U_3722),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3719,tc_HOL_Obool)),U_3720),U_3721)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3719,tc_Nat_Onat),U_3722),U_3720)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3719,tc_Nat_Onat),U_3722),U_3721))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3719,tc_Nat_Onat),U_3722),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3719,tc_HOL_Obool)),U_3720),U_3721)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3719),U_3721))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3719),U_3720)) ),
    inference(variable_rename,[status(thm)],[f_915_1]) ).

cnf(f_915_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3719,tc_Nat_Onat),U_3722),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3719,tc_HOL_Obool)),U_3720),U_3721)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3719,tc_Nat_Onat),U_3722),U_3720)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3719,tc_Nat_Onat),U_3722),U_3721))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3719,tc_Nat_Onat),U_3722),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3719,tc_HOL_Obool)),U_3720),U_3721)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3719),U_3721))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3719),U_3720)) ),
    inference(clausify,[status(thm)],[f_915_2]) ).

fof(f_916_1,plain,
    ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2))
      | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Ocomm__monoid__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum_Oinsert]) ).

fof(f_916_2,plain,
    ! [U_3727,U_3726,U_3725,U_3724,U_3723] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3724,U_3723),U_3727),hAPP(hAPP(c_Set_Oinsert(U_3724),U_3726),U_3725)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3723),hAPP(U_3727,U_3726)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3724,U_3723),U_3727),U_3725))
      | hBOOL(hAPP(hAPP(c_member(U_3724),U_3726),U_3725))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3724),U_3725))
      | ~ class_Groups_Ocomm__monoid__add(U_3723) ),
    inference(variable_rename,[status(thm)],[f_916_1]) ).

cnf(f_916_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3724,U_3723),U_3727),hAPP(hAPP(c_Set_Oinsert(U_3724),U_3726),U_3725)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3723),hAPP(U_3727,U_3726)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3724,U_3723),U_3727),U_3725))
    | hBOOL(hAPP(hAPP(c_member(U_3724),U_3726),U_3725))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3724),U_3725))
    | ~ class_Groups_Ocomm__monoid__add(U_3723) ),
    inference(clausify,[status(thm)],[f_916_2]) ).

fof(f_917_1,plain,
    ! [V_f_2,V_a_2,V_F_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_F_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_F_2))
      | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_F_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
      | ~ class_Groups_Ocomm__monoid__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__insert]) ).

fof(f_917_2,plain,
    ! [U_3732,U_3731,U_3730,U_3729,U_3728] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3729,U_3728),U_3732),hAPP(hAPP(c_Set_Oinsert(U_3729),U_3731),U_3730)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3728),hAPP(U_3732,U_3731)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3729,U_3728),U_3732),U_3730))
      | hBOOL(hAPP(hAPP(c_member(U_3729),U_3731),U_3730))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3729),U_3730))
      | ~ class_Groups_Ocomm__monoid__add(U_3728) ),
    inference(variable_rename,[status(thm)],[f_917_1]) ).

cnf(f_917_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3729,U_3728),U_3732),hAPP(hAPP(c_Set_Oinsert(U_3729),U_3731),U_3730)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3728),hAPP(U_3732,U_3731)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3729,U_3728),U_3732),U_3730))
    | hBOOL(hAPP(hAPP(c_member(U_3729),U_3731),U_3730))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3729),U_3730))
    | ~ class_Groups_Ocomm__monoid__add(U_3728) ),
    inference(clausify,[status(thm)],[f_917_2]) ).

fof(f_918_1,plain,
    ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Ocomm__monoid__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__Un__Int]) ).

fof(f_918_2,plain,
    ! [U_3737,U_3736,U_3735,U_3734,U_3733] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3733),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3734,U_3733),U_3737),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3734,tc_HOL_Obool)),U_3735),U_3736))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3734,U_3733),U_3737),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3734,tc_HOL_Obool)),U_3735),U_3736))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3733),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3734,U_3733),U_3737),U_3735)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3734,U_3733),U_3737),U_3736))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3734),U_3736))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3734),U_3735))
      | ~ class_Groups_Ocomm__monoid__add(U_3733) ),
    inference(variable_rename,[status(thm)],[f_918_1]) ).

cnf(f_918_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3733),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3734,U_3733),U_3737),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3734,tc_HOL_Obool)),U_3735),U_3736))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3734,U_3733),U_3737),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3734,tc_HOL_Obool)),U_3735),U_3736))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3733),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3734,U_3733),U_3737),U_3735)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3734,U_3733),U_3737),U_3736))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3734),U_3736))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3734),U_3735))
    | ~ class_Groups_Ocomm__monoid__add(U_3733) ),
    inference(clausify,[status(thm)],[f_918_2]) ).

fof(f_919_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ class_Lattices_Oab__semigroup__idem__mult(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_fold1__insert__idem]) ).

fof(f_919_2,plain,
    ! [U_3740,U_3739,U_3738] :
      ( hAPP(c_Finite__Set_Ofold1(U_3738,c_Groups_Otimes__class_Otimes(U_3738)),hAPP(hAPP(c_Set_Oinsert(U_3738),U_3740),U_3739)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3738),U_3740),hAPP(c_Finite__Set_Ofold1(U_3738,c_Groups_Otimes__class_Otimes(U_3738)),U_3739))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3738),U_3739))
      | U_3739 = c_Orderings_Obot__class_Obot(tc_fun(U_3738,tc_HOL_Obool))
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_3738) ),
    inference(variable_rename,[status(thm)],[f_919_1]) ).

cnf(f_919_3,plain,
    ( hAPP(c_Finite__Set_Ofold1(U_3738,c_Groups_Otimes__class_Otimes(U_3738)),hAPP(hAPP(c_Set_Oinsert(U_3738),U_3740),U_3739)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3738),U_3740),hAPP(c_Finite__Set_Ofold1(U_3738,c_Groups_Otimes__class_Otimes(U_3738)),U_3739))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3738),U_3739))
    | U_3739 = c_Orderings_Obot__class_Obot(tc_fun(U_3738,tc_HOL_Obool))
    | ~ class_Lattices_Oab__semigroup__idem__mult(U_3738) ),
    inference(clausify,[status(thm)],[f_919_2]) ).

fof(f_920_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2)),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_B_2))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Oab__semigroup__idem__mult(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_fold1__Un2]) ).

fof(f_920_2,plain,
    ! [U_3743,U_3742,U_3741] :
      ( hAPP(c_Finite__Set_Ofold1(U_3741,c_Groups_Otimes__class_Otimes(U_3741)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3741,tc_HOL_Obool)),U_3742),U_3743)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3741),hAPP(c_Finite__Set_Ofold1(U_3741,c_Groups_Otimes__class_Otimes(U_3741)),U_3742)),hAPP(c_Finite__Set_Ofold1(U_3741,c_Groups_Otimes__class_Otimes(U_3741)),U_3743))
      | U_3743 = c_Orderings_Obot__class_Obot(tc_fun(U_3741,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3741),U_3743))
      | U_3742 = c_Orderings_Obot__class_Obot(tc_fun(U_3741,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3741),U_3742))
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_3741) ),
    inference(variable_rename,[status(thm)],[f_920_1]) ).

cnf(f_920_3,plain,
    ( hAPP(c_Finite__Set_Ofold1(U_3741,c_Groups_Otimes__class_Otimes(U_3741)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3741,tc_HOL_Obool)),U_3742),U_3743)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3741),hAPP(c_Finite__Set_Ofold1(U_3741,c_Groups_Otimes__class_Otimes(U_3741)),U_3742)),hAPP(c_Finite__Set_Ofold1(U_3741,c_Groups_Otimes__class_Otimes(U_3741)),U_3743))
    | U_3743 = c_Orderings_Obot__class_Obot(tc_fun(U_3741,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3741),U_3743))
    | U_3742 = c_Orderings_Obot__class_Obot(tc_fun(U_3741,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3741),U_3742))
    | ~ class_Lattices_Oab__semigroup__idem__mult(U_3741) ),
    inference(clausify,[status(thm)],[f_920_2]) ).

fof(f_921_1,plain,
    ! [V_x_2,V_g_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Ocomm__monoid__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum_Oinsert__remove]) ).

fof(f_921_2,plain,
    ! [U_3748,U_3747,U_3746,U_3745,U_3744] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3745,U_3744),U_3747),hAPP(hAPP(c_Set_Oinsert(U_3745),U_3748),U_3746)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3744),hAPP(U_3747,U_3748)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3745,U_3744),U_3747),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3745,tc_HOL_Obool)),U_3746),hAPP(hAPP(c_Set_Oinsert(U_3745),U_3748),c_Orderings_Obot__class_Obot(tc_fun(U_3745,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3745),U_3746))
      | ~ class_Groups_Ocomm__monoid__add(U_3744) ),
    inference(variable_rename,[status(thm)],[f_921_1]) ).

cnf(f_921_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3745,U_3744),U_3747),hAPP(hAPP(c_Set_Oinsert(U_3745),U_3748),U_3746)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3744),hAPP(U_3747,U_3748)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3745,U_3744),U_3747),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3745,tc_HOL_Obool)),U_3746),hAPP(hAPP(c_Set_Oinsert(U_3745),U_3748),c_Orderings_Obot__class_Obot(tc_fun(U_3745,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3745),U_3746))
    | ~ class_Groups_Ocomm__monoid__add(U_3744) ),
    inference(clausify,[status(thm)],[f_921_2]) ).

fof(f_922_1,plain,
    ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_B_2))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Ocomm__monoid__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__Un__disjoint]) ).

fof(f_922_2,plain,
    ! [U_3753,U_3752,U_3751,U_3750,U_3749] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3750,U_3749),U_3753),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3750,tc_HOL_Obool)),U_3751),U_3752)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3749),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3750,U_3749),U_3753),U_3751)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3750,U_3749),U_3753),U_3752))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3750,tc_HOL_Obool)),U_3751),U_3752) != c_Orderings_Obot__class_Obot(tc_fun(U_3750,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3750),U_3752))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3750),U_3751))
      | ~ class_Groups_Ocomm__monoid__add(U_3749) ),
    inference(variable_rename,[status(thm)],[f_922_1]) ).

cnf(f_922_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3750,U_3749),U_3753),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3750,tc_HOL_Obool)),U_3751),U_3752)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3749),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3750,U_3749),U_3753),U_3751)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3750,U_3749),U_3753),U_3752))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3750,tc_HOL_Obool)),U_3751),U_3752) != c_Orderings_Obot__class_Obot(tc_fun(U_3750,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3750),U_3752))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3750),U_3751))
    | ~ class_Groups_Ocomm__monoid__add(U_3749) ),
    inference(clausify,[status(thm)],[f_922_2]) ).

fof(f_923_1,plain,
    ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Oab__group__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__Un]) ).

fof(f_923_2,plain,
    ! [U_3758,U_3757,U_3756,U_3755,U_3754] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3755,U_3754),U_3758),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3755,tc_HOL_Obool)),U_3756),U_3757)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3754),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3754),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3755,U_3754),U_3758),U_3756)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3755,U_3754),U_3758),U_3757))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3755,U_3754),U_3758),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3755,tc_HOL_Obool)),U_3756),U_3757)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3755),U_3757))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3755),U_3756))
      | ~ class_Groups_Oab__group__add(U_3754) ),
    inference(variable_rename,[status(thm)],[f_923_1]) ).

cnf(f_923_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3755,U_3754),U_3758),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_3755,tc_HOL_Obool)),U_3756),U_3757)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3754),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3754),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3755,U_3754),U_3758),U_3756)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3755,U_3754),U_3758),U_3757))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_3755,U_3754),U_3758),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_3755,tc_HOL_Obool)),U_3756),U_3757)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3755),U_3757))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3755),U_3756))
    | ~ class_Groups_Oab__group__add(U_3754) ),
    inference(clausify,[status(thm)],[f_923_2]) ).

fof(f_924_1,plain,
    ! [V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_y) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y))
      | ~ class_Rings_Ocomm__ring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J]) ).

fof(f_924_2,plain,
    ! [U_3761,U_3760,U_3759] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3759),U_3760),U_3761) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3759),U_3760),hAPP(c_Groups_Ouminus__class_Ouminus(U_3759),U_3761))
      | ~ class_Rings_Ocomm__ring__1(U_3759) ),
    inference(variable_rename,[status(thm)],[f_924_1]) ).

cnf(f_924_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3759),U_3760),U_3761) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3759),U_3760),hAPP(c_Groups_Ouminus__class_Ouminus(U_3759),U_3761))
    | ~ class_Rings_Ocomm__ring__1(U_3759) ),
    inference(clausify,[status(thm)],[f_924_2]) ).

fof(f_925_1,plain,
    ! [V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2)),V_A_2))
      | ? [B_x,B_y] : ~ hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Oab__semigroup__mult(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_fold1__in]) ).

fof(f_925_2,plain,
    ! [U_3765,U_3764] :
      ( hBOOL(hAPP(hAPP(c_member(U_3764),hAPP(c_Finite__Set_Ofold1(U_3764,c_Groups_Otimes__class_Otimes(U_3764)),U_3765)),U_3765))
      | ? [U_3763,U_3762] : ~ hBOOL(hAPP(hAPP(c_member(U_3764),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3764),U_3763),U_3762)),hAPP(hAPP(c_Set_Oinsert(U_3764),U_3763),hAPP(hAPP(c_Set_Oinsert(U_3764),U_3762),c_Orderings_Obot__class_Obot(tc_fun(U_3764,tc_HOL_Obool))))))
      | U_3765 = c_Orderings_Obot__class_Obot(tc_fun(U_3764,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3764),U_3765))
      | ~ class_Groups_Oab__semigroup__mult(U_3764) ),
    inference(variable_rename,[status(thm)],[f_925_1]) ).

fof(f_925_3,plain,
    ! [U_3765,U_3764] :
      ( hBOOL(hAPP(hAPP(c_member(U_3764),hAPP(c_Finite__Set_Ofold1(U_3764,c_Groups_Otimes__class_Otimes(U_3764)),U_3765)),U_3765))
      | ? [U_3762] : ~ hBOOL(hAPP(hAPP(c_member(U_3764),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3764),sK83(U_3765,U_3764)),U_3762)),hAPP(hAPP(c_Set_Oinsert(U_3764),sK83(U_3765,U_3764)),hAPP(hAPP(c_Set_Oinsert(U_3764),U_3762),c_Orderings_Obot__class_Obot(tc_fun(U_3764,tc_HOL_Obool))))))
      | U_3765 = c_Orderings_Obot__class_Obot(tc_fun(U_3764,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3764),U_3765))
      | ~ class_Groups_Oab__semigroup__mult(U_3764) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK83]),skolemize(U_3763,sK83(U_3765,U_3764))],[f_925_2]) ).

fof(f_925_4,plain,
    ! [U_3765,U_3764] :
      ( hBOOL(hAPP(hAPP(c_member(U_3764),hAPP(c_Finite__Set_Ofold1(U_3764,c_Groups_Otimes__class_Otimes(U_3764)),U_3765)),U_3765))
      | ~ hBOOL(hAPP(hAPP(c_member(U_3764),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3764),sK83(U_3765,U_3764)),sK84(U_3765,U_3764))),hAPP(hAPP(c_Set_Oinsert(U_3764),sK83(U_3765,U_3764)),hAPP(hAPP(c_Set_Oinsert(U_3764),sK84(U_3765,U_3764)),c_Orderings_Obot__class_Obot(tc_fun(U_3764,tc_HOL_Obool))))))
      | U_3765 = c_Orderings_Obot__class_Obot(tc_fun(U_3764,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3764),U_3765))
      | ~ class_Groups_Oab__semigroup__mult(U_3764) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK84]),skolemize(U_3762,sK84(U_3765,U_3764))],[f_925_3]) ).

cnf(f_925_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_3764),hAPP(c_Finite__Set_Ofold1(U_3764,c_Groups_Otimes__class_Otimes(U_3764)),U_3765)),U_3765))
    | ~ hBOOL(hAPP(hAPP(c_member(U_3764),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3764),sK83(U_3765,U_3764)),sK84(U_3765,U_3764))),hAPP(hAPP(c_Set_Oinsert(U_3764),sK83(U_3765,U_3764)),hAPP(hAPP(c_Set_Oinsert(U_3764),sK84(U_3765,U_3764)),c_Orderings_Obot__class_Obot(tc_fun(U_3764,tc_HOL_Obool))))))
    | U_3765 = c_Orderings_Obot__class_Obot(tc_fun(U_3764,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_3764),U_3765))
    | ~ class_Groups_Oab__semigroup__mult(U_3764) ),
    inference(clausify,[status(thm)],[f_925_4]) ).

fof(f_926_1,plain,
    ! [V_n_2,V_m_2,V_k_2] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_k_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_k_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2)) ),
    inference(fof_nnf,[status(thm)],[fact_le__diff__iff]) ).

fof(f_926_2,plain,
    ! [U_3768,U_3767,U_3766] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3767),U_3766)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3768),U_3766)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3767),U_3768)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3767),U_3768))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3767),U_3766)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3768),U_3766))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3766),U_3768))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3766),U_3767)) ),
    inference(variable_rename,[status(thm)],[f_926_1]) ).

cnf(f_926_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3767),U_3768))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3767),U_3766)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3768),U_3766)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3766),U_3768))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3766),U_3767)) ),
    inference(clausify,[status(thm)],[f_926_2]) ).

cnf(f_926_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3767),U_3766)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3768),U_3766)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3767),U_3768))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3766),U_3768))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3766),U_3767)) ),
    inference(clausify,[status(thm)],[f_926_2]) ).

fof(f_927_1,plain,
    ! [V_n,V_m,V_k] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_m)) ),
    inference(fof_nnf,[status(thm)],[fact_Nat_Odiff__diff__eq]) ).

fof(f_927_2,plain,
    ! [U_3771,U_3770,U_3769] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3770),U_3769)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3771),U_3769)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3770),U_3771)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3769),U_3771))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3769),U_3770)) ),
    inference(variable_rename,[status(thm)],[f_927_1]) ).

cnf(f_927_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3770),U_3769)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3771),U_3769)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3770),U_3771)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3769),U_3771))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3769),U_3770)) ),
    inference(clausify,[status(thm)],[f_927_2]) ).

fof(f_928_1,plain,
    ! [V_n_2,V_m_2,V_k_2] :
      ( ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_k_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_k_2)
          | V_m_2 != V_n_2 )
        & ( V_m_2 = V_n_2
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_k_2) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_k_2) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2)) ),
    inference(fof_nnf,[status(thm)],[fact_eq__diff__iff]) ).

fof(f_928_2,plain,
    ! [U_3774,U_3773,U_3772] :
      ( ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3773),U_3772) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3774),U_3772)
          | U_3773 != U_3774 )
        & ( U_3773 = U_3774
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3773),U_3772) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3774),U_3772) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3772),U_3774))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3772),U_3773)) ),
    inference(variable_rename,[status(thm)],[f_928_1]) ).

cnf(f_928_3,plain,
    ( U_3773 = U_3774
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3773),U_3772) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3774),U_3772)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3772),U_3774))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3772),U_3773)) ),
    inference(clausify,[status(thm)],[f_928_2]) ).

cnf(f_928_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3773),U_3772) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3774),U_3772)
    | U_3773 != U_3774
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3772),U_3774))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3772),U_3773)) ),
    inference(clausify,[status(thm)],[f_928_2]) ).

fof(f_929_1,plain,
    ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i_2),V_j_2)),V_u_2)),V_m_2)),V_n_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i_2),V_j_2)),V_u_2)),V_m_2)),V_n_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) ),
    inference(fof_nnf,[status(thm)],[fact_nat__le__add__iff1]) ).

fof(f_929_2,plain,
    ! [U_3779,U_3778,U_3777,U_3776,U_3775] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3776),U_3777)),U_3778)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3775),U_3777)),U_3779)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3776),U_3775)),U_3777)),U_3778)),U_3779)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3776),U_3775)),U_3777)),U_3778)),U_3779))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3776),U_3777)),U_3778)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3775),U_3777)),U_3779))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3775),U_3776)) ),
    inference(variable_rename,[status(thm)],[f_929_1]) ).

cnf(f_929_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3776),U_3775)),U_3777)),U_3778)),U_3779))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3776),U_3777)),U_3778)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3775),U_3777)),U_3779)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3775),U_3776)) ),
    inference(clausify,[status(thm)],[f_929_2]) ).

cnf(f_929_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3776),U_3777)),U_3778)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3775),U_3777)),U_3779)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3776),U_3775)),U_3777)),U_3778)),U_3779))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3775),U_3776)) ),
    inference(clausify,[status(thm)],[f_929_2]) ).

fof(f_930_1,plain,
    ! [V_n,V_m,V_u,V_i,V_j] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_j)),V_u)),V_m)),V_n)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i)) ),
    inference(fof_nnf,[status(thm)],[fact_nat__diff__add__eq1]) ).

fof(f_930_2,plain,
    ! [U_3784,U_3783,U_3782,U_3781,U_3780] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3781),U_3782)),U_3783)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3780),U_3782)),U_3784)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3781),U_3780)),U_3782)),U_3783)),U_3784)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3780),U_3781)) ),
    inference(variable_rename,[status(thm)],[f_930_1]) ).

cnf(f_930_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3781),U_3782)),U_3783)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3780),U_3782)),U_3784)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3781),U_3780)),U_3782)),U_3783)),U_3784)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3780),U_3781)) ),
    inference(clausify,[status(thm)],[f_930_2]) ).

fof(f_931_1,plain,
    ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i_2),V_j_2)),V_u_2)),V_m_2) != V_n_2 )
        & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i_2),V_j_2)),V_u_2)),V_m_2) = V_n_2
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) ),
    inference(fof_nnf,[status(thm)],[fact_nat__eq__add__iff1]) ).

fof(f_931_2,plain,
    ! [U_3789,U_3788,U_3787,U_3786,U_3785] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3786),U_3787)),U_3788) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3785),U_3787)),U_3789)
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3786),U_3785)),U_3787)),U_3788) != U_3789 )
        & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3786),U_3785)),U_3787)),U_3788) = U_3789
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3786),U_3787)),U_3788) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3785),U_3787)),U_3789) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3785),U_3786)) ),
    inference(variable_rename,[status(thm)],[f_931_1]) ).

cnf(f_931_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3786),U_3785)),U_3787)),U_3788) = U_3789
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3786),U_3787)),U_3788) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3785),U_3787)),U_3789)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3785),U_3786)) ),
    inference(clausify,[status(thm)],[f_931_2]) ).

cnf(f_931_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3786),U_3787)),U_3788) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3785),U_3787)),U_3789)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3786),U_3785)),U_3787)),U_3788) != U_3789
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3785),U_3786)) ),
    inference(clausify,[status(thm)],[f_931_2]) ).

fof(f_932_1,plain,
    ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_k_2))),
    inference(fof_nnf,[status(thm)],[fact_finite__lessThan]) ).

fof(f_932_2,plain,
    ! [U_3790] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_3790))),
    inference(variable_rename,[status(thm)],[f_932_1]) ).

cnf(f_932_3,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_3790))),
    inference(clausify,[status(thm)],[f_932_2]) ).

fof(f_933_1,plain,
    ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2))),
    inference(fof_nnf,[status(thm)],[fact_finite__atMost]) ).

fof(f_933_2,plain,
    ! [U_3791] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_3791))),
    inference(variable_rename,[status(thm)],[f_933_1]) ).

cnf(f_933_3,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_3791))),
    inference(clausify,[status(thm)],[f_933_2]) ).

fof(f_934_1,plain,
    ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_l_2,V_u_2))),
    inference(fof_nnf,[status(thm)],[fact_finite__atLeastAtMost]) ).

fof(f_934_2,plain,
    ! [U_3793,U_3792] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_3792,U_3793))),
    inference(variable_rename,[status(thm)],[f_934_1]) ).

cnf(f_934_3,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_3792,U_3793))),
    inference(clausify,[status(thm)],[f_934_2]) ).

fof(f_935_1,plain,
    ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_l_2,V_u_2))),
    inference(fof_nnf,[status(thm)],[fact_finite__greaterThanAtMost]) ).

fof(f_935_2,plain,
    ! [U_3795,U_3794] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_3794,U_3795))),
    inference(variable_rename,[status(thm)],[f_935_1]) ).

cnf(f_935_3,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_3794,U_3795))),
    inference(clausify,[status(thm)],[f_935_2]) ).

fof(f_936_1,plain,
    ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,V_l_2,V_u_2))),
    inference(fof_nnf,[status(thm)],[fact_finite__greaterThanLessThan]) ).

fof(f_936_2,plain,
    ! [U_3797,U_3796] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_3796,U_3797))),
    inference(variable_rename,[status(thm)],[f_936_1]) ).

cnf(f_936_3,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_3796,U_3797))),
    inference(clausify,[status(thm)],[f_936_2]) ).

fof(f_937_1,plain,
    ! [V_k,V_j,V_u,V_i] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_u)),V_k),
    inference(fof_nnf,[status(thm)],[fact_left__add__mult__distrib]) ).

fof(f_937_2,plain,
    ! [U_3801,U_3800,U_3799,U_3798] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3798),U_3799)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3800),U_3799)),U_3801)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3798),U_3800)),U_3799)),U_3801),
    inference(variable_rename,[status(thm)],[f_937_1]) ).

cnf(f_937_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3798),U_3799)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3800),U_3799)),U_3801)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3798),U_3800)),U_3799)),U_3801),
    inference(clausify,[status(thm)],[f_937_2]) ).

fof(f_938_1,plain,
    ! [V_n_2,V_k_2,V_m_2] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_k_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2)
        | V_m_2 != V_n_2 )
      & ( V_m_2 = V_n_2
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_k_2) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__add__right__cancel]) ).

fof(f_938_2,plain,
    ! [U_3804,U_3803,U_3802] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3802),U_3803) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3804),U_3803)
        | U_3802 != U_3804 )
      & ( U_3802 = U_3804
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3802),U_3803) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3804),U_3803) ) ),
    inference(variable_rename,[status(thm)],[f_938_1]) ).

fof(f_938_3,plain,
    ( ! [U_3810,U_3808,U_3806] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3806),U_3808) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3810),U_3808)
        | U_3806 != U_3810 )
    & ! [U_3809,U_3807,U_3805] :
        ( U_3805 = U_3809
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3805),U_3807) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3809),U_3807) ) ),
    inference(miniscope,[status(thm)],[f_938_2]) ).

cnf(f_938_4,plain,
    ( U_3805 = U_3809
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3805),U_3807) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3809),U_3807) ),
    inference(clausify,[status(thm)],[f_938_3]) ).

cnf(f_938_5,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3806),U_3808) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3810),U_3808)
    | U_3806 != U_3810 ),
    inference(clausify,[status(thm)],[f_938_3]) ).

fof(f_939_1,plain,
    ! [V_n_2,V_m_2,V_k_2] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2)
        | V_m_2 != V_n_2 )
      & ( V_m_2 = V_n_2
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel]) ).

fof(f_939_2,plain,
    ! [U_3813,U_3812,U_3811] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3811),U_3812) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3811),U_3813)
        | U_3812 != U_3813 )
      & ( U_3812 = U_3813
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3811),U_3812) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3811),U_3813) ) ),
    inference(variable_rename,[status(thm)],[f_939_1]) ).

fof(f_939_3,plain,
    ( ! [U_3819,U_3817] :
        ( ! [U_3815] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3815),U_3817) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3815),U_3819)
        | U_3817 != U_3819 )
    & ! [U_3818,U_3816] :
        ( ! [U_3814] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3814),U_3816) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3814),U_3818)
        | U_3816 = U_3818 ) ),
    inference(miniscope,[status(thm)],[f_939_2]) ).

cnf(f_939_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3814),U_3816) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3814),U_3818)
    | U_3816 = U_3818 ),
    inference(clausify,[status(thm)],[f_939_3]) ).

cnf(f_939_5,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3815),U_3817) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3815),U_3819)
    | U_3817 != U_3819 ),
    inference(clausify,[status(thm)],[f_939_3]) ).

fof(f_940_1,plain,
    ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)),
    inference(fof_nnf,[status(thm)],[fact_add__mult__distrib]) ).

fof(f_940_2,plain,
    ! [U_3822,U_3821,U_3820] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3820),U_3821)),U_3822) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3820),U_3822)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3821),U_3822)),
    inference(variable_rename,[status(thm)],[f_940_1]) ).

cnf(f_940_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3820),U_3821)),U_3822) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3820),U_3822)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3821),U_3822)),
    inference(clausify,[status(thm)],[f_940_2]) ).

fof(f_941_1,plain,
    ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)),
    inference(fof_nnf,[status(thm)],[fact_nat__mult__assoc]) ).

fof(f_941_2,plain,
    ! [U_3825,U_3824,U_3823] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3823),U_3824)),U_3825) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3823),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3824),U_3825)),
    inference(variable_rename,[status(thm)],[f_941_1]) ).

cnf(f_941_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3823),U_3824)),U_3825) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3823),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3824),U_3825)),
    inference(clausify,[status(thm)],[f_941_2]) ).

fof(f_942_1,plain,
    ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_k)),
    inference(fof_nnf,[status(thm)],[fact_nat__add__assoc]) ).

fof(f_942_2,plain,
    ! [U_3828,U_3827,U_3826] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3826),U_3827)),U_3828) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3826),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3827),U_3828)),
    inference(variable_rename,[status(thm)],[f_942_1]) ).

cnf(f_942_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3826),U_3827)),U_3828) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3826),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3827),U_3828)),
    inference(clausify,[status(thm)],[f_942_2]) ).

fof(f_943_1,plain,
    ! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)),
    inference(fof_nnf,[status(thm)],[fact_add__mult__distrib2]) ).

fof(f_943_2,plain,
    ! [U_3831,U_3830,U_3829] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3829),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3830),U_3831)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3829),U_3830)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3829),U_3831)),
    inference(variable_rename,[status(thm)],[f_943_1]) ).

cnf(f_943_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3829),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3830),U_3831)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3829),U_3830)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3829),U_3831)),
    inference(clausify,[status(thm)],[f_943_2]) ).

fof(f_944_1,plain,
    ! [V_z,V_y,V_x] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),V_z)),
    inference(fof_nnf,[status(thm)],[fact_nat__add__left__commute]) ).

fof(f_944_2,plain,
    ! [U_3834,U_3833,U_3832] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3832),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3833),U_3834)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3833),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3832),U_3834)),
    inference(variable_rename,[status(thm)],[f_944_1]) ).

cnf(f_944_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3832),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3833),U_3834)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3833),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3832),U_3834)),
    inference(clausify,[status(thm)],[f_944_2]) ).

fof(f_945_1,plain,
    ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m),
    inference(fof_nnf,[status(thm)],[fact_nat__mult__commute]) ).

fof(f_945_2,plain,
    ! [U_3836,U_3835] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3835),U_3836) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3836),U_3835),
    inference(variable_rename,[status(thm)],[f_945_1]) ).

cnf(f_945_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3835),U_3836) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3836),U_3835),
    inference(clausify,[status(thm)],[f_945_2]) ).

fof(f_946_1,plain,
    ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m),
    inference(fof_nnf,[status(thm)],[fact_nat__add__commute]) ).

fof(f_946_2,plain,
    ! [U_3838,U_3837] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3837),U_3838) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3838),U_3837),
    inference(variable_rename,[status(thm)],[f_946_1]) ).

cnf(f_946_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3837),U_3838) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3838),U_3837),
    inference(clausify,[status(thm)],[f_946_2]) ).

fof(f_947_1,plain,
    ! [V_k,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_k))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_k)) ),
    inference(fof_nnf,[status(thm)],[fact_add__lessD1]) ).

fof(f_947_2,plain,
    ! [U_3841,U_3840,U_3839] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3839),U_3841))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3839),U_3840)),U_3841)) ),
    inference(variable_rename,[status(thm)],[f_947_1]) ).

cnf(f_947_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3839),U_3841))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3839),U_3840)),U_3841)) ),
    inference(clausify,[status(thm)],[f_947_2]) ).

fof(f_948_1,plain,
    ! [V_n,V_m,V_l,V_k] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_l) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_n)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l)) ),
    inference(fof_nnf,[status(thm)],[fact_less__add__eq__less]) ).

fof(f_948_2,plain,
    ! [U_3845,U_3844,U_3843,U_3842] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3844),U_3845))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3844),U_3843) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3842),U_3845)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3842),U_3843)) ),
    inference(variable_rename,[status(thm)],[f_948_1]) ).

cnf(f_948_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3844),U_3845))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3844),U_3843) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3842),U_3845)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3842),U_3843)) ),
    inference(clausify,[status(thm)],[f_948_2]) ).

fof(f_949_1,plain,
    ! [V_l,V_k,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_l)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) ),
    inference(fof_nnf,[status(thm)],[fact_add__less__mono]) ).

fof(f_949_2,plain,
    ! [U_3849,U_3848,U_3847,U_3846] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3846),U_3848)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3847),U_3849)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3848),U_3849))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3846),U_3847)) ),
    inference(variable_rename,[status(thm)],[f_949_1]) ).

cnf(f_949_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3846),U_3848)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3847),U_3849)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3848),U_3849))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3846),U_3847)) ),
    inference(clausify,[status(thm)],[f_949_2]) ).

fof(f_950_1,plain,
    ! [V_k,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) ),
    inference(fof_nnf,[status(thm)],[fact_add__less__mono1]) ).

fof(f_950_2,plain,
    ! [U_3852,U_3851,U_3850] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3850),U_3852)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3851),U_3852)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3850),U_3851)) ),
    inference(variable_rename,[status(thm)],[f_950_1]) ).

cnf(f_950_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3850),U_3852)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3851),U_3852)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3850),U_3851)) ),
    inference(clausify,[status(thm)],[f_950_2]) ).

fof(f_951_1,plain,
    ! [V_m,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_j)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) ),
    inference(fof_nnf,[status(thm)],[fact_trans__less__add2]) ).

fof(f_951_2,plain,
    ! [U_3855,U_3854,U_3853] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3853),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3855),U_3854)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3853),U_3854)) ),
    inference(variable_rename,[status(thm)],[f_951_1]) ).

cnf(f_951_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3853),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3855),U_3854)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3853),U_3854)) ),
    inference(clausify,[status(thm)],[f_951_2]) ).

fof(f_952_1,plain,
    ! [V_m,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_m)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) ),
    inference(fof_nnf,[status(thm)],[fact_trans__less__add1]) ).

fof(f_952_2,plain,
    ! [U_3858,U_3857,U_3856] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3856),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3857),U_3858)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3856),U_3857)) ),
    inference(variable_rename,[status(thm)],[f_952_1]) ).

cnf(f_952_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3856),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3857),U_3858)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3856),U_3857)) ),
    inference(clausify,[status(thm)],[f_952_2]) ).

fof(f_953_1,plain,
    ! [V_n_2,V_m_2,V_k_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__less]) ).

fof(f_953_2,plain,
    ! [U_3861,U_3860,U_3859] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3859),U_3860)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3859),U_3861)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3860),U_3861)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3860),U_3861))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3859),U_3860)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3859),U_3861))) ) ),
    inference(variable_rename,[status(thm)],[f_953_1]) ).

fof(f_953_3,plain,
    ( ! [U_3867,U_3865] :
        ( ! [U_3863] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3863),U_3865)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3863),U_3867)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3865),U_3867)) )
    & ! [U_3866,U_3864] :
        ( ! [U_3862] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3862),U_3864)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3862),U_3866)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3864),U_3866)) ) ),
    inference(miniscope,[status(thm)],[f_953_2]) ).

cnf(f_953_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3862),U_3864)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3862),U_3866)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3864),U_3866)) ),
    inference(clausify,[status(thm)],[f_953_3]) ).

cnf(f_953_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3863),U_3865)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3863),U_3867)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3865),U_3867)) ),
    inference(clausify,[status(thm)],[f_953_3]) ).

fof(f_954_1,plain,
    ! [V_i,V_j] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i)),V_i)),
    inference(fof_nnf,[status(thm)],[fact_not__add__less2]) ).

fof(f_954_2,plain,
    ! [U_3869,U_3868] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3868),U_3869)),U_3869)),
    inference(variable_rename,[status(thm)],[f_954_1]) ).

cnf(f_954_3,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3868),U_3869)),U_3869)),
    inference(clausify,[status(thm)],[f_954_2]) ).

fof(f_955_1,plain,
    ! [V_j,V_i] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_i)),
    inference(fof_nnf,[status(thm)],[fact_not__add__less1]) ).

fof(f_955_2,plain,
    ! [U_3871,U_3870] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3870),U_3871)),U_3870)),
    inference(variable_rename,[status(thm)],[f_955_1]) ).

cnf(f_955_3,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3870),U_3871)),U_3870)),
    inference(clausify,[status(thm)],[f_955_2]) ).

fof(f_956_1,plain,
    ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_infinite__UNIV__nat]) ).

cnf(f_956_2,plain,
    ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_956_1]) ).

fof(f_957_1,plain,
    ! [V_N_2] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2))
        | ! [B_m] :
          ? [B_x] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_x),B_m))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) ) )
      & ( ? [B_m] :
          ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_x),B_m))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_finite__nat__set__iff__bounded]) ).

fof(f_957_2,plain,
    ! [U_3876] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3876))
        | ! [U_3875] :
          ? [U_3874] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3874),U_3875))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_3874),U_3876)) ) )
      & ( ? [U_3873] :
          ! [U_3872] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3872),U_3873))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_3872),U_3876)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3876)) ) ),
    inference(variable_rename,[status(thm)],[f_957_1]) ).

fof(f_957_3,plain,
    ( ! [U_3878] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3878))
        | ! [U_3875] :
          ? [U_3874] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3874),U_3875))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_3874),U_3878)) ) )
    & ! [U_3877] :
        ( ? [U_3873] :
          ! [U_3872] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3872),U_3873))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_3872),U_3877)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3877)) ) ),
    inference(miniscope,[status(thm)],[f_957_2]) ).

fof(f_957_4,plain,
    ( ! [U_3878] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3878))
        | ! [U_3875] :
          ? [U_3874] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3874),U_3875))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_3874),U_3878)) ) )
    & ! [U_3877] :
        ( ! [U_3872] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3872),sK85(U_3877)))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_3872),U_3877)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3877)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK85]),skolemize(U_3873,sK85(U_3877))],[f_957_3]) ).

fof(f_957_5,plain,
    ( ! [U_3878] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3878))
        | ! [U_3875] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK86(U_3878,U_3875)),U_3875))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK86(U_3878,U_3875)),U_3878)) ) )
    & ! [U_3877] :
        ( ! [U_3872] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3872),sK85(U_3877)))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_3872),U_3877)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3877)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK86]),skolemize(U_3874,sK86(U_3878,U_3875))],[f_957_4]) ).

cnf(f_957_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3872),sK85(U_3877)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_3872),U_3877))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3877)) ),
    inference(clausify,[status(thm)],[f_957_5]) ).

cnf(f_957_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK86(U_3878,U_3875)),U_3878))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3878)) ),
    inference(clausify,[status(thm)],[f_957_5]) ).

cnf(f_957_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK86(U_3878,U_3875)),U_3875))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_3878)) ),
    inference(clausify,[status(thm)],[f_957_5]) ).

fof(f_958_1,plain,
    ! [V_c,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J]) ).

fof(f_958_2,plain,
    ! [U_3881,U_3880,U_3879] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3879),U_3880),U_3881) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3879),U_3881),U_3880)
      | ~ class_Rings_Ocomm__semiring__1(U_3879) ),
    inference(variable_rename,[status(thm)],[f_958_1]) ).

cnf(f_958_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3879),U_3880),U_3881) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3879),U_3881),U_3880)
    | ~ class_Rings_Ocomm__semiring__1(U_3879) ),
    inference(clausify,[status(thm)],[f_958_2]) ).

fof(f_959_1,plain,
    ! [V_d,V_c,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_d))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J]) ).

fof(f_959_2,plain,
    ! [U_3885,U_3884,U_3883,U_3882] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3882),U_3883),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3882),U_3884),U_3885)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3882),U_3884),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3882),U_3883),U_3885))
      | ~ class_Rings_Ocomm__semiring__1(U_3882) ),
    inference(variable_rename,[status(thm)],[f_959_1]) ).

cnf(f_959_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3882),U_3883),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3882),U_3884),U_3885)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3882),U_3884),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3882),U_3883),U_3885))
    | ~ class_Rings_Ocomm__semiring__1(U_3882) ),
    inference(clausify,[status(thm)],[f_959_2]) ).

fof(f_960_1,plain,
    ! [V_d,V_c,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),V_d)
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J]) ).

fof(f_960_2,plain,
    ! [U_3889,U_3888,U_3887,U_3886] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3886),U_3887),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3886),U_3888),U_3889)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3886),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3886),U_3887),U_3888)),U_3889)
      | ~ class_Rings_Ocomm__semiring__1(U_3886) ),
    inference(variable_rename,[status(thm)],[f_960_1]) ).

cnf(f_960_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3886),U_3887),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3886),U_3888),U_3889)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3886),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3886),U_3887),U_3888)),U_3889)
    | ~ class_Rings_Ocomm__semiring__1(U_3886) ),
    inference(clausify,[status(thm)],[f_960_2]) ).

fof(f_961_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J]) ).

fof(f_961_2,plain,
    ! [U_3893,U_3892,U_3891,U_3890] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3890),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3890),U_3891),U_3892)),U_3893) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3890),U_3891),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3890),U_3892),U_3893))
      | ~ class_Rings_Ocomm__semiring__1(U_3890) ),
    inference(variable_rename,[status(thm)],[f_961_1]) ).

cnf(f_961_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3890),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3890),U_3891),U_3892)),U_3893) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3890),U_3891),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3890),U_3892),U_3893))
    | ~ class_Rings_Ocomm__semiring__1(U_3890) ),
    inference(clausify,[status(thm)],[f_961_2]) ).

fof(f_962_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),V_b)
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J]) ).

fof(f_962_2,plain,
    ! [U_3897,U_3896,U_3895,U_3894] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3894),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3894),U_3895),U_3896)),U_3897) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3894),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3894),U_3895),U_3897)),U_3896)
      | ~ class_Rings_Ocomm__semiring__1(U_3894) ),
    inference(variable_rename,[status(thm)],[f_962_1]) ).

cnf(f_962_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3894),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3894),U_3895),U_3896)),U_3897) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3894),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3894),U_3895),U_3897)),U_3896)
    | ~ class_Rings_Ocomm__semiring__1(U_3894) ),
    inference(clausify,[status(thm)],[f_962_2]) ).

fof(f_963_1,plain,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J]) ).

fof(f_963_2,plain,
    ! [U_3902,U_3901,U_3900,U_3899,U_3898] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3898),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3898),U_3899),U_3900)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3898),U_3901),U_3902)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3898),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3898),U_3899),U_3901)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3898),U_3900),U_3902))
      | ~ class_Rings_Ocomm__semiring__1(U_3898) ),
    inference(variable_rename,[status(thm)],[f_963_1]) ).

cnf(f_963_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3898),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3898),U_3899),U_3900)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3898),U_3901),U_3902)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3898),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3898),U_3899),U_3901)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3898),U_3900),U_3902))
    | ~ class_Rings_Ocomm__semiring__1(U_3898) ),
    inference(clausify,[status(thm)],[f_963_2]) ).

fof(f_964_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J]) ).

fof(f_964_2,plain,
    ! [U_3905,U_3904,U_3903] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3903),U_3904),U_3905) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3903),U_3905),U_3904)
      | ~ class_Rings_Ocomm__semiring__1(U_3903) ),
    inference(variable_rename,[status(thm)],[f_964_1]) ).

cnf(f_964_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3903),U_3904),U_3905) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3903),U_3905),U_3904)
    | ~ class_Rings_Ocomm__semiring__1(U_3903) ),
    inference(clausify,[status(thm)],[f_964_2]) ).

fof(f_965_1,plain,
    ! [V_ry,V_rx,V_lx,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ry))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J]) ).

fof(f_965_2,plain,
    ! [U_3909,U_3908,U_3907,U_3906] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3906),U_3907),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3906),U_3908),U_3909)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3906),U_3908),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3906),U_3907),U_3909))
      | ~ class_Rings_Ocomm__semiring__1(U_3906) ),
    inference(variable_rename,[status(thm)],[f_965_1]) ).

cnf(f_965_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3906),U_3907),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3906),U_3908),U_3909)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3906),U_3908),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3906),U_3907),U_3909))
    | ~ class_Rings_Ocomm__semiring__1(U_3906) ),
    inference(clausify,[status(thm)],[f_965_2]) ).

fof(f_966_1,plain,
    ! [V_ry,V_rx,V_lx,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ry)
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J]) ).

fof(f_966_2,plain,
    ! [U_3913,U_3912,U_3911,U_3910] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3910),U_3911),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3910),U_3912),U_3913)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3910),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3910),U_3911),U_3912)),U_3913)
      | ~ class_Rings_Ocomm__semiring__1(U_3910) ),
    inference(variable_rename,[status(thm)],[f_966_1]) ).

cnf(f_966_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3910),U_3911),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3910),U_3912),U_3913)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3910),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3910),U_3911),U_3912)),U_3913)
    | ~ class_Rings_Ocomm__semiring__1(U_3910) ),
    inference(clausify,[status(thm)],[f_966_2]) ).

fof(f_967_1,plain,
    ! [V_rx,V_ly,V_lx,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_rx))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J]) ).

fof(f_967_2,plain,
    ! [U_3917,U_3916,U_3915,U_3914] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3914),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3914),U_3915),U_3916)),U_3917) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3914),U_3915),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3914),U_3916),U_3917))
      | ~ class_Rings_Ocomm__semiring__1(U_3914) ),
    inference(variable_rename,[status(thm)],[f_967_1]) ).

cnf(f_967_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3914),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3914),U_3915),U_3916)),U_3917) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3914),U_3915),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3914),U_3916),U_3917))
    | ~ class_Rings_Ocomm__semiring__1(U_3914) ),
    inference(clausify,[status(thm)],[f_967_2]) ).

fof(f_968_1,plain,
    ! [V_rx,V_ly,V_lx,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ly)
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J]) ).

fof(f_968_2,plain,
    ! [U_3921,U_3920,U_3919,U_3918] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3918),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3918),U_3919),U_3920)),U_3921) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3918),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3918),U_3919),U_3921)),U_3920)
      | ~ class_Rings_Ocomm__semiring__1(U_3918) ),
    inference(variable_rename,[status(thm)],[f_968_1]) ).

cnf(f_968_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3918),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3918),U_3919),U_3920)),U_3921) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3918),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3918),U_3919),U_3921)),U_3920)
    | ~ class_Rings_Ocomm__semiring__1(U_3918) ),
    inference(clausify,[status(thm)],[f_968_2]) ).

fof(f_969_1,plain,
    ! [V_ry,V_rx,V_ly,V_lx,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J]) ).

fof(f_969_2,plain,
    ! [U_3926,U_3925,U_3924,U_3923,U_3922] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3922),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3922),U_3923),U_3924)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3922),U_3925),U_3926)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3922),U_3923),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3922),U_3924),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3922),U_3925),U_3926)))
      | ~ class_Rings_Ocomm__semiring__1(U_3922) ),
    inference(variable_rename,[status(thm)],[f_969_1]) ).

cnf(f_969_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3922),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3922),U_3923),U_3924)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3922),U_3925),U_3926)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3922),U_3923),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3922),U_3924),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3922),U_3925),U_3926)))
    | ~ class_Rings_Ocomm__semiring__1(U_3922) ),
    inference(clausify,[status(thm)],[f_969_2]) ).

fof(f_970_1,plain,
    ! [V_ry,V_rx,V_ly,V_lx,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_ry))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J]) ).

fof(f_970_2,plain,
    ! [U_3931,U_3930,U_3929,U_3928,U_3927] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3927),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3927),U_3928),U_3929)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3927),U_3930),U_3931)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3927),U_3930),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3927),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3927),U_3928),U_3929)),U_3931))
      | ~ class_Rings_Ocomm__semiring__1(U_3927) ),
    inference(variable_rename,[status(thm)],[f_970_1]) ).

cnf(f_970_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3927),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3927),U_3928),U_3929)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3927),U_3930),U_3931)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3927),U_3930),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3927),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3927),U_3928),U_3929)),U_3931))
    | ~ class_Rings_Ocomm__semiring__1(U_3927) ),
    inference(clausify,[status(thm)],[f_970_2]) ).

fof(f_971_1,plain,
    ! [V_ry,V_rx,V_ly,V_lx,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_ry))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J]) ).

fof(f_971_2,plain,
    ! [U_3936,U_3935,U_3934,U_3933,U_3932] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3932),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3932),U_3933),U_3934)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3932),U_3935),U_3936)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3932),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3932),U_3933),U_3935)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3932),U_3934),U_3936))
      | ~ class_Rings_Ocomm__semiring__1(U_3932) ),
    inference(variable_rename,[status(thm)],[f_971_1]) ).

cnf(f_971_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3932),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3932),U_3933),U_3934)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3932),U_3935),U_3936)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3932),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3932),U_3933),U_3935)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3932),U_3934),U_3936))
    | ~ class_Rings_Ocomm__semiring__1(U_3932) ),
    inference(clausify,[status(thm)],[f_971_2]) ).

fof(f_972_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
        | V_m_2 = V_n_2
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) )
      & ( ( V_m_2 != V_n_2
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__less__le]) ).

fof(f_972_2,plain,
    ! [U_3938,U_3937] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3937),U_3938))
        | U_3937 = U_3938
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3937),U_3938)) )
      & ( ( U_3937 != U_3938
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3937),U_3938)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3937),U_3938)) ) ),
    inference(variable_rename,[status(thm)],[f_972_1]) ).

fof(f_972_3,plain,
    ( ! [U_3942,U_3940] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3940),U_3942))
        | U_3940 = U_3942
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3940),U_3942)) )
    & ! [U_3941,U_3939] :
        ( ( U_3939 != U_3941
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3939),U_3941)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3939),U_3941)) ) ),
    inference(miniscope,[status(thm)],[f_972_2]) ).

cnf(f_972_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3939),U_3941))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3939),U_3941)) ),
    inference(clausify,[status(thm)],[f_972_3]) ).

cnf(f_972_5,plain,
    ( U_3939 != U_3941
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3939),U_3941)) ),
    inference(clausify,[status(thm)],[f_972_3]) ).

cnf(f_972_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3940),U_3942))
    | U_3940 = U_3942
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3940),U_3942)) ),
    inference(clausify,[status(thm)],[f_972_3]) ).

fof(f_973_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
        | ( V_m_2 != V_n_2
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) )
      & ( V_m_2 = V_n_2
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_le__eq__less__or__eq]) ).

fof(f_973_2,plain,
    ! [U_3944,U_3943] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3943),U_3944))
        | ( U_3943 != U_3944
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3943),U_3944)) ) )
      & ( U_3943 = U_3944
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3943),U_3944))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3943),U_3944)) ) ),
    inference(variable_rename,[status(thm)],[f_973_1]) ).

fof(f_973_3,plain,
    ( ! [U_3948,U_3946] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3946),U_3948))
        | ( U_3946 != U_3948
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3946),U_3948)) ) )
    & ! [U_3947,U_3945] :
        ( U_3945 = U_3947
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3945),U_3947))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3945),U_3947)) ) ),
    inference(miniscope,[status(thm)],[f_973_2]) ).

cnf(f_973_4,plain,
    ( U_3945 = U_3947
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3945),U_3947))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3945),U_3947)) ),
    inference(clausify,[status(thm)],[f_973_3]) ).

cnf(f_973_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3946),U_3948))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3946),U_3948)) ),
    inference(clausify,[status(thm)],[f_973_3]) ).

cnf(f_973_6,plain,
    ( U_3946 != U_3948
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3946),U_3948)) ),
    inference(clausify,[status(thm)],[f_973_3]) ).

fof(f_974_1,plain,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_less__imp__le__nat]) ).

fof(f_974_2,plain,
    ! [U_3950,U_3949] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3949),U_3950))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3949),U_3950)) ),
    inference(variable_rename,[status(thm)],[f_974_1]) ).

cnf(f_974_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3949),U_3950))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3949),U_3950)) ),
    inference(clausify,[status(thm)],[f_974_2]) ).

fof(f_975_1,plain,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
      | V_m = V_n
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_le__neq__implies__less]) ).

fof(f_975_2,plain,
    ! [U_3952,U_3951] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3951),U_3952))
      | U_3951 = U_3952
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3951),U_3952)) ),
    inference(variable_rename,[status(thm)],[f_975_1]) ).

cnf(f_975_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3951),U_3952))
    | U_3951 = U_3952
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3951),U_3952)) ),
    inference(clausify,[status(thm)],[f_975_2]) ).

fof(f_976_1,plain,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
      | ( V_m != V_n
        & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ),
    inference(fof_nnf,[status(thm)],[fact_less__or__eq__imp__le]) ).

fof(f_976_2,plain,
    ! [U_3954,U_3953] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3953),U_3954))
      | ( U_3953 != U_3954
        & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3953),U_3954)) ) ),
    inference(variable_rename,[status(thm)],[f_976_1]) ).

cnf(f_976_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3953),U_3954))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3953),U_3954)) ),
    inference(clausify,[status(thm)],[f_976_2]) ).

cnf(f_976_4,plain,
    ( U_3953 != U_3954
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3953),U_3954)) ),
    inference(clausify,[status(thm)],[f_976_2]) ).

fof(f_977_1,plain,
    ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_n)),
    inference(fof_nnf,[status(thm)],[fact_le__refl]) ).

fof(f_977_2,plain,
    ! [U_3955] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3955),U_3955)),
    inference(variable_rename,[status(thm)],[f_977_1]) ).

cnf(f_977_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3955),U_3955)),
    inference(clausify,[status(thm)],[f_977_2]) ).

fof(f_978_1,plain,
    ! [V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m))),
    inference(fof_nnf,[status(thm)],[fact_le__square]) ).

fof(f_978_2,plain,
    ! [U_3956] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3956),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3956),U_3956))),
    inference(variable_rename,[status(thm)],[f_978_1]) ).

cnf(f_978_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3956),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3956),U_3956))),
    inference(clausify,[status(thm)],[f_978_2]) ).

fof(f_979_1,plain,
    ! [V_m,V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))),
    inference(fof_nnf,[status(thm)],[fact_le__add2]) ).

fof(f_979_2,plain,
    ! [U_3958,U_3957] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3957),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3958),U_3957))),
    inference(variable_rename,[status(thm)],[f_979_1]) ).

cnf(f_979_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3957),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3958),U_3957))),
    inference(clausify,[status(thm)],[f_979_2]) ).

fof(f_980_1,plain,
    ! [V_m,V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m))),
    inference(fof_nnf,[status(thm)],[fact_le__add1]) ).

fof(f_980_2,plain,
    ! [U_3960,U_3959] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3959),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3959),U_3960))),
    inference(variable_rename,[status(thm)],[f_980_1]) ).

cnf(f_980_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3959),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3959),U_3960))),
    inference(clausify,[status(thm)],[f_980_2]) ).

fof(f_981_1,plain,
    ! [V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m)))),
    inference(fof_nnf,[status(thm)],[fact_le__cube]) ).

fof(f_981_2,plain,
    ! [U_3961] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3961),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3961),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3961),U_3961)))),
    inference(variable_rename,[status(thm)],[f_981_1]) ).

cnf(f_981_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3961),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3961),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3961),U_3961)))),
    inference(clausify,[status(thm)],[f_981_2]) ).

fof(f_982_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
        | ! [B_k] : V_n_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k) )
      & ( ? [B_k] : V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_le__iff__add]) ).

fof(f_982_2,plain,
    ! [U_3965,U_3964] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3964),U_3965))
        | ! [U_3963] : U_3965 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3964),U_3963) )
      & ( ? [U_3962] : U_3965 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3964),U_3962)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3964),U_3965)) ) ),
    inference(variable_rename,[status(thm)],[f_982_1]) ).

fof(f_982_3,plain,
    ( ! [U_3969,U_3967] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3967),U_3969))
        | ! [U_3963] : U_3969 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3967),U_3963) )
    & ! [U_3968,U_3966] :
        ( ? [U_3962] : U_3968 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3966),U_3962)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3966),U_3968)) ) ),
    inference(miniscope,[status(thm)],[f_982_2]) ).

fof(f_982_4,plain,
    ( ! [U_3969,U_3967] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3967),U_3969))
        | ! [U_3963] : U_3969 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3967),U_3963) )
    & ! [U_3968,U_3966] :
        ( U_3968 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3966),sK87(U_3968,U_3966))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3966),U_3968)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK87]),skolemize(U_3962,sK87(U_3968,U_3966))],[f_982_3]) ).

cnf(f_982_5,plain,
    ( U_3968 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3966),sK87(U_3968,U_3966))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3966),U_3968)) ),
    inference(clausify,[status(thm)],[f_982_4]) ).

cnf(f_982_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3967),U_3969))
    | U_3969 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3967),U_3963) ),
    inference(clausify,[status(thm)],[f_982_4]) ).

fof(f_983_1,plain,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_nat__le__linear]) ).

fof(f_983_2,plain,
    ! [U_3971,U_3970] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3971),U_3970))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3970),U_3971)) ),
    inference(variable_rename,[status(thm)],[f_983_1]) ).

cnf(f_983_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3971),U_3970))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3970),U_3971)) ),
    inference(clausify,[status(thm)],[f_983_2]) ).

fof(f_984_1,plain,
    ! [V_n_2,V_m_2,V_k_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_n_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__le]) ).

fof(f_984_2,plain,
    ! [U_3974,U_3973,U_3972] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3972),U_3973)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3972),U_3974)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3973),U_3974)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3973),U_3974))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3972),U_3973)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3972),U_3974))) ) ),
    inference(variable_rename,[status(thm)],[f_984_1]) ).

fof(f_984_3,plain,
    ( ! [U_3980,U_3978] :
        ( ! [U_3976] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3976),U_3978)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3976),U_3980)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3978),U_3980)) )
    & ! [U_3979,U_3977] :
        ( ! [U_3975] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3975),U_3977)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3975),U_3979)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3977),U_3979)) ) ),
    inference(miniscope,[status(thm)],[f_984_2]) ).

cnf(f_984_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3975),U_3977)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3975),U_3979)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3977),U_3979)) ),
    inference(clausify,[status(thm)],[f_984_3]) ).

cnf(f_984_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3976),U_3978)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3976),U_3980)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3978),U_3980)) ),
    inference(clausify,[status(thm)],[f_984_3]) ).

fof(f_985_1,plain,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
      | V_m != V_n ),
    inference(fof_nnf,[status(thm)],[fact_eq__imp__le]) ).

fof(f_985_2,plain,
    ! [U_3982,U_3981] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3981),U_3982))
      | U_3981 != U_3982 ),
    inference(variable_rename,[status(thm)],[f_985_1]) ).

cnf(f_985_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3981),U_3982))
    | U_3981 != U_3982 ),
    inference(clausify,[status(thm)],[f_985_2]) ).

fof(f_986_1,plain,
    ! [V_m,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_m)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) ),
    inference(fof_nnf,[status(thm)],[fact_trans__le__add1]) ).

fof(f_986_2,plain,
    ! [U_3985,U_3984,U_3983] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3983),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3984),U_3985)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3983),U_3984)) ),
    inference(variable_rename,[status(thm)],[f_986_1]) ).

cnf(f_986_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3983),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3984),U_3985)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3983),U_3984)) ),
    inference(clausify,[status(thm)],[f_986_2]) ).

fof(f_987_1,plain,
    ! [V_m,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_j)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) ),
    inference(fof_nnf,[status(thm)],[fact_trans__le__add2]) ).

fof(f_987_2,plain,
    ! [U_3988,U_3987,U_3986] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3986),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3988),U_3987)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3986),U_3987)) ),
    inference(variable_rename,[status(thm)],[f_987_1]) ).

cnf(f_987_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3986),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3988),U_3987)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3986),U_3987)) ),
    inference(clausify,[status(thm)],[f_987_2]) ).

fof(f_988_1,plain,
    ! [V_k,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) ),
    inference(fof_nnf,[status(thm)],[fact_add__le__mono1]) ).

fof(f_988_2,plain,
    ! [U_3991,U_3990,U_3989] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3989),U_3991)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3990),U_3991)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3989),U_3990)) ),
    inference(variable_rename,[status(thm)],[f_988_1]) ).

cnf(f_988_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3989),U_3991)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3990),U_3991)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3989),U_3990)) ),
    inference(clausify,[status(thm)],[f_988_2]) ).

fof(f_989_1,plain,
    ! [V_k,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) ),
    inference(fof_nnf,[status(thm)],[fact_mult__le__mono1]) ).

fof(f_989_2,plain,
    ! [U_3994,U_3993,U_3992] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3992),U_3994)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3993),U_3994)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3992),U_3993)) ),
    inference(variable_rename,[status(thm)],[f_989_1]) ).

cnf(f_989_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3992),U_3994)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3993),U_3994)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3992),U_3993)) ),
    inference(clausify,[status(thm)],[f_989_2]) ).

fof(f_990_1,plain,
    ! [V_k,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) ),
    inference(fof_nnf,[status(thm)],[fact_mult__le__mono2]) ).

fof(f_990_2,plain,
    ! [U_3997,U_3996,U_3995] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3997),U_3995)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3997),U_3996)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3995),U_3996)) ),
    inference(variable_rename,[status(thm)],[f_990_1]) ).

cnf(f_990_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3997),U_3995)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3997),U_3996)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3995),U_3996)) ),
    inference(clausify,[status(thm)],[f_990_2]) ).

fof(f_991_1,plain,
    ! [V_k,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_k))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_k))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) ),
    inference(fof_nnf,[status(thm)],[fact_le__trans]) ).

fof(f_991_2,plain,
    ! [U_4000,U_3999,U_3998] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3998),U_4000))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3999),U_4000))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3998),U_3999)) ),
    inference(variable_rename,[status(thm)],[f_991_1]) ).

cnf(f_991_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3998),U_4000))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3999),U_4000))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3998),U_3999)) ),
    inference(clausify,[status(thm)],[f_991_2]) ).

fof(f_992_1,plain,
    ! [V_n,V_m] :
      ( V_m = V_n
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_le__antisym]) ).

fof(f_992_2,plain,
    ! [U_4002,U_4001] :
      ( U_4001 = U_4002
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4002),U_4001))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4001),U_4002)) ),
    inference(variable_rename,[status(thm)],[f_992_1]) ).

cnf(f_992_3,plain,
    ( U_4001 = U_4002
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4002),U_4001))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4001),U_4002)) ),
    inference(clausify,[status(thm)],[f_992_2]) ).

fof(f_993_1,plain,
    ! [V_l,V_k,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_l)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) ),
    inference(fof_nnf,[status(thm)],[fact_add__le__mono]) ).

fof(f_993_2,plain,
    ! [U_4006,U_4005,U_4004,U_4003] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4003),U_4005)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4004),U_4006)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4005),U_4006))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4003),U_4004)) ),
    inference(variable_rename,[status(thm)],[f_993_1]) ).

cnf(f_993_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4003),U_4005)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4004),U_4006)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4005),U_4006))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4003),U_4004)) ),
    inference(clausify,[status(thm)],[f_993_2]) ).

fof(f_994_1,plain,
    ! [V_l,V_k,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_l)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) ),
    inference(fof_nnf,[status(thm)],[fact_mult__le__mono]) ).

fof(f_994_2,plain,
    ! [U_4010,U_4009,U_4008,U_4007] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4007),U_4009)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4008),U_4010)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4009),U_4010))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4007),U_4008)) ),
    inference(variable_rename,[status(thm)],[f_994_1]) ).

cnf(f_994_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4007),U_4009)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4008),U_4010)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4009),U_4010))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4007),U_4008)) ),
    inference(clausify,[status(thm)],[f_994_2]) ).

fof(f_995_1,plain,
    ! [V_n,V_k,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_add__leD2]) ).

fof(f_995_2,plain,
    ! [U_4013,U_4012,U_4011] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4012),U_4013))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4011),U_4012)),U_4013)) ),
    inference(variable_rename,[status(thm)],[f_995_1]) ).

fof(f_995_3,plain,
    ! [U_4013,U_4012] :
      ( ! [U_4011] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4011),U_4012)),U_4013))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4012),U_4013)) ),
    inference(miniscope,[status(thm)],[f_995_2]) ).

cnf(f_995_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4011),U_4012)),U_4013))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4012),U_4013)) ),
    inference(clausify,[status(thm)],[f_995_3]) ).

fof(f_996_1,plain,
    ! [V_n,V_k,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_add__leD1]) ).

fof(f_996_2,plain,
    ! [U_4016,U_4015,U_4014] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4014),U_4016))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4014),U_4015)),U_4016)) ),
    inference(variable_rename,[status(thm)],[f_996_1]) ).

cnf(f_996_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4014),U_4016))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4014),U_4015)),U_4016)) ),
    inference(clausify,[status(thm)],[f_996_2]) ).

fof(f_997_1,plain,
    ! [V_n,V_k,V_m] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_add__leE]) ).

fof(f_997_2,plain,
    ! [U_4019,U_4018,U_4017] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4018),U_4019))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4017),U_4019)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4017),U_4018)),U_4019)) ),
    inference(variable_rename,[status(thm)],[f_997_1]) ).

cnf(f_997_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4017),U_4019))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4017),U_4018)),U_4019)) ),
    inference(clausify,[status(thm)],[f_997_2]) ).

cnf(f_997_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4018),U_4019))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4017),U_4018)),U_4019)) ),
    inference(clausify,[status(thm)],[f_997_2]) ).

fof(f_998_1,plain,
    ! [V_k_2,V_j_2,V_i_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_k_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),V_j_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),V_j_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_k_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_less__diff__conv]) ).

fof(f_998_2,plain,
    ! [U_4022,U_4021,U_4020] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4020),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4021),U_4022)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4020),U_4022)),U_4021)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4020),U_4022)),U_4021))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4020),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4021),U_4022))) ) ),
    inference(variable_rename,[status(thm)],[f_998_1]) ).

fof(f_998_3,plain,
    ( ! [U_4028,U_4026,U_4024] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4024),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4026),U_4028)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4024),U_4028)),U_4026)) )
    & ! [U_4027,U_4025,U_4023] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4023),U_4027)),U_4025))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4023),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4025),U_4027))) ) ),
    inference(miniscope,[status(thm)],[f_998_2]) ).

cnf(f_998_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4023),U_4027)),U_4025))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4023),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4025),U_4027))) ),
    inference(clausify,[status(thm)],[f_998_3]) ).

cnf(f_998_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4024),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4026),U_4028)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4024),U_4028)),U_4026)) ),
    inference(clausify,[status(thm)],[f_998_3]) ).

fof(f_999_1,plain,
    ! [V_n,V_m] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = V_m
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_add__diff__inverse]) ).

fof(f_999_2,plain,
    ! [U_4030,U_4029] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4030),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4029),U_4030)) = U_4029
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4029),U_4030)) ),
    inference(variable_rename,[status(thm)],[f_999_1]) ).

cnf(f_999_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4030),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4029),U_4030)) = U_4029
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4029),U_4030)) ),
    inference(clausify,[status(thm)],[f_999_2]) ).

fof(f_1000_1,plain,
    ! [V_n,V_k,V_j] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_n)),V_k))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k)) ),
    inference(fof_nnf,[status(thm)],[fact_less__imp__diff__less]) ).

fof(f_1000_2,plain,
    ! [U_4033,U_4032,U_4031] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4031),U_4033)),U_4032))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4031),U_4032)) ),
    inference(variable_rename,[status(thm)],[f_1000_1]) ).

cnf(f_1000_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4031),U_4033)),U_4032))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4031),U_4032)) ),
    inference(clausify,[status(thm)],[f_1000_2]) ).

fof(f_1001_1,plain,
    ! [V_l,V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_n)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_m)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_l))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_diff__less__mono2]) ).

fof(f_1001_2,plain,
    ! [U_4036,U_4035,U_4034] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4036),U_4035)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4036),U_4034)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4034),U_4036))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4034),U_4035)) ),
    inference(variable_rename,[status(thm)],[f_1001_1]) ).

cnf(f_1001_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4036),U_4035)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4036),U_4034)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4034),U_4036))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4034),U_4035)) ),
    inference(clausify,[status(thm)],[f_1001_2]) ).

fof(f_1002_1,plain,
    ! [V_m,V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m)),V_m) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n),V_m),
    inference(fof_nnf,[status(thm)],[fact_nat__minus__add__max]) ).

fof(f_1002_2,plain,
    ! [U_4038,U_4037] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4037),U_4038)),U_4038) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_4037),U_4038),
    inference(variable_rename,[status(thm)],[f_1002_1]) ).

cnf(f_1002_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4037),U_4038)),U_4038) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_4037),U_4038),
    inference(clausify,[status(thm)],[f_1002_2]) ).

fof(f_1003_1,plain,
    ! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)),
    inference(fof_nnf,[status(thm)],[fact_diff__mult__distrib2]) ).

fof(f_1003_2,plain,
    ! [U_4041,U_4040,U_4039] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4039),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4040),U_4041)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4039),U_4040)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4039),U_4041)),
    inference(variable_rename,[status(thm)],[f_1003_1]) ).

cnf(f_1003_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4039),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4040),U_4041)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4039),U_4040)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4039),U_4041)),
    inference(clausify,[status(thm)],[f_1003_2]) ).

fof(f_1004_1,plain,
    ! [V_n,V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_n) = V_m,
    inference(fof_nnf,[status(thm)],[fact_diff__add__inverse2]) ).

fof(f_1004_2,plain,
    ! [U_4043,U_4042] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4042),U_4043)),U_4043) = U_4042,
    inference(variable_rename,[status(thm)],[f_1004_1]) ).

cnf(f_1004_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4042),U_4043)),U_4043) = U_4042,
    inference(clausify,[status(thm)],[f_1004_2]) ).

fof(f_1005_1,plain,
    ! [V_m,V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),V_n) = V_m,
    inference(fof_nnf,[status(thm)],[fact_diff__add__inverse]) ).

fof(f_1005_2,plain,
    ! [U_4045,U_4044] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4044),U_4045)),U_4044) = U_4045,
    inference(variable_rename,[status(thm)],[f_1005_1]) ).

cnf(f_1005_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4044),U_4045)),U_4044) = U_4045,
    inference(clausify,[status(thm)],[f_1005_2]) ).

fof(f_1006_1,plain,
    ! [V_k,V_j,V_i] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_j)),V_k) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k)),
    inference(fof_nnf,[status(thm)],[fact_diff__diff__left]) ).

fof(f_1006_2,plain,
    ! [U_4048,U_4047,U_4046] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4046),U_4047)),U_4048) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4046),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4047),U_4048)),
    inference(variable_rename,[status(thm)],[f_1006_1]) ).

cnf(f_1006_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4046),U_4047)),U_4048) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4046),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4047),U_4048)),
    inference(clausify,[status(thm)],[f_1006_2]) ).

fof(f_1007_1,plain,
    ! [V_k,V_j,V_i] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_j)),V_k) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_k)),V_j),
    inference(fof_nnf,[status(thm)],[fact_diff__commute]) ).

fof(f_1007_2,plain,
    ! [U_4051,U_4050,U_4049] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4049),U_4050)),U_4051) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4049),U_4051)),U_4050),
    inference(variable_rename,[status(thm)],[f_1007_1]) ).

cnf(f_1007_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4049),U_4050)),U_4051) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4049),U_4051)),U_4050),
    inference(clausify,[status(thm)],[f_1007_2]) ).

fof(f_1008_1,plain,
    ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)),
    inference(fof_nnf,[status(thm)],[fact_diff__mult__distrib]) ).

fof(f_1008_2,plain,
    ! [U_4054,U_4053,U_4052] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4052),U_4053)),U_4054) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4052),U_4054)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4053),U_4054)),
    inference(variable_rename,[status(thm)],[f_1008_1]) ).

cnf(f_1008_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4052),U_4053)),U_4054) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4052),U_4054)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4053),U_4054)),
    inference(clausify,[status(thm)],[f_1008_2]) ).

fof(f_1009_1,plain,
    ! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),
    inference(fof_nnf,[status(thm)],[fact_diff__cancel]) ).

fof(f_1009_2,plain,
    ! [U_4057,U_4056,U_4055] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4055),U_4056)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4055),U_4057)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4056),U_4057),
    inference(variable_rename,[status(thm)],[f_1009_1]) ).

cnf(f_1009_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4055),U_4056)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4055),U_4057)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4056),U_4057),
    inference(clausify,[status(thm)],[f_1009_2]) ).

fof(f_1010_1,plain,
    ! [V_n,V_k,V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),
    inference(fof_nnf,[status(thm)],[fact_diff__cancel2]) ).

fof(f_1010_2,plain,
    ! [U_4060,U_4059,U_4058] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4058),U_4059)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4060),U_4059)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4058),U_4060),
    inference(variable_rename,[status(thm)],[f_1010_1]) ).

cnf(f_1010_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4058),U_4059)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4060),U_4059)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4058),U_4060),
    inference(clausify,[status(thm)],[f_1010_2]) ).

fof(f_1011_1,plain,
    ! [V_n,V_i,V_m] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_i)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_i)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_m),V_n)),V_i),
    inference(fof_nnf,[status(thm)],[fact_min__diff]) ).

fof(f_1011_2,plain,
    ! [U_4063,U_4062,U_4061] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4061),U_4062)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4063),U_4062)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_4061),U_4063)),U_4062),
    inference(variable_rename,[status(thm)],[f_1011_1]) ).

cnf(f_1011_3,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4061),U_4062)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4063),U_4062)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_4061),U_4063)),U_4062),
    inference(clausify,[status(thm)],[f_1011_2]) ).

fof(f_1012_1,plain,
    ! [V_z,V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J]) ).

fof(f_1012_2,plain,
    ! [U_4067,U_4066,U_4065,U_4064] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4064),U_4065),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4064),U_4066),U_4067)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4064),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4064),U_4065),U_4066)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4064),U_4065),U_4067))
      | ~ class_Rings_Ocomm__semiring__1(U_4064) ),
    inference(variable_rename,[status(thm)],[f_1012_1]) ).

cnf(f_1012_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4064),U_4065),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4064),U_4066),U_4067)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4064),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4064),U_4065),U_4066)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4064),U_4065),U_4067))
    | ~ class_Rings_Ocomm__semiring__1(U_4064) ),
    inference(clausify,[status(thm)],[f_1012_2]) ).

fof(f_1013_1,plain,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
      ( ( ( ( V_c_2 != V_d_2
            & V_a_2 != V_b_2 )
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_d_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_d_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_c_2)) )
        & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_d_2)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_d_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_c_2))
          | V_c_2 = V_d_2
          | V_a_2 = V_b_2 ) )
      | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_crossproduct__noteq]) ).

fof(f_1013_2,plain,
    ! [U_4072,U_4071,U_4070,U_4069,U_4068] :
      ( ( ( ( U_4071 != U_4072
            & U_4069 != U_4070 )
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4068),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4068),U_4069),U_4071)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4068),U_4070),U_4072)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4068),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4068),U_4069),U_4072)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4068),U_4070),U_4071)) )
        & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4068),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4068),U_4069),U_4071)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4068),U_4070),U_4072)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4068),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4068),U_4069),U_4072)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4068),U_4070),U_4071))
          | U_4071 = U_4072
          | U_4069 = U_4070 ) )
      | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_4068) ),
    inference(variable_rename,[status(thm)],[f_1013_1]) ).

cnf(f_1013_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4068),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4068),U_4069),U_4071)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4068),U_4070),U_4072)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4068),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4068),U_4069),U_4072)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4068),U_4070),U_4071))
    | U_4071 = U_4072
    | U_4069 = U_4070
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_4068) ),
    inference(clausify,[status(thm)],[f_1013_2]) ).

cnf(f_1013_4,plain,
    ( U_4069 != U_4070
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4068),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4068),U_4069),U_4071)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4068),U_4070),U_4072)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4068),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4068),U_4069),U_4072)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4068),U_4070),U_4071))
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_4068) ),
    inference(clausify,[status(thm)],[f_1013_2]) ).

cnf(f_1013_5,plain,
    ( U_4071 != U_4072
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4068),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4068),U_4069),U_4071)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4068),U_4070),U_4072)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4068),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4068),U_4069),U_4072)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4068),U_4070),U_4071))
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_4068) ),
    inference(clausify,[status(thm)],[f_1013_2]) ).

fof(f_1014_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J]) ).

fof(f_1014_2,plain,
    ! [U_4076,U_4075,U_4074,U_4073] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4073),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4073),U_4074),U_4075)),U_4076) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4073),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4073),U_4074),U_4076)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4073),U_4075),U_4076))
      | ~ class_Rings_Ocomm__semiring__1(U_4073) ),
    inference(variable_rename,[status(thm)],[f_1014_1]) ).

cnf(f_1014_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4073),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4073),U_4074),U_4075)),U_4076) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4073),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4073),U_4074),U_4076)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4073),U_4075),U_4076))
    | ~ class_Rings_Ocomm__semiring__1(U_4073) ),
    inference(clausify,[status(thm)],[f_1014_2]) ).

fof(f_1015_1,plain,
    ! [V_b,V_m,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_m)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_m)
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J]) ).

fof(f_1015_2,plain,
    ! [U_4080,U_4079,U_4078,U_4077] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4077),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4077),U_4078),U_4079)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4077),U_4080),U_4079)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4077),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4077),U_4078),U_4080)),U_4079)
      | ~ class_Rings_Ocomm__semiring__1(U_4077) ),
    inference(variable_rename,[status(thm)],[f_1015_1]) ).

cnf(f_1015_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4077),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4077),U_4078),U_4079)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4077),U_4080),U_4079)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4077),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4077),U_4078),U_4080)),U_4079)
    | ~ class_Rings_Ocomm__semiring__1(U_4077) ),
    inference(clausify,[status(thm)],[f_1015_2]) ).

fof(f_1016_1,plain,
    ! [V_z_2,V_x_2,V_y_2,V_w_2,T_b] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_y_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_z_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_z_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_y_2))
          | ( V_y_2 != V_z_2
            & V_w_2 != V_x_2 ) )
        & ( V_y_2 = V_z_2
          | V_w_2 = V_x_2
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_y_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_z_2)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_z_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_y_2)) ) )
      | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_crossproduct__eq]) ).

fof(f_1016_2,plain,
    ! [U_4085,U_4084,U_4083,U_4082,U_4081] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4081),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4081),U_4082),U_4083)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4081),U_4084),U_4085)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4081),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4081),U_4082),U_4085)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4081),U_4084),U_4083))
          | ( U_4083 != U_4085
            & U_4082 != U_4084 ) )
        & ( U_4083 = U_4085
          | U_4082 = U_4084
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4081),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4081),U_4082),U_4083)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4081),U_4084),U_4085)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4081),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4081),U_4082),U_4085)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4081),U_4084),U_4083)) ) )
      | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_4081) ),
    inference(variable_rename,[status(thm)],[f_1016_1]) ).

cnf(f_1016_3,plain,
    ( U_4083 = U_4085
    | U_4082 = U_4084
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4081),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4081),U_4082),U_4083)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4081),U_4084),U_4085)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4081),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4081),U_4082),U_4085)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4081),U_4084),U_4083))
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_4081) ),
    inference(clausify,[status(thm)],[f_1016_2]) ).

cnf(f_1016_4,plain,
    ( U_4082 != U_4084
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4081),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4081),U_4082),U_4083)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4081),U_4084),U_4085)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4081),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4081),U_4082),U_4085)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4081),U_4084),U_4083))
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_4081) ),
    inference(clausify,[status(thm)],[f_1016_2]) ).

cnf(f_1016_5,plain,
    ( U_4083 != U_4085
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4081),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4081),U_4082),U_4083)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4081),U_4084),U_4085)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4081),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4081),U_4082),U_4085)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4081),U_4084),U_4083))
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_4081) ),
    inference(clausify,[status(thm)],[f_1016_2]) ).

fof(f_1017_1,plain,
    ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2)),V_u_2)),V_n_2))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2)),V_u_2)),V_n_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) ),
    inference(fof_nnf,[status(thm)],[fact_nat__less__add__iff2]) ).

fof(f_1017_2,plain,
    ! [U_4090,U_4089,U_4088,U_4087,U_4086] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4086),U_4088)),U_4089)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4087),U_4088)),U_4090)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4089),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4087),U_4086)),U_4088)),U_4090))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4089),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4087),U_4086)),U_4088)),U_4090)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4086),U_4088)),U_4089)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4087),U_4088)),U_4090))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4086),U_4087)) ),
    inference(variable_rename,[status(thm)],[f_1017_1]) ).

cnf(f_1017_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4089),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4087),U_4086)),U_4088)),U_4090)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4086),U_4088)),U_4089)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4087),U_4088)),U_4090)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4086),U_4087)) ),
    inference(clausify,[status(thm)],[f_1017_2]) ).

cnf(f_1017_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4086),U_4088)),U_4089)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4087),U_4088)),U_4090)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4089),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4087),U_4086)),U_4088)),U_4090)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4086),U_4087)) ),
    inference(clausify,[status(thm)],[f_1017_2]) ).

fof(f_1018_1,plain,
    ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i_2),V_j_2)),V_u_2)),V_m_2)),V_n_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i_2),V_j_2)),V_u_2)),V_m_2)),V_n_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) ),
    inference(fof_nnf,[status(thm)],[fact_nat__less__add__iff1]) ).

fof(f_1018_2,plain,
    ! [U_4095,U_4094,U_4093,U_4092,U_4091] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4092),U_4093)),U_4094)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4091),U_4093)),U_4095)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4092),U_4091)),U_4093)),U_4094)),U_4095)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4092),U_4091)),U_4093)),U_4094)),U_4095))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4092),U_4093)),U_4094)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4091),U_4093)),U_4095))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4091),U_4092)) ),
    inference(variable_rename,[status(thm)],[f_1018_1]) ).

cnf(f_1018_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4092),U_4091)),U_4093)),U_4094)),U_4095))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4092),U_4093)),U_4094)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4091),U_4093)),U_4095)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4091),U_4092)) ),
    inference(clausify,[status(thm)],[f_1018_2]) ).

cnf(f_1018_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4092),U_4093)),U_4094)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4091),U_4093)),U_4095)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4092),U_4091)),U_4093)),U_4094)),U_4095))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4091),U_4092)) ),
    inference(clausify,[status(thm)],[f_1018_2]) ).

fof(f_1019_1,plain,
    ! [V_c,V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a),V_c)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_b),V_c)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_c),V_a))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a),V_b)) ),
    inference(fof_nnf,[status(thm)],[fact_diff__less__mono]) ).

fof(f_1019_2,plain,
    ! [U_4098,U_4097,U_4096] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4096),U_4098)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4097),U_4098)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4098),U_4096))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4096),U_4097)) ),
    inference(variable_rename,[status(thm)],[f_1019_1]) ).

cnf(f_1019_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4096),U_4098)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4097),U_4098)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4098),U_4096))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4096),U_4097)) ),
    inference(clausify,[status(thm)],[f_1019_2]) ).

fof(f_1020_1,plain,
    ! [V_n_2,V_m_2,V_k_2] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_k_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_k_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2)) ),
    inference(fof_nnf,[status(thm)],[fact_less__diff__iff]) ).

fof(f_1020_2,plain,
    ! [U_4101,U_4100,U_4099] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4100),U_4099)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4101),U_4099)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4100),U_4101)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4100),U_4101))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4100),U_4099)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4101),U_4099))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4099),U_4101))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4099),U_4100)) ),
    inference(variable_rename,[status(thm)],[f_1020_1]) ).

cnf(f_1020_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4100),U_4101))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4100),U_4099)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4101),U_4099)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4099),U_4101))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4099),U_4100)) ),
    inference(clausify,[status(thm)],[f_1020_2]) ).

cnf(f_1020_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4100),U_4099)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4101),U_4099)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4100),U_4101))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4099),U_4101))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4099),U_4100)) ),
    inference(clausify,[status(thm)],[f_1020_2]) ).

fof(f_1021_1,plain,
    ! [V_n,V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_m)),
    inference(fof_nnf,[status(thm)],[fact_diff__le__self]) ).

fof(f_1021_2,plain,
    ! [U_4103,U_4102] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4102),U_4103)),U_4102)),
    inference(variable_rename,[status(thm)],[f_1021_1]) ).

cnf(f_1021_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4102),U_4103)),U_4102)),
    inference(clausify,[status(thm)],[f_1021_2]) ).

fof(f_1022_1,plain,
    ! [V_i,V_j,V_k] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),V_j)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) ),
    inference(fof_nnf,[status(thm)],[fact_diff__diff__right]) ).

fof(f_1022_2,plain,
    ! [U_4106,U_4105,U_4104] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4106),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4105),U_4104)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4106),U_4104)),U_4105)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4104),U_4105)) ),
    inference(variable_rename,[status(thm)],[f_1022_1]) ).

cnf(f_1022_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4106),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4105),U_4104)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4106),U_4104)),U_4105)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4104),U_4105)) ),
    inference(clausify,[status(thm)],[f_1022_2]) ).

fof(f_1023_1,plain,
    ! [V_i_2,V_k_2,V_j_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_k_2)),V_i_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_k_2)),V_i_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_le__diff__conv]) ).

fof(f_1023_2,plain,
    ! [U_4109,U_4108,U_4107] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4107),U_4108)),U_4109))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4107),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4109),U_4108))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4107),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4109),U_4108)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4107),U_4108)),U_4109)) ) ),
    inference(variable_rename,[status(thm)],[f_1023_1]) ).

fof(f_1023_3,plain,
    ( ! [U_4115,U_4113,U_4111] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4111),U_4113)),U_4115))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4111),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4115),U_4113))) )
    & ! [U_4114,U_4112,U_4110] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4110),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4114),U_4112)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4110),U_4112)),U_4114)) ) ),
    inference(miniscope,[status(thm)],[f_1023_2]) ).

cnf(f_1023_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4110),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4114),U_4112)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4110),U_4112)),U_4114)) ),
    inference(clausify,[status(thm)],[f_1023_3]) ).

cnf(f_1023_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4111),U_4113)),U_4115))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4111),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4115),U_4113))) ),
    inference(clausify,[status(thm)],[f_1023_3]) ).

fof(f_1024_1,plain,
    ! [V_m,V_n,V_k] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),V_k)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_le__add__diff]) ).

fof(f_1024_2,plain,
    ! [U_4118,U_4117,U_4116] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4118),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4117),U_4118)),U_4116)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4116),U_4117)) ),
    inference(variable_rename,[status(thm)],[f_1024_1]) ).

cnf(f_1024_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4118),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4117),U_4118)),U_4116)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4116),U_4117)) ),
    inference(clausify,[status(thm)],[f_1024_2]) ).

fof(f_1025_1,plain,
    ! [V_l,V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_n)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_m)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_diff__le__mono2]) ).

fof(f_1025_2,plain,
    ! [U_4121,U_4120,U_4119] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4121),U_4120)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4121),U_4119)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4119),U_4120)) ),
    inference(variable_rename,[status(thm)],[f_1025_1]) ).

cnf(f_1025_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4121),U_4120)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4121),U_4119)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4119),U_4120)) ),
    inference(clausify,[status(thm)],[f_1025_2]) ).

fof(f_1026_1,plain,
    ! [V_l,V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_l)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_l)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_diff__le__mono]) ).

fof(f_1026_2,plain,
    ! [U_4124,U_4123,U_4122] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4122),U_4124)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4123),U_4124)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4122),U_4123)) ),
    inference(variable_rename,[status(thm)],[f_1026_1]) ).

cnf(f_1026_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4122),U_4124)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4123),U_4124)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4122),U_4123)) ),
    inference(clausify,[status(thm)],[f_1026_2]) ).

fof(f_1027_1,plain,
    ! [V_n,V_i] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_i)) = V_i
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_diff__diff__cancel]) ).

fof(f_1027_2,plain,
    ! [U_4126,U_4125] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4126),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4126),U_4125)) = U_4125
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4125),U_4126)) ),
    inference(variable_rename,[status(thm)],[f_1027_1]) ).

cnf(f_1027_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4126),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4126),U_4125)) = U_4125
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4125),U_4126)) ),
    inference(clausify,[status(thm)],[f_1027_2]) ).

fof(f_1028_1,plain,
    ! [V_m,V_n] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = V_m
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) ),
    inference(fof_nnf,[status(thm)],[fact_le__add__diff__inverse]) ).

fof(f_1028_2,plain,
    ! [U_4128,U_4127] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4127),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4128),U_4127)) = U_4128
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4127),U_4128)) ),
    inference(variable_rename,[status(thm)],[f_1028_1]) ).

cnf(f_1028_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4127),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4128),U_4127)) = U_4128
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4127),U_4128)) ),
    inference(clausify,[status(thm)],[f_1028_2]) ).

fof(f_1029_1,plain,
    ! [V_i,V_j,V_k] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_k)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) ),
    inference(fof_nnf,[status(thm)],[fact_add__diff__assoc]) ).

fof(f_1029_2,plain,
    ! [U_4131,U_4130,U_4129] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4131),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4130),U_4129)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4131),U_4130)),U_4129)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4129),U_4130)) ),
    inference(variable_rename,[status(thm)],[f_1029_1]) ).

cnf(f_1029_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4131),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4130),U_4129)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4131),U_4130)),U_4129)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4129),U_4130)) ),
    inference(clausify,[status(thm)],[f_1029_2]) ).

fof(f_1030_1,plain,
    ! [V_i_2,V_j_2,V_k_2] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_k_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),V_j_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),V_j_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_k_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_j_2)) ),
    inference(fof_nnf,[status(thm)],[fact_le__diff__conv2]) ).

fof(f_1030_2,plain,
    ! [U_4134,U_4133,U_4132] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4134),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4133),U_4132)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4134),U_4132)),U_4133)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4134),U_4132)),U_4133))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4134),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4133),U_4132))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4132),U_4133)) ),
    inference(variable_rename,[status(thm)],[f_1030_1]) ).

cnf(f_1030_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4134),U_4132)),U_4133))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4134),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4133),U_4132)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4132),U_4133)) ),
    inference(clausify,[status(thm)],[f_1030_2]) ).

cnf(f_1030_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4134),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4133),U_4132)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4134),U_4132)),U_4133))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4132),U_4133)) ),
    inference(clausify,[status(thm)],[f_1030_2]) ).

fof(f_1031_1,plain,
    ! [V_m,V_n] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n) = V_m
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) ),
    inference(fof_nnf,[status(thm)],[fact_le__add__diff__inverse2]) ).

fof(f_1031_2,plain,
    ! [U_4136,U_4135] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4136),U_4135)),U_4135) = U_4136
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4135),U_4136)) ),
    inference(variable_rename,[status(thm)],[f_1031_1]) ).

cnf(f_1031_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4136),U_4135)),U_4135) = U_4136
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4135),U_4136)) ),
    inference(clausify,[status(thm)],[f_1031_2]) ).

fof(f_1032_1,plain,
    ! [V_k_2,V_j_2,V_i_2] :
      ( ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2) = V_k_2
          | V_j_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2) )
        & ( V_j_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2)
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2) != V_k_2 ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) ),
    inference(fof_nnf,[status(thm)],[fact_le__imp__diff__is__add]) ).

fof(f_1032_2,plain,
    ! [U_4139,U_4138,U_4137] :
      ( ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4138),U_4137) = U_4139
          | U_4138 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4139),U_4137) )
        & ( U_4138 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4139),U_4137)
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4138),U_4137) != U_4139 ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4137),U_4138)) ),
    inference(variable_rename,[status(thm)],[f_1032_1]) ).

cnf(f_1032_3,plain,
    ( U_4138 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4139),U_4137)
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4138),U_4137) != U_4139
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4137),U_4138)) ),
    inference(clausify,[status(thm)],[f_1032_2]) ).

cnf(f_1032_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4138),U_4137) = U_4139
    | U_4138 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4139),U_4137)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4137),U_4138)) ),
    inference(clausify,[status(thm)],[f_1032_2]) ).

fof(f_1033_1,plain,
    ! [V_i,V_j,V_k] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) ),
    inference(fof_nnf,[status(thm)],[fact_diff__add__assoc]) ).

fof(f_1033_2,plain,
    ! [U_4142,U_4141,U_4140] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4142),U_4141)),U_4140) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4142),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4141),U_4140))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4140),U_4141)) ),
    inference(variable_rename,[status(thm)],[f_1033_1]) ).

cnf(f_1033_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4142),U_4141)),U_4140) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4142),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4141),U_4140))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4140),U_4141)) ),
    inference(clausify,[status(thm)],[f_1033_2]) ).

fof(f_1034_1,plain,
    ! [V_i,V_j,V_k] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)),V_i) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i)),V_k)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) ),
    inference(fof_nnf,[status(thm)],[fact_add__diff__assoc2]) ).

fof(f_1034_2,plain,
    ! [U_4145,U_4144,U_4143] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4144),U_4143)),U_4145) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4144),U_4145)),U_4143)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4143),U_4144)) ),
    inference(variable_rename,[status(thm)],[f_1034_1]) ).

cnf(f_1034_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4144),U_4143)),U_4145) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4144),U_4145)),U_4143)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4143),U_4144)) ),
    inference(clausify,[status(thm)],[f_1034_2]) ).

fof(f_1035_1,plain,
    ! [V_i,V_j,V_k] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)),V_i)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) ),
    inference(fof_nnf,[status(thm)],[fact_diff__add__assoc2]) ).

fof(f_1035_2,plain,
    ! [U_4148,U_4147,U_4146] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4147),U_4148)),U_4146) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4147),U_4146)),U_4148)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4146),U_4147)) ),
    inference(variable_rename,[status(thm)],[f_1035_1]) ).

cnf(f_1035_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4147),U_4148)),U_4146) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4147),U_4146)),U_4148)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4146),U_4147)) ),
    inference(clausify,[status(thm)],[f_1035_2]) ).

fof(f_1036_1,plain,
    ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)
          | V_m_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2)),V_u_2)),V_n_2) )
        & ( V_m_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2)),V_u_2)),V_n_2)
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) ),
    inference(fof_nnf,[status(thm)],[fact_nat__eq__add__iff2]) ).

fof(f_1036_2,plain,
    ! [U_4153,U_4152,U_4151,U_4150,U_4149] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4149),U_4151)),U_4152) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4150),U_4151)),U_4153)
          | U_4152 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4150),U_4149)),U_4151)),U_4153) )
        & ( U_4152 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4150),U_4149)),U_4151)),U_4153)
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4149),U_4151)),U_4152) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4150),U_4151)),U_4153) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4149),U_4150)) ),
    inference(variable_rename,[status(thm)],[f_1036_1]) ).

cnf(f_1036_3,plain,
    ( U_4152 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4150),U_4149)),U_4151)),U_4153)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4149),U_4151)),U_4152) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4150),U_4151)),U_4153)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4149),U_4150)) ),
    inference(clausify,[status(thm)],[f_1036_2]) ).

cnf(f_1036_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4149),U_4151)),U_4152) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4150),U_4151)),U_4153)
    | U_4152 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4150),U_4149)),U_4151)),U_4153)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4149),U_4150)) ),
    inference(clausify,[status(thm)],[f_1036_2]) ).

fof(f_1037_1,plain,
    ! [V_n,V_m,V_u,V_j,V_i] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_i)),V_u)),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) ),
    inference(fof_nnf,[status(thm)],[fact_nat__diff__add__eq2]) ).

fof(f_1037_2,plain,
    ! [U_4158,U_4157,U_4156,U_4155,U_4154] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4154),U_4156)),U_4157)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4155),U_4156)),U_4158)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4157),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4155),U_4154)),U_4156)),U_4158))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4154),U_4155)) ),
    inference(variable_rename,[status(thm)],[f_1037_1]) ).

cnf(f_1037_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4154),U_4156)),U_4157)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4155),U_4156)),U_4158)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4157),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4155),U_4154)),U_4156)),U_4158))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4154),U_4155)) ),
    inference(clausify,[status(thm)],[f_1037_2]) ).

fof(f_1038_1,plain,
    ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2)),V_u_2)),V_n_2))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2)),V_u_2)),V_n_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) ),
    inference(fof_nnf,[status(thm)],[fact_nat__le__add__iff2]) ).

fof(f_1038_2,plain,
    ! [U_4163,U_4162,U_4161,U_4160,U_4159] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4159),U_4161)),U_4162)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4160),U_4161)),U_4163)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4162),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4160),U_4159)),U_4161)),U_4163))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4162),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4160),U_4159)),U_4161)),U_4163)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4159),U_4161)),U_4162)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4160),U_4161)),U_4163))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4159),U_4160)) ),
    inference(variable_rename,[status(thm)],[f_1038_1]) ).

cnf(f_1038_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4162),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4160),U_4159)),U_4161)),U_4163)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4159),U_4161)),U_4162)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4160),U_4161)),U_4163)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4159),U_4160)) ),
    inference(clausify,[status(thm)],[f_1038_2]) ).

cnf(f_1038_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4159),U_4161)),U_4162)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4160),U_4161)),U_4163)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4162),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4160),U_4159)),U_4161)),U_4163)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4159),U_4160)) ),
    inference(clausify,[status(thm)],[f_1038_2]) ).

fof(f_1039_1,plain,
    ! [V_z,V_y,V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y)) ),
    inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I3_J]) ).

fof(f_1039_2,plain,
    ! [U_4166,U_4165,U_4164] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4164),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4165),U_4166)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4164),U_4165)) ),
    inference(variable_rename,[status(thm)],[f_1039_1]) ).

cnf(f_1039_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4164),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4165),U_4166)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4164),U_4165)) ),
    inference(clausify,[status(thm)],[f_1039_2]) ).

fof(f_1040_1,plain,
    ! [V_y,V_z,V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_z)) ),
    inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I4_J]) ).

fof(f_1040_2,plain,
    ! [U_4169,U_4168,U_4167] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4167),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4169),U_4168)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4167),U_4168)) ),
    inference(variable_rename,[status(thm)],[f_1040_1]) ).

cnf(f_1040_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4167),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4169),U_4168)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4167),U_4168)) ),
    inference(clausify,[status(thm)],[f_1040_2]) ).

fof(f_1041_1,plain,
    ! [V_N_2,V_h_2,T_b] :
      ( hAPP(V_h_2,hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_N_2)) = hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2))
      | V_N_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
      | ? [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_x),B_y)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
      | ~ class_Lattices_Oab__semigroup__idem__mult(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_hom__fold1__commute]) ).

fof(f_1041_2,plain,
    ! [U_4174,U_4173,U_4172] :
      ( hAPP(U_4173,hAPP(c_Finite__Set_Ofold1(U_4172,c_Groups_Otimes__class_Otimes(U_4172)),U_4174)) = hAPP(c_Finite__Set_Ofold1(U_4172,c_Groups_Otimes__class_Otimes(U_4172)),hAPP(c_Set_Oimage(U_4172,U_4172,U_4173),U_4174))
      | U_4174 = c_Orderings_Obot__class_Obot(tc_fun(U_4172,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4172),U_4174))
      | ? [U_4171,U_4170] : hAPP(U_4173,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4172),U_4171),U_4170)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4172),hAPP(U_4173,U_4171)),hAPP(U_4173,U_4170))
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_4172) ),
    inference(variable_rename,[status(thm)],[f_1041_1]) ).

fof(f_1041_3,plain,
    ! [U_4174,U_4173,U_4172] :
      ( hAPP(U_4173,hAPP(c_Finite__Set_Ofold1(U_4172,c_Groups_Otimes__class_Otimes(U_4172)),U_4174)) = hAPP(c_Finite__Set_Ofold1(U_4172,c_Groups_Otimes__class_Otimes(U_4172)),hAPP(c_Set_Oimage(U_4172,U_4172,U_4173),U_4174))
      | U_4174 = c_Orderings_Obot__class_Obot(tc_fun(U_4172,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4172),U_4174))
      | ? [U_4170] : hAPP(U_4173,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4172),sK88(U_4174,U_4173,U_4172)),U_4170)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4172),hAPP(U_4173,sK88(U_4174,U_4173,U_4172))),hAPP(U_4173,U_4170))
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_4172) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK88]),skolemize(U_4171,sK88(U_4174,U_4173,U_4172))],[f_1041_2]) ).

fof(f_1041_4,plain,
    ! [U_4174,U_4173,U_4172] :
      ( hAPP(U_4173,hAPP(c_Finite__Set_Ofold1(U_4172,c_Groups_Otimes__class_Otimes(U_4172)),U_4174)) = hAPP(c_Finite__Set_Ofold1(U_4172,c_Groups_Otimes__class_Otimes(U_4172)),hAPP(c_Set_Oimage(U_4172,U_4172,U_4173),U_4174))
      | U_4174 = c_Orderings_Obot__class_Obot(tc_fun(U_4172,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4172),U_4174))
      | hAPP(U_4173,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4172),sK88(U_4174,U_4173,U_4172)),sK89(U_4174,U_4173,U_4172))) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4172),hAPP(U_4173,sK88(U_4174,U_4173,U_4172))),hAPP(U_4173,sK89(U_4174,U_4173,U_4172)))
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_4172) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK89]),skolemize(U_4170,sK89(U_4174,U_4173,U_4172))],[f_1041_3]) ).

cnf(f_1041_5,plain,
    ( hAPP(U_4173,hAPP(c_Finite__Set_Ofold1(U_4172,c_Groups_Otimes__class_Otimes(U_4172)),U_4174)) = hAPP(c_Finite__Set_Ofold1(U_4172,c_Groups_Otimes__class_Otimes(U_4172)),hAPP(c_Set_Oimage(U_4172,U_4172,U_4173),U_4174))
    | U_4174 = c_Orderings_Obot__class_Obot(tc_fun(U_4172,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4172),U_4174))
    | hAPP(U_4173,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4172),sK88(U_4174,U_4173,U_4172)),sK89(U_4174,U_4173,U_4172))) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4172),hAPP(U_4173,sK88(U_4174,U_4173,U_4172))),hAPP(U_4173,sK89(U_4174,U_4173,U_4172)))
    | ~ class_Lattices_Oab__semigroup__idem__mult(U_4172) ),
    inference(clausify,[status(thm)],[f_1041_4]) ).

fof(f_1042_1,plain,
    ! [V_a_2,V_x_2,V_A_2,V_b_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_a_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),V_x_2))
      | hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_b_2,V_A_2),V_x_2))
      | ~ class_Groups_Oab__semigroup__mult(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_fold__graph__permute__diff]) ).

fof(f_1042_2,plain,
    ! [U_4179,U_4178,U_4177,U_4176,U_4175] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_4175,U_4175,c_Groups_Otimes__class_Otimes(U_4175),U_4179,hAPP(hAPP(c_Set_Oinsert(U_4175),U_4176),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4175,tc_HOL_Obool)),U_4177),hAPP(hAPP(c_Set_Oinsert(U_4175),U_4179),c_Orderings_Obot__class_Obot(tc_fun(U_4175,tc_HOL_Obool)))))),U_4178))
      | hBOOL(hAPP(hAPP(c_member(U_4175),U_4176),U_4177))
      | ~ hBOOL(hAPP(hAPP(c_member(U_4175),U_4179),U_4177))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_4175,U_4175,c_Groups_Otimes__class_Otimes(U_4175),U_4176,U_4177),U_4178))
      | ~ class_Groups_Oab__semigroup__mult(U_4175) ),
    inference(variable_rename,[status(thm)],[f_1042_1]) ).

cnf(f_1042_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_4175,U_4175,c_Groups_Otimes__class_Otimes(U_4175),U_4179,hAPP(hAPP(c_Set_Oinsert(U_4175),U_4176),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4175,tc_HOL_Obool)),U_4177),hAPP(hAPP(c_Set_Oinsert(U_4175),U_4179),c_Orderings_Obot__class_Obot(tc_fun(U_4175,tc_HOL_Obool)))))),U_4178))
    | hBOOL(hAPP(hAPP(c_member(U_4175),U_4176),U_4177))
    | ~ hBOOL(hAPP(hAPP(c_member(U_4175),U_4179),U_4177))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_4175,U_4175,c_Groups_Otimes__class_Otimes(U_4175),U_4176,U_4177),U_4178))
    | ~ class_Groups_Oab__semigroup__mult(U_4175) ),
    inference(clausify,[status(thm)],[f_1042_2]) ).

fof(f_1043_1,plain,
    ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setprod_Oremove]) ).

fof(f_1043_2,plain,
    ! [U_4184,U_4183,U_4182,U_4181,U_4180] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4181,U_4180),U_4184),U_4182) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4180),hAPP(U_4184,U_4183)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4181,U_4180),U_4184),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4181,tc_HOL_Obool)),U_4182),hAPP(hAPP(c_Set_Oinsert(U_4181),U_4183),c_Orderings_Obot__class_Obot(tc_fun(U_4181,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_4181),U_4183),U_4182))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4181),U_4182))
      | ~ class_Groups_Ocomm__monoid__mult(U_4180) ),
    inference(variable_rename,[status(thm)],[f_1043_1]) ).

cnf(f_1043_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4181,U_4180),U_4184),U_4182) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4180),hAPP(U_4184,U_4183)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4181,U_4180),U_4184),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4181,tc_HOL_Obool)),U_4182),hAPP(hAPP(c_Set_Oinsert(U_4181),U_4183),c_Orderings_Obot__class_Obot(tc_fun(U_4181,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_4181),U_4183),U_4182))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4181),U_4182))
    | ~ class_Groups_Ocomm__monoid__mult(U_4180) ),
    inference(clausify,[status(thm)],[f_1043_2]) ).

fof(f_1044_1,plain,
    ! [V_g_2,V_f_2,V_d_2,V_b_2,V_c_2,V_a_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2))
      | ? [B_x] :
          ( hAPP(V_f_2,B_x) != hAPP(V_g_2,B_x)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_d_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),B_x)) )
      | V_b_2 != V_d_2
      | V_a_2 != V_c_2
      | ~ class_Orderings_Oord(T_b)
      | ~ class_Groups_Ocomm__monoid__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__ivl__cong]) ).

fof(f_1044_2,plain,
    ! [U_4193,U_4192,U_4191,U_4190,U_4189,U_4188,U_4187,U_4186] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4187,U_4186),U_4192),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_4187,U_4188),U_4190)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4187,U_4186),U_4193),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_4187,U_4189),U_4191))
      | ? [U_4185] :
          ( hAPP(U_4192,U_4185) != hAPP(U_4193,U_4185)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4187),U_4185),U_4191))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4187),U_4189),U_4185)) )
      | U_4190 != U_4191
      | U_4188 != U_4189
      | ~ class_Orderings_Oord(U_4187)
      | ~ class_Groups_Ocomm__monoid__add(U_4186) ),
    inference(variable_rename,[status(thm)],[f_1044_1]) ).

fof(f_1044_3,plain,
    ! [U_4193,U_4192,U_4191,U_4190,U_4189,U_4188,U_4187,U_4186] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4187,U_4186),U_4192),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_4187,U_4188),U_4190)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4187,U_4186),U_4193),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_4187,U_4189),U_4191))
      | ( hAPP(U_4192,sK90(U_4193,U_4192,U_4191,U_4190,U_4189,U_4188,U_4187,U_4186)) != hAPP(U_4193,sK90(U_4193,U_4192,U_4191,U_4190,U_4189,U_4188,U_4187,U_4186))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4187),sK90(U_4193,U_4192,U_4191,U_4190,U_4189,U_4188,U_4187,U_4186)),U_4191))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4187),U_4189),sK90(U_4193,U_4192,U_4191,U_4190,U_4189,U_4188,U_4187,U_4186))) )
      | U_4190 != U_4191
      | U_4188 != U_4189
      | ~ class_Orderings_Oord(U_4187)
      | ~ class_Groups_Ocomm__monoid__add(U_4186) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK90]),skolemize(U_4185,sK90(U_4193,U_4192,U_4191,U_4190,U_4189,U_4188,U_4187,U_4186))],[f_1044_2]) ).

cnf(f_1044_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4187),U_4189),sK90(U_4193,U_4192,U_4191,U_4190,U_4189,U_4188,U_4187,U_4186)))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4187,U_4186),U_4192),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_4187,U_4188),U_4190)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4187,U_4186),U_4193),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_4187,U_4189),U_4191))
    | U_4190 != U_4191
    | U_4188 != U_4189
    | ~ class_Orderings_Oord(U_4187)
    | ~ class_Groups_Ocomm__monoid__add(U_4186) ),
    inference(clausify,[status(thm)],[f_1044_3]) ).

cnf(f_1044_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4187),sK90(U_4193,U_4192,U_4191,U_4190,U_4189,U_4188,U_4187,U_4186)),U_4191))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4187,U_4186),U_4192),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_4187,U_4188),U_4190)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4187,U_4186),U_4193),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_4187,U_4189),U_4191))
    | U_4190 != U_4191
    | U_4188 != U_4189
    | ~ class_Orderings_Oord(U_4187)
    | ~ class_Groups_Ocomm__monoid__add(U_4186) ),
    inference(clausify,[status(thm)],[f_1044_3]) ).

cnf(f_1044_6,plain,
    ( hAPP(U_4192,sK90(U_4193,U_4192,U_4191,U_4190,U_4189,U_4188,U_4187,U_4186)) != hAPP(U_4193,sK90(U_4193,U_4192,U_4191,U_4190,U_4189,U_4188,U_4187,U_4186))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4187,U_4186),U_4192),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_4187,U_4188),U_4190)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_4187,U_4186),U_4193),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_4187,U_4189),U_4191))
    | U_4190 != U_4191
    | U_4188 != U_4189
    | ~ class_Orderings_Oord(U_4187)
    | ~ class_Groups_Ocomm__monoid__add(U_4186) ),
    inference(clausify,[status(thm)],[f_1044_3]) ).

fof(f_1045_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_x_2),V_A_2)
      | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oeq__fold_H]) ).

fof(f_1045_2,plain,
    ! [U_4196,U_4195,U_4194] :
      ( c_Big__Operators_Olattice_OSup__fin(U_4194,c_Orderings_Oord__class_Omax(U_4194),hAPP(hAPP(c_Set_Oinsert(U_4194),U_4196),U_4195)) = hAPP(hAPP(c_Finite__Set_Ofold(U_4194,U_4194,c_Orderings_Oord__class_Omax(U_4194)),U_4196),U_4195)
      | hBOOL(hAPP(hAPP(c_member(U_4194),U_4196),U_4195))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4194),U_4195))
      | ~ class_Orderings_Olinorder(U_4194) ),
    inference(variable_rename,[status(thm)],[f_1045_1]) ).

cnf(f_1045_3,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_4194,c_Orderings_Oord__class_Omax(U_4194),hAPP(hAPP(c_Set_Oinsert(U_4194),U_4196),U_4195)) = hAPP(hAPP(c_Finite__Set_Ofold(U_4194,U_4194,c_Orderings_Oord__class_Omax(U_4194)),U_4196),U_4195)
    | hBOOL(hAPP(hAPP(c_member(U_4194),U_4196),U_4195))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4194),U_4195))
    | ~ class_Orderings_Olinorder(U_4194) ),
    inference(clausify,[status(thm)],[f_1045_2]) ).

fof(f_1046_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_x_2),V_A_2)
      | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oeq__fold_H]) ).

fof(f_1046_2,plain,
    ! [U_4199,U_4198,U_4197] :
      ( c_Big__Operators_Olattice_OInf__fin(U_4197,c_Orderings_Oord__class_Omin(U_4197),hAPP(hAPP(c_Set_Oinsert(U_4197),U_4199),U_4198)) = hAPP(hAPP(c_Finite__Set_Ofold(U_4197,U_4197,c_Orderings_Oord__class_Omin(U_4197)),U_4199),U_4198)
      | hBOOL(hAPP(hAPP(c_member(U_4197),U_4199),U_4198))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4197),U_4198))
      | ~ class_Orderings_Olinorder(U_4197) ),
    inference(variable_rename,[status(thm)],[f_1046_1]) ).

cnf(f_1046_3,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_4197,c_Orderings_Oord__class_Omin(U_4197),hAPP(hAPP(c_Set_Oinsert(U_4197),U_4199),U_4198)) = hAPP(hAPP(c_Finite__Set_Ofold(U_4197,U_4197,c_Orderings_Oord__class_Omin(U_4197)),U_4199),U_4198)
    | hBOOL(hAPP(hAPP(c_member(U_4197),U_4199),U_4198))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4197),U_4198))
    | ~ class_Orderings_Olinorder(U_4197) ),
    inference(clausify,[status(thm)],[f_1046_2]) ).

fof(f_1047_1,plain,
    c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_sup__nat__def]) ).

cnf(f_1047_2,plain,
    c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1047_1]) ).

fof(f_1048_1,plain,
    ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)),
    inference(fof_nnf,[status(thm)],[fact_less__not__refl]) ).

fof(f_1048_2,plain,
    ! [U_4200] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4200),U_4200)),
    inference(variable_rename,[status(thm)],[f_1048_1]) ).

cnf(f_1048_3,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4200),U_4200)),
    inference(clausify,[status(thm)],[f_1048_2]) ).

fof(f_1049_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( V_m_2 != V_n_2
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
        | V_m_2 = V_n_2 ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__neq__iff]) ).

fof(f_1049_2,plain,
    ! [U_4202,U_4201] :
      ( ( U_4201 != U_4202
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4202),U_4201))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4201),U_4202)) ) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4202),U_4201))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4201),U_4202))
        | U_4201 = U_4202 ) ),
    inference(variable_rename,[status(thm)],[f_1049_1]) ).

fof(f_1049_3,plain,
    ( ! [U_4206,U_4204] :
        ( U_4204 != U_4206
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4206),U_4204))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4204),U_4206)) ) )
    & ! [U_4205,U_4203] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4205),U_4203))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4203),U_4205))
        | U_4203 = U_4205 ) ),
    inference(miniscope,[status(thm)],[f_1049_2]) ).

cnf(f_1049_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4205),U_4203))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4203),U_4205))
    | U_4203 = U_4205 ),
    inference(clausify,[status(thm)],[f_1049_3]) ).

cnf(f_1049_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4204),U_4206))
    | U_4204 != U_4206 ),
    inference(clausify,[status(thm)],[f_1049_3]) ).

cnf(f_1049_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4206),U_4204))
    | U_4204 != U_4206 ),
    inference(clausify,[status(thm)],[f_1049_3]) ).

fof(f_1050_1,plain,
    ! [V_y,V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y),V_x))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
      | V_x = V_y ),
    inference(fof_nnf,[status(thm)],[fact_linorder__neqE__nat]) ).

fof(f_1050_2,plain,
    ! [U_4208,U_4207] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4208),U_4207))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4207),U_4208))
      | U_4207 = U_4208 ),
    inference(variable_rename,[status(thm)],[f_1050_1]) ).

cnf(f_1050_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4208),U_4207))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4207),U_4208))
    | U_4207 = U_4208 ),
    inference(clausify,[status(thm)],[f_1050_2]) ).

fof(f_1051_1,plain,
    ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)),
    inference(fof_nnf,[status(thm)],[fact_less__irrefl__nat]) ).

fof(f_1051_2,plain,
    ! [U_4209] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4209),U_4209)),
    inference(variable_rename,[status(thm)],[f_1051_1]) ).

cnf(f_1051_3,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4209),U_4209)),
    inference(clausify,[status(thm)],[f_1051_2]) ).

fof(f_1052_1,plain,
    ! [V_m,V_n] :
      ( V_m != V_n
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m)) ),
    inference(fof_nnf,[status(thm)],[fact_less__not__refl2]) ).

fof(f_1052_2,plain,
    ! [U_4211,U_4210] :
      ( U_4211 != U_4210
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4210),U_4211)) ),
    inference(variable_rename,[status(thm)],[f_1052_1]) ).

cnf(f_1052_3,plain,
    ( U_4211 != U_4210
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4210),U_4211)) ),
    inference(clausify,[status(thm)],[f_1052_2]) ).

fof(f_1053_1,plain,
    ! [V_t,V_s] :
      ( V_s != V_t
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s),V_t)) ),
    inference(fof_nnf,[status(thm)],[fact_less__not__refl3]) ).

fof(f_1053_2,plain,
    ! [U_4213,U_4212] :
      ( U_4212 != U_4213
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4212),U_4213)) ),
    inference(variable_rename,[status(thm)],[f_1053_1]) ).

cnf(f_1053_3,plain,
    ( U_4212 != U_4213
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4212),U_4213)) ),
    inference(clausify,[status(thm)],[f_1053_2]) ).

fof(f_1054_1,plain,
    ! [V_P_2,V_n_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2))
      | ( ~ hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) )
      | ( ~ hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2))
        & V_m_2 = V_n_2 )
      | ( ~ hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__less__cases]) ).

fof(f_1054_2,plain,
    ! [U_4216,U_4215,U_4214] :
      ( hBOOL(hAPP(hAPP(U_4216,U_4215),U_4214))
      | ( ~ hBOOL(hAPP(hAPP(U_4216,U_4215),U_4214))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4215),U_4214)) )
      | ( ~ hBOOL(hAPP(hAPP(U_4216,U_4215),U_4214))
        & U_4214 = U_4215 )
      | ( ~ hBOOL(hAPP(hAPP(U_4216,U_4215),U_4214))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4214),U_4215)) ) ),
    inference(variable_rename,[status(thm)],[f_1054_1]) ).

cnf(f_1054_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4215),U_4214))
    | hBOOL(hAPP(hAPP(U_4216,U_4215),U_4214))
    | U_4214 = U_4215
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4214),U_4215)) ),
    inference(clausify,[status(thm)],[f_1054_2]) ).

cnf(f_1054_4,plain,
    ( ~ hBOOL(hAPP(hAPP(U_4216,U_4215),U_4214))
    | hBOOL(hAPP(hAPP(U_4216,U_4215),U_4214))
    | U_4214 = U_4215
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4214),U_4215)) ),
    inference(clausify,[status(thm)],[f_1054_2]) ).

cnf(f_1054_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4215),U_4214))
    | hBOOL(hAPP(hAPP(U_4216,U_4215),U_4214))
    | ~ hBOOL(hAPP(hAPP(U_4216,U_4215),U_4214))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4214),U_4215)) ),
    inference(clausify,[status(thm)],[f_1054_2]) ).

cnf(f_1054_6,plain,
    ( ~ hBOOL(hAPP(hAPP(U_4216,U_4215),U_4214))
    | hBOOL(hAPP(hAPP(U_4216,U_4215),U_4214))
    | ~ hBOOL(hAPP(hAPP(U_4216,U_4215),U_4214))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4214),U_4215)) ),
    inference(clausify,[status(thm)],[f_1054_2]) ).

cnf(f_1054_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4215),U_4214))
    | hBOOL(hAPP(hAPP(U_4216,U_4215),U_4214))
    | U_4214 = U_4215
    | ~ hBOOL(hAPP(hAPP(U_4216,U_4215),U_4214)) ),
    inference(clausify,[status(thm)],[f_1054_2]) ).

cnf(f_1054_8,plain,
    ( ~ hBOOL(hAPP(hAPP(U_4216,U_4215),U_4214))
    | hBOOL(hAPP(hAPP(U_4216,U_4215),U_4214))
    | U_4214 = U_4215
    | ~ hBOOL(hAPP(hAPP(U_4216,U_4215),U_4214)) ),
    inference(clausify,[status(thm)],[f_1054_2]) ).

cnf(f_1054_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4215),U_4214))
    | hBOOL(hAPP(hAPP(U_4216,U_4215),U_4214))
    | ~ hBOOL(hAPP(hAPP(U_4216,U_4215),U_4214))
    | ~ hBOOL(hAPP(hAPP(U_4216,U_4215),U_4214)) ),
    inference(clausify,[status(thm)],[f_1054_2]) ).

cnf(f_1054_10,plain,
    ( ~ hBOOL(hAPP(hAPP(U_4216,U_4215),U_4214))
    | hBOOL(hAPP(hAPP(U_4216,U_4215),U_4214))
    | ~ hBOOL(hAPP(hAPP(U_4216,U_4215),U_4214))
    | ~ hBOOL(hAPP(hAPP(U_4216,U_4215),U_4214)) ),
    inference(clausify,[status(thm)],[f_1054_2]) ).

fof(f_1055_1,plain,
    c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_inf__nat__def]) ).

cnf(f_1055_2,plain,
    c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1055_1]) ).

fof(f_1056_1,plain,
    ! [V_z_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_b,V_f_2),V_z_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_z_2,
    inference(fof_nnf,[status(thm)],[fact_fold__empty]) ).

fof(f_1056_2,plain,
    ! [U_4220,U_4219,U_4218,U_4217] : hAPP(hAPP(c_Finite__Set_Ofold(U_4217,U_4218,U_4219),U_4220),c_Orderings_Obot__class_Obot(tc_fun(U_4217,tc_HOL_Obool))) = U_4220,
    inference(variable_rename,[status(thm)],[f_1056_1]) ).

cnf(f_1056_3,plain,
    hAPP(hAPP(c_Finite__Set_Ofold(U_4217,U_4218,U_4219),U_4220),c_Orderings_Obot__class_Obot(tc_fun(U_4217,tc_HOL_Obool))) = U_4220,
    inference(clausify,[status(thm)],[f_1056_2]) ).

fof(f_1057_1,plain,
    ! [V_x_2,V_z_2,V_f_2,T_c,T_b] :
      ( V_x_2 = V_z_2
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_empty__fold__graphE]) ).

fof(f_1057_2,plain,
    ! [U_4225,U_4224,U_4223,U_4222,U_4221] :
      ( U_4225 = U_4224
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_4221,U_4222,U_4223,U_4224,c_Orderings_Obot__class_Obot(tc_fun(U_4221,tc_HOL_Obool))),U_4225)) ),
    inference(variable_rename,[status(thm)],[f_1057_1]) ).

fof(f_1057_3,plain,
    ! [U_4225,U_4224] :
      ( ! [U_4223,U_4222,U_4221] : ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_4221,U_4222,U_4223,U_4224,c_Orderings_Obot__class_Obot(tc_fun(U_4221,tc_HOL_Obool))),U_4225))
      | U_4225 = U_4224 ),
    inference(miniscope,[status(thm)],[f_1057_2]) ).

cnf(f_1057_4,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_4221,U_4222,U_4223,U_4224,c_Orderings_Obot__class_Obot(tc_fun(U_4221,tc_HOL_Obool))),U_4225))
    | U_4225 = U_4224 ),
    inference(clausify,[status(thm)],[f_1057_3]) ).

fof(f_1058_1,plain,
    ! [V_z_2,V_f_2,T_c,T_b] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_z_2)),
    inference(fof_nnf,[status(thm)],[fact_fold__graph_OemptyI]) ).

fof(f_1058_2,plain,
    ! [U_4229,U_4228,U_4227,U_4226] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_4226,U_4227,U_4228,U_4229,c_Orderings_Obot__class_Obot(tc_fun(U_4226,tc_HOL_Obool))),U_4229)),
    inference(variable_rename,[status(thm)],[f_1058_1]) ).

cnf(f_1058_3,plain,
    hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_4226,U_4227,U_4228,U_4229,c_Orderings_Obot__class_Obot(tc_fun(U_4226,tc_HOL_Obool))),U_4229)),
    inference(clausify,[status(thm)],[f_1058_2]) ).

fof(f_1059_1,plain,
    ! [V_z_2,V_f_2,T_c,T_b] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_z_2)),
    inference(fof_nnf,[status(thm)],[fact_fold__graph_Oequations_I1_J]) ).

fof(f_1059_2,plain,
    ! [U_4233,U_4232,U_4231,U_4230] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_4230,U_4231,U_4232,U_4233,c_Orderings_Obot__class_Obot(tc_fun(U_4230,tc_HOL_Obool))),U_4233)),
    inference(variable_rename,[status(thm)],[f_1059_1]) ).

cnf(f_1059_3,plain,
    hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_4230,U_4231,U_4232,U_4233,c_Orderings_Obot__class_Obot(tc_fun(U_4230,tc_HOL_Obool))),U_4233)),
    inference(clausify,[status(thm)],[f_1059_2]) ).

fof(f_1060_1,plain,
    ! [V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_fold__graph__imp__finite]) ).

fof(f_1060_2,plain,
    ! [U_4239,U_4238,U_4237,U_4236,U_4235,U_4234] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_4234),U_4238))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_4234,U_4235,U_4236,U_4237,U_4238),U_4239)) ),
    inference(variable_rename,[status(thm)],[f_1060_1]) ).

cnf(f_1060_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_4234),U_4238))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_4234,U_4235,U_4236,U_4237,U_4238),U_4239)) ),
    inference(clausify,[status(thm)],[f_1060_2]) ).

fof(f_1061_1,plain,
    ! [V_y_2,V_z_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),hAPP(hAPP(V_f_2,V_x_2),V_y_2)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
      | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_fold__graph_OinsertI]) ).

fof(f_1061_2,plain,
    ! [U_4246,U_4245,U_4244,U_4243,U_4242,U_4241,U_4240] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_4240,U_4243,U_4244,U_4245,hAPP(hAPP(c_Set_Oinsert(U_4240),U_4241),U_4242)),hAPP(hAPP(U_4244,U_4241),U_4246)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_4240,U_4243,U_4244,U_4245,U_4242),U_4246))
      | hBOOL(hAPP(hAPP(c_member(U_4240),U_4241),U_4242)) ),
    inference(variable_rename,[status(thm)],[f_1061_1]) ).

cnf(f_1061_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_4240,U_4243,U_4244,U_4245,hAPP(hAPP(c_Set_Oinsert(U_4240),U_4241),U_4242)),hAPP(hAPP(U_4244,U_4241),U_4246)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_4240,U_4243,U_4244,U_4245,U_4242),U_4246))
    | hBOOL(hAPP(hAPP(c_member(U_4240),U_4241),U_4242)) ),
    inference(clausify,[status(thm)],[f_1061_2]) ).

fof(f_1062_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,tc_fun(T_b,tc_HOL_Obool),c_Set_Oinsert(T_b)),V_B_2),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_union__fold__insert]) ).

fof(f_1062_2,plain,
    ! [U_4249,U_4248,U_4247] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4247,tc_HOL_Obool)),U_4248),U_4249) = hAPP(hAPP(c_Finite__Set_Ofold(U_4247,tc_fun(U_4247,tc_HOL_Obool),c_Set_Oinsert(U_4247)),U_4249),U_4248)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4247),U_4248)) ),
    inference(variable_rename,[status(thm)],[f_1062_1]) ).

cnf(f_1062_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4247,tc_HOL_Obool)),U_4248),U_4249) = hAPP(hAPP(c_Finite__Set_Ofold(U_4247,tc_fun(U_4247,tc_HOL_Obool),c_Set_Oinsert(U_4247)),U_4249),U_4248)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4247),U_4248)) ),
    inference(clausify,[status(thm)],[f_1062_2]) ).

fof(f_1063_1,plain,
    ! [V_a_2,V_b_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_b_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Osemilattice__sup(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_fold__sup__insert]) ).

fof(f_1063_2,plain,
    ! [U_4253,U_4252,U_4251,U_4250] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_4250,U_4250,c_Lattices_Osemilattice__sup__class_Osup(U_4250)),U_4252),hAPP(hAPP(c_Set_Oinsert(U_4250),U_4253),U_4251)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4250),U_4253),hAPP(hAPP(c_Finite__Set_Ofold(U_4250,U_4250,c_Lattices_Osemilattice__sup__class_Osup(U_4250)),U_4252),U_4251))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4250),U_4251))
      | ~ class_Lattices_Osemilattice__sup(U_4250) ),
    inference(variable_rename,[status(thm)],[f_1063_1]) ).

cnf(f_1063_3,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_4250,U_4250,c_Lattices_Osemilattice__sup__class_Osup(U_4250)),U_4252),hAPP(hAPP(c_Set_Oinsert(U_4250),U_4253),U_4251)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4250),U_4253),hAPP(hAPP(c_Finite__Set_Ofold(U_4250,U_4250,c_Lattices_Osemilattice__sup__class_Osup(U_4250)),U_4252),U_4251))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4250),U_4251))
    | ~ class_Lattices_Osemilattice__sup(U_4250) ),
    inference(clausify,[status(thm)],[f_1063_2]) ).

fof(f_1064_1,plain,
    ! [V_a_2,V_b_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_b_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Osemilattice__inf(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_fold__inf__insert]) ).

fof(f_1064_2,plain,
    ! [U_4257,U_4256,U_4255,U_4254] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_4254,U_4254,c_Lattices_Osemilattice__inf__class_Oinf(U_4254)),U_4256),hAPP(hAPP(c_Set_Oinsert(U_4254),U_4257),U_4255)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4254),U_4257),hAPP(hAPP(c_Finite__Set_Ofold(U_4254,U_4254,c_Lattices_Osemilattice__inf__class_Oinf(U_4254)),U_4256),U_4255))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4254),U_4255))
      | ~ class_Lattices_Osemilattice__inf(U_4254) ),
    inference(variable_rename,[status(thm)],[f_1064_1]) ).

cnf(f_1064_3,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_4254,U_4254,c_Lattices_Osemilattice__inf__class_Oinf(U_4254)),U_4256),hAPP(hAPP(c_Set_Oinsert(U_4254),U_4257),U_4255)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4254),U_4257),hAPP(hAPP(c_Finite__Set_Ofold(U_4254,U_4254,c_Lattices_Osemilattice__inf__class_Oinf(U_4254)),U_4256),U_4255))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4254),U_4255))
    | ~ class_Lattices_Osemilattice__inf(U_4254) ),
    inference(clausify,[status(thm)],[f_1064_2]) ).

fof(f_1065_1,plain,
    ! [V_a_2,V_b_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_b_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Ofold__inf__insert]) ).

fof(f_1065_2,plain,
    ! [U_4261,U_4260,U_4259,U_4258] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_4258,U_4258,c_Orderings_Oord__class_Omin(U_4258)),U_4260),hAPP(hAPP(c_Set_Oinsert(U_4258),U_4261),U_4259)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4258),U_4261),hAPP(hAPP(c_Finite__Set_Ofold(U_4258,U_4258,c_Orderings_Oord__class_Omin(U_4258)),U_4260),U_4259))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4258),U_4259))
      | ~ class_Orderings_Olinorder(U_4258) ),
    inference(variable_rename,[status(thm)],[f_1065_1]) ).

cnf(f_1065_3,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_4258,U_4258,c_Orderings_Oord__class_Omin(U_4258)),U_4260),hAPP(hAPP(c_Set_Oinsert(U_4258),U_4261),U_4259)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4258),U_4261),hAPP(hAPP(c_Finite__Set_Ofold(U_4258,U_4258,c_Orderings_Oord__class_Omin(U_4258)),U_4260),U_4259))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4258),U_4259))
    | ~ class_Orderings_Olinorder(U_4258) ),
    inference(clausify,[status(thm)],[f_1065_2]) ).

fof(f_1066_1,plain,
    ! [V_a_2,V_b_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_b_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Ofold__sup__insert]) ).

fof(f_1066_2,plain,
    ! [U_4265,U_4264,U_4263,U_4262] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_4262,U_4262,c_Orderings_Oord__class_Omax(U_4262)),U_4264),hAPP(hAPP(c_Set_Oinsert(U_4262),U_4265),U_4263)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_4262),U_4265),hAPP(hAPP(c_Finite__Set_Ofold(U_4262,U_4262,c_Orderings_Oord__class_Omax(U_4262)),U_4264),U_4263))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4262),U_4263))
      | ~ class_Orderings_Olinorder(U_4262) ),
    inference(variable_rename,[status(thm)],[f_1066_1]) ).

cnf(f_1066_3,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_4262,U_4262,c_Orderings_Oord__class_Omax(U_4262)),U_4264),hAPP(hAPP(c_Set_Oinsert(U_4262),U_4265),U_4263)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_4262),U_4265),hAPP(hAPP(c_Finite__Set_Ofold(U_4262,U_4262,c_Orderings_Oord__class_Omax(U_4262)),U_4264),U_4263))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4262),U_4263))
    | ~ class_Orderings_Olinorder(U_4262) ),
    inference(clausify,[status(thm)],[f_1066_2]) ).

fof(f_1067_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_B_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_B_2),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sup__Sup__fold__sup]) ).

fof(f_1067_2,plain,
    ! [U_4268,U_4267,U_4266] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4266),U_4268),c_Complete__Lattice_OSup__class_OSup(U_4266,U_4267)) = hAPP(hAPP(c_Finite__Set_Ofold(U_4266,U_4266,c_Lattices_Osemilattice__sup__class_Osup(U_4266)),U_4268),U_4267)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4266),U_4267))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_4266) ),
    inference(variable_rename,[status(thm)],[f_1067_1]) ).

cnf(f_1067_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4266),U_4268),c_Complete__Lattice_OSup__class_OSup(U_4266,U_4267)) = hAPP(hAPP(c_Finite__Set_Ofold(U_4266,U_4266,c_Lattices_Osemilattice__sup__class_Osup(U_4266)),U_4268),U_4267)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4266),U_4267))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_4266) ),
    inference(clausify,[status(thm)],[f_1067_2]) ).

fof(f_1068_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_B_2),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_B_2),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_inf__Inf__fold__inf]) ).

fof(f_1068_2,plain,
    ! [U_4271,U_4270,U_4269] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4269),U_4271),c_Complete__Lattice_OInf__class_OInf(U_4269,U_4270)) = hAPP(hAPP(c_Finite__Set_Ofold(U_4269,U_4269,c_Lattices_Osemilattice__inf__class_Oinf(U_4269)),U_4271),U_4270)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4269),U_4270))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_4269) ),
    inference(variable_rename,[status(thm)],[f_1068_1]) ).

cnf(f_1068_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4269),U_4271),c_Complete__Lattice_OInf__class_OInf(U_4269,U_4270)) = hAPP(hAPP(c_Finite__Set_Ofold(U_4269,U_4269,c_Lattices_Osemilattice__inf__class_Oinf(U_4269)),U_4271),U_4270)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4269),U_4270))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_4269) ),
    inference(clausify,[status(thm)],[f_1068_2]) ).

fof(f_1069_1,plain,
    ! [V_z,V_y,V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) ),
    inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I1_J]) ).

fof(f_1069_2,plain,
    ! [U_4274,U_4273,U_4272] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4272),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4273),U_4274)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4272),U_4273)) ),
    inference(variable_rename,[status(thm)],[f_1069_1]) ).

cnf(f_1069_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4272),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4273),U_4274)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4272),U_4273)) ),
    inference(clausify,[status(thm)],[f_1069_2]) ).

fof(f_1070_1,plain,
    ! [V_y,V_z,V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_z)) ),
    inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I2_J]) ).

fof(f_1070_2,plain,
    ! [U_4277,U_4276,U_4275] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4275),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4277),U_4276)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4275),U_4276)) ),
    inference(variable_rename,[status(thm)],[f_1070_1]) ).

cnf(f_1070_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4275),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4277),U_4276)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4275),U_4276)) ),
    inference(clausify,[status(thm)],[f_1070_2]) ).

fof(f_1071_1,plain,
    ! [V_a_2,V_A_2,V_F_2,V_f_2,T_b] :
      ( hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,V_f_2),V_a_2),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Oeq__fold__idem_H]) ).

fof(f_1071_2,plain,
    ! [U_4282,U_4281,U_4280,U_4279,U_4278] :
      ( hAPP(U_4280,hAPP(hAPP(c_Set_Oinsert(U_4278),U_4282),U_4281)) = hAPP(hAPP(c_Finite__Set_Ofold(U_4278,U_4278,U_4279),U_4282),U_4281)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4278),U_4281))
      | ~ c_Finite__Set_Ofolding__one__idem(U_4278,U_4279,U_4280) ),
    inference(variable_rename,[status(thm)],[f_1071_1]) ).

cnf(f_1071_3,plain,
    ( hAPP(U_4280,hAPP(hAPP(c_Set_Oinsert(U_4278),U_4282),U_4281)) = hAPP(hAPP(c_Finite__Set_Ofold(U_4278,U_4278,U_4279),U_4282),U_4281)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4278),U_4281))
    | ~ c_Finite__Set_Ofolding__one__idem(U_4278,U_4279,U_4280) ),
    inference(clausify,[status(thm)],[f_1071_2]) ).

fof(f_1072_1,plain,
    ! [V_y,V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) ),
    inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I5_J]) ).

fof(f_1072_2,plain,
    ! [U_4284,U_4283] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4283),U_4284))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4283),U_4284)) ),
    inference(variable_rename,[status(thm)],[f_1072_1]) ).

cnf(f_1072_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4283),U_4284))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4283),U_4284)) ),
    inference(clausify,[status(thm)],[f_1072_2]) ).

fof(f_1073_1,plain,
    ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2))
      | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__insert]) ).

fof(f_1073_2,plain,
    ! [U_4289,U_4288,U_4287,U_4286,U_4285] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4286,U_4285),U_4289),hAPP(hAPP(c_Set_Oinsert(U_4286),U_4288),U_4287)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4285),hAPP(U_4289,U_4288)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4286,U_4285),U_4289),U_4287))
      | hBOOL(hAPP(hAPP(c_member(U_4286),U_4288),U_4287))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4286),U_4287))
      | ~ class_Groups_Ocomm__monoid__mult(U_4285) ),
    inference(variable_rename,[status(thm)],[f_1073_1]) ).

cnf(f_1073_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4286,U_4285),U_4289),hAPP(hAPP(c_Set_Oinsert(U_4286),U_4288),U_4287)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4285),hAPP(U_4289,U_4288)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4286,U_4285),U_4289),U_4287))
    | hBOOL(hAPP(hAPP(c_member(U_4286),U_4288),U_4287))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4286),U_4287))
    | ~ class_Groups_Ocomm__monoid__mult(U_4285) ),
    inference(clausify,[status(thm)],[f_1073_2]) ).

fof(f_1074_1,plain,
    ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2))
      | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setprod_Oinsert]) ).

fof(f_1074_2,plain,
    ! [U_4294,U_4293,U_4292,U_4291,U_4290] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4291,U_4290),U_4294),hAPP(hAPP(c_Set_Oinsert(U_4291),U_4293),U_4292)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4290),hAPP(U_4294,U_4293)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4291,U_4290),U_4294),U_4292))
      | hBOOL(hAPP(hAPP(c_member(U_4291),U_4293),U_4292))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4291),U_4292))
      | ~ class_Groups_Ocomm__monoid__mult(U_4290) ),
    inference(variable_rename,[status(thm)],[f_1074_1]) ).

cnf(f_1074_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4291,U_4290),U_4294),hAPP(hAPP(c_Set_Oinsert(U_4291),U_4293),U_4292)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4290),hAPP(U_4294,U_4293)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4291,U_4290),U_4294),U_4292))
    | hBOOL(hAPP(hAPP(c_member(U_4291),U_4293),U_4292))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4291),U_4292))
    | ~ class_Groups_Ocomm__monoid__mult(U_4290) ),
    inference(clausify,[status(thm)],[f_1074_2]) ).

fof(f_1075_1,plain,
    ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__Un__Int]) ).

fof(f_1075_2,plain,
    ! [U_4299,U_4298,U_4297,U_4296,U_4295] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4295),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4296,U_4295),U_4299),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4296,tc_HOL_Obool)),U_4297),U_4298))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4296,U_4295),U_4299),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4296,tc_HOL_Obool)),U_4297),U_4298))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4295),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4296,U_4295),U_4299),U_4297)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4296,U_4295),U_4299),U_4298))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4296),U_4298))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4296),U_4297))
      | ~ class_Groups_Ocomm__monoid__mult(U_4295) ),
    inference(variable_rename,[status(thm)],[f_1075_1]) ).

cnf(f_1075_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4295),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4296,U_4295),U_4299),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4296,tc_HOL_Obool)),U_4297),U_4298))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4296,U_4295),U_4299),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4296,tc_HOL_Obool)),U_4297),U_4298))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4295),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4296,U_4295),U_4299),U_4297)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4296,U_4295),U_4299),U_4298))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4296),U_4298))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4296),U_4297))
    | ~ class_Groups_Ocomm__monoid__mult(U_4295) ),
    inference(clausify,[status(thm)],[f_1075_2]) ).

fof(f_1076_1,plain,
    ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setprod_Ounion__inter]) ).

fof(f_1076_2,plain,
    ! [U_4304,U_4303,U_4302,U_4301,U_4300] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4300),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4301,U_4300),U_4304),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4301,tc_HOL_Obool)),U_4302),U_4303))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4301,U_4300),U_4304),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4301,tc_HOL_Obool)),U_4302),U_4303))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4300),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4301,U_4300),U_4304),U_4302)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4301,U_4300),U_4304),U_4303))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4301),U_4303))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4301),U_4302))
      | ~ class_Groups_Ocomm__monoid__mult(U_4300) ),
    inference(variable_rename,[status(thm)],[f_1076_1]) ).

cnf(f_1076_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4300),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4301,U_4300),U_4304),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4301,tc_HOL_Obool)),U_4302),U_4303))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4301,U_4300),U_4304),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4301,tc_HOL_Obool)),U_4302),U_4303))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4300),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4301,U_4300),U_4304),U_4302)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4301,U_4300),U_4304),U_4303))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4301),U_4303))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4301),U_4302))
    | ~ class_Groups_Ocomm__monoid__mult(U_4300) ),
    inference(clausify,[status(thm)],[f_1076_2]) ).

fof(f_1077_1,plain,
    ! [V_z_2,V_y_2,V_A_2,V_b_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_z_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_z_2),V_y_2)))
      | hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_b_2,V_A_2),V_y_2))
      | ~ class_Groups_Oab__semigroup__mult(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_fold__graph__insert__swap]) ).

fof(f_1077_2,plain,
    ! [U_4309,U_4308,U_4307,U_4306,U_4305] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_4305,U_4305,c_Groups_Otimes__class_Otimes(U_4305),U_4309,hAPP(hAPP(c_Set_Oinsert(U_4305),U_4306),U_4307)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4305),U_4309),U_4308)))
      | hBOOL(hAPP(hAPP(c_member(U_4305),U_4306),U_4307))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_4305,U_4305,c_Groups_Otimes__class_Otimes(U_4305),U_4306,U_4307),U_4308))
      | ~ class_Groups_Oab__semigroup__mult(U_4305) ),
    inference(variable_rename,[status(thm)],[f_1077_1]) ).

cnf(f_1077_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_4305,U_4305,c_Groups_Otimes__class_Otimes(U_4305),U_4309,hAPP(hAPP(c_Set_Oinsert(U_4305),U_4306),U_4307)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4305),U_4309),U_4308)))
    | hBOOL(hAPP(hAPP(c_member(U_4305),U_4306),U_4307))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_4305,U_4305,c_Groups_Otimes__class_Otimes(U_4305),U_4306,U_4307),U_4308))
    | ~ class_Groups_Oab__semigroup__mult(U_4305) ),
    inference(clausify,[status(thm)],[f_1077_2]) ).

fof(f_1078_1,plain,
    ! [V_b_2,V_a_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_b_2),V_A_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Osemilattice__sup(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sup__le__fold__sup]) ).

fof(f_1078_2,plain,
    ! [U_4313,U_4312,U_4311,U_4310] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4310),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4310),U_4312),U_4313)),hAPP(hAPP(c_Finite__Set_Ofold(U_4310,U_4310,c_Lattices_Osemilattice__sup__class_Osup(U_4310)),U_4313),U_4311)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_4310),U_4312),U_4311))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4310),U_4311))
      | ~ class_Lattices_Osemilattice__sup(U_4310) ),
    inference(variable_rename,[status(thm)],[f_1078_1]) ).

cnf(f_1078_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4310),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_4310),U_4312),U_4313)),hAPP(hAPP(c_Finite__Set_Ofold(U_4310,U_4310,c_Lattices_Osemilattice__sup__class_Osup(U_4310)),U_4313),U_4311)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_4310),U_4312),U_4311))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4310),U_4311))
    | ~ class_Lattices_Osemilattice__sup(U_4310) ),
    inference(clausify,[status(thm)],[f_1078_2]) ).

fof(f_1079_1,plain,
    ! [V_b_2,V_a_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_b_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),V_b_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Osemilattice__inf(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_fold__inf__le__inf]) ).

fof(f_1079_2,plain,
    ! [U_4317,U_4316,U_4315,U_4314] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4314),hAPP(hAPP(c_Finite__Set_Ofold(U_4314,U_4314,c_Lattices_Osemilattice__inf__class_Oinf(U_4314)),U_4317),U_4315)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4314),U_4316),U_4317)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_4314),U_4316),U_4315))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4314),U_4315))
      | ~ class_Lattices_Osemilattice__inf(U_4314) ),
    inference(variable_rename,[status(thm)],[f_1079_1]) ).

cnf(f_1079_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4314),hAPP(hAPP(c_Finite__Set_Ofold(U_4314,U_4314,c_Lattices_Osemilattice__inf__class_Oinf(U_4314)),U_4317),U_4315)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_4314),U_4316),U_4317)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_4314),U_4316),U_4315))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4314),U_4315))
    | ~ class_Lattices_Osemilattice__inf(U_4314) ),
    inference(clausify,[status(thm)],[f_1079_2]) ).

fof(f_1080_1,plain,
    ! [V_b_2,V_a_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_b_2),V_A_2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_a_2),V_b_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Ofold__inf__le__inf]) ).

fof(f_1080_2,plain,
    ! [U_4321,U_4320,U_4319,U_4318] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4318),hAPP(hAPP(c_Finite__Set_Ofold(U_4318,U_4318,c_Orderings_Oord__class_Omin(U_4318)),U_4321),U_4319)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4318),U_4320),U_4321)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_4318),U_4320),U_4319))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4318),U_4319))
      | ~ class_Orderings_Olinorder(U_4318) ),
    inference(variable_rename,[status(thm)],[f_1080_1]) ).

cnf(f_1080_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4318),hAPP(hAPP(c_Finite__Set_Ofold(U_4318,U_4318,c_Orderings_Oord__class_Omin(U_4318)),U_4321),U_4319)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_4318),U_4320),U_4321)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_4318),U_4320),U_4319))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4318),U_4319))
    | ~ class_Orderings_Olinorder(U_4318) ),
    inference(clausify,[status(thm)],[f_1080_2]) ).

fof(f_1081_1,plain,
    ! [V_b_2,V_a_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_b_2),V_A_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Osup__le__fold__sup]) ).

fof(f_1081_2,plain,
    ! [U_4325,U_4324,U_4323,U_4322] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4322),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_4322),U_4324),U_4325)),hAPP(hAPP(c_Finite__Set_Ofold(U_4322,U_4322,c_Orderings_Oord__class_Omax(U_4322)),U_4325),U_4323)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_4322),U_4324),U_4323))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4322),U_4323))
      | ~ class_Orderings_Olinorder(U_4322) ),
    inference(variable_rename,[status(thm)],[f_1081_1]) ).

cnf(f_1081_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4322),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_4322),U_4324),U_4325)),hAPP(hAPP(c_Finite__Set_Ofold(U_4322,U_4322,c_Orderings_Oord__class_Omax(U_4322)),U_4325),U_4323)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_4322),U_4324),U_4323))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4322),U_4323))
    | ~ class_Orderings_Olinorder(U_4322) ),
    inference(clausify,[status(thm)],[f_1081_2]) ).

fof(f_1082_1,plain,
    ! [V_A_2,T_b] :
      ( c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),c_Orderings_Obot__class_Obot(T_b)),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__fold__sup]) ).

fof(f_1082_2,plain,
    ! [U_4327,U_4326] :
      ( c_Complete__Lattice_OSup__class_OSup(U_4326,U_4327) = hAPP(hAPP(c_Finite__Set_Ofold(U_4326,U_4326,c_Lattices_Osemilattice__sup__class_Osup(U_4326)),c_Orderings_Obot__class_Obot(U_4326)),U_4327)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4326),U_4327))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_4326) ),
    inference(variable_rename,[status(thm)],[f_1082_1]) ).

cnf(f_1082_3,plain,
    ( c_Complete__Lattice_OSup__class_OSup(U_4326,U_4327) = hAPP(hAPP(c_Finite__Set_Ofold(U_4326,U_4326,c_Lattices_Osemilattice__sup__class_Osup(U_4326)),c_Orderings_Obot__class_Obot(U_4326)),U_4327)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4326),U_4327))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_4326) ),
    inference(clausify,[status(thm)],[f_1082_2]) ).

fof(f_1083_1,plain,
    ! [V_A_2,T_b] :
      ( c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),c_Orderings_Otop__class_Otop(T_b)),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__fold__inf]) ).

fof(f_1083_2,plain,
    ! [U_4329,U_4328] :
      ( c_Complete__Lattice_OInf__class_OInf(U_4328,U_4329) = hAPP(hAPP(c_Finite__Set_Ofold(U_4328,U_4328,c_Lattices_Osemilattice__inf__class_Oinf(U_4328)),c_Orderings_Otop__class_Otop(U_4328)),U_4329)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4328),U_4329))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_4328) ),
    inference(variable_rename,[status(thm)],[f_1083_1]) ).

cnf(f_1083_3,plain,
    ( c_Complete__Lattice_OInf__class_OInf(U_4328,U_4329) = hAPP(hAPP(c_Finite__Set_Ofold(U_4328,U_4328,c_Lattices_Osemilattice__inf__class_Oinf(U_4328)),c_Orderings_Otop__class_Otop(U_4328)),U_4329)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4328),U_4329))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_4328) ),
    inference(clausify,[status(thm)],[f_1083_2]) ).

fof(f_1084_1,plain,
    ! [V_a_2,V_A_2,T_b] :
      ( hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)),V_a_2),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Oab__semigroup__idem__mult(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_fold1__eq__fold__idem]) ).

fof(f_1084_2,plain,
    ! [U_4332,U_4331,U_4330] :
      ( hAPP(c_Finite__Set_Ofold1(U_4330,c_Groups_Otimes__class_Otimes(U_4330)),hAPP(hAPP(c_Set_Oinsert(U_4330),U_4332),U_4331)) = hAPP(hAPP(c_Finite__Set_Ofold(U_4330,U_4330,c_Groups_Otimes__class_Otimes(U_4330)),U_4332),U_4331)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4330),U_4331))
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_4330) ),
    inference(variable_rename,[status(thm)],[f_1084_1]) ).

cnf(f_1084_3,plain,
    ( hAPP(c_Finite__Set_Ofold1(U_4330,c_Groups_Otimes__class_Otimes(U_4330)),hAPP(hAPP(c_Set_Oinsert(U_4330),U_4332),U_4331)) = hAPP(hAPP(c_Finite__Set_Ofold(U_4330,U_4330,c_Groups_Otimes__class_Otimes(U_4330)),U_4332),U_4331)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4330),U_4331))
    | ~ class_Lattices_Oab__semigroup__idem__mult(U_4330) ),
    inference(clausify,[status(thm)],[f_1084_2]) ).

fof(f_1085_1,plain,
    ! [V_a_2,V_A_2,T_b] :
      ( c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_a_2),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oeq__fold__idem_H]) ).

fof(f_1085_2,plain,
    ! [U_4335,U_4334,U_4333] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_4333,hAPP(hAPP(c_Set_Oinsert(U_4333),U_4335),U_4334)) = hAPP(hAPP(c_Finite__Set_Ofold(U_4333,U_4333,c_Lattices_Osemilattice__sup__class_Osup(U_4333)),U_4335),U_4334)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4333),U_4334))
      | ~ class_Lattices_Olattice(U_4333) ),
    inference(variable_rename,[status(thm)],[f_1085_1]) ).

cnf(f_1085_3,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_4333,hAPP(hAPP(c_Set_Oinsert(U_4333),U_4335),U_4334)) = hAPP(hAPP(c_Finite__Set_Ofold(U_4333,U_4333,c_Lattices_Osemilattice__sup__class_Osup(U_4333)),U_4335),U_4334)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4333),U_4334))
    | ~ class_Lattices_Olattice(U_4333) ),
    inference(clausify,[status(thm)],[f_1085_2]) ).

fof(f_1086_1,plain,
    ! [V_a_2,V_A_2,T_b] :
      ( c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_a_2),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oeq__fold__idem_H]) ).

fof(f_1086_2,plain,
    ! [U_4338,U_4337,U_4336] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_4336,hAPP(hAPP(c_Set_Oinsert(U_4336),U_4338),U_4337)) = hAPP(hAPP(c_Finite__Set_Ofold(U_4336,U_4336,c_Lattices_Osemilattice__inf__class_Oinf(U_4336)),U_4338),U_4337)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4336),U_4337))
      | ~ class_Lattices_Olattice(U_4336) ),
    inference(variable_rename,[status(thm)],[f_1086_1]) ).

cnf(f_1086_3,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_4336,hAPP(hAPP(c_Set_Oinsert(U_4336),U_4338),U_4337)) = hAPP(hAPP(c_Finite__Set_Ofold(U_4336,U_4336,c_Lattices_Osemilattice__inf__class_Oinf(U_4336)),U_4338),U_4337)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4336),U_4337))
    | ~ class_Lattices_Olattice(U_4336) ),
    inference(clausify,[status(thm)],[f_1086_2]) ).

fof(f_1087_1,plain,
    ! [V_a_2,V_A_2,T_b] :
      ( c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_a_2),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Min_Oeq__fold__idem_H]) ).

fof(f_1087_2,plain,
    ! [U_4341,U_4340,U_4339] :
      ( c_Big__Operators_Olinorder__class_OMin(U_4339,hAPP(hAPP(c_Set_Oinsert(U_4339),U_4341),U_4340)) = hAPP(hAPP(c_Finite__Set_Ofold(U_4339,U_4339,c_Orderings_Oord__class_Omin(U_4339)),U_4341),U_4340)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4339),U_4340))
      | ~ class_Orderings_Olinorder(U_4339) ),
    inference(variable_rename,[status(thm)],[f_1087_1]) ).

cnf(f_1087_3,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_4339,hAPP(hAPP(c_Set_Oinsert(U_4339),U_4341),U_4340)) = hAPP(hAPP(c_Finite__Set_Ofold(U_4339,U_4339,c_Orderings_Oord__class_Omin(U_4339)),U_4341),U_4340)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4339),U_4340))
    | ~ class_Orderings_Olinorder(U_4339) ),
    inference(clausify,[status(thm)],[f_1087_2]) ).

fof(f_1088_1,plain,
    ! [V_a_2,V_A_2,T_b] :
      ( c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_a_2),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Max_Oeq__fold__idem_H]) ).

fof(f_1088_2,plain,
    ! [U_4344,U_4343,U_4342] :
      ( c_Big__Operators_Olinorder__class_OMax(U_4342,hAPP(hAPP(c_Set_Oinsert(U_4342),U_4344),U_4343)) = hAPP(hAPP(c_Finite__Set_Ofold(U_4342,U_4342,c_Orderings_Oord__class_Omax(U_4342)),U_4344),U_4343)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4342),U_4343))
      | ~ class_Orderings_Olinorder(U_4342) ),
    inference(variable_rename,[status(thm)],[f_1088_1]) ).

cnf(f_1088_3,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_4342,hAPP(hAPP(c_Set_Oinsert(U_4342),U_4344),U_4343)) = hAPP(hAPP(c_Finite__Set_Ofold(U_4342,U_4342,c_Orderings_Oord__class_Omax(U_4342)),U_4344),U_4343)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4342),U_4343))
    | ~ class_Orderings_Olinorder(U_4342) ),
    inference(clausify,[status(thm)],[f_1088_2]) ).

fof(f_1089_1,plain,
    ! [V_a_2,V_A_2,T_b] :
      ( c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_a_2),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oeq__fold__idem_H]) ).

fof(f_1089_2,plain,
    ! [U_4347,U_4346,U_4345] :
      ( c_Big__Operators_Olattice_OInf__fin(U_4345,c_Orderings_Oord__class_Omin(U_4345),hAPP(hAPP(c_Set_Oinsert(U_4345),U_4347),U_4346)) = hAPP(hAPP(c_Finite__Set_Ofold(U_4345,U_4345,c_Orderings_Oord__class_Omin(U_4345)),U_4347),U_4346)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4345),U_4346))
      | ~ class_Orderings_Olinorder(U_4345) ),
    inference(variable_rename,[status(thm)],[f_1089_1]) ).

cnf(f_1089_3,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_4345,c_Orderings_Oord__class_Omin(U_4345),hAPP(hAPP(c_Set_Oinsert(U_4345),U_4347),U_4346)) = hAPP(hAPP(c_Finite__Set_Ofold(U_4345,U_4345,c_Orderings_Oord__class_Omin(U_4345)),U_4347),U_4346)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4345),U_4346))
    | ~ class_Orderings_Olinorder(U_4345) ),
    inference(clausify,[status(thm)],[f_1089_2]) ).

fof(f_1090_1,plain,
    ! [V_a_2,V_A_2,T_b] :
      ( c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_a_2),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oeq__fold__idem_H]) ).

fof(f_1090_2,plain,
    ! [U_4350,U_4349,U_4348] :
      ( c_Big__Operators_Olattice_OSup__fin(U_4348,c_Orderings_Oord__class_Omax(U_4348),hAPP(hAPP(c_Set_Oinsert(U_4348),U_4350),U_4349)) = hAPP(hAPP(c_Finite__Set_Ofold(U_4348,U_4348,c_Orderings_Oord__class_Omax(U_4348)),U_4350),U_4349)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4348),U_4349))
      | ~ class_Orderings_Olinorder(U_4348) ),
    inference(variable_rename,[status(thm)],[f_1090_1]) ).

cnf(f_1090_3,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_4348,c_Orderings_Oord__class_Omax(U_4348),hAPP(hAPP(c_Set_Oinsert(U_4348),U_4350),U_4349)) = hAPP(hAPP(c_Finite__Set_Ofold(U_4348,U_4348,c_Orderings_Oord__class_Omax(U_4348)),U_4350),U_4349)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4348),U_4349))
    | ~ class_Orderings_Olinorder(U_4348) ),
    inference(clausify,[status(thm)],[f_1090_2]) ).

fof(f_1091_1,plain,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
      ( hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,V_f_2),V_x_2),V_A_2)
      | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__one_Oeq__fold_H]) ).

fof(f_1091_2,plain,
    ! [U_4355,U_4354,U_4353,U_4352,U_4351] :
      ( hAPP(U_4353,hAPP(hAPP(c_Set_Oinsert(U_4351),U_4355),U_4354)) = hAPP(hAPP(c_Finite__Set_Ofold(U_4351,U_4351,U_4352),U_4355),U_4354)
      | hBOOL(hAPP(hAPP(c_member(U_4351),U_4355),U_4354))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4351),U_4354))
      | ~ c_Finite__Set_Ofolding__one(U_4351,U_4352,U_4353) ),
    inference(variable_rename,[status(thm)],[f_1091_1]) ).

cnf(f_1091_3,plain,
    ( hAPP(U_4353,hAPP(hAPP(c_Set_Oinsert(U_4351),U_4355),U_4354)) = hAPP(hAPP(c_Finite__Set_Ofold(U_4351,U_4351,U_4352),U_4355),U_4354)
    | hBOOL(hAPP(hAPP(c_member(U_4351),U_4355),U_4354))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4351),U_4354))
    | ~ c_Finite__Set_Ofolding__one(U_4351,U_4352,U_4353) ),
    inference(clausify,[status(thm)],[f_1091_2]) ).

fof(f_1092_1,plain,
    ! [V_x_2,V_g_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setprod_Oinsert__remove]) ).

fof(f_1092_2,plain,
    ! [U_4360,U_4359,U_4358,U_4357,U_4356] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4357,U_4356),U_4359),hAPP(hAPP(c_Set_Oinsert(U_4357),U_4360),U_4358)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4356),hAPP(U_4359,U_4360)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4357,U_4356),U_4359),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4357,tc_HOL_Obool)),U_4358),hAPP(hAPP(c_Set_Oinsert(U_4357),U_4360),c_Orderings_Obot__class_Obot(tc_fun(U_4357,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4357),U_4358))
      | ~ class_Groups_Ocomm__monoid__mult(U_4356) ),
    inference(variable_rename,[status(thm)],[f_1092_1]) ).

cnf(f_1092_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4357,U_4356),U_4359),hAPP(hAPP(c_Set_Oinsert(U_4357),U_4360),U_4358)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4356),hAPP(U_4359,U_4360)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4357,U_4356),U_4359),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4357,tc_HOL_Obool)),U_4358),hAPP(hAPP(c_Set_Oinsert(U_4357),U_4360),c_Orderings_Obot__class_Obot(tc_fun(U_4357,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4357),U_4358))
    | ~ class_Groups_Ocomm__monoid__mult(U_4356) ),
    inference(clausify,[status(thm)],[f_1092_2]) ).

fof(f_1093_1,plain,
    ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setprod_Ounion__disjoint]) ).

fof(f_1093_2,plain,
    ! [U_4365,U_4364,U_4363,U_4362,U_4361] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4362,U_4361),U_4365),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4362,tc_HOL_Obool)),U_4363),U_4364)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4361),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4362,U_4361),U_4365),U_4363)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4362,U_4361),U_4365),U_4364))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4362,tc_HOL_Obool)),U_4363),U_4364) != c_Orderings_Obot__class_Obot(tc_fun(U_4362,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4362),U_4364))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4362),U_4363))
      | ~ class_Groups_Ocomm__monoid__mult(U_4361) ),
    inference(variable_rename,[status(thm)],[f_1093_1]) ).

cnf(f_1093_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4362,U_4361),U_4365),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4362,tc_HOL_Obool)),U_4363),U_4364)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4361),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4362,U_4361),U_4365),U_4363)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4362,U_4361),U_4365),U_4364))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4362,tc_HOL_Obool)),U_4363),U_4364) != c_Orderings_Obot__class_Obot(tc_fun(U_4362,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4362),U_4364))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4362),U_4363))
    | ~ class_Groups_Ocomm__monoid__mult(U_4361) ),
    inference(clausify,[status(thm)],[f_1093_2]) ).

fof(f_1094_1,plain,
    ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__Un__disjoint]) ).

fof(f_1094_2,plain,
    ! [U_4370,U_4369,U_4368,U_4367,U_4366] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4367,U_4366),U_4370),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4367,tc_HOL_Obool)),U_4368),U_4369)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4366),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4367,U_4366),U_4370),U_4368)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4367,U_4366),U_4370),U_4369))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4367,tc_HOL_Obool)),U_4368),U_4369) != c_Orderings_Obot__class_Obot(tc_fun(U_4367,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4367),U_4369))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4367),U_4368))
      | ~ class_Groups_Ocomm__monoid__mult(U_4366) ),
    inference(variable_rename,[status(thm)],[f_1094_1]) ).

cnf(f_1094_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4367,U_4366),U_4370),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4367,tc_HOL_Obool)),U_4368),U_4369)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4366),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4367,U_4366),U_4370),U_4368)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4367,U_4366),U_4370),U_4369))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4367,tc_HOL_Obool)),U_4368),U_4369) != c_Orderings_Obot__class_Obot(tc_fun(U_4367,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4367),U_4369))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4367),U_4368))
    | ~ class_Groups_Ocomm__monoid__mult(U_4366) ),
    inference(clausify,[status(thm)],[f_1094_2]) ).

fof(f_1095_1,plain,
    ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),hAPP(hAPP(V_f_2,V_x_2),V_y_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Diff1__fold__graph]) ).

fof(f_1095_2,plain,
    ! [U_4377,U_4376,U_4375,U_4374,U_4373,U_4372,U_4371] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_4371,U_4372,U_4373,U_4374,U_4375),hAPP(hAPP(U_4373,U_4376),U_4377)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_4371),U_4376),U_4375))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_4371,U_4372,U_4373,U_4374,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4371,tc_HOL_Obool)),U_4375),hAPP(hAPP(c_Set_Oinsert(U_4371),U_4376),c_Orderings_Obot__class_Obot(tc_fun(U_4371,tc_HOL_Obool))))),U_4377)) ),
    inference(variable_rename,[status(thm)],[f_1095_1]) ).

cnf(f_1095_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_4371,U_4372,U_4373,U_4374,U_4375),hAPP(hAPP(U_4373,U_4376),U_4377)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_4371),U_4376),U_4375))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_4371,U_4372,U_4373,U_4374,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4371,tc_HOL_Obool)),U_4375),hAPP(hAPP(c_Set_Oinsert(U_4371),U_4376),c_Orderings_Obot__class_Obot(tc_fun(U_4371,tc_HOL_Obool))))),U_4377)) ),
    inference(clausify,[status(thm)],[f_1095_2]) ).

fof(f_1096_1,plain,
    ! [V_a_2,V_A_2,T_b] :
      ( hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)),V_a_2),V_A_2)
      | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Oab__semigroup__mult(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_fold1__eq__fold]) ).

fof(f_1096_2,plain,
    ! [U_4380,U_4379,U_4378] :
      ( hAPP(c_Finite__Set_Ofold1(U_4378,c_Groups_Otimes__class_Otimes(U_4378)),hAPP(hAPP(c_Set_Oinsert(U_4378),U_4380),U_4379)) = hAPP(hAPP(c_Finite__Set_Ofold(U_4378,U_4378,c_Groups_Otimes__class_Otimes(U_4378)),U_4380),U_4379)
      | hBOOL(hAPP(hAPP(c_member(U_4378),U_4380),U_4379))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4378),U_4379))
      | ~ class_Groups_Oab__semigroup__mult(U_4378) ),
    inference(variable_rename,[status(thm)],[f_1096_1]) ).

cnf(f_1096_3,plain,
    ( hAPP(c_Finite__Set_Ofold1(U_4378,c_Groups_Otimes__class_Otimes(U_4378)),hAPP(hAPP(c_Set_Oinsert(U_4378),U_4380),U_4379)) = hAPP(hAPP(c_Finite__Set_Ofold(U_4378,U_4378,c_Groups_Otimes__class_Otimes(U_4378)),U_4380),U_4379)
    | hBOOL(hAPP(hAPP(c_member(U_4378),U_4380),U_4379))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4378),U_4379))
    | ~ class_Groups_Oab__semigroup__mult(U_4378) ),
    inference(clausify,[status(thm)],[f_1096_2]) ).

fof(f_1097_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_x_2),V_A_2)
      | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oeq__fold_H]) ).

fof(f_1097_2,plain,
    ! [U_4383,U_4382,U_4381] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_4381,hAPP(hAPP(c_Set_Oinsert(U_4381),U_4383),U_4382)) = hAPP(hAPP(c_Finite__Set_Ofold(U_4381,U_4381,c_Lattices_Osemilattice__sup__class_Osup(U_4381)),U_4383),U_4382)
      | hBOOL(hAPP(hAPP(c_member(U_4381),U_4383),U_4382))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4381),U_4382))
      | ~ class_Lattices_Olattice(U_4381) ),
    inference(variable_rename,[status(thm)],[f_1097_1]) ).

cnf(f_1097_3,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_4381,hAPP(hAPP(c_Set_Oinsert(U_4381),U_4383),U_4382)) = hAPP(hAPP(c_Finite__Set_Ofold(U_4381,U_4381,c_Lattices_Osemilattice__sup__class_Osup(U_4381)),U_4383),U_4382)
    | hBOOL(hAPP(hAPP(c_member(U_4381),U_4383),U_4382))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4381),U_4382))
    | ~ class_Lattices_Olattice(U_4381) ),
    inference(clausify,[status(thm)],[f_1097_2]) ).

fof(f_1098_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_x_2),V_A_2)
      | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oeq__fold_H]) ).

fof(f_1098_2,plain,
    ! [U_4386,U_4385,U_4384] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_4384,hAPP(hAPP(c_Set_Oinsert(U_4384),U_4386),U_4385)) = hAPP(hAPP(c_Finite__Set_Ofold(U_4384,U_4384,c_Lattices_Osemilattice__inf__class_Oinf(U_4384)),U_4386),U_4385)
      | hBOOL(hAPP(hAPP(c_member(U_4384),U_4386),U_4385))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4384),U_4385))
      | ~ class_Lattices_Olattice(U_4384) ),
    inference(variable_rename,[status(thm)],[f_1098_1]) ).

cnf(f_1098_3,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_4384,hAPP(hAPP(c_Set_Oinsert(U_4384),U_4386),U_4385)) = hAPP(hAPP(c_Finite__Set_Ofold(U_4384,U_4384,c_Lattices_Osemilattice__inf__class_Oinf(U_4384)),U_4386),U_4385)
    | hBOOL(hAPP(hAPP(c_member(U_4384),U_4386),U_4385))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4384),U_4385))
    | ~ class_Lattices_Olattice(U_4384) ),
    inference(clausify,[status(thm)],[f_1098_2]) ).

fof(f_1099_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_x_2),V_A_2)
      | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Min_Oeq__fold_H]) ).

fof(f_1099_2,plain,
    ! [U_4389,U_4388,U_4387] :
      ( c_Big__Operators_Olinorder__class_OMin(U_4387,hAPP(hAPP(c_Set_Oinsert(U_4387),U_4389),U_4388)) = hAPP(hAPP(c_Finite__Set_Ofold(U_4387,U_4387,c_Orderings_Oord__class_Omin(U_4387)),U_4389),U_4388)
      | hBOOL(hAPP(hAPP(c_member(U_4387),U_4389),U_4388))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4387),U_4388))
      | ~ class_Orderings_Olinorder(U_4387) ),
    inference(variable_rename,[status(thm)],[f_1099_1]) ).

cnf(f_1099_3,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_4387,hAPP(hAPP(c_Set_Oinsert(U_4387),U_4389),U_4388)) = hAPP(hAPP(c_Finite__Set_Ofold(U_4387,U_4387,c_Orderings_Oord__class_Omin(U_4387)),U_4389),U_4388)
    | hBOOL(hAPP(hAPP(c_member(U_4387),U_4389),U_4388))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4387),U_4388))
    | ~ class_Orderings_Olinorder(U_4387) ),
    inference(clausify,[status(thm)],[f_1099_2]) ).

fof(f_1100_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_x_2),V_A_2)
      | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Max_Oeq__fold_H]) ).

fof(f_1100_2,plain,
    ! [U_4392,U_4391,U_4390] :
      ( c_Big__Operators_Olinorder__class_OMax(U_4390,hAPP(hAPP(c_Set_Oinsert(U_4390),U_4392),U_4391)) = hAPP(hAPP(c_Finite__Set_Ofold(U_4390,U_4390,c_Orderings_Oord__class_Omax(U_4390)),U_4392),U_4391)
      | hBOOL(hAPP(hAPP(c_member(U_4390),U_4392),U_4391))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4390),U_4391))
      | ~ class_Orderings_Olinorder(U_4390) ),
    inference(variable_rename,[status(thm)],[f_1100_1]) ).

cnf(f_1100_3,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_4390,hAPP(hAPP(c_Set_Oinsert(U_4390),U_4392),U_4391)) = hAPP(hAPP(c_Finite__Set_Ofold(U_4390,U_4390,c_Orderings_Oord__class_Omax(U_4390)),U_4392),U_4391)
    | hBOOL(hAPP(hAPP(c_member(U_4390),U_4392),U_4391))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4390),U_4391))
    | ~ class_Orderings_Olinorder(U_4390) ),
    inference(clausify,[status(thm)],[f_1100_2]) ).

fof(f_1101_1,plain,
    ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__rec]) ).

fof(f_1101_2,plain,
    ! [U_4398,U_4397,U_4396,U_4395,U_4394,U_4393] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_4393,U_4394,U_4395),U_4398),U_4396) = hAPP(hAPP(U_4395,U_4397),hAPP(hAPP(c_Finite__Set_Ofold(U_4393,U_4394,U_4395),U_4398),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4393,tc_HOL_Obool)),U_4396),hAPP(hAPP(c_Set_Oinsert(U_4393),U_4397),c_Orderings_Obot__class_Obot(tc_fun(U_4393,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_4393),U_4397),U_4396))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4393),U_4396))
      | ~ c_Finite__Set_Ofun__left__comm(U_4393,U_4394,U_4395) ),
    inference(variable_rename,[status(thm)],[f_1101_1]) ).

cnf(f_1101_3,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_4393,U_4394,U_4395),U_4398),U_4396) = hAPP(hAPP(U_4395,U_4397),hAPP(hAPP(c_Finite__Set_Ofold(U_4393,U_4394,U_4395),U_4398),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4393,tc_HOL_Obool)),U_4396),hAPP(hAPP(c_Set_Oinsert(U_4393),U_4397),c_Orderings_Obot__class_Obot(tc_fun(U_4393,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_4393),U_4397),U_4396))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4393),U_4396))
    | ~ c_Finite__Set_Ofun__left__comm(U_4393,U_4394,U_4395) ),
    inference(clausify,[status(thm)],[f_1101_2]) ).

fof(f_1102_1,plain,
    ! [V_x_2,V_A_2,V_a_2,V_f_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),V_x_2))
      | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,V_a_2,V_A_2),V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_fold1Set_Ointros]) ).

fof(f_1102_2,plain,
    ! [U_4403,U_4402,U_4401,U_4400,U_4399] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_4399,U_4400,hAPP(hAPP(c_Set_Oinsert(U_4399),U_4401),U_4402)),U_4403))
      | hBOOL(hAPP(hAPP(c_member(U_4399),U_4401),U_4402))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_4399,U_4399,U_4400,U_4401,U_4402),U_4403)) ),
    inference(variable_rename,[status(thm)],[f_1102_1]) ).

cnf(f_1102_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_4399,U_4400,hAPP(hAPP(c_Set_Oinsert(U_4399),U_4401),U_4402)),U_4403))
    | hBOOL(hAPP(hAPP(c_member(U_4399),U_4401),U_4402))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_4399,U_4399,U_4400,U_4401,U_4402),U_4403)) ),
    inference(clausify,[status(thm)],[f_1102_2]) ).

fof(f_1103_1,plain,
    ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__insert__remove]) ).

fof(f_1103_2,plain,
    ! [U_4409,U_4408,U_4407,U_4406,U_4405,U_4404] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_4404,U_4405,U_4406),U_4408),hAPP(hAPP(c_Set_Oinsert(U_4404),U_4409),U_4407)) = hAPP(hAPP(U_4406,U_4409),hAPP(hAPP(c_Finite__Set_Ofold(U_4404,U_4405,U_4406),U_4408),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4404,tc_HOL_Obool)),U_4407),hAPP(hAPP(c_Set_Oinsert(U_4404),U_4409),c_Orderings_Obot__class_Obot(tc_fun(U_4404,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4404),U_4407))
      | ~ c_Finite__Set_Ofun__left__comm(U_4404,U_4405,U_4406) ),
    inference(variable_rename,[status(thm)],[f_1103_1]) ).

cnf(f_1103_3,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_4404,U_4405,U_4406),U_4408),hAPP(hAPP(c_Set_Oinsert(U_4404),U_4409),U_4407)) = hAPP(hAPP(U_4406,U_4409),hAPP(hAPP(c_Finite__Set_Ofold(U_4404,U_4405,U_4406),U_4408),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4404,tc_HOL_Obool)),U_4407),hAPP(hAPP(c_Set_Oinsert(U_4404),U_4409),c_Orderings_Obot__class_Obot(tc_fun(U_4404,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4404),U_4407))
    | ~ c_Finite__Set_Ofun__left__comm(U_4404,U_4405,U_4406) ),
    inference(clausify,[status(thm)],[f_1103_2]) ).

fof(f_1104_1,plain,
    ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2))
      | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__insert]) ).

fof(f_1104_2,plain,
    ! [U_4415,U_4414,U_4413,U_4412,U_4411,U_4410] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_4410,U_4411,U_4412),U_4415),hAPP(hAPP(c_Set_Oinsert(U_4410),U_4414),U_4413)) = hAPP(hAPP(U_4412,U_4414),hAPP(hAPP(c_Finite__Set_Ofold(U_4410,U_4411,U_4412),U_4415),U_4413))
      | hBOOL(hAPP(hAPP(c_member(U_4410),U_4414),U_4413))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4410),U_4413))
      | ~ c_Finite__Set_Ofun__left__comm(U_4410,U_4411,U_4412) ),
    inference(variable_rename,[status(thm)],[f_1104_1]) ).

cnf(f_1104_3,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_4410,U_4411,U_4412),U_4415),hAPP(hAPP(c_Set_Oinsert(U_4410),U_4414),U_4413)) = hAPP(hAPP(U_4412,U_4414),hAPP(hAPP(c_Finite__Set_Ofold(U_4410,U_4411,U_4412),U_4415),U_4413))
    | hBOOL(hAPP(hAPP(c_member(U_4410),U_4414),U_4413))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4410),U_4413))
    | ~ c_Finite__Set_Ofun__left__comm(U_4410,U_4411,U_4412) ),
    inference(clausify,[status(thm)],[f_1104_2]) ).

fof(f_1105_1,plain,
    ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2)
      | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__insert2]) ).

fof(f_1105_2,plain,
    ! [U_4421,U_4420,U_4419,U_4418,U_4417,U_4416] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_4416,U_4417,U_4418),U_4421),hAPP(hAPP(c_Set_Oinsert(U_4416),U_4420),U_4419)) = hAPP(hAPP(c_Finite__Set_Ofold(U_4416,U_4417,U_4418),hAPP(hAPP(U_4418,U_4420),U_4421)),U_4419)
      | hBOOL(hAPP(hAPP(c_member(U_4416),U_4420),U_4419))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4416),U_4419))
      | ~ c_Finite__Set_Ofun__left__comm(U_4416,U_4417,U_4418) ),
    inference(variable_rename,[status(thm)],[f_1105_1]) ).

cnf(f_1105_3,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_4416,U_4417,U_4418),U_4421),hAPP(hAPP(c_Set_Oinsert(U_4416),U_4420),U_4419)) = hAPP(hAPP(c_Finite__Set_Ofold(U_4416,U_4417,U_4418),hAPP(hAPP(U_4418,U_4420),U_4421)),U_4419)
    | hBOOL(hAPP(hAPP(c_member(U_4416),U_4420),U_4419))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4416),U_4419))
    | ~ c_Finite__Set_Ofun__left__comm(U_4416,U_4417,U_4418) ),
    inference(clausify,[status(thm)],[f_1105_2]) ).

fof(f_1106_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__Diff1__less]) ).

fof(f_1106_2,plain,
    ! [U_4424,U_4423,U_4422] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4422),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4422,tc_HOL_Obool)),U_4423),hAPP(hAPP(c_Set_Oinsert(U_4422),U_4424),c_Orderings_Obot__class_Obot(tc_fun(U_4422,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_4422),U_4423)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_4422),U_4424),U_4423))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4422),U_4423)) ),
    inference(variable_rename,[status(thm)],[f_1106_1]) ).

cnf(f_1106_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4422),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4422,tc_HOL_Obool)),U_4423),hAPP(hAPP(c_Set_Oinsert(U_4422),U_4424),c_Orderings_Obot__class_Obot(tc_fun(U_4422,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_4422),U_4423)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_4422),U_4424),U_4423))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4422),U_4423)) ),
    inference(clausify,[status(thm)],[f_1106_2]) ).

fof(f_1107_1,plain,
    ! [V_y_2,V_x_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__Diff2__less]) ).

fof(f_1107_2,plain,
    ! [U_4428,U_4427,U_4426,U_4425] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4425),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4425,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4425,tc_HOL_Obool)),U_4426),hAPP(hAPP(c_Set_Oinsert(U_4425),U_4427),c_Orderings_Obot__class_Obot(tc_fun(U_4425,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(U_4425),U_4428),c_Orderings_Obot__class_Obot(tc_fun(U_4425,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_4425),U_4426)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_4425),U_4428),U_4426))
      | ~ hBOOL(hAPP(hAPP(c_member(U_4425),U_4427),U_4426))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4425),U_4426)) ),
    inference(variable_rename,[status(thm)],[f_1107_1]) ).

cnf(f_1107_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4425),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4425,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4425,tc_HOL_Obool)),U_4426),hAPP(hAPP(c_Set_Oinsert(U_4425),U_4427),c_Orderings_Obot__class_Obot(tc_fun(U_4425,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(U_4425),U_4428),c_Orderings_Obot__class_Obot(tc_fun(U_4425,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_4425),U_4426)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_4425),U_4428),U_4426))
    | ~ hBOOL(hAPP(hAPP(c_member(U_4425),U_4427),U_4426))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4425),U_4426)) ),
    inference(clausify,[status(thm)],[f_1107_2]) ).

fof(f_1108_1,plain,
    ! [V_z_2,V_y_2,V_x_2,V_f_2,T_c,T_b] :
      ( hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(V_f_2,V_y_2),V_z_2)) = hAPP(hAPP(V_f_2,V_y_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2))
      | ~ c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofun__left__comm]) ).

fof(f_1108_2,plain,
    ! [U_4434,U_4433,U_4432,U_4431,U_4430,U_4429] :
      ( hAPP(hAPP(U_4431,U_4432),hAPP(hAPP(U_4431,U_4433),U_4434)) = hAPP(hAPP(U_4431,U_4433),hAPP(hAPP(U_4431,U_4432),U_4434))
      | ~ c_Finite__Set_Ofun__left__comm(U_4429,U_4430,U_4431) ),
    inference(variable_rename,[status(thm)],[f_1108_1]) ).

fof(f_1108_3,plain,
    ! [U_4434,U_4433,U_4432,U_4431] :
      ( ! [U_4430,U_4429] : ~ c_Finite__Set_Ofun__left__comm(U_4429,U_4430,U_4431)
      | hAPP(hAPP(U_4431,U_4432),hAPP(hAPP(U_4431,U_4433),U_4434)) = hAPP(hAPP(U_4431,U_4433),hAPP(hAPP(U_4431,U_4432),U_4434)) ),
    inference(miniscope,[status(thm)],[f_1108_2]) ).

cnf(f_1108_4,plain,
    ( ~ c_Finite__Set_Ofun__left__comm(U_4429,U_4430,U_4431)
    | hAPP(hAPP(U_4431,U_4432),hAPP(hAPP(U_4431,U_4433),U_4434)) = hAPP(hAPP(U_4431,U_4433),hAPP(hAPP(U_4431,U_4432),U_4434)) ),
    inference(clausify,[status(thm)],[f_1108_3]) ).

fof(f_1109_1,plain,
    ! [V_u_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_u_2)) = V_u_2,
    inference(fof_nnf,[status(thm)],[fact_card__lessThan]) ).

fof(f_1109_2,plain,
    ! [U_4435] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_4435)) = U_4435,
    inference(variable_rename,[status(thm)],[f_1109_1]) ).

cnf(f_1109_3,plain,
    hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_4435)) = U_4435,
    inference(clausify,[status(thm)],[f_1109_2]) ).

fof(f_1110_1,plain,
    ! [T_b] :
      ( c_Finite__Set_Ofun__left__comm(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b))
      | ~ class_Groups_Oab__semigroup__mult(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm]) ).

fof(f_1110_2,plain,
    ! [U_4436] :
      ( c_Finite__Set_Ofun__left__comm(U_4436,U_4436,c_Groups_Otimes__class_Otimes(U_4436))
      | ~ class_Groups_Oab__semigroup__mult(U_4436) ),
    inference(variable_rename,[status(thm)],[f_1110_1]) ).

cnf(f_1110_3,plain,
    ( c_Finite__Set_Ofun__left__comm(U_4436,U_4436,c_Groups_Otimes__class_Otimes(U_4436))
    | ~ class_Groups_Oab__semigroup__mult(U_4436) ),
    inference(clausify,[status(thm)],[f_1110_2]) ).

fof(f_1111_1,plain,
    ! [V_A_2,T_b] :
      ( V_A_2 = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
      | hAPP(c_Finite__Set_Ocard(T_b),V_A_2) != hAPP(c_Finite__Set_Ocard(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ),
    inference(fof_nnf,[status(thm)],[fact_card__eq__UNIV__imp__eq__UNIV]) ).

fof(f_1111_2,plain,
    ! [U_4438,U_4437] :
      ( U_4438 = c_Orderings_Otop__class_Otop(tc_fun(U_4437,tc_HOL_Obool))
      | hAPP(c_Finite__Set_Ocard(U_4437),U_4438) != hAPP(c_Finite__Set_Ocard(U_4437),c_Orderings_Otop__class_Otop(tc_fun(U_4437,tc_HOL_Obool)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4437),c_Orderings_Otop__class_Otop(tc_fun(U_4437,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_1111_1]) ).

cnf(f_1111_3,plain,
    ( U_4438 = c_Orderings_Otop__class_Otop(tc_fun(U_4437,tc_HOL_Obool))
    | hAPP(c_Finite__Set_Ocard(U_4437),U_4438) != hAPP(c_Finite__Set_Ocard(U_4437),c_Orderings_Otop__class_Otop(tc_fun(U_4437,tc_HOL_Obool)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4437),c_Orderings_Otop__class_Otop(tc_fun(U_4437,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_1111_2]) ).

fof(f_1112_1,plain,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2)
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_card__image]) ).

fof(f_1112_2,plain,
    ! [U_4442,U_4441,U_4440,U_4439] :
      ( hAPP(c_Finite__Set_Ocard(U_4440),hAPP(c_Set_Oimage(U_4439,U_4440,U_4441),U_4442)) = hAPP(c_Finite__Set_Ocard(U_4439),U_4442)
      | ~ c_Fun_Oinj__on(U_4439,U_4440,U_4441,U_4442) ),
    inference(variable_rename,[status(thm)],[f_1112_1]) ).

cnf(f_1112_3,plain,
    ( hAPP(c_Finite__Set_Ocard(U_4440),hAPP(c_Set_Oimage(U_4439,U_4440,U_4441),U_4442)) = hAPP(c_Finite__Set_Ocard(U_4439),U_4442)
    | ~ c_Fun_Oinj__on(U_4439,U_4440,U_4441,U_4442) ),
    inference(clausify,[status(thm)],[f_1112_2]) ).

fof(f_1113_1,plain,
    ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
      ( V_y_2 = V_x_2
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_x_2))
      | ~ c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__graph__determ]) ).

fof(f_1113_2,plain,
    ! [U_4449,U_4448,U_4447,U_4446,U_4445,U_4444,U_4443] :
      ( U_4449 = U_4448
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_4443,U_4444,U_4445,U_4446,U_4447),U_4449))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_4443,U_4444,U_4445,U_4446,U_4447),U_4448))
      | ~ c_Finite__Set_Ofun__left__comm(U_4443,U_4444,U_4445) ),
    inference(variable_rename,[status(thm)],[f_1113_1]) ).

cnf(f_1113_3,plain,
    ( U_4449 = U_4448
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_4443,U_4444,U_4445,U_4446,U_4447),U_4449))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_4443,U_4444,U_4445,U_4446,U_4447),U_4448))
    | ~ c_Finite__Set_Ofun__left__comm(U_4443,U_4444,U_4445) ),
    inference(clausify,[status(thm)],[f_1113_2]) ).

fof(f_1114_1,plain,
    ! [V_x_2,V_f_2,T_b] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_x_2)),
    inference(fof_nnf,[status(thm)],[fact_empty__fold1SetE]) ).

fof(f_1114_2,plain,
    ! [U_4452,U_4451,U_4450] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_4450,U_4451,c_Orderings_Obot__class_Obot(tc_fun(U_4450,tc_HOL_Obool))),U_4452)),
    inference(variable_rename,[status(thm)],[f_1114_1]) ).

cnf(f_1114_3,plain,
    ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_4450,U_4451,c_Orderings_Obot__class_Obot(tc_fun(U_4450,tc_HOL_Obool))),U_4452)),
    inference(clausify,[status(thm)],[f_1114_2]) ).

fof(f_1115_1,plain,
    ! [V_x_2,V_A_2,V_f_2,T_b] :
      ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,V_A_2),V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_fold1Set__nonempty]) ).

fof(f_1115_2,plain,
    ! [U_4456,U_4455,U_4454,U_4453] :
      ( U_4455 != c_Orderings_Obot__class_Obot(tc_fun(U_4453,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_4453,U_4454,U_4455),U_4456)) ),
    inference(variable_rename,[status(thm)],[f_1115_1]) ).

cnf(f_1115_3,plain,
    ( U_4455 != c_Orderings_Obot__class_Obot(tc_fun(U_4453,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_4453,U_4454,U_4455),U_4456)) ),
    inference(clausify,[status(thm)],[f_1115_2]) ).

fof(f_1116_1,plain,
    ! [V_k_2,V_A_2] :
      ( V_A_2 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),V_A_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),V_A_2))))) ),
    inference(fof_nnf,[status(thm)],[fact_subset__card__intvl__is__intvl]) ).

fof(f_1116_2,plain,
    ! [U_4458,U_4457] :
      ( U_4457 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_4458),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4458),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_4457)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_4457),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_4458),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4458),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_4457))))) ),
    inference(variable_rename,[status(thm)],[f_1116_1]) ).

cnf(f_1116_3,plain,
    ( U_4457 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_4458),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4458),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_4457)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_4457),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_4458),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4458),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_4457))))) ),
    inference(clausify,[status(thm)],[f_1116_2]) ).

fof(f_1117_1,plain,
    ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_l_2),V_u_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_u_2),V_l_2),
    inference(fof_nnf,[status(thm)],[fact_card__atLeastLessThan]) ).

fof(f_1117_2,plain,
    ! [U_4460,U_4459] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_4459),U_4460)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4460),U_4459),
    inference(variable_rename,[status(thm)],[f_1117_1]) ).

cnf(f_1117_3,plain,
    hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_4459),U_4460)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4460),U_4459),
    inference(clausify,[status(thm)],[f_1117_2]) ).

fof(f_1118_1,plain,
    ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_l_2,V_u_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_u_2),V_l_2),
    inference(fof_nnf,[status(thm)],[fact_card__greaterThanAtMost]) ).

fof(f_1118_2,plain,
    ! [U_4462,U_4461] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_4461,U_4462)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4462),U_4461),
    inference(variable_rename,[status(thm)],[f_1118_1]) ).

cnf(f_1118_3,plain,
    hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_4461,U_4462)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4462),U_4461),
    inference(clausify,[status(thm)],[f_1118_2]) ).

fof(f_1119_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__insert__le]) ).

fof(f_1119_2,plain,
    ! [U_4465,U_4464,U_4463] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4463),U_4464)),hAPP(c_Finite__Set_Ocard(U_4463),hAPP(hAPP(c_Set_Oinsert(U_4463),U_4465),U_4464))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4463),U_4464)) ),
    inference(variable_rename,[status(thm)],[f_1119_1]) ).

cnf(f_1119_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4463),U_4464)),hAPP(c_Finite__Set_Ocard(U_4463),hAPP(hAPP(c_Set_Oinsert(U_4463),U_4465),U_4464))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4463),U_4464)) ),
    inference(clausify,[status(thm)],[f_1119_2]) ).

fof(f_1120_1,plain,
    ! [V_A_2,V_B_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__mono]) ).

fof(f_1120_2,plain,
    ! [U_4468,U_4467,U_4466] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4466),U_4468)),hAPP(c_Finite__Set_Ocard(U_4466),U_4467)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4466,tc_HOL_Obool)),U_4468),U_4467))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4466),U_4467)) ),
    inference(variable_rename,[status(thm)],[f_1120_1]) ).

cnf(f_1120_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4466),U_4468)),hAPP(c_Finite__Set_Ocard(U_4466),U_4467)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4466,tc_HOL_Obool)),U_4468),U_4467))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4466),U_4467)) ),
    inference(clausify,[status(thm)],[f_1120_2]) ).

fof(f_1121_1,plain,
    ! [V_A_2,V_B_2,T_b] :
      ( V_A_2 = V_B_2
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__seteq]) ).

fof(f_1121_2,plain,
    ! [U_4471,U_4470,U_4469] :
      ( U_4471 = U_4470
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4469),U_4470)),hAPP(c_Finite__Set_Ocard(U_4469),U_4471)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4469,tc_HOL_Obool)),U_4471),U_4470))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4469),U_4470)) ),
    inference(variable_rename,[status(thm)],[f_1121_1]) ).

cnf(f_1121_3,plain,
    ( U_4471 = U_4470
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4469),U_4470)),hAPP(c_Finite__Set_Ocard(U_4469),U_4471)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4469,tc_HOL_Obool)),U_4471),U_4470))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4469),U_4470)) ),
    inference(clausify,[status(thm)],[f_1121_2]) ).

fof(f_1122_1,plain,
    ! [V_f_2,T_c,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__image__le]) ).

fof(f_1122_2,plain,
    ! [U_4475,U_4474,U_4473,U_4472] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4474),hAPP(c_Set_Oimage(U_4472,U_4474,U_4475),U_4473))),hAPP(c_Finite__Set_Ocard(U_4472),U_4473)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4472),U_4473)) ),
    inference(variable_rename,[status(thm)],[f_1122_1]) ).

cnf(f_1122_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4474),hAPP(c_Set_Oimage(U_4472,U_4474,U_4475),U_4473))),hAPP(c_Finite__Set_Ocard(U_4472),U_4473)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4472),U_4473)) ),
    inference(clausify,[status(thm)],[f_1122_2]) ).

fof(f_1123_1,plain,
    ! [V_f_2,T_c,V_A_2,T_b] :
      ( ( ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
          | hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) != hAPP(c_Finite__Set_Ocard(T_b),V_A_2) )
        & ( hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2)
          | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_inj__on__iff__eq__card]) ).

fof(f_1123_2,plain,
    ! [U_4479,U_4478,U_4477,U_4476] :
      ( ( ( c_Fun_Oinj__on(U_4476,U_4478,U_4479,U_4477)
          | hAPP(c_Finite__Set_Ocard(U_4478),hAPP(c_Set_Oimage(U_4476,U_4478,U_4479),U_4477)) != hAPP(c_Finite__Set_Ocard(U_4476),U_4477) )
        & ( hAPP(c_Finite__Set_Ocard(U_4478),hAPP(c_Set_Oimage(U_4476,U_4478,U_4479),U_4477)) = hAPP(c_Finite__Set_Ocard(U_4476),U_4477)
          | ~ c_Fun_Oinj__on(U_4476,U_4478,U_4479,U_4477) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4476),U_4477)) ),
    inference(variable_rename,[status(thm)],[f_1123_1]) ).

cnf(f_1123_3,plain,
    ( hAPP(c_Finite__Set_Ocard(U_4478),hAPP(c_Set_Oimage(U_4476,U_4478,U_4479),U_4477)) = hAPP(c_Finite__Set_Ocard(U_4476),U_4477)
    | ~ c_Fun_Oinj__on(U_4476,U_4478,U_4479,U_4477)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4476),U_4477)) ),
    inference(clausify,[status(thm)],[f_1123_2]) ).

cnf(f_1123_4,plain,
    ( c_Fun_Oinj__on(U_4476,U_4478,U_4479,U_4477)
    | hAPP(c_Finite__Set_Ocard(U_4478),hAPP(c_Set_Oimage(U_4476,U_4478,U_4479),U_4477)) != hAPP(c_Finite__Set_Ocard(U_4476),U_4477)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4476),U_4477)) ),
    inference(clausify,[status(thm)],[f_1123_2]) ).

fof(f_1124_1,plain,
    ! [V_f_2,T_c,V_A_2,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
      | hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) != hAPP(c_Finite__Set_Ocard(T_b),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_eq__card__imp__inj__on]) ).

fof(f_1124_2,plain,
    ! [U_4483,U_4482,U_4481,U_4480] :
      ( c_Fun_Oinj__on(U_4480,U_4482,U_4483,U_4481)
      | hAPP(c_Finite__Set_Ocard(U_4482),hAPP(c_Set_Oimage(U_4480,U_4482,U_4483),U_4481)) != hAPP(c_Finite__Set_Ocard(U_4480),U_4481)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4480),U_4481)) ),
    inference(variable_rename,[status(thm)],[f_1124_1]) ).

cnf(f_1124_3,plain,
    ( c_Fun_Oinj__on(U_4480,U_4482,U_4483,U_4481)
    | hAPP(c_Finite__Set_Ocard(U_4482),hAPP(c_Set_Oimage(U_4480,U_4482,U_4483),U_4481)) != hAPP(c_Finite__Set_Ocard(U_4480),U_4481)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4480),U_4481)) ),
    inference(clausify,[status(thm)],[f_1124_2]) ).

fof(f_1125_1,plain,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( ~ c_Fun_Oinj__on(T_c,T_b,V_f_2,V_A_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))),hAPP(c_Finite__Set_Ocard(T_c),V_A_2))) ),
    inference(fof_nnf,[status(thm)],[fact_pigeonhole]) ).

fof(f_1125_2,plain,
    ! [U_4487,U_4486,U_4485,U_4484] :
      ( ~ c_Fun_Oinj__on(U_4485,U_4484,U_4486,U_4487)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4484),hAPP(c_Set_Oimage(U_4485,U_4484,U_4486),U_4487))),hAPP(c_Finite__Set_Ocard(U_4485),U_4487))) ),
    inference(variable_rename,[status(thm)],[f_1125_1]) ).

cnf(f_1125_3,plain,
    ( ~ c_Fun_Oinj__on(U_4485,U_4484,U_4486,U_4487)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4484),hAPP(c_Set_Oimage(U_4485,U_4484,U_4486),U_4487))),hAPP(c_Finite__Set_Ocard(U_4485),U_4487))) ),
    inference(clausify,[status(thm)],[f_1125_2]) ).

fof(f_1126_1,plain,
    ! [V_A_2,V_B_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_psubset__card__mono]) ).

fof(f_1126_2,plain,
    ! [U_4490,U_4489,U_4488] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4488),U_4490)),hAPP(c_Finite__Set_Ocard(U_4488),U_4489)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_4488,tc_HOL_Obool)),U_4490),U_4489))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4488),U_4489)) ),
    inference(variable_rename,[status(thm)],[f_1126_1]) ).

cnf(f_1126_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4488),U_4490)),hAPP(c_Finite__Set_Ocard(U_4488),U_4489)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_4488,tc_HOL_Obool)),U_4490),U_4489))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4488),U_4489)) ),
    inference(clausify,[status(thm)],[f_1126_2]) ).

fof(f_1127_1,plain,
    ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
      ( hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__fun__comm]) ).

fof(f_1127_2,plain,
    ! [U_4496,U_4495,U_4494,U_4493,U_4492,U_4491] :
      ( hAPP(hAPP(U_4493,U_4495),hAPP(hAPP(c_Finite__Set_Ofold(U_4491,U_4492,U_4493),U_4496),U_4494)) = hAPP(hAPP(c_Finite__Set_Ofold(U_4491,U_4492,U_4493),hAPP(hAPP(U_4493,U_4495),U_4496)),U_4494)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4491),U_4494))
      | ~ c_Finite__Set_Ofun__left__comm(U_4491,U_4492,U_4493) ),
    inference(variable_rename,[status(thm)],[f_1127_1]) ).

cnf(f_1127_3,plain,
    ( hAPP(hAPP(U_4493,U_4495),hAPP(hAPP(c_Finite__Set_Ofold(U_4491,U_4492,U_4493),U_4496),U_4494)) = hAPP(hAPP(c_Finite__Set_Ofold(U_4491,U_4492,U_4493),hAPP(hAPP(U_4493,U_4495),U_4496)),U_4494)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4491),U_4494))
    | ~ c_Finite__Set_Ofun__left__comm(U_4491,U_4492,U_4493) ),
    inference(clausify,[status(thm)],[f_1127_2]) ).

fof(f_1128_1,plain,
    ! [V_y_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2) = V_y_2
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
      | ~ c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__equality]) ).

fof(f_1128_2,plain,
    ! [U_4502,U_4501,U_4500,U_4499,U_4498,U_4497] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_4497,U_4498,U_4499),U_4500),U_4501) = U_4502
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_4497,U_4498,U_4499,U_4500,U_4501),U_4502))
      | ~ c_Finite__Set_Ofun__left__comm(U_4497,U_4498,U_4499) ),
    inference(variable_rename,[status(thm)],[f_1128_1]) ).

cnf(f_1128_3,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_4497,U_4498,U_4499),U_4500),U_4501) = U_4502
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_4497,U_4498,U_4499,U_4500,U_4501),U_4502))
    | ~ c_Finite__Set_Ofun__left__comm(U_4497,U_4498,U_4499) ),
    inference(clausify,[status(thm)],[f_1128_2]) ).

fof(f_1129_1,plain,
    ! [V_b_2,V_a_2,V_f_2,T_b] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_b_2))
        | V_a_2 != V_b_2 )
      & ( V_a_2 = V_b_2
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_b_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_fold1Set__sing]) ).

fof(f_1129_2,plain,
    ! [U_4506,U_4505,U_4504,U_4503] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_4503,U_4504,hAPP(hAPP(c_Set_Oinsert(U_4503),U_4505),c_Orderings_Obot__class_Obot(tc_fun(U_4503,tc_HOL_Obool)))),U_4506))
        | U_4505 != U_4506 )
      & ( U_4505 = U_4506
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_4503,U_4504,hAPP(hAPP(c_Set_Oinsert(U_4503),U_4505),c_Orderings_Obot__class_Obot(tc_fun(U_4503,tc_HOL_Obool)))),U_4506)) ) ),
    inference(variable_rename,[status(thm)],[f_1129_1]) ).

fof(f_1129_3,plain,
    ( ! [U_4514,U_4512] :
        ( ! [U_4510,U_4508] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_4508,U_4510,hAPP(hAPP(c_Set_Oinsert(U_4508),U_4512),c_Orderings_Obot__class_Obot(tc_fun(U_4508,tc_HOL_Obool)))),U_4514))
        | U_4512 != U_4514 )
    & ! [U_4513,U_4511] :
        ( ! [U_4509,U_4507] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_4507,U_4509,hAPP(hAPP(c_Set_Oinsert(U_4507),U_4511),c_Orderings_Obot__class_Obot(tc_fun(U_4507,tc_HOL_Obool)))),U_4513))
        | U_4511 = U_4513 ) ),
    inference(miniscope,[status(thm)],[f_1129_2]) ).

cnf(f_1129_4,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_4507,U_4509,hAPP(hAPP(c_Set_Oinsert(U_4507),U_4511),c_Orderings_Obot__class_Obot(tc_fun(U_4507,tc_HOL_Obool)))),U_4513))
    | U_4511 = U_4513 ),
    inference(clausify,[status(thm)],[f_1129_3]) ).

cnf(f_1129_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_4508,U_4510,hAPP(hAPP(c_Set_Oinsert(U_4508),U_4512),c_Orderings_Obot__class_Obot(tc_fun(U_4508,tc_HOL_Obool)))),U_4514))
    | U_4512 != U_4514 ),
    inference(clausify,[status(thm)],[f_1129_3]) ).

fof(f_1130_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card_Ounion__inter]) ).

fof(f_1130_2,plain,
    ! [U_4517,U_4516,U_4515] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4515),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4515,tc_HOL_Obool)),U_4516),U_4517))),hAPP(c_Finite__Set_Ocard(U_4515),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4515,tc_HOL_Obool)),U_4516),U_4517))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4515),U_4516)),hAPP(c_Finite__Set_Ocard(U_4515),U_4517))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4515),U_4517))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4515),U_4516)) ),
    inference(variable_rename,[status(thm)],[f_1130_1]) ).

cnf(f_1130_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4515),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4515,tc_HOL_Obool)),U_4516),U_4517))),hAPP(c_Finite__Set_Ocard(U_4515),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4515,tc_HOL_Obool)),U_4516),U_4517))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4515),U_4516)),hAPP(c_Finite__Set_Ocard(U_4515),U_4517))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4515),U_4517))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4515),U_4516)) ),
    inference(clausify,[status(thm)],[f_1130_2]) ).

fof(f_1131_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__Un__Int]) ).

fof(f_1131_2,plain,
    ! [U_4520,U_4519,U_4518] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4518),U_4519)),hAPP(c_Finite__Set_Ocard(U_4518),U_4520)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4518),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4518,tc_HOL_Obool)),U_4519),U_4520))),hAPP(c_Finite__Set_Ocard(U_4518),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4518,tc_HOL_Obool)),U_4519),U_4520)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4518),U_4520))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4518),U_4519)) ),
    inference(variable_rename,[status(thm)],[f_1131_1]) ).

cnf(f_1131_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4518),U_4519)),hAPP(c_Finite__Set_Ocard(U_4518),U_4520)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4518),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4518,tc_HOL_Obool)),U_4519),U_4520))),hAPP(c_Finite__Set_Ocard(U_4518),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4518,tc_HOL_Obool)),U_4519),U_4520)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4518),U_4520))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4518),U_4519)) ),
    inference(clausify,[status(thm)],[f_1131_2]) ).

fof(f_1132_1,plain,
    ! [V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_g_2),V_B_2)),V_A_2))
      | ~ c_Fun_Oinj__on(T_c,T_b,V_g_2,V_B_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),V_B_2))
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_card__bij__eq]) ).

fof(f_1132_2,plain,
    ! [U_4526,U_4525,U_4524,U_4523,U_4522,U_4521] :
      ( hAPP(c_Finite__Set_Ocard(U_4521),U_4524) = hAPP(c_Finite__Set_Ocard(U_4522),U_4525)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4522),U_4525))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4521),U_4524))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4521,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_4522,U_4521,U_4526),U_4525)),U_4524))
      | ~ c_Fun_Oinj__on(U_4522,U_4521,U_4526,U_4525)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4522,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_4521,U_4522,U_4523),U_4524)),U_4525))
      | ~ c_Fun_Oinj__on(U_4521,U_4522,U_4523,U_4524) ),
    inference(variable_rename,[status(thm)],[f_1132_1]) ).

cnf(f_1132_3,plain,
    ( hAPP(c_Finite__Set_Ocard(U_4521),U_4524) = hAPP(c_Finite__Set_Ocard(U_4522),U_4525)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4522),U_4525))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4521),U_4524))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4521,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_4522,U_4521,U_4526),U_4525)),U_4524))
    | ~ c_Fun_Oinj__on(U_4522,U_4521,U_4526,U_4525)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4522,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_4521,U_4522,U_4523),U_4524)),U_4525))
    | ~ c_Fun_Oinj__on(U_4521,U_4522,U_4523,U_4524) ),
    inference(clausify,[status(thm)],[f_1132_2]) ).

fof(f_1133_1,plain,
    ! [V_A_2,V_B_2,T_b] :
      ( hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__Diff__subset]) ).

fof(f_1133_2,plain,
    ! [U_4529,U_4528,U_4527] :
      ( hAPP(c_Finite__Set_Ocard(U_4527),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4527,tc_HOL_Obool)),U_4529),U_4528)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4527),U_4529)),hAPP(c_Finite__Set_Ocard(U_4527),U_4528))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4527,tc_HOL_Obool)),U_4528),U_4529))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4527),U_4528)) ),
    inference(variable_rename,[status(thm)],[f_1133_1]) ).

cnf(f_1133_3,plain,
    ( hAPP(c_Finite__Set_Ocard(U_4527),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4527,tc_HOL_Obool)),U_4529),U_4528)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4527),U_4529)),hAPP(c_Finite__Set_Ocard(U_4527),U_4528))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4527,tc_HOL_Obool)),U_4528),U_4529))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4527),U_4528)) ),
    inference(clausify,[status(thm)],[f_1133_2]) ).

fof(f_1134_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ),
    inference(fof_nnf,[status(thm)],[fact_card__Diff__subset__Int]) ).

fof(f_1134_2,plain,
    ! [U_4532,U_4531,U_4530] :
      ( hAPP(c_Finite__Set_Ocard(U_4530),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4530,tc_HOL_Obool)),U_4531),U_4532)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4530),U_4531)),hAPP(c_Finite__Set_Ocard(U_4530),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4530,tc_HOL_Obool)),U_4531),U_4532)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4530),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4530,tc_HOL_Obool)),U_4531),U_4532))) ),
    inference(variable_rename,[status(thm)],[f_1134_1]) ).

cnf(f_1134_3,plain,
    ( hAPP(c_Finite__Set_Ocard(U_4530),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4530,tc_HOL_Obool)),U_4531),U_4532)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4530),U_4531)),hAPP(c_Finite__Set_Ocard(U_4530),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4530,tc_HOL_Obool)),U_4531),U_4532)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4530),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4530,tc_HOL_Obool)),U_4531),U_4532))) ),
    inference(clausify,[status(thm)],[f_1134_2]) ).

fof(f_1135_1,plain,
    ! [V_A_2,V_B_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_diff__card__le__card__Diff]) ).

fof(f_1135_2,plain,
    ! [U_4535,U_4534,U_4533] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4533),U_4535)),hAPP(c_Finite__Set_Ocard(U_4533),U_4534))),hAPP(c_Finite__Set_Ocard(U_4533),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4533,tc_HOL_Obool)),U_4535),U_4534))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4533),U_4534)) ),
    inference(variable_rename,[status(thm)],[f_1135_1]) ).

cnf(f_1135_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4533),U_4535)),hAPP(c_Finite__Set_Ocard(U_4533),U_4534))),hAPP(c_Finite__Set_Ocard(U_4533),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4533,tc_HOL_Obool)),U_4535),U_4534))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4533),U_4534)) ),
    inference(clausify,[status(thm)],[f_1135_2]) ).

fof(f_1136_1,plain,
    ! [V_A_2,V_B_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__psubset]) ).

fof(f_1136_2,plain,
    ! [U_4538,U_4537,U_4536] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_4536,tc_HOL_Obool)),U_4538),U_4537))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4536),U_4538)),hAPP(c_Finite__Set_Ocard(U_4536),U_4537)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4536,tc_HOL_Obool)),U_4538),U_4537))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4536),U_4537)) ),
    inference(variable_rename,[status(thm)],[f_1136_1]) ).

cnf(f_1136_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_4536,tc_HOL_Obool)),U_4538),U_4537))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4536),U_4538)),hAPP(c_Finite__Set_Ocard(U_4536),U_4537)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4536,tc_HOL_Obool)),U_4538),U_4537))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4536),U_4537)) ),
    inference(clausify,[status(thm)],[f_1136_2]) ).

fof(f_1137_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__Un__disjoint]) ).

fof(f_1137_2,plain,
    ! [U_4541,U_4540,U_4539] :
      ( hAPP(c_Finite__Set_Ocard(U_4539),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4539,tc_HOL_Obool)),U_4540),U_4541)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4539),U_4540)),hAPP(c_Finite__Set_Ocard(U_4539),U_4541))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4539,tc_HOL_Obool)),U_4540),U_4541) != c_Orderings_Obot__class_Obot(tc_fun(U_4539,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4539),U_4541))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4539),U_4540)) ),
    inference(variable_rename,[status(thm)],[f_1137_1]) ).

cnf(f_1137_3,plain,
    ( hAPP(c_Finite__Set_Ocard(U_4539),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4539,tc_HOL_Obool)),U_4540),U_4541)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4539),U_4540)),hAPP(c_Finite__Set_Ocard(U_4539),U_4541))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4539,tc_HOL_Obool)),U_4540),U_4541) != c_Orderings_Obot__class_Obot(tc_fun(U_4539,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4539),U_4541))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4539),U_4540)) ),
    inference(clausify,[status(thm)],[f_1137_2]) ).

fof(f_1138_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__Diff1__le]) ).

fof(f_1138_2,plain,
    ! [U_4544,U_4543,U_4542] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4542),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4542,tc_HOL_Obool)),U_4543),hAPP(hAPP(c_Set_Oinsert(U_4542),U_4544),c_Orderings_Obot__class_Obot(tc_fun(U_4542,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_4542),U_4543)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4542),U_4543)) ),
    inference(variable_rename,[status(thm)],[f_1138_1]) ).

cnf(f_1138_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4542),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4542,tc_HOL_Obool)),U_4543),hAPP(hAPP(c_Set_Oinsert(U_4542),U_4544),c_Orderings_Obot__class_Obot(tc_fun(U_4542,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_4542),U_4543)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4542),U_4543)) ),
    inference(clausify,[status(thm)],[f_1138_2]) ).

fof(f_1139_1,plain,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),V_B_2))
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_card__inj__on__le]) ).

fof(f_1139_2,plain,
    ! [U_4549,U_4548,U_4547,U_4546,U_4545] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4545),U_4548)),hAPP(c_Finite__Set_Ocard(U_4546),U_4549)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4546),U_4549))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4546,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_4545,U_4546,U_4547),U_4548)),U_4549))
      | ~ c_Fun_Oinj__on(U_4545,U_4546,U_4547,U_4548) ),
    inference(variable_rename,[status(thm)],[f_1139_1]) ).

cnf(f_1139_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4545),U_4548)),hAPP(c_Finite__Set_Ocard(U_4546),U_4549)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4546),U_4549))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4546,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_4545,U_4546,U_4547),U_4548)),U_4549))
    | ~ c_Fun_Oinj__on(U_4545,U_4546,U_4547,U_4548) ),
    inference(clausify,[status(thm)],[f_1139_2]) ).

fof(f_1140_1,plain,
    ! [V_B_2,T_c,V_A_2,T_b] :
      ( ( ( ? [B_f] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,B_f),V_A_2)),V_B_2))
              & c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2)))
          | ! [B_f] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,B_f),V_A_2)),V_B_2))
              | ~ c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2) ) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_inj__on__iff__card__le]) ).

fof(f_1140_2,plain,
    ! [U_4555,U_4554,U_4553,U_4552] :
      ( ( ( ? [U_4551] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4554,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_4552,U_4554,U_4551),U_4553)),U_4555))
              & c_Fun_Oinj__on(U_4552,U_4554,U_4551,U_4553) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4552),U_4553)),hAPP(c_Finite__Set_Ocard(U_4554),U_4555))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4552),U_4553)),hAPP(c_Finite__Set_Ocard(U_4554),U_4555)))
          | ! [U_4550] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4554,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_4552,U_4554,U_4550),U_4553)),U_4555))
              | ~ c_Fun_Oinj__on(U_4552,U_4554,U_4550,U_4553) ) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4554),U_4555))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4552),U_4553)) ),
    inference(variable_rename,[status(thm)],[f_1140_1]) ).

fof(f_1140_3,plain,
    ! [U_4555,U_4554,U_4553,U_4552] :
      ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4554,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_4552,U_4554,sK91(U_4555,U_4554,U_4553,U_4552)),U_4553)),U_4555))
            & c_Fun_Oinj__on(U_4552,U_4554,sK91(U_4555,U_4554,U_4553,U_4552),U_4553) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4552),U_4553)),hAPP(c_Finite__Set_Ocard(U_4554),U_4555))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4552),U_4553)),hAPP(c_Finite__Set_Ocard(U_4554),U_4555)))
          | ! [U_4550] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4554,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_4552,U_4554,U_4550),U_4553)),U_4555))
              | ~ c_Fun_Oinj__on(U_4552,U_4554,U_4550,U_4553) ) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4554),U_4555))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4552),U_4553)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK91]),skolemize(U_4551,sK91(U_4555,U_4554,U_4553,U_4552))],[f_1140_2]) ).

cnf(f_1140_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4552),U_4553)),hAPP(c_Finite__Set_Ocard(U_4554),U_4555)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4554,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_4552,U_4554,U_4550),U_4553)),U_4555))
    | ~ c_Fun_Oinj__on(U_4552,U_4554,U_4550,U_4553)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4554),U_4555))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4552),U_4553)) ),
    inference(clausify,[status(thm)],[f_1140_3]) ).

cnf(f_1140_5,plain,
    ( c_Fun_Oinj__on(U_4552,U_4554,sK91(U_4555,U_4554,U_4553,U_4552),U_4553)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4552),U_4553)),hAPP(c_Finite__Set_Ocard(U_4554),U_4555)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4554),U_4555))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4552),U_4553)) ),
    inference(clausify,[status(thm)],[f_1140_3]) ).

cnf(f_1140_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4554,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_4552,U_4554,sK91(U_4555,U_4554,U_4553,U_4552)),U_4553)),U_4555))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4552),U_4553)),hAPP(c_Finite__Set_Ocard(U_4554),U_4555)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4554),U_4555))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4552),U_4553)) ),
    inference(clausify,[status(thm)],[f_1140_3]) ).

fof(f_1141_1,plain,
    ! [V_z_2,V_A_2,V_f_2,T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__graph__fold]) ).

fof(f_1141_2,plain,
    ! [U_4560,U_4559,U_4558,U_4557,U_4556] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_4556,U_4557,U_4558,U_4560,U_4559),hAPP(hAPP(c_Finite__Set_Ofold(U_4556,U_4557,U_4558),U_4560),U_4559)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4556),U_4559))
      | ~ c_Finite__Set_Ofun__left__comm(U_4556,U_4557,U_4558) ),
    inference(variable_rename,[status(thm)],[f_1141_1]) ).

cnf(f_1141_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_4556,U_4557,U_4558,U_4560,U_4559),hAPP(hAPP(c_Finite__Set_Ofold(U_4556,U_4557,U_4558),U_4560),U_4559)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4556),U_4559))
    | ~ c_Finite__Set_Ofun__left__comm(U_4556,U_4557,U_4558) ),
    inference(clausify,[status(thm)],[f_1141_2]) ).

fof(f_1142_1,plain,
    ! [V_a_2,V_y_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
      ( ? [B_y_H] :
          ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),B_y_H))
          & V_y_2 = hAPP(hAPP(V_f_2,V_a_2),B_y_H) )
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
      | ~ c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__graph__insertE__aux]) ).

fof(f_1142_2,plain,
    ! [U_4568,U_4567,U_4566,U_4565,U_4564,U_4563,U_4562] :
      ( ? [U_4561] :
          ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_4562,U_4563,U_4564,U_4565,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4562,tc_HOL_Obool)),U_4566),hAPP(hAPP(c_Set_Oinsert(U_4562),U_4568),c_Orderings_Obot__class_Obot(tc_fun(U_4562,tc_HOL_Obool))))),U_4561))
          & U_4567 = hAPP(hAPP(U_4564,U_4568),U_4561) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_4562),U_4568),U_4566))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_4562,U_4563,U_4564,U_4565,U_4566),U_4567))
      | ~ c_Finite__Set_Ofun__left__comm(U_4562,U_4563,U_4564) ),
    inference(variable_rename,[status(thm)],[f_1142_1]) ).

fof(f_1142_3,plain,
    ! [U_4568,U_4567,U_4566,U_4565,U_4564,U_4563,U_4562] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_4562,U_4563,U_4564,U_4565,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4562,tc_HOL_Obool)),U_4566),hAPP(hAPP(c_Set_Oinsert(U_4562),U_4568),c_Orderings_Obot__class_Obot(tc_fun(U_4562,tc_HOL_Obool))))),sK92(U_4568,U_4567,U_4566,U_4565,U_4564,U_4563,U_4562)))
        & U_4567 = hAPP(hAPP(U_4564,U_4568),sK92(U_4568,U_4567,U_4566,U_4565,U_4564,U_4563,U_4562)) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_4562),U_4568),U_4566))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_4562,U_4563,U_4564,U_4565,U_4566),U_4567))
      | ~ c_Finite__Set_Ofun__left__comm(U_4562,U_4563,U_4564) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK92]),skolemize(U_4561,sK92(U_4568,U_4567,U_4566,U_4565,U_4564,U_4563,U_4562))],[f_1142_2]) ).

cnf(f_1142_4,plain,
    ( U_4567 = hAPP(hAPP(U_4564,U_4568),sK92(U_4568,U_4567,U_4566,U_4565,U_4564,U_4563,U_4562))
    | ~ hBOOL(hAPP(hAPP(c_member(U_4562),U_4568),U_4566))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_4562,U_4563,U_4564,U_4565,U_4566),U_4567))
    | ~ c_Finite__Set_Ofun__left__comm(U_4562,U_4563,U_4564) ),
    inference(clausify,[status(thm)],[f_1142_3]) ).

cnf(f_1142_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_4562,U_4563,U_4564,U_4565,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4562,tc_HOL_Obool)),U_4566),hAPP(hAPP(c_Set_Oinsert(U_4562),U_4568),c_Orderings_Obot__class_Obot(tc_fun(U_4562,tc_HOL_Obool))))),sK92(U_4568,U_4567,U_4566,U_4565,U_4564,U_4563,U_4562)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_4562),U_4568),U_4566))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_4562,U_4563,U_4564,U_4565,U_4566),U_4567))
    | ~ c_Finite__Set_Ofun__left__comm(U_4562,U_4563,U_4564) ),
    inference(clausify,[status(thm)],[f_1142_3]) ).

fof(f_1143_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__Diff__singleton]) ).

fof(f_1143_2,plain,
    ! [U_4571,U_4570,U_4569] :
      ( hAPP(c_Finite__Set_Ocard(U_4569),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4569,tc_HOL_Obool)),U_4570),hAPP(hAPP(c_Set_Oinsert(U_4569),U_4571),c_Orderings_Obot__class_Obot(tc_fun(U_4569,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4569),U_4570)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
      | ~ hBOOL(hAPP(hAPP(c_member(U_4569),U_4571),U_4570))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4569),U_4570)) ),
    inference(variable_rename,[status(thm)],[f_1143_1]) ).

cnf(f_1143_3,plain,
    ( hAPP(c_Finite__Set_Ocard(U_4569),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4569,tc_HOL_Obool)),U_4570),hAPP(hAPP(c_Set_Oinsert(U_4569),U_4571),c_Orderings_Obot__class_Obot(tc_fun(U_4569,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4569),U_4570)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ hBOOL(hAPP(hAPP(c_member(U_4569),U_4571),U_4570))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4569),U_4570)) ),
    inference(clausify,[status(thm)],[f_1143_2]) ).

fof(f_1144_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( ( ( hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2)
          | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) )
        & ( hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
          | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__Diff__singleton__if]) ).

fof(f_1144_2,plain,
    ! [U_4574,U_4573,U_4572] :
      ( ( ( hAPP(c_Finite__Set_Ocard(U_4572),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4572,tc_HOL_Obool)),U_4573),hAPP(hAPP(c_Set_Oinsert(U_4572),U_4574),c_Orderings_Obot__class_Obot(tc_fun(U_4572,tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(U_4572),U_4573)
          | hBOOL(hAPP(hAPP(c_member(U_4572),U_4574),U_4573)) )
        & ( hAPP(c_Finite__Set_Ocard(U_4572),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4572,tc_HOL_Obool)),U_4573),hAPP(hAPP(c_Set_Oinsert(U_4572),U_4574),c_Orderings_Obot__class_Obot(tc_fun(U_4572,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4572),U_4573)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
          | ~ hBOOL(hAPP(hAPP(c_member(U_4572),U_4574),U_4573)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4572),U_4573)) ),
    inference(variable_rename,[status(thm)],[f_1144_1]) ).

cnf(f_1144_3,plain,
    ( hAPP(c_Finite__Set_Ocard(U_4572),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4572,tc_HOL_Obool)),U_4573),hAPP(hAPP(c_Set_Oinsert(U_4572),U_4574),c_Orderings_Obot__class_Obot(tc_fun(U_4572,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4572),U_4573)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ hBOOL(hAPP(hAPP(c_member(U_4572),U_4574),U_4573))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4572),U_4573)) ),
    inference(clausify,[status(thm)],[f_1144_2]) ).

cnf(f_1144_4,plain,
    ( hAPP(c_Finite__Set_Ocard(U_4572),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4572,tc_HOL_Obool)),U_4573),hAPP(hAPP(c_Set_Oinsert(U_4572),U_4574),c_Orderings_Obot__class_Obot(tc_fun(U_4572,tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(U_4572),U_4573)
    | hBOOL(hAPP(hAPP(c_member(U_4572),U_4574),U_4573))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4572),U_4573)) ),
    inference(clausify,[status(thm)],[f_1144_2]) ).

fof(f_1145_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card_Oremove]) ).

fof(f_1145_2,plain,
    ! [U_4577,U_4576,U_4575] :
      ( hAPP(c_Finite__Set_Ocard(U_4575),U_4576) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_4575),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4575,tc_HOL_Obool)),U_4576),hAPP(hAPP(c_Set_Oinsert(U_4575),U_4577),c_Orderings_Obot__class_Obot(tc_fun(U_4575,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_4575),U_4577),U_4576))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4575),U_4576)) ),
    inference(variable_rename,[status(thm)],[f_1145_1]) ).

cnf(f_1145_3,plain,
    ( hAPP(c_Finite__Set_Ocard(U_4575),U_4576) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_4575),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4575,tc_HOL_Obool)),U_4576),hAPP(hAPP(c_Set_Oinsert(U_4575),U_4577),c_Orderings_Obot__class_Obot(tc_fun(U_4575,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_4575),U_4577),U_4576))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4575),U_4576)) ),
    inference(clausify,[status(thm)],[f_1145_2]) ).

fof(f_1146_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card_Oinsert__remove]) ).

fof(f_1146_2,plain,
    ! [U_4580,U_4579,U_4578] :
      ( hAPP(c_Finite__Set_Ocard(U_4578),hAPP(hAPP(c_Set_Oinsert(U_4578),U_4580),U_4579)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_4578),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4578,tc_HOL_Obool)),U_4579),hAPP(hAPP(c_Set_Oinsert(U_4578),U_4580),c_Orderings_Obot__class_Obot(tc_fun(U_4578,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4578),U_4579)) ),
    inference(variable_rename,[status(thm)],[f_1146_1]) ).

cnf(f_1146_3,plain,
    ( hAPP(c_Finite__Set_Ocard(U_4578),hAPP(hAPP(c_Set_Oinsert(U_4578),U_4580),U_4579)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_4578),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4578,tc_HOL_Obool)),U_4579),hAPP(hAPP(c_Set_Oinsert(U_4578),U_4580),c_Orderings_Obot__class_Obot(tc_fun(U_4578,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4578),U_4579)) ),
    inference(clausify,[status(thm)],[f_1146_2]) ).

fof(f_1147_1,plain,
    ! [V_B_2,V_a_2,V_A_2,T_b] :
      ( hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Groups_Oone__class_Oone(tc_Nat_Onat))
      | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__Diff__insert]) ).

fof(f_1147_2,plain,
    ! [U_4584,U_4583,U_4582,U_4581] :
      ( hAPP(c_Finite__Set_Ocard(U_4581),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4581,tc_HOL_Obool)),U_4582),hAPP(hAPP(c_Set_Oinsert(U_4581),U_4583),U_4584))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4581),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4581,tc_HOL_Obool)),U_4582),U_4584))),c_Groups_Oone__class_Oone(tc_Nat_Onat))
      | hBOOL(hAPP(hAPP(c_member(U_4581),U_4583),U_4584))
      | ~ hBOOL(hAPP(hAPP(c_member(U_4581),U_4583),U_4582))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4581),U_4582)) ),
    inference(variable_rename,[status(thm)],[f_1147_1]) ).

cnf(f_1147_3,plain,
    ( hAPP(c_Finite__Set_Ocard(U_4581),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4581,tc_HOL_Obool)),U_4582),hAPP(hAPP(c_Set_Oinsert(U_4581),U_4583),U_4584))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_4581),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4581,tc_HOL_Obool)),U_4582),U_4584))),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | hBOOL(hAPP(hAPP(c_member(U_4581),U_4583),U_4584))
    | ~ hBOOL(hAPP(hAPP(c_member(U_4581),U_4583),U_4582))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4581),U_4582)) ),
    inference(clausify,[status(thm)],[f_1147_2]) ).

fof(f_1148_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2)
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__Suc__Diff1]) ).

fof(f_1148_2,plain,
    ! [U_4587,U_4586,U_4585] :
      ( hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_4585),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4585,tc_HOL_Obool)),U_4586),hAPP(hAPP(c_Set_Oinsert(U_4585),U_4587),c_Orderings_Obot__class_Obot(tc_fun(U_4585,tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(U_4585),U_4586)
      | ~ hBOOL(hAPP(hAPP(c_member(U_4585),U_4587),U_4586))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4585),U_4586)) ),
    inference(variable_rename,[status(thm)],[f_1148_1]) ).

cnf(f_1148_3,plain,
    ( hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_4585),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4585,tc_HOL_Obool)),U_4586),hAPP(hAPP(c_Set_Oinsert(U_4585),U_4587),c_Orderings_Obot__class_Obot(tc_fun(U_4585,tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(U_4585),U_4586)
    | ~ hBOOL(hAPP(hAPP(c_member(U_4585),U_4587),U_4586))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4585),U_4586)) ),
    inference(clausify,[status(thm)],[f_1148_2]) ).

fof(f_1149_1,plain,
    ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_n))),
    inference(fof_nnf,[status(thm)],[fact_lessI]) ).

fof(f_1149_2,plain,
    ! [U_4588] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4588),hAPP(c_Nat_OSuc,U_4588))),
    inference(variable_rename,[status(thm)],[f_1149_1]) ).

cnf(f_1149_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4588),hAPP(c_Nat_OSuc,U_4588))),
    inference(clausify,[status(thm)],[f_1149_2]) ).

fof(f_1150_1,plain,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_Suc__mono]) ).

fof(f_1150_2,plain,
    ! [U_4590,U_4589] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4589)),hAPP(c_Nat_OSuc,U_4590)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4589),U_4590)) ),
    inference(variable_rename,[status(thm)],[f_1150_1]) ).

cnf(f_1150_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4589)),hAPP(c_Nat_OSuc,U_4590)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4589),U_4590)) ),
    inference(clausify,[status(thm)],[f_1150_2]) ).

fof(f_1151_1,plain,
    hAPP(c_Finite__Set_Ocard(tc_Product__Type_Ounit),c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_card__UNIV__unit]) ).

cnf(f_1151_2,plain,
    hAPP(c_Finite__Set_Ocard(tc_Product__Type_Ounit),c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1151_1]) ).

fof(f_1152_1,plain,
    ! [V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n,
    inference(fof_nnf,[status(thm)],[fact_diff__Suc__1]) ).

fof(f_1152_2,plain,
    ! [U_4591] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4591)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_4591,
    inference(variable_rename,[status(thm)],[f_1152_1]) ).

cnf(f_1152_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4591)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_4591,
    inference(clausify,[status(thm)],[f_1152_2]) ).

fof(f_1153_1,plain,
    c_Orderings_Oorder__class_Omono(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),
    inference(fof_nnf,[status(thm)],[fact_mono__Suc]) ).

cnf(f_1153_2,plain,
    c_Orderings_Oorder__class_Omono(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),
    inference(clausify,[status(thm)],[f_1153_1]) ).

fof(f_1154_1,plain,
    ! [V_N_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,V_N_2),
    inference(fof_nnf,[status(thm)],[fact_inj__Suc]) ).

fof(f_1154_2,plain,
    ! [U_4592] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,U_4592),
    inference(variable_rename,[status(thm)],[f_1154_1]) ).

cnf(f_1154_3,plain,
    c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,U_4592),
    inference(clausify,[status(thm)],[f_1154_2]) ).

fof(f_1155_1,plain,
    ! [V_n] : V_n != hAPP(c_Nat_OSuc,V_n),
    inference(fof_nnf,[status(thm)],[fact_n__not__Suc__n]) ).

fof(f_1155_2,plain,
    ! [U_4593] : U_4593 != hAPP(c_Nat_OSuc,U_4593),
    inference(variable_rename,[status(thm)],[f_1155_1]) ).

cnf(f_1155_3,plain,
    U_4593 != hAPP(c_Nat_OSuc,U_4593),
    inference(clausify,[status(thm)],[f_1155_2]) ).

fof(f_1156_1,plain,
    ! [V_n] : hAPP(c_Nat_OSuc,V_n) != V_n,
    inference(fof_nnf,[status(thm)],[fact_Suc__n__not__n]) ).

fof(f_1156_2,plain,
    ! [U_4594] : hAPP(c_Nat_OSuc,U_4594) != U_4594,
    inference(variable_rename,[status(thm)],[f_1156_1]) ).

cnf(f_1156_3,plain,
    hAPP(c_Nat_OSuc,U_4594) != U_4594,
    inference(clausify,[status(thm)],[f_1156_2]) ).

fof(f_1157_1,plain,
    ! [V_nat_H_2,V_nat_2] :
      ( ( hAPP(c_Nat_OSuc,V_nat_2) = hAPP(c_Nat_OSuc,V_nat_H_2)
        | V_nat_2 != V_nat_H_2 )
      & ( V_nat_2 = V_nat_H_2
        | hAPP(c_Nat_OSuc,V_nat_2) != hAPP(c_Nat_OSuc,V_nat_H_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat_Oinject]) ).

fof(f_1157_2,plain,
    ! [U_4596,U_4595] :
      ( ( hAPP(c_Nat_OSuc,U_4595) = hAPP(c_Nat_OSuc,U_4596)
        | U_4595 != U_4596 )
      & ( U_4595 = U_4596
        | hAPP(c_Nat_OSuc,U_4595) != hAPP(c_Nat_OSuc,U_4596) ) ),
    inference(variable_rename,[status(thm)],[f_1157_1]) ).

fof(f_1157_3,plain,
    ( ! [U_4600,U_4598] :
        ( hAPP(c_Nat_OSuc,U_4598) = hAPP(c_Nat_OSuc,U_4600)
        | U_4598 != U_4600 )
    & ! [U_4599,U_4597] :
        ( U_4597 = U_4599
        | hAPP(c_Nat_OSuc,U_4597) != hAPP(c_Nat_OSuc,U_4599) ) ),
    inference(miniscope,[status(thm)],[f_1157_2]) ).

cnf(f_1157_4,plain,
    ( U_4597 = U_4599
    | hAPP(c_Nat_OSuc,U_4597) != hAPP(c_Nat_OSuc,U_4599) ),
    inference(clausify,[status(thm)],[f_1157_3]) ).

cnf(f_1157_5,plain,
    ( hAPP(c_Nat_OSuc,U_4598) = hAPP(c_Nat_OSuc,U_4600)
    | U_4598 != U_4600 ),
    inference(clausify,[status(thm)],[f_1157_3]) ).

fof(f_1158_1,plain,
    ! [V_y,V_x] :
      ( V_x = V_y
      | hAPP(c_Nat_OSuc,V_x) != hAPP(c_Nat_OSuc,V_y) ),
    inference(fof_nnf,[status(thm)],[fact_Suc__inject]) ).

fof(f_1158_2,plain,
    ! [U_4602,U_4601] :
      ( U_4601 = U_4602
      | hAPP(c_Nat_OSuc,U_4601) != hAPP(c_Nat_OSuc,U_4602) ),
    inference(variable_rename,[status(thm)],[f_1158_1]) ).

cnf(f_1158_3,plain,
    ( U_4601 = U_4602
    | hAPP(c_Nat_OSuc,U_4601) != hAPP(c_Nat_OSuc,U_4602) ),
    inference(clausify,[status(thm)],[f_1158_2]) ).

fof(f_1159_1,plain,
    ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),V_k_2),
    inference(fof_nnf,[status(thm)],[fact_atLeast__Suc__greaterThan]) ).

fof(f_1159_2,plain,
    ! [U_4603] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4603)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),U_4603),
    inference(variable_rename,[status(thm)],[f_1159_1]) ).

cnf(f_1159_3,plain,
    hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4603)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),U_4603),
    inference(clausify,[status(thm)],[f_1159_2]) ).

fof(f_1160_1,plain,
    ! [V_x_2,T_b] :
      ( ( ( c_Groups_Oone__class_Oone(T_b) = V_x_2
          | V_x_2 != c_Groups_Oone__class_Oone(T_b) )
        & ( V_x_2 = c_Groups_Oone__class_Oone(T_b)
          | c_Groups_Oone__class_Oone(T_b) != V_x_2 ) )
      | ~ class_Groups_Oone(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_one__reorient]) ).

fof(f_1160_2,plain,
    ! [U_4605,U_4604] :
      ( ( ( c_Groups_Oone__class_Oone(U_4604) = U_4605
          | U_4605 != c_Groups_Oone__class_Oone(U_4604) )
        & ( U_4605 = c_Groups_Oone__class_Oone(U_4604)
          | c_Groups_Oone__class_Oone(U_4604) != U_4605 ) )
      | ~ class_Groups_Oone(U_4604) ),
    inference(variable_rename,[status(thm)],[f_1160_1]) ).

cnf(f_1160_3,plain,
    ( U_4605 = c_Groups_Oone__class_Oone(U_4604)
    | c_Groups_Oone__class_Oone(U_4604) != U_4605
    | ~ class_Groups_Oone(U_4604) ),
    inference(clausify,[status(thm)],[f_1160_2]) ).

cnf(f_1160_4,plain,
    ( c_Groups_Oone__class_Oone(U_4604) = U_4605
    | U_4605 != c_Groups_Oone__class_Oone(U_4604)
    | ~ class_Groups_Oone(U_4604) ),
    inference(clausify,[status(thm)],[f_1160_2]) ).

fof(f_1161_1,plain,
    ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),V_k_2)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_greaterThan__Suc]) ).

fof(f_1161_2,plain,
    ! [U_4606] : hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4606)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),U_4606)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4606)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_1161_1]) ).

cnf(f_1161_3,plain,
    hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4606)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),U_4606)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4606)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_1161_2]) ).

fof(f_1162_1,plain,
    ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),V_k_2)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_k_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_atLeast__Suc]) ).

fof(f_1162_2,plain,
    ! [U_4607] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4607)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),U_4607)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_4607),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_1162_1]) ).

cnf(f_1162_3,plain,
    hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4607)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),U_4607)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_4607),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_1162_2]) ).

fof(f_1163_1,plain,
    ! [V_f_2,T_b] :
      ( ( ( c_Orderings_Oorder__class_Omono(tc_Nat_Onat,T_b,V_f_2)
          | ? [B_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_n)),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_n)))) )
        & ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_n)),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_n))))
          | ~ c_Orderings_Oorder__class_Omono(tc_Nat_Onat,T_b,V_f_2) ) )
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_mono__iff__le__Suc]) ).

fof(f_1163_2,plain,
    ! [U_4611,U_4610] :
      ( ( ( c_Orderings_Oorder__class_Omono(tc_Nat_Onat,U_4610,U_4611)
          | ? [U_4609] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4610),hAPP(U_4611,U_4609)),hAPP(U_4611,hAPP(c_Nat_OSuc,U_4609)))) )
        & ( ! [U_4608] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4610),hAPP(U_4611,U_4608)),hAPP(U_4611,hAPP(c_Nat_OSuc,U_4608))))
          | ~ c_Orderings_Oorder__class_Omono(tc_Nat_Onat,U_4610,U_4611) ) )
      | ~ class_Orderings_Oorder(U_4610) ),
    inference(variable_rename,[status(thm)],[f_1163_1]) ).

fof(f_1163_3,plain,
    ! [U_4611,U_4610] :
      ( ( ( c_Orderings_Oorder__class_Omono(tc_Nat_Onat,U_4610,U_4611)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4610),hAPP(U_4611,sK93(U_4611,U_4610))),hAPP(U_4611,hAPP(c_Nat_OSuc,sK93(U_4611,U_4610))))) )
        & ( ! [U_4608] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4610),hAPP(U_4611,U_4608)),hAPP(U_4611,hAPP(c_Nat_OSuc,U_4608))))
          | ~ c_Orderings_Oorder__class_Omono(tc_Nat_Onat,U_4610,U_4611) ) )
      | ~ class_Orderings_Oorder(U_4610) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK93]),skolemize(U_4609,sK93(U_4611,U_4610))],[f_1163_2]) ).

cnf(f_1163_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4610),hAPP(U_4611,U_4608)),hAPP(U_4611,hAPP(c_Nat_OSuc,U_4608))))
    | ~ c_Orderings_Oorder__class_Omono(tc_Nat_Onat,U_4610,U_4611)
    | ~ class_Orderings_Oorder(U_4610) ),
    inference(clausify,[status(thm)],[f_1163_3]) ).

cnf(f_1163_5,plain,
    ( c_Orderings_Oorder__class_Omono(tc_Nat_Onat,U_4610,U_4611)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4610),hAPP(U_4611,sK93(U_4611,U_4610))),hAPP(U_4611,hAPP(c_Nat_OSuc,sK93(U_4611,U_4610)))))
    | ~ class_Orderings_Oorder(U_4610) ),
    inference(clausify,[status(thm)],[f_1163_3]) ).

fof(f_1164_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a
      | ~ class_Groups_Omonoid__mult(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__1__left]) ).

fof(f_1164_2,plain,
    ! [U_4613,U_4612] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4612),c_Groups_Oone__class_Oone(U_4612)),U_4613) = U_4613
      | ~ class_Groups_Omonoid__mult(U_4612) ),
    inference(variable_rename,[status(thm)],[f_1164_1]) ).

cnf(f_1164_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4612),c_Groups_Oone__class_Oone(U_4612)),U_4613) = U_4613
    | ~ class_Groups_Omonoid__mult(U_4612) ),
    inference(clausify,[status(thm)],[f_1164_2]) ).

fof(f_1165_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a
      | ~ class_Groups_Ocomm__monoid__mult(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__1]) ).

fof(f_1165_2,plain,
    ! [U_4615,U_4614] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4614),c_Groups_Oone__class_Oone(U_4614)),U_4615) = U_4615
      | ~ class_Groups_Ocomm__monoid__mult(U_4614) ),
    inference(variable_rename,[status(thm)],[f_1165_1]) ).

cnf(f_1165_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4614),c_Groups_Oone__class_Oone(U_4614)),U_4615) = U_4615
    | ~ class_Groups_Ocomm__monoid__mult(U_4614) ),
    inference(clausify,[status(thm)],[f_1165_2]) ).

fof(f_1166_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a
      | ~ class_Groups_Omonoid__mult(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__1__right]) ).

fof(f_1166_2,plain,
    ! [U_4617,U_4616] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4616),U_4617),c_Groups_Oone__class_Oone(U_4616)) = U_4617
      | ~ class_Groups_Omonoid__mult(U_4616) ),
    inference(variable_rename,[status(thm)],[f_1166_1]) ).

cnf(f_1166_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4616),U_4617),c_Groups_Oone__class_Oone(U_4616)) = U_4617
    | ~ class_Groups_Omonoid__mult(U_4616) ),
    inference(clausify,[status(thm)],[f_1166_2]) ).

fof(f_1167_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a
      | ~ class_Groups_Ocomm__monoid__mult(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult_Ocomm__neutral]) ).

fof(f_1167_2,plain,
    ! [U_4619,U_4618] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4618),U_4619),c_Groups_Oone__class_Oone(U_4618)) = U_4619
      | ~ class_Groups_Ocomm__monoid__mult(U_4618) ),
    inference(variable_rename,[status(thm)],[f_1167_1]) ).

cnf(f_1167_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4618),U_4619),c_Groups_Oone__class_Oone(U_4618)) = U_4619
    | ~ class_Groups_Ocomm__monoid__mult(U_4618) ),
    inference(clausify,[status(thm)],[f_1167_2]) ).

fof(f_1168_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J]) ).

fof(f_1168_2,plain,
    ! [U_4621,U_4620] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4620),c_Groups_Oone__class_Oone(U_4620)),U_4621) = U_4621
      | ~ class_Rings_Ocomm__semiring__1(U_4620) ),
    inference(variable_rename,[status(thm)],[f_1168_1]) ).

cnf(f_1168_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4620),c_Groups_Oone__class_Oone(U_4620)),U_4621) = U_4621
    | ~ class_Rings_Ocomm__semiring__1(U_4620) ),
    inference(clausify,[status(thm)],[f_1168_2]) ).

fof(f_1169_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J]) ).

fof(f_1169_2,plain,
    ! [U_4623,U_4622] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4622),U_4623),c_Groups_Oone__class_Oone(U_4622)) = U_4623
      | ~ class_Rings_Ocomm__semiring__1(U_4622) ),
    inference(variable_rename,[status(thm)],[f_1169_1]) ).

cnf(f_1169_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4622),U_4623),c_Groups_Oone__class_Oone(U_4622)) = U_4623
    | ~ class_Rings_Ocomm__semiring__1(U_4622) ),
    inference(clausify,[status(thm)],[f_1169_2]) ).

fof(f_1170_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_not__less__eq]) ).

fof(f_1170_2,plain,
    ! [U_4625,U_4624] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4624),U_4625))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4625),hAPP(c_Nat_OSuc,U_4624))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4625),hAPP(c_Nat_OSuc,U_4624)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4624),U_4625)) ) ),
    inference(variable_rename,[status(thm)],[f_1170_1]) ).

fof(f_1170_3,plain,
    ( ! [U_4629,U_4627] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4627),U_4629))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4629),hAPP(c_Nat_OSuc,U_4627))) )
    & ! [U_4628,U_4626] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4628),hAPP(c_Nat_OSuc,U_4626)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4626),U_4628)) ) ),
    inference(miniscope,[status(thm)],[f_1170_2]) ).

cnf(f_1170_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4628),hAPP(c_Nat_OSuc,U_4626)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4626),U_4628)) ),
    inference(clausify,[status(thm)],[f_1170_3]) ).

cnf(f_1170_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4627),U_4629))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4629),hAPP(c_Nat_OSuc,U_4627))) ),
    inference(clausify,[status(thm)],[f_1170_3]) ).

fof(f_1171_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
        | ( V_m_2 != V_n_2
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) )
      & ( V_m_2 = V_n_2
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_less__Suc__eq]) ).

fof(f_1171_2,plain,
    ! [U_4631,U_4630] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4630),hAPP(c_Nat_OSuc,U_4631)))
        | ( U_4630 != U_4631
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4630),U_4631)) ) )
      & ( U_4630 = U_4631
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4630),U_4631))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4630),hAPP(c_Nat_OSuc,U_4631))) ) ),
    inference(variable_rename,[status(thm)],[f_1171_1]) ).

fof(f_1171_3,plain,
    ( ! [U_4635,U_4633] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4633),hAPP(c_Nat_OSuc,U_4635)))
        | ( U_4633 != U_4635
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4633),U_4635)) ) )
    & ! [U_4634,U_4632] :
        ( U_4632 = U_4634
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4632),U_4634))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4632),hAPP(c_Nat_OSuc,U_4634))) ) ),
    inference(miniscope,[status(thm)],[f_1171_2]) ).

cnf(f_1171_4,plain,
    ( U_4632 = U_4634
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4632),U_4634))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4632),hAPP(c_Nat_OSuc,U_4634))) ),
    inference(clausify,[status(thm)],[f_1171_3]) ).

cnf(f_1171_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4633),U_4635))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4633),hAPP(c_Nat_OSuc,U_4635))) ),
    inference(clausify,[status(thm)],[f_1171_3]) ).

cnf(f_1171_6,plain,
    ( U_4633 != U_4635
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4633),hAPP(c_Nat_OSuc,U_4635))) ),
    inference(clausify,[status(thm)],[f_1171_3]) ).

fof(f_1172_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),hAPP(c_Nat_OSuc,V_n_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),hAPP(c_Nat_OSuc,V_n_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_Suc__less__eq]) ).

fof(f_1172_2,plain,
    ! [U_4637,U_4636] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4636)),hAPP(c_Nat_OSuc,U_4637)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4636),U_4637)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4636),U_4637))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4636)),hAPP(c_Nat_OSuc,U_4637))) ) ),
    inference(variable_rename,[status(thm)],[f_1172_1]) ).

fof(f_1172_3,plain,
    ( ! [U_4641,U_4639] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4639)),hAPP(c_Nat_OSuc,U_4641)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4639),U_4641)) )
    & ! [U_4640,U_4638] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4638),U_4640))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4638)),hAPP(c_Nat_OSuc,U_4640))) ) ),
    inference(miniscope,[status(thm)],[f_1172_2]) ).

cnf(f_1172_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4638),U_4640))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4638)),hAPP(c_Nat_OSuc,U_4640))) ),
    inference(clausify,[status(thm)],[f_1172_3]) ).

cnf(f_1172_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4639)),hAPP(c_Nat_OSuc,U_4641)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4639),U_4641)) ),
    inference(clausify,[status(thm)],[f_1172_3]) ).

fof(f_1173_1,plain,
    ! [V_m_2,V_n_2] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2)))
          | V_n_2 != V_m_2 )
        & ( V_n_2 = V_m_2
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) ) )
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ),
    inference(fof_nnf,[status(thm)],[fact_not__less__less__Suc__eq]) ).

fof(f_1173_2,plain,
    ! [U_4643,U_4642] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4642),hAPP(c_Nat_OSuc,U_4643)))
          | U_4642 != U_4643 )
        & ( U_4642 = U_4643
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4642),hAPP(c_Nat_OSuc,U_4643))) ) )
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4642),U_4643)) ),
    inference(variable_rename,[status(thm)],[f_1173_1]) ).

cnf(f_1173_3,plain,
    ( U_4642 = U_4643
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4642),hAPP(c_Nat_OSuc,U_4643)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4642),U_4643)) ),
    inference(clausify,[status(thm)],[f_1173_2]) ).

cnf(f_1173_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4642),hAPP(c_Nat_OSuc,U_4643)))
    | U_4642 != U_4643
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4642),U_4643)) ),
    inference(clausify,[status(thm)],[f_1173_2]) ).

fof(f_1174_1,plain,
    ! [V_m,V_n] :
      ( V_m = V_n
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_m)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m)) ),
    inference(fof_nnf,[status(thm)],[fact_less__antisym]) ).

fof(f_1174_2,plain,
    ! [U_4645,U_4644] :
      ( U_4645 = U_4644
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4644),hAPP(c_Nat_OSuc,U_4645)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4644),U_4645)) ),
    inference(variable_rename,[status(thm)],[f_1174_1]) ).

cnf(f_1174_3,plain,
    ( U_4645 = U_4644
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4644),hAPP(c_Nat_OSuc,U_4645)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4644),U_4645)) ),
    inference(clausify,[status(thm)],[f_1174_2]) ).

fof(f_1175_1,plain,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_less__SucI]) ).

fof(f_1175_2,plain,
    ! [U_4647,U_4646] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4646),hAPP(c_Nat_OSuc,U_4647)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4646),U_4647)) ),
    inference(variable_rename,[status(thm)],[f_1175_1]) ).

cnf(f_1175_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4646),hAPP(c_Nat_OSuc,U_4647)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4646),U_4647)) ),
    inference(clausify,[status(thm)],[f_1175_2]) ).

fof(f_1176_1,plain,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
      | hAPP(c_Nat_OSuc,V_m) = V_n
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_Suc__lessI]) ).

fof(f_1176_2,plain,
    ! [U_4649,U_4648] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4648)),U_4649))
      | hAPP(c_Nat_OSuc,U_4648) = U_4649
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4648),U_4649)) ),
    inference(variable_rename,[status(thm)],[f_1176_1]) ).

cnf(f_1176_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4648)),U_4649))
    | hAPP(c_Nat_OSuc,U_4648) = U_4649
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4648),U_4649)) ),
    inference(clausify,[status(thm)],[f_1176_2]) ).

fof(f_1177_1,plain,
    ! [V_k,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_i)),V_k))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) ),
    inference(fof_nnf,[status(thm)],[fact_less__trans__Suc]) ).

fof(f_1177_2,plain,
    ! [U_4652,U_4651,U_4650] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4650)),U_4652))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4651),U_4652))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4650),U_4651)) ),
    inference(variable_rename,[status(thm)],[f_1177_1]) ).

cnf(f_1177_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4650)),U_4652))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4651),U_4652))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4650),U_4651)) ),
    inference(clausify,[status(thm)],[f_1177_2]) ).

fof(f_1178_1,plain,
    ! [V_n,V_m] :
      ( V_m = V_n
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ),
    inference(fof_nnf,[status(thm)],[fact_less__SucE]) ).

fof(f_1178_2,plain,
    ! [U_4654,U_4653] :
      ( U_4653 = U_4654
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4653),U_4654))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4653),hAPP(c_Nat_OSuc,U_4654))) ),
    inference(variable_rename,[status(thm)],[f_1178_1]) ).

cnf(f_1178_3,plain,
    ( U_4653 = U_4654
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4653),U_4654))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4653),hAPP(c_Nat_OSuc,U_4654))) ),
    inference(clausify,[status(thm)],[f_1178_2]) ).

fof(f_1179_1,plain,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_Suc__lessD]) ).

fof(f_1179_2,plain,
    ! [U_4656,U_4655] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4655),U_4656))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4655)),U_4656)) ),
    inference(variable_rename,[status(thm)],[f_1179_1]) ).

cnf(f_1179_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4655),U_4656))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4655)),U_4656)) ),
    inference(clausify,[status(thm)],[f_1179_2]) ).

fof(f_1180_1,plain,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) ),
    inference(fof_nnf,[status(thm)],[fact_Suc__less__SucD]) ).

fof(f_1180_2,plain,
    ! [U_4658,U_4657] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4657),U_4658))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4657)),hAPP(c_Nat_OSuc,U_4658))) ),
    inference(variable_rename,[status(thm)],[f_1180_1]) ).

cnf(f_1180_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4657),U_4658))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4657)),hAPP(c_Nat_OSuc,U_4658))) ),
    inference(clausify,[status(thm)],[f_1180_2]) ).

fof(f_1181_1,plain,
    ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),
    inference(fof_nnf,[status(thm)],[fact_add__Suc__right]) ).

fof(f_1181_2,plain,
    ! [U_4660,U_4659] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4659),hAPP(c_Nat_OSuc,U_4660)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4659),U_4660)),
    inference(variable_rename,[status(thm)],[f_1181_1]) ).

cnf(f_1181_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4659),hAPP(c_Nat_OSuc,U_4660)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4659),U_4660)),
    inference(clausify,[status(thm)],[f_1181_2]) ).

fof(f_1182_1,plain,
    ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),
    inference(fof_nnf,[status(thm)],[fact_add__Suc]) ).

fof(f_1182_2,plain,
    ! [U_4662,U_4661] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4661)),U_4662) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4661),U_4662)),
    inference(variable_rename,[status(thm)],[f_1182_1]) ).

cnf(f_1182_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4661)),U_4662) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4661),U_4662)),
    inference(clausify,[status(thm)],[f_1182_2]) ).

fof(f_1183_1,plain,
    ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)),
    inference(fof_nnf,[status(thm)],[fact_add__Suc__shift]) ).

fof(f_1183_2,plain,
    ! [U_4664,U_4663] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4663)),U_4664) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4663),hAPP(c_Nat_OSuc,U_4664)),
    inference(variable_rename,[status(thm)],[f_1183_1]) ).

cnf(f_1183_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4663)),U_4664) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4663),hAPP(c_Nat_OSuc,U_4664)),
    inference(clausify,[status(thm)],[f_1183_2]) ).

fof(f_1184_1,plain,
    ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)),V_n)),
    inference(fof_nnf,[status(thm)],[fact_Suc__n__not__le__n]) ).

fof(f_1184_2,plain,
    ! [U_4665] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4665)),U_4665)),
    inference(variable_rename,[status(thm)],[f_1184_1]) ).

cnf(f_1184_3,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4665)),U_4665)),
    inference(clausify,[status(thm)],[f_1184_2]) ).

fof(f_1185_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_not__less__eq__eq]) ).

fof(f_1185_2,plain,
    ! [U_4667,U_4666] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4666),U_4667))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4667)),U_4666)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4667)),U_4666))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4666),U_4667)) ) ),
    inference(variable_rename,[status(thm)],[f_1185_1]) ).

fof(f_1185_3,plain,
    ( ! [U_4671,U_4669] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4669),U_4671))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4671)),U_4669)) )
    & ! [U_4670,U_4668] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4670)),U_4668))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4668),U_4670)) ) ),
    inference(miniscope,[status(thm)],[f_1185_2]) ).

cnf(f_1185_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4670)),U_4668))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4668),U_4670)) ),
    inference(clausify,[status(thm)],[f_1185_3]) ).

cnf(f_1185_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4669),U_4671))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4671)),U_4669)) ),
    inference(clausify,[status(thm)],[f_1185_3]) ).

fof(f_1186_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
        | ( V_m_2 != hAPP(c_Nat_OSuc,V_n_2)
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) )
      & ( V_m_2 = hAPP(c_Nat_OSuc,V_n_2)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_le__Suc__eq]) ).

fof(f_1186_2,plain,
    ! [U_4673,U_4672] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4672),hAPP(c_Nat_OSuc,U_4673)))
        | ( U_4672 != hAPP(c_Nat_OSuc,U_4673)
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4672),U_4673)) ) )
      & ( U_4672 = hAPP(c_Nat_OSuc,U_4673)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4672),U_4673))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4672),hAPP(c_Nat_OSuc,U_4673))) ) ),
    inference(variable_rename,[status(thm)],[f_1186_1]) ).

fof(f_1186_3,plain,
    ( ! [U_4677,U_4675] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4675),hAPP(c_Nat_OSuc,U_4677)))
        | ( U_4675 != hAPP(c_Nat_OSuc,U_4677)
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4675),U_4677)) ) )
    & ! [U_4676,U_4674] :
        ( U_4674 = hAPP(c_Nat_OSuc,U_4676)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4674),U_4676))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4674),hAPP(c_Nat_OSuc,U_4676))) ) ),
    inference(miniscope,[status(thm)],[f_1186_2]) ).

cnf(f_1186_4,plain,
    ( U_4674 = hAPP(c_Nat_OSuc,U_4676)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4674),U_4676))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4674),hAPP(c_Nat_OSuc,U_4676))) ),
    inference(clausify,[status(thm)],[f_1186_3]) ).

cnf(f_1186_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4675),U_4677))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4675),hAPP(c_Nat_OSuc,U_4677))) ),
    inference(clausify,[status(thm)],[f_1186_3]) ).

cnf(f_1186_6,plain,
    ( U_4675 != hAPP(c_Nat_OSuc,U_4677)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4675),hAPP(c_Nat_OSuc,U_4677))) ),
    inference(clausify,[status(thm)],[f_1186_3]) ).

fof(f_1187_1,plain,
    ! [V_m_2,V_n_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Nat_OSuc,V_m_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Nat_OSuc,V_m_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_Suc__le__mono]) ).

fof(f_1187_2,plain,
    ! [U_4679,U_4678] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4678)),hAPP(c_Nat_OSuc,U_4679)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4678),U_4679)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4678),U_4679))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4678)),hAPP(c_Nat_OSuc,U_4679))) ) ),
    inference(variable_rename,[status(thm)],[f_1187_1]) ).

fof(f_1187_3,plain,
    ( ! [U_4683,U_4681] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4681)),hAPP(c_Nat_OSuc,U_4683)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4681),U_4683)) )
    & ! [U_4682,U_4680] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4680),U_4682))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4680)),hAPP(c_Nat_OSuc,U_4682))) ) ),
    inference(miniscope,[status(thm)],[f_1187_2]) ).

cnf(f_1187_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4680),U_4682))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4680)),hAPP(c_Nat_OSuc,U_4682))) ),
    inference(clausify,[status(thm)],[f_1187_3]) ).

cnf(f_1187_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4681)),hAPP(c_Nat_OSuc,U_4683)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4681),U_4683)) ),
    inference(clausify,[status(thm)],[f_1187_3]) ).

fof(f_1188_1,plain,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_le__SucI]) ).

fof(f_1188_2,plain,
    ! [U_4685,U_4684] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4684),hAPP(c_Nat_OSuc,U_4685)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4684),U_4685)) ),
    inference(variable_rename,[status(thm)],[f_1188_1]) ).

cnf(f_1188_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4684),hAPP(c_Nat_OSuc,U_4685)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4684),U_4685)) ),
    inference(clausify,[status(thm)],[f_1188_2]) ).

fof(f_1189_1,plain,
    ! [V_n,V_m] :
      ( V_m = hAPP(c_Nat_OSuc,V_n)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ),
    inference(fof_nnf,[status(thm)],[fact_le__SucE]) ).

fof(f_1189_2,plain,
    ! [U_4687,U_4686] :
      ( U_4686 = hAPP(c_Nat_OSuc,U_4687)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4686),U_4687))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4686),hAPP(c_Nat_OSuc,U_4687))) ),
    inference(variable_rename,[status(thm)],[f_1189_1]) ).

cnf(f_1189_3,plain,
    ( U_4686 = hAPP(c_Nat_OSuc,U_4687)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4686),U_4687))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4686),hAPP(c_Nat_OSuc,U_4687))) ),
    inference(clausify,[status(thm)],[f_1189_2]) ).

fof(f_1190_1,plain,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_Suc__leD]) ).

fof(f_1190_2,plain,
    ! [U_4689,U_4688] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4688),U_4689))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4688)),U_4689)) ),
    inference(variable_rename,[status(thm)],[f_1190_1]) ).

cnf(f_1190_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4688),U_4689))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4688)),U_4689)) ),
    inference(clausify,[status(thm)],[f_1190_2]) ).

fof(f_1191_1,plain,
    ! [V_f_2,V_F_2,T_b] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_F_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          | ? [B_x] :
              ( hAPP(V_f_2,B_x) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
              & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2)) ) )
        & ( ! [B_x] :
              ( hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
              | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_F_2) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__eq__1__iff]) ).

fof(f_1191_2,plain,
    ! [U_4694,U_4693,U_4692] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4692,tc_Nat_Onat),U_4694),U_4693) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          | ? [U_4691] :
              ( hAPP(U_4694,U_4691) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
              & hBOOL(hAPP(hAPP(c_member(U_4692),U_4691),U_4693)) ) )
        & ( ! [U_4690] :
              ( hAPP(U_4694,U_4690) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
              | ~ hBOOL(hAPP(hAPP(c_member(U_4692),U_4690),U_4693)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4692,tc_Nat_Onat),U_4694),U_4693) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4692),U_4693)) ),
    inference(variable_rename,[status(thm)],[f_1191_1]) ).

fof(f_1191_3,plain,
    ! [U_4694,U_4693,U_4692] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4692,tc_Nat_Onat),U_4694),U_4693) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          | ( hAPP(U_4694,sK94(U_4694,U_4693,U_4692)) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
            & hBOOL(hAPP(hAPP(c_member(U_4692),sK94(U_4694,U_4693,U_4692)),U_4693)) ) )
        & ( ! [U_4690] :
              ( hAPP(U_4694,U_4690) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
              | ~ hBOOL(hAPP(hAPP(c_member(U_4692),U_4690),U_4693)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4692,tc_Nat_Onat),U_4694),U_4693) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4692),U_4693)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK94]),skolemize(U_4691,sK94(U_4694,U_4693,U_4692))],[f_1191_2]) ).

cnf(f_1191_4,plain,
    ( hAPP(U_4694,U_4690) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(U_4692),U_4690),U_4693))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4692,tc_Nat_Onat),U_4694),U_4693) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4692),U_4693)) ),
    inference(clausify,[status(thm)],[f_1191_3]) ).

cnf(f_1191_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_4692),sK94(U_4694,U_4693,U_4692)),U_4693))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4692,tc_Nat_Onat),U_4694),U_4693) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4692),U_4693)) ),
    inference(clausify,[status(thm)],[f_1191_3]) ).

cnf(f_1191_6,plain,
    ( hAPP(U_4694,sK94(U_4694,U_4693,U_4692)) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4692,tc_Nat_Onat),U_4694),U_4693) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4692),U_4693)) ),
    inference(clausify,[status(thm)],[f_1191_3]) ).

fof(f_1192_1,plain,
    ! [V_n,V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),
    inference(fof_nnf,[status(thm)],[fact_diff__Suc__Suc]) ).

fof(f_1192_2,plain,
    ! [U_4696,U_4695] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4695)),hAPP(c_Nat_OSuc,U_4696)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4695),U_4696),
    inference(variable_rename,[status(thm)],[f_1192_1]) ).

cnf(f_1192_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4695)),hAPP(c_Nat_OSuc,U_4696)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4695),U_4696),
    inference(clausify,[status(thm)],[f_1192_2]) ).

fof(f_1193_1,plain,
    ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)),hAPP(c_Nat_OSuc,V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_k),
    inference(fof_nnf,[status(thm)],[fact_Suc__diff__diff]) ).

fof(f_1193_2,plain,
    ! [U_4699,U_4698,U_4697] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4697)),U_4698)),hAPP(c_Nat_OSuc,U_4699)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4697),U_4698)),U_4699),
    inference(variable_rename,[status(thm)],[f_1193_1]) ).

cnf(f_1193_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4697)),U_4698)),hAPP(c_Nat_OSuc,U_4699)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4697),U_4698)),U_4699),
    inference(clausify,[status(thm)],[f_1193_2]) ).

fof(f_1194_1,plain,
    ! [V_n_2,V_m_2,V_k_2] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_n_2)
        | V_m_2 != V_n_2 )
      & ( V_m_2 = V_n_2
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_m_2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_n_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_Suc__mult__cancel1]) ).

fof(f_1194_2,plain,
    ! [U_4702,U_4701,U_4700] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4700)),U_4701) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4700)),U_4702)
        | U_4701 != U_4702 )
      & ( U_4701 = U_4702
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4700)),U_4701) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4700)),U_4702) ) ),
    inference(variable_rename,[status(thm)],[f_1194_1]) ).

fof(f_1194_3,plain,
    ( ! [U_4708,U_4706] :
        ( ! [U_4704] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4704)),U_4706) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4704)),U_4708)
        | U_4706 != U_4708 )
    & ! [U_4707,U_4705] :
        ( ! [U_4703] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4703)),U_4705) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4703)),U_4707)
        | U_4705 = U_4707 ) ),
    inference(miniscope,[status(thm)],[f_1194_2]) ).

cnf(f_1194_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4703)),U_4705) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4703)),U_4707)
    | U_4705 = U_4707 ),
    inference(clausify,[status(thm)],[f_1194_3]) ).

cnf(f_1194_5,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4704)),U_4706) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4704)),U_4708)
    | U_4706 != U_4708 ),
    inference(clausify,[status(thm)],[f_1194_3]) ).

fof(f_1195_1,plain,
    ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n,
    inference(fof_nnf,[status(thm)],[fact_nat__mult__1]) ).

fof(f_1195_2,plain,
    ! [U_4709] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_4709) = U_4709,
    inference(variable_rename,[status(thm)],[f_1195_1]) ).

cnf(f_1195_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_4709) = U_4709,
    inference(clausify,[status(thm)],[f_1195_2]) ).

fof(f_1196_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)
        | V_n_2 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | V_m_2 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( ( V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          & V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__1__eq__mult__iff]) ).

fof(f_1196_2,plain,
    ! [U_4711,U_4710] :
      ( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4710),U_4711)
        | U_4711 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_4710 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( ( U_4711 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          & U_4710 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4710),U_4711) ) ),
    inference(variable_rename,[status(thm)],[f_1196_1]) ).

fof(f_1196_3,plain,
    ( ! [U_4715,U_4713] :
        ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4713),U_4715)
        | U_4715 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_4713 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
    & ! [U_4714,U_4712] :
        ( ( U_4714 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          & U_4712 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4712),U_4714) ) ),
    inference(miniscope,[status(thm)],[f_1196_2]) ).

cnf(f_1196_4,plain,
    ( U_4712 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4712),U_4714) ),
    inference(clausify,[status(thm)],[f_1196_3]) ).

cnf(f_1196_5,plain,
    ( U_4714 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4712),U_4714) ),
    inference(clausify,[status(thm)],[f_1196_3]) ).

cnf(f_1196_6,plain,
    ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4713),U_4715)
    | U_4715 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | U_4713 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1196_3]) ).

fof(f_1197_1,plain,
    ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n,
    inference(fof_nnf,[status(thm)],[fact_nat__mult__1__right]) ).

fof(f_1197_2,plain,
    ! [U_4716] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4716),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_4716,
    inference(variable_rename,[status(thm)],[f_1197_1]) ).

cnf(f_1197_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4716),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_4716,
    inference(clausify,[status(thm)],[f_1197_2]) ).

fof(f_1198_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | V_n_2 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | V_m_2 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( ( V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          & V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__mult__eq__1__iff]) ).

fof(f_1198_2,plain,
    ! [U_4718,U_4717] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4717),U_4718) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_4718 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_4717 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( ( U_4718 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          & U_4717 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4717),U_4718) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_1198_1]) ).

fof(f_1198_3,plain,
    ( ! [U_4722,U_4720] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4720),U_4722) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_4722 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_4720 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
    & ! [U_4721,U_4719] :
        ( ( U_4721 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          & U_4719 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4719),U_4721) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_1198_2]) ).

cnf(f_1198_4,plain,
    ( U_4719 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4719),U_4721) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1198_3]) ).

cnf(f_1198_5,plain,
    ( U_4721 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4719),U_4721) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1198_3]) ).

cnf(f_1198_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4720),U_4722) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | U_4722 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | U_4720 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1198_3]) ).

fof(f_1199_1,plain,
    ! [V_j_2,V_i_2] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_i_2)),hAPP(c_Nat_OSuc,V_j_2)),
    inference(fof_nnf,[status(thm)],[fact_image__Suc__atLeastLessThan]) ).

fof(f_1199_2,plain,
    ! [U_4724,U_4723] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_4723),U_4724)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_4723)),hAPP(c_Nat_OSuc,U_4724)),
    inference(variable_rename,[status(thm)],[f_1199_1]) ).

cnf(f_1199_3,plain,
    hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_4723),U_4724)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_4723)),hAPP(c_Nat_OSuc,U_4724)),
    inference(clausify,[status(thm)],[f_1199_2]) ).

fof(f_1200_1,plain,
    ! [V_m_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_m_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_m_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__singleton]) ).

fof(f_1200_2,plain,
    ! [U_4725] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_4725),hAPP(c_Nat_OSuc,U_4725)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_4725),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_1200_1]) ).

cnf(f_1200_3,plain,
    hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_4725),hAPP(c_Nat_OSuc,U_4725)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_4725),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_1200_2]) ).

fof(f_1201_1,plain,
    ! [V_j_2,V_i_2] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_i_2,V_j_2)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_i_2),hAPP(c_Nat_OSuc,V_j_2)),
    inference(fof_nnf,[status(thm)],[fact_image__Suc__atLeastAtMost]) ).

fof(f_1201_2,plain,
    ! [U_4727,U_4726] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_4726,U_4727)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_4726),hAPP(c_Nat_OSuc,U_4727)),
    inference(variable_rename,[status(thm)],[f_1201_1]) ).

cnf(f_1201_3,plain,
    hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_4726,U_4727)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_4726),hAPP(c_Nat_OSuc,U_4727)),
    inference(clausify,[status(thm)],[f_1201_2]) ).

fof(f_1202_1,plain,
    ! [V_n,V_m] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_m),V_n)),
    inference(fof_nnf,[status(thm)],[fact_min__Suc__Suc]) ).

fof(f_1202_2,plain,
    ! [U_4729,U_4728] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4728)),hAPP(c_Nat_OSuc,U_4729)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_4728),U_4729)),
    inference(variable_rename,[status(thm)],[f_1202_1]) ).

cnf(f_1202_3,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4728)),hAPP(c_Nat_OSuc,U_4729)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_4728),U_4729)),
    inference(clausify,[status(thm)],[f_1202_2]) ).

fof(f_1203_1,plain,
    ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_k_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_k_2)),
    inference(fof_nnf,[status(thm)],[fact_lessThan__Suc]) ).

fof(f_1203_2,plain,
    ! [U_4730] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4730)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_4730),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_4730)),
    inference(variable_rename,[status(thm)],[f_1203_1]) ).

cnf(f_1203_3,plain,
    hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4730)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_4730),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_4730)),
    inference(clausify,[status(thm)],[f_1203_2]) ).

fof(f_1204_1,plain,
    ! [V_n,V_m] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_m),V_n)),
    inference(fof_nnf,[status(thm)],[fact_max__Suc__Suc]) ).

fof(f_1204_2,plain,
    ! [U_4732,U_4731] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4731)),hAPP(c_Nat_OSuc,U_4732)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_4731),U_4732)),
    inference(variable_rename,[status(thm)],[f_1204_1]) ).

cnf(f_1204_3,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4731)),hAPP(c_Nat_OSuc,U_4732)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_4731),U_4732)),
    inference(clausify,[status(thm)],[f_1204_2]) ).

fof(f_1205_1,plain,
    ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2)),
    inference(fof_nnf,[status(thm)],[fact_atMost__Suc]) ).

fof(f_1205_2,plain,
    ! [U_4733] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4733)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4733)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_4733)),
    inference(variable_rename,[status(thm)],[f_1205_1]) ).

cnf(f_1205_3,plain,
    hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4733)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4733)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_4733)),
    inference(clausify,[status(thm)],[f_1205_2]) ).

fof(f_1206_1,plain,
    ! [V_u_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_u_2)) = hAPP(c_Nat_OSuc,V_u_2),
    inference(fof_nnf,[status(thm)],[fact_card__atMost]) ).

fof(f_1206_2,plain,
    ! [U_4734] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_4734)) = hAPP(c_Nat_OSuc,U_4734),
    inference(variable_rename,[status(thm)],[f_1206_1]) ).

cnf(f_1206_3,plain,
    hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_4734)) = hAPP(c_Nat_OSuc,U_4734),
    inference(clausify,[status(thm)],[f_1206_2]) ).

fof(f_1207_1,plain,
    ! [V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a))))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_less__add__one]) ).

fof(f_1207_2,plain,
    ! [U_4736,U_4735] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4735),U_4736),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4735),U_4736),c_Groups_Oone__class_Oone(U_4735))))
      | ~ class_Rings_Olinordered__semidom(U_4735) ),
    inference(variable_rename,[status(thm)],[f_1207_1]) ).

cnf(f_1207_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4735),U_4736),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4735),U_4736),c_Groups_Oone__class_Oone(U_4735))))
    | ~ class_Rings_Olinordered__semidom(U_4735) ),
    inference(clausify,[status(thm)],[f_1207_2]) ).

fof(f_1208_1,plain,
    ! [V_n,V_m,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_m),V_n)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_m))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_less__1__mult]) ).

fof(f_1208_2,plain,
    ! [U_4739,U_4738,U_4737] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4737),c_Groups_Oone__class_Oone(U_4737)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4737),U_4738),U_4739)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4737),c_Groups_Oone__class_Oone(U_4737)),U_4739))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4737),c_Groups_Oone__class_Oone(U_4737)),U_4738))
      | ~ class_Rings_Olinordered__semidom(U_4737) ),
    inference(variable_rename,[status(thm)],[f_1208_1]) ).

cnf(f_1208_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4737),c_Groups_Oone__class_Oone(U_4737)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4737),U_4738),U_4739)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4737),c_Groups_Oone__class_Oone(U_4737)),U_4739))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4737),c_Groups_Oone__class_Oone(U_4737)),U_4738))
    | ~ class_Rings_Olinordered__semidom(U_4737) ),
    inference(clausify,[status(thm)],[f_1208_2]) ).

fof(f_1209_1,plain,
    ! [V_m,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)),V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a))),V_m)
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J]) ).

fof(f_1209_2,plain,
    ! [U_4742,U_4741,U_4740] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4740),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4740),U_4741),U_4742)),U_4742) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4740),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4740),U_4741),c_Groups_Oone__class_Oone(U_4740))),U_4742)
      | ~ class_Rings_Ocomm__semiring__1(U_4740) ),
    inference(variable_rename,[status(thm)],[f_1209_1]) ).

cnf(f_1209_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4740),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4740),U_4741),U_4742)),U_4742) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4740),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4740),U_4741),c_Groups_Oone__class_Oone(U_4740))),U_4742)
    | ~ class_Rings_Ocomm__semiring__1(U_4740) ),
    inference(clausify,[status(thm)],[f_1209_2]) ).

fof(f_1210_1,plain,
    ! [V_a,V_m,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a))),V_m)
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J]) ).

fof(f_1210_2,plain,
    ! [U_4745,U_4744,U_4743] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4743),U_4744),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4743),U_4745),U_4744)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4743),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4743),U_4745),c_Groups_Oone__class_Oone(U_4743))),U_4744)
      | ~ class_Rings_Ocomm__semiring__1(U_4743) ),
    inference(variable_rename,[status(thm)],[f_1210_1]) ).

cnf(f_1210_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4743),U_4744),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4743),U_4745),U_4744)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4743),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4743),U_4745),c_Groups_Oone__class_Oone(U_4743))),U_4744)
    | ~ class_Rings_Ocomm__semiring__1(U_4743) ),
    inference(clausify,[status(thm)],[f_1210_2]) ).

fof(f_1211_1,plain,
    ! [V_m,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_m),V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a))),V_m)
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J]) ).

fof(f_1211_2,plain,
    ! [U_4747,U_4746] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4746),U_4747),U_4747) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4746),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4746),c_Groups_Oone__class_Oone(U_4746)),c_Groups_Oone__class_Oone(U_4746))),U_4747)
      | ~ class_Rings_Ocomm__semiring__1(U_4746) ),
    inference(variable_rename,[status(thm)],[f_1211_1]) ).

cnf(f_1211_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4746),U_4747),U_4747) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4746),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4746),c_Groups_Oone__class_Oone(U_4746)),c_Groups_Oone__class_Oone(U_4746))),U_4747)
    | ~ class_Rings_Ocomm__semiring__1(U_4746) ),
    inference(clausify,[status(thm)],[f_1211_2]) ).

fof(f_1212_1,plain,
    ! [V_x_2,T_b] :
      ( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_b)
          | ( V_x_2 != hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b))
            & V_x_2 != c_Groups_Oone__class_Oone(T_b) ) )
        & ( V_x_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b))
          | V_x_2 = c_Groups_Oone__class_Oone(T_b)
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2) != c_Groups_Oone__class_Oone(T_b) ) )
      | ~ class_Rings_Oring__1__no__zero__divisors(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_square__eq__1__iff]) ).

fof(f_1212_2,plain,
    ! [U_4749,U_4748] :
      ( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4748),U_4749),U_4749) = c_Groups_Oone__class_Oone(U_4748)
          | ( U_4749 != hAPP(c_Groups_Ouminus__class_Ouminus(U_4748),c_Groups_Oone__class_Oone(U_4748))
            & U_4749 != c_Groups_Oone__class_Oone(U_4748) ) )
        & ( U_4749 = hAPP(c_Groups_Ouminus__class_Ouminus(U_4748),c_Groups_Oone__class_Oone(U_4748))
          | U_4749 = c_Groups_Oone__class_Oone(U_4748)
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4748),U_4749),U_4749) != c_Groups_Oone__class_Oone(U_4748) ) )
      | ~ class_Rings_Oring__1__no__zero__divisors(U_4748) ),
    inference(variable_rename,[status(thm)],[f_1212_1]) ).

cnf(f_1212_3,plain,
    ( U_4749 = hAPP(c_Groups_Ouminus__class_Ouminus(U_4748),c_Groups_Oone__class_Oone(U_4748))
    | U_4749 = c_Groups_Oone__class_Oone(U_4748)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4748),U_4749),U_4749) != c_Groups_Oone__class_Oone(U_4748)
    | ~ class_Rings_Oring__1__no__zero__divisors(U_4748) ),
    inference(clausify,[status(thm)],[f_1212_2]) ).

cnf(f_1212_4,plain,
    ( U_4749 != c_Groups_Oone__class_Oone(U_4748)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4748),U_4749),U_4749) = c_Groups_Oone__class_Oone(U_4748)
    | ~ class_Rings_Oring__1__no__zero__divisors(U_4748) ),
    inference(clausify,[status(thm)],[f_1212_2]) ).

cnf(f_1212_5,plain,
    ( U_4749 != hAPP(c_Groups_Ouminus__class_Ouminus(U_4748),c_Groups_Oone__class_Oone(U_4748))
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4748),U_4749),U_4749) = c_Groups_Oone__class_Oone(U_4748)
    | ~ class_Rings_Oring__1__no__zero__divisors(U_4748) ),
    inference(clausify,[status(thm)],[f_1212_2]) ).

fof(f_1213_1,plain,
    ! [V_x,T_a] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),V_x)
      | ~ class_Rings_Ocomm__ring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J]) ).

fof(f_1213_2,plain,
    ! [U_4751,U_4750] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_4750),U_4751) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4750),hAPP(c_Groups_Ouminus__class_Ouminus(U_4750),c_Groups_Oone__class_Oone(U_4750))),U_4751)
      | ~ class_Rings_Ocomm__ring__1(U_4750) ),
    inference(variable_rename,[status(thm)],[f_1213_1]) ).

cnf(f_1213_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_4750),U_4751) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4750),hAPP(c_Groups_Ouminus__class_Ouminus(U_4750),c_Groups_Oone__class_Oone(U_4750))),U_4751)
    | ~ class_Rings_Ocomm__ring__1(U_4750) ),
    inference(clausify,[status(thm)],[f_1213_2]) ).

fof(f_1214_1,plain,
    ! [V_m,V_i] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m)))),
    inference(fof_nnf,[status(thm)],[fact_less__add__Suc1]) ).

fof(f_1214_2,plain,
    ! [U_4753,U_4752] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4752),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4752),U_4753)))),
    inference(variable_rename,[status(thm)],[f_1214_1]) ).

cnf(f_1214_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4752),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4752),U_4753)))),
    inference(clausify,[status(thm)],[f_1214_2]) ).

fof(f_1215_1,plain,
    ! [V_m,V_i] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_i)))),
    inference(fof_nnf,[status(thm)],[fact_less__add__Suc2]) ).

fof(f_1215_2,plain,
    ! [U_4755,U_4754] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4754),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4755),U_4754)))),
    inference(variable_rename,[status(thm)],[f_1215_1]) ).

cnf(f_1215_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4754),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4755),U_4754)))),
    inference(clausify,[status(thm)],[f_1215_2]) ).

fof(f_1216_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
        | ! [B_k] : V_n_2 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)) )
      & ( ? [B_k] : V_n_2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_less__iff__Suc__add]) ).

fof(f_1216_2,plain,
    ! [U_4759,U_4758] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4758),U_4759))
        | ! [U_4757] : U_4759 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4758),U_4757)) )
      & ( ? [U_4756] : U_4759 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4758),U_4756))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4758),U_4759)) ) ),
    inference(variable_rename,[status(thm)],[f_1216_1]) ).

fof(f_1216_3,plain,
    ( ! [U_4763,U_4761] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4761),U_4763))
        | ! [U_4757] : U_4763 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4761),U_4757)) )
    & ! [U_4762,U_4760] :
        ( ? [U_4756] : U_4762 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4760),U_4756))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4760),U_4762)) ) ),
    inference(miniscope,[status(thm)],[f_1216_2]) ).

fof(f_1216_4,plain,
    ( ! [U_4763,U_4761] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4761),U_4763))
        | ! [U_4757] : U_4763 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4761),U_4757)) )
    & ! [U_4762,U_4760] :
        ( U_4762 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4760),sK95(U_4762,U_4760)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4760),U_4762)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK95]),skolemize(U_4756,sK95(U_4762,U_4760))],[f_1216_3]) ).

cnf(f_1216_5,plain,
    ( U_4762 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4760),sK95(U_4762,U_4760)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4760),U_4762)) ),
    inference(clausify,[status(thm)],[f_1216_4]) ).

cnf(f_1216_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4761),U_4763))
    | U_4763 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4761),U_4757)) ),
    inference(clausify,[status(thm)],[f_1216_4]) ).

fof(f_1217_1,plain,
    ! [V_m_2,V_n_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_less__eq__Suc__le]) ).

fof(f_1217_2,plain,
    ! [U_4765,U_4764] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4764),U_4765))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4764)),U_4765)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4764)),U_4765))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4764),U_4765)) ) ),
    inference(variable_rename,[status(thm)],[f_1217_1]) ).

fof(f_1217_3,plain,
    ( ! [U_4769,U_4767] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4767),U_4769))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4767)),U_4769)) )
    & ! [U_4768,U_4766] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4766)),U_4768))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4766),U_4768)) ) ),
    inference(miniscope,[status(thm)],[f_1217_2]) ).

cnf(f_1217_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4766)),U_4768))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4766),U_4768)) ),
    inference(clausify,[status(thm)],[f_1217_3]) ).

cnf(f_1217_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4767),U_4769))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4767)),U_4769)) ),
    inference(clausify,[status(thm)],[f_1217_3]) ).

fof(f_1218_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_less__Suc__eq__le]) ).

fof(f_1218_2,plain,
    ! [U_4771,U_4770] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4770),hAPP(c_Nat_OSuc,U_4771)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4770),U_4771)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4770),U_4771))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4770),hAPP(c_Nat_OSuc,U_4771))) ) ),
    inference(variable_rename,[status(thm)],[f_1218_1]) ).

fof(f_1218_3,plain,
    ( ! [U_4775,U_4773] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4773),hAPP(c_Nat_OSuc,U_4775)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4773),U_4775)) )
    & ! [U_4774,U_4772] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4772),U_4774))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4772),hAPP(c_Nat_OSuc,U_4774))) ) ),
    inference(miniscope,[status(thm)],[f_1218_2]) ).

cnf(f_1218_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4772),U_4774))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4772),hAPP(c_Nat_OSuc,U_4774))) ),
    inference(clausify,[status(thm)],[f_1218_3]) ).

cnf(f_1218_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4773),hAPP(c_Nat_OSuc,U_4775)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4773),U_4775)) ),
    inference(clausify,[status(thm)],[f_1218_3]) ).

fof(f_1219_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Suc__le__eq]) ).

fof(f_1219_2,plain,
    ! [U_4777,U_4776] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4776)),U_4777))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4776),U_4777)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4776),U_4777))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4776)),U_4777)) ) ),
    inference(variable_rename,[status(thm)],[f_1219_1]) ).

fof(f_1219_3,plain,
    ( ! [U_4781,U_4779] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4779)),U_4781))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4779),U_4781)) )
    & ! [U_4780,U_4778] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4778),U_4780))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4778)),U_4780)) ) ),
    inference(miniscope,[status(thm)],[f_1219_2]) ).

cnf(f_1219_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4778),U_4780))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4778)),U_4780)) ),
    inference(clausify,[status(thm)],[f_1219_3]) ).

cnf(f_1219_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4779)),U_4781))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4779),U_4781)) ),
    inference(clausify,[status(thm)],[f_1219_3]) ).

fof(f_1220_1,plain,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_le__imp__less__Suc]) ).

fof(f_1220_2,plain,
    ! [U_4783,U_4782] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4782),hAPP(c_Nat_OSuc,U_4783)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4782),U_4783)) ),
    inference(variable_rename,[status(thm)],[f_1220_1]) ).

cnf(f_1220_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4782),hAPP(c_Nat_OSuc,U_4783)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4782),U_4783)) ),
    inference(clausify,[status(thm)],[f_1220_2]) ).

fof(f_1221_1,plain,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_Suc__leI]) ).

fof(f_1221_2,plain,
    ! [U_4785,U_4784] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4784)),U_4785))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4784),U_4785)) ),
    inference(variable_rename,[status(thm)],[f_1221_1]) ).

cnf(f_1221_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4784)),U_4785))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4784),U_4785)) ),
    inference(clausify,[status(thm)],[f_1221_2]) ).

fof(f_1222_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2)))
          | V_n_2 != V_m_2 )
        & ( V_n_2 = V_m_2
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ),
    inference(fof_nnf,[status(thm)],[fact_le__less__Suc__eq]) ).

fof(f_1222_2,plain,
    ! [U_4787,U_4786] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4787),hAPP(c_Nat_OSuc,U_4786)))
          | U_4787 != U_4786 )
        & ( U_4787 = U_4786
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4787),hAPP(c_Nat_OSuc,U_4786))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4786),U_4787)) ),
    inference(variable_rename,[status(thm)],[f_1222_1]) ).

cnf(f_1222_3,plain,
    ( U_4787 = U_4786
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4787),hAPP(c_Nat_OSuc,U_4786)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4786),U_4787)) ),
    inference(clausify,[status(thm)],[f_1222_2]) ).

cnf(f_1222_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4787),hAPP(c_Nat_OSuc,U_4786)))
    | U_4787 != U_4786
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4786),U_4787)) ),
    inference(clausify,[status(thm)],[f_1222_2]) ).

fof(f_1223_1,plain,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_Suc__le__lessD]) ).

fof(f_1223_2,plain,
    ! [U_4789,U_4788] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4788),U_4789))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4788)),U_4789)) ),
    inference(variable_rename,[status(thm)],[f_1223_1]) ).

cnf(f_1223_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4788),U_4789))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4788)),U_4789)) ),
    inference(clausify,[status(thm)],[f_1223_2]) ).

fof(f_1224_1,plain,
    ! [V_n,V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),hAPP(c_Nat_OSuc,V_m))),
    inference(fof_nnf,[status(thm)],[fact_diff__less__Suc]) ).

fof(f_1224_2,plain,
    ! [U_4791,U_4790] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4790),U_4791)),hAPP(c_Nat_OSuc,U_4790))),
    inference(variable_rename,[status(thm)],[f_1224_1]) ).

cnf(f_1224_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4790),U_4791)),hAPP(c_Nat_OSuc,U_4790))),
    inference(clausify,[status(thm)],[f_1224_2]) ).

fof(f_1225_1,plain,
    ! [V_n_2,V_m_2,V_k_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_n_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_n_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_Suc__mult__less__cancel1]) ).

fof(f_1225_2,plain,
    ! [U_4794,U_4793,U_4792] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4792)),U_4793)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4792)),U_4794)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4793),U_4794)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4793),U_4794))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4792)),U_4793)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4792)),U_4794))) ) ),
    inference(variable_rename,[status(thm)],[f_1225_1]) ).

fof(f_1225_3,plain,
    ( ! [U_4800,U_4798] :
        ( ! [U_4796] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4796)),U_4798)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4796)),U_4800)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4798),U_4800)) )
    & ! [U_4799,U_4797] :
        ( ! [U_4795] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4795)),U_4797)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4795)),U_4799)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4797),U_4799)) ) ),
    inference(miniscope,[status(thm)],[f_1225_2]) ).

cnf(f_1225_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4795)),U_4797)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4795)),U_4799)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4797),U_4799)) ),
    inference(clausify,[status(thm)],[f_1225_3]) ).

cnf(f_1225_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4796)),U_4798)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4796)),U_4800)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4798),U_4800)) ),
    inference(clausify,[status(thm)],[f_1225_3]) ).

fof(f_1226_1,plain,
    ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),
    inference(fof_nnf,[status(thm)],[fact_mult__Suc__right]) ).

fof(f_1226_2,plain,
    ! [U_4802,U_4801] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4801),hAPP(c_Nat_OSuc,U_4802)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4801),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4801),U_4802)),
    inference(variable_rename,[status(thm)],[f_1226_1]) ).

cnf(f_1226_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4801),hAPP(c_Nat_OSuc,U_4802)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4801),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4801),U_4802)),
    inference(clausify,[status(thm)],[f_1226_2]) ).

fof(f_1227_1,plain,
    ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),
    inference(fof_nnf,[status(thm)],[fact_mult__Suc]) ).

fof(f_1227_2,plain,
    ! [U_4804,U_4803] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4803)),U_4804) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4804),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4803),U_4804)),
    inference(variable_rename,[status(thm)],[f_1227_1]) ).

cnf(f_1227_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4803)),U_4804) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4804),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4803),U_4804)),
    inference(clausify,[status(thm)],[f_1227_2]) ).

fof(f_1228_1,plain,
    ! [V_m,V_n] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) ),
    inference(fof_nnf,[status(thm)],[fact_Suc__diff__le]) ).

fof(f_1228_2,plain,
    ! [U_4806,U_4805] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4806)),U_4805) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4806),U_4805))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4805),U_4806)) ),
    inference(variable_rename,[status(thm)],[f_1228_1]) ).

cnf(f_1228_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4806)),U_4805) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4806),U_4805))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4805),U_4806)) ),
    inference(clausify,[status(thm)],[f_1228_2]) ).

fof(f_1229_1,plain,
    ! [V_n_2,V_m_2,V_k_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_n_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),V_n_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_Suc__mult__le__cancel1]) ).

fof(f_1229_2,plain,
    ! [U_4809,U_4808,U_4807] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4807)),U_4808)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4807)),U_4809)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4808),U_4809)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4808),U_4809))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4807)),U_4808)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4807)),U_4809))) ) ),
    inference(variable_rename,[status(thm)],[f_1229_1]) ).

fof(f_1229_3,plain,
    ( ! [U_4815,U_4813] :
        ( ! [U_4811] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4811)),U_4813)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4811)),U_4815)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4813),U_4815)) )
    & ! [U_4814,U_4812] :
        ( ! [U_4810] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4810)),U_4812)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4810)),U_4814)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4812),U_4814)) ) ),
    inference(miniscope,[status(thm)],[f_1229_2]) ).

cnf(f_1229_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4810)),U_4812)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4810)),U_4814)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4812),U_4814)) ),
    inference(clausify,[status(thm)],[f_1229_3]) ).

cnf(f_1229_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4811)),U_4813)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4811)),U_4815)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4813),U_4815)) ),
    inference(clausify,[status(thm)],[f_1229_3]) ).

fof(f_1230_1,plain,
    ! [V_g_2,T_c,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_g_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(T_b)
      | ~ class_Groups_Ocomm__monoid__mult(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setprod_Oempty]) ).

fof(f_1230_2,plain,
    ! [U_4818,U_4817,U_4816] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4817,U_4816),U_4818),c_Orderings_Obot__class_Obot(tc_fun(U_4817,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(U_4816)
      | ~ class_Groups_Ocomm__monoid__mult(U_4816) ),
    inference(variable_rename,[status(thm)],[f_1230_1]) ).

cnf(f_1230_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4817,U_4816),U_4818),c_Orderings_Obot__class_Obot(tc_fun(U_4817,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(U_4816)
    | ~ class_Groups_Ocomm__monoid__mult(U_4816) ),
    inference(clausify,[status(thm)],[f_1230_2]) ).

fof(f_1231_1,plain,
    ! [V_f_2,T_c,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(T_b)
      | ~ class_Groups_Ocomm__monoid__mult(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__empty]) ).

fof(f_1231_2,plain,
    ! [U_4821,U_4820,U_4819] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4820,U_4819),U_4821),c_Orderings_Obot__class_Obot(tc_fun(U_4820,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(U_4819)
      | ~ class_Groups_Ocomm__monoid__mult(U_4819) ),
    inference(variable_rename,[status(thm)],[f_1231_1]) ).

cnf(f_1231_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4820,U_4819),U_4821),c_Orderings_Obot__class_Obot(tc_fun(U_4820,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(U_4819)
    | ~ class_Groups_Ocomm__monoid__mult(U_4819) ),
    inference(clausify,[status(thm)],[f_1231_2]) ).

fof(f_1232_1,plain,
    ! [V_g_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = c_Groups_Oone__class_Oone(T_c)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setprod_Oinfinite]) ).

fof(f_1232_2,plain,
    ! [U_4825,U_4824,U_4823,U_4822] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4823,U_4822),U_4825),U_4824) = c_Groups_Oone__class_Oone(U_4822)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_4823),U_4824))
      | ~ class_Groups_Ocomm__monoid__mult(U_4822) ),
    inference(variable_rename,[status(thm)],[f_1232_1]) ).

cnf(f_1232_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4823,U_4822),U_4825),U_4824) = c_Groups_Oone__class_Oone(U_4822)
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_4823),U_4824))
    | ~ class_Groups_Ocomm__monoid__mult(U_4822) ),
    inference(clausify,[status(thm)],[f_1232_2]) ).

fof(f_1233_1,plain,
    ! [V_f_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2) = c_Groups_Oone__class_Oone(T_c)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__infinite]) ).

fof(f_1233_2,plain,
    ! [U_4829,U_4828,U_4827,U_4826] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4827,U_4826),U_4829),U_4828) = c_Groups_Oone__class_Oone(U_4826)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_4827),U_4828))
      | ~ class_Groups_Ocomm__monoid__mult(U_4826) ),
    inference(variable_rename,[status(thm)],[f_1233_1]) ).

cnf(f_1233_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4827,U_4826),U_4829),U_4828) = c_Groups_Oone__class_Oone(U_4826)
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_4827),U_4828))
    | ~ class_Groups_Ocomm__monoid__mult(U_4826) ),
    inference(clausify,[status(thm)],[f_1233_2]) ).

fof(f_1234_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) )
      & ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_n_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_atLeastLessThanSuc]) ).

fof(f_1234_2,plain,
    ! [U_4831,U_4830] :
      ( ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_4830),hAPP(c_Nat_OSuc,U_4831)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4830),U_4831)) )
      & ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_4830),hAPP(c_Nat_OSuc,U_4831)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_4831),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_4830),U_4831))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4830),U_4831)) ) ),
    inference(variable_rename,[status(thm)],[f_1234_1]) ).

fof(f_1234_3,plain,
    ( ! [U_4835,U_4833] :
        ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_4833),hAPP(c_Nat_OSuc,U_4835)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4833),U_4835)) )
    & ! [U_4834,U_4832] :
        ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_4832),hAPP(c_Nat_OSuc,U_4834)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_4834),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_4832),U_4834))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4832),U_4834)) ) ),
    inference(miniscope,[status(thm)],[f_1234_2]) ).

cnf(f_1234_4,plain,
    ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_4832),hAPP(c_Nat_OSuc,U_4834)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_4834),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_4832),U_4834))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4832),U_4834)) ),
    inference(clausify,[status(thm)],[f_1234_3]) ).

cnf(f_1234_5,plain,
    ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_4833),hAPP(c_Nat_OSuc,U_4835)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4833),U_4835)) ),
    inference(clausify,[status(thm)],[f_1234_3]) ).

fof(f_1235_1,plain,
    ! [V_n_2,V_m_2] :
      ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) ),
    inference(fof_nnf,[status(thm)],[fact_atLeastAtMostSuc__conv]) ).

fof(f_1235_2,plain,
    ! [U_4837,U_4836] :
      ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_4836,hAPP(c_Nat_OSuc,U_4837)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4837)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_4836,U_4837))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4836),hAPP(c_Nat_OSuc,U_4837))) ),
    inference(variable_rename,[status(thm)],[f_1235_1]) ).

cnf(f_1235_3,plain,
    ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_4836,hAPP(c_Nat_OSuc,U_4837)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4837)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_4836,U_4837))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4836),hAPP(c_Nat_OSuc,U_4837))) ),
    inference(clausify,[status(thm)],[f_1235_2]) ).

fof(f_1236_1,plain,
    ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_l_2,V_u_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_u_2)),V_l_2),
    inference(fof_nnf,[status(thm)],[fact_card__atLeastAtMost]) ).

fof(f_1236_2,plain,
    ! [U_4839,U_4838] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_4838,U_4839)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4839)),U_4838),
    inference(variable_rename,[status(thm)],[f_1236_1]) ).

cnf(f_1236_3,plain,
    hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_4838,U_4839)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4839)),U_4838),
    inference(clausify,[status(thm)],[f_1236_2]) ).

fof(f_1237_1,plain,
    ! [V_u_2,V_l_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_l_2),hAPP(c_Nat_OSuc,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_l_2,V_u_2),
    inference(fof_nnf,[status(thm)],[fact_atLeastLessThanSuc__atLeastAtMost]) ).

fof(f_1237_2,plain,
    ! [U_4841,U_4840] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_4840),hAPP(c_Nat_OSuc,U_4841)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_4840,U_4841),
    inference(variable_rename,[status(thm)],[f_1237_1]) ).

cnf(f_1237_3,plain,
    hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_4840),hAPP(c_Nat_OSuc,U_4841)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_4840,U_4841),
    inference(clausify,[status(thm)],[f_1237_2]) ).

fof(f_1238_1,plain,
    ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2),
    inference(fof_nnf,[status(thm)],[fact_lessThan__Suc__atMost]) ).

fof(f_1238_2,plain,
    ! [U_4842] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4842)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_4842),
    inference(variable_rename,[status(thm)],[f_1238_1]) ).

cnf(f_1238_3,plain,
    hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4842)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_4842),
    inference(clausify,[status(thm)],[f_1238_2]) ).

fof(f_1239_1,plain,
    ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,V_l_2,V_u_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_u_2),hAPP(c_Nat_OSuc,V_l_2)),
    inference(fof_nnf,[status(thm)],[fact_card__greaterThanLessThan]) ).

fof(f_1239_2,plain,
    ! [U_4844,U_4843] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_4843,U_4844)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4844),hAPP(c_Nat_OSuc,U_4843)),
    inference(variable_rename,[status(thm)],[f_1239_1]) ).

cnf(f_1239_3,plain,
    hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_4843,U_4844)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4844),hAPP(c_Nat_OSuc,U_4843)),
    inference(clausify,[status(thm)],[f_1239_2]) ).

fof(f_1240_1,plain,
    ! [V_u_2,V_l_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_l_2),V_u_2) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_l_2,V_u_2),
    inference(fof_nnf,[status(thm)],[fact_atLeastSucAtMost__greaterThanAtMost]) ).

fof(f_1240_2,plain,
    ! [U_4846,U_4845] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_4845),U_4846) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_4845,U_4846),
    inference(variable_rename,[status(thm)],[f_1240_1]) ).

cnf(f_1240_3,plain,
    c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_4845),U_4846) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_4845,U_4846),
    inference(clausify,[status(thm)],[f_1240_2]) ).

fof(f_1241_1,plain,
    ! [V_u_2,V_l_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_l_2)),V_u_2) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,V_l_2,V_u_2),
    inference(fof_nnf,[status(thm)],[fact_atLeastSucLessThan__greaterThanLessThan]) ).

fof(f_1241_2,plain,
    ! [U_4848,U_4847] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_4847)),U_4848) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_4847,U_4848),
    inference(variable_rename,[status(thm)],[f_1241_1]) ).

cnf(f_1241_3,plain,
    hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_4847)),U_4848) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_4847,U_4848),
    inference(clausify,[status(thm)],[f_1241_2]) ).

fof(f_1242_1,plain,
    ! [V_m,V_j,V_k] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k))),V_m) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_j)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_m))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) ),
    inference(fof_nnf,[status(thm)],[fact_diff__Suc__diff__eq2]) ).

fof(f_1242_2,plain,
    ! [U_4851,U_4850,U_4849] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4850),U_4849))),U_4851) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4850)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4849),U_4851))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4849),U_4850)) ),
    inference(variable_rename,[status(thm)],[f_1242_1]) ).

cnf(f_1242_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4850),U_4849))),U_4851) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4850)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4849),U_4851))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4849),U_4850)) ),
    inference(clausify,[status(thm)],[f_1242_2]) ).

fof(f_1243_1,plain,
    ! [V_m,V_j,V_k] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),hAPP(c_Nat_OSuc,V_j))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) ),
    inference(fof_nnf,[status(thm)],[fact_diff__Suc__diff__eq1]) ).

fof(f_1243_2,plain,
    ! [U_4854,U_4853,U_4852] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4854),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4853),U_4852))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4854),U_4852)),hAPP(c_Nat_OSuc,U_4853))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4852),U_4853)) ),
    inference(variable_rename,[status(thm)],[f_1243_1]) ).

cnf(f_1243_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4854),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4853),U_4852))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4854),U_4852)),hAPP(c_Nat_OSuc,U_4853))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4852),U_4853)) ),
    inference(clausify,[status(thm)],[f_1243_2]) ).

fof(f_1244_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_b),V_A_2))
      | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__insert__disjoint]) ).

fof(f_1244_2,plain,
    ! [U_4857,U_4856,U_4855] :
      ( hAPP(c_Finite__Set_Ocard(U_4855),hAPP(hAPP(c_Set_Oinsert(U_4855),U_4857),U_4856)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_4855),U_4856))
      | hBOOL(hAPP(hAPP(c_member(U_4855),U_4857),U_4856))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4855),U_4856)) ),
    inference(variable_rename,[status(thm)],[f_1244_1]) ).

cnf(f_1244_3,plain,
    ( hAPP(c_Finite__Set_Ocard(U_4855),hAPP(hAPP(c_Set_Oinsert(U_4855),U_4857),U_4856)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_4855),U_4856))
    | hBOOL(hAPP(hAPP(c_member(U_4855),U_4857),U_4856))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4855),U_4856)) ),
    inference(clausify,[status(thm)],[f_1244_2]) ).

fof(f_1245_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( ( ( hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_b),V_A_2))
          | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) )
        & ( hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2)
          | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__insert__if]) ).

fof(f_1245_2,plain,
    ! [U_4860,U_4859,U_4858] :
      ( ( ( hAPP(c_Finite__Set_Ocard(U_4858),hAPP(hAPP(c_Set_Oinsert(U_4858),U_4860),U_4859)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_4858),U_4859))
          | hBOOL(hAPP(hAPP(c_member(U_4858),U_4860),U_4859)) )
        & ( hAPP(c_Finite__Set_Ocard(U_4858),hAPP(hAPP(c_Set_Oinsert(U_4858),U_4860),U_4859)) = hAPP(c_Finite__Set_Ocard(U_4858),U_4859)
          | ~ hBOOL(hAPP(hAPP(c_member(U_4858),U_4860),U_4859)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4858),U_4859)) ),
    inference(variable_rename,[status(thm)],[f_1245_1]) ).

cnf(f_1245_3,plain,
    ( hAPP(c_Finite__Set_Ocard(U_4858),hAPP(hAPP(c_Set_Oinsert(U_4858),U_4860),U_4859)) = hAPP(c_Finite__Set_Ocard(U_4858),U_4859)
    | ~ hBOOL(hAPP(hAPP(c_member(U_4858),U_4860),U_4859))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4858),U_4859)) ),
    inference(clausify,[status(thm)],[f_1245_2]) ).

cnf(f_1245_4,plain,
    ( hAPP(c_Finite__Set_Ocard(U_4858),hAPP(hAPP(c_Set_Oinsert(U_4858),U_4860),U_4859)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_4858),U_4859))
    | hBOOL(hAPP(hAPP(c_member(U_4858),U_4860),U_4859))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4858),U_4859)) ),
    inference(clausify,[status(thm)],[f_1245_2]) ).

fof(f_1246_1,plain,
    ! [V_f_2,V_n_2,V_m_2,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_f_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2)),V_n_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__head__upt__Suc]) ).

fof(f_1246_2,plain,
    ! [U_4864,U_4863,U_4862,U_4861] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_4861),U_4864),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_4862),U_4863)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4861),hAPP(U_4864,U_4862)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_4861),U_4864),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_4862)),U_4863)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4862),U_4863))
      | ~ class_Groups_Ocomm__monoid__add(U_4861) ),
    inference(variable_rename,[status(thm)],[f_1246_1]) ).

cnf(f_1246_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_4861),U_4864),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_4862),U_4863)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4861),hAPP(U_4864,U_4862)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_4861),U_4864),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_4862)),U_4863)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4862),U_4863))
    | ~ class_Groups_Ocomm__monoid__add(U_4861) ),
    inference(clausify,[status(thm)],[f_1246_2]) ).

fof(f_1247_1,plain,
    ! [V_f_2,V_n_2,V_m_2,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_f_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2),V_n_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__head__Suc]) ).

fof(f_1247_2,plain,
    ! [U_4868,U_4867,U_4866,U_4865] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_4865),U_4868),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_4866,U_4867)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4865),hAPP(U_4868,U_4866)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_4865),U_4868),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_4866),U_4867)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4866),U_4867))
      | ~ class_Groups_Ocomm__monoid__add(U_4865) ),
    inference(variable_rename,[status(thm)],[f_1247_1]) ).

cnf(f_1247_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_4865),U_4868),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_4866,U_4867)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4865),hAPP(U_4868,U_4866)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_4865),U_4868),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_4866),U_4867)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4866),U_4867))
    | ~ class_Groups_Ocomm__monoid__add(U_4865) ),
    inference(clausify,[status(thm)],[f_1247_2]) ).

fof(f_1248_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__insert]) ).

fof(f_1248_2,plain,
    ! [U_4871,U_4870,U_4869] :
      ( hAPP(c_Finite__Set_Ocard(U_4869),hAPP(hAPP(c_Set_Oinsert(U_4869),U_4871),U_4870)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_4869),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4869,tc_HOL_Obool)),U_4870),hAPP(hAPP(c_Set_Oinsert(U_4869),U_4871),c_Orderings_Obot__class_Obot(tc_fun(U_4869,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4869),U_4870)) ),
    inference(variable_rename,[status(thm)],[f_1248_1]) ).

cnf(f_1248_3,plain,
    ( hAPP(c_Finite__Set_Ocard(U_4869),hAPP(hAPP(c_Set_Oinsert(U_4869),U_4871),U_4870)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_4869),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4869,tc_HOL_Obool)),U_4870),hAPP(hAPP(c_Set_Oinsert(U_4869),U_4871),c_Orderings_Obot__class_Obot(tc_fun(U_4869,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4869),U_4870)) ),
    inference(clausify,[status(thm)],[f_1248_2]) ).

fof(f_1249_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))
      | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card_Oinsert]) ).

fof(f_1249_2,plain,
    ! [U_4874,U_4873,U_4872] :
      ( hAPP(c_Finite__Set_Ocard(U_4872),hAPP(hAPP(c_Set_Oinsert(U_4872),U_4874),U_4873)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_4872),U_4873))
      | hBOOL(hAPP(hAPP(c_member(U_4872),U_4874),U_4873))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4872),U_4873)) ),
    inference(variable_rename,[status(thm)],[f_1249_1]) ).

cnf(f_1249_3,plain,
    ( hAPP(c_Finite__Set_Ocard(U_4872),hAPP(hAPP(c_Set_Oinsert(U_4872),U_4874),U_4873)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_4872),U_4873))
    | hBOOL(hAPP(hAPP(c_member(U_4872),U_4874),U_4873))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4872),U_4873)) ),
    inference(clausify,[status(thm)],[f_1249_2]) ).

fof(f_1250_1,plain,
    ! [V_p_2,V_f_2,V_n_2,V_m_2,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_p_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_p_2))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__ub__add__nat]) ).

fof(f_1250_2,plain,
    ! [U_4879,U_4878,U_4877,U_4876,U_4875] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_4875),U_4878),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_4876,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4877),U_4879))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4875),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_4875),U_4878),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_4876,U_4877))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_4875),U_4878),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4877),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4877),U_4879))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4876),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4877),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
      | ~ class_Groups_Ocomm__monoid__add(U_4875) ),
    inference(variable_rename,[status(thm)],[f_1250_1]) ).

cnf(f_1250_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_4875),U_4878),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_4876,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4877),U_4879))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4875),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_4875),U_4878),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_4876,U_4877))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_4875),U_4878),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4877),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4877),U_4879))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4876),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4877),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | ~ class_Groups_Ocomm__monoid__add(U_4875) ),
    inference(clausify,[status(thm)],[f_1250_2]) ).

fof(f_1251_1,plain,
    ! [V_n,V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n),
    inference(fof_nnf,[status(thm)],[fact_diff__Suc__eq__diff__pred]) ).

fof(f_1251_2,plain,
    ! [U_4881,U_4880] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4880),hAPP(c_Nat_OSuc,U_4881)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4880),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_4881),
    inference(variable_rename,[status(thm)],[f_1251_1]) ).

cnf(f_1251_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4880),hAPP(c_Nat_OSuc,U_4881)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4880),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_4881),
    inference(clausify,[status(thm)],[f_1251_2]) ).

fof(f_1252_1,plain,
    ! [V_n] : hAPP(c_Nat_OSuc,V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(fof_nnf,[status(thm)],[fact_Suc__eq__plus1]) ).

fof(f_1252_2,plain,
    ! [U_4882] : hAPP(c_Nat_OSuc,U_4882) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4882),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[f_1252_1]) ).

cnf(f_1252_3,plain,
    hAPP(c_Nat_OSuc,U_4882) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4882),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(clausify,[status(thm)],[f_1252_2]) ).

fof(f_1253_1,plain,
    ! [V_n] : hAPP(c_Nat_OSuc,V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n),
    inference(fof_nnf,[status(thm)],[fact_Suc__eq__plus1__left]) ).

fof(f_1253_2,plain,
    ! [U_4883] : hAPP(c_Nat_OSuc,U_4883) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_4883),
    inference(variable_rename,[status(thm)],[f_1253_1]) ).

cnf(f_1253_3,plain,
    hAPP(c_Nat_OSuc,U_4883) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_4883),
    inference(clausify,[status(thm)],[f_1253_2]) ).

fof(f_1254_1,plain,
    ! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_S_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_T_2))
      | ? [B_x] :
          ( hAPP(V_f_2,B_x) != c_Groups_Oone__class_Oone(T_c)
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__Un__one]) ).

fof(f_1254_2,plain,
    ! [U_4889,U_4888,U_4887,U_4886,U_4885] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4886,U_4885),U_4889),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4886,tc_HOL_Obool)),U_4887),U_4888)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4885),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4886,U_4885),U_4889),U_4887)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4886,U_4885),U_4889),U_4888))
      | ? [U_4884] :
          ( hAPP(U_4889,U_4884) != c_Groups_Oone__class_Oone(U_4885)
          & hBOOL(hAPP(hAPP(c_member(U_4886),U_4884),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4886,tc_HOL_Obool)),U_4887),U_4888))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4886),U_4888))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4886),U_4887))
      | ~ class_Groups_Ocomm__monoid__mult(U_4885) ),
    inference(variable_rename,[status(thm)],[f_1254_1]) ).

fof(f_1254_3,plain,
    ! [U_4889,U_4888,U_4887,U_4886,U_4885] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4886,U_4885),U_4889),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4886,tc_HOL_Obool)),U_4887),U_4888)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4885),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4886,U_4885),U_4889),U_4887)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4886,U_4885),U_4889),U_4888))
      | ( hAPP(U_4889,sK96(U_4889,U_4888,U_4887,U_4886,U_4885)) != c_Groups_Oone__class_Oone(U_4885)
        & hBOOL(hAPP(hAPP(c_member(U_4886),sK96(U_4889,U_4888,U_4887,U_4886,U_4885)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4886,tc_HOL_Obool)),U_4887),U_4888))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4886),U_4888))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4886),U_4887))
      | ~ class_Groups_Ocomm__monoid__mult(U_4885) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK96]),skolemize(U_4884,sK96(U_4889,U_4888,U_4887,U_4886,U_4885))],[f_1254_2]) ).

cnf(f_1254_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_4886),sK96(U_4889,U_4888,U_4887,U_4886,U_4885)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4886,tc_HOL_Obool)),U_4887),U_4888)))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4886,U_4885),U_4889),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4886,tc_HOL_Obool)),U_4887),U_4888)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4885),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4886,U_4885),U_4889),U_4887)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4886,U_4885),U_4889),U_4888))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4886),U_4888))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4886),U_4887))
    | ~ class_Groups_Ocomm__monoid__mult(U_4885) ),
    inference(clausify,[status(thm)],[f_1254_3]) ).

cnf(f_1254_5,plain,
    ( hAPP(U_4889,sK96(U_4889,U_4888,U_4887,U_4886,U_4885)) != c_Groups_Oone__class_Oone(U_4885)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4886,U_4885),U_4889),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4886,tc_HOL_Obool)),U_4887),U_4888)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4885),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4886,U_4885),U_4889),U_4887)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4886,U_4885),U_4889),U_4888))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4886),U_4888))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4886),U_4887))
    | ~ class_Groups_Ocomm__monoid__mult(U_4885) ),
    inference(clausify,[status(thm)],[f_1254_3]) ).

fof(f_1255_1,plain,
    ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2))
      | ? [B_x] :
          ( hAPP(V_g_2,B_x) != c_Groups_Oone__class_Oone(T_c)
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setprod_Ounion__inter__neutral]) ).

fof(f_1255_2,plain,
    ! [U_4895,U_4894,U_4893,U_4892,U_4891] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4892,U_4891),U_4895),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4892,tc_HOL_Obool)),U_4893),U_4894)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4891),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4892,U_4891),U_4895),U_4893)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4892,U_4891),U_4895),U_4894))
      | ? [U_4890] :
          ( hAPP(U_4895,U_4890) != c_Groups_Oone__class_Oone(U_4891)
          & hBOOL(hAPP(hAPP(c_member(U_4892),U_4890),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4892,tc_HOL_Obool)),U_4893),U_4894))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4892),U_4894))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4892),U_4893))
      | ~ class_Groups_Ocomm__monoid__mult(U_4891) ),
    inference(variable_rename,[status(thm)],[f_1255_1]) ).

fof(f_1255_3,plain,
    ! [U_4895,U_4894,U_4893,U_4892,U_4891] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4892,U_4891),U_4895),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4892,tc_HOL_Obool)),U_4893),U_4894)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4891),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4892,U_4891),U_4895),U_4893)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4892,U_4891),U_4895),U_4894))
      | ( hAPP(U_4895,sK97(U_4895,U_4894,U_4893,U_4892,U_4891)) != c_Groups_Oone__class_Oone(U_4891)
        & hBOOL(hAPP(hAPP(c_member(U_4892),sK97(U_4895,U_4894,U_4893,U_4892,U_4891)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4892,tc_HOL_Obool)),U_4893),U_4894))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4892),U_4894))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4892),U_4893))
      | ~ class_Groups_Ocomm__monoid__mult(U_4891) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK97]),skolemize(U_4890,sK97(U_4895,U_4894,U_4893,U_4892,U_4891))],[f_1255_2]) ).

cnf(f_1255_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_4892),sK97(U_4895,U_4894,U_4893,U_4892,U_4891)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_4892,tc_HOL_Obool)),U_4893),U_4894)))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4892,U_4891),U_4895),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4892,tc_HOL_Obool)),U_4893),U_4894)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4891),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4892,U_4891),U_4895),U_4893)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4892,U_4891),U_4895),U_4894))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4892),U_4894))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4892),U_4893))
    | ~ class_Groups_Ocomm__monoid__mult(U_4891) ),
    inference(clausify,[status(thm)],[f_1255_3]) ).

cnf(f_1255_5,plain,
    ( hAPP(U_4895,sK97(U_4895,U_4894,U_4893,U_4892,U_4891)) != c_Groups_Oone__class_Oone(U_4891)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4892,U_4891),U_4895),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_4892,tc_HOL_Obool)),U_4893),U_4894)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4891),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4892,U_4891),U_4895),U_4893)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_4892,U_4891),U_4895),U_4894))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4892),U_4894))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_4892),U_4893))
    | ~ class_Groups_Ocomm__monoid__mult(U_4891) ),
    inference(clausify,[status(thm)],[f_1255_3]) ).

fof(f_1256_1,plain,
    ! [T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
      | hAPP(c_Finite__Set_Ocard(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,T_c),tc_HOL_Obool)))) ),
    inference(fof_nnf,[status(thm)],[fact_finite__fun__UNIVD1]) ).

fof(f_1256_2,plain,
    ! [U_4897,U_4896] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_4896),c_Orderings_Otop__class_Otop(tc_fun(U_4896,tc_HOL_Obool))))
      | hAPP(c_Finite__Set_Ocard(U_4897),c_Orderings_Otop__class_Otop(tc_fun(U_4897,tc_HOL_Obool))) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_4896,U_4897)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_4896,U_4897),tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_1256_1]) ).

cnf(f_1256_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_4896),c_Orderings_Otop__class_Otop(tc_fun(U_4896,tc_HOL_Obool))))
    | hAPP(c_Finite__Set_Ocard(U_4897),c_Orderings_Otop__class_Otop(tc_fun(U_4897,tc_HOL_Obool))) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_4896,U_4897)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_4896,U_4897),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_1256_2]) ).

fof(f_1257_1,plain,
    ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(fof_nnf,[status(thm)],[fact_less__zeroE]) ).

fof(f_1257_2,plain,
    ! [U_4898] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4898),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_1257_1]) ).

cnf(f_1257_3,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4898),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_1257_2]) ).

fof(f_1258_1,plain,
    ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)),
    inference(fof_nnf,[status(thm)],[fact_le0]) ).

fof(f_1258_2,plain,
    ! [U_4899] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4899)),
    inference(variable_rename,[status(thm)],[f_1258_1]) ).

cnf(f_1258_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4899)),
    inference(clausify,[status(thm)],[f_1258_2]) ).

fof(f_1259_1,plain,
    ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,V_n))),
    inference(fof_nnf,[status(thm)],[fact_zero__less__Suc]) ).

fof(f_1259_2,plain,
    ! [U_4900] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,U_4900))),
    inference(variable_rename,[status(thm)],[f_1259_1]) ).

cnf(f_1259_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,U_4900))),
    inference(clausify,[status(thm)],[f_1259_2]) ).

fof(f_1260_1,plain,
    ! [V_x_2,T_b] :
      ( ( ( c_Groups_Ozero__class_Ozero(T_b) = V_x_2
          | V_x_2 != c_Groups_Ozero__class_Ozero(T_b) )
        & ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
          | c_Groups_Ozero__class_Ozero(T_b) != V_x_2 ) )
      | ~ class_Groups_Ozero(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_zero__reorient]) ).

fof(f_1260_2,plain,
    ! [U_4902,U_4901] :
      ( ( ( c_Groups_Ozero__class_Ozero(U_4901) = U_4902
          | U_4902 != c_Groups_Ozero__class_Ozero(U_4901) )
        & ( U_4902 = c_Groups_Ozero__class_Ozero(U_4901)
          | c_Groups_Ozero__class_Ozero(U_4901) != U_4902 ) )
      | ~ class_Groups_Ozero(U_4901) ),
    inference(variable_rename,[status(thm)],[f_1260_1]) ).

cnf(f_1260_3,plain,
    ( U_4902 = c_Groups_Ozero__class_Ozero(U_4901)
    | c_Groups_Ozero__class_Ozero(U_4901) != U_4902
    | ~ class_Groups_Ozero(U_4901) ),
    inference(clausify,[status(thm)],[f_1260_2]) ).

cnf(f_1260_4,plain,
    ( c_Groups_Ozero__class_Ozero(U_4901) = U_4902
    | U_4902 != c_Groups_Ozero__class_Ozero(U_4901)
    | ~ class_Groups_Ozero(U_4901) ),
    inference(clausify,[status(thm)],[f_1260_2]) ).

fof(f_1261_1,plain,
    c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_bot__nat__def]) ).

cnf(f_1261_2,plain,
    c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1261_1]) ).

fof(f_1262_1,plain,
    ! [V_a_2,V_b_2,T_b] :
      ( ( ( V_b_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2)
          | V_a_2 != c_Groups_Ozero__class_Ozero(T_b) )
        & ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
          | V_b_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2) ) )
      | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_add__0__iff]) ).

fof(f_1262_2,plain,
    ! [U_4905,U_4904,U_4903] :
      ( ( ( U_4904 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4903),U_4904),U_4905)
          | U_4905 != c_Groups_Ozero__class_Ozero(U_4903) )
        & ( U_4905 = c_Groups_Ozero__class_Ozero(U_4903)
          | U_4904 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4903),U_4904),U_4905) ) )
      | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_4903) ),
    inference(variable_rename,[status(thm)],[f_1262_1]) ).

cnf(f_1262_3,plain,
    ( U_4905 = c_Groups_Ozero__class_Ozero(U_4903)
    | U_4904 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4903),U_4904),U_4905)
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_4903) ),
    inference(clausify,[status(thm)],[f_1262_2]) ).

cnf(f_1262_4,plain,
    ( U_4904 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4903),U_4904),U_4905)
    | U_4905 != c_Groups_Ozero__class_Ozero(U_4903)
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_4903) ),
    inference(clausify,[status(thm)],[f_1262_2]) ).

fof(f_1263_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J]) ).

fof(f_1263_2,plain,
    ! [U_4907,U_4906] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4906),U_4907),c_Groups_Ozero__class_Ozero(U_4906)) = U_4907
      | ~ class_Rings_Ocomm__semiring__1(U_4906) ),
    inference(variable_rename,[status(thm)],[f_1263_1]) ).

cnf(f_1263_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4906),U_4907),c_Groups_Ozero__class_Ozero(U_4906)) = U_4907
    | ~ class_Rings_Ocomm__semiring__1(U_4906) ),
    inference(clausify,[status(thm)],[f_1263_2]) ).

fof(f_1264_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J]) ).

fof(f_1264_2,plain,
    ! [U_4909,U_4908] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4908),c_Groups_Ozero__class_Ozero(U_4908)),U_4909) = U_4909
      | ~ class_Rings_Ocomm__semiring__1(U_4908) ),
    inference(variable_rename,[status(thm)],[f_1264_1]) ).

cnf(f_1264_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4908),c_Groups_Ozero__class_Ozero(U_4908)),U_4909) = U_4909
    | ~ class_Rings_Ocomm__semiring__1(U_4908) ),
    inference(clausify,[status(thm)],[f_1264_2]) ).

fof(f_1265_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a
      | ~ class_Groups_Ocomm__monoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add_Ocomm__neutral]) ).

fof(f_1265_2,plain,
    ! [U_4911,U_4910] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4910),U_4911),c_Groups_Ozero__class_Ozero(U_4910)) = U_4911
      | ~ class_Groups_Ocomm__monoid__add(U_4910) ),
    inference(variable_rename,[status(thm)],[f_1265_1]) ).

cnf(f_1265_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4910),U_4911),c_Groups_Ozero__class_Ozero(U_4910)) = U_4911
    | ~ class_Groups_Ocomm__monoid__add(U_4910) ),
    inference(clausify,[status(thm)],[f_1265_2]) ).

fof(f_1266_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a
      | ~ class_Groups_Omonoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__0__right]) ).

fof(f_1266_2,plain,
    ! [U_4913,U_4912] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4912),U_4913),c_Groups_Ozero__class_Ozero(U_4912)) = U_4913
      | ~ class_Groups_Omonoid__add(U_4912) ),
    inference(variable_rename,[status(thm)],[f_1266_1]) ).

cnf(f_1266_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4912),U_4913),c_Groups_Ozero__class_Ozero(U_4912)) = U_4913
    | ~ class_Groups_Omonoid__add(U_4912) ),
    inference(clausify,[status(thm)],[f_1266_2]) ).

fof(f_1267_1,plain,
    ! [V_a_2,T_b] :
      ( ( ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)
          | V_a_2 != c_Groups_Ozero__class_Ozero(T_b) )
        & ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
          | c_Groups_Ozero__class_Ozero(T_b) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) ) )
      | ~ class_Groups_Olinordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_double__zero__sym]) ).

fof(f_1267_2,plain,
    ! [U_4915,U_4914] :
      ( ( ( c_Groups_Ozero__class_Ozero(U_4914) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4914),U_4915),U_4915)
          | U_4915 != c_Groups_Ozero__class_Ozero(U_4914) )
        & ( U_4915 = c_Groups_Ozero__class_Ozero(U_4914)
          | c_Groups_Ozero__class_Ozero(U_4914) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4914),U_4915),U_4915) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_4914) ),
    inference(variable_rename,[status(thm)],[f_1267_1]) ).

cnf(f_1267_3,plain,
    ( U_4915 = c_Groups_Ozero__class_Ozero(U_4914)
    | c_Groups_Ozero__class_Ozero(U_4914) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4914),U_4915),U_4915)
    | ~ class_Groups_Olinordered__ab__group__add(U_4914) ),
    inference(clausify,[status(thm)],[f_1267_2]) ).

cnf(f_1267_4,plain,
    ( c_Groups_Ozero__class_Ozero(U_4914) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4914),U_4915),U_4915)
    | U_4915 != c_Groups_Ozero__class_Ozero(U_4914)
    | ~ class_Groups_Olinordered__ab__group__add(U_4914) ),
    inference(clausify,[status(thm)],[f_1267_2]) ).

fof(f_1268_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a
      | ~ class_Groups_Ocomm__monoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__0]) ).

fof(f_1268_2,plain,
    ! [U_4917,U_4916] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4916),c_Groups_Ozero__class_Ozero(U_4916)),U_4917) = U_4917
      | ~ class_Groups_Ocomm__monoid__add(U_4916) ),
    inference(variable_rename,[status(thm)],[f_1268_1]) ).

cnf(f_1268_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4916),c_Groups_Ozero__class_Ozero(U_4916)),U_4917) = U_4917
    | ~ class_Groups_Ocomm__monoid__add(U_4916) ),
    inference(clausify,[status(thm)],[f_1268_2]) ).

fof(f_1269_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a
      | ~ class_Groups_Omonoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__0__left]) ).

fof(f_1269_2,plain,
    ! [U_4919,U_4918] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4918),c_Groups_Ozero__class_Ozero(U_4918)),U_4919) = U_4919
      | ~ class_Groups_Omonoid__add(U_4918) ),
    inference(variable_rename,[status(thm)],[f_1269_1]) ).

cnf(f_1269_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4918),c_Groups_Ozero__class_Ozero(U_4918)),U_4919) = U_4919
    | ~ class_Groups_Omonoid__add(U_4918) ),
    inference(clausify,[status(thm)],[f_1269_2]) ).

fof(f_1270_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J]) ).

fof(f_1270_2,plain,
    ! [U_4921,U_4920] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4920),U_4921),c_Groups_Ozero__class_Ozero(U_4920)) = c_Groups_Ozero__class_Ozero(U_4920)
      | ~ class_Rings_Ocomm__semiring__1(U_4920) ),
    inference(variable_rename,[status(thm)],[f_1270_1]) ).

cnf(f_1270_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4920),U_4921),c_Groups_Ozero__class_Ozero(U_4920)) = c_Groups_Ozero__class_Ozero(U_4920)
    | ~ class_Rings_Ocomm__semiring__1(U_4920) ),
    inference(clausify,[status(thm)],[f_1270_2]) ).

fof(f_1271_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J]) ).

fof(f_1271_2,plain,
    ! [U_4923,U_4922] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4922),c_Groups_Ozero__class_Ozero(U_4922)),U_4923) = c_Groups_Ozero__class_Ozero(U_4922)
      | ~ class_Rings_Ocomm__semiring__1(U_4922) ),
    inference(variable_rename,[status(thm)],[f_1271_1]) ).

cnf(f_1271_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4922),c_Groups_Ozero__class_Ozero(U_4922)),U_4923) = c_Groups_Ozero__class_Ozero(U_4922)
    | ~ class_Rings_Ocomm__semiring__1(U_4922) ),
    inference(clausify,[status(thm)],[f_1271_2]) ).

fof(f_1272_1,plain,
    ! [V_b,V_a,T_a] :
      ( V_b = c_Groups_Ozero__class_Ozero(T_a)
      | V_a = c_Groups_Ozero__class_Ozero(T_a)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Rings_Ono__zero__divisors(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_divisors__zero]) ).

fof(f_1272_2,plain,
    ! [U_4926,U_4925,U_4924] :
      ( U_4926 = c_Groups_Ozero__class_Ozero(U_4924)
      | U_4925 = c_Groups_Ozero__class_Ozero(U_4924)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4924),U_4925),U_4926) != c_Groups_Ozero__class_Ozero(U_4924)
      | ~ class_Rings_Ono__zero__divisors(U_4924) ),
    inference(variable_rename,[status(thm)],[f_1272_1]) ).

cnf(f_1272_3,plain,
    ( U_4926 = c_Groups_Ozero__class_Ozero(U_4924)
    | U_4925 = c_Groups_Ozero__class_Ozero(U_4924)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4924),U_4925),U_4926) != c_Groups_Ozero__class_Ozero(U_4924)
    | ~ class_Rings_Ono__zero__divisors(U_4924) ),
    inference(clausify,[status(thm)],[f_1272_2]) ).

fof(f_1273_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a)
      | V_b = c_Groups_Ozero__class_Ozero(T_a)
      | V_a = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Rings_Ono__zero__divisors(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_no__zero__divisors]) ).

fof(f_1273_2,plain,
    ! [U_4929,U_4928,U_4927] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4927),U_4928),U_4929) != c_Groups_Ozero__class_Ozero(U_4927)
      | U_4929 = c_Groups_Ozero__class_Ozero(U_4927)
      | U_4928 = c_Groups_Ozero__class_Ozero(U_4927)
      | ~ class_Rings_Ono__zero__divisors(U_4927) ),
    inference(variable_rename,[status(thm)],[f_1273_1]) ).

cnf(f_1273_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4927),U_4928),U_4929) != c_Groups_Ozero__class_Ozero(U_4927)
    | U_4929 = c_Groups_Ozero__class_Ozero(U_4927)
    | U_4928 = c_Groups_Ozero__class_Ozero(U_4927)
    | ~ class_Rings_Ono__zero__divisors(U_4927) ),
    inference(clausify,[status(thm)],[f_1273_2]) ).

fof(f_1274_1,plain,
    ! [V_b_2,V_a_2,T_b] :
      ( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b)
          | ( V_b_2 != c_Groups_Ozero__class_Ozero(T_b)
            & V_a_2 != c_Groups_Ozero__class_Ozero(T_b) ) )
        & ( V_b_2 = c_Groups_Ozero__class_Ozero(T_b)
          | V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2) != c_Groups_Ozero__class_Ozero(T_b) ) )
      | ~ class_Rings_Oring__no__zero__divisors(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_mult__eq__0__iff]) ).

fof(f_1274_2,plain,
    ! [U_4932,U_4931,U_4930] :
      ( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4930),U_4931),U_4932) = c_Groups_Ozero__class_Ozero(U_4930)
          | ( U_4932 != c_Groups_Ozero__class_Ozero(U_4930)
            & U_4931 != c_Groups_Ozero__class_Ozero(U_4930) ) )
        & ( U_4932 = c_Groups_Ozero__class_Ozero(U_4930)
          | U_4931 = c_Groups_Ozero__class_Ozero(U_4930)
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4930),U_4931),U_4932) != c_Groups_Ozero__class_Ozero(U_4930) ) )
      | ~ class_Rings_Oring__no__zero__divisors(U_4930) ),
    inference(variable_rename,[status(thm)],[f_1274_1]) ).

cnf(f_1274_3,plain,
    ( U_4932 = c_Groups_Ozero__class_Ozero(U_4930)
    | U_4931 = c_Groups_Ozero__class_Ozero(U_4930)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4930),U_4931),U_4932) != c_Groups_Ozero__class_Ozero(U_4930)
    | ~ class_Rings_Oring__no__zero__divisors(U_4930) ),
    inference(clausify,[status(thm)],[f_1274_2]) ).

cnf(f_1274_4,plain,
    ( U_4931 != c_Groups_Ozero__class_Ozero(U_4930)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4930),U_4931),U_4932) = c_Groups_Ozero__class_Ozero(U_4930)
    | ~ class_Rings_Oring__no__zero__divisors(U_4930) ),
    inference(clausify,[status(thm)],[f_1274_2]) ).

cnf(f_1274_5,plain,
    ( U_4932 != c_Groups_Ozero__class_Ozero(U_4930)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4930),U_4931),U_4932) = c_Groups_Ozero__class_Ozero(U_4930)
    | ~ class_Rings_Oring__no__zero__divisors(U_4930) ),
    inference(clausify,[status(thm)],[f_1274_2]) ).

fof(f_1275_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Rings_Omult__zero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__zero__right]) ).

fof(f_1275_2,plain,
    ! [U_4934,U_4933] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4933),U_4934),c_Groups_Ozero__class_Ozero(U_4933)) = c_Groups_Ozero__class_Ozero(U_4933)
      | ~ class_Rings_Omult__zero(U_4933) ),
    inference(variable_rename,[status(thm)],[f_1275_1]) ).

cnf(f_1275_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4933),U_4934),c_Groups_Ozero__class_Ozero(U_4933)) = c_Groups_Ozero__class_Ozero(U_4933)
    | ~ class_Rings_Omult__zero(U_4933) ),
    inference(clausify,[status(thm)],[f_1275_2]) ).

fof(f_1276_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Rings_Omult__zero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__zero__left]) ).

fof(f_1276_2,plain,
    ! [U_4936,U_4935] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4935),c_Groups_Ozero__class_Ozero(U_4935)),U_4936) = c_Groups_Ozero__class_Ozero(U_4935)
      | ~ class_Rings_Omult__zero(U_4935) ),
    inference(variable_rename,[status(thm)],[f_1276_1]) ).

cnf(f_1276_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4935),c_Groups_Ozero__class_Ozero(U_4935)),U_4936) = c_Groups_Ozero__class_Ozero(U_4935)
    | ~ class_Rings_Omult__zero(U_4935) ),
    inference(clausify,[status(thm)],[f_1276_2]) ).

fof(f_1277_1,plain,
    ! [V_b_2,V_a_2,T_b] :
      ( ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b)
          | V_a_2 != V_b_2 )
        & ( V_a_2 = V_b_2
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) != c_Groups_Ozero__class_Ozero(T_b) ) )
      | ~ class_Groups_Ogroup__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_right__minus__eq]) ).

fof(f_1277_2,plain,
    ! [U_4939,U_4938,U_4937] :
      ( ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4937),U_4938),U_4939) = c_Groups_Ozero__class_Ozero(U_4937)
          | U_4938 != U_4939 )
        & ( U_4938 = U_4939
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4937),U_4938),U_4939) != c_Groups_Ozero__class_Ozero(U_4937) ) )
      | ~ class_Groups_Ogroup__add(U_4937) ),
    inference(variable_rename,[status(thm)],[f_1277_1]) ).

cnf(f_1277_3,plain,
    ( U_4938 = U_4939
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4937),U_4938),U_4939) != c_Groups_Ozero__class_Ozero(U_4937)
    | ~ class_Groups_Ogroup__add(U_4937) ),
    inference(clausify,[status(thm)],[f_1277_2]) ).

cnf(f_1277_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4937),U_4938),U_4939) = c_Groups_Ozero__class_Ozero(U_4937)
    | U_4938 != U_4939
    | ~ class_Groups_Ogroup__add(U_4937) ),
    inference(clausify,[status(thm)],[f_1277_2]) ).

fof(f_1278_1,plain,
    ! [V_b_2,V_a_2,T_b] :
      ( ( ( V_a_2 = V_b_2
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) != c_Groups_Ozero__class_Ozero(T_b) )
        & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b)
          | V_a_2 != V_b_2 ) )
      | ~ class_Groups_Oab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_eq__iff__diff__eq__0]) ).

fof(f_1278_2,plain,
    ! [U_4942,U_4941,U_4940] :
      ( ( ( U_4941 = U_4942
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4940),U_4941),U_4942) != c_Groups_Ozero__class_Ozero(U_4940) )
        & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4940),U_4941),U_4942) = c_Groups_Ozero__class_Ozero(U_4940)
          | U_4941 != U_4942 ) )
      | ~ class_Groups_Oab__group__add(U_4940) ),
    inference(variable_rename,[status(thm)],[f_1278_1]) ).

cnf(f_1278_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4940),U_4941),U_4942) = c_Groups_Ozero__class_Ozero(U_4940)
    | U_4941 != U_4942
    | ~ class_Groups_Oab__group__add(U_4940) ),
    inference(clausify,[status(thm)],[f_1278_2]) ).

cnf(f_1278_4,plain,
    ( U_4941 = U_4942
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4940),U_4941),U_4942) != c_Groups_Ozero__class_Ozero(U_4940)
    | ~ class_Groups_Oab__group__add(U_4940) ),
    inference(clausify,[status(thm)],[f_1278_2]) ).

fof(f_1279_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Groups_Ogroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_diff__self]) ).

fof(f_1279_2,plain,
    ! [U_4944,U_4943] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4943),U_4944),U_4944) = c_Groups_Ozero__class_Ozero(U_4943)
      | ~ class_Groups_Ogroup__add(U_4943) ),
    inference(variable_rename,[status(thm)],[f_1279_1]) ).

cnf(f_1279_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4943),U_4944),U_4944) = c_Groups_Ozero__class_Ozero(U_4943)
    | ~ class_Groups_Ogroup__add(U_4943) ),
    inference(clausify,[status(thm)],[f_1279_2]) ).

fof(f_1280_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a
      | ~ class_Groups_Ogroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_diff__0__right]) ).

fof(f_1280_2,plain,
    ! [U_4946,U_4945] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4945),U_4946),c_Groups_Ozero__class_Ozero(U_4945)) = U_4946
      | ~ class_Groups_Ogroup__add(U_4945) ),
    inference(variable_rename,[status(thm)],[f_1280_1]) ).

cnf(f_1280_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4945),U_4946),c_Groups_Ozero__class_Ozero(U_4945)) = U_4946
    | ~ class_Groups_Ogroup__add(U_4945) ),
    inference(clausify,[status(thm)],[f_1280_2]) ).

fof(f_1281_1,plain,
    ! [T_a] :
      ( c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a)
      | ~ class_Rings_Ozero__neq__one(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_zero__neq__one]) ).

fof(f_1281_2,plain,
    ! [U_4947] :
      ( c_Groups_Ozero__class_Ozero(U_4947) != c_Groups_Oone__class_Oone(U_4947)
      | ~ class_Rings_Ozero__neq__one(U_4947) ),
    inference(variable_rename,[status(thm)],[f_1281_1]) ).

cnf(f_1281_3,plain,
    ( c_Groups_Ozero__class_Ozero(U_4947) != c_Groups_Oone__class_Oone(U_4947)
    | ~ class_Rings_Ozero__neq__one(U_4947) ),
    inference(clausify,[status(thm)],[f_1281_2]) ).

fof(f_1282_1,plain,
    ! [T_a] :
      ( c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Rings_Ozero__neq__one(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_one__neq__zero]) ).

fof(f_1282_2,plain,
    ! [U_4948] :
      ( c_Groups_Oone__class_Oone(U_4948) != c_Groups_Ozero__class_Ozero(U_4948)
      | ~ class_Rings_Ozero__neq__one(U_4948) ),
    inference(variable_rename,[status(thm)],[f_1282_1]) ).

cnf(f_1282_3,plain,
    ( c_Groups_Oone__class_Oone(U_4948) != c_Groups_Ozero__class_Ozero(U_4948)
    | ~ class_Rings_Ozero__neq__one(U_4948) ),
    inference(clausify,[status(thm)],[f_1282_2]) ).

fof(f_1283_1,plain,
    ! [T_a] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Groups_Ogroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_minus__zero]) ).

fof(f_1283_2,plain,
    ! [U_4949] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_4949),c_Groups_Ozero__class_Ozero(U_4949)) = c_Groups_Ozero__class_Ozero(U_4949)
      | ~ class_Groups_Ogroup__add(U_4949) ),
    inference(variable_rename,[status(thm)],[f_1283_1]) ).

cnf(f_1283_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_4949),c_Groups_Ozero__class_Ozero(U_4949)) = c_Groups_Ozero__class_Ozero(U_4949)
    | ~ class_Groups_Ogroup__add(U_4949) ),
    inference(clausify,[status(thm)],[f_1283_2]) ).

fof(f_1284_1,plain,
    ! [V_a_2,T_b] :
      ( ( ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)
          | c_Groups_Ozero__class_Ozero(T_b) != V_a_2 )
        & ( c_Groups_Ozero__class_Ozero(T_b) = V_a_2
          | c_Groups_Ozero__class_Ozero(T_b) != hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) ) )
      | ~ class_Groups_Ogroup__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_neg__0__equal__iff__equal]) ).

fof(f_1284_2,plain,
    ! [U_4951,U_4950] :
      ( ( ( c_Groups_Ozero__class_Ozero(U_4950) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4950),U_4951)
          | c_Groups_Ozero__class_Ozero(U_4950) != U_4951 )
        & ( c_Groups_Ozero__class_Ozero(U_4950) = U_4951
          | c_Groups_Ozero__class_Ozero(U_4950) != hAPP(c_Groups_Ouminus__class_Ouminus(U_4950),U_4951) ) )
      | ~ class_Groups_Ogroup__add(U_4950) ),
    inference(variable_rename,[status(thm)],[f_1284_1]) ).

cnf(f_1284_3,plain,
    ( c_Groups_Ozero__class_Ozero(U_4950) = U_4951
    | c_Groups_Ozero__class_Ozero(U_4950) != hAPP(c_Groups_Ouminus__class_Ouminus(U_4950),U_4951)
    | ~ class_Groups_Ogroup__add(U_4950) ),
    inference(clausify,[status(thm)],[f_1284_2]) ).

cnf(f_1284_4,plain,
    ( c_Groups_Ozero__class_Ozero(U_4950) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4950),U_4951)
    | c_Groups_Ozero__class_Ozero(U_4950) != U_4951
    | ~ class_Groups_Ogroup__add(U_4950) ),
    inference(clausify,[status(thm)],[f_1284_2]) ).

fof(f_1285_1,plain,
    ! [V_a_2,T_b] :
      ( ( ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)
          | V_a_2 != c_Groups_Ozero__class_Ozero(T_b) )
        & ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
          | V_a_2 != hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) ) )
      | ~ class_Groups_Olinordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_equal__neg__zero]) ).

fof(f_1285_2,plain,
    ! [U_4953,U_4952] :
      ( ( ( U_4953 = hAPP(c_Groups_Ouminus__class_Ouminus(U_4952),U_4953)
          | U_4953 != c_Groups_Ozero__class_Ozero(U_4952) )
        & ( U_4953 = c_Groups_Ozero__class_Ozero(U_4952)
          | U_4953 != hAPP(c_Groups_Ouminus__class_Ouminus(U_4952),U_4953) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_4952) ),
    inference(variable_rename,[status(thm)],[f_1285_1]) ).

cnf(f_1285_3,plain,
    ( U_4953 = c_Groups_Ozero__class_Ozero(U_4952)
    | U_4953 != hAPP(c_Groups_Ouminus__class_Ouminus(U_4952),U_4953)
    | ~ class_Groups_Olinordered__ab__group__add(U_4952) ),
    inference(clausify,[status(thm)],[f_1285_2]) ).

cnf(f_1285_4,plain,
    ( U_4953 = hAPP(c_Groups_Ouminus__class_Ouminus(U_4952),U_4953)
    | U_4953 != c_Groups_Ozero__class_Ozero(U_4952)
    | ~ class_Groups_Olinordered__ab__group__add(U_4952) ),
    inference(clausify,[status(thm)],[f_1285_2]) ).

fof(f_1286_1,plain,
    ! [V_a_2,T_b] :
      ( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
          | V_a_2 != c_Groups_Ozero__class_Ozero(T_b) )
        & ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
          | hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) != c_Groups_Ozero__class_Ozero(T_b) ) )
      | ~ class_Groups_Ogroup__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_neg__equal__0__iff__equal]) ).

fof(f_1286_2,plain,
    ! [U_4955,U_4954] :
      ( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(U_4954),U_4955) = c_Groups_Ozero__class_Ozero(U_4954)
          | U_4955 != c_Groups_Ozero__class_Ozero(U_4954) )
        & ( U_4955 = c_Groups_Ozero__class_Ozero(U_4954)
          | hAPP(c_Groups_Ouminus__class_Ouminus(U_4954),U_4955) != c_Groups_Ozero__class_Ozero(U_4954) ) )
      | ~ class_Groups_Ogroup__add(U_4954) ),
    inference(variable_rename,[status(thm)],[f_1286_1]) ).

cnf(f_1286_3,plain,
    ( U_4955 = c_Groups_Ozero__class_Ozero(U_4954)
    | hAPP(c_Groups_Ouminus__class_Ouminus(U_4954),U_4955) != c_Groups_Ozero__class_Ozero(U_4954)
    | ~ class_Groups_Ogroup__add(U_4954) ),
    inference(clausify,[status(thm)],[f_1286_2]) ).

cnf(f_1286_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_4954),U_4955) = c_Groups_Ozero__class_Ozero(U_4954)
    | U_4955 != c_Groups_Ozero__class_Ozero(U_4954)
    | ~ class_Groups_Ogroup__add(U_4954) ),
    inference(clausify,[status(thm)],[f_1286_2]) ).

fof(f_1287_1,plain,
    ! [V_a_2,T_b] :
      ( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = V_a_2
          | V_a_2 != c_Groups_Ozero__class_Ozero(T_b) )
        & ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
          | hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) != V_a_2 ) )
      | ~ class_Groups_Olinordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_neg__equal__zero]) ).

fof(f_1287_2,plain,
    ! [U_4957,U_4956] :
      ( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(U_4956),U_4957) = U_4957
          | U_4957 != c_Groups_Ozero__class_Ozero(U_4956) )
        & ( U_4957 = c_Groups_Ozero__class_Ozero(U_4956)
          | hAPP(c_Groups_Ouminus__class_Ouminus(U_4956),U_4957) != U_4957 ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_4956) ),
    inference(variable_rename,[status(thm)],[f_1287_1]) ).

cnf(f_1287_3,plain,
    ( U_4957 = c_Groups_Ozero__class_Ozero(U_4956)
    | hAPP(c_Groups_Ouminus__class_Ouminus(U_4956),U_4957) != U_4957
    | ~ class_Groups_Olinordered__ab__group__add(U_4956) ),
    inference(clausify,[status(thm)],[f_1287_2]) ).

cnf(f_1287_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_4956),U_4957) = U_4957
    | U_4957 != c_Groups_Ozero__class_Ozero(U_4956)
    | ~ class_Groups_Olinordered__ab__group__add(U_4956) ),
    inference(clausify,[status(thm)],[f_1287_2]) ).

fof(f_1288_1,plain,
    ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_Suc__neq__Zero]) ).

fof(f_1288_2,plain,
    ! [U_4958] : hAPP(c_Nat_OSuc,U_4958) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_1288_1]) ).

cnf(f_1288_3,plain,
    hAPP(c_Nat_OSuc,U_4958) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1288_2]) ).

fof(f_1289_1,plain,
    ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m),
    inference(fof_nnf,[status(thm)],[fact_Zero__neq__Suc]) ).

fof(f_1289_2,plain,
    ! [U_4959] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_4959),
    inference(variable_rename,[status(thm)],[f_1289_1]) ).

cnf(f_1289_3,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_4959),
    inference(clausify,[status(thm)],[f_1289_2]) ).

fof(f_1290_1,plain,
    ! [V_nat_H_1] : hAPP(c_Nat_OSuc,V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_nat_Osimps_I3_J]) ).

fof(f_1290_2,plain,
    ! [U_4960] : hAPP(c_Nat_OSuc,U_4960) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_1290_1]) ).

cnf(f_1290_3,plain,
    hAPP(c_Nat_OSuc,U_4960) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1290_2]) ).

fof(f_1291_1,plain,
    ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_Suc__not__Zero]) ).

fof(f_1291_2,plain,
    ! [U_4961] : hAPP(c_Nat_OSuc,U_4961) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_1291_1]) ).

cnf(f_1291_3,plain,
    hAPP(c_Nat_OSuc,U_4961) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1291_2]) ).

fof(f_1292_1,plain,
    ! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_nat_H),
    inference(fof_nnf,[status(thm)],[fact_nat_Osimps_I2_J]) ).

fof(f_1292_2,plain,
    ! [U_4962] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_4962),
    inference(variable_rename,[status(thm)],[f_1292_1]) ).

cnf(f_1292_3,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_4962),
    inference(clausify,[status(thm)],[f_1292_2]) ).

fof(f_1293_1,plain,
    ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m),
    inference(fof_nnf,[status(thm)],[fact_Zero__not__Suc]) ).

fof(f_1293_2,plain,
    ! [U_4963] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_4963),
    inference(variable_rename,[status(thm)],[f_1293_1]) ).

cnf(f_1293_3,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_4963),
    inference(clausify,[status(thm)],[f_1293_2]) ).

fof(f_1294_1,plain,
    ! [V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
      | V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(fof_nnf,[status(thm)],[fact_gr0I]) ).

fof(f_1294_2,plain,
    ! [U_4964] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4964))
      | U_4964 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[f_1294_1]) ).

cnf(f_1294_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4964))
    | U_4964 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1294_2]) ).

fof(f_1295_1,plain,
    ! [V_n,V_m] :
      ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_gr__implies__not0]) ).

fof(f_1295_2,plain,
    ! [U_4966,U_4965] :
      ( U_4966 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4965),U_4966)) ),
    inference(variable_rename,[status(thm)],[f_1295_1]) ).

fof(f_1295_3,plain,
    ! [U_4966] :
      ( ! [U_4965] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4965),U_4966))
      | U_4966 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(miniscope,[status(thm)],[f_1295_2]) ).

cnf(f_1295_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4965),U_4966))
    | U_4966 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1295_3]) ).

fof(f_1296_1,plain,
    ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(fof_nnf,[status(thm)],[fact_less__nat__zero__code]) ).

fof(f_1296_2,plain,
    ! [U_4967] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4967),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_1296_1]) ).

cnf(f_1296_3,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4967),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_1296_2]) ).

fof(f_1297_1,plain,
    ! [V_n_2] :
      ( ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
        | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(fof_nnf,[status(thm)],[fact_neq0__conv]) ).

fof(f_1297_2,plain,
    ! [U_4968] :
      ( ( U_4968 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4968)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4968))
        | U_4968 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_1297_1]) ).

fof(f_1297_3,plain,
    ( ! [U_4970] :
        ( U_4970 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4970)) )
    & ! [U_4969] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4969))
        | U_4969 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_1297_2]) ).

cnf(f_1297_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4969))
    | U_4969 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1297_3]) ).

cnf(f_1297_5,plain,
    ( U_4970 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4970)) ),
    inference(clausify,[status(thm)],[f_1297_3]) ).

fof(f_1298_1,plain,
    ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(fof_nnf,[status(thm)],[fact_not__less0]) ).

fof(f_1298_2,plain,
    ! [U_4971] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4971),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_1298_1]) ).

cnf(f_1298_3,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4971),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_1298_2]) ).

fof(f_1299_1,plain,
    ! [V_n,V_m] :
      ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) != V_m ),
    inference(fof_nnf,[status(thm)],[fact_add__eq__self__zero]) ).

fof(f_1299_2,plain,
    ! [U_4973,U_4972] :
      ( U_4973 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4972),U_4973) != U_4972 ),
    inference(variable_rename,[status(thm)],[f_1299_1]) ).

fof(f_1299_3,plain,
    ! [U_4973] :
      ( ! [U_4972] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4972),U_4973) != U_4972
      | U_4973 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(miniscope,[status(thm)],[f_1299_2]) ).

cnf(f_1299_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4972),U_4973) != U_4972
    | U_4973 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1299_3]) ).

fof(f_1300_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(fof_nnf,[status(thm)],[fact_add__is__0]) ).

fof(f_1300_2,plain,
    ! [U_4975,U_4974] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4974),U_4975) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_4975 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_4974 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ( U_4975 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_4974 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4974),U_4975) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_1300_1]) ).

fof(f_1300_3,plain,
    ( ! [U_4979,U_4977] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4977),U_4979) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_4979 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_4977 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_4978,U_4976] :
        ( ( U_4978 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_4976 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4976),U_4978) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_1300_2]) ).

cnf(f_1300_4,plain,
    ( U_4976 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4976),U_4978) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1300_3]) ).

cnf(f_1300_5,plain,
    ( U_4978 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4976),U_4978) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1300_3]) ).

cnf(f_1300_6,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4977),U_4979) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_4979 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_4977 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1300_3]) ).

fof(f_1301_1,plain,
    ! [V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m,
    inference(fof_nnf,[status(thm)],[fact_Nat_Oadd__0__right]) ).

fof(f_1301_2,plain,
    ! [U_4980] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4980),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_4980,
    inference(variable_rename,[status(thm)],[f_1301_1]) ).

cnf(f_1301_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4980),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_4980,
    inference(clausify,[status(thm)],[f_1301_2]) ).

fof(f_1302_1,plain,
    ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n,
    inference(fof_nnf,[status(thm)],[fact_plus__nat_Oadd__0]) ).

fof(f_1302_2,plain,
    ! [U_4981] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4981) = U_4981,
    inference(variable_rename,[status(thm)],[f_1302_1]) ).

cnf(f_1302_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4981) = U_4981,
    inference(clausify,[status(thm)],[f_1302_2]) ).

fof(f_1303_1,plain,
    ! [V_n_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
    inference(fof_nnf,[status(thm)],[fact_le__0__eq]) ).

fof(f_1303_2,plain,
    ! [U_4982] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4982),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | U_4982 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( U_4982 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4982),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
    inference(variable_rename,[status(thm)],[f_1303_1]) ).

fof(f_1303_3,plain,
    ( ! [U_4984] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4984),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | U_4984 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_4983] :
        ( U_4983 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4983),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
    inference(miniscope,[status(thm)],[f_1303_2]) ).

cnf(f_1303_4,plain,
    ( U_4983 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4983),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(clausify,[status(thm)],[f_1303_3]) ).

cnf(f_1303_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4984),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | U_4984 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1303_3]) ).

fof(f_1304_1,plain,
    ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)),
    inference(fof_nnf,[status(thm)],[fact_less__eq__nat_Osimps_I1_J]) ).

fof(f_1304_2,plain,
    ! [U_4985] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4985)),
    inference(variable_rename,[status(thm)],[f_1304_1]) ).

cnf(f_1304_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4985)),
    inference(clausify,[status(thm)],[f_1304_2]) ).

fof(f_1305_1,plain,
    ! [V_n,V_m] :
      ( V_m = V_n
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(fof_nnf,[status(thm)],[fact_diffs0__imp__equal]) ).

fof(f_1305_2,plain,
    ! [U_4987,U_4986] :
      ( U_4986 = U_4987
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4987),U_4986) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4986),U_4987) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[f_1305_1]) ).

cnf(f_1305_3,plain,
    ( U_4986 = U_4987
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4987),U_4986) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4986),U_4987) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1305_2]) ).

fof(f_1306_1,plain,
    ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_diff__self__eq__0]) ).

fof(f_1306_2,plain,
    ! [U_4988] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4988),U_4988) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_1306_1]) ).

cnf(f_1306_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4988),U_4988) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1306_2]) ).

fof(f_1307_1,plain,
    ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m,
    inference(fof_nnf,[status(thm)],[fact_minus__nat_Odiff__0]) ).

fof(f_1307_2,plain,
    ! [U_4989] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4989),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_4989,
    inference(variable_rename,[status(thm)],[f_1307_1]) ).

cnf(f_1307_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4989),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_4989,
    inference(clausify,[status(thm)],[f_1307_2]) ).

fof(f_1308_1,plain,
    ! [V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_diff__0__eq__0]) ).

fof(f_1308_2,plain,
    ! [U_4990] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4990) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_1308_1]) ).

cnf(f_1308_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4990) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1308_2]) ).

fof(f_1309_1,plain,
    ! [V_n_2,V_k_2,V_m_2] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)
        | ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & V_m_2 != V_n_2 ) )
      & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | V_m_2 = V_n_2
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_mult__cancel2]) ).

fof(f_1309_2,plain,
    ! [U_4993,U_4992,U_4991] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4991),U_4992) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4993),U_4992)
        | ( U_4992 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_4991 != U_4993 ) )
      & ( U_4992 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_4991 = U_4993
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4991),U_4992) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4993),U_4992) ) ),
    inference(variable_rename,[status(thm)],[f_1309_1]) ).

fof(f_1309_3,plain,
    ( ! [U_4999,U_4997,U_4995] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4995),U_4997) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4999),U_4997)
        | ( U_4997 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_4995 != U_4999 ) )
    & ! [U_4998,U_4996,U_4994] :
        ( U_4996 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_4994 = U_4998
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4994),U_4996) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4998),U_4996) ) ),
    inference(miniscope,[status(thm)],[f_1309_2]) ).

cnf(f_1309_4,plain,
    ( U_4996 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_4994 = U_4998
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4994),U_4996) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4998),U_4996) ),
    inference(clausify,[status(thm)],[f_1309_3]) ).

cnf(f_1309_5,plain,
    ( U_4995 != U_4999
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4995),U_4997) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4999),U_4997) ),
    inference(clausify,[status(thm)],[f_1309_3]) ).

cnf(f_1309_6,plain,
    ( U_4997 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4995),U_4997) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4999),U_4997) ),
    inference(clausify,[status(thm)],[f_1309_3]) ).

fof(f_1310_1,plain,
    ! [V_n_2,V_m_2,V_k_2] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)
        | ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & V_m_2 != V_n_2 ) )
      & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | V_m_2 = V_n_2
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_mult__cancel1]) ).

fof(f_1310_2,plain,
    ! [U_5002,U_5001,U_5000] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5000),U_5001) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5000),U_5002)
        | ( U_5000 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_5001 != U_5002 ) )
      & ( U_5000 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_5001 = U_5002
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5000),U_5001) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5000),U_5002) ) ),
    inference(variable_rename,[status(thm)],[f_1310_1]) ).

fof(f_1310_3,plain,
    ( ! [U_5008,U_5006,U_5004] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5004),U_5006) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5004),U_5008)
        | ( U_5004 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_5006 != U_5008 ) )
    & ! [U_5007,U_5005,U_5003] :
        ( U_5003 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_5005 = U_5007
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5003),U_5005) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5003),U_5007) ) ),
    inference(miniscope,[status(thm)],[f_1310_2]) ).

cnf(f_1310_4,plain,
    ( U_5003 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_5005 = U_5007
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5003),U_5005) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5003),U_5007) ),
    inference(clausify,[status(thm)],[f_1310_3]) ).

cnf(f_1310_5,plain,
    ( U_5006 != U_5008
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5004),U_5006) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5004),U_5008) ),
    inference(clausify,[status(thm)],[f_1310_3]) ).

cnf(f_1310_6,plain,
    ( U_5004 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5004),U_5006) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5004),U_5008) ),
    inference(clausify,[status(thm)],[f_1310_3]) ).

fof(f_1311_1,plain,
    ! [V_n_2,V_m_2,V_k_2] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)
        | ( V_m_2 != V_n_2
          & V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( V_m_2 = V_n_2
        | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__mult__eq__cancel__disj]) ).

fof(f_1311_2,plain,
    ! [U_5011,U_5010,U_5009] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5009),U_5010) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5009),U_5011)
        | ( U_5010 != U_5011
          & U_5009 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( U_5010 = U_5011
        | U_5009 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5009),U_5010) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5009),U_5011) ) ),
    inference(variable_rename,[status(thm)],[f_1311_1]) ).

fof(f_1311_3,plain,
    ( ! [U_5017,U_5015,U_5013] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5013),U_5015) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5013),U_5017)
        | ( U_5015 != U_5017
          & U_5013 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_5016,U_5014,U_5012] :
        ( U_5014 = U_5016
        | U_5012 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5012),U_5014) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5012),U_5016) ) ),
    inference(miniscope,[status(thm)],[f_1311_2]) ).

cnf(f_1311_4,plain,
    ( U_5014 = U_5016
    | U_5012 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5012),U_5014) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5012),U_5016) ),
    inference(clausify,[status(thm)],[f_1311_3]) ).

cnf(f_1311_5,plain,
    ( U_5013 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5013),U_5015) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5013),U_5017) ),
    inference(clausify,[status(thm)],[f_1311_3]) ).

cnf(f_1311_6,plain,
    ( U_5015 != U_5017
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5013),U_5015) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5013),U_5017) ),
    inference(clausify,[status(thm)],[f_1311_3]) ).

fof(f_1312_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(fof_nnf,[status(thm)],[fact_mult__is__0]) ).

fof(f_1312_2,plain,
    ! [U_5019,U_5018] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5018),U_5019) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ( U_5019 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_5018 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( U_5019 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_5018 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5018),U_5019) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_1312_1]) ).

fof(f_1312_3,plain,
    ( ! [U_5023,U_5021] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5021),U_5023) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ( U_5023 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_5021 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_5022,U_5020] :
        ( U_5022 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_5020 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5020),U_5022) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_1312_2]) ).

cnf(f_1312_4,plain,
    ( U_5022 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_5020 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5020),U_5022) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1312_3]) ).

cnf(f_1312_5,plain,
    ( U_5021 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5021),U_5023) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1312_3]) ).

cnf(f_1312_6,plain,
    ( U_5023 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5021),U_5023) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1312_3]) ).

fof(f_1313_1,plain,
    ! [V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_mult__0__right]) ).

fof(f_1313_2,plain,
    ! [U_5024] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5024),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_1313_1]) ).

cnf(f_1313_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5024),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1313_2]) ).

fof(f_1314_1,plain,
    ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_mult__0]) ).

fof(f_1314_2,plain,
    ! [U_5025] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5025) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_1314_1]) ).

cnf(f_1314_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5025) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1314_2]) ).

fof(f_1315_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2)) = c_Groups_Ozero__class_Ozero(T_b)
          | V_y_2 != c_Groups_Ozero__class_Ozero(T_b)
          | V_x_2 != c_Groups_Ozero__class_Ozero(T_b) )
        & ( ( V_y_2 = c_Groups_Ozero__class_Ozero(T_b)
            & V_x_2 = c_Groups_Ozero__class_Ozero(T_b) )
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2)) != c_Groups_Ozero__class_Ozero(T_b) ) )
      | ~ class_Rings_Olinordered__ring__strict(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sum__squares__eq__zero__iff]) ).

fof(f_1315_2,plain,
    ! [U_5028,U_5027,U_5026] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5026),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5026),U_5027),U_5027)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5026),U_5028),U_5028)) = c_Groups_Ozero__class_Ozero(U_5026)
          | U_5028 != c_Groups_Ozero__class_Ozero(U_5026)
          | U_5027 != c_Groups_Ozero__class_Ozero(U_5026) )
        & ( ( U_5028 = c_Groups_Ozero__class_Ozero(U_5026)
            & U_5027 = c_Groups_Ozero__class_Ozero(U_5026) )
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5026),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5026),U_5027),U_5027)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5026),U_5028),U_5028)) != c_Groups_Ozero__class_Ozero(U_5026) ) )
      | ~ class_Rings_Olinordered__ring__strict(U_5026) ),
    inference(variable_rename,[status(thm)],[f_1315_1]) ).

cnf(f_1315_3,plain,
    ( U_5027 = c_Groups_Ozero__class_Ozero(U_5026)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5026),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5026),U_5027),U_5027)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5026),U_5028),U_5028)) != c_Groups_Ozero__class_Ozero(U_5026)
    | ~ class_Rings_Olinordered__ring__strict(U_5026) ),
    inference(clausify,[status(thm)],[f_1315_2]) ).

cnf(f_1315_4,plain,
    ( U_5028 = c_Groups_Ozero__class_Ozero(U_5026)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5026),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5026),U_5027),U_5027)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5026),U_5028),U_5028)) != c_Groups_Ozero__class_Ozero(U_5026)
    | ~ class_Rings_Olinordered__ring__strict(U_5026) ),
    inference(clausify,[status(thm)],[f_1315_2]) ).

cnf(f_1315_5,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5026),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5026),U_5027),U_5027)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5026),U_5028),U_5028)) = c_Groups_Ozero__class_Ozero(U_5026)
    | U_5028 != c_Groups_Ozero__class_Ozero(U_5026)
    | U_5027 != c_Groups_Ozero__class_Ozero(U_5026)
    | ~ class_Rings_Olinordered__ring__strict(U_5026) ),
    inference(clausify,[status(thm)],[f_1315_2]) ).

fof(f_1316_1,plain,
    ! [V_m_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_atLeastLessThan0]) ).

fof(f_1316_2,plain,
    ! [U_5029] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_5029),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_1316_1]) ).

cnf(f_1316_3,plain,
    hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_5029),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_1316_2]) ).

fof(f_1317_1,plain,
    hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_atLeast__0]) ).

cnf(f_1317_2,plain,
    hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_1317_1]) ).

fof(f_1318_1,plain,
    ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_min__0L]) ).

fof(f_1318_2,plain,
    ! [U_5030] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5030) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_1318_1]) ).

cnf(f_1318_3,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5030) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1318_2]) ).

fof(f_1319_1,plain,
    ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_min__0R]) ).

fof(f_1319_2,plain,
    ! [U_5031] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_5031),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_1319_1]) ).

cnf(f_1319_3,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_5031),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1319_2]) ).

fof(f_1320_1,plain,
    hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_lessThan__0]) ).

cnf(f_1320_2,plain,
    hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_1320_1]) ).

fof(f_1321_1,plain,
    ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n,
    inference(fof_nnf,[status(thm)],[fact_max__0L]) ).

fof(f_1321_2,plain,
    ! [U_5032] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5032) = U_5032,
    inference(variable_rename,[status(thm)],[f_1321_1]) ).

cnf(f_1321_3,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5032) = U_5032,
    inference(clausify,[status(thm)],[f_1321_2]) ).

fof(f_1322_1,plain,
    ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_n,
    inference(fof_nnf,[status(thm)],[fact_max__0R]) ).

fof(f_1322_2,plain,
    ! [U_5033] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_5033),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_5033,
    inference(variable_rename,[status(thm)],[f_1322_1]) ).

cnf(f_1322_3,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_5033),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_5033,
    inference(clausify,[status(thm)],[f_1322_2]) ).

fof(f_1323_1,plain,
    hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    inference(fof_nnf,[status(thm)],[fact_atMost__0]) ).

cnf(f_1323_2,plain,
    hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_1323_1]) ).

fof(f_1324_1,plain,
    ! [V_k_2,V_f_2,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
      | hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(T_b)
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__shift__lb__Suc0__0__upt]) ).

fof(f_1324_2,plain,
    ! [U_5036,U_5035,U_5034] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_5034),U_5035),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_5036)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_5034),U_5035),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5036))
      | hAPP(U_5035,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(U_5034)
      | ~ class_Groups_Ocomm__monoid__add(U_5034) ),
    inference(variable_rename,[status(thm)],[f_1324_1]) ).

cnf(f_1324_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_5034),U_5035),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_5036)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_5034),U_5035),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5036))
    | hAPP(U_5035,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(U_5034)
    | ~ class_Groups_Ocomm__monoid__add(U_5034) ),
    inference(clausify,[status(thm)],[f_1324_2]) ).

fof(f_1325_1,plain,
    ! [V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y))))
      | ~ class_Rings_Olinordered__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sum__squares__ge__zero]) ).

fof(f_1325_2,plain,
    ! [U_5039,U_5038,U_5037] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5037),c_Groups_Ozero__class_Ozero(U_5037)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5037),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5037),U_5038),U_5038)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5037),U_5039),U_5039))))
      | ~ class_Rings_Olinordered__ring(U_5037) ),
    inference(variable_rename,[status(thm)],[f_1325_1]) ).

cnf(f_1325_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5037),c_Groups_Ozero__class_Ozero(U_5037)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5037),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5037),U_5038),U_5038)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5037),U_5039),U_5039))))
    | ~ class_Rings_Olinordered__ring(U_5037) ),
    inference(clausify,[status(thm)],[f_1325_2]) ).

fof(f_1326_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2))),c_Groups_Ozero__class_Ozero(T_b)))
          | V_y_2 != c_Groups_Ozero__class_Ozero(T_b)
          | V_x_2 != c_Groups_Ozero__class_Ozero(T_b) )
        & ( ( V_y_2 = c_Groups_Ozero__class_Ozero(T_b)
            & V_x_2 = c_Groups_Ozero__class_Ozero(T_b) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2))),c_Groups_Ozero__class_Ozero(T_b))) ) )
      | ~ class_Rings_Olinordered__ring__strict(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sum__squares__le__zero__iff]) ).

fof(f_1326_2,plain,
    ! [U_5042,U_5041,U_5040] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5040),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5040),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5040),U_5041),U_5041)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5040),U_5042),U_5042))),c_Groups_Ozero__class_Ozero(U_5040)))
          | U_5042 != c_Groups_Ozero__class_Ozero(U_5040)
          | U_5041 != c_Groups_Ozero__class_Ozero(U_5040) )
        & ( ( U_5042 = c_Groups_Ozero__class_Ozero(U_5040)
            & U_5041 = c_Groups_Ozero__class_Ozero(U_5040) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5040),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5040),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5040),U_5041),U_5041)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5040),U_5042),U_5042))),c_Groups_Ozero__class_Ozero(U_5040))) ) )
      | ~ class_Rings_Olinordered__ring__strict(U_5040) ),
    inference(variable_rename,[status(thm)],[f_1326_1]) ).

cnf(f_1326_3,plain,
    ( U_5041 = c_Groups_Ozero__class_Ozero(U_5040)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5040),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5040),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5040),U_5041),U_5041)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5040),U_5042),U_5042))),c_Groups_Ozero__class_Ozero(U_5040)))
    | ~ class_Rings_Olinordered__ring__strict(U_5040) ),
    inference(clausify,[status(thm)],[f_1326_2]) ).

cnf(f_1326_4,plain,
    ( U_5042 = c_Groups_Ozero__class_Ozero(U_5040)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5040),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5040),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5040),U_5041),U_5041)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5040),U_5042),U_5042))),c_Groups_Ozero__class_Ozero(U_5040)))
    | ~ class_Rings_Olinordered__ring__strict(U_5040) ),
    inference(clausify,[status(thm)],[f_1326_2]) ).

cnf(f_1326_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5040),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5040),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5040),U_5041),U_5041)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5040),U_5042),U_5042))),c_Groups_Ozero__class_Ozero(U_5040)))
    | U_5042 != c_Groups_Ozero__class_Ozero(U_5040)
    | U_5041 != c_Groups_Ozero__class_Ozero(U_5040)
    | ~ class_Rings_Olinordered__ring__strict(U_5040) ),
    inference(clausify,[status(thm)],[f_1326_2]) ).

fof(f_1327_1,plain,
    ! [V_y,V_x,T_a] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y))),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ class_Rings_Olinordered__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_not__sum__squares__lt__zero]) ).

fof(f_1327_2,plain,
    ! [U_5045,U_5044,U_5043] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5043),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5043),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5043),U_5044),U_5044)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5043),U_5045),U_5045))),c_Groups_Ozero__class_Ozero(U_5043)))
      | ~ class_Rings_Olinordered__ring(U_5043) ),
    inference(variable_rename,[status(thm)],[f_1327_1]) ).

cnf(f_1327_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5043),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5043),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5043),U_5044),U_5044)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5043),U_5045),U_5045))),c_Groups_Ozero__class_Ozero(U_5043)))
    | ~ class_Rings_Olinordered__ring(U_5043) ),
    inference(clausify,[status(thm)],[f_1327_2]) ).

fof(f_1328_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2))))
          | ( V_y_2 = c_Groups_Ozero__class_Ozero(T_b)
            & V_x_2 = c_Groups_Ozero__class_Ozero(T_b) ) )
        & ( V_y_2 != c_Groups_Ozero__class_Ozero(T_b)
          | V_x_2 != c_Groups_Ozero__class_Ozero(T_b)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2)))) ) )
      | ~ class_Rings_Olinordered__ring__strict(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sum__squares__gt__zero__iff]) ).

fof(f_1328_2,plain,
    ! [U_5048,U_5047,U_5046] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5046),c_Groups_Ozero__class_Ozero(U_5046)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5046),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5046),U_5047),U_5047)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5046),U_5048),U_5048))))
          | ( U_5048 = c_Groups_Ozero__class_Ozero(U_5046)
            & U_5047 = c_Groups_Ozero__class_Ozero(U_5046) ) )
        & ( U_5048 != c_Groups_Ozero__class_Ozero(U_5046)
          | U_5047 != c_Groups_Ozero__class_Ozero(U_5046)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5046),c_Groups_Ozero__class_Ozero(U_5046)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5046),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5046),U_5047),U_5047)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5046),U_5048),U_5048)))) ) )
      | ~ class_Rings_Olinordered__ring__strict(U_5046) ),
    inference(variable_rename,[status(thm)],[f_1328_1]) ).

cnf(f_1328_3,plain,
    ( U_5048 != c_Groups_Ozero__class_Ozero(U_5046)
    | U_5047 != c_Groups_Ozero__class_Ozero(U_5046)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5046),c_Groups_Ozero__class_Ozero(U_5046)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5046),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5046),U_5047),U_5047)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5046),U_5048),U_5048))))
    | ~ class_Rings_Olinordered__ring__strict(U_5046) ),
    inference(clausify,[status(thm)],[f_1328_2]) ).

cnf(f_1328_4,plain,
    ( U_5047 = c_Groups_Ozero__class_Ozero(U_5046)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5046),c_Groups_Ozero__class_Ozero(U_5046)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5046),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5046),U_5047),U_5047)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5046),U_5048),U_5048))))
    | ~ class_Rings_Olinordered__ring__strict(U_5046) ),
    inference(clausify,[status(thm)],[f_1328_2]) ).

cnf(f_1328_5,plain,
    ( U_5048 = c_Groups_Ozero__class_Ozero(U_5046)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5046),c_Groups_Ozero__class_Ozero(U_5046)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5046),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5046),U_5047),U_5047)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5046),U_5048),U_5048))))
    | ~ class_Rings_Olinordered__ring__strict(U_5046) ),
    inference(clausify,[status(thm)],[f_1328_2]) ).

fof(f_1329_1,plain,
    ! [V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__nonpos__nonpos]) ).

fof(f_1329_2,plain,
    ! [U_5051,U_5050,U_5049] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5049),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5049),U_5050),U_5051)),c_Groups_Ozero__class_Ozero(U_5049)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5049),U_5051),c_Groups_Ozero__class_Ozero(U_5049)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5049),U_5050),c_Groups_Ozero__class_Ozero(U_5049)))
      | ~ class_Groups_Oordered__comm__monoid__add(U_5049) ),
    inference(variable_rename,[status(thm)],[f_1329_1]) ).

cnf(f_1329_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5049),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5049),U_5050),U_5051)),c_Groups_Ozero__class_Ozero(U_5049)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5049),U_5051),c_Groups_Ozero__class_Ozero(U_5049)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5049),U_5050),c_Groups_Ozero__class_Ozero(U_5049)))
    | ~ class_Groups_Oordered__comm__monoid__add(U_5049) ),
    inference(clausify,[status(thm)],[f_1329_2]) ).

fof(f_1330_1,plain,
    ! [V_a,V_b,V_c,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
      | ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__increasing2]) ).

fof(f_1330_2,plain,
    ! [U_5055,U_5054,U_5053,U_5052] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5052),U_5054),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5052),U_5055),U_5053)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5052),U_5054),U_5055))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5052),c_Groups_Ozero__class_Ozero(U_5052)),U_5053))
      | ~ class_Groups_Oordered__comm__monoid__add(U_5052) ),
    inference(variable_rename,[status(thm)],[f_1330_1]) ).

cnf(f_1330_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5052),U_5054),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5052),U_5055),U_5053)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5052),U_5054),U_5055))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5052),c_Groups_Ozero__class_Ozero(U_5052)),U_5053))
    | ~ class_Groups_Oordered__comm__monoid__add(U_5052) ),
    inference(clausify,[status(thm)],[f_1330_2]) ).

fof(f_1331_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
      | ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__increasing]) ).

fof(f_1331_2,plain,
    ! [U_5059,U_5058,U_5057,U_5056] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5056),U_5058),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5056),U_5057),U_5059)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5056),U_5058),U_5059))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5056),c_Groups_Ozero__class_Ozero(U_5056)),U_5057))
      | ~ class_Groups_Oordered__comm__monoid__add(U_5056) ),
    inference(variable_rename,[status(thm)],[f_1331_1]) ).

cnf(f_1331_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5056),U_5058),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5056),U_5057),U_5059)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5056),U_5058),U_5059))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5056),c_Groups_Ozero__class_Ozero(U_5056)),U_5057))
    | ~ class_Groups_Oordered__comm__monoid__add(U_5056) ),
    inference(clausify,[status(thm)],[f_1331_2]) ).

fof(f_1332_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_y_2) = c_Groups_Ozero__class_Ozero(T_b)
          | V_y_2 != c_Groups_Ozero__class_Ozero(T_b)
          | V_x_2 != c_Groups_Ozero__class_Ozero(T_b) )
        & ( ( V_y_2 = c_Groups_Ozero__class_Ozero(T_b)
            & V_x_2 = c_Groups_Ozero__class_Ozero(T_b) )
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_y_2) != c_Groups_Ozero__class_Ozero(T_b) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_y_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_x_2))
      | ~ class_Groups_Oordered__comm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_add__nonneg__eq__0__iff]) ).

fof(f_1332_2,plain,
    ! [U_5062,U_5061,U_5060] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5060),U_5061),U_5062) = c_Groups_Ozero__class_Ozero(U_5060)
          | U_5062 != c_Groups_Ozero__class_Ozero(U_5060)
          | U_5061 != c_Groups_Ozero__class_Ozero(U_5060) )
        & ( ( U_5062 = c_Groups_Ozero__class_Ozero(U_5060)
            & U_5061 = c_Groups_Ozero__class_Ozero(U_5060) )
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5060),U_5061),U_5062) != c_Groups_Ozero__class_Ozero(U_5060) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5060),c_Groups_Ozero__class_Ozero(U_5060)),U_5062))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5060),c_Groups_Ozero__class_Ozero(U_5060)),U_5061))
      | ~ class_Groups_Oordered__comm__monoid__add(U_5060) ),
    inference(variable_rename,[status(thm)],[f_1332_1]) ).

cnf(f_1332_3,plain,
    ( U_5061 = c_Groups_Ozero__class_Ozero(U_5060)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5060),U_5061),U_5062) != c_Groups_Ozero__class_Ozero(U_5060)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5060),c_Groups_Ozero__class_Ozero(U_5060)),U_5062))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5060),c_Groups_Ozero__class_Ozero(U_5060)),U_5061))
    | ~ class_Groups_Oordered__comm__monoid__add(U_5060) ),
    inference(clausify,[status(thm)],[f_1332_2]) ).

cnf(f_1332_4,plain,
    ( U_5062 = c_Groups_Ozero__class_Ozero(U_5060)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5060),U_5061),U_5062) != c_Groups_Ozero__class_Ozero(U_5060)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5060),c_Groups_Ozero__class_Ozero(U_5060)),U_5062))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5060),c_Groups_Ozero__class_Ozero(U_5060)),U_5061))
    | ~ class_Groups_Oordered__comm__monoid__add(U_5060) ),
    inference(clausify,[status(thm)],[f_1332_2]) ).

cnf(f_1332_5,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5060),U_5061),U_5062) = c_Groups_Ozero__class_Ozero(U_5060)
    | U_5062 != c_Groups_Ozero__class_Ozero(U_5060)
    | U_5061 != c_Groups_Ozero__class_Ozero(U_5060)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5060),c_Groups_Ozero__class_Ozero(U_5060)),U_5062))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5060),c_Groups_Ozero__class_Ozero(U_5060)),U_5061))
    | ~ class_Groups_Oordered__comm__monoid__add(U_5060) ),
    inference(clausify,[status(thm)],[f_1332_2]) ).

fof(f_1333_1,plain,
    ! [V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
      | ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__nonneg__nonneg]) ).

fof(f_1333_2,plain,
    ! [U_5065,U_5064,U_5063] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5063),c_Groups_Ozero__class_Ozero(U_5063)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5063),U_5064),U_5065)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5063),c_Groups_Ozero__class_Ozero(U_5063)),U_5065))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5063),c_Groups_Ozero__class_Ozero(U_5063)),U_5064))
      | ~ class_Groups_Oordered__comm__monoid__add(U_5063) ),
    inference(variable_rename,[status(thm)],[f_1333_1]) ).

cnf(f_1333_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5063),c_Groups_Ozero__class_Ozero(U_5063)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5063),U_5064),U_5065)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5063),c_Groups_Ozero__class_Ozero(U_5063)),U_5065))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5063),c_Groups_Ozero__class_Ozero(U_5063)),U_5064))
    | ~ class_Groups_Oordered__comm__monoid__add(U_5063) ),
    inference(clausify,[status(thm)],[f_1333_2]) ).

fof(f_1334_1,plain,
    ! [V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_b))) ) )
      | ~ class_Groups_Olinordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_double__add__le__zero__iff__single__add__le__zero]) ).

fof(f_1334_2,plain,
    ! [U_5067,U_5066] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5066),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5066),U_5067),U_5067)),c_Groups_Ozero__class_Ozero(U_5066)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5066),U_5067),c_Groups_Ozero__class_Ozero(U_5066))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5066),U_5067),c_Groups_Ozero__class_Ozero(U_5066)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5066),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5066),U_5067),U_5067)),c_Groups_Ozero__class_Ozero(U_5066))) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_5066) ),
    inference(variable_rename,[status(thm)],[f_1334_1]) ).

cnf(f_1334_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5066),U_5067),c_Groups_Ozero__class_Ozero(U_5066)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5066),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5066),U_5067),U_5067)),c_Groups_Ozero__class_Ozero(U_5066)))
    | ~ class_Groups_Olinordered__ab__group__add(U_5066) ),
    inference(clausify,[status(thm)],[f_1334_2]) ).

cnf(f_1334_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5066),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5066),U_5067),U_5067)),c_Groups_Ozero__class_Ozero(U_5066)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5066),U_5067),c_Groups_Ozero__class_Ozero(U_5066)))
    | ~ class_Groups_Olinordered__ab__group__add(U_5066) ),
    inference(clausify,[status(thm)],[f_1334_2]) ).

fof(f_1335_1,plain,
    ! [V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2))) ) )
      | ~ class_Groups_Olinordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_zero__le__double__add__iff__zero__le__single__add]) ).

fof(f_1335_2,plain,
    ! [U_5069,U_5068] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5068),c_Groups_Ozero__class_Ozero(U_5068)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5068),U_5069),U_5069)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5068),c_Groups_Ozero__class_Ozero(U_5068)),U_5069)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5068),c_Groups_Ozero__class_Ozero(U_5068)),U_5069))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5068),c_Groups_Ozero__class_Ozero(U_5068)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5068),U_5069),U_5069))) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_5068) ),
    inference(variable_rename,[status(thm)],[f_1335_1]) ).

cnf(f_1335_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5068),c_Groups_Ozero__class_Ozero(U_5068)),U_5069))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5068),c_Groups_Ozero__class_Ozero(U_5068)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5068),U_5069),U_5069)))
    | ~ class_Groups_Olinordered__ab__group__add(U_5068) ),
    inference(clausify,[status(thm)],[f_1335_2]) ).

cnf(f_1335_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5068),c_Groups_Ozero__class_Ozero(U_5068)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5068),U_5069),U_5069)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5068),c_Groups_Ozero__class_Ozero(U_5068)),U_5069))
    | ~ class_Groups_Olinordered__ab__group__add(U_5068) ),
    inference(clausify,[status(thm)],[f_1335_2]) ).

fof(f_1336_1,plain,
    ! [V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a)))
      | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) ) )
      | ~ class_Rings_Oordered__cancel__semiring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_split__mult__neg__le]) ).

fof(f_1336_2,plain,
    ! [U_5072,U_5071,U_5070] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5070),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5070),U_5071),U_5072)),c_Groups_Ozero__class_Ozero(U_5070)))
      | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5070),c_Groups_Ozero__class_Ozero(U_5070)),U_5072))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5070),U_5071),c_Groups_Ozero__class_Ozero(U_5070))) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5070),U_5072),c_Groups_Ozero__class_Ozero(U_5070)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5070),c_Groups_Ozero__class_Ozero(U_5070)),U_5071)) ) )
      | ~ class_Rings_Oordered__cancel__semiring(U_5070) ),
    inference(variable_rename,[status(thm)],[f_1336_1]) ).

cnf(f_1336_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5070),U_5072),c_Groups_Ozero__class_Ozero(U_5070)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5070),c_Groups_Ozero__class_Ozero(U_5070)),U_5071))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5070),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5070),U_5071),U_5072)),c_Groups_Ozero__class_Ozero(U_5070)))
    | ~ class_Rings_Oordered__cancel__semiring(U_5070) ),
    inference(clausify,[status(thm)],[f_1336_2]) ).

cnf(f_1336_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5070),c_Groups_Ozero__class_Ozero(U_5070)),U_5072))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5070),U_5071),c_Groups_Ozero__class_Ozero(U_5070)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5070),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5070),U_5071),U_5072)),c_Groups_Ozero__class_Ozero(U_5070)))
    | ~ class_Rings_Oordered__cancel__semiring(U_5070) ),
    inference(clausify,[status(thm)],[f_1336_2]) ).

fof(f_1337_1,plain,
    ! [V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))
      | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) ) )
      | ~ class_Rings_Oordered__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_split__mult__pos__le]) ).

fof(f_1337_2,plain,
    ! [U_5075,U_5074,U_5073] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5073),c_Groups_Ozero__class_Ozero(U_5073)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5073),U_5074),U_5075)))
      | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5073),U_5075),c_Groups_Ozero__class_Ozero(U_5073)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5073),U_5074),c_Groups_Ozero__class_Ozero(U_5073))) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5073),c_Groups_Ozero__class_Ozero(U_5073)),U_5075))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5073),c_Groups_Ozero__class_Ozero(U_5073)),U_5074)) ) )
      | ~ class_Rings_Oordered__ring(U_5073) ),
    inference(variable_rename,[status(thm)],[f_1337_1]) ).

cnf(f_1337_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5073),c_Groups_Ozero__class_Ozero(U_5073)),U_5075))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5073),c_Groups_Ozero__class_Ozero(U_5073)),U_5074))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5073),c_Groups_Ozero__class_Ozero(U_5073)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5073),U_5074),U_5075)))
    | ~ class_Rings_Oordered__ring(U_5073) ),
    inference(clausify,[status(thm)],[f_1337_2]) ).

cnf(f_1337_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5073),U_5075),c_Groups_Ozero__class_Ozero(U_5073)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5073),U_5074),c_Groups_Ozero__class_Ozero(U_5073)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5073),c_Groups_Ozero__class_Ozero(U_5073)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5073),U_5074),U_5075)))
    | ~ class_Rings_Oordered__ring(U_5073) ),
    inference(clausify,[status(thm)],[f_1337_2]) ).

fof(f_1338_1,plain,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
      | ~ class_Rings_Oordered__semiring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__mono]) ).

fof(f_1338_2,plain,
    ! [U_5080,U_5079,U_5078,U_5077,U_5076] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5076),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5076),U_5077),U_5079)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5076),U_5078),U_5080)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5076),c_Groups_Ozero__class_Ozero(U_5076)),U_5079))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5076),c_Groups_Ozero__class_Ozero(U_5076)),U_5078))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5076),U_5079),U_5080))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5076),U_5077),U_5078))
      | ~ class_Rings_Oordered__semiring(U_5076) ),
    inference(variable_rename,[status(thm)],[f_1338_1]) ).

cnf(f_1338_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5076),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5076),U_5077),U_5079)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5076),U_5078),U_5080)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5076),c_Groups_Ozero__class_Ozero(U_5076)),U_5079))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5076),c_Groups_Ozero__class_Ozero(U_5076)),U_5078))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5076),U_5079),U_5080))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5076),U_5077),U_5078))
    | ~ class_Rings_Oordered__semiring(U_5076) ),
    inference(clausify,[status(thm)],[f_1338_2]) ).

fof(f_1339_1,plain,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
      | ~ class_Rings_Oordered__semiring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__mono_H]) ).

fof(f_1339_2,plain,
    ! [U_5085,U_5084,U_5083,U_5082,U_5081] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5081),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5081),U_5082),U_5084)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5081),U_5083),U_5085)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5081),c_Groups_Ozero__class_Ozero(U_5081)),U_5084))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5081),c_Groups_Ozero__class_Ozero(U_5081)),U_5082))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5081),U_5084),U_5085))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5081),U_5082),U_5083))
      | ~ class_Rings_Oordered__semiring(U_5081) ),
    inference(variable_rename,[status(thm)],[f_1339_1]) ).

cnf(f_1339_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5081),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5081),U_5082),U_5084)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5081),U_5083),U_5085)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5081),c_Groups_Ozero__class_Ozero(U_5081)),U_5084))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5081),c_Groups_Ozero__class_Ozero(U_5081)),U_5082))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5081),U_5084),U_5085))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5081),U_5082),U_5083))
    | ~ class_Rings_Oordered__semiring(U_5081) ),
    inference(clausify,[status(thm)],[f_1339_2]) ).

fof(f_1340_1,plain,
    ! [V_c,V_a,V_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
      | ~ class_Rings_Oordered__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__left__mono__neg]) ).

fof(f_1340_2,plain,
    ! [U_5089,U_5088,U_5087,U_5086] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5086),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5086),U_5089),U_5088)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5086),U_5089),U_5087)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5086),U_5089),c_Groups_Ozero__class_Ozero(U_5086)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5086),U_5087),U_5088))
      | ~ class_Rings_Oordered__ring(U_5086) ),
    inference(variable_rename,[status(thm)],[f_1340_1]) ).

cnf(f_1340_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5086),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5086),U_5089),U_5088)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5086),U_5089),U_5087)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5086),U_5089),c_Groups_Ozero__class_Ozero(U_5086)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5086),U_5087),U_5088))
    | ~ class_Rings_Oordered__ring(U_5086) ),
    inference(clausify,[status(thm)],[f_1340_2]) ).

fof(f_1341_1,plain,
    ! [V_c,V_a,V_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
      | ~ class_Rings_Oordered__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__right__mono__neg]) ).

fof(f_1341_2,plain,
    ! [U_5093,U_5092,U_5091,U_5090] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5090),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5090),U_5092),U_5093)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5090),U_5091),U_5093)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5090),U_5093),c_Groups_Ozero__class_Ozero(U_5090)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5090),U_5091),U_5092))
      | ~ class_Rings_Oordered__ring(U_5090) ),
    inference(variable_rename,[status(thm)],[f_1341_1]) ).

cnf(f_1341_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5090),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5090),U_5092),U_5093)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5090),U_5091),U_5093)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5090),U_5093),c_Groups_Ozero__class_Ozero(U_5090)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5090),U_5091),U_5092))
    | ~ class_Rings_Oordered__ring(U_5090) ),
    inference(clausify,[status(thm)],[f_1341_2]) ).

fof(f_1342_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
      | ~ class_Rings_Oordered__comm__semiring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__mult__left__mono]) ).

fof(f_1342_2,plain,
    ! [U_5097,U_5096,U_5095,U_5094] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5094),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5094),U_5097),U_5095)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5094),U_5097),U_5096)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5094),c_Groups_Ozero__class_Ozero(U_5094)),U_5097))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5094),U_5095),U_5096))
      | ~ class_Rings_Oordered__comm__semiring(U_5094) ),
    inference(variable_rename,[status(thm)],[f_1342_1]) ).

cnf(f_1342_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5094),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5094),U_5097),U_5095)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5094),U_5097),U_5096)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5094),c_Groups_Ozero__class_Ozero(U_5094)),U_5097))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5094),U_5095),U_5096))
    | ~ class_Rings_Oordered__comm__semiring(U_5094) ),
    inference(clausify,[status(thm)],[f_1342_2]) ).

fof(f_1343_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
      | ~ class_Rings_Oordered__semiring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__left__mono]) ).

fof(f_1343_2,plain,
    ! [U_5101,U_5100,U_5099,U_5098] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5098),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5098),U_5101),U_5099)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5098),U_5101),U_5100)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5098),c_Groups_Ozero__class_Ozero(U_5098)),U_5101))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5098),U_5099),U_5100))
      | ~ class_Rings_Oordered__semiring(U_5098) ),
    inference(variable_rename,[status(thm)],[f_1343_1]) ).

cnf(f_1343_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5098),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5098),U_5101),U_5099)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5098),U_5101),U_5100)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5098),c_Groups_Ozero__class_Ozero(U_5098)),U_5101))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5098),U_5099),U_5100))
    | ~ class_Rings_Oordered__semiring(U_5098) ),
    inference(clausify,[status(thm)],[f_1343_2]) ).

fof(f_1344_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
      | ~ class_Rings_Oordered__semiring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__right__mono]) ).

fof(f_1344_2,plain,
    ! [U_5105,U_5104,U_5103,U_5102] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5102),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5102),U_5103),U_5105)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5102),U_5104),U_5105)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5102),c_Groups_Ozero__class_Ozero(U_5102)),U_5105))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5102),U_5103),U_5104))
      | ~ class_Rings_Oordered__semiring(U_5102) ),
    inference(variable_rename,[status(thm)],[f_1344_1]) ).

cnf(f_1344_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5102),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5102),U_5103),U_5105)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5102),U_5104),U_5105)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5102),c_Groups_Ozero__class_Ozero(U_5102)),U_5105))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5102),U_5103),U_5104))
    | ~ class_Rings_Oordered__semiring(U_5102) ),
    inference(clausify,[status(thm)],[f_1344_2]) ).

fof(f_1345_1,plain,
    ! [V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ class_Rings_Oordered__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__nonpos__nonpos]) ).

fof(f_1345_2,plain,
    ! [U_5108,U_5107,U_5106] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5106),c_Groups_Ozero__class_Ozero(U_5106)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5106),U_5107),U_5108)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5106),U_5108),c_Groups_Ozero__class_Ozero(U_5106)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5106),U_5107),c_Groups_Ozero__class_Ozero(U_5106)))
      | ~ class_Rings_Oordered__ring(U_5106) ),
    inference(variable_rename,[status(thm)],[f_1345_1]) ).

cnf(f_1345_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5106),c_Groups_Ozero__class_Ozero(U_5106)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5106),U_5107),U_5108)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5106),U_5108),c_Groups_Ozero__class_Ozero(U_5106)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5106),U_5107),c_Groups_Ozero__class_Ozero(U_5106)))
    | ~ class_Rings_Oordered__ring(U_5106) ),
    inference(clausify,[status(thm)],[f_1345_2]) ).

fof(f_1346_1,plain,
    ! [V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ class_Rings_Oordered__cancel__semiring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__nonpos__nonneg]) ).

fof(f_1346_2,plain,
    ! [U_5111,U_5110,U_5109] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5109),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5109),U_5110),U_5111)),c_Groups_Ozero__class_Ozero(U_5109)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5109),c_Groups_Ozero__class_Ozero(U_5109)),U_5111))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5109),U_5110),c_Groups_Ozero__class_Ozero(U_5109)))
      | ~ class_Rings_Oordered__cancel__semiring(U_5109) ),
    inference(variable_rename,[status(thm)],[f_1346_1]) ).

cnf(f_1346_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5109),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5109),U_5110),U_5111)),c_Groups_Ozero__class_Ozero(U_5109)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5109),c_Groups_Ozero__class_Ozero(U_5109)),U_5111))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5109),U_5110),c_Groups_Ozero__class_Ozero(U_5109)))
    | ~ class_Rings_Oordered__cancel__semiring(U_5109) ),
    inference(clausify,[status(thm)],[f_1346_2]) ).

fof(f_1347_1,plain,
    ! [V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
      | ~ class_Rings_Oordered__cancel__semiring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__nonneg__nonpos2]) ).

fof(f_1347_2,plain,
    ! [U_5114,U_5113,U_5112] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5112),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5112),U_5114),U_5113)),c_Groups_Ozero__class_Ozero(U_5112)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5112),U_5114),c_Groups_Ozero__class_Ozero(U_5112)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5112),c_Groups_Ozero__class_Ozero(U_5112)),U_5113))
      | ~ class_Rings_Oordered__cancel__semiring(U_5112) ),
    inference(variable_rename,[status(thm)],[f_1347_1]) ).

cnf(f_1347_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5112),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5112),U_5114),U_5113)),c_Groups_Ozero__class_Ozero(U_5112)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5112),U_5114),c_Groups_Ozero__class_Ozero(U_5112)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5112),c_Groups_Ozero__class_Ozero(U_5112)),U_5113))
    | ~ class_Rings_Oordered__cancel__semiring(U_5112) ),
    inference(clausify,[status(thm)],[f_1347_2]) ).

fof(f_1348_1,plain,
    ! [V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
      | ~ class_Rings_Oordered__cancel__semiring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__nonneg__nonpos]) ).

fof(f_1348_2,plain,
    ! [U_5117,U_5116,U_5115] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5115),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5115),U_5116),U_5117)),c_Groups_Ozero__class_Ozero(U_5115)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5115),U_5117),c_Groups_Ozero__class_Ozero(U_5115)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5115),c_Groups_Ozero__class_Ozero(U_5115)),U_5116))
      | ~ class_Rings_Oordered__cancel__semiring(U_5115) ),
    inference(variable_rename,[status(thm)],[f_1348_1]) ).

cnf(f_1348_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5115),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5115),U_5116),U_5117)),c_Groups_Ozero__class_Ozero(U_5115)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5115),U_5117),c_Groups_Ozero__class_Ozero(U_5115)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5115),c_Groups_Ozero__class_Ozero(U_5115)),U_5116))
    | ~ class_Rings_Oordered__cancel__semiring(U_5115) ),
    inference(clausify,[status(thm)],[f_1348_2]) ).

fof(f_1349_1,plain,
    ! [V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
      | ~ class_Rings_Oordered__cancel__semiring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__nonneg__nonneg]) ).

fof(f_1349_2,plain,
    ! [U_5120,U_5119,U_5118] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5118),c_Groups_Ozero__class_Ozero(U_5118)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5118),U_5119),U_5120)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5118),c_Groups_Ozero__class_Ozero(U_5118)),U_5120))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5118),c_Groups_Ozero__class_Ozero(U_5118)),U_5119))
      | ~ class_Rings_Oordered__cancel__semiring(U_5118) ),
    inference(variable_rename,[status(thm)],[f_1349_1]) ).

cnf(f_1349_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5118),c_Groups_Ozero__class_Ozero(U_5118)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5118),U_5119),U_5120)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5118),c_Groups_Ozero__class_Ozero(U_5118)),U_5120))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5118),c_Groups_Ozero__class_Ozero(U_5118)),U_5119))
    | ~ class_Rings_Oordered__cancel__semiring(U_5118) ),
    inference(clausify,[status(thm)],[f_1349_2]) ).

fof(f_1350_1,plain,
    ! [V_b_2,V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))) ) )
      | ~ class_Rings_Olinordered__ring__strict(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_mult__le__0__iff]) ).

fof(f_1350_2,plain,
    ! [U_5123,U_5122,U_5121] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5121),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5121),U_5122),U_5123)),c_Groups_Ozero__class_Ozero(U_5121)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5121),c_Groups_Ozero__class_Ozero(U_5121)),U_5123))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5121),U_5122),c_Groups_Ozero__class_Ozero(U_5121))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5121),U_5123),c_Groups_Ozero__class_Ozero(U_5121)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5121),c_Groups_Ozero__class_Ozero(U_5121)),U_5122)) ) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5121),c_Groups_Ozero__class_Ozero(U_5121)),U_5123))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5121),U_5122),c_Groups_Ozero__class_Ozero(U_5121))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5121),U_5123),c_Groups_Ozero__class_Ozero(U_5121)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5121),c_Groups_Ozero__class_Ozero(U_5121)),U_5122)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5121),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5121),U_5122),U_5123)),c_Groups_Ozero__class_Ozero(U_5121))) ) )
      | ~ class_Rings_Olinordered__ring__strict(U_5121) ),
    inference(variable_rename,[status(thm)],[f_1350_1]) ).

cnf(f_1350_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5121),U_5122),c_Groups_Ozero__class_Ozero(U_5121)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5121),c_Groups_Ozero__class_Ozero(U_5121)),U_5122))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5121),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5121),U_5122),U_5123)),c_Groups_Ozero__class_Ozero(U_5121)))
    | ~ class_Rings_Olinordered__ring__strict(U_5121) ),
    inference(clausify,[status(thm)],[f_1350_2]) ).

cnf(f_1350_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5121),c_Groups_Ozero__class_Ozero(U_5121)),U_5123))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5121),c_Groups_Ozero__class_Ozero(U_5121)),U_5122))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5121),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5121),U_5122),U_5123)),c_Groups_Ozero__class_Ozero(U_5121)))
    | ~ class_Rings_Olinordered__ring__strict(U_5121) ),
    inference(clausify,[status(thm)],[f_1350_2]) ).

cnf(f_1350_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5121),U_5122),c_Groups_Ozero__class_Ozero(U_5121)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5121),U_5123),c_Groups_Ozero__class_Ozero(U_5121)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5121),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5121),U_5122),U_5123)),c_Groups_Ozero__class_Ozero(U_5121)))
    | ~ class_Rings_Olinordered__ring__strict(U_5121) ),
    inference(clausify,[status(thm)],[f_1350_2]) ).

cnf(f_1350_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5121),c_Groups_Ozero__class_Ozero(U_5121)),U_5123))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5121),U_5123),c_Groups_Ozero__class_Ozero(U_5121)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5121),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5121),U_5122),U_5123)),c_Groups_Ozero__class_Ozero(U_5121)))
    | ~ class_Rings_Olinordered__ring__strict(U_5121) ),
    inference(clausify,[status(thm)],[f_1350_2]) ).

cnf(f_1350_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5121),U_5123),c_Groups_Ozero__class_Ozero(U_5121)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5121),c_Groups_Ozero__class_Ozero(U_5121)),U_5122))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5121),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5121),U_5122),U_5123)),c_Groups_Ozero__class_Ozero(U_5121)))
    | ~ class_Rings_Olinordered__ring__strict(U_5121) ),
    inference(clausify,[status(thm)],[f_1350_2]) ).

cnf(f_1350_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5121),c_Groups_Ozero__class_Ozero(U_5121)),U_5123))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5121),U_5122),c_Groups_Ozero__class_Ozero(U_5121)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5121),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5121),U_5122),U_5123)),c_Groups_Ozero__class_Ozero(U_5121)))
    | ~ class_Rings_Olinordered__ring__strict(U_5121) ),
    inference(clausify,[status(thm)],[f_1350_2]) ).

fof(f_1351_1,plain,
    ! [V_b_2,V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2))) ) )
      | ~ class_Rings_Olinordered__ring__strict(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_zero__le__mult__iff]) ).

fof(f_1351_2,plain,
    ! [U_5126,U_5125,U_5124] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5124),c_Groups_Ozero__class_Ozero(U_5124)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5124),U_5125),U_5126)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5124),U_5126),c_Groups_Ozero__class_Ozero(U_5124)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5124),U_5125),c_Groups_Ozero__class_Ozero(U_5124))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5124),c_Groups_Ozero__class_Ozero(U_5124)),U_5126))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5124),c_Groups_Ozero__class_Ozero(U_5124)),U_5125)) ) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5124),U_5126),c_Groups_Ozero__class_Ozero(U_5124)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5124),U_5125),c_Groups_Ozero__class_Ozero(U_5124))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5124),c_Groups_Ozero__class_Ozero(U_5124)),U_5126))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5124),c_Groups_Ozero__class_Ozero(U_5124)),U_5125)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5124),c_Groups_Ozero__class_Ozero(U_5124)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5124),U_5125),U_5126))) ) )
      | ~ class_Rings_Olinordered__ring__strict(U_5124) ),
    inference(variable_rename,[status(thm)],[f_1351_1]) ).

cnf(f_1351_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5124),U_5125),c_Groups_Ozero__class_Ozero(U_5124)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5124),c_Groups_Ozero__class_Ozero(U_5124)),U_5125))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5124),c_Groups_Ozero__class_Ozero(U_5124)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5124),U_5125),U_5126)))
    | ~ class_Rings_Olinordered__ring__strict(U_5124) ),
    inference(clausify,[status(thm)],[f_1351_2]) ).

cnf(f_1351_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5124),U_5126),c_Groups_Ozero__class_Ozero(U_5124)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5124),c_Groups_Ozero__class_Ozero(U_5124)),U_5125))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5124),c_Groups_Ozero__class_Ozero(U_5124)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5124),U_5125),U_5126)))
    | ~ class_Rings_Olinordered__ring__strict(U_5124) ),
    inference(clausify,[status(thm)],[f_1351_2]) ).

cnf(f_1351_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5124),U_5125),c_Groups_Ozero__class_Ozero(U_5124)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5124),c_Groups_Ozero__class_Ozero(U_5124)),U_5126))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5124),c_Groups_Ozero__class_Ozero(U_5124)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5124),U_5125),U_5126)))
    | ~ class_Rings_Olinordered__ring__strict(U_5124) ),
    inference(clausify,[status(thm)],[f_1351_2]) ).

cnf(f_1351_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5124),U_5126),c_Groups_Ozero__class_Ozero(U_5124)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5124),c_Groups_Ozero__class_Ozero(U_5124)),U_5126))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5124),c_Groups_Ozero__class_Ozero(U_5124)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5124),U_5125),U_5126)))
    | ~ class_Rings_Olinordered__ring__strict(U_5124) ),
    inference(clausify,[status(thm)],[f_1351_2]) ).

cnf(f_1351_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5124),c_Groups_Ozero__class_Ozero(U_5124)),U_5126))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5124),c_Groups_Ozero__class_Ozero(U_5124)),U_5125))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5124),c_Groups_Ozero__class_Ozero(U_5124)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5124),U_5125),U_5126)))
    | ~ class_Rings_Olinordered__ring__strict(U_5124) ),
    inference(clausify,[status(thm)],[f_1351_2]) ).

cnf(f_1351_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5124),U_5126),c_Groups_Ozero__class_Ozero(U_5124)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5124),U_5125),c_Groups_Ozero__class_Ozero(U_5124)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5124),c_Groups_Ozero__class_Ozero(U_5124)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5124),U_5125),U_5126)))
    | ~ class_Rings_Olinordered__ring__strict(U_5124) ),
    inference(clausify,[status(thm)],[f_1351_2]) ).

fof(f_1352_1,plain,
    ! [V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)))
      | ~ class_Rings_Olinordered__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_zero__le__square]) ).

fof(f_1352_2,plain,
    ! [U_5128,U_5127] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5127),c_Groups_Ozero__class_Ozero(U_5127)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5127),U_5128),U_5128)))
      | ~ class_Rings_Olinordered__ring(U_5127) ),
    inference(variable_rename,[status(thm)],[f_1352_1]) ).

cnf(f_1352_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5127),c_Groups_Ozero__class_Ozero(U_5127)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5127),U_5128),U_5128)))
    | ~ class_Rings_Olinordered__ring(U_5127) ),
    inference(clausify,[status(thm)],[f_1352_2]) ).

fof(f_1353_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_pos__add__strict]) ).

fof(f_1353_2,plain,
    ! [U_5132,U_5131,U_5130,U_5129] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5129),U_5131),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5129),U_5130),U_5132)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5129),U_5131),U_5132))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5129),c_Groups_Ozero__class_Ozero(U_5129)),U_5130))
      | ~ class_Rings_Olinordered__semidom(U_5129) ),
    inference(variable_rename,[status(thm)],[f_1353_1]) ).

cnf(f_1353_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5129),U_5131),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5129),U_5130),U_5132)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5129),U_5131),U_5132))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5129),c_Groups_Ozero__class_Ozero(U_5129)),U_5130))
    | ~ class_Rings_Olinordered__semidom(U_5129) ),
    inference(clausify,[status(thm)],[f_1353_2]) ).

fof(f_1354_1,plain,
    ! [V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2))) ) )
      | ~ class_Groups_Olinordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_zero__less__double__add__iff__zero__less__single__add]) ).

fof(f_1354_2,plain,
    ! [U_5134,U_5133] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5133),c_Groups_Ozero__class_Ozero(U_5133)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5133),U_5134),U_5134)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5133),c_Groups_Ozero__class_Ozero(U_5133)),U_5134)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5133),c_Groups_Ozero__class_Ozero(U_5133)),U_5134))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5133),c_Groups_Ozero__class_Ozero(U_5133)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5133),U_5134),U_5134))) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_5133) ),
    inference(variable_rename,[status(thm)],[f_1354_1]) ).

cnf(f_1354_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5133),c_Groups_Ozero__class_Ozero(U_5133)),U_5134))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5133),c_Groups_Ozero__class_Ozero(U_5133)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5133),U_5134),U_5134)))
    | ~ class_Groups_Olinordered__ab__group__add(U_5133) ),
    inference(clausify,[status(thm)],[f_1354_2]) ).

cnf(f_1354_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5133),c_Groups_Ozero__class_Ozero(U_5133)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5133),U_5134),U_5134)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5133),c_Groups_Ozero__class_Ozero(U_5133)),U_5134))
    | ~ class_Groups_Olinordered__ab__group__add(U_5133) ),
    inference(clausify,[status(thm)],[f_1354_2]) ).

fof(f_1355_1,plain,
    ! [V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_b))) ) )
      | ~ class_Groups_Olinordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_double__add__less__zero__iff__single__add__less__zero]) ).

fof(f_1355_2,plain,
    ! [U_5136,U_5135] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5135),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5135),U_5136),U_5136)),c_Groups_Ozero__class_Ozero(U_5135)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5135),U_5136),c_Groups_Ozero__class_Ozero(U_5135))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5135),U_5136),c_Groups_Ozero__class_Ozero(U_5135)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5135),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5135),U_5136),U_5136)),c_Groups_Ozero__class_Ozero(U_5135))) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_5135) ),
    inference(variable_rename,[status(thm)],[f_1355_1]) ).

cnf(f_1355_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5135),U_5136),c_Groups_Ozero__class_Ozero(U_5135)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5135),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5135),U_5136),U_5136)),c_Groups_Ozero__class_Ozero(U_5135)))
    | ~ class_Groups_Olinordered__ab__group__add(U_5135) ),
    inference(clausify,[status(thm)],[f_1355_2]) ).

cnf(f_1355_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5135),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5135),U_5136),U_5136)),c_Groups_Ozero__class_Ozero(U_5135)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5135),U_5136),c_Groups_Ozero__class_Ozero(U_5135)))
    | ~ class_Groups_Olinordered__ab__group__add(U_5135) ),
    inference(clausify,[status(thm)],[f_1355_2]) ).

fof(f_1356_1,plain,
    ! [V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
      | ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__pos__pos]) ).

fof(f_1356_2,plain,
    ! [U_5139,U_5138,U_5137] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5137),c_Groups_Ozero__class_Ozero(U_5137)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5137),U_5138),U_5139)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5137),c_Groups_Ozero__class_Ozero(U_5137)),U_5139))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5137),c_Groups_Ozero__class_Ozero(U_5137)),U_5138))
      | ~ class_Groups_Oordered__comm__monoid__add(U_5137) ),
    inference(variable_rename,[status(thm)],[f_1356_1]) ).

cnf(f_1356_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5137),c_Groups_Ozero__class_Ozero(U_5137)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5137),U_5138),U_5139)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5137),c_Groups_Ozero__class_Ozero(U_5137)),U_5139))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5137),c_Groups_Ozero__class_Ozero(U_5137)),U_5138))
    | ~ class_Groups_Oordered__comm__monoid__add(U_5137) ),
    inference(clausify,[status(thm)],[f_1356_2]) ).

fof(f_1357_1,plain,
    ! [V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__neg__neg]) ).

fof(f_1357_2,plain,
    ! [U_5142,U_5141,U_5140] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5140),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5140),U_5141),U_5142)),c_Groups_Ozero__class_Ozero(U_5140)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5140),U_5142),c_Groups_Ozero__class_Ozero(U_5140)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5140),U_5141),c_Groups_Ozero__class_Ozero(U_5140)))
      | ~ class_Groups_Oordered__comm__monoid__add(U_5140) ),
    inference(variable_rename,[status(thm)],[f_1357_1]) ).

cnf(f_1357_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5140),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5140),U_5141),U_5142)),c_Groups_Ozero__class_Ozero(U_5140)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5140),U_5142),c_Groups_Ozero__class_Ozero(U_5140)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5140),U_5141),c_Groups_Ozero__class_Ozero(U_5140)))
    | ~ class_Groups_Oordered__comm__monoid__add(U_5140) ),
    inference(clausify,[status(thm)],[f_1357_2]) ).

fof(f_1358_1,plain,
    ! [V_a,T_a] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ class_Rings_Olinordered__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_not__square__less__zero]) ).

fof(f_1358_2,plain,
    ! [U_5144,U_5143] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5143),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5143),U_5144),U_5144)),c_Groups_Ozero__class_Ozero(U_5143)))
      | ~ class_Rings_Olinordered__ring(U_5143) ),
    inference(variable_rename,[status(thm)],[f_1358_1]) ).

cnf(f_1358_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5143),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5143),U_5144),U_5144)),c_Groups_Ozero__class_Ozero(U_5143)))
    | ~ class_Rings_Olinordered__ring(U_5143) ),
    inference(clausify,[status(thm)],[f_1358_2]) ).

fof(f_1359_1,plain,
    ! [V_b_2,V_c_2,V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_c_2)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_c_2))) ) )
      | ~ class_Rings_Olinordered__ring__strict(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__right__disj]) ).

fof(f_1359_2,plain,
    ! [U_5148,U_5147,U_5146,U_5145] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5145),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5145),U_5146),U_5147)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5145),U_5148),U_5147)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5145),U_5148),U_5146))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5145),U_5147),c_Groups_Ozero__class_Ozero(U_5145))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5145),U_5146),U_5148))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5145),c_Groups_Ozero__class_Ozero(U_5145)),U_5147)) ) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5145),U_5148),U_5146))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5145),U_5147),c_Groups_Ozero__class_Ozero(U_5145))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5145),U_5146),U_5148))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5145),c_Groups_Ozero__class_Ozero(U_5145)),U_5147)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5145),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5145),U_5146),U_5147)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5145),U_5148),U_5147))) ) )
      | ~ class_Rings_Olinordered__ring__strict(U_5145) ),
    inference(variable_rename,[status(thm)],[f_1359_1]) ).

cnf(f_1359_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5145),U_5147),c_Groups_Ozero__class_Ozero(U_5145)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5145),c_Groups_Ozero__class_Ozero(U_5145)),U_5147))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5145),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5145),U_5146),U_5147)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5145),U_5148),U_5147)))
    | ~ class_Rings_Olinordered__ring__strict(U_5145) ),
    inference(clausify,[status(thm)],[f_1359_2]) ).

cnf(f_1359_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5145),U_5148),U_5146))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5145),c_Groups_Ozero__class_Ozero(U_5145)),U_5147))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5145),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5145),U_5146),U_5147)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5145),U_5148),U_5147)))
    | ~ class_Rings_Olinordered__ring__strict(U_5145) ),
    inference(clausify,[status(thm)],[f_1359_2]) ).

cnf(f_1359_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5145),U_5147),c_Groups_Ozero__class_Ozero(U_5145)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5145),U_5146),U_5148))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5145),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5145),U_5146),U_5147)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5145),U_5148),U_5147)))
    | ~ class_Rings_Olinordered__ring__strict(U_5145) ),
    inference(clausify,[status(thm)],[f_1359_2]) ).

cnf(f_1359_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5145),U_5148),U_5146))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5145),U_5146),U_5148))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5145),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5145),U_5146),U_5147)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5145),U_5148),U_5147)))
    | ~ class_Rings_Olinordered__ring__strict(U_5145) ),
    inference(clausify,[status(thm)],[f_1359_2]) ).

cnf(f_1359_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5145),U_5146),U_5148))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5145),c_Groups_Ozero__class_Ozero(U_5145)),U_5147))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5145),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5145),U_5146),U_5147)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5145),U_5148),U_5147)))
    | ~ class_Rings_Olinordered__ring__strict(U_5145) ),
    inference(clausify,[status(thm)],[f_1359_2]) ).

cnf(f_1359_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5145),U_5148),U_5146))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5145),U_5147),c_Groups_Ozero__class_Ozero(U_5145)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5145),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5145),U_5146),U_5147)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5145),U_5148),U_5147)))
    | ~ class_Rings_Olinordered__ring__strict(U_5145) ),
    inference(clausify,[status(thm)],[f_1359_2]) ).

fof(f_1360_1,plain,
    ! [V_b_2,V_a_2,V_c_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2))) ) )
      | ~ class_Rings_Olinordered__ring__strict(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__disj]) ).

fof(f_1360_2,plain,
    ! [U_5152,U_5151,U_5150,U_5149] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5149),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5149),U_5150),U_5151)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5149),U_5150),U_5152)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5149),U_5152),U_5151))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5149),U_5150),c_Groups_Ozero__class_Ozero(U_5149))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5149),U_5151),U_5152))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5149),c_Groups_Ozero__class_Ozero(U_5149)),U_5150)) ) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5149),U_5152),U_5151))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5149),U_5150),c_Groups_Ozero__class_Ozero(U_5149))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5149),U_5151),U_5152))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5149),c_Groups_Ozero__class_Ozero(U_5149)),U_5150)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5149),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5149),U_5150),U_5151)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5149),U_5150),U_5152))) ) )
      | ~ class_Rings_Olinordered__ring__strict(U_5149) ),
    inference(variable_rename,[status(thm)],[f_1360_1]) ).

cnf(f_1360_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5149),U_5150),c_Groups_Ozero__class_Ozero(U_5149)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5149),c_Groups_Ozero__class_Ozero(U_5149)),U_5150))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5149),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5149),U_5150),U_5151)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5149),U_5150),U_5152)))
    | ~ class_Rings_Olinordered__ring__strict(U_5149) ),
    inference(clausify,[status(thm)],[f_1360_2]) ).

cnf(f_1360_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5149),U_5152),U_5151))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5149),c_Groups_Ozero__class_Ozero(U_5149)),U_5150))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5149),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5149),U_5150),U_5151)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5149),U_5150),U_5152)))
    | ~ class_Rings_Olinordered__ring__strict(U_5149) ),
    inference(clausify,[status(thm)],[f_1360_2]) ).

cnf(f_1360_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5149),U_5150),c_Groups_Ozero__class_Ozero(U_5149)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5149),U_5151),U_5152))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5149),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5149),U_5150),U_5151)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5149),U_5150),U_5152)))
    | ~ class_Rings_Olinordered__ring__strict(U_5149) ),
    inference(clausify,[status(thm)],[f_1360_2]) ).

cnf(f_1360_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5149),U_5152),U_5151))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5149),U_5151),U_5152))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5149),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5149),U_5150),U_5151)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5149),U_5150),U_5152)))
    | ~ class_Rings_Olinordered__ring__strict(U_5149) ),
    inference(clausify,[status(thm)],[f_1360_2]) ).

cnf(f_1360_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5149),U_5151),U_5152))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5149),c_Groups_Ozero__class_Ozero(U_5149)),U_5150))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5149),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5149),U_5150),U_5151)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5149),U_5150),U_5152)))
    | ~ class_Rings_Olinordered__ring__strict(U_5149) ),
    inference(clausify,[status(thm)],[f_1360_2]) ).

cnf(f_1360_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5149),U_5152),U_5151))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5149),U_5150),c_Groups_Ozero__class_Ozero(U_5149)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5149),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5149),U_5150),U_5151)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5149),U_5150),U_5152)))
    | ~ class_Rings_Olinordered__ring__strict(U_5149) ),
    inference(clausify,[status(thm)],[f_1360_2]) ).

fof(f_1361_1,plain,
    ! [V_b_2,V_a_2,V_c_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
      | ~ class_Rings_Olinordered__ring__strict(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__pos]) ).

fof(f_1361_2,plain,
    ! [U_5156,U_5155,U_5154,U_5153] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5153),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5153),U_5154),U_5155)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5153),U_5154),U_5156)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5153),U_5155),U_5156)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5153),U_5155),U_5156))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5153),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5153),U_5154),U_5155)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5153),U_5154),U_5156))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5153),c_Groups_Ozero__class_Ozero(U_5153)),U_5154))
      | ~ class_Rings_Olinordered__ring__strict(U_5153) ),
    inference(variable_rename,[status(thm)],[f_1361_1]) ).

cnf(f_1361_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5153),U_5155),U_5156))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5153),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5153),U_5154),U_5155)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5153),U_5154),U_5156)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5153),c_Groups_Ozero__class_Ozero(U_5153)),U_5154))
    | ~ class_Rings_Olinordered__ring__strict(U_5153) ),
    inference(clausify,[status(thm)],[f_1361_2]) ).

cnf(f_1361_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5153),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5153),U_5154),U_5155)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5153),U_5154),U_5156)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5153),U_5155),U_5156))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5153),c_Groups_Ozero__class_Ozero(U_5153)),U_5154))
    | ~ class_Rings_Olinordered__ring__strict(U_5153) ),
    inference(clausify,[status(thm)],[f_1361_2]) ).

fof(f_1362_1,plain,
    ! [V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
      | ~ class_Rings_Olinordered__semiring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__pos__pos]) ).

fof(f_1362_2,plain,
    ! [U_5159,U_5158,U_5157] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5157),c_Groups_Ozero__class_Ozero(U_5157)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5157),U_5158),U_5159)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5157),c_Groups_Ozero__class_Ozero(U_5157)),U_5159))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5157),c_Groups_Ozero__class_Ozero(U_5157)),U_5158))
      | ~ class_Rings_Olinordered__semiring__strict(U_5157) ),
    inference(variable_rename,[status(thm)],[f_1362_1]) ).

cnf(f_1362_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5157),c_Groups_Ozero__class_Ozero(U_5157)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5157),U_5158),U_5159)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5157),c_Groups_Ozero__class_Ozero(U_5157)),U_5159))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5157),c_Groups_Ozero__class_Ozero(U_5157)),U_5158))
    | ~ class_Rings_Olinordered__semiring__strict(U_5157) ),
    inference(clausify,[status(thm)],[f_1362_2]) ).

fof(f_1363_1,plain,
    ! [V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
      | ~ class_Rings_Olinordered__semiring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__pos__neg]) ).

fof(f_1363_2,plain,
    ! [U_5162,U_5161,U_5160] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5160),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5160),U_5161),U_5162)),c_Groups_Ozero__class_Ozero(U_5160)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5160),U_5162),c_Groups_Ozero__class_Ozero(U_5160)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5160),c_Groups_Ozero__class_Ozero(U_5160)),U_5161))
      | ~ class_Rings_Olinordered__semiring__strict(U_5160) ),
    inference(variable_rename,[status(thm)],[f_1363_1]) ).

cnf(f_1363_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5160),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5160),U_5161),U_5162)),c_Groups_Ozero__class_Ozero(U_5160)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5160),U_5162),c_Groups_Ozero__class_Ozero(U_5160)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5160),c_Groups_Ozero__class_Ozero(U_5160)),U_5161))
    | ~ class_Rings_Olinordered__semiring__strict(U_5160) ),
    inference(clausify,[status(thm)],[f_1363_2]) ).

fof(f_1364_1,plain,
    ! [V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
      | ~ class_Rings_Olinordered__semiring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__pos__neg2]) ).

fof(f_1364_2,plain,
    ! [U_5165,U_5164,U_5163] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5163),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5163),U_5165),U_5164)),c_Groups_Ozero__class_Ozero(U_5163)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5163),U_5165),c_Groups_Ozero__class_Ozero(U_5163)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5163),c_Groups_Ozero__class_Ozero(U_5163)),U_5164))
      | ~ class_Rings_Olinordered__semiring__strict(U_5163) ),
    inference(variable_rename,[status(thm)],[f_1364_1]) ).

cnf(f_1364_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5163),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5163),U_5165),U_5164)),c_Groups_Ozero__class_Ozero(U_5163)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5163),U_5165),c_Groups_Ozero__class_Ozero(U_5163)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5163),c_Groups_Ozero__class_Ozero(U_5163)),U_5164))
    | ~ class_Rings_Olinordered__semiring__strict(U_5163) ),
    inference(clausify,[status(thm)],[f_1364_2]) ).

fof(f_1365_1,plain,
    ! [V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))
      | ~ class_Rings_Olinordered__semiring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_zero__less__mult__pos]) ).

fof(f_1365_2,plain,
    ! [U_5168,U_5167,U_5166] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5166),c_Groups_Ozero__class_Ozero(U_5166)),U_5168))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5166),c_Groups_Ozero__class_Ozero(U_5166)),U_5167))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5166),c_Groups_Ozero__class_Ozero(U_5166)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5166),U_5167),U_5168)))
      | ~ class_Rings_Olinordered__semiring__strict(U_5166) ),
    inference(variable_rename,[status(thm)],[f_1365_1]) ).

cnf(f_1365_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5166),c_Groups_Ozero__class_Ozero(U_5166)),U_5168))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5166),c_Groups_Ozero__class_Ozero(U_5166)),U_5167))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5166),c_Groups_Ozero__class_Ozero(U_5166)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5166),U_5167),U_5168)))
    | ~ class_Rings_Olinordered__semiring__strict(U_5166) ),
    inference(clausify,[status(thm)],[f_1365_2]) ).

fof(f_1366_1,plain,
    ! [V_a,V_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)))
      | ~ class_Rings_Olinordered__semiring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_zero__less__mult__pos2]) ).

fof(f_1366_2,plain,
    ! [U_5171,U_5170,U_5169] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5169),c_Groups_Ozero__class_Ozero(U_5169)),U_5170))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5169),c_Groups_Ozero__class_Ozero(U_5169)),U_5171))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5169),c_Groups_Ozero__class_Ozero(U_5169)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5169),U_5170),U_5171)))
      | ~ class_Rings_Olinordered__semiring__strict(U_5169) ),
    inference(variable_rename,[status(thm)],[f_1366_1]) ).

cnf(f_1366_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5169),c_Groups_Ozero__class_Ozero(U_5169)),U_5170))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5169),c_Groups_Ozero__class_Ozero(U_5169)),U_5171))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5169),c_Groups_Ozero__class_Ozero(U_5169)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5169),U_5170),U_5171)))
    | ~ class_Rings_Olinordered__semiring__strict(U_5169) ),
    inference(clausify,[status(thm)],[f_1366_2]) ).

fof(f_1367_1,plain,
    ! [V_b_2,V_a_2,V_c_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
      | ~ class_Rings_Olinordered__ring__strict(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__neg]) ).

fof(f_1367_2,plain,
    ! [U_5175,U_5174,U_5173,U_5172] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5172),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5172),U_5173),U_5174)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5172),U_5173),U_5175)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5172),U_5175),U_5174)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5172),U_5175),U_5174))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5172),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5172),U_5173),U_5174)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5172),U_5173),U_5175))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5172),U_5173),c_Groups_Ozero__class_Ozero(U_5172)))
      | ~ class_Rings_Olinordered__ring__strict(U_5172) ),
    inference(variable_rename,[status(thm)],[f_1367_1]) ).

cnf(f_1367_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5172),U_5175),U_5174))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5172),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5172),U_5173),U_5174)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5172),U_5173),U_5175)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5172),U_5173),c_Groups_Ozero__class_Ozero(U_5172)))
    | ~ class_Rings_Olinordered__ring__strict(U_5172) ),
    inference(clausify,[status(thm)],[f_1367_2]) ).

cnf(f_1367_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5172),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5172),U_5173),U_5174)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5172),U_5173),U_5175)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5172),U_5175),U_5174))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5172),U_5173),c_Groups_Ozero__class_Ozero(U_5172)))
    | ~ class_Rings_Olinordered__ring__strict(U_5172) ),
    inference(clausify,[status(thm)],[f_1367_2]) ).

fof(f_1368_1,plain,
    ! [V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ class_Rings_Olinordered__semiring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__neg__pos]) ).

fof(f_1368_2,plain,
    ! [U_5178,U_5177,U_5176] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5176),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5176),U_5177),U_5178)),c_Groups_Ozero__class_Ozero(U_5176)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5176),c_Groups_Ozero__class_Ozero(U_5176)),U_5178))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5176),U_5177),c_Groups_Ozero__class_Ozero(U_5176)))
      | ~ class_Rings_Olinordered__semiring__strict(U_5176) ),
    inference(variable_rename,[status(thm)],[f_1368_1]) ).

cnf(f_1368_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5176),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5176),U_5177),U_5178)),c_Groups_Ozero__class_Ozero(U_5176)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5176),c_Groups_Ozero__class_Ozero(U_5176)),U_5178))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5176),U_5177),c_Groups_Ozero__class_Ozero(U_5176)))
    | ~ class_Rings_Olinordered__semiring__strict(U_5176) ),
    inference(clausify,[status(thm)],[f_1368_2]) ).

fof(f_1369_1,plain,
    ! [V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ class_Rings_Olinordered__ring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__neg__neg]) ).

fof(f_1369_2,plain,
    ! [U_5181,U_5180,U_5179] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5179),c_Groups_Ozero__class_Ozero(U_5179)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5179),U_5180),U_5181)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5179),U_5181),c_Groups_Ozero__class_Ozero(U_5179)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5179),U_5180),c_Groups_Ozero__class_Ozero(U_5179)))
      | ~ class_Rings_Olinordered__ring__strict(U_5179) ),
    inference(variable_rename,[status(thm)],[f_1369_1]) ).

cnf(f_1369_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5179),c_Groups_Ozero__class_Ozero(U_5179)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5179),U_5180),U_5181)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5179),U_5181),c_Groups_Ozero__class_Ozero(U_5179)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5179),U_5180),c_Groups_Ozero__class_Ozero(U_5179)))
    | ~ class_Rings_Olinordered__ring__strict(U_5179) ),
    inference(clausify,[status(thm)],[f_1369_2]) ).

fof(f_1370_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
      | ~ class_Rings_Olinordered__semiring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__strict__right__mono]) ).

fof(f_1370_2,plain,
    ! [U_5185,U_5184,U_5183,U_5182] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5182),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5182),U_5183),U_5185)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5182),U_5184),U_5185)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5182),c_Groups_Ozero__class_Ozero(U_5182)),U_5185))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5182),U_5183),U_5184))
      | ~ class_Rings_Olinordered__semiring__strict(U_5182) ),
    inference(variable_rename,[status(thm)],[f_1370_1]) ).

cnf(f_1370_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5182),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5182),U_5183),U_5185)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5182),U_5184),U_5185)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5182),c_Groups_Ozero__class_Ozero(U_5182)),U_5185))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5182),U_5183),U_5184))
    | ~ class_Rings_Olinordered__semiring__strict(U_5182) ),
    inference(clausify,[status(thm)],[f_1370_2]) ).

fof(f_1371_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
      | ~ class_Rings_Olinordered__semiring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__strict__left__mono]) ).

fof(f_1371_2,plain,
    ! [U_5189,U_5188,U_5187,U_5186] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5186),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5186),U_5189),U_5187)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5186),U_5189),U_5188)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5186),c_Groups_Ozero__class_Ozero(U_5186)),U_5189))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5186),U_5187),U_5188))
      | ~ class_Rings_Olinordered__semiring__strict(U_5186) ),
    inference(variable_rename,[status(thm)],[f_1371_1]) ).

cnf(f_1371_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5186),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5186),U_5189),U_5187)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5186),U_5189),U_5188)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5186),c_Groups_Ozero__class_Ozero(U_5186)),U_5189))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5186),U_5187),U_5188))
    | ~ class_Rings_Olinordered__semiring__strict(U_5186) ),
    inference(clausify,[status(thm)],[f_1371_2]) ).

fof(f_1372_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
      | ~ class_Rings_Olinordered__comm__semiring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__mult__strict__left__mono]) ).

fof(f_1372_2,plain,
    ! [U_5193,U_5192,U_5191,U_5190] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5190),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5190),U_5193),U_5191)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5190),U_5193),U_5192)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5190),c_Groups_Ozero__class_Ozero(U_5190)),U_5193))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5190),U_5191),U_5192))
      | ~ class_Rings_Olinordered__comm__semiring__strict(U_5190) ),
    inference(variable_rename,[status(thm)],[f_1372_1]) ).

cnf(f_1372_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5190),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5190),U_5193),U_5191)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5190),U_5193),U_5192)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5190),c_Groups_Ozero__class_Ozero(U_5190)),U_5193))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5190),U_5191),U_5192))
    | ~ class_Rings_Olinordered__comm__semiring__strict(U_5190) ),
    inference(clausify,[status(thm)],[f_1372_2]) ).

fof(f_1373_1,plain,
    ! [V_c,V_a,V_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
      | ~ class_Rings_Olinordered__ring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__strict__right__mono__neg]) ).

fof(f_1373_2,plain,
    ! [U_5197,U_5196,U_5195,U_5194] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5194),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5194),U_5196),U_5197)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5194),U_5195),U_5197)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5194),U_5197),c_Groups_Ozero__class_Ozero(U_5194)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5194),U_5195),U_5196))
      | ~ class_Rings_Olinordered__ring__strict(U_5194) ),
    inference(variable_rename,[status(thm)],[f_1373_1]) ).

cnf(f_1373_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5194),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5194),U_5196),U_5197)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5194),U_5195),U_5197)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5194),U_5197),c_Groups_Ozero__class_Ozero(U_5194)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5194),U_5195),U_5196))
    | ~ class_Rings_Olinordered__ring__strict(U_5194) ),
    inference(clausify,[status(thm)],[f_1373_2]) ).

fof(f_1374_1,plain,
    ! [V_c,V_a,V_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
      | ~ class_Rings_Olinordered__ring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__strict__left__mono__neg]) ).

fof(f_1374_2,plain,
    ! [U_5201,U_5200,U_5199,U_5198] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5198),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5198),U_5201),U_5200)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5198),U_5201),U_5199)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5198),U_5201),c_Groups_Ozero__class_Ozero(U_5198)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5198),U_5199),U_5200))
      | ~ class_Rings_Olinordered__ring__strict(U_5198) ),
    inference(variable_rename,[status(thm)],[f_1374_1]) ).

cnf(f_1374_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5198),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5198),U_5201),U_5200)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5198),U_5201),U_5199)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5198),U_5201),c_Groups_Ozero__class_Ozero(U_5198)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5198),U_5199),U_5200))
    | ~ class_Rings_Olinordered__ring__strict(U_5198) ),
    inference(clausify,[status(thm)],[f_1374_2]) ).

fof(f_1375_1,plain,
    ! [V_b_2,V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) )
      | ~ class_Groups_Oordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_le__iff__diff__le__0]) ).

fof(f_1375_2,plain,
    ! [U_5204,U_5203,U_5202] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5202),U_5203),U_5204))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5202),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5202),U_5203),U_5204)),c_Groups_Ozero__class_Ozero(U_5202))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5202),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5202),U_5203),U_5204)),c_Groups_Ozero__class_Ozero(U_5202)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5202),U_5203),U_5204)) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_5202) ),
    inference(variable_rename,[status(thm)],[f_1375_1]) ).

cnf(f_1375_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5202),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5202),U_5203),U_5204)),c_Groups_Ozero__class_Ozero(U_5202)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5202),U_5203),U_5204))
    | ~ class_Groups_Oordered__ab__group__add(U_5202) ),
    inference(clausify,[status(thm)],[f_1375_2]) ).

cnf(f_1375_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5202),U_5203),U_5204))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5202),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5202),U_5203),U_5204)),c_Groups_Ozero__class_Ozero(U_5202)))
    | ~ class_Groups_Oordered__ab__group__add(U_5202) ),
    inference(clausify,[status(thm)],[f_1375_2]) ).

fof(f_1376_1,plain,
    ! [V_b_2,V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) )
      | ~ class_Groups_Oordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_less__iff__diff__less__0]) ).

fof(f_1376_2,plain,
    ! [U_5207,U_5206,U_5205] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5205),U_5206),U_5207))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5205),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5205),U_5206),U_5207)),c_Groups_Ozero__class_Ozero(U_5205))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5205),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5205),U_5206),U_5207)),c_Groups_Ozero__class_Ozero(U_5205)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5205),U_5206),U_5207)) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_5205) ),
    inference(variable_rename,[status(thm)],[f_1376_1]) ).

cnf(f_1376_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5205),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5205),U_5206),U_5207)),c_Groups_Ozero__class_Ozero(U_5205)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5205),U_5206),U_5207))
    | ~ class_Groups_Oordered__ab__group__add(U_5205) ),
    inference(clausify,[status(thm)],[f_1376_2]) ).

cnf(f_1376_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5205),U_5206),U_5207))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5205),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5205),U_5206),U_5207)),c_Groups_Ozero__class_Ozero(U_5205)))
    | ~ class_Groups_Oordered__ab__group__add(U_5205) ),
    inference(clausify,[status(thm)],[f_1376_2]) ).

fof(f_1377_1,plain,
    ! [V_d,V_c,V_b,V_a,V_r,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_c)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_d))
      | V_c = V_d
      | V_a != V_b
      | V_r = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__scale__eq__noteq]) ).

fof(f_1377_2,plain,
    ! [U_5213,U_5212,U_5211,U_5210,U_5209,U_5208] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5208),U_5210),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5208),U_5209),U_5212)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5208),U_5211),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5208),U_5209),U_5213))
      | U_5212 = U_5213
      | U_5210 != U_5211
      | U_5209 = c_Groups_Ozero__class_Ozero(U_5208)
      | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_5208) ),
    inference(variable_rename,[status(thm)],[f_1377_1]) ).

cnf(f_1377_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5208),U_5210),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5208),U_5209),U_5212)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5208),U_5211),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5208),U_5209),U_5213))
    | U_5212 = U_5213
    | U_5210 != U_5211
    | U_5209 = c_Groups_Ozero__class_Ozero(U_5208)
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_5208) ),
    inference(clausify,[status(thm)],[f_1377_2]) ).

fof(f_1378_1,plain,
    ! [T_a] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_not__one__le__zero]) ).

fof(f_1378_2,plain,
    ! [U_5214] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5214),c_Groups_Oone__class_Oone(U_5214)),c_Groups_Ozero__class_Ozero(U_5214)))
      | ~ class_Rings_Olinordered__semidom(U_5214) ),
    inference(variable_rename,[status(thm)],[f_1378_1]) ).

cnf(f_1378_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5214),c_Groups_Oone__class_Oone(U_5214)),c_Groups_Ozero__class_Ozero(U_5214)))
    | ~ class_Rings_Olinordered__semidom(U_5214) ),
    inference(clausify,[status(thm)],[f_1378_2]) ).

fof(f_1379_1,plain,
    ! [T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a)))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_zero__le__one]) ).

fof(f_1379_2,plain,
    ! [U_5215] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5215),c_Groups_Ozero__class_Ozero(U_5215)),c_Groups_Oone__class_Oone(U_5215)))
      | ~ class_Rings_Olinordered__semidom(U_5215) ),
    inference(variable_rename,[status(thm)],[f_1379_1]) ).

cnf(f_1379_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5215),c_Groups_Ozero__class_Ozero(U_5215)),c_Groups_Oone__class_Oone(U_5215)))
    | ~ class_Rings_Olinordered__semidom(U_5215) ),
    inference(clausify,[status(thm)],[f_1379_2]) ).

fof(f_1380_1,plain,
    ! [T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a)))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_zero__less__one]) ).

fof(f_1380_2,plain,
    ! [U_5216] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5216),c_Groups_Ozero__class_Ozero(U_5216)),c_Groups_Oone__class_Oone(U_5216)))
      | ~ class_Rings_Olinordered__semidom(U_5216) ),
    inference(variable_rename,[status(thm)],[f_1380_1]) ).

cnf(f_1380_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5216),c_Groups_Ozero__class_Ozero(U_5216)),c_Groups_Oone__class_Oone(U_5216)))
    | ~ class_Rings_Olinordered__semidom(U_5216) ),
    inference(clausify,[status(thm)],[f_1380_2]) ).

fof(f_1381_1,plain,
    ! [T_a] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_not__one__less__zero]) ).

fof(f_1381_2,plain,
    ! [U_5217] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5217),c_Groups_Oone__class_Oone(U_5217)),c_Groups_Ozero__class_Ozero(U_5217)))
      | ~ class_Rings_Olinordered__semidom(U_5217) ),
    inference(variable_rename,[status(thm)],[f_1381_1]) ).

cnf(f_1381_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5217),c_Groups_Oone__class_Oone(U_5217)),c_Groups_Ozero__class_Ozero(U_5217)))
    | ~ class_Rings_Olinordered__semidom(U_5217) ),
    inference(clausify,[status(thm)],[f_1381_2]) ).

fof(f_1382_1,plain,
    ! [V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) ) )
      | ~ class_Groups_Oordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_neg__0__le__iff__le]) ).

fof(f_1382_2,plain,
    ! [U_5219,U_5218] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5218),c_Groups_Ozero__class_Ozero(U_5218)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5218),U_5219)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5218),U_5219),c_Groups_Ozero__class_Ozero(U_5218))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5218),U_5219),c_Groups_Ozero__class_Ozero(U_5218)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5218),c_Groups_Ozero__class_Ozero(U_5218)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5218),U_5219))) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_5218) ),
    inference(variable_rename,[status(thm)],[f_1382_1]) ).

cnf(f_1382_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5218),U_5219),c_Groups_Ozero__class_Ozero(U_5218)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5218),c_Groups_Ozero__class_Ozero(U_5218)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5218),U_5219)))
    | ~ class_Groups_Oordered__ab__group__add(U_5218) ),
    inference(clausify,[status(thm)],[f_1382_2]) ).

cnf(f_1382_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5218),c_Groups_Ozero__class_Ozero(U_5218)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5218),U_5219)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5218),U_5219),c_Groups_Ozero__class_Ozero(U_5218)))
    | ~ class_Groups_Oordered__ab__group__add(U_5218) ),
    inference(clausify,[status(thm)],[f_1382_2]) ).

fof(f_1383_1,plain,
    ! [V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) ) )
      | ~ class_Groups_Olinordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_le__minus__self__iff]) ).

fof(f_1383_2,plain,
    ! [U_5221,U_5220] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5220),U_5221),hAPP(c_Groups_Ouminus__class_Ouminus(U_5220),U_5221)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5220),U_5221),c_Groups_Ozero__class_Ozero(U_5220))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5220),U_5221),c_Groups_Ozero__class_Ozero(U_5220)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5220),U_5221),hAPP(c_Groups_Ouminus__class_Ouminus(U_5220),U_5221))) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_5220) ),
    inference(variable_rename,[status(thm)],[f_1383_1]) ).

cnf(f_1383_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5220),U_5221),c_Groups_Ozero__class_Ozero(U_5220)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5220),U_5221),hAPP(c_Groups_Ouminus__class_Ouminus(U_5220),U_5221)))
    | ~ class_Groups_Olinordered__ab__group__add(U_5220) ),
    inference(clausify,[status(thm)],[f_1383_2]) ).

cnf(f_1383_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5220),U_5221),hAPP(c_Groups_Ouminus__class_Ouminus(U_5220),U_5221)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5220),U_5221),c_Groups_Ozero__class_Ozero(U_5220)))
    | ~ class_Groups_Olinordered__ab__group__add(U_5220) ),
    inference(clausify,[status(thm)],[f_1383_2]) ).

fof(f_1384_1,plain,
    ! [V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),c_Groups_Ozero__class_Ozero(T_b))) ) )
      | ~ class_Groups_Oordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_neg__le__0__iff__le]) ).

fof(f_1384_2,plain,
    ! [U_5223,U_5222] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5222),hAPP(c_Groups_Ouminus__class_Ouminus(U_5222),U_5223)),c_Groups_Ozero__class_Ozero(U_5222)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5222),c_Groups_Ozero__class_Ozero(U_5222)),U_5223)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5222),c_Groups_Ozero__class_Ozero(U_5222)),U_5223))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5222),hAPP(c_Groups_Ouminus__class_Ouminus(U_5222),U_5223)),c_Groups_Ozero__class_Ozero(U_5222))) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_5222) ),
    inference(variable_rename,[status(thm)],[f_1384_1]) ).

cnf(f_1384_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5222),c_Groups_Ozero__class_Ozero(U_5222)),U_5223))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5222),hAPP(c_Groups_Ouminus__class_Ouminus(U_5222),U_5223)),c_Groups_Ozero__class_Ozero(U_5222)))
    | ~ class_Groups_Oordered__ab__group__add(U_5222) ),
    inference(clausify,[status(thm)],[f_1384_2]) ).

cnf(f_1384_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5222),hAPP(c_Groups_Ouminus__class_Ouminus(U_5222),U_5223)),c_Groups_Ozero__class_Ozero(U_5222)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5222),c_Groups_Ozero__class_Ozero(U_5222)),U_5223))
    | ~ class_Groups_Oordered__ab__group__add(U_5222) ),
    inference(clausify,[status(thm)],[f_1384_2]) ).

fof(f_1385_1,plain,
    ! [V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_a_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_a_2)) ) )
      | ~ class_Groups_Olinordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_minus__le__self__iff]) ).

fof(f_1385_2,plain,
    ! [U_5225,U_5224] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5224),hAPP(c_Groups_Ouminus__class_Ouminus(U_5224),U_5225)),U_5225))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5224),c_Groups_Ozero__class_Ozero(U_5224)),U_5225)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5224),c_Groups_Ozero__class_Ozero(U_5224)),U_5225))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5224),hAPP(c_Groups_Ouminus__class_Ouminus(U_5224),U_5225)),U_5225)) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_5224) ),
    inference(variable_rename,[status(thm)],[f_1385_1]) ).

cnf(f_1385_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5224),c_Groups_Ozero__class_Ozero(U_5224)),U_5225))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5224),hAPP(c_Groups_Ouminus__class_Ouminus(U_5224),U_5225)),U_5225))
    | ~ class_Groups_Olinordered__ab__group__add(U_5224) ),
    inference(clausify,[status(thm)],[f_1385_2]) ).

cnf(f_1385_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5224),hAPP(c_Groups_Ouminus__class_Ouminus(U_5224),U_5225)),U_5225))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5224),c_Groups_Ozero__class_Ozero(U_5224)),U_5225))
    | ~ class_Groups_Olinordered__ab__group__add(U_5224) ),
    inference(clausify,[status(thm)],[f_1385_2]) ).

fof(f_1386_1,plain,
    ! [V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_a_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_a_2)) ) )
      | ~ class_Groups_Olinordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_neg__less__nonneg]) ).

fof(f_1386_2,plain,
    ! [U_5227,U_5226] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5226),hAPP(c_Groups_Ouminus__class_Ouminus(U_5226),U_5227)),U_5227))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5226),c_Groups_Ozero__class_Ozero(U_5226)),U_5227)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5226),c_Groups_Ozero__class_Ozero(U_5226)),U_5227))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5226),hAPP(c_Groups_Ouminus__class_Ouminus(U_5226),U_5227)),U_5227)) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_5226) ),
    inference(variable_rename,[status(thm)],[f_1386_1]) ).

cnf(f_1386_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5226),c_Groups_Ozero__class_Ozero(U_5226)),U_5227))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5226),hAPP(c_Groups_Ouminus__class_Ouminus(U_5226),U_5227)),U_5227))
    | ~ class_Groups_Olinordered__ab__group__add(U_5226) ),
    inference(clausify,[status(thm)],[f_1386_2]) ).

cnf(f_1386_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5226),hAPP(c_Groups_Ouminus__class_Ouminus(U_5226),U_5227)),U_5227))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5226),c_Groups_Ozero__class_Ozero(U_5226)),U_5227))
    | ~ class_Groups_Olinordered__ab__group__add(U_5226) ),
    inference(clausify,[status(thm)],[f_1386_2]) ).

fof(f_1387_1,plain,
    ! [V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),c_Groups_Ozero__class_Ozero(T_b))) ) )
      | ~ class_Groups_Oordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_neg__less__0__iff__less]) ).

fof(f_1387_2,plain,
    ! [U_5229,U_5228] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5228),hAPP(c_Groups_Ouminus__class_Ouminus(U_5228),U_5229)),c_Groups_Ozero__class_Ozero(U_5228)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5228),c_Groups_Ozero__class_Ozero(U_5228)),U_5229)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5228),c_Groups_Ozero__class_Ozero(U_5228)),U_5229))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5228),hAPP(c_Groups_Ouminus__class_Ouminus(U_5228),U_5229)),c_Groups_Ozero__class_Ozero(U_5228))) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_5228) ),
    inference(variable_rename,[status(thm)],[f_1387_1]) ).

cnf(f_1387_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5228),c_Groups_Ozero__class_Ozero(U_5228)),U_5229))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5228),hAPP(c_Groups_Ouminus__class_Ouminus(U_5228),U_5229)),c_Groups_Ozero__class_Ozero(U_5228)))
    | ~ class_Groups_Oordered__ab__group__add(U_5228) ),
    inference(clausify,[status(thm)],[f_1387_2]) ).

cnf(f_1387_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5228),hAPP(c_Groups_Ouminus__class_Ouminus(U_5228),U_5229)),c_Groups_Ozero__class_Ozero(U_5228)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5228),c_Groups_Ozero__class_Ozero(U_5228)),U_5229))
    | ~ class_Groups_Oordered__ab__group__add(U_5228) ),
    inference(clausify,[status(thm)],[f_1387_2]) ).

fof(f_1388_1,plain,
    ! [V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) ) )
      | ~ class_Groups_Oordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_neg__0__less__iff__less]) ).

fof(f_1388_2,plain,
    ! [U_5231,U_5230] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5230),c_Groups_Ozero__class_Ozero(U_5230)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5230),U_5231)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5230),U_5231),c_Groups_Ozero__class_Ozero(U_5230))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5230),U_5231),c_Groups_Ozero__class_Ozero(U_5230)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5230),c_Groups_Ozero__class_Ozero(U_5230)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5230),U_5231))) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_5230) ),
    inference(variable_rename,[status(thm)],[f_1388_1]) ).

cnf(f_1388_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5230),U_5231),c_Groups_Ozero__class_Ozero(U_5230)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5230),c_Groups_Ozero__class_Ozero(U_5230)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5230),U_5231)))
    | ~ class_Groups_Oordered__ab__group__add(U_5230) ),
    inference(clausify,[status(thm)],[f_1388_2]) ).

cnf(f_1388_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5230),c_Groups_Ozero__class_Ozero(U_5230)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5230),U_5231)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5230),U_5231),c_Groups_Ozero__class_Ozero(U_5230)))
    | ~ class_Groups_Oordered__ab__group__add(U_5230) ),
    inference(clausify,[status(thm)],[f_1388_2]) ).

fof(f_1389_1,plain,
    ! [V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) ) )
      | ~ class_Rings_Olinordered__idom(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_less__minus__self__iff]) ).

fof(f_1389_2,plain,
    ! [U_5233,U_5232] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5232),U_5233),hAPP(c_Groups_Ouminus__class_Ouminus(U_5232),U_5233)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5232),U_5233),c_Groups_Ozero__class_Ozero(U_5232))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5232),U_5233),c_Groups_Ozero__class_Ozero(U_5232)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5232),U_5233),hAPP(c_Groups_Ouminus__class_Ouminus(U_5232),U_5233))) ) )
      | ~ class_Rings_Olinordered__idom(U_5232) ),
    inference(variable_rename,[status(thm)],[f_1389_1]) ).

cnf(f_1389_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5232),U_5233),c_Groups_Ozero__class_Ozero(U_5232)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5232),U_5233),hAPP(c_Groups_Ouminus__class_Ouminus(U_5232),U_5233)))
    | ~ class_Rings_Olinordered__idom(U_5232) ),
    inference(clausify,[status(thm)],[f_1389_2]) ).

cnf(f_1389_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5232),U_5233),hAPP(c_Groups_Ouminus__class_Ouminus(U_5232),U_5233)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5232),U_5233),c_Groups_Ozero__class_Ozero(U_5232)))
    | ~ class_Rings_Olinordered__idom(U_5232) ),
    inference(clausify,[status(thm)],[f_1389_2]) ).

fof(f_1390_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Groups_Ogroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_right__minus]) ).

fof(f_1390_2,plain,
    ! [U_5235,U_5234] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5234),U_5235),hAPP(c_Groups_Ouminus__class_Ouminus(U_5234),U_5235)) = c_Groups_Ozero__class_Ozero(U_5234)
      | ~ class_Groups_Ogroup__add(U_5234) ),
    inference(variable_rename,[status(thm)],[f_1390_1]) ).

cnf(f_1390_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5234),U_5235),hAPP(c_Groups_Ouminus__class_Ouminus(U_5234),U_5235)) = c_Groups_Ozero__class_Ozero(U_5234)
    | ~ class_Groups_Ogroup__add(U_5234) ),
    inference(clausify,[status(thm)],[f_1390_2]) ).

fof(f_1391_1,plain,
    ! [V_b_2,V_a_2,T_b] :
      ( ( ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2) != c_Groups_Ozero__class_Ozero(T_b) )
        & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b)
          | V_a_2 != hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) ) )
      | ~ class_Groups_Ogroup__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_eq__neg__iff__add__eq__0]) ).

fof(f_1391_2,plain,
    ! [U_5238,U_5237,U_5236] :
      ( ( ( U_5237 = hAPP(c_Groups_Ouminus__class_Ouminus(U_5236),U_5238)
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5236),U_5237),U_5238) != c_Groups_Ozero__class_Ozero(U_5236) )
        & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5236),U_5237),U_5238) = c_Groups_Ozero__class_Ozero(U_5236)
          | U_5237 != hAPP(c_Groups_Ouminus__class_Ouminus(U_5236),U_5238) ) )
      | ~ class_Groups_Ogroup__add(U_5236) ),
    inference(variable_rename,[status(thm)],[f_1391_1]) ).

cnf(f_1391_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5236),U_5237),U_5238) = c_Groups_Ozero__class_Ozero(U_5236)
    | U_5237 != hAPP(c_Groups_Ouminus__class_Ouminus(U_5236),U_5238)
    | ~ class_Groups_Ogroup__add(U_5236) ),
    inference(clausify,[status(thm)],[f_1391_2]) ).

cnf(f_1391_4,plain,
    ( U_5237 = hAPP(c_Groups_Ouminus__class_Ouminus(U_5236),U_5238)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5236),U_5237),U_5238) != c_Groups_Ozero__class_Ozero(U_5236)
    | ~ class_Groups_Ogroup__add(U_5236) ),
    inference(clausify,[status(thm)],[f_1391_2]) ).

fof(f_1392_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Groups_Ogroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_left__minus]) ).

fof(f_1392_2,plain,
    ! [U_5240,U_5239] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5239),hAPP(c_Groups_Ouminus__class_Ouminus(U_5239),U_5240)),U_5240) = c_Groups_Ozero__class_Ozero(U_5239)
      | ~ class_Groups_Ogroup__add(U_5239) ),
    inference(variable_rename,[status(thm)],[f_1392_1]) ).

cnf(f_1392_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5239),hAPP(c_Groups_Ouminus__class_Ouminus(U_5239),U_5240)),U_5240) = c_Groups_Ozero__class_Ozero(U_5239)
    | ~ class_Groups_Ogroup__add(U_5239) ),
    inference(clausify,[status(thm)],[f_1392_2]) ).

fof(f_1393_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Groups_Oab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_ab__left__minus]) ).

fof(f_1393_2,plain,
    ! [U_5242,U_5241] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5241),hAPP(c_Groups_Ouminus__class_Ouminus(U_5241),U_5242)),U_5242) = c_Groups_Ozero__class_Ozero(U_5241)
      | ~ class_Groups_Oab__group__add(U_5241) ),
    inference(variable_rename,[status(thm)],[f_1393_1]) ).

cnf(f_1393_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5241),hAPP(c_Groups_Ouminus__class_Ouminus(U_5241),U_5242)),U_5242) = c_Groups_Ozero__class_Ozero(U_5241)
    | ~ class_Groups_Oab__group__add(U_5241) ),
    inference(clausify,[status(thm)],[f_1393_2]) ).

fof(f_1394_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) = V_b
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Groups_Ogroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_minus__unique]) ).

fof(f_1394_2,plain,
    ! [U_5245,U_5244,U_5243] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5243),U_5244) = U_5245
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5243),U_5244),U_5245) != c_Groups_Ozero__class_Ozero(U_5243)
      | ~ class_Groups_Ogroup__add(U_5243) ),
    inference(variable_rename,[status(thm)],[f_1394_1]) ).

cnf(f_1394_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5243),U_5244) = U_5245
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5243),U_5244),U_5245) != c_Groups_Ozero__class_Ozero(U_5243)
    | ~ class_Groups_Ogroup__add(U_5243) ),
    inference(clausify,[status(thm)],[f_1394_2]) ).

fof(f_1395_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)
      | ~ class_Groups_Ogroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_diff__0]) ).

fof(f_1395_2,plain,
    ! [U_5247,U_5246] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5246),c_Groups_Ozero__class_Ozero(U_5246)),U_5247) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5246),U_5247)
      | ~ class_Groups_Ogroup__add(U_5246) ),
    inference(variable_rename,[status(thm)],[f_1395_1]) ).

cnf(f_1395_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5246),c_Groups_Ozero__class_Ozero(U_5246)),U_5247) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5246),U_5247)
    | ~ class_Groups_Ogroup__add(U_5246) ),
    inference(clausify,[status(thm)],[f_1395_2]) ).

fof(f_1396_1,plain,
    ! [V_f_2,T_c,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(T_b)
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__empty]) ).

fof(f_1396_2,plain,
    ! [U_5250,U_5249,U_5248] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5249,U_5248),U_5250),c_Orderings_Obot__class_Obot(tc_fun(U_5249,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(U_5248)
      | ~ class_Groups_Ocomm__monoid__add(U_5248) ),
    inference(variable_rename,[status(thm)],[f_1396_1]) ).

cnf(f_1396_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5249,U_5248),U_5250),c_Orderings_Obot__class_Obot(tc_fun(U_5249,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(U_5248)
    | ~ class_Groups_Ocomm__monoid__add(U_5248) ),
    inference(clausify,[status(thm)],[f_1396_2]) ).

fof(f_1397_1,plain,
    ! [V_g_2,T_c,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_g_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(T_b)
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum_Oempty]) ).

fof(f_1397_2,plain,
    ! [U_5253,U_5252,U_5251] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5252,U_5251),U_5253),c_Orderings_Obot__class_Obot(tc_fun(U_5252,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(U_5251)
      | ~ class_Groups_Ocomm__monoid__add(U_5251) ),
    inference(variable_rename,[status(thm)],[f_1397_1]) ).

cnf(f_1397_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5252,U_5251),U_5253),c_Orderings_Obot__class_Obot(tc_fun(U_5252,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(U_5251)
    | ~ class_Groups_Ocomm__monoid__add(U_5251) ),
    inference(clausify,[status(thm)],[f_1397_2]) ).

fof(f_1398_1,plain,
    ! [V_g_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Ocomm__monoid__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum_Oinfinite]) ).

fof(f_1398_2,plain,
    ! [U_5257,U_5256,U_5255,U_5254] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5255,U_5254),U_5257),U_5256) = c_Groups_Ozero__class_Ozero(U_5254)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_5255),U_5256))
      | ~ class_Groups_Ocomm__monoid__add(U_5254) ),
    inference(variable_rename,[status(thm)],[f_1398_1]) ).

cnf(f_1398_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5255,U_5254),U_5257),U_5256) = c_Groups_Ozero__class_Ozero(U_5254)
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_5255),U_5256))
    | ~ class_Groups_Ocomm__monoid__add(U_5254) ),
    inference(clausify,[status(thm)],[f_1398_2]) ).

fof(f_1399_1,plain,
    ! [V_f_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Ocomm__monoid__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__infinite]) ).

fof(f_1399_2,plain,
    ! [U_5261,U_5260,U_5259,U_5258] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5259,U_5258),U_5261),U_5260) = c_Groups_Ozero__class_Ozero(U_5258)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_5259),U_5260))
      | ~ class_Groups_Ocomm__monoid__add(U_5258) ),
    inference(variable_rename,[status(thm)],[f_1399_1]) ).

cnf(f_1399_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5259,U_5258),U_5261),U_5260) = c_Groups_Ozero__class_Ozero(U_5258)
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_5259),U_5260))
    | ~ class_Groups_Ocomm__monoid__add(U_5258) ),
    inference(clausify,[status(thm)],[f_1399_2]) ).

fof(f_1400_1,plain,
    ! [V_f_2,V_S_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_S_2)))
          | ? [B_x] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(V_f_2,B_x)))
              & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) ) )
        & ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(V_f_2,B_x)))
              | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_S_2))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__pos__nat__iff]) ).

fof(f_1400_2,plain,
    ! [U_5266,U_5265,U_5264] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5264,tc_Nat_Onat),U_5266),U_5265)))
          | ? [U_5263] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_5266,U_5263)))
              & hBOOL(hAPP(hAPP(c_member(U_5264),U_5263),U_5265)) ) )
        & ( ! [U_5262] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_5266,U_5262)))
              | ~ hBOOL(hAPP(hAPP(c_member(U_5264),U_5262),U_5265)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5264,tc_Nat_Onat),U_5266),U_5265))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5264),U_5265)) ),
    inference(variable_rename,[status(thm)],[f_1400_1]) ).

fof(f_1400_3,plain,
    ! [U_5266,U_5265,U_5264] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5264,tc_Nat_Onat),U_5266),U_5265)))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_5266,sK98(U_5266,U_5265,U_5264))))
            & hBOOL(hAPP(hAPP(c_member(U_5264),sK98(U_5266,U_5265,U_5264)),U_5265)) ) )
        & ( ! [U_5262] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_5266,U_5262)))
              | ~ hBOOL(hAPP(hAPP(c_member(U_5264),U_5262),U_5265)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5264,tc_Nat_Onat),U_5266),U_5265))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5264),U_5265)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK98]),skolemize(U_5263,sK98(U_5266,U_5265,U_5264))],[f_1400_2]) ).

cnf(f_1400_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_5266,U_5262)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_5264),U_5262),U_5265))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5264,tc_Nat_Onat),U_5266),U_5265)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5264),U_5265)) ),
    inference(clausify,[status(thm)],[f_1400_3]) ).

cnf(f_1400_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_5264),sK98(U_5266,U_5265,U_5264)),U_5265))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5264,tc_Nat_Onat),U_5266),U_5265)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5264),U_5265)) ),
    inference(clausify,[status(thm)],[f_1400_3]) ).

cnf(f_1400_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_5266,sK98(U_5266,U_5265,U_5264))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5264,tc_Nat_Onat),U_5266),U_5265)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5264),U_5265)) ),
    inference(clausify,[status(thm)],[f_1400_3]) ).

fof(f_1401_1,plain,
    ! [V_f_2,V_A_2,T_b,T_c] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c)
          | ! [B_x] :
              ( hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_c)
              | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
        & ( ? [B_x] :
              ( hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c)
              & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2) != c_Groups_Ozero__class_Ozero(T_c) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Rings_Ono__zero__divisors(T_c)
      | ~ class_Rings_Ocomm__semiring__1(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__zero__iff]) ).

fof(f_1401_2,plain,
    ! [U_5272,U_5271,U_5270,U_5269] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5270,U_5269),U_5272),U_5271) = c_Groups_Ozero__class_Ozero(U_5269)
          | ! [U_5268] :
              ( hAPP(U_5272,U_5268) != c_Groups_Ozero__class_Ozero(U_5269)
              | ~ hBOOL(hAPP(hAPP(c_member(U_5270),U_5268),U_5271)) ) )
        & ( ? [U_5267] :
              ( hAPP(U_5272,U_5267) = c_Groups_Ozero__class_Ozero(U_5269)
              & hBOOL(hAPP(hAPP(c_member(U_5270),U_5267),U_5271)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5270,U_5269),U_5272),U_5271) != c_Groups_Ozero__class_Ozero(U_5269) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5270),U_5271))
      | ~ class_Rings_Ono__zero__divisors(U_5269)
      | ~ class_Rings_Ocomm__semiring__1(U_5269) ),
    inference(variable_rename,[status(thm)],[f_1401_1]) ).

fof(f_1401_3,plain,
    ! [U_5272,U_5271,U_5270,U_5269] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5270,U_5269),U_5272),U_5271) = c_Groups_Ozero__class_Ozero(U_5269)
          | ! [U_5268] :
              ( hAPP(U_5272,U_5268) != c_Groups_Ozero__class_Ozero(U_5269)
              | ~ hBOOL(hAPP(hAPP(c_member(U_5270),U_5268),U_5271)) ) )
        & ( ( hAPP(U_5272,sK99(U_5272,U_5271,U_5270,U_5269)) = c_Groups_Ozero__class_Ozero(U_5269)
            & hBOOL(hAPP(hAPP(c_member(U_5270),sK99(U_5272,U_5271,U_5270,U_5269)),U_5271)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5270,U_5269),U_5272),U_5271) != c_Groups_Ozero__class_Ozero(U_5269) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5270),U_5271))
      | ~ class_Rings_Ono__zero__divisors(U_5269)
      | ~ class_Rings_Ocomm__semiring__1(U_5269) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK99]),skolemize(U_5267,sK99(U_5272,U_5271,U_5270,U_5269))],[f_1401_2]) ).

cnf(f_1401_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_5270),sK99(U_5272,U_5271,U_5270,U_5269)),U_5271))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5270,U_5269),U_5272),U_5271) != c_Groups_Ozero__class_Ozero(U_5269)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5270),U_5271))
    | ~ class_Rings_Ono__zero__divisors(U_5269)
    | ~ class_Rings_Ocomm__semiring__1(U_5269) ),
    inference(clausify,[status(thm)],[f_1401_3]) ).

cnf(f_1401_5,plain,
    ( hAPP(U_5272,sK99(U_5272,U_5271,U_5270,U_5269)) = c_Groups_Ozero__class_Ozero(U_5269)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5270,U_5269),U_5272),U_5271) != c_Groups_Ozero__class_Ozero(U_5269)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5270),U_5271))
    | ~ class_Rings_Ono__zero__divisors(U_5269)
    | ~ class_Rings_Ocomm__semiring__1(U_5269) ),
    inference(clausify,[status(thm)],[f_1401_3]) ).

cnf(f_1401_6,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5270,U_5269),U_5272),U_5271) = c_Groups_Ozero__class_Ozero(U_5269)
    | hAPP(U_5272,U_5268) != c_Groups_Ozero__class_Ozero(U_5269)
    | ~ hBOOL(hAPP(hAPP(c_member(U_5270),U_5268),U_5271))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5270),U_5271))
    | ~ class_Rings_Ono__zero__divisors(U_5269)
    | ~ class_Rings_Ocomm__semiring__1(U_5269) ),
    inference(clausify,[status(thm)],[f_1401_3]) ).

fof(f_1402_1,plain,
    ! [V_f_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c)
      | ! [B_x] :
          ( hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_c)
          | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Rings_Ocomm__semiring__1(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__zero]) ).

fof(f_1402_2,plain,
    ! [U_5277,U_5276,U_5275,U_5274] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5275,U_5274),U_5277),U_5276) = c_Groups_Ozero__class_Ozero(U_5274)
      | ! [U_5273] :
          ( hAPP(U_5277,U_5273) != c_Groups_Ozero__class_Ozero(U_5274)
          | ~ hBOOL(hAPP(hAPP(c_member(U_5275),U_5273),U_5276)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5275),U_5276))
      | ~ class_Rings_Ocomm__semiring__1(U_5274) ),
    inference(variable_rename,[status(thm)],[f_1402_1]) ).

cnf(f_1402_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5275,U_5274),U_5277),U_5276) = c_Groups_Ozero__class_Ozero(U_5274)
    | hAPP(U_5277,U_5273) != c_Groups_Ozero__class_Ozero(U_5274)
    | ~ hBOOL(hAPP(hAPP(c_member(U_5275),U_5273),U_5276))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5275),U_5276))
    | ~ class_Rings_Ocomm__semiring__1(U_5274) ),
    inference(clausify,[status(thm)],[f_1402_2]) ).

fof(f_1403_1,plain,
    ! [V_n_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
        | ! [B_m] : V_n_2 != hAPP(c_Nat_OSuc,B_m) )
      & ( ? [B_m] : V_n_2 = hAPP(c_Nat_OSuc,B_m)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_gr0__conv__Suc]) ).

fof(f_1403_2,plain,
    ! [U_5280] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5280))
        | ! [U_5279] : U_5280 != hAPP(c_Nat_OSuc,U_5279) )
      & ( ? [U_5278] : U_5280 = hAPP(c_Nat_OSuc,U_5278)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5280)) ) ),
    inference(variable_rename,[status(thm)],[f_1403_1]) ).

fof(f_1403_3,plain,
    ( ! [U_5282] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5282))
        | ! [U_5279] : U_5282 != hAPP(c_Nat_OSuc,U_5279) )
    & ! [U_5281] :
        ( ? [U_5278] : U_5281 = hAPP(c_Nat_OSuc,U_5278)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5281)) ) ),
    inference(miniscope,[status(thm)],[f_1403_2]) ).

fof(f_1403_4,plain,
    ( ! [U_5282] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5282))
        | ! [U_5279] : U_5282 != hAPP(c_Nat_OSuc,U_5279) )
    & ! [U_5281] :
        ( U_5281 = hAPP(c_Nat_OSuc,sK100(U_5281))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5281)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK100]),skolemize(U_5278,sK100(U_5281))],[f_1403_3]) ).

cnf(f_1403_5,plain,
    ( U_5281 = hAPP(c_Nat_OSuc,sK100(U_5281))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5281)) ),
    inference(clausify,[status(thm)],[f_1403_4]) ).

cnf(f_1403_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5282))
    | U_5282 != hAPP(c_Nat_OSuc,U_5279) ),
    inference(clausify,[status(thm)],[f_1403_4]) ).

fof(f_1404_1,plain,
    ! [V_n_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
        | V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_less__Suc0]) ).

fof(f_1404_2,plain,
    ! [U_5283] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5283),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
        | U_5283 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( U_5283 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5283),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
    inference(variable_rename,[status(thm)],[f_1404_1]) ).

fof(f_1404_3,plain,
    ( ! [U_5285] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5285),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
        | U_5285 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_5284] :
        ( U_5284 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5284),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
    inference(miniscope,[status(thm)],[f_1404_2]) ).

cnf(f_1404_4,plain,
    ( U_5284 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5284),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
    inference(clausify,[status(thm)],[f_1404_3]) ).

cnf(f_1404_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5285),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
    | U_5285 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1404_3]) ).

fof(f_1405_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
        | ( ! [B_j] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_n_2))
              | V_m_2 != hAPP(c_Nat_OSuc,B_j) )
          & V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( ? [B_j] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_n_2))
            & V_m_2 = hAPP(c_Nat_OSuc,B_j) )
        | V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_less__Suc__eq__0__disj]) ).

fof(f_1405_2,plain,
    ! [U_5289,U_5288] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5288),hAPP(c_Nat_OSuc,U_5289)))
        | ( ! [U_5287] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5287),U_5289))
              | U_5288 != hAPP(c_Nat_OSuc,U_5287) )
          & U_5288 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( ? [U_5286] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5286),U_5289))
            & U_5288 = hAPP(c_Nat_OSuc,U_5286) )
        | U_5288 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5288),hAPP(c_Nat_OSuc,U_5289))) ) ),
    inference(variable_rename,[status(thm)],[f_1405_1]) ).

fof(f_1405_3,plain,
    ( ! [U_5293,U_5291] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5291),hAPP(c_Nat_OSuc,U_5293)))
        | ( ! [U_5287] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5287),U_5293))
              | U_5291 != hAPP(c_Nat_OSuc,U_5287) )
          & U_5291 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_5292,U_5290] :
        ( ? [U_5286] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5286),U_5292))
            & U_5290 = hAPP(c_Nat_OSuc,U_5286) )
        | U_5290 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5290),hAPP(c_Nat_OSuc,U_5292))) ) ),
    inference(miniscope,[status(thm)],[f_1405_2]) ).

fof(f_1405_4,plain,
    ( ! [U_5293,U_5291] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5291),hAPP(c_Nat_OSuc,U_5293)))
        | ( ! [U_5287] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5287),U_5293))
              | U_5291 != hAPP(c_Nat_OSuc,U_5287) )
          & U_5291 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_5292,U_5290] :
        ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK101(U_5292,U_5290)),U_5292))
          & U_5290 = hAPP(c_Nat_OSuc,sK101(U_5292,U_5290)) )
        | U_5290 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5290),hAPP(c_Nat_OSuc,U_5292))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK101]),skolemize(U_5286,sK101(U_5292,U_5290))],[f_1405_3]) ).

cnf(f_1405_5,plain,
    ( U_5290 = hAPP(c_Nat_OSuc,sK101(U_5292,U_5290))
    | U_5290 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5290),hAPP(c_Nat_OSuc,U_5292))) ),
    inference(clausify,[status(thm)],[f_1405_4]) ).

cnf(f_1405_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK101(U_5292,U_5290)),U_5292))
    | U_5290 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5290),hAPP(c_Nat_OSuc,U_5292))) ),
    inference(clausify,[status(thm)],[f_1405_4]) ).

cnf(f_1405_7,plain,
    ( U_5291 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5291),hAPP(c_Nat_OSuc,U_5293))) ),
    inference(clausify,[status(thm)],[f_1405_4]) ).

cnf(f_1405_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5287),U_5293))
    | U_5291 != hAPP(c_Nat_OSuc,U_5287)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5291),hAPP(c_Nat_OSuc,U_5293))) ),
    inference(clausify,[status(thm)],[f_1405_4]) ).

fof(f_1406_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)
        | ( ( V_n_2 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
            | V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | V_m_2 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
      & ( ( V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
        | hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_one__is__add]) ).

fof(f_1406_2,plain,
    ! [U_5295,U_5294] :
      ( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5294),U_5295)
        | ( ( U_5295 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
            | U_5294 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( U_5295 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | U_5294 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
      & ( ( U_5295 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & U_5294 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( U_5295 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_5294 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
        | hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5294),U_5295) ) ),
    inference(variable_rename,[status(thm)],[f_1406_1]) ).

fof(f_1406_3,plain,
    ( ! [U_5299,U_5297] :
        ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5297),U_5299)
        | ( ( U_5299 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
            | U_5297 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( U_5299 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | U_5297 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
    & ! [U_5298,U_5296] :
        ( ( U_5298 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & U_5296 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( U_5298 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_5296 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
        | hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5296),U_5298) ) ),
    inference(miniscope,[status(thm)],[f_1406_2]) ).

cnf(f_1406_4,plain,
    ( U_5296 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_5296 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5296),U_5298) ),
    inference(clausify,[status(thm)],[f_1406_3]) ).

cnf(f_1406_5,plain,
    ( U_5298 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | U_5296 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5296),U_5298) ),
    inference(clausify,[status(thm)],[f_1406_3]) ).

cnf(f_1406_6,plain,
    ( U_5296 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_5298 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5296),U_5298) ),
    inference(clausify,[status(thm)],[f_1406_3]) ).

cnf(f_1406_7,plain,
    ( U_5298 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | U_5298 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5296),U_5298) ),
    inference(clausify,[status(thm)],[f_1406_3]) ).

cnf(f_1406_8,plain,
    ( U_5299 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_5297 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5297),U_5299) ),
    inference(clausify,[status(thm)],[f_1406_3]) ).

cnf(f_1406_9,plain,
    ( U_5299 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | U_5297 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5297),U_5299) ),
    inference(clausify,[status(thm)],[f_1406_3]) ).

fof(f_1407_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ( ( V_n_2 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
            | V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | V_m_2 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
      & ( ( V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(fof_nnf,[status(thm)],[fact_add__is__1]) ).

fof(f_1407_2,plain,
    ! [U_5301,U_5300] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5300),U_5301) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ( ( U_5301 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
            | U_5300 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( U_5301 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | U_5300 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
      & ( ( U_5301 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & U_5300 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( U_5301 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_5300 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5300),U_5301) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(variable_rename,[status(thm)],[f_1407_1]) ).

fof(f_1407_3,plain,
    ( ! [U_5305,U_5303] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5303),U_5305) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ( ( U_5305 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
            | U_5303 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( U_5305 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | U_5303 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
    & ! [U_5304,U_5302] :
        ( ( U_5304 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & U_5302 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( U_5304 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_5302 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5302),U_5304) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(miniscope,[status(thm)],[f_1407_2]) ).

cnf(f_1407_4,plain,
    ( U_5302 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_5302 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5302),U_5304) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_1407_3]) ).

cnf(f_1407_5,plain,
    ( U_5304 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | U_5302 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5302),U_5304) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_1407_3]) ).

cnf(f_1407_6,plain,
    ( U_5302 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_5304 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5302),U_5304) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_1407_3]) ).

cnf(f_1407_7,plain,
    ( U_5304 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | U_5304 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5302),U_5304) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_1407_3]) ).

cnf(f_1407_8,plain,
    ( U_5305 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_5303 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5303),U_5305) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_1407_3]) ).

cnf(f_1407_9,plain,
    ( U_5305 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | U_5303 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5303),U_5305) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_1407_3]) ).

fof(f_1408_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) ) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_add__gr__0]) ).

fof(f_1408_2,plain,
    ! [U_5307,U_5306] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5306),U_5307)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5307))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5306)) ) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5307))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5306))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5306),U_5307))) ) ),
    inference(variable_rename,[status(thm)],[f_1408_1]) ).

fof(f_1408_3,plain,
    ( ! [U_5311,U_5309] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5309),U_5311)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5311))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5309)) ) )
    & ! [U_5310,U_5308] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5310))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5308))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5308),U_5310))) ) ),
    inference(miniscope,[status(thm)],[f_1408_2]) ).

cnf(f_1408_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5310))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5308))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5308),U_5310))) ),
    inference(clausify,[status(thm)],[f_1408_3]) ).

cnf(f_1408_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5309))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5309),U_5311))) ),
    inference(clausify,[status(thm)],[f_1408_3]) ).

cnf(f_1408_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5311))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5309),U_5311))) ),
    inference(clausify,[status(thm)],[f_1408_3]) ).

fof(f_1409_1,plain,
    ! [T_b] : hAPP(c_Finite__Set_Ocard(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_card_Oempty]) ).

fof(f_1409_2,plain,
    ! [U_5312] : hAPP(c_Finite__Set_Ocard(U_5312),c_Orderings_Obot__class_Obot(tc_fun(U_5312,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_1409_1]) ).

cnf(f_1409_3,plain,
    hAPP(c_Finite__Set_Ocard(U_5312),c_Orderings_Obot__class_Obot(tc_fun(U_5312,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1409_2]) ).

fof(f_1410_1,plain,
    ! [V_A_2,T_b] :
      ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__infinite]) ).

fof(f_1410_2,plain,
    ! [U_5314,U_5313] :
      ( hAPP(c_Finite__Set_Ocard(U_5313),U_5314) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_5313),U_5314)) ),
    inference(variable_rename,[status(thm)],[f_1410_1]) ).

cnf(f_1410_3,plain,
    ( hAPP(c_Finite__Set_Ocard(U_5313),U_5314) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_5313),U_5314)) ),
    inference(clausify,[status(thm)],[f_1410_2]) ).

fof(f_1411_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | V_n_2 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | V_m_2 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( ( V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(fof_nnf,[status(thm)],[fact_mult__eq__1__iff]) ).

fof(f_1411_2,plain,
    ! [U_5316,U_5315] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5315),U_5316) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_5316 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_5315 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( ( U_5316 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & U_5315 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5315),U_5316) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(variable_rename,[status(thm)],[f_1411_1]) ).

fof(f_1411_3,plain,
    ( ! [U_5320,U_5318] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5318),U_5320) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_5320 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_5318 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
    & ! [U_5319,U_5317] :
        ( ( U_5319 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & U_5317 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5317),U_5319) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(miniscope,[status(thm)],[f_1411_2]) ).

cnf(f_1411_4,plain,
    ( U_5317 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5317),U_5319) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_1411_3]) ).

cnf(f_1411_5,plain,
    ( U_5319 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5317),U_5319) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_1411_3]) ).

cnf(f_1411_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5318),U_5320) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | U_5320 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | U_5318 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_1411_3]) ).

fof(f_1412_1,plain,
    ! [V_m,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_m))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_diff__less]) ).

fof(f_1412_2,plain,
    ! [U_5322,U_5321] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5322),U_5321)),U_5322))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5322))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5321)) ),
    inference(variable_rename,[status(thm)],[f_1412_1]) ).

cnf(f_1412_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5322),U_5321)),U_5322))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5322))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5321)) ),
    inference(clausify,[status(thm)],[f_1412_2]) ).

fof(f_1413_1,plain,
    ! [V_m_2,V_n_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_m_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_m_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_zero__less__diff]) ).

fof(f_1413_2,plain,
    ! [U_5324,U_5323] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5323),U_5324)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5324),U_5323)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5324),U_5323))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5323),U_5324))) ) ),
    inference(variable_rename,[status(thm)],[f_1413_1]) ).

fof(f_1413_3,plain,
    ( ! [U_5328,U_5326] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5326),U_5328)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5328),U_5326)) )
    & ! [U_5327,U_5325] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5327),U_5325))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5325),U_5327))) ) ),
    inference(miniscope,[status(thm)],[f_1413_2]) ).

cnf(f_1413_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5327),U_5325))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5325),U_5327))) ),
    inference(clausify,[status(thm)],[f_1413_3]) ).

cnf(f_1413_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5326),U_5328)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5328),U_5326)) ),
    inference(clausify,[status(thm)],[f_1413_3]) ).

fof(f_1414_1,plain,
    ! [V_k,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) ),
    inference(fof_nnf,[status(thm)],[fact_mult__less__mono2]) ).

fof(f_1414_2,plain,
    ! [U_5331,U_5330,U_5329] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5331),U_5329)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5331),U_5330)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5331))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5329),U_5330)) ),
    inference(variable_rename,[status(thm)],[f_1414_1]) ).

cnf(f_1414_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5331),U_5329)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5331),U_5330)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5331))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5329),U_5330)) ),
    inference(clausify,[status(thm)],[f_1414_2]) ).

fof(f_1415_1,plain,
    ! [V_k,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) ),
    inference(fof_nnf,[status(thm)],[fact_mult__less__mono1]) ).

fof(f_1415_2,plain,
    ! [U_5334,U_5333,U_5332] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5332),U_5334)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5333),U_5334)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5334))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5332),U_5333)) ),
    inference(variable_rename,[status(thm)],[f_1415_1]) ).

cnf(f_1415_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5332),U_5334)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5333),U_5334)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5334))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5332),U_5333)) ),
    inference(clausify,[status(thm)],[f_1415_2]) ).

fof(f_1416_1,plain,
    ! [V_n_2,V_m_2,V_k_2] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) ),
    inference(fof_nnf,[status(thm)],[fact_nat__mult__less__cancel1]) ).

fof(f_1416_2,plain,
    ! [U_5337,U_5336,U_5335] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5335),U_5336)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5335),U_5337)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5336),U_5337)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5336),U_5337))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5335),U_5336)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5335),U_5337))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5335)) ),
    inference(variable_rename,[status(thm)],[f_1416_1]) ).

cnf(f_1416_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5336),U_5337))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5335),U_5336)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5335),U_5337)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5335)) ),
    inference(clausify,[status(thm)],[f_1416_2]) ).

cnf(f_1416_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5335),U_5336)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5335),U_5337)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5336),U_5337))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5335)) ),
    inference(clausify,[status(thm)],[f_1416_2]) ).

fof(f_1417_1,plain,
    ! [V_n_2,V_m_2,V_k_2] :
      ( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)
          | V_m_2 != V_n_2 )
        & ( V_m_2 = V_n_2
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) ),
    inference(fof_nnf,[status(thm)],[fact_nat__mult__eq__cancel1]) ).

fof(f_1417_2,plain,
    ! [U_5340,U_5339,U_5338] :
      ( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5338),U_5339) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5338),U_5340)
          | U_5339 != U_5340 )
        & ( U_5339 = U_5340
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5338),U_5339) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5338),U_5340) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5338)) ),
    inference(variable_rename,[status(thm)],[f_1417_1]) ).

cnf(f_1417_3,plain,
    ( U_5339 = U_5340
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5338),U_5339) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5338),U_5340)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5338)) ),
    inference(clausify,[status(thm)],[f_1417_2]) ).

cnf(f_1417_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5338),U_5339) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5338),U_5340)
    | U_5339 != U_5340
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5338)) ),
    inference(clausify,[status(thm)],[f_1417_2]) ).

fof(f_1418_1,plain,
    ! [V_n_2,V_k_2,V_m_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_mult__less__cancel2]) ).

fof(f_1418_2,plain,
    ! [U_5343,U_5342,U_5341] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5341),U_5342)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5343),U_5342)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5341),U_5343))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5342)) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5341),U_5343))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5342)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5341),U_5342)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5343),U_5342))) ) ),
    inference(variable_rename,[status(thm)],[f_1418_1]) ).

fof(f_1418_3,plain,
    ( ! [U_5349,U_5347,U_5345] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5345),U_5347)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5349),U_5347)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5345),U_5349))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5347)) )
    & ! [U_5348,U_5346,U_5344] :
        ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5344),U_5348))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5346)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5344),U_5346)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5348),U_5346))) ) ),
    inference(miniscope,[status(thm)],[f_1418_2]) ).

cnf(f_1418_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5346))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5344),U_5346)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5348),U_5346))) ),
    inference(clausify,[status(thm)],[f_1418_3]) ).

cnf(f_1418_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5344),U_5348))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5344),U_5346)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5348),U_5346))) ),
    inference(clausify,[status(thm)],[f_1418_3]) ).

cnf(f_1418_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5345),U_5347)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5349),U_5347)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5345),U_5349))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5347)) ),
    inference(clausify,[status(thm)],[f_1418_3]) ).

fof(f_1419_1,plain,
    ! [V_n_2,V_m_2,V_k_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_mult__less__cancel1]) ).

fof(f_1419_2,plain,
    ! [U_5352,U_5351,U_5350] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5350),U_5351)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5350),U_5352)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5351),U_5352))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5350)) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5351),U_5352))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5350)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5350),U_5351)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5350),U_5352))) ) ),
    inference(variable_rename,[status(thm)],[f_1419_1]) ).

fof(f_1419_3,plain,
    ( ! [U_5358,U_5356,U_5354] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5354),U_5356)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5354),U_5358)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5356),U_5358))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5354)) )
    & ! [U_5357,U_5355,U_5353] :
        ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5355),U_5357))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5353)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5353),U_5355)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5353),U_5357))) ) ),
    inference(miniscope,[status(thm)],[f_1419_2]) ).

cnf(f_1419_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5353))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5353),U_5355)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5353),U_5357))) ),
    inference(clausify,[status(thm)],[f_1419_3]) ).

cnf(f_1419_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5355),U_5357))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5353),U_5355)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5353),U_5357))) ),
    inference(clausify,[status(thm)],[f_1419_3]) ).

cnf(f_1419_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5354),U_5356)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5354),U_5358)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5356),U_5358))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5354)) ),
    inference(clausify,[status(thm)],[f_1419_3]) ).

fof(f_1420_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__0__less__mult__iff]) ).

fof(f_1420_2,plain,
    ! [U_5360,U_5359] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5359),U_5360)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5360))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5359)) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5360))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5359)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5359),U_5360))) ) ),
    inference(variable_rename,[status(thm)],[f_1420_1]) ).

fof(f_1420_3,plain,
    ( ! [U_5364,U_5362] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5362),U_5364)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5364))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5362)) )
    & ! [U_5363,U_5361] :
        ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5363))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5361)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5361),U_5363))) ) ),
    inference(miniscope,[status(thm)],[f_1420_2]) ).

cnf(f_1420_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5361))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5361),U_5363))) ),
    inference(clausify,[status(thm)],[f_1420_3]) ).

cnf(f_1420_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5363))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5361),U_5363))) ),
    inference(clausify,[status(thm)],[f_1420_3]) ).

cnf(f_1420_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5362),U_5364)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5364))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5362)) ),
    inference(clausify,[status(thm)],[f_1420_3]) ).

fof(f_1421_1,plain,
    ! [V_m,V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_diff__add__0]) ).

fof(f_1421_2,plain,
    ! [U_5366,U_5365] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5365),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5365),U_5366)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_1421_1]) ).

cnf(f_1421_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5365),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5365),U_5366)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1421_2]) ).

fof(f_1422_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(fof_nnf,[status(thm)],[fact_diff__is__0__eq]) ).

fof(f_1422_2,plain,
    ! [U_5368,U_5367] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5367),U_5368) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5367),U_5368)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5367),U_5368))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5367),U_5368) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_1422_1]) ).

fof(f_1422_3,plain,
    ( ! [U_5372,U_5370] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5370),U_5372) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5370),U_5372)) )
    & ! [U_5371,U_5369] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5369),U_5371))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5369),U_5371) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_1422_2]) ).

cnf(f_1422_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5369),U_5371))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5369),U_5371) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1422_3]) ).

cnf(f_1422_5,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5370),U_5372) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5370),U_5372)) ),
    inference(clausify,[status(thm)],[f_1422_3]) ).

fof(f_1423_1,plain,
    ! [V_n,V_m] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_diff__is__0__eq_H]) ).

fof(f_1423_2,plain,
    ! [U_5374,U_5373] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5373),U_5374) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5373),U_5374)) ),
    inference(variable_rename,[status(thm)],[f_1423_1]) ).

cnf(f_1423_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5373),U_5374) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5373),U_5374)) ),
    inference(clausify,[status(thm)],[f_1423_2]) ).

fof(f_1424_1,plain,
    c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(fof_nnf,[status(thm)],[fact_One__nat__def]) ).

cnf(f_1424_2,plain,
    c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(clausify,[status(thm)],[f_1424_1]) ).

fof(f_1425_1,plain,
    ! [V_n,V_m] :
      ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat)
      | V_m != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) ),
    inference(fof_nnf,[status(thm)],[fact_mult__eq__self__implies__10]) ).

fof(f_1425_2,plain,
    ! [U_5376,U_5375] :
      ( U_5375 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | U_5376 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
      | U_5375 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5375),U_5376) ),
    inference(variable_rename,[status(thm)],[f_1425_1]) ).

cnf(f_1425_3,plain,
    ( U_5375 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_5376 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | U_5375 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5375),U_5376) ),
    inference(clausify,[status(thm)],[f_1425_2]) ).

fof(f_1426_1,plain,
    ! [V_k_2,V_f_2] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2))
      | hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__shift__lb__Suc0__0]) ).

fof(f_1426_2,plain,
    ! [U_5378,U_5377] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_5377),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5378)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_5377),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_5378))
      | hAPP(U_5377,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[f_1426_1]) ).

cnf(f_1426_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_5377),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5378)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_5377),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_5378))
    | hAPP(U_5377,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1426_2]) ).

fof(f_1427_1,plain,
    ! [V_f_2,V_F_2,T_b] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_F_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          | ? [B_x] :
              ( hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
              & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2)) ) )
        & ( ! [B_x] :
              ( hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
              | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_F_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__eq__0__iff]) ).

fof(f_1427_2,plain,
    ! [U_5383,U_5382,U_5381] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5381,tc_Nat_Onat),U_5383),U_5382) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          | ? [U_5380] :
              ( hAPP(U_5383,U_5380) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
              & hBOOL(hAPP(hAPP(c_member(U_5381),U_5380),U_5382)) ) )
        & ( ! [U_5379] :
              ( hAPP(U_5383,U_5379) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
              | ~ hBOOL(hAPP(hAPP(c_member(U_5381),U_5379),U_5382)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5381,tc_Nat_Onat),U_5383),U_5382) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5381),U_5382)) ),
    inference(variable_rename,[status(thm)],[f_1427_1]) ).

fof(f_1427_3,plain,
    ! [U_5383,U_5382,U_5381] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5381,tc_Nat_Onat),U_5383),U_5382) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          | ( hAPP(U_5383,sK102(U_5383,U_5382,U_5381)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            & hBOOL(hAPP(hAPP(c_member(U_5381),sK102(U_5383,U_5382,U_5381)),U_5382)) ) )
        & ( ! [U_5379] :
              ( hAPP(U_5383,U_5379) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
              | ~ hBOOL(hAPP(hAPP(c_member(U_5381),U_5379),U_5382)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5381,tc_Nat_Onat),U_5383),U_5382) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5381),U_5382)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK102]),skolemize(U_5380,sK102(U_5383,U_5382,U_5381))],[f_1427_2]) ).

cnf(f_1427_4,plain,
    ( hAPP(U_5383,U_5379) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(U_5381),U_5379),U_5382))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5381,tc_Nat_Onat),U_5383),U_5382) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5381),U_5382)) ),
    inference(clausify,[status(thm)],[f_1427_3]) ).

cnf(f_1427_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_5381),sK102(U_5383,U_5382,U_5381)),U_5382))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5381,tc_Nat_Onat),U_5383),U_5382) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5381),U_5382)) ),
    inference(clausify,[status(thm)],[f_1427_3]) ).

cnf(f_1427_6,plain,
    ( hAPP(U_5383,sK102(U_5383,U_5382,U_5381)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5381,tc_Nat_Onat),U_5383),U_5382) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5381),U_5382)) ),
    inference(clausify,[status(thm)],[f_1427_3]) ).

fof(f_1428_1,plain,
    hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    inference(fof_nnf,[status(thm)],[fact_greaterThan__0]) ).

cnf(f_1428_2,plain,
    hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_1428_1]) ).

fof(f_1429_1,plain,
    ! [V_n_2] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))),
    inference(fof_nnf,[status(thm)],[fact_lessThan__Suc__eq__insert__0]) ).

fof(f_1429_2,plain,
    ! [U_5384] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5384)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_5384))),
    inference(variable_rename,[status(thm)],[f_1429_1]) ).

cnf(f_1429_3,plain,
    hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5384)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_5384))),
    inference(clausify,[status(thm)],[f_1429_2]) ).

fof(f_1430_1,plain,
    ! [V_n_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2),
    inference(fof_nnf,[status(thm)],[fact_atLeast0LessThan]) ).

fof(f_1430_2,plain,
    ! [U_5385] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5385) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_5385),
    inference(variable_rename,[status(thm)],[f_1430_1]) ).

cnf(f_1430_3,plain,
    hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5385) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_5385),
    inference(clausify,[status(thm)],[f_1430_2]) ).

fof(f_1431_1,plain,
    ! [V_n_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2),
    inference(fof_nnf,[status(thm)],[fact_atLeast0AtMost]) ).

fof(f_1431_2,plain,
    ! [U_5386] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_5386) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_5386),
    inference(variable_rename,[status(thm)],[f_1431_1]) ).

cnf(f_1431_3,plain,
    c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_5386) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_5386),
    inference(clausify,[status(thm)],[f_1431_2]) ).

fof(f_1432_1,plain,
    ! [V_n] :
      ( V_n = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_Suc__pred_H]) ).

fof(f_1432_2,plain,
    ! [U_5387] :
      ( U_5387 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5387),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5387)) ),
    inference(variable_rename,[status(thm)],[f_1432_1]) ).

cnf(f_1432_3,plain,
    ( U_5387 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5387),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5387)) ),
    inference(clausify,[status(thm)],[f_1432_2]) ).

fof(f_1433_1,plain,
    ! [V_n,V_m] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n))
        | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_n
        | V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(fof_nnf,[status(thm)],[fact_add__eq__if]) ).

fof(f_1433_2,plain,
    ! [U_5389,U_5388] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5388),U_5389) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5388),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_5389))
        | U_5388 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5388),U_5389) = U_5389
        | U_5388 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_1433_1]) ).

fof(f_1433_3,plain,
    ( ! [U_5393,U_5391] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5391),U_5393) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5391),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_5393))
        | U_5391 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_5392,U_5390] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5390),U_5392) = U_5392
        | U_5390 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_1433_2]) ).

cnf(f_1433_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5390),U_5392) = U_5392
    | U_5390 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1433_3]) ).

cnf(f_1433_5,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5391),U_5393) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5391),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_5393))
    | U_5391 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1433_3]) ).

fof(f_1434_1,plain,
    ! [V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__nonpos__neg]) ).

fof(f_1434_2,plain,
    ! [U_5396,U_5395,U_5394] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5394),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5394),U_5395),U_5396)),c_Groups_Ozero__class_Ozero(U_5394)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5394),U_5396),c_Groups_Ozero__class_Ozero(U_5394)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5394),U_5395),c_Groups_Ozero__class_Ozero(U_5394)))
      | ~ class_Groups_Oordered__comm__monoid__add(U_5394) ),
    inference(variable_rename,[status(thm)],[f_1434_1]) ).

cnf(f_1434_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5394),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5394),U_5395),U_5396)),c_Groups_Ozero__class_Ozero(U_5394)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5394),U_5396),c_Groups_Ozero__class_Ozero(U_5394)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5394),U_5395),c_Groups_Ozero__class_Ozero(U_5394)))
    | ~ class_Groups_Oordered__comm__monoid__add(U_5394) ),
    inference(clausify,[status(thm)],[f_1434_2]) ).

fof(f_1435_1,plain,
    ! [V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__neg__nonpos]) ).

fof(f_1435_2,plain,
    ! [U_5399,U_5398,U_5397] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5397),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5397),U_5398),U_5399)),c_Groups_Ozero__class_Ozero(U_5397)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5397),U_5399),c_Groups_Ozero__class_Ozero(U_5397)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5397),U_5398),c_Groups_Ozero__class_Ozero(U_5397)))
      | ~ class_Groups_Oordered__comm__monoid__add(U_5397) ),
    inference(variable_rename,[status(thm)],[f_1435_1]) ).

cnf(f_1435_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5397),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5397),U_5398),U_5399)),c_Groups_Ozero__class_Ozero(U_5397)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5397),U_5399),c_Groups_Ozero__class_Ozero(U_5397)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5397),U_5398),c_Groups_Ozero__class_Ozero(U_5397)))
    | ~ class_Groups_Oordered__comm__monoid__add(U_5397) ),
    inference(clausify,[status(thm)],[f_1435_2]) ).

fof(f_1436_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
      | ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__strict__increasing2]) ).

fof(f_1436_2,plain,
    ! [U_5403,U_5402,U_5401,U_5400] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5400),U_5402),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5400),U_5401),U_5403)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5400),U_5402),U_5403))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5400),c_Groups_Ozero__class_Ozero(U_5400)),U_5401))
      | ~ class_Groups_Oordered__comm__monoid__add(U_5400) ),
    inference(variable_rename,[status(thm)],[f_1436_1]) ).

cnf(f_1436_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5400),U_5402),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5400),U_5401),U_5403)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5400),U_5402),U_5403))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5400),c_Groups_Ozero__class_Ozero(U_5400)),U_5401))
    | ~ class_Groups_Oordered__comm__monoid__add(U_5400) ),
    inference(clausify,[status(thm)],[f_1436_2]) ).

fof(f_1437_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
      | ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__strict__increasing]) ).

fof(f_1437_2,plain,
    ! [U_5407,U_5406,U_5405,U_5404] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5404),U_5406),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5404),U_5405),U_5407)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5404),U_5406),U_5407))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5404),c_Groups_Ozero__class_Ozero(U_5404)),U_5405))
      | ~ class_Groups_Oordered__comm__monoid__add(U_5404) ),
    inference(variable_rename,[status(thm)],[f_1437_1]) ).

cnf(f_1437_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5404),U_5406),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5404),U_5405),U_5407)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5404),U_5406),U_5407))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5404),c_Groups_Ozero__class_Ozero(U_5404)),U_5405))
    | ~ class_Groups_Oordered__comm__monoid__add(U_5404) ),
    inference(clausify,[status(thm)],[f_1437_2]) ).

fof(f_1438_1,plain,
    ! [V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
      | ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__nonneg__pos]) ).

fof(f_1438_2,plain,
    ! [U_5410,U_5409,U_5408] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5408),c_Groups_Ozero__class_Ozero(U_5408)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5408),U_5409),U_5410)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5408),c_Groups_Ozero__class_Ozero(U_5408)),U_5410))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5408),c_Groups_Ozero__class_Ozero(U_5408)),U_5409))
      | ~ class_Groups_Oordered__comm__monoid__add(U_5408) ),
    inference(variable_rename,[status(thm)],[f_1438_1]) ).

cnf(f_1438_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5408),c_Groups_Ozero__class_Ozero(U_5408)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5408),U_5409),U_5410)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5408),c_Groups_Ozero__class_Ozero(U_5408)),U_5410))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5408),c_Groups_Ozero__class_Ozero(U_5408)),U_5409))
    | ~ class_Groups_Oordered__comm__monoid__add(U_5408) ),
    inference(clausify,[status(thm)],[f_1438_2]) ).

fof(f_1439_1,plain,
    ! [V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
      | ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__pos__nonneg]) ).

fof(f_1439_2,plain,
    ! [U_5413,U_5412,U_5411] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5411),c_Groups_Ozero__class_Ozero(U_5411)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5411),U_5412),U_5413)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5411),c_Groups_Ozero__class_Ozero(U_5411)),U_5413))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5411),c_Groups_Ozero__class_Ozero(U_5411)),U_5412))
      | ~ class_Groups_Oordered__comm__monoid__add(U_5411) ),
    inference(variable_rename,[status(thm)],[f_1439_1]) ).

cnf(f_1439_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5411),c_Groups_Ozero__class_Ozero(U_5411)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5411),U_5412),U_5413)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5411),c_Groups_Ozero__class_Ozero(U_5411)),U_5413))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5411),c_Groups_Ozero__class_Ozero(U_5411)),U_5412))
    | ~ class_Groups_Oordered__comm__monoid__add(U_5411) ),
    inference(clausify,[status(thm)],[f_1439_2]) ).

fof(f_1440_1,plain,
    ! [V_b_2,V_a_2,V_c_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
      | ~ class_Rings_Olinordered__ring__strict(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_mult__le__cancel__left__pos]) ).

fof(f_1440_2,plain,
    ! [U_5417,U_5416,U_5415,U_5414] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5414),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5414),U_5415),U_5416)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5414),U_5415),U_5417)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5414),U_5416),U_5417)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5414),U_5416),U_5417))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5414),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5414),U_5415),U_5416)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5414),U_5415),U_5417))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5414),c_Groups_Ozero__class_Ozero(U_5414)),U_5415))
      | ~ class_Rings_Olinordered__ring__strict(U_5414) ),
    inference(variable_rename,[status(thm)],[f_1440_1]) ).

cnf(f_1440_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5414),U_5416),U_5417))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5414),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5414),U_5415),U_5416)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5414),U_5415),U_5417)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5414),c_Groups_Ozero__class_Ozero(U_5414)),U_5415))
    | ~ class_Rings_Olinordered__ring__strict(U_5414) ),
    inference(clausify,[status(thm)],[f_1440_2]) ).

cnf(f_1440_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5414),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5414),U_5415),U_5416)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5414),U_5415),U_5417)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5414),U_5416),U_5417))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5414),c_Groups_Ozero__class_Ozero(U_5414)),U_5415))
    | ~ class_Rings_Olinordered__ring__strict(U_5414) ),
    inference(clausify,[status(thm)],[f_1440_2]) ).

fof(f_1441_1,plain,
    ! [V_b_2,V_a_2,V_c_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
      | ~ class_Rings_Olinordered__ring__strict(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_mult__le__cancel__left__neg]) ).

fof(f_1441_2,plain,
    ! [U_5421,U_5420,U_5419,U_5418] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5418),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5418),U_5419),U_5420)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5418),U_5419),U_5421)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5418),U_5421),U_5420)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5418),U_5421),U_5420))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5418),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5418),U_5419),U_5420)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5418),U_5419),U_5421))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5418),U_5419),c_Groups_Ozero__class_Ozero(U_5418)))
      | ~ class_Rings_Olinordered__ring__strict(U_5418) ),
    inference(variable_rename,[status(thm)],[f_1441_1]) ).

cnf(f_1441_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5418),U_5421),U_5420))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5418),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5418),U_5419),U_5420)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5418),U_5419),U_5421)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5418),U_5419),c_Groups_Ozero__class_Ozero(U_5418)))
    | ~ class_Rings_Olinordered__ring__strict(U_5418) ),
    inference(clausify,[status(thm)],[f_1441_2]) ).

cnf(f_1441_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5418),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5418),U_5419),U_5420)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5418),U_5419),U_5421)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5418),U_5421),U_5420))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5418),U_5419),c_Groups_Ozero__class_Ozero(U_5418)))
    | ~ class_Rings_Olinordered__ring__strict(U_5418) ),
    inference(clausify,[status(thm)],[f_1441_2]) ).

fof(f_1442_1,plain,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
      | ~ class_Rings_Olinordered__semiring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__strict__mono]) ).

fof(f_1442_2,plain,
    ! [U_5426,U_5425,U_5424,U_5423,U_5422] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5422),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5422),U_5423),U_5425)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5422),U_5424),U_5426)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5422),c_Groups_Ozero__class_Ozero(U_5422)),U_5425))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5422),c_Groups_Ozero__class_Ozero(U_5422)),U_5424))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5422),U_5425),U_5426))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5422),U_5423),U_5424))
      | ~ class_Rings_Olinordered__semiring__strict(U_5422) ),
    inference(variable_rename,[status(thm)],[f_1442_1]) ).

cnf(f_1442_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5422),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5422),U_5423),U_5425)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5422),U_5424),U_5426)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5422),c_Groups_Ozero__class_Ozero(U_5422)),U_5425))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5422),c_Groups_Ozero__class_Ozero(U_5422)),U_5424))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5422),U_5425),U_5426))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5422),U_5423),U_5424))
    | ~ class_Rings_Olinordered__semiring__strict(U_5422) ),
    inference(clausify,[status(thm)],[f_1442_2]) ).

fof(f_1443_1,plain,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
      | ~ class_Rings_Olinordered__semiring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__strict__mono_H]) ).

fof(f_1443_2,plain,
    ! [U_5431,U_5430,U_5429,U_5428,U_5427] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5427),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5427),U_5428),U_5430)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5427),U_5429),U_5431)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5427),c_Groups_Ozero__class_Ozero(U_5427)),U_5430))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5427),c_Groups_Ozero__class_Ozero(U_5427)),U_5428))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5427),U_5430),U_5431))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5427),U_5428),U_5429))
      | ~ class_Rings_Olinordered__semiring__strict(U_5427) ),
    inference(variable_rename,[status(thm)],[f_1443_1]) ).

cnf(f_1443_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5427),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5427),U_5428),U_5430)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5427),U_5429),U_5431)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5427),c_Groups_Ozero__class_Ozero(U_5427)),U_5430))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5427),c_Groups_Ozero__class_Ozero(U_5427)),U_5428))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5427),U_5430),U_5431))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5427),U_5428),U_5429))
    | ~ class_Rings_Olinordered__semiring__strict(U_5427) ),
    inference(clausify,[status(thm)],[f_1443_2]) ).

fof(f_1444_1,plain,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
      | ~ class_Rings_Olinordered__semiring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__less__le__imp__less]) ).

fof(f_1444_2,plain,
    ! [U_5436,U_5435,U_5434,U_5433,U_5432] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5432),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5432),U_5433),U_5435)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5432),U_5434),U_5436)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5432),c_Groups_Ozero__class_Ozero(U_5432)),U_5435))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5432),c_Groups_Ozero__class_Ozero(U_5432)),U_5433))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5432),U_5435),U_5436))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5432),U_5433),U_5434))
      | ~ class_Rings_Olinordered__semiring__strict(U_5432) ),
    inference(variable_rename,[status(thm)],[f_1444_1]) ).

cnf(f_1444_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5432),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5432),U_5433),U_5435)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5432),U_5434),U_5436)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5432),c_Groups_Ozero__class_Ozero(U_5432)),U_5435))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5432),c_Groups_Ozero__class_Ozero(U_5432)),U_5433))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5432),U_5435),U_5436))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5432),U_5433),U_5434))
    | ~ class_Rings_Olinordered__semiring__strict(U_5432) ),
    inference(clausify,[status(thm)],[f_1444_2]) ).

fof(f_1445_1,plain,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
      | ~ class_Rings_Olinordered__semiring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__le__less__imp__less]) ).

fof(f_1445_2,plain,
    ! [U_5441,U_5440,U_5439,U_5438,U_5437] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5437),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5437),U_5438),U_5440)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5437),U_5439),U_5441)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5437),c_Groups_Ozero__class_Ozero(U_5437)),U_5440))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5437),c_Groups_Ozero__class_Ozero(U_5437)),U_5438))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5437),U_5440),U_5441))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5437),U_5438),U_5439))
      | ~ class_Rings_Olinordered__semiring__strict(U_5437) ),
    inference(variable_rename,[status(thm)],[f_1445_1]) ).

cnf(f_1445_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5437),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5437),U_5438),U_5440)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5437),U_5439),U_5441)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5437),c_Groups_Ozero__class_Ozero(U_5437)),U_5440))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5437),c_Groups_Ozero__class_Ozero(U_5437)),U_5438))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5437),U_5440),U_5441))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5437),U_5438),U_5439))
    | ~ class_Rings_Olinordered__semiring__strict(U_5437) ),
    inference(clausify,[status(thm)],[f_1445_2]) ).

fof(f_1446_1,plain,
    ! [V_b,V_c,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))
      | ~ class_Rings_Olinordered__semiring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__right__less__imp__less]) ).

fof(f_1446_2,plain,
    ! [U_5445,U_5444,U_5443,U_5442] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5442),U_5443),U_5445))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5442),c_Groups_Ozero__class_Ozero(U_5442)),U_5444))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5442),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5442),U_5443),U_5444)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5442),U_5445),U_5444)))
      | ~ class_Rings_Olinordered__semiring(U_5442) ),
    inference(variable_rename,[status(thm)],[f_1446_1]) ).

cnf(f_1446_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5442),U_5443),U_5445))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5442),c_Groups_Ozero__class_Ozero(U_5442)),U_5444))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5442),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5442),U_5443),U_5444)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5442),U_5445),U_5444)))
    | ~ class_Rings_Olinordered__semiring(U_5442) ),
    inference(clausify,[status(thm)],[f_1446_2]) ).

fof(f_1447_1,plain,
    ! [V_b,V_c,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))
      | ~ class_Rings_Olinordered__semiring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__less__imp__less__right]) ).

fof(f_1447_2,plain,
    ! [U_5449,U_5448,U_5447,U_5446] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5446),U_5447),U_5449))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5446),c_Groups_Ozero__class_Ozero(U_5446)),U_5448))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5446),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5446),U_5447),U_5448)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5446),U_5449),U_5448)))
      | ~ class_Rings_Olinordered__semiring__strict(U_5446) ),
    inference(variable_rename,[status(thm)],[f_1447_1]) ).

cnf(f_1447_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5446),U_5447),U_5449))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5446),c_Groups_Ozero__class_Ozero(U_5446)),U_5448))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5446),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5446),U_5447),U_5448)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5446),U_5449),U_5448)))
    | ~ class_Rings_Olinordered__semiring__strict(U_5446) ),
    inference(clausify,[status(thm)],[f_1447_2]) ).

fof(f_1448_1,plain,
    ! [V_b,V_a,V_c,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))
      | ~ class_Rings_Olinordered__semiring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__left__less__imp__less]) ).

fof(f_1448_2,plain,
    ! [U_5453,U_5452,U_5451,U_5450] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5450),U_5452),U_5453))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5450),c_Groups_Ozero__class_Ozero(U_5450)),U_5451))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5450),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5450),U_5451),U_5452)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5450),U_5451),U_5453)))
      | ~ class_Rings_Olinordered__semiring(U_5450) ),
    inference(variable_rename,[status(thm)],[f_1448_1]) ).

cnf(f_1448_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5450),U_5452),U_5453))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5450),c_Groups_Ozero__class_Ozero(U_5450)),U_5451))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5450),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5450),U_5451),U_5452)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5450),U_5451),U_5453)))
    | ~ class_Rings_Olinordered__semiring(U_5450) ),
    inference(clausify,[status(thm)],[f_1448_2]) ).

fof(f_1449_1,plain,
    ! [V_b,V_a,V_c,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))
      | ~ class_Rings_Olinordered__semiring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__less__imp__less__left]) ).

fof(f_1449_2,plain,
    ! [U_5457,U_5456,U_5455,U_5454] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5454),U_5456),U_5457))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5454),c_Groups_Ozero__class_Ozero(U_5454)),U_5455))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5454),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5454),U_5455),U_5456)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5454),U_5455),U_5457)))
      | ~ class_Rings_Olinordered__semiring__strict(U_5454) ),
    inference(variable_rename,[status(thm)],[f_1449_1]) ).

cnf(f_1449_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5454),U_5456),U_5457))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5454),c_Groups_Ozero__class_Ozero(U_5454)),U_5455))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5454),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5454),U_5455),U_5456)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5454),U_5455),U_5457)))
    | ~ class_Rings_Olinordered__semiring__strict(U_5454) ),
    inference(clausify,[status(thm)],[f_1449_2]) ).

fof(f_1450_1,plain,
    ! [V_b,V_c,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)))
      | ~ class_Rings_Olinordered__semiring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__right__le__imp__le]) ).

fof(f_1450_2,plain,
    ! [U_5461,U_5460,U_5459,U_5458] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5458),U_5459),U_5461))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5458),c_Groups_Ozero__class_Ozero(U_5458)),U_5460))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5458),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5458),U_5459),U_5460)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5458),U_5461),U_5460)))
      | ~ class_Rings_Olinordered__semiring__strict(U_5458) ),
    inference(variable_rename,[status(thm)],[f_1450_1]) ).

cnf(f_1450_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5458),U_5459),U_5461))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5458),c_Groups_Ozero__class_Ozero(U_5458)),U_5460))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5458),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5458),U_5459),U_5460)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5458),U_5461),U_5460)))
    | ~ class_Rings_Olinordered__semiring__strict(U_5458) ),
    inference(clausify,[status(thm)],[f_1450_2]) ).

fof(f_1451_1,plain,
    ! [V_b,V_a,V_c,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)))
      | ~ class_Rings_Olinordered__semiring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__left__le__imp__le]) ).

fof(f_1451_2,plain,
    ! [U_5465,U_5464,U_5463,U_5462] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5462),U_5464),U_5465))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5462),c_Groups_Ozero__class_Ozero(U_5462)),U_5463))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5462),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5462),U_5463),U_5464)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5462),U_5463),U_5465)))
      | ~ class_Rings_Olinordered__semiring__strict(U_5462) ),
    inference(variable_rename,[status(thm)],[f_1451_1]) ).

cnf(f_1451_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5462),U_5464),U_5465))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5462),c_Groups_Ozero__class_Ozero(U_5462)),U_5463))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5462),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5462),U_5463),U_5464)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5462),U_5463),U_5465)))
    | ~ class_Rings_Olinordered__semiring__strict(U_5462) ),
    inference(clausify,[status(thm)],[f_1451_2]) ).

fof(f_1452_1,plain,
    ! [V_n,V_m] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n))
        | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(fof_nnf,[status(thm)],[fact_mult__eq__if]) ).

fof(f_1452_2,plain,
    ! [U_5467,U_5466] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5466),U_5467) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5467),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5466),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_5467))
        | U_5466 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5466),U_5467) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_5466 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_1452_1]) ).

fof(f_1452_3,plain,
    ( ! [U_5471,U_5469] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5469),U_5471) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5471),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5469),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_5471))
        | U_5469 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_5470,U_5468] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5468),U_5470) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_5468 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_1452_2]) ).

cnf(f_1452_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5468),U_5470) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_5468 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1452_3]) ).

cnf(f_1452_5,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5469),U_5471) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5471),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5469),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_5471))
    | U_5469 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1452_3]) ).

fof(f_1453_1,plain,
    ! [V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x)),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__left__le__one__le]) ).

fof(f_1453_2,plain,
    ! [U_5474,U_5473,U_5472] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5472),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5472),U_5474),U_5473)),U_5473))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5472),U_5474),c_Groups_Oone__class_Oone(U_5472)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5472),c_Groups_Ozero__class_Ozero(U_5472)),U_5474))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5472),c_Groups_Ozero__class_Ozero(U_5472)),U_5473))
      | ~ class_Rings_Olinordered__idom(U_5472) ),
    inference(variable_rename,[status(thm)],[f_1453_1]) ).

cnf(f_1453_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5472),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5472),U_5474),U_5473)),U_5473))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5472),U_5474),c_Groups_Oone__class_Oone(U_5472)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5472),c_Groups_Ozero__class_Ozero(U_5472)),U_5474))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5472),c_Groups_Ozero__class_Ozero(U_5472)),U_5473))
    | ~ class_Rings_Olinordered__idom(U_5472) ),
    inference(clausify,[status(thm)],[f_1453_2]) ).

fof(f_1454_1,plain,
    ! [V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__right__le__one__le]) ).

fof(f_1454_2,plain,
    ! [U_5477,U_5476,U_5475] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5475),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5475),U_5476),U_5477)),U_5476))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5475),U_5477),c_Groups_Oone__class_Oone(U_5475)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5475),c_Groups_Ozero__class_Ozero(U_5475)),U_5477))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5475),c_Groups_Ozero__class_Ozero(U_5475)),U_5476))
      | ~ class_Rings_Olinordered__idom(U_5475) ),
    inference(variable_rename,[status(thm)],[f_1454_1]) ).

cnf(f_1454_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5475),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5475),U_5476),U_5477)),U_5476))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5475),U_5477),c_Groups_Oone__class_Oone(U_5475)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5475),c_Groups_Ozero__class_Ozero(U_5475)),U_5477))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5475),c_Groups_Ozero__class_Ozero(U_5475)),U_5476))
    | ~ class_Rings_Olinordered__idom(U_5475) ),
    inference(clausify,[status(thm)],[f_1454_2]) ).

fof(f_1455_1,plain,
    ! [T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a))))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_zero__less__two]) ).

fof(f_1455_2,plain,
    ! [U_5478] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5478),c_Groups_Ozero__class_Ozero(U_5478)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5478),c_Groups_Oone__class_Oone(U_5478)),c_Groups_Oone__class_Oone(U_5478))))
      | ~ class_Rings_Olinordered__semidom(U_5478) ),
    inference(variable_rename,[status(thm)],[f_1455_1]) ).

cnf(f_1455_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5478),c_Groups_Ozero__class_Ozero(U_5478)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5478),c_Groups_Oone__class_Oone(U_5478)),c_Groups_Oone__class_Oone(U_5478))))
    | ~ class_Rings_Olinordered__semidom(U_5478) ),
    inference(clausify,[status(thm)],[f_1455_2]) ).

fof(f_1456_1,plain,
    ! [V_A_2,T_b] :
      ( ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
          & V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
        | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
        | hAPP(c_Finite__Set_Ocard(T_b),V_A_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(fof_nnf,[status(thm)],[fact_card__eq__0__iff]) ).

fof(f_1456_2,plain,
    ! [U_5480,U_5479] :
      ( ( hAPP(c_Finite__Set_Ocard(U_5479),U_5480) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_5479),U_5480))
          & U_5480 != c_Orderings_Obot__class_Obot(tc_fun(U_5479,tc_HOL_Obool)) ) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5479),U_5480))
        | U_5480 = c_Orderings_Obot__class_Obot(tc_fun(U_5479,tc_HOL_Obool))
        | hAPP(c_Finite__Set_Ocard(U_5479),U_5480) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_1456_1]) ).

fof(f_1456_3,plain,
    ( ! [U_5484,U_5482] :
        ( hAPP(c_Finite__Set_Ocard(U_5482),U_5484) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_5482),U_5484))
          & U_5484 != c_Orderings_Obot__class_Obot(tc_fun(U_5482,tc_HOL_Obool)) ) )
    & ! [U_5483,U_5481] :
        ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5481),U_5483))
        | U_5483 = c_Orderings_Obot__class_Obot(tc_fun(U_5481,tc_HOL_Obool))
        | hAPP(c_Finite__Set_Ocard(U_5481),U_5483) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_1456_2]) ).

cnf(f_1456_4,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5481),U_5483))
    | U_5483 = c_Orderings_Obot__class_Obot(tc_fun(U_5481,tc_HOL_Obool))
    | hAPP(c_Finite__Set_Ocard(U_5481),U_5483) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1456_3]) ).

cnf(f_1456_5,plain,
    ( U_5484 != c_Orderings_Obot__class_Obot(tc_fun(U_5482,tc_HOL_Obool))
    | hAPP(c_Finite__Set_Ocard(U_5482),U_5484) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1456_3]) ).

cnf(f_1456_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_5482),U_5484))
    | hAPP(c_Finite__Set_Ocard(U_5482),U_5484) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1456_3]) ).

fof(f_1457_1,plain,
    ! [V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ),
    inference(fof_nnf,[status(thm)],[fact_card__ge__0__finite]) ).

fof(f_1457_2,plain,
    ! [U_5486,U_5485] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_5485),U_5486))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_5485),U_5486))) ),
    inference(variable_rename,[status(thm)],[f_1457_1]) ).

cnf(f_1457_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_5485),U_5486))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_5485),U_5486))) ),
    inference(clausify,[status(thm)],[f_1457_2]) ).

fof(f_1458_1,plain,
    ! [V_n] :
      ( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = V_n
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_Suc__pred]) ).

fof(f_1458_2,plain,
    ! [U_5487] :
      ( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5487),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = U_5487
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5487)) ),
    inference(variable_rename,[status(thm)],[f_1458_1]) ).

cnf(f_1458_3,plain,
    ( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5487),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = U_5487
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5487)) ),
    inference(clausify,[status(thm)],[f_1458_2]) ).

fof(f_1459_1,plain,
    ! [V_i,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_i))),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_diff__Suc__less]) ).

fof(f_1459_2,plain,
    ! [U_5489,U_5488] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5488),hAPP(c_Nat_OSuc,U_5489))),U_5488))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5488)) ),
    inference(variable_rename,[status(thm)],[f_1459_1]) ).

cnf(f_1459_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5488),hAPP(c_Nat_OSuc,U_5489))),U_5488))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5488)) ),
    inference(clausify,[status(thm)],[f_1459_2]) ).

fof(f_1460_1,plain,
    ! [V_m,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_n__less__m__mult__n]) ).

fof(f_1460_2,plain,
    ! [U_5491,U_5490] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5490),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5491),U_5490)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_5491))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_5490)) ),
    inference(variable_rename,[status(thm)],[f_1460_1]) ).

cnf(f_1460_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5490),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5491),U_5490)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_5491))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_5490)) ),
    inference(clausify,[status(thm)],[f_1460_2]) ).

fof(f_1461_1,plain,
    ! [V_m,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_n__less__n__mult__m]) ).

fof(f_1461_2,plain,
    ! [U_5493,U_5492] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5492),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5492),U_5493)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_5493))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_5492)) ),
    inference(variable_rename,[status(thm)],[f_1461_1]) ).

cnf(f_1461_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5492),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5492),U_5493)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_5493))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_5492)) ),
    inference(clausify,[status(thm)],[f_1461_2]) ).

fof(f_1462_1,plain,
    ! [V_m,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_one__less__mult]) ).

fof(f_1462_2,plain,
    ! [U_5495,U_5494] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5495),U_5494)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_5495))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_5494)) ),
    inference(variable_rename,[status(thm)],[f_1462_1]) ).

cnf(f_1462_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5495),U_5494)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_5495))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_5494)) ),
    inference(clausify,[status(thm)],[f_1462_2]) ).

fof(f_1463_1,plain,
    ! [V_b_2,V_a_2,V_P_2] :
      ( ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
        | ? [B_d] :
            ( ~ hBOOL(hAPP(V_P_2,B_d))
            & V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) )
        | ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) ) )
      & ( ( ! [B_d] :
              ( hBOOL(hAPP(V_P_2,B_d))
              | V_a_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) )
          & ( hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) ) )
        | ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__diff__split]) ).

fof(f_1463_2,plain,
    ! [U_5500,U_5499,U_5498] :
      ( ( hBOOL(hAPP(U_5498,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5499),U_5500)))
        | ? [U_5497] :
            ( ~ hBOOL(hAPP(U_5498,U_5497))
            & U_5499 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5500),U_5497) )
        | ( ~ hBOOL(hAPP(U_5498,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5499),U_5500)) ) )
      & ( ( ! [U_5496] :
              ( hBOOL(hAPP(U_5498,U_5496))
              | U_5499 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5500),U_5496) )
          & ( hBOOL(hAPP(U_5498,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5499),U_5500)) ) )
        | ~ hBOOL(hAPP(U_5498,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5499),U_5500))) ) ),
    inference(variable_rename,[status(thm)],[f_1463_1]) ).

fof(f_1463_3,plain,
    ( ! [U_5506,U_5504,U_5502] :
        ( hBOOL(hAPP(U_5502,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5504),U_5506)))
        | ? [U_5497] :
            ( ~ hBOOL(hAPP(U_5502,U_5497))
            & U_5504 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5506),U_5497) )
        | ( ~ hBOOL(hAPP(U_5502,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5504),U_5506)) ) )
    & ! [U_5505,U_5503,U_5501] :
        ( ( ! [U_5496] :
              ( hBOOL(hAPP(U_5501,U_5496))
              | U_5503 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5505),U_5496) )
          & ( hBOOL(hAPP(U_5501,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5503),U_5505)) ) )
        | ~ hBOOL(hAPP(U_5501,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5503),U_5505))) ) ),
    inference(miniscope,[status(thm)],[f_1463_2]) ).

fof(f_1463_4,plain,
    ( ! [U_5506,U_5504,U_5502] :
        ( hBOOL(hAPP(U_5502,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5504),U_5506)))
        | ( ~ hBOOL(hAPP(U_5502,sK103(U_5506,U_5504,U_5502)))
          & U_5504 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5506),sK103(U_5506,U_5504,U_5502)) )
        | ( ~ hBOOL(hAPP(U_5502,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5504),U_5506)) ) )
    & ! [U_5505,U_5503,U_5501] :
        ( ( ! [U_5496] :
              ( hBOOL(hAPP(U_5501,U_5496))
              | U_5503 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5505),U_5496) )
          & ( hBOOL(hAPP(U_5501,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5503),U_5505)) ) )
        | ~ hBOOL(hAPP(U_5501,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5503),U_5505))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK103]),skolemize(U_5497,sK103(U_5506,U_5504,U_5502))],[f_1463_3]) ).

cnf(f_1463_5,plain,
    ( hBOOL(hAPP(U_5501,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5503),U_5505))
    | ~ hBOOL(hAPP(U_5501,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5503),U_5505))) ),
    inference(clausify,[status(thm)],[f_1463_4]) ).

cnf(f_1463_6,plain,
    ( hBOOL(hAPP(U_5501,U_5496))
    | U_5503 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5505),U_5496)
    | ~ hBOOL(hAPP(U_5501,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5503),U_5505))) ),
    inference(clausify,[status(thm)],[f_1463_4]) ).

cnf(f_1463_7,plain,
    ( U_5504 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5506),sK103(U_5506,U_5504,U_5502))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5504),U_5506))
    | hBOOL(hAPP(U_5502,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5504),U_5506))) ),
    inference(clausify,[status(thm)],[f_1463_4]) ).

cnf(f_1463_8,plain,
    ( ~ hBOOL(hAPP(U_5502,sK103(U_5506,U_5504,U_5502)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5504),U_5506))
    | hBOOL(hAPP(U_5502,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5504),U_5506))) ),
    inference(clausify,[status(thm)],[f_1463_4]) ).

cnf(f_1463_9,plain,
    ( U_5504 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5506),sK103(U_5506,U_5504,U_5502))
    | ~ hBOOL(hAPP(U_5502,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | hBOOL(hAPP(U_5502,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5504),U_5506))) ),
    inference(clausify,[status(thm)],[f_1463_4]) ).

cnf(f_1463_10,plain,
    ( ~ hBOOL(hAPP(U_5502,sK103(U_5506,U_5504,U_5502)))
    | ~ hBOOL(hAPP(U_5502,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | hBOOL(hAPP(U_5502,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5504),U_5506))) ),
    inference(clausify,[status(thm)],[f_1463_4]) ).

fof(f_1464_1,plain,
    ! [V_b_2,V_a_2,V_P_2] :
      ( ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
        | ? [B_d] :
            ( ~ hBOOL(hAPP(V_P_2,B_d))
            & V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) )
        | ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) ) )
      & ( ( ! [B_d] :
              ( hBOOL(hAPP(V_P_2,B_d))
              | V_a_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) )
          & ( hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) ) )
        | ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__diff__split__asm]) ).

fof(f_1464_2,plain,
    ! [U_5511,U_5510,U_5509] :
      ( ( hBOOL(hAPP(U_5509,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5510),U_5511)))
        | ? [U_5508] :
            ( ~ hBOOL(hAPP(U_5509,U_5508))
            & U_5510 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5511),U_5508) )
        | ( ~ hBOOL(hAPP(U_5509,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5510),U_5511)) ) )
      & ( ( ! [U_5507] :
              ( hBOOL(hAPP(U_5509,U_5507))
              | U_5510 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5511),U_5507) )
          & ( hBOOL(hAPP(U_5509,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5510),U_5511)) ) )
        | ~ hBOOL(hAPP(U_5509,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5510),U_5511))) ) ),
    inference(variable_rename,[status(thm)],[f_1464_1]) ).

fof(f_1464_3,plain,
    ( ! [U_5517,U_5515,U_5513] :
        ( hBOOL(hAPP(U_5513,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5515),U_5517)))
        | ? [U_5508] :
            ( ~ hBOOL(hAPP(U_5513,U_5508))
            & U_5515 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5517),U_5508) )
        | ( ~ hBOOL(hAPP(U_5513,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5515),U_5517)) ) )
    & ! [U_5516,U_5514,U_5512] :
        ( ( ! [U_5507] :
              ( hBOOL(hAPP(U_5512,U_5507))
              | U_5514 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5516),U_5507) )
          & ( hBOOL(hAPP(U_5512,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5514),U_5516)) ) )
        | ~ hBOOL(hAPP(U_5512,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5514),U_5516))) ) ),
    inference(miniscope,[status(thm)],[f_1464_2]) ).

fof(f_1464_4,plain,
    ( ! [U_5517,U_5515,U_5513] :
        ( hBOOL(hAPP(U_5513,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5515),U_5517)))
        | ( ~ hBOOL(hAPP(U_5513,sK104(U_5517,U_5515,U_5513)))
          & U_5515 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5517),sK104(U_5517,U_5515,U_5513)) )
        | ( ~ hBOOL(hAPP(U_5513,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5515),U_5517)) ) )
    & ! [U_5516,U_5514,U_5512] :
        ( ( ! [U_5507] :
              ( hBOOL(hAPP(U_5512,U_5507))
              | U_5514 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5516),U_5507) )
          & ( hBOOL(hAPP(U_5512,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5514),U_5516)) ) )
        | ~ hBOOL(hAPP(U_5512,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5514),U_5516))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK104]),skolemize(U_5508,sK104(U_5517,U_5515,U_5513))],[f_1464_3]) ).

cnf(f_1464_5,plain,
    ( hBOOL(hAPP(U_5512,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5514),U_5516))
    | ~ hBOOL(hAPP(U_5512,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5514),U_5516))) ),
    inference(clausify,[status(thm)],[f_1464_4]) ).

cnf(f_1464_6,plain,
    ( hBOOL(hAPP(U_5512,U_5507))
    | U_5514 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5516),U_5507)
    | ~ hBOOL(hAPP(U_5512,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5514),U_5516))) ),
    inference(clausify,[status(thm)],[f_1464_4]) ).

cnf(f_1464_7,plain,
    ( U_5515 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5517),sK104(U_5517,U_5515,U_5513))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5515),U_5517))
    | hBOOL(hAPP(U_5513,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5515),U_5517))) ),
    inference(clausify,[status(thm)],[f_1464_4]) ).

cnf(f_1464_8,plain,
    ( ~ hBOOL(hAPP(U_5513,sK104(U_5517,U_5515,U_5513)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5515),U_5517))
    | hBOOL(hAPP(U_5513,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5515),U_5517))) ),
    inference(clausify,[status(thm)],[f_1464_4]) ).

cnf(f_1464_9,plain,
    ( U_5515 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5517),sK104(U_5517,U_5515,U_5513))
    | ~ hBOOL(hAPP(U_5513,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | hBOOL(hAPP(U_5513,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5515),U_5517))) ),
    inference(clausify,[status(thm)],[f_1464_4]) ).

cnf(f_1464_10,plain,
    ( ~ hBOOL(hAPP(U_5513,sK104(U_5517,U_5515,U_5513)))
    | ~ hBOOL(hAPP(U_5513,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | hBOOL(hAPP(U_5513,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5515),U_5517))) ),
    inference(clausify,[status(thm)],[f_1464_4]) ).

fof(f_1465_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m_2)) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_m_2)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_one__le__mult__iff]) ).

fof(f_1465_2,plain,
    ! [U_5519,U_5518] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5518),U_5519)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_5519))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_5518)) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_5519))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_5518)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5518),U_5519))) ) ),
    inference(variable_rename,[status(thm)],[f_1465_1]) ).

fof(f_1465_3,plain,
    ( ! [U_5523,U_5521] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5521),U_5523)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_5523))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_5521)) )
    & ! [U_5522,U_5520] :
        ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_5522))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_5520)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5520),U_5522))) ) ),
    inference(miniscope,[status(thm)],[f_1465_2]) ).

cnf(f_1465_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_5520))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5520),U_5522))) ),
    inference(clausify,[status(thm)],[f_1465_3]) ).

cnf(f_1465_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_5522))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5520),U_5522))) ),
    inference(clausify,[status(thm)],[f_1465_3]) ).

cnf(f_1465_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5521),U_5523)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_5523))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_5521)) ),
    inference(clausify,[status(thm)],[f_1465_3]) ).

fof(f_1466_1,plain,
    ! [V_n_2,V_m_2,V_k_2] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) ),
    inference(fof_nnf,[status(thm)],[fact_nat__mult__le__cancel1]) ).

fof(f_1466_2,plain,
    ! [U_5526,U_5525,U_5524] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5524),U_5525)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5524),U_5526)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5525),U_5526)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5525),U_5526))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5524),U_5525)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5524),U_5526))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5524)) ),
    inference(variable_rename,[status(thm)],[f_1466_1]) ).

cnf(f_1466_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5525),U_5526))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5524),U_5525)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5524),U_5526)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5524)) ),
    inference(clausify,[status(thm)],[f_1466_2]) ).

cnf(f_1466_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5524),U_5525)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5524),U_5526)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5525),U_5526))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5524)) ),
    inference(clausify,[status(thm)],[f_1466_2]) ).

fof(f_1467_1,plain,
    ! [V_n_2,V_k_2,V_m_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) ) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_mult__le__cancel2]) ).

fof(f_1467_2,plain,
    ! [U_5529,U_5528,U_5527] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5527),U_5528)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5529),U_5528)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5527),U_5529))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5528)) ) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5527),U_5529))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5528))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5527),U_5528)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5529),U_5528))) ) ),
    inference(variable_rename,[status(thm)],[f_1467_1]) ).

fof(f_1467_3,plain,
    ( ! [U_5535,U_5533,U_5531] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5531),U_5533)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5535),U_5533)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5531),U_5535))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5533)) ) )
    & ! [U_5534,U_5532,U_5530] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5530),U_5534))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5532))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5530),U_5532)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5534),U_5532))) ) ),
    inference(miniscope,[status(thm)],[f_1467_2]) ).

cnf(f_1467_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5530),U_5534))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5532))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5530),U_5532)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5534),U_5532))) ),
    inference(clausify,[status(thm)],[f_1467_3]) ).

cnf(f_1467_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5533))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5531),U_5533)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5535),U_5533))) ),
    inference(clausify,[status(thm)],[f_1467_3]) ).

cnf(f_1467_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5531),U_5535))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5531),U_5533)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5535),U_5533))) ),
    inference(clausify,[status(thm)],[f_1467_3]) ).

fof(f_1468_1,plain,
    ! [V_n_2,V_m_2,V_k_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) ) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_mult__le__cancel1]) ).

fof(f_1468_2,plain,
    ! [U_5538,U_5537,U_5536] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5536),U_5537)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5536),U_5538)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5537),U_5538))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5536)) ) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5537),U_5538))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5536))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5536),U_5537)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5536),U_5538))) ) ),
    inference(variable_rename,[status(thm)],[f_1468_1]) ).

fof(f_1468_3,plain,
    ( ! [U_5544,U_5542,U_5540] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5540),U_5542)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5540),U_5544)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5542),U_5544))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5540)) ) )
    & ! [U_5543,U_5541,U_5539] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5541),U_5543))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5539))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5539),U_5541)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5539),U_5543))) ) ),
    inference(miniscope,[status(thm)],[f_1468_2]) ).

cnf(f_1468_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5541),U_5543))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5539))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5539),U_5541)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5539),U_5543))) ),
    inference(clausify,[status(thm)],[f_1468_3]) ).

cnf(f_1468_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5540))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5540),U_5542)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5540),U_5544))) ),
    inference(clausify,[status(thm)],[f_1468_3]) ).

cnf(f_1468_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5542),U_5544))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5540),U_5542)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5540),U_5544))) ),
    inference(clausify,[status(thm)],[f_1468_3]) ).

fof(f_1469_1,plain,
    ! [V_f_2,V_A_2,T_b] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          | ! [B_x] :
              ( ? [B_xa] :
                  ( hAPP(V_f_2,B_xa) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                  & B_x != B_xa
                  & hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2)) )
              | hAPP(V_f_2,B_x) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
              | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
        & ( ? [B_x] :
              ( ! [B_xa] :
                  ( hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                  | B_x = B_xa
                  | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2)) )
              & hAPP(V_f_2,B_x) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
              & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__eq__Suc0__iff]) ).

fof(f_1469_2,plain,
    ! [U_5551,U_5550,U_5549] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5549,tc_Nat_Onat),U_5551),U_5550) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          | ! [U_5548] :
              ( ? [U_5547] :
                  ( hAPP(U_5551,U_5547) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                  & U_5548 != U_5547
                  & hBOOL(hAPP(hAPP(c_member(U_5549),U_5547),U_5550)) )
              | hAPP(U_5551,U_5548) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
              | ~ hBOOL(hAPP(hAPP(c_member(U_5549),U_5548),U_5550)) ) )
        & ( ? [U_5546] :
              ( ! [U_5545] :
                  ( hAPP(U_5551,U_5545) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                  | U_5546 = U_5545
                  | ~ hBOOL(hAPP(hAPP(c_member(U_5549),U_5545),U_5550)) )
              & hAPP(U_5551,U_5546) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
              & hBOOL(hAPP(hAPP(c_member(U_5549),U_5546),U_5550)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5549,tc_Nat_Onat),U_5551),U_5550) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5549),U_5550)) ),
    inference(variable_rename,[status(thm)],[f_1469_1]) ).

fof(f_1469_3,plain,
    ! [U_5551,U_5550,U_5549] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5549,tc_Nat_Onat),U_5551),U_5550) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          | ! [U_5548] :
              ( ? [U_5547] :
                  ( hAPP(U_5551,U_5547) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                  & U_5548 != U_5547
                  & hBOOL(hAPP(hAPP(c_member(U_5549),U_5547),U_5550)) )
              | hAPP(U_5551,U_5548) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
              | ~ hBOOL(hAPP(hAPP(c_member(U_5549),U_5548),U_5550)) ) )
        & ( ( ! [U_5545] :
                ( hAPP(U_5551,U_5545) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                | sK105(U_5551,U_5550,U_5549) = U_5545
                | ~ hBOOL(hAPP(hAPP(c_member(U_5549),U_5545),U_5550)) )
            & hAPP(U_5551,sK105(U_5551,U_5550,U_5549)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
            & hBOOL(hAPP(hAPP(c_member(U_5549),sK105(U_5551,U_5550,U_5549)),U_5550)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5549,tc_Nat_Onat),U_5551),U_5550) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5549),U_5550)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK105]),skolemize(U_5546,sK105(U_5551,U_5550,U_5549))],[f_1469_2]) ).

fof(f_1469_4,plain,
    ! [U_5551,U_5550,U_5549] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5549,tc_Nat_Onat),U_5551),U_5550) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          | ! [U_5548] :
              ( ( hAPP(U_5551,sK106(U_5551,U_5550,U_5549,U_5548)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                & U_5548 != sK106(U_5551,U_5550,U_5549,U_5548)
                & hBOOL(hAPP(hAPP(c_member(U_5549),sK106(U_5551,U_5550,U_5549,U_5548)),U_5550)) )
              | hAPP(U_5551,U_5548) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
              | ~ hBOOL(hAPP(hAPP(c_member(U_5549),U_5548),U_5550)) ) )
        & ( ( ! [U_5545] :
                ( hAPP(U_5551,U_5545) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                | sK105(U_5551,U_5550,U_5549) = U_5545
                | ~ hBOOL(hAPP(hAPP(c_member(U_5549),U_5545),U_5550)) )
            & hAPP(U_5551,sK105(U_5551,U_5550,U_5549)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
            & hBOOL(hAPP(hAPP(c_member(U_5549),sK105(U_5551,U_5550,U_5549)),U_5550)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5549,tc_Nat_Onat),U_5551),U_5550) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5549),U_5550)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK106]),skolemize(U_5547,sK106(U_5551,U_5550,U_5549,U_5548))],[f_1469_3]) ).

cnf(f_1469_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_5549),sK105(U_5551,U_5550,U_5549)),U_5550))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5549,tc_Nat_Onat),U_5551),U_5550) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5549),U_5550)) ),
    inference(clausify,[status(thm)],[f_1469_4]) ).

cnf(f_1469_6,plain,
    ( hAPP(U_5551,sK105(U_5551,U_5550,U_5549)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5549,tc_Nat_Onat),U_5551),U_5550) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5549),U_5550)) ),
    inference(clausify,[status(thm)],[f_1469_4]) ).

cnf(f_1469_7,plain,
    ( hAPP(U_5551,U_5545) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | sK105(U_5551,U_5550,U_5549) = U_5545
    | ~ hBOOL(hAPP(hAPP(c_member(U_5549),U_5545),U_5550))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5549,tc_Nat_Onat),U_5551),U_5550) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5549),U_5550)) ),
    inference(clausify,[status(thm)],[f_1469_4]) ).

cnf(f_1469_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_5549),sK106(U_5551,U_5550,U_5549,U_5548)),U_5550))
    | hAPP(U_5551,U_5548) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ hBOOL(hAPP(hAPP(c_member(U_5549),U_5548),U_5550))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5549,tc_Nat_Onat),U_5551),U_5550) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5549),U_5550)) ),
    inference(clausify,[status(thm)],[f_1469_4]) ).

cnf(f_1469_9,plain,
    ( U_5548 != sK106(U_5551,U_5550,U_5549,U_5548)
    | hAPP(U_5551,U_5548) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ hBOOL(hAPP(hAPP(c_member(U_5549),U_5548),U_5550))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5549,tc_Nat_Onat),U_5551),U_5550) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5549),U_5550)) ),
    inference(clausify,[status(thm)],[f_1469_4]) ).

cnf(f_1469_10,plain,
    ( hAPP(U_5551,sK106(U_5551,U_5550,U_5549,U_5548)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(U_5551,U_5548) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ hBOOL(hAPP(hAPP(c_member(U_5549),U_5548),U_5550))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5549,tc_Nat_Onat),U_5551),U_5550) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5549),U_5550)) ),
    inference(clausify,[status(thm)],[f_1469_4]) ).

fof(f_1470_1,plain,
    ! [V_f_2,V_A_2,T_b] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          | ! [B_x] :
              ( ? [B_xa] :
                  ( hAPP(V_f_2,B_xa) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                  & B_x != B_xa
                  & hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2)) )
              | hAPP(V_f_2,B_x) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
              | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
        & ( ? [B_x] :
              ( ! [B_xa] :
                  ( hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                  | B_x = B_xa
                  | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2)) )
              & hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
              & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__eq__1__iff]) ).

fof(f_1470_2,plain,
    ! [U_5558,U_5557,U_5556] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5556,tc_Nat_Onat),U_5558),U_5557) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          | ! [U_5555] :
              ( ? [U_5554] :
                  ( hAPP(U_5558,U_5554) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                  & U_5555 != U_5554
                  & hBOOL(hAPP(hAPP(c_member(U_5556),U_5554),U_5557)) )
              | hAPP(U_5558,U_5555) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
              | ~ hBOOL(hAPP(hAPP(c_member(U_5556),U_5555),U_5557)) ) )
        & ( ? [U_5553] :
              ( ! [U_5552] :
                  ( hAPP(U_5558,U_5552) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                  | U_5553 = U_5552
                  | ~ hBOOL(hAPP(hAPP(c_member(U_5556),U_5552),U_5557)) )
              & hAPP(U_5558,U_5553) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
              & hBOOL(hAPP(hAPP(c_member(U_5556),U_5553),U_5557)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5556,tc_Nat_Onat),U_5558),U_5557) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5556),U_5557)) ),
    inference(variable_rename,[status(thm)],[f_1470_1]) ).

fof(f_1470_3,plain,
    ! [U_5558,U_5557,U_5556] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5556,tc_Nat_Onat),U_5558),U_5557) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          | ! [U_5555] :
              ( ? [U_5554] :
                  ( hAPP(U_5558,U_5554) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                  & U_5555 != U_5554
                  & hBOOL(hAPP(hAPP(c_member(U_5556),U_5554),U_5557)) )
              | hAPP(U_5558,U_5555) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
              | ~ hBOOL(hAPP(hAPP(c_member(U_5556),U_5555),U_5557)) ) )
        & ( ( ! [U_5552] :
                ( hAPP(U_5558,U_5552) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                | sK107(U_5558,U_5557,U_5556) = U_5552
                | ~ hBOOL(hAPP(hAPP(c_member(U_5556),U_5552),U_5557)) )
            & hAPP(U_5558,sK107(U_5558,U_5557,U_5556)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
            & hBOOL(hAPP(hAPP(c_member(U_5556),sK107(U_5558,U_5557,U_5556)),U_5557)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5556,tc_Nat_Onat),U_5558),U_5557) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5556),U_5557)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK107]),skolemize(U_5553,sK107(U_5558,U_5557,U_5556))],[f_1470_2]) ).

fof(f_1470_4,plain,
    ! [U_5558,U_5557,U_5556] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5556,tc_Nat_Onat),U_5558),U_5557) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          | ! [U_5555] :
              ( ( hAPP(U_5558,sK108(U_5558,U_5557,U_5556,U_5555)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                & U_5555 != sK108(U_5558,U_5557,U_5556,U_5555)
                & hBOOL(hAPP(hAPP(c_member(U_5556),sK108(U_5558,U_5557,U_5556,U_5555)),U_5557)) )
              | hAPP(U_5558,U_5555) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
              | ~ hBOOL(hAPP(hAPP(c_member(U_5556),U_5555),U_5557)) ) )
        & ( ( ! [U_5552] :
                ( hAPP(U_5558,U_5552) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                | sK107(U_5558,U_5557,U_5556) = U_5552
                | ~ hBOOL(hAPP(hAPP(c_member(U_5556),U_5552),U_5557)) )
            & hAPP(U_5558,sK107(U_5558,U_5557,U_5556)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
            & hBOOL(hAPP(hAPP(c_member(U_5556),sK107(U_5558,U_5557,U_5556)),U_5557)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5556,tc_Nat_Onat),U_5558),U_5557) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5556),U_5557)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK108]),skolemize(U_5554,sK108(U_5558,U_5557,U_5556,U_5555))],[f_1470_3]) ).

cnf(f_1470_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_5556),sK107(U_5558,U_5557,U_5556)),U_5557))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5556,tc_Nat_Onat),U_5558),U_5557) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5556),U_5557)) ),
    inference(clausify,[status(thm)],[f_1470_4]) ).

cnf(f_1470_6,plain,
    ( hAPP(U_5558,sK107(U_5558,U_5557,U_5556)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5556,tc_Nat_Onat),U_5558),U_5557) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5556),U_5557)) ),
    inference(clausify,[status(thm)],[f_1470_4]) ).

cnf(f_1470_7,plain,
    ( hAPP(U_5558,U_5552) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | sK107(U_5558,U_5557,U_5556) = U_5552
    | ~ hBOOL(hAPP(hAPP(c_member(U_5556),U_5552),U_5557))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5556,tc_Nat_Onat),U_5558),U_5557) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5556),U_5557)) ),
    inference(clausify,[status(thm)],[f_1470_4]) ).

cnf(f_1470_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_5556),sK108(U_5558,U_5557,U_5556,U_5555)),U_5557))
    | hAPP(U_5558,U_5555) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(U_5556),U_5555),U_5557))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5556,tc_Nat_Onat),U_5558),U_5557) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5556),U_5557)) ),
    inference(clausify,[status(thm)],[f_1470_4]) ).

cnf(f_1470_9,plain,
    ( U_5555 != sK108(U_5558,U_5557,U_5556,U_5555)
    | hAPP(U_5558,U_5555) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(U_5556),U_5555),U_5557))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5556,tc_Nat_Onat),U_5558),U_5557) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5556),U_5557)) ),
    inference(clausify,[status(thm)],[f_1470_4]) ).

cnf(f_1470_10,plain,
    ( hAPP(U_5558,sK108(U_5558,U_5557,U_5556,U_5555)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(U_5558,U_5555) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(U_5556),U_5555),U_5557))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5556,tc_Nat_Onat),U_5558),U_5557) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5556),U_5557)) ),
    inference(clausify,[status(thm)],[f_1470_4]) ).

fof(f_1471_1,plain,
    ! [V_v,V_u,V_y,V_a,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y))),V_a))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) != c_Groups_Oone__class_Oone(T_a)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_a))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
      | ~ class_Rings_Olinordered__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_convex__bound__le]) ).

fof(f_1471_2,plain,
    ! [U_5564,U_5563,U_5562,U_5561,U_5560,U_5559] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5559),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5559),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5559),U_5563),U_5560)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5559),U_5564),U_5562))),U_5561))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5559),U_5563),U_5564) != c_Groups_Oone__class_Oone(U_5559)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5559),c_Groups_Ozero__class_Ozero(U_5559)),U_5564))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5559),c_Groups_Ozero__class_Ozero(U_5559)),U_5563))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5559),U_5562),U_5561))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5559),U_5560),U_5561))
      | ~ class_Rings_Olinordered__semiring__1(U_5559) ),
    inference(variable_rename,[status(thm)],[f_1471_1]) ).

cnf(f_1471_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5559),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5559),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5559),U_5563),U_5560)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5559),U_5564),U_5562))),U_5561))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5559),U_5563),U_5564) != c_Groups_Oone__class_Oone(U_5559)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5559),c_Groups_Ozero__class_Ozero(U_5559)),U_5564))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5559),c_Groups_Ozero__class_Ozero(U_5559)),U_5563))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5559),U_5562),U_5561))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5559),U_5560),U_5561))
    | ~ class_Rings_Olinordered__semiring__1(U_5559) ),
    inference(clausify,[status(thm)],[f_1471_2]) ).

fof(f_1472_1,plain,
    ! [V_A_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
        | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
      & ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
          & V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_card__gt__0__iff]) ).

fof(f_1472_2,plain,
    ! [U_5566,U_5565] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_5565),U_5566)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5565),U_5566))
        | U_5566 = c_Orderings_Obot__class_Obot(tc_fun(U_5565,tc_HOL_Obool)) )
      & ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_5565),U_5566))
          & U_5566 != c_Orderings_Obot__class_Obot(tc_fun(U_5565,tc_HOL_Obool)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_5565),U_5566))) ) ),
    inference(variable_rename,[status(thm)],[f_1472_1]) ).

fof(f_1472_3,plain,
    ( ! [U_5570,U_5568] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_5568),U_5570)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5568),U_5570))
        | U_5570 = c_Orderings_Obot__class_Obot(tc_fun(U_5568,tc_HOL_Obool)) )
    & ! [U_5569,U_5567] :
        ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_5567),U_5569))
          & U_5569 != c_Orderings_Obot__class_Obot(tc_fun(U_5567,tc_HOL_Obool)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_5567),U_5569))) ) ),
    inference(miniscope,[status(thm)],[f_1472_2]) ).

cnf(f_1472_4,plain,
    ( U_5569 != c_Orderings_Obot__class_Obot(tc_fun(U_5567,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_5567),U_5569))) ),
    inference(clausify,[status(thm)],[f_1472_3]) ).

cnf(f_1472_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_5567),U_5569))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_5567),U_5569))) ),
    inference(clausify,[status(thm)],[f_1472_3]) ).

cnf(f_1472_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_5568),U_5570)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5568),U_5570))
    | U_5570 = c_Orderings_Obot__class_Obot(tc_fun(U_5568,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_1472_3]) ).

fof(f_1473_1,plain,
    ! [T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ),
    inference(fof_nnf,[status(thm)],[fact_finite__UNIV__card__ge__0]) ).

fof(f_1473_2,plain,
    ! [U_5571] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_5571),c_Orderings_Otop__class_Otop(tc_fun(U_5571,tc_HOL_Obool)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5571),c_Orderings_Otop__class_Otop(tc_fun(U_5571,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_1473_1]) ).

cnf(f_1473_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_5571),c_Orderings_Otop__class_Otop(tc_fun(U_5571,tc_HOL_Obool)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5571),c_Orderings_Otop__class_Otop(tc_fun(U_5571,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_1473_2]) ).

fof(f_1474_1,plain,
    ! [V_n] :
      ( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = V_n
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_Suc__diff__1]) ).

fof(f_1474_2,plain,
    ! [U_5572] :
      ( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5572),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = U_5572
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5572)) ),
    inference(variable_rename,[status(thm)],[f_1474_1]) ).

cnf(f_1474_3,plain,
    ( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5572),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = U_5572
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5572)) ),
    inference(clausify,[status(thm)],[f_1474_2]) ).

fof(f_1475_1,plain,
    ! [V_v,V_u,V_y,V_a,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y))),V_a))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) != c_Groups_Oone__class_Oone(T_a)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_a))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
      | ~ class_Rings_Olinordered__semiring__1__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_convex__bound__lt]) ).

fof(f_1475_2,plain,
    ! [U_5578,U_5577,U_5576,U_5575,U_5574,U_5573] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5573),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5573),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5573),U_5577),U_5574)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5573),U_5578),U_5576))),U_5575))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5573),U_5577),U_5578) != c_Groups_Oone__class_Oone(U_5573)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5573),c_Groups_Ozero__class_Ozero(U_5573)),U_5578))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5573),c_Groups_Ozero__class_Ozero(U_5573)),U_5577))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5573),U_5576),U_5575))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5573),U_5574),U_5575))
      | ~ class_Rings_Olinordered__semiring__1__strict(U_5573) ),
    inference(variable_rename,[status(thm)],[f_1475_1]) ).

cnf(f_1475_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5573),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5573),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5573),U_5577),U_5574)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5573),U_5578),U_5576))),U_5575))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5573),U_5577),U_5578) != c_Groups_Oone__class_Oone(U_5573)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5573),c_Groups_Ozero__class_Ozero(U_5573)),U_5578))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5573),c_Groups_Ozero__class_Ozero(U_5573)),U_5577))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5573),U_5576),U_5575))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5573),U_5574),U_5575))
    | ~ class_Rings_Olinordered__semiring__1__strict(U_5573) ),
    inference(clausify,[status(thm)],[f_1475_2]) ).

fof(f_1476_1,plain,
    ! [V_f_2,V_m_2,V_n_2,T_b] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2))),hAPP(V_f_2,V_n_2))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2))) = c_Groups_Ozero__class_Ozero(T_b)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) )
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__op__ivl__Suc]) ).

fof(f_1476_2,plain,
    ! [U_5582,U_5581,U_5580,U_5579] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_5579),U_5582),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_5581),hAPP(c_Nat_OSuc,U_5580))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5579),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_5579),U_5582),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_5581),U_5580))),hAPP(U_5582,U_5580))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5580),U_5581)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_5579),U_5582),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_5581),hAPP(c_Nat_OSuc,U_5580))) = c_Groups_Ozero__class_Ozero(U_5579)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5580),U_5581)) ) )
      | ~ class_Groups_Ocomm__monoid__add(U_5579) ),
    inference(variable_rename,[status(thm)],[f_1476_1]) ).

cnf(f_1476_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_5579),U_5582),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_5581),hAPP(c_Nat_OSuc,U_5580))) = c_Groups_Ozero__class_Ozero(U_5579)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5580),U_5581))
    | ~ class_Groups_Ocomm__monoid__add(U_5579) ),
    inference(clausify,[status(thm)],[f_1476_2]) ).

cnf(f_1476_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_5579),U_5582),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_5581),hAPP(c_Nat_OSuc,U_5580))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5579),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_5579),U_5582),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_5581),U_5580))),hAPP(U_5582,U_5580))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5580),U_5581))
    | ~ class_Groups_Ocomm__monoid__add(U_5579) ),
    inference(clausify,[status(thm)],[f_1476_2]) ).

fof(f_1477_1,plain,
    ! [V_f_2,V_m_2,V_n_2,T_b] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2))),hAPP(V_f_2,hAPP(c_Nat_OSuc,V_n_2)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2))) = c_Groups_Ozero__class_Ozero(T_b)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) )
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__cl__ivl__Suc]) ).

fof(f_1477_2,plain,
    ! [U_5586,U_5585,U_5584,U_5583] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_5583),U_5586),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_5585,hAPP(c_Nat_OSuc,U_5584))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5583),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_5583),U_5586),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_5585,U_5584))),hAPP(U_5586,hAPP(c_Nat_OSuc,U_5584)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5584)),U_5585)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_5583),U_5586),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_5585,hAPP(c_Nat_OSuc,U_5584))) = c_Groups_Ozero__class_Ozero(U_5583)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5584)),U_5585)) ) )
      | ~ class_Groups_Ocomm__monoid__add(U_5583) ),
    inference(variable_rename,[status(thm)],[f_1477_1]) ).

cnf(f_1477_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_5583),U_5586),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_5585,hAPP(c_Nat_OSuc,U_5584))) = c_Groups_Ozero__class_Ozero(U_5583)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5584)),U_5585))
    | ~ class_Groups_Ocomm__monoid__add(U_5583) ),
    inference(clausify,[status(thm)],[f_1477_2]) ).

cnf(f_1477_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_5583),U_5586),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_5585,hAPP(c_Nat_OSuc,U_5584))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5583),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_5583),U_5586),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_5585,U_5584))),hAPP(U_5586,hAPP(c_Nat_OSuc,U_5584)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5584)),U_5585))
    | ~ class_Groups_Ocomm__monoid__add(U_5583) ),
    inference(clausify,[status(thm)],[f_1477_2]) ).

fof(f_1478_1,plain,
    ! [V_P_2,V_n_2] :
      ( ( ? [B_m] :
            ( hBOOL(hAPP(V_P_2,B_m))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2)) )
        | ! [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2))) ) )
      & ( ? [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2))) )
        | ! [B_m] :
            ( ~ hBOOL(hAPP(V_P_2,B_m))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2)) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_ex__nat__less]) ).

fof(f_1478_2,plain,
    ! [U_5592,U_5591] :
      ( ( ? [U_5590] :
            ( hBOOL(hAPP(U_5592,U_5590))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5590),U_5591)) )
        | ! [U_5589] :
            ( ~ hBOOL(hAPP(U_5592,U_5589))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5589),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_5591))) ) )
      & ( ? [U_5588] :
            ( hBOOL(hAPP(U_5592,U_5588))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5588),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_5591))) )
        | ! [U_5587] :
            ( ~ hBOOL(hAPP(U_5592,U_5587))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5587),U_5591)) ) ) ),
    inference(variable_rename,[status(thm)],[f_1478_1]) ).

fof(f_1478_3,plain,
    ( ! [U_5596,U_5594] :
        ( ? [U_5590] :
            ( hBOOL(hAPP(U_5596,U_5590))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5590),U_5594)) )
        | ! [U_5589] :
            ( ~ hBOOL(hAPP(U_5596,U_5589))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5589),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_5594))) ) )
    & ! [U_5595,U_5593] :
        ( ? [U_5588] :
            ( hBOOL(hAPP(U_5595,U_5588))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5588),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_5593))) )
        | ! [U_5587] :
            ( ~ hBOOL(hAPP(U_5595,U_5587))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5587),U_5593)) ) ) ),
    inference(miniscope,[status(thm)],[f_1478_2]) ).

fof(f_1478_4,plain,
    ( ! [U_5596,U_5594] :
        ( ? [U_5590] :
            ( hBOOL(hAPP(U_5596,U_5590))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5590),U_5594)) )
        | ! [U_5589] :
            ( ~ hBOOL(hAPP(U_5596,U_5589))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5589),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_5594))) ) )
    & ! [U_5595,U_5593] :
        ( ( hBOOL(hAPP(U_5595,sK109(U_5595,U_5593)))
          & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK109(U_5595,U_5593)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_5593))) )
        | ! [U_5587] :
            ( ~ hBOOL(hAPP(U_5595,U_5587))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5587),U_5593)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK109]),skolemize(U_5588,sK109(U_5595,U_5593))],[f_1478_3]) ).

fof(f_1478_5,plain,
    ( ! [U_5596,U_5594] :
        ( ( hBOOL(hAPP(U_5596,sK110(U_5596,U_5594)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK110(U_5596,U_5594)),U_5594)) )
        | ! [U_5589] :
            ( ~ hBOOL(hAPP(U_5596,U_5589))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5589),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_5594))) ) )
    & ! [U_5595,U_5593] :
        ( ( hBOOL(hAPP(U_5595,sK109(U_5595,U_5593)))
          & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK109(U_5595,U_5593)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_5593))) )
        | ! [U_5587] :
            ( ~ hBOOL(hAPP(U_5595,U_5587))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5587),U_5593)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK110]),skolemize(U_5590,sK110(U_5596,U_5594))],[f_1478_4]) ).

cnf(f_1478_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK109(U_5595,U_5593)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_5593)))
    | ~ hBOOL(hAPP(U_5595,U_5587))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5587),U_5593)) ),
    inference(clausify,[status(thm)],[f_1478_5]) ).

cnf(f_1478_7,plain,
    ( hBOOL(hAPP(U_5595,sK109(U_5595,U_5593)))
    | ~ hBOOL(hAPP(U_5595,U_5587))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5587),U_5593)) ),
    inference(clausify,[status(thm)],[f_1478_5]) ).

cnf(f_1478_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK110(U_5596,U_5594)),U_5594))
    | ~ hBOOL(hAPP(U_5596,U_5589))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5589),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_5594))) ),
    inference(clausify,[status(thm)],[f_1478_5]) ).

cnf(f_1478_9,plain,
    ( hBOOL(hAPP(U_5596,sK110(U_5596,U_5594)))
    | ~ hBOOL(hAPP(U_5596,U_5589))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5589),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_5594))) ),
    inference(clausify,[status(thm)],[f_1478_5]) ).

fof(f_1479_1,plain,
    ! [V_P_2,V_n_2] :
      ( ( ! [B_m] :
            ( hBOOL(hAPP(V_P_2,B_m))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2)) )
        | ? [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2))) ) )
      & ( ! [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2))) )
        | ? [B_m] :
            ( ~ hBOOL(hAPP(V_P_2,B_m))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2)) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_all__nat__less]) ).

fof(f_1479_2,plain,
    ! [U_5602,U_5601] :
      ( ( ! [U_5600] :
            ( hBOOL(hAPP(U_5602,U_5600))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5600),U_5601)) )
        | ? [U_5599] :
            ( ~ hBOOL(hAPP(U_5602,U_5599))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5599),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_5601))) ) )
      & ( ! [U_5598] :
            ( hBOOL(hAPP(U_5602,U_5598))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5598),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_5601))) )
        | ? [U_5597] :
            ( ~ hBOOL(hAPP(U_5602,U_5597))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5597),U_5601)) ) ) ),
    inference(variable_rename,[status(thm)],[f_1479_1]) ).

fof(f_1479_3,plain,
    ( ! [U_5606,U_5604] :
        ( ! [U_5600] :
            ( hBOOL(hAPP(U_5606,U_5600))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5600),U_5604)) )
        | ? [U_5599] :
            ( ~ hBOOL(hAPP(U_5606,U_5599))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5599),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_5604))) ) )
    & ! [U_5605,U_5603] :
        ( ! [U_5598] :
            ( hBOOL(hAPP(U_5605,U_5598))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5598),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_5603))) )
        | ? [U_5597] :
            ( ~ hBOOL(hAPP(U_5605,U_5597))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5597),U_5603)) ) ) ),
    inference(miniscope,[status(thm)],[f_1479_2]) ).

fof(f_1479_4,plain,
    ( ! [U_5606,U_5604] :
        ( ! [U_5600] :
            ( hBOOL(hAPP(U_5606,U_5600))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5600),U_5604)) )
        | ? [U_5599] :
            ( ~ hBOOL(hAPP(U_5606,U_5599))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5599),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_5604))) ) )
    & ! [U_5605,U_5603] :
        ( ! [U_5598] :
            ( hBOOL(hAPP(U_5605,U_5598))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5598),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_5603))) )
        | ( ~ hBOOL(hAPP(U_5605,sK111(U_5605,U_5603)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK111(U_5605,U_5603)),U_5603)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK111]),skolemize(U_5597,sK111(U_5605,U_5603))],[f_1479_3]) ).

fof(f_1479_5,plain,
    ( ! [U_5606,U_5604] :
        ( ! [U_5600] :
            ( hBOOL(hAPP(U_5606,U_5600))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5600),U_5604)) )
        | ( ~ hBOOL(hAPP(U_5606,sK112(U_5606,U_5604)))
          & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK112(U_5606,U_5604)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_5604))) ) )
    & ! [U_5605,U_5603] :
        ( ! [U_5598] :
            ( hBOOL(hAPP(U_5605,U_5598))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5598),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_5603))) )
        | ( ~ hBOOL(hAPP(U_5605,sK111(U_5605,U_5603)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK111(U_5605,U_5603)),U_5603)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK112]),skolemize(U_5599,sK112(U_5606,U_5604))],[f_1479_4]) ).

cnf(f_1479_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK111(U_5605,U_5603)),U_5603))
    | hBOOL(hAPP(U_5605,U_5598))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5598),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_5603))) ),
    inference(clausify,[status(thm)],[f_1479_5]) ).

cnf(f_1479_7,plain,
    ( ~ hBOOL(hAPP(U_5605,sK111(U_5605,U_5603)))
    | hBOOL(hAPP(U_5605,U_5598))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5598),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_5603))) ),
    inference(clausify,[status(thm)],[f_1479_5]) ).

cnf(f_1479_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK112(U_5606,U_5604)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_5604)))
    | hBOOL(hAPP(U_5606,U_5600))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5600),U_5604)) ),
    inference(clausify,[status(thm)],[f_1479_5]) ).

cnf(f_1479_9,plain,
    ( ~ hBOOL(hAPP(U_5606,sK112(U_5606,U_5604)))
    | hBOOL(hAPP(U_5606,U_5600))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5600),U_5604)) ),
    inference(clausify,[status(thm)],[f_1479_5]) ).

fof(f_1480_1,plain,
    ! [V_P_2,V_n_2] :
      ( ( ! [B_m] :
            ( hBOOL(hAPP(V_P_2,B_m))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2)) )
        | ? [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))) ) )
      & ( ! [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))) )
        | ? [B_m] :
            ( ~ hBOOL(hAPP(V_P_2,B_m))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2)) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_all__nat__less__eq]) ).

fof(f_1480_2,plain,
    ! [U_5612,U_5611] :
      ( ( ! [U_5610] :
            ( hBOOL(hAPP(U_5612,U_5610))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5610),U_5611)) )
        | ? [U_5609] :
            ( ~ hBOOL(hAPP(U_5612,U_5609))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5609),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5611))) ) )
      & ( ! [U_5608] :
            ( hBOOL(hAPP(U_5612,U_5608))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5608),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5611))) )
        | ? [U_5607] :
            ( ~ hBOOL(hAPP(U_5612,U_5607))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5607),U_5611)) ) ) ),
    inference(variable_rename,[status(thm)],[f_1480_1]) ).

fof(f_1480_3,plain,
    ( ! [U_5616,U_5614] :
        ( ! [U_5610] :
            ( hBOOL(hAPP(U_5616,U_5610))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5610),U_5614)) )
        | ? [U_5609] :
            ( ~ hBOOL(hAPP(U_5616,U_5609))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5609),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5614))) ) )
    & ! [U_5615,U_5613] :
        ( ! [U_5608] :
            ( hBOOL(hAPP(U_5615,U_5608))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5608),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5613))) )
        | ? [U_5607] :
            ( ~ hBOOL(hAPP(U_5615,U_5607))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5607),U_5613)) ) ) ),
    inference(miniscope,[status(thm)],[f_1480_2]) ).

fof(f_1480_4,plain,
    ( ! [U_5616,U_5614] :
        ( ! [U_5610] :
            ( hBOOL(hAPP(U_5616,U_5610))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5610),U_5614)) )
        | ? [U_5609] :
            ( ~ hBOOL(hAPP(U_5616,U_5609))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5609),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5614))) ) )
    & ! [U_5615,U_5613] :
        ( ! [U_5608] :
            ( hBOOL(hAPP(U_5615,U_5608))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5608),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5613))) )
        | ( ~ hBOOL(hAPP(U_5615,sK113(U_5615,U_5613)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK113(U_5615,U_5613)),U_5613)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK113]),skolemize(U_5607,sK113(U_5615,U_5613))],[f_1480_3]) ).

fof(f_1480_5,plain,
    ( ! [U_5616,U_5614] :
        ( ! [U_5610] :
            ( hBOOL(hAPP(U_5616,U_5610))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5610),U_5614)) )
        | ( ~ hBOOL(hAPP(U_5616,sK114(U_5616,U_5614)))
          & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK114(U_5616,U_5614)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5614))) ) )
    & ! [U_5615,U_5613] :
        ( ! [U_5608] :
            ( hBOOL(hAPP(U_5615,U_5608))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5608),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5613))) )
        | ( ~ hBOOL(hAPP(U_5615,sK113(U_5615,U_5613)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK113(U_5615,U_5613)),U_5613)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK114]),skolemize(U_5609,sK114(U_5616,U_5614))],[f_1480_4]) ).

cnf(f_1480_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK113(U_5615,U_5613)),U_5613))
    | hBOOL(hAPP(U_5615,U_5608))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5608),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5613))) ),
    inference(clausify,[status(thm)],[f_1480_5]) ).

cnf(f_1480_7,plain,
    ( ~ hBOOL(hAPP(U_5615,sK113(U_5615,U_5613)))
    | hBOOL(hAPP(U_5615,U_5608))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5608),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5613))) ),
    inference(clausify,[status(thm)],[f_1480_5]) ).

cnf(f_1480_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK114(U_5616,U_5614)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5614)))
    | hBOOL(hAPP(U_5616,U_5610))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5610),U_5614)) ),
    inference(clausify,[status(thm)],[f_1480_5]) ).

cnf(f_1480_9,plain,
    ( ~ hBOOL(hAPP(U_5616,sK114(U_5616,U_5614)))
    | hBOOL(hAPP(U_5616,U_5610))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5610),U_5614)) ),
    inference(clausify,[status(thm)],[f_1480_5]) ).

fof(f_1481_1,plain,
    ! [V_P_2,V_n_2] :
      ( ( ? [B_m] :
            ( hBOOL(hAPP(V_P_2,B_m))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2)) )
        | ! [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))) ) )
      & ( ? [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))) )
        | ! [B_m] :
            ( ~ hBOOL(hAPP(V_P_2,B_m))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2)) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_ex__nat__less__eq]) ).

fof(f_1481_2,plain,
    ! [U_5622,U_5621] :
      ( ( ? [U_5620] :
            ( hBOOL(hAPP(U_5622,U_5620))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5620),U_5621)) )
        | ! [U_5619] :
            ( ~ hBOOL(hAPP(U_5622,U_5619))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5619),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5621))) ) )
      & ( ? [U_5618] :
            ( hBOOL(hAPP(U_5622,U_5618))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5618),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5621))) )
        | ! [U_5617] :
            ( ~ hBOOL(hAPP(U_5622,U_5617))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5617),U_5621)) ) ) ),
    inference(variable_rename,[status(thm)],[f_1481_1]) ).

fof(f_1481_3,plain,
    ( ! [U_5626,U_5624] :
        ( ? [U_5620] :
            ( hBOOL(hAPP(U_5626,U_5620))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5620),U_5624)) )
        | ! [U_5619] :
            ( ~ hBOOL(hAPP(U_5626,U_5619))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5619),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5624))) ) )
    & ! [U_5625,U_5623] :
        ( ? [U_5618] :
            ( hBOOL(hAPP(U_5625,U_5618))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5618),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5623))) )
        | ! [U_5617] :
            ( ~ hBOOL(hAPP(U_5625,U_5617))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5617),U_5623)) ) ) ),
    inference(miniscope,[status(thm)],[f_1481_2]) ).

fof(f_1481_4,plain,
    ( ! [U_5626,U_5624] :
        ( ? [U_5620] :
            ( hBOOL(hAPP(U_5626,U_5620))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5620),U_5624)) )
        | ! [U_5619] :
            ( ~ hBOOL(hAPP(U_5626,U_5619))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5619),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5624))) ) )
    & ! [U_5625,U_5623] :
        ( ( hBOOL(hAPP(U_5625,sK115(U_5625,U_5623)))
          & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK115(U_5625,U_5623)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5623))) )
        | ! [U_5617] :
            ( ~ hBOOL(hAPP(U_5625,U_5617))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5617),U_5623)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK115]),skolemize(U_5618,sK115(U_5625,U_5623))],[f_1481_3]) ).

fof(f_1481_5,plain,
    ( ! [U_5626,U_5624] :
        ( ( hBOOL(hAPP(U_5626,sK116(U_5626,U_5624)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK116(U_5626,U_5624)),U_5624)) )
        | ! [U_5619] :
            ( ~ hBOOL(hAPP(U_5626,U_5619))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5619),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5624))) ) )
    & ! [U_5625,U_5623] :
        ( ( hBOOL(hAPP(U_5625,sK115(U_5625,U_5623)))
          & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK115(U_5625,U_5623)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5623))) )
        | ! [U_5617] :
            ( ~ hBOOL(hAPP(U_5625,U_5617))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5617),U_5623)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK116]),skolemize(U_5620,sK116(U_5626,U_5624))],[f_1481_4]) ).

cnf(f_1481_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK115(U_5625,U_5623)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5623)))
    | ~ hBOOL(hAPP(U_5625,U_5617))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5617),U_5623)) ),
    inference(clausify,[status(thm)],[f_1481_5]) ).

cnf(f_1481_7,plain,
    ( hBOOL(hAPP(U_5625,sK115(U_5625,U_5623)))
    | ~ hBOOL(hAPP(U_5625,U_5617))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5617),U_5623)) ),
    inference(clausify,[status(thm)],[f_1481_5]) ).

cnf(f_1481_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK116(U_5626,U_5624)),U_5624))
    | ~ hBOOL(hAPP(U_5626,U_5619))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5619),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5624))) ),
    inference(clausify,[status(thm)],[f_1481_5]) ).

cnf(f_1481_9,plain,
    ( hBOOL(hAPP(U_5626,sK116(U_5626,U_5624)))
    | ~ hBOOL(hAPP(U_5626,U_5619))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_5619),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5624))) ),
    inference(clausify,[status(thm)],[f_1481_5]) ).

fof(f_1482_1,plain,
    ! [V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_b))) ) )
      | ~ class_Rings_Olinordered__idom(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_even__less__0__iff]) ).

fof(f_1482_2,plain,
    ! [U_5628,U_5627] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5627),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5627),U_5628),U_5628)),c_Groups_Ozero__class_Ozero(U_5627)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5627),U_5628),c_Groups_Ozero__class_Ozero(U_5627))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5627),U_5628),c_Groups_Ozero__class_Ozero(U_5627)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5627),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5627),U_5628),U_5628)),c_Groups_Ozero__class_Ozero(U_5627))) ) )
      | ~ class_Rings_Olinordered__idom(U_5627) ),
    inference(variable_rename,[status(thm)],[f_1482_1]) ).

cnf(f_1482_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5627),U_5628),c_Groups_Ozero__class_Ozero(U_5627)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5627),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5627),U_5628),U_5628)),c_Groups_Ozero__class_Ozero(U_5627)))
    | ~ class_Rings_Olinordered__idom(U_5627) ),
    inference(clausify,[status(thm)],[f_1482_2]) ).

cnf(f_1482_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5627),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5627),U_5628),U_5628)),c_Groups_Ozero__class_Ozero(U_5627)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5627),U_5628),c_Groups_Ozero__class_Ozero(U_5627)))
    | ~ class_Rings_Olinordered__idom(U_5627) ),
    inference(clausify,[status(thm)],[f_1482_2]) ).

fof(f_1483_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))
      | ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        & ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card_Ounion__inter__neutral]) ).

fof(f_1483_2,plain,
    ! [U_5632,U_5631,U_5630] :
      ( hAPP(c_Finite__Set_Ocard(U_5630),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5630,tc_HOL_Obool)),U_5631),U_5632)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_5630),U_5631)),hAPP(c_Finite__Set_Ocard(U_5630),U_5632))
      | ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        & ? [U_5629] : hBOOL(hAPP(hAPP(c_member(U_5630),U_5629),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5630,tc_HOL_Obool)),U_5631),U_5632))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5630),U_5632))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5630),U_5631)) ),
    inference(variable_rename,[status(thm)],[f_1483_1]) ).

fof(f_1483_3,plain,
    ! [U_5632,U_5631,U_5630] :
      ( hAPP(c_Finite__Set_Ocard(U_5630),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5630,tc_HOL_Obool)),U_5631),U_5632)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_5630),U_5631)),hAPP(c_Finite__Set_Ocard(U_5630),U_5632))
      | ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        & hBOOL(hAPP(hAPP(c_member(U_5630),sK117(U_5632,U_5631,U_5630)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5630,tc_HOL_Obool)),U_5631),U_5632))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5630),U_5632))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5630),U_5631)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK117]),skolemize(U_5629,sK117(U_5632,U_5631,U_5630))],[f_1483_2]) ).

cnf(f_1483_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_5630),sK117(U_5632,U_5631,U_5630)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5630,tc_HOL_Obool)),U_5631),U_5632)))
    | hAPP(c_Finite__Set_Ocard(U_5630),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5630,tc_HOL_Obool)),U_5631),U_5632)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_5630),U_5631)),hAPP(c_Finite__Set_Ocard(U_5630),U_5632))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5630),U_5632))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5630),U_5631)) ),
    inference(clausify,[status(thm)],[f_1483_3]) ).

cnf(f_1483_5,plain,
    ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(c_Finite__Set_Ocard(U_5630),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5630,tc_HOL_Obool)),U_5631),U_5632)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_5630),U_5631)),hAPP(c_Finite__Set_Ocard(U_5630),U_5632))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5630),U_5632))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5630),U_5631)) ),
    inference(clausify,[status(thm)],[f_1483_3]) ).

fof(f_1484_1,plain,
    ! [V_f_2,V_A_2,V_B_2,T_b,T_c] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2)))
      | ? [B_b] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_b)))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | ~ class_Groups_Oordered__comm__monoid__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__mono2]) ).

fof(f_1484_2,plain,
    ! [U_5638,U_5637,U_5636,U_5635,U_5634] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5634),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5635,U_5634),U_5638),U_5637)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5635,U_5634),U_5638),U_5636)))
      | ? [U_5633] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5634),c_Groups_Ozero__class_Ozero(U_5634)),hAPP(U_5638,U_5633)))
          & hBOOL(hAPP(hAPP(c_member(U_5635),U_5633),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5635,tc_HOL_Obool)),U_5636),U_5637))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5635,tc_HOL_Obool)),U_5637),U_5636))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5635),U_5636))
      | ~ class_Groups_Oordered__comm__monoid__add(U_5634) ),
    inference(variable_rename,[status(thm)],[f_1484_1]) ).

fof(f_1484_3,plain,
    ! [U_5638,U_5637,U_5636,U_5635,U_5634] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5634),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5635,U_5634),U_5638),U_5637)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5635,U_5634),U_5638),U_5636)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5634),c_Groups_Ozero__class_Ozero(U_5634)),hAPP(U_5638,sK118(U_5638,U_5637,U_5636,U_5635,U_5634))))
        & hBOOL(hAPP(hAPP(c_member(U_5635),sK118(U_5638,U_5637,U_5636,U_5635,U_5634)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5635,tc_HOL_Obool)),U_5636),U_5637))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5635,tc_HOL_Obool)),U_5637),U_5636))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5635),U_5636))
      | ~ class_Groups_Oordered__comm__monoid__add(U_5634) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK118]),skolemize(U_5633,sK118(U_5638,U_5637,U_5636,U_5635,U_5634))],[f_1484_2]) ).

cnf(f_1484_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_5635),sK118(U_5638,U_5637,U_5636,U_5635,U_5634)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5635,tc_HOL_Obool)),U_5636),U_5637)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5634),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5635,U_5634),U_5638),U_5637)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5635,U_5634),U_5638),U_5636)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5635,tc_HOL_Obool)),U_5637),U_5636))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5635),U_5636))
    | ~ class_Groups_Oordered__comm__monoid__add(U_5634) ),
    inference(clausify,[status(thm)],[f_1484_3]) ).

cnf(f_1484_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5634),c_Groups_Ozero__class_Ozero(U_5634)),hAPP(U_5638,sK118(U_5638,U_5637,U_5636,U_5635,U_5634))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5634),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5635,U_5634),U_5638),U_5637)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5635,U_5634),U_5638),U_5636)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5635,tc_HOL_Obool)),U_5637),U_5636))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5635),U_5636))
    | ~ class_Groups_Oordered__comm__monoid__add(U_5634) ),
    inference(clausify,[status(thm)],[f_1484_3]) ).

fof(f_1485_1,plain,
    ! [V_a_2,T_b] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
          | V_a_2 != c_Groups_Ozero__class_Ozero(T_b) )
        & ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) != c_Groups_Ozero__class_Ozero(T_b) ) )
      | ~ class_Groups_Olinordered__ab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_double__eq__0__iff]) ).

fof(f_1485_2,plain,
    ! [U_5640,U_5639] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5639),U_5640),U_5640) = c_Groups_Ozero__class_Ozero(U_5639)
          | U_5640 != c_Groups_Ozero__class_Ozero(U_5639) )
        & ( U_5640 = c_Groups_Ozero__class_Ozero(U_5639)
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5639),U_5640),U_5640) != c_Groups_Ozero__class_Ozero(U_5639) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_5639) ),
    inference(variable_rename,[status(thm)],[f_1485_1]) ).

cnf(f_1485_3,plain,
    ( U_5640 = c_Groups_Ozero__class_Ozero(U_5639)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5639),U_5640),U_5640) != c_Groups_Ozero__class_Ozero(U_5639)
    | ~ class_Groups_Olinordered__ab__group__add(U_5639) ),
    inference(clausify,[status(thm)],[f_1485_2]) ).

cnf(f_1485_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5639),U_5640),U_5640) = c_Groups_Ozero__class_Ozero(U_5639)
    | U_5640 != c_Groups_Ozero__class_Ozero(U_5639)
    | ~ class_Groups_Olinordered__ab__group__add(U_5639) ),
    inference(clausify,[status(thm)],[f_1485_2]) ).

fof(f_1486_1,plain,
    ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_B_2))
      | ? [B_x] :
          ( hAPP(V_g_2,B_x) != c_Groups_Ozero__class_Ozero(T_c)
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Ocomm__monoid__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum_Ounion__inter__neutral]) ).

fof(f_1486_2,plain,
    ! [U_5646,U_5645,U_5644,U_5643,U_5642] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5643,U_5642),U_5646),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5643,tc_HOL_Obool)),U_5644),U_5645)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5642),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5643,U_5642),U_5646),U_5644)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5643,U_5642),U_5646),U_5645))
      | ? [U_5641] :
          ( hAPP(U_5646,U_5641) != c_Groups_Ozero__class_Ozero(U_5642)
          & hBOOL(hAPP(hAPP(c_member(U_5643),U_5641),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5643,tc_HOL_Obool)),U_5644),U_5645))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5643),U_5645))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5643),U_5644))
      | ~ class_Groups_Ocomm__monoid__add(U_5642) ),
    inference(variable_rename,[status(thm)],[f_1486_1]) ).

fof(f_1486_3,plain,
    ! [U_5646,U_5645,U_5644,U_5643,U_5642] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5643,U_5642),U_5646),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5643,tc_HOL_Obool)),U_5644),U_5645)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5642),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5643,U_5642),U_5646),U_5644)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5643,U_5642),U_5646),U_5645))
      | ( hAPP(U_5646,sK119(U_5646,U_5645,U_5644,U_5643,U_5642)) != c_Groups_Ozero__class_Ozero(U_5642)
        & hBOOL(hAPP(hAPP(c_member(U_5643),sK119(U_5646,U_5645,U_5644,U_5643,U_5642)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5643,tc_HOL_Obool)),U_5644),U_5645))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5643),U_5645))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5643),U_5644))
      | ~ class_Groups_Ocomm__monoid__add(U_5642) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK119]),skolemize(U_5641,sK119(U_5646,U_5645,U_5644,U_5643,U_5642))],[f_1486_2]) ).

cnf(f_1486_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_5643),sK119(U_5646,U_5645,U_5644,U_5643,U_5642)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5643,tc_HOL_Obool)),U_5644),U_5645)))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5643,U_5642),U_5646),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5643,tc_HOL_Obool)),U_5644),U_5645)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5642),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5643,U_5642),U_5646),U_5644)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5643,U_5642),U_5646),U_5645))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5643),U_5645))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5643),U_5644))
    | ~ class_Groups_Ocomm__monoid__add(U_5642) ),
    inference(clausify,[status(thm)],[f_1486_3]) ).

cnf(f_1486_5,plain,
    ( hAPP(U_5646,sK119(U_5646,U_5645,U_5644,U_5643,U_5642)) != c_Groups_Ozero__class_Ozero(U_5642)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5643,U_5642),U_5646),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5643,tc_HOL_Obool)),U_5644),U_5645)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5642),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5643,U_5642),U_5646),U_5644)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5643,U_5642),U_5646),U_5645))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5643),U_5645))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5643),U_5644))
    | ~ class_Groups_Ocomm__monoid__add(U_5642) ),
    inference(clausify,[status(thm)],[f_1486_3]) ).

fof(f_1487_1,plain,
    ! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_S_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_T_2))
      | ? [B_x] :
          ( hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_c)
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
      | ~ class_Groups_Ocomm__monoid__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__Un__zero]) ).

fof(f_1487_2,plain,
    ! [U_5652,U_5651,U_5650,U_5649,U_5648] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5649,U_5648),U_5652),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5649,tc_HOL_Obool)),U_5650),U_5651)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5648),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5649,U_5648),U_5652),U_5650)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5649,U_5648),U_5652),U_5651))
      | ? [U_5647] :
          ( hAPP(U_5652,U_5647) != c_Groups_Ozero__class_Ozero(U_5648)
          & hBOOL(hAPP(hAPP(c_member(U_5649),U_5647),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5649,tc_HOL_Obool)),U_5650),U_5651))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5649),U_5651))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5649),U_5650))
      | ~ class_Groups_Ocomm__monoid__add(U_5648) ),
    inference(variable_rename,[status(thm)],[f_1487_1]) ).

fof(f_1487_3,plain,
    ! [U_5652,U_5651,U_5650,U_5649,U_5648] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5649,U_5648),U_5652),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5649,tc_HOL_Obool)),U_5650),U_5651)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5648),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5649,U_5648),U_5652),U_5650)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5649,U_5648),U_5652),U_5651))
      | ( hAPP(U_5652,sK120(U_5652,U_5651,U_5650,U_5649,U_5648)) != c_Groups_Ozero__class_Ozero(U_5648)
        & hBOOL(hAPP(hAPP(c_member(U_5649),sK120(U_5652,U_5651,U_5650,U_5649,U_5648)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5649,tc_HOL_Obool)),U_5650),U_5651))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5649),U_5651))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5649),U_5650))
      | ~ class_Groups_Ocomm__monoid__add(U_5648) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK120]),skolemize(U_5647,sK120(U_5652,U_5651,U_5650,U_5649,U_5648))],[f_1487_2]) ).

cnf(f_1487_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_5649),sK120(U_5652,U_5651,U_5650,U_5649,U_5648)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5649,tc_HOL_Obool)),U_5650),U_5651)))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5649,U_5648),U_5652),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5649,tc_HOL_Obool)),U_5650),U_5651)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5648),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5649,U_5648),U_5652),U_5650)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5649,U_5648),U_5652),U_5651))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5649),U_5651))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5649),U_5650))
    | ~ class_Groups_Ocomm__monoid__add(U_5648) ),
    inference(clausify,[status(thm)],[f_1487_3]) ).

cnf(f_1487_5,plain,
    ( hAPP(U_5652,sK120(U_5652,U_5651,U_5650,U_5649,U_5648)) != c_Groups_Ozero__class_Ozero(U_5648)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5649,U_5648),U_5652),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5649,tc_HOL_Obool)),U_5650),U_5651)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5648),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5649,U_5648),U_5652),U_5650)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5649,U_5648),U_5652),U_5651))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5649),U_5651))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5649),U_5650))
    | ~ class_Groups_Ocomm__monoid__add(U_5648) ),
    inference(clausify,[status(thm)],[f_1487_3]) ).

fof(f_1488_1,plain,
    ! [V_k_2,V_A_2,T_b] :
      ( ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Nat_OSuc,V_k_2)
        | ! [B_b,B_B] :
            ( ( B_B != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
              & V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
            | hAPP(c_Finite__Set_Ocard(T_b),B_B) != V_k_2
            | hBOOL(hAPP(hAPP(c_member(T_b),B_b),B_B))
            | V_A_2 != hAPP(hAPP(c_Set_Oinsert(T_b),B_b),B_B) ) )
      & ( ? [B_b,B_B] :
            ( ( B_B = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
              | V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
            & hAPP(c_Finite__Set_Ocard(T_b),B_B) = V_k_2
            & ~ hBOOL(hAPP(hAPP(c_member(T_b),B_b),B_B))
            & V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_b),B_b),B_B) )
        | hAPP(c_Finite__Set_Ocard(T_b),V_A_2) != hAPP(c_Nat_OSuc,V_k_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_card__Suc__eq]) ).

fof(f_1488_2,plain,
    ! [U_5659,U_5658,U_5657] :
      ( ( hAPP(c_Finite__Set_Ocard(U_5657),U_5658) = hAPP(c_Nat_OSuc,U_5659)
        | ! [U_5656,U_5655] :
            ( ( U_5655 != c_Orderings_Obot__class_Obot(tc_fun(U_5657,tc_HOL_Obool))
              & U_5659 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
            | hAPP(c_Finite__Set_Ocard(U_5657),U_5655) != U_5659
            | hBOOL(hAPP(hAPP(c_member(U_5657),U_5656),U_5655))
            | U_5658 != hAPP(hAPP(c_Set_Oinsert(U_5657),U_5656),U_5655) ) )
      & ( ? [U_5654,U_5653] :
            ( ( U_5653 = c_Orderings_Obot__class_Obot(tc_fun(U_5657,tc_HOL_Obool))
              | U_5659 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
            & hAPP(c_Finite__Set_Ocard(U_5657),U_5653) = U_5659
            & ~ hBOOL(hAPP(hAPP(c_member(U_5657),U_5654),U_5653))
            & U_5658 = hAPP(hAPP(c_Set_Oinsert(U_5657),U_5654),U_5653) )
        | hAPP(c_Finite__Set_Ocard(U_5657),U_5658) != hAPP(c_Nat_OSuc,U_5659) ) ),
    inference(variable_rename,[status(thm)],[f_1488_1]) ).

fof(f_1488_3,plain,
    ( ! [U_5665,U_5663,U_5661] :
        ( hAPP(c_Finite__Set_Ocard(U_5661),U_5663) = hAPP(c_Nat_OSuc,U_5665)
        | ! [U_5656,U_5655] :
            ( ( U_5655 != c_Orderings_Obot__class_Obot(tc_fun(U_5661,tc_HOL_Obool))
              & U_5665 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
            | hAPP(c_Finite__Set_Ocard(U_5661),U_5655) != U_5665
            | hBOOL(hAPP(hAPP(c_member(U_5661),U_5656),U_5655))
            | U_5663 != hAPP(hAPP(c_Set_Oinsert(U_5661),U_5656),U_5655) ) )
    & ! [U_5664,U_5662,U_5660] :
        ( ? [U_5654,U_5653] :
            ( ( U_5653 = c_Orderings_Obot__class_Obot(tc_fun(U_5660,tc_HOL_Obool))
              | U_5664 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
            & hAPP(c_Finite__Set_Ocard(U_5660),U_5653) = U_5664
            & ~ hBOOL(hAPP(hAPP(c_member(U_5660),U_5654),U_5653))
            & U_5662 = hAPP(hAPP(c_Set_Oinsert(U_5660),U_5654),U_5653) )
        | hAPP(c_Finite__Set_Ocard(U_5660),U_5662) != hAPP(c_Nat_OSuc,U_5664) ) ),
    inference(miniscope,[status(thm)],[f_1488_2]) ).

fof(f_1488_4,plain,
    ( ! [U_5665,U_5663,U_5661] :
        ( hAPP(c_Finite__Set_Ocard(U_5661),U_5663) = hAPP(c_Nat_OSuc,U_5665)
        | ! [U_5656,U_5655] :
            ( ( U_5655 != c_Orderings_Obot__class_Obot(tc_fun(U_5661,tc_HOL_Obool))
              & U_5665 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
            | hAPP(c_Finite__Set_Ocard(U_5661),U_5655) != U_5665
            | hBOOL(hAPP(hAPP(c_member(U_5661),U_5656),U_5655))
            | U_5663 != hAPP(hAPP(c_Set_Oinsert(U_5661),U_5656),U_5655) ) )
    & ! [U_5664,U_5662,U_5660] :
        ( ? [U_5653] :
            ( ( U_5653 = c_Orderings_Obot__class_Obot(tc_fun(U_5660,tc_HOL_Obool))
              | U_5664 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
            & hAPP(c_Finite__Set_Ocard(U_5660),U_5653) = U_5664
            & ~ hBOOL(hAPP(hAPP(c_member(U_5660),sK121(U_5664,U_5662,U_5660)),U_5653))
            & U_5662 = hAPP(hAPP(c_Set_Oinsert(U_5660),sK121(U_5664,U_5662,U_5660)),U_5653) )
        | hAPP(c_Finite__Set_Ocard(U_5660),U_5662) != hAPP(c_Nat_OSuc,U_5664) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK121]),skolemize(U_5654,sK121(U_5664,U_5662,U_5660))],[f_1488_3]) ).

fof(f_1488_5,plain,
    ( ! [U_5665,U_5663,U_5661] :
        ( hAPP(c_Finite__Set_Ocard(U_5661),U_5663) = hAPP(c_Nat_OSuc,U_5665)
        | ! [U_5656,U_5655] :
            ( ( U_5655 != c_Orderings_Obot__class_Obot(tc_fun(U_5661,tc_HOL_Obool))
              & U_5665 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
            | hAPP(c_Finite__Set_Ocard(U_5661),U_5655) != U_5665
            | hBOOL(hAPP(hAPP(c_member(U_5661),U_5656),U_5655))
            | U_5663 != hAPP(hAPP(c_Set_Oinsert(U_5661),U_5656),U_5655) ) )
    & ! [U_5664,U_5662,U_5660] :
        ( ( ( sK122(U_5664,U_5662,U_5660) = c_Orderings_Obot__class_Obot(tc_fun(U_5660,tc_HOL_Obool))
            | U_5664 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & hAPP(c_Finite__Set_Ocard(U_5660),sK122(U_5664,U_5662,U_5660)) = U_5664
          & ~ hBOOL(hAPP(hAPP(c_member(U_5660),sK121(U_5664,U_5662,U_5660)),sK122(U_5664,U_5662,U_5660)))
          & U_5662 = hAPP(hAPP(c_Set_Oinsert(U_5660),sK121(U_5664,U_5662,U_5660)),sK122(U_5664,U_5662,U_5660)) )
        | hAPP(c_Finite__Set_Ocard(U_5660),U_5662) != hAPP(c_Nat_OSuc,U_5664) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK122]),skolemize(U_5653,sK122(U_5664,U_5662,U_5660))],[f_1488_4]) ).

cnf(f_1488_6,plain,
    ( U_5662 = hAPP(hAPP(c_Set_Oinsert(U_5660),sK121(U_5664,U_5662,U_5660)),sK122(U_5664,U_5662,U_5660))
    | hAPP(c_Finite__Set_Ocard(U_5660),U_5662) != hAPP(c_Nat_OSuc,U_5664) ),
    inference(clausify,[status(thm)],[f_1488_5]) ).

cnf(f_1488_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_5660),sK121(U_5664,U_5662,U_5660)),sK122(U_5664,U_5662,U_5660)))
    | hAPP(c_Finite__Set_Ocard(U_5660),U_5662) != hAPP(c_Nat_OSuc,U_5664) ),
    inference(clausify,[status(thm)],[f_1488_5]) ).

cnf(f_1488_8,plain,
    ( hAPP(c_Finite__Set_Ocard(U_5660),sK122(U_5664,U_5662,U_5660)) = U_5664
    | hAPP(c_Finite__Set_Ocard(U_5660),U_5662) != hAPP(c_Nat_OSuc,U_5664) ),
    inference(clausify,[status(thm)],[f_1488_5]) ).

cnf(f_1488_9,plain,
    ( sK122(U_5664,U_5662,U_5660) = c_Orderings_Obot__class_Obot(tc_fun(U_5660,tc_HOL_Obool))
    | U_5664 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(c_Finite__Set_Ocard(U_5660),U_5662) != hAPP(c_Nat_OSuc,U_5664) ),
    inference(clausify,[status(thm)],[f_1488_5]) ).

cnf(f_1488_10,plain,
    ( U_5665 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(c_Finite__Set_Ocard(U_5661),U_5655) != U_5665
    | hBOOL(hAPP(hAPP(c_member(U_5661),U_5656),U_5655))
    | U_5663 != hAPP(hAPP(c_Set_Oinsert(U_5661),U_5656),U_5655)
    | hAPP(c_Finite__Set_Ocard(U_5661),U_5663) = hAPP(c_Nat_OSuc,U_5665) ),
    inference(clausify,[status(thm)],[f_1488_5]) ).

cnf(f_1488_11,plain,
    ( U_5655 != c_Orderings_Obot__class_Obot(tc_fun(U_5661,tc_HOL_Obool))
    | hAPP(c_Finite__Set_Ocard(U_5661),U_5655) != U_5665
    | hBOOL(hAPP(hAPP(c_member(U_5661),U_5656),U_5655))
    | U_5663 != hAPP(hAPP(c_Set_Oinsert(U_5661),U_5656),U_5655)
    | hAPP(c_Finite__Set_Ocard(U_5661),U_5663) = hAPP(c_Nat_OSuc,U_5665) ),
    inference(clausify,[status(thm)],[f_1488_5]) ).

fof(f_1489_1,plain,
    ! [V_f_2,V_A_2,V_B_2,T_b,T_c] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2)))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x)))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | ~ class_Groups_Oordered__ab__semigroup__add(T_c)
      | ~ class_Groups_Ocomm__monoid__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__mono3]) ).

fof(f_1489_2,plain,
    ! [U_5671,U_5670,U_5669,U_5668,U_5667] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5667),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5668,U_5667),U_5671),U_5670)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5668,U_5667),U_5671),U_5669)))
      | ? [U_5666] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5667),c_Groups_Ozero__class_Ozero(U_5667)),hAPP(U_5671,U_5666)))
          & hBOOL(hAPP(hAPP(c_member(U_5668),U_5666),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5668,tc_HOL_Obool)),U_5669),U_5670))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5668,tc_HOL_Obool)),U_5670),U_5669))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5668),U_5669))
      | ~ class_Groups_Oordered__ab__semigroup__add(U_5667)
      | ~ class_Groups_Ocomm__monoid__add(U_5667) ),
    inference(variable_rename,[status(thm)],[f_1489_1]) ).

fof(f_1489_3,plain,
    ! [U_5671,U_5670,U_5669,U_5668,U_5667] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5667),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5668,U_5667),U_5671),U_5670)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5668,U_5667),U_5671),U_5669)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5667),c_Groups_Ozero__class_Ozero(U_5667)),hAPP(U_5671,sK123(U_5671,U_5670,U_5669,U_5668,U_5667))))
        & hBOOL(hAPP(hAPP(c_member(U_5668),sK123(U_5671,U_5670,U_5669,U_5668,U_5667)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5668,tc_HOL_Obool)),U_5669),U_5670))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5668,tc_HOL_Obool)),U_5670),U_5669))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5668),U_5669))
      | ~ class_Groups_Oordered__ab__semigroup__add(U_5667)
      | ~ class_Groups_Ocomm__monoid__add(U_5667) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK123]),skolemize(U_5666,sK123(U_5671,U_5670,U_5669,U_5668,U_5667))],[f_1489_2]) ).

cnf(f_1489_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_5668),sK123(U_5671,U_5670,U_5669,U_5668,U_5667)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5668,tc_HOL_Obool)),U_5669),U_5670)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5667),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5668,U_5667),U_5671),U_5670)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5668,U_5667),U_5671),U_5669)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5668,tc_HOL_Obool)),U_5670),U_5669))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5668),U_5669))
    | ~ class_Groups_Oordered__ab__semigroup__add(U_5667)
    | ~ class_Groups_Ocomm__monoid__add(U_5667) ),
    inference(clausify,[status(thm)],[f_1489_3]) ).

cnf(f_1489_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5667),c_Groups_Ozero__class_Ozero(U_5667)),hAPP(U_5671,sK123(U_5671,U_5670,U_5669,U_5668,U_5667))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5667),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5668,U_5667),U_5671),U_5670)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5668,U_5667),U_5671),U_5669)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5668,tc_HOL_Obool)),U_5670),U_5669))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5668),U_5669))
    | ~ class_Groups_Oordered__ab__semigroup__add(U_5667)
    | ~ class_Groups_Ocomm__monoid__add(U_5667) ),
    inference(clausify,[status(thm)],[f_1489_3]) ).

fof(f_1490_1,plain,
    ! [V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),c_Groups_Oone__class_Oone(T_b)),V_a_2)),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),c_Groups_Oone__class_Oone(T_b)),V_a_2)),V_a_2)),c_Groups_Ozero__class_Ozero(T_b))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
      | ~ class_Rings_Olinordered__idom(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Ints__odd__less__0]) ).

fof(f_1490_2,plain,
    ! [U_5673,U_5672] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5672),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5672),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5672),c_Groups_Oone__class_Oone(U_5672)),U_5673)),U_5673)),c_Groups_Ozero__class_Ozero(U_5672)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5672),U_5673),c_Groups_Ozero__class_Ozero(U_5672))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5672),U_5673),c_Groups_Ozero__class_Ozero(U_5672)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5672),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5672),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5672),c_Groups_Oone__class_Oone(U_5672)),U_5673)),U_5673)),c_Groups_Ozero__class_Ozero(U_5672))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_5672),U_5673),c_Int_Oring__1__class_OInts(U_5672)))
      | ~ class_Rings_Olinordered__idom(U_5672) ),
    inference(variable_rename,[status(thm)],[f_1490_1]) ).

cnf(f_1490_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5672),U_5673),c_Groups_Ozero__class_Ozero(U_5672)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5672),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5672),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5672),c_Groups_Oone__class_Oone(U_5672)),U_5673)),U_5673)),c_Groups_Ozero__class_Ozero(U_5672)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_5672),U_5673),c_Int_Oring__1__class_OInts(U_5672)))
    | ~ class_Rings_Olinordered__idom(U_5672) ),
    inference(clausify,[status(thm)],[f_1490_2]) ).

cnf(f_1490_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5672),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5672),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5672),c_Groups_Oone__class_Oone(U_5672)),U_5673)),U_5673)),c_Groups_Ozero__class_Ozero(U_5672)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5672),U_5673),c_Groups_Ozero__class_Ozero(U_5672)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_5672),U_5673),c_Int_Oring__1__class_OInts(U_5672)))
    | ~ class_Rings_Olinordered__idom(U_5672) ),
    inference(clausify,[status(thm)],[f_1490_2]) ).

fof(f_1491_1,plain,
    ! [V_B_2,T_c,V_A_2,T_b] :
      ( ( hAPP(c_Finite__Set_Ocard(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) )
      & ( hAPP(c_Finite__Set_Ocard(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_card__Plus__conv__if]) ).

fof(f_1491_2,plain,
    ! [U_5677,U_5676,U_5675,U_5674] :
      ( ( hAPP(c_Finite__Set_Ocard(tc_sum(U_5674,U_5676)),c_Sum__Type_OPlus(U_5674,U_5676,U_5675,U_5677)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_5676),U_5677))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_5674),U_5675)) ) )
      & ( hAPP(c_Finite__Set_Ocard(tc_sum(U_5674,U_5676)),c_Sum__Type_OPlus(U_5674,U_5676,U_5675,U_5677)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_5674),U_5675)),hAPP(c_Finite__Set_Ocard(U_5676),U_5677))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5676),U_5677))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5674),U_5675)) ) ),
    inference(variable_rename,[status(thm)],[f_1491_1]) ).

fof(f_1491_3,plain,
    ( ! [U_5685,U_5683,U_5681,U_5679] :
        ( hAPP(c_Finite__Set_Ocard(tc_sum(U_5679,U_5683)),c_Sum__Type_OPlus(U_5679,U_5683,U_5681,U_5685)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_5683),U_5685))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_5679),U_5681)) ) )
    & ! [U_5684,U_5682,U_5680,U_5678] :
        ( hAPP(c_Finite__Set_Ocard(tc_sum(U_5678,U_5682)),c_Sum__Type_OPlus(U_5678,U_5682,U_5680,U_5684)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_5678),U_5680)),hAPP(c_Finite__Set_Ocard(U_5682),U_5684))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5682),U_5684))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5678),U_5680)) ) ),
    inference(miniscope,[status(thm)],[f_1491_2]) ).

cnf(f_1491_4,plain,
    ( hAPP(c_Finite__Set_Ocard(tc_sum(U_5678,U_5682)),c_Sum__Type_OPlus(U_5678,U_5682,U_5680,U_5684)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_5678),U_5680)),hAPP(c_Finite__Set_Ocard(U_5682),U_5684))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5682),U_5684))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5678),U_5680)) ),
    inference(clausify,[status(thm)],[f_1491_3]) ).

cnf(f_1491_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_5679),U_5681))
    | hAPP(c_Finite__Set_Ocard(tc_sum(U_5679,U_5683)),c_Sum__Type_OPlus(U_5679,U_5683,U_5681,U_5685)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1491_3]) ).

cnf(f_1491_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_5683),U_5685))
    | hAPP(c_Finite__Set_Ocard(tc_sum(U_5679,U_5683)),c_Sum__Type_OPlus(U_5679,U_5683,U_5681,U_5685)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1491_3]) ).

fof(f_1492_1,plain,
    ! [T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Int_Oring__1__class_OInts(T_b)))
      | ~ class_Rings_Oring__1(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Ints__0]) ).

fof(f_1492_2,plain,
    ! [U_5686] :
      ( hBOOL(hAPP(hAPP(c_member(U_5686),c_Groups_Ozero__class_Ozero(U_5686)),c_Int_Oring__1__class_OInts(U_5686)))
      | ~ class_Rings_Oring__1(U_5686) ),
    inference(variable_rename,[status(thm)],[f_1492_1]) ).

cnf(f_1492_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_5686),c_Groups_Ozero__class_Ozero(U_5686)),c_Int_Oring__1__class_OInts(U_5686)))
    | ~ class_Rings_Oring__1(U_5686) ),
    inference(clausify,[status(thm)],[f_1492_2]) ).

fof(f_1493_1,plain,
    ! [V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_b)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
      | ~ class_Rings_Oring__1(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Ints__add]) ).

fof(f_1493_2,plain,
    ! [U_5689,U_5688,U_5687] :
      ( hBOOL(hAPP(hAPP(c_member(U_5687),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5687),U_5688),U_5689)),c_Int_Oring__1__class_OInts(U_5687)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_5687),U_5689),c_Int_Oring__1__class_OInts(U_5687)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_5687),U_5688),c_Int_Oring__1__class_OInts(U_5687)))
      | ~ class_Rings_Oring__1(U_5687) ),
    inference(variable_rename,[status(thm)],[f_1493_1]) ).

cnf(f_1493_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_5687),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5687),U_5688),U_5689)),c_Int_Oring__1__class_OInts(U_5687)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_5687),U_5689),c_Int_Oring__1__class_OInts(U_5687)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_5687),U_5688),c_Int_Oring__1__class_OInts(U_5687)))
    | ~ class_Rings_Oring__1(U_5687) ),
    inference(clausify,[status(thm)],[f_1493_2]) ).

fof(f_1494_1,plain,
    ! [V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_b)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
      | ~ class_Rings_Oring__1(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Ints__mult]) ).

fof(f_1494_2,plain,
    ! [U_5692,U_5691,U_5690] :
      ( hBOOL(hAPP(hAPP(c_member(U_5690),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5690),U_5691),U_5692)),c_Int_Oring__1__class_OInts(U_5690)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_5690),U_5692),c_Int_Oring__1__class_OInts(U_5690)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_5690),U_5691),c_Int_Oring__1__class_OInts(U_5690)))
      | ~ class_Rings_Oring__1(U_5690) ),
    inference(variable_rename,[status(thm)],[f_1494_1]) ).

cnf(f_1494_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_5690),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5690),U_5691),U_5692)),c_Int_Oring__1__class_OInts(U_5690)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_5690),U_5692),c_Int_Oring__1__class_OInts(U_5690)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_5690),U_5691),c_Int_Oring__1__class_OInts(U_5690)))
    | ~ class_Rings_Oring__1(U_5690) ),
    inference(clausify,[status(thm)],[f_1494_2]) ).

fof(f_1495_1,plain,
    ! [V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_b)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
      | ~ class_Rings_Oring__1(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Ints__diff]) ).

fof(f_1495_2,plain,
    ! [U_5695,U_5694,U_5693] :
      ( hBOOL(hAPP(hAPP(c_member(U_5693),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5693),U_5694),U_5695)),c_Int_Oring__1__class_OInts(U_5693)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_5693),U_5695),c_Int_Oring__1__class_OInts(U_5693)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_5693),U_5694),c_Int_Oring__1__class_OInts(U_5693)))
      | ~ class_Rings_Oring__1(U_5693) ),
    inference(variable_rename,[status(thm)],[f_1495_1]) ).

cnf(f_1495_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_5693),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5693),U_5694),U_5695)),c_Int_Oring__1__class_OInts(U_5693)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_5693),U_5695),c_Int_Oring__1__class_OInts(U_5693)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_5693),U_5694),c_Int_Oring__1__class_OInts(U_5693)))
    | ~ class_Rings_Oring__1(U_5693) ),
    inference(clausify,[status(thm)],[f_1495_2]) ).

fof(f_1496_1,plain,
    ! [T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Oone__class_Oone(T_b)),c_Int_Oring__1__class_OInts(T_b)))
      | ~ class_Rings_Oring__1(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Ints__1]) ).

fof(f_1496_2,plain,
    ! [U_5696] :
      ( hBOOL(hAPP(hAPP(c_member(U_5696),c_Groups_Oone__class_Oone(U_5696)),c_Int_Oring__1__class_OInts(U_5696)))
      | ~ class_Rings_Oring__1(U_5696) ),
    inference(variable_rename,[status(thm)],[f_1496_1]) ).

cnf(f_1496_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_5696),c_Groups_Oone__class_Oone(U_5696)),c_Int_Oring__1__class_OInts(U_5696)))
    | ~ class_Rings_Oring__1(U_5696) ),
    inference(clausify,[status(thm)],[f_1496_2]) ).

fof(f_1497_1,plain,
    ! [V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),c_Int_Oring__1__class_OInts(T_b)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
      | ~ class_Rings_Oring__1(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Ints__minus]) ).

fof(f_1497_2,plain,
    ! [U_5698,U_5697] :
      ( hBOOL(hAPP(hAPP(c_member(U_5697),hAPP(c_Groups_Ouminus__class_Ouminus(U_5697),U_5698)),c_Int_Oring__1__class_OInts(U_5697)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_5697),U_5698),c_Int_Oring__1__class_OInts(U_5697)))
      | ~ class_Rings_Oring__1(U_5697) ),
    inference(variable_rename,[status(thm)],[f_1497_1]) ).

cnf(f_1497_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_5697),hAPP(c_Groups_Ouminus__class_Ouminus(U_5697),U_5698)),c_Int_Oring__1__class_OInts(U_5697)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_5697),U_5698),c_Int_Oring__1__class_OInts(U_5697)))
    | ~ class_Rings_Oring__1(U_5697) ),
    inference(clausify,[status(thm)],[f_1497_2]) ).

fof(f_1498_1,plain,
    ! [V_a_2,T_b] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
          | V_a_2 != c_Groups_Ozero__class_Ozero(T_b) )
        & ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) != c_Groups_Ozero__class_Ozero(T_b) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
      | ~ class_Int_Oring__char__0(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Ints__double__eq__0__iff]) ).

fof(f_1498_2,plain,
    ! [U_5700,U_5699] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5699),U_5700),U_5700) = c_Groups_Ozero__class_Ozero(U_5699)
          | U_5700 != c_Groups_Ozero__class_Ozero(U_5699) )
        & ( U_5700 = c_Groups_Ozero__class_Ozero(U_5699)
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5699),U_5700),U_5700) != c_Groups_Ozero__class_Ozero(U_5699) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_5699),U_5700),c_Int_Oring__1__class_OInts(U_5699)))
      | ~ class_Int_Oring__char__0(U_5699) ),
    inference(variable_rename,[status(thm)],[f_1498_1]) ).

cnf(f_1498_3,plain,
    ( U_5700 = c_Groups_Ozero__class_Ozero(U_5699)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5699),U_5700),U_5700) != c_Groups_Ozero__class_Ozero(U_5699)
    | ~ hBOOL(hAPP(hAPP(c_member(U_5699),U_5700),c_Int_Oring__1__class_OInts(U_5699)))
    | ~ class_Int_Oring__char__0(U_5699) ),
    inference(clausify,[status(thm)],[f_1498_2]) ).

cnf(f_1498_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5699),U_5700),U_5700) = c_Groups_Ozero__class_Ozero(U_5699)
    | U_5700 != c_Groups_Ozero__class_Ozero(U_5699)
    | ~ hBOOL(hAPP(hAPP(c_member(U_5699),U_5700),c_Int_Oring__1__class_OInts(U_5699)))
    | ~ class_Int_Oring__char__0(U_5699) ),
    inference(clausify,[status(thm)],[f_1498_2]) ).

fof(f_1499_1,plain,
    ! [V_B_2,V_A_2,T_c,T_b] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) )
      & ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_finite__Plus__iff]) ).

fof(f_1499_2,plain,
    ! [U_5704,U_5703,U_5702,U_5701] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_5701,U_5702)),c_Sum__Type_OPlus(U_5701,U_5702,U_5703,U_5704)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5702),U_5704))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5701),U_5703)) )
      & ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_5702),U_5704))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_5701),U_5703)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_5701,U_5702)),c_Sum__Type_OPlus(U_5701,U_5702,U_5703,U_5704))) ) ),
    inference(variable_rename,[status(thm)],[f_1499_1]) ).

fof(f_1499_3,plain,
    ( ! [U_5712,U_5710,U_5708,U_5706] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_5706,U_5708)),c_Sum__Type_OPlus(U_5706,U_5708,U_5710,U_5712)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5708),U_5712))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5706),U_5710)) )
    & ! [U_5711,U_5709,U_5707,U_5705] :
        ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_5707),U_5711))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_5705),U_5709)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_5705,U_5707)),c_Sum__Type_OPlus(U_5705,U_5707,U_5709,U_5711))) ) ),
    inference(miniscope,[status(thm)],[f_1499_2]) ).

cnf(f_1499_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_5705),U_5709))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_5705,U_5707)),c_Sum__Type_OPlus(U_5705,U_5707,U_5709,U_5711))) ),
    inference(clausify,[status(thm)],[f_1499_3]) ).

cnf(f_1499_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_5707),U_5711))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_5705,U_5707)),c_Sum__Type_OPlus(U_5705,U_5707,U_5709,U_5711))) ),
    inference(clausify,[status(thm)],[f_1499_3]) ).

cnf(f_1499_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_5706,U_5708)),c_Sum__Type_OPlus(U_5706,U_5708,U_5710,U_5712)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5708),U_5712))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5706),U_5710)) ),
    inference(clausify,[status(thm)],[f_1499_3]) ).

fof(f_1500_1,plain,
    ! [V_B_2,T_c,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__Plus]) ).

fof(f_1500_2,plain,
    ! [U_5716,U_5715,U_5714,U_5713] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_5713,U_5715)),c_Sum__Type_OPlus(U_5713,U_5715,U_5714,U_5716)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5715),U_5716))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5713),U_5714)) ),
    inference(variable_rename,[status(thm)],[f_1500_1]) ).

cnf(f_1500_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_5713,U_5715)),c_Sum__Type_OPlus(U_5713,U_5715,U_5714,U_5716)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5715),U_5716))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5713),U_5714)) ),
    inference(clausify,[status(thm)],[f_1500_2]) ).

fof(f_1501_1,plain,
    ! [V_B_2,V_A_2,T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2))) ),
    inference(fof_nnf,[status(thm)],[fact_finite__PlusD_I1_J]) ).

fof(f_1501_2,plain,
    ! [U_5720,U_5719,U_5718,U_5717] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_5717),U_5719))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_5717,U_5718)),c_Sum__Type_OPlus(U_5717,U_5718,U_5719,U_5720))) ),
    inference(variable_rename,[status(thm)],[f_1501_1]) ).

cnf(f_1501_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_5717),U_5719))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_5717,U_5718)),c_Sum__Type_OPlus(U_5717,U_5718,U_5719,U_5720))) ),
    inference(clausify,[status(thm)],[f_1501_2]) ).

fof(f_1502_1,plain,
    ! [V_B_2,V_A_2,T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2))) ),
    inference(fof_nnf,[status(thm)],[fact_finite__PlusD_I2_J]) ).

fof(f_1502_2,plain,
    ! [U_5724,U_5723,U_5722,U_5721] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_5722),U_5724))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_5721,U_5722)),c_Sum__Type_OPlus(U_5721,U_5722,U_5723,U_5724))) ),
    inference(variable_rename,[status(thm)],[f_1502_1]) ).

fof(f_1502_3,plain,
    ! [U_5724,U_5723,U_5722] :
      ( ! [U_5721] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_5721,U_5722)),c_Sum__Type_OPlus(U_5721,U_5722,U_5723,U_5724)))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_5722),U_5724)) ),
    inference(miniscope,[status(thm)],[f_1502_2]) ).

cnf(f_1502_4,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_5721,U_5722)),c_Sum__Type_OPlus(U_5721,U_5722,U_5723,U_5724)))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_5722),U_5724)) ),
    inference(clausify,[status(thm)],[f_1502_3]) ).

fof(f_1503_1,plain,
    ! [V_B_2,T_c,V_A_2,T_b] :
      ( hAPP(c_Finite__Set_Ocard(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__Plus]) ).

fof(f_1503_2,plain,
    ! [U_5728,U_5727,U_5726,U_5725] :
      ( hAPP(c_Finite__Set_Ocard(tc_sum(U_5725,U_5727)),c_Sum__Type_OPlus(U_5725,U_5727,U_5726,U_5728)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_5725),U_5726)),hAPP(c_Finite__Set_Ocard(U_5727),U_5728))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5727),U_5728))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5725),U_5726)) ),
    inference(variable_rename,[status(thm)],[f_1503_1]) ).

cnf(f_1503_3,plain,
    ( hAPP(c_Finite__Set_Ocard(tc_sum(U_5725,U_5727)),c_Sum__Type_OPlus(U_5725,U_5727,U_5726,U_5728)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_5725),U_5726)),hAPP(c_Finite__Set_Ocard(U_5727),U_5728))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5727),U_5728))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5725),U_5726)) ),
    inference(clausify,[status(thm)],[f_1503_2]) ).

fof(f_1504_1,plain,
    ! [V_a_2,T_b] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),c_Groups_Oone__class_Oone(T_b)),V_a_2)),V_a_2) != c_Groups_Ozero__class_Ozero(T_b)
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
      | ~ class_Int_Oring__char__0(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Ints__odd__nonzero]) ).

fof(f_1504_2,plain,
    ! [U_5730,U_5729] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5729),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5729),c_Groups_Oone__class_Oone(U_5729)),U_5730)),U_5730) != c_Groups_Ozero__class_Ozero(U_5729)
      | ~ hBOOL(hAPP(hAPP(c_member(U_5729),U_5730),c_Int_Oring__1__class_OInts(U_5729)))
      | ~ class_Int_Oring__char__0(U_5729) ),
    inference(variable_rename,[status(thm)],[f_1504_1]) ).

cnf(f_1504_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5729),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5729),c_Groups_Oone__class_Oone(U_5729)),U_5730)),U_5730) != c_Groups_Ozero__class_Ozero(U_5729)
    | ~ hBOOL(hAPP(hAPP(c_member(U_5729),U_5730),c_Int_Oring__1__class_OInts(U_5729)))
    | ~ class_Int_Oring__char__0(U_5729) ),
    inference(clausify,[status(thm)],[f_1504_2]) ).

fof(f_1505_1,plain,
    ! [T_c,T_b] : c_Sum__Type_OPlus(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(T_b,T_c),tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_UNIV__Plus__UNIV]) ).

fof(f_1505_2,plain,
    ! [U_5732,U_5731] : c_Sum__Type_OPlus(U_5731,U_5732,c_Orderings_Otop__class_Otop(tc_fun(U_5731,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_5732,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_5731,U_5732),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_1505_1]) ).

cnf(f_1505_3,plain,
    c_Sum__Type_OPlus(U_5731,U_5732,c_Orderings_Otop__class_Otop(tc_fun(U_5731,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_5732,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_5731,U_5732),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_1505_2]) ).

fof(f_1506_1,plain,
    ! [V_B_2,V_A_2,T_c,T_b] :
      ( ( c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(T_b,T_c),tc_HOL_Obool))
        | V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
        | V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
      & ( ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
          & V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
        | c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(tc_sum(T_b,T_c),tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Plus__eq__empty__conv]) ).

fof(f_1506_2,plain,
    ! [U_5736,U_5735,U_5734,U_5733] :
      ( ( c_Sum__Type_OPlus(U_5733,U_5734,U_5735,U_5736) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_5733,U_5734),tc_HOL_Obool))
        | U_5736 != c_Orderings_Obot__class_Obot(tc_fun(U_5734,tc_HOL_Obool))
        | U_5735 != c_Orderings_Obot__class_Obot(tc_fun(U_5733,tc_HOL_Obool)) )
      & ( ( U_5736 = c_Orderings_Obot__class_Obot(tc_fun(U_5734,tc_HOL_Obool))
          & U_5735 = c_Orderings_Obot__class_Obot(tc_fun(U_5733,tc_HOL_Obool)) )
        | c_Sum__Type_OPlus(U_5733,U_5734,U_5735,U_5736) != c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_5733,U_5734),tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_1506_1]) ).

fof(f_1506_3,plain,
    ( ! [U_5744,U_5742,U_5740,U_5738] :
        ( c_Sum__Type_OPlus(U_5738,U_5740,U_5742,U_5744) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_5738,U_5740),tc_HOL_Obool))
        | U_5744 != c_Orderings_Obot__class_Obot(tc_fun(U_5740,tc_HOL_Obool))
        | U_5742 != c_Orderings_Obot__class_Obot(tc_fun(U_5738,tc_HOL_Obool)) )
    & ! [U_5743,U_5741,U_5739,U_5737] :
        ( ( U_5743 = c_Orderings_Obot__class_Obot(tc_fun(U_5739,tc_HOL_Obool))
          & U_5741 = c_Orderings_Obot__class_Obot(tc_fun(U_5737,tc_HOL_Obool)) )
        | c_Sum__Type_OPlus(U_5737,U_5739,U_5741,U_5743) != c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_5737,U_5739),tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_1506_2]) ).

cnf(f_1506_4,plain,
    ( U_5741 = c_Orderings_Obot__class_Obot(tc_fun(U_5737,tc_HOL_Obool))
    | c_Sum__Type_OPlus(U_5737,U_5739,U_5741,U_5743) != c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_5737,U_5739),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_1506_3]) ).

cnf(f_1506_5,plain,
    ( U_5743 = c_Orderings_Obot__class_Obot(tc_fun(U_5739,tc_HOL_Obool))
    | c_Sum__Type_OPlus(U_5737,U_5739,U_5741,U_5743) != c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_5737,U_5739),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_1506_3]) ).

cnf(f_1506_6,plain,
    ( c_Sum__Type_OPlus(U_5738,U_5740,U_5742,U_5744) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_5738,U_5740),tc_HOL_Obool))
    | U_5744 != c_Orderings_Obot__class_Obot(tc_fun(U_5740,tc_HOL_Obool))
    | U_5742 != c_Orderings_Obot__class_Obot(tc_fun(U_5738,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_1506_3]) ).

fof(f_1507_1,plain,
    ! [V_a_2,V_f_2,V_A_2,T_b,T_c] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)
          | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2))
          | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) )
      | hAPP(V_f_2,V_a_2) = c_Groups_Ozero__class_Ozero(T_c)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Fields_Ofield(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__diff1]) ).

fof(f_1507_2,plain,
    ! [U_5749,U_5748,U_5747,U_5746,U_5745] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5746,U_5745),U_5748),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5746,tc_HOL_Obool)),U_5747),hAPP(hAPP(c_Set_Oinsert(U_5746),U_5749),c_Orderings_Obot__class_Obot(tc_fun(U_5746,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5746,U_5745),U_5748),U_5747)
          | hBOOL(hAPP(hAPP(c_member(U_5746),U_5749),U_5747)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5746,U_5745),U_5748),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5746,tc_HOL_Obool)),U_5747),hAPP(hAPP(c_Set_Oinsert(U_5746),U_5749),c_Orderings_Obot__class_Obot(tc_fun(U_5746,tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5745),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5746,U_5745),U_5748),U_5747)),hAPP(U_5748,U_5749))
          | ~ hBOOL(hAPP(hAPP(c_member(U_5746),U_5749),U_5747)) ) )
      | hAPP(U_5748,U_5749) = c_Groups_Ozero__class_Ozero(U_5745)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5746),U_5747))
      | ~ class_Fields_Ofield(U_5745) ),
    inference(variable_rename,[status(thm)],[f_1507_1]) ).

cnf(f_1507_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5746,U_5745),U_5748),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5746,tc_HOL_Obool)),U_5747),hAPP(hAPP(c_Set_Oinsert(U_5746),U_5749),c_Orderings_Obot__class_Obot(tc_fun(U_5746,tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5745),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5746,U_5745),U_5748),U_5747)),hAPP(U_5748,U_5749))
    | ~ hBOOL(hAPP(hAPP(c_member(U_5746),U_5749),U_5747))
    | hAPP(U_5748,U_5749) = c_Groups_Ozero__class_Ozero(U_5745)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5746),U_5747))
    | ~ class_Fields_Ofield(U_5745) ),
    inference(clausify,[status(thm)],[f_1507_2]) ).

cnf(f_1507_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5746,U_5745),U_5748),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5746,tc_HOL_Obool)),U_5747),hAPP(hAPP(c_Set_Oinsert(U_5746),U_5749),c_Orderings_Obot__class_Obot(tc_fun(U_5746,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5746,U_5745),U_5748),U_5747)
    | hBOOL(hAPP(hAPP(c_member(U_5746),U_5749),U_5747))
    | hAPP(U_5748,U_5749) = c_Groups_Ozero__class_Ozero(U_5745)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5746),U_5747))
    | ~ class_Fields_Ofield(U_5745) ),
    inference(clausify,[status(thm)],[f_1507_2]) ).

fof(f_1508_1,plain,
    ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_A_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_B_2))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_fold__Un__disjoint]) ).

fof(f_1508_2,plain,
    ! [U_5754,U_5753,U_5752,U_5751,U_5750] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5750,U_5751,c_Groups_Otimes__class_Otimes(U_5750)),U_5754),c_Groups_Oone__class_Oone(U_5750)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5751,tc_HOL_Obool)),U_5752),U_5753)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5750),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5750,U_5751,c_Groups_Otimes__class_Otimes(U_5750)),U_5754),c_Groups_Oone__class_Oone(U_5750)),U_5752)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5750,U_5751,c_Groups_Otimes__class_Otimes(U_5750)),U_5754),c_Groups_Oone__class_Oone(U_5750)),U_5753))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5751,tc_HOL_Obool)),U_5752),U_5753) != c_Orderings_Obot__class_Obot(tc_fun(U_5751,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5751),U_5753))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5751),U_5752))
      | ~ class_Groups_Ocomm__monoid__mult(U_5750) ),
    inference(variable_rename,[status(thm)],[f_1508_1]) ).

cnf(f_1508_3,plain,
    ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5750,U_5751,c_Groups_Otimes__class_Otimes(U_5750)),U_5754),c_Groups_Oone__class_Oone(U_5750)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5751,tc_HOL_Obool)),U_5752),U_5753)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5750),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5750,U_5751,c_Groups_Otimes__class_Otimes(U_5750)),U_5754),c_Groups_Oone__class_Oone(U_5750)),U_5752)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5750,U_5751,c_Groups_Otimes__class_Otimes(U_5750)),U_5754),c_Groups_Oone__class_Oone(U_5750)),U_5753))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5751,tc_HOL_Obool)),U_5752),U_5753) != c_Orderings_Obot__class_Obot(tc_fun(U_5751,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5751),U_5753))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5751),U_5752))
    | ~ class_Groups_Ocomm__monoid__mult(U_5750) ),
    inference(clausify,[status(thm)],[f_1508_2]) ).

fof(f_1509_1,plain,
    ! [V_n_2,V_P_2] :
      ( ? [B_k] :
          ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_k),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
          & ! [B_i] :
              ( ~ hBOOL(hAPP(V_P_2,B_i))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_k)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_k),V_n_2)) )
      | ~ hBOOL(hAPP(V_P_2,V_n_2))
      | hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(fof_nnf,[status(thm)],[fact_ex__least__nat__less]) ).

fof(f_1509_2,plain,
    ! [U_5758,U_5757] :
      ( ? [U_5756] :
          ( hBOOL(hAPP(U_5757,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5756),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
          & ! [U_5755] :
              ( ~ hBOOL(hAPP(U_5757,U_5755))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5755),U_5756)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5756),U_5758)) )
      | ~ hBOOL(hAPP(U_5757,U_5758))
      | hBOOL(hAPP(U_5757,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(variable_rename,[status(thm)],[f_1509_1]) ).

fof(f_1509_3,plain,
    ! [U_5758,U_5757] :
      ( ( hBOOL(hAPP(U_5757,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK124(U_5758,U_5757)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        & ! [U_5755] :
            ( ~ hBOOL(hAPP(U_5757,U_5755))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5755),sK124(U_5758,U_5757))) )
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK124(U_5758,U_5757)),U_5758)) )
      | ~ hBOOL(hAPP(U_5757,U_5758))
      | hBOOL(hAPP(U_5757,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK124]),skolemize(U_5756,sK124(U_5758,U_5757))],[f_1509_2]) ).

cnf(f_1509_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK124(U_5758,U_5757)),U_5758))
    | ~ hBOOL(hAPP(U_5757,U_5758))
    | hBOOL(hAPP(U_5757,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(clausify,[status(thm)],[f_1509_3]) ).

cnf(f_1509_5,plain,
    ( ~ hBOOL(hAPP(U_5757,U_5755))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5755),sK124(U_5758,U_5757)))
    | ~ hBOOL(hAPP(U_5757,U_5758))
    | hBOOL(hAPP(U_5757,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(clausify,[status(thm)],[f_1509_3]) ).

cnf(f_1509_6,plain,
    ( hBOOL(hAPP(U_5757,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK124(U_5758,U_5757)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | ~ hBOOL(hAPP(U_5757,U_5758))
    | hBOOL(hAPP(U_5757,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(clausify,[status(thm)],[f_1509_3]) ).

fof(f_1510_1,plain,
    ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_T_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_S_2)
      | ? [B_x] :
          ( hAPP(V_f_2,B_x) != c_Groups_Oone__class_Oone(T_c)
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_T_2),V_S_2))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__mono__one__right]) ).

fof(f_1510_2,plain,
    ! [U_5764,U_5763,U_5762,U_5761,U_5760] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5761,U_5760),U_5764),U_5762) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5761,U_5760),U_5764),U_5763)
      | ? [U_5759] :
          ( hAPP(U_5764,U_5759) != c_Groups_Oone__class_Oone(U_5760)
          & hBOOL(hAPP(hAPP(c_member(U_5761),U_5759),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5761,tc_HOL_Obool)),U_5762),U_5763))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5761,tc_HOL_Obool)),U_5763),U_5762))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5761),U_5762))
      | ~ class_Groups_Ocomm__monoid__mult(U_5760) ),
    inference(variable_rename,[status(thm)],[f_1510_1]) ).

fof(f_1510_3,plain,
    ! [U_5764,U_5763,U_5762,U_5761,U_5760] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5761,U_5760),U_5764),U_5762) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5761,U_5760),U_5764),U_5763)
      | ( hAPP(U_5764,sK125(U_5764,U_5763,U_5762,U_5761,U_5760)) != c_Groups_Oone__class_Oone(U_5760)
        & hBOOL(hAPP(hAPP(c_member(U_5761),sK125(U_5764,U_5763,U_5762,U_5761,U_5760)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5761,tc_HOL_Obool)),U_5762),U_5763))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5761,tc_HOL_Obool)),U_5763),U_5762))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5761),U_5762))
      | ~ class_Groups_Ocomm__monoid__mult(U_5760) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK125]),skolemize(U_5759,sK125(U_5764,U_5763,U_5762,U_5761,U_5760))],[f_1510_2]) ).

cnf(f_1510_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_5761),sK125(U_5764,U_5763,U_5762,U_5761,U_5760)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5761,tc_HOL_Obool)),U_5762),U_5763)))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5761,U_5760),U_5764),U_5762) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5761,U_5760),U_5764),U_5763)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5761,tc_HOL_Obool)),U_5763),U_5762))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5761),U_5762))
    | ~ class_Groups_Ocomm__monoid__mult(U_5760) ),
    inference(clausify,[status(thm)],[f_1510_3]) ).

cnf(f_1510_5,plain,
    ( hAPP(U_5764,sK125(U_5764,U_5763,U_5762,U_5761,U_5760)) != c_Groups_Oone__class_Oone(U_5760)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5761,U_5760),U_5764),U_5762) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5761,U_5760),U_5764),U_5763)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5761,tc_HOL_Obool)),U_5763),U_5762))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5761),U_5762))
    | ~ class_Groups_Ocomm__monoid__mult(U_5760) ),
    inference(clausify,[status(thm)],[f_1510_3]) ).

fof(f_1511_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Rings_Odivision__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_divide__zero__left]) ).

fof(f_1511_2,plain,
    ! [U_5766,U_5765] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5765),c_Groups_Ozero__class_Ozero(U_5765)),U_5766) = c_Groups_Ozero__class_Ozero(U_5765)
      | ~ class_Rings_Odivision__ring(U_5765) ),
    inference(variable_rename,[status(thm)],[f_1511_1]) ).

cnf(f_1511_3,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5765),c_Groups_Ozero__class_Ozero(U_5765)),U_5766) = c_Groups_Ozero__class_Ozero(U_5765)
    | ~ class_Rings_Odivision__ring(U_5765) ),
    inference(clausify,[status(thm)],[f_1511_2]) ).

fof(f_1512_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Rings_Odivision__ring__inverse__zero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_divide__zero]) ).

fof(f_1512_2,plain,
    ! [U_5768,U_5767] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5767),U_5768),c_Groups_Ozero__class_Ozero(U_5767)) = c_Groups_Ozero__class_Ozero(U_5767)
      | ~ class_Rings_Odivision__ring__inverse__zero(U_5767) ),
    inference(variable_rename,[status(thm)],[f_1512_1]) ).

cnf(f_1512_3,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5767),U_5768),c_Groups_Ozero__class_Ozero(U_5767)) = c_Groups_Ozero__class_Ozero(U_5767)
    | ~ class_Rings_Odivision__ring__inverse__zero(U_5767) ),
    inference(clausify,[status(thm)],[f_1512_2]) ).

fof(f_1513_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c))
      | ~ class_Rings_Odivision__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__divide__distrib]) ).

fof(f_1513_2,plain,
    ! [U_5772,U_5771,U_5770,U_5769] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5769),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5769),U_5770),U_5771)),U_5772) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5769),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5769),U_5770),U_5772)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5769),U_5771),U_5772))
      | ~ class_Rings_Odivision__ring(U_5769) ),
    inference(variable_rename,[status(thm)],[f_1513_1]) ).

cnf(f_1513_3,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5769),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5769),U_5770),U_5771)),U_5772) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5769),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5769),U_5770),U_5772)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5769),U_5771),U_5772))
    | ~ class_Rings_Odivision__ring(U_5769) ),
    inference(clausify,[status(thm)],[f_1513_2]) ).

fof(f_1514_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c)
      | ~ class_Rings_Odivision__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_times__divide__eq__right]) ).

fof(f_1514_2,plain,
    ! [U_5776,U_5775,U_5774,U_5773] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5773),U_5774),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5773),U_5775),U_5776)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5773),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5773),U_5774),U_5775)),U_5776)
      | ~ class_Rings_Odivision__ring(U_5773) ),
    inference(variable_rename,[status(thm)],[f_1514_1]) ).

cnf(f_1514_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5773),U_5774),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5773),U_5775),U_5776)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5773),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5773),U_5774),U_5775)),U_5776)
    | ~ class_Rings_Odivision__ring(U_5773) ),
    inference(clausify,[status(thm)],[f_1514_2]) ).

fof(f_1515_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c))
      | ~ class_Rings_Odivision__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_diff__divide__distrib]) ).

fof(f_1515_2,plain,
    ! [U_5780,U_5779,U_5778,U_5777] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5777),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5777),U_5778),U_5779)),U_5780) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5777),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5777),U_5778),U_5780)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5777),U_5779),U_5780))
      | ~ class_Rings_Odivision__ring(U_5777) ),
    inference(variable_rename,[status(thm)],[f_1515_1]) ).

cnf(f_1515_3,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5777),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5777),U_5778),U_5779)),U_5780) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5777),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5777),U_5778),U_5780)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5777),U_5779),U_5780))
    | ~ class_Rings_Odivision__ring(U_5777) ),
    inference(clausify,[status(thm)],[f_1515_2]) ).

fof(f_1516_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a
      | ~ class_Rings_Odivision__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_divide__1]) ).

fof(f_1516_2,plain,
    ! [U_5782,U_5781] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5781),U_5782),c_Groups_Oone__class_Oone(U_5781)) = U_5782
      | ~ class_Rings_Odivision__ring(U_5781) ),
    inference(variable_rename,[status(thm)],[f_1516_1]) ).

cnf(f_1516_3,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5781),U_5782),c_Groups_Oone__class_Oone(U_5781)) = U_5782
    | ~ class_Rings_Odivision__ring(U_5781) ),
    inference(clausify,[status(thm)],[f_1516_2]) ).

fof(f_1517_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)
      | ~ class_Rings_Odivision__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_minus__divide__left]) ).

fof(f_1517_2,plain,
    ! [U_5785,U_5784,U_5783] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5783),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5783),U_5784),U_5785)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5783),hAPP(c_Groups_Ouminus__class_Ouminus(U_5783),U_5784)),U_5785)
      | ~ class_Rings_Odivision__ring(U_5783) ),
    inference(variable_rename,[status(thm)],[f_1517_1]) ).

cnf(f_1517_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5783),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5783),U_5784),U_5785)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5783),hAPP(c_Groups_Ouminus__class_Ouminus(U_5783),U_5784)),U_5785)
    | ~ class_Rings_Odivision__ring(U_5783) ),
    inference(clausify,[status(thm)],[f_1517_2]) ).

fof(f_1518_1,plain,
    ! [V_z_2,V_g_2,V_f_2,T_c,T_b] : hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2),V_z_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_z_2,
    inference(fof_nnf,[status(thm)],[fact_fold__image__empty]) ).

fof(f_1518_2,plain,
    ! [U_5790,U_5789,U_5788,U_5787,U_5786] : hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5786,U_5787,U_5788),U_5789),U_5790),c_Orderings_Obot__class_Obot(tc_fun(U_5787,tc_HOL_Obool))) = U_5790,
    inference(variable_rename,[status(thm)],[f_1518_1]) ).

cnf(f_1518_3,plain,
    hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5786,U_5787,U_5788),U_5789),U_5790),c_Orderings_Obot__class_Obot(tc_fun(U_5787,tc_HOL_Obool))) = U_5790,
    inference(clausify,[status(thm)],[f_1518_2]) ).

fof(f_1519_1,plain,
    ! [V_b_2,V_a_2,V_c_2,T_b] :
      ( ( ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) != V_b_2 )
        & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) = V_b_2
          | V_a_2 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) ) )
      | V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
      | ~ class_Rings_Odivision__ring(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_nonzero__eq__divide__eq]) ).

fof(f_1519_2,plain,
    ! [U_5794,U_5793,U_5792,U_5791] :
      ( ( ( U_5793 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5791),U_5794),U_5792)
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5791),U_5793),U_5792) != U_5794 )
        & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5791),U_5793),U_5792) = U_5794
          | U_5793 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5791),U_5794),U_5792) ) )
      | U_5792 = c_Groups_Ozero__class_Ozero(U_5791)
      | ~ class_Rings_Odivision__ring(U_5791) ),
    inference(variable_rename,[status(thm)],[f_1519_1]) ).

cnf(f_1519_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5791),U_5793),U_5792) = U_5794
    | U_5793 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5791),U_5794),U_5792)
    | U_5792 = c_Groups_Ozero__class_Ozero(U_5791)
    | ~ class_Rings_Odivision__ring(U_5791) ),
    inference(clausify,[status(thm)],[f_1519_2]) ).

cnf(f_1519_4,plain,
    ( U_5793 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5791),U_5794),U_5792)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5791),U_5793),U_5792) != U_5794
    | U_5792 = c_Groups_Ozero__class_Ozero(U_5791)
    | ~ class_Rings_Odivision__ring(U_5791) ),
    inference(clausify,[status(thm)],[f_1519_2]) ).

fof(f_1520_1,plain,
    ! [V_a_2,V_b_2,V_c_2,T_b] :
      ( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) = V_a_2
          | V_b_2 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) )
        & ( V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)
          | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) != V_a_2 ) )
      | V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
      | ~ class_Rings_Odivision__ring(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_nonzero__divide__eq__eq]) ).

fof(f_1520_2,plain,
    ! [U_5798,U_5797,U_5796,U_5795] :
      ( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5795),U_5797),U_5796) = U_5798
          | U_5797 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5795),U_5798),U_5796) )
        & ( U_5797 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5795),U_5798),U_5796)
          | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5795),U_5797),U_5796) != U_5798 ) )
      | U_5796 = c_Groups_Ozero__class_Ozero(U_5795)
      | ~ class_Rings_Odivision__ring(U_5795) ),
    inference(variable_rename,[status(thm)],[f_1520_1]) ).

cnf(f_1520_3,plain,
    ( U_5797 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5795),U_5798),U_5796)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5795),U_5797),U_5796) != U_5798
    | U_5796 = c_Groups_Ozero__class_Ozero(U_5795)
    | ~ class_Rings_Odivision__ring(U_5795) ),
    inference(clausify,[status(thm)],[f_1520_2]) ).

cnf(f_1520_4,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5795),U_5797),U_5796) = U_5798
    | U_5797 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5795),U_5798),U_5796)
    | U_5796 = c_Groups_Ozero__class_Ozero(U_5795)
    | ~ class_Rings_Odivision__ring(U_5795) ),
    inference(clausify,[status(thm)],[f_1520_2]) ).

fof(f_1521_1,plain,
    ! [V_a,V_b,V_c,T_a] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) = V_a
      | V_b != hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)
      | V_c = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Rings_Odivision__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_divide__eq__imp]) ).

fof(f_1521_2,plain,
    ! [U_5802,U_5801,U_5800,U_5799] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5799),U_5801),U_5800) = U_5802
      | U_5801 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5799),U_5802),U_5800)
      | U_5800 = c_Groups_Ozero__class_Ozero(U_5799)
      | ~ class_Rings_Odivision__ring(U_5799) ),
    inference(variable_rename,[status(thm)],[f_1521_1]) ).

cnf(f_1521_3,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5799),U_5801),U_5800) = U_5802
    | U_5801 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5799),U_5802),U_5800)
    | U_5800 = c_Groups_Ozero__class_Ozero(U_5799)
    | ~ class_Rings_Odivision__ring(U_5799) ),
    inference(clausify,[status(thm)],[f_1521_2]) ).

fof(f_1522_1,plain,
    ! [V_b,V_a,V_c,T_a] :
      ( V_a = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) != V_b
      | V_c = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Rings_Odivision__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_eq__divide__imp]) ).

fof(f_1522_2,plain,
    ! [U_5806,U_5805,U_5804,U_5803] :
      ( U_5805 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5803),U_5806),U_5804)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5803),U_5805),U_5804) != U_5806
      | U_5804 = c_Groups_Ozero__class_Ozero(U_5803)
      | ~ class_Rings_Odivision__ring(U_5803) ),
    inference(variable_rename,[status(thm)],[f_1522_1]) ).

cnf(f_1522_3,plain,
    ( U_5805 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5803),U_5806),U_5804)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5803),U_5805),U_5804) != U_5806
    | U_5804 = c_Groups_Ozero__class_Ozero(U_5803)
    | ~ class_Rings_Odivision__ring(U_5803) ),
    inference(clausify,[status(thm)],[f_1522_2]) ).

fof(f_1523_1,plain,
    ! [V_a_2,V_b_2,T_b] :
      ( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2) = c_Groups_Oone__class_Oone(T_b)
          | V_a_2 != V_b_2 )
        & ( V_a_2 = V_b_2
          | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2) != c_Groups_Oone__class_Oone(T_b) ) )
      | V_b_2 = c_Groups_Ozero__class_Ozero(T_b)
      | ~ class_Rings_Odivision__ring(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_right__inverse__eq]) ).

fof(f_1523_2,plain,
    ! [U_5809,U_5808,U_5807] :
      ( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5807),U_5809),U_5808) = c_Groups_Oone__class_Oone(U_5807)
          | U_5809 != U_5808 )
        & ( U_5809 = U_5808
          | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5807),U_5809),U_5808) != c_Groups_Oone__class_Oone(U_5807) ) )
      | U_5808 = c_Groups_Ozero__class_Ozero(U_5807)
      | ~ class_Rings_Odivision__ring(U_5807) ),
    inference(variable_rename,[status(thm)],[f_1523_1]) ).

cnf(f_1523_3,plain,
    ( U_5809 = U_5808
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5807),U_5809),U_5808) != c_Groups_Oone__class_Oone(U_5807)
    | U_5808 = c_Groups_Ozero__class_Ozero(U_5807)
    | ~ class_Rings_Odivision__ring(U_5807) ),
    inference(clausify,[status(thm)],[f_1523_2]) ).

cnf(f_1523_4,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5807),U_5809),U_5808) = c_Groups_Oone__class_Oone(U_5807)
    | U_5809 != U_5808
    | U_5808 = c_Groups_Ozero__class_Ozero(U_5807)
    | ~ class_Rings_Odivision__ring(U_5807) ),
    inference(clausify,[status(thm)],[f_1523_2]) ).

fof(f_1524_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a)
      | V_a = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Rings_Odivision__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_divide__self]) ).

fof(f_1524_2,plain,
    ! [U_5811,U_5810] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5810),U_5811),U_5811) = c_Groups_Oone__class_Oone(U_5810)
      | U_5811 = c_Groups_Ozero__class_Ozero(U_5810)
      | ~ class_Rings_Odivision__ring(U_5810) ),
    inference(variable_rename,[status(thm)],[f_1524_1]) ).

cnf(f_1524_3,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5810),U_5811),U_5811) = c_Groups_Oone__class_Oone(U_5810)
    | U_5811 = c_Groups_Ozero__class_Ozero(U_5810)
    | ~ class_Rings_Odivision__ring(U_5810) ),
    inference(clausify,[status(thm)],[f_1524_2]) ).

fof(f_1525_1,plain,
    ! [V_a,T_a] :
      ( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a)
          | V_a = c_Groups_Ozero__class_Ozero(T_a) )
        & ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a)
          | V_a != c_Groups_Ozero__class_Ozero(T_a) ) )
      | ~ class_Rings_Odivision__ring__inverse__zero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_divide__self__if]) ).

fof(f_1525_2,plain,
    ! [U_5813,U_5812] :
      ( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5812),U_5813),U_5813) = c_Groups_Oone__class_Oone(U_5812)
          | U_5813 = c_Groups_Ozero__class_Ozero(U_5812) )
        & ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5812),U_5813),U_5813) = c_Groups_Ozero__class_Ozero(U_5812)
          | U_5813 != c_Groups_Ozero__class_Ozero(U_5812) ) )
      | ~ class_Rings_Odivision__ring__inverse__zero(U_5812) ),
    inference(variable_rename,[status(thm)],[f_1525_1]) ).

cnf(f_1525_3,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5812),U_5813),U_5813) = c_Groups_Ozero__class_Ozero(U_5812)
    | U_5813 != c_Groups_Ozero__class_Ozero(U_5812)
    | ~ class_Rings_Odivision__ring__inverse__zero(U_5812) ),
    inference(clausify,[status(thm)],[f_1525_2]) ).

cnf(f_1525_4,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5812),U_5813),U_5813) = c_Groups_Oone__class_Oone(U_5812)
    | U_5813 = c_Groups_Ozero__class_Ozero(U_5812)
    | ~ class_Rings_Odivision__ring__inverse__zero(U_5812) ),
    inference(clausify,[status(thm)],[f_1525_2]) ).

fof(f_1526_1,plain,
    ! [V_a,V_b,T_a] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b))
      | V_b = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Rings_Odivision__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_nonzero__minus__divide__right]) ).

fof(f_1526_2,plain,
    ! [U_5816,U_5815,U_5814] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5814),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5814),U_5816),U_5815)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5814),U_5816),hAPP(c_Groups_Ouminus__class_Ouminus(U_5814),U_5815))
      | U_5815 = c_Groups_Ozero__class_Ozero(U_5814)
      | ~ class_Rings_Odivision__ring(U_5814) ),
    inference(variable_rename,[status(thm)],[f_1526_1]) ).

cnf(f_1526_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5814),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5814),U_5816),U_5815)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5814),U_5816),hAPP(c_Groups_Ouminus__class_Ouminus(U_5814),U_5815))
    | U_5815 = c_Groups_Ozero__class_Ozero(U_5814)
    | ~ class_Rings_Odivision__ring(U_5814) ),
    inference(clausify,[status(thm)],[f_1526_2]) ).

fof(f_1527_1,plain,
    ! [V_a,V_b,T_a] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)
      | V_b = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Rings_Odivision__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_nonzero__minus__divide__divide]) ).

fof(f_1527_2,plain,
    ! [U_5819,U_5818,U_5817] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5817),hAPP(c_Groups_Ouminus__class_Ouminus(U_5817),U_5819)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5817),U_5818)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5817),U_5819),U_5818)
      | U_5818 = c_Groups_Ozero__class_Ozero(U_5817)
      | ~ class_Rings_Odivision__ring(U_5817) ),
    inference(variable_rename,[status(thm)],[f_1527_1]) ).

cnf(f_1527_3,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5817),hAPP(c_Groups_Ouminus__class_Ouminus(U_5817),U_5819)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5817),U_5818)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5817),U_5819),U_5818)
    | U_5818 = c_Groups_Ozero__class_Ozero(U_5817)
    | ~ class_Rings_Odivision__ring(U_5817) ),
    inference(clausify,[status(thm)],[f_1527_2]) ).

fof(f_1528_1,plain,
    ! [V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
      ( hAPP(V_F_2,V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2),V_z_2),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
      | ~ c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Oeq__fold__g]) ).

fof(f_1528_2,plain,
    ! [U_5826,U_5825,U_5824,U_5823,U_5822,U_5821,U_5820] :
      ( hAPP(U_5825,U_5826) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5820,U_5821,U_5822),U_5824),U_5823),U_5826)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5821),U_5826))
      | ~ c_Finite__Set_Ofolding__image__simple(U_5820,U_5821,U_5822,U_5823,U_5824,U_5825) ),
    inference(variable_rename,[status(thm)],[f_1528_1]) ).

cnf(f_1528_3,plain,
    ( hAPP(U_5825,U_5826) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5820,U_5821,U_5822),U_5824),U_5823),U_5826)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5821),U_5826))
    | ~ c_Finite__Set_Ofolding__image__simple(U_5820,U_5821,U_5822,U_5823,U_5824,U_5825) ),
    inference(clausify,[status(thm)],[f_1528_2]) ).

fof(f_1529_1,plain,
    ! [V_z_2,V_g_2,V_a_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_g_2,V_a_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),V_z_2),V_A_2))
      | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Oab__semigroup__mult(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_fold__image__insert]) ).

fof(f_1529_2,plain,
    ! [U_5832,U_5831,U_5830,U_5829,U_5828,U_5827] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5827,U_5828,c_Groups_Otimes__class_Otimes(U_5827)),U_5831),U_5832),hAPP(hAPP(c_Set_Oinsert(U_5828),U_5830),U_5829)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5827),hAPP(U_5831,U_5830)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5827,U_5828,c_Groups_Otimes__class_Otimes(U_5827)),U_5831),U_5832),U_5829))
      | hBOOL(hAPP(hAPP(c_member(U_5828),U_5830),U_5829))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5828),U_5829))
      | ~ class_Groups_Oab__semigroup__mult(U_5827) ),
    inference(variable_rename,[status(thm)],[f_1529_1]) ).

cnf(f_1529_3,plain,
    ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5827,U_5828,c_Groups_Otimes__class_Otimes(U_5827)),U_5831),U_5832),hAPP(hAPP(c_Set_Oinsert(U_5828),U_5830),U_5829)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5827),hAPP(U_5831,U_5830)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5827,U_5828,c_Groups_Otimes__class_Otimes(U_5827)),U_5831),U_5832),U_5829))
    | hBOOL(hAPP(hAPP(c_member(U_5828),U_5830),U_5829))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5828),U_5829))
    | ~ class_Groups_Oab__semigroup__mult(U_5827) ),
    inference(clausify,[status(thm)],[f_1529_2]) ).

fof(f_1530_1,plain,
    ! [V_g_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Oplus__class_Oplus(T_c)),V_g_2),c_Groups_Ozero__class_Ozero(T_c)),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Ocomm__monoid__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum_Oeq__fold]) ).

fof(f_1530_2,plain,
    ! [U_5836,U_5835,U_5834,U_5833] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5834,U_5833),U_5836),U_5835) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5833,U_5834,c_Groups_Oplus__class_Oplus(U_5833)),U_5836),c_Groups_Ozero__class_Ozero(U_5833)),U_5835)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5834),U_5835))
      | ~ class_Groups_Ocomm__monoid__add(U_5833) ),
    inference(variable_rename,[status(thm)],[f_1530_1]) ).

cnf(f_1530_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5834,U_5833),U_5836),U_5835) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5833,U_5834,c_Groups_Oplus__class_Oplus(U_5833)),U_5836),c_Groups_Ozero__class_Ozero(U_5833)),U_5835)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5834),U_5835))
    | ~ class_Groups_Ocomm__monoid__add(U_5833) ),
    inference(clausify,[status(thm)],[f_1530_2]) ).

fof(f_1531_1,plain,
    ! [V_g_2,V_A_2,T_b,T_c] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c)
          | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Oplus__class_Oplus(T_c)),V_g_2),c_Groups_Ozero__class_Ozero(T_c)),V_A_2)
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) )
      | ~ class_Groups_Ocomm__monoid__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum_OF__eq]) ).

fof(f_1531_2,plain,
    ! [U_5840,U_5839,U_5838,U_5837] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5838,U_5837),U_5840),U_5839) = c_Groups_Ozero__class_Ozero(U_5837)
          | hBOOL(hAPP(c_Finite__Set_Ofinite(U_5838),U_5839)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5838,U_5837),U_5840),U_5839) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5837,U_5838,c_Groups_Oplus__class_Oplus(U_5837)),U_5840),c_Groups_Ozero__class_Ozero(U_5837)),U_5839)
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5838),U_5839)) ) )
      | ~ class_Groups_Ocomm__monoid__add(U_5837) ),
    inference(variable_rename,[status(thm)],[f_1531_1]) ).

cnf(f_1531_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5838,U_5837),U_5840),U_5839) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5837,U_5838,c_Groups_Oplus__class_Oplus(U_5837)),U_5840),c_Groups_Ozero__class_Ozero(U_5837)),U_5839)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5838),U_5839))
    | ~ class_Groups_Ocomm__monoid__add(U_5837) ),
    inference(clausify,[status(thm)],[f_1531_2]) ).

cnf(f_1531_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_5838,U_5837),U_5840),U_5839) = c_Groups_Ozero__class_Ozero(U_5837)
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_5838),U_5839))
    | ~ class_Groups_Ocomm__monoid__add(U_5837) ),
    inference(clausify,[status(thm)],[f_1531_2]) ).

fof(f_1532_1,plain,
    ! [V_g_2,V_A_2,T_b,T_c] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = c_Groups_Oone__class_Oone(T_c)
          | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_A_2)
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) )
      | ~ class_Groups_Ocomm__monoid__mult(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setprod_OF__eq]) ).

fof(f_1532_2,plain,
    ! [U_5844,U_5843,U_5842,U_5841] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5842,U_5841),U_5844),U_5843) = c_Groups_Oone__class_Oone(U_5841)
          | hBOOL(hAPP(c_Finite__Set_Ofinite(U_5842),U_5843)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5842,U_5841),U_5844),U_5843) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5841,U_5842,c_Groups_Otimes__class_Otimes(U_5841)),U_5844),c_Groups_Oone__class_Oone(U_5841)),U_5843)
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5842),U_5843)) ) )
      | ~ class_Groups_Ocomm__monoid__mult(U_5841) ),
    inference(variable_rename,[status(thm)],[f_1532_1]) ).

cnf(f_1532_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5842,U_5841),U_5844),U_5843) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5841,U_5842,c_Groups_Otimes__class_Otimes(U_5841)),U_5844),c_Groups_Oone__class_Oone(U_5841)),U_5843)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5842),U_5843))
    | ~ class_Groups_Ocomm__monoid__mult(U_5841) ),
    inference(clausify,[status(thm)],[f_1532_2]) ).

cnf(f_1532_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5842,U_5841),U_5844),U_5843) = c_Groups_Oone__class_Oone(U_5841)
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_5842),U_5843))
    | ~ class_Groups_Ocomm__monoid__mult(U_5841) ),
    inference(clausify,[status(thm)],[f_1532_2]) ).

fof(f_1533_1,plain,
    ! [V_g_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setprod_Oeq__fold]) ).

fof(f_1533_2,plain,
    ! [U_5848,U_5847,U_5846,U_5845] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5846,U_5845),U_5848),U_5847) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5845,U_5846,c_Groups_Otimes__class_Otimes(U_5845)),U_5848),c_Groups_Oone__class_Oone(U_5845)),U_5847)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5846),U_5847))
      | ~ class_Groups_Ocomm__monoid__mult(U_5845) ),
    inference(variable_rename,[status(thm)],[f_1533_1]) ).

cnf(f_1533_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_5846,U_5845),U_5848),U_5847) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5845,U_5846,c_Groups_Otimes__class_Otimes(U_5845)),U_5848),c_Groups_Oone__class_Oone(U_5845)),U_5847)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5846),U_5847))
    | ~ class_Groups_Ocomm__monoid__mult(U_5845) ),
    inference(clausify,[status(thm)],[f_1533_2]) ).

fof(f_1534_1,plain,
    ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_A_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_fold__image__Un__Int]) ).

fof(f_1534_2,plain,
    ! [U_5853,U_5852,U_5851,U_5850,U_5849] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5849),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5849,U_5850,c_Groups_Otimes__class_Otimes(U_5849)),U_5853),c_Groups_Oone__class_Oone(U_5849)),U_5851)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5849,U_5850,c_Groups_Otimes__class_Otimes(U_5849)),U_5853),c_Groups_Oone__class_Oone(U_5849)),U_5852)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5849),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5849,U_5850,c_Groups_Otimes__class_Otimes(U_5849)),U_5853),c_Groups_Oone__class_Oone(U_5849)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5850,tc_HOL_Obool)),U_5851),U_5852))),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5849,U_5850,c_Groups_Otimes__class_Otimes(U_5849)),U_5853),c_Groups_Oone__class_Oone(U_5849)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5850,tc_HOL_Obool)),U_5851),U_5852)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5850),U_5852))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5850),U_5851))
      | ~ class_Groups_Ocomm__monoid__mult(U_5849) ),
    inference(variable_rename,[status(thm)],[f_1534_1]) ).

cnf(f_1534_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5849),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5849,U_5850,c_Groups_Otimes__class_Otimes(U_5849)),U_5853),c_Groups_Oone__class_Oone(U_5849)),U_5851)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5849,U_5850,c_Groups_Otimes__class_Otimes(U_5849)),U_5853),c_Groups_Oone__class_Oone(U_5849)),U_5852)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5849),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5849,U_5850,c_Groups_Otimes__class_Otimes(U_5849)),U_5853),c_Groups_Oone__class_Oone(U_5849)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_5850,tc_HOL_Obool)),U_5851),U_5852))),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_5849,U_5850,c_Groups_Otimes__class_Otimes(U_5849)),U_5853),c_Groups_Oone__class_Oone(U_5849)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_5850,tc_HOL_Obool)),U_5851),U_5852)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5850),U_5852))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_5850),U_5851))
    | ~ class_Groups_Ocomm__monoid__mult(U_5849) ),
    inference(clausify,[status(thm)],[f_1534_2]) ).

fof(f_1535_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
      | ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_divide__left__mono__neg]) ).

fof(f_1535_2,plain,
    ! [U_5857,U_5856,U_5855,U_5854] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5854),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5854),U_5857),U_5855)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5854),U_5857),U_5856)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5854),c_Groups_Ozero__class_Ozero(U_5854)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5854),U_5855),U_5856)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5854),U_5857),c_Groups_Ozero__class_Ozero(U_5854)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5854),U_5855),U_5856))
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5854) ),
    inference(variable_rename,[status(thm)],[f_1535_1]) ).

cnf(f_1535_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5854),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5854),U_5857),U_5855)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5854),U_5857),U_5856)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5854),c_Groups_Ozero__class_Ozero(U_5854)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5854),U_5855),U_5856)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5854),U_5857),c_Groups_Ozero__class_Ozero(U_5854)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5854),U_5855),U_5856))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5854) ),
    inference(clausify,[status(thm)],[f_1535_2]) ).

fof(f_1536_1,plain,
    ! [V_c,V_a,V_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
      | ~ class_Fields_Olinordered__field(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_divide__left__mono]) ).

fof(f_1536_2,plain,
    ! [U_5861,U_5860,U_5859,U_5858] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5858),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5858),U_5861),U_5860)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5858),U_5861),U_5859)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5858),c_Groups_Ozero__class_Ozero(U_5858)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5858),U_5860),U_5859)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5858),c_Groups_Ozero__class_Ozero(U_5858)),U_5861))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5858),U_5859),U_5860))
      | ~ class_Fields_Olinordered__field(U_5858) ),
    inference(variable_rename,[status(thm)],[f_1536_1]) ).

cnf(f_1536_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5858),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5858),U_5861),U_5860)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5858),U_5861),U_5859)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5858),c_Groups_Ozero__class_Ozero(U_5858)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5858),U_5860),U_5859)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5858),c_Groups_Ozero__class_Ozero(U_5858)),U_5861))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5858),U_5859),U_5860))
    | ~ class_Fields_Olinordered__field(U_5858) ),
    inference(clausify,[status(thm)],[f_1536_2]) ).

fof(f_1537_1,plain,
    ! [V_a_2,V_b_2,V_c_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
      | ~ class_Fields_Olinordered__field(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_neg__divide__le__eq]) ).

fof(f_1537_2,plain,
    ! [U_5865,U_5864,U_5863,U_5862] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5862),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5862),U_5864),U_5863)),U_5865))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5862),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5862),U_5865),U_5863)),U_5864)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5862),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5862),U_5865),U_5863)),U_5864))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5862),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5862),U_5864),U_5863)),U_5865)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5862),U_5863),c_Groups_Ozero__class_Ozero(U_5862)))
      | ~ class_Fields_Olinordered__field(U_5862) ),
    inference(variable_rename,[status(thm)],[f_1537_1]) ).

cnf(f_1537_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5862),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5862),U_5865),U_5863)),U_5864))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5862),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5862),U_5864),U_5863)),U_5865))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5862),U_5863),c_Groups_Ozero__class_Ozero(U_5862)))
    | ~ class_Fields_Olinordered__field(U_5862) ),
    inference(clausify,[status(thm)],[f_1537_2]) ).

cnf(f_1537_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5862),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5862),U_5864),U_5863)),U_5865))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5862),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5862),U_5865),U_5863)),U_5864))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5862),U_5863),c_Groups_Ozero__class_Ozero(U_5862)))
    | ~ class_Fields_Olinordered__field(U_5862) ),
    inference(clausify,[status(thm)],[f_1537_2]) ).

fof(f_1538_1,plain,
    ! [V_b_2,V_a_2,V_c_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
      | ~ class_Fields_Olinordered__field(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_neg__le__divide__eq]) ).

fof(f_1538_2,plain,
    ! [U_5869,U_5868,U_5867,U_5866] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5866),U_5868),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5866),U_5869),U_5867)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5866),U_5869),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5866),U_5868),U_5867))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5866),U_5869),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5866),U_5868),U_5867)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5866),U_5868),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5866),U_5869),U_5867))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5866),U_5867),c_Groups_Ozero__class_Ozero(U_5866)))
      | ~ class_Fields_Olinordered__field(U_5866) ),
    inference(variable_rename,[status(thm)],[f_1538_1]) ).

cnf(f_1538_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5866),U_5869),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5866),U_5868),U_5867)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5866),U_5868),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5866),U_5869),U_5867)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5866),U_5867),c_Groups_Ozero__class_Ozero(U_5866)))
    | ~ class_Fields_Olinordered__field(U_5866) ),
    inference(clausify,[status(thm)],[f_1538_2]) ).

cnf(f_1538_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5866),U_5868),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5866),U_5869),U_5867)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5866),U_5869),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5866),U_5868),U_5867)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5866),U_5867),c_Groups_Ozero__class_Ozero(U_5866)))
    | ~ class_Fields_Olinordered__field(U_5866) ),
    inference(clausify,[status(thm)],[f_1538_2]) ).

fof(f_1539_1,plain,
    ! [V_x,V_z,V_y,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
      | ~ class_Fields_Olinordered__field(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__imp__le__div__pos]) ).

fof(f_1539_2,plain,
    ! [U_5873,U_5872,U_5871,U_5870] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5870),U_5872),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5870),U_5873),U_5871)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5870),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5870),U_5872),U_5871)),U_5873))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5870),c_Groups_Ozero__class_Ozero(U_5870)),U_5871))
      | ~ class_Fields_Olinordered__field(U_5870) ),
    inference(variable_rename,[status(thm)],[f_1539_1]) ).

cnf(f_1539_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5870),U_5872),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5870),U_5873),U_5871)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5870),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5870),U_5872),U_5871)),U_5873))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5870),c_Groups_Ozero__class_Ozero(U_5870)),U_5871))
    | ~ class_Fields_Olinordered__field(U_5870) ),
    inference(clausify,[status(thm)],[f_1539_2]) ).

fof(f_1540_1,plain,
    ! [V_z,V_x,V_y,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),V_z))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
      | ~ class_Fields_Olinordered__field(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__imp__div__pos__le]) ).

fof(f_1540_2,plain,
    ! [U_5877,U_5876,U_5875,U_5874] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5874),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5874),U_5876),U_5875)),U_5877))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5874),U_5876),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5874),U_5877),U_5875)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5874),c_Groups_Ozero__class_Ozero(U_5874)),U_5875))
      | ~ class_Fields_Olinordered__field(U_5874) ),
    inference(variable_rename,[status(thm)],[f_1540_1]) ).

cnf(f_1540_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5874),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5874),U_5876),U_5875)),U_5877))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5874),U_5876),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5874),U_5877),U_5875)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5874),c_Groups_Ozero__class_Ozero(U_5874)),U_5875))
    | ~ class_Fields_Olinordered__field(U_5874) ),
    inference(clausify,[status(thm)],[f_1540_2]) ).

fof(f_1541_1,plain,
    ! [V_w,V_z,V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_z),V_w)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_w))
      | ~ class_Fields_Ofield__inverse__zero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_times__divide__times__eq]) ).

fof(f_1541_2,plain,
    ! [U_5882,U_5881,U_5880,U_5879,U_5878] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5878),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5878),U_5879),U_5880)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5878),U_5881),U_5882)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5878),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5878),U_5879),U_5881)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5878),U_5880),U_5882))
      | ~ class_Fields_Ofield__inverse__zero(U_5878) ),
    inference(variable_rename,[status(thm)],[f_1541_1]) ).

cnf(f_1541_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5878),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5878),U_5879),U_5880)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5878),U_5881),U_5882)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5878),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5878),U_5879),U_5881)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5878),U_5880),U_5882))
    | ~ class_Fields_Ofield__inverse__zero(U_5878) ),
    inference(clausify,[status(thm)],[f_1541_2]) ).

fof(f_1542_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)
      | ~ class_Fields_Ofield__inverse__zero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_minus__divide__divide]) ).

fof(f_1542_2,plain,
    ! [U_5885,U_5884,U_5883] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5883),hAPP(c_Groups_Ouminus__class_Ouminus(U_5883),U_5884)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5883),U_5885)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5883),U_5884),U_5885)
      | ~ class_Fields_Ofield__inverse__zero(U_5883) ),
    inference(variable_rename,[status(thm)],[f_1542_1]) ).

cnf(f_1542_3,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5883),hAPP(c_Groups_Ouminus__class_Ouminus(U_5883),U_5884)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5883),U_5885)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5883),U_5884),U_5885)
    | ~ class_Fields_Ofield__inverse__zero(U_5883) ),
    inference(clausify,[status(thm)],[f_1542_2]) ).

fof(f_1543_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b))
      | ~ class_Fields_Ofield__inverse__zero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_minus__divide__right]) ).

fof(f_1543_2,plain,
    ! [U_5888,U_5887,U_5886] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5886),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5886),U_5887),U_5888)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5886),U_5887),hAPP(c_Groups_Ouminus__class_Ouminus(U_5886),U_5888))
      | ~ class_Fields_Ofield__inverse__zero(U_5886) ),
    inference(variable_rename,[status(thm)],[f_1543_1]) ).

cnf(f_1543_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5886),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5886),U_5887),U_5888)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5886),U_5887),hAPP(c_Groups_Ouminus__class_Ouminus(U_5886),U_5888))
    | ~ class_Fields_Ofield__inverse__zero(U_5886) ),
    inference(clausify,[status(thm)],[f_1543_2]) ).

fof(f_1544_1,plain,
    ! [V_b_2,V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2))) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_zero__le__divide__iff]) ).

fof(f_1544_2,plain,
    ! [U_5891,U_5890,U_5889] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5889),c_Groups_Ozero__class_Ozero(U_5889)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5889),U_5890),U_5891)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5889),U_5891),c_Groups_Ozero__class_Ozero(U_5889)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5889),U_5890),c_Groups_Ozero__class_Ozero(U_5889))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5889),c_Groups_Ozero__class_Ozero(U_5889)),U_5891))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5889),c_Groups_Ozero__class_Ozero(U_5889)),U_5890)) ) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5889),U_5891),c_Groups_Ozero__class_Ozero(U_5889)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5889),U_5890),c_Groups_Ozero__class_Ozero(U_5889))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5889),c_Groups_Ozero__class_Ozero(U_5889)),U_5891))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5889),c_Groups_Ozero__class_Ozero(U_5889)),U_5890)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5889),c_Groups_Ozero__class_Ozero(U_5889)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5889),U_5890),U_5891))) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5889) ),
    inference(variable_rename,[status(thm)],[f_1544_1]) ).

cnf(f_1544_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5889),U_5890),c_Groups_Ozero__class_Ozero(U_5889)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5889),c_Groups_Ozero__class_Ozero(U_5889)),U_5890))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5889),c_Groups_Ozero__class_Ozero(U_5889)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5889),U_5890),U_5891)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5889) ),
    inference(clausify,[status(thm)],[f_1544_2]) ).

cnf(f_1544_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5889),U_5891),c_Groups_Ozero__class_Ozero(U_5889)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5889),c_Groups_Ozero__class_Ozero(U_5889)),U_5890))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5889),c_Groups_Ozero__class_Ozero(U_5889)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5889),U_5890),U_5891)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5889) ),
    inference(clausify,[status(thm)],[f_1544_2]) ).

cnf(f_1544_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5889),U_5890),c_Groups_Ozero__class_Ozero(U_5889)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5889),c_Groups_Ozero__class_Ozero(U_5889)),U_5891))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5889),c_Groups_Ozero__class_Ozero(U_5889)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5889),U_5890),U_5891)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5889) ),
    inference(clausify,[status(thm)],[f_1544_2]) ).

cnf(f_1544_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5889),U_5891),c_Groups_Ozero__class_Ozero(U_5889)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5889),c_Groups_Ozero__class_Ozero(U_5889)),U_5891))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5889),c_Groups_Ozero__class_Ozero(U_5889)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5889),U_5890),U_5891)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5889) ),
    inference(clausify,[status(thm)],[f_1544_2]) ).

cnf(f_1544_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5889),c_Groups_Ozero__class_Ozero(U_5889)),U_5891))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5889),c_Groups_Ozero__class_Ozero(U_5889)),U_5890))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5889),c_Groups_Ozero__class_Ozero(U_5889)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5889),U_5890),U_5891)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5889) ),
    inference(clausify,[status(thm)],[f_1544_2]) ).

cnf(f_1544_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5889),U_5891),c_Groups_Ozero__class_Ozero(U_5889)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5889),U_5890),c_Groups_Ozero__class_Ozero(U_5889)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5889),c_Groups_Ozero__class_Ozero(U_5889)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5889),U_5890),U_5891)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5889) ),
    inference(clausify,[status(thm)],[f_1544_2]) ).

fof(f_1545_1,plain,
    ! [V_b_2,V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_divide__le__0__iff]) ).

fof(f_1545_2,plain,
    ! [U_5894,U_5893,U_5892] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5892),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5892),U_5893),U_5894)),c_Groups_Ozero__class_Ozero(U_5892)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5892),c_Groups_Ozero__class_Ozero(U_5892)),U_5894))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5892),U_5893),c_Groups_Ozero__class_Ozero(U_5892))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5892),U_5894),c_Groups_Ozero__class_Ozero(U_5892)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5892),c_Groups_Ozero__class_Ozero(U_5892)),U_5893)) ) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5892),c_Groups_Ozero__class_Ozero(U_5892)),U_5894))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5892),U_5893),c_Groups_Ozero__class_Ozero(U_5892))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5892),U_5894),c_Groups_Ozero__class_Ozero(U_5892)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5892),c_Groups_Ozero__class_Ozero(U_5892)),U_5893)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5892),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5892),U_5893),U_5894)),c_Groups_Ozero__class_Ozero(U_5892))) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5892) ),
    inference(variable_rename,[status(thm)],[f_1545_1]) ).

cnf(f_1545_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5892),U_5893),c_Groups_Ozero__class_Ozero(U_5892)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5892),c_Groups_Ozero__class_Ozero(U_5892)),U_5893))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5892),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5892),U_5893),U_5894)),c_Groups_Ozero__class_Ozero(U_5892)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5892) ),
    inference(clausify,[status(thm)],[f_1545_2]) ).

cnf(f_1545_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5892),c_Groups_Ozero__class_Ozero(U_5892)),U_5894))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5892),c_Groups_Ozero__class_Ozero(U_5892)),U_5893))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5892),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5892),U_5893),U_5894)),c_Groups_Ozero__class_Ozero(U_5892)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5892) ),
    inference(clausify,[status(thm)],[f_1545_2]) ).

cnf(f_1545_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5892),U_5893),c_Groups_Ozero__class_Ozero(U_5892)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5892),U_5894),c_Groups_Ozero__class_Ozero(U_5892)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5892),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5892),U_5893),U_5894)),c_Groups_Ozero__class_Ozero(U_5892)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5892) ),
    inference(clausify,[status(thm)],[f_1545_2]) ).

cnf(f_1545_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5892),c_Groups_Ozero__class_Ozero(U_5892)),U_5894))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5892),U_5894),c_Groups_Ozero__class_Ozero(U_5892)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5892),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5892),U_5893),U_5894)),c_Groups_Ozero__class_Ozero(U_5892)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5892) ),
    inference(clausify,[status(thm)],[f_1545_2]) ).

cnf(f_1545_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5892),U_5894),c_Groups_Ozero__class_Ozero(U_5892)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5892),c_Groups_Ozero__class_Ozero(U_5892)),U_5893))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5892),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5892),U_5893),U_5894)),c_Groups_Ozero__class_Ozero(U_5892)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5892) ),
    inference(clausify,[status(thm)],[f_1545_2]) ).

cnf(f_1545_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5892),c_Groups_Ozero__class_Ozero(U_5892)),U_5894))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5892),U_5893),c_Groups_Ozero__class_Ozero(U_5892)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5892),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5892),U_5893),U_5894)),c_Groups_Ozero__class_Ozero(U_5892)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5892) ),
    inference(clausify,[status(thm)],[f_1545_2]) ).

fof(f_1546_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
      | ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_divide__right__mono]) ).

fof(f_1546_2,plain,
    ! [U_5898,U_5897,U_5896,U_5895] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5895),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5895),U_5896),U_5898)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5895),U_5897),U_5898)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5895),c_Groups_Ozero__class_Ozero(U_5895)),U_5898))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5895),U_5896),U_5897))
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5895) ),
    inference(variable_rename,[status(thm)],[f_1546_1]) ).

cnf(f_1546_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5895),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5895),U_5896),U_5898)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5895),U_5897),U_5898)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5895),c_Groups_Ozero__class_Ozero(U_5895)),U_5898))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5895),U_5896),U_5897))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5895) ),
    inference(clausify,[status(thm)],[f_1546_2]) ).

fof(f_1547_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
      | ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_divide__right__mono__neg]) ).

fof(f_1547_2,plain,
    ! [U_5902,U_5901,U_5900,U_5899] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5899),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5899),U_5901),U_5902)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5899),U_5900),U_5902)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5899),U_5902),c_Groups_Ozero__class_Ozero(U_5899)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5899),U_5900),U_5901))
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5899) ),
    inference(variable_rename,[status(thm)],[f_1547_1]) ).

cnf(f_1547_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5899),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5899),U_5901),U_5902)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5899),U_5900),U_5902)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5899),U_5902),c_Groups_Ozero__class_Ozero(U_5899)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5899),U_5900),U_5901))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5899) ),
    inference(clausify,[status(thm)],[f_1547_2]) ).

fof(f_1548_1,plain,
    ! [V_c,V_a,V_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
      | ~ class_Fields_Olinordered__field(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_divide__strict__right__mono__neg]) ).

fof(f_1548_2,plain,
    ! [U_5906,U_5905,U_5904,U_5903] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5903),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5903),U_5905),U_5906)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5903),U_5904),U_5906)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5903),U_5906),c_Groups_Ozero__class_Ozero(U_5903)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5903),U_5904),U_5905))
      | ~ class_Fields_Olinordered__field(U_5903) ),
    inference(variable_rename,[status(thm)],[f_1548_1]) ).

cnf(f_1548_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5903),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5903),U_5905),U_5906)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5903),U_5904),U_5906)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5903),U_5906),c_Groups_Ozero__class_Ozero(U_5903)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5903),U_5904),U_5905))
    | ~ class_Fields_Olinordered__field(U_5903) ),
    inference(clausify,[status(thm)],[f_1548_2]) ).

fof(f_1549_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
      | ~ class_Fields_Olinordered__field(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_divide__strict__right__mono]) ).

fof(f_1549_2,plain,
    ! [U_5910,U_5909,U_5908,U_5907] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5907),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5907),U_5908),U_5910)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5907),U_5909),U_5910)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5907),c_Groups_Ozero__class_Ozero(U_5907)),U_5910))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5907),U_5908),U_5909))
      | ~ class_Fields_Olinordered__field(U_5907) ),
    inference(variable_rename,[status(thm)],[f_1549_1]) ).

cnf(f_1549_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5907),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5907),U_5908),U_5910)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5907),U_5909),U_5910)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5907),c_Groups_Ozero__class_Ozero(U_5907)),U_5910))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5907),U_5908),U_5909))
    | ~ class_Fields_Olinordered__field(U_5907) ),
    inference(clausify,[status(thm)],[f_1549_2]) ).

fof(f_1550_1,plain,
    ! [V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ class_Fields_Olinordered__field(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_divide__neg__neg]) ).

fof(f_1550_2,plain,
    ! [U_5913,U_5912,U_5911] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5911),c_Groups_Ozero__class_Ozero(U_5911)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5911),U_5912),U_5913)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5911),U_5913),c_Groups_Ozero__class_Ozero(U_5911)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5911),U_5912),c_Groups_Ozero__class_Ozero(U_5911)))
      | ~ class_Fields_Olinordered__field(U_5911) ),
    inference(variable_rename,[status(thm)],[f_1550_1]) ).

cnf(f_1550_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5911),c_Groups_Ozero__class_Ozero(U_5911)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5911),U_5912),U_5913)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5911),U_5913),c_Groups_Ozero__class_Ozero(U_5911)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5911),U_5912),c_Groups_Ozero__class_Ozero(U_5911)))
    | ~ class_Fields_Olinordered__field(U_5911) ),
    inference(clausify,[status(thm)],[f_1550_2]) ).

fof(f_1551_1,plain,
    ! [V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ class_Fields_Olinordered__field(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_divide__neg__pos]) ).

fof(f_1551_2,plain,
    ! [U_5916,U_5915,U_5914] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5914),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5914),U_5915),U_5916)),c_Groups_Ozero__class_Ozero(U_5914)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5914),c_Groups_Ozero__class_Ozero(U_5914)),U_5916))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5914),U_5915),c_Groups_Ozero__class_Ozero(U_5914)))
      | ~ class_Fields_Olinordered__field(U_5914) ),
    inference(variable_rename,[status(thm)],[f_1551_1]) ).

cnf(f_1551_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5914),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5914),U_5915),U_5916)),c_Groups_Ozero__class_Ozero(U_5914)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5914),c_Groups_Ozero__class_Ozero(U_5914)),U_5916))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5914),U_5915),c_Groups_Ozero__class_Ozero(U_5914)))
    | ~ class_Fields_Olinordered__field(U_5914) ),
    inference(clausify,[status(thm)],[f_1551_2]) ).

fof(f_1552_1,plain,
    ! [V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
      | ~ class_Fields_Olinordered__field(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_divide__pos__neg]) ).

fof(f_1552_2,plain,
    ! [U_5919,U_5918,U_5917] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5917),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5917),U_5918),U_5919)),c_Groups_Ozero__class_Ozero(U_5917)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5917),U_5919),c_Groups_Ozero__class_Ozero(U_5917)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5917),c_Groups_Ozero__class_Ozero(U_5917)),U_5918))
      | ~ class_Fields_Olinordered__field(U_5917) ),
    inference(variable_rename,[status(thm)],[f_1552_1]) ).

cnf(f_1552_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5917),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5917),U_5918),U_5919)),c_Groups_Ozero__class_Ozero(U_5917)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5917),U_5919),c_Groups_Ozero__class_Ozero(U_5917)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5917),c_Groups_Ozero__class_Ozero(U_5917)),U_5918))
    | ~ class_Fields_Olinordered__field(U_5917) ),
    inference(clausify,[status(thm)],[f_1552_2]) ).

fof(f_1553_1,plain,
    ! [V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
      | ~ class_Fields_Olinordered__field(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_divide__pos__pos]) ).

fof(f_1553_2,plain,
    ! [U_5922,U_5921,U_5920] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5920),c_Groups_Ozero__class_Ozero(U_5920)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5920),U_5921),U_5922)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5920),c_Groups_Ozero__class_Ozero(U_5920)),U_5922))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5920),c_Groups_Ozero__class_Ozero(U_5920)),U_5921))
      | ~ class_Fields_Olinordered__field(U_5920) ),
    inference(variable_rename,[status(thm)],[f_1553_1]) ).

cnf(f_1553_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5920),c_Groups_Ozero__class_Ozero(U_5920)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5920),U_5921),U_5922)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5920),c_Groups_Ozero__class_Ozero(U_5920)),U_5922))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5920),c_Groups_Ozero__class_Ozero(U_5920)),U_5921))
    | ~ class_Fields_Olinordered__field(U_5920) ),
    inference(clausify,[status(thm)],[f_1553_2]) ).

fof(f_1554_1,plain,
    ! [V_b_2,V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_divide__less__0__iff]) ).

fof(f_1554_2,plain,
    ! [U_5925,U_5924,U_5923] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5923),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5923),U_5924),U_5925)),c_Groups_Ozero__class_Ozero(U_5923)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5923),c_Groups_Ozero__class_Ozero(U_5923)),U_5925))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5923),U_5924),c_Groups_Ozero__class_Ozero(U_5923))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5923),U_5925),c_Groups_Ozero__class_Ozero(U_5923)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5923),c_Groups_Ozero__class_Ozero(U_5923)),U_5924)) ) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5923),c_Groups_Ozero__class_Ozero(U_5923)),U_5925))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5923),U_5924),c_Groups_Ozero__class_Ozero(U_5923))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5923),U_5925),c_Groups_Ozero__class_Ozero(U_5923)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5923),c_Groups_Ozero__class_Ozero(U_5923)),U_5924)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5923),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5923),U_5924),U_5925)),c_Groups_Ozero__class_Ozero(U_5923))) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5923) ),
    inference(variable_rename,[status(thm)],[f_1554_1]) ).

cnf(f_1554_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5923),U_5924),c_Groups_Ozero__class_Ozero(U_5923)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5923),c_Groups_Ozero__class_Ozero(U_5923)),U_5924))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5923),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5923),U_5924),U_5925)),c_Groups_Ozero__class_Ozero(U_5923)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5923) ),
    inference(clausify,[status(thm)],[f_1554_2]) ).

cnf(f_1554_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5923),c_Groups_Ozero__class_Ozero(U_5923)),U_5925))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5923),c_Groups_Ozero__class_Ozero(U_5923)),U_5924))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5923),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5923),U_5924),U_5925)),c_Groups_Ozero__class_Ozero(U_5923)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5923) ),
    inference(clausify,[status(thm)],[f_1554_2]) ).

cnf(f_1554_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5923),U_5924),c_Groups_Ozero__class_Ozero(U_5923)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5923),U_5925),c_Groups_Ozero__class_Ozero(U_5923)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5923),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5923),U_5924),U_5925)),c_Groups_Ozero__class_Ozero(U_5923)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5923) ),
    inference(clausify,[status(thm)],[f_1554_2]) ).

cnf(f_1554_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5923),c_Groups_Ozero__class_Ozero(U_5923)),U_5925))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5923),U_5925),c_Groups_Ozero__class_Ozero(U_5923)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5923),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5923),U_5924),U_5925)),c_Groups_Ozero__class_Ozero(U_5923)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5923) ),
    inference(clausify,[status(thm)],[f_1554_2]) ).

cnf(f_1554_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5923),U_5925),c_Groups_Ozero__class_Ozero(U_5923)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5923),c_Groups_Ozero__class_Ozero(U_5923)),U_5924))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5923),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5923),U_5924),U_5925)),c_Groups_Ozero__class_Ozero(U_5923)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5923) ),
    inference(clausify,[status(thm)],[f_1554_2]) ).

cnf(f_1554_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5923),c_Groups_Ozero__class_Ozero(U_5923)),U_5925))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5923),U_5924),c_Groups_Ozero__class_Ozero(U_5923)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5923),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5923),U_5924),U_5925)),c_Groups_Ozero__class_Ozero(U_5923)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5923) ),
    inference(clausify,[status(thm)],[f_1554_2]) ).

fof(f_1555_1,plain,
    ! [V_b_2,V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2))) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_zero__less__divide__iff]) ).

fof(f_1555_2,plain,
    ! [U_5928,U_5927,U_5926] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5926),c_Groups_Ozero__class_Ozero(U_5926)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5926),U_5927),U_5928)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5926),U_5928),c_Groups_Ozero__class_Ozero(U_5926)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5926),U_5927),c_Groups_Ozero__class_Ozero(U_5926))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5926),c_Groups_Ozero__class_Ozero(U_5926)),U_5928))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5926),c_Groups_Ozero__class_Ozero(U_5926)),U_5927)) ) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5926),U_5928),c_Groups_Ozero__class_Ozero(U_5926)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5926),U_5927),c_Groups_Ozero__class_Ozero(U_5926))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5926),c_Groups_Ozero__class_Ozero(U_5926)),U_5928))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5926),c_Groups_Ozero__class_Ozero(U_5926)),U_5927)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5926),c_Groups_Ozero__class_Ozero(U_5926)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5926),U_5927),U_5928))) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5926) ),
    inference(variable_rename,[status(thm)],[f_1555_1]) ).

cnf(f_1555_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5926),U_5927),c_Groups_Ozero__class_Ozero(U_5926)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5926),c_Groups_Ozero__class_Ozero(U_5926)),U_5927))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5926),c_Groups_Ozero__class_Ozero(U_5926)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5926),U_5927),U_5928)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5926) ),
    inference(clausify,[status(thm)],[f_1555_2]) ).

cnf(f_1555_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5926),U_5928),c_Groups_Ozero__class_Ozero(U_5926)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5926),c_Groups_Ozero__class_Ozero(U_5926)),U_5927))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5926),c_Groups_Ozero__class_Ozero(U_5926)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5926),U_5927),U_5928)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5926) ),
    inference(clausify,[status(thm)],[f_1555_2]) ).

cnf(f_1555_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5926),U_5927),c_Groups_Ozero__class_Ozero(U_5926)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5926),c_Groups_Ozero__class_Ozero(U_5926)),U_5928))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5926),c_Groups_Ozero__class_Ozero(U_5926)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5926),U_5927),U_5928)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5926) ),
    inference(clausify,[status(thm)],[f_1555_2]) ).

cnf(f_1555_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5926),U_5928),c_Groups_Ozero__class_Ozero(U_5926)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5926),c_Groups_Ozero__class_Ozero(U_5926)),U_5928))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5926),c_Groups_Ozero__class_Ozero(U_5926)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5926),U_5927),U_5928)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5926) ),
    inference(clausify,[status(thm)],[f_1555_2]) ).

cnf(f_1555_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5926),c_Groups_Ozero__class_Ozero(U_5926)),U_5928))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5926),c_Groups_Ozero__class_Ozero(U_5926)),U_5927))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5926),c_Groups_Ozero__class_Ozero(U_5926)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5926),U_5927),U_5928)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5926) ),
    inference(clausify,[status(thm)],[f_1555_2]) ).

cnf(f_1555_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5926),U_5928),c_Groups_Ozero__class_Ozero(U_5926)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5926),U_5927),c_Groups_Ozero__class_Ozero(U_5926)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5926),c_Groups_Ozero__class_Ozero(U_5926)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5926),U_5927),U_5928)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5926) ),
    inference(clausify,[status(thm)],[f_1555_2]) ).

fof(f_1556_1,plain,
    ! [V_c_2,V_b_2,V_a_2,T_b] :
      ( ( ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)
          | ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b)
            & V_c_2 = c_Groups_Ozero__class_Ozero(T_b) )
          | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) != V_b_2
            & V_c_2 != c_Groups_Ozero__class_Ozero(T_b) ) )
        & ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
              | V_c_2 != c_Groups_Ozero__class_Ozero(T_b) )
            & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) = V_b_2
              | V_c_2 = c_Groups_Ozero__class_Ozero(T_b) ) )
          | V_a_2 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) ) )
      | ~ class_Fields_Ofield__inverse__zero(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_eq__divide__eq]) ).

fof(f_1556_2,plain,
    ! [U_5932,U_5931,U_5930,U_5929] :
      ( ( ( U_5930 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5929),U_5931),U_5932)
          | ( U_5930 != c_Groups_Ozero__class_Ozero(U_5929)
            & U_5932 = c_Groups_Ozero__class_Ozero(U_5929) )
          | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5929),U_5930),U_5932) != U_5931
            & U_5932 != c_Groups_Ozero__class_Ozero(U_5929) ) )
        & ( ( ( U_5930 = c_Groups_Ozero__class_Ozero(U_5929)
              | U_5932 != c_Groups_Ozero__class_Ozero(U_5929) )
            & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5929),U_5930),U_5932) = U_5931
              | U_5932 = c_Groups_Ozero__class_Ozero(U_5929) ) )
          | U_5930 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5929),U_5931),U_5932) ) )
      | ~ class_Fields_Ofield__inverse__zero(U_5929) ),
    inference(variable_rename,[status(thm)],[f_1556_1]) ).

cnf(f_1556_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5929),U_5930),U_5932) = U_5931
    | U_5932 = c_Groups_Ozero__class_Ozero(U_5929)
    | U_5930 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5929),U_5931),U_5932)
    | ~ class_Fields_Ofield__inverse__zero(U_5929) ),
    inference(clausify,[status(thm)],[f_1556_2]) ).

cnf(f_1556_4,plain,
    ( U_5930 = c_Groups_Ozero__class_Ozero(U_5929)
    | U_5932 != c_Groups_Ozero__class_Ozero(U_5929)
    | U_5930 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5929),U_5931),U_5932)
    | ~ class_Fields_Ofield__inverse__zero(U_5929) ),
    inference(clausify,[status(thm)],[f_1556_2]) ).

cnf(f_1556_5,plain,
    ( U_5932 = c_Groups_Ozero__class_Ozero(U_5929)
    | U_5932 != c_Groups_Ozero__class_Ozero(U_5929)
    | U_5930 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5929),U_5931),U_5932)
    | ~ class_Fields_Ofield__inverse__zero(U_5929) ),
    inference(clausify,[status(thm)],[f_1556_2]) ).

cnf(f_1556_6,plain,
    ( U_5930 != c_Groups_Ozero__class_Ozero(U_5929)
    | U_5932 != c_Groups_Ozero__class_Ozero(U_5929)
    | U_5930 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5929),U_5931),U_5932)
    | ~ class_Fields_Ofield__inverse__zero(U_5929) ),
    inference(clausify,[status(thm)],[f_1556_2]) ).

cnf(f_1556_7,plain,
    ( U_5932 = c_Groups_Ozero__class_Ozero(U_5929)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5929),U_5930),U_5932) != U_5931
    | U_5930 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5929),U_5931),U_5932)
    | ~ class_Fields_Ofield__inverse__zero(U_5929) ),
    inference(clausify,[status(thm)],[f_1556_2]) ).

cnf(f_1556_8,plain,
    ( U_5930 != c_Groups_Ozero__class_Ozero(U_5929)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5929),U_5930),U_5932) != U_5931
    | U_5930 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5929),U_5931),U_5932)
    | ~ class_Fields_Ofield__inverse__zero(U_5929) ),
    inference(clausify,[status(thm)],[f_1556_2]) ).

fof(f_1557_1,plain,
    ! [V_a_2,V_c_2,V_b_2,T_b] :
      ( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) = V_a_2
          | ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b)
            & V_c_2 = c_Groups_Ozero__class_Ozero(T_b) )
          | ( V_b_2 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)
            & V_c_2 != c_Groups_Ozero__class_Ozero(T_b) ) )
        & ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
              | V_c_2 != c_Groups_Ozero__class_Ozero(T_b) )
            & ( V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)
              | V_c_2 = c_Groups_Ozero__class_Ozero(T_b) ) )
          | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) != V_a_2 ) )
      | ~ class_Fields_Ofield__inverse__zero(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_divide__eq__eq]) ).

fof(f_1557_2,plain,
    ! [U_5936,U_5935,U_5934,U_5933] :
      ( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5933),U_5934),U_5935) = U_5936
          | ( U_5936 != c_Groups_Ozero__class_Ozero(U_5933)
            & U_5935 = c_Groups_Ozero__class_Ozero(U_5933) )
          | ( U_5934 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5933),U_5936),U_5935)
            & U_5935 != c_Groups_Ozero__class_Ozero(U_5933) ) )
        & ( ( ( U_5936 = c_Groups_Ozero__class_Ozero(U_5933)
              | U_5935 != c_Groups_Ozero__class_Ozero(U_5933) )
            & ( U_5934 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5933),U_5936),U_5935)
              | U_5935 = c_Groups_Ozero__class_Ozero(U_5933) ) )
          | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5933),U_5934),U_5935) != U_5936 ) )
      | ~ class_Fields_Ofield__inverse__zero(U_5933) ),
    inference(variable_rename,[status(thm)],[f_1557_1]) ).

cnf(f_1557_3,plain,
    ( U_5934 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5933),U_5936),U_5935)
    | U_5935 = c_Groups_Ozero__class_Ozero(U_5933)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5933),U_5934),U_5935) != U_5936
    | ~ class_Fields_Ofield__inverse__zero(U_5933) ),
    inference(clausify,[status(thm)],[f_1557_2]) ).

cnf(f_1557_4,plain,
    ( U_5936 = c_Groups_Ozero__class_Ozero(U_5933)
    | U_5935 != c_Groups_Ozero__class_Ozero(U_5933)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5933),U_5934),U_5935) != U_5936
    | ~ class_Fields_Ofield__inverse__zero(U_5933) ),
    inference(clausify,[status(thm)],[f_1557_2]) ).

cnf(f_1557_5,plain,
    ( U_5935 = c_Groups_Ozero__class_Ozero(U_5933)
    | U_5935 != c_Groups_Ozero__class_Ozero(U_5933)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5933),U_5934),U_5935) = U_5936
    | ~ class_Fields_Ofield__inverse__zero(U_5933) ),
    inference(clausify,[status(thm)],[f_1557_2]) ).

cnf(f_1557_6,plain,
    ( U_5936 != c_Groups_Ozero__class_Ozero(U_5933)
    | U_5935 != c_Groups_Ozero__class_Ozero(U_5933)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5933),U_5934),U_5935) = U_5936
    | ~ class_Fields_Ofield__inverse__zero(U_5933) ),
    inference(clausify,[status(thm)],[f_1557_2]) ).

cnf(f_1557_7,plain,
    ( U_5935 = c_Groups_Ozero__class_Ozero(U_5933)
    | U_5934 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5933),U_5936),U_5935)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5933),U_5934),U_5935) = U_5936
    | ~ class_Fields_Ofield__inverse__zero(U_5933) ),
    inference(clausify,[status(thm)],[f_1557_2]) ).

cnf(f_1557_8,plain,
    ( U_5936 != c_Groups_Ozero__class_Ozero(U_5933)
    | U_5934 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5933),U_5936),U_5935)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5933),U_5934),U_5935) = U_5936
    | ~ class_Fields_Ofield__inverse__zero(U_5933) ),
    inference(clausify,[status(thm)],[f_1557_2]) ).

fof(f_1558_1,plain,
    ! [V_b,V_a,V_c,T_a] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)
      | V_c = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Fields_Ofield__inverse__zero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__divide__mult__cancel__right]) ).

fof(f_1558_2,plain,
    ! [U_5940,U_5939,U_5938,U_5937] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5937),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5937),U_5939),U_5938)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5937),U_5940),U_5938)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5937),U_5939),U_5940)
      | U_5938 = c_Groups_Ozero__class_Ozero(U_5937)
      | ~ class_Fields_Ofield__inverse__zero(U_5937) ),
    inference(variable_rename,[status(thm)],[f_1558_1]) ).

cnf(f_1558_3,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5937),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5937),U_5939),U_5938)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5937),U_5940),U_5938)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5937),U_5939),U_5940)
    | U_5938 = c_Groups_Ozero__class_Ozero(U_5937)
    | ~ class_Fields_Ofield__inverse__zero(U_5937) ),
    inference(clausify,[status(thm)],[f_1558_2]) ).

fof(f_1559_1,plain,
    ! [V_b,V_a,V_c,T_a] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)
      | V_c = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Fields_Ofield__inverse__zero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__divide__mult__cancel__left]) ).

fof(f_1559_2,plain,
    ! [U_5944,U_5943,U_5942,U_5941] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5941),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5941),U_5942),U_5943)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5941),U_5942),U_5944)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5941),U_5943),U_5944)
      | U_5942 = c_Groups_Ozero__class_Ozero(U_5941)
      | ~ class_Fields_Ofield__inverse__zero(U_5941) ),
    inference(variable_rename,[status(thm)],[f_1559_1]) ).

cnf(f_1559_3,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5941),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5941),U_5942),U_5943)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5941),U_5942),U_5944)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5941),U_5943),U_5944)
    | U_5942 = c_Groups_Ozero__class_Ozero(U_5941)
    | ~ class_Fields_Ofield__inverse__zero(U_5941) ),
    inference(clausify,[status(thm)],[f_1559_2]) ).

fof(f_1560_1,plain,
    ! [V_w_2,V_x_2,V_z_2,V_y_2,T_b] :
      ( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_x_2),V_y_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_w_2),V_z_2)
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_z_2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_y_2) )
        & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_z_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_y_2)
          | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_x_2),V_y_2) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_w_2),V_z_2) ) )
      | V_z_2 = c_Groups_Ozero__class_Ozero(T_b)
      | V_y_2 = c_Groups_Ozero__class_Ozero(T_b)
      | ~ class_Fields_Ofield(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_frac__eq__eq]) ).

fof(f_1560_2,plain,
    ! [U_5949,U_5948,U_5947,U_5946,U_5945] :
      ( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5945),U_5948),U_5946) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5945),U_5949),U_5947)
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5945),U_5948),U_5947) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5945),U_5949),U_5946) )
        & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5945),U_5948),U_5947) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5945),U_5949),U_5946)
          | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5945),U_5948),U_5946) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5945),U_5949),U_5947) ) )
      | U_5947 = c_Groups_Ozero__class_Ozero(U_5945)
      | U_5946 = c_Groups_Ozero__class_Ozero(U_5945)
      | ~ class_Fields_Ofield(U_5945) ),
    inference(variable_rename,[status(thm)],[f_1560_1]) ).

cnf(f_1560_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5945),U_5948),U_5947) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5945),U_5949),U_5946)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5945),U_5948),U_5946) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5945),U_5949),U_5947)
    | U_5947 = c_Groups_Ozero__class_Ozero(U_5945)
    | U_5946 = c_Groups_Ozero__class_Ozero(U_5945)
    | ~ class_Fields_Ofield(U_5945) ),
    inference(clausify,[status(thm)],[f_1560_2]) ).

cnf(f_1560_4,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5945),U_5948),U_5946) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5945),U_5949),U_5947)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5945),U_5948),U_5947) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5945),U_5949),U_5946)
    | U_5947 = c_Groups_Ozero__class_Ozero(U_5945)
    | U_5946 = c_Groups_Ozero__class_Ozero(U_5945)
    | ~ class_Fields_Ofield(U_5945) ),
    inference(clausify,[status(thm)],[f_1560_2]) ).

fof(f_1561_1,plain,
    ! [V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
      | ~ class_Fields_Olinordered__field(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_divide__nonneg__pos]) ).

fof(f_1561_2,plain,
    ! [U_5952,U_5951,U_5950] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5950),c_Groups_Ozero__class_Ozero(U_5950)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5950),U_5951),U_5952)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5950),c_Groups_Ozero__class_Ozero(U_5950)),U_5952))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5950),c_Groups_Ozero__class_Ozero(U_5950)),U_5951))
      | ~ class_Fields_Olinordered__field(U_5950) ),
    inference(variable_rename,[status(thm)],[f_1561_1]) ).

cnf(f_1561_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5950),c_Groups_Ozero__class_Ozero(U_5950)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5950),U_5951),U_5952)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5950),c_Groups_Ozero__class_Ozero(U_5950)),U_5952))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5950),c_Groups_Ozero__class_Ozero(U_5950)),U_5951))
    | ~ class_Fields_Olinordered__field(U_5950) ),
    inference(clausify,[status(thm)],[f_1561_2]) ).

fof(f_1562_1,plain,
    ! [V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
      | ~ class_Fields_Olinordered__field(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_divide__nonneg__neg]) ).

fof(f_1562_2,plain,
    ! [U_5955,U_5954,U_5953] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5953),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5953),U_5954),U_5955)),c_Groups_Ozero__class_Ozero(U_5953)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5953),U_5955),c_Groups_Ozero__class_Ozero(U_5953)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5953),c_Groups_Ozero__class_Ozero(U_5953)),U_5954))
      | ~ class_Fields_Olinordered__field(U_5953) ),
    inference(variable_rename,[status(thm)],[f_1562_1]) ).

cnf(f_1562_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5953),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5953),U_5954),U_5955)),c_Groups_Ozero__class_Ozero(U_5953)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5953),U_5955),c_Groups_Ozero__class_Ozero(U_5953)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5953),c_Groups_Ozero__class_Ozero(U_5953)),U_5954))
    | ~ class_Fields_Olinordered__field(U_5953) ),
    inference(clausify,[status(thm)],[f_1562_2]) ).

fof(f_1563_1,plain,
    ! [V_z,V_w,V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_w)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_w),V_z))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
      | ~ class_Fields_Olinordered__field(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_frac__less2]) ).

fof(f_1563_2,plain,
    ! [U_5960,U_5959,U_5958,U_5957,U_5956] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5956),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5956),U_5957),U_5960)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5956),U_5958),U_5959)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5956),U_5959),U_5960))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5956),c_Groups_Ozero__class_Ozero(U_5956)),U_5959))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5956),U_5957),U_5958))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5956),c_Groups_Ozero__class_Ozero(U_5956)),U_5957))
      | ~ class_Fields_Olinordered__field(U_5956) ),
    inference(variable_rename,[status(thm)],[f_1563_1]) ).

cnf(f_1563_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5956),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5956),U_5957),U_5960)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5956),U_5958),U_5959)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5956),U_5959),U_5960))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5956),c_Groups_Ozero__class_Ozero(U_5956)),U_5959))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5956),U_5957),U_5958))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5956),c_Groups_Ozero__class_Ozero(U_5956)),U_5957))
    | ~ class_Fields_Olinordered__field(U_5956) ),
    inference(clausify,[status(thm)],[f_1563_2]) ).

fof(f_1564_1,plain,
    ! [V_z,V_w,V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_w)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
      | ~ class_Fields_Olinordered__field(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_frac__less]) ).

fof(f_1564_2,plain,
    ! [U_5965,U_5964,U_5963,U_5962,U_5961] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5961),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5961),U_5962),U_5965)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5961),U_5963),U_5964)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5961),U_5964),U_5965))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5961),c_Groups_Ozero__class_Ozero(U_5961)),U_5964))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5961),U_5962),U_5963))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5961),c_Groups_Ozero__class_Ozero(U_5961)),U_5962))
      | ~ class_Fields_Olinordered__field(U_5961) ),
    inference(variable_rename,[status(thm)],[f_1564_1]) ).

cnf(f_1564_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5961),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5961),U_5962),U_5965)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5961),U_5963),U_5964)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5961),U_5964),U_5965))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5961),c_Groups_Ozero__class_Ozero(U_5961)),U_5964))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5961),U_5962),U_5963))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5961),c_Groups_Ozero__class_Ozero(U_5961)),U_5962))
    | ~ class_Fields_Olinordered__field(U_5961) ),
    inference(clausify,[status(thm)],[f_1564_2]) ).

fof(f_1565_1,plain,
    ! [V_z,V_w,V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_w)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
      | ~ class_Fields_Olinordered__field(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_frac__le]) ).

fof(f_1565_2,plain,
    ! [U_5970,U_5969,U_5968,U_5967,U_5966] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5966),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5966),U_5967),U_5970)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5966),U_5968),U_5969)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5966),U_5969),U_5970))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5966),c_Groups_Ozero__class_Ozero(U_5966)),U_5969))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5966),U_5967),U_5968))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5966),c_Groups_Ozero__class_Ozero(U_5966)),U_5967))
      | ~ class_Fields_Olinordered__field(U_5966) ),
    inference(variable_rename,[status(thm)],[f_1565_1]) ).

cnf(f_1565_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5966),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5966),U_5967),U_5970)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5966),U_5968),U_5969)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5966),U_5969),U_5970))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5966),c_Groups_Ozero__class_Ozero(U_5966)),U_5969))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5966),U_5967),U_5968))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5966),c_Groups_Ozero__class_Ozero(U_5966)),U_5967))
    | ~ class_Fields_Olinordered__field(U_5966) ),
    inference(clausify,[status(thm)],[f_1565_2]) ).

fof(f_1566_1,plain,
    ! [V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ class_Fields_Olinordered__field(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_divide__nonpos__pos]) ).

fof(f_1566_2,plain,
    ! [U_5973,U_5972,U_5971] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5971),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5971),U_5972),U_5973)),c_Groups_Ozero__class_Ozero(U_5971)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5971),c_Groups_Ozero__class_Ozero(U_5971)),U_5973))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5971),U_5972),c_Groups_Ozero__class_Ozero(U_5971)))
      | ~ class_Fields_Olinordered__field(U_5971) ),
    inference(variable_rename,[status(thm)],[f_1566_1]) ).

cnf(f_1566_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5971),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5971),U_5972),U_5973)),c_Groups_Ozero__class_Ozero(U_5971)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5971),c_Groups_Ozero__class_Ozero(U_5971)),U_5973))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5971),U_5972),c_Groups_Ozero__class_Ozero(U_5971)))
    | ~ class_Fields_Olinordered__field(U_5971) ),
    inference(clausify,[status(thm)],[f_1566_2]) ).

fof(f_1567_1,plain,
    ! [V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ class_Fields_Olinordered__field(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_divide__nonpos__neg]) ).

fof(f_1567_2,plain,
    ! [U_5976,U_5975,U_5974] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5974),c_Groups_Ozero__class_Ozero(U_5974)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5974),U_5975),U_5976)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5974),U_5976),c_Groups_Ozero__class_Ozero(U_5974)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5974),U_5975),c_Groups_Ozero__class_Ozero(U_5974)))
      | ~ class_Fields_Olinordered__field(U_5974) ),
    inference(variable_rename,[status(thm)],[f_1567_1]) ).

cnf(f_1567_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5974),c_Groups_Ozero__class_Ozero(U_5974)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5974),U_5975),U_5976)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5974),U_5976),c_Groups_Ozero__class_Ozero(U_5974)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5974),U_5975),c_Groups_Ozero__class_Ozero(U_5974)))
    | ~ class_Fields_Olinordered__field(U_5974) ),
    inference(clausify,[status(thm)],[f_1567_2]) ).

fof(f_1568_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
      | ~ class_Fields_Olinordered__field(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_divide__strict__left__mono__neg]) ).

fof(f_1568_2,plain,
    ! [U_5980,U_5979,U_5978,U_5977] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5977),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5977),U_5980),U_5978)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5977),U_5980),U_5979)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5977),c_Groups_Ozero__class_Ozero(U_5977)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5977),U_5978),U_5979)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5977),U_5980),c_Groups_Ozero__class_Ozero(U_5977)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5977),U_5978),U_5979))
      | ~ class_Fields_Olinordered__field(U_5977) ),
    inference(variable_rename,[status(thm)],[f_1568_1]) ).

cnf(f_1568_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5977),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5977),U_5980),U_5978)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5977),U_5980),U_5979)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5977),c_Groups_Ozero__class_Ozero(U_5977)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5977),U_5978),U_5979)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5977),U_5980),c_Groups_Ozero__class_Ozero(U_5977)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5977),U_5978),U_5979))
    | ~ class_Fields_Olinordered__field(U_5977) ),
    inference(clausify,[status(thm)],[f_1568_2]) ).

fof(f_1569_1,plain,
    ! [V_c,V_a,V_b,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
      | ~ class_Fields_Olinordered__field(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_divide__strict__left__mono]) ).

fof(f_1569_2,plain,
    ! [U_5984,U_5983,U_5982,U_5981] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5981),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5981),U_5984),U_5983)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5981),U_5984),U_5982)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5981),c_Groups_Ozero__class_Ozero(U_5981)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5981),U_5983),U_5982)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5981),c_Groups_Ozero__class_Ozero(U_5981)),U_5984))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5981),U_5982),U_5983))
      | ~ class_Fields_Olinordered__field(U_5981) ),
    inference(variable_rename,[status(thm)],[f_1569_1]) ).

cnf(f_1569_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5981),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5981),U_5984),U_5983)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5981),U_5984),U_5982)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5981),c_Groups_Ozero__class_Ozero(U_5981)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5981),U_5983),U_5982)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5981),c_Groups_Ozero__class_Ozero(U_5981)),U_5984))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5981),U_5982),U_5983))
    | ~ class_Fields_Olinordered__field(U_5981) ),
    inference(clausify,[status(thm)],[f_1569_2]) ).

fof(f_1570_1,plain,
    ! [V_a_2,V_b_2,V_c_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
      | ~ class_Fields_Olinordered__field(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_neg__divide__less__eq]) ).

fof(f_1570_2,plain,
    ! [U_5988,U_5987,U_5986,U_5985] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5985),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5985),U_5987),U_5986)),U_5988))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5985),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5985),U_5988),U_5986)),U_5987)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5985),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5985),U_5988),U_5986)),U_5987))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5985),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5985),U_5987),U_5986)),U_5988)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5985),U_5986),c_Groups_Ozero__class_Ozero(U_5985)))
      | ~ class_Fields_Olinordered__field(U_5985) ),
    inference(variable_rename,[status(thm)],[f_1570_1]) ).

cnf(f_1570_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5985),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5985),U_5988),U_5986)),U_5987))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5985),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5985),U_5987),U_5986)),U_5988))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5985),U_5986),c_Groups_Ozero__class_Ozero(U_5985)))
    | ~ class_Fields_Olinordered__field(U_5985) ),
    inference(clausify,[status(thm)],[f_1570_2]) ).

cnf(f_1570_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5985),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5985),U_5987),U_5986)),U_5988))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5985),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5985),U_5988),U_5986)),U_5987))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5985),U_5986),c_Groups_Ozero__class_Ozero(U_5985)))
    | ~ class_Fields_Olinordered__field(U_5985) ),
    inference(clausify,[status(thm)],[f_1570_2]) ).

fof(f_1571_1,plain,
    ! [V_b_2,V_a_2,V_c_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
      | ~ class_Fields_Olinordered__field(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_neg__less__divide__eq]) ).

fof(f_1571_2,plain,
    ! [U_5992,U_5991,U_5990,U_5989] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5989),U_5991),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5989),U_5992),U_5990)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5989),U_5992),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5989),U_5991),U_5990))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5989),U_5992),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5989),U_5991),U_5990)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5989),U_5991),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5989),U_5992),U_5990))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5989),U_5990),c_Groups_Ozero__class_Ozero(U_5989)))
      | ~ class_Fields_Olinordered__field(U_5989) ),
    inference(variable_rename,[status(thm)],[f_1571_1]) ).

cnf(f_1571_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5989),U_5992),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5989),U_5991),U_5990)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5989),U_5991),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5989),U_5992),U_5990)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5989),U_5990),c_Groups_Ozero__class_Ozero(U_5989)))
    | ~ class_Fields_Olinordered__field(U_5989) ),
    inference(clausify,[status(thm)],[f_1571_2]) ).

cnf(f_1571_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5989),U_5991),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5989),U_5992),U_5990)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5989),U_5992),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5989),U_5991),U_5990)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5989),U_5990),c_Groups_Ozero__class_Ozero(U_5989)))
    | ~ class_Fields_Olinordered__field(U_5989) ),
    inference(clausify,[status(thm)],[f_1571_2]) ).

fof(f_1572_1,plain,
    ! [V_x,V_z,V_y,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
      | ~ class_Fields_Olinordered__field(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__imp__less__div__pos]) ).

fof(f_1572_2,plain,
    ! [U_5996,U_5995,U_5994,U_5993] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5993),U_5995),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5993),U_5996),U_5994)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5993),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5993),U_5995),U_5994)),U_5996))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5993),c_Groups_Ozero__class_Ozero(U_5993)),U_5994))
      | ~ class_Fields_Olinordered__field(U_5993) ),
    inference(variable_rename,[status(thm)],[f_1572_1]) ).

cnf(f_1572_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5993),U_5995),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5993),U_5996),U_5994)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5993),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5993),U_5995),U_5994)),U_5996))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5993),c_Groups_Ozero__class_Ozero(U_5993)),U_5994))
    | ~ class_Fields_Olinordered__field(U_5993) ),
    inference(clausify,[status(thm)],[f_1572_2]) ).

fof(f_1573_1,plain,
    ! [V_z,V_x,V_y,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),V_z))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
      | ~ class_Fields_Olinordered__field(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__imp__div__pos__less]) ).

fof(f_1573_2,plain,
    ! [U_6000,U_5999,U_5998,U_5997] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5997),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5997),U_5999),U_5998)),U_6000))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5997),U_5999),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5997),U_6000),U_5998)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5997),c_Groups_Ozero__class_Ozero(U_5997)),U_5998))
      | ~ class_Fields_Olinordered__field(U_5997) ),
    inference(variable_rename,[status(thm)],[f_1573_1]) ).

cnf(f_1573_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5997),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5997),U_5999),U_5998)),U_6000))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5997),U_5999),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5997),U_6000),U_5998)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5997),c_Groups_Ozero__class_Ozero(U_5997)),U_5998))
    | ~ class_Fields_Olinordered__field(U_5997) ),
    inference(clausify,[status(thm)],[f_1573_2]) ).

fof(f_1574_1,plain,
    ! [V_a_2,V_b_2,V_c_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
      | ~ class_Fields_Olinordered__field(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_pos__divide__less__eq]) ).

fof(f_1574_2,plain,
    ! [U_6004,U_6003,U_6002,U_6001] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6001),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6001),U_6003),U_6002)),U_6004))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6001),U_6003),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6001),U_6004),U_6002))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6001),U_6003),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6001),U_6004),U_6002)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6001),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6001),U_6003),U_6002)),U_6004)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6001),c_Groups_Ozero__class_Ozero(U_6001)),U_6002))
      | ~ class_Fields_Olinordered__field(U_6001) ),
    inference(variable_rename,[status(thm)],[f_1574_1]) ).

cnf(f_1574_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6001),U_6003),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6001),U_6004),U_6002)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6001),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6001),U_6003),U_6002)),U_6004))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6001),c_Groups_Ozero__class_Ozero(U_6001)),U_6002))
    | ~ class_Fields_Olinordered__field(U_6001) ),
    inference(clausify,[status(thm)],[f_1574_2]) ).

cnf(f_1574_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6001),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6001),U_6003),U_6002)),U_6004))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6001),U_6003),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6001),U_6004),U_6002)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6001),c_Groups_Ozero__class_Ozero(U_6001)),U_6002))
    | ~ class_Fields_Olinordered__field(U_6001) ),
    inference(clausify,[status(thm)],[f_1574_2]) ).

fof(f_1575_1,plain,
    ! [V_b_2,V_a_2,V_c_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
      | ~ class_Fields_Olinordered__field(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_pos__less__divide__eq]) ).

fof(f_1575_2,plain,
    ! [U_6008,U_6007,U_6006,U_6005] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6005),U_6007),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6005),U_6008),U_6006)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6005),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6005),U_6007),U_6006)),U_6008)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6005),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6005),U_6007),U_6006)),U_6008))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6005),U_6007),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6005),U_6008),U_6006))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6005),c_Groups_Ozero__class_Ozero(U_6005)),U_6006))
      | ~ class_Fields_Olinordered__field(U_6005) ),
    inference(variable_rename,[status(thm)],[f_1575_1]) ).

cnf(f_1575_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6005),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6005),U_6007),U_6006)),U_6008))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6005),U_6007),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6005),U_6008),U_6006)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6005),c_Groups_Ozero__class_Ozero(U_6005)),U_6006))
    | ~ class_Fields_Olinordered__field(U_6005) ),
    inference(clausify,[status(thm)],[f_1575_2]) ).

cnf(f_1575_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6005),U_6007),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6005),U_6008),U_6006)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6005),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6005),U_6007),U_6006)),U_6008))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6005),c_Groups_Ozero__class_Ozero(U_6005)),U_6006))
    | ~ class_Fields_Olinordered__field(U_6005) ),
    inference(clausify,[status(thm)],[f_1575_2]) ).

fof(f_1576_1,plain,
    ! [V_a_2,V_c_2,V_b_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2)) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_divide__less__eq]) ).

fof(f_1576_2,plain,
    ! [U_6012,U_6011,U_6010,U_6009] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6009),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6009),U_6010),U_6011)),U_6012))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6009),c_Groups_Ozero__class_Ozero(U_6009)),U_6012))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6009),U_6011),c_Groups_Ozero__class_Ozero(U_6009))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6009),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6009),U_6012),U_6011)),U_6010))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6009),U_6011),c_Groups_Ozero__class_Ozero(U_6009))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6009),c_Groups_Ozero__class_Ozero(U_6009)),U_6011)) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6009),U_6010),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6009),U_6012),U_6011)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6009),c_Groups_Ozero__class_Ozero(U_6009)),U_6011)) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6009),c_Groups_Ozero__class_Ozero(U_6009)),U_6012))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6009),U_6011),c_Groups_Ozero__class_Ozero(U_6009))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6009),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6009),U_6012),U_6011)),U_6010))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6009),U_6011),c_Groups_Ozero__class_Ozero(U_6009))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6009),c_Groups_Ozero__class_Ozero(U_6009)),U_6011)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6009),U_6010),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6009),U_6012),U_6011)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6009),c_Groups_Ozero__class_Ozero(U_6009)),U_6011)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6009),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6009),U_6010),U_6011)),U_6012)) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(U_6009) ),
    inference(variable_rename,[status(thm)],[f_1576_1]) ).

cnf(f_1576_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6009),U_6010),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6009),U_6012),U_6011)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6009),c_Groups_Ozero__class_Ozero(U_6009)),U_6011))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6009),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6009),U_6010),U_6011)),U_6012))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6009) ),
    inference(clausify,[status(thm)],[f_1576_2]) ).

cnf(f_1576_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6009),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6009),U_6012),U_6011)),U_6010))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6009),U_6011),c_Groups_Ozero__class_Ozero(U_6009)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6009),c_Groups_Ozero__class_Ozero(U_6009)),U_6011))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6009),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6009),U_6010),U_6011)),U_6012))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6009) ),
    inference(clausify,[status(thm)],[f_1576_2]) ).

cnf(f_1576_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6009),c_Groups_Ozero__class_Ozero(U_6009)),U_6012))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6009),U_6011),c_Groups_Ozero__class_Ozero(U_6009)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6009),c_Groups_Ozero__class_Ozero(U_6009)),U_6011))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6009),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6009),U_6010),U_6011)),U_6012))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6009) ),
    inference(clausify,[status(thm)],[f_1576_2]) ).

cnf(f_1576_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6009),c_Groups_Ozero__class_Ozero(U_6009)),U_6011))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6009),c_Groups_Ozero__class_Ozero(U_6009)),U_6011))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6009),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6009),U_6010),U_6011)),U_6012))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6009) ),
    inference(clausify,[status(thm)],[f_1576_2]) ).

cnf(f_1576_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6009),U_6011),c_Groups_Ozero__class_Ozero(U_6009)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6009),U_6011),c_Groups_Ozero__class_Ozero(U_6009)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6009),c_Groups_Ozero__class_Ozero(U_6009)),U_6011))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6009),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6009),U_6010),U_6011)),U_6012))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6009) ),
    inference(clausify,[status(thm)],[f_1576_2]) ).

cnf(f_1576_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6009),c_Groups_Ozero__class_Ozero(U_6009)),U_6012))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6009),U_6011),c_Groups_Ozero__class_Ozero(U_6009)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6009),c_Groups_Ozero__class_Ozero(U_6009)),U_6011))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6009),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6009),U_6010),U_6011)),U_6012))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6009) ),
    inference(clausify,[status(thm)],[f_1576_2]) ).

cnf(f_1576_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6009),U_6011),c_Groups_Ozero__class_Ozero(U_6009)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6009),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6009),U_6012),U_6011)),U_6010))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6009),c_Groups_Ozero__class_Ozero(U_6009)),U_6011))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6009),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6009),U_6010),U_6011)),U_6012))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6009) ),
    inference(clausify,[status(thm)],[f_1576_2]) ).

cnf(f_1576_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6009),c_Groups_Ozero__class_Ozero(U_6009)),U_6012))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6009),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6009),U_6012),U_6011)),U_6010))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6009),c_Groups_Ozero__class_Ozero(U_6009)),U_6011))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6009),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6009),U_6010),U_6011)),U_6012))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6009) ),
    inference(clausify,[status(thm)],[f_1576_2]) ).

cnf(f_1576_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6009),c_Groups_Ozero__class_Ozero(U_6009)),U_6011))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6009),U_6010),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6009),U_6012),U_6011)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6009),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6009),U_6010),U_6011)),U_6012))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6009) ),
    inference(clausify,[status(thm)],[f_1576_2]) ).

cnf(f_1576_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6009),U_6011),c_Groups_Ozero__class_Ozero(U_6009)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6009),U_6011),c_Groups_Ozero__class_Ozero(U_6009)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6009),U_6010),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6009),U_6012),U_6011)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6009),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6009),U_6010),U_6011)),U_6012))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6009) ),
    inference(clausify,[status(thm)],[f_1576_2]) ).

cnf(f_1576_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6009),c_Groups_Ozero__class_Ozero(U_6009)),U_6012))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6009),U_6011),c_Groups_Ozero__class_Ozero(U_6009)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6009),U_6010),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6009),U_6012),U_6011)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6009),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6009),U_6010),U_6011)),U_6012))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6009) ),
    inference(clausify,[status(thm)],[f_1576_2]) ).

cnf(f_1576_14,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6009),U_6011),c_Groups_Ozero__class_Ozero(U_6009)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6009),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6009),U_6012),U_6011)),U_6010))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6009),U_6010),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6009),U_6012),U_6011)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6009),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6009),U_6010),U_6011)),U_6012))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6009) ),
    inference(clausify,[status(thm)],[f_1576_2]) ).

cnf(f_1576_15,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6009),c_Groups_Ozero__class_Ozero(U_6009)),U_6012))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6009),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6009),U_6012),U_6011)),U_6010))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6009),U_6010),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6009),U_6012),U_6011)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6009),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6009),U_6010),U_6011)),U_6012))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6009) ),
    inference(clausify,[status(thm)],[f_1576_2]) ).

fof(f_1577_1,plain,
    ! [V_c_2,V_b_2,V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2))) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_less__divide__eq]) ).

fof(f_1577_2,plain,
    ! [U_6016,U_6015,U_6014,U_6013] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6013),U_6014),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6013),U_6015),U_6016)))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6013),U_6014),c_Groups_Ozero__class_Ozero(U_6013)))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6013),U_6016),c_Groups_Ozero__class_Ozero(U_6013))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6013),U_6015),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6013),U_6014),U_6016)))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6013),U_6016),c_Groups_Ozero__class_Ozero(U_6013))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6013),c_Groups_Ozero__class_Ozero(U_6013)),U_6016)) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6013),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6013),U_6014),U_6016)),U_6015))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6013),c_Groups_Ozero__class_Ozero(U_6013)),U_6016)) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6013),U_6014),c_Groups_Ozero__class_Ozero(U_6013)))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6013),U_6016),c_Groups_Ozero__class_Ozero(U_6013))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6013),U_6015),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6013),U_6014),U_6016)))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6013),U_6016),c_Groups_Ozero__class_Ozero(U_6013))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6013),c_Groups_Ozero__class_Ozero(U_6013)),U_6016)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6013),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6013),U_6014),U_6016)),U_6015))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6013),c_Groups_Ozero__class_Ozero(U_6013)),U_6016)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6013),U_6014),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6013),U_6015),U_6016))) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(U_6013) ),
    inference(variable_rename,[status(thm)],[f_1577_1]) ).

cnf(f_1577_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6013),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6013),U_6014),U_6016)),U_6015))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6013),c_Groups_Ozero__class_Ozero(U_6013)),U_6016))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6013),U_6014),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6013),U_6015),U_6016)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6013) ),
    inference(clausify,[status(thm)],[f_1577_2]) ).

cnf(f_1577_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6013),U_6015),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6013),U_6014),U_6016)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6013),U_6016),c_Groups_Ozero__class_Ozero(U_6013)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6013),c_Groups_Ozero__class_Ozero(U_6013)),U_6016))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6013),U_6014),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6013),U_6015),U_6016)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6013) ),
    inference(clausify,[status(thm)],[f_1577_2]) ).

cnf(f_1577_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6013),U_6014),c_Groups_Ozero__class_Ozero(U_6013)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6013),U_6016),c_Groups_Ozero__class_Ozero(U_6013)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6013),c_Groups_Ozero__class_Ozero(U_6013)),U_6016))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6013),U_6014),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6013),U_6015),U_6016)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6013) ),
    inference(clausify,[status(thm)],[f_1577_2]) ).

cnf(f_1577_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6013),c_Groups_Ozero__class_Ozero(U_6013)),U_6016))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6013),c_Groups_Ozero__class_Ozero(U_6013)),U_6016))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6013),U_6014),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6013),U_6015),U_6016)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6013) ),
    inference(clausify,[status(thm)],[f_1577_2]) ).

cnf(f_1577_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6013),U_6016),c_Groups_Ozero__class_Ozero(U_6013)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6013),U_6016),c_Groups_Ozero__class_Ozero(U_6013)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6013),c_Groups_Ozero__class_Ozero(U_6013)),U_6016))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6013),U_6014),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6013),U_6015),U_6016)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6013) ),
    inference(clausify,[status(thm)],[f_1577_2]) ).

cnf(f_1577_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6013),U_6014),c_Groups_Ozero__class_Ozero(U_6013)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6013),U_6016),c_Groups_Ozero__class_Ozero(U_6013)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6013),c_Groups_Ozero__class_Ozero(U_6013)),U_6016))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6013),U_6014),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6013),U_6015),U_6016)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6013) ),
    inference(clausify,[status(thm)],[f_1577_2]) ).

cnf(f_1577_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6013),U_6016),c_Groups_Ozero__class_Ozero(U_6013)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6013),U_6015),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6013),U_6014),U_6016)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6013),c_Groups_Ozero__class_Ozero(U_6013)),U_6016))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6013),U_6014),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6013),U_6015),U_6016)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6013) ),
    inference(clausify,[status(thm)],[f_1577_2]) ).

cnf(f_1577_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6013),U_6014),c_Groups_Ozero__class_Ozero(U_6013)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6013),U_6015),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6013),U_6014),U_6016)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6013),c_Groups_Ozero__class_Ozero(U_6013)),U_6016))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6013),U_6014),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6013),U_6015),U_6016)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6013) ),
    inference(clausify,[status(thm)],[f_1577_2]) ).

cnf(f_1577_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6013),c_Groups_Ozero__class_Ozero(U_6013)),U_6016))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6013),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6013),U_6014),U_6016)),U_6015))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6013),U_6014),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6013),U_6015),U_6016)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6013) ),
    inference(clausify,[status(thm)],[f_1577_2]) ).

cnf(f_1577_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6013),U_6016),c_Groups_Ozero__class_Ozero(U_6013)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6013),U_6016),c_Groups_Ozero__class_Ozero(U_6013)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6013),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6013),U_6014),U_6016)),U_6015))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6013),U_6014),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6013),U_6015),U_6016)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6013) ),
    inference(clausify,[status(thm)],[f_1577_2]) ).

cnf(f_1577_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6013),U_6014),c_Groups_Ozero__class_Ozero(U_6013)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6013),U_6016),c_Groups_Ozero__class_Ozero(U_6013)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6013),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6013),U_6014),U_6016)),U_6015))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6013),U_6014),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6013),U_6015),U_6016)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6013) ),
    inference(clausify,[status(thm)],[f_1577_2]) ).

cnf(f_1577_14,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6013),U_6016),c_Groups_Ozero__class_Ozero(U_6013)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6013),U_6015),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6013),U_6014),U_6016)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6013),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6013),U_6014),U_6016)),U_6015))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6013),U_6014),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6013),U_6015),U_6016)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6013) ),
    inference(clausify,[status(thm)],[f_1577_2]) ).

cnf(f_1577_15,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6013),U_6014),c_Groups_Ozero__class_Ozero(U_6013)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6013),U_6015),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6013),U_6014),U_6016)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6013),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6013),U_6014),U_6016)),U_6015))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6013),U_6014),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6013),U_6015),U_6016)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6013) ),
    inference(clausify,[status(thm)],[f_1577_2]) ).

fof(f_1578_1,plain,
    ! [V_x,V_z,V_y,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_z),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))),V_y)
      | V_y = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Fields_Ofield__inverse__zero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__num__frac]) ).

fof(f_1578_2,plain,
    ! [U_6020,U_6019,U_6018,U_6017] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6017),U_6019),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6017),U_6020),U_6018)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6017),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6017),U_6020),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6017),U_6019),U_6018))),U_6018)
      | U_6018 = c_Groups_Ozero__class_Ozero(U_6017)
      | ~ class_Fields_Ofield__inverse__zero(U_6017) ),
    inference(variable_rename,[status(thm)],[f_1578_1]) ).

cnf(f_1578_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6017),U_6019),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6017),U_6020),U_6018)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6017),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6017),U_6020),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6017),U_6019),U_6018))),U_6018)
    | U_6018 = c_Groups_Ozero__class_Ozero(U_6017)
    | ~ class_Fields_Ofield__inverse__zero(U_6017) ),
    inference(clausify,[status(thm)],[f_1578_2]) ).

fof(f_1579_1,plain,
    ! [V_y,V_x,V_z,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_x)),V_y)),V_z)
      | V_z = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Fields_Ofield(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__divide__eq__iff]) ).

fof(f_1579_2,plain,
    ! [U_6024,U_6023,U_6022,U_6021] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6021),U_6023),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6021),U_6024),U_6022)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6021),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6021),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6021),U_6022),U_6023)),U_6024)),U_6022)
      | U_6022 = c_Groups_Ozero__class_Ozero(U_6021)
      | ~ class_Fields_Ofield(U_6021) ),
    inference(variable_rename,[status(thm)],[f_1579_1]) ).

cnf(f_1579_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6021),U_6023),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6021),U_6024),U_6022)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6021),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6021),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6021),U_6022),U_6023)),U_6024)),U_6022)
    | U_6022 = c_Groups_Ozero__class_Ozero(U_6021)
    | ~ class_Fields_Ofield(U_6021) ),
    inference(clausify,[status(thm)],[f_1579_2]) ).

fof(f_1580_1,plain,
    ! [V_z,V_x,V_y,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))),V_y)
      | V_y = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Fields_Ofield__inverse__zero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__frac__num]) ).

fof(f_1580_2,plain,
    ! [U_6028,U_6027,U_6026,U_6025] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6025),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6025),U_6027),U_6026)),U_6028) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6025),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6025),U_6027),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6025),U_6028),U_6026))),U_6026)
      | U_6026 = c_Groups_Ozero__class_Ozero(U_6025)
      | ~ class_Fields_Ofield__inverse__zero(U_6025) ),
    inference(variable_rename,[status(thm)],[f_1580_1]) ).

cnf(f_1580_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6025),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6025),U_6027),U_6026)),U_6028) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6025),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6025),U_6027),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6025),U_6028),U_6026))),U_6026)
    | U_6026 = c_Groups_Ozero__class_Ozero(U_6025)
    | ~ class_Fields_Ofield__inverse__zero(U_6025) ),
    inference(clausify,[status(thm)],[f_1580_2]) ).

fof(f_1581_1,plain,
    ! [V_y,V_x,V_z,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),V_y) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))),V_z)
      | V_z = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Fields_Ofield(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_divide__add__eq__iff]) ).

fof(f_1581_2,plain,
    ! [U_6032,U_6031,U_6030,U_6029] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6029),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6029),U_6031),U_6030)),U_6032) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6029),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6029),U_6031),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6029),U_6030),U_6032))),U_6030)
      | U_6030 = c_Groups_Ozero__class_Ozero(U_6029)
      | ~ class_Fields_Ofield(U_6029) ),
    inference(variable_rename,[status(thm)],[f_1581_1]) ).

cnf(f_1581_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6029),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6029),U_6031),U_6030)),U_6032) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6029),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6029),U_6031),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6029),U_6030),U_6032))),U_6030)
    | U_6030 = c_Groups_Ozero__class_Ozero(U_6029)
    | ~ class_Fields_Ofield(U_6029) ),
    inference(clausify,[status(thm)],[f_1581_2]) ).

fof(f_1582_1,plain,
    ! [V_w,V_x,V_z,V_y,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_w),V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w),V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z))
      | V_z = c_Groups_Ozero__class_Ozero(T_a)
      | V_y = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Fields_Ofield(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__frac__eq]) ).

fof(f_1582_2,plain,
    ! [U_6037,U_6036,U_6035,U_6034,U_6033] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6033),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6033),U_6036),U_6034)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6033),U_6037),U_6035)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6033),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6033),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6033),U_6036),U_6035)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6033),U_6037),U_6034))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6033),U_6034),U_6035))
      | U_6035 = c_Groups_Ozero__class_Ozero(U_6033)
      | U_6034 = c_Groups_Ozero__class_Ozero(U_6033)
      | ~ class_Fields_Ofield(U_6033) ),
    inference(variable_rename,[status(thm)],[f_1582_1]) ).

cnf(f_1582_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6033),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6033),U_6036),U_6034)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6033),U_6037),U_6035)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6033),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6033),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6033),U_6036),U_6035)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6033),U_6037),U_6034))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6033),U_6034),U_6035))
    | U_6035 = c_Groups_Ozero__class_Ozero(U_6033)
    | U_6034 = c_Groups_Ozero__class_Ozero(U_6033)
    | ~ class_Fields_Ofield(U_6033) ),
    inference(clausify,[status(thm)],[f_1582_2]) ).

fof(f_1583_1,plain,
    ! [V_y,V_x,V_z,T_a] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_x)),V_y)),V_z)
      | V_z = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Fields_Ofield(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_diff__divide__eq__iff]) ).

fof(f_1583_2,plain,
    ! [U_6041,U_6040,U_6039,U_6038] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6038),U_6040),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6038),U_6041),U_6039)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6038),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6038),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6038),U_6039),U_6040)),U_6041)),U_6039)
      | U_6039 = c_Groups_Ozero__class_Ozero(U_6038)
      | ~ class_Fields_Ofield(U_6038) ),
    inference(variable_rename,[status(thm)],[f_1583_1]) ).

cnf(f_1583_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6038),U_6040),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6038),U_6041),U_6039)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6038),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6038),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6038),U_6039),U_6040)),U_6041)),U_6039)
    | U_6039 = c_Groups_Ozero__class_Ozero(U_6038)
    | ~ class_Fields_Ofield(U_6038) ),
    inference(clausify,[status(thm)],[f_1583_2]) ).

fof(f_1584_1,plain,
    ! [V_y,V_x,V_z,T_a] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),V_y) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))),V_z)
      | V_z = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Fields_Ofield(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_divide__diff__eq__iff]) ).

fof(f_1584_2,plain,
    ! [U_6045,U_6044,U_6043,U_6042] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6042),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6042),U_6044),U_6043)),U_6045) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6042),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6042),U_6044),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6042),U_6043),U_6045))),U_6043)
      | U_6043 = c_Groups_Ozero__class_Ozero(U_6042)
      | ~ class_Fields_Ofield(U_6042) ),
    inference(variable_rename,[status(thm)],[f_1584_1]) ).

cnf(f_1584_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6042),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6042),U_6044),U_6043)),U_6045) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6042),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6042),U_6044),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6042),U_6043),U_6045))),U_6043)
    | U_6043 = c_Groups_Ozero__class_Ozero(U_6042)
    | ~ class_Fields_Ofield(U_6042) ),
    inference(clausify,[status(thm)],[f_1584_2]) ).

fof(f_1585_1,plain,
    ! [V_w,V_x,V_z,V_y,T_a] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_w),V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w),V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z))
      | V_z = c_Groups_Ozero__class_Ozero(T_a)
      | V_y = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Fields_Ofield(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_diff__frac__eq]) ).

fof(f_1585_2,plain,
    ! [U_6050,U_6049,U_6048,U_6047,U_6046] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6046),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6046),U_6049),U_6047)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6046),U_6050),U_6048)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6046),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6046),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6046),U_6049),U_6048)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6046),U_6050),U_6047))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6046),U_6047),U_6048))
      | U_6048 = c_Groups_Ozero__class_Ozero(U_6046)
      | U_6047 = c_Groups_Ozero__class_Ozero(U_6046)
      | ~ class_Fields_Ofield(U_6046) ),
    inference(variable_rename,[status(thm)],[f_1585_1]) ).

cnf(f_1585_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6046),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6046),U_6049),U_6047)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6046),U_6050),U_6048)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6046),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6046),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6046),U_6049),U_6048)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6046),U_6050),U_6047))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6046),U_6047),U_6048))
    | U_6048 = c_Groups_Ozero__class_Ozero(U_6046)
    | U_6047 = c_Groups_Ozero__class_Ozero(U_6046)
    | ~ class_Fields_Ofield(U_6046) ),
    inference(clausify,[status(thm)],[f_1585_2]) ).

fof(f_1586_1,plain,
    ! [V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a)))),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
      | ~ class_Fields_Olinordered__field(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_gt__half__sum]) ).

fof(f_1586_2,plain,
    ! [U_6053,U_6052,U_6051] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6051),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6051),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6051),U_6052),U_6053)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6051),c_Groups_Oone__class_Oone(U_6051)),c_Groups_Oone__class_Oone(U_6051)))),U_6053))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6051),U_6052),U_6053))
      | ~ class_Fields_Olinordered__field(U_6051) ),
    inference(variable_rename,[status(thm)],[f_1586_1]) ).

cnf(f_1586_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6051),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6051),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6051),U_6052),U_6053)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6051),c_Groups_Oone__class_Oone(U_6051)),c_Groups_Oone__class_Oone(U_6051)))),U_6053))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6051),U_6052),U_6053))
    | ~ class_Fields_Olinordered__field(U_6051) ),
    inference(clausify,[status(thm)],[f_1586_2]) ).

fof(f_1587_1,plain,
    ! [V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a)))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
      | ~ class_Fields_Olinordered__field(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_less__half__sum]) ).

fof(f_1587_2,plain,
    ! [U_6056,U_6055,U_6054] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6054),U_6055),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6054),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6054),U_6055),U_6056)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6054),c_Groups_Oone__class_Oone(U_6054)),c_Groups_Oone__class_Oone(U_6054)))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6054),U_6055),U_6056))
      | ~ class_Fields_Olinordered__field(U_6054) ),
    inference(variable_rename,[status(thm)],[f_1587_1]) ).

cnf(f_1587_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6054),U_6055),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6054),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6054),U_6055),U_6056)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6054),c_Groups_Oone__class_Oone(U_6054)),c_Groups_Oone__class_Oone(U_6054)))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6054),U_6055),U_6056))
    | ~ class_Fields_Olinordered__field(U_6054) ),
    inference(clausify,[status(thm)],[f_1587_2]) ).

fof(f_1588_1,plain,
    ! [V_c_2,V_b_2,V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2))) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_le__divide__eq]) ).

fof(f_1588_2,plain,
    ! [U_6060,U_6059,U_6058,U_6057] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6057),U_6058),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6057),U_6059),U_6060)))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6057),U_6058),c_Groups_Ozero__class_Ozero(U_6057)))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6057),U_6060),c_Groups_Ozero__class_Ozero(U_6057))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6057),U_6059),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6057),U_6058),U_6060)))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6057),U_6060),c_Groups_Ozero__class_Ozero(U_6057))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6057),c_Groups_Ozero__class_Ozero(U_6057)),U_6060)) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6057),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6057),U_6058),U_6060)),U_6059))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6057),c_Groups_Ozero__class_Ozero(U_6057)),U_6060)) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6057),U_6058),c_Groups_Ozero__class_Ozero(U_6057)))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6057),U_6060),c_Groups_Ozero__class_Ozero(U_6057))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6057),U_6059),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6057),U_6058),U_6060)))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6057),U_6060),c_Groups_Ozero__class_Ozero(U_6057))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6057),c_Groups_Ozero__class_Ozero(U_6057)),U_6060)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6057),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6057),U_6058),U_6060)),U_6059))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6057),c_Groups_Ozero__class_Ozero(U_6057)),U_6060)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6057),U_6058),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6057),U_6059),U_6060))) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(U_6057) ),
    inference(variable_rename,[status(thm)],[f_1588_1]) ).

cnf(f_1588_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6057),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6057),U_6058),U_6060)),U_6059))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6057),c_Groups_Ozero__class_Ozero(U_6057)),U_6060))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6057),U_6058),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6057),U_6059),U_6060)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6057) ),
    inference(clausify,[status(thm)],[f_1588_2]) ).

cnf(f_1588_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6057),U_6059),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6057),U_6058),U_6060)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6057),U_6060),c_Groups_Ozero__class_Ozero(U_6057)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6057),c_Groups_Ozero__class_Ozero(U_6057)),U_6060))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6057),U_6058),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6057),U_6059),U_6060)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6057) ),
    inference(clausify,[status(thm)],[f_1588_2]) ).

cnf(f_1588_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6057),U_6058),c_Groups_Ozero__class_Ozero(U_6057)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6057),U_6060),c_Groups_Ozero__class_Ozero(U_6057)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6057),c_Groups_Ozero__class_Ozero(U_6057)),U_6060))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6057),U_6058),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6057),U_6059),U_6060)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6057) ),
    inference(clausify,[status(thm)],[f_1588_2]) ).

cnf(f_1588_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6057),c_Groups_Ozero__class_Ozero(U_6057)),U_6060))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6057),c_Groups_Ozero__class_Ozero(U_6057)),U_6060))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6057),U_6058),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6057),U_6059),U_6060)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6057) ),
    inference(clausify,[status(thm)],[f_1588_2]) ).

cnf(f_1588_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6057),U_6060),c_Groups_Ozero__class_Ozero(U_6057)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6057),U_6060),c_Groups_Ozero__class_Ozero(U_6057)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6057),c_Groups_Ozero__class_Ozero(U_6057)),U_6060))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6057),U_6058),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6057),U_6059),U_6060)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6057) ),
    inference(clausify,[status(thm)],[f_1588_2]) ).

cnf(f_1588_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6057),U_6058),c_Groups_Ozero__class_Ozero(U_6057)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6057),U_6060),c_Groups_Ozero__class_Ozero(U_6057)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6057),c_Groups_Ozero__class_Ozero(U_6057)),U_6060))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6057),U_6058),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6057),U_6059),U_6060)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6057) ),
    inference(clausify,[status(thm)],[f_1588_2]) ).

cnf(f_1588_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6057),U_6060),c_Groups_Ozero__class_Ozero(U_6057)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6057),U_6059),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6057),U_6058),U_6060)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6057),c_Groups_Ozero__class_Ozero(U_6057)),U_6060))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6057),U_6058),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6057),U_6059),U_6060)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6057) ),
    inference(clausify,[status(thm)],[f_1588_2]) ).

cnf(f_1588_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6057),U_6058),c_Groups_Ozero__class_Ozero(U_6057)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6057),U_6059),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6057),U_6058),U_6060)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6057),c_Groups_Ozero__class_Ozero(U_6057)),U_6060))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6057),U_6058),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6057),U_6059),U_6060)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6057) ),
    inference(clausify,[status(thm)],[f_1588_2]) ).

cnf(f_1588_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6057),c_Groups_Ozero__class_Ozero(U_6057)),U_6060))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6057),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6057),U_6058),U_6060)),U_6059))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6057),U_6058),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6057),U_6059),U_6060)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6057) ),
    inference(clausify,[status(thm)],[f_1588_2]) ).

cnf(f_1588_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6057),U_6060),c_Groups_Ozero__class_Ozero(U_6057)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6057),U_6060),c_Groups_Ozero__class_Ozero(U_6057)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6057),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6057),U_6058),U_6060)),U_6059))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6057),U_6058),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6057),U_6059),U_6060)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6057) ),
    inference(clausify,[status(thm)],[f_1588_2]) ).

cnf(f_1588_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6057),U_6058),c_Groups_Ozero__class_Ozero(U_6057)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6057),U_6060),c_Groups_Ozero__class_Ozero(U_6057)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6057),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6057),U_6058),U_6060)),U_6059))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6057),U_6058),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6057),U_6059),U_6060)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6057) ),
    inference(clausify,[status(thm)],[f_1588_2]) ).

cnf(f_1588_14,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6057),U_6060),c_Groups_Ozero__class_Ozero(U_6057)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6057),U_6059),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6057),U_6058),U_6060)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6057),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6057),U_6058),U_6060)),U_6059))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6057),U_6058),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6057),U_6059),U_6060)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6057) ),
    inference(clausify,[status(thm)],[f_1588_2]) ).

cnf(f_1588_15,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6057),U_6058),c_Groups_Ozero__class_Ozero(U_6057)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6057),U_6059),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6057),U_6058),U_6060)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6057),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6057),U_6058),U_6060)),U_6059))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6057),U_6058),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6057),U_6059),U_6060)))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6057) ),
    inference(clausify,[status(thm)],[f_1588_2]) ).

fof(f_1589_1,plain,
    ! [V_a_2,V_c_2,V_b_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2)) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_divide__le__eq]) ).

fof(f_1589_2,plain,
    ! [U_6064,U_6063,U_6062,U_6061] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6061),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6061),U_6062),U_6063)),U_6064))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6061),c_Groups_Ozero__class_Ozero(U_6061)),U_6064))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6061),U_6063),c_Groups_Ozero__class_Ozero(U_6061))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6061),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6061),U_6064),U_6063)),U_6062))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6061),U_6063),c_Groups_Ozero__class_Ozero(U_6061))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6061),c_Groups_Ozero__class_Ozero(U_6061)),U_6063)) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6061),U_6062),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6061),U_6064),U_6063)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6061),c_Groups_Ozero__class_Ozero(U_6061)),U_6063)) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6061),c_Groups_Ozero__class_Ozero(U_6061)),U_6064))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6061),U_6063),c_Groups_Ozero__class_Ozero(U_6061))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6061),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6061),U_6064),U_6063)),U_6062))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6061),U_6063),c_Groups_Ozero__class_Ozero(U_6061))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6061),c_Groups_Ozero__class_Ozero(U_6061)),U_6063)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6061),U_6062),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6061),U_6064),U_6063)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6061),c_Groups_Ozero__class_Ozero(U_6061)),U_6063)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6061),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6061),U_6062),U_6063)),U_6064)) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(U_6061) ),
    inference(variable_rename,[status(thm)],[f_1589_1]) ).

cnf(f_1589_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6061),U_6062),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6061),U_6064),U_6063)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6061),c_Groups_Ozero__class_Ozero(U_6061)),U_6063))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6061),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6061),U_6062),U_6063)),U_6064))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6061) ),
    inference(clausify,[status(thm)],[f_1589_2]) ).

cnf(f_1589_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6061),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6061),U_6064),U_6063)),U_6062))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6061),U_6063),c_Groups_Ozero__class_Ozero(U_6061)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6061),c_Groups_Ozero__class_Ozero(U_6061)),U_6063))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6061),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6061),U_6062),U_6063)),U_6064))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6061) ),
    inference(clausify,[status(thm)],[f_1589_2]) ).

cnf(f_1589_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6061),c_Groups_Ozero__class_Ozero(U_6061)),U_6064))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6061),U_6063),c_Groups_Ozero__class_Ozero(U_6061)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6061),c_Groups_Ozero__class_Ozero(U_6061)),U_6063))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6061),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6061),U_6062),U_6063)),U_6064))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6061) ),
    inference(clausify,[status(thm)],[f_1589_2]) ).

cnf(f_1589_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6061),c_Groups_Ozero__class_Ozero(U_6061)),U_6063))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6061),c_Groups_Ozero__class_Ozero(U_6061)),U_6063))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6061),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6061),U_6062),U_6063)),U_6064))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6061) ),
    inference(clausify,[status(thm)],[f_1589_2]) ).

cnf(f_1589_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6061),U_6063),c_Groups_Ozero__class_Ozero(U_6061)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6061),U_6063),c_Groups_Ozero__class_Ozero(U_6061)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6061),c_Groups_Ozero__class_Ozero(U_6061)),U_6063))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6061),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6061),U_6062),U_6063)),U_6064))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6061) ),
    inference(clausify,[status(thm)],[f_1589_2]) ).

cnf(f_1589_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6061),c_Groups_Ozero__class_Ozero(U_6061)),U_6064))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6061),U_6063),c_Groups_Ozero__class_Ozero(U_6061)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6061),c_Groups_Ozero__class_Ozero(U_6061)),U_6063))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6061),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6061),U_6062),U_6063)),U_6064))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6061) ),
    inference(clausify,[status(thm)],[f_1589_2]) ).

cnf(f_1589_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6061),U_6063),c_Groups_Ozero__class_Ozero(U_6061)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6061),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6061),U_6064),U_6063)),U_6062))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6061),c_Groups_Ozero__class_Ozero(U_6061)),U_6063))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6061),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6061),U_6062),U_6063)),U_6064))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6061) ),
    inference(clausify,[status(thm)],[f_1589_2]) ).

cnf(f_1589_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6061),c_Groups_Ozero__class_Ozero(U_6061)),U_6064))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6061),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6061),U_6064),U_6063)),U_6062))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6061),c_Groups_Ozero__class_Ozero(U_6061)),U_6063))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6061),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6061),U_6062),U_6063)),U_6064))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6061) ),
    inference(clausify,[status(thm)],[f_1589_2]) ).

cnf(f_1589_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6061),c_Groups_Ozero__class_Ozero(U_6061)),U_6063))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6061),U_6062),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6061),U_6064),U_6063)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6061),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6061),U_6062),U_6063)),U_6064))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6061) ),
    inference(clausify,[status(thm)],[f_1589_2]) ).

cnf(f_1589_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6061),U_6063),c_Groups_Ozero__class_Ozero(U_6061)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6061),U_6063),c_Groups_Ozero__class_Ozero(U_6061)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6061),U_6062),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6061),U_6064),U_6063)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6061),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6061),U_6062),U_6063)),U_6064))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6061) ),
    inference(clausify,[status(thm)],[f_1589_2]) ).

cnf(f_1589_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6061),c_Groups_Ozero__class_Ozero(U_6061)),U_6064))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6061),U_6063),c_Groups_Ozero__class_Ozero(U_6061)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6061),U_6062),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6061),U_6064),U_6063)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6061),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6061),U_6062),U_6063)),U_6064))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6061) ),
    inference(clausify,[status(thm)],[f_1589_2]) ).

cnf(f_1589_14,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6061),U_6063),c_Groups_Ozero__class_Ozero(U_6061)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6061),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6061),U_6064),U_6063)),U_6062))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6061),U_6062),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6061),U_6064),U_6063)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6061),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6061),U_6062),U_6063)),U_6064))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6061) ),
    inference(clausify,[status(thm)],[f_1589_2]) ).

cnf(f_1589_15,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6061),c_Groups_Ozero__class_Ozero(U_6061)),U_6064))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6061),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6061),U_6064),U_6063)),U_6062))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6061),U_6062),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6061),U_6064),U_6063)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6061),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6061),U_6062),U_6063)),U_6064))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6061) ),
    inference(clausify,[status(thm)],[f_1589_2]) ).

fof(f_1590_1,plain,
    ! [V_b_2,V_a_2,V_c_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
      | ~ class_Fields_Olinordered__field(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_pos__le__divide__eq]) ).

fof(f_1590_2,plain,
    ! [U_6068,U_6067,U_6066,U_6065] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6065),U_6067),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6065),U_6068),U_6066)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6065),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6065),U_6067),U_6066)),U_6068)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6065),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6065),U_6067),U_6066)),U_6068))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6065),U_6067),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6065),U_6068),U_6066))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6065),c_Groups_Ozero__class_Ozero(U_6065)),U_6066))
      | ~ class_Fields_Olinordered__field(U_6065) ),
    inference(variable_rename,[status(thm)],[f_1590_1]) ).

cnf(f_1590_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6065),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6065),U_6067),U_6066)),U_6068))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6065),U_6067),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6065),U_6068),U_6066)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6065),c_Groups_Ozero__class_Ozero(U_6065)),U_6066))
    | ~ class_Fields_Olinordered__field(U_6065) ),
    inference(clausify,[status(thm)],[f_1590_2]) ).

cnf(f_1590_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6065),U_6067),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6065),U_6068),U_6066)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6065),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6065),U_6067),U_6066)),U_6068))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6065),c_Groups_Ozero__class_Ozero(U_6065)),U_6066))
    | ~ class_Fields_Olinordered__field(U_6065) ),
    inference(clausify,[status(thm)],[f_1590_2]) ).

fof(f_1591_1,plain,
    ! [V_a_2,V_b_2,V_c_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
      | ~ class_Fields_Olinordered__field(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_pos__divide__le__eq]) ).

fof(f_1591_2,plain,
    ! [U_6072,U_6071,U_6070,U_6069] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6069),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6069),U_6071),U_6070)),U_6072))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6069),U_6071),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6069),U_6072),U_6070))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6069),U_6071),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6069),U_6072),U_6070)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6069),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6069),U_6071),U_6070)),U_6072)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6069),c_Groups_Ozero__class_Ozero(U_6069)),U_6070))
      | ~ class_Fields_Olinordered__field(U_6069) ),
    inference(variable_rename,[status(thm)],[f_1591_1]) ).

cnf(f_1591_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6069),U_6071),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6069),U_6072),U_6070)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6069),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6069),U_6071),U_6070)),U_6072))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6069),c_Groups_Ozero__class_Ozero(U_6069)),U_6070))
    | ~ class_Fields_Olinordered__field(U_6069) ),
    inference(clausify,[status(thm)],[f_1591_2]) ).

cnf(f_1591_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6069),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6069),U_6071),U_6070)),U_6072))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6069),U_6071),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6069),U_6072),U_6070)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6069),c_Groups_Ozero__class_Ozero(U_6069)),U_6070))
    | ~ class_Fields_Olinordered__field(U_6069) ),
    inference(clausify,[status(thm)],[f_1591_2]) ).

fof(f_1592_1,plain,
    ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
      ( ( ( hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2
          | hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) )
        & ( hAPP(hAPP(V_F_2,V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2),V_z_2),V_A_2)
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ) )
      | ~ c_Big__Operators_Ocomm__monoid__big(T_b,T_c,V_f_2,V_z_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_comm__monoid__big_OF__eq]) ).

fof(f_1592_2,plain,
    ! [U_6079,U_6078,U_6077,U_6076,U_6075,U_6074,U_6073] :
      ( ( ( hAPP(hAPP(U_6077,U_6079),U_6078) = U_6076
          | hBOOL(hAPP(c_Finite__Set_Ofinite(U_6074),U_6078)) )
        & ( hAPP(hAPP(U_6077,U_6079),U_6078) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_6073,U_6074,U_6075),U_6079),U_6076),U_6078)
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6074),U_6078)) ) )
      | ~ c_Big__Operators_Ocomm__monoid__big(U_6073,U_6074,U_6075,U_6076,U_6077) ),
    inference(variable_rename,[status(thm)],[f_1592_1]) ).

cnf(f_1592_3,plain,
    ( hAPP(hAPP(U_6077,U_6079),U_6078) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_6073,U_6074,U_6075),U_6079),U_6076),U_6078)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6074),U_6078))
    | ~ c_Big__Operators_Ocomm__monoid__big(U_6073,U_6074,U_6075,U_6076,U_6077) ),
    inference(clausify,[status(thm)],[f_1592_2]) ).

cnf(f_1592_4,plain,
    ( hAPP(hAPP(U_6077,U_6079),U_6078) = U_6076
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_6074),U_6078))
    | ~ c_Big__Operators_Ocomm__monoid__big(U_6073,U_6074,U_6075,U_6076,U_6077) ),
    inference(clausify,[status(thm)],[f_1592_2]) ).

fof(f_1593_1,plain,
    ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
      | ? [B_x] :
          ( hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c)
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Fields_Ofield(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__Un]) ).

fof(f_1593_2,plain,
    ! [U_6085,U_6084,U_6083,U_6082,U_6081] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_6082,U_6081),U_6085),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6082,tc_HOL_Obool)),U_6083),U_6084)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6081),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6081),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_6082,U_6081),U_6085),U_6083)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_6082,U_6081),U_6085),U_6084))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_6082,U_6081),U_6085),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_6082,tc_HOL_Obool)),U_6083),U_6084)))
      | ? [U_6080] :
          ( hAPP(U_6085,U_6080) = c_Groups_Ozero__class_Ozero(U_6081)
          & hBOOL(hAPP(hAPP(c_member(U_6082),U_6080),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_6082,tc_HOL_Obool)),U_6083),U_6084))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6082),U_6084))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6082),U_6083))
      | ~ class_Fields_Ofield(U_6081) ),
    inference(variable_rename,[status(thm)],[f_1593_1]) ).

fof(f_1593_3,plain,
    ! [U_6085,U_6084,U_6083,U_6082,U_6081] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_6082,U_6081),U_6085),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6082,tc_HOL_Obool)),U_6083),U_6084)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6081),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6081),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_6082,U_6081),U_6085),U_6083)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_6082,U_6081),U_6085),U_6084))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_6082,U_6081),U_6085),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_6082,tc_HOL_Obool)),U_6083),U_6084)))
      | ( hAPP(U_6085,sK126(U_6085,U_6084,U_6083,U_6082,U_6081)) = c_Groups_Ozero__class_Ozero(U_6081)
        & hBOOL(hAPP(hAPP(c_member(U_6082),sK126(U_6085,U_6084,U_6083,U_6082,U_6081)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_6082,tc_HOL_Obool)),U_6083),U_6084))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6082),U_6084))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6082),U_6083))
      | ~ class_Fields_Ofield(U_6081) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK126]),skolemize(U_6080,sK126(U_6085,U_6084,U_6083,U_6082,U_6081))],[f_1593_2]) ).

cnf(f_1593_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_6082),sK126(U_6085,U_6084,U_6083,U_6082,U_6081)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_6082,tc_HOL_Obool)),U_6083),U_6084)))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_6082,U_6081),U_6085),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6082,tc_HOL_Obool)),U_6083),U_6084)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6081),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6081),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_6082,U_6081),U_6085),U_6083)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_6082,U_6081),U_6085),U_6084))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_6082,U_6081),U_6085),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_6082,tc_HOL_Obool)),U_6083),U_6084)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6082),U_6084))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6082),U_6083))
    | ~ class_Fields_Ofield(U_6081) ),
    inference(clausify,[status(thm)],[f_1593_3]) ).

cnf(f_1593_5,plain,
    ( hAPP(U_6085,sK126(U_6085,U_6084,U_6083,U_6082,U_6081)) = c_Groups_Ozero__class_Ozero(U_6081)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_6082,U_6081),U_6085),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6082,tc_HOL_Obool)),U_6083),U_6084)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6081),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6081),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_6082,U_6081),U_6085),U_6083)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_6082,U_6081),U_6085),U_6084))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_6082,U_6081),U_6085),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_6082,tc_HOL_Obool)),U_6083),U_6084)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6082),U_6084))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6082),U_6083))
    | ~ class_Fields_Ofield(U_6081) ),
    inference(clausify,[status(thm)],[f_1593_3]) ).

fof(f_1594_1,plain,
    ! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_f_2),c_Groups_Oone__class_Oone(T_c)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_f_2),c_Groups_Oone__class_Oone(T_c)),V_S_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_f_2),c_Groups_Oone__class_Oone(T_c)),V_T_2))
      | ? [B_x] :
          ( hAPP(V_f_2,B_x) != c_Groups_Oone__class_Oone(T_c)
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_fold__image__Un__one]) ).

fof(f_1594_2,plain,
    ! [U_6091,U_6090,U_6089,U_6088,U_6087] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_6087,U_6088,c_Groups_Otimes__class_Otimes(U_6087)),U_6091),c_Groups_Oone__class_Oone(U_6087)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6088,tc_HOL_Obool)),U_6089),U_6090)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6087),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_6087,U_6088,c_Groups_Otimes__class_Otimes(U_6087)),U_6091),c_Groups_Oone__class_Oone(U_6087)),U_6089)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_6087,U_6088,c_Groups_Otimes__class_Otimes(U_6087)),U_6091),c_Groups_Oone__class_Oone(U_6087)),U_6090))
      | ? [U_6086] :
          ( hAPP(U_6091,U_6086) != c_Groups_Oone__class_Oone(U_6087)
          & hBOOL(hAPP(hAPP(c_member(U_6088),U_6086),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_6088,tc_HOL_Obool)),U_6089),U_6090))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6088),U_6090))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6088),U_6089))
      | ~ class_Groups_Ocomm__monoid__mult(U_6087) ),
    inference(variable_rename,[status(thm)],[f_1594_1]) ).

fof(f_1594_3,plain,
    ! [U_6091,U_6090,U_6089,U_6088,U_6087] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_6087,U_6088,c_Groups_Otimes__class_Otimes(U_6087)),U_6091),c_Groups_Oone__class_Oone(U_6087)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6088,tc_HOL_Obool)),U_6089),U_6090)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6087),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_6087,U_6088,c_Groups_Otimes__class_Otimes(U_6087)),U_6091),c_Groups_Oone__class_Oone(U_6087)),U_6089)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_6087,U_6088,c_Groups_Otimes__class_Otimes(U_6087)),U_6091),c_Groups_Oone__class_Oone(U_6087)),U_6090))
      | ( hAPP(U_6091,sK127(U_6091,U_6090,U_6089,U_6088,U_6087)) != c_Groups_Oone__class_Oone(U_6087)
        & hBOOL(hAPP(hAPP(c_member(U_6088),sK127(U_6091,U_6090,U_6089,U_6088,U_6087)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_6088,tc_HOL_Obool)),U_6089),U_6090))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6088),U_6090))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6088),U_6089))
      | ~ class_Groups_Ocomm__monoid__mult(U_6087) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK127]),skolemize(U_6086,sK127(U_6091,U_6090,U_6089,U_6088,U_6087))],[f_1594_2]) ).

cnf(f_1594_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_6088),sK127(U_6091,U_6090,U_6089,U_6088,U_6087)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_6088,tc_HOL_Obool)),U_6089),U_6090)))
    | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_6087,U_6088,c_Groups_Otimes__class_Otimes(U_6087)),U_6091),c_Groups_Oone__class_Oone(U_6087)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6088,tc_HOL_Obool)),U_6089),U_6090)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6087),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_6087,U_6088,c_Groups_Otimes__class_Otimes(U_6087)),U_6091),c_Groups_Oone__class_Oone(U_6087)),U_6089)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_6087,U_6088,c_Groups_Otimes__class_Otimes(U_6087)),U_6091),c_Groups_Oone__class_Oone(U_6087)),U_6090))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6088),U_6090))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6088),U_6089))
    | ~ class_Groups_Ocomm__monoid__mult(U_6087) ),
    inference(clausify,[status(thm)],[f_1594_3]) ).

cnf(f_1594_5,plain,
    ( hAPP(U_6091,sK127(U_6091,U_6090,U_6089,U_6088,U_6087)) != c_Groups_Oone__class_Oone(U_6087)
    | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_6087,U_6088,c_Groups_Otimes__class_Otimes(U_6087)),U_6091),c_Groups_Oone__class_Oone(U_6087)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6088,tc_HOL_Obool)),U_6089),U_6090)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6087),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_6087,U_6088,c_Groups_Otimes__class_Otimes(U_6087)),U_6091),c_Groups_Oone__class_Oone(U_6087)),U_6089)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_6087,U_6088,c_Groups_Otimes__class_Otimes(U_6087)),U_6091),c_Groups_Oone__class_Oone(U_6087)),U_6090))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6088),U_6090))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6088),U_6089))
    | ~ class_Groups_Ocomm__monoid__mult(U_6087) ),
    inference(clausify,[status(thm)],[f_1594_3]) ).

fof(f_1595_1,plain,
    ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_T_2)
      | ? [B_x] :
          ( hAPP(V_f_2,B_x) != c_Groups_Oone__class_Oone(T_c)
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_T_2),V_S_2))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__mono__one__left]) ).

fof(f_1595_2,plain,
    ! [U_6097,U_6096,U_6095,U_6094,U_6093] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_6094,U_6093),U_6097),U_6096) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_6094,U_6093),U_6097),U_6095)
      | ? [U_6092] :
          ( hAPP(U_6097,U_6092) != c_Groups_Oone__class_Oone(U_6093)
          & hBOOL(hAPP(hAPP(c_member(U_6094),U_6092),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6094,tc_HOL_Obool)),U_6095),U_6096))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6094,tc_HOL_Obool)),U_6096),U_6095))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6094),U_6095))
      | ~ class_Groups_Ocomm__monoid__mult(U_6093) ),
    inference(variable_rename,[status(thm)],[f_1595_1]) ).

fof(f_1595_3,plain,
    ! [U_6097,U_6096,U_6095,U_6094,U_6093] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_6094,U_6093),U_6097),U_6096) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_6094,U_6093),U_6097),U_6095)
      | ( hAPP(U_6097,sK128(U_6097,U_6096,U_6095,U_6094,U_6093)) != c_Groups_Oone__class_Oone(U_6093)
        & hBOOL(hAPP(hAPP(c_member(U_6094),sK128(U_6097,U_6096,U_6095,U_6094,U_6093)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6094,tc_HOL_Obool)),U_6095),U_6096))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6094,tc_HOL_Obool)),U_6096),U_6095))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6094),U_6095))
      | ~ class_Groups_Ocomm__monoid__mult(U_6093) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK128]),skolemize(U_6092,sK128(U_6097,U_6096,U_6095,U_6094,U_6093))],[f_1595_2]) ).

cnf(f_1595_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_6094),sK128(U_6097,U_6096,U_6095,U_6094,U_6093)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6094,tc_HOL_Obool)),U_6095),U_6096)))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_6094,U_6093),U_6097),U_6096) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_6094,U_6093),U_6097),U_6095)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6094,tc_HOL_Obool)),U_6096),U_6095))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6094),U_6095))
    | ~ class_Groups_Ocomm__monoid__mult(U_6093) ),
    inference(clausify,[status(thm)],[f_1595_3]) ).

cnf(f_1595_5,plain,
    ( hAPP(U_6097,sK128(U_6097,U_6096,U_6095,U_6094,U_6093)) != c_Groups_Oone__class_Oone(U_6093)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_6094,U_6093),U_6097),U_6096) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_6094,U_6093),U_6097),U_6095)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6094,tc_HOL_Obool)),U_6096),U_6095))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6094),U_6095))
    | ~ class_Groups_Ocomm__monoid__mult(U_6093) ),
    inference(clausify,[status(thm)],[f_1595_3]) ).

fof(f_1596_1,plain,
    ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_T_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_S_2)
      | ? [B_x] :
          ( hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_c)
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_T_2),V_S_2))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
      | ~ class_Groups_Ocomm__monoid__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__mono__zero__right]) ).

fof(f_1596_2,plain,
    ! [U_6103,U_6102,U_6101,U_6100,U_6099] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6100,U_6099),U_6103),U_6101) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6100,U_6099),U_6103),U_6102)
      | ? [U_6098] :
          ( hAPP(U_6103,U_6098) != c_Groups_Ozero__class_Ozero(U_6099)
          & hBOOL(hAPP(hAPP(c_member(U_6100),U_6098),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6100,tc_HOL_Obool)),U_6101),U_6102))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6100,tc_HOL_Obool)),U_6102),U_6101))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6100),U_6101))
      | ~ class_Groups_Ocomm__monoid__add(U_6099) ),
    inference(variable_rename,[status(thm)],[f_1596_1]) ).

fof(f_1596_3,plain,
    ! [U_6103,U_6102,U_6101,U_6100,U_6099] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6100,U_6099),U_6103),U_6101) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6100,U_6099),U_6103),U_6102)
      | ( hAPP(U_6103,sK129(U_6103,U_6102,U_6101,U_6100,U_6099)) != c_Groups_Ozero__class_Ozero(U_6099)
        & hBOOL(hAPP(hAPP(c_member(U_6100),sK129(U_6103,U_6102,U_6101,U_6100,U_6099)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6100,tc_HOL_Obool)),U_6101),U_6102))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6100,tc_HOL_Obool)),U_6102),U_6101))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6100),U_6101))
      | ~ class_Groups_Ocomm__monoid__add(U_6099) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK129]),skolemize(U_6098,sK129(U_6103,U_6102,U_6101,U_6100,U_6099))],[f_1596_2]) ).

cnf(f_1596_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_6100),sK129(U_6103,U_6102,U_6101,U_6100,U_6099)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6100,tc_HOL_Obool)),U_6101),U_6102)))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6100,U_6099),U_6103),U_6101) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6100,U_6099),U_6103),U_6102)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6100,tc_HOL_Obool)),U_6102),U_6101))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6100),U_6101))
    | ~ class_Groups_Ocomm__monoid__add(U_6099) ),
    inference(clausify,[status(thm)],[f_1596_3]) ).

cnf(f_1596_5,plain,
    ( hAPP(U_6103,sK129(U_6103,U_6102,U_6101,U_6100,U_6099)) != c_Groups_Ozero__class_Ozero(U_6099)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6100,U_6099),U_6103),U_6101) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6100,U_6099),U_6103),U_6102)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6100,tc_HOL_Obool)),U_6102),U_6101))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6100),U_6101))
    | ~ class_Groups_Ocomm__monoid__add(U_6099) ),
    inference(clausify,[status(thm)],[f_1596_3]) ).

fof(f_1597_1,plain,
    ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_T_2)
      | ? [B_x] :
          ( hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_c)
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_T_2),V_S_2))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
      | ~ class_Groups_Ocomm__monoid__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__mono__zero__left]) ).

fof(f_1597_2,plain,
    ! [U_6109,U_6108,U_6107,U_6106,U_6105] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6106,U_6105),U_6109),U_6108) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6106,U_6105),U_6109),U_6107)
      | ? [U_6104] :
          ( hAPP(U_6109,U_6104) != c_Groups_Ozero__class_Ozero(U_6105)
          & hBOOL(hAPP(hAPP(c_member(U_6106),U_6104),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6106,tc_HOL_Obool)),U_6107),U_6108))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6106,tc_HOL_Obool)),U_6108),U_6107))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6106),U_6107))
      | ~ class_Groups_Ocomm__monoid__add(U_6105) ),
    inference(variable_rename,[status(thm)],[f_1597_1]) ).

fof(f_1597_3,plain,
    ! [U_6109,U_6108,U_6107,U_6106,U_6105] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6106,U_6105),U_6109),U_6108) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6106,U_6105),U_6109),U_6107)
      | ( hAPP(U_6109,sK130(U_6109,U_6108,U_6107,U_6106,U_6105)) != c_Groups_Ozero__class_Ozero(U_6105)
        & hBOOL(hAPP(hAPP(c_member(U_6106),sK130(U_6109,U_6108,U_6107,U_6106,U_6105)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6106,tc_HOL_Obool)),U_6107),U_6108))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6106,tc_HOL_Obool)),U_6108),U_6107))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6106),U_6107))
      | ~ class_Groups_Ocomm__monoid__add(U_6105) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK130]),skolemize(U_6104,sK130(U_6109,U_6108,U_6107,U_6106,U_6105))],[f_1597_2]) ).

cnf(f_1597_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_6106),sK130(U_6109,U_6108,U_6107,U_6106,U_6105)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6106,tc_HOL_Obool)),U_6107),U_6108)))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6106,U_6105),U_6109),U_6108) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6106,U_6105),U_6109),U_6107)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6106,tc_HOL_Obool)),U_6108),U_6107))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6106),U_6107))
    | ~ class_Groups_Ocomm__monoid__add(U_6105) ),
    inference(clausify,[status(thm)],[f_1597_3]) ).

cnf(f_1597_5,plain,
    ( hAPP(U_6109,sK130(U_6109,U_6108,U_6107,U_6106,U_6105)) != c_Groups_Ozero__class_Ozero(U_6105)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6106,U_6105),U_6109),U_6108) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6106,U_6105),U_6109),U_6107)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6106,tc_HOL_Obool)),U_6108),U_6107))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6106),U_6107))
    | ~ class_Groups_Ocomm__monoid__add(U_6105) ),
    inference(clausify,[status(thm)],[f_1597_3]) ).

fof(f_1598_1,plain,
    ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
      ( hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2
      | hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
      | ~ c_Big__Operators_Ocomm__monoid__big(T_b,T_c,V_f_2,V_z_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_comm__monoid__big_Oinfinite]) ).

fof(f_1598_2,plain,
    ! [U_6116,U_6115,U_6114,U_6113,U_6112,U_6111,U_6110] :
      ( hAPP(hAPP(U_6114,U_6116),U_6115) = U_6113
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_6111),U_6115))
      | ~ c_Big__Operators_Ocomm__monoid__big(U_6110,U_6111,U_6112,U_6113,U_6114) ),
    inference(variable_rename,[status(thm)],[f_1598_1]) ).

fof(f_1598_3,plain,
    ! [U_6116,U_6115,U_6114,U_6113,U_6112,U_6111] :
      ( ! [U_6110] : ~ c_Big__Operators_Ocomm__monoid__big(U_6110,U_6111,U_6112,U_6113,U_6114)
      | hAPP(hAPP(U_6114,U_6116),U_6115) = U_6113
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_6111),U_6115)) ),
    inference(miniscope,[status(thm)],[f_1598_2]) ).

cnf(f_1598_4,plain,
    ( ~ c_Big__Operators_Ocomm__monoid__big(U_6110,U_6111,U_6112,U_6113,U_6114)
    | hAPP(hAPP(U_6114,U_6116),U_6115) = U_6113
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_6111),U_6115)) ),
    inference(clausify,[status(thm)],[f_1598_3]) ).

fof(f_1599_1,plain,
    ! [V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
      | ? [B_z] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_z),V_x)),V_y))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_z),c_Groups_Oone__class_Oone(T_a)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_z)) )
      | ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_field__le__mult__one__interval]) ).

fof(f_1599_2,plain,
    ! [U_6120,U_6119,U_6118] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6118),U_6119),U_6120))
      | ? [U_6117] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6118),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6118),U_6117),U_6119)),U_6120))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6118),U_6117),c_Groups_Oone__class_Oone(U_6118)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6118),c_Groups_Ozero__class_Ozero(U_6118)),U_6117)) )
      | ~ class_Fields_Olinordered__field__inverse__zero(U_6118) ),
    inference(variable_rename,[status(thm)],[f_1599_1]) ).

fof(f_1599_3,plain,
    ! [U_6120,U_6119,U_6118] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6118),U_6119),U_6120))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6118),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6118),sK131(U_6120,U_6119,U_6118)),U_6119)),U_6120))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6118),sK131(U_6120,U_6119,U_6118)),c_Groups_Oone__class_Oone(U_6118)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6118),c_Groups_Ozero__class_Ozero(U_6118)),sK131(U_6120,U_6119,U_6118))) )
      | ~ class_Fields_Olinordered__field__inverse__zero(U_6118) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK131]),skolemize(U_6117,sK131(U_6120,U_6119,U_6118))],[f_1599_2]) ).

cnf(f_1599_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6118),c_Groups_Ozero__class_Ozero(U_6118)),sK131(U_6120,U_6119,U_6118)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6118),U_6119),U_6120))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6118) ),
    inference(clausify,[status(thm)],[f_1599_3]) ).

cnf(f_1599_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6118),sK131(U_6120,U_6119,U_6118)),c_Groups_Oone__class_Oone(U_6118)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6118),U_6119),U_6120))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6118) ),
    inference(clausify,[status(thm)],[f_1599_3]) ).

cnf(f_1599_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6118),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6118),sK131(U_6120,U_6119,U_6118)),U_6119)),U_6120))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6118),U_6119),U_6120))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6118) ),
    inference(clausify,[status(thm)],[f_1599_3]) ).

fof(f_1600_1,plain,
    ! [V_a,T_a] :
      ( c_Groups_Osgn__class_Osgn(T_a,V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sgn__neg]) ).

fof(f_1600_2,plain,
    ! [U_6122,U_6121] :
      ( c_Groups_Osgn__class_Osgn(U_6121,U_6122) = hAPP(c_Groups_Ouminus__class_Ouminus(U_6121),c_Groups_Oone__class_Oone(U_6121))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6121),U_6122),c_Groups_Ozero__class_Ozero(U_6121)))
      | ~ class_Rings_Olinordered__idom(U_6121) ),
    inference(variable_rename,[status(thm)],[f_1600_1]) ).

cnf(f_1600_3,plain,
    ( c_Groups_Osgn__class_Osgn(U_6121,U_6122) = hAPP(c_Groups_Ouminus__class_Ouminus(U_6121),c_Groups_Oone__class_Oone(U_6121))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6121),U_6122),c_Groups_Ozero__class_Ozero(U_6121)))
    | ~ class_Rings_Olinordered__idom(U_6121) ),
    inference(clausify,[status(thm)],[f_1600_2]) ).

fof(f_1601_1,plain,
    ! [V_a_2,T_b] :
      ( ( ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
          | c_Groups_Osgn__class_Osgn(T_b,V_a_2) != hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b)) ) )
      | ~ class_Rings_Olinordered__idom(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sgn__1__neg]) ).

fof(f_1601_2,plain,
    ! [U_6124,U_6123] :
      ( ( ( c_Groups_Osgn__class_Osgn(U_6123,U_6124) = hAPP(c_Groups_Ouminus__class_Ouminus(U_6123),c_Groups_Oone__class_Oone(U_6123))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6123),U_6124),c_Groups_Ozero__class_Ozero(U_6123))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6123),U_6124),c_Groups_Ozero__class_Ozero(U_6123)))
          | c_Groups_Osgn__class_Osgn(U_6123,U_6124) != hAPP(c_Groups_Ouminus__class_Ouminus(U_6123),c_Groups_Oone__class_Oone(U_6123)) ) )
      | ~ class_Rings_Olinordered__idom(U_6123) ),
    inference(variable_rename,[status(thm)],[f_1601_1]) ).

cnf(f_1601_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6123),U_6124),c_Groups_Ozero__class_Ozero(U_6123)))
    | c_Groups_Osgn__class_Osgn(U_6123,U_6124) != hAPP(c_Groups_Ouminus__class_Ouminus(U_6123),c_Groups_Oone__class_Oone(U_6123))
    | ~ class_Rings_Olinordered__idom(U_6123) ),
    inference(clausify,[status(thm)],[f_1601_2]) ).

cnf(f_1601_4,plain,
    ( c_Groups_Osgn__class_Osgn(U_6123,U_6124) = hAPP(c_Groups_Ouminus__class_Ouminus(U_6123),c_Groups_Oone__class_Oone(U_6123))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6123),U_6124),c_Groups_Ozero__class_Ozero(U_6123)))
    | ~ class_Rings_Olinordered__idom(U_6123) ),
    inference(clausify,[status(thm)],[f_1601_2]) ).

fof(f_1602_1,plain,
    ! [V_x,T_a] :
      ( ( ( ( ( c_Groups_Osgn__class_Osgn(T_a,V_x) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) )
            & ( c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Oone__class_Oone(T_a)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) ) )
          | V_x = c_Groups_Ozero__class_Ozero(T_a) )
        & ( c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ozero__class_Ozero(T_a)
          | V_x != c_Groups_Ozero__class_Ozero(T_a) ) )
      | ~ class_Groups_Osgn__if(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sgn__if]) ).

fof(f_1602_2,plain,
    ! [U_6126,U_6125] :
      ( ( ( ( ( c_Groups_Osgn__class_Osgn(U_6125,U_6126) = hAPP(c_Groups_Ouminus__class_Ouminus(U_6125),c_Groups_Oone__class_Oone(U_6125))
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6125),c_Groups_Ozero__class_Ozero(U_6125)),U_6126)) )
            & ( c_Groups_Osgn__class_Osgn(U_6125,U_6126) = c_Groups_Oone__class_Oone(U_6125)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6125),c_Groups_Ozero__class_Ozero(U_6125)),U_6126)) ) )
          | U_6126 = c_Groups_Ozero__class_Ozero(U_6125) )
        & ( c_Groups_Osgn__class_Osgn(U_6125,U_6126) = c_Groups_Ozero__class_Ozero(U_6125)
          | U_6126 != c_Groups_Ozero__class_Ozero(U_6125) ) )
      | ~ class_Groups_Osgn__if(U_6125) ),
    inference(variable_rename,[status(thm)],[f_1602_1]) ).

cnf(f_1602_3,plain,
    ( c_Groups_Osgn__class_Osgn(U_6125,U_6126) = c_Groups_Ozero__class_Ozero(U_6125)
    | U_6126 != c_Groups_Ozero__class_Ozero(U_6125)
    | ~ class_Groups_Osgn__if(U_6125) ),
    inference(clausify,[status(thm)],[f_1602_2]) ).

cnf(f_1602_4,plain,
    ( c_Groups_Osgn__class_Osgn(U_6125,U_6126) = c_Groups_Oone__class_Oone(U_6125)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6125),c_Groups_Ozero__class_Ozero(U_6125)),U_6126))
    | U_6126 = c_Groups_Ozero__class_Ozero(U_6125)
    | ~ class_Groups_Osgn__if(U_6125) ),
    inference(clausify,[status(thm)],[f_1602_2]) ).

cnf(f_1602_5,plain,
    ( c_Groups_Osgn__class_Osgn(U_6125,U_6126) = hAPP(c_Groups_Ouminus__class_Ouminus(U_6125),c_Groups_Oone__class_Oone(U_6125))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6125),c_Groups_Ozero__class_Ozero(U_6125)),U_6126))
    | U_6126 = c_Groups_Ozero__class_Ozero(U_6125)
    | ~ class_Groups_Osgn__if(U_6125) ),
    inference(clausify,[status(thm)],[f_1602_2]) ).

fof(f_1603_1,plain,
    ! [V_a3_2,V_a2_2,V_a1_2,V_f_2,T_b] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),V_a2_2)),V_a3_2))
        | ! [B_a,B_A] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A))
            | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_a3_2))
            | hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),V_a2_2) != hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A) ) )
      & ( ? [B_a,B_A] :
            ( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A))
            & hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_a3_2))
            & hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),V_a2_2) = hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),V_a2_2)),V_a3_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_fold1Set_Oequations]) ).

fof(f_1603_2,plain,
    ! [U_6135,U_6134,U_6133,U_6132,U_6131] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_6131,U_6132,hAPP(hAPP(c_Set_Oinsert(U_6131),U_6133),U_6134)),U_6135))
        | ! [U_6130,U_6129] :
            ( hBOOL(hAPP(hAPP(c_member(U_6131),U_6130),U_6129))
            | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_6131,U_6131,U_6132,U_6130,U_6129),U_6135))
            | hAPP(hAPP(c_Set_Oinsert(U_6131),U_6133),U_6134) != hAPP(hAPP(c_Set_Oinsert(U_6131),U_6130),U_6129) ) )
      & ( ? [U_6128,U_6127] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_6131),U_6128),U_6127))
            & hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_6131,U_6131,U_6132,U_6128,U_6127),U_6135))
            & hAPP(hAPP(c_Set_Oinsert(U_6131),U_6133),U_6134) = hAPP(hAPP(c_Set_Oinsert(U_6131),U_6128),U_6127) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_6131,U_6132,hAPP(hAPP(c_Set_Oinsert(U_6131),U_6133),U_6134)),U_6135)) ) ),
    inference(variable_rename,[status(thm)],[f_1603_1]) ).

fof(f_1603_3,plain,
    ( ! [U_6145,U_6143,U_6141,U_6139,U_6137] :
        ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_6137,U_6139,hAPP(hAPP(c_Set_Oinsert(U_6137),U_6141),U_6143)),U_6145))
        | ! [U_6130,U_6129] :
            ( hBOOL(hAPP(hAPP(c_member(U_6137),U_6130),U_6129))
            | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_6137,U_6137,U_6139,U_6130,U_6129),U_6145))
            | hAPP(hAPP(c_Set_Oinsert(U_6137),U_6141),U_6143) != hAPP(hAPP(c_Set_Oinsert(U_6137),U_6130),U_6129) ) )
    & ! [U_6144,U_6142,U_6140,U_6138,U_6136] :
        ( ? [U_6128,U_6127] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_6136),U_6128),U_6127))
            & hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_6136,U_6136,U_6138,U_6128,U_6127),U_6144))
            & hAPP(hAPP(c_Set_Oinsert(U_6136),U_6140),U_6142) = hAPP(hAPP(c_Set_Oinsert(U_6136),U_6128),U_6127) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_6136,U_6138,hAPP(hAPP(c_Set_Oinsert(U_6136),U_6140),U_6142)),U_6144)) ) ),
    inference(miniscope,[status(thm)],[f_1603_2]) ).

fof(f_1603_4,plain,
    ( ! [U_6145,U_6143,U_6141,U_6139,U_6137] :
        ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_6137,U_6139,hAPP(hAPP(c_Set_Oinsert(U_6137),U_6141),U_6143)),U_6145))
        | ! [U_6130,U_6129] :
            ( hBOOL(hAPP(hAPP(c_member(U_6137),U_6130),U_6129))
            | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_6137,U_6137,U_6139,U_6130,U_6129),U_6145))
            | hAPP(hAPP(c_Set_Oinsert(U_6137),U_6141),U_6143) != hAPP(hAPP(c_Set_Oinsert(U_6137),U_6130),U_6129) ) )
    & ! [U_6144,U_6142,U_6140,U_6138,U_6136] :
        ( ? [U_6127] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_6136),sK132(U_6144,U_6142,U_6140,U_6138,U_6136)),U_6127))
            & hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_6136,U_6136,U_6138,sK132(U_6144,U_6142,U_6140,U_6138,U_6136),U_6127),U_6144))
            & hAPP(hAPP(c_Set_Oinsert(U_6136),U_6140),U_6142) = hAPP(hAPP(c_Set_Oinsert(U_6136),sK132(U_6144,U_6142,U_6140,U_6138,U_6136)),U_6127) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_6136,U_6138,hAPP(hAPP(c_Set_Oinsert(U_6136),U_6140),U_6142)),U_6144)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK132]),skolemize(U_6128,sK132(U_6144,U_6142,U_6140,U_6138,U_6136))],[f_1603_3]) ).

fof(f_1603_5,plain,
    ( ! [U_6145,U_6143,U_6141,U_6139,U_6137] :
        ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_6137,U_6139,hAPP(hAPP(c_Set_Oinsert(U_6137),U_6141),U_6143)),U_6145))
        | ! [U_6130,U_6129] :
            ( hBOOL(hAPP(hAPP(c_member(U_6137),U_6130),U_6129))
            | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_6137,U_6137,U_6139,U_6130,U_6129),U_6145))
            | hAPP(hAPP(c_Set_Oinsert(U_6137),U_6141),U_6143) != hAPP(hAPP(c_Set_Oinsert(U_6137),U_6130),U_6129) ) )
    & ! [U_6144,U_6142,U_6140,U_6138,U_6136] :
        ( ( ~ hBOOL(hAPP(hAPP(c_member(U_6136),sK132(U_6144,U_6142,U_6140,U_6138,U_6136)),sK133(U_6144,U_6142,U_6140,U_6138,U_6136)))
          & hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_6136,U_6136,U_6138,sK132(U_6144,U_6142,U_6140,U_6138,U_6136),sK133(U_6144,U_6142,U_6140,U_6138,U_6136)),U_6144))
          & hAPP(hAPP(c_Set_Oinsert(U_6136),U_6140),U_6142) = hAPP(hAPP(c_Set_Oinsert(U_6136),sK132(U_6144,U_6142,U_6140,U_6138,U_6136)),sK133(U_6144,U_6142,U_6140,U_6138,U_6136)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_6136,U_6138,hAPP(hAPP(c_Set_Oinsert(U_6136),U_6140),U_6142)),U_6144)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK133]),skolemize(U_6127,sK133(U_6144,U_6142,U_6140,U_6138,U_6136))],[f_1603_4]) ).

cnf(f_1603_6,plain,
    ( hAPP(hAPP(c_Set_Oinsert(U_6136),U_6140),U_6142) = hAPP(hAPP(c_Set_Oinsert(U_6136),sK132(U_6144,U_6142,U_6140,U_6138,U_6136)),sK133(U_6144,U_6142,U_6140,U_6138,U_6136))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_6136,U_6138,hAPP(hAPP(c_Set_Oinsert(U_6136),U_6140),U_6142)),U_6144)) ),
    inference(clausify,[status(thm)],[f_1603_5]) ).

cnf(f_1603_7,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_6136,U_6136,U_6138,sK132(U_6144,U_6142,U_6140,U_6138,U_6136),sK133(U_6144,U_6142,U_6140,U_6138,U_6136)),U_6144))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_6136,U_6138,hAPP(hAPP(c_Set_Oinsert(U_6136),U_6140),U_6142)),U_6144)) ),
    inference(clausify,[status(thm)],[f_1603_5]) ).

cnf(f_1603_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_6136),sK132(U_6144,U_6142,U_6140,U_6138,U_6136)),sK133(U_6144,U_6142,U_6140,U_6138,U_6136)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_6136,U_6138,hAPP(hAPP(c_Set_Oinsert(U_6136),U_6140),U_6142)),U_6144)) ),
    inference(clausify,[status(thm)],[f_1603_5]) ).

cnf(f_1603_9,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_6137,U_6139,hAPP(hAPP(c_Set_Oinsert(U_6137),U_6141),U_6143)),U_6145))
    | hBOOL(hAPP(hAPP(c_member(U_6137),U_6130),U_6129))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_6137,U_6137,U_6139,U_6130,U_6129),U_6145))
    | hAPP(hAPP(c_Set_Oinsert(U_6137),U_6141),U_6143) != hAPP(hAPP(c_Set_Oinsert(U_6137),U_6130),U_6129) ),
    inference(clausify,[status(thm)],[f_1603_5]) ).

fof(f_1604_1,plain,
    ! [V_x_2,V_X_2,V_a_2,V_f_2,T_b] :
      ( ? [B_a,B_A] :
          ( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A))
          & hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_x_2))
          & hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_X_2) = hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_X_2)),V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_insert__fold1SetE]) ).

fof(f_1604_2,plain,
    ! [U_6152,U_6151,U_6150,U_6149,U_6148] :
      ( ? [U_6147,U_6146] :
          ( ~ hBOOL(hAPP(hAPP(c_member(U_6148),U_6147),U_6146))
          & hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_6148,U_6148,U_6149,U_6147,U_6146),U_6152))
          & hAPP(hAPP(c_Set_Oinsert(U_6148),U_6150),U_6151) = hAPP(hAPP(c_Set_Oinsert(U_6148),U_6147),U_6146) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_6148,U_6149,hAPP(hAPP(c_Set_Oinsert(U_6148),U_6150),U_6151)),U_6152)) ),
    inference(variable_rename,[status(thm)],[f_1604_1]) ).

fof(f_1604_3,plain,
    ! [U_6152,U_6151,U_6150,U_6149,U_6148] :
      ( ? [U_6146] :
          ( ~ hBOOL(hAPP(hAPP(c_member(U_6148),sK134(U_6152,U_6151,U_6150,U_6149,U_6148)),U_6146))
          & hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_6148,U_6148,U_6149,sK134(U_6152,U_6151,U_6150,U_6149,U_6148),U_6146),U_6152))
          & hAPP(hAPP(c_Set_Oinsert(U_6148),U_6150),U_6151) = hAPP(hAPP(c_Set_Oinsert(U_6148),sK134(U_6152,U_6151,U_6150,U_6149,U_6148)),U_6146) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_6148,U_6149,hAPP(hAPP(c_Set_Oinsert(U_6148),U_6150),U_6151)),U_6152)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK134]),skolemize(U_6147,sK134(U_6152,U_6151,U_6150,U_6149,U_6148))],[f_1604_2]) ).

fof(f_1604_4,plain,
    ! [U_6152,U_6151,U_6150,U_6149,U_6148] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(U_6148),sK134(U_6152,U_6151,U_6150,U_6149,U_6148)),sK135(U_6152,U_6151,U_6150,U_6149,U_6148)))
        & hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_6148,U_6148,U_6149,sK134(U_6152,U_6151,U_6150,U_6149,U_6148),sK135(U_6152,U_6151,U_6150,U_6149,U_6148)),U_6152))
        & hAPP(hAPP(c_Set_Oinsert(U_6148),U_6150),U_6151) = hAPP(hAPP(c_Set_Oinsert(U_6148),sK134(U_6152,U_6151,U_6150,U_6149,U_6148)),sK135(U_6152,U_6151,U_6150,U_6149,U_6148)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_6148,U_6149,hAPP(hAPP(c_Set_Oinsert(U_6148),U_6150),U_6151)),U_6152)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK135]),skolemize(U_6146,sK135(U_6152,U_6151,U_6150,U_6149,U_6148))],[f_1604_3]) ).

cnf(f_1604_5,plain,
    ( hAPP(hAPP(c_Set_Oinsert(U_6148),U_6150),U_6151) = hAPP(hAPP(c_Set_Oinsert(U_6148),sK134(U_6152,U_6151,U_6150,U_6149,U_6148)),sK135(U_6152,U_6151,U_6150,U_6149,U_6148))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_6148,U_6149,hAPP(hAPP(c_Set_Oinsert(U_6148),U_6150),U_6151)),U_6152)) ),
    inference(clausify,[status(thm)],[f_1604_4]) ).

cnf(f_1604_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_6148,U_6148,U_6149,sK134(U_6152,U_6151,U_6150,U_6149,U_6148),sK135(U_6152,U_6151,U_6150,U_6149,U_6148)),U_6152))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_6148,U_6149,hAPP(hAPP(c_Set_Oinsert(U_6148),U_6150),U_6151)),U_6152)) ),
    inference(clausify,[status(thm)],[f_1604_4]) ).

cnf(f_1604_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_6148),sK134(U_6152,U_6151,U_6150,U_6149,U_6148)),sK135(U_6152,U_6151,U_6150,U_6149,U_6148)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_6148,U_6149,hAPP(hAPP(c_Set_Oinsert(U_6148),U_6150),U_6151)),U_6152)) ),
    inference(clausify,[status(thm)],[f_1604_4]) ).

fof(f_1605_1,plain,
    ! [V_a,T_a] :
      ( c_Groups_Osgn__class_Osgn(T_a,c_Groups_Osgn__class_Osgn(T_a,V_a)) = c_Groups_Osgn__class_Osgn(T_a,V_a)
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sgn__sgn]) ).

fof(f_1605_2,plain,
    ! [U_6154,U_6153] :
      ( c_Groups_Osgn__class_Osgn(U_6153,c_Groups_Osgn__class_Osgn(U_6153,U_6154)) = c_Groups_Osgn__class_Osgn(U_6153,U_6154)
      | ~ class_Rings_Olinordered__idom(U_6153) ),
    inference(variable_rename,[status(thm)],[f_1605_1]) ).

cnf(f_1605_3,plain,
    ( c_Groups_Osgn__class_Osgn(U_6153,c_Groups_Osgn__class_Osgn(U_6153,U_6154)) = c_Groups_Osgn__class_Osgn(U_6153,U_6154)
    | ~ class_Rings_Olinordered__idom(U_6153) ),
    inference(clausify,[status(thm)],[f_1605_2]) ).

fof(f_1606_1,plain,
    ! [V_a_2,T_b] :
      ( ( ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
          | V_a_2 != c_Groups_Ozero__class_Ozero(T_b) )
        & ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
          | c_Groups_Osgn__class_Osgn(T_b,V_a_2) != c_Groups_Ozero__class_Ozero(T_b) ) )
      | ~ class_Rings_Olinordered__idom(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sgn__0__0]) ).

fof(f_1606_2,plain,
    ! [U_6156,U_6155] :
      ( ( ( c_Groups_Osgn__class_Osgn(U_6155,U_6156) = c_Groups_Ozero__class_Ozero(U_6155)
          | U_6156 != c_Groups_Ozero__class_Ozero(U_6155) )
        & ( U_6156 = c_Groups_Ozero__class_Ozero(U_6155)
          | c_Groups_Osgn__class_Osgn(U_6155,U_6156) != c_Groups_Ozero__class_Ozero(U_6155) ) )
      | ~ class_Rings_Olinordered__idom(U_6155) ),
    inference(variable_rename,[status(thm)],[f_1606_1]) ).

cnf(f_1606_3,plain,
    ( U_6156 = c_Groups_Ozero__class_Ozero(U_6155)
    | c_Groups_Osgn__class_Osgn(U_6155,U_6156) != c_Groups_Ozero__class_Ozero(U_6155)
    | ~ class_Rings_Olinordered__idom(U_6155) ),
    inference(clausify,[status(thm)],[f_1606_2]) ).

cnf(f_1606_4,plain,
    ( c_Groups_Osgn__class_Osgn(U_6155,U_6156) = c_Groups_Ozero__class_Ozero(U_6155)
    | U_6156 != c_Groups_Ozero__class_Ozero(U_6155)
    | ~ class_Rings_Olinordered__idom(U_6155) ),
    inference(clausify,[status(thm)],[f_1606_2]) ).

fof(f_1607_1,plain,
    ! [T_a] :
      ( c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Groups_Osgn__if(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sgn0]) ).

fof(f_1607_2,plain,
    ! [U_6157] :
      ( c_Groups_Osgn__class_Osgn(U_6157,c_Groups_Ozero__class_Ozero(U_6157)) = c_Groups_Ozero__class_Ozero(U_6157)
      | ~ class_Groups_Osgn__if(U_6157) ),
    inference(variable_rename,[status(thm)],[f_1607_1]) ).

cnf(f_1607_3,plain,
    ( c_Groups_Osgn__class_Osgn(U_6157,c_Groups_Ozero__class_Ozero(U_6157)) = c_Groups_Ozero__class_Ozero(U_6157)
    | ~ class_Groups_Osgn__if(U_6157) ),
    inference(clausify,[status(thm)],[f_1607_2]) ).

fof(f_1608_1,plain,
    ! [V_b,V_a,T_a] :
      ( c_Groups_Osgn__class_Osgn(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_a)),c_Groups_Osgn__class_Osgn(T_a,V_b))
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sgn__times]) ).

fof(f_1608_2,plain,
    ! [U_6160,U_6159,U_6158] :
      ( c_Groups_Osgn__class_Osgn(U_6158,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6158),U_6159),U_6160)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6158),c_Groups_Osgn__class_Osgn(U_6158,U_6159)),c_Groups_Osgn__class_Osgn(U_6158,U_6160))
      | ~ class_Rings_Olinordered__idom(U_6158) ),
    inference(variable_rename,[status(thm)],[f_1608_1]) ).

cnf(f_1608_3,plain,
    ( c_Groups_Osgn__class_Osgn(U_6158,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6158),U_6159),U_6160)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6158),c_Groups_Osgn__class_Osgn(U_6158,U_6159)),c_Groups_Osgn__class_Osgn(U_6158,U_6160))
    | ~ class_Rings_Olinordered__idom(U_6158) ),
    inference(clausify,[status(thm)],[f_1608_2]) ).

fof(f_1609_1,plain,
    ! [V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Osgn__class_Osgn(T_b,V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Osgn__class_Osgn(T_b,V_a_2)),c_Groups_Ozero__class_Ozero(T_b))) ) )
      | ~ class_Rings_Olinordered__idom(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sgn__less]) ).

fof(f_1609_2,plain,
    ! [U_6162,U_6161] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6161),c_Groups_Osgn__class_Osgn(U_6161,U_6162)),c_Groups_Ozero__class_Ozero(U_6161)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6161),U_6162),c_Groups_Ozero__class_Ozero(U_6161))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6161),U_6162),c_Groups_Ozero__class_Ozero(U_6161)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6161),c_Groups_Osgn__class_Osgn(U_6161,U_6162)),c_Groups_Ozero__class_Ozero(U_6161))) ) )
      | ~ class_Rings_Olinordered__idom(U_6161) ),
    inference(variable_rename,[status(thm)],[f_1609_1]) ).

cnf(f_1609_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6161),U_6162),c_Groups_Ozero__class_Ozero(U_6161)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6161),c_Groups_Osgn__class_Osgn(U_6161,U_6162)),c_Groups_Ozero__class_Ozero(U_6161)))
    | ~ class_Rings_Olinordered__idom(U_6161) ),
    inference(clausify,[status(thm)],[f_1609_2]) ).

cnf(f_1609_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6161),c_Groups_Osgn__class_Osgn(U_6161,U_6162)),c_Groups_Ozero__class_Ozero(U_6161)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6161),U_6162),c_Groups_Ozero__class_Ozero(U_6161)))
    | ~ class_Rings_Olinordered__idom(U_6161) ),
    inference(clausify,[status(thm)],[f_1609_2]) ).

fof(f_1610_1,plain,
    ! [V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Groups_Osgn__class_Osgn(T_b,V_a_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Groups_Osgn__class_Osgn(T_b,V_a_2))) ) )
      | ~ class_Rings_Olinordered__idom(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sgn__greater]) ).

fof(f_1610_2,plain,
    ! [U_6164,U_6163] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6163),c_Groups_Ozero__class_Ozero(U_6163)),c_Groups_Osgn__class_Osgn(U_6163,U_6164)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6163),c_Groups_Ozero__class_Ozero(U_6163)),U_6164)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6163),c_Groups_Ozero__class_Ozero(U_6163)),U_6164))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6163),c_Groups_Ozero__class_Ozero(U_6163)),c_Groups_Osgn__class_Osgn(U_6163,U_6164))) ) )
      | ~ class_Rings_Olinordered__idom(U_6163) ),
    inference(variable_rename,[status(thm)],[f_1610_1]) ).

cnf(f_1610_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6163),c_Groups_Ozero__class_Ozero(U_6163)),U_6164))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6163),c_Groups_Ozero__class_Ozero(U_6163)),c_Groups_Osgn__class_Osgn(U_6163,U_6164)))
    | ~ class_Rings_Olinordered__idom(U_6163) ),
    inference(clausify,[status(thm)],[f_1610_2]) ).

cnf(f_1610_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6163),c_Groups_Ozero__class_Ozero(U_6163)),c_Groups_Osgn__class_Osgn(U_6163,U_6164)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6163),c_Groups_Ozero__class_Ozero(U_6163)),U_6164))
    | ~ class_Rings_Olinordered__idom(U_6163) ),
    inference(clausify,[status(thm)],[f_1610_2]) ).

fof(f_1611_1,plain,
    ! [V_a,T_a] :
      ( c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sgn__pos]) ).

fof(f_1611_2,plain,
    ! [U_6166,U_6165] :
      ( c_Groups_Osgn__class_Osgn(U_6165,U_6166) = c_Groups_Oone__class_Oone(U_6165)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6165),c_Groups_Ozero__class_Ozero(U_6165)),U_6166))
      | ~ class_Rings_Olinordered__idom(U_6165) ),
    inference(variable_rename,[status(thm)],[f_1611_1]) ).

cnf(f_1611_3,plain,
    ( c_Groups_Osgn__class_Osgn(U_6165,U_6166) = c_Groups_Oone__class_Oone(U_6165)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6165),c_Groups_Ozero__class_Ozero(U_6165)),U_6166))
    | ~ class_Rings_Olinordered__idom(U_6165) ),
    inference(clausify,[status(thm)],[f_1611_2]) ).

fof(f_1612_1,plain,
    ! [V_a_2,T_b] :
      ( ( ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Oone__class_Oone(T_b)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
          | c_Groups_Osgn__class_Osgn(T_b,V_a_2) != c_Groups_Oone__class_Oone(T_b) ) )
      | ~ class_Rings_Olinordered__idom(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sgn__1__pos]) ).

fof(f_1612_2,plain,
    ! [U_6168,U_6167] :
      ( ( ( c_Groups_Osgn__class_Osgn(U_6167,U_6168) = c_Groups_Oone__class_Oone(U_6167)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6167),c_Groups_Ozero__class_Ozero(U_6167)),U_6168)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6167),c_Groups_Ozero__class_Ozero(U_6167)),U_6168))
          | c_Groups_Osgn__class_Osgn(U_6167,U_6168) != c_Groups_Oone__class_Oone(U_6167) ) )
      | ~ class_Rings_Olinordered__idom(U_6167) ),
    inference(variable_rename,[status(thm)],[f_1612_1]) ).

cnf(f_1612_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6167),c_Groups_Ozero__class_Ozero(U_6167)),U_6168))
    | c_Groups_Osgn__class_Osgn(U_6167,U_6168) != c_Groups_Oone__class_Oone(U_6167)
    | ~ class_Rings_Olinordered__idom(U_6167) ),
    inference(clausify,[status(thm)],[f_1612_2]) ).

cnf(f_1612_4,plain,
    ( c_Groups_Osgn__class_Osgn(U_6167,U_6168) = c_Groups_Oone__class_Oone(U_6167)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6167),c_Groups_Ozero__class_Ozero(U_6167)),U_6168))
    | ~ class_Rings_Olinordered__idom(U_6167) ),
    inference(clausify,[status(thm)],[f_1612_2]) ).

fof(f_1613_1,plain,
    ! [V_f_2,V_S_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_S_2)))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(V_f_2,B_x)))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__pos__nat]) ).

fof(f_1613_2,plain,
    ! [U_6172,U_6171,U_6170] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_6170,tc_Nat_Onat),U_6172),U_6171)))
      | ? [U_6169] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_6172,U_6169)))
          & hBOOL(hAPP(hAPP(c_member(U_6170),U_6169),U_6171)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6170),U_6171)) ),
    inference(variable_rename,[status(thm)],[f_1613_1]) ).

fof(f_1613_3,plain,
    ! [U_6172,U_6171,U_6170] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_6170,tc_Nat_Onat),U_6172),U_6171)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_6172,sK136(U_6172,U_6171,U_6170))))
        & hBOOL(hAPP(hAPP(c_member(U_6170),sK136(U_6172,U_6171,U_6170)),U_6171)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6170),U_6171)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK136]),skolemize(U_6169,sK136(U_6172,U_6171,U_6170))],[f_1613_2]) ).

cnf(f_1613_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_6170),sK136(U_6172,U_6171,U_6170)),U_6171))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_6170,tc_Nat_Onat),U_6172),U_6171)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6170),U_6171)) ),
    inference(clausify,[status(thm)],[f_1613_3]) ).

cnf(f_1613_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_6172,sK136(U_6172,U_6171,U_6170))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_6170,tc_Nat_Onat),U_6172),U_6171)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6170),U_6171)) ),
    inference(clausify,[status(thm)],[f_1613_3]) ).

fof(f_1614_1,plain,
    ! [V_v_2,V_A_2,V_x_2,V_z_2,V_f_2,T_c,T_b] :
      ( ? [B_y] :
          ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),B_y))
          & V_v_2 = hAPP(hAPP(V_f_2,V_x_2),B_y) )
      | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_v_2))
      | ~ c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__graph__insertE]) ).

fof(f_1614_2,plain,
    ! [U_6180,U_6179,U_6178,U_6177,U_6176,U_6175,U_6174] :
      ( ? [U_6173] :
          ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_6174,U_6175,U_6176,U_6177,U_6179),U_6173))
          & U_6180 = hAPP(hAPP(U_6176,U_6178),U_6173) )
      | hBOOL(hAPP(hAPP(c_member(U_6174),U_6178),U_6179))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_6174,U_6175,U_6176,U_6177,hAPP(hAPP(c_Set_Oinsert(U_6174),U_6178),U_6179)),U_6180))
      | ~ c_Finite__Set_Ofun__left__comm(U_6174,U_6175,U_6176) ),
    inference(variable_rename,[status(thm)],[f_1614_1]) ).

fof(f_1614_3,plain,
    ! [U_6180,U_6179,U_6178,U_6177,U_6176,U_6175,U_6174] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_6174,U_6175,U_6176,U_6177,U_6179),sK137(U_6180,U_6179,U_6178,U_6177,U_6176,U_6175,U_6174)))
        & U_6180 = hAPP(hAPP(U_6176,U_6178),sK137(U_6180,U_6179,U_6178,U_6177,U_6176,U_6175,U_6174)) )
      | hBOOL(hAPP(hAPP(c_member(U_6174),U_6178),U_6179))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_6174,U_6175,U_6176,U_6177,hAPP(hAPP(c_Set_Oinsert(U_6174),U_6178),U_6179)),U_6180))
      | ~ c_Finite__Set_Ofun__left__comm(U_6174,U_6175,U_6176) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK137]),skolemize(U_6173,sK137(U_6180,U_6179,U_6178,U_6177,U_6176,U_6175,U_6174))],[f_1614_2]) ).

cnf(f_1614_4,plain,
    ( U_6180 = hAPP(hAPP(U_6176,U_6178),sK137(U_6180,U_6179,U_6178,U_6177,U_6176,U_6175,U_6174))
    | hBOOL(hAPP(hAPP(c_member(U_6174),U_6178),U_6179))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_6174,U_6175,U_6176,U_6177,hAPP(hAPP(c_Set_Oinsert(U_6174),U_6178),U_6179)),U_6180))
    | ~ c_Finite__Set_Ofun__left__comm(U_6174,U_6175,U_6176) ),
    inference(clausify,[status(thm)],[f_1614_3]) ).

cnf(f_1614_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_6174,U_6175,U_6176,U_6177,U_6179),sK137(U_6180,U_6179,U_6178,U_6177,U_6176,U_6175,U_6174)))
    | hBOOL(hAPP(hAPP(c_member(U_6174),U_6178),U_6179))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_6174,U_6175,U_6176,U_6177,hAPP(hAPP(c_Set_Oinsert(U_6174),U_6178),U_6179)),U_6180))
    | ~ c_Finite__Set_Ofun__left__comm(U_6174,U_6175,U_6176) ),
    inference(clausify,[status(thm)],[f_1614_3]) ).

fof(f_1615_1,plain,
    ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofold__insert__idem]) ).

fof(f_1615_2,plain,
    ! [U_6186,U_6185,U_6184,U_6183,U_6182,U_6181] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_6181,U_6182,U_6183),U_6185),hAPP(hAPP(c_Set_Oinsert(U_6181),U_6186),U_6184)) = hAPP(hAPP(U_6183,U_6186),hAPP(hAPP(c_Finite__Set_Ofold(U_6181,U_6182,U_6183),U_6185),U_6184))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6181),U_6184))
      | ~ c_Finite__Set_Ofun__left__comm__idem(U_6181,U_6182,U_6183) ),
    inference(variable_rename,[status(thm)],[f_1615_1]) ).

cnf(f_1615_3,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_6181,U_6182,U_6183),U_6185),hAPP(hAPP(c_Set_Oinsert(U_6181),U_6186),U_6184)) = hAPP(hAPP(U_6183,U_6186),hAPP(hAPP(c_Finite__Set_Ofold(U_6181,U_6182,U_6183),U_6185),U_6184))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6181),U_6184))
    | ~ c_Finite__Set_Ofun__left__comm__idem(U_6181,U_6182,U_6183) ),
    inference(clausify,[status(thm)],[f_1615_2]) ).

fof(f_1616_1,plain,
    ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofold__insert__idem2]) ).

fof(f_1616_2,plain,
    ! [U_6192,U_6191,U_6190,U_6189,U_6188,U_6187] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_6187,U_6188,U_6189),U_6191),hAPP(hAPP(c_Set_Oinsert(U_6187),U_6192),U_6190)) = hAPP(hAPP(c_Finite__Set_Ofold(U_6187,U_6188,U_6189),hAPP(hAPP(U_6189,U_6192),U_6191)),U_6190)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6187),U_6190))
      | ~ c_Finite__Set_Ofun__left__comm__idem(U_6187,U_6188,U_6189) ),
    inference(variable_rename,[status(thm)],[f_1616_1]) ).

cnf(f_1616_3,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_6187,U_6188,U_6189),U_6191),hAPP(hAPP(c_Set_Oinsert(U_6187),U_6192),U_6190)) = hAPP(hAPP(c_Finite__Set_Ofold(U_6187,U_6188,U_6189),hAPP(hAPP(U_6189,U_6192),U_6191)),U_6190)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6187),U_6190))
    | ~ c_Finite__Set_Ofun__left__comm__idem(U_6187,U_6188,U_6189) ),
    inference(clausify,[status(thm)],[f_1616_2]) ).

fof(f_1617_1,plain,
    ! [V_n_2,V_A_2,V_f_2,T_b] :
      ( ? [B_x] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(V_f_2,B_x)))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) != hAPP(c_Nat_OSuc,V_n_2) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__SucD]) ).

fof(f_1617_2,plain,
    ! [U_6197,U_6196,U_6195,U_6194] :
      ( ? [U_6193] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_6195,U_6193)))
          & hBOOL(hAPP(hAPP(c_member(U_6194),U_6193),U_6196)) )
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6194,tc_Nat_Onat),U_6195),U_6196) != hAPP(c_Nat_OSuc,U_6197) ),
    inference(variable_rename,[status(thm)],[f_1617_1]) ).

fof(f_1617_3,plain,
    ! [U_6197,U_6196,U_6195,U_6194] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_6195,sK138(U_6197,U_6196,U_6195,U_6194))))
        & hBOOL(hAPP(hAPP(c_member(U_6194),sK138(U_6197,U_6196,U_6195,U_6194)),U_6196)) )
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6194,tc_Nat_Onat),U_6195),U_6196) != hAPP(c_Nat_OSuc,U_6197) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK138]),skolemize(U_6193,sK138(U_6197,U_6196,U_6195,U_6194))],[f_1617_2]) ).

cnf(f_1617_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_6194),sK138(U_6197,U_6196,U_6195,U_6194)),U_6196))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6194,tc_Nat_Onat),U_6195),U_6196) != hAPP(c_Nat_OSuc,U_6197) ),
    inference(clausify,[status(thm)],[f_1617_3]) ).

cnf(f_1617_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_6195,sK138(U_6197,U_6196,U_6195,U_6194))))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6194,tc_Nat_Onat),U_6195),U_6196) != hAPP(c_Nat_OSuc,U_6197) ),
    inference(clausify,[status(thm)],[f_1617_3]) ).

fof(f_1618_1,plain,
    ! [V_k_2,V_C_2,T_b] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(tc_fun(T_b,tc_HOL_Obool)),V_C_2)) = hAPP(c_Finite__Set_Ocard(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2))
      | ? [B_c1] :
          ( ? [B_c2] :
              ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),B_c1),B_c2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
              & B_c1 != B_c2
              & hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c2),V_C_2)) )
          & hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c1),V_C_2)) )
      | ? [B_c] :
          ( hAPP(c_Finite__Set_Ocard(T_b),B_c) != V_k_2
          & hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c),V_C_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_C_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__partition]) ).

fof(f_1618_2,plain,
    ! [U_6203,U_6202,U_6201] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6203),hAPP(c_Finite__Set_Ocard(tc_fun(U_6201,tc_HOL_Obool)),U_6202)) = hAPP(c_Finite__Set_Ocard(U_6201),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_6201,tc_HOL_Obool),U_6202))
      | ? [U_6200] :
          ( ? [U_6199] :
              ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_6201,tc_HOL_Obool)),U_6200),U_6199) != c_Orderings_Obot__class_Obot(tc_fun(U_6201,tc_HOL_Obool))
              & U_6200 != U_6199
              & hBOOL(hAPP(hAPP(c_member(tc_fun(U_6201,tc_HOL_Obool)),U_6199),U_6202)) )
          & hBOOL(hAPP(hAPP(c_member(tc_fun(U_6201,tc_HOL_Obool)),U_6200),U_6202)) )
      | ? [U_6198] :
          ( hAPP(c_Finite__Set_Ocard(U_6201),U_6198) != U_6203
          & hBOOL(hAPP(hAPP(c_member(tc_fun(U_6201,tc_HOL_Obool)),U_6198),U_6202)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6201),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_6201,tc_HOL_Obool),U_6202)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_6201,tc_HOL_Obool)),U_6202)) ),
    inference(variable_rename,[status(thm)],[f_1618_1]) ).

fof(f_1618_3,plain,
    ! [U_6203,U_6202,U_6201] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6203),hAPP(c_Finite__Set_Ocard(tc_fun(U_6201,tc_HOL_Obool)),U_6202)) = hAPP(c_Finite__Set_Ocard(U_6201),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_6201,tc_HOL_Obool),U_6202))
      | ? [U_6200] :
          ( ? [U_6199] :
              ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_6201,tc_HOL_Obool)),U_6200),U_6199) != c_Orderings_Obot__class_Obot(tc_fun(U_6201,tc_HOL_Obool))
              & U_6200 != U_6199
              & hBOOL(hAPP(hAPP(c_member(tc_fun(U_6201,tc_HOL_Obool)),U_6199),U_6202)) )
          & hBOOL(hAPP(hAPP(c_member(tc_fun(U_6201,tc_HOL_Obool)),U_6200),U_6202)) )
      | ( hAPP(c_Finite__Set_Ocard(U_6201),sK139(U_6203,U_6202,U_6201)) != U_6203
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_6201,tc_HOL_Obool)),sK139(U_6203,U_6202,U_6201)),U_6202)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6201),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_6201,tc_HOL_Obool),U_6202)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_6201,tc_HOL_Obool)),U_6202)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK139]),skolemize(U_6198,sK139(U_6203,U_6202,U_6201))],[f_1618_2]) ).

fof(f_1618_4,plain,
    ! [U_6203,U_6202,U_6201] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6203),hAPP(c_Finite__Set_Ocard(tc_fun(U_6201,tc_HOL_Obool)),U_6202)) = hAPP(c_Finite__Set_Ocard(U_6201),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_6201,tc_HOL_Obool),U_6202))
      | ( ? [U_6199] :
            ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_6201,tc_HOL_Obool)),sK140(U_6203,U_6202,U_6201)),U_6199) != c_Orderings_Obot__class_Obot(tc_fun(U_6201,tc_HOL_Obool))
            & sK140(U_6203,U_6202,U_6201) != U_6199
            & hBOOL(hAPP(hAPP(c_member(tc_fun(U_6201,tc_HOL_Obool)),U_6199),U_6202)) )
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_6201,tc_HOL_Obool)),sK140(U_6203,U_6202,U_6201)),U_6202)) )
      | ( hAPP(c_Finite__Set_Ocard(U_6201),sK139(U_6203,U_6202,U_6201)) != U_6203
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_6201,tc_HOL_Obool)),sK139(U_6203,U_6202,U_6201)),U_6202)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6201),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_6201,tc_HOL_Obool),U_6202)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_6201,tc_HOL_Obool)),U_6202)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK140]),skolemize(U_6200,sK140(U_6203,U_6202,U_6201))],[f_1618_3]) ).

fof(f_1618_5,plain,
    ! [U_6203,U_6202,U_6201] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6203),hAPP(c_Finite__Set_Ocard(tc_fun(U_6201,tc_HOL_Obool)),U_6202)) = hAPP(c_Finite__Set_Ocard(U_6201),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_6201,tc_HOL_Obool),U_6202))
      | ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_6201,tc_HOL_Obool)),sK140(U_6203,U_6202,U_6201)),sK141(U_6203,U_6202,U_6201)) != c_Orderings_Obot__class_Obot(tc_fun(U_6201,tc_HOL_Obool))
        & sK140(U_6203,U_6202,U_6201) != sK141(U_6203,U_6202,U_6201)
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_6201,tc_HOL_Obool)),sK141(U_6203,U_6202,U_6201)),U_6202))
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_6201,tc_HOL_Obool)),sK140(U_6203,U_6202,U_6201)),U_6202)) )
      | ( hAPP(c_Finite__Set_Ocard(U_6201),sK139(U_6203,U_6202,U_6201)) != U_6203
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_6201,tc_HOL_Obool)),sK139(U_6203,U_6202,U_6201)),U_6202)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6201),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_6201,tc_HOL_Obool),U_6202)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_6201,tc_HOL_Obool)),U_6202)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK141]),skolemize(U_6199,sK141(U_6203,U_6202,U_6201))],[f_1618_4]) ).

cnf(f_1618_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_6201,tc_HOL_Obool)),sK140(U_6203,U_6202,U_6201)),U_6202))
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6203),hAPP(c_Finite__Set_Ocard(tc_fun(U_6201,tc_HOL_Obool)),U_6202)) = hAPP(c_Finite__Set_Ocard(U_6201),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_6201,tc_HOL_Obool),U_6202))
    | hBOOL(hAPP(hAPP(c_member(tc_fun(U_6201,tc_HOL_Obool)),sK139(U_6203,U_6202,U_6201)),U_6202))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6201),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_6201,tc_HOL_Obool),U_6202)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_6201,tc_HOL_Obool)),U_6202)) ),
    inference(clausify,[status(thm)],[f_1618_5]) ).

cnf(f_1618_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_6201,tc_HOL_Obool)),sK141(U_6203,U_6202,U_6201)),U_6202))
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6203),hAPP(c_Finite__Set_Ocard(tc_fun(U_6201,tc_HOL_Obool)),U_6202)) = hAPP(c_Finite__Set_Ocard(U_6201),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_6201,tc_HOL_Obool),U_6202))
    | hBOOL(hAPP(hAPP(c_member(tc_fun(U_6201,tc_HOL_Obool)),sK139(U_6203,U_6202,U_6201)),U_6202))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6201),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_6201,tc_HOL_Obool),U_6202)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_6201,tc_HOL_Obool)),U_6202)) ),
    inference(clausify,[status(thm)],[f_1618_5]) ).

cnf(f_1618_8,plain,
    ( sK140(U_6203,U_6202,U_6201) != sK141(U_6203,U_6202,U_6201)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6203),hAPP(c_Finite__Set_Ocard(tc_fun(U_6201,tc_HOL_Obool)),U_6202)) = hAPP(c_Finite__Set_Ocard(U_6201),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_6201,tc_HOL_Obool),U_6202))
    | hBOOL(hAPP(hAPP(c_member(tc_fun(U_6201,tc_HOL_Obool)),sK139(U_6203,U_6202,U_6201)),U_6202))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6201),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_6201,tc_HOL_Obool),U_6202)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_6201,tc_HOL_Obool)),U_6202)) ),
    inference(clausify,[status(thm)],[f_1618_5]) ).

cnf(f_1618_9,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_6201,tc_HOL_Obool)),sK140(U_6203,U_6202,U_6201)),sK141(U_6203,U_6202,U_6201)) != c_Orderings_Obot__class_Obot(tc_fun(U_6201,tc_HOL_Obool))
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6203),hAPP(c_Finite__Set_Ocard(tc_fun(U_6201,tc_HOL_Obool)),U_6202)) = hAPP(c_Finite__Set_Ocard(U_6201),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_6201,tc_HOL_Obool),U_6202))
    | hBOOL(hAPP(hAPP(c_member(tc_fun(U_6201,tc_HOL_Obool)),sK139(U_6203,U_6202,U_6201)),U_6202))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6201),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_6201,tc_HOL_Obool),U_6202)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_6201,tc_HOL_Obool)),U_6202)) ),
    inference(clausify,[status(thm)],[f_1618_5]) ).

cnf(f_1618_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_6201,tc_HOL_Obool)),sK140(U_6203,U_6202,U_6201)),U_6202))
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6203),hAPP(c_Finite__Set_Ocard(tc_fun(U_6201,tc_HOL_Obool)),U_6202)) = hAPP(c_Finite__Set_Ocard(U_6201),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_6201,tc_HOL_Obool),U_6202))
    | hAPP(c_Finite__Set_Ocard(U_6201),sK139(U_6203,U_6202,U_6201)) != U_6203
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6201),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_6201,tc_HOL_Obool),U_6202)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_6201,tc_HOL_Obool)),U_6202)) ),
    inference(clausify,[status(thm)],[f_1618_5]) ).

cnf(f_1618_11,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_6201,tc_HOL_Obool)),sK141(U_6203,U_6202,U_6201)),U_6202))
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6203),hAPP(c_Finite__Set_Ocard(tc_fun(U_6201,tc_HOL_Obool)),U_6202)) = hAPP(c_Finite__Set_Ocard(U_6201),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_6201,tc_HOL_Obool),U_6202))
    | hAPP(c_Finite__Set_Ocard(U_6201),sK139(U_6203,U_6202,U_6201)) != U_6203
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6201),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_6201,tc_HOL_Obool),U_6202)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_6201,tc_HOL_Obool)),U_6202)) ),
    inference(clausify,[status(thm)],[f_1618_5]) ).

cnf(f_1618_12,plain,
    ( sK140(U_6203,U_6202,U_6201) != sK141(U_6203,U_6202,U_6201)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6203),hAPP(c_Finite__Set_Ocard(tc_fun(U_6201,tc_HOL_Obool)),U_6202)) = hAPP(c_Finite__Set_Ocard(U_6201),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_6201,tc_HOL_Obool),U_6202))
    | hAPP(c_Finite__Set_Ocard(U_6201),sK139(U_6203,U_6202,U_6201)) != U_6203
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6201),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_6201,tc_HOL_Obool),U_6202)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_6201,tc_HOL_Obool)),U_6202)) ),
    inference(clausify,[status(thm)],[f_1618_5]) ).

cnf(f_1618_13,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_6201,tc_HOL_Obool)),sK140(U_6203,U_6202,U_6201)),sK141(U_6203,U_6202,U_6201)) != c_Orderings_Obot__class_Obot(tc_fun(U_6201,tc_HOL_Obool))
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6203),hAPP(c_Finite__Set_Ocard(tc_fun(U_6201,tc_HOL_Obool)),U_6202)) = hAPP(c_Finite__Set_Ocard(U_6201),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_6201,tc_HOL_Obool),U_6202))
    | hAPP(c_Finite__Set_Ocard(U_6201),sK139(U_6203,U_6202,U_6201)) != U_6203
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6201),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_6201,tc_HOL_Obool),U_6202)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_6201,tc_HOL_Obool)),U_6202)) ),
    inference(clausify,[status(thm)],[f_1618_5]) ).

fof(f_1619_1,plain,
    ! [V_z_2,V_x_2,V_f_2,T_c,T_b] :
      ( hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)) = hAPP(hAPP(V_f_2,V_x_2),V_z_2)
      | ~ c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofun__left__idem]) ).

fof(f_1619_2,plain,
    ! [U_6208,U_6207,U_6206,U_6205,U_6204] :
      ( hAPP(hAPP(U_6206,U_6207),hAPP(hAPP(U_6206,U_6207),U_6208)) = hAPP(hAPP(U_6206,U_6207),U_6208)
      | ~ c_Finite__Set_Ofun__left__comm__idem(U_6204,U_6205,U_6206) ),
    inference(variable_rename,[status(thm)],[f_1619_1]) ).

fof(f_1619_3,plain,
    ! [U_6208,U_6207,U_6206] :
      ( ! [U_6205,U_6204] : ~ c_Finite__Set_Ofun__left__comm__idem(U_6204,U_6205,U_6206)
      | hAPP(hAPP(U_6206,U_6207),hAPP(hAPP(U_6206,U_6207),U_6208)) = hAPP(hAPP(U_6206,U_6207),U_6208) ),
    inference(miniscope,[status(thm)],[f_1619_2]) ).

cnf(f_1619_4,plain,
    ( ~ c_Finite__Set_Ofun__left__comm__idem(U_6204,U_6205,U_6206)
    | hAPP(hAPP(U_6206,U_6207),hAPP(hAPP(U_6206,U_6207),U_6208)) = hAPP(hAPP(U_6206,U_6207),U_6208) ),
    inference(clausify,[status(thm)],[f_1619_3]) ).

fof(f_1620_1,plain,
    ! [T_b] : c_Finite__Set_Ofun__left__comm__idem(T_b,tc_fun(T_b,tc_HOL_Obool),c_Set_Oinsert(T_b)),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem__insert]) ).

fof(f_1620_2,plain,
    ! [U_6209] : c_Finite__Set_Ofun__left__comm__idem(U_6209,tc_fun(U_6209,tc_HOL_Obool),c_Set_Oinsert(U_6209)),
    inference(variable_rename,[status(thm)],[f_1620_1]) ).

cnf(f_1620_3,plain,
    c_Finite__Set_Ofun__left__comm__idem(U_6209,tc_fun(U_6209,tc_HOL_Obool),c_Set_Oinsert(U_6209)),
    inference(clausify,[status(thm)],[f_1620_2]) ).

fof(f_1621_1,plain,
    ! [T_b] :
      ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b))
      | ~ class_Lattices_Oab__semigroup__idem__mult(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem]) ).

fof(f_1621_2,plain,
    ! [U_6210] :
      ( c_Finite__Set_Ofun__left__comm__idem(U_6210,U_6210,c_Groups_Otimes__class_Otimes(U_6210))
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_6210) ),
    inference(variable_rename,[status(thm)],[f_1621_1]) ).

cnf(f_1621_3,plain,
    ( c_Finite__Set_Ofun__left__comm__idem(U_6210,U_6210,c_Groups_Otimes__class_Otimes(U_6210))
    | ~ class_Lattices_Oab__semigroup__idem__mult(U_6210) ),
    inference(clausify,[status(thm)],[f_1621_2]) ).

fof(f_1622_1,plain,
    ! [T_b] :
      ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b))
      | ~ class_Lattices_Osemilattice__sup(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem__sup]) ).

fof(f_1622_2,plain,
    ! [U_6211] :
      ( c_Finite__Set_Ofun__left__comm__idem(U_6211,U_6211,c_Lattices_Osemilattice__sup__class_Osup(U_6211))
      | ~ class_Lattices_Osemilattice__sup(U_6211) ),
    inference(variable_rename,[status(thm)],[f_1622_1]) ).

cnf(f_1622_3,plain,
    ( c_Finite__Set_Ofun__left__comm__idem(U_6211,U_6211,c_Lattices_Osemilattice__sup__class_Osup(U_6211))
    | ~ class_Lattices_Osemilattice__sup(U_6211) ),
    inference(clausify,[status(thm)],[f_1622_2]) ).

fof(f_1623_1,plain,
    ! [T_b] :
      ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b))
      | ~ class_Lattices_Osemilattice__inf(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem__inf]) ).

fof(f_1623_2,plain,
    ! [U_6212] :
      ( c_Finite__Set_Ofun__left__comm__idem(U_6212,U_6212,c_Lattices_Osemilattice__inf__class_Oinf(U_6212))
      | ~ class_Lattices_Osemilattice__inf(U_6212) ),
    inference(variable_rename,[status(thm)],[f_1623_1]) ).

cnf(f_1623_3,plain,
    ( c_Finite__Set_Ofun__left__comm__idem(U_6212,U_6212,c_Lattices_Osemilattice__inf__class_Oinf(U_6212))
    | ~ class_Lattices_Osemilattice__inf(U_6212) ),
    inference(clausify,[status(thm)],[f_1623_2]) ).

fof(f_1624_1,plain,
    ! [T_b] :
      ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Orderings_Oord__class_Omin(T_b))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Ofun__left__comm__idem__inf]) ).

fof(f_1624_2,plain,
    ! [U_6213] :
      ( c_Finite__Set_Ofun__left__comm__idem(U_6213,U_6213,c_Orderings_Oord__class_Omin(U_6213))
      | ~ class_Orderings_Olinorder(U_6213) ),
    inference(variable_rename,[status(thm)],[f_1624_1]) ).

cnf(f_1624_3,plain,
    ( c_Finite__Set_Ofun__left__comm__idem(U_6213,U_6213,c_Orderings_Oord__class_Omin(U_6213))
    | ~ class_Orderings_Olinorder(U_6213) ),
    inference(clausify,[status(thm)],[f_1624_2]) ).

fof(f_1625_1,plain,
    ! [T_b] :
      ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Orderings_Oord__class_Omax(T_b))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Ofun__left__comm__idem__sup]) ).

fof(f_1625_2,plain,
    ! [U_6214] :
      ( c_Finite__Set_Ofun__left__comm__idem(U_6214,U_6214,c_Orderings_Oord__class_Omax(U_6214))
      | ~ class_Orderings_Olinorder(U_6214) ),
    inference(variable_rename,[status(thm)],[f_1625_1]) ).

cnf(f_1625_3,plain,
    ( c_Finite__Set_Ofun__left__comm__idem(U_6214,U_6214,c_Orderings_Oord__class_Omax(U_6214))
    | ~ class_Orderings_Olinorder(U_6214) ),
    inference(clausify,[status(thm)],[f_1625_2]) ).

fof(f_1626_1,plain,
    ! [V_A_2,T_b] :
      ( hAPP(c_Finite__Set_Ocard(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__Pow]) ).

fof(f_1626_2,plain,
    ! [U_6216,U_6215] :
      ( hAPP(c_Finite__Set_Ocard(tc_fun(U_6215,tc_HOL_Obool)),hAPP(c_Set_OPow(U_6215),U_6216)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Finite__Set_Ocard(U_6215),U_6216))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6215),U_6216)) ),
    inference(variable_rename,[status(thm)],[f_1626_1]) ).

cnf(f_1626_3,plain,
    ( hAPP(c_Finite__Set_Ocard(tc_fun(U_6215,tc_HOL_Obool)),hAPP(c_Set_OPow(U_6215),U_6216)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Finite__Set_Ocard(U_6215),U_6216))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6215),U_6216)) ),
    inference(clausify,[status(thm)],[f_1626_2]) ).

fof(f_1627_1,plain,
    ! [V_f_2,V_S_2,T_b,T_c] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_f_2),c_Groups_Oone__class_Oone(T_c)),V_S_2) = c_Groups_Oone__class_Oone(T_c)
      | ? [B_x] :
          ( hAPP(V_f_2,B_x) != c_Groups_Oone__class_Oone(T_c)
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_fold__image__1]) ).

fof(f_1627_2,plain,
    ! [U_6221,U_6220,U_6219,U_6218] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_6218,U_6219,c_Groups_Otimes__class_Otimes(U_6218)),U_6221),c_Groups_Oone__class_Oone(U_6218)),U_6220) = c_Groups_Oone__class_Oone(U_6218)
      | ? [U_6217] :
          ( hAPP(U_6221,U_6217) != c_Groups_Oone__class_Oone(U_6218)
          & hBOOL(hAPP(hAPP(c_member(U_6219),U_6217),U_6220)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6219),U_6220))
      | ~ class_Groups_Ocomm__monoid__mult(U_6218) ),
    inference(variable_rename,[status(thm)],[f_1627_1]) ).

fof(f_1627_3,plain,
    ! [U_6221,U_6220,U_6219,U_6218] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_6218,U_6219,c_Groups_Otimes__class_Otimes(U_6218)),U_6221),c_Groups_Oone__class_Oone(U_6218)),U_6220) = c_Groups_Oone__class_Oone(U_6218)
      | ( hAPP(U_6221,sK142(U_6221,U_6220,U_6219,U_6218)) != c_Groups_Oone__class_Oone(U_6218)
        & hBOOL(hAPP(hAPP(c_member(U_6219),sK142(U_6221,U_6220,U_6219,U_6218)),U_6220)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6219),U_6220))
      | ~ class_Groups_Ocomm__monoid__mult(U_6218) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK142]),skolemize(U_6217,sK142(U_6221,U_6220,U_6219,U_6218))],[f_1627_2]) ).

cnf(f_1627_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_6219),sK142(U_6221,U_6220,U_6219,U_6218)),U_6220))
    | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_6218,U_6219,c_Groups_Otimes__class_Otimes(U_6218)),U_6221),c_Groups_Oone__class_Oone(U_6218)),U_6220) = c_Groups_Oone__class_Oone(U_6218)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6219),U_6220))
    | ~ class_Groups_Ocomm__monoid__mult(U_6218) ),
    inference(clausify,[status(thm)],[f_1627_3]) ).

cnf(f_1627_5,plain,
    ( hAPP(U_6221,sK142(U_6221,U_6220,U_6219,U_6218)) != c_Groups_Oone__class_Oone(U_6218)
    | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_6218,U_6219,c_Groups_Otimes__class_Otimes(U_6218)),U_6221),c_Groups_Oone__class_Oone(U_6218)),U_6220) = c_Groups_Oone__class_Oone(U_6218)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6219),U_6220))
    | ~ class_Groups_Ocomm__monoid__mult(U_6218) ),
    inference(clausify,[status(thm)],[f_1627_3]) ).

fof(f_1628_1,plain,
    ! [V_A_2,T_b] :
      ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        & ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card_Oneutral]) ).

fof(f_1628_2,plain,
    ! [U_6224,U_6223] :
      ( hAPP(c_Finite__Set_Ocard(U_6223),U_6224) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        & ? [U_6222] : hBOOL(hAPP(hAPP(c_member(U_6223),U_6222),U_6224)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6223),U_6224)) ),
    inference(variable_rename,[status(thm)],[f_1628_1]) ).

fof(f_1628_3,plain,
    ! [U_6224,U_6223] :
      ( hAPP(c_Finite__Set_Ocard(U_6223),U_6224) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        & hBOOL(hAPP(hAPP(c_member(U_6223),sK143(U_6224,U_6223)),U_6224)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6223),U_6224)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK143]),skolemize(U_6222,sK143(U_6224,U_6223))],[f_1628_2]) ).

cnf(f_1628_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_6223),sK143(U_6224,U_6223)),U_6224))
    | hAPP(c_Finite__Set_Ocard(U_6223),U_6224) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6223),U_6224)) ),
    inference(clausify,[status(thm)],[f_1628_3]) ).

cnf(f_1628_5,plain,
    ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(c_Finite__Set_Ocard(U_6223),U_6224) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6223),U_6224)) ),
    inference(clausify,[status(thm)],[f_1628_3]) ).

fof(f_1629_1,plain,
    ! [V_c_2,V_b_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_c_2),V_A_2)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_b_2),V_c_2)))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Ofold__sup__le__sup]) ).

fof(f_1629_2,plain,
    ! [U_6229,U_6228,U_6227,U_6226] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6226),hAPP(hAPP(c_Finite__Set_Ofold(U_6226,U_6226,c_Orderings_Oord__class_Omax(U_6226)),U_6229),U_6227)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6226),U_6228),U_6229)))
      | ? [U_6225] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6226),U_6225),U_6228))
          & hBOOL(hAPP(hAPP(c_member(U_6226),U_6225),U_6227)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6226),U_6227))
      | ~ class_Orderings_Olinorder(U_6226) ),
    inference(variable_rename,[status(thm)],[f_1629_1]) ).

fof(f_1629_3,plain,
    ! [U_6229,U_6228,U_6227,U_6226] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6226),hAPP(hAPP(c_Finite__Set_Ofold(U_6226,U_6226,c_Orderings_Oord__class_Omax(U_6226)),U_6229),U_6227)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6226),U_6228),U_6229)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6226),sK144(U_6229,U_6228,U_6227,U_6226)),U_6228))
        & hBOOL(hAPP(hAPP(c_member(U_6226),sK144(U_6229,U_6228,U_6227,U_6226)),U_6227)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6226),U_6227))
      | ~ class_Orderings_Olinorder(U_6226) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK144]),skolemize(U_6225,sK144(U_6229,U_6228,U_6227,U_6226))],[f_1629_2]) ).

cnf(f_1629_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_6226),sK144(U_6229,U_6228,U_6227,U_6226)),U_6227))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6226),hAPP(hAPP(c_Finite__Set_Ofold(U_6226,U_6226,c_Orderings_Oord__class_Omax(U_6226)),U_6229),U_6227)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6226),U_6228),U_6229)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6226),U_6227))
    | ~ class_Orderings_Olinorder(U_6226) ),
    inference(clausify,[status(thm)],[f_1629_3]) ).

cnf(f_1629_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6226),sK144(U_6229,U_6228,U_6227,U_6226)),U_6228))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6226),hAPP(hAPP(c_Finite__Set_Ofold(U_6226,U_6226,c_Orderings_Oord__class_Omax(U_6226)),U_6229),U_6227)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6226),U_6228),U_6229)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6226),U_6227))
    | ~ class_Orderings_Olinorder(U_6226) ),
    inference(clausify,[status(thm)],[f_1629_3]) ).

fof(f_1630_1,plain,
    ! [V_c_2,V_b_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_c_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_c_2),V_A_2)))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__le__fold__inf]) ).

fof(f_1630_2,plain,
    ! [U_6234,U_6233,U_6232,U_6231] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6231),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6231),U_6233),U_6234)),hAPP(hAPP(c_Finite__Set_Ofold(U_6231,U_6231,c_Orderings_Oord__class_Omin(U_6231)),U_6234),U_6232)))
      | ? [U_6230] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6231),U_6233),U_6230))
          & hBOOL(hAPP(hAPP(c_member(U_6231),U_6230),U_6232)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6231),U_6232))
      | ~ class_Orderings_Olinorder(U_6231) ),
    inference(variable_rename,[status(thm)],[f_1630_1]) ).

fof(f_1630_3,plain,
    ! [U_6234,U_6233,U_6232,U_6231] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6231),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6231),U_6233),U_6234)),hAPP(hAPP(c_Finite__Set_Ofold(U_6231,U_6231,c_Orderings_Oord__class_Omin(U_6231)),U_6234),U_6232)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6231),U_6233),sK145(U_6234,U_6233,U_6232,U_6231)))
        & hBOOL(hAPP(hAPP(c_member(U_6231),sK145(U_6234,U_6233,U_6232,U_6231)),U_6232)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6231),U_6232))
      | ~ class_Orderings_Olinorder(U_6231) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK145]),skolemize(U_6230,sK145(U_6234,U_6233,U_6232,U_6231))],[f_1630_2]) ).

cnf(f_1630_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_6231),sK145(U_6234,U_6233,U_6232,U_6231)),U_6232))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6231),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6231),U_6233),U_6234)),hAPP(hAPP(c_Finite__Set_Ofold(U_6231,U_6231,c_Orderings_Oord__class_Omin(U_6231)),U_6234),U_6232)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6231),U_6232))
    | ~ class_Orderings_Olinorder(U_6231) ),
    inference(clausify,[status(thm)],[f_1630_3]) ).

cnf(f_1630_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6231),U_6233),sK145(U_6234,U_6233,U_6232,U_6231)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6231),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6231),U_6233),U_6234)),hAPP(hAPP(c_Finite__Set_Ofold(U_6231,U_6231,c_Orderings_Oord__class_Omin(U_6231)),U_6234),U_6232)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6231),U_6232))
    | ~ class_Orderings_Olinorder(U_6231) ),
    inference(clausify,[status(thm)],[f_1630_3]) ).

fof(f_1631_1,plain,
    ! [V_z_2,V_h_2,V_g_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),V_z_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_h_2),V_z_2),V_A_2)
      | ? [B_x] :
          ( hAPP(V_g_2,B_x) != hAPP(V_h_2,B_x)
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Oab__semigroup__mult(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_fold__image__cong]) ).

fof(f_1631_2,plain,
    ! [U_6241,U_6240,U_6239,U_6238,U_6237,U_6236] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_6236,U_6237,c_Groups_Otimes__class_Otimes(U_6236)),U_6239),U_6241),U_6238) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_6236,U_6237,c_Groups_Otimes__class_Otimes(U_6236)),U_6240),U_6241),U_6238)
      | ? [U_6235] :
          ( hAPP(U_6239,U_6235) != hAPP(U_6240,U_6235)
          & hBOOL(hAPP(hAPP(c_member(U_6237),U_6235),U_6238)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6237),U_6238))
      | ~ class_Groups_Oab__semigroup__mult(U_6236) ),
    inference(variable_rename,[status(thm)],[f_1631_1]) ).

fof(f_1631_3,plain,
    ! [U_6241,U_6240,U_6239,U_6238,U_6237,U_6236] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_6236,U_6237,c_Groups_Otimes__class_Otimes(U_6236)),U_6239),U_6241),U_6238) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_6236,U_6237,c_Groups_Otimes__class_Otimes(U_6236)),U_6240),U_6241),U_6238)
      | ( hAPP(U_6239,sK146(U_6241,U_6240,U_6239,U_6238,U_6237,U_6236)) != hAPP(U_6240,sK146(U_6241,U_6240,U_6239,U_6238,U_6237,U_6236))
        & hBOOL(hAPP(hAPP(c_member(U_6237),sK146(U_6241,U_6240,U_6239,U_6238,U_6237,U_6236)),U_6238)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6237),U_6238))
      | ~ class_Groups_Oab__semigroup__mult(U_6236) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK146]),skolemize(U_6235,sK146(U_6241,U_6240,U_6239,U_6238,U_6237,U_6236))],[f_1631_2]) ).

cnf(f_1631_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_6237),sK146(U_6241,U_6240,U_6239,U_6238,U_6237,U_6236)),U_6238))
    | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_6236,U_6237,c_Groups_Otimes__class_Otimes(U_6236)),U_6239),U_6241),U_6238) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_6236,U_6237,c_Groups_Otimes__class_Otimes(U_6236)),U_6240),U_6241),U_6238)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6237),U_6238))
    | ~ class_Groups_Oab__semigroup__mult(U_6236) ),
    inference(clausify,[status(thm)],[f_1631_3]) ).

cnf(f_1631_5,plain,
    ( hAPP(U_6239,sK146(U_6241,U_6240,U_6239,U_6238,U_6237,U_6236)) != hAPP(U_6240,sK146(U_6241,U_6240,U_6239,U_6238,U_6237,U_6236))
    | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_6236,U_6237,c_Groups_Otimes__class_Otimes(U_6236)),U_6239),U_6241),U_6238) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_6236,U_6237,c_Groups_Otimes__class_Otimes(U_6236)),U_6240),U_6241),U_6238)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6237),U_6238))
    | ~ class_Groups_Oab__semigroup__mult(U_6236) ),
    inference(clausify,[status(thm)],[f_1631_3]) ).

fof(f_1632_1,plain,
    ! [V_q,V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),V_q) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_q))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J]) ).

fof(f_1632_2,plain,
    ! [U_6245,U_6244,U_6243,U_6242] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6242),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6242),U_6243),U_6244)),U_6245) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6242),hAPP(hAPP(c_Power_Opower__class_Opower(U_6242),U_6243),U_6245)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6242),U_6244),U_6245))
      | ~ class_Rings_Ocomm__semiring__1(U_6242) ),
    inference(variable_rename,[status(thm)],[f_1632_1]) ).

cnf(f_1632_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6242),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6242),U_6243),U_6244)),U_6245) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6242),hAPP(hAPP(c_Power_Opower__class_Opower(U_6242),U_6243),U_6245)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6242),U_6244),U_6245))
    | ~ class_Rings_Ocomm__semiring__1(U_6242) ),
    inference(clausify,[status(thm)],[f_1632_2]) ).

fof(f_1633_1,plain,
    ! [V_q,V_p,V_x,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),V_q) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),V_q))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J]) ).

fof(f_1633_2,plain,
    ! [U_6249,U_6248,U_6247,U_6246] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6246),hAPP(hAPP(c_Power_Opower__class_Opower(U_6246),U_6247),U_6248)),U_6249) = hAPP(hAPP(c_Power_Opower__class_Opower(U_6246),U_6247),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6248),U_6249))
      | ~ class_Rings_Ocomm__semiring__1(U_6246) ),
    inference(variable_rename,[status(thm)],[f_1633_1]) ).

cnf(f_1633_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6246),hAPP(hAPP(c_Power_Opower__class_Opower(U_6246),U_6247),U_6248)),U_6249) = hAPP(hAPP(c_Power_Opower__class_Opower(U_6246),U_6247),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6248),U_6249))
    | ~ class_Rings_Ocomm__semiring__1(U_6246) ),
    inference(clausify,[status(thm)],[f_1633_2]) ).

fof(f_1634_1,plain,
    ! [V_x,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J]) ).

fof(f_1634_2,plain,
    ! [U_6251,U_6250] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6250),U_6251),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_6251
      | ~ class_Rings_Ocomm__semiring__1(U_6250) ),
    inference(variable_rename,[status(thm)],[f_1634_1]) ).

cnf(f_1634_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6250),U_6251),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_6251
    | ~ class_Rings_Ocomm__semiring__1(U_6250) ),
    inference(clausify,[status(thm)],[f_1634_2]) ).

fof(f_1635_1,plain,
    ! [V_q,V_x,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Nat_OSuc,V_q)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J]) ).

fof(f_1635_2,plain,
    ! [U_6254,U_6253,U_6252] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6252),U_6253),hAPP(c_Nat_OSuc,U_6254)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6252),U_6253),hAPP(hAPP(c_Power_Opower__class_Opower(U_6252),U_6253),U_6254))
      | ~ class_Rings_Ocomm__semiring__1(U_6252) ),
    inference(variable_rename,[status(thm)],[f_1635_1]) ).

cnf(f_1635_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6252),U_6253),hAPP(c_Nat_OSuc,U_6254)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6252),U_6253),hAPP(hAPP(c_Power_Opower__class_Opower(U_6252),U_6253),U_6254))
    | ~ class_Rings_Ocomm__semiring__1(U_6252) ),
    inference(clausify,[status(thm)],[f_1635_2]) ).

fof(f_1636_1,plain,
    ! [V_q,V_x,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Nat_OSuc,V_q))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J]) ).

fof(f_1636_2,plain,
    ! [U_6257,U_6256,U_6255] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6255),U_6256),hAPP(hAPP(c_Power_Opower__class_Opower(U_6255),U_6256),U_6257)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_6255),U_6256),hAPP(c_Nat_OSuc,U_6257))
      | ~ class_Rings_Ocomm__semiring__1(U_6255) ),
    inference(variable_rename,[status(thm)],[f_1636_1]) ).

cnf(f_1636_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6255),U_6256),hAPP(hAPP(c_Power_Opower__class_Opower(U_6255),U_6256),U_6257)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_6255),U_6256),hAPP(c_Nat_OSuc,U_6257))
    | ~ class_Rings_Ocomm__semiring__1(U_6255) ),
    inference(clausify,[status(thm)],[f_1636_2]) ).

fof(f_1637_1,plain,
    ! [V_q,V_x,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)),V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Nat_OSuc,V_q))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J]) ).

fof(f_1637_2,plain,
    ! [U_6260,U_6259,U_6258] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6258),hAPP(hAPP(c_Power_Opower__class_Opower(U_6258),U_6259),U_6260)),U_6259) = hAPP(hAPP(c_Power_Opower__class_Opower(U_6258),U_6259),hAPP(c_Nat_OSuc,U_6260))
      | ~ class_Rings_Ocomm__semiring__1(U_6258) ),
    inference(variable_rename,[status(thm)],[f_1637_1]) ).

cnf(f_1637_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6258),hAPP(hAPP(c_Power_Opower__class_Opower(U_6258),U_6259),U_6260)),U_6259) = hAPP(hAPP(c_Power_Opower__class_Opower(U_6258),U_6259),hAPP(c_Nat_OSuc,U_6260))
    | ~ class_Rings_Ocomm__semiring__1(U_6258) ),
    inference(clausify,[status(thm)],[f_1637_2]) ).

fof(f_1638_1,plain,
    ! [V_x,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a)
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J]) ).

fof(f_1638_2,plain,
    ! [U_6262,U_6261] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6261),U_6262),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_6261)
      | ~ class_Rings_Ocomm__semiring__1(U_6261) ),
    inference(variable_rename,[status(thm)],[f_1638_1]) ).

cnf(f_1638_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6261),U_6262),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_6261)
    | ~ class_Rings_Ocomm__semiring__1(U_6261) ),
    inference(clausify,[status(thm)],[f_1638_2]) ).

fof(f_1639_1,plain,
    ! [V_q,V_p,V_x,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_p),V_q))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J]) ).

fof(f_1639_2,plain,
    ! [U_6266,U_6265,U_6264,U_6263] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6263),hAPP(hAPP(c_Power_Opower__class_Opower(U_6263),U_6264),U_6265)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6263),U_6264),U_6266)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_6263),U_6264),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6265),U_6266))
      | ~ class_Rings_Ocomm__semiring__1(U_6263) ),
    inference(variable_rename,[status(thm)],[f_1639_1]) ).

cnf(f_1639_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6263),hAPP(hAPP(c_Power_Opower__class_Opower(U_6263),U_6264),U_6265)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6263),U_6264),U_6266)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_6263),U_6264),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6265),U_6266))
    | ~ class_Rings_Ocomm__semiring__1(U_6263) ),
    inference(clausify,[status(thm)],[f_1639_2]) ).

fof(f_1640_1,plain,
    ! [V_n_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2)),c_Int_Oring__1__class_OInts(T_b)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
      | ~ class_Rings_Oring__1(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Ints__power]) ).

fof(f_1640_2,plain,
    ! [U_6269,U_6268,U_6267] :
      ( hBOOL(hAPP(hAPP(c_member(U_6267),hAPP(hAPP(c_Power_Opower__class_Opower(U_6267),U_6268),U_6269)),c_Int_Oring__1__class_OInts(U_6267)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_6267),U_6268),c_Int_Oring__1__class_OInts(U_6267)))
      | ~ class_Rings_Oring__1(U_6267) ),
    inference(variable_rename,[status(thm)],[f_1640_1]) ).

cnf(f_1640_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_6267),hAPP(hAPP(c_Power_Opower__class_Opower(U_6267),U_6268),U_6269)),c_Int_Oring__1__class_OInts(U_6267)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_6267),U_6268),c_Int_Oring__1__class_OInts(U_6267)))
    | ~ class_Rings_Oring__1(U_6267) ),
    inference(clausify,[status(thm)],[f_1640_2]) ).

fof(f_1641_1,plain,
    ! [V_p,V_m] :
      ( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(fof_nnf,[status(thm)],[fact_power__eq__if]) ).

fof(f_1641_2,plain,
    ! [U_6271,U_6270] :
      ( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6271),U_6270) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6271),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6271),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6270),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | U_6270 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6271),U_6270) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_6270 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_1641_1]) ).

fof(f_1641_3,plain,
    ( ! [U_6275,U_6273] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6275),U_6273) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6275),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6275),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6273),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | U_6273 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_6274,U_6272] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6274),U_6272) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_6272 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_1641_2]) ).

cnf(f_1641_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6274),U_6272) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | U_6272 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1641_3]) ).

cnf(f_1641_5,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6275),U_6273) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6275),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6275),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6273),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | U_6273 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1641_3]) ).

fof(f_1642_1,plain,
    ! [V_n,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__strict__mono]) ).

fof(f_1642_2,plain,
    ! [U_6279,U_6278,U_6277,U_6276] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6276),hAPP(hAPP(c_Power_Opower__class_Opower(U_6276),U_6277),U_6279)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6276),U_6278),U_6279)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6279))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6276),c_Groups_Ozero__class_Ozero(U_6276)),U_6277))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6276),U_6277),U_6278))
      | ~ class_Rings_Olinordered__semidom(U_6276) ),
    inference(variable_rename,[status(thm)],[f_1642_1]) ).

cnf(f_1642_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6276),hAPP(hAPP(c_Power_Opower__class_Opower(U_6276),U_6277),U_6279)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6276),U_6278),U_6279)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6279))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6276),c_Groups_Ozero__class_Ozero(U_6276)),U_6277))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6276),U_6277),U_6278))
    | ~ class_Rings_Olinordered__semidom(U_6276) ),
    inference(clausify,[status(thm)],[f_1642_2]) ).

fof(f_1643_1,plain,
    ! [V_m,V_n,V_a,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
      | V_a = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Fields_Ofield(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__diff]) ).

fof(f_1643_2,plain,
    ! [U_6283,U_6282,U_6281,U_6280] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6280),U_6281),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6283),U_6282)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6280),hAPP(hAPP(c_Power_Opower__class_Opower(U_6280),U_6281),U_6283)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6280),U_6281),U_6282))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6282),U_6283))
      | U_6281 = c_Groups_Ozero__class_Ozero(U_6280)
      | ~ class_Fields_Ofield(U_6280) ),
    inference(variable_rename,[status(thm)],[f_1643_1]) ).

cnf(f_1643_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6280),U_6281),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6283),U_6282)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6280),hAPP(hAPP(c_Power_Opower__class_Opower(U_6280),U_6281),U_6283)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6280),U_6281),U_6282))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6282),U_6283))
    | U_6281 = c_Groups_Ozero__class_Ozero(U_6280)
    | ~ class_Fields_Ofield(U_6280) ),
    inference(clausify,[status(thm)],[f_1643_2]) ).

fof(f_1644_1,plain,
    ! [V_n,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_one__less__power]) ).

fof(f_1644_2,plain,
    ! [U_6286,U_6285,U_6284] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6284),c_Groups_Oone__class_Oone(U_6284)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6284),U_6285),U_6286)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6286))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6284),c_Groups_Oone__class_Oone(U_6284)),U_6285))
      | ~ class_Rings_Olinordered__semidom(U_6284) ),
    inference(variable_rename,[status(thm)],[f_1644_1]) ).

cnf(f_1644_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6284),c_Groups_Oone__class_Oone(U_6284)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6284),U_6285),U_6286)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6286))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6284),c_Groups_Oone__class_Oone(U_6284)),U_6285))
    | ~ class_Rings_Olinordered__semidom(U_6284) ),
    inference(clausify,[status(thm)],[f_1644_2]) ).

fof(f_1645_1,plain,
    ! [V_n,V_m,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__le__imp__le__exp]) ).

fof(f_1645_2,plain,
    ! [U_6290,U_6289,U_6288,U_6287] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6289),U_6290))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6287),hAPP(hAPP(c_Power_Opower__class_Opower(U_6287),U_6288),U_6289)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6287),U_6288),U_6290)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6287),c_Groups_Oone__class_Oone(U_6287)),U_6288))
      | ~ class_Rings_Olinordered__semidom(U_6287) ),
    inference(variable_rename,[status(thm)],[f_1645_1]) ).

cnf(f_1645_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6289),U_6290))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6287),hAPP(hAPP(c_Power_Opower__class_Opower(U_6287),U_6288),U_6289)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6287),U_6288),U_6290)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6287),c_Groups_Oone__class_Oone(U_6287)),U_6288))
    | ~ class_Rings_Olinordered__semidom(U_6287) ),
    inference(clausify,[status(thm)],[f_1645_2]) ).

fof(f_1646_1,plain,
    ! [V_y_2,V_x_2,V_b_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_y_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_y_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_b_2))
      | ~ class_Rings_Olinordered__semidom(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_power__increasing__iff]) ).

fof(f_1646_2,plain,
    ! [U_6294,U_6293,U_6292,U_6291] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6291),hAPP(hAPP(c_Power_Opower__class_Opower(U_6291),U_6292),U_6293)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6291),U_6292),U_6294)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6293),U_6294)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6293),U_6294))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6291),hAPP(hAPP(c_Power_Opower__class_Opower(U_6291),U_6292),U_6293)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6291),U_6292),U_6294))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6291),c_Groups_Oone__class_Oone(U_6291)),U_6292))
      | ~ class_Rings_Olinordered__semidom(U_6291) ),
    inference(variable_rename,[status(thm)],[f_1646_1]) ).

cnf(f_1646_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6293),U_6294))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6291),hAPP(hAPP(c_Power_Opower__class_Opower(U_6291),U_6292),U_6293)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6291),U_6292),U_6294)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6291),c_Groups_Oone__class_Oone(U_6291)),U_6292))
    | ~ class_Rings_Olinordered__semidom(U_6291) ),
    inference(clausify,[status(thm)],[f_1646_2]) ).

cnf(f_1646_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6291),hAPP(hAPP(c_Power_Opower__class_Opower(U_6291),U_6292),U_6293)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6291),U_6292),U_6294)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6293),U_6294))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6291),c_Groups_Oone__class_Oone(U_6291)),U_6292))
    | ~ class_Rings_Olinordered__semidom(U_6291) ),
    inference(clausify,[status(thm)],[f_1646_2]) ).

fof(f_1647_1,plain,
    ! [V_a,V_N,V_n,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__decreasing]) ).

fof(f_1647_2,plain,
    ! [U_6298,U_6297,U_6296,U_6295] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6295),hAPP(hAPP(c_Power_Opower__class_Opower(U_6295),U_6298),U_6297)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6295),U_6298),U_6296)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6295),U_6298),c_Groups_Oone__class_Oone(U_6295)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6295),c_Groups_Ozero__class_Ozero(U_6295)),U_6298))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6296),U_6297))
      | ~ class_Rings_Olinordered__semidom(U_6295) ),
    inference(variable_rename,[status(thm)],[f_1647_1]) ).

cnf(f_1647_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6295),hAPP(hAPP(c_Power_Opower__class_Opower(U_6295),U_6298),U_6297)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6295),U_6298),U_6296)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6295),U_6298),c_Groups_Oone__class_Oone(U_6295)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6295),c_Groups_Ozero__class_Ozero(U_6295)),U_6298))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6296),U_6297))
    | ~ class_Rings_Olinordered__semidom(U_6295) ),
    inference(clausify,[status(thm)],[f_1647_2]) ).

fof(f_1648_1,plain,
    ! [V_z,V_y,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_z)),
    inference(fof_nnf,[status(thm)],[fact_zpower__zadd__distrib]) ).

fof(f_1648_2,plain,
    ! [U_6301,U_6300,U_6299] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_6299),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6300),U_6301)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_6299),U_6300)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_6299),U_6301)),
    inference(variable_rename,[status(thm)],[f_1648_1]) ).

cnf(f_1648_3,plain,
    hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_6299),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6300),U_6301)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_6299),U_6300)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_6299),U_6301)),
    inference(clausify,[status(thm)],[f_1648_2]) ).

fof(f_1649_1,plain,
    ! [V_z,V_y,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),V_z) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_y),V_z)),
    inference(fof_nnf,[status(thm)],[fact_zpower__zpower]) ).

fof(f_1649_2,plain,
    ! [U_6304,U_6303,U_6302] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_6302),U_6303)),U_6304) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_6302),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6303),U_6304)),
    inference(variable_rename,[status(thm)],[f_1649_1]) ).

cnf(f_1649_3,plain,
    hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_6302),U_6303)),U_6304) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_6302),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6303),U_6304)),
    inference(clausify,[status(thm)],[f_1649_2]) ).

fof(f_1650_1,plain,
    ! [V_n,V_a,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a)
      | V_a = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Rings_Oring__1__no__zero__divisors(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_field__power__not__zero]) ).

fof(f_1650_2,plain,
    ! [U_6307,U_6306,U_6305] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6305),U_6306),U_6307) != c_Groups_Ozero__class_Ozero(U_6305)
      | U_6306 = c_Groups_Ozero__class_Ozero(U_6305)
      | ~ class_Rings_Oring__1__no__zero__divisors(U_6305) ),
    inference(variable_rename,[status(thm)],[f_1650_1]) ).

cnf(f_1650_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6305),U_6306),U_6307) != c_Groups_Ozero__class_Ozero(U_6305)
    | U_6306 = c_Groups_Ozero__class_Ozero(U_6305)
    | ~ class_Rings_Oring__1__no__zero__divisors(U_6305) ),
    inference(clausify,[status(thm)],[f_1650_2]) ).

fof(f_1651_1,plain,
    ! [V_n,V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))
      | ~ class_Groups_Ocomm__monoid__mult(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__mult__distrib]) ).

fof(f_1651_2,plain,
    ! [U_6311,U_6310,U_6309,U_6308] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6308),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6308),U_6309),U_6310)),U_6311) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6308),hAPP(hAPP(c_Power_Opower__class_Opower(U_6308),U_6309),U_6311)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6308),U_6310),U_6311))
      | ~ class_Groups_Ocomm__monoid__mult(U_6308) ),
    inference(variable_rename,[status(thm)],[f_1651_1]) ).

cnf(f_1651_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6308),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6308),U_6309),U_6310)),U_6311) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6308),hAPP(hAPP(c_Power_Opower__class_Opower(U_6308),U_6309),U_6311)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6308),U_6310),U_6311))
    | ~ class_Groups_Ocomm__monoid__mult(U_6308) ),
    inference(clausify,[status(thm)],[f_1651_2]) ).

fof(f_1652_1,plain,
    ! [V_n,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
      | ~ class_Groups_Omonoid__mult(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__commutes]) ).

fof(f_1652_2,plain,
    ! [U_6314,U_6313,U_6312] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6312),hAPP(hAPP(c_Power_Opower__class_Opower(U_6312),U_6313),U_6314)),U_6313) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6312),U_6313),hAPP(hAPP(c_Power_Opower__class_Opower(U_6312),U_6313),U_6314))
      | ~ class_Groups_Omonoid__mult(U_6312) ),
    inference(variable_rename,[status(thm)],[f_1652_1]) ).

cnf(f_1652_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6312),hAPP(hAPP(c_Power_Opower__class_Opower(U_6312),U_6313),U_6314)),U_6313) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6312),U_6313),hAPP(hAPP(c_Power_Opower__class_Opower(U_6312),U_6313),U_6314))
    | ~ class_Groups_Omonoid__mult(U_6312) ),
    inference(clausify,[status(thm)],[f_1652_2]) ).

fof(f_1653_1,plain,
    ! [V_n,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),V_n) = c_Groups_Oone__class_Oone(T_a)
      | ~ class_Groups_Omonoid__mult(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__one]) ).

fof(f_1653_2,plain,
    ! [U_6316,U_6315] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6315),c_Groups_Oone__class_Oone(U_6315)),U_6316) = c_Groups_Oone__class_Oone(U_6315)
      | ~ class_Groups_Omonoid__mult(U_6315) ),
    inference(variable_rename,[status(thm)],[f_1653_1]) ).

cnf(f_1653_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6315),c_Groups_Oone__class_Oone(U_6315)),U_6316) = c_Groups_Oone__class_Oone(U_6315)
    | ~ class_Groups_Omonoid__mult(U_6315) ),
    inference(clausify,[status(thm)],[f_1653_2]) ).

fof(f_1654_1,plain,
    ! [V_n,V_m,V_a,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),V_n)
      | ~ class_Groups_Omonoid__mult(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__mult]) ).

fof(f_1654_2,plain,
    ! [U_6320,U_6319,U_6318,U_6317] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6317),U_6318),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6319),U_6320)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_6317),hAPP(hAPP(c_Power_Opower__class_Opower(U_6317),U_6318),U_6319)),U_6320)
      | ~ class_Groups_Omonoid__mult(U_6317) ),
    inference(variable_rename,[status(thm)],[f_1654_1]) ).

cnf(f_1654_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6317),U_6318),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6319),U_6320)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_6317),hAPP(hAPP(c_Power_Opower__class_Opower(U_6317),U_6318),U_6319)),U_6320)
    | ~ class_Groups_Omonoid__mult(U_6317) ),
    inference(clausify,[status(thm)],[f_1654_2]) ).

fof(f_1655_1,plain,
    ! [V_n,V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)),V_n) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))
      | ~ class_Fields_Ofield__inverse__zero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__divide]) ).

fof(f_1655_2,plain,
    ! [U_6324,U_6323,U_6322,U_6321] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6321),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6321),U_6322),U_6323)),U_6324) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6321),hAPP(hAPP(c_Power_Opower__class_Opower(U_6321),U_6322),U_6324)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6321),U_6323),U_6324))
      | ~ class_Fields_Ofield__inverse__zero(U_6321) ),
    inference(variable_rename,[status(thm)],[f_1655_1]) ).

cnf(f_1655_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6321),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6321),U_6322),U_6323)),U_6324) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6321),hAPP(hAPP(c_Power_Opower__class_Opower(U_6321),U_6322),U_6324)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6321),U_6323),U_6324))
    | ~ class_Fields_Ofield__inverse__zero(U_6321) ),
    inference(clausify,[status(thm)],[f_1655_2]) ).

fof(f_1656_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a
      | ~ class_Groups_Omonoid__mult(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__one__right]) ).

fof(f_1656_2,plain,
    ! [U_6326,U_6325] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6325),U_6326),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_6326
      | ~ class_Groups_Omonoid__mult(U_6325) ),
    inference(variable_rename,[status(thm)],[f_1656_1]) ).

cnf(f_1656_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6325),U_6326),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_6326
    | ~ class_Groups_Omonoid__mult(U_6325) ),
    inference(clausify,[status(thm)],[f_1656_2]) ).

fof(f_1657_1,plain,
    ! [V_n,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__mono]) ).

fof(f_1657_2,plain,
    ! [U_6330,U_6329,U_6328,U_6327] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6327),hAPP(hAPP(c_Power_Opower__class_Opower(U_6327),U_6328),U_6330)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6327),U_6329),U_6330)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6327),c_Groups_Ozero__class_Ozero(U_6327)),U_6328))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6327),U_6328),U_6329))
      | ~ class_Rings_Olinordered__semidom(U_6327) ),
    inference(variable_rename,[status(thm)],[f_1657_1]) ).

cnf(f_1657_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6327),hAPP(hAPP(c_Power_Opower__class_Opower(U_6327),U_6328),U_6330)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6327),U_6329),U_6330)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6327),c_Groups_Ozero__class_Ozero(U_6327)),U_6328))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6327),U_6328),U_6329))
    | ~ class_Rings_Olinordered__semidom(U_6327) ),
    inference(clausify,[status(thm)],[f_1657_2]) ).

fof(f_1658_1,plain,
    ! [V_n,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_zero__le__power]) ).

fof(f_1658_2,plain,
    ! [U_6333,U_6332,U_6331] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6331),c_Groups_Ozero__class_Ozero(U_6331)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6331),U_6332),U_6333)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6331),c_Groups_Ozero__class_Ozero(U_6331)),U_6332))
      | ~ class_Rings_Olinordered__semidom(U_6331) ),
    inference(variable_rename,[status(thm)],[f_1658_1]) ).

cnf(f_1658_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6331),c_Groups_Ozero__class_Ozero(U_6331)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6331),U_6332),U_6333)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6331),c_Groups_Ozero__class_Ozero(U_6331)),U_6332))
    | ~ class_Rings_Olinordered__semidom(U_6331) ),
    inference(clausify,[status(thm)],[f_1658_2]) ).

fof(f_1659_1,plain,
    ! [V_n,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_zero__less__power]) ).

fof(f_1659_2,plain,
    ! [U_6336,U_6335,U_6334] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6334),c_Groups_Ozero__class_Ozero(U_6334)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6334),U_6335),U_6336)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6334),c_Groups_Ozero__class_Ozero(U_6334)),U_6335))
      | ~ class_Rings_Olinordered__semidom(U_6334) ),
    inference(variable_rename,[status(thm)],[f_1659_1]) ).

cnf(f_1659_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6334),c_Groups_Ozero__class_Ozero(U_6334)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6334),U_6335),U_6336)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6334),c_Groups_Ozero__class_Ozero(U_6334)),U_6335))
    | ~ class_Rings_Olinordered__semidom(U_6334) ),
    inference(clausify,[status(thm)],[f_1659_2]) ).

fof(f_1660_1,plain,
    ! [V_n_2,V_a_2,T_b] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_b)
          | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          | V_a_2 != c_Groups_Ozero__class_Ozero(T_b) )
        & ( ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            & V_a_2 = c_Groups_Ozero__class_Ozero(T_b) )
          | hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2) != c_Groups_Ozero__class_Ozero(T_b) ) )
      | ~ class_Rings_Ozero__neq__one(T_b)
      | ~ class_Rings_Ono__zero__divisors(T_b)
      | ~ class_Rings_Omult__zero(T_b)
      | ~ class_Power_Opower(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_power__eq__0__iff]) ).

fof(f_1660_2,plain,
    ! [U_6339,U_6338,U_6337] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6337),U_6338),U_6339) = c_Groups_Ozero__class_Ozero(U_6337)
          | U_6339 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          | U_6338 != c_Groups_Ozero__class_Ozero(U_6337) )
        & ( ( U_6339 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            & U_6338 = c_Groups_Ozero__class_Ozero(U_6337) )
          | hAPP(hAPP(c_Power_Opower__class_Opower(U_6337),U_6338),U_6339) != c_Groups_Ozero__class_Ozero(U_6337) ) )
      | ~ class_Rings_Ozero__neq__one(U_6337)
      | ~ class_Rings_Ono__zero__divisors(U_6337)
      | ~ class_Rings_Omult__zero(U_6337)
      | ~ class_Power_Opower(U_6337) ),
    inference(variable_rename,[status(thm)],[f_1660_1]) ).

cnf(f_1660_3,plain,
    ( U_6338 = c_Groups_Ozero__class_Ozero(U_6337)
    | hAPP(hAPP(c_Power_Opower__class_Opower(U_6337),U_6338),U_6339) != c_Groups_Ozero__class_Ozero(U_6337)
    | ~ class_Rings_Ozero__neq__one(U_6337)
    | ~ class_Rings_Ono__zero__divisors(U_6337)
    | ~ class_Rings_Omult__zero(U_6337)
    | ~ class_Power_Opower(U_6337) ),
    inference(clausify,[status(thm)],[f_1660_2]) ).

cnf(f_1660_4,plain,
    ( U_6339 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Power_Opower__class_Opower(U_6337),U_6338),U_6339) != c_Groups_Ozero__class_Ozero(U_6337)
    | ~ class_Rings_Ozero__neq__one(U_6337)
    | ~ class_Rings_Ono__zero__divisors(U_6337)
    | ~ class_Rings_Omult__zero(U_6337)
    | ~ class_Power_Opower(U_6337) ),
    inference(clausify,[status(thm)],[f_1660_2]) ).

cnf(f_1660_5,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6337),U_6338),U_6339) = c_Groups_Ozero__class_Ozero(U_6337)
    | U_6339 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_6338 != c_Groups_Ozero__class_Ozero(U_6337)
    | ~ class_Rings_Ozero__neq__one(U_6337)
    | ~ class_Rings_Ono__zero__divisors(U_6337)
    | ~ class_Rings_Omult__zero(U_6337)
    | ~ class_Power_Opower(U_6337) ),
    inference(clausify,[status(thm)],[f_1660_2]) ).

fof(f_1661_1,plain,
    ! [V_n,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_one__le__power]) ).

fof(f_1661_2,plain,
    ! [U_6342,U_6341,U_6340] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6340),c_Groups_Oone__class_Oone(U_6340)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6340),U_6341),U_6342)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6340),c_Groups_Oone__class_Oone(U_6340)),U_6341))
      | ~ class_Rings_Olinordered__semidom(U_6340) ),
    inference(variable_rename,[status(thm)],[f_1661_1]) ).

cnf(f_1661_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6340),c_Groups_Oone__class_Oone(U_6340)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6340),U_6341),U_6342)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6340),c_Groups_Oone__class_Oone(U_6340)),U_6341))
    | ~ class_Rings_Olinordered__semidom(U_6340) ),
    inference(clausify,[status(thm)],[f_1661_2]) ).

fof(f_1662_1,plain,
    ! [V_n,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Nat_OSuc,V_n)) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Rings_Osemiring__0(T_a)
      | ~ class_Power_Opower(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__0__Suc]) ).

fof(f_1662_2,plain,
    ! [U_6344,U_6343] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6343),c_Groups_Ozero__class_Ozero(U_6343)),hAPP(c_Nat_OSuc,U_6344)) = c_Groups_Ozero__class_Ozero(U_6343)
      | ~ class_Rings_Osemiring__0(U_6343)
      | ~ class_Power_Opower(U_6343) ),
    inference(variable_rename,[status(thm)],[f_1662_1]) ).

cnf(f_1662_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6343),c_Groups_Ozero__class_Ozero(U_6343)),hAPP(c_Nat_OSuc,U_6344)) = c_Groups_Ozero__class_Ozero(U_6343)
    | ~ class_Rings_Osemiring__0(U_6343)
    | ~ class_Power_Opower(U_6343) ),
    inference(clausify,[status(thm)],[f_1662_2]) ).

fof(f_1663_1,plain,
    ! [V_n_2,V_m_2,V_a_2,T_b] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_m_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2)
          | V_m_2 != V_n_2 )
        & ( V_m_2 = V_n_2
          | hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_m_2) != hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_a_2))
      | ~ class_Rings_Olinordered__semidom(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_power__inject__exp]) ).

fof(f_1663_2,plain,
    ! [U_6348,U_6347,U_6346,U_6345] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6345),U_6346),U_6347) = hAPP(hAPP(c_Power_Opower__class_Opower(U_6345),U_6346),U_6348)
          | U_6347 != U_6348 )
        & ( U_6347 = U_6348
          | hAPP(hAPP(c_Power_Opower__class_Opower(U_6345),U_6346),U_6347) != hAPP(hAPP(c_Power_Opower__class_Opower(U_6345),U_6346),U_6348) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6345),c_Groups_Oone__class_Oone(U_6345)),U_6346))
      | ~ class_Rings_Olinordered__semidom(U_6345) ),
    inference(variable_rename,[status(thm)],[f_1663_1]) ).

cnf(f_1663_3,plain,
    ( U_6347 = U_6348
    | hAPP(hAPP(c_Power_Opower__class_Opower(U_6345),U_6346),U_6347) != hAPP(hAPP(c_Power_Opower__class_Opower(U_6345),U_6346),U_6348)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6345),c_Groups_Oone__class_Oone(U_6345)),U_6346))
    | ~ class_Rings_Olinordered__semidom(U_6345) ),
    inference(clausify,[status(thm)],[f_1663_2]) ).

cnf(f_1663_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6345),U_6346),U_6347) = hAPP(hAPP(c_Power_Opower__class_Opower(U_6345),U_6346),U_6348)
    | U_6347 != U_6348
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6345),c_Groups_Oone__class_Oone(U_6345)),U_6346))
    | ~ class_Rings_Olinordered__semidom(U_6345) ),
    inference(clausify,[status(thm)],[f_1663_2]) ).

fof(f_1664_1,plain,
    ! [V_n,V_a,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a)
      | ~ class_Groups_Omonoid__mult(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__Suc2]) ).

fof(f_1664_2,plain,
    ! [U_6351,U_6350,U_6349] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6349),U_6350),hAPP(c_Nat_OSuc,U_6351)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6349),hAPP(hAPP(c_Power_Opower__class_Opower(U_6349),U_6350),U_6351)),U_6350)
      | ~ class_Groups_Omonoid__mult(U_6349) ),
    inference(variable_rename,[status(thm)],[f_1664_1]) ).

cnf(f_1664_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6349),U_6350),hAPP(c_Nat_OSuc,U_6351)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6349),hAPP(hAPP(c_Power_Opower__class_Opower(U_6349),U_6350),U_6351)),U_6350)
    | ~ class_Groups_Omonoid__mult(U_6349) ),
    inference(clausify,[status(thm)],[f_1664_2]) ).

fof(f_1665_1,plain,
    ! [V_n,V_a,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
      | ~ class_Power_Opower(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__Suc]) ).

fof(f_1665_2,plain,
    ! [U_6354,U_6353,U_6352] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6352),U_6353),hAPP(c_Nat_OSuc,U_6354)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6352),U_6353),hAPP(hAPP(c_Power_Opower__class_Opower(U_6352),U_6353),U_6354))
      | ~ class_Power_Opower(U_6352) ),
    inference(variable_rename,[status(thm)],[f_1665_1]) ).

cnf(f_1665_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6352),U_6353),hAPP(c_Nat_OSuc,U_6354)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6352),U_6353),hAPP(hAPP(c_Power_Opower__class_Opower(U_6352),U_6353),U_6354))
    | ~ class_Power_Opower(U_6352) ),
    inference(clausify,[status(thm)],[f_1665_2]) ).

fof(f_1666_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a)
      | ~ class_Power_Opower(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__0]) ).

fof(f_1666_2,plain,
    ! [U_6356,U_6355] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6355),U_6356),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_6355)
      | ~ class_Power_Opower(U_6355) ),
    inference(variable_rename,[status(thm)],[f_1666_1]) ).

cnf(f_1666_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6355),U_6356),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_6355)
    | ~ class_Power_Opower(U_6355) ),
    inference(clausify,[status(thm)],[f_1666_2]) ).

fof(f_1667_1,plain,
    ! [V_n,V_m,V_a,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
      | ~ class_Groups_Omonoid__mult(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__add]) ).

fof(f_1667_2,plain,
    ! [U_6360,U_6359,U_6358,U_6357] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6357),U_6358),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6359),U_6360)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6357),hAPP(hAPP(c_Power_Opower__class_Opower(U_6357),U_6358),U_6359)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6357),U_6358),U_6360))
      | ~ class_Groups_Omonoid__mult(U_6357) ),
    inference(variable_rename,[status(thm)],[f_1667_1]) ).

cnf(f_1667_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6357),U_6358),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6359),U_6360)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6357),hAPP(hAPP(c_Power_Opower__class_Opower(U_6357),U_6358),U_6359)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6357),U_6358),U_6360))
    | ~ class_Groups_Omonoid__mult(U_6357) ),
    inference(clausify,[status(thm)],[f_1667_2]) ).

fof(f_1668_1,plain,
    ! [V_n,V_a,V_b,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)),V_n) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))
      | V_b = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Fields_Ofield(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_nonzero__power__divide]) ).

fof(f_1668_2,plain,
    ! [U_6364,U_6363,U_6362,U_6361] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6361),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6361),U_6363),U_6362)),U_6364) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6361),hAPP(hAPP(c_Power_Opower__class_Opower(U_6361),U_6363),U_6364)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6361),U_6362),U_6364))
      | U_6362 = c_Groups_Ozero__class_Ozero(U_6361)
      | ~ class_Fields_Ofield(U_6361) ),
    inference(variable_rename,[status(thm)],[f_1668_1]) ).

cnf(f_1668_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6361),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6361),U_6363),U_6362)),U_6364) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6361),hAPP(hAPP(c_Power_Opower__class_Opower(U_6361),U_6363),U_6364)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6361),U_6362),U_6364))
    | U_6362 = c_Groups_Ozero__class_Ozero(U_6361)
    | ~ class_Fields_Ofield(U_6361) ),
    inference(clausify,[status(thm)],[f_1668_2]) ).

fof(f_1669_1,plain,
    ! [V_n,V_a,T_a] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)),V_n)
      | ~ class_Fields_Ofield__inverse__zero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__one__over]) ).

fof(f_1669_2,plain,
    ! [U_6367,U_6366,U_6365] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6365),c_Groups_Oone__class_Oone(U_6365)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6365),U_6366),U_6367)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_6365),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6365),c_Groups_Oone__class_Oone(U_6365)),U_6366)),U_6367)
      | ~ class_Fields_Ofield__inverse__zero(U_6365) ),
    inference(variable_rename,[status(thm)],[f_1669_1]) ).

cnf(f_1669_3,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6365),c_Groups_Oone__class_Oone(U_6365)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6365),U_6366),U_6367)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_6365),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6365),c_Groups_Oone__class_Oone(U_6365)),U_6366)),U_6367)
    | ~ class_Fields_Ofield__inverse__zero(U_6365) ),
    inference(clausify,[status(thm)],[f_1669_2]) ).

fof(f_1670_1,plain,
    ! [V_n] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(fof_nnf,[status(thm)],[fact_power__Suc__0]) ).

fof(f_1670_2,plain,
    ! [U_6368] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_6368) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[f_1670_1]) ).

cnf(f_1670_3,plain,
    hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_6368) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(clausify,[status(thm)],[f_1670_2]) ).

fof(f_1671_1,plain,
    ! [V_m_2,V_x_2] :
      ( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_m_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ( V_x_2 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( V_x_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_m_2) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__power__eq__Suc__0__iff]) ).

fof(f_1671_2,plain,
    ! [U_6370,U_6369] :
      ( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6369),U_6370) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ( U_6369 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & U_6370 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( U_6369 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_6370 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6369),U_6370) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(variable_rename,[status(thm)],[f_1671_1]) ).

fof(f_1671_3,plain,
    ( ! [U_6374,U_6372] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6372),U_6374) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ( U_6372 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & U_6374 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_6373,U_6371] :
        ( U_6371 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_6373 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6371),U_6373) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(miniscope,[status(thm)],[f_1671_2]) ).

cnf(f_1671_4,plain,
    ( U_6371 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | U_6373 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6371),U_6373) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_1671_3]) ).

cnf(f_1671_5,plain,
    ( U_6374 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6372),U_6374) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_1671_3]) ).

cnf(f_1671_6,plain,
    ( U_6372 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6372),U_6374) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_1671_3]) ).

fof(f_1672_1,plain,
    ! [V_n_2,V_x_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2)))
        | ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2)) ) )
      & ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__zero__less__power__iff]) ).

fof(f_1672_2,plain,
    ! [U_6376,U_6375] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6375),U_6376)))
        | ( U_6376 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6375)) ) )
      & ( U_6376 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6375))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6375),U_6376))) ) ),
    inference(variable_rename,[status(thm)],[f_1672_1]) ).

fof(f_1672_3,plain,
    ( ! [U_6380,U_6378] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6378),U_6380)))
        | ( U_6380 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6378)) ) )
    & ! [U_6379,U_6377] :
        ( U_6379 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6377))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6377),U_6379))) ) ),
    inference(miniscope,[status(thm)],[f_1672_2]) ).

cnf(f_1672_4,plain,
    ( U_6379 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6377))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6377),U_6379))) ),
    inference(clausify,[status(thm)],[f_1672_3]) ).

cnf(f_1672_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6378))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6378),U_6380))) ),
    inference(clausify,[status(thm)],[f_1672_3]) ).

cnf(f_1672_6,plain,
    ( U_6380 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6378),U_6380))) ),
    inference(clausify,[status(thm)],[f_1672_3]) ).

fof(f_1673_1,plain,
    ! [V_n,V_m,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i)) ),
    inference(fof_nnf,[status(thm)],[fact_nat__power__less__imp__less]) ).

fof(f_1673_2,plain,
    ! [U_6383,U_6382,U_6381] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6382),U_6383))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6381),U_6382)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6381),U_6383)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6381)) ),
    inference(variable_rename,[status(thm)],[f_1673_1]) ).

cnf(f_1673_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6382),U_6383))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6381),U_6382)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6381),U_6383)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6381)) ),
    inference(clausify,[status(thm)],[f_1673_2]) ).

fof(f_1674_1,plain,
    ! [V_b,V_n,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__less__imp__less__base]) ).

fof(f_1674_2,plain,
    ! [U_6387,U_6386,U_6385,U_6384] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6384),U_6385),U_6387))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6384),c_Groups_Ozero__class_Ozero(U_6384)),U_6387))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6384),hAPP(hAPP(c_Power_Opower__class_Opower(U_6384),U_6385),U_6386)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6384),U_6387),U_6386)))
      | ~ class_Rings_Olinordered__semidom(U_6384) ),
    inference(variable_rename,[status(thm)],[f_1674_1]) ).

cnf(f_1674_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6384),U_6385),U_6387))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6384),c_Groups_Ozero__class_Ozero(U_6384)),U_6387))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6384),hAPP(hAPP(c_Power_Opower__class_Opower(U_6384),U_6385),U_6386)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6384),U_6387),U_6386)))
    | ~ class_Rings_Olinordered__semidom(U_6384) ),
    inference(clausify,[status(thm)],[f_1674_2]) ).

fof(f_1675_1,plain,
    ! [V_b,V_n,V_a,T_a] :
      ( V_a = V_b
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
      | hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n)) != hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),hAPP(c_Nat_OSuc,V_n))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__inject__base]) ).

fof(f_1675_2,plain,
    ! [U_6391,U_6390,U_6389,U_6388] :
      ( U_6389 = U_6391
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6388),c_Groups_Ozero__class_Ozero(U_6388)),U_6391))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6388),c_Groups_Ozero__class_Ozero(U_6388)),U_6389))
      | hAPP(hAPP(c_Power_Opower__class_Opower(U_6388),U_6389),hAPP(c_Nat_OSuc,U_6390)) != hAPP(hAPP(c_Power_Opower__class_Opower(U_6388),U_6391),hAPP(c_Nat_OSuc,U_6390))
      | ~ class_Rings_Olinordered__semidom(U_6388) ),
    inference(variable_rename,[status(thm)],[f_1675_1]) ).

cnf(f_1675_3,plain,
    ( U_6389 = U_6391
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6388),c_Groups_Ozero__class_Ozero(U_6388)),U_6391))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6388),c_Groups_Ozero__class_Ozero(U_6388)),U_6389))
    | hAPP(hAPP(c_Power_Opower__class_Opower(U_6388),U_6389),hAPP(c_Nat_OSuc,U_6390)) != hAPP(hAPP(c_Power_Opower__class_Opower(U_6388),U_6391),hAPP(c_Nat_OSuc,U_6390))
    | ~ class_Rings_Olinordered__semidom(U_6388) ),
    inference(clausify,[status(thm)],[f_1675_2]) ).

fof(f_1676_1,plain,
    ! [V_b,V_n,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),hAPP(c_Nat_OSuc,V_n))))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__le__imp__le__base]) ).

fof(f_1676_2,plain,
    ! [U_6395,U_6394,U_6393,U_6392] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6392),U_6393),U_6395))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6392),c_Groups_Ozero__class_Ozero(U_6392)),U_6395))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6392),hAPP(hAPP(c_Power_Opower__class_Opower(U_6392),U_6393),hAPP(c_Nat_OSuc,U_6394))),hAPP(hAPP(c_Power_Opower__class_Opower(U_6392),U_6395),hAPP(c_Nat_OSuc,U_6394))))
      | ~ class_Rings_Olinordered__semidom(U_6392) ),
    inference(variable_rename,[status(thm)],[f_1676_1]) ).

cnf(f_1676_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6392),U_6393),U_6395))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6392),c_Groups_Ozero__class_Ozero(U_6392)),U_6395))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6392),hAPP(hAPP(c_Power_Opower__class_Opower(U_6392),U_6393),hAPP(c_Nat_OSuc,U_6394))),hAPP(hAPP(c_Power_Opower__class_Opower(U_6392),U_6395),hAPP(c_Nat_OSuc,U_6394))))
    | ~ class_Rings_Olinordered__semidom(U_6392) ),
    inference(clausify,[status(thm)],[f_1676_2]) ).

fof(f_1677_1,plain,
    ! [V_n,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__gt1__lemma]) ).

fof(f_1677_2,plain,
    ! [U_6398,U_6397,U_6396] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6396),c_Groups_Oone__class_Oone(U_6396)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6396),U_6397),hAPP(hAPP(c_Power_Opower__class_Opower(U_6396),U_6397),U_6398))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6396),c_Groups_Oone__class_Oone(U_6396)),U_6397))
      | ~ class_Rings_Olinordered__semidom(U_6396) ),
    inference(variable_rename,[status(thm)],[f_1677_1]) ).

cnf(f_1677_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6396),c_Groups_Oone__class_Oone(U_6396)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6396),U_6397),hAPP(hAPP(c_Power_Opower__class_Opower(U_6396),U_6397),U_6398))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6396),c_Groups_Oone__class_Oone(U_6396)),U_6397))
    | ~ class_Rings_Olinordered__semidom(U_6396) ),
    inference(clausify,[status(thm)],[f_1677_2]) ).

fof(f_1678_1,plain,
    ! [V_n,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__less__power__Suc]) ).

fof(f_1678_2,plain,
    ! [U_6401,U_6400,U_6399] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6399),hAPP(hAPP(c_Power_Opower__class_Opower(U_6399),U_6400),U_6401)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6399),U_6400),hAPP(hAPP(c_Power_Opower__class_Opower(U_6399),U_6400),U_6401))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6399),c_Groups_Oone__class_Oone(U_6399)),U_6400))
      | ~ class_Rings_Olinordered__semidom(U_6399) ),
    inference(variable_rename,[status(thm)],[f_1678_1]) ).

cnf(f_1678_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6399),hAPP(hAPP(c_Power_Opower__class_Opower(U_6399),U_6400),U_6401)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6399),U_6400),hAPP(hAPP(c_Power_Opower__class_Opower(U_6399),U_6400),U_6401))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6399),c_Groups_Oone__class_Oone(U_6399)),U_6400))
    | ~ class_Rings_Olinordered__semidom(U_6399) ),
    inference(clausify,[status(thm)],[f_1678_2]) ).

fof(f_1679_1,plain,
    ! [V_n,T_a] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n) = c_Groups_Ozero__class_Ozero(T_a)
          | V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        & ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n) = c_Groups_Oone__class_Oone(T_a)
          | V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      | ~ class_Rings_Osemiring__0(T_a)
      | ~ class_Power_Opower(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__0__left]) ).

fof(f_1679_2,plain,
    ! [U_6403,U_6402] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6402),c_Groups_Ozero__class_Ozero(U_6402)),U_6403) = c_Groups_Ozero__class_Ozero(U_6402)
          | U_6403 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        & ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6402),c_Groups_Ozero__class_Ozero(U_6402)),U_6403) = c_Groups_Oone__class_Oone(U_6402)
          | U_6403 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      | ~ class_Rings_Osemiring__0(U_6402)
      | ~ class_Power_Opower(U_6402) ),
    inference(variable_rename,[status(thm)],[f_1679_1]) ).

cnf(f_1679_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6402),c_Groups_Ozero__class_Ozero(U_6402)),U_6403) = c_Groups_Oone__class_Oone(U_6402)
    | U_6403 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ class_Rings_Osemiring__0(U_6402)
    | ~ class_Power_Opower(U_6402) ),
    inference(clausify,[status(thm)],[f_1679_2]) ).

cnf(f_1679_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6402),c_Groups_Ozero__class_Ozero(U_6402)),U_6403) = c_Groups_Ozero__class_Ozero(U_6402)
    | U_6403 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ class_Rings_Osemiring__0(U_6402)
    | ~ class_Power_Opower(U_6402) ),
    inference(clausify,[status(thm)],[f_1679_2]) ).

fof(f_1680_1,plain,
    ! [V_n,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__gt1]) ).

fof(f_1680_2,plain,
    ! [U_6406,U_6405,U_6404] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6404),c_Groups_Oone__class_Oone(U_6404)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6404),U_6405),hAPP(c_Nat_OSuc,U_6406))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6404),c_Groups_Oone__class_Oone(U_6404)),U_6405))
      | ~ class_Rings_Olinordered__semidom(U_6404) ),
    inference(variable_rename,[status(thm)],[f_1680_1]) ).

cnf(f_1680_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6404),c_Groups_Oone__class_Oone(U_6404)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6404),U_6405),hAPP(c_Nat_OSuc,U_6406))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6404),c_Groups_Oone__class_Oone(U_6404)),U_6405))
    | ~ class_Rings_Olinordered__semidom(U_6404) ),
    inference(clausify,[status(thm)],[f_1680_2]) ).

fof(f_1681_1,plain,
    ! [V_y_2,V_x_2,V_b_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_y_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_y_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_b_2))
      | ~ class_Rings_Olinordered__semidom(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_power__strict__increasing__iff]) ).

fof(f_1681_2,plain,
    ! [U_6410,U_6409,U_6408,U_6407] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6407),hAPP(hAPP(c_Power_Opower__class_Opower(U_6407),U_6408),U_6409)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6407),U_6408),U_6410)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6409),U_6410)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6409),U_6410))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6407),hAPP(hAPP(c_Power_Opower__class_Opower(U_6407),U_6408),U_6409)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6407),U_6408),U_6410))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6407),c_Groups_Oone__class_Oone(U_6407)),U_6408))
      | ~ class_Rings_Olinordered__semidom(U_6407) ),
    inference(variable_rename,[status(thm)],[f_1681_1]) ).

cnf(f_1681_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6409),U_6410))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6407),hAPP(hAPP(c_Power_Opower__class_Opower(U_6407),U_6408),U_6409)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6407),U_6408),U_6410)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6407),c_Groups_Oone__class_Oone(U_6407)),U_6408))
    | ~ class_Rings_Olinordered__semidom(U_6407) ),
    inference(clausify,[status(thm)],[f_1681_2]) ).

cnf(f_1681_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6407),hAPP(hAPP(c_Power_Opower__class_Opower(U_6407),U_6408),U_6409)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6407),U_6408),U_6410)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6409),U_6410))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6407),c_Groups_Oone__class_Oone(U_6407)),U_6408))
    | ~ class_Rings_Olinordered__semidom(U_6407) ),
    inference(clausify,[status(thm)],[f_1681_2]) ).

fof(f_1682_1,plain,
    ! [V_n,V_m,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__less__imp__less__exp]) ).

fof(f_1682_2,plain,
    ! [U_6414,U_6413,U_6412,U_6411] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6413),U_6414))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6411),hAPP(hAPP(c_Power_Opower__class_Opower(U_6411),U_6412),U_6413)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6411),U_6412),U_6414)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6411),c_Groups_Oone__class_Oone(U_6411)),U_6412))
      | ~ class_Rings_Olinordered__semidom(U_6411) ),
    inference(variable_rename,[status(thm)],[f_1682_1]) ).

cnf(f_1682_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6413),U_6414))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6411),hAPP(hAPP(c_Power_Opower__class_Opower(U_6411),U_6412),U_6413)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6411),U_6412),U_6414)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6411),c_Groups_Oone__class_Oone(U_6411)),U_6412))
    | ~ class_Rings_Olinordered__semidom(U_6411) ),
    inference(clausify,[status(thm)],[f_1682_2]) ).

fof(f_1683_1,plain,
    ! [V_a,V_N,V_n,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__strict__increasing]) ).

fof(f_1683_2,plain,
    ! [U_6418,U_6417,U_6416,U_6415] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6415),hAPP(hAPP(c_Power_Opower__class_Opower(U_6415),U_6418),U_6416)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6415),U_6418),U_6417)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6415),c_Groups_Oone__class_Oone(U_6415)),U_6418))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6416),U_6417))
      | ~ class_Rings_Olinordered__semidom(U_6415) ),
    inference(variable_rename,[status(thm)],[f_1683_1]) ).

cnf(f_1683_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6415),hAPP(hAPP(c_Power_Opower__class_Opower(U_6415),U_6418),U_6416)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6415),U_6418),U_6417)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6415),c_Groups_Oone__class_Oone(U_6415)),U_6418))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6416),U_6417))
    | ~ class_Rings_Olinordered__semidom(U_6415) ),
    inference(clausify,[status(thm)],[f_1683_2]) ).

fof(f_1684_1,plain,
    ! [V_a,V_N,V_n,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__increasing]) ).

fof(f_1684_2,plain,
    ! [U_6422,U_6421,U_6420,U_6419] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6419),hAPP(hAPP(c_Power_Opower__class_Opower(U_6419),U_6422),U_6420)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6419),U_6422),U_6421)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6419),c_Groups_Oone__class_Oone(U_6419)),U_6422))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6420),U_6421))
      | ~ class_Rings_Olinordered__semidom(U_6419) ),
    inference(variable_rename,[status(thm)],[f_1684_1]) ).

cnf(f_1684_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6419),hAPP(hAPP(c_Power_Opower__class_Opower(U_6419),U_6422),U_6420)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6419),U_6422),U_6421)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6419),c_Groups_Oone__class_Oone(U_6419)),U_6422))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6420),U_6421))
    | ~ class_Rings_Olinordered__semidom(U_6419) ),
    inference(clausify,[status(thm)],[f_1684_2]) ).

fof(f_1685_1,plain,
    ! [V_n,V_a,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
      | ~ class_Rings_Oring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__minus]) ).

fof(f_1685_2,plain,
    ! [U_6425,U_6424,U_6423] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6423),hAPP(c_Groups_Ouminus__class_Ouminus(U_6423),U_6424)),U_6425) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6423),hAPP(hAPP(c_Power_Opower__class_Opower(U_6423),hAPP(c_Groups_Ouminus__class_Ouminus(U_6423),c_Groups_Oone__class_Oone(U_6423))),U_6425)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6423),U_6424),U_6425))
      | ~ class_Rings_Oring__1(U_6423) ),
    inference(variable_rename,[status(thm)],[f_1685_1]) ).

cnf(f_1685_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_6423),hAPP(c_Groups_Ouminus__class_Ouminus(U_6423),U_6424)),U_6425) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6423),hAPP(hAPP(c_Power_Opower__class_Opower(U_6423),hAPP(c_Groups_Ouminus__class_Ouminus(U_6423),c_Groups_Oone__class_Oone(U_6423))),U_6425)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6423),U_6424),U_6425))
    | ~ class_Rings_Oring__1(U_6423) ),
    inference(clausify,[status(thm)],[f_1685_2]) ).

fof(f_1686_1,plain,
    ! [V_n,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_i)) ),
    inference(fof_nnf,[status(thm)],[fact_nat__one__le__power]) ).

fof(f_1686_2,plain,
    ! [U_6427,U_6426] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6426),U_6427)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_6426)) ),
    inference(variable_rename,[status(thm)],[f_1686_1]) ).

cnf(f_1686_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_6426),U_6427)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_6426)) ),
    inference(clausify,[status(thm)],[f_1686_2]) ).

fof(f_1687_1,plain,
    ! [V_n,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__Suc__less]) ).

fof(f_1687_2,plain,
    ! [U_6430,U_6429,U_6428] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6428),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6428),U_6429),hAPP(hAPP(c_Power_Opower__class_Opower(U_6428),U_6429),U_6430))),hAPP(hAPP(c_Power_Opower__class_Opower(U_6428),U_6429),U_6430)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6428),U_6429),c_Groups_Oone__class_Oone(U_6428)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6428),c_Groups_Ozero__class_Ozero(U_6428)),U_6429))
      | ~ class_Rings_Olinordered__semidom(U_6428) ),
    inference(variable_rename,[status(thm)],[f_1687_1]) ).

cnf(f_1687_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6428),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6428),U_6429),hAPP(hAPP(c_Power_Opower__class_Opower(U_6428),U_6429),U_6430))),hAPP(hAPP(c_Power_Opower__class_Opower(U_6428),U_6429),U_6430)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6428),U_6429),c_Groups_Oone__class_Oone(U_6428)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6428),c_Groups_Ozero__class_Ozero(U_6428)),U_6429))
    | ~ class_Rings_Olinordered__semidom(U_6428) ),
    inference(clausify,[status(thm)],[f_1687_2]) ).

fof(f_1688_1,plain,
    ! [V_b,V_n,V_a,T_a] :
      ( V_a = V_b
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
      | hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__eq__imp__eq__base]) ).

fof(f_1688_2,plain,
    ! [U_6434,U_6433,U_6432,U_6431] :
      ( U_6432 = U_6434
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6433))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6431),c_Groups_Ozero__class_Ozero(U_6431)),U_6434))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6431),c_Groups_Ozero__class_Ozero(U_6431)),U_6432))
      | hAPP(hAPP(c_Power_Opower__class_Opower(U_6431),U_6432),U_6433) != hAPP(hAPP(c_Power_Opower__class_Opower(U_6431),U_6434),U_6433)
      | ~ class_Rings_Olinordered__semidom(U_6431) ),
    inference(variable_rename,[status(thm)],[f_1688_1]) ).

cnf(f_1688_3,plain,
    ( U_6432 = U_6434
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6433))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6431),c_Groups_Ozero__class_Ozero(U_6431)),U_6434))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6431),c_Groups_Ozero__class_Ozero(U_6431)),U_6432))
    | hAPP(hAPP(c_Power_Opower__class_Opower(U_6431),U_6432),U_6433) != hAPP(hAPP(c_Power_Opower__class_Opower(U_6431),U_6434),U_6433)
    | ~ class_Rings_Olinordered__semidom(U_6431) ),
    inference(clausify,[status(thm)],[f_1688_2]) ).

fof(f_1689_1,plain,
    ! [V_n,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n))),c_Groups_Oone__class_Oone(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__Suc__less__one]) ).

fof(f_1689_2,plain,
    ! [U_6437,U_6436,U_6435] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6435),hAPP(hAPP(c_Power_Opower__class_Opower(U_6435),U_6436),hAPP(c_Nat_OSuc,U_6437))),c_Groups_Oone__class_Oone(U_6435)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6435),U_6436),c_Groups_Oone__class_Oone(U_6435)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6435),c_Groups_Ozero__class_Ozero(U_6435)),U_6436))
      | ~ class_Rings_Olinordered__semidom(U_6435) ),
    inference(variable_rename,[status(thm)],[f_1689_1]) ).

cnf(f_1689_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6435),hAPP(hAPP(c_Power_Opower__class_Opower(U_6435),U_6436),hAPP(c_Nat_OSuc,U_6437))),c_Groups_Oone__class_Oone(U_6435)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6435),U_6436),c_Groups_Oone__class_Oone(U_6435)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6435),c_Groups_Ozero__class_Ozero(U_6435)),U_6436))
    | ~ class_Rings_Olinordered__semidom(U_6435) ),
    inference(clausify,[status(thm)],[f_1689_2]) ).

fof(f_1690_1,plain,
    ! [V_a,V_N,V_n,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__strict__decreasing]) ).

fof(f_1690_2,plain,
    ! [U_6441,U_6440,U_6439,U_6438] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6438),hAPP(hAPP(c_Power_Opower__class_Opower(U_6438),U_6441),U_6440)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6438),U_6441),U_6439)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6438),U_6441),c_Groups_Oone__class_Oone(U_6438)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6438),c_Groups_Ozero__class_Ozero(U_6438)),U_6441))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6439),U_6440))
      | ~ class_Rings_Olinordered__semidom(U_6438) ),
    inference(variable_rename,[status(thm)],[f_1690_1]) ).

cnf(f_1690_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6438),hAPP(hAPP(c_Power_Opower__class_Opower(U_6438),U_6441),U_6440)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6438),U_6441),U_6439)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6438),U_6441),c_Groups_Oone__class_Oone(U_6438)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6438),c_Groups_Ozero__class_Ozero(U_6438)),U_6441))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6439),U_6440))
    | ~ class_Rings_Olinordered__semidom(U_6438) ),
    inference(clausify,[status(thm)],[f_1690_2]) ).

fof(f_1691_1,plain,
    ! [T_b] :
      ( c_Power_Opower__class_Opower(T_b) = c_Power_Opower_Opower(T_b,c_Groups_Oone__class_Oone(T_b),c_Groups_Otimes__class_Otimes(T_b))
      | ~ class_Power_Opower(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_power__power__power]) ).

fof(f_1691_2,plain,
    ! [U_6442] :
      ( c_Power_Opower__class_Opower(U_6442) = c_Power_Opower_Opower(U_6442,c_Groups_Oone__class_Oone(U_6442),c_Groups_Otimes__class_Otimes(U_6442))
      | ~ class_Power_Opower(U_6442) ),
    inference(variable_rename,[status(thm)],[f_1691_1]) ).

cnf(f_1691_3,plain,
    ( c_Power_Opower__class_Opower(U_6442) = c_Power_Opower_Opower(U_6442,c_Groups_Oone__class_Oone(U_6442),c_Groups_Otimes__class_Otimes(U_6442))
    | ~ class_Power_Opower(U_6442) ),
    inference(clausify,[status(thm)],[f_1691_2]) ).

fof(f_1692_1,plain,
    ! [V_c_2,V_b_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_b_2),V_c_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_c_2),V_A_2)))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Osemilattice__inf(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_inf__le__fold__inf]) ).

fof(f_1692_2,plain,
    ! [U_6447,U_6446,U_6445,U_6444] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6444),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_6444),U_6446),U_6447)),hAPP(hAPP(c_Finite__Set_Ofold(U_6444,U_6444,c_Lattices_Osemilattice__inf__class_Oinf(U_6444)),U_6447),U_6445)))
      | ? [U_6443] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6444),U_6446),U_6443))
          & hBOOL(hAPP(hAPP(c_member(U_6444),U_6443),U_6445)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6444),U_6445))
      | ~ class_Lattices_Osemilattice__inf(U_6444) ),
    inference(variable_rename,[status(thm)],[f_1692_1]) ).

fof(f_1692_3,plain,
    ! [U_6447,U_6446,U_6445,U_6444] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6444),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_6444),U_6446),U_6447)),hAPP(hAPP(c_Finite__Set_Ofold(U_6444,U_6444,c_Lattices_Osemilattice__inf__class_Oinf(U_6444)),U_6447),U_6445)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6444),U_6446),sK147(U_6447,U_6446,U_6445,U_6444)))
        & hBOOL(hAPP(hAPP(c_member(U_6444),sK147(U_6447,U_6446,U_6445,U_6444)),U_6445)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6444),U_6445))
      | ~ class_Lattices_Osemilattice__inf(U_6444) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK147]),skolemize(U_6443,sK147(U_6447,U_6446,U_6445,U_6444))],[f_1692_2]) ).

cnf(f_1692_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_6444),sK147(U_6447,U_6446,U_6445,U_6444)),U_6445))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6444),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_6444),U_6446),U_6447)),hAPP(hAPP(c_Finite__Set_Ofold(U_6444,U_6444,c_Lattices_Osemilattice__inf__class_Oinf(U_6444)),U_6447),U_6445)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6444),U_6445))
    | ~ class_Lattices_Osemilattice__inf(U_6444) ),
    inference(clausify,[status(thm)],[f_1692_3]) ).

cnf(f_1692_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6444),U_6446),sK147(U_6447,U_6446,U_6445,U_6444)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6444),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_6444),U_6446),U_6447)),hAPP(hAPP(c_Finite__Set_Ofold(U_6444,U_6444,c_Lattices_Osemilattice__inf__class_Oinf(U_6444)),U_6447),U_6445)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6444),U_6445))
    | ~ class_Lattices_Osemilattice__inf(U_6444) ),
    inference(clausify,[status(thm)],[f_1692_3]) ).

fof(f_1693_1,plain,
    ! [V_c_2,V_b_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_c_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_b_2),V_c_2)))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Osemilattice__sup(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_fold__sup__le__sup]) ).

fof(f_1693_2,plain,
    ! [U_6452,U_6451,U_6450,U_6449] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6449),hAPP(hAPP(c_Finite__Set_Ofold(U_6449,U_6449,c_Lattices_Osemilattice__sup__class_Osup(U_6449)),U_6452),U_6450)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_6449),U_6451),U_6452)))
      | ? [U_6448] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6449),U_6448),U_6451))
          & hBOOL(hAPP(hAPP(c_member(U_6449),U_6448),U_6450)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6449),U_6450))
      | ~ class_Lattices_Osemilattice__sup(U_6449) ),
    inference(variable_rename,[status(thm)],[f_1693_1]) ).

fof(f_1693_3,plain,
    ! [U_6452,U_6451,U_6450,U_6449] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6449),hAPP(hAPP(c_Finite__Set_Ofold(U_6449,U_6449,c_Lattices_Osemilattice__sup__class_Osup(U_6449)),U_6452),U_6450)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_6449),U_6451),U_6452)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6449),sK148(U_6452,U_6451,U_6450,U_6449)),U_6451))
        & hBOOL(hAPP(hAPP(c_member(U_6449),sK148(U_6452,U_6451,U_6450,U_6449)),U_6450)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6449),U_6450))
      | ~ class_Lattices_Osemilattice__sup(U_6449) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK148]),skolemize(U_6448,sK148(U_6452,U_6451,U_6450,U_6449))],[f_1693_2]) ).

cnf(f_1693_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_6449),sK148(U_6452,U_6451,U_6450,U_6449)),U_6450))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6449),hAPP(hAPP(c_Finite__Set_Ofold(U_6449,U_6449,c_Lattices_Osemilattice__sup__class_Osup(U_6449)),U_6452),U_6450)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_6449),U_6451),U_6452)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6449),U_6450))
    | ~ class_Lattices_Osemilattice__sup(U_6449) ),
    inference(clausify,[status(thm)],[f_1693_3]) ).

cnf(f_1693_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6449),sK148(U_6452,U_6451,U_6450,U_6449)),U_6451))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6449),hAPP(hAPP(c_Finite__Set_Ofold(U_6449,U_6449,c_Lattices_Osemilattice__sup__class_Osup(U_6449)),U_6452),U_6450)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_6449),U_6451),U_6452)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6449),U_6450))
    | ~ class_Lattices_Osemilattice__sup(U_6449) ),
    inference(clausify,[status(thm)],[f_1693_3]) ).

fof(f_1694_1,plain,
    ! [V_v] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v))) ),
    inference(fof_nnf,[status(thm)],[fact_expand__Suc]) ).

fof(f_1694_2,plain,
    ! [U_6453] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6453) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6453)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6453))) ),
    inference(variable_rename,[status(thm)],[f_1694_1]) ).

cnf(f_1694_3,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6453) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6453)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6453))) ),
    inference(clausify,[status(thm)],[f_1694_2]) ).

fof(f_1695_1,plain,
    ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
      ( hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
      | ~ c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Ounion__idem]) ).

fof(f_1695_2,plain,
    ! [U_6461,U_6460,U_6459,U_6458,U_6457,U_6456,U_6455,U_6454] :
      ( hAPP(U_6459,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6455,tc_HOL_Obool)),U_6460),U_6461)) = hAPP(hAPP(U_6456,hAPP(U_6459,U_6460)),hAPP(U_6459,U_6461))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6455),U_6461))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6455),U_6460))
      | ~ c_Finite__Set_Ofolding__image__simple__idem(U_6454,U_6455,U_6456,U_6457,U_6458,U_6459) ),
    inference(variable_rename,[status(thm)],[f_1695_1]) ).

fof(f_1695_3,plain,
    ! [U_6461,U_6460,U_6459,U_6458,U_6457,U_6456,U_6455] :
      ( ! [U_6454] : ~ c_Finite__Set_Ofolding__image__simple__idem(U_6454,U_6455,U_6456,U_6457,U_6458,U_6459)
      | hAPP(U_6459,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6455,tc_HOL_Obool)),U_6460),U_6461)) = hAPP(hAPP(U_6456,hAPP(U_6459,U_6460)),hAPP(U_6459,U_6461))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6455),U_6461))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6455),U_6460)) ),
    inference(miniscope,[status(thm)],[f_1695_2]) ).

cnf(f_1695_4,plain,
    ( ~ c_Finite__Set_Ofolding__image__simple__idem(U_6454,U_6455,U_6456,U_6457,U_6458,U_6459)
    | hAPP(U_6459,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6455,tc_HOL_Obool)),U_6460),U_6461)) = hAPP(hAPP(U_6456,hAPP(U_6459,U_6460)),hAPP(U_6459,U_6461))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6455),U_6461))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6455),U_6460)) ),
    inference(clausify,[status(thm)],[f_1695_3]) ).

fof(f_1696_1,plain,
    ! [V_C_2,V_A_2,T_b] :
      ( ? [B_X] :
          ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2))
          & hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),B_X)) )
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2))) ),
    inference(fof_nnf,[status(thm)],[fact_UnionE]) ).

fof(f_1696_2,plain,
    ! [U_6465,U_6464,U_6463] :
      ( ? [U_6462] :
          ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_6463,tc_HOL_Obool)),U_6462),U_6465))
          & hBOOL(hAPP(hAPP(c_member(U_6463),U_6464),U_6462)) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_6463),U_6464),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_6463,tc_HOL_Obool),U_6465))) ),
    inference(variable_rename,[status(thm)],[f_1696_1]) ).

fof(f_1696_3,plain,
    ! [U_6465,U_6464,U_6463] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_6463,tc_HOL_Obool)),sK149(U_6465,U_6464,U_6463)),U_6465))
        & hBOOL(hAPP(hAPP(c_member(U_6463),U_6464),sK149(U_6465,U_6464,U_6463))) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_6463),U_6464),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_6463,tc_HOL_Obool),U_6465))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK149]),skolemize(U_6462,sK149(U_6465,U_6464,U_6463))],[f_1696_2]) ).

cnf(f_1696_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_6463),U_6464),sK149(U_6465,U_6464,U_6463)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_6463),U_6464),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_6463,tc_HOL_Obool),U_6465))) ),
    inference(clausify,[status(thm)],[f_1696_3]) ).

cnf(f_1696_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_6463,tc_HOL_Obool)),sK149(U_6465,U_6464,U_6463)),U_6465))
    | ~ hBOOL(hAPP(hAPP(c_member(U_6463),U_6464),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_6463,tc_HOL_Obool),U_6465))) ),
    inference(clausify,[status(thm)],[f_1696_3]) ).

fof(f_1697_1,plain,
    ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z,
    inference(fof_nnf,[status(thm)],[fact_zmult__1__right]) ).

fof(f_1697_2,plain,
    ! [U_6466] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6466),c_Groups_Oone__class_Oone(tc_Int_Oint)) = U_6466,
    inference(variable_rename,[status(thm)],[f_1697_1]) ).

cnf(f_1697_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6466),c_Groups_Oone__class_Oone(tc_Int_Oint)) = U_6466,
    inference(clausify,[status(thm)],[f_1697_2]) ).

fof(f_1698_1,plain,
    ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z,
    inference(fof_nnf,[status(thm)],[fact_zmult__1]) ).

fof(f_1698_2,plain,
    ! [U_6467] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_6467) = U_6467,
    inference(variable_rename,[status(thm)],[f_1698_1]) ).

cnf(f_1698_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_6467) = U_6467,
    inference(clausify,[status(thm)],[f_1698_2]) ).

fof(f_1699_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
          | V_n_2 != c_Groups_Oone__class_Oone(tc_Int_Oint)
          | V_m_2 != c_Groups_Oone__class_Oone(tc_Int_Oint) )
        & ( ( V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
            & V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) != c_Groups_Oone__class_Oone(tc_Int_Oint) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m_2)) ),
    inference(fof_nnf,[status(thm)],[fact_pos__zmult__eq__1__iff]) ).

fof(f_1699_2,plain,
    ! [U_6469,U_6468] :
      ( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6468),U_6469) = c_Groups_Oone__class_Oone(tc_Int_Oint)
          | U_6469 != c_Groups_Oone__class_Oone(tc_Int_Oint)
          | U_6468 != c_Groups_Oone__class_Oone(tc_Int_Oint) )
        & ( ( U_6469 = c_Groups_Oone__class_Oone(tc_Int_Oint)
            & U_6468 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6468),U_6469) != c_Groups_Oone__class_Oone(tc_Int_Oint) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6468)) ),
    inference(variable_rename,[status(thm)],[f_1699_1]) ).

cnf(f_1699_3,plain,
    ( U_6468 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6468),U_6469) != c_Groups_Oone__class_Oone(tc_Int_Oint)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6468)) ),
    inference(clausify,[status(thm)],[f_1699_2]) ).

cnf(f_1699_4,plain,
    ( U_6469 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6468),U_6469) != c_Groups_Oone__class_Oone(tc_Int_Oint)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6468)) ),
    inference(clausify,[status(thm)],[f_1699_2]) ).

cnf(f_1699_5,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6468),U_6469) = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | U_6469 != c_Groups_Oone__class_Oone(tc_Int_Oint)
    | U_6468 != c_Groups_Oone__class_Oone(tc_Int_Oint)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6468)) ),
    inference(clausify,[status(thm)],[f_1699_2]) ).

fof(f_1700_1,plain,
    ! [V_k,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_j)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j)) ),
    inference(fof_nnf,[status(thm)],[fact_zmult__zless__mono2]) ).

fof(f_1700_2,plain,
    ! [U_6472,U_6471,U_6470] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6472),U_6470)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6472),U_6471)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6472))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6470),U_6471)) ),
    inference(variable_rename,[status(thm)],[f_1700_1]) ).

cnf(f_1700_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6472),U_6470)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6472),U_6471)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6472))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6470),U_6471)) ),
    inference(clausify,[status(thm)],[f_1700_2]) ).

fof(f_1701_1,plain,
    ! [V_z2,V_z1,V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z1),V_z2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2)),
    inference(fof_nnf,[status(thm)],[fact_zdiff__zmult__distrib2]) ).

fof(f_1701_2,plain,
    ! [U_6475,U_6474,U_6473] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6473),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6474),U_6475)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6473),U_6474)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6473),U_6475)),
    inference(variable_rename,[status(thm)],[f_1701_1]) ).

cnf(f_1701_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6473),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6474),U_6475)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6473),U_6474)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6473),U_6475)),
    inference(clausify,[status(thm)],[f_1701_2]) ).

fof(f_1702_1,plain,
    ! [V_w,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z1),V_z2)),V_w) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w)),
    inference(fof_nnf,[status(thm)],[fact_zdiff__zmult__distrib]) ).

fof(f_1702_2,plain,
    ! [U_6478,U_6477,U_6476] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6476),U_6477)),U_6478) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6476),U_6478)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6477),U_6478)),
    inference(variable_rename,[status(thm)],[f_1702_1]) ).

cnf(f_1702_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6476),U_6477)),U_6478) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6476),U_6478)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6477),U_6478)),
    inference(clausify,[status(thm)],[f_1702_2]) ).

fof(f_1703_1,plain,
    ! [V_w,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)),V_w) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w)),
    inference(fof_nnf,[status(thm)],[fact_zadd__zmult__distrib]) ).

fof(f_1703_2,plain,
    ! [U_6481,U_6480,U_6479] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6479),U_6480)),U_6481) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6479),U_6481)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6480),U_6481)),
    inference(variable_rename,[status(thm)],[f_1703_1]) ).

cnf(f_1703_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6479),U_6480)),U_6481) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6479),U_6481)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6480),U_6481)),
    inference(clausify,[status(thm)],[f_1703_2]) ).

fof(f_1704_1,plain,
    ! [V_z3,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_z2)),V_z3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_z3)),
    inference(fof_nnf,[status(thm)],[fact_zmult__assoc]) ).

fof(f_1704_2,plain,
    ! [U_6484,U_6483,U_6482] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6482),U_6483)),U_6484) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6482),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6483),U_6484)),
    inference(variable_rename,[status(thm)],[f_1704_1]) ).

cnf(f_1704_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6482),U_6483)),U_6484) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6482),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6483),U_6484)),
    inference(clausify,[status(thm)],[f_1704_2]) ).

fof(f_1705_1,plain,
    ! [V_z2,V_z1,V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2)),
    inference(fof_nnf,[status(thm)],[fact_zadd__zmult__distrib2]) ).

fof(f_1705_2,plain,
    ! [U_6487,U_6486,U_6485] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6485),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6486),U_6487)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6485),U_6486)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6485),U_6487)),
    inference(variable_rename,[status(thm)],[f_1705_1]) ).

cnf(f_1705_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6485),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6486),U_6487)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6485),U_6486)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6485),U_6487)),
    inference(clausify,[status(thm)],[f_1705_2]) ).

fof(f_1706_1,plain,
    ! [V_w,V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_w) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z),
    inference(fof_nnf,[status(thm)],[fact_zmult__commute]) ).

fof(f_1706_2,plain,
    ! [U_6489,U_6488] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6488),U_6489) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6489),U_6488),
    inference(variable_rename,[status(thm)],[f_1706_1]) ).

cnf(f_1706_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6488),U_6489) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6489),U_6488),
    inference(clausify,[status(thm)],[f_1706_2]) ).

fof(f_1707_1,plain,
    ! [V_w,V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)),V_w) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_w)),
    inference(fof_nnf,[status(thm)],[fact_zmult__zminus]) ).

fof(f_1707_2,plain,
    ! [U_6491,U_6490] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6490)),U_6491) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6490),U_6491)),
    inference(variable_rename,[status(thm)],[f_1707_1]) ).

cnf(f_1707_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6490)),U_6491) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6490),U_6491)),
    inference(clausify,[status(thm)],[f_1707_2]) ).

fof(f_1708_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
          | V_x_2 != V_y_2 )
        & ( V_x_2 = V_y_2
          | hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) != hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2) ) )
      | ~ class_Int_Oring__char__0(T_b)
      | ~ class_Int_Onumber__ring(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_eq__number__of]) ).

fof(f_1708_2,plain,
    ! [U_6494,U_6493,U_6492] :
      ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_6492),U_6493) = hAPP(c_Int_Onumber__class_Onumber__of(U_6492),U_6494)
          | U_6493 != U_6494 )
        & ( U_6493 = U_6494
          | hAPP(c_Int_Onumber__class_Onumber__of(U_6492),U_6493) != hAPP(c_Int_Onumber__class_Onumber__of(U_6492),U_6494) ) )
      | ~ class_Int_Oring__char__0(U_6492)
      | ~ class_Int_Onumber__ring(U_6492) ),
    inference(variable_rename,[status(thm)],[f_1708_1]) ).

cnf(f_1708_3,plain,
    ( U_6493 = U_6494
    | hAPP(c_Int_Onumber__class_Onumber__of(U_6492),U_6493) != hAPP(c_Int_Onumber__class_Onumber__of(U_6492),U_6494)
    | ~ class_Int_Oring__char__0(U_6492)
    | ~ class_Int_Onumber__ring(U_6492) ),
    inference(clausify,[status(thm)],[f_1708_2]) ).

cnf(f_1708_4,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_6492),U_6493) = hAPP(c_Int_Onumber__class_Onumber__of(U_6492),U_6494)
    | U_6493 != U_6494
    | ~ class_Int_Oring__char__0(U_6492)
    | ~ class_Int_Onumber__ring(U_6492) ),
    inference(clausify,[status(thm)],[f_1708_2]) ).

fof(f_1709_1,plain,
    ! [V_x_2,V_w_2,T_b] :
      ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = V_x_2
          | V_x_2 != hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) )
        & ( V_x_2 = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)
          | hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != V_x_2 ) )
      | ~ class_Int_Onumber(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_number__of__reorient]) ).

fof(f_1709_2,plain,
    ! [U_6497,U_6496,U_6495] :
      ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_6495),U_6496) = U_6497
          | U_6497 != hAPP(c_Int_Onumber__class_Onumber__of(U_6495),U_6496) )
        & ( U_6497 = hAPP(c_Int_Onumber__class_Onumber__of(U_6495),U_6496)
          | hAPP(c_Int_Onumber__class_Onumber__of(U_6495),U_6496) != U_6497 ) )
      | ~ class_Int_Onumber(U_6495) ),
    inference(variable_rename,[status(thm)],[f_1709_1]) ).

cnf(f_1709_3,plain,
    ( U_6497 = hAPP(c_Int_Onumber__class_Onumber__of(U_6495),U_6496)
    | hAPP(c_Int_Onumber__class_Onumber__of(U_6495),U_6496) != U_6497
    | ~ class_Int_Onumber(U_6495) ),
    inference(clausify,[status(thm)],[f_1709_2]) ).

cnf(f_1709_4,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_6495),U_6496) = U_6497
    | U_6497 != hAPP(c_Int_Onumber__class_Onumber__of(U_6495),U_6496)
    | ~ class_Int_Onumber(U_6495) ),
    inference(clausify,[status(thm)],[f_1709_2]) ).

fof(f_1710_1,plain,
    ! [V_x_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
      ( hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2
      | ~ c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Oidem]) ).

fof(f_1710_2,plain,
    ! [U_6504,U_6503,U_6502,U_6501,U_6500,U_6499,U_6498] :
      ( hAPP(hAPP(U_6500,U_6504),U_6504) = U_6504
      | ~ c_Finite__Set_Ofolding__image__simple__idem(U_6498,U_6499,U_6500,U_6501,U_6502,U_6503) ),
    inference(variable_rename,[status(thm)],[f_1710_1]) ).

fof(f_1710_3,plain,
    ! [U_6504,U_6503,U_6502,U_6501,U_6500] :
      ( ! [U_6499,U_6498] : ~ c_Finite__Set_Ofolding__image__simple__idem(U_6498,U_6499,U_6500,U_6501,U_6502,U_6503)
      | hAPP(hAPP(U_6500,U_6504),U_6504) = U_6504 ),
    inference(miniscope,[status(thm)],[f_1710_2]) ).

cnf(f_1710_4,plain,
    ( ~ c_Finite__Set_Ofolding__image__simple__idem(U_6498,U_6499,U_6500,U_6501,U_6502,U_6503)
    | hAPP(hAPP(U_6500,U_6504),U_6504) = U_6504 ),
    inference(clausify,[status(thm)],[f_1710_3]) ).

fof(f_1711_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2))) ) )
      | ~ class_Rings_Olinordered__idom(T_b)
      | ~ class_Int_Onumber__ring(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_le__number__of]) ).

fof(f_1711_2,plain,
    ! [U_6507,U_6506,U_6505] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6505),hAPP(c_Int_Onumber__class_Onumber__of(U_6505),U_6506)),hAPP(c_Int_Onumber__class_Onumber__of(U_6505),U_6507)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6506),U_6507)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6506),U_6507))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6505),hAPP(c_Int_Onumber__class_Onumber__of(U_6505),U_6506)),hAPP(c_Int_Onumber__class_Onumber__of(U_6505),U_6507))) ) )
      | ~ class_Rings_Olinordered__idom(U_6505)
      | ~ class_Int_Onumber__ring(U_6505) ),
    inference(variable_rename,[status(thm)],[f_1711_1]) ).

cnf(f_1711_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6506),U_6507))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6505),hAPP(c_Int_Onumber__class_Onumber__of(U_6505),U_6506)),hAPP(c_Int_Onumber__class_Onumber__of(U_6505),U_6507)))
    | ~ class_Rings_Olinordered__idom(U_6505)
    | ~ class_Int_Onumber__ring(U_6505) ),
    inference(clausify,[status(thm)],[f_1711_2]) ).

cnf(f_1711_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6505),hAPP(c_Int_Onumber__class_Onumber__of(U_6505),U_6506)),hAPP(c_Int_Onumber__class_Onumber__of(U_6505),U_6507)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6506),U_6507))
    | ~ class_Rings_Olinordered__idom(U_6505)
    | ~ class_Int_Onumber__ring(U_6505) ),
    inference(clausify,[status(thm)],[f_1711_2]) ).

fof(f_1712_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2))) ) )
      | ~ class_Rings_Olinordered__idom(T_b)
      | ~ class_Int_Onumber__ring(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_less__number__of]) ).

fof(f_1712_2,plain,
    ! [U_6510,U_6509,U_6508] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6508),hAPP(c_Int_Onumber__class_Onumber__of(U_6508),U_6509)),hAPP(c_Int_Onumber__class_Onumber__of(U_6508),U_6510)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6509),U_6510)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6509),U_6510))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6508),hAPP(c_Int_Onumber__class_Onumber__of(U_6508),U_6509)),hAPP(c_Int_Onumber__class_Onumber__of(U_6508),U_6510))) ) )
      | ~ class_Rings_Olinordered__idom(U_6508)
      | ~ class_Int_Onumber__ring(U_6508) ),
    inference(variable_rename,[status(thm)],[f_1712_1]) ).

cnf(f_1712_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6509),U_6510))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6508),hAPP(c_Int_Onumber__class_Onumber__of(U_6508),U_6509)),hAPP(c_Int_Onumber__class_Onumber__of(U_6508),U_6510)))
    | ~ class_Rings_Olinordered__idom(U_6508)
    | ~ class_Int_Onumber__ring(U_6508) ),
    inference(clausify,[status(thm)],[f_1712_2]) ).

cnf(f_1712_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6508),hAPP(c_Int_Onumber__class_Onumber__of(U_6508),U_6509)),hAPP(c_Int_Onumber__class_Onumber__of(U_6508),U_6510)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6509),U_6510))
    | ~ class_Rings_Olinordered__idom(U_6508)
    | ~ class_Int_Onumber__ring(U_6508) ),
    inference(clausify,[status(thm)],[f_1712_2]) ).

fof(f_1713_1,plain,
    ! [V_w,V_v,T_a] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_number__of__add]) ).

fof(f_1713_2,plain,
    ! [U_6513,U_6512,U_6511] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_6511),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6512),U_6513)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6511),hAPP(c_Int_Onumber__class_Onumber__of(U_6511),U_6512)),hAPP(c_Int_Onumber__class_Onumber__of(U_6511),U_6513))
      | ~ class_Int_Onumber__ring(U_6511) ),
    inference(variable_rename,[status(thm)],[f_1713_1]) ).

cnf(f_1713_3,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_6511),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6512),U_6513)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6511),hAPP(c_Int_Onumber__class_Onumber__of(U_6511),U_6512)),hAPP(c_Int_Onumber__class_Onumber__of(U_6511),U_6513))
    | ~ class_Int_Onumber__ring(U_6511) ),
    inference(clausify,[status(thm)],[f_1713_2]) ).

fof(f_1714_1,plain,
    ! [V_w,V_v,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w))
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__number__of__eq]) ).

fof(f_1714_2,plain,
    ! [U_6516,U_6515,U_6514] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6514),hAPP(c_Int_Onumber__class_Onumber__of(U_6514),U_6515)),hAPP(c_Int_Onumber__class_Onumber__of(U_6514),U_6516)) = hAPP(c_Int_Onumber__class_Onumber__of(U_6514),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6515),U_6516))
      | ~ class_Int_Onumber__ring(U_6514) ),
    inference(variable_rename,[status(thm)],[f_1714_1]) ).

cnf(f_1714_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6514),hAPP(c_Int_Onumber__class_Onumber__of(U_6514),U_6515)),hAPP(c_Int_Onumber__class_Onumber__of(U_6514),U_6516)) = hAPP(c_Int_Onumber__class_Onumber__of(U_6514),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6515),U_6516))
    | ~ class_Int_Onumber__ring(U_6514) ),
    inference(clausify,[status(thm)],[f_1714_2]) ).

fof(f_1715_1,plain,
    ! [V_z,V_w,V_v,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w))),V_z)
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__number__of__left]) ).

fof(f_1715_2,plain,
    ! [U_6520,U_6519,U_6518,U_6517] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6517),hAPP(c_Int_Onumber__class_Onumber__of(U_6517),U_6518)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6517),hAPP(c_Int_Onumber__class_Onumber__of(U_6517),U_6519)),U_6520)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6517),hAPP(c_Int_Onumber__class_Onumber__of(U_6517),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6518),U_6519))),U_6520)
      | ~ class_Int_Onumber__ring(U_6517) ),
    inference(variable_rename,[status(thm)],[f_1715_1]) ).

cnf(f_1715_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6517),hAPP(c_Int_Onumber__class_Onumber__of(U_6517),U_6518)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6517),hAPP(c_Int_Onumber__class_Onumber__of(U_6517),U_6519)),U_6520)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6517),hAPP(c_Int_Onumber__class_Onumber__of(U_6517),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6518),U_6519))),U_6520)
    | ~ class_Int_Onumber__ring(U_6517) ),
    inference(clausify,[status(thm)],[f_1715_2]) ).

fof(f_1716_1,plain,
    ! [V_w,V_v,T_a] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_number__of__mult]) ).

fof(f_1716_2,plain,
    ! [U_6523,U_6522,U_6521] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_6521),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6522),U_6523)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6521),hAPP(c_Int_Onumber__class_Onumber__of(U_6521),U_6522)),hAPP(c_Int_Onumber__class_Onumber__of(U_6521),U_6523))
      | ~ class_Int_Onumber__ring(U_6521) ),
    inference(variable_rename,[status(thm)],[f_1716_1]) ).

cnf(f_1716_3,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_6521),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6522),U_6523)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6521),hAPP(c_Int_Onumber__class_Onumber__of(U_6521),U_6522)),hAPP(c_Int_Onumber__class_Onumber__of(U_6521),U_6523))
    | ~ class_Int_Onumber__ring(U_6521) ),
    inference(clausify,[status(thm)],[f_1716_2]) ).

fof(f_1717_1,plain,
    ! [V_w,V_v,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w))
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_arith__simps_I32_J]) ).

fof(f_1717_2,plain,
    ! [U_6526,U_6525,U_6524] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6524),hAPP(c_Int_Onumber__class_Onumber__of(U_6524),U_6525)),hAPP(c_Int_Onumber__class_Onumber__of(U_6524),U_6526)) = hAPP(c_Int_Onumber__class_Onumber__of(U_6524),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6525),U_6526))
      | ~ class_Int_Onumber__ring(U_6524) ),
    inference(variable_rename,[status(thm)],[f_1717_1]) ).

cnf(f_1717_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6524),hAPP(c_Int_Onumber__class_Onumber__of(U_6524),U_6525)),hAPP(c_Int_Onumber__class_Onumber__of(U_6524),U_6526)) = hAPP(c_Int_Onumber__class_Onumber__of(U_6524),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6525),U_6526))
    | ~ class_Int_Onumber__ring(U_6524) ),
    inference(clausify,[status(thm)],[f_1717_2]) ).

fof(f_1718_1,plain,
    ! [V_z,V_w,V_v,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)),V_z)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w))),V_z)
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__number__of__left]) ).

fof(f_1718_2,plain,
    ! [U_6530,U_6529,U_6528,U_6527] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6527),hAPP(c_Int_Onumber__class_Onumber__of(U_6527),U_6528)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6527),hAPP(c_Int_Onumber__class_Onumber__of(U_6527),U_6529)),U_6530)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6527),hAPP(c_Int_Onumber__class_Onumber__of(U_6527),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6528),U_6529))),U_6530)
      | ~ class_Int_Onumber__ring(U_6527) ),
    inference(variable_rename,[status(thm)],[f_1718_1]) ).

cnf(f_1718_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6527),hAPP(c_Int_Onumber__class_Onumber__of(U_6527),U_6528)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6527),hAPP(c_Int_Onumber__class_Onumber__of(U_6527),U_6529)),U_6530)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6527),hAPP(c_Int_Onumber__class_Onumber__of(U_6527),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6528),U_6529))),U_6530)
    | ~ class_Int_Onumber__ring(U_6527) ),
    inference(clausify,[status(thm)],[f_1718_2]) ).

fof(f_1719_1,plain,
    ! [V_w,V_v,T_a] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)))
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_diff__number__of__eq]) ).

fof(f_1719_2,plain,
    ! [U_6533,U_6532,U_6531] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6531),hAPP(c_Int_Onumber__class_Onumber__of(U_6531),U_6532)),hAPP(c_Int_Onumber__class_Onumber__of(U_6531),U_6533)) = hAPP(c_Int_Onumber__class_Onumber__of(U_6531),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6532),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6533)))
      | ~ class_Int_Onumber__ring(U_6531) ),
    inference(variable_rename,[status(thm)],[f_1719_1]) ).

cnf(f_1719_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6531),hAPP(c_Int_Onumber__class_Onumber__of(U_6531),U_6532)),hAPP(c_Int_Onumber__class_Onumber__of(U_6531),U_6533)) = hAPP(c_Int_Onumber__class_Onumber__of(U_6531),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6532),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6533)))
    | ~ class_Int_Onumber__ring(U_6531) ),
    inference(clausify,[status(thm)],[f_1719_2]) ).

fof(f_1720_1,plain,
    ! [V_w,V_v,T_a] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_v),V_w)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_number__of__diff]) ).

fof(f_1720_2,plain,
    ! [U_6536,U_6535,U_6534] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_6534),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6535),U_6536)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6534),hAPP(c_Int_Onumber__class_Onumber__of(U_6534),U_6535)),hAPP(c_Int_Onumber__class_Onumber__of(U_6534),U_6536))
      | ~ class_Int_Onumber__ring(U_6534) ),
    inference(variable_rename,[status(thm)],[f_1720_1]) ).

cnf(f_1720_3,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_6534),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6535),U_6536)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6534),hAPP(c_Int_Onumber__class_Onumber__of(U_6534),U_6535)),hAPP(c_Int_Onumber__class_Onumber__of(U_6534),U_6536))
    | ~ class_Int_Onumber__ring(U_6534) ),
    inference(clausify,[status(thm)],[f_1720_2]) ).

fof(f_1721_1,plain,
    ! [V_w,T_a] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_number__of__minus]) ).

fof(f_1721_2,plain,
    ! [U_6538,U_6537] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_6537),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6538)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_6537),hAPP(c_Int_Onumber__class_Onumber__of(U_6537),U_6538))
      | ~ class_Int_Onumber__ring(U_6537) ),
    inference(variable_rename,[status(thm)],[f_1721_1]) ).

cnf(f_1721_3,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_6537),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6538)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_6537),hAPP(c_Int_Onumber__class_Onumber__of(U_6537),U_6538))
    | ~ class_Int_Onumber__ring(U_6537) ),
    inference(clausify,[status(thm)],[f_1721_2]) ).

fof(f_1722_1,plain,
    ! [V_w,T_a] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w))
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_arith__simps_I30_J]) ).

fof(f_1722_2,plain,
    ! [U_6540,U_6539] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_6539),hAPP(c_Int_Onumber__class_Onumber__of(U_6539),U_6540)) = hAPP(c_Int_Onumber__class_Onumber__of(U_6539),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6540))
      | ~ class_Int_Onumber__ring(U_6539) ),
    inference(variable_rename,[status(thm)],[f_1722_1]) ).

cnf(f_1722_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_6539),hAPP(c_Int_Onumber__class_Onumber__of(U_6539),U_6540)) = hAPP(c_Int_Onumber__class_Onumber__of(U_6539),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6540))
    | ~ class_Int_Onumber__ring(U_6539) ),
    inference(clausify,[status(thm)],[f_1722_2]) ).

fof(f_1723_1,plain,
    ! [V_w_2,V_v_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2))) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) ) )
      | ~ class_Orderings_Olinorder(T_b)
      | ~ class_Int_Onumber(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_le__number__of__eq__not__less]) ).

fof(f_1723_2,plain,
    ! [U_6543,U_6542,U_6541] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6541),hAPP(c_Int_Onumber__class_Onumber__of(U_6541),U_6542)),hAPP(c_Int_Onumber__class_Onumber__of(U_6541),U_6543)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6541),hAPP(c_Int_Onumber__class_Onumber__of(U_6541),U_6543)),hAPP(c_Int_Onumber__class_Onumber__of(U_6541),U_6542))) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6541),hAPP(c_Int_Onumber__class_Onumber__of(U_6541),U_6543)),hAPP(c_Int_Onumber__class_Onumber__of(U_6541),U_6542)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6541),hAPP(c_Int_Onumber__class_Onumber__of(U_6541),U_6542)),hAPP(c_Int_Onumber__class_Onumber__of(U_6541),U_6543))) ) )
      | ~ class_Orderings_Olinorder(U_6541)
      | ~ class_Int_Onumber(U_6541) ),
    inference(variable_rename,[status(thm)],[f_1723_1]) ).

cnf(f_1723_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6541),hAPP(c_Int_Onumber__class_Onumber__of(U_6541),U_6543)),hAPP(c_Int_Onumber__class_Onumber__of(U_6541),U_6542)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6541),hAPP(c_Int_Onumber__class_Onumber__of(U_6541),U_6542)),hAPP(c_Int_Onumber__class_Onumber__of(U_6541),U_6543)))
    | ~ class_Orderings_Olinorder(U_6541)
    | ~ class_Int_Onumber(U_6541) ),
    inference(clausify,[status(thm)],[f_1723_2]) ).

cnf(f_1723_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6541),hAPP(c_Int_Onumber__class_Onumber__of(U_6541),U_6542)),hAPP(c_Int_Onumber__class_Onumber__of(U_6541),U_6543)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6541),hAPP(c_Int_Onumber__class_Onumber__of(U_6541),U_6543)),hAPP(c_Int_Onumber__class_Onumber__of(U_6541),U_6542)))
    | ~ class_Orderings_Olinorder(U_6541)
    | ~ class_Int_Onumber(U_6541) ),
    inference(clausify,[status(thm)],[f_1723_2]) ).

fof(f_1724_1,plain,
    ! [V_c,V_b,V_v,T_b] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b),V_c)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),V_c))
      | ~ class_Rings_Osemiring(T_b)
      | ~ class_Int_Onumber(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_right__distrib__number__of]) ).

fof(f_1724_2,plain,
    ! [U_6547,U_6546,U_6545,U_6544] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6544),hAPP(c_Int_Onumber__class_Onumber__of(U_6544),U_6545)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6544),U_6546),U_6547)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6544),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6544),hAPP(c_Int_Onumber__class_Onumber__of(U_6544),U_6545)),U_6546)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6544),hAPP(c_Int_Onumber__class_Onumber__of(U_6544),U_6545)),U_6547))
      | ~ class_Rings_Osemiring(U_6544)
      | ~ class_Int_Onumber(U_6544) ),
    inference(variable_rename,[status(thm)],[f_1724_1]) ).

cnf(f_1724_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6544),hAPP(c_Int_Onumber__class_Onumber__of(U_6544),U_6545)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6544),U_6546),U_6547)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6544),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6544),hAPP(c_Int_Onumber__class_Onumber__of(U_6544),U_6545)),U_6546)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6544),hAPP(c_Int_Onumber__class_Onumber__of(U_6544),U_6545)),U_6547))
    | ~ class_Rings_Osemiring(U_6544)
    | ~ class_Int_Onumber(U_6544) ),
    inference(clausify,[status(thm)],[f_1724_2]) ).

fof(f_1725_1,plain,
    ! [V_v,V_b,V_a,T_b] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a),V_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)))
      | ~ class_Rings_Osemiring(T_b)
      | ~ class_Int_Onumber(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_left__distrib__number__of]) ).

fof(f_1725_2,plain,
    ! [U_6551,U_6550,U_6549,U_6548] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6548),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6548),U_6549),U_6550)),hAPP(c_Int_Onumber__class_Onumber__of(U_6548),U_6551)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6548),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6548),U_6549),hAPP(c_Int_Onumber__class_Onumber__of(U_6548),U_6551))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6548),U_6550),hAPP(c_Int_Onumber__class_Onumber__of(U_6548),U_6551)))
      | ~ class_Rings_Osemiring(U_6548)
      | ~ class_Int_Onumber(U_6548) ),
    inference(variable_rename,[status(thm)],[f_1725_1]) ).

cnf(f_1725_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6548),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6548),U_6549),U_6550)),hAPP(c_Int_Onumber__class_Onumber__of(U_6548),U_6551)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6548),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6548),U_6549),hAPP(c_Int_Onumber__class_Onumber__of(U_6548),U_6551))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6548),U_6550),hAPP(c_Int_Onumber__class_Onumber__of(U_6548),U_6551)))
    | ~ class_Rings_Osemiring(U_6548)
    | ~ class_Int_Onumber(U_6548) ),
    inference(clausify,[status(thm)],[f_1725_2]) ).

fof(f_1726_1,plain,
    ! [V_w,V_c,V_v,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_c),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)))),V_c)
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__number__of__diff2]) ).

fof(f_1726_2,plain,
    ! [U_6555,U_6554,U_6553,U_6552] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6552),hAPP(c_Int_Onumber__class_Onumber__of(U_6552),U_6553)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6552),U_6554),hAPP(c_Int_Onumber__class_Onumber__of(U_6552),U_6555))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6552),hAPP(c_Int_Onumber__class_Onumber__of(U_6552),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6553),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6555)))),U_6554)
      | ~ class_Int_Onumber__ring(U_6552) ),
    inference(variable_rename,[status(thm)],[f_1726_1]) ).

cnf(f_1726_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6552),hAPP(c_Int_Onumber__class_Onumber__of(U_6552),U_6553)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6552),U_6554),hAPP(c_Int_Onumber__class_Onumber__of(U_6552),U_6555))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6552),hAPP(c_Int_Onumber__class_Onumber__of(U_6552),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6553),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6555)))),U_6554)
    | ~ class_Int_Onumber__ring(U_6552) ),
    inference(clausify,[status(thm)],[f_1726_2]) ).

fof(f_1727_1,plain,
    ! [V_c,V_w,V_v,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)),V_c)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w))),V_c)
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__number__of__diff1]) ).

fof(f_1727_2,plain,
    ! [U_6559,U_6558,U_6557,U_6556] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6556),hAPP(c_Int_Onumber__class_Onumber__of(U_6556),U_6557)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6556),hAPP(c_Int_Onumber__class_Onumber__of(U_6556),U_6558)),U_6559)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6556),hAPP(c_Int_Onumber__class_Onumber__of(U_6556),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6557),U_6558))),U_6559)
      | ~ class_Int_Onumber__ring(U_6556) ),
    inference(variable_rename,[status(thm)],[f_1727_1]) ).

cnf(f_1727_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6556),hAPP(c_Int_Onumber__class_Onumber__of(U_6556),U_6557)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6556),hAPP(c_Int_Onumber__class_Onumber__of(U_6556),U_6558)),U_6559)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6556),hAPP(c_Int_Onumber__class_Onumber__of(U_6556),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6557),U_6558))),U_6559)
    | ~ class_Int_Onumber__ring(U_6556) ),
    inference(clausify,[status(thm)],[f_1727_2]) ).

fof(f_1728_1,plain,
    ! [V_c,V_b,V_v,T_b] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b),V_c)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)),V_c))
      | ~ class_Rings_Oring(T_b)
      | ~ class_Int_Onumber(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_right__diff__distrib__number__of]) ).

fof(f_1728_2,plain,
    ! [U_6563,U_6562,U_6561,U_6560] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6560),hAPP(c_Int_Onumber__class_Onumber__of(U_6560),U_6561)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6560),U_6562),U_6563)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6560),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6560),hAPP(c_Int_Onumber__class_Onumber__of(U_6560),U_6561)),U_6562)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6560),hAPP(c_Int_Onumber__class_Onumber__of(U_6560),U_6561)),U_6563))
      | ~ class_Rings_Oring(U_6560)
      | ~ class_Int_Onumber(U_6560) ),
    inference(variable_rename,[status(thm)],[f_1728_1]) ).

cnf(f_1728_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6560),hAPP(c_Int_Onumber__class_Onumber__of(U_6560),U_6561)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6560),U_6562),U_6563)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6560),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6560),hAPP(c_Int_Onumber__class_Onumber__of(U_6560),U_6561)),U_6562)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6560),hAPP(c_Int_Onumber__class_Onumber__of(U_6560),U_6561)),U_6563))
    | ~ class_Rings_Oring(U_6560)
    | ~ class_Int_Onumber(U_6560) ),
    inference(clausify,[status(thm)],[f_1728_2]) ).

fof(f_1729_1,plain,
    ! [V_v,V_b,V_a,T_b] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a),V_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)))
      | ~ class_Rings_Oring(T_b)
      | ~ class_Int_Onumber(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_left__diff__distrib__number__of]) ).

fof(f_1729_2,plain,
    ! [U_6567,U_6566,U_6565,U_6564] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6564),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6564),U_6565),U_6566)),hAPP(c_Int_Onumber__class_Onumber__of(U_6564),U_6567)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6564),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6564),U_6565),hAPP(c_Int_Onumber__class_Onumber__of(U_6564),U_6567))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6564),U_6566),hAPP(c_Int_Onumber__class_Onumber__of(U_6564),U_6567)))
      | ~ class_Rings_Oring(U_6564)
      | ~ class_Int_Onumber(U_6564) ),
    inference(variable_rename,[status(thm)],[f_1729_1]) ).

cnf(f_1729_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6564),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6564),U_6565),U_6566)),hAPP(c_Int_Onumber__class_Onumber__of(U_6564),U_6567)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6564),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6564),U_6565),hAPP(c_Int_Onumber__class_Onumber__of(U_6564),U_6567))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6564),U_6566),hAPP(c_Int_Onumber__class_Onumber__of(U_6564),U_6567)))
    | ~ class_Rings_Oring(U_6564)
    | ~ class_Int_Onumber(U_6564) ),
    inference(clausify,[status(thm)],[f_1729_2]) ).

fof(f_1730_1,plain,
    ! [V_z,V_w,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))),V_z) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w))),V_z)
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_minus__number__of__mult]) ).

fof(f_1730_2,plain,
    ! [U_6570,U_6569,U_6568] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6568),hAPP(c_Groups_Ouminus__class_Ouminus(U_6568),hAPP(c_Int_Onumber__class_Onumber__of(U_6568),U_6569))),U_6570) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6568),hAPP(c_Int_Onumber__class_Onumber__of(U_6568),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6569))),U_6570)
      | ~ class_Int_Onumber__ring(U_6568) ),
    inference(variable_rename,[status(thm)],[f_1730_1]) ).

cnf(f_1730_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6568),hAPP(c_Groups_Ouminus__class_Ouminus(U_6568),hAPP(c_Int_Onumber__class_Onumber__of(U_6568),U_6569))),U_6570) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6568),hAPP(c_Int_Onumber__class_Onumber__of(U_6568),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6569))),U_6570)
    | ~ class_Int_Onumber__ring(U_6568) ),
    inference(clausify,[status(thm)],[f_1730_2]) ).

fof(f_1731_1,plain,
    ! [V_v,V_u,T_b] :
      ( ( ( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))) )
        & ( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))) ) )
      | ~ class_Orderings_Oord(T_b)
      | ~ class_Int_Onumber(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__number__of]) ).

fof(f_1731_2,plain,
    ! [U_6573,U_6572,U_6571] :
      ( ( ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6571),hAPP(c_Int_Onumber__class_Onumber__of(U_6571),U_6572)),hAPP(c_Int_Onumber__class_Onumber__of(U_6571),U_6573)) = hAPP(c_Int_Onumber__class_Onumber__of(U_6571),U_6573)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6571),hAPP(c_Int_Onumber__class_Onumber__of(U_6571),U_6572)),hAPP(c_Int_Onumber__class_Onumber__of(U_6571),U_6573))) )
        & ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6571),hAPP(c_Int_Onumber__class_Onumber__of(U_6571),U_6572)),hAPP(c_Int_Onumber__class_Onumber__of(U_6571),U_6573)) = hAPP(c_Int_Onumber__class_Onumber__of(U_6571),U_6572)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6571),hAPP(c_Int_Onumber__class_Onumber__of(U_6571),U_6572)),hAPP(c_Int_Onumber__class_Onumber__of(U_6571),U_6573))) ) )
      | ~ class_Orderings_Oord(U_6571)
      | ~ class_Int_Onumber(U_6571) ),
    inference(variable_rename,[status(thm)],[f_1731_1]) ).

cnf(f_1731_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6571),hAPP(c_Int_Onumber__class_Onumber__of(U_6571),U_6572)),hAPP(c_Int_Onumber__class_Onumber__of(U_6571),U_6573)) = hAPP(c_Int_Onumber__class_Onumber__of(U_6571),U_6572)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6571),hAPP(c_Int_Onumber__class_Onumber__of(U_6571),U_6572)),hAPP(c_Int_Onumber__class_Onumber__of(U_6571),U_6573)))
    | ~ class_Orderings_Oord(U_6571)
    | ~ class_Int_Onumber(U_6571) ),
    inference(clausify,[status(thm)],[f_1731_2]) ).

cnf(f_1731_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6571),hAPP(c_Int_Onumber__class_Onumber__of(U_6571),U_6572)),hAPP(c_Int_Onumber__class_Onumber__of(U_6571),U_6573)) = hAPP(c_Int_Onumber__class_Onumber__of(U_6571),U_6573)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6571),hAPP(c_Int_Onumber__class_Onumber__of(U_6571),U_6572)),hAPP(c_Int_Onumber__class_Onumber__of(U_6571),U_6573)))
    | ~ class_Orderings_Oord(U_6571)
    | ~ class_Int_Onumber(U_6571) ),
    inference(clausify,[status(thm)],[f_1731_2]) ).

fof(f_1732_1,plain,
    ! [V_v,V_u,T_b] :
      ( ( ( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))) )
        & ( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v))) ) )
      | ~ class_Orderings_Oord(T_b)
      | ~ class_Int_Onumber(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_max__number__of]) ).

fof(f_1732_2,plain,
    ! [U_6576,U_6575,U_6574] :
      ( ( ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6574),hAPP(c_Int_Onumber__class_Onumber__of(U_6574),U_6575)),hAPP(c_Int_Onumber__class_Onumber__of(U_6574),U_6576)) = hAPP(c_Int_Onumber__class_Onumber__of(U_6574),U_6575)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6574),hAPP(c_Int_Onumber__class_Onumber__of(U_6574),U_6575)),hAPP(c_Int_Onumber__class_Onumber__of(U_6574),U_6576))) )
        & ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6574),hAPP(c_Int_Onumber__class_Onumber__of(U_6574),U_6575)),hAPP(c_Int_Onumber__class_Onumber__of(U_6574),U_6576)) = hAPP(c_Int_Onumber__class_Onumber__of(U_6574),U_6576)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6574),hAPP(c_Int_Onumber__class_Onumber__of(U_6574),U_6575)),hAPP(c_Int_Onumber__class_Onumber__of(U_6574),U_6576))) ) )
      | ~ class_Orderings_Oord(U_6574)
      | ~ class_Int_Onumber(U_6574) ),
    inference(variable_rename,[status(thm)],[f_1732_1]) ).

cnf(f_1732_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6574),hAPP(c_Int_Onumber__class_Onumber__of(U_6574),U_6575)),hAPP(c_Int_Onumber__class_Onumber__of(U_6574),U_6576)) = hAPP(c_Int_Onumber__class_Onumber__of(U_6574),U_6576)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6574),hAPP(c_Int_Onumber__class_Onumber__of(U_6574),U_6575)),hAPP(c_Int_Onumber__class_Onumber__of(U_6574),U_6576)))
    | ~ class_Orderings_Oord(U_6574)
    | ~ class_Int_Onumber(U_6574) ),
    inference(clausify,[status(thm)],[f_1732_2]) ).

cnf(f_1732_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6574),hAPP(c_Int_Onumber__class_Onumber__of(U_6574),U_6575)),hAPP(c_Int_Onumber__class_Onumber__of(U_6574),U_6576)) = hAPP(c_Int_Onumber__class_Onumber__of(U_6574),U_6575)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6574),hAPP(c_Int_Onumber__class_Onumber__of(U_6574),U_6575)),hAPP(c_Int_Onumber__class_Onumber__of(U_6574),U_6576)))
    | ~ class_Orderings_Oord(U_6574)
    | ~ class_Int_Onumber(U_6574) ),
    inference(clausify,[status(thm)],[f_1732_2]) ).

fof(f_1733_1,plain,
    ! [V_w_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Int_Oring__1__class_OInts(T_b)))
      | ~ class_Int_Onumber__ring(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Ints__number__of]) ).

fof(f_1733_2,plain,
    ! [U_6578,U_6577] :
      ( hBOOL(hAPP(hAPP(c_member(U_6577),hAPP(c_Int_Onumber__class_Onumber__of(U_6577),U_6578)),c_Int_Oring__1__class_OInts(U_6577)))
      | ~ class_Int_Onumber__ring(U_6577) ),
    inference(variable_rename,[status(thm)],[f_1733_1]) ).

cnf(f_1733_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_6577),hAPP(c_Int_Onumber__class_Onumber__of(U_6577),U_6578)),c_Int_Oring__1__class_OInts(U_6577)))
    | ~ class_Int_Onumber__ring(U_6577) ),
    inference(clausify,[status(thm)],[f_1733_2]) ).

fof(f_1734_1,plain,
    ! [V_w_2,V_b_2,V_a_2,T_b] :
      ( ( ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))
          | ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b)
            & hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) )
          | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) != V_b_2
            & hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b) ) )
        & ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
              | hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b) )
            & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) = V_b_2
              | hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) ) )
          | V_a_2 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) ) )
      | ~ class_Int_Onumber(T_b)
      | ~ class_Fields_Ofield__inverse__zero(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_eq__divide__eq__number__of1]) ).

fof(f_1734_2,plain,
    ! [U_6582,U_6581,U_6580,U_6579] :
      ( ( ( U_6580 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6579),U_6581),hAPP(c_Int_Onumber__class_Onumber__of(U_6579),U_6582))
          | ( U_6580 != c_Groups_Ozero__class_Ozero(U_6579)
            & hAPP(c_Int_Onumber__class_Onumber__of(U_6579),U_6582) = c_Groups_Ozero__class_Ozero(U_6579) )
          | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6579),U_6580),hAPP(c_Int_Onumber__class_Onumber__of(U_6579),U_6582)) != U_6581
            & hAPP(c_Int_Onumber__class_Onumber__of(U_6579),U_6582) != c_Groups_Ozero__class_Ozero(U_6579) ) )
        & ( ( ( U_6580 = c_Groups_Ozero__class_Ozero(U_6579)
              | hAPP(c_Int_Onumber__class_Onumber__of(U_6579),U_6582) != c_Groups_Ozero__class_Ozero(U_6579) )
            & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6579),U_6580),hAPP(c_Int_Onumber__class_Onumber__of(U_6579),U_6582)) = U_6581
              | hAPP(c_Int_Onumber__class_Onumber__of(U_6579),U_6582) = c_Groups_Ozero__class_Ozero(U_6579) ) )
          | U_6580 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6579),U_6581),hAPP(c_Int_Onumber__class_Onumber__of(U_6579),U_6582)) ) )
      | ~ class_Int_Onumber(U_6579)
      | ~ class_Fields_Ofield__inverse__zero(U_6579) ),
    inference(variable_rename,[status(thm)],[f_1734_1]) ).

cnf(f_1734_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6579),U_6580),hAPP(c_Int_Onumber__class_Onumber__of(U_6579),U_6582)) = U_6581
    | hAPP(c_Int_Onumber__class_Onumber__of(U_6579),U_6582) = c_Groups_Ozero__class_Ozero(U_6579)
    | U_6580 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6579),U_6581),hAPP(c_Int_Onumber__class_Onumber__of(U_6579),U_6582))
    | ~ class_Int_Onumber(U_6579)
    | ~ class_Fields_Ofield__inverse__zero(U_6579) ),
    inference(clausify,[status(thm)],[f_1734_2]) ).

cnf(f_1734_4,plain,
    ( U_6580 = c_Groups_Ozero__class_Ozero(U_6579)
    | hAPP(c_Int_Onumber__class_Onumber__of(U_6579),U_6582) != c_Groups_Ozero__class_Ozero(U_6579)
    | U_6580 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6579),U_6581),hAPP(c_Int_Onumber__class_Onumber__of(U_6579),U_6582))
    | ~ class_Int_Onumber(U_6579)
    | ~ class_Fields_Ofield__inverse__zero(U_6579) ),
    inference(clausify,[status(thm)],[f_1734_2]) ).

cnf(f_1734_5,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_6579),U_6582) = c_Groups_Ozero__class_Ozero(U_6579)
    | hAPP(c_Int_Onumber__class_Onumber__of(U_6579),U_6582) != c_Groups_Ozero__class_Ozero(U_6579)
    | U_6580 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6579),U_6581),hAPP(c_Int_Onumber__class_Onumber__of(U_6579),U_6582))
    | ~ class_Int_Onumber(U_6579)
    | ~ class_Fields_Ofield__inverse__zero(U_6579) ),
    inference(clausify,[status(thm)],[f_1734_2]) ).

cnf(f_1734_6,plain,
    ( U_6580 != c_Groups_Ozero__class_Ozero(U_6579)
    | hAPP(c_Int_Onumber__class_Onumber__of(U_6579),U_6582) != c_Groups_Ozero__class_Ozero(U_6579)
    | U_6580 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6579),U_6581),hAPP(c_Int_Onumber__class_Onumber__of(U_6579),U_6582))
    | ~ class_Int_Onumber(U_6579)
    | ~ class_Fields_Ofield__inverse__zero(U_6579) ),
    inference(clausify,[status(thm)],[f_1734_2]) ).

cnf(f_1734_7,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_6579),U_6582) = c_Groups_Ozero__class_Ozero(U_6579)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6579),U_6580),hAPP(c_Int_Onumber__class_Onumber__of(U_6579),U_6582)) != U_6581
    | U_6580 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6579),U_6581),hAPP(c_Int_Onumber__class_Onumber__of(U_6579),U_6582))
    | ~ class_Int_Onumber(U_6579)
    | ~ class_Fields_Ofield__inverse__zero(U_6579) ),
    inference(clausify,[status(thm)],[f_1734_2]) ).

cnf(f_1734_8,plain,
    ( U_6580 != c_Groups_Ozero__class_Ozero(U_6579)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6579),U_6580),hAPP(c_Int_Onumber__class_Onumber__of(U_6579),U_6582)) != U_6581
    | U_6580 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6579),U_6581),hAPP(c_Int_Onumber__class_Onumber__of(U_6579),U_6582))
    | ~ class_Int_Onumber(U_6579)
    | ~ class_Fields_Ofield__inverse__zero(U_6579) ),
    inference(clausify,[status(thm)],[f_1734_2]) ).

fof(f_1735_1,plain,
    ! [V_c_2,V_b_2,V_w_2,T_b] :
      ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)
          | ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b)
            & V_c_2 = c_Groups_Ozero__class_Ozero(T_b) )
          | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2) != V_b_2
            & V_c_2 != c_Groups_Ozero__class_Ozero(T_b) ) )
        & ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b)
              | V_c_2 != c_Groups_Ozero__class_Ozero(T_b) )
            & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2) = V_b_2
              | V_c_2 = c_Groups_Ozero__class_Ozero(T_b) ) )
          | hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) ) )
      | ~ class_Int_Onumber(T_b)
      | ~ class_Fields_Ofield__inverse__zero(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_eq__divide__eq__number__of]) ).

fof(f_1735_2,plain,
    ! [U_6586,U_6585,U_6584,U_6583] :
      ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_6583),U_6584) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6583),U_6585),U_6586)
          | ( hAPP(c_Int_Onumber__class_Onumber__of(U_6583),U_6584) != c_Groups_Ozero__class_Ozero(U_6583)
            & U_6586 = c_Groups_Ozero__class_Ozero(U_6583) )
          | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6583),hAPP(c_Int_Onumber__class_Onumber__of(U_6583),U_6584)),U_6586) != U_6585
            & U_6586 != c_Groups_Ozero__class_Ozero(U_6583) ) )
        & ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_6583),U_6584) = c_Groups_Ozero__class_Ozero(U_6583)
              | U_6586 != c_Groups_Ozero__class_Ozero(U_6583) )
            & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6583),hAPP(c_Int_Onumber__class_Onumber__of(U_6583),U_6584)),U_6586) = U_6585
              | U_6586 = c_Groups_Ozero__class_Ozero(U_6583) ) )
          | hAPP(c_Int_Onumber__class_Onumber__of(U_6583),U_6584) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6583),U_6585),U_6586) ) )
      | ~ class_Int_Onumber(U_6583)
      | ~ class_Fields_Ofield__inverse__zero(U_6583) ),
    inference(variable_rename,[status(thm)],[f_1735_1]) ).

cnf(f_1735_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6583),hAPP(c_Int_Onumber__class_Onumber__of(U_6583),U_6584)),U_6586) = U_6585
    | U_6586 = c_Groups_Ozero__class_Ozero(U_6583)
    | hAPP(c_Int_Onumber__class_Onumber__of(U_6583),U_6584) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6583),U_6585),U_6586)
    | ~ class_Int_Onumber(U_6583)
    | ~ class_Fields_Ofield__inverse__zero(U_6583) ),
    inference(clausify,[status(thm)],[f_1735_2]) ).

cnf(f_1735_4,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_6583),U_6584) = c_Groups_Ozero__class_Ozero(U_6583)
    | U_6586 != c_Groups_Ozero__class_Ozero(U_6583)
    | hAPP(c_Int_Onumber__class_Onumber__of(U_6583),U_6584) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6583),U_6585),U_6586)
    | ~ class_Int_Onumber(U_6583)
    | ~ class_Fields_Ofield__inverse__zero(U_6583) ),
    inference(clausify,[status(thm)],[f_1735_2]) ).

cnf(f_1735_5,plain,
    ( U_6586 = c_Groups_Ozero__class_Ozero(U_6583)
    | U_6586 != c_Groups_Ozero__class_Ozero(U_6583)
    | hAPP(c_Int_Onumber__class_Onumber__of(U_6583),U_6584) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6583),U_6585),U_6586)
    | ~ class_Int_Onumber(U_6583)
    | ~ class_Fields_Ofield__inverse__zero(U_6583) ),
    inference(clausify,[status(thm)],[f_1735_2]) ).

cnf(f_1735_6,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_6583),U_6584) != c_Groups_Ozero__class_Ozero(U_6583)
    | U_6586 != c_Groups_Ozero__class_Ozero(U_6583)
    | hAPP(c_Int_Onumber__class_Onumber__of(U_6583),U_6584) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6583),U_6585),U_6586)
    | ~ class_Int_Onumber(U_6583)
    | ~ class_Fields_Ofield__inverse__zero(U_6583) ),
    inference(clausify,[status(thm)],[f_1735_2]) ).

cnf(f_1735_7,plain,
    ( U_6586 = c_Groups_Ozero__class_Ozero(U_6583)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6583),hAPP(c_Int_Onumber__class_Onumber__of(U_6583),U_6584)),U_6586) != U_6585
    | hAPP(c_Int_Onumber__class_Onumber__of(U_6583),U_6584) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6583),U_6585),U_6586)
    | ~ class_Int_Onumber(U_6583)
    | ~ class_Fields_Ofield__inverse__zero(U_6583) ),
    inference(clausify,[status(thm)],[f_1735_2]) ).

cnf(f_1735_8,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_6583),U_6584) != c_Groups_Ozero__class_Ozero(U_6583)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6583),hAPP(c_Int_Onumber__class_Onumber__of(U_6583),U_6584)),U_6586) != U_6585
    | hAPP(c_Int_Onumber__class_Onumber__of(U_6583),U_6584) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6583),U_6585),U_6586)
    | ~ class_Int_Onumber(U_6583)
    | ~ class_Fields_Ofield__inverse__zero(U_6583) ),
    inference(clausify,[status(thm)],[f_1735_2]) ).

fof(f_1736_1,plain,
    ! [V_w_2,V_c_2,V_b_2,T_b] :
      ( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)
          | ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b)
            & V_c_2 = c_Groups_Ozero__class_Ozero(T_b) )
          | ( V_b_2 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)
            & V_c_2 != c_Groups_Ozero__class_Ozero(T_b) ) )
        & ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b)
              | V_c_2 != c_Groups_Ozero__class_Ozero(T_b) )
            & ( V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)
              | V_c_2 = c_Groups_Ozero__class_Ozero(T_b) ) )
          | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) != hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) ) )
      | ~ class_Int_Onumber(T_b)
      | ~ class_Fields_Ofield__inverse__zero(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_divide__eq__eq__number__of]) ).

fof(f_1736_2,plain,
    ! [U_6590,U_6589,U_6588,U_6587] :
      ( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6587),U_6588),U_6589) = hAPP(c_Int_Onumber__class_Onumber__of(U_6587),U_6590)
          | ( hAPP(c_Int_Onumber__class_Onumber__of(U_6587),U_6590) != c_Groups_Ozero__class_Ozero(U_6587)
            & U_6589 = c_Groups_Ozero__class_Ozero(U_6587) )
          | ( U_6588 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6587),hAPP(c_Int_Onumber__class_Onumber__of(U_6587),U_6590)),U_6589)
            & U_6589 != c_Groups_Ozero__class_Ozero(U_6587) ) )
        & ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_6587),U_6590) = c_Groups_Ozero__class_Ozero(U_6587)
              | U_6589 != c_Groups_Ozero__class_Ozero(U_6587) )
            & ( U_6588 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6587),hAPP(c_Int_Onumber__class_Onumber__of(U_6587),U_6590)),U_6589)
              | U_6589 = c_Groups_Ozero__class_Ozero(U_6587) ) )
          | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6587),U_6588),U_6589) != hAPP(c_Int_Onumber__class_Onumber__of(U_6587),U_6590) ) )
      | ~ class_Int_Onumber(U_6587)
      | ~ class_Fields_Ofield__inverse__zero(U_6587) ),
    inference(variable_rename,[status(thm)],[f_1736_1]) ).

cnf(f_1736_3,plain,
    ( U_6588 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6587),hAPP(c_Int_Onumber__class_Onumber__of(U_6587),U_6590)),U_6589)
    | U_6589 = c_Groups_Ozero__class_Ozero(U_6587)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6587),U_6588),U_6589) != hAPP(c_Int_Onumber__class_Onumber__of(U_6587),U_6590)
    | ~ class_Int_Onumber(U_6587)
    | ~ class_Fields_Ofield__inverse__zero(U_6587) ),
    inference(clausify,[status(thm)],[f_1736_2]) ).

cnf(f_1736_4,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_6587),U_6590) = c_Groups_Ozero__class_Ozero(U_6587)
    | U_6589 != c_Groups_Ozero__class_Ozero(U_6587)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6587),U_6588),U_6589) != hAPP(c_Int_Onumber__class_Onumber__of(U_6587),U_6590)
    | ~ class_Int_Onumber(U_6587)
    | ~ class_Fields_Ofield__inverse__zero(U_6587) ),
    inference(clausify,[status(thm)],[f_1736_2]) ).

cnf(f_1736_5,plain,
    ( U_6589 = c_Groups_Ozero__class_Ozero(U_6587)
    | U_6589 != c_Groups_Ozero__class_Ozero(U_6587)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6587),U_6588),U_6589) = hAPP(c_Int_Onumber__class_Onumber__of(U_6587),U_6590)
    | ~ class_Int_Onumber(U_6587)
    | ~ class_Fields_Ofield__inverse__zero(U_6587) ),
    inference(clausify,[status(thm)],[f_1736_2]) ).

cnf(f_1736_6,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_6587),U_6590) != c_Groups_Ozero__class_Ozero(U_6587)
    | U_6589 != c_Groups_Ozero__class_Ozero(U_6587)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6587),U_6588),U_6589) = hAPP(c_Int_Onumber__class_Onumber__of(U_6587),U_6590)
    | ~ class_Int_Onumber(U_6587)
    | ~ class_Fields_Ofield__inverse__zero(U_6587) ),
    inference(clausify,[status(thm)],[f_1736_2]) ).

cnf(f_1736_7,plain,
    ( U_6589 = c_Groups_Ozero__class_Ozero(U_6587)
    | U_6588 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6587),hAPP(c_Int_Onumber__class_Onumber__of(U_6587),U_6590)),U_6589)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6587),U_6588),U_6589) = hAPP(c_Int_Onumber__class_Onumber__of(U_6587),U_6590)
    | ~ class_Int_Onumber(U_6587)
    | ~ class_Fields_Ofield__inverse__zero(U_6587) ),
    inference(clausify,[status(thm)],[f_1736_2]) ).

cnf(f_1736_8,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_6587),U_6590) != c_Groups_Ozero__class_Ozero(U_6587)
    | U_6588 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6587),hAPP(c_Int_Onumber__class_Onumber__of(U_6587),U_6590)),U_6589)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6587),U_6588),U_6589) = hAPP(c_Int_Onumber__class_Onumber__of(U_6587),U_6590)
    | ~ class_Int_Onumber(U_6587)
    | ~ class_Fields_Ofield__inverse__zero(U_6587) ),
    inference(clausify,[status(thm)],[f_1736_2]) ).

fof(f_1737_1,plain,
    ! [V_a_2,V_w_2,V_b_2,T_b] :
      ( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) = V_a_2
          | ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b)
            & hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) )
          | ( V_b_2 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))
            & hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b) ) )
        & ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
              | hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b) )
            & ( V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))
              | hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) ) )
          | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) != V_a_2 ) )
      | ~ class_Int_Onumber(T_b)
      | ~ class_Fields_Ofield__inverse__zero(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_divide__eq__eq__number__of1]) ).

fof(f_1737_2,plain,
    ! [U_6594,U_6593,U_6592,U_6591] :
      ( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6591),U_6592),hAPP(c_Int_Onumber__class_Onumber__of(U_6591),U_6593)) = U_6594
          | ( U_6594 != c_Groups_Ozero__class_Ozero(U_6591)
            & hAPP(c_Int_Onumber__class_Onumber__of(U_6591),U_6593) = c_Groups_Ozero__class_Ozero(U_6591) )
          | ( U_6592 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6591),U_6594),hAPP(c_Int_Onumber__class_Onumber__of(U_6591),U_6593))
            & hAPP(c_Int_Onumber__class_Onumber__of(U_6591),U_6593) != c_Groups_Ozero__class_Ozero(U_6591) ) )
        & ( ( ( U_6594 = c_Groups_Ozero__class_Ozero(U_6591)
              | hAPP(c_Int_Onumber__class_Onumber__of(U_6591),U_6593) != c_Groups_Ozero__class_Ozero(U_6591) )
            & ( U_6592 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6591),U_6594),hAPP(c_Int_Onumber__class_Onumber__of(U_6591),U_6593))
              | hAPP(c_Int_Onumber__class_Onumber__of(U_6591),U_6593) = c_Groups_Ozero__class_Ozero(U_6591) ) )
          | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6591),U_6592),hAPP(c_Int_Onumber__class_Onumber__of(U_6591),U_6593)) != U_6594 ) )
      | ~ class_Int_Onumber(U_6591)
      | ~ class_Fields_Ofield__inverse__zero(U_6591) ),
    inference(variable_rename,[status(thm)],[f_1737_1]) ).

cnf(f_1737_3,plain,
    ( U_6592 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6591),U_6594),hAPP(c_Int_Onumber__class_Onumber__of(U_6591),U_6593))
    | hAPP(c_Int_Onumber__class_Onumber__of(U_6591),U_6593) = c_Groups_Ozero__class_Ozero(U_6591)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6591),U_6592),hAPP(c_Int_Onumber__class_Onumber__of(U_6591),U_6593)) != U_6594
    | ~ class_Int_Onumber(U_6591)
    | ~ class_Fields_Ofield__inverse__zero(U_6591) ),
    inference(clausify,[status(thm)],[f_1737_2]) ).

cnf(f_1737_4,plain,
    ( U_6594 = c_Groups_Ozero__class_Ozero(U_6591)
    | hAPP(c_Int_Onumber__class_Onumber__of(U_6591),U_6593) != c_Groups_Ozero__class_Ozero(U_6591)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6591),U_6592),hAPP(c_Int_Onumber__class_Onumber__of(U_6591),U_6593)) != U_6594
    | ~ class_Int_Onumber(U_6591)
    | ~ class_Fields_Ofield__inverse__zero(U_6591) ),
    inference(clausify,[status(thm)],[f_1737_2]) ).

cnf(f_1737_5,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_6591),U_6593) = c_Groups_Ozero__class_Ozero(U_6591)
    | hAPP(c_Int_Onumber__class_Onumber__of(U_6591),U_6593) != c_Groups_Ozero__class_Ozero(U_6591)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6591),U_6592),hAPP(c_Int_Onumber__class_Onumber__of(U_6591),U_6593)) = U_6594
    | ~ class_Int_Onumber(U_6591)
    | ~ class_Fields_Ofield__inverse__zero(U_6591) ),
    inference(clausify,[status(thm)],[f_1737_2]) ).

cnf(f_1737_6,plain,
    ( U_6594 != c_Groups_Ozero__class_Ozero(U_6591)
    | hAPP(c_Int_Onumber__class_Onumber__of(U_6591),U_6593) != c_Groups_Ozero__class_Ozero(U_6591)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6591),U_6592),hAPP(c_Int_Onumber__class_Onumber__of(U_6591),U_6593)) = U_6594
    | ~ class_Int_Onumber(U_6591)
    | ~ class_Fields_Ofield__inverse__zero(U_6591) ),
    inference(clausify,[status(thm)],[f_1737_2]) ).

cnf(f_1737_7,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_6591),U_6593) = c_Groups_Ozero__class_Ozero(U_6591)
    | U_6592 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6591),U_6594),hAPP(c_Int_Onumber__class_Onumber__of(U_6591),U_6593))
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6591),U_6592),hAPP(c_Int_Onumber__class_Onumber__of(U_6591),U_6593)) = U_6594
    | ~ class_Int_Onumber(U_6591)
    | ~ class_Fields_Ofield__inverse__zero(U_6591) ),
    inference(clausify,[status(thm)],[f_1737_2]) ).

cnf(f_1737_8,plain,
    ( U_6594 != c_Groups_Ozero__class_Ozero(U_6591)
    | U_6592 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6591),U_6594),hAPP(c_Int_Onumber__class_Onumber__of(U_6591),U_6593))
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6591),U_6592),hAPP(c_Int_Onumber__class_Onumber__of(U_6591),U_6593)) = U_6594
    | ~ class_Int_Onumber(U_6591)
    | ~ class_Fields_Ofield__inverse__zero(U_6591) ),
    inference(clausify,[status(thm)],[f_1737_2]) ).

fof(f_1738_1,plain,
    ! [V_a_2,V_times_2,V_one_2,T_b] : hAPP(hAPP(c_Power_Opower_Opower(T_b,V_one_2,V_times_2),V_a_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_one_2,
    inference(fof_nnf,[status(thm)],[fact_power_Opower_Opower__0]) ).

fof(f_1738_2,plain,
    ! [U_6598,U_6597,U_6596,U_6595] : hAPP(hAPP(c_Power_Opower_Opower(U_6595,U_6596,U_6597),U_6598),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_6596,
    inference(variable_rename,[status(thm)],[f_1738_1]) ).

cnf(f_1738_3,plain,
    hAPP(hAPP(c_Power_Opower_Opower(U_6595,U_6596,U_6597),U_6598),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_6596,
    inference(clausify,[status(thm)],[f_1738_2]) ).

fof(f_1739_1,plain,
    ! [V_n_2,V_a_2,V_times_2,V_one_2,T_b] : hAPP(hAPP(c_Power_Opower_Opower(T_b,V_one_2,V_times_2),V_a_2),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(V_times_2,V_a_2),hAPP(hAPP(c_Power_Opower_Opower(T_b,V_one_2,V_times_2),V_a_2),V_n_2)),
    inference(fof_nnf,[status(thm)],[fact_power_Opower_Opower__Suc]) ).

fof(f_1739_2,plain,
    ! [U_6603,U_6602,U_6601,U_6600,U_6599] : hAPP(hAPP(c_Power_Opower_Opower(U_6599,U_6600,U_6601),U_6602),hAPP(c_Nat_OSuc,U_6603)) = hAPP(hAPP(U_6601,U_6602),hAPP(hAPP(c_Power_Opower_Opower(U_6599,U_6600,U_6601),U_6602),U_6603)),
    inference(variable_rename,[status(thm)],[f_1739_1]) ).

cnf(f_1739_3,plain,
    hAPP(hAPP(c_Power_Opower_Opower(U_6599,U_6600,U_6601),U_6602),hAPP(c_Nat_OSuc,U_6603)) = hAPP(hAPP(U_6601,U_6602),hAPP(hAPP(c_Power_Opower_Opower(U_6599,U_6600,U_6601),U_6602),U_6603)),
    inference(clausify,[status(thm)],[f_1739_2]) ).

fof(f_1740_1,plain,
    ! [V_a_2,V_w_2,V_b_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_a_2))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_a_2)) ) )
      | ~ class_Int_Onumber(T_b)
      | ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_divide__less__eq__number__of1]) ).

fof(f_1740_2,plain,
    ! [U_6607,U_6606,U_6605,U_6604] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6604),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6604),U_6605),hAPP(c_Int_Onumber__class_Onumber__of(U_6604),U_6606))),U_6607))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6604),c_Groups_Ozero__class_Ozero(U_6604)),U_6607))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6604),hAPP(c_Int_Onumber__class_Onumber__of(U_6604),U_6606)),c_Groups_Ozero__class_Ozero(U_6604))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6604),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6604),U_6607),hAPP(c_Int_Onumber__class_Onumber__of(U_6604),U_6606))),U_6605))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6604),hAPP(c_Int_Onumber__class_Onumber__of(U_6604),U_6606)),c_Groups_Ozero__class_Ozero(U_6604))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6604),c_Groups_Ozero__class_Ozero(U_6604)),hAPP(c_Int_Onumber__class_Onumber__of(U_6604),U_6606))) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6604),U_6605),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6604),U_6607),hAPP(c_Int_Onumber__class_Onumber__of(U_6604),U_6606))))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6604),c_Groups_Ozero__class_Ozero(U_6604)),hAPP(c_Int_Onumber__class_Onumber__of(U_6604),U_6606))) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6604),c_Groups_Ozero__class_Ozero(U_6604)),U_6607))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6604),hAPP(c_Int_Onumber__class_Onumber__of(U_6604),U_6606)),c_Groups_Ozero__class_Ozero(U_6604))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6604),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6604),U_6607),hAPP(c_Int_Onumber__class_Onumber__of(U_6604),U_6606))),U_6605))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6604),hAPP(c_Int_Onumber__class_Onumber__of(U_6604),U_6606)),c_Groups_Ozero__class_Ozero(U_6604))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6604),c_Groups_Ozero__class_Ozero(U_6604)),hAPP(c_Int_Onumber__class_Onumber__of(U_6604),U_6606))) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6604),U_6605),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6604),U_6607),hAPP(c_Int_Onumber__class_Onumber__of(U_6604),U_6606))))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6604),c_Groups_Ozero__class_Ozero(U_6604)),hAPP(c_Int_Onumber__class_Onumber__of(U_6604),U_6606))) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6604),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6604),U_6605),hAPP(c_Int_Onumber__class_Onumber__of(U_6604),U_6606))),U_6607)) ) )
      | ~ class_Int_Onumber(U_6604)
      | ~ class_Fields_Olinordered__field__inverse__zero(U_6604) ),
    inference(variable_rename,[status(thm)],[f_1740_1]) ).

cnf(f_1740_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6604),U_6605),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6604),U_6607),hAPP(c_Int_Onumber__class_Onumber__of(U_6604),U_6606))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6604),c_Groups_Ozero__class_Ozero(U_6604)),hAPP(c_Int_Onumber__class_Onumber__of(U_6604),U_6606)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6604),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6604),U_6605),hAPP(c_Int_Onumber__class_Onumber__of(U_6604),U_6606))),U_6607))
    | ~ class_Int_Onumber(U_6604)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6604) ),
    inference(clausify,[status(thm)],[f_1740_2]) ).

cnf(f_1740_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6604),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6604),U_6607),hAPP(c_Int_Onumber__class_Onumber__of(U_6604),U_6606))),U_6605))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6604),hAPP(c_Int_Onumber__class_Onumber__of(U_6604),U_6606)),c_Groups_Ozero__class_Ozero(U_6604)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6604),c_Groups_Ozero__class_Ozero(U_6604)),hAPP(c_Int_Onumber__class_Onumber__of(U_6604),U_6606)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6604),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6604),U_6605),hAPP(c_Int_Onumber__class_Onumber__of(U_6604),U_6606))),U_6607))
    | ~ class_Int_Onumber(U_6604)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6604) ),
    inference(clausify,[status(thm)],[f_1740_2]) ).

cnf(f_1740_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6604),c_Groups_Ozero__class_Ozero(U_6604)),U_6607))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6604),hAPP(c_Int_Onumber__class_Onumber__of(U_6604),U_6606)),c_Groups_Ozero__class_Ozero(U_6604)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6604),c_Groups_Ozero__class_Ozero(U_6604)),hAPP(c_Int_Onumber__class_Onumber__of(U_6604),U_6606)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6604),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6604),U_6605),hAPP(c_Int_Onumber__class_Onumber__of(U_6604),U_6606))),U_6607))
    | ~ class_Int_Onumber(U_6604)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6604) ),
    inference(clausify,[status(thm)],[f_1740_2]) ).

cnf(f_1740_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6604),c_Groups_Ozero__class_Ozero(U_6604)),hAPP(c_Int_Onumber__class_Onumber__of(U_6604),U_6606)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6604),c_Groups_Ozero__class_Ozero(U_6604)),hAPP(c_Int_Onumber__class_Onumber__of(U_6604),U_6606)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6604),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6604),U_6605),hAPP(c_Int_Onumber__class_Onumber__of(U_6604),U_6606))),U_6607))
    | ~ class_Int_Onumber(U_6604)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6604) ),
    inference(clausify,[status(thm)],[f_1740_2]) ).

cnf(f_1740_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6604),hAPP(c_Int_Onumber__class_Onumber__of(U_6604),U_6606)),c_Groups_Ozero__class_Ozero(U_6604)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6604),hAPP(c_Int_Onumber__class_Onumber__of(U_6604),U_6606)),c_Groups_Ozero__class_Ozero(U_6604)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6604),c_Groups_Ozero__class_Ozero(U_6604)),hAPP(c_Int_Onumber__class_Onumber__of(U_6604),U_6606)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6604),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6604),U_6605),hAPP(c_Int_Onumber__class_Onumber__of(U_6604),U_6606))),U_6607))
    | ~ class_Int_Onumber(U_6604)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6604) ),
    inference(clausify,[status(thm)],[f_1740_2]) ).

cnf(f_1740_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6604),c_Groups_Ozero__class_Ozero(U_6604)),U_6607))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6604),hAPP(c_Int_Onumber__class_Onumber__of(U_6604),U_6606)),c_Groups_Ozero__class_Ozero(U_6604)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6604),c_Groups_Ozero__class_Ozero(U_6604)),hAPP(c_Int_Onumber__class_Onumber__of(U_6604),U_6606)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6604),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6604),U_6605),hAPP(c_Int_Onumber__class_Onumber__of(U_6604),U_6606))),U_6607))
    | ~ class_Int_Onumber(U_6604)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6604) ),
    inference(clausify,[status(thm)],[f_1740_2]) ).

cnf(f_1740_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6604),hAPP(c_Int_Onumber__class_Onumber__of(U_6604),U_6606)),c_Groups_Ozero__class_Ozero(U_6604)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6604),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6604),U_6607),hAPP(c_Int_Onumber__class_Onumber__of(U_6604),U_6606))),U_6605))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6604),c_Groups_Ozero__class_Ozero(U_6604)),hAPP(c_Int_Onumber__class_Onumber__of(U_6604),U_6606)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6604),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6604),U_6605),hAPP(c_Int_Onumber__class_Onumber__of(U_6604),U_6606))),U_6607))
    | ~ class_Int_Onumber(U_6604)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6604) ),
    inference(clausify,[status(thm)],[f_1740_2]) ).

cnf(f_1740_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6604),c_Groups_Ozero__class_Ozero(U_6604)),U_6607))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6604),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6604),U_6607),hAPP(c_Int_Onumber__class_Onumber__of(U_6604),U_6606))),U_6605))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6604),c_Groups_Ozero__class_Ozero(U_6604)),hAPP(c_Int_Onumber__class_Onumber__of(U_6604),U_6606)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6604),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6604),U_6605),hAPP(c_Int_Onumber__class_Onumber__of(U_6604),U_6606))),U_6607))
    | ~ class_Int_Onumber(U_6604)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6604) ),
    inference(clausify,[status(thm)],[f_1740_2]) ).

cnf(f_1740_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6604),c_Groups_Ozero__class_Ozero(U_6604)),hAPP(c_Int_Onumber__class_Onumber__of(U_6604),U_6606)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6604),U_6605),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6604),U_6607),hAPP(c_Int_Onumber__class_Onumber__of(U_6604),U_6606))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6604),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6604),U_6605),hAPP(c_Int_Onumber__class_Onumber__of(U_6604),U_6606))),U_6607))
    | ~ class_Int_Onumber(U_6604)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6604) ),
    inference(clausify,[status(thm)],[f_1740_2]) ).

cnf(f_1740_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6604),hAPP(c_Int_Onumber__class_Onumber__of(U_6604),U_6606)),c_Groups_Ozero__class_Ozero(U_6604)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6604),hAPP(c_Int_Onumber__class_Onumber__of(U_6604),U_6606)),c_Groups_Ozero__class_Ozero(U_6604)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6604),U_6605),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6604),U_6607),hAPP(c_Int_Onumber__class_Onumber__of(U_6604),U_6606))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6604),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6604),U_6605),hAPP(c_Int_Onumber__class_Onumber__of(U_6604),U_6606))),U_6607))
    | ~ class_Int_Onumber(U_6604)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6604) ),
    inference(clausify,[status(thm)],[f_1740_2]) ).

cnf(f_1740_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6604),c_Groups_Ozero__class_Ozero(U_6604)),U_6607))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6604),hAPP(c_Int_Onumber__class_Onumber__of(U_6604),U_6606)),c_Groups_Ozero__class_Ozero(U_6604)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6604),U_6605),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6604),U_6607),hAPP(c_Int_Onumber__class_Onumber__of(U_6604),U_6606))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6604),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6604),U_6605),hAPP(c_Int_Onumber__class_Onumber__of(U_6604),U_6606))),U_6607))
    | ~ class_Int_Onumber(U_6604)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6604) ),
    inference(clausify,[status(thm)],[f_1740_2]) ).

cnf(f_1740_14,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6604),hAPP(c_Int_Onumber__class_Onumber__of(U_6604),U_6606)),c_Groups_Ozero__class_Ozero(U_6604)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6604),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6604),U_6607),hAPP(c_Int_Onumber__class_Onumber__of(U_6604),U_6606))),U_6605))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6604),U_6605),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6604),U_6607),hAPP(c_Int_Onumber__class_Onumber__of(U_6604),U_6606))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6604),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6604),U_6605),hAPP(c_Int_Onumber__class_Onumber__of(U_6604),U_6606))),U_6607))
    | ~ class_Int_Onumber(U_6604)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6604) ),
    inference(clausify,[status(thm)],[f_1740_2]) ).

cnf(f_1740_15,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6604),c_Groups_Ozero__class_Ozero(U_6604)),U_6607))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6604),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6604),U_6607),hAPP(c_Int_Onumber__class_Onumber__of(U_6604),U_6606))),U_6605))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6604),U_6605),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6604),U_6607),hAPP(c_Int_Onumber__class_Onumber__of(U_6604),U_6606))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6604),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6604),U_6605),hAPP(c_Int_Onumber__class_Onumber__of(U_6604),U_6606))),U_6607))
    | ~ class_Int_Onumber(U_6604)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6604) ),
    inference(clausify,[status(thm)],[f_1740_2]) ).

fof(f_1741_1,plain,
    ! [V_w_2,V_c_2,V_b_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) ) )
      | ~ class_Int_Onumber(T_b)
      | ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_divide__less__eq__number__of]) ).

fof(f_1741_2,plain,
    ! [U_6611,U_6610,U_6609,U_6608] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6608),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6608),U_6609),U_6610)),hAPP(c_Int_Onumber__class_Onumber__of(U_6608),U_6611)))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6608),c_Groups_Ozero__class_Ozero(U_6608)),hAPP(c_Int_Onumber__class_Onumber__of(U_6608),U_6611)))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6608),U_6610),c_Groups_Ozero__class_Ozero(U_6608))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6608),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6608),hAPP(c_Int_Onumber__class_Onumber__of(U_6608),U_6611)),U_6610)),U_6609))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6608),U_6610),c_Groups_Ozero__class_Ozero(U_6608))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6608),c_Groups_Ozero__class_Ozero(U_6608)),U_6610)) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6608),U_6609),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6608),hAPP(c_Int_Onumber__class_Onumber__of(U_6608),U_6611)),U_6610)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6608),c_Groups_Ozero__class_Ozero(U_6608)),U_6610)) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6608),c_Groups_Ozero__class_Ozero(U_6608)),hAPP(c_Int_Onumber__class_Onumber__of(U_6608),U_6611)))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6608),U_6610),c_Groups_Ozero__class_Ozero(U_6608))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6608),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6608),hAPP(c_Int_Onumber__class_Onumber__of(U_6608),U_6611)),U_6610)),U_6609))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6608),U_6610),c_Groups_Ozero__class_Ozero(U_6608))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6608),c_Groups_Ozero__class_Ozero(U_6608)),U_6610)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6608),U_6609),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6608),hAPP(c_Int_Onumber__class_Onumber__of(U_6608),U_6611)),U_6610)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6608),c_Groups_Ozero__class_Ozero(U_6608)),U_6610)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6608),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6608),U_6609),U_6610)),hAPP(c_Int_Onumber__class_Onumber__of(U_6608),U_6611))) ) )
      | ~ class_Int_Onumber(U_6608)
      | ~ class_Fields_Olinordered__field__inverse__zero(U_6608) ),
    inference(variable_rename,[status(thm)],[f_1741_1]) ).

cnf(f_1741_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6608),U_6609),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6608),hAPP(c_Int_Onumber__class_Onumber__of(U_6608),U_6611)),U_6610)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6608),c_Groups_Ozero__class_Ozero(U_6608)),U_6610))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6608),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6608),U_6609),U_6610)),hAPP(c_Int_Onumber__class_Onumber__of(U_6608),U_6611)))
    | ~ class_Int_Onumber(U_6608)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6608) ),
    inference(clausify,[status(thm)],[f_1741_2]) ).

cnf(f_1741_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6608),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6608),hAPP(c_Int_Onumber__class_Onumber__of(U_6608),U_6611)),U_6610)),U_6609))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6608),U_6610),c_Groups_Ozero__class_Ozero(U_6608)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6608),c_Groups_Ozero__class_Ozero(U_6608)),U_6610))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6608),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6608),U_6609),U_6610)),hAPP(c_Int_Onumber__class_Onumber__of(U_6608),U_6611)))
    | ~ class_Int_Onumber(U_6608)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6608) ),
    inference(clausify,[status(thm)],[f_1741_2]) ).

cnf(f_1741_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6608),c_Groups_Ozero__class_Ozero(U_6608)),hAPP(c_Int_Onumber__class_Onumber__of(U_6608),U_6611)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6608),U_6610),c_Groups_Ozero__class_Ozero(U_6608)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6608),c_Groups_Ozero__class_Ozero(U_6608)),U_6610))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6608),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6608),U_6609),U_6610)),hAPP(c_Int_Onumber__class_Onumber__of(U_6608),U_6611)))
    | ~ class_Int_Onumber(U_6608)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6608) ),
    inference(clausify,[status(thm)],[f_1741_2]) ).

cnf(f_1741_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6608),c_Groups_Ozero__class_Ozero(U_6608)),U_6610))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6608),c_Groups_Ozero__class_Ozero(U_6608)),U_6610))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6608),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6608),U_6609),U_6610)),hAPP(c_Int_Onumber__class_Onumber__of(U_6608),U_6611)))
    | ~ class_Int_Onumber(U_6608)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6608) ),
    inference(clausify,[status(thm)],[f_1741_2]) ).

cnf(f_1741_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6608),U_6610),c_Groups_Ozero__class_Ozero(U_6608)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6608),U_6610),c_Groups_Ozero__class_Ozero(U_6608)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6608),c_Groups_Ozero__class_Ozero(U_6608)),U_6610))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6608),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6608),U_6609),U_6610)),hAPP(c_Int_Onumber__class_Onumber__of(U_6608),U_6611)))
    | ~ class_Int_Onumber(U_6608)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6608) ),
    inference(clausify,[status(thm)],[f_1741_2]) ).

cnf(f_1741_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6608),c_Groups_Ozero__class_Ozero(U_6608)),hAPP(c_Int_Onumber__class_Onumber__of(U_6608),U_6611)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6608),U_6610),c_Groups_Ozero__class_Ozero(U_6608)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6608),c_Groups_Ozero__class_Ozero(U_6608)),U_6610))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6608),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6608),U_6609),U_6610)),hAPP(c_Int_Onumber__class_Onumber__of(U_6608),U_6611)))
    | ~ class_Int_Onumber(U_6608)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6608) ),
    inference(clausify,[status(thm)],[f_1741_2]) ).

cnf(f_1741_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6608),U_6610),c_Groups_Ozero__class_Ozero(U_6608)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6608),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6608),hAPP(c_Int_Onumber__class_Onumber__of(U_6608),U_6611)),U_6610)),U_6609))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6608),c_Groups_Ozero__class_Ozero(U_6608)),U_6610))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6608),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6608),U_6609),U_6610)),hAPP(c_Int_Onumber__class_Onumber__of(U_6608),U_6611)))
    | ~ class_Int_Onumber(U_6608)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6608) ),
    inference(clausify,[status(thm)],[f_1741_2]) ).

cnf(f_1741_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6608),c_Groups_Ozero__class_Ozero(U_6608)),hAPP(c_Int_Onumber__class_Onumber__of(U_6608),U_6611)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6608),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6608),hAPP(c_Int_Onumber__class_Onumber__of(U_6608),U_6611)),U_6610)),U_6609))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6608),c_Groups_Ozero__class_Ozero(U_6608)),U_6610))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6608),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6608),U_6609),U_6610)),hAPP(c_Int_Onumber__class_Onumber__of(U_6608),U_6611)))
    | ~ class_Int_Onumber(U_6608)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6608) ),
    inference(clausify,[status(thm)],[f_1741_2]) ).

cnf(f_1741_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6608),c_Groups_Ozero__class_Ozero(U_6608)),U_6610))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6608),U_6609),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6608),hAPP(c_Int_Onumber__class_Onumber__of(U_6608),U_6611)),U_6610)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6608),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6608),U_6609),U_6610)),hAPP(c_Int_Onumber__class_Onumber__of(U_6608),U_6611)))
    | ~ class_Int_Onumber(U_6608)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6608) ),
    inference(clausify,[status(thm)],[f_1741_2]) ).

cnf(f_1741_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6608),U_6610),c_Groups_Ozero__class_Ozero(U_6608)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6608),U_6610),c_Groups_Ozero__class_Ozero(U_6608)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6608),U_6609),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6608),hAPP(c_Int_Onumber__class_Onumber__of(U_6608),U_6611)),U_6610)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6608),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6608),U_6609),U_6610)),hAPP(c_Int_Onumber__class_Onumber__of(U_6608),U_6611)))
    | ~ class_Int_Onumber(U_6608)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6608) ),
    inference(clausify,[status(thm)],[f_1741_2]) ).

cnf(f_1741_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6608),c_Groups_Ozero__class_Ozero(U_6608)),hAPP(c_Int_Onumber__class_Onumber__of(U_6608),U_6611)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6608),U_6610),c_Groups_Ozero__class_Ozero(U_6608)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6608),U_6609),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6608),hAPP(c_Int_Onumber__class_Onumber__of(U_6608),U_6611)),U_6610)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6608),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6608),U_6609),U_6610)),hAPP(c_Int_Onumber__class_Onumber__of(U_6608),U_6611)))
    | ~ class_Int_Onumber(U_6608)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6608) ),
    inference(clausify,[status(thm)],[f_1741_2]) ).

cnf(f_1741_14,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6608),U_6610),c_Groups_Ozero__class_Ozero(U_6608)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6608),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6608),hAPP(c_Int_Onumber__class_Onumber__of(U_6608),U_6611)),U_6610)),U_6609))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6608),U_6609),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6608),hAPP(c_Int_Onumber__class_Onumber__of(U_6608),U_6611)),U_6610)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6608),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6608),U_6609),U_6610)),hAPP(c_Int_Onumber__class_Onumber__of(U_6608),U_6611)))
    | ~ class_Int_Onumber(U_6608)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6608) ),
    inference(clausify,[status(thm)],[f_1741_2]) ).

cnf(f_1741_15,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6608),c_Groups_Ozero__class_Ozero(U_6608)),hAPP(c_Int_Onumber__class_Onumber__of(U_6608),U_6611)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6608),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6608),hAPP(c_Int_Onumber__class_Onumber__of(U_6608),U_6611)),U_6610)),U_6609))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6608),U_6609),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6608),hAPP(c_Int_Onumber__class_Onumber__of(U_6608),U_6611)),U_6610)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6608),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6608),U_6609),U_6610)),hAPP(c_Int_Onumber__class_Onumber__of(U_6608),U_6611)))
    | ~ class_Int_Onumber(U_6608)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6608) ),
    inference(clausify,[status(thm)],[f_1741_2]) ).

fof(f_1742_1,plain,
    ! [V_c_2,V_b_2,V_w_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2))) ) )
      | ~ class_Int_Onumber(T_b)
      | ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_less__divide__eq__number__of]) ).

fof(f_1742_2,plain,
    ! [U_6615,U_6614,U_6613,U_6612] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6612),hAPP(c_Int_Onumber__class_Onumber__of(U_6612),U_6613)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6612),U_6614),U_6615)))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6612),hAPP(c_Int_Onumber__class_Onumber__of(U_6612),U_6613)),c_Groups_Ozero__class_Ozero(U_6612)))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6612),U_6615),c_Groups_Ozero__class_Ozero(U_6612))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6612),U_6614),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6612),hAPP(c_Int_Onumber__class_Onumber__of(U_6612),U_6613)),U_6615)))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6612),U_6615),c_Groups_Ozero__class_Ozero(U_6612))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6612),c_Groups_Ozero__class_Ozero(U_6612)),U_6615)) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6612),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6612),hAPP(c_Int_Onumber__class_Onumber__of(U_6612),U_6613)),U_6615)),U_6614))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6612),c_Groups_Ozero__class_Ozero(U_6612)),U_6615)) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6612),hAPP(c_Int_Onumber__class_Onumber__of(U_6612),U_6613)),c_Groups_Ozero__class_Ozero(U_6612)))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6612),U_6615),c_Groups_Ozero__class_Ozero(U_6612))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6612),U_6614),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6612),hAPP(c_Int_Onumber__class_Onumber__of(U_6612),U_6613)),U_6615)))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6612),U_6615),c_Groups_Ozero__class_Ozero(U_6612))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6612),c_Groups_Ozero__class_Ozero(U_6612)),U_6615)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6612),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6612),hAPP(c_Int_Onumber__class_Onumber__of(U_6612),U_6613)),U_6615)),U_6614))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6612),c_Groups_Ozero__class_Ozero(U_6612)),U_6615)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6612),hAPP(c_Int_Onumber__class_Onumber__of(U_6612),U_6613)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6612),U_6614),U_6615))) ) )
      | ~ class_Int_Onumber(U_6612)
      | ~ class_Fields_Olinordered__field__inverse__zero(U_6612) ),
    inference(variable_rename,[status(thm)],[f_1742_1]) ).

cnf(f_1742_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6612),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6612),hAPP(c_Int_Onumber__class_Onumber__of(U_6612),U_6613)),U_6615)),U_6614))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6612),c_Groups_Ozero__class_Ozero(U_6612)),U_6615))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6612),hAPP(c_Int_Onumber__class_Onumber__of(U_6612),U_6613)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6612),U_6614),U_6615)))
    | ~ class_Int_Onumber(U_6612)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6612) ),
    inference(clausify,[status(thm)],[f_1742_2]) ).

cnf(f_1742_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6612),U_6614),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6612),hAPP(c_Int_Onumber__class_Onumber__of(U_6612),U_6613)),U_6615)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6612),U_6615),c_Groups_Ozero__class_Ozero(U_6612)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6612),c_Groups_Ozero__class_Ozero(U_6612)),U_6615))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6612),hAPP(c_Int_Onumber__class_Onumber__of(U_6612),U_6613)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6612),U_6614),U_6615)))
    | ~ class_Int_Onumber(U_6612)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6612) ),
    inference(clausify,[status(thm)],[f_1742_2]) ).

cnf(f_1742_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6612),hAPP(c_Int_Onumber__class_Onumber__of(U_6612),U_6613)),c_Groups_Ozero__class_Ozero(U_6612)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6612),U_6615),c_Groups_Ozero__class_Ozero(U_6612)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6612),c_Groups_Ozero__class_Ozero(U_6612)),U_6615))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6612),hAPP(c_Int_Onumber__class_Onumber__of(U_6612),U_6613)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6612),U_6614),U_6615)))
    | ~ class_Int_Onumber(U_6612)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6612) ),
    inference(clausify,[status(thm)],[f_1742_2]) ).

cnf(f_1742_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6612),c_Groups_Ozero__class_Ozero(U_6612)),U_6615))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6612),c_Groups_Ozero__class_Ozero(U_6612)),U_6615))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6612),hAPP(c_Int_Onumber__class_Onumber__of(U_6612),U_6613)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6612),U_6614),U_6615)))
    | ~ class_Int_Onumber(U_6612)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6612) ),
    inference(clausify,[status(thm)],[f_1742_2]) ).

cnf(f_1742_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6612),U_6615),c_Groups_Ozero__class_Ozero(U_6612)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6612),U_6615),c_Groups_Ozero__class_Ozero(U_6612)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6612),c_Groups_Ozero__class_Ozero(U_6612)),U_6615))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6612),hAPP(c_Int_Onumber__class_Onumber__of(U_6612),U_6613)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6612),U_6614),U_6615)))
    | ~ class_Int_Onumber(U_6612)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6612) ),
    inference(clausify,[status(thm)],[f_1742_2]) ).

cnf(f_1742_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6612),hAPP(c_Int_Onumber__class_Onumber__of(U_6612),U_6613)),c_Groups_Ozero__class_Ozero(U_6612)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6612),U_6615),c_Groups_Ozero__class_Ozero(U_6612)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6612),c_Groups_Ozero__class_Ozero(U_6612)),U_6615))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6612),hAPP(c_Int_Onumber__class_Onumber__of(U_6612),U_6613)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6612),U_6614),U_6615)))
    | ~ class_Int_Onumber(U_6612)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6612) ),
    inference(clausify,[status(thm)],[f_1742_2]) ).

cnf(f_1742_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6612),U_6615),c_Groups_Ozero__class_Ozero(U_6612)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6612),U_6614),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6612),hAPP(c_Int_Onumber__class_Onumber__of(U_6612),U_6613)),U_6615)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6612),c_Groups_Ozero__class_Ozero(U_6612)),U_6615))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6612),hAPP(c_Int_Onumber__class_Onumber__of(U_6612),U_6613)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6612),U_6614),U_6615)))
    | ~ class_Int_Onumber(U_6612)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6612) ),
    inference(clausify,[status(thm)],[f_1742_2]) ).

cnf(f_1742_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6612),hAPP(c_Int_Onumber__class_Onumber__of(U_6612),U_6613)),c_Groups_Ozero__class_Ozero(U_6612)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6612),U_6614),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6612),hAPP(c_Int_Onumber__class_Onumber__of(U_6612),U_6613)),U_6615)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6612),c_Groups_Ozero__class_Ozero(U_6612)),U_6615))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6612),hAPP(c_Int_Onumber__class_Onumber__of(U_6612),U_6613)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6612),U_6614),U_6615)))
    | ~ class_Int_Onumber(U_6612)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6612) ),
    inference(clausify,[status(thm)],[f_1742_2]) ).

cnf(f_1742_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6612),c_Groups_Ozero__class_Ozero(U_6612)),U_6615))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6612),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6612),hAPP(c_Int_Onumber__class_Onumber__of(U_6612),U_6613)),U_6615)),U_6614))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6612),hAPP(c_Int_Onumber__class_Onumber__of(U_6612),U_6613)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6612),U_6614),U_6615)))
    | ~ class_Int_Onumber(U_6612)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6612) ),
    inference(clausify,[status(thm)],[f_1742_2]) ).

cnf(f_1742_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6612),U_6615),c_Groups_Ozero__class_Ozero(U_6612)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6612),U_6615),c_Groups_Ozero__class_Ozero(U_6612)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6612),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6612),hAPP(c_Int_Onumber__class_Onumber__of(U_6612),U_6613)),U_6615)),U_6614))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6612),hAPP(c_Int_Onumber__class_Onumber__of(U_6612),U_6613)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6612),U_6614),U_6615)))
    | ~ class_Int_Onumber(U_6612)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6612) ),
    inference(clausify,[status(thm)],[f_1742_2]) ).

cnf(f_1742_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6612),hAPP(c_Int_Onumber__class_Onumber__of(U_6612),U_6613)),c_Groups_Ozero__class_Ozero(U_6612)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6612),U_6615),c_Groups_Ozero__class_Ozero(U_6612)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6612),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6612),hAPP(c_Int_Onumber__class_Onumber__of(U_6612),U_6613)),U_6615)),U_6614))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6612),hAPP(c_Int_Onumber__class_Onumber__of(U_6612),U_6613)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6612),U_6614),U_6615)))
    | ~ class_Int_Onumber(U_6612)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6612) ),
    inference(clausify,[status(thm)],[f_1742_2]) ).

cnf(f_1742_14,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6612),U_6615),c_Groups_Ozero__class_Ozero(U_6612)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6612),U_6614),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6612),hAPP(c_Int_Onumber__class_Onumber__of(U_6612),U_6613)),U_6615)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6612),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6612),hAPP(c_Int_Onumber__class_Onumber__of(U_6612),U_6613)),U_6615)),U_6614))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6612),hAPP(c_Int_Onumber__class_Onumber__of(U_6612),U_6613)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6612),U_6614),U_6615)))
    | ~ class_Int_Onumber(U_6612)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6612) ),
    inference(clausify,[status(thm)],[f_1742_2]) ).

cnf(f_1742_15,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6612),hAPP(c_Int_Onumber__class_Onumber__of(U_6612),U_6613)),c_Groups_Ozero__class_Ozero(U_6612)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6612),U_6614),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6612),hAPP(c_Int_Onumber__class_Onumber__of(U_6612),U_6613)),U_6615)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6612),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6612),hAPP(c_Int_Onumber__class_Onumber__of(U_6612),U_6613)),U_6615)),U_6614))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6612),hAPP(c_Int_Onumber__class_Onumber__of(U_6612),U_6613)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6612),U_6614),U_6615)))
    | ~ class_Int_Onumber(U_6612)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6612) ),
    inference(clausify,[status(thm)],[f_1742_2]) ).

fof(f_1743_1,plain,
    ! [V_w_2,V_b_2,V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))) ) )
      | ~ class_Int_Onumber(T_b)
      | ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_less__divide__eq__number__of1]) ).

fof(f_1743_2,plain,
    ! [U_6619,U_6618,U_6617,U_6616] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6616),U_6617),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6616),U_6618),hAPP(c_Int_Onumber__class_Onumber__of(U_6616),U_6619))))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6616),U_6617),c_Groups_Ozero__class_Ozero(U_6616)))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6616),hAPP(c_Int_Onumber__class_Onumber__of(U_6616),U_6619)),c_Groups_Ozero__class_Ozero(U_6616))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6616),U_6618),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6616),U_6617),hAPP(c_Int_Onumber__class_Onumber__of(U_6616),U_6619))))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6616),hAPP(c_Int_Onumber__class_Onumber__of(U_6616),U_6619)),c_Groups_Ozero__class_Ozero(U_6616))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6616),c_Groups_Ozero__class_Ozero(U_6616)),hAPP(c_Int_Onumber__class_Onumber__of(U_6616),U_6619))) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6616),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6616),U_6617),hAPP(c_Int_Onumber__class_Onumber__of(U_6616),U_6619))),U_6618))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6616),c_Groups_Ozero__class_Ozero(U_6616)),hAPP(c_Int_Onumber__class_Onumber__of(U_6616),U_6619))) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6616),U_6617),c_Groups_Ozero__class_Ozero(U_6616)))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6616),hAPP(c_Int_Onumber__class_Onumber__of(U_6616),U_6619)),c_Groups_Ozero__class_Ozero(U_6616))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6616),U_6618),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6616),U_6617),hAPP(c_Int_Onumber__class_Onumber__of(U_6616),U_6619))))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6616),hAPP(c_Int_Onumber__class_Onumber__of(U_6616),U_6619)),c_Groups_Ozero__class_Ozero(U_6616))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6616),c_Groups_Ozero__class_Ozero(U_6616)),hAPP(c_Int_Onumber__class_Onumber__of(U_6616),U_6619))) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6616),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6616),U_6617),hAPP(c_Int_Onumber__class_Onumber__of(U_6616),U_6619))),U_6618))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6616),c_Groups_Ozero__class_Ozero(U_6616)),hAPP(c_Int_Onumber__class_Onumber__of(U_6616),U_6619))) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6616),U_6617),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6616),U_6618),hAPP(c_Int_Onumber__class_Onumber__of(U_6616),U_6619)))) ) )
      | ~ class_Int_Onumber(U_6616)
      | ~ class_Fields_Olinordered__field__inverse__zero(U_6616) ),
    inference(variable_rename,[status(thm)],[f_1743_1]) ).

cnf(f_1743_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6616),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6616),U_6617),hAPP(c_Int_Onumber__class_Onumber__of(U_6616),U_6619))),U_6618))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6616),c_Groups_Ozero__class_Ozero(U_6616)),hAPP(c_Int_Onumber__class_Onumber__of(U_6616),U_6619)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6616),U_6617),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6616),U_6618),hAPP(c_Int_Onumber__class_Onumber__of(U_6616),U_6619))))
    | ~ class_Int_Onumber(U_6616)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6616) ),
    inference(clausify,[status(thm)],[f_1743_2]) ).

cnf(f_1743_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6616),U_6618),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6616),U_6617),hAPP(c_Int_Onumber__class_Onumber__of(U_6616),U_6619))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6616),hAPP(c_Int_Onumber__class_Onumber__of(U_6616),U_6619)),c_Groups_Ozero__class_Ozero(U_6616)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6616),c_Groups_Ozero__class_Ozero(U_6616)),hAPP(c_Int_Onumber__class_Onumber__of(U_6616),U_6619)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6616),U_6617),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6616),U_6618),hAPP(c_Int_Onumber__class_Onumber__of(U_6616),U_6619))))
    | ~ class_Int_Onumber(U_6616)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6616) ),
    inference(clausify,[status(thm)],[f_1743_2]) ).

cnf(f_1743_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6616),U_6617),c_Groups_Ozero__class_Ozero(U_6616)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6616),hAPP(c_Int_Onumber__class_Onumber__of(U_6616),U_6619)),c_Groups_Ozero__class_Ozero(U_6616)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6616),c_Groups_Ozero__class_Ozero(U_6616)),hAPP(c_Int_Onumber__class_Onumber__of(U_6616),U_6619)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6616),U_6617),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6616),U_6618),hAPP(c_Int_Onumber__class_Onumber__of(U_6616),U_6619))))
    | ~ class_Int_Onumber(U_6616)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6616) ),
    inference(clausify,[status(thm)],[f_1743_2]) ).

cnf(f_1743_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6616),c_Groups_Ozero__class_Ozero(U_6616)),hAPP(c_Int_Onumber__class_Onumber__of(U_6616),U_6619)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6616),c_Groups_Ozero__class_Ozero(U_6616)),hAPP(c_Int_Onumber__class_Onumber__of(U_6616),U_6619)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6616),U_6617),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6616),U_6618),hAPP(c_Int_Onumber__class_Onumber__of(U_6616),U_6619))))
    | ~ class_Int_Onumber(U_6616)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6616) ),
    inference(clausify,[status(thm)],[f_1743_2]) ).

cnf(f_1743_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6616),hAPP(c_Int_Onumber__class_Onumber__of(U_6616),U_6619)),c_Groups_Ozero__class_Ozero(U_6616)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6616),hAPP(c_Int_Onumber__class_Onumber__of(U_6616),U_6619)),c_Groups_Ozero__class_Ozero(U_6616)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6616),c_Groups_Ozero__class_Ozero(U_6616)),hAPP(c_Int_Onumber__class_Onumber__of(U_6616),U_6619)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6616),U_6617),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6616),U_6618),hAPP(c_Int_Onumber__class_Onumber__of(U_6616),U_6619))))
    | ~ class_Int_Onumber(U_6616)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6616) ),
    inference(clausify,[status(thm)],[f_1743_2]) ).

cnf(f_1743_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6616),U_6617),c_Groups_Ozero__class_Ozero(U_6616)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6616),hAPP(c_Int_Onumber__class_Onumber__of(U_6616),U_6619)),c_Groups_Ozero__class_Ozero(U_6616)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6616),c_Groups_Ozero__class_Ozero(U_6616)),hAPP(c_Int_Onumber__class_Onumber__of(U_6616),U_6619)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6616),U_6617),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6616),U_6618),hAPP(c_Int_Onumber__class_Onumber__of(U_6616),U_6619))))
    | ~ class_Int_Onumber(U_6616)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6616) ),
    inference(clausify,[status(thm)],[f_1743_2]) ).

cnf(f_1743_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6616),hAPP(c_Int_Onumber__class_Onumber__of(U_6616),U_6619)),c_Groups_Ozero__class_Ozero(U_6616)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6616),U_6618),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6616),U_6617),hAPP(c_Int_Onumber__class_Onumber__of(U_6616),U_6619))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6616),c_Groups_Ozero__class_Ozero(U_6616)),hAPP(c_Int_Onumber__class_Onumber__of(U_6616),U_6619)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6616),U_6617),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6616),U_6618),hAPP(c_Int_Onumber__class_Onumber__of(U_6616),U_6619))))
    | ~ class_Int_Onumber(U_6616)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6616) ),
    inference(clausify,[status(thm)],[f_1743_2]) ).

cnf(f_1743_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6616),U_6617),c_Groups_Ozero__class_Ozero(U_6616)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6616),U_6618),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6616),U_6617),hAPP(c_Int_Onumber__class_Onumber__of(U_6616),U_6619))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6616),c_Groups_Ozero__class_Ozero(U_6616)),hAPP(c_Int_Onumber__class_Onumber__of(U_6616),U_6619)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6616),U_6617),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6616),U_6618),hAPP(c_Int_Onumber__class_Onumber__of(U_6616),U_6619))))
    | ~ class_Int_Onumber(U_6616)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6616) ),
    inference(clausify,[status(thm)],[f_1743_2]) ).

cnf(f_1743_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6616),c_Groups_Ozero__class_Ozero(U_6616)),hAPP(c_Int_Onumber__class_Onumber__of(U_6616),U_6619)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6616),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6616),U_6617),hAPP(c_Int_Onumber__class_Onumber__of(U_6616),U_6619))),U_6618))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6616),U_6617),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6616),U_6618),hAPP(c_Int_Onumber__class_Onumber__of(U_6616),U_6619))))
    | ~ class_Int_Onumber(U_6616)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6616) ),
    inference(clausify,[status(thm)],[f_1743_2]) ).

cnf(f_1743_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6616),hAPP(c_Int_Onumber__class_Onumber__of(U_6616),U_6619)),c_Groups_Ozero__class_Ozero(U_6616)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6616),hAPP(c_Int_Onumber__class_Onumber__of(U_6616),U_6619)),c_Groups_Ozero__class_Ozero(U_6616)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6616),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6616),U_6617),hAPP(c_Int_Onumber__class_Onumber__of(U_6616),U_6619))),U_6618))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6616),U_6617),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6616),U_6618),hAPP(c_Int_Onumber__class_Onumber__of(U_6616),U_6619))))
    | ~ class_Int_Onumber(U_6616)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6616) ),
    inference(clausify,[status(thm)],[f_1743_2]) ).

cnf(f_1743_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6616),U_6617),c_Groups_Ozero__class_Ozero(U_6616)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6616),hAPP(c_Int_Onumber__class_Onumber__of(U_6616),U_6619)),c_Groups_Ozero__class_Ozero(U_6616)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6616),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6616),U_6617),hAPP(c_Int_Onumber__class_Onumber__of(U_6616),U_6619))),U_6618))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6616),U_6617),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6616),U_6618),hAPP(c_Int_Onumber__class_Onumber__of(U_6616),U_6619))))
    | ~ class_Int_Onumber(U_6616)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6616) ),
    inference(clausify,[status(thm)],[f_1743_2]) ).

cnf(f_1743_14,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6616),hAPP(c_Int_Onumber__class_Onumber__of(U_6616),U_6619)),c_Groups_Ozero__class_Ozero(U_6616)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6616),U_6618),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6616),U_6617),hAPP(c_Int_Onumber__class_Onumber__of(U_6616),U_6619))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6616),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6616),U_6617),hAPP(c_Int_Onumber__class_Onumber__of(U_6616),U_6619))),U_6618))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6616),U_6617),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6616),U_6618),hAPP(c_Int_Onumber__class_Onumber__of(U_6616),U_6619))))
    | ~ class_Int_Onumber(U_6616)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6616) ),
    inference(clausify,[status(thm)],[f_1743_2]) ).

cnf(f_1743_15,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6616),U_6617),c_Groups_Ozero__class_Ozero(U_6616)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6616),U_6618),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6616),U_6617),hAPP(c_Int_Onumber__class_Onumber__of(U_6616),U_6619))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6616),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6616),U_6617),hAPP(c_Int_Onumber__class_Onumber__of(U_6616),U_6619))),U_6618))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6616),U_6617),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6616),U_6618),hAPP(c_Int_Onumber__class_Onumber__of(U_6616),U_6619))))
    | ~ class_Int_Onumber(U_6616)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6616) ),
    inference(clausify,[status(thm)],[f_1743_2]) ).

fof(f_1744_1,plain,
    ! [V_w_2,V_b_2,V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))) ) )
      | ~ class_Int_Onumber(T_b)
      | ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_le__divide__eq__number__of1]) ).

fof(f_1744_2,plain,
    ! [U_6623,U_6622,U_6621,U_6620] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6620),U_6621),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6620),U_6622),hAPP(c_Int_Onumber__class_Onumber__of(U_6620),U_6623))))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6620),U_6621),c_Groups_Ozero__class_Ozero(U_6620)))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6620),hAPP(c_Int_Onumber__class_Onumber__of(U_6620),U_6623)),c_Groups_Ozero__class_Ozero(U_6620))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6620),U_6622),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6620),U_6621),hAPP(c_Int_Onumber__class_Onumber__of(U_6620),U_6623))))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6620),hAPP(c_Int_Onumber__class_Onumber__of(U_6620),U_6623)),c_Groups_Ozero__class_Ozero(U_6620))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6620),c_Groups_Ozero__class_Ozero(U_6620)),hAPP(c_Int_Onumber__class_Onumber__of(U_6620),U_6623))) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6620),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6620),U_6621),hAPP(c_Int_Onumber__class_Onumber__of(U_6620),U_6623))),U_6622))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6620),c_Groups_Ozero__class_Ozero(U_6620)),hAPP(c_Int_Onumber__class_Onumber__of(U_6620),U_6623))) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6620),U_6621),c_Groups_Ozero__class_Ozero(U_6620)))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6620),hAPP(c_Int_Onumber__class_Onumber__of(U_6620),U_6623)),c_Groups_Ozero__class_Ozero(U_6620))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6620),U_6622),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6620),U_6621),hAPP(c_Int_Onumber__class_Onumber__of(U_6620),U_6623))))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6620),hAPP(c_Int_Onumber__class_Onumber__of(U_6620),U_6623)),c_Groups_Ozero__class_Ozero(U_6620))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6620),c_Groups_Ozero__class_Ozero(U_6620)),hAPP(c_Int_Onumber__class_Onumber__of(U_6620),U_6623))) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6620),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6620),U_6621),hAPP(c_Int_Onumber__class_Onumber__of(U_6620),U_6623))),U_6622))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6620),c_Groups_Ozero__class_Ozero(U_6620)),hAPP(c_Int_Onumber__class_Onumber__of(U_6620),U_6623))) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6620),U_6621),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6620),U_6622),hAPP(c_Int_Onumber__class_Onumber__of(U_6620),U_6623)))) ) )
      | ~ class_Int_Onumber(U_6620)
      | ~ class_Fields_Olinordered__field__inverse__zero(U_6620) ),
    inference(variable_rename,[status(thm)],[f_1744_1]) ).

cnf(f_1744_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6620),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6620),U_6621),hAPP(c_Int_Onumber__class_Onumber__of(U_6620),U_6623))),U_6622))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6620),c_Groups_Ozero__class_Ozero(U_6620)),hAPP(c_Int_Onumber__class_Onumber__of(U_6620),U_6623)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6620),U_6621),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6620),U_6622),hAPP(c_Int_Onumber__class_Onumber__of(U_6620),U_6623))))
    | ~ class_Int_Onumber(U_6620)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6620) ),
    inference(clausify,[status(thm)],[f_1744_2]) ).

cnf(f_1744_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6620),U_6622),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6620),U_6621),hAPP(c_Int_Onumber__class_Onumber__of(U_6620),U_6623))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6620),hAPP(c_Int_Onumber__class_Onumber__of(U_6620),U_6623)),c_Groups_Ozero__class_Ozero(U_6620)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6620),c_Groups_Ozero__class_Ozero(U_6620)),hAPP(c_Int_Onumber__class_Onumber__of(U_6620),U_6623)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6620),U_6621),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6620),U_6622),hAPP(c_Int_Onumber__class_Onumber__of(U_6620),U_6623))))
    | ~ class_Int_Onumber(U_6620)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6620) ),
    inference(clausify,[status(thm)],[f_1744_2]) ).

cnf(f_1744_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6620),U_6621),c_Groups_Ozero__class_Ozero(U_6620)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6620),hAPP(c_Int_Onumber__class_Onumber__of(U_6620),U_6623)),c_Groups_Ozero__class_Ozero(U_6620)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6620),c_Groups_Ozero__class_Ozero(U_6620)),hAPP(c_Int_Onumber__class_Onumber__of(U_6620),U_6623)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6620),U_6621),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6620),U_6622),hAPP(c_Int_Onumber__class_Onumber__of(U_6620),U_6623))))
    | ~ class_Int_Onumber(U_6620)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6620) ),
    inference(clausify,[status(thm)],[f_1744_2]) ).

cnf(f_1744_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6620),c_Groups_Ozero__class_Ozero(U_6620)),hAPP(c_Int_Onumber__class_Onumber__of(U_6620),U_6623)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6620),c_Groups_Ozero__class_Ozero(U_6620)),hAPP(c_Int_Onumber__class_Onumber__of(U_6620),U_6623)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6620),U_6621),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6620),U_6622),hAPP(c_Int_Onumber__class_Onumber__of(U_6620),U_6623))))
    | ~ class_Int_Onumber(U_6620)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6620) ),
    inference(clausify,[status(thm)],[f_1744_2]) ).

cnf(f_1744_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6620),hAPP(c_Int_Onumber__class_Onumber__of(U_6620),U_6623)),c_Groups_Ozero__class_Ozero(U_6620)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6620),hAPP(c_Int_Onumber__class_Onumber__of(U_6620),U_6623)),c_Groups_Ozero__class_Ozero(U_6620)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6620),c_Groups_Ozero__class_Ozero(U_6620)),hAPP(c_Int_Onumber__class_Onumber__of(U_6620),U_6623)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6620),U_6621),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6620),U_6622),hAPP(c_Int_Onumber__class_Onumber__of(U_6620),U_6623))))
    | ~ class_Int_Onumber(U_6620)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6620) ),
    inference(clausify,[status(thm)],[f_1744_2]) ).

cnf(f_1744_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6620),U_6621),c_Groups_Ozero__class_Ozero(U_6620)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6620),hAPP(c_Int_Onumber__class_Onumber__of(U_6620),U_6623)),c_Groups_Ozero__class_Ozero(U_6620)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6620),c_Groups_Ozero__class_Ozero(U_6620)),hAPP(c_Int_Onumber__class_Onumber__of(U_6620),U_6623)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6620),U_6621),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6620),U_6622),hAPP(c_Int_Onumber__class_Onumber__of(U_6620),U_6623))))
    | ~ class_Int_Onumber(U_6620)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6620) ),
    inference(clausify,[status(thm)],[f_1744_2]) ).

cnf(f_1744_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6620),hAPP(c_Int_Onumber__class_Onumber__of(U_6620),U_6623)),c_Groups_Ozero__class_Ozero(U_6620)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6620),U_6622),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6620),U_6621),hAPP(c_Int_Onumber__class_Onumber__of(U_6620),U_6623))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6620),c_Groups_Ozero__class_Ozero(U_6620)),hAPP(c_Int_Onumber__class_Onumber__of(U_6620),U_6623)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6620),U_6621),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6620),U_6622),hAPP(c_Int_Onumber__class_Onumber__of(U_6620),U_6623))))
    | ~ class_Int_Onumber(U_6620)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6620) ),
    inference(clausify,[status(thm)],[f_1744_2]) ).

cnf(f_1744_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6620),U_6621),c_Groups_Ozero__class_Ozero(U_6620)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6620),U_6622),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6620),U_6621),hAPP(c_Int_Onumber__class_Onumber__of(U_6620),U_6623))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6620),c_Groups_Ozero__class_Ozero(U_6620)),hAPP(c_Int_Onumber__class_Onumber__of(U_6620),U_6623)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6620),U_6621),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6620),U_6622),hAPP(c_Int_Onumber__class_Onumber__of(U_6620),U_6623))))
    | ~ class_Int_Onumber(U_6620)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6620) ),
    inference(clausify,[status(thm)],[f_1744_2]) ).

cnf(f_1744_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6620),c_Groups_Ozero__class_Ozero(U_6620)),hAPP(c_Int_Onumber__class_Onumber__of(U_6620),U_6623)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6620),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6620),U_6621),hAPP(c_Int_Onumber__class_Onumber__of(U_6620),U_6623))),U_6622))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6620),U_6621),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6620),U_6622),hAPP(c_Int_Onumber__class_Onumber__of(U_6620),U_6623))))
    | ~ class_Int_Onumber(U_6620)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6620) ),
    inference(clausify,[status(thm)],[f_1744_2]) ).

cnf(f_1744_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6620),hAPP(c_Int_Onumber__class_Onumber__of(U_6620),U_6623)),c_Groups_Ozero__class_Ozero(U_6620)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6620),hAPP(c_Int_Onumber__class_Onumber__of(U_6620),U_6623)),c_Groups_Ozero__class_Ozero(U_6620)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6620),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6620),U_6621),hAPP(c_Int_Onumber__class_Onumber__of(U_6620),U_6623))),U_6622))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6620),U_6621),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6620),U_6622),hAPP(c_Int_Onumber__class_Onumber__of(U_6620),U_6623))))
    | ~ class_Int_Onumber(U_6620)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6620) ),
    inference(clausify,[status(thm)],[f_1744_2]) ).

cnf(f_1744_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6620),U_6621),c_Groups_Ozero__class_Ozero(U_6620)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6620),hAPP(c_Int_Onumber__class_Onumber__of(U_6620),U_6623)),c_Groups_Ozero__class_Ozero(U_6620)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6620),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6620),U_6621),hAPP(c_Int_Onumber__class_Onumber__of(U_6620),U_6623))),U_6622))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6620),U_6621),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6620),U_6622),hAPP(c_Int_Onumber__class_Onumber__of(U_6620),U_6623))))
    | ~ class_Int_Onumber(U_6620)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6620) ),
    inference(clausify,[status(thm)],[f_1744_2]) ).

cnf(f_1744_14,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6620),hAPP(c_Int_Onumber__class_Onumber__of(U_6620),U_6623)),c_Groups_Ozero__class_Ozero(U_6620)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6620),U_6622),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6620),U_6621),hAPP(c_Int_Onumber__class_Onumber__of(U_6620),U_6623))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6620),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6620),U_6621),hAPP(c_Int_Onumber__class_Onumber__of(U_6620),U_6623))),U_6622))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6620),U_6621),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6620),U_6622),hAPP(c_Int_Onumber__class_Onumber__of(U_6620),U_6623))))
    | ~ class_Int_Onumber(U_6620)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6620) ),
    inference(clausify,[status(thm)],[f_1744_2]) ).

cnf(f_1744_15,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6620),U_6621),c_Groups_Ozero__class_Ozero(U_6620)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6620),U_6622),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6620),U_6621),hAPP(c_Int_Onumber__class_Onumber__of(U_6620),U_6623))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6620),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6620),U_6621),hAPP(c_Int_Onumber__class_Onumber__of(U_6620),U_6623))),U_6622))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6620),U_6621),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6620),U_6622),hAPP(c_Int_Onumber__class_Onumber__of(U_6620),U_6623))))
    | ~ class_Int_Onumber(U_6620)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6620) ),
    inference(clausify,[status(thm)],[f_1744_2]) ).

fof(f_1745_1,plain,
    ! [V_c_2,V_b_2,V_w_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2))) ) )
      | ~ class_Int_Onumber(T_b)
      | ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_le__divide__eq__number__of]) ).

fof(f_1745_2,plain,
    ! [U_6627,U_6626,U_6625,U_6624] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6624),hAPP(c_Int_Onumber__class_Onumber__of(U_6624),U_6625)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6624),U_6626),U_6627)))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6624),hAPP(c_Int_Onumber__class_Onumber__of(U_6624),U_6625)),c_Groups_Ozero__class_Ozero(U_6624)))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6624),U_6627),c_Groups_Ozero__class_Ozero(U_6624))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6624),U_6626),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6624),hAPP(c_Int_Onumber__class_Onumber__of(U_6624),U_6625)),U_6627)))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6624),U_6627),c_Groups_Ozero__class_Ozero(U_6624))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6624),c_Groups_Ozero__class_Ozero(U_6624)),U_6627)) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6624),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6624),hAPP(c_Int_Onumber__class_Onumber__of(U_6624),U_6625)),U_6627)),U_6626))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6624),c_Groups_Ozero__class_Ozero(U_6624)),U_6627)) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6624),hAPP(c_Int_Onumber__class_Onumber__of(U_6624),U_6625)),c_Groups_Ozero__class_Ozero(U_6624)))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6624),U_6627),c_Groups_Ozero__class_Ozero(U_6624))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6624),U_6626),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6624),hAPP(c_Int_Onumber__class_Onumber__of(U_6624),U_6625)),U_6627)))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6624),U_6627),c_Groups_Ozero__class_Ozero(U_6624))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6624),c_Groups_Ozero__class_Ozero(U_6624)),U_6627)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6624),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6624),hAPP(c_Int_Onumber__class_Onumber__of(U_6624),U_6625)),U_6627)),U_6626))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6624),c_Groups_Ozero__class_Ozero(U_6624)),U_6627)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6624),hAPP(c_Int_Onumber__class_Onumber__of(U_6624),U_6625)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6624),U_6626),U_6627))) ) )
      | ~ class_Int_Onumber(U_6624)
      | ~ class_Fields_Olinordered__field__inverse__zero(U_6624) ),
    inference(variable_rename,[status(thm)],[f_1745_1]) ).

cnf(f_1745_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6624),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6624),hAPP(c_Int_Onumber__class_Onumber__of(U_6624),U_6625)),U_6627)),U_6626))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6624),c_Groups_Ozero__class_Ozero(U_6624)),U_6627))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6624),hAPP(c_Int_Onumber__class_Onumber__of(U_6624),U_6625)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6624),U_6626),U_6627)))
    | ~ class_Int_Onumber(U_6624)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6624) ),
    inference(clausify,[status(thm)],[f_1745_2]) ).

cnf(f_1745_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6624),U_6626),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6624),hAPP(c_Int_Onumber__class_Onumber__of(U_6624),U_6625)),U_6627)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6624),U_6627),c_Groups_Ozero__class_Ozero(U_6624)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6624),c_Groups_Ozero__class_Ozero(U_6624)),U_6627))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6624),hAPP(c_Int_Onumber__class_Onumber__of(U_6624),U_6625)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6624),U_6626),U_6627)))
    | ~ class_Int_Onumber(U_6624)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6624) ),
    inference(clausify,[status(thm)],[f_1745_2]) ).

cnf(f_1745_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6624),hAPP(c_Int_Onumber__class_Onumber__of(U_6624),U_6625)),c_Groups_Ozero__class_Ozero(U_6624)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6624),U_6627),c_Groups_Ozero__class_Ozero(U_6624)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6624),c_Groups_Ozero__class_Ozero(U_6624)),U_6627))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6624),hAPP(c_Int_Onumber__class_Onumber__of(U_6624),U_6625)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6624),U_6626),U_6627)))
    | ~ class_Int_Onumber(U_6624)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6624) ),
    inference(clausify,[status(thm)],[f_1745_2]) ).

cnf(f_1745_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6624),c_Groups_Ozero__class_Ozero(U_6624)),U_6627))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6624),c_Groups_Ozero__class_Ozero(U_6624)),U_6627))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6624),hAPP(c_Int_Onumber__class_Onumber__of(U_6624),U_6625)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6624),U_6626),U_6627)))
    | ~ class_Int_Onumber(U_6624)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6624) ),
    inference(clausify,[status(thm)],[f_1745_2]) ).

cnf(f_1745_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6624),U_6627),c_Groups_Ozero__class_Ozero(U_6624)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6624),U_6627),c_Groups_Ozero__class_Ozero(U_6624)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6624),c_Groups_Ozero__class_Ozero(U_6624)),U_6627))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6624),hAPP(c_Int_Onumber__class_Onumber__of(U_6624),U_6625)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6624),U_6626),U_6627)))
    | ~ class_Int_Onumber(U_6624)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6624) ),
    inference(clausify,[status(thm)],[f_1745_2]) ).

cnf(f_1745_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6624),hAPP(c_Int_Onumber__class_Onumber__of(U_6624),U_6625)),c_Groups_Ozero__class_Ozero(U_6624)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6624),U_6627),c_Groups_Ozero__class_Ozero(U_6624)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6624),c_Groups_Ozero__class_Ozero(U_6624)),U_6627))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6624),hAPP(c_Int_Onumber__class_Onumber__of(U_6624),U_6625)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6624),U_6626),U_6627)))
    | ~ class_Int_Onumber(U_6624)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6624) ),
    inference(clausify,[status(thm)],[f_1745_2]) ).

cnf(f_1745_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6624),U_6627),c_Groups_Ozero__class_Ozero(U_6624)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6624),U_6626),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6624),hAPP(c_Int_Onumber__class_Onumber__of(U_6624),U_6625)),U_6627)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6624),c_Groups_Ozero__class_Ozero(U_6624)),U_6627))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6624),hAPP(c_Int_Onumber__class_Onumber__of(U_6624),U_6625)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6624),U_6626),U_6627)))
    | ~ class_Int_Onumber(U_6624)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6624) ),
    inference(clausify,[status(thm)],[f_1745_2]) ).

cnf(f_1745_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6624),hAPP(c_Int_Onumber__class_Onumber__of(U_6624),U_6625)),c_Groups_Ozero__class_Ozero(U_6624)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6624),U_6626),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6624),hAPP(c_Int_Onumber__class_Onumber__of(U_6624),U_6625)),U_6627)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6624),c_Groups_Ozero__class_Ozero(U_6624)),U_6627))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6624),hAPP(c_Int_Onumber__class_Onumber__of(U_6624),U_6625)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6624),U_6626),U_6627)))
    | ~ class_Int_Onumber(U_6624)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6624) ),
    inference(clausify,[status(thm)],[f_1745_2]) ).

cnf(f_1745_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6624),c_Groups_Ozero__class_Ozero(U_6624)),U_6627))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6624),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6624),hAPP(c_Int_Onumber__class_Onumber__of(U_6624),U_6625)),U_6627)),U_6626))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6624),hAPP(c_Int_Onumber__class_Onumber__of(U_6624),U_6625)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6624),U_6626),U_6627)))
    | ~ class_Int_Onumber(U_6624)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6624) ),
    inference(clausify,[status(thm)],[f_1745_2]) ).

cnf(f_1745_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6624),U_6627),c_Groups_Ozero__class_Ozero(U_6624)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6624),U_6627),c_Groups_Ozero__class_Ozero(U_6624)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6624),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6624),hAPP(c_Int_Onumber__class_Onumber__of(U_6624),U_6625)),U_6627)),U_6626))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6624),hAPP(c_Int_Onumber__class_Onumber__of(U_6624),U_6625)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6624),U_6626),U_6627)))
    | ~ class_Int_Onumber(U_6624)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6624) ),
    inference(clausify,[status(thm)],[f_1745_2]) ).

cnf(f_1745_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6624),hAPP(c_Int_Onumber__class_Onumber__of(U_6624),U_6625)),c_Groups_Ozero__class_Ozero(U_6624)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6624),U_6627),c_Groups_Ozero__class_Ozero(U_6624)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6624),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6624),hAPP(c_Int_Onumber__class_Onumber__of(U_6624),U_6625)),U_6627)),U_6626))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6624),hAPP(c_Int_Onumber__class_Onumber__of(U_6624),U_6625)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6624),U_6626),U_6627)))
    | ~ class_Int_Onumber(U_6624)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6624) ),
    inference(clausify,[status(thm)],[f_1745_2]) ).

cnf(f_1745_14,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6624),U_6627),c_Groups_Ozero__class_Ozero(U_6624)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6624),U_6626),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6624),hAPP(c_Int_Onumber__class_Onumber__of(U_6624),U_6625)),U_6627)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6624),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6624),hAPP(c_Int_Onumber__class_Onumber__of(U_6624),U_6625)),U_6627)),U_6626))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6624),hAPP(c_Int_Onumber__class_Onumber__of(U_6624),U_6625)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6624),U_6626),U_6627)))
    | ~ class_Int_Onumber(U_6624)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6624) ),
    inference(clausify,[status(thm)],[f_1745_2]) ).

cnf(f_1745_15,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6624),hAPP(c_Int_Onumber__class_Onumber__of(U_6624),U_6625)),c_Groups_Ozero__class_Ozero(U_6624)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6624),U_6626),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6624),hAPP(c_Int_Onumber__class_Onumber__of(U_6624),U_6625)),U_6627)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6624),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6624),hAPP(c_Int_Onumber__class_Onumber__of(U_6624),U_6625)),U_6627)),U_6626))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6624),hAPP(c_Int_Onumber__class_Onumber__of(U_6624),U_6625)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6624),U_6626),U_6627)))
    | ~ class_Int_Onumber(U_6624)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6624) ),
    inference(clausify,[status(thm)],[f_1745_2]) ).

fof(f_1746_1,plain,
    ! [V_w_2,V_c_2,V_b_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) ) )
      | ~ class_Int_Onumber(T_b)
      | ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_divide__le__eq__number__of]) ).

fof(f_1746_2,plain,
    ! [U_6631,U_6630,U_6629,U_6628] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6628),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6628),U_6629),U_6630)),hAPP(c_Int_Onumber__class_Onumber__of(U_6628),U_6631)))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6628),c_Groups_Ozero__class_Ozero(U_6628)),hAPP(c_Int_Onumber__class_Onumber__of(U_6628),U_6631)))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6628),U_6630),c_Groups_Ozero__class_Ozero(U_6628))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6628),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6628),hAPP(c_Int_Onumber__class_Onumber__of(U_6628),U_6631)),U_6630)),U_6629))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6628),U_6630),c_Groups_Ozero__class_Ozero(U_6628))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6628),c_Groups_Ozero__class_Ozero(U_6628)),U_6630)) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6628),U_6629),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6628),hAPP(c_Int_Onumber__class_Onumber__of(U_6628),U_6631)),U_6630)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6628),c_Groups_Ozero__class_Ozero(U_6628)),U_6630)) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6628),c_Groups_Ozero__class_Ozero(U_6628)),hAPP(c_Int_Onumber__class_Onumber__of(U_6628),U_6631)))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6628),U_6630),c_Groups_Ozero__class_Ozero(U_6628))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6628),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6628),hAPP(c_Int_Onumber__class_Onumber__of(U_6628),U_6631)),U_6630)),U_6629))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6628),U_6630),c_Groups_Ozero__class_Ozero(U_6628))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6628),c_Groups_Ozero__class_Ozero(U_6628)),U_6630)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6628),U_6629),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6628),hAPP(c_Int_Onumber__class_Onumber__of(U_6628),U_6631)),U_6630)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6628),c_Groups_Ozero__class_Ozero(U_6628)),U_6630)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6628),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6628),U_6629),U_6630)),hAPP(c_Int_Onumber__class_Onumber__of(U_6628),U_6631))) ) )
      | ~ class_Int_Onumber(U_6628)
      | ~ class_Fields_Olinordered__field__inverse__zero(U_6628) ),
    inference(variable_rename,[status(thm)],[f_1746_1]) ).

cnf(f_1746_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6628),U_6629),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6628),hAPP(c_Int_Onumber__class_Onumber__of(U_6628),U_6631)),U_6630)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6628),c_Groups_Ozero__class_Ozero(U_6628)),U_6630))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6628),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6628),U_6629),U_6630)),hAPP(c_Int_Onumber__class_Onumber__of(U_6628),U_6631)))
    | ~ class_Int_Onumber(U_6628)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6628) ),
    inference(clausify,[status(thm)],[f_1746_2]) ).

cnf(f_1746_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6628),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6628),hAPP(c_Int_Onumber__class_Onumber__of(U_6628),U_6631)),U_6630)),U_6629))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6628),U_6630),c_Groups_Ozero__class_Ozero(U_6628)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6628),c_Groups_Ozero__class_Ozero(U_6628)),U_6630))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6628),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6628),U_6629),U_6630)),hAPP(c_Int_Onumber__class_Onumber__of(U_6628),U_6631)))
    | ~ class_Int_Onumber(U_6628)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6628) ),
    inference(clausify,[status(thm)],[f_1746_2]) ).

cnf(f_1746_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6628),c_Groups_Ozero__class_Ozero(U_6628)),hAPP(c_Int_Onumber__class_Onumber__of(U_6628),U_6631)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6628),U_6630),c_Groups_Ozero__class_Ozero(U_6628)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6628),c_Groups_Ozero__class_Ozero(U_6628)),U_6630))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6628),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6628),U_6629),U_6630)),hAPP(c_Int_Onumber__class_Onumber__of(U_6628),U_6631)))
    | ~ class_Int_Onumber(U_6628)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6628) ),
    inference(clausify,[status(thm)],[f_1746_2]) ).

cnf(f_1746_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6628),c_Groups_Ozero__class_Ozero(U_6628)),U_6630))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6628),c_Groups_Ozero__class_Ozero(U_6628)),U_6630))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6628),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6628),U_6629),U_6630)),hAPP(c_Int_Onumber__class_Onumber__of(U_6628),U_6631)))
    | ~ class_Int_Onumber(U_6628)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6628) ),
    inference(clausify,[status(thm)],[f_1746_2]) ).

cnf(f_1746_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6628),U_6630),c_Groups_Ozero__class_Ozero(U_6628)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6628),U_6630),c_Groups_Ozero__class_Ozero(U_6628)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6628),c_Groups_Ozero__class_Ozero(U_6628)),U_6630))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6628),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6628),U_6629),U_6630)),hAPP(c_Int_Onumber__class_Onumber__of(U_6628),U_6631)))
    | ~ class_Int_Onumber(U_6628)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6628) ),
    inference(clausify,[status(thm)],[f_1746_2]) ).

cnf(f_1746_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6628),c_Groups_Ozero__class_Ozero(U_6628)),hAPP(c_Int_Onumber__class_Onumber__of(U_6628),U_6631)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6628),U_6630),c_Groups_Ozero__class_Ozero(U_6628)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6628),c_Groups_Ozero__class_Ozero(U_6628)),U_6630))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6628),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6628),U_6629),U_6630)),hAPP(c_Int_Onumber__class_Onumber__of(U_6628),U_6631)))
    | ~ class_Int_Onumber(U_6628)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6628) ),
    inference(clausify,[status(thm)],[f_1746_2]) ).

cnf(f_1746_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6628),U_6630),c_Groups_Ozero__class_Ozero(U_6628)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6628),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6628),hAPP(c_Int_Onumber__class_Onumber__of(U_6628),U_6631)),U_6630)),U_6629))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6628),c_Groups_Ozero__class_Ozero(U_6628)),U_6630))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6628),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6628),U_6629),U_6630)),hAPP(c_Int_Onumber__class_Onumber__of(U_6628),U_6631)))
    | ~ class_Int_Onumber(U_6628)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6628) ),
    inference(clausify,[status(thm)],[f_1746_2]) ).

cnf(f_1746_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6628),c_Groups_Ozero__class_Ozero(U_6628)),hAPP(c_Int_Onumber__class_Onumber__of(U_6628),U_6631)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6628),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6628),hAPP(c_Int_Onumber__class_Onumber__of(U_6628),U_6631)),U_6630)),U_6629))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6628),c_Groups_Ozero__class_Ozero(U_6628)),U_6630))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6628),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6628),U_6629),U_6630)),hAPP(c_Int_Onumber__class_Onumber__of(U_6628),U_6631)))
    | ~ class_Int_Onumber(U_6628)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6628) ),
    inference(clausify,[status(thm)],[f_1746_2]) ).

cnf(f_1746_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6628),c_Groups_Ozero__class_Ozero(U_6628)),U_6630))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6628),U_6629),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6628),hAPP(c_Int_Onumber__class_Onumber__of(U_6628),U_6631)),U_6630)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6628),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6628),U_6629),U_6630)),hAPP(c_Int_Onumber__class_Onumber__of(U_6628),U_6631)))
    | ~ class_Int_Onumber(U_6628)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6628) ),
    inference(clausify,[status(thm)],[f_1746_2]) ).

cnf(f_1746_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6628),U_6630),c_Groups_Ozero__class_Ozero(U_6628)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6628),U_6630),c_Groups_Ozero__class_Ozero(U_6628)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6628),U_6629),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6628),hAPP(c_Int_Onumber__class_Onumber__of(U_6628),U_6631)),U_6630)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6628),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6628),U_6629),U_6630)),hAPP(c_Int_Onumber__class_Onumber__of(U_6628),U_6631)))
    | ~ class_Int_Onumber(U_6628)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6628) ),
    inference(clausify,[status(thm)],[f_1746_2]) ).

cnf(f_1746_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6628),c_Groups_Ozero__class_Ozero(U_6628)),hAPP(c_Int_Onumber__class_Onumber__of(U_6628),U_6631)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6628),U_6630),c_Groups_Ozero__class_Ozero(U_6628)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6628),U_6629),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6628),hAPP(c_Int_Onumber__class_Onumber__of(U_6628),U_6631)),U_6630)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6628),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6628),U_6629),U_6630)),hAPP(c_Int_Onumber__class_Onumber__of(U_6628),U_6631)))
    | ~ class_Int_Onumber(U_6628)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6628) ),
    inference(clausify,[status(thm)],[f_1746_2]) ).

cnf(f_1746_14,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6628),U_6630),c_Groups_Ozero__class_Ozero(U_6628)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6628),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6628),hAPP(c_Int_Onumber__class_Onumber__of(U_6628),U_6631)),U_6630)),U_6629))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6628),U_6629),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6628),hAPP(c_Int_Onumber__class_Onumber__of(U_6628),U_6631)),U_6630)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6628),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6628),U_6629),U_6630)),hAPP(c_Int_Onumber__class_Onumber__of(U_6628),U_6631)))
    | ~ class_Int_Onumber(U_6628)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6628) ),
    inference(clausify,[status(thm)],[f_1746_2]) ).

cnf(f_1746_15,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6628),c_Groups_Ozero__class_Ozero(U_6628)),hAPP(c_Int_Onumber__class_Onumber__of(U_6628),U_6631)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6628),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6628),hAPP(c_Int_Onumber__class_Onumber__of(U_6628),U_6631)),U_6630)),U_6629))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6628),U_6629),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6628),hAPP(c_Int_Onumber__class_Onumber__of(U_6628),U_6631)),U_6630)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6628),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6628),U_6629),U_6630)),hAPP(c_Int_Onumber__class_Onumber__of(U_6628),U_6631)))
    | ~ class_Int_Onumber(U_6628)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6628) ),
    inference(clausify,[status(thm)],[f_1746_2]) ).

fof(f_1747_1,plain,
    ! [V_a_2,V_w_2,V_b_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_a_2))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_a_2)) ) )
      | ~ class_Int_Onumber(T_b)
      | ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_divide__le__eq__number__of1]) ).

fof(f_1747_2,plain,
    ! [U_6635,U_6634,U_6633,U_6632] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6632),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6632),U_6633),hAPP(c_Int_Onumber__class_Onumber__of(U_6632),U_6634))),U_6635))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6632),c_Groups_Ozero__class_Ozero(U_6632)),U_6635))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6632),hAPP(c_Int_Onumber__class_Onumber__of(U_6632),U_6634)),c_Groups_Ozero__class_Ozero(U_6632))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6632),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6632),U_6635),hAPP(c_Int_Onumber__class_Onumber__of(U_6632),U_6634))),U_6633))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6632),hAPP(c_Int_Onumber__class_Onumber__of(U_6632),U_6634)),c_Groups_Ozero__class_Ozero(U_6632))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6632),c_Groups_Ozero__class_Ozero(U_6632)),hAPP(c_Int_Onumber__class_Onumber__of(U_6632),U_6634))) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6632),U_6633),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6632),U_6635),hAPP(c_Int_Onumber__class_Onumber__of(U_6632),U_6634))))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6632),c_Groups_Ozero__class_Ozero(U_6632)),hAPP(c_Int_Onumber__class_Onumber__of(U_6632),U_6634))) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6632),c_Groups_Ozero__class_Ozero(U_6632)),U_6635))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6632),hAPP(c_Int_Onumber__class_Onumber__of(U_6632),U_6634)),c_Groups_Ozero__class_Ozero(U_6632))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6632),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6632),U_6635),hAPP(c_Int_Onumber__class_Onumber__of(U_6632),U_6634))),U_6633))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6632),hAPP(c_Int_Onumber__class_Onumber__of(U_6632),U_6634)),c_Groups_Ozero__class_Ozero(U_6632))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6632),c_Groups_Ozero__class_Ozero(U_6632)),hAPP(c_Int_Onumber__class_Onumber__of(U_6632),U_6634))) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6632),U_6633),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6632),U_6635),hAPP(c_Int_Onumber__class_Onumber__of(U_6632),U_6634))))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6632),c_Groups_Ozero__class_Ozero(U_6632)),hAPP(c_Int_Onumber__class_Onumber__of(U_6632),U_6634))) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6632),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6632),U_6633),hAPP(c_Int_Onumber__class_Onumber__of(U_6632),U_6634))),U_6635)) ) )
      | ~ class_Int_Onumber(U_6632)
      | ~ class_Fields_Olinordered__field__inverse__zero(U_6632) ),
    inference(variable_rename,[status(thm)],[f_1747_1]) ).

cnf(f_1747_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6632),U_6633),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6632),U_6635),hAPP(c_Int_Onumber__class_Onumber__of(U_6632),U_6634))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6632),c_Groups_Ozero__class_Ozero(U_6632)),hAPP(c_Int_Onumber__class_Onumber__of(U_6632),U_6634)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6632),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6632),U_6633),hAPP(c_Int_Onumber__class_Onumber__of(U_6632),U_6634))),U_6635))
    | ~ class_Int_Onumber(U_6632)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6632) ),
    inference(clausify,[status(thm)],[f_1747_2]) ).

cnf(f_1747_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6632),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6632),U_6635),hAPP(c_Int_Onumber__class_Onumber__of(U_6632),U_6634))),U_6633))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6632),hAPP(c_Int_Onumber__class_Onumber__of(U_6632),U_6634)),c_Groups_Ozero__class_Ozero(U_6632)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6632),c_Groups_Ozero__class_Ozero(U_6632)),hAPP(c_Int_Onumber__class_Onumber__of(U_6632),U_6634)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6632),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6632),U_6633),hAPP(c_Int_Onumber__class_Onumber__of(U_6632),U_6634))),U_6635))
    | ~ class_Int_Onumber(U_6632)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6632) ),
    inference(clausify,[status(thm)],[f_1747_2]) ).

cnf(f_1747_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6632),c_Groups_Ozero__class_Ozero(U_6632)),U_6635))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6632),hAPP(c_Int_Onumber__class_Onumber__of(U_6632),U_6634)),c_Groups_Ozero__class_Ozero(U_6632)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6632),c_Groups_Ozero__class_Ozero(U_6632)),hAPP(c_Int_Onumber__class_Onumber__of(U_6632),U_6634)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6632),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6632),U_6633),hAPP(c_Int_Onumber__class_Onumber__of(U_6632),U_6634))),U_6635))
    | ~ class_Int_Onumber(U_6632)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6632) ),
    inference(clausify,[status(thm)],[f_1747_2]) ).

cnf(f_1747_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6632),c_Groups_Ozero__class_Ozero(U_6632)),hAPP(c_Int_Onumber__class_Onumber__of(U_6632),U_6634)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6632),c_Groups_Ozero__class_Ozero(U_6632)),hAPP(c_Int_Onumber__class_Onumber__of(U_6632),U_6634)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6632),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6632),U_6633),hAPP(c_Int_Onumber__class_Onumber__of(U_6632),U_6634))),U_6635))
    | ~ class_Int_Onumber(U_6632)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6632) ),
    inference(clausify,[status(thm)],[f_1747_2]) ).

cnf(f_1747_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6632),hAPP(c_Int_Onumber__class_Onumber__of(U_6632),U_6634)),c_Groups_Ozero__class_Ozero(U_6632)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6632),hAPP(c_Int_Onumber__class_Onumber__of(U_6632),U_6634)),c_Groups_Ozero__class_Ozero(U_6632)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6632),c_Groups_Ozero__class_Ozero(U_6632)),hAPP(c_Int_Onumber__class_Onumber__of(U_6632),U_6634)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6632),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6632),U_6633),hAPP(c_Int_Onumber__class_Onumber__of(U_6632),U_6634))),U_6635))
    | ~ class_Int_Onumber(U_6632)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6632) ),
    inference(clausify,[status(thm)],[f_1747_2]) ).

cnf(f_1747_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6632),c_Groups_Ozero__class_Ozero(U_6632)),U_6635))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6632),hAPP(c_Int_Onumber__class_Onumber__of(U_6632),U_6634)),c_Groups_Ozero__class_Ozero(U_6632)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6632),c_Groups_Ozero__class_Ozero(U_6632)),hAPP(c_Int_Onumber__class_Onumber__of(U_6632),U_6634)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6632),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6632),U_6633),hAPP(c_Int_Onumber__class_Onumber__of(U_6632),U_6634))),U_6635))
    | ~ class_Int_Onumber(U_6632)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6632) ),
    inference(clausify,[status(thm)],[f_1747_2]) ).

cnf(f_1747_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6632),hAPP(c_Int_Onumber__class_Onumber__of(U_6632),U_6634)),c_Groups_Ozero__class_Ozero(U_6632)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6632),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6632),U_6635),hAPP(c_Int_Onumber__class_Onumber__of(U_6632),U_6634))),U_6633))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6632),c_Groups_Ozero__class_Ozero(U_6632)),hAPP(c_Int_Onumber__class_Onumber__of(U_6632),U_6634)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6632),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6632),U_6633),hAPP(c_Int_Onumber__class_Onumber__of(U_6632),U_6634))),U_6635))
    | ~ class_Int_Onumber(U_6632)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6632) ),
    inference(clausify,[status(thm)],[f_1747_2]) ).

cnf(f_1747_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6632),c_Groups_Ozero__class_Ozero(U_6632)),U_6635))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6632),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6632),U_6635),hAPP(c_Int_Onumber__class_Onumber__of(U_6632),U_6634))),U_6633))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6632),c_Groups_Ozero__class_Ozero(U_6632)),hAPP(c_Int_Onumber__class_Onumber__of(U_6632),U_6634)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6632),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6632),U_6633),hAPP(c_Int_Onumber__class_Onumber__of(U_6632),U_6634))),U_6635))
    | ~ class_Int_Onumber(U_6632)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6632) ),
    inference(clausify,[status(thm)],[f_1747_2]) ).

cnf(f_1747_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6632),c_Groups_Ozero__class_Ozero(U_6632)),hAPP(c_Int_Onumber__class_Onumber__of(U_6632),U_6634)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6632),U_6633),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6632),U_6635),hAPP(c_Int_Onumber__class_Onumber__of(U_6632),U_6634))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6632),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6632),U_6633),hAPP(c_Int_Onumber__class_Onumber__of(U_6632),U_6634))),U_6635))
    | ~ class_Int_Onumber(U_6632)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6632) ),
    inference(clausify,[status(thm)],[f_1747_2]) ).

cnf(f_1747_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6632),hAPP(c_Int_Onumber__class_Onumber__of(U_6632),U_6634)),c_Groups_Ozero__class_Ozero(U_6632)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6632),hAPP(c_Int_Onumber__class_Onumber__of(U_6632),U_6634)),c_Groups_Ozero__class_Ozero(U_6632)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6632),U_6633),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6632),U_6635),hAPP(c_Int_Onumber__class_Onumber__of(U_6632),U_6634))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6632),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6632),U_6633),hAPP(c_Int_Onumber__class_Onumber__of(U_6632),U_6634))),U_6635))
    | ~ class_Int_Onumber(U_6632)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6632) ),
    inference(clausify,[status(thm)],[f_1747_2]) ).

cnf(f_1747_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6632),c_Groups_Ozero__class_Ozero(U_6632)),U_6635))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6632),hAPP(c_Int_Onumber__class_Onumber__of(U_6632),U_6634)),c_Groups_Ozero__class_Ozero(U_6632)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6632),U_6633),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6632),U_6635),hAPP(c_Int_Onumber__class_Onumber__of(U_6632),U_6634))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6632),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6632),U_6633),hAPP(c_Int_Onumber__class_Onumber__of(U_6632),U_6634))),U_6635))
    | ~ class_Int_Onumber(U_6632)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6632) ),
    inference(clausify,[status(thm)],[f_1747_2]) ).

cnf(f_1747_14,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6632),hAPP(c_Int_Onumber__class_Onumber__of(U_6632),U_6634)),c_Groups_Ozero__class_Ozero(U_6632)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6632),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6632),U_6635),hAPP(c_Int_Onumber__class_Onumber__of(U_6632),U_6634))),U_6633))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6632),U_6633),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6632),U_6635),hAPP(c_Int_Onumber__class_Onumber__of(U_6632),U_6634))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6632),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6632),U_6633),hAPP(c_Int_Onumber__class_Onumber__of(U_6632),U_6634))),U_6635))
    | ~ class_Int_Onumber(U_6632)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6632) ),
    inference(clausify,[status(thm)],[f_1747_2]) ).

cnf(f_1747_15,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6632),c_Groups_Ozero__class_Ozero(U_6632)),U_6635))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6632),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6632),U_6635),hAPP(c_Int_Onumber__class_Onumber__of(U_6632),U_6634))),U_6633))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6632),U_6633),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6632),U_6635),hAPP(c_Int_Onumber__class_Onumber__of(U_6632),U_6634))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6632),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6632),U_6633),hAPP(c_Int_Onumber__class_Onumber__of(U_6632),U_6634))),U_6635))
    | ~ class_Int_Onumber(U_6632)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6632) ),
    inference(clausify,[status(thm)],[f_1747_2]) ).

fof(f_1748_1,plain,
    ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
      ( hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2)
      | ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
      | ~ c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Oin__idem]) ).

fof(f_1748_2,plain,
    ! [U_6643,U_6642,U_6641,U_6640,U_6639,U_6638,U_6637,U_6636] :
      ( hAPP(hAPP(U_6638,hAPP(U_6640,U_6643)),hAPP(U_6641,U_6642)) = hAPP(U_6641,U_6642)
      | ~ hBOOL(hAPP(hAPP(c_member(U_6637),U_6643),U_6642))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6637),U_6642))
      | ~ c_Finite__Set_Ofolding__image__simple__idem(U_6636,U_6637,U_6638,U_6639,U_6640,U_6641) ),
    inference(variable_rename,[status(thm)],[f_1748_1]) ).

fof(f_1748_3,plain,
    ! [U_6643,U_6642,U_6641,U_6640,U_6639,U_6638,U_6637] :
      ( ! [U_6636] : ~ c_Finite__Set_Ofolding__image__simple__idem(U_6636,U_6637,U_6638,U_6639,U_6640,U_6641)
      | hAPP(hAPP(U_6638,hAPP(U_6640,U_6643)),hAPP(U_6641,U_6642)) = hAPP(U_6641,U_6642)
      | ~ hBOOL(hAPP(hAPP(c_member(U_6637),U_6643),U_6642))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6637),U_6642)) ),
    inference(miniscope,[status(thm)],[f_1748_2]) ).

cnf(f_1748_4,plain,
    ( ~ c_Finite__Set_Ofolding__image__simple__idem(U_6636,U_6637,U_6638,U_6639,U_6640,U_6641)
    | hAPP(hAPP(U_6638,hAPP(U_6640,U_6643)),hAPP(U_6641,U_6642)) = hAPP(U_6641,U_6642)
    | ~ hBOOL(hAPP(hAPP(c_member(U_6637),U_6643),U_6642))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6637),U_6642)) ),
    inference(clausify,[status(thm)],[f_1748_3]) ).

fof(f_1749_1,plain,
    ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
      ( hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
      | ~ c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Oinsert__idem]) ).

fof(f_1749_2,plain,
    ! [U_6651,U_6650,U_6649,U_6648,U_6647,U_6646,U_6645,U_6644] :
      ( hAPP(U_6649,hAPP(hAPP(c_Set_Oinsert(U_6645),U_6651),U_6650)) = hAPP(hAPP(U_6646,hAPP(U_6648,U_6651)),hAPP(U_6649,U_6650))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6645),U_6650))
      | ~ c_Finite__Set_Ofolding__image__simple__idem(U_6644,U_6645,U_6646,U_6647,U_6648,U_6649) ),
    inference(variable_rename,[status(thm)],[f_1749_1]) ).

fof(f_1749_3,plain,
    ! [U_6651,U_6650,U_6649,U_6648,U_6647,U_6646,U_6645] :
      ( ! [U_6644] : ~ c_Finite__Set_Ofolding__image__simple__idem(U_6644,U_6645,U_6646,U_6647,U_6648,U_6649)
      | hAPP(U_6649,hAPP(hAPP(c_Set_Oinsert(U_6645),U_6651),U_6650)) = hAPP(hAPP(U_6646,hAPP(U_6648,U_6651)),hAPP(U_6649,U_6650))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6645),U_6650)) ),
    inference(miniscope,[status(thm)],[f_1749_2]) ).

cnf(f_1749_4,plain,
    ( ~ c_Finite__Set_Ofolding__image__simple__idem(U_6644,U_6645,U_6646,U_6647,U_6648,U_6649)
    | hAPP(U_6649,hAPP(hAPP(c_Set_Oinsert(U_6645),U_6651),U_6650)) = hAPP(hAPP(U_6646,hAPP(U_6648,U_6651)),hAPP(U_6649,U_6650))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6645),U_6650)) ),
    inference(clausify,[status(thm)],[f_1749_3]) ).

fof(f_1750_1,plain,
    ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
      ( hAPP(hAPP(V_f_2,hAPP(V_F_2,V_B_2)),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
      | ~ c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Osubset__idem]) ).

fof(f_1750_2,plain,
    ! [U_6659,U_6658,U_6657,U_6656,U_6655,U_6654,U_6653,U_6652] :
      ( hAPP(hAPP(U_6654,hAPP(U_6657,U_6659)),hAPP(U_6657,U_6658)) = hAPP(U_6657,U_6658)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6653,tc_HOL_Obool)),U_6659),U_6658))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6653),U_6658))
      | ~ c_Finite__Set_Ofolding__image__simple__idem(U_6652,U_6653,U_6654,U_6655,U_6656,U_6657) ),
    inference(variable_rename,[status(thm)],[f_1750_1]) ).

fof(f_1750_3,plain,
    ! [U_6659,U_6658,U_6657,U_6656,U_6655,U_6654,U_6653] :
      ( ! [U_6652] : ~ c_Finite__Set_Ofolding__image__simple__idem(U_6652,U_6653,U_6654,U_6655,U_6656,U_6657)
      | hAPP(hAPP(U_6654,hAPP(U_6657,U_6659)),hAPP(U_6657,U_6658)) = hAPP(U_6657,U_6658)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6653,tc_HOL_Obool)),U_6659),U_6658))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6653),U_6658)) ),
    inference(miniscope,[status(thm)],[f_1750_2]) ).

cnf(f_1750_4,plain,
    ( ~ c_Finite__Set_Ofolding__image__simple__idem(U_6652,U_6653,U_6654,U_6655,U_6656,U_6657)
    | hAPP(hAPP(U_6654,hAPP(U_6657,U_6659)),hAPP(U_6657,U_6658)) = hAPP(U_6657,U_6658)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6653,tc_HOL_Obool)),U_6659),U_6658))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6653),U_6658)) ),
    inference(clausify,[status(thm)],[f_1750_3]) ).

fof(f_1751_1,plain,
    ! [V_w,T_a] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_Opred(V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_number__of__pred]) ).

fof(f_1751_2,plain,
    ! [U_6661,U_6660] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_6660),c_Int_Opred(U_6661)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6660),hAPP(c_Groups_Ouminus__class_Ouminus(U_6660),c_Groups_Oone__class_Oone(U_6660))),hAPP(c_Int_Onumber__class_Onumber__of(U_6660),U_6661))
      | ~ class_Int_Onumber__ring(U_6660) ),
    inference(variable_rename,[status(thm)],[f_1751_1]) ).

cnf(f_1751_3,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_6660),c_Int_Opred(U_6661)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6660),hAPP(c_Groups_Ouminus__class_Ouminus(U_6660),c_Groups_Oone__class_Oone(U_6660))),hAPP(c_Int_Onumber__class_Onumber__of(U_6660),U_6661))
    | ~ class_Int_Onumber__ring(U_6660) ),
    inference(clausify,[status(thm)],[f_1751_2]) ).

fof(f_1752_1,plain,
    ! [V_f_2,V_A_2,T_b,T_c] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x)))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
      | ~ class_Rings_Olinordered__semidom(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__pos]) ).

fof(f_1752_2,plain,
    ! [U_6666,U_6665,U_6664,U_6663] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6663),c_Groups_Ozero__class_Ozero(U_6663)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_6664,U_6663),U_6666),U_6665)))
      | ? [U_6662] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6663),c_Groups_Ozero__class_Ozero(U_6663)),hAPP(U_6666,U_6662)))
          & hBOOL(hAPP(hAPP(c_member(U_6664),U_6662),U_6665)) )
      | ~ class_Rings_Olinordered__semidom(U_6663) ),
    inference(variable_rename,[status(thm)],[f_1752_1]) ).

fof(f_1752_3,plain,
    ! [U_6666,U_6665,U_6664,U_6663] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6663),c_Groups_Ozero__class_Ozero(U_6663)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_6664,U_6663),U_6666),U_6665)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6663),c_Groups_Ozero__class_Ozero(U_6663)),hAPP(U_6666,sK150(U_6666,U_6665,U_6664,U_6663))))
        & hBOOL(hAPP(hAPP(c_member(U_6664),sK150(U_6666,U_6665,U_6664,U_6663)),U_6665)) )
      | ~ class_Rings_Olinordered__semidom(U_6663) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK150]),skolemize(U_6662,sK150(U_6666,U_6665,U_6664,U_6663))],[f_1752_2]) ).

cnf(f_1752_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_6664),sK150(U_6666,U_6665,U_6664,U_6663)),U_6665))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6663),c_Groups_Ozero__class_Ozero(U_6663)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_6664,U_6663),U_6666),U_6665)))
    | ~ class_Rings_Olinordered__semidom(U_6663) ),
    inference(clausify,[status(thm)],[f_1752_3]) ).

cnf(f_1752_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6663),c_Groups_Ozero__class_Ozero(U_6663)),hAPP(U_6666,sK150(U_6666,U_6665,U_6664,U_6663))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6663),c_Groups_Ozero__class_Ozero(U_6663)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_6664,U_6663),U_6666),U_6665)))
    | ~ class_Rings_Olinordered__semidom(U_6663) ),
    inference(clausify,[status(thm)],[f_1752_3]) ).

fof(f_1753_1,plain,
    ! [V_f_2,V_A_2,T_b,T_c] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x)))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
      | ~ class_Rings_Olinordered__semidom(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__nonneg]) ).

fof(f_1753_2,plain,
    ! [U_6671,U_6670,U_6669,U_6668] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6668),c_Groups_Ozero__class_Ozero(U_6668)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_6669,U_6668),U_6671),U_6670)))
      | ? [U_6667] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6668),c_Groups_Ozero__class_Ozero(U_6668)),hAPP(U_6671,U_6667)))
          & hBOOL(hAPP(hAPP(c_member(U_6669),U_6667),U_6670)) )
      | ~ class_Rings_Olinordered__semidom(U_6668) ),
    inference(variable_rename,[status(thm)],[f_1753_1]) ).

fof(f_1753_3,plain,
    ! [U_6671,U_6670,U_6669,U_6668] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6668),c_Groups_Ozero__class_Ozero(U_6668)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_6669,U_6668),U_6671),U_6670)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6668),c_Groups_Ozero__class_Ozero(U_6668)),hAPP(U_6671,sK151(U_6671,U_6670,U_6669,U_6668))))
        & hBOOL(hAPP(hAPP(c_member(U_6669),sK151(U_6671,U_6670,U_6669,U_6668)),U_6670)) )
      | ~ class_Rings_Olinordered__semidom(U_6668) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK151]),skolemize(U_6667,sK151(U_6671,U_6670,U_6669,U_6668))],[f_1753_2]) ).

cnf(f_1753_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_6669),sK151(U_6671,U_6670,U_6669,U_6668)),U_6670))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6668),c_Groups_Ozero__class_Ozero(U_6668)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_6669,U_6668),U_6671),U_6670)))
    | ~ class_Rings_Olinordered__semidom(U_6668) ),
    inference(clausify,[status(thm)],[f_1753_3]) ).

cnf(f_1753_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6668),c_Groups_Ozero__class_Ozero(U_6668)),hAPP(U_6671,sK151(U_6671,U_6670,U_6669,U_6668))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6668),c_Groups_Ozero__class_Ozero(U_6668)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_6669,U_6668),U_6671),U_6670)))
    | ~ class_Rings_Olinordered__semidom(U_6668) ),
    inference(clausify,[status(thm)],[f_1753_3]) ).

fof(f_1754_1,plain,
    ! [V_P_2,V_F_2,T_b] :
      ( hBOOL(hAPP(V_P_2,V_F_2))
      | ? [B_x,B_F] :
          ( ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Set_Oinsert(T_b),B_x),B_F)))
          & hBOOL(hAPP(V_P_2,B_F))
          & ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_F))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_F)) )
      | ~ hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__induct]) ).

fof(f_1754_2,plain,
    ! [U_6676,U_6675,U_6674] :
      ( hBOOL(hAPP(U_6676,U_6675))
      | ? [U_6673,U_6672] :
          ( ~ hBOOL(hAPP(U_6676,hAPP(hAPP(c_Set_Oinsert(U_6674),U_6673),U_6672)))
          & hBOOL(hAPP(U_6676,U_6672))
          & ~ hBOOL(hAPP(hAPP(c_member(U_6674),U_6673),U_6672))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_6674),U_6672)) )
      | ~ hBOOL(hAPP(U_6676,c_Orderings_Obot__class_Obot(tc_fun(U_6674,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6674),U_6675)) ),
    inference(variable_rename,[status(thm)],[f_1754_1]) ).

fof(f_1754_3,plain,
    ! [U_6676,U_6675,U_6674] :
      ( hBOOL(hAPP(U_6676,U_6675))
      | ? [U_6672] :
          ( ~ hBOOL(hAPP(U_6676,hAPP(hAPP(c_Set_Oinsert(U_6674),sK152(U_6676,U_6675,U_6674)),U_6672)))
          & hBOOL(hAPP(U_6676,U_6672))
          & ~ hBOOL(hAPP(hAPP(c_member(U_6674),sK152(U_6676,U_6675,U_6674)),U_6672))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_6674),U_6672)) )
      | ~ hBOOL(hAPP(U_6676,c_Orderings_Obot__class_Obot(tc_fun(U_6674,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6674),U_6675)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK152]),skolemize(U_6673,sK152(U_6676,U_6675,U_6674))],[f_1754_2]) ).

fof(f_1754_4,plain,
    ! [U_6676,U_6675,U_6674] :
      ( hBOOL(hAPP(U_6676,U_6675))
      | ( ~ hBOOL(hAPP(U_6676,hAPP(hAPP(c_Set_Oinsert(U_6674),sK152(U_6676,U_6675,U_6674)),sK153(U_6676,U_6675,U_6674))))
        & hBOOL(hAPP(U_6676,sK153(U_6676,U_6675,U_6674)))
        & ~ hBOOL(hAPP(hAPP(c_member(U_6674),sK152(U_6676,U_6675,U_6674)),sK153(U_6676,U_6675,U_6674)))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(U_6674),sK153(U_6676,U_6675,U_6674))) )
      | ~ hBOOL(hAPP(U_6676,c_Orderings_Obot__class_Obot(tc_fun(U_6674,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6674),U_6675)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK153]),skolemize(U_6672,sK153(U_6676,U_6675,U_6674))],[f_1754_3]) ).

cnf(f_1754_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_6674),sK153(U_6676,U_6675,U_6674)))
    | hBOOL(hAPP(U_6676,U_6675))
    | ~ hBOOL(hAPP(U_6676,c_Orderings_Obot__class_Obot(tc_fun(U_6674,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6674),U_6675)) ),
    inference(clausify,[status(thm)],[f_1754_4]) ).

cnf(f_1754_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_6674),sK152(U_6676,U_6675,U_6674)),sK153(U_6676,U_6675,U_6674)))
    | hBOOL(hAPP(U_6676,U_6675))
    | ~ hBOOL(hAPP(U_6676,c_Orderings_Obot__class_Obot(tc_fun(U_6674,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6674),U_6675)) ),
    inference(clausify,[status(thm)],[f_1754_4]) ).

cnf(f_1754_7,plain,
    ( hBOOL(hAPP(U_6676,sK153(U_6676,U_6675,U_6674)))
    | hBOOL(hAPP(U_6676,U_6675))
    | ~ hBOOL(hAPP(U_6676,c_Orderings_Obot__class_Obot(tc_fun(U_6674,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6674),U_6675)) ),
    inference(clausify,[status(thm)],[f_1754_4]) ).

cnf(f_1754_8,plain,
    ( ~ hBOOL(hAPP(U_6676,hAPP(hAPP(c_Set_Oinsert(U_6674),sK152(U_6676,U_6675,U_6674)),sK153(U_6676,U_6675,U_6674))))
    | hBOOL(hAPP(U_6676,U_6675))
    | ~ hBOOL(hAPP(U_6676,c_Orderings_Obot__class_Obot(tc_fun(U_6674,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_6674),U_6675)) ),
    inference(clausify,[status(thm)],[f_1754_4]) ).

fof(f_1755_1,plain,
    ! [V_y_2,V_z_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
      ( c_Nitpick_Ofold__graph_H(T_b,T_c,V_f_2,V_z_2,V_A_2,hAPP(hAPP(V_f_2,V_x_2),V_y_2))
      | ~ c_Nitpick_Ofold__graph_H(T_b,T_c,V_f_2,V_z_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_y_2)
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_fold__graph_H_Ointros_I2_J]) ).

fof(f_1755_2,plain,
    ! [U_6683,U_6682,U_6681,U_6680,U_6679,U_6678,U_6677] :
      ( c_Nitpick_Ofold__graph_H(U_6677,U_6680,U_6681,U_6682,U_6679,hAPP(hAPP(U_6681,U_6678),U_6683))
      | ~ c_Nitpick_Ofold__graph_H(U_6677,U_6680,U_6681,U_6682,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6677,tc_HOL_Obool)),U_6679),hAPP(hAPP(c_Set_Oinsert(U_6677),U_6678),c_Orderings_Obot__class_Obot(tc_fun(U_6677,tc_HOL_Obool)))),U_6683)
      | ~ hBOOL(hAPP(hAPP(c_member(U_6677),U_6678),U_6679)) ),
    inference(variable_rename,[status(thm)],[f_1755_1]) ).

cnf(f_1755_3,plain,
    ( c_Nitpick_Ofold__graph_H(U_6677,U_6680,U_6681,U_6682,U_6679,hAPP(hAPP(U_6681,U_6678),U_6683))
    | ~ c_Nitpick_Ofold__graph_H(U_6677,U_6680,U_6681,U_6682,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6677,tc_HOL_Obool)),U_6679),hAPP(hAPP(c_Set_Oinsert(U_6677),U_6678),c_Orderings_Obot__class_Obot(tc_fun(U_6677,tc_HOL_Obool)))),U_6683)
    | ~ hBOOL(hAPP(hAPP(c_member(U_6677),U_6678),U_6679)) ),
    inference(clausify,[status(thm)],[f_1755_2]) ).

fof(f_1756_1,plain,
    ! [V_k,T_a] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_Osucc(V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_k))
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_number__of__succ]) ).

fof(f_1756_2,plain,
    ! [U_6685,U_6684] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_6684),c_Int_Osucc(U_6685)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6684),c_Groups_Oone__class_Oone(U_6684)),hAPP(c_Int_Onumber__class_Onumber__of(U_6684),U_6685))
      | ~ class_Int_Onumber__ring(U_6684) ),
    inference(variable_rename,[status(thm)],[f_1756_1]) ).

cnf(f_1756_3,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_6684),c_Int_Osucc(U_6685)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6684),c_Groups_Oone__class_Oone(U_6684)),hAPP(c_Int_Onumber__class_Onumber__of(U_6684),U_6685))
    | ~ class_Int_Onumber__ring(U_6684) ),
    inference(clausify,[status(thm)],[f_1756_2]) ).

fof(f_1757_1,plain,
    ! [V_w,V_v] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w))),
    inference(fof_nnf,[status(thm)],[fact_minus__numeral__code_I6_J]) ).

fof(f_1757_2,plain,
    ! [U_6687,U_6686] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6686)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6687)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6686),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6687))),
    inference(variable_rename,[status(thm)],[f_1757_1]) ).

cnf(f_1757_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6686)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6687)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6686),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6687))),
    inference(clausify,[status(thm)],[f_1757_2]) ).

fof(f_1758_1,plain,
    ! [V_w,V_v] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w)),
    inference(fof_nnf,[status(thm)],[fact_plus__numeral__code_I9_J]) ).

fof(f_1758_2,plain,
    ! [U_6689,U_6688] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6688)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6689)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6688),U_6689)),
    inference(variable_rename,[status(thm)],[f_1758_1]) ).

cnf(f_1758_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6688)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6689)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6688),U_6689)),
    inference(clausify,[status(thm)],[f_1758_2]) ).

fof(f_1759_1,plain,
    ! [V_w] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)),
    inference(fof_nnf,[status(thm)],[fact_minus__numeral__code_I5_J]) ).

fof(f_1759_2,plain,
    ! [U_6690] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6690)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6690)),
    inference(variable_rename,[status(thm)],[f_1759_1]) ).

cnf(f_1759_3,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6690)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6690)),
    inference(clausify,[status(thm)],[f_1759_2]) ).

fof(f_1760_1,plain,
    ! [V_l_2,V_k_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_l_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_l_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_less__number__of__int__code]) ).

fof(f_1760_2,plain,
    ! [U_6692,U_6691] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6691)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6692)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6691),U_6692)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6691),U_6692))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6691)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6692))) ) ),
    inference(variable_rename,[status(thm)],[f_1760_1]) ).

fof(f_1760_3,plain,
    ( ! [U_6696,U_6694] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6694)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6696)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6694),U_6696)) )
    & ! [U_6695,U_6693] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6693),U_6695))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6693)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6695))) ) ),
    inference(miniscope,[status(thm)],[f_1760_2]) ).

cnf(f_1760_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6693),U_6695))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6693)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6695))) ),
    inference(clausify,[status(thm)],[f_1760_3]) ).

cnf(f_1760_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6694)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6696)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6694),U_6696)) ),
    inference(clausify,[status(thm)],[f_1760_3]) ).

fof(f_1761_1,plain,
    ! [V_l_2,V_k_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_l_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_l_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_less__eq__number__of__int__code]) ).

fof(f_1761_2,plain,
    ! [U_6698,U_6697] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6697)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6698)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6697),U_6698)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6697),U_6698))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6697)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6698))) ) ),
    inference(variable_rename,[status(thm)],[f_1761_1]) ).

fof(f_1761_3,plain,
    ( ! [U_6702,U_6700] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6700)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6702)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6700),U_6702)) )
    & ! [U_6701,U_6699] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6699),U_6701))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6699)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6701))) ) ),
    inference(miniscope,[status(thm)],[f_1761_2]) ).

cnf(f_1761_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6699),U_6701))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6699)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6701))) ),
    inference(clausify,[status(thm)],[f_1761_3]) ).

cnf(f_1761_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6700)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6702)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6700),U_6702)) ),
    inference(clausify,[status(thm)],[f_1761_3]) ).

fof(f_1762_1,plain,
    ! [V_i] :
      ( ( ( ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i)) )
          & ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Oone__class_Oone(tc_Int_Oint)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i)) ) )
        | V_i = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | V_i != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(fof_nnf,[status(thm)],[fact_zsgn__def]) ).

fof(f_1762_2,plain,
    ! [U_6703] :
      ( ( ( ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_6703) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6703)) )
          & ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_6703) = c_Groups_Oone__class_Oone(tc_Int_Oint)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6703)) ) )
        | U_6703 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_6703) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | U_6703 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[f_1762_1]) ).

fof(f_1762_3,plain,
    ( ! [U_6705] :
        ( ( ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_6705) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6705)) )
          & ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_6705) = c_Groups_Oone__class_Oone(tc_Int_Oint)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6705)) ) )
        | U_6705 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
    & ! [U_6704] :
        ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_6704) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | U_6704 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(miniscope,[status(thm)],[f_1762_2]) ).

cnf(f_1762_4,plain,
    ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_6704) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_6704 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1762_3]) ).

cnf(f_1762_5,plain,
    ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_6705) = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6705))
    | U_6705 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1762_3]) ).

cnf(f_1762_6,plain,
    ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_6705) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6705))
    | U_6705 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1762_3]) ).

fof(f_1763_1,plain,
    ! [V_u_2,V_l_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_l_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_u_2),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_l_2,V_u_2),
    inference(fof_nnf,[status(thm)],[fact_atLeastLessThanPlusOne__atLeastAtMost__int]) ).

fof(f_1763_2,plain,
    ! [U_6707,U_6706] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_6706),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6707),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_6706,U_6707),
    inference(variable_rename,[status(thm)],[f_1763_1]) ).

cnf(f_1763_3,plain,
    hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_6706),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6707),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_6706,U_6707),
    inference(clausify,[status(thm)],[f_1763_2]) ).

fof(f_1764_1,plain,
    ! [V_u_2,V_l_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_l_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_u_2) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,V_l_2,V_u_2),
    inference(fof_nnf,[status(thm)],[fact_atLeastPlusOneAtMost__greaterThanAtMost__int]) ).

fof(f_1764_2,plain,
    ! [U_6709,U_6708] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6708),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_6709) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_6708,U_6709),
    inference(variable_rename,[status(thm)],[f_1764_1]) ).

cnf(f_1764_3,plain,
    c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6708),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_6709) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_6708,U_6709),
    inference(clausify,[status(thm)],[f_1764_2]) ).

fof(f_1765_1,plain,
    ! [V_u_2,V_l_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_l_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_u_2) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,V_l_2,V_u_2),
    inference(fof_nnf,[status(thm)],[fact_atLeastPlusOneLessThan__greaterThanLessThan__int]) ).

fof(f_1765_2,plain,
    ! [U_6711,U_6710] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6710),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_6711) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_6710,U_6711),
    inference(variable_rename,[status(thm)],[f_1765_1]) ).

cnf(f_1765_3,plain,
    hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6710),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_6711) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_6710,U_6711),
    inference(clausify,[status(thm)],[f_1765_2]) ).

fof(f_1766_1,plain,
    ! [V_k,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_i)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_j)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) ),
    inference(fof_nnf,[status(thm)],[fact_zadd__left__mono]) ).

fof(f_1766_2,plain,
    ! [U_6714,U_6713,U_6712] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6714),U_6712)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6714),U_6713)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6712),U_6713)) ),
    inference(variable_rename,[status(thm)],[f_1766_1]) ).

cnf(f_1766_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6714),U_6712)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6714),U_6713)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6712),U_6713)) ),
    inference(clausify,[status(thm)],[f_1766_2]) ).

fof(f_1767_1,plain,
    ! [V_w] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_w)),
    inference(fof_nnf,[status(thm)],[fact_zle__refl]) ).

fof(f_1767_2,plain,
    ! [U_6715] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6715),U_6715)),
    inference(variable_rename,[status(thm)],[f_1767_1]) ).

cnf(f_1767_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6715),U_6715)),
    inference(clausify,[status(thm)],[f_1767_2]) ).

fof(f_1768_1,plain,
    ! [V_w,V_z] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w)) ),
    inference(fof_nnf,[status(thm)],[fact_zle__linear]) ).

fof(f_1768_2,plain,
    ! [U_6717,U_6716] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6717),U_6716))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6716),U_6717)) ),
    inference(variable_rename,[status(thm)],[f_1768_1]) ).

cnf(f_1768_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6717),U_6716))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6716),U_6717)) ),
    inference(clausify,[status(thm)],[f_1768_2]) ).

fof(f_1769_1,plain,
    ! [V_k,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_k))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_j),V_k))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) ),
    inference(fof_nnf,[status(thm)],[fact_zle__trans]) ).

fof(f_1769_2,plain,
    ! [U_6720,U_6719,U_6718] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6718),U_6720))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6719),U_6720))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6718),U_6719)) ),
    inference(variable_rename,[status(thm)],[f_1769_1]) ).

cnf(f_1769_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6718),U_6720))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6719),U_6720))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6718),U_6719)) ),
    inference(clausify,[status(thm)],[f_1769_2]) ).

fof(f_1770_1,plain,
    ! [V_w,V_z] :
      ( V_z = V_w
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w)) ),
    inference(fof_nnf,[status(thm)],[fact_zle__antisym]) ).

fof(f_1770_2,plain,
    ! [U_6722,U_6721] :
      ( U_6721 = U_6722
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6722),U_6721))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6721),U_6722)) ),
    inference(variable_rename,[status(thm)],[f_1770_1]) ).

cnf(f_1770_3,plain,
    ( U_6721 = U_6722
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6722),U_6721))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6721),U_6722)) ),
    inference(clausify,[status(thm)],[f_1770_2]) ).

fof(f_1771_1,plain,
    ! [V_w_2,V_z_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),V_w_2))
        | V_z_2 = V_w_2
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),V_w_2)) )
      & ( ( V_z_2 != V_w_2
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),V_w_2)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),V_w_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_zless__le]) ).

fof(f_1771_2,plain,
    ! [U_6724,U_6723] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6723),U_6724))
        | U_6723 = U_6724
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6723),U_6724)) )
      & ( ( U_6723 != U_6724
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6723),U_6724)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6723),U_6724)) ) ),
    inference(variable_rename,[status(thm)],[f_1771_1]) ).

fof(f_1771_3,plain,
    ( ! [U_6728,U_6726] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6726),U_6728))
        | U_6726 = U_6728
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6726),U_6728)) )
    & ! [U_6727,U_6725] :
        ( ( U_6725 != U_6727
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6725),U_6727)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6725),U_6727)) ) ),
    inference(miniscope,[status(thm)],[f_1771_2]) ).

cnf(f_1771_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6725),U_6727))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6725),U_6727)) ),
    inference(clausify,[status(thm)],[f_1771_3]) ).

cnf(f_1771_5,plain,
    ( U_6725 != U_6727
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6725),U_6727)) ),
    inference(clausify,[status(thm)],[f_1771_3]) ).

cnf(f_1771_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6726),U_6728))
    | U_6726 = U_6728
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6726),U_6728)) ),
    inference(clausify,[status(thm)],[f_1771_3]) ).

fof(f_1772_1,plain,
    ! [V_l_2,V_k_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(V_k_2)),V_l_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(V_k_2)),V_l_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_le__iff__pred__less]) ).

fof(f_1772_2,plain,
    ! [U_6730,U_6729] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6729),U_6730))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(U_6729)),U_6730)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(U_6729)),U_6730))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6729),U_6730)) ) ),
    inference(variable_rename,[status(thm)],[f_1772_1]) ).

fof(f_1772_3,plain,
    ( ! [U_6734,U_6732] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6732),U_6734))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(U_6732)),U_6734)) )
    & ! [U_6733,U_6731] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(U_6731)),U_6733))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6731),U_6733)) ) ),
    inference(miniscope,[status(thm)],[f_1772_2]) ).

cnf(f_1772_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(U_6731)),U_6733))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6731),U_6733)) ),
    inference(clausify,[status(thm)],[f_1772_3]) ).

cnf(f_1772_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6732),U_6734))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(U_6732)),U_6734)) ),
    inference(clausify,[status(thm)],[f_1772_3]) ).

fof(f_1773_1,plain,
    ! [V_z,V_z_H,V_w,V_w_H] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_H),V_z_H)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),V_z)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_H),V_w)) ),
    inference(fof_nnf,[status(thm)],[fact_zadd__zless__mono]) ).

fof(f_1773_2,plain,
    ! [U_6738,U_6737,U_6736,U_6735] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6735),U_6737)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6736),U_6738)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6737),U_6738))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6735),U_6736)) ),
    inference(variable_rename,[status(thm)],[f_1773_1]) ).

cnf(f_1773_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6735),U_6737)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6736),U_6738)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6737),U_6738))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6735),U_6736)) ),
    inference(clausify,[status(thm)],[f_1773_2]) ).

fof(f_1774_1,plain,
    ! [V_k,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_j),V_k)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j)) ),
    inference(fof_nnf,[status(thm)],[fact_zadd__strict__right__mono]) ).

fof(f_1774_2,plain,
    ! [U_6741,U_6740,U_6739] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6739),U_6741)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6740),U_6741)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6739),U_6740)) ),
    inference(variable_rename,[status(thm)],[f_1774_1]) ).

cnf(f_1774_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6739),U_6741)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6740),U_6741)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6739),U_6740)) ),
    inference(clausify,[status(thm)],[f_1774_2]) ).

fof(f_1775_1,plain,
    ! [V_y,V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_x))
      | V_x = V_y
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),V_y)) ),
    inference(fof_nnf,[status(thm)],[fact_zless__linear]) ).

fof(f_1775_2,plain,
    ! [U_6743,U_6742] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6743),U_6742))
      | U_6742 = U_6743
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6742),U_6743)) ),
    inference(variable_rename,[status(thm)],[f_1775_1]) ).

cnf(f_1775_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6743),U_6742))
    | U_6742 = U_6743
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6742),U_6743)) ),
    inference(clausify,[status(thm)],[f_1775_2]) ).

fof(f_1776_1,plain,
    ! [V_z] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)) = V_z,
    inference(fof_nnf,[status(thm)],[fact_zminus__zminus]) ).

fof(f_1776_2,plain,
    ! [U_6744] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6744)) = U_6744,
    inference(variable_rename,[status(thm)],[f_1776_1]) ).

cnf(f_1776_3,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6744)) = U_6744,
    inference(clausify,[status(thm)],[f_1776_2]) ).

fof(f_1777_1,plain,
    ! [V_x] : c_Int_Osucc(c_Int_Opred(V_x)) = V_x,
    inference(fof_nnf,[status(thm)],[fact_succ__pred]) ).

fof(f_1777_2,plain,
    ! [U_6745] : c_Int_Osucc(c_Int_Opred(U_6745)) = U_6745,
    inference(variable_rename,[status(thm)],[f_1777_1]) ).

cnf(f_1777_3,plain,
    c_Int_Osucc(c_Int_Opred(U_6745)) = U_6745,
    inference(clausify,[status(thm)],[f_1777_2]) ).

fof(f_1778_1,plain,
    ! [V_w,V_z] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)),
    inference(fof_nnf,[status(thm)],[fact_zminus__zadd__distrib]) ).

fof(f_1778_2,plain,
    ! [U_6747,U_6746] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6746),U_6747)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6746)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6747)),
    inference(variable_rename,[status(thm)],[f_1778_1]) ).

cnf(f_1778_3,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6746),U_6747)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6746)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6747)),
    inference(clausify,[status(thm)],[f_1778_2]) ).

fof(f_1779_1,plain,
    ! [V_w,V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),V_w) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),V_z),
    inference(fof_nnf,[status(thm)],[fact_zadd__commute]) ).

fof(f_1779_2,plain,
    ! [U_6749,U_6748] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6748),U_6749) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6749),U_6748),
    inference(variable_rename,[status(thm)],[f_1779_1]) ).

cnf(f_1779_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6748),U_6749) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6749),U_6748),
    inference(clausify,[status(thm)],[f_1779_2]) ).

fof(f_1780_1,plain,
    ! [V_z,V_y,V_x] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_y),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_y),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_z)),
    inference(fof_nnf,[status(thm)],[fact_zadd__left__commute]) ).

fof(f_1780_2,plain,
    ! [U_6752,U_6751,U_6750] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6750),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6751),U_6752)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6751),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6750),U_6752)),
    inference(variable_rename,[status(thm)],[f_1780_1]) ).

cnf(f_1780_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6750),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6751),U_6752)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6751),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6750),U_6752)),
    inference(clausify,[status(thm)],[f_1780_2]) ).

fof(f_1781_1,plain,
    ! [V_z3,V_z2,V_z1] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)),V_z3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z2),V_z3)),
    inference(fof_nnf,[status(thm)],[fact_zadd__assoc]) ).

fof(f_1781_2,plain,
    ! [U_6755,U_6754,U_6753] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6753),U_6754)),U_6755) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6753),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6754),U_6755)),
    inference(variable_rename,[status(thm)],[f_1781_1]) ).

cnf(f_1781_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6753),U_6754)),U_6755) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6753),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6754),U_6755)),
    inference(clausify,[status(thm)],[f_1781_2]) ).

fof(f_1782_1,plain,
    ! [V_w,V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z),V_w),
    inference(fof_nnf,[status(thm)],[fact_diff__int__def__symmetric]) ).

fof(f_1782_2,plain,
    ! [U_6757,U_6756] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6756),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6757)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6756),U_6757),
    inference(variable_rename,[status(thm)],[f_1782_1]) ).

cnf(f_1782_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6756),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6757)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6756),U_6757),
    inference(clausify,[status(thm)],[f_1782_2]) ).

fof(f_1783_1,plain,
    ! [V_w,V_z] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z),V_w) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)),
    inference(fof_nnf,[status(thm)],[fact_diff__int__def]) ).

fof(f_1783_2,plain,
    ! [U_6759,U_6758] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6758),U_6759) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6758),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6759)),
    inference(variable_rename,[status(thm)],[f_1783_1]) ).

cnf(f_1783_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6758),U_6759) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6758),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6759)),
    inference(clausify,[status(thm)],[f_1783_2]) ).

fof(f_1784_1,plain,
    ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z,
    inference(fof_nnf,[status(thm)],[fact_zadd__0__right]) ).

fof(f_1784_2,plain,
    ! [U_6760] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6760),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_6760,
    inference(variable_rename,[status(thm)],[f_1784_1]) ).

cnf(f_1784_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6760),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_6760,
    inference(clausify,[status(thm)],[f_1784_2]) ).

fof(f_1785_1,plain,
    ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z) = V_z,
    inference(fof_nnf,[status(thm)],[fact_zadd__0]) ).

fof(f_1785_2,plain,
    ! [U_6761] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6761) = U_6761,
    inference(variable_rename,[status(thm)],[f_1785_1]) ).

cnf(f_1785_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6761) = U_6761,
    inference(clausify,[status(thm)],[f_1785_2]) ).

fof(f_1786_1,plain,
    ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)),V_z) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[fact_zadd__zminus__inverse2]) ).

fof(f_1786_2,plain,
    ! [U_6762] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6762)),U_6762) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[f_1786_1]) ).

cnf(f_1786_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6762)),U_6762) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1786_2]) ).

fof(f_1787_1,plain,
    ! [V_u_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2))),
    inference(fof_nnf,[status(thm)],[fact_finite__atLeastZeroLessThan__int]) ).

fof(f_1787_2,plain,
    ! [U_6763] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6763))),
    inference(variable_rename,[status(thm)],[f_1787_1]) ).

cnf(f_1787_3,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6763))),
    inference(clausify,[status(thm)],[f_1787_2]) ).

fof(f_1788_1,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[fact_zminus__0]) ).

cnf(f_1788_2,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1788_1]) ).

fof(f_1789_1,plain,
    ! [V_l_2,V_k_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k_2),V_l_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k_2),V_l_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_less__bin__lemma]) ).

fof(f_1789_2,plain,
    ! [U_6765,U_6764] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6764),U_6765))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6764),U_6765)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6764),U_6765)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6764),U_6765)) ) ),
    inference(variable_rename,[status(thm)],[f_1789_1]) ).

fof(f_1789_3,plain,
    ( ! [U_6769,U_6767] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6767),U_6769))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6767),U_6769)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_6768,U_6766] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6766),U_6768)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6766),U_6768)) ) ),
    inference(miniscope,[status(thm)],[f_1789_2]) ).

cnf(f_1789_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6766),U_6768)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6766),U_6768)) ),
    inference(clausify,[status(thm)],[f_1789_3]) ).

cnf(f_1789_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6767),U_6769))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6767),U_6769)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1789_3]) ).

fof(f_1790_1,plain,
    ! [V_z_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)),V_z_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)),V_z_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(fof_nnf,[status(thm)],[fact_odd__less__0]) ).

fof(f_1790_2,plain,
    ! [U_6770] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_6770)),U_6770)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6770),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6770),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_6770)),U_6770)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(variable_rename,[status(thm)],[f_1790_1]) ).

fof(f_1790_3,plain,
    ( ! [U_6772] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_6772)),U_6772)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6772),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_6771] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6771),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_6771)),U_6771)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(miniscope,[status(thm)],[f_1790_2]) ).

cnf(f_1790_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6771),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_6771)),U_6771)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1790_3]) ).

cnf(f_1790_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_6772)),U_6772)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6772),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1790_3]) ).

fof(f_1791_1,plain,
    ! [V_z_2,V_w_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | ( V_w_2 != V_z_2
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) )
      & ( V_w_2 = V_z_2
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_zless__add1__eq]) ).

fof(f_1791_2,plain,
    ! [U_6774,U_6773] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6773),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6774),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | ( U_6773 != U_6774
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6773),U_6774)) ) )
      & ( U_6773 = U_6774
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6773),U_6774))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6773),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6774),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
    inference(variable_rename,[status(thm)],[f_1791_1]) ).

fof(f_1791_3,plain,
    ( ! [U_6778,U_6776] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6776),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6778),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | ( U_6776 != U_6778
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6776),U_6778)) ) )
    & ! [U_6777,U_6775] :
        ( U_6775 = U_6777
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6775),U_6777))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6775),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6777),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
    inference(miniscope,[status(thm)],[f_1791_2]) ).

cnf(f_1791_4,plain,
    ( U_6775 = U_6777
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6775),U_6777))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6775),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6777),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
    inference(clausify,[status(thm)],[f_1791_3]) ).

cnf(f_1791_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6776),U_6778))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6776),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6778),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
    inference(clausify,[status(thm)],[f_1791_3]) ).

cnf(f_1791_6,plain,
    ( U_6776 != U_6778
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6776),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6778),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
    inference(clausify,[status(thm)],[f_1791_3]) ).

fof(f_1792_1,plain,
    ! [V_z,V_w] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_z))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w),V_z)) ),
    inference(fof_nnf,[status(thm)],[fact_zless__imp__add1__zle]) ).

fof(f_1792_2,plain,
    ! [U_6780,U_6779] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6779),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_6780))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6779),U_6780)) ),
    inference(variable_rename,[status(thm)],[f_1792_1]) ).

cnf(f_1792_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6779),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_6780))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6779),U_6780)) ),
    inference(clausify,[status(thm)],[f_1792_2]) ).

fof(f_1793_1,plain,
    ! [V_z] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) ),
    inference(fof_nnf,[status(thm)],[fact_le__imp__0__less]) ).

fof(f_1793_2,plain,
    ! [U_6781] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_6781)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6781)) ),
    inference(variable_rename,[status(thm)],[f_1793_1]) ).

cnf(f_1793_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_6781)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6781)) ),
    inference(clausify,[status(thm)],[f_1793_2]) ).

fof(f_1794_1,plain,
    ! [V_z_2,V_w_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_z_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_z_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_add1__zle__eq]) ).

fof(f_1794_2,plain,
    ! [U_6783,U_6782] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6782),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_6783))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6782),U_6783)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6782),U_6783))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6782),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_6783)) ) ),
    inference(variable_rename,[status(thm)],[f_1794_1]) ).

fof(f_1794_3,plain,
    ( ! [U_6787,U_6785] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6785),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_6787))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6785),U_6787)) )
    & ! [U_6786,U_6784] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6784),U_6786))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6784),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_6786)) ) ),
    inference(miniscope,[status(thm)],[f_1794_2]) ).

cnf(f_1794_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6784),U_6786))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6784),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_6786)) ),
    inference(clausify,[status(thm)],[f_1794_3]) ).

cnf(f_1794_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6785),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_6787))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6785),U_6787)) ),
    inference(clausify,[status(thm)],[f_1794_3]) ).

fof(f_1795_1,plain,
    ! [V_z_2,V_w_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_zle__add1__eq__le]) ).

fof(f_1795_2,plain,
    ! [U_6789,U_6788] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6788),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6789),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6788),U_6789)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6788),U_6789))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6788),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6789),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
    inference(variable_rename,[status(thm)],[f_1795_1]) ).

fof(f_1795_3,plain,
    ( ! [U_6793,U_6791] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6791),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6793),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6791),U_6793)) )
    & ! [U_6792,U_6790] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6790),U_6792))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6790),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6792),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
    inference(miniscope,[status(thm)],[f_1795_2]) ).

cnf(f_1795_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6790),U_6792))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6790),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6792),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
    inference(clausify,[status(thm)],[f_1795_3]) ).

cnf(f_1795_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6791),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6793),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6791),U_6793)) ),
    inference(clausify,[status(thm)],[f_1795_3]) ).

fof(f_1796_1,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(fof_nnf,[status(thm)],[fact_int__0__less__1]) ).

cnf(f_1796_2,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(clausify,[status(thm)],[f_1796_1]) ).

fof(f_1797_1,plain,
    ! [V_z_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_int__one__le__iff__zero__less]) ).

fof(f_1797_2,plain,
    ! [U_6794] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_6794))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6794)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6794))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_6794)) ) ),
    inference(variable_rename,[status(thm)],[f_1797_1]) ).

fof(f_1797_3,plain,
    ( ! [U_6796] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_6796))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6796)) )
    & ! [U_6795] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6795))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_6795)) ) ),
    inference(miniscope,[status(thm)],[f_1797_2]) ).

cnf(f_1797_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6795))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_6795)) ),
    inference(clausify,[status(thm)],[f_1797_3]) ).

cnf(f_1797_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_6796))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6796)) ),
    inference(clausify,[status(thm)],[f_1797_3]) ).

fof(f_1798_1,plain,
    ! [V_z_2,V_w_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_zle__diff1__eq]) ).

fof(f_1798_2,plain,
    ! [U_6798,U_6797] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6797),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6798),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6797),U_6798)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6797),U_6798))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6797),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6798),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
    inference(variable_rename,[status(thm)],[f_1798_1]) ).

fof(f_1798_3,plain,
    ( ! [U_6802,U_6800] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6800),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6802),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6800),U_6802)) )
    & ! [U_6801,U_6799] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6799),U_6801))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6799),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6801),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
    inference(miniscope,[status(thm)],[f_1798_2]) ).

cnf(f_1798_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6799),U_6801))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6799),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6801),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
    inference(clausify,[status(thm)],[f_1798_3]) ).

cnf(f_1798_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6800),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6802),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6800),U_6802)) ),
    inference(clausify,[status(thm)],[f_1798_3]) ).

fof(f_1799_1,plain,
    ! [V_k] : c_Int_Opred(V_k) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(fof_nnf,[status(thm)],[fact_pred__def]) ).

fof(f_1799_2,plain,
    ! [U_6803] : c_Int_Opred(U_6803) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6803),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(variable_rename,[status(thm)],[f_1799_1]) ).

cnf(f_1799_3,plain,
    c_Int_Opred(U_6803) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6803),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(clausify,[status(thm)],[f_1799_2]) ).

fof(f_1800_1,plain,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[fact_int__0__neq__1]) ).

cnf(f_1800_2,plain,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1800_1]) ).

fof(f_1801_1,plain,
    ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z)),V_z) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[fact_odd__nonzero]) ).

fof(f_1801_2,plain,
    ! [U_6804] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_6804)),U_6804) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[f_1801_1]) ).

cnf(f_1801_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_6804)),U_6804) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1801_2]) ).

fof(f_1802_1,plain,
    ! [V_k] : c_Int_Osucc(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(fof_nnf,[status(thm)],[fact_succ__def]) ).

fof(f_1802_2,plain,
    ! [U_6805] : c_Int_Osucc(U_6805) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6805),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(variable_rename,[status(thm)],[f_1802_1]) ).

cnf(f_1802_3,plain,
    c_Int_Osucc(U_6805) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6805),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(clausify,[status(thm)],[f_1802_2]) ).

fof(f_1803_1,plain,
    ! [V_z_2,V_f_2,T_c,T_b] : c_Nitpick_Ofold__graph_H(T_b,T_c,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_z_2),
    inference(fof_nnf,[status(thm)],[fact_fold__graph_H_Ointros_I1_J]) ).

fof(f_1803_2,plain,
    ! [U_6809,U_6808,U_6807,U_6806] : c_Nitpick_Ofold__graph_H(U_6806,U_6807,U_6808,U_6809,c_Orderings_Obot__class_Obot(tc_fun(U_6806,tc_HOL_Obool)),U_6809),
    inference(variable_rename,[status(thm)],[f_1803_1]) ).

cnf(f_1803_3,plain,
    c_Nitpick_Ofold__graph_H(U_6806,U_6807,U_6808,U_6809,c_Orderings_Obot__class_Obot(tc_fun(U_6806,tc_HOL_Obool)),U_6809),
    inference(clausify,[status(thm)],[f_1803_2]) ).

fof(f_1804_1,plain,
    ! [V_a2_2,V_a1_2,T_c,T_b] : c_Nitpick_Ofold__graph_H(T_b,T_c,V_a1_2,V_a2_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_a2_2),
    inference(fof_nnf,[status(thm)],[fact_fold__graph_H_Oequations_I1_J]) ).

fof(f_1804_2,plain,
    ! [U_6813,U_6812,U_6811,U_6810] : c_Nitpick_Ofold__graph_H(U_6810,U_6811,U_6812,U_6813,c_Orderings_Obot__class_Obot(tc_fun(U_6810,tc_HOL_Obool)),U_6813),
    inference(variable_rename,[status(thm)],[f_1804_1]) ).

cnf(f_1804_3,plain,
    c_Nitpick_Ofold__graph_H(U_6810,U_6811,U_6812,U_6813,c_Orderings_Obot__class_Obot(tc_fun(U_6810,tc_HOL_Obool)),U_6813),
    inference(clausify,[status(thm)],[f_1804_2]) ).

fof(f_1805_1,plain,
    ! [V_w,V_v] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w)),
    inference(fof_nnf,[status(thm)],[fact_times__numeral__code_I5_J]) ).

fof(f_1805_2,plain,
    ! [U_6815,U_6814] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6814)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6815)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6814),U_6815)),
    inference(variable_rename,[status(thm)],[f_1805_1]) ).

cnf(f_1805_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6814)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6815)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6814),U_6815)),
    inference(clausify,[status(thm)],[f_1805_2]) ).

fof(f_1806_1,plain,
    ! [V_q,V_r,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_q))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_a))
      | V_a != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) ),
    inference(fof_nnf,[status(thm)],[fact_self__quotient__aux1]) ).

fof(f_1806_2,plain,
    ! [U_6818,U_6817,U_6816] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_6818))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6817),U_6816))
      | U_6816 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6817),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6816),U_6818))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6816)) ),
    inference(variable_rename,[status(thm)],[f_1806_1]) ).

cnf(f_1806_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_6818))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6817),U_6816))
    | U_6816 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6817),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6816),U_6818))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6816)) ),
    inference(clausify,[status(thm)],[f_1806_2]) ).

fof(f_1807_1,plain,
    ! [V_q,V_r,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),c_Groups_Oone__class_Oone(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
      | V_a != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) ),
    inference(fof_nnf,[status(thm)],[fact_self__quotient__aux2]) ).

fof(f_1807_2,plain,
    ! [U_6821,U_6820,U_6819] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6821),c_Groups_Oone__class_Oone(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6820))
      | U_6819 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6820),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6819),U_6821))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6819)) ),
    inference(variable_rename,[status(thm)],[f_1807_1]) ).

cnf(f_1807_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6821),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6820))
    | U_6819 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6820),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6819),U_6821))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6819)) ),
    inference(clausify,[status(thm)],[f_1807_2]) ).

fof(f_1808_1,plain,
    ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H) ),
    inference(fof_nnf,[status(thm)],[fact_zdiv__mono2__neg__lemma]) ).

fof(f_1808_2,plain,
    ! [U_6827,U_6826,U_6825,U_6824,U_6823,U_6822] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6826),U_6823))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6825),U_6822))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6825))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6827))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6824),U_6822))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6825),U_6826)),U_6827)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6822),U_6823)),U_6824) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6825),U_6826)),U_6827) ),
    inference(variable_rename,[status(thm)],[f_1808_1]) ).

cnf(f_1808_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6826),U_6823))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6825),U_6822))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6825))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6827))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6824),U_6822))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6825),U_6826)),U_6827)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6822),U_6823)),U_6824) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6825),U_6826)),U_6827) ),
    inference(clausify,[status(thm)],[f_1808_2]) ).

fof(f_1809_1,plain,
    ! [V_r,V_q,V_r_H,V_q_H,V_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r_H))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H)),V_r_H)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r))) ),
    inference(fof_nnf,[status(thm)],[fact_unique__quotient__lemma__neg]) ).

fof(f_1809_2,plain,
    ! [U_6832,U_6831,U_6830,U_6829,U_6828] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6831),U_6829))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6828),U_6830))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6828),U_6832))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6832),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6828),U_6829)),U_6830)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6828),U_6831)),U_6832))) ),
    inference(variable_rename,[status(thm)],[f_1809_1]) ).

cnf(f_1809_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6831),U_6829))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6828),U_6830))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6828),U_6832))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6832),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6828),U_6829)),U_6830)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6828),U_6831)),U_6832))) ),
    inference(clausify,[status(thm)],[f_1809_2]) ).

fof(f_1810_1,plain,
    ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H) ),
    inference(fof_nnf,[status(thm)],[fact_zdiv__mono2__lemma]) ).

fof(f_1810_2,plain,
    ! [U_6838,U_6837,U_6836,U_6835,U_6834,U_6833] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6834),U_6837))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6836),U_6833))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6836))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6835))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6838),U_6836))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6836),U_6837)),U_6838)))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6833),U_6834)),U_6835) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6836),U_6837)),U_6838) ),
    inference(variable_rename,[status(thm)],[f_1810_1]) ).

cnf(f_1810_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6834),U_6837))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6836),U_6833))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6836))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6835))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6838),U_6836))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6836),U_6837)),U_6838)))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6833),U_6834)),U_6835) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6836),U_6837)),U_6838) ),
    inference(clausify,[status(thm)],[f_1810_2]) ).

fof(f_1811_1,plain,
    ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_l_2,V_u_2))),
    inference(fof_nnf,[status(thm)],[fact_finite__atLeastAtMost__int]) ).

fof(f_1811_2,plain,
    ! [U_6840,U_6839] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_6839,U_6840))),
    inference(variable_rename,[status(thm)],[f_1811_1]) ).

cnf(f_1811_3,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_6839,U_6840))),
    inference(clausify,[status(thm)],[f_1811_2]) ).

fof(f_1812_1,plain,
    ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_l_2),V_u_2))),
    inference(fof_nnf,[status(thm)],[fact_finite__atLeastLessThan__int]) ).

fof(f_1812_2,plain,
    ! [U_6842,U_6841] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_6841),U_6842))),
    inference(variable_rename,[status(thm)],[f_1812_1]) ).

cnf(f_1812_3,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_6841),U_6842))),
    inference(clausify,[status(thm)],[f_1812_2]) ).

fof(f_1813_1,plain,
    ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,V_l_2,V_u_2))),
    inference(fof_nnf,[status(thm)],[fact_finite__greaterThanAtMost__int]) ).

fof(f_1813_2,plain,
    ! [U_6844,U_6843] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_6843,U_6844))),
    inference(variable_rename,[status(thm)],[f_1813_1]) ).

cnf(f_1813_3,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_6843,U_6844))),
    inference(clausify,[status(thm)],[f_1813_2]) ).

fof(f_1814_1,plain,
    ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,V_l_2,V_u_2))),
    inference(fof_nnf,[status(thm)],[fact_finite__greaterThanLessThan__int]) ).

fof(f_1814_2,plain,
    ! [U_6846,U_6845] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_6845,U_6846))),
    inference(variable_rename,[status(thm)],[f_1814_1]) ).

cnf(f_1814_3,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_6845,U_6846))),
    inference(clausify,[status(thm)],[f_1814_2]) ).

fof(f_1815_1,plain,
    ! [V_k] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k) = V_k,
    inference(fof_nnf,[status(thm)],[fact_number__of__is__id]) ).

fof(f_1815_2,plain,
    ! [U_6847] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6847) = U_6847,
    inference(variable_rename,[status(thm)],[f_1815_1]) ).

cnf(f_1815_3,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6847) = U_6847,
    inference(clausify,[status(thm)],[f_1815_2]) ).

fof(f_1816_1,plain,
    ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_infinite__UNIV__int]) ).

cnf(f_1816_2,plain,
    ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_1816_1]) ).

fof(f_1817_1,plain,
    ! [V_r_H,V_q_H,V_b_H] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_q_H))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H))) ),
    inference(fof_nnf,[status(thm)],[fact_q__pos__lemma]) ).

fof(f_1817_2,plain,
    ! [U_6850,U_6849,U_6848] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6849))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6848))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6850),U_6848))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6848),U_6849)),U_6850))) ),
    inference(variable_rename,[status(thm)],[f_1817_1]) ).

cnf(f_1817_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6849))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6848))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6850),U_6848))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6848),U_6849)),U_6850))) ),
    inference(clausify,[status(thm)],[f_1817_2]) ).

fof(f_1818_1,plain,
    ! [V_r_H,V_q_H,V_b_H] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(fof_nnf,[status(thm)],[fact_q__neg__lemma]) ).

fof(f_1818_2,plain,
    ! [U_6853,U_6852,U_6851] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6852),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6851))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6853))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6851),U_6852)),U_6853)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_1818_1]) ).

cnf(f_1818_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6852),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6851))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6853))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6851),U_6852)),U_6853)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1818_2]) ).

fof(f_1819_1,plain,
    ! [V_r,V_q,V_r_H,V_q_H,V_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H)),V_r_H)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r))) ),
    inference(fof_nnf,[status(thm)],[fact_unique__quotient__lemma]) ).

fof(f_1819_2,plain,
    ! [U_6858,U_6857,U_6856,U_6855,U_6854] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6855),U_6857))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6858),U_6854))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6856),U_6854))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6856))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6854),U_6855)),U_6856)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6854),U_6857)),U_6858))) ),
    inference(variable_rename,[status(thm)],[f_1819_1]) ).

cnf(f_1819_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6855),U_6857))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6858),U_6854))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6856),U_6854))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6856))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6854),U_6855)),U_6856)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6854),U_6857)),U_6858))) ),
    inference(clausify,[status(thm)],[f_1819_2]) ).

fof(f_1820_1,plain,
    ! [V_i_2,V_j_2] :
      ( ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),V_i_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_j_2))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2)) )
      & ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_simp__from__to]) ).

fof(f_1820_2,plain,
    ! [U_6860,U_6859] :
      ( ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_6860,U_6859) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),U_6860),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6860),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_6859))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6859),U_6860)) )
      & ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_6860,U_6859) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6859),U_6860)) ) ),
    inference(variable_rename,[status(thm)],[f_1820_1]) ).

fof(f_1820_3,plain,
    ( ! [U_6864,U_6862] :
        ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_6864,U_6862) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),U_6864),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6864),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_6862))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6862),U_6864)) )
    & ! [U_6863,U_6861] :
        ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_6863,U_6861) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6861),U_6863)) ) ),
    inference(miniscope,[status(thm)],[f_1820_2]) ).

cnf(f_1820_4,plain,
    ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_6863,U_6861) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6861),U_6863)) ),
    inference(clausify,[status(thm)],[f_1820_3]) ).

cnf(f_1820_5,plain,
    ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_6864,U_6862) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),U_6864),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6864),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_6862))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6862),U_6864)) ),
    inference(clausify,[status(thm)],[f_1820_3]) ).

fof(f_1821_1,plain,
    ! [V_n,V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) ),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J]) ).

fof(f_1821_2,plain,
    ! [U_6866,U_6865] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_6865),U_6866)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6865)) ),
    inference(variable_rename,[status(thm)],[f_1821_1]) ).

cnf(f_1821_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_6865),U_6866)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6865)) ),
    inference(clausify,[status(thm)],[f_1821_2]) ).

fof(f_1822_1,plain,
    ! [V_y,V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) ),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J]) ).

fof(f_1822_2,plain,
    ! [U_6868,U_6867] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6867),U_6868)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6868))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6867)) ),
    inference(variable_rename,[status(thm)],[f_1822_1]) ).

cnf(f_1822_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6867),U_6868)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6868))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6867)) ),
    inference(clausify,[status(thm)],[f_1822_2]) ).

fof(f_1823_1,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J]) ).

cnf(f_1823_2,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(clausify,[status(thm)],[f_1823_1]) ).

fof(f_1824_1,plain,
    ! [V_y,V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) ),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J]) ).

fof(f_1824_2,plain,
    ! [U_6870,U_6869] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6869),U_6870)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6870))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6869)) ),
    inference(variable_rename,[status(thm)],[f_1824_1]) ).

cnf(f_1824_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6869),U_6870)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6870))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6869)) ),
    inference(clausify,[status(thm)],[f_1824_2]) ).

fof(f_1825_1,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J]) ).

cnf(f_1825_2,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(clausify,[status(thm)],[f_1825_1]) ).

fof(f_1826_1,plain,
    ! [V_B_2,V_t_2,V_D_2] :
      ( ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x))
          | ? [B_xa] :
              ( ? [B_xb] :
                  ( B_x = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) ),
    inference(fof_nnf,[status(thm)],[fact_bset_I8_J]) ).

fof(f_1826_2,plain,
    ! [U_6876,U_6875,U_6874] :
      ( ! [U_6873] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6875),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6873),U_6874)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6875),U_6873))
          | ? [U_6872] :
              ( ? [U_6871] :
                  ( U_6873 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6871),U_6872)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6871),U_6876)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6872),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6874))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6875),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_6876))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6874)) ),
    inference(variable_rename,[status(thm)],[f_1826_1]) ).

fof(f_1826_3,plain,
    ! [U_6876,U_6875,U_6874] :
      ( ! [U_6873] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6875),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6873),U_6874)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6875),U_6873))
          | ( ? [U_6871] :
                ( U_6873 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6871),sK154(U_6876,U_6875,U_6874,U_6873))
                & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6871),U_6876)) )
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK154(U_6876,U_6875,U_6874,U_6873)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6874))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6875),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_6876))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6874)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK154]),skolemize(U_6872,sK154(U_6876,U_6875,U_6874,U_6873))],[f_1826_2]) ).

fof(f_1826_4,plain,
    ! [U_6876,U_6875,U_6874] :
      ( ! [U_6873] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6875),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6873),U_6874)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6875),U_6873))
          | ( U_6873 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK155(U_6876,U_6875,U_6874,U_6873)),sK154(U_6876,U_6875,U_6874,U_6873))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK155(U_6876,U_6875,U_6874,U_6873)),U_6876))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK154(U_6876,U_6875,U_6874,U_6873)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6874))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6875),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_6876))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6874)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK155]),skolemize(U_6871,sK155(U_6876,U_6875,U_6874,U_6873))],[f_1826_3]) ).

cnf(f_1826_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK154(U_6876,U_6875,U_6874,U_6873)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6874)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6875),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6873),U_6874)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6875),U_6873))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6875),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_6876))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6874)) ),
    inference(clausify,[status(thm)],[f_1826_4]) ).

cnf(f_1826_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK155(U_6876,U_6875,U_6874,U_6873)),U_6876))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6875),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6873),U_6874)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6875),U_6873))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6875),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_6876))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6874)) ),
    inference(clausify,[status(thm)],[f_1826_4]) ).

cnf(f_1826_7,plain,
    ( U_6873 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK155(U_6876,U_6875,U_6874,U_6873)),sK154(U_6876,U_6875,U_6874,U_6873))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6875),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6873),U_6874)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6875),U_6873))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6875),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_6876))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6874)) ),
    inference(clausify,[status(thm)],[f_1826_4]) ).

fof(f_1827_1,plain,
    ! [V_A_2,V_t_2,V_D_2] :
      ( ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2)),V_t_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2))
          | ? [B_xa] :
              ( ? [B_xb] :
                  ( B_x = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) ),
    inference(fof_nnf,[status(thm)],[fact_aset_I6_J]) ).

fof(f_1827_2,plain,
    ! [U_6882,U_6881,U_6880] :
      ( ! [U_6879] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6879),U_6880)),U_6881))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6879),U_6881))
          | ? [U_6878] :
              ( ? [U_6877] :
                  ( U_6879 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6877),U_6878)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6877),U_6882)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6878),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6880))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6881),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_6882))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6880)) ),
    inference(variable_rename,[status(thm)],[f_1827_1]) ).

fof(f_1827_3,plain,
    ! [U_6882,U_6881,U_6880] :
      ( ! [U_6879] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6879),U_6880)),U_6881))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6879),U_6881))
          | ( ? [U_6877] :
                ( U_6879 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6877),sK156(U_6882,U_6881,U_6880,U_6879))
                & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6877),U_6882)) )
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK156(U_6882,U_6881,U_6880,U_6879)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6880))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6881),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_6882))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6880)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK156]),skolemize(U_6878,sK156(U_6882,U_6881,U_6880,U_6879))],[f_1827_2]) ).

fof(f_1827_4,plain,
    ! [U_6882,U_6881,U_6880] :
      ( ! [U_6879] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6879),U_6880)),U_6881))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6879),U_6881))
          | ( U_6879 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK157(U_6882,U_6881,U_6880,U_6879)),sK156(U_6882,U_6881,U_6880,U_6879))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK157(U_6882,U_6881,U_6880,U_6879)),U_6882))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK156(U_6882,U_6881,U_6880,U_6879)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6880))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6881),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_6882))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6880)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK157]),skolemize(U_6877,sK157(U_6882,U_6881,U_6880,U_6879))],[f_1827_3]) ).

cnf(f_1827_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK156(U_6882,U_6881,U_6880,U_6879)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6880)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6879),U_6880)),U_6881))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6879),U_6881))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6881),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_6882))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6880)) ),
    inference(clausify,[status(thm)],[f_1827_4]) ).

cnf(f_1827_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK157(U_6882,U_6881,U_6880,U_6879)),U_6882))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6879),U_6880)),U_6881))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6879),U_6881))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6881),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_6882))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6880)) ),
    inference(clausify,[status(thm)],[f_1827_4]) ).

cnf(f_1827_7,plain,
    ( U_6879 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK157(U_6882,U_6881,U_6880,U_6879)),sK156(U_6882,U_6881,U_6880,U_6879))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6879),U_6880)),U_6881))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6879),U_6881))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6881),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_6882))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6880)) ),
    inference(clausify,[status(thm)],[f_1827_4]) ).

fof(f_1828_1,plain,
    ! [V_t_2,V_A_2,V_D_2] :
      ( ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x))
          | ? [B_xa] :
              ( ? [B_xb] :
                  ( B_x = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) ),
    inference(fof_nnf,[status(thm)],[fact_aset_I8_J]) ).

fof(f_1828_2,plain,
    ! [U_6888,U_6887,U_6886] :
      ( ! [U_6885] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6888),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6885),U_6886)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6888),U_6885))
          | ? [U_6884] :
              ( ? [U_6883] :
                  ( U_6885 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6883),U_6884)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6883),U_6887)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6884),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6886))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6886)) ),
    inference(variable_rename,[status(thm)],[f_1828_1]) ).

fof(f_1828_3,plain,
    ! [U_6888,U_6887,U_6886] :
      ( ! [U_6885] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6888),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6885),U_6886)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6888),U_6885))
          | ( ? [U_6883] :
                ( U_6885 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6883),sK158(U_6888,U_6887,U_6886,U_6885))
                & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6883),U_6887)) )
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK158(U_6888,U_6887,U_6886,U_6885)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6886))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6886)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK158]),skolemize(U_6884,sK158(U_6888,U_6887,U_6886,U_6885))],[f_1828_2]) ).

fof(f_1828_4,plain,
    ! [U_6888,U_6887,U_6886] :
      ( ! [U_6885] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6888),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6885),U_6886)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6888),U_6885))
          | ( U_6885 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK159(U_6888,U_6887,U_6886,U_6885)),sK158(U_6888,U_6887,U_6886,U_6885))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK159(U_6888,U_6887,U_6886,U_6885)),U_6887))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK158(U_6888,U_6887,U_6886,U_6885)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6886))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6886)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK159]),skolemize(U_6883,sK159(U_6888,U_6887,U_6886,U_6885))],[f_1828_3]) ).

cnf(f_1828_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK158(U_6888,U_6887,U_6886,U_6885)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6886)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6888),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6885),U_6886)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6888),U_6885))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6886)) ),
    inference(clausify,[status(thm)],[f_1828_4]) ).

cnf(f_1828_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK159(U_6888,U_6887,U_6886,U_6885)),U_6887))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6888),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6885),U_6886)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6888),U_6885))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6886)) ),
    inference(clausify,[status(thm)],[f_1828_4]) ).

cnf(f_1828_7,plain,
    ( U_6885 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK159(U_6888,U_6887,U_6886,U_6885)),sK158(U_6888,U_6887,U_6886,U_6885))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6888),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6885),U_6886)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6888),U_6885))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6886)) ),
    inference(clausify,[status(thm)],[f_1828_4]) ).

fof(f_1829_1,plain,
    ! [V_t_2,V_B_2,V_D_2] :
      ( ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2)),V_t_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2))
          | ? [B_xa] :
              ( ? [B_xb] :
                  ( B_x = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) ),
    inference(fof_nnf,[status(thm)],[fact_bset_I6_J]) ).

fof(f_1829_2,plain,
    ! [U_6894,U_6893,U_6892] :
      ( ! [U_6891] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6891),U_6892)),U_6894))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6891),U_6894))
          | ? [U_6890] :
              ( ? [U_6889] :
                  ( U_6891 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6889),U_6890)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6889),U_6893)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6890),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6892))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6892)) ),
    inference(variable_rename,[status(thm)],[f_1829_1]) ).

fof(f_1829_3,plain,
    ! [U_6894,U_6893,U_6892] :
      ( ! [U_6891] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6891),U_6892)),U_6894))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6891),U_6894))
          | ( ? [U_6889] :
                ( U_6891 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6889),sK160(U_6894,U_6893,U_6892,U_6891))
                & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6889),U_6893)) )
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK160(U_6894,U_6893,U_6892,U_6891)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6892))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6892)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK160]),skolemize(U_6890,sK160(U_6894,U_6893,U_6892,U_6891))],[f_1829_2]) ).

fof(f_1829_4,plain,
    ! [U_6894,U_6893,U_6892] :
      ( ! [U_6891] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6891),U_6892)),U_6894))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6891),U_6894))
          | ( U_6891 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK161(U_6894,U_6893,U_6892,U_6891)),sK160(U_6894,U_6893,U_6892,U_6891))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK161(U_6894,U_6893,U_6892,U_6891)),U_6893))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK160(U_6894,U_6893,U_6892,U_6891)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6892))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6892)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK161]),skolemize(U_6889,sK161(U_6894,U_6893,U_6892,U_6891))],[f_1829_3]) ).

cnf(f_1829_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK160(U_6894,U_6893,U_6892,U_6891)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6892)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6891),U_6892)),U_6894))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6891),U_6894))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6892)) ),
    inference(clausify,[status(thm)],[f_1829_4]) ).

cnf(f_1829_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK161(U_6894,U_6893,U_6892,U_6891)),U_6893))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6891),U_6892)),U_6894))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6891),U_6894))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6892)) ),
    inference(clausify,[status(thm)],[f_1829_4]) ).

cnf(f_1829_7,plain,
    ( U_6891 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK161(U_6894,U_6893,U_6892,U_6891)),sK160(U_6894,U_6893,U_6892,U_6891))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6891),U_6892)),U_6894))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6891),U_6894))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6892)) ),
    inference(clausify,[status(thm)],[f_1829_4]) ).

fof(f_1830_1,plain,
    ! [V_P_2,V_d_2] :
      ( ( ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
          | ! [B_x] :
              ( ~ hBOOL(hAPP(V_P_2,B_x))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_d_2))) ) )
        & ( ? [B_x] :
              ( hBOOL(hAPP(V_P_2,B_x))
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_d_2))) )
          | ! [B_x1] : ~ hBOOL(hAPP(V_P_2,B_x1)) ) )
      | ? [B_x,B_k] :
          ( ( ~ hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B_k),V_d_2)))) )
          | ( ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B_k),V_d_2))))
            & hBOOL(hAPP(V_P_2,B_x)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) ),
    inference(fof_nnf,[status(thm)],[fact_periodic__finite__ex]) ).

fof(f_1830_2,plain,
    ! [U_6902,U_6901] :
      ( ( ( ? [U_6900] : hBOOL(hAPP(U_6902,U_6900))
          | ! [U_6899] :
              ( ~ hBOOL(hAPP(U_6902,U_6899))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6899),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6901))) ) )
        & ( ? [U_6898] :
              ( hBOOL(hAPP(U_6902,U_6898))
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6898),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6901))) )
          | ! [U_6897] : ~ hBOOL(hAPP(U_6902,U_6897)) ) )
      | ? [U_6896,U_6895] :
          ( ( ~ hBOOL(hAPP(U_6902,U_6896))
            & hBOOL(hAPP(U_6902,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6896),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6895),U_6901)))) )
          | ( ~ hBOOL(hAPP(U_6902,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6896),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6895),U_6901))))
            & hBOOL(hAPP(U_6902,U_6896)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6901)) ),
    inference(variable_rename,[status(thm)],[f_1830_1]) ).

fof(f_1830_3,plain,
    ! [U_6902,U_6901] :
      ( ( ( ? [U_6900] : hBOOL(hAPP(U_6902,U_6900))
          | ! [U_6899] :
              ( ~ hBOOL(hAPP(U_6902,U_6899))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6899),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6901))) ) )
        & ( ? [U_6898] :
              ( hBOOL(hAPP(U_6902,U_6898))
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6898),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6901))) )
          | ! [U_6897] : ~ hBOOL(hAPP(U_6902,U_6897)) ) )
      | ? [U_6906] :
          ( ? [U_6904] : hBOOL(hAPP(U_6902,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6906),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6904),U_6901))))
          & ~ hBOOL(hAPP(U_6902,U_6906)) )
      | ? [U_6905] :
          ( ? [U_6903] : ~ hBOOL(hAPP(U_6902,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6905),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6903),U_6901))))
          & hBOOL(hAPP(U_6902,U_6905)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6901)) ),
    inference(miniscope,[status(thm)],[f_1830_2]) ).

fof(f_1830_4,plain,
    ! [U_6902,U_6901] :
      ( ( ( ? [U_6900] : hBOOL(hAPP(U_6902,U_6900))
          | ! [U_6899] :
              ( ~ hBOOL(hAPP(U_6902,U_6899))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6899),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6901))) ) )
        & ( ? [U_6898] :
              ( hBOOL(hAPP(U_6902,U_6898))
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6898),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6901))) )
          | ! [U_6897] : ~ hBOOL(hAPP(U_6902,U_6897)) ) )
      | ? [U_6906] :
          ( ? [U_6904] : hBOOL(hAPP(U_6902,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6906),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6904),U_6901))))
          & ~ hBOOL(hAPP(U_6902,U_6906)) )
      | ( ? [U_6903] : ~ hBOOL(hAPP(U_6902,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK162(U_6902,U_6901)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6903),U_6901))))
        & hBOOL(hAPP(U_6902,sK162(U_6902,U_6901))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6901)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK162]),skolemize(U_6905,sK162(U_6902,U_6901))],[f_1830_3]) ).

fof(f_1830_5,plain,
    ! [U_6902,U_6901] :
      ( ( ( ? [U_6900] : hBOOL(hAPP(U_6902,U_6900))
          | ! [U_6899] :
              ( ~ hBOOL(hAPP(U_6902,U_6899))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6899),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6901))) ) )
        & ( ? [U_6898] :
              ( hBOOL(hAPP(U_6902,U_6898))
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6898),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6901))) )
          | ! [U_6897] : ~ hBOOL(hAPP(U_6902,U_6897)) ) )
      | ? [U_6906] :
          ( ? [U_6904] : hBOOL(hAPP(U_6902,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6906),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6904),U_6901))))
          & ~ hBOOL(hAPP(U_6902,U_6906)) )
      | ( ~ hBOOL(hAPP(U_6902,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK162(U_6902,U_6901)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK163(U_6902,U_6901)),U_6901))))
        & hBOOL(hAPP(U_6902,sK162(U_6902,U_6901))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6901)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK163]),skolemize(U_6903,sK163(U_6902,U_6901))],[f_1830_4]) ).

fof(f_1830_6,plain,
    ! [U_6902,U_6901] :
      ( ( ( ? [U_6900] : hBOOL(hAPP(U_6902,U_6900))
          | ! [U_6899] :
              ( ~ hBOOL(hAPP(U_6902,U_6899))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6899),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6901))) ) )
        & ( ? [U_6898] :
              ( hBOOL(hAPP(U_6902,U_6898))
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6898),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6901))) )
          | ! [U_6897] : ~ hBOOL(hAPP(U_6902,U_6897)) ) )
      | ( ? [U_6904] : hBOOL(hAPP(U_6902,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK164(U_6902,U_6901)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6904),U_6901))))
        & ~ hBOOL(hAPP(U_6902,sK164(U_6902,U_6901))) )
      | ( ~ hBOOL(hAPP(U_6902,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK162(U_6902,U_6901)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK163(U_6902,U_6901)),U_6901))))
        & hBOOL(hAPP(U_6902,sK162(U_6902,U_6901))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6901)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK164]),skolemize(U_6906,sK164(U_6902,U_6901))],[f_1830_5]) ).

fof(f_1830_7,plain,
    ! [U_6902,U_6901] :
      ( ( ( ? [U_6900] : hBOOL(hAPP(U_6902,U_6900))
          | ! [U_6899] :
              ( ~ hBOOL(hAPP(U_6902,U_6899))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6899),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6901))) ) )
        & ( ? [U_6898] :
              ( hBOOL(hAPP(U_6902,U_6898))
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6898),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6901))) )
          | ! [U_6897] : ~ hBOOL(hAPP(U_6902,U_6897)) ) )
      | ( hBOOL(hAPP(U_6902,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK164(U_6902,U_6901)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK165(U_6902,U_6901)),U_6901))))
        & ~ hBOOL(hAPP(U_6902,sK164(U_6902,U_6901))) )
      | ( ~ hBOOL(hAPP(U_6902,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK162(U_6902,U_6901)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK163(U_6902,U_6901)),U_6901))))
        & hBOOL(hAPP(U_6902,sK162(U_6902,U_6901))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6901)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK165]),skolemize(U_6904,sK165(U_6902,U_6901))],[f_1830_6]) ).

fof(f_1830_8,plain,
    ! [U_6902,U_6901] :
      ( ( ( ? [U_6900] : hBOOL(hAPP(U_6902,U_6900))
          | ! [U_6899] :
              ( ~ hBOOL(hAPP(U_6902,U_6899))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6899),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6901))) ) )
        & ( ( hBOOL(hAPP(U_6902,sK166(U_6902,U_6901)))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK166(U_6902,U_6901)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6901))) )
          | ! [U_6897] : ~ hBOOL(hAPP(U_6902,U_6897)) ) )
      | ( hBOOL(hAPP(U_6902,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK164(U_6902,U_6901)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK165(U_6902,U_6901)),U_6901))))
        & ~ hBOOL(hAPP(U_6902,sK164(U_6902,U_6901))) )
      | ( ~ hBOOL(hAPP(U_6902,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK162(U_6902,U_6901)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK163(U_6902,U_6901)),U_6901))))
        & hBOOL(hAPP(U_6902,sK162(U_6902,U_6901))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6901)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK166]),skolemize(U_6898,sK166(U_6902,U_6901))],[f_1830_7]) ).

fof(f_1830_9,plain,
    ! [U_6902,U_6901] :
      ( ( ( hBOOL(hAPP(U_6902,sK167(U_6902,U_6901)))
          | ! [U_6899] :
              ( ~ hBOOL(hAPP(U_6902,U_6899))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6899),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6901))) ) )
        & ( ( hBOOL(hAPP(U_6902,sK166(U_6902,U_6901)))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK166(U_6902,U_6901)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6901))) )
          | ! [U_6897] : ~ hBOOL(hAPP(U_6902,U_6897)) ) )
      | ( hBOOL(hAPP(U_6902,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK164(U_6902,U_6901)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK165(U_6902,U_6901)),U_6901))))
        & ~ hBOOL(hAPP(U_6902,sK164(U_6902,U_6901))) )
      | ( ~ hBOOL(hAPP(U_6902,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK162(U_6902,U_6901)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK163(U_6902,U_6901)),U_6901))))
        & hBOOL(hAPP(U_6902,sK162(U_6902,U_6901))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6901)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK167]),skolemize(U_6900,sK167(U_6902,U_6901))],[f_1830_8]) ).

cnf(f_1830_10,plain,
    ( ~ hBOOL(hAPP(U_6902,sK164(U_6902,U_6901)))
    | hBOOL(hAPP(U_6902,sK162(U_6902,U_6901)))
    | hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK166(U_6902,U_6901)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6901)))
    | ~ hBOOL(hAPP(U_6902,U_6897))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6901)) ),
    inference(clausify,[status(thm)],[f_1830_9]) ).

cnf(f_1830_11,plain,
    ( hBOOL(hAPP(U_6902,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK164(U_6902,U_6901)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK165(U_6902,U_6901)),U_6901))))
    | hBOOL(hAPP(U_6902,sK162(U_6902,U_6901)))
    | hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK166(U_6902,U_6901)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6901)))
    | ~ hBOOL(hAPP(U_6902,U_6897))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6901)) ),
    inference(clausify,[status(thm)],[f_1830_9]) ).

cnf(f_1830_12,plain,
    ( ~ hBOOL(hAPP(U_6902,sK164(U_6902,U_6901)))
    | hBOOL(hAPP(U_6902,sK162(U_6902,U_6901)))
    | hBOOL(hAPP(U_6902,sK166(U_6902,U_6901)))
    | ~ hBOOL(hAPP(U_6902,U_6897))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6901)) ),
    inference(clausify,[status(thm)],[f_1830_9]) ).

cnf(f_1830_13,plain,
    ( hBOOL(hAPP(U_6902,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK164(U_6902,U_6901)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK165(U_6902,U_6901)),U_6901))))
    | hBOOL(hAPP(U_6902,sK162(U_6902,U_6901)))
    | hBOOL(hAPP(U_6902,sK166(U_6902,U_6901)))
    | ~ hBOOL(hAPP(U_6902,U_6897))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6901)) ),
    inference(clausify,[status(thm)],[f_1830_9]) ).

cnf(f_1830_14,plain,
    ( ~ hBOOL(hAPP(U_6902,sK164(U_6902,U_6901)))
    | ~ hBOOL(hAPP(U_6902,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK162(U_6902,U_6901)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK163(U_6902,U_6901)),U_6901))))
    | hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK166(U_6902,U_6901)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6901)))
    | ~ hBOOL(hAPP(U_6902,U_6897))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6901)) ),
    inference(clausify,[status(thm)],[f_1830_9]) ).

cnf(f_1830_15,plain,
    ( hBOOL(hAPP(U_6902,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK164(U_6902,U_6901)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK165(U_6902,U_6901)),U_6901))))
    | ~ hBOOL(hAPP(U_6902,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK162(U_6902,U_6901)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK163(U_6902,U_6901)),U_6901))))
    | hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK166(U_6902,U_6901)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6901)))
    | ~ hBOOL(hAPP(U_6902,U_6897))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6901)) ),
    inference(clausify,[status(thm)],[f_1830_9]) ).

cnf(f_1830_16,plain,
    ( ~ hBOOL(hAPP(U_6902,sK164(U_6902,U_6901)))
    | ~ hBOOL(hAPP(U_6902,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK162(U_6902,U_6901)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK163(U_6902,U_6901)),U_6901))))
    | hBOOL(hAPP(U_6902,sK166(U_6902,U_6901)))
    | ~ hBOOL(hAPP(U_6902,U_6897))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6901)) ),
    inference(clausify,[status(thm)],[f_1830_9]) ).

cnf(f_1830_17,plain,
    ( hBOOL(hAPP(U_6902,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK164(U_6902,U_6901)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK165(U_6902,U_6901)),U_6901))))
    | ~ hBOOL(hAPP(U_6902,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK162(U_6902,U_6901)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK163(U_6902,U_6901)),U_6901))))
    | hBOOL(hAPP(U_6902,sK166(U_6902,U_6901)))
    | ~ hBOOL(hAPP(U_6902,U_6897))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6901)) ),
    inference(clausify,[status(thm)],[f_1830_9]) ).

cnf(f_1830_18,plain,
    ( ~ hBOOL(hAPP(U_6902,sK164(U_6902,U_6901)))
    | hBOOL(hAPP(U_6902,sK162(U_6902,U_6901)))
    | hBOOL(hAPP(U_6902,sK167(U_6902,U_6901)))
    | ~ hBOOL(hAPP(U_6902,U_6899))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6899),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6901)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6901)) ),
    inference(clausify,[status(thm)],[f_1830_9]) ).

cnf(f_1830_19,plain,
    ( hBOOL(hAPP(U_6902,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK164(U_6902,U_6901)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK165(U_6902,U_6901)),U_6901))))
    | hBOOL(hAPP(U_6902,sK162(U_6902,U_6901)))
    | hBOOL(hAPP(U_6902,sK167(U_6902,U_6901)))
    | ~ hBOOL(hAPP(U_6902,U_6899))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6899),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6901)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6901)) ),
    inference(clausify,[status(thm)],[f_1830_9]) ).

cnf(f_1830_20,plain,
    ( ~ hBOOL(hAPP(U_6902,sK164(U_6902,U_6901)))
    | ~ hBOOL(hAPP(U_6902,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK162(U_6902,U_6901)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK163(U_6902,U_6901)),U_6901))))
    | hBOOL(hAPP(U_6902,sK167(U_6902,U_6901)))
    | ~ hBOOL(hAPP(U_6902,U_6899))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6899),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6901)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6901)) ),
    inference(clausify,[status(thm)],[f_1830_9]) ).

cnf(f_1830_21,plain,
    ( hBOOL(hAPP(U_6902,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK164(U_6902,U_6901)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK165(U_6902,U_6901)),U_6901))))
    | ~ hBOOL(hAPP(U_6902,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK162(U_6902,U_6901)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK163(U_6902,U_6901)),U_6901))))
    | hBOOL(hAPP(U_6902,sK167(U_6902,U_6901)))
    | ~ hBOOL(hAPP(U_6902,U_6899))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6899),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6901)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6901)) ),
    inference(clausify,[status(thm)],[f_1830_9]) ).

fof(f_1831_1,plain,
    ! [V_B_2,V_t_2,V_D_2] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2
      | ? [B_x] :
          ( ? [B_xa] :
              ( V_t_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xa),B_x)
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_B_2)) )
          & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) ),
    inference(fof_nnf,[status(thm)],[fact_bset_I3_J]) ).

fof(f_1831_2,plain,
    ! [U_6911,U_6910,U_6909] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6910),U_6909) = U_6910
      | ? [U_6908] :
          ( ? [U_6907] :
              ( U_6910 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6907),U_6908)
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6907),U_6911)) )
          & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6908),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6909))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6910),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_6911))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6909)) ),
    inference(variable_rename,[status(thm)],[f_1831_1]) ).

fof(f_1831_3,plain,
    ! [U_6911,U_6910,U_6909] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6910),U_6909) = U_6910
      | ( ? [U_6907] :
            ( U_6910 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6907),sK168(U_6911,U_6910,U_6909))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6907),U_6911)) )
        & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK168(U_6911,U_6910,U_6909)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6909))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6910),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_6911))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6909)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK168]),skolemize(U_6908,sK168(U_6911,U_6910,U_6909))],[f_1831_2]) ).

fof(f_1831_4,plain,
    ! [U_6911,U_6910,U_6909] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6910),U_6909) = U_6910
      | ( U_6910 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK169(U_6911,U_6910,U_6909)),sK168(U_6911,U_6910,U_6909))
        & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK169(U_6911,U_6910,U_6909)),U_6911))
        & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK168(U_6911,U_6910,U_6909)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6909))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6910),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_6911))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6909)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK169]),skolemize(U_6907,sK169(U_6911,U_6910,U_6909))],[f_1831_3]) ).

cnf(f_1831_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK168(U_6911,U_6910,U_6909)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6909)))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6910),U_6909) = U_6910
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6910),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_6911))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6909)) ),
    inference(clausify,[status(thm)],[f_1831_4]) ).

cnf(f_1831_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK169(U_6911,U_6910,U_6909)),U_6911))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6910),U_6909) = U_6910
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6910),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_6911))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6909)) ),
    inference(clausify,[status(thm)],[f_1831_4]) ).

cnf(f_1831_7,plain,
    ( U_6910 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK169(U_6911,U_6910,U_6909)),sK168(U_6911,U_6910,U_6909))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6910),U_6909) = U_6910
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6910),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_6911))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6909)) ),
    inference(clausify,[status(thm)],[f_1831_4]) ).

fof(f_1832_1,plain,
    ! [V_A_2,V_t_2,V_D_2] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2
      | ? [B_x] :
          ( ? [B_xa] :
              ( V_t_2 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xa),B_x)
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_A_2)) )
          & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) ),
    inference(fof_nnf,[status(thm)],[fact_aset_I3_J]) ).

fof(f_1832_2,plain,
    ! [U_6916,U_6915,U_6914] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6915),U_6914) = U_6915
      | ? [U_6913] :
          ( ? [U_6912] :
              ( U_6915 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6912),U_6913)
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6912),U_6916)) )
          & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6913),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6914))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6915),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_6916))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6914)) ),
    inference(variable_rename,[status(thm)],[f_1832_1]) ).

fof(f_1832_3,plain,
    ! [U_6916,U_6915,U_6914] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6915),U_6914) = U_6915
      | ( ? [U_6912] :
            ( U_6915 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6912),sK170(U_6916,U_6915,U_6914))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6912),U_6916)) )
        & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK170(U_6916,U_6915,U_6914)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6914))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6915),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_6916))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6914)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK170]),skolemize(U_6913,sK170(U_6916,U_6915,U_6914))],[f_1832_2]) ).

fof(f_1832_4,plain,
    ! [U_6916,U_6915,U_6914] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6915),U_6914) = U_6915
      | ( U_6915 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK171(U_6916,U_6915,U_6914)),sK170(U_6916,U_6915,U_6914))
        & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK171(U_6916,U_6915,U_6914)),U_6916))
        & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK170(U_6916,U_6915,U_6914)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6914))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6915),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_6916))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6914)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK171]),skolemize(U_6912,sK171(U_6916,U_6915,U_6914))],[f_1832_3]) ).

cnf(f_1832_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK170(U_6916,U_6915,U_6914)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6914)))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6915),U_6914) = U_6915
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6915),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_6916))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6914)) ),
    inference(clausify,[status(thm)],[f_1832_4]) ).

cnf(f_1832_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK171(U_6916,U_6915,U_6914)),U_6916))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6915),U_6914) = U_6915
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6915),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_6916))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6914)) ),
    inference(clausify,[status(thm)],[f_1832_4]) ).

cnf(f_1832_7,plain,
    ( U_6915 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK171(U_6916,U_6915,U_6914)),sK170(U_6916,U_6915,U_6914))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6915),U_6914) = U_6915
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6915),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_6916))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6914)) ),
    inference(clausify,[status(thm)],[f_1832_4]) ).

fof(f_1833_1,plain,
    ! [V_A_2,V_t_2,V_D_2] :
      ( ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2)),V_t_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2))
          | ? [B_xa] :
              ( ? [B_xb] :
                  ( B_x = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) ),
    inference(fof_nnf,[status(thm)],[fact_aset_I5_J]) ).

fof(f_1833_2,plain,
    ! [U_6922,U_6921,U_6920] :
      ( ! [U_6919] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6919),U_6920)),U_6921))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6919),U_6921))
          | ? [U_6918] :
              ( ? [U_6917] :
                  ( U_6919 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6917),U_6918)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6917),U_6922)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6918),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6920))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6921),U_6922))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6920)) ),
    inference(variable_rename,[status(thm)],[f_1833_1]) ).

fof(f_1833_3,plain,
    ! [U_6922,U_6921,U_6920] :
      ( ! [U_6919] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6919),U_6920)),U_6921))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6919),U_6921))
          | ( ? [U_6917] :
                ( U_6919 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6917),sK172(U_6922,U_6921,U_6920,U_6919))
                & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6917),U_6922)) )
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK172(U_6922,U_6921,U_6920,U_6919)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6920))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6921),U_6922))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6920)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK172]),skolemize(U_6918,sK172(U_6922,U_6921,U_6920,U_6919))],[f_1833_2]) ).

fof(f_1833_4,plain,
    ! [U_6922,U_6921,U_6920] :
      ( ! [U_6919] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6919),U_6920)),U_6921))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6919),U_6921))
          | ( U_6919 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK173(U_6922,U_6921,U_6920,U_6919)),sK172(U_6922,U_6921,U_6920,U_6919))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK173(U_6922,U_6921,U_6920,U_6919)),U_6922))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK172(U_6922,U_6921,U_6920,U_6919)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6920))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6921),U_6922))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6920)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK173]),skolemize(U_6917,sK173(U_6922,U_6921,U_6920,U_6919))],[f_1833_3]) ).

cnf(f_1833_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK172(U_6922,U_6921,U_6920,U_6919)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6920)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6919),U_6920)),U_6921))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6919),U_6921))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6921),U_6922))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6920)) ),
    inference(clausify,[status(thm)],[f_1833_4]) ).

cnf(f_1833_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK173(U_6922,U_6921,U_6920,U_6919)),U_6922))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6919),U_6920)),U_6921))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6919),U_6921))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6921),U_6922))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6920)) ),
    inference(clausify,[status(thm)],[f_1833_4]) ).

cnf(f_1833_7,plain,
    ( U_6919 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK173(U_6922,U_6921,U_6920,U_6919)),sK172(U_6922,U_6921,U_6920,U_6919))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6919),U_6920)),U_6921))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6919),U_6921))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6921),U_6922))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6920)) ),
    inference(clausify,[status(thm)],[f_1833_4]) ).

fof(f_1834_1,plain,
    ! [V_B_2,V_t_2,V_D_2] :
      ( ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x))
          | ? [B_xa] :
              ( ? [B_xb] :
                  ( B_x = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) ),
    inference(fof_nnf,[status(thm)],[fact_bset_I7_J]) ).

fof(f_1834_2,plain,
    ! [U_6928,U_6927,U_6926] :
      ( ! [U_6925] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6927),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6925),U_6926)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6927),U_6925))
          | ? [U_6924] :
              ( ? [U_6923] :
                  ( U_6925 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6923),U_6924)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6923),U_6928)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6924),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6926))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6927),U_6928))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6926)) ),
    inference(variable_rename,[status(thm)],[f_1834_1]) ).

fof(f_1834_3,plain,
    ! [U_6928,U_6927,U_6926] :
      ( ! [U_6925] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6927),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6925),U_6926)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6927),U_6925))
          | ( ? [U_6923] :
                ( U_6925 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6923),sK174(U_6928,U_6927,U_6926,U_6925))
                & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6923),U_6928)) )
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK174(U_6928,U_6927,U_6926,U_6925)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6926))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6927),U_6928))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6926)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK174]),skolemize(U_6924,sK174(U_6928,U_6927,U_6926,U_6925))],[f_1834_2]) ).

fof(f_1834_4,plain,
    ! [U_6928,U_6927,U_6926] :
      ( ! [U_6925] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6927),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6925),U_6926)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6927),U_6925))
          | ( U_6925 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK175(U_6928,U_6927,U_6926,U_6925)),sK174(U_6928,U_6927,U_6926,U_6925))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK175(U_6928,U_6927,U_6926,U_6925)),U_6928))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK174(U_6928,U_6927,U_6926,U_6925)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6926))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6927),U_6928))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6926)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK175]),skolemize(U_6923,sK175(U_6928,U_6927,U_6926,U_6925))],[f_1834_3]) ).

cnf(f_1834_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK174(U_6928,U_6927,U_6926,U_6925)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6926)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6927),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6925),U_6926)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6927),U_6925))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6927),U_6928))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6926)) ),
    inference(clausify,[status(thm)],[f_1834_4]) ).

cnf(f_1834_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK175(U_6928,U_6927,U_6926,U_6925)),U_6928))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6927),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6925),U_6926)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6927),U_6925))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6927),U_6928))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6926)) ),
    inference(clausify,[status(thm)],[f_1834_4]) ).

cnf(f_1834_7,plain,
    ( U_6925 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK175(U_6928,U_6927,U_6926,U_6925)),sK174(U_6928,U_6927,U_6926,U_6925))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6927),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6925),U_6926)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6927),U_6925))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6927),U_6928))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6926)) ),
    inference(clausify,[status(thm)],[f_1834_4]) ).

fof(f_1835_1,plain,
    ! [V_B_2,V_t_2,V_D_2] :
      ( ! [B_x] :
          ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2) != V_t_2
          | B_x = V_t_2
          | ? [B_xa] :
              ( ? [B_xb] :
                  ( B_x = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) ),
    inference(fof_nnf,[status(thm)],[fact_bset_I4_J]) ).

fof(f_1835_2,plain,
    ! [U_6934,U_6933,U_6932] :
      ( ! [U_6931] :
          ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6931),U_6932) != U_6933
          | U_6931 = U_6933
          | ? [U_6930] :
              ( ? [U_6929] :
                  ( U_6931 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6929),U_6930)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6929),U_6934)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6930),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6932))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6933),U_6934))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6932)) ),
    inference(variable_rename,[status(thm)],[f_1835_1]) ).

fof(f_1835_3,plain,
    ! [U_6934,U_6933,U_6932] :
      ( ! [U_6931] :
          ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6931),U_6932) != U_6933
          | U_6931 = U_6933
          | ( ? [U_6929] :
                ( U_6931 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6929),sK176(U_6934,U_6933,U_6932,U_6931))
                & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6929),U_6934)) )
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK176(U_6934,U_6933,U_6932,U_6931)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6932))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6933),U_6934))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6932)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK176]),skolemize(U_6930,sK176(U_6934,U_6933,U_6932,U_6931))],[f_1835_2]) ).

fof(f_1835_4,plain,
    ! [U_6934,U_6933,U_6932] :
      ( ! [U_6931] :
          ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6931),U_6932) != U_6933
          | U_6931 = U_6933
          | ( U_6931 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK177(U_6934,U_6933,U_6932,U_6931)),sK176(U_6934,U_6933,U_6932,U_6931))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK177(U_6934,U_6933,U_6932,U_6931)),U_6934))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK176(U_6934,U_6933,U_6932,U_6931)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6932))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6933),U_6934))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6932)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK177]),skolemize(U_6929,sK177(U_6934,U_6933,U_6932,U_6931))],[f_1835_3]) ).

cnf(f_1835_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK176(U_6934,U_6933,U_6932,U_6931)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6932)))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6931),U_6932) != U_6933
    | U_6931 = U_6933
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6933),U_6934))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6932)) ),
    inference(clausify,[status(thm)],[f_1835_4]) ).

cnf(f_1835_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK177(U_6934,U_6933,U_6932,U_6931)),U_6934))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6931),U_6932) != U_6933
    | U_6931 = U_6933
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6933),U_6934))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6932)) ),
    inference(clausify,[status(thm)],[f_1835_4]) ).

cnf(f_1835_7,plain,
    ( U_6931 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK177(U_6934,U_6933,U_6932,U_6931)),sK176(U_6934,U_6933,U_6932,U_6931))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6931),U_6932) != U_6933
    | U_6931 = U_6933
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6933),U_6934))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6932)) ),
    inference(clausify,[status(thm)],[f_1835_4]) ).

fof(f_1836_1,plain,
    ! [V_A_2,V_t_2,V_D_2] :
      ( ! [B_x] :
          ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2) != V_t_2
          | B_x = V_t_2
          | ? [B_xa] :
              ( ? [B_xb] :
                  ( B_x = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) ),
    inference(fof_nnf,[status(thm)],[fact_aset_I4_J]) ).

fof(f_1836_2,plain,
    ! [U_6940,U_6939,U_6938] :
      ( ! [U_6937] :
          ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6937),U_6938) != U_6939
          | U_6937 = U_6939
          | ? [U_6936] :
              ( ? [U_6935] :
                  ( U_6937 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6935),U_6936)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6935),U_6940)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6936),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6938))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6939),U_6940))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6938)) ),
    inference(variable_rename,[status(thm)],[f_1836_1]) ).

fof(f_1836_3,plain,
    ! [U_6940,U_6939,U_6938] :
      ( ! [U_6937] :
          ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6937),U_6938) != U_6939
          | U_6937 = U_6939
          | ( ? [U_6935] :
                ( U_6937 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6935),sK178(U_6940,U_6939,U_6938,U_6937))
                & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6935),U_6940)) )
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK178(U_6940,U_6939,U_6938,U_6937)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6938))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6939),U_6940))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6938)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK178]),skolemize(U_6936,sK178(U_6940,U_6939,U_6938,U_6937))],[f_1836_2]) ).

fof(f_1836_4,plain,
    ! [U_6940,U_6939,U_6938] :
      ( ! [U_6937] :
          ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6937),U_6938) != U_6939
          | U_6937 = U_6939
          | ( U_6937 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK179(U_6940,U_6939,U_6938,U_6937)),sK178(U_6940,U_6939,U_6938,U_6937))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK179(U_6940,U_6939,U_6938,U_6937)),U_6940))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK178(U_6940,U_6939,U_6938,U_6937)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6938))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6939),U_6940))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6938)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK179]),skolemize(U_6935,sK179(U_6940,U_6939,U_6938,U_6937))],[f_1836_3]) ).

cnf(f_1836_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK178(U_6940,U_6939,U_6938,U_6937)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6938)))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6937),U_6938) != U_6939
    | U_6937 = U_6939
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6939),U_6940))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6938)) ),
    inference(clausify,[status(thm)],[f_1836_4]) ).

cnf(f_1836_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK179(U_6940,U_6939,U_6938,U_6937)),U_6940))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6937),U_6938) != U_6939
    | U_6937 = U_6939
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6939),U_6940))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6938)) ),
    inference(clausify,[status(thm)],[f_1836_4]) ).

cnf(f_1836_7,plain,
    ( U_6937 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK179(U_6940,U_6939,U_6938,U_6937)),sK178(U_6940,U_6939,U_6938,U_6937))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6937),U_6938) != U_6939
    | U_6937 = U_6939
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6939),U_6940))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6938)) ),
    inference(clausify,[status(thm)],[f_1836_4]) ).

fof(f_1837_1,plain,
    ! [V_t_2,V_A_2,V_D_2] :
      ( ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x))
          | ? [B_xa] :
              ( ? [B_xb] :
                  ( B_x = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) ),
    inference(fof_nnf,[status(thm)],[fact_aset_I7_J]) ).

fof(f_1837_2,plain,
    ! [U_6946,U_6945,U_6944] :
      ( ! [U_6943] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6946),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6943),U_6944)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6946),U_6943))
          | ? [U_6942] :
              ( ? [U_6941] :
                  ( U_6943 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6941),U_6942)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6941),U_6945)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6942),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6944))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6944)) ),
    inference(variable_rename,[status(thm)],[f_1837_1]) ).

fof(f_1837_3,plain,
    ! [U_6946,U_6945,U_6944] :
      ( ! [U_6943] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6946),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6943),U_6944)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6946),U_6943))
          | ( ? [U_6941] :
                ( U_6943 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6941),sK180(U_6946,U_6945,U_6944,U_6943))
                & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6941),U_6945)) )
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK180(U_6946,U_6945,U_6944,U_6943)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6944))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6944)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK180]),skolemize(U_6942,sK180(U_6946,U_6945,U_6944,U_6943))],[f_1837_2]) ).

fof(f_1837_4,plain,
    ! [U_6946,U_6945,U_6944] :
      ( ! [U_6943] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6946),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6943),U_6944)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6946),U_6943))
          | ( U_6943 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK181(U_6946,U_6945,U_6944,U_6943)),sK180(U_6946,U_6945,U_6944,U_6943))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK181(U_6946,U_6945,U_6944,U_6943)),U_6945))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK180(U_6946,U_6945,U_6944,U_6943)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6944))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6944)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK181]),skolemize(U_6941,sK181(U_6946,U_6945,U_6944,U_6943))],[f_1837_3]) ).

cnf(f_1837_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK180(U_6946,U_6945,U_6944,U_6943)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6944)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6946),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6943),U_6944)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6946),U_6943))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6944)) ),
    inference(clausify,[status(thm)],[f_1837_4]) ).

cnf(f_1837_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK181(U_6946,U_6945,U_6944,U_6943)),U_6945))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6946),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6943),U_6944)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6946),U_6943))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6944)) ),
    inference(clausify,[status(thm)],[f_1837_4]) ).

cnf(f_1837_7,plain,
    ( U_6943 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK181(U_6946,U_6945,U_6944,U_6943)),sK180(U_6946,U_6945,U_6944,U_6943))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6946),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6943),U_6944)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6946),U_6943))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6944)) ),
    inference(clausify,[status(thm)],[f_1837_4]) ).

fof(f_1838_1,plain,
    ! [V_t_2,V_B_2,V_D_2] :
      ( ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2)),V_t_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2))
          | ? [B_xa] :
              ( ? [B_xb] :
                  ( B_x = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) ),
    inference(fof_nnf,[status(thm)],[fact_bset_I5_J]) ).

fof(f_1838_2,plain,
    ! [U_6952,U_6951,U_6950] :
      ( ! [U_6949] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6949),U_6950)),U_6952))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6949),U_6952))
          | ? [U_6948] :
              ( ? [U_6947] :
                  ( U_6949 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6947),U_6948)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6947),U_6951)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6948),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6950))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6950)) ),
    inference(variable_rename,[status(thm)],[f_1838_1]) ).

fof(f_1838_3,plain,
    ! [U_6952,U_6951,U_6950] :
      ( ! [U_6949] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6949),U_6950)),U_6952))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6949),U_6952))
          | ( ? [U_6947] :
                ( U_6949 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6947),sK182(U_6952,U_6951,U_6950,U_6949))
                & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6947),U_6951)) )
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK182(U_6952,U_6951,U_6950,U_6949)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6950))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6950)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK182]),skolemize(U_6948,sK182(U_6952,U_6951,U_6950,U_6949))],[f_1838_2]) ).

fof(f_1838_4,plain,
    ! [U_6952,U_6951,U_6950] :
      ( ! [U_6949] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6949),U_6950)),U_6952))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6949),U_6952))
          | ( U_6949 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK183(U_6952,U_6951,U_6950,U_6949)),sK182(U_6952,U_6951,U_6950,U_6949))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK183(U_6952,U_6951,U_6950,U_6949)),U_6951))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK182(U_6952,U_6951,U_6950,U_6949)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6950))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6950)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK183]),skolemize(U_6947,sK183(U_6952,U_6951,U_6950,U_6949))],[f_1838_3]) ).

cnf(f_1838_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK182(U_6952,U_6951,U_6950,U_6949)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6950)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6949),U_6950)),U_6952))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6949),U_6952))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6950)) ),
    inference(clausify,[status(thm)],[f_1838_4]) ).

cnf(f_1838_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK183(U_6952,U_6951,U_6950,U_6949)),U_6951))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6949),U_6950)),U_6952))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6949),U_6952))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6950)) ),
    inference(clausify,[status(thm)],[f_1838_4]) ).

cnf(f_1838_7,plain,
    ( U_6949 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK183(U_6952,U_6951,U_6950,U_6949)),sK182(U_6952,U_6951,U_6950,U_6949))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6949),U_6950)),U_6952))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6949),U_6952))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6950)) ),
    inference(clausify,[status(thm)],[f_1838_4]) ).

fof(f_1839_1,plain,
    ! [V_n,V_v] :
      ( ( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(V_v))),V_n)
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) )
      & ( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) ) ),
    inference(fof_nnf,[status(thm)],[fact_Suc__nat__number__of__add]) ).

fof(f_1839_2,plain,
    ! [U_6954,U_6953] :
      ( ( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6953)),U_6954)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_6953))),U_6954)
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6953))) )
      & ( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6953)),U_6954)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_6954)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6953))) ) ),
    inference(variable_rename,[status(thm)],[f_1839_1]) ).

fof(f_1839_3,plain,
    ( ! [U_6958,U_6956] :
        ( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6956)),U_6958)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_6956))),U_6958)
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6956))) )
    & ! [U_6957,U_6955] :
        ( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6955)),U_6957)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_6957)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6955))) ) ),
    inference(miniscope,[status(thm)],[f_1839_2]) ).

cnf(f_1839_4,plain,
    ( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6955)),U_6957)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_6957)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6955))) ),
    inference(clausify,[status(thm)],[f_1839_3]) ).

cnf(f_1839_5,plain,
    ( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6956)),U_6958)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_6956))),U_6958)
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6956))) ),
    inference(clausify,[status(thm)],[f_1839_3]) ).

fof(f_1840_1,plain,
    ! [V_x,V_y] :
      ( ( c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x)) )
      & ( c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x)) ) ),
    inference(fof_nnf,[status(thm)],[fact_tsub__def]) ).

fof(f_1840_2,plain,
    ! [U_6960,U_6959] :
      ( ( c_Nat__Transfer_Otsub(U_6960,U_6959) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6959),U_6960)) )
      & ( c_Nat__Transfer_Otsub(U_6960,U_6959) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6960),U_6959)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6959),U_6960)) ) ),
    inference(variable_rename,[status(thm)],[f_1840_1]) ).

fof(f_1840_3,plain,
    ( ! [U_6964,U_6962] :
        ( c_Nat__Transfer_Otsub(U_6964,U_6962) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6962),U_6964)) )
    & ! [U_6963,U_6961] :
        ( c_Nat__Transfer_Otsub(U_6963,U_6961) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6963),U_6961)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6961),U_6963)) ) ),
    inference(miniscope,[status(thm)],[f_1840_2]) ).

cnf(f_1840_4,plain,
    ( c_Nat__Transfer_Otsub(U_6963,U_6961) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6963),U_6961)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6961),U_6963)) ),
    inference(clausify,[status(thm)],[f_1840_3]) ).

cnf(f_1840_5,plain,
    ( c_Nat__Transfer_Otsub(U_6964,U_6962) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6962),U_6964)) ),
    inference(clausify,[status(thm)],[f_1840_3]) ).

fof(f_1841_1,plain,
    ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(fof_nnf,[status(thm)],[fact_not__neg__0]) ).

cnf(f_1841_2,plain,
    ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(clausify,[status(thm)],[f_1841_1]) ).

fof(f_1842_1,plain,
    ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(fof_nnf,[status(thm)],[fact_not__neg__1]) ).

cnf(f_1842_2,plain,
    ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(clausify,[status(thm)],[f_1842_1]) ).

fof(f_1843_1,plain,
    ! [V_x_2] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_x_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,V_x_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_not__neg__eq__ge__0]) ).

fof(f_1843_2,plain,
    ! [U_6965] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_6965))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6965)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6965))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,U_6965)) ) ),
    inference(variable_rename,[status(thm)],[f_1843_1]) ).

fof(f_1843_3,plain,
    ( ! [U_6967] :
        ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_6967))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6967)) )
    & ! [U_6966] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6966))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,U_6966)) ) ),
    inference(miniscope,[status(thm)],[f_1843_2]) ).

cnf(f_1843_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6966))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,U_6966)) ),
    inference(clausify,[status(thm)],[f_1843_3]) ).

cnf(f_1843_5,plain,
    ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_6967))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6967)) ),
    inference(clausify,[status(thm)],[f_1843_3]) ).

fof(f_1844_1,plain,
    ! [V_Z_2] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_Z_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_Z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_Z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_Z_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_neg__def]) ).

fof(f_1844_2,plain,
    ! [U_6968] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,U_6968))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6968),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6968),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_6968)) ) ),
    inference(variable_rename,[status(thm)],[f_1844_1]) ).

fof(f_1844_3,plain,
    ( ! [U_6970] :
        ( hBOOL(hAPP(c_Nat__Numeral_Oneg,U_6970))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6970),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_6969] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6969),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_6969)) ) ),
    inference(miniscope,[status(thm)],[f_1844_2]) ).

cnf(f_1844_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6969),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_6969)) ),
    inference(clausify,[status(thm)],[f_1844_3]) ).

cnf(f_1844_5,plain,
    ( hBOOL(hAPP(c_Nat__Numeral_Oneg,U_6970))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6970),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1844_3]) ).

fof(f_1845_1,plain,
    ! [V_v] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) ),
    inference(fof_nnf,[status(thm)],[fact_neg__imp__number__of__eq__0]) ).

fof(f_1845_2,plain,
    ! [U_6971] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6971) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6971))) ),
    inference(variable_rename,[status(thm)],[f_1845_1]) ).

cnf(f_1845_3,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6971) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6971))) ),
    inference(clausify,[status(thm)],[f_1845_2]) ).

fof(f_1846_1,plain,
    ! [V_v_H_2,V_v_2] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2)
        | ( ( ( V_v_2 != V_v_H_2
              & ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2))) )
            | ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
              & hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2))) ) )
          & ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))) )
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))) ) )
      & ( ( ( ( ( V_v_2 = V_v_H_2
                | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2))) )
              & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
                | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2))) ) )
            | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))) ) )
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_eq__nat__number__of]) ).

fof(f_1846_2,plain,
    ! [U_6973,U_6972] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6972) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6973)
        | ( ( ( U_6972 != U_6973
              & ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6973))) )
            | ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6972) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
              & hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6973))) ) )
          & ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6972))) )
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6973)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6972))) ) )
      & ( ( ( ( ( U_6972 = U_6973
                | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6973))) )
              & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6972) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
                | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6973))) ) )
            | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6972))) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6973)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6972))) ) )
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6972) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6973) ) ),
    inference(variable_rename,[status(thm)],[f_1846_1]) ).

fof(f_1846_3,plain,
    ( ! [U_6977,U_6975] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6975) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6977)
        | ( ( ( U_6975 != U_6977
              & ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6977))) )
            | ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6975) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
              & hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6977))) ) )
          & ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6975))) )
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6977)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6975))) ) )
    & ! [U_6976,U_6974] :
        ( ( ( ( ( U_6974 = U_6976
                | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6976))) )
              & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6974) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
                | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6976))) ) )
            | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6974))) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6976)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6974))) ) )
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6974) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6976) ) ),
    inference(miniscope,[status(thm)],[f_1846_2]) ).

cnf(f_1846_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6976)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6974)))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6974) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6976) ),
    inference(clausify,[status(thm)],[f_1846_3]) ).

cnf(f_1846_5,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6974) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6976)))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6974)))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6974) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6976) ),
    inference(clausify,[status(thm)],[f_1846_3]) ).

cnf(f_1846_6,plain,
    ( U_6974 = U_6976
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6976)))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6974)))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6974) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6976) ),
    inference(clausify,[status(thm)],[f_1846_3]) ).

cnf(f_1846_7,plain,
    ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6975)))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6975)))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6975) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6977) ),
    inference(clausify,[status(thm)],[f_1846_3]) ).

cnf(f_1846_8,plain,
    ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6977)))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6977)))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6975)))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6975) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6977) ),
    inference(clausify,[status(thm)],[f_1846_3]) ).

cnf(f_1846_9,plain,
    ( U_6975 != U_6977
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6977)))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6975)))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6975) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6977) ),
    inference(clausify,[status(thm)],[f_1846_3]) ).

cnf(f_1846_10,plain,
    ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6977)))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6975) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6975)))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6975) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6977) ),
    inference(clausify,[status(thm)],[f_1846_3]) ).

cnf(f_1846_11,plain,
    ( U_6975 != U_6977
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6975) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6975)))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6975) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6977) ),
    inference(clausify,[status(thm)],[f_1846_3]) ).

cnf(f_1846_12,plain,
    ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6975)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6977)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6975) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6977) ),
    inference(clausify,[status(thm)],[f_1846_3]) ).

cnf(f_1846_13,plain,
    ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6977)))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6977)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6977)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6975) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6977) ),
    inference(clausify,[status(thm)],[f_1846_3]) ).

cnf(f_1846_14,plain,
    ( U_6975 != U_6977
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6977)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6977)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6975) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6977) ),
    inference(clausify,[status(thm)],[f_1846_3]) ).

cnf(f_1846_15,plain,
    ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6977)))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6975) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6977)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6975) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6977) ),
    inference(clausify,[status(thm)],[f_1846_3]) ).

cnf(f_1846_16,plain,
    ( U_6975 != U_6977
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6975) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6977)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6975) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6977) ),
    inference(clausify,[status(thm)],[f_1846_3]) ).

fof(f_1847_1,plain,
    ! [V_k,V_v_H,V_v] :
      ( ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_v_H))),V_k)
            | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) )
          & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),V_k)
            | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) ) )
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) )
      & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__number__of__add__left]) ).

fof(f_1847_2,plain,
    ! [U_6980,U_6979,U_6978] :
      ( ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6978)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6979)),U_6980)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6978),U_6979))),U_6980)
            | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6979))) )
          & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6978)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6979)),U_6980)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6978)),U_6980)
            | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6979))) ) )
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6978))) )
      & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6978)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6979)),U_6980)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6979)),U_6980)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6978))) ) ),
    inference(variable_rename,[status(thm)],[f_1847_1]) ).

fof(f_1847_3,plain,
    ( ! [U_6986,U_6984,U_6982] :
        ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6982)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6984)),U_6986)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6982),U_6984))),U_6986)
            | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6984))) )
          & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6982)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6984)),U_6986)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6982)),U_6986)
            | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6984))) ) )
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6982))) )
    & ! [U_6985,U_6983,U_6981] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6981)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6983)),U_6985)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6983)),U_6985)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6981))) ) ),
    inference(miniscope,[status(thm)],[f_1847_2]) ).

cnf(f_1847_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6981)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6983)),U_6985)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6983)),U_6985)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6981))) ),
    inference(clausify,[status(thm)],[f_1847_3]) ).

cnf(f_1847_5,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6982)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6984)),U_6986)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6982)),U_6986)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6984)))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6982))) ),
    inference(clausify,[status(thm)],[f_1847_3]) ).

cnf(f_1847_6,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6982)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6984)),U_6986)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6982),U_6984))),U_6986)
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6984)))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6982))) ),
    inference(clausify,[status(thm)],[f_1847_3]) ).

fof(f_1848_1,plain,
    ! [V_y,V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Nat__Transfer_Otsub(V_x,V_y)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) ),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J]) ).

fof(f_1848_2,plain,
    ! [U_6988,U_6987] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Nat__Transfer_Otsub(U_6987,U_6988)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6988))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6987)) ),
    inference(variable_rename,[status(thm)],[f_1848_1]) ).

cnf(f_1848_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Nat__Transfer_Otsub(U_6987,U_6988)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6988))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6987)) ),
    inference(clausify,[status(thm)],[f_1848_2]) ).

fof(f_1849_1,plain,
    ! [V_v_2] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_neg__number__of__pred__iff__0]) ).

fof(f_1849_2,plain,
    ! [U_6989] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_6989))))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6989) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6989) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_6989)))) ) ),
    inference(variable_rename,[status(thm)],[f_1849_1]) ).

fof(f_1849_3,plain,
    ( ! [U_6991] :
        ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_6991))))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6991) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_6990] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6990) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_6990)))) ) ),
    inference(miniscope,[status(thm)],[f_1849_2]) ).

cnf(f_1849_4,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6990) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_6990)))) ),
    inference(clausify,[status(thm)],[f_1849_3]) ).

cnf(f_1849_5,plain,
    ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_6991))))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6991) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1849_3]) ).

fof(f_1850_1,plain,
    ! [V_x,V_y] :
      ( c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x)) ),
    inference(fof_nnf,[status(thm)],[fact_tsub__eq]) ).

fof(f_1850_2,plain,
    ! [U_6993,U_6992] :
      ( c_Nat__Transfer_Otsub(U_6993,U_6992) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6993),U_6992)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6992),U_6993)) ),
    inference(variable_rename,[status(thm)],[f_1850_1]) ).

cnf(f_1850_3,plain,
    ( c_Nat__Transfer_Otsub(U_6993,U_6992) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6993),U_6992)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6992),U_6993)) ),
    inference(clausify,[status(thm)],[f_1850_2]) ).

fof(f_1851_1,plain,
    ! [V_v] :
      ( ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(V_v))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) )
      & ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) ) ),
    inference(fof_nnf,[status(thm)],[fact_Suc__nat__number__of]) ).

fof(f_1851_2,plain,
    ! [U_6994] :
      ( ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6994)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_6994))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6994))) )
      & ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6994)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6994))) ) ),
    inference(variable_rename,[status(thm)],[f_1851_1]) ).

fof(f_1851_3,plain,
    ( ! [U_6996] :
        ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6996)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_6996))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6996))) )
    & ! [U_6995] :
        ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6995)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6995))) ) ),
    inference(miniscope,[status(thm)],[f_1851_2]) ).

cnf(f_1851_4,plain,
    ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6995)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6995))) ),
    inference(clausify,[status(thm)],[f_1851_3]) ).

cnf(f_1851_5,plain,
    ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6996)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_6996))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6996))) ),
    inference(clausify,[status(thm)],[f_1851_3]) ).

fof(f_1852_1,plain,
    ! [V_a5_2,V_a1_2,V_a2_2,V_a4_2,V_a3_2,T_c,T_b] :
      ( ( c_Nitpick_Ofold__graph_H(T_b,T_c,V_a3_2,V_a4_2,V_a2_2,hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2))
        | ( ! [B_x,B_y] :
              ( ~ c_Nitpick_Ofold__graph_H(T_b,T_c,V_a3_2,V_a4_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_a2_2),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),B_y)
              | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a2_2))
              | hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) != hAPP(hAPP(V_a3_2,B_x),B_y) )
          & ( hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) != V_a4_2
            | V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) )
      & ( ? [B_x,B_y] :
            ( c_Nitpick_Ofold__graph_H(T_b,T_c,V_a3_2,V_a4_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_a2_2),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),B_y)
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a2_2))
            & hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = hAPP(hAPP(V_a3_2,B_x),B_y) )
        | ( hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = V_a4_2
          & V_a2_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
        | ~ c_Nitpick_Ofold__graph_H(T_b,T_c,V_a3_2,V_a4_2,V_a2_2,hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_fold__graph_H_Oequations_I2_J]) ).

fof(f_1852_2,plain,
    ! [U_7007,U_7006,U_7005,U_7004,U_7003,U_7002,U_7001] :
      ( ( c_Nitpick_Ofold__graph_H(U_7001,U_7002,U_7003,U_7004,U_7005,hAPP(hAPP(U_7003,U_7006),U_7007))
        | ( ! [U_7000,U_6999] :
              ( ~ c_Nitpick_Ofold__graph_H(U_7001,U_7002,U_7003,U_7004,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7001,tc_HOL_Obool)),U_7005),hAPP(hAPP(c_Set_Oinsert(U_7001),U_7000),c_Orderings_Obot__class_Obot(tc_fun(U_7001,tc_HOL_Obool)))),U_6999)
              | ~ hBOOL(hAPP(hAPP(c_member(U_7001),U_7000),U_7005))
              | hAPP(hAPP(U_7003,U_7006),U_7007) != hAPP(hAPP(U_7003,U_7000),U_6999) )
          & ( hAPP(hAPP(U_7003,U_7006),U_7007) != U_7004
            | U_7005 != c_Orderings_Obot__class_Obot(tc_fun(U_7001,tc_HOL_Obool)) ) ) )
      & ( ? [U_6998,U_6997] :
            ( c_Nitpick_Ofold__graph_H(U_7001,U_7002,U_7003,U_7004,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7001,tc_HOL_Obool)),U_7005),hAPP(hAPP(c_Set_Oinsert(U_7001),U_6998),c_Orderings_Obot__class_Obot(tc_fun(U_7001,tc_HOL_Obool)))),U_6997)
            & hBOOL(hAPP(hAPP(c_member(U_7001),U_6998),U_7005))
            & hAPP(hAPP(U_7003,U_7006),U_7007) = hAPP(hAPP(U_7003,U_6998),U_6997) )
        | ( hAPP(hAPP(U_7003,U_7006),U_7007) = U_7004
          & U_7005 = c_Orderings_Obot__class_Obot(tc_fun(U_7001,tc_HOL_Obool)) )
        | ~ c_Nitpick_Ofold__graph_H(U_7001,U_7002,U_7003,U_7004,U_7005,hAPP(hAPP(U_7003,U_7006),U_7007)) ) ),
    inference(variable_rename,[status(thm)],[f_1852_1]) ).

fof(f_1852_3,plain,
    ( ! [U_7021,U_7019,U_7017,U_7015,U_7013,U_7011,U_7009] :
        ( c_Nitpick_Ofold__graph_H(U_7009,U_7011,U_7013,U_7015,U_7017,hAPP(hAPP(U_7013,U_7019),U_7021))
        | ( ! [U_7000] :
              ( ! [U_6999] :
                  ( ~ c_Nitpick_Ofold__graph_H(U_7009,U_7011,U_7013,U_7015,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7009,tc_HOL_Obool)),U_7017),hAPP(hAPP(c_Set_Oinsert(U_7009),U_7000),c_Orderings_Obot__class_Obot(tc_fun(U_7009,tc_HOL_Obool)))),U_6999)
                  | hAPP(hAPP(U_7013,U_7019),U_7021) != hAPP(hAPP(U_7013,U_7000),U_6999) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_7009),U_7000),U_7017)) )
          & ( hAPP(hAPP(U_7013,U_7019),U_7021) != U_7015
            | U_7017 != c_Orderings_Obot__class_Obot(tc_fun(U_7009,tc_HOL_Obool)) ) ) )
    & ! [U_7020,U_7018,U_7016,U_7014,U_7012,U_7010,U_7008] :
        ( ? [U_6998] :
            ( ? [U_6997] :
                ( c_Nitpick_Ofold__graph_H(U_7008,U_7010,U_7012,U_7014,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7008,tc_HOL_Obool)),U_7016),hAPP(hAPP(c_Set_Oinsert(U_7008),U_6998),c_Orderings_Obot__class_Obot(tc_fun(U_7008,tc_HOL_Obool)))),U_6997)
                & hAPP(hAPP(U_7012,U_7018),U_7020) = hAPP(hAPP(U_7012,U_6998),U_6997) )
            & hBOOL(hAPP(hAPP(c_member(U_7008),U_6998),U_7016)) )
        | ( hAPP(hAPP(U_7012,U_7018),U_7020) = U_7014
          & U_7016 = c_Orderings_Obot__class_Obot(tc_fun(U_7008,tc_HOL_Obool)) )
        | ~ c_Nitpick_Ofold__graph_H(U_7008,U_7010,U_7012,U_7014,U_7016,hAPP(hAPP(U_7012,U_7018),U_7020)) ) ),
    inference(miniscope,[status(thm)],[f_1852_2]) ).

fof(f_1852_4,plain,
    ( ! [U_7021,U_7019,U_7017,U_7015,U_7013,U_7011,U_7009] :
        ( c_Nitpick_Ofold__graph_H(U_7009,U_7011,U_7013,U_7015,U_7017,hAPP(hAPP(U_7013,U_7019),U_7021))
        | ( ! [U_7000] :
              ( ! [U_6999] :
                  ( ~ c_Nitpick_Ofold__graph_H(U_7009,U_7011,U_7013,U_7015,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7009,tc_HOL_Obool)),U_7017),hAPP(hAPP(c_Set_Oinsert(U_7009),U_7000),c_Orderings_Obot__class_Obot(tc_fun(U_7009,tc_HOL_Obool)))),U_6999)
                  | hAPP(hAPP(U_7013,U_7019),U_7021) != hAPP(hAPP(U_7013,U_7000),U_6999) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_7009),U_7000),U_7017)) )
          & ( hAPP(hAPP(U_7013,U_7019),U_7021) != U_7015
            | U_7017 != c_Orderings_Obot__class_Obot(tc_fun(U_7009,tc_HOL_Obool)) ) ) )
    & ! [U_7020,U_7018,U_7016,U_7014,U_7012,U_7010,U_7008] :
        ( ( ? [U_6997] :
              ( c_Nitpick_Ofold__graph_H(U_7008,U_7010,U_7012,U_7014,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7008,tc_HOL_Obool)),U_7016),hAPP(hAPP(c_Set_Oinsert(U_7008),sK184(U_7020,U_7018,U_7016,U_7014,U_7012,U_7010,U_7008)),c_Orderings_Obot__class_Obot(tc_fun(U_7008,tc_HOL_Obool)))),U_6997)
              & hAPP(hAPP(U_7012,U_7018),U_7020) = hAPP(hAPP(U_7012,sK184(U_7020,U_7018,U_7016,U_7014,U_7012,U_7010,U_7008)),U_6997) )
          & hBOOL(hAPP(hAPP(c_member(U_7008),sK184(U_7020,U_7018,U_7016,U_7014,U_7012,U_7010,U_7008)),U_7016)) )
        | ( hAPP(hAPP(U_7012,U_7018),U_7020) = U_7014
          & U_7016 = c_Orderings_Obot__class_Obot(tc_fun(U_7008,tc_HOL_Obool)) )
        | ~ c_Nitpick_Ofold__graph_H(U_7008,U_7010,U_7012,U_7014,U_7016,hAPP(hAPP(U_7012,U_7018),U_7020)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK184]),skolemize(U_6998,sK184(U_7020,U_7018,U_7016,U_7014,U_7012,U_7010,U_7008))],[f_1852_3]) ).

fof(f_1852_5,plain,
    ( ! [U_7021,U_7019,U_7017,U_7015,U_7013,U_7011,U_7009] :
        ( c_Nitpick_Ofold__graph_H(U_7009,U_7011,U_7013,U_7015,U_7017,hAPP(hAPP(U_7013,U_7019),U_7021))
        | ( ! [U_7000] :
              ( ! [U_6999] :
                  ( ~ c_Nitpick_Ofold__graph_H(U_7009,U_7011,U_7013,U_7015,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7009,tc_HOL_Obool)),U_7017),hAPP(hAPP(c_Set_Oinsert(U_7009),U_7000),c_Orderings_Obot__class_Obot(tc_fun(U_7009,tc_HOL_Obool)))),U_6999)
                  | hAPP(hAPP(U_7013,U_7019),U_7021) != hAPP(hAPP(U_7013,U_7000),U_6999) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_7009),U_7000),U_7017)) )
          & ( hAPP(hAPP(U_7013,U_7019),U_7021) != U_7015
            | U_7017 != c_Orderings_Obot__class_Obot(tc_fun(U_7009,tc_HOL_Obool)) ) ) )
    & ! [U_7020,U_7018,U_7016,U_7014,U_7012,U_7010,U_7008] :
        ( ( c_Nitpick_Ofold__graph_H(U_7008,U_7010,U_7012,U_7014,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7008,tc_HOL_Obool)),U_7016),hAPP(hAPP(c_Set_Oinsert(U_7008),sK184(U_7020,U_7018,U_7016,U_7014,U_7012,U_7010,U_7008)),c_Orderings_Obot__class_Obot(tc_fun(U_7008,tc_HOL_Obool)))),sK185(U_7020,U_7018,U_7016,U_7014,U_7012,U_7010,U_7008))
          & hAPP(hAPP(U_7012,U_7018),U_7020) = hAPP(hAPP(U_7012,sK184(U_7020,U_7018,U_7016,U_7014,U_7012,U_7010,U_7008)),sK185(U_7020,U_7018,U_7016,U_7014,U_7012,U_7010,U_7008))
          & hBOOL(hAPP(hAPP(c_member(U_7008),sK184(U_7020,U_7018,U_7016,U_7014,U_7012,U_7010,U_7008)),U_7016)) )
        | ( hAPP(hAPP(U_7012,U_7018),U_7020) = U_7014
          & U_7016 = c_Orderings_Obot__class_Obot(tc_fun(U_7008,tc_HOL_Obool)) )
        | ~ c_Nitpick_Ofold__graph_H(U_7008,U_7010,U_7012,U_7014,U_7016,hAPP(hAPP(U_7012,U_7018),U_7020)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK185]),skolemize(U_6997,sK185(U_7020,U_7018,U_7016,U_7014,U_7012,U_7010,U_7008))],[f_1852_4]) ).

cnf(f_1852_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7008),sK184(U_7020,U_7018,U_7016,U_7014,U_7012,U_7010,U_7008)),U_7016))
    | U_7016 = c_Orderings_Obot__class_Obot(tc_fun(U_7008,tc_HOL_Obool))
    | ~ c_Nitpick_Ofold__graph_H(U_7008,U_7010,U_7012,U_7014,U_7016,hAPP(hAPP(U_7012,U_7018),U_7020)) ),
    inference(clausify,[status(thm)],[f_1852_5]) ).

cnf(f_1852_7,plain,
    ( hAPP(hAPP(U_7012,U_7018),U_7020) = hAPP(hAPP(U_7012,sK184(U_7020,U_7018,U_7016,U_7014,U_7012,U_7010,U_7008)),sK185(U_7020,U_7018,U_7016,U_7014,U_7012,U_7010,U_7008))
    | U_7016 = c_Orderings_Obot__class_Obot(tc_fun(U_7008,tc_HOL_Obool))
    | ~ c_Nitpick_Ofold__graph_H(U_7008,U_7010,U_7012,U_7014,U_7016,hAPP(hAPP(U_7012,U_7018),U_7020)) ),
    inference(clausify,[status(thm)],[f_1852_5]) ).

cnf(f_1852_8,plain,
    ( c_Nitpick_Ofold__graph_H(U_7008,U_7010,U_7012,U_7014,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7008,tc_HOL_Obool)),U_7016),hAPP(hAPP(c_Set_Oinsert(U_7008),sK184(U_7020,U_7018,U_7016,U_7014,U_7012,U_7010,U_7008)),c_Orderings_Obot__class_Obot(tc_fun(U_7008,tc_HOL_Obool)))),sK185(U_7020,U_7018,U_7016,U_7014,U_7012,U_7010,U_7008))
    | U_7016 = c_Orderings_Obot__class_Obot(tc_fun(U_7008,tc_HOL_Obool))
    | ~ c_Nitpick_Ofold__graph_H(U_7008,U_7010,U_7012,U_7014,U_7016,hAPP(hAPP(U_7012,U_7018),U_7020)) ),
    inference(clausify,[status(thm)],[f_1852_5]) ).

cnf(f_1852_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7008),sK184(U_7020,U_7018,U_7016,U_7014,U_7012,U_7010,U_7008)),U_7016))
    | hAPP(hAPP(U_7012,U_7018),U_7020) = U_7014
    | ~ c_Nitpick_Ofold__graph_H(U_7008,U_7010,U_7012,U_7014,U_7016,hAPP(hAPP(U_7012,U_7018),U_7020)) ),
    inference(clausify,[status(thm)],[f_1852_5]) ).

cnf(f_1852_10,plain,
    ( hAPP(hAPP(U_7012,U_7018),U_7020) = hAPP(hAPP(U_7012,sK184(U_7020,U_7018,U_7016,U_7014,U_7012,U_7010,U_7008)),sK185(U_7020,U_7018,U_7016,U_7014,U_7012,U_7010,U_7008))
    | hAPP(hAPP(U_7012,U_7018),U_7020) = U_7014
    | ~ c_Nitpick_Ofold__graph_H(U_7008,U_7010,U_7012,U_7014,U_7016,hAPP(hAPP(U_7012,U_7018),U_7020)) ),
    inference(clausify,[status(thm)],[f_1852_5]) ).

cnf(f_1852_11,plain,
    ( c_Nitpick_Ofold__graph_H(U_7008,U_7010,U_7012,U_7014,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7008,tc_HOL_Obool)),U_7016),hAPP(hAPP(c_Set_Oinsert(U_7008),sK184(U_7020,U_7018,U_7016,U_7014,U_7012,U_7010,U_7008)),c_Orderings_Obot__class_Obot(tc_fun(U_7008,tc_HOL_Obool)))),sK185(U_7020,U_7018,U_7016,U_7014,U_7012,U_7010,U_7008))
    | hAPP(hAPP(U_7012,U_7018),U_7020) = U_7014
    | ~ c_Nitpick_Ofold__graph_H(U_7008,U_7010,U_7012,U_7014,U_7016,hAPP(hAPP(U_7012,U_7018),U_7020)) ),
    inference(clausify,[status(thm)],[f_1852_5]) ).

cnf(f_1852_12,plain,
    ( hAPP(hAPP(U_7013,U_7019),U_7021) != U_7015
    | U_7017 != c_Orderings_Obot__class_Obot(tc_fun(U_7009,tc_HOL_Obool))
    | c_Nitpick_Ofold__graph_H(U_7009,U_7011,U_7013,U_7015,U_7017,hAPP(hAPP(U_7013,U_7019),U_7021)) ),
    inference(clausify,[status(thm)],[f_1852_5]) ).

cnf(f_1852_13,plain,
    ( ~ c_Nitpick_Ofold__graph_H(U_7009,U_7011,U_7013,U_7015,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7009,tc_HOL_Obool)),U_7017),hAPP(hAPP(c_Set_Oinsert(U_7009),U_7000),c_Orderings_Obot__class_Obot(tc_fun(U_7009,tc_HOL_Obool)))),U_6999)
    | hAPP(hAPP(U_7013,U_7019),U_7021) != hAPP(hAPP(U_7013,U_7000),U_6999)
    | ~ hBOOL(hAPP(hAPP(c_member(U_7009),U_7000),U_7017))
    | c_Nitpick_Ofold__graph_H(U_7009,U_7011,U_7013,U_7015,U_7017,hAPP(hAPP(U_7013,U_7019),U_7021)) ),
    inference(clausify,[status(thm)],[f_1852_5]) ).

fof(f_1853_1,plain,
    ! [V_k,V_m] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_k),V_m)),V_k) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) ),
    inference(fof_nnf,[status(thm)],[fact_int__power__div__base]) ).

fof(f_1853_2,plain,
    ! [U_7023,U_7022] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_7023),U_7022)),U_7023) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_7023),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7022),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7023))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7022)) ),
    inference(variable_rename,[status(thm)],[f_1853_1]) ).

cnf(f_1853_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_7023),U_7022)),U_7023) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_7023),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7022),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7023))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7022)) ),
    inference(clausify,[status(thm)],[f_1853_2]) ).

fof(f_1854_1,plain,
    ! [V_v] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(V_v))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls)) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls)) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__number__of__diff__1]) ).

fof(f_1854_2,plain,
    ! [U_7024] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7024)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(U_7024))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7024),c_Int_OPls)) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7024)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7024),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[f_1854_1]) ).

fof(f_1854_3,plain,
    ( ! [U_7026] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7026)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(U_7026))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7026),c_Int_OPls)) )
    & ! [U_7025] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7025)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7025),c_Int_OPls)) ) ),
    inference(miniscope,[status(thm)],[f_1854_2]) ).

cnf(f_1854_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7025)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7025),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1854_3]) ).

cnf(f_1854_5,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7026)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(U_7026))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7026),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1854_3]) ).

fof(f_1855_1,plain,
    ! [V_k_2,V_P_2,V_d_2] :
      ( ! [B_x] :
          ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2))))
          | ~ hBOOL(hAPP(V_P_2,B_x)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_d_2)))
          & hBOOL(hAPP(V_P_2,B_x)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) ),
    inference(fof_nnf,[status(thm)],[fact_decr__mult__lemma]) ).

fof(f_1855_2,plain,
    ! [U_7031,U_7030,U_7029] :
      ( ! [U_7028] :
          ( hBOOL(hAPP(U_7030,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7028),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7031),U_7029))))
          | ~ hBOOL(hAPP(U_7030,U_7028)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7031))
      | ? [U_7027] :
          ( ~ hBOOL(hAPP(U_7030,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7027),U_7029)))
          & hBOOL(hAPP(U_7030,U_7027)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7029)) ),
    inference(variable_rename,[status(thm)],[f_1855_1]) ).

fof(f_1855_3,plain,
    ! [U_7031,U_7030,U_7029] :
      ( ! [U_7028] :
          ( hBOOL(hAPP(U_7030,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7028),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7031),U_7029))))
          | ~ hBOOL(hAPP(U_7030,U_7028)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7031))
      | ( ~ hBOOL(hAPP(U_7030,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK186(U_7031,U_7030,U_7029)),U_7029)))
        & hBOOL(hAPP(U_7030,sK186(U_7031,U_7030,U_7029))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7029)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK186]),skolemize(U_7027,sK186(U_7031,U_7030,U_7029))],[f_1855_2]) ).

cnf(f_1855_4,plain,
    ( hBOOL(hAPP(U_7030,sK186(U_7031,U_7030,U_7029)))
    | hBOOL(hAPP(U_7030,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7028),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7031),U_7029))))
    | ~ hBOOL(hAPP(U_7030,U_7028))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7031))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7029)) ),
    inference(clausify,[status(thm)],[f_1855_3]) ).

cnf(f_1855_5,plain,
    ( ~ hBOOL(hAPP(U_7030,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK186(U_7031,U_7030,U_7029)),U_7029)))
    | hBOOL(hAPP(U_7030,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7028),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7031),U_7029))))
    | ~ hBOOL(hAPP(U_7030,U_7028))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7031))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7029)) ),
    inference(clausify,[status(thm)],[f_1855_3]) ).

fof(f_1856_1,plain,
    ! [V_k_2,V_P_2,V_d_2] :
      ( ! [B_x] :
          ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2))))
          | ~ hBOOL(hAPP(V_P_2,B_x)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_d_2)))
          & hBOOL(hAPP(V_P_2,B_x)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) ),
    inference(fof_nnf,[status(thm)],[fact_incr__mult__lemma]) ).

fof(f_1856_2,plain,
    ! [U_7036,U_7035,U_7034] :
      ( ! [U_7033] :
          ( hBOOL(hAPP(U_7035,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7033),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7036),U_7034))))
          | ~ hBOOL(hAPP(U_7035,U_7033)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7036))
      | ? [U_7032] :
          ( ~ hBOOL(hAPP(U_7035,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7032),U_7034)))
          & hBOOL(hAPP(U_7035,U_7032)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7034)) ),
    inference(variable_rename,[status(thm)],[f_1856_1]) ).

fof(f_1856_3,plain,
    ! [U_7036,U_7035,U_7034] :
      ( ! [U_7033] :
          ( hBOOL(hAPP(U_7035,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7033),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7036),U_7034))))
          | ~ hBOOL(hAPP(U_7035,U_7033)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7036))
      | ( ~ hBOOL(hAPP(U_7035,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK187(U_7036,U_7035,U_7034)),U_7034)))
        & hBOOL(hAPP(U_7035,sK187(U_7036,U_7035,U_7034))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7034)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK187]),skolemize(U_7032,sK187(U_7036,U_7035,U_7034))],[f_1856_2]) ).

cnf(f_1856_4,plain,
    ( hBOOL(hAPP(U_7035,sK187(U_7036,U_7035,U_7034)))
    | hBOOL(hAPP(U_7035,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7033),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7036),U_7034))))
    | ~ hBOOL(hAPP(U_7035,U_7033))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7036))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7034)) ),
    inference(clausify,[status(thm)],[f_1856_3]) ).

cnf(f_1856_5,plain,
    ( ~ hBOOL(hAPP(U_7035,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK187(U_7036,U_7035,U_7034)),U_7034)))
    | hBOOL(hAPP(U_7035,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7033),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7036),U_7034))))
    | ~ hBOOL(hAPP(U_7035,U_7033))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7036))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7034)) ),
    inference(clausify,[status(thm)],[f_1856_3]) ).

fof(f_1857_1,plain,
    ! [V_b] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[fact_zdiv__zero]) ).

fof(f_1857_2,plain,
    ! [U_7037] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7037) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[f_1857_1]) ).

cnf(f_1857_3,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7037) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1857_2]) ).

fof(f_1858_1,plain,
    ! [V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a)),V_b),
    inference(fof_nnf,[status(thm)],[fact_zdiv__zminus2]) ).

fof(f_1858_2,plain,
    ! [U_7039,U_7038] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7038),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7039)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7038)),U_7039),
    inference(variable_rename,[status(thm)],[f_1858_1]) ).

cnf(f_1858_3,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7038),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7039)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7038)),U_7039),
    inference(clausify,[status(thm)],[f_1858_2]) ).

fof(f_1859_1,plain,
    ! [V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b),
    inference(fof_nnf,[status(thm)],[fact_zdiv__zminus__zminus]) ).

fof(f_1859_2,plain,
    ! [U_7041,U_7040] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7040)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7041)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7040),U_7041),
    inference(variable_rename,[status(thm)],[f_1859_1]) ).

cnf(f_1859_3,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7040)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7041)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7040),U_7041),
    inference(clausify,[status(thm)],[f_1859_2]) ).

fof(f_1860_1,plain,
    c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[fact_Pls__def]) ).

cnf(f_1860_2,plain,
    c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1860_1]) ).

fof(f_1861_1,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I19_J]) ).

cnf(f_1861_2,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),
    inference(clausify,[status(thm)],[f_1861_1]) ).

fof(f_1862_1,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I2_J]) ).

cnf(f_1862_2,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),
    inference(clausify,[status(thm)],[f_1862_1]) ).

fof(f_1863_1,plain,
    ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),V_k) = V_k,
    inference(fof_nnf,[status(thm)],[fact_add__Pls]) ).

fof(f_1863_2,plain,
    ! [U_7042] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),U_7042) = U_7042,
    inference(variable_rename,[status(thm)],[f_1863_1]) ).

cnf(f_1863_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),U_7042) = U_7042,
    inference(clausify,[status(thm)],[f_1863_2]) ).

fof(f_1864_1,plain,
    ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OPls) = V_k,
    inference(fof_nnf,[status(thm)],[fact_add__Pls__right]) ).

fof(f_1864_2,plain,
    ! [U_7043] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7043),c_Int_OPls) = U_7043,
    inference(variable_rename,[status(thm)],[f_1864_1]) ).

cnf(f_1864_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7043),c_Int_OPls) = U_7043,
    inference(clausify,[status(thm)],[f_1864_2]) ).

fof(f_1865_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_div__0]) ).

fof(f_1865_2,plain,
    ! [U_7045,U_7044] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7044),c_Groups_Ozero__class_Ozero(U_7044)),U_7045) = c_Groups_Ozero__class_Ozero(U_7044)
      | ~ class_Divides_Osemiring__div(U_7044) ),
    inference(variable_rename,[status(thm)],[f_1865_1]) ).

cnf(f_1865_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7044),c_Groups_Ozero__class_Ozero(U_7044)),U_7045) = c_Groups_Ozero__class_Ozero(U_7044)
    | ~ class_Divides_Osemiring__div(U_7044) ),
    inference(clausify,[status(thm)],[f_1865_2]) ).

fof(f_1866_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_div__by__0]) ).

fof(f_1866_2,plain,
    ! [U_7047,U_7046] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7046),U_7047),c_Groups_Ozero__class_Ozero(U_7046)) = c_Groups_Ozero__class_Ozero(U_7046)
      | ~ class_Divides_Osemiring__div(U_7046) ),
    inference(variable_rename,[status(thm)],[f_1866_1]) ).

cnf(f_1866_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7046),U_7047),c_Groups_Ozero__class_Ozero(U_7046)) = c_Groups_Ozero__class_Ozero(U_7046)
    | ~ class_Divides_Osemiring__div(U_7046) ),
    inference(clausify,[status(thm)],[f_1866_2]) ).

fof(f_1867_1,plain,
    ! [V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),V_w) = c_Int_OPls,
    inference(fof_nnf,[status(thm)],[fact_mult__Pls]) ).

fof(f_1867_2,plain,
    ! [U_7048] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),U_7048) = c_Int_OPls,
    inference(variable_rename,[status(thm)],[f_1867_1]) ).

cnf(f_1867_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),U_7048) = c_Int_OPls,
    inference(clausify,[status(thm)],[f_1867_2]) ).

fof(f_1868_1,plain,
    ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OPls) = V_k,
    inference(fof_nnf,[status(thm)],[fact_diff__bin__simps_I1_J]) ).

fof(f_1868_2,plain,
    ! [U_7049] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7049),c_Int_OPls) = U_7049,
    inference(variable_rename,[status(thm)],[f_1868_1]) ).

cnf(f_1868_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7049),c_Int_OPls) = U_7049,
    inference(clausify,[status(thm)],[f_1868_2]) ).

fof(f_1869_1,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls,
    inference(fof_nnf,[status(thm)],[fact_minus__Pls]) ).

cnf(f_1869_2,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls,
    inference(clausify,[status(thm)],[f_1869_1]) ).

fof(f_1870_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_div__by__1]) ).

fof(f_1870_2,plain,
    ! [U_7051,U_7050] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7050),U_7051),c_Groups_Oone__class_Oone(U_7050)) = U_7051
      | ~ class_Divides_Osemiring__div(U_7050) ),
    inference(variable_rename,[status(thm)],[f_1870_1]) ).

cnf(f_1870_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7050),U_7051),c_Groups_Oone__class_Oone(U_7050)) = U_7051
    | ~ class_Divides_Osemiring__div(U_7050) ),
    inference(clausify,[status(thm)],[f_1870_2]) ).

fof(f_1871_1,plain,
    ! [V_y,V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) ),
    inference(fof_nnf,[status(thm)],[fact_Divides_Otransfer__nat__int__function__closures_I1_J]) ).

fof(f_1871_2,plain,
    ! [U_7053,U_7052] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7052),U_7053)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7053))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7052)) ),
    inference(variable_rename,[status(thm)],[f_1871_1]) ).

cnf(f_1871_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7052),U_7053)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7053))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7052)) ),
    inference(clausify,[status(thm)],[f_1871_2]) ).

fof(f_1872_1,plain,
    ! [V_a_2,V_b_2] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) ),
    inference(fof_nnf,[status(thm)],[fact_pos__imp__zdiv__neg__iff]) ).

fof(f_1872_2,plain,
    ! [U_7055,U_7054] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7055),U_7054)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7055),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7055),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7055),U_7054)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7054)) ),
    inference(variable_rename,[status(thm)],[f_1872_1]) ).

cnf(f_1872_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7055),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7055),U_7054)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7054)) ),
    inference(clausify,[status(thm)],[f_1872_2]) ).

cnf(f_1872_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7055),U_7054)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7055),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7054)) ),
    inference(clausify,[status(thm)],[f_1872_2]) ).

fof(f_1873_1,plain,
    ! [V_a_2,V_b_2] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(fof_nnf,[status(thm)],[fact_neg__imp__zdiv__neg__iff]) ).

fof(f_1873_2,plain,
    ! [U_7057,U_7056] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7057),U_7056)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7057)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7057))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7057),U_7056)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7056),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_1873_1]) ).

cnf(f_1873_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7057))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7057),U_7056)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7056),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1873_2]) ).

cnf(f_1873_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7057),U_7056)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7057))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7056),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1873_2]) ).

fof(f_1874_1,plain,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(fof_nnf,[status(thm)],[fact_div__neg__pos__less0]) ).

fof(f_1874_2,plain,
    ! [U_7059,U_7058] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7058),U_7059)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7059))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7058),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_1874_1]) ).

cnf(f_1874_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7058),U_7059)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7059))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7058),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1874_2]) ).

fof(f_1875_1,plain,
    ! [V_a] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_a) = c_Groups_Oone__class_Oone(tc_Int_Oint)
      | V_a = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(fof_nnf,[status(thm)],[fact_zdiv__self]) ).

fof(f_1875_2,plain,
    ! [U_7060] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7060),U_7060) = c_Groups_Oone__class_Oone(tc_Int_Oint)
      | U_7060 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_1875_1]) ).

cnf(f_1875_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7060),U_7060) = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | U_7060 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1875_2]) ).

fof(f_1876_1,plain,
    ! [T_a] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_number__of__Pls]) ).

fof(f_1876_2,plain,
    ! [U_7061] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_7061),c_Int_OPls) = c_Groups_Ozero__class_Ozero(U_7061)
      | ~ class_Int_Onumber__ring(U_7061) ),
    inference(variable_rename,[status(thm)],[f_1876_1]) ).

cnf(f_1876_3,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_7061),c_Int_OPls) = c_Groups_Ozero__class_Ozero(U_7061)
    | ~ class_Int_Onumber__ring(U_7061) ),
    inference(clausify,[status(thm)],[f_1876_2]) ).

fof(f_1877_1,plain,
    ! [T_a] :
      ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_semiring__norm_I112_J]) ).

fof(f_1877_2,plain,
    ! [U_7062] :
      ( c_Groups_Ozero__class_Ozero(U_7062) = hAPP(c_Int_Onumber__class_Onumber__of(U_7062),c_Int_OPls)
      | ~ class_Int_Onumber__ring(U_7062) ),
    inference(variable_rename,[status(thm)],[f_1877_1]) ).

cnf(f_1877_3,plain,
    ( c_Groups_Ozero__class_Ozero(U_7062) = hAPP(c_Int_Onumber__class_Onumber__of(U_7062),c_Int_OPls)
    | ~ class_Int_Onumber__ring(U_7062) ),
    inference(clausify,[status(thm)],[f_1877_2]) ).

fof(f_1878_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) = V_a
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__numeral__0__right]) ).

fof(f_1878_2,plain,
    ! [U_7064,U_7063] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7063),U_7064),hAPP(c_Int_Onumber__class_Onumber__of(U_7063),c_Int_OPls)) = U_7064
      | ~ class_Int_Onumber__ring(U_7063) ),
    inference(variable_rename,[status(thm)],[f_1878_1]) ).

cnf(f_1878_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7063),U_7064),hAPP(c_Int_Onumber__class_Onumber__of(U_7063),c_Int_OPls)) = U_7064
    | ~ class_Int_Onumber__ring(U_7063) ),
    inference(clausify,[status(thm)],[f_1878_2]) ).

fof(f_1879_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)),V_a) = V_a
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__numeral__0]) ).

fof(f_1879_2,plain,
    ! [U_7066,U_7065] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7065),hAPP(c_Int_Onumber__class_Onumber__of(U_7065),c_Int_OPls)),U_7066) = U_7066
      | ~ class_Int_Onumber__ring(U_7065) ),
    inference(variable_rename,[status(thm)],[f_1879_1]) ).

cnf(f_1879_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7065),hAPP(c_Int_Onumber__class_Onumber__of(U_7065),c_Int_OPls)),U_7066) = U_7066
    | ~ class_Int_Onumber__ring(U_7065) ),
    inference(clausify,[status(thm)],[f_1879_2]) ).

fof(f_1880_1,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(fof_nnf,[status(thm)],[fact_bin__less__0__simps_I1_J]) ).

cnf(f_1880_2,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(clausify,[status(thm)],[f_1880_1]) ).

fof(f_1881_1,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_nat__number__of__Pls]) ).

cnf(f_1881_2,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1881_1]) ).

fof(f_1882_1,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls),
    inference(fof_nnf,[status(thm)],[fact_semiring__norm_I113_J]) ).

cnf(f_1882_2,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls),
    inference(clausify,[status(thm)],[f_1882_1]) ).

fof(f_1883_1,plain,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls),
    inference(fof_nnf,[status(thm)],[fact_zero__is__num__zero]) ).

cnf(f_1883_2,plain,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls),
    inference(clausify,[status(thm)],[f_1883_1]) ).

fof(f_1884_1,plain,
    ! [V_b,V_a,V_c,T_a] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)
      | V_c = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_div__mult__mult1]) ).

fof(f_1884_2,plain,
    ! [U_7070,U_7069,U_7068,U_7067] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7067),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7067),U_7068),U_7069)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7067),U_7068),U_7070)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7067),U_7069),U_7070)
      | U_7068 = c_Groups_Ozero__class_Ozero(U_7067)
      | ~ class_Divides_Osemiring__div(U_7067) ),
    inference(variable_rename,[status(thm)],[f_1884_1]) ).

cnf(f_1884_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7067),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7067),U_7068),U_7069)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7067),U_7068),U_7070)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7067),U_7069),U_7070)
    | U_7068 = c_Groups_Ozero__class_Ozero(U_7067)
    | ~ class_Divides_Osemiring__div(U_7067) ),
    inference(clausify,[status(thm)],[f_1884_2]) ).

fof(f_1885_1,plain,
    ! [V_b,V_a,V_c,T_a] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)
      | V_c = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_div__mult__mult2]) ).

fof(f_1885_2,plain,
    ! [U_7074,U_7073,U_7072,U_7071] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7071),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7071),U_7073),U_7072)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7071),U_7074),U_7072)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7071),U_7073),U_7074)
      | U_7072 = c_Groups_Ozero__class_Ozero(U_7071)
      | ~ class_Divides_Osemiring__div(U_7071) ),
    inference(variable_rename,[status(thm)],[f_1885_1]) ).

cnf(f_1885_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7071),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7071),U_7073),U_7072)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7071),U_7074),U_7072)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7071),U_7073),U_7074)
    | U_7072 = c_Groups_Ozero__class_Ozero(U_7071)
    | ~ class_Divides_Osemiring__div(U_7071) ),
    inference(clausify,[status(thm)],[f_1885_2]) ).

fof(f_1886_1,plain,
    ! [V_a,V_b,T_a] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)),V_b) = V_a
      | V_b = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_div__mult__self1__is__id]) ).

fof(f_1886_2,plain,
    ! [U_7077,U_7076,U_7075] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7075),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7075),U_7076),U_7077)),U_7076) = U_7077
      | U_7076 = c_Groups_Ozero__class_Ozero(U_7075)
      | ~ class_Divides_Osemiring__div(U_7075) ),
    inference(variable_rename,[status(thm)],[f_1886_1]) ).

cnf(f_1886_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7075),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7075),U_7076),U_7077)),U_7076) = U_7077
    | U_7076 = c_Groups_Ozero__class_Ozero(U_7075)
    | ~ class_Divides_Osemiring__div(U_7075) ),
    inference(clausify,[status(thm)],[f_1886_2]) ).

fof(f_1887_1,plain,
    ! [V_a,V_b,T_a] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_b) = V_a
      | V_b = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_div__mult__self2__is__id]) ).

fof(f_1887_2,plain,
    ! [U_7080,U_7079,U_7078] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7078),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7078),U_7080),U_7079)),U_7079) = U_7080
      | U_7079 = c_Groups_Ozero__class_Ozero(U_7078)
      | ~ class_Divides_Osemiring__div(U_7078) ),
    inference(variable_rename,[status(thm)],[f_1887_1]) ).

cnf(f_1887_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7078),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7078),U_7080),U_7079)),U_7079) = U_7080
    | U_7079 = c_Groups_Ozero__class_Ozero(U_7078)
    | ~ class_Divides_Osemiring__div(U_7078) ),
    inference(clausify,[status(thm)],[f_1887_2]) ).

fof(f_1888_1,plain,
    ! [V_b,V_a,V_c,T_a] :
      ( ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)
          | V_c = c_Groups_Ozero__class_Ozero(T_a) )
        & ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = c_Groups_Ozero__class_Ozero(T_a)
          | V_c != c_Groups_Ozero__class_Ozero(T_a) ) )
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_div__mult__mult1__if]) ).

fof(f_1888_2,plain,
    ! [U_7084,U_7083,U_7082,U_7081] :
      ( ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7081),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7081),U_7082),U_7083)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7081),U_7082),U_7084)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7081),U_7083),U_7084)
          | U_7082 = c_Groups_Ozero__class_Ozero(U_7081) )
        & ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7081),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7081),U_7082),U_7083)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7081),U_7082),U_7084)) = c_Groups_Ozero__class_Ozero(U_7081)
          | U_7082 != c_Groups_Ozero__class_Ozero(U_7081) ) )
      | ~ class_Divides_Osemiring__div(U_7081) ),
    inference(variable_rename,[status(thm)],[f_1888_1]) ).

cnf(f_1888_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7081),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7081),U_7082),U_7083)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7081),U_7082),U_7084)) = c_Groups_Ozero__class_Ozero(U_7081)
    | U_7082 != c_Groups_Ozero__class_Ozero(U_7081)
    | ~ class_Divides_Osemiring__div(U_7081) ),
    inference(clausify,[status(thm)],[f_1888_2]) ).

cnf(f_1888_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7081),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7081),U_7082),U_7083)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7081),U_7082),U_7084)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7081),U_7083),U_7084)
    | U_7082 = c_Groups_Ozero__class_Ozero(U_7081)
    | ~ class_Divides_Osemiring__div(U_7081) ),
    inference(clausify,[status(thm)],[f_1888_2]) ).

fof(f_1889_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a)
      | V_a = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_div__self]) ).

fof(f_1889_2,plain,
    ! [U_7086,U_7085] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7085),U_7086),U_7086) = c_Groups_Oone__class_Oone(U_7085)
      | U_7086 = c_Groups_Ozero__class_Ozero(U_7085)
      | ~ class_Divides_Osemiring__div(U_7085) ),
    inference(variable_rename,[status(thm)],[f_1889_1]) ).

cnf(f_1889_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7085),U_7086),U_7086) = c_Groups_Oone__class_Oone(U_7085)
    | U_7086 = c_Groups_Ozero__class_Ozero(U_7085)
    | ~ class_Divides_Osemiring__div(U_7085) ),
    inference(clausify,[status(thm)],[f_1889_2]) ).

fof(f_1890_1,plain,
    ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))),
    inference(fof_nnf,[status(thm)],[fact_not__neg__number__of__Pls]) ).

cnf(f_1890_2,plain,
    ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))),
    inference(clausify,[status(thm)],[f_1890_1]) ).

fof(f_1891_1,plain,
    ! [V_k_2,V_i_2] :
      ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_i_2))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),V_k_2))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2)) )
          & V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_i_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),V_k_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2)) )
        | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(fof_nnf,[status(thm)],[fact_zdiv__eq__0__iff]) ).

fof(f_1891_2,plain,
    ! [U_7088,U_7087] :
      ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7087),U_7088) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7088),U_7087))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7087),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7087),U_7088))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7087)) )
          & U_7088 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7088),U_7087))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7087),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7087),U_7088))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7087)) )
        | U_7088 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7087),U_7088) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[f_1891_1]) ).

fof(f_1891_3,plain,
    ( ! [U_7092,U_7090] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7090),U_7092) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7092),U_7090))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7090),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7090),U_7092))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7090)) )
          & U_7092 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_7091,U_7089] :
        ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7091),U_7089))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7089),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7089),U_7091))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7089)) )
        | U_7091 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7089),U_7091) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(miniscope,[status(thm)],[f_1891_2]) ).

cnf(f_1891_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7089),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7089))
    | U_7091 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7089),U_7091) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1891_3]) ).

cnf(f_1891_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7091),U_7089))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7089))
    | U_7091 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7089),U_7091) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1891_3]) ).

cnf(f_1891_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7089),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7089),U_7091))
    | U_7091 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7089),U_7091) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1891_3]) ).

cnf(f_1891_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7091),U_7089))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7089),U_7091))
    | U_7091 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7089),U_7091) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1891_3]) ).

cnf(f_1891_8,plain,
    ( U_7092 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7090),U_7092) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1891_3]) ).

cnf(f_1891_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7090),U_7092))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7090))
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7090),U_7092) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1891_3]) ).

cnf(f_1891_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7092),U_7090))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7090),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7090),U_7092) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1891_3]) ).

fof(f_1892_1,plain,
    ! [V_a_2,V_b_2] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) ),
    inference(fof_nnf,[status(thm)],[fact_pos__imp__zdiv__nonneg__iff]) ).

fof(f_1892_2,plain,
    ! [U_7094,U_7093] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7094),U_7093)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7094)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7094))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7094),U_7093))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7093)) ),
    inference(variable_rename,[status(thm)],[f_1892_1]) ).

cnf(f_1892_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7094))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7094),U_7093)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7093)) ),
    inference(clausify,[status(thm)],[f_1892_2]) ).

cnf(f_1892_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7094),U_7093)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7094))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7093)) ),
    inference(clausify,[status(thm)],[f_1892_2]) ).

fof(f_1893_1,plain,
    ! [V_i_2,V_k_2] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_i_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_i_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) ),
    inference(fof_nnf,[status(thm)],[fact_pos__imp__zdiv__pos__iff]) ).

fof(f_1893_2,plain,
    ! [U_7096,U_7095] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7096),U_7095)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7095),U_7096)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7095),U_7096))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7096),U_7095))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7095)) ),
    inference(variable_rename,[status(thm)],[f_1893_1]) ).

cnf(f_1893_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7095),U_7096))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7096),U_7095)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7095)) ),
    inference(clausify,[status(thm)],[f_1893_2]) ).

cnf(f_1893_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7096),U_7095)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7095),U_7096))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7095)) ),
    inference(clausify,[status(thm)],[f_1893_2]) ).

fof(f_1894_1,plain,
    ! [V_b_2,V_a_2] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),V_a_2)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),V_a_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ),
    inference(fof_nnf,[status(thm)],[fact_nonneg1__imp__zdiv__pos__iff]) ).

fof(f_1894_2,plain,
    ! [U_7098,U_7097] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7097),U_7098)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7098))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7098),U_7097)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7098))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7098),U_7097)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7097),U_7098))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7097)) ),
    inference(variable_rename,[status(thm)],[f_1894_1]) ).

cnf(f_1894_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7098),U_7097))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7097),U_7098)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7097)) ),
    inference(clausify,[status(thm)],[f_1894_2]) ).

cnf(f_1894_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7098))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7097),U_7098)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7097)) ),
    inference(clausify,[status(thm)],[f_1894_2]) ).

cnf(f_1894_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7097),U_7098)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7098))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7098),U_7097))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7097)) ),
    inference(clausify,[status(thm)],[f_1894_2]) ).

fof(f_1895_1,plain,
    ! [V_b,V_b_H,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b_H)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) ),
    inference(fof_nnf,[status(thm)],[fact_zdiv__mono2]) ).

fof(f_1895_2,plain,
    ! [U_7101,U_7100,U_7099] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7099),U_7101)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7099),U_7100)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7100),U_7101))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7100))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7099)) ),
    inference(variable_rename,[status(thm)],[f_1895_1]) ).

cnf(f_1895_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7099),U_7101)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7099),U_7100)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7100),U_7101))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7100))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7099)) ),
    inference(clausify,[status(thm)],[f_1895_2]) ).

fof(f_1896_1,plain,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) ),
    inference(fof_nnf,[status(thm)],[fact_div__nonneg__neg__le0]) ).

fof(f_1896_2,plain,
    ! [U_7103,U_7102] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7102),U_7103)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7103),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7102)) ),
    inference(variable_rename,[status(thm)],[f_1896_1]) ).

cnf(f_1896_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7102),U_7103)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7103),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7102)) ),
    inference(clausify,[status(thm)],[f_1896_2]) ).

fof(f_1897_1,plain,
    ! [V_b,V_a] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) ),
    inference(fof_nnf,[status(thm)],[fact_div__pos__pos__trivial]) ).

fof(f_1897_2,plain,
    ! [U_7105,U_7104] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7104),U_7105) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7104),U_7105))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7104)) ),
    inference(variable_rename,[status(thm)],[f_1897_1]) ).

cnf(f_1897_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7104),U_7105) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7104),U_7105))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7104)) ),
    inference(clausify,[status(thm)],[f_1897_2]) ).

fof(f_1898_1,plain,
    ! [V_a_2,V_b_2] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(fof_nnf,[status(thm)],[fact_neg__imp__zdiv__nonneg__iff]) ).

fof(f_1898_2,plain,
    ! [U_7107,U_7106] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7107),U_7106)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7107),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7107),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7107),U_7106))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7106),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_1898_1]) ).

cnf(f_1898_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7107),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7107),U_7106)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7106),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1898_2]) ).

cnf(f_1898_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7107),U_7106)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7107),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7106),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1898_2]) ).

fof(f_1899_1,plain,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(fof_nnf,[status(thm)],[fact_div__nonpos__pos__le0]) ).

fof(f_1899_2,plain,
    ! [U_7109,U_7108] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7108),U_7109)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7109))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7108),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_1899_1]) ).

cnf(f_1899_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7108),U_7109)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7109))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7108),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1899_2]) ).

fof(f_1900_1,plain,
    ! [V_b,V_b_H,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b_H)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(fof_nnf,[status(thm)],[fact_zdiv__mono2__neg]) ).

fof(f_1900_2,plain,
    ! [U_7112,U_7111,U_7110] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7110),U_7111)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7110),U_7112)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7111),U_7112))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7111))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7110),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_1900_1]) ).

cnf(f_1900_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7110),U_7111)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7110),U_7112)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7111),U_7112))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7111))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7110),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1900_2]) ).

fof(f_1901_1,plain,
    ! [V_b,V_a] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(fof_nnf,[status(thm)],[fact_div__neg__neg__trivial]) ).

fof(f_1901_2,plain,
    ! [U_7114,U_7113] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7113),U_7114) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7114),U_7113))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7113),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_1901_1]) ).

cnf(f_1901_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7113),U_7114) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7114),U_7113))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7113),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1901_2]) ).

fof(f_1902_1,plain,
    ! [V_b,V_a_H,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_H),V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H)) ),
    inference(fof_nnf,[status(thm)],[fact_zdiv__mono1]) ).

fof(f_1902_2,plain,
    ! [U_7117,U_7116,U_7115] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7115),U_7117)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7116),U_7117)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7117))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7115),U_7116)) ),
    inference(variable_rename,[status(thm)],[f_1902_1]) ).

cnf(f_1902_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7115),U_7117)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7116),U_7117)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7117))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7115),U_7116)) ),
    inference(clausify,[status(thm)],[f_1902_2]) ).

fof(f_1903_1,plain,
    ! [V_b,V_a_H,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_H),V_b)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H)) ),
    inference(fof_nnf,[status(thm)],[fact_zdiv__mono1__neg]) ).

fof(f_1903_2,plain,
    ! [U_7120,U_7119,U_7118] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7119),U_7120)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7118),U_7120)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7120),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7118),U_7119)) ),
    inference(variable_rename,[status(thm)],[f_1903_1]) ).

cnf(f_1903_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7119),U_7120)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7118),U_7120)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7120),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7118),U_7119)) ),
    inference(clausify,[status(thm)],[f_1903_2]) ).

fof(f_1904_1,plain,
    ! [V_k,V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_k)),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) ),
    inference(fof_nnf,[status(thm)],[fact_int__div__less__self]) ).

fof(f_1904_2,plain,
    ! [U_7122,U_7121] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7121),U_7122)),U_7121))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_7122))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7121)) ),
    inference(variable_rename,[status(thm)],[f_1904_1]) ).

cnf(f_1904_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7121),U_7122)),U_7121))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_7122))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7121)) ),
    inference(clausify,[status(thm)],[f_1904_2]) ).

fof(f_1905_1,plain,
    ! [V_b,V_a,V_c] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),V_c)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) ),
    inference(fof_nnf,[status(thm)],[fact_zdiv__zmult2__eq]) ).

fof(f_1905_2,plain,
    ! [U_7125,U_7124,U_7123] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7124),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7125),U_7123)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7124),U_7125)),U_7123)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7123)) ),
    inference(variable_rename,[status(thm)],[f_1905_1]) ).

cnf(f_1905_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7124),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7125),U_7123)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7124),U_7125)),U_7123)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7123)) ),
    inference(clausify,[status(thm)],[f_1905_2]) ).

fof(f_1906_1,plain,
    ! [V_x,T_a] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Int_Onumber__ring(T_a)
      | ~ class_Fields_Ofield__inverse__zero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_divide__Numeral0]) ).

fof(f_1906_2,plain,
    ! [U_7127,U_7126] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7126),U_7127),hAPP(c_Int_Onumber__class_Onumber__of(U_7126),c_Int_OPls)) = c_Groups_Ozero__class_Ozero(U_7126)
      | ~ class_Int_Onumber__ring(U_7126)
      | ~ class_Fields_Ofield__inverse__zero(U_7126) ),
    inference(variable_rename,[status(thm)],[f_1906_1]) ).

cnf(f_1906_3,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7126),U_7127),hAPP(c_Int_Onumber__class_Onumber__of(U_7126),c_Int_OPls)) = c_Groups_Ozero__class_Ozero(U_7126)
    | ~ class_Int_Onumber__ring(U_7126)
    | ~ class_Fields_Ofield__inverse__zero(U_7126) ),
    inference(clausify,[status(thm)],[f_1906_2]) ).

fof(f_1907_1,plain,
    ! [V_v_2] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(fof_nnf,[status(thm)],[fact_eq__number__of__0]) ).

fof(f_1907_2,plain,
    ! [U_7128] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7128) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7128),c_Int_OPls)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7128),c_Int_OPls))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7128) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_1907_1]) ).

fof(f_1907_3,plain,
    ( ! [U_7130] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7130) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7130),c_Int_OPls)) )
    & ! [U_7129] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7129),c_Int_OPls))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7129) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_1907_2]) ).

cnf(f_1907_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7129),c_Int_OPls))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7129) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1907_3]) ).

cnf(f_1907_5,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7130) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7130),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1907_3]) ).

fof(f_1908_1,plain,
    ! [V_v_2] :
      ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls))
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_eq__0__number__of]) ).

fof(f_1908_2,plain,
    ! [U_7131] :
      ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7131)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7131),c_Int_OPls)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7131),c_Int_OPls))
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7131) ) ),
    inference(variable_rename,[status(thm)],[f_1908_1]) ).

fof(f_1908_3,plain,
    ( ! [U_7133] :
        ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7133)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7133),c_Int_OPls)) )
    & ! [U_7132] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7132),c_Int_OPls))
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7132) ) ),
    inference(miniscope,[status(thm)],[f_1908_2]) ).

cnf(f_1908_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7132),c_Int_OPls))
    | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7132) ),
    inference(clausify,[status(thm)],[f_1908_3]) ).

cnf(f_1908_5,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7133)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7133),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1908_3]) ).

fof(f_1909_1,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))),
    inference(fof_nnf,[status(thm)],[fact_number__of2]) ).

cnf(f_1909_2,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))),
    inference(clausify,[status(thm)],[f_1909_1]) ).

fof(f_1910_1,plain,
    ! [V_v_H_2,V_v_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_H_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2)) ) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2))
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_H_2))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2)) ) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_less__nat__number__of]) ).

fof(f_1910_2,plain,
    ! [U_7135,U_7134] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7134)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7135)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7134),U_7135))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_7135))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7134),U_7135)) ) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7134),U_7135))
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_7135))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7134),U_7135)) ) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7134)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7135))) ) ),
    inference(variable_rename,[status(thm)],[f_1910_1]) ).

fof(f_1910_3,plain,
    ( ! [U_7139,U_7137] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7137)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7139)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7137),U_7139))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_7139))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7137),U_7139)) ) )
    & ! [U_7138,U_7136] :
        ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7136),U_7138))
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_7138))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7136),U_7138)) ) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7136)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7138))) ) ),
    inference(miniscope,[status(thm)],[f_1910_2]) ).

cnf(f_1910_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_7138))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7136),U_7138))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7136)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7138))) ),
    inference(clausify,[status(thm)],[f_1910_3]) ).

cnf(f_1910_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7136),U_7138))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7136)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7138))) ),
    inference(clausify,[status(thm)],[f_1910_3]) ).

cnf(f_1910_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7137),U_7139))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7137),U_7139))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7137)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7139))) ),
    inference(clausify,[status(thm)],[f_1910_3]) ).

cnf(f_1910_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_7139))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7137),U_7139))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7137)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7139))) ),
    inference(clausify,[status(thm)],[f_1910_3]) ).

fof(f_1911_1,plain,
    ! [V_v_H_2,V_v_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),V_v_H_2)) ) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),V_v_H_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_le__nat__number__of]) ).

fof(f_1911_2,plain,
    ! [U_7141,U_7140] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7140)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7141)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7140),c_Int_OPls))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7140),U_7141)) ) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7140),c_Int_OPls))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7140),U_7141))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7140)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7141))) ) ),
    inference(variable_rename,[status(thm)],[f_1911_1]) ).

fof(f_1911_3,plain,
    ( ! [U_7145,U_7143] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7143)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7145)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7143),c_Int_OPls))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7143),U_7145)) ) )
    & ! [U_7144,U_7142] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7142),c_Int_OPls))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7142),U_7144))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7142)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7144))) ) ),
    inference(miniscope,[status(thm)],[f_1911_2]) ).

cnf(f_1911_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7142),c_Int_OPls))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7142),U_7144))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7142)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7144))) ),
    inference(clausify,[status(thm)],[f_1911_3]) ).

cnf(f_1911_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7143),U_7145))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7143)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7145))) ),
    inference(clausify,[status(thm)],[f_1911_3]) ).

cnf(f_1911_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7143),c_Int_OPls))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7143)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7145))) ),
    inference(clausify,[status(thm)],[f_1911_3]) ).

fof(f_1912_1,plain,
    ! [V_c,V_a,V_b,T_a] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b))
      | V_b = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_div__mult__self2]) ).

fof(f_1912_2,plain,
    ! [U_7149,U_7148,U_7147,U_7146] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7146),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7146),U_7148),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7146),U_7147),U_7149))),U_7147) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7146),U_7149),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7146),U_7148),U_7147))
      | U_7147 = c_Groups_Ozero__class_Ozero(U_7146)
      | ~ class_Divides_Osemiring__div(U_7146) ),
    inference(variable_rename,[status(thm)],[f_1912_1]) ).

cnf(f_1912_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7146),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7146),U_7148),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7146),U_7147),U_7149))),U_7147) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7146),U_7149),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7146),U_7148),U_7147))
    | U_7147 = c_Groups_Ozero__class_Ozero(U_7146)
    | ~ class_Divides_Osemiring__div(U_7146) ),
    inference(clausify,[status(thm)],[f_1912_2]) ).

fof(f_1913_1,plain,
    ! [V_c,V_a,V_b,T_a] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b))
      | V_b = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_div__mult__self1]) ).

fof(f_1913_2,plain,
    ! [U_7153,U_7152,U_7151,U_7150] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7150),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7150),U_7152),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7150),U_7153),U_7151))),U_7151) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7150),U_7153),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7150),U_7152),U_7151))
      | U_7151 = c_Groups_Ozero__class_Ozero(U_7150)
      | ~ class_Divides_Osemiring__div(U_7150) ),
    inference(variable_rename,[status(thm)],[f_1913_1]) ).

cnf(f_1913_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7150),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7150),U_7152),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7150),U_7153),U_7151))),U_7151) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7150),U_7153),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7150),U_7152),U_7151))
    | U_7151 = c_Groups_Ozero__class_Ozero(U_7150)
    | ~ class_Divides_Osemiring__div(U_7150) ),
    inference(clausify,[status(thm)],[f_1913_2]) ).

fof(f_1914_1,plain,
    ! [V_a,V_b,T_a] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),c_Groups_Oone__class_Oone(T_a))
      | V_b = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_div__add__self2]) ).

fof(f_1914_2,plain,
    ! [U_7156,U_7155,U_7154] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7154),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7154),U_7156),U_7155)),U_7155) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7154),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7154),U_7156),U_7155)),c_Groups_Oone__class_Oone(U_7154))
      | U_7155 = c_Groups_Ozero__class_Ozero(U_7154)
      | ~ class_Divides_Osemiring__div(U_7154) ),
    inference(variable_rename,[status(thm)],[f_1914_1]) ).

cnf(f_1914_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7154),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7154),U_7156),U_7155)),U_7155) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7154),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7154),U_7156),U_7155)),c_Groups_Oone__class_Oone(U_7154))
    | U_7155 = c_Groups_Ozero__class_Ozero(U_7154)
    | ~ class_Divides_Osemiring__div(U_7154) ),
    inference(clausify,[status(thm)],[f_1914_2]) ).

fof(f_1915_1,plain,
    ! [V_a,V_b,T_a] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a)),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),c_Groups_Oone__class_Oone(T_a))
      | V_b = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_div__add__self1]) ).

fof(f_1915_2,plain,
    ! [U_7159,U_7158,U_7157] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7157),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7157),U_7158),U_7159)),U_7158) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7157),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7157),U_7159),U_7158)),c_Groups_Oone__class_Oone(U_7157))
      | U_7158 = c_Groups_Ozero__class_Ozero(U_7157)
      | ~ class_Divides_Osemiring__div(U_7157) ),
    inference(variable_rename,[status(thm)],[f_1915_1]) ).

cnf(f_1915_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7157),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7157),U_7158),U_7159)),U_7158) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7157),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7157),U_7159),U_7158)),c_Groups_Oone__class_Oone(U_7157))
    | U_7158 = c_Groups_Ozero__class_Ozero(U_7157)
    | ~ class_Divides_Osemiring__div(U_7157) ),
    inference(clausify,[status(thm)],[f_1915_2]) ).

fof(f_1916_1,plain,
    ! [V_x_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Ozero__class_Ozero(T_b)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OPls)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OPls))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Ozero__class_Ozero(T_b))) ) )
      | ~ class_Rings_Olinordered__idom(T_b)
      | ~ class_Int_Onumber__ring(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_le__special_I3_J]) ).

fof(f_1916_2,plain,
    ! [U_7161,U_7160] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7160),hAPP(c_Int_Onumber__class_Onumber__of(U_7160),U_7161)),c_Groups_Ozero__class_Ozero(U_7160)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7161),c_Int_OPls)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7161),c_Int_OPls))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7160),hAPP(c_Int_Onumber__class_Onumber__of(U_7160),U_7161)),c_Groups_Ozero__class_Ozero(U_7160))) ) )
      | ~ class_Rings_Olinordered__idom(U_7160)
      | ~ class_Int_Onumber__ring(U_7160) ),
    inference(variable_rename,[status(thm)],[f_1916_1]) ).

cnf(f_1916_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7161),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7160),hAPP(c_Int_Onumber__class_Onumber__of(U_7160),U_7161)),c_Groups_Ozero__class_Ozero(U_7160)))
    | ~ class_Rings_Olinordered__idom(U_7160)
    | ~ class_Int_Onumber__ring(U_7160) ),
    inference(clausify,[status(thm)],[f_1916_2]) ).

cnf(f_1916_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7160),hAPP(c_Int_Onumber__class_Onumber__of(U_7160),U_7161)),c_Groups_Ozero__class_Ozero(U_7160)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7161),c_Int_OPls))
    | ~ class_Rings_Olinordered__idom(U_7160)
    | ~ class_Int_Onumber__ring(U_7160) ),
    inference(clausify,[status(thm)],[f_1916_2]) ).

fof(f_1917_1,plain,
    ! [V_y_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_y_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_y_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2))) ) )
      | ~ class_Rings_Olinordered__idom(T_b)
      | ~ class_Int_Onumber__ring(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_le__special_I1_J]) ).

fof(f_1917_2,plain,
    ! [U_7163,U_7162] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7162),c_Groups_Ozero__class_Ozero(U_7162)),hAPP(c_Int_Onumber__class_Onumber__of(U_7162),U_7163)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_7163)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_7163))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7162),c_Groups_Ozero__class_Ozero(U_7162)),hAPP(c_Int_Onumber__class_Onumber__of(U_7162),U_7163))) ) )
      | ~ class_Rings_Olinordered__idom(U_7162)
      | ~ class_Int_Onumber__ring(U_7162) ),
    inference(variable_rename,[status(thm)],[f_1917_1]) ).

cnf(f_1917_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_7163))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7162),c_Groups_Ozero__class_Ozero(U_7162)),hAPP(c_Int_Onumber__class_Onumber__of(U_7162),U_7163)))
    | ~ class_Rings_Olinordered__idom(U_7162)
    | ~ class_Int_Onumber__ring(U_7162) ),
    inference(clausify,[status(thm)],[f_1917_2]) ).

cnf(f_1917_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7162),c_Groups_Ozero__class_Ozero(U_7162)),hAPP(c_Int_Onumber__class_Onumber__of(U_7162),U_7163)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_7163))
    | ~ class_Rings_Olinordered__idom(U_7162)
    | ~ class_Int_Onumber__ring(U_7162) ),
    inference(clausify,[status(thm)],[f_1917_2]) ).

fof(f_1918_1,plain,
    ! [V_y_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_y_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_y_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2))) ) )
      | ~ class_Rings_Olinordered__idom(T_b)
      | ~ class_Int_Onumber__ring(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_less__special_I1_J]) ).

fof(f_1918_2,plain,
    ! [U_7165,U_7164] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7164),c_Groups_Ozero__class_Ozero(U_7164)),hAPP(c_Int_Onumber__class_Onumber__of(U_7164),U_7165)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_7165)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_7165))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7164),c_Groups_Ozero__class_Ozero(U_7164)),hAPP(c_Int_Onumber__class_Onumber__of(U_7164),U_7165))) ) )
      | ~ class_Rings_Olinordered__idom(U_7164)
      | ~ class_Int_Onumber__ring(U_7164) ),
    inference(variable_rename,[status(thm)],[f_1918_1]) ).

cnf(f_1918_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_7165))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7164),c_Groups_Ozero__class_Ozero(U_7164)),hAPP(c_Int_Onumber__class_Onumber__of(U_7164),U_7165)))
    | ~ class_Rings_Olinordered__idom(U_7164)
    | ~ class_Int_Onumber__ring(U_7164) ),
    inference(clausify,[status(thm)],[f_1918_2]) ).

cnf(f_1918_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7164),c_Groups_Ozero__class_Ozero(U_7164)),hAPP(c_Int_Onumber__class_Onumber__of(U_7164),U_7165)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_7165))
    | ~ class_Rings_Olinordered__idom(U_7164)
    | ~ class_Int_Onumber__ring(U_7164) ),
    inference(clausify,[status(thm)],[f_1918_2]) ).

fof(f_1919_1,plain,
    ! [V_x_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Ozero__class_Ozero(T_b)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OPls)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OPls))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Ozero__class_Ozero(T_b))) ) )
      | ~ class_Rings_Olinordered__idom(T_b)
      | ~ class_Int_Onumber__ring(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_less__special_I3_J]) ).

fof(f_1919_2,plain,
    ! [U_7167,U_7166] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7166),hAPP(c_Int_Onumber__class_Onumber__of(U_7166),U_7167)),c_Groups_Ozero__class_Ozero(U_7166)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7167),c_Int_OPls)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7167),c_Int_OPls))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7166),hAPP(c_Int_Onumber__class_Onumber__of(U_7166),U_7167)),c_Groups_Ozero__class_Ozero(U_7166))) ) )
      | ~ class_Rings_Olinordered__idom(U_7166)
      | ~ class_Int_Onumber__ring(U_7166) ),
    inference(variable_rename,[status(thm)],[f_1919_1]) ).

cnf(f_1919_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7167),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7166),hAPP(c_Int_Onumber__class_Onumber__of(U_7166),U_7167)),c_Groups_Ozero__class_Ozero(U_7166)))
    | ~ class_Rings_Olinordered__idom(U_7166)
    | ~ class_Int_Onumber__ring(U_7166) ),
    inference(clausify,[status(thm)],[f_1919_2]) ).

cnf(f_1919_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7166),hAPP(c_Int_Onumber__class_Onumber__of(U_7166),U_7167)),c_Groups_Ozero__class_Ozero(U_7166)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7167),c_Int_OPls))
    | ~ class_Rings_Olinordered__idom(U_7166)
    | ~ class_Int_Onumber__ring(U_7166) ),
    inference(clausify,[status(thm)],[f_1919_2]) ).

fof(f_1920_1,plain,
    ! [V_v_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_less__0__number__of]) ).

fof(f_1920_2,plain,
    ! [U_7168] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7168)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_7168)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_7168))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7168))) ) ),
    inference(variable_rename,[status(thm)],[f_1920_1]) ).

fof(f_1920_3,plain,
    ( ! [U_7170] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7170)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_7170)) )
    & ! [U_7169] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_7169))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7169))) ) ),
    inference(miniscope,[status(thm)],[f_1920_2]) ).

cnf(f_1920_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_7169))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7169))) ),
    inference(clausify,[status(thm)],[f_1920_3]) ).

cnf(f_1920_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7170)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_7170)) ),
    inference(clausify,[status(thm)],[f_1920_3]) ).

fof(f_1921_1,plain,
    ! [V_v_H,V_v] :
      ( ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_v_H))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls)) )
          & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls)) ) )
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) )
      & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) ) ),
    inference(fof_nnf,[status(thm)],[fact_add__nat__number__of]) ).

fof(f_1921_2,plain,
    ! [U_7172,U_7171] :
      ( ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7171)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7172)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7171),U_7172))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7172),c_Int_OPls)) )
          & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7171)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7172)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7171)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7172),c_Int_OPls)) ) )
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7171),c_Int_OPls)) )
      & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7171)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7172)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7172)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7171),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[f_1921_1]) ).

fof(f_1921_3,plain,
    ( ! [U_7176,U_7174] :
        ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7174)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7176)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7174),U_7176))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7176),c_Int_OPls)) )
          & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7174)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7176)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7174)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7176),c_Int_OPls)) ) )
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7174),c_Int_OPls)) )
    & ! [U_7175,U_7173] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7173)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7175)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7175)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7173),c_Int_OPls)) ) ),
    inference(miniscope,[status(thm)],[f_1921_2]) ).

cnf(f_1921_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7173)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7175)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7175)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7173),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1921_3]) ).

cnf(f_1921_5,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7174)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7176)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7174)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7176),c_Int_OPls))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7174),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1921_3]) ).

cnf(f_1921_6,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7174)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7176)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7174),U_7176))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7176),c_Int_OPls))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7174),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1921_3]) ).

fof(f_1922_1,plain,
    ! [V_k_2,V_n_2,V_P_2] :
      ( ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)))
        | ( ? [B_i] :
              ( ~ hBOOL(hAPP(V_P_2,B_i))
              & ? [B_j] :
                  ( V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) ) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ? [B_i] :
              ( ~ hBOOL(hAPP(V_P_2,B_i))
              & ? [B_j] :
                  ( V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) ) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) )
        | ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
      & ( ( ( ! [B_i] :
                ( hBOOL(hAPP(V_P_2,B_i))
                | ! [B_j] :
                    ( V_n_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [B_i] :
                ( hBOOL(hAPP(V_P_2,B_i))
                | ! [B_j] :
                    ( V_n_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) )
          & ( hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_split__zdiv]) ).

fof(f_1922_2,plain,
    ! [U_7187,U_7186,U_7185] :
      ( ( hBOOL(hAPP(U_7185,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7186),U_7187)))
        | ( ? [U_7184] :
              ( ~ hBOOL(hAPP(U_7185,U_7184))
              & ? [U_7183] :
                  ( U_7186 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7187),U_7184)),U_7183)
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7183),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7187),U_7183)) ) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7187),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ? [U_7182] :
              ( ~ hBOOL(hAPP(U_7185,U_7182))
              & ? [U_7181] :
                  ( U_7186 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7187),U_7182)),U_7181)
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7181),U_7187))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7181)) ) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7187)) )
        | ( ~ hBOOL(hAPP(U_7185,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & U_7187 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
      & ( ( ( ! [U_7180] :
                ( hBOOL(hAPP(U_7185,U_7180))
                | ! [U_7179] :
                    ( U_7186 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7187),U_7180)),U_7179)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7179),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7187),U_7179)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7187),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [U_7178] :
                ( hBOOL(hAPP(U_7185,U_7178))
                | ! [U_7177] :
                    ( U_7186 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7187),U_7178)),U_7177)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7177),U_7187))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7177)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7187)) )
          & ( hBOOL(hAPP(U_7185,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | U_7187 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_7185,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7186),U_7187))) ) ),
    inference(variable_rename,[status(thm)],[f_1922_1]) ).

fof(f_1922_3,plain,
    ( ! [U_7193,U_7191,U_7189] :
        ( hBOOL(hAPP(U_7189,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7191),U_7193)))
        | ( ? [U_7184] :
              ( ~ hBOOL(hAPP(U_7189,U_7184))
              & ? [U_7183] :
                  ( U_7191 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7193),U_7184)),U_7183)
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7183),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7193),U_7183)) ) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7193),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ? [U_7182] :
              ( ~ hBOOL(hAPP(U_7189,U_7182))
              & ? [U_7181] :
                  ( U_7191 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7193),U_7182)),U_7181)
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7181),U_7193))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7181)) ) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7193)) )
        | ( ~ hBOOL(hAPP(U_7189,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & U_7193 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_7192,U_7190,U_7188] :
        ( ( ( ! [U_7180] :
                ( hBOOL(hAPP(U_7188,U_7180))
                | ! [U_7179] :
                    ( U_7190 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7192),U_7180)),U_7179)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7179),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7192),U_7179)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7192),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [U_7178] :
                ( hBOOL(hAPP(U_7188,U_7178))
                | ! [U_7177] :
                    ( U_7190 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7192),U_7178)),U_7177)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7177),U_7192))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7177)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7192)) )
          & ( hBOOL(hAPP(U_7188,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | U_7192 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_7188,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7190),U_7192))) ) ),
    inference(miniscope,[status(thm)],[f_1922_2]) ).

fof(f_1922_4,plain,
    ( ! [U_7193,U_7191,U_7189] :
        ( hBOOL(hAPP(U_7189,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7191),U_7193)))
        | ( ? [U_7184] :
              ( ~ hBOOL(hAPP(U_7189,U_7184))
              & ? [U_7183] :
                  ( U_7191 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7193),U_7184)),U_7183)
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7183),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7193),U_7183)) ) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7193),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ~ hBOOL(hAPP(U_7189,sK188(U_7193,U_7191,U_7189)))
          & ? [U_7181] :
              ( U_7191 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7193),sK188(U_7193,U_7191,U_7189))),U_7181)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7181),U_7193))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7181)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7193)) )
        | ( ~ hBOOL(hAPP(U_7189,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & U_7193 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_7192,U_7190,U_7188] :
        ( ( ( ! [U_7180] :
                ( hBOOL(hAPP(U_7188,U_7180))
                | ! [U_7179] :
                    ( U_7190 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7192),U_7180)),U_7179)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7179),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7192),U_7179)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7192),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [U_7178] :
                ( hBOOL(hAPP(U_7188,U_7178))
                | ! [U_7177] :
                    ( U_7190 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7192),U_7178)),U_7177)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7177),U_7192))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7177)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7192)) )
          & ( hBOOL(hAPP(U_7188,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | U_7192 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_7188,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7190),U_7192))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK188]),skolemize(U_7182,sK188(U_7193,U_7191,U_7189))],[f_1922_3]) ).

fof(f_1922_5,plain,
    ( ! [U_7193,U_7191,U_7189] :
        ( hBOOL(hAPP(U_7189,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7191),U_7193)))
        | ( ? [U_7184] :
              ( ~ hBOOL(hAPP(U_7189,U_7184))
              & ? [U_7183] :
                  ( U_7191 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7193),U_7184)),U_7183)
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7183),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7193),U_7183)) ) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7193),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ~ hBOOL(hAPP(U_7189,sK188(U_7193,U_7191,U_7189)))
          & U_7191 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7193),sK188(U_7193,U_7191,U_7189))),sK189(U_7193,U_7191,U_7189))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK189(U_7193,U_7191,U_7189)),U_7193))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK189(U_7193,U_7191,U_7189)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7193)) )
        | ( ~ hBOOL(hAPP(U_7189,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & U_7193 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_7192,U_7190,U_7188] :
        ( ( ( ! [U_7180] :
                ( hBOOL(hAPP(U_7188,U_7180))
                | ! [U_7179] :
                    ( U_7190 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7192),U_7180)),U_7179)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7179),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7192),U_7179)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7192),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [U_7178] :
                ( hBOOL(hAPP(U_7188,U_7178))
                | ! [U_7177] :
                    ( U_7190 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7192),U_7178)),U_7177)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7177),U_7192))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7177)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7192)) )
          & ( hBOOL(hAPP(U_7188,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | U_7192 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_7188,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7190),U_7192))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK189]),skolemize(U_7181,sK189(U_7193,U_7191,U_7189))],[f_1922_4]) ).

fof(f_1922_6,plain,
    ( ! [U_7193,U_7191,U_7189] :
        ( hBOOL(hAPP(U_7189,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7191),U_7193)))
        | ( ~ hBOOL(hAPP(U_7189,sK190(U_7193,U_7191,U_7189)))
          & ? [U_7183] :
              ( U_7191 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7193),sK190(U_7193,U_7191,U_7189))),U_7183)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7183),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7193),U_7183)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7193),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ~ hBOOL(hAPP(U_7189,sK188(U_7193,U_7191,U_7189)))
          & U_7191 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7193),sK188(U_7193,U_7191,U_7189))),sK189(U_7193,U_7191,U_7189))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK189(U_7193,U_7191,U_7189)),U_7193))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK189(U_7193,U_7191,U_7189)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7193)) )
        | ( ~ hBOOL(hAPP(U_7189,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & U_7193 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_7192,U_7190,U_7188] :
        ( ( ( ! [U_7180] :
                ( hBOOL(hAPP(U_7188,U_7180))
                | ! [U_7179] :
                    ( U_7190 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7192),U_7180)),U_7179)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7179),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7192),U_7179)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7192),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [U_7178] :
                ( hBOOL(hAPP(U_7188,U_7178))
                | ! [U_7177] :
                    ( U_7190 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7192),U_7178)),U_7177)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7177),U_7192))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7177)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7192)) )
          & ( hBOOL(hAPP(U_7188,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | U_7192 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_7188,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7190),U_7192))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK190]),skolemize(U_7184,sK190(U_7193,U_7191,U_7189))],[f_1922_5]) ).

fof(f_1922_7,plain,
    ( ! [U_7193,U_7191,U_7189] :
        ( hBOOL(hAPP(U_7189,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7191),U_7193)))
        | ( ~ hBOOL(hAPP(U_7189,sK190(U_7193,U_7191,U_7189)))
          & U_7191 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7193),sK190(U_7193,U_7191,U_7189))),sK191(U_7193,U_7191,U_7189))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK191(U_7193,U_7191,U_7189)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7193),sK191(U_7193,U_7191,U_7189)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7193),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ~ hBOOL(hAPP(U_7189,sK188(U_7193,U_7191,U_7189)))
          & U_7191 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7193),sK188(U_7193,U_7191,U_7189))),sK189(U_7193,U_7191,U_7189))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK189(U_7193,U_7191,U_7189)),U_7193))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK189(U_7193,U_7191,U_7189)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7193)) )
        | ( ~ hBOOL(hAPP(U_7189,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & U_7193 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_7192,U_7190,U_7188] :
        ( ( ( ! [U_7180] :
                ( hBOOL(hAPP(U_7188,U_7180))
                | ! [U_7179] :
                    ( U_7190 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7192),U_7180)),U_7179)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7179),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7192),U_7179)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7192),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [U_7178] :
                ( hBOOL(hAPP(U_7188,U_7178))
                | ! [U_7177] :
                    ( U_7190 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7192),U_7178)),U_7177)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7177),U_7192))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7177)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7192)) )
          & ( hBOOL(hAPP(U_7188,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | U_7192 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_7188,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7190),U_7192))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK191]),skolemize(U_7183,sK191(U_7193,U_7191,U_7189))],[f_1922_6]) ).

cnf(f_1922_8,plain,
    ( hBOOL(hAPP(U_7188,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | U_7192 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(U_7188,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7190),U_7192))) ),
    inference(clausify,[status(thm)],[f_1922_7]) ).

cnf(f_1922_9,plain,
    ( hBOOL(hAPP(U_7188,U_7178))
    | U_7190 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7192),U_7178)),U_7177)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7177),U_7192))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7177))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7192))
    | ~ hBOOL(hAPP(U_7188,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7190),U_7192))) ),
    inference(clausify,[status(thm)],[f_1922_7]) ).

cnf(f_1922_10,plain,
    ( hBOOL(hAPP(U_7188,U_7180))
    | U_7190 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7192),U_7180)),U_7179)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7179),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7192),U_7179))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7192),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(U_7188,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7190),U_7192))) ),
    inference(clausify,[status(thm)],[f_1922_7]) ).

cnf(f_1922_11,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7193))
    | U_7193 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7193),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_7189,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7191),U_7193))) ),
    inference(clausify,[status(thm)],[f_1922_7]) ).

cnf(f_1922_12,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK189(U_7193,U_7191,U_7189)))
    | U_7193 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7193),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_7189,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7191),U_7193))) ),
    inference(clausify,[status(thm)],[f_1922_7]) ).

cnf(f_1922_13,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK189(U_7193,U_7191,U_7189)),U_7193))
    | U_7193 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7193),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_7189,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7191),U_7193))) ),
    inference(clausify,[status(thm)],[f_1922_7]) ).

cnf(f_1922_14,plain,
    ( U_7191 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7193),sK188(U_7193,U_7191,U_7189))),sK189(U_7193,U_7191,U_7189))
    | U_7193 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7193),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_7189,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7191),U_7193))) ),
    inference(clausify,[status(thm)],[f_1922_7]) ).

cnf(f_1922_15,plain,
    ( ~ hBOOL(hAPP(U_7189,sK188(U_7193,U_7191,U_7189)))
    | U_7193 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7193),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_7189,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7191),U_7193))) ),
    inference(clausify,[status(thm)],[f_1922_7]) ).

cnf(f_1922_16,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7193))
    | ~ hBOOL(hAPP(U_7189,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7193),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_7189,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7191),U_7193))) ),
    inference(clausify,[status(thm)],[f_1922_7]) ).

cnf(f_1922_17,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK189(U_7193,U_7191,U_7189)))
    | ~ hBOOL(hAPP(U_7189,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7193),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_7189,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7191),U_7193))) ),
    inference(clausify,[status(thm)],[f_1922_7]) ).

cnf(f_1922_18,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK189(U_7193,U_7191,U_7189)),U_7193))
    | ~ hBOOL(hAPP(U_7189,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7193),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_7189,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7191),U_7193))) ),
    inference(clausify,[status(thm)],[f_1922_7]) ).

cnf(f_1922_19,plain,
    ( U_7191 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7193),sK188(U_7193,U_7191,U_7189))),sK189(U_7193,U_7191,U_7189))
    | ~ hBOOL(hAPP(U_7189,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7193),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_7189,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7191),U_7193))) ),
    inference(clausify,[status(thm)],[f_1922_7]) ).

cnf(f_1922_20,plain,
    ( ~ hBOOL(hAPP(U_7189,sK188(U_7193,U_7191,U_7189)))
    | ~ hBOOL(hAPP(U_7189,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7193),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_7189,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7191),U_7193))) ),
    inference(clausify,[status(thm)],[f_1922_7]) ).

cnf(f_1922_21,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7193))
    | U_7193 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7193),sK191(U_7193,U_7191,U_7189)))
    | hBOOL(hAPP(U_7189,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7191),U_7193))) ),
    inference(clausify,[status(thm)],[f_1922_7]) ).

cnf(f_1922_22,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK189(U_7193,U_7191,U_7189)))
    | U_7193 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7193),sK191(U_7193,U_7191,U_7189)))
    | hBOOL(hAPP(U_7189,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7191),U_7193))) ),
    inference(clausify,[status(thm)],[f_1922_7]) ).

cnf(f_1922_23,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK189(U_7193,U_7191,U_7189)),U_7193))
    | U_7193 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7193),sK191(U_7193,U_7191,U_7189)))
    | hBOOL(hAPP(U_7189,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7191),U_7193))) ),
    inference(clausify,[status(thm)],[f_1922_7]) ).

cnf(f_1922_24,plain,
    ( U_7191 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7193),sK188(U_7193,U_7191,U_7189))),sK189(U_7193,U_7191,U_7189))
    | U_7193 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7193),sK191(U_7193,U_7191,U_7189)))
    | hBOOL(hAPP(U_7189,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7191),U_7193))) ),
    inference(clausify,[status(thm)],[f_1922_7]) ).

cnf(f_1922_25,plain,
    ( ~ hBOOL(hAPP(U_7189,sK188(U_7193,U_7191,U_7189)))
    | U_7193 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7193),sK191(U_7193,U_7191,U_7189)))
    | hBOOL(hAPP(U_7189,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7191),U_7193))) ),
    inference(clausify,[status(thm)],[f_1922_7]) ).

cnf(f_1922_26,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7193))
    | U_7193 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK191(U_7193,U_7191,U_7189)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_7189,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7191),U_7193))) ),
    inference(clausify,[status(thm)],[f_1922_7]) ).

cnf(f_1922_27,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK189(U_7193,U_7191,U_7189)))
    | U_7193 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK191(U_7193,U_7191,U_7189)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_7189,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7191),U_7193))) ),
    inference(clausify,[status(thm)],[f_1922_7]) ).

cnf(f_1922_28,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK189(U_7193,U_7191,U_7189)),U_7193))
    | U_7193 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK191(U_7193,U_7191,U_7189)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_7189,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7191),U_7193))) ),
    inference(clausify,[status(thm)],[f_1922_7]) ).

cnf(f_1922_29,plain,
    ( U_7191 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7193),sK188(U_7193,U_7191,U_7189))),sK189(U_7193,U_7191,U_7189))
    | U_7193 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK191(U_7193,U_7191,U_7189)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_7189,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7191),U_7193))) ),
    inference(clausify,[status(thm)],[f_1922_7]) ).

cnf(f_1922_30,plain,
    ( ~ hBOOL(hAPP(U_7189,sK188(U_7193,U_7191,U_7189)))
    | U_7193 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK191(U_7193,U_7191,U_7189)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_7189,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7191),U_7193))) ),
    inference(clausify,[status(thm)],[f_1922_7]) ).

cnf(f_1922_31,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7193))
    | U_7193 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_7191 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7193),sK190(U_7193,U_7191,U_7189))),sK191(U_7193,U_7191,U_7189))
    | hBOOL(hAPP(U_7189,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7191),U_7193))) ),
    inference(clausify,[status(thm)],[f_1922_7]) ).

cnf(f_1922_32,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK189(U_7193,U_7191,U_7189)))
    | U_7193 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_7191 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7193),sK190(U_7193,U_7191,U_7189))),sK191(U_7193,U_7191,U_7189))
    | hBOOL(hAPP(U_7189,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7191),U_7193))) ),
    inference(clausify,[status(thm)],[f_1922_7]) ).

cnf(f_1922_33,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK189(U_7193,U_7191,U_7189)),U_7193))
    | U_7193 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_7191 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7193),sK190(U_7193,U_7191,U_7189))),sK191(U_7193,U_7191,U_7189))
    | hBOOL(hAPP(U_7189,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7191),U_7193))) ),
    inference(clausify,[status(thm)],[f_1922_7]) ).

cnf(f_1922_34,plain,
    ( U_7191 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7193),sK188(U_7193,U_7191,U_7189))),sK189(U_7193,U_7191,U_7189))
    | U_7193 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_7191 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7193),sK190(U_7193,U_7191,U_7189))),sK191(U_7193,U_7191,U_7189))
    | hBOOL(hAPP(U_7189,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7191),U_7193))) ),
    inference(clausify,[status(thm)],[f_1922_7]) ).

cnf(f_1922_35,plain,
    ( ~ hBOOL(hAPP(U_7189,sK188(U_7193,U_7191,U_7189)))
    | U_7193 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_7191 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7193),sK190(U_7193,U_7191,U_7189))),sK191(U_7193,U_7191,U_7189))
    | hBOOL(hAPP(U_7189,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7191),U_7193))) ),
    inference(clausify,[status(thm)],[f_1922_7]) ).

cnf(f_1922_36,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7193))
    | U_7193 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(U_7189,sK190(U_7193,U_7191,U_7189)))
    | hBOOL(hAPP(U_7189,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7191),U_7193))) ),
    inference(clausify,[status(thm)],[f_1922_7]) ).

cnf(f_1922_37,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK189(U_7193,U_7191,U_7189)))
    | U_7193 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(U_7189,sK190(U_7193,U_7191,U_7189)))
    | hBOOL(hAPP(U_7189,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7191),U_7193))) ),
    inference(clausify,[status(thm)],[f_1922_7]) ).

cnf(f_1922_38,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK189(U_7193,U_7191,U_7189)),U_7193))
    | U_7193 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(U_7189,sK190(U_7193,U_7191,U_7189)))
    | hBOOL(hAPP(U_7189,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7191),U_7193))) ),
    inference(clausify,[status(thm)],[f_1922_7]) ).

cnf(f_1922_39,plain,
    ( U_7191 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7193),sK188(U_7193,U_7191,U_7189))),sK189(U_7193,U_7191,U_7189))
    | U_7193 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(U_7189,sK190(U_7193,U_7191,U_7189)))
    | hBOOL(hAPP(U_7189,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7191),U_7193))) ),
    inference(clausify,[status(thm)],[f_1922_7]) ).

cnf(f_1922_40,plain,
    ( ~ hBOOL(hAPP(U_7189,sK188(U_7193,U_7191,U_7189)))
    | U_7193 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(U_7189,sK190(U_7193,U_7191,U_7189)))
    | hBOOL(hAPP(U_7189,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7191),U_7193))) ),
    inference(clausify,[status(thm)],[f_1922_7]) ).

cnf(f_1922_41,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7193))
    | ~ hBOOL(hAPP(U_7189,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7193),sK191(U_7193,U_7191,U_7189)))
    | hBOOL(hAPP(U_7189,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7191),U_7193))) ),
    inference(clausify,[status(thm)],[f_1922_7]) ).

cnf(f_1922_42,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK189(U_7193,U_7191,U_7189)))
    | ~ hBOOL(hAPP(U_7189,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7193),sK191(U_7193,U_7191,U_7189)))
    | hBOOL(hAPP(U_7189,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7191),U_7193))) ),
    inference(clausify,[status(thm)],[f_1922_7]) ).

cnf(f_1922_43,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK189(U_7193,U_7191,U_7189)),U_7193))
    | ~ hBOOL(hAPP(U_7189,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7193),sK191(U_7193,U_7191,U_7189)))
    | hBOOL(hAPP(U_7189,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7191),U_7193))) ),
    inference(clausify,[status(thm)],[f_1922_7]) ).

cnf(f_1922_44,plain,
    ( U_7191 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7193),sK188(U_7193,U_7191,U_7189))),sK189(U_7193,U_7191,U_7189))
    | ~ hBOOL(hAPP(U_7189,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7193),sK191(U_7193,U_7191,U_7189)))
    | hBOOL(hAPP(U_7189,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7191),U_7193))) ),
    inference(clausify,[status(thm)],[f_1922_7]) ).

cnf(f_1922_45,plain,
    ( ~ hBOOL(hAPP(U_7189,sK188(U_7193,U_7191,U_7189)))
    | ~ hBOOL(hAPP(U_7189,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7193),sK191(U_7193,U_7191,U_7189)))
    | hBOOL(hAPP(U_7189,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7191),U_7193))) ),
    inference(clausify,[status(thm)],[f_1922_7]) ).

cnf(f_1922_46,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7193))
    | ~ hBOOL(hAPP(U_7189,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK191(U_7193,U_7191,U_7189)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_7189,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7191),U_7193))) ),
    inference(clausify,[status(thm)],[f_1922_7]) ).

cnf(f_1922_47,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK189(U_7193,U_7191,U_7189)))
    | ~ hBOOL(hAPP(U_7189,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK191(U_7193,U_7191,U_7189)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_7189,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7191),U_7193))) ),
    inference(clausify,[status(thm)],[f_1922_7]) ).

cnf(f_1922_48,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK189(U_7193,U_7191,U_7189)),U_7193))
    | ~ hBOOL(hAPP(U_7189,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK191(U_7193,U_7191,U_7189)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_7189,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7191),U_7193))) ),
    inference(clausify,[status(thm)],[f_1922_7]) ).

cnf(f_1922_49,plain,
    ( U_7191 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7193),sK188(U_7193,U_7191,U_7189))),sK189(U_7193,U_7191,U_7189))
    | ~ hBOOL(hAPP(U_7189,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK191(U_7193,U_7191,U_7189)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_7189,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7191),U_7193))) ),
    inference(clausify,[status(thm)],[f_1922_7]) ).

cnf(f_1922_50,plain,
    ( ~ hBOOL(hAPP(U_7189,sK188(U_7193,U_7191,U_7189)))
    | ~ hBOOL(hAPP(U_7189,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK191(U_7193,U_7191,U_7189)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_7189,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7191),U_7193))) ),
    inference(clausify,[status(thm)],[f_1922_7]) ).

cnf(f_1922_51,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7193))
    | ~ hBOOL(hAPP(U_7189,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | U_7191 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7193),sK190(U_7193,U_7191,U_7189))),sK191(U_7193,U_7191,U_7189))
    | hBOOL(hAPP(U_7189,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7191),U_7193))) ),
    inference(clausify,[status(thm)],[f_1922_7]) ).

cnf(f_1922_52,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK189(U_7193,U_7191,U_7189)))
    | ~ hBOOL(hAPP(U_7189,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | U_7191 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7193),sK190(U_7193,U_7191,U_7189))),sK191(U_7193,U_7191,U_7189))
    | hBOOL(hAPP(U_7189,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7191),U_7193))) ),
    inference(clausify,[status(thm)],[f_1922_7]) ).

cnf(f_1922_53,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK189(U_7193,U_7191,U_7189)),U_7193))
    | ~ hBOOL(hAPP(U_7189,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | U_7191 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7193),sK190(U_7193,U_7191,U_7189))),sK191(U_7193,U_7191,U_7189))
    | hBOOL(hAPP(U_7189,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7191),U_7193))) ),
    inference(clausify,[status(thm)],[f_1922_7]) ).

cnf(f_1922_54,plain,
    ( U_7191 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7193),sK188(U_7193,U_7191,U_7189))),sK189(U_7193,U_7191,U_7189))
    | ~ hBOOL(hAPP(U_7189,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | U_7191 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7193),sK190(U_7193,U_7191,U_7189))),sK191(U_7193,U_7191,U_7189))
    | hBOOL(hAPP(U_7189,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7191),U_7193))) ),
    inference(clausify,[status(thm)],[f_1922_7]) ).

cnf(f_1922_55,plain,
    ( ~ hBOOL(hAPP(U_7189,sK188(U_7193,U_7191,U_7189)))
    | ~ hBOOL(hAPP(U_7189,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | U_7191 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7193),sK190(U_7193,U_7191,U_7189))),sK191(U_7193,U_7191,U_7189))
    | hBOOL(hAPP(U_7189,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7191),U_7193))) ),
    inference(clausify,[status(thm)],[f_1922_7]) ).

cnf(f_1922_56,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7193))
    | ~ hBOOL(hAPP(U_7189,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(U_7189,sK190(U_7193,U_7191,U_7189)))
    | hBOOL(hAPP(U_7189,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7191),U_7193))) ),
    inference(clausify,[status(thm)],[f_1922_7]) ).

cnf(f_1922_57,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK189(U_7193,U_7191,U_7189)))
    | ~ hBOOL(hAPP(U_7189,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(U_7189,sK190(U_7193,U_7191,U_7189)))
    | hBOOL(hAPP(U_7189,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7191),U_7193))) ),
    inference(clausify,[status(thm)],[f_1922_7]) ).

cnf(f_1922_58,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK189(U_7193,U_7191,U_7189)),U_7193))
    | ~ hBOOL(hAPP(U_7189,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(U_7189,sK190(U_7193,U_7191,U_7189)))
    | hBOOL(hAPP(U_7189,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7191),U_7193))) ),
    inference(clausify,[status(thm)],[f_1922_7]) ).

cnf(f_1922_59,plain,
    ( U_7191 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7193),sK188(U_7193,U_7191,U_7189))),sK189(U_7193,U_7191,U_7189))
    | ~ hBOOL(hAPP(U_7189,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(U_7189,sK190(U_7193,U_7191,U_7189)))
    | hBOOL(hAPP(U_7189,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7191),U_7193))) ),
    inference(clausify,[status(thm)],[f_1922_7]) ).

cnf(f_1922_60,plain,
    ( ~ hBOOL(hAPP(U_7189,sK188(U_7193,U_7191,U_7189)))
    | ~ hBOOL(hAPP(U_7189,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(U_7189,sK190(U_7193,U_7191,U_7189)))
    | hBOOL(hAPP(U_7189,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7191),U_7193))) ),
    inference(clausify,[status(thm)],[f_1922_7]) ).

fof(f_1923_1,plain,
    ! [V_r_1,V_y,V_b_1,V_a_1] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_1),V_b_1) = V_y
      | V_b_1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r_1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_r_1)) )
        & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) )
      | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_1),V_b_1))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_1)) )
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) )
      | V_a_1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_1),V_y)),V_r_1) ),
    inference(fof_nnf,[status(thm)],[fact_divmod__int__rel__div__eq]) ).

fof(f_1923_2,plain,
    ! [U_7197,U_7196,U_7195,U_7194] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7194),U_7195) = U_7196
      | U_7195 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7197),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7195),U_7197)) )
        & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7195)) )
      | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7197),U_7195))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7197)) )
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7195)) )
      | U_7194 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7195),U_7196)),U_7197) ),
    inference(variable_rename,[status(thm)],[f_1923_1]) ).

cnf(f_1923_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7195))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7195))
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7194),U_7195) = U_7196
    | U_7195 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_7194 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7195),U_7196)),U_7197) ),
    inference(clausify,[status(thm)],[f_1923_2]) ).

cnf(f_1923_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7197),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7195),U_7197))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7195))
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7194),U_7195) = U_7196
    | U_7195 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_7194 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7195),U_7196)),U_7197) ),
    inference(clausify,[status(thm)],[f_1923_2]) ).

cnf(f_1923_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7195))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7197),U_7195))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7197))
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7194),U_7195) = U_7196
    | U_7195 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_7194 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7195),U_7196)),U_7197) ),
    inference(clausify,[status(thm)],[f_1923_2]) ).

cnf(f_1923_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7197),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7195),U_7197))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7197),U_7195))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7197))
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7194),U_7195) = U_7196
    | U_7195 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_7194 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7195),U_7196)),U_7197) ),
    inference(clausify,[status(thm)],[f_1923_2]) ).

fof(f_1924_1,plain,
    ! [V_k,V_v_H,V_v] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_v_H))),V_k)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) )
      & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)),V_k)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__number__of__mult__left]) ).

fof(f_1924_2,plain,
    ! [U_7200,U_7199,U_7198] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7198)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7199)),U_7200)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7198),U_7199))),U_7200)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7198),c_Int_OPls)) )
      & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7198)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7199)),U_7200)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7198),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[f_1924_1]) ).

fof(f_1924_3,plain,
    ( ! [U_7206,U_7204,U_7202] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7202)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7204)),U_7206)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7202),U_7204))),U_7206)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7202),c_Int_OPls)) )
    & ! [U_7205,U_7203,U_7201] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7201)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7203)),U_7205)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7201),c_Int_OPls)) ) ),
    inference(miniscope,[status(thm)],[f_1924_2]) ).

cnf(f_1924_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7201)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7203)),U_7205)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7201),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1924_3]) ).

cnf(f_1924_5,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7202)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7204)),U_7206)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7202),U_7204))),U_7206)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7202),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1924_3]) ).

fof(f_1925_1,plain,
    ! [V_v_H,V_v] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_v_H))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) )
      & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) ) ),
    inference(fof_nnf,[status(thm)],[fact_mult__nat__number__of]) ).

fof(f_1925_2,plain,
    ! [U_7208,U_7207] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7207)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7208)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7207),U_7208))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7207),c_Int_OPls)) )
      & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7207)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7208)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7207),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[f_1925_1]) ).

fof(f_1925_3,plain,
    ( ! [U_7212,U_7210] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7210)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7212)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7210),U_7212))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7210),c_Int_OPls)) )
    & ! [U_7211,U_7209] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7209)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7211)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7209),c_Int_OPls)) ) ),
    inference(miniscope,[status(thm)],[f_1925_2]) ).

cnf(f_1925_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7209)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7211)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7209),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1925_3]) ).

cnf(f_1925_5,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7210)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7212)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7210),U_7212))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7210),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1925_3]) ).

fof(f_1926_1,plain,
    ! [V_m,V_v] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(V_v)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v)) ),
    inference(fof_nnf,[status(thm)],[fact_Suc__diff__number__of]) ).

fof(f_1926_2,plain,
    ! [U_7214,U_7213] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_7214)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7213)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7214),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(U_7213)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_7213)) ),
    inference(variable_rename,[status(thm)],[f_1926_1]) ).

cnf(f_1926_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_7214)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7213)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7214),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(U_7213)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_7213)) ),
    inference(clausify,[status(thm)],[f_1926_2]) ).

fof(f_1927_1,plain,
    ! [V_v] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(V_v))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) )
      & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__1__add__number__of]) ).

fof(f_1927_2,plain,
    ! [U_7215] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7215)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_7215))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7215),c_Int_OPls)) )
      & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7215)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7215),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[f_1927_1]) ).

fof(f_1927_3,plain,
    ( ! [U_7217] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7217)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_7217))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7217),c_Int_OPls)) )
    & ! [U_7216] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7216)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7216),c_Int_OPls)) ) ),
    inference(miniscope,[status(thm)],[f_1927_2]) ).

cnf(f_1927_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7216)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7216),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1927_3]) ).

cnf(f_1927_5,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7217)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_7217))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7217),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1927_3]) ).

fof(f_1928_1,plain,
    ! [V_v] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(V_v))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) )
      & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__number__of__add__1]) ).

fof(f_1928_2,plain,
    ! [U_7218] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7218)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_7218))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7218),c_Int_OPls)) )
      & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7218)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7218),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[f_1928_1]) ).

fof(f_1928_3,plain,
    ( ! [U_7220] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7220)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_7220))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7220),c_Int_OPls)) )
    & ! [U_7219] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7219)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7219),c_Int_OPls)) ) ),
    inference(miniscope,[status(thm)],[f_1928_2]) ).

cnf(f_1928_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7219)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7219),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1928_3]) ).

cnf(f_1928_5,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7220)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_7220))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7220),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1928_3]) ).

fof(f_1929_1,plain,
    ! [V_k,V_l] :
      ( ( c_SMT_Oz3div(V_k,V_l) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_l)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) )
      & ( c_SMT_Oz3div(V_k,V_l) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) ) ),
    inference(fof_nnf,[status(thm)],[fact_z3div__def]) ).

fof(f_1929_2,plain,
    ! [U_7222,U_7221] :
      ( ( c_SMT_Oz3div(U_7222,U_7221) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7222),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7221)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7221)) )
      & ( c_SMT_Oz3div(U_7222,U_7221) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7222),U_7221)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7221)) ) ),
    inference(variable_rename,[status(thm)],[f_1929_1]) ).

fof(f_1929_3,plain,
    ( ! [U_7226,U_7224] :
        ( c_SMT_Oz3div(U_7226,U_7224) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7226),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7224)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7224)) )
    & ! [U_7225,U_7223] :
        ( c_SMT_Oz3div(U_7225,U_7223) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7225),U_7223)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7223)) ) ),
    inference(miniscope,[status(thm)],[f_1929_2]) ).

cnf(f_1929_4,plain,
    ( c_SMT_Oz3div(U_7225,U_7223) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7225),U_7223)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7223)) ),
    inference(clausify,[status(thm)],[f_1929_3]) ).

cnf(f_1929_5,plain,
    ( c_SMT_Oz3div(U_7226,U_7224) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7226),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7224)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7224)) ),
    inference(clausify,[status(thm)],[f_1929_3]) ).

fof(f_1930_1,plain,
    ! [V_x_2,T_b] :
      ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = c_Groups_Ozero__class_Ozero(T_b)
          | ~ c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls)))) )
        & ( c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls))))
          | hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) != c_Groups_Ozero__class_Ozero(T_b) ) )
      | ~ class_Int_Onumber__ring(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_eq__special_I3_J]) ).

fof(f_1930_2,plain,
    ! [U_7228,U_7227] :
      ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_7227),U_7228) = c_Groups_Ozero__class_Ozero(U_7227)
          | ~ c_Int_Oiszero(U_7227,hAPP(c_Int_Onumber__class_Onumber__of(U_7227),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7228),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls)))) )
        & ( c_Int_Oiszero(U_7227,hAPP(c_Int_Onumber__class_Onumber__of(U_7227),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7228),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls))))
          | hAPP(c_Int_Onumber__class_Onumber__of(U_7227),U_7228) != c_Groups_Ozero__class_Ozero(U_7227) ) )
      | ~ class_Int_Onumber__ring(U_7227) ),
    inference(variable_rename,[status(thm)],[f_1930_1]) ).

cnf(f_1930_3,plain,
    ( c_Int_Oiszero(U_7227,hAPP(c_Int_Onumber__class_Onumber__of(U_7227),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7228),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls))))
    | hAPP(c_Int_Onumber__class_Onumber__of(U_7227),U_7228) != c_Groups_Ozero__class_Ozero(U_7227)
    | ~ class_Int_Onumber__ring(U_7227) ),
    inference(clausify,[status(thm)],[f_1930_2]) ).

cnf(f_1930_4,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_7227),U_7228) = c_Groups_Ozero__class_Ozero(U_7227)
    | ~ c_Int_Oiszero(U_7227,hAPP(c_Int_Onumber__class_Onumber__of(U_7227),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7228),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls))))
    | ~ class_Int_Onumber__ring(U_7227) ),
    inference(clausify,[status(thm)],[f_1930_2]) ).

fof(f_1931_1,plain,
    ! [V_y_2,T_b] :
      ( ( ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
          | ~ c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_y_2)))) )
        & ( c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_y_2))))
          | c_Groups_Ozero__class_Ozero(T_b) != hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2) ) )
      | ~ class_Int_Onumber__ring(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_eq__special_I1_J]) ).

fof(f_1931_2,plain,
    ! [U_7230,U_7229] :
      ( ( ( c_Groups_Ozero__class_Ozero(U_7229) = hAPP(c_Int_Onumber__class_Onumber__of(U_7229),U_7230)
          | ~ c_Int_Oiszero(U_7229,hAPP(c_Int_Onumber__class_Onumber__of(U_7229),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7230)))) )
        & ( c_Int_Oiszero(U_7229,hAPP(c_Int_Onumber__class_Onumber__of(U_7229),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7230))))
          | c_Groups_Ozero__class_Ozero(U_7229) != hAPP(c_Int_Onumber__class_Onumber__of(U_7229),U_7230) ) )
      | ~ class_Int_Onumber__ring(U_7229) ),
    inference(variable_rename,[status(thm)],[f_1931_1]) ).

cnf(f_1931_3,plain,
    ( c_Int_Oiszero(U_7229,hAPP(c_Int_Onumber__class_Onumber__of(U_7229),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7230))))
    | c_Groups_Ozero__class_Ozero(U_7229) != hAPP(c_Int_Onumber__class_Onumber__of(U_7229),U_7230)
    | ~ class_Int_Onumber__ring(U_7229) ),
    inference(clausify,[status(thm)],[f_1931_2]) ).

cnf(f_1931_4,plain,
    ( c_Groups_Ozero__class_Ozero(U_7229) = hAPP(c_Int_Onumber__class_Onumber__of(U_7229),U_7230)
    | ~ c_Int_Oiszero(U_7229,hAPP(c_Int_Onumber__class_Onumber__of(U_7229),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7230))))
    | ~ class_Int_Onumber__ring(U_7229) ),
    inference(clausify,[status(thm)],[f_1931_2]) ).

fof(f_1932_1,plain,
    ! [V_w_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Nat_Osemiring__1__class_ONats(T_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_w_2))
      | ~ class_Int_Onumber__ring(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Nats__number__of]) ).

fof(f_1932_2,plain,
    ! [U_7232,U_7231] :
      ( hBOOL(hAPP(hAPP(c_member(U_7231),hAPP(c_Int_Onumber__class_Onumber__of(U_7231),U_7232)),c_Nat_Osemiring__1__class_ONats(U_7231)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_7232))
      | ~ class_Int_Onumber__ring(U_7231) ),
    inference(variable_rename,[status(thm)],[f_1932_1]) ).

cnf(f_1932_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7231),hAPP(c_Int_Onumber__class_Onumber__of(U_7231),U_7232)),c_Nat_Osemiring__1__class_ONats(U_7231)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_7232))
    | ~ class_Int_Onumber__ring(U_7231) ),
    inference(clausify,[status(thm)],[f_1932_2]) ).

fof(f_1933_1,plain,
    ! [V_w,V_v] :
      ( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) )
      & ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) ) ),
    inference(fof_nnf,[status(thm)],[fact_power__nat__number__of__number__of]) ).

fof(f_1933_2,plain,
    ! [U_7234,U_7233] :
      ( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7233)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7234)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7233)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7234)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7233))) )
      & ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7233)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7234)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7234))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7233))) ) ),
    inference(variable_rename,[status(thm)],[f_1933_1]) ).

fof(f_1933_3,plain,
    ( ! [U_7238,U_7236] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7236)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7238)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7236)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7238)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7236))) )
    & ! [U_7237,U_7235] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7235)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7237)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7237))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7235))) ) ),
    inference(miniscope,[status(thm)],[f_1933_2]) ).

cnf(f_1933_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7235)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7237)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7237))
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7235))) ),
    inference(clausify,[status(thm)],[f_1933_3]) ).

cnf(f_1933_5,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7236)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7238)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7236)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7238)))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7236))) ),
    inference(clausify,[status(thm)],[f_1933_3]) ).

fof(f_1934_1,plain,
    ! [V_k,V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n),V_k)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_div__le__mono]) ).

fof(f_1934_2,plain,
    ! [U_7241,U_7240,U_7239] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7239),U_7241)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7240),U_7241)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7239),U_7240)) ),
    inference(variable_rename,[status(thm)],[f_1934_1]) ).

cnf(f_1934_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7239),U_7241)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7240),U_7241)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7239),U_7240)) ),
    inference(clausify,[status(thm)],[f_1934_2]) ).

fof(f_1935_1,plain,
    ! [V_n,V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),V_m)),
    inference(fof_nnf,[status(thm)],[fact_div__le__dividend]) ).

fof(f_1935_2,plain,
    ! [U_7243,U_7242] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7242),U_7243)),U_7242)),
    inference(variable_rename,[status(thm)],[f_1935_1]) ).

cnf(f_1935_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7242),U_7243)),U_7242)),
    inference(clausify,[status(thm)],[f_1935_2]) ).

fof(f_1936_1,plain,
    ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),V_b)),V_c),
    inference(fof_nnf,[status(thm)],[fact_div__mult2__eq]) ).

fof(f_1936_2,plain,
    ! [U_7246,U_7245,U_7244] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7244),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7245),U_7246)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7244),U_7245)),U_7246),
    inference(variable_rename,[status(thm)],[f_1936_1]) ).

cnf(f_1936_3,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7244),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7245),U_7246)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7244),U_7245)),U_7246),
    inference(clausify,[status(thm)],[f_1936_2]) ).

fof(f_1937_1,plain,
    ! [V_y,V_x] :
      ( hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) ),
    inference(fof_nnf,[status(thm)],[fact_nat__div__distrib]) ).

fof(f_1937_2,plain,
    ! [U_7248,U_7247] :
      ( hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7247),U_7248)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,U_7247)),hAPP(c_Int_Onat,U_7248))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7247)) ),
    inference(variable_rename,[status(thm)],[f_1937_1]) ).

cnf(f_1937_3,plain,
    ( hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7247),U_7248)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,U_7247)),hAPP(c_Int_Onat,U_7248))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7247)) ),
    inference(clausify,[status(thm)],[f_1937_2]) ).

fof(f_1938_1,plain,
    ! [V_y,V_x] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) ),
    inference(fof_nnf,[status(thm)],[fact_Divides_Otransfer__nat__int__functions_I1_J]) ).

fof(f_1938_2,plain,
    ! [U_7250,U_7249] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,U_7249)),hAPP(c_Int_Onat,U_7250)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7249),U_7250))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7250))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7249)) ),
    inference(variable_rename,[status(thm)],[f_1938_1]) ).

cnf(f_1938_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,U_7249)),hAPP(c_Int_Onat,U_7250)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7249),U_7250))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7250))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7249)) ),
    inference(clausify,[status(thm)],[f_1938_2]) ).

fof(f_1939_1,plain,
    ! [T_a] :
      ( c_Int_Oiszero(T_a,c_Groups_Ozero__class_Ozero(T_a))
      | ~ class_Rings_Osemiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_iszero__0]) ).

fof(f_1939_2,plain,
    ! [U_7251] :
      ( c_Int_Oiszero(U_7251,c_Groups_Ozero__class_Ozero(U_7251))
      | ~ class_Rings_Osemiring__1(U_7251) ),
    inference(variable_rename,[status(thm)],[f_1939_1]) ).

cnf(f_1939_3,plain,
    ( c_Int_Oiszero(U_7251,c_Groups_Ozero__class_Ozero(U_7251))
    | ~ class_Rings_Osemiring__1(U_7251) ),
    inference(clausify,[status(thm)],[f_1939_2]) ).

fof(f_1940_1,plain,
    ! [V_z_2,T_b] :
      ( ( ( c_Int_Oiszero(T_b,V_z_2)
          | V_z_2 != c_Groups_Ozero__class_Ozero(T_b) )
        & ( V_z_2 = c_Groups_Ozero__class_Ozero(T_b)
          | ~ c_Int_Oiszero(T_b,V_z_2) ) )
      | ~ class_Rings_Osemiring__1(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_iszero__def]) ).

fof(f_1940_2,plain,
    ! [U_7253,U_7252] :
      ( ( ( c_Int_Oiszero(U_7252,U_7253)
          | U_7253 != c_Groups_Ozero__class_Ozero(U_7252) )
        & ( U_7253 = c_Groups_Ozero__class_Ozero(U_7252)
          | ~ c_Int_Oiszero(U_7252,U_7253) ) )
      | ~ class_Rings_Osemiring__1(U_7252) ),
    inference(variable_rename,[status(thm)],[f_1940_1]) ).

cnf(f_1940_3,plain,
    ( U_7253 = c_Groups_Ozero__class_Ozero(U_7252)
    | ~ c_Int_Oiszero(U_7252,U_7253)
    | ~ class_Rings_Osemiring__1(U_7252) ),
    inference(clausify,[status(thm)],[f_1940_2]) ).

cnf(f_1940_4,plain,
    ( c_Int_Oiszero(U_7252,U_7253)
    | U_7253 != c_Groups_Ozero__class_Ozero(U_7252)
    | ~ class_Rings_Osemiring__1(U_7252) ),
    inference(clausify,[status(thm)],[f_1940_2]) ).

fof(f_1941_1,plain,
    ! [V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = V_m,
    inference(fof_nnf,[status(thm)],[fact_div__1]) ).

fof(f_1941_2,plain,
    ! [U_7254] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7254),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = U_7254,
    inference(variable_rename,[status(thm)],[f_1941_1]) ).

cnf(f_1941_3,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7254),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = U_7254,
    inference(clausify,[status(thm)],[f_1941_2]) ).

fof(f_1942_1,plain,
    ! [V_n,V_m] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_div__less]) ).

fof(f_1942_2,plain,
    ! [U_7256,U_7255] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7255),U_7256) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7255),U_7256)) ),
    inference(variable_rename,[status(thm)],[f_1942_1]) ).

cnf(f_1942_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7255),U_7256) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7255),U_7256)) ),
    inference(clausify,[status(thm)],[f_1942_2]) ).

fof(f_1943_1,plain,
    ! [V_n,V_m,V_k] :
      ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)
        | V_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | V_k != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__mult__div__cancel__disj]) ).

fof(f_1943_2,plain,
    ! [U_7259,U_7258,U_7257] :
      ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7257),U_7258)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7257),U_7259)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7258),U_7259)
        | U_7257 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7257),U_7258)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7257),U_7259)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_7257 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_1943_1]) ).

fof(f_1943_3,plain,
    ( ! [U_7265,U_7263,U_7261] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7261),U_7263)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7261),U_7265)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7263),U_7265)
        | U_7261 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_7264,U_7262,U_7260] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7260),U_7262)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7260),U_7264)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_7260 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_1943_2]) ).

cnf(f_1943_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7260),U_7262)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7260),U_7264)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_7260 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1943_3]) ).

cnf(f_1943_5,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7261),U_7263)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7261),U_7265)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7263),U_7265)
    | U_7261 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1943_3]) ).

fof(f_1944_1,plain,
    hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_nat__0]) ).

cnf(f_1944_2,plain,
    hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1944_1]) ).

fof(f_1945_1,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__numerals_I1_J]) ).

cnf(f_1945_2,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    inference(clausify,[status(thm)],[f_1945_1]) ).

fof(f_1946_1,plain,
    ! [T_a] :
      ( ~ c_Int_Oiszero(T_a,c_Groups_Oone__class_Oone(T_a))
      | ~ class_Rings_Osemiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_not__iszero__1]) ).

fof(f_1946_2,plain,
    ! [U_7266] :
      ( ~ c_Int_Oiszero(U_7266,c_Groups_Oone__class_Oone(U_7266))
      | ~ class_Rings_Osemiring__1(U_7266) ),
    inference(variable_rename,[status(thm)],[f_1946_1]) ).

cnf(f_1946_3,plain,
    ( ~ c_Int_Oiszero(U_7266,c_Groups_Oone__class_Oone(U_7266))
    | ~ class_Rings_Osemiring__1(U_7266) ),
    inference(clausify,[status(thm)],[f_1946_2]) ).

fof(f_1947_1,plain,
    ! [V_z_H_2,V_z_2] :
      ( ( ( hAPP(c_Int_Onat,V_z_2) = hAPP(c_Int_Onat,V_z_H_2)
          | V_z_2 != V_z_H_2 )
        & ( V_z_2 = V_z_H_2
          | hAPP(c_Int_Onat,V_z_2) != hAPP(c_Int_Onat,V_z_H_2) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ),
    inference(fof_nnf,[status(thm)],[fact_eq__nat__nat__iff]) ).

fof(f_1947_2,plain,
    ! [U_7268,U_7267] :
      ( ( ( hAPP(c_Int_Onat,U_7267) = hAPP(c_Int_Onat,U_7268)
          | U_7267 != U_7268 )
        & ( U_7267 = U_7268
          | hAPP(c_Int_Onat,U_7267) != hAPP(c_Int_Onat,U_7268) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7268))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7267)) ),
    inference(variable_rename,[status(thm)],[f_1947_1]) ).

cnf(f_1947_3,plain,
    ( U_7267 = U_7268
    | hAPP(c_Int_Onat,U_7267) != hAPP(c_Int_Onat,U_7268)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7268))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7267)) ),
    inference(clausify,[status(thm)],[f_1947_2]) ).

cnf(f_1947_4,plain,
    ( hAPP(c_Int_Onat,U_7267) = hAPP(c_Int_Onat,U_7268)
    | U_7267 != U_7268
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7268))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7267)) ),
    inference(clausify,[status(thm)],[f_1947_2]) ).

fof(f_1948_1,plain,
    ! [V_P_2] :
      ( ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
        | ! [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) )
      & ( ? [B_x] :
            ( hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) )
        | ! [B_x1] : ~ hBOOL(hAPP(V_P_2,B_x1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_ex__nat]) ).

fof(f_1948_2,plain,
    ! [U_7273] :
      ( ( ? [U_7272] : hBOOL(hAPP(U_7273,U_7272))
        | ! [U_7271] :
            ( ~ hBOOL(hAPP(U_7273,hAPP(c_Int_Onat,U_7271)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7271)) ) )
      & ( ? [U_7270] :
            ( hBOOL(hAPP(U_7273,hAPP(c_Int_Onat,U_7270)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7270)) )
        | ! [U_7269] : ~ hBOOL(hAPP(U_7273,U_7269)) ) ),
    inference(variable_rename,[status(thm)],[f_1948_1]) ).

fof(f_1948_3,plain,
    ( ! [U_7275] :
        ( ? [U_7272] : hBOOL(hAPP(U_7275,U_7272))
        | ! [U_7271] :
            ( ~ hBOOL(hAPP(U_7275,hAPP(c_Int_Onat,U_7271)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7271)) ) )
    & ! [U_7274] :
        ( ? [U_7270] :
            ( hBOOL(hAPP(U_7274,hAPP(c_Int_Onat,U_7270)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7270)) )
        | ! [U_7269] : ~ hBOOL(hAPP(U_7274,U_7269)) ) ),
    inference(miniscope,[status(thm)],[f_1948_2]) ).

fof(f_1948_4,plain,
    ( ! [U_7275] :
        ( ? [U_7272] : hBOOL(hAPP(U_7275,U_7272))
        | ! [U_7271] :
            ( ~ hBOOL(hAPP(U_7275,hAPP(c_Int_Onat,U_7271)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7271)) ) )
    & ! [U_7274] :
        ( ( hBOOL(hAPP(U_7274,hAPP(c_Int_Onat,sK192(U_7274))))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK192(U_7274))) )
        | ! [U_7269] : ~ hBOOL(hAPP(U_7274,U_7269)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK192]),skolemize(U_7270,sK192(U_7274))],[f_1948_3]) ).

fof(f_1948_5,plain,
    ( ! [U_7275] :
        ( hBOOL(hAPP(U_7275,sK193(U_7275)))
        | ! [U_7271] :
            ( ~ hBOOL(hAPP(U_7275,hAPP(c_Int_Onat,U_7271)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7271)) ) )
    & ! [U_7274] :
        ( ( hBOOL(hAPP(U_7274,hAPP(c_Int_Onat,sK192(U_7274))))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK192(U_7274))) )
        | ! [U_7269] : ~ hBOOL(hAPP(U_7274,U_7269)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK193]),skolemize(U_7272,sK193(U_7275))],[f_1948_4]) ).

cnf(f_1948_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK192(U_7274)))
    | ~ hBOOL(hAPP(U_7274,U_7269)) ),
    inference(clausify,[status(thm)],[f_1948_5]) ).

cnf(f_1948_7,plain,
    ( hBOOL(hAPP(U_7274,hAPP(c_Int_Onat,sK192(U_7274))))
    | ~ hBOOL(hAPP(U_7274,U_7269)) ),
    inference(clausify,[status(thm)],[f_1948_5]) ).

cnf(f_1948_8,plain,
    ( hBOOL(hAPP(U_7275,sK193(U_7275)))
    | ~ hBOOL(hAPP(U_7275,hAPP(c_Int_Onat,U_7271)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7271)) ),
    inference(clausify,[status(thm)],[f_1948_5]) ).

fof(f_1949_1,plain,
    ! [V_P_2] :
      ( ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
        | ? [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) )
      & ( ! [B_x] :
            ( hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) )
        | ? [B_x1] : ~ hBOOL(hAPP(V_P_2,B_x1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_all__nat]) ).

fof(f_1949_2,plain,
    ! [U_7280] :
      ( ( ! [U_7279] : hBOOL(hAPP(U_7280,U_7279))
        | ? [U_7278] :
            ( ~ hBOOL(hAPP(U_7280,hAPP(c_Int_Onat,U_7278)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7278)) ) )
      & ( ! [U_7277] :
            ( hBOOL(hAPP(U_7280,hAPP(c_Int_Onat,U_7277)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7277)) )
        | ? [U_7276] : ~ hBOOL(hAPP(U_7280,U_7276)) ) ),
    inference(variable_rename,[status(thm)],[f_1949_1]) ).

fof(f_1949_3,plain,
    ( ! [U_7282] :
        ( ! [U_7279] : hBOOL(hAPP(U_7282,U_7279))
        | ? [U_7278] :
            ( ~ hBOOL(hAPP(U_7282,hAPP(c_Int_Onat,U_7278)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7278)) ) )
    & ! [U_7281] :
        ( ! [U_7277] :
            ( hBOOL(hAPP(U_7281,hAPP(c_Int_Onat,U_7277)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7277)) )
        | ? [U_7276] : ~ hBOOL(hAPP(U_7281,U_7276)) ) ),
    inference(miniscope,[status(thm)],[f_1949_2]) ).

fof(f_1949_4,plain,
    ( ! [U_7282] :
        ( ! [U_7279] : hBOOL(hAPP(U_7282,U_7279))
        | ? [U_7278] :
            ( ~ hBOOL(hAPP(U_7282,hAPP(c_Int_Onat,U_7278)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7278)) ) )
    & ! [U_7281] :
        ( ! [U_7277] :
            ( hBOOL(hAPP(U_7281,hAPP(c_Int_Onat,U_7277)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7277)) )
        | ~ hBOOL(hAPP(U_7281,sK194(U_7281))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK194]),skolemize(U_7276,sK194(U_7281))],[f_1949_3]) ).

fof(f_1949_5,plain,
    ( ! [U_7282] :
        ( ! [U_7279] : hBOOL(hAPP(U_7282,U_7279))
        | ( ~ hBOOL(hAPP(U_7282,hAPP(c_Int_Onat,sK195(U_7282))))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK195(U_7282))) ) )
    & ! [U_7281] :
        ( ! [U_7277] :
            ( hBOOL(hAPP(U_7281,hAPP(c_Int_Onat,U_7277)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7277)) )
        | ~ hBOOL(hAPP(U_7281,sK194(U_7281))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK195]),skolemize(U_7278,sK195(U_7282))],[f_1949_4]) ).

cnf(f_1949_6,plain,
    ( hBOOL(hAPP(U_7281,hAPP(c_Int_Onat,U_7277)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7277))
    | ~ hBOOL(hAPP(U_7281,sK194(U_7281))) ),
    inference(clausify,[status(thm)],[f_1949_5]) ).

cnf(f_1949_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK195(U_7282)))
    | hBOOL(hAPP(U_7282,U_7279)) ),
    inference(clausify,[status(thm)],[f_1949_5]) ).

cnf(f_1949_8,plain,
    ( ~ hBOOL(hAPP(U_7282,hAPP(c_Int_Onat,sK195(U_7282))))
    | hBOOL(hAPP(U_7282,U_7279)) ),
    inference(clausify,[status(thm)],[f_1949_5]) ).

fof(f_1950_1,plain,
    ! [V_y_2,V_x_2] :
      ( ( ( hAPP(c_Int_Onat,V_x_2) = hAPP(c_Int_Onat,V_y_2)
          | V_x_2 != V_y_2 )
        & ( V_x_2 = V_y_2
          | hAPP(c_Int_Onat,V_x_2) != hAPP(c_Int_Onat,V_y_2) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__relations_I1_J]) ).

fof(f_1950_2,plain,
    ! [U_7284,U_7283] :
      ( ( ( hAPP(c_Int_Onat,U_7283) = hAPP(c_Int_Onat,U_7284)
          | U_7283 != U_7284 )
        & ( U_7283 = U_7284
          | hAPP(c_Int_Onat,U_7283) != hAPP(c_Int_Onat,U_7284) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7284))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7283)) ),
    inference(variable_rename,[status(thm)],[f_1950_1]) ).

cnf(f_1950_3,plain,
    ( U_7283 = U_7284
    | hAPP(c_Int_Onat,U_7283) != hAPP(c_Int_Onat,U_7284)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7284))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7283)) ),
    inference(clausify,[status(thm)],[f_1950_2]) ).

cnf(f_1950_4,plain,
    ( hAPP(c_Int_Onat,U_7283) = hAPP(c_Int_Onat,U_7284)
    | U_7283 != U_7284
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7284))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7283)) ),
    inference(clausify,[status(thm)],[f_1950_2]) ).

fof(f_1951_1,plain,
    ! [V_v] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),
    inference(fof_nnf,[status(thm)],[fact_nat__number__of__def]) ).

fof(f_1951_2,plain,
    ! [U_7285] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7285) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7285)),
    inference(variable_rename,[status(thm)],[f_1951_1]) ).

cnf(f_1951_3,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7285) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7285)),
    inference(clausify,[status(thm)],[f_1951_2]) ).

fof(f_1952_1,plain,
    ! [V_w] : hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w),
    inference(fof_nnf,[status(thm)],[fact_nat__number__of]) ).

fof(f_1952_2,plain,
    ! [U_7286] : hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7286)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7286),
    inference(variable_rename,[status(thm)],[f_1952_1]) ).

cnf(f_1952_3,plain,
    hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7286)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7286),
    inference(clausify,[status(thm)],[f_1952_2]) ).

fof(f_1953_1,plain,
    c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__numerals_I2_J]) ).

cnf(f_1953_2,plain,
    c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(clausify,[status(thm)],[f_1953_1]) ).

fof(f_1954_1,plain,
    ! [V_z] :
      ( hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z)) ),
    inference(fof_nnf,[status(thm)],[fact_neg__nat]) ).

fof(f_1954_2,plain,
    ! [U_7287] :
      ( hAPP(c_Int_Onat,U_7287) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_7287)) ),
    inference(variable_rename,[status(thm)],[f_1954_1]) ).

cnf(f_1954_3,plain,
    ( hAPP(c_Int_Onat,U_7287) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_7287)) ),
    inference(clausify,[status(thm)],[f_1954_2]) ).

fof(f_1955_1,plain,
    ! [V_u_2] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2)) = hAPP(c_Int_Onat,V_u_2),
    inference(fof_nnf,[status(thm)],[fact_card__atLeastZeroLessThan__int]) ).

fof(f_1955_2,plain,
    ! [U_7288] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7288)) = hAPP(c_Int_Onat,U_7288),
    inference(variable_rename,[status(thm)],[f_1955_1]) ).

cnf(f_1955_3,plain,
    hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7288)) = hAPP(c_Int_Onat,U_7288),
    inference(clausify,[status(thm)],[f_1955_2]) ).

fof(f_1956_1,plain,
    ! [V_v_H,V_v] :
      ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) )
      & ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) ) ),
    inference(fof_nnf,[status(thm)],[fact_div__nat__number__of]) ).

fof(f_1956_2,plain,
    ! [U_7290,U_7289] :
      ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7289)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7290)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7289)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7290)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7289))) )
      & ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7289)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7290)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7289))) ) ),
    inference(variable_rename,[status(thm)],[f_1956_1]) ).

fof(f_1956_3,plain,
    ( ! [U_7294,U_7292] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7292)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7294)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7292)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7294)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7292))) )
    & ! [U_7293,U_7291] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7291)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7293)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7291))) ) ),
    inference(miniscope,[status(thm)],[f_1956_2]) ).

cnf(f_1956_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7291)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7293)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7291))) ),
    inference(clausify,[status(thm)],[f_1956_3]) ).

cnf(f_1956_5,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7292)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7294)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7292)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7294)))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7292))) ),
    inference(clausify,[status(thm)],[f_1956_3]) ).

fof(f_1957_1,plain,
    ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_l_2),V_u_2)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_u_2),V_l_2)),
    inference(fof_nnf,[status(thm)],[fact_card__atLeastLessThan__int]) ).

fof(f_1957_2,plain,
    ! [U_7296,U_7295] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_7295),U_7296)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7296),U_7295)),
    inference(variable_rename,[status(thm)],[f_1957_1]) ).

cnf(f_1957_3,plain,
    hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_7295),U_7296)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7296),U_7295)),
    inference(clausify,[status(thm)],[f_1957_2]) ).

fof(f_1958_1,plain,
    ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,V_l_2,V_u_2)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_u_2),V_l_2)),
    inference(fof_nnf,[status(thm)],[fact_card__greaterThanAtMost__int]) ).

fof(f_1958_2,plain,
    ! [U_7298,U_7297] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_7297,U_7298)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7298),U_7297)),
    inference(variable_rename,[status(thm)],[f_1958_1]) ).

cnf(f_1958_3,plain,
    hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_7297,U_7298)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7298),U_7297)),
    inference(clausify,[status(thm)],[f_1958_2]) ).

fof(f_1959_1,plain,
    ! [V_v_H] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))),
    inference(fof_nnf,[status(thm)],[fact_one__div__nat__number__of]) ).

fof(f_1959_2,plain,
    ! [U_7299] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7299)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7299))),
    inference(variable_rename,[status(thm)],[f_1959_1]) ).

cnf(f_1959_3,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7299)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7299))),
    inference(clausify,[status(thm)],[f_1959_2]) ).

fof(f_1960_1,plain,
    c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__set__functions_I2_J]) ).

cnf(f_1960_2,plain,
    c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_1960_1]) ).

fof(f_1961_1,plain,
    ! [V_k,V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_k),V_n)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_k),V_m)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) ),
    inference(fof_nnf,[status(thm)],[fact_div__le__mono2]) ).

fof(f_1961_2,plain,
    ! [U_7302,U_7301,U_7300] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7302),U_7301)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7302),U_7300)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7300),U_7301))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7300)) ),
    inference(variable_rename,[status(thm)],[f_1961_1]) ).

cnf(f_1961_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7302),U_7301)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7302),U_7300)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7300),U_7301))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7300)) ),
    inference(clausify,[status(thm)],[f_1961_2]) ).

fof(f_1962_1,plain,
    ! [V_m,V_n] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m)),V_n) = V_m
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_div__mult__self1__is__m]) ).

fof(f_1962_2,plain,
    ! [U_7304,U_7303] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7303),U_7304)),U_7303) = U_7304
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7303)) ),
    inference(variable_rename,[status(thm)],[f_1962_1]) ).

cnf(f_1962_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7303),U_7304)),U_7303) = U_7304
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7303)) ),
    inference(clausify,[status(thm)],[f_1962_2]) ).

fof(f_1963_1,plain,
    ! [V_m,V_n] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),V_n) = V_m
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_div__mult__self__is__m]) ).

fof(f_1963_2,plain,
    ! [U_7306,U_7305] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7306),U_7305)),U_7305) = U_7306
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7305)) ),
    inference(variable_rename,[status(thm)],[f_1963_1]) ).

cnf(f_1963_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7306),U_7305)),U_7305) = U_7306
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7305)) ),
    inference(clausify,[status(thm)],[f_1963_2]) ).

fof(f_1964_1,plain,
    ! [V_n,V_m,V_k] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) ),
    inference(fof_nnf,[status(thm)],[fact_nat__mult__div__cancel1]) ).

fof(f_1964_2,plain,
    ! [U_7309,U_7308,U_7307] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7307),U_7308)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7307),U_7309)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7308),U_7309)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7307)) ),
    inference(variable_rename,[status(thm)],[f_1964_1]) ).

cnf(f_1964_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7307),U_7308)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7307),U_7309)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7308),U_7309)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7307)) ),
    inference(clausify,[status(thm)],[f_1964_2]) ).

fof(f_1965_1,plain,
    ! [V_m,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),V_m))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_div__less__dividend]) ).

fof(f_1965_2,plain,
    ! [U_7311,U_7310] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7311),U_7310)),U_7311))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7311))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_7310)) ),
    inference(variable_rename,[status(thm)],[f_1965_1]) ).

cnf(f_1965_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7311),U_7310)),U_7311))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7311))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_7310)) ),
    inference(clausify,[status(thm)],[f_1965_2]) ).

fof(f_1966_1,plain,
    ! [V_z] :
      ( hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(fof_nnf,[status(thm)],[fact_nat__le__0]) ).

fof(f_1966_2,plain,
    ! [U_7312] :
      ( hAPP(c_Int_Onat,U_7312) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7312),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_1966_1]) ).

cnf(f_1966_3,plain,
    ( hAPP(c_Int_Onat,U_7312) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7312),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1966_2]) ).

fof(f_1967_1,plain,
    ! [V_i_2] :
      ( ( hAPP(c_Int_Onat,V_i_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hAPP(c_Int_Onat,V_i_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__0__iff]) ).

fof(f_1967_2,plain,
    ! [U_7313] :
      ( ( hAPP(c_Int_Onat,U_7313) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7313),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7313),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hAPP(c_Int_Onat,U_7313) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_1967_1]) ).

fof(f_1967_3,plain,
    ( ! [U_7315] :
        ( hAPP(c_Int_Onat,U_7315) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7315),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_7314] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7314),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hAPP(c_Int_Onat,U_7314) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_1967_2]) ).

cnf(f_1967_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7314),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hAPP(c_Int_Onat,U_7314) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1967_3]) ).

cnf(f_1967_5,plain,
    ( hAPP(c_Int_Onat,U_7315) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7315),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1967_3]) ).

fof(f_1968_1,plain,
    ! [V_z_2,V_w_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),hAPP(c_Int_Onat,V_z_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),hAPP(c_Int_Onat,V_z_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_zless__nat__conj]) ).

fof(f_1968_2,plain,
    ! [U_7317,U_7316] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7316)),hAPP(c_Int_Onat,U_7317)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7316),U_7317))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7317)) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7316),U_7317))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7317)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7316)),hAPP(c_Int_Onat,U_7317))) ) ),
    inference(variable_rename,[status(thm)],[f_1968_1]) ).

fof(f_1968_3,plain,
    ( ! [U_7321,U_7319] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7319)),hAPP(c_Int_Onat,U_7321)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7319),U_7321))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7321)) )
    & ! [U_7320,U_7318] :
        ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7318),U_7320))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7320)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7318)),hAPP(c_Int_Onat,U_7320))) ) ),
    inference(miniscope,[status(thm)],[f_1968_2]) ).

cnf(f_1968_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7320))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7318)),hAPP(c_Int_Onat,U_7320))) ),
    inference(clausify,[status(thm)],[f_1968_3]) ).

cnf(f_1968_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7318),U_7320))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7318)),hAPP(c_Int_Onat,U_7320))) ),
    inference(clausify,[status(thm)],[f_1968_3]) ).

cnf(f_1968_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7319)),hAPP(c_Int_Onat,U_7321)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7319),U_7321))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7321)) ),
    inference(clausify,[status(thm)],[f_1968_3]) ).

fof(f_1969_1,plain,
    ! [V_w_2,V_z_2] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),hAPP(c_Int_Onat,V_z_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),hAPP(c_Int_Onat,V_z_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ),
    inference(fof_nnf,[status(thm)],[fact_nat__mono__iff]) ).

fof(f_1969_2,plain,
    ! [U_7323,U_7322] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7323)),hAPP(c_Int_Onat,U_7322)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7323),U_7322)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7323),U_7322))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7323)),hAPP(c_Int_Onat,U_7322))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7322)) ),
    inference(variable_rename,[status(thm)],[f_1969_1]) ).

cnf(f_1969_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7323),U_7322))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7323)),hAPP(c_Int_Onat,U_7322)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7322)) ),
    inference(clausify,[status(thm)],[f_1969_2]) ).

cnf(f_1969_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7323)),hAPP(c_Int_Onat,U_7322)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7323),U_7322))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7322)) ),
    inference(clausify,[status(thm)],[f_1969_2]) ).

fof(f_1970_1,plain,
    ! [V_y_2,V_x_2] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,V_x_2)),hAPP(c_Int_Onat,V_y_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,V_x_2)),hAPP(c_Int_Onat,V_y_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__relations_I3_J]) ).

fof(f_1970_2,plain,
    ! [U_7325,U_7324] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_7324)),hAPP(c_Int_Onat,U_7325)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7324),U_7325)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7324),U_7325))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_7324)),hAPP(c_Int_Onat,U_7325))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7325))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7324)) ),
    inference(variable_rename,[status(thm)],[f_1970_1]) ).

cnf(f_1970_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7324),U_7325))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_7324)),hAPP(c_Int_Onat,U_7325)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7325))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7324)) ),
    inference(clausify,[status(thm)],[f_1970_2]) ).

cnf(f_1970_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_7324)),hAPP(c_Int_Onat,U_7325)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7324),U_7325))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7325))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7324)) ),
    inference(clausify,[status(thm)],[f_1970_2]) ).

fof(f_1971_1,plain,
    hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(fof_nnf,[status(thm)],[fact_nat__1]) ).

cnf(f_1971_2,plain,
    hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(clausify,[status(thm)],[f_1971_1]) ).

fof(f_1972_1,plain,
    ! [T_a] :
      ( c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls))
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_iszero__Numeral0]) ).

fof(f_1972_2,plain,
    ! [U_7326] :
      ( c_Int_Oiszero(U_7326,hAPP(c_Int_Onumber__class_Onumber__of(U_7326),c_Int_OPls))
      | ~ class_Int_Onumber__ring(U_7326) ),
    inference(variable_rename,[status(thm)],[f_1972_1]) ).

cnf(f_1972_3,plain,
    ( c_Int_Oiszero(U_7326,hAPP(c_Int_Onumber__class_Onumber__of(U_7326),c_Int_OPls))
    | ~ class_Int_Onumber__ring(U_7326) ),
    inference(clausify,[status(thm)],[f_1972_2]) ).

fof(f_1973_1,plain,
    ! [T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Nat_Osemiring__1__class_ONats(T_b)))
      | ~ class_Rings_Osemiring__1(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Nats__0]) ).

fof(f_1973_2,plain,
    ! [U_7327] :
      ( hBOOL(hAPP(hAPP(c_member(U_7327),c_Groups_Ozero__class_Ozero(U_7327)),c_Nat_Osemiring__1__class_ONats(U_7327)))
      | ~ class_Rings_Osemiring__1(U_7327) ),
    inference(variable_rename,[status(thm)],[f_1973_1]) ).

cnf(f_1973_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7327),c_Groups_Ozero__class_Ozero(U_7327)),c_Nat_Osemiring__1__class_ONats(U_7327)))
    | ~ class_Rings_Osemiring__1(U_7327) ),
    inference(clausify,[status(thm)],[f_1973_2]) ).

fof(f_1974_1,plain,
    ! [V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2)),c_Nat_Osemiring__1__class_ONats(T_b)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Nat_Osemiring__1__class_ONats(T_b)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Nat_Osemiring__1__class_ONats(T_b)))
      | ~ class_Rings_Osemiring__1(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Nats__add]) ).

fof(f_1974_2,plain,
    ! [U_7330,U_7329,U_7328] :
      ( hBOOL(hAPP(hAPP(c_member(U_7328),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7328),U_7329),U_7330)),c_Nat_Osemiring__1__class_ONats(U_7328)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7328),U_7330),c_Nat_Osemiring__1__class_ONats(U_7328)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7328),U_7329),c_Nat_Osemiring__1__class_ONats(U_7328)))
      | ~ class_Rings_Osemiring__1(U_7328) ),
    inference(variable_rename,[status(thm)],[f_1974_1]) ).

cnf(f_1974_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7328),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7328),U_7329),U_7330)),c_Nat_Osemiring__1__class_ONats(U_7328)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7328),U_7330),c_Nat_Osemiring__1__class_ONats(U_7328)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7328),U_7329),c_Nat_Osemiring__1__class_ONats(U_7328)))
    | ~ class_Rings_Osemiring__1(U_7328) ),
    inference(clausify,[status(thm)],[f_1974_2]) ).

fof(f_1975_1,plain,
    ! [V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)),c_Nat_Osemiring__1__class_ONats(T_b)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Nat_Osemiring__1__class_ONats(T_b)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Nat_Osemiring__1__class_ONats(T_b)))
      | ~ class_Rings_Osemiring__1(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Nats__mult]) ).

fof(f_1975_2,plain,
    ! [U_7333,U_7332,U_7331] :
      ( hBOOL(hAPP(hAPP(c_member(U_7331),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7331),U_7332),U_7333)),c_Nat_Osemiring__1__class_ONats(U_7331)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7331),U_7333),c_Nat_Osemiring__1__class_ONats(U_7331)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7331),U_7332),c_Nat_Osemiring__1__class_ONats(U_7331)))
      | ~ class_Rings_Osemiring__1(U_7331) ),
    inference(variable_rename,[status(thm)],[f_1975_1]) ).

cnf(f_1975_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7331),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7331),U_7332),U_7333)),c_Nat_Osemiring__1__class_ONats(U_7331)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7331),U_7333),c_Nat_Osemiring__1__class_ONats(U_7331)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7331),U_7332),c_Nat_Osemiring__1__class_ONats(U_7331)))
    | ~ class_Rings_Osemiring__1(U_7331) ),
    inference(clausify,[status(thm)],[f_1975_2]) ).

fof(f_1976_1,plain,
    ! [T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Oone__class_Oone(T_b)),c_Nat_Osemiring__1__class_ONats(T_b)))
      | ~ class_Rings_Osemiring__1(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Nats__1]) ).

fof(f_1976_2,plain,
    ! [U_7334] :
      ( hBOOL(hAPP(hAPP(c_member(U_7334),c_Groups_Oone__class_Oone(U_7334)),c_Nat_Osemiring__1__class_ONats(U_7334)))
      | ~ class_Rings_Osemiring__1(U_7334) ),
    inference(variable_rename,[status(thm)],[f_1976_1]) ).

cnf(f_1976_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7334),c_Groups_Oone__class_Oone(U_7334)),c_Nat_Osemiring__1__class_ONats(U_7334)))
    | ~ class_Rings_Osemiring__1(U_7334) ),
    inference(clausify,[status(thm)],[f_1976_2]) ).

fof(f_1977_1,plain,
    ! [V_m,V_n] :
      ( ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) )
        & ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_div__if]) ).

fof(f_1977_2,plain,
    ! [U_7336,U_7335] :
      ( ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7336),U_7335) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7336),U_7335)),U_7335))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7336),U_7335)) )
        & ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7336),U_7335) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7336),U_7335)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7335)) ),
    inference(variable_rename,[status(thm)],[f_1977_1]) ).

cnf(f_1977_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7336),U_7335) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7336),U_7335))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7335)) ),
    inference(clausify,[status(thm)],[f_1977_2]) ).

cnf(f_1977_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7336),U_7335) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7336),U_7335)),U_7335))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7336),U_7335))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7335)) ),
    inference(clausify,[status(thm)],[f_1977_2]) ).

fof(f_1978_1,plain,
    ! [V_m,V_n] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_div__geq]) ).

fof(f_1978_2,plain,
    ! [U_7338,U_7337] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7338),U_7337) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7338),U_7337)),U_7337))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7338),U_7337))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7337)) ),
    inference(variable_rename,[status(thm)],[f_1978_1]) ).

cnf(f_1978_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7338),U_7337) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7338),U_7337)),U_7337))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7338),U_7337))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7337)) ),
    inference(clausify,[status(thm)],[f_1978_2]) ).

fof(f_1979_1,plain,
    ! [V_k_2,V_n_2,V_P_2] :
      ( ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n_2),V_k_2)))
        | ( ? [B_i,B_j] :
              ( ~ hBOOL(hAPP(V_P_2,B_i))
              & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),B_i)),B_j)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2)) )
          & V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( ( ( ! [B_i,B_j] :
                ( hBOOL(hAPP(V_P_2,B_i))
                | V_n_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),B_i)),B_j)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2)) )
            | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
        | ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n_2),V_k_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_split__div]) ).

fof(f_1979_2,plain,
    ! [U_7345,U_7344,U_7343] :
      ( ( hBOOL(hAPP(U_7343,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7344),U_7345)))
        | ( ? [U_7342,U_7341] :
              ( ~ hBOOL(hAPP(U_7343,U_7342))
              & U_7344 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7345),U_7342)),U_7341)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7341),U_7345)) )
          & U_7345 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( ~ hBOOL(hAPP(U_7343,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & U_7345 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( ( ( ! [U_7340,U_7339] :
                ( hBOOL(hAPP(U_7343,U_7340))
                | U_7344 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7345),U_7340)),U_7339)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7339),U_7345)) )
            | U_7345 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( hBOOL(hAPP(U_7343,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | U_7345 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
        | ~ hBOOL(hAPP(U_7343,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7344),U_7345))) ) ),
    inference(variable_rename,[status(thm)],[f_1979_1]) ).

fof(f_1979_3,plain,
    ( ! [U_7351,U_7349,U_7347] :
        ( hBOOL(hAPP(U_7347,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7349),U_7351)))
        | ( ? [U_7342,U_7341] :
              ( ~ hBOOL(hAPP(U_7347,U_7342))
              & U_7349 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7351),U_7342)),U_7341)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7341),U_7351)) )
          & U_7351 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( ~ hBOOL(hAPP(U_7347,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & U_7351 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_7350,U_7348,U_7346] :
        ( ( ( ! [U_7340,U_7339] :
                ( hBOOL(hAPP(U_7346,U_7340))
                | U_7348 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7350),U_7340)),U_7339)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7339),U_7350)) )
            | U_7350 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( hBOOL(hAPP(U_7346,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | U_7350 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
        | ~ hBOOL(hAPP(U_7346,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7348),U_7350))) ) ),
    inference(miniscope,[status(thm)],[f_1979_2]) ).

fof(f_1979_4,plain,
    ( ! [U_7351,U_7349,U_7347] :
        ( hBOOL(hAPP(U_7347,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7349),U_7351)))
        | ( ? [U_7341] :
              ( ~ hBOOL(hAPP(U_7347,sK196(U_7351,U_7349,U_7347)))
              & U_7349 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7351),sK196(U_7351,U_7349,U_7347))),U_7341)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7341),U_7351)) )
          & U_7351 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( ~ hBOOL(hAPP(U_7347,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & U_7351 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_7350,U_7348,U_7346] :
        ( ( ( ! [U_7340,U_7339] :
                ( hBOOL(hAPP(U_7346,U_7340))
                | U_7348 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7350),U_7340)),U_7339)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7339),U_7350)) )
            | U_7350 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( hBOOL(hAPP(U_7346,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | U_7350 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
        | ~ hBOOL(hAPP(U_7346,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7348),U_7350))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK196]),skolemize(U_7342,sK196(U_7351,U_7349,U_7347))],[f_1979_3]) ).

fof(f_1979_5,plain,
    ( ! [U_7351,U_7349,U_7347] :
        ( hBOOL(hAPP(U_7347,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7349),U_7351)))
        | ( ~ hBOOL(hAPP(U_7347,sK196(U_7351,U_7349,U_7347)))
          & U_7349 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7351),sK196(U_7351,U_7349,U_7347))),sK197(U_7351,U_7349,U_7347))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK197(U_7351,U_7349,U_7347)),U_7351))
          & U_7351 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( ~ hBOOL(hAPP(U_7347,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & U_7351 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_7350,U_7348,U_7346] :
        ( ( ( ! [U_7340,U_7339] :
                ( hBOOL(hAPP(U_7346,U_7340))
                | U_7348 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7350),U_7340)),U_7339)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7339),U_7350)) )
            | U_7350 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( hBOOL(hAPP(U_7346,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | U_7350 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
        | ~ hBOOL(hAPP(U_7346,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7348),U_7350))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK197]),skolemize(U_7341,sK197(U_7351,U_7349,U_7347))],[f_1979_4]) ).

cnf(f_1979_6,plain,
    ( hBOOL(hAPP(U_7346,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | U_7350 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(U_7346,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7348),U_7350))) ),
    inference(clausify,[status(thm)],[f_1979_5]) ).

cnf(f_1979_7,plain,
    ( hBOOL(hAPP(U_7346,U_7340))
    | U_7348 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7350),U_7340)),U_7339)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7339),U_7350))
    | U_7350 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(U_7346,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7348),U_7350))) ),
    inference(clausify,[status(thm)],[f_1979_5]) ).

cnf(f_1979_8,plain,
    ( U_7351 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_7351 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(U_7347,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7349),U_7351))) ),
    inference(clausify,[status(thm)],[f_1979_5]) ).

cnf(f_1979_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK197(U_7351,U_7349,U_7347)),U_7351))
    | U_7351 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(U_7347,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7349),U_7351))) ),
    inference(clausify,[status(thm)],[f_1979_5]) ).

cnf(f_1979_10,plain,
    ( U_7349 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7351),sK196(U_7351,U_7349,U_7347))),sK197(U_7351,U_7349,U_7347))
    | U_7351 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(U_7347,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7349),U_7351))) ),
    inference(clausify,[status(thm)],[f_1979_5]) ).

cnf(f_1979_11,plain,
    ( ~ hBOOL(hAPP(U_7347,sK196(U_7351,U_7349,U_7347)))
    | U_7351 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(U_7347,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7349),U_7351))) ),
    inference(clausify,[status(thm)],[f_1979_5]) ).

cnf(f_1979_12,plain,
    ( U_7351 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(U_7347,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | hBOOL(hAPP(U_7347,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7349),U_7351))) ),
    inference(clausify,[status(thm)],[f_1979_5]) ).

cnf(f_1979_13,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK197(U_7351,U_7349,U_7347)),U_7351))
    | ~ hBOOL(hAPP(U_7347,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | hBOOL(hAPP(U_7347,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7349),U_7351))) ),
    inference(clausify,[status(thm)],[f_1979_5]) ).

cnf(f_1979_14,plain,
    ( U_7349 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7351),sK196(U_7351,U_7349,U_7347))),sK197(U_7351,U_7349,U_7347))
    | ~ hBOOL(hAPP(U_7347,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | hBOOL(hAPP(U_7347,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7349),U_7351))) ),
    inference(clausify,[status(thm)],[f_1979_5]) ).

cnf(f_1979_15,plain,
    ( ~ hBOOL(hAPP(U_7347,sK196(U_7351,U_7349,U_7347)))
    | ~ hBOOL(hAPP(U_7347,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | hBOOL(hAPP(U_7347,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7349),U_7351))) ),
    inference(clausify,[status(thm)],[f_1979_5]) ).

fof(f_1980_1,plain,
    ! [V_z_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,V_z_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,V_z_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_zero__less__nat__eq]) ).

fof(f_1980_2,plain,
    ! [U_7352] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,U_7352)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7352)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7352))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,U_7352))) ) ),
    inference(variable_rename,[status(thm)],[f_1980_1]) ).

fof(f_1980_3,plain,
    ( ! [U_7354] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,U_7354)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7354)) )
    & ! [U_7353] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7353))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,U_7353))) ) ),
    inference(miniscope,[status(thm)],[f_1980_2]) ).

cnf(f_1980_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7353))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,U_7353))) ),
    inference(clausify,[status(thm)],[f_1980_3]) ).

cnf(f_1980_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,U_7354)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7354)) ),
    inference(clausify,[status(thm)],[f_1980_3]) ).

fof(f_1981_1,plain,
    ! [V_z_2,V_w_2] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),hAPP(c_Int_Onat,V_z_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),hAPP(c_Int_Onat,V_z_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) ),
    inference(fof_nnf,[status(thm)],[fact_nat__less__eq__zless]) ).

fof(f_1981_2,plain,
    ! [U_7356,U_7355] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7355)),hAPP(c_Int_Onat,U_7356)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7355),U_7356)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7355),U_7356))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7355)),hAPP(c_Int_Onat,U_7356))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7355)) ),
    inference(variable_rename,[status(thm)],[f_1981_1]) ).

cnf(f_1981_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7355),U_7356))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7355)),hAPP(c_Int_Onat,U_7356)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7355)) ),
    inference(clausify,[status(thm)],[f_1981_2]) ).

cnf(f_1981_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7355)),hAPP(c_Int_Onat,U_7356)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7355),U_7356))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7355)) ),
    inference(clausify,[status(thm)],[f_1981_2]) ).

fof(f_1982_1,plain,
    ! [V_y_2,V_x_2] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_x_2)),hAPP(c_Int_Onat,V_y_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_x_2)),hAPP(c_Int_Onat,V_y_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__relations_I2_J]) ).

fof(f_1982_2,plain,
    ! [U_7358,U_7357] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7357)),hAPP(c_Int_Onat,U_7358)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7357),U_7358)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7357),U_7358))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7357)),hAPP(c_Int_Onat,U_7358))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7358))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7357)) ),
    inference(variable_rename,[status(thm)],[f_1982_1]) ).

cnf(f_1982_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7357),U_7358))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7357)),hAPP(c_Int_Onat,U_7358)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7358))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7357)) ),
    inference(clausify,[status(thm)],[f_1982_2]) ).

cnf(f_1982_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7357)),hAPP(c_Int_Onat,U_7358)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7357),U_7358))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7358))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7357)) ),
    inference(clausify,[status(thm)],[f_1982_2]) ).

fof(f_1983_1,plain,
    ! [V_z_2,V_w_2] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),hAPP(c_Int_Onat,V_z_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),hAPP(c_Int_Onat,V_z_2))) ) )
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
        & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__le__eq__zle]) ).

fof(f_1983_2,plain,
    ! [U_7360,U_7359] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_7359)),hAPP(c_Int_Onat,U_7360)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7359),U_7360)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7359),U_7360))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_7359)),hAPP(c_Int_Onat,U_7360))) ) )
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7360))
        & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7359)) ) ),
    inference(variable_rename,[status(thm)],[f_1983_1]) ).

cnf(f_1983_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7359),U_7360))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_7359)),hAPP(c_Int_Onat,U_7360)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7359)) ),
    inference(clausify,[status(thm)],[f_1983_2]) ).

cnf(f_1983_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_7359)),hAPP(c_Int_Onat,U_7360)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7359),U_7360))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7359)) ),
    inference(clausify,[status(thm)],[f_1983_2]) ).

cnf(f_1983_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7359),U_7360))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_7359)),hAPP(c_Int_Onat,U_7360)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7360)) ),
    inference(clausify,[status(thm)],[f_1983_2]) ).

cnf(f_1983_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_7359)),hAPP(c_Int_Onat,U_7360)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7359),U_7360))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7360)) ),
    inference(clausify,[status(thm)],[f_1983_2]) ).

fof(f_1984_1,plain,
    ! [V_z_H,V_z] :
      ( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),V_z_H)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,V_z)),hAPP(c_Int_Onat,V_z_H))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) ),
    inference(fof_nnf,[status(thm)],[fact_nat__add__distrib]) ).

fof(f_1984_2,plain,
    ! [U_7362,U_7361] :
      ( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7361),U_7362)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_7361)),hAPP(c_Int_Onat,U_7362))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7362))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7361)) ),
    inference(variable_rename,[status(thm)],[f_1984_1]) ).

cnf(f_1984_3,plain,
    ( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7361),U_7362)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_7361)),hAPP(c_Int_Onat,U_7362))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7362))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7361)) ),
    inference(clausify,[status(thm)],[f_1984_2]) ).

fof(f_1985_1,plain,
    ! [V_y,V_x] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) ),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J]) ).

fof(f_1985_2,plain,
    ! [U_7364,U_7363] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_7363)),hAPP(c_Int_Onat,U_7364)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7363),U_7364))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7364))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7363)) ),
    inference(variable_rename,[status(thm)],[f_1985_1]) ).

cnf(f_1985_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_7363)),hAPP(c_Int_Onat,U_7364)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7363),U_7364))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7364))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7363)) ),
    inference(clausify,[status(thm)],[f_1985_2]) ).

fof(f_1986_1,plain,
    ! [V_z_H,V_z] :
      ( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_z_H)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,V_z)),hAPP(c_Int_Onat,V_z_H))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) ),
    inference(fof_nnf,[status(thm)],[fact_nat__mult__distrib]) ).

fof(f_1986_2,plain,
    ! [U_7366,U_7365] :
      ( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7365),U_7366)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,U_7365)),hAPP(c_Int_Onat,U_7366))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7365)) ),
    inference(variable_rename,[status(thm)],[f_1986_1]) ).

cnf(f_1986_3,plain,
    ( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7365),U_7366)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,U_7365)),hAPP(c_Int_Onat,U_7366))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7365)) ),
    inference(clausify,[status(thm)],[f_1986_2]) ).

fof(f_1987_1,plain,
    ! [V_y,V_x] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) ),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J]) ).

fof(f_1987_2,plain,
    ! [U_7368,U_7367] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,U_7367)),hAPP(c_Int_Onat,U_7368)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7367),U_7368))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7368))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7367)) ),
    inference(variable_rename,[status(thm)],[f_1987_1]) ).

cnf(f_1987_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,U_7367)),hAPP(c_Int_Onat,U_7368)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7367),U_7368))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7368))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7367)) ),
    inference(clausify,[status(thm)],[f_1987_2]) ).

fof(f_1988_1,plain,
    ! [V_z,V_z_H] :
      ( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z),V_z_H)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,V_z)),hAPP(c_Int_Onat,V_z_H))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H)) ),
    inference(fof_nnf,[status(thm)],[fact_nat__diff__distrib]) ).

fof(f_1988_2,plain,
    ! [U_7370,U_7369] :
      ( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7370),U_7369)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_7370)),hAPP(c_Int_Onat,U_7369))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7369),U_7370))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7369)) ),
    inference(variable_rename,[status(thm)],[f_1988_1]) ).

cnf(f_1988_3,plain,
    ( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7370),U_7369)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_7370)),hAPP(c_Int_Onat,U_7369))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7369),U_7370))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7369)) ),
    inference(clausify,[status(thm)],[f_1988_2]) ).

fof(f_1989_1,plain,
    ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_l_2,V_u_2)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_u_2),V_l_2)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(fof_nnf,[status(thm)],[fact_card__atLeastAtMost__int]) ).

fof(f_1989_2,plain,
    ! [U_7372,U_7371] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_7371,U_7372)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7372),U_7371)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(variable_rename,[status(thm)],[f_1989_1]) ).

cnf(f_1989_3,plain,
    hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_7371,U_7372)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7372),U_7371)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(clausify,[status(thm)],[f_1989_2]) ).

fof(f_1990_1,plain,
    ! [V_n,V_x] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),V_n) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) ),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J]) ).

fof(f_1990_2,plain,
    ! [U_7374,U_7373] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,U_7373)),U_7374) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_7373),U_7374))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7373)) ),
    inference(variable_rename,[status(thm)],[f_1990_1]) ).

cnf(f_1990_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,U_7373)),U_7374) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_7373),U_7374))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7373)) ),
    inference(clausify,[status(thm)],[f_1990_2]) ).

fof(f_1991_1,plain,
    ! [V_n,V_z] :
      ( hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,V_z)),V_n)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) ),
    inference(fof_nnf,[status(thm)],[fact_nat__power__eq]) ).

fof(f_1991_2,plain,
    ! [U_7376,U_7375] :
      ( hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_7375),U_7376)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,U_7375)),U_7376)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7375)) ),
    inference(variable_rename,[status(thm)],[f_1991_1]) ).

cnf(f_1991_3,plain,
    ( hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_7375),U_7376)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,U_7375)),U_7376)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7375)) ),
    inference(clausify,[status(thm)],[f_1991_2]) ).

fof(f_1992_1,plain,
    ! [V_y,V_x] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,c_Nat__Transfer_Otsub(V_x,V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) ),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J]) ).

fof(f_1992_2,plain,
    ! [U_7378,U_7377] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_7377)),hAPP(c_Int_Onat,U_7378)) = hAPP(c_Int_Onat,c_Nat__Transfer_Otsub(U_7377,U_7378))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7378))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7377)) ),
    inference(variable_rename,[status(thm)],[f_1992_1]) ).

cnf(f_1992_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_7377)),hAPP(c_Int_Onat,U_7378)) = hAPP(c_Int_Onat,c_Nat__Transfer_Otsub(U_7377,U_7378))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7378))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7377)) ),
    inference(clausify,[status(thm)],[f_1992_2]) ).

fof(f_1993_1,plain,
    ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,V_l_2,V_u_2)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_u_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_l_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    inference(fof_nnf,[status(thm)],[fact_card__greaterThanLessThan__int]) ).

fof(f_1993_2,plain,
    ! [U_7380,U_7379] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_7379,U_7380)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7380),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7379),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    inference(variable_rename,[status(thm)],[f_1993_1]) ).

cnf(f_1993_3,plain,
    hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_7379,U_7380)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7380),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7379),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    inference(clausify,[status(thm)],[f_1993_2]) ).

fof(f_1994_1,plain,
    ! [V_m,V_n] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_le__div__geq]) ).

fof(f_1994_2,plain,
    ! [U_7382,U_7381] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7382),U_7381) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7382),U_7381)),U_7381))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7381),U_7382))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7381)) ),
    inference(variable_rename,[status(thm)],[f_1994_1]) ).

cnf(f_1994_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7382),U_7381) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7382),U_7381)),U_7381))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7381),U_7382))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7381)) ),
    inference(clausify,[status(thm)],[f_1994_2]) ).

fof(f_1995_1,plain,
    ! [V_m_2,V_q_2,V_n_2] :
      ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_q_2))))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_q_2)),V_m_2)) )
          | V_q_2 != hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2) )
        & ( V_q_2 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_q_2))))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_q_2)),V_m_2)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ),
    inference(fof_nnf,[status(thm)],[fact_split__div__lemma]) ).

fof(f_1995_2,plain,
    ! [U_7385,U_7384,U_7383] :
      ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7385),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7383),hAPP(c_Nat_OSuc,U_7384))))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7383),U_7384)),U_7385)) )
          | U_7384 != hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7385),U_7383) )
        & ( U_7384 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7385),U_7383)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7385),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7383),hAPP(c_Nat_OSuc,U_7384))))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7383),U_7384)),U_7385)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7383)) ),
    inference(variable_rename,[status(thm)],[f_1995_1]) ).

cnf(f_1995_3,plain,
    ( U_7384 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7385),U_7383)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7385),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7383),hAPP(c_Nat_OSuc,U_7384))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7383),U_7384)),U_7385))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7383)) ),
    inference(clausify,[status(thm)],[f_1995_2]) ).

cnf(f_1995_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7383),U_7384)),U_7385))
    | U_7384 != hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7385),U_7383)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7383)) ),
    inference(clausify,[status(thm)],[f_1995_2]) ).

cnf(f_1995_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7385),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7383),hAPP(c_Nat_OSuc,U_7384))))
    | U_7384 != hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7385),U_7383)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7383)) ),
    inference(clausify,[status(thm)],[f_1995_2]) ).

fof(f_1996_1,plain,
    ! [V_n_2,V_m_2,V_P_2] :
      ( ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2)))
        | ( ! [B_q] :
              ( ~ hBOOL(hAPP(V_P_2,B_q))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,B_q))))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),B_q)),V_m_2)) )
          & ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) )
      & ( ? [B_q] :
            ( hBOOL(hAPP(V_P_2,B_q))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,B_q))))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),B_q)),V_m_2)) )
        | ( hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_split__div_H]) ).

fof(f_1996_2,plain,
    ! [U_7390,U_7389,U_7388] :
      ( ( hBOOL(hAPP(U_7388,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7389),U_7390)))
        | ( ! [U_7387] :
              ( ~ hBOOL(hAPP(U_7388,U_7387))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7389),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7390),hAPP(c_Nat_OSuc,U_7387))))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7390),U_7387)),U_7389)) )
          & ( ~ hBOOL(hAPP(U_7388,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | U_7390 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) )
      & ( ? [U_7386] :
            ( hBOOL(hAPP(U_7388,U_7386))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7389),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7390),hAPP(c_Nat_OSuc,U_7386))))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7390),U_7386)),U_7389)) )
        | ( hBOOL(hAPP(U_7388,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & U_7390 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ~ hBOOL(hAPP(U_7388,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7389),U_7390))) ) ),
    inference(variable_rename,[status(thm)],[f_1996_1]) ).

fof(f_1996_3,plain,
    ( ! [U_7396,U_7394,U_7392] :
        ( hBOOL(hAPP(U_7392,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7394),U_7396)))
        | ( ! [U_7387] :
              ( ~ hBOOL(hAPP(U_7392,U_7387))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7394),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7396),hAPP(c_Nat_OSuc,U_7387))))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7396),U_7387)),U_7394)) )
          & ( ~ hBOOL(hAPP(U_7392,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | U_7396 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) )
    & ! [U_7395,U_7393,U_7391] :
        ( ? [U_7386] :
            ( hBOOL(hAPP(U_7391,U_7386))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7393),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7395),hAPP(c_Nat_OSuc,U_7386))))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7395),U_7386)),U_7393)) )
        | ( hBOOL(hAPP(U_7391,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & U_7395 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ~ hBOOL(hAPP(U_7391,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7393),U_7395))) ) ),
    inference(miniscope,[status(thm)],[f_1996_2]) ).

fof(f_1996_4,plain,
    ( ! [U_7396,U_7394,U_7392] :
        ( hBOOL(hAPP(U_7392,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7394),U_7396)))
        | ( ! [U_7387] :
              ( ~ hBOOL(hAPP(U_7392,U_7387))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7394),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7396),hAPP(c_Nat_OSuc,U_7387))))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7396),U_7387)),U_7394)) )
          & ( ~ hBOOL(hAPP(U_7392,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | U_7396 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) )
    & ! [U_7395,U_7393,U_7391] :
        ( ( hBOOL(hAPP(U_7391,sK198(U_7395,U_7393,U_7391)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7393),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7395),hAPP(c_Nat_OSuc,sK198(U_7395,U_7393,U_7391)))))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7395),sK198(U_7395,U_7393,U_7391))),U_7393)) )
        | ( hBOOL(hAPP(U_7391,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & U_7395 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ~ hBOOL(hAPP(U_7391,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7393),U_7395))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK198]),skolemize(U_7386,sK198(U_7395,U_7393,U_7391))],[f_1996_3]) ).

cnf(f_1996_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7395),sK198(U_7395,U_7393,U_7391))),U_7393))
    | U_7395 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(U_7391,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7393),U_7395))) ),
    inference(clausify,[status(thm)],[f_1996_4]) ).

cnf(f_1996_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7393),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7395),hAPP(c_Nat_OSuc,sK198(U_7395,U_7393,U_7391)))))
    | U_7395 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(U_7391,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7393),U_7395))) ),
    inference(clausify,[status(thm)],[f_1996_4]) ).

cnf(f_1996_7,plain,
    ( hBOOL(hAPP(U_7391,sK198(U_7395,U_7393,U_7391)))
    | U_7395 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(U_7391,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7393),U_7395))) ),
    inference(clausify,[status(thm)],[f_1996_4]) ).

cnf(f_1996_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7395),sK198(U_7395,U_7393,U_7391))),U_7393))
    | hBOOL(hAPP(U_7391,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(U_7391,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7393),U_7395))) ),
    inference(clausify,[status(thm)],[f_1996_4]) ).

cnf(f_1996_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7393),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7395),hAPP(c_Nat_OSuc,sK198(U_7395,U_7393,U_7391)))))
    | hBOOL(hAPP(U_7391,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(U_7391,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7393),U_7395))) ),
    inference(clausify,[status(thm)],[f_1996_4]) ).

cnf(f_1996_10,plain,
    ( hBOOL(hAPP(U_7391,sK198(U_7395,U_7393,U_7391)))
    | hBOOL(hAPP(U_7391,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(U_7391,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7393),U_7395))) ),
    inference(clausify,[status(thm)],[f_1996_4]) ).

cnf(f_1996_11,plain,
    ( ~ hBOOL(hAPP(U_7392,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | U_7396 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(U_7392,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7394),U_7396))) ),
    inference(clausify,[status(thm)],[f_1996_4]) ).

cnf(f_1996_12,plain,
    ( ~ hBOOL(hAPP(U_7392,U_7387))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7394),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7396),hAPP(c_Nat_OSuc,U_7387))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7396),U_7387)),U_7394))
    | hBOOL(hAPP(U_7392,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7394),U_7396))) ),
    inference(clausify,[status(thm)],[f_1996_4]) ).

fof(f_1997_1,plain,
    ! [V_z_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onat,V_z_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onat,V_z_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_one__less__nat__eq]) ).

fof(f_1997_2,plain,
    ! [U_7397] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onat,U_7397)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_7397)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_7397))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onat,U_7397))) ) ),
    inference(variable_rename,[status(thm)],[f_1997_1]) ).

fof(f_1997_3,plain,
    ( ! [U_7399] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onat,U_7399)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_7399)) )
    & ! [U_7398] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_7398))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onat,U_7398))) ) ),
    inference(miniscope,[status(thm)],[f_1997_2]) ).

cnf(f_1997_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_7398))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onat,U_7398))) ),
    inference(clausify,[status(thm)],[f_1997_3]) ).

cnf(f_1997_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onat,U_7399)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_7399)) ),
    inference(clausify,[status(thm)],[f_1997_3]) ).

fof(f_1998_1,plain,
    ! [V_z] :
      ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,V_z)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) ),
    inference(fof_nnf,[status(thm)],[fact_Suc__nat__eq__nat__zadd1]) ).

fof(f_1998_2,plain,
    ! [U_7400] :
      ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,U_7400)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_7400))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7400)) ),
    inference(variable_rename,[status(thm)],[f_1998_1]) ).

cnf(f_1998_3,plain,
    ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,U_7400)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_7400))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7400)) ),
    inference(clausify,[status(thm)],[f_1998_2]) ).

fof(f_1999_1,plain,
    ! [V_z_H,V_z] :
      ( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_z_H)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z))),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z_H)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(fof_nnf,[status(thm)],[fact_nat__mult__distrib__neg]) ).

fof(f_1999_2,plain,
    ! [U_7402,U_7401] :
      ( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7401),U_7402)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7401))),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7402)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7401),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_1999_1]) ).

cnf(f_1999_3,plain,
    ( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7401),U_7402)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7401))),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7402)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7401),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1999_2]) ).

fof(f_2000_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
          | ~ c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_y_2)))) )
        & ( c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_y_2))))
          | hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) != hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2) ) )
      | ~ class_Int_Onumber__ring(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_eq__number__of__eq]) ).

fof(f_2000_2,plain,
    ! [U_7405,U_7404,U_7403] :
      ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_7403),U_7404) = hAPP(c_Int_Onumber__class_Onumber__of(U_7403),U_7405)
          | ~ c_Int_Oiszero(U_7403,hAPP(c_Int_Onumber__class_Onumber__of(U_7403),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7404),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7405)))) )
        & ( c_Int_Oiszero(U_7403,hAPP(c_Int_Onumber__class_Onumber__of(U_7403),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7404),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7405))))
          | hAPP(c_Int_Onumber__class_Onumber__of(U_7403),U_7404) != hAPP(c_Int_Onumber__class_Onumber__of(U_7403),U_7405) ) )
      | ~ class_Int_Onumber__ring(U_7403) ),
    inference(variable_rename,[status(thm)],[f_2000_1]) ).

cnf(f_2000_3,plain,
    ( c_Int_Oiszero(U_7403,hAPP(c_Int_Onumber__class_Onumber__of(U_7403),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7404),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7405))))
    | hAPP(c_Int_Onumber__class_Onumber__of(U_7403),U_7404) != hAPP(c_Int_Onumber__class_Onumber__of(U_7403),U_7405)
    | ~ class_Int_Onumber__ring(U_7403) ),
    inference(clausify,[status(thm)],[f_2000_2]) ).

cnf(f_2000_4,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_7403),U_7404) = hAPP(c_Int_Onumber__class_Onumber__of(U_7403),U_7405)
    | ~ c_Int_Oiszero(U_7403,hAPP(c_Int_Onumber__class_Onumber__of(U_7403),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7404),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7405))))
    | ~ class_Int_Onumber__ring(U_7403) ),
    inference(clausify,[status(thm)],[f_2000_2]) ).

fof(f_2001_1,plain,
    ! [V_n,V_v] :
      ( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),V_n) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),V_n))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) )
      & ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),V_n) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) ) ),
    inference(fof_nnf,[status(thm)],[fact_power__nat__number__of]) ).

fof(f_2001_2,plain,
    ! [U_7407,U_7406] :
      ( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7406)),U_7407) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7406)),U_7407))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7406))) )
      & ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7406)),U_7407) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7407)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7406))) ) ),
    inference(variable_rename,[status(thm)],[f_2001_1]) ).

fof(f_2001_3,plain,
    ( ! [U_7411,U_7409] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7409)),U_7411) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7409)),U_7411))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7409))) )
    & ! [U_7410,U_7408] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7408)),U_7410) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7410)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7408))) ) ),
    inference(miniscope,[status(thm)],[f_2001_2]) ).

cnf(f_2001_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7408)),U_7410) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7410)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7408))) ),
    inference(clausify,[status(thm)],[f_2001_3]) ).

cnf(f_2001_5,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7409)),U_7411) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7409)),U_7411))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7409))) ),
    inference(clausify,[status(thm)],[f_2001_3]) ).

fof(f_2002_1,plain,
    ! [V_n,V_i] : c_Int_Onat__aux(V_i,V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,V_i)),V_n),
    inference(fof_nnf,[status(thm)],[fact_nat__aux__def]) ).

fof(f_2002_2,plain,
    ! [U_7413,U_7412] : c_Int_Onat__aux(U_7412,U_7413) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_7412)),U_7413),
    inference(variable_rename,[status(thm)],[f_2002_1]) ).

cnf(f_2002_3,plain,
    c_Int_Onat__aux(U_7412,U_7413) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_7412)),U_7413),
    inference(clausify,[status(thm)],[f_2002_2]) ).

fof(f_2003_1,plain,
    c_Nat__Transfer_Otransfer__morphism(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(fof_nnf,[status(thm)],[fact_transfer__morphism__nat__int]) ).

cnf(f_2003_2,plain,
    c_Nat__Transfer_Otransfer__morphism(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(clausify,[status(thm)],[f_2003_1]) ).

fof(f_2004_1,plain,
    ! [V_y_2,T_b] :
      ( ( ( c_Groups_Oone__class_Oone(T_b) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
          | ~ c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_y_2)))) )
        & ( c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_y_2))))
          | c_Groups_Oone__class_Oone(T_b) != hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2) ) )
      | ~ class_Int_Onumber__ring(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_eq__special_I2_J]) ).

fof(f_2004_2,plain,
    ! [U_7415,U_7414] :
      ( ( ( c_Groups_Oone__class_Oone(U_7414) = hAPP(c_Int_Onumber__class_Onumber__of(U_7414),U_7415)
          | ~ c_Int_Oiszero(U_7414,hAPP(c_Int_Onumber__class_Onumber__of(U_7414),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7415)))) )
        & ( c_Int_Oiszero(U_7414,hAPP(c_Int_Onumber__class_Onumber__of(U_7414),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7415))))
          | c_Groups_Oone__class_Oone(U_7414) != hAPP(c_Int_Onumber__class_Onumber__of(U_7414),U_7415) ) )
      | ~ class_Int_Onumber__ring(U_7414) ),
    inference(variable_rename,[status(thm)],[f_2004_1]) ).

cnf(f_2004_3,plain,
    ( c_Int_Oiszero(U_7414,hAPP(c_Int_Onumber__class_Onumber__of(U_7414),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7415))))
    | c_Groups_Oone__class_Oone(U_7414) != hAPP(c_Int_Onumber__class_Onumber__of(U_7414),U_7415)
    | ~ class_Int_Onumber__ring(U_7414) ),
    inference(clausify,[status(thm)],[f_2004_2]) ).

cnf(f_2004_4,plain,
    ( c_Groups_Oone__class_Oone(U_7414) = hAPP(c_Int_Onumber__class_Onumber__of(U_7414),U_7415)
    | ~ c_Int_Oiszero(U_7414,hAPP(c_Int_Onumber__class_Onumber__of(U_7414),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7415))))
    | ~ class_Int_Onumber__ring(U_7414) ),
    inference(clausify,[status(thm)],[f_2004_2]) ).

fof(f_2005_1,plain,
    ! [V_x_2,T_b] :
      ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = c_Groups_Oone__class_Oone(T_b)
          | ~ c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls))))) )
        & ( c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))))
          | hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) != c_Groups_Oone__class_Oone(T_b) ) )
      | ~ class_Int_Onumber__ring(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_eq__special_I4_J]) ).

fof(f_2005_2,plain,
    ! [U_7417,U_7416] :
      ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_7416),U_7417) = c_Groups_Oone__class_Oone(U_7416)
          | ~ c_Int_Oiszero(U_7416,hAPP(c_Int_Onumber__class_Onumber__of(U_7416),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7417),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls))))) )
        & ( c_Int_Oiszero(U_7416,hAPP(c_Int_Onumber__class_Onumber__of(U_7416),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7417),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))))
          | hAPP(c_Int_Onumber__class_Onumber__of(U_7416),U_7417) != c_Groups_Oone__class_Oone(U_7416) ) )
      | ~ class_Int_Onumber__ring(U_7416) ),
    inference(variable_rename,[status(thm)],[f_2005_1]) ).

cnf(f_2005_3,plain,
    ( c_Int_Oiszero(U_7416,hAPP(c_Int_Onumber__class_Onumber__of(U_7416),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7417),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))))
    | hAPP(c_Int_Onumber__class_Onumber__of(U_7416),U_7417) != c_Groups_Oone__class_Oone(U_7416)
    | ~ class_Int_Onumber__ring(U_7416) ),
    inference(clausify,[status(thm)],[f_2005_2]) ).

cnf(f_2005_4,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_7416),U_7417) = c_Groups_Oone__class_Oone(U_7416)
    | ~ c_Int_Oiszero(U_7416,hAPP(c_Int_Onumber__class_Onumber__of(U_7416),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7417),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))))
    | ~ class_Int_Onumber__ring(U_7416) ),
    inference(clausify,[status(thm)],[f_2005_2]) ).

fof(f_2006_1,plain,
    ! [V_v,T_a] :
      ( ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Ozero__class_Ozero(T_a)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) )
        & ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) ) )
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__number__of__lemma]) ).

fof(f_2006_2,plain,
    ! [U_7419,U_7418] :
      ( ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7418),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7419)) = c_Groups_Ozero__class_Ozero(U_7418)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7419))) )
        & ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7418),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7419)) = hAPP(c_Int_Onumber__class_Onumber__of(U_7418),U_7419)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7419))) ) )
      | ~ class_Int_Onumber__ring(U_7418) ),
    inference(variable_rename,[status(thm)],[f_2006_1]) ).

cnf(f_2006_3,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7418),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7419)) = hAPP(c_Int_Onumber__class_Onumber__of(U_7418),U_7419)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7419)))
    | ~ class_Int_Onumber__ring(U_7418) ),
    inference(clausify,[status(thm)],[f_2006_2]) ).

cnf(f_2006_4,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7418),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7419)) = c_Groups_Ozero__class_Ozero(U_7418)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7419)))
    | ~ class_Int_Onumber__ring(U_7418) ),
    inference(clausify,[status(thm)],[f_2006_2]) ).

fof(f_2007_1,plain,
    ! [V_m,V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m))),
    inference(fof_nnf,[status(thm)],[fact_negative__zle]) ).

fof(f_2007_2,plain,
    ! [U_7421,U_7420] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7420))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7421))),
    inference(variable_rename,[status(thm)],[f_2007_1]) ).

cnf(f_2007_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7420))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7421))),
    inference(clausify,[status(thm)],[f_2007_2]) ).

fof(f_2008_1,plain,
    ! [V_m,V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,V_n)))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m))),
    inference(fof_nnf,[status(thm)],[fact_negative__zless]) ).

fof(f_2008_2,plain,
    ! [U_7423,U_7422] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_7422)))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7423))),
    inference(variable_rename,[status(thm)],[f_2008_1]) ).

cnf(f_2008_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_7422)))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7423))),
    inference(clausify,[status(thm)],[f_2008_2]) ).

fof(f_2009_1,plain,
    ! [V_A_2] : hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)) = V_A_2,
    inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__set__return__embed]) ).

fof(f_2009_2,plain,
    ! [U_7424] : hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7424)) = U_7424,
    inference(variable_rename,[status(thm)],[f_2009_1]) ).

cnf(f_2009_3,plain,
    hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7424)) = U_7424,
    inference(clausify,[status(thm)],[f_2009_2]) ).

fof(f_2010_1,plain,
    ! [V_B_2,V_A_2] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2))),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J]) ).

fof(f_2010_2,plain,
    ! [U_7426,U_7425] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_7425),U_7426) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7425)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7426))),
    inference(variable_rename,[status(thm)],[f_2010_1]) ).

cnf(f_2010_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_7425),U_7426) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7425)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7426))),
    inference(clausify,[status(thm)],[f_2010_2]) ).

fof(f_2011_1,plain,
    ! [V_n] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = V_n,
    inference(fof_nnf,[status(thm)],[fact_nat__int]) ).

fof(f_2011_2,plain,
    ! [U_7427] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7427)) = U_7427,
    inference(variable_rename,[status(thm)],[f_2011_1]) ).

cnf(f_2011_3,plain,
    hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7427)) = U_7427,
    inference(clausify,[status(thm)],[f_2011_2]) ).

fof(f_2012_1,plain,
    ! [V_k] : c_Int_OBit1(V_k) != c_Int_OPls,
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I46_J]) ).

fof(f_2012_2,plain,
    ! [U_7428] : c_Int_OBit1(U_7428) != c_Int_OPls,
    inference(variable_rename,[status(thm)],[f_2012_1]) ).

cnf(f_2012_3,plain,
    c_Int_OBit1(U_7428) != c_Int_OPls,
    inference(clausify,[status(thm)],[f_2012_2]) ).

fof(f_2013_1,plain,
    ! [V_l] : c_Int_OPls != c_Int_OBit1(V_l),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I39_J]) ).

fof(f_2013_2,plain,
    ! [U_7429] : c_Int_OPls != c_Int_OBit1(U_7429),
    inference(variable_rename,[status(thm)],[f_2013_1]) ).

cnf(f_2013_3,plain,
    c_Int_OPls != c_Int_OBit1(U_7429),
    inference(clausify,[status(thm)],[f_2013_2]) ).

fof(f_2014_1,plain,
    ! [V_n_2,V_m_2,T_b] :
      ( ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_m_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)
          | V_m_2 != V_n_2 )
        & ( V_m_2 = V_n_2
          | hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_m_2) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2) ) )
      | ~ class_Nat_Osemiring__char__0(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__eq__iff]) ).

fof(f_2014_2,plain,
    ! [U_7432,U_7431,U_7430] :
      ( ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7430),U_7431) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7430),U_7432)
          | U_7431 != U_7432 )
        & ( U_7431 = U_7432
          | hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7430),U_7431) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7430),U_7432) ) )
      | ~ class_Nat_Osemiring__char__0(U_7430) ),
    inference(variable_rename,[status(thm)],[f_2014_1]) ).

cnf(f_2014_3,plain,
    ( U_7431 = U_7432
    | hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7430),U_7431) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7430),U_7432)
    | ~ class_Nat_Osemiring__char__0(U_7430) ),
    inference(clausify,[status(thm)],[f_2014_2]) ).

cnf(f_2014_4,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7430),U_7431) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7430),U_7432)
    | U_7431 != U_7432
    | ~ class_Nat_Osemiring__char__0(U_7430) ),
    inference(clausify,[status(thm)],[f_2014_2]) ).

fof(f_2015_1,plain,
    ! [V_l_2,V_k_2] :
      ( ( c_Int_OBit1(V_k_2) = c_Int_OBit1(V_l_2)
        | V_k_2 != V_l_2 )
      & ( V_k_2 = V_l_2
        | c_Int_OBit1(V_k_2) != c_Int_OBit1(V_l_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I51_J]) ).

fof(f_2015_2,plain,
    ! [U_7434,U_7433] :
      ( ( c_Int_OBit1(U_7433) = c_Int_OBit1(U_7434)
        | U_7433 != U_7434 )
      & ( U_7433 = U_7434
        | c_Int_OBit1(U_7433) != c_Int_OBit1(U_7434) ) ),
    inference(variable_rename,[status(thm)],[f_2015_1]) ).

fof(f_2015_3,plain,
    ( ! [U_7438,U_7436] :
        ( c_Int_OBit1(U_7436) = c_Int_OBit1(U_7438)
        | U_7436 != U_7438 )
    & ! [U_7437,U_7435] :
        ( U_7435 = U_7437
        | c_Int_OBit1(U_7435) != c_Int_OBit1(U_7437) ) ),
    inference(miniscope,[status(thm)],[f_2015_2]) ).

cnf(f_2015_4,plain,
    ( U_7435 = U_7437
    | c_Int_OBit1(U_7435) != c_Int_OBit1(U_7437) ),
    inference(clausify,[status(thm)],[f_2015_3]) ).

cnf(f_2015_5,plain,
    ( c_Int_OBit1(U_7436) = c_Int_OBit1(U_7438)
    | U_7436 != U_7438 ),
    inference(clausify,[status(thm)],[f_2015_3]) ).

fof(f_2016_1,plain,
    ! [V_l_2,V_k_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I17_J]) ).

fof(f_2016_2,plain,
    ! [U_7440,U_7439] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7439)),c_Int_OBit1(U_7440)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7439),U_7440)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7439),U_7440))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7439)),c_Int_OBit1(U_7440))) ) ),
    inference(variable_rename,[status(thm)],[f_2016_1]) ).

fof(f_2016_3,plain,
    ( ! [U_7444,U_7442] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7442)),c_Int_OBit1(U_7444)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7442),U_7444)) )
    & ! [U_7443,U_7441] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7441),U_7443))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7441)),c_Int_OBit1(U_7443))) ) ),
    inference(miniscope,[status(thm)],[f_2016_2]) ).

cnf(f_2016_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7441),U_7443))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7441)),c_Int_OBit1(U_7443))) ),
    inference(clausify,[status(thm)],[f_2016_3]) ).

cnf(f_2016_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7442)),c_Int_OBit1(U_7444)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7442),U_7444)) ),
    inference(clausify,[status(thm)],[f_2016_3]) ).

fof(f_2017_1,plain,
    ! [V_k2_2,V_k1_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_less__int__code_I16_J]) ).

fof(f_2017_2,plain,
    ! [U_7446,U_7445] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7445)),c_Int_OBit1(U_7446)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7445),U_7446)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7445),U_7446))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7445)),c_Int_OBit1(U_7446))) ) ),
    inference(variable_rename,[status(thm)],[f_2017_1]) ).

fof(f_2017_3,plain,
    ( ! [U_7450,U_7448] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7448)),c_Int_OBit1(U_7450)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7448),U_7450)) )
    & ! [U_7449,U_7447] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7447),U_7449))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7447)),c_Int_OBit1(U_7449))) ) ),
    inference(miniscope,[status(thm)],[f_2017_2]) ).

cnf(f_2017_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7447),U_7449))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7447)),c_Int_OBit1(U_7449))) ),
    inference(clausify,[status(thm)],[f_2017_3]) ).

cnf(f_2017_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7448)),c_Int_OBit1(U_7450)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7448),U_7450)) ),
    inference(clausify,[status(thm)],[f_2017_3]) ).

fof(f_2018_1,plain,
    ! [V_k2_2,V_k1_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_less__eq__int__code_I16_J]) ).

fof(f_2018_2,plain,
    ! [U_7452,U_7451] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7451)),c_Int_OBit1(U_7452)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7451),U_7452)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7451),U_7452))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7451)),c_Int_OBit1(U_7452))) ) ),
    inference(variable_rename,[status(thm)],[f_2018_1]) ).

fof(f_2018_3,plain,
    ( ! [U_7456,U_7454] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7454)),c_Int_OBit1(U_7456)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7454),U_7456)) )
    & ! [U_7455,U_7453] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7453),U_7455))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7453)),c_Int_OBit1(U_7455))) ) ),
    inference(miniscope,[status(thm)],[f_2018_2]) ).

cnf(f_2018_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7453),U_7455))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7453)),c_Int_OBit1(U_7455))) ),
    inference(clausify,[status(thm)],[f_2018_3]) ).

cnf(f_2018_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7454)),c_Int_OBit1(U_7456)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7454),U_7456)) ),
    inference(clausify,[status(thm)],[f_2018_3]) ).

fof(f_2019_1,plain,
    ! [V_l_2,V_k_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I34_J]) ).

fof(f_2019_2,plain,
    ! [U_7458,U_7457] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7457)),c_Int_OBit1(U_7458)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7457),U_7458)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7457),U_7458))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7457)),c_Int_OBit1(U_7458))) ) ),
    inference(variable_rename,[status(thm)],[f_2019_1]) ).

fof(f_2019_3,plain,
    ( ! [U_7462,U_7460] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7460)),c_Int_OBit1(U_7462)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7460),U_7462)) )
    & ! [U_7461,U_7459] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7459),U_7461))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7459)),c_Int_OBit1(U_7461))) ) ),
    inference(miniscope,[status(thm)],[f_2019_2]) ).

cnf(f_2019_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7459),U_7461))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7459)),c_Int_OBit1(U_7461))) ),
    inference(clausify,[status(thm)],[f_2019_3]) ).

cnf(f_2019_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7460)),c_Int_OBit1(U_7462)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7460),U_7462)) ),
    inference(clausify,[status(thm)],[f_2019_3]) ).

fof(f_2020_1,plain,
    ! [V_y,V_x] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_x),V_y)),
    inference(fof_nnf,[status(thm)],[fact_Divides_Otransfer__int__nat__functions_I1_J]) ).

fof(f_2020_2,plain,
    ! [U_7464,U_7463] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7463)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7464)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7463),U_7464)),
    inference(variable_rename,[status(thm)],[f_2020_1]) ).

cnf(f_2020_3,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7463)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7464)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7463),U_7464)),
    inference(clausify,[status(thm)],[f_2020_2]) ).

fof(f_2021_1,plain,
    ! [V_b,V_a] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_a)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_b)),
    inference(fof_nnf,[status(thm)],[fact_zdiv__int]) ).

fof(f_2021_2,plain,
    ! [U_7466,U_7465] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7465),U_7466)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7465)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7466)),
    inference(variable_rename,[status(thm)],[f_2021_1]) ).

cnf(f_2021_3,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7465),U_7466)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7465)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7466)),
    inference(clausify,[status(thm)],[f_2021_2]) ).

fof(f_2022_1,plain,
    ! [V_n] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))),
    inference(fof_nnf,[status(thm)],[fact_not__neg__int]) ).

fof(f_2022_2,plain,
    ! [U_7467] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7467))),
    inference(variable_rename,[status(thm)],[f_2022_1]) ).

cnf(f_2022_3,plain,
    ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7467))),
    inference(clausify,[status(thm)],[f_2022_2]) ).

fof(f_2023_1,plain,
    c_Fun_Oinj__on(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    inference(fof_nnf,[status(thm)],[fact_inj__int]) ).

cnf(f_2023_2,plain,
    c_Fun_Oinj__on(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_2023_1]) ).

fof(f_2024_1,plain,
    ! [V_A_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),V_A_2) = hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J]) ).

fof(f_2024_2,plain,
    ! [U_7468] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_7468) = hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7468)),
    inference(variable_rename,[status(thm)],[f_2024_1]) ).

cnf(f_2024_3,plain,
    hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_7468) = hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7468)),
    inference(clausify,[status(thm)],[f_2024_2]) ).

fof(f_2025_1,plain,
    ! [V_A_2,V_x_2] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),V_A_2))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),V_A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__relations_I2_J]) ).

fof(f_2025_2,plain,
    ! [U_7470,U_7469] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7469),U_7470))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7469)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7470))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7469)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7470)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7469),U_7470)) ) ),
    inference(variable_rename,[status(thm)],[f_2025_1]) ).

fof(f_2025_3,plain,
    ( ! [U_7474,U_7472] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7472),U_7474))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7472)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7474))) )
    & ! [U_7473,U_7471] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7471)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7473)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7471),U_7473)) ) ),
    inference(miniscope,[status(thm)],[f_2025_2]) ).

cnf(f_2025_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7471)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7473)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7471),U_7473)) ),
    inference(clausify,[status(thm)],[f_2025_3]) ).

cnf(f_2025_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7472),U_7474))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7472)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7474))) ),
    inference(clausify,[status(thm)],[f_2025_3]) ).

fof(f_2026_1,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),
    inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__numerals_I4_J]) ).

cnf(f_2026_2,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),
    inference(clausify,[status(thm)],[f_2026_1]) ).

fof(f_2027_1,plain,
    ! [V_B_2,V_A_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__relations_I5_J]) ).

fof(f_2027_2,plain,
    ! [U_7476,U_7475] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_7475),U_7476))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7475)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7476))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7475)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7476)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_7475),U_7476)) ) ),
    inference(variable_rename,[status(thm)],[f_2027_1]) ).

fof(f_2027_3,plain,
    ( ! [U_7480,U_7478] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_7478),U_7480))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7478)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7480))) )
    & ! [U_7479,U_7477] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7477)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7479)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_7477),U_7479)) ) ),
    inference(miniscope,[status(thm)],[f_2027_2]) ).

cnf(f_2027_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7477)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7479)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_7477),U_7479)) ),
    inference(clausify,[status(thm)],[f_2027_3]) ).

cnf(f_2027_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_7478),U_7480))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7478)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7480))) ),
    inference(clausify,[status(thm)],[f_2027_3]) ).

fof(f_2028_1,plain,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__numerals_I1_J]) ).

cnf(f_2028_2,plain,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(clausify,[status(thm)],[f_2028_1]) ).

fof(f_2029_1,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[fact_int__0]) ).

cnf(f_2029_2,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_2029_1]) ).

fof(f_2030_1,plain,
    ! [V_n_2] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(fof_nnf,[status(thm)],[fact_int__eq__0__conv]) ).

fof(f_2030_2,plain,
    ! [U_7481] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7481) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | U_7481 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( U_7481 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7481) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[f_2030_1]) ).

fof(f_2030_3,plain,
    ( ! [U_7483] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7483) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | U_7483 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_7482] :
        ( U_7482 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7482) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(miniscope,[status(thm)],[f_2030_2]) ).

cnf(f_2030_4,plain,
    ( U_7482 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7482) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2030_3]) ).

cnf(f_2030_5,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7483) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_7483 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_2030_3]) ).

fof(f_2031_1,plain,
    ! [V_P_2] :
      ( ( ! [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) )
        | ? [B_x] : ~ hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) )
      & ( ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x)))
        | ? [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__quantifiers_I1_J]) ).

fof(f_2031_2,plain,
    ! [U_7488] :
      ( ( ! [U_7487] :
            ( hBOOL(hAPP(U_7488,U_7487))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7487)) )
        | ? [U_7486] : ~ hBOOL(hAPP(U_7488,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7486))) )
      & ( ! [U_7485] : hBOOL(hAPP(U_7488,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7485)))
        | ? [U_7484] :
            ( ~ hBOOL(hAPP(U_7488,U_7484))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7484)) ) ) ),
    inference(variable_rename,[status(thm)],[f_2031_1]) ).

fof(f_2031_3,plain,
    ( ! [U_7490] :
        ( ! [U_7487] :
            ( hBOOL(hAPP(U_7490,U_7487))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7487)) )
        | ? [U_7486] : ~ hBOOL(hAPP(U_7490,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7486))) )
    & ! [U_7489] :
        ( ! [U_7485] : hBOOL(hAPP(U_7489,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7485)))
        | ? [U_7484] :
            ( ~ hBOOL(hAPP(U_7489,U_7484))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7484)) ) ) ),
    inference(miniscope,[status(thm)],[f_2031_2]) ).

fof(f_2031_4,plain,
    ( ! [U_7490] :
        ( ! [U_7487] :
            ( hBOOL(hAPP(U_7490,U_7487))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7487)) )
        | ? [U_7486] : ~ hBOOL(hAPP(U_7490,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7486))) )
    & ! [U_7489] :
        ( ! [U_7485] : hBOOL(hAPP(U_7489,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7485)))
        | ( ~ hBOOL(hAPP(U_7489,sK199(U_7489)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK199(U_7489))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK199]),skolemize(U_7484,sK199(U_7489))],[f_2031_3]) ).

fof(f_2031_5,plain,
    ( ! [U_7490] :
        ( ! [U_7487] :
            ( hBOOL(hAPP(U_7490,U_7487))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7487)) )
        | ~ hBOOL(hAPP(U_7490,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK200(U_7490)))) )
    & ! [U_7489] :
        ( ! [U_7485] : hBOOL(hAPP(U_7489,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7485)))
        | ( ~ hBOOL(hAPP(U_7489,sK199(U_7489)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK199(U_7489))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK200]),skolemize(U_7486,sK200(U_7490))],[f_2031_4]) ).

cnf(f_2031_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK199(U_7489)))
    | hBOOL(hAPP(U_7489,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7485))) ),
    inference(clausify,[status(thm)],[f_2031_5]) ).

cnf(f_2031_7,plain,
    ( ~ hBOOL(hAPP(U_7489,sK199(U_7489)))
    | hBOOL(hAPP(U_7489,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7485))) ),
    inference(clausify,[status(thm)],[f_2031_5]) ).

cnf(f_2031_8,plain,
    ( hBOOL(hAPP(U_7490,U_7487))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7487))
    | ~ hBOOL(hAPP(U_7490,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK200(U_7490)))) ),
    inference(clausify,[status(thm)],[f_2031_5]) ).

fof(f_2032_1,plain,
    ! [V_P_2] :
      ( ( ? [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) )
        | ! [B_x] : ~ hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) )
      & ( ? [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x)))
        | ! [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__quantifiers_I2_J]) ).

fof(f_2032_2,plain,
    ! [U_7495] :
      ( ( ? [U_7494] :
            ( hBOOL(hAPP(U_7495,U_7494))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7494)) )
        | ! [U_7493] : ~ hBOOL(hAPP(U_7495,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7493))) )
      & ( ? [U_7492] : hBOOL(hAPP(U_7495,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7492)))
        | ! [U_7491] :
            ( ~ hBOOL(hAPP(U_7495,U_7491))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7491)) ) ) ),
    inference(variable_rename,[status(thm)],[f_2032_1]) ).

fof(f_2032_3,plain,
    ( ! [U_7497] :
        ( ? [U_7494] :
            ( hBOOL(hAPP(U_7497,U_7494))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7494)) )
        | ! [U_7493] : ~ hBOOL(hAPP(U_7497,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7493))) )
    & ! [U_7496] :
        ( ? [U_7492] : hBOOL(hAPP(U_7496,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7492)))
        | ! [U_7491] :
            ( ~ hBOOL(hAPP(U_7496,U_7491))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7491)) ) ) ),
    inference(miniscope,[status(thm)],[f_2032_2]) ).

fof(f_2032_4,plain,
    ( ! [U_7497] :
        ( ? [U_7494] :
            ( hBOOL(hAPP(U_7497,U_7494))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7494)) )
        | ! [U_7493] : ~ hBOOL(hAPP(U_7497,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7493))) )
    & ! [U_7496] :
        ( hBOOL(hAPP(U_7496,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK201(U_7496))))
        | ! [U_7491] :
            ( ~ hBOOL(hAPP(U_7496,U_7491))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7491)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK201]),skolemize(U_7492,sK201(U_7496))],[f_2032_3]) ).

fof(f_2032_5,plain,
    ( ! [U_7497] :
        ( ( hBOOL(hAPP(U_7497,sK202(U_7497)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK202(U_7497))) )
        | ! [U_7493] : ~ hBOOL(hAPP(U_7497,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7493))) )
    & ! [U_7496] :
        ( hBOOL(hAPP(U_7496,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK201(U_7496))))
        | ! [U_7491] :
            ( ~ hBOOL(hAPP(U_7496,U_7491))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7491)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK202]),skolemize(U_7494,sK202(U_7497))],[f_2032_4]) ).

cnf(f_2032_6,plain,
    ( hBOOL(hAPP(U_7496,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK201(U_7496))))
    | ~ hBOOL(hAPP(U_7496,U_7491))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7491)) ),
    inference(clausify,[status(thm)],[f_2032_5]) ).

cnf(f_2032_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK202(U_7497)))
    | ~ hBOOL(hAPP(U_7497,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7493))) ),
    inference(clausify,[status(thm)],[f_2032_5]) ).

cnf(f_2032_8,plain,
    ( hBOOL(hAPP(U_7497,sK202(U_7497)))
    | ~ hBOOL(hAPP(U_7497,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7493))) ),
    inference(clausify,[status(thm)],[f_2032_5]) ).

fof(f_2033_1,plain,
    ! [V_z] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z))),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J]) ).

fof(f_2033_2,plain,
    ! [U_7498] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7498))),
    inference(variable_rename,[status(thm)],[f_2033_1]) ).

cnf(f_2033_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7498))),
    inference(clausify,[status(thm)],[f_2033_2]) ).

fof(f_2034_1,plain,
    ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))),
    inference(fof_nnf,[status(thm)],[fact_zero__zle__int]) ).

fof(f_2034_2,plain,
    ! [U_7499] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7499))),
    inference(variable_rename,[status(thm)],[f_2034_1]) ).

cnf(f_2034_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7499))),
    inference(clausify,[status(thm)],[f_2034_2]) ).

fof(f_2035_1,plain,
    ! [V_k] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_k)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(fof_nnf,[status(thm)],[fact_int__less__0__conv]) ).

fof(f_2035_2,plain,
    ! [U_7500] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7500)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(variable_rename,[status(thm)],[f_2035_1]) ).

cnf(f_2035_3,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7500)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(clausify,[status(thm)],[f_2035_2]) ).

fof(f_2036_1,plain,
    ! [V_y_2,V_x_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__relations_I2_J]) ).

fof(f_2036_2,plain,
    ! [U_7502,U_7501] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7501)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7502)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7501),U_7502)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7501),U_7502))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7501)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7502))) ) ),
    inference(variable_rename,[status(thm)],[f_2036_1]) ).

fof(f_2036_3,plain,
    ( ! [U_7506,U_7504] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7504)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7506)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7504),U_7506)) )
    & ! [U_7505,U_7503] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7503),U_7505))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7503)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7505))) ) ),
    inference(miniscope,[status(thm)],[f_2036_2]) ).

cnf(f_2036_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7503),U_7505))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7503)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7505))) ),
    inference(clausify,[status(thm)],[f_2036_3]) ).

cnf(f_2036_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7504)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7506)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7504),U_7506)) ),
    inference(clausify,[status(thm)],[f_2036_3]) ).

fof(f_2037_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_zless__int]) ).

fof(f_2037_2,plain,
    ! [U_7508,U_7507] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7507)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7508)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7507),U_7508)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7507),U_7508))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7507)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7508))) ) ),
    inference(variable_rename,[status(thm)],[f_2037_1]) ).

fof(f_2037_3,plain,
    ( ! [U_7512,U_7510] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7510)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7512)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7510),U_7512)) )
    & ! [U_7511,U_7509] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7509),U_7511))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7509)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7511))) ) ),
    inference(miniscope,[status(thm)],[f_2037_2]) ).

cnf(f_2037_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7509),U_7511))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7509)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7511))) ),
    inference(clausify,[status(thm)],[f_2037_3]) ).

cnf(f_2037_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7510)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7512)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7510),U_7512)) ),
    inference(clausify,[status(thm)],[f_2037_3]) ).

fof(f_2038_1,plain,
    ! [V_w_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_w_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_w_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(fof_nnf,[status(thm)],[fact_bin__less__0__simps_I4_J]) ).

fof(f_2038_2,plain,
    ! [U_7513] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7513)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7513),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7513),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7513)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(variable_rename,[status(thm)],[f_2038_1]) ).

fof(f_2038_3,plain,
    ( ! [U_7515] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7515)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7515),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_7514] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7514),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7514)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(miniscope,[status(thm)],[f_2038_2]) ).

cnf(f_2038_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7514),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7514)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2038_3]) ).

cnf(f_2038_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7515)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7515),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2038_3]) ).

fof(f_2039_1,plain,
    ! [V_y_2,V_x_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__relations_I3_J]) ).

fof(f_2039_2,plain,
    ! [U_7517,U_7516] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7516)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7517)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7516),U_7517)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7516),U_7517))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7516)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7517))) ) ),
    inference(variable_rename,[status(thm)],[f_2039_1]) ).

fof(f_2039_3,plain,
    ( ! [U_7521,U_7519] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7519)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7521)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7519),U_7521)) )
    & ! [U_7520,U_7518] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7518),U_7520))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7518)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7520))) ) ),
    inference(miniscope,[status(thm)],[f_2039_2]) ).

cnf(f_2039_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7518),U_7520))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7518)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7520))) ),
    inference(clausify,[status(thm)],[f_2039_3]) ).

cnf(f_2039_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7519)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7521)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7519),U_7521)) ),
    inference(clausify,[status(thm)],[f_2039_3]) ).

fof(f_2040_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_zle__int]) ).

fof(f_2040_2,plain,
    ! [U_7523,U_7522] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7522)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7523)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7522),U_7523)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7522),U_7523))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7522)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7523))) ) ),
    inference(variable_rename,[status(thm)],[f_2040_1]) ).

fof(f_2040_3,plain,
    ( ! [U_7527,U_7525] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7525)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7527)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7525),U_7527)) )
    & ! [U_7526,U_7524] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7524),U_7526))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7524)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7526))) ) ),
    inference(miniscope,[status(thm)],[f_2040_2]) ).

cnf(f_2040_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7524),U_7526))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7524)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7526))) ),
    inference(clausify,[status(thm)],[f_2040_3]) ).

cnf(f_2040_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7525)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7527)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7525),U_7527)) ),
    inference(clausify,[status(thm)],[f_2040_3]) ).

fof(f_2041_1,plain,
    ! [V_y,V_x] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),V_y)),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J]) ).

fof(f_2041_2,plain,
    ! [U_7529,U_7528] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7528)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7529)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7528),U_7529)),
    inference(variable_rename,[status(thm)],[f_2041_1]) ).

cnf(f_2041_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7528)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7529)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7528),U_7529)),
    inference(clausify,[status(thm)],[f_2041_2]) ).

fof(f_2042_1,plain,
    ! [V_z,V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))),V_z),
    inference(fof_nnf,[status(thm)],[fact_zadd__int__left]) ).

fof(f_2042_2,plain,
    ! [U_7532,U_7531,U_7530] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7530)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7531)),U_7532)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7530),U_7531))),U_7532),
    inference(variable_rename,[status(thm)],[f_2042_1]) ).

cnf(f_2042_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7530)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7531)),U_7532)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7530),U_7531))),U_7532),
    inference(clausify,[status(thm)],[f_2042_2]) ).

fof(f_2043_1,plain,
    ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),
    inference(fof_nnf,[status(thm)],[fact_zadd__int]) ).

fof(f_2043_2,plain,
    ! [U_7534,U_7533] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7533)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7534)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7533),U_7534)),
    inference(variable_rename,[status(thm)],[f_2043_1]) ).

cnf(f_2043_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7533)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7534)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7533),U_7534)),
    inference(clausify,[status(thm)],[f_2043_2]) ).

fof(f_2044_1,plain,
    ! [V_z_2,V_w_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2))
        | ! [B_n] : V_z_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n)) )
      & ( ? [B_n] : V_z_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_zle__iff__zadd]) ).

fof(f_2044_2,plain,
    ! [U_7538,U_7537] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7537),U_7538))
        | ! [U_7536] : U_7538 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7537),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7536)) )
      & ( ? [U_7535] : U_7538 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7537),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7535))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7537),U_7538)) ) ),
    inference(variable_rename,[status(thm)],[f_2044_1]) ).

fof(f_2044_3,plain,
    ( ! [U_7542,U_7540] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7540),U_7542))
        | ! [U_7536] : U_7542 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7540),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7536)) )
    & ! [U_7541,U_7539] :
        ( ? [U_7535] : U_7541 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7539),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7535))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7539),U_7541)) ) ),
    inference(miniscope,[status(thm)],[f_2044_2]) ).

fof(f_2044_4,plain,
    ( ! [U_7542,U_7540] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7540),U_7542))
        | ! [U_7536] : U_7542 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7540),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7536)) )
    & ! [U_7541,U_7539] :
        ( U_7541 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7539),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK203(U_7541,U_7539)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7539),U_7541)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK203]),skolemize(U_7535,sK203(U_7541,U_7539))],[f_2044_3]) ).

cnf(f_2044_5,plain,
    ( U_7541 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7539),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK203(U_7541,U_7539)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7539),U_7541)) ),
    inference(clausify,[status(thm)],[f_2044_4]) ).

cnf(f_2044_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7540),U_7542))
    | U_7542 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7540),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7536)) ),
    inference(clausify,[status(thm)],[f_2044_4]) ).

fof(f_2045_1,plain,
    ! [V_k_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I22_J]) ).

fof(f_2045_2,plain,
    ! [U_7543] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_7543)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_7543)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_7543))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_7543))) ) ),
    inference(variable_rename,[status(thm)],[f_2045_1]) ).

fof(f_2045_3,plain,
    ( ! [U_7545] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_7545)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_7545)) )
    & ! [U_7544] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_7544))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_7544))) ) ),
    inference(miniscope,[status(thm)],[f_2045_2]) ).

cnf(f_2045_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_7544))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_7544))) ),
    inference(clausify,[status(thm)],[f_2045_3]) ).

cnf(f_2045_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_7545)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_7545)) ),
    inference(clausify,[status(thm)],[f_2045_3]) ).

fof(f_2046_1,plain,
    ! [V_k_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls)) ) ),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I12_J]) ).

fof(f_2046_2,plain,
    ! [U_7546] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7546)),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7546),c_Int_OPls)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7546),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7546)),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[f_2046_1]) ).

fof(f_2046_3,plain,
    ( ! [U_7548] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7548)),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7548),c_Int_OPls)) )
    & ! [U_7547] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7547),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7547)),c_Int_OPls)) ) ),
    inference(miniscope,[status(thm)],[f_2046_2]) ).

cnf(f_2046_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7547),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7547)),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_2046_3]) ).

cnf(f_2046_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7548)),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7548),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_2046_3]) ).

fof(f_2047_1,plain,
    ! [V_m,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_zero__le__imp__of__nat]) ).

fof(f_2047_2,plain,
    ! [U_7550,U_7549] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7549),c_Groups_Ozero__class_Ozero(U_7549)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7549),U_7550)))
      | ~ class_Rings_Olinordered__semidom(U_7549) ),
    inference(variable_rename,[status(thm)],[f_2047_1]) ).

cnf(f_2047_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7549),c_Groups_Ozero__class_Ozero(U_7549)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7549),U_7550)))
    | ~ class_Rings_Olinordered__semidom(U_7549) ),
    inference(clausify,[status(thm)],[f_2047_2]) ).

fof(f_2048_1,plain,
    ! [V_n,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__0__le__iff]) ).

fof(f_2048_2,plain,
    ! [U_7552,U_7551] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7551),c_Groups_Ozero__class_Ozero(U_7551)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7551),U_7552)))
      | ~ class_Rings_Olinordered__semidom(U_7551) ),
    inference(variable_rename,[status(thm)],[f_2048_1]) ).

cnf(f_2048_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7551),c_Groups_Ozero__class_Ozero(U_7551)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7551),U_7552)))
    | ~ class_Rings_Olinordered__semidom(U_7551) ),
    inference(clausify,[status(thm)],[f_2048_2]) ).

fof(f_2049_1,plain,
    ! [V_m_2,V_n_2] :
      ( ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)
        | V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_negative__eq__positive]) ).

fof(f_2049_2,plain,
    ! [U_7554,U_7553] :
      ( ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7553)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7554)
        | U_7554 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_7553 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ( U_7554 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_7553 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7553)) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7554) ) ),
    inference(variable_rename,[status(thm)],[f_2049_1]) ).

fof(f_2049_3,plain,
    ( ! [U_7558,U_7556] :
        ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7556)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7558)
        | U_7558 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_7556 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_7557,U_7555] :
        ( ( U_7557 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_7555 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7555)) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7557) ) ),
    inference(miniscope,[status(thm)],[f_2049_2]) ).

cnf(f_2049_4,plain,
    ( U_7555 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7555)) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7557) ),
    inference(clausify,[status(thm)],[f_2049_3]) ).

cnf(f_2049_5,plain,
    ( U_7557 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7555)) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7557) ),
    inference(clausify,[status(thm)],[f_2049_3]) ).

cnf(f_2049_6,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7556)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7558)
    | U_7558 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_7556 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_2049_3]) ).

fof(f_2050_1,plain,
    ! [V_m,T_a] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__less__0__iff]) ).

fof(f_2050_2,plain,
    ! [U_7560,U_7559] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7559),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7559),U_7560)),c_Groups_Ozero__class_Ozero(U_7559)))
      | ~ class_Rings_Olinordered__semidom(U_7559) ),
    inference(variable_rename,[status(thm)],[f_2050_1]) ).

cnf(f_2050_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7559),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7559),U_7560)),c_Groups_Ozero__class_Ozero(U_7559)))
    | ~ class_Rings_Olinordered__semidom(U_7559) ),
    inference(clausify,[status(thm)],[f_2050_2]) ).

fof(f_2051_1,plain,
    ! [V_k] : c_Int_OBit1(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k)),V_k),
    inference(fof_nnf,[status(thm)],[fact_Bit1__def]) ).

fof(f_2051_2,plain,
    ! [U_7561] : c_Int_OBit1(U_7561) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_7561)),U_7561),
    inference(variable_rename,[status(thm)],[f_2051_1]) ).

cnf(f_2051_3,plain,
    c_Int_OBit1(U_7561) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_7561)),U_7561),
    inference(clausify,[status(thm)],[f_2051_2]) ).

fof(f_2052_1,plain,
    ! [V_m,V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)))),
    inference(fof_nnf,[status(thm)],[fact_not__int__zless__negative]) ).

fof(f_2052_2,plain,
    ! [U_7563,U_7562] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7562)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7563)))),
    inference(variable_rename,[status(thm)],[f_2052_1]) ).

cnf(f_2052_3,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7562)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7563)))),
    inference(clausify,[status(thm)],[f_2052_2]) ).

fof(f_2053_1,plain,
    ! [V_y,V_x] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_x),V_y)),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J]) ).

fof(f_2053_2,plain,
    ! [U_7565,U_7564] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7564)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7565)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7564),U_7565)),
    inference(variable_rename,[status(thm)],[f_2053_1]) ).

cnf(f_2053_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7564)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7565)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7564),U_7565)),
    inference(clausify,[status(thm)],[f_2053_2]) ).

fof(f_2054_1,plain,
    ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),
    inference(fof_nnf,[status(thm)],[fact_zmult__int]) ).

fof(f_2054_2,plain,
    ! [U_7567,U_7566] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7566)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7567)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7566),U_7567)),
    inference(variable_rename,[status(thm)],[f_2054_1]) ).

cnf(f_2054_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7566)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7567)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7566),U_7567)),
    inference(clausify,[status(thm)],[f_2054_2]) ).

fof(f_2055_1,plain,
    ! [V_n,V_m] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)),
    inference(fof_nnf,[status(thm)],[fact_int__mult]) ).

fof(f_2055_2,plain,
    ! [U_7569,U_7568] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7568),U_7569)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7568)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7569)),
    inference(variable_rename,[status(thm)],[f_2055_1]) ).

cnf(f_2055_3,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7568),U_7569)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7568)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7569)),
    inference(clausify,[status(thm)],[f_2055_2]) ).

fof(f_2056_1,plain,
    ! [T_a] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Rings_Osemiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__0]) ).

fof(f_2056_2,plain,
    ! [U_7570] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7570),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(U_7570)
      | ~ class_Rings_Osemiring__1(U_7570) ),
    inference(variable_rename,[status(thm)],[f_2056_1]) ).

cnf(f_2056_3,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7570),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(U_7570)
    | ~ class_Rings_Osemiring__1(U_7570) ),
    inference(clausify,[status(thm)],[f_2056_2]) ).

fof(f_2057_1,plain,
    ! [V_n_2,V_m_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2))) ) )
      | ~ class_Rings_Olinordered__semidom(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__less__iff]) ).

fof(f_2057_2,plain,
    ! [U_7573,U_7572,U_7571] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7571),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7571),U_7572)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7571),U_7573)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7572),U_7573)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7572),U_7573))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7571),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7571),U_7572)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7571),U_7573))) ) )
      | ~ class_Rings_Olinordered__semidom(U_7571) ),
    inference(variable_rename,[status(thm)],[f_2057_1]) ).

cnf(f_2057_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7572),U_7573))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7571),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7571),U_7572)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7571),U_7573)))
    | ~ class_Rings_Olinordered__semidom(U_7571) ),
    inference(clausify,[status(thm)],[f_2057_2]) ).

cnf(f_2057_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7571),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7571),U_7572)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7571),U_7573)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7572),U_7573))
    | ~ class_Rings_Olinordered__semidom(U_7571) ),
    inference(clausify,[status(thm)],[f_2057_2]) ).

fof(f_2058_1,plain,
    ! [V_n,V_m,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_less__imp__of__nat__less]) ).

fof(f_2058_2,plain,
    ! [U_7576,U_7575,U_7574] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7574),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7574),U_7575)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7574),U_7576)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7575),U_7576))
      | ~ class_Rings_Olinordered__semidom(U_7574) ),
    inference(variable_rename,[status(thm)],[f_2058_1]) ).

cnf(f_2058_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7574),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7574),U_7575)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7574),U_7576)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7575),U_7576))
    | ~ class_Rings_Olinordered__semidom(U_7574) ),
    inference(clausify,[status(thm)],[f_2058_2]) ).

fof(f_2059_1,plain,
    ! [V_n,V_m,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__less__imp__less]) ).

fof(f_2059_2,plain,
    ! [U_7579,U_7578,U_7577] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7578),U_7579))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7577),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7577),U_7578)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7577),U_7579)))
      | ~ class_Rings_Olinordered__semidom(U_7577) ),
    inference(variable_rename,[status(thm)],[f_2059_1]) ).

cnf(f_2059_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7578),U_7579))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7577),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7577),U_7578)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7577),U_7579)))
    | ~ class_Rings_Olinordered__semidom(U_7577) ),
    inference(clausify,[status(thm)],[f_2059_2]) ).

fof(f_2060_1,plain,
    c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__numerals_I2_J]) ).

cnf(f_2060_2,plain,
    c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(clausify,[status(thm)],[f_2060_1]) ).

fof(f_2061_1,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[fact_int__1]) ).

cnf(f_2061_2,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_2061_1]) ).

fof(f_2062_1,plain,
    ! [V_n_2,V_m_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2))) ) )
      | ~ class_Rings_Olinordered__semidom(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__le__iff]) ).

fof(f_2062_2,plain,
    ! [U_7582,U_7581,U_7580] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7580),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7580),U_7581)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7580),U_7582)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7581),U_7582)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7581),U_7582))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7580),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7580),U_7581)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7580),U_7582))) ) )
      | ~ class_Rings_Olinordered__semidom(U_7580) ),
    inference(variable_rename,[status(thm)],[f_2062_1]) ).

cnf(f_2062_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7581),U_7582))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7580),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7580),U_7581)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7580),U_7582)))
    | ~ class_Rings_Olinordered__semidom(U_7580) ),
    inference(clausify,[status(thm)],[f_2062_2]) ).

cnf(f_2062_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7580),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7580),U_7581)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7580),U_7582)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7581),U_7582))
    | ~ class_Rings_Olinordered__semidom(U_7580) ),
    inference(clausify,[status(thm)],[f_2062_2]) ).

fof(f_2063_1,plain,
    ! [V_n,V_m,T_a] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n))
      | ~ class_Rings_Osemiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__add]) ).

fof(f_2063_2,plain,
    ! [U_7585,U_7584,U_7583] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7583),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7584),U_7585)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7583),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7583),U_7584)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7583),U_7585))
      | ~ class_Rings_Osemiring__1(U_7583) ),
    inference(variable_rename,[status(thm)],[f_2063_1]) ).

cnf(f_2063_3,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7583),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7584),U_7585)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7583),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7583),U_7584)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7583),U_7585))
    | ~ class_Rings_Osemiring__1(U_7583) ),
    inference(clausify,[status(thm)],[f_2063_2]) ).

fof(f_2064_1,plain,
    ! [V_n,V_m,T_a] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n))
      | ~ class_Rings_Osemiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__mult]) ).

fof(f_2064_2,plain,
    ! [U_7588,U_7587,U_7586] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7586),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7587),U_7588)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7586),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7586),U_7587)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7586),U_7588))
      | ~ class_Rings_Osemiring__1(U_7586) ),
    inference(variable_rename,[status(thm)],[f_2064_1]) ).

cnf(f_2064_3,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7586),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7587),U_7588)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7586),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7586),U_7587)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7586),U_7588))
    | ~ class_Rings_Osemiring__1(U_7586) ),
    inference(clausify,[status(thm)],[f_2064_2]) ).

fof(f_2065_1,plain,
    ! [V_w_2] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_w_2))))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_w_2)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_neg__number__of__Bit1]) ).

fof(f_2065_2,plain,
    ! [U_7589] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_7589))))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7589))) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7589)))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_7589)))) ) ),
    inference(variable_rename,[status(thm)],[f_2065_1]) ).

fof(f_2065_3,plain,
    ( ! [U_7591] :
        ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_7591))))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7591))) )
    & ! [U_7590] :
        ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7590)))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_7590)))) ) ),
    inference(miniscope,[status(thm)],[f_2065_2]) ).

cnf(f_2065_4,plain,
    ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7590)))
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_7590)))) ),
    inference(clausify,[status(thm)],[f_2065_3]) ).

cnf(f_2065_5,plain,
    ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_7591))))
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7591))) ),
    inference(clausify,[status(thm)],[f_2065_3]) ).

fof(f_2066_1,plain,
    ! [V_z] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z
      | hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z)) ),
    inference(fof_nnf,[status(thm)],[fact_not__neg__nat]) ).

fof(f_2066_2,plain,
    ! [U_7592] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_7592)) = U_7592
      | hBOOL(hAPP(c_Nat__Numeral_Oneg,U_7592)) ),
    inference(variable_rename,[status(thm)],[f_2066_1]) ).

cnf(f_2066_3,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_7592)) = U_7592
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,U_7592)) ),
    inference(clausify,[status(thm)],[f_2066_2]) ).

fof(f_2067_1,plain,
    ! [T_a] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a)
      | ~ class_Rings_Osemiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__1]) ).

fof(f_2067_2,plain,
    ! [U_7593] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7593),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_7593)
      | ~ class_Rings_Osemiring__1(U_7593) ),
    inference(variable_rename,[status(thm)],[f_2067_1]) ).

cnf(f_2067_3,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7593),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_7593)
    | ~ class_Rings_Osemiring__1(U_7593) ),
    inference(clausify,[status(thm)],[f_2067_2]) ).

fof(f_2068_1,plain,
    ! [V_k] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(V_k)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k))),
    inference(fof_nnf,[status(thm)],[fact_minus__Bit1]) ).

fof(f_2068_2,plain,
    ! [U_7594] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(U_7594)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7594))),
    inference(variable_rename,[status(thm)],[f_2068_1]) ).

cnf(f_2068_3,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(U_7594)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7594))),
    inference(clausify,[status(thm)],[f_2068_2]) ).

fof(f_2069_1,plain,
    ! [V_w,T_a] :
      ( ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(V_w)))
      | ~ class_Int_Oring__char__0(T_a)
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_iszero__number__of__Bit1]) ).

fof(f_2069_2,plain,
    ! [U_7596,U_7595] :
      ( ~ c_Int_Oiszero(U_7595,hAPP(c_Int_Onumber__class_Onumber__of(U_7595),c_Int_OBit1(U_7596)))
      | ~ class_Int_Oring__char__0(U_7595)
      | ~ class_Int_Onumber__ring(U_7595) ),
    inference(variable_rename,[status(thm)],[f_2069_1]) ).

cnf(f_2069_3,plain,
    ( ~ c_Int_Oiszero(U_7595,hAPP(c_Int_Onumber__class_Onumber__of(U_7595),c_Int_OBit1(U_7596)))
    | ~ class_Int_Oring__char__0(U_7595)
    | ~ class_Int_Onumber__ring(U_7595) ),
    inference(clausify,[status(thm)],[f_2069_2]) ).

fof(f_2070_1,plain,
    ! [V_n_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)),c_Int_Oring__1__class_OInts(T_b)))
      | ~ class_Rings_Oring__1(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Ints__of__nat]) ).

fof(f_2070_2,plain,
    ! [U_7598,U_7597] :
      ( hBOOL(hAPP(hAPP(c_member(U_7597),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7597),U_7598)),c_Int_Oring__1__class_OInts(U_7597)))
      | ~ class_Rings_Oring__1(U_7597) ),
    inference(variable_rename,[status(thm)],[f_2070_1]) ).

cnf(f_2070_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7597),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7597),U_7598)),c_Int_Oring__1__class_OInts(U_7597)))
    | ~ class_Rings_Oring__1(U_7597) ),
    inference(clausify,[status(thm)],[f_2070_2]) ).

fof(f_2071_1,plain,
    c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls),
    inference(fof_nnf,[status(thm)],[fact_succ__Pls]) ).

cnf(f_2071_2,plain,
    c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls),
    inference(clausify,[status(thm)],[f_2071_1]) ).

fof(f_2072_1,plain,
    ! [V_n,V_m,T_a] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),V_n)
      | ~ class_Rings_Osemiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__power]) ).

fof(f_2072_2,plain,
    ! [U_7601,U_7600,U_7599] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7599),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_7600),U_7601)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_7599),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7599),U_7600)),U_7601)
      | ~ class_Rings_Osemiring__1(U_7599) ),
    inference(variable_rename,[status(thm)],[f_2072_1]) ).

cnf(f_2072_3,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7599),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_7600),U_7601)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_7599),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7599),U_7600)),U_7601)
    | ~ class_Rings_Osemiring__1(U_7599) ),
    inference(clausify,[status(thm)],[f_2072_2]) ).

fof(f_2073_1,plain,
    ! [V_n,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x)),V_n) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x),V_n)),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J]) ).

fof(f_2073_2,plain,
    ! [U_7603,U_7602] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7602)),U_7603) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_7602),U_7603)),
    inference(variable_rename,[status(thm)],[f_2073_1]) ).

cnf(f_2073_3,plain,
    hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7602)),U_7603) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_7602),U_7603)),
    inference(clausify,[status(thm)],[f_2073_2]) ).

fof(f_2074_1,plain,
    ! [V_n,V_m] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),V_n) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)),
    inference(fof_nnf,[status(thm)],[fact_zpower__int]) ).

fof(f_2074_2,plain,
    ! [U_7605,U_7604] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7604)),U_7605) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_7604),U_7605)),
    inference(variable_rename,[status(thm)],[f_2074_1]) ).

cnf(f_2074_3,plain,
    hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7604)),U_7605) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_7604),U_7605)),
    inference(clausify,[status(thm)],[f_2074_2]) ).

fof(f_2075_1,plain,
    ! [V_n,V_m] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),V_n),
    inference(fof_nnf,[status(thm)],[fact_int__power]) ).

fof(f_2075_2,plain,
    ! [U_7607,U_7606] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_7606),U_7607)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7606)),U_7607),
    inference(variable_rename,[status(thm)],[f_2075_1]) ).

cnf(f_2075_3,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_7606),U_7607)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7606)),U_7607),
    inference(clausify,[status(thm)],[f_2075_2]) ).

fof(f_2076_1,plain,
    ! [V_n_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)),c_Nat_Osemiring__1__class_ONats(T_b)))
      | ~ class_Rings_Osemiring__1(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__in__Nats]) ).

fof(f_2076_2,plain,
    ! [U_7609,U_7608] :
      ( hBOOL(hAPP(hAPP(c_member(U_7608),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7608),U_7609)),c_Nat_Osemiring__1__class_ONats(U_7608)))
      | ~ class_Rings_Osemiring__1(U_7608) ),
    inference(variable_rename,[status(thm)],[f_2076_1]) ).

cnf(f_2076_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7608),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7608),U_7609)),c_Nat_Osemiring__1__class_ONats(U_7608)))
    | ~ class_Rings_Osemiring__1(U_7608) ),
    inference(clausify,[status(thm)],[f_2076_2]) ).

fof(f_2077_1,plain,
    ! [V_y,V_x] : c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x),V_y)),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J]) ).

fof(f_2077_2,plain,
    ! [U_7611,U_7610] : c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7610),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7611)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7610),U_7611)),
    inference(variable_rename,[status(thm)],[f_2077_1]) ).

cnf(f_2077_3,plain,
    c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7610),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7611)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7610),U_7611)),
    inference(clausify,[status(thm)],[f_2077_2]) ).

fof(f_2078_1,plain,
    ! [V_A_2] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_A_2))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2))) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__relations_I1_J]) ).

fof(f_2078_2,plain,
    ! [U_7612] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_7612))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7612))) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7612)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_7612)) ) ),
    inference(variable_rename,[status(thm)],[f_2078_1]) ).

fof(f_2078_3,plain,
    ( ! [U_7614] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_7614))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7614))) )
    & ! [U_7613] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7613)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_7613)) ) ),
    inference(miniscope,[status(thm)],[f_2078_2]) ).

cnf(f_2078_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7613)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_7613)) ),
    inference(clausify,[status(thm)],[f_2078_3]) ).

cnf(f_2078_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_7614))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7614))) ),
    inference(clausify,[status(thm)],[f_2078_3]) ).

fof(f_2079_1,plain,
    ! [T_b] :
      ( c_Fun_Oinj__on(tc_Nat_Onat,T_b,c_Nat_Osemiring__1__class_Oof__nat(T_b),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
      | ~ class_Nat_Osemiring__char__0(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_inj__of__nat]) ).

fof(f_2079_2,plain,
    ! [U_7615] :
      ( c_Fun_Oinj__on(tc_Nat_Onat,U_7615,c_Nat_Osemiring__1__class_Oof__nat(U_7615),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
      | ~ class_Nat_Osemiring__char__0(U_7615) ),
    inference(variable_rename,[status(thm)],[f_2079_1]) ).

cnf(f_2079_3,plain,
    ( c_Fun_Oinj__on(tc_Nat_Onat,U_7615,c_Nat_Osemiring__1__class_Oof__nat(U_7615),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
    | ~ class_Nat_Osemiring__char__0(U_7615) ),
    inference(clausify,[status(thm)],[f_2079_2]) ).

fof(f_2080_1,plain,
    ! [V_B_2,V_A_2] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2))),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__set__functions_I3_J]) ).

fof(f_2080_2,plain,
    ! [U_7617,U_7616] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_7616),U_7617) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7616)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7617))),
    inference(variable_rename,[status(thm)],[f_2080_1]) ).

cnf(f_2080_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_7616),U_7617) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7616)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7617))),
    inference(clausify,[status(thm)],[f_2080_2]) ).

fof(f_2081_1,plain,
    c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J]) ).

cnf(f_2081_2,plain,
    c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_2081_1]) ).

fof(f_2082_1,plain,
    ! [V_w,T_a] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_number__of__Bit1]) ).

fof(f_2082_2,plain,
    ! [U_7619,U_7618] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_7618),c_Int_OBit1(U_7619)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7618),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7618),c_Groups_Oone__class_Oone(U_7618)),hAPP(c_Int_Onumber__class_Onumber__of(U_7618),U_7619))),hAPP(c_Int_Onumber__class_Onumber__of(U_7618),U_7619))
      | ~ class_Int_Onumber__ring(U_7618) ),
    inference(variable_rename,[status(thm)],[f_2082_1]) ).

cnf(f_2082_3,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_7618),c_Int_OBit1(U_7619)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7618),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7618),c_Groups_Oone__class_Oone(U_7618)),hAPP(c_Int_Onumber__class_Onumber__of(U_7618),U_7619))),hAPP(c_Int_Onumber__class_Onumber__of(U_7618),U_7619))
    | ~ class_Int_Onumber__ring(U_7618) ),
    inference(clausify,[status(thm)],[f_2082_2]) ).

fof(f_2083_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))),V_a) = V_a
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__numeral__1]) ).

fof(f_2083_2,plain,
    ! [U_7621,U_7620] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7620),hAPP(c_Int_Onumber__class_Onumber__of(U_7620),c_Int_OBit1(c_Int_OPls))),U_7621) = U_7621
      | ~ class_Int_Onumber__ring(U_7620) ),
    inference(variable_rename,[status(thm)],[f_2083_1]) ).

cnf(f_2083_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7620),hAPP(c_Int_Onumber__class_Onumber__of(U_7620),c_Int_OBit1(c_Int_OPls))),U_7621) = U_7621
    | ~ class_Int_Onumber__ring(U_7620) ),
    inference(clausify,[status(thm)],[f_2083_2]) ).

fof(f_2084_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) = V_a
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__numeral__1__right]) ).

fof(f_2084_2,plain,
    ! [U_7623,U_7622] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7622),U_7623),hAPP(c_Int_Onumber__class_Onumber__of(U_7622),c_Int_OBit1(c_Int_OPls))) = U_7623
      | ~ class_Int_Onumber__ring(U_7622) ),
    inference(variable_rename,[status(thm)],[f_2084_1]) ).

cnf(f_2084_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7622),U_7623),hAPP(c_Int_Onumber__class_Onumber__of(U_7622),c_Int_OBit1(c_Int_OPls))) = U_7623
    | ~ class_Int_Onumber__ring(U_7622) ),
    inference(clausify,[status(thm)],[f_2084_2]) ).

fof(f_2085_1,plain,
    ! [V_n_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(fof_nnf,[status(thm)],[fact_int__le__0__conv]) ).

fof(f_2085_2,plain,
    ! [U_7624] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7624)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | U_7624 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( U_7624 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7624)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(variable_rename,[status(thm)],[f_2085_1]) ).

fof(f_2085_3,plain,
    ( ! [U_7626] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7626)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | U_7626 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_7625] :
        ( U_7625 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7625)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(miniscope,[status(thm)],[f_2085_2]) ).

cnf(f_2085_4,plain,
    ( U_7625 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7625)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2085_3]) ).

cnf(f_2085_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7626)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | U_7626 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_2085_3]) ).

fof(f_2086_1,plain,
    ! [T_a] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(T_a)
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_numeral__1__eq__1]) ).

fof(f_2086_2,plain,
    ! [U_7627] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_7627),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(U_7627)
      | ~ class_Int_Onumber__ring(U_7627) ),
    inference(variable_rename,[status(thm)],[f_2086_1]) ).

cnf(f_2086_3,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_7627),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(U_7627)
    | ~ class_Int_Onumber__ring(U_7627) ),
    inference(clausify,[status(thm)],[f_2086_2]) ).

fof(f_2087_1,plain,
    ! [T_a] :
      ( c_Groups_Oone__class_Oone(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_semiring__norm_I110_J]) ).

fof(f_2087_2,plain,
    ! [U_7628] :
      ( c_Groups_Oone__class_Oone(U_7628) = hAPP(c_Int_Onumber__class_Onumber__of(U_7628),c_Int_OBit1(c_Int_OPls))
      | ~ class_Int_Onumber__ring(U_7628) ),
    inference(variable_rename,[status(thm)],[f_2087_1]) ).

cnf(f_2087_3,plain,
    ( c_Groups_Oone__class_Oone(U_7628) = hAPP(c_Int_Onumber__class_Onumber__of(U_7628),c_Int_OBit1(c_Int_OPls))
    | ~ class_Int_Onumber__ring(U_7628) ),
    inference(clausify,[status(thm)],[f_2087_2]) ).

fof(f_2088_1,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[fact_int__Suc0__eq__1]) ).

cnf(f_2088_2,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_2088_1]) ).

fof(f_2089_1,plain,
    ! [V_z_2,V_w_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
        | ! [B_n] : V_z_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,B_n))) )
      & ( ? [B_n] : V_z_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,B_n)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_zless__iff__Suc__zadd]) ).

fof(f_2089_2,plain,
    ! [U_7632,U_7631] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7631),U_7632))
        | ! [U_7630] : U_7632 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7631),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_7630))) )
      & ( ? [U_7629] : U_7632 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7631),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_7629)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7631),U_7632)) ) ),
    inference(variable_rename,[status(thm)],[f_2089_1]) ).

fof(f_2089_3,plain,
    ( ! [U_7636,U_7634] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7634),U_7636))
        | ! [U_7630] : U_7636 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7634),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_7630))) )
    & ! [U_7635,U_7633] :
        ( ? [U_7629] : U_7635 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7633),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_7629)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7633),U_7635)) ) ),
    inference(miniscope,[status(thm)],[f_2089_2]) ).

fof(f_2089_4,plain,
    ( ! [U_7636,U_7634] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7634),U_7636))
        | ! [U_7630] : U_7636 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7634),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_7630))) )
    & ! [U_7635,U_7633] :
        ( U_7635 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7633),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,sK204(U_7635,U_7633))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7633),U_7635)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK204]),skolemize(U_7629,sK204(U_7635,U_7633))],[f_2089_3]) ).

cnf(f_2089_5,plain,
    ( U_7635 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7633),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,sK204(U_7635,U_7633))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7633),U_7635)) ),
    inference(clausify,[status(thm)],[f_2089_4]) ).

cnf(f_2089_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7634),U_7636))
    | U_7636 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7634),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_7630))) ),
    inference(clausify,[status(thm)],[f_2089_4]) ).

fof(f_2090_1,plain,
    ! [V_z] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) )
      & ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) ) ),
    inference(fof_nnf,[status(thm)],[fact_int__nat__eq]) ).

fof(f_2090_2,plain,
    ! [U_7637] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_7637)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7637)) )
      & ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_7637)) = U_7637
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7637)) ) ),
    inference(variable_rename,[status(thm)],[f_2090_1]) ).

fof(f_2090_3,plain,
    ( ! [U_7639] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_7639)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7639)) )
    & ! [U_7638] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_7638)) = U_7638
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7638)) ) ),
    inference(miniscope,[status(thm)],[f_2090_2]) ).

cnf(f_2090_4,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_7638)) = U_7638
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7638)) ),
    inference(clausify,[status(thm)],[f_2090_3]) ).

cnf(f_2090_5,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_7639)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7639)) ),
    inference(clausify,[status(thm)],[f_2090_3]) ).

fof(f_2091_1,plain,
    ! [V_z_2,V_m_2] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = V_z_2
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
        | V_m_2 != hAPP(c_Int_Onat,V_z_2) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
          & V_m_2 = hAPP(c_Int_Onat,V_z_2) )
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) != V_z_2 ) ),
    inference(fof_nnf,[status(thm)],[fact_int__eq__iff]) ).

fof(f_2091_2,plain,
    ! [U_7641,U_7640] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7640) = U_7641
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7641))
        | U_7640 != hAPP(c_Int_Onat,U_7641) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7641))
          & U_7640 = hAPP(c_Int_Onat,U_7641) )
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7640) != U_7641 ) ),
    inference(variable_rename,[status(thm)],[f_2091_1]) ).

fof(f_2091_3,plain,
    ( ! [U_7645,U_7643] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7643) = U_7645
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7645))
        | U_7643 != hAPP(c_Int_Onat,U_7645) )
    & ! [U_7644,U_7642] :
        ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7644))
          & U_7642 = hAPP(c_Int_Onat,U_7644) )
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7642) != U_7644 ) ),
    inference(miniscope,[status(thm)],[f_2091_2]) ).

cnf(f_2091_4,plain,
    ( U_7642 = hAPP(c_Int_Onat,U_7644)
    | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7642) != U_7644 ),
    inference(clausify,[status(thm)],[f_2091_3]) ).

cnf(f_2091_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7644))
    | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7642) != U_7644 ),
    inference(clausify,[status(thm)],[f_2091_3]) ).

cnf(f_2091_6,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7643) = U_7645
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7645))
    | U_7643 != hAPP(c_Int_Onat,U_7645) ),
    inference(clausify,[status(thm)],[f_2091_3]) ).

fof(f_2092_1,plain,
    ! [V_z] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) ),
    inference(fof_nnf,[status(thm)],[fact_nat__0__le]) ).

fof(f_2092_2,plain,
    ! [U_7646] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_7646)) = U_7646
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7646)) ),
    inference(variable_rename,[status(thm)],[f_2092_1]) ).

cnf(f_2092_3,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_7646)) = U_7646
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7646)) ),
    inference(clausify,[status(thm)],[f_2092_2]) ).

fof(f_2093_1,plain,
    ! [V_z_2,V_m_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Int_Onat,V_z_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)),V_z_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)),V_z_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Int_Onat,V_z_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_zless__nat__eq__int__zless]) ).

fof(f_2093_2,plain,
    ! [U_7648,U_7647] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7647),hAPP(c_Int_Onat,U_7648)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7647)),U_7648)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7647)),U_7648))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7647),hAPP(c_Int_Onat,U_7648))) ) ),
    inference(variable_rename,[status(thm)],[f_2093_1]) ).

fof(f_2093_3,plain,
    ( ! [U_7652,U_7650] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7650),hAPP(c_Int_Onat,U_7652)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7650)),U_7652)) )
    & ! [U_7651,U_7649] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7649)),U_7651))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7649),hAPP(c_Int_Onat,U_7651))) ) ),
    inference(miniscope,[status(thm)],[f_2093_2]) ).

cnf(f_2093_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7649)),U_7651))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7649),hAPP(c_Int_Onat,U_7651))) ),
    inference(clausify,[status(thm)],[f_2093_3]) ).

cnf(f_2093_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7650),hAPP(c_Int_Onat,U_7652)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7650)),U_7652)) ),
    inference(clausify,[status(thm)],[f_2093_3]) ).

fof(f_2094_1,plain,
    ! [V_k_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I5_J]) ).

fof(f_2094_2,plain,
    ! [U_7653] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_7653)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_7653)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_7653))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_7653))) ) ),
    inference(variable_rename,[status(thm)],[f_2094_1]) ).

fof(f_2094_3,plain,
    ( ! [U_7655] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_7655)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_7655)) )
    & ! [U_7654] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_7654))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_7654))) ) ),
    inference(miniscope,[status(thm)],[f_2094_2]) ).

cnf(f_2094_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_7654))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_7654))) ),
    inference(clausify,[status(thm)],[f_2094_3]) ).

cnf(f_2094_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_7655)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_7655)) ),
    inference(clausify,[status(thm)],[f_2094_3]) ).

fof(f_2095_1,plain,
    ! [V_k_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls)) ) ),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I29_J]) ).

fof(f_2095_2,plain,
    ! [U_7656] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7656)),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7656),c_Int_OPls)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7656),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7656)),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[f_2095_1]) ).

fof(f_2095_3,plain,
    ( ! [U_7658] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7658)),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7658),c_Int_OPls)) )
    & ! [U_7657] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7657),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7657)),c_Int_OPls)) ) ),
    inference(miniscope,[status(thm)],[f_2095_2]) ).

cnf(f_2095_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7657),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7657)),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_2095_3]) ).

cnf(f_2095_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7658)),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7658),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_2095_3]) ).

fof(f_2096_1,plain,
    ! [V_m_2,V_n_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2))))
        | V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_int__zle__neg]) ).

fof(f_2096_2,plain,
    ! [U_7660,U_7659] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7659)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7660))))
        | U_7660 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_7659 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ( U_7660 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_7659 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7659)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7660)))) ) ),
    inference(variable_rename,[status(thm)],[f_2096_1]) ).

fof(f_2096_3,plain,
    ( ! [U_7664,U_7662] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7662)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7664))))
        | U_7664 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_7662 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_7663,U_7661] :
        ( ( U_7663 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_7661 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7661)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7663)))) ) ),
    inference(miniscope,[status(thm)],[f_2096_2]) ).

cnf(f_2096_4,plain,
    ( U_7661 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7661)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7663)))) ),
    inference(clausify,[status(thm)],[f_2096_3]) ).

cnf(f_2096_5,plain,
    ( U_7663 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7661)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7663)))) ),
    inference(clausify,[status(thm)],[f_2096_3]) ).

cnf(f_2096_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7662)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7664))))
    | U_7664 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_7662 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_2096_3]) ).

fof(f_2097_1,plain,
    ! [V_m] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,V_m)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),
    inference(fof_nnf,[status(thm)],[fact_int__Suc]) ).

fof(f_2097_2,plain,
    ! [U_7665] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_7665)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7665)),
    inference(variable_rename,[status(thm)],[f_2097_1]) ).

cnf(f_2097_3,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_7665)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7665)),
    inference(clausify,[status(thm)],[f_2097_2]) ).

fof(f_2098_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) = V_a
      | ~ class_Int_Onumber__ring(T_a)
      | ~ class_Fields_Ofield(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_divide__numeral__1]) ).

fof(f_2098_2,plain,
    ! [U_7667,U_7666] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7666),U_7667),hAPP(c_Int_Onumber__class_Onumber__of(U_7666),c_Int_OBit1(c_Int_OPls))) = U_7667
      | ~ class_Int_Onumber__ring(U_7666)
      | ~ class_Fields_Ofield(U_7666) ),
    inference(variable_rename,[status(thm)],[f_2098_1]) ).

cnf(f_2098_3,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7666),U_7667),hAPP(c_Int_Onumber__class_Onumber__of(U_7666),c_Int_OBit1(c_Int_OPls))) = U_7667
    | ~ class_Int_Onumber__ring(U_7666)
    | ~ class_Fields_Ofield(U_7666) ),
    inference(clausify,[status(thm)],[f_2098_2]) ).

fof(f_2099_1,plain,
    ! [V_x,T_a] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) = V_x
      | ~ class_Int_Onumber__ring(T_a)
      | ~ class_Fields_Ofield(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_divide__Numeral1]) ).

fof(f_2099_2,plain,
    ! [U_7669,U_7668] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7668),U_7669),hAPP(c_Int_Onumber__class_Onumber__of(U_7668),c_Int_OBit1(c_Int_OPls))) = U_7669
      | ~ class_Int_Onumber__ring(U_7668)
      | ~ class_Fields_Ofield(U_7668) ),
    inference(variable_rename,[status(thm)],[f_2099_1]) ).

cnf(f_2099_3,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7668),U_7669),hAPP(c_Int_Onumber__class_Onumber__of(U_7668),c_Int_OBit1(c_Int_OPls))) = U_7669
    | ~ class_Int_Onumber__ring(U_7668)
    | ~ class_Fields_Ofield(U_7668) ),
    inference(clausify,[status(thm)],[f_2099_2]) ).

fof(f_2100_1,plain,
    ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(fof_nnf,[status(thm)],[fact_negative__zle__0]) ).

fof(f_2100_2,plain,
    ! [U_7670] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7670))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(variable_rename,[status(thm)],[f_2100_1]) ).

cnf(f_2100_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7670))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(clausify,[status(thm)],[f_2100_2]) ).

fof(f_2101_1,plain,
    ! [V_n] : hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_nat__zminus__int]) ).

fof(f_2101_2,plain,
    ! [U_7671] : hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7671))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_2101_1]) ).

cnf(f_2101_3,plain,
    hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7671))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_2101_2]) ).

fof(f_2102_1,plain,
    c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),
    inference(fof_nnf,[status(thm)],[fact_one__is__num__one]) ).

cnf(f_2102_2,plain,
    c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),
    inference(clausify,[status(thm)],[f_2102_1]) ).

fof(f_2103_1,plain,
    ! [V_m,V_n] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) ),
    inference(fof_nnf,[status(thm)],[fact_zdiff__int]) ).

fof(f_2103_2,plain,
    ! [U_7673,U_7672] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7673)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7672)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7673),U_7672))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7672),U_7673)) ),
    inference(variable_rename,[status(thm)],[f_2103_1]) ).

cnf(f_2103_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7673)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7672)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7673),U_7672))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7672),U_7673)) ),
    inference(clausify,[status(thm)],[f_2103_2]) ).

fof(f_2104_1,plain,
    c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)),
    inference(fof_nnf,[status(thm)],[fact_Numeral1__eq1__nat]) ).

cnf(f_2104_2,plain,
    c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)),
    inference(clausify,[status(thm)],[f_2104_1]) ).

fof(f_2105_1,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_nat__numeral__1__eq__1]) ).

cnf(f_2105_2,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_2105_1]) ).

fof(f_2106_1,plain,
    ! [V_m,T_a] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Nat_OSuc,V_m)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m))
      | ~ class_Rings_Osemiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__Suc]) ).

fof(f_2106_2,plain,
    ! [U_7675,U_7674] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7674),hAPP(c_Nat_OSuc,U_7675)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7674),c_Groups_Oone__class_Oone(U_7674)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7674),U_7675))
      | ~ class_Rings_Osemiring__1(U_7674) ),
    inference(variable_rename,[status(thm)],[f_2106_1]) ).

cnf(f_2106_3,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7674),hAPP(c_Nat_OSuc,U_7675)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7674),c_Groups_Oone__class_Oone(U_7674)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7674),U_7675))
    | ~ class_Rings_Osemiring__1(U_7674) ),
    inference(clausify,[status(thm)],[f_2106_2]) ).

fof(f_2107_1,plain,
    ! [V_n] : hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,V_n))))),
    inference(fof_nnf,[status(thm)],[fact_neg__zminus__int]) ).

fof(f_2107_2,plain,
    ! [U_7676] : hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_7676))))),
    inference(variable_rename,[status(thm)],[f_2107_1]) ).

cnf(f_2107_3,plain,
    hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_7676))))),
    inference(clausify,[status(thm)],[f_2107_2]) ).

fof(f_2108_1,plain,
    ! [V_m,V_n,T_a] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
      | ~ class_Rings_Oring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__diff]) ).

fof(f_2108_2,plain,
    ! [U_7679,U_7678,U_7677] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7677),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7679),U_7678)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7677),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7677),U_7679)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7677),U_7678))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7678),U_7679))
      | ~ class_Rings_Oring__1(U_7677) ),
    inference(variable_rename,[status(thm)],[f_2108_1]) ).

cnf(f_2108_3,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7677),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7679),U_7678)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7677),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7677),U_7679)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7677),U_7678))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7678),U_7679))
    | ~ class_Rings_Oring__1(U_7677) ),
    inference(clausify,[status(thm)],[f_2108_2]) ).

fof(f_2109_1,plain,
    ! [T_a] :
      ( ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)))
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_not__iszero__Numeral1]) ).

fof(f_2109_2,plain,
    ! [U_7680] :
      ( ~ c_Int_Oiszero(U_7680,hAPP(c_Int_Onumber__class_Onumber__of(U_7680),c_Int_OBit1(c_Int_OPls)))
      | ~ class_Int_Onumber__ring(U_7680) ),
    inference(variable_rename,[status(thm)],[f_2109_1]) ).

cnf(f_2109_3,plain,
    ( ~ c_Int_Oiszero(U_7680,hAPP(c_Int_Onumber__class_Onumber__of(U_7680),c_Int_OBit1(c_Int_OPls)))
    | ~ class_Int_Onumber__ring(U_7680) ),
    inference(clausify,[status(thm)],[f_2109_2]) ).

fof(f_2110_1,plain,
    ! [V_n_2,V_m_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2))),
    inference(fof_nnf,[status(thm)],[fact_SetInterval_Otransfer__nat__int__set__functions_I2_J]) ).

fof(f_2110_2,plain,
    ! [U_7682,U_7681] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_7681,U_7682) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7681),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7682))),
    inference(variable_rename,[status(thm)],[f_2110_1]) ).

cnf(f_2110_3,plain,
    c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_7681,U_7682) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7681),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7682))),
    inference(clausify,[status(thm)],[f_2110_2]) ).

fof(f_2111_1,plain,
    ! [V_n_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_zero__less__int__conv]) ).

fof(f_2111_2,plain,
    ! [U_7683] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7683)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7683)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7683))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7683))) ) ),
    inference(variable_rename,[status(thm)],[f_2111_1]) ).

fof(f_2111_3,plain,
    ( ! [U_7685] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7685)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7685)) )
    & ! [U_7684] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7684))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7684))) ) ),
    inference(miniscope,[status(thm)],[f_2111_2]) ).

cnf(f_2111_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7684))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7684))) ),
    inference(clausify,[status(thm)],[f_2111_3]) ).

cnf(f_2111_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7685)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7685)) ),
    inference(clausify,[status(thm)],[f_2111_3]) ).

fof(f_2112_1,plain,
    ! [V_m_2,V_w_2] :
      ( ( hAPP(c_Int_Onat,V_w_2) = V_m_2
        | ( V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) )
        | ( V_w_2 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) ) )
      & ( ( ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) )
          & ( V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) ) )
        | hAPP(c_Int_Onat,V_w_2) != V_m_2 ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__eq__iff]) ).

fof(f_2112_2,plain,
    ! [U_7687,U_7686] :
      ( ( hAPP(c_Int_Onat,U_7686) = U_7687
        | ( U_7687 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7686)) )
        | ( U_7686 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7687)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7686)) ) )
      & ( ( ( U_7687 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7686)) )
          & ( U_7686 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7687)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7686)) ) )
        | hAPP(c_Int_Onat,U_7686) != U_7687 ) ),
    inference(variable_rename,[status(thm)],[f_2112_1]) ).

fof(f_2112_3,plain,
    ( ! [U_7691,U_7689] :
        ( hAPP(c_Int_Onat,U_7689) = U_7691
        | ( U_7691 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7689)) )
        | ( U_7689 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7691)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7689)) ) )
    & ! [U_7690,U_7688] :
        ( ( ( U_7690 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7688)) )
          & ( U_7688 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7690)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7688)) ) )
        | hAPP(c_Int_Onat,U_7688) != U_7690 ) ),
    inference(miniscope,[status(thm)],[f_2112_2]) ).

cnf(f_2112_4,plain,
    ( U_7688 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7690)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7688))
    | hAPP(c_Int_Onat,U_7688) != U_7690 ),
    inference(clausify,[status(thm)],[f_2112_3]) ).

cnf(f_2112_5,plain,
    ( U_7690 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7688))
    | hAPP(c_Int_Onat,U_7688) != U_7690 ),
    inference(clausify,[status(thm)],[f_2112_3]) ).

cnf(f_2112_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7689))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7689))
    | hAPP(c_Int_Onat,U_7689) = U_7691 ),
    inference(clausify,[status(thm)],[f_2112_3]) ).

cnf(f_2112_7,plain,
    ( U_7691 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7689))
    | hAPP(c_Int_Onat,U_7689) = U_7691 ),
    inference(clausify,[status(thm)],[f_2112_3]) ).

cnf(f_2112_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7689))
    | U_7689 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7691)
    | hAPP(c_Int_Onat,U_7689) = U_7691 ),
    inference(clausify,[status(thm)],[f_2112_3]) ).

cnf(f_2112_9,plain,
    ( U_7691 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_7689 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7691)
    | hAPP(c_Int_Onat,U_7689) = U_7691 ),
    inference(clausify,[status(thm)],[f_2112_3]) ).

fof(f_2113_1,plain,
    ! [V_w_2,V_m_2] :
      ( ( V_m_2 = hAPP(c_Int_Onat,V_w_2)
        | ( V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) )
        | ( V_w_2 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) ) )
      & ( ( ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) )
          & ( V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) ) )
        | V_m_2 != hAPP(c_Int_Onat,V_w_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__eq__iff2]) ).

fof(f_2113_2,plain,
    ! [U_7693,U_7692] :
      ( ( U_7692 = hAPP(c_Int_Onat,U_7693)
        | ( U_7692 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7693)) )
        | ( U_7693 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7692)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7693)) ) )
      & ( ( ( U_7692 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7693)) )
          & ( U_7693 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7692)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7693)) ) )
        | U_7692 != hAPP(c_Int_Onat,U_7693) ) ),
    inference(variable_rename,[status(thm)],[f_2113_1]) ).

fof(f_2113_3,plain,
    ( ! [U_7697,U_7695] :
        ( U_7695 = hAPP(c_Int_Onat,U_7697)
        | ( U_7695 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7697)) )
        | ( U_7697 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7695)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7697)) ) )
    & ! [U_7696,U_7694] :
        ( ( ( U_7694 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7696)) )
          & ( U_7696 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7694)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7696)) ) )
        | U_7694 != hAPP(c_Int_Onat,U_7696) ) ),
    inference(miniscope,[status(thm)],[f_2113_2]) ).

cnf(f_2113_4,plain,
    ( U_7696 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7694)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7696))
    | U_7694 != hAPP(c_Int_Onat,U_7696) ),
    inference(clausify,[status(thm)],[f_2113_3]) ).

cnf(f_2113_5,plain,
    ( U_7694 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7696))
    | U_7694 != hAPP(c_Int_Onat,U_7696) ),
    inference(clausify,[status(thm)],[f_2113_3]) ).

cnf(f_2113_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7697))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7697))
    | U_7695 = hAPP(c_Int_Onat,U_7697) ),
    inference(clausify,[status(thm)],[f_2113_3]) ).

cnf(f_2113_7,plain,
    ( U_7695 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7697))
    | U_7695 = hAPP(c_Int_Onat,U_7697) ),
    inference(clausify,[status(thm)],[f_2113_3]) ).

cnf(f_2113_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7697))
    | U_7697 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7695)
    | U_7695 = hAPP(c_Int_Onat,U_7697) ),
    inference(clausify,[status(thm)],[f_2113_3]) ).

cnf(f_2113_9,plain,
    ( U_7695 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_7697 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7695)
    | U_7695 = hAPP(c_Int_Onat,U_7697) ),
    inference(clausify,[status(thm)],[f_2113_3]) ).

fof(f_2114_1,plain,
    ! [V_i_2,V_P_2] :
      ( ( hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,V_i_2)))
        | ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ? [B_n] :
            ( ~ hBOOL(hAPP(V_P_2,B_n))
            & V_i_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) ) )
      & ( ( ( hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ! [B_n] :
              ( hBOOL(hAPP(V_P_2,B_n))
              | V_i_2 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) ) )
        | ~ hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,V_i_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_split__nat]) ).

fof(f_2114_2,plain,
    ! [U_7701,U_7700] :
      ( ( hBOOL(hAPP(U_7700,hAPP(c_Int_Onat,U_7701)))
        | ( ~ hBOOL(hAPP(U_7700,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7701),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ? [U_7699] :
            ( ~ hBOOL(hAPP(U_7700,U_7699))
            & U_7701 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7699) ) )
      & ( ( ( hBOOL(hAPP(U_7700,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7701),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ! [U_7698] :
              ( hBOOL(hAPP(U_7700,U_7698))
              | U_7701 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7698) ) )
        | ~ hBOOL(hAPP(U_7700,hAPP(c_Int_Onat,U_7701))) ) ),
    inference(variable_rename,[status(thm)],[f_2114_1]) ).

fof(f_2114_3,plain,
    ( ! [U_7705,U_7703] :
        ( hBOOL(hAPP(U_7703,hAPP(c_Int_Onat,U_7705)))
        | ( ~ hBOOL(hAPP(U_7703,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7705),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ? [U_7699] :
            ( ~ hBOOL(hAPP(U_7703,U_7699))
            & U_7705 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7699) ) )
    & ! [U_7704,U_7702] :
        ( ( ( hBOOL(hAPP(U_7702,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7704),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ! [U_7698] :
              ( hBOOL(hAPP(U_7702,U_7698))
              | U_7704 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7698) ) )
        | ~ hBOOL(hAPP(U_7702,hAPP(c_Int_Onat,U_7704))) ) ),
    inference(miniscope,[status(thm)],[f_2114_2]) ).

fof(f_2114_4,plain,
    ( ! [U_7705,U_7703] :
        ( hBOOL(hAPP(U_7703,hAPP(c_Int_Onat,U_7705)))
        | ( ~ hBOOL(hAPP(U_7703,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7705),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ~ hBOOL(hAPP(U_7703,sK205(U_7705,U_7703)))
          & U_7705 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK205(U_7705,U_7703)) ) )
    & ! [U_7704,U_7702] :
        ( ( ( hBOOL(hAPP(U_7702,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7704),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ! [U_7698] :
              ( hBOOL(hAPP(U_7702,U_7698))
              | U_7704 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7698) ) )
        | ~ hBOOL(hAPP(U_7702,hAPP(c_Int_Onat,U_7704))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK205]),skolemize(U_7699,sK205(U_7705,U_7703))],[f_2114_3]) ).

cnf(f_2114_5,plain,
    ( hBOOL(hAPP(U_7702,U_7698))
    | U_7704 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7698)
    | ~ hBOOL(hAPP(U_7702,hAPP(c_Int_Onat,U_7704))) ),
    inference(clausify,[status(thm)],[f_2114_4]) ).

cnf(f_2114_6,plain,
    ( hBOOL(hAPP(U_7702,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7704),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(U_7702,hAPP(c_Int_Onat,U_7704))) ),
    inference(clausify,[status(thm)],[f_2114_4]) ).

cnf(f_2114_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7705),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | U_7705 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK205(U_7705,U_7703))
    | hBOOL(hAPP(U_7703,hAPP(c_Int_Onat,U_7705))) ),
    inference(clausify,[status(thm)],[f_2114_4]) ).

cnf(f_2114_8,plain,
    ( ~ hBOOL(hAPP(U_7703,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | U_7705 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK205(U_7705,U_7703))
    | hBOOL(hAPP(U_7703,hAPP(c_Int_Onat,U_7705))) ),
    inference(clausify,[status(thm)],[f_2114_4]) ).

cnf(f_2114_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7705),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(U_7703,sK205(U_7705,U_7703)))
    | hBOOL(hAPP(U_7703,hAPP(c_Int_Onat,U_7705))) ),
    inference(clausify,[status(thm)],[f_2114_4]) ).

cnf(f_2114_10,plain,
    ( ~ hBOOL(hAPP(U_7703,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(U_7703,sK205(U_7705,U_7703)))
    | hBOOL(hAPP(U_7703,hAPP(c_Int_Onat,U_7705))) ),
    inference(clausify,[status(thm)],[f_2114_4]) ).

fof(f_2115_1,plain,
    ! [V_k,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_k)),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_k)),V_j)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j)) ),
    inference(fof_nnf,[status(thm)],[fact_zmult__zless__mono2__lemma]) ).

fof(f_2115_2,plain,
    ! [U_7708,U_7707,U_7706] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7708)),U_7706)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7708)),U_7707)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7708))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7706),U_7707)) ),
    inference(variable_rename,[status(thm)],[f_2115_1]) ).

cnf(f_2115_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7708)),U_7706)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7708)),U_7707)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7708))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7706),U_7707)) ),
    inference(clausify,[status(thm)],[f_2115_2]) ).

fof(f_2116_1,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(fof_nnf,[status(thm)],[fact_numeral__1__eq__Suc__0]) ).

cnf(f_2116_2,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(clausify,[status(thm)],[f_2116_1]) ).

fof(f_2117_1,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
    inference(fof_nnf,[status(thm)],[fact_numeral__3__eq__3]) ).

cnf(f_2117_2,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
    inference(clausify,[status(thm)],[f_2117_1]) ).

fof(f_2118_1,plain,
    ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,V_n))))),
    inference(fof_nnf,[status(thm)],[fact_not__zle__0__negative]) ).

fof(f_2118_2,plain,
    ! [U_7709] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_7709))))),
    inference(variable_rename,[status(thm)],[f_2118_1]) ).

cnf(f_2118_3,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_7709))))),
    inference(clausify,[status(thm)],[f_2118_2]) ).

fof(f_2119_1,plain,
    ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,V_n)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(fof_nnf,[status(thm)],[fact_negative__zless__0]) ).

fof(f_2119_2,plain,
    ! [U_7710] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_7710)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(variable_rename,[status(thm)],[f_2119_1]) ).

cnf(f_2119_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_7710)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(clausify,[status(thm)],[f_2119_2]) ).

fof(f_2120_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)),V_a)
      | ~ class_Groups_Omonoid__mult(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power3__eq__cube]) ).

fof(f_2120_2,plain,
    ! [U_7712,U_7711] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_7711),U_7712),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7711),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7711),U_7712),U_7712)),U_7712)
      | ~ class_Groups_Omonoid__mult(U_7711) ),
    inference(variable_rename,[status(thm)],[f_2120_1]) ).

cnf(f_2120_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_7711),U_7712),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7711),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7711),U_7712),U_7712)),U_7712)
    | ~ class_Groups_Omonoid__mult(U_7711) ),
    inference(clausify,[status(thm)],[f_2120_2]) ).

fof(f_2121_1,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))))),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J]) ).

cnf(f_2121_2,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))))),
    inference(clausify,[status(thm)],[f_2121_1]) ).

fof(f_2122_1,plain,
    ! [V_n] : hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_n),
    inference(fof_nnf,[status(thm)],[fact_Suc3__eq__add__3]) ).

fof(f_2122_2,plain,
    ! [U_7713] : hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_7713))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),U_7713),
    inference(variable_rename,[status(thm)],[f_2122_1]) ).

cnf(f_2122_3,plain,
    hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_7713))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),U_7713),
    inference(clausify,[status(thm)],[f_2122_2]) ).

fof(f_2123_1,plain,
    ! [V_v,V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),
    inference(fof_nnf,[status(thm)],[fact_Suc__div__eq__add3__div__number__of]) ).

fof(f_2123_2,plain,
    ! [U_7715,U_7714] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_7714)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7715)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),U_7714)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7715)),
    inference(variable_rename,[status(thm)],[f_2123_1]) ).

cnf(f_2123_3,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_7714)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7715)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),U_7714)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7715)),
    inference(clausify,[status(thm)],[f_2123_2]) ).

fof(f_2124_1,plain,
    ! [V_n,V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m)))),V_n) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_m)),V_n),
    inference(fof_nnf,[status(thm)],[fact_Suc__div__eq__add3__div]) ).

fof(f_2124_2,plain,
    ! [U_7717,U_7716] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_7716)))),U_7717) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),U_7716)),U_7717),
    inference(variable_rename,[status(thm)],[f_2124_1]) ).

cnf(f_2124_3,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_7716)))),U_7717) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),U_7716)),U_7717),
    inference(clausify,[status(thm)],[f_2124_2]) ).

fof(f_2125_1,plain,
    ! [V_n,V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_n)),
    inference(fof_nnf,[status(thm)],[fact_div__Suc__eq__div__add3]) ).

fof(f_2125_2,plain,
    ! [U_7719,U_7718] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7718),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_7719)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7718),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),U_7719)),
    inference(variable_rename,[status(thm)],[f_2125_1]) ).

cnf(f_2125_3,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7718),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_7719)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7718),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),U_7719)),
    inference(clausify,[status(thm)],[f_2125_2]) ).

fof(f_2126_1,plain,
    ! [V_v_2,V_m_2] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)))
        | V_m_2 != hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)))
          & V_m_2 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)) )
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_int__eq__iff__number__of]) ).

fof(f_2126_2,plain,
    ! [U_7721,U_7720] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7720) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7721)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7721)))
        | U_7720 != hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7721)) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7721)))
          & U_7720 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7721)) )
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7720) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7721) ) ),
    inference(variable_rename,[status(thm)],[f_2126_1]) ).

fof(f_2126_3,plain,
    ( ! [U_7725,U_7723] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7723) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7725)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7725)))
        | U_7723 != hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7725)) )
    & ! [U_7724,U_7722] :
        ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7724)))
          & U_7722 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7724)) )
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7722) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7724) ) ),
    inference(miniscope,[status(thm)],[f_2126_2]) ).

cnf(f_2126_4,plain,
    ( U_7722 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7724))
    | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7722) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7724) ),
    inference(clausify,[status(thm)],[f_2126_3]) ).

cnf(f_2126_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7724)))
    | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7722) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7724) ),
    inference(clausify,[status(thm)],[f_2126_3]) ).

cnf(f_2126_6,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7723) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7725)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7725)))
    | U_7723 != hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7725)) ),
    inference(clausify,[status(thm)],[f_2126_3]) ).

fof(f_2127_1,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),
    inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__numerals_I4_J]) ).

cnf(f_2127_2,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),
    inference(clausify,[status(thm)],[f_2127_1]) ).

fof(f_2128_1,plain,
    ! [V_n_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2))) ) )
      | ~ class_Rings_Olinordered__semidom(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__0__less__iff]) ).

fof(f_2128_2,plain,
    ! [U_7727,U_7726] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7726),c_Groups_Ozero__class_Ozero(U_7726)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7726),U_7727)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7727)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7727))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7726),c_Groups_Ozero__class_Ozero(U_7726)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7726),U_7727))) ) )
      | ~ class_Rings_Olinordered__semidom(U_7726) ),
    inference(variable_rename,[status(thm)],[f_2128_1]) ).

cnf(f_2128_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7727))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7726),c_Groups_Ozero__class_Ozero(U_7726)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7726),U_7727)))
    | ~ class_Rings_Olinordered__semidom(U_7726) ),
    inference(clausify,[status(thm)],[f_2128_2]) ).

cnf(f_2128_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7726),c_Groups_Ozero__class_Ozero(U_7726)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7726),U_7727)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7727))
    | ~ class_Rings_Olinordered__semidom(U_7726) ),
    inference(clausify,[status(thm)],[f_2128_2]) ).

fof(f_2129_1,plain,
    ! [V_v] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) )
      & ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) ) ),
    inference(fof_nnf,[status(thm)],[fact_int__nat__number__of]) ).

fof(f_2129_2,plain,
    ! [U_7728] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7728)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7728)
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7728))) )
      & ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7728)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7728))) ) ),
    inference(variable_rename,[status(thm)],[f_2129_1]) ).

fof(f_2129_3,plain,
    ( ! [U_7730] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7730)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7730)
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7730))) )
    & ! [U_7729] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7729)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7729))) ) ),
    inference(miniscope,[status(thm)],[f_2129_2]) ).

cnf(f_2129_4,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7729)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7729))) ),
    inference(clausify,[status(thm)],[f_2129_3]) ).

cnf(f_2129_5,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7730)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7730)
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7730))) ),
    inference(clausify,[status(thm)],[f_2129_3]) ).

fof(f_2130_1,plain,
    ! [V_n_2] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2))),
    inference(fof_nnf,[status(thm)],[fact_SetInterval_Otransfer__nat__int__set__functions_I1_J]) ).

fof(f_2130_2,plain,
    ! [U_7731] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_7731) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7731))),
    inference(variable_rename,[status(thm)],[f_2130_1]) ).

cnf(f_2130_3,plain,
    hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_7731) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7731))),
    inference(clausify,[status(thm)],[f_2130_2]) ).

fof(f_2131_1,plain,
    ! [V_x_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Oone__class_Oone(T_b)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Oone__class_Oone(T_b))) ) )
      | ~ class_Rings_Olinordered__idom(T_b)
      | ~ class_Int_Onumber__ring(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_le__special_I4_J]) ).

fof(f_2131_2,plain,
    ! [U_7733,U_7732] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7732),hAPP(c_Int_Onumber__class_Onumber__of(U_7732),U_7733)),c_Groups_Oone__class_Oone(U_7732)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7733),c_Int_OBit1(c_Int_OPls))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7733),c_Int_OBit1(c_Int_OPls)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7732),hAPP(c_Int_Onumber__class_Onumber__of(U_7732),U_7733)),c_Groups_Oone__class_Oone(U_7732))) ) )
      | ~ class_Rings_Olinordered__idom(U_7732)
      | ~ class_Int_Onumber__ring(U_7732) ),
    inference(variable_rename,[status(thm)],[f_2131_1]) ).

cnf(f_2131_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7733),c_Int_OBit1(c_Int_OPls)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7732),hAPP(c_Int_Onumber__class_Onumber__of(U_7732),U_7733)),c_Groups_Oone__class_Oone(U_7732)))
    | ~ class_Rings_Olinordered__idom(U_7732)
    | ~ class_Int_Onumber__ring(U_7732) ),
    inference(clausify,[status(thm)],[f_2131_2]) ).

cnf(f_2131_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7732),hAPP(c_Int_Onumber__class_Onumber__of(U_7732),U_7733)),c_Groups_Oone__class_Oone(U_7732)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7733),c_Int_OBit1(c_Int_OPls)))
    | ~ class_Rings_Olinordered__idom(U_7732)
    | ~ class_Int_Onumber__ring(U_7732) ),
    inference(clausify,[status(thm)],[f_2131_2]) ).

fof(f_2132_1,plain,
    ! [V_y_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Oone__class_Oone(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Oone__class_Oone(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2))) ) )
      | ~ class_Rings_Olinordered__idom(T_b)
      | ~ class_Int_Onumber__ring(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_le__special_I2_J]) ).

fof(f_2132_2,plain,
    ! [U_7735,U_7734] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7734),c_Groups_Oone__class_Oone(U_7734)),hAPP(c_Int_Onumber__class_Onumber__of(U_7734),U_7735)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_7735)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_7735))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7734),c_Groups_Oone__class_Oone(U_7734)),hAPP(c_Int_Onumber__class_Onumber__of(U_7734),U_7735))) ) )
      | ~ class_Rings_Olinordered__idom(U_7734)
      | ~ class_Int_Onumber__ring(U_7734) ),
    inference(variable_rename,[status(thm)],[f_2132_1]) ).

cnf(f_2132_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_7735))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7734),c_Groups_Oone__class_Oone(U_7734)),hAPP(c_Int_Onumber__class_Onumber__of(U_7734),U_7735)))
    | ~ class_Rings_Olinordered__idom(U_7734)
    | ~ class_Int_Onumber__ring(U_7734) ),
    inference(clausify,[status(thm)],[f_2132_2]) ).

cnf(f_2132_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7734),c_Groups_Oone__class_Oone(U_7734)),hAPP(c_Int_Onumber__class_Onumber__of(U_7734),U_7735)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_7735))
    | ~ class_Rings_Olinordered__idom(U_7734)
    | ~ class_Int_Onumber__ring(U_7734) ),
    inference(clausify,[status(thm)],[f_2132_2]) ).

fof(f_2133_1,plain,
    ! [V_x_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Oone__class_Oone(T_b)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Oone__class_Oone(T_b))) ) )
      | ~ class_Rings_Olinordered__idom(T_b)
      | ~ class_Int_Onumber__ring(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_less__special_I4_J]) ).

fof(f_2133_2,plain,
    ! [U_7737,U_7736] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7736),hAPP(c_Int_Onumber__class_Onumber__of(U_7736),U_7737)),c_Groups_Oone__class_Oone(U_7736)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7737),c_Int_OBit1(c_Int_OPls))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7737),c_Int_OBit1(c_Int_OPls)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7736),hAPP(c_Int_Onumber__class_Onumber__of(U_7736),U_7737)),c_Groups_Oone__class_Oone(U_7736))) ) )
      | ~ class_Rings_Olinordered__idom(U_7736)
      | ~ class_Int_Onumber__ring(U_7736) ),
    inference(variable_rename,[status(thm)],[f_2133_1]) ).

cnf(f_2133_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7737),c_Int_OBit1(c_Int_OPls)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7736),hAPP(c_Int_Onumber__class_Onumber__of(U_7736),U_7737)),c_Groups_Oone__class_Oone(U_7736)))
    | ~ class_Rings_Olinordered__idom(U_7736)
    | ~ class_Int_Onumber__ring(U_7736) ),
    inference(clausify,[status(thm)],[f_2133_2]) ).

cnf(f_2133_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7736),hAPP(c_Int_Onumber__class_Onumber__of(U_7736),U_7737)),c_Groups_Oone__class_Oone(U_7736)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7737),c_Int_OBit1(c_Int_OPls)))
    | ~ class_Rings_Olinordered__idom(U_7736)
    | ~ class_Int_Onumber__ring(U_7736) ),
    inference(clausify,[status(thm)],[f_2133_2]) ).

fof(f_2134_1,plain,
    ! [V_y_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2))) ) )
      | ~ class_Rings_Olinordered__idom(T_b)
      | ~ class_Int_Onumber__ring(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_less__special_I2_J]) ).

fof(f_2134_2,plain,
    ! [U_7739,U_7738] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7738),c_Groups_Oone__class_Oone(U_7738)),hAPP(c_Int_Onumber__class_Onumber__of(U_7738),U_7739)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_7739)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_7739))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7738),c_Groups_Oone__class_Oone(U_7738)),hAPP(c_Int_Onumber__class_Onumber__of(U_7738),U_7739))) ) )
      | ~ class_Rings_Olinordered__idom(U_7738)
      | ~ class_Int_Onumber__ring(U_7738) ),
    inference(variable_rename,[status(thm)],[f_2134_1]) ).

cnf(f_2134_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_7739))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7738),c_Groups_Oone__class_Oone(U_7738)),hAPP(c_Int_Onumber__class_Onumber__of(U_7738),U_7739)))
    | ~ class_Rings_Olinordered__idom(U_7738)
    | ~ class_Int_Onumber__ring(U_7738) ),
    inference(clausify,[status(thm)],[f_2134_2]) ).

cnf(f_2134_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7738),c_Groups_Oone__class_Oone(U_7738)),hAPP(c_Int_Onumber__class_Onumber__of(U_7738),U_7739)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_7739))
    | ~ class_Rings_Olinordered__idom(U_7738)
    | ~ class_Int_Onumber__ring(U_7738) ),
    inference(clausify,[status(thm)],[f_2134_2]) ).

fof(f_2135_1,plain,
    ! [V_w,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_w))
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__special_I2_J]) ).

fof(f_2135_2,plain,
    ! [U_7741,U_7740] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7740),c_Groups_Oone__class_Oone(U_7740)),hAPP(c_Int_Onumber__class_Onumber__of(U_7740),U_7741)) = hAPP(c_Int_Onumber__class_Onumber__of(U_7740),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_7741))
      | ~ class_Int_Onumber__ring(U_7740) ),
    inference(variable_rename,[status(thm)],[f_2135_1]) ).

cnf(f_2135_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7740),c_Groups_Oone__class_Oone(U_7740)),hAPP(c_Int_Onumber__class_Onumber__of(U_7740),U_7741)) = hAPP(c_Int_Onumber__class_Onumber__of(U_7740),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_7741))
    | ~ class_Int_Onumber__ring(U_7740) ),
    inference(clausify,[status(thm)],[f_2135_2]) ).

fof(f_2136_1,plain,
    ! [V_v,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),c_Groups_Oone__class_Oone(T_a)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),c_Int_OBit1(c_Int_OPls)))
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__special_I3_J]) ).

fof(f_2136_2,plain,
    ! [U_7743,U_7742] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7742),hAPP(c_Int_Onumber__class_Onumber__of(U_7742),U_7743)),c_Groups_Oone__class_Oone(U_7742)) = hAPP(c_Int_Onumber__class_Onumber__of(U_7742),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7743),c_Int_OBit1(c_Int_OPls)))
      | ~ class_Int_Onumber__ring(U_7742) ),
    inference(variable_rename,[status(thm)],[f_2136_1]) ).

cnf(f_2136_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7742),hAPP(c_Int_Onumber__class_Onumber__of(U_7742),U_7743)),c_Groups_Oone__class_Oone(U_7742)) = hAPP(c_Int_Onumber__class_Onumber__of(U_7742),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7743),c_Int_OBit1(c_Int_OPls)))
    | ~ class_Int_Onumber__ring(U_7742) ),
    inference(clausify,[status(thm)],[f_2136_2]) ).

fof(f_2137_1,plain,
    ! [V_m_2,V_w_2] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),V_m_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),V_m_2)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) ),
    inference(fof_nnf,[status(thm)],[fact_nat__less__iff]) ).

fof(f_2137_2,plain,
    ! [U_7745,U_7744] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7744)),U_7745))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7744),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7745))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7744),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7745)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7744)),U_7745)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7744)) ),
    inference(variable_rename,[status(thm)],[f_2137_1]) ).

cnf(f_2137_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7744),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7745)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7744)),U_7745))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7744)) ),
    inference(clausify,[status(thm)],[f_2137_2]) ).

cnf(f_2137_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_7744)),U_7745))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7744),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7745)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7744)) ),
    inference(clausify,[status(thm)],[f_2137_2]) ).

fof(f_2138_1,plain,
    ! [V_m,V_n] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls)),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_Suc__diff__eq__diff__pred]) ).

fof(f_2138_2,plain,
    ! [U_7747,U_7746] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_7747)),U_7746) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7747),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7746),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls)),U_7746)) ),
    inference(variable_rename,[status(thm)],[f_2138_1]) ).

cnf(f_2138_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_7747)),U_7746) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7747),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7746),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls)),U_7746)) ),
    inference(clausify,[status(thm)],[f_2138_2]) ).

fof(f_2139_1,plain,
    ! [V_y_2,V_x_2,V_P_2] :
      ( ( hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_y_2))))
        | ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) )
        | ( ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2))))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),V_x_2)) ) )
      & ( ( ( hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) )
          & ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2))))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),V_x_2)) ) )
        | ~ hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_y_2)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_zdiff__int__split]) ).

fof(f_2139_2,plain,
    ! [U_7750,U_7749,U_7748] :
      ( ( hBOOL(hAPP(U_7748,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7749),U_7750))))
        | ( ~ hBOOL(hAPP(U_7748,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7749),U_7750)) )
        | ( ~ hBOOL(hAPP(U_7748,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7749)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7750))))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7750),U_7749)) ) )
      & ( ( ( hBOOL(hAPP(U_7748,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7749),U_7750)) )
          & ( hBOOL(hAPP(U_7748,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7749)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7750))))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7750),U_7749)) ) )
        | ~ hBOOL(hAPP(U_7748,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7749),U_7750)))) ) ),
    inference(variable_rename,[status(thm)],[f_2139_1]) ).

fof(f_2139_3,plain,
    ( ! [U_7756,U_7754,U_7752] :
        ( hBOOL(hAPP(U_7752,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7754),U_7756))))
        | ( ~ hBOOL(hAPP(U_7752,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7754),U_7756)) )
        | ( ~ hBOOL(hAPP(U_7752,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7754)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7756))))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7756),U_7754)) ) )
    & ! [U_7755,U_7753,U_7751] :
        ( ( ( hBOOL(hAPP(U_7751,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7753),U_7755)) )
          & ( hBOOL(hAPP(U_7751,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7753)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7755))))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7755),U_7753)) ) )
        | ~ hBOOL(hAPP(U_7751,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7753),U_7755)))) ) ),
    inference(miniscope,[status(thm)],[f_2139_2]) ).

cnf(f_2139_4,plain,
    ( hBOOL(hAPP(U_7751,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7753)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7755))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7755),U_7753))
    | ~ hBOOL(hAPP(U_7751,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7753),U_7755)))) ),
    inference(clausify,[status(thm)],[f_2139_3]) ).

cnf(f_2139_5,plain,
    ( hBOOL(hAPP(U_7751,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7753),U_7755))
    | ~ hBOOL(hAPP(U_7751,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7753),U_7755)))) ),
    inference(clausify,[status(thm)],[f_2139_3]) ).

cnf(f_2139_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7754),U_7756))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7756),U_7754))
    | hBOOL(hAPP(U_7752,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7754),U_7756)))) ),
    inference(clausify,[status(thm)],[f_2139_3]) ).

cnf(f_2139_7,plain,
    ( ~ hBOOL(hAPP(U_7752,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7756),U_7754))
    | hBOOL(hAPP(U_7752,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7754),U_7756)))) ),
    inference(clausify,[status(thm)],[f_2139_3]) ).

cnf(f_2139_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7754),U_7756))
    | ~ hBOOL(hAPP(U_7752,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7754)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7756))))
    | hBOOL(hAPP(U_7752,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7754),U_7756)))) ),
    inference(clausify,[status(thm)],[f_2139_3]) ).

cnf(f_2139_9,plain,
    ( ~ hBOOL(hAPP(U_7752,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(U_7752,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7754)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7756))))
    | hBOOL(hAPP(U_7752,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7754),U_7756)))) ),
    inference(clausify,[status(thm)],[f_2139_3]) ).

fof(f_2140_1,plain,
    ! [V_v,T_a] :
      ( ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)
          | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) )
        & ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Ozero__class_Ozero(T_a)
          | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) ) )
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__number__of__eq]) ).

fof(f_2140_2,plain,
    ! [U_7758,U_7757] :
      ( ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7757),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7758)) = hAPP(c_Int_Onumber__class_Onumber__of(U_7757),U_7758)
          | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7758))) )
        & ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7757),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7758)) = c_Groups_Ozero__class_Ozero(U_7757)
          | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7758))) ) )
      | ~ class_Int_Onumber__ring(U_7757) ),
    inference(variable_rename,[status(thm)],[f_2140_1]) ).

cnf(f_2140_3,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7757),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7758)) = c_Groups_Ozero__class_Ozero(U_7757)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7758)))
    | ~ class_Int_Onumber__ring(U_7757) ),
    inference(clausify,[status(thm)],[f_2140_2]) ).

cnf(f_2140_4,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7757),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7758)) = hAPP(c_Int_Onumber__class_Onumber__of(U_7757),U_7758)
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7758)))
    | ~ class_Int_Onumber__ring(U_7757) ),
    inference(clausify,[status(thm)],[f_2140_2]) ).

fof(f_2141_1,plain,
    ! [V_u_2] :
      ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Int_Onat,V_u_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2)) ),
    inference(fof_nnf,[status(thm)],[fact_image__atLeastZeroLessThan__int]) ).

fof(f_2141_2,plain,
    ! [U_7759] :
      ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7759) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Int_Onat,U_7759)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7759)) ),
    inference(variable_rename,[status(thm)],[f_2141_1]) ).

cnf(f_2141_3,plain,
    ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7759) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Int_Onat,U_7759)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7759)) ),
    inference(clausify,[status(thm)],[f_2141_2]) ).

fof(f_2142_1,plain,
    ! [V_w,T_a] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)))
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_diff__special_I1_J]) ).

fof(f_2142_2,plain,
    ! [U_7761,U_7760] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7760),c_Groups_Oone__class_Oone(U_7760)),hAPP(c_Int_Onumber__class_Onumber__of(U_7760),U_7761)) = hAPP(c_Int_Onumber__class_Onumber__of(U_7760),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7761)))
      | ~ class_Int_Onumber__ring(U_7760) ),
    inference(variable_rename,[status(thm)],[f_2142_1]) ).

cnf(f_2142_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7760),c_Groups_Oone__class_Oone(U_7760)),hAPP(c_Int_Onumber__class_Onumber__of(U_7760),U_7761)) = hAPP(c_Int_Onumber__class_Onumber__of(U_7760),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7761)))
    | ~ class_Int_Onumber__ring(U_7760) ),
    inference(clausify,[status(thm)],[f_2142_2]) ).

fof(f_2143_1,plain,
    ! [V_v,T_a] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),c_Groups_Oone__class_Oone(T_a)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls))))
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_diff__special_I2_J]) ).

fof(f_2143_2,plain,
    ! [U_7763,U_7762] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7762),hAPP(c_Int_Onumber__class_Onumber__of(U_7762),U_7763)),c_Groups_Oone__class_Oone(U_7762)) = hAPP(c_Int_Onumber__class_Onumber__of(U_7762),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7763),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls))))
      | ~ class_Int_Onumber__ring(U_7762) ),
    inference(variable_rename,[status(thm)],[f_2143_1]) ).

cnf(f_2143_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7762),hAPP(c_Int_Onumber__class_Onumber__of(U_7762),U_7763)),c_Groups_Oone__class_Oone(U_7762)) = hAPP(c_Int_Onumber__class_Onumber__of(U_7762),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7763),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls))))
    | ~ class_Int_Onumber__ring(U_7762) ),
    inference(clausify,[status(thm)],[f_2143_2]) ).

fof(f_2144_1,plain,
    ! [V_b,V_a] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b),V_a)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) ),
    inference(fof_nnf,[status(thm)],[fact_pos__zdiv__mult__2]) ).

fof(f_2144_2,plain,
    ! [U_7765,U_7764] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_7765))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_7764)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7765),U_7764)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7764)) ),
    inference(variable_rename,[status(thm)],[f_2144_1]) ).

cnf(f_2144_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_7765))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_7764)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7765),U_7764)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7764)) ),
    inference(clausify,[status(thm)],[f_2144_2]) ).

fof(f_2145_1,plain,
    ! [V_b,V_a] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_b),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_a)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(fof_nnf,[status(thm)],[fact_neg__zdiv__mult__2]) ).

fof(f_2145_2,plain,
    ! [U_7767,U_7766] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_7767))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_7766)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7767),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_7766)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7766),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_2145_1]) ).

cnf(f_2145_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_7767))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_7766)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7767),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_7766)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7766),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2145_2]) ).

fof(f_2146_1,plain,
    ! [V_x,T_a] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,V_x))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,V_x)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
      | ~ class_Rings_Osemiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__double]) ).

fof(f_2146_2,plain,
    ! [U_7769,U_7768] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7768),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_7769))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7768),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7768),hAPP(c_Int_Onat,U_7769))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7768),hAPP(c_Int_Onat,U_7769)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7769))
      | ~ class_Rings_Osemiring__1(U_7768) ),
    inference(variable_rename,[status(thm)],[f_2146_1]) ).

cnf(f_2146_3,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7768),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_7769))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7768),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7768),hAPP(c_Int_Onat,U_7769))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_7768),hAPP(c_Int_Onat,U_7769)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7769))
    | ~ class_Rings_Osemiring__1(U_7768) ),
    inference(clausify,[status(thm)],[f_2146_2]) ).

fof(f_2147_1,plain,
    ! [V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_Suc__n__div__2__gt__zero]) ).

fof(f_2147_2,plain,
    ! [U_7770] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7770),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7770)) ),
    inference(variable_rename,[status(thm)],[f_2147_1]) ).

cnf(f_2147_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7770),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7770)) ),
    inference(clausify,[status(thm)],[f_2147_2]) ).

fof(f_2148_1,plain,
    ! [V_n,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))
      | ~ class_Rings_Oring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__minus1__odd]) ).

fof(f_2148_2,plain,
    ! [U_7772,U_7771] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_7771),hAPP(c_Groups_Ouminus__class_Ouminus(U_7771),c_Groups_Oone__class_Oone(U_7771))),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_7772))) = hAPP(c_Groups_Ouminus__class_Ouminus(U_7771),c_Groups_Oone__class_Oone(U_7771))
      | ~ class_Rings_Oring__1(U_7771) ),
    inference(variable_rename,[status(thm)],[f_2148_1]) ).

cnf(f_2148_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_7771),hAPP(c_Groups_Ouminus__class_Ouminus(U_7771),c_Groups_Oone__class_Oone(U_7771))),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_7772))) = hAPP(c_Groups_Ouminus__class_Ouminus(U_7771),c_Groups_Oone__class_Oone(U_7771))
    | ~ class_Rings_Oring__1(U_7771) ),
    inference(clausify,[status(thm)],[f_2148_2]) ).

fof(f_2149_1,plain,
    ! [V_l,V_k] : c_Int_OBit0(V_k) != c_Int_OBit1(V_l),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I49_J]) ).

fof(f_2149_2,plain,
    ! [U_7774,U_7773] : c_Int_OBit0(U_7773) != c_Int_OBit1(U_7774),
    inference(variable_rename,[status(thm)],[f_2149_1]) ).

cnf(f_2149_3,plain,
    c_Int_OBit0(U_7773) != c_Int_OBit1(U_7774),
    inference(clausify,[status(thm)],[f_2149_2]) ).

fof(f_2150_1,plain,
    ! [V_l,V_k] : c_Int_OBit1(V_k) != c_Int_OBit0(V_l),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I50_J]) ).

fof(f_2150_2,plain,
    ! [U_7776,U_7775] : c_Int_OBit1(U_7775) != c_Int_OBit0(U_7776),
    inference(variable_rename,[status(thm)],[f_2150_1]) ).

cnf(f_2150_3,plain,
    c_Int_OBit1(U_7775) != c_Int_OBit0(U_7776),
    inference(clausify,[status(thm)],[f_2150_2]) ).

fof(f_2151_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)
        | V_m_2 != V_n_2 )
      & ( V_m_2 = V_n_2
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_int__int__eq]) ).

fof(f_2151_2,plain,
    ! [U_7778,U_7777] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7777) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7778)
        | U_7777 != U_7778 )
      & ( U_7777 = U_7778
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7777) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7778) ) ),
    inference(variable_rename,[status(thm)],[f_2151_1]) ).

fof(f_2151_3,plain,
    ( ! [U_7782,U_7780] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7780) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7782)
        | U_7780 != U_7782 )
    & ! [U_7781,U_7779] :
        ( U_7779 = U_7781
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7779) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7781) ) ),
    inference(miniscope,[status(thm)],[f_2151_2]) ).

cnf(f_2151_4,plain,
    ( U_7779 = U_7781
    | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7779) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7781) ),
    inference(clausify,[status(thm)],[f_2151_3]) ).

cnf(f_2151_5,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7780) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7782)
    | U_7780 != U_7782 ),
    inference(clausify,[status(thm)],[f_2151_3]) ).

fof(f_2152_1,plain,
    ! [V_B_2,V_A_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__relations_I4_J]) ).

fof(f_2152_2,plain,
    ! [U_7784,U_7783] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_7783),U_7784))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7783)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7784))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7783)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7784)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_7783),U_7784)) ) ),
    inference(variable_rename,[status(thm)],[f_2152_1]) ).

fof(f_2152_3,plain,
    ( ! [U_7788,U_7786] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_7786),U_7788))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7786)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7788))) )
    & ! [U_7787,U_7785] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7785)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7787)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_7785),U_7787)) ) ),
    inference(miniscope,[status(thm)],[f_2152_2]) ).

cnf(f_2152_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7785)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7787)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_7785),U_7787)) ),
    inference(clausify,[status(thm)],[f_2152_3]) ).

cnf(f_2152_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_7786),U_7788))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7786)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7788))) ),
    inference(clausify,[status(thm)],[f_2152_3]) ).

fof(f_2153_1,plain,
    ! [V_y_2,V_x_2] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2)
        | V_x_2 != V_y_2 )
      & ( V_x_2 = V_y_2
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__relations_I1_J]) ).

fof(f_2153_2,plain,
    ! [U_7790,U_7789] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7789) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7790)
        | U_7789 != U_7790 )
      & ( U_7789 = U_7790
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7789) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7790) ) ),
    inference(variable_rename,[status(thm)],[f_2153_1]) ).

fof(f_2153_3,plain,
    ( ! [U_7794,U_7792] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7792) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7794)
        | U_7792 != U_7794 )
    & ! [U_7793,U_7791] :
        ( U_7791 = U_7793
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7791) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7793) ) ),
    inference(miniscope,[status(thm)],[f_2153_2]) ).

cnf(f_2153_4,plain,
    ( U_7791 = U_7793
    | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7791) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7793) ),
    inference(clausify,[status(thm)],[f_2153_3]) ).

cnf(f_2153_5,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7792) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7794)
    | U_7792 != U_7794 ),
    inference(clausify,[status(thm)],[f_2153_3]) ).

fof(f_2154_1,plain,
    ! [V_B_2,V_A_2] :
      ( ( V_A_2 = V_B_2
        | hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2) != hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2) )
      & ( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2)
        | V_A_2 != V_B_2 ) ),
    inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__relations_I3_J]) ).

fof(f_2154_2,plain,
    ! [U_7796,U_7795] :
      ( ( U_7795 = U_7796
        | hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7795) != hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7796) )
      & ( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7795) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7796)
        | U_7795 != U_7796 ) ),
    inference(variable_rename,[status(thm)],[f_2154_1]) ).

fof(f_2154_3,plain,
    ( ! [U_7800,U_7798] :
        ( U_7798 = U_7800
        | hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7798) != hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7800) )
    & ! [U_7799,U_7797] :
        ( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7797) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7799)
        | U_7797 != U_7799 ) ),
    inference(miniscope,[status(thm)],[f_2154_2]) ).

cnf(f_2154_4,plain,
    ( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7797) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7799)
    | U_7797 != U_7799 ),
    inference(clausify,[status(thm)],[f_2154_3]) ).

cnf(f_2154_5,plain,
    ( U_7798 = U_7800
    | hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7798) != hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7800) ),
    inference(clausify,[status(thm)],[f_2154_3]) ).

fof(f_2155_1,plain,
    c_Int_OBit0(c_Int_OPls) = c_Int_OPls,
    inference(fof_nnf,[status(thm)],[fact_Bit0__Pls]) ).

cnf(f_2155_2,plain,
    c_Int_OBit0(c_Int_OPls) = c_Int_OPls,
    inference(clausify,[status(thm)],[f_2155_1]) ).

fof(f_2156_1,plain,
    ! [V_l_2] :
      ( ( c_Int_OPls = c_Int_OBit0(V_l_2)
        | c_Int_OPls != V_l_2 )
      & ( c_Int_OPls = V_l_2
        | c_Int_OPls != c_Int_OBit0(V_l_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I38_J]) ).

fof(f_2156_2,plain,
    ! [U_7801] :
      ( ( c_Int_OPls = c_Int_OBit0(U_7801)
        | c_Int_OPls != U_7801 )
      & ( c_Int_OPls = U_7801
        | c_Int_OPls != c_Int_OBit0(U_7801) ) ),
    inference(variable_rename,[status(thm)],[f_2156_1]) ).

fof(f_2156_3,plain,
    ( ! [U_7803] :
        ( c_Int_OPls = c_Int_OBit0(U_7803)
        | c_Int_OPls != U_7803 )
    & ! [U_7802] :
        ( c_Int_OPls = U_7802
        | c_Int_OPls != c_Int_OBit0(U_7802) ) ),
    inference(miniscope,[status(thm)],[f_2156_2]) ).

cnf(f_2156_4,plain,
    ( c_Int_OPls = U_7802
    | c_Int_OPls != c_Int_OBit0(U_7802) ),
    inference(clausify,[status(thm)],[f_2156_3]) ).

cnf(f_2156_5,plain,
    ( c_Int_OPls = c_Int_OBit0(U_7803)
    | c_Int_OPls != U_7803 ),
    inference(clausify,[status(thm)],[f_2156_3]) ).

fof(f_2157_1,plain,
    ! [V_k_2] :
      ( ( c_Int_OBit0(V_k_2) = c_Int_OPls
        | V_k_2 != c_Int_OPls )
      & ( V_k_2 = c_Int_OPls
        | c_Int_OBit0(V_k_2) != c_Int_OPls ) ),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I44_J]) ).

fof(f_2157_2,plain,
    ! [U_7804] :
      ( ( c_Int_OBit0(U_7804) = c_Int_OPls
        | U_7804 != c_Int_OPls )
      & ( U_7804 = c_Int_OPls
        | c_Int_OBit0(U_7804) != c_Int_OPls ) ),
    inference(variable_rename,[status(thm)],[f_2157_1]) ).

fof(f_2157_3,plain,
    ( ! [U_7806] :
        ( c_Int_OBit0(U_7806) = c_Int_OPls
        | U_7806 != c_Int_OPls )
    & ! [U_7805] :
        ( U_7805 = c_Int_OPls
        | c_Int_OBit0(U_7805) != c_Int_OPls ) ),
    inference(miniscope,[status(thm)],[f_2157_2]) ).

cnf(f_2157_4,plain,
    ( U_7805 = c_Int_OPls
    | c_Int_OBit0(U_7805) != c_Int_OPls ),
    inference(clausify,[status(thm)],[f_2157_3]) ).

cnf(f_2157_5,plain,
    ( c_Int_OBit0(U_7806) = c_Int_OPls
    | U_7806 != c_Int_OPls ),
    inference(clausify,[status(thm)],[f_2157_3]) ).

fof(f_2158_1,plain,
    ! [V_k] : c_Int_OBit0(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_k),
    inference(fof_nnf,[status(thm)],[fact_Bit0__def]) ).

fof(f_2158_2,plain,
    ! [U_7807] : c_Int_OBit0(U_7807) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7807),U_7807),
    inference(variable_rename,[status(thm)],[f_2158_1]) ).

cnf(f_2158_3,plain,
    c_Int_OBit0(U_7807) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7807),U_7807),
    inference(clausify,[status(thm)],[f_2158_2]) ).

fof(f_2159_1,plain,
    ! [V_l,V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(V_k)),c_Int_OBit0(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_l)),
    inference(fof_nnf,[status(thm)],[fact_add__Bit0__Bit0]) ).

fof(f_2159_2,plain,
    ! [U_7809,U_7808] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(U_7808)),c_Int_OBit0(U_7809)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7808),U_7809)),
    inference(variable_rename,[status(thm)],[f_2159_1]) ).

cnf(f_2159_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(U_7808)),c_Int_OBit0(U_7809)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7808),U_7809)),
    inference(clausify,[status(thm)],[f_2159_2]) ).

fof(f_2160_1,plain,
    ! [V_l_2,V_k_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I31_J]) ).

fof(f_2160_2,plain,
    ! [U_7811,U_7810] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7810)),c_Int_OBit0(U_7811)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7810),U_7811)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7810),U_7811))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7810)),c_Int_OBit0(U_7811))) ) ),
    inference(variable_rename,[status(thm)],[f_2160_1]) ).

fof(f_2160_3,plain,
    ( ! [U_7815,U_7813] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7813)),c_Int_OBit0(U_7815)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7813),U_7815)) )
    & ! [U_7814,U_7812] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7812),U_7814))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7812)),c_Int_OBit0(U_7814))) ) ),
    inference(miniscope,[status(thm)],[f_2160_2]) ).

cnf(f_2160_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7812),U_7814))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7812)),c_Int_OBit0(U_7814))) ),
    inference(clausify,[status(thm)],[f_2160_3]) ).

cnf(f_2160_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7813)),c_Int_OBit0(U_7815)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7813),U_7815)) ),
    inference(clausify,[status(thm)],[f_2160_3]) ).

fof(f_2161_1,plain,
    ! [V_k2_2,V_k1_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_less__eq__int__code_I13_J]) ).

fof(f_2161_2,plain,
    ! [U_7817,U_7816] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7816)),c_Int_OBit0(U_7817)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7816),U_7817)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7816),U_7817))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7816)),c_Int_OBit0(U_7817))) ) ),
    inference(variable_rename,[status(thm)],[f_2161_1]) ).

fof(f_2161_3,plain,
    ( ! [U_7821,U_7819] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7819)),c_Int_OBit0(U_7821)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7819),U_7821)) )
    & ! [U_7820,U_7818] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7818),U_7820))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7818)),c_Int_OBit0(U_7820))) ) ),
    inference(miniscope,[status(thm)],[f_2161_2]) ).

cnf(f_2161_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7818),U_7820))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7818)),c_Int_OBit0(U_7820))) ),
    inference(clausify,[status(thm)],[f_2161_3]) ).

cnf(f_2161_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7819)),c_Int_OBit0(U_7821)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7819),U_7821)) ),
    inference(clausify,[status(thm)],[f_2161_3]) ).

fof(f_2162_1,plain,
    ! [V_k2_2,V_k1_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_less__int__code_I13_J]) ).

fof(f_2162_2,plain,
    ! [U_7823,U_7822] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7822)),c_Int_OBit0(U_7823)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7822),U_7823)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7822),U_7823))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7822)),c_Int_OBit0(U_7823))) ) ),
    inference(variable_rename,[status(thm)],[f_2162_1]) ).

fof(f_2162_3,plain,
    ( ! [U_7827,U_7825] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7825)),c_Int_OBit0(U_7827)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7825),U_7827)) )
    & ! [U_7826,U_7824] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7824),U_7826))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7824)),c_Int_OBit0(U_7826))) ) ),
    inference(miniscope,[status(thm)],[f_2162_2]) ).

cnf(f_2162_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7824),U_7826))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7824)),c_Int_OBit0(U_7826))) ),
    inference(clausify,[status(thm)],[f_2162_3]) ).

cnf(f_2162_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7825)),c_Int_OBit0(U_7827)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7825),U_7827)) ),
    inference(clausify,[status(thm)],[f_2162_3]) ).

fof(f_2163_1,plain,
    ! [V_l_2,V_k_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I14_J]) ).

fof(f_2163_2,plain,
    ! [U_7829,U_7828] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7828)),c_Int_OBit0(U_7829)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7828),U_7829)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7828),U_7829))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7828)),c_Int_OBit0(U_7829))) ) ),
    inference(variable_rename,[status(thm)],[f_2163_1]) ).

fof(f_2163_3,plain,
    ( ! [U_7833,U_7831] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7831)),c_Int_OBit0(U_7833)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7831),U_7833)) )
    & ! [U_7832,U_7830] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7830),U_7832))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7830)),c_Int_OBit0(U_7832))) ) ),
    inference(miniscope,[status(thm)],[f_2163_2]) ).

cnf(f_2163_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7830),U_7832))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7830)),c_Int_OBit0(U_7832))) ),
    inference(clausify,[status(thm)],[f_2163_3]) ).

cnf(f_2163_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7831)),c_Int_OBit0(U_7833)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7831),U_7833)) ),
    inference(clausify,[status(thm)],[f_2163_3]) ).

fof(f_2164_1,plain,
    ! [V_l_2,V_k_2] :
      ( ( c_Int_OBit0(V_k_2) = c_Int_OBit0(V_l_2)
        | V_k_2 != V_l_2 )
      & ( V_k_2 = V_l_2
        | c_Int_OBit0(V_k_2) != c_Int_OBit0(V_l_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I48_J]) ).

fof(f_2164_2,plain,
    ! [U_7835,U_7834] :
      ( ( c_Int_OBit0(U_7834) = c_Int_OBit0(U_7835)
        | U_7834 != U_7835 )
      & ( U_7834 = U_7835
        | c_Int_OBit0(U_7834) != c_Int_OBit0(U_7835) ) ),
    inference(variable_rename,[status(thm)],[f_2164_1]) ).

fof(f_2164_3,plain,
    ( ! [U_7839,U_7837] :
        ( c_Int_OBit0(U_7837) = c_Int_OBit0(U_7839)
        | U_7837 != U_7839 )
    & ! [U_7838,U_7836] :
        ( U_7836 = U_7838
        | c_Int_OBit0(U_7836) != c_Int_OBit0(U_7838) ) ),
    inference(miniscope,[status(thm)],[f_2164_2]) ).

cnf(f_2164_4,plain,
    ( U_7836 = U_7838
    | c_Int_OBit0(U_7836) != c_Int_OBit0(U_7838) ),
    inference(clausify,[status(thm)],[f_2164_3]) ).

cnf(f_2164_5,plain,
    ( c_Int_OBit0(U_7837) = c_Int_OBit0(U_7839)
    | U_7837 != U_7839 ),
    inference(clausify,[status(thm)],[f_2164_3]) ).

fof(f_2165_1,plain,
    ! [V_k] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit0(V_k)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k)),
    inference(fof_nnf,[status(thm)],[fact_minus__Bit0]) ).

fof(f_2165_2,plain,
    ! [U_7840] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit0(U_7840)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7840)),
    inference(variable_rename,[status(thm)],[f_2165_1]) ).

cnf(f_2165_3,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit0(U_7840)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7840)),
    inference(clausify,[status(thm)],[f_2165_2]) ).

fof(f_2166_1,plain,
    ! [V_l,V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(V_k)),c_Int_OBit0(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),V_l)),
    inference(fof_nnf,[status(thm)],[fact_diff__bin__simps_I7_J]) ).

fof(f_2166_2,plain,
    ! [U_7842,U_7841] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(U_7841)),c_Int_OBit0(U_7842)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7841),U_7842)),
    inference(variable_rename,[status(thm)],[f_2166_1]) ).

cnf(f_2166_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(U_7841)),c_Int_OBit0(U_7842)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7841),U_7842)),
    inference(clausify,[status(thm)],[f_2166_2]) ).

fof(f_2167_1,plain,
    ! [V_l,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit0(V_k)),V_l) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_l)),
    inference(fof_nnf,[status(thm)],[fact_mult__Bit0]) ).

fof(f_2167_2,plain,
    ! [U_7844,U_7843] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit0(U_7843)),U_7844) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7843),U_7844)),
    inference(variable_rename,[status(thm)],[f_2167_1]) ).

cnf(f_2167_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit0(U_7843)),U_7844) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7843),U_7844)),
    inference(clausify,[status(thm)],[f_2167_2]) ).

fof(f_2168_1,plain,
    ! [V_w_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_w_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_w_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(fof_nnf,[status(thm)],[fact_bin__less__0__simps_I3_J]) ).

fof(f_2168_2,plain,
    ! [U_7845] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7845)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7845),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7845),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7845)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(variable_rename,[status(thm)],[f_2168_1]) ).

fof(f_2168_3,plain,
    ( ! [U_7847] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7847)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7847),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_7846] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7846),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7846)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(miniscope,[status(thm)],[f_2168_2]) ).

cnf(f_2168_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7846),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7846)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2168_3]) ).

cnf(f_2168_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7847)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7847),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2168_3]) ).

fof(f_2169_1,plain,
    ! [V_k_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I21_J]) ).

fof(f_2169_2,plain,
    ! [U_7848] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_7848)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_7848)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_7848))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_7848))) ) ),
    inference(variable_rename,[status(thm)],[f_2169_1]) ).

fof(f_2169_3,plain,
    ( ! [U_7850] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_7850)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_7850)) )
    & ! [U_7849] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_7849))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_7849))) ) ),
    inference(miniscope,[status(thm)],[f_2169_2]) ).

cnf(f_2169_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_7849))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_7849))) ),
    inference(clausify,[status(thm)],[f_2169_3]) ).

cnf(f_2169_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_7850)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_7850)) ),
    inference(clausify,[status(thm)],[f_2169_3]) ).

fof(f_2170_1,plain,
    ! [V_k_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OPls)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls)) ) ),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I27_J]) ).

fof(f_2170_2,plain,
    ! [U_7851] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7851)),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7851),c_Int_OPls)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7851),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7851)),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[f_2170_1]) ).

fof(f_2170_3,plain,
    ( ! [U_7853] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7853)),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7853),c_Int_OPls)) )
    & ! [U_7852] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7852),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7852)),c_Int_OPls)) ) ),
    inference(miniscope,[status(thm)],[f_2170_2]) ).

cnf(f_2170_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7852),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7852)),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_2170_3]) ).

cnf(f_2170_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7853)),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7853),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_2170_3]) ).

fof(f_2171_1,plain,
    ! [V_l_2,V_k_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I32_J]) ).

fof(f_2171_2,plain,
    ! [U_7855,U_7854] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7854)),c_Int_OBit1(U_7855)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7854),U_7855)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7854),U_7855))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7854)),c_Int_OBit1(U_7855))) ) ),
    inference(variable_rename,[status(thm)],[f_2171_1]) ).

fof(f_2171_3,plain,
    ( ! [U_7859,U_7857] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7857)),c_Int_OBit1(U_7859)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7857),U_7859)) )
    & ! [U_7858,U_7856] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7856),U_7858))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7856)),c_Int_OBit1(U_7858))) ) ),
    inference(miniscope,[status(thm)],[f_2171_2]) ).

cnf(f_2171_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7856),U_7858))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7856)),c_Int_OBit1(U_7858))) ),
    inference(clausify,[status(thm)],[f_2171_3]) ).

cnf(f_2171_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7857)),c_Int_OBit1(U_7859)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7857),U_7859)) ),
    inference(clausify,[status(thm)],[f_2171_3]) ).

fof(f_2172_1,plain,
    ! [V_k2_2,V_k1_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_less__eq__int__code_I14_J]) ).

fof(f_2172_2,plain,
    ! [U_7861,U_7860] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7860)),c_Int_OBit1(U_7861)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7860),U_7861)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7860),U_7861))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7860)),c_Int_OBit1(U_7861))) ) ),
    inference(variable_rename,[status(thm)],[f_2172_1]) ).

fof(f_2172_3,plain,
    ( ! [U_7865,U_7863] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7863)),c_Int_OBit1(U_7865)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7863),U_7865)) )
    & ! [U_7864,U_7862] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7862),U_7864))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7862)),c_Int_OBit1(U_7864))) ) ),
    inference(miniscope,[status(thm)],[f_2172_2]) ).

cnf(f_2172_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7862),U_7864))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7862)),c_Int_OBit1(U_7864))) ),
    inference(clausify,[status(thm)],[f_2172_3]) ).

cnf(f_2172_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_7863)),c_Int_OBit1(U_7865)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7863),U_7865)) ),
    inference(clausify,[status(thm)],[f_2172_3]) ).

fof(f_2173_1,plain,
    ! [V_k_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls)) ) ),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I10_J]) ).

fof(f_2173_2,plain,
    ! [U_7866] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7866)),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7866),c_Int_OPls)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7866),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7866)),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[f_2173_1]) ).

fof(f_2173_3,plain,
    ( ! [U_7868] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7868)),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7868),c_Int_OPls)) )
    & ! [U_7867] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7867),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7867)),c_Int_OPls)) ) ),
    inference(miniscope,[status(thm)],[f_2173_2]) ).

cnf(f_2173_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7867),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7867)),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_2173_3]) ).

cnf(f_2173_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7868)),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7868),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_2173_3]) ).

fof(f_2174_1,plain,
    ! [V_k_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_k_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_k_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I4_J]) ).

fof(f_2174_2,plain,
    ! [U_7869] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_7869)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_7869)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_7869))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_7869))) ) ),
    inference(variable_rename,[status(thm)],[f_2174_1]) ).

fof(f_2174_3,plain,
    ( ! [U_7871] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_7871)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_7871)) )
    & ! [U_7870] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_7870))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_7870))) ) ),
    inference(miniscope,[status(thm)],[f_2174_2]) ).

cnf(f_2174_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_7870))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_7870))) ),
    inference(clausify,[status(thm)],[f_2174_3]) ).

cnf(f_2174_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_7871)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_7871)) ),
    inference(clausify,[status(thm)],[f_2174_3]) ).

fof(f_2175_1,plain,
    ! [V_k2_2,V_k1_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_less__int__code_I15_J]) ).

fof(f_2175_2,plain,
    ! [U_7873,U_7872] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7872)),c_Int_OBit0(U_7873)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7872),U_7873)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7872),U_7873))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7872)),c_Int_OBit0(U_7873))) ) ),
    inference(variable_rename,[status(thm)],[f_2175_1]) ).

fof(f_2175_3,plain,
    ( ! [U_7877,U_7875] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7875)),c_Int_OBit0(U_7877)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7875),U_7877)) )
    & ! [U_7876,U_7874] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7874),U_7876))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7874)),c_Int_OBit0(U_7876))) ) ),
    inference(miniscope,[status(thm)],[f_2175_2]) ).

cnf(f_2175_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7874),U_7876))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7874)),c_Int_OBit0(U_7876))) ),
    inference(clausify,[status(thm)],[f_2175_3]) ).

cnf(f_2175_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7875)),c_Int_OBit0(U_7877)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7875),U_7877)) ),
    inference(clausify,[status(thm)],[f_2175_3]) ).

fof(f_2176_1,plain,
    ! [V_l_2,V_k_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I16_J]) ).

fof(f_2176_2,plain,
    ! [U_7879,U_7878] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7878)),c_Int_OBit0(U_7879)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7878),U_7879)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7878),U_7879))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7878)),c_Int_OBit0(U_7879))) ) ),
    inference(variable_rename,[status(thm)],[f_2176_1]) ).

fof(f_2176_3,plain,
    ( ! [U_7883,U_7881] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7881)),c_Int_OBit0(U_7883)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7881),U_7883)) )
    & ! [U_7882,U_7880] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7880),U_7882))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7880)),c_Int_OBit0(U_7882))) ) ),
    inference(miniscope,[status(thm)],[f_2176_2]) ).

cnf(f_2176_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7880),U_7882))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7880)),c_Int_OBit0(U_7882))) ),
    inference(clausify,[status(thm)],[f_2176_3]) ).

cnf(f_2176_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_7881)),c_Int_OBit0(U_7883)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7881),U_7883)) ),
    inference(clausify,[status(thm)],[f_2176_3]) ).

fof(f_2177_1,plain,
    ! [V_l,V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(V_k)),c_Int_OBit1(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_l)),
    inference(fof_nnf,[status(thm)],[fact_add__Bit0__Bit1]) ).

fof(f_2177_2,plain,
    ! [U_7885,U_7884] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(U_7884)),c_Int_OBit1(U_7885)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7884),U_7885)),
    inference(variable_rename,[status(thm)],[f_2177_1]) ).

cnf(f_2177_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(U_7884)),c_Int_OBit1(U_7885)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7884),U_7885)),
    inference(clausify,[status(thm)],[f_2177_2]) ).

fof(f_2178_1,plain,
    ! [V_l,V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(V_k)),c_Int_OBit0(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_l)),
    inference(fof_nnf,[status(thm)],[fact_add__Bit1__Bit0]) ).

fof(f_2178_2,plain,
    ! [U_7887,U_7886] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(U_7886)),c_Int_OBit0(U_7887)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7886),U_7887)),
    inference(variable_rename,[status(thm)],[f_2178_1]) ).

cnf(f_2178_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(U_7886)),c_Int_OBit0(U_7887)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7886),U_7887)),
    inference(clausify,[status(thm)],[f_2178_2]) ).

fof(f_2179_1,plain,
    ! [V_l] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),V_l)),
    inference(fof_nnf,[status(thm)],[fact_diff__bin__simps_I3_J]) ).

fof(f_2179_2,plain,
    ! [U_7888] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_7888)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),U_7888)),
    inference(variable_rename,[status(thm)],[f_2179_1]) ).

cnf(f_2179_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_7888)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),U_7888)),
    inference(clausify,[status(thm)],[f_2179_2]) ).

fof(f_2180_1,plain,
    ! [V_l,V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(V_k)),c_Int_OBit0(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),V_l)),
    inference(fof_nnf,[status(thm)],[fact_diff__bin__simps_I9_J]) ).

fof(f_2180_2,plain,
    ! [U_7890,U_7889] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(U_7889)),c_Int_OBit0(U_7890)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7889),U_7890)),
    inference(variable_rename,[status(thm)],[f_2180_1]) ).

cnf(f_2180_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(U_7889)),c_Int_OBit0(U_7890)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7889),U_7890)),
    inference(clausify,[status(thm)],[f_2180_2]) ).

fof(f_2181_1,plain,
    ! [V_l,V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(V_k)),c_Int_OBit1(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),V_l)),
    inference(fof_nnf,[status(thm)],[fact_diff__bin__simps_I10_J]) ).

fof(f_2181_2,plain,
    ! [U_7892,U_7891] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(U_7891)),c_Int_OBit1(U_7892)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7891),U_7892)),
    inference(variable_rename,[status(thm)],[f_2181_1]) ).

cnf(f_2181_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(U_7891)),c_Int_OBit1(U_7892)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7891),U_7892)),
    inference(clausify,[status(thm)],[f_2181_2]) ).

fof(f_2182_1,plain,
    ! [V_w,V_v] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_v))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),
    inference(fof_nnf,[status(thm)],[fact_zdiv__number__of__Bit0]) ).

fof(f_2182_2,plain,
    ! [U_7894,U_7893] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_7893))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_7894))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7893)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7894)),
    inference(variable_rename,[status(thm)],[f_2182_1]) ).

cnf(f_2182_3,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_7893))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_7894))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7893)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7894)),
    inference(clausify,[status(thm)],[f_2182_2]) ).

fof(f_2183_1,plain,
    ! [V_w_2] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w_2))))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w_2)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_neg__number__of__Bit0]) ).

fof(f_2183_2,plain,
    ! [U_7895] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_7895))))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7895))) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7895)))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_7895)))) ) ),
    inference(variable_rename,[status(thm)],[f_2183_1]) ).

fof(f_2183_3,plain,
    ( ! [U_7897] :
        ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_7897))))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7897))) )
    & ! [U_7896] :
        ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7896)))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_7896)))) ) ),
    inference(miniscope,[status(thm)],[f_2183_2]) ).

cnf(f_2183_4,plain,
    ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7896)))
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_7896)))) ),
    inference(clausify,[status(thm)],[f_2183_3]) ).

cnf(f_2183_5,plain,
    ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_7897))))
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7897))) ),
    inference(clausify,[status(thm)],[f_2183_3]) ).

fof(f_2184_1,plain,
    ! [V_k] : c_Int_Opred(c_Int_OBit1(V_k)) = c_Int_OBit0(V_k),
    inference(fof_nnf,[status(thm)],[fact_pred__Bit1]) ).

fof(f_2184_2,plain,
    ! [U_7898] : c_Int_Opred(c_Int_OBit1(U_7898)) = c_Int_OBit0(U_7898),
    inference(variable_rename,[status(thm)],[f_2184_1]) ).

cnf(f_2184_3,plain,
    c_Int_Opred(c_Int_OBit1(U_7898)) = c_Int_OBit0(U_7898),
    inference(clausify,[status(thm)],[f_2184_2]) ).

fof(f_2185_1,plain,
    ! [V_k] : c_Int_Opred(c_Int_OBit0(V_k)) = c_Int_OBit1(c_Int_Opred(V_k)),
    inference(fof_nnf,[status(thm)],[fact_pred__Bit0]) ).

fof(f_2185_2,plain,
    ! [U_7899] : c_Int_Opred(c_Int_OBit0(U_7899)) = c_Int_OBit1(c_Int_Opred(U_7899)),
    inference(variable_rename,[status(thm)],[f_2185_1]) ).

cnf(f_2185_3,plain,
    c_Int_Opred(c_Int_OBit0(U_7899)) = c_Int_OBit1(c_Int_Opred(U_7899)),
    inference(clausify,[status(thm)],[f_2185_2]) ).

fof(f_2186_1,plain,
    ! [V_w_2,T_b] :
      ( ( ( c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),c_Int_OBit0(V_w_2)))
          | ~ c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) )
        & ( c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))
          | ~ c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),c_Int_OBit0(V_w_2))) ) )
      | ~ class_Int_Oring__char__0(T_b)
      | ~ class_Int_Onumber__ring(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_iszero__number__of__Bit0]) ).

fof(f_2186_2,plain,
    ! [U_7901,U_7900] :
      ( ( ( c_Int_Oiszero(U_7900,hAPP(c_Int_Onumber__class_Onumber__of(U_7900),c_Int_OBit0(U_7901)))
          | ~ c_Int_Oiszero(U_7900,hAPP(c_Int_Onumber__class_Onumber__of(U_7900),U_7901)) )
        & ( c_Int_Oiszero(U_7900,hAPP(c_Int_Onumber__class_Onumber__of(U_7900),U_7901))
          | ~ c_Int_Oiszero(U_7900,hAPP(c_Int_Onumber__class_Onumber__of(U_7900),c_Int_OBit0(U_7901))) ) )
      | ~ class_Int_Oring__char__0(U_7900)
      | ~ class_Int_Onumber__ring(U_7900) ),
    inference(variable_rename,[status(thm)],[f_2186_1]) ).

cnf(f_2186_3,plain,
    ( c_Int_Oiszero(U_7900,hAPP(c_Int_Onumber__class_Onumber__of(U_7900),U_7901))
    | ~ c_Int_Oiszero(U_7900,hAPP(c_Int_Onumber__class_Onumber__of(U_7900),c_Int_OBit0(U_7901)))
    | ~ class_Int_Oring__char__0(U_7900)
    | ~ class_Int_Onumber__ring(U_7900) ),
    inference(clausify,[status(thm)],[f_2186_2]) ).

cnf(f_2186_4,plain,
    ( c_Int_Oiszero(U_7900,hAPP(c_Int_Onumber__class_Onumber__of(U_7900),c_Int_OBit0(U_7901)))
    | ~ c_Int_Oiszero(U_7900,hAPP(c_Int_Onumber__class_Onumber__of(U_7900),U_7901))
    | ~ class_Int_Oring__char__0(U_7900)
    | ~ class_Int_Onumber__ring(U_7900) ),
    inference(clausify,[status(thm)],[f_2186_2]) ).

fof(f_2187_1,plain,
    ! [V_k] : c_Int_Osucc(c_Int_OBit0(V_k)) = c_Int_OBit1(V_k),
    inference(fof_nnf,[status(thm)],[fact_succ__Bit0]) ).

fof(f_2187_2,plain,
    ! [U_7902] : c_Int_Osucc(c_Int_OBit0(U_7902)) = c_Int_OBit1(U_7902),
    inference(variable_rename,[status(thm)],[f_2187_1]) ).

cnf(f_2187_3,plain,
    c_Int_Osucc(c_Int_OBit0(U_7902)) = c_Int_OBit1(U_7902),
    inference(clausify,[status(thm)],[f_2187_2]) ).

fof(f_2188_1,plain,
    ! [V_k] : c_Int_Osucc(c_Int_OBit1(V_k)) = c_Int_OBit0(c_Int_Osucc(V_k)),
    inference(fof_nnf,[status(thm)],[fact_succ__Bit1]) ).

fof(f_2188_2,plain,
    ! [U_7903] : c_Int_Osucc(c_Int_OBit1(U_7903)) = c_Int_OBit0(c_Int_Osucc(U_7903)),
    inference(variable_rename,[status(thm)],[f_2188_1]) ).

cnf(f_2188_3,plain,
    c_Int_Osucc(c_Int_OBit1(U_7903)) = c_Int_OBit0(c_Int_Osucc(U_7903)),
    inference(clausify,[status(thm)],[f_2188_2]) ).

fof(f_2189_1,plain,
    ! [V_w,T_a] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_number__of__Bit0]) ).

fof(f_2189_2,plain,
    ! [U_7905,U_7904] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_7904),c_Int_OBit0(U_7905)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7904),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7904),c_Groups_Ozero__class_Ozero(U_7904)),hAPP(c_Int_Onumber__class_Onumber__of(U_7904),U_7905))),hAPP(c_Int_Onumber__class_Onumber__of(U_7904),U_7905))
      | ~ class_Int_Onumber__ring(U_7904) ),
    inference(variable_rename,[status(thm)],[f_2189_1]) ).

cnf(f_2189_3,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_7904),c_Int_OBit0(U_7905)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7904),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7904),c_Groups_Ozero__class_Ozero(U_7904)),hAPP(c_Int_Onumber__class_Onumber__of(U_7904),U_7905))),hAPP(c_Int_Onumber__class_Onumber__of(U_7904),U_7905))
    | ~ class_Int_Onumber__ring(U_7904) ),
    inference(clausify,[status(thm)],[f_2189_2]) ).

fof(f_2190_1,plain,
    ! [V_k2_2,V_k1_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_less__eq__int__code_I15_J]) ).

fof(f_2190_2,plain,
    ! [U_7907,U_7906] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7906)),c_Int_OBit0(U_7907)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7906),U_7907)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7906),U_7907))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7906)),c_Int_OBit0(U_7907))) ) ),
    inference(variable_rename,[status(thm)],[f_2190_1]) ).

fof(f_2190_3,plain,
    ( ! [U_7911,U_7909] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7909)),c_Int_OBit0(U_7911)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7909),U_7911)) )
    & ! [U_7910,U_7908] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7908),U_7910))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7908)),c_Int_OBit0(U_7910))) ) ),
    inference(miniscope,[status(thm)],[f_2190_2]) ).

cnf(f_2190_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7908),U_7910))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7908)),c_Int_OBit0(U_7910))) ),
    inference(clausify,[status(thm)],[f_2190_3]) ).

cnf(f_2190_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7909)),c_Int_OBit0(U_7911)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7909),U_7911)) ),
    inference(clausify,[status(thm)],[f_2190_3]) ).

fof(f_2191_1,plain,
    ! [V_l_2,V_k_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I33_J]) ).

fof(f_2191_2,plain,
    ! [U_7913,U_7912] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7912)),c_Int_OBit0(U_7913)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7912),U_7913)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7912),U_7913))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7912)),c_Int_OBit0(U_7913))) ) ),
    inference(variable_rename,[status(thm)],[f_2191_1]) ).

fof(f_2191_3,plain,
    ( ! [U_7917,U_7915] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7915)),c_Int_OBit0(U_7917)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7915),U_7917)) )
    & ! [U_7916,U_7914] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7914),U_7916))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7914)),c_Int_OBit0(U_7916))) ) ),
    inference(miniscope,[status(thm)],[f_2191_2]) ).

cnf(f_2191_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7914),U_7916))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7914)),c_Int_OBit0(U_7916))) ),
    inference(clausify,[status(thm)],[f_2191_3]) ).

cnf(f_2191_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_7915)),c_Int_OBit0(U_7917)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7915),U_7917)) ),
    inference(clausify,[status(thm)],[f_2191_3]) ).

fof(f_2192_1,plain,
    ! [V_k2_2,V_k1_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_less__int__code_I14_J]) ).

fof(f_2192_2,plain,
    ! [U_7919,U_7918] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7918)),c_Int_OBit1(U_7919)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7918),U_7919)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7918),U_7919))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7918)),c_Int_OBit1(U_7919))) ) ),
    inference(variable_rename,[status(thm)],[f_2192_1]) ).

fof(f_2192_3,plain,
    ( ! [U_7923,U_7921] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7921)),c_Int_OBit1(U_7923)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7921),U_7923)) )
    & ! [U_7922,U_7920] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7920),U_7922))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7920)),c_Int_OBit1(U_7922))) ) ),
    inference(miniscope,[status(thm)],[f_2192_2]) ).

cnf(f_2192_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7920),U_7922))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7920)),c_Int_OBit1(U_7922))) ),
    inference(clausify,[status(thm)],[f_2192_3]) ).

cnf(f_2192_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7921)),c_Int_OBit1(U_7923)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7921),U_7923)) ),
    inference(clausify,[status(thm)],[f_2192_3]) ).

fof(f_2193_1,plain,
    ! [V_l_2,V_k_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I15_J]) ).

fof(f_2193_2,plain,
    ! [U_7925,U_7924] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7924)),c_Int_OBit1(U_7925)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7924),U_7925)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7924),U_7925))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7924)),c_Int_OBit1(U_7925))) ) ),
    inference(variable_rename,[status(thm)],[f_2193_1]) ).

fof(f_2193_3,plain,
    ( ! [U_7929,U_7927] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7927)),c_Int_OBit1(U_7929)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7927),U_7929)) )
    & ! [U_7928,U_7926] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7926),U_7928))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7926)),c_Int_OBit1(U_7928))) ) ),
    inference(miniscope,[status(thm)],[f_2193_2]) ).

cnf(f_2193_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7926),U_7928))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7926)),c_Int_OBit1(U_7928))) ),
    inference(clausify,[status(thm)],[f_2193_3]) ).

cnf(f_2193_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_7927)),c_Int_OBit1(U_7929)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7927),U_7929)) ),
    inference(clausify,[status(thm)],[f_2193_3]) ).

fof(f_2194_1,plain,
    hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
    inference(fof_nnf,[status(thm)],[fact_card__UNIV__bool]) ).

cnf(f_2194_2,plain,
    hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
    inference(clausify,[status(thm)],[f_2194_1]) ).

fof(f_2195_1,plain,
    ! [V_l,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit1(V_k)),V_l) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_l))),V_l),
    inference(fof_nnf,[status(thm)],[fact_mult__Bit1]) ).

fof(f_2195_2,plain,
    ! [U_7931,U_7930] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit1(U_7930)),U_7931) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7930),U_7931))),U_7931),
    inference(variable_rename,[status(thm)],[f_2195_1]) ).

cnf(f_2195_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit1(U_7930)),U_7931) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7930),U_7931))),U_7931),
    inference(clausify,[status(thm)],[f_2195_2]) ).

fof(f_2196_1,plain,
    ! [V_l,V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(V_k)),c_Int_OBit1(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_Opred(V_k)),V_l)),
    inference(fof_nnf,[status(thm)],[fact_diff__bin__simps_I8_J]) ).

fof(f_2196_2,plain,
    ! [U_7933,U_7932] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(U_7932)),c_Int_OBit1(U_7933)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_Opred(U_7932)),U_7933)),
    inference(variable_rename,[status(thm)],[f_2196_1]) ).

cnf(f_2196_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(U_7932)),c_Int_OBit1(U_7933)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_Opred(U_7932)),U_7933)),
    inference(clausify,[status(thm)],[f_2196_2]) ).

fof(f_2197_1,plain,
    ! [V_l,V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(V_k)),c_Int_OBit1(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_Osucc(V_l))),
    inference(fof_nnf,[status(thm)],[fact_add__Bit1__Bit1]) ).

fof(f_2197_2,plain,
    ! [U_7935,U_7934] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(U_7934)),c_Int_OBit1(U_7935)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7934),c_Int_Osucc(U_7935))),
    inference(variable_rename,[status(thm)],[f_2197_1]) ).

cnf(f_2197_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(U_7934)),c_Int_OBit1(U_7935)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7934),c_Int_Osucc(U_7935))),
    inference(clausify,[status(thm)],[f_2197_2]) ).

fof(f_2198_1,plain,
    ! [V_w,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a))),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(V_w))
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_double__number__of__Bit0]) ).

fof(f_2198_2,plain,
    ! [U_7937,U_7936] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7936),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7936),c_Groups_Oone__class_Oone(U_7936)),c_Groups_Oone__class_Oone(U_7936))),hAPP(c_Int_Onumber__class_Onumber__of(U_7936),U_7937)) = hAPP(c_Int_Onumber__class_Onumber__of(U_7936),c_Int_OBit0(U_7937))
      | ~ class_Int_Onumber__ring(U_7936) ),
    inference(variable_rename,[status(thm)],[f_2198_1]) ).

cnf(f_2198_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7936),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7936),c_Groups_Oone__class_Oone(U_7936)),c_Groups_Oone__class_Oone(U_7936))),hAPP(c_Int_Onumber__class_Onumber__of(U_7936),U_7937)) = hAPP(c_Int_Onumber__class_Onumber__of(U_7936),c_Int_OBit0(U_7937))
    | ~ class_Int_Onumber__ring(U_7936) ),
    inference(clausify,[status(thm)],[f_2198_2]) ).

fof(f_2199_1,plain,
    ! [V_n] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_n))))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_n)))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n))) ),
    inference(fof_nnf,[status(thm)],[fact_number__of1]) ).

fof(f_2199_2,plain,
    ! [U_7938] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_7938))))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_7938)))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7938))) ),
    inference(variable_rename,[status(thm)],[f_2199_1]) ).

cnf(f_2199_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_7938))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7938))) ),
    inference(clausify,[status(thm)],[f_2199_2]) ).

cnf(f_2199_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_7938))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7938))) ),
    inference(clausify,[status(thm)],[f_2199_2]) ).

fof(f_2200_1,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
    inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__numerals_I3_J]) ).

cnf(f_2200_2,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
    inference(clausify,[status(thm)],[f_2200_1]) ).

fof(f_2201_1,plain,
    ! [V_z,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_z),V_z)
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__2__right]) ).

fof(f_2201_2,plain,
    ! [U_7940,U_7939] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7939),U_7940),hAPP(c_Int_Onumber__class_Onumber__of(U_7939),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7939),U_7940),U_7940)
      | ~ class_Int_Onumber__ring(U_7939) ),
    inference(variable_rename,[status(thm)],[f_2201_1]) ).

cnf(f_2201_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7939),U_7940),hAPP(c_Int_Onumber__class_Onumber__of(U_7939),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7939),U_7940),U_7940)
    | ~ class_Int_Onumber__ring(U_7939) ),
    inference(clausify,[status(thm)],[f_2201_2]) ).

fof(f_2202_1,plain,
    ! [V_z,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_z) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_z),V_z)
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__2]) ).

fof(f_2202_2,plain,
    ! [U_7942,U_7941] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7941),hAPP(c_Int_Onumber__class_Onumber__of(U_7941),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_7942) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7941),U_7942),U_7942)
      | ~ class_Int_Onumber__ring(U_7941) ),
    inference(variable_rename,[status(thm)],[f_2202_1]) ).

cnf(f_2202_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7941),hAPP(c_Int_Onumber__class_Onumber__of(U_7941),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_7942) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7941),U_7942),U_7942)
    | ~ class_Int_Onumber__ring(U_7941) ),
    inference(clausify,[status(thm)],[f_2202_2]) ).

fof(f_2203_1,plain,
    ! [T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_one__add__one__is__two]) ).

fof(f_2203_2,plain,
    ! [U_7943] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7943),c_Groups_Oone__class_Oone(U_7943)),c_Groups_Oone__class_Oone(U_7943)) = hAPP(c_Int_Onumber__class_Onumber__of(U_7943),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))
      | ~ class_Int_Onumber__ring(U_7943) ),
    inference(variable_rename,[status(thm)],[f_2203_1]) ).

cnf(f_2203_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7943),c_Groups_Oone__class_Oone(U_7943)),c_Groups_Oone__class_Oone(U_7943)) = hAPP(c_Int_Onumber__class_Onumber__of(U_7943),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))
    | ~ class_Int_Onumber__ring(U_7943) ),
    inference(clausify,[status(thm)],[f_2203_2]) ).

fof(f_2204_1,plain,
    ! [V_a_2,T_b] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(T_b)
          | V_a_2 != c_Groups_Ozero__class_Ozero(T_b) )
        & ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
          | hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(T_b) ) )
      | ~ class_Rings_Oring__1__no__zero__divisors(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_zero__eq__power2]) ).

fof(f_2204_2,plain,
    ! [U_7945,U_7944] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_7944),U_7945),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(U_7944)
          | U_7945 != c_Groups_Ozero__class_Ozero(U_7944) )
        & ( U_7945 = c_Groups_Ozero__class_Ozero(U_7944)
          | hAPP(hAPP(c_Power_Opower__class_Opower(U_7944),U_7945),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(U_7944) ) )
      | ~ class_Rings_Oring__1__no__zero__divisors(U_7944) ),
    inference(variable_rename,[status(thm)],[f_2204_1]) ).

cnf(f_2204_3,plain,
    ( U_7945 = c_Groups_Ozero__class_Ozero(U_7944)
    | hAPP(hAPP(c_Power_Opower__class_Opower(U_7944),U_7945),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(U_7944)
    | ~ class_Rings_Oring__1__no__zero__divisors(U_7944) ),
    inference(clausify,[status(thm)],[f_2204_2]) ).

cnf(f_2204_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_7944),U_7945),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(U_7944)
    | U_7945 != c_Groups_Ozero__class_Ozero(U_7944)
    | ~ class_Rings_Oring__1__no__zero__divisors(U_7944) ),
    inference(clausify,[status(thm)],[f_2204_2]) ).

fof(f_2205_1,plain,
    ! [T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Rings_Osemiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_zero__power2]) ).

fof(f_2205_2,plain,
    ! [U_7946] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_7946),c_Groups_Ozero__class_Ozero(U_7946)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(U_7946)
      | ~ class_Rings_Osemiring__1(U_7946) ),
    inference(variable_rename,[status(thm)],[f_2205_1]) ).

cnf(f_2205_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_7946),c_Groups_Ozero__class_Ozero(U_7946)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(U_7946)
    | ~ class_Rings_Osemiring__1(U_7946) ),
    inference(clausify,[status(thm)],[f_2205_2]) ).

fof(f_2206_1,plain,
    hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
    inference(fof_nnf,[status(thm)],[fact_semiring__norm_I115_J]) ).

cnf(f_2206_2,plain,
    hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
    inference(clausify,[status(thm)],[f_2206_1]) ).

fof(f_2207_1,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(fof_nnf,[status(thm)],[fact_numeral__2__eq__2]) ).

cnf(f_2207_2,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_2207_1]) ).

fof(f_2208_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)
      | ~ class_Groups_Omonoid__mult(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power2__eq__square]) ).

fof(f_2208_2,plain,
    ! [U_7948,U_7947] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_7947),U_7948),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7947),U_7948),U_7948)
      | ~ class_Groups_Omonoid__mult(U_7947) ),
    inference(variable_rename,[status(thm)],[f_2208_1]) ).

cnf(f_2208_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_7947),U_7948),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7947),U_7948),U_7948)
    | ~ class_Groups_Omonoid__mult(U_7947) ),
    inference(clausify,[status(thm)],[f_2208_2]) ).

fof(f_2209_1,plain,
    ! [V_x,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J]) ).

fof(f_2209_2,plain,
    ! [U_7950,U_7949] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7949),U_7950),U_7950) = hAPP(hAPP(c_Power_Opower__class_Opower(U_7949),U_7950),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
      | ~ class_Rings_Ocomm__semiring__1(U_7949) ),
    inference(variable_rename,[status(thm)],[f_2209_1]) ).

cnf(f_2209_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7949),U_7950),U_7950) = hAPP(hAPP(c_Power_Opower__class_Opower(U_7949),U_7950),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
    | ~ class_Rings_Ocomm__semiring__1(U_7949) ),
    inference(clausify,[status(thm)],[f_2209_2]) ).

fof(f_2210_1,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J]) ).

cnf(f_2210_2,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
    inference(clausify,[status(thm)],[f_2210_1]) ).

fof(f_2211_1,plain,
    ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n)),
    inference(fof_nnf,[status(thm)],[fact_add__2__eq__Suc]) ).

fof(f_2211_2,plain,
    ! [U_7951] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_7951) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_7951)),
    inference(variable_rename,[status(thm)],[f_2211_1]) ).

cnf(f_2211_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_7951) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_7951)),
    inference(clausify,[status(thm)],[f_2211_2]) ).

fof(f_2212_1,plain,
    ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n)),
    inference(fof_nnf,[status(thm)],[fact_add__2__eq__Suc_H]) ).

fof(f_2212_2,plain,
    ! [U_7952] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7952),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_7952)),
    inference(variable_rename,[status(thm)],[f_2212_1]) ).

cnf(f_2212_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7952),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_7952)),
    inference(clausify,[status(thm)],[f_2212_2]) ).

fof(f_2213_1,plain,
    ! [T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(T_a)
      | ~ class_Rings_Osemiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_one__power2]) ).

fof(f_2213_2,plain,
    ! [U_7953] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_7953),c_Groups_Oone__class_Oone(U_7953)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(U_7953)
      | ~ class_Rings_Osemiring__1(U_7953) ),
    inference(variable_rename,[status(thm)],[f_2213_1]) ).

cnf(f_2213_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_7953),c_Groups_Oone__class_Oone(U_7953)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(U_7953)
    | ~ class_Rings_Osemiring__1(U_7953) ),
    inference(clausify,[status(thm)],[f_2213_2]) ).

fof(f_2214_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
      | ~ class_Rings_Oring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power2__minus]) ).

fof(f_2214_2,plain,
    ! [U_7955,U_7954] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_7954),hAPP(c_Groups_Ouminus__class_Ouminus(U_7954),U_7955)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(U_7954),U_7955),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
      | ~ class_Rings_Oring__1(U_7954) ),
    inference(variable_rename,[status(thm)],[f_2214_1]) ).

cnf(f_2214_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_7954),hAPP(c_Groups_Ouminus__class_Ouminus(U_7954),U_7955)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(U_7954),U_7955),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
    | ~ class_Rings_Oring__1(U_7954) ),
    inference(clausify,[status(thm)],[f_2214_2]) ).

fof(f_2215_1,plain,
    ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_z),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_z),V_z),
    inference(fof_nnf,[status(thm)],[fact_nat__mult__2__right]) ).

fof(f_2215_2,plain,
    ! [U_7956] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7956),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7956),U_7956),
    inference(variable_rename,[status(thm)],[f_2215_1]) ).

cnf(f_2215_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7956),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7956),U_7956),
    inference(clausify,[status(thm)],[f_2215_2]) ).

fof(f_2216_1,plain,
    ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_z) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_z),V_z),
    inference(fof_nnf,[status(thm)],[fact_nat__mult__2]) ).

fof(f_2216_2,plain,
    ! [U_7957] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_7957) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7957),U_7957),
    inference(variable_rename,[status(thm)],[f_2216_1]) ).

cnf(f_2216_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_7957) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7957),U_7957),
    inference(clausify,[status(thm)],[f_2216_2]) ).

fof(f_2217_1,plain,
    ! [V_n,V_a,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
      | ~ class_Groups_Omonoid__mult(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__even__eq]) ).

fof(f_2217_2,plain,
    ! [U_7960,U_7959,U_7958] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_7958),U_7959),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_7960)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_7958),hAPP(hAPP(c_Power_Opower__class_Opower(U_7958),U_7959),U_7960)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
      | ~ class_Groups_Omonoid__mult(U_7958) ),
    inference(variable_rename,[status(thm)],[f_2217_1]) ).

cnf(f_2217_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_7958),U_7959),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_7960)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_7958),hAPP(hAPP(c_Power_Opower__class_Opower(U_7958),U_7959),U_7960)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
    | ~ class_Groups_Omonoid__mult(U_7958) ),
    inference(clausify,[status(thm)],[f_2217_2]) ).

fof(f_2218_1,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
    inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__numerals_I3_J]) ).

cnf(f_2218_2,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
    inference(clausify,[status(thm)],[f_2218_1]) ).

fof(f_2219_1,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
    inference(fof_nnf,[status(thm)],[fact_nat__1__add__1]) ).

cnf(f_2219_2,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
    inference(clausify,[status(thm)],[f_2219_1]) ).

fof(f_2220_1,plain,
    ! [V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
    inference(fof_nnf,[status(thm)],[fact_div2__Suc__Suc]) ).

fof(f_2220_2,plain,
    ! [U_7961] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_7961))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7961),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
    inference(variable_rename,[status(thm)],[f_2220_1]) ).

cnf(f_2220_3,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_7961))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_7961),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
    inference(clausify,[status(thm)],[f_2220_2]) ).

fof(f_2221_1,plain,
    ! [V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = V_m,
    inference(fof_nnf,[status(thm)],[fact_add__self__div__2]) ).

fof(f_2221_2,plain,
    ! [U_7962] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7962),U_7962)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = U_7962,
    inference(variable_rename,[status(thm)],[f_2221_1]) ).

cnf(f_2221_3,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7962),U_7962)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = U_7962,
    inference(clausify,[status(thm)],[f_2221_2]) ).

fof(f_2222_1,plain,
    ! [V_r_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_r_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_r_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_r_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_r_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) )
      | ~ class_Int_Onumber__ring(T_b)
      | ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_half__gt__zero__iff]) ).

fof(f_2222_2,plain,
    ! [U_7964,U_7963] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7963),c_Groups_Ozero__class_Ozero(U_7963)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7963),U_7964),hAPP(c_Int_Onumber__class_Onumber__of(U_7963),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7963),c_Groups_Ozero__class_Ozero(U_7963)),U_7964)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7963),c_Groups_Ozero__class_Ozero(U_7963)),U_7964))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7963),c_Groups_Ozero__class_Ozero(U_7963)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7963),U_7964),hAPP(c_Int_Onumber__class_Onumber__of(U_7963),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) )
      | ~ class_Int_Onumber__ring(U_7963)
      | ~ class_Fields_Olinordered__field__inverse__zero(U_7963) ),
    inference(variable_rename,[status(thm)],[f_2222_1]) ).

cnf(f_2222_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7963),c_Groups_Ozero__class_Ozero(U_7963)),U_7964))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7963),c_Groups_Ozero__class_Ozero(U_7963)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7963),U_7964),hAPP(c_Int_Onumber__class_Onumber__of(U_7963),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | ~ class_Int_Onumber__ring(U_7963)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_7963) ),
    inference(clausify,[status(thm)],[f_2222_2]) ).

cnf(f_2222_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7963),c_Groups_Ozero__class_Ozero(U_7963)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7963),U_7964),hAPP(c_Int_Onumber__class_Onumber__of(U_7963),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7963),c_Groups_Ozero__class_Ozero(U_7963)),U_7964))
    | ~ class_Int_Onumber__ring(U_7963)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_7963) ),
    inference(clausify,[status(thm)],[f_2222_2]) ).

fof(f_2223_1,plain,
    ! [V_r,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_r),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_r))
      | ~ class_Int_Onumber__ring(T_a)
      | ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_half__gt__zero]) ).

fof(f_2223_2,plain,
    ! [U_7966,U_7965] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7965),c_Groups_Ozero__class_Ozero(U_7965)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7965),U_7966),hAPP(c_Int_Onumber__class_Onumber__of(U_7965),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7965),c_Groups_Ozero__class_Ozero(U_7965)),U_7966))
      | ~ class_Int_Onumber__ring(U_7965)
      | ~ class_Fields_Olinordered__field__inverse__zero(U_7965) ),
    inference(variable_rename,[status(thm)],[f_2223_1]) ).

cnf(f_2223_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7965),c_Groups_Ozero__class_Ozero(U_7965)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_7965),U_7966),hAPP(c_Int_Onumber__class_Onumber__of(U_7965),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7965),c_Groups_Ozero__class_Ozero(U_7965)),U_7966))
    | ~ class_Int_Onumber__ring(U_7965)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_7965) ),
    inference(clausify,[status(thm)],[f_2223_2]) ).

fof(f_2224_1,plain,
    ! [V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_zero__le__power2]) ).

fof(f_2224_2,plain,
    ! [U_7968,U_7967] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7967),c_Groups_Ozero__class_Ozero(U_7967)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7967),U_7968),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
      | ~ class_Rings_Olinordered__idom(U_7967) ),
    inference(variable_rename,[status(thm)],[f_2224_1]) ).

cnf(f_2224_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7967),c_Groups_Ozero__class_Ozero(U_7967)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7967),U_7968),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | ~ class_Rings_Olinordered__idom(U_7967) ),
    inference(clausify,[status(thm)],[f_2224_2]) ).

fof(f_2225_1,plain,
    ! [V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power2__le__imp__le]) ).

fof(f_2225_2,plain,
    ! [U_7971,U_7970,U_7969] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7969),U_7970),U_7971))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7969),c_Groups_Ozero__class_Ozero(U_7969)),U_7971))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7969),hAPP(hAPP(c_Power_Opower__class_Opower(U_7969),U_7970),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(U_7969),U_7971),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
      | ~ class_Rings_Olinordered__semidom(U_7969) ),
    inference(variable_rename,[status(thm)],[f_2225_1]) ).

cnf(f_2225_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7969),U_7970),U_7971))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7969),c_Groups_Ozero__class_Ozero(U_7969)),U_7971))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7969),hAPP(hAPP(c_Power_Opower__class_Opower(U_7969),U_7970),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(U_7969),U_7971),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | ~ class_Rings_Olinordered__semidom(U_7969) ),
    inference(clausify,[status(thm)],[f_2225_2]) ).

fof(f_2226_1,plain,
    ! [V_y,V_x,T_a] :
      ( V_x = V_y
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
      | hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power2__eq__imp__eq]) ).

fof(f_2226_2,plain,
    ! [U_7974,U_7973,U_7972] :
      ( U_7973 = U_7974
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7972),c_Groups_Ozero__class_Ozero(U_7972)),U_7974))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7972),c_Groups_Ozero__class_Ozero(U_7972)),U_7973))
      | hAPP(hAPP(c_Power_Opower__class_Opower(U_7972),U_7973),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != hAPP(hAPP(c_Power_Opower__class_Opower(U_7972),U_7974),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
      | ~ class_Rings_Olinordered__semidom(U_7972) ),
    inference(variable_rename,[status(thm)],[f_2226_1]) ).

cnf(f_2226_3,plain,
    ( U_7973 = U_7974
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7972),c_Groups_Ozero__class_Ozero(U_7972)),U_7974))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7972),c_Groups_Ozero__class_Ozero(U_7972)),U_7973))
    | hAPP(hAPP(c_Power_Opower__class_Opower(U_7972),U_7973),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != hAPP(hAPP(c_Power_Opower__class_Opower(U_7972),U_7974),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
    | ~ class_Rings_Olinordered__semidom(U_7972) ),
    inference(clausify,[status(thm)],[f_2226_2]) ).

fof(f_2227_1,plain,
    ! [V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
          | V_a_2 = c_Groups_Ozero__class_Ozero(T_b) )
        & ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) )
      | ~ class_Rings_Olinordered__idom(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_zero__less__power2]) ).

fof(f_2227_2,plain,
    ! [U_7976,U_7975] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7975),c_Groups_Ozero__class_Ozero(U_7975)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7975),U_7976),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
          | U_7976 = c_Groups_Ozero__class_Ozero(U_7975) )
        & ( U_7976 != c_Groups_Ozero__class_Ozero(U_7975)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7975),c_Groups_Ozero__class_Ozero(U_7975)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7975),U_7976),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) )
      | ~ class_Rings_Olinordered__idom(U_7975) ),
    inference(variable_rename,[status(thm)],[f_2227_1]) ).

cnf(f_2227_3,plain,
    ( U_7976 != c_Groups_Ozero__class_Ozero(U_7975)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7975),c_Groups_Ozero__class_Ozero(U_7975)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7975),U_7976),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | ~ class_Rings_Olinordered__idom(U_7975) ),
    inference(clausify,[status(thm)],[f_2227_2]) ).

cnf(f_2227_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7975),c_Groups_Ozero__class_Ozero(U_7975)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7975),U_7976),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | U_7976 = c_Groups_Ozero__class_Ozero(U_7975)
    | ~ class_Rings_Olinordered__idom(U_7975) ),
    inference(clausify,[status(thm)],[f_2227_2]) ).

fof(f_2228_1,plain,
    ! [V_a,T_a] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power2__less__0]) ).

fof(f_2228_2,plain,
    ! [U_7978,U_7977] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7977),hAPP(hAPP(c_Power_Opower__class_Opower(U_7977),U_7978),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(U_7977)))
      | ~ class_Rings_Olinordered__idom(U_7977) ),
    inference(variable_rename,[status(thm)],[f_2228_1]) ).

cnf(f_2228_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7977),hAPP(hAPP(c_Power_Opower__class_Opower(U_7977),U_7978),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(U_7977)))
    | ~ class_Rings_Olinordered__idom(U_7977) ),
    inference(clausify,[status(thm)],[f_2228_2]) ).

fof(f_2229_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(T_b)
          | V_y_2 != c_Groups_Ozero__class_Ozero(T_b)
          | V_x_2 != c_Groups_Ozero__class_Ozero(T_b) )
        & ( ( V_y_2 = c_Groups_Ozero__class_Ozero(T_b)
            & V_x_2 = c_Groups_Ozero__class_Ozero(T_b) )
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(T_b) ) )
      | ~ class_Rings_Olinordered__idom(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sum__power2__eq__zero__iff]) ).

fof(f_2229_2,plain,
    ! [U_7981,U_7980,U_7979] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7979),hAPP(hAPP(c_Power_Opower__class_Opower(U_7979),U_7980),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(U_7979),U_7981),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(U_7979)
          | U_7981 != c_Groups_Ozero__class_Ozero(U_7979)
          | U_7980 != c_Groups_Ozero__class_Ozero(U_7979) )
        & ( ( U_7981 = c_Groups_Ozero__class_Ozero(U_7979)
            & U_7980 = c_Groups_Ozero__class_Ozero(U_7979) )
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7979),hAPP(hAPP(c_Power_Opower__class_Opower(U_7979),U_7980),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(U_7979),U_7981),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(U_7979) ) )
      | ~ class_Rings_Olinordered__idom(U_7979) ),
    inference(variable_rename,[status(thm)],[f_2229_1]) ).

cnf(f_2229_3,plain,
    ( U_7980 = c_Groups_Ozero__class_Ozero(U_7979)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7979),hAPP(hAPP(c_Power_Opower__class_Opower(U_7979),U_7980),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(U_7979),U_7981),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(U_7979)
    | ~ class_Rings_Olinordered__idom(U_7979) ),
    inference(clausify,[status(thm)],[f_2229_2]) ).

cnf(f_2229_4,plain,
    ( U_7981 = c_Groups_Ozero__class_Ozero(U_7979)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7979),hAPP(hAPP(c_Power_Opower__class_Opower(U_7979),U_7980),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(U_7979),U_7981),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(U_7979)
    | ~ class_Rings_Olinordered__idom(U_7979) ),
    inference(clausify,[status(thm)],[f_2229_2]) ).

cnf(f_2229_5,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7979),hAPP(hAPP(c_Power_Opower__class_Opower(U_7979),U_7980),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(U_7979),U_7981),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(U_7979)
    | U_7981 != c_Groups_Ozero__class_Ozero(U_7979)
    | U_7980 != c_Groups_Ozero__class_Ozero(U_7979)
    | ~ class_Rings_Olinordered__idom(U_7979) ),
    inference(clausify,[status(thm)],[f_2229_2]) ).

fof(f_2230_1,plain,
    ! [V_w,T_b] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w))
      | ~ class_Int_Onumber(T_b)
      | ~ class_Groups_Omonoid__mult(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_power2__eq__square__number__of]) ).

fof(f_2230_2,plain,
    ! [U_7983,U_7982] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_7982),hAPP(c_Int_Onumber__class_Onumber__of(U_7982),U_7983)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7982),hAPP(c_Int_Onumber__class_Onumber__of(U_7982),U_7983)),hAPP(c_Int_Onumber__class_Onumber__of(U_7982),U_7983))
      | ~ class_Int_Onumber(U_7982)
      | ~ class_Groups_Omonoid__mult(U_7982) ),
    inference(variable_rename,[status(thm)],[f_2230_1]) ).

cnf(f_2230_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_7982),hAPP(c_Int_Onumber__class_Onumber__of(U_7982),U_7983)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7982),hAPP(c_Int_Onumber__class_Onumber__of(U_7982),U_7983)),hAPP(c_Int_Onumber__class_Onumber__of(U_7982),U_7983))
    | ~ class_Int_Onumber(U_7982)
    | ~ class_Groups_Omonoid__mult(U_7982) ),
    inference(clausify,[status(thm)],[f_2230_2]) ).

fof(f_2231_1,plain,
    ! [V_n] :
      ( V_n = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
      | V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
    inference(fof_nnf,[status(thm)],[fact_less__2__cases]) ).

fof(f_2231_2,plain,
    ! [U_7984] :
      ( U_7984 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
      | U_7984 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7984),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
    inference(variable_rename,[status(thm)],[f_2231_1]) ).

cnf(f_2231_3,plain,
    ( U_7984 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | U_7984 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7984),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
    inference(clausify,[status(thm)],[f_2231_2]) ).

fof(f_2232_1,plain,
    hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(fof_nnf,[status(thm)],[fact_nat__2]) ).

cnf(f_2232_2,plain,
    hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_2232_1]) ).

fof(f_2233_1,plain,
    ! [V_a_2,T_b] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(T_b)
          | ( V_a_2 != hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b))
            & V_a_2 != c_Groups_Oone__class_Oone(T_b) ) )
        & ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b))
          | V_a_2 = c_Groups_Oone__class_Oone(T_b)
          | hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Oone__class_Oone(T_b) ) )
      | ~ class_Rings_Oring__1__no__zero__divisors(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_power2__eq__1__iff]) ).

fof(f_2233_2,plain,
    ! [U_7986,U_7985] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_7985),U_7986),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(U_7985)
          | ( U_7986 != hAPP(c_Groups_Ouminus__class_Ouminus(U_7985),c_Groups_Oone__class_Oone(U_7985))
            & U_7986 != c_Groups_Oone__class_Oone(U_7985) ) )
        & ( U_7986 = hAPP(c_Groups_Ouminus__class_Ouminus(U_7985),c_Groups_Oone__class_Oone(U_7985))
          | U_7986 = c_Groups_Oone__class_Oone(U_7985)
          | hAPP(hAPP(c_Power_Opower__class_Opower(U_7985),U_7986),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Oone__class_Oone(U_7985) ) )
      | ~ class_Rings_Oring__1__no__zero__divisors(U_7985) ),
    inference(variable_rename,[status(thm)],[f_2233_1]) ).

cnf(f_2233_3,plain,
    ( U_7986 = hAPP(c_Groups_Ouminus__class_Ouminus(U_7985),c_Groups_Oone__class_Oone(U_7985))
    | U_7986 = c_Groups_Oone__class_Oone(U_7985)
    | hAPP(hAPP(c_Power_Opower__class_Opower(U_7985),U_7986),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Oone__class_Oone(U_7985)
    | ~ class_Rings_Oring__1__no__zero__divisors(U_7985) ),
    inference(clausify,[status(thm)],[f_2233_2]) ).

cnf(f_2233_4,plain,
    ( U_7986 != c_Groups_Oone__class_Oone(U_7985)
    | hAPP(hAPP(c_Power_Opower__class_Opower(U_7985),U_7986),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(U_7985)
    | ~ class_Rings_Oring__1__no__zero__divisors(U_7985) ),
    inference(clausify,[status(thm)],[f_2233_2]) ).

cnf(f_2233_5,plain,
    ( U_7986 != hAPP(c_Groups_Ouminus__class_Ouminus(U_7985),c_Groups_Oone__class_Oone(U_7985))
    | hAPP(hAPP(c_Power_Opower__class_Opower(U_7985),U_7986),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(U_7985)
    | ~ class_Rings_Oring__1__no__zero__divisors(U_7985) ),
    inference(clausify,[status(thm)],[f_2233_2]) ).

fof(f_2234_1,plain,
    ! [V_n,V_x,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J]) ).

fof(f_2234_2,plain,
    ! [U_7989,U_7988,U_7987] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_7987),U_7988),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_7989)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7987),hAPP(hAPP(c_Power_Opower__class_Opower(U_7987),U_7988),U_7989)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7987),U_7988),U_7989))
      | ~ class_Rings_Ocomm__semiring__1(U_7987) ),
    inference(variable_rename,[status(thm)],[f_2234_1]) ).

cnf(f_2234_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_7987),U_7988),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_7989)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7987),hAPP(hAPP(c_Power_Opower__class_Opower(U_7987),U_7988),U_7989)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7987),U_7988),U_7989))
    | ~ class_Rings_Ocomm__semiring__1(U_7987) ),
    inference(clausify,[status(thm)],[f_2234_2]) ).

fof(f_2235_1,plain,
    ! [V_n,V_a,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))
      | ~ class_Rings_Oring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__minus__even]) ).

fof(f_2235_2,plain,
    ! [U_7992,U_7991,U_7990] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_7990),hAPP(c_Groups_Ouminus__class_Ouminus(U_7990),U_7991)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_7992)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_7990),U_7991),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_7992))
      | ~ class_Rings_Oring__1(U_7990) ),
    inference(variable_rename,[status(thm)],[f_2235_1]) ).

cnf(f_2235_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_7990),hAPP(c_Groups_Ouminus__class_Ouminus(U_7990),U_7991)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_7992)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_7990),U_7991),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_7992))
    | ~ class_Rings_Oring__1(U_7990) ),
    inference(clausify,[status(thm)],[f_2235_2]) ).

fof(f_2236_1,plain,
    ! [V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power2__less__imp__less]) ).

fof(f_2236_2,plain,
    ! [U_7995,U_7994,U_7993] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7993),U_7994),U_7995))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7993),c_Groups_Ozero__class_Ozero(U_7993)),U_7995))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7993),hAPP(hAPP(c_Power_Opower__class_Opower(U_7993),U_7994),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(U_7993),U_7995),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
      | ~ class_Rings_Olinordered__semidom(U_7993) ),
    inference(variable_rename,[status(thm)],[f_2236_1]) ).

cnf(f_2236_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7993),U_7994),U_7995))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7993),c_Groups_Ozero__class_Ozero(U_7993)),U_7995))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7993),hAPP(hAPP(c_Power_Opower__class_Opower(U_7993),U_7994),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(U_7993),U_7995),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | ~ class_Rings_Olinordered__semidom(U_7993) ),
    inference(clausify,[status(thm)],[f_2236_2]) ).

fof(f_2237_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(T_b)))
          | V_y_2 != c_Groups_Ozero__class_Ozero(T_b)
          | V_x_2 != c_Groups_Ozero__class_Ozero(T_b) )
        & ( ( V_y_2 = c_Groups_Ozero__class_Ozero(T_b)
            & V_x_2 = c_Groups_Ozero__class_Ozero(T_b) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(T_b))) ) )
      | ~ class_Rings_Olinordered__idom(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sum__power2__le__zero__iff]) ).

fof(f_2237_2,plain,
    ! [U_7998,U_7997,U_7996] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7996),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7996),hAPP(hAPP(c_Power_Opower__class_Opower(U_7996),U_7997),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(U_7996),U_7998),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(U_7996)))
          | U_7998 != c_Groups_Ozero__class_Ozero(U_7996)
          | U_7997 != c_Groups_Ozero__class_Ozero(U_7996) )
        & ( ( U_7998 = c_Groups_Ozero__class_Ozero(U_7996)
            & U_7997 = c_Groups_Ozero__class_Ozero(U_7996) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7996),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7996),hAPP(hAPP(c_Power_Opower__class_Opower(U_7996),U_7997),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(U_7996),U_7998),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(U_7996))) ) )
      | ~ class_Rings_Olinordered__idom(U_7996) ),
    inference(variable_rename,[status(thm)],[f_2237_1]) ).

cnf(f_2237_3,plain,
    ( U_7997 = c_Groups_Ozero__class_Ozero(U_7996)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7996),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7996),hAPP(hAPP(c_Power_Opower__class_Opower(U_7996),U_7997),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(U_7996),U_7998),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(U_7996)))
    | ~ class_Rings_Olinordered__idom(U_7996) ),
    inference(clausify,[status(thm)],[f_2237_2]) ).

cnf(f_2237_4,plain,
    ( U_7998 = c_Groups_Ozero__class_Ozero(U_7996)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7996),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7996),hAPP(hAPP(c_Power_Opower__class_Opower(U_7996),U_7997),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(U_7996),U_7998),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(U_7996)))
    | ~ class_Rings_Olinordered__idom(U_7996) ),
    inference(clausify,[status(thm)],[f_2237_2]) ).

cnf(f_2237_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7996),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7996),hAPP(hAPP(c_Power_Opower__class_Opower(U_7996),U_7997),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(U_7996),U_7998),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(U_7996)))
    | U_7998 != c_Groups_Ozero__class_Ozero(U_7996)
    | U_7997 != c_Groups_Ozero__class_Ozero(U_7996)
    | ~ class_Rings_Olinordered__idom(U_7996) ),
    inference(clausify,[status(thm)],[f_2237_2]) ).

fof(f_2238_1,plain,
    ! [V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sum__power2__ge__zero]) ).

fof(f_2238_2,plain,
    ! [U_8001,U_8000,U_7999] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7999),c_Groups_Ozero__class_Ozero(U_7999)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7999),hAPP(hAPP(c_Power_Opower__class_Opower(U_7999),U_8000),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(U_7999),U_8001),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
      | ~ class_Rings_Olinordered__idom(U_7999) ),
    inference(variable_rename,[status(thm)],[f_2238_1]) ).

cnf(f_2238_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7999),c_Groups_Ozero__class_Ozero(U_7999)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7999),hAPP(hAPP(c_Power_Opower__class_Opower(U_7999),U_8000),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(U_7999),U_8001),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
    | ~ class_Rings_Olinordered__idom(U_7999) ),
    inference(clausify,[status(thm)],[f_2238_2]) ).

fof(f_2239_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
          | ( V_y_2 = c_Groups_Ozero__class_Ozero(T_b)
            & V_x_2 = c_Groups_Ozero__class_Ozero(T_b) ) )
        & ( V_y_2 != c_Groups_Ozero__class_Ozero(T_b)
          | V_x_2 != c_Groups_Ozero__class_Ozero(T_b)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) ) )
      | ~ class_Rings_Olinordered__idom(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sum__power2__gt__zero__iff]) ).

fof(f_2239_2,plain,
    ! [U_8004,U_8003,U_8002] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8002),c_Groups_Ozero__class_Ozero(U_8002)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8002),hAPP(hAPP(c_Power_Opower__class_Opower(U_8002),U_8003),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(U_8002),U_8004),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
          | ( U_8004 = c_Groups_Ozero__class_Ozero(U_8002)
            & U_8003 = c_Groups_Ozero__class_Ozero(U_8002) ) )
        & ( U_8004 != c_Groups_Ozero__class_Ozero(U_8002)
          | U_8003 != c_Groups_Ozero__class_Ozero(U_8002)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8002),c_Groups_Ozero__class_Ozero(U_8002)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8002),hAPP(hAPP(c_Power_Opower__class_Opower(U_8002),U_8003),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(U_8002),U_8004),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) ) )
      | ~ class_Rings_Olinordered__idom(U_8002) ),
    inference(variable_rename,[status(thm)],[f_2239_1]) ).

cnf(f_2239_3,plain,
    ( U_8004 != c_Groups_Ozero__class_Ozero(U_8002)
    | U_8003 != c_Groups_Ozero__class_Ozero(U_8002)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8002),c_Groups_Ozero__class_Ozero(U_8002)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8002),hAPP(hAPP(c_Power_Opower__class_Opower(U_8002),U_8003),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(U_8002),U_8004),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
    | ~ class_Rings_Olinordered__idom(U_8002) ),
    inference(clausify,[status(thm)],[f_2239_2]) ).

cnf(f_2239_4,plain,
    ( U_8003 = c_Groups_Ozero__class_Ozero(U_8002)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8002),c_Groups_Ozero__class_Ozero(U_8002)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8002),hAPP(hAPP(c_Power_Opower__class_Opower(U_8002),U_8003),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(U_8002),U_8004),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
    | ~ class_Rings_Olinordered__idom(U_8002) ),
    inference(clausify,[status(thm)],[f_2239_2]) ).

cnf(f_2239_5,plain,
    ( U_8004 = c_Groups_Ozero__class_Ozero(U_8002)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8002),c_Groups_Ozero__class_Ozero(U_8002)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8002),hAPP(hAPP(c_Power_Opower__class_Opower(U_8002),U_8003),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(U_8002),U_8004),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
    | ~ class_Rings_Olinordered__idom(U_8002) ),
    inference(clausify,[status(thm)],[f_2239_2]) ).

fof(f_2240_1,plain,
    ! [V_y,V_x,T_a] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_not__sum__power2__lt__zero]) ).

fof(f_2240_2,plain,
    ! [U_8007,U_8006,U_8005] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8005),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8005),hAPP(hAPP(c_Power_Opower__class_Opower(U_8005),U_8006),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(U_8005),U_8007),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(U_8005)))
      | ~ class_Rings_Olinordered__idom(U_8005) ),
    inference(variable_rename,[status(thm)],[f_2240_1]) ).

cnf(f_2240_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8005),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8005),hAPP(hAPP(c_Power_Opower__class_Opower(U_8005),U_8006),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(U_8005),U_8007),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(U_8005)))
    | ~ class_Rings_Olinordered__idom(U_8005) ),
    inference(clausify,[status(thm)],[f_2240_2]) ).

fof(f_2241_1,plain,
    ! [V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x)),V_y))
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power2__sum]) ).

fof(f_2241_2,plain,
    ! [U_8010,U_8009,U_8008] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_8008),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8008),U_8009),U_8010)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8008),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8008),hAPP(hAPP(c_Power_Opower__class_Opower(U_8008),U_8009),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(U_8008),U_8010),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8008),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8008),hAPP(c_Int_Onumber__class_Onumber__of(U_8008),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_8009)),U_8010))
      | ~ class_Int_Onumber__ring(U_8008) ),
    inference(variable_rename,[status(thm)],[f_2241_1]) ).

cnf(f_2241_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_8008),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8008),U_8009),U_8010)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8008),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8008),hAPP(hAPP(c_Power_Opower__class_Opower(U_8008),U_8009),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(U_8008),U_8010),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8008),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8008),hAPP(c_Int_Onumber__class_Onumber__of(U_8008),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_8009)),U_8010))
    | ~ class_Int_Onumber__ring(U_8008) ),
    inference(clausify,[status(thm)],[f_2241_2]) ).

fof(f_2242_1,plain,
    ! [V_n,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))))
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_zero__le__even__power_H]) ).

fof(f_2242_2,plain,
    ! [U_8013,U_8012,U_8011] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8011),c_Groups_Ozero__class_Ozero(U_8011)),hAPP(hAPP(c_Power_Opower__class_Opower(U_8011),U_8012),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_8013))))
      | ~ class_Rings_Olinordered__idom(U_8011) ),
    inference(variable_rename,[status(thm)],[f_2242_1]) ).

cnf(f_2242_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8011),c_Groups_Ozero__class_Ozero(U_8011)),hAPP(hAPP(c_Power_Opower__class_Opower(U_8011),U_8012),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_8013))))
    | ~ class_Rings_Olinordered__idom(U_8011) ),
    inference(clausify,[status(thm)],[f_2242_2]) ).

fof(f_2243_1,plain,
    ! [V_n,V_x,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J]) ).

fof(f_2243_2,plain,
    ! [U_8016,U_8015,U_8014] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_8014),U_8015),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_8016))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8014),U_8015),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8014),hAPP(hAPP(c_Power_Opower__class_Opower(U_8014),U_8015),U_8016)),hAPP(hAPP(c_Power_Opower__class_Opower(U_8014),U_8015),U_8016)))
      | ~ class_Rings_Ocomm__semiring__1(U_8014) ),
    inference(variable_rename,[status(thm)],[f_2243_1]) ).

cnf(f_2243_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_8014),U_8015),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_8016))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8014),U_8015),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8014),hAPP(hAPP(c_Power_Opower__class_Opower(U_8014),U_8015),U_8016)),hAPP(hAPP(c_Power_Opower__class_Opower(U_8014),U_8015),U_8016)))
    | ~ class_Rings_Ocomm__semiring__1(U_8014) ),
    inference(clausify,[status(thm)],[f_2243_2]) ).

fof(f_2244_1,plain,
    ! [V_n,V_a,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
      | ~ class_Groups_Omonoid__mult(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__odd__eq]) ).

fof(f_2244_2,plain,
    ! [U_8019,U_8018,U_8017] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_8017),U_8018),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_8019))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8017),U_8018),hAPP(hAPP(c_Power_Opower__class_Opower(U_8017),hAPP(hAPP(c_Power_Opower__class_Opower(U_8017),U_8018),U_8019)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
      | ~ class_Groups_Omonoid__mult(U_8017) ),
    inference(variable_rename,[status(thm)],[f_2244_1]) ).

cnf(f_2244_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_8017),U_8018),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_8019))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8017),U_8018),hAPP(hAPP(c_Power_Opower__class_Opower(U_8017),hAPP(hAPP(c_Power_Opower__class_Opower(U_8017),U_8018),U_8019)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
    | ~ class_Groups_Omonoid__mult(U_8017) ),
    inference(clausify,[status(thm)],[f_2244_2]) ).

fof(f_2245_1,plain,
    ! [V_n,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = c_Groups_Oone__class_Oone(T_a)
      | ~ class_Rings_Oring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__minus1__even]) ).

fof(f_2245_2,plain,
    ! [U_8021,U_8020] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_8020),hAPP(c_Groups_Ouminus__class_Ouminus(U_8020),c_Groups_Oone__class_Oone(U_8020))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_8021)) = c_Groups_Oone__class_Oone(U_8020)
      | ~ class_Rings_Oring__1(U_8020) ),
    inference(variable_rename,[status(thm)],[f_2245_1]) ).

cnf(f_2245_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_8020),hAPP(c_Groups_Ouminus__class_Ouminus(U_8020),c_Groups_Oone__class_Oone(U_8020))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_8021)) = c_Groups_Oone__class_Oone(U_8020)
    | ~ class_Rings_Oring__1(U_8020) ),
    inference(clausify,[status(thm)],[f_2245_2]) ).

fof(f_2246_1,plain,
    ! [V_v,V_w] :
      ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_v))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) )
      & ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_v))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) ) ),
    inference(fof_nnf,[status(thm)],[fact_zdiv__number__of__Bit1]) ).

fof(f_2246_2,plain,
    ! [U_8023,U_8022] :
      ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_8023))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_8022))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8023)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8022))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8022))) )
      & ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_8023))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_8022))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8023)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8022))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8022))) ) ),
    inference(variable_rename,[status(thm)],[f_2246_1]) ).

fof(f_2246_3,plain,
    ( ! [U_8027,U_8025] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_8027))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_8025))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8027)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8025))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8025))) )
    & ! [U_8026,U_8024] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_8026))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_8024))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8026)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8024))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8024))) ) ),
    inference(miniscope,[status(thm)],[f_2246_2]) ).

cnf(f_2246_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_8026))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_8024))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8026)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8024))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8024))) ),
    inference(clausify,[status(thm)],[f_2246_3]) ).

cnf(f_2246_5,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_8027))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_8025))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8027)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8025))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8025))) ),
    inference(clausify,[status(thm)],[f_2246_3]) ).

fof(f_2247_1,plain,
    ! [V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_div__2__gt__zero]) ).

fof(f_2247_2,plain,
    ! [U_8028] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_8028),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_8028)) ),
    inference(variable_rename,[status(thm)],[f_2247_1]) ).

cnf(f_2247_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_8028),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_8028)) ),
    inference(clausify,[status(thm)],[f_2247_2]) ).

fof(f_2248_1,plain,
    ! [V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_y)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x)),V_y))
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power2__diff]) ).

fof(f_2248_2,plain,
    ! [U_8031,U_8030,U_8029] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_8029),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8029),U_8030),U_8031)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8029),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8029),hAPP(hAPP(c_Power_Opower__class_Opower(U_8029),U_8030),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(U_8029),U_8031),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8029),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8029),hAPP(c_Int_Onumber__class_Onumber__of(U_8029),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_8030)),U_8031))
      | ~ class_Int_Onumber__ring(U_8029) ),
    inference(variable_rename,[status(thm)],[f_2248_1]) ).

cnf(f_2248_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_8029),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8029),U_8030),U_8031)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8029),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8029),hAPP(hAPP(c_Power_Opower__class_Opower(U_8029),U_8030),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(U_8029),U_8031),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8029),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8029),hAPP(c_Int_Onumber__class_Onumber__of(U_8029),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_8030)),U_8031))
    | ~ class_Int_Onumber__ring(U_8029) ),
    inference(clausify,[status(thm)],[f_2248_2]) ).

fof(f_2249_1,plain,
    ! [V_n,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)))))
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_odd__0__le__power__imp__0__le]) ).

fof(f_2249_2,plain,
    ! [U_8034,U_8033,U_8032] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8032),c_Groups_Ozero__class_Ozero(U_8032)),U_8033))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8032),c_Groups_Ozero__class_Ozero(U_8032)),hAPP(hAPP(c_Power_Opower__class_Opower(U_8032),U_8033),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_8034)))))
      | ~ class_Rings_Olinordered__idom(U_8032) ),
    inference(variable_rename,[status(thm)],[f_2249_1]) ).

cnf(f_2249_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8032),c_Groups_Ozero__class_Ozero(U_8032)),U_8033))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8032),c_Groups_Ozero__class_Ozero(U_8032)),hAPP(hAPP(c_Power_Opower__class_Opower(U_8032),U_8033),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_8034)))))
    | ~ class_Rings_Olinordered__idom(U_8032) ),
    inference(clausify,[status(thm)],[f_2249_2]) ).

fof(f_2250_1,plain,
    ! [V_n,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)))),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_odd__power__less__zero]) ).

fof(f_2250_2,plain,
    ! [U_8037,U_8036,U_8035] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8035),hAPP(hAPP(c_Power_Opower__class_Opower(U_8035),U_8036),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_8037)))),c_Groups_Ozero__class_Ozero(U_8035)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8035),U_8036),c_Groups_Ozero__class_Ozero(U_8035)))
      | ~ class_Rings_Olinordered__idom(U_8035) ),
    inference(variable_rename,[status(thm)],[f_2250_1]) ).

cnf(f_2250_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8035),hAPP(hAPP(c_Power_Opower__class_Opower(U_8035),U_8036),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_8037)))),c_Groups_Ozero__class_Ozero(U_8035)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8035),U_8036),c_Groups_Ozero__class_Ozero(U_8035)))
    | ~ class_Rings_Olinordered__idom(U_8035) ),
    inference(clausify,[status(thm)],[f_2250_2]) ).

fof(f_2251_1,plain,
    ! [V_B_2,V_A_2] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2)))
      | ~ c_Nat__Transfer_Onat__set(V_B_2)
      | ~ c_Nat__Transfer_Onat__set(V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J]) ).

fof(f_2251_2,plain,
    ! [U_8039,U_8038] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_8038),U_8039) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8038)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8039)))
      | ~ c_Nat__Transfer_Onat__set(U_8039)
      | ~ c_Nat__Transfer_Onat__set(U_8038) ),
    inference(variable_rename,[status(thm)],[f_2251_1]) ).

cnf(f_2251_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_8038),U_8039) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8038)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8039)))
    | ~ c_Nat__Transfer_Onat__set(U_8039)
    | ~ c_Nat__Transfer_Onat__set(U_8038) ),
    inference(clausify,[status(thm)],[f_2251_2]) ).

fof(f_2252_1,plain,
    ! [V_B_2,V_A_2] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2)))
      | ~ c_Nat__Transfer_Onat__set(V_B_2)
      | ~ c_Nat__Transfer_Onat__set(V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J]) ).

fof(f_2252_2,plain,
    ! [U_8041,U_8040] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_8040),U_8041) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8040)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8041)))
      | ~ c_Nat__Transfer_Onat__set(U_8041)
      | ~ c_Nat__Transfer_Onat__set(U_8040) ),
    inference(variable_rename,[status(thm)],[f_2252_1]) ).

cnf(f_2252_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_8040),U_8041) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8040)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8041)))
    | ~ c_Nat__Transfer_Onat__set(U_8041)
    | ~ c_Nat__Transfer_Onat__set(U_8040) ),
    inference(clausify,[status(thm)],[f_2252_2]) ).

fof(f_2253_1,plain,
    ! [V_v,V_w] :
      ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))),c_Groups_Oone__class_Oone(tc_Int_Oint))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) )
      & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))),c_Groups_Oone__class_Oone(tc_Int_Oint))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) ) ),
    inference(fof_nnf,[status(thm)],[fact_zmod__number__of__Bit1]) ).

fof(f_2253_2,plain,
    ! [U_8043,U_8042] :
      ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_8043)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_8042))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8043)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8042)))),c_Groups_Oone__class_Oone(tc_Int_Oint))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8042))) )
      & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_8043)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_8042))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8043),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8042)))),c_Groups_Oone__class_Oone(tc_Int_Oint))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8042))) ) ),
    inference(variable_rename,[status(thm)],[f_2253_1]) ).

fof(f_2253_3,plain,
    ( ! [U_8047,U_8045] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_8047)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_8045))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8047)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8045)))),c_Groups_Oone__class_Oone(tc_Int_Oint))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8045))) )
    & ! [U_8046,U_8044] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_8046)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_8044))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8046),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8044)))),c_Groups_Oone__class_Oone(tc_Int_Oint))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8044))) ) ),
    inference(miniscope,[status(thm)],[f_2253_2]) ).

cnf(f_2253_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_8046)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_8044))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8046),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8044)))),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8044))) ),
    inference(clausify,[status(thm)],[f_2253_3]) ).

cnf(f_2253_5,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_8047)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_8045))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8047)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8045)))),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8045))) ),
    inference(clausify,[status(thm)],[f_2253_3]) ).

fof(f_2254_1,plain,
    ! [V_b,V_a] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_b),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_a))),c_Groups_Oone__class_Oone(tc_Int_Oint))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(fof_nnf,[status(thm)],[fact_neg__zmod__mult__2]) ).

fof(f_2254_2,plain,
    ! [U_8049,U_8048] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_8049)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_8048)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8049),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_8048))),c_Groups_Oone__class_Oone(tc_Int_Oint))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8048),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_2254_1]) ).

cnf(f_2254_3,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_8049)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_8048)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8049),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_8048))),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8048),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2254_2]) ).

fof(f_2255_1,plain,
    ! [V_b,V_a] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) ),
    inference(fof_nnf,[status(thm)],[fact_pos__zmod__mult__2]) ).

fof(f_2255_2,plain,
    ! [U_8051,U_8050] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_8051)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_8050)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8051,U_8050)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8050)) ),
    inference(variable_rename,[status(thm)],[f_2255_1]) ).

cnf(f_2255_3,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_8051)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_8050)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8051,U_8050)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8050)) ),
    inference(clausify,[status(thm)],[f_2255_2]) ).

fof(f_2256_1,plain,
    ! [V_c,V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c)),V_c) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b),V_c),
    inference(fof_nnf,[status(thm)],[fact_zmod__simps_I3_J]) ).

fof(f_2256_2,plain,
    ! [U_8054,U_8053,U_8052] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8052),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8053,U_8054)),U_8054) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8052),U_8053),U_8054),
    inference(variable_rename,[status(thm)],[f_2256_1]) ).

cnf(f_2256_3,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8052),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8053,U_8054)),U_8054) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8052),U_8053),U_8054),
    inference(clausify,[status(thm)],[f_2256_2]) ).

fof(f_2257_1,plain,
    ! [V_c,V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c)),V_c),
    inference(fof_nnf,[status(thm)],[fact_zmod__zmult1__eq]) ).

fof(f_2257_2,plain,
    ! [U_8057,U_8056,U_8055] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8055),U_8056),U_8057) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8055),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8056,U_8057)),U_8057),
    inference(variable_rename,[status(thm)],[f_2257_1]) ).

cnf(f_2257_3,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8055),U_8056),U_8057) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8055),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8056,U_8057)),U_8057),
    inference(clausify,[status(thm)],[f_2257_2]) ).

fof(f_2258_1,plain,
    ! [V_y,V_m,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_m)),V_y),V_m) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y),V_m),
    inference(fof_nnf,[status(thm)],[fact_zdiff__zmod__left]) ).

fof(f_2258_2,plain,
    ! [U_8060,U_8059,U_8058] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8058,U_8059)),U_8060),U_8059) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8058),U_8060),U_8059),
    inference(variable_rename,[status(thm)],[f_2258_1]) ).

cnf(f_2258_3,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8058,U_8059)),U_8060),U_8059) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8058),U_8060),U_8059),
    inference(clausify,[status(thm)],[f_2258_2]) ).

fof(f_2259_1,plain,
    ! [V_m,V_y,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_y,V_m)),V_m) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y),V_m),
    inference(fof_nnf,[status(thm)],[fact_zdiff__zmod__right]) ).

fof(f_2259_2,plain,
    ! [U_8063,U_8062,U_8061] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8061),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8062,U_8063)),U_8063) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8061),U_8062),U_8063),
    inference(variable_rename,[status(thm)],[f_2259_1]) ).

cnf(f_2259_3,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8061),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8062,U_8063)),U_8063) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8061),U_8062),U_8063),
    inference(clausify,[status(thm)],[f_2259_2]) ).

fof(f_2260_1,plain,
    ! [V_m,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_m)),V_m) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_x),V_m),
    inference(fof_nnf,[status(thm)],[fact_zminus__zmod]) ).

fof(f_2260_2,plain,
    ! [U_8065,U_8064] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8064,U_8065)),U_8065) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8064),U_8065),
    inference(variable_rename,[status(thm)],[f_2260_1]) ).

cnf(f_2260_3,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8064,U_8065)),U_8065) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8064),U_8065),
    inference(clausify,[status(thm)],[f_2260_2]) ).

fof(f_2261_1,plain,
    ! [V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),
    inference(fof_nnf,[status(thm)],[fact_zmod__zminus__zminus]) ).

fof(f_2261_2,plain,
    ! [U_8067,U_8066] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8066),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8067)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8066,U_8067)),
    inference(variable_rename,[status(thm)],[f_2261_1]) ).

cnf(f_2261_3,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8066),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8067)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8066,U_8067)),
    inference(clausify,[status(thm)],[f_2261_2]) ).

fof(f_2262_1,plain,
    ! [V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),V_b)),
    inference(fof_nnf,[status(thm)],[fact_zmod__zminus2]) ).

fof(f_2262_2,plain,
    ! [U_8069,U_8068] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8068,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8069)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8068),U_8069)),
    inference(variable_rename,[status(thm)],[f_2262_1]) ).

cnf(f_2262_3,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8068,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8069)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8068),U_8069)),
    inference(clausify,[status(thm)],[f_2262_2]) ).

fof(f_2263_1,plain,
    ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
      ( c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_H),V_b_H),V_c)
      | c_Divides_Odiv__class_Omod(T_a,V_b,V_c) != c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
      | c_Divides_Odiv__class_Omod(T_a,V_a,V_c) != c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
      | ~ class_Divides_Oring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mod__diff__cong]) ).

fof(f_2263_2,plain,
    ! [U_8075,U_8074,U_8073,U_8072,U_8071,U_8070] :
      ( c_Divides_Odiv__class_Omod(U_8070,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8070),U_8071),U_8074),U_8072) = c_Divides_Odiv__class_Omod(U_8070,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8070),U_8073),U_8075),U_8072)
      | c_Divides_Odiv__class_Omod(U_8070,U_8074,U_8072) != c_Divides_Odiv__class_Omod(U_8070,U_8075,U_8072)
      | c_Divides_Odiv__class_Omod(U_8070,U_8071,U_8072) != c_Divides_Odiv__class_Omod(U_8070,U_8073,U_8072)
      | ~ class_Divides_Oring__div(U_8070) ),
    inference(variable_rename,[status(thm)],[f_2263_1]) ).

cnf(f_2263_3,plain,
    ( c_Divides_Odiv__class_Omod(U_8070,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8070),U_8071),U_8074),U_8072) = c_Divides_Odiv__class_Omod(U_8070,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8070),U_8073),U_8075),U_8072)
    | c_Divides_Odiv__class_Omod(U_8070,U_8074,U_8072) != c_Divides_Odiv__class_Omod(U_8070,U_8075,U_8072)
    | c_Divides_Odiv__class_Omod(U_8070,U_8071,U_8072) != c_Divides_Odiv__class_Omod(U_8070,U_8073,U_8072)
    | ~ class_Divides_Oring__div(U_8070) ),
    inference(clausify,[status(thm)],[f_2263_2]) ).

fof(f_2264_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c)
      | ~ class_Divides_Oring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mod__diff__eq]) ).

fof(f_2264_2,plain,
    ! [U_8079,U_8078,U_8077,U_8076] :
      ( c_Divides_Odiv__class_Omod(U_8076,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8076),U_8077),U_8078),U_8079) = c_Divides_Odiv__class_Omod(U_8076,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8076),c_Divides_Odiv__class_Omod(U_8076,U_8077,U_8079)),c_Divides_Odiv__class_Omod(U_8076,U_8078,U_8079)),U_8079)
      | ~ class_Divides_Oring__div(U_8076) ),
    inference(variable_rename,[status(thm)],[f_2264_1]) ).

cnf(f_2264_3,plain,
    ( c_Divides_Odiv__class_Omod(U_8076,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8076),U_8077),U_8078),U_8079) = c_Divides_Odiv__class_Omod(U_8076,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8076),c_Divides_Odiv__class_Omod(U_8076,U_8077,U_8079)),c_Divides_Odiv__class_Omod(U_8076,U_8078,U_8079)),U_8079)
    | ~ class_Divides_Oring__div(U_8076) ),
    inference(clausify,[status(thm)],[f_2264_2]) ).

fof(f_2265_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c)
      | ~ class_Divides_Oring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mod__diff__left__eq]) ).

fof(f_2265_2,plain,
    ! [U_8083,U_8082,U_8081,U_8080] :
      ( c_Divides_Odiv__class_Omod(U_8080,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8080),U_8081),U_8082),U_8083) = c_Divides_Odiv__class_Omod(U_8080,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8080),c_Divides_Odiv__class_Omod(U_8080,U_8081,U_8083)),U_8082),U_8083)
      | ~ class_Divides_Oring__div(U_8080) ),
    inference(variable_rename,[status(thm)],[f_2265_1]) ).

cnf(f_2265_3,plain,
    ( c_Divides_Odiv__class_Omod(U_8080,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8080),U_8081),U_8082),U_8083) = c_Divides_Odiv__class_Omod(U_8080,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8080),c_Divides_Odiv__class_Omod(U_8080,U_8081,U_8083)),U_8082),U_8083)
    | ~ class_Divides_Oring__div(U_8080) ),
    inference(clausify,[status(thm)],[f_2265_2]) ).

fof(f_2266_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c)
      | ~ class_Divides_Oring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mod__diff__right__eq]) ).

fof(f_2266_2,plain,
    ! [U_8087,U_8086,U_8085,U_8084] :
      ( c_Divides_Odiv__class_Omod(U_8084,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8084),U_8085),U_8086),U_8087) = c_Divides_Odiv__class_Omod(U_8084,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8084),U_8085),c_Divides_Odiv__class_Omod(U_8084,U_8086,U_8087)),U_8087)
      | ~ class_Divides_Oring__div(U_8084) ),
    inference(variable_rename,[status(thm)],[f_2266_1]) ).

cnf(f_2266_3,plain,
    ( c_Divides_Odiv__class_Omod(U_8084,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8084),U_8085),U_8086),U_8087) = c_Divides_Odiv__class_Omod(U_8084,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8084),U_8085),c_Divides_Odiv__class_Omod(U_8084,U_8086,U_8087)),U_8087)
    | ~ class_Divides_Oring__div(U_8084) ),
    inference(clausify,[status(thm)],[f_2266_2]) ).

fof(f_2267_1,plain,
    ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
      ( c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_H),V_b_H),V_c)
      | c_Divides_Odiv__class_Omod(T_a,V_b,V_c) != c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
      | c_Divides_Odiv__class_Omod(T_a,V_a,V_c) != c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mod__add__cong]) ).

fof(f_2267_2,plain,
    ! [U_8093,U_8092,U_8091,U_8090,U_8089,U_8088] :
      ( c_Divides_Odiv__class_Omod(U_8088,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8088),U_8089),U_8092),U_8090) = c_Divides_Odiv__class_Omod(U_8088,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8088),U_8091),U_8093),U_8090)
      | c_Divides_Odiv__class_Omod(U_8088,U_8092,U_8090) != c_Divides_Odiv__class_Omod(U_8088,U_8093,U_8090)
      | c_Divides_Odiv__class_Omod(U_8088,U_8089,U_8090) != c_Divides_Odiv__class_Omod(U_8088,U_8091,U_8090)
      | ~ class_Divides_Osemiring__div(U_8088) ),
    inference(variable_rename,[status(thm)],[f_2267_1]) ).

cnf(f_2267_3,plain,
    ( c_Divides_Odiv__class_Omod(U_8088,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8088),U_8089),U_8092),U_8090) = c_Divides_Odiv__class_Omod(U_8088,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8088),U_8091),U_8093),U_8090)
    | c_Divides_Odiv__class_Omod(U_8088,U_8092,U_8090) != c_Divides_Odiv__class_Omod(U_8088,U_8093,U_8090)
    | c_Divides_Odiv__class_Omod(U_8088,U_8089,U_8090) != c_Divides_Odiv__class_Omod(U_8088,U_8091,U_8090)
    | ~ class_Divides_Osemiring__div(U_8088) ),
    inference(clausify,[status(thm)],[f_2267_2]) ).

fof(f_2268_1,plain,
    ! [V_b,V_c,V_a,T_a] :
      ( c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_zmod__simps_I1_J]) ).

fof(f_2268_2,plain,
    ! [U_8097,U_8096,U_8095,U_8094] :
      ( c_Divides_Odiv__class_Omod(U_8094,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8094),c_Divides_Odiv__class_Omod(U_8094,U_8095,U_8096)),U_8097),U_8096) = c_Divides_Odiv__class_Omod(U_8094,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8094),U_8095),U_8097),U_8096)
      | ~ class_Divides_Osemiring__div(U_8094) ),
    inference(variable_rename,[status(thm)],[f_2268_1]) ).

cnf(f_2268_3,plain,
    ( c_Divides_Odiv__class_Omod(U_8094,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8094),c_Divides_Odiv__class_Omod(U_8094,U_8095,U_8096)),U_8097),U_8096) = c_Divides_Odiv__class_Omod(U_8094,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8094),U_8095),U_8097),U_8096)
    | ~ class_Divides_Osemiring__div(U_8094) ),
    inference(clausify,[status(thm)],[f_2268_2]) ).

fof(f_2269_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_zmod__simps_I2_J]) ).

fof(f_2269_2,plain,
    ! [U_8101,U_8100,U_8099,U_8098] :
      ( c_Divides_Odiv__class_Omod(U_8098,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8098),U_8099),c_Divides_Odiv__class_Omod(U_8098,U_8100,U_8101)),U_8101) = c_Divides_Odiv__class_Omod(U_8098,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8098),U_8099),U_8100),U_8101)
      | ~ class_Divides_Osemiring__div(U_8098) ),
    inference(variable_rename,[status(thm)],[f_2269_1]) ).

cnf(f_2269_3,plain,
    ( c_Divides_Odiv__class_Omod(U_8098,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8098),U_8099),c_Divides_Odiv__class_Omod(U_8098,U_8100,U_8101)),U_8101) = c_Divides_Odiv__class_Omod(U_8098,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8098),U_8099),U_8100),U_8101)
    | ~ class_Divides_Osemiring__div(U_8098) ),
    inference(clausify,[status(thm)],[f_2269_2]) ).

fof(f_2270_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mod__add__eq]) ).

fof(f_2270_2,plain,
    ! [U_8105,U_8104,U_8103,U_8102] :
      ( c_Divides_Odiv__class_Omod(U_8102,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8102),U_8103),U_8104),U_8105) = c_Divides_Odiv__class_Omod(U_8102,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8102),c_Divides_Odiv__class_Omod(U_8102,U_8103,U_8105)),c_Divides_Odiv__class_Omod(U_8102,U_8104,U_8105)),U_8105)
      | ~ class_Divides_Osemiring__div(U_8102) ),
    inference(variable_rename,[status(thm)],[f_2270_1]) ).

cnf(f_2270_3,plain,
    ( c_Divides_Odiv__class_Omod(U_8102,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8102),U_8103),U_8104),U_8105) = c_Divides_Odiv__class_Omod(U_8102,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8102),c_Divides_Odiv__class_Omod(U_8102,U_8103,U_8105)),c_Divides_Odiv__class_Omod(U_8102,U_8104,U_8105)),U_8105)
    | ~ class_Divides_Osemiring__div(U_8102) ),
    inference(clausify,[status(thm)],[f_2270_2]) ).

fof(f_2271_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mod__add__left__eq]) ).

fof(f_2271_2,plain,
    ! [U_8109,U_8108,U_8107,U_8106] :
      ( c_Divides_Odiv__class_Omod(U_8106,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8106),U_8107),U_8108),U_8109) = c_Divides_Odiv__class_Omod(U_8106,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8106),c_Divides_Odiv__class_Omod(U_8106,U_8107,U_8109)),U_8108),U_8109)
      | ~ class_Divides_Osemiring__div(U_8106) ),
    inference(variable_rename,[status(thm)],[f_2271_1]) ).

cnf(f_2271_3,plain,
    ( c_Divides_Odiv__class_Omod(U_8106,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8106),U_8107),U_8108),U_8109) = c_Divides_Odiv__class_Omod(U_8106,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8106),c_Divides_Odiv__class_Omod(U_8106,U_8107,U_8109)),U_8108),U_8109)
    | ~ class_Divides_Osemiring__div(U_8106) ),
    inference(clausify,[status(thm)],[f_2271_2]) ).

fof(f_2272_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mod__add__right__eq]) ).

fof(f_2272_2,plain,
    ! [U_8113,U_8112,U_8111,U_8110] :
      ( c_Divides_Odiv__class_Omod(U_8110,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8110),U_8111),U_8112),U_8113) = c_Divides_Odiv__class_Omod(U_8110,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8110),U_8111),c_Divides_Odiv__class_Omod(U_8110,U_8112,U_8113)),U_8113)
      | ~ class_Divides_Osemiring__div(U_8110) ),
    inference(variable_rename,[status(thm)],[f_2272_1]) ).

cnf(f_2272_3,plain,
    ( c_Divides_Odiv__class_Omod(U_8110,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8110),U_8111),U_8112),U_8113) = c_Divides_Odiv__class_Omod(U_8110,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8110),U_8111),c_Divides_Odiv__class_Omod(U_8110,U_8112,U_8113)),U_8113)
    | ~ class_Divides_Osemiring__div(U_8110) ),
    inference(clausify,[status(thm)],[f_2272_2]) ).

fof(f_2273_1,plain,
    ! [V_a,V_b,T_a] :
      ( c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mod__add__self1]) ).

fof(f_2273_2,plain,
    ! [U_8116,U_8115,U_8114] :
      ( c_Divides_Odiv__class_Omod(U_8114,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8114),U_8115),U_8116),U_8115) = c_Divides_Odiv__class_Omod(U_8114,U_8116,U_8115)
      | ~ class_Divides_Osemiring__div(U_8114) ),
    inference(variable_rename,[status(thm)],[f_2273_1]) ).

cnf(f_2273_3,plain,
    ( c_Divides_Odiv__class_Omod(U_8114,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8114),U_8115),U_8116),U_8115) = c_Divides_Odiv__class_Omod(U_8114,U_8116,U_8115)
    | ~ class_Divides_Osemiring__div(U_8114) ),
    inference(clausify,[status(thm)],[f_2273_2]) ).

fof(f_2274_1,plain,
    ! [V_b,V_a,T_a] :
      ( c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mod__add__self2]) ).

fof(f_2274_2,plain,
    ! [U_8119,U_8118,U_8117] :
      ( c_Divides_Odiv__class_Omod(U_8117,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8117),U_8118),U_8119),U_8119) = c_Divides_Odiv__class_Omod(U_8117,U_8118,U_8119)
      | ~ class_Divides_Osemiring__div(U_8117) ),
    inference(variable_rename,[status(thm)],[f_2274_1]) ).

cnf(f_2274_3,plain,
    ( c_Divides_Odiv__class_Omod(U_8117,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8117),U_8118),U_8119),U_8119) = c_Divides_Odiv__class_Omod(U_8117,U_8118,U_8119)
    | ~ class_Divides_Osemiring__div(U_8117) ),
    inference(clausify,[status(thm)],[f_2274_2]) ).

fof(f_2275_1,plain,
    ! [V_b,V_a,T_a] :
      ( c_Divides_Odiv__class_Omod(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a),V_b) = c_Divides_Odiv__class_Omod(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_b)
      | ~ class_Divides_Oring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mod__minus__eq]) ).

fof(f_2275_2,plain,
    ! [U_8122,U_8121,U_8120] :
      ( c_Divides_Odiv__class_Omod(U_8120,hAPP(c_Groups_Ouminus__class_Ouminus(U_8120),U_8121),U_8122) = c_Divides_Odiv__class_Omod(U_8120,hAPP(c_Groups_Ouminus__class_Ouminus(U_8120),c_Divides_Odiv__class_Omod(U_8120,U_8121,U_8122)),U_8122)
      | ~ class_Divides_Oring__div(U_8120) ),
    inference(variable_rename,[status(thm)],[f_2275_1]) ).

cnf(f_2275_3,plain,
    ( c_Divides_Odiv__class_Omod(U_8120,hAPP(c_Groups_Ouminus__class_Ouminus(U_8120),U_8121),U_8122) = c_Divides_Odiv__class_Omod(U_8120,hAPP(c_Groups_Ouminus__class_Ouminus(U_8120),c_Divides_Odiv__class_Omod(U_8120,U_8121,U_8122)),U_8122)
    | ~ class_Divides_Oring__div(U_8120) ),
    inference(clausify,[status(thm)],[f_2275_2]) ).

fof(f_2276_1,plain,
    ! [V_a_H,V_b,V_a,T_a] :
      ( c_Divides_Odiv__class_Omod(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a),V_b) = c_Divides_Odiv__class_Omod(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_H),V_b)
      | c_Divides_Odiv__class_Omod(T_a,V_a,V_b) != c_Divides_Odiv__class_Omod(T_a,V_a_H,V_b)
      | ~ class_Divides_Oring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mod__minus__cong]) ).

fof(f_2276_2,plain,
    ! [U_8126,U_8125,U_8124,U_8123] :
      ( c_Divides_Odiv__class_Omod(U_8123,hAPP(c_Groups_Ouminus__class_Ouminus(U_8123),U_8124),U_8125) = c_Divides_Odiv__class_Omod(U_8123,hAPP(c_Groups_Ouminus__class_Ouminus(U_8123),U_8126),U_8125)
      | c_Divides_Odiv__class_Omod(U_8123,U_8124,U_8125) != c_Divides_Odiv__class_Omod(U_8123,U_8126,U_8125)
      | ~ class_Divides_Oring__div(U_8123) ),
    inference(variable_rename,[status(thm)],[f_2276_1]) ).

cnf(f_2276_3,plain,
    ( c_Divides_Odiv__class_Omod(U_8123,hAPP(c_Groups_Ouminus__class_Ouminus(U_8123),U_8124),U_8125) = c_Divides_Odiv__class_Omod(U_8123,hAPP(c_Groups_Ouminus__class_Ouminus(U_8123),U_8126),U_8125)
    | c_Divides_Odiv__class_Omod(U_8123,U_8124,U_8125) != c_Divides_Odiv__class_Omod(U_8123,U_8126,U_8125)
    | ~ class_Divides_Oring__div(U_8123) ),
    inference(clausify,[status(thm)],[f_2276_2]) ).

fof(f_2277_1,plain,
    ! [V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_a) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[fact_zmod__self]) ).

fof(f_2277_2,plain,
    ! [U_8127] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8127,U_8127) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[f_2277_1]) ).

cnf(f_2277_3,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8127,U_8127) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_2277_2]) ).

fof(f_2278_1,plain,
    ! [V_a,T_a] :
      ( c_Divides_Odiv__class_Omod(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mod__self]) ).

fof(f_2278_2,plain,
    ! [U_8129,U_8128] :
      ( c_Divides_Odiv__class_Omod(U_8128,U_8129,U_8129) = c_Groups_Ozero__class_Ozero(U_8128)
      | ~ class_Divides_Osemiring__div(U_8128) ),
    inference(variable_rename,[status(thm)],[f_2278_1]) ).

cnf(f_2278_3,plain,
    ( c_Divides_Odiv__class_Omod(U_8128,U_8129,U_8129) = c_Groups_Ozero__class_Ozero(U_8128)
    | ~ class_Divides_Osemiring__div(U_8128) ),
    inference(clausify,[status(thm)],[f_2278_2]) ).

fof(f_2279_1,plain,
    ! [V_a,T_a] :
      ( c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mod__by__0]) ).

fof(f_2279_2,plain,
    ! [U_8131,U_8130] :
      ( c_Divides_Odiv__class_Omod(U_8130,U_8131,c_Groups_Ozero__class_Ozero(U_8130)) = U_8131
      | ~ class_Divides_Osemiring__div(U_8130) ),
    inference(variable_rename,[status(thm)],[f_2279_1]) ).

cnf(f_2279_3,plain,
    ( c_Divides_Odiv__class_Omod(U_8130,U_8131,c_Groups_Ozero__class_Ozero(U_8130)) = U_8131
    | ~ class_Divides_Osemiring__div(U_8130) ),
    inference(clausify,[status(thm)],[f_2279_2]) ).

fof(f_2280_1,plain,
    ! [V_b] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[fact_zmod__zero]) ).

fof(f_2280_2,plain,
    ! [U_8132] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_8132) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[f_2280_1]) ).

cnf(f_2280_3,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_8132) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_2280_2]) ).

fof(f_2281_1,plain,
    ! [V_a,T_a] :
      ( c_Divides_Odiv__class_Omod(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mod__0]) ).

fof(f_2281_2,plain,
    ! [U_8134,U_8133] :
      ( c_Divides_Odiv__class_Omod(U_8133,c_Groups_Ozero__class_Ozero(U_8133),U_8134) = c_Groups_Ozero__class_Ozero(U_8133)
      | ~ class_Divides_Osemiring__div(U_8133) ),
    inference(variable_rename,[status(thm)],[f_2281_1]) ).

cnf(f_2281_3,plain,
    ( c_Divides_Odiv__class_Omod(U_8133,c_Groups_Ozero__class_Ozero(U_8133),U_8134) = c_Groups_Ozero__class_Ozero(U_8133)
    | ~ class_Divides_Osemiring__div(U_8133) ),
    inference(clausify,[status(thm)],[f_2281_2]) ).

fof(f_2282_1,plain,
    ! [V_b,V_a,T_a] :
      ( c_Divides_Odiv__class_Omod(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mod__mod__trivial]) ).

fof(f_2282_2,plain,
    ! [U_8137,U_8136,U_8135] :
      ( c_Divides_Odiv__class_Omod(U_8135,c_Divides_Odiv__class_Omod(U_8135,U_8136,U_8137),U_8137) = c_Divides_Odiv__class_Omod(U_8135,U_8136,U_8137)
      | ~ class_Divides_Osemiring__div(U_8135) ),
    inference(variable_rename,[status(thm)],[f_2282_1]) ).

cnf(f_2282_3,plain,
    ( c_Divides_Odiv__class_Omod(U_8135,c_Divides_Odiv__class_Omod(U_8135,U_8136,U_8137),U_8137) = c_Divides_Odiv__class_Omod(U_8135,U_8136,U_8137)
    | ~ class_Divides_Osemiring__div(U_8135) ),
    inference(clausify,[status(thm)],[f_2282_2]) ).

fof(f_2283_1,plain,
    ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
      ( c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_H),V_b_H),V_c)
      | c_Divides_Odiv__class_Omod(T_a,V_b,V_c) != c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
      | c_Divides_Odiv__class_Omod(T_a,V_a,V_c) != c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mod__mult__cong]) ).

fof(f_2283_2,plain,
    ! [U_8143,U_8142,U_8141,U_8140,U_8139,U_8138] :
      ( c_Divides_Odiv__class_Omod(U_8138,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8138),U_8139),U_8142),U_8140) = c_Divides_Odiv__class_Omod(U_8138,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8138),U_8141),U_8143),U_8140)
      | c_Divides_Odiv__class_Omod(U_8138,U_8142,U_8140) != c_Divides_Odiv__class_Omod(U_8138,U_8143,U_8140)
      | c_Divides_Odiv__class_Omod(U_8138,U_8139,U_8140) != c_Divides_Odiv__class_Omod(U_8138,U_8141,U_8140)
      | ~ class_Divides_Osemiring__div(U_8138) ),
    inference(variable_rename,[status(thm)],[f_2283_1]) ).

cnf(f_2283_3,plain,
    ( c_Divides_Odiv__class_Omod(U_8138,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8138),U_8139),U_8142),U_8140) = c_Divides_Odiv__class_Omod(U_8138,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8138),U_8141),U_8143),U_8140)
    | c_Divides_Odiv__class_Omod(U_8138,U_8142,U_8140) != c_Divides_Odiv__class_Omod(U_8138,U_8143,U_8140)
    | c_Divides_Odiv__class_Omod(U_8138,U_8139,U_8140) != c_Divides_Odiv__class_Omod(U_8138,U_8141,U_8140)
    | ~ class_Divides_Osemiring__div(U_8138) ),
    inference(clausify,[status(thm)],[f_2283_2]) ).

fof(f_2284_1,plain,
    ! [V_b,V_c,V_a,T_a] :
      ( c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_zmod__simps_I4_J]) ).

fof(f_2284_2,plain,
    ! [U_8147,U_8146,U_8145,U_8144] :
      ( c_Divides_Odiv__class_Omod(U_8144,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8144),c_Divides_Odiv__class_Omod(U_8144,U_8145,U_8146)),U_8147),U_8146) = c_Divides_Odiv__class_Omod(U_8144,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8144),U_8145),U_8147),U_8146)
      | ~ class_Divides_Osemiring__div(U_8144) ),
    inference(variable_rename,[status(thm)],[f_2284_1]) ).

cnf(f_2284_3,plain,
    ( c_Divides_Odiv__class_Omod(U_8144,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8144),c_Divides_Odiv__class_Omod(U_8144,U_8145,U_8146)),U_8147),U_8146) = c_Divides_Odiv__class_Omod(U_8144,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8144),U_8145),U_8147),U_8146)
    | ~ class_Divides_Osemiring__div(U_8144) ),
    inference(clausify,[status(thm)],[f_2284_2]) ).

fof(f_2285_1,plain,
    ! [V_b,V_c,V_a,T_a] :
      ( c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_c)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mod__mult__mult2]) ).

fof(f_2285_2,plain,
    ! [U_8151,U_8150,U_8149,U_8148] :
      ( c_Divides_Odiv__class_Omod(U_8148,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8148),U_8149),U_8150),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8148),U_8151),U_8150)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8148),c_Divides_Odiv__class_Omod(U_8148,U_8149,U_8151)),U_8150)
      | ~ class_Divides_Osemiring__div(U_8148) ),
    inference(variable_rename,[status(thm)],[f_2285_1]) ).

cnf(f_2285_3,plain,
    ( c_Divides_Odiv__class_Omod(U_8148,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8148),U_8149),U_8150),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8148),U_8151),U_8150)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8148),c_Divides_Odiv__class_Omod(U_8148,U_8149,U_8151)),U_8150)
    | ~ class_Divides_Osemiring__div(U_8148) ),
    inference(clausify,[status(thm)],[f_2285_2]) ).

fof(f_2286_1,plain,
    ! [V_b,V_a,V_c,T_a] :
      ( c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),c_Divides_Odiv__class_Omod(T_a,V_a,V_b))
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mod__mult__mult1]) ).

fof(f_2286_2,plain,
    ! [U_8155,U_8154,U_8153,U_8152] :
      ( c_Divides_Odiv__class_Omod(U_8152,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8152),U_8153),U_8154),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8152),U_8153),U_8155)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8152),U_8153),c_Divides_Odiv__class_Omod(U_8152,U_8154,U_8155))
      | ~ class_Divides_Osemiring__div(U_8152) ),
    inference(variable_rename,[status(thm)],[f_2286_1]) ).

cnf(f_2286_3,plain,
    ( c_Divides_Odiv__class_Omod(U_8152,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8152),U_8153),U_8154),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8152),U_8153),U_8155)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8152),U_8153),c_Divides_Odiv__class_Omod(U_8152,U_8154,U_8155))
    | ~ class_Divides_Osemiring__div(U_8152) ),
    inference(clausify,[status(thm)],[f_2286_2]) ).

fof(f_2287_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mod__mult__eq]) ).

fof(f_2287_2,plain,
    ! [U_8159,U_8158,U_8157,U_8156] :
      ( c_Divides_Odiv__class_Omod(U_8156,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8156),U_8157),U_8158),U_8159) = c_Divides_Odiv__class_Omod(U_8156,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8156),c_Divides_Odiv__class_Omod(U_8156,U_8157,U_8159)),c_Divides_Odiv__class_Omod(U_8156,U_8158,U_8159)),U_8159)
      | ~ class_Divides_Osemiring__div(U_8156) ),
    inference(variable_rename,[status(thm)],[f_2287_1]) ).

cnf(f_2287_3,plain,
    ( c_Divides_Odiv__class_Omod(U_8156,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8156),U_8157),U_8158),U_8159) = c_Divides_Odiv__class_Omod(U_8156,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8156),c_Divides_Odiv__class_Omod(U_8156,U_8157,U_8159)),c_Divides_Odiv__class_Omod(U_8156,U_8158,U_8159)),U_8159)
    | ~ class_Divides_Osemiring__div(U_8156) ),
    inference(clausify,[status(thm)],[f_2287_2]) ).

fof(f_2288_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mod__mult__left__eq]) ).

fof(f_2288_2,plain,
    ! [U_8163,U_8162,U_8161,U_8160] :
      ( c_Divides_Odiv__class_Omod(U_8160,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8160),U_8161),U_8162),U_8163) = c_Divides_Odiv__class_Omod(U_8160,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8160),c_Divides_Odiv__class_Omod(U_8160,U_8161,U_8163)),U_8162),U_8163)
      | ~ class_Divides_Osemiring__div(U_8160) ),
    inference(variable_rename,[status(thm)],[f_2288_1]) ).

cnf(f_2288_3,plain,
    ( c_Divides_Odiv__class_Omod(U_8160,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8160),U_8161),U_8162),U_8163) = c_Divides_Odiv__class_Omod(U_8160,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8160),c_Divides_Odiv__class_Omod(U_8160,U_8161,U_8163)),U_8162),U_8163)
    | ~ class_Divides_Osemiring__div(U_8160) ),
    inference(clausify,[status(thm)],[f_2288_2]) ).

fof(f_2289_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mod__mult__right__eq]) ).

fof(f_2289_2,plain,
    ! [U_8167,U_8166,U_8165,U_8164] :
      ( c_Divides_Odiv__class_Omod(U_8164,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8164),U_8165),U_8166),U_8167) = c_Divides_Odiv__class_Omod(U_8164,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8164),U_8165),c_Divides_Odiv__class_Omod(U_8164,U_8166,U_8167)),U_8167)
      | ~ class_Divides_Osemiring__div(U_8164) ),
    inference(variable_rename,[status(thm)],[f_2289_1]) ).

cnf(f_2289_3,plain,
    ( c_Divides_Odiv__class_Omod(U_8164,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8164),U_8165),U_8166),U_8167) = c_Divides_Odiv__class_Omod(U_8164,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8164),U_8165),c_Divides_Odiv__class_Omod(U_8164,U_8166,U_8167)),U_8167)
    | ~ class_Divides_Osemiring__div(U_8164) ),
    inference(clausify,[status(thm)],[f_2289_2]) ).

fof(f_2290_1,plain,
    ! [V_y,V_m,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_m)),V_y),V_m) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y),V_m),
    inference(fof_nnf,[status(thm)],[fact_zpower__zmod]) ).

fof(f_2290_2,plain,
    ! [U_8170,U_8169,U_8168] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8168,U_8169)),U_8170),U_8169) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_8168),U_8170),U_8169),
    inference(variable_rename,[status(thm)],[f_2290_1]) ).

cnf(f_2290_3,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8168,U_8169)),U_8170),U_8169) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_8168),U_8170),U_8169),
    inference(clausify,[status(thm)],[f_2290_2]) ).

fof(f_2291_1,plain,
    ! [V_a,V_b,T_a] :
      ( c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mod__mult__self1__is__0]) ).

fof(f_2291_2,plain,
    ! [U_8173,U_8172,U_8171] :
      ( c_Divides_Odiv__class_Omod(U_8171,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8171),U_8172),U_8173),U_8172) = c_Groups_Ozero__class_Ozero(U_8171)
      | ~ class_Divides_Osemiring__div(U_8171) ),
    inference(variable_rename,[status(thm)],[f_2291_1]) ).

cnf(f_2291_3,plain,
    ( c_Divides_Odiv__class_Omod(U_8171,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8171),U_8172),U_8173),U_8172) = c_Groups_Ozero__class_Ozero(U_8171)
    | ~ class_Divides_Osemiring__div(U_8171) ),
    inference(clausify,[status(thm)],[f_2291_2]) ).

fof(f_2292_1,plain,
    ! [V_b,V_a,T_a] :
      ( c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_b) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mod__mult__self2__is__0]) ).

fof(f_2292_2,plain,
    ! [U_8176,U_8175,U_8174] :
      ( c_Divides_Odiv__class_Omod(U_8174,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8174),U_8175),U_8176),U_8176) = c_Groups_Ozero__class_Ozero(U_8174)
      | ~ class_Divides_Osemiring__div(U_8174) ),
    inference(variable_rename,[status(thm)],[f_2292_1]) ).

cnf(f_2292_3,plain,
    ( c_Divides_Odiv__class_Omod(U_8174,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8174),U_8175),U_8176),U_8176) = c_Groups_Ozero__class_Ozero(U_8174)
    | ~ class_Divides_Osemiring__div(U_8174) ),
    inference(clausify,[status(thm)],[f_2292_2]) ).

fof(f_2293_1,plain,
    ! [V_b,V_c,V_a,T_a] :
      ( c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mod__mult__self1]) ).

fof(f_2293_2,plain,
    ! [U_8180,U_8179,U_8178,U_8177] :
      ( c_Divides_Odiv__class_Omod(U_8177,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8177),U_8178),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8177),U_8179),U_8180)),U_8180) = c_Divides_Odiv__class_Omod(U_8177,U_8178,U_8180)
      | ~ class_Divides_Osemiring__div(U_8177) ),
    inference(variable_rename,[status(thm)],[f_2293_1]) ).

cnf(f_2293_3,plain,
    ( c_Divides_Odiv__class_Omod(U_8177,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8177),U_8178),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8177),U_8179),U_8180)),U_8180) = c_Divides_Odiv__class_Omod(U_8177,U_8178,U_8180)
    | ~ class_Divides_Osemiring__div(U_8177) ),
    inference(clausify,[status(thm)],[f_2293_2]) ).

fof(f_2294_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mod__mult__self2]) ).

fof(f_2294_2,plain,
    ! [U_8184,U_8183,U_8182,U_8181] :
      ( c_Divides_Odiv__class_Omod(U_8181,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8181),U_8182),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8181),U_8183),U_8184)),U_8183) = c_Divides_Odiv__class_Omod(U_8181,U_8182,U_8183)
      | ~ class_Divides_Osemiring__div(U_8181) ),
    inference(variable_rename,[status(thm)],[f_2294_1]) ).

cnf(f_2294_3,plain,
    ( c_Divides_Odiv__class_Omod(U_8181,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8181),U_8182),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8181),U_8183),U_8184)),U_8183) = c_Divides_Odiv__class_Omod(U_8181,U_8182,U_8183)
    | ~ class_Divides_Osemiring__div(U_8181) ),
    inference(clausify,[status(thm)],[f_2294_2]) ).

fof(f_2295_1,plain,
    ! [V_a,T_a] :
      ( c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mod__by__1]) ).

fof(f_2295_2,plain,
    ! [U_8186,U_8185] :
      ( c_Divides_Odiv__class_Omod(U_8185,U_8186,c_Groups_Oone__class_Oone(U_8185)) = c_Groups_Ozero__class_Ozero(U_8185)
      | ~ class_Divides_Osemiring__div(U_8185) ),
    inference(variable_rename,[status(thm)],[f_2295_1]) ).

cnf(f_2295_3,plain,
    ( c_Divides_Odiv__class_Omod(U_8185,U_8186,c_Groups_Oone__class_Oone(U_8185)) = c_Groups_Ozero__class_Ozero(U_8185)
    | ~ class_Divides_Osemiring__div(U_8185) ),
    inference(clausify,[status(thm)],[f_2295_2]) ).

fof(f_2296_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_b) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mod__div__trivial]) ).

fof(f_2296_2,plain,
    ! [U_8189,U_8188,U_8187] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_8187),c_Divides_Odiv__class_Omod(U_8187,U_8188,U_8189)),U_8189) = c_Groups_Ozero__class_Ozero(U_8187)
      | ~ class_Divides_Osemiring__div(U_8187) ),
    inference(variable_rename,[status(thm)],[f_2296_1]) ).

cnf(f_2296_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_8187),c_Divides_Odiv__class_Omod(U_8187,U_8188,U_8189)),U_8189) = c_Groups_Ozero__class_Ozero(U_8187)
    | ~ class_Divides_Osemiring__div(U_8187) ),
    inference(clausify,[status(thm)],[f_2296_2]) ).

fof(f_2297_1,plain,
    ! [V_y,V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) ),
    inference(fof_nnf,[status(thm)],[fact_Divides_Otransfer__nat__int__function__closures_I2_J]) ).

fof(f_2297_2,plain,
    ! [U_8191,U_8190] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8190,U_8191)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8191))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8190)) ),
    inference(variable_rename,[status(thm)],[f_2297_1]) ).

cnf(f_2297_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8190,U_8191)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8191))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8190)) ),
    inference(clausify,[status(thm)],[f_2297_2]) ).

fof(f_2298_1,plain,
    ! [V_k,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_k)),V_m))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m)) ),
    inference(fof_nnf,[status(thm)],[fact_zmod__le__nonneg__dividend]) ).

fof(f_2298_2,plain,
    ! [U_8193,U_8192] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8192,U_8193)),U_8192))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8192)) ),
    inference(variable_rename,[status(thm)],[f_2298_1]) ).

cnf(f_2298_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8192,U_8193)),U_8192))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8192)) ),
    inference(clausify,[status(thm)],[f_2298_2]) ).

fof(f_2299_1,plain,
    ! [V_a,V_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) ),
    inference(fof_nnf,[status(thm)],[fact_pos__mod__bound]) ).

fof(f_2299_2,plain,
    ! [U_8195,U_8194] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8195,U_8194)),U_8194))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8194)) ),
    inference(variable_rename,[status(thm)],[f_2299_1]) ).

cnf(f_2299_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8195,U_8194)),U_8194))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8194)) ),
    inference(clausify,[status(thm)],[f_2299_2]) ).

fof(f_2300_1,plain,
    ! [V_a,V_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(fof_nnf,[status(thm)],[fact_neg__mod__bound]) ).

fof(f_2300_2,plain,
    ! [U_8197,U_8196] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8196),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8197,U_8196)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8196),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_2300_1]) ).

cnf(f_2300_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8196),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8197,U_8196)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8196),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2300_2]) ).

fof(f_2301_1,plain,
    ! [V_d_2,V_m_2] :
      ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ! [B_q] : V_m_2 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_d_2),B_q) )
      & ( ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_d_2),B_q)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m_2,V_d_2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(fof_nnf,[status(thm)],[fact_zmod__eq__0__iff]) ).

fof(f_2301_2,plain,
    ! [U_8201,U_8200] :
      ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8200,U_8201) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ! [U_8199] : U_8200 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8201),U_8199) )
      & ( ? [U_8198] : U_8200 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8201),U_8198)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8200,U_8201) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[f_2301_1]) ).

fof(f_2301_3,plain,
    ( ! [U_8205,U_8203] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8203,U_8205) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ! [U_8199] : U_8203 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8205),U_8199) )
    & ! [U_8204,U_8202] :
        ( ? [U_8198] : U_8202 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8204),U_8198)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8202,U_8204) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(miniscope,[status(thm)],[f_2301_2]) ).

fof(f_2301_4,plain,
    ( ! [U_8205,U_8203] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8203,U_8205) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ! [U_8199] : U_8203 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8205),U_8199) )
    & ! [U_8204,U_8202] :
        ( U_8202 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8204),sK206(U_8204,U_8202))
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8202,U_8204) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK206]),skolemize(U_8198,sK206(U_8204,U_8202))],[f_2301_3]) ).

cnf(f_2301_5,plain,
    ( U_8202 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8204),sK206(U_8204,U_8202))
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8202,U_8204) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2301_4]) ).

cnf(f_2301_6,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8203,U_8205) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_8203 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8205),U_8199) ),
    inference(clausify,[status(thm)],[f_2301_4]) ).

fof(f_2302_1,plain,
    ! [V_l,V_k] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k),V_l) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(fof_nnf,[status(thm)],[fact_zmod__zminus1__not__zero]) ).

fof(f_2302_2,plain,
    ! [U_8207,U_8206] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8206,U_8207) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8206),U_8207) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_2302_1]) ).

cnf(f_2302_3,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8206,U_8207) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8206),U_8207) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2302_2]) ).

fof(f_2303_1,plain,
    ! [V_l,V_k] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_l)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(fof_nnf,[status(thm)],[fact_zmod__zminus2__not__zero]) ).

fof(f_2303_2,plain,
    ! [U_8209,U_8208] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8208,U_8209) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8208,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8209)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_2303_1]) ).

cnf(f_2303_3,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8208,U_8209) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8208,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8209)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2303_2]) ).

fof(f_2304_1,plain,
    ! [V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[fact_zmod__zdiv__trivial]) ).

fof(f_2304_2,plain,
    ! [U_8211,U_8210] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8210,U_8211)),U_8211) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[f_2304_1]) ).

cnf(f_2304_3,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8210,U_8211)),U_8211) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_2304_2]) ).

fof(f_2305_1,plain,
    ! [V_a] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_a
      & hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(fof_nnf,[status(thm)],[fact_DIVISION__BY__ZERO]) ).

fof(f_2305_2,plain,
    ! [U_8212] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8212,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_8212
      & hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8212),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_2305_1]) ).

fof(f_2305_3,plain,
    ( ! [U_8214] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8214,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_8214
    & ! [U_8213] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8213),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(miniscope,[status(thm)],[f_2305_2]) ).

cnf(f_2305_4,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8213),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_2305_3]) ).

cnf(f_2305_5,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8214,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_8214,
    inference(clausify,[status(thm)],[f_2305_3]) ).

fof(f_2306_1,plain,
    ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_c)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b),V_c))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_c)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c))),V_c)),
    inference(fof_nnf,[status(thm)],[fact_zdiv__zadd1__eq]) ).

fof(f_2306_2,plain,
    ! [U_8217,U_8216,U_8215] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8215),U_8216)),U_8217) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8215),U_8217)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8216),U_8217))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8215,U_8217)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8216,U_8217))),U_8217)),
    inference(variable_rename,[status(thm)],[f_2306_1]) ).

cnf(f_2306_3,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8215),U_8216)),U_8217) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8215),U_8217)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8216),U_8217))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8215,U_8217)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8216,U_8217))),U_8217)),
    inference(clausify,[status(thm)],[f_2306_2]) ).

fof(f_2307_1,plain,
    c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J]) ).

cnf(f_2307_2,plain,
    c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_2307_1]) ).

fof(f_2308_1,plain,
    ! [V_B_2,V_A_2] :
      ( c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2))
      | ~ c_Nat__Transfer_Onat__set(V_B_2)
      | ~ c_Nat__Transfer_Onat__set(V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J]) ).

fof(f_2308_2,plain,
    ! [U_8219,U_8218] :
      ( c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_8218),U_8219))
      | ~ c_Nat__Transfer_Onat__set(U_8219)
      | ~ c_Nat__Transfer_Onat__set(U_8218) ),
    inference(variable_rename,[status(thm)],[f_2308_1]) ).

cnf(f_2308_3,plain,
    ( c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_8218),U_8219))
    | ~ c_Nat__Transfer_Onat__set(U_8219)
    | ~ c_Nat__Transfer_Onat__set(U_8218) ),
    inference(clausify,[status(thm)],[f_2308_2]) ).

fof(f_2309_1,plain,
    ! [V_B_2,V_A_2] :
      ( c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2))
      | ~ c_Nat__Transfer_Onat__set(V_B_2)
      | ~ c_Nat__Transfer_Onat__set(V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J]) ).

fof(f_2309_2,plain,
    ! [U_8221,U_8220] :
      ( c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_8220),U_8221))
      | ~ c_Nat__Transfer_Onat__set(U_8221)
      | ~ c_Nat__Transfer_Onat__set(U_8220) ),
    inference(variable_rename,[status(thm)],[f_2309_1]) ).

cnf(f_2309_3,plain,
    ( c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_8220),U_8221))
    | ~ c_Nat__Transfer_Onat__set(U_8221)
    | ~ c_Nat__Transfer_Onat__set(U_8220) ),
    inference(clausify,[status(thm)],[f_2309_2]) ).

fof(f_2310_1,plain,
    ! [V_S_2] :
      ( ( c_Nat__Transfer_Onat__set(V_S_2)
        | ? [B_x] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),V_S_2)) ) )
      & ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),V_S_2)) )
        | ~ c_Nat__Transfer_Onat__set(V_S_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__set__def]) ).

fof(f_2310_2,plain,
    ! [U_8224] :
      ( ( c_Nat__Transfer_Onat__set(U_8224)
        | ? [U_8223] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8223))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8223),U_8224)) ) )
      & ( ! [U_8222] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8222))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8222),U_8224)) )
        | ~ c_Nat__Transfer_Onat__set(U_8224) ) ),
    inference(variable_rename,[status(thm)],[f_2310_1]) ).

fof(f_2310_3,plain,
    ( ! [U_8226] :
        ( c_Nat__Transfer_Onat__set(U_8226)
        | ? [U_8223] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8223))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8223),U_8226)) ) )
    & ! [U_8225] :
        ( ! [U_8222] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8222))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8222),U_8225)) )
        | ~ c_Nat__Transfer_Onat__set(U_8225) ) ),
    inference(miniscope,[status(thm)],[f_2310_2]) ).

fof(f_2310_4,plain,
    ( ! [U_8226] :
        ( c_Nat__Transfer_Onat__set(U_8226)
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK207(U_8226)))
          & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK207(U_8226)),U_8226)) ) )
    & ! [U_8225] :
        ( ! [U_8222] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8222))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8222),U_8225)) )
        | ~ c_Nat__Transfer_Onat__set(U_8225) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK207]),skolemize(U_8223,sK207(U_8226))],[f_2310_3]) ).

cnf(f_2310_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8222))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8222),U_8225))
    | ~ c_Nat__Transfer_Onat__set(U_8225) ),
    inference(clausify,[status(thm)],[f_2310_4]) ).

cnf(f_2310_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK207(U_8226)),U_8226))
    | c_Nat__Transfer_Onat__set(U_8226) ),
    inference(clausify,[status(thm)],[f_2310_4]) ).

cnf(f_2310_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK207(U_8226)))
    | c_Nat__Transfer_Onat__set(U_8226) ),
    inference(clausify,[status(thm)],[f_2310_4]) ).

fof(f_2311_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),V_b)) = V_a
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_semiring__div__class_Omod__div__equality_H]) ).

fof(f_2311_2,plain,
    ! [U_8229,U_8228,U_8227] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8227),c_Divides_Odiv__class_Omod(U_8227,U_8228,U_8229)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8227),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_8227),U_8228),U_8229)),U_8229)) = U_8228
      | ~ class_Divides_Osemiring__div(U_8227) ),
    inference(variable_rename,[status(thm)],[f_2311_1]) ).

cnf(f_2311_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8227),c_Divides_Odiv__class_Omod(U_8227,U_8228,U_8229)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8227),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_8227),U_8228),U_8229)),U_8229)) = U_8228
    | ~ class_Divides_Osemiring__div(U_8227) ),
    inference(clausify,[status(thm)],[f_2311_2]) ).

fof(f_2312_1,plain,
    ! [V_a,V_b,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b))),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) = V_a
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mod__div__equality2]) ).

fof(f_2312_2,plain,
    ! [U_8232,U_8231,U_8230] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8230),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8230),U_8231),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_8230),U_8232),U_8231))),c_Divides_Odiv__class_Omod(U_8230,U_8232,U_8231)) = U_8232
      | ~ class_Divides_Osemiring__div(U_8230) ),
    inference(variable_rename,[status(thm)],[f_2312_1]) ).

cnf(f_2312_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8230),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8230),U_8231),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_8230),U_8232),U_8231))),c_Divides_Odiv__class_Omod(U_8230,U_8232,U_8231)) = U_8232
    | ~ class_Divides_Osemiring__div(U_8230) ),
    inference(clausify,[status(thm)],[f_2312_2]) ).

fof(f_2313_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),V_b)),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) = V_a
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mod__div__equality]) ).

fof(f_2313_2,plain,
    ! [U_8235,U_8234,U_8233] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8233),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8233),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_8233),U_8234),U_8235)),U_8235)),c_Divides_Odiv__class_Omod(U_8233,U_8234,U_8235)) = U_8234
      | ~ class_Divides_Osemiring__div(U_8233) ),
    inference(variable_rename,[status(thm)],[f_2313_1]) ).

cnf(f_2313_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8233),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8233),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_8233),U_8234),U_8235)),U_8235)),c_Divides_Odiv__class_Omod(U_8233,U_8234,U_8235)) = U_8234
    | ~ class_Divides_Osemiring__div(U_8233) ),
    inference(clausify,[status(thm)],[f_2313_2]) ).

fof(f_2314_1,plain,
    ! [V_c,V_a,V_b,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b))),c_Divides_Odiv__class_Omod(T_a,V_a,V_b))),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_div__mod__equality2]) ).

fof(f_2314_2,plain,
    ! [U_8239,U_8238,U_8237,U_8236] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8236),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8236),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8236),U_8237),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_8236),U_8238),U_8237))),c_Divides_Odiv__class_Omod(U_8236,U_8238,U_8237))),U_8239) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8236),U_8238),U_8239)
      | ~ class_Divides_Osemiring__div(U_8236) ),
    inference(variable_rename,[status(thm)],[f_2314_1]) ).

cnf(f_2314_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8236),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8236),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8236),U_8237),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_8236),U_8238),U_8237))),c_Divides_Odiv__class_Omod(U_8236,U_8238,U_8237))),U_8239) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8236),U_8238),U_8239)
    | ~ class_Divides_Osemiring__div(U_8236) ),
    inference(clausify,[status(thm)],[f_2314_2]) ).

fof(f_2315_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),V_b)),c_Divides_Odiv__class_Omod(T_a,V_a,V_b))),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_div__mod__equality]) ).

fof(f_2315_2,plain,
    ! [U_8243,U_8242,U_8241,U_8240] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8240),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8240),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8240),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_8240),U_8241),U_8242)),U_8242)),c_Divides_Odiv__class_Omod(U_8240,U_8241,U_8242))),U_8243) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8240),U_8241),U_8243)
      | ~ class_Divides_Osemiring__div(U_8240) ),
    inference(variable_rename,[status(thm)],[f_2315_1]) ).

cnf(f_2315_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8240),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8240),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8240),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_8240),U_8241),U_8242)),U_8242)),c_Divides_Odiv__class_Omod(U_8240,U_8241,U_8242))),U_8243) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8240),U_8241),U_8243)
    | ~ class_Divides_Osemiring__div(U_8240) ),
    inference(clausify,[status(thm)],[f_2315_2]) ).

fof(f_2316_1,plain,
    ! [V_a,V_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) ),
    inference(fof_nnf,[status(thm)],[fact_pos__mod__sign]) ).

fof(f_2316_2,plain,
    ! [U_8245,U_8244] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8245,U_8244)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8244)) ),
    inference(variable_rename,[status(thm)],[f_2316_1]) ).

cnf(f_2316_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8245,U_8244)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8244)) ),
    inference(clausify,[status(thm)],[f_2316_2]) ).

fof(f_2317_1,plain,
    ! [V_a,V_b] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_b))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) ),
    inference(fof_nnf,[status(thm)],[fact_pos__mod__conj]) ).

fof(f_2317_2,plain,
    ! [U_8247,U_8246] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8247,U_8246)),U_8246))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8247,U_8246))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8246)) ),
    inference(variable_rename,[status(thm)],[f_2317_1]) ).

cnf(f_2317_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8247,U_8246)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8246)) ),
    inference(clausify,[status(thm)],[f_2317_2]) ).

cnf(f_2317_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8247,U_8246)),U_8246))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8246)) ),
    inference(clausify,[status(thm)],[f_2317_2]) ).

fof(f_2318_1,plain,
    ! [V_b,V_a] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) ),
    inference(fof_nnf,[status(thm)],[fact_mod__pos__pos__trivial]) ).

fof(f_2318_2,plain,
    ! [U_8249,U_8248] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8248,U_8249) = U_8248
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8248),U_8249))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8248)) ),
    inference(variable_rename,[status(thm)],[f_2318_1]) ).

cnf(f_2318_3,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8248,U_8249) = U_8248
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8248),U_8249))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8248)) ),
    inference(clausify,[status(thm)],[f_2318_2]) ).

fof(f_2319_1,plain,
    ! [V_a,V_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(fof_nnf,[status(thm)],[fact_neg__mod__sign]) ).

fof(f_2319_2,plain,
    ! [U_8251,U_8250] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8251,U_8250)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8250),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_2319_1]) ).

cnf(f_2319_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8251,U_8250)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8250),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2319_2]) ).

fof(f_2320_1,plain,
    ! [V_a,V_b] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(fof_nnf,[status(thm)],[fact_neg__mod__conj]) ).

fof(f_2320_2,plain,
    ! [U_8253,U_8252] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8252),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8253,U_8252)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8253,U_8252)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8252),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_2320_1]) ).

cnf(f_2320_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8253,U_8252)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8252),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2320_2]) ).

cnf(f_2320_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8252),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8253,U_8252)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8252),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2320_2]) ).

fof(f_2321_1,plain,
    ! [V_b,V_a] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(fof_nnf,[status(thm)],[fact_mod__neg__neg__trivial]) ).

fof(f_2321_2,plain,
    ! [U_8255,U_8254] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8254,U_8255) = U_8254
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8255),U_8254))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8254),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_2321_1]) ).

cnf(f_2321_3,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8254,U_8255) = U_8254
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8255),U_8254))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8254),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2321_2]) ).

fof(f_2322_1,plain,
    ! [V_C_2] : c_Nat__Transfer_Onat__set(hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_C_2)),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J]) ).

fof(f_2322_2,plain,
    ! [U_8256] : c_Nat__Transfer_Onat__set(hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8256)),
    inference(variable_rename,[status(thm)],[f_2322_1]) ).

cnf(f_2322_3,plain,
    c_Nat__Transfer_Onat__set(hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8256)),
    inference(clausify,[status(thm)],[f_2322_2]) ).

fof(f_2323_1,plain,
    ! [V_B_2,V_A_2] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2)) ) )
      | ~ c_Nat__Transfer_Onat__set(V_B_2)
      | ~ c_Nat__Transfer_Onat__set(V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__set__relations_I4_J]) ).

fof(f_2323_2,plain,
    ! [U_8258,U_8257] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_8257),U_8258))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8257)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8258))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8257)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8258)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_8257),U_8258)) ) )
      | ~ c_Nat__Transfer_Onat__set(U_8258)
      | ~ c_Nat__Transfer_Onat__set(U_8257) ),
    inference(variable_rename,[status(thm)],[f_2323_1]) ).

cnf(f_2323_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8257)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8258)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_8257),U_8258))
    | ~ c_Nat__Transfer_Onat__set(U_8258)
    | ~ c_Nat__Transfer_Onat__set(U_8257) ),
    inference(clausify,[status(thm)],[f_2323_2]) ).

cnf(f_2323_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_8257),U_8258))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8257)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8258)))
    | ~ c_Nat__Transfer_Onat__set(U_8258)
    | ~ c_Nat__Transfer_Onat__set(U_8257) ),
    inference(clausify,[status(thm)],[f_2323_2]) ).

fof(f_2324_1,plain,
    ! [V_B_2,V_A_2] :
      ( ( ( V_A_2 = V_B_2
          | hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2) != hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2) )
        & ( hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2)
          | V_A_2 != V_B_2 ) )
      | ~ c_Nat__Transfer_Onat__set(V_B_2)
      | ~ c_Nat__Transfer_Onat__set(V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__set__relations_I3_J]) ).

fof(f_2324_2,plain,
    ! [U_8260,U_8259] :
      ( ( ( U_8259 = U_8260
          | hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8259) != hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8260) )
        & ( hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8259) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8260)
          | U_8259 != U_8260 ) )
      | ~ c_Nat__Transfer_Onat__set(U_8260)
      | ~ c_Nat__Transfer_Onat__set(U_8259) ),
    inference(variable_rename,[status(thm)],[f_2324_1]) ).

cnf(f_2324_3,plain,
    ( hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8259) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8260)
    | U_8259 != U_8260
    | ~ c_Nat__Transfer_Onat__set(U_8260)
    | ~ c_Nat__Transfer_Onat__set(U_8259) ),
    inference(clausify,[status(thm)],[f_2324_2]) ).

cnf(f_2324_4,plain,
    ( U_8259 = U_8260
    | hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8259) != hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8260)
    | ~ c_Nat__Transfer_Onat__set(U_8260)
    | ~ c_Nat__Transfer_Onat__set(U_8259) ),
    inference(clausify,[status(thm)],[f_2324_2]) ).

fof(f_2325_1,plain,
    ! [V_b,V_a] :
      ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_b)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(fof_nnf,[status(thm)],[fact_zmod__zminus2__eq__if]) ).

fof(f_2325_2,plain,
    ! [U_8262,U_8261] :
      ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8261,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8262)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8261,U_8262)),U_8262)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8261,U_8262) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8261,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8262)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8261,U_8262) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[f_2325_1]) ).

fof(f_2325_3,plain,
    ( ! [U_8266,U_8264] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8264,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8266)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8264,U_8266)),U_8266)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8264,U_8266) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
    & ! [U_8265,U_8263] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8263,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8265)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8263,U_8265) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(miniscope,[status(thm)],[f_2325_2]) ).

cnf(f_2325_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8263,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8265)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8263,U_8265) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2325_3]) ).

cnf(f_2325_5,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8264,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8266)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8264,U_8266)),U_8266)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8264,U_8266) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2325_3]) ).

fof(f_2326_1,plain,
    ! [V_b,V_a] :
      ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),V_b) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(fof_nnf,[status(thm)],[fact_zmod__zminus1__eq__if]) ).

fof(f_2326_2,plain,
    ! [U_8268,U_8267] :
      ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8267),U_8268) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8268),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8267,U_8268))
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8267,U_8268) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8267),U_8268) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8267,U_8268) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[f_2326_1]) ).

fof(f_2326_3,plain,
    ( ! [U_8272,U_8270] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8270),U_8272) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8272),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8270,U_8272))
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8270,U_8272) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
    & ! [U_8271,U_8269] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8269),U_8271) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8269,U_8271) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(miniscope,[status(thm)],[f_2326_2]) ).

cnf(f_2326_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8269),U_8271) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8269,U_8271) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2326_3]) ).

cnf(f_2326_5,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8270),U_8272) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8272),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8270,U_8272))
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8270,U_8272) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2326_3]) ).

fof(f_2327_1,plain,
    ! [V_b,V_a] : V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),
    inference(fof_nnf,[status(thm)],[fact_zmod__zdiv__equality]) ).

fof(f_2327_2,plain,
    ! [U_8274,U_8273] : U_8273 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8274),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8273),U_8274))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8273,U_8274)),
    inference(variable_rename,[status(thm)],[f_2327_1]) ).

cnf(f_2327_3,plain,
    U_8273 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8274),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8273),U_8274))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8273,U_8274)),
    inference(clausify,[status(thm)],[f_2327_2]) ).

fof(f_2328_1,plain,
    ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b),V_c))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_c))),V_c)),
    inference(fof_nnf,[status(thm)],[fact_zdiv__zmult1__eq]) ).

fof(f_2328_2,plain,
    ! [U_8277,U_8276,U_8275] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8275),U_8276)),U_8277) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8275),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8276),U_8277))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8275),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8276,U_8277))),U_8277)),
    inference(variable_rename,[status(thm)],[f_2328_1]) ).

cnf(f_2328_3,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8275),U_8276)),U_8277) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8275),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8276),U_8277))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8275),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8276,U_8277))),U_8277)),
    inference(clausify,[status(thm)],[f_2328_2]) ).

fof(f_2329_1,plain,
    ! [V_k,V_a,V_b] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_k),
    inference(fof_nnf,[status(thm)],[fact_zdiv__zmod__equality]) ).

fof(f_2329_2,plain,
    ! [U_8280,U_8279,U_8278] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8278),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8279),U_8278))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8279,U_8278))),U_8280) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8279),U_8280),
    inference(variable_rename,[status(thm)],[f_2329_1]) ).

cnf(f_2329_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8278),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8279),U_8278))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8279,U_8278))),U_8280) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8279),U_8280),
    inference(clausify,[status(thm)],[f_2329_2]) ).

fof(f_2330_1,plain,
    ! [V_k,V_b,V_a] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),V_b)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_k),
    inference(fof_nnf,[status(thm)],[fact_zdiv__zmod__equality2]) ).

fof(f_2330_2,plain,
    ! [U_8283,U_8282,U_8281] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8281),U_8282)),U_8282)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8281,U_8282))),U_8283) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8281),U_8283),
    inference(variable_rename,[status(thm)],[f_2330_1]) ).

cnf(f_2330_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8281),U_8282)),U_8282)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8281,U_8282))),U_8283) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8281),U_8283),
    inference(clausify,[status(thm)],[f_2330_2]) ).

fof(f_2331_1,plain,
    ! [V_m,V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_n),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_m),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_m),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n)),
    inference(fof_nnf,[status(thm)],[fact_zmult__div__cancel]) ).

fof(f_2331_2,plain,
    ! [U_8285,U_8284] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8284),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8285),U_8284)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8285),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8285,U_8284)),
    inference(variable_rename,[status(thm)],[f_2331_1]) ).

cnf(f_2331_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8284),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8285),U_8284)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8285),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8285,U_8284)),
    inference(clausify,[status(thm)],[f_2331_2]) ).

fof(f_2332_1,plain,
    ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_m),V_n)),V_n)),
    inference(fof_nnf,[status(thm)],[fact_zmod__zdiv__equality_H]) ).

fof(f_2332_2,plain,
    ! [U_8287,U_8286] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8286,U_8287) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8286),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8286),U_8287)),U_8287)),
    inference(variable_rename,[status(thm)],[f_2332_1]) ).

cnf(f_2332_3,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8286,U_8287) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8286),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8286),U_8287)),U_8287)),
    inference(clausify,[status(thm)],[f_2332_2]) ).

fof(f_2333_1,plain,
    ! [V_b,V_a] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) ),
    inference(fof_nnf,[status(thm)],[fact_mod__pos__neg__trivial]) ).

fof(f_2333_2,plain,
    ! [U_8289,U_8288] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8288,U_8289) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8288),U_8289)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8288),U_8289)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8288)) ),
    inference(variable_rename,[status(thm)],[f_2333_1]) ).

cnf(f_2333_3,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8288,U_8289) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8288),U_8289)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8288),U_8289)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8288)) ),
    inference(clausify,[status(thm)],[f_2333_2]) ).

fof(f_2334_1,plain,
    ! [V_y_2,V_x_2] :
      ( c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_SetInterval_Otransfer__nat__int__set__function__closures]) ).

fof(f_2334_2,plain,
    ! [U_8291,U_8290] :
      ( c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_8290,U_8291))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8290)) ),
    inference(variable_rename,[status(thm)],[f_2334_1]) ).

cnf(f_2334_3,plain,
    ( c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_8290,U_8291))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8290)) ),
    inference(clausify,[status(thm)],[f_2334_2]) ).

fof(f_2335_1,plain,
    ! [V_x_2,V_A_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
      | ~ c_Nat__Transfer_Onat__set(V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J]) ).

fof(f_2335_2,plain,
    ! [U_8293,U_8292] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8293))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8293),U_8292))
      | ~ c_Nat__Transfer_Onat__set(U_8292) ),
    inference(variable_rename,[status(thm)],[f_2335_1]) ).

cnf(f_2335_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8293))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8293),U_8292))
    | ~ c_Nat__Transfer_Onat__set(U_8292) ),
    inference(clausify,[status(thm)],[f_2335_2]) ).

fof(f_2336_1,plain,
    ! [V_k_2,V_n_2,V_P_2] :
      ( ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
        | ( ? [B_i,B_j] :
              ( ~ hBOOL(hAPP(V_P_2,B_j))
              & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ? [B_i,B_j] :
              ( ~ hBOOL(hAPP(V_P_2,B_j))
              & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) )
        | ( ~ hBOOL(hAPP(V_P_2,V_n_2))
          & V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
      & ( ( ( ! [B_i,B_j] :
                ( hBOOL(hAPP(V_P_2,B_j))
                | V_n_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [B_i,B_j] :
                ( hBOOL(hAPP(V_P_2,B_j))
                | V_n_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) )
          & ( hBOOL(hAPP(V_P_2,V_n_2))
            | V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_split__zmod]) ).

fof(f_2336_2,plain,
    ! [U_8304,U_8303,U_8302] :
      ( ( hBOOL(hAPP(U_8302,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8303,U_8304)))
        | ( ? [U_8301,U_8300] :
              ( ~ hBOOL(hAPP(U_8302,U_8300))
              & U_8303 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8304),U_8301)),U_8300)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8300),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8304),U_8300)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8304),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ? [U_8299,U_8298] :
              ( ~ hBOOL(hAPP(U_8302,U_8298))
              & U_8303 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8304),U_8299)),U_8298)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8298),U_8304))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8298)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8304)) )
        | ( ~ hBOOL(hAPP(U_8302,U_8303))
          & U_8304 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
      & ( ( ( ! [U_8297,U_8296] :
                ( hBOOL(hAPP(U_8302,U_8296))
                | U_8303 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8304),U_8297)),U_8296)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8296),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8304),U_8296)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8304),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [U_8295,U_8294] :
                ( hBOOL(hAPP(U_8302,U_8294))
                | U_8303 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8304),U_8295)),U_8294)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8294),U_8304))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8294)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8304)) )
          & ( hBOOL(hAPP(U_8302,U_8303))
            | U_8304 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_8302,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8303,U_8304))) ) ),
    inference(variable_rename,[status(thm)],[f_2336_1]) ).

fof(f_2336_3,plain,
    ( ! [U_8310,U_8308,U_8306] :
        ( hBOOL(hAPP(U_8306,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8308,U_8310)))
        | ( ? [U_8301,U_8300] :
              ( ~ hBOOL(hAPP(U_8306,U_8300))
              & U_8308 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8310),U_8301)),U_8300)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8300),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8310),U_8300)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8310),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ? [U_8299,U_8298] :
              ( ~ hBOOL(hAPP(U_8306,U_8298))
              & U_8308 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8310),U_8299)),U_8298)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8298),U_8310))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8298)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8310)) )
        | ( ~ hBOOL(hAPP(U_8306,U_8308))
          & U_8310 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_8309,U_8307,U_8305] :
        ( ( ( ! [U_8297,U_8296] :
                ( hBOOL(hAPP(U_8305,U_8296))
                | U_8307 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8309),U_8297)),U_8296)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8296),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8309),U_8296)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8309),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [U_8295,U_8294] :
                ( hBOOL(hAPP(U_8305,U_8294))
                | U_8307 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8309),U_8295)),U_8294)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8294),U_8309))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8294)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8309)) )
          & ( hBOOL(hAPP(U_8305,U_8307))
            | U_8309 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_8305,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8307,U_8309))) ) ),
    inference(miniscope,[status(thm)],[f_2336_2]) ).

fof(f_2336_4,plain,
    ( ! [U_8310,U_8308,U_8306] :
        ( hBOOL(hAPP(U_8306,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8308,U_8310)))
        | ( ? [U_8301,U_8300] :
              ( ~ hBOOL(hAPP(U_8306,U_8300))
              & U_8308 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8310),U_8301)),U_8300)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8300),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8310),U_8300)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8310),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ? [U_8298] :
              ( ~ hBOOL(hAPP(U_8306,U_8298))
              & U_8308 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8310),sK208(U_8310,U_8308,U_8306))),U_8298)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8298),U_8310))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8298)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8310)) )
        | ( ~ hBOOL(hAPP(U_8306,U_8308))
          & U_8310 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_8309,U_8307,U_8305] :
        ( ( ( ! [U_8297,U_8296] :
                ( hBOOL(hAPP(U_8305,U_8296))
                | U_8307 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8309),U_8297)),U_8296)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8296),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8309),U_8296)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8309),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [U_8295,U_8294] :
                ( hBOOL(hAPP(U_8305,U_8294))
                | U_8307 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8309),U_8295)),U_8294)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8294),U_8309))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8294)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8309)) )
          & ( hBOOL(hAPP(U_8305,U_8307))
            | U_8309 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_8305,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8307,U_8309))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK208]),skolemize(U_8299,sK208(U_8310,U_8308,U_8306))],[f_2336_3]) ).

fof(f_2336_5,plain,
    ( ! [U_8310,U_8308,U_8306] :
        ( hBOOL(hAPP(U_8306,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8308,U_8310)))
        | ( ? [U_8301,U_8300] :
              ( ~ hBOOL(hAPP(U_8306,U_8300))
              & U_8308 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8310),U_8301)),U_8300)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8300),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8310),U_8300)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8310),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ~ hBOOL(hAPP(U_8306,sK209(U_8310,U_8308,U_8306)))
          & U_8308 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8310),sK208(U_8310,U_8308,U_8306))),sK209(U_8310,U_8308,U_8306))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK209(U_8310,U_8308,U_8306)),U_8310))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK209(U_8310,U_8308,U_8306)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8310)) )
        | ( ~ hBOOL(hAPP(U_8306,U_8308))
          & U_8310 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_8309,U_8307,U_8305] :
        ( ( ( ! [U_8297,U_8296] :
                ( hBOOL(hAPP(U_8305,U_8296))
                | U_8307 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8309),U_8297)),U_8296)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8296),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8309),U_8296)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8309),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [U_8295,U_8294] :
                ( hBOOL(hAPP(U_8305,U_8294))
                | U_8307 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8309),U_8295)),U_8294)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8294),U_8309))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8294)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8309)) )
          & ( hBOOL(hAPP(U_8305,U_8307))
            | U_8309 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_8305,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8307,U_8309))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK209]),skolemize(U_8298,sK209(U_8310,U_8308,U_8306))],[f_2336_4]) ).

fof(f_2336_6,plain,
    ( ! [U_8310,U_8308,U_8306] :
        ( hBOOL(hAPP(U_8306,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8308,U_8310)))
        | ( ? [U_8300] :
              ( ~ hBOOL(hAPP(U_8306,U_8300))
              & U_8308 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8310),sK210(U_8310,U_8308,U_8306))),U_8300)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8300),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8310),U_8300)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8310),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ~ hBOOL(hAPP(U_8306,sK209(U_8310,U_8308,U_8306)))
          & U_8308 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8310),sK208(U_8310,U_8308,U_8306))),sK209(U_8310,U_8308,U_8306))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK209(U_8310,U_8308,U_8306)),U_8310))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK209(U_8310,U_8308,U_8306)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8310)) )
        | ( ~ hBOOL(hAPP(U_8306,U_8308))
          & U_8310 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_8309,U_8307,U_8305] :
        ( ( ( ! [U_8297,U_8296] :
                ( hBOOL(hAPP(U_8305,U_8296))
                | U_8307 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8309),U_8297)),U_8296)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8296),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8309),U_8296)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8309),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [U_8295,U_8294] :
                ( hBOOL(hAPP(U_8305,U_8294))
                | U_8307 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8309),U_8295)),U_8294)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8294),U_8309))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8294)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8309)) )
          & ( hBOOL(hAPP(U_8305,U_8307))
            | U_8309 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_8305,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8307,U_8309))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK210]),skolemize(U_8301,sK210(U_8310,U_8308,U_8306))],[f_2336_5]) ).

fof(f_2336_7,plain,
    ( ! [U_8310,U_8308,U_8306] :
        ( hBOOL(hAPP(U_8306,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8308,U_8310)))
        | ( ~ hBOOL(hAPP(U_8306,sK211(U_8310,U_8308,U_8306)))
          & U_8308 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8310),sK210(U_8310,U_8308,U_8306))),sK211(U_8310,U_8308,U_8306))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK211(U_8310,U_8308,U_8306)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8310),sK211(U_8310,U_8308,U_8306)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8310),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ~ hBOOL(hAPP(U_8306,sK209(U_8310,U_8308,U_8306)))
          & U_8308 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8310),sK208(U_8310,U_8308,U_8306))),sK209(U_8310,U_8308,U_8306))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK209(U_8310,U_8308,U_8306)),U_8310))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK209(U_8310,U_8308,U_8306)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8310)) )
        | ( ~ hBOOL(hAPP(U_8306,U_8308))
          & U_8310 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_8309,U_8307,U_8305] :
        ( ( ( ! [U_8297,U_8296] :
                ( hBOOL(hAPP(U_8305,U_8296))
                | U_8307 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8309),U_8297)),U_8296)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8296),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8309),U_8296)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8309),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [U_8295,U_8294] :
                ( hBOOL(hAPP(U_8305,U_8294))
                | U_8307 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8309),U_8295)),U_8294)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8294),U_8309))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8294)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8309)) )
          & ( hBOOL(hAPP(U_8305,U_8307))
            | U_8309 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_8305,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8307,U_8309))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK211]),skolemize(U_8300,sK211(U_8310,U_8308,U_8306))],[f_2336_6]) ).

cnf(f_2336_8,plain,
    ( hBOOL(hAPP(U_8305,U_8307))
    | U_8309 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(U_8305,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8307,U_8309))) ),
    inference(clausify,[status(thm)],[f_2336_7]) ).

cnf(f_2336_9,plain,
    ( hBOOL(hAPP(U_8305,U_8294))
    | U_8307 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8309),U_8295)),U_8294)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8294),U_8309))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8294))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8309))
    | ~ hBOOL(hAPP(U_8305,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8307,U_8309))) ),
    inference(clausify,[status(thm)],[f_2336_7]) ).

cnf(f_2336_10,plain,
    ( hBOOL(hAPP(U_8305,U_8296))
    | U_8307 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8309),U_8297)),U_8296)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8296),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8309),U_8296))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8309),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(U_8305,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8307,U_8309))) ),
    inference(clausify,[status(thm)],[f_2336_7]) ).

cnf(f_2336_11,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8310))
    | U_8310 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8310),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_8306,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8308,U_8310))) ),
    inference(clausify,[status(thm)],[f_2336_7]) ).

cnf(f_2336_12,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK209(U_8310,U_8308,U_8306)))
    | U_8310 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8310),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_8306,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8308,U_8310))) ),
    inference(clausify,[status(thm)],[f_2336_7]) ).

cnf(f_2336_13,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK209(U_8310,U_8308,U_8306)),U_8310))
    | U_8310 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8310),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_8306,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8308,U_8310))) ),
    inference(clausify,[status(thm)],[f_2336_7]) ).

cnf(f_2336_14,plain,
    ( U_8308 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8310),sK208(U_8310,U_8308,U_8306))),sK209(U_8310,U_8308,U_8306))
    | U_8310 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8310),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_8306,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8308,U_8310))) ),
    inference(clausify,[status(thm)],[f_2336_7]) ).

cnf(f_2336_15,plain,
    ( ~ hBOOL(hAPP(U_8306,sK209(U_8310,U_8308,U_8306)))
    | U_8310 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8310),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_8306,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8308,U_8310))) ),
    inference(clausify,[status(thm)],[f_2336_7]) ).

cnf(f_2336_16,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8310))
    | ~ hBOOL(hAPP(U_8306,U_8308))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8310),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_8306,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8308,U_8310))) ),
    inference(clausify,[status(thm)],[f_2336_7]) ).

cnf(f_2336_17,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK209(U_8310,U_8308,U_8306)))
    | ~ hBOOL(hAPP(U_8306,U_8308))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8310),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_8306,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8308,U_8310))) ),
    inference(clausify,[status(thm)],[f_2336_7]) ).

cnf(f_2336_18,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK209(U_8310,U_8308,U_8306)),U_8310))
    | ~ hBOOL(hAPP(U_8306,U_8308))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8310),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_8306,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8308,U_8310))) ),
    inference(clausify,[status(thm)],[f_2336_7]) ).

cnf(f_2336_19,plain,
    ( U_8308 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8310),sK208(U_8310,U_8308,U_8306))),sK209(U_8310,U_8308,U_8306))
    | ~ hBOOL(hAPP(U_8306,U_8308))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8310),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_8306,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8308,U_8310))) ),
    inference(clausify,[status(thm)],[f_2336_7]) ).

cnf(f_2336_20,plain,
    ( ~ hBOOL(hAPP(U_8306,sK209(U_8310,U_8308,U_8306)))
    | ~ hBOOL(hAPP(U_8306,U_8308))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8310),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_8306,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8308,U_8310))) ),
    inference(clausify,[status(thm)],[f_2336_7]) ).

cnf(f_2336_21,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8310))
    | U_8310 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8310),sK211(U_8310,U_8308,U_8306)))
    | hBOOL(hAPP(U_8306,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8308,U_8310))) ),
    inference(clausify,[status(thm)],[f_2336_7]) ).

cnf(f_2336_22,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK209(U_8310,U_8308,U_8306)))
    | U_8310 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8310),sK211(U_8310,U_8308,U_8306)))
    | hBOOL(hAPP(U_8306,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8308,U_8310))) ),
    inference(clausify,[status(thm)],[f_2336_7]) ).

cnf(f_2336_23,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK209(U_8310,U_8308,U_8306)),U_8310))
    | U_8310 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8310),sK211(U_8310,U_8308,U_8306)))
    | hBOOL(hAPP(U_8306,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8308,U_8310))) ),
    inference(clausify,[status(thm)],[f_2336_7]) ).

cnf(f_2336_24,plain,
    ( U_8308 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8310),sK208(U_8310,U_8308,U_8306))),sK209(U_8310,U_8308,U_8306))
    | U_8310 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8310),sK211(U_8310,U_8308,U_8306)))
    | hBOOL(hAPP(U_8306,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8308,U_8310))) ),
    inference(clausify,[status(thm)],[f_2336_7]) ).

cnf(f_2336_25,plain,
    ( ~ hBOOL(hAPP(U_8306,sK209(U_8310,U_8308,U_8306)))
    | U_8310 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8310),sK211(U_8310,U_8308,U_8306)))
    | hBOOL(hAPP(U_8306,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8308,U_8310))) ),
    inference(clausify,[status(thm)],[f_2336_7]) ).

cnf(f_2336_26,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8310))
    | U_8310 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK211(U_8310,U_8308,U_8306)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_8306,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8308,U_8310))) ),
    inference(clausify,[status(thm)],[f_2336_7]) ).

cnf(f_2336_27,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK209(U_8310,U_8308,U_8306)))
    | U_8310 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK211(U_8310,U_8308,U_8306)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_8306,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8308,U_8310))) ),
    inference(clausify,[status(thm)],[f_2336_7]) ).

cnf(f_2336_28,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK209(U_8310,U_8308,U_8306)),U_8310))
    | U_8310 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK211(U_8310,U_8308,U_8306)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_8306,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8308,U_8310))) ),
    inference(clausify,[status(thm)],[f_2336_7]) ).

cnf(f_2336_29,plain,
    ( U_8308 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8310),sK208(U_8310,U_8308,U_8306))),sK209(U_8310,U_8308,U_8306))
    | U_8310 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK211(U_8310,U_8308,U_8306)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_8306,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8308,U_8310))) ),
    inference(clausify,[status(thm)],[f_2336_7]) ).

cnf(f_2336_30,plain,
    ( ~ hBOOL(hAPP(U_8306,sK209(U_8310,U_8308,U_8306)))
    | U_8310 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK211(U_8310,U_8308,U_8306)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_8306,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8308,U_8310))) ),
    inference(clausify,[status(thm)],[f_2336_7]) ).

cnf(f_2336_31,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8310))
    | U_8310 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_8308 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8310),sK210(U_8310,U_8308,U_8306))),sK211(U_8310,U_8308,U_8306))
    | hBOOL(hAPP(U_8306,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8308,U_8310))) ),
    inference(clausify,[status(thm)],[f_2336_7]) ).

cnf(f_2336_32,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK209(U_8310,U_8308,U_8306)))
    | U_8310 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_8308 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8310),sK210(U_8310,U_8308,U_8306))),sK211(U_8310,U_8308,U_8306))
    | hBOOL(hAPP(U_8306,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8308,U_8310))) ),
    inference(clausify,[status(thm)],[f_2336_7]) ).

cnf(f_2336_33,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK209(U_8310,U_8308,U_8306)),U_8310))
    | U_8310 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_8308 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8310),sK210(U_8310,U_8308,U_8306))),sK211(U_8310,U_8308,U_8306))
    | hBOOL(hAPP(U_8306,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8308,U_8310))) ),
    inference(clausify,[status(thm)],[f_2336_7]) ).

cnf(f_2336_34,plain,
    ( U_8308 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8310),sK208(U_8310,U_8308,U_8306))),sK209(U_8310,U_8308,U_8306))
    | U_8310 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_8308 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8310),sK210(U_8310,U_8308,U_8306))),sK211(U_8310,U_8308,U_8306))
    | hBOOL(hAPP(U_8306,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8308,U_8310))) ),
    inference(clausify,[status(thm)],[f_2336_7]) ).

cnf(f_2336_35,plain,
    ( ~ hBOOL(hAPP(U_8306,sK209(U_8310,U_8308,U_8306)))
    | U_8310 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_8308 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8310),sK210(U_8310,U_8308,U_8306))),sK211(U_8310,U_8308,U_8306))
    | hBOOL(hAPP(U_8306,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8308,U_8310))) ),
    inference(clausify,[status(thm)],[f_2336_7]) ).

cnf(f_2336_36,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8310))
    | U_8310 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(U_8306,sK211(U_8310,U_8308,U_8306)))
    | hBOOL(hAPP(U_8306,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8308,U_8310))) ),
    inference(clausify,[status(thm)],[f_2336_7]) ).

cnf(f_2336_37,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK209(U_8310,U_8308,U_8306)))
    | U_8310 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(U_8306,sK211(U_8310,U_8308,U_8306)))
    | hBOOL(hAPP(U_8306,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8308,U_8310))) ),
    inference(clausify,[status(thm)],[f_2336_7]) ).

cnf(f_2336_38,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK209(U_8310,U_8308,U_8306)),U_8310))
    | U_8310 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(U_8306,sK211(U_8310,U_8308,U_8306)))
    | hBOOL(hAPP(U_8306,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8308,U_8310))) ),
    inference(clausify,[status(thm)],[f_2336_7]) ).

cnf(f_2336_39,plain,
    ( U_8308 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8310),sK208(U_8310,U_8308,U_8306))),sK209(U_8310,U_8308,U_8306))
    | U_8310 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(U_8306,sK211(U_8310,U_8308,U_8306)))
    | hBOOL(hAPP(U_8306,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8308,U_8310))) ),
    inference(clausify,[status(thm)],[f_2336_7]) ).

cnf(f_2336_40,plain,
    ( ~ hBOOL(hAPP(U_8306,sK209(U_8310,U_8308,U_8306)))
    | U_8310 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(U_8306,sK211(U_8310,U_8308,U_8306)))
    | hBOOL(hAPP(U_8306,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8308,U_8310))) ),
    inference(clausify,[status(thm)],[f_2336_7]) ).

cnf(f_2336_41,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8310))
    | ~ hBOOL(hAPP(U_8306,U_8308))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8310),sK211(U_8310,U_8308,U_8306)))
    | hBOOL(hAPP(U_8306,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8308,U_8310))) ),
    inference(clausify,[status(thm)],[f_2336_7]) ).

cnf(f_2336_42,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK209(U_8310,U_8308,U_8306)))
    | ~ hBOOL(hAPP(U_8306,U_8308))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8310),sK211(U_8310,U_8308,U_8306)))
    | hBOOL(hAPP(U_8306,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8308,U_8310))) ),
    inference(clausify,[status(thm)],[f_2336_7]) ).

cnf(f_2336_43,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK209(U_8310,U_8308,U_8306)),U_8310))
    | ~ hBOOL(hAPP(U_8306,U_8308))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8310),sK211(U_8310,U_8308,U_8306)))
    | hBOOL(hAPP(U_8306,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8308,U_8310))) ),
    inference(clausify,[status(thm)],[f_2336_7]) ).

cnf(f_2336_44,plain,
    ( U_8308 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8310),sK208(U_8310,U_8308,U_8306))),sK209(U_8310,U_8308,U_8306))
    | ~ hBOOL(hAPP(U_8306,U_8308))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8310),sK211(U_8310,U_8308,U_8306)))
    | hBOOL(hAPP(U_8306,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8308,U_8310))) ),
    inference(clausify,[status(thm)],[f_2336_7]) ).

cnf(f_2336_45,plain,
    ( ~ hBOOL(hAPP(U_8306,sK209(U_8310,U_8308,U_8306)))
    | ~ hBOOL(hAPP(U_8306,U_8308))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8310),sK211(U_8310,U_8308,U_8306)))
    | hBOOL(hAPP(U_8306,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8308,U_8310))) ),
    inference(clausify,[status(thm)],[f_2336_7]) ).

cnf(f_2336_46,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8310))
    | ~ hBOOL(hAPP(U_8306,U_8308))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK211(U_8310,U_8308,U_8306)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_8306,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8308,U_8310))) ),
    inference(clausify,[status(thm)],[f_2336_7]) ).

cnf(f_2336_47,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK209(U_8310,U_8308,U_8306)))
    | ~ hBOOL(hAPP(U_8306,U_8308))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK211(U_8310,U_8308,U_8306)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_8306,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8308,U_8310))) ),
    inference(clausify,[status(thm)],[f_2336_7]) ).

cnf(f_2336_48,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK209(U_8310,U_8308,U_8306)),U_8310))
    | ~ hBOOL(hAPP(U_8306,U_8308))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK211(U_8310,U_8308,U_8306)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_8306,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8308,U_8310))) ),
    inference(clausify,[status(thm)],[f_2336_7]) ).

cnf(f_2336_49,plain,
    ( U_8308 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8310),sK208(U_8310,U_8308,U_8306))),sK209(U_8310,U_8308,U_8306))
    | ~ hBOOL(hAPP(U_8306,U_8308))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK211(U_8310,U_8308,U_8306)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_8306,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8308,U_8310))) ),
    inference(clausify,[status(thm)],[f_2336_7]) ).

cnf(f_2336_50,plain,
    ( ~ hBOOL(hAPP(U_8306,sK209(U_8310,U_8308,U_8306)))
    | ~ hBOOL(hAPP(U_8306,U_8308))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK211(U_8310,U_8308,U_8306)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(U_8306,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8308,U_8310))) ),
    inference(clausify,[status(thm)],[f_2336_7]) ).

cnf(f_2336_51,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8310))
    | ~ hBOOL(hAPP(U_8306,U_8308))
    | U_8308 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8310),sK210(U_8310,U_8308,U_8306))),sK211(U_8310,U_8308,U_8306))
    | hBOOL(hAPP(U_8306,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8308,U_8310))) ),
    inference(clausify,[status(thm)],[f_2336_7]) ).

cnf(f_2336_52,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK209(U_8310,U_8308,U_8306)))
    | ~ hBOOL(hAPP(U_8306,U_8308))
    | U_8308 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8310),sK210(U_8310,U_8308,U_8306))),sK211(U_8310,U_8308,U_8306))
    | hBOOL(hAPP(U_8306,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8308,U_8310))) ),
    inference(clausify,[status(thm)],[f_2336_7]) ).

cnf(f_2336_53,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK209(U_8310,U_8308,U_8306)),U_8310))
    | ~ hBOOL(hAPP(U_8306,U_8308))
    | U_8308 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8310),sK210(U_8310,U_8308,U_8306))),sK211(U_8310,U_8308,U_8306))
    | hBOOL(hAPP(U_8306,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8308,U_8310))) ),
    inference(clausify,[status(thm)],[f_2336_7]) ).

cnf(f_2336_54,plain,
    ( U_8308 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8310),sK208(U_8310,U_8308,U_8306))),sK209(U_8310,U_8308,U_8306))
    | ~ hBOOL(hAPP(U_8306,U_8308))
    | U_8308 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8310),sK210(U_8310,U_8308,U_8306))),sK211(U_8310,U_8308,U_8306))
    | hBOOL(hAPP(U_8306,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8308,U_8310))) ),
    inference(clausify,[status(thm)],[f_2336_7]) ).

cnf(f_2336_55,plain,
    ( ~ hBOOL(hAPP(U_8306,sK209(U_8310,U_8308,U_8306)))
    | ~ hBOOL(hAPP(U_8306,U_8308))
    | U_8308 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8310),sK210(U_8310,U_8308,U_8306))),sK211(U_8310,U_8308,U_8306))
    | hBOOL(hAPP(U_8306,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8308,U_8310))) ),
    inference(clausify,[status(thm)],[f_2336_7]) ).

cnf(f_2336_56,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8310))
    | ~ hBOOL(hAPP(U_8306,U_8308))
    | ~ hBOOL(hAPP(U_8306,sK211(U_8310,U_8308,U_8306)))
    | hBOOL(hAPP(U_8306,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8308,U_8310))) ),
    inference(clausify,[status(thm)],[f_2336_7]) ).

cnf(f_2336_57,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK209(U_8310,U_8308,U_8306)))
    | ~ hBOOL(hAPP(U_8306,U_8308))
    | ~ hBOOL(hAPP(U_8306,sK211(U_8310,U_8308,U_8306)))
    | hBOOL(hAPP(U_8306,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8308,U_8310))) ),
    inference(clausify,[status(thm)],[f_2336_7]) ).

cnf(f_2336_58,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK209(U_8310,U_8308,U_8306)),U_8310))
    | ~ hBOOL(hAPP(U_8306,U_8308))
    | ~ hBOOL(hAPP(U_8306,sK211(U_8310,U_8308,U_8306)))
    | hBOOL(hAPP(U_8306,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8308,U_8310))) ),
    inference(clausify,[status(thm)],[f_2336_7]) ).

cnf(f_2336_59,plain,
    ( U_8308 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8310),sK208(U_8310,U_8308,U_8306))),sK209(U_8310,U_8308,U_8306))
    | ~ hBOOL(hAPP(U_8306,U_8308))
    | ~ hBOOL(hAPP(U_8306,sK211(U_8310,U_8308,U_8306)))
    | hBOOL(hAPP(U_8306,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8308,U_8310))) ),
    inference(clausify,[status(thm)],[f_2336_7]) ).

cnf(f_2336_60,plain,
    ( ~ hBOOL(hAPP(U_8306,sK209(U_8310,U_8308,U_8306)))
    | ~ hBOOL(hAPP(U_8306,U_8308))
    | ~ hBOOL(hAPP(U_8306,sK211(U_8310,U_8308,U_8306)))
    | hBOOL(hAPP(U_8306,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8308,U_8310))) ),
    inference(clausify,[status(thm)],[f_2336_7]) ).

fof(f_2337_1,plain,
    ! [V_q,V_b,V_r,V_c] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) ),
    inference(fof_nnf,[status(thm)],[fact_zmult2__lemma__aux3]) ).

fof(f_2337_2,plain,
    ! [U_8314,U_8313,U_8312,U_8311] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8313),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8314,U_8311))),U_8312)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8312),U_8313))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8312))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8311)) ),
    inference(variable_rename,[status(thm)],[f_2337_1]) ).

cnf(f_2337_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8313),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8314,U_8311))),U_8312)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8312),U_8313))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8312))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8311)) ),
    inference(clausify,[status(thm)],[f_2337_2]) ).

fof(f_2338_1,plain,
    ! [V_q,V_b,V_r,V_c] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) ),
    inference(fof_nnf,[status(thm)],[fact_zmult2__lemma__aux4]) ).

fof(f_2338_2,plain,
    ! [U_8318,U_8317,U_8316,U_8315] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8317),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8318,U_8315))),U_8316)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8317),U_8315)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8316),U_8317))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8316))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8315)) ),
    inference(variable_rename,[status(thm)],[f_2338_1]) ).

cnf(f_2338_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8317),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8318,U_8315))),U_8316)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8317),U_8315)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8316),U_8317))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8316))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8315)) ),
    inference(clausify,[status(thm)],[f_2338_2]) ).

fof(f_2339_1,plain,
    ! [V_q,V_r,V_b,V_c] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) ),
    inference(fof_nnf,[status(thm)],[fact_zmult2__lemma__aux1]) ).

fof(f_2339_2,plain,
    ! [U_8322,U_8321,U_8320,U_8319] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8320),U_8319)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8320),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8322,U_8319))),U_8321)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8321),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8320),U_8321))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8319)) ),
    inference(variable_rename,[status(thm)],[f_2339_1]) ).

cnf(f_2339_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8320),U_8319)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8320),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8322,U_8319))),U_8321)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8321),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8320),U_8321))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8319)) ),
    inference(clausify,[status(thm)],[f_2339_2]) ).

fof(f_2340_1,plain,
    ! [V_q,V_r,V_b,V_c] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) ),
    inference(fof_nnf,[status(thm)],[fact_zmult2__lemma__aux2]) ).

fof(f_2340_2,plain,
    ! [U_8326,U_8325,U_8324,U_8323] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8324),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8326,U_8323))),U_8325)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8325),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8324),U_8325))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8323)) ),
    inference(variable_rename,[status(thm)],[f_2340_1]) ).

cnf(f_2340_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8324),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8326,U_8323))),U_8325)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8325),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8324),U_8325))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8323)) ),
    inference(clausify,[status(thm)],[f_2340_2]) ).

fof(f_2341_1,plain,
    ! [V_y,V_q_1,V_b_1,V_a_1] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a_1,V_b_1) = V_y
      | V_b_1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_y)) )
        & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) )
      | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_b_1))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) )
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) )
      | V_a_1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_1),V_q_1)),V_y) ),
    inference(fof_nnf,[status(thm)],[fact_divmod__int__rel__mod__eq]) ).

fof(f_2341_2,plain,
    ! [U_8330,U_8329,U_8328,U_8327] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8327,U_8328) = U_8330
      | U_8328 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8330),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8328),U_8330)) )
        & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8328)) )
      | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8330),U_8328))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8330)) )
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8328)) )
      | U_8327 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8328),U_8329)),U_8330) ),
    inference(variable_rename,[status(thm)],[f_2341_1]) ).

cnf(f_2341_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8328))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8328))
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8327,U_8328) = U_8330
    | U_8328 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_8327 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8328),U_8329)),U_8330) ),
    inference(clausify,[status(thm)],[f_2341_2]) ).

cnf(f_2341_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8330),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8328),U_8330))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8328))
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8327,U_8328) = U_8330
    | U_8328 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_8327 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8328),U_8329)),U_8330) ),
    inference(clausify,[status(thm)],[f_2341_2]) ).

cnf(f_2341_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8328))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8330),U_8328))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8330))
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8327,U_8328) = U_8330
    | U_8328 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_8327 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8328),U_8329)),U_8330) ),
    inference(clausify,[status(thm)],[f_2341_2]) ).

cnf(f_2341_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8330),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8328),U_8330))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8330),U_8328))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8330))
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8327,U_8328) = U_8330
    | U_8328 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_8327 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8328),U_8329)),U_8330) ),
    inference(clausify,[status(thm)],[f_2341_2]) ).

fof(f_2342_1,plain,
    ! [V_w,V_v] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))),
    inference(fof_nnf,[status(thm)],[fact_zmod__number__of__Bit0]) ).

fof(f_2342_2,plain,
    ! [U_8332,U_8331] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_8331)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_8332))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8331),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8332))),
    inference(variable_rename,[status(thm)],[f_2342_1]) ).

cnf(f_2342_3,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_8331)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_8332))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8331),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8332))),
    inference(clausify,[status(thm)],[f_2342_2]) ).

fof(f_2343_1,plain,
    ! [V_b,V_a,V_c] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b),V_c))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) ),
    inference(fof_nnf,[status(thm)],[fact_zmod__zmult2__eq]) ).

fof(f_2343_2,plain,
    ! [U_8335,U_8334,U_8333] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8334,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8335),U_8333)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8335),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8334),U_8335),U_8333))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8334,U_8335))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8333)) ),
    inference(variable_rename,[status(thm)],[f_2343_1]) ).

cnf(f_2343_3,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8334,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8335),U_8333)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8335),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8334),U_8335),U_8333))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8334,U_8335))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8333)) ),
    inference(clausify,[status(thm)],[f_2343_2]) ).

fof(f_2344_1,plain,
    ! [V_a,V_b] :
      ( ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a)),V_b) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))),c_Groups_Oone__class_Oone(tc_Int_Oint))
          | c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
        & ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a)),V_b) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))
          | c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
      | V_b = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(fof_nnf,[status(thm)],[fact_zdiv__zminus1__eq__if]) ).

fof(f_2344_2,plain,
    ! [U_8337,U_8336] :
      ( ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8337)),U_8336) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8337),U_8336))),c_Groups_Oone__class_Oone(tc_Int_Oint))
          | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8337,U_8336) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
        & ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8337)),U_8336) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8337),U_8336))
          | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8337,U_8336) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
      | U_8336 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_2344_1]) ).

cnf(f_2344_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8337)),U_8336) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8337),U_8336))
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8337,U_8336) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_8336 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2344_2]) ).

cnf(f_2344_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8337)),U_8336) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8337),U_8336))),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8337,U_8336) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_8336 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2344_2]) ).

fof(f_2345_1,plain,
    ! [V_a,V_b] :
      ( ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))),c_Groups_Oone__class_Oone(tc_Int_Oint))
          | c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
        & ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))
          | c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
      | V_b = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(fof_nnf,[status(thm)],[fact_zdiv__zminus2__eq__if]) ).

fof(f_2345_2,plain,
    ! [U_8339,U_8338] :
      ( ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8339),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8338)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8339),U_8338))),c_Groups_Oone__class_Oone(tc_Int_Oint))
          | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8339,U_8338) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
        & ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8339),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8338)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8339),U_8338))
          | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8339,U_8338) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
      | U_8338 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_2345_1]) ).

cnf(f_2345_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8339),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8338)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8339),U_8338))
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8339,U_8338) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_8338 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2345_2]) ).

cnf(f_2345_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8339),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8338)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8339),U_8338))),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8339,U_8338) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_8338 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2345_2]) ).

fof(f_2346_1,plain,
    ! [V_A_2] :
      ( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)) = V_A_2
      | ~ c_Nat__Transfer_Onat__set(V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__return__embed]) ).

fof(f_2346_2,plain,
    ! [U_8340] :
      ( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8340)) = U_8340
      | ~ c_Nat__Transfer_Onat__set(U_8340) ),
    inference(variable_rename,[status(thm)],[f_2346_1]) ).

cnf(f_2346_3,plain,
    ( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8340)) = U_8340
    | ~ c_Nat__Transfer_Onat__set(U_8340) ),
    inference(clausify,[status(thm)],[f_2346_2]) ).

fof(f_2347_1,plain,
    ! [V_n_2,V_P_2,V_k_2] :
      ( ( ( hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
          | ? [B_i,B_j] :
              ( ~ hBOOL(hAPP(hAPP(V_P_2,B_i),B_j))
              & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) ) )
        & ( ! [B_i,B_j] :
              ( hBOOL(hAPP(hAPP(V_P_2,B_i),B_j))
              | V_n_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) )
          | ~ hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) ),
    inference(fof_nnf,[status(thm)],[fact_split__pos__lemma]) ).

fof(f_2347_2,plain,
    ! [U_8347,U_8346,U_8345] :
      ( ( ( hBOOL(hAPP(hAPP(U_8346,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8347),U_8345)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8347,U_8345)))
          | ? [U_8344,U_8343] :
              ( ~ hBOOL(hAPP(hAPP(U_8346,U_8344),U_8343))
              & U_8347 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8345),U_8344)),U_8343)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8343),U_8345))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8343)) ) )
        & ( ! [U_8342,U_8341] :
              ( hBOOL(hAPP(hAPP(U_8346,U_8342),U_8341))
              | U_8347 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8345),U_8342)),U_8341)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8341),U_8345))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8341)) )
          | ~ hBOOL(hAPP(hAPP(U_8346,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8347),U_8345)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8347,U_8345))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8345)) ),
    inference(variable_rename,[status(thm)],[f_2347_1]) ).

fof(f_2347_3,plain,
    ! [U_8347,U_8346,U_8345] :
      ( ( ( hBOOL(hAPP(hAPP(U_8346,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8347),U_8345)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8347,U_8345)))
          | ? [U_8343] :
              ( ~ hBOOL(hAPP(hAPP(U_8346,sK212(U_8347,U_8346,U_8345)),U_8343))
              & U_8347 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8345),sK212(U_8347,U_8346,U_8345))),U_8343)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8343),U_8345))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8343)) ) )
        & ( ! [U_8342,U_8341] :
              ( hBOOL(hAPP(hAPP(U_8346,U_8342),U_8341))
              | U_8347 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8345),U_8342)),U_8341)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8341),U_8345))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8341)) )
          | ~ hBOOL(hAPP(hAPP(U_8346,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8347),U_8345)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8347,U_8345))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8345)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK212]),skolemize(U_8344,sK212(U_8347,U_8346,U_8345))],[f_2347_2]) ).

fof(f_2347_4,plain,
    ! [U_8347,U_8346,U_8345] :
      ( ( ( hBOOL(hAPP(hAPP(U_8346,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8347),U_8345)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8347,U_8345)))
          | ( ~ hBOOL(hAPP(hAPP(U_8346,sK212(U_8347,U_8346,U_8345)),sK213(U_8347,U_8346,U_8345)))
            & U_8347 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8345),sK212(U_8347,U_8346,U_8345))),sK213(U_8347,U_8346,U_8345))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK213(U_8347,U_8346,U_8345)),U_8345))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK213(U_8347,U_8346,U_8345))) ) )
        & ( ! [U_8342,U_8341] :
              ( hBOOL(hAPP(hAPP(U_8346,U_8342),U_8341))
              | U_8347 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8345),U_8342)),U_8341)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8341),U_8345))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8341)) )
          | ~ hBOOL(hAPP(hAPP(U_8346,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8347),U_8345)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8347,U_8345))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8345)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK213]),skolemize(U_8343,sK213(U_8347,U_8346,U_8345))],[f_2347_3]) ).

cnf(f_2347_5,plain,
    ( hBOOL(hAPP(hAPP(U_8346,U_8342),U_8341))
    | U_8347 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8345),U_8342)),U_8341)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8341),U_8345))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8341))
    | ~ hBOOL(hAPP(hAPP(U_8346,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8347),U_8345)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8347,U_8345)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8345)) ),
    inference(clausify,[status(thm)],[f_2347_4]) ).

cnf(f_2347_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK213(U_8347,U_8346,U_8345)))
    | hBOOL(hAPP(hAPP(U_8346,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8347),U_8345)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8347,U_8345)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8345)) ),
    inference(clausify,[status(thm)],[f_2347_4]) ).

cnf(f_2347_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK213(U_8347,U_8346,U_8345)),U_8345))
    | hBOOL(hAPP(hAPP(U_8346,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8347),U_8345)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8347,U_8345)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8345)) ),
    inference(clausify,[status(thm)],[f_2347_4]) ).

cnf(f_2347_8,plain,
    ( U_8347 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8345),sK212(U_8347,U_8346,U_8345))),sK213(U_8347,U_8346,U_8345))
    | hBOOL(hAPP(hAPP(U_8346,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8347),U_8345)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8347,U_8345)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8345)) ),
    inference(clausify,[status(thm)],[f_2347_4]) ).

cnf(f_2347_9,plain,
    ( ~ hBOOL(hAPP(hAPP(U_8346,sK212(U_8347,U_8346,U_8345)),sK213(U_8347,U_8346,U_8345)))
    | hBOOL(hAPP(hAPP(U_8346,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8347),U_8345)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8347,U_8345)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8345)) ),
    inference(clausify,[status(thm)],[f_2347_4]) ).

fof(f_2348_1,plain,
    ! [V_n_2,V_P_2,V_k_2] :
      ( ( ( hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
          | ? [B_i,B_j] :
              ( ~ hBOOL(hAPP(hAPP(V_P_2,B_i),B_j))
              & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) ) )
        & ( ! [B_i,B_j] :
              ( hBOOL(hAPP(hAPP(V_P_2,B_i),B_j))
              | V_n_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) )
          | ~ hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(fof_nnf,[status(thm)],[fact_split__neg__lemma]) ).

fof(f_2348_2,plain,
    ! [U_8354,U_8353,U_8352] :
      ( ( ( hBOOL(hAPP(hAPP(U_8353,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8354),U_8352)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8354,U_8352)))
          | ? [U_8351,U_8350] :
              ( ~ hBOOL(hAPP(hAPP(U_8353,U_8351),U_8350))
              & U_8354 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8352),U_8351)),U_8350)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8350),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8352),U_8350)) ) )
        & ( ! [U_8349,U_8348] :
              ( hBOOL(hAPP(hAPP(U_8353,U_8349),U_8348))
              | U_8354 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8352),U_8349)),U_8348)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8348),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8352),U_8348)) )
          | ~ hBOOL(hAPP(hAPP(U_8353,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8354),U_8352)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8354,U_8352))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8352),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_2348_1]) ).

fof(f_2348_3,plain,
    ! [U_8354,U_8353,U_8352] :
      ( ( ( hBOOL(hAPP(hAPP(U_8353,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8354),U_8352)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8354,U_8352)))
          | ? [U_8350] :
              ( ~ hBOOL(hAPP(hAPP(U_8353,sK214(U_8354,U_8353,U_8352)),U_8350))
              & U_8354 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8352),sK214(U_8354,U_8353,U_8352))),U_8350)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8350),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8352),U_8350)) ) )
        & ( ! [U_8349,U_8348] :
              ( hBOOL(hAPP(hAPP(U_8353,U_8349),U_8348))
              | U_8354 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8352),U_8349)),U_8348)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8348),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8352),U_8348)) )
          | ~ hBOOL(hAPP(hAPP(U_8353,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8354),U_8352)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8354,U_8352))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8352),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK214]),skolemize(U_8351,sK214(U_8354,U_8353,U_8352))],[f_2348_2]) ).

fof(f_2348_4,plain,
    ! [U_8354,U_8353,U_8352] :
      ( ( ( hBOOL(hAPP(hAPP(U_8353,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8354),U_8352)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8354,U_8352)))
          | ( ~ hBOOL(hAPP(hAPP(U_8353,sK214(U_8354,U_8353,U_8352)),sK215(U_8354,U_8353,U_8352)))
            & U_8354 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8352),sK214(U_8354,U_8353,U_8352))),sK215(U_8354,U_8353,U_8352))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK215(U_8354,U_8353,U_8352)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8352),sK215(U_8354,U_8353,U_8352))) ) )
        & ( ! [U_8349,U_8348] :
              ( hBOOL(hAPP(hAPP(U_8353,U_8349),U_8348))
              | U_8354 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8352),U_8349)),U_8348)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8348),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8352),U_8348)) )
          | ~ hBOOL(hAPP(hAPP(U_8353,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8354),U_8352)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8354,U_8352))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8352),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK215]),skolemize(U_8350,sK215(U_8354,U_8353,U_8352))],[f_2348_3]) ).

cnf(f_2348_5,plain,
    ( hBOOL(hAPP(hAPP(U_8353,U_8349),U_8348))
    | U_8354 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8352),U_8349)),U_8348)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8348),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8352),U_8348))
    | ~ hBOOL(hAPP(hAPP(U_8353,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8354),U_8352)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8354,U_8352)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8352),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2348_4]) ).

cnf(f_2348_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8352),sK215(U_8354,U_8353,U_8352)))
    | hBOOL(hAPP(hAPP(U_8353,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8354),U_8352)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8354,U_8352)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8352),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2348_4]) ).

cnf(f_2348_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK215(U_8354,U_8353,U_8352)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(U_8353,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8354),U_8352)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8354,U_8352)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8352),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2348_4]) ).

cnf(f_2348_8,plain,
    ( U_8354 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8352),sK214(U_8354,U_8353,U_8352))),sK215(U_8354,U_8353,U_8352))
    | hBOOL(hAPP(hAPP(U_8353,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8354),U_8352)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8354,U_8352)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8352),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2348_4]) ).

cnf(f_2348_9,plain,
    ( ~ hBOOL(hAPP(hAPP(U_8353,sK214(U_8354,U_8353,U_8352)),sK215(U_8354,U_8353,U_8352)))
    | hBOOL(hAPP(hAPP(U_8353,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8354),U_8352)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8354,U_8352)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8352),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2348_4]) ).

fof(f_2349_1,plain,
    ! [V_A_2] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),V_A_2))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2))) )
        & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),V_A_2)) ) )
      | ~ c_Nat__Transfer_Onat__set(V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__set__relations_I1_J]) ).

fof(f_2349_2,plain,
    ! [U_8355] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),U_8355))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8355))) )
        & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8355)))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),U_8355)) ) )
      | ~ c_Nat__Transfer_Onat__set(U_8355) ),
    inference(variable_rename,[status(thm)],[f_2349_1]) ).

cnf(f_2349_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8355)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),U_8355))
    | ~ c_Nat__Transfer_Onat__set(U_8355) ),
    inference(clausify,[status(thm)],[f_2349_2]) ).

cnf(f_2349_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),U_8355))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8355)))
    | ~ c_Nat__Transfer_Onat__set(U_8355) ),
    inference(clausify,[status(thm)],[f_2349_2]) ).

fof(f_2350_1,plain,
    ! [V_A_2] :
      ( hAPP(c_Finite__Set_Ocard(tc_Int_Oint),V_A_2) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2))
      | ~ c_Nat__Transfer_Onat__set(V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J]) ).

fof(f_2350_2,plain,
    ! [U_8356] :
      ( hAPP(c_Finite__Set_Ocard(tc_Int_Oint),U_8356) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8356))
      | ~ c_Nat__Transfer_Onat__set(U_8356) ),
    inference(variable_rename,[status(thm)],[f_2350_1]) ).

cnf(f_2350_3,plain,
    ( hAPP(c_Finite__Set_Ocard(tc_Int_Oint),U_8356) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8356))
    | ~ c_Nat__Transfer_Onat__set(U_8356) ),
    inference(clausify,[status(thm)],[f_2350_2]) ).

fof(f_2351_1,plain,
    ! [V_B_2,V_A_2] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2)) ) )
      | ~ c_Nat__Transfer_Onat__set(V_B_2)
      | ~ c_Nat__Transfer_Onat__set(V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__set__relations_I5_J]) ).

fof(f_2351_2,plain,
    ! [U_8358,U_8357] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_8357),U_8358))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8357)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8358))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8357)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8358)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_8357),U_8358)) ) )
      | ~ c_Nat__Transfer_Onat__set(U_8358)
      | ~ c_Nat__Transfer_Onat__set(U_8357) ),
    inference(variable_rename,[status(thm)],[f_2351_1]) ).

cnf(f_2351_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8357)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8358)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_8357),U_8358))
    | ~ c_Nat__Transfer_Onat__set(U_8358)
    | ~ c_Nat__Transfer_Onat__set(U_8357) ),
    inference(clausify,[status(thm)],[f_2351_2]) ).

cnf(f_2351_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_8357),U_8358))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8357)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8358)))
    | ~ c_Nat__Transfer_Onat__set(U_8358)
    | ~ c_Nat__Transfer_Onat__set(U_8357) ),
    inference(clausify,[status(thm)],[f_2351_2]) ).

fof(f_2352_1,plain,
    ! [V_k,V_l] :
      ( ( c_SMT_Oz3mod(V_k,V_l) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_l))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) )
      & ( c_SMT_Oz3mod(V_k,V_l) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) ) ),
    inference(fof_nnf,[status(thm)],[fact_z3mod__def]) ).

fof(f_2352_2,plain,
    ! [U_8360,U_8359] :
      ( ( c_SMT_Oz3mod(U_8360,U_8359) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8360,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8359))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8359)) )
      & ( c_SMT_Oz3mod(U_8360,U_8359) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8360,U_8359)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8359)) ) ),
    inference(variable_rename,[status(thm)],[f_2352_1]) ).

fof(f_2352_3,plain,
    ( ! [U_8364,U_8362] :
        ( c_SMT_Oz3mod(U_8364,U_8362) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8364,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8362))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8362)) )
    & ! [U_8363,U_8361] :
        ( c_SMT_Oz3mod(U_8363,U_8361) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8363,U_8361)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8361)) ) ),
    inference(miniscope,[status(thm)],[f_2352_2]) ).

cnf(f_2352_4,plain,
    ( c_SMT_Oz3mod(U_8363,U_8361) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8363,U_8361)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8361)) ),
    inference(clausify,[status(thm)],[f_2352_3]) ).

cnf(f_2352_5,plain,
    ( c_SMT_Oz3mod(U_8364,U_8362) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8364,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8362))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8362)) ),
    inference(clausify,[status(thm)],[f_2352_3]) ).

fof(f_2353_1,plain,
    ! [V_n,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__m1__odd]) ).

fof(f_2353_2,plain,
    ! [U_8366,U_8365] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_8365),hAPP(c_Int_Onumber__class_Onumber__of(U_8365),c_Int_OMin)),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_8366))) = hAPP(c_Int_Onumber__class_Onumber__of(U_8365),c_Int_OMin)
      | ~ class_Int_Onumber__ring(U_8365) ),
    inference(variable_rename,[status(thm)],[f_2353_1]) ).

cnf(f_2353_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_8365),hAPP(c_Int_Onumber__class_Onumber__of(U_8365),c_Int_OMin)),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_8366))) = hAPP(c_Int_Onumber__class_Onumber__of(U_8365),c_Int_OMin)
    | ~ class_Int_Onumber__ring(U_8365) ),
    inference(clausify,[status(thm)],[f_2353_2]) ).

fof(f_2354_1,plain,
    ! [V_n,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = c_Groups_Oone__class_Oone(T_a)
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__m1__even]) ).

fof(f_2354_2,plain,
    ! [U_8368,U_8367] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_8367),hAPP(c_Int_Onumber__class_Onumber__of(U_8367),c_Int_OMin)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_8368)) = c_Groups_Oone__class_Oone(U_8367)
      | ~ class_Int_Onumber__ring(U_8367) ),
    inference(variable_rename,[status(thm)],[f_2354_1]) ).

cnf(f_2354_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_8367),hAPP(c_Int_Onumber__class_Onumber__of(U_8367),c_Int_OMin)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_8368)) = c_Groups_Oone__class_Oone(U_8367)
    | ~ class_Int_Onumber__ring(U_8367) ),
    inference(clausify,[status(thm)],[f_2354_2]) ).

fof(f_2355_1,plain,
    ! [V_v_H] :
      ( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) )
      & ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) ) ),
    inference(fof_nnf,[status(thm)],[fact_one__mod__nat__number__of]) ).

fof(f_2355_2,plain,
    ! [U_8369] :
      ( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_8369)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8369)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8369))) )
      & ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_8369)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8369))) ) ),
    inference(variable_rename,[status(thm)],[f_2355_1]) ).

fof(f_2355_3,plain,
    ( ! [U_8371] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_8371)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8371)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8371))) )
    & ! [U_8370] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_8370)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8370))) ) ),
    inference(miniscope,[status(thm)],[f_2355_2]) ).

cnf(f_2355_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_8370)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8370))) ),
    inference(clausify,[status(thm)],[f_2355_3]) ).

cnf(f_2355_5,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_8371)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8371)))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8371))) ),
    inference(clausify,[status(thm)],[f_2355_3]) ).

fof(f_2356_1,plain,
    ! [V_n,V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_m)),
    inference(fof_nnf,[status(thm)],[fact_mod__less__eq__dividend]) ).

fof(f_2356_2,plain,
    ! [U_8373,U_8372] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8372,U_8373)),U_8372)),
    inference(variable_rename,[status(thm)],[f_2356_1]) ).

cnf(f_2356_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8372,U_8373)),U_8372)),
    inference(clausify,[status(thm)],[f_2356_2]) ).

fof(f_2357_1,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I7_J]) ).

cnf(f_2357_2,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),
    inference(clausify,[status(thm)],[f_2357_1]) ).

fof(f_2358_1,plain,
    ! [V_n,V_m] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_mod__less]) ).

fof(f_2358_2,plain,
    ! [U_8375,U_8374] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8374,U_8375) = U_8374
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8374),U_8375)) ),
    inference(variable_rename,[status(thm)],[f_2358_1]) ).

cnf(f_2358_3,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8374,U_8375) = U_8374
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8374),U_8375)) ),
    inference(clausify,[status(thm)],[f_2358_2]) ).

fof(f_2359_1,plain,
    ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_n),
    inference(fof_nnf,[status(thm)],[fact_mod__Suc__eq__Suc__mod]) ).

fof(f_2359_2,plain,
    ! [U_8377,U_8376] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_8376),U_8377) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8376,U_8377)),U_8377),
    inference(variable_rename,[status(thm)],[f_2359_1]) ).

cnf(f_2359_3,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_8376),U_8377) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8376,U_8377)),U_8377),
    inference(clausify,[status(thm)],[f_2359_2]) ).

fof(f_2360_1,plain,
    ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_k) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)),
    inference(fof_nnf,[status(thm)],[fact_mod__mult__distrib]) ).

fof(f_2360_2,plain,
    ! [U_8380,U_8379,U_8378] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8378,U_8379)),U_8380) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8378),U_8380),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8379),U_8380)),
    inference(variable_rename,[status(thm)],[f_2360_1]) ).

cnf(f_2360_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8378,U_8379)),U_8380) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8378),U_8380),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8379),U_8380)),
    inference(clausify,[status(thm)],[f_2360_2]) ).

fof(f_2361_1,plain,
    ! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)),
    inference(fof_nnf,[status(thm)],[fact_mod__mult__distrib2]) ).

fof(f_2361_2,plain,
    ! [U_8383,U_8382,U_8381] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8381),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8382,U_8383)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8381),U_8382),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8381),U_8383)),
    inference(variable_rename,[status(thm)],[f_2361_1]) ).

cnf(f_2361_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8381),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8382,U_8383)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8381),U_8382),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8381),U_8383)),
    inference(clausify,[status(thm)],[f_2361_2]) ).

fof(f_2362_1,plain,
    c_Int_OBit1(c_Int_OMin) = c_Int_OMin,
    inference(fof_nnf,[status(thm)],[fact_Bit1__Min]) ).

cnf(f_2362_2,plain,
    c_Int_OBit1(c_Int_OMin) = c_Int_OMin,
    inference(clausify,[status(thm)],[f_2362_1]) ).

fof(f_2363_1,plain,
    ! [V_l_2] :
      ( ( c_Int_OMin = c_Int_OBit1(V_l_2)
        | c_Int_OMin != V_l_2 )
      & ( c_Int_OMin = V_l_2
        | c_Int_OMin != c_Int_OBit1(V_l_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I43_J]) ).

fof(f_2363_2,plain,
    ! [U_8384] :
      ( ( c_Int_OMin = c_Int_OBit1(U_8384)
        | c_Int_OMin != U_8384 )
      & ( c_Int_OMin = U_8384
        | c_Int_OMin != c_Int_OBit1(U_8384) ) ),
    inference(variable_rename,[status(thm)],[f_2363_1]) ).

fof(f_2363_3,plain,
    ( ! [U_8386] :
        ( c_Int_OMin = c_Int_OBit1(U_8386)
        | c_Int_OMin != U_8386 )
    & ! [U_8385] :
        ( c_Int_OMin = U_8385
        | c_Int_OMin != c_Int_OBit1(U_8385) ) ),
    inference(miniscope,[status(thm)],[f_2363_2]) ).

cnf(f_2363_4,plain,
    ( c_Int_OMin = U_8385
    | c_Int_OMin != c_Int_OBit1(U_8385) ),
    inference(clausify,[status(thm)],[f_2363_3]) ).

cnf(f_2363_5,plain,
    ( c_Int_OMin = c_Int_OBit1(U_8386)
    | c_Int_OMin != U_8386 ),
    inference(clausify,[status(thm)],[f_2363_3]) ).

fof(f_2364_1,plain,
    ! [V_k_2] :
      ( ( c_Int_OBit1(V_k_2) = c_Int_OMin
        | V_k_2 != c_Int_OMin )
      & ( V_k_2 = c_Int_OMin
        | c_Int_OBit1(V_k_2) != c_Int_OMin ) ),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I47_J]) ).

fof(f_2364_2,plain,
    ! [U_8387] :
      ( ( c_Int_OBit1(U_8387) = c_Int_OMin
        | U_8387 != c_Int_OMin )
      & ( U_8387 = c_Int_OMin
        | c_Int_OBit1(U_8387) != c_Int_OMin ) ),
    inference(variable_rename,[status(thm)],[f_2364_1]) ).

fof(f_2364_3,plain,
    ( ! [U_8389] :
        ( c_Int_OBit1(U_8389) = c_Int_OMin
        | U_8389 != c_Int_OMin )
    & ! [U_8388] :
        ( U_8388 = c_Int_OMin
        | c_Int_OBit1(U_8388) != c_Int_OMin ) ),
    inference(miniscope,[status(thm)],[f_2364_2]) ).

cnf(f_2364_4,plain,
    ( U_8388 = c_Int_OMin
    | c_Int_OBit1(U_8388) != c_Int_OMin ),
    inference(clausify,[status(thm)],[f_2364_3]) ).

cnf(f_2364_5,plain,
    ( c_Int_OBit1(U_8389) = c_Int_OMin
    | U_8389 != c_Int_OMin ),
    inference(clausify,[status(thm)],[f_2364_3]) ).

fof(f_2365_1,plain,
    c_Int_OMin != c_Int_OPls,
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I40_J]) ).

cnf(f_2365_2,plain,
    c_Int_OMin != c_Int_OPls,
    inference(clausify,[status(thm)],[f_2365_1]) ).

fof(f_2366_1,plain,
    c_Int_OPls != c_Int_OMin,
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I37_J]) ).

cnf(f_2366_2,plain,
    c_Int_OPls != c_Int_OMin,
    inference(clausify,[status(thm)],[f_2366_1]) ).

fof(f_2367_1,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I24_J]) ).

cnf(f_2367_2,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),
    inference(clausify,[status(thm)],[f_2367_1]) ).

fof(f_2368_1,plain,
    ! [V_l] : c_Int_OMin != c_Int_OBit0(V_l),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I42_J]) ).

fof(f_2368_2,plain,
    ! [U_8390] : c_Int_OMin != c_Int_OBit0(U_8390),
    inference(variable_rename,[status(thm)],[f_2368_1]) ).

cnf(f_2368_3,plain,
    c_Int_OMin != c_Int_OBit0(U_8390),
    inference(clausify,[status(thm)],[f_2368_2]) ).

fof(f_2369_1,plain,
    ! [V_k] : c_Int_OBit0(V_k) != c_Int_OMin,
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I45_J]) ).

fof(f_2369_2,plain,
    ! [U_8391] : c_Int_OBit0(U_8391) != c_Int_OMin,
    inference(variable_rename,[status(thm)],[f_2369_1]) ).

cnf(f_2369_3,plain,
    c_Int_OBit0(U_8391) != c_Int_OMin,
    inference(clausify,[status(thm)],[f_2369_2]) ).

fof(f_2370_1,plain,
    ! [V_n,V_m] :
      ( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n))
        | hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = V_n )
      & ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) != V_n ) ),
    inference(fof_nnf,[status(thm)],[fact_mod__Suc]) ).

fof(f_2370_2,plain,
    ! [U_8393,U_8392] :
      ( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_8392),U_8393) = hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8392,U_8393))
        | hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8392,U_8393)) = U_8393 )
      & ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_8392),U_8393) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8392,U_8393)) != U_8393 ) ),
    inference(variable_rename,[status(thm)],[f_2370_1]) ).

fof(f_2370_3,plain,
    ( ! [U_8397,U_8395] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_8395),U_8397) = hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8395,U_8397))
        | hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8395,U_8397)) = U_8397 )
    & ! [U_8396,U_8394] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_8394),U_8396) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8394,U_8396)) != U_8396 ) ),
    inference(miniscope,[status(thm)],[f_2370_2]) ).

cnf(f_2370_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_8394),U_8396) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8394,U_8396)) != U_8396 ),
    inference(clausify,[status(thm)],[f_2370_3]) ).

cnf(f_2370_5,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_8395),U_8397) = hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8395,U_8397))
    | hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8395,U_8397)) = U_8397 ),
    inference(clausify,[status(thm)],[f_2370_3]) ).

fof(f_2371_1,plain,
    ! [V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_mod__1]) ).

fof(f_2371_2,plain,
    ! [U_8398] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8398,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_2371_1]) ).

cnf(f_2371_3,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8398,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_2371_2]) ).

fof(f_2372_1,plain,
    ! [V_m,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_mod__less__divisor]) ).

fof(f_2372_2,plain,
    ! [U_8400,U_8399] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8400,U_8399)),U_8399))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8399)) ),
    inference(variable_rename,[status(thm)],[f_2372_1]) ).

cnf(f_2372_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8400,U_8399)),U_8399))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8399)) ),
    inference(clausify,[status(thm)],[f_2372_2]) ).

fof(f_2373_1,plain,
    ! [V_d_2,V_m_2] :
      ( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ! [B_q] : V_m_2 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_d_2),B_q) )
      & ( ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_d_2),B_q)
        | c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,V_d_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(fof_nnf,[status(thm)],[fact_mod__eq__0__iff]) ).

fof(f_2373_2,plain,
    ! [U_8404,U_8403] :
      ( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8403,U_8404) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ! [U_8402] : U_8403 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8404),U_8402) )
      & ( ? [U_8401] : U_8403 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8404),U_8401)
        | c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8403,U_8404) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_2373_1]) ).

fof(f_2373_3,plain,
    ( ! [U_8408,U_8406] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8406,U_8408) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ! [U_8402] : U_8406 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8408),U_8402) )
    & ! [U_8407,U_8405] :
        ( ? [U_8401] : U_8405 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8407),U_8401)
        | c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8405,U_8407) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_2373_2]) ).

fof(f_2373_4,plain,
    ( ! [U_8408,U_8406] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8406,U_8408) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ! [U_8402] : U_8406 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8408),U_8402) )
    & ! [U_8407,U_8405] :
        ( U_8405 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8407),sK216(U_8407,U_8405))
        | c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8405,U_8407) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK216]),skolemize(U_8401,sK216(U_8407,U_8405))],[f_2373_3]) ).

cnf(f_2373_5,plain,
    ( U_8405 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8407),sK216(U_8407,U_8405))
    | c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8405,U_8407) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_2373_4]) ).

cnf(f_2373_6,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8406,U_8408) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_8406 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8408),U_8402) ),
    inference(clausify,[status(thm)],[f_2373_4]) ).

fof(f_2374_1,plain,
    ! [V_n,V_m] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_n)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_mod__geq]) ).

fof(f_2374_2,plain,
    ! [U_8410,U_8409] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8409,U_8410) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_8409),U_8410),U_8410)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8409),U_8410)) ),
    inference(variable_rename,[status(thm)],[f_2374_1]) ).

cnf(f_2374_3,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8409,U_8410) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_8409),U_8410),U_8410)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8409),U_8410)) ),
    inference(clausify,[status(thm)],[f_2374_2]) ).

fof(f_2375_1,plain,
    ! [V_n,V_m] :
      ( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_n)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) )
      & ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ),
    inference(fof_nnf,[status(thm)],[fact_mod__if]) ).

fof(f_2375_2,plain,
    ! [U_8412,U_8411] :
      ( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8411,U_8412) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_8411),U_8412),U_8412)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8411),U_8412)) )
      & ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8411,U_8412) = U_8411
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8411),U_8412)) ) ),
    inference(variable_rename,[status(thm)],[f_2375_1]) ).

fof(f_2375_3,plain,
    ( ! [U_8416,U_8414] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8414,U_8416) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_8414),U_8416),U_8416)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8414),U_8416)) )
    & ! [U_8415,U_8413] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8413,U_8415) = U_8413
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8413),U_8415)) ) ),
    inference(miniscope,[status(thm)],[f_2375_2]) ).

cnf(f_2375_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8413,U_8415) = U_8413
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8413),U_8415)) ),
    inference(clausify,[status(thm)],[f_2375_3]) ).

cnf(f_2375_5,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8414,U_8416) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_8414),U_8416),U_8416)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8414),U_8416)) ),
    inference(clausify,[status(thm)],[f_2375_3]) ).

fof(f_2376_1,plain,
    ! [V_m,V_n,V_k] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)),V_m),V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n),
    inference(fof_nnf,[status(thm)],[fact_mod__mult__self3]) ).

fof(f_2376_2,plain,
    ! [U_8419,U_8418,U_8417] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8417),U_8418)),U_8419),U_8418) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8419,U_8418),
    inference(variable_rename,[status(thm)],[f_2376_1]) ).

cnf(f_2376_3,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8417),U_8418)),U_8419),U_8418) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8419,U_8418),
    inference(clausify,[status(thm)],[f_2376_2]) ).

fof(f_2377_1,plain,
    ! [V_m,V_n] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_n)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) ),
    inference(fof_nnf,[status(thm)],[fact_le__mod__geq]) ).

fof(f_2377_2,plain,
    ! [U_8421,U_8420] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8421,U_8420) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_8421),U_8420),U_8420)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8420),U_8421)) ),
    inference(variable_rename,[status(thm)],[f_2377_1]) ).

cnf(f_2377_3,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8421,U_8420) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_8421),U_8420),U_8420)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8420),U_8421)) ),
    inference(clausify,[status(thm)],[f_2377_2]) ).

fof(f_2378_1,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(fof_nnf,[status(thm)],[fact_bin__less__0__simps_I2_J]) ).

cnf(f_2378_2,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(clausify,[status(thm)],[f_2378_1]) ).

fof(f_2379_1,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I23_J]) ).

cnf(f_2379_2,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
    inference(clausify,[status(thm)],[f_2379_1]) ).

fof(f_2380_1,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I20_J]) ).

cnf(f_2380_2,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
    inference(clausify,[status(thm)],[f_2380_1]) ).

fof(f_2381_1,plain,
    ! [V_k_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),V_k_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),V_k_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I26_J]) ).

fof(f_2381_2,plain,
    ! [U_8422] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_8422)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),U_8422)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),U_8422))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_8422))) ) ),
    inference(variable_rename,[status(thm)],[f_2381_1]) ).

fof(f_2381_3,plain,
    ( ! [U_8424] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_8424)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),U_8424)) )
    & ! [U_8423] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),U_8423))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_8423))) ) ),
    inference(miniscope,[status(thm)],[f_2381_2]) ).

cnf(f_2381_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),U_8423))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_8423))) ),
    inference(clausify,[status(thm)],[f_2381_3]) ).

cnf(f_2381_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_8424)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),U_8424)) ),
    inference(clausify,[status(thm)],[f_2381_3]) ).

fof(f_2382_1,plain,
    ! [V_k_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin)) ) ),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I30_J]) ).

fof(f_2382_2,plain,
    ! [U_8425] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_8425)),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8425),c_Int_OMin)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8425),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_8425)),c_Int_OMin)) ) ),
    inference(variable_rename,[status(thm)],[f_2382_1]) ).

fof(f_2382_3,plain,
    ( ! [U_8427] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_8427)),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8427),c_Int_OMin)) )
    & ! [U_8426] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8426),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_8426)),c_Int_OMin)) ) ),
    inference(miniscope,[status(thm)],[f_2382_2]) ).

cnf(f_2382_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8426),c_Int_OMin))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_8426)),c_Int_OMin)) ),
    inference(clausify,[status(thm)],[f_2382_3]) ).

cnf(f_2382_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_8427)),c_Int_OMin))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8427),c_Int_OMin)) ),
    inference(clausify,[status(thm)],[f_2382_3]) ).

fof(f_2383_1,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I3_J]) ).

cnf(f_2383_2,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
    inference(clausify,[status(thm)],[f_2383_1]) ).

fof(f_2384_1,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I6_J]) ).

cnf(f_2384_2,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
    inference(clausify,[status(thm)],[f_2384_1]) ).

fof(f_2385_1,plain,
    ! [V_k_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OMin)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin)) ) ),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I13_J]) ).

fof(f_2385_2,plain,
    ! [U_8428] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_8428)),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8428),c_Int_OMin)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8428),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_8428)),c_Int_OMin)) ) ),
    inference(variable_rename,[status(thm)],[f_2385_1]) ).

fof(f_2385_3,plain,
    ( ! [U_8430] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_8430)),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8430),c_Int_OMin)) )
    & ! [U_8429] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8429),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_8429)),c_Int_OMin)) ) ),
    inference(miniscope,[status(thm)],[f_2385_2]) ).

cnf(f_2385_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8429),c_Int_OMin))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_8429)),c_Int_OMin)) ),
    inference(clausify,[status(thm)],[f_2385_3]) ).

cnf(f_2385_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_8430)),c_Int_OMin))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8430),c_Int_OMin)) ),
    inference(clausify,[status(thm)],[f_2385_3]) ).

fof(f_2386_1,plain,
    ! [V_k_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I9_J]) ).

fof(f_2386_2,plain,
    ! [U_8431] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_8431)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_8431)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_8431))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_8431))) ) ),
    inference(variable_rename,[status(thm)],[f_2386_1]) ).

fof(f_2386_3,plain,
    ( ! [U_8433] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_8433)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_8433)) )
    & ! [U_8432] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_8432))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_8432))) ) ),
    inference(miniscope,[status(thm)],[f_2386_2]) ).

cnf(f_2386_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_8432))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_8432))) ),
    inference(clausify,[status(thm)],[f_2386_3]) ).

cnf(f_2386_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_8433)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_8433)) ),
    inference(clausify,[status(thm)],[f_2386_3]) ).

fof(f_2387_1,plain,
    ! [V_k_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin)) ) ),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I28_J]) ).

fof(f_2387_2,plain,
    ! [U_8434] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_8434)),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8434),c_Int_OMin)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8434),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_8434)),c_Int_OMin)) ) ),
    inference(variable_rename,[status(thm)],[f_2387_1]) ).

fof(f_2387_3,plain,
    ( ! [U_8436] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_8436)),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8436),c_Int_OMin)) )
    & ! [U_8435] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8435),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_8435)),c_Int_OMin)) ) ),
    inference(miniscope,[status(thm)],[f_2387_2]) ).

cnf(f_2387_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8435),c_Int_OMin))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_8435)),c_Int_OMin)) ),
    inference(clausify,[status(thm)],[f_2387_3]) ).

cnf(f_2387_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_8436)),c_Int_OMin))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8436),c_Int_OMin)) ),
    inference(clausify,[status(thm)],[f_2387_3]) ).

fof(f_2388_1,plain,
    ! [V_k_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I8_J]) ).

fof(f_2388_2,plain,
    ! [U_8437] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_8437)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_8437)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_8437))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_8437))) ) ),
    inference(variable_rename,[status(thm)],[f_2388_1]) ).

fof(f_2388_3,plain,
    ( ! [U_8439] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_8439)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_8439)) )
    & ! [U_8438] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_8438))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_8438))) ) ),
    inference(miniscope,[status(thm)],[f_2388_2]) ).

cnf(f_2388_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_8438))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_8438))) ),
    inference(clausify,[status(thm)],[f_2388_3]) ).

cnf(f_2388_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_8439)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_8439)) ),
    inference(clausify,[status(thm)],[f_2388_3]) ).

fof(f_2389_1,plain,
    ! [V_y,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_y)),
    inference(fof_nnf,[status(thm)],[fact_Divides_Otransfer__int__nat__functions_I2_J]) ).

fof(f_2389_2,plain,
    ! [U_8441,U_8440] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8440),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8441)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8440,U_8441)),
    inference(variable_rename,[status(thm)],[f_2389_1]) ).

cnf(f_2389_3,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8440),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8441)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8440,U_8441)),
    inference(clausify,[status(thm)],[f_2389_2]) ).

fof(f_2390_1,plain,
    ! [V_b,V_a] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,V_b)) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_b)),
    inference(fof_nnf,[status(thm)],[fact_zmod__int]) ).

fof(f_2390_2,plain,
    ! [U_8443,U_8442] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8442,U_8443)) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8442),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8443)),
    inference(variable_rename,[status(thm)],[f_2390_1]) ).

cnf(f_2390_3,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8442,U_8443)) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8442),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8443)),
    inference(clausify,[status(thm)],[f_2390_2]) ).

fof(f_2391_1,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),
    inference(fof_nnf,[status(thm)],[fact_eq__number__of__Pls__Min]) ).

cnf(f_2391_2,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),
    inference(clausify,[status(thm)],[f_2391_1]) ).

fof(f_2392_1,plain,
    ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),V_c)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_b),V_c))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,V_c)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_b,V_c))),V_c)),
    inference(fof_nnf,[status(thm)],[fact_div__add1__eq]) ).

fof(f_2392_2,plain,
    ! [U_8446,U_8445,U_8444] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8444),U_8445)),U_8446) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_8444),U_8446)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_8445),U_8446))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8444,U_8446)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8445,U_8446))),U_8446)),
    inference(variable_rename,[status(thm)],[f_2392_1]) ).

cnf(f_2392_3,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8444),U_8445)),U_8446) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_8444),U_8446)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_8445),U_8446))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8444,U_8446)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8445,U_8446))),U_8446)),
    inference(clausify,[status(thm)],[f_2392_2]) ).

fof(f_2393_1,plain,
    c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(fof_nnf,[status(thm)],[fact_Int_OMin__def]) ).

cnf(f_2393_2,plain,
    c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(clausify,[status(thm)],[f_2393_1]) ).

fof(f_2394_1,plain,
    ! [V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),V_k) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k),
    inference(fof_nnf,[status(thm)],[fact_mult__Min]) ).

fof(f_2394_2,plain,
    ! [U_8447] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),U_8447) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8447),
    inference(variable_rename,[status(thm)],[f_2394_1]) ).

cnf(f_2394_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),U_8447) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8447),
    inference(clausify,[status(thm)],[f_2394_2]) ).

fof(f_2395_1,plain,
    hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))),
    inference(fof_nnf,[status(thm)],[fact_neg__number__of__Min]) ).

cnf(f_2395_2,plain,
    hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))),
    inference(clausify,[status(thm)],[f_2395_1]) ).

fof(f_2396_1,plain,
    c_Int_Opred(c_Int_OPls) = c_Int_OMin,
    inference(fof_nnf,[status(thm)],[fact_pred__Pls]) ).

cnf(f_2396_2,plain,
    c_Int_Opred(c_Int_OPls) = c_Int_OMin,
    inference(clausify,[status(thm)],[f_2396_1]) ).

fof(f_2397_1,plain,
    ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Opred(V_k),
    inference(fof_nnf,[status(thm)],[fact_add__Min__right]) ).

fof(f_2397_2,plain,
    ! [U_8448] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8448),c_Int_OMin) = c_Int_Opred(U_8448),
    inference(variable_rename,[status(thm)],[f_2397_1]) ).

cnf(f_2397_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8448),c_Int_OMin) = c_Int_Opred(U_8448),
    inference(clausify,[status(thm)],[f_2397_2]) ).

fof(f_2398_1,plain,
    ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),V_k) = c_Int_Opred(V_k),
    inference(fof_nnf,[status(thm)],[fact_add__Min]) ).

fof(f_2398_2,plain,
    ! [U_8449] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),U_8449) = c_Int_Opred(U_8449),
    inference(variable_rename,[status(thm)],[f_2398_1]) ).

cnf(f_2398_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),U_8449) = c_Int_Opred(U_8449),
    inference(clausify,[status(thm)],[f_2398_2]) ).

fof(f_2399_1,plain,
    c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin),
    inference(fof_nnf,[status(thm)],[fact_pred__Min]) ).

cnf(f_2399_2,plain,
    c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin),
    inference(clausify,[status(thm)],[f_2399_1]) ).

fof(f_2400_1,plain,
    ! [T_a] :
      ( ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin))
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_nonzero__number__of__Min]) ).

fof(f_2400_2,plain,
    ! [U_8450] :
      ( ~ c_Int_Oiszero(U_8450,hAPP(c_Int_Onumber__class_Onumber__of(U_8450),c_Int_OMin))
      | ~ class_Int_Onumber__ring(U_8450) ),
    inference(variable_rename,[status(thm)],[f_2400_1]) ).

cnf(f_2400_3,plain,
    ( ~ c_Int_Oiszero(U_8450,hAPP(c_Int_Onumber__class_Onumber__of(U_8450),c_Int_OMin))
    | ~ class_Int_Onumber__ring(U_8450) ),
    inference(clausify,[status(thm)],[f_2400_2]) ).

fof(f_2401_1,plain,
    c_Int_Osucc(c_Int_OMin) = c_Int_OPls,
    inference(fof_nnf,[status(thm)],[fact_succ__Min]) ).

cnf(f_2401_2,plain,
    c_Int_Osucc(c_Int_OMin) = c_Int_OPls,
    inference(clausify,[status(thm)],[f_2401_1]) ).

fof(f_2402_1,plain,
    ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Osucc(V_k),
    inference(fof_nnf,[status(thm)],[fact_diff__bin__simps_I2_J]) ).

fof(f_2402_2,plain,
    ! [U_8451] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8451),c_Int_OMin) = c_Int_Osucc(U_8451),
    inference(variable_rename,[status(thm)],[f_2402_1]) ).

cnf(f_2402_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8451),c_Int_OMin) = c_Int_Osucc(U_8451),
    inference(clausify,[status(thm)],[f_2402_2]) ).

fof(f_2403_1,plain,
    ! [V_m,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_mod__le__divisor]) ).

fof(f_2403_2,plain,
    ! [U_8453,U_8452] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8453,U_8452)),U_8452))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8452)) ),
    inference(variable_rename,[status(thm)],[f_2403_1]) ).

cnf(f_2403_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8453,U_8452)),U_8452))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8452)) ),
    inference(clausify,[status(thm)],[f_2403_2]) ).

fof(f_2404_1,plain,
    ! [V_m,V_n,V_k] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)),V_m)),V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n),
    inference(fof_nnf,[status(thm)],[fact_mod__mult__self4]) ).

fof(f_2404_2,plain,
    ! [U_8456,U_8455,U_8454] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8454),U_8455)),U_8456)),U_8455) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_8456),U_8455),
    inference(variable_rename,[status(thm)],[f_2404_1]) ).

cnf(f_2404_3,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8454),U_8455)),U_8456)),U_8455) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_8456),U_8455),
    inference(clausify,[status(thm)],[f_2404_2]) ).

fof(f_2405_1,plain,
    ! [V_z,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)),V_z) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_z)
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__minus1]) ).

fof(f_2405_2,plain,
    ! [U_8458,U_8457] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8457),hAPP(c_Int_Onumber__class_Onumber__of(U_8457),c_Int_OMin)),U_8458) = hAPP(c_Groups_Ouminus__class_Ouminus(U_8457),U_8458)
      | ~ class_Int_Onumber__ring(U_8457) ),
    inference(variable_rename,[status(thm)],[f_2405_1]) ).

cnf(f_2405_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8457),hAPP(c_Int_Onumber__class_Onumber__of(U_8457),c_Int_OMin)),U_8458) = hAPP(c_Groups_Ouminus__class_Ouminus(U_8457),U_8458)
    | ~ class_Int_Onumber__ring(U_8457) ),
    inference(clausify,[status(thm)],[f_2405_2]) ).

fof(f_2406_1,plain,
    ! [V_z,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_z)
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__minus1__right]) ).

fof(f_2406_2,plain,
    ! [U_8460,U_8459] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8459),U_8460),hAPP(c_Int_Onumber__class_Onumber__of(U_8459),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_8459),U_8460)
      | ~ class_Int_Onumber__ring(U_8459) ),
    inference(variable_rename,[status(thm)],[f_2406_1]) ).

cnf(f_2406_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8459),U_8460),hAPP(c_Int_Onumber__class_Onumber__of(U_8459),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_8459),U_8460)
    | ~ class_Int_Onumber__ring(U_8459) ),
    inference(clausify,[status(thm)],[f_2406_2]) ).

fof(f_2407_1,plain,
    ! [T_a] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_number__of__Min]) ).

fof(f_2407_2,plain,
    ! [U_8461] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_8461),c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(U_8461),c_Groups_Oone__class_Oone(U_8461))
      | ~ class_Int_Onumber__ring(U_8461) ),
    inference(variable_rename,[status(thm)],[f_2407_1]) ).

cnf(f_2407_3,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_8461),c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(U_8461),c_Groups_Oone__class_Oone(U_8461))
    | ~ class_Int_Onumber__ring(U_8461) ),
    inference(clausify,[status(thm)],[f_2407_2]) ).

fof(f_2408_1,plain,
    ! [T_a] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_arith__simps_I31_J]) ).

fof(f_2408_2,plain,
    ! [U_8462] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_8462),c_Groups_Oone__class_Oone(U_8462)) = hAPP(c_Int_Onumber__class_Onumber__of(U_8462),c_Int_OMin)
      | ~ class_Int_Onumber__ring(U_8462) ),
    inference(variable_rename,[status(thm)],[f_2408_1]) ).

cnf(f_2408_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_8462),c_Groups_Oone__class_Oone(U_8462)) = hAPP(c_Int_Onumber__class_Onumber__of(U_8462),c_Int_OMin)
    | ~ class_Int_Onumber__ring(U_8462) ),
    inference(clausify,[status(thm)],[f_2408_2]) ).

fof(f_2409_1,plain,
    ! [V_x,T_a] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)
      | ~ class_Int_Onumber__ring(T_a)
      | ~ class_Fields_Ofield__inverse__zero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_divide__minus1]) ).

fof(f_2409_2,plain,
    ! [U_8464,U_8463] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8463),U_8464),hAPP(c_Int_Onumber__class_Onumber__of(U_8463),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_8463),U_8464)
      | ~ class_Int_Onumber__ring(U_8463)
      | ~ class_Fields_Ofield__inverse__zero(U_8463) ),
    inference(variable_rename,[status(thm)],[f_2409_1]) ).

cnf(f_2409_3,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8463),U_8464),hAPP(c_Int_Onumber__class_Onumber__of(U_8463),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_8463),U_8464)
    | ~ class_Int_Onumber__ring(U_8463)
    | ~ class_Fields_Ofield__inverse__zero(U_8463) ),
    inference(clausify,[status(thm)],[f_2409_2]) ).

fof(f_2410_1,plain,
    ! [V_k_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin)) ) ),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I11_J]) ).

fof(f_2410_2,plain,
    ! [U_8465] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_8465)),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8465),c_Int_OMin)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8465),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_8465)),c_Int_OMin)) ) ),
    inference(variable_rename,[status(thm)],[f_2410_1]) ).

fof(f_2410_3,plain,
    ( ! [U_8467] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_8467)),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8467),c_Int_OMin)) )
    & ! [U_8466] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8466),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_8466)),c_Int_OMin)) ) ),
    inference(miniscope,[status(thm)],[f_2410_2]) ).

cnf(f_2410_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8466),c_Int_OMin))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_8466)),c_Int_OMin)) ),
    inference(clausify,[status(thm)],[f_2410_3]) ).

cnf(f_2410_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_8467)),c_Int_OMin))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8467),c_Int_OMin)) ),
    inference(clausify,[status(thm)],[f_2410_3]) ).

fof(f_2411_1,plain,
    ! [V_k_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I25_J]) ).

fof(f_2411_2,plain,
    ! [U_8468] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_8468)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_8468)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_8468))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_8468))) ) ),
    inference(variable_rename,[status(thm)],[f_2411_1]) ).

fof(f_2411_3,plain,
    ( ! [U_8470] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_8470)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_8470)) )
    & ! [U_8469] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_8469))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_8469))) ) ),
    inference(miniscope,[status(thm)],[f_2411_2]) ).

cnf(f_2411_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_8469))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_8469))) ),
    inference(clausify,[status(thm)],[f_2411_3]) ).

cnf(f_2411_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_8470)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_8470)) ),
    inference(clausify,[status(thm)],[f_2411_3]) ).

fof(f_2412_1,plain,
    ! [V_c,V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),V_b),V_c))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,V_b)),
    inference(fof_nnf,[status(thm)],[fact_mod__mult2__eq]) ).

fof(f_2412_2,plain,
    ! [U_8473,U_8472,U_8471] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8471,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8472),U_8473)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8472),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_8471),U_8472),U_8473))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8471,U_8472)),
    inference(variable_rename,[status(thm)],[f_2412_1]) ).

cnf(f_2412_3,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8471,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8472),U_8473)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8472),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_8471),U_8472),U_8473))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8471,U_8472)),
    inference(clausify,[status(thm)],[f_2412_2]) ).

fof(f_2413_1,plain,
    ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_b),V_c))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_b,V_c))),V_c)),
    inference(fof_nnf,[status(thm)],[fact_div__mult1__eq]) ).

fof(f_2413_2,plain,
    ! [U_8476,U_8475,U_8474] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8474),U_8475)),U_8476) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8474),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_8475),U_8476))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8474),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8475,U_8476))),U_8476)),
    inference(variable_rename,[status(thm)],[f_2413_1]) ).

cnf(f_2413_3,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8474),U_8475)),U_8476) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8474),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_8475),U_8476))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8474),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8475,U_8476))),U_8476)),
    inference(clausify,[status(thm)],[f_2413_2]) ).

fof(f_2414_1,plain,
    ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),
    inference(fof_nnf,[status(thm)],[fact_div__mod__equality_H]) ).

fof(f_2414_2,plain,
    ! [U_8478,U_8477] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_8477),U_8478)),U_8478) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_8477),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8477,U_8478)),
    inference(variable_rename,[status(thm)],[f_2414_1]) ).

cnf(f_2414_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_8477),U_8478)),U_8478) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_8477),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8477,U_8478)),
    inference(clausify,[status(thm)],[f_2414_2]) ).

fof(f_2415_1,plain,
    ! [V_m,V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),
    inference(fof_nnf,[status(thm)],[fact_mult__div__cancel]) ).

fof(f_2415_2,plain,
    ! [U_8480,U_8479] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8479),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_8480),U_8479)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_8480),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8480,U_8479)),
    inference(variable_rename,[status(thm)],[f_2415_1]) ).

cnf(f_2415_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8479),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_8480),U_8479)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_8480),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8480,U_8479)),
    inference(clausify,[status(thm)],[f_2415_2]) ).

fof(f_2416_1,plain,
    ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),V_n)),
    inference(fof_nnf,[status(thm)],[fact_Divides_Omod__div__equality_H]) ).

fof(f_2416_2,plain,
    ! [U_8482,U_8481] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8481,U_8482) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_8481),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_8481),U_8482)),U_8482)),
    inference(variable_rename,[status(thm)],[f_2416_1]) ).

cnf(f_2416_3,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8481,U_8482) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_8481),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_8481),U_8482)),U_8482)),
    inference(clausify,[status(thm)],[f_2416_2]) ).

fof(f_2417_1,plain,
    ! [V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[fact_zmod__minus1__right]) ).

fof(f_2417_2,plain,
    ! [U_8483] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8483,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[f_2417_1]) ).

cnf(f_2417_3,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8483,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_2417_2]) ).

fof(f_2418_1,plain,
    ! [V_l] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),V_l)),
    inference(fof_nnf,[status(thm)],[fact_diff__bin__simps_I4_J]) ).

fof(f_2418_2,plain,
    ! [U_8484] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_8484)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_8484)),
    inference(variable_rename,[status(thm)],[f_2418_1]) ).

cnf(f_2418_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_8484)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_8484)),
    inference(clausify,[status(thm)],[f_2418_2]) ).

fof(f_2419_1,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = c_Int_OBit1(c_Int_OPls),
    inference(fof_nnf,[status(thm)],[fact_minus__Min]) ).

cnf(f_2419_2,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = c_Int_OBit1(c_Int_OPls),
    inference(clausify,[status(thm)],[f_2419_1]) ).

fof(f_2420_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | ( ( V_n_2 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
            | V_m_2 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) )
          & ( V_n_2 != c_Groups_Oone__class_Oone(tc_Int_Oint)
            | V_m_2 != c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) )
      & ( ( V_n_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
          & V_m_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) )
        | ( V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
          & V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) != c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
    inference(fof_nnf,[status(thm)],[fact_zmult__eq__1__iff]) ).

fof(f_2420_2,plain,
    ! [U_8486,U_8485] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8485),U_8486) = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | ( ( U_8486 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
            | U_8485 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) )
          & ( U_8486 != c_Groups_Oone__class_Oone(tc_Int_Oint)
            | U_8485 != c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) )
      & ( ( U_8486 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
          & U_8485 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) )
        | ( U_8486 = c_Groups_Oone__class_Oone(tc_Int_Oint)
          & U_8485 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8485),U_8486) != c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[f_2420_1]) ).

fof(f_2420_3,plain,
    ( ! [U_8490,U_8488] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8488),U_8490) = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | ( ( U_8490 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
            | U_8488 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) )
          & ( U_8490 != c_Groups_Oone__class_Oone(tc_Int_Oint)
            | U_8488 != c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) )
    & ! [U_8489,U_8487] :
        ( ( U_8489 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
          & U_8487 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) )
        | ( U_8489 = c_Groups_Oone__class_Oone(tc_Int_Oint)
          & U_8487 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8487),U_8489) != c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
    inference(miniscope,[status(thm)],[f_2420_2]) ).

cnf(f_2420_4,plain,
    ( U_8487 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
    | U_8487 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8487),U_8489) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2420_3]) ).

cnf(f_2420_5,plain,
    ( U_8489 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
    | U_8487 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8487),U_8489) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2420_3]) ).

cnf(f_2420_6,plain,
    ( U_8487 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
    | U_8489 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8487),U_8489) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2420_3]) ).

cnf(f_2420_7,plain,
    ( U_8489 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
    | U_8489 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8487),U_8489) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2420_3]) ).

cnf(f_2420_8,plain,
    ( U_8490 != c_Groups_Oone__class_Oone(tc_Int_Oint)
    | U_8488 != c_Groups_Oone__class_Oone(tc_Int_Oint)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8488),U_8490) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2420_3]) ).

cnf(f_2420_9,plain,
    ( U_8490 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
    | U_8488 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8488),U_8490) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2420_3]) ).

fof(f_2421_1,plain,
    ! [V_n,V_m] :
      ( V_m = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
      | V_m = c_Groups_Oone__class_Oone(tc_Int_Oint)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(fof_nnf,[status(thm)],[fact_pos__zmult__eq__1__iff__lemma]) ).

fof(f_2421_2,plain,
    ! [U_8492,U_8491] :
      ( U_8491 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
      | U_8491 = c_Groups_Oone__class_Oone(tc_Int_Oint)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8491),U_8492) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_2421_1]) ).

cnf(f_2421_3,plain,
    ( U_8491 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
    | U_8491 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8491),U_8492) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2421_2]) ).

fof(f_2422_1,plain,
    ! [V_l] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),V_l)),
    inference(fof_nnf,[status(thm)],[fact_diff__bin__simps_I6_J]) ).

fof(f_2422_2,plain,
    ! [U_8493] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_8493)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_8493)),
    inference(variable_rename,[status(thm)],[f_2422_1]) ).

cnf(f_2422_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_8493)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_8493)),
    inference(clausify,[status(thm)],[f_2422_2]) ).

fof(f_2423_1,plain,
    ! [V_l] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),V_l)),
    inference(fof_nnf,[status(thm)],[fact_diff__bin__simps_I5_J]) ).

fof(f_2423_2,plain,
    ! [U_8494] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_8494)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_8494)),
    inference(variable_rename,[status(thm)],[f_2423_1]) ).

cnf(f_2423_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_8494)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_8494)),
    inference(clausify,[status(thm)],[f_2423_2]) ).

fof(f_2424_1,plain,
    ! [V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),
    inference(fof_nnf,[status(thm)],[fact_zdiv__minus1__right]) ).

fof(f_2424_2,plain,
    ! [U_8495] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8495),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8495),
    inference(variable_rename,[status(thm)],[f_2424_1]) ).

cnf(f_2424_3,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8495),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8495),
    inference(clausify,[status(thm)],[f_2424_2]) ).

fof(f_2425_1,plain,
    ! [V_k_2,V_n_2,V_P_2] :
      ( ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2)))
        | ( ? [B_i,B_j] :
              ( ~ hBOOL(hAPP(V_P_2,B_j))
              & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),B_i)),B_j)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2)) )
          & V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( ~ hBOOL(hAPP(V_P_2,V_n_2))
          & V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( ( ( ! [B_i,B_j] :
                ( hBOOL(hAPP(V_P_2,B_j))
                | V_n_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),B_i)),B_j)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2)) )
            | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( hBOOL(hAPP(V_P_2,V_n_2))
            | V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
        | ~ hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_split__mod]) ).

fof(f_2425_2,plain,
    ! [U_8502,U_8501,U_8500] :
      ( ( hBOOL(hAPP(U_8500,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8501,U_8502)))
        | ( ? [U_8499,U_8498] :
              ( ~ hBOOL(hAPP(U_8500,U_8498))
              & U_8501 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8502),U_8499)),U_8498)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8498),U_8502)) )
          & U_8502 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( ~ hBOOL(hAPP(U_8500,U_8501))
          & U_8502 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( ( ( ! [U_8497,U_8496] :
                ( hBOOL(hAPP(U_8500,U_8496))
                | U_8501 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8502),U_8497)),U_8496)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8496),U_8502)) )
            | U_8502 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( hBOOL(hAPP(U_8500,U_8501))
            | U_8502 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
        | ~ hBOOL(hAPP(U_8500,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8501,U_8502))) ) ),
    inference(variable_rename,[status(thm)],[f_2425_1]) ).

fof(f_2425_3,plain,
    ( ! [U_8508,U_8506,U_8504] :
        ( hBOOL(hAPP(U_8504,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8506,U_8508)))
        | ( ? [U_8499,U_8498] :
              ( ~ hBOOL(hAPP(U_8504,U_8498))
              & U_8506 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8508),U_8499)),U_8498)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8498),U_8508)) )
          & U_8508 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( ~ hBOOL(hAPP(U_8504,U_8506))
          & U_8508 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_8507,U_8505,U_8503] :
        ( ( ( ! [U_8497,U_8496] :
                ( hBOOL(hAPP(U_8503,U_8496))
                | U_8505 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8507),U_8497)),U_8496)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8496),U_8507)) )
            | U_8507 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( hBOOL(hAPP(U_8503,U_8505))
            | U_8507 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
        | ~ hBOOL(hAPP(U_8503,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8505,U_8507))) ) ),
    inference(miniscope,[status(thm)],[f_2425_2]) ).

fof(f_2425_4,plain,
    ( ! [U_8508,U_8506,U_8504] :
        ( hBOOL(hAPP(U_8504,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8506,U_8508)))
        | ( ? [U_8498] :
              ( ~ hBOOL(hAPP(U_8504,U_8498))
              & U_8506 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8508),sK217(U_8508,U_8506,U_8504))),U_8498)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8498),U_8508)) )
          & U_8508 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( ~ hBOOL(hAPP(U_8504,U_8506))
          & U_8508 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_8507,U_8505,U_8503] :
        ( ( ( ! [U_8497,U_8496] :
                ( hBOOL(hAPP(U_8503,U_8496))
                | U_8505 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8507),U_8497)),U_8496)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8496),U_8507)) )
            | U_8507 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( hBOOL(hAPP(U_8503,U_8505))
            | U_8507 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
        | ~ hBOOL(hAPP(U_8503,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8505,U_8507))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK217]),skolemize(U_8499,sK217(U_8508,U_8506,U_8504))],[f_2425_3]) ).

fof(f_2425_5,plain,
    ( ! [U_8508,U_8506,U_8504] :
        ( hBOOL(hAPP(U_8504,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8506,U_8508)))
        | ( ~ hBOOL(hAPP(U_8504,sK218(U_8508,U_8506,U_8504)))
          & U_8506 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8508),sK217(U_8508,U_8506,U_8504))),sK218(U_8508,U_8506,U_8504))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK218(U_8508,U_8506,U_8504)),U_8508))
          & U_8508 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( ~ hBOOL(hAPP(U_8504,U_8506))
          & U_8508 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_8507,U_8505,U_8503] :
        ( ( ( ! [U_8497,U_8496] :
                ( hBOOL(hAPP(U_8503,U_8496))
                | U_8505 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8507),U_8497)),U_8496)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8496),U_8507)) )
            | U_8507 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( hBOOL(hAPP(U_8503,U_8505))
            | U_8507 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
        | ~ hBOOL(hAPP(U_8503,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8505,U_8507))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK218]),skolemize(U_8498,sK218(U_8508,U_8506,U_8504))],[f_2425_4]) ).

cnf(f_2425_6,plain,
    ( hBOOL(hAPP(U_8503,U_8505))
    | U_8507 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(U_8503,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8505,U_8507))) ),
    inference(clausify,[status(thm)],[f_2425_5]) ).

cnf(f_2425_7,plain,
    ( hBOOL(hAPP(U_8503,U_8496))
    | U_8505 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8507),U_8497)),U_8496)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8496),U_8507))
    | U_8507 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(U_8503,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8505,U_8507))) ),
    inference(clausify,[status(thm)],[f_2425_5]) ).

cnf(f_2425_8,plain,
    ( U_8508 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_8508 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(U_8504,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8506,U_8508))) ),
    inference(clausify,[status(thm)],[f_2425_5]) ).

cnf(f_2425_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK218(U_8508,U_8506,U_8504)),U_8508))
    | U_8508 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(U_8504,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8506,U_8508))) ),
    inference(clausify,[status(thm)],[f_2425_5]) ).

cnf(f_2425_10,plain,
    ( U_8506 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8508),sK217(U_8508,U_8506,U_8504))),sK218(U_8508,U_8506,U_8504))
    | U_8508 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(U_8504,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8506,U_8508))) ),
    inference(clausify,[status(thm)],[f_2425_5]) ).

cnf(f_2425_11,plain,
    ( ~ hBOOL(hAPP(U_8504,sK218(U_8508,U_8506,U_8504)))
    | U_8508 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(U_8504,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8506,U_8508))) ),
    inference(clausify,[status(thm)],[f_2425_5]) ).

cnf(f_2425_12,plain,
    ( U_8508 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(U_8504,U_8506))
    | hBOOL(hAPP(U_8504,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8506,U_8508))) ),
    inference(clausify,[status(thm)],[f_2425_5]) ).

cnf(f_2425_13,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK218(U_8508,U_8506,U_8504)),U_8508))
    | ~ hBOOL(hAPP(U_8504,U_8506))
    | hBOOL(hAPP(U_8504,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8506,U_8508))) ),
    inference(clausify,[status(thm)],[f_2425_5]) ).

cnf(f_2425_14,plain,
    ( U_8506 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8508),sK217(U_8508,U_8506,U_8504))),sK218(U_8508,U_8506,U_8504))
    | ~ hBOOL(hAPP(U_8504,U_8506))
    | hBOOL(hAPP(U_8504,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8506,U_8508))) ),
    inference(clausify,[status(thm)],[f_2425_5]) ).

cnf(f_2425_15,plain,
    ( ~ hBOOL(hAPP(U_8504,sK218(U_8508,U_8506,U_8504)))
    | ~ hBOOL(hAPP(U_8504,U_8506))
    | hBOOL(hAPP(U_8504,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8506,U_8508))) ),
    inference(clausify,[status(thm)],[f_2425_5]) ).

fof(f_2426_1,plain,
    ! [V_q,V_b,V_r,V_c] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_q,V_c))),V_r)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_r),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) ),
    inference(fof_nnf,[status(thm)],[fact_mod__lemma]) ).

fof(f_2426_2,plain,
    ! [U_8512,U_8511,U_8510,U_8509] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8511),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8512,U_8509))),U_8510)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8511),U_8509)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8510),U_8511))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8509)) ),
    inference(variable_rename,[status(thm)],[f_2426_1]) ).

cnf(f_2426_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8511),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8512,U_8509))),U_8510)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8511),U_8509)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8510),U_8511))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8509)) ),
    inference(clausify,[status(thm)],[f_2426_2]) ).

fof(f_2427_1,plain,
    ! [V_m,V_k] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),V_k) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_k)) ),
    inference(fof_nnf,[status(thm)],[fact_Suc__times__mod__eq]) ).

fof(f_2427_2,plain,
    ! [U_8514,U_8513] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8513),U_8514)),U_8513) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_8513)) ),
    inference(variable_rename,[status(thm)],[f_2427_1]) ).

cnf(f_2427_3,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8513),U_8514)),U_8513) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_8513)) ),
    inference(clausify,[status(thm)],[f_2427_2]) ).

fof(f_2428_1,plain,
    ! [V_y,V_x] :
      ( hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,V_x),hAPP(c_Int_Onat,V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) ),
    inference(fof_nnf,[status(thm)],[fact_nat__mod__distrib]) ).

fof(f_2428_2,plain,
    ! [U_8516,U_8515] :
      ( hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8515,U_8516)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,U_8515),hAPP(c_Int_Onat,U_8516))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8516))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8515)) ),
    inference(variable_rename,[status(thm)],[f_2428_1]) ).

cnf(f_2428_3,plain,
    ( hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8515,U_8516)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,U_8515),hAPP(c_Int_Onat,U_8516))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8516))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8515)) ),
    inference(clausify,[status(thm)],[f_2428_2]) ).

fof(f_2429_1,plain,
    ! [V_y,V_x] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,V_x),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) ),
    inference(fof_nnf,[status(thm)],[fact_Divides_Otransfer__nat__int__functions_I2_J]) ).

fof(f_2429_2,plain,
    ! [U_8518,U_8517] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,U_8517),hAPP(c_Int_Onat,U_8518)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8517,U_8518))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8518))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8517)) ),
    inference(variable_rename,[status(thm)],[f_2429_1]) ).

cnf(f_2429_3,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,U_8517),hAPP(c_Int_Onat,U_8518)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8517,U_8518))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8518))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8517)) ),
    inference(clausify,[status(thm)],[f_2429_2]) ).

fof(f_2430_1,plain,
    ! [V_x,T_a] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)),V_x) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Oone__class_Oone(T_a)),V_x))
      | ~ class_Int_Onumber__ring(T_a)
      | ~ class_Fields_Ofield__inverse__zero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_minus1__divide]) ).

fof(f_2430_2,plain,
    ! [U_8520,U_8519] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8519),hAPP(c_Int_Onumber__class_Onumber__of(U_8519),c_Int_OMin)),U_8520) = hAPP(c_Groups_Ouminus__class_Ouminus(U_8519),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8519),c_Groups_Oone__class_Oone(U_8519)),U_8520))
      | ~ class_Int_Onumber__ring(U_8519)
      | ~ class_Fields_Ofield__inverse__zero(U_8519) ),
    inference(variable_rename,[status(thm)],[f_2430_1]) ).

cnf(f_2430_3,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8519),hAPP(c_Int_Onumber__class_Onumber__of(U_8519),c_Int_OMin)),U_8520) = hAPP(c_Groups_Ouminus__class_Ouminus(U_8519),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8519),c_Groups_Oone__class_Oone(U_8519)),U_8520))
    | ~ class_Int_Onumber__ring(U_8519)
    | ~ class_Fields_Ofield__inverse__zero(U_8519) ),
    inference(clausify,[status(thm)],[f_2430_2]) ).

fof(f_2431_1,plain,
    ! [V_b] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),V_b) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) ),
    inference(fof_nnf,[status(thm)],[fact_div__eq__minus1]) ).

fof(f_2431_2,plain,
    ! [U_8521] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),U_8521) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8521)) ),
    inference(variable_rename,[status(thm)],[f_2431_1]) ).

cnf(f_2431_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),U_8521) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8521)) ),
    inference(clausify,[status(thm)],[f_2431_2]) ).

fof(f_2432_1,plain,
    ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_n)),
    inference(fof_nnf,[status(thm)],[fact_mod__Suc__eq__mod__add3]) ).

fof(f_2432_2,plain,
    ! [U_8523,U_8522] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8522,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_8523)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8522,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),U_8523)),
    inference(variable_rename,[status(thm)],[f_2432_1]) ).

cnf(f_2432_3,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8522,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_8523)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8522,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),U_8523)),
    inference(clausify,[status(thm)],[f_2432_2]) ).

fof(f_2433_1,plain,
    ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m))),V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_m),V_n),
    inference(fof_nnf,[status(thm)],[fact_Suc__mod__eq__add3__mod]) ).

fof(f_2433_2,plain,
    ! [U_8525,U_8524] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_8524))),U_8525) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),U_8524),U_8525),
    inference(variable_rename,[status(thm)],[f_2433_1]) ).

cnf(f_2433_3,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_8524))),U_8525) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),U_8524),U_8525),
    inference(clausify,[status(thm)],[f_2433_2]) ).

fof(f_2434_1,plain,
    ! [V_v,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),
    inference(fof_nnf,[status(thm)],[fact_Suc__mod__eq__add3__mod__number__of]) ).

fof(f_2434_2,plain,
    ! [U_8527,U_8526] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_8526))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_8527)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),U_8526),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_8527)),
    inference(variable_rename,[status(thm)],[f_2434_1]) ).

cnf(f_2434_3,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_8526))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_8527)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),U_8526),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_8527)),
    inference(clausify,[status(thm)],[f_2434_2]) ).

fof(f_2435_1,plain,
    ! [V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
    inference(fof_nnf,[status(thm)],[fact_mod2__Suc__Suc]) ).

fof(f_2435_2,plain,
    ! [U_8528] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_8528)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8528,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
    inference(variable_rename,[status(thm)],[f_2435_1]) ).

cnf(f_2435_3,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_8528)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8528,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
    inference(clausify,[status(thm)],[f_2435_2]) ).

fof(f_2436_1,plain,
    ! [V_v_H,V_v] :
      ( ( ( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
            | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) )
          & ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)
            | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) ) )
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) )
      & ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) ) ),
    inference(fof_nnf,[status(thm)],[fact_mod__nat__number__of]) ).

fof(f_2436_2,plain,
    ! [U_8530,U_8529] :
      ( ( ( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_8529),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_8530)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8529),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8530)))
            | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8530))) )
          & ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_8529),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_8530)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_8529)
            | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8530))) ) )
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8529))) )
      & ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_8529),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_8530)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8529))) ) ),
    inference(variable_rename,[status(thm)],[f_2436_1]) ).

fof(f_2436_3,plain,
    ( ! [U_8534,U_8532] :
        ( ( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_8532),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_8534)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8532),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8534)))
            | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8534))) )
          & ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_8532),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_8534)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_8532)
            | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8534))) ) )
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8532))) )
    & ! [U_8533,U_8531] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_8531),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_8533)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8531))) ) ),
    inference(miniscope,[status(thm)],[f_2436_2]) ).

cnf(f_2436_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_8531),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_8533)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8531))) ),
    inference(clausify,[status(thm)],[f_2436_3]) ).

cnf(f_2436_5,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_8532),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_8534)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_8532)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8534)))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8532))) ),
    inference(clausify,[status(thm)],[f_2436_3]) ).

cnf(f_2436_6,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_8532),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_8534)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8532),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8534)))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8534)))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8532))) ),
    inference(clausify,[status(thm)],[f_2436_3]) ).

fof(f_2437_1,plain,
    ! [V_b,V_a] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) ),
    inference(fof_nnf,[status(thm)],[fact_div__pos__neg__trivial]) ).

fof(f_2437_2,plain,
    ! [U_8536,U_8535] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8535),U_8536) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8535),U_8536)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8535)) ),
    inference(variable_rename,[status(thm)],[f_2437_1]) ).

cnf(f_2437_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8535),U_8536) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8535),U_8536)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8535)) ),
    inference(clausify,[status(thm)],[f_2437_2]) ).

fof(f_2438_1,plain,
    ! [V_b] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),V_b) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_b),c_Groups_Oone__class_Oone(tc_Int_Oint))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) ),
    inference(fof_nnf,[status(thm)],[fact_zmod__minus1]) ).

fof(f_2438_2,plain,
    ! [U_8537] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),U_8537) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8537),c_Groups_Oone__class_Oone(tc_Int_Oint))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8537)) ),
    inference(variable_rename,[status(thm)],[f_2438_1]) ).

cnf(f_2438_3,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),U_8537) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8537),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8537)) ),
    inference(clausify,[status(thm)],[f_2438_2]) ).

fof(f_2439_1,plain,
    ! [V_m_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
        | c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ),
    inference(fof_nnf,[status(thm)],[fact_mod2__gr__0]) ).

fof(f_2439_2,plain,
    ! [U_8538] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8538,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
        | c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8538,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8538,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8538,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ),
    inference(variable_rename,[status(thm)],[f_2439_1]) ).

fof(f_2439_3,plain,
    ( ! [U_8540] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8540,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
        | c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8540,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
    & ! [U_8539] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8539,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8539,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ),
    inference(miniscope,[status(thm)],[f_2439_2]) ).

cnf(f_2439_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8539,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8539,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ),
    inference(clausify,[status(thm)],[f_2439_3]) ).

cnf(f_2439_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8540,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8540,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_2439_3]) ).

fof(f_2440_1,plain,
    ! [V_k] :
      ( ( ( ( hAPP(c_Code__Numeral_Oint__of,V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_k),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),c_Groups_Oone__class_Oone(tc_Int_Oint))
            | c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,V_k,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
          & ( hAPP(c_Code__Numeral_Oint__of,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_k),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
            | c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,V_k,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) )
        | V_k = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
      & ( hAPP(c_Code__Numeral_Oint__of,V_k) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | V_k != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(fof_nnf,[status(thm)],[fact_int__of__code]) ).

fof(f_2440_2,plain,
    ! [U_8541] :
      ( ( ( ( hAPP(c_Code__Numeral_Oint__of,U_8541) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),U_8541),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),c_Groups_Oone__class_Oone(tc_Int_Oint))
            | c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,U_8541,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
          & ( hAPP(c_Code__Numeral_Oint__of,U_8541) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),U_8541),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
            | c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,U_8541,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) )
        | U_8541 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
      & ( hAPP(c_Code__Numeral_Oint__of,U_8541) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | U_8541 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(variable_rename,[status(thm)],[f_2440_1]) ).

fof(f_2440_3,plain,
    ( ! [U_8543] :
        ( ( ( hAPP(c_Code__Numeral_Oint__of,U_8543) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),U_8543),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),c_Groups_Oone__class_Oone(tc_Int_Oint))
            | c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,U_8543,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
          & ( hAPP(c_Code__Numeral_Oint__of,U_8543) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),U_8543),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
            | c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,U_8543,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) )
        | U_8543 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
    & ! [U_8542] :
        ( hAPP(c_Code__Numeral_Oint__of,U_8542) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | U_8542 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(miniscope,[status(thm)],[f_2440_2]) ).

cnf(f_2440_4,plain,
    ( hAPP(c_Code__Numeral_Oint__of,U_8542) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_8542 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_2440_3]) ).

cnf(f_2440_5,plain,
    ( hAPP(c_Code__Numeral_Oint__of,U_8543) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),U_8543),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,U_8543,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
    | U_8543 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_2440_3]) ).

cnf(f_2440_6,plain,
    ( hAPP(c_Code__Numeral_Oint__of,U_8543) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),U_8543),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,U_8543,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
    | U_8543 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_2440_3]) ).

fof(f_2441_1,plain,
    ! [V_A_2,V_x_2] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
          | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,V_x_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2))) )
        & ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,V_x_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)))
          | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2)) ) )
      | ~ c_Nat__Transfer_Onat__set(V_A_2)
      | ~ c_Nat__Transfer_Ois__nat(V_x_2) ),
    inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__set__relations_I2_J]) ).

fof(f_2441_2,plain,
    ! [U_8545,U_8544] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8544),U_8545))
          | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,U_8544)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8545))) )
        & ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,U_8544)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8545)))
          | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8544),U_8545)) ) )
      | ~ c_Nat__Transfer_Onat__set(U_8545)
      | ~ c_Nat__Transfer_Ois__nat(U_8544) ),
    inference(variable_rename,[status(thm)],[f_2441_1]) ).

cnf(f_2441_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,U_8544)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8545)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8544),U_8545))
    | ~ c_Nat__Transfer_Onat__set(U_8545)
    | ~ c_Nat__Transfer_Ois__nat(U_8544) ),
    inference(clausify,[status(thm)],[f_2441_2]) ).

cnf(f_2441_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8544),U_8545))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,U_8544)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8545)))
    | ~ c_Nat__Transfer_Onat__set(U_8545)
    | ~ c_Nat__Transfer_Ois__nat(U_8544) ),
    inference(clausify,[status(thm)],[f_2441_2]) ).

fof(f_2442_1,plain,
    ! [V_K_2,V_f_2,V_A_2,T_b,T_c] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))),V_K_2)))
      | ? [B_i] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_i)),V_K_2))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_A_2)) )
      | ~ class_Rings_Osemiring__1(T_c)
      | ~ class_Groups_Oordered__ab__semigroup__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__bounded]) ).

fof(f_2442_2,plain,
    ! [U_8551,U_8550,U_8549,U_8548,U_8547] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8547),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8548,U_8547),U_8550),U_8549)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8547),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_8547),hAPP(c_Finite__Set_Ocard(U_8548),U_8549))),U_8551)))
      | ? [U_8546] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8547),hAPP(U_8550,U_8546)),U_8551))
          & hBOOL(hAPP(hAPP(c_member(U_8548),U_8546),U_8549)) )
      | ~ class_Rings_Osemiring__1(U_8547)
      | ~ class_Groups_Oordered__ab__semigroup__add(U_8547) ),
    inference(variable_rename,[status(thm)],[f_2442_1]) ).

fof(f_2442_3,plain,
    ! [U_8551,U_8550,U_8549,U_8548,U_8547] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8547),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8548,U_8547),U_8550),U_8549)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8547),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_8547),hAPP(c_Finite__Set_Ocard(U_8548),U_8549))),U_8551)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8547),hAPP(U_8550,sK219(U_8551,U_8550,U_8549,U_8548,U_8547))),U_8551))
        & hBOOL(hAPP(hAPP(c_member(U_8548),sK219(U_8551,U_8550,U_8549,U_8548,U_8547)),U_8549)) )
      | ~ class_Rings_Osemiring__1(U_8547)
      | ~ class_Groups_Oordered__ab__semigroup__add(U_8547) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK219]),skolemize(U_8546,sK219(U_8551,U_8550,U_8549,U_8548,U_8547))],[f_2442_2]) ).

cnf(f_2442_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8548),sK219(U_8551,U_8550,U_8549,U_8548,U_8547)),U_8549))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8547),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8548,U_8547),U_8550),U_8549)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8547),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_8547),hAPP(c_Finite__Set_Ocard(U_8548),U_8549))),U_8551)))
    | ~ class_Rings_Osemiring__1(U_8547)
    | ~ class_Groups_Oordered__ab__semigroup__add(U_8547) ),
    inference(clausify,[status(thm)],[f_2442_3]) ).

cnf(f_2442_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8547),hAPP(U_8550,sK219(U_8551,U_8550,U_8549,U_8548,U_8547))),U_8551))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8547),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8548,U_8547),U_8550),U_8549)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8547),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_8547),hAPP(c_Finite__Set_Ocard(U_8548),U_8549))),U_8551)))
    | ~ class_Rings_Osemiring__1(U_8547)
    | ~ class_Groups_Oordered__ab__semigroup__add(U_8547) ),
    inference(clausify,[status(thm)],[f_2442_3]) ).

fof(f_2443_1,plain,
    ! [V_n_2,V_m_2] :
      ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_m_2,V_n_2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Int_Onat,V_m_2),hAPP(c_Int_Onat,V_n_2)))
      | ~ c_Nat__Transfer_Ois__nat(V_n_2)
      | ~ c_Nat__Transfer_Ois__nat(V_m_2) ),
    inference(fof_nnf,[status(thm)],[fact_SetInterval_Otransfer__int__nat__set__functions]) ).

fof(f_2443_2,plain,
    ! [U_8553,U_8552] :
      ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_8552,U_8553) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Int_Onat,U_8552),hAPP(c_Int_Onat,U_8553)))
      | ~ c_Nat__Transfer_Ois__nat(U_8553)
      | ~ c_Nat__Transfer_Ois__nat(U_8552) ),
    inference(variable_rename,[status(thm)],[f_2443_1]) ).

cnf(f_2443_3,plain,
    ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_8552,U_8553) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Int_Onat,U_8552),hAPP(c_Int_Onat,U_8553)))
    | ~ c_Nat__Transfer_Ois__nat(U_8553)
    | ~ c_Nat__Transfer_Ois__nat(U_8552) ),
    inference(clausify,[status(thm)],[f_2443_2]) ).

fof(f_2444_1,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[fact_code__numeral__zero__minus__one]) ).

cnf(f_2444_2,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_2444_1]) ).

fof(f_2445_1,plain,
    c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J]) ).

cnf(f_2445_2,plain,
    c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    inference(clausify,[status(thm)],[f_2445_1]) ).

fof(f_2446_1,plain,
    ! [V_y,V_x] :
      ( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y))
      | ~ c_Nat__Transfer_Ois__nat(V_y)
      | ~ c_Nat__Transfer_Ois__nat(V_x) ),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J]) ).

fof(f_2446_2,plain,
    ! [U_8555,U_8554] :
      ( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8554),U_8555))
      | ~ c_Nat__Transfer_Ois__nat(U_8555)
      | ~ c_Nat__Transfer_Ois__nat(U_8554) ),
    inference(variable_rename,[status(thm)],[f_2446_1]) ).

cnf(f_2446_3,plain,
    ( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8554),U_8555))
    | ~ c_Nat__Transfer_Ois__nat(U_8555)
    | ~ c_Nat__Transfer_Ois__nat(U_8554) ),
    inference(clausify,[status(thm)],[f_2446_2]) ).

fof(f_2447_1,plain,
    ! [V_z] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z)),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J]) ).

fof(f_2447_2,plain,
    ! [U_8556] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8556)),
    inference(variable_rename,[status(thm)],[f_2447_1]) ).

cnf(f_2447_3,plain,
    c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8556)),
    inference(clausify,[status(thm)],[f_2447_2]) ).

fof(f_2448_1,plain,
    c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J]) ).

cnf(f_2448_2,plain,
    c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(clausify,[status(thm)],[f_2448_1]) ).

fof(f_2449_1,plain,
    ! [V_y,V_x] :
      ( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y))
      | ~ c_Nat__Transfer_Ois__nat(V_y)
      | ~ c_Nat__Transfer_Ois__nat(V_x) ),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J]) ).

fof(f_2449_2,plain,
    ! [U_8558,U_8557] :
      ( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8557),U_8558))
      | ~ c_Nat__Transfer_Ois__nat(U_8558)
      | ~ c_Nat__Transfer_Ois__nat(U_8557) ),
    inference(variable_rename,[status(thm)],[f_2449_1]) ).

cnf(f_2449_3,plain,
    ( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8557),U_8558))
    | ~ c_Nat__Transfer_Ois__nat(U_8558)
    | ~ c_Nat__Transfer_Ois__nat(U_8557) ),
    inference(clausify,[status(thm)],[f_2449_2]) ).

fof(f_2450_1,plain,
    ! [V_y,V_x] :
      ( c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y))
      | ~ c_Nat__Transfer_Ois__nat(V_y)
      | ~ c_Nat__Transfer_Ois__nat(V_x) ),
    inference(fof_nnf,[status(thm)],[fact_Divides_Otransfer__int__nat__function__closures_I2_J]) ).

fof(f_2450_2,plain,
    ! [U_8560,U_8559] :
      ( c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8559,U_8560))
      | ~ c_Nat__Transfer_Ois__nat(U_8560)
      | ~ c_Nat__Transfer_Ois__nat(U_8559) ),
    inference(variable_rename,[status(thm)],[f_2450_1]) ).

cnf(f_2450_3,plain,
    ( c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,U_8559,U_8560))
    | ~ c_Nat__Transfer_Ois__nat(U_8560)
    | ~ c_Nat__Transfer_Ois__nat(U_8559) ),
    inference(clausify,[status(thm)],[f_2450_2]) ).

fof(f_2451_1,plain,
    ! [V_y,V_x] :
      ( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y))
      | ~ c_Nat__Transfer_Ois__nat(V_y)
      | ~ c_Nat__Transfer_Ois__nat(V_x) ),
    inference(fof_nnf,[status(thm)],[fact_Divides_Otransfer__int__nat__function__closures_I1_J]) ).

fof(f_2451_2,plain,
    ! [U_8562,U_8561] :
      ( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8561),U_8562))
      | ~ c_Nat__Transfer_Ois__nat(U_8562)
      | ~ c_Nat__Transfer_Ois__nat(U_8561) ),
    inference(variable_rename,[status(thm)],[f_2451_1]) ).

cnf(f_2451_3,plain,
    ( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_8561),U_8562))
    | ~ c_Nat__Transfer_Ois__nat(U_8562)
    | ~ c_Nat__Transfer_Ois__nat(U_8561) ),
    inference(clausify,[status(thm)],[f_2451_2]) ).

fof(f_2452_1,plain,
    ! [V_n,V_x] :
      ( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n))
      | ~ c_Nat__Transfer_Ois__nat(V_x) ),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J]) ).

fof(f_2452_2,plain,
    ! [U_8564,U_8563] :
      ( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_8563),U_8564))
      | ~ c_Nat__Transfer_Ois__nat(U_8563) ),
    inference(variable_rename,[status(thm)],[f_2452_1]) ).

cnf(f_2452_3,plain,
    ( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_8563),U_8564))
    | ~ c_Nat__Transfer_Ois__nat(U_8563) ),
    inference(clausify,[status(thm)],[f_2452_2]) ).

fof(f_2453_1,plain,
    ! [V_y,V_x] :
      ( c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(V_x,V_y))
      | ~ c_Nat__Transfer_Ois__nat(V_y)
      | ~ c_Nat__Transfer_Ois__nat(V_x) ),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J]) ).

fof(f_2453_2,plain,
    ! [U_8566,U_8565] :
      ( c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(U_8565,U_8566))
      | ~ c_Nat__Transfer_Ois__nat(U_8566)
      | ~ c_Nat__Transfer_Ois__nat(U_8565) ),
    inference(variable_rename,[status(thm)],[f_2453_1]) ).

cnf(f_2453_3,plain,
    ( c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(U_8565,U_8566))
    | ~ c_Nat__Transfer_Ois__nat(U_8566)
    | ~ c_Nat__Transfer_Ois__nat(U_8565) ),
    inference(clausify,[status(thm)],[f_2453_2]) ).

fof(f_2454_1,plain,
    ! [V_x_2] :
      ( ( c_Nat__Transfer_Ois__nat(V_x_2)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
        | ~ c_Nat__Transfer_Ois__nat(V_x_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_is__nat__def]) ).

fof(f_2454_2,plain,
    ! [U_8567] :
      ( ( c_Nat__Transfer_Ois__nat(U_8567)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8567)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8567))
        | ~ c_Nat__Transfer_Ois__nat(U_8567) ) ),
    inference(variable_rename,[status(thm)],[f_2454_1]) ).

fof(f_2454_3,plain,
    ( ! [U_8569] :
        ( c_Nat__Transfer_Ois__nat(U_8569)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8569)) )
    & ! [U_8568] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8568))
        | ~ c_Nat__Transfer_Ois__nat(U_8568) ) ),
    inference(miniscope,[status(thm)],[f_2454_2]) ).

cnf(f_2454_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8568))
    | ~ c_Nat__Transfer_Ois__nat(U_8568) ),
    inference(clausify,[status(thm)],[f_2454_3]) ).

cnf(f_2454_5,plain,
    ( c_Nat__Transfer_Ois__nat(U_8569)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8569)) ),
    inference(clausify,[status(thm)],[f_2454_3]) ).

fof(f_2455_1,plain,
    ! [V_y_2,V_x_2] :
      ( c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2))
      | ~ c_Nat__Transfer_Ois__nat(V_x_2) ),
    inference(fof_nnf,[status(thm)],[fact_SetInterval_Otransfer__int__nat__set__function__closures]) ).

fof(f_2455_2,plain,
    ! [U_8571,U_8570] :
      ( c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_8570,U_8571))
      | ~ c_Nat__Transfer_Ois__nat(U_8570) ),
    inference(variable_rename,[status(thm)],[f_2455_1]) ).

cnf(f_2455_3,plain,
    ( c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_8570,U_8571))
    | ~ c_Nat__Transfer_Ois__nat(U_8570) ),
    inference(clausify,[status(thm)],[f_2455_2]) ).

fof(f_2456_1,plain,
    ! [V_x_2,V_A_2] :
      ( c_Nat__Transfer_Ois__nat(V_x_2)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
      | ~ c_Nat__Transfer_Onat__set(V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J]) ).

fof(f_2456_2,plain,
    ! [U_8573,U_8572] :
      ( c_Nat__Transfer_Ois__nat(U_8573)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8573),U_8572))
      | ~ c_Nat__Transfer_Onat__set(U_8572) ),
    inference(variable_rename,[status(thm)],[f_2456_1]) ).

cnf(f_2456_3,plain,
    ( c_Nat__Transfer_Ois__nat(U_8573)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8573),U_8572))
    | ~ c_Nat__Transfer_Onat__set(U_8572) ),
    inference(clausify,[status(thm)],[f_2456_2]) ).

fof(f_2457_1,plain,
    c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OPls),
    inference(fof_nnf,[status(thm)],[fact_zero__code__numeral__code]) ).

cnf(f_2457_2,plain,
    c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OPls),
    inference(clausify,[status(thm)],[f_2457_1]) ).

fof(f_2458_1,plain,
    c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I8_J]) ).

cnf(f_2458_2,plain,
    c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),
    inference(clausify,[status(thm)],[f_2458_1]) ).

fof(f_2459_1,plain,
    c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I7_J]) ).

cnf(f_2459_2,plain,
    c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
    inference(clausify,[status(thm)],[f_2459_1]) ).

fof(f_2460_1,plain,
    c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit1(c_Int_OPls)),
    inference(fof_nnf,[status(thm)],[fact_one__code__numeral__code]) ).

cnf(f_2460_2,plain,
    c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit1(c_Int_OPls)),
    inference(clausify,[status(thm)],[f_2460_1]) ).

fof(f_2461_1,plain,
    c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_code__numeral_Osize_I1_J]) ).

cnf(f_2461_2,plain,
    c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_2461_1]) ).

fof(f_2462_1,plain,
    ! [V_k,T_a] :
      ( ( ( hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,V_k))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        & ( hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k))))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) )
      | ~ class_Rings_Oring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__int__of__nat]) ).

fof(f_2462_2,plain,
    ! [U_8575,U_8574] :
      ( ( ( hAPP(c_Int_Oring__1__class_Oof__int(U_8574),U_8575) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_8574),hAPP(c_Int_Onat,U_8575))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8575),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        & ( hAPP(c_Int_Oring__1__class_Oof__int(U_8574),U_8575) = hAPP(c_Groups_Ouminus__class_Ouminus(U_8574),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_8574),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8575))))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8575),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) )
      | ~ class_Rings_Oring__1(U_8574) ),
    inference(variable_rename,[status(thm)],[f_2462_1]) ).

cnf(f_2462_3,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_8574),U_8575) = hAPP(c_Groups_Ouminus__class_Ouminus(U_8574),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_8574),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8575))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8575),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ class_Rings_Oring__1(U_8574) ),
    inference(clausify,[status(thm)],[f_2462_2]) ).

cnf(f_2462_4,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_8574),U_8575) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_8574),hAPP(c_Int_Onat,U_8575))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8575),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ class_Rings_Oring__1(U_8574) ),
    inference(clausify,[status(thm)],[f_2462_2]) ).

fof(f_2463_1,plain,
    ! [V_n,V_i] :
      ( ( c_Code__Numeral_Onat__of__aux(V_i,V_n) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_i),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,V_n))
        | V_i = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
      & ( c_Code__Numeral_Onat__of__aux(V_i,V_n) = V_n
        | V_i != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__of__aux__code]) ).

fof(f_2463_2,plain,
    ! [U_8577,U_8576] :
      ( ( c_Code__Numeral_Onat__of__aux(U_8576,U_8577) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_8576),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,U_8577))
        | U_8576 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
      & ( c_Code__Numeral_Onat__of__aux(U_8576,U_8577) = U_8577
        | U_8576 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(variable_rename,[status(thm)],[f_2463_1]) ).

fof(f_2463_3,plain,
    ( ! [U_8581,U_8579] :
        ( c_Code__Numeral_Onat__of__aux(U_8579,U_8581) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_8579),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,U_8581))
        | U_8579 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
    & ! [U_8580,U_8578] :
        ( c_Code__Numeral_Onat__of__aux(U_8578,U_8580) = U_8580
        | U_8578 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(miniscope,[status(thm)],[f_2463_2]) ).

cnf(f_2463_4,plain,
    ( c_Code__Numeral_Onat__of__aux(U_8578,U_8580) = U_8580
    | U_8578 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_2463_3]) ).

cnf(f_2463_5,plain,
    ( c_Code__Numeral_Onat__of__aux(U_8579,U_8581) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_8579),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,U_8581))
    | U_8579 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_2463_3]) ).

fof(f_2464_1,plain,
    ! [V_x] :
      ( ? [B_n] : V_x = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,B_n)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(fof_nnf,[status(thm)],[fact_negD]) ).

fof(f_2464_2,plain,
    ! [U_8583] :
      ( ? [U_8582] : U_8583 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_8582)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8583),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_2464_1]) ).

fof(f_2464_3,plain,
    ! [U_8583] :
      ( U_8583 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,sK220(U_8583))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8583),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK220]),skolemize(U_8582,sK220(U_8583))],[f_2464_2]) ).

cnf(f_2464_4,plain,
    ( U_8583 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,sK220(U_8583))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8583),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2464_3]) ).

fof(f_2465_1,plain,
    ! [V_k,T_a] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_k) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k)
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_number__of__eq]) ).

fof(f_2465_2,plain,
    ! [U_8585,U_8584] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_8584),U_8585) = hAPP(c_Int_Oring__1__class_Oof__int(U_8584),U_8585)
      | ~ class_Int_Onumber__ring(U_8584) ),
    inference(variable_rename,[status(thm)],[f_2465_1]) ).

cnf(f_2465_3,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_8584),U_8585) = hAPP(c_Int_Oring__1__class_Oof__int(U_8584),U_8585)
    | ~ class_Int_Onumber__ring(U_8584) ),
    inference(clausify,[status(thm)],[f_2465_2]) ).

fof(f_2466_1,plain,
    ! [V_w] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),V_w),
    inference(fof_nnf,[status(thm)],[fact_int__number__of__def]) ).

fof(f_2466_2,plain,
    ! [U_8586] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8586) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),U_8586),
    inference(variable_rename,[status(thm)],[f_2466_1]) ).

cnf(f_2466_3,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8586) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),U_8586),
    inference(clausify,[status(thm)],[f_2466_2]) ).

fof(f_2467_1,plain,
    ! [V_n] : hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n),
    inference(fof_nnf,[status(thm)],[fact_of__int__int__eq]) ).

fof(f_2467_2,plain,
    ! [U_8587] : hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8587)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8587),
    inference(variable_rename,[status(thm)],[f_2467_1]) ).

cnf(f_2467_3,plain,
    hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8587)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8587),
    inference(clausify,[status(thm)],[f_2467_2]) ).

fof(f_2468_1,plain,
    ! [V_z_2,V_w_2,T_b] :
      ( ( ( hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_w_2) = hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)
          | V_w_2 != V_z_2 )
        & ( V_w_2 = V_z_2
          | hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_w_2) != hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2) ) )
      | ~ class_Int_Oring__char__0(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_of__int__eq__iff]) ).

fof(f_2468_2,plain,
    ! [U_8590,U_8589,U_8588] :
      ( ( ( hAPP(c_Int_Oring__1__class_Oof__int(U_8588),U_8589) = hAPP(c_Int_Oring__1__class_Oof__int(U_8588),U_8590)
          | U_8589 != U_8590 )
        & ( U_8589 = U_8590
          | hAPP(c_Int_Oring__1__class_Oof__int(U_8588),U_8589) != hAPP(c_Int_Oring__1__class_Oof__int(U_8588),U_8590) ) )
      | ~ class_Int_Oring__char__0(U_8588) ),
    inference(variable_rename,[status(thm)],[f_2468_1]) ).

cnf(f_2468_3,plain,
    ( U_8589 = U_8590
    | hAPP(c_Int_Oring__1__class_Oof__int(U_8588),U_8589) != hAPP(c_Int_Oring__1__class_Oof__int(U_8588),U_8590)
    | ~ class_Int_Oring__char__0(U_8588) ),
    inference(clausify,[status(thm)],[f_2468_2]) ).

cnf(f_2468_4,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_8588),U_8589) = hAPP(c_Int_Oring__1__class_Oof__int(U_8588),U_8590)
    | U_8589 != U_8590
    | ~ class_Int_Oring__char__0(U_8588) ),
    inference(clausify,[status(thm)],[f_2468_2]) ).

fof(f_2469_1,plain,
    ! [V_z_2,T_b] :
      ( ( ( hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2) = c_Groups_Ozero__class_Ozero(T_b)
          | V_z_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
        & ( V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
          | hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2) != c_Groups_Ozero__class_Ozero(T_b) ) )
      | ~ class_Int_Oring__char__0(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_of__int__eq__0__iff]) ).

fof(f_2469_2,plain,
    ! [U_8592,U_8591] :
      ( ( ( hAPP(c_Int_Oring__1__class_Oof__int(U_8591),U_8592) = c_Groups_Ozero__class_Ozero(U_8591)
          | U_8592 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
        & ( U_8592 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
          | hAPP(c_Int_Oring__1__class_Oof__int(U_8591),U_8592) != c_Groups_Ozero__class_Ozero(U_8591) ) )
      | ~ class_Int_Oring__char__0(U_8591) ),
    inference(variable_rename,[status(thm)],[f_2469_1]) ).

cnf(f_2469_3,plain,
    ( U_8592 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hAPP(c_Int_Oring__1__class_Oof__int(U_8591),U_8592) != c_Groups_Ozero__class_Ozero(U_8591)
    | ~ class_Int_Oring__char__0(U_8591) ),
    inference(clausify,[status(thm)],[f_2469_2]) ).

cnf(f_2469_4,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_8591),U_8592) = c_Groups_Ozero__class_Ozero(U_8591)
    | U_8592 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ class_Int_Oring__char__0(U_8591) ),
    inference(clausify,[status(thm)],[f_2469_2]) ).

fof(f_2470_1,plain,
    ! [V_z_2,T_b] :
      ( ( ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)
          | V_z_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
        & ( V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
          | c_Groups_Ozero__class_Ozero(T_b) != hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2) ) )
      | ~ class_Int_Oring__char__0(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_of__int__0__eq__iff]) ).

fof(f_2470_2,plain,
    ! [U_8594,U_8593] :
      ( ( ( c_Groups_Ozero__class_Ozero(U_8593) = hAPP(c_Int_Oring__1__class_Oof__int(U_8593),U_8594)
          | U_8594 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
        & ( U_8594 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
          | c_Groups_Ozero__class_Ozero(U_8593) != hAPP(c_Int_Oring__1__class_Oof__int(U_8593),U_8594) ) )
      | ~ class_Int_Oring__char__0(U_8593) ),
    inference(variable_rename,[status(thm)],[f_2470_1]) ).

cnf(f_2470_3,plain,
    ( U_8594 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Groups_Ozero__class_Ozero(U_8593) != hAPP(c_Int_Oring__1__class_Oof__int(U_8593),U_8594)
    | ~ class_Int_Oring__char__0(U_8593) ),
    inference(clausify,[status(thm)],[f_2470_2]) ).

cnf(f_2470_4,plain,
    ( c_Groups_Ozero__class_Ozero(U_8593) = hAPP(c_Int_Oring__1__class_Oof__int(U_8593),U_8594)
    | U_8594 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ class_Int_Oring__char__0(U_8593) ),
    inference(clausify,[status(thm)],[f_2470_2]) ).

fof(f_2471_1,plain,
    ! [T_a] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(T_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Rings_Oring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__int__0]) ).

fof(f_2471_2,plain,
    ! [U_8595] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_8595),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(U_8595)
      | ~ class_Rings_Oring__1(U_8595) ),
    inference(variable_rename,[status(thm)],[f_2471_1]) ).

cnf(f_2471_3,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_8595),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(U_8595)
    | ~ class_Rings_Oring__1(U_8595) ),
    inference(clausify,[status(thm)],[f_2471_2]) ).

fof(f_2472_1,plain,
    ! [V_z_2,V_w_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_w_2)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_w_2)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2))) ) )
      | ~ class_Rings_Olinordered__idom(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_of__int__le__iff]) ).

fof(f_2472_2,plain,
    ! [U_8598,U_8597,U_8596] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8596),hAPP(c_Int_Oring__1__class_Oof__int(U_8596),U_8597)),hAPP(c_Int_Oring__1__class_Oof__int(U_8596),U_8598)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8597),U_8598)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8597),U_8598))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8596),hAPP(c_Int_Oring__1__class_Oof__int(U_8596),U_8597)),hAPP(c_Int_Oring__1__class_Oof__int(U_8596),U_8598))) ) )
      | ~ class_Rings_Olinordered__idom(U_8596) ),
    inference(variable_rename,[status(thm)],[f_2472_1]) ).

cnf(f_2472_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8597),U_8598))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8596),hAPP(c_Int_Oring__1__class_Oof__int(U_8596),U_8597)),hAPP(c_Int_Oring__1__class_Oof__int(U_8596),U_8598)))
    | ~ class_Rings_Olinordered__idom(U_8596) ),
    inference(clausify,[status(thm)],[f_2472_2]) ).

cnf(f_2472_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8596),hAPP(c_Int_Oring__1__class_Oof__int(U_8596),U_8597)),hAPP(c_Int_Oring__1__class_Oof__int(U_8596),U_8598)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8597),U_8598))
    | ~ class_Rings_Olinordered__idom(U_8596) ),
    inference(clausify,[status(thm)],[f_2472_2]) ).

fof(f_2473_1,plain,
    ! [V_z_2,V_w_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_w_2)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_w_2)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2))) ) )
      | ~ class_Rings_Olinordered__idom(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_of__int__less__iff]) ).

fof(f_2473_2,plain,
    ! [U_8601,U_8600,U_8599] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8599),hAPP(c_Int_Oring__1__class_Oof__int(U_8599),U_8600)),hAPP(c_Int_Oring__1__class_Oof__int(U_8599),U_8601)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8600),U_8601)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8600),U_8601))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8599),hAPP(c_Int_Oring__1__class_Oof__int(U_8599),U_8600)),hAPP(c_Int_Oring__1__class_Oof__int(U_8599),U_8601))) ) )
      | ~ class_Rings_Olinordered__idom(U_8599) ),
    inference(variable_rename,[status(thm)],[f_2473_1]) ).

cnf(f_2473_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8600),U_8601))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8599),hAPP(c_Int_Oring__1__class_Oof__int(U_8599),U_8600)),hAPP(c_Int_Oring__1__class_Oof__int(U_8599),U_8601)))
    | ~ class_Rings_Olinordered__idom(U_8599) ),
    inference(clausify,[status(thm)],[f_2473_2]) ).

cnf(f_2473_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8599),hAPP(c_Int_Oring__1__class_Oof__int(U_8599),U_8600)),hAPP(c_Int_Oring__1__class_Oof__int(U_8599),U_8601)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8600),U_8601))
    | ~ class_Rings_Olinordered__idom(U_8599) ),
    inference(clausify,[status(thm)],[f_2473_2]) ).

fof(f_2474_1,plain,
    ! [V_z,V_w,T_a] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_w)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z))
      | ~ class_Rings_Oring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__int__add]) ).

fof(f_2474_2,plain,
    ! [U_8604,U_8603,U_8602] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_8602),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8603),U_8604)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8602),hAPP(c_Int_Oring__1__class_Oof__int(U_8602),U_8603)),hAPP(c_Int_Oring__1__class_Oof__int(U_8602),U_8604))
      | ~ class_Rings_Oring__1(U_8602) ),
    inference(variable_rename,[status(thm)],[f_2474_1]) ).

cnf(f_2474_3,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_8602),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8603),U_8604)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8602),hAPP(c_Int_Oring__1__class_Oof__int(U_8602),U_8603)),hAPP(c_Int_Oring__1__class_Oof__int(U_8602),U_8604))
    | ~ class_Rings_Oring__1(U_8602) ),
    inference(clausify,[status(thm)],[f_2474_2]) ).

fof(f_2475_1,plain,
    ! [V_v,T_a] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__int__number__of__eq]) ).

fof(f_2475_2,plain,
    ! [U_8606,U_8605] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_8605),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8606)) = hAPP(c_Int_Onumber__class_Onumber__of(U_8605),U_8606)
      | ~ class_Int_Onumber__ring(U_8605) ),
    inference(variable_rename,[status(thm)],[f_2475_1]) ).

cnf(f_2475_3,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_8605),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8606)) = hAPP(c_Int_Onumber__class_Onumber__of(U_8605),U_8606)
    | ~ class_Int_Onumber__ring(U_8605) ),
    inference(clausify,[status(thm)],[f_2475_2]) ).

fof(f_2476_1,plain,
    ! [V_z,V_w,T_a] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_w)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z))
      | ~ class_Rings_Oring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__int__mult]) ).

fof(f_2476_2,plain,
    ! [U_8609,U_8608,U_8607] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_8607),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8608),U_8609)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8607),hAPP(c_Int_Oring__1__class_Oof__int(U_8607),U_8608)),hAPP(c_Int_Oring__1__class_Oof__int(U_8607),U_8609))
      | ~ class_Rings_Oring__1(U_8607) ),
    inference(variable_rename,[status(thm)],[f_2476_1]) ).

cnf(f_2476_3,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_8607),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8608),U_8609)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8607),hAPP(c_Int_Oring__1__class_Oof__int(U_8607),U_8608)),hAPP(c_Int_Oring__1__class_Oof__int(U_8607),U_8609))
    | ~ class_Rings_Oring__1(U_8607) ),
    inference(clausify,[status(thm)],[f_2476_2]) ).

fof(f_2477_1,plain,
    ! [T_a] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(T_a),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(T_a)
      | ~ class_Rings_Oring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__int__1]) ).

fof(f_2477_2,plain,
    ! [U_8610] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_8610),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(U_8610)
      | ~ class_Rings_Oring__1(U_8610) ),
    inference(variable_rename,[status(thm)],[f_2477_1]) ).

cnf(f_2477_3,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_8610),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(U_8610)
    | ~ class_Rings_Oring__1(U_8610) ),
    inference(clausify,[status(thm)],[f_2477_2]) ).

fof(f_2478_1,plain,
    ! [V_z,V_w,T_a] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_w),V_z)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_w)),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z))
      | ~ class_Rings_Oring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__int__diff]) ).

fof(f_2478_2,plain,
    ! [U_8613,U_8612,U_8611] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_8611),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8612),U_8613)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8611),hAPP(c_Int_Oring__1__class_Oof__int(U_8611),U_8612)),hAPP(c_Int_Oring__1__class_Oof__int(U_8611),U_8613))
      | ~ class_Rings_Oring__1(U_8611) ),
    inference(variable_rename,[status(thm)],[f_2478_1]) ).

cnf(f_2478_3,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_8611),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8612),U_8613)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8611),hAPP(c_Int_Oring__1__class_Oof__int(U_8611),U_8612)),hAPP(c_Int_Oring__1__class_Oof__int(U_8611),U_8613))
    | ~ class_Rings_Oring__1(U_8611) ),
    inference(clausify,[status(thm)],[f_2478_2]) ).

fof(f_2479_1,plain,
    ! [V_n,T_a] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)
      | ~ class_Rings_Oring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__int__of__nat__eq]) ).

fof(f_2479_2,plain,
    ! [U_8615,U_8614] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_8614),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8615)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_8614),U_8615)
      | ~ class_Rings_Oring__1(U_8614) ),
    inference(variable_rename,[status(thm)],[f_2479_1]) ).

cnf(f_2479_3,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_8614),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8615)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_8614),U_8615)
    | ~ class_Rings_Oring__1(U_8614) ),
    inference(clausify,[status(thm)],[f_2479_2]) ).

fof(f_2480_1,plain,
    ! [V_z,T_a] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z))
      | ~ class_Rings_Oring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__int__minus]) ).

fof(f_2480_2,plain,
    ! [U_8617,U_8616] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_8616),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8617)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_8616),hAPP(c_Int_Oring__1__class_Oof__int(U_8616),U_8617))
      | ~ class_Rings_Oring__1(U_8616) ),
    inference(variable_rename,[status(thm)],[f_2480_1]) ).

cnf(f_2480_3,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_8616),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8617)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_8616),hAPP(c_Int_Oring__1__class_Oof__int(U_8616),U_8617))
    | ~ class_Rings_Oring__1(U_8616) ),
    inference(clausify,[status(thm)],[f_2480_2]) ).

fof(f_2481_1,plain,
    ! [V_z_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)),c_Int_Oring__1__class_OInts(T_b)))
      | ~ class_Rings_Oring__1(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Ints__of__int]) ).

fof(f_2481_2,plain,
    ! [U_8619,U_8618] :
      ( hBOOL(hAPP(hAPP(c_member(U_8618),hAPP(c_Int_Oring__1__class_Oof__int(U_8618),U_8619)),c_Int_Oring__1__class_OInts(U_8618)))
      | ~ class_Rings_Oring__1(U_8618) ),
    inference(variable_rename,[status(thm)],[f_2481_1]) ).

cnf(f_2481_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8618),hAPP(c_Int_Oring__1__class_Oof__int(U_8618),U_8619)),c_Int_Oring__1__class_OInts(U_8618)))
    | ~ class_Rings_Oring__1(U_8618) ),
    inference(clausify,[status(thm)],[f_2481_2]) ).

fof(f_2482_1,plain,
    ! [V_n,V_z,T_a] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z)),V_n)
      | ~ class_Rings_Oring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__int__power]) ).

fof(f_2482_2,plain,
    ! [U_8622,U_8621,U_8620] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_8620),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_8621),U_8622)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_8620),hAPP(c_Int_Oring__1__class_Oof__int(U_8620),U_8621)),U_8622)
      | ~ class_Rings_Oring__1(U_8620) ),
    inference(variable_rename,[status(thm)],[f_2482_1]) ).

cnf(f_2482_3,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_8620),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_8621),U_8622)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_8620),hAPP(c_Int_Oring__1__class_Oof__int(U_8620),U_8621)),U_8622)
    | ~ class_Rings_Oring__1(U_8620) ),
    inference(clausify,[status(thm)],[f_2482_2]) ).

fof(f_2483_1,plain,
    ! [T_a] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__int__m1]) ).

fof(f_2483_2,plain,
    ! [U_8623] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_8623),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(U_8623),c_Int_OMin)
      | ~ class_Int_Onumber__ring(U_8623) ),
    inference(variable_rename,[status(thm)],[f_2483_1]) ).

cnf(f_2483_3,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_8623),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(U_8623),c_Int_OMin)
    | ~ class_Int_Onumber__ring(U_8623) ),
    inference(clausify,[status(thm)],[f_2483_2]) ).

fof(f_2484_1,plain,
    ! [V_z_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2))) ) )
      | ~ class_Rings_Olinordered__idom(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_of__int__0__le__iff]) ).

fof(f_2484_2,plain,
    ! [U_8625,U_8624] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8624),c_Groups_Ozero__class_Ozero(U_8624)),hAPP(c_Int_Oring__1__class_Oof__int(U_8624),U_8625)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8625)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8625))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8624),c_Groups_Ozero__class_Ozero(U_8624)),hAPP(c_Int_Oring__1__class_Oof__int(U_8624),U_8625))) ) )
      | ~ class_Rings_Olinordered__idom(U_8624) ),
    inference(variable_rename,[status(thm)],[f_2484_1]) ).

cnf(f_2484_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8625))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8624),c_Groups_Ozero__class_Ozero(U_8624)),hAPP(c_Int_Oring__1__class_Oof__int(U_8624),U_8625)))
    | ~ class_Rings_Olinordered__idom(U_8624) ),
    inference(clausify,[status(thm)],[f_2484_2]) ).

cnf(f_2484_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8624),c_Groups_Ozero__class_Ozero(U_8624)),hAPP(c_Int_Oring__1__class_Oof__int(U_8624),U_8625)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8625))
    | ~ class_Rings_Olinordered__idom(U_8624) ),
    inference(clausify,[status(thm)],[f_2484_2]) ).

fof(f_2485_1,plain,
    ! [V_z_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)),c_Groups_Ozero__class_Ozero(T_b)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)),c_Groups_Ozero__class_Ozero(T_b))) ) )
      | ~ class_Rings_Olinordered__idom(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_of__int__le__0__iff]) ).

fof(f_2485_2,plain,
    ! [U_8627,U_8626] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8626),hAPP(c_Int_Oring__1__class_Oof__int(U_8626),U_8627)),c_Groups_Ozero__class_Ozero(U_8626)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8627),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8627),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8626),hAPP(c_Int_Oring__1__class_Oof__int(U_8626),U_8627)),c_Groups_Ozero__class_Ozero(U_8626))) ) )
      | ~ class_Rings_Olinordered__idom(U_8626) ),
    inference(variable_rename,[status(thm)],[f_2485_1]) ).

cnf(f_2485_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8627),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8626),hAPP(c_Int_Oring__1__class_Oof__int(U_8626),U_8627)),c_Groups_Ozero__class_Ozero(U_8626)))
    | ~ class_Rings_Olinordered__idom(U_8626) ),
    inference(clausify,[status(thm)],[f_2485_2]) ).

cnf(f_2485_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8626),hAPP(c_Int_Oring__1__class_Oof__int(U_8626),U_8627)),c_Groups_Ozero__class_Ozero(U_8626)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8627),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ class_Rings_Olinordered__idom(U_8626) ),
    inference(clausify,[status(thm)],[f_2485_2]) ).

fof(f_2486_1,plain,
    ! [V_z_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)),c_Groups_Ozero__class_Ozero(T_b)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)),c_Groups_Ozero__class_Ozero(T_b))) ) )
      | ~ class_Rings_Olinordered__idom(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_of__int__less__0__iff]) ).

fof(f_2486_2,plain,
    ! [U_8629,U_8628] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8628),hAPP(c_Int_Oring__1__class_Oof__int(U_8628),U_8629)),c_Groups_Ozero__class_Ozero(U_8628)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8629),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8629),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8628),hAPP(c_Int_Oring__1__class_Oof__int(U_8628),U_8629)),c_Groups_Ozero__class_Ozero(U_8628))) ) )
      | ~ class_Rings_Olinordered__idom(U_8628) ),
    inference(variable_rename,[status(thm)],[f_2486_1]) ).

cnf(f_2486_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8629),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8628),hAPP(c_Int_Oring__1__class_Oof__int(U_8628),U_8629)),c_Groups_Ozero__class_Ozero(U_8628)))
    | ~ class_Rings_Olinordered__idom(U_8628) ),
    inference(clausify,[status(thm)],[f_2486_2]) ).

cnf(f_2486_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8628),hAPP(c_Int_Oring__1__class_Oof__int(U_8628),U_8629)),c_Groups_Ozero__class_Ozero(U_8628)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8629),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ class_Rings_Olinordered__idom(U_8628) ),
    inference(clausify,[status(thm)],[f_2486_2]) ).

fof(f_2487_1,plain,
    ! [V_z_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2))) ) )
      | ~ class_Rings_Olinordered__idom(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_of__int__0__less__iff]) ).

fof(f_2487_2,plain,
    ! [U_8631,U_8630] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8630),c_Groups_Ozero__class_Ozero(U_8630)),hAPP(c_Int_Oring__1__class_Oof__int(U_8630),U_8631)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8631)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8631))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8630),c_Groups_Ozero__class_Ozero(U_8630)),hAPP(c_Int_Oring__1__class_Oof__int(U_8630),U_8631))) ) )
      | ~ class_Rings_Olinordered__idom(U_8630) ),
    inference(variable_rename,[status(thm)],[f_2487_1]) ).

cnf(f_2487_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8631))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8630),c_Groups_Ozero__class_Ozero(U_8630)),hAPP(c_Int_Oring__1__class_Oof__int(U_8630),U_8631)))
    | ~ class_Rings_Olinordered__idom(U_8630) ),
    inference(clausify,[status(thm)],[f_2487_2]) ).

cnf(f_2487_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8630),c_Groups_Ozero__class_Ozero(U_8630)),hAPP(c_Int_Oring__1__class_Oof__int(U_8630),U_8631)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8631))
    | ~ class_Rings_Olinordered__idom(U_8630) ),
    inference(clausify,[status(thm)],[f_2487_2]) ).

fof(f_2488_1,plain,
    ! [V_z,T_a] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,V_z)) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
      | ~ class_Rings_Oring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__nat]) ).

fof(f_2488_2,plain,
    ! [U_8633,U_8632] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_8632),hAPP(c_Int_Onat,U_8633)) = hAPP(c_Int_Oring__1__class_Oof__int(U_8632),U_8633)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8633))
      | ~ class_Rings_Oring__1(U_8632) ),
    inference(variable_rename,[status(thm)],[f_2488_1]) ).

cnf(f_2488_3,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_8632),hAPP(c_Int_Onat,U_8633)) = hAPP(c_Int_Oring__1__class_Oof__int(U_8632),U_8633)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8633))
    | ~ class_Rings_Oring__1(U_8632) ),
    inference(clausify,[status(thm)],[f_2488_2]) ).

fof(f_2489_1,plain,
    ! [V_code__numeral] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(V_code__numeral)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(V_code__numeral)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(fof_nnf,[status(thm)],[fact_code__numeral_Osize_I2_J]) ).

fof(f_2489_2,plain,
    ! [U_8634] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(U_8634)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(U_8634)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_2489_1]) ).

cnf(f_2489_3,plain,
    c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(U_8634)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(U_8634)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_2489_2]) ).

fof(f_2490_1,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_code__numeral_Osize_I3_J]) ).

cnf(f_2490_2,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_2490_1]) ).

fof(f_2491_1,plain,
    ! [V_k] :
      ( ? [B_n] :
          ( V_k = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) ),
    inference(fof_nnf,[status(thm)],[fact_zero__less__imp__eq__int]) ).

fof(f_2491_2,plain,
    ! [U_8636] :
      ( ? [U_8635] :
          ( U_8636 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8635)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8635)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8636)) ),
    inference(variable_rename,[status(thm)],[f_2491_1]) ).

fof(f_2491_3,plain,
    ! [U_8636] :
      ( ( U_8636 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK221(U_8636))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK221(U_8636))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8636)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK221]),skolemize(U_8635,sK221(U_8636))],[f_2491_2]) ).

cnf(f_2491_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK221(U_8636)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8636)) ),
    inference(clausify,[status(thm)],[f_2491_3]) ).

cnf(f_2491_5,plain,
    ( U_8636 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK221(U_8636))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8636)) ),
    inference(clausify,[status(thm)],[f_2491_3]) ).

fof(f_2492_1,plain,
    ! [V_z,V_x,V_d] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_z))),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_d))),V_z))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d)) ),
    inference(fof_nnf,[status(thm)],[fact_decr__lemma]) ).

fof(f_2492_2,plain,
    ! [U_8639,U_8638,U_8637] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8638),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8638),U_8639))),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_8637))),U_8639))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8637)) ),
    inference(variable_rename,[status(thm)],[f_2492_1]) ).

cnf(f_2492_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8638),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8638),U_8639))),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_8637))),U_8639))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8637)) ),
    inference(clausify,[status(thm)],[f_2492_2]) ).

fof(f_2493_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)) = hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_a))
      | ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__minus__commute]) ).

fof(f_2493_2,plain,
    ! [U_8642,U_8641,U_8640] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_8640),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8640),U_8641),U_8642)) = hAPP(c_Groups_Oabs__class_Oabs(U_8640),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8640),U_8642),U_8641))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_8640) ),
    inference(variable_rename,[status(thm)],[f_2493_1]) ).

cnf(f_2493_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_8640),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8640),U_8641),U_8642)) = hAPP(c_Groups_Oabs__class_Oabs(U_8640),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8640),U_8642),U_8641))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_8640) ),
    inference(clausify,[status(thm)],[f_2493_2]) ).

fof(f_2494_1,plain,
    ! [T_a] :
      ( hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a)
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__one]) ).

fof(f_2494_2,plain,
    ! [U_8643] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_8643),c_Groups_Oone__class_Oone(U_8643)) = c_Groups_Oone__class_Oone(U_8643)
      | ~ class_Rings_Olinordered__idom(U_8643) ),
    inference(variable_rename,[status(thm)],[f_2494_1]) ).

cnf(f_2494_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_8643),c_Groups_Oone__class_Oone(U_8643)) = c_Groups_Oone__class_Oone(U_8643)
    | ~ class_Rings_Olinordered__idom(U_8643) ),
    inference(clausify,[status(thm)],[f_2494_2]) ).

fof(f_2495_1,plain,
    ! [V_n,T_a] :
      ( hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__of__nat]) ).

fof(f_2495_2,plain,
    ! [U_8645,U_8644] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_8644),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_8644),U_8645)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_8644),U_8645)
      | ~ class_Rings_Olinordered__idom(U_8644) ),
    inference(variable_rename,[status(thm)],[f_2495_1]) ).

cnf(f_2495_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_8644),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_8644),U_8645)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_8644),U_8645)
    | ~ class_Rings_Olinordered__idom(U_8644) ),
    inference(clausify,[status(thm)],[f_2495_2]) ).

fof(f_2496_1,plain,
    ! [V_m] : hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m),
    inference(fof_nnf,[status(thm)],[fact_abs__int__eq]) ).

fof(f_2496_2,plain,
    ! [U_8646] : hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8646)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8646),
    inference(variable_rename,[status(thm)],[f_2496_1]) ).

cnf(f_2496_3,plain,
    hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8646)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8646),
    inference(clausify,[status(thm)],[f_2496_2]) ).

fof(f_2497_1,plain,
    ! [V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b))
      | ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__le__D1]) ).

fof(f_2497_2,plain,
    ! [U_8649,U_8648,U_8647] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8647),U_8648),U_8649))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8647),hAPP(c_Groups_Oabs__class_Oabs(U_8647),U_8648)),U_8649))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_8647) ),
    inference(variable_rename,[status(thm)],[f_2497_1]) ).

cnf(f_2497_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8647),U_8648),U_8649))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8647),hAPP(c_Groups_Oabs__class_Oabs(U_8647),U_8648)),U_8649))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_8647) ),
    inference(clausify,[status(thm)],[f_2497_2]) ).

fof(f_2498_1,plain,
    ! [V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)))
      | ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__ge__self]) ).

fof(f_2498_2,plain,
    ! [U_8651,U_8650] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8650),U_8651),hAPP(c_Groups_Oabs__class_Oabs(U_8650),U_8651)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_8650) ),
    inference(variable_rename,[status(thm)],[f_2498_1]) ).

cnf(f_2498_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8650),U_8651),hAPP(c_Groups_Oabs__class_Oabs(U_8650),U_8651)))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_8650) ),
    inference(clausify,[status(thm)],[f_2498_2]) ).

fof(f_2499_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))
      | ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__divide]) ).

fof(f_2499_2,plain,
    ! [U_8654,U_8653,U_8652] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_8652),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8652),U_8653),U_8654)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8652),hAPP(c_Groups_Oabs__class_Oabs(U_8652),U_8653)),hAPP(c_Groups_Oabs__class_Oabs(U_8652),U_8654))
      | ~ class_Fields_Olinordered__field__inverse__zero(U_8652) ),
    inference(variable_rename,[status(thm)],[f_2499_1]) ).

cnf(f_2499_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_8652),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8652),U_8653),U_8654)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8652),hAPP(c_Groups_Oabs__class_Oabs(U_8652),U_8653)),hAPP(c_Groups_Oabs__class_Oabs(U_8652),U_8654))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_8652) ),
    inference(clausify,[status(thm)],[f_2499_2]) ).

fof(f_2500_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__mult__self]) ).

fof(f_2500_2,plain,
    ! [U_8656,U_8655] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8655),hAPP(c_Groups_Oabs__class_Oabs(U_8655),U_8656)),hAPP(c_Groups_Oabs__class_Oabs(U_8655),U_8656)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8655),U_8656),U_8656)
      | ~ class_Rings_Olinordered__idom(U_8655) ),
    inference(variable_rename,[status(thm)],[f_2500_1]) ).

cnf(f_2500_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8655),hAPP(c_Groups_Oabs__class_Oabs(U_8655),U_8656)),hAPP(c_Groups_Oabs__class_Oabs(U_8655),U_8656)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8655),U_8656),U_8656)
    | ~ class_Rings_Olinordered__idom(U_8655) ),
    inference(clausify,[status(thm)],[f_2500_2]) ).

fof(f_2501_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__mult]) ).

fof(f_2501_2,plain,
    ! [U_8659,U_8658,U_8657] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_8657),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8657),U_8658),U_8659)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8657),hAPP(c_Groups_Oabs__class_Oabs(U_8657),U_8658)),hAPP(c_Groups_Oabs__class_Oabs(U_8657),U_8659))
      | ~ class_Rings_Olinordered__idom(U_8657) ),
    inference(variable_rename,[status(thm)],[f_2501_1]) ).

cnf(f_2501_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_8657),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8657),U_8658),U_8659)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8657),hAPP(c_Groups_Oabs__class_Oabs(U_8657),U_8658)),hAPP(c_Groups_Oabs__class_Oabs(U_8657),U_8659))
    | ~ class_Rings_Olinordered__idom(U_8657) ),
    inference(clausify,[status(thm)],[f_2501_2]) ).

fof(f_2502_1,plain,
    ! [V_a,T_a] :
      ( hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)) = hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)
      | ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__idempotent]) ).

fof(f_2502_2,plain,
    ! [U_8661,U_8660] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_8660),hAPP(c_Groups_Oabs__class_Oabs(U_8660),U_8661)) = hAPP(c_Groups_Oabs__class_Oabs(U_8660),U_8661)
      | ~ class_Groups_Oordered__ab__group__add__abs(U_8660) ),
    inference(variable_rename,[status(thm)],[f_2502_1]) ).

cnf(f_2502_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_8660),hAPP(c_Groups_Oabs__class_Oabs(U_8660),U_8661)) = hAPP(c_Groups_Oabs__class_Oabs(U_8660),U_8661)
    | ~ class_Groups_Oordered__ab__group__add__abs(U_8660) ),
    inference(clausify,[status(thm)],[f_2502_2]) ).

fof(f_2503_1,plain,
    ! [V_n,V_a,T_a] :
      ( hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_n)
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__abs]) ).

fof(f_2503_2,plain,
    ! [U_8664,U_8663,U_8662] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_8662),hAPP(hAPP(c_Power_Opower__class_Opower(U_8662),U_8663),U_8664)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_8662),hAPP(c_Groups_Oabs__class_Oabs(U_8662),U_8663)),U_8664)
      | ~ class_Rings_Olinordered__idom(U_8662) ),
    inference(variable_rename,[status(thm)],[f_2503_1]) ).

cnf(f_2503_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_8662),hAPP(hAPP(c_Power_Opower__class_Opower(U_8662),U_8663),U_8664)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_8662),hAPP(c_Groups_Oabs__class_Oabs(U_8662),U_8663)),U_8664)
    | ~ class_Rings_Olinordered__idom(U_8662) ),
    inference(clausify,[status(thm)],[f_2503_2]) ).

fof(f_2504_1,plain,
    ! [V_a,T_a] :
      ( hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)
      | ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__minus__cancel]) ).

fof(f_2504_2,plain,
    ! [U_8666,U_8665] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_8665),hAPP(c_Groups_Ouminus__class_Ouminus(U_8665),U_8666)) = hAPP(c_Groups_Oabs__class_Oabs(U_8665),U_8666)
      | ~ class_Groups_Oordered__ab__group__add__abs(U_8665) ),
    inference(variable_rename,[status(thm)],[f_2504_1]) ).

cnf(f_2504_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_8665),hAPP(c_Groups_Ouminus__class_Ouminus(U_8665),U_8666)) = hAPP(c_Groups_Oabs__class_Oabs(U_8665),U_8666)
    | ~ class_Groups_Oordered__ab__group__add__abs(U_8665) ),
    inference(clausify,[status(thm)],[f_2504_2]) ).

fof(f_2505_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))
      | ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__add__abs]) ).

fof(f_2505_2,plain,
    ! [U_8669,U_8668,U_8667] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_8667),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8667),hAPP(c_Groups_Oabs__class_Oabs(U_8667),U_8668)),hAPP(c_Groups_Oabs__class_Oabs(U_8667),U_8669))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8667),hAPP(c_Groups_Oabs__class_Oabs(U_8667),U_8668)),hAPP(c_Groups_Oabs__class_Oabs(U_8667),U_8669))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_8667) ),
    inference(variable_rename,[status(thm)],[f_2505_1]) ).

cnf(f_2505_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_8667),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8667),hAPP(c_Groups_Oabs__class_Oabs(U_8667),U_8668)),hAPP(c_Groups_Oabs__class_Oabs(U_8667),U_8669))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8667),hAPP(c_Groups_Oabs__class_Oabs(U_8667),U_8668)),hAPP(c_Groups_Oabs__class_Oabs(U_8667),U_8669))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_8667) ),
    inference(clausify,[status(thm)],[f_2505_2]) ).

fof(f_2506_1,plain,
    ! [V_a_2,T_b] :
      ( ( ( hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
          | V_a_2 != c_Groups_Ozero__class_Ozero(T_b) )
        & ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
          | hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2) != c_Groups_Ozero__class_Ozero(T_b) ) )
      | ~ class_Groups_Oordered__ab__group__add__abs(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_abs__eq__0]) ).

fof(f_2506_2,plain,
    ! [U_8671,U_8670] :
      ( ( ( hAPP(c_Groups_Oabs__class_Oabs(U_8670),U_8671) = c_Groups_Ozero__class_Ozero(U_8670)
          | U_8671 != c_Groups_Ozero__class_Ozero(U_8670) )
        & ( U_8671 = c_Groups_Ozero__class_Ozero(U_8670)
          | hAPP(c_Groups_Oabs__class_Oabs(U_8670),U_8671) != c_Groups_Ozero__class_Ozero(U_8670) ) )
      | ~ class_Groups_Oordered__ab__group__add__abs(U_8670) ),
    inference(variable_rename,[status(thm)],[f_2506_1]) ).

cnf(f_2506_3,plain,
    ( U_8671 = c_Groups_Ozero__class_Ozero(U_8670)
    | hAPP(c_Groups_Oabs__class_Oabs(U_8670),U_8671) != c_Groups_Ozero__class_Ozero(U_8670)
    | ~ class_Groups_Oordered__ab__group__add__abs(U_8670) ),
    inference(clausify,[status(thm)],[f_2506_2]) ).

cnf(f_2506_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_8670),U_8671) = c_Groups_Ozero__class_Ozero(U_8670)
    | U_8671 != c_Groups_Ozero__class_Ozero(U_8670)
    | ~ class_Groups_Oordered__ab__group__add__abs(U_8670) ),
    inference(clausify,[status(thm)],[f_2506_2]) ).

fof(f_2507_1,plain,
    ! [T_a] :
      ( hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__zero]) ).

fof(f_2507_2,plain,
    ! [U_8672] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_8672),c_Groups_Ozero__class_Ozero(U_8672)) = c_Groups_Ozero__class_Ozero(U_8672)
      | ~ class_Groups_Oordered__ab__group__add__abs(U_8672) ),
    inference(variable_rename,[status(thm)],[f_2507_1]) ).

cnf(f_2507_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_8672),c_Groups_Ozero__class_Ozero(U_8672)) = c_Groups_Ozero__class_Ozero(U_8672)
    | ~ class_Groups_Oordered__ab__group__add__abs(U_8672) ),
    inference(clausify,[status(thm)],[f_2507_2]) ).

fof(f_2508_1,plain,
    ! [V_code__numeral_H_2,V_code__numeral_2] :
      ( ( c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2) = c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H_2)
        | V_code__numeral_2 != V_code__numeral_H_2 )
      & ( V_code__numeral_2 = V_code__numeral_H_2
        | c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2) != c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_code__numeral_Oinject]) ).

fof(f_2508_2,plain,
    ! [U_8674,U_8673] :
      ( ( c_Code__Numeral_OSuc__code__numeral(U_8673) = c_Code__Numeral_OSuc__code__numeral(U_8674)
        | U_8673 != U_8674 )
      & ( U_8673 = U_8674
        | c_Code__Numeral_OSuc__code__numeral(U_8673) != c_Code__Numeral_OSuc__code__numeral(U_8674) ) ),
    inference(variable_rename,[status(thm)],[f_2508_1]) ).

fof(f_2508_3,plain,
    ( ! [U_8678,U_8676] :
        ( c_Code__Numeral_OSuc__code__numeral(U_8676) = c_Code__Numeral_OSuc__code__numeral(U_8678)
        | U_8676 != U_8678 )
    & ! [U_8677,U_8675] :
        ( U_8675 = U_8677
        | c_Code__Numeral_OSuc__code__numeral(U_8675) != c_Code__Numeral_OSuc__code__numeral(U_8677) ) ),
    inference(miniscope,[status(thm)],[f_2508_2]) ).

cnf(f_2508_4,plain,
    ( U_8675 = U_8677
    | c_Code__Numeral_OSuc__code__numeral(U_8675) != c_Code__Numeral_OSuc__code__numeral(U_8677) ),
    inference(clausify,[status(thm)],[f_2508_3]) ).

cnf(f_2508_5,plain,
    ( c_Code__Numeral_OSuc__code__numeral(U_8676) = c_Code__Numeral_OSuc__code__numeral(U_8678)
    | U_8676 != U_8678 ),
    inference(clausify,[status(thm)],[f_2508_3]) ).

fof(f_2509_1,plain,
    ! [V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)))
      | ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__ge__zero]) ).

fof(f_2509_2,plain,
    ! [U_8680,U_8679] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8679),c_Groups_Ozero__class_Ozero(U_8679)),hAPP(c_Groups_Oabs__class_Oabs(U_8679),U_8680)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_8679) ),
    inference(variable_rename,[status(thm)],[f_2509_1]) ).

cnf(f_2509_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8679),c_Groups_Ozero__class_Ozero(U_8679)),hAPP(c_Groups_Oabs__class_Oabs(U_8679),U_8680)))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_8679) ),
    inference(clausify,[status(thm)],[f_2509_2]) ).

fof(f_2510_1,plain,
    ! [V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
          | V_a_2 != c_Groups_Ozero__class_Ozero(T_b) )
        & ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),c_Groups_Ozero__class_Ozero(T_b))) ) )
      | ~ class_Groups_Oordered__ab__group__add__abs(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_abs__le__zero__iff]) ).

fof(f_2510_2,plain,
    ! [U_8682,U_8681] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8681),hAPP(c_Groups_Oabs__class_Oabs(U_8681),U_8682)),c_Groups_Ozero__class_Ozero(U_8681)))
          | U_8682 != c_Groups_Ozero__class_Ozero(U_8681) )
        & ( U_8682 = c_Groups_Ozero__class_Ozero(U_8681)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8681),hAPP(c_Groups_Oabs__class_Oabs(U_8681),U_8682)),c_Groups_Ozero__class_Ozero(U_8681))) ) )
      | ~ class_Groups_Oordered__ab__group__add__abs(U_8681) ),
    inference(variable_rename,[status(thm)],[f_2510_1]) ).

cnf(f_2510_3,plain,
    ( U_8682 = c_Groups_Ozero__class_Ozero(U_8681)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8681),hAPP(c_Groups_Oabs__class_Oabs(U_8681),U_8682)),c_Groups_Ozero__class_Ozero(U_8681)))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_8681) ),
    inference(clausify,[status(thm)],[f_2510_2]) ).

cnf(f_2510_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8681),hAPP(c_Groups_Oabs__class_Oabs(U_8681),U_8682)),c_Groups_Ozero__class_Ozero(U_8681)))
    | U_8682 != c_Groups_Ozero__class_Ozero(U_8681)
    | ~ class_Groups_Oordered__ab__group__add__abs(U_8681) ),
    inference(clausify,[status(thm)],[f_2510_2]) ).

fof(f_2511_1,plain,
    ! [V_a,T_a] :
      ( hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
      | ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__of__nonneg]) ).

fof(f_2511_2,plain,
    ! [U_8684,U_8683] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_8683),U_8684) = U_8684
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8683),c_Groups_Ozero__class_Ozero(U_8683)),U_8684))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_8683) ),
    inference(variable_rename,[status(thm)],[f_2511_1]) ).

cnf(f_2511_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_8683),U_8684) = U_8684
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8683),c_Groups_Ozero__class_Ozero(U_8683)),U_8684))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_8683) ),
    inference(clausify,[status(thm)],[f_2511_2]) ).

fof(f_2512_1,plain,
    ! [V_a,T_a] :
      ( hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
      | ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__of__pos]) ).

fof(f_2512_2,plain,
    ! [U_8686,U_8685] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_8685),U_8686) = U_8686
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8685),c_Groups_Ozero__class_Ozero(U_8685)),U_8686))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_8685) ),
    inference(variable_rename,[status(thm)],[f_2512_1]) ).

cnf(f_2512_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_8685),U_8686) = U_8686
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8685),c_Groups_Ozero__class_Ozero(U_8685)),U_8686))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_8685) ),
    inference(clausify,[status(thm)],[f_2512_2]) ).

fof(f_2513_1,plain,
    ! [V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)))
          | V_a_2 = c_Groups_Ozero__class_Ozero(T_b) )
        & ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2))) ) )
      | ~ class_Groups_Oordered__ab__group__add__abs(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_zero__less__abs__iff]) ).

fof(f_2513_2,plain,
    ! [U_8688,U_8687] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8687),c_Groups_Ozero__class_Ozero(U_8687)),hAPP(c_Groups_Oabs__class_Oabs(U_8687),U_8688)))
          | U_8688 = c_Groups_Ozero__class_Ozero(U_8687) )
        & ( U_8688 != c_Groups_Ozero__class_Ozero(U_8687)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8687),c_Groups_Ozero__class_Ozero(U_8687)),hAPP(c_Groups_Oabs__class_Oabs(U_8687),U_8688))) ) )
      | ~ class_Groups_Oordered__ab__group__add__abs(U_8687) ),
    inference(variable_rename,[status(thm)],[f_2513_1]) ).

cnf(f_2513_3,plain,
    ( U_8688 != c_Groups_Ozero__class_Ozero(U_8687)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8687),c_Groups_Ozero__class_Ozero(U_8687)),hAPP(c_Groups_Oabs__class_Oabs(U_8687),U_8688)))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_8687) ),
    inference(clausify,[status(thm)],[f_2513_2]) ).

cnf(f_2513_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8687),c_Groups_Ozero__class_Ozero(U_8687)),hAPP(c_Groups_Oabs__class_Oabs(U_8687),U_8688)))
    | U_8688 = c_Groups_Ozero__class_Ozero(U_8687)
    | ~ class_Groups_Oordered__ab__group__add__abs(U_8687) ),
    inference(clausify,[status(thm)],[f_2513_2]) ).

fof(f_2514_1,plain,
    ! [V_a,T_a] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__not__less__zero]) ).

fof(f_2514_2,plain,
    ! [U_8690,U_8689] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8689),hAPP(c_Groups_Oabs__class_Oabs(U_8689),U_8690)),c_Groups_Ozero__class_Ozero(U_8689)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_8689) ),
    inference(variable_rename,[status(thm)],[f_2514_1]) ).

cnf(f_2514_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8689),hAPP(c_Groups_Oabs__class_Oabs(U_8689),U_8690)),c_Groups_Ozero__class_Ozero(U_8689)))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_8689) ),
    inference(clausify,[status(thm)],[f_2514_2]) ).

fof(f_2515_1,plain,
    ! [V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))))
      | ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq]) ).

fof(f_2515_2,plain,
    ! [U_8693,U_8692,U_8691] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8691),hAPP(c_Groups_Oabs__class_Oabs(U_8691),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8691),U_8692),U_8693))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8691),hAPP(c_Groups_Oabs__class_Oabs(U_8691),U_8692)),hAPP(c_Groups_Oabs__class_Oabs(U_8691),U_8693))))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_8691) ),
    inference(variable_rename,[status(thm)],[f_2515_1]) ).

cnf(f_2515_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8691),hAPP(c_Groups_Oabs__class_Oabs(U_8691),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8691),U_8692),U_8693))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8691),hAPP(c_Groups_Oabs__class_Oabs(U_8691),U_8692)),hAPP(c_Groups_Oabs__class_Oabs(U_8691),U_8693))))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_8691) ),
    inference(clausify,[status(thm)],[f_2515_2]) ).

fof(f_2516_1,plain,
    ! [V_d,V_b,V_c,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_d)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)),V_d))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_c))
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__mult__less]) ).

fof(f_2516_2,plain,
    ! [U_8698,U_8697,U_8696,U_8695,U_8694] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8694),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8694),hAPP(c_Groups_Oabs__class_Oabs(U_8694),U_8695)),hAPP(c_Groups_Oabs__class_Oabs(U_8694),U_8697))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8694),U_8696),U_8698)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8694),hAPP(c_Groups_Oabs__class_Oabs(U_8694),U_8697)),U_8698))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8694),hAPP(c_Groups_Oabs__class_Oabs(U_8694),U_8695)),U_8696))
      | ~ class_Rings_Olinordered__idom(U_8694) ),
    inference(variable_rename,[status(thm)],[f_2516_1]) ).

cnf(f_2516_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8694),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8694),hAPP(c_Groups_Oabs__class_Oabs(U_8694),U_8695)),hAPP(c_Groups_Oabs__class_Oabs(U_8694),U_8697))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8694),U_8696),U_8698)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8694),hAPP(c_Groups_Oabs__class_Oabs(U_8694),U_8697)),U_8698))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8694),hAPP(c_Groups_Oabs__class_Oabs(U_8694),U_8695)),U_8696))
    | ~ class_Rings_Olinordered__idom(U_8694) ),
    inference(clausify,[status(thm)],[f_2516_2]) ).

fof(f_2517_1,plain,
    ! [V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)))),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b))))
      | ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq3]) ).

fof(f_2517_2,plain,
    ! [U_8701,U_8700,U_8699] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8699),hAPP(c_Groups_Oabs__class_Oabs(U_8699),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8699),hAPP(c_Groups_Oabs__class_Oabs(U_8699),U_8700)),hAPP(c_Groups_Oabs__class_Oabs(U_8699),U_8701)))),hAPP(c_Groups_Oabs__class_Oabs(U_8699),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8699),U_8700),U_8701))))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_8699) ),
    inference(variable_rename,[status(thm)],[f_2517_1]) ).

cnf(f_2517_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8699),hAPP(c_Groups_Oabs__class_Oabs(U_8699),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8699),hAPP(c_Groups_Oabs__class_Oabs(U_8699),U_8700)),hAPP(c_Groups_Oabs__class_Oabs(U_8699),U_8701)))),hAPP(c_Groups_Oabs__class_Oabs(U_8699),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8699),U_8700),U_8701))))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_8699) ),
    inference(clausify,[status(thm)],[f_2517_2]) ).

fof(f_2518_1,plain,
    ! [V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b))))
      | ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq2]) ).

fof(f_2518_2,plain,
    ! [U_8704,U_8703,U_8702] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8702),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8702),hAPP(c_Groups_Oabs__class_Oabs(U_8702),U_8703)),hAPP(c_Groups_Oabs__class_Oabs(U_8702),U_8704))),hAPP(c_Groups_Oabs__class_Oabs(U_8702),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8702),U_8703),U_8704))))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_8702) ),
    inference(variable_rename,[status(thm)],[f_2518_1]) ).

cnf(f_2518_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8702),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8702),hAPP(c_Groups_Oabs__class_Oabs(U_8702),U_8703)),hAPP(c_Groups_Oabs__class_Oabs(U_8702),U_8704))),hAPP(c_Groups_Oabs__class_Oabs(U_8702),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8702),U_8703),U_8704))))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_8702) ),
    inference(clausify,[status(thm)],[f_2518_2]) ).

fof(f_2519_1,plain,
    ! [V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_a))))
      | ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq2__sym]) ).

fof(f_2519_2,plain,
    ! [U_8707,U_8706,U_8705] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8705),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8705),hAPP(c_Groups_Oabs__class_Oabs(U_8705),U_8706)),hAPP(c_Groups_Oabs__class_Oabs(U_8705),U_8707))),hAPP(c_Groups_Oabs__class_Oabs(U_8705),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8705),U_8707),U_8706))))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_8705) ),
    inference(variable_rename,[status(thm)],[f_2519_1]) ).

cnf(f_2519_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8705),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8705),hAPP(c_Groups_Oabs__class_Oabs(U_8705),U_8706)),hAPP(c_Groups_Oabs__class_Oabs(U_8705),U_8707))),hAPP(c_Groups_Oabs__class_Oabs(U_8705),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8705),U_8707),U_8706))))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_8705) ),
    inference(clausify,[status(thm)],[f_2519_2]) ).

fof(f_2520_1,plain,
    ! [V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b))
      | ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__le__D2]) ).

fof(f_2520_2,plain,
    ! [U_8710,U_8709,U_8708] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8708),hAPP(c_Groups_Ouminus__class_Ouminus(U_8708),U_8709)),U_8710))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8708),hAPP(c_Groups_Oabs__class_Oabs(U_8708),U_8709)),U_8710))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_8708) ),
    inference(variable_rename,[status(thm)],[f_2520_1]) ).

cnf(f_2520_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8708),hAPP(c_Groups_Ouminus__class_Ouminus(U_8708),U_8709)),U_8710))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8708),hAPP(c_Groups_Oabs__class_Oabs(U_8708),U_8709)),U_8710))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_8708) ),
    inference(clausify,[status(thm)],[f_2520_2]) ).

fof(f_2521_1,plain,
    ! [V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
      | ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__leI]) ).

fof(f_2521_2,plain,
    ! [U_8713,U_8712,U_8711] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8711),hAPP(c_Groups_Oabs__class_Oabs(U_8711),U_8712)),U_8713))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8711),hAPP(c_Groups_Ouminus__class_Ouminus(U_8711),U_8712)),U_8713))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8711),U_8712),U_8713))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_8711) ),
    inference(variable_rename,[status(thm)],[f_2521_1]) ).

cnf(f_2521_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8711),hAPP(c_Groups_Oabs__class_Oabs(U_8711),U_8712)),U_8713))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8711),hAPP(c_Groups_Ouminus__class_Ouminus(U_8711),U_8712)),U_8713))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8711),U_8712),U_8713))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_8711) ),
    inference(clausify,[status(thm)],[f_2521_2]) ).

fof(f_2522_1,plain,
    ! [V_b_2,V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),V_b_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),V_b_2)) ) )
      | ~ class_Groups_Oordered__ab__group__add__abs(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_abs__le__iff]) ).

fof(f_2522_2,plain,
    ! [U_8716,U_8715,U_8714] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8714),hAPP(c_Groups_Oabs__class_Oabs(U_8714),U_8715)),U_8716))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8714),hAPP(c_Groups_Ouminus__class_Ouminus(U_8714),U_8715)),U_8716))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8714),U_8715),U_8716)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8714),hAPP(c_Groups_Ouminus__class_Ouminus(U_8714),U_8715)),U_8716))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8714),U_8715),U_8716)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8714),hAPP(c_Groups_Oabs__class_Oabs(U_8714),U_8715)),U_8716)) ) )
      | ~ class_Groups_Oordered__ab__group__add__abs(U_8714) ),
    inference(variable_rename,[status(thm)],[f_2522_1]) ).

cnf(f_2522_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8714),U_8715),U_8716))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8714),hAPP(c_Groups_Oabs__class_Oabs(U_8714),U_8715)),U_8716))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_8714) ),
    inference(clausify,[status(thm)],[f_2522_2]) ).

cnf(f_2522_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8714),hAPP(c_Groups_Ouminus__class_Ouminus(U_8714),U_8715)),U_8716))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8714),hAPP(c_Groups_Oabs__class_Oabs(U_8714),U_8715)),U_8716))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_8714) ),
    inference(clausify,[status(thm)],[f_2522_2]) ).

cnf(f_2522_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8714),hAPP(c_Groups_Oabs__class_Oabs(U_8714),U_8715)),U_8716))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8714),hAPP(c_Groups_Ouminus__class_Ouminus(U_8714),U_8715)),U_8716))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8714),U_8715),U_8716))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_8714) ),
    inference(clausify,[status(thm)],[f_2522_2]) ).

fof(f_2523_1,plain,
    ! [V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)))
      | ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__ge__minus__self]) ).

fof(f_2523_2,plain,
    ! [U_8718,U_8717] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8717),hAPP(c_Groups_Ouminus__class_Ouminus(U_8717),U_8718)),hAPP(c_Groups_Oabs__class_Oabs(U_8717),U_8718)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_8717) ),
    inference(variable_rename,[status(thm)],[f_2523_1]) ).

cnf(f_2523_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8717),hAPP(c_Groups_Ouminus__class_Ouminus(U_8717),U_8718)),hAPP(c_Groups_Oabs__class_Oabs(U_8717),U_8718)))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_8717) ),
    inference(clausify,[status(thm)],[f_2523_2]) ).

fof(f_2524_1,plain,
    ! [V_b_2,V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),V_b_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),V_b_2)) ) )
      | ~ class_Rings_Olinordered__idom(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_abs__less__iff]) ).

fof(f_2524_2,plain,
    ! [U_8721,U_8720,U_8719] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8719),hAPP(c_Groups_Oabs__class_Oabs(U_8719),U_8720)),U_8721))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8719),hAPP(c_Groups_Ouminus__class_Ouminus(U_8719),U_8720)),U_8721))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8719),U_8720),U_8721)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8719),hAPP(c_Groups_Ouminus__class_Ouminus(U_8719),U_8720)),U_8721))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8719),U_8720),U_8721)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8719),hAPP(c_Groups_Oabs__class_Oabs(U_8719),U_8720)),U_8721)) ) )
      | ~ class_Rings_Olinordered__idom(U_8719) ),
    inference(variable_rename,[status(thm)],[f_2524_1]) ).

cnf(f_2524_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8719),U_8720),U_8721))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8719),hAPP(c_Groups_Oabs__class_Oabs(U_8719),U_8720)),U_8721))
    | ~ class_Rings_Olinordered__idom(U_8719) ),
    inference(clausify,[status(thm)],[f_2524_2]) ).

cnf(f_2524_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8719),hAPP(c_Groups_Ouminus__class_Ouminus(U_8719),U_8720)),U_8721))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8719),hAPP(c_Groups_Oabs__class_Oabs(U_8719),U_8720)),U_8721))
    | ~ class_Rings_Olinordered__idom(U_8719) ),
    inference(clausify,[status(thm)],[f_2524_2]) ).

cnf(f_2524_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8719),hAPP(c_Groups_Oabs__class_Oabs(U_8719),U_8720)),U_8721))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8719),hAPP(c_Groups_Ouminus__class_Ouminus(U_8719),U_8720)),U_8721))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8719),U_8720),U_8721))
    | ~ class_Rings_Olinordered__idom(U_8719) ),
    inference(clausify,[status(thm)],[f_2524_2]) ).

fof(f_2525_1,plain,
    ! [V_a,V_b,T_a] :
      ( hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))
      | V_b = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Fields_Olinordered__field(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_nonzero__abs__divide]) ).

fof(f_2525_2,plain,
    ! [U_8724,U_8723,U_8722] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_8722),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8722),U_8724),U_8723)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8722),hAPP(c_Groups_Oabs__class_Oabs(U_8722),U_8724)),hAPP(c_Groups_Oabs__class_Oabs(U_8722),U_8723))
      | U_8723 = c_Groups_Ozero__class_Ozero(U_8722)
      | ~ class_Fields_Olinordered__field(U_8722) ),
    inference(variable_rename,[status(thm)],[f_2525_1]) ).

cnf(f_2525_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_8722),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8722),U_8724),U_8723)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8722),hAPP(c_Groups_Oabs__class_Oabs(U_8722),U_8724)),hAPP(c_Groups_Oabs__class_Oabs(U_8722),U_8723))
    | U_8723 = c_Groups_Ozero__class_Ozero(U_8722)
    | ~ class_Fields_Olinordered__field(U_8722) ),
    inference(clausify,[status(thm)],[f_2525_2]) ).

fof(f_2526_1,plain,
    ! [V_n,V_a,T_a] :
      ( hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_n)) = hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__power__minus]) ).

fof(f_2526_2,plain,
    ! [U_8727,U_8726,U_8725] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_8725),hAPP(hAPP(c_Power_Opower__class_Opower(U_8725),hAPP(c_Groups_Ouminus__class_Ouminus(U_8725),U_8726)),U_8727)) = hAPP(c_Groups_Oabs__class_Oabs(U_8725),hAPP(hAPP(c_Power_Opower__class_Opower(U_8725),U_8726),U_8727))
      | ~ class_Rings_Olinordered__idom(U_8725) ),
    inference(variable_rename,[status(thm)],[f_2526_1]) ).

cnf(f_2526_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_8725),hAPP(hAPP(c_Power_Opower__class_Opower(U_8725),hAPP(c_Groups_Ouminus__class_Ouminus(U_8725),U_8726)),U_8727)) = hAPP(c_Groups_Oabs__class_Oabs(U_8725),hAPP(hAPP(c_Power_Opower__class_Opower(U_8725),U_8726),U_8727))
    | ~ class_Rings_Olinordered__idom(U_8725) ),
    inference(clausify,[status(thm)],[f_2526_2]) ).

fof(f_2527_1,plain,
    ! [V_n,V_m] :
      ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_m) = c_Groups_Oone__class_Oone(tc_Int_Oint)
      | hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n)) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(fof_nnf,[status(thm)],[fact_abs__zmult__eq__1]) ).

fof(f_2527_2,plain,
    ! [U_8729,U_8728] :
      ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_8728) = c_Groups_Oone__class_Oone(tc_Int_Oint)
      | hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8728),U_8729)) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_2527_1]) ).

cnf(f_2527_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_8728) = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8728),U_8729)) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2527_2]) ).

fof(f_2528_1,plain,
    ! [V_k,T_a] :
      ( hAPP(c_Groups_Oabs__class_Oabs(T_a),V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k))
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__sgn]) ).

fof(f_2528_2,plain,
    ! [U_8731,U_8730] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_8730),U_8731) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8730),U_8731),c_Groups_Osgn__class_Osgn(U_8730,U_8731))
      | ~ class_Rings_Olinordered__idom(U_8730) ),
    inference(variable_rename,[status(thm)],[f_2528_1]) ).

cnf(f_2528_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_8730),U_8731) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8730),U_8731),c_Groups_Osgn__class_Osgn(U_8730,U_8731))
    | ~ class_Rings_Olinordered__idom(U_8730) ),
    inference(clausify,[status(thm)],[f_2528_2]) ).

fof(f_2529_1,plain,
    ! [V_x,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_x)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_x)) = V_x
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__sgn__abs]) ).

fof(f_2529_2,plain,
    ! [U_8733,U_8732] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8732),c_Groups_Osgn__class_Osgn(U_8732,U_8733)),hAPP(c_Groups_Oabs__class_Oabs(U_8732),U_8733)) = U_8733
      | ~ class_Rings_Olinordered__idom(U_8732) ),
    inference(variable_rename,[status(thm)],[f_2529_1]) ).

cnf(f_2529_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8732),c_Groups_Osgn__class_Osgn(U_8732,U_8733)),hAPP(c_Groups_Oabs__class_Oabs(U_8732),U_8733)) = U_8733
    | ~ class_Rings_Olinordered__idom(U_8732) ),
    inference(clausify,[status(thm)],[f_2529_2]) ).

fof(f_2530_1,plain,
    ! [V_code__numeral_H] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H),
    inference(fof_nnf,[status(thm)],[fact_code__numeral_Osimps_I2_J]) ).

fof(f_2530_2,plain,
    ! [U_8734] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(U_8734),
    inference(variable_rename,[status(thm)],[f_2530_1]) ).

cnf(f_2530_3,plain,
    c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(U_8734),
    inference(clausify,[status(thm)],[f_2530_2]) ).

fof(f_2531_1,plain,
    ! [V_code__numeral_H_1] : c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H_1) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[fact_code__numeral_Osimps_I3_J]) ).

fof(f_2531_2,plain,
    ! [U_8735] : c_Code__Numeral_OSuc__code__numeral(U_8735) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
    inference(variable_rename,[status(thm)],[f_2531_1]) ).

cnf(f_2531_3,plain,
    c_Code__Numeral_OSuc__code__numeral(U_8735) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_2531_2]) ).

fof(f_2532_1,plain,
    ! [V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_y)),V_x) = hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__mult__pos]) ).

fof(f_2532_2,plain,
    ! [U_8738,U_8737,U_8736] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8736),hAPP(c_Groups_Oabs__class_Oabs(U_8736),U_8738)),U_8737) = hAPP(c_Groups_Oabs__class_Oabs(U_8736),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8736),U_8738),U_8737))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8736),c_Groups_Ozero__class_Ozero(U_8736)),U_8737))
      | ~ class_Rings_Olinordered__idom(U_8736) ),
    inference(variable_rename,[status(thm)],[f_2532_1]) ).

cnf(f_2532_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8736),hAPP(c_Groups_Oabs__class_Oabs(U_8736),U_8738)),U_8737) = hAPP(c_Groups_Oabs__class_Oabs(U_8736),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8736),U_8738),U_8737))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8736),c_Groups_Ozero__class_Ozero(U_8736)),U_8737))
    | ~ class_Rings_Olinordered__idom(U_8736) ),
    inference(clausify,[status(thm)],[f_2532_2]) ).

fof(f_2533_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
        & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) )
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
        & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) )
      | ~ class_Rings_Oordered__ring__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__eq__mult]) ).

fof(f_2533_2,plain,
    ! [U_8741,U_8740,U_8739] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_8739),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8739),U_8740),U_8741)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8739),hAPP(c_Groups_Oabs__class_Oabs(U_8739),U_8740)),hAPP(c_Groups_Oabs__class_Oabs(U_8739),U_8741))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8739),U_8741),c_Groups_Ozero__class_Ozero(U_8739)))
        & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8739),c_Groups_Ozero__class_Ozero(U_8739)),U_8741)) )
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8739),U_8740),c_Groups_Ozero__class_Ozero(U_8739)))
        & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8739),c_Groups_Ozero__class_Ozero(U_8739)),U_8740)) )
      | ~ class_Rings_Oordered__ring__abs(U_8739) ),
    inference(variable_rename,[status(thm)],[f_2533_1]) ).

cnf(f_2533_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8739),c_Groups_Ozero__class_Ozero(U_8739)),U_8741))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8739),c_Groups_Ozero__class_Ozero(U_8739)),U_8740))
    | hAPP(c_Groups_Oabs__class_Oabs(U_8739),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8739),U_8740),U_8741)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8739),hAPP(c_Groups_Oabs__class_Oabs(U_8739),U_8740)),hAPP(c_Groups_Oabs__class_Oabs(U_8739),U_8741))
    | ~ class_Rings_Oordered__ring__abs(U_8739) ),
    inference(clausify,[status(thm)],[f_2533_2]) ).

cnf(f_2533_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8739),U_8741),c_Groups_Ozero__class_Ozero(U_8739)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8739),c_Groups_Ozero__class_Ozero(U_8739)),U_8740))
    | hAPP(c_Groups_Oabs__class_Oabs(U_8739),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8739),U_8740),U_8741)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8739),hAPP(c_Groups_Oabs__class_Oabs(U_8739),U_8740)),hAPP(c_Groups_Oabs__class_Oabs(U_8739),U_8741))
    | ~ class_Rings_Oordered__ring__abs(U_8739) ),
    inference(clausify,[status(thm)],[f_2533_2]) ).

cnf(f_2533_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8739),c_Groups_Ozero__class_Ozero(U_8739)),U_8741))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8739),U_8740),c_Groups_Ozero__class_Ozero(U_8739)))
    | hAPP(c_Groups_Oabs__class_Oabs(U_8739),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8739),U_8740),U_8741)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8739),hAPP(c_Groups_Oabs__class_Oabs(U_8739),U_8740)),hAPP(c_Groups_Oabs__class_Oabs(U_8739),U_8741))
    | ~ class_Rings_Oordered__ring__abs(U_8739) ),
    inference(clausify,[status(thm)],[f_2533_2]) ).

cnf(f_2533_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8739),U_8741),c_Groups_Ozero__class_Ozero(U_8739)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8739),U_8740),c_Groups_Ozero__class_Ozero(U_8739)))
    | hAPP(c_Groups_Oabs__class_Oabs(U_8739),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8739),U_8740),U_8741)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8739),hAPP(c_Groups_Oabs__class_Oabs(U_8739),U_8740)),hAPP(c_Groups_Oabs__class_Oabs(U_8739),U_8741))
    | ~ class_Rings_Oordered__ring__abs(U_8739) ),
    inference(clausify,[status(thm)],[f_2533_2]) ).

fof(f_2534_1,plain,
    ! [V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))))
      | ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq4]) ).

fof(f_2534_2,plain,
    ! [U_8744,U_8743,U_8742] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8742),hAPP(c_Groups_Oabs__class_Oabs(U_8742),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8742),U_8743),U_8744))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8742),hAPP(c_Groups_Oabs__class_Oabs(U_8742),U_8743)),hAPP(c_Groups_Oabs__class_Oabs(U_8742),U_8744))))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_8742) ),
    inference(variable_rename,[status(thm)],[f_2534_1]) ).

cnf(f_2534_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8742),hAPP(c_Groups_Oabs__class_Oabs(U_8742),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8742),U_8743),U_8744))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8742),hAPP(c_Groups_Oabs__class_Oabs(U_8742),U_8743)),hAPP(c_Groups_Oabs__class_Oabs(U_8742),U_8744))))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_8742) ),
    inference(clausify,[status(thm)],[f_2534_2]) ).

fof(f_2535_1,plain,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_d)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_c))),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_d)))))
      | ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__diff__triangle__ineq]) ).

fof(f_2535_2,plain,
    ! [U_8749,U_8748,U_8747,U_8746,U_8745] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8745),hAPP(c_Groups_Oabs__class_Oabs(U_8745),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8745),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8745),U_8746),U_8747)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8745),U_8748),U_8749)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8745),hAPP(c_Groups_Oabs__class_Oabs(U_8745),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8745),U_8746),U_8748))),hAPP(c_Groups_Oabs__class_Oabs(U_8745),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8745),U_8747),U_8749)))))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_8745) ),
    inference(variable_rename,[status(thm)],[f_2535_1]) ).

cnf(f_2535_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8745),hAPP(c_Groups_Oabs__class_Oabs(U_8745),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8745),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8745),U_8746),U_8747)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8745),U_8748),U_8749)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8745),hAPP(c_Groups_Oabs__class_Oabs(U_8745),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8745),U_8746),U_8748))),hAPP(c_Groups_Oabs__class_Oabs(U_8745),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8745),U_8747),U_8749)))))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_8745) ),
    inference(clausify,[status(thm)],[f_2535_2]) ).

fof(f_2536_1,plain,
    ! [V_a,T_a] :
      ( hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__of__nonpos]) ).

fof(f_2536_2,plain,
    ! [U_8751,U_8750] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_8750),U_8751) = hAPP(c_Groups_Ouminus__class_Ouminus(U_8750),U_8751)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8750),U_8751),c_Groups_Ozero__class_Ozero(U_8750)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_8750) ),
    inference(variable_rename,[status(thm)],[f_2536_1]) ).

cnf(f_2536_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_8750),U_8751) = hAPP(c_Groups_Ouminus__class_Ouminus(U_8750),U_8751)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8750),U_8751),c_Groups_Ozero__class_Ozero(U_8750)))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_8750) ),
    inference(clausify,[status(thm)],[f_2536_2]) ).

fof(f_2537_1,plain,
    ! [V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__minus__le__zero]) ).

fof(f_2537_2,plain,
    ! [U_8753,U_8752] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8752),hAPP(c_Groups_Ouminus__class_Ouminus(U_8752),hAPP(c_Groups_Oabs__class_Oabs(U_8752),U_8753))),c_Groups_Ozero__class_Ozero(U_8752)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_8752) ),
    inference(variable_rename,[status(thm)],[f_2537_1]) ).

cnf(f_2537_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8752),hAPP(c_Groups_Ouminus__class_Ouminus(U_8752),hAPP(c_Groups_Oabs__class_Oabs(U_8752),U_8753))),c_Groups_Ozero__class_Ozero(U_8752)))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_8752) ),
    inference(clausify,[status(thm)],[f_2537_2]) ).

fof(f_2538_1,plain,
    ! [V_a,T_a] :
      ( hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__of__neg]) ).

fof(f_2538_2,plain,
    ! [U_8755,U_8754] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_8754),U_8755) = hAPP(c_Groups_Ouminus__class_Ouminus(U_8754),U_8755)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8754),U_8755),c_Groups_Ozero__class_Ozero(U_8754)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_8754) ),
    inference(variable_rename,[status(thm)],[f_2538_1]) ).

cnf(f_2538_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_8754),U_8755) = hAPP(c_Groups_Ouminus__class_Ouminus(U_8754),U_8755)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8754),U_8755),c_Groups_Ozero__class_Ozero(U_8754)))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_8754) ),
    inference(clausify,[status(thm)],[f_2538_2]) ).

fof(f_2539_1,plain,
    ! [V_a,T_a] :
      ( ( ( hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) )
        & ( hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) ) )
      | ~ class_Groups_Oabs__if(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__if]) ).

fof(f_2539_2,plain,
    ! [U_8757,U_8756] :
      ( ( ( hAPP(c_Groups_Oabs__class_Oabs(U_8756),U_8757) = U_8757
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8756),U_8757),c_Groups_Ozero__class_Ozero(U_8756))) )
        & ( hAPP(c_Groups_Oabs__class_Oabs(U_8756),U_8757) = hAPP(c_Groups_Ouminus__class_Ouminus(U_8756),U_8757)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8756),U_8757),c_Groups_Ozero__class_Ozero(U_8756))) ) )
      | ~ class_Groups_Oabs__if(U_8756) ),
    inference(variable_rename,[status(thm)],[f_2539_1]) ).

cnf(f_2539_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_8756),U_8757) = hAPP(c_Groups_Ouminus__class_Ouminus(U_8756),U_8757)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8756),U_8757),c_Groups_Ozero__class_Ozero(U_8756)))
    | ~ class_Groups_Oabs__if(U_8756) ),
    inference(clausify,[status(thm)],[f_2539_2]) ).

cnf(f_2539_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_8756),U_8757) = U_8757
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8756),U_8757),c_Groups_Ozero__class_Ozero(U_8756)))
    | ~ class_Groups_Oabs__if(U_8756) ),
    inference(clausify,[status(thm)],[f_2539_2]) ).

fof(f_2540_1,plain,
    ! [V_n,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_n)))
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_zero__le__power__abs]) ).

fof(f_2540_2,plain,
    ! [U_8760,U_8759,U_8758] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8758),c_Groups_Ozero__class_Ozero(U_8758)),hAPP(hAPP(c_Power_Opower__class_Opower(U_8758),hAPP(c_Groups_Oabs__class_Oabs(U_8758),U_8759)),U_8760)))
      | ~ class_Rings_Olinordered__idom(U_8758) ),
    inference(variable_rename,[status(thm)],[f_2540_1]) ).

cnf(f_2540_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8758),c_Groups_Ozero__class_Ozero(U_8758)),hAPP(hAPP(c_Power_Opower__class_Opower(U_8758),hAPP(c_Groups_Oabs__class_Oabs(U_8758),U_8759)),U_8760)))
    | ~ class_Rings_Olinordered__idom(U_8758) ),
    inference(clausify,[status(thm)],[f_2540_2]) ).

fof(f_2541_1,plain,
    ! [V_x,V_y,T_a] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_x)),V_y) = hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
      | ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__div__pos]) ).

fof(f_2541_2,plain,
    ! [U_8763,U_8762,U_8761] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8761),hAPP(c_Groups_Oabs__class_Oabs(U_8761),U_8763)),U_8762) = hAPP(c_Groups_Oabs__class_Oabs(U_8761),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8761),U_8763),U_8762))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8761),c_Groups_Ozero__class_Ozero(U_8761)),U_8762))
      | ~ class_Fields_Olinordered__field__inverse__zero(U_8761) ),
    inference(variable_rename,[status(thm)],[f_2541_1]) ).

cnf(f_2541_3,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8761),hAPP(c_Groups_Oabs__class_Oabs(U_8761),U_8763)),U_8762) = hAPP(c_Groups_Oabs__class_Oabs(U_8761),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_8761),U_8763),U_8762))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8761),c_Groups_Ozero__class_Ozero(U_8761)),U_8762))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_8761) ),
    inference(clausify,[status(thm)],[f_2541_2]) ).

fof(f_2542_1,plain,
    ! [T_a] :
      ( hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) = c_Groups_Oone__class_Oone(T_a)
      | ~ class_Rings_Olinordered__idom(T_a)
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__minus__one]) ).

fof(f_2542_2,plain,
    ! [U_8764] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_8764),hAPP(c_Int_Onumber__class_Onumber__of(U_8764),c_Int_OMin)) = c_Groups_Oone__class_Oone(U_8764)
      | ~ class_Rings_Olinordered__idom(U_8764)
      | ~ class_Int_Onumber__ring(U_8764) ),
    inference(variable_rename,[status(thm)],[f_2542_1]) ).

cnf(f_2542_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_8764),hAPP(c_Int_Onumber__class_Onumber__of(U_8764),c_Int_OMin)) = c_Groups_Oone__class_Oone(U_8764)
    | ~ class_Rings_Olinordered__idom(U_8764)
    | ~ class_Int_Onumber__ring(U_8764) ),
    inference(clausify,[status(thm)],[f_2542_2]) ).

fof(f_2543_1,plain,
    ! [V_z_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_z_2)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | V_z_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_z_2)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
    inference(fof_nnf,[status(thm)],[fact_zabs__less__one__iff]) ).

fof(f_2543_2,plain,
    ! [U_8765] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_8765)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | U_8765 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( U_8765 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_8765)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
    inference(variable_rename,[status(thm)],[f_2543_1]) ).

fof(f_2543_3,plain,
    ( ! [U_8767] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_8767)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | U_8767 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
    & ! [U_8766] :
        ( U_8766 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_8766)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
    inference(miniscope,[status(thm)],[f_2543_2]) ).

cnf(f_2543_4,plain,
    ( U_8766 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_8766)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2543_3]) ).

cnf(f_2543_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_8767)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | U_8767 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2543_3]) ).

fof(f_2544_1,plain,
    ! [V_i] :
      ( ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = V_i
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_i)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(fof_nnf,[status(thm)],[fact_zabs__def]) ).

fof(f_2544_2,plain,
    ! [U_8768] :
      ( ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_8768) = U_8768
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8768),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_8768) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8768)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8768),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(variable_rename,[status(thm)],[f_2544_1]) ).

fof(f_2544_3,plain,
    ( ! [U_8770] :
        ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_8770) = U_8770
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8770),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_8769] :
        ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_8769) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8769)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8769),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(miniscope,[status(thm)],[f_2544_2]) ).

cnf(f_2544_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_8769) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_8769)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8769),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2544_3]) ).

cnf(f_2544_5,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_8770) = U_8770
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8770),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2544_3]) ).

fof(f_2545_1,plain,
    ! [V_z,V_w] : hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_w))),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_z))),
    inference(fof_nnf,[status(thm)],[fact_nat__abs__mult__distrib]) ).

fof(f_2545_2,plain,
    ! [U_8772,U_8771] : hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8771),U_8772))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_8771))),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_8772))),
    inference(variable_rename,[status(thm)],[f_2545_1]) ).

cnf(f_2545_3,plain,
    hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_8771),U_8772))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_8771))),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_8772))),
    inference(clausify,[status(thm)],[f_2545_2]) ).

fof(f_2546_1,plain,
    ! [V_code__numeral] : hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(V_code__numeral)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),V_code__numeral)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(fof_nnf,[status(thm)],[fact_code__numeral_Osize_I4_J]) ).

fof(f_2546_2,plain,
    ! [U_8773] : hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(U_8773)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),U_8773)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_2546_1]) ).

cnf(f_2546_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(U_8773)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),U_8773)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_2546_2]) ).

fof(f_2547_1,plain,
    ! [V_n,V_x] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x)),V_n))),
    inference(fof_nnf,[status(thm)],[fact_zero__le__zpower__abs]) ).

fof(f_2547_2,plain,
    ! [U_8775,U_8774] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_8774)),U_8775))),
    inference(variable_rename,[status(thm)],[f_2547_1]) ).

cnf(f_2547_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_8774)),U_8775))),
    inference(clausify,[status(thm)],[f_2547_2]) ).

fof(f_2548_1,plain,
    ! [V_x,T_a] :
      ( ( ( hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)),c_Groups_Ozero__class_Ozero(T_a))) )
        & ( hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)),c_Groups_Ozero__class_Ozero(T_a))) ) )
      | ~ class_Rings_Olinordered__idom(T_a)
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__number__of]) ).

fof(f_2548_2,plain,
    ! [U_8777,U_8776] :
      ( ( ( hAPP(c_Groups_Oabs__class_Oabs(U_8776),hAPP(c_Int_Onumber__class_Onumber__of(U_8776),U_8777)) = hAPP(c_Int_Onumber__class_Onumber__of(U_8776),U_8777)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8776),hAPP(c_Int_Onumber__class_Onumber__of(U_8776),U_8777)),c_Groups_Ozero__class_Ozero(U_8776))) )
        & ( hAPP(c_Groups_Oabs__class_Oabs(U_8776),hAPP(c_Int_Onumber__class_Onumber__of(U_8776),U_8777)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_8776),hAPP(c_Int_Onumber__class_Onumber__of(U_8776),U_8777))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8776),hAPP(c_Int_Onumber__class_Onumber__of(U_8776),U_8777)),c_Groups_Ozero__class_Ozero(U_8776))) ) )
      | ~ class_Rings_Olinordered__idom(U_8776)
      | ~ class_Int_Onumber__ring(U_8776) ),
    inference(variable_rename,[status(thm)],[f_2548_1]) ).

cnf(f_2548_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_8776),hAPP(c_Int_Onumber__class_Onumber__of(U_8776),U_8777)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_8776),hAPP(c_Int_Onumber__class_Onumber__of(U_8776),U_8777))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8776),hAPP(c_Int_Onumber__class_Onumber__of(U_8776),U_8777)),c_Groups_Ozero__class_Ozero(U_8776)))
    | ~ class_Rings_Olinordered__idom(U_8776)
    | ~ class_Int_Onumber__ring(U_8776) ),
    inference(clausify,[status(thm)],[f_2548_2]) ).

cnf(f_2548_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_8776),hAPP(c_Int_Onumber__class_Onumber__of(U_8776),U_8777)) = hAPP(c_Int_Onumber__class_Onumber__of(U_8776),U_8777)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8776),hAPP(c_Int_Onumber__class_Onumber__of(U_8776),U_8777)),c_Groups_Ozero__class_Ozero(U_8776)))
    | ~ class_Rings_Olinordered__idom(U_8776)
    | ~ class_Int_Onumber__ring(U_8776) ),
    inference(clausify,[status(thm)],[f_2548_2]) ).

fof(f_2549_1,plain,
    ! [V_n,T_a] :
      ( hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)),V_n)) = c_Groups_Oone__class_Oone(T_a)
      | ~ class_Rings_Olinordered__idom(T_a)
      | ~ class_Int_Onumber__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__power__minus__one]) ).

fof(f_2549_2,plain,
    ! [U_8779,U_8778] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_8778),hAPP(hAPP(c_Power_Opower__class_Opower(U_8778),hAPP(c_Int_Onumber__class_Onumber__of(U_8778),c_Int_OMin)),U_8779)) = c_Groups_Oone__class_Oone(U_8778)
      | ~ class_Rings_Olinordered__idom(U_8778)
      | ~ class_Int_Onumber__ring(U_8778) ),
    inference(variable_rename,[status(thm)],[f_2549_1]) ).

cnf(f_2549_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_8778),hAPP(hAPP(c_Power_Opower__class_Opower(U_8778),hAPP(c_Int_Onumber__class_Onumber__of(U_8778),c_Int_OMin)),U_8779)) = c_Groups_Oone__class_Oone(U_8778)
    | ~ class_Rings_Olinordered__idom(U_8778)
    | ~ class_Int_Onumber__ring(U_8778) ),
    inference(clausify,[status(thm)],[f_2549_2]) ).

fof(f_2550_1,plain,
    ! [V_n_2,V_x_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x_2)),V_n_2)))
        | ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & V_x_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
      & ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | V_x_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x_2)),V_n_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_zero__less__zpower__abs__iff]) ).

fof(f_2550_2,plain,
    ! [U_8781,U_8780] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_8780)),U_8781)))
        | ( U_8781 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_8780 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
      & ( U_8781 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_8780 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_8780)),U_8781))) ) ),
    inference(variable_rename,[status(thm)],[f_2550_1]) ).

fof(f_2550_3,plain,
    ( ! [U_8785,U_8783] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_8783)),U_8785)))
        | ( U_8785 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_8783 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_8784,U_8782] :
        ( U_8784 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_8782 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_8782)),U_8784))) ) ),
    inference(miniscope,[status(thm)],[f_2550_2]) ).

cnf(f_2550_4,plain,
    ( U_8784 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_8782 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_8782)),U_8784))) ),
    inference(clausify,[status(thm)],[f_2550_3]) ).

cnf(f_2550_5,plain,
    ( U_8783 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_8783)),U_8785))) ),
    inference(clausify,[status(thm)],[f_2550_3]) ).

cnf(f_2550_6,plain,
    ( U_8785 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_8783)),U_8785))) ),
    inference(clausify,[status(thm)],[f_2550_3]) ).

fof(f_2551_1,plain,
    ! [V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(V_n)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = V_n,
    inference(fof_nnf,[status(thm)],[fact_Suc__code__numeral__minus__one]) ).

fof(f_2551_2,plain,
    ! [U_8786] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(U_8786)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = U_8786,
    inference(variable_rename,[status(thm)],[f_2551_1]) ).

cnf(f_2551_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(U_8786)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = U_8786,
    inference(clausify,[status(thm)],[f_2551_2]) ).

fof(f_2552_1,plain,
    ! [V_a,T_a] :
      ( hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_abs__power2]) ).

fof(f_2552_2,plain,
    ! [U_8788,U_8787] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_8787),hAPP(hAPP(c_Power_Opower__class_Opower(U_8787),U_8788),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = hAPP(hAPP(c_Power_Opower__class_Opower(U_8787),U_8788),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
      | ~ class_Rings_Olinordered__idom(U_8787) ),
    inference(variable_rename,[status(thm)],[f_2552_1]) ).

cnf(f_2552_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_8787),hAPP(hAPP(c_Power_Opower__class_Opower(U_8787),U_8788),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = hAPP(hAPP(c_Power_Opower__class_Opower(U_8787),U_8788),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
    | ~ class_Rings_Olinordered__idom(U_8787) ),
    inference(clausify,[status(thm)],[f_2552_2]) ).

fof(f_2553_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power2__abs]) ).

fof(f_2553_2,plain,
    ! [U_8790,U_8789] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_8789),hAPP(c_Groups_Oabs__class_Oabs(U_8789),U_8790)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(U_8789),U_8790),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
      | ~ class_Rings_Olinordered__idom(U_8789) ),
    inference(variable_rename,[status(thm)],[f_2553_1]) ).

cnf(f_2553_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_8789),hAPP(c_Groups_Oabs__class_Oabs(U_8789),U_8790)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(U_8789),U_8790),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
    | ~ class_Rings_Olinordered__idom(U_8789) ),
    inference(clausify,[status(thm)],[f_2553_2]) ).

fof(f_2554_1,plain,
    ! [V_x,V_z,V_d] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_z))),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_d))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d)) ),
    inference(fof_nnf,[status(thm)],[fact_incr__lemma]) ).

fof(f_2554_2,plain,
    ! [U_8793,U_8792,U_8791] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8792),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8793),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8793),U_8792))),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_8791))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8791)) ),
    inference(variable_rename,[status(thm)],[f_2554_1]) ).

cnf(f_2554_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8792),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8793),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8793),U_8792))),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_8791))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8791)) ),
    inference(clausify,[status(thm)],[f_2554_2]) ).

fof(f_2555_1,plain,
    ! [V_y,V_x] : c_Nitpick_Oint__lcm(V_x,V_y) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nitpick_Onat__lcm(hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_y)))),
    inference(fof_nnf,[status(thm)],[fact_Nitpick_Oint__lcm__def]) ).

fof(f_2555_2,plain,
    ! [U_8795,U_8794] : c_Nitpick_Oint__lcm(U_8794,U_8795) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nitpick_Onat__lcm(hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_8794)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_8795)))),
    inference(variable_rename,[status(thm)],[f_2555_1]) ).

cnf(f_2555_3,plain,
    c_Nitpick_Oint__lcm(U_8794,U_8795) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nitpick_Onat__lcm(hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_8794)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_8795)))),
    inference(clausify,[status(thm)],[f_2555_2]) ).

fof(f_2556_1,plain,
    ! [V_code__numeral_2,V_f2_2,V_f1_2,T_b] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(T_b,V_f1_2,V_f2_2,c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2)) = hAPP(V_f2_2,V_code__numeral_2),
    inference(fof_nnf,[status(thm)],[fact_code__numeral_Osimps_I5_J]) ).

fof(f_2556_2,plain,
    ! [U_8799,U_8798,U_8797,U_8796] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(U_8796,U_8797,U_8798,c_Code__Numeral_OSuc__code__numeral(U_8799)) = hAPP(U_8798,U_8799),
    inference(variable_rename,[status(thm)],[f_2556_1]) ).

cnf(f_2556_3,plain,
    c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(U_8796,U_8797,U_8798,c_Code__Numeral_OSuc__code__numeral(U_8799)) = hAPP(U_8798,U_8799),
    inference(clausify,[status(thm)],[f_2556_2]) ).

fof(f_2557_1,plain,
    ! [V_k_2,V_f_2,V_n_2] :
      ( ? [B_i] :
          ( hAPP(V_f_2,B_i) = V_k_2
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k_2))
      | ? [B_i] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_i),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(V_f_2,B_i)))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat0__intermed__int__val]) ).

fof(f_2557_2,plain,
    ! [U_8804,U_8803,U_8802] :
      ( ? [U_8801] :
          ( hAPP(U_8803,U_8801) = U_8804
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8801),U_8802)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8804),hAPP(U_8803,U_8802)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8803,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_8804))
      | ? [U_8800] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(U_8803,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8800),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_8803,U_8800)))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8800),U_8802)) ) ),
    inference(variable_rename,[status(thm)],[f_2557_1]) ).

fof(f_2557_3,plain,
    ! [U_8804,U_8803,U_8802] :
      ( ? [U_8801] :
          ( hAPP(U_8803,U_8801) = U_8804
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8801),U_8802)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8804),hAPP(U_8803,U_8802)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8803,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_8804))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(U_8803,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK222(U_8804,U_8803,U_8802)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_8803,sK222(U_8804,U_8803,U_8802))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK222(U_8804,U_8803,U_8802)),U_8802)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK222]),skolemize(U_8800,sK222(U_8804,U_8803,U_8802))],[f_2557_2]) ).

fof(f_2557_4,plain,
    ! [U_8804,U_8803,U_8802] :
      ( ( hAPP(U_8803,sK223(U_8804,U_8803,U_8802)) = U_8804
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK223(U_8804,U_8803,U_8802)),U_8802)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8804),hAPP(U_8803,U_8802)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8803,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_8804))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(U_8803,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK222(U_8804,U_8803,U_8802)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_8803,sK222(U_8804,U_8803,U_8802))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK222(U_8804,U_8803,U_8802)),U_8802)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK223]),skolemize(U_8801,sK223(U_8804,U_8803,U_8802))],[f_2557_3]) ).

cnf(f_2557_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK223(U_8804,U_8803,U_8802)),U_8802))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8804),hAPP(U_8803,U_8802)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8803,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_8804))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK222(U_8804,U_8803,U_8802)),U_8802)) ),
    inference(clausify,[status(thm)],[f_2557_4]) ).

cnf(f_2557_6,plain,
    ( hAPP(U_8803,sK223(U_8804,U_8803,U_8802)) = U_8804
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8804),hAPP(U_8803,U_8802)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8803,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_8804))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK222(U_8804,U_8803,U_8802)),U_8802)) ),
    inference(clausify,[status(thm)],[f_2557_4]) ).

cnf(f_2557_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK223(U_8804,U_8803,U_8802)),U_8802))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8804),hAPP(U_8803,U_8802)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8803,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_8804))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(U_8803,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK222(U_8804,U_8803,U_8802)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_8803,sK222(U_8804,U_8803,U_8802))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2557_4]) ).

cnf(f_2557_8,plain,
    ( hAPP(U_8803,sK223(U_8804,U_8803,U_8802)) = U_8804
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8804),hAPP(U_8803,U_8802)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8803,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_8804))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(U_8803,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK222(U_8804,U_8803,U_8802)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_8803,sK222(U_8804,U_8803,U_8802))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2557_4]) ).

fof(f_2558_1,plain,
    ! [V_k_2,V_f_2,V_n_2] :
      ( ? [B_i] :
          ( hAPP(V_f_2,B_i) = V_k_2
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k_2))
      | ? [B_i] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_i),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(V_f_2,B_i)))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_int__val__lemma]) ).

fof(f_2558_2,plain,
    ! [U_8809,U_8808,U_8807] :
      ( ? [U_8806] :
          ( hAPP(U_8808,U_8806) = U_8809
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8806),U_8807)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8809),hAPP(U_8808,U_8807)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8808,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_8809))
      | ? [U_8805] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(U_8808,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8805),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_8808,U_8805)))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8805),U_8807)) ) ),
    inference(variable_rename,[status(thm)],[f_2558_1]) ).

fof(f_2558_3,plain,
    ! [U_8809,U_8808,U_8807] :
      ( ? [U_8806] :
          ( hAPP(U_8808,U_8806) = U_8809
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8806),U_8807)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8809),hAPP(U_8808,U_8807)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8808,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_8809))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(U_8808,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK224(U_8809,U_8808,U_8807)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_8808,sK224(U_8809,U_8808,U_8807))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK224(U_8809,U_8808,U_8807)),U_8807)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK224]),skolemize(U_8805,sK224(U_8809,U_8808,U_8807))],[f_2558_2]) ).

fof(f_2558_4,plain,
    ! [U_8809,U_8808,U_8807] :
      ( ( hAPP(U_8808,sK225(U_8809,U_8808,U_8807)) = U_8809
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK225(U_8809,U_8808,U_8807)),U_8807)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8809),hAPP(U_8808,U_8807)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8808,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_8809))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(U_8808,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK224(U_8809,U_8808,U_8807)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_8808,sK224(U_8809,U_8808,U_8807))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK224(U_8809,U_8808,U_8807)),U_8807)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK225]),skolemize(U_8806,sK225(U_8809,U_8808,U_8807))],[f_2558_3]) ).

cnf(f_2558_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK225(U_8809,U_8808,U_8807)),U_8807))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8809),hAPP(U_8808,U_8807)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8808,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_8809))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK224(U_8809,U_8808,U_8807)),U_8807)) ),
    inference(clausify,[status(thm)],[f_2558_4]) ).

cnf(f_2558_6,plain,
    ( hAPP(U_8808,sK225(U_8809,U_8808,U_8807)) = U_8809
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8809),hAPP(U_8808,U_8807)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8808,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_8809))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK224(U_8809,U_8808,U_8807)),U_8807)) ),
    inference(clausify,[status(thm)],[f_2558_4]) ).

cnf(f_2558_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK225(U_8809,U_8808,U_8807)),U_8807))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8809),hAPP(U_8808,U_8807)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8808,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_8809))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(U_8808,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK224(U_8809,U_8808,U_8807)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_8808,sK224(U_8809,U_8808,U_8807))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2558_4]) ).

cnf(f_2558_8,plain,
    ( hAPP(U_8808,sK225(U_8809,U_8808,U_8807)) = U_8809
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8809),hAPP(U_8808,U_8807)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8808,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_8809))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(U_8808,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK224(U_8809,U_8808,U_8807)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_8808,sK224(U_8809,U_8808,U_8807))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2558_4]) ).

fof(f_2559_1,plain,
    ! [V_f2_2,V_f1_2,T_b] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(T_b,V_f1_2,V_f2_2,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = V_f1_2,
    inference(fof_nnf,[status(thm)],[fact_code__numeral_Osimps_I4_J]) ).

fof(f_2559_2,plain,
    ! [U_8812,U_8811,U_8810] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(U_8810,U_8811,U_8812,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = U_8811,
    inference(variable_rename,[status(thm)],[f_2559_1]) ).

cnf(f_2559_3,plain,
    c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(U_8810,U_8811,U_8812,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = U_8811,
    inference(clausify,[status(thm)],[f_2559_2]) ).

fof(f_2560_1,plain,
    ! [V_y,V_x] : c_Nitpick_Onat__lcm(V_x,V_y) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_x),V_y)),c_Nitpick_Onat__gcd(V_x,V_y)),
    inference(fof_nnf,[status(thm)],[fact_Nitpick_Onat__lcm__def]) ).

fof(f_2560_2,plain,
    ! [U_8814,U_8813] : c_Nitpick_Onat__lcm(U_8813,U_8814) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8813),U_8814)),c_Nitpick_Onat__gcd(U_8813,U_8814)),
    inference(variable_rename,[status(thm)],[f_2560_1]) ).

cnf(f_2560_3,plain,
    c_Nitpick_Onat__lcm(U_8813,U_8814) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8813),U_8814)),c_Nitpick_Onat__gcd(U_8813,U_8814)),
    inference(clausify,[status(thm)],[f_2560_2]) ).

fof(f_2561_1,plain,
    ! [V_y,V_n,V_x] :
      ( ? [B_q] : V_x = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),B_q))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y),V_x))
      | c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_n) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_y,V_n) ),
    inference(fof_nnf,[status(thm)],[fact_nat__mod__eq__lemma]) ).

fof(f_2561_2,plain,
    ! [U_8818,U_8817,U_8816] :
      ( ? [U_8815] : U_8816 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8818),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8817),U_8815))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8818),U_8816))
      | c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8816,U_8817) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8818,U_8817) ),
    inference(variable_rename,[status(thm)],[f_2561_1]) ).

fof(f_2561_3,plain,
    ! [U_8818,U_8817,U_8816] :
      ( U_8816 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8818),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8817),sK226(U_8818,U_8817,U_8816)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8818),U_8816))
      | c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8816,U_8817) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8818,U_8817) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK226]),skolemize(U_8815,sK226(U_8818,U_8817,U_8816))],[f_2561_2]) ).

cnf(f_2561_4,plain,
    ( U_8816 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8818),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_8817),sK226(U_8818,U_8817,U_8816)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8818),U_8816))
    | c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8816,U_8817) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8818,U_8817) ),
    inference(clausify,[status(thm)],[f_2561_3]) ).

fof(f_2562_1,plain,
    ! [V_i_2,V_P_2,V_p_2] :
      ( hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_p_2))
      | ~ hBOOL(hAPP(V_P_2,V_i_2))
      | ? [B_i] :
          ( ~ hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,B_i),V_p_2)))
          & hBOOL(hAPP(V_P_2,B_i))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_p_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_mod__induct__0]) ).

fof(f_2562_2,plain,
    ! [U_8822,U_8821,U_8820] :
      ( hBOOL(hAPP(U_8821,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8822),U_8820))
      | ~ hBOOL(hAPP(U_8821,U_8822))
      | ? [U_8819] :
          ( ~ hBOOL(hAPP(U_8821,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_8819),U_8820)))
          & hBOOL(hAPP(U_8821,U_8819))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8819),U_8820)) ) ),
    inference(variable_rename,[status(thm)],[f_2562_1]) ).

fof(f_2562_3,plain,
    ! [U_8822,U_8821,U_8820] :
      ( hBOOL(hAPP(U_8821,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8822),U_8820))
      | ~ hBOOL(hAPP(U_8821,U_8822))
      | ( ~ hBOOL(hAPP(U_8821,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,sK227(U_8822,U_8821,U_8820)),U_8820)))
        & hBOOL(hAPP(U_8821,sK227(U_8822,U_8821,U_8820)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK227(U_8822,U_8821,U_8820)),U_8820)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK227]),skolemize(U_8819,sK227(U_8822,U_8821,U_8820))],[f_2562_2]) ).

cnf(f_2562_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK227(U_8822,U_8821,U_8820)),U_8820))
    | hBOOL(hAPP(U_8821,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8822),U_8820))
    | ~ hBOOL(hAPP(U_8821,U_8822)) ),
    inference(clausify,[status(thm)],[f_2562_3]) ).

cnf(f_2562_5,plain,
    ( hBOOL(hAPP(U_8821,sK227(U_8822,U_8821,U_8820)))
    | hBOOL(hAPP(U_8821,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8822),U_8820))
    | ~ hBOOL(hAPP(U_8821,U_8822)) ),
    inference(clausify,[status(thm)],[f_2562_3]) ).

cnf(f_2562_6,plain,
    ( ~ hBOOL(hAPP(U_8821,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,sK227(U_8822,U_8821,U_8820)),U_8820)))
    | hBOOL(hAPP(U_8821,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8822),U_8820))
    | ~ hBOOL(hAPP(U_8821,U_8822)) ),
    inference(clausify,[status(thm)],[f_2562_3]) ).

fof(f_2563_1,plain,
    ! [V_k_2,V_f_2,V_n_2,V_m_2] :
      ( ? [B_i] :
          ( hAPP(V_f_2,B_i) = V_k_2
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,V_m_2)),V_k_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
      | ? [B_i] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_i),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(V_f_2,B_i)))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i)) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__intermed__int__val]) ).

fof(f_2563_2,plain,
    ! [U_8828,U_8827,U_8826,U_8825] :
      ( ? [U_8824] :
          ( hAPP(U_8827,U_8824) = U_8828
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8824),U_8826))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8825),U_8824)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8828),hAPP(U_8827,U_8826)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8827,U_8825)),U_8828))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8825),U_8826))
      | ? [U_8823] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(U_8827,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_8823),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_8827,U_8823)))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8823),U_8826))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8825),U_8823)) ) ),
    inference(variable_rename,[status(thm)],[f_2563_1]) ).

fof(f_2563_3,plain,
    ! [U_8828,U_8827,U_8826,U_8825] :
      ( ? [U_8824] :
          ( hAPP(U_8827,U_8824) = U_8828
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8824),U_8826))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8825),U_8824)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8828),hAPP(U_8827,U_8826)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8827,U_8825)),U_8828))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8825),U_8826))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(U_8827,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK228(U_8828,U_8827,U_8826,U_8825)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_8827,sK228(U_8828,U_8827,U_8826,U_8825))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK228(U_8828,U_8827,U_8826,U_8825)),U_8826))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8825),sK228(U_8828,U_8827,U_8826,U_8825))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK228]),skolemize(U_8823,sK228(U_8828,U_8827,U_8826,U_8825))],[f_2563_2]) ).

fof(f_2563_4,plain,
    ! [U_8828,U_8827,U_8826,U_8825] :
      ( ( hAPP(U_8827,sK229(U_8828,U_8827,U_8826,U_8825)) = U_8828
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK229(U_8828,U_8827,U_8826,U_8825)),U_8826))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8825),sK229(U_8828,U_8827,U_8826,U_8825))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8828),hAPP(U_8827,U_8826)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8827,U_8825)),U_8828))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8825),U_8826))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(U_8827,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK228(U_8828,U_8827,U_8826,U_8825)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_8827,sK228(U_8828,U_8827,U_8826,U_8825))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK228(U_8828,U_8827,U_8826,U_8825)),U_8826))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8825),sK228(U_8828,U_8827,U_8826,U_8825))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK229]),skolemize(U_8824,sK229(U_8828,U_8827,U_8826,U_8825))],[f_2563_3]) ).

cnf(f_2563_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8825),sK229(U_8828,U_8827,U_8826,U_8825)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8828),hAPP(U_8827,U_8826)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8827,U_8825)),U_8828))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8825),U_8826))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8825),sK228(U_8828,U_8827,U_8826,U_8825))) ),
    inference(clausify,[status(thm)],[f_2563_4]) ).

cnf(f_2563_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK229(U_8828,U_8827,U_8826,U_8825)),U_8826))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8828),hAPP(U_8827,U_8826)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8827,U_8825)),U_8828))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8825),U_8826))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8825),sK228(U_8828,U_8827,U_8826,U_8825))) ),
    inference(clausify,[status(thm)],[f_2563_4]) ).

cnf(f_2563_7,plain,
    ( hAPP(U_8827,sK229(U_8828,U_8827,U_8826,U_8825)) = U_8828
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8828),hAPP(U_8827,U_8826)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8827,U_8825)),U_8828))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8825),U_8826))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8825),sK228(U_8828,U_8827,U_8826,U_8825))) ),
    inference(clausify,[status(thm)],[f_2563_4]) ).

cnf(f_2563_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8825),sK229(U_8828,U_8827,U_8826,U_8825)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8828),hAPP(U_8827,U_8826)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8827,U_8825)),U_8828))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8825),U_8826))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK228(U_8828,U_8827,U_8826,U_8825)),U_8826)) ),
    inference(clausify,[status(thm)],[f_2563_4]) ).

cnf(f_2563_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK229(U_8828,U_8827,U_8826,U_8825)),U_8826))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8828),hAPP(U_8827,U_8826)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8827,U_8825)),U_8828))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8825),U_8826))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK228(U_8828,U_8827,U_8826,U_8825)),U_8826)) ),
    inference(clausify,[status(thm)],[f_2563_4]) ).

cnf(f_2563_10,plain,
    ( hAPP(U_8827,sK229(U_8828,U_8827,U_8826,U_8825)) = U_8828
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8828),hAPP(U_8827,U_8826)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8827,U_8825)),U_8828))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8825),U_8826))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK228(U_8828,U_8827,U_8826,U_8825)),U_8826)) ),
    inference(clausify,[status(thm)],[f_2563_4]) ).

cnf(f_2563_11,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8825),sK229(U_8828,U_8827,U_8826,U_8825)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8828),hAPP(U_8827,U_8826)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8827,U_8825)),U_8828))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8825),U_8826))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(U_8827,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK228(U_8828,U_8827,U_8826,U_8825)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_8827,sK228(U_8828,U_8827,U_8826,U_8825))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2563_4]) ).

cnf(f_2563_12,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK229(U_8828,U_8827,U_8826,U_8825)),U_8826))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8828),hAPP(U_8827,U_8826)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8827,U_8825)),U_8828))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8825),U_8826))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(U_8827,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK228(U_8828,U_8827,U_8826,U_8825)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_8827,sK228(U_8828,U_8827,U_8826,U_8825))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2563_4]) ).

cnf(f_2563_13,plain,
    ( hAPP(U_8827,sK229(U_8828,U_8827,U_8826,U_8825)) = U_8828
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8828),hAPP(U_8827,U_8826)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_8827,U_8825)),U_8828))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8825),U_8826))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(U_8827,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK228(U_8828,U_8827,U_8826,U_8825)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_8827,sK228(U_8828,U_8827,U_8826,U_8825))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2563_4]) ).

fof(f_2564_1,plain,
    ! [V_x,V_y] :
      ( ( c_Nitpick_Onat__gcd(V_x,V_y) = c_Nitpick_Onat__gcd(V_y,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_y))
        | V_y = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( c_Nitpick_Onat__gcd(V_x,V_y) = V_x
        | V_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__gcd_Osimps]) ).

fof(f_2564_2,plain,
    ! [U_8830,U_8829] :
      ( ( c_Nitpick_Onat__gcd(U_8830,U_8829) = c_Nitpick_Onat__gcd(U_8829,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8830,U_8829))
        | U_8829 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( c_Nitpick_Onat__gcd(U_8830,U_8829) = U_8830
        | U_8829 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_2564_1]) ).

fof(f_2564_3,plain,
    ( ! [U_8834,U_8832] :
        ( c_Nitpick_Onat__gcd(U_8834,U_8832) = c_Nitpick_Onat__gcd(U_8832,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8834,U_8832))
        | U_8832 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_8833,U_8831] :
        ( c_Nitpick_Onat__gcd(U_8833,U_8831) = U_8833
        | U_8831 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_2564_2]) ).

cnf(f_2564_4,plain,
    ( c_Nitpick_Onat__gcd(U_8833,U_8831) = U_8833
    | U_8831 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_2564_3]) ).

cnf(f_2564_5,plain,
    ( c_Nitpick_Onat__gcd(U_8834,U_8832) = c_Nitpick_Onat__gcd(U_8832,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_8834,U_8832))
    | U_8832 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_2564_3]) ).

fof(f_2565_1,plain,
    ! [V_y,V_x] : hAPP(hAPP(c_Nitpick_Oint__gcd,V_x),V_y) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nitpick_Onat__gcd(hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_y)))),
    inference(fof_nnf,[status(thm)],[fact_Nitpick_Oint__gcd__def]) ).

fof(f_2565_2,plain,
    ! [U_8836,U_8835] : hAPP(hAPP(c_Nitpick_Oint__gcd,U_8835),U_8836) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nitpick_Onat__gcd(hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_8835)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_8836)))),
    inference(variable_rename,[status(thm)],[f_2565_1]) ).

cnf(f_2565_3,plain,
    hAPP(hAPP(c_Nitpick_Oint__gcd,U_8835),U_8836) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nitpick_Onat__gcd(hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_8835)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_8836)))),
    inference(clausify,[status(thm)],[f_2565_2]) ).

fof(f_2566_1,plain,
    ! [V_i,V_b] :
      ( ( c_Random_Olog(V_b,V_i) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),c_Random_Olog(V_b,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_i),V_b)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_b),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) )
      & ( c_Random_Olog(V_b,V_i) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_b),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_log_Osimps]) ).

fof(f_2566_2,plain,
    ! [U_8838,U_8837] :
      ( ( c_Random_Olog(U_8837,U_8838) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),c_Random_Olog(U_8837,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),U_8838),U_8837)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_8838),U_8837))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_8837),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) )
      & ( c_Random_Olog(U_8837,U_8838) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_8838),U_8837))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_8837),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) ) ) ),
    inference(variable_rename,[status(thm)],[f_2566_1]) ).

fof(f_2566_3,plain,
    ( ! [U_8842,U_8840] :
        ( c_Random_Olog(U_8840,U_8842) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),c_Random_Olog(U_8840,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),U_8842),U_8840)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_8842),U_8840))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_8840),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) )
    & ! [U_8841,U_8839] :
        ( c_Random_Olog(U_8839,U_8841) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_8841),U_8839))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_8839),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) ) ) ),
    inference(miniscope,[status(thm)],[f_2566_2]) ).

cnf(f_2566_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_8839),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))
    | c_Random_Olog(U_8839,U_8841) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_2566_3]) ).

cnf(f_2566_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_8841),U_8839))
    | c_Random_Olog(U_8839,U_8841) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_2566_3]) ).

cnf(f_2566_6,plain,
    ( c_Random_Olog(U_8840,U_8842) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),c_Random_Olog(U_8840,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),U_8842),U_8840)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_8842),U_8840))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_8840),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) ),
    inference(clausify,[status(thm)],[f_2566_3]) ).

fof(f_2567_1,plain,
    ! [V_b,V_a,T_a] :
      ( V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),V_b)),c_Divides_Odiv__class_Omod(T_a,V_a,V_b))
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mod__div__decomp]) ).

fof(f_2567_2,plain,
    ! [U_8845,U_8844,U_8843] :
      ( U_8844 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8843),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8843),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_8843),U_8844),U_8845)),U_8845)),c_Divides_Odiv__class_Omod(U_8843,U_8844,U_8845))
      | ~ class_Divides_Osemiring__div(U_8843) ),
    inference(variable_rename,[status(thm)],[f_2567_1]) ).

cnf(f_2567_3,plain,
    ( U_8844 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8843),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_8843),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_8843),U_8844),U_8845)),U_8845)),c_Divides_Odiv__class_Omod(U_8843,U_8844,U_8845))
    | ~ class_Divides_Osemiring__div(U_8843) ),
    inference(clausify,[status(thm)],[f_2567_2]) ).

fof(f_2568_1,plain,
    ! [V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
      | ? [B_e] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),B_e)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_e)) )
      | ~ class_Fields_Olinordered__field(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_field__le__epsilon]) ).

fof(f_2568_2,plain,
    ! [U_8849,U_8848,U_8847] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8847),U_8848),U_8849))
      | ? [U_8846] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8847),U_8848),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8847),U_8849),U_8846)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8847),c_Groups_Ozero__class_Ozero(U_8847)),U_8846)) )
      | ~ class_Fields_Olinordered__field(U_8847) ),
    inference(variable_rename,[status(thm)],[f_2568_1]) ).

fof(f_2568_3,plain,
    ! [U_8849,U_8848,U_8847] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8847),U_8848),U_8849))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8847),U_8848),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8847),U_8849),sK230(U_8849,U_8848,U_8847))))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8847),c_Groups_Ozero__class_Ozero(U_8847)),sK230(U_8849,U_8848,U_8847))) )
      | ~ class_Fields_Olinordered__field(U_8847) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK230]),skolemize(U_8846,sK230(U_8849,U_8848,U_8847))],[f_2568_2]) ).

cnf(f_2568_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8847),c_Groups_Ozero__class_Ozero(U_8847)),sK230(U_8849,U_8848,U_8847)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8847),U_8848),U_8849))
    | ~ class_Fields_Olinordered__field(U_8847) ),
    inference(clausify,[status(thm)],[f_2568_3]) ).

cnf(f_2568_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8847),U_8848),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8847),U_8849),sK230(U_8849,U_8848,U_8847))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8847),U_8848),U_8849))
    | ~ class_Fields_Olinordered__field(U_8847) ),
    inference(clausify,[status(thm)],[f_2568_3]) ).

fof(f_2569_1,plain,
    ! [V_r,V_l,V_k] :
      ( ( c_Random_Ominus__shift(V_r,V_k,V_l) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_k),V_l)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l)) )
      & ( c_Random_Ominus__shift(V_r,V_k,V_l) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),V_r),V_k)),V_l)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l)) ) ),
    inference(fof_nnf,[status(thm)],[fact_minus__shift__def]) ).

fof(f_2569_2,plain,
    ! [U_8852,U_8851,U_8850] :
      ( ( c_Random_Ominus__shift(U_8852,U_8850,U_8851) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_8850),U_8851)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_8850),U_8851)) )
      & ( c_Random_Ominus__shift(U_8852,U_8850,U_8851) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),U_8852),U_8850)),U_8851)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_8850),U_8851)) ) ),
    inference(variable_rename,[status(thm)],[f_2569_1]) ).

fof(f_2569_3,plain,
    ( ! [U_8858,U_8856,U_8854] :
        ( c_Random_Ominus__shift(U_8858,U_8854,U_8856) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_8854),U_8856)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_8854),U_8856)) )
    & ! [U_8857,U_8855,U_8853] :
        ( c_Random_Ominus__shift(U_8857,U_8853,U_8855) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),U_8857),U_8853)),U_8855)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_8853),U_8855)) ) ),
    inference(miniscope,[status(thm)],[f_2569_2]) ).

cnf(f_2569_4,plain,
    ( c_Random_Ominus__shift(U_8857,U_8853,U_8855) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),U_8857),U_8853)),U_8855)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_8853),U_8855)) ),
    inference(clausify,[status(thm)],[f_2569_3]) ).

cnf(f_2569_5,plain,
    ( c_Random_Ominus__shift(U_8858,U_8854,U_8856) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_8854),U_8856)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_8854),U_8856)) ),
    inference(clausify,[status(thm)],[f_2569_3]) ).

fof(f_2570_1,plain,
    ! [V_k,V_v] :
      ( ( c_Random_Oinc__shift(V_v,V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),V_k),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))
        | V_v = V_k )
      & ( c_Random_Oinc__shift(V_v,V_k) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)
        | V_v != V_k ) ),
    inference(fof_nnf,[status(thm)],[fact_inc__shift__def]) ).

fof(f_2570_2,plain,
    ! [U_8860,U_8859] :
      ( ( c_Random_Oinc__shift(U_8859,U_8860) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),U_8860),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))
        | U_8859 = U_8860 )
      & ( c_Random_Oinc__shift(U_8859,U_8860) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)
        | U_8859 != U_8860 ) ),
    inference(variable_rename,[status(thm)],[f_2570_1]) ).

fof(f_2570_3,plain,
    ( ! [U_8864,U_8862] :
        ( c_Random_Oinc__shift(U_8862,U_8864) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),U_8864),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))
        | U_8862 = U_8864 )
    & ! [U_8863,U_8861] :
        ( c_Random_Oinc__shift(U_8861,U_8863) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)
        | U_8861 != U_8863 ) ),
    inference(miniscope,[status(thm)],[f_2570_2]) ).

cnf(f_2570_4,plain,
    ( c_Random_Oinc__shift(U_8861,U_8863) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)
    | U_8861 != U_8863 ),
    inference(clausify,[status(thm)],[f_2570_3]) ).

cnf(f_2570_5,plain,
    ( c_Random_Oinc__shift(U_8862,U_8864) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),U_8864),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))
    | U_8862 = U_8864 ),
    inference(clausify,[status(thm)],[f_2570_3]) ).

fof(f_2571_1,plain,
    c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[fact_subtract__code__numeral__def]) ).

cnf(f_2571_2,plain,
    c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_2571_1]) ).

fof(f_2572_1,plain,
    ! [V_m,V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_n),V_m) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,V_n),V_m),
    inference(fof_nnf,[status(thm)],[fact_minus__code__numeral__code]) ).

fof(f_2572_2,plain,
    ! [U_8866,U_8865] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_8865),U_8866) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,U_8865),U_8866),
    inference(variable_rename,[status(thm)],[f_2572_1]) ).

cnf(f_2572_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_8865),U_8866) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,U_8865),U_8866),
    inference(clausify,[status(thm)],[f_2572_2]) ).

fof(f_2573_1,plain,
    ! [V_b_2,V_a_2,V_fb_2,V_fa_2,T_c,T_b] : c_Nitpick_Opair__box_Opair__box__size(T_b,T_c,V_fa_2,V_fb_2,c_Nitpick_Opair__box_OPairBox(T_b,T_c,V_a_2,V_b_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_fa_2,V_a_2)),hAPP(V_fb_2,V_b_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(fof_nnf,[status(thm)],[fact_pair__box_Osize_I1_J]) ).

fof(f_2573_2,plain,
    ! [U_8872,U_8871,U_8870,U_8869,U_8868,U_8867] : c_Nitpick_Opair__box_Opair__box__size(U_8867,U_8868,U_8869,U_8870,c_Nitpick_Opair__box_OPairBox(U_8867,U_8868,U_8871,U_8872)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_8869,U_8871)),hAPP(U_8870,U_8872))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_2573_1]) ).

cnf(f_2573_3,plain,
    c_Nitpick_Opair__box_Opair__box__size(U_8867,U_8868,U_8869,U_8870,c_Nitpick_Opair__box_OPairBox(U_8867,U_8868,U_8871,U_8872)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_8869,U_8871)),hAPP(U_8870,U_8872))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_2573_2]) ).

fof(f_2574_1,plain,
    ! [V_n_2,V_d_2,V_a_2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),V_d_2))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_d_2)))),
    inference(fof_nnf,[status(thm)],[fact_arith__series__int]) ).

fof(f_2574_2,plain,
    ! [U_8875,U_8874,U_8873] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8873)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),U_8874))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_8875))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8875)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8873),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8873),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_8875),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),U_8874)))),
    inference(variable_rename,[status(thm)],[f_2574_1]) ).

cnf(f_2574_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8873)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),U_8874))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_8875))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8875)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8873),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8873),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_8875),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),U_8874)))),
    inference(clausify,[status(thm)],[f_2574_2]) ).

fof(f_2575_1,plain,
    ! [V_w] :
      ( ( ( c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))) )
        & ( c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) ),
    inference(fof_nnf,[status(thm)],[fact_negDivAlg__eqn__1__number__of]) ).

fof(f_2575_2,plain,
    ! [U_8876] :
      ( ( ( c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8876)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8876)),c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8876))))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8876)))) )
        & ( c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8876)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8876)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8876)))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8876))) ),
    inference(variable_rename,[status(thm)],[f_2575_1]) ).

cnf(f_2575_3,plain,
    ( c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8876)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8876)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8876))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8876))) ),
    inference(clausify,[status(thm)],[f_2575_2]) ).

cnf(f_2575_4,plain,
    ( c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8876)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8876)),c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8876))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8876))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_8876))) ),
    inference(clausify,[status(thm)],[f_2575_2]) ).

fof(f_2576_1,plain,
    ! [V_z_2,V_g_2,V_h_2,T_c,V_A_2,T_b,T_d] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Otimes__class_Otimes(T_d)),V_g_2),V_z_2),hAPP(c_Set_Oimage(T_b,T_c,V_h_2),V_A_2)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_b,c_Groups_Otimes__class_Otimes(T_d)),hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_g_2),V_h_2)),V_z_2),V_A_2)
      | ~ c_Fun_Oinj__on(T_b,T_c,V_h_2,V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Oab__semigroup__mult(T_d) ),
    inference(fof_nnf,[status(thm)],[fact_fold__image__reindex]) ).

fof(f_2576_2,plain,
    ! [U_8883,U_8882,U_8881,U_8880,U_8879,U_8878,U_8877] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_8877,U_8880,c_Groups_Otimes__class_Otimes(U_8877)),U_8882),U_8883),hAPP(c_Set_Oimage(U_8878,U_8880,U_8881),U_8879)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_8877,U_8878,c_Groups_Otimes__class_Otimes(U_8877)),hAPP(c_Fun_Ocomp(U_8880,U_8877,U_8878,U_8882),U_8881)),U_8883),U_8879)
      | ~ c_Fun_Oinj__on(U_8878,U_8880,U_8881,U_8879)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8878),U_8879))
      | ~ class_Groups_Oab__semigroup__mult(U_8877) ),
    inference(variable_rename,[status(thm)],[f_2576_1]) ).

cnf(f_2576_3,plain,
    ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_8877,U_8880,c_Groups_Otimes__class_Otimes(U_8877)),U_8882),U_8883),hAPP(c_Set_Oimage(U_8878,U_8880,U_8881),U_8879)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_8877,U_8878,c_Groups_Otimes__class_Otimes(U_8877)),hAPP(c_Fun_Ocomp(U_8880,U_8877,U_8878,U_8882),U_8881)),U_8883),U_8879)
    | ~ c_Fun_Oinj__on(U_8878,U_8880,U_8881,U_8879)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8878),U_8879))
    | ~ class_Groups_Oab__semigroup__mult(U_8877) ),
    inference(clausify,[status(thm)],[f_2576_2]) ).

fof(f_2577_1,plain,
    ! [T_d,T_c,V_c_2,V_b_2,V_B_2,V_A_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2))
      | ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_SUP2__I]) ).

fof(f_2577_2,plain,
    ! [U_8891,U_8890,U_8889,U_8888,U_8887,U_8886,U_8885,U_8884] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8884,tc_fun(U_8890,tc_fun(U_8891,tc_HOL_Obool))),U_8886),U_8887),U_8888),U_8889))
      | ~ hBOOL(hAPP(hAPP(hAPP(U_8887,U_8885),U_8888),U_8889))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8884),U_8885),U_8886)) ),
    inference(variable_rename,[status(thm)],[f_2577_1]) ).

cnf(f_2577_3,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8884,tc_fun(U_8890,tc_fun(U_8891,tc_HOL_Obool))),U_8886),U_8887),U_8888),U_8889))
    | ~ hBOOL(hAPP(hAPP(hAPP(U_8887,U_8885),U_8888),U_8889))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8884),U_8885),U_8886)) ),
    inference(clausify,[status(thm)],[f_2577_2]) ).

fof(f_2578_1,plain,
    ! [V_a_2,V_b_2,V_B_2,V_A_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2)) ),
    inference(fof_nnf,[status(thm)],[fact_INF1__D]) ).

fof(f_2578_2,plain,
    ! [U_8897,U_8896,U_8895,U_8894,U_8893,U_8892] :
      ( hBOOL(hAPP(hAPP(U_8895,U_8897),U_8896))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8892),U_8897),U_8894))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8892,tc_fun(U_8893,tc_HOL_Obool)),U_8894),U_8895),U_8896)) ),
    inference(variable_rename,[status(thm)],[f_2578_1]) ).

cnf(f_2578_3,plain,
    ( hBOOL(hAPP(hAPP(U_8895,U_8897),U_8896))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8892),U_8897),U_8894))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8892,tc_fun(U_8893,tc_HOL_Obool)),U_8894),U_8895),U_8896)) ),
    inference(clausify,[status(thm)],[f_2578_2]) ).

fof(f_2579_1,plain,
    ! [V_a_2,V_b_2,V_B_2,V_A_2,T_c,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2)) ),
    inference(fof_nnf,[status(thm)],[fact_INF1__E]) ).

fof(f_2579_2,plain,
    ! [U_8903,U_8902,U_8901,U_8900,U_8899,U_8898] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_8898),U_8903),U_8900))
      | hBOOL(hAPP(hAPP(U_8901,U_8903),U_8902))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8898,tc_fun(U_8899,tc_HOL_Obool)),U_8900),U_8901),U_8902)) ),
    inference(variable_rename,[status(thm)],[f_2579_1]) ).

cnf(f_2579_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_8898),U_8903),U_8900))
    | hBOOL(hAPP(hAPP(U_8901,U_8903),U_8902))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8898,tc_fun(U_8899,tc_HOL_Obool)),U_8900),U_8901),U_8902)) ),
    inference(clausify,[status(thm)],[f_2579_2]) ).

fof(f_2580_1,plain,
    ! [V_a_2,V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) ),
    inference(fof_nnf,[status(thm)],[fact_INF2__D]) ).

fof(f_2580_2,plain,
    ! [U_8911,U_8910,U_8909,U_8908,U_8907,U_8906,U_8905,U_8904] :
      ( hBOOL(hAPP(hAPP(hAPP(U_8908,U_8911),U_8909),U_8910))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8904),U_8911),U_8907))
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8904,tc_fun(U_8905,tc_fun(U_8906,tc_HOL_Obool))),U_8907),U_8908),U_8909),U_8910)) ),
    inference(variable_rename,[status(thm)],[f_2580_1]) ).

cnf(f_2580_3,plain,
    ( hBOOL(hAPP(hAPP(hAPP(U_8908,U_8911),U_8909),U_8910))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8904),U_8911),U_8907))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8904,tc_fun(U_8905,tc_fun(U_8906,tc_HOL_Obool))),U_8907),U_8908),U_8909),U_8910)) ),
    inference(clausify,[status(thm)],[f_2580_2]) ).

fof(f_2581_1,plain,
    ! [V_a_2,V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2))
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) ),
    inference(fof_nnf,[status(thm)],[fact_INF2__E]) ).

fof(f_2581_2,plain,
    ! [U_8919,U_8918,U_8917,U_8916,U_8915,U_8914,U_8913,U_8912] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_8912),U_8919),U_8915))
      | hBOOL(hAPP(hAPP(hAPP(U_8916,U_8919),U_8917),U_8918))
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8912,tc_fun(U_8913,tc_fun(U_8914,tc_HOL_Obool))),U_8915),U_8916),U_8917),U_8918)) ),
    inference(variable_rename,[status(thm)],[f_2581_1]) ).

cnf(f_2581_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_8912),U_8919),U_8915))
    | hBOOL(hAPP(hAPP(hAPP(U_8916,U_8919),U_8917),U_8918))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8912,tc_fun(U_8913,tc_fun(U_8914,tc_HOL_Obool))),U_8915),U_8916),U_8917),U_8918)) ),
    inference(clausify,[status(thm)],[f_2581_2]) ).

fof(f_2582_1,plain,
    ! [V_a_2,V_B_2,V_A_2,T_c,V_b_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
      | hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ),
    inference(fof_nnf,[status(thm)],[fact_INT__E]) ).

fof(f_2582_2,plain,
    ! [U_8925,U_8924,U_8923,U_8922,U_8921,U_8920] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_8922),U_8925),U_8923))
      | hBOOL(hAPP(hAPP(c_member(U_8920),U_8921),hAPP(U_8924,U_8925)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8920),U_8921),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8922,tc_fun(U_8920,tc_HOL_Obool)),U_8923),U_8924))) ),
    inference(variable_rename,[status(thm)],[f_2582_1]) ).

cnf(f_2582_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_8922),U_8925),U_8923))
    | hBOOL(hAPP(hAPP(c_member(U_8920),U_8921),hAPP(U_8924,U_8925)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8920),U_8921),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8922,tc_fun(U_8920,tc_HOL_Obool)),U_8923),U_8924))) ),
    inference(clausify,[status(thm)],[f_2582_2]) ).

fof(f_2583_1,plain,
    ! [V_a_2,V_B_2,V_A_2,T_c,V_b_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ),
    inference(fof_nnf,[status(thm)],[fact_INT__D]) ).

fof(f_2583_2,plain,
    ! [U_8931,U_8930,U_8929,U_8928,U_8927,U_8926] :
      ( hBOOL(hAPP(hAPP(c_member(U_8926),U_8927),hAPP(U_8930,U_8931)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8928),U_8931),U_8929))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8926),U_8927),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8928,tc_fun(U_8926,tc_HOL_Obool)),U_8929),U_8930))) ),
    inference(variable_rename,[status(thm)],[f_2583_1]) ).

cnf(f_2583_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8926),U_8927),hAPP(U_8930,U_8931)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8928),U_8931),U_8929))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8926),U_8927),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8928,tc_fun(U_8926,tc_HOL_Obool)),U_8929),U_8930))) ),
    inference(clausify,[status(thm)],[f_2583_2]) ).

fof(f_2584_1,plain,
    ! [V_A_2,T_c,V_I_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)))
      | ! [B_x] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_A_2,B_x)))
          | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_finite__INT]) ).

fof(f_2584_2,plain,
    ! [U_8936,U_8935,U_8934,U_8933] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8935),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8933,tc_fun(U_8935,tc_HOL_Obool)),U_8934),U_8936)))
      | ! [U_8932] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8935),hAPP(U_8936,U_8932)))
          | ~ hBOOL(hAPP(hAPP(c_member(U_8933),U_8932),U_8934)) ) ),
    inference(variable_rename,[status(thm)],[f_2584_1]) ).

cnf(f_2584_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8935),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8933,tc_fun(U_8935,tc_HOL_Obool)),U_8934),U_8936)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8935),hAPP(U_8936,U_8932)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8933),U_8932),U_8934)) ),
    inference(clausify,[status(thm)],[f_2584_2]) ).

fof(f_2585_1,plain,
    ! [V_B_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_UN__I]) ).

fof(f_2585_2,plain,
    ! [U_8942,U_8941,U_8940,U_8939,U_8938,U_8937] :
      ( hBOOL(hAPP(hAPP(c_member(U_8940),U_8941),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8937,tc_fun(U_8940,tc_HOL_Obool)),U_8939),U_8942)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8940),U_8941),hAPP(U_8942,U_8938)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8937),U_8938),U_8939)) ),
    inference(variable_rename,[status(thm)],[f_2585_1]) ).

cnf(f_2585_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8940),U_8941),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8937,tc_fun(U_8940,tc_HOL_Obool)),U_8939),U_8942)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8940),U_8941),hAPP(U_8942,U_8938)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8937),U_8938),U_8939)) ),
    inference(clausify,[status(thm)],[f_2585_2]) ).

fof(f_2586_1,plain,
    ! [T_c,V_b_2,V_B_2,V_A_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2))
      | ~ hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_SUP1__I]) ).

fof(f_2586_2,plain,
    ! [U_8948,U_8947,U_8946,U_8945,U_8944,U_8943] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8943,tc_fun(U_8948,tc_HOL_Obool)),U_8945),U_8946),U_8947))
      | ~ hBOOL(hAPP(hAPP(U_8946,U_8944),U_8947))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8943),U_8944),U_8945)) ),
    inference(variable_rename,[status(thm)],[f_2586_1]) ).

cnf(f_2586_3,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8943,tc_fun(U_8948,tc_HOL_Obool)),U_8945),U_8946),U_8947))
    | ~ hBOOL(hAPP(hAPP(U_8946,U_8944),U_8947))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8943),U_8944),U_8945)) ),
    inference(clausify,[status(thm)],[f_2586_2]) ).

fof(f_2587_1,plain,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2)))
      | ~ class_Groups_Oordered__ab__group__add__abs(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__abs]) ).

fof(f_2587_2,plain,
    ! [U_8952,U_8951,U_8950,U_8949] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8949),hAPP(c_Groups_Oabs__class_Oabs(U_8949),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8950,U_8949),U_8951),U_8952))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8950,U_8949),hAPP(hAPP(c_COMBB(U_8949,U_8949,U_8950),c_Groups_Oabs__class_Oabs(U_8949)),U_8951)),U_8952)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_8949) ),
    inference(variable_rename,[status(thm)],[f_2587_1]) ).

cnf(f_2587_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8949),hAPP(c_Groups_Oabs__class_Oabs(U_8949),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8950,U_8949),U_8951),U_8952))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8950,U_8949),hAPP(hAPP(c_COMBB(U_8949,U_8949,U_8950),c_Groups_Oabs__class_Oabs(U_8949)),U_8951)),U_8952)))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_8949) ),
    inference(clausify,[status(thm)],[f_2587_2]) ).

fof(f_2588_1,plain,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2)))
      | ~ class_Groups_Oordered__ab__group__add__abs(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__abs__ge__zero]) ).

fof(f_2588_2,plain,
    ! [U_8956,U_8955,U_8954,U_8953] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8953),c_Groups_Ozero__class_Ozero(U_8953)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8954,U_8953),hAPP(hAPP(c_COMBB(U_8953,U_8953,U_8954),c_Groups_Oabs__class_Oabs(U_8953)),U_8955)),U_8956)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_8953) ),
    inference(variable_rename,[status(thm)],[f_2588_1]) ).

cnf(f_2588_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8953),c_Groups_Ozero__class_Ozero(U_8953)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8954,U_8953),hAPP(hAPP(c_COMBB(U_8953,U_8953,U_8954),c_Groups_Oabs__class_Oabs(U_8953)),U_8955)),U_8956)))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_8953) ),
    inference(clausify,[status(thm)],[f_2588_2]) ).

fof(f_2589_1,plain,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,tc_Int_Oint),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_b,T_c),c_Int_Oring__1__class_Oof__int(T_b)),V_f_2)),V_A_2)
      | ~ class_Rings_Oring__1(T_b)
      | ~ class_Groups_Ocomm__monoid__mult(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_of__int__setprod]) ).

fof(f_2589_2,plain,
    ! [U_8960,U_8959,U_8958,U_8957] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_8957),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8958,tc_Int_Oint),U_8959),U_8960)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8958,U_8957),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_8957,U_8958),c_Int_Oring__1__class_Oof__int(U_8957)),U_8959)),U_8960)
      | ~ class_Rings_Oring__1(U_8957)
      | ~ class_Groups_Ocomm__monoid__mult(U_8957) ),
    inference(variable_rename,[status(thm)],[f_2589_1]) ).

cnf(f_2589_3,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_8957),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8958,tc_Int_Oint),U_8959),U_8960)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_8958,U_8957),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_8957,U_8958),c_Int_Oring__1__class_Oof__int(U_8957)),U_8959)),U_8960)
    | ~ class_Rings_Oring__1(U_8957)
    | ~ class_Groups_Ocomm__monoid__mult(U_8957) ),
    inference(clausify,[status(thm)],[f_2589_2]) ).

fof(f_2590_1,plain,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Int_Oint),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_b,T_c),c_Int_Oring__1__class_Oof__int(T_b)),V_f_2)),V_A_2)
      | ~ class_Rings_Oring__1(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_of__int__setsum]) ).

fof(f_2590_2,plain,
    ! [U_8964,U_8963,U_8962,U_8961] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_8961),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8962,tc_Int_Oint),U_8963),U_8964)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8962,U_8961),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_8961,U_8962),c_Int_Oring__1__class_Oof__int(U_8961)),U_8963)),U_8964)
      | ~ class_Rings_Oring__1(U_8961) ),
    inference(variable_rename,[status(thm)],[f_2590_1]) ).

cnf(f_2590_3,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_8961),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8962,tc_Int_Oint),U_8963),U_8964)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8962,U_8961),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_8961,U_8962),c_Int_Oring__1__class_Oof__int(U_8961)),U_8963)),U_8964)
    | ~ class_Rings_Oring__1(U_8961) ),
    inference(clausify,[status(thm)],[f_2590_2]) ).

fof(f_2591_1,plain,
    ! [V_A_2,T_c,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(c_COMBK(T_b,T_c),c_Groups_Ozero__class_Ozero(T_b))),V_A_2) = c_Groups_Ozero__class_Ozero(T_b)
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__0]) ).

fof(f_2591_2,plain,
    ! [U_8967,U_8966,U_8965] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8966,U_8965),hAPP(c_COMBK(U_8965,U_8966),c_Groups_Ozero__class_Ozero(U_8965))),U_8967) = c_Groups_Ozero__class_Ozero(U_8965)
      | ~ class_Groups_Ocomm__monoid__add(U_8965) ),
    inference(variable_rename,[status(thm)],[f_2591_1]) ).

cnf(f_2591_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8966,U_8965),hAPP(c_COMBK(U_8965,U_8966),c_Groups_Ozero__class_Ozero(U_8965))),U_8967) = c_Groups_Ozero__class_Ozero(U_8965)
    | ~ class_Groups_Ocomm__monoid__add(U_8965) ),
    inference(clausify,[status(thm)],[f_2591_2]) ).

fof(f_2592_1,plain,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,T_c),c_Nat_Osemiring__1__class_Oof__nat(T_b)),V_f_2)),V_A_2)
      | ~ class_Rings_Osemiring__1(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__setsum]) ).

fof(f_2592_2,plain,
    ! [U_8971,U_8970,U_8969,U_8968] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_8968),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8969,tc_Nat_Onat),U_8970),U_8971)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8969,U_8968),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_8968,U_8969),c_Nat_Osemiring__1__class_Oof__nat(U_8968)),U_8970)),U_8971)
      | ~ class_Rings_Osemiring__1(U_8968) ),
    inference(variable_rename,[status(thm)],[f_2592_1]) ).

cnf(f_2592_3,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_8968),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8969,tc_Nat_Onat),U_8970),U_8971)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8969,U_8968),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_8968,U_8969),c_Nat_Osemiring__1__class_Oof__nat(U_8968)),U_8970)),U_8971)
    | ~ class_Rings_Osemiring__1(U_8968) ),
    inference(clausify,[status(thm)],[f_2592_2]) ).

fof(f_2593_1,plain,
    ! [V_n_2,V_m_2,V_f_2,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2)),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2))
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__shift__bounds__Suc__ivl]) ).

fof(f_2593_2,plain,
    ! [U_8975,U_8974,U_8973,U_8972] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_8972),U_8973),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_8974)),hAPP(c_Nat_OSuc,U_8975))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_8972),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_8972,tc_Nat_Onat),U_8973),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_8974),U_8975))
      | ~ class_Groups_Ocomm__monoid__add(U_8972) ),
    inference(variable_rename,[status(thm)],[f_2593_1]) ).

cnf(f_2593_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_8972),U_8973),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_8974)),hAPP(c_Nat_OSuc,U_8975))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_8972),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_8972,tc_Nat_Onat),U_8973),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_8974),U_8975))
    | ~ class_Groups_Ocomm__monoid__add(U_8972) ),
    inference(clausify,[status(thm)],[f_2593_2]) ).

fof(f_2594_1,plain,
    ! [V_A_2,V_f_2,T_b] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_b),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__sum__prod2_I1_J]) ).

fof(f_2594_2,plain,
    ! [U_8978,U_8977,U_8976] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8976,tc_Nat_Onat),U_8977),U_8978) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8976,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_8976),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8977)),U_8978)),
    inference(variable_rename,[status(thm)],[f_2594_1]) ).

cnf(f_2594_3,plain,
    hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8976,tc_Nat_Onat),U_8977),U_8978) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8976,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_8976),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8977)),U_8978)),
    inference(clausify,[status(thm)],[f_2594_2]) ).

fof(f_2595_1,plain,
    ! [V_g_2,V_f_2,T_d,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,hAPP(hAPP(c_COMBB(T_d,T_b,T_c),V_f_2),V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = hAPP(c_Set_Oimage(T_d,T_b,V_f_2),hAPP(c_Set_Oimage(T_c,T_d,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_range__composition]) ).

fof(f_2595_2,plain,
    ! [U_8983,U_8982,U_8981,U_8980,U_8979] : hAPP(c_Set_Oimage(U_8979,U_8980,hAPP(hAPP(c_COMBB(U_8981,U_8980,U_8979),U_8982),U_8983)),c_Orderings_Otop__class_Otop(tc_fun(U_8979,tc_HOL_Obool))) = hAPP(c_Set_Oimage(U_8981,U_8980,U_8982),hAPP(c_Set_Oimage(U_8979,U_8981,U_8983),c_Orderings_Otop__class_Otop(tc_fun(U_8979,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_2595_1]) ).

cnf(f_2595_3,plain,
    hAPP(c_Set_Oimage(U_8979,U_8980,hAPP(hAPP(c_COMBB(U_8981,U_8980,U_8979),U_8982),U_8983)),c_Orderings_Otop__class_Otop(tc_fun(U_8979,tc_HOL_Obool))) = hAPP(c_Set_Oimage(U_8981,U_8980,U_8982),hAPP(c_Set_Oimage(U_8979,U_8981,U_8983),c_Orderings_Otop__class_Otop(tc_fun(U_8979,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_2595_2]) ).

fof(f_2596_1,plain,
    ! [T_d,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,tc_fun(T_d,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_d,T_c),T_b),c_COMBK(T_c,T_d)),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_inj__fun]) ).

fof(f_2596_2,plain,
    ! [U_8987,U_8986,U_8985,U_8984] :
      ( c_Fun_Oinj__on(U_8984,tc_fun(U_8987,U_8985),hAPP(hAPP(c_COMBB(U_8985,tc_fun(U_8987,U_8985),U_8984),c_COMBK(U_8985,U_8987)),U_8986),c_Orderings_Otop__class_Otop(tc_fun(U_8984,tc_HOL_Obool)))
      | ~ c_Fun_Oinj__on(U_8984,U_8985,U_8986,c_Orderings_Otop__class_Otop(tc_fun(U_8984,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_2596_1]) ).

cnf(f_2596_3,plain,
    ( c_Fun_Oinj__on(U_8984,tc_fun(U_8987,U_8985),hAPP(hAPP(c_COMBB(U_8985,tc_fun(U_8987,U_8985),U_8984),c_COMBK(U_8985,U_8987)),U_8986),c_Orderings_Otop__class_Otop(tc_fun(U_8984,tc_HOL_Obool)))
    | ~ c_Fun_Oinj__on(U_8984,U_8985,U_8986,c_Orderings_Otop__class_Otop(tc_fun(U_8984,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_2596_2]) ).

fof(f_2597_1,plain,
    ! [V_x_2,V_r_2,T_c,T_b] :
      ( ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c))),V_r_2)),V_x_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2))) )
      & ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2)))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c))),V_r_2)),V_x_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_INF__INT__eq]) ).

fof(f_2597_2,plain,
    ! [U_8991,U_8990,U_8989,U_8988] :
      ( ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8988,tc_fun(U_8989,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_8988,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_8989,tc_HOL_Obool),tc_fun(U_8989,tc_HOL_Obool),U_8988),hAPP(c_COMBC(U_8989,tc_fun(U_8989,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8989))),U_8990)),U_8991))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8989),U_8991),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8988,tc_fun(U_8989,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_8988,tc_HOL_Obool))),U_8990))) )
      & ( hBOOL(hAPP(hAPP(c_member(U_8989),U_8991),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8988,tc_fun(U_8989,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_8988,tc_HOL_Obool))),U_8990)))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8988,tc_fun(U_8989,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_8988,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_8989,tc_HOL_Obool),tc_fun(U_8989,tc_HOL_Obool),U_8988),hAPP(c_COMBC(U_8989,tc_fun(U_8989,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8989))),U_8990)),U_8991)) ) ),
    inference(variable_rename,[status(thm)],[f_2597_1]) ).

fof(f_2597_3,plain,
    ( ! [U_8999,U_8997,U_8995,U_8993] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8993,tc_fun(U_8995,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_8993,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_8995,tc_HOL_Obool),tc_fun(U_8995,tc_HOL_Obool),U_8993),hAPP(c_COMBC(U_8995,tc_fun(U_8995,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8995))),U_8997)),U_8999))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8995),U_8999),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8993,tc_fun(U_8995,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_8993,tc_HOL_Obool))),U_8997))) )
    & ! [U_8998,U_8996,U_8994,U_8992] :
        ( hBOOL(hAPP(hAPP(c_member(U_8994),U_8998),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8992,tc_fun(U_8994,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_8992,tc_HOL_Obool))),U_8996)))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8992,tc_fun(U_8994,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_8992,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_8994,tc_HOL_Obool),tc_fun(U_8994,tc_HOL_Obool),U_8992),hAPP(c_COMBC(U_8994,tc_fun(U_8994,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8994))),U_8996)),U_8998)) ) ),
    inference(miniscope,[status(thm)],[f_2597_2]) ).

cnf(f_2597_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8994),U_8998),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8992,tc_fun(U_8994,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_8992,tc_HOL_Obool))),U_8996)))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8992,tc_fun(U_8994,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_8992,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_8994,tc_HOL_Obool),tc_fun(U_8994,tc_HOL_Obool),U_8992),hAPP(c_COMBC(U_8994,tc_fun(U_8994,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8994))),U_8996)),U_8998)) ),
    inference(clausify,[status(thm)],[f_2597_3]) ).

cnf(f_2597_5,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8993,tc_fun(U_8995,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_8993,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_8995,tc_HOL_Obool),tc_fun(U_8995,tc_HOL_Obool),U_8993),hAPP(c_COMBC(U_8995,tc_fun(U_8995,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8995))),U_8997)),U_8999))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8995),U_8999),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8993,tc_fun(U_8995,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_8993,tc_HOL_Obool))),U_8997))) ),
    inference(clausify,[status(thm)],[f_2597_3]) ).

fof(f_2598_1,plain,
    ! [V_y_2,V_x_2,V_r_2,T_d,T_c,T_b] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),T_b),hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_c,T_d)))),c_Product__Type_OPair(T_c,T_d))))),V_r_2)),V_x_2),V_y_2))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2)))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),T_b),hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_c,T_d)))),c_Product__Type_OPair(T_c,T_d))))),V_r_2)),V_x_2),V_y_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_INF__INT__eq2]) ).

fof(f_2598_2,plain,
    ! [U_9005,U_9004,U_9003,U_9002,U_9001,U_9000] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9000,tc_fun(U_9001,tc_fun(U_9002,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_9000,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_9001,U_9002),tc_HOL_Obool),tc_fun(U_9001,tc_fun(U_9002,tc_HOL_Obool)),U_9000),hAPP(c_COMBC(U_9001,tc_fun(tc_prod(U_9001,U_9002),tc_HOL_Obool),tc_fun(U_9002,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9002,tc_fun(tc_fun(tc_prod(U_9001,U_9002),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9001,U_9002),tc_HOL_Obool),tc_fun(U_9002,tc_HOL_Obool)),U_9001),c_COMBC(U_9002,tc_fun(tc_prod(U_9001,U_9002),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9002,tc_prod(U_9001,U_9002)),tc_fun(U_9002,tc_fun(tc_fun(tc_prod(U_9001,U_9002),tc_HOL_Obool),tc_HOL_Obool)),U_9001),hAPP(c_COMBB(tc_prod(U_9001,U_9002),tc_fun(tc_fun(tc_prod(U_9001,U_9002),tc_HOL_Obool),tc_HOL_Obool),U_9002),c_member(tc_prod(U_9001,U_9002)))),c_Product__Type_OPair(U_9001,U_9002))))),U_9003)),U_9004),U_9005))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9001,U_9002)),hAPP(hAPP(c_Product__Type_OPair(U_9001,U_9002),U_9004),U_9005)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9000,tc_fun(tc_prod(U_9001,U_9002),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9000,tc_HOL_Obool))),U_9003))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9001,U_9002)),hAPP(hAPP(c_Product__Type_OPair(U_9001,U_9002),U_9004),U_9005)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9000,tc_fun(tc_prod(U_9001,U_9002),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9000,tc_HOL_Obool))),U_9003)))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9000,tc_fun(U_9001,tc_fun(U_9002,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_9000,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_9001,U_9002),tc_HOL_Obool),tc_fun(U_9001,tc_fun(U_9002,tc_HOL_Obool)),U_9000),hAPP(c_COMBC(U_9001,tc_fun(tc_prod(U_9001,U_9002),tc_HOL_Obool),tc_fun(U_9002,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9002,tc_fun(tc_fun(tc_prod(U_9001,U_9002),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9001,U_9002),tc_HOL_Obool),tc_fun(U_9002,tc_HOL_Obool)),U_9001),c_COMBC(U_9002,tc_fun(tc_prod(U_9001,U_9002),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9002,tc_prod(U_9001,U_9002)),tc_fun(U_9002,tc_fun(tc_fun(tc_prod(U_9001,U_9002),tc_HOL_Obool),tc_HOL_Obool)),U_9001),hAPP(c_COMBB(tc_prod(U_9001,U_9002),tc_fun(tc_fun(tc_prod(U_9001,U_9002),tc_HOL_Obool),tc_HOL_Obool),U_9002),c_member(tc_prod(U_9001,U_9002)))),c_Product__Type_OPair(U_9001,U_9002))))),U_9003)),U_9004),U_9005)) ) ),
    inference(variable_rename,[status(thm)],[f_2598_1]) ).

fof(f_2598_3,plain,
    ( ! [U_9017,U_9015,U_9013,U_9011,U_9009,U_9007] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9007,tc_fun(U_9009,tc_fun(U_9011,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_9007,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_9009,U_9011),tc_HOL_Obool),tc_fun(U_9009,tc_fun(U_9011,tc_HOL_Obool)),U_9007),hAPP(c_COMBC(U_9009,tc_fun(tc_prod(U_9009,U_9011),tc_HOL_Obool),tc_fun(U_9011,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9011,tc_fun(tc_fun(tc_prod(U_9009,U_9011),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9009,U_9011),tc_HOL_Obool),tc_fun(U_9011,tc_HOL_Obool)),U_9009),c_COMBC(U_9011,tc_fun(tc_prod(U_9009,U_9011),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9011,tc_prod(U_9009,U_9011)),tc_fun(U_9011,tc_fun(tc_fun(tc_prod(U_9009,U_9011),tc_HOL_Obool),tc_HOL_Obool)),U_9009),hAPP(c_COMBB(tc_prod(U_9009,U_9011),tc_fun(tc_fun(tc_prod(U_9009,U_9011),tc_HOL_Obool),tc_HOL_Obool),U_9011),c_member(tc_prod(U_9009,U_9011)))),c_Product__Type_OPair(U_9009,U_9011))))),U_9013)),U_9015),U_9017))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9009,U_9011)),hAPP(hAPP(c_Product__Type_OPair(U_9009,U_9011),U_9015),U_9017)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9007,tc_fun(tc_prod(U_9009,U_9011),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9007,tc_HOL_Obool))),U_9013))) )
    & ! [U_9016,U_9014,U_9012,U_9010,U_9008,U_9006] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9008,U_9010)),hAPP(hAPP(c_Product__Type_OPair(U_9008,U_9010),U_9014),U_9016)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9006,tc_fun(tc_prod(U_9008,U_9010),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9006,tc_HOL_Obool))),U_9012)))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9006,tc_fun(U_9008,tc_fun(U_9010,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_9006,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_9008,U_9010),tc_HOL_Obool),tc_fun(U_9008,tc_fun(U_9010,tc_HOL_Obool)),U_9006),hAPP(c_COMBC(U_9008,tc_fun(tc_prod(U_9008,U_9010),tc_HOL_Obool),tc_fun(U_9010,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9010,tc_fun(tc_fun(tc_prod(U_9008,U_9010),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9008,U_9010),tc_HOL_Obool),tc_fun(U_9010,tc_HOL_Obool)),U_9008),c_COMBC(U_9010,tc_fun(tc_prod(U_9008,U_9010),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9010,tc_prod(U_9008,U_9010)),tc_fun(U_9010,tc_fun(tc_fun(tc_prod(U_9008,U_9010),tc_HOL_Obool),tc_HOL_Obool)),U_9008),hAPP(c_COMBB(tc_prod(U_9008,U_9010),tc_fun(tc_fun(tc_prod(U_9008,U_9010),tc_HOL_Obool),tc_HOL_Obool),U_9010),c_member(tc_prod(U_9008,U_9010)))),c_Product__Type_OPair(U_9008,U_9010))))),U_9012)),U_9014),U_9016)) ) ),
    inference(miniscope,[status(thm)],[f_2598_2]) ).

cnf(f_2598_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9008,U_9010)),hAPP(hAPP(c_Product__Type_OPair(U_9008,U_9010),U_9014),U_9016)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9006,tc_fun(tc_prod(U_9008,U_9010),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9006,tc_HOL_Obool))),U_9012)))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9006,tc_fun(U_9008,tc_fun(U_9010,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_9006,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_9008,U_9010),tc_HOL_Obool),tc_fun(U_9008,tc_fun(U_9010,tc_HOL_Obool)),U_9006),hAPP(c_COMBC(U_9008,tc_fun(tc_prod(U_9008,U_9010),tc_HOL_Obool),tc_fun(U_9010,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9010,tc_fun(tc_fun(tc_prod(U_9008,U_9010),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9008,U_9010),tc_HOL_Obool),tc_fun(U_9010,tc_HOL_Obool)),U_9008),c_COMBC(U_9010,tc_fun(tc_prod(U_9008,U_9010),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9010,tc_prod(U_9008,U_9010)),tc_fun(U_9010,tc_fun(tc_fun(tc_prod(U_9008,U_9010),tc_HOL_Obool),tc_HOL_Obool)),U_9008),hAPP(c_COMBB(tc_prod(U_9008,U_9010),tc_fun(tc_fun(tc_prod(U_9008,U_9010),tc_HOL_Obool),tc_HOL_Obool),U_9010),c_member(tc_prod(U_9008,U_9010)))),c_Product__Type_OPair(U_9008,U_9010))))),U_9012)),U_9014),U_9016)) ),
    inference(clausify,[status(thm)],[f_2598_3]) ).

cnf(f_2598_5,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9007,tc_fun(U_9009,tc_fun(U_9011,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_9007,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_9009,U_9011),tc_HOL_Obool),tc_fun(U_9009,tc_fun(U_9011,tc_HOL_Obool)),U_9007),hAPP(c_COMBC(U_9009,tc_fun(tc_prod(U_9009,U_9011),tc_HOL_Obool),tc_fun(U_9011,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9011,tc_fun(tc_fun(tc_prod(U_9009,U_9011),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9009,U_9011),tc_HOL_Obool),tc_fun(U_9011,tc_HOL_Obool)),U_9009),c_COMBC(U_9011,tc_fun(tc_prod(U_9009,U_9011),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9011,tc_prod(U_9009,U_9011)),tc_fun(U_9011,tc_fun(tc_fun(tc_prod(U_9009,U_9011),tc_HOL_Obool),tc_HOL_Obool)),U_9009),hAPP(c_COMBB(tc_prod(U_9009,U_9011),tc_fun(tc_fun(tc_prod(U_9009,U_9011),tc_HOL_Obool),tc_HOL_Obool),U_9011),c_member(tc_prod(U_9009,U_9011)))),c_Product__Type_OPair(U_9009,U_9011))))),U_9013)),U_9015),U_9017))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9009,U_9011)),hAPP(hAPP(c_Product__Type_OPair(U_9009,U_9011),U_9015),U_9017)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9007,tc_fun(tc_prod(U_9009,U_9011),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9007,tc_HOL_Obool))),U_9013))) ),
    inference(clausify,[status(thm)],[f_2598_3]) ).

fof(f_2599_1,plain,
    ! [V_y_2,V_x_2,V_r_2,T_d,T_c,T_b] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),T_b),hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_c,T_d)))),c_Product__Type_OPair(T_c,T_d))))),V_r_2)),V_x_2),V_y_2))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2)))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),T_b),hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_c,T_d)))),c_Product__Type_OPair(T_c,T_d))))),V_r_2)),V_x_2),V_y_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_SUP__UN__eq2]) ).

fof(f_2599_2,plain,
    ! [U_9023,U_9022,U_9021,U_9020,U_9019,U_9018] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9018,tc_fun(U_9019,tc_fun(U_9020,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_9018,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_9019,U_9020),tc_HOL_Obool),tc_fun(U_9019,tc_fun(U_9020,tc_HOL_Obool)),U_9018),hAPP(c_COMBC(U_9019,tc_fun(tc_prod(U_9019,U_9020),tc_HOL_Obool),tc_fun(U_9020,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9020,tc_fun(tc_fun(tc_prod(U_9019,U_9020),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9019,U_9020),tc_HOL_Obool),tc_fun(U_9020,tc_HOL_Obool)),U_9019),c_COMBC(U_9020,tc_fun(tc_prod(U_9019,U_9020),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9020,tc_prod(U_9019,U_9020)),tc_fun(U_9020,tc_fun(tc_fun(tc_prod(U_9019,U_9020),tc_HOL_Obool),tc_HOL_Obool)),U_9019),hAPP(c_COMBB(tc_prod(U_9019,U_9020),tc_fun(tc_fun(tc_prod(U_9019,U_9020),tc_HOL_Obool),tc_HOL_Obool),U_9020),c_member(tc_prod(U_9019,U_9020)))),c_Product__Type_OPair(U_9019,U_9020))))),U_9021)),U_9022),U_9023))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9019,U_9020)),hAPP(hAPP(c_Product__Type_OPair(U_9019,U_9020),U_9022),U_9023)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9018,tc_fun(tc_prod(U_9019,U_9020),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9018,tc_HOL_Obool))),U_9021))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9019,U_9020)),hAPP(hAPP(c_Product__Type_OPair(U_9019,U_9020),U_9022),U_9023)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9018,tc_fun(tc_prod(U_9019,U_9020),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9018,tc_HOL_Obool))),U_9021)))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9018,tc_fun(U_9019,tc_fun(U_9020,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_9018,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_9019,U_9020),tc_HOL_Obool),tc_fun(U_9019,tc_fun(U_9020,tc_HOL_Obool)),U_9018),hAPP(c_COMBC(U_9019,tc_fun(tc_prod(U_9019,U_9020),tc_HOL_Obool),tc_fun(U_9020,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9020,tc_fun(tc_fun(tc_prod(U_9019,U_9020),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9019,U_9020),tc_HOL_Obool),tc_fun(U_9020,tc_HOL_Obool)),U_9019),c_COMBC(U_9020,tc_fun(tc_prod(U_9019,U_9020),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9020,tc_prod(U_9019,U_9020)),tc_fun(U_9020,tc_fun(tc_fun(tc_prod(U_9019,U_9020),tc_HOL_Obool),tc_HOL_Obool)),U_9019),hAPP(c_COMBB(tc_prod(U_9019,U_9020),tc_fun(tc_fun(tc_prod(U_9019,U_9020),tc_HOL_Obool),tc_HOL_Obool),U_9020),c_member(tc_prod(U_9019,U_9020)))),c_Product__Type_OPair(U_9019,U_9020))))),U_9021)),U_9022),U_9023)) ) ),
    inference(variable_rename,[status(thm)],[f_2599_1]) ).

fof(f_2599_3,plain,
    ( ! [U_9035,U_9033,U_9031,U_9029,U_9027,U_9025] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9025,tc_fun(U_9027,tc_fun(U_9029,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_9025,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_9027,U_9029),tc_HOL_Obool),tc_fun(U_9027,tc_fun(U_9029,tc_HOL_Obool)),U_9025),hAPP(c_COMBC(U_9027,tc_fun(tc_prod(U_9027,U_9029),tc_HOL_Obool),tc_fun(U_9029,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9029,tc_fun(tc_fun(tc_prod(U_9027,U_9029),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9027,U_9029),tc_HOL_Obool),tc_fun(U_9029,tc_HOL_Obool)),U_9027),c_COMBC(U_9029,tc_fun(tc_prod(U_9027,U_9029),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9029,tc_prod(U_9027,U_9029)),tc_fun(U_9029,tc_fun(tc_fun(tc_prod(U_9027,U_9029),tc_HOL_Obool),tc_HOL_Obool)),U_9027),hAPP(c_COMBB(tc_prod(U_9027,U_9029),tc_fun(tc_fun(tc_prod(U_9027,U_9029),tc_HOL_Obool),tc_HOL_Obool),U_9029),c_member(tc_prod(U_9027,U_9029)))),c_Product__Type_OPair(U_9027,U_9029))))),U_9031)),U_9033),U_9035))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9027,U_9029)),hAPP(hAPP(c_Product__Type_OPair(U_9027,U_9029),U_9033),U_9035)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9025,tc_fun(tc_prod(U_9027,U_9029),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9025,tc_HOL_Obool))),U_9031))) )
    & ! [U_9034,U_9032,U_9030,U_9028,U_9026,U_9024] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9026,U_9028)),hAPP(hAPP(c_Product__Type_OPair(U_9026,U_9028),U_9032),U_9034)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9024,tc_fun(tc_prod(U_9026,U_9028),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9024,tc_HOL_Obool))),U_9030)))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9024,tc_fun(U_9026,tc_fun(U_9028,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_9024,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_9026,U_9028),tc_HOL_Obool),tc_fun(U_9026,tc_fun(U_9028,tc_HOL_Obool)),U_9024),hAPP(c_COMBC(U_9026,tc_fun(tc_prod(U_9026,U_9028),tc_HOL_Obool),tc_fun(U_9028,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9028,tc_fun(tc_fun(tc_prod(U_9026,U_9028),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9026,U_9028),tc_HOL_Obool),tc_fun(U_9028,tc_HOL_Obool)),U_9026),c_COMBC(U_9028,tc_fun(tc_prod(U_9026,U_9028),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9028,tc_prod(U_9026,U_9028)),tc_fun(U_9028,tc_fun(tc_fun(tc_prod(U_9026,U_9028),tc_HOL_Obool),tc_HOL_Obool)),U_9026),hAPP(c_COMBB(tc_prod(U_9026,U_9028),tc_fun(tc_fun(tc_prod(U_9026,U_9028),tc_HOL_Obool),tc_HOL_Obool),U_9028),c_member(tc_prod(U_9026,U_9028)))),c_Product__Type_OPair(U_9026,U_9028))))),U_9030)),U_9032),U_9034)) ) ),
    inference(miniscope,[status(thm)],[f_2599_2]) ).

cnf(f_2599_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9026,U_9028)),hAPP(hAPP(c_Product__Type_OPair(U_9026,U_9028),U_9032),U_9034)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9024,tc_fun(tc_prod(U_9026,U_9028),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9024,tc_HOL_Obool))),U_9030)))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9024,tc_fun(U_9026,tc_fun(U_9028,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_9024,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_9026,U_9028),tc_HOL_Obool),tc_fun(U_9026,tc_fun(U_9028,tc_HOL_Obool)),U_9024),hAPP(c_COMBC(U_9026,tc_fun(tc_prod(U_9026,U_9028),tc_HOL_Obool),tc_fun(U_9028,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9028,tc_fun(tc_fun(tc_prod(U_9026,U_9028),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9026,U_9028),tc_HOL_Obool),tc_fun(U_9028,tc_HOL_Obool)),U_9026),c_COMBC(U_9028,tc_fun(tc_prod(U_9026,U_9028),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9028,tc_prod(U_9026,U_9028)),tc_fun(U_9028,tc_fun(tc_fun(tc_prod(U_9026,U_9028),tc_HOL_Obool),tc_HOL_Obool)),U_9026),hAPP(c_COMBB(tc_prod(U_9026,U_9028),tc_fun(tc_fun(tc_prod(U_9026,U_9028),tc_HOL_Obool),tc_HOL_Obool),U_9028),c_member(tc_prod(U_9026,U_9028)))),c_Product__Type_OPair(U_9026,U_9028))))),U_9030)),U_9032),U_9034)) ),
    inference(clausify,[status(thm)],[f_2599_3]) ).

cnf(f_2599_5,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9025,tc_fun(U_9027,tc_fun(U_9029,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_9025,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_9027,U_9029),tc_HOL_Obool),tc_fun(U_9027,tc_fun(U_9029,tc_HOL_Obool)),U_9025),hAPP(c_COMBC(U_9027,tc_fun(tc_prod(U_9027,U_9029),tc_HOL_Obool),tc_fun(U_9029,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9029,tc_fun(tc_fun(tc_prod(U_9027,U_9029),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9027,U_9029),tc_HOL_Obool),tc_fun(U_9029,tc_HOL_Obool)),U_9027),c_COMBC(U_9029,tc_fun(tc_prod(U_9027,U_9029),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9029,tc_prod(U_9027,U_9029)),tc_fun(U_9029,tc_fun(tc_fun(tc_prod(U_9027,U_9029),tc_HOL_Obool),tc_HOL_Obool)),U_9027),hAPP(c_COMBB(tc_prod(U_9027,U_9029),tc_fun(tc_fun(tc_prod(U_9027,U_9029),tc_HOL_Obool),tc_HOL_Obool),U_9029),c_member(tc_prod(U_9027,U_9029)))),c_Product__Type_OPair(U_9027,U_9029))))),U_9031)),U_9033),U_9035))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9027,U_9029)),hAPP(hAPP(c_Product__Type_OPair(U_9027,U_9029),U_9033),U_9035)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9025,tc_fun(tc_prod(U_9027,U_9029),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9025,tc_HOL_Obool))),U_9031))) ),
    inference(clausify,[status(thm)],[f_2599_3]) ).

fof(f_2600_1,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_UN__atLeast__UNIV]) ).

cnf(f_2600_2,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2600_1]) ).

fof(f_2601_1,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_UN__lessThan__UNIV]) ).

cnf(f_2601_2,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2601_1]) ).

fof(f_2602_1,plain,
    ! [V_B_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_INT__empty]) ).

fof(f_2602_2,plain,
    ! [U_9038,U_9037,U_9036] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9036,tc_fun(U_9037,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_9036,tc_HOL_Obool))),U_9038) = c_Orderings_Otop__class_Otop(tc_fun(U_9037,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2602_1]) ).

cnf(f_2602_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9036,tc_fun(U_9037,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_9036,tc_HOL_Obool))),U_9038) = c_Orderings_Otop__class_Otop(tc_fun(U_9037,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2602_2]) ).

fof(f_2603_1,plain,
    ! [V_c_2,T_c,T_b,V_A_2] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_c_2)) = V_c_2
        | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_c_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))
        | V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_INT__constant]) ).

fof(f_2603_2,plain,
    ! [U_9042,U_9041,U_9040,U_9039] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9040,tc_fun(U_9041,tc_HOL_Obool)),U_9039),hAPP(c_COMBK(tc_fun(U_9041,tc_HOL_Obool),U_9040),U_9042)) = U_9042
        | U_9039 = c_Orderings_Obot__class_Obot(tc_fun(U_9040,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9040,tc_fun(U_9041,tc_HOL_Obool)),U_9039),hAPP(c_COMBK(tc_fun(U_9041,tc_HOL_Obool),U_9040),U_9042)) = c_Orderings_Otop__class_Otop(tc_fun(U_9041,tc_HOL_Obool))
        | U_9039 != c_Orderings_Obot__class_Obot(tc_fun(U_9040,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2603_1]) ).

fof(f_2603_3,plain,
    ( ! [U_9050,U_9048,U_9046,U_9044] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9046,tc_fun(U_9048,tc_HOL_Obool)),U_9044),hAPP(c_COMBK(tc_fun(U_9048,tc_HOL_Obool),U_9046),U_9050)) = U_9050
        | U_9044 = c_Orderings_Obot__class_Obot(tc_fun(U_9046,tc_HOL_Obool)) )
    & ! [U_9049,U_9047,U_9045,U_9043] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9045,tc_fun(U_9047,tc_HOL_Obool)),U_9043),hAPP(c_COMBK(tc_fun(U_9047,tc_HOL_Obool),U_9045),U_9049)) = c_Orderings_Otop__class_Otop(tc_fun(U_9047,tc_HOL_Obool))
        | U_9043 != c_Orderings_Obot__class_Obot(tc_fun(U_9045,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2603_2]) ).

cnf(f_2603_4,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9045,tc_fun(U_9047,tc_HOL_Obool)),U_9043),hAPP(c_COMBK(tc_fun(U_9047,tc_HOL_Obool),U_9045),U_9049)) = c_Orderings_Otop__class_Otop(tc_fun(U_9047,tc_HOL_Obool))
    | U_9043 != c_Orderings_Obot__class_Obot(tc_fun(U_9045,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2603_3]) ).

cnf(f_2603_5,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9046,tc_fun(U_9048,tc_HOL_Obool)),U_9044),hAPP(c_COMBK(tc_fun(U_9048,tc_HOL_Obool),U_9046),U_9050)) = U_9050
    | U_9044 = c_Orderings_Obot__class_Obot(tc_fun(U_9046,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2603_3]) ).

fof(f_2604_1,plain,
    ! [V_B_2,V_A_2,T_b,T_c] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
        | ? [B_x] :
            ( hAPP(V_B_2,B_x) != c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) )
      & ( ! [B_x] :
            ( hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_INTER__UNIV__conv_I2_J]) ).

fof(f_2604_2,plain,
    ! [U_9056,U_9055,U_9054,U_9053] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9053,tc_fun(U_9054,tc_HOL_Obool)),U_9055),U_9056) = c_Orderings_Otop__class_Otop(tc_fun(U_9054,tc_HOL_Obool))
        | ? [U_9052] :
            ( hAPP(U_9056,U_9052) != c_Orderings_Otop__class_Otop(tc_fun(U_9054,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(U_9053),U_9052),U_9055)) ) )
      & ( ! [U_9051] :
            ( hAPP(U_9056,U_9051) = c_Orderings_Otop__class_Otop(tc_fun(U_9054,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_9053),U_9051),U_9055)) )
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9053,tc_fun(U_9054,tc_HOL_Obool)),U_9055),U_9056) != c_Orderings_Otop__class_Otop(tc_fun(U_9054,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2604_1]) ).

fof(f_2604_3,plain,
    ( ! [U_9064,U_9062,U_9060,U_9058] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9058,tc_fun(U_9060,tc_HOL_Obool)),U_9062),U_9064) = c_Orderings_Otop__class_Otop(tc_fun(U_9060,tc_HOL_Obool))
        | ? [U_9052] :
            ( hAPP(U_9064,U_9052) != c_Orderings_Otop__class_Otop(tc_fun(U_9060,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(U_9058),U_9052),U_9062)) ) )
    & ! [U_9063,U_9061,U_9059,U_9057] :
        ( ! [U_9051] :
            ( hAPP(U_9063,U_9051) = c_Orderings_Otop__class_Otop(tc_fun(U_9059,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_9057),U_9051),U_9061)) )
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9057,tc_fun(U_9059,tc_HOL_Obool)),U_9061),U_9063) != c_Orderings_Otop__class_Otop(tc_fun(U_9059,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2604_2]) ).

fof(f_2604_4,plain,
    ( ! [U_9064,U_9062,U_9060,U_9058] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9058,tc_fun(U_9060,tc_HOL_Obool)),U_9062),U_9064) = c_Orderings_Otop__class_Otop(tc_fun(U_9060,tc_HOL_Obool))
        | ( hAPP(U_9064,sK231(U_9064,U_9062,U_9060,U_9058)) != c_Orderings_Otop__class_Otop(tc_fun(U_9060,tc_HOL_Obool))
          & hBOOL(hAPP(hAPP(c_member(U_9058),sK231(U_9064,U_9062,U_9060,U_9058)),U_9062)) ) )
    & ! [U_9063,U_9061,U_9059,U_9057] :
        ( ! [U_9051] :
            ( hAPP(U_9063,U_9051) = c_Orderings_Otop__class_Otop(tc_fun(U_9059,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_9057),U_9051),U_9061)) )
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9057,tc_fun(U_9059,tc_HOL_Obool)),U_9061),U_9063) != c_Orderings_Otop__class_Otop(tc_fun(U_9059,tc_HOL_Obool)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK231]),skolemize(U_9052,sK231(U_9064,U_9062,U_9060,U_9058))],[f_2604_3]) ).

cnf(f_2604_5,plain,
    ( hAPP(U_9063,U_9051) = c_Orderings_Otop__class_Otop(tc_fun(U_9059,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9057),U_9051),U_9061))
    | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9057,tc_fun(U_9059,tc_HOL_Obool)),U_9061),U_9063) != c_Orderings_Otop__class_Otop(tc_fun(U_9059,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2604_4]) ).

cnf(f_2604_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9058),sK231(U_9064,U_9062,U_9060,U_9058)),U_9062))
    | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9058,tc_fun(U_9060,tc_HOL_Obool)),U_9062),U_9064) = c_Orderings_Otop__class_Otop(tc_fun(U_9060,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2604_4]) ).

cnf(f_2604_7,plain,
    ( hAPP(U_9064,sK231(U_9064,U_9062,U_9060,U_9058)) != c_Orderings_Otop__class_Otop(tc_fun(U_9060,tc_HOL_Obool))
    | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9058,tc_fun(U_9060,tc_HOL_Obool)),U_9062),U_9064) = c_Orderings_Otop__class_Otop(tc_fun(U_9060,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2604_4]) ).

fof(f_2605_1,plain,
    ! [V_B_2,V_A_2,T_c,T_b] :
      ( ( c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)
        | ? [B_x] :
            ( hAPP(V_B_2,B_x) != c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) )
      & ( ! [B_x] :
            ( hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
        | c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_INTER__UNIV__conv_I1_J]) ).

fof(f_2605_2,plain,
    ! [U_9070,U_9069,U_9068,U_9067] :
      ( ( c_Orderings_Otop__class_Otop(tc_fun(U_9067,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9068,tc_fun(U_9067,tc_HOL_Obool)),U_9069),U_9070)
        | ? [U_9066] :
            ( hAPP(U_9070,U_9066) != c_Orderings_Otop__class_Otop(tc_fun(U_9067,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(U_9068),U_9066),U_9069)) ) )
      & ( ! [U_9065] :
            ( hAPP(U_9070,U_9065) = c_Orderings_Otop__class_Otop(tc_fun(U_9067,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_9068),U_9065),U_9069)) )
        | c_Orderings_Otop__class_Otop(tc_fun(U_9067,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9068,tc_fun(U_9067,tc_HOL_Obool)),U_9069),U_9070) ) ),
    inference(variable_rename,[status(thm)],[f_2605_1]) ).

fof(f_2605_3,plain,
    ( ! [U_9078,U_9076,U_9074,U_9072] :
        ( c_Orderings_Otop__class_Otop(tc_fun(U_9072,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9074,tc_fun(U_9072,tc_HOL_Obool)),U_9076),U_9078)
        | ? [U_9066] :
            ( hAPP(U_9078,U_9066) != c_Orderings_Otop__class_Otop(tc_fun(U_9072,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(U_9074),U_9066),U_9076)) ) )
    & ! [U_9077,U_9075,U_9073,U_9071] :
        ( ! [U_9065] :
            ( hAPP(U_9077,U_9065) = c_Orderings_Otop__class_Otop(tc_fun(U_9071,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_9073),U_9065),U_9075)) )
        | c_Orderings_Otop__class_Otop(tc_fun(U_9071,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9073,tc_fun(U_9071,tc_HOL_Obool)),U_9075),U_9077) ) ),
    inference(miniscope,[status(thm)],[f_2605_2]) ).

fof(f_2605_4,plain,
    ( ! [U_9078,U_9076,U_9074,U_9072] :
        ( c_Orderings_Otop__class_Otop(tc_fun(U_9072,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9074,tc_fun(U_9072,tc_HOL_Obool)),U_9076),U_9078)
        | ( hAPP(U_9078,sK232(U_9078,U_9076,U_9074,U_9072)) != c_Orderings_Otop__class_Otop(tc_fun(U_9072,tc_HOL_Obool))
          & hBOOL(hAPP(hAPP(c_member(U_9074),sK232(U_9078,U_9076,U_9074,U_9072)),U_9076)) ) )
    & ! [U_9077,U_9075,U_9073,U_9071] :
        ( ! [U_9065] :
            ( hAPP(U_9077,U_9065) = c_Orderings_Otop__class_Otop(tc_fun(U_9071,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_9073),U_9065),U_9075)) )
        | c_Orderings_Otop__class_Otop(tc_fun(U_9071,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9073,tc_fun(U_9071,tc_HOL_Obool)),U_9075),U_9077) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK232]),skolemize(U_9066,sK232(U_9078,U_9076,U_9074,U_9072))],[f_2605_3]) ).

cnf(f_2605_5,plain,
    ( hAPP(U_9077,U_9065) = c_Orderings_Otop__class_Otop(tc_fun(U_9071,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9073),U_9065),U_9075))
    | c_Orderings_Otop__class_Otop(tc_fun(U_9071,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9073,tc_fun(U_9071,tc_HOL_Obool)),U_9075),U_9077) ),
    inference(clausify,[status(thm)],[f_2605_4]) ).

cnf(f_2605_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9074),sK232(U_9078,U_9076,U_9074,U_9072)),U_9076))
    | c_Orderings_Otop__class_Otop(tc_fun(U_9072,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9074,tc_fun(U_9072,tc_HOL_Obool)),U_9076),U_9078) ),
    inference(clausify,[status(thm)],[f_2605_4]) ).

cnf(f_2605_7,plain,
    ( hAPP(U_9078,sK232(U_9078,U_9076,U_9074,U_9072)) != c_Orderings_Otop__class_Otop(tc_fun(U_9072,tc_HOL_Obool))
    | c_Orderings_Otop__class_Otop(tc_fun(U_9072,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9074,tc_fun(U_9072,tc_HOL_Obool)),U_9076),U_9078) ),
    inference(clausify,[status(thm)],[f_2605_4]) ).

fof(f_2606_1,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OatMost(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_UN__atMost__UNIV]) ).

cnf(f_2606_2,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OatMost(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2606_1]) ).

fof(f_2607_1,plain,
    ! [V_x_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_x_2)) = hAPP(V_f_2,V_x_2)
      | ~ c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofun__comp__idem]) ).

fof(f_2607_2,plain,
    ! [U_9082,U_9081,U_9080,U_9079] :
      ( hAPP(c_Fun_Ocomp(U_9080,U_9080,U_9080,hAPP(U_9081,U_9082)),hAPP(U_9081,U_9082)) = hAPP(U_9081,U_9082)
      | ~ c_Finite__Set_Ofun__left__comm__idem(U_9079,U_9080,U_9081) ),
    inference(variable_rename,[status(thm)],[f_2607_1]) ).

fof(f_2607_3,plain,
    ! [U_9082,U_9081,U_9080] :
      ( ! [U_9079] : ~ c_Finite__Set_Ofun__left__comm__idem(U_9079,U_9080,U_9081)
      | hAPP(c_Fun_Ocomp(U_9080,U_9080,U_9080,hAPP(U_9081,U_9082)),hAPP(U_9081,U_9082)) = hAPP(U_9081,U_9082) ),
    inference(miniscope,[status(thm)],[f_2607_2]) ).

cnf(f_2607_4,plain,
    ( ~ c_Finite__Set_Ofun__left__comm__idem(U_9079,U_9080,U_9081)
    | hAPP(c_Fun_Ocomp(U_9080,U_9080,U_9080,hAPP(U_9081,U_9082)),hAPP(U_9081,U_9082)) = hAPP(U_9081,U_9082) ),
    inference(clausify,[status(thm)],[f_2607_3]) ).

fof(f_2608_1,plain,
    ! [T_b] : c_Fun_Oinj__on(T_b,tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),
    inference(fof_nnf,[status(thm)],[fact_inj__singleton]) ).

fof(f_2608_2,plain,
    ! [U_9083] : c_Fun_Oinj__on(U_9083,tc_fun(U_9083,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_9083,tc_fun(U_9083,tc_HOL_Obool),tc_fun(U_9083,tc_HOL_Obool)),c_Set_Oinsert(U_9083)),c_Orderings_Obot__class_Obot(tc_fun(U_9083,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_9083,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_2608_1]) ).

cnf(f_2608_3,plain,
    c_Fun_Oinj__on(U_9083,tc_fun(U_9083,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_9083,tc_fun(U_9083,tc_HOL_Obool),tc_fun(U_9083,tc_HOL_Obool)),c_Set_Oinsert(U_9083)),c_Orderings_Obot__class_Obot(tc_fun(U_9083,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_9083,tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_2608_2]) ).

fof(f_2609_1,plain,
    ! [V_B_2,V_a_2,T_c,V_A_2,V_u_2,T_b] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_u_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_UN__insert__distrib]) ).

fof(f_2609_2,plain,
    ! [U_9089,U_9088,U_9087,U_9086,U_9085,U_9084] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9084,tc_fun(U_9087,tc_HOL_Obool)),U_9086),hAPP(hAPP(c_COMBB(tc_fun(U_9087,tc_HOL_Obool),tc_fun(U_9087,tc_HOL_Obool),U_9084),hAPP(c_Set_Oinsert(U_9087),U_9088)),U_9089)) = hAPP(hAPP(c_Set_Oinsert(U_9087),U_9088),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9084,tc_fun(U_9087,tc_HOL_Obool)),U_9086),U_9089))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9084),U_9085),U_9086)) ),
    inference(variable_rename,[status(thm)],[f_2609_1]) ).

cnf(f_2609_3,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9084,tc_fun(U_9087,tc_HOL_Obool)),U_9086),hAPP(hAPP(c_COMBB(tc_fun(U_9087,tc_HOL_Obool),tc_fun(U_9087,tc_HOL_Obool),U_9084),hAPP(c_Set_Oinsert(U_9087),U_9088)),U_9089)) = hAPP(hAPP(c_Set_Oinsert(U_9087),U_9088),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9084,tc_fun(U_9087,tc_HOL_Obool)),U_9086),U_9089))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9084),U_9085),U_9086)) ),
    inference(clausify,[status(thm)],[f_2609_2]) ).

fof(f_2610_1,plain,
    ! [V_c_2,T_c,T_b,V_A_2] :
      ( ( hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_c_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))
        | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
      & ( hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_c_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
        | V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_image__constant__conv]) ).

fof(f_2610_2,plain,
    ! [U_9093,U_9092,U_9091,U_9090] :
      ( ( hAPP(c_Set_Oimage(U_9091,U_9092,hAPP(c_COMBK(U_9092,U_9091),U_9093)),U_9090) = hAPP(hAPP(c_Set_Oinsert(U_9092),U_9093),c_Orderings_Obot__class_Obot(tc_fun(U_9092,tc_HOL_Obool)))
        | U_9090 = c_Orderings_Obot__class_Obot(tc_fun(U_9091,tc_HOL_Obool)) )
      & ( hAPP(c_Set_Oimage(U_9091,U_9092,hAPP(c_COMBK(U_9092,U_9091),U_9093)),U_9090) = c_Orderings_Obot__class_Obot(tc_fun(U_9092,tc_HOL_Obool))
        | U_9090 != c_Orderings_Obot__class_Obot(tc_fun(U_9091,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2610_1]) ).

fof(f_2610_3,plain,
    ( ! [U_9101,U_9099,U_9097,U_9095] :
        ( hAPP(c_Set_Oimage(U_9097,U_9099,hAPP(c_COMBK(U_9099,U_9097),U_9101)),U_9095) = hAPP(hAPP(c_Set_Oinsert(U_9099),U_9101),c_Orderings_Obot__class_Obot(tc_fun(U_9099,tc_HOL_Obool)))
        | U_9095 = c_Orderings_Obot__class_Obot(tc_fun(U_9097,tc_HOL_Obool)) )
    & ! [U_9100,U_9098,U_9096,U_9094] :
        ( hAPP(c_Set_Oimage(U_9096,U_9098,hAPP(c_COMBK(U_9098,U_9096),U_9100)),U_9094) = c_Orderings_Obot__class_Obot(tc_fun(U_9098,tc_HOL_Obool))
        | U_9094 != c_Orderings_Obot__class_Obot(tc_fun(U_9096,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2610_2]) ).

cnf(f_2610_4,plain,
    ( hAPP(c_Set_Oimage(U_9096,U_9098,hAPP(c_COMBK(U_9098,U_9096),U_9100)),U_9094) = c_Orderings_Obot__class_Obot(tc_fun(U_9098,tc_HOL_Obool))
    | U_9094 != c_Orderings_Obot__class_Obot(tc_fun(U_9096,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2610_3]) ).

cnf(f_2610_5,plain,
    ( hAPP(c_Set_Oimage(U_9097,U_9099,hAPP(c_COMBK(U_9099,U_9097),U_9101)),U_9095) = hAPP(hAPP(c_Set_Oinsert(U_9099),U_9101),c_Orderings_Obot__class_Obot(tc_fun(U_9099,tc_HOL_Obool)))
    | U_9095 = c_Orderings_Obot__class_Obot(tc_fun(U_9097,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2610_3]) ).

fof(f_2611_1,plain,
    ! [V_x_2,V_r_2,T_c,T_b] :
      ( ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c))),V_r_2)),V_x_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2))) )
      & ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2)))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c))),V_r_2)),V_x_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_SUP__UN__eq]) ).

fof(f_2611_2,plain,
    ! [U_9105,U_9104,U_9103,U_9102] :
      ( ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9102,tc_fun(U_9103,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9102,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9103,tc_HOL_Obool),tc_fun(U_9103,tc_HOL_Obool),U_9102),hAPP(c_COMBC(U_9103,tc_fun(U_9103,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9103))),U_9104)),U_9105))
        | ~ hBOOL(hAPP(hAPP(c_member(U_9103),U_9105),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9102,tc_fun(U_9103,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9102,tc_HOL_Obool))),U_9104))) )
      & ( hBOOL(hAPP(hAPP(c_member(U_9103),U_9105),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9102,tc_fun(U_9103,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9102,tc_HOL_Obool))),U_9104)))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9102,tc_fun(U_9103,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9102,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9103,tc_HOL_Obool),tc_fun(U_9103,tc_HOL_Obool),U_9102),hAPP(c_COMBC(U_9103,tc_fun(U_9103,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9103))),U_9104)),U_9105)) ) ),
    inference(variable_rename,[status(thm)],[f_2611_1]) ).

fof(f_2611_3,plain,
    ( ! [U_9113,U_9111,U_9109,U_9107] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9107,tc_fun(U_9109,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9107,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9109,tc_HOL_Obool),tc_fun(U_9109,tc_HOL_Obool),U_9107),hAPP(c_COMBC(U_9109,tc_fun(U_9109,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9109))),U_9111)),U_9113))
        | ~ hBOOL(hAPP(hAPP(c_member(U_9109),U_9113),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9107,tc_fun(U_9109,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9107,tc_HOL_Obool))),U_9111))) )
    & ! [U_9112,U_9110,U_9108,U_9106] :
        ( hBOOL(hAPP(hAPP(c_member(U_9108),U_9112),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9106,tc_fun(U_9108,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9106,tc_HOL_Obool))),U_9110)))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9106,tc_fun(U_9108,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9106,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9108,tc_HOL_Obool),tc_fun(U_9108,tc_HOL_Obool),U_9106),hAPP(c_COMBC(U_9108,tc_fun(U_9108,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9108))),U_9110)),U_9112)) ) ),
    inference(miniscope,[status(thm)],[f_2611_2]) ).

cnf(f_2611_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9108),U_9112),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9106,tc_fun(U_9108,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9106,tc_HOL_Obool))),U_9110)))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9106,tc_fun(U_9108,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9106,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9108,tc_HOL_Obool),tc_fun(U_9108,tc_HOL_Obool),U_9106),hAPP(c_COMBC(U_9108,tc_fun(U_9108,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9108))),U_9110)),U_9112)) ),
    inference(clausify,[status(thm)],[f_2611_3]) ).

cnf(f_2611_5,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9107,tc_fun(U_9109,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9107,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9109,tc_HOL_Obool),tc_fun(U_9109,tc_HOL_Obool),U_9107),hAPP(c_COMBC(U_9109,tc_fun(U_9109,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9109))),U_9111)),U_9113))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9109),U_9113),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9107,tc_fun(U_9109,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_9107,tc_HOL_Obool))),U_9111))) ),
    inference(clausify,[status(thm)],[f_2611_3]) ).

fof(f_2612_1,plain,
    ! [V_f_2,T_d,V_g_2,T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),hAPP(c_Set_Oimage(T_c,T_d,hAPP(hAPP(c_COMBB(T_b,T_d,T_c),V_f_2),V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_c,T_b,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) ),
    inference(fof_nnf,[status(thm)],[fact_finite__range__imageI]) ).

fof(f_2612_2,plain,
    ! [U_9118,U_9117,U_9116,U_9115,U_9114] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9117),hAPP(c_Set_Oimage(U_9115,U_9117,hAPP(hAPP(c_COMBB(U_9114,U_9117,U_9115),U_9118),U_9116)),c_Orderings_Otop__class_Otop(tc_fun(U_9115,tc_HOL_Obool)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9114),hAPP(c_Set_Oimage(U_9115,U_9114,U_9116),c_Orderings_Otop__class_Otop(tc_fun(U_9115,tc_HOL_Obool))))) ),
    inference(variable_rename,[status(thm)],[f_2612_1]) ).

cnf(f_2612_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9117),hAPP(c_Set_Oimage(U_9115,U_9117,hAPP(hAPP(c_COMBB(U_9114,U_9117,U_9115),U_9118),U_9116)),c_Orderings_Otop__class_Otop(tc_fun(U_9115,tc_HOL_Obool)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9114),hAPP(c_Set_Oimage(U_9115,U_9114,U_9116),c_Orderings_Otop__class_Otop(tc_fun(U_9115,tc_HOL_Obool))))) ),
    inference(clausify,[status(thm)],[f_2612_2]) ).

fof(f_2613_1,plain,
    ! [V_A_2,T_c,V_I_2,V_k_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_A_2,V_k_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_k_2),V_I_2)) ),
    inference(fof_nnf,[status(thm)],[fact_UN__absorb]) ).

fof(f_2613_2,plain,
    ! [U_9123,U_9122,U_9121,U_9120,U_9119] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9122,tc_HOL_Obool)),hAPP(U_9123,U_9120)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9119,tc_fun(U_9122,tc_HOL_Obool)),U_9121),U_9123)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9119,tc_fun(U_9122,tc_HOL_Obool)),U_9121),U_9123)
      | ~ hBOOL(hAPP(hAPP(c_member(U_9119),U_9120),U_9121)) ),
    inference(variable_rename,[status(thm)],[f_2613_1]) ).

cnf(f_2613_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9122,tc_HOL_Obool)),hAPP(U_9123,U_9120)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9119,tc_fun(U_9122,tc_HOL_Obool)),U_9121),U_9123)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9119,tc_fun(U_9122,tc_HOL_Obool)),U_9121),U_9123)
    | ~ hBOOL(hAPP(hAPP(c_member(U_9119),U_9120),U_9121)) ),
    inference(clausify,[status(thm)],[f_2613_2]) ).

fof(f_2614_1,plain,
    ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2))
        | V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))
        | V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_INT__simps_I2_J]) ).

fof(f_2614_2,plain,
    ! [U_9128,U_9127,U_9126,U_9125,U_9124] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9125,tc_fun(U_9126,tc_HOL_Obool)),U_9124),hAPP(hAPP(c_COMBB(tc_fun(U_9126,tc_HOL_Obool),tc_fun(U_9126,tc_HOL_Obool),U_9125),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9126,tc_HOL_Obool)),U_9127)),U_9128)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9126,tc_HOL_Obool)),U_9127),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9125,tc_fun(U_9126,tc_HOL_Obool)),U_9124),U_9128))
        | U_9124 = c_Orderings_Obot__class_Obot(tc_fun(U_9125,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9125,tc_fun(U_9126,tc_HOL_Obool)),U_9124),hAPP(hAPP(c_COMBB(tc_fun(U_9126,tc_HOL_Obool),tc_fun(U_9126,tc_HOL_Obool),U_9125),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9126,tc_HOL_Obool)),U_9127)),U_9128)) = c_Orderings_Otop__class_Otop(tc_fun(U_9126,tc_HOL_Obool))
        | U_9124 != c_Orderings_Obot__class_Obot(tc_fun(U_9125,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2614_1]) ).

fof(f_2614_3,plain,
    ( ! [U_9138,U_9136,U_9134,U_9132,U_9130] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9132,tc_fun(U_9134,tc_HOL_Obool)),U_9130),hAPP(hAPP(c_COMBB(tc_fun(U_9134,tc_HOL_Obool),tc_fun(U_9134,tc_HOL_Obool),U_9132),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9134,tc_HOL_Obool)),U_9136)),U_9138)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9134,tc_HOL_Obool)),U_9136),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9132,tc_fun(U_9134,tc_HOL_Obool)),U_9130),U_9138))
        | U_9130 = c_Orderings_Obot__class_Obot(tc_fun(U_9132,tc_HOL_Obool)) )
    & ! [U_9137,U_9135,U_9133,U_9131,U_9129] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9131,tc_fun(U_9133,tc_HOL_Obool)),U_9129),hAPP(hAPP(c_COMBB(tc_fun(U_9133,tc_HOL_Obool),tc_fun(U_9133,tc_HOL_Obool),U_9131),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9133,tc_HOL_Obool)),U_9135)),U_9137)) = c_Orderings_Otop__class_Otop(tc_fun(U_9133,tc_HOL_Obool))
        | U_9129 != c_Orderings_Obot__class_Obot(tc_fun(U_9131,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2614_2]) ).

cnf(f_2614_4,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9131,tc_fun(U_9133,tc_HOL_Obool)),U_9129),hAPP(hAPP(c_COMBB(tc_fun(U_9133,tc_HOL_Obool),tc_fun(U_9133,tc_HOL_Obool),U_9131),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9133,tc_HOL_Obool)),U_9135)),U_9137)) = c_Orderings_Otop__class_Otop(tc_fun(U_9133,tc_HOL_Obool))
    | U_9129 != c_Orderings_Obot__class_Obot(tc_fun(U_9131,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2614_3]) ).

cnf(f_2614_5,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9132,tc_fun(U_9134,tc_HOL_Obool)),U_9130),hAPP(hAPP(c_COMBB(tc_fun(U_9134,tc_HOL_Obool),tc_fun(U_9134,tc_HOL_Obool),U_9132),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9134,tc_HOL_Obool)),U_9136)),U_9138)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9134,tc_HOL_Obool)),U_9136),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9132,tc_fun(U_9134,tc_HOL_Obool)),U_9130),U_9138))
    | U_9130 = c_Orderings_Obot__class_Obot(tc_fun(U_9132,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2614_3]) ).

fof(f_2615_1,plain,
    ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2)
        | V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))
        | V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_INT__simps_I1_J]) ).

fof(f_2615_2,plain,
    ! [U_9143,U_9142,U_9141,U_9140,U_9139] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9140,tc_fun(U_9141,tc_HOL_Obool)),U_9139),hAPP(hAPP(c_COMBC(U_9140,tc_fun(U_9141,tc_HOL_Obool),tc_fun(U_9141,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9141,tc_HOL_Obool),tc_fun(tc_fun(U_9141,tc_HOL_Obool),tc_fun(U_9141,tc_HOL_Obool)),U_9140),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9141,tc_HOL_Obool))),U_9142)),U_9143)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9141,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9140,tc_fun(U_9141,tc_HOL_Obool)),U_9139),U_9142)),U_9143)
        | U_9139 = c_Orderings_Obot__class_Obot(tc_fun(U_9140,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9140,tc_fun(U_9141,tc_HOL_Obool)),U_9139),hAPP(hAPP(c_COMBC(U_9140,tc_fun(U_9141,tc_HOL_Obool),tc_fun(U_9141,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9141,tc_HOL_Obool),tc_fun(tc_fun(U_9141,tc_HOL_Obool),tc_fun(U_9141,tc_HOL_Obool)),U_9140),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9141,tc_HOL_Obool))),U_9142)),U_9143)) = c_Orderings_Otop__class_Otop(tc_fun(U_9141,tc_HOL_Obool))
        | U_9139 != c_Orderings_Obot__class_Obot(tc_fun(U_9140,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2615_1]) ).

fof(f_2615_3,plain,
    ( ! [U_9153,U_9151,U_9149,U_9147,U_9145] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9147,tc_fun(U_9149,tc_HOL_Obool)),U_9145),hAPP(hAPP(c_COMBC(U_9147,tc_fun(U_9149,tc_HOL_Obool),tc_fun(U_9149,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9149,tc_HOL_Obool),tc_fun(tc_fun(U_9149,tc_HOL_Obool),tc_fun(U_9149,tc_HOL_Obool)),U_9147),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9149,tc_HOL_Obool))),U_9151)),U_9153)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9149,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9147,tc_fun(U_9149,tc_HOL_Obool)),U_9145),U_9151)),U_9153)
        | U_9145 = c_Orderings_Obot__class_Obot(tc_fun(U_9147,tc_HOL_Obool)) )
    & ! [U_9152,U_9150,U_9148,U_9146,U_9144] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9146,tc_fun(U_9148,tc_HOL_Obool)),U_9144),hAPP(hAPP(c_COMBC(U_9146,tc_fun(U_9148,tc_HOL_Obool),tc_fun(U_9148,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9148,tc_HOL_Obool),tc_fun(tc_fun(U_9148,tc_HOL_Obool),tc_fun(U_9148,tc_HOL_Obool)),U_9146),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9148,tc_HOL_Obool))),U_9150)),U_9152)) = c_Orderings_Otop__class_Otop(tc_fun(U_9148,tc_HOL_Obool))
        | U_9144 != c_Orderings_Obot__class_Obot(tc_fun(U_9146,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2615_2]) ).

cnf(f_2615_4,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9146,tc_fun(U_9148,tc_HOL_Obool)),U_9144),hAPP(hAPP(c_COMBC(U_9146,tc_fun(U_9148,tc_HOL_Obool),tc_fun(U_9148,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9148,tc_HOL_Obool),tc_fun(tc_fun(U_9148,tc_HOL_Obool),tc_fun(U_9148,tc_HOL_Obool)),U_9146),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9148,tc_HOL_Obool))),U_9150)),U_9152)) = c_Orderings_Otop__class_Otop(tc_fun(U_9148,tc_HOL_Obool))
    | U_9144 != c_Orderings_Obot__class_Obot(tc_fun(U_9146,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2615_3]) ).

cnf(f_2615_5,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9147,tc_fun(U_9149,tc_HOL_Obool)),U_9145),hAPP(hAPP(c_COMBC(U_9147,tc_fun(U_9149,tc_HOL_Obool),tc_fun(U_9149,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9149,tc_HOL_Obool),tc_fun(tc_fun(U_9149,tc_HOL_Obool),tc_fun(U_9149,tc_HOL_Obool)),U_9147),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9149,tc_HOL_Obool))),U_9151)),U_9153)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9149,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9147,tc_fun(U_9149,tc_HOL_Obool)),U_9145),U_9151)),U_9153)
    | U_9145 = c_Orderings_Obot__class_Obot(tc_fun(U_9147,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2615_3]) ).

fof(f_2616_1,plain,
    ! [V_B_2,V_a_2,T_c,T_b,V_C_2] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2))
        | V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
        | V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_UN__simps_I1_J]) ).

fof(f_2616_2,plain,
    ! [U_9158,U_9157,U_9156,U_9155,U_9154] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9155,tc_fun(U_9156,tc_HOL_Obool)),U_9154),hAPP(hAPP(c_COMBB(tc_fun(U_9156,tc_HOL_Obool),tc_fun(U_9156,tc_HOL_Obool),U_9155),hAPP(c_Set_Oinsert(U_9156),U_9157)),U_9158)) = hAPP(hAPP(c_Set_Oinsert(U_9156),U_9157),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9155,tc_fun(U_9156,tc_HOL_Obool)),U_9154),U_9158))
        | U_9154 = c_Orderings_Obot__class_Obot(tc_fun(U_9155,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9155,tc_fun(U_9156,tc_HOL_Obool)),U_9154),hAPP(hAPP(c_COMBB(tc_fun(U_9156,tc_HOL_Obool),tc_fun(U_9156,tc_HOL_Obool),U_9155),hAPP(c_Set_Oinsert(U_9156),U_9157)),U_9158)) = c_Orderings_Obot__class_Obot(tc_fun(U_9156,tc_HOL_Obool))
        | U_9154 != c_Orderings_Obot__class_Obot(tc_fun(U_9155,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2616_1]) ).

fof(f_2616_3,plain,
    ( ! [U_9168,U_9166,U_9164,U_9162,U_9160] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9162,tc_fun(U_9164,tc_HOL_Obool)),U_9160),hAPP(hAPP(c_COMBB(tc_fun(U_9164,tc_HOL_Obool),tc_fun(U_9164,tc_HOL_Obool),U_9162),hAPP(c_Set_Oinsert(U_9164),U_9166)),U_9168)) = hAPP(hAPP(c_Set_Oinsert(U_9164),U_9166),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9162,tc_fun(U_9164,tc_HOL_Obool)),U_9160),U_9168))
        | U_9160 = c_Orderings_Obot__class_Obot(tc_fun(U_9162,tc_HOL_Obool)) )
    & ! [U_9167,U_9165,U_9163,U_9161,U_9159] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9161,tc_fun(U_9163,tc_HOL_Obool)),U_9159),hAPP(hAPP(c_COMBB(tc_fun(U_9163,tc_HOL_Obool),tc_fun(U_9163,tc_HOL_Obool),U_9161),hAPP(c_Set_Oinsert(U_9163),U_9165)),U_9167)) = c_Orderings_Obot__class_Obot(tc_fun(U_9163,tc_HOL_Obool))
        | U_9159 != c_Orderings_Obot__class_Obot(tc_fun(U_9161,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2616_2]) ).

cnf(f_2616_4,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9161,tc_fun(U_9163,tc_HOL_Obool)),U_9159),hAPP(hAPP(c_COMBB(tc_fun(U_9163,tc_HOL_Obool),tc_fun(U_9163,tc_HOL_Obool),U_9161),hAPP(c_Set_Oinsert(U_9163),U_9165)),U_9167)) = c_Orderings_Obot__class_Obot(tc_fun(U_9163,tc_HOL_Obool))
    | U_9159 != c_Orderings_Obot__class_Obot(tc_fun(U_9161,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2616_3]) ).

cnf(f_2616_5,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9162,tc_fun(U_9164,tc_HOL_Obool)),U_9160),hAPP(hAPP(c_COMBB(tc_fun(U_9164,tc_HOL_Obool),tc_fun(U_9164,tc_HOL_Obool),U_9162),hAPP(c_Set_Oinsert(U_9164),U_9166)),U_9168)) = hAPP(hAPP(c_Set_Oinsert(U_9164),U_9166),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9162,tc_fun(U_9164,tc_HOL_Obool)),U_9160),U_9168))
    | U_9160 = c_Orderings_Obot__class_Obot(tc_fun(U_9162,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2616_3]) ).

fof(f_2617_1,plain,
    ! [V_A_2,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_A_2,
    inference(fof_nnf,[status(thm)],[fact_UN__singleton]) ).

fof(f_2617_2,plain,
    ! [U_9170,U_9169] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9169,tc_fun(U_9169,tc_HOL_Obool)),U_9170),hAPP(hAPP(c_COMBC(U_9169,tc_fun(U_9169,tc_HOL_Obool),tc_fun(U_9169,tc_HOL_Obool)),c_Set_Oinsert(U_9169)),c_Orderings_Obot__class_Obot(tc_fun(U_9169,tc_HOL_Obool)))) = U_9170,
    inference(variable_rename,[status(thm)],[f_2617_1]) ).

cnf(f_2617_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9169,tc_fun(U_9169,tc_HOL_Obool)),U_9170),hAPP(hAPP(c_COMBC(U_9169,tc_fun(U_9169,tc_HOL_Obool),tc_fun(U_9169,tc_HOL_Obool)),c_Set_Oinsert(U_9169)),c_Orderings_Obot__class_Obot(tc_fun(U_9169,tc_HOL_Obool)))) = U_9170,
    inference(clausify,[status(thm)],[f_2617_2]) ).

fof(f_2618_1,plain,
    ! [V_B_2,V_a_2,T_c,T_b,V_C_2] :
      ( ( hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2))
        | V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))
        | V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I1_J]) ).

fof(f_2618_2,plain,
    ! [U_9175,U_9174,U_9173,U_9172,U_9171] :
      ( ( hAPP(hAPP(c_Set_Oinsert(U_9173),U_9174),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9172,tc_fun(U_9173,tc_HOL_Obool)),U_9171),U_9175)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9172,tc_fun(U_9173,tc_HOL_Obool)),U_9171),hAPP(hAPP(c_COMBB(tc_fun(U_9173,tc_HOL_Obool),tc_fun(U_9173,tc_HOL_Obool),U_9172),hAPP(c_Set_Oinsert(U_9173),U_9174)),U_9175))
        | U_9171 = c_Orderings_Obot__class_Obot(tc_fun(U_9172,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Set_Oinsert(U_9173),U_9174),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9172,tc_fun(U_9173,tc_HOL_Obool)),U_9171),U_9175)) = hAPP(hAPP(c_Set_Oinsert(U_9173),U_9174),c_Orderings_Obot__class_Obot(tc_fun(U_9173,tc_HOL_Obool)))
        | U_9171 != c_Orderings_Obot__class_Obot(tc_fun(U_9172,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2618_1]) ).

fof(f_2618_3,plain,
    ( ! [U_9185,U_9183,U_9181,U_9179,U_9177] :
        ( hAPP(hAPP(c_Set_Oinsert(U_9181),U_9183),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9179,tc_fun(U_9181,tc_HOL_Obool)),U_9177),U_9185)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9179,tc_fun(U_9181,tc_HOL_Obool)),U_9177),hAPP(hAPP(c_COMBB(tc_fun(U_9181,tc_HOL_Obool),tc_fun(U_9181,tc_HOL_Obool),U_9179),hAPP(c_Set_Oinsert(U_9181),U_9183)),U_9185))
        | U_9177 = c_Orderings_Obot__class_Obot(tc_fun(U_9179,tc_HOL_Obool)) )
    & ! [U_9184,U_9182,U_9180,U_9178,U_9176] :
        ( hAPP(hAPP(c_Set_Oinsert(U_9180),U_9182),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9178,tc_fun(U_9180,tc_HOL_Obool)),U_9176),U_9184)) = hAPP(hAPP(c_Set_Oinsert(U_9180),U_9182),c_Orderings_Obot__class_Obot(tc_fun(U_9180,tc_HOL_Obool)))
        | U_9176 != c_Orderings_Obot__class_Obot(tc_fun(U_9178,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2618_2]) ).

cnf(f_2618_4,plain,
    ( hAPP(hAPP(c_Set_Oinsert(U_9180),U_9182),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9178,tc_fun(U_9180,tc_HOL_Obool)),U_9176),U_9184)) = hAPP(hAPP(c_Set_Oinsert(U_9180),U_9182),c_Orderings_Obot__class_Obot(tc_fun(U_9180,tc_HOL_Obool)))
    | U_9176 != c_Orderings_Obot__class_Obot(tc_fun(U_9178,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2618_3]) ).

cnf(f_2618_5,plain,
    ( hAPP(hAPP(c_Set_Oinsert(U_9181),U_9183),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9179,tc_fun(U_9181,tc_HOL_Obool)),U_9177),U_9185)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9179,tc_fun(U_9181,tc_HOL_Obool)),U_9177),hAPP(hAPP(c_COMBB(tc_fun(U_9181,tc_HOL_Obool),tc_fun(U_9181,tc_HOL_Obool),U_9179),hAPP(c_Set_Oinsert(U_9181),U_9183)),U_9185))
    | U_9177 = c_Orderings_Obot__class_Obot(tc_fun(U_9179,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2618_3]) ).

fof(f_2619_1,plain,
    ! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Groups_Otimes__class_Otimes(T_c)),V_g_2)),V_h_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_h_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setprod_Odistrib]) ).

fof(f_2619_2,plain,
    ! [U_9190,U_9189,U_9188,U_9187,U_9186] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9187,U_9186),hAPP(hAPP(c_COMBS(U_9187,U_9186,U_9186),hAPP(hAPP(c_COMBB(U_9186,tc_fun(U_9186,U_9186),U_9187),c_Groups_Otimes__class_Otimes(U_9186)),U_9189)),U_9190)),U_9188) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9186),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9187,U_9186),U_9189),U_9188)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9187,U_9186),U_9190),U_9188))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9187),U_9188))
      | ~ class_Groups_Ocomm__monoid__mult(U_9186) ),
    inference(variable_rename,[status(thm)],[f_2619_1]) ).

cnf(f_2619_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9187,U_9186),hAPP(hAPP(c_COMBS(U_9187,U_9186,U_9186),hAPP(hAPP(c_COMBB(U_9186,tc_fun(U_9186,U_9186),U_9187),c_Groups_Otimes__class_Otimes(U_9186)),U_9189)),U_9190)),U_9188) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9186),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9187,U_9186),U_9189),U_9188)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9187,U_9186),U_9190),U_9188))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9187),U_9188))
    | ~ class_Groups_Ocomm__monoid__mult(U_9186) ),
    inference(clausify,[status(thm)],[f_2619_2]) ).

fof(f_2620_1,plain,
    ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2))
        | V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = V_B_2
        | V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I2_J]) ).

fof(f_2620_2,plain,
    ! [U_9195,U_9194,U_9193,U_9192,U_9191] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9193,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9192,tc_fun(U_9193,tc_HOL_Obool)),U_9191),U_9194)),U_9195) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9192,tc_fun(U_9193,tc_HOL_Obool)),U_9191),hAPP(hAPP(c_COMBC(U_9192,tc_fun(U_9193,tc_HOL_Obool),tc_fun(U_9193,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9193,tc_HOL_Obool),tc_fun(tc_fun(U_9193,tc_HOL_Obool),tc_fun(U_9193,tc_HOL_Obool)),U_9192),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9193,tc_HOL_Obool))),U_9194)),U_9195))
        | U_9191 = c_Orderings_Obot__class_Obot(tc_fun(U_9192,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9193,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9192,tc_fun(U_9193,tc_HOL_Obool)),U_9191),U_9194)),U_9195) = U_9195
        | U_9191 != c_Orderings_Obot__class_Obot(tc_fun(U_9192,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2620_1]) ).

fof(f_2620_3,plain,
    ( ! [U_9205,U_9203,U_9201,U_9199,U_9197] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9201,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9199,tc_fun(U_9201,tc_HOL_Obool)),U_9197),U_9203)),U_9205) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9199,tc_fun(U_9201,tc_HOL_Obool)),U_9197),hAPP(hAPP(c_COMBC(U_9199,tc_fun(U_9201,tc_HOL_Obool),tc_fun(U_9201,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9201,tc_HOL_Obool),tc_fun(tc_fun(U_9201,tc_HOL_Obool),tc_fun(U_9201,tc_HOL_Obool)),U_9199),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9201,tc_HOL_Obool))),U_9203)),U_9205))
        | U_9197 = c_Orderings_Obot__class_Obot(tc_fun(U_9199,tc_HOL_Obool)) )
    & ! [U_9204,U_9202,U_9200,U_9198,U_9196] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9200,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9198,tc_fun(U_9200,tc_HOL_Obool)),U_9196),U_9202)),U_9204) = U_9204
        | U_9196 != c_Orderings_Obot__class_Obot(tc_fun(U_9198,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2620_2]) ).

cnf(f_2620_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9200,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9198,tc_fun(U_9200,tc_HOL_Obool)),U_9196),U_9202)),U_9204) = U_9204
    | U_9196 != c_Orderings_Obot__class_Obot(tc_fun(U_9198,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2620_3]) ).

cnf(f_2620_5,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9201,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9199,tc_fun(U_9201,tc_HOL_Obool)),U_9197),U_9203)),U_9205) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9199,tc_fun(U_9201,tc_HOL_Obool)),U_9197),hAPP(hAPP(c_COMBC(U_9199,tc_fun(U_9201,tc_HOL_Obool),tc_fun(U_9201,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9201,tc_HOL_Obool),tc_fun(tc_fun(U_9201,tc_HOL_Obool),tc_fun(U_9201,tc_HOL_Obool)),U_9199),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9201,tc_HOL_Obool))),U_9203)),U_9205))
    | U_9197 = c_Orderings_Obot__class_Obot(tc_fun(U_9199,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2620_3]) ).

fof(f_2621_1,plain,
    ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2))
        | V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2
        | V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I3_J]) ).

fof(f_2621_2,plain,
    ! [U_9210,U_9209,U_9208,U_9207,U_9206] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9208,tc_HOL_Obool)),U_9209),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9207,tc_fun(U_9208,tc_HOL_Obool)),U_9206),U_9210)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9207,tc_fun(U_9208,tc_HOL_Obool)),U_9206),hAPP(hAPP(c_COMBB(tc_fun(U_9208,tc_HOL_Obool),tc_fun(U_9208,tc_HOL_Obool),U_9207),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9208,tc_HOL_Obool)),U_9209)),U_9210))
        | U_9206 = c_Orderings_Obot__class_Obot(tc_fun(U_9207,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9208,tc_HOL_Obool)),U_9209),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9207,tc_fun(U_9208,tc_HOL_Obool)),U_9206),U_9210)) = U_9209
        | U_9206 != c_Orderings_Obot__class_Obot(tc_fun(U_9207,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2621_1]) ).

fof(f_2621_3,plain,
    ( ! [U_9220,U_9218,U_9216,U_9214,U_9212] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9216,tc_HOL_Obool)),U_9218),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9214,tc_fun(U_9216,tc_HOL_Obool)),U_9212),U_9220)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9214,tc_fun(U_9216,tc_HOL_Obool)),U_9212),hAPP(hAPP(c_COMBB(tc_fun(U_9216,tc_HOL_Obool),tc_fun(U_9216,tc_HOL_Obool),U_9214),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9216,tc_HOL_Obool)),U_9218)),U_9220))
        | U_9212 = c_Orderings_Obot__class_Obot(tc_fun(U_9214,tc_HOL_Obool)) )
    & ! [U_9219,U_9217,U_9215,U_9213,U_9211] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9215,tc_HOL_Obool)),U_9217),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9213,tc_fun(U_9215,tc_HOL_Obool)),U_9211),U_9219)) = U_9217
        | U_9211 != c_Orderings_Obot__class_Obot(tc_fun(U_9213,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2621_2]) ).

cnf(f_2621_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9215,tc_HOL_Obool)),U_9217),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9213,tc_fun(U_9215,tc_HOL_Obool)),U_9211),U_9219)) = U_9217
    | U_9211 != c_Orderings_Obot__class_Obot(tc_fun(U_9213,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2621_3]) ).

cnf(f_2621_5,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9216,tc_HOL_Obool)),U_9218),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9214,tc_fun(U_9216,tc_HOL_Obool)),U_9212),U_9220)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9214,tc_fun(U_9216,tc_HOL_Obool)),U_9212),hAPP(hAPP(c_COMBB(tc_fun(U_9216,tc_HOL_Obool),tc_fun(U_9216,tc_HOL_Obool),U_9214),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9216,tc_HOL_Obool)),U_9218)),U_9220))
    | U_9212 = c_Orderings_Obot__class_Obot(tc_fun(U_9214,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2621_3]) ).

fof(f_2622_1,plain,
    ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2)
        | V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
        | V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_UN__simps_I2_J]) ).

fof(f_2622_2,plain,
    ! [U_9225,U_9224,U_9223,U_9222,U_9221] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9222,tc_fun(U_9223,tc_HOL_Obool)),U_9221),hAPP(hAPP(c_COMBC(U_9222,tc_fun(U_9223,tc_HOL_Obool),tc_fun(U_9223,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9223,tc_HOL_Obool),tc_fun(tc_fun(U_9223,tc_HOL_Obool),tc_fun(U_9223,tc_HOL_Obool)),U_9222),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9223,tc_HOL_Obool))),U_9224)),U_9225)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9223,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9222,tc_fun(U_9223,tc_HOL_Obool)),U_9221),U_9224)),U_9225)
        | U_9221 = c_Orderings_Obot__class_Obot(tc_fun(U_9222,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9222,tc_fun(U_9223,tc_HOL_Obool)),U_9221),hAPP(hAPP(c_COMBC(U_9222,tc_fun(U_9223,tc_HOL_Obool),tc_fun(U_9223,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9223,tc_HOL_Obool),tc_fun(tc_fun(U_9223,tc_HOL_Obool),tc_fun(U_9223,tc_HOL_Obool)),U_9222),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9223,tc_HOL_Obool))),U_9224)),U_9225)) = c_Orderings_Obot__class_Obot(tc_fun(U_9223,tc_HOL_Obool))
        | U_9221 != c_Orderings_Obot__class_Obot(tc_fun(U_9222,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2622_1]) ).

fof(f_2622_3,plain,
    ( ! [U_9235,U_9233,U_9231,U_9229,U_9227] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9229,tc_fun(U_9231,tc_HOL_Obool)),U_9227),hAPP(hAPP(c_COMBC(U_9229,tc_fun(U_9231,tc_HOL_Obool),tc_fun(U_9231,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9231,tc_HOL_Obool),tc_fun(tc_fun(U_9231,tc_HOL_Obool),tc_fun(U_9231,tc_HOL_Obool)),U_9229),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9231,tc_HOL_Obool))),U_9233)),U_9235)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9231,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9229,tc_fun(U_9231,tc_HOL_Obool)),U_9227),U_9233)),U_9235)
        | U_9227 = c_Orderings_Obot__class_Obot(tc_fun(U_9229,tc_HOL_Obool)) )
    & ! [U_9234,U_9232,U_9230,U_9228,U_9226] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9228,tc_fun(U_9230,tc_HOL_Obool)),U_9226),hAPP(hAPP(c_COMBC(U_9228,tc_fun(U_9230,tc_HOL_Obool),tc_fun(U_9230,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9230,tc_HOL_Obool),tc_fun(tc_fun(U_9230,tc_HOL_Obool),tc_fun(U_9230,tc_HOL_Obool)),U_9228),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9230,tc_HOL_Obool))),U_9232)),U_9234)) = c_Orderings_Obot__class_Obot(tc_fun(U_9230,tc_HOL_Obool))
        | U_9226 != c_Orderings_Obot__class_Obot(tc_fun(U_9228,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2622_2]) ).

cnf(f_2622_4,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9228,tc_fun(U_9230,tc_HOL_Obool)),U_9226),hAPP(hAPP(c_COMBC(U_9228,tc_fun(U_9230,tc_HOL_Obool),tc_fun(U_9230,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9230,tc_HOL_Obool),tc_fun(tc_fun(U_9230,tc_HOL_Obool),tc_fun(U_9230,tc_HOL_Obool)),U_9228),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9230,tc_HOL_Obool))),U_9232)),U_9234)) = c_Orderings_Obot__class_Obot(tc_fun(U_9230,tc_HOL_Obool))
    | U_9226 != c_Orderings_Obot__class_Obot(tc_fun(U_9228,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2622_3]) ).

cnf(f_2622_5,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9229,tc_fun(U_9231,tc_HOL_Obool)),U_9227),hAPP(hAPP(c_COMBC(U_9229,tc_fun(U_9231,tc_HOL_Obool),tc_fun(U_9231,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9231,tc_HOL_Obool),tc_fun(tc_fun(U_9231,tc_HOL_Obool),tc_fun(U_9231,tc_HOL_Obool)),U_9229),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9231,tc_HOL_Obool))),U_9233)),U_9235)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9231,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9229,tc_fun(U_9231,tc_HOL_Obool)),U_9227),U_9233)),U_9235)
    | U_9227 = c_Orderings_Obot__class_Obot(tc_fun(U_9229,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2622_3]) ).

fof(f_2623_1,plain,
    ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2))
        | V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
        | V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_UN__simps_I3_J]) ).

fof(f_2623_2,plain,
    ! [U_9240,U_9239,U_9238,U_9237,U_9236] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9237,tc_fun(U_9238,tc_HOL_Obool)),U_9236),hAPP(hAPP(c_COMBB(tc_fun(U_9238,tc_HOL_Obool),tc_fun(U_9238,tc_HOL_Obool),U_9237),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9238,tc_HOL_Obool)),U_9239)),U_9240)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9238,tc_HOL_Obool)),U_9239),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9237,tc_fun(U_9238,tc_HOL_Obool)),U_9236),U_9240))
        | U_9236 = c_Orderings_Obot__class_Obot(tc_fun(U_9237,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9237,tc_fun(U_9238,tc_HOL_Obool)),U_9236),hAPP(hAPP(c_COMBB(tc_fun(U_9238,tc_HOL_Obool),tc_fun(U_9238,tc_HOL_Obool),U_9237),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9238,tc_HOL_Obool)),U_9239)),U_9240)) = c_Orderings_Obot__class_Obot(tc_fun(U_9238,tc_HOL_Obool))
        | U_9236 != c_Orderings_Obot__class_Obot(tc_fun(U_9237,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2623_1]) ).

fof(f_2623_3,plain,
    ( ! [U_9250,U_9248,U_9246,U_9244,U_9242] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9244,tc_fun(U_9246,tc_HOL_Obool)),U_9242),hAPP(hAPP(c_COMBB(tc_fun(U_9246,tc_HOL_Obool),tc_fun(U_9246,tc_HOL_Obool),U_9244),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9246,tc_HOL_Obool)),U_9248)),U_9250)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9246,tc_HOL_Obool)),U_9248),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9244,tc_fun(U_9246,tc_HOL_Obool)),U_9242),U_9250))
        | U_9242 = c_Orderings_Obot__class_Obot(tc_fun(U_9244,tc_HOL_Obool)) )
    & ! [U_9249,U_9247,U_9245,U_9243,U_9241] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9243,tc_fun(U_9245,tc_HOL_Obool)),U_9241),hAPP(hAPP(c_COMBB(tc_fun(U_9245,tc_HOL_Obool),tc_fun(U_9245,tc_HOL_Obool),U_9243),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9245,tc_HOL_Obool)),U_9247)),U_9249)) = c_Orderings_Obot__class_Obot(tc_fun(U_9245,tc_HOL_Obool))
        | U_9241 != c_Orderings_Obot__class_Obot(tc_fun(U_9243,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2623_2]) ).

cnf(f_2623_4,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9243,tc_fun(U_9245,tc_HOL_Obool)),U_9241),hAPP(hAPP(c_COMBB(tc_fun(U_9245,tc_HOL_Obool),tc_fun(U_9245,tc_HOL_Obool),U_9243),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9245,tc_HOL_Obool)),U_9247)),U_9249)) = c_Orderings_Obot__class_Obot(tc_fun(U_9245,tc_HOL_Obool))
    | U_9241 != c_Orderings_Obot__class_Obot(tc_fun(U_9243,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2623_3]) ).

cnf(f_2623_5,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9244,tc_fun(U_9246,tc_HOL_Obool)),U_9242),hAPP(hAPP(c_COMBB(tc_fun(U_9246,tc_HOL_Obool),tc_fun(U_9246,tc_HOL_Obool),U_9244),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9246,tc_HOL_Obool)),U_9248)),U_9250)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9246,tc_HOL_Obool)),U_9248),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9244,tc_fun(U_9246,tc_HOL_Obool)),U_9242),U_9250))
    | U_9242 = c_Orderings_Obot__class_Obot(tc_fun(U_9244,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2623_3]) ).

fof(f_2624_1,plain,
    ! [V_B_2,V_A_2,V_a_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_B_2,V_a_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_UN__insert]) ).

fof(f_2624_2,plain,
    ! [U_9255,U_9254,U_9253,U_9252,U_9251] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9251,tc_fun(U_9252,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_9251),U_9253),U_9254)),U_9255) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9252,tc_HOL_Obool)),hAPP(U_9255,U_9253)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9251,tc_fun(U_9252,tc_HOL_Obool)),U_9254),U_9255)),
    inference(variable_rename,[status(thm)],[f_2624_1]) ).

cnf(f_2624_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9251,tc_fun(U_9252,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_9251),U_9253),U_9254)),U_9255) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9252,tc_HOL_Obool)),hAPP(U_9255,U_9253)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9251,tc_fun(U_9252,tc_HOL_Obool)),U_9254),U_9255)),
    inference(clausify,[status(thm)],[f_2624_2]) ).

fof(f_2625_1,plain,
    ! [V_B_2,V_C_2,T_c,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Set_Oinsert(T_b),V_a_2)),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I5_J]) ).

fof(f_2625_2,plain,
    ! [U_9260,U_9259,U_9258,U_9257,U_9256] : hAPP(hAPP(c_Set_Oinsert(U_9256),U_9257),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9258,tc_fun(U_9256,tc_HOL_Obool)),U_9259),U_9260)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9258,tc_fun(U_9256,tc_HOL_Obool)),U_9259),hAPP(hAPP(c_COMBB(tc_fun(U_9256,tc_HOL_Obool),tc_fun(U_9256,tc_HOL_Obool),U_9258),hAPP(c_Set_Oinsert(U_9256),U_9257)),U_9260)),
    inference(variable_rename,[status(thm)],[f_2625_1]) ).

cnf(f_2625_3,plain,
    hAPP(hAPP(c_Set_Oinsert(U_9256),U_9257),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9258,tc_fun(U_9256,tc_HOL_Obool)),U_9259),U_9260)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9258,tc_fun(U_9256,tc_HOL_Obool)),U_9259),hAPP(hAPP(c_COMBB(tc_fun(U_9256,tc_HOL_Obool),tc_fun(U_9256,tc_HOL_Obool),U_9258),hAPP(c_Set_Oinsert(U_9256),U_9257)),U_9260)),
    inference(clausify,[status(thm)],[f_2625_2]) ).

fof(f_2626_1,plain,
    ! [V_B_2,V_a_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Set_Oinsert(T_b),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_INT__simps_I5_J]) ).

fof(f_2626_2,plain,
    ! [U_9265,U_9264,U_9263,U_9262,U_9261] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9261,tc_fun(U_9262,tc_HOL_Obool)),U_9263),hAPP(hAPP(c_COMBB(tc_fun(U_9262,tc_HOL_Obool),tc_fun(U_9262,tc_HOL_Obool),U_9261),hAPP(c_Set_Oinsert(U_9262),U_9264)),U_9265)) = hAPP(hAPP(c_Set_Oinsert(U_9262),U_9264),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9261,tc_fun(U_9262,tc_HOL_Obool)),U_9263),U_9265)),
    inference(variable_rename,[status(thm)],[f_2626_1]) ).

cnf(f_2626_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9261,tc_fun(U_9262,tc_HOL_Obool)),U_9263),hAPP(hAPP(c_COMBB(tc_fun(U_9262,tc_HOL_Obool),tc_fun(U_9262,tc_HOL_Obool),U_9261),hAPP(c_Set_Oinsert(U_9262),U_9264)),U_9265)) = hAPP(hAPP(c_Set_Oinsert(U_9262),U_9264),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9261,tc_fun(U_9262,tc_HOL_Obool)),U_9263),U_9265)),
    inference(clausify,[status(thm)],[f_2626_2]) ).

fof(f_2627_1,plain,
    ! [V_x_2,T_c,T_b] :
      ( hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b)
      | ~ class_Orderings_Obot(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_bot__fun__def]) ).

fof(f_2627_2,plain,
    ! [U_9268,U_9267,U_9266] :
      ( hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_9267,U_9266)),U_9268) = c_Orderings_Obot__class_Obot(U_9266)
      | ~ class_Orderings_Obot(U_9266) ),
    inference(variable_rename,[status(thm)],[f_2627_1]) ).

cnf(f_2627_3,plain,
    ( hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_9267,U_9266)),U_9268) = c_Orderings_Obot__class_Obot(U_9266)
    | ~ class_Orderings_Obot(U_9266) ),
    inference(clausify,[status(thm)],[f_2627_2]) ).

fof(f_2628_1,plain,
    ! [V_M_2,T_b,V_A_2,T_c] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),hAPP(c_COMBK(T_c,T_b),V_M_2)) = V_M_2
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_SUP__const]) ).

fof(f_2628_2,plain,
    ! [U_9272,U_9271,U_9270,U_9269] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9271,U_9269),U_9270),hAPP(c_COMBK(U_9269,U_9271),U_9272)) = U_9272
      | U_9270 = c_Orderings_Obot__class_Obot(tc_fun(U_9271,tc_HOL_Obool))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_9269) ),
    inference(variable_rename,[status(thm)],[f_2628_1]) ).

cnf(f_2628_3,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9271,U_9269),U_9270),hAPP(c_COMBK(U_9269,U_9271),U_9272)) = U_9272
    | U_9270 = c_Orderings_Obot__class_Obot(tc_fun(U_9271,tc_HOL_Obool))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_9269) ),
    inference(clausify,[status(thm)],[f_2628_2]) ).

fof(f_2629_1,plain,
    ! [V_B_2,V_A_2,T_c,T_b] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)
        | ? [B_x] :
            ( hAPP(V_B_2,B_x) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) )
      & ( ! [B_x] :
            ( hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
        | c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_UNION__empty__conv_I1_J]) ).

fof(f_2629_2,plain,
    ! [U_9278,U_9277,U_9276,U_9275] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(U_9275,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9276,tc_fun(U_9275,tc_HOL_Obool)),U_9277),U_9278)
        | ? [U_9274] :
            ( hAPP(U_9278,U_9274) != c_Orderings_Obot__class_Obot(tc_fun(U_9275,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(U_9276),U_9274),U_9277)) ) )
      & ( ! [U_9273] :
            ( hAPP(U_9278,U_9273) = c_Orderings_Obot__class_Obot(tc_fun(U_9275,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_9276),U_9273),U_9277)) )
        | c_Orderings_Obot__class_Obot(tc_fun(U_9275,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9276,tc_fun(U_9275,tc_HOL_Obool)),U_9277),U_9278) ) ),
    inference(variable_rename,[status(thm)],[f_2629_1]) ).

fof(f_2629_3,plain,
    ( ! [U_9286,U_9284,U_9282,U_9280] :
        ( c_Orderings_Obot__class_Obot(tc_fun(U_9280,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9282,tc_fun(U_9280,tc_HOL_Obool)),U_9284),U_9286)
        | ? [U_9274] :
            ( hAPP(U_9286,U_9274) != c_Orderings_Obot__class_Obot(tc_fun(U_9280,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(U_9282),U_9274),U_9284)) ) )
    & ! [U_9285,U_9283,U_9281,U_9279] :
        ( ! [U_9273] :
            ( hAPP(U_9285,U_9273) = c_Orderings_Obot__class_Obot(tc_fun(U_9279,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_9281),U_9273),U_9283)) )
        | c_Orderings_Obot__class_Obot(tc_fun(U_9279,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9281,tc_fun(U_9279,tc_HOL_Obool)),U_9283),U_9285) ) ),
    inference(miniscope,[status(thm)],[f_2629_2]) ).

fof(f_2629_4,plain,
    ( ! [U_9286,U_9284,U_9282,U_9280] :
        ( c_Orderings_Obot__class_Obot(tc_fun(U_9280,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9282,tc_fun(U_9280,tc_HOL_Obool)),U_9284),U_9286)
        | ( hAPP(U_9286,sK233(U_9286,U_9284,U_9282,U_9280)) != c_Orderings_Obot__class_Obot(tc_fun(U_9280,tc_HOL_Obool))
          & hBOOL(hAPP(hAPP(c_member(U_9282),sK233(U_9286,U_9284,U_9282,U_9280)),U_9284)) ) )
    & ! [U_9285,U_9283,U_9281,U_9279] :
        ( ! [U_9273] :
            ( hAPP(U_9285,U_9273) = c_Orderings_Obot__class_Obot(tc_fun(U_9279,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_9281),U_9273),U_9283)) )
        | c_Orderings_Obot__class_Obot(tc_fun(U_9279,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9281,tc_fun(U_9279,tc_HOL_Obool)),U_9283),U_9285) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK233]),skolemize(U_9274,sK233(U_9286,U_9284,U_9282,U_9280))],[f_2629_3]) ).

cnf(f_2629_5,plain,
    ( hAPP(U_9285,U_9273) = c_Orderings_Obot__class_Obot(tc_fun(U_9279,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9281),U_9273),U_9283))
    | c_Orderings_Obot__class_Obot(tc_fun(U_9279,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9281,tc_fun(U_9279,tc_HOL_Obool)),U_9283),U_9285) ),
    inference(clausify,[status(thm)],[f_2629_4]) ).

cnf(f_2629_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9282),sK233(U_9286,U_9284,U_9282,U_9280)),U_9284))
    | c_Orderings_Obot__class_Obot(tc_fun(U_9280,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9282,tc_fun(U_9280,tc_HOL_Obool)),U_9284),U_9286) ),
    inference(clausify,[status(thm)],[f_2629_4]) ).

cnf(f_2629_7,plain,
    ( hAPP(U_9286,sK233(U_9286,U_9284,U_9282,U_9280)) != c_Orderings_Obot__class_Obot(tc_fun(U_9280,tc_HOL_Obool))
    | c_Orderings_Obot__class_Obot(tc_fun(U_9280,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9282,tc_fun(U_9280,tc_HOL_Obool)),U_9284),U_9286) ),
    inference(clausify,[status(thm)],[f_2629_4]) ).

fof(f_2630_1,plain,
    ! [V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_UN__empty2]) ).

fof(f_2630_2,plain,
    ! [U_9289,U_9288,U_9287] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9287,tc_fun(U_9288,tc_HOL_Obool)),U_9289),hAPP(c_COMBK(tc_fun(U_9288,tc_HOL_Obool),U_9287),c_Orderings_Obot__class_Obot(tc_fun(U_9288,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9288,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2630_1]) ).

cnf(f_2630_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9287,tc_fun(U_9288,tc_HOL_Obool)),U_9289),hAPP(c_COMBK(tc_fun(U_9288,tc_HOL_Obool),U_9287),c_Orderings_Obot__class_Obot(tc_fun(U_9288,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9288,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2630_2]) ).

fof(f_2631_1,plain,
    ! [V_c_2,T_c,T_b,V_A_2] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_c_2)) = V_c_2
        | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_c_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
        | V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_UN__constant]) ).

fof(f_2631_2,plain,
    ! [U_9293,U_9292,U_9291,U_9290] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9291,tc_fun(U_9292,tc_HOL_Obool)),U_9290),hAPP(c_COMBK(tc_fun(U_9292,tc_HOL_Obool),U_9291),U_9293)) = U_9293
        | U_9290 = c_Orderings_Obot__class_Obot(tc_fun(U_9291,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9291,tc_fun(U_9292,tc_HOL_Obool)),U_9290),hAPP(c_COMBK(tc_fun(U_9292,tc_HOL_Obool),U_9291),U_9293)) = c_Orderings_Obot__class_Obot(tc_fun(U_9292,tc_HOL_Obool))
        | U_9290 != c_Orderings_Obot__class_Obot(tc_fun(U_9291,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2631_1]) ).

fof(f_2631_3,plain,
    ( ! [U_9301,U_9299,U_9297,U_9295] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9297,tc_fun(U_9299,tc_HOL_Obool)),U_9295),hAPP(c_COMBK(tc_fun(U_9299,tc_HOL_Obool),U_9297),U_9301)) = U_9301
        | U_9295 = c_Orderings_Obot__class_Obot(tc_fun(U_9297,tc_HOL_Obool)) )
    & ! [U_9300,U_9298,U_9296,U_9294] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9296,tc_fun(U_9298,tc_HOL_Obool)),U_9294),hAPP(c_COMBK(tc_fun(U_9298,tc_HOL_Obool),U_9296),U_9300)) = c_Orderings_Obot__class_Obot(tc_fun(U_9298,tc_HOL_Obool))
        | U_9294 != c_Orderings_Obot__class_Obot(tc_fun(U_9296,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2631_2]) ).

cnf(f_2631_4,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9296,tc_fun(U_9298,tc_HOL_Obool)),U_9294),hAPP(c_COMBK(tc_fun(U_9298,tc_HOL_Obool),U_9296),U_9300)) = c_Orderings_Obot__class_Obot(tc_fun(U_9298,tc_HOL_Obool))
    | U_9294 != c_Orderings_Obot__class_Obot(tc_fun(U_9296,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2631_3]) ).

cnf(f_2631_5,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9297,tc_fun(U_9299,tc_HOL_Obool)),U_9295),hAPP(c_COMBK(tc_fun(U_9299,tc_HOL_Obool),U_9297),U_9301)) = U_9301
    | U_9295 = c_Orderings_Obot__class_Obot(tc_fun(U_9297,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2631_3]) ).

fof(f_2632_1,plain,
    ! [V_B_2,V_A_2,T_b,T_c] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
        | ? [B_x] :
            ( hAPP(V_B_2,B_x) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) )
      & ( ! [B_x] :
            ( hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_UNION__empty__conv_I2_J]) ).

fof(f_2632_2,plain,
    ! [U_9307,U_9306,U_9305,U_9304] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9304,tc_fun(U_9305,tc_HOL_Obool)),U_9306),U_9307) = c_Orderings_Obot__class_Obot(tc_fun(U_9305,tc_HOL_Obool))
        | ? [U_9303] :
            ( hAPP(U_9307,U_9303) != c_Orderings_Obot__class_Obot(tc_fun(U_9305,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(U_9304),U_9303),U_9306)) ) )
      & ( ! [U_9302] :
            ( hAPP(U_9307,U_9302) = c_Orderings_Obot__class_Obot(tc_fun(U_9305,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_9304),U_9302),U_9306)) )
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9304,tc_fun(U_9305,tc_HOL_Obool)),U_9306),U_9307) != c_Orderings_Obot__class_Obot(tc_fun(U_9305,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2632_1]) ).

fof(f_2632_3,plain,
    ( ! [U_9315,U_9313,U_9311,U_9309] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9309,tc_fun(U_9311,tc_HOL_Obool)),U_9313),U_9315) = c_Orderings_Obot__class_Obot(tc_fun(U_9311,tc_HOL_Obool))
        | ? [U_9303] :
            ( hAPP(U_9315,U_9303) != c_Orderings_Obot__class_Obot(tc_fun(U_9311,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(U_9309),U_9303),U_9313)) ) )
    & ! [U_9314,U_9312,U_9310,U_9308] :
        ( ! [U_9302] :
            ( hAPP(U_9314,U_9302) = c_Orderings_Obot__class_Obot(tc_fun(U_9310,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_9308),U_9302),U_9312)) )
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9308,tc_fun(U_9310,tc_HOL_Obool)),U_9312),U_9314) != c_Orderings_Obot__class_Obot(tc_fun(U_9310,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2632_2]) ).

fof(f_2632_4,plain,
    ( ! [U_9315,U_9313,U_9311,U_9309] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9309,tc_fun(U_9311,tc_HOL_Obool)),U_9313),U_9315) = c_Orderings_Obot__class_Obot(tc_fun(U_9311,tc_HOL_Obool))
        | ( hAPP(U_9315,sK234(U_9315,U_9313,U_9311,U_9309)) != c_Orderings_Obot__class_Obot(tc_fun(U_9311,tc_HOL_Obool))
          & hBOOL(hAPP(hAPP(c_member(U_9309),sK234(U_9315,U_9313,U_9311,U_9309)),U_9313)) ) )
    & ! [U_9314,U_9312,U_9310,U_9308] :
        ( ! [U_9302] :
            ( hAPP(U_9314,U_9302) = c_Orderings_Obot__class_Obot(tc_fun(U_9310,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_9308),U_9302),U_9312)) )
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9308,tc_fun(U_9310,tc_HOL_Obool)),U_9312),U_9314) != c_Orderings_Obot__class_Obot(tc_fun(U_9310,tc_HOL_Obool)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK234]),skolemize(U_9303,sK234(U_9315,U_9313,U_9311,U_9309))],[f_2632_3]) ).

cnf(f_2632_5,plain,
    ( hAPP(U_9314,U_9302) = c_Orderings_Obot__class_Obot(tc_fun(U_9310,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9308),U_9302),U_9312))
    | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9308,tc_fun(U_9310,tc_HOL_Obool)),U_9312),U_9314) != c_Orderings_Obot__class_Obot(tc_fun(U_9310,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2632_4]) ).

cnf(f_2632_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9309),sK234(U_9315,U_9313,U_9311,U_9309)),U_9313))
    | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9309,tc_fun(U_9311,tc_HOL_Obool)),U_9313),U_9315) = c_Orderings_Obot__class_Obot(tc_fun(U_9311,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2632_4]) ).

cnf(f_2632_7,plain,
    ( hAPP(U_9315,sK234(U_9315,U_9313,U_9311,U_9309)) != c_Orderings_Obot__class_Obot(tc_fun(U_9311,tc_HOL_Obool))
    | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9309,tc_fun(U_9311,tc_HOL_Obool)),U_9313),U_9315) = c_Orderings_Obot__class_Obot(tc_fun(U_9311,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2632_4]) ).

fof(f_2633_1,plain,
    ! [V_M_2,T_b,V_A_2,T_c] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),hAPP(c_COMBK(T_c,T_b),V_M_2)) = V_M_2
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_INF__const]) ).

fof(f_2633_2,plain,
    ! [U_9319,U_9318,U_9317,U_9316] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9318,U_9316),U_9317),hAPP(c_COMBK(U_9316,U_9318),U_9319)) = U_9319
      | U_9317 = c_Orderings_Obot__class_Obot(tc_fun(U_9318,tc_HOL_Obool))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_9316) ),
    inference(variable_rename,[status(thm)],[f_2633_1]) ).

cnf(f_2633_3,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9318,U_9316),U_9317),hAPP(c_COMBK(U_9316,U_9318),U_9319)) = U_9319
    | U_9317 = c_Orderings_Obot__class_Obot(tc_fun(U_9318,tc_HOL_Obool))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_9316) ),
    inference(clausify,[status(thm)],[f_2633_2]) ).

fof(f_2634_1,plain,
    ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
      ( ( c_Nitpick_Opair__box_OPairBox(T_b,T_c,V_a_2,V_b_2) = c_Nitpick_Opair__box_OPairBox(T_b,T_c,V_a_H_2,V_b_H_2)
        | V_b_2 != V_b_H_2
        | V_a_2 != V_a_H_2 )
      & ( ( V_b_2 = V_b_H_2
          & V_a_2 = V_a_H_2 )
        | c_Nitpick_Opair__box_OPairBox(T_b,T_c,V_a_2,V_b_2) != c_Nitpick_Opair__box_OPairBox(T_b,T_c,V_a_H_2,V_b_H_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_pair__box_Oinject]) ).

fof(f_2634_2,plain,
    ! [U_9325,U_9324,U_9323,U_9322,U_9321,U_9320] :
      ( ( c_Nitpick_Opair__box_OPairBox(U_9320,U_9321,U_9322,U_9323) = c_Nitpick_Opair__box_OPairBox(U_9320,U_9321,U_9324,U_9325)
        | U_9323 != U_9325
        | U_9322 != U_9324 )
      & ( ( U_9323 = U_9325
          & U_9322 = U_9324 )
        | c_Nitpick_Opair__box_OPairBox(U_9320,U_9321,U_9322,U_9323) != c_Nitpick_Opair__box_OPairBox(U_9320,U_9321,U_9324,U_9325) ) ),
    inference(variable_rename,[status(thm)],[f_2634_1]) ).

fof(f_2634_3,plain,
    ( ! [U_9337,U_9335,U_9333,U_9331] :
        ( ! [U_9329,U_9327] : c_Nitpick_Opair__box_OPairBox(U_9327,U_9329,U_9331,U_9333) = c_Nitpick_Opair__box_OPairBox(U_9327,U_9329,U_9335,U_9337)
        | U_9333 != U_9337
        | U_9331 != U_9335 )
    & ! [U_9336,U_9334,U_9332,U_9330] :
        ( ! [U_9328,U_9326] : c_Nitpick_Opair__box_OPairBox(U_9326,U_9328,U_9330,U_9332) != c_Nitpick_Opair__box_OPairBox(U_9326,U_9328,U_9334,U_9336)
        | ( U_9332 = U_9336
          & U_9330 = U_9334 ) ) ),
    inference(miniscope,[status(thm)],[f_2634_2]) ).

cnf(f_2634_4,plain,
    ( U_9330 = U_9334
    | c_Nitpick_Opair__box_OPairBox(U_9326,U_9328,U_9330,U_9332) != c_Nitpick_Opair__box_OPairBox(U_9326,U_9328,U_9334,U_9336) ),
    inference(clausify,[status(thm)],[f_2634_3]) ).

cnf(f_2634_5,plain,
    ( U_9332 = U_9336
    | c_Nitpick_Opair__box_OPairBox(U_9326,U_9328,U_9330,U_9332) != c_Nitpick_Opair__box_OPairBox(U_9326,U_9328,U_9334,U_9336) ),
    inference(clausify,[status(thm)],[f_2634_3]) ).

cnf(f_2634_6,plain,
    ( c_Nitpick_Opair__box_OPairBox(U_9327,U_9329,U_9331,U_9333) = c_Nitpick_Opair__box_OPairBox(U_9327,U_9329,U_9335,U_9337)
    | U_9333 != U_9337
    | U_9331 != U_9335 ),
    inference(clausify,[status(thm)],[f_2634_3]) ).

fof(f_2635_1,plain,
    ! [V_B_2,V_A_2,T_c,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool))),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_Compl__INT]) ).

fof(f_2635_2,plain,
    ! [U_9341,U_9340,U_9339,U_9338] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9338,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9339,tc_fun(U_9338,tc_HOL_Obool)),U_9340),U_9341)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9339,tc_fun(U_9338,tc_HOL_Obool)),U_9340),hAPP(hAPP(c_COMBB(tc_fun(U_9338,tc_HOL_Obool),tc_fun(U_9338,tc_HOL_Obool),U_9339),c_Groups_Ouminus__class_Ouminus(tc_fun(U_9338,tc_HOL_Obool))),U_9341)),
    inference(variable_rename,[status(thm)],[f_2635_1]) ).

cnf(f_2635_3,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9338,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9339,tc_fun(U_9338,tc_HOL_Obool)),U_9340),U_9341)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9339,tc_fun(U_9338,tc_HOL_Obool)),U_9340),hAPP(hAPP(c_COMBB(tc_fun(U_9338,tc_HOL_Obool),tc_fun(U_9338,tc_HOL_Obool),U_9339),c_Groups_Ouminus__class_Ouminus(tc_fun(U_9338,tc_HOL_Obool))),U_9341)),
    inference(clausify,[status(thm)],[f_2635_2]) ).

fof(f_2636_1,plain,
    ! [V_B_2,V_A_2,T_c,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool))),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_Compl__UN]) ).

fof(f_2636_2,plain,
    ! [U_9345,U_9344,U_9343,U_9342] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9342,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9343,tc_fun(U_9342,tc_HOL_Obool)),U_9344),U_9345)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9343,tc_fun(U_9342,tc_HOL_Obool)),U_9344),hAPP(hAPP(c_COMBB(tc_fun(U_9342,tc_HOL_Obool),tc_fun(U_9342,tc_HOL_Obool),U_9343),c_Groups_Ouminus__class_Ouminus(tc_fun(U_9342,tc_HOL_Obool))),U_9345)),
    inference(variable_rename,[status(thm)],[f_2636_1]) ).

cnf(f_2636_3,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9342,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9343,tc_fun(U_9342,tc_HOL_Obool)),U_9344),U_9345)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9343,tc_fun(U_9342,tc_HOL_Obool)),U_9344),hAPP(hAPP(c_COMBB(tc_fun(U_9342,tc_HOL_Obool),tc_fun(U_9342,tc_HOL_Obool),U_9343),c_Groups_Ouminus__class_Ouminus(tc_fun(U_9342,tc_HOL_Obool))),U_9345)),
    inference(clausify,[status(thm)],[f_2636_2]) ).

fof(f_2637_1,plain,
    ! [V_x_2,V_A_2,T_c,T_b] :
      ( hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,T_b)),V_A_2),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(V_A_2,V_x_2))
      | ~ class_Groups_Ouminus(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_fun__Compl__def]) ).

fof(f_2637_2,plain,
    ! [U_9349,U_9348,U_9347,U_9346] :
      ( hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9347,U_9346)),U_9348),U_9349) = hAPP(c_Groups_Ouminus__class_Ouminus(U_9346),hAPP(U_9348,U_9349))
      | ~ class_Groups_Ouminus(U_9346) ),
    inference(variable_rename,[status(thm)],[f_2637_1]) ).

cnf(f_2637_3,plain,
    ( hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9347,U_9346)),U_9348),U_9349) = hAPP(c_Groups_Ouminus__class_Ouminus(U_9346),hAPP(U_9348,U_9349))
    | ~ class_Groups_Ouminus(U_9346) ),
    inference(clausify,[status(thm)],[f_2637_2]) ).

fof(f_2638_1,plain,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Ouminus__class_Ouminus(T_b)),V_f_2)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2))
      | ~ class_Groups_Oab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__negf]) ).

fof(f_2638_2,plain,
    ! [U_9353,U_9352,U_9351,U_9350] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9351,U_9350),hAPP(hAPP(c_COMBB(U_9350,U_9350,U_9351),c_Groups_Ouminus__class_Ouminus(U_9350)),U_9352)),U_9353) = hAPP(c_Groups_Ouminus__class_Ouminus(U_9350),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9351,U_9350),U_9352),U_9353))
      | ~ class_Groups_Oab__group__add(U_9350) ),
    inference(variable_rename,[status(thm)],[f_2638_1]) ).

cnf(f_2638_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9351,U_9350),hAPP(hAPP(c_COMBB(U_9350,U_9350,U_9351),c_Groups_Ouminus__class_Ouminus(U_9350)),U_9352)),U_9353) = hAPP(c_Groups_Ouminus__class_Ouminus(U_9350),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9351,U_9350),U_9352),U_9353))
    | ~ class_Groups_Oab__group__add(U_9350) ),
    inference(clausify,[status(thm)],[f_2638_2]) ).

fof(f_2639_1,plain,
    ! [V_g_2,V_f_2,T_c,T_b] : hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2) = c_Finite__Set_Ofold(T_c,T_b,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),V_f_2),V_g_2)),
    inference(fof_nnf,[status(thm)],[fact_fold__image__def]) ).

fof(f_2639_2,plain,
    ! [U_9357,U_9356,U_9355,U_9354] : hAPP(c_Finite__Set_Ofold__image(U_9354,U_9355,U_9356),U_9357) = c_Finite__Set_Ofold(U_9355,U_9354,hAPP(hAPP(c_COMBB(U_9354,tc_fun(U_9354,U_9354),U_9355),U_9356),U_9357)),
    inference(variable_rename,[status(thm)],[f_2639_1]) ).

cnf(f_2639_3,plain,
    hAPP(c_Finite__Set_Ofold__image(U_9354,U_9355,U_9356),U_9357) = c_Finite__Set_Ofold(U_9355,U_9354,hAPP(hAPP(c_COMBB(U_9354,tc_fun(U_9354,U_9354),U_9355),U_9356),U_9357)),
    inference(clausify,[status(thm)],[f_2639_2]) ).

fof(f_2640_1,plain,
    ! [V_r_2,V_A_2,V_f_2,T_c,T_b] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),V_r_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Rings_Oinverse__class_Odivide(T_b)),V_f_2)),V_r_2)),V_A_2)
      | ~ class_Fields_Ofield(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__divide__distrib]) ).

fof(f_2640_2,plain,
    ! [U_9362,U_9361,U_9360,U_9359,U_9358] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9358),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9359,U_9358),U_9360),U_9361)),U_9362) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9359,U_9358),hAPP(hAPP(c_COMBC(U_9359,U_9358,U_9358),hAPP(hAPP(c_COMBB(U_9358,tc_fun(U_9358,U_9358),U_9359),c_Rings_Oinverse__class_Odivide(U_9358)),U_9360)),U_9362)),U_9361)
      | ~ class_Fields_Ofield(U_9358) ),
    inference(variable_rename,[status(thm)],[f_2640_1]) ).

cnf(f_2640_3,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9358),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9359,U_9358),U_9360),U_9361)),U_9362) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9359,U_9358),hAPP(hAPP(c_COMBC(U_9359,U_9358,U_9358),hAPP(hAPP(c_COMBB(U_9358,tc_fun(U_9358,U_9358),U_9359),c_Rings_Oinverse__class_Odivide(U_9358)),U_9360)),U_9362)),U_9361)
    | ~ class_Fields_Ofield(U_9358) ),
    inference(clausify,[status(thm)],[f_2640_2]) ).

fof(f_2641_1,plain,
    ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)),V_B_2),
    inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I8_J]) ).

fof(f_2641_2,plain,
    ! [U_9366,U_9365,U_9364,U_9363] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_9363,tc_HOL_Obool),tc_fun(U_9364,tc_HOL_Obool)),U_9365),hAPP(hAPP(c_COMBC(tc_fun(U_9363,tc_HOL_Obool),tc_fun(U_9363,tc_fun(U_9364,tc_HOL_Obool)),tc_fun(U_9364,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9363,tc_fun(U_9364,tc_HOL_Obool))),U_9366)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9363,tc_fun(U_9364,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9363,tc_HOL_Obool),U_9365)),U_9366),
    inference(variable_rename,[status(thm)],[f_2641_1]) ).

cnf(f_2641_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_9363,tc_HOL_Obool),tc_fun(U_9364,tc_HOL_Obool)),U_9365),hAPP(hAPP(c_COMBC(tc_fun(U_9363,tc_HOL_Obool),tc_fun(U_9363,tc_fun(U_9364,tc_HOL_Obool)),tc_fun(U_9364,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9363,tc_fun(U_9364,tc_HOL_Obool))),U_9366)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9363,tc_fun(U_9364,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9363,tc_HOL_Obool),U_9365)),U_9366),
    inference(clausify,[status(thm)],[f_2641_2]) ).

fof(f_2642_1,plain,
    ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_UN__simps_I8_J]) ).

fof(f_2642_2,plain,
    ! [U_9370,U_9369,U_9368,U_9367] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9367,tc_fun(U_9368,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9367,tc_HOL_Obool),U_9369)),U_9370) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_9367,tc_HOL_Obool),tc_fun(U_9368,tc_HOL_Obool)),U_9369),hAPP(hAPP(c_COMBC(tc_fun(U_9367,tc_HOL_Obool),tc_fun(U_9367,tc_fun(U_9368,tc_HOL_Obool)),tc_fun(U_9368,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9367,tc_fun(U_9368,tc_HOL_Obool))),U_9370)),
    inference(variable_rename,[status(thm)],[f_2642_1]) ).

cnf(f_2642_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9367,tc_fun(U_9368,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9367,tc_HOL_Obool),U_9369)),U_9370) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_9367,tc_HOL_Obool),tc_fun(U_9368,tc_HOL_Obool)),U_9369),hAPP(hAPP(c_COMBC(tc_fun(U_9367,tc_HOL_Obool),tc_fun(U_9367,tc_fun(U_9368,tc_HOL_Obool)),tc_fun(U_9368,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9367,tc_fun(U_9368,tc_HOL_Obool))),U_9370)),
    inference(clausify,[status(thm)],[f_2642_2]) ).

fof(f_2643_1,plain,
    ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_b),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_b),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_b),T_d),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b)),hAPP(c_COMBC(T_c,T_d,T_b),V_f_2))),V_A_2)),V_B_2)
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__commute]) ).

fof(f_2643_2,plain,
    ! [U_9376,U_9375,U_9374,U_9373,U_9372,U_9371] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9372,U_9371),hAPP(hAPP(c_COMBC(U_9372,tc_fun(U_9373,tc_HOL_Obool),U_9371),hAPP(hAPP(c_COMBB(tc_fun(U_9373,U_9371),tc_fun(tc_fun(U_9373,tc_HOL_Obool),U_9371),U_9372),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9373,U_9371)),U_9374)),U_9375)),U_9376) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9373,U_9371),hAPP(hAPP(c_COMBC(U_9373,tc_fun(U_9372,tc_HOL_Obool),U_9371),hAPP(hAPP(c_COMBB(tc_fun(U_9372,U_9371),tc_fun(tc_fun(U_9372,tc_HOL_Obool),U_9371),U_9373),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9372,U_9371)),hAPP(c_COMBC(U_9372,U_9373,U_9371),U_9374))),U_9376)),U_9375)
      | ~ class_Groups_Ocomm__monoid__add(U_9371) ),
    inference(variable_rename,[status(thm)],[f_2643_1]) ).

cnf(f_2643_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9372,U_9371),hAPP(hAPP(c_COMBC(U_9372,tc_fun(U_9373,tc_HOL_Obool),U_9371),hAPP(hAPP(c_COMBB(tc_fun(U_9373,U_9371),tc_fun(tc_fun(U_9373,tc_HOL_Obool),U_9371),U_9372),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9373,U_9371)),U_9374)),U_9375)),U_9376) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9373,U_9371),hAPP(hAPP(c_COMBC(U_9373,tc_fun(U_9372,tc_HOL_Obool),U_9371),hAPP(hAPP(c_COMBB(tc_fun(U_9372,U_9371),tc_fun(tc_fun(U_9372,tc_HOL_Obool),U_9371),U_9373),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9372,U_9371)),hAPP(c_COMBC(U_9372,U_9373,U_9371),U_9374))),U_9376)),U_9375)
    | ~ class_Groups_Ocomm__monoid__add(U_9371) ),
    inference(clausify,[status(thm)],[f_2643_2]) ).

fof(f_2644_1,plain,
    ! [V_x_2,V_f_2,V_A_2,T_d,T_c,T_b] :
      ( hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,T_b)),V_A_2),V_f_2),V_x_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2),hAPP(hAPP(c_COMBC(T_c,T_d,T_b),V_f_2),V_x_2))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_SUPR__apply]) ).

fof(f_2644_2,plain,
    ! [U_9382,U_9381,U_9380,U_9379,U_9378,U_9377] :
      ( hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9378,tc_fun(U_9379,U_9377)),U_9380),U_9381),U_9382) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9378,U_9377),U_9380),hAPP(hAPP(c_COMBC(U_9378,U_9379,U_9377),U_9381),U_9382))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_9377) ),
    inference(variable_rename,[status(thm)],[f_2644_1]) ).

cnf(f_2644_3,plain,
    ( hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9378,tc_fun(U_9379,U_9377)),U_9380),U_9381),U_9382) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9378,U_9377),U_9380),hAPP(hAPP(c_COMBC(U_9378,U_9379,U_9377),U_9381),U_9382))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_9377) ),
    inference(clausify,[status(thm)],[f_2644_2]) ).

fof(f_2645_1,plain,
    ! [T_f,T_e,T_d,T_b,T_c,V_x_H_2,V_g_H_2,V_f_H_2,V_x_2,V_g_2,V_f_2] :
      ( hAPP(hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Fun_Ocomp(T_e,T_b,T_f,V_f_H_2),V_g_H_2),V_x_H_2)
      | hAPP(V_f_2,hAPP(V_g_2,V_x_2)) != hAPP(V_f_H_2,hAPP(V_g_H_2,V_x_H_2)) ),
    inference(fof_nnf,[status(thm)],[fact_comp__cong]) ).

fof(f_2645_2,plain,
    ! [U_9393,U_9392,U_9391,U_9390,U_9389,U_9388,U_9387,U_9386,U_9385,U_9384,U_9383] :
      ( hAPP(hAPP(c_Fun_Ocomp(U_9389,U_9390,U_9391,U_9383),U_9384),U_9385) = hAPP(hAPP(c_Fun_Ocomp(U_9392,U_9390,U_9393,U_9386),U_9387),U_9388)
      | hAPP(U_9383,hAPP(U_9384,U_9385)) != hAPP(U_9386,hAPP(U_9387,U_9388)) ),
    inference(variable_rename,[status(thm)],[f_2645_1]) ).

cnf(f_2645_3,plain,
    ( hAPP(hAPP(c_Fun_Ocomp(U_9389,U_9390,U_9391,U_9383),U_9384),U_9385) = hAPP(hAPP(c_Fun_Ocomp(U_9392,U_9390,U_9393,U_9386),U_9387),U_9388)
    | hAPP(U_9383,hAPP(U_9384,U_9385)) != hAPP(U_9386,hAPP(U_9387,U_9388)) ),
    inference(clausify,[status(thm)],[f_2645_2]) ).

fof(f_2646_1,plain,
    ! [V_v_2,V_c_2,V_b_2,V_a_2,T_b,T_c,T_d] :
      ( hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,V_v_2)
      | hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) != V_c_2 ),
    inference(fof_nnf,[status(thm)],[fact_o__eq__dest__lhs]) ).

fof(f_2646_2,plain,
    ! [U_9400,U_9399,U_9398,U_9397,U_9396,U_9395,U_9394] :
      ( hAPP(U_9397,hAPP(U_9398,U_9400)) = hAPP(U_9399,U_9400)
      | hAPP(c_Fun_Ocomp(U_9394,U_9395,U_9396,U_9397),U_9398) != U_9399 ),
    inference(variable_rename,[status(thm)],[f_2646_1]) ).

fof(f_2646_3,plain,
    ! [U_9400,U_9399,U_9398,U_9397] :
      ( ! [U_9396,U_9395,U_9394] : hAPP(c_Fun_Ocomp(U_9394,U_9395,U_9396,U_9397),U_9398) != U_9399
      | hAPP(U_9397,hAPP(U_9398,U_9400)) = hAPP(U_9399,U_9400) ),
    inference(miniscope,[status(thm)],[f_2646_2]) ).

cnf(f_2646_4,plain,
    ( hAPP(c_Fun_Ocomp(U_9394,U_9395,U_9396,U_9397),U_9398) != U_9399
    | hAPP(U_9397,hAPP(U_9398,U_9400)) = hAPP(U_9399,U_9400) ),
    inference(clausify,[status(thm)],[f_2646_3]) ).

fof(f_2647_1,plain,
    ! [V_x_2,V_f_2,V_c_2,T_d,T_b,T_c] : hAPP(hAPP(c_Fun_Ocomp(T_c,T_b,T_d,hAPP(c_COMBK(T_b,T_c),V_c_2)),V_f_2),V_x_2) = V_c_2,
    inference(fof_nnf,[status(thm)],[fact_K__record__comp]) ).

fof(f_2647_2,plain,
    ! [U_9406,U_9405,U_9404,U_9403,U_9402,U_9401] : hAPP(hAPP(c_Fun_Ocomp(U_9401,U_9402,U_9403,hAPP(c_COMBK(U_9402,U_9401),U_9404)),U_9405),U_9406) = U_9404,
    inference(variable_rename,[status(thm)],[f_2647_1]) ).

cnf(f_2647_3,plain,
    hAPP(hAPP(c_Fun_Ocomp(U_9401,U_9402,U_9403,hAPP(c_COMBK(U_9402,U_9401),U_9404)),U_9405),U_9406) = U_9404,
    inference(clausify,[status(thm)],[f_2647_2]) ).

fof(f_2648_1,plain,
    ! [V_f_2,V_B_2,T_d,V_A_2,T_c,T_b] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),T_b,T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,T_b),V_B_2)),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,T_b),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_b),T_b,T_d),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2)),hAPP(c_COMBC(T_c,T_d,T_b),V_f_2)))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_SUP__commute]) ).

fof(f_2648_2,plain,
    ! [U_9412,U_9411,U_9410,U_9409,U_9408,U_9407] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9408,U_9407),U_9409),hAPP(hAPP(c_COMBB(tc_fun(U_9410,U_9407),U_9407,U_9408),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9410,U_9407),U_9411)),U_9412)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9410,U_9407),U_9411),hAPP(hAPP(c_COMBB(tc_fun(U_9408,U_9407),U_9407,U_9410),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9408,U_9407),U_9409)),hAPP(c_COMBC(U_9408,U_9410,U_9407),U_9412)))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_9407) ),
    inference(variable_rename,[status(thm)],[f_2648_1]) ).

cnf(f_2648_3,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9408,U_9407),U_9409),hAPP(hAPP(c_COMBB(tc_fun(U_9410,U_9407),U_9407,U_9408),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9410,U_9407),U_9411)),U_9412)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9410,U_9407),U_9411),hAPP(hAPP(c_COMBB(tc_fun(U_9408,U_9407),U_9407,U_9410),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9408,U_9407),U_9409)),hAPP(c_COMBC(U_9408,U_9410,U_9407),U_9412)))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_9407) ),
    inference(clausify,[status(thm)],[f_2648_2]) ).

fof(f_2649_1,plain,
    ! [V_C_2,V_B_2,T_d,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2),
    inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I9_J]) ).

fof(f_2649_2,plain,
    ! [U_9418,U_9417,U_9416,U_9415,U_9414,U_9413] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9413,tc_fun(U_9414,tc_HOL_Obool)),U_9415),hAPP(hAPP(c_COMBC(U_9413,tc_fun(U_9416,tc_fun(U_9414,tc_HOL_Obool)),tc_fun(U_9414,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9416,tc_HOL_Obool),tc_fun(tc_fun(U_9416,tc_fun(U_9414,tc_HOL_Obool)),tc_fun(U_9414,tc_HOL_Obool)),U_9413),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9416,tc_fun(U_9414,tc_HOL_Obool))),U_9417)),U_9418)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9416,tc_fun(U_9414,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9413,tc_fun(U_9416,tc_HOL_Obool)),U_9415),U_9417)),U_9418),
    inference(variable_rename,[status(thm)],[f_2649_1]) ).

cnf(f_2649_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9413,tc_fun(U_9414,tc_HOL_Obool)),U_9415),hAPP(hAPP(c_COMBC(U_9413,tc_fun(U_9416,tc_fun(U_9414,tc_HOL_Obool)),tc_fun(U_9414,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9416,tc_HOL_Obool),tc_fun(tc_fun(U_9416,tc_fun(U_9414,tc_HOL_Obool)),tc_fun(U_9414,tc_HOL_Obool)),U_9413),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9416,tc_fun(U_9414,tc_HOL_Obool))),U_9417)),U_9418)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9416,tc_fun(U_9414,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9413,tc_fun(U_9416,tc_HOL_Obool)),U_9415),U_9417)),U_9418),
    inference(clausify,[status(thm)],[f_2649_2]) ).

fof(f_2650_1,plain,
    ! [V_C_2,V_B_2,T_d,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2),
    inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I9_J]) ).

fof(f_2650_2,plain,
    ! [U_9424,U_9423,U_9422,U_9421,U_9420,U_9419] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9419,tc_fun(U_9420,tc_HOL_Obool)),U_9421),hAPP(hAPP(c_COMBC(U_9419,tc_fun(U_9422,tc_fun(U_9420,tc_HOL_Obool)),tc_fun(U_9420,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9422,tc_HOL_Obool),tc_fun(tc_fun(U_9422,tc_fun(U_9420,tc_HOL_Obool)),tc_fun(U_9420,tc_HOL_Obool)),U_9419),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9422,tc_fun(U_9420,tc_HOL_Obool))),U_9423)),U_9424)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9422,tc_fun(U_9420,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9419,tc_fun(U_9422,tc_HOL_Obool)),U_9421),U_9423)),U_9424),
    inference(variable_rename,[status(thm)],[f_2650_1]) ).

cnf(f_2650_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9419,tc_fun(U_9420,tc_HOL_Obool)),U_9421),hAPP(hAPP(c_COMBC(U_9419,tc_fun(U_9422,tc_fun(U_9420,tc_HOL_Obool)),tc_fun(U_9420,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9422,tc_HOL_Obool),tc_fun(tc_fun(U_9422,tc_fun(U_9420,tc_HOL_Obool)),tc_fun(U_9420,tc_HOL_Obool)),U_9419),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9422,tc_fun(U_9420,tc_HOL_Obool))),U_9423)),U_9424)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9422,tc_fun(U_9420,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9419,tc_fun(U_9422,tc_HOL_Obool)),U_9421),U_9423)),U_9424),
    inference(clausify,[status(thm)],[f_2650_2]) ).

fof(f_2651_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_d,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_d),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2)),
    inference(fof_nnf,[status(thm)],[fact_INT__simps_I9_J]) ).

fof(f_2651_2,plain,
    ! [U_9430,U_9429,U_9428,U_9427,U_9426,U_9425] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9425,tc_fun(U_9426,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9427,tc_fun(U_9425,tc_HOL_Obool)),U_9428),U_9429)),U_9430) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9427,tc_fun(U_9426,tc_HOL_Obool)),U_9428),hAPP(hAPP(c_COMBC(U_9427,tc_fun(U_9425,tc_fun(U_9426,tc_HOL_Obool)),tc_fun(U_9426,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9425,tc_HOL_Obool),tc_fun(tc_fun(U_9425,tc_fun(U_9426,tc_HOL_Obool)),tc_fun(U_9426,tc_HOL_Obool)),U_9427),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9425,tc_fun(U_9426,tc_HOL_Obool))),U_9429)),U_9430)),
    inference(variable_rename,[status(thm)],[f_2651_1]) ).

cnf(f_2651_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9425,tc_fun(U_9426,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9427,tc_fun(U_9425,tc_HOL_Obool)),U_9428),U_9429)),U_9430) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9427,tc_fun(U_9426,tc_HOL_Obool)),U_9428),hAPP(hAPP(c_COMBC(U_9427,tc_fun(U_9425,tc_fun(U_9426,tc_HOL_Obool)),tc_fun(U_9426,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9425,tc_HOL_Obool),tc_fun(tc_fun(U_9425,tc_fun(U_9426,tc_HOL_Obool)),tc_fun(U_9426,tc_HOL_Obool)),U_9427),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9425,tc_fun(U_9426,tc_HOL_Obool))),U_9429)),U_9430)),
    inference(clausify,[status(thm)],[f_2651_2]) ).

fof(f_2652_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_d,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_d),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2)),
    inference(fof_nnf,[status(thm)],[fact_UN__simps_I9_J]) ).

fof(f_2652_2,plain,
    ! [U_9436,U_9435,U_9434,U_9433,U_9432,U_9431] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9431,tc_fun(U_9432,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9433,tc_fun(U_9431,tc_HOL_Obool)),U_9434),U_9435)),U_9436) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9433,tc_fun(U_9432,tc_HOL_Obool)),U_9434),hAPP(hAPP(c_COMBC(U_9433,tc_fun(U_9431,tc_fun(U_9432,tc_HOL_Obool)),tc_fun(U_9432,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9431,tc_HOL_Obool),tc_fun(tc_fun(U_9431,tc_fun(U_9432,tc_HOL_Obool)),tc_fun(U_9432,tc_HOL_Obool)),U_9433),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9431,tc_fun(U_9432,tc_HOL_Obool))),U_9435)),U_9436)),
    inference(variable_rename,[status(thm)],[f_2652_1]) ).

cnf(f_2652_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9431,tc_fun(U_9432,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9433,tc_fun(U_9431,tc_HOL_Obool)),U_9434),U_9435)),U_9436) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9433,tc_fun(U_9432,tc_HOL_Obool)),U_9434),hAPP(hAPP(c_COMBC(U_9433,tc_fun(U_9431,tc_fun(U_9432,tc_HOL_Obool)),tc_fun(U_9432,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9431,tc_HOL_Obool),tc_fun(tc_fun(U_9431,tc_fun(U_9432,tc_HOL_Obool)),tc_fun(U_9432,tc_HOL_Obool)),U_9433),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9431,tc_fun(U_9432,tc_HOL_Obool))),U_9435)),U_9436)),
    inference(clausify,[status(thm)],[f_2652_2]) ).

fof(f_2653_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_d,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_d),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2)),
    inference(fof_nnf,[status(thm)],[fact_UN__UN__flatten]) ).

fof(f_2653_2,plain,
    ! [U_9442,U_9441,U_9440,U_9439,U_9438,U_9437] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9437,tc_fun(U_9438,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9439,tc_fun(U_9437,tc_HOL_Obool)),U_9440),U_9441)),U_9442) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9439,tc_fun(U_9438,tc_HOL_Obool)),U_9440),hAPP(hAPP(c_COMBC(U_9439,tc_fun(U_9437,tc_fun(U_9438,tc_HOL_Obool)),tc_fun(U_9438,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9437,tc_HOL_Obool),tc_fun(tc_fun(U_9437,tc_fun(U_9438,tc_HOL_Obool)),tc_fun(U_9438,tc_HOL_Obool)),U_9439),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9437,tc_fun(U_9438,tc_HOL_Obool))),U_9441)),U_9442)),
    inference(variable_rename,[status(thm)],[f_2653_1]) ).

cnf(f_2653_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9437,tc_fun(U_9438,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9439,tc_fun(U_9437,tc_HOL_Obool)),U_9440),U_9441)),U_9442) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9439,tc_fun(U_9438,tc_HOL_Obool)),U_9440),hAPP(hAPP(c_COMBC(U_9439,tc_fun(U_9437,tc_fun(U_9438,tc_HOL_Obool)),tc_fun(U_9438,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9437,tc_HOL_Obool),tc_fun(tc_fun(U_9437,tc_fun(U_9438,tc_HOL_Obool)),tc_fun(U_9438,tc_HOL_Obool)),U_9439),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9437,tc_fun(U_9438,tc_HOL_Obool))),U_9441)),U_9442)),
    inference(clausify,[status(thm)],[f_2653_2]) ).

fof(f_2654_1,plain,
    ! [V_b_2,V_B_2,V_A_2,T_c,T_b] :
      ( ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2))
        | ! [B_x] :
            ( ~ hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2))
            | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
      & ( ? [B_x] :
            ( hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_SUP1__iff]) ).

fof(f_2654_2,plain,
    ! [U_9449,U_9448,U_9447,U_9446,U_9445] :
      ( ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9445,tc_fun(U_9446,tc_HOL_Obool)),U_9447),U_9448),U_9449))
        | ! [U_9444] :
            ( ~ hBOOL(hAPP(hAPP(U_9448,U_9444),U_9449))
            | ~ hBOOL(hAPP(hAPP(c_member(U_9445),U_9444),U_9447)) ) )
      & ( ? [U_9443] :
            ( hBOOL(hAPP(hAPP(U_9448,U_9443),U_9449))
            & hBOOL(hAPP(hAPP(c_member(U_9445),U_9443),U_9447)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9445,tc_fun(U_9446,tc_HOL_Obool)),U_9447),U_9448),U_9449)) ) ),
    inference(variable_rename,[status(thm)],[f_2654_1]) ).

fof(f_2654_3,plain,
    ( ! [U_9459,U_9457,U_9455,U_9453,U_9451] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9451,tc_fun(U_9453,tc_HOL_Obool)),U_9455),U_9457),U_9459))
        | ! [U_9444] :
            ( ~ hBOOL(hAPP(hAPP(U_9457,U_9444),U_9459))
            | ~ hBOOL(hAPP(hAPP(c_member(U_9451),U_9444),U_9455)) ) )
    & ! [U_9458,U_9456,U_9454,U_9452,U_9450] :
        ( ? [U_9443] :
            ( hBOOL(hAPP(hAPP(U_9456,U_9443),U_9458))
            & hBOOL(hAPP(hAPP(c_member(U_9450),U_9443),U_9454)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9450,tc_fun(U_9452,tc_HOL_Obool)),U_9454),U_9456),U_9458)) ) ),
    inference(miniscope,[status(thm)],[f_2654_2]) ).

fof(f_2654_4,plain,
    ( ! [U_9459,U_9457,U_9455,U_9453,U_9451] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9451,tc_fun(U_9453,tc_HOL_Obool)),U_9455),U_9457),U_9459))
        | ! [U_9444] :
            ( ~ hBOOL(hAPP(hAPP(U_9457,U_9444),U_9459))
            | ~ hBOOL(hAPP(hAPP(c_member(U_9451),U_9444),U_9455)) ) )
    & ! [U_9458,U_9456,U_9454,U_9452,U_9450] :
        ( ( hBOOL(hAPP(hAPP(U_9456,sK235(U_9458,U_9456,U_9454,U_9452,U_9450)),U_9458))
          & hBOOL(hAPP(hAPP(c_member(U_9450),sK235(U_9458,U_9456,U_9454,U_9452,U_9450)),U_9454)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9450,tc_fun(U_9452,tc_HOL_Obool)),U_9454),U_9456),U_9458)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK235]),skolemize(U_9443,sK235(U_9458,U_9456,U_9454,U_9452,U_9450))],[f_2654_3]) ).

cnf(f_2654_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9450),sK235(U_9458,U_9456,U_9454,U_9452,U_9450)),U_9454))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9450,tc_fun(U_9452,tc_HOL_Obool)),U_9454),U_9456),U_9458)) ),
    inference(clausify,[status(thm)],[f_2654_4]) ).

cnf(f_2654_6,plain,
    ( hBOOL(hAPP(hAPP(U_9456,sK235(U_9458,U_9456,U_9454,U_9452,U_9450)),U_9458))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9450,tc_fun(U_9452,tc_HOL_Obool)),U_9454),U_9456),U_9458)) ),
    inference(clausify,[status(thm)],[f_2654_4]) ).

cnf(f_2654_7,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9451,tc_fun(U_9453,tc_HOL_Obool)),U_9455),U_9457),U_9459))
    | ~ hBOOL(hAPP(hAPP(U_9457,U_9444),U_9459))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9451),U_9444),U_9455)) ),
    inference(clausify,[status(thm)],[f_2654_4]) ).

fof(f_2655_1,plain,
    ! [V_S_2,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_S_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_COMBI(tc_fun(T_b,tc_HOL_Obool))),
    inference(fof_nnf,[status(thm)],[fact_Union__def]) ).

fof(f_2655_2,plain,
    ! [U_9461,U_9460] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9460,tc_HOL_Obool),U_9461) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_9460,tc_HOL_Obool),tc_fun(U_9460,tc_HOL_Obool)),U_9461),c_COMBI(tc_fun(U_9460,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_2655_1]) ).

cnf(f_2655_3,plain,
    c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9460,tc_HOL_Obool),U_9461) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_9460,tc_HOL_Obool),tc_fun(U_9460,tc_HOL_Obool)),U_9461),c_COMBI(tc_fun(U_9460,tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_2655_2]) ).

fof(f_2656_1,plain,
    ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_INT__simps_I8_J]) ).

fof(f_2656_2,plain,
    ! [U_9465,U_9464,U_9463,U_9462] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9462,tc_fun(U_9463,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9462,tc_HOL_Obool),U_9464)),U_9465) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_9462,tc_HOL_Obool),tc_fun(U_9463,tc_HOL_Obool)),U_9464),hAPP(hAPP(c_COMBC(tc_fun(U_9462,tc_HOL_Obool),tc_fun(U_9462,tc_fun(U_9463,tc_HOL_Obool)),tc_fun(U_9463,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9462,tc_fun(U_9463,tc_HOL_Obool))),U_9465)),
    inference(variable_rename,[status(thm)],[f_2656_1]) ).

cnf(f_2656_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9462,tc_fun(U_9463,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9462,tc_HOL_Obool),U_9464)),U_9465) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_9462,tc_HOL_Obool),tc_fun(U_9463,tc_HOL_Obool)),U_9464),hAPP(hAPP(c_COMBC(tc_fun(U_9462,tc_HOL_Obool),tc_fun(U_9462,tc_fun(U_9463,tc_HOL_Obool)),tc_fun(U_9463,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9462,tc_fun(U_9463,tc_HOL_Obool))),U_9465)),
    inference(clausify,[status(thm)],[f_2656_2]) ).

fof(f_2657_1,plain,
    ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)),V_B_2),
    inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I8_J]) ).

fof(f_2657_2,plain,
    ! [U_9469,U_9468,U_9467,U_9466] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_9466,tc_HOL_Obool),tc_fun(U_9467,tc_HOL_Obool)),U_9468),hAPP(hAPP(c_COMBC(tc_fun(U_9466,tc_HOL_Obool),tc_fun(U_9466,tc_fun(U_9467,tc_HOL_Obool)),tc_fun(U_9467,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9466,tc_fun(U_9467,tc_HOL_Obool))),U_9469)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9466,tc_fun(U_9467,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9466,tc_HOL_Obool),U_9468)),U_9469),
    inference(variable_rename,[status(thm)],[f_2657_1]) ).

cnf(f_2657_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_9466,tc_HOL_Obool),tc_fun(U_9467,tc_HOL_Obool)),U_9468),hAPP(hAPP(c_COMBC(tc_fun(U_9466,tc_HOL_Obool),tc_fun(U_9466,tc_fun(U_9467,tc_HOL_Obool)),tc_fun(U_9467,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9466,tc_fun(U_9467,tc_HOL_Obool))),U_9469)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9466,tc_fun(U_9467,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9466,tc_HOL_Obool),U_9468)),U_9469),
    inference(clausify,[status(thm)],[f_2657_2]) ).

fof(f_2658_1,plain,
    ! [V_x_2,V_f_2,V_A_2,T_d,T_c,T_b] :
      ( hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,T_b)),V_A_2),V_f_2),V_x_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2),hAPP(hAPP(c_COMBC(T_c,T_d,T_b),V_f_2),V_x_2))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_INFI__apply]) ).

fof(f_2658_2,plain,
    ! [U_9475,U_9474,U_9473,U_9472,U_9471,U_9470] :
      ( hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9471,tc_fun(U_9472,U_9470)),U_9473),U_9474),U_9475) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9471,U_9470),U_9473),hAPP(hAPP(c_COMBC(U_9471,U_9472,U_9470),U_9474),U_9475))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_9470) ),
    inference(variable_rename,[status(thm)],[f_2658_1]) ).

cnf(f_2658_3,plain,
    ( hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9471,tc_fun(U_9472,U_9470)),U_9473),U_9474),U_9475) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9471,U_9470),U_9473),hAPP(hAPP(c_COMBC(U_9471,U_9472,U_9470),U_9474),U_9475))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_9470) ),
    inference(clausify,[status(thm)],[f_2658_2]) ).

fof(f_2659_1,plain,
    ! [V_f_2,V_B_2,T_d,V_A_2,T_c,T_b] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),T_b,T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,T_b),V_B_2)),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,T_b),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_b),T_b,T_d),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2)),hAPP(c_COMBC(T_c,T_d,T_b),V_f_2)))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_INF__commute]) ).

fof(f_2659_2,plain,
    ! [U_9481,U_9480,U_9479,U_9478,U_9477,U_9476] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9477,U_9476),U_9478),hAPP(hAPP(c_COMBB(tc_fun(U_9479,U_9476),U_9476,U_9477),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9479,U_9476),U_9480)),U_9481)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9479,U_9476),U_9480),hAPP(hAPP(c_COMBB(tc_fun(U_9477,U_9476),U_9476,U_9479),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9477,U_9476),U_9478)),hAPP(c_COMBC(U_9477,U_9479,U_9476),U_9481)))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_9476) ),
    inference(variable_rename,[status(thm)],[f_2659_1]) ).

cnf(f_2659_3,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9477,U_9476),U_9478),hAPP(hAPP(c_COMBB(tc_fun(U_9479,U_9476),U_9476,U_9477),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9479,U_9476),U_9480)),U_9481)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9479,U_9476),U_9480),hAPP(hAPP(c_COMBB(tc_fun(U_9477,U_9476),U_9476,U_9479),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9477,U_9476),U_9478)),hAPP(c_COMBC(U_9477,U_9479,U_9476),U_9481)))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_9476) ),
    inference(clausify,[status(thm)],[f_2659_2]) ).

fof(f_2660_1,plain,
    ! [V_S_2,T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_S_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_COMBI(tc_fun(T_b,tc_HOL_Obool))),
    inference(fof_nnf,[status(thm)],[fact_Inter__def]) ).

fof(f_2660_2,plain,
    ! [U_9483,U_9482] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_9482,tc_HOL_Obool),U_9483) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_9482,tc_HOL_Obool),tc_fun(U_9482,tc_HOL_Obool)),U_9483),c_COMBI(tc_fun(U_9482,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_2660_1]) ).

cnf(f_2660_3,plain,
    c_Complete__Lattice_OInf__class_OInf(tc_fun(U_9482,tc_HOL_Obool),U_9483) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_9482,tc_HOL_Obool),tc_fun(U_9482,tc_HOL_Obool)),U_9483),c_COMBI(tc_fun(U_9482,tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_2660_2]) ).

fof(f_2661_1,plain,
    ! [V_B_2,V_A_2,T_c,T_b] : hAPP(c_Set_OPow(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),T_c),c_Set_OPow(T_b)),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_Pow__INT__eq]) ).

fof(f_2661_2,plain,
    ! [U_9487,U_9486,U_9485,U_9484] : hAPP(c_Set_OPow(U_9484),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9485,tc_fun(U_9484,tc_HOL_Obool)),U_9486),U_9487)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9485,tc_fun(tc_fun(U_9484,tc_HOL_Obool),tc_HOL_Obool)),U_9486),hAPP(hAPP(c_COMBB(tc_fun(U_9484,tc_HOL_Obool),tc_fun(tc_fun(U_9484,tc_HOL_Obool),tc_HOL_Obool),U_9485),c_Set_OPow(U_9484)),U_9487)),
    inference(variable_rename,[status(thm)],[f_2661_1]) ).

cnf(f_2661_3,plain,
    hAPP(c_Set_OPow(U_9484),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9485,tc_fun(U_9484,tc_HOL_Obool)),U_9486),U_9487)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9485,tc_fun(tc_fun(U_9484,tc_HOL_Obool),tc_HOL_Obool)),U_9486),hAPP(hAPP(c_COMBB(tc_fun(U_9484,tc_HOL_Obool),tc_fun(tc_fun(U_9484,tc_HOL_Obool),tc_HOL_Obool),U_9485),c_Set_OPow(U_9484)),U_9487)),
    inference(clausify,[status(thm)],[f_2661_2]) ).

fof(f_2662_1,plain,
    ! [V_d_2,V_c_2,T_e,V_b_2,V_a_2,T_b,T_c,T_d] :
      ( ! [B_v] : hAPP(V_a_2,hAPP(V_b_2,B_v)) = hAPP(V_c_2,hAPP(V_d_2,B_v))
      | hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) != hAPP(c_Fun_Ocomp(T_e,T_c,T_b,V_c_2),V_d_2) ),
    inference(fof_nnf,[status(thm)],[fact_o__eq__elim]) ).

fof(f_2662_2,plain,
    ! [U_9496,U_9495,U_9494,U_9493,U_9492,U_9491,U_9490,U_9489] :
      ( ! [U_9488] : hAPP(U_9492,hAPP(U_9493,U_9488)) = hAPP(U_9495,hAPP(U_9496,U_9488))
      | hAPP(c_Fun_Ocomp(U_9489,U_9490,U_9491,U_9492),U_9493) != hAPP(c_Fun_Ocomp(U_9494,U_9490,U_9491,U_9495),U_9496) ),
    inference(variable_rename,[status(thm)],[f_2662_1]) ).

fof(f_2662_3,plain,
    ! [U_9496,U_9495,U_9494,U_9493,U_9492] :
      ( ! [U_9491,U_9490,U_9489] : hAPP(c_Fun_Ocomp(U_9489,U_9490,U_9491,U_9492),U_9493) != hAPP(c_Fun_Ocomp(U_9494,U_9490,U_9491,U_9495),U_9496)
      | ! [U_9488] : hAPP(U_9492,hAPP(U_9493,U_9488)) = hAPP(U_9495,hAPP(U_9496,U_9488)) ),
    inference(miniscope,[status(thm)],[f_2662_2]) ).

cnf(f_2662_4,plain,
    ( hAPP(c_Fun_Ocomp(U_9489,U_9490,U_9491,U_9492),U_9493) != hAPP(c_Fun_Ocomp(U_9494,U_9490,U_9491,U_9495),U_9496)
    | hAPP(U_9492,hAPP(U_9493,U_9488)) = hAPP(U_9495,hAPP(U_9496,U_9488)) ),
    inference(clausify,[status(thm)],[f_2662_3]) ).

fof(f_2663_1,plain,
    ! [V_v_2,V_d_2,V_c_2,T_e,V_b_2,V_a_2,T_b,T_c,T_d] :
      ( hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,hAPP(V_d_2,V_v_2))
      | hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) != hAPP(c_Fun_Ocomp(T_e,T_c,T_b,V_c_2),V_d_2) ),
    inference(fof_nnf,[status(thm)],[fact_o__eq__dest]) ).

fof(f_2663_2,plain,
    ! [U_9505,U_9504,U_9503,U_9502,U_9501,U_9500,U_9499,U_9498,U_9497] :
      ( hAPP(U_9500,hAPP(U_9501,U_9505)) = hAPP(U_9503,hAPP(U_9504,U_9505))
      | hAPP(c_Fun_Ocomp(U_9497,U_9498,U_9499,U_9500),U_9501) != hAPP(c_Fun_Ocomp(U_9502,U_9498,U_9499,U_9503),U_9504) ),
    inference(variable_rename,[status(thm)],[f_2663_1]) ).

fof(f_2663_3,plain,
    ! [U_9505,U_9504,U_9503,U_9502,U_9501,U_9500] :
      ( ! [U_9499,U_9498,U_9497] : hAPP(c_Fun_Ocomp(U_9497,U_9498,U_9499,U_9500),U_9501) != hAPP(c_Fun_Ocomp(U_9502,U_9498,U_9499,U_9503),U_9504)
      | hAPP(U_9500,hAPP(U_9501,U_9505)) = hAPP(U_9503,hAPP(U_9504,U_9505)) ),
    inference(miniscope,[status(thm)],[f_2663_2]) ).

cnf(f_2663_4,plain,
    ( hAPP(c_Fun_Ocomp(U_9497,U_9498,U_9499,U_9500),U_9501) != hAPP(c_Fun_Ocomp(U_9502,U_9498,U_9499,U_9503),U_9504)
    | hAPP(U_9500,hAPP(U_9501,U_9505)) = hAPP(U_9503,hAPP(U_9504,U_9505)) ),
    inference(clausify,[status(thm)],[f_2663_3]) ).

fof(f_2664_1,plain,
    ! [V_x_2,V_g_2,V_f_2,T_d,T_b,T_c] : hAPP(hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2),V_x_2) = hAPP(V_f_2,hAPP(V_g_2,V_x_2)),
    inference(fof_nnf,[status(thm)],[fact_o__apply]) ).

fof(f_2664_2,plain,
    ! [U_9511,U_9510,U_9509,U_9508,U_9507,U_9506] : hAPP(hAPP(c_Fun_Ocomp(U_9506,U_9507,U_9508,U_9509),U_9510),U_9511) = hAPP(U_9509,hAPP(U_9510,U_9511)),
    inference(variable_rename,[status(thm)],[f_2664_1]) ).

cnf(f_2664_3,plain,
    hAPP(hAPP(c_Fun_Ocomp(U_9506,U_9507,U_9508,U_9509),U_9510),U_9511) = hAPP(U_9509,hAPP(U_9510,U_9511)),
    inference(clausify,[status(thm)],[f_2664_2]) ).

fof(f_2665_1,plain,
    ! [V_h_2,V_g_2,T_e,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),hAPP(c_Fun_Ocomp(T_e,T_d,T_b,V_g_2),V_h_2)) = hAPP(c_Fun_Ocomp(T_e,T_c,T_b,hAPP(c_Fun_Ocomp(T_d,T_c,T_e,V_f_2),V_g_2)),V_h_2),
    inference(fof_nnf,[status(thm)],[fact_o__assoc]) ).

fof(f_2665_2,plain,
    ! [U_9518,U_9517,U_9516,U_9515,U_9514,U_9513,U_9512] : hAPP(c_Fun_Ocomp(U_9512,U_9513,U_9514,U_9515),hAPP(c_Fun_Ocomp(U_9516,U_9512,U_9514,U_9517),U_9518)) = hAPP(c_Fun_Ocomp(U_9516,U_9513,U_9514,hAPP(c_Fun_Ocomp(U_9512,U_9513,U_9516,U_9515),U_9517)),U_9518),
    inference(variable_rename,[status(thm)],[f_2665_1]) ).

cnf(f_2665_3,plain,
    hAPP(c_Fun_Ocomp(U_9512,U_9513,U_9514,U_9515),hAPP(c_Fun_Ocomp(U_9516,U_9512,U_9514,U_9517),U_9518)) = hAPP(c_Fun_Ocomp(U_9516,U_9513,U_9514,hAPP(c_Fun_Ocomp(U_9512,U_9513,U_9516,U_9515),U_9517)),U_9518),
    inference(clausify,[status(thm)],[f_2665_2]) ).

fof(f_2666_1,plain,
    ! [V_x_2,V_g_2,V_f_2,T_d,T_b,T_c] : hAPP(hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2),V_x_2) = hAPP(V_f_2,hAPP(V_g_2,V_x_2)),
    inference(fof_nnf,[status(thm)],[fact_o__def]) ).

fof(f_2666_2,plain,
    ! [U_9524,U_9523,U_9522,U_9521,U_9520,U_9519] : hAPP(hAPP(c_Fun_Ocomp(U_9519,U_9520,U_9521,U_9522),U_9523),U_9524) = hAPP(U_9522,hAPP(U_9523,U_9524)),
    inference(variable_rename,[status(thm)],[f_2666_1]) ).

cnf(f_2666_3,plain,
    hAPP(hAPP(c_Fun_Ocomp(U_9519,U_9520,U_9521,U_9522),U_9523),U_9524) = hAPP(U_9522,hAPP(U_9523,U_9524)),
    inference(clausify,[status(thm)],[f_2666_2]) ).

fof(f_2667_1,plain,
    ! [V_b_2,V_f_2,T_c,T_b,V_a_2,V_x_2] :
      ( ( hAPP(c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_a_2,V_b_2),V_x_2) = hAPP(V_f_2,V_x_2)
        | V_x_2 = V_a_2 )
      & ( hAPP(c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_a_2,V_b_2),V_x_2) = V_b_2
        | V_x_2 != V_a_2 ) ),
    inference(fof_nnf,[status(thm)],[fact_fun__upd__def]) ).

fof(f_2667_2,plain,
    ! [U_9530,U_9529,U_9528,U_9527,U_9526,U_9525] :
      ( ( hAPP(c_Fun_Ofun__upd(U_9527,U_9528,U_9529,U_9526,U_9530),U_9525) = hAPP(U_9529,U_9525)
        | U_9525 = U_9526 )
      & ( hAPP(c_Fun_Ofun__upd(U_9527,U_9528,U_9529,U_9526,U_9530),U_9525) = U_9530
        | U_9525 != U_9526 ) ),
    inference(variable_rename,[status(thm)],[f_2667_1]) ).

fof(f_2667_3,plain,
    ( ! [U_9542,U_9540,U_9538,U_9536,U_9534,U_9532] :
        ( hAPP(c_Fun_Ofun__upd(U_9536,U_9538,U_9540,U_9534,U_9542),U_9532) = hAPP(U_9540,U_9532)
        | U_9532 = U_9534 )
    & ! [U_9541,U_9539,U_9537,U_9535,U_9533,U_9531] :
        ( hAPP(c_Fun_Ofun__upd(U_9535,U_9537,U_9539,U_9533,U_9541),U_9531) = U_9541
        | U_9531 != U_9533 ) ),
    inference(miniscope,[status(thm)],[f_2667_2]) ).

cnf(f_2667_4,plain,
    ( hAPP(c_Fun_Ofun__upd(U_9535,U_9537,U_9539,U_9533,U_9541),U_9531) = U_9541
    | U_9531 != U_9533 ),
    inference(clausify,[status(thm)],[f_2667_3]) ).

cnf(f_2667_5,plain,
    ( hAPP(c_Fun_Ofun__upd(U_9536,U_9538,U_9540,U_9534,U_9542),U_9532) = hAPP(U_9540,U_9532)
    | U_9532 = U_9534 ),
    inference(clausify,[status(thm)],[f_2667_3]) ).

fof(f_2668_1,plain,
    ! [V_g_2,T_d,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofun__left__comm(T_d,T_c,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,T_c),T_d),V_f_2),V_g_2))
      | ~ c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofun__left__comm__apply]) ).

fof(f_2668_2,plain,
    ! [U_9547,U_9546,U_9545,U_9544,U_9543] :
      ( c_Finite__Set_Ofun__left__comm(U_9546,U_9544,hAPP(hAPP(c_COMBB(U_9543,tc_fun(U_9544,U_9544),U_9546),U_9545),U_9547))
      | ~ c_Finite__Set_Ofun__left__comm(U_9543,U_9544,U_9545) ),
    inference(variable_rename,[status(thm)],[f_2668_1]) ).

cnf(f_2668_3,plain,
    ( c_Finite__Set_Ofun__left__comm(U_9546,U_9544,hAPP(hAPP(c_COMBB(U_9543,tc_fun(U_9544,U_9544),U_9546),U_9545),U_9547))
    | ~ c_Finite__Set_Ofun__left__comm(U_9543,U_9544,U_9545) ),
    inference(clausify,[status(thm)],[f_2668_2]) ).

fof(f_2669_1,plain,
    ! [V_g_2,T_d,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofun__left__comm__idem(T_d,T_c,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,T_c),T_d),V_f_2),V_g_2))
      | ~ c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofun__left__comm__idem__apply]) ).

fof(f_2669_2,plain,
    ! [U_9552,U_9551,U_9550,U_9549,U_9548] :
      ( c_Finite__Set_Ofun__left__comm__idem(U_9551,U_9549,hAPP(hAPP(c_COMBB(U_9548,tc_fun(U_9549,U_9549),U_9551),U_9550),U_9552))
      | ~ c_Finite__Set_Ofun__left__comm__idem(U_9548,U_9549,U_9550) ),
    inference(variable_rename,[status(thm)],[f_2669_1]) ).

cnf(f_2669_3,plain,
    ( c_Finite__Set_Ofun__left__comm__idem(U_9551,U_9549,hAPP(hAPP(c_COMBB(U_9548,tc_fun(U_9549,U_9549),U_9551),U_9550),U_9552))
    | ~ c_Finite__Set_Ofun__left__comm__idem(U_9548,U_9549,U_9550) ),
    inference(clausify,[status(thm)],[f_2669_2]) ).

fof(f_2670_1,plain,
    ! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Otimes__class_Otimes(T_b)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_g_2),V_A_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__timesf]) ).

fof(f_2670_2,plain,
    ! [U_9557,U_9556,U_9555,U_9554,U_9553] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9554,U_9553),hAPP(hAPP(c_COMBS(U_9554,U_9553,U_9553),hAPP(hAPP(c_COMBB(U_9553,tc_fun(U_9553,U_9553),U_9554),c_Groups_Otimes__class_Otimes(U_9553)),U_9555)),U_9556)),U_9557) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9553),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9554,U_9553),U_9555),U_9557)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9554,U_9553),U_9556),U_9557))
      | ~ class_Groups_Ocomm__monoid__mult(U_9553) ),
    inference(variable_rename,[status(thm)],[f_2670_1]) ).

cnf(f_2670_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9554,U_9553),hAPP(hAPP(c_COMBS(U_9554,U_9553,U_9553),hAPP(hAPP(c_COMBB(U_9553,tc_fun(U_9553,U_9553),U_9554),c_Groups_Otimes__class_Otimes(U_9553)),U_9555)),U_9556)),U_9557) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9553),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9554,U_9553),U_9555),U_9557)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9554,U_9553),U_9556),U_9557))
    | ~ class_Groups_Ocomm__monoid__mult(U_9553) ),
    inference(clausify,[status(thm)],[f_2670_2]) ).

fof(f_2671_1,plain,
    ! [V_A_2,V_f_2,T_c,V_r_2,T_b] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_r_2),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),hAPP(c_Groups_Otimes__class_Otimes(T_b),V_r_2)),V_f_2)),V_A_2)
      | ~ class_Rings_Osemiring__0(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__right__distrib]) ).

fof(f_2671_2,plain,
    ! [U_9562,U_9561,U_9560,U_9559,U_9558] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9558),U_9559),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9560,U_9558),U_9561),U_9562)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9560,U_9558),hAPP(hAPP(c_COMBB(U_9558,U_9558,U_9560),hAPP(c_Groups_Otimes__class_Otimes(U_9558),U_9559)),U_9561)),U_9562)
      | ~ class_Rings_Osemiring__0(U_9558) ),
    inference(variable_rename,[status(thm)],[f_2671_1]) ).

cnf(f_2671_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9558),U_9559),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9560,U_9558),U_9561),U_9562)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9560,U_9558),hAPP(hAPP(c_COMBB(U_9558,U_9558,U_9560),hAPP(c_Groups_Otimes__class_Otimes(U_9558),U_9559)),U_9561)),U_9562)
    | ~ class_Rings_Osemiring__0(U_9558) ),
    inference(clausify,[status(thm)],[f_2671_2]) ).

fof(f_2672_1,plain,
    ! [V_r_2,V_A_2,V_f_2,T_c,T_b] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),V_r_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Otimes__class_Otimes(T_b)),V_f_2)),V_r_2)),V_A_2)
      | ~ class_Rings_Osemiring__0(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__left__distrib]) ).

fof(f_2672_2,plain,
    ! [U_9567,U_9566,U_9565,U_9564,U_9563] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9563),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9564,U_9563),U_9565),U_9566)),U_9567) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9564,U_9563),hAPP(hAPP(c_COMBC(U_9564,U_9563,U_9563),hAPP(hAPP(c_COMBB(U_9563,tc_fun(U_9563,U_9563),U_9564),c_Groups_Otimes__class_Otimes(U_9563)),U_9565)),U_9567)),U_9566)
      | ~ class_Rings_Osemiring__0(U_9563) ),
    inference(variable_rename,[status(thm)],[f_2672_1]) ).

cnf(f_2672_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9563),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9564,U_9563),U_9565),U_9566)),U_9567) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9564,U_9563),hAPP(hAPP(c_COMBC(U_9564,U_9563,U_9563),hAPP(hAPP(c_COMBB(U_9563,tc_fun(U_9563,U_9563),U_9564),c_Groups_Otimes__class_Otimes(U_9563)),U_9565)),U_9567)),U_9566)
    | ~ class_Rings_Osemiring__0(U_9563) ),
    inference(clausify,[status(thm)],[f_2672_2]) ).

fof(f_2673_1,plain,
    ! [V_B_2,V_g_2,T_d,V_A_2,V_f_2,T_c,T_b] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b),V_g_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_b),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,T_b),tc_fun(T_d,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_b),tc_fun(tc_fun(T_d,T_b),tc_fun(T_d,T_b)),T_c),c_COMBB(T_b,T_b,T_d)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Otimes__class_Otimes(T_b)),V_f_2))),V_g_2))),V_B_2)),V_A_2)
      | ~ class_Rings_Osemiring__0(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__product]) ).

fof(f_2673_2,plain,
    ! [U_9574,U_9573,U_9572,U_9571,U_9570,U_9569,U_9568] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9568),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9569,U_9568),U_9570),U_9571)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9572,U_9568),U_9573),U_9574)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9569,U_9568),hAPP(hAPP(c_COMBC(U_9569,tc_fun(U_9572,tc_HOL_Obool),U_9568),hAPP(hAPP(c_COMBB(tc_fun(U_9572,U_9568),tc_fun(tc_fun(U_9572,tc_HOL_Obool),U_9568),U_9569),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9572,U_9568)),hAPP(hAPP(c_COMBC(U_9569,tc_fun(U_9572,U_9568),tc_fun(U_9572,U_9568)),hAPP(hAPP(c_COMBB(tc_fun(U_9568,U_9568),tc_fun(tc_fun(U_9572,U_9568),tc_fun(U_9572,U_9568)),U_9569),c_COMBB(U_9568,U_9568,U_9572)),hAPP(hAPP(c_COMBB(U_9568,tc_fun(U_9568,U_9568),U_9569),c_Groups_Otimes__class_Otimes(U_9568)),U_9570))),U_9573))),U_9574)),U_9571)
      | ~ class_Rings_Osemiring__0(U_9568) ),
    inference(variable_rename,[status(thm)],[f_2673_1]) ).

cnf(f_2673_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9568),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9569,U_9568),U_9570),U_9571)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9572,U_9568),U_9573),U_9574)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9569,U_9568),hAPP(hAPP(c_COMBC(U_9569,tc_fun(U_9572,tc_HOL_Obool),U_9568),hAPP(hAPP(c_COMBB(tc_fun(U_9572,U_9568),tc_fun(tc_fun(U_9572,tc_HOL_Obool),U_9568),U_9569),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9572,U_9568)),hAPP(hAPP(c_COMBC(U_9569,tc_fun(U_9572,U_9568),tc_fun(U_9572,U_9568)),hAPP(hAPP(c_COMBB(tc_fun(U_9568,U_9568),tc_fun(tc_fun(U_9572,U_9568),tc_fun(U_9572,U_9568)),U_9569),c_COMBB(U_9568,U_9568,U_9572)),hAPP(hAPP(c_COMBB(U_9568,tc_fun(U_9568,U_9568),U_9569),c_Groups_Otimes__class_Otimes(U_9568)),U_9570))),U_9573))),U_9574)),U_9571)
    | ~ class_Rings_Osemiring__0(U_9568) ),
    inference(clausify,[status(thm)],[f_2673_2]) ).

fof(f_2674_1,plain,
    ! [V_y_2,V_x_2,V_g_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),c_Fun_Ofun__upd(T_b,T_d,V_g_2,V_x_2,V_y_2)) = c_Fun_Ofun__upd(T_b,T_c,hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),V_g_2),V_x_2,hAPP(V_f_2,V_y_2)),
    inference(fof_nnf,[status(thm)],[fact_fun__upd__comp]) ).

fof(f_2674_2,plain,
    ! [U_9581,U_9580,U_9579,U_9578,U_9577,U_9576,U_9575] : hAPP(c_Fun_Ocomp(U_9575,U_9576,U_9577,U_9578),c_Fun_Ofun__upd(U_9577,U_9575,U_9579,U_9580,U_9581)) = c_Fun_Ofun__upd(U_9577,U_9576,hAPP(c_Fun_Ocomp(U_9575,U_9576,U_9577,U_9578),U_9579),U_9580,hAPP(U_9578,U_9581)),
    inference(variable_rename,[status(thm)],[f_2674_1]) ).

cnf(f_2674_3,plain,
    hAPP(c_Fun_Ocomp(U_9575,U_9576,U_9577,U_9578),c_Fun_Ofun__upd(U_9577,U_9575,U_9579,U_9580,U_9581)) = c_Fun_Ofun__upd(U_9577,U_9576,hAPP(c_Fun_Ocomp(U_9575,U_9576,U_9577,U_9578),U_9579),U_9580,hAPP(U_9578,U_9581)),
    inference(clausify,[status(thm)],[f_2674_2]) ).

fof(f_2675_1,plain,
    ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_y_2)),hAPP(V_f_2,V_x_2))
      | ~ c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofun__comp__comm]) ).

fof(f_2675_2,plain,
    ! [U_9586,U_9585,U_9584,U_9583,U_9582] :
      ( hAPP(c_Fun_Ocomp(U_9583,U_9583,U_9583,hAPP(U_9584,U_9585)),hAPP(U_9584,U_9586)) = hAPP(c_Fun_Ocomp(U_9583,U_9583,U_9583,hAPP(U_9584,U_9586)),hAPP(U_9584,U_9585))
      | ~ c_Finite__Set_Ofun__left__comm(U_9582,U_9583,U_9584) ),
    inference(variable_rename,[status(thm)],[f_2675_1]) ).

fof(f_2675_3,plain,
    ! [U_9586,U_9585,U_9584,U_9583] :
      ( ! [U_9582] : ~ c_Finite__Set_Ofun__left__comm(U_9582,U_9583,U_9584)
      | hAPP(c_Fun_Ocomp(U_9583,U_9583,U_9583,hAPP(U_9584,U_9585)),hAPP(U_9584,U_9586)) = hAPP(c_Fun_Ocomp(U_9583,U_9583,U_9583,hAPP(U_9584,U_9586)),hAPP(U_9584,U_9585)) ),
    inference(miniscope,[status(thm)],[f_2675_2]) ).

cnf(f_2675_4,plain,
    ( ~ c_Finite__Set_Ofun__left__comm(U_9582,U_9583,U_9584)
    | hAPP(c_Fun_Ocomp(U_9583,U_9583,U_9583,hAPP(U_9584,U_9585)),hAPP(U_9584,U_9586)) = hAPP(c_Fun_Ocomp(U_9583,U_9583,U_9583,hAPP(U_9584,U_9586)),hAPP(U_9584,U_9585)) ),
    inference(clausify,[status(thm)],[f_2675_3]) ).

fof(f_2676_1,plain,
    ! [V_B_2,V_a_2,T_c,V_A_2,V_u_2,T_b] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_u_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_INT__insert__distrib]) ).

fof(f_2676_2,plain,
    ! [U_9592,U_9591,U_9590,U_9589,U_9588,U_9587] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9587,tc_fun(U_9590,tc_HOL_Obool)),U_9589),hAPP(hAPP(c_COMBB(tc_fun(U_9590,tc_HOL_Obool),tc_fun(U_9590,tc_HOL_Obool),U_9587),hAPP(c_Set_Oinsert(U_9590),U_9591)),U_9592)) = hAPP(hAPP(c_Set_Oinsert(U_9590),U_9591),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9587,tc_fun(U_9590,tc_HOL_Obool)),U_9589),U_9592))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9587),U_9588),U_9589)) ),
    inference(variable_rename,[status(thm)],[f_2676_1]) ).

cnf(f_2676_3,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9587,tc_fun(U_9590,tc_HOL_Obool)),U_9589),hAPP(hAPP(c_COMBB(tc_fun(U_9590,tc_HOL_Obool),tc_fun(U_9590,tc_HOL_Obool),U_9587),hAPP(c_Set_Oinsert(U_9590),U_9591)),U_9592)) = hAPP(hAPP(c_Set_Oinsert(U_9590),U_9591),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9587,tc_fun(U_9590,tc_HOL_Obool)),U_9589),U_9592))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9587),U_9588),U_9589)) ),
    inference(clausify,[status(thm)],[f_2676_2]) ).

fof(f_2677_1,plain,
    ! [V_y_2,V_x_2,T_c,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_x_2),V_y_2))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_x_2),V_y_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_bot__empty__eq2]) ).

fof(f_2677_2,plain,
    ! [U_9596,U_9595,U_9594,U_9593] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_9593,tc_fun(U_9594,tc_HOL_Obool))),U_9595),U_9596))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9593,U_9594)),hAPP(hAPP(c_Product__Type_OPair(U_9593,U_9594),U_9595),U_9596)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9593,U_9594),tc_HOL_Obool)))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9593,U_9594)),hAPP(hAPP(c_Product__Type_OPair(U_9593,U_9594),U_9595),U_9596)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9593,U_9594),tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_9593,tc_fun(U_9594,tc_HOL_Obool))),U_9595),U_9596)) ) ),
    inference(variable_rename,[status(thm)],[f_2677_1]) ).

fof(f_2677_3,plain,
    ( ! [U_9604,U_9602,U_9600,U_9598] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_9598,tc_fun(U_9600,tc_HOL_Obool))),U_9602),U_9604))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9598,U_9600)),hAPP(hAPP(c_Product__Type_OPair(U_9598,U_9600),U_9602),U_9604)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9598,U_9600),tc_HOL_Obool)))) )
    & ! [U_9603,U_9601,U_9599,U_9597] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9597,U_9599)),hAPP(hAPP(c_Product__Type_OPair(U_9597,U_9599),U_9601),U_9603)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9597,U_9599),tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_9597,tc_fun(U_9599,tc_HOL_Obool))),U_9601),U_9603)) ) ),
    inference(miniscope,[status(thm)],[f_2677_2]) ).

cnf(f_2677_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9597,U_9599)),hAPP(hAPP(c_Product__Type_OPair(U_9597,U_9599),U_9601),U_9603)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9597,U_9599),tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_9597,tc_fun(U_9599,tc_HOL_Obool))),U_9601),U_9603)) ),
    inference(clausify,[status(thm)],[f_2677_3]) ).

cnf(f_2677_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_9598,tc_fun(U_9600,tc_HOL_Obool))),U_9602),U_9604))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9598,U_9600)),hAPP(hAPP(c_Product__Type_OPair(U_9598,U_9600),U_9602),U_9604)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9598,U_9600),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_2677_3]) ).

fof(f_2678_1,plain,
    ! [V_x_2,T_b] :
      ( ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_x_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) )
      & ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_x_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_bot__empty__eq]) ).

fof(f_2678_2,plain,
    ! [U_9606,U_9605] :
      ( ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_9605,tc_HOL_Obool)),U_9606))
        | ~ hBOOL(hAPP(hAPP(c_member(U_9605),U_9606),c_Orderings_Obot__class_Obot(tc_fun(U_9605,tc_HOL_Obool)))) )
      & ( hBOOL(hAPP(hAPP(c_member(U_9605),U_9606),c_Orderings_Obot__class_Obot(tc_fun(U_9605,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_9605,tc_HOL_Obool)),U_9606)) ) ),
    inference(variable_rename,[status(thm)],[f_2678_1]) ).

fof(f_2678_3,plain,
    ( ! [U_9610,U_9608] :
        ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_9608,tc_HOL_Obool)),U_9610))
        | ~ hBOOL(hAPP(hAPP(c_member(U_9608),U_9610),c_Orderings_Obot__class_Obot(tc_fun(U_9608,tc_HOL_Obool)))) )
    & ! [U_9609,U_9607] :
        ( hBOOL(hAPP(hAPP(c_member(U_9607),U_9609),c_Orderings_Obot__class_Obot(tc_fun(U_9607,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_9607,tc_HOL_Obool)),U_9609)) ) ),
    inference(miniscope,[status(thm)],[f_2678_2]) ).

cnf(f_2678_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9607),U_9609),c_Orderings_Obot__class_Obot(tc_fun(U_9607,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_9607,tc_HOL_Obool)),U_9609)) ),
    inference(clausify,[status(thm)],[f_2678_3]) ).

cnf(f_2678_5,plain,
    ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_9608,tc_HOL_Obool)),U_9610))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9608),U_9610),c_Orderings_Obot__class_Obot(tc_fun(U_9608,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_2678_3]) ).

fof(f_2679_1,plain,
    ! [V_x_2,V_S_2,V_R_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)),V_x_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2))) )
      & ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2)))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)),V_x_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_sup__Un__eq]) ).

fof(f_2679_2,plain,
    ! [U_9614,U_9613,U_9612,U_9611] :
      ( ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9611,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_9611,tc_fun(U_9611,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9611)),U_9612)),hAPP(hAPP(c_COMBC(U_9611,tc_fun(U_9611,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9611)),U_9613)),U_9614))
        | ~ hBOOL(hAPP(hAPP(c_member(U_9611),U_9614),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9611,tc_HOL_Obool)),U_9612),U_9613))) )
      & ( hBOOL(hAPP(hAPP(c_member(U_9611),U_9614),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9611,tc_HOL_Obool)),U_9612),U_9613)))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9611,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_9611,tc_fun(U_9611,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9611)),U_9612)),hAPP(hAPP(c_COMBC(U_9611,tc_fun(U_9611,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9611)),U_9613)),U_9614)) ) ),
    inference(variable_rename,[status(thm)],[f_2679_1]) ).

fof(f_2679_3,plain,
    ( ! [U_9622,U_9620,U_9618,U_9616] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9616,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_9616,tc_fun(U_9616,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9616)),U_9618)),hAPP(hAPP(c_COMBC(U_9616,tc_fun(U_9616,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9616)),U_9620)),U_9622))
        | ~ hBOOL(hAPP(hAPP(c_member(U_9616),U_9622),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9616,tc_HOL_Obool)),U_9618),U_9620))) )
    & ! [U_9621,U_9619,U_9617,U_9615] :
        ( hBOOL(hAPP(hAPP(c_member(U_9615),U_9621),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9615,tc_HOL_Obool)),U_9617),U_9619)))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9615,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_9615,tc_fun(U_9615,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9615)),U_9617)),hAPP(hAPP(c_COMBC(U_9615,tc_fun(U_9615,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9615)),U_9619)),U_9621)) ) ),
    inference(miniscope,[status(thm)],[f_2679_2]) ).

cnf(f_2679_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9615),U_9621),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9615,tc_HOL_Obool)),U_9617),U_9619)))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9615,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_9615,tc_fun(U_9615,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9615)),U_9617)),hAPP(hAPP(c_COMBC(U_9615,tc_fun(U_9615,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9615)),U_9619)),U_9621)) ),
    inference(clausify,[status(thm)],[f_2679_3]) ).

cnf(f_2679_5,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9616,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_9616,tc_fun(U_9616,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9616)),U_9618)),hAPP(hAPP(c_COMBC(U_9616,tc_fun(U_9616,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9616)),U_9620)),U_9622))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9616),U_9622),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9616,tc_HOL_Obool)),U_9618),U_9620))) ),
    inference(clausify,[status(thm)],[f_2679_3]) ).

fof(f_2680_1,plain,
    ! [V_x_2,V_S_2,V_R_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)),V_x_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2))) )
      & ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2)))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)),V_x_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_inf__Int__eq]) ).

fof(f_2680_2,plain,
    ! [U_9626,U_9625,U_9624,U_9623] :
      ( ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9623,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_9623,tc_fun(U_9623,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9623)),U_9624)),hAPP(hAPP(c_COMBC(U_9623,tc_fun(U_9623,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9623)),U_9625)),U_9626))
        | ~ hBOOL(hAPP(hAPP(c_member(U_9623),U_9626),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9623,tc_HOL_Obool)),U_9624),U_9625))) )
      & ( hBOOL(hAPP(hAPP(c_member(U_9623),U_9626),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9623,tc_HOL_Obool)),U_9624),U_9625)))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9623,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_9623,tc_fun(U_9623,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9623)),U_9624)),hAPP(hAPP(c_COMBC(U_9623,tc_fun(U_9623,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9623)),U_9625)),U_9626)) ) ),
    inference(variable_rename,[status(thm)],[f_2680_1]) ).

fof(f_2680_3,plain,
    ( ! [U_9634,U_9632,U_9630,U_9628] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9628,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_9628,tc_fun(U_9628,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9628)),U_9630)),hAPP(hAPP(c_COMBC(U_9628,tc_fun(U_9628,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9628)),U_9632)),U_9634))
        | ~ hBOOL(hAPP(hAPP(c_member(U_9628),U_9634),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9628,tc_HOL_Obool)),U_9630),U_9632))) )
    & ! [U_9633,U_9631,U_9629,U_9627] :
        ( hBOOL(hAPP(hAPP(c_member(U_9627),U_9633),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9627,tc_HOL_Obool)),U_9629),U_9631)))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9627,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_9627,tc_fun(U_9627,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9627)),U_9629)),hAPP(hAPP(c_COMBC(U_9627,tc_fun(U_9627,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9627)),U_9631)),U_9633)) ) ),
    inference(miniscope,[status(thm)],[f_2680_2]) ).

cnf(f_2680_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9627),U_9633),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9627,tc_HOL_Obool)),U_9629),U_9631)))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9627,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_9627,tc_fun(U_9627,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9627)),U_9629)),hAPP(hAPP(c_COMBC(U_9627,tc_fun(U_9627,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9627)),U_9631)),U_9633)) ),
    inference(clausify,[status(thm)],[f_2680_3]) ).

cnf(f_2680_5,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9628,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_9628,tc_fun(U_9628,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9628)),U_9630)),hAPP(hAPP(c_COMBC(U_9628,tc_fun(U_9628,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9628)),U_9632)),U_9634))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9628),U_9634),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9628,tc_HOL_Obool)),U_9630),U_9632))) ),
    inference(clausify,[status(thm)],[f_2680_3]) ).

fof(f_2681_1,plain,
    ! [V_A_2,T_c,V_I_2,V_k_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_A_2,V_k_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_k_2),V_I_2)) ),
    inference(fof_nnf,[status(thm)],[fact_INT__absorb]) ).

fof(f_2681_2,plain,
    ! [U_9639,U_9638,U_9637,U_9636,U_9635] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9638,tc_HOL_Obool)),hAPP(U_9639,U_9636)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9635,tc_fun(U_9638,tc_HOL_Obool)),U_9637),U_9639)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9635,tc_fun(U_9638,tc_HOL_Obool)),U_9637),U_9639)
      | ~ hBOOL(hAPP(hAPP(c_member(U_9635),U_9636),U_9637)) ),
    inference(variable_rename,[status(thm)],[f_2681_1]) ).

cnf(f_2681_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9638,tc_HOL_Obool)),hAPP(U_9639,U_9636)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9635,tc_fun(U_9638,tc_HOL_Obool)),U_9637),U_9639)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9635,tc_fun(U_9638,tc_HOL_Obool)),U_9637),U_9639)
    | ~ hBOOL(hAPP(hAPP(c_member(U_9635),U_9636),U_9637)) ),
    inference(clausify,[status(thm)],[f_2681_2]) ).

fof(f_2682_1,plain,
    ! [V_B_2,V_A_2,T_c,V_b_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
        | ! [B_x] :
            ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,B_x)))
            | ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) )
      & ( ? [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,B_x)))
            & hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_UN__iff]) ).

fof(f_2682_2,plain,
    ! [U_9646,U_9645,U_9644,U_9643,U_9642] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_9642),U_9643),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9644,tc_fun(U_9642,tc_HOL_Obool)),U_9645),U_9646)))
        | ! [U_9641] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_9642),U_9643),hAPP(U_9646,U_9641)))
            | ~ hBOOL(hAPP(hAPP(c_member(U_9644),U_9641),U_9645)) ) )
      & ( ? [U_9640] :
            ( hBOOL(hAPP(hAPP(c_member(U_9642),U_9643),hAPP(U_9646,U_9640)))
            & hBOOL(hAPP(hAPP(c_member(U_9644),U_9640),U_9645)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_9642),U_9643),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9644,tc_fun(U_9642,tc_HOL_Obool)),U_9645),U_9646))) ) ),
    inference(variable_rename,[status(thm)],[f_2682_1]) ).

fof(f_2682_3,plain,
    ( ! [U_9656,U_9654,U_9652,U_9650,U_9648] :
        ( hBOOL(hAPP(hAPP(c_member(U_9648),U_9650),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9652,tc_fun(U_9648,tc_HOL_Obool)),U_9654),U_9656)))
        | ! [U_9641] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_9648),U_9650),hAPP(U_9656,U_9641)))
            | ~ hBOOL(hAPP(hAPP(c_member(U_9652),U_9641),U_9654)) ) )
    & ! [U_9655,U_9653,U_9651,U_9649,U_9647] :
        ( ? [U_9640] :
            ( hBOOL(hAPP(hAPP(c_member(U_9647),U_9649),hAPP(U_9655,U_9640)))
            & hBOOL(hAPP(hAPP(c_member(U_9651),U_9640),U_9653)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_9647),U_9649),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9651,tc_fun(U_9647,tc_HOL_Obool)),U_9653),U_9655))) ) ),
    inference(miniscope,[status(thm)],[f_2682_2]) ).

fof(f_2682_4,plain,
    ( ! [U_9656,U_9654,U_9652,U_9650,U_9648] :
        ( hBOOL(hAPP(hAPP(c_member(U_9648),U_9650),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9652,tc_fun(U_9648,tc_HOL_Obool)),U_9654),U_9656)))
        | ! [U_9641] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_9648),U_9650),hAPP(U_9656,U_9641)))
            | ~ hBOOL(hAPP(hAPP(c_member(U_9652),U_9641),U_9654)) ) )
    & ! [U_9655,U_9653,U_9651,U_9649,U_9647] :
        ( ( hBOOL(hAPP(hAPP(c_member(U_9647),U_9649),hAPP(U_9655,sK236(U_9655,U_9653,U_9651,U_9649,U_9647))))
          & hBOOL(hAPP(hAPP(c_member(U_9651),sK236(U_9655,U_9653,U_9651,U_9649,U_9647)),U_9653)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_9647),U_9649),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9651,tc_fun(U_9647,tc_HOL_Obool)),U_9653),U_9655))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK236]),skolemize(U_9640,sK236(U_9655,U_9653,U_9651,U_9649,U_9647))],[f_2682_3]) ).

cnf(f_2682_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9651),sK236(U_9655,U_9653,U_9651,U_9649,U_9647)),U_9653))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9647),U_9649),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9651,tc_fun(U_9647,tc_HOL_Obool)),U_9653),U_9655))) ),
    inference(clausify,[status(thm)],[f_2682_4]) ).

cnf(f_2682_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9647),U_9649),hAPP(U_9655,sK236(U_9655,U_9653,U_9651,U_9649,U_9647))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9647),U_9649),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9651,tc_fun(U_9647,tc_HOL_Obool)),U_9653),U_9655))) ),
    inference(clausify,[status(thm)],[f_2682_4]) ).

cnf(f_2682_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9648),U_9650),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9652,tc_fun(U_9648,tc_HOL_Obool)),U_9654),U_9656)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9648),U_9650),hAPP(U_9656,U_9641)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9652),U_9641),U_9654)) ),
    inference(clausify,[status(thm)],[f_2682_4]) ).

fof(f_2683_1,plain,
    ! [V_B_2,V_A_2,T_c,V_b_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
        | ? [B_x] :
            ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,B_x)))
            & hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) )
      & ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,B_x)))
            | ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_INT__iff]) ).

fof(f_2683_2,plain,
    ! [U_9663,U_9662,U_9661,U_9660,U_9659] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_9659),U_9660),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9661,tc_fun(U_9659,tc_HOL_Obool)),U_9662),U_9663)))
        | ? [U_9658] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_9659),U_9660),hAPP(U_9663,U_9658)))
            & hBOOL(hAPP(hAPP(c_member(U_9661),U_9658),U_9662)) ) )
      & ( ! [U_9657] :
            ( hBOOL(hAPP(hAPP(c_member(U_9659),U_9660),hAPP(U_9663,U_9657)))
            | ~ hBOOL(hAPP(hAPP(c_member(U_9661),U_9657),U_9662)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_9659),U_9660),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9661,tc_fun(U_9659,tc_HOL_Obool)),U_9662),U_9663))) ) ),
    inference(variable_rename,[status(thm)],[f_2683_1]) ).

fof(f_2683_3,plain,
    ( ! [U_9673,U_9671,U_9669,U_9667,U_9665] :
        ( hBOOL(hAPP(hAPP(c_member(U_9665),U_9667),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9669,tc_fun(U_9665,tc_HOL_Obool)),U_9671),U_9673)))
        | ? [U_9658] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_9665),U_9667),hAPP(U_9673,U_9658)))
            & hBOOL(hAPP(hAPP(c_member(U_9669),U_9658),U_9671)) ) )
    & ! [U_9672,U_9670,U_9668,U_9666,U_9664] :
        ( ! [U_9657] :
            ( hBOOL(hAPP(hAPP(c_member(U_9664),U_9666),hAPP(U_9672,U_9657)))
            | ~ hBOOL(hAPP(hAPP(c_member(U_9668),U_9657),U_9670)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_9664),U_9666),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9668,tc_fun(U_9664,tc_HOL_Obool)),U_9670),U_9672))) ) ),
    inference(miniscope,[status(thm)],[f_2683_2]) ).

fof(f_2683_4,plain,
    ( ! [U_9673,U_9671,U_9669,U_9667,U_9665] :
        ( hBOOL(hAPP(hAPP(c_member(U_9665),U_9667),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9669,tc_fun(U_9665,tc_HOL_Obool)),U_9671),U_9673)))
        | ( ~ hBOOL(hAPP(hAPP(c_member(U_9665),U_9667),hAPP(U_9673,sK237(U_9673,U_9671,U_9669,U_9667,U_9665))))
          & hBOOL(hAPP(hAPP(c_member(U_9669),sK237(U_9673,U_9671,U_9669,U_9667,U_9665)),U_9671)) ) )
    & ! [U_9672,U_9670,U_9668,U_9666,U_9664] :
        ( ! [U_9657] :
            ( hBOOL(hAPP(hAPP(c_member(U_9664),U_9666),hAPP(U_9672,U_9657)))
            | ~ hBOOL(hAPP(hAPP(c_member(U_9668),U_9657),U_9670)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_9664),U_9666),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9668,tc_fun(U_9664,tc_HOL_Obool)),U_9670),U_9672))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK237]),skolemize(U_9658,sK237(U_9673,U_9671,U_9669,U_9667,U_9665))],[f_2683_3]) ).

cnf(f_2683_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9664),U_9666),hAPP(U_9672,U_9657)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9668),U_9657),U_9670))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9664),U_9666),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9668,tc_fun(U_9664,tc_HOL_Obool)),U_9670),U_9672))) ),
    inference(clausify,[status(thm)],[f_2683_4]) ).

cnf(f_2683_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9669),sK237(U_9673,U_9671,U_9669,U_9667,U_9665)),U_9671))
    | hBOOL(hAPP(hAPP(c_member(U_9665),U_9667),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9669,tc_fun(U_9665,tc_HOL_Obool)),U_9671),U_9673))) ),
    inference(clausify,[status(thm)],[f_2683_4]) ).

cnf(f_2683_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_9665),U_9667),hAPP(U_9673,sK237(U_9673,U_9671,U_9669,U_9667,U_9665))))
    | hBOOL(hAPP(hAPP(c_member(U_9665),U_9667),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9669,tc_fun(U_9665,tc_HOL_Obool)),U_9671),U_9673))) ),
    inference(clausify,[status(thm)],[f_2683_4]) ).

fof(f_2684_1,plain,
    ! [V_S_2,V_R_2,T_b] :
      ( ( hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2) = hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)
        | V_R_2 != V_S_2 )
      & ( V_R_2 = V_S_2
        | hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2) != hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_pred__equals__eq]) ).

fof(f_2684_2,plain,
    ! [U_9676,U_9675,U_9674] :
      ( ( hAPP(hAPP(c_COMBC(U_9674,tc_fun(U_9674,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9674)),U_9675) = hAPP(hAPP(c_COMBC(U_9674,tc_fun(U_9674,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9674)),U_9676)
        | U_9675 != U_9676 )
      & ( U_9675 = U_9676
        | hAPP(hAPP(c_COMBC(U_9674,tc_fun(U_9674,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9674)),U_9675) != hAPP(hAPP(c_COMBC(U_9674,tc_fun(U_9674,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9674)),U_9676) ) ),
    inference(variable_rename,[status(thm)],[f_2684_1]) ).

fof(f_2684_3,plain,
    ( ! [U_9682,U_9680] :
        ( ! [U_9678] : hAPP(hAPP(c_COMBC(U_9678,tc_fun(U_9678,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9678)),U_9680) = hAPP(hAPP(c_COMBC(U_9678,tc_fun(U_9678,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9678)),U_9682)
        | U_9680 != U_9682 )
    & ! [U_9681,U_9679] :
        ( ! [U_9677] : hAPP(hAPP(c_COMBC(U_9677,tc_fun(U_9677,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9677)),U_9679) != hAPP(hAPP(c_COMBC(U_9677,tc_fun(U_9677,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9677)),U_9681)
        | U_9679 = U_9681 ) ),
    inference(miniscope,[status(thm)],[f_2684_2]) ).

cnf(f_2684_4,plain,
    ( hAPP(hAPP(c_COMBC(U_9677,tc_fun(U_9677,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9677)),U_9679) != hAPP(hAPP(c_COMBC(U_9677,tc_fun(U_9677,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9677)),U_9681)
    | U_9679 = U_9681 ),
    inference(clausify,[status(thm)],[f_2684_3]) ).

cnf(f_2684_5,plain,
    ( hAPP(hAPP(c_COMBC(U_9678,tc_fun(U_9678,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9678)),U_9680) = hAPP(hAPP(c_COMBC(U_9678,tc_fun(U_9678,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9678)),U_9682)
    | U_9680 != U_9682 ),
    inference(clausify,[status(thm)],[f_2684_3]) ).

fof(f_2685_1,plain,
    ! [V_S_2,V_R_2,T_c,T_b] :
      ( ( hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_R_2) = hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_S_2)
        | V_R_2 != V_S_2 )
      & ( V_R_2 = V_S_2
        | hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_R_2) != hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_S_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_pred__equals__eq2]) ).

fof(f_2685_2,plain,
    ! [U_9686,U_9685,U_9684,U_9683] :
      ( ( hAPP(hAPP(c_COMBC(U_9683,tc_fun(tc_prod(U_9683,U_9684),tc_HOL_Obool),tc_fun(U_9684,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9684,tc_fun(tc_fun(tc_prod(U_9683,U_9684),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9683,U_9684),tc_HOL_Obool),tc_fun(U_9684,tc_HOL_Obool)),U_9683),c_COMBC(U_9684,tc_fun(tc_prod(U_9683,U_9684),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9684,tc_prod(U_9683,U_9684)),tc_fun(U_9684,tc_fun(tc_fun(tc_prod(U_9683,U_9684),tc_HOL_Obool),tc_HOL_Obool)),U_9683),hAPP(c_COMBB(tc_prod(U_9683,U_9684),tc_fun(tc_fun(tc_prod(U_9683,U_9684),tc_HOL_Obool),tc_HOL_Obool),U_9684),c_member(tc_prod(U_9683,U_9684)))),c_Product__Type_OPair(U_9683,U_9684)))),U_9685) = hAPP(hAPP(c_COMBC(U_9683,tc_fun(tc_prod(U_9683,U_9684),tc_HOL_Obool),tc_fun(U_9684,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9684,tc_fun(tc_fun(tc_prod(U_9683,U_9684),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9683,U_9684),tc_HOL_Obool),tc_fun(U_9684,tc_HOL_Obool)),U_9683),c_COMBC(U_9684,tc_fun(tc_prod(U_9683,U_9684),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9684,tc_prod(U_9683,U_9684)),tc_fun(U_9684,tc_fun(tc_fun(tc_prod(U_9683,U_9684),tc_HOL_Obool),tc_HOL_Obool)),U_9683),hAPP(c_COMBB(tc_prod(U_9683,U_9684),tc_fun(tc_fun(tc_prod(U_9683,U_9684),tc_HOL_Obool),tc_HOL_Obool),U_9684),c_member(tc_prod(U_9683,U_9684)))),c_Product__Type_OPair(U_9683,U_9684)))),U_9686)
        | U_9685 != U_9686 )
      & ( U_9685 = U_9686
        | hAPP(hAPP(c_COMBC(U_9683,tc_fun(tc_prod(U_9683,U_9684),tc_HOL_Obool),tc_fun(U_9684,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9684,tc_fun(tc_fun(tc_prod(U_9683,U_9684),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9683,U_9684),tc_HOL_Obool),tc_fun(U_9684,tc_HOL_Obool)),U_9683),c_COMBC(U_9684,tc_fun(tc_prod(U_9683,U_9684),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9684,tc_prod(U_9683,U_9684)),tc_fun(U_9684,tc_fun(tc_fun(tc_prod(U_9683,U_9684),tc_HOL_Obool),tc_HOL_Obool)),U_9683),hAPP(c_COMBB(tc_prod(U_9683,U_9684),tc_fun(tc_fun(tc_prod(U_9683,U_9684),tc_HOL_Obool),tc_HOL_Obool),U_9684),c_member(tc_prod(U_9683,U_9684)))),c_Product__Type_OPair(U_9683,U_9684)))),U_9685) != hAPP(hAPP(c_COMBC(U_9683,tc_fun(tc_prod(U_9683,U_9684),tc_HOL_Obool),tc_fun(U_9684,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9684,tc_fun(tc_fun(tc_prod(U_9683,U_9684),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9683,U_9684),tc_HOL_Obool),tc_fun(U_9684,tc_HOL_Obool)),U_9683),c_COMBC(U_9684,tc_fun(tc_prod(U_9683,U_9684),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9684,tc_prod(U_9683,U_9684)),tc_fun(U_9684,tc_fun(tc_fun(tc_prod(U_9683,U_9684),tc_HOL_Obool),tc_HOL_Obool)),U_9683),hAPP(c_COMBB(tc_prod(U_9683,U_9684),tc_fun(tc_fun(tc_prod(U_9683,U_9684),tc_HOL_Obool),tc_HOL_Obool),U_9684),c_member(tc_prod(U_9683,U_9684)))),c_Product__Type_OPair(U_9683,U_9684)))),U_9686) ) ),
    inference(variable_rename,[status(thm)],[f_2685_1]) ).

fof(f_2685_3,plain,
    ( ! [U_9694,U_9692] :
        ( ! [U_9690,U_9688] : hAPP(hAPP(c_COMBC(U_9688,tc_fun(tc_prod(U_9688,U_9690),tc_HOL_Obool),tc_fun(U_9690,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9690,tc_fun(tc_fun(tc_prod(U_9688,U_9690),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9688,U_9690),tc_HOL_Obool),tc_fun(U_9690,tc_HOL_Obool)),U_9688),c_COMBC(U_9690,tc_fun(tc_prod(U_9688,U_9690),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9690,tc_prod(U_9688,U_9690)),tc_fun(U_9690,tc_fun(tc_fun(tc_prod(U_9688,U_9690),tc_HOL_Obool),tc_HOL_Obool)),U_9688),hAPP(c_COMBB(tc_prod(U_9688,U_9690),tc_fun(tc_fun(tc_prod(U_9688,U_9690),tc_HOL_Obool),tc_HOL_Obool),U_9690),c_member(tc_prod(U_9688,U_9690)))),c_Product__Type_OPair(U_9688,U_9690)))),U_9692) = hAPP(hAPP(c_COMBC(U_9688,tc_fun(tc_prod(U_9688,U_9690),tc_HOL_Obool),tc_fun(U_9690,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9690,tc_fun(tc_fun(tc_prod(U_9688,U_9690),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9688,U_9690),tc_HOL_Obool),tc_fun(U_9690,tc_HOL_Obool)),U_9688),c_COMBC(U_9690,tc_fun(tc_prod(U_9688,U_9690),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9690,tc_prod(U_9688,U_9690)),tc_fun(U_9690,tc_fun(tc_fun(tc_prod(U_9688,U_9690),tc_HOL_Obool),tc_HOL_Obool)),U_9688),hAPP(c_COMBB(tc_prod(U_9688,U_9690),tc_fun(tc_fun(tc_prod(U_9688,U_9690),tc_HOL_Obool),tc_HOL_Obool),U_9690),c_member(tc_prod(U_9688,U_9690)))),c_Product__Type_OPair(U_9688,U_9690)))),U_9694)
        | U_9692 != U_9694 )
    & ! [U_9693,U_9691] :
        ( ! [U_9689,U_9687] : hAPP(hAPP(c_COMBC(U_9687,tc_fun(tc_prod(U_9687,U_9689),tc_HOL_Obool),tc_fun(U_9689,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9689,tc_fun(tc_fun(tc_prod(U_9687,U_9689),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9687,U_9689),tc_HOL_Obool),tc_fun(U_9689,tc_HOL_Obool)),U_9687),c_COMBC(U_9689,tc_fun(tc_prod(U_9687,U_9689),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9689,tc_prod(U_9687,U_9689)),tc_fun(U_9689,tc_fun(tc_fun(tc_prod(U_9687,U_9689),tc_HOL_Obool),tc_HOL_Obool)),U_9687),hAPP(c_COMBB(tc_prod(U_9687,U_9689),tc_fun(tc_fun(tc_prod(U_9687,U_9689),tc_HOL_Obool),tc_HOL_Obool),U_9689),c_member(tc_prod(U_9687,U_9689)))),c_Product__Type_OPair(U_9687,U_9689)))),U_9691) != hAPP(hAPP(c_COMBC(U_9687,tc_fun(tc_prod(U_9687,U_9689),tc_HOL_Obool),tc_fun(U_9689,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9689,tc_fun(tc_fun(tc_prod(U_9687,U_9689),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9687,U_9689),tc_HOL_Obool),tc_fun(U_9689,tc_HOL_Obool)),U_9687),c_COMBC(U_9689,tc_fun(tc_prod(U_9687,U_9689),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9689,tc_prod(U_9687,U_9689)),tc_fun(U_9689,tc_fun(tc_fun(tc_prod(U_9687,U_9689),tc_HOL_Obool),tc_HOL_Obool)),U_9687),hAPP(c_COMBB(tc_prod(U_9687,U_9689),tc_fun(tc_fun(tc_prod(U_9687,U_9689),tc_HOL_Obool),tc_HOL_Obool),U_9689),c_member(tc_prod(U_9687,U_9689)))),c_Product__Type_OPair(U_9687,U_9689)))),U_9693)
        | U_9691 = U_9693 ) ),
    inference(miniscope,[status(thm)],[f_2685_2]) ).

cnf(f_2685_4,plain,
    ( hAPP(hAPP(c_COMBC(U_9687,tc_fun(tc_prod(U_9687,U_9689),tc_HOL_Obool),tc_fun(U_9689,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9689,tc_fun(tc_fun(tc_prod(U_9687,U_9689),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9687,U_9689),tc_HOL_Obool),tc_fun(U_9689,tc_HOL_Obool)),U_9687),c_COMBC(U_9689,tc_fun(tc_prod(U_9687,U_9689),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9689,tc_prod(U_9687,U_9689)),tc_fun(U_9689,tc_fun(tc_fun(tc_prod(U_9687,U_9689),tc_HOL_Obool),tc_HOL_Obool)),U_9687),hAPP(c_COMBB(tc_prod(U_9687,U_9689),tc_fun(tc_fun(tc_prod(U_9687,U_9689),tc_HOL_Obool),tc_HOL_Obool),U_9689),c_member(tc_prod(U_9687,U_9689)))),c_Product__Type_OPair(U_9687,U_9689)))),U_9691) != hAPP(hAPP(c_COMBC(U_9687,tc_fun(tc_prod(U_9687,U_9689),tc_HOL_Obool),tc_fun(U_9689,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9689,tc_fun(tc_fun(tc_prod(U_9687,U_9689),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9687,U_9689),tc_HOL_Obool),tc_fun(U_9689,tc_HOL_Obool)),U_9687),c_COMBC(U_9689,tc_fun(tc_prod(U_9687,U_9689),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9689,tc_prod(U_9687,U_9689)),tc_fun(U_9689,tc_fun(tc_fun(tc_prod(U_9687,U_9689),tc_HOL_Obool),tc_HOL_Obool)),U_9687),hAPP(c_COMBB(tc_prod(U_9687,U_9689),tc_fun(tc_fun(tc_prod(U_9687,U_9689),tc_HOL_Obool),tc_HOL_Obool),U_9689),c_member(tc_prod(U_9687,U_9689)))),c_Product__Type_OPair(U_9687,U_9689)))),U_9693)
    | U_9691 = U_9693 ),
    inference(clausify,[status(thm)],[f_2685_3]) ).

cnf(f_2685_5,plain,
    ( hAPP(hAPP(c_COMBC(U_9688,tc_fun(tc_prod(U_9688,U_9690),tc_HOL_Obool),tc_fun(U_9690,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9690,tc_fun(tc_fun(tc_prod(U_9688,U_9690),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9688,U_9690),tc_HOL_Obool),tc_fun(U_9690,tc_HOL_Obool)),U_9688),c_COMBC(U_9690,tc_fun(tc_prod(U_9688,U_9690),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9690,tc_prod(U_9688,U_9690)),tc_fun(U_9690,tc_fun(tc_fun(tc_prod(U_9688,U_9690),tc_HOL_Obool),tc_HOL_Obool)),U_9688),hAPP(c_COMBB(tc_prod(U_9688,U_9690),tc_fun(tc_fun(tc_prod(U_9688,U_9690),tc_HOL_Obool),tc_HOL_Obool),U_9690),c_member(tc_prod(U_9688,U_9690)))),c_Product__Type_OPair(U_9688,U_9690)))),U_9692) = hAPP(hAPP(c_COMBC(U_9688,tc_fun(tc_prod(U_9688,U_9690),tc_HOL_Obool),tc_fun(U_9690,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9690,tc_fun(tc_fun(tc_prod(U_9688,U_9690),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9688,U_9690),tc_HOL_Obool),tc_fun(U_9690,tc_HOL_Obool)),U_9688),c_COMBC(U_9690,tc_fun(tc_prod(U_9688,U_9690),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9690,tc_prod(U_9688,U_9690)),tc_fun(U_9690,tc_fun(tc_fun(tc_prod(U_9688,U_9690),tc_HOL_Obool),tc_HOL_Obool)),U_9688),hAPP(c_COMBB(tc_prod(U_9688,U_9690),tc_fun(tc_fun(tc_prod(U_9688,U_9690),tc_HOL_Obool),tc_HOL_Obool),U_9690),c_member(tc_prod(U_9688,U_9690)))),c_Product__Type_OPair(U_9688,U_9690)))),U_9694)
    | U_9692 != U_9694 ),
    inference(clausify,[status(thm)],[f_2685_3]) ).

fof(f_2686_1,plain,
    ! [V_y_2,V_x_2,V_S_2,V_R_2,T_c,T_b] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_S_2)),V_x_2),V_y_2))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_R_2),V_S_2))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_R_2),V_S_2)))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_S_2)),V_x_2),V_y_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_sup__Un__eq2]) ).

fof(f_2686_2,plain,
    ! [U_9700,U_9699,U_9698,U_9697,U_9696,U_9695] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9695,tc_fun(U_9696,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_9695,tc_fun(tc_prod(U_9695,U_9696),tc_HOL_Obool),tc_fun(U_9696,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9696,tc_fun(tc_fun(tc_prod(U_9695,U_9696),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9695,U_9696),tc_HOL_Obool),tc_fun(U_9696,tc_HOL_Obool)),U_9695),c_COMBC(U_9696,tc_fun(tc_prod(U_9695,U_9696),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9696,tc_prod(U_9695,U_9696)),tc_fun(U_9696,tc_fun(tc_fun(tc_prod(U_9695,U_9696),tc_HOL_Obool),tc_HOL_Obool)),U_9695),hAPP(c_COMBB(tc_prod(U_9695,U_9696),tc_fun(tc_fun(tc_prod(U_9695,U_9696),tc_HOL_Obool),tc_HOL_Obool),U_9696),c_member(tc_prod(U_9695,U_9696)))),c_Product__Type_OPair(U_9695,U_9696)))),U_9697)),hAPP(hAPP(c_COMBC(U_9695,tc_fun(tc_prod(U_9695,U_9696),tc_HOL_Obool),tc_fun(U_9696,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9696,tc_fun(tc_fun(tc_prod(U_9695,U_9696),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9695,U_9696),tc_HOL_Obool),tc_fun(U_9696,tc_HOL_Obool)),U_9695),c_COMBC(U_9696,tc_fun(tc_prod(U_9695,U_9696),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9696,tc_prod(U_9695,U_9696)),tc_fun(U_9696,tc_fun(tc_fun(tc_prod(U_9695,U_9696),tc_HOL_Obool),tc_HOL_Obool)),U_9695),hAPP(c_COMBB(tc_prod(U_9695,U_9696),tc_fun(tc_fun(tc_prod(U_9695,U_9696),tc_HOL_Obool),tc_HOL_Obool),U_9696),c_member(tc_prod(U_9695,U_9696)))),c_Product__Type_OPair(U_9695,U_9696)))),U_9698)),U_9699),U_9700))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9695,U_9696)),hAPP(hAPP(c_Product__Type_OPair(U_9695,U_9696),U_9699),U_9700)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_9695,U_9696),tc_HOL_Obool)),U_9697),U_9698))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9695,U_9696)),hAPP(hAPP(c_Product__Type_OPair(U_9695,U_9696),U_9699),U_9700)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_9695,U_9696),tc_HOL_Obool)),U_9697),U_9698)))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9695,tc_fun(U_9696,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_9695,tc_fun(tc_prod(U_9695,U_9696),tc_HOL_Obool),tc_fun(U_9696,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9696,tc_fun(tc_fun(tc_prod(U_9695,U_9696),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9695,U_9696),tc_HOL_Obool),tc_fun(U_9696,tc_HOL_Obool)),U_9695),c_COMBC(U_9696,tc_fun(tc_prod(U_9695,U_9696),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9696,tc_prod(U_9695,U_9696)),tc_fun(U_9696,tc_fun(tc_fun(tc_prod(U_9695,U_9696),tc_HOL_Obool),tc_HOL_Obool)),U_9695),hAPP(c_COMBB(tc_prod(U_9695,U_9696),tc_fun(tc_fun(tc_prod(U_9695,U_9696),tc_HOL_Obool),tc_HOL_Obool),U_9696),c_member(tc_prod(U_9695,U_9696)))),c_Product__Type_OPair(U_9695,U_9696)))),U_9697)),hAPP(hAPP(c_COMBC(U_9695,tc_fun(tc_prod(U_9695,U_9696),tc_HOL_Obool),tc_fun(U_9696,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9696,tc_fun(tc_fun(tc_prod(U_9695,U_9696),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9695,U_9696),tc_HOL_Obool),tc_fun(U_9696,tc_HOL_Obool)),U_9695),c_COMBC(U_9696,tc_fun(tc_prod(U_9695,U_9696),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9696,tc_prod(U_9695,U_9696)),tc_fun(U_9696,tc_fun(tc_fun(tc_prod(U_9695,U_9696),tc_HOL_Obool),tc_HOL_Obool)),U_9695),hAPP(c_COMBB(tc_prod(U_9695,U_9696),tc_fun(tc_fun(tc_prod(U_9695,U_9696),tc_HOL_Obool),tc_HOL_Obool),U_9696),c_member(tc_prod(U_9695,U_9696)))),c_Product__Type_OPair(U_9695,U_9696)))),U_9698)),U_9699),U_9700)) ) ),
    inference(variable_rename,[status(thm)],[f_2686_1]) ).

fof(f_2686_3,plain,
    ( ! [U_9712,U_9710,U_9708,U_9706,U_9704,U_9702] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9702,tc_fun(U_9704,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_9702,tc_fun(tc_prod(U_9702,U_9704),tc_HOL_Obool),tc_fun(U_9704,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9704,tc_fun(tc_fun(tc_prod(U_9702,U_9704),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9702,U_9704),tc_HOL_Obool),tc_fun(U_9704,tc_HOL_Obool)),U_9702),c_COMBC(U_9704,tc_fun(tc_prod(U_9702,U_9704),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9704,tc_prod(U_9702,U_9704)),tc_fun(U_9704,tc_fun(tc_fun(tc_prod(U_9702,U_9704),tc_HOL_Obool),tc_HOL_Obool)),U_9702),hAPP(c_COMBB(tc_prod(U_9702,U_9704),tc_fun(tc_fun(tc_prod(U_9702,U_9704),tc_HOL_Obool),tc_HOL_Obool),U_9704),c_member(tc_prod(U_9702,U_9704)))),c_Product__Type_OPair(U_9702,U_9704)))),U_9706)),hAPP(hAPP(c_COMBC(U_9702,tc_fun(tc_prod(U_9702,U_9704),tc_HOL_Obool),tc_fun(U_9704,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9704,tc_fun(tc_fun(tc_prod(U_9702,U_9704),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9702,U_9704),tc_HOL_Obool),tc_fun(U_9704,tc_HOL_Obool)),U_9702),c_COMBC(U_9704,tc_fun(tc_prod(U_9702,U_9704),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9704,tc_prod(U_9702,U_9704)),tc_fun(U_9704,tc_fun(tc_fun(tc_prod(U_9702,U_9704),tc_HOL_Obool),tc_HOL_Obool)),U_9702),hAPP(c_COMBB(tc_prod(U_9702,U_9704),tc_fun(tc_fun(tc_prod(U_9702,U_9704),tc_HOL_Obool),tc_HOL_Obool),U_9704),c_member(tc_prod(U_9702,U_9704)))),c_Product__Type_OPair(U_9702,U_9704)))),U_9708)),U_9710),U_9712))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9702,U_9704)),hAPP(hAPP(c_Product__Type_OPair(U_9702,U_9704),U_9710),U_9712)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_9702,U_9704),tc_HOL_Obool)),U_9706),U_9708))) )
    & ! [U_9711,U_9709,U_9707,U_9705,U_9703,U_9701] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9701,U_9703)),hAPP(hAPP(c_Product__Type_OPair(U_9701,U_9703),U_9709),U_9711)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_9701,U_9703),tc_HOL_Obool)),U_9705),U_9707)))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9701,tc_fun(U_9703,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_9701,tc_fun(tc_prod(U_9701,U_9703),tc_HOL_Obool),tc_fun(U_9703,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9703,tc_fun(tc_fun(tc_prod(U_9701,U_9703),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9701,U_9703),tc_HOL_Obool),tc_fun(U_9703,tc_HOL_Obool)),U_9701),c_COMBC(U_9703,tc_fun(tc_prod(U_9701,U_9703),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9703,tc_prod(U_9701,U_9703)),tc_fun(U_9703,tc_fun(tc_fun(tc_prod(U_9701,U_9703),tc_HOL_Obool),tc_HOL_Obool)),U_9701),hAPP(c_COMBB(tc_prod(U_9701,U_9703),tc_fun(tc_fun(tc_prod(U_9701,U_9703),tc_HOL_Obool),tc_HOL_Obool),U_9703),c_member(tc_prod(U_9701,U_9703)))),c_Product__Type_OPair(U_9701,U_9703)))),U_9705)),hAPP(hAPP(c_COMBC(U_9701,tc_fun(tc_prod(U_9701,U_9703),tc_HOL_Obool),tc_fun(U_9703,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9703,tc_fun(tc_fun(tc_prod(U_9701,U_9703),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9701,U_9703),tc_HOL_Obool),tc_fun(U_9703,tc_HOL_Obool)),U_9701),c_COMBC(U_9703,tc_fun(tc_prod(U_9701,U_9703),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9703,tc_prod(U_9701,U_9703)),tc_fun(U_9703,tc_fun(tc_fun(tc_prod(U_9701,U_9703),tc_HOL_Obool),tc_HOL_Obool)),U_9701),hAPP(c_COMBB(tc_prod(U_9701,U_9703),tc_fun(tc_fun(tc_prod(U_9701,U_9703),tc_HOL_Obool),tc_HOL_Obool),U_9703),c_member(tc_prod(U_9701,U_9703)))),c_Product__Type_OPair(U_9701,U_9703)))),U_9707)),U_9709),U_9711)) ) ),
    inference(miniscope,[status(thm)],[f_2686_2]) ).

cnf(f_2686_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9701,U_9703)),hAPP(hAPP(c_Product__Type_OPair(U_9701,U_9703),U_9709),U_9711)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_9701,U_9703),tc_HOL_Obool)),U_9705),U_9707)))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9701,tc_fun(U_9703,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_9701,tc_fun(tc_prod(U_9701,U_9703),tc_HOL_Obool),tc_fun(U_9703,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9703,tc_fun(tc_fun(tc_prod(U_9701,U_9703),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9701,U_9703),tc_HOL_Obool),tc_fun(U_9703,tc_HOL_Obool)),U_9701),c_COMBC(U_9703,tc_fun(tc_prod(U_9701,U_9703),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9703,tc_prod(U_9701,U_9703)),tc_fun(U_9703,tc_fun(tc_fun(tc_prod(U_9701,U_9703),tc_HOL_Obool),tc_HOL_Obool)),U_9701),hAPP(c_COMBB(tc_prod(U_9701,U_9703),tc_fun(tc_fun(tc_prod(U_9701,U_9703),tc_HOL_Obool),tc_HOL_Obool),U_9703),c_member(tc_prod(U_9701,U_9703)))),c_Product__Type_OPair(U_9701,U_9703)))),U_9705)),hAPP(hAPP(c_COMBC(U_9701,tc_fun(tc_prod(U_9701,U_9703),tc_HOL_Obool),tc_fun(U_9703,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9703,tc_fun(tc_fun(tc_prod(U_9701,U_9703),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9701,U_9703),tc_HOL_Obool),tc_fun(U_9703,tc_HOL_Obool)),U_9701),c_COMBC(U_9703,tc_fun(tc_prod(U_9701,U_9703),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9703,tc_prod(U_9701,U_9703)),tc_fun(U_9703,tc_fun(tc_fun(tc_prod(U_9701,U_9703),tc_HOL_Obool),tc_HOL_Obool)),U_9701),hAPP(c_COMBB(tc_prod(U_9701,U_9703),tc_fun(tc_fun(tc_prod(U_9701,U_9703),tc_HOL_Obool),tc_HOL_Obool),U_9703),c_member(tc_prod(U_9701,U_9703)))),c_Product__Type_OPair(U_9701,U_9703)))),U_9707)),U_9709),U_9711)) ),
    inference(clausify,[status(thm)],[f_2686_3]) ).

cnf(f_2686_5,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9702,tc_fun(U_9704,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_9702,tc_fun(tc_prod(U_9702,U_9704),tc_HOL_Obool),tc_fun(U_9704,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9704,tc_fun(tc_fun(tc_prod(U_9702,U_9704),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9702,U_9704),tc_HOL_Obool),tc_fun(U_9704,tc_HOL_Obool)),U_9702),c_COMBC(U_9704,tc_fun(tc_prod(U_9702,U_9704),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9704,tc_prod(U_9702,U_9704)),tc_fun(U_9704,tc_fun(tc_fun(tc_prod(U_9702,U_9704),tc_HOL_Obool),tc_HOL_Obool)),U_9702),hAPP(c_COMBB(tc_prod(U_9702,U_9704),tc_fun(tc_fun(tc_prod(U_9702,U_9704),tc_HOL_Obool),tc_HOL_Obool),U_9704),c_member(tc_prod(U_9702,U_9704)))),c_Product__Type_OPair(U_9702,U_9704)))),U_9706)),hAPP(hAPP(c_COMBC(U_9702,tc_fun(tc_prod(U_9702,U_9704),tc_HOL_Obool),tc_fun(U_9704,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9704,tc_fun(tc_fun(tc_prod(U_9702,U_9704),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9702,U_9704),tc_HOL_Obool),tc_fun(U_9704,tc_HOL_Obool)),U_9702),c_COMBC(U_9704,tc_fun(tc_prod(U_9702,U_9704),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9704,tc_prod(U_9702,U_9704)),tc_fun(U_9704,tc_fun(tc_fun(tc_prod(U_9702,U_9704),tc_HOL_Obool),tc_HOL_Obool)),U_9702),hAPP(c_COMBB(tc_prod(U_9702,U_9704),tc_fun(tc_fun(tc_prod(U_9702,U_9704),tc_HOL_Obool),tc_HOL_Obool),U_9704),c_member(tc_prod(U_9702,U_9704)))),c_Product__Type_OPair(U_9702,U_9704)))),U_9708)),U_9710),U_9712))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9702,U_9704)),hAPP(hAPP(c_Product__Type_OPair(U_9702,U_9704),U_9710),U_9712)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_9702,U_9704),tc_HOL_Obool)),U_9706),U_9708))) ),
    inference(clausify,[status(thm)],[f_2686_3]) ).

fof(f_2687_1,plain,
    ! [V_y_2,V_x_2,V_S_2,V_R_2,T_c,T_b] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_S_2)),V_x_2),V_y_2))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_R_2),V_S_2))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_R_2),V_S_2)))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_S_2)),V_x_2),V_y_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_inf__Int__eq2]) ).

fof(f_2687_2,plain,
    ! [U_9718,U_9717,U_9716,U_9715,U_9714,U_9713] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9713,tc_fun(U_9714,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_9713,tc_fun(tc_prod(U_9713,U_9714),tc_HOL_Obool),tc_fun(U_9714,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9714,tc_fun(tc_fun(tc_prod(U_9713,U_9714),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9713,U_9714),tc_HOL_Obool),tc_fun(U_9714,tc_HOL_Obool)),U_9713),c_COMBC(U_9714,tc_fun(tc_prod(U_9713,U_9714),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9714,tc_prod(U_9713,U_9714)),tc_fun(U_9714,tc_fun(tc_fun(tc_prod(U_9713,U_9714),tc_HOL_Obool),tc_HOL_Obool)),U_9713),hAPP(c_COMBB(tc_prod(U_9713,U_9714),tc_fun(tc_fun(tc_prod(U_9713,U_9714),tc_HOL_Obool),tc_HOL_Obool),U_9714),c_member(tc_prod(U_9713,U_9714)))),c_Product__Type_OPair(U_9713,U_9714)))),U_9715)),hAPP(hAPP(c_COMBC(U_9713,tc_fun(tc_prod(U_9713,U_9714),tc_HOL_Obool),tc_fun(U_9714,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9714,tc_fun(tc_fun(tc_prod(U_9713,U_9714),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9713,U_9714),tc_HOL_Obool),tc_fun(U_9714,tc_HOL_Obool)),U_9713),c_COMBC(U_9714,tc_fun(tc_prod(U_9713,U_9714),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9714,tc_prod(U_9713,U_9714)),tc_fun(U_9714,tc_fun(tc_fun(tc_prod(U_9713,U_9714),tc_HOL_Obool),tc_HOL_Obool)),U_9713),hAPP(c_COMBB(tc_prod(U_9713,U_9714),tc_fun(tc_fun(tc_prod(U_9713,U_9714),tc_HOL_Obool),tc_HOL_Obool),U_9714),c_member(tc_prod(U_9713,U_9714)))),c_Product__Type_OPair(U_9713,U_9714)))),U_9716)),U_9717),U_9718))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9713,U_9714)),hAPP(hAPP(c_Product__Type_OPair(U_9713,U_9714),U_9717),U_9718)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_9713,U_9714),tc_HOL_Obool)),U_9715),U_9716))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9713,U_9714)),hAPP(hAPP(c_Product__Type_OPair(U_9713,U_9714),U_9717),U_9718)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_9713,U_9714),tc_HOL_Obool)),U_9715),U_9716)))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9713,tc_fun(U_9714,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_9713,tc_fun(tc_prod(U_9713,U_9714),tc_HOL_Obool),tc_fun(U_9714,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9714,tc_fun(tc_fun(tc_prod(U_9713,U_9714),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9713,U_9714),tc_HOL_Obool),tc_fun(U_9714,tc_HOL_Obool)),U_9713),c_COMBC(U_9714,tc_fun(tc_prod(U_9713,U_9714),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9714,tc_prod(U_9713,U_9714)),tc_fun(U_9714,tc_fun(tc_fun(tc_prod(U_9713,U_9714),tc_HOL_Obool),tc_HOL_Obool)),U_9713),hAPP(c_COMBB(tc_prod(U_9713,U_9714),tc_fun(tc_fun(tc_prod(U_9713,U_9714),tc_HOL_Obool),tc_HOL_Obool),U_9714),c_member(tc_prod(U_9713,U_9714)))),c_Product__Type_OPair(U_9713,U_9714)))),U_9715)),hAPP(hAPP(c_COMBC(U_9713,tc_fun(tc_prod(U_9713,U_9714),tc_HOL_Obool),tc_fun(U_9714,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9714,tc_fun(tc_fun(tc_prod(U_9713,U_9714),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9713,U_9714),tc_HOL_Obool),tc_fun(U_9714,tc_HOL_Obool)),U_9713),c_COMBC(U_9714,tc_fun(tc_prod(U_9713,U_9714),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9714,tc_prod(U_9713,U_9714)),tc_fun(U_9714,tc_fun(tc_fun(tc_prod(U_9713,U_9714),tc_HOL_Obool),tc_HOL_Obool)),U_9713),hAPP(c_COMBB(tc_prod(U_9713,U_9714),tc_fun(tc_fun(tc_prod(U_9713,U_9714),tc_HOL_Obool),tc_HOL_Obool),U_9714),c_member(tc_prod(U_9713,U_9714)))),c_Product__Type_OPair(U_9713,U_9714)))),U_9716)),U_9717),U_9718)) ) ),
    inference(variable_rename,[status(thm)],[f_2687_1]) ).

fof(f_2687_3,plain,
    ( ! [U_9730,U_9728,U_9726,U_9724,U_9722,U_9720] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9720,tc_fun(U_9722,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_9720,tc_fun(tc_prod(U_9720,U_9722),tc_HOL_Obool),tc_fun(U_9722,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9722,tc_fun(tc_fun(tc_prod(U_9720,U_9722),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9720,U_9722),tc_HOL_Obool),tc_fun(U_9722,tc_HOL_Obool)),U_9720),c_COMBC(U_9722,tc_fun(tc_prod(U_9720,U_9722),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9722,tc_prod(U_9720,U_9722)),tc_fun(U_9722,tc_fun(tc_fun(tc_prod(U_9720,U_9722),tc_HOL_Obool),tc_HOL_Obool)),U_9720),hAPP(c_COMBB(tc_prod(U_9720,U_9722),tc_fun(tc_fun(tc_prod(U_9720,U_9722),tc_HOL_Obool),tc_HOL_Obool),U_9722),c_member(tc_prod(U_9720,U_9722)))),c_Product__Type_OPair(U_9720,U_9722)))),U_9724)),hAPP(hAPP(c_COMBC(U_9720,tc_fun(tc_prod(U_9720,U_9722),tc_HOL_Obool),tc_fun(U_9722,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9722,tc_fun(tc_fun(tc_prod(U_9720,U_9722),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9720,U_9722),tc_HOL_Obool),tc_fun(U_9722,tc_HOL_Obool)),U_9720),c_COMBC(U_9722,tc_fun(tc_prod(U_9720,U_9722),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9722,tc_prod(U_9720,U_9722)),tc_fun(U_9722,tc_fun(tc_fun(tc_prod(U_9720,U_9722),tc_HOL_Obool),tc_HOL_Obool)),U_9720),hAPP(c_COMBB(tc_prod(U_9720,U_9722),tc_fun(tc_fun(tc_prod(U_9720,U_9722),tc_HOL_Obool),tc_HOL_Obool),U_9722),c_member(tc_prod(U_9720,U_9722)))),c_Product__Type_OPair(U_9720,U_9722)))),U_9726)),U_9728),U_9730))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9720,U_9722)),hAPP(hAPP(c_Product__Type_OPair(U_9720,U_9722),U_9728),U_9730)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_9720,U_9722),tc_HOL_Obool)),U_9724),U_9726))) )
    & ! [U_9729,U_9727,U_9725,U_9723,U_9721,U_9719] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9719,U_9721)),hAPP(hAPP(c_Product__Type_OPair(U_9719,U_9721),U_9727),U_9729)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_9719,U_9721),tc_HOL_Obool)),U_9723),U_9725)))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9719,tc_fun(U_9721,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_9719,tc_fun(tc_prod(U_9719,U_9721),tc_HOL_Obool),tc_fun(U_9721,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9721,tc_fun(tc_fun(tc_prod(U_9719,U_9721),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9719,U_9721),tc_HOL_Obool),tc_fun(U_9721,tc_HOL_Obool)),U_9719),c_COMBC(U_9721,tc_fun(tc_prod(U_9719,U_9721),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9721,tc_prod(U_9719,U_9721)),tc_fun(U_9721,tc_fun(tc_fun(tc_prod(U_9719,U_9721),tc_HOL_Obool),tc_HOL_Obool)),U_9719),hAPP(c_COMBB(tc_prod(U_9719,U_9721),tc_fun(tc_fun(tc_prod(U_9719,U_9721),tc_HOL_Obool),tc_HOL_Obool),U_9721),c_member(tc_prod(U_9719,U_9721)))),c_Product__Type_OPair(U_9719,U_9721)))),U_9723)),hAPP(hAPP(c_COMBC(U_9719,tc_fun(tc_prod(U_9719,U_9721),tc_HOL_Obool),tc_fun(U_9721,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9721,tc_fun(tc_fun(tc_prod(U_9719,U_9721),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9719,U_9721),tc_HOL_Obool),tc_fun(U_9721,tc_HOL_Obool)),U_9719),c_COMBC(U_9721,tc_fun(tc_prod(U_9719,U_9721),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9721,tc_prod(U_9719,U_9721)),tc_fun(U_9721,tc_fun(tc_fun(tc_prod(U_9719,U_9721),tc_HOL_Obool),tc_HOL_Obool)),U_9719),hAPP(c_COMBB(tc_prod(U_9719,U_9721),tc_fun(tc_fun(tc_prod(U_9719,U_9721),tc_HOL_Obool),tc_HOL_Obool),U_9721),c_member(tc_prod(U_9719,U_9721)))),c_Product__Type_OPair(U_9719,U_9721)))),U_9725)),U_9727),U_9729)) ) ),
    inference(miniscope,[status(thm)],[f_2687_2]) ).

cnf(f_2687_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9719,U_9721)),hAPP(hAPP(c_Product__Type_OPair(U_9719,U_9721),U_9727),U_9729)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_9719,U_9721),tc_HOL_Obool)),U_9723),U_9725)))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9719,tc_fun(U_9721,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_9719,tc_fun(tc_prod(U_9719,U_9721),tc_HOL_Obool),tc_fun(U_9721,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9721,tc_fun(tc_fun(tc_prod(U_9719,U_9721),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9719,U_9721),tc_HOL_Obool),tc_fun(U_9721,tc_HOL_Obool)),U_9719),c_COMBC(U_9721,tc_fun(tc_prod(U_9719,U_9721),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9721,tc_prod(U_9719,U_9721)),tc_fun(U_9721,tc_fun(tc_fun(tc_prod(U_9719,U_9721),tc_HOL_Obool),tc_HOL_Obool)),U_9719),hAPP(c_COMBB(tc_prod(U_9719,U_9721),tc_fun(tc_fun(tc_prod(U_9719,U_9721),tc_HOL_Obool),tc_HOL_Obool),U_9721),c_member(tc_prod(U_9719,U_9721)))),c_Product__Type_OPair(U_9719,U_9721)))),U_9723)),hAPP(hAPP(c_COMBC(U_9719,tc_fun(tc_prod(U_9719,U_9721),tc_HOL_Obool),tc_fun(U_9721,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9721,tc_fun(tc_fun(tc_prod(U_9719,U_9721),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9719,U_9721),tc_HOL_Obool),tc_fun(U_9721,tc_HOL_Obool)),U_9719),c_COMBC(U_9721,tc_fun(tc_prod(U_9719,U_9721),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9721,tc_prod(U_9719,U_9721)),tc_fun(U_9721,tc_fun(tc_fun(tc_prod(U_9719,U_9721),tc_HOL_Obool),tc_HOL_Obool)),U_9719),hAPP(c_COMBB(tc_prod(U_9719,U_9721),tc_fun(tc_fun(tc_prod(U_9719,U_9721),tc_HOL_Obool),tc_HOL_Obool),U_9721),c_member(tc_prod(U_9719,U_9721)))),c_Product__Type_OPair(U_9719,U_9721)))),U_9725)),U_9727),U_9729)) ),
    inference(clausify,[status(thm)],[f_2687_3]) ).

cnf(f_2687_5,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9720,tc_fun(U_9722,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_9720,tc_fun(tc_prod(U_9720,U_9722),tc_HOL_Obool),tc_fun(U_9722,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9722,tc_fun(tc_fun(tc_prod(U_9720,U_9722),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9720,U_9722),tc_HOL_Obool),tc_fun(U_9722,tc_HOL_Obool)),U_9720),c_COMBC(U_9722,tc_fun(tc_prod(U_9720,U_9722),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9722,tc_prod(U_9720,U_9722)),tc_fun(U_9722,tc_fun(tc_fun(tc_prod(U_9720,U_9722),tc_HOL_Obool),tc_HOL_Obool)),U_9720),hAPP(c_COMBB(tc_prod(U_9720,U_9722),tc_fun(tc_fun(tc_prod(U_9720,U_9722),tc_HOL_Obool),tc_HOL_Obool),U_9722),c_member(tc_prod(U_9720,U_9722)))),c_Product__Type_OPair(U_9720,U_9722)))),U_9724)),hAPP(hAPP(c_COMBC(U_9720,tc_fun(tc_prod(U_9720,U_9722),tc_HOL_Obool),tc_fun(U_9722,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9722,tc_fun(tc_fun(tc_prod(U_9720,U_9722),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9720,U_9722),tc_HOL_Obool),tc_fun(U_9722,tc_HOL_Obool)),U_9720),c_COMBC(U_9722,tc_fun(tc_prod(U_9720,U_9722),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9722,tc_prod(U_9720,U_9722)),tc_fun(U_9722,tc_fun(tc_fun(tc_prod(U_9720,U_9722),tc_HOL_Obool),tc_HOL_Obool)),U_9720),hAPP(c_COMBB(tc_prod(U_9720,U_9722),tc_fun(tc_fun(tc_prod(U_9720,U_9722),tc_HOL_Obool),tc_HOL_Obool),U_9722),c_member(tc_prod(U_9720,U_9722)))),c_Product__Type_OPair(U_9720,U_9722)))),U_9726)),U_9728),U_9730))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9720,U_9722)),hAPP(hAPP(c_Product__Type_OPair(U_9720,U_9722),U_9728),U_9730)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_9720,U_9722),tc_HOL_Obool)),U_9724),U_9726))) ),
    inference(clausify,[status(thm)],[f_2687_3]) ).

fof(f_2688_1,plain,
    ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_Un__Inter]) ).

fof(f_2688_2,plain,
    ! [U_9733,U_9732,U_9731] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9731,tc_HOL_Obool)),U_9732),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_9731,tc_HOL_Obool),U_9733)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_9731,tc_HOL_Obool),tc_fun(U_9731,tc_HOL_Obool)),U_9733),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9731,tc_HOL_Obool)),U_9732)),
    inference(variable_rename,[status(thm)],[f_2688_1]) ).

cnf(f_2688_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9731,tc_HOL_Obool)),U_9732),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_9731,tc_HOL_Obool),U_9733)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_9731,tc_HOL_Obool),tc_fun(U_9731,tc_HOL_Obool)),U_9733),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9731,tc_HOL_Obool)),U_9732)),
    inference(clausify,[status(thm)],[f_2688_2]) ).

fof(f_2689_1,plain,
    ! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,T_b,c_COMBI(T_b),V_A_2),
    inference(fof_nnf,[status(thm)],[fact_inj__on__id2]) ).

fof(f_2689_2,plain,
    ! [U_9735,U_9734] : c_Fun_Oinj__on(U_9734,U_9734,c_COMBI(U_9734),U_9735),
    inference(variable_rename,[status(thm)],[f_2689_1]) ).

cnf(f_2689_3,plain,
    c_Fun_Oinj__on(U_9734,U_9734,c_COMBI(U_9734),U_9735),
    inference(clausify,[status(thm)],[f_2689_2]) ).

fof(f_2690_1,plain,
    ! [V_B_2,V_A_2,V_I_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_INT__Int__distrib]) ).

fof(f_2690_2,plain,
    ! [U_9740,U_9739,U_9738,U_9737,U_9736] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9736,tc_fun(U_9737,tc_HOL_Obool)),U_9738),hAPP(hAPP(c_COMBS(U_9736,tc_fun(U_9737,tc_HOL_Obool),tc_fun(U_9737,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9737,tc_HOL_Obool),tc_fun(tc_fun(U_9737,tc_HOL_Obool),tc_fun(U_9737,tc_HOL_Obool)),U_9736),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9737,tc_HOL_Obool))),U_9739)),U_9740)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9737,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9736,tc_fun(U_9737,tc_HOL_Obool)),U_9738),U_9739)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9736,tc_fun(U_9737,tc_HOL_Obool)),U_9738),U_9740)),
    inference(variable_rename,[status(thm)],[f_2690_1]) ).

cnf(f_2690_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9736,tc_fun(U_9737,tc_HOL_Obool)),U_9738),hAPP(hAPP(c_COMBS(U_9736,tc_fun(U_9737,tc_HOL_Obool),tc_fun(U_9737,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9737,tc_HOL_Obool),tc_fun(tc_fun(U_9737,tc_HOL_Obool),tc_fun(U_9737,tc_HOL_Obool)),U_9736),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9737,tc_HOL_Obool))),U_9739)),U_9740)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9737,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9736,tc_fun(U_9737,tc_HOL_Obool)),U_9738),U_9739)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9736,tc_fun(U_9737,tc_HOL_Obool)),U_9738),U_9740)),
    inference(clausify,[status(thm)],[f_2690_2]) ).

fof(f_2691_1,plain,
    ! [V_B_2,V_J_2,T_d,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_J_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_J_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool))),T_c),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2))),V_B_2))),
    inference(fof_nnf,[status(thm)],[fact_Un__INT__distrib2]) ).

fof(f_2691_2,plain,
    ! [U_9747,U_9746,U_9745,U_9744,U_9743,U_9742,U_9741] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9741,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9742,tc_fun(U_9741,tc_HOL_Obool)),U_9743),U_9744)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9745,tc_fun(U_9741,tc_HOL_Obool)),U_9746),U_9747)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9742,tc_fun(U_9741,tc_HOL_Obool)),U_9743),hAPP(hAPP(c_COMBB(tc_fun(U_9745,tc_fun(U_9741,tc_HOL_Obool)),tc_fun(U_9741,tc_HOL_Obool),U_9742),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9745,tc_fun(U_9741,tc_HOL_Obool)),U_9746)),hAPP(hAPP(c_COMBC(U_9742,tc_fun(U_9745,tc_fun(U_9741,tc_HOL_Obool)),tc_fun(U_9745,tc_fun(U_9741,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_9741,tc_HOL_Obool),tc_fun(U_9741,tc_HOL_Obool)),tc_fun(tc_fun(U_9745,tc_fun(U_9741,tc_HOL_Obool)),tc_fun(U_9745,tc_fun(U_9741,tc_HOL_Obool))),U_9742),c_COMBB(tc_fun(U_9741,tc_HOL_Obool),tc_fun(U_9741,tc_HOL_Obool),U_9745)),hAPP(hAPP(c_COMBB(tc_fun(U_9741,tc_HOL_Obool),tc_fun(tc_fun(U_9741,tc_HOL_Obool),tc_fun(U_9741,tc_HOL_Obool)),U_9742),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9741,tc_HOL_Obool))),U_9744))),U_9747))),
    inference(variable_rename,[status(thm)],[f_2691_1]) ).

cnf(f_2691_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9741,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9742,tc_fun(U_9741,tc_HOL_Obool)),U_9743),U_9744)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9745,tc_fun(U_9741,tc_HOL_Obool)),U_9746),U_9747)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9742,tc_fun(U_9741,tc_HOL_Obool)),U_9743),hAPP(hAPP(c_COMBB(tc_fun(U_9745,tc_fun(U_9741,tc_HOL_Obool)),tc_fun(U_9741,tc_HOL_Obool),U_9742),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9745,tc_fun(U_9741,tc_HOL_Obool)),U_9746)),hAPP(hAPP(c_COMBC(U_9742,tc_fun(U_9745,tc_fun(U_9741,tc_HOL_Obool)),tc_fun(U_9745,tc_fun(U_9741,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_9741,tc_HOL_Obool),tc_fun(U_9741,tc_HOL_Obool)),tc_fun(tc_fun(U_9745,tc_fun(U_9741,tc_HOL_Obool)),tc_fun(U_9745,tc_fun(U_9741,tc_HOL_Obool))),U_9742),c_COMBB(tc_fun(U_9741,tc_HOL_Obool),tc_fun(U_9741,tc_HOL_Obool),U_9745)),hAPP(hAPP(c_COMBB(tc_fun(U_9741,tc_HOL_Obool),tc_fun(tc_fun(U_9741,tc_HOL_Obool),tc_fun(U_9741,tc_HOL_Obool)),U_9742),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9741,tc_HOL_Obool))),U_9744))),U_9747))),
    inference(clausify,[status(thm)],[f_2691_2]) ).

fof(f_2692_1,plain,
    ! [V_B_2,V_A_2,V_C_2,T_c,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I6_J]) ).

fof(f_2692_2,plain,
    ! [U_9752,U_9751,U_9750,U_9749,U_9748] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9748,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9749,tc_fun(U_9748,tc_HOL_Obool)),U_9750),U_9751)),U_9752) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9749,tc_fun(U_9748,tc_HOL_Obool)),U_9750),hAPP(hAPP(c_COMBC(U_9749,tc_fun(U_9748,tc_HOL_Obool),tc_fun(U_9748,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9748,tc_HOL_Obool),tc_fun(tc_fun(U_9748,tc_HOL_Obool),tc_fun(U_9748,tc_HOL_Obool)),U_9749),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9748,tc_HOL_Obool))),U_9751)),U_9752)),
    inference(variable_rename,[status(thm)],[f_2692_1]) ).

cnf(f_2692_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9748,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9749,tc_fun(U_9748,tc_HOL_Obool)),U_9750),U_9751)),U_9752) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9749,tc_fun(U_9748,tc_HOL_Obool)),U_9750),hAPP(hAPP(c_COMBC(U_9749,tc_fun(U_9748,tc_HOL_Obool),tc_fun(U_9748,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9748,tc_HOL_Obool),tc_fun(tc_fun(U_9748,tc_HOL_Obool),tc_fun(U_9748,tc_HOL_Obool)),U_9749),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9748,tc_HOL_Obool))),U_9751)),U_9752)),
    inference(clausify,[status(thm)],[f_2692_2]) ).

fof(f_2693_1,plain,
    ! [V_A_2,V_I_2,T_c,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2)),V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_Un__INT__distrib]) ).

fof(f_2693_2,plain,
    ! [U_9757,U_9756,U_9755,U_9754,U_9753] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9753,tc_HOL_Obool)),U_9754),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9755,tc_fun(U_9753,tc_HOL_Obool)),U_9756),U_9757)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9755,tc_fun(U_9753,tc_HOL_Obool)),U_9756),hAPP(hAPP(c_COMBB(tc_fun(U_9753,tc_HOL_Obool),tc_fun(U_9753,tc_HOL_Obool),U_9755),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9753,tc_HOL_Obool)),U_9754)),U_9757)),
    inference(variable_rename,[status(thm)],[f_2693_1]) ).

cnf(f_2693_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9753,tc_HOL_Obool)),U_9754),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9755,tc_fun(U_9753,tc_HOL_Obool)),U_9756),U_9757)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9755,tc_fun(U_9753,tc_HOL_Obool)),U_9756),hAPP(hAPP(c_COMBB(tc_fun(U_9753,tc_HOL_Obool),tc_fun(U_9753,tc_HOL_Obool),U_9755),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9753,tc_HOL_Obool)),U_9754)),U_9757)),
    inference(clausify,[status(thm)],[f_2693_2]) ).

fof(f_2694_1,plain,
    ! [V_B_2,V_C_2,T_c,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I7_J]) ).

fof(f_2694_2,plain,
    ! [U_9762,U_9761,U_9760,U_9759,U_9758] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9758,tc_HOL_Obool)),U_9759),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9760,tc_fun(U_9758,tc_HOL_Obool)),U_9761),U_9762)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9760,tc_fun(U_9758,tc_HOL_Obool)),U_9761),hAPP(hAPP(c_COMBB(tc_fun(U_9758,tc_HOL_Obool),tc_fun(U_9758,tc_HOL_Obool),U_9760),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9758,tc_HOL_Obool)),U_9759)),U_9762)),
    inference(variable_rename,[status(thm)],[f_2694_1]) ).

cnf(f_2694_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9758,tc_HOL_Obool)),U_9759),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9760,tc_fun(U_9758,tc_HOL_Obool)),U_9761),U_9762)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9760,tc_fun(U_9758,tc_HOL_Obool)),U_9761),hAPP(hAPP(c_COMBB(tc_fun(U_9758,tc_HOL_Obool),tc_fun(U_9758,tc_HOL_Obool),U_9760),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9758,tc_HOL_Obool)),U_9759)),U_9762)),
    inference(clausify,[status(thm)],[f_2694_2]) ).

fof(f_2695_1,plain,
    ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2),
    inference(fof_nnf,[status(thm)],[fact_INT__simps_I6_J]) ).

fof(f_2695_2,plain,
    ! [U_9767,U_9766,U_9765,U_9764,U_9763] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9763,tc_fun(U_9764,tc_HOL_Obool)),U_9765),hAPP(hAPP(c_COMBC(U_9763,tc_fun(U_9764,tc_HOL_Obool),tc_fun(U_9764,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9764,tc_HOL_Obool),tc_fun(tc_fun(U_9764,tc_HOL_Obool),tc_fun(U_9764,tc_HOL_Obool)),U_9763),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9764,tc_HOL_Obool))),U_9766)),U_9767)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9764,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9763,tc_fun(U_9764,tc_HOL_Obool)),U_9765),U_9766)),U_9767),
    inference(variable_rename,[status(thm)],[f_2695_1]) ).

cnf(f_2695_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9763,tc_fun(U_9764,tc_HOL_Obool)),U_9765),hAPP(hAPP(c_COMBC(U_9763,tc_fun(U_9764,tc_HOL_Obool),tc_fun(U_9764,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9764,tc_HOL_Obool),tc_fun(tc_fun(U_9764,tc_HOL_Obool),tc_fun(U_9764,tc_HOL_Obool)),U_9763),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9764,tc_HOL_Obool))),U_9766)),U_9767)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9764,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9763,tc_fun(U_9764,tc_HOL_Obool)),U_9765),U_9766)),U_9767),
    inference(clausify,[status(thm)],[f_2695_2]) ).

fof(f_2696_1,plain,
    ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_INT__simps_I7_J]) ).

fof(f_2696_2,plain,
    ! [U_9772,U_9771,U_9770,U_9769,U_9768] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9768,tc_fun(U_9769,tc_HOL_Obool)),U_9770),hAPP(hAPP(c_COMBB(tc_fun(U_9769,tc_HOL_Obool),tc_fun(U_9769,tc_HOL_Obool),U_9768),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9769,tc_HOL_Obool)),U_9771)),U_9772)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9769,tc_HOL_Obool)),U_9771),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9768,tc_fun(U_9769,tc_HOL_Obool)),U_9770),U_9772)),
    inference(variable_rename,[status(thm)],[f_2696_1]) ).

cnf(f_2696_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9768,tc_fun(U_9769,tc_HOL_Obool)),U_9770),hAPP(hAPP(c_COMBB(tc_fun(U_9769,tc_HOL_Obool),tc_fun(U_9769,tc_HOL_Obool),U_9768),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9769,tc_HOL_Obool)),U_9771)),U_9772)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9769,tc_HOL_Obool)),U_9771),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9768,tc_fun(U_9769,tc_HOL_Obool)),U_9770),U_9772)),
    inference(clausify,[status(thm)],[f_2696_2]) ).

fof(f_2697_1,plain,
    ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_Int__Union]) ).

fof(f_2697_2,plain,
    ! [U_9775,U_9774,U_9773] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9773,tc_HOL_Obool)),U_9774),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9773,tc_HOL_Obool),U_9775)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_9773,tc_HOL_Obool),tc_fun(U_9773,tc_HOL_Obool)),U_9775),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9773,tc_HOL_Obool)),U_9774)),
    inference(variable_rename,[status(thm)],[f_2697_1]) ).

cnf(f_2697_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9773,tc_HOL_Obool)),U_9774),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9773,tc_HOL_Obool),U_9775)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_9773,tc_HOL_Obool),tc_fun(U_9773,tc_HOL_Obool)),U_9775),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9773,tc_HOL_Obool)),U_9774)),
    inference(clausify,[status(thm)],[f_2697_2]) ).

fof(f_2698_1,plain,
    ! [V_A_2,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_Int__Union2]) ).

fof(f_2698_2,plain,
    ! [U_9778,U_9777,U_9776] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9776,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9776,tc_HOL_Obool),U_9777)),U_9778) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_9776,tc_HOL_Obool),tc_fun(U_9776,tc_HOL_Obool)),U_9777),hAPP(hAPP(c_COMBC(tc_fun(U_9776,tc_HOL_Obool),tc_fun(U_9776,tc_HOL_Obool),tc_fun(U_9776,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9776,tc_HOL_Obool))),U_9778)),
    inference(variable_rename,[status(thm)],[f_2698_1]) ).

cnf(f_2698_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9776,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9776,tc_HOL_Obool),U_9777)),U_9778) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_9776,tc_HOL_Obool),tc_fun(U_9776,tc_HOL_Obool)),U_9777),hAPP(hAPP(c_COMBC(tc_fun(U_9776,tc_HOL_Obool),tc_fun(U_9776,tc_HOL_Obool),tc_fun(U_9776,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9776,tc_HOL_Obool))),U_9778)),
    inference(clausify,[status(thm)],[f_2698_2]) ).

fof(f_2699_1,plain,
    ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_UN__simps_I5_J]) ).

fof(f_2699_2,plain,
    ! [U_9783,U_9782,U_9781,U_9780,U_9779] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9779,tc_fun(U_9780,tc_HOL_Obool)),U_9781),hAPP(hAPP(c_COMBB(tc_fun(U_9780,tc_HOL_Obool),tc_fun(U_9780,tc_HOL_Obool),U_9779),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9780,tc_HOL_Obool)),U_9782)),U_9783)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9780,tc_HOL_Obool)),U_9782),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9779,tc_fun(U_9780,tc_HOL_Obool)),U_9781),U_9783)),
    inference(variable_rename,[status(thm)],[f_2699_1]) ).

cnf(f_2699_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9779,tc_fun(U_9780,tc_HOL_Obool)),U_9781),hAPP(hAPP(c_COMBB(tc_fun(U_9780,tc_HOL_Obool),tc_fun(U_9780,tc_HOL_Obool),U_9779),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9780,tc_HOL_Obool)),U_9782)),U_9783)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9780,tc_HOL_Obool)),U_9782),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9779,tc_fun(U_9780,tc_HOL_Obool)),U_9781),U_9783)),
    inference(clausify,[status(thm)],[f_2699_2]) ).

fof(f_2700_1,plain,
    ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2),
    inference(fof_nnf,[status(thm)],[fact_UN__simps_I4_J]) ).

fof(f_2700_2,plain,
    ! [U_9788,U_9787,U_9786,U_9785,U_9784] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9784,tc_fun(U_9785,tc_HOL_Obool)),U_9786),hAPP(hAPP(c_COMBC(U_9784,tc_fun(U_9785,tc_HOL_Obool),tc_fun(U_9785,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9785,tc_HOL_Obool),tc_fun(tc_fun(U_9785,tc_HOL_Obool),tc_fun(U_9785,tc_HOL_Obool)),U_9784),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9785,tc_HOL_Obool))),U_9787)),U_9788)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9785,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9784,tc_fun(U_9785,tc_HOL_Obool)),U_9786),U_9787)),U_9788),
    inference(variable_rename,[status(thm)],[f_2700_1]) ).

cnf(f_2700_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9784,tc_fun(U_9785,tc_HOL_Obool)),U_9786),hAPP(hAPP(c_COMBC(U_9784,tc_fun(U_9785,tc_HOL_Obool),tc_fun(U_9785,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9785,tc_HOL_Obool),tc_fun(tc_fun(U_9785,tc_HOL_Obool),tc_fun(U_9785,tc_HOL_Obool)),U_9784),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9785,tc_HOL_Obool))),U_9787)),U_9788)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9785,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9784,tc_fun(U_9785,tc_HOL_Obool)),U_9786),U_9787)),U_9788),
    inference(clausify,[status(thm)],[f_2700_2]) ).

fof(f_2701_1,plain,
    ! [V_B_2,V_C_2,T_c,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I5_J]) ).

fof(f_2701_2,plain,
    ! [U_9793,U_9792,U_9791,U_9790,U_9789] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9789,tc_HOL_Obool)),U_9790),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9791,tc_fun(U_9789,tc_HOL_Obool)),U_9792),U_9793)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9791,tc_fun(U_9789,tc_HOL_Obool)),U_9792),hAPP(hAPP(c_COMBB(tc_fun(U_9789,tc_HOL_Obool),tc_fun(U_9789,tc_HOL_Obool),U_9791),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9789,tc_HOL_Obool)),U_9790)),U_9793)),
    inference(variable_rename,[status(thm)],[f_2701_1]) ).

cnf(f_2701_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9789,tc_HOL_Obool)),U_9790),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9791,tc_fun(U_9789,tc_HOL_Obool)),U_9792),U_9793)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9791,tc_fun(U_9789,tc_HOL_Obool)),U_9792),hAPP(hAPP(c_COMBB(tc_fun(U_9789,tc_HOL_Obool),tc_fun(U_9789,tc_HOL_Obool),U_9791),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9789,tc_HOL_Obool)),U_9790)),U_9793)),
    inference(clausify,[status(thm)],[f_2701_2]) ).

fof(f_2702_1,plain,
    ! [V_A_2,V_I_2,T_c,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2)),V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_Int__UN__distrib]) ).

fof(f_2702_2,plain,
    ! [U_9798,U_9797,U_9796,U_9795,U_9794] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9794,tc_HOL_Obool)),U_9795),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9796,tc_fun(U_9794,tc_HOL_Obool)),U_9797),U_9798)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9796,tc_fun(U_9794,tc_HOL_Obool)),U_9797),hAPP(hAPP(c_COMBB(tc_fun(U_9794,tc_HOL_Obool),tc_fun(U_9794,tc_HOL_Obool),U_9796),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9794,tc_HOL_Obool)),U_9795)),U_9798)),
    inference(variable_rename,[status(thm)],[f_2702_1]) ).

cnf(f_2702_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9794,tc_HOL_Obool)),U_9795),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9796,tc_fun(U_9794,tc_HOL_Obool)),U_9797),U_9798)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9796,tc_fun(U_9794,tc_HOL_Obool)),U_9797),hAPP(hAPP(c_COMBB(tc_fun(U_9794,tc_HOL_Obool),tc_fun(U_9794,tc_HOL_Obool),U_9796),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9794,tc_HOL_Obool)),U_9795)),U_9798)),
    inference(clausify,[status(thm)],[f_2702_2]) ).

fof(f_2703_1,plain,
    ! [V_B_2,V_A_2,V_C_2,T_c,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I4_J]) ).

fof(f_2703_2,plain,
    ! [U_9803,U_9802,U_9801,U_9800,U_9799] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9799,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9800,tc_fun(U_9799,tc_HOL_Obool)),U_9801),U_9802)),U_9803) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9800,tc_fun(U_9799,tc_HOL_Obool)),U_9801),hAPP(hAPP(c_COMBC(U_9800,tc_fun(U_9799,tc_HOL_Obool),tc_fun(U_9799,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9799,tc_HOL_Obool),tc_fun(tc_fun(U_9799,tc_HOL_Obool),tc_fun(U_9799,tc_HOL_Obool)),U_9800),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9799,tc_HOL_Obool))),U_9802)),U_9803)),
    inference(variable_rename,[status(thm)],[f_2703_1]) ).

cnf(f_2703_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9799,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9800,tc_fun(U_9799,tc_HOL_Obool)),U_9801),U_9802)),U_9803) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9800,tc_fun(U_9799,tc_HOL_Obool)),U_9801),hAPP(hAPP(c_COMBC(U_9800,tc_fun(U_9799,tc_HOL_Obool),tc_fun(U_9799,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9799,tc_HOL_Obool),tc_fun(tc_fun(U_9799,tc_HOL_Obool),tc_fun(U_9799,tc_HOL_Obool)),U_9800),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9799,tc_HOL_Obool))),U_9802)),U_9803)),
    inference(clausify,[status(thm)],[f_2703_2]) ).

fof(f_2704_1,plain,
    ! [V_B_2,V_J_2,T_d,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_J_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_J_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool))),T_c),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2))),V_B_2))),
    inference(fof_nnf,[status(thm)],[fact_Int__UN__distrib2]) ).

fof(f_2704_2,plain,
    ! [U_9810,U_9809,U_9808,U_9807,U_9806,U_9805,U_9804] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9804,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9805,tc_fun(U_9804,tc_HOL_Obool)),U_9806),U_9807)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9808,tc_fun(U_9804,tc_HOL_Obool)),U_9809),U_9810)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9805,tc_fun(U_9804,tc_HOL_Obool)),U_9806),hAPP(hAPP(c_COMBB(tc_fun(U_9808,tc_fun(U_9804,tc_HOL_Obool)),tc_fun(U_9804,tc_HOL_Obool),U_9805),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9808,tc_fun(U_9804,tc_HOL_Obool)),U_9809)),hAPP(hAPP(c_COMBC(U_9805,tc_fun(U_9808,tc_fun(U_9804,tc_HOL_Obool)),tc_fun(U_9808,tc_fun(U_9804,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_9804,tc_HOL_Obool),tc_fun(U_9804,tc_HOL_Obool)),tc_fun(tc_fun(U_9808,tc_fun(U_9804,tc_HOL_Obool)),tc_fun(U_9808,tc_fun(U_9804,tc_HOL_Obool))),U_9805),c_COMBB(tc_fun(U_9804,tc_HOL_Obool),tc_fun(U_9804,tc_HOL_Obool),U_9808)),hAPP(hAPP(c_COMBB(tc_fun(U_9804,tc_HOL_Obool),tc_fun(tc_fun(U_9804,tc_HOL_Obool),tc_fun(U_9804,tc_HOL_Obool)),U_9805),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9804,tc_HOL_Obool))),U_9807))),U_9810))),
    inference(variable_rename,[status(thm)],[f_2704_1]) ).

cnf(f_2704_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9804,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9805,tc_fun(U_9804,tc_HOL_Obool)),U_9806),U_9807)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9808,tc_fun(U_9804,tc_HOL_Obool)),U_9809),U_9810)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9805,tc_fun(U_9804,tc_HOL_Obool)),U_9806),hAPP(hAPP(c_COMBB(tc_fun(U_9808,tc_fun(U_9804,tc_HOL_Obool)),tc_fun(U_9804,tc_HOL_Obool),U_9805),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9808,tc_fun(U_9804,tc_HOL_Obool)),U_9809)),hAPP(hAPP(c_COMBC(U_9805,tc_fun(U_9808,tc_fun(U_9804,tc_HOL_Obool)),tc_fun(U_9808,tc_fun(U_9804,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_9804,tc_HOL_Obool),tc_fun(U_9804,tc_HOL_Obool)),tc_fun(tc_fun(U_9808,tc_fun(U_9804,tc_HOL_Obool)),tc_fun(U_9808,tc_fun(U_9804,tc_HOL_Obool))),U_9805),c_COMBB(tc_fun(U_9804,tc_HOL_Obool),tc_fun(U_9804,tc_HOL_Obool),U_9808)),hAPP(hAPP(c_COMBB(tc_fun(U_9804,tc_HOL_Obool),tc_fun(tc_fun(U_9804,tc_HOL_Obool),tc_fun(U_9804,tc_HOL_Obool)),U_9805),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9804,tc_HOL_Obool))),U_9807))),U_9810))),
    inference(clausify,[status(thm)],[f_2704_2]) ).

fof(f_2705_1,plain,
    ! [V_B_2,V_A_2,V_I_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_UN__Un__distrib]) ).

fof(f_2705_2,plain,
    ! [U_9815,U_9814,U_9813,U_9812,U_9811] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9811,tc_fun(U_9812,tc_HOL_Obool)),U_9813),hAPP(hAPP(c_COMBS(U_9811,tc_fun(U_9812,tc_HOL_Obool),tc_fun(U_9812,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9812,tc_HOL_Obool),tc_fun(tc_fun(U_9812,tc_HOL_Obool),tc_fun(U_9812,tc_HOL_Obool)),U_9811),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9812,tc_HOL_Obool))),U_9814)),U_9815)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9812,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9811,tc_fun(U_9812,tc_HOL_Obool)),U_9813),U_9814)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9811,tc_fun(U_9812,tc_HOL_Obool)),U_9813),U_9815)),
    inference(variable_rename,[status(thm)],[f_2705_1]) ).

cnf(f_2705_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9811,tc_fun(U_9812,tc_HOL_Obool)),U_9813),hAPP(hAPP(c_COMBS(U_9811,tc_fun(U_9812,tc_HOL_Obool),tc_fun(U_9812,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9812,tc_HOL_Obool),tc_fun(tc_fun(U_9812,tc_HOL_Obool),tc_fun(U_9812,tc_HOL_Obool)),U_9811),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9812,tc_HOL_Obool))),U_9814)),U_9815)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9812,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9811,tc_fun(U_9812,tc_HOL_Obool)),U_9813),U_9814)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9811,tc_fun(U_9812,tc_HOL_Obool)),U_9813),U_9815)),
    inference(clausify,[status(thm)],[f_2705_2]) ).

fof(f_2706_1,plain,
    ! [V_M_2,V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_M_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_M_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_M_2)),
    inference(fof_nnf,[status(thm)],[fact_UN__Un]) ).

fof(f_2706_2,plain,
    ! [U_9820,U_9819,U_9818,U_9817,U_9816] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9816,tc_fun(U_9817,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9816,tc_HOL_Obool)),U_9818),U_9819)),U_9820) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9817,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9816,tc_fun(U_9817,tc_HOL_Obool)),U_9818),U_9820)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9816,tc_fun(U_9817,tc_HOL_Obool)),U_9819),U_9820)),
    inference(variable_rename,[status(thm)],[f_2706_1]) ).

cnf(f_2706_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9816,tc_fun(U_9817,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9816,tc_HOL_Obool)),U_9818),U_9819)),U_9820) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9817,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9816,tc_fun(U_9817,tc_HOL_Obool)),U_9818),U_9820)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9816,tc_fun(U_9817,tc_HOL_Obool)),U_9819),U_9820)),
    inference(clausify,[status(thm)],[f_2706_2]) ).

fof(f_2707_1,plain,
    ! [V_M_2,V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_M_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_M_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_M_2)),
    inference(fof_nnf,[status(thm)],[fact_INT__Un]) ).

fof(f_2707_2,plain,
    ! [U_9825,U_9824,U_9823,U_9822,U_9821] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9821,tc_fun(U_9822,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9821,tc_HOL_Obool)),U_9823),U_9824)),U_9825) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9822,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9821,tc_fun(U_9822,tc_HOL_Obool)),U_9823),U_9825)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9821,tc_fun(U_9822,tc_HOL_Obool)),U_9824),U_9825)),
    inference(variable_rename,[status(thm)],[f_2707_1]) ).

cnf(f_2707_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9821,tc_fun(U_9822,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9821,tc_HOL_Obool)),U_9823),U_9824)),U_9825) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9822,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9821,tc_fun(U_9822,tc_HOL_Obool)),U_9823),U_9825)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9821,tc_fun(U_9822,tc_HOL_Obool)),U_9824),U_9825)),
    inference(clausify,[status(thm)],[f_2707_2]) ).

fof(f_2708_1,plain,
    ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
      ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,T_b)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_inf__fun__def]) ).

fof(f_2708_2,plain,
    ! [U_9830,U_9829,U_9828,U_9827,U_9826] :
      ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9827,U_9826)),U_9828),U_9829),U_9830) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9826),hAPP(U_9828,U_9830)),hAPP(U_9829,U_9830))
      | ~ class_Lattices_Olattice(U_9826) ),
    inference(variable_rename,[status(thm)],[f_2708_1]) ).

cnf(f_2708_3,plain,
    ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9827,U_9826)),U_9828),U_9829),U_9830) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_9826),hAPP(U_9828,U_9830)),hAPP(U_9829,U_9830))
    | ~ class_Lattices_Olattice(U_9826) ),
    inference(clausify,[status(thm)],[f_2708_2]) ).

fof(f_2709_1,plain,
    ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
      ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,T_b)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sup__fun__def]) ).

fof(f_2709_2,plain,
    ! [U_9835,U_9834,U_9833,U_9832,U_9831] :
      ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9832,U_9831)),U_9833),U_9834),U_9835) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9831),hAPP(U_9833,U_9835)),hAPP(U_9834,U_9835))
      | ~ class_Lattices_Olattice(U_9831) ),
    inference(variable_rename,[status(thm)],[f_2709_1]) ).

cnf(f_2709_3,plain,
    ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9832,U_9831)),U_9833),U_9834),U_9835) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9831),hAPP(U_9833,U_9835)),hAPP(U_9834,U_9835))
    | ~ class_Lattices_Olattice(U_9831) ),
    inference(clausify,[status(thm)],[f_2709_2]) ).

fof(f_2710_1,plain,
    ! [V_A_2,V_f_2,V_f_H_2,T_d,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_d,V_f_2,V_A_2)
      | ~ c_Fun_Oinj__on(T_b,T_c,hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_H_2),V_f_2),V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_inj__on__imageI2]) ).

fof(f_2710_2,plain,
    ! [U_9841,U_9840,U_9839,U_9838,U_9837,U_9836] :
      ( c_Fun_Oinj__on(U_9836,U_9838,U_9840,U_9841)
      | ~ c_Fun_Oinj__on(U_9836,U_9837,hAPP(c_Fun_Ocomp(U_9838,U_9837,U_9836,U_9839),U_9840),U_9841) ),
    inference(variable_rename,[status(thm)],[f_2710_1]) ).

cnf(f_2710_3,plain,
    ( c_Fun_Oinj__on(U_9836,U_9838,U_9840,U_9841)
    | ~ c_Fun_Oinj__on(U_9836,U_9837,hAPP(c_Fun_Ocomp(U_9838,U_9837,U_9836,U_9839),U_9840),U_9841) ),
    inference(clausify,[status(thm)],[f_2710_2]) ).

fof(f_2711_1,plain,
    ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2))
        | V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2
        | V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I2_J]) ).

fof(f_2711_2,plain,
    ! [U_9846,U_9845,U_9844,U_9843,U_9842] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9844,tc_HOL_Obool)),U_9845),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9843,tc_fun(U_9844,tc_HOL_Obool)),U_9842),U_9846)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9843,tc_fun(U_9844,tc_HOL_Obool)),U_9842),hAPP(hAPP(c_COMBB(tc_fun(U_9844,tc_HOL_Obool),tc_fun(U_9844,tc_HOL_Obool),U_9843),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9844,tc_HOL_Obool)),U_9845)),U_9846))
        | U_9842 = c_Orderings_Obot__class_Obot(tc_fun(U_9843,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9844,tc_HOL_Obool)),U_9845),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9843,tc_fun(U_9844,tc_HOL_Obool)),U_9842),U_9846)) = U_9845
        | U_9842 != c_Orderings_Obot__class_Obot(tc_fun(U_9843,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2711_1]) ).

fof(f_2711_3,plain,
    ( ! [U_9856,U_9854,U_9852,U_9850,U_9848] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9852,tc_HOL_Obool)),U_9854),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9850,tc_fun(U_9852,tc_HOL_Obool)),U_9848),U_9856)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9850,tc_fun(U_9852,tc_HOL_Obool)),U_9848),hAPP(hAPP(c_COMBB(tc_fun(U_9852,tc_HOL_Obool),tc_fun(U_9852,tc_HOL_Obool),U_9850),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9852,tc_HOL_Obool)),U_9854)),U_9856))
        | U_9848 = c_Orderings_Obot__class_Obot(tc_fun(U_9850,tc_HOL_Obool)) )
    & ! [U_9855,U_9853,U_9851,U_9849,U_9847] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9851,tc_HOL_Obool)),U_9853),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9849,tc_fun(U_9851,tc_HOL_Obool)),U_9847),U_9855)) = U_9853
        | U_9847 != c_Orderings_Obot__class_Obot(tc_fun(U_9849,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2711_2]) ).

cnf(f_2711_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9851,tc_HOL_Obool)),U_9853),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9849,tc_fun(U_9851,tc_HOL_Obool)),U_9847),U_9855)) = U_9853
    | U_9847 != c_Orderings_Obot__class_Obot(tc_fun(U_9849,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2711_3]) ).

cnf(f_2711_5,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9852,tc_HOL_Obool)),U_9854),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9850,tc_fun(U_9852,tc_HOL_Obool)),U_9848),U_9856)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9850,tc_fun(U_9852,tc_HOL_Obool)),U_9848),hAPP(hAPP(c_COMBB(tc_fun(U_9852,tc_HOL_Obool),tc_fun(U_9852,tc_HOL_Obool),U_9850),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9852,tc_HOL_Obool)),U_9854)),U_9856))
    | U_9848 = c_Orderings_Obot__class_Obot(tc_fun(U_9850,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2711_3]) ).

fof(f_2712_1,plain,
    ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2))
        | V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = V_B_2
        | V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I1_J]) ).

fof(f_2712_2,plain,
    ! [U_9861,U_9860,U_9859,U_9858,U_9857] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9859,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9858,tc_fun(U_9859,tc_HOL_Obool)),U_9857),U_9860)),U_9861) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9858,tc_fun(U_9859,tc_HOL_Obool)),U_9857),hAPP(hAPP(c_COMBC(U_9858,tc_fun(U_9859,tc_HOL_Obool),tc_fun(U_9859,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9859,tc_HOL_Obool),tc_fun(tc_fun(U_9859,tc_HOL_Obool),tc_fun(U_9859,tc_HOL_Obool)),U_9858),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9859,tc_HOL_Obool))),U_9860)),U_9861))
        | U_9857 = c_Orderings_Obot__class_Obot(tc_fun(U_9858,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9859,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9858,tc_fun(U_9859,tc_HOL_Obool)),U_9857),U_9860)),U_9861) = U_9861
        | U_9857 != c_Orderings_Obot__class_Obot(tc_fun(U_9858,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2712_1]) ).

fof(f_2712_3,plain,
    ( ! [U_9871,U_9869,U_9867,U_9865,U_9863] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9867,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9865,tc_fun(U_9867,tc_HOL_Obool)),U_9863),U_9869)),U_9871) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9865,tc_fun(U_9867,tc_HOL_Obool)),U_9863),hAPP(hAPP(c_COMBC(U_9865,tc_fun(U_9867,tc_HOL_Obool),tc_fun(U_9867,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9867,tc_HOL_Obool),tc_fun(tc_fun(U_9867,tc_HOL_Obool),tc_fun(U_9867,tc_HOL_Obool)),U_9865),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9867,tc_HOL_Obool))),U_9869)),U_9871))
        | U_9863 = c_Orderings_Obot__class_Obot(tc_fun(U_9865,tc_HOL_Obool)) )
    & ! [U_9870,U_9868,U_9866,U_9864,U_9862] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9866,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9864,tc_fun(U_9866,tc_HOL_Obool)),U_9862),U_9868)),U_9870) = U_9870
        | U_9862 != c_Orderings_Obot__class_Obot(tc_fun(U_9864,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2712_2]) ).

cnf(f_2712_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9866,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9864,tc_fun(U_9866,tc_HOL_Obool)),U_9862),U_9868)),U_9870) = U_9870
    | U_9862 != c_Orderings_Obot__class_Obot(tc_fun(U_9864,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2712_3]) ).

cnf(f_2712_5,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9867,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9865,tc_fun(U_9867,tc_HOL_Obool)),U_9863),U_9869)),U_9871) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9865,tc_fun(U_9867,tc_HOL_Obool)),U_9863),hAPP(hAPP(c_COMBC(U_9865,tc_fun(U_9867,tc_HOL_Obool),tc_fun(U_9867,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9867,tc_HOL_Obool),tc_fun(tc_fun(U_9867,tc_HOL_Obool),tc_fun(U_9867,tc_HOL_Obool)),U_9865),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9867,tc_HOL_Obool))),U_9869)),U_9871))
    | U_9863 = c_Orderings_Obot__class_Obot(tc_fun(U_9865,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2712_3]) ).

fof(f_2713_1,plain,
    ! [V_B_2,V_A_2,V_a_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_B_2,V_a_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_INT__insert]) ).

fof(f_2713_2,plain,
    ! [U_9876,U_9875,U_9874,U_9873,U_9872] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9872,tc_fun(U_9873,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_9872),U_9874),U_9875)),U_9876) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9873,tc_HOL_Obool)),hAPP(U_9876,U_9874)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9872,tc_fun(U_9873,tc_HOL_Obool)),U_9875),U_9876)),
    inference(variable_rename,[status(thm)],[f_2713_1]) ).

cnf(f_2713_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9872,tc_fun(U_9873,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_9872),U_9874),U_9875)),U_9876) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_9873,tc_HOL_Obool)),hAPP(U_9876,U_9874)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9872,tc_fun(U_9873,tc_HOL_Obool)),U_9875),U_9876)),
    inference(clausify,[status(thm)],[f_2713_2]) ).

fof(f_2714_1,plain,
    ! [V_g_2,V_f_2,T_c,V_A_2,V_a_2,T_b] :
      ( ( hAPP(c_Fun_Ooverride__on(T_b,T_c,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_f_2,V_a_2)
        | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) )
      & ( hAPP(c_Fun_Ooverride__on(T_b,T_c,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_g_2,V_a_2)
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_override__on__def]) ).

fof(f_2714_2,plain,
    ! [U_9882,U_9881,U_9880,U_9879,U_9878,U_9877] :
      ( ( hAPP(c_Fun_Ooverride__on(U_9877,U_9880,U_9881,U_9882,U_9879),U_9878) = hAPP(U_9881,U_9878)
        | hBOOL(hAPP(hAPP(c_member(U_9877),U_9878),U_9879)) )
      & ( hAPP(c_Fun_Ooverride__on(U_9877,U_9880,U_9881,U_9882,U_9879),U_9878) = hAPP(U_9882,U_9878)
        | ~ hBOOL(hAPP(hAPP(c_member(U_9877),U_9878),U_9879)) ) ),
    inference(variable_rename,[status(thm)],[f_2714_1]) ).

fof(f_2714_3,plain,
    ( ! [U_9894,U_9892,U_9890,U_9888,U_9886,U_9884] :
        ( hAPP(c_Fun_Ooverride__on(U_9884,U_9890,U_9892,U_9894,U_9888),U_9886) = hAPP(U_9892,U_9886)
        | hBOOL(hAPP(hAPP(c_member(U_9884),U_9886),U_9888)) )
    & ! [U_9893,U_9891,U_9889,U_9887,U_9885,U_9883] :
        ( hAPP(c_Fun_Ooverride__on(U_9883,U_9889,U_9891,U_9893,U_9887),U_9885) = hAPP(U_9893,U_9885)
        | ~ hBOOL(hAPP(hAPP(c_member(U_9883),U_9885),U_9887)) ) ),
    inference(miniscope,[status(thm)],[f_2714_2]) ).

cnf(f_2714_4,plain,
    ( hAPP(c_Fun_Ooverride__on(U_9883,U_9889,U_9891,U_9893,U_9887),U_9885) = hAPP(U_9893,U_9885)
    | ~ hBOOL(hAPP(hAPP(c_member(U_9883),U_9885),U_9887)) ),
    inference(clausify,[status(thm)],[f_2714_3]) ).

cnf(f_2714_5,plain,
    ( hAPP(c_Fun_Ooverride__on(U_9884,U_9890,U_9892,U_9894,U_9888),U_9886) = hAPP(U_9892,U_9886)
    | hBOOL(hAPP(hAPP(c_member(U_9884),U_9886),U_9888)) ),
    inference(clausify,[status(thm)],[f_2714_3]) ).

fof(f_2715_1,plain,
    ! [V_A_2,V_f_2,T_b] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_b),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2),
    inference(fof_nnf,[status(thm)],[fact_int__setprod]) ).

fof(f_2715_2,plain,
    ! [U_9897,U_9896,U_9895] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9895,tc_Nat_Onat),U_9896),U_9897)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9895,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_9895),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9896)),U_9897),
    inference(variable_rename,[status(thm)],[f_2715_1]) ).

cnf(f_2715_3,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9895,tc_Nat_Onat),U_9896),U_9897)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9895,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_9895),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9896)),U_9897),
    inference(clausify,[status(thm)],[f_2715_2]) ).

fof(f_2716_1,plain,
    ! [V_A_2,V_f_2,T_b] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_b),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2),
    inference(fof_nnf,[status(thm)],[fact_int__setsum]) ).

fof(f_2716_2,plain,
    ! [U_9900,U_9899,U_9898] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9898,tc_Nat_Onat),U_9899),U_9900)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9898,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_9898),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9899)),U_9900),
    inference(variable_rename,[status(thm)],[f_2716_1]) ).

cnf(f_2716_3,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9898,tc_Nat_Onat),U_9899),U_9900)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9898,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_9898),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9899)),U_9900),
    inference(clausify,[status(thm)],[f_2716_2]) ).

fof(f_2717_1,plain,
    ! [V_f_2,V_B_2,T_d,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),V_B_2),
    inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I10_J]) ).

fof(f_2717_2,plain,
    ! [U_9906,U_9905,U_9904,U_9903,U_9902,U_9901] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9901,tc_fun(U_9902,tc_HOL_Obool)),U_9903),hAPP(hAPP(c_COMBB(U_9904,tc_fun(U_9902,tc_HOL_Obool),U_9901),U_9905),U_9906)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9904,tc_fun(U_9902,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_9901,U_9904,U_9906),U_9903)),U_9905),
    inference(variable_rename,[status(thm)],[f_2717_1]) ).

cnf(f_2717_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9901,tc_fun(U_9902,tc_HOL_Obool)),U_9903),hAPP(hAPP(c_COMBB(U_9904,tc_fun(U_9902,tc_HOL_Obool),U_9901),U_9905),U_9906)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9904,tc_fun(U_9902,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_9901,U_9904,U_9906),U_9903)),U_9905),
    inference(clausify,[status(thm)],[f_2717_2]) ).

fof(f_2718_1,plain,
    ! [V_B_2,V_A_2,T_d,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Set_Oimage(T_c,T_b,V_f_2)),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_image__UN]) ).

fof(f_2718_2,plain,
    ! [U_9912,U_9911,U_9910,U_9909,U_9908,U_9907] : hAPP(c_Set_Oimage(U_9907,U_9908,U_9909),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9910,tc_fun(U_9907,tc_HOL_Obool)),U_9911),U_9912)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9910,tc_fun(U_9908,tc_HOL_Obool)),U_9911),hAPP(hAPP(c_COMBB(tc_fun(U_9907,tc_HOL_Obool),tc_fun(U_9908,tc_HOL_Obool),U_9910),c_Set_Oimage(U_9907,U_9908,U_9909)),U_9912)),
    inference(variable_rename,[status(thm)],[f_2718_1]) ).

cnf(f_2718_3,plain,
    hAPP(c_Set_Oimage(U_9907,U_9908,U_9909),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9910,tc_fun(U_9907,tc_HOL_Obool)),U_9911),U_9912)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9910,tc_fun(U_9908,tc_HOL_Obool)),U_9911),hAPP(hAPP(c_COMBB(tc_fun(U_9907,tc_HOL_Obool),tc_fun(U_9908,tc_HOL_Obool),U_9910),c_Set_Oimage(U_9907,U_9908,U_9909)),U_9912)),
    inference(clausify,[status(thm)],[f_2718_2]) ).

fof(f_2719_1,plain,
    ! [V_B_2,V_A_2,V_f_2,T_d,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_b,tc_HOL_Obool),T_d),V_B_2),V_f_2)),
    inference(fof_nnf,[status(thm)],[fact_UN__simps_I10_J]) ).

fof(f_2719_2,plain,
    ! [U_9918,U_9917,U_9916,U_9915,U_9914,U_9913] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9913,tc_fun(U_9914,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_9915,U_9913,U_9916),U_9917)),U_9918) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9915,tc_fun(U_9914,tc_HOL_Obool)),U_9917),hAPP(hAPP(c_COMBB(U_9913,tc_fun(U_9914,tc_HOL_Obool),U_9915),U_9918),U_9916)),
    inference(variable_rename,[status(thm)],[f_2719_1]) ).

cnf(f_2719_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9913,tc_fun(U_9914,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_9915,U_9913,U_9916),U_9917)),U_9918) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9915,tc_fun(U_9914,tc_HOL_Obool)),U_9917),hAPP(hAPP(c_COMBB(U_9913,tc_fun(U_9914,tc_HOL_Obool),U_9915),U_9918),U_9916)),
    inference(clausify,[status(thm)],[f_2719_2]) ).

fof(f_2720_1,plain,
    ! [V_S_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_Set_Oimage(T_c,T_b,V_f_2)),
    inference(fof_nnf,[status(thm)],[fact_image__Union]) ).

fof(f_2720_2,plain,
    ! [U_9922,U_9921,U_9920,U_9919] : hAPP(c_Set_Oimage(U_9919,U_9920,U_9921),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9919,tc_HOL_Obool),U_9922)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_9919,tc_HOL_Obool),tc_fun(U_9920,tc_HOL_Obool)),U_9922),c_Set_Oimage(U_9919,U_9920,U_9921)),
    inference(variable_rename,[status(thm)],[f_2720_1]) ).

cnf(f_2720_3,plain,
    hAPP(c_Set_Oimage(U_9919,U_9920,U_9921),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_9919,tc_HOL_Obool),U_9922)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_9919,tc_HOL_Obool),tc_fun(U_9920,tc_HOL_Obool)),U_9922),c_Set_Oimage(U_9919,U_9920,U_9921)),
    inference(clausify,[status(thm)],[f_2720_2]) ).

fof(f_2721_1,plain,
    ! [V_A_2,V_g_2,T_d,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Oimage(T_d,T_c,V_g_2),V_A_2)) = hAPP(c_Set_Oimage(T_d,T_b,hAPP(hAPP(c_COMBB(T_c,T_b,T_d),V_f_2),V_g_2)),V_A_2),
    inference(fof_nnf,[status(thm)],[fact_image__image]) ).

fof(f_2721_2,plain,
    ! [U_9928,U_9927,U_9926,U_9925,U_9924,U_9923] : hAPP(c_Set_Oimage(U_9923,U_9924,U_9925),hAPP(c_Set_Oimage(U_9926,U_9923,U_9927),U_9928)) = hAPP(c_Set_Oimage(U_9926,U_9924,hAPP(hAPP(c_COMBB(U_9923,U_9924,U_9926),U_9925),U_9927)),U_9928),
    inference(variable_rename,[status(thm)],[f_2721_1]) ).

cnf(f_2721_3,plain,
    hAPP(c_Set_Oimage(U_9923,U_9924,U_9925),hAPP(c_Set_Oimage(U_9926,U_9923,U_9927),U_9928)) = hAPP(c_Set_Oimage(U_9926,U_9924,hAPP(hAPP(c_COMBB(U_9923,U_9924,U_9926),U_9925),U_9927)),U_9928),
    inference(clausify,[status(thm)],[f_2721_2]) ).

fof(f_2722_1,plain,
    ! [V_Y_2,T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_COMBI(T_b)),V_Y_2) = V_Y_2,
    inference(fof_nnf,[status(thm)],[fact_image__ident]) ).

fof(f_2722_2,plain,
    ! [U_9930,U_9929] : hAPP(c_Set_Oimage(U_9929,U_9929,c_COMBI(U_9929)),U_9930) = U_9930,
    inference(variable_rename,[status(thm)],[f_2722_1]) ).

cnf(f_2722_3,plain,
    hAPP(c_Set_Oimage(U_9929,U_9929,c_COMBI(U_9929)),U_9930) = U_9930,
    inference(clausify,[status(thm)],[f_2722_2]) ).

fof(f_2723_1,plain,
    ! [V_f_2,V_B_2,T_d,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),V_B_2),
    inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I10_J]) ).

fof(f_2723_2,plain,
    ! [U_9936,U_9935,U_9934,U_9933,U_9932,U_9931] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9931,tc_fun(U_9932,tc_HOL_Obool)),U_9933),hAPP(hAPP(c_COMBB(U_9934,tc_fun(U_9932,tc_HOL_Obool),U_9931),U_9935),U_9936)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9934,tc_fun(U_9932,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_9931,U_9934,U_9936),U_9933)),U_9935),
    inference(variable_rename,[status(thm)],[f_2723_1]) ).

cnf(f_2723_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9931,tc_fun(U_9932,tc_HOL_Obool)),U_9933),hAPP(hAPP(c_COMBB(U_9934,tc_fun(U_9932,tc_HOL_Obool),U_9931),U_9935),U_9936)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9934,tc_fun(U_9932,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_9931,U_9934,U_9936),U_9933)),U_9935),
    inference(clausify,[status(thm)],[f_2723_2]) ).

fof(f_2724_1,plain,
    ! [V_B_2,V_A_2,V_f_2,T_d,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_b,tc_HOL_Obool),T_d),V_B_2),V_f_2)),
    inference(fof_nnf,[status(thm)],[fact_INT__simps_I10_J]) ).

fof(f_2724_2,plain,
    ! [U_9942,U_9941,U_9940,U_9939,U_9938,U_9937] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9937,tc_fun(U_9938,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_9939,U_9937,U_9940),U_9941)),U_9942) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9939,tc_fun(U_9938,tc_HOL_Obool)),U_9941),hAPP(hAPP(c_COMBB(U_9937,tc_fun(U_9938,tc_HOL_Obool),U_9939),U_9942),U_9940)),
    inference(variable_rename,[status(thm)],[f_2724_1]) ).

cnf(f_2724_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9937,tc_fun(U_9938,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_9939,U_9937,U_9940),U_9941)),U_9942) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9939,tc_fun(U_9938,tc_HOL_Obool)),U_9941),hAPP(hAPP(c_COMBB(U_9937,tc_fun(U_9938,tc_HOL_Obool),U_9939),U_9942),U_9940)),
    inference(clausify,[status(thm)],[f_2724_2]) ).

fof(f_2725_1,plain,
    ! [V_r_2,V_g_2,V_f_2,T_d,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,hAPP(c_Fun_Ocomp(T_d,T_b,T_c,V_f_2),V_g_2)),V_r_2) = hAPP(c_Set_Oimage(T_d,T_b,V_f_2),hAPP(c_Set_Oimage(T_c,T_d,V_g_2),V_r_2)),
    inference(fof_nnf,[status(thm)],[fact_image__compose]) ).

fof(f_2725_2,plain,
    ! [U_9948,U_9947,U_9946,U_9945,U_9944,U_9943] : hAPP(c_Set_Oimage(U_9943,U_9944,hAPP(c_Fun_Ocomp(U_9945,U_9944,U_9943,U_9946),U_9947)),U_9948) = hAPP(c_Set_Oimage(U_9945,U_9944,U_9946),hAPP(c_Set_Oimage(U_9943,U_9945,U_9947),U_9948)),
    inference(variable_rename,[status(thm)],[f_2725_1]) ).

cnf(f_2725_3,plain,
    hAPP(c_Set_Oimage(U_9943,U_9944,hAPP(c_Fun_Ocomp(U_9945,U_9944,U_9943,U_9946),U_9947)),U_9948) = hAPP(c_Set_Oimage(U_9945,U_9944,U_9946),hAPP(c_Set_Oimage(U_9943,U_9945,U_9947),U_9948)),
    inference(clausify,[status(thm)],[f_2725_2]) ).

fof(f_2726_1,plain,
    ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_INTER__eq__Inter__image]) ).

fof(f_2726_2,plain,
    ! [U_9952,U_9951,U_9950,U_9949] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9949,tc_fun(U_9950,tc_HOL_Obool)),U_9951),U_9952) = c_Complete__Lattice_OInf__class_OInf(tc_fun(U_9950,tc_HOL_Obool),hAPP(c_Set_Oimage(U_9949,tc_fun(U_9950,tc_HOL_Obool),U_9952),U_9951)),
    inference(variable_rename,[status(thm)],[f_2726_1]) ).

cnf(f_2726_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9949,tc_fun(U_9950,tc_HOL_Obool)),U_9951),U_9952) = c_Complete__Lattice_OInf__class_OInf(tc_fun(U_9950,tc_HOL_Obool),hAPP(c_Set_Oimage(U_9949,tc_fun(U_9950,tc_HOL_Obool),U_9952),U_9951)),
    inference(clausify,[status(thm)],[f_2726_2]) ).

fof(f_2727_1,plain,
    ! [V_A_2,V_B_2,T_c,T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),
    inference(fof_nnf,[status(thm)],[fact_Inter__image__eq]) ).

fof(f_2727_2,plain,
    ! [U_9956,U_9955,U_9954,U_9953] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_9953,tc_HOL_Obool),hAPP(c_Set_Oimage(U_9954,tc_fun(U_9953,tc_HOL_Obool),U_9955),U_9956)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9954,tc_fun(U_9953,tc_HOL_Obool)),U_9956),U_9955),
    inference(variable_rename,[status(thm)],[f_2727_1]) ).

cnf(f_2727_3,plain,
    c_Complete__Lattice_OInf__class_OInf(tc_fun(U_9953,tc_HOL_Obool),hAPP(c_Set_Oimage(U_9954,tc_fun(U_9953,tc_HOL_Obool),U_9955),U_9956)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9954,tc_fun(U_9953,tc_HOL_Obool)),U_9956),U_9955),
    inference(clausify,[status(thm)],[f_2727_2]) ).

fof(f_2728_1,plain,
    ! [V_g_2,V_f_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Rings_Oinverse__class_Odivide(T_c)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Fields_Ofield__inverse__zero(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__dividef]) ).

fof(f_2728_2,plain,
    ! [U_9961,U_9960,U_9959,U_9958,U_9957] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9958,U_9957),hAPP(hAPP(c_COMBS(U_9958,U_9957,U_9957),hAPP(hAPP(c_COMBB(U_9957,tc_fun(U_9957,U_9957),U_9958),c_Rings_Oinverse__class_Odivide(U_9957)),U_9960)),U_9961)),U_9959) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9957),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9958,U_9957),U_9960),U_9959)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9958,U_9957),U_9961),U_9959))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9958),U_9959))
      | ~ class_Fields_Ofield__inverse__zero(U_9957) ),
    inference(variable_rename,[status(thm)],[f_2728_1]) ).

cnf(f_2728_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9958,U_9957),hAPP(hAPP(c_COMBS(U_9958,U_9957,U_9957),hAPP(hAPP(c_COMBB(U_9957,tc_fun(U_9957,U_9957),U_9958),c_Rings_Oinverse__class_Odivide(U_9957)),U_9960)),U_9961)),U_9959) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9957),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9958,U_9957),U_9960),U_9959)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9958,U_9957),U_9961),U_9959))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9958),U_9959))
    | ~ class_Fields_Ofield__inverse__zero(U_9957) ),
    inference(clausify,[status(thm)],[f_2728_2]) ).

fof(f_2729_1,plain,
    ! [V_A_2,V_f_2,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),V_f_2),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_b)
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__sum__prod_I2_J]) ).

fof(f_2729_2,plain,
    ! [U_9964,U_9963,U_9962] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,U_9962),U_9963),U_9964) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_9962),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_9962,tc_Int_Oint),U_9963),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9964))
      | ~ class_Groups_Ocomm__monoid__mult(U_9962)
      | ~ class_Groups_Ocomm__monoid__add(U_9962) ),
    inference(variable_rename,[status(thm)],[f_2729_1]) ).

cnf(f_2729_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,U_9962),U_9963),U_9964) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_9962),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_9962,tc_Int_Oint),U_9963),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9964))
    | ~ class_Groups_Ocomm__monoid__mult(U_9962)
    | ~ class_Groups_Ocomm__monoid__add(U_9962) ),
    inference(clausify,[status(thm)],[f_2729_2]) ).

fof(f_2730_1,plain,
    ! [V_n_2,V_m_2,V_f_2,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),c_Nat_OSuc)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2))
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__shift__bounds__cl__Suc__ivl]) ).

fof(f_2730_2,plain,
    ! [U_9968,U_9967,U_9966,U_9965] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_9965),U_9966),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_9967),hAPP(c_Nat_OSuc,U_9968))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_9965),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_9965,tc_Nat_Onat),U_9966),c_Nat_OSuc)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_9967,U_9968))
      | ~ class_Groups_Ocomm__monoid__add(U_9965) ),
    inference(variable_rename,[status(thm)],[f_2730_1]) ).

cnf(f_2730_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_9965),U_9966),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_9967),hAPP(c_Nat_OSuc,U_9968))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_9965),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_9965,tc_Nat_Onat),U_9966),c_Nat_OSuc)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_9967,U_9968))
    | ~ class_Groups_Ocomm__monoid__add(U_9965) ),
    inference(clausify,[status(thm)],[f_2730_2]) ).

fof(f_2731_1,plain,
    ! [V_A_2,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),tc_Nat_Onat),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2),
    inference(fof_nnf,[status(thm)],[fact_UN__UN__finite__eq]) ).

fof(f_2731_2,plain,
    ! [U_9970,U_9969] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_9969,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_fun(U_9969,tc_HOL_Obool)),tc_fun(U_9969,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_fun(U_9969,tc_HOL_Obool)),tc_fun(U_9969,tc_HOL_Obool)),tc_Nat_Onat),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_9969,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),U_9970)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_9969,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_9970),
    inference(variable_rename,[status(thm)],[f_2731_1]) ).

cnf(f_2731_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_9969,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_fun(U_9969,tc_HOL_Obool)),tc_fun(U_9969,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_fun(U_9969,tc_HOL_Obool)),tc_fun(U_9969,tc_HOL_Obool)),tc_Nat_Onat),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_9969,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),U_9970)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_9969,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_9970),
    inference(clausify,[status(thm)],[f_2731_2]) ).

fof(f_2732_1,plain,
    ! [V_A_2,T_b] : hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,T_b),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_A_2),
    inference(fof_nnf,[status(thm)],[fact_card__eq__setsum]) ).

fof(f_2732_2,plain,
    ! [U_9972,U_9971] : hAPP(c_Finite__Set_Ocard(U_9971),U_9972) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9971,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,U_9971),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_9972),
    inference(variable_rename,[status(thm)],[f_2732_1]) ).

cnf(f_2732_3,plain,
    hAPP(c_Finite__Set_Ocard(U_9971),U_9972) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9971,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,U_9971),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_9972),
    inference(clausify,[status(thm)],[f_2732_2]) ).

fof(f_2733_1,plain,
    ! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Ominus__class_Ominus(T_b)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_g_2),V_A_2))
      | ~ class_Groups_Oab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__subtractf]) ).

fof(f_2733_2,plain,
    ! [U_9977,U_9976,U_9975,U_9974,U_9973] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9974,U_9973),hAPP(hAPP(c_COMBS(U_9974,U_9973,U_9973),hAPP(hAPP(c_COMBB(U_9973,tc_fun(U_9973,U_9973),U_9974),c_Groups_Ominus__class_Ominus(U_9973)),U_9975)),U_9976)),U_9977) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_9973),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9974,U_9973),U_9975),U_9977)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9974,U_9973),U_9976),U_9977))
      | ~ class_Groups_Oab__group__add(U_9973) ),
    inference(variable_rename,[status(thm)],[f_2733_1]) ).

cnf(f_2733_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9974,U_9973),hAPP(hAPP(c_COMBS(U_9974,U_9973,U_9973),hAPP(hAPP(c_COMBB(U_9973,tc_fun(U_9973,U_9973),U_9974),c_Groups_Ominus__class_Ominus(U_9973)),U_9975)),U_9976)),U_9977) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_9973),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9974,U_9973),U_9975),U_9977)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9974,U_9973),U_9976),U_9977))
    | ~ class_Groups_Oab__group__add(U_9973) ),
    inference(clausify,[status(thm)],[f_2733_2]) ).

fof(f_2734_1,plain,
    ! [V_x_2,V_B_2,V_A_2,T_c,T_b] :
      ( hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,T_b)),V_A_2),V_B_2),V_x_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(V_A_2,V_x_2)),hAPP(V_B_2,V_x_2))
      | ~ class_Groups_Ominus(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_fun__diff__def]) ).

fof(f_2734_2,plain,
    ! [U_9982,U_9981,U_9980,U_9979,U_9978] :
      ( hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9979,U_9978)),U_9980),U_9981),U_9982) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_9978),hAPP(U_9980,U_9982)),hAPP(U_9981,U_9982))
      | ~ class_Groups_Ominus(U_9978) ),
    inference(variable_rename,[status(thm)],[f_2734_1]) ).

cnf(f_2734_3,plain,
    ( hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9979,U_9978)),U_9980),U_9981),U_9982) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_9978),hAPP(U_9980,U_9982)),hAPP(U_9981,U_9982))
    | ~ class_Groups_Ominus(U_9978) ),
    inference(clausify,[status(thm)],[f_2734_2]) ).

fof(f_2735_1,plain,
    ! [V_A_2,T_c,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(c_COMBK(T_b,T_c),c_Groups_Oone__class_Oone(T_b))),V_A_2) = c_Groups_Oone__class_Oone(T_b)
      | ~ class_Groups_Ocomm__monoid__mult(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__1]) ).

fof(f_2735_2,plain,
    ! [U_9985,U_9984,U_9983] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9984,U_9983),hAPP(c_COMBK(U_9983,U_9984),c_Groups_Oone__class_Oone(U_9983))),U_9985) = c_Groups_Oone__class_Oone(U_9983)
      | ~ class_Groups_Ocomm__monoid__mult(U_9983) ),
    inference(variable_rename,[status(thm)],[f_2735_1]) ).

cnf(f_2735_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9984,U_9983),hAPP(c_COMBK(U_9983,U_9984),c_Groups_Oone__class_Oone(U_9983))),U_9985) = c_Groups_Oone__class_Oone(U_9983)
    | ~ class_Groups_Ocomm__monoid__mult(U_9983) ),
    inference(clausify,[status(thm)],[f_2735_2]) ).

fof(f_2736_1,plain,
    ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_UN__simps_I7_J]) ).

fof(f_2736_2,plain,
    ! [U_9990,U_9989,U_9988,U_9987,U_9986] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9986,tc_fun(U_9987,tc_HOL_Obool)),U_9988),hAPP(hAPP(c_COMBB(tc_fun(U_9987,tc_HOL_Obool),tc_fun(U_9987,tc_HOL_Obool),U_9986),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9987,tc_HOL_Obool)),U_9989)),U_9990)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9987,tc_HOL_Obool)),U_9989),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9986,tc_fun(U_9987,tc_HOL_Obool)),U_9988),U_9990)),
    inference(variable_rename,[status(thm)],[f_2736_1]) ).

cnf(f_2736_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9986,tc_fun(U_9987,tc_HOL_Obool)),U_9988),hAPP(hAPP(c_COMBB(tc_fun(U_9987,tc_HOL_Obool),tc_fun(U_9987,tc_HOL_Obool),U_9986),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9987,tc_HOL_Obool)),U_9989)),U_9990)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9987,tc_HOL_Obool)),U_9989),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9986,tc_fun(U_9987,tc_HOL_Obool)),U_9988),U_9990)),
    inference(clausify,[status(thm)],[f_2736_2]) ).

fof(f_2737_1,plain,
    ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2),
    inference(fof_nnf,[status(thm)],[fact_UN__simps_I6_J]) ).

fof(f_2737_2,plain,
    ! [U_9995,U_9994,U_9993,U_9992,U_9991] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9991,tc_fun(U_9992,tc_HOL_Obool)),U_9993),hAPP(hAPP(c_COMBC(U_9991,tc_fun(U_9992,tc_HOL_Obool),tc_fun(U_9992,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9992,tc_HOL_Obool),tc_fun(tc_fun(U_9992,tc_HOL_Obool),tc_fun(U_9992,tc_HOL_Obool)),U_9991),c_Groups_Ominus__class_Ominus(tc_fun(U_9992,tc_HOL_Obool))),U_9994)),U_9995)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9992,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9991,tc_fun(U_9992,tc_HOL_Obool)),U_9993),U_9994)),U_9995),
    inference(variable_rename,[status(thm)],[f_2737_1]) ).

cnf(f_2737_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9991,tc_fun(U_9992,tc_HOL_Obool)),U_9993),hAPP(hAPP(c_COMBC(U_9991,tc_fun(U_9992,tc_HOL_Obool),tc_fun(U_9992,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9992,tc_HOL_Obool),tc_fun(tc_fun(U_9992,tc_HOL_Obool),tc_fun(U_9992,tc_HOL_Obool)),U_9991),c_Groups_Ominus__class_Ominus(tc_fun(U_9992,tc_HOL_Obool))),U_9994)),U_9995)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9992,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9991,tc_fun(U_9992,tc_HOL_Obool)),U_9993),U_9994)),U_9995),
    inference(clausify,[status(thm)],[f_2737_2]) ).

fof(f_2738_1,plain,
    ! [V_B_2,V_C_2,T_c,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I7_J]) ).

fof(f_2738_2,plain,
    ! [U_10000,U_9999,U_9998,U_9997,U_9996] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9996,tc_HOL_Obool)),U_9997),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9998,tc_fun(U_9996,tc_HOL_Obool)),U_9999),U_10000)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9998,tc_fun(U_9996,tc_HOL_Obool)),U_9999),hAPP(hAPP(c_COMBB(tc_fun(U_9996,tc_HOL_Obool),tc_fun(U_9996,tc_HOL_Obool),U_9998),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9996,tc_HOL_Obool)),U_9997)),U_10000)),
    inference(variable_rename,[status(thm)],[f_2738_1]) ).

cnf(f_2738_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9996,tc_HOL_Obool)),U_9997),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9998,tc_fun(U_9996,tc_HOL_Obool)),U_9999),U_10000)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9998,tc_fun(U_9996,tc_HOL_Obool)),U_9999),hAPP(hAPP(c_COMBB(tc_fun(U_9996,tc_HOL_Obool),tc_fun(U_9996,tc_HOL_Obool),U_9998),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9996,tc_HOL_Obool)),U_9997)),U_10000)),
    inference(clausify,[status(thm)],[f_2738_2]) ).

fof(f_2739_1,plain,
    ! [V_B_2,V_A_2,V_C_2,T_c,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I6_J]) ).

fof(f_2739_2,plain,
    ! [U_10005,U_10004,U_10003,U_10002,U_10001] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10001,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10002,tc_fun(U_10001,tc_HOL_Obool)),U_10003),U_10004)),U_10005) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10002,tc_fun(U_10001,tc_HOL_Obool)),U_10003),hAPP(hAPP(c_COMBC(U_10002,tc_fun(U_10001,tc_HOL_Obool),tc_fun(U_10001,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10001,tc_HOL_Obool),tc_fun(tc_fun(U_10001,tc_HOL_Obool),tc_fun(U_10001,tc_HOL_Obool)),U_10002),c_Groups_Ominus__class_Ominus(tc_fun(U_10001,tc_HOL_Obool))),U_10004)),U_10005)),
    inference(variable_rename,[status(thm)],[f_2739_1]) ).

cnf(f_2739_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10001,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10002,tc_fun(U_10001,tc_HOL_Obool)),U_10003),U_10004)),U_10005) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10002,tc_fun(U_10001,tc_HOL_Obool)),U_10003),hAPP(hAPP(c_COMBC(U_10002,tc_fun(U_10001,tc_HOL_Obool),tc_fun(U_10001,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10001,tc_HOL_Obool),tc_fun(tc_fun(U_10001,tc_HOL_Obool),tc_fun(U_10001,tc_HOL_Obool)),U_10002),c_Groups_Ominus__class_Ominus(tc_fun(U_10001,tc_HOL_Obool))),U_10004)),U_10005)),
    inference(clausify,[status(thm)],[f_2739_2]) ).

fof(f_2740_1,plain,
    ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2))
        | V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2
        | V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I4_J]) ).

fof(f_2740_2,plain,
    ! [U_10010,U_10009,U_10008,U_10007,U_10006] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10008,tc_HOL_Obool)),U_10009),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10007,tc_fun(U_10008,tc_HOL_Obool)),U_10006),U_10010)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10007,tc_fun(U_10008,tc_HOL_Obool)),U_10006),hAPP(hAPP(c_COMBB(tc_fun(U_10008,tc_HOL_Obool),tc_fun(U_10008,tc_HOL_Obool),U_10007),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10008,tc_HOL_Obool)),U_10009)),U_10010))
        | U_10006 = c_Orderings_Obot__class_Obot(tc_fun(U_10007,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10008,tc_HOL_Obool)),U_10009),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10007,tc_fun(U_10008,tc_HOL_Obool)),U_10006),U_10010)) = U_10009
        | U_10006 != c_Orderings_Obot__class_Obot(tc_fun(U_10007,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2740_1]) ).

fof(f_2740_3,plain,
    ( ! [U_10020,U_10018,U_10016,U_10014,U_10012] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10016,tc_HOL_Obool)),U_10018),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10014,tc_fun(U_10016,tc_HOL_Obool)),U_10012),U_10020)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10014,tc_fun(U_10016,tc_HOL_Obool)),U_10012),hAPP(hAPP(c_COMBB(tc_fun(U_10016,tc_HOL_Obool),tc_fun(U_10016,tc_HOL_Obool),U_10014),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10016,tc_HOL_Obool)),U_10018)),U_10020))
        | U_10012 = c_Orderings_Obot__class_Obot(tc_fun(U_10014,tc_HOL_Obool)) )
    & ! [U_10019,U_10017,U_10015,U_10013,U_10011] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10015,tc_HOL_Obool)),U_10017),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10013,tc_fun(U_10015,tc_HOL_Obool)),U_10011),U_10019)) = U_10017
        | U_10011 != c_Orderings_Obot__class_Obot(tc_fun(U_10013,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2740_2]) ).

cnf(f_2740_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10015,tc_HOL_Obool)),U_10017),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10013,tc_fun(U_10015,tc_HOL_Obool)),U_10011),U_10019)) = U_10017
    | U_10011 != c_Orderings_Obot__class_Obot(tc_fun(U_10013,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2740_3]) ).

cnf(f_2740_5,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10016,tc_HOL_Obool)),U_10018),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10014,tc_fun(U_10016,tc_HOL_Obool)),U_10012),U_10020)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10014,tc_fun(U_10016,tc_HOL_Obool)),U_10012),hAPP(hAPP(c_COMBB(tc_fun(U_10016,tc_HOL_Obool),tc_fun(U_10016,tc_HOL_Obool),U_10014),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10016,tc_HOL_Obool)),U_10018)),U_10020))
    | U_10012 = c_Orderings_Obot__class_Obot(tc_fun(U_10014,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2740_3]) ).

fof(f_2741_1,plain,
    ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2))
        | V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))),V_B_2)
        | V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I3_J]) ).

fof(f_2741_2,plain,
    ! [U_10025,U_10024,U_10023,U_10022,U_10021] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10023,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10022,tc_fun(U_10023,tc_HOL_Obool)),U_10021),U_10024)),U_10025) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10022,tc_fun(U_10023,tc_HOL_Obool)),U_10021),hAPP(hAPP(c_COMBC(U_10022,tc_fun(U_10023,tc_HOL_Obool),tc_fun(U_10023,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10023,tc_HOL_Obool),tc_fun(tc_fun(U_10023,tc_HOL_Obool),tc_fun(U_10023,tc_HOL_Obool)),U_10022),c_Groups_Ominus__class_Ominus(tc_fun(U_10023,tc_HOL_Obool))),U_10024)),U_10025))
        | U_10021 = c_Orderings_Obot__class_Obot(tc_fun(U_10022,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10023,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10022,tc_fun(U_10023,tc_HOL_Obool)),U_10021),U_10024)),U_10025) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10023,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_10023,tc_HOL_Obool))),U_10025)
        | U_10021 != c_Orderings_Obot__class_Obot(tc_fun(U_10022,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2741_1]) ).

fof(f_2741_3,plain,
    ( ! [U_10035,U_10033,U_10031,U_10029,U_10027] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10031,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10029,tc_fun(U_10031,tc_HOL_Obool)),U_10027),U_10033)),U_10035) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10029,tc_fun(U_10031,tc_HOL_Obool)),U_10027),hAPP(hAPP(c_COMBC(U_10029,tc_fun(U_10031,tc_HOL_Obool),tc_fun(U_10031,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10031,tc_HOL_Obool),tc_fun(tc_fun(U_10031,tc_HOL_Obool),tc_fun(U_10031,tc_HOL_Obool)),U_10029),c_Groups_Ominus__class_Ominus(tc_fun(U_10031,tc_HOL_Obool))),U_10033)),U_10035))
        | U_10027 = c_Orderings_Obot__class_Obot(tc_fun(U_10029,tc_HOL_Obool)) )
    & ! [U_10034,U_10032,U_10030,U_10028,U_10026] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10030,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10028,tc_fun(U_10030,tc_HOL_Obool)),U_10026),U_10032)),U_10034) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10030,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_10030,tc_HOL_Obool))),U_10034)
        | U_10026 != c_Orderings_Obot__class_Obot(tc_fun(U_10028,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2741_2]) ).

cnf(f_2741_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10030,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10028,tc_fun(U_10030,tc_HOL_Obool)),U_10026),U_10032)),U_10034) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10030,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_10030,tc_HOL_Obool))),U_10034)
    | U_10026 != c_Orderings_Obot__class_Obot(tc_fun(U_10028,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2741_3]) ).

cnf(f_2741_5,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10031,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10029,tc_fun(U_10031,tc_HOL_Obool)),U_10027),U_10033)),U_10035) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10029,tc_fun(U_10031,tc_HOL_Obool)),U_10027),hAPP(hAPP(c_COMBC(U_10029,tc_fun(U_10031,tc_HOL_Obool),tc_fun(U_10031,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10031,tc_HOL_Obool),tc_fun(tc_fun(U_10031,tc_HOL_Obool),tc_fun(U_10031,tc_HOL_Obool)),U_10029),c_Groups_Ominus__class_Ominus(tc_fun(U_10031,tc_HOL_Obool))),U_10033)),U_10035))
    | U_10027 = c_Orderings_Obot__class_Obot(tc_fun(U_10029,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2741_3]) ).

fof(f_2742_1,plain,
    ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2)
        | V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))
        | V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_INT__simps_I3_J]) ).

fof(f_2742_2,plain,
    ! [U_10040,U_10039,U_10038,U_10037,U_10036] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10037,tc_fun(U_10038,tc_HOL_Obool)),U_10036),hAPP(hAPP(c_COMBC(U_10037,tc_fun(U_10038,tc_HOL_Obool),tc_fun(U_10038,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10038,tc_HOL_Obool),tc_fun(tc_fun(U_10038,tc_HOL_Obool),tc_fun(U_10038,tc_HOL_Obool)),U_10037),c_Groups_Ominus__class_Ominus(tc_fun(U_10038,tc_HOL_Obool))),U_10039)),U_10040)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10038,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10037,tc_fun(U_10038,tc_HOL_Obool)),U_10036),U_10039)),U_10040)
        | U_10036 = c_Orderings_Obot__class_Obot(tc_fun(U_10037,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10037,tc_fun(U_10038,tc_HOL_Obool)),U_10036),hAPP(hAPP(c_COMBC(U_10037,tc_fun(U_10038,tc_HOL_Obool),tc_fun(U_10038,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10038,tc_HOL_Obool),tc_fun(tc_fun(U_10038,tc_HOL_Obool),tc_fun(U_10038,tc_HOL_Obool)),U_10037),c_Groups_Ominus__class_Ominus(tc_fun(U_10038,tc_HOL_Obool))),U_10039)),U_10040)) = c_Orderings_Otop__class_Otop(tc_fun(U_10038,tc_HOL_Obool))
        | U_10036 != c_Orderings_Obot__class_Obot(tc_fun(U_10037,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2742_1]) ).

fof(f_2742_3,plain,
    ( ! [U_10050,U_10048,U_10046,U_10044,U_10042] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10044,tc_fun(U_10046,tc_HOL_Obool)),U_10042),hAPP(hAPP(c_COMBC(U_10044,tc_fun(U_10046,tc_HOL_Obool),tc_fun(U_10046,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10046,tc_HOL_Obool),tc_fun(tc_fun(U_10046,tc_HOL_Obool),tc_fun(U_10046,tc_HOL_Obool)),U_10044),c_Groups_Ominus__class_Ominus(tc_fun(U_10046,tc_HOL_Obool))),U_10048)),U_10050)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10046,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10044,tc_fun(U_10046,tc_HOL_Obool)),U_10042),U_10048)),U_10050)
        | U_10042 = c_Orderings_Obot__class_Obot(tc_fun(U_10044,tc_HOL_Obool)) )
    & ! [U_10049,U_10047,U_10045,U_10043,U_10041] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10043,tc_fun(U_10045,tc_HOL_Obool)),U_10041),hAPP(hAPP(c_COMBC(U_10043,tc_fun(U_10045,tc_HOL_Obool),tc_fun(U_10045,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10045,tc_HOL_Obool),tc_fun(tc_fun(U_10045,tc_HOL_Obool),tc_fun(U_10045,tc_HOL_Obool)),U_10043),c_Groups_Ominus__class_Ominus(tc_fun(U_10045,tc_HOL_Obool))),U_10047)),U_10049)) = c_Orderings_Otop__class_Otop(tc_fun(U_10045,tc_HOL_Obool))
        | U_10041 != c_Orderings_Obot__class_Obot(tc_fun(U_10043,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2742_2]) ).

cnf(f_2742_4,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10043,tc_fun(U_10045,tc_HOL_Obool)),U_10041),hAPP(hAPP(c_COMBC(U_10043,tc_fun(U_10045,tc_HOL_Obool),tc_fun(U_10045,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10045,tc_HOL_Obool),tc_fun(tc_fun(U_10045,tc_HOL_Obool),tc_fun(U_10045,tc_HOL_Obool)),U_10043),c_Groups_Ominus__class_Ominus(tc_fun(U_10045,tc_HOL_Obool))),U_10047)),U_10049)) = c_Orderings_Otop__class_Otop(tc_fun(U_10045,tc_HOL_Obool))
    | U_10041 != c_Orderings_Obot__class_Obot(tc_fun(U_10043,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2742_3]) ).

cnf(f_2742_5,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10044,tc_fun(U_10046,tc_HOL_Obool)),U_10042),hAPP(hAPP(c_COMBC(U_10044,tc_fun(U_10046,tc_HOL_Obool),tc_fun(U_10046,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10046,tc_HOL_Obool),tc_fun(tc_fun(U_10046,tc_HOL_Obool),tc_fun(U_10046,tc_HOL_Obool)),U_10044),c_Groups_Ominus__class_Ominus(tc_fun(U_10046,tc_HOL_Obool))),U_10048)),U_10050)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10046,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10044,tc_fun(U_10046,tc_HOL_Obool)),U_10042),U_10048)),U_10050)
    | U_10042 = c_Orderings_Obot__class_Obot(tc_fun(U_10044,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2742_3]) ).

fof(f_2743_1,plain,
    ! [V_A_2,V_B_2,T_c,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),
    inference(fof_nnf,[status(thm)],[fact_Union__image__eq]) ).

fof(f_2743_2,plain,
    ! [U_10054,U_10053,U_10052,U_10051] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_10051,tc_HOL_Obool),hAPP(c_Set_Oimage(U_10052,tc_fun(U_10051,tc_HOL_Obool),U_10053),U_10054)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10052,tc_fun(U_10051,tc_HOL_Obool)),U_10054),U_10053),
    inference(variable_rename,[status(thm)],[f_2743_1]) ).

cnf(f_2743_3,plain,
    c_Complete__Lattice_OSup__class_OSup(tc_fun(U_10051,tc_HOL_Obool),hAPP(c_Set_Oimage(U_10052,tc_fun(U_10051,tc_HOL_Obool),U_10053),U_10054)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10052,tc_fun(U_10051,tc_HOL_Obool)),U_10054),U_10053),
    inference(clausify,[status(thm)],[f_2743_2]) ).

fof(f_2744_1,plain,
    ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_UNION__eq__Union__image]) ).

fof(f_2744_2,plain,
    ! [U_10058,U_10057,U_10056,U_10055] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10055,tc_fun(U_10056,tc_HOL_Obool)),U_10057),U_10058) = c_Complete__Lattice_OSup__class_OSup(tc_fun(U_10056,tc_HOL_Obool),hAPP(c_Set_Oimage(U_10055,tc_fun(U_10056,tc_HOL_Obool),U_10058),U_10057)),
    inference(variable_rename,[status(thm)],[f_2744_1]) ).

cnf(f_2744_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10055,tc_fun(U_10056,tc_HOL_Obool)),U_10057),U_10058) = c_Complete__Lattice_OSup__class_OSup(tc_fun(U_10056,tc_HOL_Obool),hAPP(c_Set_Oimage(U_10055,tc_fun(U_10056,tc_HOL_Obool),U_10058),U_10057)),
    inference(clausify,[status(thm)],[f_2744_2]) ).

fof(f_2745_1,plain,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Groups_Oabs__class_Oabs(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2)
      | ~ class_Groups_Oordered__ab__group__add__abs(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_abs__setsum__abs]) ).

fof(f_2745_2,plain,
    ! [U_10062,U_10061,U_10060,U_10059] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_10059),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10060,U_10059),hAPP(hAPP(c_COMBB(U_10059,U_10059,U_10060),c_Groups_Oabs__class_Oabs(U_10059)),U_10061)),U_10062)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10060,U_10059),hAPP(hAPP(c_COMBB(U_10059,U_10059,U_10060),c_Groups_Oabs__class_Oabs(U_10059)),U_10061)),U_10062)
      | ~ class_Groups_Oordered__ab__group__add__abs(U_10059) ),
    inference(variable_rename,[status(thm)],[f_2745_1]) ).

cnf(f_2745_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_10059),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10060,U_10059),hAPP(hAPP(c_COMBB(U_10059,U_10059,U_10060),c_Groups_Oabs__class_Oabs(U_10059)),U_10061)),U_10062)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10060,U_10059),hAPP(hAPP(c_COMBB(U_10059,U_10059,U_10060),c_Groups_Oabs__class_Oabs(U_10059)),U_10061)),U_10062)
    | ~ class_Groups_Oordered__ab__group__add__abs(U_10059) ),
    inference(clausify,[status(thm)],[f_2745_2]) ).

fof(f_2746_1,plain,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Groups_Oabs__class_Oabs(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2)
      | ~ class_Fields_Olinordered__field(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_abs__setprod]) ).

fof(f_2746_2,plain,
    ! [U_10066,U_10065,U_10064,U_10063] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_10063),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10064,U_10063),U_10065),U_10066)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10064,U_10063),hAPP(hAPP(c_COMBB(U_10063,U_10063,U_10064),c_Groups_Oabs__class_Oabs(U_10063)),U_10065)),U_10066)
      | ~ class_Fields_Olinordered__field(U_10063) ),
    inference(variable_rename,[status(thm)],[f_2746_1]) ).

cnf(f_2746_3,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_10063),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10064,U_10063),U_10065),U_10066)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10064,U_10063),hAPP(hAPP(c_COMBB(U_10063,U_10063,U_10064),c_Groups_Oabs__class_Oabs(U_10063)),U_10065)),U_10066)
    | ~ class_Fields_Olinordered__field(U_10063) ),
    inference(clausify,[status(thm)],[f_2746_2]) ).

fof(f_2747_1,plain,
    ! [V_n_2,V_k_2,V_m_2,V_f_2,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2))
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__shift__bounds__cl__nat__ivl]) ).

fof(f_2747_2,plain,
    ! [U_10071,U_10070,U_10069,U_10068,U_10067] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10067),U_10068),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10069),U_10070),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10071),U_10070))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10067),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10067,tc_Nat_Onat),U_10068),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_10070))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_10069,U_10071))
      | ~ class_Groups_Ocomm__monoid__add(U_10067) ),
    inference(variable_rename,[status(thm)],[f_2747_1]) ).

cnf(f_2747_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10067),U_10068),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10069),U_10070),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10071),U_10070))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10067),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10067,tc_Nat_Onat),U_10068),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_10070))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_10069,U_10071))
    | ~ class_Groups_Ocomm__monoid__add(U_10067) ),
    inference(clausify,[status(thm)],[f_2747_2]) ).

fof(f_2748_1,plain,
    ! [V_A_2,V_I_2,T_c,V_B_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)))
        | ? [B_x] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(V_A_2,B_x)))
            & hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2)) ) )
      & ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(V_A_2,B_x)))
            | ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_INT__subset__iff]) ).

fof(f_2748_2,plain,
    ! [U_10078,U_10077,U_10076,U_10075,U_10074] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10074,tc_HOL_Obool)),U_10075),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10076,tc_fun(U_10074,tc_HOL_Obool)),U_10077),U_10078)))
        | ? [U_10073] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10074,tc_HOL_Obool)),U_10075),hAPP(U_10078,U_10073)))
            & hBOOL(hAPP(hAPP(c_member(U_10076),U_10073),U_10077)) ) )
      & ( ! [U_10072] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10074,tc_HOL_Obool)),U_10075),hAPP(U_10078,U_10072)))
            | ~ hBOOL(hAPP(hAPP(c_member(U_10076),U_10072),U_10077)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10074,tc_HOL_Obool)),U_10075),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10076,tc_fun(U_10074,tc_HOL_Obool)),U_10077),U_10078))) ) ),
    inference(variable_rename,[status(thm)],[f_2748_1]) ).

fof(f_2748_3,plain,
    ( ! [U_10088,U_10086,U_10084,U_10082,U_10080] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10080,tc_HOL_Obool)),U_10082),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10084,tc_fun(U_10080,tc_HOL_Obool)),U_10086),U_10088)))
        | ? [U_10073] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10080,tc_HOL_Obool)),U_10082),hAPP(U_10088,U_10073)))
            & hBOOL(hAPP(hAPP(c_member(U_10084),U_10073),U_10086)) ) )
    & ! [U_10087,U_10085,U_10083,U_10081,U_10079] :
        ( ! [U_10072] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10079,tc_HOL_Obool)),U_10081),hAPP(U_10087,U_10072)))
            | ~ hBOOL(hAPP(hAPP(c_member(U_10083),U_10072),U_10085)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10079,tc_HOL_Obool)),U_10081),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10083,tc_fun(U_10079,tc_HOL_Obool)),U_10085),U_10087))) ) ),
    inference(miniscope,[status(thm)],[f_2748_2]) ).

fof(f_2748_4,plain,
    ( ! [U_10088,U_10086,U_10084,U_10082,U_10080] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10080,tc_HOL_Obool)),U_10082),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10084,tc_fun(U_10080,tc_HOL_Obool)),U_10086),U_10088)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10080,tc_HOL_Obool)),U_10082),hAPP(U_10088,sK238(U_10088,U_10086,U_10084,U_10082,U_10080))))
          & hBOOL(hAPP(hAPP(c_member(U_10084),sK238(U_10088,U_10086,U_10084,U_10082,U_10080)),U_10086)) ) )
    & ! [U_10087,U_10085,U_10083,U_10081,U_10079] :
        ( ! [U_10072] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10079,tc_HOL_Obool)),U_10081),hAPP(U_10087,U_10072)))
            | ~ hBOOL(hAPP(hAPP(c_member(U_10083),U_10072),U_10085)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10079,tc_HOL_Obool)),U_10081),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10083,tc_fun(U_10079,tc_HOL_Obool)),U_10085),U_10087))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK238]),skolemize(U_10073,sK238(U_10088,U_10086,U_10084,U_10082,U_10080))],[f_2748_3]) ).

cnf(f_2748_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10079,tc_HOL_Obool)),U_10081),hAPP(U_10087,U_10072)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10083),U_10072),U_10085))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10079,tc_HOL_Obool)),U_10081),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10083,tc_fun(U_10079,tc_HOL_Obool)),U_10085),U_10087))) ),
    inference(clausify,[status(thm)],[f_2748_4]) ).

cnf(f_2748_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10084),sK238(U_10088,U_10086,U_10084,U_10082,U_10080)),U_10086))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10080,tc_HOL_Obool)),U_10082),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10084,tc_fun(U_10080,tc_HOL_Obool)),U_10086),U_10088))) ),
    inference(clausify,[status(thm)],[f_2748_4]) ).

cnf(f_2748_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10080,tc_HOL_Obool)),U_10082),hAPP(U_10088,sK238(U_10088,U_10086,U_10084,U_10082,U_10080))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10080,tc_HOL_Obool)),U_10082),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10084,tc_fun(U_10080,tc_HOL_Obool)),U_10086),U_10088))) ),
    inference(clausify,[status(thm)],[f_2748_4]) ).

fof(f_2749_1,plain,
    ! [V_B_2,V_A_2,V_I_2,T_c,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),V_B_2))
        | ? [B_x] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_A_2,B_x)),V_B_2))
            & hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2)) ) )
      & ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_A_2,B_x)),V_B_2))
            | ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),V_B_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_UN__subset__iff]) ).

fof(f_2749_2,plain,
    ! [U_10095,U_10094,U_10093,U_10092,U_10091] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10091,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10092,tc_fun(U_10091,tc_HOL_Obool)),U_10093),U_10094)),U_10095))
        | ? [U_10090] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10091,tc_HOL_Obool)),hAPP(U_10094,U_10090)),U_10095))
            & hBOOL(hAPP(hAPP(c_member(U_10092),U_10090),U_10093)) ) )
      & ( ! [U_10089] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10091,tc_HOL_Obool)),hAPP(U_10094,U_10089)),U_10095))
            | ~ hBOOL(hAPP(hAPP(c_member(U_10092),U_10089),U_10093)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10091,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10092,tc_fun(U_10091,tc_HOL_Obool)),U_10093),U_10094)),U_10095)) ) ),
    inference(variable_rename,[status(thm)],[f_2749_1]) ).

fof(f_2749_3,plain,
    ( ! [U_10105,U_10103,U_10101,U_10099,U_10097] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10097,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10099,tc_fun(U_10097,tc_HOL_Obool)),U_10101),U_10103)),U_10105))
        | ? [U_10090] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10097,tc_HOL_Obool)),hAPP(U_10103,U_10090)),U_10105))
            & hBOOL(hAPP(hAPP(c_member(U_10099),U_10090),U_10101)) ) )
    & ! [U_10104,U_10102,U_10100,U_10098,U_10096] :
        ( ! [U_10089] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10096,tc_HOL_Obool)),hAPP(U_10102,U_10089)),U_10104))
            | ~ hBOOL(hAPP(hAPP(c_member(U_10098),U_10089),U_10100)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10096,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10098,tc_fun(U_10096,tc_HOL_Obool)),U_10100),U_10102)),U_10104)) ) ),
    inference(miniscope,[status(thm)],[f_2749_2]) ).

fof(f_2749_4,plain,
    ( ! [U_10105,U_10103,U_10101,U_10099,U_10097] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10097,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10099,tc_fun(U_10097,tc_HOL_Obool)),U_10101),U_10103)),U_10105))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10097,tc_HOL_Obool)),hAPP(U_10103,sK239(U_10105,U_10103,U_10101,U_10099,U_10097))),U_10105))
          & hBOOL(hAPP(hAPP(c_member(U_10099),sK239(U_10105,U_10103,U_10101,U_10099,U_10097)),U_10101)) ) )
    & ! [U_10104,U_10102,U_10100,U_10098,U_10096] :
        ( ! [U_10089] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10096,tc_HOL_Obool)),hAPP(U_10102,U_10089)),U_10104))
            | ~ hBOOL(hAPP(hAPP(c_member(U_10098),U_10089),U_10100)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10096,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10098,tc_fun(U_10096,tc_HOL_Obool)),U_10100),U_10102)),U_10104)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK239]),skolemize(U_10090,sK239(U_10105,U_10103,U_10101,U_10099,U_10097))],[f_2749_3]) ).

cnf(f_2749_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10096,tc_HOL_Obool)),hAPP(U_10102,U_10089)),U_10104))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10098),U_10089),U_10100))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10096,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10098,tc_fun(U_10096,tc_HOL_Obool)),U_10100),U_10102)),U_10104)) ),
    inference(clausify,[status(thm)],[f_2749_4]) ).

cnf(f_2749_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10099),sK239(U_10105,U_10103,U_10101,U_10099,U_10097)),U_10101))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10097,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10099,tc_fun(U_10097,tc_HOL_Obool)),U_10101),U_10103)),U_10105)) ),
    inference(clausify,[status(thm)],[f_2749_4]) ).

cnf(f_2749_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10097,tc_HOL_Obool)),hAPP(U_10103,sK239(U_10105,U_10103,U_10101,U_10099,U_10097))),U_10105))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10097,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10099,tc_fun(U_10097,tc_HOL_Obool)),U_10101),U_10103)),U_10105)) ),
    inference(clausify,[status(thm)],[f_2749_4]) ).

fof(f_2750_1,plain,
    ! [V_M_2,V_A_2,T_c,V_u_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_u_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2),V_M_2)))
          | ? [B_x] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_u_2),hAPP(V_M_2,B_x)))
              & hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) )
        & ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_u_2),hAPP(V_M_2,B_x)))
              | ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_u_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2),V_M_2))) ) )
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_le__INF__iff]) ).

fof(f_2750_2,plain,
    ! [U_10112,U_10111,U_10110,U_10109,U_10108] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10108),U_10109),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10110,U_10108),U_10111),U_10112)))
          | ? [U_10107] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10108),U_10109),hAPP(U_10112,U_10107)))
              & hBOOL(hAPP(hAPP(c_member(U_10110),U_10107),U_10111)) ) )
        & ( ! [U_10106] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10108),U_10109),hAPP(U_10112,U_10106)))
              | ~ hBOOL(hAPP(hAPP(c_member(U_10110),U_10106),U_10111)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10108),U_10109),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10110,U_10108),U_10111),U_10112))) ) )
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_10108) ),
    inference(variable_rename,[status(thm)],[f_2750_1]) ).

fof(f_2750_3,plain,
    ! [U_10112,U_10111,U_10110,U_10109,U_10108] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10108),U_10109),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10110,U_10108),U_10111),U_10112)))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10108),U_10109),hAPP(U_10112,sK240(U_10112,U_10111,U_10110,U_10109,U_10108))))
            & hBOOL(hAPP(hAPP(c_member(U_10110),sK240(U_10112,U_10111,U_10110,U_10109,U_10108)),U_10111)) ) )
        & ( ! [U_10106] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10108),U_10109),hAPP(U_10112,U_10106)))
              | ~ hBOOL(hAPP(hAPP(c_member(U_10110),U_10106),U_10111)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10108),U_10109),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10110,U_10108),U_10111),U_10112))) ) )
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_10108) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK240]),skolemize(U_10107,sK240(U_10112,U_10111,U_10110,U_10109,U_10108))],[f_2750_2]) ).

cnf(f_2750_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10108),U_10109),hAPP(U_10112,U_10106)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10110),U_10106),U_10111))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10108),U_10109),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10110,U_10108),U_10111),U_10112)))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_10108) ),
    inference(clausify,[status(thm)],[f_2750_3]) ).

cnf(f_2750_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10110),sK240(U_10112,U_10111,U_10110,U_10109,U_10108)),U_10111))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10108),U_10109),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10110,U_10108),U_10111),U_10112)))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_10108) ),
    inference(clausify,[status(thm)],[f_2750_3]) ).

cnf(f_2750_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10108),U_10109),hAPP(U_10112,sK240(U_10112,U_10111,U_10110,U_10109,U_10108))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10108),U_10109),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10110,U_10108),U_10111),U_10112)))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_10108) ),
    inference(clausify,[status(thm)],[f_2750_3]) ).

fof(f_2751_1,plain,
    ! [V_u_2,V_M_2,V_A_2,T_c,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2),V_M_2)),V_u_2))
          | ? [B_x] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_M_2,B_x)),V_u_2))
              & hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) )
        & ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_M_2,B_x)),V_u_2))
              | ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2),V_M_2)),V_u_2)) ) )
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_SUP__le__iff]) ).

fof(f_2751_2,plain,
    ! [U_10119,U_10118,U_10117,U_10116,U_10115] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10115),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10116,U_10115),U_10117),U_10118)),U_10119))
          | ? [U_10114] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10115),hAPP(U_10118,U_10114)),U_10119))
              & hBOOL(hAPP(hAPP(c_member(U_10116),U_10114),U_10117)) ) )
        & ( ! [U_10113] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10115),hAPP(U_10118,U_10113)),U_10119))
              | ~ hBOOL(hAPP(hAPP(c_member(U_10116),U_10113),U_10117)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10115),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10116,U_10115),U_10117),U_10118)),U_10119)) ) )
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_10115) ),
    inference(variable_rename,[status(thm)],[f_2751_1]) ).

fof(f_2751_3,plain,
    ! [U_10119,U_10118,U_10117,U_10116,U_10115] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10115),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10116,U_10115),U_10117),U_10118)),U_10119))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10115),hAPP(U_10118,sK241(U_10119,U_10118,U_10117,U_10116,U_10115))),U_10119))
            & hBOOL(hAPP(hAPP(c_member(U_10116),sK241(U_10119,U_10118,U_10117,U_10116,U_10115)),U_10117)) ) )
        & ( ! [U_10113] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10115),hAPP(U_10118,U_10113)),U_10119))
              | ~ hBOOL(hAPP(hAPP(c_member(U_10116),U_10113),U_10117)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10115),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10116,U_10115),U_10117),U_10118)),U_10119)) ) )
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_10115) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK241]),skolemize(U_10114,sK241(U_10119,U_10118,U_10117,U_10116,U_10115))],[f_2751_2]) ).

cnf(f_2751_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10115),hAPP(U_10118,U_10113)),U_10119))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10116),U_10113),U_10117))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10115),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10116,U_10115),U_10117),U_10118)),U_10119))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_10115) ),
    inference(clausify,[status(thm)],[f_2751_3]) ).

cnf(f_2751_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10116),sK241(U_10119,U_10118,U_10117,U_10116,U_10115)),U_10117))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10115),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10116,U_10115),U_10117),U_10118)),U_10119))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_10115) ),
    inference(clausify,[status(thm)],[f_2751_3]) ).

cnf(f_2751_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10115),hAPP(U_10118,sK241(U_10119,U_10118,U_10117,U_10116,U_10115))),U_10119))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10115),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10116,U_10115),U_10117),U_10118)),U_10119))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_10115) ),
    inference(clausify,[status(thm)],[f_2751_3]) ).

fof(f_2752_1,plain,
    ! [V_B_2,T_c,V_A_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(V_B_2,V_a_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_INT__lower]) ).

fof(f_2752_2,plain,
    ! [U_10124,U_10123,U_10122,U_10121,U_10120] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10123,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10120,tc_fun(U_10123,tc_HOL_Obool)),U_10122),U_10124)),hAPP(U_10124,U_10121)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10120),U_10121),U_10122)) ),
    inference(variable_rename,[status(thm)],[f_2752_1]) ).

cnf(f_2752_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10123,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10120,tc_fun(U_10123,tc_HOL_Obool)),U_10122),U_10124)),hAPP(U_10124,U_10121)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10120),U_10121),U_10122)) ),
    inference(clausify,[status(thm)],[f_2752_2]) ).

fof(f_2753_1,plain,
    ! [V_S_2,V_R_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_pred__subset__eq]) ).

fof(f_2753_2,plain,
    ! [U_10127,U_10126,U_10125] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10125,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_10125,tc_fun(U_10125,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10125)),U_10126)),hAPP(hAPP(c_COMBC(U_10125,tc_fun(U_10125,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10125)),U_10127)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10125,tc_HOL_Obool)),U_10126),U_10127)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10125,tc_HOL_Obool)),U_10126),U_10127))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10125,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_10125,tc_fun(U_10125,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10125)),U_10126)),hAPP(hAPP(c_COMBC(U_10125,tc_fun(U_10125,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10125)),U_10127))) ) ),
    inference(variable_rename,[status(thm)],[f_2753_1]) ).

fof(f_2753_3,plain,
    ( ! [U_10133,U_10131,U_10129] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10129,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_10129,tc_fun(U_10129,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10129)),U_10131)),hAPP(hAPP(c_COMBC(U_10129,tc_fun(U_10129,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10129)),U_10133)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10129,tc_HOL_Obool)),U_10131),U_10133)) )
    & ! [U_10132,U_10130,U_10128] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10128,tc_HOL_Obool)),U_10130),U_10132))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10128,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_10128,tc_fun(U_10128,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10128)),U_10130)),hAPP(hAPP(c_COMBC(U_10128,tc_fun(U_10128,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10128)),U_10132))) ) ),
    inference(miniscope,[status(thm)],[f_2753_2]) ).

cnf(f_2753_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10128,tc_HOL_Obool)),U_10130),U_10132))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10128,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_10128,tc_fun(U_10128,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10128)),U_10130)),hAPP(hAPP(c_COMBC(U_10128,tc_fun(U_10128,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10128)),U_10132))) ),
    inference(clausify,[status(thm)],[f_2753_3]) ).

cnf(f_2753_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10129,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_10129,tc_fun(U_10129,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10129)),U_10131)),hAPP(hAPP(c_COMBC(U_10129,tc_fun(U_10129,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10129)),U_10133)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10129,tc_HOL_Obool)),U_10131),U_10133)) ),
    inference(clausify,[status(thm)],[f_2753_3]) ).

fof(f_2754_1,plain,
    ! [V_S_2,V_R_2,T_c,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_S_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_R_2),V_S_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_R_2),V_S_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_S_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_pred__subset__eq2]) ).

fof(f_2754_2,plain,
    ! [U_10137,U_10136,U_10135,U_10134] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10134,tc_fun(U_10135,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_10134,tc_fun(tc_prod(U_10134,U_10135),tc_HOL_Obool),tc_fun(U_10135,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10135,tc_fun(tc_fun(tc_prod(U_10134,U_10135),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_10134,U_10135),tc_HOL_Obool),tc_fun(U_10135,tc_HOL_Obool)),U_10134),c_COMBC(U_10135,tc_fun(tc_prod(U_10134,U_10135),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10135,tc_prod(U_10134,U_10135)),tc_fun(U_10135,tc_fun(tc_fun(tc_prod(U_10134,U_10135),tc_HOL_Obool),tc_HOL_Obool)),U_10134),hAPP(c_COMBB(tc_prod(U_10134,U_10135),tc_fun(tc_fun(tc_prod(U_10134,U_10135),tc_HOL_Obool),tc_HOL_Obool),U_10135),c_member(tc_prod(U_10134,U_10135)))),c_Product__Type_OPair(U_10134,U_10135)))),U_10136)),hAPP(hAPP(c_COMBC(U_10134,tc_fun(tc_prod(U_10134,U_10135),tc_HOL_Obool),tc_fun(U_10135,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10135,tc_fun(tc_fun(tc_prod(U_10134,U_10135),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_10134,U_10135),tc_HOL_Obool),tc_fun(U_10135,tc_HOL_Obool)),U_10134),c_COMBC(U_10135,tc_fun(tc_prod(U_10134,U_10135),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10135,tc_prod(U_10134,U_10135)),tc_fun(U_10135,tc_fun(tc_fun(tc_prod(U_10134,U_10135),tc_HOL_Obool),tc_HOL_Obool)),U_10134),hAPP(c_COMBB(tc_prod(U_10134,U_10135),tc_fun(tc_fun(tc_prod(U_10134,U_10135),tc_HOL_Obool),tc_HOL_Obool),U_10135),c_member(tc_prod(U_10134,U_10135)))),c_Product__Type_OPair(U_10134,U_10135)))),U_10137)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_10134,U_10135),tc_HOL_Obool)),U_10136),U_10137)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_10134,U_10135),tc_HOL_Obool)),U_10136),U_10137))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10134,tc_fun(U_10135,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_10134,tc_fun(tc_prod(U_10134,U_10135),tc_HOL_Obool),tc_fun(U_10135,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10135,tc_fun(tc_fun(tc_prod(U_10134,U_10135),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_10134,U_10135),tc_HOL_Obool),tc_fun(U_10135,tc_HOL_Obool)),U_10134),c_COMBC(U_10135,tc_fun(tc_prod(U_10134,U_10135),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10135,tc_prod(U_10134,U_10135)),tc_fun(U_10135,tc_fun(tc_fun(tc_prod(U_10134,U_10135),tc_HOL_Obool),tc_HOL_Obool)),U_10134),hAPP(c_COMBB(tc_prod(U_10134,U_10135),tc_fun(tc_fun(tc_prod(U_10134,U_10135),tc_HOL_Obool),tc_HOL_Obool),U_10135),c_member(tc_prod(U_10134,U_10135)))),c_Product__Type_OPair(U_10134,U_10135)))),U_10136)),hAPP(hAPP(c_COMBC(U_10134,tc_fun(tc_prod(U_10134,U_10135),tc_HOL_Obool),tc_fun(U_10135,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10135,tc_fun(tc_fun(tc_prod(U_10134,U_10135),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_10134,U_10135),tc_HOL_Obool),tc_fun(U_10135,tc_HOL_Obool)),U_10134),c_COMBC(U_10135,tc_fun(tc_prod(U_10134,U_10135),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10135,tc_prod(U_10134,U_10135)),tc_fun(U_10135,tc_fun(tc_fun(tc_prod(U_10134,U_10135),tc_HOL_Obool),tc_HOL_Obool)),U_10134),hAPP(c_COMBB(tc_prod(U_10134,U_10135),tc_fun(tc_fun(tc_prod(U_10134,U_10135),tc_HOL_Obool),tc_HOL_Obool),U_10135),c_member(tc_prod(U_10134,U_10135)))),c_Product__Type_OPair(U_10134,U_10135)))),U_10137))) ) ),
    inference(variable_rename,[status(thm)],[f_2754_1]) ).

fof(f_2754_3,plain,
    ( ! [U_10145,U_10143,U_10141,U_10139] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10139,tc_fun(U_10141,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_10139,tc_fun(tc_prod(U_10139,U_10141),tc_HOL_Obool),tc_fun(U_10141,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10141,tc_fun(tc_fun(tc_prod(U_10139,U_10141),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_10139,U_10141),tc_HOL_Obool),tc_fun(U_10141,tc_HOL_Obool)),U_10139),c_COMBC(U_10141,tc_fun(tc_prod(U_10139,U_10141),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10141,tc_prod(U_10139,U_10141)),tc_fun(U_10141,tc_fun(tc_fun(tc_prod(U_10139,U_10141),tc_HOL_Obool),tc_HOL_Obool)),U_10139),hAPP(c_COMBB(tc_prod(U_10139,U_10141),tc_fun(tc_fun(tc_prod(U_10139,U_10141),tc_HOL_Obool),tc_HOL_Obool),U_10141),c_member(tc_prod(U_10139,U_10141)))),c_Product__Type_OPair(U_10139,U_10141)))),U_10143)),hAPP(hAPP(c_COMBC(U_10139,tc_fun(tc_prod(U_10139,U_10141),tc_HOL_Obool),tc_fun(U_10141,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10141,tc_fun(tc_fun(tc_prod(U_10139,U_10141),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_10139,U_10141),tc_HOL_Obool),tc_fun(U_10141,tc_HOL_Obool)),U_10139),c_COMBC(U_10141,tc_fun(tc_prod(U_10139,U_10141),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10141,tc_prod(U_10139,U_10141)),tc_fun(U_10141,tc_fun(tc_fun(tc_prod(U_10139,U_10141),tc_HOL_Obool),tc_HOL_Obool)),U_10139),hAPP(c_COMBB(tc_prod(U_10139,U_10141),tc_fun(tc_fun(tc_prod(U_10139,U_10141),tc_HOL_Obool),tc_HOL_Obool),U_10141),c_member(tc_prod(U_10139,U_10141)))),c_Product__Type_OPair(U_10139,U_10141)))),U_10145)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_10139,U_10141),tc_HOL_Obool)),U_10143),U_10145)) )
    & ! [U_10144,U_10142,U_10140,U_10138] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_10138,U_10140),tc_HOL_Obool)),U_10142),U_10144))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10138,tc_fun(U_10140,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_10138,tc_fun(tc_prod(U_10138,U_10140),tc_HOL_Obool),tc_fun(U_10140,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10140,tc_fun(tc_fun(tc_prod(U_10138,U_10140),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_10138,U_10140),tc_HOL_Obool),tc_fun(U_10140,tc_HOL_Obool)),U_10138),c_COMBC(U_10140,tc_fun(tc_prod(U_10138,U_10140),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10140,tc_prod(U_10138,U_10140)),tc_fun(U_10140,tc_fun(tc_fun(tc_prod(U_10138,U_10140),tc_HOL_Obool),tc_HOL_Obool)),U_10138),hAPP(c_COMBB(tc_prod(U_10138,U_10140),tc_fun(tc_fun(tc_prod(U_10138,U_10140),tc_HOL_Obool),tc_HOL_Obool),U_10140),c_member(tc_prod(U_10138,U_10140)))),c_Product__Type_OPair(U_10138,U_10140)))),U_10142)),hAPP(hAPP(c_COMBC(U_10138,tc_fun(tc_prod(U_10138,U_10140),tc_HOL_Obool),tc_fun(U_10140,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10140,tc_fun(tc_fun(tc_prod(U_10138,U_10140),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_10138,U_10140),tc_HOL_Obool),tc_fun(U_10140,tc_HOL_Obool)),U_10138),c_COMBC(U_10140,tc_fun(tc_prod(U_10138,U_10140),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10140,tc_prod(U_10138,U_10140)),tc_fun(U_10140,tc_fun(tc_fun(tc_prod(U_10138,U_10140),tc_HOL_Obool),tc_HOL_Obool)),U_10138),hAPP(c_COMBB(tc_prod(U_10138,U_10140),tc_fun(tc_fun(tc_prod(U_10138,U_10140),tc_HOL_Obool),tc_HOL_Obool),U_10140),c_member(tc_prod(U_10138,U_10140)))),c_Product__Type_OPair(U_10138,U_10140)))),U_10144))) ) ),
    inference(miniscope,[status(thm)],[f_2754_2]) ).

cnf(f_2754_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_10138,U_10140),tc_HOL_Obool)),U_10142),U_10144))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10138,tc_fun(U_10140,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_10138,tc_fun(tc_prod(U_10138,U_10140),tc_HOL_Obool),tc_fun(U_10140,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10140,tc_fun(tc_fun(tc_prod(U_10138,U_10140),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_10138,U_10140),tc_HOL_Obool),tc_fun(U_10140,tc_HOL_Obool)),U_10138),c_COMBC(U_10140,tc_fun(tc_prod(U_10138,U_10140),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10140,tc_prod(U_10138,U_10140)),tc_fun(U_10140,tc_fun(tc_fun(tc_prod(U_10138,U_10140),tc_HOL_Obool),tc_HOL_Obool)),U_10138),hAPP(c_COMBB(tc_prod(U_10138,U_10140),tc_fun(tc_fun(tc_prod(U_10138,U_10140),tc_HOL_Obool),tc_HOL_Obool),U_10140),c_member(tc_prod(U_10138,U_10140)))),c_Product__Type_OPair(U_10138,U_10140)))),U_10142)),hAPP(hAPP(c_COMBC(U_10138,tc_fun(tc_prod(U_10138,U_10140),tc_HOL_Obool),tc_fun(U_10140,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10140,tc_fun(tc_fun(tc_prod(U_10138,U_10140),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_10138,U_10140),tc_HOL_Obool),tc_fun(U_10140,tc_HOL_Obool)),U_10138),c_COMBC(U_10140,tc_fun(tc_prod(U_10138,U_10140),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10140,tc_prod(U_10138,U_10140)),tc_fun(U_10140,tc_fun(tc_fun(tc_prod(U_10138,U_10140),tc_HOL_Obool),tc_HOL_Obool)),U_10138),hAPP(c_COMBB(tc_prod(U_10138,U_10140),tc_fun(tc_fun(tc_prod(U_10138,U_10140),tc_HOL_Obool),tc_HOL_Obool),U_10140),c_member(tc_prod(U_10138,U_10140)))),c_Product__Type_OPair(U_10138,U_10140)))),U_10144))) ),
    inference(clausify,[status(thm)],[f_2754_3]) ).

cnf(f_2754_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10139,tc_fun(U_10141,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_10139,tc_fun(tc_prod(U_10139,U_10141),tc_HOL_Obool),tc_fun(U_10141,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10141,tc_fun(tc_fun(tc_prod(U_10139,U_10141),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_10139,U_10141),tc_HOL_Obool),tc_fun(U_10141,tc_HOL_Obool)),U_10139),c_COMBC(U_10141,tc_fun(tc_prod(U_10139,U_10141),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10141,tc_prod(U_10139,U_10141)),tc_fun(U_10141,tc_fun(tc_fun(tc_prod(U_10139,U_10141),tc_HOL_Obool),tc_HOL_Obool)),U_10139),hAPP(c_COMBB(tc_prod(U_10139,U_10141),tc_fun(tc_fun(tc_prod(U_10139,U_10141),tc_HOL_Obool),tc_HOL_Obool),U_10141),c_member(tc_prod(U_10139,U_10141)))),c_Product__Type_OPair(U_10139,U_10141)))),U_10143)),hAPP(hAPP(c_COMBC(U_10139,tc_fun(tc_prod(U_10139,U_10141),tc_HOL_Obool),tc_fun(U_10141,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10141,tc_fun(tc_fun(tc_prod(U_10139,U_10141),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_10139,U_10141),tc_HOL_Obool),tc_fun(U_10141,tc_HOL_Obool)),U_10139),c_COMBC(U_10141,tc_fun(tc_prod(U_10139,U_10141),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10141,tc_prod(U_10139,U_10141)),tc_fun(U_10141,tc_fun(tc_fun(tc_prod(U_10139,U_10141),tc_HOL_Obool),tc_HOL_Obool)),U_10139),hAPP(c_COMBB(tc_prod(U_10139,U_10141),tc_fun(tc_fun(tc_prod(U_10139,U_10141),tc_HOL_Obool),tc_HOL_Obool),U_10141),c_member(tc_prod(U_10139,U_10141)))),c_Product__Type_OPair(U_10139,U_10141)))),U_10145)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_10139,U_10141),tc_HOL_Obool)),U_10143),U_10145)) ),
    inference(clausify,[status(thm)],[f_2754_3]) ).

fof(f_2755_1,plain,
    ! [V_N_2,V_k_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2),V_N_2),
    inference(fof_nnf,[status(thm)],[fact_inj__on__add__nat]) ).

fof(f_2755_2,plain,
    ! [U_10147,U_10146] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_10146),U_10147),
    inference(variable_rename,[status(thm)],[f_2755_1]) ).

cnf(f_2755_3,plain,
    c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_10146),U_10147),
    inference(clausify,[status(thm)],[f_2755_2]) ).

fof(f_2756_1,plain,
    ! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Oplus__class_Oplus(T_b)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_g_2),V_A_2))
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__addf]) ).

fof(f_2756_2,plain,
    ! [U_10152,U_10151,U_10150,U_10149,U_10148] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10149,U_10148),hAPP(hAPP(c_COMBS(U_10149,U_10148,U_10148),hAPP(hAPP(c_COMBB(U_10148,tc_fun(U_10148,U_10148),U_10149),c_Groups_Oplus__class_Oplus(U_10148)),U_10150)),U_10151)),U_10152) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10148),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10149,U_10148),U_10150),U_10152)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10149,U_10148),U_10151),U_10152))
      | ~ class_Groups_Ocomm__monoid__add(U_10148) ),
    inference(variable_rename,[status(thm)],[f_2756_1]) ).

cnf(f_2756_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10149,U_10148),hAPP(hAPP(c_COMBS(U_10149,U_10148,U_10148),hAPP(hAPP(c_COMBB(U_10148,tc_fun(U_10148,U_10148),U_10149),c_Groups_Oplus__class_Oplus(U_10148)),U_10150)),U_10151)),U_10152) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10148),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10149,U_10148),U_10150),U_10152)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10149,U_10148),U_10151),U_10152))
    | ~ class_Groups_Ocomm__monoid__add(U_10148) ),
    inference(clausify,[status(thm)],[f_2756_2]) ).

fof(f_2757_1,plain,
    ! [V_n_2] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),
    inference(fof_nnf,[status(thm)],[fact_less__eq__Suc__le__raw]) ).

fof(f_2757_2,plain,
    ! [U_10153] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10153) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10153)),
    inference(variable_rename,[status(thm)],[f_2757_1]) ).

cnf(f_2757_3,plain,
    hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10153) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10153)),
    inference(clausify,[status(thm)],[f_2757_2]) ).

fof(f_2758_1,plain,
    ! [V_B_2,T_c,V_A_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_B_2,V_a_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_UN__upper]) ).

fof(f_2758_2,plain,
    ! [U_10158,U_10157,U_10156,U_10155,U_10154] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10157,tc_HOL_Obool)),hAPP(U_10158,U_10155)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10154,tc_fun(U_10157,tc_HOL_Obool)),U_10156),U_10158)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10154),U_10155),U_10156)) ),
    inference(variable_rename,[status(thm)],[f_2758_1]) ).

cnf(f_2758_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10157,tc_HOL_Obool)),hAPP(U_10158,U_10155)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10154,tc_fun(U_10157,tc_HOL_Obool)),U_10156),U_10158)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10154),U_10155),U_10156)) ),
    inference(clausify,[status(thm)],[f_2758_2]) ).

fof(f_2759_1,plain,
    ! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Groups_Oplus__class_Oplus(T_c)),V_g_2)),V_h_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_h_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Ocomm__monoid__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum_Odistrib]) ).

fof(f_2759_2,plain,
    ! [U_10163,U_10162,U_10161,U_10160,U_10159] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10160,U_10159),hAPP(hAPP(c_COMBS(U_10160,U_10159,U_10159),hAPP(hAPP(c_COMBB(U_10159,tc_fun(U_10159,U_10159),U_10160),c_Groups_Oplus__class_Oplus(U_10159)),U_10162)),U_10163)),U_10161) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10159),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10160,U_10159),U_10162),U_10161)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10160,U_10159),U_10163),U_10161))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10160),U_10161))
      | ~ class_Groups_Ocomm__monoid__add(U_10159) ),
    inference(variable_rename,[status(thm)],[f_2759_1]) ).

cnf(f_2759_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10160,U_10159),hAPP(hAPP(c_COMBS(U_10160,U_10159,U_10159),hAPP(hAPP(c_COMBB(U_10159,tc_fun(U_10159,U_10159),U_10160),c_Groups_Oplus__class_Oplus(U_10159)),U_10162)),U_10163)),U_10161) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10159),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10160,U_10159),U_10162),U_10161)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10160,U_10159),U_10163),U_10161))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10160),U_10161))
    | ~ class_Groups_Ocomm__monoid__add(U_10159) ),
    inference(clausify,[status(thm)],[f_2759_2]) ).

fof(f_2760_1,plain,
    ! [V_M_2,V_A_2,V_i_2,T_b,T_c] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),V_M_2)),hAPP(V_M_2,V_i_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_INF__leI]) ).

fof(f_2760_2,plain,
    ! [U_10168,U_10167,U_10166,U_10165,U_10164] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10164),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10165,U_10164),U_10167),U_10168)),hAPP(U_10168,U_10166)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10165),U_10166),U_10167))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_10164) ),
    inference(variable_rename,[status(thm)],[f_2760_1]) ).

cnf(f_2760_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10164),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10165,U_10164),U_10167),U_10168)),hAPP(U_10168,U_10166)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10165),U_10166),U_10167))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_10164) ),
    inference(clausify,[status(thm)],[f_2760_2]) ).

fof(f_2761_1,plain,
    ! [V_M_2,V_A_2,V_i_2,T_b,T_c] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_M_2,V_i_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),V_M_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_le__SUPI]) ).

fof(f_2761_2,plain,
    ! [U_10173,U_10172,U_10171,U_10170,U_10169] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10169),hAPP(U_10173,U_10171)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10170,U_10169),U_10172),U_10173)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10170),U_10171),U_10172))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_10169) ),
    inference(variable_rename,[status(thm)],[f_2761_1]) ).

cnf(f_2761_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10169),hAPP(U_10173,U_10171)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10170,U_10169),U_10172),U_10173)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10170),U_10171),U_10172))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_10169) ),
    inference(clausify,[status(thm)],[f_2761_2]) ).

fof(f_2762_1,plain,
    ! [V_a_2,V_f_2,V_A_2,T_c,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2),V_f_2)),V_a_2))
          | ! [B_x] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_x)),V_a_2))
              | ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) )
        & ( ? [B_x] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_x)),V_a_2))
              & hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2),V_f_2)),V_a_2)) ) )
      | ~ class_Orderings_Olinorder(T_b)
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_INF__less__iff]) ).

fof(f_2762_2,plain,
    ! [U_10180,U_10179,U_10178,U_10177,U_10176] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10176),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10177,U_10176),U_10178),U_10179)),U_10180))
          | ! [U_10175] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10176),hAPP(U_10179,U_10175)),U_10180))
              | ~ hBOOL(hAPP(hAPP(c_member(U_10177),U_10175),U_10178)) ) )
        & ( ? [U_10174] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10176),hAPP(U_10179,U_10174)),U_10180))
              & hBOOL(hAPP(hAPP(c_member(U_10177),U_10174),U_10178)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10176),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10177,U_10176),U_10178),U_10179)),U_10180)) ) )
      | ~ class_Orderings_Olinorder(U_10176)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_10176) ),
    inference(variable_rename,[status(thm)],[f_2762_1]) ).

fof(f_2762_3,plain,
    ! [U_10180,U_10179,U_10178,U_10177,U_10176] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10176),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10177,U_10176),U_10178),U_10179)),U_10180))
          | ! [U_10175] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10176),hAPP(U_10179,U_10175)),U_10180))
              | ~ hBOOL(hAPP(hAPP(c_member(U_10177),U_10175),U_10178)) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10176),hAPP(U_10179,sK242(U_10180,U_10179,U_10178,U_10177,U_10176))),U_10180))
            & hBOOL(hAPP(hAPP(c_member(U_10177),sK242(U_10180,U_10179,U_10178,U_10177,U_10176)),U_10178)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10176),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10177,U_10176),U_10178),U_10179)),U_10180)) ) )
      | ~ class_Orderings_Olinorder(U_10176)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_10176) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK242]),skolemize(U_10174,sK242(U_10180,U_10179,U_10178,U_10177,U_10176))],[f_2762_2]) ).

cnf(f_2762_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10177),sK242(U_10180,U_10179,U_10178,U_10177,U_10176)),U_10178))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10176),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10177,U_10176),U_10178),U_10179)),U_10180))
    | ~ class_Orderings_Olinorder(U_10176)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_10176) ),
    inference(clausify,[status(thm)],[f_2762_3]) ).

cnf(f_2762_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10176),hAPP(U_10179,sK242(U_10180,U_10179,U_10178,U_10177,U_10176))),U_10180))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10176),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10177,U_10176),U_10178),U_10179)),U_10180))
    | ~ class_Orderings_Olinorder(U_10176)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_10176) ),
    inference(clausify,[status(thm)],[f_2762_3]) ).

cnf(f_2762_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10176),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10177,U_10176),U_10178),U_10179)),U_10180))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10176),hAPP(U_10179,U_10175)),U_10180))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10177),U_10175),U_10178))
    | ~ class_Orderings_Olinorder(U_10176)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_10176) ),
    inference(clausify,[status(thm)],[f_2762_3]) ).

fof(f_2763_1,plain,
    ! [V_f_2,V_A_2,T_c,V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2),V_f_2)))
          | ! [B_x] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(V_f_2,B_x)))
              | ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) )
        & ( ? [B_x] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(V_f_2,B_x)))
              & hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2),V_f_2))) ) )
      | ~ class_Orderings_Olinorder(T_b)
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_less__SUP__iff]) ).

fof(f_2763_2,plain,
    ! [U_10187,U_10186,U_10185,U_10184,U_10183] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10183),U_10184),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10185,U_10183),U_10186),U_10187)))
          | ! [U_10182] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10183),U_10184),hAPP(U_10187,U_10182)))
              | ~ hBOOL(hAPP(hAPP(c_member(U_10185),U_10182),U_10186)) ) )
        & ( ? [U_10181] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10183),U_10184),hAPP(U_10187,U_10181)))
              & hBOOL(hAPP(hAPP(c_member(U_10185),U_10181),U_10186)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10183),U_10184),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10185,U_10183),U_10186),U_10187))) ) )
      | ~ class_Orderings_Olinorder(U_10183)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_10183) ),
    inference(variable_rename,[status(thm)],[f_2763_1]) ).

fof(f_2763_3,plain,
    ! [U_10187,U_10186,U_10185,U_10184,U_10183] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10183),U_10184),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10185,U_10183),U_10186),U_10187)))
          | ! [U_10182] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10183),U_10184),hAPP(U_10187,U_10182)))
              | ~ hBOOL(hAPP(hAPP(c_member(U_10185),U_10182),U_10186)) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10183),U_10184),hAPP(U_10187,sK243(U_10187,U_10186,U_10185,U_10184,U_10183))))
            & hBOOL(hAPP(hAPP(c_member(U_10185),sK243(U_10187,U_10186,U_10185,U_10184,U_10183)),U_10186)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10183),U_10184),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10185,U_10183),U_10186),U_10187))) ) )
      | ~ class_Orderings_Olinorder(U_10183)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_10183) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK243]),skolemize(U_10181,sK243(U_10187,U_10186,U_10185,U_10184,U_10183))],[f_2763_2]) ).

cnf(f_2763_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10185),sK243(U_10187,U_10186,U_10185,U_10184,U_10183)),U_10186))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10183),U_10184),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10185,U_10183),U_10186),U_10187)))
    | ~ class_Orderings_Olinorder(U_10183)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_10183) ),
    inference(clausify,[status(thm)],[f_2763_3]) ).

cnf(f_2763_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10183),U_10184),hAPP(U_10187,sK243(U_10187,U_10186,U_10185,U_10184,U_10183))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10183),U_10184),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10185,U_10183),U_10186),U_10187)))
    | ~ class_Orderings_Olinorder(U_10183)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_10183) ),
    inference(clausify,[status(thm)],[f_2763_3]) ).

cnf(f_2763_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10183),U_10184),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10185,U_10183),U_10186),U_10187)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10183),U_10184),hAPP(U_10187,U_10182)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10185),U_10182),U_10186))
    | ~ class_Orderings_Olinorder(U_10183)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_10183) ),
    inference(clausify,[status(thm)],[f_2763_3]) ).

fof(f_2764_1,plain,
    ! [V_n_2,V_k_2,V_m_2,V_f_2,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2))
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__shift__bounds__nat__ivl]) ).

fof(f_2764_2,plain,
    ! [U_10192,U_10191,U_10190,U_10189,U_10188] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10188),U_10189),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10190),U_10191)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10192),U_10191))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10188),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10188,tc_Nat_Onat),U_10189),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_10191))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10190),U_10192))
      | ~ class_Groups_Ocomm__monoid__add(U_10188) ),
    inference(variable_rename,[status(thm)],[f_2764_1]) ).

cnf(f_2764_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10188),U_10189),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10190),U_10191)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10192),U_10191))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10188),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10188,tc_Nat_Onat),U_10189),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_10191))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10190),U_10192))
    | ~ class_Groups_Ocomm__monoid__add(U_10188) ),
    inference(clausify,[status(thm)],[f_2764_2]) ).

fof(f_2765_1,plain,
    ! [V_w_2] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(V_w_2)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat))),
    inference(fof_nnf,[status(thm)],[fact_nat__number__of__Bit0]) ).

fof(f_2765_2,plain,
    ! [U_10193] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_10193)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10193)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_2765_1]) ).

cnf(f_2765_3,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_10193)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10193)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_2765_2]) ).

fof(f_2766_1,plain,
    ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_A_2),V_C_2))),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_C_2))),
    inference(fof_nnf,[status(thm)],[fact_Int__Inter__image]) ).

fof(f_2766_2,plain,
    ! [U_10198,U_10197,U_10196,U_10195,U_10194] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10194,tc_fun(U_10195,tc_HOL_Obool)),U_10196),hAPP(hAPP(c_COMBS(U_10194,tc_fun(U_10195,tc_HOL_Obool),tc_fun(U_10195,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10195,tc_HOL_Obool),tc_fun(tc_fun(U_10195,tc_HOL_Obool),tc_fun(U_10195,tc_HOL_Obool)),U_10194),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10195,tc_HOL_Obool))),U_10197)),U_10198)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10195,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_10195,tc_HOL_Obool),hAPP(c_Set_Oimage(U_10194,tc_fun(U_10195,tc_HOL_Obool),U_10197),U_10196))),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_10195,tc_HOL_Obool),hAPP(c_Set_Oimage(U_10194,tc_fun(U_10195,tc_HOL_Obool),U_10198),U_10196))),
    inference(variable_rename,[status(thm)],[f_2766_1]) ).

cnf(f_2766_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10194,tc_fun(U_10195,tc_HOL_Obool)),U_10196),hAPP(hAPP(c_COMBS(U_10194,tc_fun(U_10195,tc_HOL_Obool),tc_fun(U_10195,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10195,tc_HOL_Obool),tc_fun(tc_fun(U_10195,tc_HOL_Obool),tc_fun(U_10195,tc_HOL_Obool)),U_10194),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10195,tc_HOL_Obool))),U_10197)),U_10198)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10195,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_10195,tc_HOL_Obool),hAPP(c_Set_Oimage(U_10194,tc_fun(U_10195,tc_HOL_Obool),U_10197),U_10196))),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_10195,tc_HOL_Obool),hAPP(c_Set_Oimage(U_10194,tc_fun(U_10195,tc_HOL_Obool),U_10198),U_10196))),
    inference(clausify,[status(thm)],[f_2766_2]) ).

fof(f_2767_1,plain,
    ! [V_k_2,V_M_2,V_n_2,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool),tc_Nat_Onat),V_M_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_k_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2))),V_M_2),
    inference(fof_nnf,[status(thm)],[fact_UN__le__add__shift]) ).

fof(f_2767_2,plain,
    ! [U_10202,U_10201,U_10200,U_10199] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_10199,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_10200)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_10199,tc_HOL_Obool),tc_Nat_Onat),U_10201),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_10202))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_10199,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_10202,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10200),U_10202))),U_10201),
    inference(variable_rename,[status(thm)],[f_2767_1]) ).

cnf(f_2767_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_10199,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_10200)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_10199,tc_HOL_Obool),tc_Nat_Onat),U_10201),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_10202))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_10199,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_10202,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10200),U_10202))),U_10201),
    inference(clausify,[status(thm)],[f_2767_2]) ).

fof(f_2768_1,plain,
    ! [V_B_2,V_A_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),T_c),c_Set_OPow(T_b)),V_B_2))),hAPP(c_Set_OPow(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))),
    inference(fof_nnf,[status(thm)],[fact_UN__Pow__subset]) ).

fof(f_2768_2,plain,
    ! [U_10206,U_10205,U_10204,U_10203] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_10203,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10204,tc_fun(tc_fun(U_10203,tc_HOL_Obool),tc_HOL_Obool)),U_10205),hAPP(hAPP(c_COMBB(tc_fun(U_10203,tc_HOL_Obool),tc_fun(tc_fun(U_10203,tc_HOL_Obool),tc_HOL_Obool),U_10204),c_Set_OPow(U_10203)),U_10206))),hAPP(c_Set_OPow(U_10203),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10204,tc_fun(U_10203,tc_HOL_Obool)),U_10205),U_10206)))),
    inference(variable_rename,[status(thm)],[f_2768_1]) ).

cnf(f_2768_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_10203,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10204,tc_fun(tc_fun(U_10203,tc_HOL_Obool),tc_HOL_Obool)),U_10205),hAPP(hAPP(c_COMBB(tc_fun(U_10203,tc_HOL_Obool),tc_fun(tc_fun(U_10203,tc_HOL_Obool),tc_HOL_Obool),U_10204),c_Set_OPow(U_10203)),U_10206))),hAPP(c_Set_OPow(U_10203),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10204,tc_fun(U_10203,tc_HOL_Obool)),U_10205),U_10206)))),
    inference(clausify,[status(thm)],[f_2768_2]) ).

fof(f_2769_1,plain,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,T_c),c_Nat_Osemiring__1__class_Oof__nat(T_b)),V_f_2)),V_A_2)
      | ~ class_Rings_Osemiring__1(T_b)
      | ~ class_Groups_Ocomm__monoid__mult(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__setprod]) ).

fof(f_2769_2,plain,
    ! [U_10210,U_10209,U_10208,U_10207] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10207),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10208,tc_Nat_Onat),U_10209),U_10210)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10208,U_10207),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10207,U_10208),c_Nat_Osemiring__1__class_Oof__nat(U_10207)),U_10209)),U_10210)
      | ~ class_Rings_Osemiring__1(U_10207)
      | ~ class_Groups_Ocomm__monoid__mult(U_10207) ),
    inference(variable_rename,[status(thm)],[f_2769_1]) ).

cnf(f_2769_3,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10207),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10208,tc_Nat_Onat),U_10209),U_10210)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10208,U_10207),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10207,U_10208),c_Nat_Osemiring__1__class_Oof__nat(U_10207)),U_10209)),U_10210)
    | ~ class_Rings_Osemiring__1(U_10207)
    | ~ class_Groups_Ocomm__monoid__mult(U_10207) ),
    inference(clausify,[status(thm)],[f_2769_2]) ).

fof(f_2770_1,plain,
    ! [V_A_2,V_f_2,T_b] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_b),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__sum__prod2_I2_J]) ).

fof(f_2770_2,plain,
    ! [U_10213,U_10212,U_10211] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10211,tc_Nat_Onat),U_10212),U_10213) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10211,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_10211),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10212)),U_10213)),
    inference(variable_rename,[status(thm)],[f_2770_1]) ).

cnf(f_2770_3,plain,
    hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10211,tc_Nat_Onat),U_10212),U_10213) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10211,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_10211),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10212)),U_10213)),
    inference(clausify,[status(thm)],[f_2770_2]) ).

fof(f_2771_1,plain,
    ! [V_j_2,V_i_2,V_k_2] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),V_k_2)),
    inference(fof_nnf,[status(thm)],[fact_image__add__atLeastLessThan]) ).

fof(f_2771_2,plain,
    ! [U_10216,U_10215,U_10214] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_10214)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10215),U_10216)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10215),U_10214)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10216),U_10214)),
    inference(variable_rename,[status(thm)],[f_2771_1]) ).

cnf(f_2771_3,plain,
    hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_10214)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10215),U_10216)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10215),U_10214)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10216),U_10214)),
    inference(clausify,[status(thm)],[f_2771_2]) ).

fof(f_2772_1,plain,
    ! [V_j_2,V_i_2,V_k_2] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_i_2,V_j_2)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),V_k_2)),
    inference(fof_nnf,[status(thm)],[fact_image__add__atLeastAtMost]) ).

fof(f_2772_2,plain,
    ! [U_10219,U_10218,U_10217] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_10217)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_10218,U_10219)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10218),U_10217),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10219),U_10217)),
    inference(variable_rename,[status(thm)],[f_2772_1]) ).

cnf(f_2772_3,plain,
    hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_10217)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_10218,U_10219)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10218),U_10217),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10219),U_10217)),
    inference(clausify,[status(thm)],[f_2772_2]) ).

fof(f_2773_1,plain,
    ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = c_Groups_Ozero__class_Ozero(T_c)
          | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = hAPP(V_b_2,V_a_2)
          | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
      | ~ class_Groups_Ocomm__monoid__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__delta_H]) ).

fof(f_2773_2,plain,
    ! [U_10224,U_10223,U_10222,U_10221,U_10220] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10221,U_10220),hAPP(hAPP(c_COMBC(U_10221,U_10220,U_10220),hAPP(hAPP(c_COMBS(U_10221,U_10220,tc_fun(U_10220,U_10220)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10220,tc_fun(U_10220,U_10220)),U_10221),c_If(U_10220)),hAPP(c_fequal,U_10223))),U_10224)),c_Groups_Ozero__class_Ozero(U_10220))),U_10222) = c_Groups_Ozero__class_Ozero(U_10220)
          | hBOOL(hAPP(hAPP(c_member(U_10221),U_10223),U_10222)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10221,U_10220),hAPP(hAPP(c_COMBC(U_10221,U_10220,U_10220),hAPP(hAPP(c_COMBS(U_10221,U_10220,tc_fun(U_10220,U_10220)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10220,tc_fun(U_10220,U_10220)),U_10221),c_If(U_10220)),hAPP(c_fequal,U_10223))),U_10224)),c_Groups_Ozero__class_Ozero(U_10220))),U_10222) = hAPP(U_10224,U_10223)
          | ~ hBOOL(hAPP(hAPP(c_member(U_10221),U_10223),U_10222)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10221),U_10222))
      | ~ class_Groups_Ocomm__monoid__add(U_10220) ),
    inference(variable_rename,[status(thm)],[f_2773_1]) ).

cnf(f_2773_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10221,U_10220),hAPP(hAPP(c_COMBC(U_10221,U_10220,U_10220),hAPP(hAPP(c_COMBS(U_10221,U_10220,tc_fun(U_10220,U_10220)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10220,tc_fun(U_10220,U_10220)),U_10221),c_If(U_10220)),hAPP(c_fequal,U_10223))),U_10224)),c_Groups_Ozero__class_Ozero(U_10220))),U_10222) = hAPP(U_10224,U_10223)
    | ~ hBOOL(hAPP(hAPP(c_member(U_10221),U_10223),U_10222))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10221),U_10222))
    | ~ class_Groups_Ocomm__monoid__add(U_10220) ),
    inference(clausify,[status(thm)],[f_2773_2]) ).

cnf(f_2773_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10221,U_10220),hAPP(hAPP(c_COMBC(U_10221,U_10220,U_10220),hAPP(hAPP(c_COMBS(U_10221,U_10220,tc_fun(U_10220,U_10220)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10220,tc_fun(U_10220,U_10220)),U_10221),c_If(U_10220)),hAPP(c_fequal,U_10223))),U_10224)),c_Groups_Ozero__class_Ozero(U_10220))),U_10222) = c_Groups_Ozero__class_Ozero(U_10220)
    | hBOOL(hAPP(hAPP(c_member(U_10221),U_10223),U_10222))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10221),U_10222))
    | ~ class_Groups_Ocomm__monoid__add(U_10220) ),
    inference(clausify,[status(thm)],[f_2773_2]) ).

fof(f_2774_1,plain,
    ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = c_Groups_Ozero__class_Ozero(T_c)
          | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = hAPP(V_b_2,V_a_2)
          | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
      | ~ class_Groups_Ocomm__monoid__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__delta]) ).

fof(f_2774_2,plain,
    ! [U_10229,U_10228,U_10227,U_10226,U_10225] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10226,U_10225),hAPP(hAPP(c_COMBC(U_10226,U_10225,U_10225),hAPP(hAPP(c_COMBS(U_10226,U_10225,tc_fun(U_10225,U_10225)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10225,tc_fun(U_10225,U_10225)),U_10226),c_If(U_10225)),hAPP(hAPP(c_COMBC(U_10226,U_10226,tc_HOL_Obool),c_fequal),U_10228))),U_10229)),c_Groups_Ozero__class_Ozero(U_10225))),U_10227) = c_Groups_Ozero__class_Ozero(U_10225)
          | hBOOL(hAPP(hAPP(c_member(U_10226),U_10228),U_10227)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10226,U_10225),hAPP(hAPP(c_COMBC(U_10226,U_10225,U_10225),hAPP(hAPP(c_COMBS(U_10226,U_10225,tc_fun(U_10225,U_10225)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10225,tc_fun(U_10225,U_10225)),U_10226),c_If(U_10225)),hAPP(hAPP(c_COMBC(U_10226,U_10226,tc_HOL_Obool),c_fequal),U_10228))),U_10229)),c_Groups_Ozero__class_Ozero(U_10225))),U_10227) = hAPP(U_10229,U_10228)
          | ~ hBOOL(hAPP(hAPP(c_member(U_10226),U_10228),U_10227)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10226),U_10227))
      | ~ class_Groups_Ocomm__monoid__add(U_10225) ),
    inference(variable_rename,[status(thm)],[f_2774_1]) ).

cnf(f_2774_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10226,U_10225),hAPP(hAPP(c_COMBC(U_10226,U_10225,U_10225),hAPP(hAPP(c_COMBS(U_10226,U_10225,tc_fun(U_10225,U_10225)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10225,tc_fun(U_10225,U_10225)),U_10226),c_If(U_10225)),hAPP(hAPP(c_COMBC(U_10226,U_10226,tc_HOL_Obool),c_fequal),U_10228))),U_10229)),c_Groups_Ozero__class_Ozero(U_10225))),U_10227) = hAPP(U_10229,U_10228)
    | ~ hBOOL(hAPP(hAPP(c_member(U_10226),U_10228),U_10227))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10226),U_10227))
    | ~ class_Groups_Ocomm__monoid__add(U_10225) ),
    inference(clausify,[status(thm)],[f_2774_2]) ).

cnf(f_2774_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10226,U_10225),hAPP(hAPP(c_COMBC(U_10226,U_10225,U_10225),hAPP(hAPP(c_COMBS(U_10226,U_10225,tc_fun(U_10225,U_10225)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10225,tc_fun(U_10225,U_10225)),U_10226),c_If(U_10225)),hAPP(hAPP(c_COMBC(U_10226,U_10226,tc_HOL_Obool),c_fequal),U_10228))),U_10229)),c_Groups_Ozero__class_Ozero(U_10225))),U_10227) = c_Groups_Ozero__class_Ozero(U_10225)
    | hBOOL(hAPP(hAPP(c_member(U_10226),U_10228),U_10227))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10226),U_10227))
    | ~ class_Groups_Ocomm__monoid__add(U_10225) ),
    inference(clausify,[status(thm)],[f_2774_2]) ).

fof(f_2775_1,plain,
    ! [V_c_2,T_c,V_A_2,V_x_2,T_b] :
      ( hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_c_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_image__constant]) ).

fof(f_2775_2,plain,
    ! [U_10234,U_10233,U_10232,U_10231,U_10230] :
      ( hAPP(c_Set_Oimage(U_10230,U_10233,hAPP(c_COMBK(U_10233,U_10230),U_10234)),U_10232) = hAPP(hAPP(c_Set_Oinsert(U_10233),U_10234),c_Orderings_Obot__class_Obot(tc_fun(U_10233,tc_HOL_Obool)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10230),U_10231),U_10232)) ),
    inference(variable_rename,[status(thm)],[f_2775_1]) ).

cnf(f_2775_3,plain,
    ( hAPP(c_Set_Oimage(U_10230,U_10233,hAPP(c_COMBK(U_10233,U_10230),U_10234)),U_10232) = hAPP(hAPP(c_Set_Oinsert(U_10233),U_10234),c_Orderings_Obot__class_Obot(tc_fun(U_10233,tc_HOL_Obool)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10230),U_10231),U_10232)) ),
    inference(clausify,[status(thm)],[f_2775_2]) ).

fof(f_2776_1,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_INT__greaterThan__UNIV]) ).

cnf(f_2776_2,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2776_1]) ).

fof(f_2777_1,plain,
    ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = c_Groups_Oone__class_Oone(T_c)
          | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = hAPP(V_b_2,V_a_2)
          | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__delta]) ).

fof(f_2777_2,plain,
    ! [U_10239,U_10238,U_10237,U_10236,U_10235] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10236,U_10235),hAPP(hAPP(c_COMBC(U_10236,U_10235,U_10235),hAPP(hAPP(c_COMBS(U_10236,U_10235,tc_fun(U_10235,U_10235)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10235,tc_fun(U_10235,U_10235)),U_10236),c_If(U_10235)),hAPP(hAPP(c_COMBC(U_10236,U_10236,tc_HOL_Obool),c_fequal),U_10238))),U_10239)),c_Groups_Oone__class_Oone(U_10235))),U_10237) = c_Groups_Oone__class_Oone(U_10235)
          | hBOOL(hAPP(hAPP(c_member(U_10236),U_10238),U_10237)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10236,U_10235),hAPP(hAPP(c_COMBC(U_10236,U_10235,U_10235),hAPP(hAPP(c_COMBS(U_10236,U_10235,tc_fun(U_10235,U_10235)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10235,tc_fun(U_10235,U_10235)),U_10236),c_If(U_10235)),hAPP(hAPP(c_COMBC(U_10236,U_10236,tc_HOL_Obool),c_fequal),U_10238))),U_10239)),c_Groups_Oone__class_Oone(U_10235))),U_10237) = hAPP(U_10239,U_10238)
          | ~ hBOOL(hAPP(hAPP(c_member(U_10236),U_10238),U_10237)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10236),U_10237))
      | ~ class_Groups_Ocomm__monoid__mult(U_10235) ),
    inference(variable_rename,[status(thm)],[f_2777_1]) ).

cnf(f_2777_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10236,U_10235),hAPP(hAPP(c_COMBC(U_10236,U_10235,U_10235),hAPP(hAPP(c_COMBS(U_10236,U_10235,tc_fun(U_10235,U_10235)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10235,tc_fun(U_10235,U_10235)),U_10236),c_If(U_10235)),hAPP(hAPP(c_COMBC(U_10236,U_10236,tc_HOL_Obool),c_fequal),U_10238))),U_10239)),c_Groups_Oone__class_Oone(U_10235))),U_10237) = hAPP(U_10239,U_10238)
    | ~ hBOOL(hAPP(hAPP(c_member(U_10236),U_10238),U_10237))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10236),U_10237))
    | ~ class_Groups_Ocomm__monoid__mult(U_10235) ),
    inference(clausify,[status(thm)],[f_2777_2]) ).

cnf(f_2777_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10236,U_10235),hAPP(hAPP(c_COMBC(U_10236,U_10235,U_10235),hAPP(hAPP(c_COMBS(U_10236,U_10235,tc_fun(U_10235,U_10235)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10235,tc_fun(U_10235,U_10235)),U_10236),c_If(U_10235)),hAPP(hAPP(c_COMBC(U_10236,U_10236,tc_HOL_Obool),c_fequal),U_10238))),U_10239)),c_Groups_Oone__class_Oone(U_10235))),U_10237) = c_Groups_Oone__class_Oone(U_10235)
    | hBOOL(hAPP(hAPP(c_member(U_10236),U_10238),U_10237))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10236),U_10237))
    | ~ class_Groups_Ocomm__monoid__mult(U_10235) ),
    inference(clausify,[status(thm)],[f_2777_2]) ).

fof(f_2778_1,plain,
    ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = c_Groups_Oone__class_Oone(T_c)
          | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = hAPP(V_b_2,V_a_2)
          | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__delta_H]) ).

fof(f_2778_2,plain,
    ! [U_10244,U_10243,U_10242,U_10241,U_10240] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10241,U_10240),hAPP(hAPP(c_COMBC(U_10241,U_10240,U_10240),hAPP(hAPP(c_COMBS(U_10241,U_10240,tc_fun(U_10240,U_10240)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10240,tc_fun(U_10240,U_10240)),U_10241),c_If(U_10240)),hAPP(c_fequal,U_10243))),U_10244)),c_Groups_Oone__class_Oone(U_10240))),U_10242) = c_Groups_Oone__class_Oone(U_10240)
          | hBOOL(hAPP(hAPP(c_member(U_10241),U_10243),U_10242)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10241,U_10240),hAPP(hAPP(c_COMBC(U_10241,U_10240,U_10240),hAPP(hAPP(c_COMBS(U_10241,U_10240,tc_fun(U_10240,U_10240)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10240,tc_fun(U_10240,U_10240)),U_10241),c_If(U_10240)),hAPP(c_fequal,U_10243))),U_10244)),c_Groups_Oone__class_Oone(U_10240))),U_10242) = hAPP(U_10244,U_10243)
          | ~ hBOOL(hAPP(hAPP(c_member(U_10241),U_10243),U_10242)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10241),U_10242))
      | ~ class_Groups_Ocomm__monoid__mult(U_10240) ),
    inference(variable_rename,[status(thm)],[f_2778_1]) ).

cnf(f_2778_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10241,U_10240),hAPP(hAPP(c_COMBC(U_10241,U_10240,U_10240),hAPP(hAPP(c_COMBS(U_10241,U_10240,tc_fun(U_10240,U_10240)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10240,tc_fun(U_10240,U_10240)),U_10241),c_If(U_10240)),hAPP(c_fequal,U_10243))),U_10244)),c_Groups_Oone__class_Oone(U_10240))),U_10242) = hAPP(U_10244,U_10243)
    | ~ hBOOL(hAPP(hAPP(c_member(U_10241),U_10243),U_10242))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10241),U_10242))
    | ~ class_Groups_Ocomm__monoid__mult(U_10240) ),
    inference(clausify,[status(thm)],[f_2778_2]) ).

cnf(f_2778_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10241,U_10240),hAPP(hAPP(c_COMBC(U_10241,U_10240,U_10240),hAPP(hAPP(c_COMBS(U_10241,U_10240,tc_fun(U_10240,U_10240)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10240,tc_fun(U_10240,U_10240)),U_10241),c_If(U_10240)),hAPP(c_fequal,U_10243))),U_10244)),c_Groups_Oone__class_Oone(U_10240))),U_10242) = c_Groups_Oone__class_Oone(U_10240)
    | hBOOL(hAPP(hAPP(c_member(U_10241),U_10243),U_10242))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10241),U_10242))
    | ~ class_Groups_Ocomm__monoid__mult(U_10240) ),
    inference(clausify,[status(thm)],[f_2778_2]) ).

fof(f_2779_1,plain,
    ! [V_A_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Set_Oinsert(T_b)),V_f_2)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_image__eq__UN]) ).

fof(f_2779_2,plain,
    ! [U_10248,U_10247,U_10246,U_10245] : hAPP(c_Set_Oimage(U_10245,U_10246,U_10247),U_10248) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10245,tc_fun(U_10246,tc_HOL_Obool)),U_10248),hAPP(hAPP(c_COMBC(U_10245,tc_fun(U_10246,tc_HOL_Obool),tc_fun(U_10246,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(U_10246,tc_fun(tc_fun(U_10246,tc_HOL_Obool),tc_fun(U_10246,tc_HOL_Obool)),U_10245),c_Set_Oinsert(U_10246)),U_10247)),c_Orderings_Obot__class_Obot(tc_fun(U_10246,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_2779_1]) ).

cnf(f_2779_3,plain,
    hAPP(c_Set_Oimage(U_10245,U_10246,U_10247),U_10248) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10245,tc_fun(U_10246,tc_HOL_Obool)),U_10248),hAPP(hAPP(c_COMBC(U_10245,tc_fun(U_10246,tc_HOL_Obool),tc_fun(U_10246,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(U_10246,tc_fun(tc_fun(U_10246,tc_HOL_Obool),tc_fun(U_10246,tc_HOL_Obool)),U_10245),c_Set_Oinsert(U_10246)),U_10247)),c_Orderings_Obot__class_Obot(tc_fun(U_10246,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_2779_2]) ).

fof(f_2780_1,plain,
    ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2))
        | V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))
        | V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_INT__simps_I4_J]) ).

fof(f_2780_2,plain,
    ! [U_10253,U_10252,U_10251,U_10250,U_10249] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10250,tc_fun(U_10251,tc_HOL_Obool)),U_10249),hAPP(hAPP(c_COMBB(tc_fun(U_10251,tc_HOL_Obool),tc_fun(U_10251,tc_HOL_Obool),U_10250),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10251,tc_HOL_Obool)),U_10252)),U_10253)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10251,tc_HOL_Obool)),U_10252),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10250,tc_fun(U_10251,tc_HOL_Obool)),U_10249),U_10253))
        | U_10249 = c_Orderings_Obot__class_Obot(tc_fun(U_10250,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10250,tc_fun(U_10251,tc_HOL_Obool)),U_10249),hAPP(hAPP(c_COMBB(tc_fun(U_10251,tc_HOL_Obool),tc_fun(U_10251,tc_HOL_Obool),U_10250),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10251,tc_HOL_Obool)),U_10252)),U_10253)) = c_Orderings_Otop__class_Otop(tc_fun(U_10251,tc_HOL_Obool))
        | U_10249 != c_Orderings_Obot__class_Obot(tc_fun(U_10250,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2780_1]) ).

fof(f_2780_3,plain,
    ( ! [U_10263,U_10261,U_10259,U_10257,U_10255] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10257,tc_fun(U_10259,tc_HOL_Obool)),U_10255),hAPP(hAPP(c_COMBB(tc_fun(U_10259,tc_HOL_Obool),tc_fun(U_10259,tc_HOL_Obool),U_10257),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10259,tc_HOL_Obool)),U_10261)),U_10263)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10259,tc_HOL_Obool)),U_10261),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10257,tc_fun(U_10259,tc_HOL_Obool)),U_10255),U_10263))
        | U_10255 = c_Orderings_Obot__class_Obot(tc_fun(U_10257,tc_HOL_Obool)) )
    & ! [U_10262,U_10260,U_10258,U_10256,U_10254] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10256,tc_fun(U_10258,tc_HOL_Obool)),U_10254),hAPP(hAPP(c_COMBB(tc_fun(U_10258,tc_HOL_Obool),tc_fun(U_10258,tc_HOL_Obool),U_10256),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10258,tc_HOL_Obool)),U_10260)),U_10262)) = c_Orderings_Otop__class_Otop(tc_fun(U_10258,tc_HOL_Obool))
        | U_10254 != c_Orderings_Obot__class_Obot(tc_fun(U_10256,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2780_2]) ).

cnf(f_2780_4,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10256,tc_fun(U_10258,tc_HOL_Obool)),U_10254),hAPP(hAPP(c_COMBB(tc_fun(U_10258,tc_HOL_Obool),tc_fun(U_10258,tc_HOL_Obool),U_10256),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10258,tc_HOL_Obool)),U_10260)),U_10262)) = c_Orderings_Otop__class_Otop(tc_fun(U_10258,tc_HOL_Obool))
    | U_10254 != c_Orderings_Obot__class_Obot(tc_fun(U_10256,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2780_3]) ).

cnf(f_2780_5,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10257,tc_fun(U_10259,tc_HOL_Obool)),U_10255),hAPP(hAPP(c_COMBB(tc_fun(U_10259,tc_HOL_Obool),tc_fun(U_10259,tc_HOL_Obool),U_10257),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10259,tc_HOL_Obool)),U_10261)),U_10263)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10259,tc_HOL_Obool)),U_10261),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10257,tc_fun(U_10259,tc_HOL_Obool)),U_10255),U_10263))
    | U_10255 = c_Orderings_Obot__class_Obot(tc_fun(U_10257,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2780_3]) ).

fof(f_2781_1,plain,
    ! [V_A_2,V_y_2,T_c,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(c_COMBK(T_b,T_c),V_y_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(c_Finite__Set_Ocard(T_c),V_A_2))),V_y_2)
      | ~ class_Rings_Osemiring__1(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__constant]) ).

fof(f_2781_2,plain,
    ! [U_10267,U_10266,U_10265,U_10264] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10265,U_10264),hAPP(c_COMBK(U_10264,U_10265),U_10266)),U_10267) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10264),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10264),hAPP(c_Finite__Set_Ocard(U_10265),U_10267))),U_10266)
      | ~ class_Rings_Osemiring__1(U_10264) ),
    inference(variable_rename,[status(thm)],[f_2781_1]) ).

cnf(f_2781_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10265,U_10264),hAPP(c_COMBK(U_10264,U_10265),U_10266)),U_10267) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10264),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10264),hAPP(c_Finite__Set_Ocard(U_10265),U_10267))),U_10266)
    | ~ class_Rings_Osemiring__1(U_10264) ),
    inference(clausify,[status(thm)],[f_2781_2]) ).

fof(f_2782_1,plain,
    ! [V_w_2,V_z_2,T_b] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(V_w_2))) = hAPP(hAPP(c_HOL_OLet(T_b,T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),c_Groups_Otimes__class_Otimes(T_b)),c_COMBI(T_b)))
      | ~ class_Int_Onumber__ring(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_power__number__of__even]) ).

fof(f_2782_2,plain,
    ! [U_10270,U_10269,U_10268] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_10268),U_10269),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_10270))) = hAPP(hAPP(c_HOL_OLet(U_10268,U_10268),hAPP(hAPP(c_Power_Opower__class_Opower(U_10268),U_10269),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10270))),hAPP(hAPP(c_COMBS(U_10268,U_10268,U_10268),c_Groups_Otimes__class_Otimes(U_10268)),c_COMBI(U_10268)))
      | ~ class_Int_Onumber__ring(U_10268) ),
    inference(variable_rename,[status(thm)],[f_2782_1]) ).

cnf(f_2782_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_10268),U_10269),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_10270))) = hAPP(hAPP(c_HOL_OLet(U_10268,U_10268),hAPP(hAPP(c_Power_Opower__class_Opower(U_10268),U_10269),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10270))),hAPP(hAPP(c_COMBS(U_10268,U_10268,U_10268),c_Groups_Otimes__class_Otimes(U_10268)),c_COMBI(U_10268)))
    | ~ class_Int_Onumber__ring(U_10268) ),
    inference(clausify,[status(thm)],[f_2782_2]) ).

fof(f_2783_1,plain,
    ! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Groups_Otimes__class_Otimes(T_c)),V_g_2)),V_h_2)),c_Groups_Oone__class_Oone(T_c)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_A_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_h_2),c_Groups_Oone__class_Oone(T_c)),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_fold__image__distrib]) ).

fof(f_2783_2,plain,
    ! [U_10275,U_10274,U_10273,U_10272,U_10271] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10271,U_10272,c_Groups_Otimes__class_Otimes(U_10271)),hAPP(hAPP(c_COMBS(U_10272,U_10271,U_10271),hAPP(hAPP(c_COMBB(U_10271,tc_fun(U_10271,U_10271),U_10272),c_Groups_Otimes__class_Otimes(U_10271)),U_10274)),U_10275)),c_Groups_Oone__class_Oone(U_10271)),U_10273) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10271),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10271,U_10272,c_Groups_Otimes__class_Otimes(U_10271)),U_10274),c_Groups_Oone__class_Oone(U_10271)),U_10273)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10271,U_10272,c_Groups_Otimes__class_Otimes(U_10271)),U_10275),c_Groups_Oone__class_Oone(U_10271)),U_10273))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10272),U_10273))
      | ~ class_Groups_Ocomm__monoid__mult(U_10271) ),
    inference(variable_rename,[status(thm)],[f_2783_1]) ).

cnf(f_2783_3,plain,
    ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10271,U_10272,c_Groups_Otimes__class_Otimes(U_10271)),hAPP(hAPP(c_COMBS(U_10272,U_10271,U_10271),hAPP(hAPP(c_COMBB(U_10271,tc_fun(U_10271,U_10271),U_10272),c_Groups_Otimes__class_Otimes(U_10271)),U_10274)),U_10275)),c_Groups_Oone__class_Oone(U_10271)),U_10273) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10271),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10271,U_10272,c_Groups_Otimes__class_Otimes(U_10271)),U_10274),c_Groups_Oone__class_Oone(U_10271)),U_10273)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_10271,U_10272,c_Groups_Otimes__class_Otimes(U_10271)),U_10275),c_Groups_Oone__class_Oone(U_10271)),U_10273))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10272),U_10273))
    | ~ class_Groups_Ocomm__monoid__mult(U_10271) ),
    inference(clausify,[status(thm)],[f_2783_2]) ).

fof(f_2784_1,plain,
    ! [T_b] :
      ( c_Orderings_Oord_Omax(T_b,hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_b))) = c_Orderings_Oord__class_Omin(T_b)
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_dual__max]) ).

fof(f_2784_2,plain,
    ! [U_10276] :
      ( c_Orderings_Oord_Omax(U_10276,hAPP(c_COMBC(U_10276,U_10276,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(U_10276))) = c_Orderings_Oord__class_Omin(U_10276)
      | ~ class_Orderings_Olinorder(U_10276) ),
    inference(variable_rename,[status(thm)],[f_2784_1]) ).

cnf(f_2784_3,plain,
    ( c_Orderings_Oord_Omax(U_10276,hAPP(c_COMBC(U_10276,U_10276,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(U_10276))) = c_Orderings_Oord__class_Omin(U_10276)
    | ~ class_Orderings_Olinorder(U_10276) ),
    inference(clausify,[status(thm)],[f_2784_2]) ).

fof(f_2785_1,plain,
    ! [T_b] :
      ( c_Orderings_Oord_Omin(T_b,hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_b))) = c_Orderings_Oord__class_Omax(T_b)
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_dual__min]) ).

fof(f_2785_2,plain,
    ! [U_10277] :
      ( c_Orderings_Oord_Omin(U_10277,hAPP(c_COMBC(U_10277,U_10277,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(U_10277))) = c_Orderings_Oord__class_Omax(U_10277)
      | ~ class_Orderings_Olinorder(U_10277) ),
    inference(variable_rename,[status(thm)],[f_2785_1]) ).

cnf(f_2785_3,plain,
    ( c_Orderings_Oord_Omin(U_10277,hAPP(c_COMBC(U_10277,U_10277,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(U_10277))) = c_Orderings_Oord__class_Omax(U_10277)
    | ~ class_Orderings_Olinorder(U_10277) ),
    inference(clausify,[status(thm)],[f_2785_2]) ).

fof(f_2786_1,plain,
    ! [V_y_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(c_COMBK(T_c,T_b),V_y_2)),V_A_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_y_2),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__constant]) ).

fof(f_2786_2,plain,
    ! [U_10281,U_10280,U_10279,U_10278] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10279,U_10278),hAPP(c_COMBK(U_10278,U_10279),U_10281)),U_10280) = hAPP(hAPP(c_Power_Opower__class_Opower(U_10278),U_10281),hAPP(c_Finite__Set_Ocard(U_10279),U_10280))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10279),U_10280))
      | ~ class_Groups_Ocomm__monoid__mult(U_10278) ),
    inference(variable_rename,[status(thm)],[f_2786_1]) ).

cnf(f_2786_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10279,U_10278),hAPP(c_COMBK(U_10278,U_10279),U_10281)),U_10280) = hAPP(hAPP(c_Power_Opower__class_Opower(U_10278),U_10281),hAPP(c_Finite__Set_Ocard(U_10279),U_10280))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10279),U_10280))
    | ~ class_Groups_Ocomm__monoid__mult(U_10278) ),
    inference(clausify,[status(thm)],[f_2786_2]) ).

fof(f_2787_1,plain,
    ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),V_f_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Lattices_Osemilattice__sup__class_Osup(T_c)),V_f_2)),V_B_2),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_sup__SUPR__fold__sup]) ).

fof(f_2787_2,plain,
    ! [U_10286,U_10285,U_10284,U_10283,U_10282] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10282),U_10285),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10283,U_10282),U_10284),U_10286)) = hAPP(hAPP(c_Finite__Set_Ofold(U_10283,U_10282,hAPP(hAPP(c_COMBB(U_10282,tc_fun(U_10282,U_10282),U_10283),c_Lattices_Osemilattice__sup__class_Osup(U_10282)),U_10286)),U_10285),U_10284)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10283),U_10284))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_10282) ),
    inference(variable_rename,[status(thm)],[f_2787_1]) ).

cnf(f_2787_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10282),U_10285),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10283,U_10282),U_10284),U_10286)) = hAPP(hAPP(c_Finite__Set_Ofold(U_10283,U_10282,hAPP(hAPP(c_COMBB(U_10282,tc_fun(U_10282,U_10282),U_10283),c_Lattices_Osemilattice__sup__class_Osup(U_10282)),U_10286)),U_10285),U_10284)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10283),U_10284))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_10282) ),
    inference(clausify,[status(thm)],[f_2787_2]) ).

fof(f_2788_1,plain,
    ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),V_f_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Lattices_Osemilattice__inf__class_Oinf(T_c)),V_f_2)),V_B_2),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_inf__INFI__fold__inf]) ).

fof(f_2788_2,plain,
    ! [U_10291,U_10290,U_10289,U_10288,U_10287] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10287),U_10290),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10288,U_10287),U_10289),U_10291)) = hAPP(hAPP(c_Finite__Set_Ofold(U_10288,U_10287,hAPP(hAPP(c_COMBB(U_10287,tc_fun(U_10287,U_10287),U_10288),c_Lattices_Osemilattice__inf__class_Oinf(U_10287)),U_10291)),U_10290),U_10289)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10288),U_10289))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_10287) ),
    inference(variable_rename,[status(thm)],[f_2788_1]) ).

cnf(f_2788_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10287),U_10290),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10288,U_10287),U_10289),U_10291)) = hAPP(hAPP(c_Finite__Set_Ofold(U_10288,U_10287,hAPP(hAPP(c_COMBB(U_10287,tc_fun(U_10287,U_10287),U_10288),c_Lattices_Osemilattice__inf__class_Oinf(U_10287)),U_10291)),U_10290),U_10289)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10288),U_10289))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_10287) ),
    inference(clausify,[status(thm)],[f_2788_2]) ).

fof(f_2789_1,plain,
    ! [V_w_2,V_z_2] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(V_w_2))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_COMBI(tc_Int_Oint))),
    inference(fof_nnf,[status(thm)],[fact_zpower__number__of__even]) ).

fof(f_2789_2,plain,
    ! [U_10293,U_10292] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_10292),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_10293))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_10292),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10293))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_COMBI(tc_Int_Oint))),
    inference(variable_rename,[status(thm)],[f_2789_1]) ).

cnf(f_2789_3,plain,
    hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_10292),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_10293))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_10292),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10293))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),c_COMBI(tc_Int_Oint))),
    inference(clausify,[status(thm)],[f_2789_2]) ).

fof(f_2790_1,plain,
    ! [V_g_2,T_d,V_f_2,T_b,T_c] :
      ( hAPP(c_Set_Oimage(T_c,T_d,hAPP(c_Fun_Ocomp(T_b,T_d,T_c,V_g_2),V_f_2)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))
      | hAPP(c_Set_Oimage(T_b,T_d,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))
      | hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ),
    inference(fof_nnf,[status(thm)],[fact_comp__surj]) ).

fof(f_2790_2,plain,
    ! [U_10298,U_10297,U_10296,U_10295,U_10294] :
      ( hAPP(c_Set_Oimage(U_10294,U_10297,hAPP(c_Fun_Ocomp(U_10295,U_10297,U_10294,U_10298),U_10296)),c_Orderings_Otop__class_Otop(tc_fun(U_10294,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_10297,tc_HOL_Obool))
      | hAPP(c_Set_Oimage(U_10295,U_10297,U_10298),c_Orderings_Otop__class_Otop(tc_fun(U_10295,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_10297,tc_HOL_Obool))
      | hAPP(c_Set_Oimage(U_10294,U_10295,U_10296),c_Orderings_Otop__class_Otop(tc_fun(U_10294,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_10295,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_2790_1]) ).

cnf(f_2790_3,plain,
    ( hAPP(c_Set_Oimage(U_10294,U_10297,hAPP(c_Fun_Ocomp(U_10295,U_10297,U_10294,U_10298),U_10296)),c_Orderings_Otop__class_Otop(tc_fun(U_10294,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_10297,tc_HOL_Obool))
    | hAPP(c_Set_Oimage(U_10295,U_10297,U_10298),c_Orderings_Otop__class_Otop(tc_fun(U_10295,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_10297,tc_HOL_Obool))
    | hAPP(c_Set_Oimage(U_10294,U_10295,U_10296),c_Orderings_Otop__class_Otop(tc_fun(U_10294,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_10295,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2790_2]) ).

fof(f_2791_1,plain,
    ! [V_n_2,V_f_2,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))),hAPP(V_f_2,V_n_2))
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__lessThan__Suc]) ).

fof(f_2791_2,plain,
    ! [U_10301,U_10300,U_10299] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10299),U_10300),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10301))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10299),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10299),U_10300),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_10301))),hAPP(U_10300,U_10301))
      | ~ class_Groups_Ocomm__monoid__add(U_10299) ),
    inference(variable_rename,[status(thm)],[f_2791_1]) ).

cnf(f_2791_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10299),U_10300),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10301))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10299),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10299),U_10300),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_10301))),hAPP(U_10300,U_10301))
    | ~ class_Groups_Ocomm__monoid__add(U_10299) ),
    inference(clausify,[status(thm)],[f_2791_2]) ).

fof(f_2792_1,plain,
    ! [V_f_2,V_g_2,T_d,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Fun_Ocomp(T_d,tc_fun(T_b,tc_HOL_Obool),T_c,V_g_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),V_g_2),
    inference(fof_nnf,[status(thm)],[fact_UN__o]) ).

fof(f_2792_2,plain,
    ! [U_10307,U_10306,U_10305,U_10304,U_10303,U_10302] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10302,tc_fun(U_10303,tc_HOL_Obool)),U_10304),hAPP(c_Fun_Ocomp(U_10305,tc_fun(U_10303,tc_HOL_Obool),U_10302,U_10306),U_10307)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10305,tc_fun(U_10303,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_10302,U_10305,U_10307),U_10304)),U_10306),
    inference(variable_rename,[status(thm)],[f_2792_1]) ).

cnf(f_2792_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10302,tc_fun(U_10303,tc_HOL_Obool)),U_10304),hAPP(c_Fun_Ocomp(U_10305,tc_fun(U_10303,tc_HOL_Obool),U_10302,U_10306),U_10307)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10305,tc_fun(U_10303,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_10302,U_10305,U_10307),U_10304)),U_10306),
    inference(clausify,[status(thm)],[f_2792_2]) ).

fof(f_2793_1,plain,
    ! [V_g_2,T_d,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_d,T_c,hAPP(c_Fun_Ocomp(T_b,T_c,T_d,V_f_2),V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)))
      | ~ c_Fun_Oinj__on(T_d,T_b,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)))
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_inj__comp]) ).

fof(f_2793_2,plain,
    ! [U_10312,U_10311,U_10310,U_10309,U_10308] :
      ( c_Fun_Oinj__on(U_10311,U_10309,hAPP(c_Fun_Ocomp(U_10308,U_10309,U_10311,U_10310),U_10312),c_Orderings_Otop__class_Otop(tc_fun(U_10311,tc_HOL_Obool)))
      | ~ c_Fun_Oinj__on(U_10311,U_10308,U_10312,c_Orderings_Otop__class_Otop(tc_fun(U_10311,tc_HOL_Obool)))
      | ~ c_Fun_Oinj__on(U_10308,U_10309,U_10310,c_Orderings_Otop__class_Otop(tc_fun(U_10308,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_2793_1]) ).

cnf(f_2793_3,plain,
    ( c_Fun_Oinj__on(U_10311,U_10309,hAPP(c_Fun_Ocomp(U_10308,U_10309,U_10311,U_10310),U_10312),c_Orderings_Otop__class_Otop(tc_fun(U_10311,tc_HOL_Obool)))
    | ~ c_Fun_Oinj__on(U_10311,U_10308,U_10312,c_Orderings_Otop__class_Otop(tc_fun(U_10311,tc_HOL_Obool)))
    | ~ c_Fun_Oinj__on(U_10308,U_10309,U_10310,c_Orderings_Otop__class_Otop(tc_fun(U_10308,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_2793_2]) ).

fof(f_2794_1,plain,
    ! [V_f_H_2,T_d,V_A_2,V_f_2,T_c,T_b] :
      ( ( ( c_Fun_Oinj__on(T_c,T_d,V_f_H_2,hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))
          | ~ c_Fun_Oinj__on(T_b,T_d,hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_f_H_2),V_f_2),V_A_2) )
        & ( c_Fun_Oinj__on(T_b,T_d,hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_f_H_2),V_f_2),V_A_2)
          | ~ c_Fun_Oinj__on(T_c,T_d,V_f_H_2,hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) ) )
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_comp__inj__on__iff]) ).

fof(f_2794_2,plain,
    ! [U_10318,U_10317,U_10316,U_10315,U_10314,U_10313] :
      ( ( ( c_Fun_Oinj__on(U_10314,U_10317,U_10318,hAPP(c_Set_Oimage(U_10313,U_10314,U_10315),U_10316))
          | ~ c_Fun_Oinj__on(U_10313,U_10317,hAPP(c_Fun_Ocomp(U_10314,U_10317,U_10313,U_10318),U_10315),U_10316) )
        & ( c_Fun_Oinj__on(U_10313,U_10317,hAPP(c_Fun_Ocomp(U_10314,U_10317,U_10313,U_10318),U_10315),U_10316)
          | ~ c_Fun_Oinj__on(U_10314,U_10317,U_10318,hAPP(c_Set_Oimage(U_10313,U_10314,U_10315),U_10316)) ) )
      | ~ c_Fun_Oinj__on(U_10313,U_10314,U_10315,U_10316) ),
    inference(variable_rename,[status(thm)],[f_2794_1]) ).

cnf(f_2794_3,plain,
    ( c_Fun_Oinj__on(U_10313,U_10317,hAPP(c_Fun_Ocomp(U_10314,U_10317,U_10313,U_10318),U_10315),U_10316)
    | ~ c_Fun_Oinj__on(U_10314,U_10317,U_10318,hAPP(c_Set_Oimage(U_10313,U_10314,U_10315),U_10316))
    | ~ c_Fun_Oinj__on(U_10313,U_10314,U_10315,U_10316) ),
    inference(clausify,[status(thm)],[f_2794_2]) ).

cnf(f_2794_4,plain,
    ( c_Fun_Oinj__on(U_10314,U_10317,U_10318,hAPP(c_Set_Oimage(U_10313,U_10314,U_10315),U_10316))
    | ~ c_Fun_Oinj__on(U_10313,U_10317,hAPP(c_Fun_Ocomp(U_10314,U_10317,U_10313,U_10318),U_10315),U_10316)
    | ~ c_Fun_Oinj__on(U_10313,U_10314,U_10315,U_10316) ),
    inference(clausify,[status(thm)],[f_2794_2]) ).

fof(f_2795_1,plain,
    ! [V_g_2,T_d,V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_d,hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_g_2),V_f_2),V_A_2)
      | ~ c_Fun_Oinj__on(T_c,T_d,V_g_2,hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_comp__inj__on]) ).

fof(f_2795_2,plain,
    ! [U_10324,U_10323,U_10322,U_10321,U_10320,U_10319] :
      ( c_Fun_Oinj__on(U_10319,U_10323,hAPP(c_Fun_Ocomp(U_10320,U_10323,U_10319,U_10324),U_10321),U_10322)
      | ~ c_Fun_Oinj__on(U_10320,U_10323,U_10324,hAPP(c_Set_Oimage(U_10319,U_10320,U_10321),U_10322))
      | ~ c_Fun_Oinj__on(U_10319,U_10320,U_10321,U_10322) ),
    inference(variable_rename,[status(thm)],[f_2795_1]) ).

cnf(f_2795_3,plain,
    ( c_Fun_Oinj__on(U_10319,U_10323,hAPP(c_Fun_Ocomp(U_10320,U_10323,U_10319,U_10324),U_10321),U_10322)
    | ~ c_Fun_Oinj__on(U_10320,U_10323,U_10324,hAPP(c_Set_Oimage(U_10319,U_10320,U_10321),U_10322))
    | ~ c_Fun_Oinj__on(U_10319,U_10320,U_10321,U_10322) ),
    inference(clausify,[status(thm)],[f_2795_2]) ).

fof(f_2796_1,plain,
    ! [V_A_2,V_f_2,V_g_2,T_d,T_c,T_b] :
      ( c_Fun_Oinj__on(T_d,T_c,V_g_2,hAPP(c_Set_Oimage(T_b,T_d,V_f_2),V_A_2))
      | ~ c_Fun_Oinj__on(T_b,T_c,hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_g_2),V_f_2),V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_inj__on__imageI]) ).

fof(f_2796_2,plain,
    ! [U_10330,U_10329,U_10328,U_10327,U_10326,U_10325] :
      ( c_Fun_Oinj__on(U_10327,U_10326,U_10328,hAPP(c_Set_Oimage(U_10325,U_10327,U_10329),U_10330))
      | ~ c_Fun_Oinj__on(U_10325,U_10326,hAPP(c_Fun_Ocomp(U_10327,U_10326,U_10325,U_10328),U_10329),U_10330) ),
    inference(variable_rename,[status(thm)],[f_2796_1]) ).

cnf(f_2796_3,plain,
    ( c_Fun_Oinj__on(U_10327,U_10326,U_10328,hAPP(c_Set_Oimage(U_10325,U_10327,U_10329),U_10330))
    | ~ c_Fun_Oinj__on(U_10325,U_10326,hAPP(c_Fun_Ocomp(U_10327,U_10326,U_10325,U_10328),U_10329),U_10330) ),
    inference(clausify,[status(thm)],[f_2796_2]) ).

fof(f_2797_1,plain,
    ! [V_n_2,V_f_2,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2))),hAPP(V_f_2,hAPP(c_Nat_OSuc,V_n_2)))
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__atMost__Suc]) ).

fof(f_2797_2,plain,
    ! [U_10333,U_10332,U_10331] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10331),U_10332),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10333))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10331),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10331),U_10332),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_10333))),hAPP(U_10332,hAPP(c_Nat_OSuc,U_10333)))
      | ~ class_Groups_Ocomm__monoid__add(U_10331) ),
    inference(variable_rename,[status(thm)],[f_2797_1]) ).

cnf(f_2797_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10331),U_10332),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10333))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10331),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10331),U_10332),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_10333))),hAPP(U_10332,hAPP(c_Nat_OSuc,U_10333)))
    | ~ class_Groups_Ocomm__monoid__add(U_10331) ),
    inference(clausify,[status(thm)],[f_2797_2]) ).

fof(f_2798_1,plain,
    ! [V_A_2,V_f_2,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),V_f_2),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_b)
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__sum__prod_I1_J]) ).

fof(f_2798_2,plain,
    ! [U_10336,U_10335,U_10334] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10334),U_10335),U_10336) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_10334),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10334,tc_Int_Oint),U_10335),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10336))
      | ~ class_Groups_Ocomm__monoid__mult(U_10334)
      | ~ class_Groups_Ocomm__monoid__add(U_10334) ),
    inference(variable_rename,[status(thm)],[f_2798_1]) ).

cnf(f_2798_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10334),U_10335),U_10336) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_10334),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10334,tc_Int_Oint),U_10335),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10336))
    | ~ class_Groups_Ocomm__monoid__mult(U_10334)
    | ~ class_Groups_Ocomm__monoid__add(U_10334) ),
    inference(clausify,[status(thm)],[f_2798_2]) ).

fof(f_2799_1,plain,
    ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_A_2),V_C_2))),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_C_2))),
    inference(fof_nnf,[status(thm)],[fact_Un__Union__image]) ).

fof(f_2799_2,plain,
    ! [U_10341,U_10340,U_10339,U_10338,U_10337] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10337,tc_fun(U_10338,tc_HOL_Obool)),U_10339),hAPP(hAPP(c_COMBS(U_10337,tc_fun(U_10338,tc_HOL_Obool),tc_fun(U_10338,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10338,tc_HOL_Obool),tc_fun(tc_fun(U_10338,tc_HOL_Obool),tc_fun(U_10338,tc_HOL_Obool)),U_10337),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10338,tc_HOL_Obool))),U_10340)),U_10341)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10338,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_10338,tc_HOL_Obool),hAPP(c_Set_Oimage(U_10337,tc_fun(U_10338,tc_HOL_Obool),U_10340),U_10339))),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_10338,tc_HOL_Obool),hAPP(c_Set_Oimage(U_10337,tc_fun(U_10338,tc_HOL_Obool),U_10341),U_10339))),
    inference(variable_rename,[status(thm)],[f_2799_1]) ).

cnf(f_2799_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10337,tc_fun(U_10338,tc_HOL_Obool)),U_10339),hAPP(hAPP(c_COMBS(U_10337,tc_fun(U_10338,tc_HOL_Obool),tc_fun(U_10338,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10338,tc_HOL_Obool),tc_fun(tc_fun(U_10338,tc_HOL_Obool),tc_fun(U_10338,tc_HOL_Obool)),U_10337),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10338,tc_HOL_Obool))),U_10340)),U_10341)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10338,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_10338,tc_HOL_Obool),hAPP(c_Set_Oimage(U_10337,tc_fun(U_10338,tc_HOL_Obool),U_10340),U_10339))),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_10338,tc_HOL_Obool),hAPP(c_Set_Oimage(U_10337,tc_fun(U_10338,tc_HOL_Obool),U_10341),U_10339))),
    inference(clausify,[status(thm)],[f_2799_2]) ).

fof(f_2800_1,plain,
    ! [V_u_2,V_l_2] : hAPP(c_Set_Oimage(tc_Int_Oint,tc_Int_Oint,hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),V_l_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_u_2),V_l_2))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_l_2),V_u_2),
    inference(fof_nnf,[status(thm)],[fact_image__add__int__atLeastLessThan]) ).

fof(f_2800_2,plain,
    ! [U_10343,U_10342] : hAPP(c_Set_Oimage(tc_Int_Oint,tc_Int_Oint,hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),U_10342)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_10343),U_10342))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_10342),U_10343),
    inference(variable_rename,[status(thm)],[f_2800_1]) ).

cnf(f_2800_3,plain,
    hAPP(c_Set_Oimage(tc_Int_Oint,tc_Int_Oint,hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),U_10342)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_10343),U_10342))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_10342),U_10343),
    inference(clausify,[status(thm)],[f_2800_2]) ).

fof(f_2801_1,plain,
    ! [V_f_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_b,tc_Nat_Onat),V_f_2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2))
      | ~ c_Nat__Transfer_Onat__set(V_A_2)
      | ~ class_Groups_Ocomm__monoid__mult(T_b)
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__sum__prod_I2_J]) ).

fof(f_2801_2,plain,
    ! [U_10346,U_10345,U_10344] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_10344),U_10346),U_10345) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,U_10344),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_10344,tc_Nat_Onat),U_10346),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_10345))
      | ~ c_Nat__Transfer_Onat__set(U_10345)
      | ~ class_Groups_Ocomm__monoid__mult(U_10344)
      | ~ class_Groups_Ocomm__monoid__add(U_10344) ),
    inference(variable_rename,[status(thm)],[f_2801_1]) ).

cnf(f_2801_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_10344),U_10346),U_10345) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,U_10344),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_10344,tc_Nat_Onat),U_10346),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_10345))
    | ~ c_Nat__Transfer_Onat__set(U_10345)
    | ~ class_Groups_Ocomm__monoid__mult(U_10344)
    | ~ class_Groups_Ocomm__monoid__add(U_10344) ),
    inference(clausify,[status(thm)],[f_2801_2]) ).

fof(f_2802_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( ( hBOOL(hAPP(c_Predicate_OPowp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)),V_x_2))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),hAPP(c_Set_OPow(T_b),V_A_2))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),hAPP(c_Set_OPow(T_b),V_A_2)))
        | ~ hBOOL(hAPP(c_Predicate_OPowp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)),V_x_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Powp__Pow__eq]) ).

fof(f_2802_2,plain,
    ! [U_10349,U_10348,U_10347] :
      ( ( hBOOL(hAPP(c_Predicate_OPowp(U_10347,hAPP(hAPP(c_COMBC(U_10347,tc_fun(U_10347,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10347)),U_10348)),U_10349))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10347,tc_HOL_Obool)),U_10349),hAPP(c_Set_OPow(U_10347),U_10348))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_10347,tc_HOL_Obool)),U_10349),hAPP(c_Set_OPow(U_10347),U_10348)))
        | ~ hBOOL(hAPP(c_Predicate_OPowp(U_10347,hAPP(hAPP(c_COMBC(U_10347,tc_fun(U_10347,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10347)),U_10348)),U_10349)) ) ),
    inference(variable_rename,[status(thm)],[f_2802_1]) ).

fof(f_2802_3,plain,
    ( ! [U_10355,U_10353,U_10351] :
        ( hBOOL(hAPP(c_Predicate_OPowp(U_10351,hAPP(hAPP(c_COMBC(U_10351,tc_fun(U_10351,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10351)),U_10353)),U_10355))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10351,tc_HOL_Obool)),U_10355),hAPP(c_Set_OPow(U_10351),U_10353))) )
    & ! [U_10354,U_10352,U_10350] :
        ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_10350,tc_HOL_Obool)),U_10354),hAPP(c_Set_OPow(U_10350),U_10352)))
        | ~ hBOOL(hAPP(c_Predicate_OPowp(U_10350,hAPP(hAPP(c_COMBC(U_10350,tc_fun(U_10350,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10350)),U_10352)),U_10354)) ) ),
    inference(miniscope,[status(thm)],[f_2802_2]) ).

cnf(f_2802_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_10350,tc_HOL_Obool)),U_10354),hAPP(c_Set_OPow(U_10350),U_10352)))
    | ~ hBOOL(hAPP(c_Predicate_OPowp(U_10350,hAPP(hAPP(c_COMBC(U_10350,tc_fun(U_10350,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10350)),U_10352)),U_10354)) ),
    inference(clausify,[status(thm)],[f_2802_3]) ).

cnf(f_2802_5,plain,
    ( hBOOL(hAPP(c_Predicate_OPowp(U_10351,hAPP(hAPP(c_COMBC(U_10351,tc_fun(U_10351,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10351)),U_10353)),U_10355))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10351,tc_HOL_Obool)),U_10355),hAPP(c_Set_OPow(U_10351),U_10353))) ),
    inference(clausify,[status(thm)],[f_2802_3]) ).

fof(f_2803_1,plain,
    ! [V_B_2,V_f_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_f_2)),c_Groups_Ozero__class_Ozero(T_c))),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Ocomm__monoid__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__restrict__set]) ).

fof(f_2803_2,plain,
    ! [U_10360,U_10359,U_10358,U_10357,U_10356] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10357,U_10356),U_10359),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10357,tc_HOL_Obool)),U_10358),U_10360)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10357,U_10356),hAPP(hAPP(c_COMBC(U_10357,U_10356,U_10356),hAPP(hAPP(c_COMBS(U_10357,U_10356,tc_fun(U_10356,U_10356)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10356,tc_fun(U_10356,U_10356)),U_10357),c_If(U_10356)),hAPP(hAPP(c_COMBC(U_10357,tc_fun(U_10357,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10357)),U_10360))),U_10359)),c_Groups_Ozero__class_Ozero(U_10356))),U_10358)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10357),U_10358))
      | ~ class_Groups_Ocomm__monoid__add(U_10356) ),
    inference(variable_rename,[status(thm)],[f_2803_1]) ).

cnf(f_2803_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10357,U_10356),U_10359),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10357,tc_HOL_Obool)),U_10358),U_10360)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10357,U_10356),hAPP(hAPP(c_COMBC(U_10357,U_10356,U_10356),hAPP(hAPP(c_COMBS(U_10357,U_10356,tc_fun(U_10356,U_10356)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10356,tc_fun(U_10356,U_10356)),U_10357),c_If(U_10356)),hAPP(hAPP(c_COMBC(U_10357,tc_fun(U_10357,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10357)),U_10360))),U_10359)),c_Groups_Ozero__class_Ozero(U_10356))),U_10358)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10357),U_10358))
    | ~ class_Groups_Ocomm__monoid__add(U_10356) ),
    inference(clausify,[status(thm)],[f_2803_2]) ).

fof(f_2804_1,plain,
    ! [V_f_2,T_c,V_A_2,T_b] :
      ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(T_c,tc_HOL_Obool),T_b,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(T_c,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Set_Oinsert(T_c)),V_f_2)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_image__eq__fold__image]) ).

fof(f_2804_2,plain,
    ! [U_10364,U_10363,U_10362,U_10361] :
      ( hAPP(c_Set_Oimage(U_10361,U_10363,U_10364),U_10362) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(U_10363,tc_HOL_Obool),U_10361,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10363,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_10361,tc_fun(U_10363,tc_HOL_Obool),tc_fun(U_10363,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(U_10363,tc_fun(tc_fun(U_10363,tc_HOL_Obool),tc_fun(U_10363,tc_HOL_Obool)),U_10361),c_Set_Oinsert(U_10363)),U_10364)),c_Orderings_Obot__class_Obot(tc_fun(U_10363,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(U_10363,tc_HOL_Obool))),U_10362)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10361),U_10362)) ),
    inference(variable_rename,[status(thm)],[f_2804_1]) ).

cnf(f_2804_3,plain,
    ( hAPP(c_Set_Oimage(U_10361,U_10363,U_10364),U_10362) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(U_10363,tc_HOL_Obool),U_10361,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10363,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_10361,tc_fun(U_10363,tc_HOL_Obool),tc_fun(U_10363,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(U_10363,tc_fun(tc_fun(U_10363,tc_HOL_Obool),tc_fun(U_10363,tc_HOL_Obool)),U_10361),c_Set_Oinsert(U_10363)),U_10364)),c_Orderings_Obot__class_Obot(tc_fun(U_10363,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(U_10363,tc_HOL_Obool))),U_10362)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10361),U_10362)) ),
    inference(clausify,[status(thm)],[f_2804_2]) ).

fof(f_2805_1,plain,
    ! [V_w_2,V_v_2,T_b] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(V_w_2))) = hAPP(hAPP(c_HOL_OLet(T_b,T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),c_Groups_Otimes__class_Otimes(T_b)),c_COMBI(T_b)))
      | ~ class_Int_Onumber__ring(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_power__number__of__even__number__of]) ).

fof(f_2805_2,plain,
    ! [U_10367,U_10366,U_10365] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_10365),hAPP(c_Int_Onumber__class_Onumber__of(U_10365),U_10366)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_10367))) = hAPP(hAPP(c_HOL_OLet(U_10365,U_10365),hAPP(hAPP(c_Power_Opower__class_Opower(U_10365),hAPP(c_Int_Onumber__class_Onumber__of(U_10365),U_10366)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10367))),hAPP(hAPP(c_COMBS(U_10365,U_10365,U_10365),c_Groups_Otimes__class_Otimes(U_10365)),c_COMBI(U_10365)))
      | ~ class_Int_Onumber__ring(U_10365) ),
    inference(variable_rename,[status(thm)],[f_2805_1]) ).

cnf(f_2805_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_10365),hAPP(c_Int_Onumber__class_Onumber__of(U_10365),U_10366)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_10367))) = hAPP(hAPP(c_HOL_OLet(U_10365,U_10365),hAPP(hAPP(c_Power_Opower__class_Opower(U_10365),hAPP(c_Int_Onumber__class_Onumber__of(U_10365),U_10366)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10367))),hAPP(hAPP(c_COMBS(U_10365,U_10365,U_10365),c_Groups_Otimes__class_Otimes(U_10365)),c_COMBI(U_10365)))
    | ~ class_Int_Onumber__ring(U_10365) ),
    inference(clausify,[status(thm)],[f_2805_2]) ).

fof(f_2806_1,plain,
    ! [V_f_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),V_f_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Lattices_Osemilattice__sup__class_Osup(T_c)),V_f_2)),c_Orderings_Obot__class_Obot(T_c)),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_SUPR__fold__sup]) ).

fof(f_2806_2,plain,
    ! [U_10371,U_10370,U_10369,U_10368] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10369,U_10368),U_10370),U_10371) = hAPP(hAPP(c_Finite__Set_Ofold(U_10369,U_10368,hAPP(hAPP(c_COMBB(U_10368,tc_fun(U_10368,U_10368),U_10369),c_Lattices_Osemilattice__sup__class_Osup(U_10368)),U_10371)),c_Orderings_Obot__class_Obot(U_10368)),U_10370)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10369),U_10370))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_10368) ),
    inference(variable_rename,[status(thm)],[f_2806_1]) ).

cnf(f_2806_3,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10369,U_10368),U_10370),U_10371) = hAPP(hAPP(c_Finite__Set_Ofold(U_10369,U_10368,hAPP(hAPP(c_COMBB(U_10368,tc_fun(U_10368,U_10368),U_10369),c_Lattices_Osemilattice__sup__class_Osup(U_10368)),U_10371)),c_Orderings_Obot__class_Obot(U_10368)),U_10370)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10369),U_10370))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_10368) ),
    inference(clausify,[status(thm)],[f_2806_2]) ).

fof(f_2807_1,plain,
    ! [V_A_2,T_b] :
      ( ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) )
      & ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,T_b,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,T_b),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_card__def]) ).

fof(f_2807_2,plain,
    ! [U_10373,U_10372] :
      ( ( hAPP(c_Finite__Set_Ocard(U_10372),U_10373) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(c_Finite__Set_Ofinite(U_10372),U_10373)) )
      & ( hAPP(c_Finite__Set_Ocard(U_10372),U_10373) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,U_10372,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,U_10372),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10373)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10372),U_10373)) ) ),
    inference(variable_rename,[status(thm)],[f_2807_1]) ).

fof(f_2807_3,plain,
    ( ! [U_10377,U_10375] :
        ( hAPP(c_Finite__Set_Ocard(U_10375),U_10377) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(c_Finite__Set_Ofinite(U_10375),U_10377)) )
    & ! [U_10376,U_10374] :
        ( hAPP(c_Finite__Set_Ocard(U_10374),U_10376) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,U_10374,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,U_10374),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10376)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10374),U_10376)) ) ),
    inference(miniscope,[status(thm)],[f_2807_2]) ).

cnf(f_2807_4,plain,
    ( hAPP(c_Finite__Set_Ocard(U_10374),U_10376) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,U_10374,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,U_10374),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10376)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10374),U_10376)) ),
    inference(clausify,[status(thm)],[f_2807_3]) ).

cnf(f_2807_5,plain,
    ( hAPP(c_Finite__Set_Ocard(U_10375),U_10377) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_10375),U_10377)) ),
    inference(clausify,[status(thm)],[f_2807_3]) ).

fof(f_2808_1,plain,
    ! [V_A_2,T_b] :
      ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,T_b,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,T_b),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card_Oeq__fold__g]) ).

fof(f_2808_2,plain,
    ! [U_10379,U_10378] :
      ( hAPP(c_Finite__Set_Ocard(U_10378),U_10379) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,U_10378,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,U_10378),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10379)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10378),U_10379)) ),
    inference(variable_rename,[status(thm)],[f_2808_1]) ).

cnf(f_2808_3,plain,
    ( hAPP(c_Finite__Set_Ocard(U_10378),U_10379) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,U_10378,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,U_10378),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10379)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10378),U_10379)) ),
    inference(clausify,[status(thm)],[f_2808_2]) ).

fof(f_2809_1,plain,
    ! [T_b] : c_Finite__Set_Ofun__left__comm__idem(T_b,tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem__remove]) ).

fof(f_2809_2,plain,
    ! [U_10380] : c_Finite__Set_Ofun__left__comm__idem(U_10380,tc_fun(U_10380,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_10380,tc_HOL_Obool),tc_fun(tc_fun(U_10380,tc_HOL_Obool),tc_fun(U_10380,tc_HOL_Obool)),U_10380),hAPP(c_COMBC(tc_fun(U_10380,tc_HOL_Obool),tc_fun(U_10380,tc_HOL_Obool),tc_fun(U_10380,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(U_10380,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(U_10380,tc_fun(U_10380,tc_HOL_Obool),tc_fun(U_10380,tc_HOL_Obool)),c_Set_Oinsert(U_10380)),c_Orderings_Obot__class_Obot(tc_fun(U_10380,tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_2809_1]) ).

cnf(f_2809_3,plain,
    c_Finite__Set_Ofun__left__comm__idem(U_10380,tc_fun(U_10380,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_10380,tc_HOL_Obool),tc_fun(tc_fun(U_10380,tc_HOL_Obool),tc_fun(U_10380,tc_HOL_Obool)),U_10380),hAPP(c_COMBC(tc_fun(U_10380,tc_HOL_Obool),tc_fun(U_10380,tc_HOL_Obool),tc_fun(U_10380,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(U_10380,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(U_10380,tc_fun(U_10380,tc_HOL_Obool),tc_fun(U_10380,tc_HOL_Obool)),c_Set_Oinsert(U_10380)),c_Orderings_Obot__class_Obot(tc_fun(U_10380,tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_2809_2]) ).

fof(f_2810_1,plain,
    ! [V_f_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),V_f_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Lattices_Osemilattice__inf__class_Oinf(T_c)),V_f_2)),c_Orderings_Otop__class_Otop(T_c)),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_INFI__fold__inf]) ).

fof(f_2810_2,plain,
    ! [U_10384,U_10383,U_10382,U_10381] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10382,U_10381),U_10383),U_10384) = hAPP(hAPP(c_Finite__Set_Ofold(U_10382,U_10381,hAPP(hAPP(c_COMBB(U_10381,tc_fun(U_10381,U_10381),U_10382),c_Lattices_Osemilattice__inf__class_Oinf(U_10381)),U_10384)),c_Orderings_Otop__class_Otop(U_10381)),U_10383)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10382),U_10383))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_10381) ),
    inference(variable_rename,[status(thm)],[f_2810_1]) ).

cnf(f_2810_3,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10382,U_10381),U_10383),U_10384) = hAPP(hAPP(c_Finite__Set_Ofold(U_10382,U_10381,hAPP(hAPP(c_COMBB(U_10381,tc_fun(U_10381,U_10381),U_10382),c_Lattices_Osemilattice__inf__class_Oinf(U_10381)),U_10384)),c_Orderings_Otop__class_Otop(U_10381)),U_10383)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10382),U_10383))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_10381) ),
    inference(clausify,[status(thm)],[f_2810_2]) ).

fof(f_2811_1,plain,
    ! [V_z_2,V_z_H_2] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,V_z_2)),hAPP(c_Int_Onat,V_z_H_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z_2),V_z_H_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2)) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,V_z_2)),hAPP(c_Int_Onat,V_z_H_2)) = hAPP(c_Int_Onat,V_z_2)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_diff__nat__eq__if]) ).

fof(f_2811_2,plain,
    ! [U_10386,U_10385] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_10386)),hAPP(c_Int_Onat,U_10385)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_10386),U_10385)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,U_10385)) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_10386)),hAPP(c_Int_Onat,U_10385)) = hAPP(c_Int_Onat,U_10386)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_10385)) ) ),
    inference(variable_rename,[status(thm)],[f_2811_1]) ).

fof(f_2811_3,plain,
    ( ! [U_10390,U_10388] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_10390)),hAPP(c_Int_Onat,U_10388)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_10390),U_10388)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,U_10388)) )
    & ! [U_10389,U_10387] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_10389)),hAPP(c_Int_Onat,U_10387)) = hAPP(c_Int_Onat,U_10389)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_10387)) ) ),
    inference(miniscope,[status(thm)],[f_2811_2]) ).

cnf(f_2811_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_10389)),hAPP(c_Int_Onat,U_10387)) = hAPP(c_Int_Onat,U_10389)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_10387)) ),
    inference(clausify,[status(thm)],[f_2811_3]) ).

cnf(f_2811_5,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_10390)),hAPP(c_Int_Onat,U_10388)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_10390),U_10388)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,U_10388)) ),
    inference(clausify,[status(thm)],[f_2811_3]) ).

fof(f_2812_1,plain,
    ! [V_l,V_k] :
      ( c_Divides_OnegDivAlg(V_k,V_l) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(fof_nnf,[status(thm)],[fact_negDivAlg__div__mod]) ).

fof(f_2812_2,plain,
    ! [U_10392,U_10391] :
      ( c_Divides_OnegDivAlg(U_10391,U_10392) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10391),U_10392)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10391,U_10392))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10392))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10391),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_2812_1]) ).

cnf(f_2812_3,plain,
    ( c_Divides_OnegDivAlg(U_10391,U_10392) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10391),U_10392)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10391,U_10392))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10392))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10391),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2812_2]) ).

fof(f_2813_1,plain,
    ! [V_b] : c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_b),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(fof_nnf,[status(thm)],[fact_negDivAlg__minus1]) ).

fof(f_2813_2,plain,
    ! [U_10393] : c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),U_10393) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_10393),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(variable_rename,[status(thm)],[f_2813_1]) ).

cnf(f_2813_3,plain,
    c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),U_10393) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_10393),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(clausify,[status(thm)],[f_2813_2]) ).

fof(f_2814_1,plain,
    ! [V_M_2,V_n_2,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2)),V_M_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n_2)),V_M_2)),hAPP(V_M_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(fof_nnf,[status(thm)],[fact_UN__le__eq__Un0]) ).

fof(f_2814_2,plain,
    ! [U_10396,U_10395,U_10394] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_10394,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_10395)),U_10396) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10394,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_10394,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_10395)),U_10396)),hAPP(U_10396,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_2814_1]) ).

cnf(f_2814_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_10394,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_10395)),U_10396) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10394,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_10394,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_10395)),U_10396)),hAPP(U_10396,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_2814_2]) ).

fof(f_2815_1,plain,
    ! [V_f_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_b,tc_Nat_Onat),V_f_2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2))
      | ~ c_Nat__Transfer_Onat__set(V_A_2)
      | ~ class_Groups_Ocomm__monoid__mult(T_b)
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__sum__prod_I1_J]) ).

fof(f_2815_2,plain,
    ! [U_10399,U_10398,U_10397] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_10397),U_10399),U_10398) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10397),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_10397,tc_Nat_Onat),U_10399),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_10398))
      | ~ c_Nat__Transfer_Onat__set(U_10398)
      | ~ class_Groups_Ocomm__monoid__mult(U_10397)
      | ~ class_Groups_Ocomm__monoid__add(U_10397) ),
    inference(variable_rename,[status(thm)],[f_2815_1]) ).

cnf(f_2815_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_10397),U_10399),U_10398) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10397),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_10397,tc_Nat_Onat),U_10399),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_10398))
    | ~ c_Nat__Transfer_Onat__set(U_10398)
    | ~ class_Groups_Ocomm__monoid__mult(U_10397)
    | ~ class_Groups_Ocomm__monoid__add(U_10397) ),
    inference(clausify,[status(thm)],[f_2815_2]) ).

fof(f_2816_1,plain,
    ! [V_r_2,V_q_2,V_b_2] : hAPP(c_Divides_Oadjust(V_b_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q_2),V_r_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_r_2),V_b_2)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_q_2)),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_q_2)),V_r_2))),
    inference(fof_nnf,[status(thm)],[fact_adjust__eq]) ).

fof(f_2816_2,plain,
    ! [U_10402,U_10401,U_10400] : hAPP(c_Divides_Oadjust(U_10400),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_10401),U_10402)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_10402),U_10400)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_10401)),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_10401)),U_10402))),
    inference(variable_rename,[status(thm)],[f_2816_1]) ).

cnf(f_2816_3,plain,
    hAPP(c_Divides_Oadjust(U_10400),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_10401),U_10402)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_10402),U_10400)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_10401)),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_10401)),U_10402))),
    inference(clausify,[status(thm)],[f_2816_2]) ).

fof(f_2817_1,plain,
    ! [V_P_2,V_n_2,V_m_2,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_P_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_P_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_P_2),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_m_2,V_n_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__head]) ).

fof(f_2817_2,plain,
    ! [U_10406,U_10405,U_10404,U_10403] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10403),U_10406),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_10404,U_10405)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10403),hAPP(U_10406,U_10404)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10403),U_10406),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_10404,U_10405)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10404),U_10405))
      | ~ class_Groups_Ocomm__monoid__add(U_10403) ),
    inference(variable_rename,[status(thm)],[f_2817_1]) ).

cnf(f_2817_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10403),U_10406),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_10404,U_10405)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10403),hAPP(U_10406,U_10404)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10403),U_10406),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_10404,U_10405)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10404),U_10405))
    | ~ class_Groups_Ocomm__monoid__add(U_10403) ),
    inference(clausify,[status(thm)],[f_2817_2]) ).

fof(f_2818_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_B_2),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_minus__fold__remove]) ).

fof(f_2818_2,plain,
    ! [U_10409,U_10408,U_10407] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10407,tc_HOL_Obool)),U_10409),U_10408) = hAPP(hAPP(c_Finite__Set_Ofold(U_10407,tc_fun(U_10407,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_10407,tc_HOL_Obool),tc_fun(tc_fun(U_10407,tc_HOL_Obool),tc_fun(U_10407,tc_HOL_Obool)),U_10407),hAPP(c_COMBC(tc_fun(U_10407,tc_HOL_Obool),tc_fun(U_10407,tc_HOL_Obool),tc_fun(U_10407,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(U_10407,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(U_10407,tc_fun(U_10407,tc_HOL_Obool),tc_fun(U_10407,tc_HOL_Obool)),c_Set_Oinsert(U_10407)),c_Orderings_Obot__class_Obot(tc_fun(U_10407,tc_HOL_Obool))))),U_10409),U_10408)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10407),U_10408)) ),
    inference(variable_rename,[status(thm)],[f_2818_1]) ).

cnf(f_2818_3,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10407,tc_HOL_Obool)),U_10409),U_10408) = hAPP(hAPP(c_Finite__Set_Ofold(U_10407,tc_fun(U_10407,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_10407,tc_HOL_Obool),tc_fun(tc_fun(U_10407,tc_HOL_Obool),tc_fun(U_10407,tc_HOL_Obool)),U_10407),hAPP(c_COMBC(tc_fun(U_10407,tc_HOL_Obool),tc_fun(U_10407,tc_HOL_Obool),tc_fun(U_10407,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(U_10407,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(U_10407,tc_fun(U_10407,tc_HOL_Obool),tc_fun(U_10407,tc_HOL_Obool)),c_Set_Oinsert(U_10407)),c_Orderings_Obot__class_Obot(tc_fun(U_10407,tc_HOL_Obool))))),U_10409),U_10408)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10407),U_10408)) ),
    inference(clausify,[status(thm)],[f_2818_2]) ).

fof(f_2819_1,plain,
    ! [V_h_2,V_B_2,V_f_2,T_c,T_b,T_d] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_h_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)),V_B_2)
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
      | ~ class_Groups_Ocomm__monoid__add(T_d) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__reindex]) ).

fof(f_2819_2,plain,
    ! [U_10415,U_10414,U_10413,U_10412,U_10411,U_10410] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10412,U_10410),U_10415),hAPP(c_Set_Oimage(U_10411,U_10412,U_10413),U_10414)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10411,U_10410),hAPP(c_Fun_Ocomp(U_10412,U_10410,U_10411,U_10415),U_10413)),U_10414)
      | ~ c_Fun_Oinj__on(U_10411,U_10412,U_10413,U_10414)
      | ~ class_Groups_Ocomm__monoid__add(U_10410) ),
    inference(variable_rename,[status(thm)],[f_2819_1]) ).

cnf(f_2819_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10412,U_10410),U_10415),hAPP(c_Set_Oimage(U_10411,U_10412,U_10413),U_10414)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10411,U_10410),hAPP(c_Fun_Ocomp(U_10412,U_10410,U_10411,U_10415),U_10413)),U_10414)
    | ~ c_Fun_Oinj__on(U_10411,U_10412,U_10413,U_10414)
    | ~ class_Groups_Ocomm__monoid__add(U_10410) ),
    inference(clausify,[status(thm)],[f_2819_2]) ).

fof(f_2820_1,plain,
    ! [V_n_2,V_v_2] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = hAPP(c_Nat_OSuc,V_n_2)
        | ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),V_n_2))))) )
      & ( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),V_n_2)))))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) != hAPP(c_Nat_OSuc,V_n_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_eq__number__of__Suc]) ).

fof(f_2820_2,plain,
    ! [U_10417,U_10416] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10416) = hAPP(c_Nat_OSuc,U_10417)
        | ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10416))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),U_10417))))) )
      & ( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10416))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),U_10417)))))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10416) != hAPP(c_Nat_OSuc,U_10417) ) ),
    inference(variable_rename,[status(thm)],[f_2820_1]) ).

fof(f_2820_3,plain,
    ( ! [U_10421,U_10419] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10419) = hAPP(c_Nat_OSuc,U_10421)
        | ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10419))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),U_10421))))) )
    & ! [U_10420,U_10418] :
        ( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10418))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),U_10420)))))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10418) != hAPP(c_Nat_OSuc,U_10420) ) ),
    inference(miniscope,[status(thm)],[f_2820_2]) ).

cnf(f_2820_4,plain,
    ( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10418))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),U_10420)))))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10418) != hAPP(c_Nat_OSuc,U_10420) ),
    inference(clausify,[status(thm)],[f_2820_3]) ).

cnf(f_2820_5,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10419) = hAPP(c_Nat_OSuc,U_10421)
    | ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10419))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),U_10421))))) ),
    inference(clausify,[status(thm)],[f_2820_3]) ).

fof(f_2821_1,plain,
    ! [V_v_2,V_n_2] :
      ( ( hAPP(c_Nat_OSuc,V_n_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)
        | ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),V_n_2))))) )
      & ( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),V_n_2)))))
        | hAPP(c_Nat_OSuc,V_n_2) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_Suc__eq__number__of]) ).

fof(f_2821_2,plain,
    ! [U_10423,U_10422] :
      ( ( hAPP(c_Nat_OSuc,U_10422) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10423)
        | ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10423))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),U_10422))))) )
      & ( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10423))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),U_10422)))))
        | hAPP(c_Nat_OSuc,U_10422) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10423) ) ),
    inference(variable_rename,[status(thm)],[f_2821_1]) ).

fof(f_2821_3,plain,
    ( ! [U_10427,U_10425] :
        ( hAPP(c_Nat_OSuc,U_10425) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10427)
        | ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10427))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),U_10425))))) )
    & ! [U_10426,U_10424] :
        ( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10426))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),U_10424)))))
        | hAPP(c_Nat_OSuc,U_10424) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10426) ) ),
    inference(miniscope,[status(thm)],[f_2821_2]) ).

cnf(f_2821_4,plain,
    ( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10426))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),U_10424)))))
    | hAPP(c_Nat_OSuc,U_10424) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10426) ),
    inference(clausify,[status(thm)],[f_2821_3]) ).

cnf(f_2821_5,plain,
    ( hAPP(c_Nat_OSuc,U_10425) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10427)
    | ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10427))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),U_10425))))) ),
    inference(clausify,[status(thm)],[f_2821_3]) ).

fof(f_2822_1,plain,
    ! [V_h_2,V_B_2,V_f_2,T_c,T_b,T_d] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_h_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_d),hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)),V_B_2)
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
      | ~ class_Groups_Ocomm__monoid__mult(T_d) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__reindex]) ).

fof(f_2822_2,plain,
    ! [U_10433,U_10432,U_10431,U_10430,U_10429,U_10428] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10430,U_10428),U_10433),hAPP(c_Set_Oimage(U_10429,U_10430,U_10431),U_10432)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10429,U_10428),hAPP(c_Fun_Ocomp(U_10430,U_10428,U_10429,U_10433),U_10431)),U_10432)
      | ~ c_Fun_Oinj__on(U_10429,U_10430,U_10431,U_10432)
      | ~ class_Groups_Ocomm__monoid__mult(U_10428) ),
    inference(variable_rename,[status(thm)],[f_2822_1]) ).

cnf(f_2822_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10430,U_10428),U_10433),hAPP(c_Set_Oimage(U_10429,U_10430,U_10431),U_10432)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10429,U_10428),hAPP(c_Fun_Ocomp(U_10430,U_10428,U_10429,U_10433),U_10431)),U_10432)
    | ~ c_Fun_Oinj__on(U_10429,U_10430,U_10431,U_10432)
    | ~ class_Groups_Ocomm__monoid__mult(U_10428) ),
    inference(clausify,[status(thm)],[f_2822_2]) ).

fof(f_2823_1,plain,
    ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_d),V_g_2),V_A_2)
      | V_g_2 != hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)
      | V_B_2 != hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
      | ~ class_Groups_Ocomm__monoid__mult(T_d) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__reindex__cong]) ).

fof(f_2823_2,plain,
    ! [U_10441,U_10440,U_10439,U_10438,U_10437,U_10436,U_10435,U_10434] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10436,U_10434),U_10441),U_10439) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10435,U_10434),U_10440),U_10438)
      | U_10440 != hAPP(c_Fun_Ocomp(U_10436,U_10434,U_10435,U_10441),U_10437)
      | U_10439 != hAPP(c_Set_Oimage(U_10435,U_10436,U_10437),U_10438)
      | ~ c_Fun_Oinj__on(U_10435,U_10436,U_10437,U_10438)
      | ~ class_Groups_Ocomm__monoid__mult(U_10434) ),
    inference(variable_rename,[status(thm)],[f_2823_1]) ).

cnf(f_2823_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10436,U_10434),U_10441),U_10439) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10435,U_10434),U_10440),U_10438)
    | U_10440 != hAPP(c_Fun_Ocomp(U_10436,U_10434,U_10435,U_10441),U_10437)
    | U_10439 != hAPP(c_Set_Oimage(U_10435,U_10436,U_10437),U_10438)
    | ~ c_Fun_Oinj__on(U_10435,U_10436,U_10437,U_10438)
    | ~ class_Groups_Ocomm__monoid__mult(U_10434) ),
    inference(clausify,[status(thm)],[f_2823_2]) ).

fof(f_2824_1,plain,
    ! [V_w_2] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat))))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__number__of__Bit1]) ).

fof(f_2824_2,plain,
    ! [U_10442] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10442)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10442)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat))))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10442))) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10442)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10442))) ) ),
    inference(variable_rename,[status(thm)],[f_2824_1]) ).

fof(f_2824_3,plain,
    ( ! [U_10444] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10444)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10444)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat))))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10444))) )
    & ! [U_10443] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10443)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10443))) ) ),
    inference(miniscope,[status(thm)],[f_2824_2]) ).

cnf(f_2824_4,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10443)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10443))) ),
    inference(clausify,[status(thm)],[f_2824_3]) ).

cnf(f_2824_5,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10444)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10444)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat))))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10444))) ),
    inference(clausify,[status(thm)],[f_2824_3]) ).

fof(f_2825_1,plain,
    ! [V_n_2,V_x_2,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(c_Power_Opower__class_Opower(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),V_n_2)),c_Groups_Oone__class_Oone(T_b))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_x_2),c_Groups_Oone__class_Oone(T_b)))
      | V_x_2 = c_Groups_Oone__class_Oone(T_b)
      | ~ class_Fields_Ofield(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_geometric__sum]) ).

fof(f_2825_2,plain,
    ! [U_10447,U_10446,U_10445] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10445),hAPP(c_Power_Opower__class_Opower(U_10445),U_10446)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10447)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10445),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10445),hAPP(hAPP(c_Power_Opower__class_Opower(U_10445),U_10446),U_10447)),c_Groups_Oone__class_Oone(U_10445))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10445),U_10446),c_Groups_Oone__class_Oone(U_10445)))
      | U_10446 = c_Groups_Oone__class_Oone(U_10445)
      | ~ class_Fields_Ofield(U_10445) ),
    inference(variable_rename,[status(thm)],[f_2825_1]) ).

cnf(f_2825_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10445),hAPP(c_Power_Opower__class_Opower(U_10445),U_10446)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10447)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10445),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10445),hAPP(hAPP(c_Power_Opower__class_Opower(U_10445),U_10446),U_10447)),c_Groups_Oone__class_Oone(U_10445))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10445),U_10446),c_Groups_Oone__class_Oone(U_10445)))
    | U_10446 = c_Groups_Oone__class_Oone(U_10445)
    | ~ class_Fields_Ofield(U_10445) ),
    inference(clausify,[status(thm)],[f_2825_2]) ).

fof(f_2826_1,plain,
    ! [V_n_2,T_b] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),c_Groups_Oone__class_Oone(T_b)),c_Groups_Oone__class_Oone(T_b))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),c_Nat_Osemiring__1__class_Oof__nat(T_b)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)),c_Groups_Oone__class_Oone(T_b)))
      | ~ class_Rings_Ocomm__semiring__1(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_gauss__sum]) ).

fof(f_2826_2,plain,
    ! [U_10449,U_10448] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10448),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10448),c_Groups_Oone__class_Oone(U_10448)),c_Groups_Oone__class_Oone(U_10448))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10448),c_Nat_Osemiring__1__class_Oof__nat(U_10448)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_10449))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10448),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10448),U_10449)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10448),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10448),U_10449)),c_Groups_Oone__class_Oone(U_10448)))
      | ~ class_Rings_Ocomm__semiring__1(U_10448) ),
    inference(variable_rename,[status(thm)],[f_2826_1]) ).

cnf(f_2826_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10448),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10448),c_Groups_Oone__class_Oone(U_10448)),c_Groups_Oone__class_Oone(U_10448))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10448),c_Nat_Osemiring__1__class_Oof__nat(U_10448)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_10449))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10448),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10448),U_10449)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10448),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10448),U_10449)),c_Groups_Oone__class_Oone(U_10448)))
    | ~ class_Rings_Ocomm__semiring__1(U_10448) ),
    inference(clausify,[status(thm)],[f_2826_2]) ).

fof(f_2827_1,plain,
    ! [V_f_2,V_n_2,V_m_2,T_b] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(T_b)),V_f_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) = c_Groups_Ozero__class_Ozero(T_b)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(T_b)),V_f_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(V_f_2,V_m_2)),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) )
      | ~ class_Groups_Oab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__natinterval__difff]) ).

fof(f_2827_2,plain,
    ! [U_10453,U_10452,U_10451,U_10450] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10450),hAPP(hAPP(c_COMBS(tc_Nat_Onat,U_10450,U_10450),hAPP(hAPP(c_COMBB(U_10450,tc_fun(U_10450,U_10450),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(U_10450)),U_10453)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10450,tc_Nat_Onat),U_10453),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_10451,U_10452)) = c_Groups_Ozero__class_Ozero(U_10450)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10451),U_10452)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10450),hAPP(hAPP(c_COMBS(tc_Nat_Onat,U_10450,U_10450),hAPP(hAPP(c_COMBB(U_10450,tc_fun(U_10450,U_10450),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(U_10450)),U_10453)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10450,tc_Nat_Onat),U_10453),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_10451,U_10452)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10450),hAPP(U_10453,U_10451)),hAPP(U_10453,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10452),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10451),U_10452)) ) )
      | ~ class_Groups_Oab__group__add(U_10450) ),
    inference(variable_rename,[status(thm)],[f_2827_1]) ).

cnf(f_2827_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10450),hAPP(hAPP(c_COMBS(tc_Nat_Onat,U_10450,U_10450),hAPP(hAPP(c_COMBB(U_10450,tc_fun(U_10450,U_10450),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(U_10450)),U_10453)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10450,tc_Nat_Onat),U_10453),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_10451,U_10452)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10450),hAPP(U_10453,U_10451)),hAPP(U_10453,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10452),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10451),U_10452))
    | ~ class_Groups_Oab__group__add(U_10450) ),
    inference(clausify,[status(thm)],[f_2827_2]) ).

cnf(f_2827_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10450),hAPP(hAPP(c_COMBS(tc_Nat_Onat,U_10450,U_10450),hAPP(hAPP(c_COMBB(U_10450,tc_fun(U_10450,U_10450),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(U_10450)),U_10453)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10450,tc_Nat_Onat),U_10453),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_10451,U_10452)) = c_Groups_Ozero__class_Ozero(U_10450)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10451),U_10452))
    | ~ class_Groups_Oab__group__add(U_10450) ),
    inference(clausify,[status(thm)],[f_2827_2]) ).

fof(f_2828_1,plain,
    ! [V_n_2,V_v_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Nat_OSuc,V_n_2)))
        | ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Int_Onat)),V_n_2)))) )
      & ( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Int_Onat)),V_n_2))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Nat_OSuc,V_n_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_less__number__of__Suc]) ).

fof(f_2828_2,plain,
    ! [U_10455,U_10454] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10454)),hAPP(c_Nat_OSuc,U_10455)))
        | ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10454))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Int_Onat)),U_10455)))) )
      & ( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10454))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Int_Onat)),U_10455))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10454)),hAPP(c_Nat_OSuc,U_10455))) ) ),
    inference(variable_rename,[status(thm)],[f_2828_1]) ).

fof(f_2828_3,plain,
    ( ! [U_10459,U_10457] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10457)),hAPP(c_Nat_OSuc,U_10459)))
        | ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10457))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Int_Onat)),U_10459)))) )
    & ! [U_10458,U_10456] :
        ( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10456))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Int_Onat)),U_10458))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10456)),hAPP(c_Nat_OSuc,U_10458))) ) ),
    inference(miniscope,[status(thm)],[f_2828_2]) ).

cnf(f_2828_4,plain,
    ( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10456))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Int_Onat)),U_10458))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10456)),hAPP(c_Nat_OSuc,U_10458))) ),
    inference(clausify,[status(thm)],[f_2828_3]) ).

cnf(f_2828_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10457)),hAPP(c_Nat_OSuc,U_10459)))
    | ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10457))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Int_Onat)),U_10459)))) ),
    inference(clausify,[status(thm)],[f_2828_3]) ).

fof(f_2829_1,plain,
    ! [V_v_2,V_n_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)))
        | ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2)),c_Int_Onat))))) )
      & ( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2)),c_Int_Onat)))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_less__Suc__number__of]) ).

fof(f_2829_2,plain,
    ! [U_10461,U_10460] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10460)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10461)))
        | ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10461))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10460)),c_Int_Onat))))) )
      & ( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10461))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10460)),c_Int_Onat)))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10460)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10461))) ) ),
    inference(variable_rename,[status(thm)],[f_2829_1]) ).

fof(f_2829_3,plain,
    ( ! [U_10465,U_10463] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10463)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10465)))
        | ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10465))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10463)),c_Int_Onat))))) )
    & ! [U_10464,U_10462] :
        ( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10464))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10462)),c_Int_Onat)))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10462)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10464))) ) ),
    inference(miniscope,[status(thm)],[f_2829_2]) ).

cnf(f_2829_4,plain,
    ( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10464))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10462)),c_Int_Onat)))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10462)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10464))) ),
    inference(clausify,[status(thm)],[f_2829_3]) ).

cnf(f_2829_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10463)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10465)))
    | ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10465))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10463)),c_Int_Onat))))) ),
    inference(clausify,[status(thm)],[f_2829_3]) ).

fof(f_2830_1,plain,
    ! [V_n_2,V_v_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Nat_OSuc,V_n_2)))
        | ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Int_Onat)),V_n_2)))) )
      & ( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Int_Onat)),V_n_2))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Nat_OSuc,V_n_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_le__number__of__Suc]) ).

fof(f_2830_2,plain,
    ! [U_10467,U_10466] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10466)),hAPP(c_Nat_OSuc,U_10467)))
        | ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10466))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Int_Onat)),U_10467)))) )
      & ( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10466))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Int_Onat)),U_10467))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10466)),hAPP(c_Nat_OSuc,U_10467))) ) ),
    inference(variable_rename,[status(thm)],[f_2830_1]) ).

fof(f_2830_3,plain,
    ( ! [U_10471,U_10469] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10469)),hAPP(c_Nat_OSuc,U_10471)))
        | ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10469))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Int_Onat)),U_10471)))) )
    & ! [U_10470,U_10468] :
        ( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10468))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Int_Onat)),U_10470))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10468)),hAPP(c_Nat_OSuc,U_10470))) ) ),
    inference(miniscope,[status(thm)],[f_2830_2]) ).

cnf(f_2830_4,plain,
    ( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10468))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Int_Onat)),U_10470))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10468)),hAPP(c_Nat_OSuc,U_10470))) ),
    inference(clausify,[status(thm)],[f_2830_3]) ).

cnf(f_2830_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10469)),hAPP(c_Nat_OSuc,U_10471)))
    | ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10469))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Int_Onat)),U_10471)))) ),
    inference(clausify,[status(thm)],[f_2830_3]) ).

fof(f_2831_1,plain,
    ! [V_v_2,V_n_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)))
        | ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2)),c_Int_Onat))))) )
      & ( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2)),c_Int_Onat)))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_le__Suc__number__of]) ).

fof(f_2831_2,plain,
    ! [U_10473,U_10472] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10472)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10473)))
        | ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10473))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10472)),c_Int_Onat))))) )
      & ( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10473))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10472)),c_Int_Onat)))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10472)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10473))) ) ),
    inference(variable_rename,[status(thm)],[f_2831_1]) ).

fof(f_2831_3,plain,
    ( ! [U_10477,U_10475] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10475)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10477)))
        | ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10477))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10475)),c_Int_Onat))))) )
    & ! [U_10476,U_10474] :
        ( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10476))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10474)),c_Int_Onat)))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10474)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10476))) ) ),
    inference(miniscope,[status(thm)],[f_2831_2]) ).

cnf(f_2831_4,plain,
    ( hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10476))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10474)),c_Int_Onat)))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10474)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10476))) ),
    inference(clausify,[status(thm)],[f_2831_3]) ).

cnf(f_2831_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10475)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10477)))
    | ~ hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10477))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10475)),c_Int_Onat))))) ),
    inference(clausify,[status(thm)],[f_2831_3]) ).

fof(f_2832_1,plain,
    ! [V_v_2,V_n_2] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_OSuc,V_n_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n_2)),c_Int_Onat)))),
    inference(fof_nnf,[status(thm)],[fact_max__number__of__Suc]) ).

fof(f_2832_2,plain,
    ! [U_10479,U_10478] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10478)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10479)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10479))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_OSuc,U_10478))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_10478)),c_Int_Onat)))),
    inference(variable_rename,[status(thm)],[f_2832_1]) ).

cnf(f_2832_3,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10478)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10479)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10479))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_OSuc,U_10478))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_10478)),c_Int_Onat)))),
    inference(clausify,[status(thm)],[f_2832_2]) ).

fof(f_2833_1,plain,
    ! [V_n_2,V_v_2] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_OSuc,V_n_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Int_Onat)),V_n_2)))),
    inference(fof_nnf,[status(thm)],[fact_max__Suc__number__of]) ).

fof(f_2833_2,plain,
    ! [U_10481,U_10480] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10480)),hAPP(c_Nat_OSuc,U_10481)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10480))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_OSuc,U_10481))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Int_Onat)),U_10481)))),
    inference(variable_rename,[status(thm)],[f_2833_1]) ).

cnf(f_2833_3,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10480)),hAPP(c_Nat_OSuc,U_10481)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10480))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_OSuc,U_10481))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Int_Onat)),U_10481)))),
    inference(clausify,[status(thm)],[f_2833_2]) ).

fof(f_2834_1,plain,
    ! [V_z_2,V_w_2,T_b] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = c_Groups_Oone__class_Oone(T_b)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) )
        & ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = hAPP(hAPP(c_HOL_OLet(T_b,T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_b),c_Groups_Otimes__class_Otimes(T_b)),hAPP(c_Groups_Otimes__class_Otimes(T_b),V_z_2))),c_COMBI(T_b)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) )
      | ~ class_Int_Onumber__ring(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_power__number__of__odd]) ).

fof(f_2834_2,plain,
    ! [U_10484,U_10483,U_10482] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_10482),U_10484),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10483))) = c_Groups_Oone__class_Oone(U_10482)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10483))) )
        & ( hAPP(hAPP(c_Power_Opower__class_Opower(U_10482),U_10484),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10483))) = hAPP(hAPP(c_HOL_OLet(U_10482,U_10482),hAPP(hAPP(c_Power_Opower__class_Opower(U_10482),U_10484),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10483))),hAPP(hAPP(c_COMBS(U_10482,U_10482,U_10482),hAPP(hAPP(c_COMBB(U_10482,tc_fun(U_10482,U_10482),U_10482),c_Groups_Otimes__class_Otimes(U_10482)),hAPP(c_Groups_Otimes__class_Otimes(U_10482),U_10484))),c_COMBI(U_10482)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10483))) ) )
      | ~ class_Int_Onumber__ring(U_10482) ),
    inference(variable_rename,[status(thm)],[f_2834_1]) ).

cnf(f_2834_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_10482),U_10484),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10483))) = hAPP(hAPP(c_HOL_OLet(U_10482,U_10482),hAPP(hAPP(c_Power_Opower__class_Opower(U_10482),U_10484),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10483))),hAPP(hAPP(c_COMBS(U_10482,U_10482,U_10482),hAPP(hAPP(c_COMBB(U_10482,tc_fun(U_10482,U_10482),U_10482),c_Groups_Otimes__class_Otimes(U_10482)),hAPP(c_Groups_Otimes__class_Otimes(U_10482),U_10484))),c_COMBI(U_10482)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10483)))
    | ~ class_Int_Onumber__ring(U_10482) ),
    inference(clausify,[status(thm)],[f_2834_2]) ).

cnf(f_2834_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_10482),U_10484),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10483))) = c_Groups_Oone__class_Oone(U_10482)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10483)))
    | ~ class_Int_Onumber__ring(U_10482) ),
    inference(clausify,[status(thm)],[f_2834_2]) ).

fof(f_2835_1,plain,
    ! [V_c_2,V_b_2,V_a_2,V_S_2,T_b,T_c] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),V_c_2)),V_S_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_c_2),hAPP(c_Finite__Set_Ocard(T_b),V_S_2))
          | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),V_c_2)),V_S_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_b_2,V_a_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_S_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
          | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__gen__delta]) ).

fof(f_2835_2,plain,
    ! [U_10490,U_10489,U_10488,U_10487,U_10486,U_10485] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10486,U_10485),hAPP(hAPP(c_COMBC(U_10486,U_10485,U_10485),hAPP(hAPP(c_COMBS(U_10486,U_10485,tc_fun(U_10485,U_10485)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10485,tc_fun(U_10485,U_10485)),U_10486),c_If(U_10485)),hAPP(hAPP(c_COMBC(U_10486,U_10486,tc_HOL_Obool),c_fequal),U_10488))),U_10489)),U_10490)),U_10487) = hAPP(hAPP(c_Power_Opower__class_Opower(U_10485),U_10490),hAPP(c_Finite__Set_Ocard(U_10486),U_10487))
          | hBOOL(hAPP(hAPP(c_member(U_10486),U_10488),U_10487)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10486,U_10485),hAPP(hAPP(c_COMBC(U_10486,U_10485,U_10485),hAPP(hAPP(c_COMBS(U_10486,U_10485,tc_fun(U_10485,U_10485)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10485,tc_fun(U_10485,U_10485)),U_10486),c_If(U_10485)),hAPP(hAPP(c_COMBC(U_10486,U_10486,tc_HOL_Obool),c_fequal),U_10488))),U_10489)),U_10490)),U_10487) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10485),hAPP(U_10489,U_10488)),hAPP(hAPP(c_Power_Opower__class_Opower(U_10485),U_10490),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10486),U_10487)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
          | ~ hBOOL(hAPP(hAPP(c_member(U_10486),U_10488),U_10487)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10486),U_10487))
      | ~ class_Groups_Ocomm__monoid__mult(U_10485) ),
    inference(variable_rename,[status(thm)],[f_2835_1]) ).

cnf(f_2835_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10486,U_10485),hAPP(hAPP(c_COMBC(U_10486,U_10485,U_10485),hAPP(hAPP(c_COMBS(U_10486,U_10485,tc_fun(U_10485,U_10485)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10485,tc_fun(U_10485,U_10485)),U_10486),c_If(U_10485)),hAPP(hAPP(c_COMBC(U_10486,U_10486,tc_HOL_Obool),c_fequal),U_10488))),U_10489)),U_10490)),U_10487) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10485),hAPP(U_10489,U_10488)),hAPP(hAPP(c_Power_Opower__class_Opower(U_10485),U_10490),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10486),U_10487)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10486),U_10488),U_10487))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10486),U_10487))
    | ~ class_Groups_Ocomm__monoid__mult(U_10485) ),
    inference(clausify,[status(thm)],[f_2835_2]) ).

cnf(f_2835_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10486,U_10485),hAPP(hAPP(c_COMBC(U_10486,U_10485,U_10485),hAPP(hAPP(c_COMBS(U_10486,U_10485,tc_fun(U_10485,U_10485)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10485,tc_fun(U_10485,U_10485)),U_10486),c_If(U_10485)),hAPP(hAPP(c_COMBC(U_10486,U_10486,tc_HOL_Obool),c_fequal),U_10488))),U_10489)),U_10490)),U_10487) = hAPP(hAPP(c_Power_Opower__class_Opower(U_10485),U_10490),hAPP(c_Finite__Set_Ocard(U_10486),U_10487))
    | hBOOL(hAPP(hAPP(c_member(U_10486),U_10488),U_10487))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10486),U_10487))
    | ~ class_Groups_Ocomm__monoid__mult(U_10485) ),
    inference(clausify,[status(thm)],[f_2835_2]) ).

fof(f_2836_1,plain,
    ! [V_x_2,V_y_2,V_c_2] :
      ( ( ( ( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_c_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) )
          & ( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_c_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) )
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_c_2),V_y_2)) )
      & ( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_c_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_c_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_y_2),V_c_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_c_2),V_y_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_image__minus__const__atLeastLessThan__nat]) ).

fof(f_2836_2,plain,
    ! [U_10493,U_10492,U_10491] :
      ( ( ( ( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),U_10491)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10493),U_10492)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10493),U_10492)) )
          & ( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),U_10491)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10493),U_10492)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10493),U_10492)) ) )
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10491),U_10492)) )
      & ( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),U_10491)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10493),U_10492)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10493),U_10491)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10492),U_10491))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10491),U_10492)) ) ),
    inference(variable_rename,[status(thm)],[f_2836_1]) ).

fof(f_2836_3,plain,
    ( ! [U_10499,U_10497,U_10495] :
        ( ( ( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),U_10495)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10499),U_10497)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10499),U_10497)) )
          & ( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),U_10495)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10499),U_10497)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10499),U_10497)) ) )
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10495),U_10497)) )
    & ! [U_10498,U_10496,U_10494] :
        ( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),U_10494)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10498),U_10496)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10498),U_10494)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10496),U_10494))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10494),U_10496)) ) ),
    inference(miniscope,[status(thm)],[f_2836_2]) ).

cnf(f_2836_4,plain,
    ( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),U_10494)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10498),U_10496)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10498),U_10494)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10496),U_10494))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10494),U_10496)) ),
    inference(clausify,[status(thm)],[f_2836_3]) ).

cnf(f_2836_5,plain,
    ( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),U_10495)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10499),U_10497)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10499),U_10497))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10495),U_10497)) ),
    inference(clausify,[status(thm)],[f_2836_3]) ).

cnf(f_2836_6,plain,
    ( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),U_10495)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_10499),U_10497)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10499),U_10497))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10495),U_10497)) ),
    inference(clausify,[status(thm)],[f_2836_3]) ).

fof(f_2837_1,plain,
    ! [V_g_2,V_h_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(c_Fun_Ocomp(T_b,T_c,T_b,V_g_2),V_h_2)),V_A_2)
      | ~ c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Ocomm__monoid__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum_Oreindex]) ).

fof(f_2837_2,plain,
    ! [U_10504,U_10503,U_10502,U_10501,U_10500] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10501,U_10500),U_10504),hAPP(c_Set_Oimage(U_10501,U_10501,U_10503),U_10502)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10501,U_10500),hAPP(c_Fun_Ocomp(U_10501,U_10500,U_10501,U_10504),U_10503)),U_10502)
      | ~ c_Fun_Oinj__on(U_10501,U_10501,U_10503,U_10502)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10501),U_10502))
      | ~ class_Groups_Ocomm__monoid__add(U_10500) ),
    inference(variable_rename,[status(thm)],[f_2837_1]) ).

cnf(f_2837_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10501,U_10500),U_10504),hAPP(c_Set_Oimage(U_10501,U_10501,U_10503),U_10502)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10501,U_10500),hAPP(c_Fun_Ocomp(U_10501,U_10500,U_10501,U_10504),U_10503)),U_10502)
    | ~ c_Fun_Oinj__on(U_10501,U_10501,U_10503,U_10502)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10501),U_10502))
    | ~ class_Groups_Ocomm__monoid__add(U_10500) ),
    inference(clausify,[status(thm)],[f_2837_2]) ).

fof(f_2838_1,plain,
    ! [V_z_2,V_w_2] :
      ( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) )
      & ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z_2))),c_COMBI(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_zpower__number__of__odd]) ).

fof(f_2838_2,plain,
    ! [U_10506,U_10505] :
      ( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_10506),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10505))) = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10505))) )
      & ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_10506),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10505))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_10506),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10505))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10506))),c_COMBI(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10505))) ) ),
    inference(variable_rename,[status(thm)],[f_2838_1]) ).

fof(f_2838_3,plain,
    ( ! [U_10510,U_10508] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_10510),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10508))) = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10508))) )
    & ! [U_10509,U_10507] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_10509),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10507))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_10509),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10507))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10509))),c_COMBI(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10507))) ) ),
    inference(miniscope,[status(thm)],[f_2838_2]) ).

cnf(f_2838_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_10509),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10507))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_10509),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10507))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_10509))),c_COMBI(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10507))) ),
    inference(clausify,[status(thm)],[f_2838_3]) ).

cnf(f_2838_5,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_10510),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10508))) = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10508))) ),
    inference(clausify,[status(thm)],[f_2838_3]) ).

fof(f_2839_1,plain,
    ! [V_g_2,V_h_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(c_Fun_Ocomp(T_b,T_c,T_b,V_g_2),V_h_2)),V_A_2)
      | ~ c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setprod_Oreindex]) ).

fof(f_2839_2,plain,
    ! [U_10515,U_10514,U_10513,U_10512,U_10511] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10512,U_10511),U_10515),hAPP(c_Set_Oimage(U_10512,U_10512,U_10514),U_10513)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10512,U_10511),hAPP(c_Fun_Ocomp(U_10512,U_10511,U_10512,U_10515),U_10514)),U_10513)
      | ~ c_Fun_Oinj__on(U_10512,U_10512,U_10514,U_10513)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10512),U_10513))
      | ~ class_Groups_Ocomm__monoid__mult(U_10511) ),
    inference(variable_rename,[status(thm)],[f_2839_1]) ).

cnf(f_2839_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10512,U_10511),U_10515),hAPP(c_Set_Oimage(U_10512,U_10512,U_10514),U_10513)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10512,U_10511),hAPP(c_Fun_Ocomp(U_10512,U_10511,U_10512,U_10515),U_10514)),U_10513)
    | ~ c_Fun_Oinj__on(U_10512,U_10512,U_10514,U_10513)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10512),U_10513))
    | ~ class_Groups_Ocomm__monoid__mult(U_10511) ),
    inference(clausify,[status(thm)],[f_2839_2]) ).

fof(f_2840_1,plain,
    ! [V_n_2,V_d_2,V_a_2,T_b] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),c_Groups_Oone__class_Oone(T_b)),c_Groups_Oone__class_Oone(T_b))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(T_b)),c_Nat_Osemiring__1__class_Oof__nat(T_b))),V_d_2))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_d_2))))
      | ~ class_Rings_Ocomm__semiring__1(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_arith__series__general]) ).

fof(f_2840_2,plain,
    ! [U_10519,U_10518,U_10517,U_10516] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10516),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10516),c_Groups_Oone__class_Oone(U_10516)),c_Groups_Oone__class_Oone(U_10516))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10516),hAPP(hAPP(c_COMBB(U_10516,U_10516,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(U_10516),U_10517)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,U_10516,U_10516),hAPP(hAPP(c_COMBB(U_10516,tc_fun(U_10516,U_10516),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(U_10516)),c_Nat_Osemiring__1__class_Oof__nat(U_10516))),U_10518))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_10519))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10516),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10516),U_10519)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10516),U_10517),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10516),U_10517),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10516),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10516),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10519),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),U_10518))))
      | ~ class_Rings_Ocomm__semiring__1(U_10516) ),
    inference(variable_rename,[status(thm)],[f_2840_1]) ).

cnf(f_2840_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10516),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10516),c_Groups_Oone__class_Oone(U_10516)),c_Groups_Oone__class_Oone(U_10516))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_10516),hAPP(hAPP(c_COMBB(U_10516,U_10516,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(U_10516),U_10517)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,U_10516,U_10516),hAPP(hAPP(c_COMBB(U_10516,tc_fun(U_10516,U_10516),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(U_10516)),c_Nat_Osemiring__1__class_Oof__nat(U_10516))),U_10518))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_10519))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10516),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10516),U_10519)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10516),U_10517),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10516),U_10517),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10516),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10516),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10519),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),U_10518))))
    | ~ class_Rings_Ocomm__semiring__1(U_10516) ),
    inference(clausify,[status(thm)],[f_2840_2]) ).

fof(f_2841_1,plain,
    ! [V_b,V_a] :
      ( ( c_Divides_OnegDivAlg(V_a,V_b) = hAPP(c_Divides_Oadjust(V_b),c_Divides_OnegDivAlg(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b))) )
      & ( c_Divides_OnegDivAlg(V_a,V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b))) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_negDivAlg_Osimps]) ).

fof(f_2841_2,plain,
    ! [U_10521,U_10520] :
      ( ( c_Divides_OnegDivAlg(U_10520,U_10521) = hAPP(c_Divides_Oadjust(U_10521),c_Divides_OnegDivAlg(U_10520,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_10521)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10521),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10520),U_10521))) )
      & ( c_Divides_OnegDivAlg(U_10520,U_10521) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10520),U_10521))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10521),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10520),U_10521))) ) ) ),
    inference(variable_rename,[status(thm)],[f_2841_1]) ).

fof(f_2841_3,plain,
    ( ! [U_10525,U_10523] :
        ( c_Divides_OnegDivAlg(U_10523,U_10525) = hAPP(c_Divides_Oadjust(U_10525),c_Divides_OnegDivAlg(U_10523,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_10525)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10525),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10523),U_10525))) )
    & ! [U_10524,U_10522] :
        ( c_Divides_OnegDivAlg(U_10522,U_10524) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10522),U_10524))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10524),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10522),U_10524))) ) ) ),
    inference(miniscope,[status(thm)],[f_2841_2]) ).

cnf(f_2841_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10522),U_10524)))
    | c_Divides_OnegDivAlg(U_10522,U_10524) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10522),U_10524)) ),
    inference(clausify,[status(thm)],[f_2841_3]) ).

cnf(f_2841_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10524),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | c_Divides_OnegDivAlg(U_10522,U_10524) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10522),U_10524)) ),
    inference(clausify,[status(thm)],[f_2841_3]) ).

cnf(f_2841_6,plain,
    ( c_Divides_OnegDivAlg(U_10523,U_10525) = hAPP(c_Divides_Oadjust(U_10525),c_Divides_OnegDivAlg(U_10523,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_10525)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10525),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10523),U_10525))) ),
    inference(clausify,[status(thm)],[f_2841_3]) ).

fof(f_2842_1,plain,
    ! [V_v_2,V_n_2] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_n_2)),c_Int_Onat)))),
    inference(fof_nnf,[status(thm)],[fact_min__number__of__Suc]) ).

fof(f_2842_2,plain,
    ! [U_10527,U_10526] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10526)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10527)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10527))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_10526)),c_Int_Onat)))),
    inference(variable_rename,[status(thm)],[f_2842_1]) ).

cnf(f_2842_3,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10526)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10527)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10527))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_10526)),c_Int_Onat)))),
    inference(clausify,[status(thm)],[f_2842_2]) ).

fof(f_2843_1,plain,
    ! [V_n_2,V_v_2] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Orderings_Oord__class_Omin(tc_Nat_Onat)),c_Int_Onat)),V_n_2)))),
    inference(fof_nnf,[status(thm)],[fact_min__Suc__number__of]) ).

fof(f_2843_2,plain,
    ! [U_10529,U_10528] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10528)),hAPP(c_Nat_OSuc,U_10529)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10528))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Orderings_Oord__class_Omin(tc_Nat_Onat)),c_Int_Onat)),U_10529)))),
    inference(variable_rename,[status(thm)],[f_2843_1]) ).

cnf(f_2843_3,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10528)),hAPP(c_Nat_OSuc,U_10529)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10528))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Int_Oint),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Orderings_Oord__class_Omin(tc_Nat_Onat)),c_Int_Onat)),U_10529)))),
    inference(clausify,[status(thm)],[f_2843_2]) ).

fof(f_2844_1,plain,
    ! [V_n_2,V_d_2,V_a_2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),V_d_2))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_d_2)))),
    inference(fof_nnf,[status(thm)],[fact_arith__series__nat]) ).

fof(f_2844_2,plain,
    ! [U_10532,U_10531,U_10530] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10530)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),U_10531))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_10532))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10532),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10530),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10530),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10532),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_10531)))),
    inference(variable_rename,[status(thm)],[f_2844_1]) ).

cnf(f_2844_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10530)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),U_10531))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_10532))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10532),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10530),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10530),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10532),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_10531)))),
    inference(clausify,[status(thm)],[f_2844_2]) ).

fof(f_2845_1,plain,
    ! [V_x_2,V_A_2,V_g_2,T_d,V_f_2,T_c,T_b] :
      ( hAPP(c_Fun_Othe__inv__into(T_d,T_c,V_A_2,hAPP(c_Fun_Ocomp(T_b,T_c,T_d,V_f_2),V_g_2)),V_x_2) = hAPP(hAPP(c_Fun_Ocomp(T_b,T_d,T_c,c_Fun_Othe__inv__into(T_d,T_b,V_A_2,V_g_2)),c_Fun_Othe__inv__into(T_b,T_c,hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2),V_f_2)),V_x_2)
      | ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2))))
      | ~ c_Fun_Oinj__on(T_d,T_b,V_g_2,V_A_2)
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_the__inv__into__comp]) ).

fof(f_2845_2,plain,
    ! [U_10539,U_10538,U_10537,U_10536,U_10535,U_10534,U_10533] :
      ( hAPP(c_Fun_Othe__inv__into(U_10536,U_10534,U_10538,hAPP(c_Fun_Ocomp(U_10533,U_10534,U_10536,U_10535),U_10537)),U_10539) = hAPP(hAPP(c_Fun_Ocomp(U_10533,U_10536,U_10534,c_Fun_Othe__inv__into(U_10536,U_10533,U_10538,U_10537)),c_Fun_Othe__inv__into(U_10533,U_10534,hAPP(c_Set_Oimage(U_10536,U_10533,U_10537),U_10538),U_10535)),U_10539)
      | ~ hBOOL(hAPP(hAPP(c_member(U_10534),U_10539),hAPP(c_Set_Oimage(U_10533,U_10534,U_10535),hAPP(c_Set_Oimage(U_10536,U_10533,U_10537),U_10538))))
      | ~ c_Fun_Oinj__on(U_10536,U_10533,U_10537,U_10538)
      | ~ c_Fun_Oinj__on(U_10533,U_10534,U_10535,hAPP(c_Set_Oimage(U_10536,U_10533,U_10537),U_10538)) ),
    inference(variable_rename,[status(thm)],[f_2845_1]) ).

cnf(f_2845_3,plain,
    ( hAPP(c_Fun_Othe__inv__into(U_10536,U_10534,U_10538,hAPP(c_Fun_Ocomp(U_10533,U_10534,U_10536,U_10535),U_10537)),U_10539) = hAPP(hAPP(c_Fun_Ocomp(U_10533,U_10536,U_10534,c_Fun_Othe__inv__into(U_10536,U_10533,U_10538,U_10537)),c_Fun_Othe__inv__into(U_10533,U_10534,hAPP(c_Set_Oimage(U_10536,U_10533,U_10537),U_10538),U_10535)),U_10539)
    | ~ hBOOL(hAPP(hAPP(c_member(U_10534),U_10539),hAPP(c_Set_Oimage(U_10533,U_10534,U_10535),hAPP(c_Set_Oimage(U_10536,U_10533,U_10537),U_10538))))
    | ~ c_Fun_Oinj__on(U_10536,U_10533,U_10537,U_10538)
    | ~ c_Fun_Oinj__on(U_10533,U_10534,U_10535,hAPP(c_Set_Oimage(U_10536,U_10533,U_10537),U_10538)) ),
    inference(clausify,[status(thm)],[f_2845_2]) ).

fof(f_2846_1,plain,
    ! [V_v_2,V_w_2,T_b] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = c_Groups_Oone__class_Oone(T_b)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) )
        & ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = hAPP(hAPP(c_HOL_OLet(T_b,T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_b),c_Groups_Otimes__class_Otimes(T_b)),hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)))),c_COMBI(T_b)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) )
      | ~ class_Int_Onumber__ring(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_power__number__of__odd__number__of]) ).

fof(f_2846_2,plain,
    ! [U_10542,U_10541,U_10540] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_10540),hAPP(c_Int_Onumber__class_Onumber__of(U_10540),U_10542)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10541))) = c_Groups_Oone__class_Oone(U_10540)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10541))) )
        & ( hAPP(hAPP(c_Power_Opower__class_Opower(U_10540),hAPP(c_Int_Onumber__class_Onumber__of(U_10540),U_10542)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10541))) = hAPP(hAPP(c_HOL_OLet(U_10540,U_10540),hAPP(hAPP(c_Power_Opower__class_Opower(U_10540),hAPP(c_Int_Onumber__class_Onumber__of(U_10540),U_10542)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10541))),hAPP(hAPP(c_COMBS(U_10540,U_10540,U_10540),hAPP(hAPP(c_COMBB(U_10540,tc_fun(U_10540,U_10540),U_10540),c_Groups_Otimes__class_Otimes(U_10540)),hAPP(c_Groups_Otimes__class_Otimes(U_10540),hAPP(c_Int_Onumber__class_Onumber__of(U_10540),U_10542)))),c_COMBI(U_10540)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10541))) ) )
      | ~ class_Int_Onumber__ring(U_10540) ),
    inference(variable_rename,[status(thm)],[f_2846_1]) ).

cnf(f_2846_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_10540),hAPP(c_Int_Onumber__class_Onumber__of(U_10540),U_10542)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10541))) = hAPP(hAPP(c_HOL_OLet(U_10540,U_10540),hAPP(hAPP(c_Power_Opower__class_Opower(U_10540),hAPP(c_Int_Onumber__class_Onumber__of(U_10540),U_10542)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10541))),hAPP(hAPP(c_COMBS(U_10540,U_10540,U_10540),hAPP(hAPP(c_COMBB(U_10540,tc_fun(U_10540,U_10540),U_10540),c_Groups_Otimes__class_Otimes(U_10540)),hAPP(c_Groups_Otimes__class_Otimes(U_10540),hAPP(c_Int_Onumber__class_Onumber__of(U_10540),U_10542)))),c_COMBI(U_10540)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10541)))
    | ~ class_Int_Onumber__ring(U_10540) ),
    inference(clausify,[status(thm)],[f_2846_2]) ).

cnf(f_2846_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_10540),hAPP(c_Int_Onumber__class_Onumber__of(U_10540),U_10542)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_10541))) = c_Groups_Oone__class_Oone(U_10540)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10541)))
    | ~ class_Int_Onumber__ring(U_10540) ),
    inference(clausify,[status(thm)],[f_2846_2]) ).

fof(f_2847_1,plain,
    ! [V_a,V_b] :
      ( ( ( c_Divides_OnegDivAlg(V_a,V_b) = hAPP(c_Divides_Oadjust(V_b),c_Divides_OnegDivAlg(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b))) )
        & ( c_Divides_OnegDivAlg(V_a,V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) ),
    inference(fof_nnf,[status(thm)],[fact_negDivAlg__eqn]) ).

fof(f_2847_2,plain,
    ! [U_10544,U_10543] :
      ( ( ( c_Divides_OnegDivAlg(U_10544,U_10543) = hAPP(c_Divides_Oadjust(U_10543),c_Divides_OnegDivAlg(U_10544,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_10543)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10544),U_10543))) )
        & ( c_Divides_OnegDivAlg(U_10544,U_10543) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10544),U_10543))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10544),U_10543))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10543)) ),
    inference(variable_rename,[status(thm)],[f_2847_1]) ).

cnf(f_2847_3,plain,
    ( c_Divides_OnegDivAlg(U_10544,U_10543) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10544),U_10543))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10544),U_10543)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10543)) ),
    inference(clausify,[status(thm)],[f_2847_2]) ).

cnf(f_2847_4,plain,
    ( c_Divides_OnegDivAlg(U_10544,U_10543) = hAPP(c_Divides_Oadjust(U_10543),c_Divides_OnegDivAlg(U_10544,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_10543)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10544),U_10543)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10543)) ),
    inference(clausify,[status(thm)],[f_2847_2]) ).

fof(f_2848_1,plain,
    ! [V_w,V_v] :
      ( ( ( c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))) )
        & ( c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) ),
    inference(fof_nnf,[status(thm)],[fact_negDivAlg__eqn__number__of]) ).

fof(f_2848_2,plain,
    ! [U_10546,U_10545] :
      ( ( ( c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10546),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10545)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10545)),c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10546),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10545))))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10546)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10545)))) )
        & ( c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10546),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10545)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10546)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10545)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10546)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10545)))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10545))) ),
    inference(variable_rename,[status(thm)],[f_2848_1]) ).

cnf(f_2848_3,plain,
    ( c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10546),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10545)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10546)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10545)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10546)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10545))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10545))) ),
    inference(clausify,[status(thm)],[f_2848_2]) ).

cnf(f_2848_4,plain,
    ( c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10546),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10545)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10545)),c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10546),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10545))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10546)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10545))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10545))) ),
    inference(clausify,[status(thm)],[f_2848_2]) ).

fof(f_2849_1,plain,
    ! [V_v_2,V_v_H_2] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_v_H_2)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls)) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls)) ) ),
    inference(fof_nnf,[status(thm)],[fact_diff__nat__number__of]) ).

fof(f_2849_2,plain,
    ! [U_10548,U_10547] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10548)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10547)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10548),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10547)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10547),c_Int_OPls)) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10548)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10547)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10548)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10547),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[f_2849_1]) ).

fof(f_2849_3,plain,
    ( ! [U_10552,U_10550] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10552)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10550)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10552),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10550)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10550),c_Int_OPls)) )
    & ! [U_10551,U_10549] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10551)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10549)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10551)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10549),c_Int_OPls)) ) ),
    inference(miniscope,[status(thm)],[f_2849_2]) ).

cnf(f_2849_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10551)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10549)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10551)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10549),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_2849_3]) ).

cnf(f_2849_5,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10552)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10550)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10552),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10550)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10550),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_2849_3]) ).

fof(f_2850_1,plain,
    ! [V_a_2,V_b_2] :
      ( ( ( ( c_Nitpick_Onorm__frac(V_a_2,V_b_2) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,V_a_2),V_b_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b_2)))
            | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
            | V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
          & ( c_Nitpick_Onorm__frac(V_a_2,V_b_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
            | ( V_b_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
              & V_a_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) )
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( c_Nitpick_Onorm__frac(V_a_2,V_b_2) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(fof_nnf,[status(thm)],[fact_norm__frac_Osimps]) ).

fof(f_2850_2,plain,
    ! [U_10554,U_10553] :
      ( ( ( ( c_Nitpick_Onorm__frac(U_10554,U_10553) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,U_10554),U_10553)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10554))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10553)))
            | U_10553 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
            | U_10554 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
          & ( c_Nitpick_Onorm__frac(U_10554,U_10553) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
            | ( U_10553 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
              & U_10554 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) )
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10553),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( c_Nitpick_Onorm__frac(U_10554,U_10553) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10554),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10553))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10553),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(variable_rename,[status(thm)],[f_2850_1]) ).

fof(f_2850_3,plain,
    ( ! [U_10558,U_10556] :
        ( ( ( c_Nitpick_Onorm__frac(U_10558,U_10556) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,U_10558),U_10556)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10558))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10556)))
            | U_10556 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
            | U_10558 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
          & ( c_Nitpick_Onorm__frac(U_10558,U_10556) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
            | ( U_10556 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
              & U_10558 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) )
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10556),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_10557,U_10555] :
        ( c_Nitpick_Onorm__frac(U_10557,U_10555) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10557),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10555))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10555),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(miniscope,[status(thm)],[f_2850_2]) ).

cnf(f_2850_4,plain,
    ( c_Nitpick_Onorm__frac(U_10557,U_10555) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10557),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10555))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10555),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2850_3]) ).

cnf(f_2850_5,plain,
    ( U_10558 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Nitpick_Onorm__frac(U_10558,U_10556) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10556),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2850_3]) ).

cnf(f_2850_6,plain,
    ( U_10556 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Nitpick_Onorm__frac(U_10558,U_10556) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10556),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2850_3]) ).

cnf(f_2850_7,plain,
    ( c_Nitpick_Onorm__frac(U_10558,U_10556) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,U_10558),U_10556)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10558))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10556)))
    | U_10556 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_10558 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10556),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2850_3]) ).

fof(f_2851_1,plain,
    ! [V_n_2,V_v_2,V_f_2,V_a_2,T_b] : c_Nat_Onat_Onat__case(T_b,V_a_2,V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),V_n_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_b),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),tc_Int_Oint),c_If(T_b)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(T_b,V_a_2,V_f_2,V_n_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),V_f_2),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),V_n_2)))),
    inference(fof_nnf,[status(thm)],[fact_nat__case__add__eq__if]) ).

fof(f_2851_2,plain,
    ! [U_10563,U_10562,U_10561,U_10560,U_10559] : c_Nat_Onat_Onat__case(U_10559,U_10560,U_10561,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10562)),U_10563)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_10559),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10562))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_10559,U_10559),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_10559,tc_fun(U_10559,U_10559)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10559,tc_fun(U_10559,U_10559)),tc_Int_Oint),c_If(U_10559)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(U_10559,U_10560,U_10561,U_10563))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10559,tc_Int_Oint),U_10561),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),U_10563)))),
    inference(variable_rename,[status(thm)],[f_2851_1]) ).

cnf(f_2851_3,plain,
    c_Nat_Onat_Onat__case(U_10559,U_10560,U_10561,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10562)),U_10563)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_10559),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10562))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_10559,U_10559),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_10559,tc_fun(U_10559,U_10559)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10559,tc_fun(U_10559,U_10559)),tc_Int_Oint),c_If(U_10559)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(U_10559,U_10560,U_10561,U_10563))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10559,tc_Int_Oint),U_10561),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),U_10563)))),
    inference(clausify,[status(thm)],[f_2851_2]) ).

fof(f_2852_1,plain,
    ! [V_w] :
      ( ( ( c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) )
        & ( c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) ),
    inference(fof_nnf,[status(thm)],[fact_posDivAlg__eqn__1__number__of]) ).

fof(f_2852_2,plain,
    ! [U_10564] :
      ( ( ( c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10564)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10564)),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10564))))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10564))) )
        & ( c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10564)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10564))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10564))) ),
    inference(variable_rename,[status(thm)],[f_2852_1]) ).

cnf(f_2852_3,plain,
    ( c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10564)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10564)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10564))) ),
    inference(clausify,[status(thm)],[f_2852_2]) ).

cnf(f_2852_4,plain,
    ( c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10564)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10564)),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10564))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10564)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10564))) ),
    inference(clausify,[status(thm)],[f_2852_2]) ).

fof(f_2853_1,plain,
    ! [V_b,V_a] :
      ( ( c_Divides_OposDivAlg(V_a,V_b) = hAPP(c_Divides_Oadjust(V_b),c_Divides_OposDivAlg(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) )
      & ( c_Divides_OposDivAlg(V_a,V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_posDivAlg_Osimps]) ).

fof(f_2853_2,plain,
    ! [U_10566,U_10565] :
      ( ( c_Divides_OposDivAlg(U_10565,U_10566) = hAPP(c_Divides_Oadjust(U_10566),c_Divides_OposDivAlg(U_10565,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_10566)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10566),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10565),U_10566)) )
      & ( c_Divides_OposDivAlg(U_10565,U_10566) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10565)
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10566),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10565),U_10566)) ) ) ),
    inference(variable_rename,[status(thm)],[f_2853_1]) ).

fof(f_2853_3,plain,
    ( ! [U_10570,U_10568] :
        ( c_Divides_OposDivAlg(U_10568,U_10570) = hAPP(c_Divides_Oadjust(U_10570),c_Divides_OposDivAlg(U_10568,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_10570)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10570),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10568),U_10570)) )
    & ! [U_10569,U_10567] :
        ( c_Divides_OposDivAlg(U_10567,U_10569) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10567)
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10569),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10567),U_10569)) ) ) ),
    inference(miniscope,[status(thm)],[f_2853_2]) ).

cnf(f_2853_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10567),U_10569))
    | c_Divides_OposDivAlg(U_10567,U_10569) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10567) ),
    inference(clausify,[status(thm)],[f_2853_3]) ).

cnf(f_2853_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10569),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | c_Divides_OposDivAlg(U_10567,U_10569) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10567) ),
    inference(clausify,[status(thm)],[f_2853_3]) ).

cnf(f_2853_6,plain,
    ( c_Divides_OposDivAlg(U_10568,U_10570) = hAPP(c_Divides_Oadjust(U_10570),c_Divides_OposDivAlg(U_10568,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_10570)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_10570),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10568),U_10570)) ),
    inference(clausify,[status(thm)],[f_2853_3]) ).

fof(f_2854_1,plain,
    ! [T_c,T_b,V_A_2,V_y_2,V_x_2,V_B_2] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2))
      | ( ~ hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
        & ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_sup2CI]) ).

fof(f_2854_2,plain,
    ! [U_10576,U_10575,U_10574,U_10573,U_10572,U_10571] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10575,tc_fun(U_10576,tc_HOL_Obool))),U_10574),U_10571),U_10572),U_10573))
      | ( ~ hBOOL(hAPP(hAPP(U_10574,U_10572),U_10573))
        & ~ hBOOL(hAPP(hAPP(U_10571,U_10572),U_10573)) ) ),
    inference(variable_rename,[status(thm)],[f_2854_1]) ).

cnf(f_2854_3,plain,
    ( ~ hBOOL(hAPP(hAPP(U_10571,U_10572),U_10573))
    | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10575,tc_fun(U_10576,tc_HOL_Obool))),U_10574),U_10571),U_10572),U_10573)) ),
    inference(clausify,[status(thm)],[f_2854_2]) ).

cnf(f_2854_4,plain,
    ( ~ hBOOL(hAPP(hAPP(U_10574,U_10572),U_10573))
    | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10575,tc_fun(U_10576,tc_HOL_Obool))),U_10574),U_10571),U_10572),U_10573)) ),
    inference(clausify,[status(thm)],[f_2854_2]) ).

fof(f_2855_1,plain,
    ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
      | hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_sup2E]) ).

fof(f_2855_2,plain,
    ! [U_10582,U_10581,U_10580,U_10579,U_10578,U_10577] :
      ( hBOOL(hAPP(hAPP(U_10580,U_10581),U_10582))
      | hBOOL(hAPP(hAPP(U_10579,U_10581),U_10582))
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10577,tc_fun(U_10578,tc_HOL_Obool))),U_10579),U_10580),U_10581),U_10582)) ),
    inference(variable_rename,[status(thm)],[f_2855_1]) ).

fof(f_2855_3,plain,
    ! [U_10582,U_10581,U_10580,U_10579] :
      ( ! [U_10578,U_10577] : ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10577,tc_fun(U_10578,tc_HOL_Obool))),U_10579),U_10580),U_10581),U_10582))
      | hBOOL(hAPP(hAPP(U_10580,U_10581),U_10582))
      | hBOOL(hAPP(hAPP(U_10579,U_10581),U_10582)) ),
    inference(miniscope,[status(thm)],[f_2855_2]) ).

cnf(f_2855_4,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10577,tc_fun(U_10578,tc_HOL_Obool))),U_10579),U_10580),U_10581),U_10582))
    | hBOOL(hAPP(hAPP(U_10580,U_10581),U_10582))
    | hBOOL(hAPP(hAPP(U_10579,U_10581),U_10582)) ),
    inference(clausify,[status(thm)],[f_2855_3]) ).

fof(f_2856_1,plain,
    ! [T_c,T_b,V_B_2,V_y_2,V_x_2,V_A_2] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2))
      | ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
      | ~ hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_inf2I]) ).

fof(f_2856_2,plain,
    ! [U_10588,U_10587,U_10586,U_10585,U_10584,U_10583] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10587,tc_fun(U_10588,tc_HOL_Obool))),U_10583),U_10586),U_10584),U_10585))
      | ~ hBOOL(hAPP(hAPP(U_10586,U_10584),U_10585))
      | ~ hBOOL(hAPP(hAPP(U_10583,U_10584),U_10585)) ),
    inference(variable_rename,[status(thm)],[f_2856_1]) ).

cnf(f_2856_3,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10587,tc_fun(U_10588,tc_HOL_Obool))),U_10583),U_10586),U_10584),U_10585))
    | ~ hBOOL(hAPP(hAPP(U_10586,U_10584),U_10585))
    | ~ hBOOL(hAPP(hAPP(U_10583,U_10584),U_10585)) ),
    inference(clausify,[status(thm)],[f_2856_2]) ).

fof(f_2857_1,plain,
    ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
      ( ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
        & hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) )
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_inf2E]) ).

fof(f_2857_2,plain,
    ! [U_10594,U_10593,U_10592,U_10591,U_10590,U_10589] :
      ( ( hBOOL(hAPP(hAPP(U_10592,U_10593),U_10594))
        & hBOOL(hAPP(hAPP(U_10591,U_10593),U_10594)) )
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10589,tc_fun(U_10590,tc_HOL_Obool))),U_10591),U_10592),U_10593),U_10594)) ),
    inference(variable_rename,[status(thm)],[f_2857_1]) ).

fof(f_2857_3,plain,
    ! [U_10594,U_10593,U_10592,U_10591] :
      ( ! [U_10590,U_10589] : ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10589,tc_fun(U_10590,tc_HOL_Obool))),U_10591),U_10592),U_10593),U_10594))
      | ( hBOOL(hAPP(hAPP(U_10592,U_10593),U_10594))
        & hBOOL(hAPP(hAPP(U_10591,U_10593),U_10594)) ) ),
    inference(miniscope,[status(thm)],[f_2857_2]) ).

cnf(f_2857_4,plain,
    ( hBOOL(hAPP(hAPP(U_10591,U_10593),U_10594))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10589,tc_fun(U_10590,tc_HOL_Obool))),U_10591),U_10592),U_10593),U_10594)) ),
    inference(clausify,[status(thm)],[f_2857_3]) ).

cnf(f_2857_5,plain,
    ( hBOOL(hAPP(hAPP(U_10592,U_10593),U_10594))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10589,tc_fun(U_10590,tc_HOL_Obool))),U_10591),U_10592),U_10593),U_10594)) ),
    inference(clausify,[status(thm)],[f_2857_3]) ).

fof(f_2858_1,plain,
    ! [V_y_2,V_x_2,T_c,T_b] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_x_2),V_y_2)),
    inference(fof_nnf,[status(thm)],[fact_bot2E]) ).

fof(f_2858_2,plain,
    ! [U_10598,U_10597,U_10596,U_10595] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_10595,tc_fun(U_10596,tc_HOL_Obool))),U_10597),U_10598)),
    inference(variable_rename,[status(thm)],[f_2858_1]) ).

cnf(f_2858_3,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_10595,tc_fun(U_10596,tc_HOL_Obool))),U_10597),U_10598)),
    inference(clausify,[status(thm)],[f_2858_2]) ).

fof(f_2859_1,plain,
    ! [V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2))
        | ! [B_x] :
            ( ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2))
            | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
      & ( ? [B_x] :
            ( hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_SUP2__iff]) ).

fof(f_2859_2,plain,
    ! [U_10607,U_10606,U_10605,U_10604,U_10603,U_10602,U_10601] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10601,tc_fun(U_10602,tc_fun(U_10603,tc_HOL_Obool))),U_10604),U_10605),U_10606),U_10607))
        | ! [U_10600] :
            ( ~ hBOOL(hAPP(hAPP(hAPP(U_10605,U_10600),U_10606),U_10607))
            | ~ hBOOL(hAPP(hAPP(c_member(U_10601),U_10600),U_10604)) ) )
      & ( ? [U_10599] :
            ( hBOOL(hAPP(hAPP(hAPP(U_10605,U_10599),U_10606),U_10607))
            & hBOOL(hAPP(hAPP(c_member(U_10601),U_10599),U_10604)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10601,tc_fun(U_10602,tc_fun(U_10603,tc_HOL_Obool))),U_10604),U_10605),U_10606),U_10607)) ) ),
    inference(variable_rename,[status(thm)],[f_2859_1]) ).

fof(f_2859_3,plain,
    ( ! [U_10621,U_10619,U_10617,U_10615,U_10613,U_10611,U_10609] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10609,tc_fun(U_10611,tc_fun(U_10613,tc_HOL_Obool))),U_10615),U_10617),U_10619),U_10621))
        | ! [U_10600] :
            ( ~ hBOOL(hAPP(hAPP(hAPP(U_10617,U_10600),U_10619),U_10621))
            | ~ hBOOL(hAPP(hAPP(c_member(U_10609),U_10600),U_10615)) ) )
    & ! [U_10620,U_10618,U_10616,U_10614,U_10612,U_10610,U_10608] :
        ( ? [U_10599] :
            ( hBOOL(hAPP(hAPP(hAPP(U_10616,U_10599),U_10618),U_10620))
            & hBOOL(hAPP(hAPP(c_member(U_10608),U_10599),U_10614)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10608,tc_fun(U_10610,tc_fun(U_10612,tc_HOL_Obool))),U_10614),U_10616),U_10618),U_10620)) ) ),
    inference(miniscope,[status(thm)],[f_2859_2]) ).

fof(f_2859_4,plain,
    ( ! [U_10621,U_10619,U_10617,U_10615,U_10613,U_10611,U_10609] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10609,tc_fun(U_10611,tc_fun(U_10613,tc_HOL_Obool))),U_10615),U_10617),U_10619),U_10621))
        | ! [U_10600] :
            ( ~ hBOOL(hAPP(hAPP(hAPP(U_10617,U_10600),U_10619),U_10621))
            | ~ hBOOL(hAPP(hAPP(c_member(U_10609),U_10600),U_10615)) ) )
    & ! [U_10620,U_10618,U_10616,U_10614,U_10612,U_10610,U_10608] :
        ( ( hBOOL(hAPP(hAPP(hAPP(U_10616,sK244(U_10620,U_10618,U_10616,U_10614,U_10612,U_10610,U_10608)),U_10618),U_10620))
          & hBOOL(hAPP(hAPP(c_member(U_10608),sK244(U_10620,U_10618,U_10616,U_10614,U_10612,U_10610,U_10608)),U_10614)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10608,tc_fun(U_10610,tc_fun(U_10612,tc_HOL_Obool))),U_10614),U_10616),U_10618),U_10620)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK244]),skolemize(U_10599,sK244(U_10620,U_10618,U_10616,U_10614,U_10612,U_10610,U_10608))],[f_2859_3]) ).

cnf(f_2859_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10608),sK244(U_10620,U_10618,U_10616,U_10614,U_10612,U_10610,U_10608)),U_10614))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10608,tc_fun(U_10610,tc_fun(U_10612,tc_HOL_Obool))),U_10614),U_10616),U_10618),U_10620)) ),
    inference(clausify,[status(thm)],[f_2859_4]) ).

cnf(f_2859_6,plain,
    ( hBOOL(hAPP(hAPP(hAPP(U_10616,sK244(U_10620,U_10618,U_10616,U_10614,U_10612,U_10610,U_10608)),U_10618),U_10620))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10608,tc_fun(U_10610,tc_fun(U_10612,tc_HOL_Obool))),U_10614),U_10616),U_10618),U_10620)) ),
    inference(clausify,[status(thm)],[f_2859_4]) ).

cnf(f_2859_7,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10609,tc_fun(U_10611,tc_fun(U_10613,tc_HOL_Obool))),U_10615),U_10617),U_10619),U_10621))
    | ~ hBOOL(hAPP(hAPP(hAPP(U_10617,U_10600),U_10619),U_10621))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10609),U_10600),U_10615)) ),
    inference(clausify,[status(thm)],[f_2859_4]) ).

fof(f_2860_1,plain,
    ! [V_b_2,V_B_2,V_A_2,T_c,T_b] :
      ( ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2))
        | ? [B_x] :
            ( ~ hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
      & ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2))
            | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_INF1__iff]) ).

fof(f_2860_2,plain,
    ! [U_10628,U_10627,U_10626,U_10625,U_10624] :
      ( ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10624,tc_fun(U_10625,tc_HOL_Obool)),U_10626),U_10627),U_10628))
        | ? [U_10623] :
            ( ~ hBOOL(hAPP(hAPP(U_10627,U_10623),U_10628))
            & hBOOL(hAPP(hAPP(c_member(U_10624),U_10623),U_10626)) ) )
      & ( ! [U_10622] :
            ( hBOOL(hAPP(hAPP(U_10627,U_10622),U_10628))
            | ~ hBOOL(hAPP(hAPP(c_member(U_10624),U_10622),U_10626)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10624,tc_fun(U_10625,tc_HOL_Obool)),U_10626),U_10627),U_10628)) ) ),
    inference(variable_rename,[status(thm)],[f_2860_1]) ).

fof(f_2860_3,plain,
    ( ! [U_10638,U_10636,U_10634,U_10632,U_10630] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10630,tc_fun(U_10632,tc_HOL_Obool)),U_10634),U_10636),U_10638))
        | ? [U_10623] :
            ( ~ hBOOL(hAPP(hAPP(U_10636,U_10623),U_10638))
            & hBOOL(hAPP(hAPP(c_member(U_10630),U_10623),U_10634)) ) )
    & ! [U_10637,U_10635,U_10633,U_10631,U_10629] :
        ( ! [U_10622] :
            ( hBOOL(hAPP(hAPP(U_10635,U_10622),U_10637))
            | ~ hBOOL(hAPP(hAPP(c_member(U_10629),U_10622),U_10633)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10629,tc_fun(U_10631,tc_HOL_Obool)),U_10633),U_10635),U_10637)) ) ),
    inference(miniscope,[status(thm)],[f_2860_2]) ).

fof(f_2860_4,plain,
    ( ! [U_10638,U_10636,U_10634,U_10632,U_10630] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10630,tc_fun(U_10632,tc_HOL_Obool)),U_10634),U_10636),U_10638))
        | ( ~ hBOOL(hAPP(hAPP(U_10636,sK245(U_10638,U_10636,U_10634,U_10632,U_10630)),U_10638))
          & hBOOL(hAPP(hAPP(c_member(U_10630),sK245(U_10638,U_10636,U_10634,U_10632,U_10630)),U_10634)) ) )
    & ! [U_10637,U_10635,U_10633,U_10631,U_10629] :
        ( ! [U_10622] :
            ( hBOOL(hAPP(hAPP(U_10635,U_10622),U_10637))
            | ~ hBOOL(hAPP(hAPP(c_member(U_10629),U_10622),U_10633)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10629,tc_fun(U_10631,tc_HOL_Obool)),U_10633),U_10635),U_10637)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK245]),skolemize(U_10623,sK245(U_10638,U_10636,U_10634,U_10632,U_10630))],[f_2860_3]) ).

cnf(f_2860_5,plain,
    ( hBOOL(hAPP(hAPP(U_10635,U_10622),U_10637))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10629),U_10622),U_10633))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10629,tc_fun(U_10631,tc_HOL_Obool)),U_10633),U_10635),U_10637)) ),
    inference(clausify,[status(thm)],[f_2860_4]) ).

cnf(f_2860_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10630),sK245(U_10638,U_10636,U_10634,U_10632,U_10630)),U_10634))
    | hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10630,tc_fun(U_10632,tc_HOL_Obool)),U_10634),U_10636),U_10638)) ),
    inference(clausify,[status(thm)],[f_2860_4]) ).

cnf(f_2860_7,plain,
    ( ~ hBOOL(hAPP(hAPP(U_10636,sK245(U_10638,U_10636,U_10634,U_10632,U_10630)),U_10638))
    | hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10630,tc_fun(U_10632,tc_HOL_Obool)),U_10634),U_10636),U_10638)) ),
    inference(clausify,[status(thm)],[f_2860_4]) ).

fof(f_2861_1,plain,
    ! [V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2))
        | ? [B_x] :
            ( ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
      & ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2))
            | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_INF2__iff]) ).

fof(f_2861_2,plain,
    ! [U_10647,U_10646,U_10645,U_10644,U_10643,U_10642,U_10641] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10641,tc_fun(U_10642,tc_fun(U_10643,tc_HOL_Obool))),U_10644),U_10645),U_10646),U_10647))
        | ? [U_10640] :
            ( ~ hBOOL(hAPP(hAPP(hAPP(U_10645,U_10640),U_10646),U_10647))
            & hBOOL(hAPP(hAPP(c_member(U_10641),U_10640),U_10644)) ) )
      & ( ! [U_10639] :
            ( hBOOL(hAPP(hAPP(hAPP(U_10645,U_10639),U_10646),U_10647))
            | ~ hBOOL(hAPP(hAPP(c_member(U_10641),U_10639),U_10644)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10641,tc_fun(U_10642,tc_fun(U_10643,tc_HOL_Obool))),U_10644),U_10645),U_10646),U_10647)) ) ),
    inference(variable_rename,[status(thm)],[f_2861_1]) ).

fof(f_2861_3,plain,
    ( ! [U_10661,U_10659,U_10657,U_10655,U_10653,U_10651,U_10649] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10649,tc_fun(U_10651,tc_fun(U_10653,tc_HOL_Obool))),U_10655),U_10657),U_10659),U_10661))
        | ? [U_10640] :
            ( ~ hBOOL(hAPP(hAPP(hAPP(U_10657,U_10640),U_10659),U_10661))
            & hBOOL(hAPP(hAPP(c_member(U_10649),U_10640),U_10655)) ) )
    & ! [U_10660,U_10658,U_10656,U_10654,U_10652,U_10650,U_10648] :
        ( ! [U_10639] :
            ( hBOOL(hAPP(hAPP(hAPP(U_10656,U_10639),U_10658),U_10660))
            | ~ hBOOL(hAPP(hAPP(c_member(U_10648),U_10639),U_10654)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10648,tc_fun(U_10650,tc_fun(U_10652,tc_HOL_Obool))),U_10654),U_10656),U_10658),U_10660)) ) ),
    inference(miniscope,[status(thm)],[f_2861_2]) ).

fof(f_2861_4,plain,
    ( ! [U_10661,U_10659,U_10657,U_10655,U_10653,U_10651,U_10649] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10649,tc_fun(U_10651,tc_fun(U_10653,tc_HOL_Obool))),U_10655),U_10657),U_10659),U_10661))
        | ( ~ hBOOL(hAPP(hAPP(hAPP(U_10657,sK246(U_10661,U_10659,U_10657,U_10655,U_10653,U_10651,U_10649)),U_10659),U_10661))
          & hBOOL(hAPP(hAPP(c_member(U_10649),sK246(U_10661,U_10659,U_10657,U_10655,U_10653,U_10651,U_10649)),U_10655)) ) )
    & ! [U_10660,U_10658,U_10656,U_10654,U_10652,U_10650,U_10648] :
        ( ! [U_10639] :
            ( hBOOL(hAPP(hAPP(hAPP(U_10656,U_10639),U_10658),U_10660))
            | ~ hBOOL(hAPP(hAPP(c_member(U_10648),U_10639),U_10654)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10648,tc_fun(U_10650,tc_fun(U_10652,tc_HOL_Obool))),U_10654),U_10656),U_10658),U_10660)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK246]),skolemize(U_10640,sK246(U_10661,U_10659,U_10657,U_10655,U_10653,U_10651,U_10649))],[f_2861_3]) ).

cnf(f_2861_5,plain,
    ( hBOOL(hAPP(hAPP(hAPP(U_10656,U_10639),U_10658),U_10660))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10648),U_10639),U_10654))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10648,tc_fun(U_10650,tc_fun(U_10652,tc_HOL_Obool))),U_10654),U_10656),U_10658),U_10660)) ),
    inference(clausify,[status(thm)],[f_2861_4]) ).

cnf(f_2861_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10649),sK246(U_10661,U_10659,U_10657,U_10655,U_10653,U_10651,U_10649)),U_10655))
    | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10649,tc_fun(U_10651,tc_fun(U_10653,tc_HOL_Obool))),U_10655),U_10657),U_10659),U_10661)) ),
    inference(clausify,[status(thm)],[f_2861_4]) ).

cnf(f_2861_7,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(U_10657,sK246(U_10661,U_10659,U_10657,U_10655,U_10653,U_10651,U_10649)),U_10659),U_10661))
    | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10649,tc_fun(U_10651,tc_fun(U_10653,tc_HOL_Obool))),U_10655),U_10657),U_10659),U_10661)) ),
    inference(clausify,[status(thm)],[f_2861_4]) ).

fof(f_2862_1,plain,
    ! [V_y_2,V_x_2,V_Q_2,V_P_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2))
      | ~ hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_P_2),V_Q_2)) ),
    inference(fof_nnf,[status(thm)],[fact_predicate2D]) ).

fof(f_2862_2,plain,
    ! [U_10667,U_10666,U_10665,U_10664,U_10663,U_10662] :
      ( hBOOL(hAPP(hAPP(U_10665,U_10666),U_10667))
      | ~ hBOOL(hAPP(hAPP(U_10664,U_10666),U_10667))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10662,tc_fun(U_10663,tc_HOL_Obool))),U_10664),U_10665)) ),
    inference(variable_rename,[status(thm)],[f_2862_1]) ).

fof(f_2862_3,plain,
    ! [U_10667,U_10666,U_10665,U_10664] :
      ( ! [U_10663,U_10662] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10662,tc_fun(U_10663,tc_HOL_Obool))),U_10664),U_10665))
      | hBOOL(hAPP(hAPP(U_10665,U_10666),U_10667))
      | ~ hBOOL(hAPP(hAPP(U_10664,U_10666),U_10667)) ),
    inference(miniscope,[status(thm)],[f_2862_2]) ).

cnf(f_2862_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10662,tc_fun(U_10663,tc_HOL_Obool))),U_10664),U_10665))
    | hBOOL(hAPP(hAPP(U_10665,U_10666),U_10667))
    | ~ hBOOL(hAPP(hAPP(U_10664,U_10666),U_10667)) ),
    inference(clausify,[status(thm)],[f_2862_3]) ).

fof(f_2863_1,plain,
    ! [V_Q_2,T_c,T_b,V_y_2,V_x_2,V_P_2] :
      ( hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_P_2),V_Q_2))
      | ~ hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_rev__predicate2D]) ).

fof(f_2863_2,plain,
    ! [U_10673,U_10672,U_10671,U_10670,U_10669,U_10668] :
      ( hBOOL(hAPP(hAPP(U_10673,U_10669),U_10670))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10671,tc_fun(U_10672,tc_HOL_Obool))),U_10668),U_10673))
      | ~ hBOOL(hAPP(hAPP(U_10668,U_10669),U_10670)) ),
    inference(variable_rename,[status(thm)],[f_2863_1]) ).

cnf(f_2863_3,plain,
    ( hBOOL(hAPP(hAPP(U_10673,U_10669),U_10670))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10671,tc_fun(U_10672,tc_HOL_Obool))),U_10668),U_10673))
    | ~ hBOOL(hAPP(hAPP(U_10668,U_10669),U_10670)) ),
    inference(clausify,[status(thm)],[f_2863_2]) ).

fof(f_2864_1,plain,
    ! [V_B_2,T_b,V_A_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_A_2),V_B_2))
      | V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) ),
    inference(fof_nnf,[status(thm)],[fact_less__by__empty]) ).

fof(f_2864_2,plain,
    ! [U_10676,U_10675,U_10674] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_10675,U_10675),tc_HOL_Obool)),U_10674),U_10676))
      | U_10674 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_10675,U_10675),tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_2864_1]) ).

cnf(f_2864_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_10675,U_10675),tc_HOL_Obool)),U_10674),U_10676))
    | U_10674 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_10675,U_10675),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2864_2]) ).

fof(f_2865_1,plain,
    ! [V_A_2,T_c,T_b,V_y_2,V_x_2,V_B_2] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2))
      | ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_sup2I2]) ).

fof(f_2865_2,plain,
    ! [U_10682,U_10681,U_10680,U_10679,U_10678,U_10677] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10680,tc_fun(U_10681,tc_HOL_Obool))),U_10682),U_10677),U_10678),U_10679))
      | ~ hBOOL(hAPP(hAPP(U_10677,U_10678),U_10679)) ),
    inference(variable_rename,[status(thm)],[f_2865_1]) ).

cnf(f_2865_3,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10680,tc_fun(U_10681,tc_HOL_Obool))),U_10682),U_10677),U_10678),U_10679))
    | ~ hBOOL(hAPP(hAPP(U_10677,U_10678),U_10679)) ),
    inference(clausify,[status(thm)],[f_2865_2]) ).

fof(f_2866_1,plain,
    ! [V_B_2,T_c,T_b,V_y_2,V_x_2,V_A_2] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2))
      | ~ hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_sup2I1]) ).

fof(f_2866_2,plain,
    ! [U_10688,U_10687,U_10686,U_10685,U_10684,U_10683] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10686,tc_fun(U_10687,tc_HOL_Obool))),U_10683),U_10688),U_10684),U_10685))
      | ~ hBOOL(hAPP(hAPP(U_10683,U_10684),U_10685)) ),
    inference(variable_rename,[status(thm)],[f_2866_1]) ).

cnf(f_2866_3,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10686,tc_fun(U_10687,tc_HOL_Obool))),U_10683),U_10688),U_10684),U_10685))
    | ~ hBOOL(hAPP(hAPP(U_10683,U_10684),U_10685)) ),
    inference(clausify,[status(thm)],[f_2866_2]) ).

fof(f_2867_1,plain,
    ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_inf2D1]) ).

fof(f_2867_2,plain,
    ! [U_10694,U_10693,U_10692,U_10691,U_10690,U_10689] :
      ( hBOOL(hAPP(hAPP(U_10691,U_10693),U_10694))
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10689,tc_fun(U_10690,tc_HOL_Obool))),U_10691),U_10692),U_10693),U_10694)) ),
    inference(variable_rename,[status(thm)],[f_2867_1]) ).

fof(f_2867_3,plain,
    ! [U_10694,U_10693,U_10692,U_10691] :
      ( ! [U_10690,U_10689] : ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10689,tc_fun(U_10690,tc_HOL_Obool))),U_10691),U_10692),U_10693),U_10694))
      | hBOOL(hAPP(hAPP(U_10691,U_10693),U_10694)) ),
    inference(miniscope,[status(thm)],[f_2867_2]) ).

cnf(f_2867_4,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10689,tc_fun(U_10690,tc_HOL_Obool))),U_10691),U_10692),U_10693),U_10694))
    | hBOOL(hAPP(hAPP(U_10691,U_10693),U_10694)) ),
    inference(clausify,[status(thm)],[f_2867_3]) ).

fof(f_2868_1,plain,
    ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_inf2D2]) ).

fof(f_2868_2,plain,
    ! [U_10700,U_10699,U_10698,U_10697,U_10696,U_10695] :
      ( hBOOL(hAPP(hAPP(U_10698,U_10699),U_10700))
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10695,tc_fun(U_10696,tc_HOL_Obool))),U_10697),U_10698),U_10699),U_10700)) ),
    inference(variable_rename,[status(thm)],[f_2868_1]) ).

fof(f_2868_3,plain,
    ! [U_10700,U_10699,U_10698] :
      ( ! [U_10697,U_10696,U_10695] : ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10695,tc_fun(U_10696,tc_HOL_Obool))),U_10697),U_10698),U_10699),U_10700))
      | hBOOL(hAPP(hAPP(U_10698,U_10699),U_10700)) ),
    inference(miniscope,[status(thm)],[f_2868_2]) ).

cnf(f_2868_4,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10695,tc_fun(U_10696,tc_HOL_Obool))),U_10697),U_10698),U_10699),U_10700))
    | hBOOL(hAPP(hAPP(U_10698,U_10699),U_10700)) ),
    inference(clausify,[status(thm)],[f_2868_3]) ).

fof(f_2869_1,plain,
    ! [V_f2_2,V_f1_2,T_b] : c_Nat_Onat_Onat__case(T_b,V_f1_2,V_f2_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_f1_2,
    inference(fof_nnf,[status(thm)],[fact_nat__case__0]) ).

fof(f_2869_2,plain,
    ! [U_10703,U_10702,U_10701] : c_Nat_Onat_Onat__case(U_10701,U_10702,U_10703,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_10702,
    inference(variable_rename,[status(thm)],[f_2869_1]) ).

cnf(f_2869_3,plain,
    c_Nat_Onat_Onat__case(U_10701,U_10702,U_10703,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_10702,
    inference(clausify,[status(thm)],[f_2869_2]) ).

fof(f_2870_1,plain,
    ! [V_nat_2,V_f2_2,V_f1_2,T_b] : c_Nat_Onat_Onat__case(T_b,V_f1_2,V_f2_2,hAPP(c_Nat_OSuc,V_nat_2)) = hAPP(V_f2_2,V_nat_2),
    inference(fof_nnf,[status(thm)],[fact_nat__case__Suc]) ).

fof(f_2870_2,plain,
    ! [U_10707,U_10706,U_10705,U_10704] : c_Nat_Onat_Onat__case(U_10704,U_10705,U_10706,hAPP(c_Nat_OSuc,U_10707)) = hAPP(U_10706,U_10707),
    inference(variable_rename,[status(thm)],[f_2870_1]) ).

cnf(f_2870_3,plain,
    c_Nat_Onat_Onat__case(U_10704,U_10705,U_10706,hAPP(c_Nat_OSuc,U_10707)) = hAPP(U_10706,U_10707),
    inference(clausify,[status(thm)],[f_2870_2]) ).

fof(f_2871_1,plain,
    ! [V_b] : c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    inference(fof_nnf,[status(thm)],[fact_posDivAlg__0]) ).

fof(f_2871_2,plain,
    ! [U_10708] : c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_10708) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    inference(variable_rename,[status(thm)],[f_2871_1]) ).

cnf(f_2871_3,plain,
    c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_10708) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    inference(clausify,[status(thm)],[f_2871_2]) ).

fof(f_2872_1,plain,
    ! [V_m_2,V_n_2] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n_2),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n_2)),V_m_2),
    inference(fof_nnf,[status(thm)],[fact_max__Suc1]) ).

fof(f_2872_2,plain,
    ! [U_10710,U_10709] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10709)),U_10710) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_10709),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_10709)),U_10710),
    inference(variable_rename,[status(thm)],[f_2872_1]) ).

cnf(f_2872_3,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10709)),U_10710) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_10709),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_10709)),U_10710),
    inference(clausify,[status(thm)],[f_2872_2]) ).

fof(f_2873_1,plain,
    ! [V_n_2,V_m_2] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n_2),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),V_n_2)),V_m_2),
    inference(fof_nnf,[status(thm)],[fact_max__Suc2]) ).

fof(f_2873_2,plain,
    ! [U_10712,U_10711] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_10711),hAPP(c_Nat_OSuc,U_10712)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_10712),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),U_10712)),U_10711),
    inference(variable_rename,[status(thm)],[f_2873_1]) ).

cnf(f_2873_3,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_10711),hAPP(c_Nat_OSuc,U_10712)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_10712),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),U_10712)),U_10711),
    inference(clausify,[status(thm)],[f_2873_2]) ).

fof(f_2874_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2))
        | ~ hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) )
      & ( hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_less__eq__nat_Osimps_I2_J]) ).

fof(f_2874_2,plain,
    ! [U_10714,U_10713] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10713)),U_10714))
        | ~ hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10713),U_10714)) )
      & ( hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10713),U_10714))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10713)),U_10714)) ) ),
    inference(variable_rename,[status(thm)],[f_2874_1]) ).

fof(f_2874_3,plain,
    ( ! [U_10718,U_10716] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10716)),U_10718))
        | ~ hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10716),U_10718)) )
    & ! [U_10717,U_10715] :
        ( hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10715),U_10717))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10715)),U_10717)) ) ),
    inference(miniscope,[status(thm)],[f_2874_2]) ).

cnf(f_2874_4,plain,
    ( hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10715),U_10717))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10715)),U_10717)) ),
    inference(clausify,[status(thm)],[f_2874_3]) ).

cnf(f_2874_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10716)),U_10718))
    | ~ hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10716),U_10718)) ),
    inference(clausify,[status(thm)],[f_2874_3]) ).

fof(f_2875_1,plain,
    ! [V_n_2,V_m_2] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_COMBI(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2)),
    inference(fof_nnf,[status(thm)],[fact_diff__Suc]) ).

fof(f_2875_2,plain,
    ! [U_10720,U_10719] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10719),hAPP(c_Nat_OSuc,U_10720)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_COMBI(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10719),U_10720)),
    inference(variable_rename,[status(thm)],[f_2875_1]) ).

cnf(f_2875_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10719),hAPP(c_Nat_OSuc,U_10720)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_COMBI(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10719),U_10720)),
    inference(clausify,[status(thm)],[f_2875_2]) ).

fof(f_2876_1,plain,
    ! [V_m_2,V_n_2] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_n_2)),V_m_2),
    inference(fof_nnf,[status(thm)],[fact_min__Suc1]) ).

fof(f_2876_2,plain,
    ! [U_10722,U_10721] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10721)),U_10722) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_10721)),U_10722),
    inference(variable_rename,[status(thm)],[f_2876_1]) ).

cnf(f_2876_3,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_10721)),U_10722) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_10721)),U_10722),
    inference(clausify,[status(thm)],[f_2876_2]) ).

fof(f_2877_1,plain,
    ! [V_n_2,V_m_2] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Oord__class_Omin(tc_Nat_Onat)),V_n_2)),V_m_2),
    inference(fof_nnf,[status(thm)],[fact_min__Suc2]) ).

fof(f_2877_2,plain,
    ! [U_10724,U_10723] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_10723),hAPP(c_Nat_OSuc,U_10724)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Oord__class_Omin(tc_Nat_Onat)),U_10724)),U_10723),
    inference(variable_rename,[status(thm)],[f_2877_1]) ).

cnf(f_2877_3,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_10723),hAPP(c_Nat_OSuc,U_10724)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Oord__class_Omin(tc_Nat_Onat)),U_10724)),U_10723),
    inference(clausify,[status(thm)],[f_2877_2]) ).

fof(f_2878_1,plain,
    ! [V_l,V_k] :
      ( c_Divides_OposDivAlg(V_k,V_l) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) ),
    inference(fof_nnf,[status(thm)],[fact_posDivAlg__div__mod]) ).

fof(f_2878_2,plain,
    ! [U_10726,U_10725] :
      ( c_Divides_OposDivAlg(U_10725,U_10726) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10725),U_10726)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10725,U_10726))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10726))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10725)) ),
    inference(variable_rename,[status(thm)],[f_2878_1]) ).

cnf(f_2878_3,plain,
    ( c_Divides_OposDivAlg(U_10725,U_10726) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10725),U_10726)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10725,U_10726))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10726))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10725)) ),
    inference(clausify,[status(thm)],[f_2878_2]) ).

fof(f_2879_1,plain,
    ! [V_v_2,V_f_2,V_a_2,T_b] : c_Nat_Onat_Onat__case(T_b,V_a_2,V_f_2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_b),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),tc_Int_Oint),c_If(T_b)),c_Nat__Numeral_Oneg)),V_a_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),V_f_2),c_Int_Onat))),
    inference(fof_nnf,[status(thm)],[fact_nat__case__number__of]) ).

fof(f_2879_2,plain,
    ! [U_10730,U_10729,U_10728,U_10727] : c_Nat_Onat_Onat__case(U_10727,U_10728,U_10729,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10730)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_10727),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10730))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_10727,U_10727),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_10727,tc_fun(U_10727,U_10727)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10727,tc_fun(U_10727,U_10727)),tc_Int_Oint),c_If(U_10727)),c_Nat__Numeral_Oneg)),U_10728)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10727,tc_Int_Oint),U_10729),c_Int_Onat))),
    inference(variable_rename,[status(thm)],[f_2879_1]) ).

cnf(f_2879_3,plain,
    c_Nat_Onat_Onat__case(U_10727,U_10728,U_10729,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10730)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_10727),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10730))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_10727,U_10727),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_10727,tc_fun(U_10727,U_10727)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10727,tc_fun(U_10727,U_10727)),tc_Int_Oint),c_If(U_10727)),c_Nat__Numeral_Oneg)),U_10728)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10727,tc_Int_Oint),U_10729),c_Int_Onat))),
    inference(clausify,[status(thm)],[f_2879_2]) ).

fof(f_2880_1,plain,
    ! [V_a,V_b] :
      ( ( ( c_Divides_OposDivAlg(V_a,V_b) = hAPP(c_Divides_Oadjust(V_b),c_Divides_OposDivAlg(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) )
        & ( c_Divides_OposDivAlg(V_a,V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) ),
    inference(fof_nnf,[status(thm)],[fact_posDivAlg__eqn]) ).

fof(f_2880_2,plain,
    ! [U_10732,U_10731] :
      ( ( ( c_Divides_OposDivAlg(U_10732,U_10731) = hAPP(c_Divides_Oadjust(U_10731),c_Divides_OposDivAlg(U_10732,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_10731)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10732),U_10731)) )
        & ( c_Divides_OposDivAlg(U_10732,U_10731) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10732)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10732),U_10731)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10731)) ),
    inference(variable_rename,[status(thm)],[f_2880_1]) ).

cnf(f_2880_3,plain,
    ( c_Divides_OposDivAlg(U_10732,U_10731) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10732)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10732),U_10731))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10731)) ),
    inference(clausify,[status(thm)],[f_2880_2]) ).

cnf(f_2880_4,plain,
    ( c_Divides_OposDivAlg(U_10732,U_10731) = hAPP(c_Divides_Oadjust(U_10731),c_Divides_OposDivAlg(U_10732,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_10731)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10732),U_10731))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10731)) ),
    inference(clausify,[status(thm)],[f_2880_2]) ).

fof(f_2881_1,plain,
    ! [V_w,V_v] :
      ( ( ( c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) )
        & ( c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) ),
    inference(fof_nnf,[status(thm)],[fact_posDivAlg__eqn__number__of]) ).

fof(f_2881_2,plain,
    ! [U_10734,U_10733] :
      ( ( ( c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10734),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10733)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10733)),c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10734),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10733))))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10734)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10733))) )
        & ( c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10734),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10733)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10734))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10734)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10733))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10733))) ),
    inference(variable_rename,[status(thm)],[f_2881_1]) ).

cnf(f_2881_3,plain,
    ( c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10734),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10733)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10734))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10734)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10733)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10733))) ),
    inference(clausify,[status(thm)],[f_2881_2]) ).

cnf(f_2881_4,plain,
    ( c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10734),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10733)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10733)),c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10734),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10733))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10734)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10733)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_10733))) ),
    inference(clausify,[status(thm)],[f_2881_2]) ).

fof(f_2882_1,plain,
    ! [V_y_2,V_x_2,V_R_2,T_c,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(T_b,T_c,V_R_2),V_x_2),V_y_2))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),V_R_2)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),V_R_2))
        | ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(T_b,T_c,V_R_2),V_x_2),V_y_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_in__rel__def]) ).

fof(f_2882_2,plain,
    ! [U_10739,U_10738,U_10737,U_10736,U_10735] :
      ( ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_10735,U_10736,U_10737),U_10738),U_10739))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10735,U_10736)),hAPP(hAPP(c_Product__Type_OPair(U_10735,U_10736),U_10738),U_10739)),U_10737)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10735,U_10736)),hAPP(hAPP(c_Product__Type_OPair(U_10735,U_10736),U_10738),U_10739)),U_10737))
        | ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_10735,U_10736,U_10737),U_10738),U_10739)) ) ),
    inference(variable_rename,[status(thm)],[f_2882_1]) ).

fof(f_2882_3,plain,
    ( ! [U_10749,U_10747,U_10745,U_10743,U_10741] :
        ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_10741,U_10743,U_10745),U_10747),U_10749))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10741,U_10743)),hAPP(hAPP(c_Product__Type_OPair(U_10741,U_10743),U_10747),U_10749)),U_10745)) )
    & ! [U_10748,U_10746,U_10744,U_10742,U_10740] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10740,U_10742)),hAPP(hAPP(c_Product__Type_OPair(U_10740,U_10742),U_10746),U_10748)),U_10744))
        | ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_10740,U_10742,U_10744),U_10746),U_10748)) ) ),
    inference(miniscope,[status(thm)],[f_2882_2]) ).

cnf(f_2882_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10740,U_10742)),hAPP(hAPP(c_Product__Type_OPair(U_10740,U_10742),U_10746),U_10748)),U_10744))
    | ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_10740,U_10742,U_10744),U_10746),U_10748)) ),
    inference(clausify,[status(thm)],[f_2882_3]) ).

cnf(f_2882_5,plain,
    ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_10741,U_10743,U_10745),U_10747),U_10749))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10741,U_10743)),hAPP(hAPP(c_Product__Type_OPair(U_10741,U_10743),U_10747),U_10749)),U_10745)) ),
    inference(clausify,[status(thm)],[f_2882_3]) ).

fof(f_2883_1,plain,
    ! [V_m,V_n] : c_Code__Numeral_Odiv__mod__code__numeral(V_n,V_m) = hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_n),V_m)),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,V_n,V_m)),
    inference(fof_nnf,[status(thm)],[fact_div__mod__code__numeral__def]) ).

fof(f_2883_2,plain,
    ! [U_10751,U_10750] : c_Code__Numeral_Odiv__mod__code__numeral(U_10750,U_10751) = hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),U_10750),U_10751)),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,U_10750,U_10751)),
    inference(variable_rename,[status(thm)],[f_2883_1]) ).

cnf(f_2883_3,plain,
    c_Code__Numeral_Odiv__mod__code__numeral(U_10750,U_10751) = hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),U_10750),U_10751)),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,U_10750,U_10751)),
    inference(clausify,[status(thm)],[f_2883_2]) ).

fof(f_2884_1,plain,
    ! [V_r_2,T_b] :
      ( ( c_Nitpick_Orefl_H(T_b,V_r_2)
        | ? [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) )
      & ( ! [B_x] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2))
        | ~ c_Nitpick_Orefl_H(T_b,V_r_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_Nitpick_Orefl_H__def]) ).

fof(f_2884_2,plain,
    ! [U_10755,U_10754] :
      ( ( c_Nitpick_Orefl_H(U_10754,U_10755)
        | ? [U_10753] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10754,U_10754)),hAPP(hAPP(c_Product__Type_OPair(U_10754,U_10754),U_10753),U_10753)),U_10755)) )
      & ( ! [U_10752] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_10754,U_10754)),hAPP(hAPP(c_Product__Type_OPair(U_10754,U_10754),U_10752),U_10752)),U_10755))
        | ~ c_Nitpick_Orefl_H(U_10754,U_10755) ) ),
    inference(variable_rename,[status(thm)],[f_2884_1]) ).

fof(f_2884_3,plain,
    ( ! [U_10759,U_10757] :
        ( c_Nitpick_Orefl_H(U_10757,U_10759)
        | ? [U_10753] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10757,U_10757)),hAPP(hAPP(c_Product__Type_OPair(U_10757,U_10757),U_10753),U_10753)),U_10759)) )
    & ! [U_10758,U_10756] :
        ( ! [U_10752] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_10756,U_10756)),hAPP(hAPP(c_Product__Type_OPair(U_10756,U_10756),U_10752),U_10752)),U_10758))
        | ~ c_Nitpick_Orefl_H(U_10756,U_10758) ) ),
    inference(miniscope,[status(thm)],[f_2884_2]) ).

fof(f_2884_4,plain,
    ( ! [U_10759,U_10757] :
        ( c_Nitpick_Orefl_H(U_10757,U_10759)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10757,U_10757)),hAPP(hAPP(c_Product__Type_OPair(U_10757,U_10757),sK247(U_10759,U_10757)),sK247(U_10759,U_10757))),U_10759)) )
    & ! [U_10758,U_10756] :
        ( ! [U_10752] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_10756,U_10756)),hAPP(hAPP(c_Product__Type_OPair(U_10756,U_10756),U_10752),U_10752)),U_10758))
        | ~ c_Nitpick_Orefl_H(U_10756,U_10758) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK247]),skolemize(U_10753,sK247(U_10759,U_10757))],[f_2884_3]) ).

cnf(f_2884_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10756,U_10756)),hAPP(hAPP(c_Product__Type_OPair(U_10756,U_10756),U_10752),U_10752)),U_10758))
    | ~ c_Nitpick_Orefl_H(U_10756,U_10758) ),
    inference(clausify,[status(thm)],[f_2884_4]) ).

cnf(f_2884_6,plain,
    ( c_Nitpick_Orefl_H(U_10757,U_10759)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10757,U_10757)),hAPP(hAPP(c_Product__Type_OPair(U_10757,U_10757),sK247(U_10759,U_10757)),sK247(U_10759,U_10757))),U_10759)) ),
    inference(clausify,[status(thm)],[f_2884_4]) ).

fof(f_2885_1,plain,
    ! [V_b_2] : c_Divides_Oadjust(V_b_2) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),V_b_2))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),V_b_2))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
    inference(fof_nnf,[status(thm)],[fact_adjust__def]) ).

fof(f_2885_2,plain,
    ! [U_10760] : c_Divides_Oadjust(U_10760) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),U_10760))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),U_10760))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
    inference(variable_rename,[status(thm)],[f_2885_1]) ).

cnf(f_2885_3,plain,
    c_Divides_Oadjust(U_10760) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),U_10760))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),U_10760))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
    inference(clausify,[status(thm)],[f_2885_2]) ).

fof(f_2886_1,plain,
    ! [V_m,V_n] :
      ( c_Divides_Odivmod__nat(V_m,V_n) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_divmod__nat__step]) ).

fof(f_2886_2,plain,
    ! [U_10762,U_10761] :
      ( c_Divides_Odivmod__nat(U_10762,U_10761) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10762),U_10761)),U_10761))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10762),U_10761),U_10761))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10761),U_10762))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10761)) ),
    inference(variable_rename,[status(thm)],[f_2886_1]) ).

cnf(f_2886_3,plain,
    ( c_Divides_Odivmod__nat(U_10762,U_10761) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10762),U_10761)),U_10761))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10762),U_10761),U_10761))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10761),U_10762))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10761)) ),
    inference(clausify,[status(thm)],[f_2886_2]) ).

fof(f_2887_1,plain,
    ! [V_n_2,V_v_2,V_f_2,V_a_2,T_b] : hAPP(c_Nat_Onat_Onat__rec(T_b,V_a_2,V_f_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),V_n_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_b),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),tc_Int_Oint),c_If(T_b)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(T_b,V_a_2,V_f_2),V_n_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_b,T_b),tc_Int_Oint),V_f_2),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),V_n_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),c_Nat_Onat_Onat__rec(T_b,V_a_2,V_f_2)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),V_n_2))))),
    inference(fof_nnf,[status(thm)],[fact_nat__rec__add__eq__if]) ).

fof(f_2887_2,plain,
    ! [U_10767,U_10766,U_10765,U_10764,U_10763] : hAPP(c_Nat_Onat_Onat__rec(U_10763,U_10764,U_10765),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10766)),U_10767)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_10763),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10766))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_10763,U_10763),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_10763,tc_fun(U_10763,U_10763)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10763,tc_fun(U_10763,U_10763)),tc_Int_Oint),c_If(U_10763)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(U_10763,U_10764,U_10765),U_10767))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_10763,U_10763),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_10763,U_10763),tc_Int_Oint),U_10765),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),U_10767))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10763,tc_Int_Oint),c_Nat_Onat_Onat__rec(U_10763,U_10764,U_10765)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),U_10767))))),
    inference(variable_rename,[status(thm)],[f_2887_1]) ).

cnf(f_2887_3,plain,
    hAPP(c_Nat_Onat_Onat__rec(U_10763,U_10764,U_10765),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10766)),U_10767)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_10763),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10766))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_10763,U_10763),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_10763,tc_fun(U_10763,U_10763)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10763,tc_fun(U_10763,U_10763)),tc_Int_Oint),c_If(U_10763)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(U_10763,U_10764,U_10765),U_10767))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_10763,U_10763),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_10763,U_10763),tc_Int_Oint),U_10765),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),U_10767))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10763,tc_Int_Oint),c_Nat_Onat_Onat__rec(U_10763,U_10764,U_10765)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),U_10767))))),
    inference(clausify,[status(thm)],[f_2887_2]) ).

fof(f_2888_1,plain,
    ! [V_f2_2,V_f1_2,T_b] : hAPP(c_Nat_Onat_Onat__rec(T_b,V_f1_2,V_f2_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_f1_2,
    inference(fof_nnf,[status(thm)],[fact_nat__rec__0]) ).

fof(f_2888_2,plain,
    ! [U_10770,U_10769,U_10768] : hAPP(c_Nat_Onat_Onat__rec(U_10768,U_10769,U_10770),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_10769,
    inference(variable_rename,[status(thm)],[f_2888_1]) ).

cnf(f_2888_3,plain,
    hAPP(c_Nat_Onat_Onat__rec(U_10768,U_10769,U_10770),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_10769,
    inference(clausify,[status(thm)],[f_2888_2]) ).

fof(f_2889_1,plain,
    ! [V_nat_2,V_f2_2,V_f1_2,T_b] : hAPP(c_Nat_Onat_Onat__rec(T_b,V_f1_2,V_f2_2),hAPP(c_Nat_OSuc,V_nat_2)) = hAPP(hAPP(V_f2_2,V_nat_2),hAPP(c_Nat_Onat_Onat__rec(T_b,V_f1_2,V_f2_2),V_nat_2)),
    inference(fof_nnf,[status(thm)],[fact_nat__rec__Suc]) ).

fof(f_2889_2,plain,
    ! [U_10774,U_10773,U_10772,U_10771] : hAPP(c_Nat_Onat_Onat__rec(U_10771,U_10772,U_10773),hAPP(c_Nat_OSuc,U_10774)) = hAPP(hAPP(U_10773,U_10774),hAPP(c_Nat_Onat_Onat__rec(U_10771,U_10772,U_10773),U_10774)),
    inference(variable_rename,[status(thm)],[f_2889_1]) ).

cnf(f_2889_3,plain,
    hAPP(c_Nat_Onat_Onat__rec(U_10771,U_10772,U_10773),hAPP(c_Nat_OSuc,U_10774)) = hAPP(hAPP(U_10773,U_10774),hAPP(c_Nat_Onat_Onat__rec(U_10771,U_10772,U_10773),U_10774)),
    inference(clausify,[status(thm)],[f_2889_2]) ).

fof(f_2890_1,plain,
    ! [V_m] : c_Divides_Odivmod__nat(V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m),
    inference(fof_nnf,[status(thm)],[fact_divmod__nat__zero]) ).

fof(f_2890_2,plain,
    ! [U_10775] : c_Divides_Odivmod__nat(U_10775,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10775),
    inference(variable_rename,[status(thm)],[f_2890_1]) ).

cnf(f_2890_3,plain,
    c_Divides_Odivmod__nat(U_10775,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10775),
    inference(clausify,[status(thm)],[f_2890_2]) ).

fof(f_2891_1,plain,
    ! [V_n,V_m] :
      ( c_Divides_Odivmod__nat(V_m,V_n) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_divmod__nat__base]) ).

fof(f_2891_2,plain,
    ! [U_10777,U_10776] :
      ( c_Divides_Odivmod__nat(U_10776,U_10777) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10776)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10776),U_10777)) ),
    inference(variable_rename,[status(thm)],[f_2891_1]) ).

cnf(f_2891_3,plain,
    ( c_Divides_Odivmod__nat(U_10776,U_10777) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10776)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10776),U_10777)) ),
    inference(clausify,[status(thm)],[f_2891_2]) ).

fof(f_2892_1,plain,
    ! [V_n,V_m] : c_Divides_Odivmod__nat(V_m,V_n) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),
    inference(fof_nnf,[status(thm)],[fact_divmod__nat__div__mod]) ).

fof(f_2892_2,plain,
    ! [U_10779,U_10778] : c_Divides_Odivmod__nat(U_10778,U_10779) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10778),U_10779)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10778,U_10779)),
    inference(variable_rename,[status(thm)],[f_2892_1]) ).

cnf(f_2892_3,plain,
    c_Divides_Odivmod__nat(U_10778,U_10779) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10778),U_10779)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10778,U_10779)),
    inference(clausify,[status(thm)],[f_2892_2]) ).

fof(f_2893_1,plain,
    ! [V_v_2,V_f_2,V_a_2,T_b] : hAPP(c_Nat_Onat_Onat__rec(T_b,V_a_2,V_f_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_b),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),tc_Int_Oint),c_If(T_b)),c_Nat__Numeral_Oneg)),V_a_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_b,T_b),tc_Int_Oint),V_f_2),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),c_Nat_Onat_Onat__rec(T_b,V_a_2,V_f_2)),c_Int_Onat)))),
    inference(fof_nnf,[status(thm)],[fact_nat__rec__number__of]) ).

fof(f_2893_2,plain,
    ! [U_10783,U_10782,U_10781,U_10780] : hAPP(c_Nat_Onat_Onat__rec(U_10780,U_10781,U_10782),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10783)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_10780),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10783))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_10780,U_10780),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_10780,tc_fun(U_10780,U_10780)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10780,tc_fun(U_10780,U_10780)),tc_Int_Oint),c_If(U_10780)),c_Nat__Numeral_Oneg)),U_10781)),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_10780,U_10780),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_10780,U_10780),tc_Int_Oint),U_10782),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10780,tc_Int_Oint),c_Nat_Onat_Onat__rec(U_10780,U_10781,U_10782)),c_Int_Onat)))),
    inference(variable_rename,[status(thm)],[f_2893_1]) ).

cnf(f_2893_3,plain,
    hAPP(c_Nat_Onat_Onat__rec(U_10780,U_10781,U_10782),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_10783)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_10780),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_10783))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_10780,U_10780),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_10780,tc_fun(U_10780,U_10780)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10780,tc_fun(U_10780,U_10780)),tc_Int_Oint),c_If(U_10780)),c_Nat__Numeral_Oneg)),U_10781)),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_10780,U_10780),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_10780,U_10780),tc_Int_Oint),U_10782),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10780,tc_Int_Oint),c_Nat_Onat_Onat__rec(U_10780,U_10781,U_10782)),c_Int_Onat)))),
    inference(clausify,[status(thm)],[f_2893_2]) ).

fof(f_2894_1,plain,
    ! [V_f_2,T_d,V_A_2,V_b_2,V_a_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_d),hAPP(hAPP(V_f_2,V_a_2),V_b_2)),hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_d,hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_f_2)),V_A_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_pair__imageI]) ).

fof(f_2894_2,plain,
    ! [U_10790,U_10789,U_10788,U_10787,U_10786,U_10785,U_10784] :
      ( hBOOL(hAPP(hAPP(c_member(U_10789),hAPP(hAPP(U_10790,U_10786),U_10787)),hAPP(c_Set_Oimage(tc_prod(U_10784,U_10785),U_10789,hAPP(c_Product__Type_Oprod_Oprod__case(U_10784,U_10785,U_10789),U_10790)),U_10788)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10784,U_10785)),hAPP(hAPP(c_Product__Type_OPair(U_10784,U_10785),U_10786),U_10787)),U_10788)) ),
    inference(variable_rename,[status(thm)],[f_2894_1]) ).

cnf(f_2894_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10789),hAPP(hAPP(U_10790,U_10786),U_10787)),hAPP(c_Set_Oimage(tc_prod(U_10784,U_10785),U_10789,hAPP(c_Product__Type_Oprod_Oprod__case(U_10784,U_10785,U_10789),U_10790)),U_10788)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10784,U_10785)),hAPP(hAPP(c_Product__Type_OPair(U_10784,U_10785),U_10786),U_10787)),U_10788)) ),
    inference(clausify,[status(thm)],[f_2894_2]) ).

fof(f_2895_1,plain,
    ! [V_k_2,T_b] :
      ( ( ( ( ( hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_k_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(T_b,T_b)),tc_fun(tc_Int_Oint,T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),T_b),tc_fun(tc_fun(tc_Int_Oint,tc_fun(T_b,T_b)),tc_fun(tc_Int_Oint,T_b)),tc_Int_Oint),c_COMBB(tc_fun(T_b,T_b),T_b,tc_Int_Oint)),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_fun(T_b,T_b),T_b),tc_Int_Oint),c_HOL_OLet(T_b,T_b)),c_Int_Oring__1__class_Oof__int(T_b)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(T_b,T_b),tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,T_b)),tc_Int_Oint),c_COMBS(T_b,T_b,T_b)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(T_b,T_b),tc_fun(T_b,tc_fun(T_b,T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_fun(T_b,T_b))),tc_Int_Oint),c_COMBB(T_b,tc_fun(T_b,T_b),T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),tc_Int_Oint),c_If(T_b)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),c_Groups_Oplus__class_Oplus(T_b)),c_COMBI(T_b))))),hAPP(hAPP(c_COMBC(T_b,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_b),c_Groups_Oplus__class_Oplus(T_b)),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),c_Groups_Oplus__class_Oplus(T_b)),c_COMBI(T_b)))),c_Groups_Oone__class_Oone(T_b))))),c_Divides_Odivmod__int(V_k_2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
            & ( hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_k_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k_2)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) )
          | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
        & ( hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_k_2) = c_Groups_Ozero__class_Ozero(T_b)
          | V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
      | ~ class_Rings_Oring__1(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_of__int__num]) ).

fof(f_2895_2,plain,
    ! [U_10792,U_10791] :
      ( ( ( ( ( hAPP(c_Int_Oring__1__class_Oof__int(U_10791),U_10792) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,U_10791),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(U_10791,U_10791)),tc_fun(tc_Int_Oint,U_10791)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_10791,U_10791),U_10791),tc_fun(tc_fun(tc_Int_Oint,tc_fun(U_10791,U_10791)),tc_fun(tc_Int_Oint,U_10791)),tc_Int_Oint),c_COMBB(tc_fun(U_10791,U_10791),U_10791,tc_Int_Oint)),hAPP(hAPP(c_COMBB(U_10791,tc_fun(tc_fun(U_10791,U_10791),U_10791),tc_Int_Oint),c_HOL_OLet(U_10791,U_10791)),c_Int_Oring__1__class_Oof__int(U_10791)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(U_10791,U_10791),tc_fun(U_10791,U_10791)),hAPP(hAPP(c_COMBB(tc_fun(U_10791,tc_fun(U_10791,U_10791)),tc_fun(tc_fun(U_10791,U_10791),tc_fun(U_10791,U_10791)),tc_Int_Oint),c_COMBS(U_10791,U_10791,U_10791)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(U_10791,U_10791),tc_fun(U_10791,tc_fun(U_10791,U_10791))),hAPP(hAPP(c_COMBB(tc_fun(U_10791,tc_fun(U_10791,U_10791)),tc_fun(tc_fun(U_10791,U_10791),tc_fun(U_10791,tc_fun(U_10791,U_10791))),tc_Int_Oint),c_COMBB(U_10791,tc_fun(U_10791,U_10791),U_10791)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10791,tc_fun(U_10791,U_10791)),tc_Int_Oint),c_If(U_10791)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBS(U_10791,U_10791,U_10791),c_Groups_Oplus__class_Oplus(U_10791)),c_COMBI(U_10791))))),hAPP(hAPP(c_COMBC(U_10791,U_10791,U_10791),hAPP(hAPP(c_COMBB(U_10791,tc_fun(U_10791,U_10791),U_10791),c_Groups_Oplus__class_Oplus(U_10791)),hAPP(hAPP(c_COMBS(U_10791,U_10791,U_10791),c_Groups_Oplus__class_Oplus(U_10791)),c_COMBI(U_10791)))),c_Groups_Oone__class_Oone(U_10791))))),c_Divides_Odivmod__int(U_10792,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10792),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
            & ( hAPP(c_Int_Oring__1__class_Oof__int(U_10791),U_10792) = hAPP(c_Groups_Ouminus__class_Ouminus(U_10791),hAPP(c_Int_Oring__1__class_Oof__int(U_10791),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10792)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10792),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) )
          | U_10792 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
        & ( hAPP(c_Int_Oring__1__class_Oof__int(U_10791),U_10792) = c_Groups_Ozero__class_Ozero(U_10791)
          | U_10792 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
      | ~ class_Rings_Oring__1(U_10791) ),
    inference(variable_rename,[status(thm)],[f_2895_1]) ).

cnf(f_2895_3,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_10791),U_10792) = c_Groups_Ozero__class_Ozero(U_10791)
    | U_10792 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ class_Rings_Oring__1(U_10791) ),
    inference(clausify,[status(thm)],[f_2895_2]) ).

cnf(f_2895_4,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_10791),U_10792) = hAPP(c_Groups_Ouminus__class_Ouminus(U_10791),hAPP(c_Int_Oring__1__class_Oof__int(U_10791),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10792)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10792),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | U_10792 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ class_Rings_Oring__1(U_10791) ),
    inference(clausify,[status(thm)],[f_2895_2]) ).

cnf(f_2895_5,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_10791),U_10792) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,U_10791),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(U_10791,U_10791)),tc_fun(tc_Int_Oint,U_10791)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_10791,U_10791),U_10791),tc_fun(tc_fun(tc_Int_Oint,tc_fun(U_10791,U_10791)),tc_fun(tc_Int_Oint,U_10791)),tc_Int_Oint),c_COMBB(tc_fun(U_10791,U_10791),U_10791,tc_Int_Oint)),hAPP(hAPP(c_COMBB(U_10791,tc_fun(tc_fun(U_10791,U_10791),U_10791),tc_Int_Oint),c_HOL_OLet(U_10791,U_10791)),c_Int_Oring__1__class_Oof__int(U_10791)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(U_10791,U_10791),tc_fun(U_10791,U_10791)),hAPP(hAPP(c_COMBB(tc_fun(U_10791,tc_fun(U_10791,U_10791)),tc_fun(tc_fun(U_10791,U_10791),tc_fun(U_10791,U_10791)),tc_Int_Oint),c_COMBS(U_10791,U_10791,U_10791)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(U_10791,U_10791),tc_fun(U_10791,tc_fun(U_10791,U_10791))),hAPP(hAPP(c_COMBB(tc_fun(U_10791,tc_fun(U_10791,U_10791)),tc_fun(tc_fun(U_10791,U_10791),tc_fun(U_10791,tc_fun(U_10791,U_10791))),tc_Int_Oint),c_COMBB(U_10791,tc_fun(U_10791,U_10791),U_10791)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10791,tc_fun(U_10791,U_10791)),tc_Int_Oint),c_If(U_10791)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBS(U_10791,U_10791,U_10791),c_Groups_Oplus__class_Oplus(U_10791)),c_COMBI(U_10791))))),hAPP(hAPP(c_COMBC(U_10791,U_10791,U_10791),hAPP(hAPP(c_COMBB(U_10791,tc_fun(U_10791,U_10791),U_10791),c_Groups_Oplus__class_Oplus(U_10791)),hAPP(hAPP(c_COMBS(U_10791,U_10791,U_10791),c_Groups_Oplus__class_Oplus(U_10791)),c_COMBI(U_10791)))),c_Groups_Oone__class_Oone(U_10791))))),c_Divides_Odivmod__int(U_10792,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10792),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | U_10792 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ class_Rings_Oring__1(U_10791) ),
    inference(clausify,[status(thm)],[f_2895_2]) ).

fof(f_2896_1,plain,
    ! [V_n_2,T_b] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2) = c_Nat_Osemiring__1__class_Oof__nat__aux(T_b,hAPP(hAPP(c_COMBC(T_b,T_b,T_b),c_Groups_Oplus__class_Oplus(T_b)),c_Groups_Oone__class_Oone(T_b)),V_n_2,c_Groups_Ozero__class_Ozero(T_b))
      | ~ class_Rings_Osemiring__1(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_semiring__1__class_Oof__nat__code]) ).

fof(f_2896_2,plain,
    ! [U_10794,U_10793] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10793),U_10794) = c_Nat_Osemiring__1__class_Oof__nat__aux(U_10793,hAPP(hAPP(c_COMBC(U_10793,U_10793,U_10793),c_Groups_Oplus__class_Oplus(U_10793)),c_Groups_Oone__class_Oone(U_10793)),U_10794,c_Groups_Ozero__class_Ozero(U_10793))
      | ~ class_Rings_Osemiring__1(U_10793) ),
    inference(variable_rename,[status(thm)],[f_2896_1]) ).

cnf(f_2896_3,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10793),U_10794) = c_Nat_Osemiring__1__class_Oof__nat__aux(U_10793,hAPP(hAPP(c_COMBC(U_10793,U_10793,U_10793),c_Groups_Oplus__class_Oplus(U_10793)),c_Groups_Oone__class_Oone(U_10793)),U_10794,c_Groups_Ozero__class_Ozero(U_10793))
    | ~ class_Rings_Osemiring__1(U_10793) ),
    inference(clausify,[status(thm)],[f_2896_2]) ).

fof(f_2897_1,plain,
    ! [T_c,T_b,V_b_2,V_a_2,V_f_2] :
      ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)))
      | ~ hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2)) ),
    inference(fof_nnf,[status(thm)],[fact_splitI]) ).

fof(f_2897_2,plain,
    ! [U_10799,U_10798,U_10797,U_10796,U_10795] :
      ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10798,U_10799,tc_HOL_Obool),U_10795),hAPP(hAPP(c_Product__Type_OPair(U_10798,U_10799),U_10796),U_10797)))
      | ~ hBOOL(hAPP(hAPP(U_10795,U_10796),U_10797)) ),
    inference(variable_rename,[status(thm)],[f_2897_1]) ).

cnf(f_2897_3,plain,
    ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10798,U_10799,tc_HOL_Obool),U_10795),hAPP(hAPP(c_Product__Type_OPair(U_10798,U_10799),U_10796),U_10797)))
    | ~ hBOOL(hAPP(hAPP(U_10795,U_10796),U_10797)) ),
    inference(clausify,[status(thm)],[f_2897_2]) ).

fof(f_2898_1,plain,
    ! [T_c,T_b,V_b_2,V_a_2,V_f1_2] :
      ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_f1_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)))
      | ~ hBOOL(hAPP(hAPP(V_f1_2,V_a_2),V_b_2)) ),
    inference(fof_nnf,[status(thm)],[fact_prod__caseI]) ).

fof(f_2898_2,plain,
    ! [U_10804,U_10803,U_10802,U_10801,U_10800] :
      ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10803,U_10804,tc_HOL_Obool),U_10800),hAPP(hAPP(c_Product__Type_OPair(U_10803,U_10804),U_10801),U_10802)))
      | ~ hBOOL(hAPP(hAPP(U_10800,U_10801),U_10802)) ),
    inference(variable_rename,[status(thm)],[f_2898_1]) ).

cnf(f_2898_3,plain,
    ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10803,U_10804,tc_HOL_Obool),U_10800),hAPP(hAPP(c_Product__Type_OPair(U_10803,U_10804),U_10801),U_10802)))
    | ~ hBOOL(hAPP(hAPP(U_10800,U_10801),U_10802)) ),
    inference(clausify,[status(thm)],[f_2898_2]) ).

fof(f_2899_1,plain,
    ! [T_d,T_c,V_b_2,V_a_2,V_c_2,V_z_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_fun(T_b,tc_HOL_Obool)),V_c_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2))))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_c_2,V_a_2),V_b_2))) ),
    inference(fof_nnf,[status(thm)],[fact_mem__splitI]) ).

fof(f_2899_2,plain,
    ! [U_10811,U_10810,U_10809,U_10808,U_10807,U_10806,U_10805] :
      ( hBOOL(hAPP(hAPP(c_member(U_10805),U_10806),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10810,U_10811,tc_fun(U_10805,tc_HOL_Obool)),U_10807),hAPP(hAPP(c_Product__Type_OPair(U_10810,U_10811),U_10808),U_10809))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10805),U_10806),hAPP(hAPP(U_10807,U_10808),U_10809))) ),
    inference(variable_rename,[status(thm)],[f_2899_1]) ).

cnf(f_2899_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10805),U_10806),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10810,U_10811,tc_fun(U_10805,tc_HOL_Obool)),U_10807),hAPP(hAPP(c_Product__Type_OPair(U_10810,U_10811),U_10808),U_10809))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10805),U_10806),hAPP(hAPP(U_10807,U_10808),U_10809))) ),
    inference(clausify,[status(thm)],[f_2899_2]) ).

fof(f_2900_1,plain,
    ! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2))
      | ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ),
    inference(fof_nnf,[status(thm)],[fact_splitD]) ).

fof(f_2900_2,plain,
    ! [U_10816,U_10815,U_10814,U_10813,U_10812] :
      ( hBOOL(hAPP(hAPP(U_10814,U_10815),U_10816))
      | ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10812,U_10813,tc_HOL_Obool),U_10814),hAPP(hAPP(c_Product__Type_OPair(U_10812,U_10813),U_10815),U_10816))) ),
    inference(variable_rename,[status(thm)],[f_2900_1]) ).

fof(f_2900_3,plain,
    ! [U_10816,U_10815,U_10814] :
      ( ! [U_10813,U_10812] : ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10812,U_10813,tc_HOL_Obool),U_10814),hAPP(hAPP(c_Product__Type_OPair(U_10812,U_10813),U_10815),U_10816)))
      | hBOOL(hAPP(hAPP(U_10814,U_10815),U_10816)) ),
    inference(miniscope,[status(thm)],[f_2900_2]) ).

cnf(f_2900_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10812,U_10813,tc_HOL_Obool),U_10814),hAPP(hAPP(c_Product__Type_OPair(U_10812,U_10813),U_10815),U_10816)))
    | hBOOL(hAPP(hAPP(U_10814,U_10815),U_10816)) ),
    inference(clausify,[status(thm)],[f_2900_3]) ).

fof(f_2901_1,plain,
    ! [V_c_2,V_b_2,V_a_2,V_R_2,T_d,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(hAPP(V_R_2,V_a_2),V_b_2),V_c_2))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_d,tc_HOL_Obool)),V_R_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_c_2)) ),
    inference(fof_nnf,[status(thm)],[fact_splitD_H]) ).

fof(f_2901_2,plain,
    ! [U_10823,U_10822,U_10821,U_10820,U_10819,U_10818,U_10817] :
      ( hBOOL(hAPP(hAPP(hAPP(U_10820,U_10821),U_10822),U_10823))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10817,U_10818,tc_fun(U_10819,tc_HOL_Obool)),U_10820),hAPP(hAPP(c_Product__Type_OPair(U_10817,U_10818),U_10821),U_10822)),U_10823)) ),
    inference(variable_rename,[status(thm)],[f_2901_1]) ).

fof(f_2901_3,plain,
    ! [U_10823,U_10822,U_10821,U_10820] :
      ( ! [U_10819,U_10818,U_10817] : ~ hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10817,U_10818,tc_fun(U_10819,tc_HOL_Obool)),U_10820),hAPP(hAPP(c_Product__Type_OPair(U_10817,U_10818),U_10821),U_10822)),U_10823))
      | hBOOL(hAPP(hAPP(hAPP(U_10820,U_10821),U_10822),U_10823)) ),
    inference(miniscope,[status(thm)],[f_2901_2]) ).

cnf(f_2901_4,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10817,U_10818,tc_fun(U_10819,tc_HOL_Obool)),U_10820),hAPP(hAPP(c_Product__Type_OPair(U_10817,U_10818),U_10821),U_10822)),U_10823))
    | hBOOL(hAPP(hAPP(hAPP(U_10820,U_10821),U_10822),U_10823)) ),
    inference(clausify,[status(thm)],[f_2901_3]) ).

fof(f_2902_1,plain,
    ! [V_i_2,V_inc_2,T_b] :
      ( c_Nat_Osemiring__1__class_Oof__nat__aux(T_b,V_inc_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i_2) = V_i_2
      | ~ class_Rings_Osemiring__1(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__aux_Osimps_I1_J]) ).

fof(f_2902_2,plain,
    ! [U_10826,U_10825,U_10824] :
      ( c_Nat_Osemiring__1__class_Oof__nat__aux(U_10824,U_10825,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_10826) = U_10826
      | ~ class_Rings_Osemiring__1(U_10824) ),
    inference(variable_rename,[status(thm)],[f_2902_1]) ).

cnf(f_2902_3,plain,
    ( c_Nat_Osemiring__1__class_Oof__nat__aux(U_10824,U_10825,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_10826) = U_10826
    | ~ class_Rings_Osemiring__1(U_10824) ),
    inference(clausify,[status(thm)],[f_2902_2]) ).

fof(f_2903_1,plain,
    ! [V_i_2,V_n_2,V_inc_2,T_b] :
      ( c_Nat_Osemiring__1__class_Oof__nat__aux(T_b,V_inc_2,hAPP(c_Nat_OSuc,V_n_2),V_i_2) = c_Nat_Osemiring__1__class_Oof__nat__aux(T_b,V_inc_2,V_n_2,hAPP(V_inc_2,V_i_2))
      | ~ class_Rings_Osemiring__1(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__aux_Osimps_I2_J]) ).

fof(f_2903_2,plain,
    ! [U_10830,U_10829,U_10828,U_10827] :
      ( c_Nat_Osemiring__1__class_Oof__nat__aux(U_10827,U_10828,hAPP(c_Nat_OSuc,U_10829),U_10830) = c_Nat_Osemiring__1__class_Oof__nat__aux(U_10827,U_10828,U_10829,hAPP(U_10828,U_10830))
      | ~ class_Rings_Osemiring__1(U_10827) ),
    inference(variable_rename,[status(thm)],[f_2903_1]) ).

cnf(f_2903_3,plain,
    ( c_Nat_Osemiring__1__class_Oof__nat__aux(U_10827,U_10828,hAPP(c_Nat_OSuc,U_10829),U_10830) = c_Nat_Osemiring__1__class_Oof__nat__aux(U_10827,U_10828,U_10829,hAPP(U_10828,U_10830))
    | ~ class_Rings_Osemiring__1(U_10827) ),
    inference(clausify,[status(thm)],[f_2903_2]) ).

fof(f_2904_1,plain,
    ! [T_c,T_b,V_P_2] :
      ( ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
        | ? [B_a,B_b] : ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b))) )
      & ( ! [B_a,B_b] : hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b)))
        | ? [B_x1] : ~ hBOOL(hAPP(V_P_2,B_x1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_split__paired__All]) ).

fof(f_2904_2,plain,
    ! [U_10839,U_10838,U_10837] :
      ( ( ! [U_10836] : hBOOL(hAPP(U_10837,U_10836))
        | ? [U_10835,U_10834] : ~ hBOOL(hAPP(U_10837,hAPP(hAPP(c_Product__Type_OPair(U_10838,U_10839),U_10835),U_10834))) )
      & ( ! [U_10833,U_10832] : hBOOL(hAPP(U_10837,hAPP(hAPP(c_Product__Type_OPair(U_10838,U_10839),U_10833),U_10832)))
        | ? [U_10831] : ~ hBOOL(hAPP(U_10837,U_10831)) ) ),
    inference(variable_rename,[status(thm)],[f_2904_1]) ).

fof(f_2904_3,plain,
    ( ! [U_10845,U_10843,U_10841] :
        ( ! [U_10836] : hBOOL(hAPP(U_10841,U_10836))
        | ? [U_10835,U_10834] : ~ hBOOL(hAPP(U_10841,hAPP(hAPP(c_Product__Type_OPair(U_10843,U_10845),U_10835),U_10834))) )
    & ! [U_10844,U_10842,U_10840] :
        ( ! [U_10833,U_10832] : hBOOL(hAPP(U_10840,hAPP(hAPP(c_Product__Type_OPair(U_10842,U_10844),U_10833),U_10832)))
        | ? [U_10831] : ~ hBOOL(hAPP(U_10840,U_10831)) ) ),
    inference(miniscope,[status(thm)],[f_2904_2]) ).

fof(f_2904_4,plain,
    ( ! [U_10845,U_10843,U_10841] :
        ( ! [U_10836] : hBOOL(hAPP(U_10841,U_10836))
        | ? [U_10835,U_10834] : ~ hBOOL(hAPP(U_10841,hAPP(hAPP(c_Product__Type_OPair(U_10843,U_10845),U_10835),U_10834))) )
    & ! [U_10844,U_10842,U_10840] :
        ( ! [U_10833,U_10832] : hBOOL(hAPP(U_10840,hAPP(hAPP(c_Product__Type_OPair(U_10842,U_10844),U_10833),U_10832)))
        | ~ hBOOL(hAPP(U_10840,sK248(U_10844,U_10842,U_10840))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK248]),skolemize(U_10831,sK248(U_10844,U_10842,U_10840))],[f_2904_3]) ).

fof(f_2904_5,plain,
    ( ! [U_10845,U_10843,U_10841] :
        ( ! [U_10836] : hBOOL(hAPP(U_10841,U_10836))
        | ? [U_10834] : ~ hBOOL(hAPP(U_10841,hAPP(hAPP(c_Product__Type_OPair(U_10843,U_10845),sK249(U_10845,U_10843,U_10841)),U_10834))) )
    & ! [U_10844,U_10842,U_10840] :
        ( ! [U_10833,U_10832] : hBOOL(hAPP(U_10840,hAPP(hAPP(c_Product__Type_OPair(U_10842,U_10844),U_10833),U_10832)))
        | ~ hBOOL(hAPP(U_10840,sK248(U_10844,U_10842,U_10840))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK249]),skolemize(U_10835,sK249(U_10845,U_10843,U_10841))],[f_2904_4]) ).

fof(f_2904_6,plain,
    ( ! [U_10845,U_10843,U_10841] :
        ( ! [U_10836] : hBOOL(hAPP(U_10841,U_10836))
        | ~ hBOOL(hAPP(U_10841,hAPP(hAPP(c_Product__Type_OPair(U_10843,U_10845),sK249(U_10845,U_10843,U_10841)),sK250(U_10845,U_10843,U_10841)))) )
    & ! [U_10844,U_10842,U_10840] :
        ( ! [U_10833,U_10832] : hBOOL(hAPP(U_10840,hAPP(hAPP(c_Product__Type_OPair(U_10842,U_10844),U_10833),U_10832)))
        | ~ hBOOL(hAPP(U_10840,sK248(U_10844,U_10842,U_10840))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK250]),skolemize(U_10834,sK250(U_10845,U_10843,U_10841))],[f_2904_5]) ).

cnf(f_2904_7,plain,
    ( hBOOL(hAPP(U_10840,hAPP(hAPP(c_Product__Type_OPair(U_10842,U_10844),U_10833),U_10832)))
    | ~ hBOOL(hAPP(U_10840,sK248(U_10844,U_10842,U_10840))) ),
    inference(clausify,[status(thm)],[f_2904_6]) ).

cnf(f_2904_8,plain,
    ( hBOOL(hAPP(U_10841,U_10836))
    | ~ hBOOL(hAPP(U_10841,hAPP(hAPP(c_Product__Type_OPair(U_10843,U_10845),sK249(U_10845,U_10843,U_10841)),sK250(U_10845,U_10843,U_10841)))) ),
    inference(clausify,[status(thm)],[f_2904_6]) ).

fof(f_2905_1,plain,
    ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
      ( ( hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_H_2),V_b_H_2)
        | V_b_2 != V_b_H_2
        | V_a_2 != V_a_H_2 )
      & ( ( V_b_2 = V_b_H_2
          & V_a_2 = V_a_H_2 )
        | hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2) != hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_H_2),V_b_H_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_Pair__eq]) ).

fof(f_2905_2,plain,
    ! [U_10851,U_10850,U_10849,U_10848,U_10847,U_10846] :
      ( ( hAPP(hAPP(c_Product__Type_OPair(U_10846,U_10847),U_10848),U_10849) = hAPP(hAPP(c_Product__Type_OPair(U_10846,U_10847),U_10850),U_10851)
        | U_10849 != U_10851
        | U_10848 != U_10850 )
      & ( ( U_10849 = U_10851
          & U_10848 = U_10850 )
        | hAPP(hAPP(c_Product__Type_OPair(U_10846,U_10847),U_10848),U_10849) != hAPP(hAPP(c_Product__Type_OPair(U_10846,U_10847),U_10850),U_10851) ) ),
    inference(variable_rename,[status(thm)],[f_2905_1]) ).

fof(f_2905_3,plain,
    ( ! [U_10863,U_10861,U_10859,U_10857] :
        ( ! [U_10855,U_10853] : hAPP(hAPP(c_Product__Type_OPair(U_10853,U_10855),U_10857),U_10859) = hAPP(hAPP(c_Product__Type_OPair(U_10853,U_10855),U_10861),U_10863)
        | U_10859 != U_10863
        | U_10857 != U_10861 )
    & ! [U_10862,U_10860,U_10858,U_10856] :
        ( ! [U_10854,U_10852] : hAPP(hAPP(c_Product__Type_OPair(U_10852,U_10854),U_10856),U_10858) != hAPP(hAPP(c_Product__Type_OPair(U_10852,U_10854),U_10860),U_10862)
        | ( U_10858 = U_10862
          & U_10856 = U_10860 ) ) ),
    inference(miniscope,[status(thm)],[f_2905_2]) ).

cnf(f_2905_4,plain,
    ( U_10856 = U_10860
    | hAPP(hAPP(c_Product__Type_OPair(U_10852,U_10854),U_10856),U_10858) != hAPP(hAPP(c_Product__Type_OPair(U_10852,U_10854),U_10860),U_10862) ),
    inference(clausify,[status(thm)],[f_2905_3]) ).

cnf(f_2905_5,plain,
    ( U_10858 = U_10862
    | hAPP(hAPP(c_Product__Type_OPair(U_10852,U_10854),U_10856),U_10858) != hAPP(hAPP(c_Product__Type_OPair(U_10852,U_10854),U_10860),U_10862) ),
    inference(clausify,[status(thm)],[f_2905_3]) ).

cnf(f_2905_6,plain,
    ( hAPP(hAPP(c_Product__Type_OPair(U_10853,U_10855),U_10857),U_10859) = hAPP(hAPP(c_Product__Type_OPair(U_10853,U_10855),U_10861),U_10863)
    | U_10859 != U_10863
    | U_10857 != U_10861 ),
    inference(clausify,[status(thm)],[f_2905_3]) ).

fof(f_2906_1,plain,
    ! [V_b_H,V_a_H,V_b,V_a,T_b,T_a] :
      ( ( V_b = V_b_H
        & V_a = V_a_H )
      | hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a),V_b) != hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_H),V_b_H) ),
    inference(fof_nnf,[status(thm)],[fact_Pair__inject]) ).

fof(f_2906_2,plain,
    ! [U_10869,U_10868,U_10867,U_10866,U_10865,U_10864] :
      ( ( U_10867 = U_10869
        & U_10866 = U_10868 )
      | hAPP(hAPP(c_Product__Type_OPair(U_10864,U_10865),U_10866),U_10867) != hAPP(hAPP(c_Product__Type_OPair(U_10864,U_10865),U_10868),U_10869) ),
    inference(variable_rename,[status(thm)],[f_2906_1]) ).

fof(f_2906_3,plain,
    ! [U_10869,U_10868,U_10867,U_10866] :
      ( ! [U_10865,U_10864] : hAPP(hAPP(c_Product__Type_OPair(U_10864,U_10865),U_10866),U_10867) != hAPP(hAPP(c_Product__Type_OPair(U_10864,U_10865),U_10868),U_10869)
      | ( U_10867 = U_10869
        & U_10866 = U_10868 ) ),
    inference(miniscope,[status(thm)],[f_2906_2]) ).

cnf(f_2906_4,plain,
    ( U_10866 = U_10868
    | hAPP(hAPP(c_Product__Type_OPair(U_10864,U_10865),U_10866),U_10867) != hAPP(hAPP(c_Product__Type_OPair(U_10864,U_10865),U_10868),U_10869) ),
    inference(clausify,[status(thm)],[f_2906_3]) ).

cnf(f_2906_5,plain,
    ( U_10867 = U_10869
    | hAPP(hAPP(c_Product__Type_OPair(U_10864,U_10865),U_10866),U_10867) != hAPP(hAPP(c_Product__Type_OPair(U_10864,U_10865),U_10868),U_10869) ),
    inference(clausify,[status(thm)],[f_2906_3]) ).

fof(f_2907_1,plain,
    ! [V_c_2,T_d,T_c,T_b,V_q_2,V_p_2] :
      ( hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_c_2),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_c_2),V_q_2)
      | V_p_2 != V_q_2 ),
    inference(fof_nnf,[status(thm)],[fact_split__weak__cong]) ).

fof(f_2907_2,plain,
    ! [U_10875,U_10874,U_10873,U_10872,U_10871,U_10870] :
      ( hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10872,U_10873,U_10874),U_10875),U_10870) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10872,U_10873,U_10874),U_10875),U_10871)
      | U_10870 != U_10871 ),
    inference(variable_rename,[status(thm)],[f_2907_1]) ).

cnf(f_2907_3,plain,
    ( hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10872,U_10873,U_10874),U_10875),U_10870) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10872,U_10873,U_10874),U_10875),U_10871)
    | U_10870 != U_10871 ),
    inference(clausify,[status(thm)],[f_2907_2]) ).

fof(f_2908_1,plain,
    ! [V_q,V_p] : c_Divides_Odivmod__int(V_p,V_q) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_p),V_q)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_p,V_q)),
    inference(fof_nnf,[status(thm)],[fact_divmod__int__mod__div]) ).

fof(f_2908_2,plain,
    ! [U_10877,U_10876] : c_Divides_Odivmod__int(U_10876,U_10877) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10876),U_10877)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10876,U_10877)),
    inference(variable_rename,[status(thm)],[f_2908_1]) ).

cnf(f_2908_3,plain,
    c_Divides_Odivmod__int(U_10876,U_10877) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_10876),U_10877)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_10876,U_10877)),
    inference(clausify,[status(thm)],[f_2908_2]) ).

fof(f_2909_1,plain,
    ! [V_b_2,V_a_2,V_f1_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f1_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2),
    inference(fof_nnf,[status(thm)],[fact_prod_Osimps_I2_J]) ).

fof(f_2909_2,plain,
    ! [U_10883,U_10882,U_10881,U_10880,U_10879,U_10878] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10878,U_10879,U_10880),U_10881),hAPP(hAPP(c_Product__Type_OPair(U_10878,U_10879),U_10882),U_10883)) = hAPP(hAPP(U_10881,U_10882),U_10883),
    inference(variable_rename,[status(thm)],[f_2909_1]) ).

cnf(f_2909_3,plain,
    hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10878,U_10879,U_10880),U_10881),hAPP(hAPP(c_Product__Type_OPair(U_10878,U_10879),U_10882),U_10883)) = hAPP(hAPP(U_10881,U_10882),U_10883),
    inference(clausify,[status(thm)],[f_2909_2]) ).

fof(f_2910_1,plain,
    ! [V_b_2,V_a_2,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(V_f_2,V_a_2),V_b_2),
    inference(fof_nnf,[status(thm)],[fact_split__conv]) ).

fof(f_2910_2,plain,
    ! [U_10889,U_10888,U_10887,U_10886,U_10885,U_10884] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10884,U_10885,U_10886),U_10887),hAPP(hAPP(c_Product__Type_OPair(U_10884,U_10885),U_10888),U_10889)) = hAPP(hAPP(U_10887,U_10888),U_10889),
    inference(variable_rename,[status(thm)],[f_2910_1]) ).

cnf(f_2910_3,plain,
    hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10884,U_10885,U_10886),U_10887),hAPP(hAPP(c_Product__Type_OPair(U_10884,U_10885),U_10888),U_10889)) = hAPP(hAPP(U_10887,U_10888),U_10889),
    inference(clausify,[status(thm)],[f_2910_2]) ).

fof(f_2911_1,plain,
    ! [V_m_2,V_n_2] :
      ( ( c_Divides_Odivmod__nat(V_m_2,V_n_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat)),c_Nat_OSuc)),c_Divides_Odivmod__nat(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2),V_n_2))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
        | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( c_Divides_Odivmod__nat(V_m_2,V_n_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
          & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_divmod__nat__if]) ).

fof(f_2911_2,plain,
    ! [U_10891,U_10890] :
      ( ( c_Divides_Odivmod__nat(U_10891,U_10890) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat)),c_Nat_OSuc)),c_Divides_Odivmod__nat(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10891),U_10890),U_10890))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10891),U_10890))
        | U_10890 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( c_Divides_Odivmod__nat(U_10891,U_10890) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10891)
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10891),U_10890))
          & U_10890 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
    inference(variable_rename,[status(thm)],[f_2911_1]) ).

fof(f_2911_3,plain,
    ( ! [U_10895,U_10893] :
        ( c_Divides_Odivmod__nat(U_10895,U_10893) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat)),c_Nat_OSuc)),c_Divides_Odivmod__nat(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10895),U_10893),U_10893))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10895),U_10893))
        | U_10893 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_10894,U_10892] :
        ( c_Divides_Odivmod__nat(U_10894,U_10892) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10894)
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10894),U_10892))
          & U_10892 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
    inference(miniscope,[status(thm)],[f_2911_2]) ).

cnf(f_2911_4,plain,
    ( U_10892 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Divides_Odivmod__nat(U_10894,U_10892) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10894) ),
    inference(clausify,[status(thm)],[f_2911_3]) ).

cnf(f_2911_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10894),U_10892))
    | c_Divides_Odivmod__nat(U_10894,U_10892) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10894) ),
    inference(clausify,[status(thm)],[f_2911_3]) ).

cnf(f_2911_6,plain,
    ( c_Divides_Odivmod__nat(U_10895,U_10893) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat)),c_Nat_OSuc)),c_Divides_Odivmod__nat(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10895),U_10893),U_10893))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_10895),U_10893))
    | U_10893 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_2911_3]) ).

fof(f_2912_1,plain,
    ! [V_f_2,T_d,T_c,T_b] : hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,T_d),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),T_d,T_c),V_f_2)),c_Product__Type_OPair(T_b,T_c))) = V_f_2,
    inference(fof_nnf,[status(thm)],[fact_split__eta]) ).

fof(f_2912_2,plain,
    ! [U_10899,U_10898,U_10897,U_10896] : hAPP(c_Product__Type_Oprod_Oprod__case(U_10896,U_10897,U_10898),hAPP(hAPP(c_COMBB(tc_fun(U_10897,tc_prod(U_10896,U_10897)),tc_fun(U_10897,U_10898),U_10896),hAPP(c_COMBB(tc_prod(U_10896,U_10897),U_10898,U_10897),U_10899)),c_Product__Type_OPair(U_10896,U_10897))) = U_10899,
    inference(variable_rename,[status(thm)],[f_2912_1]) ).

cnf(f_2912_3,plain,
    hAPP(c_Product__Type_Oprod_Oprod__case(U_10896,U_10897,U_10898),hAPP(hAPP(c_COMBB(tc_fun(U_10897,tc_prod(U_10896,U_10897)),tc_fun(U_10897,U_10898),U_10896),hAPP(c_COMBB(tc_prod(U_10896,U_10897),U_10898,U_10897),U_10899)),c_Product__Type_OPair(U_10896,U_10897))) = U_10899,
    inference(clausify,[status(thm)],[f_2912_2]) ).

fof(f_2913_1,plain,
    ! [V_A_2,T_c,T_b] : c_Fun_Oinj__on(tc_prod(T_b,T_c),tc_prod(T_c,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_prod(T_c,T_b)),hAPP(c_COMBC(T_c,T_b,tc_prod(T_c,T_b)),c_Product__Type_OPair(T_c,T_b))),V_A_2),
    inference(fof_nnf,[status(thm)],[fact_swap__inj__on]) ).

fof(f_2913_2,plain,
    ! [U_10902,U_10901,U_10900] : c_Fun_Oinj__on(tc_prod(U_10900,U_10901),tc_prod(U_10901,U_10900),hAPP(c_Product__Type_Oprod_Oprod__case(U_10900,U_10901,tc_prod(U_10901,U_10900)),hAPP(c_COMBC(U_10901,U_10900,tc_prod(U_10901,U_10900)),c_Product__Type_OPair(U_10901,U_10900))),U_10902),
    inference(variable_rename,[status(thm)],[f_2913_1]) ).

cnf(f_2913_3,plain,
    c_Fun_Oinj__on(tc_prod(U_10900,U_10901),tc_prod(U_10901,U_10900),hAPP(c_Product__Type_Oprod_Oprod__case(U_10900,U_10901,tc_prod(U_10901,U_10900)),hAPP(c_COMBC(U_10901,U_10900,tc_prod(U_10901,U_10900)),c_Product__Type_OPair(U_10901,U_10900))),U_10902),
    inference(clausify,[status(thm)],[f_2913_2]) ).

fof(f_2914_1,plain,
    ! [V_p_2,V_g_2,T_f,T_e,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_e,T_f,tc_prod(T_c,T_d)),V_g_2),V_p_2)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_e,T_f,T_b),hAPP(hAPP(c_COMBB(tc_fun(T_f,tc_prod(T_c,T_d)),tc_fun(T_f,T_b),T_e),hAPP(c_COMBB(tc_prod(T_c,T_d),T_b,T_f),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2))),V_g_2)),V_p_2),
    inference(fof_nnf,[status(thm)],[fact_split__twice]) ).

fof(f_2914_2,plain,
    ! [U_10910,U_10909,U_10908,U_10907,U_10906,U_10905,U_10904,U_10903] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10903,U_10904,U_10905),U_10906),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10907,U_10908,tc_prod(U_10903,U_10904)),U_10909),U_10910)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10907,U_10908,U_10905),hAPP(hAPP(c_COMBB(tc_fun(U_10908,tc_prod(U_10903,U_10904)),tc_fun(U_10908,U_10905),U_10907),hAPP(c_COMBB(tc_prod(U_10903,U_10904),U_10905,U_10908),hAPP(c_Product__Type_Oprod_Oprod__case(U_10903,U_10904,U_10905),U_10906))),U_10909)),U_10910),
    inference(variable_rename,[status(thm)],[f_2914_1]) ).

cnf(f_2914_3,plain,
    hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10903,U_10904,U_10905),U_10906),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10907,U_10908,tc_prod(U_10903,U_10904)),U_10909),U_10910)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_10907,U_10908,U_10905),hAPP(hAPP(c_COMBB(tc_fun(U_10908,tc_prod(U_10903,U_10904)),tc_fun(U_10908,U_10905),U_10907),hAPP(c_COMBB(tc_prod(U_10903,U_10904),U_10905,U_10908),hAPP(c_Product__Type_Oprod_Oprod__case(U_10903,U_10904,U_10905),U_10906))),U_10909)),U_10910),
    inference(clausify,[status(thm)],[f_2914_2]) ).

fof(f_2915_1,plain,
    c_Nitpick_OFrac = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),c_fequal)),c_Nitpick_Oint__gcd))),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    inference(fof_nnf,[status(thm)],[fact_Nitpick_OFrac__def]) ).

cnf(f_2915_2,plain,
    c_Nitpick_OFrac = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),c_fequal)),c_Nitpick_Oint__gcd))),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    inference(clausify,[status(thm)],[f_2915_1]) ).

fof(f_2916_1,plain,
    ! [V_b,V_a] :
      ( ( ( ( c_Divides_Odivmod__int(V_a,V_b) = hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) )
          & ( c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OnegDivAlg(V_a,V_b)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) ) )
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) )
      & ( ( ( ( ( c_Divides_Odivmod__int(V_a,V_b) = hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)))
                | V_a = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
              & ( c_Divides_Odivmod__int(V_a,V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
                | V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) )
          & ( c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OposDivAlg(V_a,V_b)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) ) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) ) ),
    inference(fof_nnf,[status(thm)],[fact_divmod__int__def]) ).

fof(f_2916_2,plain,
    ! [U_10912,U_10911] :
      ( ( ( ( c_Divides_Odivmod__int(U_10911,U_10912) = hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10911),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10912)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10912)) )
          & ( c_Divides_Odivmod__int(U_10911,U_10912) = c_Divides_OnegDivAlg(U_10911,U_10912)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10912)) ) )
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10911)) )
      & ( ( ( ( ( c_Divides_Odivmod__int(U_10911,U_10912) = hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10911),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10912)))
                | U_10911 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
              & ( c_Divides_Odivmod__int(U_10911,U_10912) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
                | U_10911 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10912)) )
          & ( c_Divides_Odivmod__int(U_10911,U_10912) = c_Divides_OposDivAlg(U_10911,U_10912)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10912)) ) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10911)) ) ),
    inference(variable_rename,[status(thm)],[f_2916_1]) ).

fof(f_2916_3,plain,
    ( ! [U_10916,U_10914] :
        ( ( ( c_Divides_Odivmod__int(U_10914,U_10916) = hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10914),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10916)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10916)) )
          & ( c_Divides_Odivmod__int(U_10914,U_10916) = c_Divides_OnegDivAlg(U_10914,U_10916)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10916)) ) )
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10914)) )
    & ! [U_10915,U_10913] :
        ( ( ( ( ( c_Divides_Odivmod__int(U_10913,U_10915) = hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10913),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10915)))
                | U_10913 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
              & ( c_Divides_Odivmod__int(U_10913,U_10915) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
                | U_10913 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10915)) )
          & ( c_Divides_Odivmod__int(U_10913,U_10915) = c_Divides_OposDivAlg(U_10913,U_10915)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10915)) ) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10913)) ) ),
    inference(miniscope,[status(thm)],[f_2916_2]) ).

cnf(f_2916_4,plain,
    ( c_Divides_Odivmod__int(U_10913,U_10915) = c_Divides_OposDivAlg(U_10913,U_10915)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10915))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10913)) ),
    inference(clausify,[status(thm)],[f_2916_3]) ).

cnf(f_2916_5,plain,
    ( c_Divides_Odivmod__int(U_10913,U_10915) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | U_10913 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10915))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10913)) ),
    inference(clausify,[status(thm)],[f_2916_3]) ).

cnf(f_2916_6,plain,
    ( c_Divides_Odivmod__int(U_10913,U_10915) = hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10913),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10915)))
    | U_10913 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10915))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10913)) ),
    inference(clausify,[status(thm)],[f_2916_3]) ).

cnf(f_2916_7,plain,
    ( c_Divides_Odivmod__int(U_10914,U_10916) = c_Divides_OnegDivAlg(U_10914,U_10916)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10916))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10914)) ),
    inference(clausify,[status(thm)],[f_2916_3]) ).

cnf(f_2916_8,plain,
    ( c_Divides_Odivmod__int(U_10914,U_10916) = hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10914),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10916)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10916))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10914)) ),
    inference(clausify,[status(thm)],[f_2916_3]) ).

fof(f_2917_1,plain,
    ! [V_l_2,V_k_2] :
      ( ( ( ( c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_l_2))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fdisj,hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l_2)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_l_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(V_k_2,V_l_2)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_l_2))))),c_Divides_Opdivmod(V_k_2,V_l_2))))
            | V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
          & ( c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)
            | V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(fof_nnf,[status(thm)],[fact_divmod__int__pdivmod]) ).

fof(f_2917_2,plain,
    ! [U_10918,U_10917] :
      ( ( ( ( c_Divides_Odivmod__int(U_10917,U_10918) = hAPP(c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_10918))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fdisj,hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10918)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10917))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10918),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10917),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(U_10917,U_10918)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_10918))))),c_Divides_Opdivmod(U_10917,U_10918))))
            | U_10918 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
          & ( c_Divides_Odivmod__int(U_10917,U_10918) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10917)
            | U_10918 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | U_10917 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Divides_Odivmod__int(U_10917,U_10918) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | U_10917 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[f_2917_1]) ).

fof(f_2917_3,plain,
    ( ! [U_10922,U_10920] :
        ( ( ( c_Divides_Odivmod__int(U_10920,U_10922) = hAPP(c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_10922))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fdisj,hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10922)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10920))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10922),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10920),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(U_10920,U_10922)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_10922))))),c_Divides_Opdivmod(U_10920,U_10922))))
            | U_10922 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
          & ( c_Divides_Odivmod__int(U_10920,U_10922) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10920)
            | U_10922 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | U_10920 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
    & ! [U_10921,U_10919] :
        ( c_Divides_Odivmod__int(U_10919,U_10921) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | U_10919 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(miniscope,[status(thm)],[f_2917_2]) ).

cnf(f_2917_4,plain,
    ( c_Divides_Odivmod__int(U_10919,U_10921) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | U_10919 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2917_3]) ).

cnf(f_2917_5,plain,
    ( c_Divides_Odivmod__int(U_10920,U_10922) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10920)
    | U_10922 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_10920 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2917_3]) ).

cnf(f_2917_6,plain,
    ( c_Divides_Odivmod__int(U_10920,U_10922) = hAPP(c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_10922))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fdisj,hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10922)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10920))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10922),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_10920),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(U_10920,U_10922)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_10922))))),c_Divides_Opdivmod(U_10920,U_10922))))
    | U_10922 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_10920 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2917_3]) ).

fof(f_2918_1,plain,
    ! [V_y_2,V_x_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),V_x_2),V_y_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),hAPP(V_f_2,V_y_2)),
    inference(fof_nnf,[status(thm)],[fact_apsnd__conv]) ).

fof(f_2918_2,plain,
    ! [U_10928,U_10927,U_10926,U_10925,U_10924,U_10923] : hAPP(c_Product__Type_Oapsnd(U_10923,U_10924,U_10925,U_10926),hAPP(hAPP(c_Product__Type_OPair(U_10925,U_10923),U_10927),U_10928)) = hAPP(hAPP(c_Product__Type_OPair(U_10925,U_10924),U_10927),hAPP(U_10926,U_10928)),
    inference(variable_rename,[status(thm)],[f_2918_1]) ).

cnf(f_2918_3,plain,
    hAPP(c_Product__Type_Oapsnd(U_10923,U_10924,U_10925,U_10926),hAPP(hAPP(c_Product__Type_OPair(U_10925,U_10923),U_10927),U_10928)) = hAPP(hAPP(c_Product__Type_OPair(U_10925,U_10924),U_10927),hAPP(U_10926,U_10928)),
    inference(clausify,[status(thm)],[f_2918_2]) ).

fof(f_2919_1,plain,
    c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)),
    inference(fof_nnf,[status(thm)],[fact_negateSnd__def]) ).

cnf(f_2919_2,plain,
    c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)),
    inference(clausify,[status(thm)],[f_2919_1]) ).

fof(f_2920_1,plain,
    ! [V_x_2,V_g_2,T_e,V_f_2,T_b,T_c,T_d] : hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),hAPP(c_Product__Type_Oapsnd(T_e,T_d,T_b,V_g_2),V_x_2)) = hAPP(c_Product__Type_Oapsnd(T_e,T_c,T_b,hAPP(c_Fun_Ocomp(T_d,T_c,T_e,V_f_2),V_g_2)),V_x_2),
    inference(fof_nnf,[status(thm)],[fact_apsnd__compose]) ).

fof(f_2920_2,plain,
    ! [U_10935,U_10934,U_10933,U_10932,U_10931,U_10930,U_10929] : hAPP(c_Product__Type_Oapsnd(U_10929,U_10930,U_10931,U_10932),hAPP(c_Product__Type_Oapsnd(U_10933,U_10929,U_10931,U_10934),U_10935)) = hAPP(c_Product__Type_Oapsnd(U_10933,U_10930,U_10931,hAPP(c_Fun_Ocomp(U_10929,U_10930,U_10933,U_10932),U_10934)),U_10935),
    inference(variable_rename,[status(thm)],[f_2920_1]) ).

cnf(f_2920_3,plain,
    hAPP(c_Product__Type_Oapsnd(U_10929,U_10930,U_10931,U_10932),hAPP(c_Product__Type_Oapsnd(U_10933,U_10929,U_10931,U_10934),U_10935)) = hAPP(c_Product__Type_Oapsnd(U_10933,U_10930,U_10931,hAPP(c_Fun_Ocomp(U_10929,U_10930,U_10933,U_10932),U_10934)),U_10935),
    inference(clausify,[status(thm)],[f_2920_2]) ).

fof(f_2921_1,plain,
    ! [V_r,V_q] : hAPP(c_Divides_OnegateSnd,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_r)),
    inference(fof_nnf,[status(thm)],[fact_negateSnd__eq]) ).

fof(f_2921_2,plain,
    ! [U_10937,U_10936] : hAPP(c_Divides_OnegateSnd,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_10936),U_10937)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_10936),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10937)),
    inference(variable_rename,[status(thm)],[f_2921_1]) ).

cnf(f_2921_3,plain,
    hAPP(c_Divides_OnegateSnd,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_10936),U_10937)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_10936),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10937)),
    inference(clausify,[status(thm)],[f_2921_2]) ).

fof(f_2922_1,plain,
    ! [V_l,V_k] : c_Divides_Opdivmod(V_k,V_l) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_k)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_l))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_k),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_l))),
    inference(fof_nnf,[status(thm)],[fact_pdivmod__def]) ).

fof(f_2922_2,plain,
    ! [U_10939,U_10938] : c_Divides_Opdivmod(U_10938,U_10939) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_10938)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_10939))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_10938),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_10939))),
    inference(variable_rename,[status(thm)],[f_2922_1]) ).

cnf(f_2922_3,plain,
    c_Divides_Opdivmod(U_10938,U_10939) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_10938)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_10939))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_10938),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_10939))),
    inference(clausify,[status(thm)],[f_2922_2]) ).

fof(f_2923_1,plain,
    ! [V_k,V_l] :
      ( ( c_Divides_Opdivmod(V_k,V_l) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_k),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_l))
        | V_l = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Divides_Opdivmod(V_k,V_l) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_k))
        | V_l != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(fof_nnf,[status(thm)],[fact_pdivmod__posDivAlg]) ).

fof(f_2923_2,plain,
    ! [U_10941,U_10940] :
      ( ( c_Divides_Opdivmod(U_10941,U_10940) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_10941),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_10940))
        | U_10940 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Divides_Opdivmod(U_10941,U_10940) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_10941))
        | U_10940 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[f_2923_1]) ).

fof(f_2923_3,plain,
    ( ! [U_10945,U_10943] :
        ( c_Divides_Opdivmod(U_10945,U_10943) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_10945),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_10943))
        | U_10943 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
    & ! [U_10944,U_10942] :
        ( c_Divides_Opdivmod(U_10944,U_10942) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_10944))
        | U_10942 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(miniscope,[status(thm)],[f_2923_2]) ).

cnf(f_2923_4,plain,
    ( c_Divides_Opdivmod(U_10944,U_10942) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_10944))
    | U_10942 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2923_3]) ).

cnf(f_2923_5,plain,
    ( c_Divides_Opdivmod(U_10945,U_10943) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_10945),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_10943))
    | U_10943 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2923_3]) ).

fof(f_2924_1,plain,
    ! [V_l_2,V_k_2] :
      ( ( ( ( c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_l_2))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fequal,c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_k_2)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_l_2))),c_Divides_Opdivmod(V_k_2,V_l_2)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_l_2))))),c_Divides_Opdivmod(V_k_2,V_l_2))))
            | V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
          & ( c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)
            | V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(fof_nnf,[status(thm)],[fact_divmod__int__code]) ).

fof(f_2924_2,plain,
    ! [U_10947,U_10946] :
      ( ( ( ( c_Divides_Odivmod__int(U_10946,U_10947) = hAPP(c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_10947))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fequal,c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_10946)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_10947))),c_Divides_Opdivmod(U_10946,U_10947)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_10947))))),c_Divides_Opdivmod(U_10946,U_10947))))
            | U_10947 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
          & ( c_Divides_Odivmod__int(U_10946,U_10947) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10946)
            | U_10947 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | U_10946 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Divides_Odivmod__int(U_10946,U_10947) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | U_10946 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[f_2924_1]) ).

fof(f_2924_3,plain,
    ( ! [U_10951,U_10949] :
        ( ( ( c_Divides_Odivmod__int(U_10949,U_10951) = hAPP(c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_10951))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fequal,c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_10949)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_10951))),c_Divides_Opdivmod(U_10949,U_10951)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_10951))))),c_Divides_Opdivmod(U_10949,U_10951))))
            | U_10951 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
          & ( c_Divides_Odivmod__int(U_10949,U_10951) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10949)
            | U_10951 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | U_10949 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
    & ! [U_10950,U_10948] :
        ( c_Divides_Odivmod__int(U_10948,U_10950) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | U_10948 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(miniscope,[status(thm)],[f_2924_2]) ).

cnf(f_2924_4,plain,
    ( c_Divides_Odivmod__int(U_10948,U_10950) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | U_10948 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2924_3]) ).

cnf(f_2924_5,plain,
    ( c_Divides_Odivmod__int(U_10949,U_10951) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_10949)
    | U_10951 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_10949 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2924_3]) ).

cnf(f_2924_6,plain,
    ( c_Divides_Odivmod__int(U_10949,U_10951) = hAPP(c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_10951))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fequal,c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_10949)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_10951))),c_Divides_Opdivmod(U_10949,U_10951)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_10951))))),c_Divides_Opdivmod(U_10949,U_10951))))
    | U_10951 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_10949 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2924_3]) ).

fof(f_2925_1,plain,
    ! [V_a,V_r,V_q,V_c,V_b] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_b),V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_q)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_r)),V_c))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_r),V_c))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_b,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_q),V_r))) ),
    inference(fof_nnf,[status(thm)],[fact_divmod__nat__rel__mult1__eq]) ).

fof(f_2925_2,plain,
    ! [U_10956,U_10955,U_10954,U_10953,U_10952] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10956),U_10952),U_10953),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10956),U_10954)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10956),U_10955)),U_10953))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10956),U_10955),U_10953))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10953))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_10952,U_10953),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10954),U_10955))) ),
    inference(variable_rename,[status(thm)],[f_2925_1]) ).

cnf(f_2925_3,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10956),U_10952),U_10953),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10956),U_10954)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10956),U_10955)),U_10953))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10956),U_10955),U_10953))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10953))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_10952,U_10953),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10954),U_10955))) ),
    inference(clausify,[status(thm)],[f_2925_2]) ).

fof(f_2926_1,plain,
    ! [V_c,V_r,V_q,V_b,V_a] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_q),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_q,V_c))),V_r))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_b))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_q),V_r))) ),
    inference(fof_nnf,[status(thm)],[fact_divmod__nat__rel__mult2__eq]) ).

fof(f_2926_2,plain,
    ! [U_10961,U_10960,U_10959,U_10958,U_10957] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_10957,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10958),U_10961)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10959),U_10961)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10958),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10959,U_10961))),U_10960))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10961))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10958))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_10957,U_10958),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10959),U_10960))) ),
    inference(variable_rename,[status(thm)],[f_2926_1]) ).

cnf(f_2926_3,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_10957,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10958),U_10961)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10959),U_10961)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10958),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10959,U_10961))),U_10960))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10961))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10958))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_10957,U_10958),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10959),U_10960))) ),
    inference(clausify,[status(thm)],[f_2926_2]) ).

fof(f_2927_1,plain,
    ! [V_b,V_a,T_b,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(T_a,T_b)),c_Nitpick_Opair__box_OPairBox(T_a,T_b,V_a,V_b)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_pair__box_Osize_I2_J]) ).

fof(f_2927_2,plain,
    ! [U_10965,U_10964,U_10963,U_10962] : hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(U_10962,U_10963)),c_Nitpick_Opair__box_OPairBox(U_10962,U_10963,U_10964,U_10965)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_2927_1]) ).

cnf(f_2927_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(U_10962,U_10963)),c_Nitpick_Opair__box_OPairBox(U_10962,U_10963,U_10964,U_10965)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_2927_2]) ).

fof(f_2928_1,plain,
    ! [V_qr_H,V_qr,V_n,V_m] :
      ( V_qr = V_qr_H
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr_H))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr)) ),
    inference(fof_nnf,[status(thm)],[fact_divmod__nat__rel__unique]) ).

fof(f_2928_2,plain,
    ! [U_10969,U_10968,U_10967,U_10966] :
      ( U_10968 = U_10969
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_10966,U_10967),U_10969))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_10966,U_10967),U_10968)) ),
    inference(variable_rename,[status(thm)],[f_2928_1]) ).

cnf(f_2928_3,plain,
    ( U_10968 = U_10969
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_10966,U_10967),U_10969))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_10966,U_10967),U_10968)) ),
    inference(clausify,[status(thm)],[f_2928_2]) ).

fof(f_2929_1,plain,
    ! [V_qr,V_n,V_m] :
      ( c_Divides_Odivmod__nat(V_m,V_n) = V_qr
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr)) ),
    inference(fof_nnf,[status(thm)],[fact_divmod__nat__eq]) ).

fof(f_2929_2,plain,
    ! [U_10972,U_10971,U_10970] :
      ( c_Divides_Odivmod__nat(U_10970,U_10971) = U_10972
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_10970,U_10971),U_10972)) ),
    inference(variable_rename,[status(thm)],[f_2929_1]) ).

cnf(f_2929_3,plain,
    ( c_Divides_Odivmod__nat(U_10970,U_10971) = U_10972
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_10970,U_10971),U_10972)) ),
    inference(clausify,[status(thm)],[f_2929_2]) ).

fof(f_2930_1,plain,
    ! [V_n,V_m] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),c_Divides_Odivmod__nat(V_m,V_n))),
    inference(fof_nnf,[status(thm)],[fact_divmod__nat__rel__divmod__nat]) ).

fof(f_2930_2,plain,
    ! [U_10974,U_10973] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_10973,U_10974),c_Divides_Odivmod__nat(U_10973,U_10974))),
    inference(variable_rename,[status(thm)],[f_2930_1]) ).

cnf(f_2930_3,plain,
    hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_10973,U_10974),c_Divides_Odivmod__nat(U_10973,U_10974))),
    inference(clausify,[status(thm)],[f_2930_2]) ).

fof(f_2931_1,plain,
    ! [V_r,V_q,V_n,V_m] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_r
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_q),V_r))) ),
    inference(fof_nnf,[status(thm)],[fact_mod__eq]) ).

fof(f_2931_2,plain,
    ! [U_10978,U_10977,U_10976,U_10975] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10975,U_10976) = U_10978
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_10975,U_10976),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10977),U_10978))) ),
    inference(variable_rename,[status(thm)],[f_2931_1]) ).

cnf(f_2931_3,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10975,U_10976) = U_10978
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_10975,U_10976),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10977),U_10978))) ),
    inference(clausify,[status(thm)],[f_2931_2]) ).

fof(f_2932_1,plain,
    ! [V_r,V_q,V_n,V_m] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = V_q
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_q),V_r))) ),
    inference(fof_nnf,[status(thm)],[fact_div__eq]) ).

fof(f_2932_2,plain,
    ! [U_10982,U_10981,U_10980,U_10979] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10979),U_10980) = U_10981
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_10979,U_10980),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10981),U_10982))) ),
    inference(variable_rename,[status(thm)],[f_2932_1]) ).

cnf(f_2932_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10979),U_10980) = U_10981
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_10979,U_10980),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10981),U_10982))) ),
    inference(clausify,[status(thm)],[f_2932_2]) ).

fof(f_2933_1,plain,
    ! [V_n,V_m] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)))),
    inference(fof_nnf,[status(thm)],[fact_divmod__nat__rel]) ).

fof(f_2933_2,plain,
    ! [U_10984,U_10983] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_10983,U_10984),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10983),U_10984)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10983,U_10984)))),
    inference(variable_rename,[status(thm)],[f_2933_1]) ).

cnf(f_2933_3,plain,
    hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_10983,U_10984),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_10983),U_10984)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_10983,U_10984)))),
    inference(clausify,[status(thm)],[f_2933_2]) ).

fof(f_2934_1,plain,
    ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a),V_b),V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_aq),V_bq)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_ar),V_br)),V_c))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_ar),V_br),V_c))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_b,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_bq),V_br)))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_a,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_aq),V_ar))) ),
    inference(fof_nnf,[status(thm)],[fact_divmod__nat__rel__add1__eq]) ).

fof(f_2934_2,plain,
    ! [U_10991,U_10990,U_10989,U_10988,U_10987,U_10986,U_10985] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10985),U_10989),U_10986),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10987),U_10990)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10988),U_10991)),U_10986))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10988),U_10991),U_10986))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10986))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_10989,U_10986),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10990),U_10991)))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_10985,U_10986),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10987),U_10988))) ),
    inference(variable_rename,[status(thm)],[f_2934_1]) ).

cnf(f_2934_3,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10985),U_10989),U_10986),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10987),U_10990)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10988),U_10991)),U_10986))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10988),U_10991),U_10986))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_10986))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_10989,U_10986),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10990),U_10991)))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_10985,U_10986),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10987),U_10988))) ),
    inference(clausify,[status(thm)],[f_2934_2]) ).

fof(f_2935_1,plain,
    ! [V_b_2,V_a_2,V_f1_2,T_b,T_d,T_c] : c_Nitpick_Opair__box_Opair__box__case(T_c,T_d,T_b,V_f1_2,c_Nitpick_Opair__box_OPairBox(T_c,T_d,V_a_2,V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2),
    inference(fof_nnf,[status(thm)],[fact_pair__box_Osimps_I2_J]) ).

fof(f_2935_2,plain,
    ! [U_10997,U_10996,U_10995,U_10994,U_10993,U_10992] : c_Nitpick_Opair__box_Opair__box__case(U_10992,U_10993,U_10994,U_10995,c_Nitpick_Opair__box_OPairBox(U_10992,U_10993,U_10996,U_10997)) = hAPP(hAPP(U_10995,U_10996),U_10997),
    inference(variable_rename,[status(thm)],[f_2935_1]) ).

cnf(f_2935_3,plain,
    c_Nitpick_Opair__box_Opair__box__case(U_10992,U_10993,U_10994,U_10995,c_Nitpick_Opair__box_OPairBox(U_10992,U_10993,U_10996,U_10997)) = hAPP(hAPP(U_10995,U_10996),U_10997),
    inference(clausify,[status(thm)],[f_2935_2]) ).

fof(f_2936_1,plain,
    ! [V_b_2,V_a_2,V_f1_2,T_b,T_d,T_c] : c_Nitpick_Opair__box_Opair__box__rec(T_c,T_d,T_b,V_f1_2,c_Nitpick_Opair__box_OPairBox(T_c,T_d,V_a_2,V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2),
    inference(fof_nnf,[status(thm)],[fact_pair__box_Orecs]) ).

fof(f_2936_2,plain,
    ! [U_11003,U_11002,U_11001,U_11000,U_10999,U_10998] : c_Nitpick_Opair__box_Opair__box__rec(U_10998,U_10999,U_11000,U_11001,c_Nitpick_Opair__box_OPairBox(U_10998,U_10999,U_11002,U_11003)) = hAPP(hAPP(U_11001,U_11002),U_11003),
    inference(variable_rename,[status(thm)],[f_2936_1]) ).

cnf(f_2936_3,plain,
    c_Nitpick_Opair__box_Opair__box__rec(U_10998,U_10999,U_11000,U_11001,c_Nitpick_Opair__box_OPairBox(U_10998,U_10999,U_11002,U_11003)) = hAPP(hAPP(U_11001,U_11002),U_11003),
    inference(clausify,[status(thm)],[f_2936_2]) ).

fof(f_2937_1,plain,
    ! [V_b_2,V_a_2] :
      ( ( ( c_Divides_OnegDivAlg(V_a_2,V_b_2) = hAPP(c_Divides_Oadjust(V_b_2),c_Divides_OnegDivAlg(V_a_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b_2)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),V_b_2))) )
        & ( c_Divides_OnegDivAlg(V_a_2,V_b_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),V_b_2))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),V_b_2))) ) ) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a_2),V_b_2))) ),
    inference(fof_nnf,[status(thm)],[fact_negDivAlg_Opsimps]) ).

fof(f_2937_2,plain,
    ! [U_11005,U_11004] :
      ( ( ( c_Divides_OnegDivAlg(U_11004,U_11005) = hAPP(c_Divides_Oadjust(U_11005),c_Divides_OnegDivAlg(U_11004,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_11005)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11005),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11004),U_11005))) )
        & ( c_Divides_OnegDivAlg(U_11004,U_11005) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11004),U_11005))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11005),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11004),U_11005))) ) ) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11004),U_11005))) ),
    inference(variable_rename,[status(thm)],[f_2937_1]) ).

cnf(f_2937_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11004),U_11005)))
    | c_Divides_OnegDivAlg(U_11004,U_11005) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11004),U_11005))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11004),U_11005))) ),
    inference(clausify,[status(thm)],[f_2937_2]) ).

cnf(f_2937_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11005),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | c_Divides_OnegDivAlg(U_11004,U_11005) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11004),U_11005))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11004),U_11005))) ),
    inference(clausify,[status(thm)],[f_2937_2]) ).

cnf(f_2937_5,plain,
    ( c_Divides_OnegDivAlg(U_11004,U_11005) = hAPP(c_Divides_Oadjust(U_11005),c_Divides_OnegDivAlg(U_11004,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_11005)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11005),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11004),U_11005)))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11004),U_11005))) ),
    inference(clausify,[status(thm)],[f_2937_2]) ).

fof(f_2938_1,plain,
    ! [V_b_2,V_a_2] :
      ( ( ( c_Divides_OposDivAlg(V_a_2,V_b_2) = hAPP(c_Divides_Oadjust(V_b_2),c_Divides_OposDivAlg(V_a_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b_2)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2)) )
        & ( c_Divides_OposDivAlg(V_a_2,V_b_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2)) ) ) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a_2),V_b_2))) ),
    inference(fof_nnf,[status(thm)],[fact_posDivAlg_Opsimps]) ).

fof(f_2938_2,plain,
    ! [U_11007,U_11006] :
      ( ( ( c_Divides_OposDivAlg(U_11006,U_11007) = hAPP(c_Divides_Oadjust(U_11007),c_Divides_OposDivAlg(U_11006,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_11007)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11007),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11006),U_11007)) )
        & ( c_Divides_OposDivAlg(U_11006,U_11007) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11006)
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11007),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11006),U_11007)) ) ) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11006),U_11007))) ),
    inference(variable_rename,[status(thm)],[f_2938_1]) ).

cnf(f_2938_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11006),U_11007))
    | c_Divides_OposDivAlg(U_11006,U_11007) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11006)
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11006),U_11007))) ),
    inference(clausify,[status(thm)],[f_2938_2]) ).

cnf(f_2938_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11007),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | c_Divides_OposDivAlg(U_11006,U_11007) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11006)
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11006),U_11007))) ),
    inference(clausify,[status(thm)],[f_2938_2]) ).

cnf(f_2938_5,plain,
    ( c_Divides_OposDivAlg(U_11006,U_11007) = hAPP(c_Divides_Oadjust(U_11007),c_Divides_OposDivAlg(U_11006,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_11007)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11007),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11006),U_11007))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11006),U_11007))) ),
    inference(clausify,[status(thm)],[f_2938_2]) ).

fof(f_2939_1,plain,
    ! [V_b_2,V_a_2] :
      ( ( ( ( ( c_Nitpick_Onorm__frac(V_a_2,V_b_2) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,V_a_2),V_b_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b_2)))
              | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
              | V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
            & ( c_Nitpick_Onorm__frac(V_a_2,V_b_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
              | ( V_b_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
                & V_a_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) )
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        & ( c_Nitpick_Onorm__frac(V_a_2,V_b_2) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a_2),V_b_2))) ),
    inference(fof_nnf,[status(thm)],[fact_norm__frac_Opsimps]) ).

fof(f_2939_2,plain,
    ! [U_11009,U_11008] :
      ( ( ( ( ( c_Nitpick_Onorm__frac(U_11008,U_11009) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,U_11008),U_11009)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11008))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11009)))
              | U_11009 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
              | U_11008 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
            & ( c_Nitpick_Onorm__frac(U_11008,U_11009) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
              | ( U_11009 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
                & U_11008 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) )
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11009),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        & ( c_Nitpick_Onorm__frac(U_11008,U_11009) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11008),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11009))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11009),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11008),U_11009))) ),
    inference(variable_rename,[status(thm)],[f_2939_1]) ).

cnf(f_2939_3,plain,
    ( c_Nitpick_Onorm__frac(U_11008,U_11009) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11008),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11009))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11009),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11008),U_11009))) ),
    inference(clausify,[status(thm)],[f_2939_2]) ).

cnf(f_2939_4,plain,
    ( U_11008 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Nitpick_Onorm__frac(U_11008,U_11009) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11009),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11008),U_11009))) ),
    inference(clausify,[status(thm)],[f_2939_2]) ).

cnf(f_2939_5,plain,
    ( U_11009 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Nitpick_Onorm__frac(U_11008,U_11009) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11009),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11008),U_11009))) ),
    inference(clausify,[status(thm)],[f_2939_2]) ).

cnf(f_2939_6,plain,
    ( c_Nitpick_Onorm__frac(U_11008,U_11009) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,U_11008),U_11009)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11008))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11009)))
    | U_11009 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_11008 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11009),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11008),U_11009))) ),
    inference(clausify,[status(thm)],[f_2939_2]) ).

fof(f_2940_1,plain,
    ! [V_P_2,V_a1_2,V_a0_2] :
      ( hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2))
      | ? [B_a,B_b] :
          ( ~ hBOOL(hAPP(hAPP(V_P_2,B_a),B_b))
          & ( hBOOL(hAPP(hAPP(V_P_2,B_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),B_b)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_a),B_b))) )
          & hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_a),B_b))) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2))) ),
    inference(fof_nnf,[status(thm)],[fact_negDivAlg_Opinduct]) ).

fof(f_2940_2,plain,
    ! [U_11014,U_11013,U_11012] :
      ( hBOOL(hAPP(hAPP(U_11014,U_11012),U_11013))
      | ? [U_11011,U_11010] :
          ( ~ hBOOL(hAPP(hAPP(U_11014,U_11011),U_11010))
          & ( hBOOL(hAPP(hAPP(U_11014,U_11011),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_11010)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11010),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11011),U_11010))) )
          & hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11011),U_11010))) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11012),U_11013))) ),
    inference(variable_rename,[status(thm)],[f_2940_1]) ).

fof(f_2940_3,plain,
    ! [U_11014,U_11013,U_11012] :
      ( hBOOL(hAPP(hAPP(U_11014,U_11012),U_11013))
      | ? [U_11010] :
          ( ~ hBOOL(hAPP(hAPP(U_11014,sK251(U_11014,U_11013,U_11012)),U_11010))
          & ( hBOOL(hAPP(hAPP(U_11014,sK251(U_11014,U_11013,U_11012)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_11010)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11010),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK251(U_11014,U_11013,U_11012)),U_11010))) )
          & hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),sK251(U_11014,U_11013,U_11012)),U_11010))) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11012),U_11013))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK251]),skolemize(U_11011,sK251(U_11014,U_11013,U_11012))],[f_2940_2]) ).

fof(f_2940_4,plain,
    ! [U_11014,U_11013,U_11012] :
      ( hBOOL(hAPP(hAPP(U_11014,U_11012),U_11013))
      | ( ~ hBOOL(hAPP(hAPP(U_11014,sK251(U_11014,U_11013,U_11012)),sK252(U_11014,U_11013,U_11012)))
        & ( hBOOL(hAPP(hAPP(U_11014,sK251(U_11014,U_11013,U_11012)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),sK252(U_11014,U_11013,U_11012))))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK252(U_11014,U_11013,U_11012)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK251(U_11014,U_11013,U_11012)),sK252(U_11014,U_11013,U_11012)))) )
        & hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),sK251(U_11014,U_11013,U_11012)),sK252(U_11014,U_11013,U_11012)))) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11012),U_11013))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK252]),skolemize(U_11010,sK252(U_11014,U_11013,U_11012))],[f_2940_3]) ).

cnf(f_2940_5,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),sK251(U_11014,U_11013,U_11012)),sK252(U_11014,U_11013,U_11012))))
    | hBOOL(hAPP(hAPP(U_11014,U_11012),U_11013))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11012),U_11013))) ),
    inference(clausify,[status(thm)],[f_2940_4]) ).

cnf(f_2940_6,plain,
    ( hBOOL(hAPP(hAPP(U_11014,sK251(U_11014,U_11013,U_11012)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),sK252(U_11014,U_11013,U_11012))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK252(U_11014,U_11013,U_11012)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK251(U_11014,U_11013,U_11012)),sK252(U_11014,U_11013,U_11012))))
    | hBOOL(hAPP(hAPP(U_11014,U_11012),U_11013))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11012),U_11013))) ),
    inference(clausify,[status(thm)],[f_2940_4]) ).

cnf(f_2940_7,plain,
    ( ~ hBOOL(hAPP(hAPP(U_11014,sK251(U_11014,U_11013,U_11012)),sK252(U_11014,U_11013,U_11012)))
    | hBOOL(hAPP(hAPP(U_11014,U_11012),U_11013))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11012),U_11013))) ),
    inference(clausify,[status(thm)],[f_2940_4]) ).

fof(f_2941_1,plain,
    ! [V_P_2,V_a1_2,V_a0_2] :
      ( hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2))
      | ? [B_a,B_b] :
          ( ~ hBOOL(hAPP(hAPP(V_P_2,B_a),B_b))
          & ( hBOOL(hAPP(hAPP(V_P_2,B_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),B_b)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_a),B_b)) )
          & hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_a),B_b))) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2))) ),
    inference(fof_nnf,[status(thm)],[fact_posDivAlg_Opinduct]) ).

fof(f_2941_2,plain,
    ! [U_11019,U_11018,U_11017] :
      ( hBOOL(hAPP(hAPP(U_11019,U_11017),U_11018))
      | ? [U_11016,U_11015] :
          ( ~ hBOOL(hAPP(hAPP(U_11019,U_11016),U_11015))
          & ( hBOOL(hAPP(hAPP(U_11019,U_11016),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_11015)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11015),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11016),U_11015)) )
          & hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11016),U_11015))) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11017),U_11018))) ),
    inference(variable_rename,[status(thm)],[f_2941_1]) ).

fof(f_2941_3,plain,
    ! [U_11019,U_11018,U_11017] :
      ( hBOOL(hAPP(hAPP(U_11019,U_11017),U_11018))
      | ? [U_11015] :
          ( ~ hBOOL(hAPP(hAPP(U_11019,sK253(U_11019,U_11018,U_11017)),U_11015))
          & ( hBOOL(hAPP(hAPP(U_11019,sK253(U_11019,U_11018,U_11017)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_11015)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11015),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK253(U_11019,U_11018,U_11017)),U_11015)) )
          & hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),sK253(U_11019,U_11018,U_11017)),U_11015))) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11017),U_11018))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK253]),skolemize(U_11016,sK253(U_11019,U_11018,U_11017))],[f_2941_2]) ).

fof(f_2941_4,plain,
    ! [U_11019,U_11018,U_11017] :
      ( hBOOL(hAPP(hAPP(U_11019,U_11017),U_11018))
      | ( ~ hBOOL(hAPP(hAPP(U_11019,sK253(U_11019,U_11018,U_11017)),sK254(U_11019,U_11018,U_11017)))
        & ( hBOOL(hAPP(hAPP(U_11019,sK253(U_11019,U_11018,U_11017)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),sK254(U_11019,U_11018,U_11017))))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK254(U_11019,U_11018,U_11017)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK253(U_11019,U_11018,U_11017)),sK254(U_11019,U_11018,U_11017))) )
        & hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),sK253(U_11019,U_11018,U_11017)),sK254(U_11019,U_11018,U_11017)))) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11017),U_11018))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK254]),skolemize(U_11015,sK254(U_11019,U_11018,U_11017))],[f_2941_3]) ).

cnf(f_2941_5,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),sK253(U_11019,U_11018,U_11017)),sK254(U_11019,U_11018,U_11017))))
    | hBOOL(hAPP(hAPP(U_11019,U_11017),U_11018))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11017),U_11018))) ),
    inference(clausify,[status(thm)],[f_2941_4]) ).

cnf(f_2941_6,plain,
    ( hBOOL(hAPP(hAPP(U_11019,sK253(U_11019,U_11018,U_11017)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),sK254(U_11019,U_11018,U_11017))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK254(U_11019,U_11018,U_11017)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK253(U_11019,U_11018,U_11017)),sK254(U_11019,U_11018,U_11017)))
    | hBOOL(hAPP(hAPP(U_11019,U_11017),U_11018))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11017),U_11018))) ),
    inference(clausify,[status(thm)],[f_2941_4]) ).

cnf(f_2941_7,plain,
    ( ~ hBOOL(hAPP(hAPP(U_11019,sK253(U_11019,U_11018,U_11017)),sK254(U_11019,U_11018,U_11017)))
    | hBOOL(hAPP(hAPP(U_11019,U_11017),U_11018))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11017),U_11018))) ),
    inference(clausify,[status(thm)],[f_2941_4]) ).

fof(f_2942_1,plain,
    ! [V_R2_2,V_R1_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Wellfounded_Oaccp(T_b,V_R2_2)),c_Wellfounded_Oaccp(T_b,V_R1_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),V_R1_2),V_R2_2)) ),
    inference(fof_nnf,[status(thm)],[fact_accp__subset]) ).

fof(f_2942_2,plain,
    ! [U_11022,U_11021,U_11020] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11020,tc_HOL_Obool)),c_Wellfounded_Oaccp(U_11020,U_11022)),c_Wellfounded_Oaccp(U_11020,U_11021)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11020,tc_fun(U_11020,tc_HOL_Obool))),U_11021),U_11022)) ),
    inference(variable_rename,[status(thm)],[f_2942_1]) ).

cnf(f_2942_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11020,tc_HOL_Obool)),c_Wellfounded_Oaccp(U_11020,U_11022)),c_Wellfounded_Oaccp(U_11020,U_11021)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11020,tc_fun(U_11020,tc_HOL_Obool))),U_11021),U_11022)) ),
    inference(clausify,[status(thm)],[f_2942_2]) ).

fof(f_2943_1,plain,
    ! [V_c,V_r,V_q,V_b,V_a] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_q),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
      | V_b = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r))) ),
    inference(fof_nnf,[status(thm)],[fact_zmult2__lemma]) ).

fof(f_2943_2,plain,
    ! [U_11027,U_11026,U_11025,U_11024,U_11023] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11023,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11024),U_11027)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11025),U_11027)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11024),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11025,U_11027))),U_11026))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11027))
      | U_11024 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11023,U_11024),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11025),U_11026))) ),
    inference(variable_rename,[status(thm)],[f_2943_1]) ).

cnf(f_2943_3,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11023,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11024),U_11027)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11025),U_11027)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11024),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11025,U_11027))),U_11026))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11027))
    | U_11024 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11023,U_11024),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11025),U_11026))) ),
    inference(clausify,[status(thm)],[f_2943_2]) ).

fof(f_2944_1,plain,
    ! [V_b] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))
      | V_b = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(fof_nnf,[status(thm)],[fact_divmod__int__rel__0]) ).

fof(f_2944_2,plain,
    ! [U_11028] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_11028),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))
      | U_11028 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_2944_1]) ).

cnf(f_2944_3,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_11028),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))
    | U_11028 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2944_2]) ).

fof(f_2945_1,plain,
    ! [V_r,V_q,V_a] :
      ( V_r = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | V_a = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_a),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r))) ),
    inference(fof_nnf,[status(thm)],[fact_self__remainder]) ).

fof(f_2945_2,plain,
    ! [U_11031,U_11030,U_11029] :
      ( U_11031 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | U_11029 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11029,U_11029),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11030),U_11031))) ),
    inference(variable_rename,[status(thm)],[f_2945_1]) ).

cnf(f_2945_3,plain,
    ( U_11031 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_11029 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11029,U_11029),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11030),U_11031))) ),
    inference(clausify,[status(thm)],[f_2945_2]) ).

fof(f_2946_1,plain,
    ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] :
      ( V_q = V_q_H
      | V_b = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q_H),V_r_H)))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r))) ),
    inference(fof_nnf,[status(thm)],[fact_unique__quotient]) ).

fof(f_2946_2,plain,
    ! [U_11037,U_11036,U_11035,U_11034,U_11033,U_11032] :
      ( U_11034 = U_11036
      | U_11033 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11032,U_11033),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11036),U_11037)))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11032,U_11033),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11034),U_11035))) ),
    inference(variable_rename,[status(thm)],[f_2946_1]) ).

cnf(f_2946_3,plain,
    ( U_11034 = U_11036
    | U_11033 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11032,U_11033),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11036),U_11037)))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11032,U_11033),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11034),U_11035))) ),
    inference(clausify,[status(thm)],[f_2946_2]) ).

fof(f_2947_1,plain,
    ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] :
      ( V_r = V_r_H
      | V_b = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q_H),V_r_H)))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r))) ),
    inference(fof_nnf,[status(thm)],[fact_unique__remainder]) ).

fof(f_2947_2,plain,
    ! [U_11043,U_11042,U_11041,U_11040,U_11039,U_11038] :
      ( U_11041 = U_11043
      | U_11039 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11038,U_11039),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11042),U_11043)))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11038,U_11039),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11040),U_11041))) ),
    inference(variable_rename,[status(thm)],[f_2947_1]) ).

cnf(f_2947_3,plain,
    ( U_11041 = U_11043
    | U_11039 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11038,U_11039),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11042),U_11043)))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11038,U_11039),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11040),U_11041))) ),
    inference(clausify,[status(thm)],[f_2947_2]) ).

fof(f_2948_1,plain,
    ! [V_qr,V_b,V_a] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(c_Divides_OnegateSnd,V_qr)))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)),V_qr)) ),
    inference(fof_nnf,[status(thm)],[fact_divmod__int__rel__neg]) ).

fof(f_2948_2,plain,
    ! [U_11046,U_11045,U_11044] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11044,U_11045),hAPP(c_Divides_OnegateSnd,U_11046)))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11044),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11045)),U_11046)) ),
    inference(variable_rename,[status(thm)],[f_2948_1]) ).

cnf(f_2948_3,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11044,U_11045),hAPP(c_Divides_OnegateSnd,U_11046)))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11044),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11045)),U_11046)) ),
    inference(clausify,[status(thm)],[f_2948_2]) ).

fof(f_2949_1,plain,
    ! [V_a,V_b] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_Odivmod__int(V_a,V_b)))
      | V_b = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(fof_nnf,[status(thm)],[fact_divmod__int__correct]) ).

fof(f_2949_2,plain,
    ! [U_11048,U_11047] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11048,U_11047),c_Divides_Odivmod__int(U_11048,U_11047)))
      | U_11047 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_2949_1]) ).

cnf(f_2949_3,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11048,U_11047),c_Divides_Odivmod__int(U_11048,U_11047)))
    | U_11047 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2949_2]) ).

fof(f_2950_1,plain,
    ! [V_a_2,V_b_2,V_r_2,T_b] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2))
      | ~ hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_b_2)) ),
    inference(fof_nnf,[status(thm)],[fact_accp__downward]) ).

fof(f_2950_2,plain,
    ! [U_11052,U_11051,U_11050,U_11049] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_11049,U_11050),U_11052))
      | ~ hBOOL(hAPP(hAPP(U_11050,U_11052),U_11051))
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_11049,U_11050),U_11051)) ),
    inference(variable_rename,[status(thm)],[f_2950_1]) ).

cnf(f_2950_3,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_11049,U_11050),U_11052))
    | ~ hBOOL(hAPP(hAPP(U_11050,U_11052),U_11051))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_11049,U_11050),U_11051)) ),
    inference(clausify,[status(thm)],[f_2950_2]) ).

fof(f_2951_1,plain,
    ! [V_a_2,V_r_2,T_b] :
      ( ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2))
        | ? [B_x] :
            ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x))
            & hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2)) ) )
      & ( ! [B_x] :
            ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x))
            | ~ hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2)) )
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_accp_Oequations]) ).

fof(f_2951_2,plain,
    ! [U_11057,U_11056,U_11055] :
      ( ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_11055,U_11056),U_11057))
        | ? [U_11054] :
            ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_11055,U_11056),U_11054))
            & hBOOL(hAPP(hAPP(U_11056,U_11054),U_11057)) ) )
      & ( ! [U_11053] :
            ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_11055,U_11056),U_11053))
            | ~ hBOOL(hAPP(hAPP(U_11056,U_11053),U_11057)) )
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_11055,U_11056),U_11057)) ) ),
    inference(variable_rename,[status(thm)],[f_2951_1]) ).

fof(f_2951_3,plain,
    ( ! [U_11063,U_11061,U_11059] :
        ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_11059,U_11061),U_11063))
        | ? [U_11054] :
            ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_11059,U_11061),U_11054))
            & hBOOL(hAPP(hAPP(U_11061,U_11054),U_11063)) ) )
    & ! [U_11062,U_11060,U_11058] :
        ( ! [U_11053] :
            ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_11058,U_11060),U_11053))
            | ~ hBOOL(hAPP(hAPP(U_11060,U_11053),U_11062)) )
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_11058,U_11060),U_11062)) ) ),
    inference(miniscope,[status(thm)],[f_2951_2]) ).

fof(f_2951_4,plain,
    ( ! [U_11063,U_11061,U_11059] :
        ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_11059,U_11061),U_11063))
        | ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_11059,U_11061),sK255(U_11063,U_11061,U_11059)))
          & hBOOL(hAPP(hAPP(U_11061,sK255(U_11063,U_11061,U_11059)),U_11063)) ) )
    & ! [U_11062,U_11060,U_11058] :
        ( ! [U_11053] :
            ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_11058,U_11060),U_11053))
            | ~ hBOOL(hAPP(hAPP(U_11060,U_11053),U_11062)) )
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_11058,U_11060),U_11062)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK255]),skolemize(U_11054,sK255(U_11063,U_11061,U_11059))],[f_2951_3]) ).

cnf(f_2951_5,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_11058,U_11060),U_11053))
    | ~ hBOOL(hAPP(hAPP(U_11060,U_11053),U_11062))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_11058,U_11060),U_11062)) ),
    inference(clausify,[status(thm)],[f_2951_4]) ).

cnf(f_2951_6,plain,
    ( hBOOL(hAPP(hAPP(U_11061,sK255(U_11063,U_11061,U_11059)),U_11063))
    | hBOOL(hAPP(c_Wellfounded_Oaccp(U_11059,U_11061),U_11063)) ),
    inference(clausify,[status(thm)],[f_2951_4]) ).

cnf(f_2951_7,plain,
    ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_11059,U_11061),sK255(U_11063,U_11061,U_11059)))
    | hBOOL(hAPP(c_Wellfounded_Oaccp(U_11059,U_11061),U_11063)) ),
    inference(clausify,[status(thm)],[f_2951_4]) ).

fof(f_2952_1,plain,
    ! [V_a_2,V_r_2,T_b] :
      ( ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2))
        | ? [B_x] :
            ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x))
            & hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2)) ) )
      & ( ! [B_x] :
            ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x))
            | ~ hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2)) )
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_accp_Osimps]) ).

fof(f_2952_2,plain,
    ! [U_11068,U_11067,U_11066] :
      ( ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_11066,U_11067),U_11068))
        | ? [U_11065] :
            ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_11066,U_11067),U_11065))
            & hBOOL(hAPP(hAPP(U_11067,U_11065),U_11068)) ) )
      & ( ! [U_11064] :
            ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_11066,U_11067),U_11064))
            | ~ hBOOL(hAPP(hAPP(U_11067,U_11064),U_11068)) )
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_11066,U_11067),U_11068)) ) ),
    inference(variable_rename,[status(thm)],[f_2952_1]) ).

fof(f_2952_3,plain,
    ( ! [U_11074,U_11072,U_11070] :
        ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_11070,U_11072),U_11074))
        | ? [U_11065] :
            ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_11070,U_11072),U_11065))
            & hBOOL(hAPP(hAPP(U_11072,U_11065),U_11074)) ) )
    & ! [U_11073,U_11071,U_11069] :
        ( ! [U_11064] :
            ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_11069,U_11071),U_11064))
            | ~ hBOOL(hAPP(hAPP(U_11071,U_11064),U_11073)) )
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_11069,U_11071),U_11073)) ) ),
    inference(miniscope,[status(thm)],[f_2952_2]) ).

fof(f_2952_4,plain,
    ( ! [U_11074,U_11072,U_11070] :
        ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_11070,U_11072),U_11074))
        | ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_11070,U_11072),sK256(U_11074,U_11072,U_11070)))
          & hBOOL(hAPP(hAPP(U_11072,sK256(U_11074,U_11072,U_11070)),U_11074)) ) )
    & ! [U_11073,U_11071,U_11069] :
        ( ! [U_11064] :
            ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_11069,U_11071),U_11064))
            | ~ hBOOL(hAPP(hAPP(U_11071,U_11064),U_11073)) )
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_11069,U_11071),U_11073)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK256]),skolemize(U_11065,sK256(U_11074,U_11072,U_11070))],[f_2952_3]) ).

cnf(f_2952_5,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_11069,U_11071),U_11064))
    | ~ hBOOL(hAPP(hAPP(U_11071,U_11064),U_11073))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_11069,U_11071),U_11073)) ),
    inference(clausify,[status(thm)],[f_2952_4]) ).

cnf(f_2952_6,plain,
    ( hBOOL(hAPP(hAPP(U_11072,sK256(U_11074,U_11072,U_11070)),U_11074))
    | hBOOL(hAPP(c_Wellfounded_Oaccp(U_11070,U_11072),U_11074)) ),
    inference(clausify,[status(thm)],[f_2952_4]) ).

cnf(f_2952_7,plain,
    ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_11070,U_11072),sK256(U_11074,U_11072,U_11070)))
    | hBOOL(hAPP(c_Wellfounded_Oaccp(U_11070,U_11072),U_11074)) ),
    inference(clausify,[status(thm)],[f_2952_4]) ).

fof(f_2953_1,plain,
    ! [V_r,V_q,V_a] :
      ( V_q = c_Groups_Oone__class_Oone(tc_Int_Oint)
      | V_a = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_a),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r))) ),
    inference(fof_nnf,[status(thm)],[fact_self__quotient]) ).

fof(f_2953_2,plain,
    ! [U_11077,U_11076,U_11075] :
      ( U_11076 = c_Groups_Oone__class_Oone(tc_Int_Oint)
      | U_11075 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11075,U_11075),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11076),U_11077))) ),
    inference(variable_rename,[status(thm)],[f_2953_1]) ).

cnf(f_2953_3,plain,
    ( U_11076 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | U_11075 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11075,U_11075),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11076),U_11077))) ),
    inference(clausify,[status(thm)],[f_2953_2]) ).

fof(f_2954_1,plain,
    ! [V_r,V_q,V_b,V_a] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_r
      | V_b = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r))) ),
    inference(fof_nnf,[status(thm)],[fact_divmod__int__rel__mod]) ).

fof(f_2954_2,plain,
    ! [U_11081,U_11080,U_11079,U_11078] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11078,U_11079) = U_11081
      | U_11079 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11078,U_11079),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11080),U_11081))) ),
    inference(variable_rename,[status(thm)],[f_2954_1]) ).

cnf(f_2954_3,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11078,U_11079) = U_11081
    | U_11079 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11078,U_11079),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11080),U_11081))) ),
    inference(clausify,[status(thm)],[f_2954_2]) ).

fof(f_2955_1,plain,
    ! [V_r,V_q,V_b,V_a] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = V_q
      | V_b = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r))) ),
    inference(fof_nnf,[status(thm)],[fact_divmod__int__rel__div]) ).

fof(f_2955_2,plain,
    ! [U_11085,U_11084,U_11083,U_11082] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11082),U_11083) = U_11084
      | U_11083 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11082,U_11083),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11084),U_11085))) ),
    inference(variable_rename,[status(thm)],[f_2955_1]) ).

cnf(f_2955_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11082),U_11083) = U_11084
    | U_11083 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11082,U_11083),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11084),U_11085))) ),
    inference(clausify,[status(thm)],[f_2955_2]) ).

fof(f_2956_1,plain,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OnegDivAlg(V_a,V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(fof_nnf,[status(thm)],[fact_negDivAlg__correct]) ).

fof(f_2956_2,plain,
    ! [U_11087,U_11086] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11086,U_11087),c_Divides_OnegDivAlg(U_11086,U_11087)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11087))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11086),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_2956_1]) ).

cnf(f_2956_3,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11086,U_11087),c_Divides_OnegDivAlg(U_11086,U_11087)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11087))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11086),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2956_2]) ).

fof(f_2957_1,plain,
    ! [V_a,V_b] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))))
      | V_b = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(fof_nnf,[status(thm)],[fact_divmod__int__rel__div__mod]) ).

fof(f_2957_2,plain,
    ! [U_11089,U_11088] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11089,U_11088),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11089),U_11088)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11089,U_11088))))
      | U_11088 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_2957_1]) ).

cnf(f_2957_3,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11089,U_11088),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11089),U_11088)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11089,U_11088))))
    | U_11088 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2957_2]) ).

fof(f_2958_1,plain,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OposDivAlg(V_a,V_b)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) ),
    inference(fof_nnf,[status(thm)],[fact_posDivAlg__correct]) ).

fof(f_2958_2,plain,
    ! [U_11091,U_11090] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11090,U_11091),c_Divides_OposDivAlg(U_11090,U_11091)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11091))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11090)) ),
    inference(variable_rename,[status(thm)],[f_2958_1]) ).

cnf(f_2958_3,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11090,U_11091),c_Divides_OposDivAlg(U_11090,U_11091)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11091))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11090)) ),
    inference(clausify,[status(thm)],[f_2958_2]) ).

fof(f_2959_1,plain,
    ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b),V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_aq),V_bq)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_ar),V_br)),V_c))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_ar),V_br),V_c))))
      | V_c = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_b,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_bq),V_br)))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_aq),V_ar))) ),
    inference(fof_nnf,[status(thm)],[fact_zadd1__lemma]) ).

fof(f_2959_2,plain,
    ! [U_11098,U_11097,U_11096,U_11095,U_11094,U_11093,U_11092] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11092),U_11096),U_11093),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11094),U_11097)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11095),U_11098)),U_11093))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11095),U_11098),U_11093))))
      | U_11093 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11096,U_11093),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11097),U_11098)))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11092,U_11093),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11094),U_11095))) ),
    inference(variable_rename,[status(thm)],[f_2959_1]) ).

cnf(f_2959_3,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11092),U_11096),U_11093),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11094),U_11097)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11095),U_11098)),U_11093))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11095),U_11098),U_11093))))
    | U_11093 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11096,U_11093),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11097),U_11098)))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11092,U_11093),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11094),U_11095))) ),
    inference(clausify,[status(thm)],[f_2959_2]) ).

fof(f_2960_1,plain,
    ! [V_r_2,V_q_2,V_b_2,V_a_2] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a_2),V_b_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,V_r_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_q_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_q_2)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,V_r_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_b_2),V_r_2)))))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a_2,V_b_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q_2),V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_zminus1__lemma]) ).

fof(f_2960_2,plain,
    ! [U_11102,U_11101,U_11100,U_11099] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11099),U_11100),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,U_11102),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11101)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11101)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,U_11102),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11100),U_11102)))))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11099,U_11100),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11101),U_11102))) ),
    inference(variable_rename,[status(thm)],[f_2960_1]) ).

cnf(f_2960_3,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11099),U_11100),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,U_11102),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11101)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11101)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,U_11102),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11100),U_11102)))))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11099,U_11100),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11101),U_11102))) ),
    inference(clausify,[status(thm)],[f_2960_2]) ).

fof(f_2961_1,plain,
    ! [V_r,V_q,V_b,V_a] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r)))
      | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) )
        & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) )
      | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) )
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) )
      | V_a != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r) ),
    inference(fof_nnf,[status(thm)],[fact_divmod__int__relI]) ).

fof(f_2961_2,plain,
    ! [U_11106,U_11105,U_11104,U_11103] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11103,U_11104),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11105),U_11106)))
      | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11106),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11104),U_11106)) )
        & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11104)) )
      | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11106),U_11104))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11106)) )
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11104)) )
      | U_11103 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11104),U_11105)),U_11106) ),
    inference(variable_rename,[status(thm)],[f_2961_1]) ).

cnf(f_2961_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11104))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11104))
    | hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11103,U_11104),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11105),U_11106)))
    | U_11103 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11104),U_11105)),U_11106) ),
    inference(clausify,[status(thm)],[f_2961_2]) ).

cnf(f_2961_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11106),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11104),U_11106))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11104))
    | hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11103,U_11104),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11105),U_11106)))
    | U_11103 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11104),U_11105)),U_11106) ),
    inference(clausify,[status(thm)],[f_2961_2]) ).

cnf(f_2961_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11104))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11106),U_11104))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11106))
    | hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11103,U_11104),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11105),U_11106)))
    | U_11103 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11104),U_11105)),U_11106) ),
    inference(clausify,[status(thm)],[f_2961_2]) ).

cnf(f_2961_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11106),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11104),U_11106))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11106),U_11104))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11106))
    | hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11103,U_11104),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11105),U_11106)))
    | U_11103 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11104),U_11105)),U_11106) ),
    inference(clausify,[status(thm)],[f_2961_2]) ).

fof(f_2962_1,plain,
    ! [V_a,V_r,V_q,V_c,V_b] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b),V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_r)),V_c))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_r),V_c))))
      | V_c = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_b,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r))) ),
    inference(fof_nnf,[status(thm)],[fact_zmult1__lemma]) ).

fof(f_2962_2,plain,
    ! [U_11111,U_11110,U_11109,U_11108,U_11107] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11111),U_11107),U_11108),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11111),U_11109)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11111),U_11110)),U_11108))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11111),U_11110),U_11108))))
      | U_11108 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11107,U_11108),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11109),U_11110))) ),
    inference(variable_rename,[status(thm)],[f_2962_1]) ).

cnf(f_2962_3,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11111),U_11107),U_11108),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11111),U_11109)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11111),U_11110)),U_11108))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11111),U_11110),U_11108))))
    | U_11108 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_11107,U_11108),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11109),U_11110))) ),
    inference(clausify,[status(thm)],[f_2962_2]) ).

fof(f_2963_1,plain,
    ! [V_b_2,V_a_2] : c_Divides_Odivmod__int__rel(V_a_2,V_b_2) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fequal,V_a_2))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_2)))))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fimplies,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Int_Oint)),V_b_2))))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fimplies,hAPP(c_fNot,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))))),
    inference(fof_nnf,[status(thm)],[fact_divmod__int__rel__def]) ).

fof(f_2963_2,plain,
    ! [U_11113,U_11112] : c_Divides_Odivmod__int__rel(U_11112,U_11113) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fequal,U_11112))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11113)))))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fimplies,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11113))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Int_Oint)),U_11113))))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fimplies,hAPP(c_fNot,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11113)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11113))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))))),
    inference(variable_rename,[status(thm)],[f_2963_1]) ).

cnf(f_2963_3,plain,
    c_Divides_Odivmod__int__rel(U_11112,U_11113) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fequal,U_11112))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11113)))))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fimplies,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11113))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Int_Oint)),U_11113))))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fimplies,hAPP(c_fNot,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11113)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11113))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))))),
    inference(clausify,[status(thm)],[f_2963_2]) ).

fof(f_2964_1,plain,
    ! [V_y_2,V_x_2] :
      ( ( ( c_Nitpick_Onat__gcd(V_x_2,V_y_2) = c_Nitpick_Onat__gcd(V_y_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x_2,V_y_2))
          | V_y_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        & ( c_Nitpick_Onat__gcd(V_x_2,V_y_2) = V_x_2
          | V_y_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2))) ),
    inference(fof_nnf,[status(thm)],[fact_nat__gcd_Opsimps]) ).

fof(f_2964_2,plain,
    ! [U_11115,U_11114] :
      ( ( ( c_Nitpick_Onat__gcd(U_11114,U_11115) = c_Nitpick_Onat__gcd(U_11115,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_11114,U_11115))
          | U_11115 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        & ( c_Nitpick_Onat__gcd(U_11114,U_11115) = U_11114
          | U_11115 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11114),U_11115))) ),
    inference(variable_rename,[status(thm)],[f_2964_1]) ).

cnf(f_2964_3,plain,
    ( c_Nitpick_Onat__gcd(U_11114,U_11115) = U_11114
    | U_11115 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11114),U_11115))) ),
    inference(clausify,[status(thm)],[f_2964_2]) ).

cnf(f_2964_4,plain,
    ( c_Nitpick_Onat__gcd(U_11114,U_11115) = c_Nitpick_Onat__gcd(U_11115,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_11114,U_11115))
    | U_11115 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11114),U_11115))) ),
    inference(clausify,[status(thm)],[f_2964_2]) ).

fof(f_2965_1,plain,
    ! [V_nat] : c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,V_nat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(V_nat)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(fof_nnf,[status(thm)],[fact_nat_Osize_I2_J]) ).

fof(f_2965_2,plain,
    ! [U_11116] : c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,U_11116)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(U_11116)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_2965_1]) ).

cnf(f_2965_3,plain,
    c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,U_11116)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(U_11116)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_2965_2]) ).

fof(f_2966_1,plain,
    ! [V_B_2,V_X_2,V_f_2,T_c,T_b] :
      ( c_Orderings_Oorder__class_Omono(T_b,tc_fun(T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_f_2)),V_X_2))),V_B_2))
      | ~ c_Orderings_Oorder__class_Omono(T_b,tc_fun(T_c,tc_HOL_Obool),V_f_2)
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_coinduct3__mono__lemma]) ).

fof(f_2966_2,plain,
    ! [U_11121,U_11120,U_11119,U_11118,U_11117] :
      ( c_Orderings_Oorder__class_Omono(U_11117,tc_fun(U_11118,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11117,tc_fun(U_11118,tc_HOL_Obool),tc_fun(U_11118,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11118,tc_HOL_Obool),tc_fun(tc_fun(U_11118,tc_HOL_Obool),tc_fun(U_11118,tc_HOL_Obool)),U_11117),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11118,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_11117,tc_fun(U_11118,tc_HOL_Obool),tc_fun(U_11118,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11118,tc_HOL_Obool),tc_fun(tc_fun(U_11118,tc_HOL_Obool),tc_fun(U_11118,tc_HOL_Obool)),U_11117),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11118,tc_HOL_Obool))),U_11119)),U_11120))),U_11121))
      | ~ c_Orderings_Oorder__class_Omono(U_11117,tc_fun(U_11118,tc_HOL_Obool),U_11119)
      | ~ class_Orderings_Oorder(U_11117) ),
    inference(variable_rename,[status(thm)],[f_2966_1]) ).

cnf(f_2966_3,plain,
    ( c_Orderings_Oorder__class_Omono(U_11117,tc_fun(U_11118,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11117,tc_fun(U_11118,tc_HOL_Obool),tc_fun(U_11118,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11118,tc_HOL_Obool),tc_fun(tc_fun(U_11118,tc_HOL_Obool),tc_fun(U_11118,tc_HOL_Obool)),U_11117),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11118,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_11117,tc_fun(U_11118,tc_HOL_Obool),tc_fun(U_11118,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11118,tc_HOL_Obool),tc_fun(tc_fun(U_11118,tc_HOL_Obool),tc_fun(U_11118,tc_HOL_Obool)),U_11117),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11118,tc_HOL_Obool))),U_11119)),U_11120))),U_11121))
    | ~ c_Orderings_Oorder__class_Omono(U_11117,tc_fun(U_11118,tc_HOL_Obool),U_11119)
    | ~ class_Orderings_Oorder(U_11117) ),
    inference(clausify,[status(thm)],[f_2966_2]) ).

fof(f_2967_1,plain,
    c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_nat_Osize_I1_J]) ).

cnf(f_2967_2,plain,
    c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_2967_1]) ).

fof(f_2968_1,plain,
    ! [V_f_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Int_Oint),V_f_2),V_A_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,T_b),c_Int_Onat),V_f_2)),V_A_2))
      | ? [B_x] :
          ( ~ c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__sum__prod2_I2_J]) ).

fof(f_2968_2,plain,
    ! [U_11125,U_11124,U_11123] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11123,tc_Int_Oint),U_11125),U_11124) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11123,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_11123),c_Int_Onat),U_11125)),U_11124))
      | ? [U_11122] :
          ( ~ c_Nat__Transfer_Ois__nat(hAPP(U_11125,U_11122))
          & hBOOL(hAPP(hAPP(c_member(U_11123),U_11122),U_11124)) ) ),
    inference(variable_rename,[status(thm)],[f_2968_1]) ).

fof(f_2968_3,plain,
    ! [U_11125,U_11124,U_11123] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11123,tc_Int_Oint),U_11125),U_11124) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11123,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_11123),c_Int_Onat),U_11125)),U_11124))
      | ( ~ c_Nat__Transfer_Ois__nat(hAPP(U_11125,sK257(U_11125,U_11124,U_11123)))
        & hBOOL(hAPP(hAPP(c_member(U_11123),sK257(U_11125,U_11124,U_11123)),U_11124)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK257]),skolemize(U_11122,sK257(U_11125,U_11124,U_11123))],[f_2968_2]) ).

cnf(f_2968_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11123),sK257(U_11125,U_11124,U_11123)),U_11124))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11123,tc_Int_Oint),U_11125),U_11124) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11123,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_11123),c_Int_Onat),U_11125)),U_11124)) ),
    inference(clausify,[status(thm)],[f_2968_3]) ).

cnf(f_2968_5,plain,
    ( ~ c_Nat__Transfer_Ois__nat(hAPP(U_11125,sK257(U_11125,U_11124,U_11123)))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11123,tc_Int_Oint),U_11125),U_11124) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11123,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_11123),c_Int_Onat),U_11125)),U_11124)) ),
    inference(clausify,[status(thm)],[f_2968_3]) ).

fof(f_2969_1,plain,
    ! [V_w] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(fof_nnf,[status(thm)],[fact_mod__pos__neg__1__number__of]) ).

fof(f_2969_2,plain,
    ! [U_11126] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11126)) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11126)))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11126)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_2969_1]) ).

cnf(f_2969_3,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11126)) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11126)))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11126)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2969_2]) ).

fof(f_2970_1,plain,
    ! [V_f_2,V_y_2,V_x_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(c_Wellfounded_Omeasure(T_b),V_f_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(c_Wellfounded_Omeasure(T_b),V_f_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_in__measure]) ).

fof(f_2970_2,plain,
    ! [U_11130,U_11129,U_11128,U_11127] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11127,U_11127)),hAPP(hAPP(c_Product__Type_OPair(U_11127,U_11127),U_11128),U_11129)),hAPP(c_Wellfounded_Omeasure(U_11127),U_11130)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_11130,U_11128)),hAPP(U_11130,U_11129))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_11130,U_11128)),hAPP(U_11130,U_11129)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11127,U_11127)),hAPP(hAPP(c_Product__Type_OPair(U_11127,U_11127),U_11128),U_11129)),hAPP(c_Wellfounded_Omeasure(U_11127),U_11130))) ) ),
    inference(variable_rename,[status(thm)],[f_2970_1]) ).

fof(f_2970_3,plain,
    ( ! [U_11138,U_11136,U_11134] :
        ( ! [U_11132] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_11132,U_11132)),hAPP(hAPP(c_Product__Type_OPair(U_11132,U_11132),U_11134),U_11136)),hAPP(c_Wellfounded_Omeasure(U_11132),U_11138)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_11138,U_11134)),hAPP(U_11138,U_11136))) )
    & ! [U_11137,U_11135,U_11133] :
        ( ! [U_11131] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11131,U_11131)),hAPP(hAPP(c_Product__Type_OPair(U_11131,U_11131),U_11133),U_11135)),hAPP(c_Wellfounded_Omeasure(U_11131),U_11137)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_11137,U_11133)),hAPP(U_11137,U_11135))) ) ),
    inference(miniscope,[status(thm)],[f_2970_2]) ).

cnf(f_2970_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11131,U_11131)),hAPP(hAPP(c_Product__Type_OPair(U_11131,U_11131),U_11133),U_11135)),hAPP(c_Wellfounded_Omeasure(U_11131),U_11137)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_11137,U_11133)),hAPP(U_11137,U_11135))) ),
    inference(clausify,[status(thm)],[f_2970_3]) ).

cnf(f_2970_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11132,U_11132)),hAPP(hAPP(c_Product__Type_OPair(U_11132,U_11132),U_11134),U_11136)),hAPP(c_Wellfounded_Omeasure(U_11132),U_11138)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_11138,U_11134)),hAPP(U_11138,U_11136))) ),
    inference(clausify,[status(thm)],[f_2970_3]) ).

fof(f_2971_1,plain,
    ! [V_x_2,V_f_2,T_d,T_b,T_c] : hAPP(c_Product__Type_Osnd(T_c,T_b),hAPP(c_Product__Type_Oapsnd(T_d,T_b,T_c,V_f_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_c,T_d),V_x_2)),
    inference(fof_nnf,[status(thm)],[fact_snd__apsnd]) ).

fof(f_2971_2,plain,
    ! [U_11143,U_11142,U_11141,U_11140,U_11139] : hAPP(c_Product__Type_Osnd(U_11139,U_11140),hAPP(c_Product__Type_Oapsnd(U_11141,U_11140,U_11139,U_11142),U_11143)) = hAPP(U_11142,hAPP(c_Product__Type_Osnd(U_11139,U_11141),U_11143)),
    inference(variable_rename,[status(thm)],[f_2971_1]) ).

cnf(f_2971_3,plain,
    hAPP(c_Product__Type_Osnd(U_11139,U_11140),hAPP(c_Product__Type_Oapsnd(U_11141,U_11140,U_11139,U_11142),U_11143)) = hAPP(U_11142,hAPP(c_Product__Type_Osnd(U_11139,U_11141),U_11143)),
    inference(clausify,[status(thm)],[f_2971_2]) ).

fof(f_2972_1,plain,
    ! [V_g_2,V_x_2,V_f_2,T_b,T_c,T_d] :
      ( ( hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),V_x_2) = hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_g_2),V_x_2)
        | hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_b,T_d),V_x_2)) != hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_b,T_d),V_x_2)) )
      & ( hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_b,T_d),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_b,T_d),V_x_2))
        | hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),V_x_2) != hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_g_2),V_x_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_apsnd__eq__conv]) ).

fof(f_2972_2,plain,
    ! [U_11149,U_11148,U_11147,U_11146,U_11145,U_11144] :
      ( ( hAPP(c_Product__Type_Oapsnd(U_11144,U_11145,U_11146,U_11147),U_11148) = hAPP(c_Product__Type_Oapsnd(U_11144,U_11145,U_11146,U_11149),U_11148)
        | hAPP(U_11147,hAPP(c_Product__Type_Osnd(U_11146,U_11144),U_11148)) != hAPP(U_11149,hAPP(c_Product__Type_Osnd(U_11146,U_11144),U_11148)) )
      & ( hAPP(U_11147,hAPP(c_Product__Type_Osnd(U_11146,U_11144),U_11148)) = hAPP(U_11149,hAPP(c_Product__Type_Osnd(U_11146,U_11144),U_11148))
        | hAPP(c_Product__Type_Oapsnd(U_11144,U_11145,U_11146,U_11147),U_11148) != hAPP(c_Product__Type_Oapsnd(U_11144,U_11145,U_11146,U_11149),U_11148) ) ),
    inference(variable_rename,[status(thm)],[f_2972_1]) ).

fof(f_2972_3,plain,
    ( ! [U_11161,U_11159,U_11157,U_11155,U_11153,U_11151] :
        ( hAPP(c_Product__Type_Oapsnd(U_11151,U_11153,U_11155,U_11157),U_11159) = hAPP(c_Product__Type_Oapsnd(U_11151,U_11153,U_11155,U_11161),U_11159)
        | hAPP(U_11157,hAPP(c_Product__Type_Osnd(U_11155,U_11151),U_11159)) != hAPP(U_11161,hAPP(c_Product__Type_Osnd(U_11155,U_11151),U_11159)) )
    & ! [U_11160,U_11158,U_11156,U_11154,U_11152,U_11150] :
        ( hAPP(U_11156,hAPP(c_Product__Type_Osnd(U_11154,U_11150),U_11158)) = hAPP(U_11160,hAPP(c_Product__Type_Osnd(U_11154,U_11150),U_11158))
        | hAPP(c_Product__Type_Oapsnd(U_11150,U_11152,U_11154,U_11156),U_11158) != hAPP(c_Product__Type_Oapsnd(U_11150,U_11152,U_11154,U_11160),U_11158) ) ),
    inference(miniscope,[status(thm)],[f_2972_2]) ).

cnf(f_2972_4,plain,
    ( hAPP(U_11156,hAPP(c_Product__Type_Osnd(U_11154,U_11150),U_11158)) = hAPP(U_11160,hAPP(c_Product__Type_Osnd(U_11154,U_11150),U_11158))
    | hAPP(c_Product__Type_Oapsnd(U_11150,U_11152,U_11154,U_11156),U_11158) != hAPP(c_Product__Type_Oapsnd(U_11150,U_11152,U_11154,U_11160),U_11158) ),
    inference(clausify,[status(thm)],[f_2972_3]) ).

cnf(f_2972_5,plain,
    ( hAPP(c_Product__Type_Oapsnd(U_11151,U_11153,U_11155,U_11157),U_11159) = hAPP(c_Product__Type_Oapsnd(U_11151,U_11153,U_11155,U_11161),U_11159)
    | hAPP(U_11157,hAPP(c_Product__Type_Osnd(U_11155,U_11151),U_11159)) != hAPP(U_11161,hAPP(c_Product__Type_Osnd(U_11155,U_11151),U_11159)) ),
    inference(clausify,[status(thm)],[f_2972_3]) ).

fof(f_2973_1,plain,
    ! [V_b,V_a,T_a,T_b] : hAPP(c_Product__Type_Osnd(T_b,T_a),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_a),V_b)) = V_b,
    inference(fof_nnf,[status(thm)],[fact_snd__conv]) ).

fof(f_2973_2,plain,
    ! [U_11165,U_11164,U_11163,U_11162] : hAPP(c_Product__Type_Osnd(U_11162,U_11163),hAPP(hAPP(c_Product__Type_OPair(U_11162,U_11163),U_11164),U_11165)) = U_11165,
    inference(variable_rename,[status(thm)],[f_2973_1]) ).

cnf(f_2973_3,plain,
    hAPP(c_Product__Type_Osnd(U_11162,U_11163),hAPP(hAPP(c_Product__Type_OPair(U_11162,U_11163),U_11164),U_11165)) = U_11165,
    inference(clausify,[status(thm)],[f_2973_2]) ).

fof(f_2974_1,plain,
    ! [V_a,V_y,V_x,T_a,T_b] :
      ( V_y = V_a
      | hAPP(c_Product__Type_Osnd(T_b,T_a),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_x),V_y)) != V_a ),
    inference(fof_nnf,[status(thm)],[fact_snd__eqD]) ).

fof(f_2974_2,plain,
    ! [U_11170,U_11169,U_11168,U_11167,U_11166] :
      ( U_11169 = U_11170
      | hAPP(c_Product__Type_Osnd(U_11166,U_11167),hAPP(hAPP(c_Product__Type_OPair(U_11166,U_11167),U_11168),U_11169)) != U_11170 ),
    inference(variable_rename,[status(thm)],[f_2974_1]) ).

fof(f_2974_3,plain,
    ! [U_11170,U_11169] :
      ( ! [U_11168,U_11167,U_11166] : hAPP(c_Product__Type_Osnd(U_11166,U_11167),hAPP(hAPP(c_Product__Type_OPair(U_11166,U_11167),U_11168),U_11169)) != U_11170
      | U_11169 = U_11170 ),
    inference(miniscope,[status(thm)],[f_2974_2]) ).

cnf(f_2974_4,plain,
    ( hAPP(c_Product__Type_Osnd(U_11166,U_11167),hAPP(hAPP(c_Product__Type_OPair(U_11166,U_11167),U_11168),U_11169)) != U_11170
    | U_11169 = U_11170 ),
    inference(clausify,[status(thm)],[f_2974_3]) ).

fof(f_2975_1,plain,
    ! [V_p_2,T_b,T_c] : hAPP(c_Product__Type_Osnd(T_c,T_b),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,T_b),hAPP(c_COMBK(tc_fun(T_b,T_b),T_c),c_COMBI(T_b))),V_p_2),
    inference(fof_nnf,[status(thm)],[fact_snd__def]) ).

fof(f_2975_2,plain,
    ! [U_11173,U_11172,U_11171] : hAPP(c_Product__Type_Osnd(U_11171,U_11172),U_11173) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11171,U_11172,U_11172),hAPP(c_COMBK(tc_fun(U_11172,U_11172),U_11171),c_COMBI(U_11172))),U_11173),
    inference(variable_rename,[status(thm)],[f_2975_1]) ).

cnf(f_2975_3,plain,
    hAPP(c_Product__Type_Osnd(U_11171,U_11172),U_11173) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11171,U_11172,U_11172),hAPP(c_COMBK(tc_fun(U_11172,U_11172),U_11171),c_COMBI(U_11172))),U_11173),
    inference(clausify,[status(thm)],[f_2975_2]) ).

fof(f_2976_1,plain,
    ! [V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(V_a,V_b)),
    inference(fof_nnf,[status(thm)],[fact_mod__int__def]) ).

fof(f_2976_2,plain,
    ! [U_11175,U_11174] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11174,U_11175) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(U_11174,U_11175)),
    inference(variable_rename,[status(thm)],[f_2976_1]) ).

cnf(f_2976_3,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11174,U_11175) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(U_11174,U_11175)),
    inference(clausify,[status(thm)],[f_2976_2]) ).

fof(f_2977_1,plain,
    ! [V_b,V_a] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(V_a,V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(fof_nnf,[status(thm)],[fact_mod__neg__pos]) ).

fof(f_2977_2,plain,
    ! [U_11177,U_11176] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11176,U_11177) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(U_11176,U_11177))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11177))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11176),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_2977_1]) ).

cnf(f_2977_3,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11176,U_11177) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(U_11176,U_11177))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11177))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11176),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2977_2]) ).

fof(f_2978_1,plain,
    ! [V_b,V_a] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(V_a,V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) ),
    inference(fof_nnf,[status(thm)],[fact_mod__pos__pos]) ).

fof(f_2978_2,plain,
    ! [U_11179,U_11178] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11178,U_11179) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(U_11178,U_11179))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11179))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11178)) ),
    inference(variable_rename,[status(thm)],[f_2978_1]) ).

cnf(f_2978_3,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11178,U_11179) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(U_11178,U_11179))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11179))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11178)) ),
    inference(clausify,[status(thm)],[f_2978_2]) ).

fof(f_2979_1,plain,
    ! [V_w] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) ),
    inference(fof_nnf,[status(thm)],[fact_mod__pos__pos__1__number__of]) ).

fof(f_2979_2,plain,
    ! [U_11180] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11180)) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11180)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11180))) ),
    inference(variable_rename,[status(thm)],[f_2979_1]) ).

cnf(f_2979_3,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11180)) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11180)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11180))) ),
    inference(clausify,[status(thm)],[f_2979_2]) ).

fof(f_2980_1,plain,
    ! [V_b,V_a] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) ),
    inference(fof_nnf,[status(thm)],[fact_mod__pos__neg]) ).

fof(f_2980_2,plain,
    ! [U_11182,U_11181] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11181,U_11182) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11181),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11182))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11182),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11181)) ),
    inference(variable_rename,[status(thm)],[f_2980_1]) ).

cnf(f_2980_3,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11181,U_11182) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11181),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11182))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11182),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11181)) ),
    inference(clausify,[status(thm)],[f_2980_2]) ).

fof(f_2981_1,plain,
    ! [V_b,V_a] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(fof_nnf,[status(thm)],[fact_mod__neg__neg]) ).

fof(f_2981_2,plain,
    ! [U_11184,U_11183] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11183,U_11184) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11183),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11184))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11184),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11183),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_2981_1]) ).

cnf(f_2981_3,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_11183,U_11184) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11183),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11184))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11184),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11183),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2981_2]) ).

fof(f_2982_1,plain,
    ! [V_f_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Int_Oint),V_f_2),V_A_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,T_b),c_Int_Onat),V_f_2)),V_A_2))
      | ? [B_x] :
          ( ~ c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__sum__prod2_I1_J]) ).

fof(f_2982_2,plain,
    ! [U_11188,U_11187,U_11186] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11186,tc_Int_Oint),U_11188),U_11187) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11186,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_11186),c_Int_Onat),U_11188)),U_11187))
      | ? [U_11185] :
          ( ~ c_Nat__Transfer_Ois__nat(hAPP(U_11188,U_11185))
          & hBOOL(hAPP(hAPP(c_member(U_11186),U_11185),U_11187)) ) ),
    inference(variable_rename,[status(thm)],[f_2982_1]) ).

fof(f_2982_3,plain,
    ! [U_11188,U_11187,U_11186] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11186,tc_Int_Oint),U_11188),U_11187) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11186,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_11186),c_Int_Onat),U_11188)),U_11187))
      | ( ~ c_Nat__Transfer_Ois__nat(hAPP(U_11188,sK258(U_11188,U_11187,U_11186)))
        & hBOOL(hAPP(hAPP(c_member(U_11186),sK258(U_11188,U_11187,U_11186)),U_11187)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK258]),skolemize(U_11185,sK258(U_11188,U_11187,U_11186))],[f_2982_2]) ).

cnf(f_2982_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11186),sK258(U_11188,U_11187,U_11186)),U_11187))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11186,tc_Int_Oint),U_11188),U_11187) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11186,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_11186),c_Int_Onat),U_11188)),U_11187)) ),
    inference(clausify,[status(thm)],[f_2982_3]) ).

cnf(f_2982_5,plain,
    ( ~ c_Nat__Transfer_Ois__nat(hAPP(U_11188,sK258(U_11188,U_11187,U_11186)))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11186,tc_Int_Oint),U_11188),U_11187) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11186,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_11186),c_Int_Onat),U_11188)),U_11187)) ),
    inference(clausify,[status(thm)],[f_2982_3]) ).

fof(f_2983_1,plain,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
      ( hAPP(V_F_2,V_A_2) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(V_f_2,V_x_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding_Oremove]) ).

fof(f_2983_2,plain,
    ! [U_11194,U_11193,U_11192,U_11191,U_11190,U_11189] :
      ( hAPP(U_11192,U_11193) = hAPP(c_Fun_Ocomp(U_11190,U_11190,U_11190,hAPP(U_11192,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11189,tc_HOL_Obool)),U_11193),hAPP(hAPP(c_Set_Oinsert(U_11189),U_11194),c_Orderings_Obot__class_Obot(tc_fun(U_11189,tc_HOL_Obool)))))),hAPP(U_11191,U_11194))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11189),U_11194),U_11193))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11189),U_11193))
      | ~ c_Finite__Set_Ofolding(U_11189,U_11190,U_11191,U_11192) ),
    inference(variable_rename,[status(thm)],[f_2983_1]) ).

cnf(f_2983_3,plain,
    ( hAPP(U_11192,U_11193) = hAPP(c_Fun_Ocomp(U_11190,U_11190,U_11190,hAPP(U_11192,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11189,tc_HOL_Obool)),U_11193),hAPP(hAPP(c_Set_Oinsert(U_11189),U_11194),c_Orderings_Obot__class_Obot(tc_fun(U_11189,tc_HOL_Obool)))))),hAPP(U_11191,U_11194))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11189),U_11194),U_11193))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11189),U_11193))
    | ~ c_Finite__Set_Ofolding(U_11189,U_11190,U_11191,U_11192) ),
    inference(clausify,[status(thm)],[f_2983_2]) ).

fof(f_2984_1,plain,
    ! [V_P_2,V_a1_2,V_a0_2] :
      ( hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2))
      | ? [B_a,B_b] :
          ( ~ hBOOL(hAPP(hAPP(V_P_2,B_a),B_b))
          & ( hBOOL(hAPP(hAPP(V_P_2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B_a)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B_b)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_a),B_b))) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2))) ),
    inference(fof_nnf,[status(thm)],[fact_norm__frac_Opinduct]) ).

fof(f_2984_2,plain,
    ! [U_11199,U_11198,U_11197] :
      ( hBOOL(hAPP(hAPP(U_11199,U_11197),U_11198))
      | ? [U_11196,U_11195] :
          ( ~ hBOOL(hAPP(hAPP(U_11199,U_11196),U_11195))
          & ( hBOOL(hAPP(hAPP(U_11199,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11196)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11195)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11195),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11196),U_11195))) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11197),U_11198))) ),
    inference(variable_rename,[status(thm)],[f_2984_1]) ).

fof(f_2984_3,plain,
    ! [U_11199,U_11198,U_11197] :
      ( hBOOL(hAPP(hAPP(U_11199,U_11197),U_11198))
      | ? [U_11195] :
          ( ~ hBOOL(hAPP(hAPP(U_11199,sK259(U_11199,U_11198,U_11197)),U_11195))
          & ( hBOOL(hAPP(hAPP(U_11199,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),sK259(U_11199,U_11198,U_11197))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11195)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11195),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),sK259(U_11199,U_11198,U_11197)),U_11195))) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11197),U_11198))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK259]),skolemize(U_11196,sK259(U_11199,U_11198,U_11197))],[f_2984_2]) ).

fof(f_2984_4,plain,
    ! [U_11199,U_11198,U_11197] :
      ( hBOOL(hAPP(hAPP(U_11199,U_11197),U_11198))
      | ( ~ hBOOL(hAPP(hAPP(U_11199,sK259(U_11199,U_11198,U_11197)),sK260(U_11199,U_11198,U_11197)))
        & ( hBOOL(hAPP(hAPP(U_11199,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),sK259(U_11199,U_11198,U_11197))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),sK260(U_11199,U_11198,U_11197))))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK260(U_11199,U_11198,U_11197)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        & hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),sK259(U_11199,U_11198,U_11197)),sK260(U_11199,U_11198,U_11197)))) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11197),U_11198))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK260]),skolemize(U_11195,sK260(U_11199,U_11198,U_11197))],[f_2984_3]) ).

cnf(f_2984_5,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),sK259(U_11199,U_11198,U_11197)),sK260(U_11199,U_11198,U_11197))))
    | hBOOL(hAPP(hAPP(U_11199,U_11197),U_11198))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11197),U_11198))) ),
    inference(clausify,[status(thm)],[f_2984_4]) ).

cnf(f_2984_6,plain,
    ( hBOOL(hAPP(hAPP(U_11199,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),sK259(U_11199,U_11198,U_11197))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),sK260(U_11199,U_11198,U_11197))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK260(U_11199,U_11198,U_11197)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(U_11199,U_11197),U_11198))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11197),U_11198))) ),
    inference(clausify,[status(thm)],[f_2984_4]) ).

cnf(f_2984_7,plain,
    ( ~ hBOOL(hAPP(hAPP(U_11199,sK259(U_11199,U_11198,U_11197)),sK260(U_11199,U_11198,U_11197)))
    | hBOOL(hAPP(hAPP(U_11199,U_11197),U_11198))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_11197),U_11198))) ),
    inference(clausify,[status(thm)],[f_2984_4]) ).

fof(f_2985_1,plain,
    ! [V_g_2,V_x_2,V_y_2,T_d,V_F_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_y_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_y_2)),V_g_2))
      | ~ c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__left__comp]) ).

fof(f_2985_2,plain,
    ! [U_11207,U_11206,U_11205,U_11204,U_11203,U_11202,U_11201,U_11200] :
      ( hAPP(c_Fun_Ocomp(U_11201,U_11201,U_11204,hAPP(U_11202,U_11205)),hAPP(c_Fun_Ocomp(U_11201,U_11201,U_11204,hAPP(U_11202,U_11206)),U_11207)) = hAPP(c_Fun_Ocomp(U_11201,U_11201,U_11204,hAPP(U_11202,U_11206)),hAPP(c_Fun_Ocomp(U_11201,U_11201,U_11204,hAPP(U_11202,U_11205)),U_11207))
      | ~ c_Finite__Set_Ofolding(U_11200,U_11201,U_11202,U_11203) ),
    inference(variable_rename,[status(thm)],[f_2985_1]) ).

fof(f_2985_3,plain,
    ! [U_11207,U_11206,U_11205,U_11204,U_11203,U_11202,U_11201] :
      ( ! [U_11200] : ~ c_Finite__Set_Ofolding(U_11200,U_11201,U_11202,U_11203)
      | hAPP(c_Fun_Ocomp(U_11201,U_11201,U_11204,hAPP(U_11202,U_11205)),hAPP(c_Fun_Ocomp(U_11201,U_11201,U_11204,hAPP(U_11202,U_11206)),U_11207)) = hAPP(c_Fun_Ocomp(U_11201,U_11201,U_11204,hAPP(U_11202,U_11206)),hAPP(c_Fun_Ocomp(U_11201,U_11201,U_11204,hAPP(U_11202,U_11205)),U_11207)) ),
    inference(miniscope,[status(thm)],[f_2985_2]) ).

cnf(f_2985_4,plain,
    ( ~ c_Finite__Set_Ofolding(U_11200,U_11201,U_11202,U_11203)
    | hAPP(c_Fun_Ocomp(U_11201,U_11201,U_11204,hAPP(U_11202,U_11205)),hAPP(c_Fun_Ocomp(U_11201,U_11201,U_11204,hAPP(U_11202,U_11206)),U_11207)) = hAPP(c_Fun_Ocomp(U_11201,U_11201,U_11204,hAPP(U_11202,U_11206)),hAPP(c_Fun_Ocomp(U_11201,U_11201,U_11204,hAPP(U_11202,U_11205)),U_11207)) ),
    inference(clausify,[status(thm)],[f_2985_3]) ).

fof(f_2986_1,plain,
    ! [V_x_2,V_y_2,V_F_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_y_2)),hAPP(V_f_2,V_x_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))
      | ~ c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__comp]) ).

fof(f_2986_2,plain,
    ! [U_11213,U_11212,U_11211,U_11210,U_11209,U_11208] :
      ( hAPP(c_Fun_Ocomp(U_11209,U_11209,U_11209,hAPP(U_11210,U_11212)),hAPP(U_11210,U_11213)) = hAPP(c_Fun_Ocomp(U_11209,U_11209,U_11209,hAPP(U_11210,U_11213)),hAPP(U_11210,U_11212))
      | ~ c_Finite__Set_Ofolding(U_11208,U_11209,U_11210,U_11211) ),
    inference(variable_rename,[status(thm)],[f_2986_1]) ).

fof(f_2986_3,plain,
    ! [U_11213,U_11212,U_11211,U_11210,U_11209] :
      ( ! [U_11208] : ~ c_Finite__Set_Ofolding(U_11208,U_11209,U_11210,U_11211)
      | hAPP(c_Fun_Ocomp(U_11209,U_11209,U_11209,hAPP(U_11210,U_11212)),hAPP(U_11210,U_11213)) = hAPP(c_Fun_Ocomp(U_11209,U_11209,U_11209,hAPP(U_11210,U_11213)),hAPP(U_11210,U_11212)) ),
    inference(miniscope,[status(thm)],[f_2986_2]) ).

cnf(f_2986_4,plain,
    ( ~ c_Finite__Set_Ofolding(U_11208,U_11209,U_11210,U_11211)
    | hAPP(c_Fun_Ocomp(U_11209,U_11209,U_11209,hAPP(U_11210,U_11212)),hAPP(U_11210,U_11213)) = hAPP(c_Fun_Ocomp(U_11209,U_11209,U_11209,hAPP(U_11210,U_11213)),hAPP(U_11210,U_11212)) ),
    inference(clausify,[status(thm)],[f_2986_3]) ).

fof(f_2987_1,plain,
    ! [V_h_2,V_g_2,T_g,V_f_2,T_d,T_e,T_f,V_F_2,V_fa_2,T_c,T_b] :
      ( hAPP(c_Fun_Ocomp(T_f,T_e,T_d,V_f_2),hAPP(c_Fun_Ocomp(T_g,T_f,T_d,V_g_2),V_h_2)) = hAPP(c_Fun_Ocomp(T_g,T_e,T_d,hAPP(c_Fun_Ocomp(T_f,T_e,T_g,V_f_2),V_g_2)),V_h_2)
      | ~ c_Finite__Set_Ofolding(T_b,T_c,V_fa_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__comps_I1_J]) ).

fof(f_2987_2,plain,
    ! [U_11224,U_11223,U_11222,U_11221,U_11220,U_11219,U_11218,U_11217,U_11216,U_11215,U_11214] :
      ( hAPP(c_Fun_Ocomp(U_11218,U_11219,U_11220,U_11221),hAPP(c_Fun_Ocomp(U_11222,U_11218,U_11220,U_11223),U_11224)) = hAPP(c_Fun_Ocomp(U_11222,U_11219,U_11220,hAPP(c_Fun_Ocomp(U_11218,U_11219,U_11222,U_11221),U_11223)),U_11224)
      | ~ c_Finite__Set_Ofolding(U_11214,U_11215,U_11216,U_11217) ),
    inference(variable_rename,[status(thm)],[f_2987_1]) ).

fof(f_2987_3,plain,
    ( ! [U_11224,U_11223,U_11222,U_11221,U_11220,U_11219,U_11218] : hAPP(c_Fun_Ocomp(U_11218,U_11219,U_11220,U_11221),hAPP(c_Fun_Ocomp(U_11222,U_11218,U_11220,U_11223),U_11224)) = hAPP(c_Fun_Ocomp(U_11222,U_11219,U_11220,hAPP(c_Fun_Ocomp(U_11218,U_11219,U_11222,U_11221),U_11223)),U_11224)
    | ! [U_11217,U_11216,U_11215,U_11214] : ~ c_Finite__Set_Ofolding(U_11214,U_11215,U_11216,U_11217) ),
    inference(miniscope,[status(thm)],[f_2987_2]) ).

cnf(f_2987_4,plain,
    ( hAPP(c_Fun_Ocomp(U_11218,U_11219,U_11220,U_11221),hAPP(c_Fun_Ocomp(U_11222,U_11218,U_11220,U_11223),U_11224)) = hAPP(c_Fun_Ocomp(U_11222,U_11219,U_11220,hAPP(c_Fun_Ocomp(U_11218,U_11219,U_11222,U_11221),U_11223)),U_11224)
    | ~ c_Finite__Set_Ofolding(U_11214,U_11215,U_11216,U_11217) ),
    inference(clausify,[status(thm)],[f_2987_3]) ).

fof(f_2988_1,plain,
    ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(V_m,V_n)),
    inference(fof_nnf,[status(thm)],[fact_mod__nat__def]) ).

fof(f_2988_2,plain,
    ! [U_11226,U_11225] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_11225,U_11226) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(U_11225,U_11226)),
    inference(variable_rename,[status(thm)],[f_2988_1]) ).

cnf(f_2988_3,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_11225,U_11226) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(U_11225,U_11226)),
    inference(clausify,[status(thm)],[f_2988_2]) ).

fof(f_2989_1,plain,
    ! [V_g_2,T_d,V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_B_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_A_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_A_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_B_2)),V_g_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__left__comp_H_H]) ).

fof(f_2989_2,plain,
    ! [U_11234,U_11233,U_11232,U_11231,U_11230,U_11229,U_11228,U_11227] :
      ( hAPP(c_Fun_Ocomp(U_11228,U_11228,U_11233,hAPP(U_11230,U_11232)),hAPP(c_Fun_Ocomp(U_11228,U_11228,U_11233,hAPP(U_11230,U_11231)),U_11234)) = hAPP(c_Fun_Ocomp(U_11228,U_11228,U_11233,hAPP(U_11230,U_11231)),hAPP(c_Fun_Ocomp(U_11228,U_11228,U_11233,hAPP(U_11230,U_11232)),U_11234))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11227),U_11232))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11227),U_11231))
      | ~ c_Finite__Set_Ofolding(U_11227,U_11228,U_11229,U_11230) ),
    inference(variable_rename,[status(thm)],[f_2989_1]) ).

cnf(f_2989_3,plain,
    ( hAPP(c_Fun_Ocomp(U_11228,U_11228,U_11233,hAPP(U_11230,U_11232)),hAPP(c_Fun_Ocomp(U_11228,U_11228,U_11233,hAPP(U_11230,U_11231)),U_11234)) = hAPP(c_Fun_Ocomp(U_11228,U_11228,U_11233,hAPP(U_11230,U_11231)),hAPP(c_Fun_Ocomp(U_11228,U_11228,U_11233,hAPP(U_11230,U_11232)),U_11234))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11227),U_11232))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11227),U_11231))
    | ~ c_Finite__Set_Ofolding(U_11227,U_11228,U_11229,U_11230) ),
    inference(clausify,[status(thm)],[f_2989_2]) ).

fof(f_2990_1,plain,
    ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_B_2)),hAPP(V_F_2,V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__comp_H_H]) ).

fof(f_2990_2,plain,
    ! [U_11240,U_11239,U_11238,U_11237,U_11236,U_11235] :
      ( hAPP(c_Fun_Ocomp(U_11236,U_11236,U_11236,hAPP(U_11238,U_11240)),hAPP(U_11238,U_11239)) = hAPP(c_Fun_Ocomp(U_11236,U_11236,U_11236,hAPP(U_11238,U_11239)),hAPP(U_11238,U_11240))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11235),U_11240))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11235),U_11239))
      | ~ c_Finite__Set_Ofolding(U_11235,U_11236,U_11237,U_11238) ),
    inference(variable_rename,[status(thm)],[f_2990_1]) ).

cnf(f_2990_3,plain,
    ( hAPP(c_Fun_Ocomp(U_11236,U_11236,U_11236,hAPP(U_11238,U_11240)),hAPP(U_11238,U_11239)) = hAPP(c_Fun_Ocomp(U_11236,U_11236,U_11236,hAPP(U_11238,U_11239)),hAPP(U_11238,U_11240))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11235),U_11240))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11235),U_11239))
    | ~ c_Finite__Set_Ofolding(U_11235,U_11236,U_11237,U_11238) ),
    inference(clausify,[status(thm)],[f_2990_2]) ).

fof(f_2991_1,plain,
    ! [V_g_2,V_x_2,T_d,V_A_2,V_F_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_A_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_A_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),V_g_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__left__comp_H]) ).

fof(f_2991_2,plain,
    ! [U_11248,U_11247,U_11246,U_11245,U_11244,U_11243,U_11242,U_11241] :
      ( hAPP(c_Fun_Ocomp(U_11242,U_11242,U_11246,hAPP(U_11243,U_11247)),hAPP(c_Fun_Ocomp(U_11242,U_11242,U_11246,hAPP(U_11244,U_11245)),U_11248)) = hAPP(c_Fun_Ocomp(U_11242,U_11242,U_11246,hAPP(U_11244,U_11245)),hAPP(c_Fun_Ocomp(U_11242,U_11242,U_11246,hAPP(U_11243,U_11247)),U_11248))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11241),U_11245))
      | ~ c_Finite__Set_Ofolding(U_11241,U_11242,U_11243,U_11244) ),
    inference(variable_rename,[status(thm)],[f_2991_1]) ).

cnf(f_2991_3,plain,
    ( hAPP(c_Fun_Ocomp(U_11242,U_11242,U_11246,hAPP(U_11243,U_11247)),hAPP(c_Fun_Ocomp(U_11242,U_11242,U_11246,hAPP(U_11244,U_11245)),U_11248)) = hAPP(c_Fun_Ocomp(U_11242,U_11242,U_11246,hAPP(U_11244,U_11245)),hAPP(c_Fun_Ocomp(U_11242,U_11242,U_11246,hAPP(U_11243,U_11247)),U_11248))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11241),U_11245))
    | ~ c_Finite__Set_Ofolding(U_11241,U_11242,U_11243,U_11244) ),
    inference(clausify,[status(thm)],[f_2991_2]) ).

fof(f_2992_1,plain,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_F_2,V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__comp_H]) ).

fof(f_2992_2,plain,
    ! [U_11254,U_11253,U_11252,U_11251,U_11250,U_11249] :
      ( hAPP(c_Fun_Ocomp(U_11250,U_11250,U_11250,hAPP(U_11251,U_11254)),hAPP(U_11252,U_11253)) = hAPP(c_Fun_Ocomp(U_11250,U_11250,U_11250,hAPP(U_11252,U_11253)),hAPP(U_11251,U_11254))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11249),U_11253))
      | ~ c_Finite__Set_Ofolding(U_11249,U_11250,U_11251,U_11252) ),
    inference(variable_rename,[status(thm)],[f_2992_1]) ).

cnf(f_2992_3,plain,
    ( hAPP(c_Fun_Ocomp(U_11250,U_11250,U_11250,hAPP(U_11251,U_11254)),hAPP(U_11252,U_11253)) = hAPP(c_Fun_Ocomp(U_11250,U_11250,U_11250,hAPP(U_11252,U_11253)),hAPP(U_11251,U_11254))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11249),U_11253))
    | ~ c_Finite__Set_Ofolding(U_11249,U_11250,U_11251,U_11252) ),
    inference(clausify,[status(thm)],[f_2992_2]) ).

fof(f_2993_1,plain,
    ! [V_s_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
      ( hAPP(hAPP(V_F_2,V_A_2),V_s_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_s_2),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding_Oeq__fold]) ).

fof(f_2993_2,plain,
    ! [U_11260,U_11259,U_11258,U_11257,U_11256,U_11255] :
      ( hAPP(hAPP(U_11258,U_11259),U_11260) = hAPP(hAPP(c_Finite__Set_Ofold(U_11255,U_11256,U_11257),U_11260),U_11259)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11255),U_11259))
      | ~ c_Finite__Set_Ofolding(U_11255,U_11256,U_11257,U_11258) ),
    inference(variable_rename,[status(thm)],[f_2993_1]) ).

cnf(f_2993_3,plain,
    ( hAPP(hAPP(U_11258,U_11259),U_11260) = hAPP(hAPP(c_Finite__Set_Ofold(U_11255,U_11256,U_11257),U_11260),U_11259)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11255),U_11259))
    | ~ c_Finite__Set_Ofolding(U_11255,U_11256,U_11257,U_11258) ),
    inference(clausify,[status(thm)],[f_2993_2]) ).

fof(f_2994_1,plain,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
      ( hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2))
      | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding_Oinsert]) ).

fof(f_2994_2,plain,
    ! [U_11266,U_11265,U_11264,U_11263,U_11262,U_11261] :
      ( hAPP(U_11264,hAPP(hAPP(c_Set_Oinsert(U_11261),U_11266),U_11265)) = hAPP(c_Fun_Ocomp(U_11262,U_11262,U_11262,hAPP(U_11264,U_11265)),hAPP(U_11263,U_11266))
      | hBOOL(hAPP(hAPP(c_member(U_11261),U_11266),U_11265))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11261),U_11265))
      | ~ c_Finite__Set_Ofolding(U_11261,U_11262,U_11263,U_11264) ),
    inference(variable_rename,[status(thm)],[f_2994_1]) ).

cnf(f_2994_3,plain,
    ( hAPP(U_11264,hAPP(hAPP(c_Set_Oinsert(U_11261),U_11266),U_11265)) = hAPP(c_Fun_Ocomp(U_11262,U_11262,U_11262,hAPP(U_11264,U_11265)),hAPP(U_11263,U_11266))
    | hBOOL(hAPP(hAPP(c_member(U_11261),U_11266),U_11265))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11261),U_11265))
    | ~ c_Finite__Set_Ofolding(U_11261,U_11262,U_11263,U_11264) ),
    inference(clausify,[status(thm)],[f_2994_2]) ).

fof(f_2995_1,plain,
    ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding_Ounion__inter]) ).

fof(f_2995_2,plain,
    ! [U_11272,U_11271,U_11270,U_11269,U_11268,U_11267] :
      ( hAPP(c_Fun_Ocomp(U_11268,U_11268,U_11268,hAPP(U_11270,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11267,tc_HOL_Obool)),U_11271),U_11272))),hAPP(U_11270,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11267,tc_HOL_Obool)),U_11271),U_11272))) = hAPP(c_Fun_Ocomp(U_11268,U_11268,U_11268,hAPP(U_11270,U_11271)),hAPP(U_11270,U_11272))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11267),U_11272))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11267),U_11271))
      | ~ c_Finite__Set_Ofolding(U_11267,U_11268,U_11269,U_11270) ),
    inference(variable_rename,[status(thm)],[f_2995_1]) ).

cnf(f_2995_3,plain,
    ( hAPP(c_Fun_Ocomp(U_11268,U_11268,U_11268,hAPP(U_11270,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11267,tc_HOL_Obool)),U_11271),U_11272))),hAPP(U_11270,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11267,tc_HOL_Obool)),U_11271),U_11272))) = hAPP(c_Fun_Ocomp(U_11268,U_11268,U_11268,hAPP(U_11270,U_11271)),hAPP(U_11270,U_11272))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11267),U_11272))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11267),U_11271))
    | ~ c_Finite__Set_Ofolding(U_11267,U_11268,U_11269,U_11270) ),
    inference(clausify,[status(thm)],[f_2995_2]) ).

fof(f_2996_1,plain,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
      ( hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(V_f_2,V_x_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding_Oinsert__remove]) ).

fof(f_2996_2,plain,
    ! [U_11278,U_11277,U_11276,U_11275,U_11274,U_11273] :
      ( hAPP(U_11276,hAPP(hAPP(c_Set_Oinsert(U_11273),U_11278),U_11277)) = hAPP(c_Fun_Ocomp(U_11274,U_11274,U_11274,hAPP(U_11276,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11273,tc_HOL_Obool)),U_11277),hAPP(hAPP(c_Set_Oinsert(U_11273),U_11278),c_Orderings_Obot__class_Obot(tc_fun(U_11273,tc_HOL_Obool)))))),hAPP(U_11275,U_11278))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11273),U_11277))
      | ~ c_Finite__Set_Ofolding(U_11273,U_11274,U_11275,U_11276) ),
    inference(variable_rename,[status(thm)],[f_2996_1]) ).

cnf(f_2996_3,plain,
    ( hAPP(U_11276,hAPP(hAPP(c_Set_Oinsert(U_11273),U_11278),U_11277)) = hAPP(c_Fun_Ocomp(U_11274,U_11274,U_11274,hAPP(U_11276,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11273,tc_HOL_Obool)),U_11277),hAPP(hAPP(c_Set_Oinsert(U_11273),U_11278),c_Orderings_Obot__class_Obot(tc_fun(U_11273,tc_HOL_Obool)))))),hAPP(U_11275,U_11278))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11273),U_11277))
    | ~ c_Finite__Set_Ofolding(U_11273,U_11274,U_11275,U_11276) ),
    inference(clausify,[status(thm)],[f_2996_2]) ).

fof(f_2997_1,plain,
    ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
      ( hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding_Ounion]) ).

fof(f_2997_2,plain,
    ! [U_11284,U_11283,U_11282,U_11281,U_11280,U_11279] :
      ( hAPP(U_11282,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11279,tc_HOL_Obool)),U_11283),U_11284)) = hAPP(c_Fun_Ocomp(U_11280,U_11280,U_11280,hAPP(U_11282,U_11283)),hAPP(U_11282,U_11284))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11279,tc_HOL_Obool)),U_11283),U_11284) != c_Orderings_Obot__class_Obot(tc_fun(U_11279,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11279),U_11284))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11279),U_11283))
      | ~ c_Finite__Set_Ofolding(U_11279,U_11280,U_11281,U_11282) ),
    inference(variable_rename,[status(thm)],[f_2997_1]) ).

cnf(f_2997_3,plain,
    ( hAPP(U_11282,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11279,tc_HOL_Obool)),U_11283),U_11284)) = hAPP(c_Fun_Ocomp(U_11280,U_11280,U_11280,hAPP(U_11282,U_11283)),hAPP(U_11282,U_11284))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11279,tc_HOL_Obool)),U_11283),U_11284) != c_Orderings_Obot__class_Obot(tc_fun(U_11279,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11279),U_11284))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11279),U_11283))
    | ~ c_Finite__Set_Ofolding(U_11279,U_11280,U_11281,U_11282) ),
    inference(clausify,[status(thm)],[f_2997_2]) ).

fof(f_2998_1,plain,
    ! [V_w] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(fof_nnf,[status(thm)],[fact_div__pos__neg__1__number__of]) ).

fof(f_2998_2,plain,
    ! [U_11285] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11285)) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11285)))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11285)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_2998_1]) ).

cnf(f_2998_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11285)) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11285)))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11285)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2998_2]) ).

fof(f_2999_1,plain,
    ! [V_z_2] : hAPP(c_Int_Onat,V_z_2) = c_Set_Othe__elem(tc_Nat_Onat,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,V_z_2)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_Set_Oinsert(tc_Nat_Onat))),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))))),
    inference(fof_nnf,[status(thm)],[fact_nat__def]) ).

fof(f_2999_2,plain,
    ! [U_11286] : hAPP(c_Int_Onat,U_11286) = c_Set_Othe__elem(tc_Nat_Onat,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,U_11286)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_Set_Oinsert(tc_Nat_Onat))),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))))),
    inference(variable_rename,[status(thm)],[f_2999_1]) ).

cnf(f_2999_3,plain,
    hAPP(c_Int_Onat,U_11286) = c_Set_Othe__elem(tc_Nat_Onat,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,U_11286)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_Set_Oinsert(tc_Nat_Onat))),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))))),
    inference(clausify,[status(thm)],[f_2999_2]) ).

fof(f_3000_1,plain,
    ! [V_B_2,V_k_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_B_2)))
      | ? [B_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_n),V_k_2))),V_B_2))) ),
    inference(fof_nnf,[status(thm)],[fact_UN__finite2__subset]) ).

fof(f_3000_2,plain,
    ! [U_11291,U_11290,U_11289,U_11288] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11288,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11288,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_11289)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11288,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_11291)))
      | ? [U_11287] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11288,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11288,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11287)),U_11289)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11288,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11287),U_11290))),U_11291))) ),
    inference(variable_rename,[status(thm)],[f_3000_1]) ).

fof(f_3000_3,plain,
    ! [U_11291,U_11290,U_11289,U_11288] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11288,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11288,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_11289)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11288,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_11291)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11288,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11288,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK261(U_11291,U_11290,U_11289,U_11288))),U_11289)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11288,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK261(U_11291,U_11290,U_11289,U_11288)),U_11290))),U_11291))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK261]),skolemize(U_11287,sK261(U_11291,U_11290,U_11289,U_11288))],[f_3000_2]) ).

cnf(f_3000_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11288,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11288,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_11289)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11288,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_11291)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11288,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11288,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK261(U_11291,U_11290,U_11289,U_11288))),U_11289)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11288,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK261(U_11291,U_11290,U_11289,U_11288)),U_11290))),U_11291))) ),
    inference(clausify,[status(thm)],[f_3000_3]) ).

fof(f_3001_1,plain,
    ! [T_c,T_b,V_t_2,V_s_2] :
      ( ( V_s_2 = V_t_2
        | hAPP(c_Product__Type_Osnd(T_b,T_c),V_s_2) != hAPP(c_Product__Type_Osnd(T_b,T_c),V_t_2)
        | hAPP(c_Product__Type_Ofst(T_b,T_c),V_s_2) != hAPP(c_Product__Type_Ofst(T_b,T_c),V_t_2) )
      & ( ( hAPP(c_Product__Type_Osnd(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Osnd(T_b,T_c),V_t_2)
          & hAPP(c_Product__Type_Ofst(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Ofst(T_b,T_c),V_t_2) )
        | V_s_2 != V_t_2 ) ),
    inference(fof_nnf,[status(thm)],[fact_Pair__fst__snd__eq]) ).

fof(f_3001_2,plain,
    ! [U_11295,U_11294,U_11293,U_11292] :
      ( ( U_11292 = U_11293
        | hAPP(c_Product__Type_Osnd(U_11294,U_11295),U_11292) != hAPP(c_Product__Type_Osnd(U_11294,U_11295),U_11293)
        | hAPP(c_Product__Type_Ofst(U_11294,U_11295),U_11292) != hAPP(c_Product__Type_Ofst(U_11294,U_11295),U_11293) )
      & ( ( hAPP(c_Product__Type_Osnd(U_11294,U_11295),U_11292) = hAPP(c_Product__Type_Osnd(U_11294,U_11295),U_11293)
          & hAPP(c_Product__Type_Ofst(U_11294,U_11295),U_11292) = hAPP(c_Product__Type_Ofst(U_11294,U_11295),U_11293) )
        | U_11292 != U_11293 ) ),
    inference(variable_rename,[status(thm)],[f_3001_1]) ).

fof(f_3001_3,plain,
    ( ! [U_11303,U_11301,U_11299,U_11297] :
        ( U_11297 = U_11299
        | hAPP(c_Product__Type_Osnd(U_11301,U_11303),U_11297) != hAPP(c_Product__Type_Osnd(U_11301,U_11303),U_11299)
        | hAPP(c_Product__Type_Ofst(U_11301,U_11303),U_11297) != hAPP(c_Product__Type_Ofst(U_11301,U_11303),U_11299) )
    & ! [U_11302,U_11300,U_11298,U_11296] :
        ( ( hAPP(c_Product__Type_Osnd(U_11300,U_11302),U_11296) = hAPP(c_Product__Type_Osnd(U_11300,U_11302),U_11298)
          & hAPP(c_Product__Type_Ofst(U_11300,U_11302),U_11296) = hAPP(c_Product__Type_Ofst(U_11300,U_11302),U_11298) )
        | U_11296 != U_11298 ) ),
    inference(miniscope,[status(thm)],[f_3001_2]) ).

cnf(f_3001_4,plain,
    ( hAPP(c_Product__Type_Ofst(U_11300,U_11302),U_11296) = hAPP(c_Product__Type_Ofst(U_11300,U_11302),U_11298)
    | U_11296 != U_11298 ),
    inference(clausify,[status(thm)],[f_3001_3]) ).

cnf(f_3001_5,plain,
    ( hAPP(c_Product__Type_Osnd(U_11300,U_11302),U_11296) = hAPP(c_Product__Type_Osnd(U_11300,U_11302),U_11298)
    | U_11296 != U_11298 ),
    inference(clausify,[status(thm)],[f_3001_3]) ).

cnf(f_3001_6,plain,
    ( U_11297 = U_11299
    | hAPP(c_Product__Type_Osnd(U_11301,U_11303),U_11297) != hAPP(c_Product__Type_Osnd(U_11301,U_11303),U_11299)
    | hAPP(c_Product__Type_Ofst(U_11301,U_11303),U_11297) != hAPP(c_Product__Type_Ofst(U_11301,U_11303),U_11299) ),
    inference(clausify,[status(thm)],[f_3001_3]) ).

fof(f_3002_1,plain,
    ! [V_q,V_p,T_b,T_a] :
      ( V_p = V_q
      | hAPP(c_Product__Type_Osnd(T_a,T_b),V_p) != hAPP(c_Product__Type_Osnd(T_a,T_b),V_q)
      | hAPP(c_Product__Type_Ofst(T_a,T_b),V_p) != hAPP(c_Product__Type_Ofst(T_a,T_b),V_q) ),
    inference(fof_nnf,[status(thm)],[fact_prod__eqI]) ).

fof(f_3002_2,plain,
    ! [U_11307,U_11306,U_11305,U_11304] :
      ( U_11306 = U_11307
      | hAPP(c_Product__Type_Osnd(U_11304,U_11305),U_11306) != hAPP(c_Product__Type_Osnd(U_11304,U_11305),U_11307)
      | hAPP(c_Product__Type_Ofst(U_11304,U_11305),U_11306) != hAPP(c_Product__Type_Ofst(U_11304,U_11305),U_11307) ),
    inference(variable_rename,[status(thm)],[f_3002_1]) ).

cnf(f_3002_3,plain,
    ( U_11306 = U_11307
    | hAPP(c_Product__Type_Osnd(U_11304,U_11305),U_11306) != hAPP(c_Product__Type_Osnd(U_11304,U_11305),U_11307)
    | hAPP(c_Product__Type_Ofst(U_11304,U_11305),U_11306) != hAPP(c_Product__Type_Ofst(U_11304,U_11305),U_11307) ),
    inference(clausify,[status(thm)],[f_3002_2]) ).

fof(f_3003_1,plain,
    ! [V_x_2,V_f_2,T_d,T_c,T_b] : hAPP(c_Product__Type_Ofst(T_b,T_c),hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),V_x_2)) = hAPP(c_Product__Type_Ofst(T_b,T_d),V_x_2),
    inference(fof_nnf,[status(thm)],[fact_fst__apsnd]) ).

fof(f_3003_2,plain,
    ! [U_11312,U_11311,U_11310,U_11309,U_11308] : hAPP(c_Product__Type_Ofst(U_11308,U_11309),hAPP(c_Product__Type_Oapsnd(U_11310,U_11309,U_11308,U_11311),U_11312)) = hAPP(c_Product__Type_Ofst(U_11308,U_11310),U_11312),
    inference(variable_rename,[status(thm)],[f_3003_1]) ).

cnf(f_3003_3,plain,
    hAPP(c_Product__Type_Ofst(U_11308,U_11309),hAPP(c_Product__Type_Oapsnd(U_11310,U_11309,U_11308,U_11311),U_11312)) = hAPP(c_Product__Type_Ofst(U_11308,U_11310),U_11312),
    inference(clausify,[status(thm)],[f_3003_2]) ).

fof(f_3004_1,plain,
    ! [V_b,V_a,T_b,T_a] : hAPP(c_Product__Type_Ofst(T_a,T_b),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a),V_b)) = V_a,
    inference(fof_nnf,[status(thm)],[fact_fst__conv]) ).

fof(f_3004_2,plain,
    ! [U_11316,U_11315,U_11314,U_11313] : hAPP(c_Product__Type_Ofst(U_11313,U_11314),hAPP(hAPP(c_Product__Type_OPair(U_11313,U_11314),U_11315),U_11316)) = U_11315,
    inference(variable_rename,[status(thm)],[f_3004_1]) ).

cnf(f_3004_3,plain,
    hAPP(c_Product__Type_Ofst(U_11313,U_11314),hAPP(hAPP(c_Product__Type_OPair(U_11313,U_11314),U_11315),U_11316)) = U_11315,
    inference(clausify,[status(thm)],[f_3004_2]) ).

fof(f_3005_1,plain,
    ! [V_a,V_y,V_x,T_b,T_a] :
      ( V_x = V_a
      | hAPP(c_Product__Type_Ofst(T_a,T_b),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x),V_y)) != V_a ),
    inference(fof_nnf,[status(thm)],[fact_fst__eqD]) ).

fof(f_3005_2,plain,
    ! [U_11321,U_11320,U_11319,U_11318,U_11317] :
      ( U_11319 = U_11321
      | hAPP(c_Product__Type_Ofst(U_11317,U_11318),hAPP(hAPP(c_Product__Type_OPair(U_11317,U_11318),U_11319),U_11320)) != U_11321 ),
    inference(variable_rename,[status(thm)],[f_3005_1]) ).

fof(f_3005_3,plain,
    ! [U_11321,U_11320,U_11319] :
      ( ! [U_11318,U_11317] : hAPP(c_Product__Type_Ofst(U_11317,U_11318),hAPP(hAPP(c_Product__Type_OPair(U_11317,U_11318),U_11319),U_11320)) != U_11321
      | U_11319 = U_11321 ),
    inference(miniscope,[status(thm)],[f_3005_2]) ).

cnf(f_3005_4,plain,
    ( hAPP(c_Product__Type_Ofst(U_11317,U_11318),hAPP(hAPP(c_Product__Type_OPair(U_11317,U_11318),U_11319),U_11320)) != U_11321
    | U_11319 = U_11321 ),
    inference(clausify,[status(thm)],[f_3005_3]) ).

fof(f_3006_1,plain,
    ! [V_y_2,V_x_2] :
      ( ( hAPP(c_Int_ORep__Integ,V_x_2) = hAPP(c_Int_ORep__Integ,V_y_2)
        | V_x_2 != V_y_2 )
      & ( V_x_2 = V_y_2
        | hAPP(c_Int_ORep__Integ,V_x_2) != hAPP(c_Int_ORep__Integ,V_y_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_Rep__Integ__inject]) ).

fof(f_3006_2,plain,
    ! [U_11323,U_11322] :
      ( ( hAPP(c_Int_ORep__Integ,U_11322) = hAPP(c_Int_ORep__Integ,U_11323)
        | U_11322 != U_11323 )
      & ( U_11322 = U_11323
        | hAPP(c_Int_ORep__Integ,U_11322) != hAPP(c_Int_ORep__Integ,U_11323) ) ),
    inference(variable_rename,[status(thm)],[f_3006_1]) ).

fof(f_3006_3,plain,
    ( ! [U_11327,U_11325] :
        ( hAPP(c_Int_ORep__Integ,U_11325) = hAPP(c_Int_ORep__Integ,U_11327)
        | U_11325 != U_11327 )
    & ! [U_11326,U_11324] :
        ( U_11324 = U_11326
        | hAPP(c_Int_ORep__Integ,U_11324) != hAPP(c_Int_ORep__Integ,U_11326) ) ),
    inference(miniscope,[status(thm)],[f_3006_2]) ).

cnf(f_3006_4,plain,
    ( U_11324 = U_11326
    | hAPP(c_Int_ORep__Integ,U_11324) != hAPP(c_Int_ORep__Integ,U_11326) ),
    inference(clausify,[status(thm)],[f_3006_3]) ).

cnf(f_3006_5,plain,
    ( hAPP(c_Int_ORep__Integ,U_11325) = hAPP(c_Int_ORep__Integ,U_11327)
    | U_11325 != U_11327 ),
    inference(clausify,[status(thm)],[f_3006_3]) ).

fof(f_3007_1,plain,
    ! [V_p_2,T_c,T_b] : hAPP(c_Product__Type_Ofst(T_b,T_c),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_b),c_COMBK(T_b,T_c)),V_p_2),
    inference(fof_nnf,[status(thm)],[fact_fst__def]) ).

fof(f_3007_2,plain,
    ! [U_11330,U_11329,U_11328] : hAPP(c_Product__Type_Ofst(U_11328,U_11329),U_11330) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11328,U_11329,U_11328),c_COMBK(U_11328,U_11329)),U_11330),
    inference(variable_rename,[status(thm)],[f_3007_1]) ).

cnf(f_3007_3,plain,
    hAPP(c_Product__Type_Ofst(U_11328,U_11329),U_11330) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11328,U_11329,U_11328),c_COMBK(U_11328,U_11329)),U_11330),
    inference(clausify,[status(thm)],[f_3007_2]) ).

fof(f_3008_1,plain,
    ! [T_b,T_a,V_t] : V_t = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(c_Product__Type_Ofst(T_a,T_b),V_t)),hAPP(c_Product__Type_Osnd(T_a,T_b),V_t)),
    inference(fof_nnf,[status(thm)],[fact_surjective__pairing]) ).

fof(f_3008_2,plain,
    ! [U_11333,U_11332,U_11331] : U_11331 = hAPP(hAPP(c_Product__Type_OPair(U_11332,U_11333),hAPP(c_Product__Type_Ofst(U_11332,U_11333),U_11331)),hAPP(c_Product__Type_Osnd(U_11332,U_11333),U_11331)),
    inference(variable_rename,[status(thm)],[f_3008_1]) ).

cnf(f_3008_3,plain,
    U_11331 = hAPP(hAPP(c_Product__Type_OPair(U_11332,U_11333),hAPP(c_Product__Type_Ofst(U_11332,U_11333),U_11331)),hAPP(c_Product__Type_Osnd(U_11332,U_11333),U_11331)),
    inference(clausify,[status(thm)],[f_3008_2]) ).

fof(f_3009_1,plain,
    ! [V_p,T_b,T_a] : hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(c_Product__Type_Ofst(T_a,T_b),V_p)),hAPP(c_Product__Type_Osnd(T_a,T_b),V_p)) = V_p,
    inference(fof_nnf,[status(thm)],[fact_pair__collapse]) ).

fof(f_3009_2,plain,
    ! [U_11336,U_11335,U_11334] : hAPP(hAPP(c_Product__Type_OPair(U_11334,U_11335),hAPP(c_Product__Type_Ofst(U_11334,U_11335),U_11336)),hAPP(c_Product__Type_Osnd(U_11334,U_11335),U_11336)) = U_11336,
    inference(variable_rename,[status(thm)],[f_3009_1]) ).

cnf(f_3009_3,plain,
    hAPP(hAPP(c_Product__Type_OPair(U_11334,U_11335),hAPP(c_Product__Type_Ofst(U_11334,U_11335),U_11336)),hAPP(c_Product__Type_Osnd(U_11334,U_11335),U_11336)) = U_11336,
    inference(clausify,[status(thm)],[f_3009_2]) ).

fof(f_3010_1,plain,
    ! [V_p_2,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2),V_p_2) = hAPP(hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_p_2)),hAPP(c_Product__Type_Osnd(T_c,T_d),V_p_2)),
    inference(fof_nnf,[status(thm)],[fact_prod__case__beta]) ).

fof(f_3010_2,plain,
    ! [U_11341,U_11340,U_11339,U_11338,U_11337] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11337,U_11338,U_11339),U_11340),U_11341) = hAPP(hAPP(U_11340,hAPP(c_Product__Type_Ofst(U_11337,U_11338),U_11341)),hAPP(c_Product__Type_Osnd(U_11337,U_11338),U_11341)),
    inference(variable_rename,[status(thm)],[f_3010_1]) ).

cnf(f_3010_3,plain,
    hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11337,U_11338,U_11339),U_11340),U_11341) = hAPP(hAPP(U_11340,hAPP(c_Product__Type_Ofst(U_11337,U_11338),U_11341)),hAPP(c_Product__Type_Osnd(U_11337,U_11338),U_11341)),
    inference(clausify,[status(thm)],[f_3010_2]) ).

fof(f_3011_1,plain,
    ! [V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(V_a,V_b)),
    inference(fof_nnf,[status(thm)],[fact_div__int__def]) ).

fof(f_3011_2,plain,
    ! [U_11343,U_11342] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11342),U_11343) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(U_11342,U_11343)),
    inference(variable_rename,[status(thm)],[f_3011_1]) ).

cnf(f_3011_3,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11342),U_11343) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(U_11342,U_11343)),
    inference(clausify,[status(thm)],[f_3011_2]) ).

fof(f_3012_1,plain,
    ! [V_z_2,V_P_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_P_2),V_z_2) = hAPP(hAPP(V_P_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_z_2)),hAPP(c_Product__Type_Osnd(T_c,T_d),V_z_2)),
    inference(fof_nnf,[status(thm)],[fact_split__beta]) ).

fof(f_3012_2,plain,
    ! [U_11348,U_11347,U_11346,U_11345,U_11344] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11344,U_11345,U_11346),U_11347),U_11348) = hAPP(hAPP(U_11347,hAPP(c_Product__Type_Ofst(U_11344,U_11345),U_11348)),hAPP(c_Product__Type_Osnd(U_11344,U_11345),U_11348)),
    inference(variable_rename,[status(thm)],[f_3012_1]) ).

cnf(f_3012_3,plain,
    hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11344,U_11345,U_11346),U_11347),U_11348) = hAPP(hAPP(U_11347,hAPP(c_Product__Type_Ofst(U_11344,U_11345),U_11348)),hAPP(c_Product__Type_Osnd(U_11344,U_11345),U_11348)),
    inference(clausify,[status(thm)],[f_3012_2]) ).

fof(f_3013_1,plain,
    ! [V_g_2,V_f_2,T_e,T_d,T_c,T_b] : hAPP(hAPP(c_COMBS(tc_prod(T_b,T_c),T_c,T_d),hAPP(hAPP(c_COMBB(T_e,tc_fun(T_c,T_d),tc_prod(T_b,T_c)),V_f_2),hAPP(hAPP(c_COMBB(T_b,T_e,tc_prod(T_b,T_c)),V_g_2),c_Product__Type_Ofst(T_b,T_c)))),c_Product__Type_Osnd(T_b,T_c)) = hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),hAPP(hAPP(c_COMBB(T_e,tc_fun(T_c,T_d),T_b),V_f_2),V_g_2)),
    inference(fof_nnf,[status(thm)],[fact_split__comp__eq]) ).

fof(f_3013_2,plain,
    ! [U_11354,U_11353,U_11352,U_11351,U_11350,U_11349] : hAPP(hAPP(c_COMBS(tc_prod(U_11349,U_11350),U_11350,U_11351),hAPP(hAPP(c_COMBB(U_11352,tc_fun(U_11350,U_11351),tc_prod(U_11349,U_11350)),U_11353),hAPP(hAPP(c_COMBB(U_11349,U_11352,tc_prod(U_11349,U_11350)),U_11354),c_Product__Type_Ofst(U_11349,U_11350)))),c_Product__Type_Osnd(U_11349,U_11350)) = hAPP(c_Product__Type_Oprod_Oprod__case(U_11349,U_11350,U_11351),hAPP(hAPP(c_COMBB(U_11352,tc_fun(U_11350,U_11351),U_11349),U_11353),U_11354)),
    inference(variable_rename,[status(thm)],[f_3013_1]) ).

cnf(f_3013_3,plain,
    hAPP(hAPP(c_COMBS(tc_prod(U_11349,U_11350),U_11350,U_11351),hAPP(hAPP(c_COMBB(U_11352,tc_fun(U_11350,U_11351),tc_prod(U_11349,U_11350)),U_11353),hAPP(hAPP(c_COMBB(U_11349,U_11352,tc_prod(U_11349,U_11350)),U_11354),c_Product__Type_Ofst(U_11349,U_11350)))),c_Product__Type_Osnd(U_11349,U_11350)) = hAPP(c_Product__Type_Oprod_Oprod__case(U_11349,U_11350,U_11351),hAPP(hAPP(c_COMBB(U_11352,tc_fun(U_11350,U_11351),U_11349),U_11353),U_11354)),
    inference(clausify,[status(thm)],[f_3013_2]) ).

fof(f_3014_1,plain,
    ! [V_p_2,V_c_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_c_2),V_p_2) = hAPP(hAPP(V_c_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_p_2)),hAPP(c_Product__Type_Osnd(T_c,T_d),V_p_2)),
    inference(fof_nnf,[status(thm)],[fact_split__def]) ).

fof(f_3014_2,plain,
    ! [U_11359,U_11358,U_11357,U_11356,U_11355] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11355,U_11356,U_11357),U_11358),U_11359) = hAPP(hAPP(U_11358,hAPP(c_Product__Type_Ofst(U_11355,U_11356),U_11359)),hAPP(c_Product__Type_Osnd(U_11355,U_11356),U_11359)),
    inference(variable_rename,[status(thm)],[f_3014_1]) ).

cnf(f_3014_3,plain,
    hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11355,U_11356,U_11357),U_11358),U_11359) = hAPP(hAPP(U_11358,hAPP(c_Product__Type_Ofst(U_11355,U_11356),U_11359)),hAPP(c_Product__Type_Osnd(U_11355,U_11356),U_11359)),
    inference(clausify,[status(thm)],[f_3014_2]) ).

fof(f_3015_1,plain,
    ! [V_x_2,V_g_2,V_f_2,T_e,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),hAPP(c_Fun_Ocomp(T_e,tc_fun(T_d,T_b),T_c,V_f_2),V_g_2)),V_x_2) = hAPP(hAPP(V_f_2,hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_x_2))),hAPP(c_Product__Type_Osnd(T_c,T_d),V_x_2)),
    inference(fof_nnf,[status(thm)],[fact_split__comp]) ).

fof(f_3015_2,plain,
    ! [U_11366,U_11365,U_11364,U_11363,U_11362,U_11361,U_11360] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11360,U_11361,U_11362),hAPP(c_Fun_Ocomp(U_11363,tc_fun(U_11361,U_11362),U_11360,U_11364),U_11365)),U_11366) = hAPP(hAPP(U_11364,hAPP(U_11365,hAPP(c_Product__Type_Ofst(U_11360,U_11361),U_11366))),hAPP(c_Product__Type_Osnd(U_11360,U_11361),U_11366)),
    inference(variable_rename,[status(thm)],[f_3015_1]) ).

cnf(f_3015_3,plain,
    hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11360,U_11361,U_11362),hAPP(c_Fun_Ocomp(U_11363,tc_fun(U_11361,U_11362),U_11360,U_11364),U_11365)),U_11366) = hAPP(hAPP(U_11364,hAPP(U_11365,hAPP(c_Product__Type_Ofst(U_11360,U_11361),U_11366))),hAPP(c_Product__Type_Osnd(U_11360,U_11361),U_11366)),
    inference(clausify,[status(thm)],[f_3015_2]) ).

fof(f_3016_1,plain,
    ! [V_b,V_a] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(V_a,V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(fof_nnf,[status(thm)],[fact_div__neg__pos]) ).

fof(f_3016_2,plain,
    ! [U_11368,U_11367] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11367),U_11368) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(U_11367,U_11368))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11368))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11367),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_3016_1]) ).

cnf(f_3016_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11367),U_11368) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(U_11367,U_11368))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11368))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11367),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_3016_2]) ).

fof(f_3017_1,plain,
    ! [V_b,V_a] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(V_a,V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) ),
    inference(fof_nnf,[status(thm)],[fact_div__pos__pos]) ).

fof(f_3017_2,plain,
    ! [U_11370,U_11369] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11369),U_11370) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(U_11369,U_11370))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11370))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11369)) ),
    inference(variable_rename,[status(thm)],[f_3017_1]) ).

cnf(f_3017_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11369),U_11370) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(U_11369,U_11370))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11370))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11369)) ),
    inference(clausify,[status(thm)],[f_3017_2]) ).

fof(f_3018_1,plain,
    ! [V_w] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) ),
    inference(fof_nnf,[status(thm)],[fact_div__pos__pos__1__number__of]) ).

fof(f_3018_2,plain,
    ! [U_11371] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11371)) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11371)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11371))) ),
    inference(variable_rename,[status(thm)],[f_3018_1]) ).

cnf(f_3018_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11371)) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11371)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_11371))) ),
    inference(clausify,[status(thm)],[f_3018_2]) ).

fof(f_3019_1,plain,
    ! [V_b,V_a] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) ),
    inference(fof_nnf,[status(thm)],[fact_div__pos__neg]) ).

fof(f_3019_2,plain,
    ! [U_11373,U_11372] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11372),U_11373) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11372),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11373))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11373),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11372)) ),
    inference(variable_rename,[status(thm)],[f_3019_1]) ).

cnf(f_3019_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11372),U_11373) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11372),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11373))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11373),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11372)) ),
    inference(clausify,[status(thm)],[f_3019_2]) ).

fof(f_3020_1,plain,
    ! [V_b,V_a] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(fof_nnf,[status(thm)],[fact_div__neg__neg]) ).

fof(f_3020_2,plain,
    ! [U_11375,U_11374] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11374),U_11375) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11374),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11375))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11375),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11374),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_3020_1]) ).

cnf(f_3020_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_11374),U_11375) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11374),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11375))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11375),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11374),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_3020_2]) ).

fof(f_3021_1,plain,
    ! [V_p_2,V_g_2,V_f_2,T_c,T_b] : c_Product__Type_Oprod_Oprod__size(T_b,T_c,V_f_2,V_g_2,V_p_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_b,T_c),V_p_2))),hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_b,T_c),V_p_2)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(fof_nnf,[status(thm)],[fact_prod__size__simp]) ).

fof(f_3021_2,plain,
    ! [U_11380,U_11379,U_11378,U_11377,U_11376] : c_Product__Type_Oprod_Oprod__size(U_11376,U_11377,U_11378,U_11379,U_11380) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_11378,hAPP(c_Product__Type_Ofst(U_11376,U_11377),U_11380))),hAPP(U_11379,hAPP(c_Product__Type_Osnd(U_11376,U_11377),U_11380)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_3021_1]) ).

cnf(f_3021_3,plain,
    c_Product__Type_Oprod_Oprod__size(U_11376,U_11377,U_11378,U_11379,U_11380) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_11378,hAPP(c_Product__Type_Ofst(U_11376,U_11377),U_11380))),hAPP(U_11379,hAPP(c_Product__Type_Osnd(U_11376,U_11377),U_11380)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_3021_2]) ).

fof(f_3022_1,plain,
    ! [T_b,T_c,V_x_2,V_y_2,V_P_2] :
      ( hBOOL(hAPP(hAPP(V_P_2,hAPP(c_Product__Type_Osnd(T_c,T_b),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2),V_y_2))),hAPP(c_Product__Type_Ofst(T_c,T_b),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2),V_y_2))))
      | ~ hBOOL(hAPP(hAPP(V_P_2,V_y_2),V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_exI__realizer]) ).

fof(f_3022_2,plain,
    ! [U_11385,U_11384,U_11383,U_11382,U_11381] :
      ( hBOOL(hAPP(hAPP(U_11381,hAPP(c_Product__Type_Osnd(U_11384,U_11385),hAPP(hAPP(c_Product__Type_OPair(U_11384,U_11385),U_11383),U_11382))),hAPP(c_Product__Type_Ofst(U_11384,U_11385),hAPP(hAPP(c_Product__Type_OPair(U_11384,U_11385),U_11383),U_11382))))
      | ~ hBOOL(hAPP(hAPP(U_11381,U_11382),U_11383)) ),
    inference(variable_rename,[status(thm)],[f_3022_1]) ).

cnf(f_3022_3,plain,
    ( hBOOL(hAPP(hAPP(U_11381,hAPP(c_Product__Type_Osnd(U_11384,U_11385),hAPP(hAPP(c_Product__Type_OPair(U_11384,U_11385),U_11383),U_11382))),hAPP(c_Product__Type_Ofst(U_11384,U_11385),hAPP(hAPP(c_Product__Type_OPair(U_11384,U_11385),U_11383),U_11382))))
    | ~ hBOOL(hAPP(hAPP(U_11381,U_11382),U_11383)) ),
    inference(clausify,[status(thm)],[f_3022_2]) ).

fof(f_3023_1,plain,
    ! [T_c,T_b,V_q_2,V_Q_2,V_p_2,V_P_2] :
      ( ( hBOOL(hAPP(V_Q_2,hAPP(c_Product__Type_Osnd(T_b,T_c),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_p_2),V_q_2))))
        & hBOOL(hAPP(V_P_2,hAPP(c_Product__Type_Ofst(T_b,T_c),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_p_2),V_q_2)))) )
      | ~ hBOOL(hAPP(V_Q_2,V_q_2))
      | ~ hBOOL(hAPP(V_P_2,V_p_2)) ),
    inference(fof_nnf,[status(thm)],[fact_conjI__realizer]) ).

fof(f_3023_2,plain,
    ! [U_11391,U_11390,U_11389,U_11388,U_11387,U_11386] :
      ( ( hBOOL(hAPP(U_11388,hAPP(c_Product__Type_Osnd(U_11390,U_11391),hAPP(hAPP(c_Product__Type_OPair(U_11390,U_11391),U_11387),U_11389))))
        & hBOOL(hAPP(U_11386,hAPP(c_Product__Type_Ofst(U_11390,U_11391),hAPP(hAPP(c_Product__Type_OPair(U_11390,U_11391),U_11387),U_11389)))) )
      | ~ hBOOL(hAPP(U_11388,U_11389))
      | ~ hBOOL(hAPP(U_11386,U_11387)) ),
    inference(variable_rename,[status(thm)],[f_3023_1]) ).

cnf(f_3023_3,plain,
    ( hBOOL(hAPP(U_11386,hAPP(c_Product__Type_Ofst(U_11390,U_11391),hAPP(hAPP(c_Product__Type_OPair(U_11390,U_11391),U_11387),U_11389))))
    | ~ hBOOL(hAPP(U_11388,U_11389))
    | ~ hBOOL(hAPP(U_11386,U_11387)) ),
    inference(clausify,[status(thm)],[f_3023_2]) ).

cnf(f_3023_4,plain,
    ( hBOOL(hAPP(U_11388,hAPP(c_Product__Type_Osnd(U_11390,U_11391),hAPP(hAPP(c_Product__Type_OPair(U_11390,U_11391),U_11387),U_11389))))
    | ~ hBOOL(hAPP(U_11388,U_11389))
    | ~ hBOOL(hAPP(U_11386,U_11387)) ),
    inference(clausify,[status(thm)],[f_3023_2]) ).

fof(f_3024_1,plain,
    ! [V_n,V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(V_m,V_n)),
    inference(fof_nnf,[status(thm)],[fact_div__nat__def]) ).

fof(f_3024_2,plain,
    ! [U_11393,U_11392] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_11392),U_11393) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(U_11392,U_11393)),
    inference(variable_rename,[status(thm)],[f_3024_1]) ).

cnf(f_3024_3,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_11392),U_11393) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(U_11392,U_11393)),
    inference(clausify,[status(thm)],[f_3024_2]) ).

fof(f_3025_1,plain,
    ! [V_qr_2,V_n_2,V_m_2] :
      ( ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m_2,V_n_2),V_qr_2))
        | ( ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2))) )
              & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) )
            | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)),V_n_2))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2))) )
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) )
          & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),V_qr_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | V_m_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)),V_n_2)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)) )
      & ( ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2))) )
                | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) )
              & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)),V_n_2))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2))) )
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) )
            | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),V_qr_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & V_m_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)),V_n_2)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)) )
        | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m_2,V_n_2),V_qr_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_divmod__nat__rel__def]) ).

fof(f_3025_2,plain,
    ! [U_11396,U_11395,U_11394] :
      ( ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11394,U_11395),U_11396))
        | ( ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11396)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11395),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11396))) )
              & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11395)) )
            | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11396)),U_11395))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11396))) )
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11395)) ) )
          & U_11395 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_11396) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_11395 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | U_11394 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_11396)),U_11395)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11396)) )
      & ( ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11396)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11395),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11396))) )
                | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11395)) )
              & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11396)),U_11395))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11396))) )
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11395)) ) )
            | U_11395 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_11396) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | U_11395 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & U_11394 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_11396)),U_11395)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11396)) )
        | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11394,U_11395),U_11396)) ) ),
    inference(variable_rename,[status(thm)],[f_3025_1]) ).

fof(f_3025_3,plain,
    ( ! [U_11402,U_11400,U_11398] :
        ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11398,U_11400),U_11402))
        | ( ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11402)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11400),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11402))) )
              & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11400)) )
            | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11402)),U_11400))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11402))) )
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11400)) ) )
          & U_11400 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_11402) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_11400 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | U_11398 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_11402)),U_11400)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11402)) )
    & ! [U_11401,U_11399,U_11397] :
        ( ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11401)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11399),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11401))) )
                | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11399)) )
              & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11401)),U_11399))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11401))) )
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11399)) ) )
            | U_11399 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_11401) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | U_11399 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & U_11397 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_11401)),U_11399)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11401)) )
        | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11397,U_11399),U_11401)) ) ),
    inference(miniscope,[status(thm)],[f_3025_2]) ).

cnf(f_3025_4,plain,
    ( U_11397 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_11401)),U_11399)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11401))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11397,U_11399),U_11401)) ),
    inference(clausify,[status(thm)],[f_3025_3]) ).

cnf(f_3025_5,plain,
    ( hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_11401) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_11399 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11397,U_11399),U_11401)) ),
    inference(clausify,[status(thm)],[f_3025_3]) ).

cnf(f_3025_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11401)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11399))
    | U_11399 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11397,U_11399),U_11401)) ),
    inference(clausify,[status(thm)],[f_3025_3]) ).

cnf(f_3025_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11401)),U_11399))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11399))
    | U_11399 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11397,U_11399),U_11401)) ),
    inference(clausify,[status(thm)],[f_3025_3]) ).

cnf(f_3025_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11399),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11401)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11399))
    | U_11399 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11397,U_11399),U_11401)) ),
    inference(clausify,[status(thm)],[f_3025_3]) ).

cnf(f_3025_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11401)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11399))
    | U_11399 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11397,U_11399),U_11401)) ),
    inference(clausify,[status(thm)],[f_3025_3]) ).

cnf(f_3025_10,plain,
    ( U_11400 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_11400 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_11398 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_11402)),U_11400)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11402))
    | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11398,U_11400),U_11402)) ),
    inference(clausify,[status(thm)],[f_3025_3]) ).

cnf(f_3025_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11400))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11400))
    | U_11400 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_11398 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_11402)),U_11400)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11402))
    | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11398,U_11400),U_11402)) ),
    inference(clausify,[status(thm)],[f_3025_3]) ).

cnf(f_3025_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11402)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11400),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11402)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11400))
    | U_11400 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_11398 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_11402)),U_11400)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11402))
    | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11398,U_11400),U_11402)) ),
    inference(clausify,[status(thm)],[f_3025_3]) ).

cnf(f_3025_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11400))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11402)),U_11400))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11402)))
    | U_11400 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_11398 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_11402)),U_11400)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11402))
    | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11398,U_11400),U_11402)) ),
    inference(clausify,[status(thm)],[f_3025_3]) ).

cnf(f_3025_14,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11402)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11400),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11402)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11402)),U_11400))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11402)))
    | U_11400 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_11398 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_11402)),U_11400)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11402))
    | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11398,U_11400),U_11402)) ),
    inference(clausify,[status(thm)],[f_3025_3]) ).

cnf(f_3025_15,plain,
    ( U_11400 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_11402) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_11398 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_11402)),U_11400)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11402))
    | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11398,U_11400),U_11402)) ),
    inference(clausify,[status(thm)],[f_3025_3]) ).

cnf(f_3025_16,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11400))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11400))
    | hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_11402) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_11398 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_11402)),U_11400)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11402))
    | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11398,U_11400),U_11402)) ),
    inference(clausify,[status(thm)],[f_3025_3]) ).

cnf(f_3025_17,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11402)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11400),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11402)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11400))
    | hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_11402) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_11398 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_11402)),U_11400)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11402))
    | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11398,U_11400),U_11402)) ),
    inference(clausify,[status(thm)],[f_3025_3]) ).

cnf(f_3025_18,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11400))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11402)),U_11400))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11402)))
    | hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_11402) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_11398 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_11402)),U_11400)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11402))
    | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11398,U_11400),U_11402)) ),
    inference(clausify,[status(thm)],[f_3025_3]) ).

cnf(f_3025_19,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11402)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11400),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11402)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11402)),U_11400))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11402)))
    | hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_11402) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_11398 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_11402)),U_11400)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_11402))
    | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_11398,U_11400),U_11402)) ),
    inference(clausify,[status(thm)],[f_3025_3]) ).

fof(f_3026_1,plain,
    ! [V_P_2,V_a1_2,V_a0_2] :
      ( hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2))
      | ? [B_x,B_y] :
          ( ~ hBOOL(hAPP(hAPP(V_P_2,B_x),B_y))
          & ( hBOOL(hAPP(hAPP(V_P_2,B_y),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B_x,B_y)))
            | B_y = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),B_x),B_y))) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a0_2),V_a1_2))) ),
    inference(fof_nnf,[status(thm)],[fact_nat__gcd_Opinduct]) ).

fof(f_3026_2,plain,
    ! [U_11407,U_11406,U_11405] :
      ( hBOOL(hAPP(hAPP(U_11407,U_11405),U_11406))
      | ? [U_11404,U_11403] :
          ( ~ hBOOL(hAPP(hAPP(U_11407,U_11404),U_11403))
          & ( hBOOL(hAPP(hAPP(U_11407,U_11403),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_11404,U_11403)))
            | U_11403 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11404),U_11403))) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11405),U_11406))) ),
    inference(variable_rename,[status(thm)],[f_3026_1]) ).

fof(f_3026_3,plain,
    ! [U_11407,U_11406,U_11405] :
      ( hBOOL(hAPP(hAPP(U_11407,U_11405),U_11406))
      | ? [U_11403] :
          ( ~ hBOOL(hAPP(hAPP(U_11407,sK262(U_11407,U_11406,U_11405)),U_11403))
          & ( hBOOL(hAPP(hAPP(U_11407,U_11403),c_Divides_Odiv__class_Omod(tc_Nat_Onat,sK262(U_11407,U_11406,U_11405),U_11403)))
            | U_11403 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),sK262(U_11407,U_11406,U_11405)),U_11403))) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11405),U_11406))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK262]),skolemize(U_11404,sK262(U_11407,U_11406,U_11405))],[f_3026_2]) ).

fof(f_3026_4,plain,
    ! [U_11407,U_11406,U_11405] :
      ( hBOOL(hAPP(hAPP(U_11407,U_11405),U_11406))
      | ( ~ hBOOL(hAPP(hAPP(U_11407,sK262(U_11407,U_11406,U_11405)),sK263(U_11407,U_11406,U_11405)))
        & ( hBOOL(hAPP(hAPP(U_11407,sK263(U_11407,U_11406,U_11405)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,sK262(U_11407,U_11406,U_11405),sK263(U_11407,U_11406,U_11405))))
          | sK263(U_11407,U_11406,U_11405) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        & hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),sK262(U_11407,U_11406,U_11405)),sK263(U_11407,U_11406,U_11405)))) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11405),U_11406))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK263]),skolemize(U_11403,sK263(U_11407,U_11406,U_11405))],[f_3026_3]) ).

cnf(f_3026_5,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),sK262(U_11407,U_11406,U_11405)),sK263(U_11407,U_11406,U_11405))))
    | hBOOL(hAPP(hAPP(U_11407,U_11405),U_11406))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11405),U_11406))) ),
    inference(clausify,[status(thm)],[f_3026_4]) ).

cnf(f_3026_6,plain,
    ( hBOOL(hAPP(hAPP(U_11407,sK263(U_11407,U_11406,U_11405)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,sK262(U_11407,U_11406,U_11405),sK263(U_11407,U_11406,U_11405))))
    | sK263(U_11407,U_11406,U_11405) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(hAPP(U_11407,U_11405),U_11406))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11405),U_11406))) ),
    inference(clausify,[status(thm)],[f_3026_4]) ).

cnf(f_3026_7,plain,
    ( ~ hBOOL(hAPP(hAPP(U_11407,sK262(U_11407,U_11406,U_11405)),sK263(U_11407,U_11406,U_11405)))
    | hBOOL(hAPP(hAPP(U_11407,U_11405),U_11406))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11405),U_11406))) ),
    inference(clausify,[status(thm)],[f_3026_4]) ).

fof(f_3027_1,plain,
    ! [V_s,V_k] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Orange(V_k),V_s))),V_k))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),V_k)) ),
    inference(fof_nnf,[status(thm)],[fact_range]) ).

fof(f_3027_2,plain,
    ! [U_11409,U_11408] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Orange(U_11408),U_11409))),U_11408))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),U_11408)) ),
    inference(variable_rename,[status(thm)],[f_3027_1]) ).

cnf(f_3027_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Orange(U_11408),U_11409))),U_11408))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),U_11408)) ),
    inference(clausify,[status(thm)],[f_3027_2]) ).

fof(f_3028_1,plain,
    ! [V_R_2,T_b,V_y_2,V_x_2,V_f_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_R_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) ),
    inference(fof_nnf,[status(thm)],[fact_mlex__leq]) ).

fof(f_3028_2,plain,
    ! [U_11414,U_11413,U_11412,U_11411,U_11410] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11413,U_11413)),hAPP(hAPP(c_Product__Type_OPair(U_11413,U_11413),U_11411),U_11412)),c_Wellfounded_Omlex__prod(U_11413,U_11410,U_11414)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11413,U_11413)),hAPP(hAPP(c_Product__Type_OPair(U_11413,U_11413),U_11411),U_11412)),U_11414))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(U_11410,U_11411)),hAPP(U_11410,U_11412))) ),
    inference(variable_rename,[status(thm)],[f_3028_1]) ).

cnf(f_3028_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11413,U_11413)),hAPP(hAPP(c_Product__Type_OPair(U_11413,U_11413),U_11411),U_11412)),c_Wellfounded_Omlex__prod(U_11413,U_11410,U_11414)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11413,U_11413)),hAPP(hAPP(c_Product__Type_OPair(U_11413,U_11413),U_11411),U_11412)),U_11414))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(U_11410,U_11411)),hAPP(U_11410,U_11412))) ),
    inference(clausify,[status(thm)],[f_3028_2]) ).

fof(f_3029_1,plain,
    ! [V_R_2,T_b,V_y_2,V_x_2,V_f_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) ),
    inference(fof_nnf,[status(thm)],[fact_mlex__less]) ).

fof(f_3029_2,plain,
    ! [U_11419,U_11418,U_11417,U_11416,U_11415] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11418,U_11418)),hAPP(hAPP(c_Product__Type_OPair(U_11418,U_11418),U_11416),U_11417)),c_Wellfounded_Omlex__prod(U_11418,U_11415,U_11419)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_11415,U_11416)),hAPP(U_11415,U_11417))) ),
    inference(variable_rename,[status(thm)],[f_3029_1]) ).

cnf(f_3029_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11418,U_11418)),hAPP(hAPP(c_Product__Type_OPair(U_11418,U_11418),U_11416),U_11417)),c_Wellfounded_Omlex__prod(U_11418,U_11415,U_11419)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_11415,U_11416)),hAPP(U_11415,U_11417))) ),
    inference(clausify,[status(thm)],[f_3029_2]) ).

fof(f_3030_1,plain,
    ! [V_S_2,V_f_2,T_b,T_c] :
      ( c_Orderings_Oord__class_OLeast(T_c,hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_S_2))) = hAPP(V_f_2,c_Orderings_Oord__class_OLeast(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)))
      | ! [B_x] :
          ( ? [B_xa] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),B_xa))
              & hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_S_2)) )
          | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) )
      | ~ c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
      | ~ class_Orderings_Oorder(T_b)
      | ~ class_Orderings_Oorder(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_Least__mono]) ).

fof(f_3030_2,plain,
    ! [U_11425,U_11424,U_11423,U_11422] :
      ( c_Orderings_Oord__class_OLeast(U_11422,hAPP(hAPP(c_COMBC(U_11422,tc_fun(U_11422,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11422)),hAPP(c_Set_Oimage(U_11423,U_11422,U_11424),U_11425))) = hAPP(U_11424,c_Orderings_Oord__class_OLeast(U_11423,hAPP(hAPP(c_COMBC(U_11423,tc_fun(U_11423,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11423)),U_11425)))
      | ! [U_11421] :
          ( ? [U_11420] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11423),U_11421),U_11420))
              & hBOOL(hAPP(hAPP(c_member(U_11423),U_11420),U_11425)) )
          | ~ hBOOL(hAPP(hAPP(c_member(U_11423),U_11421),U_11425)) )
      | ~ c_Orderings_Oorder__class_Omono(U_11423,U_11422,U_11424)
      | ~ class_Orderings_Oorder(U_11423)
      | ~ class_Orderings_Oorder(U_11422) ),
    inference(variable_rename,[status(thm)],[f_3030_1]) ).

fof(f_3030_3,plain,
    ! [U_11425,U_11424,U_11423,U_11422] :
      ( c_Orderings_Oord__class_OLeast(U_11422,hAPP(hAPP(c_COMBC(U_11422,tc_fun(U_11422,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11422)),hAPP(c_Set_Oimage(U_11423,U_11422,U_11424),U_11425))) = hAPP(U_11424,c_Orderings_Oord__class_OLeast(U_11423,hAPP(hAPP(c_COMBC(U_11423,tc_fun(U_11423,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11423)),U_11425)))
      | ! [U_11421] :
          ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11423),U_11421),sK264(U_11425,U_11424,U_11423,U_11422,U_11421)))
            & hBOOL(hAPP(hAPP(c_member(U_11423),sK264(U_11425,U_11424,U_11423,U_11422,U_11421)),U_11425)) )
          | ~ hBOOL(hAPP(hAPP(c_member(U_11423),U_11421),U_11425)) )
      | ~ c_Orderings_Oorder__class_Omono(U_11423,U_11422,U_11424)
      | ~ class_Orderings_Oorder(U_11423)
      | ~ class_Orderings_Oorder(U_11422) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK264]),skolemize(U_11420,sK264(U_11425,U_11424,U_11423,U_11422,U_11421))],[f_3030_2]) ).

cnf(f_3030_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11423),sK264(U_11425,U_11424,U_11423,U_11422,U_11421)),U_11425))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11423),U_11421),U_11425))
    | c_Orderings_Oord__class_OLeast(U_11422,hAPP(hAPP(c_COMBC(U_11422,tc_fun(U_11422,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11422)),hAPP(c_Set_Oimage(U_11423,U_11422,U_11424),U_11425))) = hAPP(U_11424,c_Orderings_Oord__class_OLeast(U_11423,hAPP(hAPP(c_COMBC(U_11423,tc_fun(U_11423,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11423)),U_11425)))
    | ~ c_Orderings_Oorder__class_Omono(U_11423,U_11422,U_11424)
    | ~ class_Orderings_Oorder(U_11423)
    | ~ class_Orderings_Oorder(U_11422) ),
    inference(clausify,[status(thm)],[f_3030_3]) ).

cnf(f_3030_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11423),U_11421),sK264(U_11425,U_11424,U_11423,U_11422,U_11421)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11423),U_11421),U_11425))
    | c_Orderings_Oord__class_OLeast(U_11422,hAPP(hAPP(c_COMBC(U_11422,tc_fun(U_11422,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11422)),hAPP(c_Set_Oimage(U_11423,U_11422,U_11424),U_11425))) = hAPP(U_11424,c_Orderings_Oord__class_OLeast(U_11423,hAPP(hAPP(c_COMBC(U_11423,tc_fun(U_11423,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11423)),U_11425)))
    | ~ c_Orderings_Oorder__class_Omono(U_11423,U_11422,U_11424)
    | ~ class_Orderings_Oorder(U_11423)
    | ~ class_Orderings_Oorder(U_11422) ),
    inference(clausify,[status(thm)],[f_3030_3]) ).

fof(f_3031_1,plain,
    ! [V_g_2,V_h_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
      ( hAPP(hAPP(V_F_2,V_g_2),hAPP(c_Set_Oimage(T_c,T_c,V_h_2),V_A_2)) = hAPP(hAPP(V_F_2,hAPP(c_Fun_Ocomp(T_c,T_b,T_c,V_g_2),V_h_2)),V_A_2)
      | ~ c_Fun_Oinj__on(T_c,T_c,V_h_2,V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
      | ~ c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__image_Oreindex]) ).

fof(f_3031_2,plain,
    ! [U_11433,U_11432,U_11431,U_11430,U_11429,U_11428,U_11427,U_11426] :
      ( hAPP(hAPP(U_11430,U_11433),hAPP(c_Set_Oimage(U_11427,U_11427,U_11432),U_11431)) = hAPP(hAPP(U_11430,hAPP(c_Fun_Ocomp(U_11427,U_11426,U_11427,U_11433),U_11432)),U_11431)
      | ~ c_Fun_Oinj__on(U_11427,U_11427,U_11432,U_11431)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11427),U_11431))
      | ~ c_Finite__Set_Ofolding__image(U_11426,U_11427,U_11428,U_11429,U_11430) ),
    inference(variable_rename,[status(thm)],[f_3031_1]) ).

cnf(f_3031_3,plain,
    ( hAPP(hAPP(U_11430,U_11433),hAPP(c_Set_Oimage(U_11427,U_11427,U_11432),U_11431)) = hAPP(hAPP(U_11430,hAPP(c_Fun_Ocomp(U_11427,U_11426,U_11427,U_11433),U_11432)),U_11431)
    | ~ c_Fun_Oinj__on(U_11427,U_11427,U_11432,U_11431)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11427),U_11431))
    | ~ c_Finite__Set_Ofolding__image(U_11426,U_11427,U_11428,U_11429,U_11430) ),
    inference(clausify,[status(thm)],[f_3031_2]) ).

fof(f_3032_1,plain,
    ! [V_nat] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_nat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),V_nat)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(fof_nnf,[status(thm)],[fact_nat_Osize_I4_J]) ).

fof(f_3032_2,plain,
    ! [U_11434] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_11434)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),U_11434)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_3032_1]) ).

cnf(f_3032_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_11434)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),U_11434)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_3032_2]) ).

fof(f_3033_1,plain,
    ! [V_n] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),V_n) = V_n,
    inference(fof_nnf,[status(thm)],[fact_nat__size]) ).

fof(f_3033_2,plain,
    ! [U_11435] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),U_11435) = U_11435,
    inference(variable_rename,[status(thm)],[f_3033_1]) ).

cnf(f_3033_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),U_11435) = U_11435,
    inference(clausify,[status(thm)],[f_3033_2]) ).

fof(f_3034_1,plain,
    ! [V_P_2,T_b] :
      ( hBOOL(hAPP(V_P_2,c_Orderings_Oord__class_OLeast(T_b,V_P_2)))
      | ! [B_x1] : ~ hBOOL(hAPP(V_P_2,B_x1))
      | ~ class_Orderings_Owellorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_LeastI__ex]) ).

fof(f_3034_2,plain,
    ! [U_11438,U_11437] :
      ( hBOOL(hAPP(U_11438,c_Orderings_Oord__class_OLeast(U_11437,U_11438)))
      | ! [U_11436] : ~ hBOOL(hAPP(U_11438,U_11436))
      | ~ class_Orderings_Owellorder(U_11437) ),
    inference(variable_rename,[status(thm)],[f_3034_1]) ).

cnf(f_3034_3,plain,
    ( hBOOL(hAPP(U_11438,c_Orderings_Oord__class_OLeast(U_11437,U_11438)))
    | ~ hBOOL(hAPP(U_11438,U_11436))
    | ~ class_Orderings_Owellorder(U_11437) ),
    inference(clausify,[status(thm)],[f_3034_2]) ).

fof(f_3035_1,plain,
    ! [V_k_2,V_P_2,T_b] :
      ( hBOOL(hAPP(V_P_2,c_Orderings_Oord__class_OLeast(T_b,V_P_2)))
      | ~ hBOOL(hAPP(V_P_2,V_k_2))
      | ~ class_Orderings_Owellorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_LeastI]) ).

fof(f_3035_2,plain,
    ! [U_11441,U_11440,U_11439] :
      ( hBOOL(hAPP(U_11440,c_Orderings_Oord__class_OLeast(U_11439,U_11440)))
      | ~ hBOOL(hAPP(U_11440,U_11441))
      | ~ class_Orderings_Owellorder(U_11439) ),
    inference(variable_rename,[status(thm)],[f_3035_1]) ).

cnf(f_3035_3,plain,
    ( hBOOL(hAPP(U_11440,c_Orderings_Oord__class_OLeast(U_11439,U_11440)))
    | ~ hBOOL(hAPP(U_11440,U_11441))
    | ~ class_Orderings_Owellorder(U_11439) ),
    inference(clausify,[status(thm)],[f_3035_2]) ).

fof(f_3036_1,plain,
    ! [V_k_2,V_P_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Orderings_Oord__class_OLeast(T_b,V_P_2)),V_k_2))
      | ~ hBOOL(hAPP(V_P_2,V_k_2))
      | ~ class_Orderings_Owellorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Least__le]) ).

fof(f_3036_2,plain,
    ! [U_11444,U_11443,U_11442] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11442),c_Orderings_Oord__class_OLeast(U_11442,U_11443)),U_11444))
      | ~ hBOOL(hAPP(U_11443,U_11444))
      | ~ class_Orderings_Owellorder(U_11442) ),
    inference(variable_rename,[status(thm)],[f_3036_1]) ).

cnf(f_3036_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11442),c_Orderings_Oord__class_OLeast(U_11442,U_11443)),U_11444))
    | ~ hBOOL(hAPP(U_11443,U_11444))
    | ~ class_Orderings_Owellorder(U_11442) ),
    inference(clausify,[status(thm)],[f_3036_2]) ).

fof(f_3037_1,plain,
    ! [V_P_2,V_k_2,T_b] :
      ( ~ hBOOL(hAPP(V_P_2,V_k_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),c_Orderings_Oord__class_OLeast(T_b,V_P_2)))
      | ~ class_Orderings_Owellorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_not__less__Least]) ).

fof(f_3037_2,plain,
    ! [U_11447,U_11446,U_11445] :
      ( ~ hBOOL(hAPP(U_11447,U_11446))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11445),U_11446),c_Orderings_Oord__class_OLeast(U_11445,U_11447)))
      | ~ class_Orderings_Owellorder(U_11445) ),
    inference(variable_rename,[status(thm)],[f_3037_1]) ).

cnf(f_3037_3,plain,
    ( ~ hBOOL(hAPP(U_11447,U_11446))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11445),U_11446),c_Orderings_Oord__class_OLeast(U_11445,U_11447)))
    | ~ class_Orderings_Owellorder(U_11445) ),
    inference(clausify,[status(thm)],[f_3037_2]) ).

fof(f_3038_1,plain,
    ! [V_h_2,V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
      ( hAPP(hAPP(V_F_2,hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),V_f_2),V_g_2)),V_h_2)),V_A_2) = hAPP(hAPP(V_f_2,hAPP(hAPP(V_F_2,V_g_2),V_A_2)),hAPP(hAPP(V_F_2,V_h_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
      | ~ c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__image_Odistrib]) ).

fof(f_3038_2,plain,
    ! [U_11455,U_11454,U_11453,U_11452,U_11451,U_11450,U_11449,U_11448] :
      ( hAPP(hAPP(U_11452,hAPP(hAPP(c_COMBS(U_11449,U_11448,U_11448),hAPP(hAPP(c_COMBB(U_11448,tc_fun(U_11448,U_11448),U_11449),U_11450),U_11454)),U_11455)),U_11453) = hAPP(hAPP(U_11450,hAPP(hAPP(U_11452,U_11454),U_11453)),hAPP(hAPP(U_11452,U_11455),U_11453))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11449),U_11453))
      | ~ c_Finite__Set_Ofolding__image(U_11448,U_11449,U_11450,U_11451,U_11452) ),
    inference(variable_rename,[status(thm)],[f_3038_1]) ).

cnf(f_3038_3,plain,
    ( hAPP(hAPP(U_11452,hAPP(hAPP(c_COMBS(U_11449,U_11448,U_11448),hAPP(hAPP(c_COMBB(U_11448,tc_fun(U_11448,U_11448),U_11449),U_11450),U_11454)),U_11455)),U_11453) = hAPP(hAPP(U_11450,hAPP(hAPP(U_11452,U_11454),U_11453)),hAPP(hAPP(U_11452,U_11455),U_11453))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11449),U_11453))
    | ~ c_Finite__Set_Ofolding__image(U_11448,U_11449,U_11450,U_11451,U_11452) ),
    inference(clausify,[status(thm)],[f_3038_2]) ).

fof(f_3039_1,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_nat_Osize_I3_J]) ).

cnf(f_3039_2,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_3039_1]) ).

fof(f_3040_1,plain,
    ! [V_n_2,V_P_2] :
      ( c_Orderings_Oord__class_OLeast(tc_Nat_Onat,V_P_2) = hAPP(c_Nat_OSuc,c_Orderings_Oord__class_OLeast(tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Nat_Onat),V_P_2),c_Nat_OSuc)))
      | hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
      | ~ hBOOL(hAPP(V_P_2,V_n_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Least__Suc]) ).

fof(f_3040_2,plain,
    ! [U_11457,U_11456] :
      ( c_Orderings_Oord__class_OLeast(tc_Nat_Onat,U_11456) = hAPP(c_Nat_OSuc,c_Orderings_Oord__class_OLeast(tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Nat_Onat),U_11456),c_Nat_OSuc)))
      | hBOOL(hAPP(U_11456,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
      | ~ hBOOL(hAPP(U_11456,U_11457)) ),
    inference(variable_rename,[status(thm)],[f_3040_1]) ).

cnf(f_3040_3,plain,
    ( c_Orderings_Oord__class_OLeast(tc_Nat_Onat,U_11456) = hAPP(c_Nat_OSuc,c_Orderings_Oord__class_OLeast(tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Nat_Onat),U_11456),c_Nat_OSuc)))
    | hBOOL(hAPP(U_11456,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(U_11456,U_11457)) ),
    inference(clausify,[status(thm)],[f_3040_2]) ).

fof(f_3041_1,plain,
    ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
      ( hAPP(hAPP(V_F_2,V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2),V_z_2),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
      | ~ c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__image_Oeq__fold]) ).

fof(f_3041_2,plain,
    ! [U_11464,U_11463,U_11462,U_11461,U_11460,U_11459,U_11458] :
      ( hAPP(hAPP(U_11462,U_11464),U_11463) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11458,U_11459,U_11460),U_11464),U_11461),U_11463)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11459),U_11463))
      | ~ c_Finite__Set_Ofolding__image(U_11458,U_11459,U_11460,U_11461,U_11462) ),
    inference(variable_rename,[status(thm)],[f_3041_1]) ).

cnf(f_3041_3,plain,
    ( hAPP(hAPP(U_11462,U_11464),U_11463) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11458,U_11459,U_11460),U_11464),U_11461),U_11463)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11459),U_11463))
    | ~ c_Finite__Set_Ofolding__image(U_11458,U_11459,U_11460,U_11461,U_11462) ),
    inference(clausify,[status(thm)],[f_3041_2]) ).

fof(f_3042_1,plain,
    ! [V_b_2,V_a_2,V_f1_2,T_b,T_d,T_c] : c_Product__Type_Oprod_Oprod__rec(T_c,T_d,T_b,V_f1_2,hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2),
    inference(fof_nnf,[status(thm)],[fact_prod_Orecs]) ).

fof(f_3042_2,plain,
    ! [U_11470,U_11469,U_11468,U_11467,U_11466,U_11465] : c_Product__Type_Oprod_Oprod__rec(U_11465,U_11466,U_11467,U_11468,hAPP(hAPP(c_Product__Type_OPair(U_11465,U_11466),U_11469),U_11470)) = hAPP(hAPP(U_11468,U_11469),U_11470),
    inference(variable_rename,[status(thm)],[f_3042_1]) ).

cnf(f_3042_3,plain,
    c_Product__Type_Oprod_Oprod__rec(U_11465,U_11466,U_11467,U_11468,hAPP(hAPP(c_Product__Type_OPair(U_11465,U_11466),U_11469),U_11470)) = hAPP(hAPP(U_11468,U_11469),U_11470),
    inference(clausify,[status(thm)],[f_3042_2]) ).

fof(f_3043_1,plain,
    ! [T_c,V_h_2,V_f_2,V_S_2,T_b,T_d] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_h_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_S_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)),V_S_2)
      | ? [B_x] :
          ( ? [B_y] :
              ( hAPP(V_h_2,hAPP(V_f_2,B_x)) != c_Groups_Ozero__class_Ozero(T_d)
              & hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y)
              & B_x != B_y
              & hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_S_2)) )
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
      | ~ class_Groups_Ocomm__monoid__add(T_d) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__reindex__nonzero]) ).

fof(f_3043_2,plain,
    ! [U_11478,U_11477,U_11476,U_11475,U_11474,U_11473] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11478,U_11473),U_11477),hAPP(c_Set_Oimage(U_11474,U_11478,U_11476),U_11475)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11474,U_11473),hAPP(c_Fun_Ocomp(U_11478,U_11473,U_11474,U_11477),U_11476)),U_11475)
      | ? [U_11472] :
          ( ? [U_11471] :
              ( hAPP(U_11477,hAPP(U_11476,U_11472)) != c_Groups_Ozero__class_Ozero(U_11473)
              & hAPP(U_11476,U_11472) = hAPP(U_11476,U_11471)
              & U_11472 != U_11471
              & hBOOL(hAPP(hAPP(c_member(U_11474),U_11471),U_11475)) )
          & hBOOL(hAPP(hAPP(c_member(U_11474),U_11472),U_11475)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11474),U_11475))
      | ~ class_Groups_Ocomm__monoid__add(U_11473) ),
    inference(variable_rename,[status(thm)],[f_3043_1]) ).

fof(f_3043_3,plain,
    ! [U_11478,U_11477,U_11476,U_11475,U_11474,U_11473] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11478,U_11473),U_11477),hAPP(c_Set_Oimage(U_11474,U_11478,U_11476),U_11475)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11474,U_11473),hAPP(c_Fun_Ocomp(U_11478,U_11473,U_11474,U_11477),U_11476)),U_11475)
      | ( ? [U_11471] :
            ( hAPP(U_11477,hAPP(U_11476,sK265(U_11478,U_11477,U_11476,U_11475,U_11474,U_11473))) != c_Groups_Ozero__class_Ozero(U_11473)
            & hAPP(U_11476,sK265(U_11478,U_11477,U_11476,U_11475,U_11474,U_11473)) = hAPP(U_11476,U_11471)
            & sK265(U_11478,U_11477,U_11476,U_11475,U_11474,U_11473) != U_11471
            & hBOOL(hAPP(hAPP(c_member(U_11474),U_11471),U_11475)) )
        & hBOOL(hAPP(hAPP(c_member(U_11474),sK265(U_11478,U_11477,U_11476,U_11475,U_11474,U_11473)),U_11475)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11474),U_11475))
      | ~ class_Groups_Ocomm__monoid__add(U_11473) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK265]),skolemize(U_11472,sK265(U_11478,U_11477,U_11476,U_11475,U_11474,U_11473))],[f_3043_2]) ).

fof(f_3043_4,plain,
    ! [U_11478,U_11477,U_11476,U_11475,U_11474,U_11473] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11478,U_11473),U_11477),hAPP(c_Set_Oimage(U_11474,U_11478,U_11476),U_11475)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11474,U_11473),hAPP(c_Fun_Ocomp(U_11478,U_11473,U_11474,U_11477),U_11476)),U_11475)
      | ( hAPP(U_11477,hAPP(U_11476,sK265(U_11478,U_11477,U_11476,U_11475,U_11474,U_11473))) != c_Groups_Ozero__class_Ozero(U_11473)
        & hAPP(U_11476,sK265(U_11478,U_11477,U_11476,U_11475,U_11474,U_11473)) = hAPP(U_11476,sK266(U_11478,U_11477,U_11476,U_11475,U_11474,U_11473))
        & sK265(U_11478,U_11477,U_11476,U_11475,U_11474,U_11473) != sK266(U_11478,U_11477,U_11476,U_11475,U_11474,U_11473)
        & hBOOL(hAPP(hAPP(c_member(U_11474),sK266(U_11478,U_11477,U_11476,U_11475,U_11474,U_11473)),U_11475))
        & hBOOL(hAPP(hAPP(c_member(U_11474),sK265(U_11478,U_11477,U_11476,U_11475,U_11474,U_11473)),U_11475)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11474),U_11475))
      | ~ class_Groups_Ocomm__monoid__add(U_11473) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK266]),skolemize(U_11471,sK266(U_11478,U_11477,U_11476,U_11475,U_11474,U_11473))],[f_3043_3]) ).

cnf(f_3043_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11474),sK265(U_11478,U_11477,U_11476,U_11475,U_11474,U_11473)),U_11475))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11478,U_11473),U_11477),hAPP(c_Set_Oimage(U_11474,U_11478,U_11476),U_11475)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11474,U_11473),hAPP(c_Fun_Ocomp(U_11478,U_11473,U_11474,U_11477),U_11476)),U_11475)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11474),U_11475))
    | ~ class_Groups_Ocomm__monoid__add(U_11473) ),
    inference(clausify,[status(thm)],[f_3043_4]) ).

cnf(f_3043_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11474),sK266(U_11478,U_11477,U_11476,U_11475,U_11474,U_11473)),U_11475))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11478,U_11473),U_11477),hAPP(c_Set_Oimage(U_11474,U_11478,U_11476),U_11475)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11474,U_11473),hAPP(c_Fun_Ocomp(U_11478,U_11473,U_11474,U_11477),U_11476)),U_11475)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11474),U_11475))
    | ~ class_Groups_Ocomm__monoid__add(U_11473) ),
    inference(clausify,[status(thm)],[f_3043_4]) ).

cnf(f_3043_7,plain,
    ( sK265(U_11478,U_11477,U_11476,U_11475,U_11474,U_11473) != sK266(U_11478,U_11477,U_11476,U_11475,U_11474,U_11473)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11478,U_11473),U_11477),hAPP(c_Set_Oimage(U_11474,U_11478,U_11476),U_11475)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11474,U_11473),hAPP(c_Fun_Ocomp(U_11478,U_11473,U_11474,U_11477),U_11476)),U_11475)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11474),U_11475))
    | ~ class_Groups_Ocomm__monoid__add(U_11473) ),
    inference(clausify,[status(thm)],[f_3043_4]) ).

cnf(f_3043_8,plain,
    ( hAPP(U_11476,sK265(U_11478,U_11477,U_11476,U_11475,U_11474,U_11473)) = hAPP(U_11476,sK266(U_11478,U_11477,U_11476,U_11475,U_11474,U_11473))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11478,U_11473),U_11477),hAPP(c_Set_Oimage(U_11474,U_11478,U_11476),U_11475)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11474,U_11473),hAPP(c_Fun_Ocomp(U_11478,U_11473,U_11474,U_11477),U_11476)),U_11475)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11474),U_11475))
    | ~ class_Groups_Ocomm__monoid__add(U_11473) ),
    inference(clausify,[status(thm)],[f_3043_4]) ).

cnf(f_3043_9,plain,
    ( hAPP(U_11477,hAPP(U_11476,sK265(U_11478,U_11477,U_11476,U_11475,U_11474,U_11473))) != c_Groups_Ozero__class_Ozero(U_11473)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11478,U_11473),U_11477),hAPP(c_Set_Oimage(U_11474,U_11478,U_11476),U_11475)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11474,U_11473),hAPP(c_Fun_Ocomp(U_11478,U_11473,U_11474,U_11477),U_11476)),U_11475)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11474),U_11475))
    | ~ class_Groups_Ocomm__monoid__add(U_11473) ),
    inference(clausify,[status(thm)],[f_3043_4]) ).

fof(f_3044_1,plain,
    ! [V_B_2,V_k_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_B_2)
      | ? [B_n] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)),V_A_2) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_n),V_k_2))),V_B_2) ),
    inference(fof_nnf,[status(thm)],[fact_UN__finite2__eq]) ).

fof(f_3044_2,plain,
    ! [U_11483,U_11482,U_11481,U_11480] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11480,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_11481) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11480,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_11483)
      | ? [U_11479] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11480,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11479)),U_11481) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11480,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11479),U_11482))),U_11483) ),
    inference(variable_rename,[status(thm)],[f_3044_1]) ).

fof(f_3044_3,plain,
    ! [U_11483,U_11482,U_11481,U_11480] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11480,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_11481) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11480,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_11483)
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11480,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK267(U_11483,U_11482,U_11481,U_11480))),U_11481) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11480,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK267(U_11483,U_11482,U_11481,U_11480)),U_11482))),U_11483) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK267]),skolemize(U_11479,sK267(U_11483,U_11482,U_11481,U_11480))],[f_3044_2]) ).

cnf(f_3044_4,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11480,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_11481) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11480,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_11483)
    | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11480,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK267(U_11483,U_11482,U_11481,U_11480))),U_11481) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11480,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK267(U_11483,U_11482,U_11481,U_11480)),U_11482))),U_11483) ),
    inference(clausify,[status(thm)],[f_3044_3]) ).

fof(f_3045_1,plain,
    ! [V_C_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2)),V_C_2))
      | ? [B_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)),V_A_2)),V_C_2)) ),
    inference(fof_nnf,[status(thm)],[fact_UN__finite__subset]) ).

fof(f_3045_2,plain,
    ! [U_11487,U_11486,U_11485] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11485,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11485,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_11486)),U_11487))
      | ? [U_11484] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11485,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11485,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11484)),U_11486)),U_11487)) ),
    inference(variable_rename,[status(thm)],[f_3045_1]) ).

fof(f_3045_3,plain,
    ! [U_11487,U_11486,U_11485] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11485,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11485,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_11486)),U_11487))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11485,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11485,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK268(U_11487,U_11486,U_11485))),U_11486)),U_11487)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK268]),skolemize(U_11484,sK268(U_11487,U_11486,U_11485))],[f_3045_2]) ).

cnf(f_3045_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11485,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11485,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_11486)),U_11487))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11485,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_11485,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK268(U_11487,U_11486,U_11485))),U_11486)),U_11487)) ),
    inference(clausify,[status(thm)],[f_3045_3]) ).

fof(f_3046_1,plain,
    ! [V_j_2,V_B_2,V_A_2,T_d,V_C_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_d),c_Set_Oimage(T_b,T_c,V_f_2)),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_d),V_j_2),V_A_2))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_B_2,B_x)),V_C_2))
          & hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2)) )
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2) ),
    inference(fof_nnf,[status(thm)],[fact_image__INT]) ).

fof(f_3046_2,plain,
    ! [U_11496,U_11495,U_11494,U_11493,U_11492,U_11491,U_11490,U_11489] :
      ( hAPP(c_Set_Oimage(U_11489,U_11490,U_11491),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11493,tc_fun(U_11489,tc_HOL_Obool)),U_11494),U_11495)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11493,tc_fun(U_11490,tc_HOL_Obool)),U_11494),hAPP(hAPP(c_COMBB(tc_fun(U_11489,tc_HOL_Obool),tc_fun(U_11490,tc_HOL_Obool),U_11493),c_Set_Oimage(U_11489,U_11490,U_11491)),U_11495))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11493),U_11496),U_11494))
      | ? [U_11488] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11489,tc_HOL_Obool)),hAPP(U_11495,U_11488)),U_11492))
          & hBOOL(hAPP(hAPP(c_member(U_11493),U_11488),U_11494)) )
      | ~ c_Fun_Oinj__on(U_11489,U_11490,U_11491,U_11492) ),
    inference(variable_rename,[status(thm)],[f_3046_1]) ).

fof(f_3046_3,plain,
    ! [U_11496,U_11495,U_11494,U_11493,U_11492,U_11491,U_11490,U_11489] :
      ( hAPP(c_Set_Oimage(U_11489,U_11490,U_11491),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11493,tc_fun(U_11489,tc_HOL_Obool)),U_11494),U_11495)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11493,tc_fun(U_11490,tc_HOL_Obool)),U_11494),hAPP(hAPP(c_COMBB(tc_fun(U_11489,tc_HOL_Obool),tc_fun(U_11490,tc_HOL_Obool),U_11493),c_Set_Oimage(U_11489,U_11490,U_11491)),U_11495))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11493),U_11496),U_11494))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11489,tc_HOL_Obool)),hAPP(U_11495,sK269(U_11496,U_11495,U_11494,U_11493,U_11492,U_11491,U_11490,U_11489))),U_11492))
        & hBOOL(hAPP(hAPP(c_member(U_11493),sK269(U_11496,U_11495,U_11494,U_11493,U_11492,U_11491,U_11490,U_11489)),U_11494)) )
      | ~ c_Fun_Oinj__on(U_11489,U_11490,U_11491,U_11492) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK269]),skolemize(U_11488,sK269(U_11496,U_11495,U_11494,U_11493,U_11492,U_11491,U_11490,U_11489))],[f_3046_2]) ).

cnf(f_3046_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11493),sK269(U_11496,U_11495,U_11494,U_11493,U_11492,U_11491,U_11490,U_11489)),U_11494))
    | hAPP(c_Set_Oimage(U_11489,U_11490,U_11491),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11493,tc_fun(U_11489,tc_HOL_Obool)),U_11494),U_11495)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11493,tc_fun(U_11490,tc_HOL_Obool)),U_11494),hAPP(hAPP(c_COMBB(tc_fun(U_11489,tc_HOL_Obool),tc_fun(U_11490,tc_HOL_Obool),U_11493),c_Set_Oimage(U_11489,U_11490,U_11491)),U_11495))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11493),U_11496),U_11494))
    | ~ c_Fun_Oinj__on(U_11489,U_11490,U_11491,U_11492) ),
    inference(clausify,[status(thm)],[f_3046_3]) ).

cnf(f_3046_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11489,tc_HOL_Obool)),hAPP(U_11495,sK269(U_11496,U_11495,U_11494,U_11493,U_11492,U_11491,U_11490,U_11489))),U_11492))
    | hAPP(c_Set_Oimage(U_11489,U_11490,U_11491),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11493,tc_fun(U_11489,tc_HOL_Obool)),U_11494),U_11495)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11493,tc_fun(U_11490,tc_HOL_Obool)),U_11494),hAPP(hAPP(c_COMBB(tc_fun(U_11489,tc_HOL_Obool),tc_fun(U_11490,tc_HOL_Obool),U_11493),c_Set_Oimage(U_11489,U_11490,U_11491)),U_11495))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11493),U_11496),U_11494))
    | ~ c_Fun_Oinj__on(U_11489,U_11490,U_11491,U_11492) ),
    inference(clausify,[status(thm)],[f_3046_3]) ).

fof(f_3047_1,plain,
    ! [V_s_2,V_r_2,V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_H_2),V_b_H_2))),c_Wellfounded_Olex__prod(T_b,T_c,V_r_2,V_s_2)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_b_2),V_b_H_2)),V_s_2))
            | V_a_2 != V_a_H_2 )
          & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_H_2)),V_r_2)) ) )
      & ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_b_2),V_b_H_2)),V_s_2))
          & V_a_2 = V_a_H_2 )
        | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_H_2)),V_r_2))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_H_2),V_b_H_2))),c_Wellfounded_Olex__prod(T_b,T_c,V_r_2,V_s_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_in__lex__prod]) ).

fof(f_3047_2,plain,
    ! [U_11504,U_11503,U_11502,U_11501,U_11500,U_11499,U_11498,U_11497] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_11497,U_11498),tc_prod(U_11497,U_11498))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_11497,U_11498),tc_prod(U_11497,U_11498)),hAPP(hAPP(c_Product__Type_OPair(U_11497,U_11498),U_11499),U_11500)),hAPP(hAPP(c_Product__Type_OPair(U_11497,U_11498),U_11501),U_11502))),c_Wellfounded_Olex__prod(U_11497,U_11498,U_11503,U_11504)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11498,U_11498)),hAPP(hAPP(c_Product__Type_OPair(U_11498,U_11498),U_11500),U_11502)),U_11504))
            | U_11499 != U_11501 )
          & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11497,U_11497)),hAPP(hAPP(c_Product__Type_OPair(U_11497,U_11497),U_11499),U_11501)),U_11503)) ) )
      & ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11498,U_11498)),hAPP(hAPP(c_Product__Type_OPair(U_11498,U_11498),U_11500),U_11502)),U_11504))
          & U_11499 = U_11501 )
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_11497,U_11497)),hAPP(hAPP(c_Product__Type_OPair(U_11497,U_11497),U_11499),U_11501)),U_11503))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_11497,U_11498),tc_prod(U_11497,U_11498))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_11497,U_11498),tc_prod(U_11497,U_11498)),hAPP(hAPP(c_Product__Type_OPair(U_11497,U_11498),U_11499),U_11500)),hAPP(hAPP(c_Product__Type_OPair(U_11497,U_11498),U_11501),U_11502))),c_Wellfounded_Olex__prod(U_11497,U_11498,U_11503,U_11504))) ) ),
    inference(variable_rename,[status(thm)],[f_3047_1]) ).

fof(f_3047_3,plain,
    ( ! [U_11520,U_11518,U_11516,U_11514,U_11512,U_11510,U_11508,U_11506] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_11506,U_11508),tc_prod(U_11506,U_11508))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_11506,U_11508),tc_prod(U_11506,U_11508)),hAPP(hAPP(c_Product__Type_OPair(U_11506,U_11508),U_11510),U_11512)),hAPP(hAPP(c_Product__Type_OPair(U_11506,U_11508),U_11514),U_11516))),c_Wellfounded_Olex__prod(U_11506,U_11508,U_11518,U_11520)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11508,U_11508)),hAPP(hAPP(c_Product__Type_OPair(U_11508,U_11508),U_11512),U_11516)),U_11520))
            | U_11510 != U_11514 )
          & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11506,U_11506)),hAPP(hAPP(c_Product__Type_OPair(U_11506,U_11506),U_11510),U_11514)),U_11518)) ) )
    & ! [U_11519,U_11517,U_11515,U_11513,U_11511,U_11509,U_11507,U_11505] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11507,U_11507)),hAPP(hAPP(c_Product__Type_OPair(U_11507,U_11507),U_11511),U_11515)),U_11519))
          & U_11509 = U_11513 )
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_11505,U_11505)),hAPP(hAPP(c_Product__Type_OPair(U_11505,U_11505),U_11509),U_11513)),U_11517))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_11505,U_11507),tc_prod(U_11505,U_11507))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_11505,U_11507),tc_prod(U_11505,U_11507)),hAPP(hAPP(c_Product__Type_OPair(U_11505,U_11507),U_11509),U_11511)),hAPP(hAPP(c_Product__Type_OPair(U_11505,U_11507),U_11513),U_11515))),c_Wellfounded_Olex__prod(U_11505,U_11507,U_11517,U_11519))) ) ),
    inference(miniscope,[status(thm)],[f_3047_2]) ).

cnf(f_3047_4,plain,
    ( U_11509 = U_11513
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_11505,U_11505)),hAPP(hAPP(c_Product__Type_OPair(U_11505,U_11505),U_11509),U_11513)),U_11517))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_11505,U_11507),tc_prod(U_11505,U_11507))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_11505,U_11507),tc_prod(U_11505,U_11507)),hAPP(hAPP(c_Product__Type_OPair(U_11505,U_11507),U_11509),U_11511)),hAPP(hAPP(c_Product__Type_OPair(U_11505,U_11507),U_11513),U_11515))),c_Wellfounded_Olex__prod(U_11505,U_11507,U_11517,U_11519))) ),
    inference(clausify,[status(thm)],[f_3047_3]) ).

cnf(f_3047_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11507,U_11507)),hAPP(hAPP(c_Product__Type_OPair(U_11507,U_11507),U_11511),U_11515)),U_11519))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_11505,U_11505)),hAPP(hAPP(c_Product__Type_OPair(U_11505,U_11505),U_11509),U_11513)),U_11517))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_11505,U_11507),tc_prod(U_11505,U_11507))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_11505,U_11507),tc_prod(U_11505,U_11507)),hAPP(hAPP(c_Product__Type_OPair(U_11505,U_11507),U_11509),U_11511)),hAPP(hAPP(c_Product__Type_OPair(U_11505,U_11507),U_11513),U_11515))),c_Wellfounded_Olex__prod(U_11505,U_11507,U_11517,U_11519))) ),
    inference(clausify,[status(thm)],[f_3047_3]) ).

cnf(f_3047_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11506,U_11506)),hAPP(hAPP(c_Product__Type_OPair(U_11506,U_11506),U_11510),U_11514)),U_11518))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_11506,U_11508),tc_prod(U_11506,U_11508))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_11506,U_11508),tc_prod(U_11506,U_11508)),hAPP(hAPP(c_Product__Type_OPair(U_11506,U_11508),U_11510),U_11512)),hAPP(hAPP(c_Product__Type_OPair(U_11506,U_11508),U_11514),U_11516))),c_Wellfounded_Olex__prod(U_11506,U_11508,U_11518,U_11520))) ),
    inference(clausify,[status(thm)],[f_3047_3]) ).

cnf(f_3047_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11508,U_11508)),hAPP(hAPP(c_Product__Type_OPair(U_11508,U_11508),U_11512),U_11516)),U_11520))
    | U_11510 != U_11514
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_11506,U_11508),tc_prod(U_11506,U_11508))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_11506,U_11508),tc_prod(U_11506,U_11508)),hAPP(hAPP(c_Product__Type_OPair(U_11506,U_11508),U_11510),U_11512)),hAPP(hAPP(c_Product__Type_OPair(U_11506,U_11508),U_11514),U_11516))),c_Wellfounded_Olex__prod(U_11506,U_11508,U_11518,U_11520))) ),
    inference(clausify,[status(thm)],[f_3047_3]) ).

fof(f_3048_1,plain,
    ! [T_b,V_R_2,V_y_2,V_y_H_2,T_c,V_x_2,V_P_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_H_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2))),c_Recdef_Osame__fst(T_b,T_c,V_P_2,V_R_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_y_H_2),V_y_2)),hAPP(V_R_2,V_x_2)))
      | ~ hBOOL(hAPP(V_P_2,V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_same__fstI]) ).

fof(f_3048_2,plain,
    ! [U_11527,U_11526,U_11525,U_11524,U_11523,U_11522,U_11521] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_11527,U_11523),tc_prod(U_11527,U_11523))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_11527,U_11523),tc_prod(U_11527,U_11523)),hAPP(hAPP(c_Product__Type_OPair(U_11527,U_11523),U_11522),U_11524)),hAPP(hAPP(c_Product__Type_OPair(U_11527,U_11523),U_11522),U_11525))),c_Recdef_Osame__fst(U_11527,U_11523,U_11521,U_11526)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11523,U_11523)),hAPP(hAPP(c_Product__Type_OPair(U_11523,U_11523),U_11524),U_11525)),hAPP(U_11526,U_11522)))
      | ~ hBOOL(hAPP(U_11521,U_11522)) ),
    inference(variable_rename,[status(thm)],[f_3048_1]) ).

cnf(f_3048_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_11527,U_11523),tc_prod(U_11527,U_11523))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_11527,U_11523),tc_prod(U_11527,U_11523)),hAPP(hAPP(c_Product__Type_OPair(U_11527,U_11523),U_11522),U_11524)),hAPP(hAPP(c_Product__Type_OPair(U_11527,U_11523),U_11522),U_11525))),c_Recdef_Osame__fst(U_11527,U_11523,U_11521,U_11526)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11523,U_11523)),hAPP(hAPP(c_Product__Type_OPair(U_11523,U_11523),U_11524),U_11525)),hAPP(U_11526,U_11522)))
    | ~ hBOOL(hAPP(U_11521,U_11522)) ),
    inference(clausify,[status(thm)],[f_3048_2]) ).

fof(f_3049_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),c_Wellfounded_Ofinite__psubset(T_b)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
      & ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),c_Wellfounded_Ofinite__psubset(T_b))) ) ),
    inference(fof_nnf,[status(thm)],[fact_in__finite__psubset]) ).

fof(f_3049_2,plain,
    ! [U_11530,U_11529,U_11528] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_11528,tc_HOL_Obool),tc_fun(U_11528,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_11528,tc_HOL_Obool),tc_fun(U_11528,tc_HOL_Obool)),U_11529),U_11530)),c_Wellfounded_Ofinite__psubset(U_11528)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11528),U_11530))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_11528,tc_HOL_Obool)),U_11529),U_11530)) )
      & ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_11528),U_11530))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_11528,tc_HOL_Obool)),U_11529),U_11530)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_11528,tc_HOL_Obool),tc_fun(U_11528,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_11528,tc_HOL_Obool),tc_fun(U_11528,tc_HOL_Obool)),U_11529),U_11530)),c_Wellfounded_Ofinite__psubset(U_11528))) ) ),
    inference(variable_rename,[status(thm)],[f_3049_1]) ).

fof(f_3049_3,plain,
    ( ! [U_11536,U_11534,U_11532] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_11532,tc_HOL_Obool),tc_fun(U_11532,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_11532,tc_HOL_Obool),tc_fun(U_11532,tc_HOL_Obool)),U_11534),U_11536)),c_Wellfounded_Ofinite__psubset(U_11532)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11532),U_11536))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_11532,tc_HOL_Obool)),U_11534),U_11536)) )
    & ! [U_11535,U_11533,U_11531] :
        ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_11531),U_11535))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_11531,tc_HOL_Obool)),U_11533),U_11535)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_11531,tc_HOL_Obool),tc_fun(U_11531,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_11531,tc_HOL_Obool),tc_fun(U_11531,tc_HOL_Obool)),U_11533),U_11535)),c_Wellfounded_Ofinite__psubset(U_11531))) ) ),
    inference(miniscope,[status(thm)],[f_3049_2]) ).

cnf(f_3049_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_11531,tc_HOL_Obool)),U_11533),U_11535))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_11531,tc_HOL_Obool),tc_fun(U_11531,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_11531,tc_HOL_Obool),tc_fun(U_11531,tc_HOL_Obool)),U_11533),U_11535)),c_Wellfounded_Ofinite__psubset(U_11531))) ),
    inference(clausify,[status(thm)],[f_3049_3]) ).

cnf(f_3049_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_11531),U_11535))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_11531,tc_HOL_Obool),tc_fun(U_11531,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_11531,tc_HOL_Obool),tc_fun(U_11531,tc_HOL_Obool)),U_11533),U_11535)),c_Wellfounded_Ofinite__psubset(U_11531))) ),
    inference(clausify,[status(thm)],[f_3049_3]) ).

cnf(f_3049_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_11532,tc_HOL_Obool),tc_fun(U_11532,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_11532,tc_HOL_Obool),tc_fun(U_11532,tc_HOL_Obool)),U_11534),U_11536)),c_Wellfounded_Ofinite__psubset(U_11532)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11532),U_11536))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_11532,tc_HOL_Obool)),U_11534),U_11536)) ),
    inference(clausify,[status(thm)],[f_3049_3]) ).

fof(f_3050_1,plain,
    ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
      ( hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__idem_Ounion__idem]) ).

fof(f_3050_2,plain,
    ! [U_11542,U_11541,U_11540,U_11539,U_11538,U_11537] :
      ( hAPP(U_11540,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11537,tc_HOL_Obool)),U_11541),U_11542)) = hAPP(c_Fun_Ocomp(U_11538,U_11538,U_11538,hAPP(U_11540,U_11541)),hAPP(U_11540,U_11542))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11537),U_11542))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11537),U_11541))
      | ~ c_Finite__Set_Ofolding__idem(U_11537,U_11538,U_11539,U_11540) ),
    inference(variable_rename,[status(thm)],[f_3050_1]) ).

cnf(f_3050_3,plain,
    ( hAPP(U_11540,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11537,tc_HOL_Obool)),U_11541),U_11542)) = hAPP(c_Fun_Ocomp(U_11538,U_11538,U_11538,hAPP(U_11540,U_11541)),hAPP(U_11540,U_11542))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11537),U_11542))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11537),U_11541))
    | ~ c_Finite__Set_Ofolding__idem(U_11537,U_11538,U_11539,U_11540) ),
    inference(clausify,[status(thm)],[f_3050_2]) ).

fof(f_3051_1,plain,
    ! [V_x_2,V_F_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_x_2)) = hAPP(V_f_2,V_x_2)
      | ~ c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__idem_Oidem__comp]) ).

fof(f_3051_2,plain,
    ! [U_11547,U_11546,U_11545,U_11544,U_11543] :
      ( hAPP(c_Fun_Ocomp(U_11544,U_11544,U_11544,hAPP(U_11545,U_11547)),hAPP(U_11545,U_11547)) = hAPP(U_11545,U_11547)
      | ~ c_Finite__Set_Ofolding__idem(U_11543,U_11544,U_11545,U_11546) ),
    inference(variable_rename,[status(thm)],[f_3051_1]) ).

fof(f_3051_3,plain,
    ! [U_11547,U_11546,U_11545,U_11544] :
      ( ! [U_11543] : ~ c_Finite__Set_Ofolding__idem(U_11543,U_11544,U_11545,U_11546)
      | hAPP(c_Fun_Ocomp(U_11544,U_11544,U_11544,hAPP(U_11545,U_11547)),hAPP(U_11545,U_11547)) = hAPP(U_11545,U_11547) ),
    inference(miniscope,[status(thm)],[f_3051_2]) ).

cnf(f_3051_4,plain,
    ( ~ c_Finite__Set_Ofolding__idem(U_11543,U_11544,U_11545,U_11546)
    | hAPP(c_Fun_Ocomp(U_11544,U_11544,U_11544,hAPP(U_11545,U_11547)),hAPP(U_11545,U_11547)) = hAPP(U_11545,U_11547) ),
    inference(clausify,[status(thm)],[f_3051_3]) ).

fof(f_3052_1,plain,
    ! [V_g_2,V_x_2,T_d,V_F_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),V_g_2)
      | ~ c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__idem_Oidem__left__comp]) ).

fof(f_3052_2,plain,
    ! [U_11554,U_11553,U_11552,U_11551,U_11550,U_11549,U_11548] :
      ( hAPP(c_Fun_Ocomp(U_11549,U_11549,U_11552,hAPP(U_11550,U_11553)),hAPP(c_Fun_Ocomp(U_11549,U_11549,U_11552,hAPP(U_11550,U_11553)),U_11554)) = hAPP(c_Fun_Ocomp(U_11549,U_11549,U_11552,hAPP(U_11550,U_11553)),U_11554)
      | ~ c_Finite__Set_Ofolding__idem(U_11548,U_11549,U_11550,U_11551) ),
    inference(variable_rename,[status(thm)],[f_3052_1]) ).

fof(f_3052_3,plain,
    ! [U_11554,U_11553,U_11552,U_11551,U_11550,U_11549] :
      ( ! [U_11548] : ~ c_Finite__Set_Ofolding__idem(U_11548,U_11549,U_11550,U_11551)
      | hAPP(c_Fun_Ocomp(U_11549,U_11549,U_11552,hAPP(U_11550,U_11553)),hAPP(c_Fun_Ocomp(U_11549,U_11549,U_11552,hAPP(U_11550,U_11553)),U_11554)) = hAPP(c_Fun_Ocomp(U_11549,U_11549,U_11552,hAPP(U_11550,U_11553)),U_11554) ),
    inference(miniscope,[status(thm)],[f_3052_2]) ).

cnf(f_3052_4,plain,
    ( ~ c_Finite__Set_Ofolding__idem(U_11548,U_11549,U_11550,U_11551)
    | hAPP(c_Fun_Ocomp(U_11549,U_11549,U_11552,hAPP(U_11550,U_11553)),hAPP(c_Fun_Ocomp(U_11549,U_11549,U_11552,hAPP(U_11550,U_11553)),U_11554)) = hAPP(c_Fun_Ocomp(U_11549,U_11549,U_11552,hAPP(U_11550,U_11553)),U_11554) ),
    inference(clausify,[status(thm)],[f_3052_3]) ).

fof(f_3053_1,plain,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) = hAPP(V_F_2,V_A_2)
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__idem_Oin__comp__idem]) ).

fof(f_3053_2,plain,
    ! [U_11560,U_11559,U_11558,U_11557,U_11556,U_11555] :
      ( hAPP(c_Fun_Ocomp(U_11556,U_11556,U_11556,hAPP(U_11558,U_11559)),hAPP(U_11557,U_11560)) = hAPP(U_11558,U_11559)
      | ~ hBOOL(hAPP(hAPP(c_member(U_11555),U_11560),U_11559))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11555),U_11559))
      | ~ c_Finite__Set_Ofolding__idem(U_11555,U_11556,U_11557,U_11558) ),
    inference(variable_rename,[status(thm)],[f_3053_1]) ).

cnf(f_3053_3,plain,
    ( hAPP(c_Fun_Ocomp(U_11556,U_11556,U_11556,hAPP(U_11558,U_11559)),hAPP(U_11557,U_11560)) = hAPP(U_11558,U_11559)
    | ~ hBOOL(hAPP(hAPP(c_member(U_11555),U_11560),U_11559))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11555),U_11559))
    | ~ c_Finite__Set_Ofolding__idem(U_11555,U_11556,U_11557,U_11558) ),
    inference(clausify,[status(thm)],[f_3053_2]) ).

fof(f_3054_1,plain,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
      ( hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__idem_Oinsert__idem]) ).

fof(f_3054_2,plain,
    ! [U_11566,U_11565,U_11564,U_11563,U_11562,U_11561] :
      ( hAPP(U_11564,hAPP(hAPP(c_Set_Oinsert(U_11561),U_11566),U_11565)) = hAPP(c_Fun_Ocomp(U_11562,U_11562,U_11562,hAPP(U_11564,U_11565)),hAPP(U_11563,U_11566))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11561),U_11565))
      | ~ c_Finite__Set_Ofolding__idem(U_11561,U_11562,U_11563,U_11564) ),
    inference(variable_rename,[status(thm)],[f_3054_1]) ).

cnf(f_3054_3,plain,
    ( hAPP(U_11564,hAPP(hAPP(c_Set_Oinsert(U_11561),U_11566),U_11565)) = hAPP(c_Fun_Ocomp(U_11562,U_11562,U_11562,hAPP(U_11564,U_11565)),hAPP(U_11563,U_11566))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11561),U_11565))
    | ~ c_Finite__Set_Ofolding__idem(U_11561,U_11562,U_11563,U_11564) ),
    inference(clausify,[status(thm)],[f_3054_2]) ).

fof(f_3055_1,plain,
    ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) = hAPP(V_F_2,V_A_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__idem_Osubset__comp__idem]) ).

fof(f_3055_2,plain,
    ! [U_11572,U_11571,U_11570,U_11569,U_11568,U_11567] :
      ( hAPP(c_Fun_Ocomp(U_11568,U_11568,U_11568,hAPP(U_11570,U_11571)),hAPP(U_11570,U_11572)) = hAPP(U_11570,U_11571)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11567,tc_HOL_Obool)),U_11572),U_11571))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11567),U_11571))
      | ~ c_Finite__Set_Ofolding__idem(U_11567,U_11568,U_11569,U_11570) ),
    inference(variable_rename,[status(thm)],[f_3055_1]) ).

cnf(f_3055_3,plain,
    ( hAPP(c_Fun_Ocomp(U_11568,U_11568,U_11568,hAPP(U_11570,U_11571)),hAPP(U_11570,U_11572)) = hAPP(U_11570,U_11571)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11567,tc_HOL_Obool)),U_11572),U_11571))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11567),U_11571))
    | ~ c_Finite__Set_Ofolding__idem(U_11567,U_11568,U_11569,U_11570) ),
    inference(clausify,[status(thm)],[f_3055_2]) ).

fof(f_3056_1,plain,
    ! [V_i_2,V_B_2,V_f_2,V_s_2,T_b,T_c] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_i_2)),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_s_2))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_s_2) != V_B_2
      | ? [B_i] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_i)))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_s_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
      | ~ class_Groups_Oordered__ab__group__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__nonneg__leq__bound]) ).

fof(f_3056_2,plain,
    ! [U_11579,U_11578,U_11577,U_11576,U_11575,U_11574] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11574),hAPP(U_11577,U_11579)),U_11578))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11575),U_11579),U_11576))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11575,U_11574),U_11577),U_11576) != U_11578
      | ? [U_11573] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11574),c_Groups_Ozero__class_Ozero(U_11574)),hAPP(U_11577,U_11573)))
          & hBOOL(hAPP(hAPP(c_member(U_11575),U_11573),U_11576)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11575),U_11576))
      | ~ class_Groups_Oordered__ab__group__add(U_11574) ),
    inference(variable_rename,[status(thm)],[f_3056_1]) ).

fof(f_3056_3,plain,
    ! [U_11579,U_11578,U_11577,U_11576,U_11575,U_11574] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11574),hAPP(U_11577,U_11579)),U_11578))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11575),U_11579),U_11576))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11575,U_11574),U_11577),U_11576) != U_11578
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11574),c_Groups_Ozero__class_Ozero(U_11574)),hAPP(U_11577,sK270(U_11579,U_11578,U_11577,U_11576,U_11575,U_11574))))
        & hBOOL(hAPP(hAPP(c_member(U_11575),sK270(U_11579,U_11578,U_11577,U_11576,U_11575,U_11574)),U_11576)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11575),U_11576))
      | ~ class_Groups_Oordered__ab__group__add(U_11574) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK270]),skolemize(U_11573,sK270(U_11579,U_11578,U_11577,U_11576,U_11575,U_11574))],[f_3056_2]) ).

cnf(f_3056_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11575),sK270(U_11579,U_11578,U_11577,U_11576,U_11575,U_11574)),U_11576))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11574),hAPP(U_11577,U_11579)),U_11578))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11575),U_11579),U_11576))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11575,U_11574),U_11577),U_11576) != U_11578
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11575),U_11576))
    | ~ class_Groups_Oordered__ab__group__add(U_11574) ),
    inference(clausify,[status(thm)],[f_3056_3]) ).

cnf(f_3056_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11574),c_Groups_Ozero__class_Ozero(U_11574)),hAPP(U_11577,sK270(U_11579,U_11578,U_11577,U_11576,U_11575,U_11574))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11574),hAPP(U_11577,U_11579)),U_11578))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11575),U_11579),U_11576))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11575,U_11574),U_11577),U_11576) != U_11578
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11575),U_11576))
    | ~ class_Groups_Oordered__ab__group__add(U_11574) ),
    inference(clausify,[status(thm)],[f_3056_3]) ).

fof(f_3057_1,plain,
    ! [V_i_2,V_f_2,V_s_2,T_b,T_c] :
      ( hAPP(V_f_2,V_i_2) = c_Groups_Ozero__class_Ozero(T_c)
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_s_2))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_s_2) != c_Groups_Ozero__class_Ozero(T_c)
      | ? [B_i] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_i)))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_s_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
      | ~ class_Groups_Oordered__ab__group__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__nonneg__0]) ).

fof(f_3057_2,plain,
    ! [U_11585,U_11584,U_11583,U_11582,U_11581] :
      ( hAPP(U_11584,U_11585) = c_Groups_Ozero__class_Ozero(U_11581)
      | ~ hBOOL(hAPP(hAPP(c_member(U_11582),U_11585),U_11583))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11582,U_11581),U_11584),U_11583) != c_Groups_Ozero__class_Ozero(U_11581)
      | ? [U_11580] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11581),c_Groups_Ozero__class_Ozero(U_11581)),hAPP(U_11584,U_11580)))
          & hBOOL(hAPP(hAPP(c_member(U_11582),U_11580),U_11583)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11582),U_11583))
      | ~ class_Groups_Oordered__ab__group__add(U_11581) ),
    inference(variable_rename,[status(thm)],[f_3057_1]) ).

fof(f_3057_3,plain,
    ! [U_11585,U_11584,U_11583,U_11582,U_11581] :
      ( hAPP(U_11584,U_11585) = c_Groups_Ozero__class_Ozero(U_11581)
      | ~ hBOOL(hAPP(hAPP(c_member(U_11582),U_11585),U_11583))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11582,U_11581),U_11584),U_11583) != c_Groups_Ozero__class_Ozero(U_11581)
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11581),c_Groups_Ozero__class_Ozero(U_11581)),hAPP(U_11584,sK271(U_11585,U_11584,U_11583,U_11582,U_11581))))
        & hBOOL(hAPP(hAPP(c_member(U_11582),sK271(U_11585,U_11584,U_11583,U_11582,U_11581)),U_11583)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11582),U_11583))
      | ~ class_Groups_Oordered__ab__group__add(U_11581) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK271]),skolemize(U_11580,sK271(U_11585,U_11584,U_11583,U_11582,U_11581))],[f_3057_2]) ).

cnf(f_3057_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11582),sK271(U_11585,U_11584,U_11583,U_11582,U_11581)),U_11583))
    | hAPP(U_11584,U_11585) = c_Groups_Ozero__class_Ozero(U_11581)
    | ~ hBOOL(hAPP(hAPP(c_member(U_11582),U_11585),U_11583))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11582,U_11581),U_11584),U_11583) != c_Groups_Ozero__class_Ozero(U_11581)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11582),U_11583))
    | ~ class_Groups_Oordered__ab__group__add(U_11581) ),
    inference(clausify,[status(thm)],[f_3057_3]) ).

cnf(f_3057_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11581),c_Groups_Ozero__class_Ozero(U_11581)),hAPP(U_11584,sK271(U_11585,U_11584,U_11583,U_11582,U_11581))))
    | hAPP(U_11584,U_11585) = c_Groups_Ozero__class_Ozero(U_11581)
    | ~ hBOOL(hAPP(hAPP(c_member(U_11582),U_11585),U_11583))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11582,U_11581),U_11584),U_11583) != c_Groups_Ozero__class_Ozero(U_11581)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11582),U_11583))
    | ~ class_Groups_Oordered__ab__group__add(U_11581) ),
    inference(clausify,[status(thm)],[f_3057_3]) ).

fof(f_3058_1,plain,
    ! [V_n_2,V_P_2,V_Q_2] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_P_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_Q_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_P_2)),V_Q_2)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))
      | ? [B_x] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_Q_2,B_x)),hAPP(V_P_2,B_x))) ),
    inference(fof_nnf,[status(thm)],[fact_sum__diff__distrib]) ).

fof(f_3058_2,plain,
    ! [U_11589,U_11588,U_11587] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_11588),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_11589))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_11587),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_11589))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),U_11588)),U_11587)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_11589))
      | ? [U_11586] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(U_11587,U_11586)),hAPP(U_11588,U_11586))) ),
    inference(variable_rename,[status(thm)],[f_3058_1]) ).

fof(f_3058_3,plain,
    ! [U_11589,U_11588,U_11587] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_11588),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_11589))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_11587),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_11589))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),U_11588)),U_11587)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_11589))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(U_11587,sK272(U_11589,U_11588,U_11587))),hAPP(U_11588,sK272(U_11589,U_11588,U_11587)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK272]),skolemize(U_11586,sK272(U_11589,U_11588,U_11587))],[f_3058_2]) ).

cnf(f_3058_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_11588),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_11589))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_11587),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_11589))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),U_11588)),U_11587)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_11589))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(U_11587,sK272(U_11589,U_11588,U_11587))),hAPP(U_11588,sK272(U_11589,U_11588,U_11587)))) ),
    inference(clausify,[status(thm)],[f_3058_3]) ).

fof(f_3059_1,plain,
    ! [V_x_2,V_g_2,T_e,V_f_2,T_b,T_c,T_d] : hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),hAPP(c_Product__Type_Oapfst(T_e,T_b,T_d,V_g_2),V_x_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_e,T_d),V_x_2))),hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_e,T_d),V_x_2))),
    inference(fof_nnf,[status(thm)],[fact_apsnd__apfst]) ).

fof(f_3059_2,plain,
    ! [U_11596,U_11595,U_11594,U_11593,U_11592,U_11591,U_11590] : hAPP(c_Product__Type_Oapsnd(U_11590,U_11591,U_11592,U_11593),hAPP(c_Product__Type_Oapfst(U_11594,U_11592,U_11590,U_11595),U_11596)) = hAPP(hAPP(c_Product__Type_OPair(U_11592,U_11591),hAPP(U_11595,hAPP(c_Product__Type_Ofst(U_11594,U_11590),U_11596))),hAPP(U_11593,hAPP(c_Product__Type_Osnd(U_11594,U_11590),U_11596))),
    inference(variable_rename,[status(thm)],[f_3059_1]) ).

cnf(f_3059_3,plain,
    hAPP(c_Product__Type_Oapsnd(U_11590,U_11591,U_11592,U_11593),hAPP(c_Product__Type_Oapfst(U_11594,U_11592,U_11590,U_11595),U_11596)) = hAPP(hAPP(c_Product__Type_OPair(U_11592,U_11591),hAPP(U_11595,hAPP(c_Product__Type_Ofst(U_11594,U_11590),U_11596))),hAPP(U_11593,hAPP(c_Product__Type_Osnd(U_11594,U_11590),U_11596))),
    inference(clausify,[status(thm)],[f_3059_2]) ).

fof(f_3060_1,plain,
    ! [V_x_2,V_g_2,T_e,V_f_2,T_c,T_b,T_d] : hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),hAPP(c_Product__Type_Oapsnd(T_e,T_c,T_d,V_g_2),V_x_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_d,T_e),V_x_2))),hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_d,T_e),V_x_2))),
    inference(fof_nnf,[status(thm)],[fact_apfst__apsnd]) ).

fof(f_3060_2,plain,
    ! [U_11603,U_11602,U_11601,U_11600,U_11599,U_11598,U_11597] : hAPP(c_Product__Type_Oapfst(U_11597,U_11598,U_11599,U_11600),hAPP(c_Product__Type_Oapsnd(U_11601,U_11599,U_11597,U_11602),U_11603)) = hAPP(hAPP(c_Product__Type_OPair(U_11598,U_11599),hAPP(U_11600,hAPP(c_Product__Type_Ofst(U_11597,U_11601),U_11603))),hAPP(U_11602,hAPP(c_Product__Type_Osnd(U_11597,U_11601),U_11603))),
    inference(variable_rename,[status(thm)],[f_3060_1]) ).

cnf(f_3060_3,plain,
    hAPP(c_Product__Type_Oapfst(U_11597,U_11598,U_11599,U_11600),hAPP(c_Product__Type_Oapsnd(U_11601,U_11599,U_11597,U_11602),U_11603)) = hAPP(hAPP(c_Product__Type_OPair(U_11598,U_11599),hAPP(U_11600,hAPP(c_Product__Type_Ofst(U_11597,U_11601),U_11603))),hAPP(U_11602,hAPP(c_Product__Type_Osnd(U_11597,U_11601),U_11603))),
    inference(clausify,[status(thm)],[f_3060_2]) ).

fof(f_3061_1,plain,
    ! [V_t_2,V_s_2,V_b_2,V_a_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_b_2),V_t_2))),c_FunDef_Opair__less))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s_2),V_t_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2)) ),
    inference(fof_nnf,[status(thm)],[fact_pair__lessI2]) ).

fof(f_3061_2,plain,
    ! [U_11607,U_11606,U_11605,U_11604] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11604),U_11606)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11605),U_11607))),c_FunDef_Opair__less))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11606),U_11607))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11604),U_11605)) ),
    inference(variable_rename,[status(thm)],[f_3061_1]) ).

cnf(f_3061_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11604),U_11606)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11605),U_11607))),c_FunDef_Opair__less))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11606),U_11607))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11604),U_11605)) ),
    inference(clausify,[status(thm)],[f_3061_2]) ).

fof(f_3062_1,plain,
    ! [V_g_2,V_x_2,V_f_2,T_c,T_b,T_d] :
      ( ( hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),V_x_2) = hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_g_2),V_x_2)
        | hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_d,T_c),V_x_2)) != hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_d,T_c),V_x_2)) )
      & ( hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_d,T_c),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_d,T_c),V_x_2))
        | hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),V_x_2) != hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_g_2),V_x_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_apfst__eq__conv]) ).

fof(f_3062_2,plain,
    ! [U_11613,U_11612,U_11611,U_11610,U_11609,U_11608] :
      ( ( hAPP(c_Product__Type_Oapfst(U_11608,U_11609,U_11610,U_11611),U_11612) = hAPP(c_Product__Type_Oapfst(U_11608,U_11609,U_11610,U_11613),U_11612)
        | hAPP(U_11611,hAPP(c_Product__Type_Ofst(U_11608,U_11610),U_11612)) != hAPP(U_11613,hAPP(c_Product__Type_Ofst(U_11608,U_11610),U_11612)) )
      & ( hAPP(U_11611,hAPP(c_Product__Type_Ofst(U_11608,U_11610),U_11612)) = hAPP(U_11613,hAPP(c_Product__Type_Ofst(U_11608,U_11610),U_11612))
        | hAPP(c_Product__Type_Oapfst(U_11608,U_11609,U_11610,U_11611),U_11612) != hAPP(c_Product__Type_Oapfst(U_11608,U_11609,U_11610,U_11613),U_11612) ) ),
    inference(variable_rename,[status(thm)],[f_3062_1]) ).

fof(f_3062_3,plain,
    ( ! [U_11625,U_11623,U_11621,U_11619,U_11617,U_11615] :
        ( hAPP(c_Product__Type_Oapfst(U_11615,U_11617,U_11619,U_11621),U_11623) = hAPP(c_Product__Type_Oapfst(U_11615,U_11617,U_11619,U_11625),U_11623)
        | hAPP(U_11621,hAPP(c_Product__Type_Ofst(U_11615,U_11619),U_11623)) != hAPP(U_11625,hAPP(c_Product__Type_Ofst(U_11615,U_11619),U_11623)) )
    & ! [U_11624,U_11622,U_11620,U_11618,U_11616,U_11614] :
        ( hAPP(U_11620,hAPP(c_Product__Type_Ofst(U_11614,U_11618),U_11622)) = hAPP(U_11624,hAPP(c_Product__Type_Ofst(U_11614,U_11618),U_11622))
        | hAPP(c_Product__Type_Oapfst(U_11614,U_11616,U_11618,U_11620),U_11622) != hAPP(c_Product__Type_Oapfst(U_11614,U_11616,U_11618,U_11624),U_11622) ) ),
    inference(miniscope,[status(thm)],[f_3062_2]) ).

cnf(f_3062_4,plain,
    ( hAPP(U_11620,hAPP(c_Product__Type_Ofst(U_11614,U_11618),U_11622)) = hAPP(U_11624,hAPP(c_Product__Type_Ofst(U_11614,U_11618),U_11622))
    | hAPP(c_Product__Type_Oapfst(U_11614,U_11616,U_11618,U_11620),U_11622) != hAPP(c_Product__Type_Oapfst(U_11614,U_11616,U_11618,U_11624),U_11622) ),
    inference(clausify,[status(thm)],[f_3062_3]) ).

cnf(f_3062_5,plain,
    ( hAPP(c_Product__Type_Oapfst(U_11615,U_11617,U_11619,U_11621),U_11623) = hAPP(c_Product__Type_Oapfst(U_11615,U_11617,U_11619,U_11625),U_11623)
    | hAPP(U_11621,hAPP(c_Product__Type_Ofst(U_11615,U_11619),U_11623)) != hAPP(U_11625,hAPP(c_Product__Type_Ofst(U_11615,U_11619),U_11623)) ),
    inference(clausify,[status(thm)],[f_3062_3]) ).

fof(f_3063_1,plain,
    ! [V_x_2,V_f_2,T_d,T_c,T_b] : hAPP(c_Product__Type_Ofst(T_b,T_c),hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_d,T_c),V_x_2)),
    inference(fof_nnf,[status(thm)],[fact_fst__apfst]) ).

fof(f_3063_2,plain,
    ! [U_11630,U_11629,U_11628,U_11627,U_11626] : hAPP(c_Product__Type_Ofst(U_11626,U_11627),hAPP(c_Product__Type_Oapfst(U_11628,U_11626,U_11627,U_11629),U_11630)) = hAPP(U_11629,hAPP(c_Product__Type_Ofst(U_11628,U_11627),U_11630)),
    inference(variable_rename,[status(thm)],[f_3063_1]) ).

cnf(f_3063_3,plain,
    hAPP(c_Product__Type_Ofst(U_11626,U_11627),hAPP(c_Product__Type_Oapfst(U_11628,U_11626,U_11627,U_11629),U_11630)) = hAPP(U_11629,hAPP(c_Product__Type_Ofst(U_11628,U_11627),U_11630)),
    inference(clausify,[status(thm)],[f_3063_2]) ).

fof(f_3064_1,plain,
    ! [V_x_2,V_g_2,T_e,V_f_2,T_c,T_b,T_d] : hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),hAPP(c_Product__Type_Oapfst(T_e,T_d,T_c,V_g_2),V_x_2)) = hAPP(c_Product__Type_Oapfst(T_e,T_b,T_c,hAPP(c_Fun_Ocomp(T_d,T_b,T_e,V_f_2),V_g_2)),V_x_2),
    inference(fof_nnf,[status(thm)],[fact_apfst__compose]) ).

fof(f_3064_2,plain,
    ! [U_11637,U_11636,U_11635,U_11634,U_11633,U_11632,U_11631] : hAPP(c_Product__Type_Oapfst(U_11631,U_11632,U_11633,U_11634),hAPP(c_Product__Type_Oapfst(U_11635,U_11631,U_11633,U_11636),U_11637)) = hAPP(c_Product__Type_Oapfst(U_11635,U_11632,U_11633,hAPP(c_Fun_Ocomp(U_11631,U_11632,U_11635,U_11634),U_11636)),U_11637),
    inference(variable_rename,[status(thm)],[f_3064_1]) ).

cnf(f_3064_3,plain,
    hAPP(c_Product__Type_Oapfst(U_11631,U_11632,U_11633,U_11634),hAPP(c_Product__Type_Oapfst(U_11635,U_11631,U_11633,U_11636),U_11637)) = hAPP(c_Product__Type_Oapfst(U_11635,U_11632,U_11633,hAPP(c_Fun_Ocomp(U_11631,U_11632,U_11635,U_11634),U_11636)),U_11637),
    inference(clausify,[status(thm)],[f_3064_2]) ).

fof(f_3065_1,plain,
    ! [V_y_2,V_x_2,V_f_2,T_c,T_b,T_d] : hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_d,T_c),V_x_2),V_y_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,V_x_2)),V_y_2),
    inference(fof_nnf,[status(thm)],[fact_apfst__conv]) ).

fof(f_3065_2,plain,
    ! [U_11643,U_11642,U_11641,U_11640,U_11639,U_11638] : hAPP(c_Product__Type_Oapfst(U_11638,U_11639,U_11640,U_11641),hAPP(hAPP(c_Product__Type_OPair(U_11638,U_11640),U_11642),U_11643)) = hAPP(hAPP(c_Product__Type_OPair(U_11639,U_11640),hAPP(U_11641,U_11642)),U_11643),
    inference(variable_rename,[status(thm)],[f_3065_1]) ).

cnf(f_3065_3,plain,
    hAPP(c_Product__Type_Oapfst(U_11638,U_11639,U_11640,U_11641),hAPP(hAPP(c_Product__Type_OPair(U_11638,U_11640),U_11642),U_11643)) = hAPP(hAPP(c_Product__Type_OPair(U_11639,U_11640),hAPP(U_11641,U_11642)),U_11643),
    inference(clausify,[status(thm)],[f_3065_2]) ).

fof(f_3066_1,plain,
    ! [V_x_2,V_f_2,T_d,T_b,T_c] : hAPP(c_Product__Type_Osnd(T_c,T_b),hAPP(c_Product__Type_Oapfst(T_d,T_c,T_b,V_f_2),V_x_2)) = hAPP(c_Product__Type_Osnd(T_d,T_b),V_x_2),
    inference(fof_nnf,[status(thm)],[fact_snd__apfst]) ).

fof(f_3066_2,plain,
    ! [U_11648,U_11647,U_11646,U_11645,U_11644] : hAPP(c_Product__Type_Osnd(U_11644,U_11645),hAPP(c_Product__Type_Oapfst(U_11646,U_11644,U_11645,U_11647),U_11648)) = hAPP(c_Product__Type_Osnd(U_11646,U_11645),U_11648),
    inference(variable_rename,[status(thm)],[f_3066_1]) ).

cnf(f_3066_3,plain,
    hAPP(c_Product__Type_Osnd(U_11644,U_11645),hAPP(c_Product__Type_Oapfst(U_11646,U_11644,U_11645,U_11647),U_11648)) = hAPP(c_Product__Type_Osnd(U_11646,U_11645),U_11648),
    inference(clausify,[status(thm)],[f_3066_2]) ).

fof(f_3067_1,plain,
    ! [V_p_2,V_g_2,T_e,V_f_2,T_b,T_c,T_d] : hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),hAPP(c_Product__Type_Oapfst(T_e,T_b,T_d,V_g_2),V_p_2)) = hAPP(c_Product__Type_Oapfst(T_e,T_b,T_c,V_g_2),hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_e,V_f_2),V_p_2)),
    inference(fof_nnf,[status(thm)],[fact_apsnd__apfst__commute]) ).

fof(f_3067_2,plain,
    ! [U_11655,U_11654,U_11653,U_11652,U_11651,U_11650,U_11649] : hAPP(c_Product__Type_Oapsnd(U_11649,U_11650,U_11651,U_11652),hAPP(c_Product__Type_Oapfst(U_11653,U_11651,U_11649,U_11654),U_11655)) = hAPP(c_Product__Type_Oapfst(U_11653,U_11651,U_11650,U_11654),hAPP(c_Product__Type_Oapsnd(U_11649,U_11650,U_11653,U_11652),U_11655)),
    inference(variable_rename,[status(thm)],[f_3067_1]) ).

cnf(f_3067_3,plain,
    hAPP(c_Product__Type_Oapsnd(U_11649,U_11650,U_11651,U_11652),hAPP(c_Product__Type_Oapfst(U_11653,U_11651,U_11649,U_11654),U_11655)) = hAPP(c_Product__Type_Oapfst(U_11653,U_11651,U_11650,U_11654),hAPP(c_Product__Type_Oapsnd(U_11649,U_11650,U_11653,U_11652),U_11655)),
    inference(clausify,[status(thm)],[f_3067_2]) ).

fof(f_3068_1,plain,
    ! [V_t_2,V_s_2,V_b_2,V_a_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_b_2),V_t_2))),c_FunDef_Opair__less))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) ),
    inference(fof_nnf,[status(thm)],[fact_pair__lessI1]) ).

fof(f_3068_2,plain,
    ! [U_11659,U_11658,U_11657,U_11656] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11656),U_11658)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11657),U_11659))),c_FunDef_Opair__less))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11656),U_11657)) ),
    inference(variable_rename,[status(thm)],[f_3068_1]) ).

cnf(f_3068_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11656),U_11658)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11657),U_11659))),c_FunDef_Opair__less))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11656),U_11657)) ),
    inference(clausify,[status(thm)],[f_3068_2]) ).

fof(f_3069_1,plain,
    ! [V_t_2,V_s_2,V_b_2,V_a_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_b_2),V_t_2))),c_FunDef_Opair__leq))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_s_2),V_t_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2)) ),
    inference(fof_nnf,[status(thm)],[fact_pair__leqI2]) ).

fof(f_3069_2,plain,
    ! [U_11663,U_11662,U_11661,U_11660] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11660),U_11662)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11661),U_11663))),c_FunDef_Opair__leq))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11662),U_11663))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11660),U_11661)) ),
    inference(variable_rename,[status(thm)],[f_3069_1]) ).

cnf(f_3069_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11660),U_11662)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11661),U_11663))),c_FunDef_Opair__leq))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11662),U_11663))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11660),U_11661)) ),
    inference(clausify,[status(thm)],[f_3069_2]) ).

fof(f_3070_1,plain,
    ! [V_YS_2,V_y_2,V_XS_2,V_x_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2))),c_FunDef_Omin__strict))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),V_YS_2)),c_FunDef_Omin__strict))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_FunDef_Opair__less))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2)) ),
    inference(fof_nnf,[status(thm)],[fact_smin__insertI]) ).

fof(f_3070_2,plain,
    ! [U_11667,U_11666,U_11665,U_11664] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_11665),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11666),U_11667))),c_FunDef_Omin__strict))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_11665),U_11667)),c_FunDef_Omin__strict))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11664),U_11666)),c_FunDef_Opair__less))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11664),U_11665)) ),
    inference(variable_rename,[status(thm)],[f_3070_1]) ).

cnf(f_3070_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_11665),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11666),U_11667))),c_FunDef_Omin__strict))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_11665),U_11667)),c_FunDef_Omin__strict))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11664),U_11666)),c_FunDef_Opair__less))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11664),U_11665)) ),
    inference(clausify,[status(thm)],[f_3070_2]) ).

fof(f_3071_1,plain,
    ! [V_X_2,V_x_2,V_Y_2,V_y_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_X_2)),V_Y_2)),c_FunDef_Omax__strict))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_X_2),V_Y_2)),c_FunDef_Omax__strict))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_FunDef_Opair__less))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_smax__insertI]) ).

fof(f_3071_2,plain,
    ! [U_11671,U_11670,U_11669,U_11668] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11670),U_11671)),U_11669)),c_FunDef_Omax__strict))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_11671),U_11669)),c_FunDef_Omax__strict))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11670),U_11668)),c_FunDef_Opair__less))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11668),U_11669)) ),
    inference(variable_rename,[status(thm)],[f_3071_1]) ).

cnf(f_3071_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11670),U_11671)),U_11669)),c_FunDef_Omax__strict))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_11671),U_11669)),c_FunDef_Omax__strict))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11670),U_11668)),c_FunDef_Opair__less))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11668),U_11669)) ),
    inference(clausify,[status(thm)],[f_3071_2]) ).

fof(f_3072_1,plain,
    ! [V_X_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_X_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__strict))
      | V_X_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)) ),
    inference(fof_nnf,[status(thm)],[fact_smin__emptyI]) ).

fof(f_3072_2,plain,
    ! [U_11672] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_11672),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__strict))
      | U_11672 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_3072_1]) ).

cnf(f_3072_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_11672),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__strict))
    | U_11672 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3072_2]) ).

fof(f_3073_1,plain,
    ! [V_Y_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),V_Y_2)),c_FunDef_Omax__strict))
      | V_Y_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_Y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_smax__emptyI]) ).

fof(f_3073_2,plain,
    ! [U_11673] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),U_11673)),c_FunDef_Omax__strict))
      | U_11673 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11673)) ),
    inference(variable_rename,[status(thm)],[f_3073_1]) ).

cnf(f_3073_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),U_11673)),c_FunDef_Omax__strict))
    | U_11673 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11673)) ),
    inference(clausify,[status(thm)],[f_3073_2]) ).

fof(f_3074_1,plain,
    ! [V_t_2,V_s_2,V_b_2,V_a_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_b_2),V_t_2))),c_FunDef_Opair__leq))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) ),
    inference(fof_nnf,[status(thm)],[fact_pair__leqI1]) ).

fof(f_3074_2,plain,
    ! [U_11677,U_11676,U_11675,U_11674] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11674),U_11676)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11675),U_11677))),c_FunDef_Opair__leq))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11674),U_11675)) ),
    inference(variable_rename,[status(thm)],[f_3074_1]) ).

cnf(f_3074_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11674),U_11676)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11675),U_11677))),c_FunDef_Opair__leq))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11674),U_11675)) ),
    inference(clausify,[status(thm)],[f_3074_2]) ).

fof(f_3075_1,plain,
    ! [V_XS_2,V_x_2,V_YS_2,V_y_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2)),V_YS_2)),c_FunDef_Omax__weak))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),V_YS_2)),c_FunDef_Omax__weak))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_FunDef_Opair__leq))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2)) ),
    inference(fof_nnf,[status(thm)],[fact_wmax__insertI]) ).

fof(f_3075_2,plain,
    ! [U_11681,U_11680,U_11679,U_11678] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11680),U_11681)),U_11679)),c_FunDef_Omax__weak))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_11681),U_11679)),c_FunDef_Omax__weak))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11680),U_11678)),c_FunDef_Opair__leq))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11678),U_11679)) ),
    inference(variable_rename,[status(thm)],[f_3075_1]) ).

cnf(f_3075_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11680),U_11681)),U_11679)),c_FunDef_Omax__weak))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_11681),U_11679)),c_FunDef_Omax__weak))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11680),U_11678)),c_FunDef_Opair__leq))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11678),U_11679)) ),
    inference(clausify,[status(thm)],[f_3075_2]) ).

fof(f_3076_1,plain,
    ! [V_YS_2,V_y_2,V_XS_2,V_x_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2))),c_FunDef_Omin__weak))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),V_YS_2)),c_FunDef_Omin__weak))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_FunDef_Opair__leq))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2)) ),
    inference(fof_nnf,[status(thm)],[fact_wmin__insertI]) ).

fof(f_3076_2,plain,
    ! [U_11685,U_11684,U_11683,U_11682] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_11683),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11684),U_11685))),c_FunDef_Omin__weak))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_11683),U_11685)),c_FunDef_Omin__weak))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11682),U_11684)),c_FunDef_Opair__leq))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11682),U_11683)) ),
    inference(variable_rename,[status(thm)],[f_3076_1]) ).

cnf(f_3076_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_11683),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11684),U_11685))),c_FunDef_Omin__weak))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_11683),U_11685)),c_FunDef_Omin__weak))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11682),U_11684)),c_FunDef_Opair__leq))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11682),U_11683)) ),
    inference(clausify,[status(thm)],[f_3076_2]) ).

fof(f_3077_1,plain,
    ! [V_X_2] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_X_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__weak)),
    inference(fof_nnf,[status(thm)],[fact_wmin__emptyI]) ).

fof(f_3077_2,plain,
    ! [U_11686] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_11686),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__weak)),
    inference(variable_rename,[status(thm)],[f_3077_1]) ).

cnf(f_3077_3,plain,
    hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_11686),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__weak)),
    inference(clausify,[status(thm)],[f_3077_2]) ).

fof(f_3078_1,plain,
    ! [V_X_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),V_X_2)),c_FunDef_Omax__weak))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_X_2)) ),
    inference(fof_nnf,[status(thm)],[fact_wmax__emptyI]) ).

fof(f_3078_2,plain,
    ! [U_11687] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),U_11687)),c_FunDef_Omax__weak))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11687)) ),
    inference(variable_rename,[status(thm)],[f_3078_1]) ).

cnf(f_3078_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),U_11687)),c_FunDef_Omax__weak))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11687)) ),
    inference(clausify,[status(thm)],[f_3078_2]) ).

fof(f_3079_1,plain,
    c_FunDef_Omin__weak = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_min__weak__def]) ).

cnf(f_3079_2,plain,
    c_FunDef_Omin__weak = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_3079_1]) ).

fof(f_3080_1,plain,
    c_FunDef_Omax__weak = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_max__weak__def]) ).

cnf(f_3080_2,plain,
    c_FunDef_Omax__weak = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_3080_1]) ).

fof(f_3081_1,plain,
    c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_FunDef_Omin__strict),c_FunDef_Omin__weak)),
    inference(fof_nnf,[status(thm)],[fact_min__rpair__set]) ).

cnf(f_3081_2,plain,
    c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_FunDef_Omin__strict),c_FunDef_Omin__weak)),
    inference(clausify,[status(thm)],[f_3081_1]) ).

fof(f_3082_1,plain,
    c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
    inference(fof_nnf,[status(thm)],[fact_max__strict__def]) ).

cnf(f_3082_2,plain,
    c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
    inference(clausify,[status(thm)],[f_3082_1]) ).

fof(f_3083_1,plain,
    ! [V_D_2,V_C_2,V_R_2,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2))),c_Wellfounded_Omax__ext(T_b,V_R_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2)),c_Wellfounded_Omax__ext(T_b,V_R_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),c_Wellfounded_Omax__ext(T_b,V_R_2))) ),
    inference(fof_nnf,[status(thm)],[fact_max__ext__additive]) ).

fof(f_3083_2,plain,
    ! [U_11693,U_11692,U_11691,U_11690,U_11689,U_11688] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_11688,tc_HOL_Obool),tc_fun(U_11688,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_11688,tc_HOL_Obool),tc_fun(U_11688,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11688,tc_HOL_Obool)),U_11689),U_11692)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11688,tc_HOL_Obool)),U_11690),U_11693))),c_Wellfounded_Omax__ext(U_11688,U_11691)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_11688,tc_HOL_Obool),tc_fun(U_11688,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_11688,tc_HOL_Obool),tc_fun(U_11688,tc_HOL_Obool)),U_11692),U_11693)),c_Wellfounded_Omax__ext(U_11688,U_11691)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_11688,tc_HOL_Obool),tc_fun(U_11688,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_11688,tc_HOL_Obool),tc_fun(U_11688,tc_HOL_Obool)),U_11689),U_11690)),c_Wellfounded_Omax__ext(U_11688,U_11691))) ),
    inference(variable_rename,[status(thm)],[f_3083_1]) ).

cnf(f_3083_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_11688,tc_HOL_Obool),tc_fun(U_11688,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_11688,tc_HOL_Obool),tc_fun(U_11688,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11688,tc_HOL_Obool)),U_11689),U_11692)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11688,tc_HOL_Obool)),U_11690),U_11693))),c_Wellfounded_Omax__ext(U_11688,U_11691)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_11688,tc_HOL_Obool),tc_fun(U_11688,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_11688,tc_HOL_Obool),tc_fun(U_11688,tc_HOL_Obool)),U_11692),U_11693)),c_Wellfounded_Omax__ext(U_11688,U_11691)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_11688,tc_HOL_Obool),tc_fun(U_11688,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_11688,tc_HOL_Obool),tc_fun(U_11688,tc_HOL_Obool)),U_11689),U_11690)),c_Wellfounded_Omax__ext(U_11688,U_11691))) ),
    inference(clausify,[status(thm)],[f_3083_2]) ).

fof(f_3084_1,plain,
    c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
    inference(fof_nnf,[status(thm)],[fact_min__strict__def]) ).

cnf(f_3084_2,plain,
    c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
    inference(clausify,[status(thm)],[f_3084_1]) ).

fof(f_3085_1,plain,
    c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_FunDef_Omax__strict),c_FunDef_Omax__weak)),
    inference(fof_nnf,[status(thm)],[fact_max__rpair__set]) ).

cnf(f_3085_2,plain,
    c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_FunDef_Omax__strict),c_FunDef_Omax__weak)),
    inference(clausify,[status(thm)],[f_3085_1]) ).

fof(f_3086_1,plain,
    ! [V_xa_2,V_x_2,V_R_2,T_b] :
      ( ( c_Wellfounded_Omax__extp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_R_2),V_x_2,V_xa_2)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_xa_2)),c_Wellfounded_Omax__ext(T_b,V_R_2))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_xa_2)),c_Wellfounded_Omax__ext(T_b,V_R_2)))
        | ~ c_Wellfounded_Omax__extp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_R_2),V_x_2,V_xa_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_max__extp__max__ext__eq]) ).

fof(f_3086_2,plain,
    ! [U_11697,U_11696,U_11695,U_11694] :
      ( ( c_Wellfounded_Omax__extp(U_11694,hAPP(hAPP(c_COMBC(U_11694,tc_fun(tc_prod(U_11694,U_11694),tc_HOL_Obool),tc_fun(U_11694,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11694,tc_fun(tc_fun(tc_prod(U_11694,U_11694),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11694,U_11694),tc_HOL_Obool),tc_fun(U_11694,tc_HOL_Obool)),U_11694),c_COMBC(U_11694,tc_fun(tc_prod(U_11694,U_11694),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11694,tc_prod(U_11694,U_11694)),tc_fun(U_11694,tc_fun(tc_fun(tc_prod(U_11694,U_11694),tc_HOL_Obool),tc_HOL_Obool)),U_11694),hAPP(c_COMBB(tc_prod(U_11694,U_11694),tc_fun(tc_fun(tc_prod(U_11694,U_11694),tc_HOL_Obool),tc_HOL_Obool),U_11694),c_member(tc_prod(U_11694,U_11694)))),c_Product__Type_OPair(U_11694,U_11694)))),U_11695),U_11696,U_11697)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_11694,tc_HOL_Obool),tc_fun(U_11694,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_11694,tc_HOL_Obool),tc_fun(U_11694,tc_HOL_Obool)),U_11696),U_11697)),c_Wellfounded_Omax__ext(U_11694,U_11695))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_11694,tc_HOL_Obool),tc_fun(U_11694,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_11694,tc_HOL_Obool),tc_fun(U_11694,tc_HOL_Obool)),U_11696),U_11697)),c_Wellfounded_Omax__ext(U_11694,U_11695)))
        | ~ c_Wellfounded_Omax__extp(U_11694,hAPP(hAPP(c_COMBC(U_11694,tc_fun(tc_prod(U_11694,U_11694),tc_HOL_Obool),tc_fun(U_11694,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11694,tc_fun(tc_fun(tc_prod(U_11694,U_11694),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11694,U_11694),tc_HOL_Obool),tc_fun(U_11694,tc_HOL_Obool)),U_11694),c_COMBC(U_11694,tc_fun(tc_prod(U_11694,U_11694),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11694,tc_prod(U_11694,U_11694)),tc_fun(U_11694,tc_fun(tc_fun(tc_prod(U_11694,U_11694),tc_HOL_Obool),tc_HOL_Obool)),U_11694),hAPP(c_COMBB(tc_prod(U_11694,U_11694),tc_fun(tc_fun(tc_prod(U_11694,U_11694),tc_HOL_Obool),tc_HOL_Obool),U_11694),c_member(tc_prod(U_11694,U_11694)))),c_Product__Type_OPair(U_11694,U_11694)))),U_11695),U_11696,U_11697) ) ),
    inference(variable_rename,[status(thm)],[f_3086_1]) ).

fof(f_3086_3,plain,
    ( ! [U_11705,U_11703,U_11701,U_11699] :
        ( c_Wellfounded_Omax__extp(U_11699,hAPP(hAPP(c_COMBC(U_11699,tc_fun(tc_prod(U_11699,U_11699),tc_HOL_Obool),tc_fun(U_11699,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11699,tc_fun(tc_fun(tc_prod(U_11699,U_11699),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11699,U_11699),tc_HOL_Obool),tc_fun(U_11699,tc_HOL_Obool)),U_11699),c_COMBC(U_11699,tc_fun(tc_prod(U_11699,U_11699),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11699,tc_prod(U_11699,U_11699)),tc_fun(U_11699,tc_fun(tc_fun(tc_prod(U_11699,U_11699),tc_HOL_Obool),tc_HOL_Obool)),U_11699),hAPP(c_COMBB(tc_prod(U_11699,U_11699),tc_fun(tc_fun(tc_prod(U_11699,U_11699),tc_HOL_Obool),tc_HOL_Obool),U_11699),c_member(tc_prod(U_11699,U_11699)))),c_Product__Type_OPair(U_11699,U_11699)))),U_11701),U_11703,U_11705)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_11699,tc_HOL_Obool),tc_fun(U_11699,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_11699,tc_HOL_Obool),tc_fun(U_11699,tc_HOL_Obool)),U_11703),U_11705)),c_Wellfounded_Omax__ext(U_11699,U_11701))) )
    & ! [U_11704,U_11702,U_11700,U_11698] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_11698,tc_HOL_Obool),tc_fun(U_11698,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_11698,tc_HOL_Obool),tc_fun(U_11698,tc_HOL_Obool)),U_11702),U_11704)),c_Wellfounded_Omax__ext(U_11698,U_11700)))
        | ~ c_Wellfounded_Omax__extp(U_11698,hAPP(hAPP(c_COMBC(U_11698,tc_fun(tc_prod(U_11698,U_11698),tc_HOL_Obool),tc_fun(U_11698,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11698,tc_fun(tc_fun(tc_prod(U_11698,U_11698),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11698,U_11698),tc_HOL_Obool),tc_fun(U_11698,tc_HOL_Obool)),U_11698),c_COMBC(U_11698,tc_fun(tc_prod(U_11698,U_11698),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11698,tc_prod(U_11698,U_11698)),tc_fun(U_11698,tc_fun(tc_fun(tc_prod(U_11698,U_11698),tc_HOL_Obool),tc_HOL_Obool)),U_11698),hAPP(c_COMBB(tc_prod(U_11698,U_11698),tc_fun(tc_fun(tc_prod(U_11698,U_11698),tc_HOL_Obool),tc_HOL_Obool),U_11698),c_member(tc_prod(U_11698,U_11698)))),c_Product__Type_OPair(U_11698,U_11698)))),U_11700),U_11702,U_11704) ) ),
    inference(miniscope,[status(thm)],[f_3086_2]) ).

cnf(f_3086_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_11698,tc_HOL_Obool),tc_fun(U_11698,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_11698,tc_HOL_Obool),tc_fun(U_11698,tc_HOL_Obool)),U_11702),U_11704)),c_Wellfounded_Omax__ext(U_11698,U_11700)))
    | ~ c_Wellfounded_Omax__extp(U_11698,hAPP(hAPP(c_COMBC(U_11698,tc_fun(tc_prod(U_11698,U_11698),tc_HOL_Obool),tc_fun(U_11698,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11698,tc_fun(tc_fun(tc_prod(U_11698,U_11698),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11698,U_11698),tc_HOL_Obool),tc_fun(U_11698,tc_HOL_Obool)),U_11698),c_COMBC(U_11698,tc_fun(tc_prod(U_11698,U_11698),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11698,tc_prod(U_11698,U_11698)),tc_fun(U_11698,tc_fun(tc_fun(tc_prod(U_11698,U_11698),tc_HOL_Obool),tc_HOL_Obool)),U_11698),hAPP(c_COMBB(tc_prod(U_11698,U_11698),tc_fun(tc_fun(tc_prod(U_11698,U_11698),tc_HOL_Obool),tc_HOL_Obool),U_11698),c_member(tc_prod(U_11698,U_11698)))),c_Product__Type_OPair(U_11698,U_11698)))),U_11700),U_11702,U_11704) ),
    inference(clausify,[status(thm)],[f_3086_3]) ).

cnf(f_3086_5,plain,
    ( c_Wellfounded_Omax__extp(U_11699,hAPP(hAPP(c_COMBC(U_11699,tc_fun(tc_prod(U_11699,U_11699),tc_HOL_Obool),tc_fun(U_11699,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11699,tc_fun(tc_fun(tc_prod(U_11699,U_11699),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11699,U_11699),tc_HOL_Obool),tc_fun(U_11699,tc_HOL_Obool)),U_11699),c_COMBC(U_11699,tc_fun(tc_prod(U_11699,U_11699),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11699,tc_prod(U_11699,U_11699)),tc_fun(U_11699,tc_fun(tc_fun(tc_prod(U_11699,U_11699),tc_HOL_Obool),tc_HOL_Obool)),U_11699),hAPP(c_COMBB(tc_prod(U_11699,U_11699),tc_fun(tc_fun(tc_prod(U_11699,U_11699),tc_HOL_Obool),tc_HOL_Obool),U_11699),c_member(tc_prod(U_11699,U_11699)))),c_Product__Type_OPair(U_11699,U_11699)))),U_11701),U_11703,U_11705)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_11699,tc_HOL_Obool),tc_fun(U_11699,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_11699,tc_HOL_Obool),tc_fun(U_11699,tc_HOL_Obool)),U_11703),U_11705)),c_Wellfounded_Omax__ext(U_11699,U_11701))) ),
    inference(clausify,[status(thm)],[f_3086_3]) ).

fof(f_3087_1,plain,
    ! [V_y_2,V_x_2] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Wellfounded_Oless__than))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Wellfounded_Oless__than)) ) ),
    inference(fof_nnf,[status(thm)],[fact_less__than__iff]) ).

fof(f_3087_2,plain,
    ! [U_11707,U_11706] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11706),U_11707)),c_Wellfounded_Oless__than))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11706),U_11707)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11706),U_11707))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11706),U_11707)),c_Wellfounded_Oless__than)) ) ),
    inference(variable_rename,[status(thm)],[f_3087_1]) ).

fof(f_3087_3,plain,
    ( ! [U_11711,U_11709] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11709),U_11711)),c_Wellfounded_Oless__than))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11709),U_11711)) )
    & ! [U_11710,U_11708] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11708),U_11710))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11708),U_11710)),c_Wellfounded_Oless__than)) ) ),
    inference(miniscope,[status(thm)],[f_3087_2]) ).

cnf(f_3087_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11708),U_11710))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11708),U_11710)),c_Wellfounded_Oless__than)) ),
    inference(clausify,[status(thm)],[f_3087_3]) ).

cnf(f_3087_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11709),U_11711)),c_Wellfounded_Oless__than))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11709),U_11711)) ),
    inference(clausify,[status(thm)],[f_3087_3]) ).

fof(f_3088_1,plain,
    ! [V_v_2,V_u_2,V_y_2,V_x_2] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2))),c_Int_Ointrel))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_v_2) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_u_2),V_y_2) )
      & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_v_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_u_2),V_y_2)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2))),c_Int_Ointrel)) ) ),
    inference(fof_nnf,[status(thm)],[fact_intrel__iff]) ).

fof(f_3088_2,plain,
    ! [U_11715,U_11714,U_11713,U_11712] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11712),U_11713)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11714),U_11715))),c_Int_Ointrel))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11712),U_11715) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11714),U_11713) )
      & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11712),U_11715) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11714),U_11713)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11712),U_11713)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11714),U_11715))),c_Int_Ointrel)) ) ),
    inference(variable_rename,[status(thm)],[f_3088_1]) ).

fof(f_3088_3,plain,
    ( ! [U_11723,U_11721,U_11719,U_11717] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11717),U_11719)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11721),U_11723))),c_Int_Ointrel))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11717),U_11723) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11721),U_11719) )
    & ! [U_11722,U_11720,U_11718,U_11716] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11716),U_11722) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11720),U_11718)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11716),U_11718)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11720),U_11722))),c_Int_Ointrel)) ) ),
    inference(miniscope,[status(thm)],[f_3088_2]) ).

cnf(f_3088_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11716),U_11722) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11720),U_11718)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11716),U_11718)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11720),U_11722))),c_Int_Ointrel)) ),
    inference(clausify,[status(thm)],[f_3088_3]) ).

cnf(f_3088_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11717),U_11719)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11721),U_11723))),c_Int_Ointrel))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11717),U_11723) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11721),U_11719) ),
    inference(clausify,[status(thm)],[f_3088_3]) ).

fof(f_3089_1,plain,
    c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than),
    inference(fof_nnf,[status(thm)],[fact_pair__less__def]) ).

cnf(f_3089_2,plain,
    c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than),
    inference(clausify,[status(thm)],[f_3089_1]) ).

fof(f_3090_1,plain,
    ! [V_R_2,V_f_2,T_b] : c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,T_b),T_b),c_Wellfounded_Olex__prod(tc_Nat_Onat,T_b,c_Wellfounded_Oless__than,V_R_2)),hAPP(hAPP(c_COMBS(T_b,T_b,tc_prod(tc_Nat_Onat,T_b)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_b,tc_prod(tc_Nat_Onat,T_b)),T_b),c_Product__Type_OPair(tc_Nat_Onat,T_b)),V_f_2)),c_COMBI(T_b))),
    inference(fof_nnf,[status(thm)],[fact_mlex__prod__def]) ).

fof(f_3090_2,plain,
    ! [U_11726,U_11725,U_11724] : c_Wellfounded_Omlex__prod(U_11724,U_11725,U_11726) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,U_11724),U_11724),c_Wellfounded_Olex__prod(tc_Nat_Onat,U_11724,c_Wellfounded_Oless__than,U_11726)),hAPP(hAPP(c_COMBS(U_11724,U_11724,tc_prod(tc_Nat_Onat,U_11724)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_11724,tc_prod(tc_Nat_Onat,U_11724)),U_11724),c_Product__Type_OPair(tc_Nat_Onat,U_11724)),U_11725)),c_COMBI(U_11724))),
    inference(variable_rename,[status(thm)],[f_3090_1]) ).

cnf(f_3090_3,plain,
    c_Wellfounded_Omlex__prod(U_11724,U_11725,U_11726) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,U_11724),U_11724),c_Wellfounded_Olex__prod(tc_Nat_Onat,U_11724,c_Wellfounded_Oless__than,U_11726)),hAPP(hAPP(c_COMBS(U_11724,U_11724,tc_prod(tc_Nat_Onat,U_11724)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_11724,tc_prod(tc_Nat_Onat,U_11724)),U_11724),c_Product__Type_OPair(tc_Nat_Onat,U_11724)),U_11725)),c_COMBI(U_11724))),
    inference(clausify,[status(thm)],[f_3090_2]) ).

fof(f_3091_1,plain,
    ! [V_f_2,T_c,V_P_2,T_b] :
      ( c_FunDef_Oreduction__pair(T_c,hAPP(hAPP(c_FunDef_Orp__inv__image(T_b,T_c),V_P_2),V_f_2))
      | ~ c_FunDef_Oreduction__pair(T_b,V_P_2) ),
    inference(fof_nnf,[status(thm)],[fact_rp__inv__image__rp]) ).

fof(f_3091_2,plain,
    ! [U_11730,U_11729,U_11728,U_11727] :
      ( c_FunDef_Oreduction__pair(U_11729,hAPP(hAPP(c_FunDef_Orp__inv__image(U_11727,U_11729),U_11728),U_11730))
      | ~ c_FunDef_Oreduction__pair(U_11727,U_11728) ),
    inference(variable_rename,[status(thm)],[f_3091_1]) ).

cnf(f_3091_3,plain,
    ( c_FunDef_Oreduction__pair(U_11729,hAPP(hAPP(c_FunDef_Orp__inv__image(U_11727,U_11729),U_11728),U_11730))
    | ~ c_FunDef_Oreduction__pair(U_11727,U_11728) ),
    inference(clausify,[status(thm)],[f_3091_2]) ).

fof(f_3092_1,plain,
    ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_d),V_g_2),V_A_2)
      | ? [B_x] :
          ( hAPP(V_g_2,B_x) != hAPP(hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2),B_x)
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
      | V_B_2 != hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
      | ~ class_Groups_Ocomm__monoid__mult(T_d) ),
    inference(fof_nnf,[status(thm)],[fact_strong__setprod__reindex__cong]) ).

fof(f_3092_2,plain,
    ! [U_11739,U_11738,U_11737,U_11736,U_11735,U_11734,U_11733,U_11732] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11734,U_11732),U_11739),U_11737) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11733,U_11732),U_11738),U_11736)
      | ? [U_11731] :
          ( hAPP(U_11738,U_11731) != hAPP(hAPP(c_Fun_Ocomp(U_11734,U_11732,U_11733,U_11739),U_11735),U_11731)
          & hBOOL(hAPP(hAPP(c_member(U_11733),U_11731),U_11736)) )
      | U_11737 != hAPP(c_Set_Oimage(U_11733,U_11734,U_11735),U_11736)
      | ~ c_Fun_Oinj__on(U_11733,U_11734,U_11735,U_11736)
      | ~ class_Groups_Ocomm__monoid__mult(U_11732) ),
    inference(variable_rename,[status(thm)],[f_3092_1]) ).

fof(f_3092_3,plain,
    ! [U_11739,U_11738,U_11737,U_11736,U_11735,U_11734,U_11733,U_11732] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11734,U_11732),U_11739),U_11737) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11733,U_11732),U_11738),U_11736)
      | ( hAPP(U_11738,sK273(U_11739,U_11738,U_11737,U_11736,U_11735,U_11734,U_11733,U_11732)) != hAPP(hAPP(c_Fun_Ocomp(U_11734,U_11732,U_11733,U_11739),U_11735),sK273(U_11739,U_11738,U_11737,U_11736,U_11735,U_11734,U_11733,U_11732))
        & hBOOL(hAPP(hAPP(c_member(U_11733),sK273(U_11739,U_11738,U_11737,U_11736,U_11735,U_11734,U_11733,U_11732)),U_11736)) )
      | U_11737 != hAPP(c_Set_Oimage(U_11733,U_11734,U_11735),U_11736)
      | ~ c_Fun_Oinj__on(U_11733,U_11734,U_11735,U_11736)
      | ~ class_Groups_Ocomm__monoid__mult(U_11732) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK273]),skolemize(U_11731,sK273(U_11739,U_11738,U_11737,U_11736,U_11735,U_11734,U_11733,U_11732))],[f_3092_2]) ).

cnf(f_3092_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11733),sK273(U_11739,U_11738,U_11737,U_11736,U_11735,U_11734,U_11733,U_11732)),U_11736))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11734,U_11732),U_11739),U_11737) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11733,U_11732),U_11738),U_11736)
    | U_11737 != hAPP(c_Set_Oimage(U_11733,U_11734,U_11735),U_11736)
    | ~ c_Fun_Oinj__on(U_11733,U_11734,U_11735,U_11736)
    | ~ class_Groups_Ocomm__monoid__mult(U_11732) ),
    inference(clausify,[status(thm)],[f_3092_3]) ).

cnf(f_3092_5,plain,
    ( hAPP(U_11738,sK273(U_11739,U_11738,U_11737,U_11736,U_11735,U_11734,U_11733,U_11732)) != hAPP(hAPP(c_Fun_Ocomp(U_11734,U_11732,U_11733,U_11739),U_11735),sK273(U_11739,U_11738,U_11737,U_11736,U_11735,U_11734,U_11733,U_11732))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11734,U_11732),U_11739),U_11737) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11733,U_11732),U_11738),U_11736)
    | U_11737 != hAPP(c_Set_Oimage(U_11733,U_11734,U_11735),U_11736)
    | ~ c_Fun_Oinj__on(U_11733,U_11734,U_11735,U_11736)
    | ~ class_Groups_Ocomm__monoid__mult(U_11732) ),
    inference(clausify,[status(thm)],[f_3092_3]) ).

fof(f_3093_1,plain,
    ! [T_c,T_b] : c_FunDef_Orp__inv__image(T_b,T_c) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))))),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_COMBS(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_c,T_b),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))),tc_fun(T_c,T_b)),c_Product__Type_OPair(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),c_Relation_Oinv__image(T_b,T_c))))),c_Relation_Oinv__image(T_b,T_c))),
    inference(fof_nnf,[status(thm)],[fact_rp__inv__image__def]) ).

fof(f_3093_2,plain,
    ! [U_11741,U_11740] : c_FunDef_Orp__inv__image(U_11740,U_11741) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(U_11740,U_11740),tc_HOL_Obool),tc_fun(tc_prod(U_11740,U_11740),tc_HOL_Obool),tc_fun(tc_fun(U_11741,U_11740),tc_prod(tc_fun(tc_prod(U_11741,U_11741),tc_HOL_Obool),tc_fun(tc_prod(U_11741,U_11741),tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(tc_fun(tc_prod(U_11740,U_11740),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_11740,U_11740),tc_HOL_Obool),tc_fun(tc_fun(U_11741,U_11740),tc_fun(tc_prod(U_11741,U_11741),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(U_11740,U_11740),tc_HOL_Obool),tc_fun(tc_fun(U_11741,U_11740),tc_prod(tc_fun(tc_prod(U_11741,U_11741),tc_HOL_Obool),tc_fun(tc_prod(U_11741,U_11741),tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(U_11741,U_11740),tc_fun(tc_prod(U_11741,U_11741),tc_HOL_Obool)),tc_fun(tc_fun(U_11741,U_11740),tc_prod(tc_fun(tc_prod(U_11741,U_11741),tc_HOL_Obool),tc_fun(tc_prod(U_11741,U_11741),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(tc_prod(U_11740,U_11740),tc_HOL_Obool),tc_fun(tc_fun(U_11741,U_11740),tc_fun(tc_prod(U_11741,U_11741),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(U_11740,U_11740),tc_HOL_Obool),tc_fun(tc_fun(U_11741,U_11740),tc_prod(tc_fun(tc_prod(U_11741,U_11741),tc_HOL_Obool),tc_fun(tc_prod(U_11741,U_11741),tc_HOL_Obool))))),tc_fun(tc_prod(U_11740,U_11740),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(U_11741,U_11740),tc_fun(tc_prod(U_11741,U_11741),tc_HOL_Obool)),tc_fun(tc_fun(U_11741,U_11740),tc_prod(tc_fun(tc_prod(U_11741,U_11741),tc_HOL_Obool),tc_fun(tc_prod(U_11741,U_11741),tc_HOL_Obool))),tc_fun(tc_prod(U_11740,U_11740),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_11741,U_11740),tc_fun(tc_fun(tc_prod(U_11741,U_11741),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_11741,U_11741),tc_HOL_Obool),tc_fun(tc_prod(U_11741,U_11741),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(U_11741,U_11740),tc_fun(tc_prod(U_11741,U_11741),tc_HOL_Obool)),tc_fun(tc_fun(U_11741,U_11740),tc_prod(tc_fun(tc_prod(U_11741,U_11741),tc_HOL_Obool),tc_fun(tc_prod(U_11741,U_11741),tc_HOL_Obool)))),tc_fun(tc_prod(U_11740,U_11740),tc_HOL_Obool)),c_COMBS(tc_fun(U_11741,U_11740),tc_fun(tc_prod(U_11741,U_11741),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_11741,U_11741),tc_HOL_Obool),tc_fun(tc_prod(U_11741,U_11741),tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_11741,U_11740),tc_fun(tc_prod(U_11741,U_11741),tc_HOL_Obool)),tc_fun(tc_fun(U_11741,U_11740),tc_fun(tc_fun(tc_prod(U_11741,U_11741),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_11741,U_11741),tc_HOL_Obool),tc_fun(tc_prod(U_11741,U_11741),tc_HOL_Obool)))),tc_fun(tc_prod(U_11740,U_11740),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(U_11741,U_11741),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_11741,U_11741),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_11741,U_11741),tc_HOL_Obool),tc_fun(tc_prod(U_11741,U_11741),tc_HOL_Obool))),tc_fun(U_11741,U_11740)),c_Product__Type_OPair(tc_fun(tc_prod(U_11741,U_11741),tc_HOL_Obool),tc_fun(tc_prod(U_11741,U_11741),tc_HOL_Obool)))),c_Relation_Oinv__image(U_11740,U_11741))))),c_Relation_Oinv__image(U_11740,U_11741))),
    inference(variable_rename,[status(thm)],[f_3093_1]) ).

cnf(f_3093_3,plain,
    c_FunDef_Orp__inv__image(U_11740,U_11741) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(U_11740,U_11740),tc_HOL_Obool),tc_fun(tc_prod(U_11740,U_11740),tc_HOL_Obool),tc_fun(tc_fun(U_11741,U_11740),tc_prod(tc_fun(tc_prod(U_11741,U_11741),tc_HOL_Obool),tc_fun(tc_prod(U_11741,U_11741),tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(tc_fun(tc_prod(U_11740,U_11740),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_11740,U_11740),tc_HOL_Obool),tc_fun(tc_fun(U_11741,U_11740),tc_fun(tc_prod(U_11741,U_11741),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(U_11740,U_11740),tc_HOL_Obool),tc_fun(tc_fun(U_11741,U_11740),tc_prod(tc_fun(tc_prod(U_11741,U_11741),tc_HOL_Obool),tc_fun(tc_prod(U_11741,U_11741),tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(U_11741,U_11740),tc_fun(tc_prod(U_11741,U_11741),tc_HOL_Obool)),tc_fun(tc_fun(U_11741,U_11740),tc_prod(tc_fun(tc_prod(U_11741,U_11741),tc_HOL_Obool),tc_fun(tc_prod(U_11741,U_11741),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(tc_prod(U_11740,U_11740),tc_HOL_Obool),tc_fun(tc_fun(U_11741,U_11740),tc_fun(tc_prod(U_11741,U_11741),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(U_11740,U_11740),tc_HOL_Obool),tc_fun(tc_fun(U_11741,U_11740),tc_prod(tc_fun(tc_prod(U_11741,U_11741),tc_HOL_Obool),tc_fun(tc_prod(U_11741,U_11741),tc_HOL_Obool))))),tc_fun(tc_prod(U_11740,U_11740),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(U_11741,U_11740),tc_fun(tc_prod(U_11741,U_11741),tc_HOL_Obool)),tc_fun(tc_fun(U_11741,U_11740),tc_prod(tc_fun(tc_prod(U_11741,U_11741),tc_HOL_Obool),tc_fun(tc_prod(U_11741,U_11741),tc_HOL_Obool))),tc_fun(tc_prod(U_11740,U_11740),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_11741,U_11740),tc_fun(tc_fun(tc_prod(U_11741,U_11741),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_11741,U_11741),tc_HOL_Obool),tc_fun(tc_prod(U_11741,U_11741),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(U_11741,U_11740),tc_fun(tc_prod(U_11741,U_11741),tc_HOL_Obool)),tc_fun(tc_fun(U_11741,U_11740),tc_prod(tc_fun(tc_prod(U_11741,U_11741),tc_HOL_Obool),tc_fun(tc_prod(U_11741,U_11741),tc_HOL_Obool)))),tc_fun(tc_prod(U_11740,U_11740),tc_HOL_Obool)),c_COMBS(tc_fun(U_11741,U_11740),tc_fun(tc_prod(U_11741,U_11741),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_11741,U_11741),tc_HOL_Obool),tc_fun(tc_prod(U_11741,U_11741),tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_11741,U_11740),tc_fun(tc_prod(U_11741,U_11741),tc_HOL_Obool)),tc_fun(tc_fun(U_11741,U_11740),tc_fun(tc_fun(tc_prod(U_11741,U_11741),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_11741,U_11741),tc_HOL_Obool),tc_fun(tc_prod(U_11741,U_11741),tc_HOL_Obool)))),tc_fun(tc_prod(U_11740,U_11740),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(U_11741,U_11741),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_11741,U_11741),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_11741,U_11741),tc_HOL_Obool),tc_fun(tc_prod(U_11741,U_11741),tc_HOL_Obool))),tc_fun(U_11741,U_11740)),c_Product__Type_OPair(tc_fun(tc_prod(U_11741,U_11741),tc_HOL_Obool),tc_fun(tc_prod(U_11741,U_11741),tc_HOL_Obool)))),c_Relation_Oinv__image(U_11740,U_11741))))),c_Relation_Oinv__image(U_11740,U_11741))),
    inference(clausify,[status(thm)],[f_3093_2]) ).

fof(f_3094_1,plain,
    ! [V_f_2,V_r_2,T_c,V_y_2,V_x_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Relation_Oinv__image(T_c,T_b),V_r_2),V_f_2)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))),V_r_2)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))),V_r_2))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Relation_Oinv__image(T_c,T_b),V_r_2),V_f_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_in__inv__image]) ).

fof(f_3094_2,plain,
    ! [U_11747,U_11746,U_11745,U_11744,U_11743,U_11742] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11742,U_11742)),hAPP(hAPP(c_Product__Type_OPair(U_11742,U_11742),U_11743),U_11744)),hAPP(hAPP(c_Relation_Oinv__image(U_11745,U_11742),U_11746),U_11747)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11745,U_11745)),hAPP(hAPP(c_Product__Type_OPair(U_11745,U_11745),hAPP(U_11747,U_11743)),hAPP(U_11747,U_11744))),U_11746)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11745,U_11745)),hAPP(hAPP(c_Product__Type_OPair(U_11745,U_11745),hAPP(U_11747,U_11743)),hAPP(U_11747,U_11744))),U_11746))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11742,U_11742)),hAPP(hAPP(c_Product__Type_OPair(U_11742,U_11742),U_11743),U_11744)),hAPP(hAPP(c_Relation_Oinv__image(U_11745,U_11742),U_11746),U_11747))) ) ),
    inference(variable_rename,[status(thm)],[f_3094_1]) ).

fof(f_3094_3,plain,
    ( ! [U_11759,U_11757,U_11755,U_11753,U_11751] :
        ( ! [U_11749] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_11749,U_11749)),hAPP(hAPP(c_Product__Type_OPair(U_11749,U_11749),U_11751),U_11753)),hAPP(hAPP(c_Relation_Oinv__image(U_11755,U_11749),U_11757),U_11759)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11755,U_11755)),hAPP(hAPP(c_Product__Type_OPair(U_11755,U_11755),hAPP(U_11759,U_11751)),hAPP(U_11759,U_11753))),U_11757)) )
    & ! [U_11758,U_11756,U_11754,U_11752,U_11750] :
        ( ! [U_11748] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11748,U_11748)),hAPP(hAPP(c_Product__Type_OPair(U_11748,U_11748),U_11750),U_11752)),hAPP(hAPP(c_Relation_Oinv__image(U_11754,U_11748),U_11756),U_11758)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_11754,U_11754)),hAPP(hAPP(c_Product__Type_OPair(U_11754,U_11754),hAPP(U_11758,U_11750)),hAPP(U_11758,U_11752))),U_11756)) ) ),
    inference(miniscope,[status(thm)],[f_3094_2]) ).

cnf(f_3094_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11748,U_11748)),hAPP(hAPP(c_Product__Type_OPair(U_11748,U_11748),U_11750),U_11752)),hAPP(hAPP(c_Relation_Oinv__image(U_11754,U_11748),U_11756),U_11758)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_11754,U_11754)),hAPP(hAPP(c_Product__Type_OPair(U_11754,U_11754),hAPP(U_11758,U_11750)),hAPP(U_11758,U_11752))),U_11756)) ),
    inference(clausify,[status(thm)],[f_3094_3]) ).

cnf(f_3094_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11749,U_11749)),hAPP(hAPP(c_Product__Type_OPair(U_11749,U_11749),U_11751),U_11753)),hAPP(hAPP(c_Relation_Oinv__image(U_11755,U_11749),U_11757),U_11759)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11755,U_11755)),hAPP(hAPP(c_Product__Type_OPair(U_11755,U_11755),hAPP(U_11759,U_11751)),hAPP(U_11759,U_11753))),U_11757)) ),
    inference(clausify,[status(thm)],[f_3094_3]) ).

fof(f_3095_1,plain,
    ! [V_y_2,V_x_2] :
      ( ( hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) = hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_Int_Ointrel)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_Int_Ointrel))
        | hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) != hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_equiv__intrel__iff]) ).

fof(f_3095_2,plain,
    ! [U_11761,U_11760] :
      ( ( hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11760),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) = hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11761),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11760),U_11761)),c_Int_Ointrel)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11760),U_11761)),c_Int_Ointrel))
        | hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11760),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) != hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11761),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) ) ),
    inference(variable_rename,[status(thm)],[f_3095_1]) ).

fof(f_3095_3,plain,
    ( ! [U_11765,U_11763] :
        ( hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11763),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) = hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11765),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11763),U_11765)),c_Int_Ointrel)) )
    & ! [U_11764,U_11762] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11762),U_11764)),c_Int_Ointrel))
        | hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11762),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) != hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11764),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) ) ),
    inference(miniscope,[status(thm)],[f_3095_2]) ).

cnf(f_3095_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11762),U_11764)),c_Int_Ointrel))
    | hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11762),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) != hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11764),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_3095_3]) ).

cnf(f_3095_5,plain,
    ( hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11763),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) = hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11765),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_11763),U_11765)),c_Int_Ointrel)) ),
    inference(clausify,[status(thm)],[f_3095_3]) ).

fof(f_3096_1,plain,
    ! [V_g_2,V_f_2,V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_b),V_g_2),V_B_2)
      | ? [B_x] :
          ( hAPP(V_f_2,B_x) != hAPP(V_g_2,B_x)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) )
      | ~ c_Nat__Transfer_Onat__set(V_B_2)
      | V_A_2 != V_B_2
      | ~ class_Groups_Ocomm__monoid__mult(T_b)
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__sum__prod__cong_I2_J]) ).

fof(f_3096_2,plain,
    ! [U_11771,U_11770,U_11769,U_11768,U_11767] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_11767),U_11770),U_11768) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_11767),U_11771),U_11769)
      | ? [U_11766] :
          ( hAPP(U_11770,U_11766) != hAPP(U_11771,U_11766)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11766)) )
      | ~ c_Nat__Transfer_Onat__set(U_11769)
      | U_11768 != U_11769
      | ~ class_Groups_Ocomm__monoid__mult(U_11767)
      | ~ class_Groups_Ocomm__monoid__add(U_11767) ),
    inference(variable_rename,[status(thm)],[f_3096_1]) ).

fof(f_3096_3,plain,
    ! [U_11771,U_11770,U_11769,U_11768,U_11767] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_11767),U_11770),U_11768) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_11767),U_11771),U_11769)
      | ( hAPP(U_11770,sK274(U_11771,U_11770,U_11769,U_11768,U_11767)) != hAPP(U_11771,sK274(U_11771,U_11770,U_11769,U_11768,U_11767))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK274(U_11771,U_11770,U_11769,U_11768,U_11767))) )
      | ~ c_Nat__Transfer_Onat__set(U_11769)
      | U_11768 != U_11769
      | ~ class_Groups_Ocomm__monoid__mult(U_11767)
      | ~ class_Groups_Ocomm__monoid__add(U_11767) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK274]),skolemize(U_11766,sK274(U_11771,U_11770,U_11769,U_11768,U_11767))],[f_3096_2]) ).

cnf(f_3096_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK274(U_11771,U_11770,U_11769,U_11768,U_11767)))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_11767),U_11770),U_11768) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_11767),U_11771),U_11769)
    | ~ c_Nat__Transfer_Onat__set(U_11769)
    | U_11768 != U_11769
    | ~ class_Groups_Ocomm__monoid__mult(U_11767)
    | ~ class_Groups_Ocomm__monoid__add(U_11767) ),
    inference(clausify,[status(thm)],[f_3096_3]) ).

cnf(f_3096_5,plain,
    ( hAPP(U_11770,sK274(U_11771,U_11770,U_11769,U_11768,U_11767)) != hAPP(U_11771,sK274(U_11771,U_11770,U_11769,U_11768,U_11767))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_11767),U_11770),U_11768) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_11767),U_11771),U_11769)
    | ~ c_Nat__Transfer_Onat__set(U_11769)
    | U_11768 != U_11769
    | ~ class_Groups_Ocomm__monoid__mult(U_11767)
    | ~ class_Groups_Ocomm__monoid__add(U_11767) ),
    inference(clausify,[status(thm)],[f_3096_3]) ).

fof(f_3097_1,plain,
    ! [V_R_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,V_R_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Image__empty]) ).

fof(f_3097_2,plain,
    ! [U_11774,U_11773,U_11772] : hAPP(c_Relation_OImage(U_11772,U_11773,U_11774),c_Orderings_Obot__class_Obot(tc_fun(U_11772,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_11773,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3097_1]) ).

cnf(f_3097_3,plain,
    hAPP(c_Relation_OImage(U_11772,U_11773,U_11774),c_Orderings_Obot__class_Obot(tc_fun(U_11772,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_11773,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3097_2]) ).

fof(f_3098_1,plain,
    ! [V_A_2,V_S_2,V_R_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_R_2),V_S_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_c,T_b,V_S_2),V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_Un__Image]) ).

fof(f_3098_2,plain,
    ! [U_11779,U_11778,U_11777,U_11776,U_11775] : hAPP(c_Relation_OImage(U_11775,U_11776,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_11775,U_11776),tc_HOL_Obool)),U_11777),U_11778)),U_11779) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11776,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11775,U_11776,U_11777),U_11779)),hAPP(c_Relation_OImage(U_11775,U_11776,U_11778),U_11779)),
    inference(variable_rename,[status(thm)],[f_3098_1]) ).

cnf(f_3098_3,plain,
    hAPP(c_Relation_OImage(U_11775,U_11776,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_11775,U_11776),tc_HOL_Obool)),U_11777),U_11778)),U_11779) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11776,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11775,U_11776,U_11777),U_11779)),hAPP(c_Relation_OImage(U_11775,U_11776,U_11778),U_11779)),
    inference(clausify,[status(thm)],[f_3098_2]) ).

fof(f_3099_1,plain,
    ! [V_B_2,V_A_2,V_R_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_Image__Un]) ).

fof(f_3099_2,plain,
    ! [U_11784,U_11783,U_11782,U_11781,U_11780] : hAPP(c_Relation_OImage(U_11780,U_11781,U_11782),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11780,tc_HOL_Obool)),U_11783),U_11784)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11781,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11780,U_11781,U_11782),U_11783)),hAPP(c_Relation_OImage(U_11780,U_11781,U_11782),U_11784)),
    inference(variable_rename,[status(thm)],[f_3099_1]) ).

cnf(f_3099_3,plain,
    hAPP(c_Relation_OImage(U_11780,U_11781,U_11782),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11780,tc_HOL_Obool)),U_11783),U_11784)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11781,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11780,U_11781,U_11782),U_11783)),hAPP(c_Relation_OImage(U_11780,U_11781,U_11782),U_11784)),
    inference(clausify,[status(thm)],[f_3099_2]) ).

fof(f_3100_1,plain,
    ! [V_B_2,V_A_2,T_d,V_r_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Relation_OImage(T_c,T_b,V_r_2)),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_Image__UN]) ).

fof(f_3100_2,plain,
    ! [U_11790,U_11789,U_11788,U_11787,U_11786,U_11785] : hAPP(c_Relation_OImage(U_11785,U_11786,U_11787),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11788,tc_fun(U_11785,tc_HOL_Obool)),U_11789),U_11790)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11788,tc_fun(U_11786,tc_HOL_Obool)),U_11789),hAPP(hAPP(c_COMBB(tc_fun(U_11785,tc_HOL_Obool),tc_fun(U_11786,tc_HOL_Obool),U_11788),c_Relation_OImage(U_11785,U_11786,U_11787)),U_11790)),
    inference(variable_rename,[status(thm)],[f_3100_1]) ).

cnf(f_3100_3,plain,
    hAPP(c_Relation_OImage(U_11785,U_11786,U_11787),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11788,tc_fun(U_11785,tc_HOL_Obool)),U_11789),U_11790)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11788,tc_fun(U_11786,tc_HOL_Obool)),U_11789),hAPP(hAPP(c_COMBB(tc_fun(U_11785,tc_HOL_Obool),tc_fun(U_11786,tc_HOL_Obool),U_11788),c_Relation_OImage(U_11785,U_11786,U_11787)),U_11790)),
    inference(clausify,[status(thm)],[f_3100_2]) ).

fof(f_3101_1,plain,
    ! [V_B_2,V_A_2,T_d,V_r_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Relation_OImage(T_c,T_b,V_r_2)),V_B_2)))),
    inference(fof_nnf,[status(thm)],[fact_Image__INT__subset]) ).

fof(f_3101_2,plain,
    ! [U_11796,U_11795,U_11794,U_11793,U_11792,U_11791] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11791,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11792,U_11791,U_11793),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11794,tc_fun(U_11792,tc_HOL_Obool)),U_11795),U_11796))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11794,tc_fun(U_11791,tc_HOL_Obool)),U_11795),hAPP(hAPP(c_COMBB(tc_fun(U_11792,tc_HOL_Obool),tc_fun(U_11791,tc_HOL_Obool),U_11794),c_Relation_OImage(U_11792,U_11791,U_11793)),U_11796)))),
    inference(variable_rename,[status(thm)],[f_3101_1]) ).

cnf(f_3101_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11791,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11792,U_11791,U_11793),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11794,tc_fun(U_11792,tc_HOL_Obool)),U_11795),U_11796))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11794,tc_fun(U_11791,tc_HOL_Obool)),U_11795),hAPP(hAPP(c_COMBB(tc_fun(U_11792,tc_HOL_Obool),tc_fun(U_11791,tc_HOL_Obool),U_11794),c_Relation_OImage(U_11792,U_11791,U_11793)),U_11796)))),
    inference(clausify,[status(thm)],[f_3101_2]) ).

fof(f_3102_1,plain,
    ! [V_B_2,V_A_2,V_R_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_B_2)))),
    inference(fof_nnf,[status(thm)],[fact_Image__Int__subset]) ).

fof(f_3102_2,plain,
    ! [U_11801,U_11800,U_11799,U_11798,U_11797] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11797,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11798,U_11797,U_11799),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11798,tc_HOL_Obool)),U_11800),U_11801))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11797,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11798,U_11797,U_11799),U_11800)),hAPP(c_Relation_OImage(U_11798,U_11797,U_11799),U_11801)))),
    inference(variable_rename,[status(thm)],[f_3102_1]) ).

cnf(f_3102_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11797,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11798,U_11797,U_11799),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11798,tc_HOL_Obool)),U_11800),U_11801))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11797,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11798,U_11797,U_11799),U_11800)),hAPP(c_Relation_OImage(U_11798,U_11797,U_11799),U_11801)))),
    inference(clausify,[status(thm)],[f_3102_2]) ).

fof(f_3103_1,plain,
    ! [V_A_2,V_A_H_2,V_r_2,V_r_H_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_c,V_r_H_2),V_A_H_2)),hAPP(c_Relation_OImage(T_b,T_c,V_r_2),V_A_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_H_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_H_2),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Image__mono]) ).

fof(f_3103_2,plain,
    ! [U_11807,U_11806,U_11805,U_11804,U_11803,U_11802] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11803,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11802,U_11803,U_11804),U_11806)),hAPP(c_Relation_OImage(U_11802,U_11803,U_11805),U_11807)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11802,tc_HOL_Obool)),U_11806),U_11807))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_11802,U_11803),tc_HOL_Obool)),U_11804),U_11805)) ),
    inference(variable_rename,[status(thm)],[f_3103_1]) ).

cnf(f_3103_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11803,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11802,U_11803,U_11804),U_11806)),hAPP(c_Relation_OImage(U_11802,U_11803,U_11805),U_11807)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11802,tc_HOL_Obool)),U_11806),U_11807))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_11802,U_11803),tc_HOL_Obool)),U_11804),U_11805)) ),
    inference(clausify,[status(thm)],[f_3103_2]) ).

fof(f_3104_1,plain,
    ! [V_A_2,V_r_2,T_c,V_b_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2)))
        | ! [B_x] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),V_b_2)),V_r_2))
            | ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) )
      & ( ? [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),V_b_2)),V_r_2))
            & hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_Image__iff]) ).

fof(f_3104_2,plain,
    ! [U_11814,U_11813,U_11812,U_11811,U_11810] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_11810),U_11811),hAPP(c_Relation_OImage(U_11812,U_11810,U_11813),U_11814)))
        | ! [U_11809] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11812,U_11810)),hAPP(hAPP(c_Product__Type_OPair(U_11812,U_11810),U_11809),U_11811)),U_11813))
            | ~ hBOOL(hAPP(hAPP(c_member(U_11812),U_11809),U_11814)) ) )
      & ( ? [U_11808] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11812,U_11810)),hAPP(hAPP(c_Product__Type_OPair(U_11812,U_11810),U_11808),U_11811)),U_11813))
            & hBOOL(hAPP(hAPP(c_member(U_11812),U_11808),U_11814)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_11810),U_11811),hAPP(c_Relation_OImage(U_11812,U_11810,U_11813),U_11814))) ) ),
    inference(variable_rename,[status(thm)],[f_3104_1]) ).

fof(f_3104_3,plain,
    ( ! [U_11824,U_11822,U_11820,U_11818,U_11816] :
        ( hBOOL(hAPP(hAPP(c_member(U_11816),U_11818),hAPP(c_Relation_OImage(U_11820,U_11816,U_11822),U_11824)))
        | ! [U_11809] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11820,U_11816)),hAPP(hAPP(c_Product__Type_OPair(U_11820,U_11816),U_11809),U_11818)),U_11822))
            | ~ hBOOL(hAPP(hAPP(c_member(U_11820),U_11809),U_11824)) ) )
    & ! [U_11823,U_11821,U_11819,U_11817,U_11815] :
        ( ? [U_11808] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11819,U_11815)),hAPP(hAPP(c_Product__Type_OPair(U_11819,U_11815),U_11808),U_11817)),U_11821))
            & hBOOL(hAPP(hAPP(c_member(U_11819),U_11808),U_11823)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_11815),U_11817),hAPP(c_Relation_OImage(U_11819,U_11815,U_11821),U_11823))) ) ),
    inference(miniscope,[status(thm)],[f_3104_2]) ).

fof(f_3104_4,plain,
    ( ! [U_11824,U_11822,U_11820,U_11818,U_11816] :
        ( hBOOL(hAPP(hAPP(c_member(U_11816),U_11818),hAPP(c_Relation_OImage(U_11820,U_11816,U_11822),U_11824)))
        | ! [U_11809] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11820,U_11816)),hAPP(hAPP(c_Product__Type_OPair(U_11820,U_11816),U_11809),U_11818)),U_11822))
            | ~ hBOOL(hAPP(hAPP(c_member(U_11820),U_11809),U_11824)) ) )
    & ! [U_11823,U_11821,U_11819,U_11817,U_11815] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11819,U_11815)),hAPP(hAPP(c_Product__Type_OPair(U_11819,U_11815),sK275(U_11823,U_11821,U_11819,U_11817,U_11815)),U_11817)),U_11821))
          & hBOOL(hAPP(hAPP(c_member(U_11819),sK275(U_11823,U_11821,U_11819,U_11817,U_11815)),U_11823)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_11815),U_11817),hAPP(c_Relation_OImage(U_11819,U_11815,U_11821),U_11823))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK275]),skolemize(U_11808,sK275(U_11823,U_11821,U_11819,U_11817,U_11815))],[f_3104_3]) ).

cnf(f_3104_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11819),sK275(U_11823,U_11821,U_11819,U_11817,U_11815)),U_11823))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11815),U_11817),hAPP(c_Relation_OImage(U_11819,U_11815,U_11821),U_11823))) ),
    inference(clausify,[status(thm)],[f_3104_4]) ).

cnf(f_3104_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11819,U_11815)),hAPP(hAPP(c_Product__Type_OPair(U_11819,U_11815),sK275(U_11823,U_11821,U_11819,U_11817,U_11815)),U_11817)),U_11821))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11815),U_11817),hAPP(c_Relation_OImage(U_11819,U_11815,U_11821),U_11823))) ),
    inference(clausify,[status(thm)],[f_3104_4]) ).

cnf(f_3104_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11816),U_11818),hAPP(c_Relation_OImage(U_11820,U_11816,U_11822),U_11824)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11820,U_11816)),hAPP(hAPP(c_Product__Type_OPair(U_11820,U_11816),U_11809),U_11818)),U_11822))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11820),U_11809),U_11824)) ),
    inference(clausify,[status(thm)],[f_3104_4]) ).

fof(f_3105_1,plain,
    ! [V_r_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Relation_OImage(T_b,T_c,V_r_2),V_A_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_rev__ImageI]) ).

fof(f_3105_2,plain,
    ! [U_11830,U_11829,U_11828,U_11827,U_11826,U_11825] :
      ( hBOOL(hAPP(hAPP(c_member(U_11828),U_11829),hAPP(c_Relation_OImage(U_11825,U_11828,U_11830),U_11827)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11825,U_11828)),hAPP(hAPP(c_Product__Type_OPair(U_11825,U_11828),U_11826),U_11829)),U_11830))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11825),U_11826),U_11827)) ),
    inference(variable_rename,[status(thm)],[f_3105_1]) ).

cnf(f_3105_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11828),U_11829),hAPP(c_Relation_OImage(U_11825,U_11828,U_11830),U_11827)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11825,U_11828)),hAPP(hAPP(c_Product__Type_OPair(U_11825,U_11828),U_11826),U_11829)),U_11830))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11825),U_11826),U_11827)) ),
    inference(clausify,[status(thm)],[f_3105_2]) ).

fof(f_3106_1,plain,
    ! [V_B_2,V_r_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Relation_OImage(T_c,T_b,V_r_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),c_Set_Oinsert(T_c)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))),
    inference(fof_nnf,[status(thm)],[fact_Image__eq__UN]) ).

fof(f_3106_2,plain,
    ! [U_11834,U_11833,U_11832,U_11831] : hAPP(c_Relation_OImage(U_11831,U_11832,U_11833),U_11834) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11831,tc_fun(U_11832,tc_HOL_Obool)),U_11834),hAPP(hAPP(c_COMBB(tc_fun(U_11831,tc_HOL_Obool),tc_fun(U_11832,tc_HOL_Obool),U_11831),c_Relation_OImage(U_11831,U_11832,U_11833)),hAPP(hAPP(c_COMBC(U_11831,tc_fun(U_11831,tc_HOL_Obool),tc_fun(U_11831,tc_HOL_Obool)),c_Set_Oinsert(U_11831)),c_Orderings_Obot__class_Obot(tc_fun(U_11831,tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_3106_1]) ).

cnf(f_3106_3,plain,
    hAPP(c_Relation_OImage(U_11831,U_11832,U_11833),U_11834) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11831,tc_fun(U_11832,tc_HOL_Obool)),U_11834),hAPP(hAPP(c_COMBB(tc_fun(U_11831,tc_HOL_Obool),tc_fun(U_11832,tc_HOL_Obool),U_11831),c_Relation_OImage(U_11831,U_11832,U_11833)),hAPP(hAPP(c_COMBC(U_11831,tc_fun(U_11831,tc_HOL_Obool),tc_fun(U_11831,tc_HOL_Obool)),c_Set_Oinsert(U_11831)),c_Orderings_Obot__class_Obot(tc_fun(U_11831,tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_3106_2]) ).

fof(f_3107_1,plain,
    ! [V_a_2,V_r_2,T_c,V_b_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_a_2),V_b_2)),V_r_2)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_a_2),V_b_2)),V_r_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))) ) ),
    inference(fof_nnf,[status(thm)],[fact_Image__singleton__iff]) ).

fof(f_3107_2,plain,
    ! [U_11839,U_11838,U_11837,U_11836,U_11835] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_11835),U_11836),hAPP(c_Relation_OImage(U_11837,U_11835,U_11838),hAPP(hAPP(c_Set_Oinsert(U_11837),U_11839),c_Orderings_Obot__class_Obot(tc_fun(U_11837,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11837,U_11835)),hAPP(hAPP(c_Product__Type_OPair(U_11837,U_11835),U_11839),U_11836)),U_11838)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11837,U_11835)),hAPP(hAPP(c_Product__Type_OPair(U_11837,U_11835),U_11839),U_11836)),U_11838))
        | ~ hBOOL(hAPP(hAPP(c_member(U_11835),U_11836),hAPP(c_Relation_OImage(U_11837,U_11835,U_11838),hAPP(hAPP(c_Set_Oinsert(U_11837),U_11839),c_Orderings_Obot__class_Obot(tc_fun(U_11837,tc_HOL_Obool)))))) ) ),
    inference(variable_rename,[status(thm)],[f_3107_1]) ).

fof(f_3107_3,plain,
    ( ! [U_11849,U_11847,U_11845,U_11843,U_11841] :
        ( hBOOL(hAPP(hAPP(c_member(U_11841),U_11843),hAPP(c_Relation_OImage(U_11845,U_11841,U_11847),hAPP(hAPP(c_Set_Oinsert(U_11845),U_11849),c_Orderings_Obot__class_Obot(tc_fun(U_11845,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11845,U_11841)),hAPP(hAPP(c_Product__Type_OPair(U_11845,U_11841),U_11849),U_11843)),U_11847)) )
    & ! [U_11848,U_11846,U_11844,U_11842,U_11840] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11844,U_11840)),hAPP(hAPP(c_Product__Type_OPair(U_11844,U_11840),U_11848),U_11842)),U_11846))
        | ~ hBOOL(hAPP(hAPP(c_member(U_11840),U_11842),hAPP(c_Relation_OImage(U_11844,U_11840,U_11846),hAPP(hAPP(c_Set_Oinsert(U_11844),U_11848),c_Orderings_Obot__class_Obot(tc_fun(U_11844,tc_HOL_Obool)))))) ) ),
    inference(miniscope,[status(thm)],[f_3107_2]) ).

cnf(f_3107_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11844,U_11840)),hAPP(hAPP(c_Product__Type_OPair(U_11844,U_11840),U_11848),U_11842)),U_11846))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11840),U_11842),hAPP(c_Relation_OImage(U_11844,U_11840,U_11846),hAPP(hAPP(c_Set_Oinsert(U_11844),U_11848),c_Orderings_Obot__class_Obot(tc_fun(U_11844,tc_HOL_Obool)))))) ),
    inference(clausify,[status(thm)],[f_3107_3]) ).

cnf(f_3107_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11841),U_11843),hAPP(c_Relation_OImage(U_11845,U_11841,U_11847),hAPP(hAPP(c_Set_Oinsert(U_11845),U_11849),c_Orderings_Obot__class_Obot(tc_fun(U_11845,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11845,U_11841)),hAPP(hAPP(c_Product__Type_OPair(U_11845,U_11841),U_11849),U_11843)),U_11847)) ),
    inference(clausify,[status(thm)],[f_3107_3]) ).

fof(f_3108_1,plain,
    ! [T_b] : c_Wellfounded_Omeasure(T_b) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,T_b),c_Wellfounded_Oless__than),
    inference(fof_nnf,[status(thm)],[fact_measure__def]) ).

fof(f_3108_2,plain,
    ! [U_11850] : c_Wellfounded_Omeasure(U_11850) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,U_11850),c_Wellfounded_Oless__than),
    inference(variable_rename,[status(thm)],[f_3108_1]) ).

cnf(f_3108_3,plain,
    c_Wellfounded_Omeasure(U_11850) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,U_11850),c_Wellfounded_Oless__than),
    inference(clausify,[status(thm)],[f_3108_2]) ).

fof(f_3109_1,plain,
    ! [V_j_2,V_i_2,T_b] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_i_2),V_j_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_i_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_j_2))
      | ~ class_Rings_Oring__1(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_of__int]) ).

fof(f_3109_2,plain,
    ! [U_11853,U_11852,U_11851] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_11851),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11852),U_11853)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_11851),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_11851),U_11852)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_11851),U_11853))
      | ~ class_Rings_Oring__1(U_11851) ),
    inference(variable_rename,[status(thm)],[f_3109_1]) ).

cnf(f_3109_3,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_11851),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11852),U_11853)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_11851),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_11851),U_11852)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_11851),U_11853))
    | ~ class_Rings_Oring__1(U_11851) ),
    inference(clausify,[status(thm)],[f_3109_2]) ).

fof(f_3110_1,plain,
    c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(fof_nnf,[status(thm)],[fact_One__int__def]) ).

cnf(f_3110_2,plain,
    c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_3110_1]) ).

fof(f_3111_1,plain,
    ! [V_v_2,V_u_2,V_y_2,V_x_2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_x_2),V_u_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_y_2),V_v_2))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_x_2),V_v_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_y_2),V_u_2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(fof_nnf,[status(thm)],[fact_mult]) ).

fof(f_3111_2,plain,
    ! [U_11857,U_11856,U_11855,U_11854] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11854),U_11855)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11856),U_11857)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_11854),U_11856)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_11855),U_11857))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_11854),U_11857)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_11855),U_11856)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_3111_1]) ).

cnf(f_3111_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11854),U_11855)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11856),U_11857)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_11854),U_11856)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_11855),U_11857))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_11854),U_11857)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_11855),U_11856)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_3111_2]) ).

fof(f_3112_1,plain,
    ! [V_x_2] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,V_x_2)) = V_x_2,
    inference(fof_nnf,[status(thm)],[fact_Rep__Integ__inverse]) ).

fof(f_3112_2,plain,
    ! [U_11858] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,U_11858)) = U_11858,
    inference(variable_rename,[status(thm)],[f_3112_1]) ).

cnf(f_3112_3,plain,
    hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,U_11858)) = U_11858,
    inference(clausify,[status(thm)],[f_3112_2]) ).

fof(f_3113_1,plain,
    ! [V_y_2,V_x_2] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_y_2),V_x_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(fof_nnf,[status(thm)],[fact_minus]) ).

fof(f_3113_2,plain,
    ! [U_11860,U_11859] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11859),U_11860)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11860),U_11859)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_3113_1]) ).

cnf(f_3113_3,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11859),U_11860)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11860),U_11859)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_3113_2]) ).

fof(f_3114_1,plain,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(fof_nnf,[status(thm)],[fact_Zero__int__def]) ).

cnf(f_3114_2,plain,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_3114_1]) ).

fof(f_3115_1,plain,
    ! [V_m_2] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_m_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(fof_nnf,[status(thm)],[fact_int__def]) ).

fof(f_3115_2,plain,
    ! [U_11861] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_11861) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11861),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_3115_1]) ).

cnf(f_3115_3,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_11861) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11861),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_3115_2]) ).

fof(f_3116_1,plain,
    ! [V_v_2,V_u_2,V_y_2,V_x_2] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_u_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y_2),V_v_2))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(fof_nnf,[status(thm)],[fact_add]) ).

fof(f_3116_2,plain,
    ! [U_11865,U_11864,U_11863,U_11862] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11862),U_11863)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11864),U_11865)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11862),U_11864)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11863),U_11865))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_3116_1]) ).

cnf(f_3116_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11862),U_11863)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11864),U_11865)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11862),U_11864)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11863),U_11865))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_3116_2]) ).

fof(f_3117_1,plain,
    ! [V_y_2,V_x_2] : hAPP(c_Int_Onat,hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_y_2),
    inference(fof_nnf,[status(thm)],[fact_nat]) ).

fof(f_3117_2,plain,
    ! [U_11867,U_11866] : hAPP(c_Int_Onat,hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11866),U_11867)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_11866),U_11867),
    inference(variable_rename,[status(thm)],[f_3117_1]) ).

cnf(f_3117_3,plain,
    hAPP(c_Int_Onat,hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11866),U_11867)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_11866),U_11867),
    inference(clausify,[status(thm)],[f_3117_2]) ).

fof(f_3118_1,plain,
    ! [V_z_2] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z_2) = hAPP(c_Int_OAbs__Integ,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,V_z_2)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_Nat_Onat),c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_Nat_Onat),c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_Nat_Onat),c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)))),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat))))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))),
    inference(fof_nnf,[status(thm)],[fact_minus__int__def]) ).

fof(f_3118_2,plain,
    ! [U_11868] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11868) = hAPP(c_Int_OAbs__Integ,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,U_11868)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_Nat_Onat),c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_Nat_Onat),c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_Nat_Onat),c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)))),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat))))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))),
    inference(variable_rename,[status(thm)],[f_3118_1]) ).

cnf(f_3118_3,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_11868) = hAPP(c_Int_OAbs__Integ,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,U_11868)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_Nat_Onat),c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_Nat_Onat),c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_Nat_Onat),c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)))),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat))))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))),
    inference(clausify,[status(thm)],[f_3118_2]) ).

fof(f_3119_1,plain,
    ! [V_v_2,V_u_2,V_y_2,V_x_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_v_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_u_2),V_y_2))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_v_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_u_2),V_y_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ) ),
    inference(fof_nnf,[status(thm)],[fact_less]) ).

fof(f_3119_2,plain,
    ! [U_11872,U_11871,U_11870,U_11869] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11869),U_11870)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11871),U_11872)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11869),U_11872)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11871),U_11870))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11869),U_11872)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11871),U_11870)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11869),U_11870)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11871),U_11872)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ) ),
    inference(variable_rename,[status(thm)],[f_3119_1]) ).

fof(f_3119_3,plain,
    ( ! [U_11880,U_11878,U_11876,U_11874] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11874),U_11876)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11878),U_11880)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11874),U_11880)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11878),U_11876))) )
    & ! [U_11879,U_11877,U_11875,U_11873] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11873),U_11879)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11877),U_11875)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11873),U_11875)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11877),U_11879)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ) ),
    inference(miniscope,[status(thm)],[f_3119_2]) ).

cnf(f_3119_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11873),U_11879)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11877),U_11875)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11873),U_11875)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11877),U_11879)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ),
    inference(clausify,[status(thm)],[f_3119_3]) ).

cnf(f_3119_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11874),U_11876)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11878),U_11880)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11874),U_11880)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11878),U_11876))) ),
    inference(clausify,[status(thm)],[f_3119_3]) ).

fof(f_3120_1,plain,
    ! [V_v_2,V_u_2,V_y_2,V_x_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_v_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_u_2),V_y_2))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_v_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_u_2),V_y_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ) ),
    inference(fof_nnf,[status(thm)],[fact_le]) ).

fof(f_3120_2,plain,
    ! [U_11884,U_11883,U_11882,U_11881] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11881),U_11882)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11883),U_11884)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11881),U_11884)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11883),U_11882))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11881),U_11884)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11883),U_11882)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11881),U_11882)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11883),U_11884)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ) ),
    inference(variable_rename,[status(thm)],[f_3120_1]) ).

fof(f_3120_3,plain,
    ( ! [U_11892,U_11890,U_11888,U_11886] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11886),U_11888)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11890),U_11892)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11886),U_11892)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11890),U_11888))) )
    & ! [U_11891,U_11889,U_11887,U_11885] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11885),U_11891)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11889),U_11887)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11885),U_11887)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11889),U_11891)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ) ),
    inference(miniscope,[status(thm)],[f_3120_2]) ).

cnf(f_3120_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11885),U_11891)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11889),U_11887)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11885),U_11887)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11889),U_11891)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ),
    inference(clausify,[status(thm)],[f_3120_3]) ).

cnf(f_3120_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11886),U_11888)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11890),U_11892)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11886),U_11892)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11890),U_11888))) ),
    inference(clausify,[status(thm)],[f_3120_3]) ).

fof(f_3121_1,plain,
    ! [V_r_2,T_b] :
      ( ( c_Relation_Oirrefl(T_b,V_r_2)
        | ? [B_x] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) )
      & ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2))
        | ~ c_Relation_Oirrefl(T_b,V_r_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_irrefl__def]) ).

fof(f_3121_2,plain,
    ! [U_11896,U_11895] :
      ( ( c_Relation_Oirrefl(U_11895,U_11896)
        | ? [U_11894] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_11895,U_11895)),hAPP(hAPP(c_Product__Type_OPair(U_11895,U_11895),U_11894),U_11894)),U_11896)) )
      & ( ! [U_11893] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11895,U_11895)),hAPP(hAPP(c_Product__Type_OPair(U_11895,U_11895),U_11893),U_11893)),U_11896))
        | ~ c_Relation_Oirrefl(U_11895,U_11896) ) ),
    inference(variable_rename,[status(thm)],[f_3121_1]) ).

fof(f_3121_3,plain,
    ( ! [U_11900,U_11898] :
        ( c_Relation_Oirrefl(U_11898,U_11900)
        | ? [U_11894] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_11898,U_11898)),hAPP(hAPP(c_Product__Type_OPair(U_11898,U_11898),U_11894),U_11894)),U_11900)) )
    & ! [U_11899,U_11897] :
        ( ! [U_11893] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11897,U_11897)),hAPP(hAPP(c_Product__Type_OPair(U_11897,U_11897),U_11893),U_11893)),U_11899))
        | ~ c_Relation_Oirrefl(U_11897,U_11899) ) ),
    inference(miniscope,[status(thm)],[f_3121_2]) ).

fof(f_3121_4,plain,
    ( ! [U_11900,U_11898] :
        ( c_Relation_Oirrefl(U_11898,U_11900)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_11898,U_11898)),hAPP(hAPP(c_Product__Type_OPair(U_11898,U_11898),sK276(U_11900,U_11898)),sK276(U_11900,U_11898))),U_11900)) )
    & ! [U_11899,U_11897] :
        ( ! [U_11893] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11897,U_11897)),hAPP(hAPP(c_Product__Type_OPair(U_11897,U_11897),U_11893),U_11893)),U_11899))
        | ~ c_Relation_Oirrefl(U_11897,U_11899) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK276]),skolemize(U_11894,sK276(U_11900,U_11898))],[f_3121_3]) ).

cnf(f_3121_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11897,U_11897)),hAPP(hAPP(c_Product__Type_OPair(U_11897,U_11897),U_11893),U_11893)),U_11899))
    | ~ c_Relation_Oirrefl(U_11897,U_11899) ),
    inference(clausify,[status(thm)],[f_3121_4]) ).

cnf(f_3121_6,plain,
    ( c_Relation_Oirrefl(U_11898,U_11900)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_11898,U_11898)),hAPP(hAPP(c_Product__Type_OPair(U_11898,U_11898),sK276(U_11900,U_11898)),sK276(U_11900,U_11898))),U_11900)) ),
    inference(clausify,[status(thm)],[f_3121_4]) ).

fof(f_3122_1,plain,
    ! [V_z_2] :
    ? [B_x,B_y] : V_z_2 = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),B_x),B_y)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(fof_nnf,[status(thm)],[fact_eq__Abs__Integ]) ).

fof(f_3122_2,plain,
    ! [U_11903] :
    ? [U_11902,U_11901] : U_11903 = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_11902),U_11901)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_3122_1]) ).

fof(f_3122_3,plain,
    ! [U_11903] :
    ? [U_11901] : U_11903 = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),sK277(U_11903)),U_11901)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK277]),skolemize(U_11902,sK277(U_11903))],[f_3122_2]) ).

fof(f_3122_4,plain,
    ! [U_11903] : U_11903 = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),sK277(U_11903)),sK278(U_11903))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK278]),skolemize(U_11901,sK278(U_11903))],[f_3122_3]) ).

cnf(f_3122_5,plain,
    U_11903 = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),sK277(U_11903)),sK278(U_11903))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_3122_4]) ).

fof(f_3123_1,plain,
    ! [V_r_2,V_b_2,V_a_2,T_b] : hAPP(c_Relation_OField(T_b),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(c_Relation_OField(T_b),V_r_2)),
    inference(fof_nnf,[status(thm)],[fact_Field__insert]) ).

fof(f_3123_2,plain,
    ! [U_11907,U_11906,U_11905,U_11904] : hAPP(c_Relation_OField(U_11904),hAPP(hAPP(c_Set_Oinsert(tc_prod(U_11904,U_11904)),hAPP(hAPP(c_Product__Type_OPair(U_11904,U_11904),U_11905),U_11906)),U_11907)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11904,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_11904),U_11905),hAPP(hAPP(c_Set_Oinsert(U_11904),U_11906),c_Orderings_Obot__class_Obot(tc_fun(U_11904,tc_HOL_Obool))))),hAPP(c_Relation_OField(U_11904),U_11907)),
    inference(variable_rename,[status(thm)],[f_3123_1]) ).

cnf(f_3123_3,plain,
    hAPP(c_Relation_OField(U_11904),hAPP(hAPP(c_Set_Oinsert(tc_prod(U_11904,U_11904)),hAPP(hAPP(c_Product__Type_OPair(U_11904,U_11904),U_11905),U_11906)),U_11907)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11904,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_11904),U_11905),hAPP(hAPP(c_Set_Oinsert(U_11904),U_11906),c_Orderings_Obot__class_Obot(tc_fun(U_11904,tc_HOL_Obool))))),hAPP(c_Relation_OField(U_11904),U_11907)),
    inference(clausify,[status(thm)],[f_3123_2]) ).

fof(f_3124_1,plain,
    ! [V_R_2,T_b] : hAPP(c_Relation_OField(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),V_R_2)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),c_Relation_OField(T_b)),V_R_2)),
    inference(fof_nnf,[status(thm)],[fact_Field__Union]) ).

fof(f_3124_2,plain,
    ! [U_11909,U_11908] : hAPP(c_Relation_OField(U_11908),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(U_11908,U_11908),tc_HOL_Obool),U_11909)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(U_11908,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_fun(tc_prod(U_11908,U_11908),tc_HOL_Obool),tc_fun(U_11908,tc_HOL_Obool),c_Relation_OField(U_11908)),U_11909)),
    inference(variable_rename,[status(thm)],[f_3124_1]) ).

cnf(f_3124_3,plain,
    hAPP(c_Relation_OField(U_11908),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(U_11908,U_11908),tc_HOL_Obool),U_11909)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(U_11908,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_fun(tc_prod(U_11908,U_11908),tc_HOL_Obool),tc_fun(U_11908,tc_HOL_Obool),c_Relation_OField(U_11908)),U_11909)),
    inference(clausify,[status(thm)],[f_3124_2]) ).

fof(f_3125_1,plain,
    ! [T_b] : hAPP(c_Relation_OField(T_b),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Field__empty]) ).

fof(f_3125_2,plain,
    ! [U_11910] : hAPP(c_Relation_OField(U_11910),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_11910,U_11910),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_11910,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3125_1]) ).

cnf(f_3125_3,plain,
    hAPP(c_Relation_OField(U_11910),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_11910,U_11910),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_11910,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3125_2]) ).

fof(f_3126_1,plain,
    ! [V_s_2,V_r_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OField(T_b),V_r_2)),hAPP(c_Relation_OField(T_b),V_s_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ),
    inference(fof_nnf,[status(thm)],[fact_mono__Field]) ).

fof(f_3126_2,plain,
    ! [U_11913,U_11912,U_11911] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11911,tc_HOL_Obool)),hAPP(c_Relation_OField(U_11911),U_11912)),hAPP(c_Relation_OField(U_11911),U_11913)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_11911,U_11911),tc_HOL_Obool)),U_11912),U_11913)) ),
    inference(variable_rename,[status(thm)],[f_3126_1]) ).

cnf(f_3126_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11911,tc_HOL_Obool)),hAPP(c_Relation_OField(U_11911),U_11912)),hAPP(c_Relation_OField(U_11911),U_11913)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_11911,U_11911),tc_HOL_Obool)),U_11912),U_11913)) ),
    inference(clausify,[status(thm)],[f_3126_2]) ).

fof(f_3127_1,plain,
    ! [V_s_2,V_r_2,T_b] : hAPP(c_Relation_OField(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OField(T_b),V_r_2)),hAPP(c_Relation_OField(T_b),V_s_2)),
    inference(fof_nnf,[status(thm)],[fact_Field__Un]) ).

fof(f_3127_2,plain,
    ! [U_11916,U_11915,U_11914] : hAPP(c_Relation_OField(U_11914),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_11914,U_11914),tc_HOL_Obool)),U_11915),U_11916)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11914,tc_HOL_Obool)),hAPP(c_Relation_OField(U_11914),U_11915)),hAPP(c_Relation_OField(U_11914),U_11916)),
    inference(variable_rename,[status(thm)],[f_3127_1]) ).

cnf(f_3127_3,plain,
    hAPP(c_Relation_OField(U_11914),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_11914,U_11914),tc_HOL_Obool)),U_11915),U_11916)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11914,tc_HOL_Obool)),hAPP(c_Relation_OField(U_11914),U_11915)),hAPP(c_Relation_OField(U_11914),U_11916)),
    inference(clausify,[status(thm)],[f_3127_2]) ).

fof(f_3128_1,plain,
    ! [V_r_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_OField(T_b),V_r_2)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__Field]) ).

fof(f_3128_2,plain,
    ! [U_11918,U_11917] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_11917),hAPP(c_Relation_OField(U_11917),U_11918)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_11917,U_11917)),U_11918)) ),
    inference(variable_rename,[status(thm)],[f_3128_1]) ).

cnf(f_3128_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_11917),hAPP(c_Relation_OField(U_11917),U_11918)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_11917,U_11917)),U_11918)) ),
    inference(clausify,[status(thm)],[f_3128_2]) ).

fof(f_3129_1,plain,
    ! [V_A_2,T_b] : c_Relation_OId__on(T_b,V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),T_b),c_Set_Oinsert(tc_prod(T_b,T_b))),hAPP(hAPP(c_COMBS(T_b,T_b,tc_prod(T_b,T_b)),c_Product__Type_OPair(T_b,T_b)),c_COMBI(T_b)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_Id__on__def]) ).

fof(f_3129_2,plain,
    ! [U_11920,U_11919] : c_Relation_OId__on(U_11919,U_11920) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11919,tc_fun(tc_prod(U_11919,U_11919),tc_HOL_Obool)),U_11920),hAPP(hAPP(c_COMBC(U_11919,tc_fun(tc_prod(U_11919,U_11919),tc_HOL_Obool),tc_fun(tc_prod(U_11919,U_11919),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_prod(U_11919,U_11919),tc_fun(tc_fun(tc_prod(U_11919,U_11919),tc_HOL_Obool),tc_fun(tc_prod(U_11919,U_11919),tc_HOL_Obool)),U_11919),c_Set_Oinsert(tc_prod(U_11919,U_11919))),hAPP(hAPP(c_COMBS(U_11919,U_11919,tc_prod(U_11919,U_11919)),c_Product__Type_OPair(U_11919,U_11919)),c_COMBI(U_11919)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_11919,U_11919),tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_3129_1]) ).

cnf(f_3129_3,plain,
    c_Relation_OId__on(U_11919,U_11920) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11919,tc_fun(tc_prod(U_11919,U_11919),tc_HOL_Obool)),U_11920),hAPP(hAPP(c_COMBC(U_11919,tc_fun(tc_prod(U_11919,U_11919),tc_HOL_Obool),tc_fun(tc_prod(U_11919,U_11919),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_prod(U_11919,U_11919),tc_fun(tc_fun(tc_prod(U_11919,U_11919),tc_HOL_Obool),tc_fun(tc_prod(U_11919,U_11919),tc_HOL_Obool)),U_11919),c_Set_Oinsert(tc_prod(U_11919,U_11919))),hAPP(hAPP(c_COMBS(U_11919,U_11919,tc_prod(U_11919,U_11919)),c_Product__Type_OPair(U_11919,U_11919)),c_COMBI(U_11919)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_11919,U_11919),tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_3129_2]) ).

fof(f_3130_1,plain,
    ! [V_r_2,V_A_2,T_b] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),T_b),c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),c_Relation_OImage(T_b,T_b,V_r_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_quotient__def]) ).

fof(f_3130_2,plain,
    ! [U_11923,U_11922,U_11921] : hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11921),U_11922),U_11923) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11921,tc_fun(tc_fun(U_11921,tc_HOL_Obool),tc_HOL_Obool)),U_11922),hAPP(hAPP(c_COMBC(U_11921,tc_fun(tc_fun(U_11921,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_11921,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11921,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(U_11921,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_11921,tc_HOL_Obool),tc_HOL_Obool)),U_11921),c_Set_Oinsert(tc_fun(U_11921,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_11921,tc_HOL_Obool),tc_fun(U_11921,tc_HOL_Obool),U_11921),c_Relation_OImage(U_11921,U_11921,U_11923)),hAPP(hAPP(c_COMBC(U_11921,tc_fun(U_11921,tc_HOL_Obool),tc_fun(U_11921,tc_HOL_Obool)),c_Set_Oinsert(U_11921)),c_Orderings_Obot__class_Obot(tc_fun(U_11921,tc_HOL_Obool)))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_11921,tc_HOL_Obool),tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_3130_1]) ).

cnf(f_3130_3,plain,
    hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11921),U_11922),U_11923) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11921,tc_fun(tc_fun(U_11921,tc_HOL_Obool),tc_HOL_Obool)),U_11922),hAPP(hAPP(c_COMBC(U_11921,tc_fun(tc_fun(U_11921,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_11921,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11921,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(U_11921,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_11921,tc_HOL_Obool),tc_HOL_Obool)),U_11921),c_Set_Oinsert(tc_fun(U_11921,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_11921,tc_HOL_Obool),tc_fun(U_11921,tc_HOL_Obool),U_11921),c_Relation_OImage(U_11921,U_11921,U_11923)),hAPP(hAPP(c_COMBC(U_11921,tc_fun(U_11921,tc_HOL_Obool),tc_fun(U_11921,tc_HOL_Obool)),c_Set_Oinsert(U_11921)),c_Orderings_Obot__class_Obot(tc_fun(U_11921,tc_HOL_Obool)))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_11921,tc_HOL_Obool),tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_3130_2]) ).

fof(f_3131_1,plain,
    ! [V_A_2,V_r_2,T_c,V_b_2,T_b] :
      ( ? [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),V_b_2)),V_r_2)) )
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2))) ),
    inference(fof_nnf,[status(thm)],[fact_ImageE]) ).

fof(f_3131_2,plain,
    ! [U_11929,U_11928,U_11927,U_11926,U_11925] :
      ( ? [U_11924] :
          ( hBOOL(hAPP(hAPP(c_member(U_11927),U_11924),U_11929))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_11927,U_11925)),hAPP(hAPP(c_Product__Type_OPair(U_11927,U_11925),U_11924),U_11926)),U_11928)) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_11925),U_11926),hAPP(c_Relation_OImage(U_11927,U_11925,U_11928),U_11929))) ),
    inference(variable_rename,[status(thm)],[f_3131_1]) ).

fof(f_3131_3,plain,
    ! [U_11929,U_11928,U_11927,U_11926,U_11925] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_11927),sK279(U_11929,U_11928,U_11927,U_11926,U_11925)),U_11929))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_11927,U_11925)),hAPP(hAPP(c_Product__Type_OPair(U_11927,U_11925),sK279(U_11929,U_11928,U_11927,U_11926,U_11925)),U_11926)),U_11928)) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_11925),U_11926),hAPP(c_Relation_OImage(U_11927,U_11925,U_11928),U_11929))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK279]),skolemize(U_11924,sK279(U_11929,U_11928,U_11927,U_11926,U_11925))],[f_3131_2]) ).

cnf(f_3131_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11927,U_11925)),hAPP(hAPP(c_Product__Type_OPair(U_11927,U_11925),sK279(U_11929,U_11928,U_11927,U_11926,U_11925)),U_11926)),U_11928))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11925),U_11926),hAPP(c_Relation_OImage(U_11927,U_11925,U_11928),U_11929))) ),
    inference(clausify,[status(thm)],[f_3131_3]) ).

cnf(f_3131_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11927),sK279(U_11929,U_11928,U_11927,U_11926,U_11925)),U_11929))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11925),U_11926),hAPP(c_Relation_OImage(U_11927,U_11925,U_11928),U_11929))) ),
    inference(clausify,[status(thm)],[f_3131_3]) ).

fof(f_3132_1,plain,
    ! [V_r_2,T_b] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_quotient__empty]) ).

fof(f_3132_2,plain,
    ! [U_11931,U_11930] : hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11930),c_Orderings_Obot__class_Obot(tc_fun(U_11930,tc_HOL_Obool))),U_11931) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_11930,tc_HOL_Obool),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3132_1]) ).

cnf(f_3132_3,plain,
    hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11930),c_Orderings_Obot__class_Obot(tc_fun(U_11930,tc_HOL_Obool))),U_11931) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_11930,tc_HOL_Obool),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3132_2]) ).

fof(f_3133_1,plain,
    ! [V_r_2,V_A_2,T_b] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)
        | V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
      & ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
        | c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)) != hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_quotient__is__empty2]) ).

fof(f_3133_2,plain,
    ! [U_11934,U_11933,U_11932] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_11932,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11932),U_11933),U_11934)
        | U_11933 != c_Orderings_Obot__class_Obot(tc_fun(U_11932,tc_HOL_Obool)) )
      & ( U_11933 = c_Orderings_Obot__class_Obot(tc_fun(U_11932,tc_HOL_Obool))
        | c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_11932,tc_HOL_Obool),tc_HOL_Obool)) != hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11932),U_11933),U_11934) ) ),
    inference(variable_rename,[status(thm)],[f_3133_1]) ).

fof(f_3133_3,plain,
    ( ! [U_11940,U_11938,U_11936] :
        ( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_11936,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11936),U_11938),U_11940)
        | U_11938 != c_Orderings_Obot__class_Obot(tc_fun(U_11936,tc_HOL_Obool)) )
    & ! [U_11939,U_11937,U_11935] :
        ( U_11937 = c_Orderings_Obot__class_Obot(tc_fun(U_11935,tc_HOL_Obool))
        | c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_11935,tc_HOL_Obool),tc_HOL_Obool)) != hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11935),U_11937),U_11939) ) ),
    inference(miniscope,[status(thm)],[f_3133_2]) ).

cnf(f_3133_4,plain,
    ( U_11937 = c_Orderings_Obot__class_Obot(tc_fun(U_11935,tc_HOL_Obool))
    | c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_11935,tc_HOL_Obool),tc_HOL_Obool)) != hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11935),U_11937),U_11939) ),
    inference(clausify,[status(thm)],[f_3133_3]) ).

cnf(f_3133_5,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_11936,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11936),U_11938),U_11940)
    | U_11938 != c_Orderings_Obot__class_Obot(tc_fun(U_11936,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3133_3]) ).

fof(f_3134_1,plain,
    ! [V_r_2,V_A_2,T_b] :
      ( ( hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))
        | V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
      & ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
        | hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_quotient__is__empty]) ).

fof(f_3134_2,plain,
    ! [U_11943,U_11942,U_11941] :
      ( ( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11941),U_11942),U_11943) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_11941,tc_HOL_Obool),tc_HOL_Obool))
        | U_11942 != c_Orderings_Obot__class_Obot(tc_fun(U_11941,tc_HOL_Obool)) )
      & ( U_11942 = c_Orderings_Obot__class_Obot(tc_fun(U_11941,tc_HOL_Obool))
        | hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11941),U_11942),U_11943) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_11941,tc_HOL_Obool),tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_3134_1]) ).

fof(f_3134_3,plain,
    ( ! [U_11949,U_11947,U_11945] :
        ( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11945),U_11947),U_11949) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_11945,tc_HOL_Obool),tc_HOL_Obool))
        | U_11947 != c_Orderings_Obot__class_Obot(tc_fun(U_11945,tc_HOL_Obool)) )
    & ! [U_11948,U_11946,U_11944] :
        ( U_11946 = c_Orderings_Obot__class_Obot(tc_fun(U_11944,tc_HOL_Obool))
        | hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11944),U_11946),U_11948) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_11944,tc_HOL_Obool),tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_3134_2]) ).

cnf(f_3134_4,plain,
    ( U_11946 = c_Orderings_Obot__class_Obot(tc_fun(U_11944,tc_HOL_Obool))
    | hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11944),U_11946),U_11948) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_11944,tc_HOL_Obool),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3134_3]) ).

cnf(f_3134_5,plain,
    ( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11945),U_11947),U_11949) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_11945,tc_HOL_Obool),tc_HOL_Obool))
    | U_11947 != c_Orderings_Obot__class_Obot(tc_fun(U_11945,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3134_3]) ).

fof(f_3135_1,plain,
    ! [V_A_2,T_b] : c_Relation_OId__on(T_b,V_A_2) = hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),c_fequal))),V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_Id__on__def_H]) ).

fof(f_3135_2,plain,
    ! [U_11951,U_11950] : c_Relation_OId__on(U_11950,U_11951) = hAPP(c_Product__Type_Oprod_Oprod__case(U_11950,U_11950,tc_HOL_Obool),hAPP(hAPP(c_COMBS(U_11950,tc_HOL_Obool,tc_fun(U_11950,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11950,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_HOL_Obool,tc_fun(U_11950,tc_HOL_Obool)),U_11950),c_COMBC(U_11950,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11950,tc_HOL_Obool),tc_fun(U_11950,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_11950),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11950),c_fconj)),c_fequal))),U_11951)),
    inference(variable_rename,[status(thm)],[f_3135_1]) ).

cnf(f_3135_3,plain,
    c_Relation_OId__on(U_11950,U_11951) = hAPP(c_Product__Type_Oprod_Oprod__case(U_11950,U_11950,tc_HOL_Obool),hAPP(hAPP(c_COMBS(U_11950,tc_HOL_Obool,tc_fun(U_11950,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11950,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_HOL_Obool,tc_fun(U_11950,tc_HOL_Obool)),U_11950),c_COMBC(U_11950,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11950,tc_HOL_Obool),tc_fun(U_11950,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_11950),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11950),c_fconj)),c_fequal))),U_11951)),
    inference(clausify,[status(thm)],[f_3135_2]) ).

fof(f_3136_1,plain,
    ! [T_b] : c_Relation_OId__on(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Id__on__empty]) ).

fof(f_3136_2,plain,
    ! [U_11952] : c_Relation_OId__on(U_11952,c_Orderings_Obot__class_Obot(tc_fun(U_11952,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_11952,U_11952),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3136_1]) ).

cnf(f_3136_3,plain,
    c_Relation_OId__on(U_11952,c_Orderings_Obot__class_Obot(tc_fun(U_11952,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_11952,U_11952),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3136_2]) ).

fof(f_3137_1,plain,
    ! [V_B_2,V_A_2,T_b] : hAPP(c_Relation_OImage(T_b,T_b,c_Relation_OId__on(T_b,V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),
    inference(fof_nnf,[status(thm)],[fact_Image__Id__on]) ).

fof(f_3137_2,plain,
    ! [U_11955,U_11954,U_11953] : hAPP(c_Relation_OImage(U_11953,U_11953,c_Relation_OId__on(U_11953,U_11954)),U_11955) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11953,tc_HOL_Obool)),U_11954),U_11955),
    inference(variable_rename,[status(thm)],[f_3137_1]) ).

cnf(f_3137_3,plain,
    hAPP(c_Relation_OImage(U_11953,U_11953,c_Relation_OId__on(U_11953,U_11954)),U_11955) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11953,tc_HOL_Obool)),U_11954),U_11955),
    inference(clausify,[status(thm)],[f_3137_2]) ).

fof(f_3138_1,plain,
    ! [V_a_2,V_A_2,V_r_2,T_b] :
      ( hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_r_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_r_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | ~ c_Fun_Oinj__on(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),T_b),c_Equiv__Relations_Oquotient(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_r_2),V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_quotient__diff1]) ).

fof(f_3138_2,plain,
    ! [U_11959,U_11958,U_11957,U_11956] :
      ( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11956),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11956,tc_HOL_Obool)),U_11958),hAPP(hAPP(c_Set_Oinsert(U_11956),U_11959),c_Orderings_Obot__class_Obot(tc_fun(U_11956,tc_HOL_Obool))))),U_11957) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(U_11956,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11956),U_11958),U_11957)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11956),hAPP(hAPP(c_Set_Oinsert(U_11956),U_11959),c_Orderings_Obot__class_Obot(tc_fun(U_11956,tc_HOL_Obool)))),U_11957))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11956),U_11959),U_11958))
      | ~ c_Fun_Oinj__on(U_11956,tc_fun(tc_fun(U_11956,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11956,tc_fun(tc_prod(U_11956,U_11956),tc_HOL_Obool),tc_fun(tc_fun(U_11956,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11956,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_11956,U_11956),tc_HOL_Obool),tc_fun(tc_fun(U_11956,tc_HOL_Obool),tc_HOL_Obool)),U_11956),c_Equiv__Relations_Oquotient(U_11956)),hAPP(hAPP(c_COMBC(U_11956,tc_fun(U_11956,tc_HOL_Obool),tc_fun(U_11956,tc_HOL_Obool)),c_Set_Oinsert(U_11956)),c_Orderings_Obot__class_Obot(tc_fun(U_11956,tc_HOL_Obool))))),U_11957),U_11958) ),
    inference(variable_rename,[status(thm)],[f_3138_1]) ).

cnf(f_3138_3,plain,
    ( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11956),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11956,tc_HOL_Obool)),U_11958),hAPP(hAPP(c_Set_Oinsert(U_11956),U_11959),c_Orderings_Obot__class_Obot(tc_fun(U_11956,tc_HOL_Obool))))),U_11957) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(U_11956,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11956),U_11958),U_11957)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11956),hAPP(hAPP(c_Set_Oinsert(U_11956),U_11959),c_Orderings_Obot__class_Obot(tc_fun(U_11956,tc_HOL_Obool)))),U_11957))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11956),U_11959),U_11958))
    | ~ c_Fun_Oinj__on(U_11956,tc_fun(tc_fun(U_11956,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11956,tc_fun(tc_prod(U_11956,U_11956),tc_HOL_Obool),tc_fun(tc_fun(U_11956,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11956,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_11956,U_11956),tc_HOL_Obool),tc_fun(tc_fun(U_11956,tc_HOL_Obool),tc_HOL_Obool)),U_11956),c_Equiv__Relations_Oquotient(U_11956)),hAPP(hAPP(c_COMBC(U_11956,tc_fun(U_11956,tc_HOL_Obool),tc_fun(U_11956,tc_HOL_Obool)),c_Set_Oinsert(U_11956)),c_Orderings_Obot__class_Obot(tc_fun(U_11956,tc_HOL_Obool))))),U_11957),U_11958) ),
    inference(clausify,[status(thm)],[f_3138_2]) ).

fof(f_3139_1,plain,
    ! [V_r_2,V_A_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_quotientI]) ).

fof(f_3139_2,plain,
    ! [U_11963,U_11962,U_11961,U_11960] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_11960,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11960,U_11960,U_11963),hAPP(hAPP(c_Set_Oinsert(U_11960),U_11961),c_Orderings_Obot__class_Obot(tc_fun(U_11960,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11960),U_11962),U_11963)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11960),U_11961),U_11962)) ),
    inference(variable_rename,[status(thm)],[f_3139_1]) ).

cnf(f_3139_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_11960,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11960,U_11960,U_11963),hAPP(hAPP(c_Set_Oinsert(U_11960),U_11961),c_Orderings_Obot__class_Obot(tc_fun(U_11960,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11960),U_11962),U_11963)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11960),U_11961),U_11962)) ),
    inference(clausify,[status(thm)],[f_3139_2]) ).

fof(f_3140_1,plain,
    ! [V_A_2,T_b,V_b_2,V_a_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Relation_OId__on(T_b,V_A_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | V_a_2 != V_b_2 ),
    inference(fof_nnf,[status(thm)],[fact_Id__on__eqI]) ).

fof(f_3140_2,plain,
    ! [U_11967,U_11966,U_11965,U_11964] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11966,U_11966)),hAPP(hAPP(c_Product__Type_OPair(U_11966,U_11966),U_11964),U_11965)),c_Relation_OId__on(U_11966,U_11967)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11966),U_11964),U_11967))
      | U_11964 != U_11965 ),
    inference(variable_rename,[status(thm)],[f_3140_1]) ).

cnf(f_3140_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11966,U_11966)),hAPP(hAPP(c_Product__Type_OPair(U_11966,U_11966),U_11964),U_11965)),c_Relation_OId__on(U_11966,U_11967)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11966),U_11964),U_11967))
    | U_11964 != U_11965 ),
    inference(clausify,[status(thm)],[f_3140_2]) ).

fof(f_3141_1,plain,
    ! [V_A_2,V_y_2,V_x_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Relation_OId__on(T_b,V_A_2)))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
        | V_x_2 != V_y_2 )
      & ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
          & V_x_2 = V_y_2 )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Relation_OId__on(T_b,V_A_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_Id__on__iff]) ).

fof(f_3141_2,plain,
    ! [U_11971,U_11970,U_11969,U_11968] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11968,U_11968)),hAPP(hAPP(c_Product__Type_OPair(U_11968,U_11968),U_11969),U_11970)),c_Relation_OId__on(U_11968,U_11971)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_11968),U_11969),U_11971))
        | U_11969 != U_11970 )
      & ( ( hBOOL(hAPP(hAPP(c_member(U_11968),U_11969),U_11971))
          & U_11969 = U_11970 )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11968,U_11968)),hAPP(hAPP(c_Product__Type_OPair(U_11968,U_11968),U_11969),U_11970)),c_Relation_OId__on(U_11968,U_11971))) ) ),
    inference(variable_rename,[status(thm)],[f_3141_1]) ).

fof(f_3141_3,plain,
    ( ! [U_11979,U_11977,U_11975,U_11973] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11973,U_11973)),hAPP(hAPP(c_Product__Type_OPair(U_11973,U_11973),U_11975),U_11977)),c_Relation_OId__on(U_11973,U_11979)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_11973),U_11975),U_11979))
        | U_11975 != U_11977 )
    & ! [U_11978,U_11976,U_11974,U_11972] :
        ( ( hBOOL(hAPP(hAPP(c_member(U_11972),U_11974),U_11978))
          & U_11974 = U_11976 )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11972,U_11972)),hAPP(hAPP(c_Product__Type_OPair(U_11972,U_11972),U_11974),U_11976)),c_Relation_OId__on(U_11972,U_11978))) ) ),
    inference(miniscope,[status(thm)],[f_3141_2]) ).

cnf(f_3141_4,plain,
    ( U_11974 = U_11976
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11972,U_11972)),hAPP(hAPP(c_Product__Type_OPair(U_11972,U_11972),U_11974),U_11976)),c_Relation_OId__on(U_11972,U_11978))) ),
    inference(clausify,[status(thm)],[f_3141_3]) ).

cnf(f_3141_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11972),U_11974),U_11978))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11972,U_11972)),hAPP(hAPP(c_Product__Type_OPair(U_11972,U_11972),U_11974),U_11976)),c_Relation_OId__on(U_11972,U_11978))) ),
    inference(clausify,[status(thm)],[f_3141_3]) ).

cnf(f_3141_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11973,U_11973)),hAPP(hAPP(c_Product__Type_OPair(U_11973,U_11973),U_11975),U_11977)),c_Relation_OId__on(U_11973,U_11979)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11973),U_11975),U_11979))
    | U_11975 != U_11977 ),
    inference(clausify,[status(thm)],[f_3141_3]) ).

fof(f_3142_1,plain,
    ! [V_r_2,V_x_2,T_b] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_r_2) = hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))),
    inference(fof_nnf,[status(thm)],[fact_singleton__quotient]) ).

fof(f_3142_2,plain,
    ! [U_11982,U_11981,U_11980] : hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11980),hAPP(hAPP(c_Set_Oinsert(U_11980),U_11981),c_Orderings_Obot__class_Obot(tc_fun(U_11980,tc_HOL_Obool)))),U_11982) = hAPP(hAPP(c_Set_Oinsert(tc_fun(U_11980,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11980,U_11980,U_11982),hAPP(hAPP(c_Set_Oinsert(U_11980),U_11981),c_Orderings_Obot__class_Obot(tc_fun(U_11980,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_11980,tc_HOL_Obool),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_3142_1]) ).

cnf(f_3142_3,plain,
    hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11980),hAPP(hAPP(c_Set_Oinsert(U_11980),U_11981),c_Orderings_Obot__class_Obot(tc_fun(U_11980,tc_HOL_Obool)))),U_11982) = hAPP(hAPP(c_Set_Oinsert(tc_fun(U_11980,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11980,U_11980,U_11982),hAPP(hAPP(c_Set_Oinsert(U_11980),U_11981),c_Orderings_Obot__class_Obot(tc_fun(U_11980,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_11980,tc_HOL_Obool),tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_3142_2]) ).

fof(f_3143_1,plain,
    ! [V_r_2,V_A_2,T_b] :
      ( hAPP(c_Finite__Set_Ocard(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2)
      | ~ c_Fun_Oinj__on(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),T_b),c_Equiv__Relations_Oquotient(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_r_2),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__quotient__disjoint]) ).

fof(f_3143_2,plain,
    ! [U_11985,U_11984,U_11983] :
      ( hAPP(c_Finite__Set_Ocard(tc_fun(U_11983,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11983),U_11984),U_11985)) = hAPP(c_Finite__Set_Ocard(U_11983),U_11984)
      | ~ c_Fun_Oinj__on(U_11983,tc_fun(tc_fun(U_11983,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11983,tc_fun(tc_prod(U_11983,U_11983),tc_HOL_Obool),tc_fun(tc_fun(U_11983,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11983,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_11983,U_11983),tc_HOL_Obool),tc_fun(tc_fun(U_11983,tc_HOL_Obool),tc_HOL_Obool)),U_11983),c_Equiv__Relations_Oquotient(U_11983)),hAPP(hAPP(c_COMBC(U_11983,tc_fun(U_11983,tc_HOL_Obool),tc_fun(U_11983,tc_HOL_Obool)),c_Set_Oinsert(U_11983)),c_Orderings_Obot__class_Obot(tc_fun(U_11983,tc_HOL_Obool))))),U_11985),U_11984)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11983),U_11984)) ),
    inference(variable_rename,[status(thm)],[f_3143_1]) ).

cnf(f_3143_3,plain,
    ( hAPP(c_Finite__Set_Ocard(tc_fun(U_11983,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11983),U_11984),U_11985)) = hAPP(c_Finite__Set_Ocard(U_11983),U_11984)
    | ~ c_Fun_Oinj__on(U_11983,tc_fun(tc_fun(U_11983,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11983,tc_fun(tc_prod(U_11983,U_11983),tc_HOL_Obool),tc_fun(tc_fun(U_11983,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11983,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_11983,U_11983),tc_HOL_Obool),tc_fun(tc_fun(U_11983,tc_HOL_Obool),tc_HOL_Obool)),U_11983),c_Equiv__Relations_Oquotient(U_11983)),hAPP(hAPP(c_COMBC(U_11983,tc_fun(U_11983,tc_HOL_Obool),tc_fun(U_11983,tc_HOL_Obool)),c_Set_Oinsert(U_11983)),c_Orderings_Obot__class_Obot(tc_fun(U_11983,tc_HOL_Obool))))),U_11985),U_11984)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11983),U_11984)) ),
    inference(clausify,[status(thm)],[f_3143_2]) ).

fof(f_3144_1,plain,
    ! [V_b_2,V_a_2,V_x_2,V_r_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))))
      | ~ c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_equiv__class__nondisjoint]) ).

fof(f_3144_2,plain,
    ! [U_11991,U_11990,U_11989,U_11988,U_11987,U_11986] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11986,U_11986)),hAPP(hAPP(c_Product__Type_OPair(U_11986,U_11986),U_11990),U_11991)),U_11988))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11986),U_11989),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11986,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11986,U_11986,U_11988),hAPP(hAPP(c_Set_Oinsert(U_11986),U_11990),c_Orderings_Obot__class_Obot(tc_fun(U_11986,tc_HOL_Obool))))),hAPP(c_Relation_OImage(U_11986,U_11986,U_11988),hAPP(hAPP(c_Set_Oinsert(U_11986),U_11991),c_Orderings_Obot__class_Obot(tc_fun(U_11986,tc_HOL_Obool)))))))
      | ~ c_Equiv__Relations_Oequiv(U_11986,U_11987,U_11988) ),
    inference(variable_rename,[status(thm)],[f_3144_1]) ).

cnf(f_3144_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11986,U_11986)),hAPP(hAPP(c_Product__Type_OPair(U_11986,U_11986),U_11990),U_11991)),U_11988))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11986),U_11989),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11986,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11986,U_11986,U_11988),hAPP(hAPP(c_Set_Oinsert(U_11986),U_11990),c_Orderings_Obot__class_Obot(tc_fun(U_11986,tc_HOL_Obool))))),hAPP(c_Relation_OImage(U_11986,U_11986,U_11988),hAPP(hAPP(c_Set_Oinsert(U_11986),U_11991),c_Orderings_Obot__class_Obot(tc_fun(U_11986,tc_HOL_Obool)))))))
    | ~ c_Equiv__Relations_Oequiv(U_11986,U_11987,U_11988) ),
    inference(clausify,[status(thm)],[f_3144_2]) ).

fof(f_3145_1,plain,
    ! [V_a_2,V_b_2,V_r_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
      | ~ c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_subset__equiv__class]) ).

fof(f_3145_2,plain,
    ! [U_11996,U_11995,U_11994,U_11993,U_11992] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11992,U_11992)),hAPP(hAPP(c_Product__Type_OPair(U_11992,U_11992),U_11996),U_11995)),U_11994))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11992),U_11995),U_11993))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11992,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11992,U_11992,U_11994),hAPP(hAPP(c_Set_Oinsert(U_11992),U_11995),c_Orderings_Obot__class_Obot(tc_fun(U_11992,tc_HOL_Obool))))),hAPP(c_Relation_OImage(U_11992,U_11992,U_11994),hAPP(hAPP(c_Set_Oinsert(U_11992),U_11996),c_Orderings_Obot__class_Obot(tc_fun(U_11992,tc_HOL_Obool))))))
      | ~ c_Equiv__Relations_Oequiv(U_11992,U_11993,U_11994) ),
    inference(variable_rename,[status(thm)],[f_3145_1]) ).

cnf(f_3145_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11992,U_11992)),hAPP(hAPP(c_Product__Type_OPair(U_11992,U_11992),U_11996),U_11995)),U_11994))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11992),U_11995),U_11993))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11992,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11992,U_11992,U_11994),hAPP(hAPP(c_Set_Oinsert(U_11992),U_11995),c_Orderings_Obot__class_Obot(tc_fun(U_11992,tc_HOL_Obool))))),hAPP(c_Relation_OImage(U_11992,U_11992,U_11994),hAPP(hAPP(c_Set_Oinsert(U_11992),U_11996),c_Orderings_Obot__class_Obot(tc_fun(U_11992,tc_HOL_Obool))))))
    | ~ c_Equiv__Relations_Oequiv(U_11992,U_11993,U_11994) ),
    inference(clausify,[status(thm)],[f_3145_2]) ).

fof(f_3146_1,plain,
    ! [V_r_2,V_A_2,V_X_2,T_b] :
      ( ? [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
          & V_X_2 = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_quotientE]) ).

fof(f_3146_2,plain,
    ! [U_12001,U_12000,U_11999,U_11998] :
      ( ? [U_11997] :
          ( hBOOL(hAPP(hAPP(c_member(U_11998),U_11997),U_12000))
          & U_11999 = hAPP(c_Relation_OImage(U_11998,U_11998,U_12001),hAPP(hAPP(c_Set_Oinsert(U_11998),U_11997),c_Orderings_Obot__class_Obot(tc_fun(U_11998,tc_HOL_Obool)))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11998,tc_HOL_Obool)),U_11999),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11998),U_12000),U_12001))) ),
    inference(variable_rename,[status(thm)],[f_3146_1]) ).

fof(f_3146_3,plain,
    ! [U_12001,U_12000,U_11999,U_11998] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_11998),sK280(U_12001,U_12000,U_11999,U_11998)),U_12000))
        & U_11999 = hAPP(c_Relation_OImage(U_11998,U_11998,U_12001),hAPP(hAPP(c_Set_Oinsert(U_11998),sK280(U_12001,U_12000,U_11999,U_11998)),c_Orderings_Obot__class_Obot(tc_fun(U_11998,tc_HOL_Obool)))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11998,tc_HOL_Obool)),U_11999),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11998),U_12000),U_12001))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK280]),skolemize(U_11997,sK280(U_12001,U_12000,U_11999,U_11998))],[f_3146_2]) ).

cnf(f_3146_4,plain,
    ( U_11999 = hAPP(c_Relation_OImage(U_11998,U_11998,U_12001),hAPP(hAPP(c_Set_Oinsert(U_11998),sK280(U_12001,U_12000,U_11999,U_11998)),c_Orderings_Obot__class_Obot(tc_fun(U_11998,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11998,tc_HOL_Obool)),U_11999),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11998),U_12000),U_12001))) ),
    inference(clausify,[status(thm)],[f_3146_3]) ).

cnf(f_3146_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11998),sK280(U_12001,U_12000,U_11999,U_11998)),U_12000))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11998,tc_HOL_Obool)),U_11999),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11998),U_12000),U_12001))) ),
    inference(clausify,[status(thm)],[f_3146_3]) ).

fof(f_3147_1,plain,
    c_Equiv__Relations_Oequiv(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Int_Ointrel),
    inference(fof_nnf,[status(thm)],[fact_equiv__intrel]) ).

cnf(f_3147_2,plain,
    c_Equiv__Relations_Oequiv(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Int_Ointrel),
    inference(clausify,[status(thm)],[f_3147_1]) ).

fof(f_3148_1,plain,
    ! [V_r_2,V_A_2,T_b] :
      ( c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)) = V_A_2
      | ~ c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_Union__quotient]) ).

fof(f_3148_2,plain,
    ! [U_12004,U_12003,U_12002] :
      ( c_Complete__Lattice_OSup__class_OSup(tc_fun(U_12002,tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12002),U_12003),U_12004)) = U_12003
      | ~ c_Equiv__Relations_Oequiv(U_12002,U_12003,U_12004) ),
    inference(variable_rename,[status(thm)],[f_3148_1]) ).

cnf(f_3148_3,plain,
    ( c_Complete__Lattice_OSup__class_OSup(tc_fun(U_12002,tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12002),U_12003),U_12004)) = U_12003
    | ~ c_Equiv__Relations_Oequiv(U_12002,U_12003,U_12004) ),
    inference(clausify,[status(thm)],[f_3148_2]) ).

fof(f_3149_1,plain,
    ! [V_a_2,V_r_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | ~ c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_equiv__class__self]) ).

fof(f_3149_2,plain,
    ! [U_12008,U_12007,U_12006,U_12005] :
      ( hBOOL(hAPP(hAPP(c_member(U_12005),U_12008),hAPP(c_Relation_OImage(U_12005,U_12005,U_12007),hAPP(hAPP(c_Set_Oinsert(U_12005),U_12008),c_Orderings_Obot__class_Obot(tc_fun(U_12005,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12005),U_12008),U_12006))
      | ~ c_Equiv__Relations_Oequiv(U_12005,U_12006,U_12007) ),
    inference(variable_rename,[status(thm)],[f_3149_1]) ).

cnf(f_3149_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12005),U_12008),hAPP(c_Relation_OImage(U_12005,U_12005,U_12007),hAPP(hAPP(c_Set_Oinsert(U_12005),U_12008),c_Orderings_Obot__class_Obot(tc_fun(U_12005,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12005),U_12008),U_12006))
    | ~ c_Equiv__Relations_Oequiv(U_12005,U_12006,U_12007) ),
    inference(clausify,[status(thm)],[f_3149_2]) ).

fof(f_3150_1,plain,
    ! [V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_Y_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | V_X_2 = V_Y_2
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
      | ~ c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_quotient__disj]) ).

fof(f_3150_2,plain,
    ! [U_12013,U_12012,U_12011,U_12010,U_12009] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12009,tc_HOL_Obool)),U_12012),U_12013) = c_Orderings_Obot__class_Obot(tc_fun(U_12009,tc_HOL_Obool))
      | U_12012 = U_12013
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12009,tc_HOL_Obool)),U_12013),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12009),U_12010),U_12011)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12009,tc_HOL_Obool)),U_12012),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12009),U_12010),U_12011)))
      | ~ c_Equiv__Relations_Oequiv(U_12009,U_12010,U_12011) ),
    inference(variable_rename,[status(thm)],[f_3150_1]) ).

cnf(f_3150_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12009,tc_HOL_Obool)),U_12012),U_12013) = c_Orderings_Obot__class_Obot(tc_fun(U_12009,tc_HOL_Obool))
    | U_12012 = U_12013
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12009,tc_HOL_Obool)),U_12013),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12009),U_12010),U_12011)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12009,tc_HOL_Obool)),U_12012),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12009),U_12010),U_12011)))
    | ~ c_Equiv__Relations_Oequiv(U_12009,U_12010,U_12011) ),
    inference(clausify,[status(thm)],[f_3150_2]) ).

fof(f_3151_1,plain,
    ! [V_b_2,V_a_2,V_r_2,V_A_2,T_b] :
      ( hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
      | ~ c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_equiv__class__eq]) ).

fof(f_3151_2,plain,
    ! [U_12018,U_12017,U_12016,U_12015,U_12014] :
      ( hAPP(c_Relation_OImage(U_12014,U_12014,U_12016),hAPP(hAPP(c_Set_Oinsert(U_12014),U_12017),c_Orderings_Obot__class_Obot(tc_fun(U_12014,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(U_12014,U_12014,U_12016),hAPP(hAPP(c_Set_Oinsert(U_12014),U_12018),c_Orderings_Obot__class_Obot(tc_fun(U_12014,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12014,U_12014)),hAPP(hAPP(c_Product__Type_OPair(U_12014,U_12014),U_12017),U_12018)),U_12016))
      | ~ c_Equiv__Relations_Oequiv(U_12014,U_12015,U_12016) ),
    inference(variable_rename,[status(thm)],[f_3151_1]) ).

cnf(f_3151_3,plain,
    ( hAPP(c_Relation_OImage(U_12014,U_12014,U_12016),hAPP(hAPP(c_Set_Oinsert(U_12014),U_12017),c_Orderings_Obot__class_Obot(tc_fun(U_12014,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(U_12014,U_12014,U_12016),hAPP(hAPP(c_Set_Oinsert(U_12014),U_12018),c_Orderings_Obot__class_Obot(tc_fun(U_12014,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12014,U_12014)),hAPP(hAPP(c_Product__Type_OPair(U_12014,U_12014),U_12017),U_12018)),U_12016))
    | ~ c_Equiv__Relations_Oequiv(U_12014,U_12015,U_12016) ),
    inference(clausify,[status(thm)],[f_3151_2]) ).

fof(f_3152_1,plain,
    ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
      ( ( ( V_X_2 = V_Y_2
          | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) )
        & ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
          | V_X_2 != V_Y_2 ) )
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_Y_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_X_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
      | ~ c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_quotient__eq__iff]) ).

fof(f_3152_2,plain,
    ! [U_12025,U_12024,U_12023,U_12022,U_12021,U_12020,U_12019] :
      ( ( ( U_12022 = U_12023
          | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12019,U_12019)),hAPP(hAPP(c_Product__Type_OPair(U_12019,U_12019),U_12024),U_12025)),U_12021)) )
        & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12019,U_12019)),hAPP(hAPP(c_Product__Type_OPair(U_12019,U_12019),U_12024),U_12025)),U_12021))
          | U_12022 != U_12023 ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_12019),U_12025),U_12023))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12019),U_12024),U_12022))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12019,tc_HOL_Obool)),U_12023),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12019),U_12020),U_12021)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12019,tc_HOL_Obool)),U_12022),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12019),U_12020),U_12021)))
      | ~ c_Equiv__Relations_Oequiv(U_12019,U_12020,U_12021) ),
    inference(variable_rename,[status(thm)],[f_3152_1]) ).

cnf(f_3152_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12019,U_12019)),hAPP(hAPP(c_Product__Type_OPair(U_12019,U_12019),U_12024),U_12025)),U_12021))
    | U_12022 != U_12023
    | ~ hBOOL(hAPP(hAPP(c_member(U_12019),U_12025),U_12023))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12019),U_12024),U_12022))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12019,tc_HOL_Obool)),U_12023),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12019),U_12020),U_12021)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12019,tc_HOL_Obool)),U_12022),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12019),U_12020),U_12021)))
    | ~ c_Equiv__Relations_Oequiv(U_12019,U_12020,U_12021) ),
    inference(clausify,[status(thm)],[f_3152_2]) ).

cnf(f_3152_4,plain,
    ( U_12022 = U_12023
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12019,U_12019)),hAPP(hAPP(c_Product__Type_OPair(U_12019,U_12019),U_12024),U_12025)),U_12021))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12019),U_12025),U_12023))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12019),U_12024),U_12022))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12019,tc_HOL_Obool)),U_12023),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12019),U_12020),U_12021)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12019,tc_HOL_Obool)),U_12022),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12019),U_12020),U_12021)))
    | ~ c_Equiv__Relations_Oequiv(U_12019,U_12020,U_12021) ),
    inference(clausify,[status(thm)],[f_3152_2]) ).

fof(f_3153_1,plain,
    ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
      ( V_X_2 = V_Y_2
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_Y_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_X_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
      | ~ c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_quotient__eqI]) ).

fof(f_3153_2,plain,
    ! [U_12032,U_12031,U_12030,U_12029,U_12028,U_12027,U_12026] :
      ( U_12029 = U_12030
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12026,U_12026)),hAPP(hAPP(c_Product__Type_OPair(U_12026,U_12026),U_12031),U_12032)),U_12028))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12026),U_12032),U_12030))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12026),U_12031),U_12029))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12026,tc_HOL_Obool)),U_12030),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12026),U_12027),U_12028)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12026,tc_HOL_Obool)),U_12029),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12026),U_12027),U_12028)))
      | ~ c_Equiv__Relations_Oequiv(U_12026,U_12027,U_12028) ),
    inference(variable_rename,[status(thm)],[f_3153_1]) ).

cnf(f_3153_3,plain,
    ( U_12029 = U_12030
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12026,U_12026)),hAPP(hAPP(c_Product__Type_OPair(U_12026,U_12026),U_12031),U_12032)),U_12028))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12026),U_12032),U_12030))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12026),U_12031),U_12029))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12026,tc_HOL_Obool)),U_12030),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12026),U_12027),U_12028)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12026,tc_HOL_Obool)),U_12029),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12026),U_12027),U_12028)))
    | ~ c_Equiv__Relations_Oequiv(U_12026,U_12027,U_12028) ),
    inference(clausify,[status(thm)],[f_3153_2]) ).

fof(f_3154_1,plain,
    ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
          | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
          | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
          | hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) )
        & ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
            & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
            & hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) )
          | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) ) )
      | ~ c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_equiv__class__eq__iff]) ).

fof(f_3154_2,plain,
    ! [U_12037,U_12036,U_12035,U_12034,U_12033] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12033,U_12033)),hAPP(hAPP(c_Product__Type_OPair(U_12033,U_12033),U_12036),U_12037)),U_12035))
          | ~ hBOOL(hAPP(hAPP(c_member(U_12033),U_12037),U_12034))
          | ~ hBOOL(hAPP(hAPP(c_member(U_12033),U_12036),U_12034))
          | hAPP(c_Relation_OImage(U_12033,U_12033,U_12035),hAPP(hAPP(c_Set_Oinsert(U_12033),U_12036),c_Orderings_Obot__class_Obot(tc_fun(U_12033,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(U_12033,U_12033,U_12035),hAPP(hAPP(c_Set_Oinsert(U_12033),U_12037),c_Orderings_Obot__class_Obot(tc_fun(U_12033,tc_HOL_Obool)))) )
        & ( ( hBOOL(hAPP(hAPP(c_member(U_12033),U_12037),U_12034))
            & hBOOL(hAPP(hAPP(c_member(U_12033),U_12036),U_12034))
            & hAPP(c_Relation_OImage(U_12033,U_12033,U_12035),hAPP(hAPP(c_Set_Oinsert(U_12033),U_12036),c_Orderings_Obot__class_Obot(tc_fun(U_12033,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(U_12033,U_12033,U_12035),hAPP(hAPP(c_Set_Oinsert(U_12033),U_12037),c_Orderings_Obot__class_Obot(tc_fun(U_12033,tc_HOL_Obool)))) )
          | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12033,U_12033)),hAPP(hAPP(c_Product__Type_OPair(U_12033,U_12033),U_12036),U_12037)),U_12035)) ) )
      | ~ c_Equiv__Relations_Oequiv(U_12033,U_12034,U_12035) ),
    inference(variable_rename,[status(thm)],[f_3154_1]) ).

cnf(f_3154_3,plain,
    ( hAPP(c_Relation_OImage(U_12033,U_12033,U_12035),hAPP(hAPP(c_Set_Oinsert(U_12033),U_12036),c_Orderings_Obot__class_Obot(tc_fun(U_12033,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(U_12033,U_12033,U_12035),hAPP(hAPP(c_Set_Oinsert(U_12033),U_12037),c_Orderings_Obot__class_Obot(tc_fun(U_12033,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12033,U_12033)),hAPP(hAPP(c_Product__Type_OPair(U_12033,U_12033),U_12036),U_12037)),U_12035))
    | ~ c_Equiv__Relations_Oequiv(U_12033,U_12034,U_12035) ),
    inference(clausify,[status(thm)],[f_3154_2]) ).

cnf(f_3154_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12033),U_12036),U_12034))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12033,U_12033)),hAPP(hAPP(c_Product__Type_OPair(U_12033,U_12033),U_12036),U_12037)),U_12035))
    | ~ c_Equiv__Relations_Oequiv(U_12033,U_12034,U_12035) ),
    inference(clausify,[status(thm)],[f_3154_2]) ).

cnf(f_3154_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12033),U_12037),U_12034))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12033,U_12033)),hAPP(hAPP(c_Product__Type_OPair(U_12033,U_12033),U_12036),U_12037)),U_12035))
    | ~ c_Equiv__Relations_Oequiv(U_12033,U_12034,U_12035) ),
    inference(clausify,[status(thm)],[f_3154_2]) ).

cnf(f_3154_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12033,U_12033)),hAPP(hAPP(c_Product__Type_OPair(U_12033,U_12033),U_12036),U_12037)),U_12035))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12033),U_12037),U_12034))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12033),U_12036),U_12034))
    | hAPP(c_Relation_OImage(U_12033,U_12033,U_12035),hAPP(hAPP(c_Set_Oinsert(U_12033),U_12036),c_Orderings_Obot__class_Obot(tc_fun(U_12033,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(U_12033,U_12033,U_12035),hAPP(hAPP(c_Set_Oinsert(U_12033),U_12037),c_Orderings_Obot__class_Obot(tc_fun(U_12033,tc_HOL_Obool))))
    | ~ c_Equiv__Relations_Oequiv(U_12033,U_12034,U_12035) ),
    inference(clausify,[status(thm)],[f_3154_2]) ).

fof(f_3155_1,plain,
    ! [V_A_2,V_b_2,V_a_2,V_r_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
      | ~ c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
      | hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ),
    inference(fof_nnf,[status(thm)],[fact_eq__equiv__class]) ).

fof(f_3155_2,plain,
    ! [U_12042,U_12041,U_12040,U_12039,U_12038] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12038,U_12038)),hAPP(hAPP(c_Product__Type_OPair(U_12038,U_12038),U_12040),U_12041)),U_12039))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12038),U_12041),U_12042))
      | ~ c_Equiv__Relations_Oequiv(U_12038,U_12042,U_12039)
      | hAPP(c_Relation_OImage(U_12038,U_12038,U_12039),hAPP(hAPP(c_Set_Oinsert(U_12038),U_12040),c_Orderings_Obot__class_Obot(tc_fun(U_12038,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(U_12038,U_12038,U_12039),hAPP(hAPP(c_Set_Oinsert(U_12038),U_12041),c_Orderings_Obot__class_Obot(tc_fun(U_12038,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_3155_1]) ).

cnf(f_3155_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12038,U_12038)),hAPP(hAPP(c_Product__Type_OPair(U_12038,U_12038),U_12040),U_12041)),U_12039))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12038),U_12041),U_12042))
    | ~ c_Equiv__Relations_Oequiv(U_12038,U_12042,U_12039)
    | hAPP(c_Relation_OImage(U_12038,U_12038,U_12039),hAPP(hAPP(c_Set_Oinsert(U_12038),U_12040),c_Orderings_Obot__class_Obot(tc_fun(U_12038,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(U_12038,U_12038,U_12039),hAPP(hAPP(c_Set_Oinsert(U_12038),U_12041),c_Orderings_Obot__class_Obot(tc_fun(U_12038,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_3155_2]) ).

fof(f_3156_1,plain,
    ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
      ( ( ( hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
          | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) )
        & ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
          | hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_eq__equiv__class__iff]) ).

fof(f_3156_2,plain,
    ! [U_12047,U_12046,U_12045,U_12044,U_12043] :
      ( ( ( hAPP(c_Relation_OImage(U_12043,U_12043,U_12045),hAPP(hAPP(c_Set_Oinsert(U_12043),U_12046),c_Orderings_Obot__class_Obot(tc_fun(U_12043,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(U_12043,U_12043,U_12045),hAPP(hAPP(c_Set_Oinsert(U_12043),U_12047),c_Orderings_Obot__class_Obot(tc_fun(U_12043,tc_HOL_Obool))))
          | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12043,U_12043)),hAPP(hAPP(c_Product__Type_OPair(U_12043,U_12043),U_12046),U_12047)),U_12045)) )
        & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12043,U_12043)),hAPP(hAPP(c_Product__Type_OPair(U_12043,U_12043),U_12046),U_12047)),U_12045))
          | hAPP(c_Relation_OImage(U_12043,U_12043,U_12045),hAPP(hAPP(c_Set_Oinsert(U_12043),U_12046),c_Orderings_Obot__class_Obot(tc_fun(U_12043,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(U_12043,U_12043,U_12045),hAPP(hAPP(c_Set_Oinsert(U_12043),U_12047),c_Orderings_Obot__class_Obot(tc_fun(U_12043,tc_HOL_Obool)))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_12043),U_12047),U_12044))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12043),U_12046),U_12044))
      | ~ c_Equiv__Relations_Oequiv(U_12043,U_12044,U_12045) ),
    inference(variable_rename,[status(thm)],[f_3156_1]) ).

cnf(f_3156_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12043,U_12043)),hAPP(hAPP(c_Product__Type_OPair(U_12043,U_12043),U_12046),U_12047)),U_12045))
    | hAPP(c_Relation_OImage(U_12043,U_12043,U_12045),hAPP(hAPP(c_Set_Oinsert(U_12043),U_12046),c_Orderings_Obot__class_Obot(tc_fun(U_12043,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(U_12043,U_12043,U_12045),hAPP(hAPP(c_Set_Oinsert(U_12043),U_12047),c_Orderings_Obot__class_Obot(tc_fun(U_12043,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12043),U_12047),U_12044))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12043),U_12046),U_12044))
    | ~ c_Equiv__Relations_Oequiv(U_12043,U_12044,U_12045) ),
    inference(clausify,[status(thm)],[f_3156_2]) ).

cnf(f_3156_4,plain,
    ( hAPP(c_Relation_OImage(U_12043,U_12043,U_12045),hAPP(hAPP(c_Set_Oinsert(U_12043),U_12046),c_Orderings_Obot__class_Obot(tc_fun(U_12043,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(U_12043,U_12043,U_12045),hAPP(hAPP(c_Set_Oinsert(U_12043),U_12047),c_Orderings_Obot__class_Obot(tc_fun(U_12043,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12043,U_12043)),hAPP(hAPP(c_Product__Type_OPair(U_12043,U_12043),U_12046),U_12047)),U_12045))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12043),U_12047),U_12044))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12043),U_12046),U_12044))
    | ~ c_Equiv__Relations_Oequiv(U_12043,U_12044,U_12045) ),
    inference(clausify,[status(thm)],[f_3156_2]) ).

fof(f_3157_1,plain,
    ! [V_b_2,V_a_2,V_r_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
      | ~ c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_equiv__class__subset]) ).

fof(f_3157_2,plain,
    ! [U_12052,U_12051,U_12050,U_12049,U_12048] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12048,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12048,U_12048,U_12050),hAPP(hAPP(c_Set_Oinsert(U_12048),U_12051),c_Orderings_Obot__class_Obot(tc_fun(U_12048,tc_HOL_Obool))))),hAPP(c_Relation_OImage(U_12048,U_12048,U_12050),hAPP(hAPP(c_Set_Oinsert(U_12048),U_12052),c_Orderings_Obot__class_Obot(tc_fun(U_12048,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12048,U_12048)),hAPP(hAPP(c_Product__Type_OPair(U_12048,U_12048),U_12051),U_12052)),U_12050))
      | ~ c_Equiv__Relations_Oequiv(U_12048,U_12049,U_12050) ),
    inference(variable_rename,[status(thm)],[f_3157_1]) ).

cnf(f_3157_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12048,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12048,U_12048,U_12050),hAPP(hAPP(c_Set_Oinsert(U_12048),U_12051),c_Orderings_Obot__class_Obot(tc_fun(U_12048,tc_HOL_Obool))))),hAPP(c_Relation_OImage(U_12048,U_12048,U_12050),hAPP(hAPP(c_Set_Oinsert(U_12048),U_12052),c_Orderings_Obot__class_Obot(tc_fun(U_12048,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12048,U_12048)),hAPP(hAPP(c_Product__Type_OPair(U_12048,U_12048),U_12051),U_12052)),U_12050))
    | ~ c_Equiv__Relations_Oequiv(U_12048,U_12049,U_12050) ),
    inference(clausify,[status(thm)],[f_3157_2]) ).

fof(f_3158_1,plain,
    ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
      ( ( ( hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_r_2) = hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_r_2)
          | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) )
        & ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
          | hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_r_2) != hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_r_2) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_eq__equiv__class__iff2]) ).

fof(f_3158_2,plain,
    ! [U_12057,U_12056,U_12055,U_12054,U_12053] :
      ( ( ( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12053),hAPP(hAPP(c_Set_Oinsert(U_12053),U_12056),c_Orderings_Obot__class_Obot(tc_fun(U_12053,tc_HOL_Obool)))),U_12055) = hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12053),hAPP(hAPP(c_Set_Oinsert(U_12053),U_12057),c_Orderings_Obot__class_Obot(tc_fun(U_12053,tc_HOL_Obool)))),U_12055)
          | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12053,U_12053)),hAPP(hAPP(c_Product__Type_OPair(U_12053,U_12053),U_12056),U_12057)),U_12055)) )
        & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12053,U_12053)),hAPP(hAPP(c_Product__Type_OPair(U_12053,U_12053),U_12056),U_12057)),U_12055))
          | hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12053),hAPP(hAPP(c_Set_Oinsert(U_12053),U_12056),c_Orderings_Obot__class_Obot(tc_fun(U_12053,tc_HOL_Obool)))),U_12055) != hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12053),hAPP(hAPP(c_Set_Oinsert(U_12053),U_12057),c_Orderings_Obot__class_Obot(tc_fun(U_12053,tc_HOL_Obool)))),U_12055) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_12053),U_12057),U_12054))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12053),U_12056),U_12054))
      | ~ c_Equiv__Relations_Oequiv(U_12053,U_12054,U_12055) ),
    inference(variable_rename,[status(thm)],[f_3158_1]) ).

cnf(f_3158_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12053,U_12053)),hAPP(hAPP(c_Product__Type_OPair(U_12053,U_12053),U_12056),U_12057)),U_12055))
    | hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12053),hAPP(hAPP(c_Set_Oinsert(U_12053),U_12056),c_Orderings_Obot__class_Obot(tc_fun(U_12053,tc_HOL_Obool)))),U_12055) != hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12053),hAPP(hAPP(c_Set_Oinsert(U_12053),U_12057),c_Orderings_Obot__class_Obot(tc_fun(U_12053,tc_HOL_Obool)))),U_12055)
    | ~ hBOOL(hAPP(hAPP(c_member(U_12053),U_12057),U_12054))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12053),U_12056),U_12054))
    | ~ c_Equiv__Relations_Oequiv(U_12053,U_12054,U_12055) ),
    inference(clausify,[status(thm)],[f_3158_2]) ).

cnf(f_3158_4,plain,
    ( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12053),hAPP(hAPP(c_Set_Oinsert(U_12053),U_12056),c_Orderings_Obot__class_Obot(tc_fun(U_12053,tc_HOL_Obool)))),U_12055) = hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12053),hAPP(hAPP(c_Set_Oinsert(U_12053),U_12057),c_Orderings_Obot__class_Obot(tc_fun(U_12053,tc_HOL_Obool)))),U_12055)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12053,U_12053)),hAPP(hAPP(c_Product__Type_OPair(U_12053,U_12053),U_12056),U_12057)),U_12055))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12053),U_12057),U_12054))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12053),U_12056),U_12054))
    | ~ c_Equiv__Relations_Oequiv(U_12053,U_12054,U_12055) ),
    inference(clausify,[status(thm)],[f_3158_2]) ).

fof(f_3159_1,plain,
    ! [V_a2_2,V_a1_2,V_f_2,T_d,V_r2_2,V_A2_2,T_c,V_r1_2,V_A1_2,T_b] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r1_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_c,V_r2_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a2_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))),V_f_2)) = hAPP(hAPP(V_f_2,V_a1_2),V_a2_2)
      | ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a2_2),V_A2_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a1_2),V_A1_2))
      | ~ c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
      | ~ c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
      | ~ c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2) ),
    inference(fof_nnf,[status(thm)],[fact_UN__equiv__class2]) ).

fof(f_3159_2,plain,
    ! [U_12067,U_12066,U_12065,U_12064,U_12063,U_12062,U_12061,U_12060,U_12059,U_12058] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12058,tc_fun(U_12064,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12058,U_12058,U_12060),hAPP(hAPP(c_Set_Oinsert(U_12058),U_12066),c_Orderings_Obot__class_Obot(tc_fun(U_12058,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(U_12061,tc_fun(U_12064,tc_HOL_Obool)),tc_fun(U_12064,tc_HOL_Obool),U_12058),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12061,tc_fun(U_12064,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12061,U_12061,U_12063),hAPP(hAPP(c_Set_Oinsert(U_12061),U_12067),c_Orderings_Obot__class_Obot(tc_fun(U_12061,tc_HOL_Obool)))))),U_12065)) = hAPP(hAPP(U_12065,U_12066),U_12067)
      | ~ hBOOL(hAPP(hAPP(c_member(U_12061),U_12067),U_12062))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12058),U_12066),U_12059))
      | ~ c_Equiv__Relations_Ocongruent2(U_12058,U_12061,tc_fun(U_12064,tc_HOL_Obool),U_12060,U_12063,U_12065)
      | ~ c_Equiv__Relations_Oequiv(U_12061,U_12062,U_12063)
      | ~ c_Equiv__Relations_Oequiv(U_12058,U_12059,U_12060) ),
    inference(variable_rename,[status(thm)],[f_3159_1]) ).

cnf(f_3159_3,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12058,tc_fun(U_12064,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12058,U_12058,U_12060),hAPP(hAPP(c_Set_Oinsert(U_12058),U_12066),c_Orderings_Obot__class_Obot(tc_fun(U_12058,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(U_12061,tc_fun(U_12064,tc_HOL_Obool)),tc_fun(U_12064,tc_HOL_Obool),U_12058),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12061,tc_fun(U_12064,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12061,U_12061,U_12063),hAPP(hAPP(c_Set_Oinsert(U_12061),U_12067),c_Orderings_Obot__class_Obot(tc_fun(U_12061,tc_HOL_Obool)))))),U_12065)) = hAPP(hAPP(U_12065,U_12066),U_12067)
    | ~ hBOOL(hAPP(hAPP(c_member(U_12061),U_12067),U_12062))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12058),U_12066),U_12059))
    | ~ c_Equiv__Relations_Ocongruent2(U_12058,U_12061,tc_fun(U_12064,tc_HOL_Obool),U_12060,U_12063,U_12065)
    | ~ c_Equiv__Relations_Oequiv(U_12061,U_12062,U_12063)
    | ~ c_Equiv__Relations_Oequiv(U_12058,U_12059,U_12060) ),
    inference(clausify,[status(thm)],[f_3159_2]) ).

fof(f_3160_1,plain,
    ! [V_a_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_f_2) = hAPP(V_f_2,V_a_2)
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | ~ c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
      | ~ c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_UN__equiv__class]) ).

fof(f_3160_2,plain,
    ! [U_12073,U_12072,U_12071,U_12070,U_12069,U_12068] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12068,tc_fun(U_12071,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12068,U_12068,U_12070),hAPP(hAPP(c_Set_Oinsert(U_12068),U_12073),c_Orderings_Obot__class_Obot(tc_fun(U_12068,tc_HOL_Obool))))),U_12072) = hAPP(U_12072,U_12073)
      | ~ hBOOL(hAPP(hAPP(c_member(U_12068),U_12073),U_12069))
      | ~ c_Equiv__Relations_Ocongruent(U_12068,tc_fun(U_12071,tc_HOL_Obool),U_12070,U_12072)
      | ~ c_Equiv__Relations_Oequiv(U_12068,U_12069,U_12070) ),
    inference(variable_rename,[status(thm)],[f_3160_1]) ).

cnf(f_3160_3,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12068,tc_fun(U_12071,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12068,U_12068,U_12070),hAPP(hAPP(c_Set_Oinsert(U_12068),U_12073),c_Orderings_Obot__class_Obot(tc_fun(U_12068,tc_HOL_Obool))))),U_12072) = hAPP(U_12072,U_12073)
    | ~ hBOOL(hAPP(hAPP(c_member(U_12068),U_12073),U_12069))
    | ~ c_Equiv__Relations_Ocongruent(U_12068,tc_fun(U_12071,tc_HOL_Obool),U_12070,U_12072)
    | ~ c_Equiv__Relations_Oequiv(U_12068,U_12069,U_12070) ),
    inference(clausify,[status(thm)],[f_3160_2]) ).

fof(f_3161_1,plain,
    ! [V_A_2,T_b] :
      ( ( c_Equiv__Relations_Oequiv(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_A_2)
        | ~ c_Equiv__Relations_Oequivp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_A_2)) )
      & ( c_Equiv__Relations_Oequivp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_A_2))
        | ~ c_Equiv__Relations_Oequiv(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_A_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_equivp__equiv]) ).

fof(f_3161_2,plain,
    ! [U_12075,U_12074] :
      ( ( c_Equiv__Relations_Oequiv(U_12074,c_Orderings_Otop__class_Otop(tc_fun(U_12074,tc_HOL_Obool)),U_12075)
        | ~ c_Equiv__Relations_Oequivp(U_12074,hAPP(hAPP(c_COMBC(U_12074,tc_fun(tc_prod(U_12074,U_12074),tc_HOL_Obool),tc_fun(U_12074,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12074,tc_fun(tc_fun(tc_prod(U_12074,U_12074),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12074,U_12074),tc_HOL_Obool),tc_fun(U_12074,tc_HOL_Obool)),U_12074),c_COMBC(U_12074,tc_fun(tc_prod(U_12074,U_12074),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12074,tc_prod(U_12074,U_12074)),tc_fun(U_12074,tc_fun(tc_fun(tc_prod(U_12074,U_12074),tc_HOL_Obool),tc_HOL_Obool)),U_12074),hAPP(c_COMBB(tc_prod(U_12074,U_12074),tc_fun(tc_fun(tc_prod(U_12074,U_12074),tc_HOL_Obool),tc_HOL_Obool),U_12074),c_member(tc_prod(U_12074,U_12074)))),c_Product__Type_OPair(U_12074,U_12074)))),U_12075)) )
      & ( c_Equiv__Relations_Oequivp(U_12074,hAPP(hAPP(c_COMBC(U_12074,tc_fun(tc_prod(U_12074,U_12074),tc_HOL_Obool),tc_fun(U_12074,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12074,tc_fun(tc_fun(tc_prod(U_12074,U_12074),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12074,U_12074),tc_HOL_Obool),tc_fun(U_12074,tc_HOL_Obool)),U_12074),c_COMBC(U_12074,tc_fun(tc_prod(U_12074,U_12074),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12074,tc_prod(U_12074,U_12074)),tc_fun(U_12074,tc_fun(tc_fun(tc_prod(U_12074,U_12074),tc_HOL_Obool),tc_HOL_Obool)),U_12074),hAPP(c_COMBB(tc_prod(U_12074,U_12074),tc_fun(tc_fun(tc_prod(U_12074,U_12074),tc_HOL_Obool),tc_HOL_Obool),U_12074),c_member(tc_prod(U_12074,U_12074)))),c_Product__Type_OPair(U_12074,U_12074)))),U_12075))
        | ~ c_Equiv__Relations_Oequiv(U_12074,c_Orderings_Otop__class_Otop(tc_fun(U_12074,tc_HOL_Obool)),U_12075) ) ),
    inference(variable_rename,[status(thm)],[f_3161_1]) ).

fof(f_3161_3,plain,
    ( ! [U_12079,U_12077] :
        ( c_Equiv__Relations_Oequiv(U_12077,c_Orderings_Otop__class_Otop(tc_fun(U_12077,tc_HOL_Obool)),U_12079)
        | ~ c_Equiv__Relations_Oequivp(U_12077,hAPP(hAPP(c_COMBC(U_12077,tc_fun(tc_prod(U_12077,U_12077),tc_HOL_Obool),tc_fun(U_12077,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12077,tc_fun(tc_fun(tc_prod(U_12077,U_12077),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12077,U_12077),tc_HOL_Obool),tc_fun(U_12077,tc_HOL_Obool)),U_12077),c_COMBC(U_12077,tc_fun(tc_prod(U_12077,U_12077),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12077,tc_prod(U_12077,U_12077)),tc_fun(U_12077,tc_fun(tc_fun(tc_prod(U_12077,U_12077),tc_HOL_Obool),tc_HOL_Obool)),U_12077),hAPP(c_COMBB(tc_prod(U_12077,U_12077),tc_fun(tc_fun(tc_prod(U_12077,U_12077),tc_HOL_Obool),tc_HOL_Obool),U_12077),c_member(tc_prod(U_12077,U_12077)))),c_Product__Type_OPair(U_12077,U_12077)))),U_12079)) )
    & ! [U_12078,U_12076] :
        ( c_Equiv__Relations_Oequivp(U_12076,hAPP(hAPP(c_COMBC(U_12076,tc_fun(tc_prod(U_12076,U_12076),tc_HOL_Obool),tc_fun(U_12076,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12076,tc_fun(tc_fun(tc_prod(U_12076,U_12076),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12076,U_12076),tc_HOL_Obool),tc_fun(U_12076,tc_HOL_Obool)),U_12076),c_COMBC(U_12076,tc_fun(tc_prod(U_12076,U_12076),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12076,tc_prod(U_12076,U_12076)),tc_fun(U_12076,tc_fun(tc_fun(tc_prod(U_12076,U_12076),tc_HOL_Obool),tc_HOL_Obool)),U_12076),hAPP(c_COMBB(tc_prod(U_12076,U_12076),tc_fun(tc_fun(tc_prod(U_12076,U_12076),tc_HOL_Obool),tc_HOL_Obool),U_12076),c_member(tc_prod(U_12076,U_12076)))),c_Product__Type_OPair(U_12076,U_12076)))),U_12078))
        | ~ c_Equiv__Relations_Oequiv(U_12076,c_Orderings_Otop__class_Otop(tc_fun(U_12076,tc_HOL_Obool)),U_12078) ) ),
    inference(miniscope,[status(thm)],[f_3161_2]) ).

cnf(f_3161_4,plain,
    ( c_Equiv__Relations_Oequivp(U_12076,hAPP(hAPP(c_COMBC(U_12076,tc_fun(tc_prod(U_12076,U_12076),tc_HOL_Obool),tc_fun(U_12076,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12076,tc_fun(tc_fun(tc_prod(U_12076,U_12076),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12076,U_12076),tc_HOL_Obool),tc_fun(U_12076,tc_HOL_Obool)),U_12076),c_COMBC(U_12076,tc_fun(tc_prod(U_12076,U_12076),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12076,tc_prod(U_12076,U_12076)),tc_fun(U_12076,tc_fun(tc_fun(tc_prod(U_12076,U_12076),tc_HOL_Obool),tc_HOL_Obool)),U_12076),hAPP(c_COMBB(tc_prod(U_12076,U_12076),tc_fun(tc_fun(tc_prod(U_12076,U_12076),tc_HOL_Obool),tc_HOL_Obool),U_12076),c_member(tc_prod(U_12076,U_12076)))),c_Product__Type_OPair(U_12076,U_12076)))),U_12078))
    | ~ c_Equiv__Relations_Oequiv(U_12076,c_Orderings_Otop__class_Otop(tc_fun(U_12076,tc_HOL_Obool)),U_12078) ),
    inference(clausify,[status(thm)],[f_3161_3]) ).

cnf(f_3161_5,plain,
    ( c_Equiv__Relations_Oequiv(U_12077,c_Orderings_Otop__class_Otop(tc_fun(U_12077,tc_HOL_Obool)),U_12079)
    | ~ c_Equiv__Relations_Oequivp(U_12077,hAPP(hAPP(c_COMBC(U_12077,tc_fun(tc_prod(U_12077,U_12077),tc_HOL_Obool),tc_fun(U_12077,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12077,tc_fun(tc_fun(tc_prod(U_12077,U_12077),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12077,U_12077),tc_HOL_Obool),tc_fun(U_12077,tc_HOL_Obool)),U_12077),c_COMBC(U_12077,tc_fun(tc_prod(U_12077,U_12077),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12077,tc_prod(U_12077,U_12077)),tc_fun(U_12077,tc_fun(tc_fun(tc_prod(U_12077,U_12077),tc_HOL_Obool),tc_HOL_Obool)),U_12077),hAPP(c_COMBB(tc_prod(U_12077,U_12077),tc_fun(tc_fun(tc_prod(U_12077,U_12077),tc_HOL_Obool),tc_HOL_Obool),U_12077),c_member(tc_prod(U_12077,U_12077)))),c_Product__Type_OPair(U_12077,U_12077)))),U_12079)) ),
    inference(clausify,[status(thm)],[f_3161_3]) ).

fof(f_3162_1,plain,
    ! [V_z_2,V_y_2,V_x_2,V_R_2,T_b] :
      ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_z_2))
      | ~ hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_z_2))
      | ~ hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
      | ~ c_Equiv__Relations_Oequivp(T_b,V_R_2) ),
    inference(fof_nnf,[status(thm)],[fact_equivp__transp]) ).

fof(f_3162_2,plain,
    ! [U_12084,U_12083,U_12082,U_12081,U_12080] :
      ( hBOOL(hAPP(hAPP(U_12081,U_12082),U_12084))
      | ~ hBOOL(hAPP(hAPP(U_12081,U_12083),U_12084))
      | ~ hBOOL(hAPP(hAPP(U_12081,U_12082),U_12083))
      | ~ c_Equiv__Relations_Oequivp(U_12080,U_12081) ),
    inference(variable_rename,[status(thm)],[f_3162_1]) ).

fof(f_3162_3,plain,
    ! [U_12084,U_12083,U_12082,U_12081] :
      ( ! [U_12080] : ~ c_Equiv__Relations_Oequivp(U_12080,U_12081)
      | hBOOL(hAPP(hAPP(U_12081,U_12082),U_12084))
      | ~ hBOOL(hAPP(hAPP(U_12081,U_12083),U_12084))
      | ~ hBOOL(hAPP(hAPP(U_12081,U_12082),U_12083)) ),
    inference(miniscope,[status(thm)],[f_3162_2]) ).

cnf(f_3162_4,plain,
    ( ~ c_Equiv__Relations_Oequivp(U_12080,U_12081)
    | hBOOL(hAPP(hAPP(U_12081,U_12082),U_12084))
    | ~ hBOOL(hAPP(hAPP(U_12081,U_12083),U_12084))
    | ~ hBOOL(hAPP(hAPP(U_12081,U_12082),U_12083)) ),
    inference(clausify,[status(thm)],[f_3162_3]) ).

fof(f_3163_1,plain,
    ! [V_y_2,V_x_2,V_R_2,T_b] :
      ( hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2))
      | ~ hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
      | ~ c_Equiv__Relations_Oequivp(T_b,V_R_2) ),
    inference(fof_nnf,[status(thm)],[fact_equivp__symp]) ).

fof(f_3163_2,plain,
    ! [U_12088,U_12087,U_12086,U_12085] :
      ( hBOOL(hAPP(hAPP(U_12086,U_12088),U_12087))
      | ~ hBOOL(hAPP(hAPP(U_12086,U_12087),U_12088))
      | ~ c_Equiv__Relations_Oequivp(U_12085,U_12086) ),
    inference(variable_rename,[status(thm)],[f_3163_1]) ).

fof(f_3163_3,plain,
    ! [U_12088,U_12087,U_12086] :
      ( ! [U_12085] : ~ c_Equiv__Relations_Oequivp(U_12085,U_12086)
      | hBOOL(hAPP(hAPP(U_12086,U_12088),U_12087))
      | ~ hBOOL(hAPP(hAPP(U_12086,U_12087),U_12088)) ),
    inference(miniscope,[status(thm)],[f_3163_2]) ).

cnf(f_3163_4,plain,
    ( ~ c_Equiv__Relations_Oequivp(U_12085,U_12086)
    | hBOOL(hAPP(hAPP(U_12086,U_12088),U_12087))
    | ~ hBOOL(hAPP(hAPP(U_12086,U_12087),U_12088)) ),
    inference(clausify,[status(thm)],[f_3163_3]) ).

fof(f_3164_1,plain,
    ! [V_x_2,V_R_2,T_b] :
      ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2))
      | ~ c_Equiv__Relations_Oequivp(T_b,V_R_2) ),
    inference(fof_nnf,[status(thm)],[fact_equivp__reflp]) ).

fof(f_3164_2,plain,
    ! [U_12091,U_12090,U_12089] :
      ( hBOOL(hAPP(hAPP(U_12090,U_12091),U_12091))
      | ~ c_Equiv__Relations_Oequivp(U_12089,U_12090) ),
    inference(variable_rename,[status(thm)],[f_3164_1]) ).

fof(f_3164_3,plain,
    ! [U_12091,U_12090] :
      ( ! [U_12089] : ~ c_Equiv__Relations_Oequivp(U_12089,U_12090)
      | hBOOL(hAPP(hAPP(U_12090,U_12091),U_12091)) ),
    inference(miniscope,[status(thm)],[f_3164_2]) ).

cnf(f_3164_4,plain,
    ( ~ c_Equiv__Relations_Oequivp(U_12089,U_12090)
    | hBOOL(hAPP(hAPP(U_12090,U_12091),U_12091)) ),
    inference(clausify,[status(thm)],[f_3164_3]) ).

fof(f_3165_1,plain,
    ! [V_R_2,T_b] :
      ( ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
        | ? [B_x,B_y] :
            ( ( ~ hBOOL(hAPP(hAPP(V_R_2,B_x),B_y))
              & hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y) )
            | ( hAPP(V_R_2,B_x) != hAPP(V_R_2,B_y)
              & hBOOL(hAPP(hAPP(V_R_2,B_x),B_y)) ) ) )
      & ( ! [B_x,B_y] :
            ( ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_y))
              | hAPP(V_R_2,B_x) != hAPP(V_R_2,B_y) )
            & ( hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y)
              | ~ hBOOL(hAPP(hAPP(V_R_2,B_x),B_y)) ) )
        | ~ c_Equiv__Relations_Oequivp(T_b,V_R_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_equivp__def]) ).

fof(f_3165_2,plain,
    ! [U_12097,U_12096] :
      ( ( c_Equiv__Relations_Oequivp(U_12096,U_12097)
        | ? [U_12095,U_12094] :
            ( ( ~ hBOOL(hAPP(hAPP(U_12097,U_12095),U_12094))
              & hAPP(U_12097,U_12095) = hAPP(U_12097,U_12094) )
            | ( hAPP(U_12097,U_12095) != hAPP(U_12097,U_12094)
              & hBOOL(hAPP(hAPP(U_12097,U_12095),U_12094)) ) ) )
      & ( ! [U_12093,U_12092] :
            ( ( hBOOL(hAPP(hAPP(U_12097,U_12093),U_12092))
              | hAPP(U_12097,U_12093) != hAPP(U_12097,U_12092) )
            & ( hAPP(U_12097,U_12093) = hAPP(U_12097,U_12092)
              | ~ hBOOL(hAPP(hAPP(U_12097,U_12093),U_12092)) ) )
        | ~ c_Equiv__Relations_Oequivp(U_12096,U_12097) ) ),
    inference(variable_rename,[status(thm)],[f_3165_1]) ).

fof(f_3165_3,plain,
    ( ! [U_12109] :
        ( ! [U_12107] : c_Equiv__Relations_Oequivp(U_12107,U_12109)
        | ? [U_12105,U_12103] :
            ( ~ hBOOL(hAPP(hAPP(U_12109,U_12105),U_12103))
            & hAPP(U_12109,U_12105) = hAPP(U_12109,U_12103) )
        | ? [U_12104,U_12102] :
            ( hAPP(U_12109,U_12104) != hAPP(U_12109,U_12102)
            & hBOOL(hAPP(hAPP(U_12109,U_12104),U_12102)) ) )
    & ! [U_12108] :
        ( ! [U_12106] : ~ c_Equiv__Relations_Oequivp(U_12106,U_12108)
        | ( ! [U_12101,U_12099] :
              ( hBOOL(hAPP(hAPP(U_12108,U_12101),U_12099))
              | hAPP(U_12108,U_12101) != hAPP(U_12108,U_12099) )
          & ! [U_12100,U_12098] :
              ( hAPP(U_12108,U_12100) = hAPP(U_12108,U_12098)
              | ~ hBOOL(hAPP(hAPP(U_12108,U_12100),U_12098)) ) ) ) ),
    inference(miniscope,[status(thm)],[f_3165_2]) ).

fof(f_3165_4,plain,
    ( ! [U_12109] :
        ( ! [U_12107] : c_Equiv__Relations_Oequivp(U_12107,U_12109)
        | ? [U_12105,U_12103] :
            ( ~ hBOOL(hAPP(hAPP(U_12109,U_12105),U_12103))
            & hAPP(U_12109,U_12105) = hAPP(U_12109,U_12103) )
        | ? [U_12102] :
            ( hAPP(U_12109,sK281(U_12109)) != hAPP(U_12109,U_12102)
            & hBOOL(hAPP(hAPP(U_12109,sK281(U_12109)),U_12102)) ) )
    & ! [U_12108] :
        ( ! [U_12106] : ~ c_Equiv__Relations_Oequivp(U_12106,U_12108)
        | ( ! [U_12101,U_12099] :
              ( hBOOL(hAPP(hAPP(U_12108,U_12101),U_12099))
              | hAPP(U_12108,U_12101) != hAPP(U_12108,U_12099) )
          & ! [U_12100,U_12098] :
              ( hAPP(U_12108,U_12100) = hAPP(U_12108,U_12098)
              | ~ hBOOL(hAPP(hAPP(U_12108,U_12100),U_12098)) ) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK281]),skolemize(U_12104,sK281(U_12109))],[f_3165_3]) ).

fof(f_3165_5,plain,
    ( ! [U_12109] :
        ( ! [U_12107] : c_Equiv__Relations_Oequivp(U_12107,U_12109)
        | ? [U_12105,U_12103] :
            ( ~ hBOOL(hAPP(hAPP(U_12109,U_12105),U_12103))
            & hAPP(U_12109,U_12105) = hAPP(U_12109,U_12103) )
        | ( hAPP(U_12109,sK281(U_12109)) != hAPP(U_12109,sK282(U_12109))
          & hBOOL(hAPP(hAPP(U_12109,sK281(U_12109)),sK282(U_12109))) ) )
    & ! [U_12108] :
        ( ! [U_12106] : ~ c_Equiv__Relations_Oequivp(U_12106,U_12108)
        | ( ! [U_12101,U_12099] :
              ( hBOOL(hAPP(hAPP(U_12108,U_12101),U_12099))
              | hAPP(U_12108,U_12101) != hAPP(U_12108,U_12099) )
          & ! [U_12100,U_12098] :
              ( hAPP(U_12108,U_12100) = hAPP(U_12108,U_12098)
              | ~ hBOOL(hAPP(hAPP(U_12108,U_12100),U_12098)) ) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK282]),skolemize(U_12102,sK282(U_12109))],[f_3165_4]) ).

fof(f_3165_6,plain,
    ( ! [U_12109] :
        ( ! [U_12107] : c_Equiv__Relations_Oequivp(U_12107,U_12109)
        | ? [U_12103] :
            ( ~ hBOOL(hAPP(hAPP(U_12109,sK283(U_12109)),U_12103))
            & hAPP(U_12109,sK283(U_12109)) = hAPP(U_12109,U_12103) )
        | ( hAPP(U_12109,sK281(U_12109)) != hAPP(U_12109,sK282(U_12109))
          & hBOOL(hAPP(hAPP(U_12109,sK281(U_12109)),sK282(U_12109))) ) )
    & ! [U_12108] :
        ( ! [U_12106] : ~ c_Equiv__Relations_Oequivp(U_12106,U_12108)
        | ( ! [U_12101,U_12099] :
              ( hBOOL(hAPP(hAPP(U_12108,U_12101),U_12099))
              | hAPP(U_12108,U_12101) != hAPP(U_12108,U_12099) )
          & ! [U_12100,U_12098] :
              ( hAPP(U_12108,U_12100) = hAPP(U_12108,U_12098)
              | ~ hBOOL(hAPP(hAPP(U_12108,U_12100),U_12098)) ) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK283]),skolemize(U_12105,sK283(U_12109))],[f_3165_5]) ).

fof(f_3165_7,plain,
    ( ! [U_12109] :
        ( ! [U_12107] : c_Equiv__Relations_Oequivp(U_12107,U_12109)
        | ( ~ hBOOL(hAPP(hAPP(U_12109,sK283(U_12109)),sK284(U_12109)))
          & hAPP(U_12109,sK283(U_12109)) = hAPP(U_12109,sK284(U_12109)) )
        | ( hAPP(U_12109,sK281(U_12109)) != hAPP(U_12109,sK282(U_12109))
          & hBOOL(hAPP(hAPP(U_12109,sK281(U_12109)),sK282(U_12109))) ) )
    & ! [U_12108] :
        ( ! [U_12106] : ~ c_Equiv__Relations_Oequivp(U_12106,U_12108)
        | ( ! [U_12101,U_12099] :
              ( hBOOL(hAPP(hAPP(U_12108,U_12101),U_12099))
              | hAPP(U_12108,U_12101) != hAPP(U_12108,U_12099) )
          & ! [U_12100,U_12098] :
              ( hAPP(U_12108,U_12100) = hAPP(U_12108,U_12098)
              | ~ hBOOL(hAPP(hAPP(U_12108,U_12100),U_12098)) ) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK284]),skolemize(U_12103,sK284(U_12109))],[f_3165_6]) ).

cnf(f_3165_8,plain,
    ( hAPP(U_12108,U_12100) = hAPP(U_12108,U_12098)
    | ~ hBOOL(hAPP(hAPP(U_12108,U_12100),U_12098))
    | ~ c_Equiv__Relations_Oequivp(U_12106,U_12108) ),
    inference(clausify,[status(thm)],[f_3165_7]) ).

cnf(f_3165_9,plain,
    ( hBOOL(hAPP(hAPP(U_12108,U_12101),U_12099))
    | hAPP(U_12108,U_12101) != hAPP(U_12108,U_12099)
    | ~ c_Equiv__Relations_Oequivp(U_12106,U_12108) ),
    inference(clausify,[status(thm)],[f_3165_7]) ).

cnf(f_3165_10,plain,
    ( hAPP(U_12109,sK283(U_12109)) = hAPP(U_12109,sK284(U_12109))
    | hBOOL(hAPP(hAPP(U_12109,sK281(U_12109)),sK282(U_12109)))
    | c_Equiv__Relations_Oequivp(U_12107,U_12109) ),
    inference(clausify,[status(thm)],[f_3165_7]) ).

cnf(f_3165_11,plain,
    ( ~ hBOOL(hAPP(hAPP(U_12109,sK283(U_12109)),sK284(U_12109)))
    | hBOOL(hAPP(hAPP(U_12109,sK281(U_12109)),sK282(U_12109)))
    | c_Equiv__Relations_Oequivp(U_12107,U_12109) ),
    inference(clausify,[status(thm)],[f_3165_7]) ).

cnf(f_3165_12,plain,
    ( hAPP(U_12109,sK283(U_12109)) = hAPP(U_12109,sK284(U_12109))
    | hAPP(U_12109,sK281(U_12109)) != hAPP(U_12109,sK282(U_12109))
    | c_Equiv__Relations_Oequivp(U_12107,U_12109) ),
    inference(clausify,[status(thm)],[f_3165_7]) ).

cnf(f_3165_13,plain,
    ( ~ hBOOL(hAPP(hAPP(U_12109,sK283(U_12109)),sK284(U_12109)))
    | hAPP(U_12109,sK281(U_12109)) != hAPP(U_12109,sK282(U_12109))
    | c_Equiv__Relations_Oequivp(U_12107,U_12109) ),
    inference(clausify,[status(thm)],[f_3165_7]) ).

fof(f_3166_1,plain,
    ! [T_b] : c_Equiv__Relations_Oequivp(T_b,c_fequal),
    inference(fof_nnf,[status(thm)],[fact_identity__equivp]) ).

fof(f_3166_2,plain,
    ! [U_12110] : c_Equiv__Relations_Oequivp(U_12110,c_fequal),
    inference(variable_rename,[status(thm)],[f_3166_1]) ).

cnf(f_3166_3,plain,
    c_Equiv__Relations_Oequivp(U_12110,c_fequal),
    inference(clausify,[status(thm)],[f_3166_2]) ).

fof(f_3167_1,plain,
    ! [V_a_2,V_f_2,V_r2_2,T_d,T_c,V_r1_2,V_A_2,T_b] :
      ( c_Equiv__Relations_Ocongruent(T_c,T_d,V_r2_2,hAPP(V_f_2,V_a_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | ~ c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2)
      | ~ c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r1_2) ),
    inference(fof_nnf,[status(thm)],[fact_congruent2__implies__congruent]) ).

fof(f_3167_2,plain,
    ! [U_12118,U_12117,U_12116,U_12115,U_12114,U_12113,U_12112,U_12111] :
      ( c_Equiv__Relations_Ocongruent(U_12114,U_12115,U_12116,hAPP(U_12117,U_12118))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12111),U_12118),U_12112))
      | ~ c_Equiv__Relations_Ocongruent2(U_12111,U_12114,U_12115,U_12113,U_12116,U_12117)
      | ~ c_Equiv__Relations_Oequiv(U_12111,U_12112,U_12113) ),
    inference(variable_rename,[status(thm)],[f_3167_1]) ).

cnf(f_3167_3,plain,
    ( c_Equiv__Relations_Ocongruent(U_12114,U_12115,U_12116,hAPP(U_12117,U_12118))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12111),U_12118),U_12112))
    | ~ c_Equiv__Relations_Ocongruent2(U_12111,U_12114,U_12115,U_12113,U_12116,U_12117)
    | ~ c_Equiv__Relations_Oequiv(U_12111,U_12112,U_12113) ),
    inference(clausify,[status(thm)],[f_3167_2]) ).

fof(f_3168_1,plain,
    ! [V_z2_2,V_y2_2,V_z1_2,V_y1_2,V_f_2,V_r2_2,V_r1_2,T_d,T_c,T_b] :
      ( hAPP(hAPP(V_f_2,V_y1_2),V_y2_2) = hAPP(hAPP(V_f_2,V_z1_2),V_z2_2)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_y2_2),V_z2_2)),V_r2_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y1_2),V_z1_2)),V_r1_2))
      | ~ c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_congruent2D]) ).

fof(f_3168_2,plain,
    ! [U_12128,U_12127,U_12126,U_12125,U_12124,U_12123,U_12122,U_12121,U_12120,U_12119] :
      ( hAPP(hAPP(U_12124,U_12125),U_12127) = hAPP(hAPP(U_12124,U_12126),U_12128)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12120,U_12120)),hAPP(hAPP(c_Product__Type_OPair(U_12120,U_12120),U_12127),U_12128)),U_12123))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12119,U_12119)),hAPP(hAPP(c_Product__Type_OPair(U_12119,U_12119),U_12125),U_12126)),U_12122))
      | ~ c_Equiv__Relations_Ocongruent2(U_12119,U_12120,U_12121,U_12122,U_12123,U_12124) ),
    inference(variable_rename,[status(thm)],[f_3168_1]) ).

cnf(f_3168_3,plain,
    ( hAPP(hAPP(U_12124,U_12125),U_12127) = hAPP(hAPP(U_12124,U_12126),U_12128)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12120,U_12120)),hAPP(hAPP(c_Product__Type_OPair(U_12120,U_12120),U_12127),U_12128)),U_12123))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12119,U_12119)),hAPP(hAPP(c_Product__Type_OPair(U_12119,U_12119),U_12125),U_12126)),U_12122))
    | ~ c_Equiv__Relations_Ocongruent2(U_12119,U_12120,U_12121,U_12122,U_12123,U_12124) ),
    inference(clausify,[status(thm)],[f_3168_2]) ).

fof(f_3169_1,plain,
    ! [V_z_2,V_y_2,V_f_2,V_r_2,T_c,T_b] :
      ( hAPP(V_f_2,V_y_2) = hAPP(V_f_2,V_z_2)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),V_r_2))
      | ~ c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_congruentD]) ).

fof(f_3169_2,plain,
    ! [U_12134,U_12133,U_12132,U_12131,U_12130,U_12129] :
      ( hAPP(U_12132,U_12133) = hAPP(U_12132,U_12134)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12129,U_12129)),hAPP(hAPP(c_Product__Type_OPair(U_12129,U_12129),U_12133),U_12134)),U_12131))
      | ~ c_Equiv__Relations_Ocongruent(U_12129,U_12130,U_12131,U_12132) ),
    inference(variable_rename,[status(thm)],[f_3169_1]) ).

cnf(f_3169_3,plain,
    ( hAPP(U_12132,U_12133) = hAPP(U_12132,U_12134)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12129,U_12129)),hAPP(hAPP(c_Product__Type_OPair(U_12129,U_12129),U_12133),U_12134)),U_12131))
    | ~ c_Equiv__Relations_Ocongruent(U_12129,U_12130,U_12131,U_12132) ),
    inference(clausify,[status(thm)],[f_3169_2]) ).

fof(f_3170_1,plain,
    ! [V_a_2,V_f_2,T_d,V_r2_2,V_A2_2,T_c,V_r1_2,V_A1_2,T_b] :
      ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_d,tc_HOL_Obool),V_r1_2,hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_c,V_r2_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))),V_f_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A2_2))
      | ~ c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
      | ~ c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
      | ~ c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2) ),
    inference(fof_nnf,[status(thm)],[fact_congruent2__implies__congruent__UN]) ).

fof(f_3170_2,plain,
    ! [U_12143,U_12142,U_12141,U_12140,U_12139,U_12138,U_12137,U_12136,U_12135] :
      ( c_Equiv__Relations_Ocongruent(U_12135,tc_fun(U_12141,tc_HOL_Obool),U_12137,hAPP(hAPP(c_COMBB(tc_fun(U_12138,tc_fun(U_12141,tc_HOL_Obool)),tc_fun(U_12141,tc_HOL_Obool),U_12135),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12138,tc_fun(U_12141,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12138,U_12138,U_12140),hAPP(hAPP(c_Set_Oinsert(U_12138),U_12143),c_Orderings_Obot__class_Obot(tc_fun(U_12138,tc_HOL_Obool)))))),U_12142))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12138),U_12143),U_12139))
      | ~ c_Equiv__Relations_Ocongruent2(U_12135,U_12138,tc_fun(U_12141,tc_HOL_Obool),U_12137,U_12140,U_12142)
      | ~ c_Equiv__Relations_Oequiv(U_12138,U_12139,U_12140)
      | ~ c_Equiv__Relations_Oequiv(U_12135,U_12136,U_12137) ),
    inference(variable_rename,[status(thm)],[f_3170_1]) ).

cnf(f_3170_3,plain,
    ( c_Equiv__Relations_Ocongruent(U_12135,tc_fun(U_12141,tc_HOL_Obool),U_12137,hAPP(hAPP(c_COMBB(tc_fun(U_12138,tc_fun(U_12141,tc_HOL_Obool)),tc_fun(U_12141,tc_HOL_Obool),U_12135),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12138,tc_fun(U_12141,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12138,U_12138,U_12140),hAPP(hAPP(c_Set_Oinsert(U_12138),U_12143),c_Orderings_Obot__class_Obot(tc_fun(U_12138,tc_HOL_Obool)))))),U_12142))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12138),U_12143),U_12139))
    | ~ c_Equiv__Relations_Ocongruent2(U_12135,U_12138,tc_fun(U_12141,tc_HOL_Obool),U_12137,U_12140,U_12142)
    | ~ c_Equiv__Relations_Oequiv(U_12138,U_12139,U_12140)
    | ~ c_Equiv__Relations_Oequiv(U_12135,U_12136,U_12137) ),
    inference(clausify,[status(thm)],[f_3170_2]) ).

fof(f_3171_1,plain,
    ! [V_Y_2,V_X_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
      ( V_X_2 = V_Y_2
      | ? [B_x] :
          ( ? [B_y] :
              ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_r_2))
              & hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y)
              & hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2)) )
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_X_2),V_f_2) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_Y_2),V_f_2)
      | ~ c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
      | ~ c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_UN__equiv__class__inject]) ).

fof(f_3171_2,plain,
    ! [U_12152,U_12151,U_12150,U_12149,U_12148,U_12147,U_12146] :
      ( U_12151 = U_12152
      | ? [U_12145] :
          ( ? [U_12144] :
              ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12146,U_12146)),hAPP(hAPP(c_Product__Type_OPair(U_12146,U_12146),U_12145),U_12144)),U_12148))
              & hAPP(U_12150,U_12145) = hAPP(U_12150,U_12144)
              & hBOOL(hAPP(hAPP(c_member(U_12146),U_12144),U_12147)) )
          & hBOOL(hAPP(hAPP(c_member(U_12146),U_12145),U_12147)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12146,tc_HOL_Obool)),U_12152),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12146),U_12147),U_12148)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12146,tc_HOL_Obool)),U_12151),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12146),U_12147),U_12148)))
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12146,tc_fun(U_12149,tc_HOL_Obool)),U_12151),U_12150) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12146,tc_fun(U_12149,tc_HOL_Obool)),U_12152),U_12150)
      | ~ c_Equiv__Relations_Ocongruent(U_12146,tc_fun(U_12149,tc_HOL_Obool),U_12148,U_12150)
      | ~ c_Equiv__Relations_Oequiv(U_12146,U_12147,U_12148) ),
    inference(variable_rename,[status(thm)],[f_3171_1]) ).

fof(f_3171_3,plain,
    ! [U_12152,U_12151,U_12150,U_12149,U_12148,U_12147,U_12146] :
      ( U_12151 = U_12152
      | ( ? [U_12144] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12146,U_12146)),hAPP(hAPP(c_Product__Type_OPair(U_12146,U_12146),sK285(U_12152,U_12151,U_12150,U_12149,U_12148,U_12147,U_12146)),U_12144)),U_12148))
            & hAPP(U_12150,sK285(U_12152,U_12151,U_12150,U_12149,U_12148,U_12147,U_12146)) = hAPP(U_12150,U_12144)
            & hBOOL(hAPP(hAPP(c_member(U_12146),U_12144),U_12147)) )
        & hBOOL(hAPP(hAPP(c_member(U_12146),sK285(U_12152,U_12151,U_12150,U_12149,U_12148,U_12147,U_12146)),U_12147)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12146,tc_HOL_Obool)),U_12152),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12146),U_12147),U_12148)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12146,tc_HOL_Obool)),U_12151),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12146),U_12147),U_12148)))
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12146,tc_fun(U_12149,tc_HOL_Obool)),U_12151),U_12150) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12146,tc_fun(U_12149,tc_HOL_Obool)),U_12152),U_12150)
      | ~ c_Equiv__Relations_Ocongruent(U_12146,tc_fun(U_12149,tc_HOL_Obool),U_12148,U_12150)
      | ~ c_Equiv__Relations_Oequiv(U_12146,U_12147,U_12148) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK285]),skolemize(U_12145,sK285(U_12152,U_12151,U_12150,U_12149,U_12148,U_12147,U_12146))],[f_3171_2]) ).

fof(f_3171_4,plain,
    ! [U_12152,U_12151,U_12150,U_12149,U_12148,U_12147,U_12146] :
      ( U_12151 = U_12152
      | ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12146,U_12146)),hAPP(hAPP(c_Product__Type_OPair(U_12146,U_12146),sK285(U_12152,U_12151,U_12150,U_12149,U_12148,U_12147,U_12146)),sK286(U_12152,U_12151,U_12150,U_12149,U_12148,U_12147,U_12146))),U_12148))
        & hAPP(U_12150,sK285(U_12152,U_12151,U_12150,U_12149,U_12148,U_12147,U_12146)) = hAPP(U_12150,sK286(U_12152,U_12151,U_12150,U_12149,U_12148,U_12147,U_12146))
        & hBOOL(hAPP(hAPP(c_member(U_12146),sK286(U_12152,U_12151,U_12150,U_12149,U_12148,U_12147,U_12146)),U_12147))
        & hBOOL(hAPP(hAPP(c_member(U_12146),sK285(U_12152,U_12151,U_12150,U_12149,U_12148,U_12147,U_12146)),U_12147)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12146,tc_HOL_Obool)),U_12152),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12146),U_12147),U_12148)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12146,tc_HOL_Obool)),U_12151),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12146),U_12147),U_12148)))
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12146,tc_fun(U_12149,tc_HOL_Obool)),U_12151),U_12150) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12146,tc_fun(U_12149,tc_HOL_Obool)),U_12152),U_12150)
      | ~ c_Equiv__Relations_Ocongruent(U_12146,tc_fun(U_12149,tc_HOL_Obool),U_12148,U_12150)
      | ~ c_Equiv__Relations_Oequiv(U_12146,U_12147,U_12148) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK286]),skolemize(U_12144,sK286(U_12152,U_12151,U_12150,U_12149,U_12148,U_12147,U_12146))],[f_3171_3]) ).

cnf(f_3171_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12146),sK285(U_12152,U_12151,U_12150,U_12149,U_12148,U_12147,U_12146)),U_12147))
    | U_12151 = U_12152
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12146,tc_HOL_Obool)),U_12152),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12146),U_12147),U_12148)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12146,tc_HOL_Obool)),U_12151),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12146),U_12147),U_12148)))
    | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12146,tc_fun(U_12149,tc_HOL_Obool)),U_12151),U_12150) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12146,tc_fun(U_12149,tc_HOL_Obool)),U_12152),U_12150)
    | ~ c_Equiv__Relations_Ocongruent(U_12146,tc_fun(U_12149,tc_HOL_Obool),U_12148,U_12150)
    | ~ c_Equiv__Relations_Oequiv(U_12146,U_12147,U_12148) ),
    inference(clausify,[status(thm)],[f_3171_4]) ).

cnf(f_3171_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12146),sK286(U_12152,U_12151,U_12150,U_12149,U_12148,U_12147,U_12146)),U_12147))
    | U_12151 = U_12152
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12146,tc_HOL_Obool)),U_12152),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12146),U_12147),U_12148)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12146,tc_HOL_Obool)),U_12151),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12146),U_12147),U_12148)))
    | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12146,tc_fun(U_12149,tc_HOL_Obool)),U_12151),U_12150) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12146,tc_fun(U_12149,tc_HOL_Obool)),U_12152),U_12150)
    | ~ c_Equiv__Relations_Ocongruent(U_12146,tc_fun(U_12149,tc_HOL_Obool),U_12148,U_12150)
    | ~ c_Equiv__Relations_Oequiv(U_12146,U_12147,U_12148) ),
    inference(clausify,[status(thm)],[f_3171_4]) ).

cnf(f_3171_7,plain,
    ( hAPP(U_12150,sK285(U_12152,U_12151,U_12150,U_12149,U_12148,U_12147,U_12146)) = hAPP(U_12150,sK286(U_12152,U_12151,U_12150,U_12149,U_12148,U_12147,U_12146))
    | U_12151 = U_12152
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12146,tc_HOL_Obool)),U_12152),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12146),U_12147),U_12148)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12146,tc_HOL_Obool)),U_12151),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12146),U_12147),U_12148)))
    | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12146,tc_fun(U_12149,tc_HOL_Obool)),U_12151),U_12150) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12146,tc_fun(U_12149,tc_HOL_Obool)),U_12152),U_12150)
    | ~ c_Equiv__Relations_Ocongruent(U_12146,tc_fun(U_12149,tc_HOL_Obool),U_12148,U_12150)
    | ~ c_Equiv__Relations_Oequiv(U_12146,U_12147,U_12148) ),
    inference(clausify,[status(thm)],[f_3171_4]) ).

cnf(f_3171_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12146,U_12146)),hAPP(hAPP(c_Product__Type_OPair(U_12146,U_12146),sK285(U_12152,U_12151,U_12150,U_12149,U_12148,U_12147,U_12146)),sK286(U_12152,U_12151,U_12150,U_12149,U_12148,U_12147,U_12146))),U_12148))
    | U_12151 = U_12152
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12146,tc_HOL_Obool)),U_12152),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12146),U_12147),U_12148)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12146,tc_HOL_Obool)),U_12151),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12146),U_12147),U_12148)))
    | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12146,tc_fun(U_12149,tc_HOL_Obool)),U_12151),U_12150) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12146,tc_fun(U_12149,tc_HOL_Obool)),U_12152),U_12150)
    | ~ c_Equiv__Relations_Ocongruent(U_12146,tc_fun(U_12149,tc_HOL_Obool),U_12148,U_12150)
    | ~ c_Equiv__Relations_Oequiv(U_12146,U_12147,U_12148) ),
    inference(clausify,[status(thm)],[f_3171_4]) ).

fof(f_3172_1,plain,
    ! [V_B_2,V_X2_2,V_X1_2,V_f_2,T_d,V_r2_2,V_A2_2,T_c,V_r1_2,V_A1_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_d,tc_HOL_Obool)),V_X1_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_X2_2)),V_f_2))),V_B_2))
      | ? [B_x1] :
          ( ? [B_x2] :
              ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(V_f_2,B_x1),B_x2)),V_B_2))
              & hBOOL(hAPP(hAPP(c_member(T_c),B_x2),V_A2_2)) )
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x1),V_A1_2)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_X2_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),V_A2_2),V_r2_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X1_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A1_2),V_r1_2)))
      | ~ c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
      | ~ c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
      | ~ c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2) ),
    inference(fof_nnf,[status(thm)],[fact_UN__equiv__class__type2]) ).

fof(f_3172_2,plain,
    ! [U_12165,U_12164,U_12163,U_12162,U_12161,U_12160,U_12159,U_12158,U_12157,U_12156,U_12155] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_12161,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12155,tc_fun(U_12161,tc_HOL_Obool)),U_12163),hAPP(hAPP(c_COMBB(tc_fun(U_12158,tc_fun(U_12161,tc_HOL_Obool)),tc_fun(U_12161,tc_HOL_Obool),U_12155),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12158,tc_fun(U_12161,tc_HOL_Obool)),U_12164)),U_12162))),U_12165))
      | ? [U_12154] :
          ( ? [U_12153] :
              ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12161,tc_HOL_Obool)),hAPP(hAPP(U_12162,U_12154),U_12153)),U_12165))
              & hBOOL(hAPP(hAPP(c_member(U_12158),U_12153),U_12159)) )
          & hBOOL(hAPP(hAPP(c_member(U_12155),U_12154),U_12156)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12158,tc_HOL_Obool)),U_12164),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12158),U_12159),U_12160)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12155,tc_HOL_Obool)),U_12163),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12155),U_12156),U_12157)))
      | ~ c_Equiv__Relations_Ocongruent2(U_12155,U_12158,tc_fun(U_12161,tc_HOL_Obool),U_12157,U_12160,U_12162)
      | ~ c_Equiv__Relations_Oequiv(U_12158,U_12159,U_12160)
      | ~ c_Equiv__Relations_Oequiv(U_12155,U_12156,U_12157) ),
    inference(variable_rename,[status(thm)],[f_3172_1]) ).

fof(f_3172_3,plain,
    ! [U_12165,U_12164,U_12163,U_12162,U_12161,U_12160,U_12159,U_12158,U_12157,U_12156,U_12155] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_12161,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12155,tc_fun(U_12161,tc_HOL_Obool)),U_12163),hAPP(hAPP(c_COMBB(tc_fun(U_12158,tc_fun(U_12161,tc_HOL_Obool)),tc_fun(U_12161,tc_HOL_Obool),U_12155),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12158,tc_fun(U_12161,tc_HOL_Obool)),U_12164)),U_12162))),U_12165))
      | ( ? [U_12153] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12161,tc_HOL_Obool)),hAPP(hAPP(U_12162,sK287(U_12165,U_12164,U_12163,U_12162,U_12161,U_12160,U_12159,U_12158,U_12157,U_12156,U_12155)),U_12153)),U_12165))
            & hBOOL(hAPP(hAPP(c_member(U_12158),U_12153),U_12159)) )
        & hBOOL(hAPP(hAPP(c_member(U_12155),sK287(U_12165,U_12164,U_12163,U_12162,U_12161,U_12160,U_12159,U_12158,U_12157,U_12156,U_12155)),U_12156)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12158,tc_HOL_Obool)),U_12164),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12158),U_12159),U_12160)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12155,tc_HOL_Obool)),U_12163),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12155),U_12156),U_12157)))
      | ~ c_Equiv__Relations_Ocongruent2(U_12155,U_12158,tc_fun(U_12161,tc_HOL_Obool),U_12157,U_12160,U_12162)
      | ~ c_Equiv__Relations_Oequiv(U_12158,U_12159,U_12160)
      | ~ c_Equiv__Relations_Oequiv(U_12155,U_12156,U_12157) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK287]),skolemize(U_12154,sK287(U_12165,U_12164,U_12163,U_12162,U_12161,U_12160,U_12159,U_12158,U_12157,U_12156,U_12155))],[f_3172_2]) ).

fof(f_3172_4,plain,
    ! [U_12165,U_12164,U_12163,U_12162,U_12161,U_12160,U_12159,U_12158,U_12157,U_12156,U_12155] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_12161,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12155,tc_fun(U_12161,tc_HOL_Obool)),U_12163),hAPP(hAPP(c_COMBB(tc_fun(U_12158,tc_fun(U_12161,tc_HOL_Obool)),tc_fun(U_12161,tc_HOL_Obool),U_12155),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12158,tc_fun(U_12161,tc_HOL_Obool)),U_12164)),U_12162))),U_12165))
      | ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12161,tc_HOL_Obool)),hAPP(hAPP(U_12162,sK287(U_12165,U_12164,U_12163,U_12162,U_12161,U_12160,U_12159,U_12158,U_12157,U_12156,U_12155)),sK288(U_12165,U_12164,U_12163,U_12162,U_12161,U_12160,U_12159,U_12158,U_12157,U_12156,U_12155))),U_12165))
        & hBOOL(hAPP(hAPP(c_member(U_12158),sK288(U_12165,U_12164,U_12163,U_12162,U_12161,U_12160,U_12159,U_12158,U_12157,U_12156,U_12155)),U_12159))
        & hBOOL(hAPP(hAPP(c_member(U_12155),sK287(U_12165,U_12164,U_12163,U_12162,U_12161,U_12160,U_12159,U_12158,U_12157,U_12156,U_12155)),U_12156)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12158,tc_HOL_Obool)),U_12164),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12158),U_12159),U_12160)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12155,tc_HOL_Obool)),U_12163),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12155),U_12156),U_12157)))
      | ~ c_Equiv__Relations_Ocongruent2(U_12155,U_12158,tc_fun(U_12161,tc_HOL_Obool),U_12157,U_12160,U_12162)
      | ~ c_Equiv__Relations_Oequiv(U_12158,U_12159,U_12160)
      | ~ c_Equiv__Relations_Oequiv(U_12155,U_12156,U_12157) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK288]),skolemize(U_12153,sK288(U_12165,U_12164,U_12163,U_12162,U_12161,U_12160,U_12159,U_12158,U_12157,U_12156,U_12155))],[f_3172_3]) ).

cnf(f_3172_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12155),sK287(U_12165,U_12164,U_12163,U_12162,U_12161,U_12160,U_12159,U_12158,U_12157,U_12156,U_12155)),U_12156))
    | hBOOL(hAPP(hAPP(c_member(tc_fun(U_12161,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12155,tc_fun(U_12161,tc_HOL_Obool)),U_12163),hAPP(hAPP(c_COMBB(tc_fun(U_12158,tc_fun(U_12161,tc_HOL_Obool)),tc_fun(U_12161,tc_HOL_Obool),U_12155),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12158,tc_fun(U_12161,tc_HOL_Obool)),U_12164)),U_12162))),U_12165))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12158,tc_HOL_Obool)),U_12164),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12158),U_12159),U_12160)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12155,tc_HOL_Obool)),U_12163),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12155),U_12156),U_12157)))
    | ~ c_Equiv__Relations_Ocongruent2(U_12155,U_12158,tc_fun(U_12161,tc_HOL_Obool),U_12157,U_12160,U_12162)
    | ~ c_Equiv__Relations_Oequiv(U_12158,U_12159,U_12160)
    | ~ c_Equiv__Relations_Oequiv(U_12155,U_12156,U_12157) ),
    inference(clausify,[status(thm)],[f_3172_4]) ).

cnf(f_3172_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12158),sK288(U_12165,U_12164,U_12163,U_12162,U_12161,U_12160,U_12159,U_12158,U_12157,U_12156,U_12155)),U_12159))
    | hBOOL(hAPP(hAPP(c_member(tc_fun(U_12161,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12155,tc_fun(U_12161,tc_HOL_Obool)),U_12163),hAPP(hAPP(c_COMBB(tc_fun(U_12158,tc_fun(U_12161,tc_HOL_Obool)),tc_fun(U_12161,tc_HOL_Obool),U_12155),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12158,tc_fun(U_12161,tc_HOL_Obool)),U_12164)),U_12162))),U_12165))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12158,tc_HOL_Obool)),U_12164),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12158),U_12159),U_12160)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12155,tc_HOL_Obool)),U_12163),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12155),U_12156),U_12157)))
    | ~ c_Equiv__Relations_Ocongruent2(U_12155,U_12158,tc_fun(U_12161,tc_HOL_Obool),U_12157,U_12160,U_12162)
    | ~ c_Equiv__Relations_Oequiv(U_12158,U_12159,U_12160)
    | ~ c_Equiv__Relations_Oequiv(U_12155,U_12156,U_12157) ),
    inference(clausify,[status(thm)],[f_3172_4]) ).

cnf(f_3172_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12161,tc_HOL_Obool)),hAPP(hAPP(U_12162,sK287(U_12165,U_12164,U_12163,U_12162,U_12161,U_12160,U_12159,U_12158,U_12157,U_12156,U_12155)),sK288(U_12165,U_12164,U_12163,U_12162,U_12161,U_12160,U_12159,U_12158,U_12157,U_12156,U_12155))),U_12165))
    | hBOOL(hAPP(hAPP(c_member(tc_fun(U_12161,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12155,tc_fun(U_12161,tc_HOL_Obool)),U_12163),hAPP(hAPP(c_COMBB(tc_fun(U_12158,tc_fun(U_12161,tc_HOL_Obool)),tc_fun(U_12161,tc_HOL_Obool),U_12155),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12158,tc_fun(U_12161,tc_HOL_Obool)),U_12164)),U_12162))),U_12165))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12158,tc_HOL_Obool)),U_12164),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12158),U_12159),U_12160)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12155,tc_HOL_Obool)),U_12163),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12155),U_12156),U_12157)))
    | ~ c_Equiv__Relations_Ocongruent2(U_12155,U_12158,tc_fun(U_12161,tc_HOL_Obool),U_12157,U_12160,U_12162)
    | ~ c_Equiv__Relations_Oequiv(U_12158,U_12159,U_12160)
    | ~ c_Equiv__Relations_Oequiv(U_12155,U_12156,U_12157) ),
    inference(clausify,[status(thm)],[f_3172_4]) ).

fof(f_3173_1,plain,
    ! [V_B_2,V_X_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_X_2),V_f_2)),V_B_2))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_f_2,B_x)),V_B_2))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
      | ~ c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
      | ~ c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_UN__equiv__class__type]) ).

fof(f_3173_2,plain,
    ! [U_12173,U_12172,U_12171,U_12170,U_12169,U_12168,U_12167] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_12170,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12167,tc_fun(U_12170,tc_HOL_Obool)),U_12172),U_12171)),U_12173))
      | ? [U_12166] :
          ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12170,tc_HOL_Obool)),hAPP(U_12171,U_12166)),U_12173))
          & hBOOL(hAPP(hAPP(c_member(U_12167),U_12166),U_12168)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12167,tc_HOL_Obool)),U_12172),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12167),U_12168),U_12169)))
      | ~ c_Equiv__Relations_Ocongruent(U_12167,tc_fun(U_12170,tc_HOL_Obool),U_12169,U_12171)
      | ~ c_Equiv__Relations_Oequiv(U_12167,U_12168,U_12169) ),
    inference(variable_rename,[status(thm)],[f_3173_1]) ).

fof(f_3173_3,plain,
    ! [U_12173,U_12172,U_12171,U_12170,U_12169,U_12168,U_12167] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_12170,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12167,tc_fun(U_12170,tc_HOL_Obool)),U_12172),U_12171)),U_12173))
      | ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12170,tc_HOL_Obool)),hAPP(U_12171,sK289(U_12173,U_12172,U_12171,U_12170,U_12169,U_12168,U_12167))),U_12173))
        & hBOOL(hAPP(hAPP(c_member(U_12167),sK289(U_12173,U_12172,U_12171,U_12170,U_12169,U_12168,U_12167)),U_12168)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12167,tc_HOL_Obool)),U_12172),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12167),U_12168),U_12169)))
      | ~ c_Equiv__Relations_Ocongruent(U_12167,tc_fun(U_12170,tc_HOL_Obool),U_12169,U_12171)
      | ~ c_Equiv__Relations_Oequiv(U_12167,U_12168,U_12169) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK289]),skolemize(U_12166,sK289(U_12173,U_12172,U_12171,U_12170,U_12169,U_12168,U_12167))],[f_3173_2]) ).

cnf(f_3173_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12167),sK289(U_12173,U_12172,U_12171,U_12170,U_12169,U_12168,U_12167)),U_12168))
    | hBOOL(hAPP(hAPP(c_member(tc_fun(U_12170,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12167,tc_fun(U_12170,tc_HOL_Obool)),U_12172),U_12171)),U_12173))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12167,tc_HOL_Obool)),U_12172),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12167),U_12168),U_12169)))
    | ~ c_Equiv__Relations_Ocongruent(U_12167,tc_fun(U_12170,tc_HOL_Obool),U_12169,U_12171)
    | ~ c_Equiv__Relations_Oequiv(U_12167,U_12168,U_12169) ),
    inference(clausify,[status(thm)],[f_3173_3]) ).

cnf(f_3173_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12170,tc_HOL_Obool)),hAPP(U_12171,sK289(U_12173,U_12172,U_12171,U_12170,U_12169,U_12168,U_12167))),U_12173))
    | hBOOL(hAPP(hAPP(c_member(tc_fun(U_12170,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12167,tc_fun(U_12170,tc_HOL_Obool)),U_12172),U_12171)),U_12173))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12167,tc_HOL_Obool)),U_12172),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12167),U_12168),U_12169)))
    | ~ c_Equiv__Relations_Ocongruent(U_12167,tc_fun(U_12170,tc_HOL_Obool),U_12169,U_12171)
    | ~ c_Equiv__Relations_Oequiv(U_12167,U_12168,U_12169) ),
    inference(clausify,[status(thm)],[f_3173_3]) ).

fof(f_3174_1,plain,
    c_Int_OInteg = hAPP(hAPP(c_Equiv__Relations_Oquotient(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Int_Ointrel),
    inference(fof_nnf,[status(thm)],[fact_Integ__def]) ).

cnf(f_3174_2,plain,
    c_Int_OInteg = hAPP(hAPP(c_Equiv__Relations_Oquotient(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Int_Ointrel),
    inference(clausify,[status(thm)],[f_3174_1]) ).

fof(f_3175_1,plain,
    ! [V_A_2,V_c_2,T_b] :
      ( ? [B_x] :
          ( V_c_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_c_2),c_Relation_OId__on(T_b,V_A_2))) ),
    inference(fof_nnf,[status(thm)],[fact_Id__onE]) ).

fof(f_3175_2,plain,
    ! [U_12177,U_12176,U_12175] :
      ( ? [U_12174] :
          ( U_12176 = hAPP(hAPP(c_Product__Type_OPair(U_12175,U_12175),U_12174),U_12174)
          & hBOOL(hAPP(hAPP(c_member(U_12175),U_12174),U_12177)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12175,U_12175)),U_12176),c_Relation_OId__on(U_12175,U_12177))) ),
    inference(variable_rename,[status(thm)],[f_3175_1]) ).

fof(f_3175_3,plain,
    ! [U_12177,U_12176,U_12175] :
      ( ( U_12176 = hAPP(hAPP(c_Product__Type_OPair(U_12175,U_12175),sK290(U_12177,U_12176,U_12175)),sK290(U_12177,U_12176,U_12175))
        & hBOOL(hAPP(hAPP(c_member(U_12175),sK290(U_12177,U_12176,U_12175)),U_12177)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12175,U_12175)),U_12176),c_Relation_OId__on(U_12175,U_12177))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK290]),skolemize(U_12174,sK290(U_12177,U_12176,U_12175))],[f_3175_2]) ).

cnf(f_3175_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12175),sK290(U_12177,U_12176,U_12175)),U_12177))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12175,U_12175)),U_12176),c_Relation_OId__on(U_12175,U_12177))) ),
    inference(clausify,[status(thm)],[f_3175_3]) ).

cnf(f_3175_5,plain,
    ( U_12176 = hAPP(hAPP(c_Product__Type_OPair(U_12175,U_12175),sK290(U_12177,U_12176,U_12175)),sK290(U_12177,U_12176,U_12175))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12175,U_12175)),U_12176),c_Relation_OId__on(U_12175,U_12177))) ),
    inference(clausify,[status(thm)],[f_3175_3]) ).

fof(f_3176_1,plain,
    ! [V_g_2,V_f_2,V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),V_g_2),V_B_2)
      | ? [B_x] :
          ( hAPP(V_f_2,B_x) != hAPP(V_g_2,B_x)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) )
      | ~ c_Nat__Transfer_Onat__set(V_B_2)
      | V_A_2 != V_B_2
      | ~ class_Groups_Ocomm__monoid__mult(T_b)
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__sum__prod__cong_I1_J]) ).

fof(f_3176_2,plain,
    ! [U_12183,U_12182,U_12181,U_12180,U_12179] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_12179),U_12182),U_12180) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_12179),U_12183),U_12181)
      | ? [U_12178] :
          ( hAPP(U_12182,U_12178) != hAPP(U_12183,U_12178)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12178)) )
      | ~ c_Nat__Transfer_Onat__set(U_12181)
      | U_12180 != U_12181
      | ~ class_Groups_Ocomm__monoid__mult(U_12179)
      | ~ class_Groups_Ocomm__monoid__add(U_12179) ),
    inference(variable_rename,[status(thm)],[f_3176_1]) ).

fof(f_3176_3,plain,
    ! [U_12183,U_12182,U_12181,U_12180,U_12179] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_12179),U_12182),U_12180) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_12179),U_12183),U_12181)
      | ( hAPP(U_12182,sK291(U_12183,U_12182,U_12181,U_12180,U_12179)) != hAPP(U_12183,sK291(U_12183,U_12182,U_12181,U_12180,U_12179))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK291(U_12183,U_12182,U_12181,U_12180,U_12179))) )
      | ~ c_Nat__Transfer_Onat__set(U_12181)
      | U_12180 != U_12181
      | ~ class_Groups_Ocomm__monoid__mult(U_12179)
      | ~ class_Groups_Ocomm__monoid__add(U_12179) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK291]),skolemize(U_12178,sK291(U_12183,U_12182,U_12181,U_12180,U_12179))],[f_3176_2]) ).

cnf(f_3176_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK291(U_12183,U_12182,U_12181,U_12180,U_12179)))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_12179),U_12182),U_12180) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_12179),U_12183),U_12181)
    | ~ c_Nat__Transfer_Onat__set(U_12181)
    | U_12180 != U_12181
    | ~ class_Groups_Ocomm__monoid__mult(U_12179)
    | ~ class_Groups_Ocomm__monoid__add(U_12179) ),
    inference(clausify,[status(thm)],[f_3176_3]) ).

cnf(f_3176_5,plain,
    ( hAPP(U_12182,sK291(U_12183,U_12182,U_12181,U_12180,U_12179)) != hAPP(U_12183,sK291(U_12183,U_12182,U_12181,U_12180,U_12179))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_12179),U_12182),U_12180) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_12179),U_12183),U_12181)
    | ~ c_Nat__Transfer_Onat__set(U_12181)
    | U_12180 != U_12181
    | ~ class_Groups_Ocomm__monoid__mult(U_12179)
    | ~ class_Groups_Ocomm__monoid__add(U_12179) ),
    inference(clausify,[status(thm)],[f_3176_3]) ).

fof(f_3177_1,plain,
    ! [V_x_2] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,V_x_2)),c_Int_OInteg)),
    inference(fof_nnf,[status(thm)],[fact_Rep__Integ]) ).

fof(f_3177_2,plain,
    ! [U_12184] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,U_12184)),c_Int_OInteg)),
    inference(variable_rename,[status(thm)],[f_3177_1]) ).

cnf(f_3177_3,plain,
    hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,U_12184)),c_Int_OInteg)),
    inference(clausify,[status(thm)],[f_3177_2]) ).

fof(f_3178_1,plain,
    c_Typedef_Otype__definition(tc_Int_Oint,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Int_ORep__Integ,c_Int_OAbs__Integ,c_Int_OInteg),
    inference(fof_nnf,[status(thm)],[fact_type__definition__Integ]) ).

cnf(f_3178_2,plain,
    c_Typedef_Otype__definition(tc_Int_Oint,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Int_ORep__Integ,c_Int_OAbs__Integ,c_Int_OInteg),
    inference(clausify,[status(thm)],[f_3178_1]) ).

fof(f_3179_1,plain,
    ! [V_x_2,V_r_2,T_b] :
      ( ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2)),V_x_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) )
      & ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2)))
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2)),V_x_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_accp__acc__eq]) ).

fof(f_3179_2,plain,
    ! [U_12187,U_12186,U_12185] :
      ( ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_12185,hAPP(hAPP(c_COMBC(U_12185,tc_fun(tc_prod(U_12185,U_12185),tc_HOL_Obool),tc_fun(U_12185,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12185,tc_fun(tc_fun(tc_prod(U_12185,U_12185),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12185,U_12185),tc_HOL_Obool),tc_fun(U_12185,tc_HOL_Obool)),U_12185),c_COMBC(U_12185,tc_fun(tc_prod(U_12185,U_12185),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12185,tc_prod(U_12185,U_12185)),tc_fun(U_12185,tc_fun(tc_fun(tc_prod(U_12185,U_12185),tc_HOL_Obool),tc_HOL_Obool)),U_12185),hAPP(c_COMBB(tc_prod(U_12185,U_12185),tc_fun(tc_fun(tc_prod(U_12185,U_12185),tc_HOL_Obool),tc_HOL_Obool),U_12185),c_member(tc_prod(U_12185,U_12185)))),c_Product__Type_OPair(U_12185,U_12185)))),U_12186)),U_12187))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12185),U_12187),c_Wellfounded_Oacc(U_12185,U_12186))) )
      & ( hBOOL(hAPP(hAPP(c_member(U_12185),U_12187),c_Wellfounded_Oacc(U_12185,U_12186)))
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_12185,hAPP(hAPP(c_COMBC(U_12185,tc_fun(tc_prod(U_12185,U_12185),tc_HOL_Obool),tc_fun(U_12185,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12185,tc_fun(tc_fun(tc_prod(U_12185,U_12185),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12185,U_12185),tc_HOL_Obool),tc_fun(U_12185,tc_HOL_Obool)),U_12185),c_COMBC(U_12185,tc_fun(tc_prod(U_12185,U_12185),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12185,tc_prod(U_12185,U_12185)),tc_fun(U_12185,tc_fun(tc_fun(tc_prod(U_12185,U_12185),tc_HOL_Obool),tc_HOL_Obool)),U_12185),hAPP(c_COMBB(tc_prod(U_12185,U_12185),tc_fun(tc_fun(tc_prod(U_12185,U_12185),tc_HOL_Obool),tc_HOL_Obool),U_12185),c_member(tc_prod(U_12185,U_12185)))),c_Product__Type_OPair(U_12185,U_12185)))),U_12186)),U_12187)) ) ),
    inference(variable_rename,[status(thm)],[f_3179_1]) ).

fof(f_3179_3,plain,
    ( ! [U_12193,U_12191,U_12189] :
        ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_12189,hAPP(hAPP(c_COMBC(U_12189,tc_fun(tc_prod(U_12189,U_12189),tc_HOL_Obool),tc_fun(U_12189,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12189,tc_fun(tc_fun(tc_prod(U_12189,U_12189),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12189,U_12189),tc_HOL_Obool),tc_fun(U_12189,tc_HOL_Obool)),U_12189),c_COMBC(U_12189,tc_fun(tc_prod(U_12189,U_12189),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12189,tc_prod(U_12189,U_12189)),tc_fun(U_12189,tc_fun(tc_fun(tc_prod(U_12189,U_12189),tc_HOL_Obool),tc_HOL_Obool)),U_12189),hAPP(c_COMBB(tc_prod(U_12189,U_12189),tc_fun(tc_fun(tc_prod(U_12189,U_12189),tc_HOL_Obool),tc_HOL_Obool),U_12189),c_member(tc_prod(U_12189,U_12189)))),c_Product__Type_OPair(U_12189,U_12189)))),U_12191)),U_12193))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12189),U_12193),c_Wellfounded_Oacc(U_12189,U_12191))) )
    & ! [U_12192,U_12190,U_12188] :
        ( hBOOL(hAPP(hAPP(c_member(U_12188),U_12192),c_Wellfounded_Oacc(U_12188,U_12190)))
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_12188,hAPP(hAPP(c_COMBC(U_12188,tc_fun(tc_prod(U_12188,U_12188),tc_HOL_Obool),tc_fun(U_12188,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12188,tc_fun(tc_fun(tc_prod(U_12188,U_12188),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12188,U_12188),tc_HOL_Obool),tc_fun(U_12188,tc_HOL_Obool)),U_12188),c_COMBC(U_12188,tc_fun(tc_prod(U_12188,U_12188),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12188,tc_prod(U_12188,U_12188)),tc_fun(U_12188,tc_fun(tc_fun(tc_prod(U_12188,U_12188),tc_HOL_Obool),tc_HOL_Obool)),U_12188),hAPP(c_COMBB(tc_prod(U_12188,U_12188),tc_fun(tc_fun(tc_prod(U_12188,U_12188),tc_HOL_Obool),tc_HOL_Obool),U_12188),c_member(tc_prod(U_12188,U_12188)))),c_Product__Type_OPair(U_12188,U_12188)))),U_12190)),U_12192)) ) ),
    inference(miniscope,[status(thm)],[f_3179_2]) ).

cnf(f_3179_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12188),U_12192),c_Wellfounded_Oacc(U_12188,U_12190)))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_12188,hAPP(hAPP(c_COMBC(U_12188,tc_fun(tc_prod(U_12188,U_12188),tc_HOL_Obool),tc_fun(U_12188,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12188,tc_fun(tc_fun(tc_prod(U_12188,U_12188),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12188,U_12188),tc_HOL_Obool),tc_fun(U_12188,tc_HOL_Obool)),U_12188),c_COMBC(U_12188,tc_fun(tc_prod(U_12188,U_12188),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12188,tc_prod(U_12188,U_12188)),tc_fun(U_12188,tc_fun(tc_fun(tc_prod(U_12188,U_12188),tc_HOL_Obool),tc_HOL_Obool)),U_12188),hAPP(c_COMBB(tc_prod(U_12188,U_12188),tc_fun(tc_fun(tc_prod(U_12188,U_12188),tc_HOL_Obool),tc_HOL_Obool),U_12188),c_member(tc_prod(U_12188,U_12188)))),c_Product__Type_OPair(U_12188,U_12188)))),U_12190)),U_12192)) ),
    inference(clausify,[status(thm)],[f_3179_3]) ).

cnf(f_3179_5,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_12189,hAPP(hAPP(c_COMBC(U_12189,tc_fun(tc_prod(U_12189,U_12189),tc_HOL_Obool),tc_fun(U_12189,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12189,tc_fun(tc_fun(tc_prod(U_12189,U_12189),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12189,U_12189),tc_HOL_Obool),tc_fun(U_12189,tc_HOL_Obool)),U_12189),c_COMBC(U_12189,tc_fun(tc_prod(U_12189,U_12189),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12189,tc_prod(U_12189,U_12189)),tc_fun(U_12189,tc_fun(tc_fun(tc_prod(U_12189,U_12189),tc_HOL_Obool),tc_HOL_Obool)),U_12189),hAPP(c_COMBB(tc_prod(U_12189,U_12189),tc_fun(tc_fun(tc_prod(U_12189,U_12189),tc_HOL_Obool),tc_HOL_Obool),U_12189),c_member(tc_prod(U_12189,U_12189)))),c_Product__Type_OPair(U_12189,U_12189)))),U_12191)),U_12193))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12189),U_12193),c_Wellfounded_Oacc(U_12189,U_12191))) ),
    inference(clausify,[status(thm)],[f_3179_3]) ).

fof(f_3180_1,plain,
    ! [V_a2_2,V_a1_2,V_R_2,T_b] :
      ( ( c_Wellfounded_Omax__extp(T_b,V_R_2,V_a1_2,V_a2_2)
        | ? [B_x] :
            ( ! [B_xa] :
                ( ~ hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa))
                | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2)) )
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2)) )
        | V_a2_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2)) )
      & ( ( ! [B_x] :
              ( ? [B_xa] :
                  ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa))
                  & hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2)) )
              | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2)) )
          & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2)) )
        | ~ c_Wellfounded_Omax__extp(T_b,V_R_2,V_a1_2,V_a2_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_max__extp_Oequations]) ).

fof(f_3180_2,plain,
    ! [U_12201,U_12200,U_12199,U_12198] :
      ( ( c_Wellfounded_Omax__extp(U_12198,U_12199,U_12200,U_12201)
        | ? [U_12197] :
            ( ! [U_12196] :
                ( ~ hBOOL(hAPP(hAPP(U_12199,U_12197),U_12196))
                | ~ hBOOL(hAPP(hAPP(c_member(U_12198),U_12196),U_12201)) )
            & hBOOL(hAPP(hAPP(c_member(U_12198),U_12197),U_12200)) )
        | U_12201 = c_Orderings_Obot__class_Obot(tc_fun(U_12198,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12198),U_12201))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12198),U_12200)) )
      & ( ( ! [U_12195] :
              ( ? [U_12194] :
                  ( hBOOL(hAPP(hAPP(U_12199,U_12195),U_12194))
                  & hBOOL(hAPP(hAPP(c_member(U_12198),U_12194),U_12201)) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_12198),U_12195),U_12200)) )
          & U_12201 != c_Orderings_Obot__class_Obot(tc_fun(U_12198,tc_HOL_Obool))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_12198),U_12201))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_12198),U_12200)) )
        | ~ c_Wellfounded_Omax__extp(U_12198,U_12199,U_12200,U_12201) ) ),
    inference(variable_rename,[status(thm)],[f_3180_1]) ).

fof(f_3180_3,plain,
    ( ! [U_12209,U_12207,U_12205,U_12203] :
        ( c_Wellfounded_Omax__extp(U_12203,U_12205,U_12207,U_12209)
        | ? [U_12197] :
            ( ! [U_12196] :
                ( ~ hBOOL(hAPP(hAPP(U_12205,U_12197),U_12196))
                | ~ hBOOL(hAPP(hAPP(c_member(U_12203),U_12196),U_12209)) )
            & hBOOL(hAPP(hAPP(c_member(U_12203),U_12197),U_12207)) )
        | U_12209 = c_Orderings_Obot__class_Obot(tc_fun(U_12203,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12203),U_12209))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12203),U_12207)) )
    & ! [U_12208,U_12206,U_12204,U_12202] :
        ( ( ! [U_12195] :
              ( ? [U_12194] :
                  ( hBOOL(hAPP(hAPP(U_12204,U_12195),U_12194))
                  & hBOOL(hAPP(hAPP(c_member(U_12202),U_12194),U_12208)) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_12202),U_12195),U_12206)) )
          & U_12208 != c_Orderings_Obot__class_Obot(tc_fun(U_12202,tc_HOL_Obool))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_12202),U_12208))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_12202),U_12206)) )
        | ~ c_Wellfounded_Omax__extp(U_12202,U_12204,U_12206,U_12208) ) ),
    inference(miniscope,[status(thm)],[f_3180_2]) ).

fof(f_3180_4,plain,
    ( ! [U_12209,U_12207,U_12205,U_12203] :
        ( c_Wellfounded_Omax__extp(U_12203,U_12205,U_12207,U_12209)
        | ? [U_12197] :
            ( ! [U_12196] :
                ( ~ hBOOL(hAPP(hAPP(U_12205,U_12197),U_12196))
                | ~ hBOOL(hAPP(hAPP(c_member(U_12203),U_12196),U_12209)) )
            & hBOOL(hAPP(hAPP(c_member(U_12203),U_12197),U_12207)) )
        | U_12209 = c_Orderings_Obot__class_Obot(tc_fun(U_12203,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12203),U_12209))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12203),U_12207)) )
    & ! [U_12208,U_12206,U_12204,U_12202] :
        ( ( ! [U_12195] :
              ( ( hBOOL(hAPP(hAPP(U_12204,U_12195),sK292(U_12208,U_12206,U_12204,U_12202,U_12195)))
                & hBOOL(hAPP(hAPP(c_member(U_12202),sK292(U_12208,U_12206,U_12204,U_12202,U_12195)),U_12208)) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_12202),U_12195),U_12206)) )
          & U_12208 != c_Orderings_Obot__class_Obot(tc_fun(U_12202,tc_HOL_Obool))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_12202),U_12208))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_12202),U_12206)) )
        | ~ c_Wellfounded_Omax__extp(U_12202,U_12204,U_12206,U_12208) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK292]),skolemize(U_12194,sK292(U_12208,U_12206,U_12204,U_12202,U_12195))],[f_3180_3]) ).

fof(f_3180_5,plain,
    ( ! [U_12209,U_12207,U_12205,U_12203] :
        ( c_Wellfounded_Omax__extp(U_12203,U_12205,U_12207,U_12209)
        | ( ! [U_12196] :
              ( ~ hBOOL(hAPP(hAPP(U_12205,sK293(U_12209,U_12207,U_12205,U_12203)),U_12196))
              | ~ hBOOL(hAPP(hAPP(c_member(U_12203),U_12196),U_12209)) )
          & hBOOL(hAPP(hAPP(c_member(U_12203),sK293(U_12209,U_12207,U_12205,U_12203)),U_12207)) )
        | U_12209 = c_Orderings_Obot__class_Obot(tc_fun(U_12203,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12203),U_12209))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12203),U_12207)) )
    & ! [U_12208,U_12206,U_12204,U_12202] :
        ( ( ! [U_12195] :
              ( ( hBOOL(hAPP(hAPP(U_12204,U_12195),sK292(U_12208,U_12206,U_12204,U_12202,U_12195)))
                & hBOOL(hAPP(hAPP(c_member(U_12202),sK292(U_12208,U_12206,U_12204,U_12202,U_12195)),U_12208)) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_12202),U_12195),U_12206)) )
          & U_12208 != c_Orderings_Obot__class_Obot(tc_fun(U_12202,tc_HOL_Obool))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_12202),U_12208))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_12202),U_12206)) )
        | ~ c_Wellfounded_Omax__extp(U_12202,U_12204,U_12206,U_12208) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK293]),skolemize(U_12197,sK293(U_12209,U_12207,U_12205,U_12203))],[f_3180_4]) ).

cnf(f_3180_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12202),U_12206))
    | ~ c_Wellfounded_Omax__extp(U_12202,U_12204,U_12206,U_12208) ),
    inference(clausify,[status(thm)],[f_3180_5]) ).

cnf(f_3180_7,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12202),U_12208))
    | ~ c_Wellfounded_Omax__extp(U_12202,U_12204,U_12206,U_12208) ),
    inference(clausify,[status(thm)],[f_3180_5]) ).

cnf(f_3180_8,plain,
    ( U_12208 != c_Orderings_Obot__class_Obot(tc_fun(U_12202,tc_HOL_Obool))
    | ~ c_Wellfounded_Omax__extp(U_12202,U_12204,U_12206,U_12208) ),
    inference(clausify,[status(thm)],[f_3180_5]) ).

cnf(f_3180_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12202),sK292(U_12208,U_12206,U_12204,U_12202,U_12195)),U_12208))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12202),U_12195),U_12206))
    | ~ c_Wellfounded_Omax__extp(U_12202,U_12204,U_12206,U_12208) ),
    inference(clausify,[status(thm)],[f_3180_5]) ).

cnf(f_3180_10,plain,
    ( hBOOL(hAPP(hAPP(U_12204,U_12195),sK292(U_12208,U_12206,U_12204,U_12202,U_12195)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12202),U_12195),U_12206))
    | ~ c_Wellfounded_Omax__extp(U_12202,U_12204,U_12206,U_12208) ),
    inference(clausify,[status(thm)],[f_3180_5]) ).

cnf(f_3180_11,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12203),sK293(U_12209,U_12207,U_12205,U_12203)),U_12207))
    | U_12209 = c_Orderings_Obot__class_Obot(tc_fun(U_12203,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12203),U_12209))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12203),U_12207))
    | c_Wellfounded_Omax__extp(U_12203,U_12205,U_12207,U_12209) ),
    inference(clausify,[status(thm)],[f_3180_5]) ).

cnf(f_3180_12,plain,
    ( ~ hBOOL(hAPP(hAPP(U_12205,sK293(U_12209,U_12207,U_12205,U_12203)),U_12196))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12203),U_12196),U_12209))
    | U_12209 = c_Orderings_Obot__class_Obot(tc_fun(U_12203,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12203),U_12209))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12203),U_12207))
    | c_Wellfounded_Omax__extp(U_12203,U_12205,U_12207,U_12209) ),
    inference(clausify,[status(thm)],[f_3180_5]) ).

fof(f_3181_1,plain,
    ! [V_R2_2,V_R1_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Wellfounded_Oacc(T_b,V_R2_2)),c_Wellfounded_Oacc(T_b,V_R1_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R1_2),V_R2_2)) ),
    inference(fof_nnf,[status(thm)],[fact_acc__subset]) ).

fof(f_3181_2,plain,
    ! [U_12212,U_12211,U_12210] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12210,tc_HOL_Obool)),c_Wellfounded_Oacc(U_12210,U_12212)),c_Wellfounded_Oacc(U_12210,U_12211)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12210,U_12210),tc_HOL_Obool)),U_12211),U_12212)) ),
    inference(variable_rename,[status(thm)],[f_3181_1]) ).

cnf(f_3181_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12210,tc_HOL_Obool)),c_Wellfounded_Oacc(U_12210,U_12212)),c_Wellfounded_Oacc(U_12210,U_12211)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12210,U_12210),tc_HOL_Obool)),U_12211),U_12212)) ),
    inference(clausify,[status(thm)],[f_3181_2]) ).

fof(f_3182_1,plain,
    ! [V_a_2,V_r_2,V_b_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_acc__downward]) ).

fof(f_3182_2,plain,
    ! [U_12216,U_12215,U_12214,U_12213] :
      ( hBOOL(hAPP(hAPP(c_member(U_12213),U_12216),c_Wellfounded_Oacc(U_12213,U_12215)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12213,U_12213)),hAPP(hAPP(c_Product__Type_OPair(U_12213,U_12213),U_12216),U_12214)),U_12215))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12213),U_12214),c_Wellfounded_Oacc(U_12213,U_12215))) ),
    inference(variable_rename,[status(thm)],[f_3182_1]) ).

cnf(f_3182_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12213),U_12216),c_Wellfounded_Oacc(U_12213,U_12215)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12213,U_12213)),hAPP(hAPP(c_Product__Type_OPair(U_12213,U_12213),U_12216),U_12214)),U_12215))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12213),U_12214),c_Wellfounded_Oacc(U_12213,U_12215))) ),
    inference(clausify,[status(thm)],[f_3182_2]) ).

fof(f_3183_1,plain,
    ! [V_r_2,V_a_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
        | ? [B_x] :
            ( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2)))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),V_a_2)),V_r_2)) ) )
      & ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2)))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),V_a_2)),V_r_2)) )
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_acc_Osimps]) ).

fof(f_3183_2,plain,
    ! [U_12221,U_12220,U_12219] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_12219),U_12220),c_Wellfounded_Oacc(U_12219,U_12221)))
        | ? [U_12218] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_12219),U_12218),c_Wellfounded_Oacc(U_12219,U_12221)))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_12219,U_12219)),hAPP(hAPP(c_Product__Type_OPair(U_12219,U_12219),U_12218),U_12220)),U_12221)) ) )
      & ( ! [U_12217] :
            ( hBOOL(hAPP(hAPP(c_member(U_12219),U_12217),c_Wellfounded_Oacc(U_12219,U_12221)))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12219,U_12219)),hAPP(hAPP(c_Product__Type_OPair(U_12219,U_12219),U_12217),U_12220)),U_12221)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_12219),U_12220),c_Wellfounded_Oacc(U_12219,U_12221))) ) ),
    inference(variable_rename,[status(thm)],[f_3183_1]) ).

fof(f_3183_3,plain,
    ( ! [U_12227,U_12225,U_12223] :
        ( hBOOL(hAPP(hAPP(c_member(U_12223),U_12225),c_Wellfounded_Oacc(U_12223,U_12227)))
        | ? [U_12218] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_12223),U_12218),c_Wellfounded_Oacc(U_12223,U_12227)))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_12223,U_12223)),hAPP(hAPP(c_Product__Type_OPair(U_12223,U_12223),U_12218),U_12225)),U_12227)) ) )
    & ! [U_12226,U_12224,U_12222] :
        ( ! [U_12217] :
            ( hBOOL(hAPP(hAPP(c_member(U_12222),U_12217),c_Wellfounded_Oacc(U_12222,U_12226)))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12222,U_12222)),hAPP(hAPP(c_Product__Type_OPair(U_12222,U_12222),U_12217),U_12224)),U_12226)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_12222),U_12224),c_Wellfounded_Oacc(U_12222,U_12226))) ) ),
    inference(miniscope,[status(thm)],[f_3183_2]) ).

fof(f_3183_4,plain,
    ( ! [U_12227,U_12225,U_12223] :
        ( hBOOL(hAPP(hAPP(c_member(U_12223),U_12225),c_Wellfounded_Oacc(U_12223,U_12227)))
        | ( ~ hBOOL(hAPP(hAPP(c_member(U_12223),sK294(U_12227,U_12225,U_12223)),c_Wellfounded_Oacc(U_12223,U_12227)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_12223,U_12223)),hAPP(hAPP(c_Product__Type_OPair(U_12223,U_12223),sK294(U_12227,U_12225,U_12223)),U_12225)),U_12227)) ) )
    & ! [U_12226,U_12224,U_12222] :
        ( ! [U_12217] :
            ( hBOOL(hAPP(hAPP(c_member(U_12222),U_12217),c_Wellfounded_Oacc(U_12222,U_12226)))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12222,U_12222)),hAPP(hAPP(c_Product__Type_OPair(U_12222,U_12222),U_12217),U_12224)),U_12226)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_12222),U_12224),c_Wellfounded_Oacc(U_12222,U_12226))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK294]),skolemize(U_12218,sK294(U_12227,U_12225,U_12223))],[f_3183_3]) ).

cnf(f_3183_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12222),U_12217),c_Wellfounded_Oacc(U_12222,U_12226)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12222,U_12222)),hAPP(hAPP(c_Product__Type_OPair(U_12222,U_12222),U_12217),U_12224)),U_12226))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12222),U_12224),c_Wellfounded_Oacc(U_12222,U_12226))) ),
    inference(clausify,[status(thm)],[f_3183_4]) ).

cnf(f_3183_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12223,U_12223)),hAPP(hAPP(c_Product__Type_OPair(U_12223,U_12223),sK294(U_12227,U_12225,U_12223)),U_12225)),U_12227))
    | hBOOL(hAPP(hAPP(c_member(U_12223),U_12225),c_Wellfounded_Oacc(U_12223,U_12227))) ),
    inference(clausify,[status(thm)],[f_3183_4]) ).

cnf(f_3183_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_12223),sK294(U_12227,U_12225,U_12223)),c_Wellfounded_Oacc(U_12223,U_12227)))
    | hBOOL(hAPP(hAPP(c_member(U_12223),U_12225),c_Wellfounded_Oacc(U_12223,U_12227))) ),
    inference(clausify,[status(thm)],[f_3183_4]) ).

fof(f_3184_1,plain,
    ! [V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
      ( hAPP(c_Set_Oimage(T_b,T_c,V_Rep_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = V_A_2
      | ~ c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_type__definition_ORep__range]) ).

fof(f_3184_2,plain,
    ! [U_12232,U_12231,U_12230,U_12229,U_12228] :
      ( hAPP(c_Set_Oimage(U_12228,U_12229,U_12230),c_Orderings_Otop__class_Otop(tc_fun(U_12228,tc_HOL_Obool))) = U_12232
      | ~ c_Typedef_Otype__definition(U_12228,U_12229,U_12230,U_12231,U_12232) ),
    inference(variable_rename,[status(thm)],[f_3184_1]) ).

cnf(f_3184_3,plain,
    ( hAPP(c_Set_Oimage(U_12228,U_12229,U_12230),c_Orderings_Otop__class_Otop(tc_fun(U_12228,tc_HOL_Obool))) = U_12232
    | ~ c_Typedef_Otype__definition(U_12228,U_12229,U_12230,U_12231,U_12232) ),
    inference(clausify,[status(thm)],[f_3184_2]) ).

fof(f_3185_1,plain,
    ! [V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
      ( hAPP(c_Set_Oimage(T_c,T_b,V_Abs_2),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
      | ~ c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_type__definition_OAbs__image]) ).

fof(f_3185_2,plain,
    ! [U_12237,U_12236,U_12235,U_12234,U_12233] :
      ( hAPP(c_Set_Oimage(U_12234,U_12233,U_12236),U_12237) = c_Orderings_Otop__class_Otop(tc_fun(U_12233,tc_HOL_Obool))
      | ~ c_Typedef_Otype__definition(U_12233,U_12234,U_12235,U_12236,U_12237) ),
    inference(variable_rename,[status(thm)],[f_3185_1]) ).

cnf(f_3185_3,plain,
    ( hAPP(c_Set_Oimage(U_12234,U_12233,U_12236),U_12237) = c_Orderings_Otop__class_Otop(tc_fun(U_12233,tc_HOL_Obool))
    | ~ c_Typedef_Otype__definition(U_12233,U_12234,U_12235,U_12236,U_12237) ),
    inference(clausify,[status(thm)],[f_3185_2]) ).

fof(f_3186_1,plain,
    ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
      ( ( ( hAPP(V_Abs_2,V_x_2) = hAPP(V_Abs_2,V_y_2)
          | V_x_2 != V_y_2 )
        & ( V_x_2 = V_y_2
          | hAPP(V_Abs_2,V_x_2) != hAPP(V_Abs_2,V_y_2) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
      | ~ c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_type__definition_OAbs__inject]) ).

fof(f_3186_2,plain,
    ! [U_12244,U_12243,U_12242,U_12241,U_12240,U_12239,U_12238] :
      ( ( ( hAPP(U_12241,U_12243) = hAPP(U_12241,U_12244)
          | U_12243 != U_12244 )
        & ( U_12243 = U_12244
          | hAPP(U_12241,U_12243) != hAPP(U_12241,U_12244) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_12239),U_12244),U_12242))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12239),U_12243),U_12242))
      | ~ c_Typedef_Otype__definition(U_12238,U_12239,U_12240,U_12241,U_12242) ),
    inference(variable_rename,[status(thm)],[f_3186_1]) ).

fof(f_3186_3,plain,
    ! [U_12244,U_12243,U_12242,U_12241,U_12240,U_12239] :
      ( ! [U_12238] : ~ c_Typedef_Otype__definition(U_12238,U_12239,U_12240,U_12241,U_12242)
      | ( ( hAPP(U_12241,U_12243) = hAPP(U_12241,U_12244)
          | U_12243 != U_12244 )
        & ( U_12243 = U_12244
          | hAPP(U_12241,U_12243) != hAPP(U_12241,U_12244) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_12239),U_12244),U_12242))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12239),U_12243),U_12242)) ),
    inference(miniscope,[status(thm)],[f_3186_2]) ).

cnf(f_3186_4,plain,
    ( U_12243 = U_12244
    | hAPP(U_12241,U_12243) != hAPP(U_12241,U_12244)
    | ~ hBOOL(hAPP(hAPP(c_member(U_12239),U_12244),U_12242))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12239),U_12243),U_12242))
    | ~ c_Typedef_Otype__definition(U_12238,U_12239,U_12240,U_12241,U_12242) ),
    inference(clausify,[status(thm)],[f_3186_3]) ).

cnf(f_3186_5,plain,
    ( hAPP(U_12241,U_12243) = hAPP(U_12241,U_12244)
    | U_12243 != U_12244
    | ~ hBOOL(hAPP(hAPP(c_member(U_12239),U_12244),U_12242))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12239),U_12243),U_12242))
    | ~ c_Typedef_Otype__definition(U_12238,U_12239,U_12240,U_12241,U_12242) ),
    inference(clausify,[status(thm)],[f_3186_3]) ).

fof(f_3187_1,plain,
    ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
      ( hAPP(V_Abs_2,hAPP(V_Rep_2,V_x_2)) = V_x_2
      | ~ c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_type__definition_ORep__inverse]) ).

fof(f_3187_2,plain,
    ! [U_12250,U_12249,U_12248,U_12247,U_12246,U_12245] :
      ( hAPP(U_12248,hAPP(U_12247,U_12250)) = U_12250
      | ~ c_Typedef_Otype__definition(U_12245,U_12246,U_12247,U_12248,U_12249) ),
    inference(variable_rename,[status(thm)],[f_3187_1]) ).

fof(f_3187_3,plain,
    ! [U_12250,U_12249,U_12248,U_12247] :
      ( ! [U_12246,U_12245] : ~ c_Typedef_Otype__definition(U_12245,U_12246,U_12247,U_12248,U_12249)
      | hAPP(U_12248,hAPP(U_12247,U_12250)) = U_12250 ),
    inference(miniscope,[status(thm)],[f_3187_2]) ).

cnf(f_3187_4,plain,
    ( ~ c_Typedef_Otype__definition(U_12245,U_12246,U_12247,U_12248,U_12249)
    | hAPP(U_12248,hAPP(U_12247,U_12250)) = U_12250 ),
    inference(clausify,[status(thm)],[f_3187_3]) ).

fof(f_3188_1,plain,
    ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
      ( ( ( hAPP(V_Rep_2,V_x_2) = hAPP(V_Rep_2,V_y_2)
          | V_x_2 != V_y_2 )
        & ( V_x_2 = V_y_2
          | hAPP(V_Rep_2,V_x_2) != hAPP(V_Rep_2,V_y_2) ) )
      | ~ c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_type__definition_ORep__inject]) ).

fof(f_3188_2,plain,
    ! [U_12257,U_12256,U_12255,U_12254,U_12253,U_12252,U_12251] :
      ( ( ( hAPP(U_12253,U_12256) = hAPP(U_12253,U_12257)
          | U_12256 != U_12257 )
        & ( U_12256 = U_12257
          | hAPP(U_12253,U_12256) != hAPP(U_12253,U_12257) ) )
      | ~ c_Typedef_Otype__definition(U_12251,U_12252,U_12253,U_12254,U_12255) ),
    inference(variable_rename,[status(thm)],[f_3188_1]) ).

fof(f_3188_3,plain,
    ! [U_12257,U_12256,U_12255,U_12254,U_12253] :
      ( ! [U_12252,U_12251] : ~ c_Typedef_Otype__definition(U_12251,U_12252,U_12253,U_12254,U_12255)
      | ( ( hAPP(U_12253,U_12256) = hAPP(U_12253,U_12257)
          | U_12256 != U_12257 )
        & ( U_12256 = U_12257
          | hAPP(U_12253,U_12256) != hAPP(U_12253,U_12257) ) ) ),
    inference(miniscope,[status(thm)],[f_3188_2]) ).

cnf(f_3188_4,plain,
    ( U_12256 = U_12257
    | hAPP(U_12253,U_12256) != hAPP(U_12253,U_12257)
    | ~ c_Typedef_Otype__definition(U_12251,U_12252,U_12253,U_12254,U_12255) ),
    inference(clausify,[status(thm)],[f_3188_3]) ).

cnf(f_3188_5,plain,
    ( hAPP(U_12253,U_12256) = hAPP(U_12253,U_12257)
    | U_12256 != U_12257
    | ~ c_Typedef_Otype__definition(U_12251,U_12252,U_12253,U_12254,U_12255) ),
    inference(clausify,[status(thm)],[f_3188_3]) ).

fof(f_3189_1,plain,
    ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_Rep_2,V_x_2)),V_A_2))
      | ~ c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_type__definition_ORep]) ).

fof(f_3189_2,plain,
    ! [U_12263,U_12262,U_12261,U_12260,U_12259,U_12258] :
      ( hBOOL(hAPP(hAPP(c_member(U_12259),hAPP(U_12260,U_12263)),U_12262))
      | ~ c_Typedef_Otype__definition(U_12258,U_12259,U_12260,U_12261,U_12262) ),
    inference(variable_rename,[status(thm)],[f_3189_1]) ).

fof(f_3189_3,plain,
    ! [U_12263,U_12262,U_12261,U_12260,U_12259] :
      ( ! [U_12258] : ~ c_Typedef_Otype__definition(U_12258,U_12259,U_12260,U_12261,U_12262)
      | hBOOL(hAPP(hAPP(c_member(U_12259),hAPP(U_12260,U_12263)),U_12262)) ),
    inference(miniscope,[status(thm)],[f_3189_2]) ).

cnf(f_3189_4,plain,
    ( ~ c_Typedef_Otype__definition(U_12258,U_12259,U_12260,U_12261,U_12262)
    | hBOOL(hAPP(hAPP(c_member(U_12259),hAPP(U_12260,U_12263)),U_12262)) ),
    inference(clausify,[status(thm)],[f_3189_3]) ).

fof(f_3190_1,plain,
    ! [V_y_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
      ( hAPP(V_Rep_2,hAPP(V_Abs_2,V_y_2)) = V_y_2
      | ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2))
      | ~ c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_type__definition_OAbs__inverse]) ).

fof(f_3190_2,plain,
    ! [U_12269,U_12268,U_12267,U_12266,U_12265,U_12264] :
      ( hAPP(U_12266,hAPP(U_12267,U_12269)) = U_12269
      | ~ hBOOL(hAPP(hAPP(c_member(U_12265),U_12269),U_12268))
      | ~ c_Typedef_Otype__definition(U_12264,U_12265,U_12266,U_12267,U_12268) ),
    inference(variable_rename,[status(thm)],[f_3190_1]) ).

fof(f_3190_3,plain,
    ! [U_12269,U_12268,U_12267,U_12266,U_12265] :
      ( ! [U_12264] : ~ c_Typedef_Otype__definition(U_12264,U_12265,U_12266,U_12267,U_12268)
      | hAPP(U_12266,hAPP(U_12267,U_12269)) = U_12269
      | ~ hBOOL(hAPP(hAPP(c_member(U_12265),U_12269),U_12268)) ),
    inference(miniscope,[status(thm)],[f_3190_2]) ).

cnf(f_3190_4,plain,
    ( ~ c_Typedef_Otype__definition(U_12264,U_12265,U_12266,U_12267,U_12268)
    | hAPP(U_12266,hAPP(U_12267,U_12269)) = U_12269
    | ~ hBOOL(hAPP(hAPP(c_member(U_12265),U_12269),U_12268)) ),
    inference(clausify,[status(thm)],[f_3190_3]) ).

fof(f_3191_1,plain,
    ! [V_R_2,V_Y_2,V_X_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_Y_2)),c_Wellfounded_Omax__ext(T_b,V_R_2)))
      | ? [B_x] :
          ( ! [B_xa] :
              ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_xa)),V_R_2))
              | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_Y_2)) )
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_X_2)) )
      | V_Y_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Y_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2)) ),
    inference(fof_nnf,[status(thm)],[fact_max__ext_Ointros]) ).

fof(f_3191_2,plain,
    ! [U_12275,U_12274,U_12273,U_12272] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_12272,tc_HOL_Obool),tc_fun(U_12272,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_12272,tc_HOL_Obool),tc_fun(U_12272,tc_HOL_Obool)),U_12273),U_12274)),c_Wellfounded_Omax__ext(U_12272,U_12275)))
      | ? [U_12271] :
          ( ! [U_12270] :
              ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12272,U_12272)),hAPP(hAPP(c_Product__Type_OPair(U_12272,U_12272),U_12271),U_12270)),U_12275))
              | ~ hBOOL(hAPP(hAPP(c_member(U_12272),U_12270),U_12274)) )
          & hBOOL(hAPP(hAPP(c_member(U_12272),U_12271),U_12273)) )
      | U_12274 = c_Orderings_Obot__class_Obot(tc_fun(U_12272,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12272),U_12274))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12272),U_12273)) ),
    inference(variable_rename,[status(thm)],[f_3191_1]) ).

fof(f_3191_3,plain,
    ! [U_12275,U_12274,U_12273,U_12272] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_12272,tc_HOL_Obool),tc_fun(U_12272,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_12272,tc_HOL_Obool),tc_fun(U_12272,tc_HOL_Obool)),U_12273),U_12274)),c_Wellfounded_Omax__ext(U_12272,U_12275)))
      | ( ! [U_12270] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12272,U_12272)),hAPP(hAPP(c_Product__Type_OPair(U_12272,U_12272),sK295(U_12275,U_12274,U_12273,U_12272)),U_12270)),U_12275))
            | ~ hBOOL(hAPP(hAPP(c_member(U_12272),U_12270),U_12274)) )
        & hBOOL(hAPP(hAPP(c_member(U_12272),sK295(U_12275,U_12274,U_12273,U_12272)),U_12273)) )
      | U_12274 = c_Orderings_Obot__class_Obot(tc_fun(U_12272,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12272),U_12274))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12272),U_12273)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK295]),skolemize(U_12271,sK295(U_12275,U_12274,U_12273,U_12272))],[f_3191_2]) ).

cnf(f_3191_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12272),sK295(U_12275,U_12274,U_12273,U_12272)),U_12273))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_12272,tc_HOL_Obool),tc_fun(U_12272,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_12272,tc_HOL_Obool),tc_fun(U_12272,tc_HOL_Obool)),U_12273),U_12274)),c_Wellfounded_Omax__ext(U_12272,U_12275)))
    | U_12274 = c_Orderings_Obot__class_Obot(tc_fun(U_12272,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12272),U_12274))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12272),U_12273)) ),
    inference(clausify,[status(thm)],[f_3191_3]) ).

cnf(f_3191_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12272,U_12272)),hAPP(hAPP(c_Product__Type_OPair(U_12272,U_12272),sK295(U_12275,U_12274,U_12273,U_12272)),U_12270)),U_12275))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12272),U_12270),U_12274))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_12272,tc_HOL_Obool),tc_fun(U_12272,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_12272,tc_HOL_Obool),tc_fun(U_12272,tc_HOL_Obool)),U_12273),U_12274)),c_Wellfounded_Omax__ext(U_12272,U_12275)))
    | U_12274 = c_Orderings_Obot__class_Obot(tc_fun(U_12272,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12272),U_12274))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12272),U_12273)) ),
    inference(clausify,[status(thm)],[f_3191_3]) ).

fof(f_3192_1,plain,
    ! [T_a] : c_Nitpick_Ozero__frac(T_a) = c_Nitpick_OAbs__Frac(T_a,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(fof_nnf,[status(thm)],[fact_Nitpick_Ozero__frac__def]) ).

fof(f_3192_2,plain,
    ! [U_12276] : c_Nitpick_Ozero__frac(U_12276) = c_Nitpick_OAbs__Frac(U_12276,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(variable_rename,[status(thm)],[f_3192_1]) ).

cnf(f_3192_3,plain,
    c_Nitpick_Ozero__frac(U_12276) = c_Nitpick_OAbs__Frac(U_12276,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(clausify,[status(thm)],[f_3192_2]) ).

fof(f_3193_1,plain,
    ! [V_X_2,T_b] : c_Set_Othe__elem(T_b,V_X_2) = c_HOL_OThe(T_b,hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),hAPP(c_fequal,V_X_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),
    inference(fof_nnf,[status(thm)],[fact_the__elem__def]) ).

fof(f_3193_2,plain,
    ! [U_12278,U_12277] : c_Set_Othe__elem(U_12277,U_12278) = c_HOL_OThe(U_12277,hAPP(hAPP(c_COMBB(tc_fun(U_12277,tc_HOL_Obool),tc_HOL_Obool,U_12277),hAPP(c_fequal,U_12278)),hAPP(hAPP(c_COMBC(U_12277,tc_fun(U_12277,tc_HOL_Obool),tc_fun(U_12277,tc_HOL_Obool)),c_Set_Oinsert(U_12277)),c_Orderings_Obot__class_Obot(tc_fun(U_12277,tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_3193_1]) ).

cnf(f_3193_3,plain,
    c_Set_Othe__elem(U_12277,U_12278) = c_HOL_OThe(U_12277,hAPP(hAPP(c_COMBB(tc_fun(U_12277,tc_HOL_Obool),tc_HOL_Obool,U_12277),hAPP(c_fequal,U_12278)),hAPP(hAPP(c_COMBC(U_12277,tc_fun(U_12277,tc_HOL_Obool),tc_fun(U_12277,tc_HOL_Obool)),c_Set_Oinsert(U_12277)),c_Orderings_Obot__class_Obot(tc_fun(U_12277,tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_3193_2]) ).

fof(f_3194_1,plain,
    ! [V_y_2,V_x_2,T_c,T_b] : c_HOL_OThe(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_x_2)))),hAPP(c_fequal,V_y_2)))) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2),
    inference(fof_nnf,[status(thm)],[fact_The__split__eq]) ).

fof(f_3194_2,plain,
    ! [U_12282,U_12281,U_12280,U_12279] : c_HOL_OThe(tc_prod(U_12279,U_12280),hAPP(c_Product__Type_Oprod_Oprod__case(U_12279,U_12280,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_12279,tc_fun(U_12280,tc_HOL_Obool),tc_fun(U_12280,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_12280,tc_HOL_Obool),tc_fun(U_12280,tc_HOL_Obool)),U_12279),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_12280)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12279),c_fconj),hAPP(c_fequal,U_12281)))),hAPP(c_fequal,U_12282)))) = hAPP(hAPP(c_Product__Type_OPair(U_12279,U_12280),U_12281),U_12282),
    inference(variable_rename,[status(thm)],[f_3194_1]) ).

cnf(f_3194_3,plain,
    c_HOL_OThe(tc_prod(U_12279,U_12280),hAPP(c_Product__Type_Oprod_Oprod__case(U_12279,U_12280,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_12279,tc_fun(U_12280,tc_HOL_Obool),tc_fun(U_12280,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_12280,tc_HOL_Obool),tc_fun(U_12280,tc_HOL_Obool)),U_12279),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_12280)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12279),c_fconj),hAPP(c_fequal,U_12281)))),hAPP(c_fequal,U_12282)))) = hAPP(hAPP(c_Product__Type_OPair(U_12279,U_12280),U_12281),U_12282),
    inference(clausify,[status(thm)],[f_3194_2]) ).

fof(f_3195_1,plain,
    ! [V_P_2,T_c,T_b] : c_HOL_OThe(tc_prod(T_b,T_c),V_P_2) = c_HOL_OThe(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,T_c),V_P_2)),c_Product__Type_OPair(T_b,T_c)))),
    inference(fof_nnf,[status(thm)],[fact_split__paired__The]) ).

fof(f_3195_2,plain,
    ! [U_12285,U_12284,U_12283] : c_HOL_OThe(tc_prod(U_12283,U_12284),U_12285) = c_HOL_OThe(tc_prod(U_12283,U_12284),hAPP(c_Product__Type_Oprod_Oprod__case(U_12283,U_12284,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_12284,tc_prod(U_12283,U_12284)),tc_fun(U_12284,tc_HOL_Obool),U_12283),hAPP(c_COMBB(tc_prod(U_12283,U_12284),tc_HOL_Obool,U_12284),U_12285)),c_Product__Type_OPair(U_12283,U_12284)))),
    inference(variable_rename,[status(thm)],[f_3195_1]) ).

cnf(f_3195_3,plain,
    c_HOL_OThe(tc_prod(U_12283,U_12284),U_12285) = c_HOL_OThe(tc_prod(U_12283,U_12284),hAPP(c_Product__Type_Oprod_Oprod__case(U_12283,U_12284,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_12284,tc_prod(U_12283,U_12284)),tc_fun(U_12284,tc_HOL_Obool),U_12283),hAPP(c_COMBB(tc_prod(U_12283,U_12284),tc_HOL_Obool,U_12284),U_12285)),c_Product__Type_OPair(U_12283,U_12284)))),
    inference(clausify,[status(thm)],[f_3195_2]) ).

fof(f_3196_1,plain,
    ! [V_x_2,V_f_2,V_A_2,T_c,T_b] : hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_x_2) = c_HOL_OThe(T_b,hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),V_x_2))),
    inference(fof_nnf,[status(thm)],[fact_the__inv__into__def]) ).

fof(f_3196_2,plain,
    ! [U_12290,U_12289,U_12288,U_12287,U_12286] : hAPP(c_Fun_Othe__inv__into(U_12286,U_12287,U_12288,U_12289),U_12290) = c_HOL_OThe(U_12286,hAPP(hAPP(c_COMBS(U_12286,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12286),c_fconj),hAPP(hAPP(c_COMBC(U_12286,tc_fun(U_12286,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12286)),U_12288))),hAPP(hAPP(c_COMBC(U_12286,U_12287,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_12287,tc_fun(U_12287,tc_HOL_Obool),U_12286),c_fequal),U_12289)),U_12290))),
    inference(variable_rename,[status(thm)],[f_3196_1]) ).

cnf(f_3196_3,plain,
    hAPP(c_Fun_Othe__inv__into(U_12286,U_12287,U_12288,U_12289),U_12290) = c_HOL_OThe(U_12286,hAPP(hAPP(c_COMBS(U_12286,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12286),c_fconj),hAPP(hAPP(c_COMBC(U_12286,tc_fun(U_12286,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12286)),U_12288))),hAPP(hAPP(c_COMBC(U_12286,U_12287,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_12287,tc_fun(U_12287,tc_HOL_Obool),U_12286),c_fequal),U_12289)),U_12290))),
    inference(clausify,[status(thm)],[f_3196_2]) ).

fof(f_3197_1,plain,
    ! [V_A_2,V_z_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_b,V_f_2),V_z_2),V_A_2) = c_HOL_OThe(T_b,c_Finite__Set_Ofold__graph(T_c,T_b,V_f_2,V_z_2,V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_fold__def]) ).

fof(f_3197_2,plain,
    ! [U_12295,U_12294,U_12293,U_12292,U_12291] : hAPP(hAPP(c_Finite__Set_Ofold(U_12291,U_12292,U_12293),U_12294),U_12295) = c_HOL_OThe(U_12292,c_Finite__Set_Ofold__graph(U_12291,U_12292,U_12293,U_12294,U_12295)),
    inference(variable_rename,[status(thm)],[f_3197_1]) ).

cnf(f_3197_3,plain,
    hAPP(hAPP(c_Finite__Set_Ofold(U_12291,U_12292,U_12293),U_12294),U_12295) = c_HOL_OThe(U_12292,c_Finite__Set_Ofold__graph(U_12291,U_12292,U_12293,U_12294,U_12295)),
    inference(clausify,[status(thm)],[f_3197_2]) ).

fof(f_3198_1,plain,
    ! [V_n_2,V_m_2] : c_Divides_Odivmod__nat(V_m_2,V_n_2) = c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(V_m_2,V_n_2)),
    inference(fof_nnf,[status(thm)],[fact_divmod__nat__def]) ).

fof(f_3198_2,plain,
    ! [U_12297,U_12296] : c_Divides_Odivmod__nat(U_12296,U_12297) = c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(U_12296,U_12297)),
    inference(variable_rename,[status(thm)],[f_3198_1]) ).

cnf(f_3198_3,plain,
    c_Divides_Odivmod__nat(U_12296,U_12297) = c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(U_12296,U_12297)),
    inference(clausify,[status(thm)],[f_3198_2]) ).

fof(f_3199_1,plain,
    ! [V_A_2,V_f_2,T_b] : hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) = c_HOL_OThe(T_b,c_Finite__Set_Ofold1Set(T_b,V_f_2,V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_fold1__def]) ).

fof(f_3199_2,plain,
    ! [U_12300,U_12299,U_12298] : hAPP(c_Finite__Set_Ofold1(U_12298,U_12299),U_12300) = c_HOL_OThe(U_12298,c_Finite__Set_Ofold1Set(U_12298,U_12299,U_12300)),
    inference(variable_rename,[status(thm)],[f_3199_1]) ).

cnf(f_3199_3,plain,
    hAPP(c_Finite__Set_Ofold1(U_12298,U_12299),U_12300) = c_HOL_OThe(U_12298,c_Finite__Set_Ofold1Set(U_12298,U_12299,U_12300)),
    inference(clausify,[status(thm)],[f_3199_2]) ).

fof(f_3200_1,plain,
    ! [V_P_2,T_c,T_b] : c_HOL_OThe(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_P_2)) = c_HOL_OThe(tc_prod(T_b,T_c),hAPP(hAPP(c_COMBS(tc_prod(T_b,T_c),T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_HOL_Obool),tc_prod(T_b,T_c)),V_P_2),c_Product__Type_Ofst(T_b,T_c))),c_Product__Type_Osnd(T_b,T_c))),
    inference(fof_nnf,[status(thm)],[fact_The__split]) ).

fof(f_3200_2,plain,
    ! [U_12303,U_12302,U_12301] : c_HOL_OThe(tc_prod(U_12301,U_12302),hAPP(c_Product__Type_Oprod_Oprod__case(U_12301,U_12302,tc_HOL_Obool),U_12303)) = c_HOL_OThe(tc_prod(U_12301,U_12302),hAPP(hAPP(c_COMBS(tc_prod(U_12301,U_12302),U_12302,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_12301,tc_fun(U_12302,tc_HOL_Obool),tc_prod(U_12301,U_12302)),U_12303),c_Product__Type_Ofst(U_12301,U_12302))),c_Product__Type_Osnd(U_12301,U_12302))),
    inference(variable_rename,[status(thm)],[f_3200_1]) ).

cnf(f_3200_3,plain,
    c_HOL_OThe(tc_prod(U_12301,U_12302),hAPP(c_Product__Type_Oprod_Oprod__case(U_12301,U_12302,tc_HOL_Obool),U_12303)) = c_HOL_OThe(tc_prod(U_12301,U_12302),hAPP(hAPP(c_COMBS(tc_prod(U_12301,U_12302),U_12302,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_12301,tc_fun(U_12302,tc_HOL_Obool),tc_prod(U_12301,U_12302)),U_12303),c_Product__Type_Ofst(U_12301,U_12302))),c_Product__Type_Osnd(U_12301,U_12302))),
    inference(clausify,[status(thm)],[f_3200_2]) ).

fof(f_3201_1,plain,
    ! [T_a] : c_Nitpick_Oone__frac(T_a) = c_Nitpick_OAbs__Frac(T_a,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(fof_nnf,[status(thm)],[fact_Nitpick_Oone__frac__def]) ).

fof(f_3201_2,plain,
    ! [U_12304] : c_Nitpick_Oone__frac(U_12304) = c_Nitpick_OAbs__Frac(U_12304,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(variable_rename,[status(thm)],[f_3201_1]) ).

cnf(f_3201_3,plain,
    c_Nitpick_Oone__frac(U_12304) = c_Nitpick_OAbs__Frac(U_12304,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(clausify,[status(thm)],[f_3201_2]) ).

fof(f_3202_1,plain,
    ! [V_n,T_a] : c_Nitpick_Onumber__of__frac(T_a,V_n) = c_Nitpick_OAbs__Frac(T_a,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_n),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(fof_nnf,[status(thm)],[fact_Nitpick_Onumber__of__frac__def]) ).

fof(f_3202_2,plain,
    ! [U_12306,U_12305] : c_Nitpick_Onumber__of__frac(U_12305,U_12306) = c_Nitpick_OAbs__Frac(U_12305,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_12306),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(variable_rename,[status(thm)],[f_3202_1]) ).

cnf(f_3202_3,plain,
    c_Nitpick_Onumber__of__frac(U_12305,U_12306) = c_Nitpick_OAbs__Frac(U_12305,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_12306),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(clausify,[status(thm)],[f_3202_2]) ).

fof(f_3203_1,plain,
    ! [V_b,V_a,T_a] : hAPP(hAPP(c_Nitpick_Ofrac(T_a),V_a),V_b) = c_Nitpick_OAbs__Frac(T_a,c_Nitpick_Onorm__frac(V_a,V_b)),
    inference(fof_nnf,[status(thm)],[fact_Nitpick_Ofrac__def]) ).

fof(f_3203_2,plain,
    ! [U_12309,U_12308,U_12307] : hAPP(hAPP(c_Nitpick_Ofrac(U_12307),U_12308),U_12309) = c_Nitpick_OAbs__Frac(U_12307,c_Nitpick_Onorm__frac(U_12308,U_12309)),
    inference(variable_rename,[status(thm)],[f_3203_1]) ).

cnf(f_3203_3,plain,
    hAPP(hAPP(c_Nitpick_Ofrac(U_12307),U_12308),U_12309) = c_Nitpick_OAbs__Frac(U_12307,c_Nitpick_Onorm__frac(U_12308,U_12309)),
    inference(clausify,[status(thm)],[f_3203_2]) ).

fof(f_3204_1,plain,
    ! [V_b_2,V_A_2,T_b] :
      ( ( c_Partial__Function_Oflat__lub(T_b,V_b_2,V_A_2) = c_HOL_OThe(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) )
      & ( c_Partial__Function_Oflat__lub(T_b,V_b_2,V_A_2) = V_b_2
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) ) ),
    inference(fof_nnf,[status(thm)],[fact_flat__lub__def]) ).

fof(f_3204_2,plain,
    ! [U_12312,U_12311,U_12310] :
      ( ( c_Partial__Function_Oflat__lub(U_12310,U_12312,U_12311) = c_HOL_OThe(U_12310,hAPP(hAPP(c_COMBC(U_12310,tc_fun(U_12310,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12310)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12310,tc_HOL_Obool)),U_12311),hAPP(hAPP(c_Set_Oinsert(U_12310),U_12312),c_Orderings_Obot__class_Obot(tc_fun(U_12310,tc_HOL_Obool))))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12310,tc_HOL_Obool)),U_12311),hAPP(hAPP(c_Set_Oinsert(U_12310),U_12312),c_Orderings_Obot__class_Obot(tc_fun(U_12310,tc_HOL_Obool))))) )
      & ( c_Partial__Function_Oflat__lub(U_12310,U_12312,U_12311) = U_12312
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12310,tc_HOL_Obool)),U_12311),hAPP(hAPP(c_Set_Oinsert(U_12310),U_12312),c_Orderings_Obot__class_Obot(tc_fun(U_12310,tc_HOL_Obool))))) ) ),
    inference(variable_rename,[status(thm)],[f_3204_1]) ).

fof(f_3204_3,plain,
    ( ! [U_12318,U_12316,U_12314] :
        ( c_Partial__Function_Oflat__lub(U_12314,U_12318,U_12316) = c_HOL_OThe(U_12314,hAPP(hAPP(c_COMBC(U_12314,tc_fun(U_12314,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12314)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12314,tc_HOL_Obool)),U_12316),hAPP(hAPP(c_Set_Oinsert(U_12314),U_12318),c_Orderings_Obot__class_Obot(tc_fun(U_12314,tc_HOL_Obool))))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12314,tc_HOL_Obool)),U_12316),hAPP(hAPP(c_Set_Oinsert(U_12314),U_12318),c_Orderings_Obot__class_Obot(tc_fun(U_12314,tc_HOL_Obool))))) )
    & ! [U_12317,U_12315,U_12313] :
        ( c_Partial__Function_Oflat__lub(U_12313,U_12317,U_12315) = U_12317
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12313,tc_HOL_Obool)),U_12315),hAPP(hAPP(c_Set_Oinsert(U_12313),U_12317),c_Orderings_Obot__class_Obot(tc_fun(U_12313,tc_HOL_Obool))))) ) ),
    inference(miniscope,[status(thm)],[f_3204_2]) ).

cnf(f_3204_4,plain,
    ( c_Partial__Function_Oflat__lub(U_12313,U_12317,U_12315) = U_12317
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12313,tc_HOL_Obool)),U_12315),hAPP(hAPP(c_Set_Oinsert(U_12313),U_12317),c_Orderings_Obot__class_Obot(tc_fun(U_12313,tc_HOL_Obool))))) ),
    inference(clausify,[status(thm)],[f_3204_3]) ).

cnf(f_3204_5,plain,
    ( c_Partial__Function_Oflat__lub(U_12314,U_12318,U_12316) = c_HOL_OThe(U_12314,hAPP(hAPP(c_COMBC(U_12314,tc_fun(U_12314,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12314)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12314,tc_HOL_Obool)),U_12316),hAPP(hAPP(c_Set_Oinsert(U_12314),U_12318),c_Orderings_Obot__class_Obot(tc_fun(U_12314,tc_HOL_Obool))))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12314,tc_HOL_Obool)),U_12316),hAPP(hAPP(c_Set_Oinsert(U_12314),U_12318),c_Orderings_Obot__class_Obot(tc_fun(U_12314,tc_HOL_Obool))))) ),
    inference(clausify,[status(thm)],[f_3204_3]) ).

fof(f_3205_1,plain,
    ! [V_a_2,V_f_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(T_b),c_HOL_OThe(T_b,hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),V_a_2))),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_inj__vimage__singleton]) ).

fof(f_3205_2,plain,
    ! [U_12322,U_12321,U_12320,U_12319] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12319,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_12319,U_12320,U_12321),hAPP(hAPP(c_Set_Oinsert(U_12320),U_12322),c_Orderings_Obot__class_Obot(tc_fun(U_12320,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(U_12319),c_HOL_OThe(U_12319,hAPP(hAPP(c_COMBC(U_12319,U_12320,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_12320,tc_fun(U_12320,tc_HOL_Obool),U_12319),c_fequal),U_12321)),U_12322))),c_Orderings_Obot__class_Obot(tc_fun(U_12319,tc_HOL_Obool)))))
      | ~ c_Fun_Oinj__on(U_12319,U_12320,U_12321,c_Orderings_Otop__class_Otop(tc_fun(U_12319,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_3205_1]) ).

cnf(f_3205_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12319,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_12319,U_12320,U_12321),hAPP(hAPP(c_Set_Oinsert(U_12320),U_12322),c_Orderings_Obot__class_Obot(tc_fun(U_12320,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(U_12319),c_HOL_OThe(U_12319,hAPP(hAPP(c_COMBC(U_12319,U_12320,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_12320,tc_fun(U_12320,tc_HOL_Obool),U_12319),c_fequal),U_12321)),U_12322))),c_Orderings_Obot__class_Obot(tc_fun(U_12319,tc_HOL_Obool)))))
    | ~ c_Fun_Oinj__on(U_12319,U_12320,U_12321,c_Orderings_Otop__class_Otop(tc_fun(U_12319,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_3205_2]) ).

fof(f_3206_1,plain,
    ! [V_y_2] :
      ( ? [B_x] : V_y_2 = hAPP(c_Int_ORep__Integ,B_x)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg)) ),
    inference(fof_nnf,[status(thm)],[fact_Rep__Integ__cases]) ).

fof(f_3206_2,plain,
    ! [U_12324] :
      ( ? [U_12323] : U_12324 = hAPP(c_Int_ORep__Integ,U_12323)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_12324),c_Int_OInteg)) ),
    inference(variable_rename,[status(thm)],[f_3206_1]) ).

fof(f_3206_3,plain,
    ! [U_12324] :
      ( U_12324 = hAPP(c_Int_ORep__Integ,sK296(U_12324))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_12324),c_Int_OInteg)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK296]),skolemize(U_12323,sK296(U_12324))],[f_3206_2]) ).

cnf(f_3206_4,plain,
    ( U_12324 = hAPP(c_Int_ORep__Integ,sK296(U_12324))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_12324),c_Int_OInteg)) ),
    inference(clausify,[status(thm)],[f_3206_3]) ).

fof(f_3207_1,plain,
    ! [T_c,V_B_2,T_b,V_b_2,V_a_2,V_f_2] :
      ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_B_2))
      | hAPP(V_f_2,V_a_2) != V_b_2 ),
    inference(fof_nnf,[status(thm)],[fact_vimageI]) ).

fof(f_3207_2,plain,
    ! [U_12330,U_12329,U_12328,U_12327,U_12326,U_12325] :
      ( hBOOL(hAPP(hAPP(c_member(U_12330),U_12326),hAPP(c_Set_Ovimage(U_12330,U_12328,U_12325),U_12329)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12328),U_12327),U_12329))
      | hAPP(U_12325,U_12326) != U_12327 ),
    inference(variable_rename,[status(thm)],[f_3207_1]) ).

cnf(f_3207_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12330),U_12326),hAPP(c_Set_Ovimage(U_12330,U_12328,U_12325),U_12329)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12328),U_12327),U_12329))
    | hAPP(U_12325,U_12326) != U_12327 ),
    inference(clausify,[status(thm)],[f_3207_2]) ).

fof(f_3208_1,plain,
    ! [V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_vimage__UNIV]) ).

fof(f_3208_2,plain,
    ! [U_12333,U_12332,U_12331] : hAPP(c_Set_Ovimage(U_12331,U_12332,U_12333),c_Orderings_Otop__class_Otop(tc_fun(U_12332,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_12331,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3208_1]) ).

cnf(f_3208_3,plain,
    hAPP(c_Set_Ovimage(U_12331,U_12332,U_12333),c_Orderings_Otop__class_Otop(tc_fun(U_12332,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_12331,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3208_2]) ).

fof(f_3209_1,plain,
    ! [V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_vimage__empty]) ).

fof(f_3209_2,plain,
    ! [U_12336,U_12335,U_12334] : hAPP(c_Set_Ovimage(U_12334,U_12335,U_12336),c_Orderings_Obot__class_Obot(tc_fun(U_12335,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_12334,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3209_1]) ).

cnf(f_3209_3,plain,
    hAPP(c_Set_Ovimage(U_12334,U_12335,U_12336),c_Orderings_Obot__class_Obot(tc_fun(U_12335,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_12334,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3209_2]) ).

fof(f_3210_1,plain,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_vimage__Un]) ).

fof(f_3210_2,plain,
    ! [U_12341,U_12340,U_12339,U_12338,U_12337] : hAPP(c_Set_Ovimage(U_12337,U_12338,U_12339),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12338,tc_HOL_Obool)),U_12340),U_12341)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12337,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_12337,U_12338,U_12339),U_12340)),hAPP(c_Set_Ovimage(U_12337,U_12338,U_12339),U_12341)),
    inference(variable_rename,[status(thm)],[f_3210_1]) ).

cnf(f_3210_3,plain,
    hAPP(c_Set_Ovimage(U_12337,U_12338,U_12339),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12338,tc_HOL_Obool)),U_12340),U_12341)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12337,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_12337,U_12338,U_12339),U_12340)),hAPP(c_Set_Ovimage(U_12337,U_12338,U_12339),U_12341)),
    inference(clausify,[status(thm)],[f_3210_2]) ).

fof(f_3211_1,plain,
    ! [V_B_2,V_A_2,T_d,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Set_Ovimage(T_b,T_c,V_f_2)),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_vimage__INT]) ).

fof(f_3211_2,plain,
    ! [U_12347,U_12346,U_12345,U_12344,U_12343,U_12342] : hAPP(c_Set_Ovimage(U_12342,U_12343,U_12344),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12345,tc_fun(U_12343,tc_HOL_Obool)),U_12346),U_12347)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12345,tc_fun(U_12342,tc_HOL_Obool)),U_12346),hAPP(hAPP(c_COMBB(tc_fun(U_12343,tc_HOL_Obool),tc_fun(U_12342,tc_HOL_Obool),U_12345),c_Set_Ovimage(U_12342,U_12343,U_12344)),U_12347)),
    inference(variable_rename,[status(thm)],[f_3211_1]) ).

cnf(f_3211_3,plain,
    hAPP(c_Set_Ovimage(U_12342,U_12343,U_12344),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12345,tc_fun(U_12343,tc_HOL_Obool)),U_12346),U_12347)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12345,tc_fun(U_12342,tc_HOL_Obool)),U_12346),hAPP(hAPP(c_COMBB(tc_fun(U_12343,tc_HOL_Obool),tc_fun(U_12342,tc_HOL_Obool),U_12345),c_Set_Ovimage(U_12342,U_12343,U_12344)),U_12347)),
    inference(clausify,[status(thm)],[f_3211_2]) ).

fof(f_3212_1,plain,
    ! [V_x_2,V_f_2,V_g_2,T_d,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_g_2),V_f_2)),V_x_2) = hAPP(c_Set_Ovimage(T_b,T_d,V_f_2),hAPP(c_Set_Ovimage(T_d,T_c,V_g_2),V_x_2)),
    inference(fof_nnf,[status(thm)],[fact_vimage__compose]) ).

fof(f_3212_2,plain,
    ! [U_12353,U_12352,U_12351,U_12350,U_12349,U_12348] : hAPP(c_Set_Ovimage(U_12348,U_12349,hAPP(c_Fun_Ocomp(U_12350,U_12349,U_12348,U_12351),U_12352)),U_12353) = hAPP(c_Set_Ovimage(U_12348,U_12350,U_12352),hAPP(c_Set_Ovimage(U_12350,U_12349,U_12351),U_12353)),
    inference(variable_rename,[status(thm)],[f_3212_1]) ).

cnf(f_3212_3,plain,
    hAPP(c_Set_Ovimage(U_12348,U_12349,hAPP(c_Fun_Ocomp(U_12350,U_12349,U_12348,U_12351),U_12352)),U_12353) = hAPP(c_Set_Ovimage(U_12348,U_12350,U_12352),hAPP(c_Set_Ovimage(U_12350,U_12349,U_12351),U_12353)),
    inference(clausify,[status(thm)],[f_3212_2]) ).

fof(f_3213_1,plain,
    ! [V_Y_2,T_b] : hAPP(c_Set_Ovimage(T_b,T_b,c_COMBI(T_b)),V_Y_2) = V_Y_2,
    inference(fof_nnf,[status(thm)],[fact_vimage__ident]) ).

fof(f_3213_2,plain,
    ! [U_12355,U_12354] : hAPP(c_Set_Ovimage(U_12354,U_12354,c_COMBI(U_12354)),U_12355) = U_12355,
    inference(variable_rename,[status(thm)],[f_3213_1]) ).

cnf(f_3213_3,plain,
    hAPP(c_Set_Ovimage(U_12354,U_12354,c_COMBI(U_12354)),U_12355) = U_12355,
    inference(clausify,[status(thm)],[f_3213_2]) ).

fof(f_3214_1,plain,
    ! [V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_vimage__Compl]) ).

fof(f_3214_2,plain,
    ! [U_12359,U_12358,U_12357,U_12356] : hAPP(c_Set_Ovimage(U_12356,U_12357,U_12358),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12357,tc_HOL_Obool)),U_12359)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12356,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_12356,U_12357,U_12358),U_12359)),
    inference(variable_rename,[status(thm)],[f_3214_1]) ).

cnf(f_3214_3,plain,
    hAPP(c_Set_Ovimage(U_12356,U_12357,U_12358),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12357,tc_HOL_Obool)),U_12359)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12356,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_12356,U_12357,U_12358),U_12359)),
    inference(clausify,[status(thm)],[f_3214_2]) ).

fof(f_3215_1,plain,
    ! [V_x_2,V_A_2,V_f_2,T_c,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2),V_x_2))
        | ~ hBOOL(hAPP(V_A_2,hAPP(V_f_2,V_x_2))) )
      & ( hBOOL(hAPP(V_A_2,hAPP(V_f_2,V_x_2)))
        | ~ hBOOL(hAPP(hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2),V_x_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_vimage__code]) ).

fof(f_3215_2,plain,
    ! [U_12364,U_12363,U_12362,U_12361,U_12360] :
      ( ( hBOOL(hAPP(hAPP(c_Set_Ovimage(U_12360,U_12361,U_12362),U_12363),U_12364))
        | ~ hBOOL(hAPP(U_12363,hAPP(U_12362,U_12364))) )
      & ( hBOOL(hAPP(U_12363,hAPP(U_12362,U_12364)))
        | ~ hBOOL(hAPP(hAPP(c_Set_Ovimage(U_12360,U_12361,U_12362),U_12363),U_12364)) ) ),
    inference(variable_rename,[status(thm)],[f_3215_1]) ).

fof(f_3215_3,plain,
    ( ! [U_12374,U_12372,U_12370] :
        ( ! [U_12368,U_12366] : hBOOL(hAPP(hAPP(c_Set_Ovimage(U_12366,U_12368,U_12370),U_12372),U_12374))
        | ~ hBOOL(hAPP(U_12372,hAPP(U_12370,U_12374))) )
    & ! [U_12373,U_12371,U_12369] :
        ( ! [U_12367,U_12365] : ~ hBOOL(hAPP(hAPP(c_Set_Ovimage(U_12365,U_12367,U_12369),U_12371),U_12373))
        | hBOOL(hAPP(U_12371,hAPP(U_12369,U_12373))) ) ),
    inference(miniscope,[status(thm)],[f_3215_2]) ).

cnf(f_3215_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Set_Ovimage(U_12365,U_12367,U_12369),U_12371),U_12373))
    | hBOOL(hAPP(U_12371,hAPP(U_12369,U_12373))) ),
    inference(clausify,[status(thm)],[f_3215_3]) ).

cnf(f_3215_5,plain,
    ( hBOOL(hAPP(hAPP(c_Set_Ovimage(U_12366,U_12368,U_12370),U_12372),U_12374))
    | ~ hBOOL(hAPP(U_12372,hAPP(U_12370,U_12374))) ),
    inference(clausify,[status(thm)],[f_3215_3]) ).

fof(f_3216_1,plain,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_vimage__Int]) ).

fof(f_3216_2,plain,
    ! [U_12379,U_12378,U_12377,U_12376,U_12375] : hAPP(c_Set_Ovimage(U_12375,U_12376,U_12377),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12376,tc_HOL_Obool)),U_12378),U_12379)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12375,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_12375,U_12376,U_12377),U_12378)),hAPP(c_Set_Ovimage(U_12375,U_12376,U_12377),U_12379)),
    inference(variable_rename,[status(thm)],[f_3216_1]) ).

cnf(f_3216_3,plain,
    hAPP(c_Set_Ovimage(U_12375,U_12376,U_12377),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12376,tc_HOL_Obool)),U_12378),U_12379)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12375,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_12375,U_12376,U_12377),U_12378)),hAPP(c_Set_Ovimage(U_12375,U_12376,U_12377),U_12379)),
    inference(clausify,[status(thm)],[f_3216_2]) ).

fof(f_3217_1,plain,
    ! [V_f_2,T_c,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_vimage__mono]) ).

fof(f_3217_2,plain,
    ! [U_12384,U_12383,U_12382,U_12381,U_12380] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12383,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_12383,U_12380,U_12384),U_12381)),hAPP(c_Set_Ovimage(U_12383,U_12380,U_12384),U_12382)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12380,tc_HOL_Obool)),U_12381),U_12382)) ),
    inference(variable_rename,[status(thm)],[f_3217_1]) ).

cnf(f_3217_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12383,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_12383,U_12380,U_12384),U_12381)),hAPP(c_Set_Ovimage(U_12383,U_12380,U_12384),U_12382)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12380,tc_HOL_Obool)),U_12381),U_12382)) ),
    inference(clausify,[status(thm)],[f_3217_2]) ).

fof(f_3218_1,plain,
    ! [V_B_2,V_A_2,T_d,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Set_Ovimage(T_b,T_c,V_f_2)),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_vimage__UN]) ).

fof(f_3218_2,plain,
    ! [U_12390,U_12389,U_12388,U_12387,U_12386,U_12385] : hAPP(c_Set_Ovimage(U_12385,U_12386,U_12387),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12388,tc_fun(U_12386,tc_HOL_Obool)),U_12389),U_12390)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12388,tc_fun(U_12385,tc_HOL_Obool)),U_12389),hAPP(hAPP(c_COMBB(tc_fun(U_12386,tc_HOL_Obool),tc_fun(U_12385,tc_HOL_Obool),U_12388),c_Set_Ovimage(U_12385,U_12386,U_12387)),U_12390)),
    inference(variable_rename,[status(thm)],[f_3218_1]) ).

cnf(f_3218_3,plain,
    hAPP(c_Set_Ovimage(U_12385,U_12386,U_12387),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12388,tc_fun(U_12386,tc_HOL_Obool)),U_12389),U_12390)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12388,tc_fun(U_12385,tc_HOL_Obool)),U_12389),hAPP(hAPP(c_COMBB(tc_fun(U_12386,tc_HOL_Obool),tc_fun(U_12385,tc_HOL_Obool),U_12388),c_Set_Ovimage(U_12385,U_12386,U_12387)),U_12390)),
    inference(clausify,[status(thm)],[f_3218_2]) ).

fof(f_3219_1,plain,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_vimage__Diff]) ).

fof(f_3219_2,plain,
    ! [U_12395,U_12394,U_12393,U_12392,U_12391] : hAPP(c_Set_Ovimage(U_12391,U_12392,U_12393),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12392,tc_HOL_Obool)),U_12394),U_12395)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12391,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_12391,U_12392,U_12393),U_12394)),hAPP(c_Set_Ovimage(U_12391,U_12392,U_12393),U_12395)),
    inference(variable_rename,[status(thm)],[f_3219_1]) ).

cnf(f_3219_3,plain,
    hAPP(c_Set_Ovimage(U_12391,U_12392,U_12393),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12392,tc_HOL_Obool)),U_12394),U_12395)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12391,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_12391,U_12392,U_12393),U_12394)),hAPP(c_Set_Ovimage(U_12391,U_12392,U_12393),U_12395)),
    inference(clausify,[status(thm)],[f_3219_2]) ).

fof(f_3220_1,plain,
    ! [T_c,V_A_2,V_a_2,V_f_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_vimageI2]) ).

fof(f_3220_2,plain,
    ! [U_12400,U_12399,U_12398,U_12397,U_12396] :
      ( hBOOL(hAPP(hAPP(c_member(U_12400),U_12398),hAPP(c_Set_Ovimage(U_12400,U_12396,U_12397),U_12399)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12396),hAPP(U_12397,U_12398)),U_12399)) ),
    inference(variable_rename,[status(thm)],[f_3220_1]) ).

cnf(f_3220_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12400),U_12398),hAPP(c_Set_Ovimage(U_12400,U_12396,U_12397),U_12399)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12396),hAPP(U_12397,U_12398)),U_12399)) ),
    inference(clausify,[status(thm)],[f_3220_2]) ).

fof(f_3221_1,plain,
    ! [V_A_2,V_f_2,T_c,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2))) ),
    inference(fof_nnf,[status(thm)],[fact_vimageD]) ).

fof(f_3221_2,plain,
    ! [U_12405,U_12404,U_12403,U_12402,U_12401] :
      ( hBOOL(hAPP(hAPP(c_member(U_12403),hAPP(U_12404,U_12402)),U_12405))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12401),U_12402),hAPP(c_Set_Ovimage(U_12401,U_12403,U_12404),U_12405))) ),
    inference(variable_rename,[status(thm)],[f_3221_1]) ).

fof(f_3221_3,plain,
    ! [U_12405,U_12404,U_12403,U_12402] :
      ( ! [U_12401] : ~ hBOOL(hAPP(hAPP(c_member(U_12401),U_12402),hAPP(c_Set_Ovimage(U_12401,U_12403,U_12404),U_12405)))
      | hBOOL(hAPP(hAPP(c_member(U_12403),hAPP(U_12404,U_12402)),U_12405)) ),
    inference(miniscope,[status(thm)],[f_3221_2]) ).

cnf(f_3221_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_12401),U_12402),hAPP(c_Set_Ovimage(U_12401,U_12403,U_12404),U_12405)))
    | hBOOL(hAPP(hAPP(c_member(U_12403),hAPP(U_12404,U_12402)),U_12405)) ),
    inference(clausify,[status(thm)],[f_3221_3]) ).

fof(f_3222_1,plain,
    ! [V_B_2,V_f_2,T_c,V_a_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)))
        | ~ hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_B_2)) )
      & ( hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_B_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_vimage__eq]) ).

fof(f_3222_2,plain,
    ! [U_12410,U_12409,U_12408,U_12407,U_12406] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_12406),U_12407),hAPP(c_Set_Ovimage(U_12406,U_12408,U_12409),U_12410)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12408),hAPP(U_12409,U_12407)),U_12410)) )
      & ( hBOOL(hAPP(hAPP(c_member(U_12408),hAPP(U_12409,U_12407)),U_12410))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12406),U_12407),hAPP(c_Set_Ovimage(U_12406,U_12408,U_12409),U_12410))) ) ),
    inference(variable_rename,[status(thm)],[f_3222_1]) ).

fof(f_3222_3,plain,
    ( ! [U_12420,U_12418,U_12416,U_12414] :
        ( ! [U_12412] : hBOOL(hAPP(hAPP(c_member(U_12412),U_12414),hAPP(c_Set_Ovimage(U_12412,U_12416,U_12418),U_12420)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12416),hAPP(U_12418,U_12414)),U_12420)) )
    & ! [U_12419,U_12417,U_12415,U_12413] :
        ( ! [U_12411] : ~ hBOOL(hAPP(hAPP(c_member(U_12411),U_12413),hAPP(c_Set_Ovimage(U_12411,U_12415,U_12417),U_12419)))
        | hBOOL(hAPP(hAPP(c_member(U_12415),hAPP(U_12417,U_12413)),U_12419)) ) ),
    inference(miniscope,[status(thm)],[f_3222_2]) ).

cnf(f_3222_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_12411),U_12413),hAPP(c_Set_Ovimage(U_12411,U_12415,U_12417),U_12419)))
    | hBOOL(hAPP(hAPP(c_member(U_12415),hAPP(U_12417,U_12413)),U_12419)) ),
    inference(clausify,[status(thm)],[f_3222_3]) ).

cnf(f_3222_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12412),U_12414),hAPP(c_Set_Ovimage(U_12412,U_12416,U_12418),U_12420)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12416),hAPP(U_12418,U_12414)),U_12420)) ),
    inference(clausify,[status(thm)],[f_3222_3]) ).

fof(f_3223_1,plain,
    ! [V_A_2,V_f_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2))),V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_image__vimage__subset]) ).

fof(f_3223_2,plain,
    ! [U_12424,U_12423,U_12422,U_12421] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12421,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_12422,U_12421,U_12423),hAPP(c_Set_Ovimage(U_12422,U_12421,U_12423),U_12424))),U_12424)),
    inference(variable_rename,[status(thm)],[f_3223_1]) ).

cnf(f_3223_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12421,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_12422,U_12421,U_12423),hAPP(c_Set_Ovimage(U_12422,U_12421,U_12423),U_12424))),U_12424)),
    inference(clausify,[status(thm)],[f_3223_2]) ).

fof(f_3224_1,plain,
    ! [V_A_2,V_f_2,T_b,T_c] :
      ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2)) = V_A_2
      | hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ),
    inference(fof_nnf,[status(thm)],[fact_surj__image__vimage__eq]) ).

fof(f_3224_2,plain,
    ! [U_12428,U_12427,U_12426,U_12425] :
      ( hAPP(c_Set_Oimage(U_12425,U_12426,U_12427),hAPP(c_Set_Ovimage(U_12425,U_12426,U_12427),U_12428)) = U_12428
      | hAPP(c_Set_Oimage(U_12425,U_12426,U_12427),c_Orderings_Otop__class_Otop(tc_fun(U_12425,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_12426,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_3224_1]) ).

cnf(f_3224_3,plain,
    ( hAPP(c_Set_Oimage(U_12425,U_12426,U_12427),hAPP(c_Set_Ovimage(U_12425,U_12426,U_12427),U_12428)) = U_12428
    | hAPP(c_Set_Oimage(U_12425,U_12426,U_12427),c_Orderings_Otop__class_Otop(tc_fun(U_12425,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_12426,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3224_2]) ).

fof(f_3225_1,plain,
    ! [V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Set_Ovimage(T_b,T_c,V_f_2)),
    inference(fof_nnf,[status(thm)],[fact_vimage__Union]) ).

fof(f_3225_2,plain,
    ! [U_12432,U_12431,U_12430,U_12429] : hAPP(c_Set_Ovimage(U_12429,U_12430,U_12431),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_12430,tc_HOL_Obool),U_12432)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_12430,tc_HOL_Obool),tc_fun(U_12429,tc_HOL_Obool)),U_12432),c_Set_Ovimage(U_12429,U_12430,U_12431)),
    inference(variable_rename,[status(thm)],[f_3225_1]) ).

cnf(f_3225_3,plain,
    hAPP(c_Set_Ovimage(U_12429,U_12430,U_12431),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_12430,tc_HOL_Obool),U_12432)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_12430,tc_HOL_Obool),tc_fun(U_12429,tc_HOL_Obool)),U_12432),c_Set_Ovimage(U_12429,U_12430,U_12431)),
    inference(clausify,[status(thm)],[f_3225_2]) ).

fof(f_3226_1,plain,
    ! [V_b_2,V_f_2,T_c,V_a_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))))
        | hAPP(V_f_2,V_a_2) != V_b_2 )
      & ( hAPP(V_f_2,V_a_2) = V_b_2
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))) ) ),
    inference(fof_nnf,[status(thm)],[fact_vimage__singleton__eq]) ).

fof(f_3226_2,plain,
    ! [U_12437,U_12436,U_12435,U_12434,U_12433] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_12433),U_12434),hAPP(c_Set_Ovimage(U_12433,U_12435,U_12436),hAPP(hAPP(c_Set_Oinsert(U_12435),U_12437),c_Orderings_Obot__class_Obot(tc_fun(U_12435,tc_HOL_Obool))))))
        | hAPP(U_12436,U_12434) != U_12437 )
      & ( hAPP(U_12436,U_12434) = U_12437
        | ~ hBOOL(hAPP(hAPP(c_member(U_12433),U_12434),hAPP(c_Set_Ovimage(U_12433,U_12435,U_12436),hAPP(hAPP(c_Set_Oinsert(U_12435),U_12437),c_Orderings_Obot__class_Obot(tc_fun(U_12435,tc_HOL_Obool)))))) ) ),
    inference(variable_rename,[status(thm)],[f_3226_1]) ).

fof(f_3226_3,plain,
    ( ! [U_12447,U_12445,U_12443,U_12441] :
        ( ! [U_12439] : hBOOL(hAPP(hAPP(c_member(U_12439),U_12441),hAPP(c_Set_Ovimage(U_12439,U_12443,U_12445),hAPP(hAPP(c_Set_Oinsert(U_12443),U_12447),c_Orderings_Obot__class_Obot(tc_fun(U_12443,tc_HOL_Obool))))))
        | hAPP(U_12445,U_12441) != U_12447 )
    & ! [U_12446,U_12444,U_12442,U_12440] :
        ( ! [U_12438] : ~ hBOOL(hAPP(hAPP(c_member(U_12438),U_12440),hAPP(c_Set_Ovimage(U_12438,U_12442,U_12444),hAPP(hAPP(c_Set_Oinsert(U_12442),U_12446),c_Orderings_Obot__class_Obot(tc_fun(U_12442,tc_HOL_Obool))))))
        | hAPP(U_12444,U_12440) = U_12446 ) ),
    inference(miniscope,[status(thm)],[f_3226_2]) ).

cnf(f_3226_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_12438),U_12440),hAPP(c_Set_Ovimage(U_12438,U_12442,U_12444),hAPP(hAPP(c_Set_Oinsert(U_12442),U_12446),c_Orderings_Obot__class_Obot(tc_fun(U_12442,tc_HOL_Obool))))))
    | hAPP(U_12444,U_12440) = U_12446 ),
    inference(clausify,[status(thm)],[f_3226_3]) ).

cnf(f_3226_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12439),U_12441),hAPP(c_Set_Ovimage(U_12439,U_12443,U_12445),hAPP(hAPP(c_Set_Oinsert(U_12443),U_12447),c_Orderings_Obot__class_Obot(tc_fun(U_12443,tc_HOL_Obool))))))
    | hAPP(U_12445,U_12441) != U_12447 ),
    inference(clausify,[status(thm)],[f_3226_3]) ).

fof(f_3227_1,plain,
    ! [V_B_2,V_a_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_vimage__insert]) ).

fof(f_3227_2,plain,
    ! [U_12452,U_12451,U_12450,U_12449,U_12448] : hAPP(c_Set_Ovimage(U_12448,U_12449,U_12450),hAPP(hAPP(c_Set_Oinsert(U_12449),U_12451),U_12452)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12448,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_12448,U_12449,U_12450),hAPP(hAPP(c_Set_Oinsert(U_12449),U_12451),c_Orderings_Obot__class_Obot(tc_fun(U_12449,tc_HOL_Obool))))),hAPP(c_Set_Ovimage(U_12448,U_12449,U_12450),U_12452)),
    inference(variable_rename,[status(thm)],[f_3227_1]) ).

cnf(f_3227_3,plain,
    hAPP(c_Set_Ovimage(U_12448,U_12449,U_12450),hAPP(hAPP(c_Set_Oinsert(U_12449),U_12451),U_12452)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12448,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_12448,U_12449,U_12450),hAPP(hAPP(c_Set_Oinsert(U_12449),U_12451),c_Orderings_Obot__class_Obot(tc_fun(U_12449,tc_HOL_Obool))))),hAPP(c_Set_Ovimage(U_12448,U_12449,U_12450),U_12452)),
    inference(clausify,[status(thm)],[f_3227_2]) ).

fof(f_3228_1,plain,
    ! [V_F_2,V_h_2,T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2))
      | hAPP(c_Set_Oimage(T_b,T_c,V_h_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_c,V_h_2),V_F_2))) ),
    inference(fof_nnf,[status(thm)],[fact_finite__vimageD]) ).

fof(f_3228_2,plain,
    ! [U_12456,U_12455,U_12454,U_12453] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12454),U_12456))
      | hAPP(c_Set_Oimage(U_12453,U_12454,U_12455),c_Orderings_Otop__class_Otop(tc_fun(U_12453,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_12454,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12453),hAPP(c_Set_Ovimage(U_12453,U_12454,U_12455),U_12456))) ),
    inference(variable_rename,[status(thm)],[f_3228_1]) ).

cnf(f_3228_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12454),U_12456))
    | hAPP(c_Set_Oimage(U_12453,U_12454,U_12455),c_Orderings_Otop__class_Otop(tc_fun(U_12453,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_12454,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12453),hAPP(c_Set_Ovimage(U_12453,U_12454,U_12455),U_12456))) ),
    inference(clausify,[status(thm)],[f_3228_2]) ).

fof(f_3229_1,plain,
    ! [V_A_2,V_B_2,V_f_2,T_b,T_c] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_B_2)),V_A_2))
      | hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ),
    inference(fof_nnf,[status(thm)],[fact_vimage__subsetD]) ).

fof(f_3229_2,plain,
    ! [U_12461,U_12460,U_12459,U_12458,U_12457] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12458,tc_HOL_Obool)),U_12460),hAPP(c_Set_Oimage(U_12457,U_12458,U_12459),U_12461)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12457,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_12457,U_12458,U_12459),U_12460)),U_12461))
      | hAPP(c_Set_Oimage(U_12457,U_12458,U_12459),c_Orderings_Otop__class_Otop(tc_fun(U_12457,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_12458,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_3229_1]) ).

cnf(f_3229_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12458,tc_HOL_Obool)),U_12460),hAPP(c_Set_Oimage(U_12457,U_12458,U_12459),U_12461)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12457,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_12457,U_12458,U_12459),U_12460)),U_12461))
    | hAPP(c_Set_Oimage(U_12457,U_12458,U_12459),c_Orderings_Otop__class_Otop(tc_fun(U_12457,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_12458,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3229_2]) ).

fof(f_3230_1,plain,
    ! [V_A_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_image__vimage__eq]) ).

fof(f_3230_2,plain,
    ! [U_12465,U_12464,U_12463,U_12462] : hAPP(c_Set_Oimage(U_12462,U_12463,U_12464),hAPP(c_Set_Ovimage(U_12462,U_12463,U_12464),U_12465)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12463,tc_HOL_Obool)),U_12465),hAPP(c_Set_Oimage(U_12462,U_12463,U_12464),c_Orderings_Otop__class_Otop(tc_fun(U_12462,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_3230_1]) ).

cnf(f_3230_3,plain,
    hAPP(c_Set_Oimage(U_12462,U_12463,U_12464),hAPP(c_Set_Ovimage(U_12462,U_12463,U_12464),U_12465)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12463,tc_HOL_Obool)),U_12465),hAPP(c_Set_Oimage(U_12462,U_12463,U_12464),c_Orderings_Otop__class_Otop(tc_fun(U_12462,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_3230_2]) ).

fof(f_3231_1,plain,
    ! [V_h_2,T_c,V_F_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Ovimage(T_c,T_b,V_h_2),V_F_2)))
      | ~ c_Fun_Oinj__on(T_c,T_b,V_h_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__vimageI]) ).

fof(f_3231_2,plain,
    ! [U_12469,U_12468,U_12467,U_12466] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12468),hAPP(c_Set_Ovimage(U_12468,U_12466,U_12469),U_12467)))
      | ~ c_Fun_Oinj__on(U_12468,U_12466,U_12469,c_Orderings_Otop__class_Otop(tc_fun(U_12468,tc_HOL_Obool)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12466),U_12467)) ),
    inference(variable_rename,[status(thm)],[f_3231_1]) ).

cnf(f_3231_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12468),hAPP(c_Set_Ovimage(U_12468,U_12466,U_12469),U_12467)))
    | ~ c_Fun_Oinj__on(U_12468,U_12466,U_12469,c_Orderings_Otop__class_Otop(tc_fun(U_12468,tc_HOL_Obool)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12466),U_12467)) ),
    inference(clausify,[status(thm)],[f_3231_2]) ).

fof(f_3232_1,plain,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = V_A_2
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_inj__vimage__image__eq]) ).

fof(f_3232_2,plain,
    ! [U_12473,U_12472,U_12471,U_12470] :
      ( hAPP(c_Set_Ovimage(U_12470,U_12471,U_12472),hAPP(c_Set_Oimage(U_12470,U_12471,U_12472),U_12473)) = U_12473
      | ~ c_Fun_Oinj__on(U_12470,U_12471,U_12472,c_Orderings_Otop__class_Otop(tc_fun(U_12470,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_3232_1]) ).

cnf(f_3232_3,plain,
    ( hAPP(c_Set_Ovimage(U_12470,U_12471,U_12472),hAPP(c_Set_Oimage(U_12470,U_12471,U_12472),U_12473)) = U_12473
    | ~ c_Fun_Oinj__on(U_12470,U_12471,U_12472,c_Orderings_Otop__class_Otop(tc_fun(U_12470,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_3232_2]) ).

fof(f_3233_1,plain,
    ! [T_c,V_A_2,V_c_2,T_b] :
      ( ( hAPP(c_Set_Ovimage(T_c,T_b,hAPP(c_COMBK(T_b,T_c),V_c_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) )
      & ( hAPP(c_Set_Ovimage(T_c,T_b,hAPP(c_COMBK(T_b,T_c),V_c_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_vimage__const]) ).

fof(f_3233_2,plain,
    ! [U_12477,U_12476,U_12475,U_12474] :
      ( ( hAPP(c_Set_Ovimage(U_12477,U_12474,hAPP(c_COMBK(U_12474,U_12477),U_12475)),U_12476) = c_Orderings_Obot__class_Obot(tc_fun(U_12477,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_member(U_12474),U_12475),U_12476)) )
      & ( hAPP(c_Set_Ovimage(U_12477,U_12474,hAPP(c_COMBK(U_12474,U_12477),U_12475)),U_12476) = c_Orderings_Otop__class_Otop(tc_fun(U_12477,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12474),U_12475),U_12476)) ) ),
    inference(variable_rename,[status(thm)],[f_3233_1]) ).

fof(f_3233_3,plain,
    ( ! [U_12485,U_12483,U_12481,U_12479] :
        ( hAPP(c_Set_Ovimage(U_12485,U_12479,hAPP(c_COMBK(U_12479,U_12485),U_12481)),U_12483) = c_Orderings_Obot__class_Obot(tc_fun(U_12485,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_member(U_12479),U_12481),U_12483)) )
    & ! [U_12484,U_12482,U_12480,U_12478] :
        ( hAPP(c_Set_Ovimage(U_12484,U_12478,hAPP(c_COMBK(U_12478,U_12484),U_12480)),U_12482) = c_Orderings_Otop__class_Otop(tc_fun(U_12484,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12478),U_12480),U_12482)) ) ),
    inference(miniscope,[status(thm)],[f_3233_2]) ).

cnf(f_3233_4,plain,
    ( hAPP(c_Set_Ovimage(U_12484,U_12478,hAPP(c_COMBK(U_12478,U_12484),U_12480)),U_12482) = c_Orderings_Otop__class_Otop(tc_fun(U_12484,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12478),U_12480),U_12482)) ),
    inference(clausify,[status(thm)],[f_3233_3]) ).

cnf(f_3233_5,plain,
    ( hAPP(c_Set_Ovimage(U_12485,U_12479,hAPP(c_COMBK(U_12479,U_12485),U_12481)),U_12483) = c_Orderings_Obot__class_Obot(tc_fun(U_12485,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(U_12479),U_12481),U_12483)) ),
    inference(clausify,[status(thm)],[f_3233_3]) ).

fof(f_3234_1,plain,
    ! [V_B_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Set_Ovimage(T_b,T_c,V_f_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),c_Set_Oinsert(T_c)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))),
    inference(fof_nnf,[status(thm)],[fact_vimage__eq__UN]) ).

fof(f_3234_2,plain,
    ! [U_12489,U_12488,U_12487,U_12486] : hAPP(c_Set_Ovimage(U_12486,U_12487,U_12488),U_12489) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12487,tc_fun(U_12486,tc_HOL_Obool)),U_12489),hAPP(hAPP(c_COMBB(tc_fun(U_12487,tc_HOL_Obool),tc_fun(U_12486,tc_HOL_Obool),U_12487),c_Set_Ovimage(U_12486,U_12487,U_12488)),hAPP(hAPP(c_COMBC(U_12487,tc_fun(U_12487,tc_HOL_Obool),tc_fun(U_12487,tc_HOL_Obool)),c_Set_Oinsert(U_12487)),c_Orderings_Obot__class_Obot(tc_fun(U_12487,tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_3234_1]) ).

cnf(f_3234_3,plain,
    hAPP(c_Set_Ovimage(U_12486,U_12487,U_12488),U_12489) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12487,tc_fun(U_12486,tc_HOL_Obool)),U_12489),hAPP(hAPP(c_COMBB(tc_fun(U_12487,tc_HOL_Obool),tc_fun(U_12486,tc_HOL_Obool),U_12487),c_Set_Ovimage(U_12486,U_12487,U_12488)),hAPP(hAPP(c_COMBC(U_12487,tc_fun(U_12487,tc_HOL_Obool),tc_fun(U_12487,tc_HOL_Obool)),c_Set_Oinsert(U_12487)),c_Orderings_Obot__class_Obot(tc_fun(U_12487,tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_3234_2]) ).

fof(f_3235_1,plain,
    ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_vimage__subsetI]) ).

fof(f_3235_2,plain,
    ! [U_12494,U_12493,U_12492,U_12491,U_12490] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12490,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_12490,U_12491,U_12492),U_12493)),U_12494))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12491,tc_HOL_Obool)),U_12493),hAPP(c_Set_Oimage(U_12490,U_12491,U_12492),U_12494)))
      | ~ c_Fun_Oinj__on(U_12490,U_12491,U_12492,c_Orderings_Otop__class_Otop(tc_fun(U_12490,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_3235_1]) ).

cnf(f_3235_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12490,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_12490,U_12491,U_12492),U_12493)),U_12494))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12491,tc_HOL_Obool)),U_12493),hAPP(c_Set_Oimage(U_12490,U_12491,U_12492),U_12494)))
    | ~ c_Fun_Oinj__on(U_12490,U_12491,U_12492,c_Orderings_Otop__class_Otop(tc_fun(U_12490,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_3235_2]) ).

fof(f_3236_1,plain,
    ! [V_B_2,T_c,V_d_2,V_A_2,V_c_2,T_b] :
      ( ( ( ( hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
            | hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2)) )
          & ( hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_B_2)
            | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2)) ) )
        | hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) )
      & ( ( ( hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = V_B_2
            | hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2)) )
          & ( hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2)) ) )
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_vimage__if]) ).

fof(f_3236_2,plain,
    ! [U_12500,U_12499,U_12498,U_12497,U_12496,U_12495] :
      ( ( ( ( hAPP(c_Set_Ovimage(U_12499,U_12495,hAPP(hAPP(c_COMBC(U_12499,U_12495,U_12495),hAPP(hAPP(c_COMBC(U_12499,U_12495,tc_fun(U_12495,U_12495)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12495,tc_fun(U_12495,U_12495)),U_12499),c_If(U_12495)),hAPP(hAPP(c_COMBC(U_12499,tc_fun(U_12499,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12499)),U_12500))),U_12496)),U_12498)),U_12497) = c_Orderings_Obot__class_Obot(tc_fun(U_12499,tc_HOL_Obool))
            | hBOOL(hAPP(hAPP(c_member(U_12495),U_12498),U_12497)) )
          & ( hAPP(c_Set_Ovimage(U_12499,U_12495,hAPP(hAPP(c_COMBC(U_12499,U_12495,U_12495),hAPP(hAPP(c_COMBC(U_12499,U_12495,tc_fun(U_12495,U_12495)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12495,tc_fun(U_12495,U_12495)),U_12499),c_If(U_12495)),hAPP(hAPP(c_COMBC(U_12499,tc_fun(U_12499,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12499)),U_12500))),U_12496)),U_12498)),U_12497) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12499,tc_HOL_Obool)),U_12500)
            | ~ hBOOL(hAPP(hAPP(c_member(U_12495),U_12498),U_12497)) ) )
        | hBOOL(hAPP(hAPP(c_member(U_12495),U_12496),U_12497)) )
      & ( ( ( hAPP(c_Set_Ovimage(U_12499,U_12495,hAPP(hAPP(c_COMBC(U_12499,U_12495,U_12495),hAPP(hAPP(c_COMBC(U_12499,U_12495,tc_fun(U_12495,U_12495)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12495,tc_fun(U_12495,U_12495)),U_12499),c_If(U_12495)),hAPP(hAPP(c_COMBC(U_12499,tc_fun(U_12499,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12499)),U_12500))),U_12496)),U_12498)),U_12497) = U_12500
            | hBOOL(hAPP(hAPP(c_member(U_12495),U_12498),U_12497)) )
          & ( hAPP(c_Set_Ovimage(U_12499,U_12495,hAPP(hAPP(c_COMBC(U_12499,U_12495,U_12495),hAPP(hAPP(c_COMBC(U_12499,U_12495,tc_fun(U_12495,U_12495)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12495,tc_fun(U_12495,U_12495)),U_12499),c_If(U_12495)),hAPP(hAPP(c_COMBC(U_12499,tc_fun(U_12499,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12499)),U_12500))),U_12496)),U_12498)),U_12497) = c_Orderings_Otop__class_Otop(tc_fun(U_12499,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_12495),U_12498),U_12497)) ) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_12495),U_12496),U_12497)) ) ),
    inference(variable_rename,[status(thm)],[f_3236_1]) ).

fof(f_3236_3,plain,
    ( ! [U_12512,U_12510,U_12508,U_12506,U_12504,U_12502] :
        ( ( ( hAPP(c_Set_Ovimage(U_12510,U_12502,hAPP(hAPP(c_COMBC(U_12510,U_12502,U_12502),hAPP(hAPP(c_COMBC(U_12510,U_12502,tc_fun(U_12502,U_12502)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12502,tc_fun(U_12502,U_12502)),U_12510),c_If(U_12502)),hAPP(hAPP(c_COMBC(U_12510,tc_fun(U_12510,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12510)),U_12512))),U_12504)),U_12508)),U_12506) = c_Orderings_Obot__class_Obot(tc_fun(U_12510,tc_HOL_Obool))
            | hBOOL(hAPP(hAPP(c_member(U_12502),U_12508),U_12506)) )
          & ( hAPP(c_Set_Ovimage(U_12510,U_12502,hAPP(hAPP(c_COMBC(U_12510,U_12502,U_12502),hAPP(hAPP(c_COMBC(U_12510,U_12502,tc_fun(U_12502,U_12502)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12502,tc_fun(U_12502,U_12502)),U_12510),c_If(U_12502)),hAPP(hAPP(c_COMBC(U_12510,tc_fun(U_12510,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12510)),U_12512))),U_12504)),U_12508)),U_12506) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12510,tc_HOL_Obool)),U_12512)
            | ~ hBOOL(hAPP(hAPP(c_member(U_12502),U_12508),U_12506)) ) )
        | hBOOL(hAPP(hAPP(c_member(U_12502),U_12504),U_12506)) )
    & ! [U_12511,U_12509,U_12507,U_12505,U_12503,U_12501] :
        ( ( ( hAPP(c_Set_Ovimage(U_12509,U_12501,hAPP(hAPP(c_COMBC(U_12509,U_12501,U_12501),hAPP(hAPP(c_COMBC(U_12509,U_12501,tc_fun(U_12501,U_12501)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12501,tc_fun(U_12501,U_12501)),U_12509),c_If(U_12501)),hAPP(hAPP(c_COMBC(U_12509,tc_fun(U_12509,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12509)),U_12511))),U_12503)),U_12507)),U_12505) = U_12511
            | hBOOL(hAPP(hAPP(c_member(U_12501),U_12507),U_12505)) )
          & ( hAPP(c_Set_Ovimage(U_12509,U_12501,hAPP(hAPP(c_COMBC(U_12509,U_12501,U_12501),hAPP(hAPP(c_COMBC(U_12509,U_12501,tc_fun(U_12501,U_12501)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12501,tc_fun(U_12501,U_12501)),U_12509),c_If(U_12501)),hAPP(hAPP(c_COMBC(U_12509,tc_fun(U_12509,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12509)),U_12511))),U_12503)),U_12507)),U_12505) = c_Orderings_Otop__class_Otop(tc_fun(U_12509,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_12501),U_12507),U_12505)) ) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_12501),U_12503),U_12505)) ) ),
    inference(miniscope,[status(thm)],[f_3236_2]) ).

cnf(f_3236_4,plain,
    ( hAPP(c_Set_Ovimage(U_12509,U_12501,hAPP(hAPP(c_COMBC(U_12509,U_12501,U_12501),hAPP(hAPP(c_COMBC(U_12509,U_12501,tc_fun(U_12501,U_12501)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12501,tc_fun(U_12501,U_12501)),U_12509),c_If(U_12501)),hAPP(hAPP(c_COMBC(U_12509,tc_fun(U_12509,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12509)),U_12511))),U_12503)),U_12507)),U_12505) = c_Orderings_Otop__class_Otop(tc_fun(U_12509,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12501),U_12507),U_12505))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12501),U_12503),U_12505)) ),
    inference(clausify,[status(thm)],[f_3236_3]) ).

cnf(f_3236_5,plain,
    ( hAPP(c_Set_Ovimage(U_12509,U_12501,hAPP(hAPP(c_COMBC(U_12509,U_12501,U_12501),hAPP(hAPP(c_COMBC(U_12509,U_12501,tc_fun(U_12501,U_12501)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12501,tc_fun(U_12501,U_12501)),U_12509),c_If(U_12501)),hAPP(hAPP(c_COMBC(U_12509,tc_fun(U_12509,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12509)),U_12511))),U_12503)),U_12507)),U_12505) = U_12511
    | hBOOL(hAPP(hAPP(c_member(U_12501),U_12507),U_12505))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12501),U_12503),U_12505)) ),
    inference(clausify,[status(thm)],[f_3236_3]) ).

cnf(f_3236_6,plain,
    ( hAPP(c_Set_Ovimage(U_12510,U_12502,hAPP(hAPP(c_COMBC(U_12510,U_12502,U_12502),hAPP(hAPP(c_COMBC(U_12510,U_12502,tc_fun(U_12502,U_12502)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12502,tc_fun(U_12502,U_12502)),U_12510),c_If(U_12502)),hAPP(hAPP(c_COMBC(U_12510,tc_fun(U_12510,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12510)),U_12512))),U_12504)),U_12508)),U_12506) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12510,tc_HOL_Obool)),U_12512)
    | ~ hBOOL(hAPP(hAPP(c_member(U_12502),U_12508),U_12506))
    | hBOOL(hAPP(hAPP(c_member(U_12502),U_12504),U_12506)) ),
    inference(clausify,[status(thm)],[f_3236_3]) ).

cnf(f_3236_7,plain,
    ( hAPP(c_Set_Ovimage(U_12510,U_12502,hAPP(hAPP(c_COMBC(U_12510,U_12502,U_12502),hAPP(hAPP(c_COMBC(U_12510,U_12502,tc_fun(U_12502,U_12502)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12502,tc_fun(U_12502,U_12502)),U_12510),c_If(U_12502)),hAPP(hAPP(c_COMBC(U_12510,tc_fun(U_12510,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12510)),U_12512))),U_12504)),U_12508)),U_12506) = c_Orderings_Obot__class_Obot(tc_fun(U_12510,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(U_12502),U_12508),U_12506))
    | hBOOL(hAPP(hAPP(c_member(U_12502),U_12504),U_12506)) ),
    inference(clausify,[status(thm)],[f_3236_3]) ).

fof(f_3237_1,plain,
    ! [V_A_2,V_g_2,V_f_2,T_c,T_b,T_d] : hAPP(c_Set_Oimage(T_d,tc_prod(T_b,T_c),hAPP(hAPP(c_COMBS(T_d,T_c,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_prod(T_b,T_c)),T_d),c_Product__Type_OPair(T_b,T_c)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_Oimage(T_d,T_b,V_f_2),V_A_2)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_Oimage(T_d,T_c,V_g_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_b),c_Set_Ovimage(T_d,T_b,V_f_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),V_A_2))),
    inference(fof_nnf,[status(thm)],[fact_image__split__eq__Sigma]) ).

fof(f_3237_2,plain,
    ! [U_12518,U_12517,U_12516,U_12515,U_12514,U_12513] : hAPP(c_Set_Oimage(U_12513,tc_prod(U_12514,U_12515),hAPP(hAPP(c_COMBS(U_12513,U_12515,tc_prod(U_12514,U_12515)),hAPP(hAPP(c_COMBB(U_12514,tc_fun(U_12515,tc_prod(U_12514,U_12515)),U_12513),c_Product__Type_OPair(U_12514,U_12515)),U_12516)),U_12517)),U_12518) = hAPP(hAPP(c_Product__Type_OSigma(U_12514,U_12515),hAPP(c_Set_Oimage(U_12513,U_12514,U_12516),U_12518)),hAPP(hAPP(c_COMBB(tc_fun(U_12513,tc_HOL_Obool),tc_fun(U_12515,tc_HOL_Obool),U_12514),c_Set_Oimage(U_12513,U_12515,U_12517)),hAPP(hAPP(c_COMBC(U_12514,tc_fun(U_12513,tc_HOL_Obool),tc_fun(U_12513,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12513,tc_HOL_Obool),tc_fun(tc_fun(U_12513,tc_HOL_Obool),tc_fun(U_12513,tc_HOL_Obool)),U_12514),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12513,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_12514,tc_HOL_Obool),tc_fun(U_12513,tc_HOL_Obool),U_12514),c_Set_Ovimage(U_12513,U_12514,U_12516)),hAPP(hAPP(c_COMBC(U_12514,tc_fun(U_12514,tc_HOL_Obool),tc_fun(U_12514,tc_HOL_Obool)),c_Set_Oinsert(U_12514)),c_Orderings_Obot__class_Obot(tc_fun(U_12514,tc_HOL_Obool)))))),U_12518))),
    inference(variable_rename,[status(thm)],[f_3237_1]) ).

cnf(f_3237_3,plain,
    hAPP(c_Set_Oimage(U_12513,tc_prod(U_12514,U_12515),hAPP(hAPP(c_COMBS(U_12513,U_12515,tc_prod(U_12514,U_12515)),hAPP(hAPP(c_COMBB(U_12514,tc_fun(U_12515,tc_prod(U_12514,U_12515)),U_12513),c_Product__Type_OPair(U_12514,U_12515)),U_12516)),U_12517)),U_12518) = hAPP(hAPP(c_Product__Type_OSigma(U_12514,U_12515),hAPP(c_Set_Oimage(U_12513,U_12514,U_12516),U_12518)),hAPP(hAPP(c_COMBB(tc_fun(U_12513,tc_HOL_Obool),tc_fun(U_12515,tc_HOL_Obool),U_12514),c_Set_Oimage(U_12513,U_12515,U_12517)),hAPP(hAPP(c_COMBC(U_12514,tc_fun(U_12513,tc_HOL_Obool),tc_fun(U_12513,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12513,tc_HOL_Obool),tc_fun(tc_fun(U_12513,tc_HOL_Obool),tc_fun(U_12513,tc_HOL_Obool)),U_12514),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12513,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_12514,tc_HOL_Obool),tc_fun(U_12513,tc_HOL_Obool),U_12514),c_Set_Ovimage(U_12513,U_12514,U_12516)),hAPP(hAPP(c_COMBC(U_12514,tc_fun(U_12514,tc_HOL_Obool),tc_fun(U_12514,tc_HOL_Obool)),c_Set_Oinsert(U_12514)),c_Orderings_Obot__class_Obot(tc_fun(U_12514,tc_HOL_Obool)))))),U_12518))),
    inference(clausify,[status(thm)],[f_3237_2]) ).

fof(f_3238_1,plain,
    ! [V_P_2,V_y_2] :
      ( hBOOL(hAPP(V_P_2,V_y_2))
      | ? [B_x] : ~ hBOOL(hAPP(V_P_2,hAPP(c_Int_ORep__Integ,B_x)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg)) ),
    inference(fof_nnf,[status(thm)],[fact_Rep__Integ__induct]) ).

fof(f_3238_2,plain,
    ! [U_12521,U_12520] :
      ( hBOOL(hAPP(U_12521,U_12520))
      | ? [U_12519] : ~ hBOOL(hAPP(U_12521,hAPP(c_Int_ORep__Integ,U_12519)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_12520),c_Int_OInteg)) ),
    inference(variable_rename,[status(thm)],[f_3238_1]) ).

fof(f_3238_3,plain,
    ! [U_12521,U_12520] :
      ( hBOOL(hAPP(U_12521,U_12520))
      | ~ hBOOL(hAPP(U_12521,hAPP(c_Int_ORep__Integ,sK297(U_12521,U_12520))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_12520),c_Int_OInteg)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK297]),skolemize(U_12519,sK297(U_12521,U_12520))],[f_3238_2]) ).

cnf(f_3238_4,plain,
    ( hBOOL(hAPP(U_12521,U_12520))
    | ~ hBOOL(hAPP(U_12521,hAPP(c_Int_ORep__Integ,sK297(U_12521,U_12520))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_12520),c_Int_OInteg)) ),
    inference(clausify,[status(thm)],[f_3238_3]) ).

fof(f_3239_1,plain,
    ! [V_A_2,V_f_2,T_d,T_c,T_b,V_I_2] :
      ( c_Fun_Oinj__on(T_c,T_d,V_f_2,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2))
      | ? [B_i] :
          ( ~ c_Fun_Oinj__on(T_c,T_d,V_f_2,hAPP(V_A_2,B_i))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_I_2)) )
      | V_I_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
    inference(fof_nnf,[status(thm)],[fact_inj__on__INTER]) ).

fof(f_3239_2,plain,
    ! [U_12528,U_12527,U_12526,U_12525,U_12524,U_12523] :
      ( c_Fun_Oinj__on(U_12525,U_12526,U_12527,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12524,tc_fun(U_12525,tc_HOL_Obool)),U_12523),U_12528))
      | ? [U_12522] :
          ( ~ c_Fun_Oinj__on(U_12525,U_12526,U_12527,hAPP(U_12528,U_12522))
          & hBOOL(hAPP(hAPP(c_member(U_12524),U_12522),U_12523)) )
      | U_12523 = c_Orderings_Obot__class_Obot(tc_fun(U_12524,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_3239_1]) ).

fof(f_3239_3,plain,
    ! [U_12528,U_12527,U_12526,U_12525,U_12524,U_12523] :
      ( c_Fun_Oinj__on(U_12525,U_12526,U_12527,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12524,tc_fun(U_12525,tc_HOL_Obool)),U_12523),U_12528))
      | ( ~ c_Fun_Oinj__on(U_12525,U_12526,U_12527,hAPP(U_12528,sK298(U_12528,U_12527,U_12526,U_12525,U_12524,U_12523)))
        & hBOOL(hAPP(hAPP(c_member(U_12524),sK298(U_12528,U_12527,U_12526,U_12525,U_12524,U_12523)),U_12523)) )
      | U_12523 = c_Orderings_Obot__class_Obot(tc_fun(U_12524,tc_HOL_Obool)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK298]),skolemize(U_12522,sK298(U_12528,U_12527,U_12526,U_12525,U_12524,U_12523))],[f_3239_2]) ).

cnf(f_3239_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12524),sK298(U_12528,U_12527,U_12526,U_12525,U_12524,U_12523)),U_12523))
    | c_Fun_Oinj__on(U_12525,U_12526,U_12527,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12524,tc_fun(U_12525,tc_HOL_Obool)),U_12523),U_12528))
    | U_12523 = c_Orderings_Obot__class_Obot(tc_fun(U_12524,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3239_3]) ).

cnf(f_3239_5,plain,
    ( ~ c_Fun_Oinj__on(U_12525,U_12526,U_12527,hAPP(U_12528,sK298(U_12528,U_12527,U_12526,U_12525,U_12524,U_12523)))
    | c_Fun_Oinj__on(U_12525,U_12526,U_12527,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12524,tc_fun(U_12525,tc_HOL_Obool)),U_12523),U_12528))
    | U_12523 = c_Orderings_Obot__class_Obot(tc_fun(U_12524,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3239_3]) ).

fof(f_3240_1,plain,
    ! [V_B_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_SigmaI]) ).

fof(f_3240_2,plain,
    ! [U_12534,U_12533,U_12532,U_12531,U_12530,U_12529] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12529,U_12532)),hAPP(hAPP(c_Product__Type_OPair(U_12529,U_12532),U_12530),U_12533)),hAPP(hAPP(c_Product__Type_OSigma(U_12529,U_12532),U_12531),U_12534)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12532),U_12533),hAPP(U_12534,U_12530)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12529),U_12530),U_12531)) ),
    inference(variable_rename,[status(thm)],[f_3240_1]) ).

cnf(f_3240_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12529,U_12532)),hAPP(hAPP(c_Product__Type_OPair(U_12529,U_12532),U_12530),U_12533)),hAPP(hAPP(c_Product__Type_OSigma(U_12529,U_12532),U_12531),U_12534)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12532),U_12533),hAPP(U_12534,U_12530)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12529),U_12530),U_12531)) ),
    inference(clausify,[status(thm)],[f_3240_2]) ).

fof(f_3241_1,plain,
    ! [V_B_2,V_A_2,T_c,V_C_2,V_x_2,T_b] :
      ( ( ( hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_C_2)) = hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_B_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_C_2))
          | V_A_2 != V_B_2 )
        & ( V_A_2 = V_B_2
          | hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_C_2)) != hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_B_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_C_2)) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_C_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Times__eq__cancel2]) ).

fof(f_3241_2,plain,
    ! [U_12540,U_12539,U_12538,U_12537,U_12536,U_12535] :
      ( ( ( hAPP(hAPP(c_Product__Type_OSigma(U_12538,U_12535),U_12539),hAPP(c_COMBK(tc_fun(U_12535,tc_HOL_Obool),U_12538),U_12537)) = hAPP(hAPP(c_Product__Type_OSigma(U_12538,U_12535),U_12540),hAPP(c_COMBK(tc_fun(U_12535,tc_HOL_Obool),U_12538),U_12537))
          | U_12539 != U_12540 )
        & ( U_12539 = U_12540
          | hAPP(hAPP(c_Product__Type_OSigma(U_12538,U_12535),U_12539),hAPP(c_COMBK(tc_fun(U_12535,tc_HOL_Obool),U_12538),U_12537)) != hAPP(hAPP(c_Product__Type_OSigma(U_12538,U_12535),U_12540),hAPP(c_COMBK(tc_fun(U_12535,tc_HOL_Obool),U_12538),U_12537)) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_12535),U_12536),U_12537)) ),
    inference(variable_rename,[status(thm)],[f_3241_1]) ).

cnf(f_3241_3,plain,
    ( U_12539 = U_12540
    | hAPP(hAPP(c_Product__Type_OSigma(U_12538,U_12535),U_12539),hAPP(c_COMBK(tc_fun(U_12535,tc_HOL_Obool),U_12538),U_12537)) != hAPP(hAPP(c_Product__Type_OSigma(U_12538,U_12535),U_12540),hAPP(c_COMBK(tc_fun(U_12535,tc_HOL_Obool),U_12538),U_12537))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12535),U_12536),U_12537)) ),
    inference(clausify,[status(thm)],[f_3241_2]) ).

cnf(f_3241_4,plain,
    ( hAPP(hAPP(c_Product__Type_OSigma(U_12538,U_12535),U_12539),hAPP(c_COMBK(tc_fun(U_12535,tc_HOL_Obool),U_12538),U_12537)) = hAPP(hAPP(c_Product__Type_OSigma(U_12538,U_12535),U_12540),hAPP(c_COMBK(tc_fun(U_12535,tc_HOL_Obool),U_12538),U_12537))
    | U_12539 != U_12540
    | ~ hBOOL(hAPP(hAPP(c_member(U_12535),U_12536),U_12537)) ),
    inference(clausify,[status(thm)],[f_3241_2]) ).

fof(f_3242_1,plain,
    ! [V_B_2,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_Sigma__Diff__distrib2]) ).

fof(f_3242_2,plain,
    ! [U_12545,U_12544,U_12543,U_12542,U_12541] : hAPP(hAPP(c_Product__Type_OSigma(U_12541,U_12542),U_12543),hAPP(hAPP(c_COMBS(U_12541,tc_fun(U_12542,tc_HOL_Obool),tc_fun(U_12542,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12542,tc_HOL_Obool),tc_fun(tc_fun(U_12542,tc_HOL_Obool),tc_fun(U_12542,tc_HOL_Obool)),U_12541),c_Groups_Ominus__class_Ominus(tc_fun(U_12542,tc_HOL_Obool))),U_12544)),U_12545)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_12541,U_12542),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12541,U_12542),U_12543),U_12544)),hAPP(hAPP(c_Product__Type_OSigma(U_12541,U_12542),U_12543),U_12545)),
    inference(variable_rename,[status(thm)],[f_3242_1]) ).

cnf(f_3242_3,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_12541,U_12542),U_12543),hAPP(hAPP(c_COMBS(U_12541,tc_fun(U_12542,tc_HOL_Obool),tc_fun(U_12542,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12542,tc_HOL_Obool),tc_fun(tc_fun(U_12542,tc_HOL_Obool),tc_fun(U_12542,tc_HOL_Obool)),U_12541),c_Groups_Ominus__class_Ominus(tc_fun(U_12542,tc_HOL_Obool))),U_12544)),U_12545)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_12541,U_12542),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12541,U_12542),U_12543),U_12544)),hAPP(hAPP(c_Product__Type_OSigma(U_12541,U_12542),U_12543),U_12545)),
    inference(clausify,[status(thm)],[f_3242_2]) ).

fof(f_3243_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_B_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))),
    inference(fof_nnf,[status(thm)],[fact_Times__Diff__distrib1]) ).

fof(f_3243_2,plain,
    ! [U_12550,U_12549,U_12548,U_12547,U_12546] : hAPP(hAPP(c_Product__Type_OSigma(U_12546,U_12547),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12546,tc_HOL_Obool)),U_12548),U_12549)),hAPP(c_COMBK(tc_fun(U_12547,tc_HOL_Obool),U_12546),U_12550)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_12546,U_12547),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12546,U_12547),U_12548),hAPP(c_COMBK(tc_fun(U_12547,tc_HOL_Obool),U_12546),U_12550))),hAPP(hAPP(c_Product__Type_OSigma(U_12546,U_12547),U_12549),hAPP(c_COMBK(tc_fun(U_12547,tc_HOL_Obool),U_12546),U_12550))),
    inference(variable_rename,[status(thm)],[f_3243_1]) ).

cnf(f_3243_3,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_12546,U_12547),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12546,tc_HOL_Obool)),U_12548),U_12549)),hAPP(c_COMBK(tc_fun(U_12547,tc_HOL_Obool),U_12546),U_12550)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_12546,U_12547),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12546,U_12547),U_12548),hAPP(c_COMBK(tc_fun(U_12547,tc_HOL_Obool),U_12546),U_12550))),hAPP(hAPP(c_Product__Type_OSigma(U_12546,U_12547),U_12549),hAPP(c_COMBK(tc_fun(U_12547,tc_HOL_Obool),U_12546),U_12550))),
    inference(clausify,[status(thm)],[f_3243_2]) ).

fof(f_3244_1,plain,
    ! [V_C_2,V_J_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_J_2)),V_C_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_J_2),V_C_2)),
    inference(fof_nnf,[status(thm)],[fact_Sigma__Diff__distrib1]) ).

fof(f_3244_2,plain,
    ! [U_12555,U_12554,U_12553,U_12552,U_12551] : hAPP(hAPP(c_Product__Type_OSigma(U_12551,U_12552),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12551,tc_HOL_Obool)),U_12553),U_12554)),U_12555) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_12551,U_12552),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12551,U_12552),U_12553),U_12555)),hAPP(hAPP(c_Product__Type_OSigma(U_12551,U_12552),U_12554),U_12555)),
    inference(variable_rename,[status(thm)],[f_3244_1]) ).

cnf(f_3244_3,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_12551,U_12552),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12551,tc_HOL_Obool)),U_12553),U_12554)),U_12555) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_12551,U_12552),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12551,U_12552),U_12553),U_12555)),hAPP(hAPP(c_Product__Type_OSigma(U_12551,U_12552),U_12554),U_12555)),
    inference(clausify,[status(thm)],[f_3244_2]) ).

fof(f_3245_1,plain,
    ! [V_B_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Sigma__empty1]) ).

fof(f_3245_2,plain,
    ! [U_12558,U_12557,U_12556] : hAPP(hAPP(c_Product__Type_OSigma(U_12556,U_12557),c_Orderings_Obot__class_Obot(tc_fun(U_12556,tc_HOL_Obool))),U_12558) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_12556,U_12557),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3245_1]) ).

cnf(f_3245_3,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_12556,U_12557),c_Orderings_Obot__class_Obot(tc_fun(U_12556,tc_HOL_Obool))),U_12558) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_12556,U_12557),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3245_2]) ).

fof(f_3246_1,plain,
    ! [V_B_2,V_X_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_X_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),c_Product__Type_OSigma(T_b,T_c)),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_Sigma__Union]) ).

fof(f_3246_2,plain,
    ! [U_12562,U_12561,U_12560,U_12559] : hAPP(hAPP(c_Product__Type_OSigma(U_12559,U_12560),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_12559,tc_HOL_Obool),U_12561)),U_12562) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_12559,tc_HOL_Obool),tc_fun(tc_prod(U_12559,U_12560),tc_HOL_Obool)),U_12561),hAPP(hAPP(c_COMBC(tc_fun(U_12559,tc_HOL_Obool),tc_fun(U_12559,tc_fun(U_12560,tc_HOL_Obool)),tc_fun(tc_prod(U_12559,U_12560),tc_HOL_Obool)),c_Product__Type_OSigma(U_12559,U_12560)),U_12562)),
    inference(variable_rename,[status(thm)],[f_3246_1]) ).

cnf(f_3246_3,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_12559,U_12560),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_12559,tc_HOL_Obool),U_12561)),U_12562) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_12559,tc_HOL_Obool),tc_fun(tc_prod(U_12559,U_12560),tc_HOL_Obool)),U_12561),hAPP(hAPP(c_COMBC(tc_fun(U_12559,tc_HOL_Obool),tc_fun(U_12559,tc_fun(U_12560,tc_HOL_Obool)),tc_fun(tc_prod(U_12559,U_12560),tc_HOL_Obool)),c_Product__Type_OSigma(U_12559,U_12560)),U_12562)),
    inference(clausify,[status(thm)],[f_3246_2]) ).

fof(f_3247_1,plain,
    ! [V_B_2,V_A_2,T_c,T_b] : hAPP(c_Finite__Set_Ocard(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_card__cartesian__product]) ).

fof(f_3247_2,plain,
    ! [U_12566,U_12565,U_12564,U_12563] : hAPP(c_Finite__Set_Ocard(tc_prod(U_12563,U_12564)),hAPP(hAPP(c_Product__Type_OSigma(U_12563,U_12564),U_12565),hAPP(c_COMBK(tc_fun(U_12564,tc_HOL_Obool),U_12563),U_12566))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_12563),U_12565)),hAPP(c_Finite__Set_Ocard(U_12564),U_12566)),
    inference(variable_rename,[status(thm)],[f_3247_1]) ).

cnf(f_3247_3,plain,
    hAPP(c_Finite__Set_Ocard(tc_prod(U_12563,U_12564)),hAPP(hAPP(c_Product__Type_OSigma(U_12563,U_12564),U_12565),hAPP(c_COMBK(tc_fun(U_12564,tc_HOL_Obool),U_12563),U_12566))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_12563),U_12565)),hAPP(c_Finite__Set_Ocard(U_12564),U_12566)),
    inference(clausify,[status(thm)],[f_3247_2]) ).

fof(f_3248_1,plain,
    ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_b),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(T_c,T_d),T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_B_2)))
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__cartesian__product]) ).

fof(f_3248_2,plain,
    ! [U_12572,U_12571,U_12570,U_12569,U_12568,U_12567] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12568,U_12567),hAPP(hAPP(c_COMBC(U_12568,tc_fun(U_12569,tc_HOL_Obool),U_12567),hAPP(hAPP(c_COMBB(tc_fun(U_12569,U_12567),tc_fun(tc_fun(U_12569,tc_HOL_Obool),U_12567),U_12568),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12569,U_12567)),U_12570)),U_12571)),U_12572) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(U_12568,U_12569),U_12567),hAPP(c_Product__Type_Oprod_Oprod__case(U_12568,U_12569,U_12567),U_12570)),hAPP(hAPP(c_Product__Type_OSigma(U_12568,U_12569),U_12572),hAPP(c_COMBK(tc_fun(U_12569,tc_HOL_Obool),U_12568),U_12571)))
      | ~ class_Groups_Ocomm__monoid__add(U_12567) ),
    inference(variable_rename,[status(thm)],[f_3248_1]) ).

cnf(f_3248_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12568,U_12567),hAPP(hAPP(c_COMBC(U_12568,tc_fun(U_12569,tc_HOL_Obool),U_12567),hAPP(hAPP(c_COMBB(tc_fun(U_12569,U_12567),tc_fun(tc_fun(U_12569,tc_HOL_Obool),U_12567),U_12568),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12569,U_12567)),U_12570)),U_12571)),U_12572) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(U_12568,U_12569),U_12567),hAPP(c_Product__Type_Oprod_Oprod__case(U_12568,U_12569,U_12567),U_12570)),hAPP(hAPP(c_Product__Type_OSigma(U_12568,U_12569),U_12572),hAPP(c_COMBK(tc_fun(U_12569,tc_HOL_Obool),U_12568),U_12571)))
    | ~ class_Groups_Ocomm__monoid__add(U_12567) ),
    inference(clausify,[status(thm)],[f_3248_2]) ).

fof(f_3249_1,plain,
    ! [V_B_2,V_A_2,T_c,T_b] :
      ( ( hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))
        | ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
          & V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) )
      & ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
        | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
        | hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Times__empty]) ).

fof(f_3249_2,plain,
    ! [U_12576,U_12575,U_12574,U_12573] :
      ( ( hAPP(hAPP(c_Product__Type_OSigma(U_12573,U_12574),U_12575),hAPP(c_COMBK(tc_fun(U_12574,tc_HOL_Obool),U_12573),U_12576)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_12573,U_12574),tc_HOL_Obool))
        | ( U_12576 != c_Orderings_Obot__class_Obot(tc_fun(U_12574,tc_HOL_Obool))
          & U_12575 != c_Orderings_Obot__class_Obot(tc_fun(U_12573,tc_HOL_Obool)) ) )
      & ( U_12576 = c_Orderings_Obot__class_Obot(tc_fun(U_12574,tc_HOL_Obool))
        | U_12575 = c_Orderings_Obot__class_Obot(tc_fun(U_12573,tc_HOL_Obool))
        | hAPP(hAPP(c_Product__Type_OSigma(U_12573,U_12574),U_12575),hAPP(c_COMBK(tc_fun(U_12574,tc_HOL_Obool),U_12573),U_12576)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_12573,U_12574),tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_3249_1]) ).

fof(f_3249_3,plain,
    ( ! [U_12584,U_12582,U_12580,U_12578] :
        ( hAPP(hAPP(c_Product__Type_OSigma(U_12578,U_12580),U_12582),hAPP(c_COMBK(tc_fun(U_12580,tc_HOL_Obool),U_12578),U_12584)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_12578,U_12580),tc_HOL_Obool))
        | ( U_12584 != c_Orderings_Obot__class_Obot(tc_fun(U_12580,tc_HOL_Obool))
          & U_12582 != c_Orderings_Obot__class_Obot(tc_fun(U_12578,tc_HOL_Obool)) ) )
    & ! [U_12583,U_12581,U_12579,U_12577] :
        ( U_12583 = c_Orderings_Obot__class_Obot(tc_fun(U_12579,tc_HOL_Obool))
        | U_12581 = c_Orderings_Obot__class_Obot(tc_fun(U_12577,tc_HOL_Obool))
        | hAPP(hAPP(c_Product__Type_OSigma(U_12577,U_12579),U_12581),hAPP(c_COMBK(tc_fun(U_12579,tc_HOL_Obool),U_12577),U_12583)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_12577,U_12579),tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_3249_2]) ).

cnf(f_3249_4,plain,
    ( U_12583 = c_Orderings_Obot__class_Obot(tc_fun(U_12579,tc_HOL_Obool))
    | U_12581 = c_Orderings_Obot__class_Obot(tc_fun(U_12577,tc_HOL_Obool))
    | hAPP(hAPP(c_Product__Type_OSigma(U_12577,U_12579),U_12581),hAPP(c_COMBK(tc_fun(U_12579,tc_HOL_Obool),U_12577),U_12583)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_12577,U_12579),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3249_3]) ).

cnf(f_3249_5,plain,
    ( U_12582 != c_Orderings_Obot__class_Obot(tc_fun(U_12578,tc_HOL_Obool))
    | hAPP(hAPP(c_Product__Type_OSigma(U_12578,U_12580),U_12582),hAPP(c_COMBK(tc_fun(U_12580,tc_HOL_Obool),U_12578),U_12584)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_12578,U_12580),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3249_3]) ).

cnf(f_3249_6,plain,
    ( U_12584 != c_Orderings_Obot__class_Obot(tc_fun(U_12580,tc_HOL_Obool))
    | hAPP(hAPP(c_Product__Type_OSigma(U_12578,U_12580),U_12582),hAPP(c_COMBK(tc_fun(U_12580,tc_HOL_Obool),U_12578),U_12584)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_12578,U_12580),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3249_3]) ).

fof(f_3250_1,plain,
    ! [V_A_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Sigma__empty2]) ).

fof(f_3250_2,plain,
    ! [U_12587,U_12586,U_12585] : hAPP(hAPP(c_Product__Type_OSigma(U_12585,U_12586),U_12587),hAPP(c_COMBK(tc_fun(U_12586,tc_HOL_Obool),U_12585),c_Orderings_Obot__class_Obot(tc_fun(U_12586,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_12585,U_12586),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3250_1]) ).

cnf(f_3250_3,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_12585,U_12586),U_12587),hAPP(c_COMBK(tc_fun(U_12586,tc_HOL_Obool),U_12585),c_Orderings_Obot__class_Obot(tc_fun(U_12586,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_12585,U_12586),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3250_2]) ).

fof(f_3251_1,plain,
    ! [V_A_2,T_c,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_Compl__Times__UNIV2]) ).

fof(f_3251_2,plain,
    ! [U_12590,U_12589,U_12588] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(U_12588,U_12589),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12588,U_12589),U_12590),hAPP(c_COMBK(tc_fun(U_12589,tc_HOL_Obool),U_12588),c_Orderings_Otop__class_Otop(tc_fun(U_12589,tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(U_12588,U_12589),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12588,tc_HOL_Obool)),U_12590)),hAPP(c_COMBK(tc_fun(U_12589,tc_HOL_Obool),U_12588),c_Orderings_Otop__class_Otop(tc_fun(U_12589,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_3251_1]) ).

cnf(f_3251_3,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(U_12588,U_12589),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12588,U_12589),U_12590),hAPP(c_COMBK(tc_fun(U_12589,tc_HOL_Obool),U_12588),c_Orderings_Otop__class_Otop(tc_fun(U_12589,tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(U_12588,U_12589),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12588,tc_HOL_Obool)),U_12590)),hAPP(c_COMBK(tc_fun(U_12589,tc_HOL_Obool),U_12588),c_Orderings_Otop__class_Otop(tc_fun(U_12589,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_3251_2]) ).

fof(f_3252_1,plain,
    ! [V_A_2,T_c,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_A_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2))),
    inference(fof_nnf,[status(thm)],[fact_Compl__Times__UNIV1]) ).

fof(f_3252_2,plain,
    ! [U_12593,U_12592,U_12591] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(U_12591,U_12592),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12591,U_12592),c_Orderings_Otop__class_Otop(tc_fun(U_12591,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(U_12592,tc_HOL_Obool),U_12591),U_12593))) = hAPP(hAPP(c_Product__Type_OSigma(U_12591,U_12592),c_Orderings_Otop__class_Otop(tc_fun(U_12591,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(U_12592,tc_HOL_Obool),U_12591),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12592,tc_HOL_Obool)),U_12593))),
    inference(variable_rename,[status(thm)],[f_3252_1]) ).

cnf(f_3252_3,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(U_12591,U_12592),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12591,U_12592),c_Orderings_Otop__class_Otop(tc_fun(U_12591,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(U_12592,tc_HOL_Obool),U_12591),U_12593))) = hAPP(hAPP(c_Product__Type_OSigma(U_12591,U_12592),c_Orderings_Otop__class_Otop(tc_fun(U_12591,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(U_12592,tc_HOL_Obool),U_12591),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12592,tc_HOL_Obool)),U_12593))),
    inference(clausify,[status(thm)],[f_3252_2]) ).

fof(f_3253_1,plain,
    ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_b),T_c),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_d,T_b)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(T_c,T_d),T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_B_2)))
      | ~ class_Groups_Ocomm__monoid__mult(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__cartesian__product]) ).

fof(f_3253_2,plain,
    ! [U_12599,U_12598,U_12597,U_12596,U_12595,U_12594] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_12595,U_12594),hAPP(hAPP(c_COMBC(U_12595,tc_fun(U_12596,tc_HOL_Obool),U_12594),hAPP(hAPP(c_COMBB(tc_fun(U_12596,U_12594),tc_fun(tc_fun(U_12596,tc_HOL_Obool),U_12594),U_12595),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_12596,U_12594)),U_12597)),U_12598)),U_12599) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(U_12595,U_12596),U_12594),hAPP(c_Product__Type_Oprod_Oprod__case(U_12595,U_12596,U_12594),U_12597)),hAPP(hAPP(c_Product__Type_OSigma(U_12595,U_12596),U_12599),hAPP(c_COMBK(tc_fun(U_12596,tc_HOL_Obool),U_12595),U_12598)))
      | ~ class_Groups_Ocomm__monoid__mult(U_12594) ),
    inference(variable_rename,[status(thm)],[f_3253_1]) ).

cnf(f_3253_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_12595,U_12594),hAPP(hAPP(c_COMBC(U_12595,tc_fun(U_12596,tc_HOL_Obool),U_12594),hAPP(hAPP(c_COMBB(tc_fun(U_12596,U_12594),tc_fun(tc_fun(U_12596,tc_HOL_Obool),U_12594),U_12595),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_12596,U_12594)),U_12597)),U_12598)),U_12599) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(U_12595,U_12596),U_12594),hAPP(c_Product__Type_Oprod_Oprod__case(U_12595,U_12596,U_12594),U_12597)),hAPP(hAPP(c_Product__Type_OSigma(U_12595,U_12596),U_12599),hAPP(c_COMBK(tc_fun(U_12596,tc_HOL_Obool),U_12595),U_12598)))
    | ~ class_Groups_Ocomm__monoid__mult(U_12594) ),
    inference(clausify,[status(thm)],[f_3253_2]) ).

fof(f_3254_1,plain,
    ! [V_C_2,V_J_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_J_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_J_2),V_C_2)),
    inference(fof_nnf,[status(thm)],[fact_Sigma__Un__distrib1]) ).

fof(f_3254_2,plain,
    ! [U_12604,U_12603,U_12602,U_12601,U_12600] : hAPP(hAPP(c_Product__Type_OSigma(U_12600,U_12601),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12600,tc_HOL_Obool)),U_12602),U_12603)),U_12604) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_12600,U_12601),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12600,U_12601),U_12602),U_12604)),hAPP(hAPP(c_Product__Type_OSigma(U_12600,U_12601),U_12603),U_12604)),
    inference(variable_rename,[status(thm)],[f_3254_1]) ).

cnf(f_3254_3,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_12600,U_12601),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12600,tc_HOL_Obool)),U_12602),U_12603)),U_12604) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_12600,U_12601),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12600,U_12601),U_12602),U_12604)),hAPP(hAPP(c_Product__Type_OSigma(U_12600,U_12601),U_12603),U_12604)),
    inference(clausify,[status(thm)],[f_3254_2]) ).

fof(f_3255_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_B_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))),
    inference(fof_nnf,[status(thm)],[fact_Times__Un__distrib1]) ).

fof(f_3255_2,plain,
    ! [U_12609,U_12608,U_12607,U_12606,U_12605] : hAPP(hAPP(c_Product__Type_OSigma(U_12605,U_12606),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12605,tc_HOL_Obool)),U_12607),U_12608)),hAPP(c_COMBK(tc_fun(U_12606,tc_HOL_Obool),U_12605),U_12609)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_12605,U_12606),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12605,U_12606),U_12607),hAPP(c_COMBK(tc_fun(U_12606,tc_HOL_Obool),U_12605),U_12609))),hAPP(hAPP(c_Product__Type_OSigma(U_12605,U_12606),U_12608),hAPP(c_COMBK(tc_fun(U_12606,tc_HOL_Obool),U_12605),U_12609))),
    inference(variable_rename,[status(thm)],[f_3255_1]) ).

cnf(f_3255_3,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_12605,U_12606),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12605,tc_HOL_Obool)),U_12607),U_12608)),hAPP(c_COMBK(tc_fun(U_12606,tc_HOL_Obool),U_12605),U_12609)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_12605,U_12606),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12605,U_12606),U_12607),hAPP(c_COMBK(tc_fun(U_12606,tc_HOL_Obool),U_12605),U_12609))),hAPP(hAPP(c_Product__Type_OSigma(U_12605,U_12606),U_12608),hAPP(c_COMBK(tc_fun(U_12606,tc_HOL_Obool),U_12605),U_12609))),
    inference(clausify,[status(thm)],[f_3255_2]) ).

fof(f_3256_1,plain,
    ! [V_B_2,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_Sigma__Un__distrib2]) ).

fof(f_3256_2,plain,
    ! [U_12614,U_12613,U_12612,U_12611,U_12610] : hAPP(hAPP(c_Product__Type_OSigma(U_12610,U_12611),U_12612),hAPP(hAPP(c_COMBS(U_12610,tc_fun(U_12611,tc_HOL_Obool),tc_fun(U_12611,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12611,tc_HOL_Obool),tc_fun(tc_fun(U_12611,tc_HOL_Obool),tc_fun(U_12611,tc_HOL_Obool)),U_12610),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12611,tc_HOL_Obool))),U_12613)),U_12614)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_12610,U_12611),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12610,U_12611),U_12612),U_12613)),hAPP(hAPP(c_Product__Type_OSigma(U_12610,U_12611),U_12612),U_12614)),
    inference(variable_rename,[status(thm)],[f_3256_1]) ).

cnf(f_3256_3,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_12610,U_12611),U_12612),hAPP(hAPP(c_COMBS(U_12610,tc_fun(U_12611,tc_HOL_Obool),tc_fun(U_12611,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12611,tc_HOL_Obool),tc_fun(tc_fun(U_12611,tc_HOL_Obool),tc_fun(U_12611,tc_HOL_Obool)),U_12610),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12611,tc_HOL_Obool))),U_12613)),U_12614)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_12610,U_12611),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12610,U_12611),U_12612),U_12613)),hAPP(hAPP(c_Product__Type_OSigma(U_12610,U_12611),U_12612),U_12614)),
    inference(clausify,[status(thm)],[f_3256_2]) ).

fof(f_3257_1,plain,
    ! [V_B_2,V_A_2,T_b,T_c] : hAPP(c_Set_Oimage(tc_prod(T_c,T_b),tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,tc_prod(T_b,T_c)),hAPP(c_COMBC(T_b,T_c,tc_prod(T_b,T_c)),c_Product__Type_OPair(T_b,T_c)))),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_B_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_swap__product]) ).

fof(f_3257_2,plain,
    ! [U_12618,U_12617,U_12616,U_12615] : hAPP(c_Set_Oimage(tc_prod(U_12615,U_12616),tc_prod(U_12616,U_12615),hAPP(c_Product__Type_Oprod_Oprod__case(U_12615,U_12616,tc_prod(U_12616,U_12615)),hAPP(c_COMBC(U_12616,U_12615,tc_prod(U_12616,U_12615)),c_Product__Type_OPair(U_12616,U_12615)))),hAPP(hAPP(c_Product__Type_OSigma(U_12615,U_12616),U_12617),hAPP(c_COMBK(tc_fun(U_12616,tc_HOL_Obool),U_12615),U_12618))) = hAPP(hAPP(c_Product__Type_OSigma(U_12616,U_12615),U_12618),hAPP(c_COMBK(tc_fun(U_12615,tc_HOL_Obool),U_12616),U_12617)),
    inference(variable_rename,[status(thm)],[f_3257_1]) ).

cnf(f_3257_3,plain,
    hAPP(c_Set_Oimage(tc_prod(U_12615,U_12616),tc_prod(U_12616,U_12615),hAPP(c_Product__Type_Oprod_Oprod__case(U_12615,U_12616,tc_prod(U_12616,U_12615)),hAPP(c_COMBC(U_12616,U_12615,tc_prod(U_12616,U_12615)),c_Product__Type_OPair(U_12616,U_12615)))),hAPP(hAPP(c_Product__Type_OSigma(U_12615,U_12616),U_12617),hAPP(c_COMBK(tc_fun(U_12616,tc_HOL_Obool),U_12615),U_12618))) = hAPP(hAPP(c_Product__Type_OSigma(U_12616,U_12615),U_12618),hAPP(c_COMBK(tc_fun(U_12615,tc_HOL_Obool),U_12616),U_12617)),
    inference(clausify,[status(thm)],[f_3257_2]) ).

fof(f_3258_1,plain,
    ! [V_B_2,T_c,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__cartesian__product]) ).

fof(f_3258_2,plain,
    ! [U_12622,U_12621,U_12620,U_12619] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_12619,U_12621)),hAPP(hAPP(c_Product__Type_OSigma(U_12619,U_12621),U_12620),hAPP(c_COMBK(tc_fun(U_12621,tc_HOL_Obool),U_12619),U_12622))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12621),U_12622))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12619),U_12620)) ),
    inference(variable_rename,[status(thm)],[f_3258_1]) ).

cnf(f_3258_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_12619,U_12621)),hAPP(hAPP(c_Product__Type_OSigma(U_12619,U_12621),U_12620),hAPP(c_COMBK(tc_fun(U_12621,tc_HOL_Obool),U_12619),U_12622))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12621),U_12622))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12619),U_12620)) ),
    inference(clausify,[status(thm)],[f_3258_2]) ).

fof(f_3259_1,plain,
    ! [V_r_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
      | ~ c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_equiv__type]) ).

fof(f_3259_2,plain,
    ! [U_12625,U_12624,U_12623] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12623,U_12623),tc_HOL_Obool)),U_12625),hAPP(hAPP(c_Product__Type_OSigma(U_12623,U_12623),U_12624),hAPP(c_COMBK(tc_fun(U_12623,tc_HOL_Obool),U_12623),U_12624))))
      | ~ c_Equiv__Relations_Oequiv(U_12623,U_12624,U_12625) ),
    inference(variable_rename,[status(thm)],[f_3259_1]) ).

cnf(f_3259_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12623,U_12623),tc_HOL_Obool)),U_12625),hAPP(hAPP(c_Product__Type_OSigma(U_12623,U_12623),U_12624),hAPP(c_COMBK(tc_fun(U_12623,tc_HOL_Obool),U_12623),U_12624))))
    | ~ c_Equiv__Relations_Oequiv(U_12623,U_12624,U_12625) ),
    inference(clausify,[status(thm)],[f_3259_2]) ).

fof(f_3260_1,plain,
    ! [V_B_2,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_Sigma__Int__distrib2]) ).

fof(f_3260_2,plain,
    ! [U_12630,U_12629,U_12628,U_12627,U_12626] : hAPP(hAPP(c_Product__Type_OSigma(U_12626,U_12627),U_12628),hAPP(hAPP(c_COMBS(U_12626,tc_fun(U_12627,tc_HOL_Obool),tc_fun(U_12627,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12627,tc_HOL_Obool),tc_fun(tc_fun(U_12627,tc_HOL_Obool),tc_fun(U_12627,tc_HOL_Obool)),U_12626),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12627,tc_HOL_Obool))),U_12629)),U_12630)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_12626,U_12627),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12626,U_12627),U_12628),U_12629)),hAPP(hAPP(c_Product__Type_OSigma(U_12626,U_12627),U_12628),U_12630)),
    inference(variable_rename,[status(thm)],[f_3260_1]) ).

cnf(f_3260_3,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_12626,U_12627),U_12628),hAPP(hAPP(c_COMBS(U_12626,tc_fun(U_12627,tc_HOL_Obool),tc_fun(U_12627,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12627,tc_HOL_Obool),tc_fun(tc_fun(U_12627,tc_HOL_Obool),tc_fun(U_12627,tc_HOL_Obool)),U_12626),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12627,tc_HOL_Obool))),U_12629)),U_12630)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_12626,U_12627),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12626,U_12627),U_12628),U_12629)),hAPP(hAPP(c_Product__Type_OSigma(U_12626,U_12627),U_12628),U_12630)),
    inference(clausify,[status(thm)],[f_3260_2]) ).

fof(f_3261_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_B_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))),
    inference(fof_nnf,[status(thm)],[fact_Times__Int__distrib1]) ).

fof(f_3261_2,plain,
    ! [U_12635,U_12634,U_12633,U_12632,U_12631] : hAPP(hAPP(c_Product__Type_OSigma(U_12631,U_12632),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12631,tc_HOL_Obool)),U_12633),U_12634)),hAPP(c_COMBK(tc_fun(U_12632,tc_HOL_Obool),U_12631),U_12635)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_12631,U_12632),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12631,U_12632),U_12633),hAPP(c_COMBK(tc_fun(U_12632,tc_HOL_Obool),U_12631),U_12635))),hAPP(hAPP(c_Product__Type_OSigma(U_12631,U_12632),U_12634),hAPP(c_COMBK(tc_fun(U_12632,tc_HOL_Obool),U_12631),U_12635))),
    inference(variable_rename,[status(thm)],[f_3261_1]) ).

cnf(f_3261_3,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_12631,U_12632),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12631,tc_HOL_Obool)),U_12633),U_12634)),hAPP(c_COMBK(tc_fun(U_12632,tc_HOL_Obool),U_12631),U_12635)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_12631,U_12632),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12631,U_12632),U_12633),hAPP(c_COMBK(tc_fun(U_12632,tc_HOL_Obool),U_12631),U_12635))),hAPP(hAPP(c_Product__Type_OSigma(U_12631,U_12632),U_12634),hAPP(c_COMBK(tc_fun(U_12632,tc_HOL_Obool),U_12631),U_12635))),
    inference(clausify,[status(thm)],[f_3261_2]) ).

fof(f_3262_1,plain,
    ! [V_C_2,V_J_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_J_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_J_2),V_C_2)),
    inference(fof_nnf,[status(thm)],[fact_Sigma__Int__distrib1]) ).

fof(f_3262_2,plain,
    ! [U_12640,U_12639,U_12638,U_12637,U_12636] : hAPP(hAPP(c_Product__Type_OSigma(U_12636,U_12637),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12636,tc_HOL_Obool)),U_12638),U_12639)),U_12640) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_12636,U_12637),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12636,U_12637),U_12638),U_12640)),hAPP(hAPP(c_Product__Type_OSigma(U_12636,U_12637),U_12639),U_12640)),
    inference(variable_rename,[status(thm)],[f_3262_1]) ).

cnf(f_3262_3,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_12636,U_12637),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12636,tc_HOL_Obool)),U_12638),U_12639)),U_12640) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_12636,U_12637),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12636,U_12637),U_12638),U_12640)),hAPP(hAPP(c_Product__Type_OSigma(U_12636,U_12637),U_12639),U_12640)),
    inference(clausify,[status(thm)],[f_3262_2]) ).

fof(f_3263_1,plain,
    ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Relation_OId__on(T_b,V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))),
    inference(fof_nnf,[status(thm)],[fact_Id__on__subset__Times]) ).

fof(f_3263_2,plain,
    ! [U_12642,U_12641] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12641,U_12641),tc_HOL_Obool)),c_Relation_OId__on(U_12641,U_12642)),hAPP(hAPP(c_Product__Type_OSigma(U_12641,U_12641),U_12642),hAPP(c_COMBK(tc_fun(U_12641,tc_HOL_Obool),U_12641),U_12642)))),
    inference(variable_rename,[status(thm)],[f_3263_1]) ).

cnf(f_3263_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12641,U_12641),tc_HOL_Obool)),c_Relation_OId__on(U_12641,U_12642)),hAPP(hAPP(c_Product__Type_OSigma(U_12641,U_12641),U_12642),hAPP(c_COMBK(tc_fun(U_12641,tc_HOL_Obool),U_12641),U_12642)))),
    inference(clausify,[status(thm)],[f_3263_2]) ).

fof(f_3264_1,plain,
    ! [T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_UNIV__Times__UNIV]) ).

fof(f_3264_2,plain,
    ! [U_12644,U_12643] : hAPP(hAPP(c_Product__Type_OSigma(U_12643,U_12644),c_Orderings_Otop__class_Otop(tc_fun(U_12643,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(U_12644,tc_HOL_Obool),U_12643),c_Orderings_Otop__class_Otop(tc_fun(U_12644,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_12643,U_12644),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3264_1]) ).

cnf(f_3264_3,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_12643,U_12644),c_Orderings_Otop__class_Otop(tc_fun(U_12643,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(U_12644,tc_HOL_Obool),U_12643),c_Orderings_Otop__class_Otop(tc_fun(U_12644,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_12643,U_12644),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3264_2]) ).

fof(f_3265_1,plain,
    ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2)))
        & hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))) ),
    inference(fof_nnf,[status(thm)],[fact_SigmaE2]) ).

fof(f_3265_2,plain,
    ! [U_12650,U_12649,U_12648,U_12647,U_12646,U_12645] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_12646),U_12648),hAPP(U_12650,U_12647)))
        & hBOOL(hAPP(hAPP(c_member(U_12645),U_12647),U_12649)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12645,U_12646)),hAPP(hAPP(c_Product__Type_OPair(U_12645,U_12646),U_12647),U_12648)),hAPP(hAPP(c_Product__Type_OSigma(U_12645,U_12646),U_12649),U_12650))) ),
    inference(variable_rename,[status(thm)],[f_3265_1]) ).

cnf(f_3265_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12645),U_12647),U_12649))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12645,U_12646)),hAPP(hAPP(c_Product__Type_OPair(U_12645,U_12646),U_12647),U_12648)),hAPP(hAPP(c_Product__Type_OSigma(U_12645,U_12646),U_12649),U_12650))) ),
    inference(clausify,[status(thm)],[f_3265_2]) ).

cnf(f_3265_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12646),U_12648),hAPP(U_12650,U_12647)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12645,U_12646)),hAPP(hAPP(c_Product__Type_OPair(U_12645,U_12646),U_12647),U_12648)),hAPP(hAPP(c_Product__Type_OSigma(U_12645,U_12646),U_12649),U_12650))) ),
    inference(clausify,[status(thm)],[f_3265_2]) ).

fof(f_3266_1,plain,
    ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))) ),
    inference(fof_nnf,[status(thm)],[fact_SigmaD2]) ).

fof(f_3266_2,plain,
    ! [U_12656,U_12655,U_12654,U_12653,U_12652,U_12651] :
      ( hBOOL(hAPP(hAPP(c_member(U_12652),U_12654),hAPP(U_12656,U_12653)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12651,U_12652)),hAPP(hAPP(c_Product__Type_OPair(U_12651,U_12652),U_12653),U_12654)),hAPP(hAPP(c_Product__Type_OSigma(U_12651,U_12652),U_12655),U_12656))) ),
    inference(variable_rename,[status(thm)],[f_3266_1]) ).

fof(f_3266_3,plain,
    ! [U_12656,U_12655,U_12654,U_12653,U_12652] :
      ( ! [U_12651] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12651,U_12652)),hAPP(hAPP(c_Product__Type_OPair(U_12651,U_12652),U_12653),U_12654)),hAPP(hAPP(c_Product__Type_OSigma(U_12651,U_12652),U_12655),U_12656)))
      | hBOOL(hAPP(hAPP(c_member(U_12652),U_12654),hAPP(U_12656,U_12653))) ),
    inference(miniscope,[status(thm)],[f_3266_2]) ).

cnf(f_3266_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12651,U_12652)),hAPP(hAPP(c_Product__Type_OPair(U_12651,U_12652),U_12653),U_12654)),hAPP(hAPP(c_Product__Type_OSigma(U_12651,U_12652),U_12655),U_12656)))
    | hBOOL(hAPP(hAPP(c_member(U_12652),U_12654),hAPP(U_12656,U_12653))) ),
    inference(clausify,[status(thm)],[f_3266_3]) ).

fof(f_3267_1,plain,
    ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))) ),
    inference(fof_nnf,[status(thm)],[fact_SigmaD1]) ).

fof(f_3267_2,plain,
    ! [U_12662,U_12661,U_12660,U_12659,U_12658,U_12657] :
      ( hBOOL(hAPP(hAPP(c_member(U_12657),U_12659),U_12661))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12657,U_12658)),hAPP(hAPP(c_Product__Type_OPair(U_12657,U_12658),U_12659),U_12660)),hAPP(hAPP(c_Product__Type_OSigma(U_12657,U_12658),U_12661),U_12662))) ),
    inference(variable_rename,[status(thm)],[f_3267_1]) ).

cnf(f_3267_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12657),U_12659),U_12661))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12657,U_12658)),hAPP(hAPP(c_Product__Type_OPair(U_12657,U_12658),U_12659),U_12660)),hAPP(hAPP(c_Product__Type_OSigma(U_12657,U_12658),U_12661),U_12662))) ),
    inference(clausify,[status(thm)],[f_3267_2]) ).

fof(f_3268_1,plain,
    ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)))
        | ~ hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2)))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) )
      & ( ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2)))
          & hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_mem__Sigma__iff]) ).

fof(f_3268_2,plain,
    ! [U_12668,U_12667,U_12666,U_12665,U_12664,U_12663] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12663,U_12664)),hAPP(hAPP(c_Product__Type_OPair(U_12663,U_12664),U_12665),U_12666)),hAPP(hAPP(c_Product__Type_OSigma(U_12663,U_12664),U_12667),U_12668)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12664),U_12666),hAPP(U_12668,U_12665)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12663),U_12665),U_12667)) )
      & ( ( hBOOL(hAPP(hAPP(c_member(U_12664),U_12666),hAPP(U_12668,U_12665)))
          & hBOOL(hAPP(hAPP(c_member(U_12663),U_12665),U_12667)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12663,U_12664)),hAPP(hAPP(c_Product__Type_OPair(U_12663,U_12664),U_12665),U_12666)),hAPP(hAPP(c_Product__Type_OSigma(U_12663,U_12664),U_12667),U_12668))) ) ),
    inference(variable_rename,[status(thm)],[f_3268_1]) ).

fof(f_3268_3,plain,
    ( ! [U_12680,U_12678,U_12676,U_12674,U_12672,U_12670] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12670,U_12672)),hAPP(hAPP(c_Product__Type_OPair(U_12670,U_12672),U_12674),U_12676)),hAPP(hAPP(c_Product__Type_OSigma(U_12670,U_12672),U_12678),U_12680)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12672),U_12676),hAPP(U_12680,U_12674)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12670),U_12674),U_12678)) )
    & ! [U_12679,U_12677,U_12675,U_12673,U_12671,U_12669] :
        ( ( hBOOL(hAPP(hAPP(c_member(U_12671),U_12675),hAPP(U_12679,U_12673)))
          & hBOOL(hAPP(hAPP(c_member(U_12669),U_12673),U_12677)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12669,U_12671)),hAPP(hAPP(c_Product__Type_OPair(U_12669,U_12671),U_12673),U_12675)),hAPP(hAPP(c_Product__Type_OSigma(U_12669,U_12671),U_12677),U_12679))) ) ),
    inference(miniscope,[status(thm)],[f_3268_2]) ).

cnf(f_3268_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12669),U_12673),U_12677))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12669,U_12671)),hAPP(hAPP(c_Product__Type_OPair(U_12669,U_12671),U_12673),U_12675)),hAPP(hAPP(c_Product__Type_OSigma(U_12669,U_12671),U_12677),U_12679))) ),
    inference(clausify,[status(thm)],[f_3268_3]) ).

cnf(f_3268_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12671),U_12675),hAPP(U_12679,U_12673)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12669,U_12671)),hAPP(hAPP(c_Product__Type_OPair(U_12669,U_12671),U_12673),U_12675)),hAPP(hAPP(c_Product__Type_OSigma(U_12669,U_12671),U_12677),U_12679))) ),
    inference(clausify,[status(thm)],[f_3268_3]) ).

cnf(f_3268_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12670,U_12672)),hAPP(hAPP(c_Product__Type_OPair(U_12670,U_12672),U_12674),U_12676)),hAPP(hAPP(c_Product__Type_OSigma(U_12670,U_12672),U_12678),U_12680)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12672),U_12676),hAPP(U_12680,U_12674)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12670),U_12674),U_12678)) ),
    inference(clausify,[status(thm)],[f_3268_3]) ).

fof(f_3269_1,plain,
    ! [V_A_2,V_x_2,T_c,T_b] : hAPP(c_Finite__Set_Ocard(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_A_2))) = hAPP(c_Finite__Set_Ocard(T_c),V_A_2),
    inference(fof_nnf,[status(thm)],[fact_card__cartesian__product__singleton]) ).

fof(f_3269_2,plain,
    ! [U_12684,U_12683,U_12682,U_12681] : hAPP(c_Finite__Set_Ocard(tc_prod(U_12681,U_12682)),hAPP(hAPP(c_Product__Type_OSigma(U_12681,U_12682),hAPP(hAPP(c_Set_Oinsert(U_12681),U_12683),c_Orderings_Obot__class_Obot(tc_fun(U_12681,tc_HOL_Obool)))),hAPP(c_COMBK(tc_fun(U_12682,tc_HOL_Obool),U_12681),U_12684))) = hAPP(c_Finite__Set_Ocard(U_12682),U_12684),
    inference(variable_rename,[status(thm)],[f_3269_1]) ).

cnf(f_3269_3,plain,
    hAPP(c_Finite__Set_Ocard(tc_prod(U_12681,U_12682)),hAPP(hAPP(c_Product__Type_OSigma(U_12681,U_12682),hAPP(hAPP(c_Set_Oinsert(U_12681),U_12683),c_Orderings_Obot__class_Obot(tc_fun(U_12681,tc_HOL_Obool)))),hAPP(c_COMBK(tc_fun(U_12682,tc_HOL_Obool),U_12681),U_12684))) = hAPP(c_Finite__Set_Ocard(U_12682),U_12684),
    inference(clausify,[status(thm)],[f_3269_2]) ).

fof(f_3270_1,plain,
    ! [V_B_2,V_A_2,T_c,V_C_2,V_x_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_B_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_C_2))))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_B_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_C_2)))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_C_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Times__subset__cancel2]) ).

fof(f_3270_2,plain,
    ! [U_12690,U_12689,U_12688,U_12687,U_12686,U_12685] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12688,U_12685),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12688,U_12685),U_12689),hAPP(c_COMBK(tc_fun(U_12685,tc_HOL_Obool),U_12688),U_12687))),hAPP(hAPP(c_Product__Type_OSigma(U_12688,U_12685),U_12690),hAPP(c_COMBK(tc_fun(U_12685,tc_HOL_Obool),U_12688),U_12687))))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12688,tc_HOL_Obool)),U_12689),U_12690)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12688,tc_HOL_Obool)),U_12689),U_12690))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12688,U_12685),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12688,U_12685),U_12689),hAPP(c_COMBK(tc_fun(U_12685,tc_HOL_Obool),U_12688),U_12687))),hAPP(hAPP(c_Product__Type_OSigma(U_12688,U_12685),U_12690),hAPP(c_COMBK(tc_fun(U_12685,tc_HOL_Obool),U_12688),U_12687)))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_12685),U_12686),U_12687)) ),
    inference(variable_rename,[status(thm)],[f_3270_1]) ).

cnf(f_3270_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12688,tc_HOL_Obool)),U_12689),U_12690))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12688,U_12685),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12688,U_12685),U_12689),hAPP(c_COMBK(tc_fun(U_12685,tc_HOL_Obool),U_12688),U_12687))),hAPP(hAPP(c_Product__Type_OSigma(U_12688,U_12685),U_12690),hAPP(c_COMBK(tc_fun(U_12685,tc_HOL_Obool),U_12688),U_12687))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12685),U_12686),U_12687)) ),
    inference(clausify,[status(thm)],[f_3270_2]) ).

cnf(f_3270_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12688,U_12685),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12688,U_12685),U_12689),hAPP(c_COMBK(tc_fun(U_12685,tc_HOL_Obool),U_12688),U_12687))),hAPP(hAPP(c_Product__Type_OSigma(U_12688,U_12685),U_12690),hAPP(c_COMBK(tc_fun(U_12685,tc_HOL_Obool),U_12688),U_12687))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12688,tc_HOL_Obool)),U_12689),U_12690))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12685),U_12686),U_12687)) ),
    inference(clausify,[status(thm)],[f_3270_2]) ).

fof(f_3271_1,plain,
    ! [V_C_2,V_B_2,V_A_2,V_r_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_c,V_r_2),V_C_2)),V_B_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_Image__subset]) ).

fof(f_3271_2,plain,
    ! [U_12696,U_12695,U_12694,U_12693,U_12692,U_12691] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12692,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12691,U_12692,U_12693),U_12696)),U_12695))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12691,U_12692),tc_HOL_Obool)),U_12693),hAPP(hAPP(c_Product__Type_OSigma(U_12691,U_12692),U_12694),hAPP(c_COMBK(tc_fun(U_12692,tc_HOL_Obool),U_12691),U_12695)))) ),
    inference(variable_rename,[status(thm)],[f_3271_1]) ).

cnf(f_3271_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12692,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12691,U_12692,U_12693),U_12696)),U_12695))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12691,U_12692),tc_HOL_Obool)),U_12693),hAPP(hAPP(c_Product__Type_OSigma(U_12691,U_12692),U_12694),hAPP(c_COMBK(tc_fun(U_12692,tc_HOL_Obool),U_12691),U_12695)))) ),
    inference(clausify,[status(thm)],[f_3271_2]) ).

fof(f_3272_1,plain,
    ! [V_B_2,V_A_2,T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_finite__cartesian__productD1]) ).

fof(f_3272_2,plain,
    ! [U_12700,U_12699,U_12698,U_12697] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12697),U_12699))
      | U_12700 = c_Orderings_Obot__class_Obot(tc_fun(U_12698,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_12697,U_12698)),hAPP(hAPP(c_Product__Type_OSigma(U_12697,U_12698),U_12699),hAPP(c_COMBK(tc_fun(U_12698,tc_HOL_Obool),U_12697),U_12700)))) ),
    inference(variable_rename,[status(thm)],[f_3272_1]) ).

cnf(f_3272_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12697),U_12699))
    | U_12700 = c_Orderings_Obot__class_Obot(tc_fun(U_12698,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_12697,U_12698)),hAPP(hAPP(c_Product__Type_OSigma(U_12697,U_12698),U_12699),hAPP(c_COMBK(tc_fun(U_12698,tc_HOL_Obool),U_12697),U_12700)))) ),
    inference(clausify,[status(thm)],[f_3272_2]) ).

fof(f_3273_1,plain,
    ! [V_B_2,V_A_2,T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_finite__cartesian__productD2]) ).

fof(f_3273_2,plain,
    ! [U_12704,U_12703,U_12702,U_12701] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12702),U_12704))
      | U_12703 = c_Orderings_Obot__class_Obot(tc_fun(U_12701,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_12701,U_12702)),hAPP(hAPP(c_Product__Type_OSigma(U_12701,U_12702),U_12703),hAPP(c_COMBK(tc_fun(U_12702,tc_HOL_Obool),U_12701),U_12704)))) ),
    inference(variable_rename,[status(thm)],[f_3273_1]) ).

cnf(f_3273_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12702),U_12704))
    | U_12703 = c_Orderings_Obot__class_Obot(tc_fun(U_12701,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_12701,U_12702)),hAPP(hAPP(c_Product__Type_OSigma(U_12701,U_12702),U_12703),hAPP(c_COMBK(tc_fun(U_12702,tc_HOL_Obool),U_12701),U_12704)))) ),
    inference(clausify,[status(thm)],[f_3273_2]) ).

fof(f_3274_1,plain,
    ! [V_A_2,T_c,T_b,V_B_2] :
      ( ( hAPP(c_Set_Oimage(tc_prod(T_c,T_b),T_c,c_Product__Type_Ofst(T_c,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2))) = V_A_2
        | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
      & ( hAPP(c_Set_Oimage(tc_prod(T_c,T_b),T_c,c_Product__Type_Ofst(T_c,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
        | V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_fst__image__times]) ).

fof(f_3274_2,plain,
    ! [U_12708,U_12707,U_12706,U_12705] :
      ( ( hAPP(c_Set_Oimage(tc_prod(U_12707,U_12706),U_12707,c_Product__Type_Ofst(U_12707,U_12706)),hAPP(hAPP(c_Product__Type_OSigma(U_12707,U_12706),U_12708),hAPP(c_COMBK(tc_fun(U_12706,tc_HOL_Obool),U_12707),U_12705))) = U_12708
        | U_12705 = c_Orderings_Obot__class_Obot(tc_fun(U_12706,tc_HOL_Obool)) )
      & ( hAPP(c_Set_Oimage(tc_prod(U_12707,U_12706),U_12707,c_Product__Type_Ofst(U_12707,U_12706)),hAPP(hAPP(c_Product__Type_OSigma(U_12707,U_12706),U_12708),hAPP(c_COMBK(tc_fun(U_12706,tc_HOL_Obool),U_12707),U_12705))) = c_Orderings_Obot__class_Obot(tc_fun(U_12707,tc_HOL_Obool))
        | U_12705 != c_Orderings_Obot__class_Obot(tc_fun(U_12706,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_3274_1]) ).

fof(f_3274_3,plain,
    ( ! [U_12716,U_12714,U_12712,U_12710] :
        ( hAPP(c_Set_Oimage(tc_prod(U_12714,U_12712),U_12714,c_Product__Type_Ofst(U_12714,U_12712)),hAPP(hAPP(c_Product__Type_OSigma(U_12714,U_12712),U_12716),hAPP(c_COMBK(tc_fun(U_12712,tc_HOL_Obool),U_12714),U_12710))) = U_12716
        | U_12710 = c_Orderings_Obot__class_Obot(tc_fun(U_12712,tc_HOL_Obool)) )
    & ! [U_12715,U_12713,U_12711,U_12709] :
        ( hAPP(c_Set_Oimage(tc_prod(U_12713,U_12711),U_12713,c_Product__Type_Ofst(U_12713,U_12711)),hAPP(hAPP(c_Product__Type_OSigma(U_12713,U_12711),U_12715),hAPP(c_COMBK(tc_fun(U_12711,tc_HOL_Obool),U_12713),U_12709))) = c_Orderings_Obot__class_Obot(tc_fun(U_12713,tc_HOL_Obool))
        | U_12709 != c_Orderings_Obot__class_Obot(tc_fun(U_12711,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_3274_2]) ).

cnf(f_3274_4,plain,
    ( hAPP(c_Set_Oimage(tc_prod(U_12713,U_12711),U_12713,c_Product__Type_Ofst(U_12713,U_12711)),hAPP(hAPP(c_Product__Type_OSigma(U_12713,U_12711),U_12715),hAPP(c_COMBK(tc_fun(U_12711,tc_HOL_Obool),U_12713),U_12709))) = c_Orderings_Obot__class_Obot(tc_fun(U_12713,tc_HOL_Obool))
    | U_12709 != c_Orderings_Obot__class_Obot(tc_fun(U_12711,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3274_3]) ).

cnf(f_3274_5,plain,
    ( hAPP(c_Set_Oimage(tc_prod(U_12714,U_12712),U_12714,c_Product__Type_Ofst(U_12714,U_12712)),hAPP(hAPP(c_Product__Type_OSigma(U_12714,U_12712),U_12716),hAPP(c_COMBK(tc_fun(U_12712,tc_HOL_Obool),U_12714),U_12710))) = U_12716
    | U_12710 = c_Orderings_Obot__class_Obot(tc_fun(U_12712,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3274_3]) ).

fof(f_3275_1,plain,
    ! [V_B_2,T_c,T_b,V_A_2] :
      ( ( hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_c,c_Product__Type_Osnd(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))) = V_B_2
        | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
      & ( hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_c,c_Product__Type_Osnd(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
        | V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_snd__image__times]) ).

fof(f_3275_2,plain,
    ! [U_12720,U_12719,U_12718,U_12717] :
      ( ( hAPP(c_Set_Oimage(tc_prod(U_12718,U_12719),U_12719,c_Product__Type_Osnd(U_12718,U_12719)),hAPP(hAPP(c_Product__Type_OSigma(U_12718,U_12719),U_12717),hAPP(c_COMBK(tc_fun(U_12719,tc_HOL_Obool),U_12718),U_12720))) = U_12720
        | U_12717 = c_Orderings_Obot__class_Obot(tc_fun(U_12718,tc_HOL_Obool)) )
      & ( hAPP(c_Set_Oimage(tc_prod(U_12718,U_12719),U_12719,c_Product__Type_Osnd(U_12718,U_12719)),hAPP(hAPP(c_Product__Type_OSigma(U_12718,U_12719),U_12717),hAPP(c_COMBK(tc_fun(U_12719,tc_HOL_Obool),U_12718),U_12720))) = c_Orderings_Obot__class_Obot(tc_fun(U_12719,tc_HOL_Obool))
        | U_12717 != c_Orderings_Obot__class_Obot(tc_fun(U_12718,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_3275_1]) ).

fof(f_3275_3,plain,
    ( ! [U_12728,U_12726,U_12724,U_12722] :
        ( hAPP(c_Set_Oimage(tc_prod(U_12724,U_12726),U_12726,c_Product__Type_Osnd(U_12724,U_12726)),hAPP(hAPP(c_Product__Type_OSigma(U_12724,U_12726),U_12722),hAPP(c_COMBK(tc_fun(U_12726,tc_HOL_Obool),U_12724),U_12728))) = U_12728
        | U_12722 = c_Orderings_Obot__class_Obot(tc_fun(U_12724,tc_HOL_Obool)) )
    & ! [U_12727,U_12725,U_12723,U_12721] :
        ( hAPP(c_Set_Oimage(tc_prod(U_12723,U_12725),U_12725,c_Product__Type_Osnd(U_12723,U_12725)),hAPP(hAPP(c_Product__Type_OSigma(U_12723,U_12725),U_12721),hAPP(c_COMBK(tc_fun(U_12725,tc_HOL_Obool),U_12723),U_12727))) = c_Orderings_Obot__class_Obot(tc_fun(U_12725,tc_HOL_Obool))
        | U_12721 != c_Orderings_Obot__class_Obot(tc_fun(U_12723,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_3275_2]) ).

cnf(f_3275_4,plain,
    ( hAPP(c_Set_Oimage(tc_prod(U_12723,U_12725),U_12725,c_Product__Type_Osnd(U_12723,U_12725)),hAPP(hAPP(c_Product__Type_OSigma(U_12723,U_12725),U_12721),hAPP(c_COMBK(tc_fun(U_12725,tc_HOL_Obool),U_12723),U_12727))) = c_Orderings_Obot__class_Obot(tc_fun(U_12725,tc_HOL_Obool))
    | U_12721 != c_Orderings_Obot__class_Obot(tc_fun(U_12723,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3275_3]) ).

cnf(f_3275_5,plain,
    ( hAPP(c_Set_Oimage(tc_prod(U_12724,U_12726),U_12726,c_Product__Type_Osnd(U_12724,U_12726)),hAPP(hAPP(c_Product__Type_OSigma(U_12724,U_12726),U_12722),hAPP(c_COMBK(tc_fun(U_12726,tc_HOL_Obool),U_12724),U_12728))) = U_12728
    | U_12722 = c_Orderings_Obot__class_Obot(tc_fun(U_12724,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3275_3]) ).

fof(f_3276_1,plain,
    ! [V_B_2,V_b_2,V_A_2,V_a_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),V_B_2))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),V_B_2)))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2)))),
    inference(fof_nnf,[status(thm)],[fact_insert__times__insert]) ).

fof(f_3276_2,plain,
    ! [U_12734,U_12733,U_12732,U_12731,U_12730,U_12729] : hAPP(hAPP(c_Product__Type_OSigma(U_12729,U_12730),hAPP(hAPP(c_Set_Oinsert(U_12729),U_12731),U_12732)),hAPP(c_COMBK(tc_fun(U_12730,tc_HOL_Obool),U_12729),hAPP(hAPP(c_Set_Oinsert(U_12730),U_12733),U_12734))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(U_12729,U_12730)),hAPP(hAPP(c_Product__Type_OPair(U_12729,U_12730),U_12731),U_12733)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_12729,U_12730),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12729,U_12730),U_12732),hAPP(c_COMBK(tc_fun(U_12730,tc_HOL_Obool),U_12729),hAPP(hAPP(c_Set_Oinsert(U_12730),U_12733),U_12734)))),hAPP(hAPP(c_Product__Type_OSigma(U_12729,U_12730),hAPP(hAPP(c_Set_Oinsert(U_12729),U_12731),U_12732)),hAPP(c_COMBK(tc_fun(U_12730,tc_HOL_Obool),U_12729),U_12734)))),
    inference(variable_rename,[status(thm)],[f_3276_1]) ).

cnf(f_3276_3,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_12729,U_12730),hAPP(hAPP(c_Set_Oinsert(U_12729),U_12731),U_12732)),hAPP(c_COMBK(tc_fun(U_12730,tc_HOL_Obool),U_12729),hAPP(hAPP(c_Set_Oinsert(U_12730),U_12733),U_12734))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(U_12729,U_12730)),hAPP(hAPP(c_Product__Type_OPair(U_12729,U_12730),U_12731),U_12733)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_12729,U_12730),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12729,U_12730),U_12732),hAPP(c_COMBK(tc_fun(U_12730,tc_HOL_Obool),U_12729),hAPP(hAPP(c_Set_Oinsert(U_12730),U_12733),U_12734)))),hAPP(hAPP(c_Product__Type_OSigma(U_12729,U_12730),hAPP(hAPP(c_Set_Oinsert(U_12729),U_12731),U_12732)),hAPP(c_COMBK(tc_fun(U_12730,tc_HOL_Obool),U_12729),U_12734)))),
    inference(clausify,[status(thm)],[f_3276_2]) ).

fof(f_3277_1,plain,
    ! [V_X_2,V_r_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__equiv__class]) ).

fof(f_3277_2,plain,
    ! [U_12738,U_12737,U_12736,U_12735] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12735),U_12738))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12735,tc_HOL_Obool)),U_12738),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12735),U_12736),U_12737)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12735,U_12735),tc_HOL_Obool)),U_12737),hAPP(hAPP(c_Product__Type_OSigma(U_12735,U_12735),U_12736),hAPP(c_COMBK(tc_fun(U_12735,tc_HOL_Obool),U_12735),U_12736))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12735),U_12736)) ),
    inference(variable_rename,[status(thm)],[f_3277_1]) ).

cnf(f_3277_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12735),U_12738))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12735,tc_HOL_Obool)),U_12738),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12735),U_12736),U_12737)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12735,U_12735),tc_HOL_Obool)),U_12737),hAPP(hAPP(c_Product__Type_OSigma(U_12735,U_12735),U_12736),hAPP(c_COMBK(tc_fun(U_12735,tc_HOL_Obool),U_12735),U_12736))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12735),U_12736)) ),
    inference(clausify,[status(thm)],[f_3277_2]) ).

fof(f_3278_1,plain,
    ! [V_B_2,V_A_2,V_f_2,T_d,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,tc_prod(T_c,T_d),V_f_2),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,hAPP(c_Fun_Ocomp(tc_prod(T_c,T_d),T_c,T_b,c_Product__Type_Ofst(T_c,T_d)),V_f_2)),V_A_2)),hAPP(c_Set_Ovimage(T_b,T_d,hAPP(c_Fun_Ocomp(tc_prod(T_c,T_d),T_d,T_b,c_Product__Type_Osnd(T_c,T_d)),V_f_2)),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_vimage__Times]) ).

fof(f_3278_2,plain,
    ! [U_12744,U_12743,U_12742,U_12741,U_12740,U_12739] : hAPP(c_Set_Ovimage(U_12739,tc_prod(U_12740,U_12741),U_12742),hAPP(hAPP(c_Product__Type_OSigma(U_12740,U_12741),U_12743),hAPP(c_COMBK(tc_fun(U_12741,tc_HOL_Obool),U_12740),U_12744))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12739,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_12739,U_12740,hAPP(c_Fun_Ocomp(tc_prod(U_12740,U_12741),U_12740,U_12739,c_Product__Type_Ofst(U_12740,U_12741)),U_12742)),U_12743)),hAPP(c_Set_Ovimage(U_12739,U_12741,hAPP(c_Fun_Ocomp(tc_prod(U_12740,U_12741),U_12741,U_12739,c_Product__Type_Osnd(U_12740,U_12741)),U_12742)),U_12744)),
    inference(variable_rename,[status(thm)],[f_3278_1]) ).

cnf(f_3278_3,plain,
    hAPP(c_Set_Ovimage(U_12739,tc_prod(U_12740,U_12741),U_12742),hAPP(hAPP(c_Product__Type_OSigma(U_12740,U_12741),U_12743),hAPP(c_COMBK(tc_fun(U_12741,tc_HOL_Obool),U_12740),U_12744))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12739,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_12739,U_12740,hAPP(c_Fun_Ocomp(tc_prod(U_12740,U_12741),U_12740,U_12739,c_Product__Type_Ofst(U_12740,U_12741)),U_12742)),U_12743)),hAPP(c_Set_Ovimage(U_12739,U_12741,hAPP(c_Fun_Ocomp(tc_prod(U_12740,U_12741),U_12741,U_12739,c_Product__Type_Osnd(U_12740,U_12741)),U_12742)),U_12744)),
    inference(clausify,[status(thm)],[f_3278_2]) ).

fof(f_3279_1,plain,
    ! [V_F_2,V_E_2,V_B_2,V_A_2,T_c,T_b,T_e,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(T_d,T_e),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_d,T_e),V_A_2),hAPP(c_COMBK(tc_fun(T_e,tc_HOL_Obool),T_d),V_B_2))),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_e,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),tc_fun(T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_e,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),tc_fun(T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),T_d),c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),T_e)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),T_d),c_Product__Type_OSigma(T_b,T_c)),V_E_2))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),T_e),c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b)),V_F_2)))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_E_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_F_2))),
    inference(fof_nnf,[status(thm)],[fact_UN__Times__distrib]) ).

fof(f_3279_2,plain,
    ! [U_12752,U_12751,U_12750,U_12749,U_12748,U_12747,U_12746,U_12745] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(U_12745,U_12746),tc_fun(tc_prod(U_12747,U_12748),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12745,U_12746),U_12749),hAPP(c_COMBK(tc_fun(U_12746,tc_HOL_Obool),U_12745),U_12750))),hAPP(c_Product__Type_Oprod_Oprod__case(U_12745,U_12746,tc_fun(tc_prod(U_12747,U_12748),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_12745,tc_fun(U_12746,tc_fun(U_12747,tc_fun(U_12748,tc_HOL_Obool))),tc_fun(U_12746,tc_fun(tc_prod(U_12747,U_12748),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_12747,tc_fun(U_12748,tc_HOL_Obool)),tc_fun(tc_prod(U_12747,U_12748),tc_HOL_Obool)),tc_fun(tc_fun(U_12746,tc_fun(U_12747,tc_fun(U_12748,tc_HOL_Obool))),tc_fun(U_12746,tc_fun(tc_prod(U_12747,U_12748),tc_HOL_Obool))),U_12745),c_COMBB(tc_fun(U_12747,tc_fun(U_12748,tc_HOL_Obool)),tc_fun(tc_prod(U_12747,U_12748),tc_HOL_Obool),U_12746)),hAPP(hAPP(c_COMBB(tc_fun(U_12747,tc_HOL_Obool),tc_fun(tc_fun(U_12747,tc_fun(U_12748,tc_HOL_Obool)),tc_fun(tc_prod(U_12747,U_12748),tc_HOL_Obool)),U_12745),c_Product__Type_OSigma(U_12747,U_12748)),U_12751))),hAPP(hAPP(c_COMBB(tc_fun(U_12748,tc_HOL_Obool),tc_fun(U_12747,tc_fun(U_12748,tc_HOL_Obool)),U_12746),c_COMBK(tc_fun(U_12748,tc_HOL_Obool),U_12747)),U_12752)))) = hAPP(hAPP(c_Product__Type_OSigma(U_12747,U_12748),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12745,tc_fun(U_12747,tc_HOL_Obool)),U_12749),U_12751)),hAPP(c_COMBK(tc_fun(U_12748,tc_HOL_Obool),U_12747),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12746,tc_fun(U_12748,tc_HOL_Obool)),U_12750),U_12752))),
    inference(variable_rename,[status(thm)],[f_3279_1]) ).

cnf(f_3279_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(U_12745,U_12746),tc_fun(tc_prod(U_12747,U_12748),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12745,U_12746),U_12749),hAPP(c_COMBK(tc_fun(U_12746,tc_HOL_Obool),U_12745),U_12750))),hAPP(c_Product__Type_Oprod_Oprod__case(U_12745,U_12746,tc_fun(tc_prod(U_12747,U_12748),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_12745,tc_fun(U_12746,tc_fun(U_12747,tc_fun(U_12748,tc_HOL_Obool))),tc_fun(U_12746,tc_fun(tc_prod(U_12747,U_12748),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_12747,tc_fun(U_12748,tc_HOL_Obool)),tc_fun(tc_prod(U_12747,U_12748),tc_HOL_Obool)),tc_fun(tc_fun(U_12746,tc_fun(U_12747,tc_fun(U_12748,tc_HOL_Obool))),tc_fun(U_12746,tc_fun(tc_prod(U_12747,U_12748),tc_HOL_Obool))),U_12745),c_COMBB(tc_fun(U_12747,tc_fun(U_12748,tc_HOL_Obool)),tc_fun(tc_prod(U_12747,U_12748),tc_HOL_Obool),U_12746)),hAPP(hAPP(c_COMBB(tc_fun(U_12747,tc_HOL_Obool),tc_fun(tc_fun(U_12747,tc_fun(U_12748,tc_HOL_Obool)),tc_fun(tc_prod(U_12747,U_12748),tc_HOL_Obool)),U_12745),c_Product__Type_OSigma(U_12747,U_12748)),U_12751))),hAPP(hAPP(c_COMBB(tc_fun(U_12748,tc_HOL_Obool),tc_fun(U_12747,tc_fun(U_12748,tc_HOL_Obool)),U_12746),c_COMBK(tc_fun(U_12748,tc_HOL_Obool),U_12747)),U_12752)))) = hAPP(hAPP(c_Product__Type_OSigma(U_12747,U_12748),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12745,tc_fun(U_12747,tc_HOL_Obool)),U_12749),U_12751)),hAPP(c_COMBK(tc_fun(U_12748,tc_HOL_Obool),U_12747),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12746,tc_fun(U_12748,tc_HOL_Obool)),U_12750),U_12752))),
    inference(clausify,[status(thm)],[f_3279_2]) ).

fof(f_3280_1,plain,
    ! [V_B_2,V_A_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),T_b),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),V_B_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),T_c),c_Set_Oinsert(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))))),
    inference(fof_nnf,[status(thm)],[fact_Sigma__def]) ).

fof(f_3280_2,plain,
    ! [U_12756,U_12755,U_12754,U_12753] : hAPP(hAPP(c_Product__Type_OSigma(U_12753,U_12754),U_12755),U_12756) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12753,tc_fun(tc_prod(U_12753,U_12754),tc_HOL_Obool)),U_12755),hAPP(hAPP(c_COMBS(U_12753,tc_fun(U_12754,tc_fun(tc_prod(U_12753,U_12754),tc_HOL_Obool)),tc_fun(tc_prod(U_12753,U_12754),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12754,tc_HOL_Obool),tc_fun(tc_fun(U_12754,tc_fun(tc_prod(U_12753,U_12754),tc_HOL_Obool)),tc_fun(tc_prod(U_12753,U_12754),tc_HOL_Obool)),U_12753),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12754,tc_fun(tc_prod(U_12753,U_12754),tc_HOL_Obool))),U_12756)),hAPP(hAPP(c_COMBC(U_12753,tc_fun(tc_prod(U_12753,U_12754),tc_HOL_Obool),tc_fun(U_12754,tc_fun(tc_prod(U_12753,U_12754),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_12754,tc_fun(tc_fun(tc_prod(U_12753,U_12754),tc_HOL_Obool),tc_fun(tc_prod(U_12753,U_12754),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(U_12753,U_12754),tc_HOL_Obool),tc_fun(U_12754,tc_fun(tc_prod(U_12753,U_12754),tc_HOL_Obool))),U_12753),c_COMBC(U_12754,tc_fun(tc_prod(U_12753,U_12754),tc_HOL_Obool),tc_fun(tc_prod(U_12753,U_12754),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_12754,tc_prod(U_12753,U_12754)),tc_fun(U_12754,tc_fun(tc_fun(tc_prod(U_12753,U_12754),tc_HOL_Obool),tc_fun(tc_prod(U_12753,U_12754),tc_HOL_Obool))),U_12753),hAPP(c_COMBB(tc_prod(U_12753,U_12754),tc_fun(tc_fun(tc_prod(U_12753,U_12754),tc_HOL_Obool),tc_fun(tc_prod(U_12753,U_12754),tc_HOL_Obool)),U_12754),c_Set_Oinsert(tc_prod(U_12753,U_12754)))),c_Product__Type_OPair(U_12753,U_12754)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_12753,U_12754),tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_3280_1]) ).

cnf(f_3280_3,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_12753,U_12754),U_12755),U_12756) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12753,tc_fun(tc_prod(U_12753,U_12754),tc_HOL_Obool)),U_12755),hAPP(hAPP(c_COMBS(U_12753,tc_fun(U_12754,tc_fun(tc_prod(U_12753,U_12754),tc_HOL_Obool)),tc_fun(tc_prod(U_12753,U_12754),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12754,tc_HOL_Obool),tc_fun(tc_fun(U_12754,tc_fun(tc_prod(U_12753,U_12754),tc_HOL_Obool)),tc_fun(tc_prod(U_12753,U_12754),tc_HOL_Obool)),U_12753),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12754,tc_fun(tc_prod(U_12753,U_12754),tc_HOL_Obool))),U_12756)),hAPP(hAPP(c_COMBC(U_12753,tc_fun(tc_prod(U_12753,U_12754),tc_HOL_Obool),tc_fun(U_12754,tc_fun(tc_prod(U_12753,U_12754),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_12754,tc_fun(tc_fun(tc_prod(U_12753,U_12754),tc_HOL_Obool),tc_fun(tc_prod(U_12753,U_12754),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(U_12753,U_12754),tc_HOL_Obool),tc_fun(U_12754,tc_fun(tc_prod(U_12753,U_12754),tc_HOL_Obool))),U_12753),c_COMBC(U_12754,tc_fun(tc_prod(U_12753,U_12754),tc_HOL_Obool),tc_fun(tc_prod(U_12753,U_12754),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_12754,tc_prod(U_12753,U_12754)),tc_fun(U_12754,tc_fun(tc_fun(tc_prod(U_12753,U_12754),tc_HOL_Obool),tc_fun(tc_prod(U_12753,U_12754),tc_HOL_Obool))),U_12753),hAPP(c_COMBB(tc_prod(U_12753,U_12754),tc_fun(tc_fun(tc_prod(U_12753,U_12754),tc_HOL_Obool),tc_fun(tc_prod(U_12753,U_12754),tc_HOL_Obool)),U_12754),c_Set_Oinsert(tc_prod(U_12753,U_12754)))),c_Product__Type_OPair(U_12753,U_12754)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_12753,U_12754),tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_3280_2]) ).

fof(f_3281_1,plain,
    ! [V_r_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__quotient]) ).

fof(f_3281_2,plain,
    ! [U_12759,U_12758,U_12757] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_12757,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12757),U_12758),U_12759)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12757,U_12757),tc_HOL_Obool)),U_12759),hAPP(hAPP(c_Product__Type_OSigma(U_12757,U_12757),U_12758),hAPP(c_COMBK(tc_fun(U_12757,tc_HOL_Obool),U_12757),U_12758))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12757),U_12758)) ),
    inference(variable_rename,[status(thm)],[f_3281_1]) ).

cnf(f_3281_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_12757,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12757),U_12758),U_12759)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12757,U_12757),tc_HOL_Obool)),U_12759),hAPP(hAPP(c_Product__Type_OSigma(U_12757,U_12757),U_12758),hAPP(c_COMBK(tc_fun(U_12757,tc_HOL_Obool),U_12757),U_12758))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12757),U_12758)) ),
    inference(clausify,[status(thm)],[f_3281_2]) ).

fof(f_3282_1,plain,
    ! [V_A_2,V_I_2,T_c,T_b] :
    ? [B_f] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,tc_prod(T_c,T_b),B_f),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2))),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_I_2),V_A_2)))
      & c_Fun_Oinj__on(T_b,tc_prod(T_c,T_b),B_f,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Ex__inj__on__UNION__Sigma]) ).

fof(f_3282_2,plain,
    ! [U_12764,U_12763,U_12762,U_12761] :
    ? [U_12760] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12762,U_12761),tc_HOL_Obool)),hAPP(c_Set_Oimage(U_12761,tc_prod(U_12762,U_12761),U_12760),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12762,tc_fun(U_12761,tc_HOL_Obool)),U_12763),U_12764))),hAPP(hAPP(c_Product__Type_OSigma(U_12762,U_12761),U_12763),U_12764)))
      & c_Fun_Oinj__on(U_12761,tc_prod(U_12762,U_12761),U_12760,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12762,tc_fun(U_12761,tc_HOL_Obool)),U_12763),U_12764)) ),
    inference(variable_rename,[status(thm)],[f_3282_1]) ).

fof(f_3282_3,plain,
    ! [U_12764,U_12763,U_12762,U_12761] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12762,U_12761),tc_HOL_Obool)),hAPP(c_Set_Oimage(U_12761,tc_prod(U_12762,U_12761),sK299(U_12764,U_12763,U_12762,U_12761)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12762,tc_fun(U_12761,tc_HOL_Obool)),U_12763),U_12764))),hAPP(hAPP(c_Product__Type_OSigma(U_12762,U_12761),U_12763),U_12764)))
      & c_Fun_Oinj__on(U_12761,tc_prod(U_12762,U_12761),sK299(U_12764,U_12763,U_12762,U_12761),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12762,tc_fun(U_12761,tc_HOL_Obool)),U_12763),U_12764)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK299]),skolemize(U_12760,sK299(U_12764,U_12763,U_12762,U_12761))],[f_3282_2]) ).

cnf(f_3282_4,plain,
    c_Fun_Oinj__on(U_12761,tc_prod(U_12762,U_12761),sK299(U_12764,U_12763,U_12762,U_12761),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12762,tc_fun(U_12761,tc_HOL_Obool)),U_12763),U_12764)),
    inference(clausify,[status(thm)],[f_3282_3]) ).

cnf(f_3282_5,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12762,U_12761),tc_HOL_Obool)),hAPP(c_Set_Oimage(U_12761,tc_prod(U_12762,U_12761),sK299(U_12764,U_12763,U_12762,U_12761)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12762,tc_fun(U_12761,tc_HOL_Obool)),U_12763),U_12764))),hAPP(hAPP(c_Product__Type_OSigma(U_12762,U_12761),U_12763),U_12764))),
    inference(clausify,[status(thm)],[f_3282_3]) ).

fof(f_3283_1,plain,
    ! [V_g_2,V_B_2,T_c,V_A_2,T_b,T_d] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_b,c_Groups_Otimes__class_Otimes(T_d)),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBC(T_b,T_d,tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_d),tc_fun(T_d,tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d)),T_b),c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Otimes__class_Otimes(T_d))),V_g_2)),c_Groups_Oone__class_Oone(T_d))),V_B_2)),c_Groups_Oone__class_Oone(T_d)),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,tc_prod(T_b,T_c),c_Groups_Otimes__class_Otimes(T_d)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_g_2)),c_Groups_Oone__class_Oone(T_d)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x)))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_d) ),
    inference(fof_nnf,[status(thm)],[fact_fold__image__Sigma]) ).

fof(f_3283_2,plain,
    ! [U_12771,U_12770,U_12769,U_12768,U_12767,U_12766] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_12766,U_12767,c_Groups_Otimes__class_Otimes(U_12766)),hAPP(hAPP(c_COMBS(U_12767,tc_fun(U_12769,tc_HOL_Obool),U_12766),hAPP(hAPP(c_COMBC(U_12767,U_12766,tc_fun(tc_fun(U_12769,tc_HOL_Obool),U_12766)),hAPP(hAPP(c_COMBB(tc_fun(U_12769,U_12766),tc_fun(U_12766,tc_fun(tc_fun(U_12769,tc_HOL_Obool),U_12766)),U_12767),c_Finite__Set_Ofold__image(U_12766,U_12769,c_Groups_Otimes__class_Otimes(U_12766))),U_12771)),c_Groups_Oone__class_Oone(U_12766))),U_12770)),c_Groups_Oone__class_Oone(U_12766)),U_12768) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_12766,tc_prod(U_12767,U_12769),c_Groups_Otimes__class_Otimes(U_12766)),hAPP(c_Product__Type_Oprod_Oprod__case(U_12767,U_12769,U_12766),U_12771)),c_Groups_Oone__class_Oone(U_12766)),hAPP(hAPP(c_Product__Type_OSigma(U_12767,U_12769),U_12768),U_12770))
      | ? [U_12765] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12769),hAPP(U_12770,U_12765)))
          & hBOOL(hAPP(hAPP(c_member(U_12767),U_12765),U_12768)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12767),U_12768))
      | ~ class_Groups_Ocomm__monoid__mult(U_12766) ),
    inference(variable_rename,[status(thm)],[f_3283_1]) ).

fof(f_3283_3,plain,
    ! [U_12771,U_12770,U_12769,U_12768,U_12767,U_12766] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_12766,U_12767,c_Groups_Otimes__class_Otimes(U_12766)),hAPP(hAPP(c_COMBS(U_12767,tc_fun(U_12769,tc_HOL_Obool),U_12766),hAPP(hAPP(c_COMBC(U_12767,U_12766,tc_fun(tc_fun(U_12769,tc_HOL_Obool),U_12766)),hAPP(hAPP(c_COMBB(tc_fun(U_12769,U_12766),tc_fun(U_12766,tc_fun(tc_fun(U_12769,tc_HOL_Obool),U_12766)),U_12767),c_Finite__Set_Ofold__image(U_12766,U_12769,c_Groups_Otimes__class_Otimes(U_12766))),U_12771)),c_Groups_Oone__class_Oone(U_12766))),U_12770)),c_Groups_Oone__class_Oone(U_12766)),U_12768) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_12766,tc_prod(U_12767,U_12769),c_Groups_Otimes__class_Otimes(U_12766)),hAPP(c_Product__Type_Oprod_Oprod__case(U_12767,U_12769,U_12766),U_12771)),c_Groups_Oone__class_Oone(U_12766)),hAPP(hAPP(c_Product__Type_OSigma(U_12767,U_12769),U_12768),U_12770))
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12769),hAPP(U_12770,sK300(U_12771,U_12770,U_12769,U_12768,U_12767,U_12766))))
        & hBOOL(hAPP(hAPP(c_member(U_12767),sK300(U_12771,U_12770,U_12769,U_12768,U_12767,U_12766)),U_12768)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12767),U_12768))
      | ~ class_Groups_Ocomm__monoid__mult(U_12766) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK300]),skolemize(U_12765,sK300(U_12771,U_12770,U_12769,U_12768,U_12767,U_12766))],[f_3283_2]) ).

cnf(f_3283_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12767),sK300(U_12771,U_12770,U_12769,U_12768,U_12767,U_12766)),U_12768))
    | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_12766,U_12767,c_Groups_Otimes__class_Otimes(U_12766)),hAPP(hAPP(c_COMBS(U_12767,tc_fun(U_12769,tc_HOL_Obool),U_12766),hAPP(hAPP(c_COMBC(U_12767,U_12766,tc_fun(tc_fun(U_12769,tc_HOL_Obool),U_12766)),hAPP(hAPP(c_COMBB(tc_fun(U_12769,U_12766),tc_fun(U_12766,tc_fun(tc_fun(U_12769,tc_HOL_Obool),U_12766)),U_12767),c_Finite__Set_Ofold__image(U_12766,U_12769,c_Groups_Otimes__class_Otimes(U_12766))),U_12771)),c_Groups_Oone__class_Oone(U_12766))),U_12770)),c_Groups_Oone__class_Oone(U_12766)),U_12768) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_12766,tc_prod(U_12767,U_12769),c_Groups_Otimes__class_Otimes(U_12766)),hAPP(c_Product__Type_Oprod_Oprod__case(U_12767,U_12769,U_12766),U_12771)),c_Groups_Oone__class_Oone(U_12766)),hAPP(hAPP(c_Product__Type_OSigma(U_12767,U_12769),U_12768),U_12770))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12767),U_12768))
    | ~ class_Groups_Ocomm__monoid__mult(U_12766) ),
    inference(clausify,[status(thm)],[f_3283_3]) ).

cnf(f_3283_5,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12769),hAPP(U_12770,sK300(U_12771,U_12770,U_12769,U_12768,U_12767,U_12766))))
    | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_12766,U_12767,c_Groups_Otimes__class_Otimes(U_12766)),hAPP(hAPP(c_COMBS(U_12767,tc_fun(U_12769,tc_HOL_Obool),U_12766),hAPP(hAPP(c_COMBC(U_12767,U_12766,tc_fun(tc_fun(U_12769,tc_HOL_Obool),U_12766)),hAPP(hAPP(c_COMBB(tc_fun(U_12769,U_12766),tc_fun(U_12766,tc_fun(tc_fun(U_12769,tc_HOL_Obool),U_12766)),U_12767),c_Finite__Set_Ofold__image(U_12766,U_12769,c_Groups_Otimes__class_Otimes(U_12766))),U_12771)),c_Groups_Oone__class_Oone(U_12766))),U_12770)),c_Groups_Oone__class_Oone(U_12766)),U_12768) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_12766,tc_prod(U_12767,U_12769),c_Groups_Otimes__class_Otimes(U_12766)),hAPP(c_Product__Type_Oprod_Oprod__case(U_12767,U_12769,U_12766),U_12771)),c_Groups_Oone__class_Oone(U_12766)),hAPP(hAPP(c_Product__Type_OSigma(U_12767,U_12769),U_12768),U_12770))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12767),U_12768))
    | ~ class_Groups_Ocomm__monoid__mult(U_12766) ),
    inference(clausify,[status(thm)],[f_3283_3]) ).

fof(f_3284_1,plain,
    ! [V_B_2,T_c,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)))
      | ? [B_a] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_a)))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__SigmaI]) ).

fof(f_3284_2,plain,
    ! [U_12776,U_12775,U_12774,U_12773] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_12773,U_12775)),hAPP(hAPP(c_Product__Type_OSigma(U_12773,U_12775),U_12774),U_12776)))
      | ? [U_12772] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12775),hAPP(U_12776,U_12772)))
          & hBOOL(hAPP(hAPP(c_member(U_12773),U_12772),U_12774)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12773),U_12774)) ),
    inference(variable_rename,[status(thm)],[f_3284_1]) ).

fof(f_3284_3,plain,
    ! [U_12776,U_12775,U_12774,U_12773] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_12773,U_12775)),hAPP(hAPP(c_Product__Type_OSigma(U_12773,U_12775),U_12774),U_12776)))
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12775),hAPP(U_12776,sK301(U_12776,U_12775,U_12774,U_12773))))
        & hBOOL(hAPP(hAPP(c_member(U_12773),sK301(U_12776,U_12775,U_12774,U_12773)),U_12774)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12773),U_12774)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK301]),skolemize(U_12772,sK301(U_12776,U_12775,U_12774,U_12773))],[f_3284_2]) ).

cnf(f_3284_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12773),sK301(U_12776,U_12775,U_12774,U_12773)),U_12774))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_12773,U_12775)),hAPP(hAPP(c_Product__Type_OSigma(U_12773,U_12775),U_12774),U_12776)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12773),U_12774)) ),
    inference(clausify,[status(thm)],[f_3284_3]) ).

cnf(f_3284_5,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12775),hAPP(U_12776,sK301(U_12776,U_12775,U_12774,U_12773))))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_12773,U_12775)),hAPP(hAPP(c_Product__Type_OSigma(U_12773,U_12775),U_12774),U_12776)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12773),U_12774)) ),
    inference(clausify,[status(thm)],[f_3284_3]) ).

fof(f_3285_1,plain,
    ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_d),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_d),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d),T_b),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(T_b,T_c),T_d),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x)))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_d) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__Sigma]) ).

fof(f_3285_2,plain,
    ! [U_12783,U_12782,U_12781,U_12780,U_12779,U_12778] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_12779,U_12778),hAPP(hAPP(c_COMBS(U_12779,tc_fun(U_12781,tc_HOL_Obool),U_12778),hAPP(hAPP(c_COMBB(tc_fun(U_12781,U_12778),tc_fun(tc_fun(U_12781,tc_HOL_Obool),U_12778),U_12779),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_12781,U_12778)),U_12783)),U_12782)),U_12780) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(U_12779,U_12781),U_12778),hAPP(c_Product__Type_Oprod_Oprod__case(U_12779,U_12781,U_12778),U_12783)),hAPP(hAPP(c_Product__Type_OSigma(U_12779,U_12781),U_12780),U_12782))
      | ? [U_12777] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12781),hAPP(U_12782,U_12777)))
          & hBOOL(hAPP(hAPP(c_member(U_12779),U_12777),U_12780)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12779),U_12780))
      | ~ class_Groups_Ocomm__monoid__mult(U_12778) ),
    inference(variable_rename,[status(thm)],[f_3285_1]) ).

fof(f_3285_3,plain,
    ! [U_12783,U_12782,U_12781,U_12780,U_12779,U_12778] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_12779,U_12778),hAPP(hAPP(c_COMBS(U_12779,tc_fun(U_12781,tc_HOL_Obool),U_12778),hAPP(hAPP(c_COMBB(tc_fun(U_12781,U_12778),tc_fun(tc_fun(U_12781,tc_HOL_Obool),U_12778),U_12779),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_12781,U_12778)),U_12783)),U_12782)),U_12780) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(U_12779,U_12781),U_12778),hAPP(c_Product__Type_Oprod_Oprod__case(U_12779,U_12781,U_12778),U_12783)),hAPP(hAPP(c_Product__Type_OSigma(U_12779,U_12781),U_12780),U_12782))
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12781),hAPP(U_12782,sK302(U_12783,U_12782,U_12781,U_12780,U_12779,U_12778))))
        & hBOOL(hAPP(hAPP(c_member(U_12779),sK302(U_12783,U_12782,U_12781,U_12780,U_12779,U_12778)),U_12780)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12779),U_12780))
      | ~ class_Groups_Ocomm__monoid__mult(U_12778) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK302]),skolemize(U_12777,sK302(U_12783,U_12782,U_12781,U_12780,U_12779,U_12778))],[f_3285_2]) ).

cnf(f_3285_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12779),sK302(U_12783,U_12782,U_12781,U_12780,U_12779,U_12778)),U_12780))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_12779,U_12778),hAPP(hAPP(c_COMBS(U_12779,tc_fun(U_12781,tc_HOL_Obool),U_12778),hAPP(hAPP(c_COMBB(tc_fun(U_12781,U_12778),tc_fun(tc_fun(U_12781,tc_HOL_Obool),U_12778),U_12779),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_12781,U_12778)),U_12783)),U_12782)),U_12780) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(U_12779,U_12781),U_12778),hAPP(c_Product__Type_Oprod_Oprod__case(U_12779,U_12781,U_12778),U_12783)),hAPP(hAPP(c_Product__Type_OSigma(U_12779,U_12781),U_12780),U_12782))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12779),U_12780))
    | ~ class_Groups_Ocomm__monoid__mult(U_12778) ),
    inference(clausify,[status(thm)],[f_3285_3]) ).

cnf(f_3285_5,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12781),hAPP(U_12782,sK302(U_12783,U_12782,U_12781,U_12780,U_12779,U_12778))))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_12779,U_12778),hAPP(hAPP(c_COMBS(U_12779,tc_fun(U_12781,tc_HOL_Obool),U_12778),hAPP(hAPP(c_COMBB(tc_fun(U_12781,U_12778),tc_fun(tc_fun(U_12781,tc_HOL_Obool),U_12778),U_12779),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_12781,U_12778)),U_12783)),U_12782)),U_12780) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(U_12779,U_12781),U_12778),hAPP(c_Product__Type_Oprod_Oprod__case(U_12779,U_12781,U_12778),U_12783)),hAPP(hAPP(c_Product__Type_OSigma(U_12779,U_12781),U_12780),U_12782))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12779),U_12780))
    | ~ class_Groups_Ocomm__monoid__mult(U_12778) ),
    inference(clausify,[status(thm)],[f_3285_3]) ).

fof(f_3286_1,plain,
    ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_d),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d),T_b),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(T_b,T_c),T_d),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x)))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Ocomm__monoid__add(T_d) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__Sigma]) ).

fof(f_3286_2,plain,
    ! [U_12790,U_12789,U_12788,U_12787,U_12786,U_12785] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12786,U_12785),hAPP(hAPP(c_COMBS(U_12786,tc_fun(U_12788,tc_HOL_Obool),U_12785),hAPP(hAPP(c_COMBB(tc_fun(U_12788,U_12785),tc_fun(tc_fun(U_12788,tc_HOL_Obool),U_12785),U_12786),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12788,U_12785)),U_12790)),U_12789)),U_12787) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(U_12786,U_12788),U_12785),hAPP(c_Product__Type_Oprod_Oprod__case(U_12786,U_12788,U_12785),U_12790)),hAPP(hAPP(c_Product__Type_OSigma(U_12786,U_12788),U_12787),U_12789))
      | ? [U_12784] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12788),hAPP(U_12789,U_12784)))
          & hBOOL(hAPP(hAPP(c_member(U_12786),U_12784),U_12787)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12786),U_12787))
      | ~ class_Groups_Ocomm__monoid__add(U_12785) ),
    inference(variable_rename,[status(thm)],[f_3286_1]) ).

fof(f_3286_3,plain,
    ! [U_12790,U_12789,U_12788,U_12787,U_12786,U_12785] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12786,U_12785),hAPP(hAPP(c_COMBS(U_12786,tc_fun(U_12788,tc_HOL_Obool),U_12785),hAPP(hAPP(c_COMBB(tc_fun(U_12788,U_12785),tc_fun(tc_fun(U_12788,tc_HOL_Obool),U_12785),U_12786),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12788,U_12785)),U_12790)),U_12789)),U_12787) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(U_12786,U_12788),U_12785),hAPP(c_Product__Type_Oprod_Oprod__case(U_12786,U_12788,U_12785),U_12790)),hAPP(hAPP(c_Product__Type_OSigma(U_12786,U_12788),U_12787),U_12789))
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12788),hAPP(U_12789,sK303(U_12790,U_12789,U_12788,U_12787,U_12786,U_12785))))
        & hBOOL(hAPP(hAPP(c_member(U_12786),sK303(U_12790,U_12789,U_12788,U_12787,U_12786,U_12785)),U_12787)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12786),U_12787))
      | ~ class_Groups_Ocomm__monoid__add(U_12785) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK303]),skolemize(U_12784,sK303(U_12790,U_12789,U_12788,U_12787,U_12786,U_12785))],[f_3286_2]) ).

cnf(f_3286_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12786),sK303(U_12790,U_12789,U_12788,U_12787,U_12786,U_12785)),U_12787))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12786,U_12785),hAPP(hAPP(c_COMBS(U_12786,tc_fun(U_12788,tc_HOL_Obool),U_12785),hAPP(hAPP(c_COMBB(tc_fun(U_12788,U_12785),tc_fun(tc_fun(U_12788,tc_HOL_Obool),U_12785),U_12786),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12788,U_12785)),U_12790)),U_12789)),U_12787) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(U_12786,U_12788),U_12785),hAPP(c_Product__Type_Oprod_Oprod__case(U_12786,U_12788,U_12785),U_12790)),hAPP(hAPP(c_Product__Type_OSigma(U_12786,U_12788),U_12787),U_12789))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12786),U_12787))
    | ~ class_Groups_Ocomm__monoid__add(U_12785) ),
    inference(clausify,[status(thm)],[f_3286_3]) ).

cnf(f_3286_5,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12788),hAPP(U_12789,sK303(U_12790,U_12789,U_12788,U_12787,U_12786,U_12785))))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12786,U_12785),hAPP(hAPP(c_COMBS(U_12786,tc_fun(U_12788,tc_HOL_Obool),U_12785),hAPP(hAPP(c_COMBB(tc_fun(U_12788,U_12785),tc_fun(tc_fun(U_12788,tc_HOL_Obool),U_12785),U_12786),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12788,U_12785)),U_12790)),U_12789)),U_12787) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(U_12786,U_12788),U_12785),hAPP(c_Product__Type_Oprod_Oprod__case(U_12786,U_12788,U_12785),U_12790)),hAPP(hAPP(c_Product__Type_OSigma(U_12786,U_12788),U_12787),U_12789))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12786),U_12787))
    | ~ class_Groups_Ocomm__monoid__add(U_12785) ),
    inference(clausify,[status(thm)],[f_3286_3]) ).

fof(f_3287_1,plain,
    ! [V_B_2,T_c,V_A_2,T_b] :
      ( hAPP(c_Finite__Set_Ocard(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_Nat_Onat,T_b),c_Finite__Set_Ocard(T_c)),V_B_2)),V_A_2)
      | ? [B_x] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x)))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__SigmaI]) ).

fof(f_3287_2,plain,
    ! [U_12795,U_12794,U_12793,U_12792] :
      ( hAPP(c_Finite__Set_Ocard(tc_prod(U_12792,U_12794)),hAPP(hAPP(c_Product__Type_OSigma(U_12792,U_12794),U_12793),U_12795)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12792,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_12794,tc_HOL_Obool),tc_Nat_Onat,U_12792),c_Finite__Set_Ocard(U_12794)),U_12795)),U_12793)
      | ? [U_12791] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12794),hAPP(U_12795,U_12791)))
          & hBOOL(hAPP(hAPP(c_member(U_12792),U_12791),U_12793)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12792),U_12793)) ),
    inference(variable_rename,[status(thm)],[f_3287_1]) ).

fof(f_3287_3,plain,
    ! [U_12795,U_12794,U_12793,U_12792] :
      ( hAPP(c_Finite__Set_Ocard(tc_prod(U_12792,U_12794)),hAPP(hAPP(c_Product__Type_OSigma(U_12792,U_12794),U_12793),U_12795)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12792,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_12794,tc_HOL_Obool),tc_Nat_Onat,U_12792),c_Finite__Set_Ocard(U_12794)),U_12795)),U_12793)
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12794),hAPP(U_12795,sK304(U_12795,U_12794,U_12793,U_12792))))
        & hBOOL(hAPP(hAPP(c_member(U_12792),sK304(U_12795,U_12794,U_12793,U_12792)),U_12793)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12792),U_12793)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK304]),skolemize(U_12791,sK304(U_12795,U_12794,U_12793,U_12792))],[f_3287_2]) ).

cnf(f_3287_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12792),sK304(U_12795,U_12794,U_12793,U_12792)),U_12793))
    | hAPP(c_Finite__Set_Ocard(tc_prod(U_12792,U_12794)),hAPP(hAPP(c_Product__Type_OSigma(U_12792,U_12794),U_12793),U_12795)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12792,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_12794,tc_HOL_Obool),tc_Nat_Onat,U_12792),c_Finite__Set_Ocard(U_12794)),U_12795)),U_12793)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12792),U_12793)) ),
    inference(clausify,[status(thm)],[f_3287_3]) ).

cnf(f_3287_5,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12794),hAPP(U_12795,sK304(U_12795,U_12794,U_12793,U_12792))))
    | hAPP(c_Finite__Set_Ocard(tc_prod(U_12792,U_12794)),hAPP(hAPP(c_Product__Type_OSigma(U_12792,U_12794),U_12793),U_12795)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12792,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_12794,tc_HOL_Obool),tc_Nat_Onat,U_12792),c_Finite__Set_Ocard(U_12794)),U_12795)),U_12793)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12792),U_12793)) ),
    inference(clausify,[status(thm)],[f_3287_3]) ).

fof(f_3288_1,plain,
    ! [V_B_2,V_A_2,V_c_2,T_c,T_b] :
      ( ? [B_x] :
          ( ? [B_y] :
              ( V_c_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y)
              & hBOOL(hAPP(hAPP(c_member(T_c),B_y),hAPP(V_B_2,B_x))) )
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_c_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))) ),
    inference(fof_nnf,[status(thm)],[fact_SigmaE]) ).

fof(f_3288_2,plain,
    ! [U_12802,U_12801,U_12800,U_12799,U_12798] :
      ( ? [U_12797] :
          ( ? [U_12796] :
              ( U_12800 = hAPP(hAPP(c_Product__Type_OPair(U_12798,U_12799),U_12797),U_12796)
              & hBOOL(hAPP(hAPP(c_member(U_12799),U_12796),hAPP(U_12802,U_12797))) )
          & hBOOL(hAPP(hAPP(c_member(U_12798),U_12797),U_12801)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12798,U_12799)),U_12800),hAPP(hAPP(c_Product__Type_OSigma(U_12798,U_12799),U_12801),U_12802))) ),
    inference(variable_rename,[status(thm)],[f_3288_1]) ).

fof(f_3288_3,plain,
    ! [U_12802,U_12801,U_12800,U_12799,U_12798] :
      ( ( ? [U_12796] :
            ( U_12800 = hAPP(hAPP(c_Product__Type_OPair(U_12798,U_12799),sK305(U_12802,U_12801,U_12800,U_12799,U_12798)),U_12796)
            & hBOOL(hAPP(hAPP(c_member(U_12799),U_12796),hAPP(U_12802,sK305(U_12802,U_12801,U_12800,U_12799,U_12798)))) )
        & hBOOL(hAPP(hAPP(c_member(U_12798),sK305(U_12802,U_12801,U_12800,U_12799,U_12798)),U_12801)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12798,U_12799)),U_12800),hAPP(hAPP(c_Product__Type_OSigma(U_12798,U_12799),U_12801),U_12802))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK305]),skolemize(U_12797,sK305(U_12802,U_12801,U_12800,U_12799,U_12798))],[f_3288_2]) ).

fof(f_3288_4,plain,
    ! [U_12802,U_12801,U_12800,U_12799,U_12798] :
      ( ( U_12800 = hAPP(hAPP(c_Product__Type_OPair(U_12798,U_12799),sK305(U_12802,U_12801,U_12800,U_12799,U_12798)),sK306(U_12802,U_12801,U_12800,U_12799,U_12798))
        & hBOOL(hAPP(hAPP(c_member(U_12799),sK306(U_12802,U_12801,U_12800,U_12799,U_12798)),hAPP(U_12802,sK305(U_12802,U_12801,U_12800,U_12799,U_12798))))
        & hBOOL(hAPP(hAPP(c_member(U_12798),sK305(U_12802,U_12801,U_12800,U_12799,U_12798)),U_12801)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12798,U_12799)),U_12800),hAPP(hAPP(c_Product__Type_OSigma(U_12798,U_12799),U_12801),U_12802))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK306]),skolemize(U_12796,sK306(U_12802,U_12801,U_12800,U_12799,U_12798))],[f_3288_3]) ).

cnf(f_3288_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12798),sK305(U_12802,U_12801,U_12800,U_12799,U_12798)),U_12801))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12798,U_12799)),U_12800),hAPP(hAPP(c_Product__Type_OSigma(U_12798,U_12799),U_12801),U_12802))) ),
    inference(clausify,[status(thm)],[f_3288_4]) ).

cnf(f_3288_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12799),sK306(U_12802,U_12801,U_12800,U_12799,U_12798)),hAPP(U_12802,sK305(U_12802,U_12801,U_12800,U_12799,U_12798))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12798,U_12799)),U_12800),hAPP(hAPP(c_Product__Type_OSigma(U_12798,U_12799),U_12801),U_12802))) ),
    inference(clausify,[status(thm)],[f_3288_4]) ).

cnf(f_3288_7,plain,
    ( U_12800 = hAPP(hAPP(c_Product__Type_OPair(U_12798,U_12799),sK305(U_12802,U_12801,U_12800,U_12799,U_12798)),sK306(U_12802,U_12801,U_12800,U_12799,U_12798))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12798,U_12799)),U_12800),hAPP(hAPP(c_Product__Type_OSigma(U_12798,U_12799),U_12801),U_12802))) ),
    inference(clausify,[status(thm)],[f_3288_4]) ).

fof(f_3289_1,plain,
    ! [V_g_2,T_d,T_e,V_f_2,T_b,T_c] :
      ( hAPP(c_Set_Oimage(tc_prod(T_c,T_e),tc_prod(T_b,T_d),c_Product__Type_Omap__pair(T_c,T_b,T_e,T_d,V_f_2,V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_c,T_e),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool))
      | hAPP(c_Set_Oimage(T_e,T_d,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_e,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))
      | hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ),
    inference(fof_nnf,[status(thm)],[fact_map__pair__surj]) ).

fof(f_3289_2,plain,
    ! [U_12808,U_12807,U_12806,U_12805,U_12804,U_12803] :
      ( hAPP(c_Set_Oimage(tc_prod(U_12803,U_12806),tc_prod(U_12804,U_12807),c_Product__Type_Omap__pair(U_12803,U_12804,U_12806,U_12807,U_12805,U_12808)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_12803,U_12806),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_12804,U_12807),tc_HOL_Obool))
      | hAPP(c_Set_Oimage(U_12806,U_12807,U_12808),c_Orderings_Otop__class_Otop(tc_fun(U_12806,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_12807,tc_HOL_Obool))
      | hAPP(c_Set_Oimage(U_12803,U_12804,U_12805),c_Orderings_Otop__class_Otop(tc_fun(U_12803,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_12804,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_3289_1]) ).

cnf(f_3289_3,plain,
    ( hAPP(c_Set_Oimage(tc_prod(U_12803,U_12806),tc_prod(U_12804,U_12807),c_Product__Type_Omap__pair(U_12803,U_12804,U_12806,U_12807,U_12805,U_12808)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_12803,U_12806),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_12804,U_12807),tc_HOL_Obool))
    | hAPP(c_Set_Oimage(U_12806,U_12807,U_12808),c_Orderings_Otop__class_Otop(tc_fun(U_12806,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_12807,tc_HOL_Obool))
    | hAPP(c_Set_Oimage(U_12803,U_12804,U_12805),c_Orderings_Otop__class_Otop(tc_fun(U_12803,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_12804,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3289_2]) ).

fof(f_3290_1,plain,
    ! [V_B_2,V_g_2,T_e,T_d,V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(tc_prod(T_b,T_d),tc_prod(T_c,T_e),c_Product__Type_Omap__pair(T_b,T_c,T_d,T_e,V_f_2,V_g_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_b),V_B_2)))
      | ~ c_Fun_Oinj__on(T_d,T_e,V_g_2,V_B_2)
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_map__pair__inj__on]) ).

fof(f_3290_2,plain,
    ! [U_12816,U_12815,U_12814,U_12813,U_12812,U_12811,U_12810,U_12809] :
      ( c_Fun_Oinj__on(tc_prod(U_12809,U_12813),tc_prod(U_12810,U_12814),c_Product__Type_Omap__pair(U_12809,U_12810,U_12813,U_12814,U_12811,U_12815),hAPP(hAPP(c_Product__Type_OSigma(U_12809,U_12813),U_12812),hAPP(c_COMBK(tc_fun(U_12813,tc_HOL_Obool),U_12809),U_12816)))
      | ~ c_Fun_Oinj__on(U_12813,U_12814,U_12815,U_12816)
      | ~ c_Fun_Oinj__on(U_12809,U_12810,U_12811,U_12812) ),
    inference(variable_rename,[status(thm)],[f_3290_1]) ).

cnf(f_3290_3,plain,
    ( c_Fun_Oinj__on(tc_prod(U_12809,U_12813),tc_prod(U_12810,U_12814),c_Product__Type_Omap__pair(U_12809,U_12810,U_12813,U_12814,U_12811,U_12815),hAPP(hAPP(c_Product__Type_OSigma(U_12809,U_12813),U_12812),hAPP(c_COMBK(tc_fun(U_12813,tc_HOL_Obool),U_12809),U_12816)))
    | ~ c_Fun_Oinj__on(U_12813,U_12814,U_12815,U_12816)
    | ~ c_Fun_Oinj__on(U_12809,U_12810,U_12811,U_12812) ),
    inference(clausify,[status(thm)],[f_3290_2]) ).

fof(f_3291_1,plain,
    ! [V_g_2,V_f_2,T_e,T_d,V_R_2,V_b_2,V_a_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_e)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),hAPP(V_f_2,V_a_2)),hAPP(V_g_2,V_b_2))),hAPP(c_Set_Oimage(tc_prod(T_b,T_c),tc_prod(T_d,T_e),c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,V_f_2,V_g_2)),V_R_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_R_2)) ),
    inference(fof_nnf,[status(thm)],[fact_map__pair__imageI]) ).

fof(f_3291_2,plain,
    ! [U_12825,U_12824,U_12823,U_12822,U_12821,U_12820,U_12819,U_12818,U_12817] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12822,U_12823)),hAPP(hAPP(c_Product__Type_OPair(U_12822,U_12823),hAPP(U_12824,U_12819)),hAPP(U_12825,U_12820))),hAPP(c_Set_Oimage(tc_prod(U_12817,U_12818),tc_prod(U_12822,U_12823),c_Product__Type_Omap__pair(U_12817,U_12822,U_12818,U_12823,U_12824,U_12825)),U_12821)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12817,U_12818)),hAPP(hAPP(c_Product__Type_OPair(U_12817,U_12818),U_12819),U_12820)),U_12821)) ),
    inference(variable_rename,[status(thm)],[f_3291_1]) ).

cnf(f_3291_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12822,U_12823)),hAPP(hAPP(c_Product__Type_OPair(U_12822,U_12823),hAPP(U_12824,U_12819)),hAPP(U_12825,U_12820))),hAPP(c_Set_Oimage(tc_prod(U_12817,U_12818),tc_prod(U_12822,U_12823),c_Product__Type_Omap__pair(U_12817,U_12822,U_12818,U_12823,U_12824,U_12825)),U_12821)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12817,U_12818)),hAPP(hAPP(c_Product__Type_OPair(U_12817,U_12818),U_12819),U_12820)),U_12821)) ),
    inference(clausify,[status(thm)],[f_3291_2]) ).

fof(f_3292_1,plain,
    ! [V_z_2,T_c,T_b] : hAPP(c_Product__Type_Omap__pair(T_b,T_b,T_c,T_c,c_COMBI(T_b),c_COMBI(T_c)),V_z_2) = V_z_2,
    inference(fof_nnf,[status(thm)],[fact_map__pair__ident]) ).

fof(f_3292_2,plain,
    ! [U_12828,U_12827,U_12826] : hAPP(c_Product__Type_Omap__pair(U_12826,U_12826,U_12827,U_12827,c_COMBI(U_12826),c_COMBI(U_12827)),U_12828) = U_12828,
    inference(variable_rename,[status(thm)],[f_3292_1]) ).

cnf(f_3292_3,plain,
    hAPP(c_Product__Type_Omap__pair(U_12826,U_12826,U_12827,U_12827,c_COMBI(U_12826),c_COMBI(U_12827)),U_12828) = U_12828,
    inference(clausify,[status(thm)],[f_3292_2]) ).

fof(f_3293_1,plain,
    ! [V_x_2,V_g_2,V_f_2,T_e,T_d,T_b,T_c] : hAPP(c_Product__Type_Osnd(T_c,T_b),hAPP(c_Product__Type_Omap__pair(T_d,T_c,T_e,T_b,V_f_2,V_g_2),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_d,T_e),V_x_2)),
    inference(fof_nnf,[status(thm)],[fact_snd__prod__fun]) ).

fof(f_3293_2,plain,
    ! [U_12835,U_12834,U_12833,U_12832,U_12831,U_12830,U_12829] : hAPP(c_Product__Type_Osnd(U_12829,U_12830),hAPP(c_Product__Type_Omap__pair(U_12831,U_12829,U_12832,U_12830,U_12833,U_12834),U_12835)) = hAPP(U_12834,hAPP(c_Product__Type_Osnd(U_12831,U_12832),U_12835)),
    inference(variable_rename,[status(thm)],[f_3293_1]) ).

cnf(f_3293_3,plain,
    hAPP(c_Product__Type_Osnd(U_12829,U_12830),hAPP(c_Product__Type_Omap__pair(U_12831,U_12829,U_12832,U_12830,U_12833,U_12834),U_12835)) = hAPP(U_12834,hAPP(c_Product__Type_Osnd(U_12831,U_12832),U_12835)),
    inference(clausify,[status(thm)],[f_3293_2]) ).

fof(f_3294_1,plain,
    ! [V_x_2,V_g_2,V_f_2,T_e,T_d,T_c,T_b] : hAPP(c_Product__Type_Ofst(T_b,T_c),hAPP(c_Product__Type_Omap__pair(T_d,T_b,T_e,T_c,V_f_2,V_g_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_d,T_e),V_x_2)),
    inference(fof_nnf,[status(thm)],[fact_fst__map__pair]) ).

fof(f_3294_2,plain,
    ! [U_12842,U_12841,U_12840,U_12839,U_12838,U_12837,U_12836] : hAPP(c_Product__Type_Ofst(U_12836,U_12837),hAPP(c_Product__Type_Omap__pair(U_12838,U_12836,U_12839,U_12837,U_12840,U_12841),U_12842)) = hAPP(U_12840,hAPP(c_Product__Type_Ofst(U_12838,U_12839),U_12842)),
    inference(variable_rename,[status(thm)],[f_3294_1]) ).

cnf(f_3294_3,plain,
    hAPP(c_Product__Type_Ofst(U_12836,U_12837),hAPP(c_Product__Type_Omap__pair(U_12838,U_12836,U_12839,U_12837,U_12840,U_12841),U_12842)) = hAPP(U_12840,hAPP(c_Product__Type_Ofst(U_12838,U_12839),U_12842)),
    inference(clausify,[status(thm)],[f_3294_2]) ).

fof(f_3295_1,plain,
    ! [V_b_2,V_a_2,V_g_2,V_f_2,T_c,T_e,T_b,T_d] : hAPP(c_Product__Type_Omap__pair(T_d,T_b,T_e,T_c,V_f_2,V_g_2),hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),V_a_2),V_b_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,V_a_2)),hAPP(V_g_2,V_b_2)),
    inference(fof_nnf,[status(thm)],[fact_map__pair__simp]) ).

fof(f_3295_2,plain,
    ! [U_12850,U_12849,U_12848,U_12847,U_12846,U_12845,U_12844,U_12843] : hAPP(c_Product__Type_Omap__pair(U_12843,U_12844,U_12845,U_12846,U_12847,U_12848),hAPP(hAPP(c_Product__Type_OPair(U_12843,U_12845),U_12849),U_12850)) = hAPP(hAPP(c_Product__Type_OPair(U_12844,U_12846),hAPP(U_12847,U_12849)),hAPP(U_12848,U_12850)),
    inference(variable_rename,[status(thm)],[f_3295_1]) ).

cnf(f_3295_3,plain,
    hAPP(c_Product__Type_Omap__pair(U_12843,U_12844,U_12845,U_12846,U_12847,U_12848),hAPP(hAPP(c_Product__Type_OPair(U_12843,U_12845),U_12849),U_12850)) = hAPP(hAPP(c_Product__Type_OPair(U_12844,U_12846),hAPP(U_12847,U_12849)),hAPP(U_12848,U_12850)),
    inference(clausify,[status(thm)],[f_3295_2]) ).

fof(f_3296_1,plain,
    ! [V_g_2,V_f_2,T_c,T_b,T_e,T_d] : hAPP(c_Fun_Ocomp(tc_prod(T_d,T_e),T_d,tc_prod(T_b,T_c),c_Product__Type_Ofst(T_d,T_e)),c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,V_f_2,V_g_2)) = hAPP(c_Fun_Ocomp(T_b,T_d,tc_prod(T_b,T_c),V_f_2),c_Product__Type_Ofst(T_b,T_c)),
    inference(fof_nnf,[status(thm)],[fact_fst__comp__map__pair]) ).

fof(f_3296_2,plain,
    ! [U_12856,U_12855,U_12854,U_12853,U_12852,U_12851] : hAPP(c_Fun_Ocomp(tc_prod(U_12851,U_12852),U_12851,tc_prod(U_12853,U_12854),c_Product__Type_Ofst(U_12851,U_12852)),c_Product__Type_Omap__pair(U_12853,U_12851,U_12854,U_12852,U_12855,U_12856)) = hAPP(c_Fun_Ocomp(U_12853,U_12851,tc_prod(U_12853,U_12854),U_12855),c_Product__Type_Ofst(U_12853,U_12854)),
    inference(variable_rename,[status(thm)],[f_3296_1]) ).

cnf(f_3296_3,plain,
    hAPP(c_Fun_Ocomp(tc_prod(U_12851,U_12852),U_12851,tc_prod(U_12853,U_12854),c_Product__Type_Ofst(U_12851,U_12852)),c_Product__Type_Omap__pair(U_12853,U_12851,U_12854,U_12852,U_12855,U_12856)) = hAPP(c_Fun_Ocomp(U_12853,U_12851,tc_prod(U_12853,U_12854),U_12855),c_Product__Type_Ofst(U_12853,U_12854)),
    inference(clausify,[status(thm)],[f_3296_2]) ).

fof(f_3297_1,plain,
    ! [V_i_2,V_h_2,V_g_2,V_f_2,T_c,T_b,T_e,T_d,T_g,T_f] : hAPP(c_Fun_Ocomp(tc_prod(T_f,T_g),tc_prod(T_d,T_e),tc_prod(T_b,T_c),c_Product__Type_Omap__pair(T_f,T_d,T_g,T_e,V_f_2,V_g_2)),c_Product__Type_Omap__pair(T_b,T_f,T_c,T_g,V_h_2,V_i_2)) = c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,hAPP(c_Fun_Ocomp(T_f,T_d,T_b,V_f_2),V_h_2),hAPP(c_Fun_Ocomp(T_g,T_e,T_c,V_g_2),V_i_2)),
    inference(fof_nnf,[status(thm)],[fact_map__pair_Ocomp]) ).

fof(f_3297_2,plain,
    ! [U_12866,U_12865,U_12864,U_12863,U_12862,U_12861,U_12860,U_12859,U_12858,U_12857] : hAPP(c_Fun_Ocomp(tc_prod(U_12857,U_12858),tc_prod(U_12859,U_12860),tc_prod(U_12861,U_12862),c_Product__Type_Omap__pair(U_12857,U_12859,U_12858,U_12860,U_12863,U_12864)),c_Product__Type_Omap__pair(U_12861,U_12857,U_12862,U_12858,U_12865,U_12866)) = c_Product__Type_Omap__pair(U_12861,U_12859,U_12862,U_12860,hAPP(c_Fun_Ocomp(U_12857,U_12859,U_12861,U_12863),U_12865),hAPP(c_Fun_Ocomp(U_12858,U_12860,U_12862,U_12864),U_12866)),
    inference(variable_rename,[status(thm)],[f_3297_1]) ).

cnf(f_3297_3,plain,
    hAPP(c_Fun_Ocomp(tc_prod(U_12857,U_12858),tc_prod(U_12859,U_12860),tc_prod(U_12861,U_12862),c_Product__Type_Omap__pair(U_12857,U_12859,U_12858,U_12860,U_12863,U_12864)),c_Product__Type_Omap__pair(U_12861,U_12857,U_12862,U_12858,U_12865,U_12866)) = c_Product__Type_Omap__pair(U_12861,U_12859,U_12862,U_12860,hAPP(c_Fun_Ocomp(U_12857,U_12859,U_12861,U_12863),U_12865),hAPP(c_Fun_Ocomp(U_12858,U_12860,U_12862,U_12864),U_12866)),
    inference(clausify,[status(thm)],[f_3297_2]) ).

fof(f_3298_1,plain,
    ! [V_g2_2,V_g1_2,T_g,V_f2_2,V_f1_2,T_f,T_e,T_c,T_d,T_b] : c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,hAPP(c_Fun_Ocomp(T_f,T_d,T_b,V_f1_2),V_f2_2),hAPP(c_Fun_Ocomp(T_g,T_e,T_c,V_g1_2),V_g2_2)) = hAPP(c_Fun_Ocomp(tc_prod(T_f,T_g),tc_prod(T_d,T_e),tc_prod(T_b,T_c),c_Product__Type_Omap__pair(T_f,T_d,T_g,T_e,V_f1_2,V_g1_2)),c_Product__Type_Omap__pair(T_b,T_f,T_c,T_g,V_f2_2,V_g2_2)),
    inference(fof_nnf,[status(thm)],[fact_map__pair__compose]) ).

fof(f_3298_2,plain,
    ! [U_12876,U_12875,U_12874,U_12873,U_12872,U_12871,U_12870,U_12869,U_12868,U_12867] : c_Product__Type_Omap__pair(U_12867,U_12868,U_12869,U_12870,hAPP(c_Fun_Ocomp(U_12871,U_12868,U_12867,U_12872),U_12873),hAPP(c_Fun_Ocomp(U_12874,U_12870,U_12869,U_12875),U_12876)) = hAPP(c_Fun_Ocomp(tc_prod(U_12871,U_12874),tc_prod(U_12868,U_12870),tc_prod(U_12867,U_12869),c_Product__Type_Omap__pair(U_12871,U_12868,U_12874,U_12870,U_12872,U_12875)),c_Product__Type_Omap__pair(U_12867,U_12871,U_12869,U_12874,U_12873,U_12876)),
    inference(variable_rename,[status(thm)],[f_3298_1]) ).

cnf(f_3298_3,plain,
    c_Product__Type_Omap__pair(U_12867,U_12868,U_12869,U_12870,hAPP(c_Fun_Ocomp(U_12871,U_12868,U_12867,U_12872),U_12873),hAPP(c_Fun_Ocomp(U_12874,U_12870,U_12869,U_12875),U_12876)) = hAPP(c_Fun_Ocomp(tc_prod(U_12871,U_12874),tc_prod(U_12868,U_12870),tc_prod(U_12867,U_12869),c_Product__Type_Omap__pair(U_12871,U_12868,U_12874,U_12870,U_12872,U_12875)),c_Product__Type_Omap__pair(U_12867,U_12871,U_12869,U_12874,U_12873,U_12876)),
    inference(clausify,[status(thm)],[f_3298_2]) ).

fof(f_3299_1,plain,
    ! [V_prod_2,V_i_2,V_h_2,T_g,T_f,V_g_2,V_f_2,T_c,T_e,T_b,T_d] : hAPP(c_Product__Type_Omap__pair(T_d,T_b,T_e,T_c,V_f_2,V_g_2),hAPP(c_Product__Type_Omap__pair(T_f,T_d,T_g,T_e,V_h_2,V_i_2),V_prod_2)) = hAPP(c_Product__Type_Omap__pair(T_f,T_b,T_g,T_c,hAPP(c_Fun_Ocomp(T_d,T_b,T_f,V_f_2),V_h_2),hAPP(c_Fun_Ocomp(T_e,T_c,T_g,V_g_2),V_i_2)),V_prod_2),
    inference(fof_nnf,[status(thm)],[fact_map__pair_Ocompositionality]) ).

fof(f_3299_2,plain,
    ! [U_12887,U_12886,U_12885,U_12884,U_12883,U_12882,U_12881,U_12880,U_12879,U_12878,U_12877] : hAPP(c_Product__Type_Omap__pair(U_12877,U_12878,U_12879,U_12880,U_12881,U_12882),hAPP(c_Product__Type_Omap__pair(U_12883,U_12877,U_12884,U_12879,U_12885,U_12886),U_12887)) = hAPP(c_Product__Type_Omap__pair(U_12883,U_12878,U_12884,U_12880,hAPP(c_Fun_Ocomp(U_12877,U_12878,U_12883,U_12881),U_12885),hAPP(c_Fun_Ocomp(U_12879,U_12880,U_12884,U_12882),U_12886)),U_12887),
    inference(variable_rename,[status(thm)],[f_3299_1]) ).

cnf(f_3299_3,plain,
    hAPP(c_Product__Type_Omap__pair(U_12877,U_12878,U_12879,U_12880,U_12881,U_12882),hAPP(c_Product__Type_Omap__pair(U_12883,U_12877,U_12884,U_12879,U_12885,U_12886),U_12887)) = hAPP(c_Product__Type_Omap__pair(U_12883,U_12878,U_12884,U_12880,hAPP(c_Fun_Ocomp(U_12877,U_12878,U_12883,U_12881),U_12885),hAPP(c_Fun_Ocomp(U_12879,U_12880,U_12884,U_12882),U_12886)),U_12887),
    inference(clausify,[status(thm)],[f_3299_2]) ).

fof(f_3300_1,plain,
    ! [V_g_2,V_f_2,T_c,T_b,T_d,T_e] : hAPP(c_Fun_Ocomp(tc_prod(T_e,T_d),T_d,tc_prod(T_b,T_c),c_Product__Type_Osnd(T_e,T_d)),c_Product__Type_Omap__pair(T_b,T_e,T_c,T_d,V_f_2,V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_d,tc_prod(T_b,T_c),V_g_2),c_Product__Type_Osnd(T_b,T_c)),
    inference(fof_nnf,[status(thm)],[fact_snd__comp__map__pair]) ).

fof(f_3300_2,plain,
    ! [U_12893,U_12892,U_12891,U_12890,U_12889,U_12888] : hAPP(c_Fun_Ocomp(tc_prod(U_12888,U_12889),U_12889,tc_prod(U_12890,U_12891),c_Product__Type_Osnd(U_12888,U_12889)),c_Product__Type_Omap__pair(U_12890,U_12888,U_12891,U_12889,U_12892,U_12893)) = hAPP(c_Fun_Ocomp(U_12891,U_12889,tc_prod(U_12890,U_12891),U_12893),c_Product__Type_Osnd(U_12890,U_12891)),
    inference(variable_rename,[status(thm)],[f_3300_1]) ).

cnf(f_3300_3,plain,
    hAPP(c_Fun_Ocomp(tc_prod(U_12888,U_12889),U_12889,tc_prod(U_12890,U_12891),c_Product__Type_Osnd(U_12888,U_12889)),c_Product__Type_Omap__pair(U_12890,U_12888,U_12891,U_12889,U_12892,U_12893)) = hAPP(c_Fun_Ocomp(U_12891,U_12889,tc_prod(U_12890,U_12891),U_12893),c_Product__Type_Osnd(U_12890,U_12891)),
    inference(clausify,[status(thm)],[f_3300_2]) ).

fof(f_3301_1,plain,
    ! [V_g_2,V_f_2,T_e,T_c,T_d,T_b] : c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,V_f_2,V_g_2) = hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_prod(T_d,T_e)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,T_e),tc_fun(T_c,tc_prod(T_d,T_e))),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_prod(T_d,T_e)),tc_fun(tc_fun(T_c,T_e),tc_fun(T_c,tc_prod(T_d,T_e))),T_b),c_COMBB(T_e,tc_prod(T_d,T_e),T_c)),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_e,tc_prod(T_d,T_e)),T_b),c_Product__Type_OPair(T_d,T_e)),V_f_2))),V_g_2)),
    inference(fof_nnf,[status(thm)],[fact_map__pair__def]) ).

fof(f_3301_2,plain,
    ! [U_12899,U_12898,U_12897,U_12896,U_12895,U_12894] : c_Product__Type_Omap__pair(U_12894,U_12895,U_12896,U_12897,U_12898,U_12899) = hAPP(c_Product__Type_Oprod_Oprod__case(U_12894,U_12896,tc_prod(U_12895,U_12897)),hAPP(hAPP(c_COMBC(U_12894,tc_fun(U_12896,U_12897),tc_fun(U_12896,tc_prod(U_12895,U_12897))),hAPP(hAPP(c_COMBB(tc_fun(U_12897,tc_prod(U_12895,U_12897)),tc_fun(tc_fun(U_12896,U_12897),tc_fun(U_12896,tc_prod(U_12895,U_12897))),U_12894),c_COMBB(U_12897,tc_prod(U_12895,U_12897),U_12896)),hAPP(hAPP(c_COMBB(U_12895,tc_fun(U_12897,tc_prod(U_12895,U_12897)),U_12894),c_Product__Type_OPair(U_12895,U_12897)),U_12898))),U_12899)),
    inference(variable_rename,[status(thm)],[f_3301_1]) ).

cnf(f_3301_3,plain,
    c_Product__Type_Omap__pair(U_12894,U_12895,U_12896,U_12897,U_12898,U_12899) = hAPP(c_Product__Type_Oprod_Oprod__case(U_12894,U_12896,tc_prod(U_12895,U_12897)),hAPP(hAPP(c_COMBC(U_12894,tc_fun(U_12896,U_12897),tc_fun(U_12896,tc_prod(U_12895,U_12897))),hAPP(hAPP(c_COMBB(tc_fun(U_12897,tc_prod(U_12895,U_12897)),tc_fun(tc_fun(U_12896,U_12897),tc_fun(U_12896,tc_prod(U_12895,U_12897))),U_12894),c_COMBB(U_12897,tc_prod(U_12895,U_12897),U_12896)),hAPP(hAPP(c_COMBB(U_12895,tc_fun(U_12897,tc_prod(U_12895,U_12897)),U_12894),c_Product__Type_OPair(U_12895,U_12897)),U_12898))),U_12899)),
    inference(clausify,[status(thm)],[f_3301_2]) ).

fof(f_3302_1,plain,
    ! [V_B_H_2,V_B_2,V_g_2,T_d,T_e,V_A_H_2,V_A_2,V_f_2,T_b,T_c] :
      ( hAPP(c_Set_Oimage(tc_prod(T_c,T_e),tc_prod(T_b,T_d),c_Product__Type_Omap__pair(T_c,T_b,T_e,T_d,V_f_2,V_g_2)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_e),V_A_2),hAPP(c_COMBK(tc_fun(T_e,tc_HOL_Obool),T_c),V_B_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_d),V_A_H_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_b),V_B_H_2))
      | hAPP(c_Set_Oimage(T_e,T_d,V_g_2),V_B_2) != V_B_H_2
      | hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) != V_A_H_2 ),
    inference(fof_nnf,[status(thm)],[fact_map__pair__surj__on]) ).

fof(f_3302_2,plain,
    ! [U_12909,U_12908,U_12907,U_12906,U_12905,U_12904,U_12903,U_12902,U_12901,U_12900] :
      ( hAPP(c_Set_Oimage(tc_prod(U_12900,U_12905),tc_prod(U_12901,U_12906),c_Product__Type_Omap__pair(U_12900,U_12901,U_12905,U_12906,U_12902,U_12907)),hAPP(hAPP(c_Product__Type_OSigma(U_12900,U_12905),U_12903),hAPP(c_COMBK(tc_fun(U_12905,tc_HOL_Obool),U_12900),U_12908))) = hAPP(hAPP(c_Product__Type_OSigma(U_12901,U_12906),U_12904),hAPP(c_COMBK(tc_fun(U_12906,tc_HOL_Obool),U_12901),U_12909))
      | hAPP(c_Set_Oimage(U_12905,U_12906,U_12907),U_12908) != U_12909
      | hAPP(c_Set_Oimage(U_12900,U_12901,U_12902),U_12903) != U_12904 ),
    inference(variable_rename,[status(thm)],[f_3302_1]) ).

cnf(f_3302_3,plain,
    ( hAPP(c_Set_Oimage(tc_prod(U_12900,U_12905),tc_prod(U_12901,U_12906),c_Product__Type_Omap__pair(U_12900,U_12901,U_12905,U_12906,U_12902,U_12907)),hAPP(hAPP(c_Product__Type_OSigma(U_12900,U_12905),U_12903),hAPP(c_COMBK(tc_fun(U_12905,tc_HOL_Obool),U_12900),U_12908))) = hAPP(hAPP(c_Product__Type_OSigma(U_12901,U_12906),U_12904),hAPP(c_COMBK(tc_fun(U_12906,tc_HOL_Obool),U_12901),U_12909))
    | hAPP(c_Set_Oimage(U_12905,U_12906,U_12907),U_12908) != U_12909
    | hAPP(c_Set_Oimage(U_12900,U_12901,U_12902),U_12903) != U_12904 ),
    inference(clausify,[status(thm)],[f_3302_2]) ).

fof(f_3303_1,plain,
    ! [V_R_2,V_g_2,V_f_2,T_e,T_d,V_c_2,T_c,T_b] :
      ( ? [B_x,B_y] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_e)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),B_x),B_y)),V_R_2))
          & V_c_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_y)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_c_2),hAPP(c_Set_Oimage(tc_prod(T_d,T_e),tc_prod(T_b,T_c),c_Product__Type_Omap__pair(T_d,T_b,T_e,T_c,V_f_2,V_g_2)),V_R_2))) ),
    inference(fof_nnf,[status(thm)],[fact_prod__fun__imageE]) ).

fof(f_3303_2,plain,
    ! [U_12919,U_12918,U_12917,U_12916,U_12915,U_12914,U_12913,U_12912] :
      ( ? [U_12911,U_12910] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12915,U_12916)),hAPP(hAPP(c_Product__Type_OPair(U_12915,U_12916),U_12911),U_12910)),U_12919))
          & U_12914 = hAPP(hAPP(c_Product__Type_OPair(U_12912,U_12913),hAPP(U_12917,U_12911)),hAPP(U_12918,U_12910)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12912,U_12913)),U_12914),hAPP(c_Set_Oimage(tc_prod(U_12915,U_12916),tc_prod(U_12912,U_12913),c_Product__Type_Omap__pair(U_12915,U_12912,U_12916,U_12913,U_12917,U_12918)),U_12919))) ),
    inference(variable_rename,[status(thm)],[f_3303_1]) ).

fof(f_3303_3,plain,
    ! [U_12919,U_12918,U_12917,U_12916,U_12915,U_12914,U_12913,U_12912] :
      ( ? [U_12910] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12915,U_12916)),hAPP(hAPP(c_Product__Type_OPair(U_12915,U_12916),sK307(U_12919,U_12918,U_12917,U_12916,U_12915,U_12914,U_12913,U_12912)),U_12910)),U_12919))
          & U_12914 = hAPP(hAPP(c_Product__Type_OPair(U_12912,U_12913),hAPP(U_12917,sK307(U_12919,U_12918,U_12917,U_12916,U_12915,U_12914,U_12913,U_12912))),hAPP(U_12918,U_12910)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12912,U_12913)),U_12914),hAPP(c_Set_Oimage(tc_prod(U_12915,U_12916),tc_prod(U_12912,U_12913),c_Product__Type_Omap__pair(U_12915,U_12912,U_12916,U_12913,U_12917,U_12918)),U_12919))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK307]),skolemize(U_12911,sK307(U_12919,U_12918,U_12917,U_12916,U_12915,U_12914,U_12913,U_12912))],[f_3303_2]) ).

fof(f_3303_4,plain,
    ! [U_12919,U_12918,U_12917,U_12916,U_12915,U_12914,U_12913,U_12912] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12915,U_12916)),hAPP(hAPP(c_Product__Type_OPair(U_12915,U_12916),sK307(U_12919,U_12918,U_12917,U_12916,U_12915,U_12914,U_12913,U_12912)),sK308(U_12919,U_12918,U_12917,U_12916,U_12915,U_12914,U_12913,U_12912))),U_12919))
        & U_12914 = hAPP(hAPP(c_Product__Type_OPair(U_12912,U_12913),hAPP(U_12917,sK307(U_12919,U_12918,U_12917,U_12916,U_12915,U_12914,U_12913,U_12912))),hAPP(U_12918,sK308(U_12919,U_12918,U_12917,U_12916,U_12915,U_12914,U_12913,U_12912))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12912,U_12913)),U_12914),hAPP(c_Set_Oimage(tc_prod(U_12915,U_12916),tc_prod(U_12912,U_12913),c_Product__Type_Omap__pair(U_12915,U_12912,U_12916,U_12913,U_12917,U_12918)),U_12919))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK308]),skolemize(U_12910,sK308(U_12919,U_12918,U_12917,U_12916,U_12915,U_12914,U_12913,U_12912))],[f_3303_3]) ).

cnf(f_3303_5,plain,
    ( U_12914 = hAPP(hAPP(c_Product__Type_OPair(U_12912,U_12913),hAPP(U_12917,sK307(U_12919,U_12918,U_12917,U_12916,U_12915,U_12914,U_12913,U_12912))),hAPP(U_12918,sK308(U_12919,U_12918,U_12917,U_12916,U_12915,U_12914,U_12913,U_12912)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12912,U_12913)),U_12914),hAPP(c_Set_Oimage(tc_prod(U_12915,U_12916),tc_prod(U_12912,U_12913),c_Product__Type_Omap__pair(U_12915,U_12912,U_12916,U_12913,U_12917,U_12918)),U_12919))) ),
    inference(clausify,[status(thm)],[f_3303_4]) ).

cnf(f_3303_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12915,U_12916)),hAPP(hAPP(c_Product__Type_OPair(U_12915,U_12916),sK307(U_12919,U_12918,U_12917,U_12916,U_12915,U_12914,U_12913,U_12912)),sK308(U_12919,U_12918,U_12917,U_12916,U_12915,U_12914,U_12913,U_12912))),U_12919))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12912,U_12913)),U_12914),hAPP(c_Set_Oimage(tc_prod(U_12915,U_12916),tc_prod(U_12912,U_12913),c_Product__Type_Omap__pair(U_12915,U_12912,U_12916,U_12913,U_12917,U_12918)),U_12919))) ),
    inference(clausify,[status(thm)],[f_3303_4]) ).

fof(f_3304_1,plain,
    ! [V_r_2,V_A_2,T_b] :
      ( ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
        | ? [B_x] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) )
      & ( ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2))
              | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) )
        | ~ c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_refl__on__def]) ).

fof(f_3304_2,plain,
    ! [U_12924,U_12923,U_12922] :
      ( ( c_Relation_Orefl__on(U_12922,U_12923,U_12924)
        | ? [U_12921] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12922,U_12922)),hAPP(hAPP(c_Product__Type_OPair(U_12922,U_12922),U_12921),U_12921)),U_12924))
            & hBOOL(hAPP(hAPP(c_member(U_12922),U_12921),U_12923)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12922,U_12922),tc_HOL_Obool)),U_12924),hAPP(hAPP(c_Product__Type_OSigma(U_12922,U_12922),U_12923),hAPP(c_COMBK(tc_fun(U_12922,tc_HOL_Obool),U_12922),U_12923)))) )
      & ( ( ! [U_12920] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12922,U_12922)),hAPP(hAPP(c_Product__Type_OPair(U_12922,U_12922),U_12920),U_12920)),U_12924))
              | ~ hBOOL(hAPP(hAPP(c_member(U_12922),U_12920),U_12923)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12922,U_12922),tc_HOL_Obool)),U_12924),hAPP(hAPP(c_Product__Type_OSigma(U_12922,U_12922),U_12923),hAPP(c_COMBK(tc_fun(U_12922,tc_HOL_Obool),U_12922),U_12923)))) )
        | ~ c_Relation_Orefl__on(U_12922,U_12923,U_12924) ) ),
    inference(variable_rename,[status(thm)],[f_3304_1]) ).

fof(f_3304_3,plain,
    ( ! [U_12930,U_12928,U_12926] :
        ( c_Relation_Orefl__on(U_12926,U_12928,U_12930)
        | ? [U_12921] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12926,U_12926)),hAPP(hAPP(c_Product__Type_OPair(U_12926,U_12926),U_12921),U_12921)),U_12930))
            & hBOOL(hAPP(hAPP(c_member(U_12926),U_12921),U_12928)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12926,U_12926),tc_HOL_Obool)),U_12930),hAPP(hAPP(c_Product__Type_OSigma(U_12926,U_12926),U_12928),hAPP(c_COMBK(tc_fun(U_12926,tc_HOL_Obool),U_12926),U_12928)))) )
    & ! [U_12929,U_12927,U_12925] :
        ( ( ! [U_12920] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12925,U_12925)),hAPP(hAPP(c_Product__Type_OPair(U_12925,U_12925),U_12920),U_12920)),U_12929))
              | ~ hBOOL(hAPP(hAPP(c_member(U_12925),U_12920),U_12927)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12925,U_12925),tc_HOL_Obool)),U_12929),hAPP(hAPP(c_Product__Type_OSigma(U_12925,U_12925),U_12927),hAPP(c_COMBK(tc_fun(U_12925,tc_HOL_Obool),U_12925),U_12927)))) )
        | ~ c_Relation_Orefl__on(U_12925,U_12927,U_12929) ) ),
    inference(miniscope,[status(thm)],[f_3304_2]) ).

fof(f_3304_4,plain,
    ( ! [U_12930,U_12928,U_12926] :
        ( c_Relation_Orefl__on(U_12926,U_12928,U_12930)
        | ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12926,U_12926)),hAPP(hAPP(c_Product__Type_OPair(U_12926,U_12926),sK309(U_12930,U_12928,U_12926)),sK309(U_12930,U_12928,U_12926))),U_12930))
          & hBOOL(hAPP(hAPP(c_member(U_12926),sK309(U_12930,U_12928,U_12926)),U_12928)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12926,U_12926),tc_HOL_Obool)),U_12930),hAPP(hAPP(c_Product__Type_OSigma(U_12926,U_12926),U_12928),hAPP(c_COMBK(tc_fun(U_12926,tc_HOL_Obool),U_12926),U_12928)))) )
    & ! [U_12929,U_12927,U_12925] :
        ( ( ! [U_12920] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12925,U_12925)),hAPP(hAPP(c_Product__Type_OPair(U_12925,U_12925),U_12920),U_12920)),U_12929))
              | ~ hBOOL(hAPP(hAPP(c_member(U_12925),U_12920),U_12927)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12925,U_12925),tc_HOL_Obool)),U_12929),hAPP(hAPP(c_Product__Type_OSigma(U_12925,U_12925),U_12927),hAPP(c_COMBK(tc_fun(U_12925,tc_HOL_Obool),U_12925),U_12927)))) )
        | ~ c_Relation_Orefl__on(U_12925,U_12927,U_12929) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK309]),skolemize(U_12921,sK309(U_12930,U_12928,U_12926))],[f_3304_3]) ).

cnf(f_3304_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12925,U_12925),tc_HOL_Obool)),U_12929),hAPP(hAPP(c_Product__Type_OSigma(U_12925,U_12925),U_12927),hAPP(c_COMBK(tc_fun(U_12925,tc_HOL_Obool),U_12925),U_12927))))
    | ~ c_Relation_Orefl__on(U_12925,U_12927,U_12929) ),
    inference(clausify,[status(thm)],[f_3304_4]) ).

cnf(f_3304_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12925,U_12925)),hAPP(hAPP(c_Product__Type_OPair(U_12925,U_12925),U_12920),U_12920)),U_12929))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12925),U_12920),U_12927))
    | ~ c_Relation_Orefl__on(U_12925,U_12927,U_12929) ),
    inference(clausify,[status(thm)],[f_3304_4]) ).

cnf(f_3304_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12926),sK309(U_12930,U_12928,U_12926)),U_12928))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12926,U_12926),tc_HOL_Obool)),U_12930),hAPP(hAPP(c_Product__Type_OSigma(U_12926,U_12926),U_12928),hAPP(c_COMBK(tc_fun(U_12926,tc_HOL_Obool),U_12926),U_12928))))
    | c_Relation_Orefl__on(U_12926,U_12928,U_12930) ),
    inference(clausify,[status(thm)],[f_3304_4]) ).

cnf(f_3304_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12926,U_12926)),hAPP(hAPP(c_Product__Type_OPair(U_12926,U_12926),sK309(U_12930,U_12928,U_12926)),sK309(U_12930,U_12928,U_12926))),U_12930))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12926,U_12926),tc_HOL_Obool)),U_12930),hAPP(hAPP(c_Product__Type_OSigma(U_12926,U_12926),U_12928),hAPP(c_COMBK(tc_fun(U_12926,tc_HOL_Obool),U_12926),U_12928))))
    | c_Relation_Orefl__on(U_12926,U_12928,U_12930) ),
    inference(clausify,[status(thm)],[f_3304_4]) ).

fof(f_3305_1,plain,
    ! [V_i_2,V_M_2] :
      ( hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),V_M_2))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_i_2)))) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_M_2))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,V_i_2)))))
      | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__less__Suc2]) ).

fof(f_3305_2,plain,
    ! [U_12932,U_12931] :
      ( hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),U_12931))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_12932)))) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),U_12931))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,U_12932)))))
      | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12931)) ),
    inference(variable_rename,[status(thm)],[f_3305_1]) ).

cnf(f_3305_3,plain,
    ( hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),U_12931))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_12932)))) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),U_12931))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,U_12932)))))
    | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12931)) ),
    inference(clausify,[status(thm)],[f_3305_2]) ).

fof(f_3306_1,plain,
    ! [T_b,V_a_2,V_P_2] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2)))
      | ~ hBOOL(hAPP(V_P_2,V_a_2)) ),
    inference(fof_nnf,[status(thm)],[fact_CollectI]) ).

fof(f_3306_2,plain,
    ! [U_12935,U_12934,U_12933] :
      ( hBOOL(hAPP(hAPP(c_member(U_12935),U_12934),hAPP(c_Set_OCollect(U_12935),U_12933)))
      | ~ hBOOL(hAPP(U_12933,U_12934)) ),
    inference(variable_rename,[status(thm)],[f_3306_1]) ).

cnf(f_3306_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12935),U_12934),hAPP(c_Set_OCollect(U_12935),U_12933)))
    | ~ hBOOL(hAPP(U_12933,U_12934)) ),
    inference(clausify,[status(thm)],[f_3306_2]) ).

fof(f_3307_1,plain,
    ! [V_Q_2,V_P_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_P_2)),V_Q_2))))
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Q_2)))
        & ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_finite__Collect__conjI]) ).

fof(f_3307_2,plain,
    ! [U_12938,U_12937,U_12936] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12936),hAPP(c_Set_OCollect(U_12936),hAPP(hAPP(c_COMBS(U_12936,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12936),c_fconj),U_12937)),U_12938))))
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12936),hAPP(c_Set_OCollect(U_12936),U_12938)))
        & ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12936),hAPP(c_Set_OCollect(U_12936),U_12937))) ) ),
    inference(variable_rename,[status(thm)],[f_3307_1]) ).

cnf(f_3307_3,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12936),hAPP(c_Set_OCollect(U_12936),U_12937)))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_12936),hAPP(c_Set_OCollect(U_12936),hAPP(hAPP(c_COMBS(U_12936,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12936),c_fconj),U_12937)),U_12938)))) ),
    inference(clausify,[status(thm)],[f_3307_2]) ).

cnf(f_3307_4,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12936),hAPP(c_Set_OCollect(U_12936),U_12938)))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_12936),hAPP(c_Set_OCollect(U_12936),hAPP(hAPP(c_COMBS(U_12936,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12936),c_fconj),U_12937)),U_12938)))) ),
    inference(clausify,[status(thm)],[f_3307_2]) ).

fof(f_3308_1,plain,
    ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_k_2)))),
    inference(fof_nnf,[status(thm)],[fact_finite__Collect__less__nat]) ).

fof(f_3308_2,plain,
    ! [U_12939] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_12939)))),
    inference(variable_rename,[status(thm)],[f_3308_1]) ).

cnf(f_3308_3,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_12939)))),
    inference(clausify,[status(thm)],[f_3308_2]) ).

fof(f_3309_1,plain,
    ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),V_k_2)))),
    inference(fof_nnf,[status(thm)],[fact_finite__Collect__le__nat]) ).

fof(f_3309_2,plain,
    ! [U_12940] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),U_12940)))),
    inference(variable_rename,[status(thm)],[f_3309_1]) ).

cnf(f_3309_3,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),U_12940)))),
    inference(clausify,[status(thm)],[f_3309_2]) ).

fof(f_3310_1,plain,
    ! [V_Q_2,V_P_2,T_c,T_b] : hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_P_2))),V_Q_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_OCollect(T_b),V_P_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_OCollect(T_c),V_Q_2))),
    inference(fof_nnf,[status(thm)],[fact_Collect__split]) ).

fof(f_3310_2,plain,
    ! [U_12944,U_12943,U_12942,U_12941] : hAPP(c_Set_OCollect(tc_prod(U_12941,U_12942)),hAPP(c_Product__Type_Oprod_Oprod__case(U_12941,U_12942,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_12941,tc_fun(U_12942,tc_HOL_Obool),tc_fun(U_12942,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_12942,tc_HOL_Obool),tc_fun(U_12942,tc_HOL_Obool)),U_12941),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_12942)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12941),c_fconj),U_12943))),U_12944))) = hAPP(hAPP(c_Product__Type_OSigma(U_12941,U_12942),hAPP(c_Set_OCollect(U_12941),U_12943)),hAPP(c_COMBK(tc_fun(U_12942,tc_HOL_Obool),U_12941),hAPP(c_Set_OCollect(U_12942),U_12944))),
    inference(variable_rename,[status(thm)],[f_3310_1]) ).

cnf(f_3310_3,plain,
    hAPP(c_Set_OCollect(tc_prod(U_12941,U_12942)),hAPP(c_Product__Type_Oprod_Oprod__case(U_12941,U_12942,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_12941,tc_fun(U_12942,tc_HOL_Obool),tc_fun(U_12942,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_12942,tc_HOL_Obool),tc_fun(U_12942,tc_HOL_Obool)),U_12941),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_12942)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12941),c_fconj),U_12943))),U_12944))) = hAPP(hAPP(c_Product__Type_OSigma(U_12941,U_12942),hAPP(c_Set_OCollect(U_12941),U_12943)),hAPP(c_COMBK(tc_fun(U_12942,tc_HOL_Obool),U_12941),hAPP(c_Set_OCollect(U_12942),U_12944))),
    inference(clausify,[status(thm)],[f_3310_2]) ).

fof(f_3311_1,plain,
    ! [V_Q_2,V_P_2,T_c,T_b] : hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_P_2))),V_Q_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_OCollect(T_b),V_P_2)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_OCollect(T_c)),V_Q_2)),
    inference(fof_nnf,[status(thm)],[fact_SetCompr__Sigma__eq]) ).

fof(f_3311_2,plain,
    ! [U_12948,U_12947,U_12946,U_12945] : hAPP(c_Set_OCollect(tc_prod(U_12945,U_12946)),hAPP(c_Product__Type_Oprod_Oprod__case(U_12945,U_12946,tc_HOL_Obool),hAPP(hAPP(c_COMBS(U_12945,tc_fun(U_12946,tc_HOL_Obool),tc_fun(U_12946,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_12946,tc_HOL_Obool),tc_fun(U_12946,tc_HOL_Obool)),U_12945),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_12946)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12945),c_fconj),U_12947))),U_12948))) = hAPP(hAPP(c_Product__Type_OSigma(U_12945,U_12946),hAPP(c_Set_OCollect(U_12945),U_12947)),hAPP(hAPP(c_COMBB(tc_fun(U_12946,tc_HOL_Obool),tc_fun(U_12946,tc_HOL_Obool),U_12945),c_Set_OCollect(U_12946)),U_12948)),
    inference(variable_rename,[status(thm)],[f_3311_1]) ).

cnf(f_3311_3,plain,
    hAPP(c_Set_OCollect(tc_prod(U_12945,U_12946)),hAPP(c_Product__Type_Oprod_Oprod__case(U_12945,U_12946,tc_HOL_Obool),hAPP(hAPP(c_COMBS(U_12945,tc_fun(U_12946,tc_HOL_Obool),tc_fun(U_12946,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_12946,tc_HOL_Obool),tc_fun(U_12946,tc_HOL_Obool)),U_12945),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_12946)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12945),c_fconj),U_12947))),U_12948))) = hAPP(hAPP(c_Product__Type_OSigma(U_12945,U_12946),hAPP(c_Set_OCollect(U_12945),U_12947)),hAPP(hAPP(c_COMBB(tc_fun(U_12946,tc_HOL_Obool),tc_fun(U_12946,tc_HOL_Obool),U_12945),c_Set_OCollect(U_12946)),U_12948)),
    inference(clausify,[status(thm)],[f_3311_2]) ).

fof(f_3312_1,plain,
    ! [V_P_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_P_2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_P_2)),
    inference(fof_nnf,[status(thm)],[fact_Collect__neg__eq]) ).

fof(f_3312_2,plain,
    ! [U_12950,U_12949] : hAPP(c_Set_OCollect(U_12949),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_12949),c_fNot),U_12950)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12949,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_12949),U_12950)),
    inference(variable_rename,[status(thm)],[f_3312_1]) ).

cnf(f_3312_3,plain,
    hAPP(c_Set_OCollect(U_12949),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_12949),c_fNot),U_12950)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12949,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_12949),U_12950)),
    inference(clausify,[status(thm)],[f_3312_2]) ).

fof(f_3313_1,plain,
    ! [V_P_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(c_Set_OCollect(T_c),V_P_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(T_c,tc_HOL_Obool,T_b),V_P_2),V_f_2)),
    inference(fof_nnf,[status(thm)],[fact_vimage__Collect__eq]) ).

fof(f_3313_2,plain,
    ! [U_12954,U_12953,U_12952,U_12951] : hAPP(c_Set_Ovimage(U_12951,U_12952,U_12953),hAPP(c_Set_OCollect(U_12952),U_12954)) = hAPP(c_Set_OCollect(U_12951),hAPP(hAPP(c_COMBB(U_12952,tc_HOL_Obool,U_12951),U_12954),U_12953)),
    inference(variable_rename,[status(thm)],[f_3313_1]) ).

cnf(f_3313_3,plain,
    hAPP(c_Set_Ovimage(U_12951,U_12952,U_12953),hAPP(c_Set_OCollect(U_12952),U_12954)) = hAPP(c_Set_OCollect(U_12951),hAPP(hAPP(c_COMBB(U_12952,tc_HOL_Obool,U_12951),U_12954),U_12953)),
    inference(clausify,[status(thm)],[f_3313_2]) ).

fof(f_3314_1,plain,
    ! [V_P_2,V_a_2,T_b] :
      ( hBOOL(hAPP(V_P_2,V_a_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2))) ),
    inference(fof_nnf,[status(thm)],[fact_CollectE]) ).

fof(f_3314_2,plain,
    ! [U_12957,U_12956,U_12955] :
      ( hBOOL(hAPP(U_12957,U_12956))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12955),U_12956),hAPP(c_Set_OCollect(U_12955),U_12957))) ),
    inference(variable_rename,[status(thm)],[f_3314_1]) ).

fof(f_3314_3,plain,
    ! [U_12957,U_12956] :
      ( ! [U_12955] : ~ hBOOL(hAPP(hAPP(c_member(U_12955),U_12956),hAPP(c_Set_OCollect(U_12955),U_12957)))
      | hBOOL(hAPP(U_12957,U_12956)) ),
    inference(miniscope,[status(thm)],[f_3314_2]) ).

cnf(f_3314_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_12955),U_12956),hAPP(c_Set_OCollect(U_12955),U_12957)))
    | hBOOL(hAPP(U_12957,U_12956)) ),
    inference(clausify,[status(thm)],[f_3314_3]) ).

fof(f_3315_1,plain,
    ! [V_P_2,V_a_2,T_b] :
      ( hBOOL(hAPP(V_P_2,V_a_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2))) ),
    inference(fof_nnf,[status(thm)],[fact_CollectD]) ).

fof(f_3315_2,plain,
    ! [U_12960,U_12959,U_12958] :
      ( hBOOL(hAPP(U_12960,U_12959))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12958),U_12959),hAPP(c_Set_OCollect(U_12958),U_12960))) ),
    inference(variable_rename,[status(thm)],[f_3315_1]) ).

fof(f_3315_3,plain,
    ! [U_12960,U_12959] :
      ( ! [U_12958] : ~ hBOOL(hAPP(hAPP(c_member(U_12958),U_12959),hAPP(c_Set_OCollect(U_12958),U_12960)))
      | hBOOL(hAPP(U_12960,U_12959)) ),
    inference(miniscope,[status(thm)],[f_3315_2]) ).

cnf(f_3315_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_12958),U_12959),hAPP(c_Set_OCollect(U_12958),U_12960)))
    | hBOOL(hAPP(U_12960,U_12959)) ),
    inference(clausify,[status(thm)],[f_3315_3]) ).

fof(f_3316_1,plain,
    ! [V_P_2,V_a_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2)))
        | ~ hBOOL(hAPP(V_P_2,V_a_2)) )
      & ( hBOOL(hAPP(V_P_2,V_a_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_mem__Collect__eq]) ).

fof(f_3316_2,plain,
    ! [U_12963,U_12962,U_12961] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_12961),U_12962),hAPP(c_Set_OCollect(U_12961),U_12963)))
        | ~ hBOOL(hAPP(U_12963,U_12962)) )
      & ( hBOOL(hAPP(U_12963,U_12962))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12961),U_12962),hAPP(c_Set_OCollect(U_12961),U_12963))) ) ),
    inference(variable_rename,[status(thm)],[f_3316_1]) ).

fof(f_3316_3,plain,
    ( ! [U_12969,U_12967] :
        ( ! [U_12965] : hBOOL(hAPP(hAPP(c_member(U_12965),U_12967),hAPP(c_Set_OCollect(U_12965),U_12969)))
        | ~ hBOOL(hAPP(U_12969,U_12967)) )
    & ! [U_12968,U_12966] :
        ( ! [U_12964] : ~ hBOOL(hAPP(hAPP(c_member(U_12964),U_12966),hAPP(c_Set_OCollect(U_12964),U_12968)))
        | hBOOL(hAPP(U_12968,U_12966)) ) ),
    inference(miniscope,[status(thm)],[f_3316_2]) ).

cnf(f_3316_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_12964),U_12966),hAPP(c_Set_OCollect(U_12964),U_12968)))
    | hBOOL(hAPP(U_12968,U_12966)) ),
    inference(clausify,[status(thm)],[f_3316_3]) ).

cnf(f_3316_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12965),U_12967),hAPP(c_Set_OCollect(U_12965),U_12969)))
    | ~ hBOOL(hAPP(U_12969,U_12967)) ),
    inference(clausify,[status(thm)],[f_3316_3]) ).

fof(f_3317_1,plain,
    ! [V_A_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)) = V_A_2,
    inference(fof_nnf,[status(thm)],[fact_Collect__mem__eq]) ).

fof(f_3317_2,plain,
    ! [U_12971,U_12970] : hAPP(c_Set_OCollect(U_12970),hAPP(hAPP(c_COMBC(U_12970,tc_fun(U_12970,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12970)),U_12971)) = U_12971,
    inference(variable_rename,[status(thm)],[f_3317_1]) ).

cnf(f_3317_3,plain,
    hAPP(c_Set_OCollect(U_12970),hAPP(hAPP(c_COMBC(U_12970,tc_fun(U_12970,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12970)),U_12971)) = U_12971,
    inference(clausify,[status(thm)],[f_3317_2]) ).

fof(f_3318_1,plain,
    ! [V_P_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2)))),V_P_2)),
    inference(fof_nnf,[status(thm)],[fact_insert__Collect]) ).

fof(f_3318_2,plain,
    ! [U_12974,U_12973,U_12972] : hAPP(hAPP(c_Set_Oinsert(U_12972),U_12973),hAPP(c_Set_OCollect(U_12972),U_12974)) = hAPP(c_Set_OCollect(U_12972),hAPP(hAPP(c_COMBS(U_12972,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12972),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_12972),c_fNot),hAPP(hAPP(c_COMBC(U_12972,U_12972,tc_HOL_Obool),c_fequal),U_12973)))),U_12974)),
    inference(variable_rename,[status(thm)],[f_3318_1]) ).

cnf(f_3318_3,plain,
    hAPP(hAPP(c_Set_Oinsert(U_12972),U_12973),hAPP(c_Set_OCollect(U_12972),U_12974)) = hAPP(c_Set_OCollect(U_12972),hAPP(hAPP(c_COMBS(U_12972,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12972),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_12972),c_fNot),hAPP(hAPP(c_COMBC(U_12972,U_12972,tc_HOL_Obool),c_fequal),U_12973)))),U_12974)),
    inference(clausify,[status(thm)],[f_3318_2]) ).

fof(f_3319_1,plain,
    ! [V_Q_2,V_P_2,T_b] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),V_P_2)),V_Q_2))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Q_2)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2))) )
      & ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Q_2)))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2))) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),V_P_2)),V_Q_2)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_finite__Collect__disjI]) ).

fof(f_3319_2,plain,
    ! [U_12977,U_12976,U_12975] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12975),hAPP(c_Set_OCollect(U_12975),hAPP(hAPP(c_COMBS(U_12975,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12975),c_fdisj),U_12976)),U_12977))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12975),hAPP(c_Set_OCollect(U_12975),U_12977)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12975),hAPP(c_Set_OCollect(U_12975),U_12976))) )
      & ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12975),hAPP(c_Set_OCollect(U_12975),U_12977)))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_12975),hAPP(c_Set_OCollect(U_12975),U_12976))) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12975),hAPP(c_Set_OCollect(U_12975),hAPP(hAPP(c_COMBS(U_12975,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12975),c_fdisj),U_12976)),U_12977)))) ) ),
    inference(variable_rename,[status(thm)],[f_3319_1]) ).

fof(f_3319_3,plain,
    ( ! [U_12983,U_12981,U_12979] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12979),hAPP(c_Set_OCollect(U_12979),hAPP(hAPP(c_COMBS(U_12979,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12979),c_fdisj),U_12981)),U_12983))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12979),hAPP(c_Set_OCollect(U_12979),U_12983)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12979),hAPP(c_Set_OCollect(U_12979),U_12981))) )
    & ! [U_12982,U_12980,U_12978] :
        ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12978),hAPP(c_Set_OCollect(U_12978),U_12982)))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_12978),hAPP(c_Set_OCollect(U_12978),U_12980))) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12978),hAPP(c_Set_OCollect(U_12978),hAPP(hAPP(c_COMBS(U_12978,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12978),c_fdisj),U_12980)),U_12982)))) ) ),
    inference(miniscope,[status(thm)],[f_3319_2]) ).

cnf(f_3319_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12978),hAPP(c_Set_OCollect(U_12978),U_12980)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12978),hAPP(c_Set_OCollect(U_12978),hAPP(hAPP(c_COMBS(U_12978,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12978),c_fdisj),U_12980)),U_12982)))) ),
    inference(clausify,[status(thm)],[f_3319_3]) ).

cnf(f_3319_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12978),hAPP(c_Set_OCollect(U_12978),U_12982)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12978),hAPP(c_Set_OCollect(U_12978),hAPP(hAPP(c_COMBS(U_12978,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12978),c_fdisj),U_12980)),U_12982)))) ),
    inference(clausify,[status(thm)],[f_3319_3]) ).

cnf(f_3319_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12979),hAPP(c_Set_OCollect(U_12979),hAPP(hAPP(c_COMBS(U_12979,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12979),c_fdisj),U_12981)),U_12983))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12979),hAPP(c_Set_OCollect(U_12979),U_12983)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12979),hAPP(c_Set_OCollect(U_12979),U_12981))) ),
    inference(clausify,[status(thm)],[f_3319_3]) ).

fof(f_3320_1,plain,
    ! [V_P_2,T_b] : hAPP(c_Set_OCollect(T_b),V_P_2) = V_P_2,
    inference(fof_nnf,[status(thm)],[fact_Collect__def]) ).

fof(f_3320_2,plain,
    ! [U_12985,U_12984] : hAPP(c_Set_OCollect(U_12984),U_12985) = U_12985,
    inference(variable_rename,[status(thm)],[f_3320_1]) ).

cnf(f_3320_3,plain,
    hAPP(c_Set_OCollect(U_12984),U_12985) = U_12985,
    inference(clausify,[status(thm)],[f_3320_2]) ).

fof(f_3321_1,plain,
    ! [V_Q_2,V_P_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_P_2)),V_Q_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_P_2)),hAPP(c_Set_OCollect(T_b),V_Q_2)),
    inference(fof_nnf,[status(thm)],[fact_Collect__conj__eq]) ).

fof(f_3321_2,plain,
    ! [U_12988,U_12987,U_12986] : hAPP(c_Set_OCollect(U_12986),hAPP(hAPP(c_COMBS(U_12986,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12986),c_fconj),U_12987)),U_12988)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12986,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_12986),U_12987)),hAPP(c_Set_OCollect(U_12986),U_12988)),
    inference(variable_rename,[status(thm)],[f_3321_1]) ).

cnf(f_3321_3,plain,
    hAPP(c_Set_OCollect(U_12986),hAPP(hAPP(c_COMBS(U_12986,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12986),c_fconj),U_12987)),U_12988)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12986,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_12986),U_12987)),hAPP(c_Set_OCollect(U_12986),U_12988)),
    inference(clausify,[status(thm)],[f_3321_2]) ).

fof(f_3322_1,plain,
    ! [V_Q_2,V_P_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),V_P_2)),V_Q_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_P_2)),hAPP(c_Set_OCollect(T_b),V_Q_2)),
    inference(fof_nnf,[status(thm)],[fact_Collect__disj__eq]) ).

fof(f_3322_2,plain,
    ! [U_12991,U_12990,U_12989] : hAPP(c_Set_OCollect(U_12989),hAPP(hAPP(c_COMBS(U_12989,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12989),c_fdisj),U_12990)),U_12991)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12989,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_12989),U_12990)),hAPP(c_Set_OCollect(U_12989),U_12991)),
    inference(variable_rename,[status(thm)],[f_3322_1]) ).

cnf(f_3322_3,plain,
    hAPP(c_Set_OCollect(U_12989),hAPP(hAPP(c_COMBS(U_12989,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12989),c_fdisj),U_12990)),U_12991)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12989,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_12989),U_12990)),hAPP(c_Set_OCollect(U_12989),U_12991)),
    inference(clausify,[status(thm)],[f_3322_2]) ).

fof(f_3323_1,plain,
    ! [V_P_2,T_b] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),V_P_2)
        | ? [B_x] : hBOOL(hAPP(V_P_2,B_x)) )
      & ( ! [B_x] : ~ hBOOL(hAPP(V_P_2,B_x))
        | c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) != hAPP(c_Set_OCollect(T_b),V_P_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_empty__Collect__eq]) ).

fof(f_3323_2,plain,
    ! [U_12995,U_12994] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(U_12994,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_12994),U_12995)
        | ? [U_12993] : hBOOL(hAPP(U_12995,U_12993)) )
      & ( ! [U_12992] : ~ hBOOL(hAPP(U_12995,U_12992))
        | c_Orderings_Obot__class_Obot(tc_fun(U_12994,tc_HOL_Obool)) != hAPP(c_Set_OCollect(U_12994),U_12995) ) ),
    inference(variable_rename,[status(thm)],[f_3323_1]) ).

fof(f_3323_3,plain,
    ( ! [U_12999] :
        ( ! [U_12997] : c_Orderings_Obot__class_Obot(tc_fun(U_12997,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_12997),U_12999)
        | ? [U_12993] : hBOOL(hAPP(U_12999,U_12993)) )
    & ! [U_12998] :
        ( ! [U_12996] : c_Orderings_Obot__class_Obot(tc_fun(U_12996,tc_HOL_Obool)) != hAPP(c_Set_OCollect(U_12996),U_12998)
        | ! [U_12992] : ~ hBOOL(hAPP(U_12998,U_12992)) ) ),
    inference(miniscope,[status(thm)],[f_3323_2]) ).

fof(f_3323_4,plain,
    ( ! [U_12999] :
        ( ! [U_12997] : c_Orderings_Obot__class_Obot(tc_fun(U_12997,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_12997),U_12999)
        | hBOOL(hAPP(U_12999,sK310(U_12999))) )
    & ! [U_12998] :
        ( ! [U_12996] : c_Orderings_Obot__class_Obot(tc_fun(U_12996,tc_HOL_Obool)) != hAPP(c_Set_OCollect(U_12996),U_12998)
        | ! [U_12992] : ~ hBOOL(hAPP(U_12998,U_12992)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK310]),skolemize(U_12993,sK310(U_12999))],[f_3323_3]) ).

cnf(f_3323_5,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(U_12996,tc_HOL_Obool)) != hAPP(c_Set_OCollect(U_12996),U_12998)
    | ~ hBOOL(hAPP(U_12998,U_12992)) ),
    inference(clausify,[status(thm)],[f_3323_4]) ).

cnf(f_3323_6,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(U_12997,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_12997),U_12999)
    | hBOOL(hAPP(U_12999,sK310(U_12999))) ),
    inference(clausify,[status(thm)],[f_3323_4]) ).

fof(f_3324_1,plain,
    ! [V_P_2,T_b] :
      ( ( hAPP(c_Set_OCollect(T_b),V_P_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
        | ? [B_x] : hBOOL(hAPP(V_P_2,B_x)) )
      & ( ! [B_x] : ~ hBOOL(hAPP(V_P_2,B_x))
        | hAPP(c_Set_OCollect(T_b),V_P_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Collect__empty__eq]) ).

fof(f_3324_2,plain,
    ! [U_13003,U_13002] :
      ( ( hAPP(c_Set_OCollect(U_13002),U_13003) = c_Orderings_Obot__class_Obot(tc_fun(U_13002,tc_HOL_Obool))
        | ? [U_13001] : hBOOL(hAPP(U_13003,U_13001)) )
      & ( ! [U_13000] : ~ hBOOL(hAPP(U_13003,U_13000))
        | hAPP(c_Set_OCollect(U_13002),U_13003) != c_Orderings_Obot__class_Obot(tc_fun(U_13002,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_3324_1]) ).

fof(f_3324_3,plain,
    ( ! [U_13007] :
        ( ! [U_13005] : hAPP(c_Set_OCollect(U_13005),U_13007) = c_Orderings_Obot__class_Obot(tc_fun(U_13005,tc_HOL_Obool))
        | ? [U_13001] : hBOOL(hAPP(U_13007,U_13001)) )
    & ! [U_13006] :
        ( ! [U_13004] : hAPP(c_Set_OCollect(U_13004),U_13006) != c_Orderings_Obot__class_Obot(tc_fun(U_13004,tc_HOL_Obool))
        | ! [U_13000] : ~ hBOOL(hAPP(U_13006,U_13000)) ) ),
    inference(miniscope,[status(thm)],[f_3324_2]) ).

fof(f_3324_4,plain,
    ( ! [U_13007] :
        ( ! [U_13005] : hAPP(c_Set_OCollect(U_13005),U_13007) = c_Orderings_Obot__class_Obot(tc_fun(U_13005,tc_HOL_Obool))
        | hBOOL(hAPP(U_13007,sK311(U_13007))) )
    & ! [U_13006] :
        ( ! [U_13004] : hAPP(c_Set_OCollect(U_13004),U_13006) != c_Orderings_Obot__class_Obot(tc_fun(U_13004,tc_HOL_Obool))
        | ! [U_13000] : ~ hBOOL(hAPP(U_13006,U_13000)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK311]),skolemize(U_13001,sK311(U_13007))],[f_3324_3]) ).

cnf(f_3324_5,plain,
    ( hAPP(c_Set_OCollect(U_13004),U_13006) != c_Orderings_Obot__class_Obot(tc_fun(U_13004,tc_HOL_Obool))
    | ~ hBOOL(hAPP(U_13006,U_13000)) ),
    inference(clausify,[status(thm)],[f_3324_4]) ).

cnf(f_3324_6,plain,
    ( hAPP(c_Set_OCollect(U_13005),U_13007) = c_Orderings_Obot__class_Obot(tc_fun(U_13005,tc_HOL_Obool))
    | hBOOL(hAPP(U_13007,sK311(U_13007))) ),
    inference(clausify,[status(thm)],[f_3324_4]) ).

fof(f_3325_1,plain,
    ! [T_b] : c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),hAPP(c_COMBK(tc_HOL_Obool,T_b),c_fFalse)),
    inference(fof_nnf,[status(thm)],[fact_empty__def]) ).

fof(f_3325_2,plain,
    ! [U_13008] : c_Orderings_Obot__class_Obot(tc_fun(U_13008,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_13008),hAPP(c_COMBK(tc_HOL_Obool,U_13008),c_fFalse)),
    inference(variable_rename,[status(thm)],[f_3325_1]) ).

cnf(f_3325_3,plain,
    c_Orderings_Obot__class_Obot(tc_fun(U_13008,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_13008),hAPP(c_COMBK(tc_HOL_Obool,U_13008),c_fFalse)),
    inference(clausify,[status(thm)],[f_3325_2]) ).

fof(f_3326_1,plain,
    ! [V_A_2,T_b] : c_Relation_Orefl__on(T_b,V_A_2,c_Relation_OId__on(T_b,V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_refl__on__Id__on]) ).

fof(f_3326_2,plain,
    ! [U_13010,U_13009] : c_Relation_Orefl__on(U_13009,U_13010,c_Relation_OId__on(U_13009,U_13010)),
    inference(variable_rename,[status(thm)],[f_3326_1]) ).

cnf(f_3326_3,plain,
    c_Relation_Orefl__on(U_13009,U_13010,c_Relation_OId__on(U_13009,U_13010)),
    inference(clausify,[status(thm)],[f_3326_2]) ).

fof(f_3327_1,plain,
    ! [T_b] : c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),hAPP(c_COMBK(tc_HOL_Obool,T_b),c_fTrue)),
    inference(fof_nnf,[status(thm)],[fact_UNIV__def]) ).

fof(f_3327_2,plain,
    ! [U_13011] : c_Orderings_Otop__class_Otop(tc_fun(U_13011,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_13011),hAPP(c_COMBK(tc_HOL_Obool,U_13011),c_fTrue)),
    inference(variable_rename,[status(thm)],[f_3327_1]) ).

cnf(f_3327_3,plain,
    c_Orderings_Otop__class_Otop(tc_fun(U_13011,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_13011),hAPP(c_COMBK(tc_HOL_Obool,U_13011),c_fTrue)),
    inference(clausify,[status(thm)],[f_3327_2]) ).

fof(f_3328_1,plain,
    ! [V_B_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),
    inference(fof_nnf,[status(thm)],[fact_insert__compr__raw]) ).

fof(f_3328_2,plain,
    ! [U_13014,U_13013,U_13012] : hAPP(hAPP(c_Set_Oinsert(U_13012),U_13013),U_13014) = hAPP(c_Set_OCollect(U_13012),hAPP(hAPP(c_COMBS(U_13012,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13012),c_fdisj),hAPP(hAPP(c_COMBC(U_13012,U_13012,tc_HOL_Obool),c_fequal),U_13013))),hAPP(hAPP(c_COMBC(U_13012,tc_fun(U_13012,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13012)),U_13014))),
    inference(variable_rename,[status(thm)],[f_3328_1]) ).

cnf(f_3328_3,plain,
    hAPP(hAPP(c_Set_Oinsert(U_13012),U_13013),U_13014) = hAPP(c_Set_OCollect(U_13012),hAPP(hAPP(c_COMBS(U_13012,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13012),c_fdisj),hAPP(hAPP(c_COMBC(U_13012,U_13012,tc_HOL_Obool),c_fequal),U_13013))),hAPP(hAPP(c_COMBC(U_13012,tc_fun(U_13012,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13012)),U_13014))),
    inference(clausify,[status(thm)],[f_3328_2]) ).

fof(f_3329_1,plain,
    ! [V_B_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),
    inference(fof_nnf,[status(thm)],[fact_insert__compr]) ).

fof(f_3329_2,plain,
    ! [U_13017,U_13016,U_13015] : hAPP(hAPP(c_Set_Oinsert(U_13015),U_13016),U_13017) = hAPP(c_Set_OCollect(U_13015),hAPP(hAPP(c_COMBS(U_13015,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13015),c_fdisj),hAPP(hAPP(c_COMBC(U_13015,U_13015,tc_HOL_Obool),c_fequal),U_13016))),hAPP(hAPP(c_COMBC(U_13015,tc_fun(U_13015,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13015)),U_13017))),
    inference(variable_rename,[status(thm)],[f_3329_1]) ).

cnf(f_3329_3,plain,
    hAPP(hAPP(c_Set_Oinsert(U_13015),U_13016),U_13017) = hAPP(c_Set_OCollect(U_13015),hAPP(hAPP(c_COMBS(U_13015,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13015),c_fdisj),hAPP(hAPP(c_COMBC(U_13015,U_13015,tc_HOL_Obool),c_fequal),U_13016))),hAPP(hAPP(c_COMBC(U_13015,tc_fun(U_13015,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13015)),U_13017))),
    inference(clausify,[status(thm)],[f_3329_2]) ).

fof(f_3330_1,plain,
    ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),
    inference(fof_nnf,[status(thm)],[fact_Un__def]) ).

fof(f_3330_2,plain,
    ! [U_13020,U_13019,U_13018] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13018,tc_HOL_Obool)),U_13019),U_13020) = hAPP(c_Set_OCollect(U_13018),hAPP(hAPP(c_COMBS(U_13018,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13018),c_fdisj),hAPP(hAPP(c_COMBC(U_13018,tc_fun(U_13018,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13018)),U_13019))),hAPP(hAPP(c_COMBC(U_13018,tc_fun(U_13018,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13018)),U_13020))),
    inference(variable_rename,[status(thm)],[f_3330_1]) ).

cnf(f_3330_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13018,tc_HOL_Obool)),U_13019),U_13020) = hAPP(c_Set_OCollect(U_13018),hAPP(hAPP(c_COMBS(U_13018,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13018),c_fdisj),hAPP(hAPP(c_COMBC(U_13018,tc_fun(U_13018,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13018)),U_13019))),hAPP(hAPP(c_COMBC(U_13018,tc_fun(U_13018,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13018)),U_13020))),
    inference(clausify,[status(thm)],[f_3330_2]) ).

fof(f_3331_1,plain,
    ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),
    inference(fof_nnf,[status(thm)],[fact_Int__def]) ).

fof(f_3331_2,plain,
    ! [U_13023,U_13022,U_13021] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13021,tc_HOL_Obool)),U_13022),U_13023) = hAPP(c_Set_OCollect(U_13021),hAPP(hAPP(c_COMBS(U_13021,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13021),c_fconj),hAPP(hAPP(c_COMBC(U_13021,tc_fun(U_13021,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13021)),U_13022))),hAPP(hAPP(c_COMBC(U_13021,tc_fun(U_13021,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13021)),U_13023))),
    inference(variable_rename,[status(thm)],[f_3331_1]) ).

cnf(f_3331_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13021,tc_HOL_Obool)),U_13022),U_13023) = hAPP(c_Set_OCollect(U_13021),hAPP(hAPP(c_COMBS(U_13021,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13021),c_fconj),hAPP(hAPP(c_COMBC(U_13021,tc_fun(U_13021,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13021)),U_13022))),hAPP(hAPP(c_COMBC(U_13021,tc_fun(U_13021,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13021)),U_13023))),
    inference(clausify,[status(thm)],[f_3331_2]) ).

fof(f_3332_1,plain,
    ! [V_P_2,V_A_2,V_x_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_P_2))))
        | ~ hBOOL(hAPP(V_P_2,V_x_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) )
      & ( ( hBOOL(hAPP(V_P_2,V_x_2))
          & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) )
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_P_2)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_Int__Collect]) ).

fof(f_3332_2,plain,
    ! [U_13027,U_13026,U_13025,U_13024] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_13024),U_13025),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13024,tc_HOL_Obool)),U_13026),hAPP(c_Set_OCollect(U_13024),U_13027))))
        | ~ hBOOL(hAPP(U_13027,U_13025))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13024),U_13025),U_13026)) )
      & ( ( hBOOL(hAPP(U_13027,U_13025))
          & hBOOL(hAPP(hAPP(c_member(U_13024),U_13025),U_13026)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_13024),U_13025),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13024,tc_HOL_Obool)),U_13026),hAPP(c_Set_OCollect(U_13024),U_13027)))) ) ),
    inference(variable_rename,[status(thm)],[f_3332_1]) ).

fof(f_3332_3,plain,
    ( ! [U_13035,U_13033,U_13031,U_13029] :
        ( hBOOL(hAPP(hAPP(c_member(U_13029),U_13031),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13029,tc_HOL_Obool)),U_13033),hAPP(c_Set_OCollect(U_13029),U_13035))))
        | ~ hBOOL(hAPP(U_13035,U_13031))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13029),U_13031),U_13033)) )
    & ! [U_13034,U_13032,U_13030,U_13028] :
        ( ( hBOOL(hAPP(U_13034,U_13030))
          & hBOOL(hAPP(hAPP(c_member(U_13028),U_13030),U_13032)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_13028),U_13030),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13028,tc_HOL_Obool)),U_13032),hAPP(c_Set_OCollect(U_13028),U_13034)))) ) ),
    inference(miniscope,[status(thm)],[f_3332_2]) ).

cnf(f_3332_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13028),U_13030),U_13032))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13028),U_13030),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13028,tc_HOL_Obool)),U_13032),hAPP(c_Set_OCollect(U_13028),U_13034)))) ),
    inference(clausify,[status(thm)],[f_3332_3]) ).

cnf(f_3332_5,plain,
    ( hBOOL(hAPP(U_13034,U_13030))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13028),U_13030),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13028,tc_HOL_Obool)),U_13032),hAPP(c_Set_OCollect(U_13028),U_13034)))) ),
    inference(clausify,[status(thm)],[f_3332_3]) ).

cnf(f_3332_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13029),U_13031),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13029,tc_HOL_Obool)),U_13033),hAPP(c_Set_OCollect(U_13029),U_13035))))
    | ~ hBOOL(hAPP(U_13035,U_13031))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13029),U_13031),U_13033)) ),
    inference(clausify,[status(thm)],[f_3332_3]) ).

fof(f_3333_1,plain,
    ! [T_b,V_a_2,V_P_2] :
      ( ( hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_P_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
        | hBOOL(hAPP(V_P_2,V_a_2)) )
      & ( hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_P_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))
        | ~ hBOOL(hAPP(V_P_2,V_a_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Collect__conv__if]) ).

fof(f_3333_2,plain,
    ! [U_13038,U_13037,U_13036] :
      ( ( hAPP(c_Set_OCollect(U_13038),hAPP(hAPP(c_COMBS(U_13038,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13038),c_fconj),hAPP(hAPP(c_COMBC(U_13038,U_13038,tc_HOL_Obool),c_fequal),U_13037))),U_13036)) = c_Orderings_Obot__class_Obot(tc_fun(U_13038,tc_HOL_Obool))
        | hBOOL(hAPP(U_13036,U_13037)) )
      & ( hAPP(c_Set_OCollect(U_13038),hAPP(hAPP(c_COMBS(U_13038,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13038),c_fconj),hAPP(hAPP(c_COMBC(U_13038,U_13038,tc_HOL_Obool),c_fequal),U_13037))),U_13036)) = hAPP(hAPP(c_Set_Oinsert(U_13038),U_13037),c_Orderings_Obot__class_Obot(tc_fun(U_13038,tc_HOL_Obool)))
        | ~ hBOOL(hAPP(U_13036,U_13037)) ) ),
    inference(variable_rename,[status(thm)],[f_3333_1]) ).

fof(f_3333_3,plain,
    ( ! [U_13044,U_13042,U_13040] :
        ( hAPP(c_Set_OCollect(U_13044),hAPP(hAPP(c_COMBS(U_13044,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13044),c_fconj),hAPP(hAPP(c_COMBC(U_13044,U_13044,tc_HOL_Obool),c_fequal),U_13042))),U_13040)) = c_Orderings_Obot__class_Obot(tc_fun(U_13044,tc_HOL_Obool))
        | hBOOL(hAPP(U_13040,U_13042)) )
    & ! [U_13043,U_13041,U_13039] :
        ( hAPP(c_Set_OCollect(U_13043),hAPP(hAPP(c_COMBS(U_13043,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13043),c_fconj),hAPP(hAPP(c_COMBC(U_13043,U_13043,tc_HOL_Obool),c_fequal),U_13041))),U_13039)) = hAPP(hAPP(c_Set_Oinsert(U_13043),U_13041),c_Orderings_Obot__class_Obot(tc_fun(U_13043,tc_HOL_Obool)))
        | ~ hBOOL(hAPP(U_13039,U_13041)) ) ),
    inference(miniscope,[status(thm)],[f_3333_2]) ).

cnf(f_3333_4,plain,
    ( hAPP(c_Set_OCollect(U_13043),hAPP(hAPP(c_COMBS(U_13043,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13043),c_fconj),hAPP(hAPP(c_COMBC(U_13043,U_13043,tc_HOL_Obool),c_fequal),U_13041))),U_13039)) = hAPP(hAPP(c_Set_Oinsert(U_13043),U_13041),c_Orderings_Obot__class_Obot(tc_fun(U_13043,tc_HOL_Obool)))
    | ~ hBOOL(hAPP(U_13039,U_13041)) ),
    inference(clausify,[status(thm)],[f_3333_3]) ).

cnf(f_3333_5,plain,
    ( hAPP(c_Set_OCollect(U_13044),hAPP(hAPP(c_COMBS(U_13044,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13044),c_fconj),hAPP(hAPP(c_COMBC(U_13044,U_13044,tc_HOL_Obool),c_fequal),U_13042))),U_13040)) = c_Orderings_Obot__class_Obot(tc_fun(U_13044,tc_HOL_Obool))
    | hBOOL(hAPP(U_13040,U_13042)) ),
    inference(clausify,[status(thm)],[f_3333_3]) ).

fof(f_3334_1,plain,
    ! [T_b,V_a_2,V_P_2] :
      ( ( hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_a_2))),V_P_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
        | hBOOL(hAPP(V_P_2,V_a_2)) )
      & ( hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_a_2))),V_P_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))
        | ~ hBOOL(hAPP(V_P_2,V_a_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Collect__conv__if2]) ).

fof(f_3334_2,plain,
    ! [U_13047,U_13046,U_13045] :
      ( ( hAPP(c_Set_OCollect(U_13047),hAPP(hAPP(c_COMBS(U_13047,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13047),c_fconj),hAPP(c_fequal,U_13046))),U_13045)) = c_Orderings_Obot__class_Obot(tc_fun(U_13047,tc_HOL_Obool))
        | hBOOL(hAPP(U_13045,U_13046)) )
      & ( hAPP(c_Set_OCollect(U_13047),hAPP(hAPP(c_COMBS(U_13047,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13047),c_fconj),hAPP(c_fequal,U_13046))),U_13045)) = hAPP(hAPP(c_Set_Oinsert(U_13047),U_13046),c_Orderings_Obot__class_Obot(tc_fun(U_13047,tc_HOL_Obool)))
        | ~ hBOOL(hAPP(U_13045,U_13046)) ) ),
    inference(variable_rename,[status(thm)],[f_3334_1]) ).

fof(f_3334_3,plain,
    ( ! [U_13053,U_13051,U_13049] :
        ( hAPP(c_Set_OCollect(U_13053),hAPP(hAPP(c_COMBS(U_13053,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13053),c_fconj),hAPP(c_fequal,U_13051))),U_13049)) = c_Orderings_Obot__class_Obot(tc_fun(U_13053,tc_HOL_Obool))
        | hBOOL(hAPP(U_13049,U_13051)) )
    & ! [U_13052,U_13050,U_13048] :
        ( hAPP(c_Set_OCollect(U_13052),hAPP(hAPP(c_COMBS(U_13052,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13052),c_fconj),hAPP(c_fequal,U_13050))),U_13048)) = hAPP(hAPP(c_Set_Oinsert(U_13052),U_13050),c_Orderings_Obot__class_Obot(tc_fun(U_13052,tc_HOL_Obool)))
        | ~ hBOOL(hAPP(U_13048,U_13050)) ) ),
    inference(miniscope,[status(thm)],[f_3334_2]) ).

cnf(f_3334_4,plain,
    ( hAPP(c_Set_OCollect(U_13052),hAPP(hAPP(c_COMBS(U_13052,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13052),c_fconj),hAPP(c_fequal,U_13050))),U_13048)) = hAPP(hAPP(c_Set_Oinsert(U_13052),U_13050),c_Orderings_Obot__class_Obot(tc_fun(U_13052,tc_HOL_Obool)))
    | ~ hBOOL(hAPP(U_13048,U_13050)) ),
    inference(clausify,[status(thm)],[f_3334_3]) ).

cnf(f_3334_5,plain,
    ( hAPP(c_Set_OCollect(U_13053),hAPP(hAPP(c_COMBS(U_13053,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13053),c_fconj),hAPP(c_fequal,U_13051))),U_13049)) = c_Orderings_Obot__class_Obot(tc_fun(U_13053,tc_HOL_Obool))
    | hBOOL(hAPP(U_13049,U_13051)) ),
    inference(clausify,[status(thm)],[f_3334_3]) ).

fof(f_3335_1,plain,
    ! [V_a_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),
    inference(fof_nnf,[status(thm)],[fact_singleton__conv]) ).

fof(f_3335_2,plain,
    ! [U_13055,U_13054] : hAPP(c_Set_OCollect(U_13054),hAPP(hAPP(c_COMBC(U_13054,U_13054,tc_HOL_Obool),c_fequal),U_13055)) = hAPP(hAPP(c_Set_Oinsert(U_13054),U_13055),c_Orderings_Obot__class_Obot(tc_fun(U_13054,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_3335_1]) ).

cnf(f_3335_3,plain,
    hAPP(c_Set_OCollect(U_13054),hAPP(hAPP(c_COMBC(U_13054,U_13054,tc_HOL_Obool),c_fequal),U_13055)) = hAPP(hAPP(c_Set_Oinsert(U_13054),U_13055),c_Orderings_Obot__class_Obot(tc_fun(U_13054,tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_3335_2]) ).

fof(f_3336_1,plain,
    ! [V_a_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(c_fequal,V_a_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),
    inference(fof_nnf,[status(thm)],[fact_singleton__conv2]) ).

fof(f_3336_2,plain,
    ! [U_13057,U_13056] : hAPP(c_Set_OCollect(U_13056),hAPP(c_fequal,U_13057)) = hAPP(hAPP(c_Set_Oinsert(U_13056),U_13057),c_Orderings_Obot__class_Obot(tc_fun(U_13056,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_3336_1]) ).

cnf(f_3336_3,plain,
    hAPP(c_Set_OCollect(U_13056),hAPP(c_fequal,U_13057)) = hAPP(hAPP(c_Set_Oinsert(U_13056),U_13057),c_Orderings_Obot__class_Obot(tc_fun(U_13056,tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_3336_2]) ).

fof(f_3337_1,plain,
    ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2)))),
    inference(fof_nnf,[status(thm)],[fact_set__diff__eq]) ).

fof(f_3337_2,plain,
    ! [U_13060,U_13059,U_13058] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13058,tc_HOL_Obool)),U_13059),U_13060) = hAPP(c_Set_OCollect(U_13058),hAPP(hAPP(c_COMBS(U_13058,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13058),c_fconj),hAPP(hAPP(c_COMBC(U_13058,tc_fun(U_13058,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13058)),U_13059))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13058),c_fNot),hAPP(hAPP(c_COMBC(U_13058,tc_fun(U_13058,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13058)),U_13060)))),
    inference(variable_rename,[status(thm)],[f_3337_1]) ).

cnf(f_3337_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13058,tc_HOL_Obool)),U_13059),U_13060) = hAPP(c_Set_OCollect(U_13058),hAPP(hAPP(c_COMBS(U_13058,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13058),c_fconj),hAPP(hAPP(c_COMBC(U_13058,tc_fun(U_13058,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13058)),U_13059))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13058),c_fNot),hAPP(hAPP(c_COMBC(U_13058,tc_fun(U_13058,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13058)),U_13060)))),
    inference(clausify,[status(thm)],[f_3337_2]) ).

fof(f_3338_1,plain,
    ! [V_P_2,T_b] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_P_2))))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) )
        & ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_P_2)))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2))) ),
    inference(fof_nnf,[status(thm)],[fact_finite__Collect__not]) ).

fof(f_3338_2,plain,
    ! [U_13062,U_13061] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13061),hAPP(c_Set_OCollect(U_13061),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13061),c_fNot),U_13062))))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13061),c_Orderings_Otop__class_Otop(tc_fun(U_13061,tc_HOL_Obool)))) )
        & ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13061),c_Orderings_Otop__class_Otop(tc_fun(U_13061,tc_HOL_Obool))))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13061),hAPP(c_Set_OCollect(U_13061),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13061),c_fNot),U_13062)))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13061),hAPP(c_Set_OCollect(U_13061),U_13062))) ),
    inference(variable_rename,[status(thm)],[f_3338_1]) ).

cnf(f_3338_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13061),c_Orderings_Otop__class_Otop(tc_fun(U_13061,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13061),hAPP(c_Set_OCollect(U_13061),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13061),c_fNot),U_13062))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13061),hAPP(c_Set_OCollect(U_13061),U_13062))) ),
    inference(clausify,[status(thm)],[f_3338_2]) ).

cnf(f_3338_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13061),hAPP(c_Set_OCollect(U_13061),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13061),c_fNot),U_13062))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13061),c_Orderings_Otop__class_Otop(tc_fun(U_13061,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13061),hAPP(c_Set_OCollect(U_13061),U_13062))) ),
    inference(clausify,[status(thm)],[f_3338_2]) ).

fof(f_3339_1,plain,
    ! [V_B_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_B_2),
    inference(fof_nnf,[status(thm)],[fact_insert__def]) ).

fof(f_3339_2,plain,
    ! [U_13065,U_13064,U_13063] : hAPP(hAPP(c_Set_Oinsert(U_13063),U_13064),U_13065) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13063,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_13063),hAPP(hAPP(c_COMBC(U_13063,U_13063,tc_HOL_Obool),c_fequal),U_13064))),U_13065),
    inference(variable_rename,[status(thm)],[f_3339_1]) ).

cnf(f_3339_3,plain,
    hAPP(hAPP(c_Set_Oinsert(U_13063),U_13064),U_13065) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13063,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_13063),hAPP(hAPP(c_COMBC(U_13063,U_13063,tc_HOL_Obool),c_fequal),U_13064))),U_13065),
    inference(clausify,[status(thm)],[f_3339_2]) ).

fof(f_3340_1,plain,
    ! [V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),
    inference(fof_nnf,[status(thm)],[fact_Compl__eq]) ).

fof(f_3340_2,plain,
    ! [U_13067,U_13066] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13066,tc_HOL_Obool)),U_13067) = hAPP(c_Set_OCollect(U_13066),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13066),c_fNot),hAPP(hAPP(c_COMBC(U_13066,tc_fun(U_13066,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13066)),U_13067))),
    inference(variable_rename,[status(thm)],[f_3340_1]) ).

cnf(f_3340_3,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13066,tc_HOL_Obool)),U_13067) = hAPP(c_Set_OCollect(U_13066),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13066),c_fNot),hAPP(hAPP(c_COMBC(U_13066,tc_fun(U_13066,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13066)),U_13067))),
    inference(clausify,[status(thm)],[f_3340_2]) ).

fof(f_3341_1,plain,
    ! [V_B_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(T_c)),V_f_2)),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_vimage__def]) ).

fof(f_3341_2,plain,
    ! [U_13071,U_13070,U_13069,U_13068] : hAPP(c_Set_Ovimage(U_13068,U_13069,U_13070),U_13071) = hAPP(c_Set_OCollect(U_13068),hAPP(hAPP(c_COMBC(U_13068,tc_fun(U_13069,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_13069,tc_fun(tc_fun(U_13069,tc_HOL_Obool),tc_HOL_Obool),U_13068),c_member(U_13069)),U_13070)),U_13071)),
    inference(variable_rename,[status(thm)],[f_3341_1]) ).

cnf(f_3341_3,plain,
    hAPP(c_Set_Ovimage(U_13068,U_13069,U_13070),U_13071) = hAPP(c_Set_OCollect(U_13068),hAPP(hAPP(c_COMBC(U_13068,tc_fun(U_13069,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_13069,tc_fun(tc_fun(U_13069,tc_HOL_Obool),tc_HOL_Obool),U_13068),c_member(U_13069)),U_13070)),U_13071)),
    inference(clausify,[status(thm)],[f_3341_2]) ).

fof(f_3342_1,plain,
    ! [V_Q_2,V_P_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),V_P_2)),V_Q_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_P_2))),hAPP(c_Set_OCollect(T_b),V_Q_2)),
    inference(fof_nnf,[status(thm)],[fact_Collect__imp__eq]) ).

fof(f_3342_2,plain,
    ! [U_13074,U_13073,U_13072] : hAPP(c_Set_OCollect(U_13072),hAPP(hAPP(c_COMBS(U_13072,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13072),c_fimplies),U_13073)),U_13074)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13072,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13072,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_13072),U_13073))),hAPP(c_Set_OCollect(U_13072),U_13074)),
    inference(variable_rename,[status(thm)],[f_3342_1]) ).

cnf(f_3342_3,plain,
    hAPP(c_Set_OCollect(U_13072),hAPP(hAPP(c_COMBS(U_13072,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13072),c_fimplies),U_13073)),U_13074)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13072,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13072,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_13072),U_13073))),hAPP(c_Set_OCollect(U_13072),U_13074)),
    inference(clausify,[status(thm)],[f_3342_2]) ).

fof(f_3343_1,plain,
    ! [V_i_2,V_P_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),V_P_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_i_2))))),
    inference(fof_nnf,[status(thm)],[fact_finite__M__bounded__by__nat]) ).

fof(f_3343_2,plain,
    ! [U_13076,U_13075] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),U_13075)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_13076))))),
    inference(variable_rename,[status(thm)],[f_3343_1]) ).

cnf(f_3343_3,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),U_13075)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_13076))))),
    inference(clausify,[status(thm)],[f_3343_2]) ).

fof(f_3344_1,plain,
    ! [T_b] : c_Relation_Orefl__on(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))),
    inference(fof_nnf,[status(thm)],[fact_refl__on__empty]) ).

fof(f_3344_2,plain,
    ! [U_13077] : c_Relation_Orefl__on(U_13077,c_Orderings_Obot__class_Obot(tc_fun(U_13077,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13077,U_13077),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_3344_1]) ).

cnf(f_3344_3,plain,
    c_Relation_Orefl__on(U_13077,c_Orderings_Obot__class_Obot(tc_fun(U_13077,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13077,U_13077),tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_3344_2]) ).

fof(f_3345_1,plain,
    ! [V_s_2,V_B_2,V_r_2,V_A_2,T_b] :
      ( c_Relation_Orefl__on(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
      | ~ c_Relation_Orefl__on(T_b,V_B_2,V_s_2)
      | ~ c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_refl__on__Un]) ).

fof(f_3345_2,plain,
    ! [U_13082,U_13081,U_13080,U_13079,U_13078] :
      ( c_Relation_Orefl__on(U_13078,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13078,tc_HOL_Obool)),U_13079),U_13081),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13078,U_13078),tc_HOL_Obool)),U_13080),U_13082))
      | ~ c_Relation_Orefl__on(U_13078,U_13081,U_13082)
      | ~ c_Relation_Orefl__on(U_13078,U_13079,U_13080) ),
    inference(variable_rename,[status(thm)],[f_3345_1]) ).

cnf(f_3345_3,plain,
    ( c_Relation_Orefl__on(U_13078,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13078,tc_HOL_Obool)),U_13079),U_13081),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13078,U_13078),tc_HOL_Obool)),U_13080),U_13082))
    | ~ c_Relation_Orefl__on(U_13078,U_13081,U_13082)
    | ~ c_Relation_Orefl__on(U_13078,U_13079,U_13080) ),
    inference(clausify,[status(thm)],[f_3345_2]) ).

fof(f_3346_1,plain,
    ! [V_s_2,V_B_2,V_r_2,V_A_2,T_b] :
      ( c_Relation_Orefl__on(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
      | ~ c_Relation_Orefl__on(T_b,V_B_2,V_s_2)
      | ~ c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_refl__on__Int]) ).

fof(f_3346_2,plain,
    ! [U_13087,U_13086,U_13085,U_13084,U_13083] :
      ( c_Relation_Orefl__on(U_13083,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13083,tc_HOL_Obool)),U_13084),U_13086),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_13083,U_13083),tc_HOL_Obool)),U_13085),U_13087))
      | ~ c_Relation_Orefl__on(U_13083,U_13086,U_13087)
      | ~ c_Relation_Orefl__on(U_13083,U_13084,U_13085) ),
    inference(variable_rename,[status(thm)],[f_3346_1]) ).

cnf(f_3346_3,plain,
    ( c_Relation_Orefl__on(U_13083,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13083,tc_HOL_Obool)),U_13084),U_13086),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_13083,U_13083),tc_HOL_Obool)),U_13085),U_13087))
    | ~ c_Relation_Orefl__on(U_13083,U_13086,U_13087)
    | ~ c_Relation_Orefl__on(U_13083,U_13084,U_13085) ),
    inference(clausify,[status(thm)],[f_3346_2]) ).

fof(f_3347_1,plain,
    ! [V_R_2,V_f_2,V_T_2,T_c,V_S_2,T_b,T_d] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_d),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d),T_b),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d)),V_f_2)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_OCollect(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_T_2)))),V_R_2)))),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_b,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_d),tc_fun(tc_fun(T_b,tc_HOL_Obool),T_d),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d)),hAPP(c_COMBC(T_b,T_c,T_d),V_f_2))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Set_OCollect(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)))),hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),V_R_2))))),V_T_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
      | ~ class_Groups_Ocomm__monoid__add(T_d) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__setsum__restrict]) ).

fof(f_3347_2,plain,
    ! [U_13094,U_13093,U_13092,U_13091,U_13090,U_13089,U_13088] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13089,U_13088),hAPP(hAPP(c_COMBS(U_13089,tc_fun(U_13091,tc_HOL_Obool),U_13088),hAPP(hAPP(c_COMBB(tc_fun(U_13091,U_13088),tc_fun(tc_fun(U_13091,tc_HOL_Obool),U_13088),U_13089),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13091,U_13088)),U_13093)),hAPP(hAPP(c_COMBB(tc_fun(U_13091,tc_HOL_Obool),tc_fun(U_13091,tc_HOL_Obool),U_13089),c_Set_OCollect(U_13091)),hAPP(hAPP(c_COMBB(tc_fun(U_13091,tc_HOL_Obool),tc_fun(U_13091,tc_HOL_Obool),U_13089),hAPP(c_COMBS(U_13091,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13091),c_fconj),hAPP(hAPP(c_COMBC(U_13091,tc_fun(U_13091,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13091)),U_13092)))),U_13094)))),U_13090) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13091,U_13088),hAPP(hAPP(c_COMBS(U_13091,tc_fun(U_13089,tc_HOL_Obool),U_13088),hAPP(hAPP(c_COMBB(tc_fun(U_13089,U_13088),tc_fun(tc_fun(U_13089,tc_HOL_Obool),U_13088),U_13091),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13089,U_13088)),hAPP(c_COMBC(U_13089,U_13091,U_13088),U_13093))),hAPP(hAPP(c_COMBB(tc_fun(U_13089,tc_HOL_Obool),tc_fun(U_13089,tc_HOL_Obool),U_13091),c_Set_OCollect(U_13089)),hAPP(hAPP(c_COMBB(tc_fun(U_13089,tc_HOL_Obool),tc_fun(U_13089,tc_HOL_Obool),U_13091),hAPP(c_COMBS(U_13089,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13089),c_fconj),hAPP(hAPP(c_COMBC(U_13089,tc_fun(U_13089,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13089)),U_13090)))),hAPP(c_COMBC(U_13089,U_13091,tc_HOL_Obool),U_13094))))),U_13092)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13091),U_13092))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13089),U_13090))
      | ~ class_Groups_Ocomm__monoid__add(U_13088) ),
    inference(variable_rename,[status(thm)],[f_3347_1]) ).

cnf(f_3347_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13089,U_13088),hAPP(hAPP(c_COMBS(U_13089,tc_fun(U_13091,tc_HOL_Obool),U_13088),hAPP(hAPP(c_COMBB(tc_fun(U_13091,U_13088),tc_fun(tc_fun(U_13091,tc_HOL_Obool),U_13088),U_13089),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13091,U_13088)),U_13093)),hAPP(hAPP(c_COMBB(tc_fun(U_13091,tc_HOL_Obool),tc_fun(U_13091,tc_HOL_Obool),U_13089),c_Set_OCollect(U_13091)),hAPP(hAPP(c_COMBB(tc_fun(U_13091,tc_HOL_Obool),tc_fun(U_13091,tc_HOL_Obool),U_13089),hAPP(c_COMBS(U_13091,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13091),c_fconj),hAPP(hAPP(c_COMBC(U_13091,tc_fun(U_13091,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13091)),U_13092)))),U_13094)))),U_13090) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13091,U_13088),hAPP(hAPP(c_COMBS(U_13091,tc_fun(U_13089,tc_HOL_Obool),U_13088),hAPP(hAPP(c_COMBB(tc_fun(U_13089,U_13088),tc_fun(tc_fun(U_13089,tc_HOL_Obool),U_13088),U_13091),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13089,U_13088)),hAPP(c_COMBC(U_13089,U_13091,U_13088),U_13093))),hAPP(hAPP(c_COMBB(tc_fun(U_13089,tc_HOL_Obool),tc_fun(U_13089,tc_HOL_Obool),U_13091),c_Set_OCollect(U_13089)),hAPP(hAPP(c_COMBB(tc_fun(U_13089,tc_HOL_Obool),tc_fun(U_13089,tc_HOL_Obool),U_13091),hAPP(c_COMBS(U_13089,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13089),c_fconj),hAPP(hAPP(c_COMBC(U_13089,tc_fun(U_13089,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13089)),U_13090)))),hAPP(c_COMBC(U_13089,U_13091,tc_HOL_Obool),U_13094))))),U_13092)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13091),U_13092))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13089),U_13090))
    | ~ class_Groups_Ocomm__monoid__add(U_13088) ),
    inference(clausify,[status(thm)],[f_3347_2]) ).

fof(f_3348_1,plain,
    ! [V_S_2,V_g_2,V_f_2,V_P_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),V_P_2)),V_f_2)),V_g_2)),V_S_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_S_2),hAPP(c_Set_OCollect(T_c),V_P_2)))),hAPP(c_Set_Oimage(T_c,T_b,V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_S_2),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c),c_fNot),V_P_2))))),
    inference(fof_nnf,[status(thm)],[fact_if__image__distrib]) ).

fof(f_3348_2,plain,
    ! [U_13100,U_13099,U_13098,U_13097,U_13096,U_13095] : hAPP(c_Set_Oimage(U_13095,U_13096,hAPP(hAPP(c_COMBS(U_13095,U_13096,U_13096),hAPP(hAPP(c_COMBS(U_13095,U_13096,tc_fun(U_13096,U_13096)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_13096,tc_fun(U_13096,U_13096)),U_13095),c_If(U_13096)),U_13097)),U_13098)),U_13099)),U_13100) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13096,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13095,U_13096,U_13098),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13095,tc_HOL_Obool)),U_13100),hAPP(c_Set_OCollect(U_13095),U_13097)))),hAPP(c_Set_Oimage(U_13095,U_13096,U_13099),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13095,tc_HOL_Obool)),U_13100),hAPP(c_Set_OCollect(U_13095),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13095),c_fNot),U_13097))))),
    inference(variable_rename,[status(thm)],[f_3348_1]) ).

cnf(f_3348_3,plain,
    hAPP(c_Set_Oimage(U_13095,U_13096,hAPP(hAPP(c_COMBS(U_13095,U_13096,U_13096),hAPP(hAPP(c_COMBS(U_13095,U_13096,tc_fun(U_13096,U_13096)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_13096,tc_fun(U_13096,U_13096)),U_13095),c_If(U_13096)),U_13097)),U_13098)),U_13099)),U_13100) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13096,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13095,U_13096,U_13098),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13095,tc_HOL_Obool)),U_13100),hAPP(c_Set_OCollect(U_13095),U_13097)))),hAPP(c_Set_Oimage(U_13095,U_13096,U_13099),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13095,tc_HOL_Obool)),U_13100),hAPP(c_Set_OCollect(U_13095),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13095),c_fNot),U_13097))))),
    inference(clausify,[status(thm)],[f_3348_2]) ).

fof(f_3349_1,plain,
    ! [V_n_2,V_f_2,T_b,V_A_2] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | V_A_2 != hAPP(c_Set_Oimage(tc_Nat_Onat,T_b,V_f_2),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_n_2))) ),
    inference(fof_nnf,[status(thm)],[fact_nat__seg__image__imp__finite]) ).

fof(f_3349_2,plain,
    ! [U_13104,U_13103,U_13102,U_13101] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13102),U_13101))
      | U_13101 != hAPP(c_Set_Oimage(tc_Nat_Onat,U_13102,U_13103),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_13104))) ),
    inference(variable_rename,[status(thm)],[f_3349_1]) ).

cnf(f_3349_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13102),U_13101))
    | U_13101 != hAPP(c_Set_Oimage(tc_Nat_Onat,U_13102,U_13103),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_13104))) ),
    inference(clausify,[status(thm)],[f_3349_2]) ).

fof(f_3350_1,plain,
    ! [V_a_2,V_r_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),V_r_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | ~ c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_refl__onD]) ).

fof(f_3350_2,plain,
    ! [U_13108,U_13107,U_13106,U_13105] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13105,U_13105)),hAPP(hAPP(c_Product__Type_OPair(U_13105,U_13105),U_13108),U_13108)),U_13107))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13105),U_13108),U_13106))
      | ~ c_Relation_Orefl__on(U_13105,U_13106,U_13107) ),
    inference(variable_rename,[status(thm)],[f_3350_1]) ).

cnf(f_3350_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13105,U_13105)),hAPP(hAPP(c_Product__Type_OPair(U_13105,U_13105),U_13108),U_13108)),U_13107))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13105),U_13108),U_13106))
    | ~ c_Relation_Orefl__on(U_13105,U_13106,U_13107) ),
    inference(clausify,[status(thm)],[f_3350_2]) ).

fof(f_3351_1,plain,
    ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
      | ~ c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_refl__onD1]) ).

fof(f_3351_2,plain,
    ! [U_13113,U_13112,U_13111,U_13110,U_13109] :
      ( hBOOL(hAPP(hAPP(c_member(U_13109),U_13112),U_13110))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13109,U_13109)),hAPP(hAPP(c_Product__Type_OPair(U_13109,U_13109),U_13112),U_13113)),U_13111))
      | ~ c_Relation_Orefl__on(U_13109,U_13110,U_13111) ),
    inference(variable_rename,[status(thm)],[f_3351_1]) ).

cnf(f_3351_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13109),U_13112),U_13110))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13109,U_13109)),hAPP(hAPP(c_Product__Type_OPair(U_13109,U_13109),U_13112),U_13113)),U_13111))
    | ~ c_Relation_Orefl__on(U_13109,U_13110,U_13111) ),
    inference(clausify,[status(thm)],[f_3351_2]) ).

fof(f_3352_1,plain,
    ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
      | ~ c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_refl__onD2]) ).

fof(f_3352_2,plain,
    ! [U_13118,U_13117,U_13116,U_13115,U_13114] :
      ( hBOOL(hAPP(hAPP(c_member(U_13114),U_13118),U_13115))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13114,U_13114)),hAPP(hAPP(c_Product__Type_OPair(U_13114,U_13114),U_13117),U_13118)),U_13116))
      | ~ c_Relation_Orefl__on(U_13114,U_13115,U_13116) ),
    inference(variable_rename,[status(thm)],[f_3352_1]) ).

cnf(f_3352_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13114),U_13118),U_13115))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13114,U_13114)),hAPP(hAPP(c_Product__Type_OPair(U_13114,U_13114),U_13117),U_13118)),U_13116))
    | ~ c_Relation_Orefl__on(U_13114,U_13115,U_13116) ),
    inference(clausify,[status(thm)],[f_3352_2]) ).

fof(f_3353_1,plain,
    ! [V_B_2,V_f_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_f_2)),c_Groups_Ozero__class_Ozero(T_c))),V_A_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Ocomm__monoid__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__restrict__set_H]) ).

fof(f_3353_2,plain,
    ! [U_13123,U_13122,U_13121,U_13120,U_13119] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13120,U_13119),U_13122),hAPP(c_Set_OCollect(U_13120),hAPP(hAPP(c_COMBS(U_13120,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13120),c_fconj),hAPP(hAPP(c_COMBC(U_13120,tc_fun(U_13120,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13120)),U_13121))),hAPP(hAPP(c_COMBC(U_13120,tc_fun(U_13120,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13120)),U_13123)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13120,U_13119),hAPP(hAPP(c_COMBC(U_13120,U_13119,U_13119),hAPP(hAPP(c_COMBS(U_13120,U_13119,tc_fun(U_13119,U_13119)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_13119,tc_fun(U_13119,U_13119)),U_13120),c_If(U_13119)),hAPP(hAPP(c_COMBC(U_13120,tc_fun(U_13120,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13120)),U_13123))),U_13122)),c_Groups_Ozero__class_Ozero(U_13119))),U_13121)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13120),U_13121))
      | ~ class_Groups_Ocomm__monoid__add(U_13119) ),
    inference(variable_rename,[status(thm)],[f_3353_1]) ).

cnf(f_3353_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13120,U_13119),U_13122),hAPP(c_Set_OCollect(U_13120),hAPP(hAPP(c_COMBS(U_13120,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13120),c_fconj),hAPP(hAPP(c_COMBC(U_13120,tc_fun(U_13120,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13120)),U_13121))),hAPP(hAPP(c_COMBC(U_13120,tc_fun(U_13120,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13120)),U_13123)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13120,U_13119),hAPP(hAPP(c_COMBC(U_13120,U_13119,U_13119),hAPP(hAPP(c_COMBS(U_13120,U_13119,tc_fun(U_13119,U_13119)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_13119,tc_fun(U_13119,U_13119)),U_13120),c_If(U_13119)),hAPP(hAPP(c_COMBC(U_13120,tc_fun(U_13120,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13120)),U_13123))),U_13122)),c_Groups_Ozero__class_Ozero(U_13119))),U_13121)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13120),U_13121))
    | ~ class_Groups_Ocomm__monoid__add(U_13119) ),
    inference(clausify,[status(thm)],[f_3353_2]) ).

fof(f_3354_1,plain,
    ! [V_f_2,T_d,V_g_2,V_S_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),T_c,T_d),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Set_OCollect(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)))),hAPP(c_COMBC(T_b,T_d,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,tc_HOL_Obool),T_b),c_fequal),V_f_2)))))),hAPP(c_Set_Oimage(T_b,T_d,V_f_2),V_S_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
      | ~ class_Groups_Ocomm__monoid__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__image__gen]) ).

fof(f_3354_2,plain,
    ! [U_13129,U_13128,U_13127,U_13126,U_13125,U_13124] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13125,U_13124),U_13127),U_13126) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13128,U_13124),hAPP(hAPP(c_COMBB(tc_fun(U_13125,tc_HOL_Obool),U_13124,U_13128),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13125,U_13124),U_13127)),hAPP(hAPP(c_COMBB(tc_fun(U_13125,tc_HOL_Obool),tc_fun(U_13125,tc_HOL_Obool),U_13128),c_Set_OCollect(U_13125)),hAPP(hAPP(c_COMBB(tc_fun(U_13125,tc_HOL_Obool),tc_fun(U_13125,tc_HOL_Obool),U_13128),hAPP(c_COMBS(U_13125,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13125),c_fconj),hAPP(hAPP(c_COMBC(U_13125,tc_fun(U_13125,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13125)),U_13126)))),hAPP(c_COMBC(U_13125,U_13128,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_13128,tc_fun(U_13128,tc_HOL_Obool),U_13125),c_fequal),U_13129)))))),hAPP(c_Set_Oimage(U_13125,U_13128,U_13129),U_13126))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13125),U_13126))
      | ~ class_Groups_Ocomm__monoid__add(U_13124) ),
    inference(variable_rename,[status(thm)],[f_3354_1]) ).

cnf(f_3354_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13125,U_13124),U_13127),U_13126) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13128,U_13124),hAPP(hAPP(c_COMBB(tc_fun(U_13125,tc_HOL_Obool),U_13124,U_13128),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13125,U_13124),U_13127)),hAPP(hAPP(c_COMBB(tc_fun(U_13125,tc_HOL_Obool),tc_fun(U_13125,tc_HOL_Obool),U_13128),c_Set_OCollect(U_13125)),hAPP(hAPP(c_COMBB(tc_fun(U_13125,tc_HOL_Obool),tc_fun(U_13125,tc_HOL_Obool),U_13128),hAPP(c_COMBS(U_13125,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13125),c_fconj),hAPP(hAPP(c_COMBC(U_13125,tc_fun(U_13125,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13125)),U_13126)))),hAPP(c_COMBC(U_13125,U_13128,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_13128,tc_fun(U_13128,tc_HOL_Obool),U_13125),c_fequal),U_13129)))))),hAPP(c_Set_Oimage(U_13125,U_13128,U_13129),U_13126))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13125),U_13126))
    | ~ class_Groups_Ocomm__monoid__add(U_13124) ),
    inference(clausify,[status(thm)],[f_3354_2]) ).

fof(f_3355_1,plain,
    ! [V_a_2,V_r_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(T_c,T_b),tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_c,T_b))),hAPP(c_Product__Type_OPair(T_c,T_b),V_a_2))),V_r_2)),
    inference(fof_nnf,[status(thm)],[fact_Image__singleton]) ).

fof(f_3355_2,plain,
    ! [U_13133,U_13132,U_13131,U_13130] : hAPP(c_Relation_OImage(U_13130,U_13131,U_13132),hAPP(hAPP(c_Set_Oinsert(U_13130),U_13133),c_Orderings_Obot__class_Obot(tc_fun(U_13130,tc_HOL_Obool)))) = hAPP(c_Set_OCollect(U_13131),hAPP(hAPP(c_COMBC(U_13131,tc_fun(tc_prod(U_13130,U_13131),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(U_13130,U_13131),tc_fun(tc_fun(tc_prod(U_13130,U_13131),tc_HOL_Obool),tc_HOL_Obool),U_13131),c_member(tc_prod(U_13130,U_13131))),hAPP(c_Product__Type_OPair(U_13130,U_13131),U_13133))),U_13132)),
    inference(variable_rename,[status(thm)],[f_3355_1]) ).

cnf(f_3355_3,plain,
    hAPP(c_Relation_OImage(U_13130,U_13131,U_13132),hAPP(hAPP(c_Set_Oinsert(U_13130),U_13133),c_Orderings_Obot__class_Obot(tc_fun(U_13130,tc_HOL_Obool)))) = hAPP(c_Set_OCollect(U_13131),hAPP(hAPP(c_COMBC(U_13131,tc_fun(tc_prod(U_13130,U_13131),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(U_13130,U_13131),tc_fun(tc_fun(tc_prod(U_13130,U_13131),tc_HOL_Obool),tc_HOL_Obool),U_13131),c_member(tc_prod(U_13130,U_13131))),hAPP(c_Product__Type_OPair(U_13130,U_13131),U_13133))),U_13132)),
    inference(clausify,[status(thm)],[f_3355_2]) ).

fof(f_3356_1,plain,
    ! [V_g_2,V_f_2,V_P_2,V_A_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),V_P_2)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_P_2)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_P_2)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Groups_Ocomm__monoid__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__cases]) ).

fof(f_3356_2,plain,
    ! [U_13139,U_13138,U_13137,U_13136,U_13135,U_13134] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13135,U_13134),hAPP(hAPP(c_COMBS(U_13135,U_13134,U_13134),hAPP(hAPP(c_COMBS(U_13135,U_13134,tc_fun(U_13134,U_13134)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_13134,tc_fun(U_13134,U_13134)),U_13135),c_If(U_13134)),U_13137)),U_13138)),U_13139)),U_13136) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_13134),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13135,U_13134),U_13138),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13135,tc_HOL_Obool)),U_13136),hAPP(c_Set_OCollect(U_13135),U_13137)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13135,U_13134),U_13139),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13135,tc_HOL_Obool)),U_13136),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13135,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_13135),U_13137)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13135),U_13136))
      | ~ class_Groups_Ocomm__monoid__add(U_13134) ),
    inference(variable_rename,[status(thm)],[f_3356_1]) ).

cnf(f_3356_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13135,U_13134),hAPP(hAPP(c_COMBS(U_13135,U_13134,U_13134),hAPP(hAPP(c_COMBS(U_13135,U_13134,tc_fun(U_13134,U_13134)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_13134,tc_fun(U_13134,U_13134)),U_13135),c_If(U_13134)),U_13137)),U_13138)),U_13139)),U_13136) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_13134),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13135,U_13134),U_13138),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13135,tc_HOL_Obool)),U_13136),hAPP(c_Set_OCollect(U_13135),U_13137)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13135,U_13134),U_13139),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13135,tc_HOL_Obool)),U_13136),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13135,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_13135),U_13137)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13135),U_13136))
    | ~ class_Groups_Ocomm__monoid__add(U_13134) ),
    inference(clausify,[status(thm)],[f_3356_2]) ).

fof(f_3357_1,plain,
    ! [V_i_2,V_M_2] :
      ( hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),V_M_2))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_i_2))))) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_M_2))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,V_i_2)))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__less__Suc]) ).

fof(f_3357_2,plain,
    ! [U_13141,U_13140] :
      ( hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),U_13140))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_13141))))) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),U_13140))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,U_13141)))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_13140)) ),
    inference(variable_rename,[status(thm)],[f_3357_1]) ).

cnf(f_3357_3,plain,
    ( hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),U_13140))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_13141))))) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),U_13140))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,U_13141)))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_13140)) ),
    inference(clausify,[status(thm)],[f_3357_2]) ).

fof(f_3358_1,plain,
    ! [V_i_2,V_M_2] :
      ( hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_M_2))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,V_i_2))))) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2)) ),
    inference(fof_nnf,[status(thm)],[fact_card__less]) ).

fof(f_3358_2,plain,
    ! [U_13143,U_13142] :
      ( hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),U_13142))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,U_13143))))) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_13142)) ),
    inference(variable_rename,[status(thm)],[f_3358_1]) ).

cnf(f_3358_3,plain,
    ( hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),U_13142))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,U_13143))))) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_13142)) ),
    inference(clausify,[status(thm)],[f_3358_2]) ).

fof(f_3359_1,plain,
    ! [V_A_2,V_r_2,T_b] :
      ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
      | ? [B_x] :
          ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_refl__onI]) ).

fof(f_3359_2,plain,
    ! [U_13147,U_13146,U_13145] :
      ( c_Relation_Orefl__on(U_13145,U_13147,U_13146)
      | ? [U_13144] :
          ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13145,U_13145)),hAPP(hAPP(c_Product__Type_OPair(U_13145,U_13145),U_13144),U_13144)),U_13146))
          & hBOOL(hAPP(hAPP(c_member(U_13145),U_13144),U_13147)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13145,U_13145),tc_HOL_Obool)),U_13146),hAPP(hAPP(c_Product__Type_OSigma(U_13145,U_13145),U_13147),hAPP(c_COMBK(tc_fun(U_13145,tc_HOL_Obool),U_13145),U_13147)))) ),
    inference(variable_rename,[status(thm)],[f_3359_1]) ).

fof(f_3359_3,plain,
    ! [U_13147,U_13146,U_13145] :
      ( c_Relation_Orefl__on(U_13145,U_13147,U_13146)
      | ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13145,U_13145)),hAPP(hAPP(c_Product__Type_OPair(U_13145,U_13145),sK312(U_13147,U_13146,U_13145)),sK312(U_13147,U_13146,U_13145))),U_13146))
        & hBOOL(hAPP(hAPP(c_member(U_13145),sK312(U_13147,U_13146,U_13145)),U_13147)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13145,U_13145),tc_HOL_Obool)),U_13146),hAPP(hAPP(c_Product__Type_OSigma(U_13145,U_13145),U_13147),hAPP(c_COMBK(tc_fun(U_13145,tc_HOL_Obool),U_13145),U_13147)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK312]),skolemize(U_13144,sK312(U_13147,U_13146,U_13145))],[f_3359_2]) ).

cnf(f_3359_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13145),sK312(U_13147,U_13146,U_13145)),U_13147))
    | c_Relation_Orefl__on(U_13145,U_13147,U_13146)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13145,U_13145),tc_HOL_Obool)),U_13146),hAPP(hAPP(c_Product__Type_OSigma(U_13145,U_13145),U_13147),hAPP(c_COMBK(tc_fun(U_13145,tc_HOL_Obool),U_13145),U_13147)))) ),
    inference(clausify,[status(thm)],[f_3359_3]) ).

cnf(f_3359_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13145,U_13145)),hAPP(hAPP(c_Product__Type_OPair(U_13145,U_13145),sK312(U_13147,U_13146,U_13145)),sK312(U_13147,U_13146,U_13145))),U_13146))
    | c_Relation_Orefl__on(U_13145,U_13147,U_13146)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13145,U_13145),tc_HOL_Obool)),U_13146),hAPP(hAPP(c_Product__Type_OSigma(U_13145,U_13145),U_13147),hAPP(c_COMBK(tc_fun(U_13145,tc_HOL_Obool),U_13145),U_13147)))) ),
    inference(clausify,[status(thm)],[f_3359_3]) ).

fof(f_3360_1,plain,
    ! [V_k_2,V_R_2,V_T_2,T_c,V_S_2,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_Nat_Onat,T_b),c_Finite__Set_Ocard(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_OCollect(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_T_2)))),V_R_2)))),V_S_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(T_c),V_T_2))
      | ? [B_x] :
          ( hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),V_R_2),B_x)))) != V_k_2
          & hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_T_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__multicount]) ).

fof(f_3360_2,plain,
    ! [U_13154,U_13153,U_13152,U_13151,U_13150,U_13149] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13149,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_13151,tc_HOL_Obool),tc_Nat_Onat,U_13149),c_Finite__Set_Ocard(U_13151)),hAPP(hAPP(c_COMBB(tc_fun(U_13151,tc_HOL_Obool),tc_fun(U_13151,tc_HOL_Obool),U_13149),c_Set_OCollect(U_13151)),hAPP(hAPP(c_COMBB(tc_fun(U_13151,tc_HOL_Obool),tc_fun(U_13151,tc_HOL_Obool),U_13149),hAPP(c_COMBS(U_13151,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13151),c_fconj),hAPP(hAPP(c_COMBC(U_13151,tc_fun(U_13151,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13151)),U_13152)))),U_13153)))),U_13150) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_13154),hAPP(c_Finite__Set_Ocard(U_13151),U_13152))
      | ? [U_13148] :
          ( hAPP(c_Finite__Set_Ocard(U_13149),hAPP(c_Set_OCollect(U_13149),hAPP(hAPP(c_COMBS(U_13149,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13149),c_fconj),hAPP(hAPP(c_COMBC(U_13149,tc_fun(U_13149,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13149)),U_13150))),hAPP(hAPP(c_COMBC(U_13149,U_13151,tc_HOL_Obool),U_13153),U_13148)))) != U_13154
          & hBOOL(hAPP(hAPP(c_member(U_13151),U_13148),U_13152)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13151),U_13152))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13149),U_13150)) ),
    inference(variable_rename,[status(thm)],[f_3360_1]) ).

fof(f_3360_3,plain,
    ! [U_13154,U_13153,U_13152,U_13151,U_13150,U_13149] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13149,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_13151,tc_HOL_Obool),tc_Nat_Onat,U_13149),c_Finite__Set_Ocard(U_13151)),hAPP(hAPP(c_COMBB(tc_fun(U_13151,tc_HOL_Obool),tc_fun(U_13151,tc_HOL_Obool),U_13149),c_Set_OCollect(U_13151)),hAPP(hAPP(c_COMBB(tc_fun(U_13151,tc_HOL_Obool),tc_fun(U_13151,tc_HOL_Obool),U_13149),hAPP(c_COMBS(U_13151,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13151),c_fconj),hAPP(hAPP(c_COMBC(U_13151,tc_fun(U_13151,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13151)),U_13152)))),U_13153)))),U_13150) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_13154),hAPP(c_Finite__Set_Ocard(U_13151),U_13152))
      | ( hAPP(c_Finite__Set_Ocard(U_13149),hAPP(c_Set_OCollect(U_13149),hAPP(hAPP(c_COMBS(U_13149,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13149),c_fconj),hAPP(hAPP(c_COMBC(U_13149,tc_fun(U_13149,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13149)),U_13150))),hAPP(hAPP(c_COMBC(U_13149,U_13151,tc_HOL_Obool),U_13153),sK313(U_13154,U_13153,U_13152,U_13151,U_13150,U_13149))))) != U_13154
        & hBOOL(hAPP(hAPP(c_member(U_13151),sK313(U_13154,U_13153,U_13152,U_13151,U_13150,U_13149)),U_13152)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13151),U_13152))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13149),U_13150)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK313]),skolemize(U_13148,sK313(U_13154,U_13153,U_13152,U_13151,U_13150,U_13149))],[f_3360_2]) ).

cnf(f_3360_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13151),sK313(U_13154,U_13153,U_13152,U_13151,U_13150,U_13149)),U_13152))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13149,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_13151,tc_HOL_Obool),tc_Nat_Onat,U_13149),c_Finite__Set_Ocard(U_13151)),hAPP(hAPP(c_COMBB(tc_fun(U_13151,tc_HOL_Obool),tc_fun(U_13151,tc_HOL_Obool),U_13149),c_Set_OCollect(U_13151)),hAPP(hAPP(c_COMBB(tc_fun(U_13151,tc_HOL_Obool),tc_fun(U_13151,tc_HOL_Obool),U_13149),hAPP(c_COMBS(U_13151,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13151),c_fconj),hAPP(hAPP(c_COMBC(U_13151,tc_fun(U_13151,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13151)),U_13152)))),U_13153)))),U_13150) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_13154),hAPP(c_Finite__Set_Ocard(U_13151),U_13152))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13151),U_13152))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13149),U_13150)) ),
    inference(clausify,[status(thm)],[f_3360_3]) ).

cnf(f_3360_5,plain,
    ( hAPP(c_Finite__Set_Ocard(U_13149),hAPP(c_Set_OCollect(U_13149),hAPP(hAPP(c_COMBS(U_13149,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13149),c_fconj),hAPP(hAPP(c_COMBC(U_13149,tc_fun(U_13149,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13149)),U_13150))),hAPP(hAPP(c_COMBC(U_13149,U_13151,tc_HOL_Obool),U_13153),sK313(U_13154,U_13153,U_13152,U_13151,U_13150,U_13149))))) != U_13154
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13149,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_13151,tc_HOL_Obool),tc_Nat_Onat,U_13149),c_Finite__Set_Ocard(U_13151)),hAPP(hAPP(c_COMBB(tc_fun(U_13151,tc_HOL_Obool),tc_fun(U_13151,tc_HOL_Obool),U_13149),c_Set_OCollect(U_13151)),hAPP(hAPP(c_COMBB(tc_fun(U_13151,tc_HOL_Obool),tc_fun(U_13151,tc_HOL_Obool),U_13149),hAPP(c_COMBS(U_13151,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13151),c_fconj),hAPP(hAPP(c_COMBC(U_13151,tc_fun(U_13151,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13151)),U_13152)))),U_13153)))),U_13150) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_13154),hAPP(c_Finite__Set_Ocard(U_13151),U_13152))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13151),U_13152))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13149),U_13150)) ),
    inference(clausify,[status(thm)],[f_3360_3]) ).

fof(f_3361_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Osup__Inf1__distrib]) ).

fof(f_3361_2,plain,
    ! [U_13157,U_13156,U_13155] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_13155),U_13157),c_Big__Operators_Olattice_OInf__fin(U_13155,c_Orderings_Oord__class_Omin(U_13155),U_13156)) = c_Big__Operators_Olattice_OInf__fin(U_13155,c_Orderings_Oord__class_Omin(U_13155),hAPP(c_Set_OCollect(U_13155),hAPP(hAPP(c_COMBB(tc_fun(U_13155,tc_HOL_Obool),tc_HOL_Obool,U_13155),c_HOL_OEx(U_13155)),hAPP(hAPP(c_COMBC(U_13155,tc_fun(U_13155,tc_HOL_Obool),tc_fun(U_13155,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13155,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13155,tc_HOL_Obool),tc_fun(U_13155,tc_HOL_Obool)),U_13155),c_COMBS(U_13155,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13155,tc_HOL_Obool),tc_fun(U_13155,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13155),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13155),c_fconj)),hAPP(hAPP(c_COMBC(U_13155,tc_fun(U_13155,U_13155),tc_fun(U_13155,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13155,tc_HOL_Obool),tc_fun(tc_fun(U_13155,U_13155),tc_fun(U_13155,tc_HOL_Obool)),U_13155),c_COMBB(U_13155,tc_HOL_Obool,U_13155)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(U_13155),U_13157))))),hAPP(hAPP(c_COMBC(U_13155,tc_fun(U_13155,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13155)),U_13156)))))
      | U_13156 = c_Orderings_Obot__class_Obot(tc_fun(U_13155,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13155),U_13156))
      | ~ class_Orderings_Olinorder(U_13155) ),
    inference(variable_rename,[status(thm)],[f_3361_1]) ).

cnf(f_3361_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_13155),U_13157),c_Big__Operators_Olattice_OInf__fin(U_13155,c_Orderings_Oord__class_Omin(U_13155),U_13156)) = c_Big__Operators_Olattice_OInf__fin(U_13155,c_Orderings_Oord__class_Omin(U_13155),hAPP(c_Set_OCollect(U_13155),hAPP(hAPP(c_COMBB(tc_fun(U_13155,tc_HOL_Obool),tc_HOL_Obool,U_13155),c_HOL_OEx(U_13155)),hAPP(hAPP(c_COMBC(U_13155,tc_fun(U_13155,tc_HOL_Obool),tc_fun(U_13155,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13155,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13155,tc_HOL_Obool),tc_fun(U_13155,tc_HOL_Obool)),U_13155),c_COMBS(U_13155,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13155,tc_HOL_Obool),tc_fun(U_13155,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13155),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13155),c_fconj)),hAPP(hAPP(c_COMBC(U_13155,tc_fun(U_13155,U_13155),tc_fun(U_13155,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13155,tc_HOL_Obool),tc_fun(tc_fun(U_13155,U_13155),tc_fun(U_13155,tc_HOL_Obool)),U_13155),c_COMBB(U_13155,tc_HOL_Obool,U_13155)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(U_13155),U_13157))))),hAPP(hAPP(c_COMBC(U_13155,tc_fun(U_13155,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13155)),U_13156)))))
    | U_13156 = c_Orderings_Obot__class_Obot(tc_fun(U_13155,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13155),U_13156))
    | ~ class_Orderings_Olinorder(U_13155) ),
    inference(clausify,[status(thm)],[f_3361_2]) ).

fof(f_3362_1,plain,
    ! [V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),V_A_2))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__Collect__subsets]) ).

fof(f_3362_2,plain,
    ! [U_13159,U_13158] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_13158,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_fun(U_13158,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(U_13158,tc_HOL_Obool),tc_fun(U_13158,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(U_13158,tc_HOL_Obool))),U_13159))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13158),U_13159)) ),
    inference(variable_rename,[status(thm)],[f_3362_1]) ).

cnf(f_3362_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_13158,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_fun(U_13158,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(U_13158,tc_HOL_Obool),tc_fun(U_13158,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(U_13158,tc_HOL_Obool))),U_13159))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13158),U_13159)) ),
    inference(clausify,[status(thm)],[f_3362_2]) ).

fof(f_3363_1,plain,
    ! [V_A_2,T_b] : hAPP(c_Set_OPow(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = hAPP(c_Set_OCollect(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),c_HOL_OEx(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBS(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),c_Set_OPow(T_b))))),
    inference(fof_nnf,[status(thm)],[fact_Pow__Compl]) ).

fof(f_3363_2,plain,
    ! [U_13161,U_13160] : hAPP(c_Set_OPow(U_13160),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13160,tc_HOL_Obool)),U_13161)) = hAPP(c_Set_OCollect(tc_fun(U_13160,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13160,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_13160,tc_HOL_Obool)),c_HOL_OEx(tc_fun(U_13160,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(U_13160,tc_HOL_Obool),tc_fun(tc_fun(U_13160,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_13160,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13160,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(U_13160,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_13160,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(U_13160,tc_HOL_Obool)),c_COMBS(tc_fun(U_13160,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13160,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_13160,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(U_13160,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(U_13160,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(U_13160,tc_HOL_Obool),tc_fun(tc_fun(U_13160,tc_HOL_Obool),tc_fun(U_13160,tc_HOL_Obool)),tc_fun(tc_fun(U_13160,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13160,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(U_13160,tc_HOL_Obool),tc_fun(U_13160,tc_HOL_Obool)),tc_fun(tc_fun(U_13160,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(U_13160,tc_HOL_Obool)),c_COMBB(tc_fun(U_13160,tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_13160,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(U_13160,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13160,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_13160,tc_HOL_Obool)),hAPP(c_member(tc_fun(U_13160,tc_HOL_Obool)),U_13161)),c_Set_OPow(U_13160))))),
    inference(variable_rename,[status(thm)],[f_3363_1]) ).

cnf(f_3363_3,plain,
    hAPP(c_Set_OPow(U_13160),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13160,tc_HOL_Obool)),U_13161)) = hAPP(c_Set_OCollect(tc_fun(U_13160,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13160,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_13160,tc_HOL_Obool)),c_HOL_OEx(tc_fun(U_13160,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(U_13160,tc_HOL_Obool),tc_fun(tc_fun(U_13160,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_13160,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13160,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(U_13160,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_13160,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(U_13160,tc_HOL_Obool)),c_COMBS(tc_fun(U_13160,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13160,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_13160,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(U_13160,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(U_13160,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(U_13160,tc_HOL_Obool),tc_fun(tc_fun(U_13160,tc_HOL_Obool),tc_fun(U_13160,tc_HOL_Obool)),tc_fun(tc_fun(U_13160,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13160,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(U_13160,tc_HOL_Obool),tc_fun(U_13160,tc_HOL_Obool)),tc_fun(tc_fun(U_13160,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(U_13160,tc_HOL_Obool)),c_COMBB(tc_fun(U_13160,tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_13160,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(U_13160,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13160,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_13160,tc_HOL_Obool)),hAPP(c_member(tc_fun(U_13160,tc_HOL_Obool)),U_13161)),c_Set_OPow(U_13160))))),
    inference(clausify,[status(thm)],[f_3363_2]) ).

fof(f_3364_1,plain,
    ! [V_A_2,T_b] : hAPP(c_Set_OPow(T_b),V_A_2) = hAPP(c_Set_OCollect(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_Pow__def]) ).

fof(f_3364_2,plain,
    ! [U_13163,U_13162] : hAPP(c_Set_OPow(U_13162),U_13163) = hAPP(c_Set_OCollect(tc_fun(U_13162,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(U_13162,tc_HOL_Obool),tc_fun(U_13162,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(U_13162,tc_HOL_Obool))),U_13163)),
    inference(variable_rename,[status(thm)],[f_3364_1]) ).

cnf(f_3364_3,plain,
    hAPP(c_Set_OPow(U_13162),U_13163) = hAPP(c_Set_OCollect(tc_fun(U_13162,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(U_13162,tc_HOL_Obool),tc_fun(U_13162,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(U_13162,tc_HOL_Obool))),U_13163)),
    inference(clausify,[status(thm)],[f_3364_2]) ).

fof(f_3365_1,plain,
    ! [V_Q_2,T_c,V_P_2,T_b] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_P_2))),V_Q_2)))))
          | ? [B_y] :
              ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),V_Q_2),B_y))))
              & hBOOL(hAPP(V_P_2,B_y)) ) )
        & ( ! [B_y] :
              ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),V_Q_2),B_y))))
              | ~ hBOOL(hAPP(V_P_2,B_y)) )
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_P_2))),V_Q_2))))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2))) ),
    inference(fof_nnf,[status(thm)],[fact_finite__Collect__bounded__ex]) ).

fof(f_3365_2,plain,
    ! [U_13169,U_13168,U_13167,U_13166] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13168),hAPP(c_Set_OCollect(U_13168),hAPP(hAPP(c_COMBB(tc_fun(U_13166,tc_HOL_Obool),tc_HOL_Obool,U_13168),c_HOL_OEx(U_13166)),hAPP(hAPP(c_COMBB(tc_fun(U_13166,tc_HOL_Obool),tc_fun(U_13166,tc_HOL_Obool),U_13168),hAPP(c_COMBS(U_13166,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13166),c_fconj),U_13167))),U_13169)))))
          | ? [U_13165] :
              ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13168),hAPP(c_Set_OCollect(U_13168),hAPP(hAPP(c_COMBC(U_13168,U_13166,tc_HOL_Obool),U_13169),U_13165))))
              & hBOOL(hAPP(U_13167,U_13165)) ) )
        & ( ! [U_13164] :
              ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13168),hAPP(c_Set_OCollect(U_13168),hAPP(hAPP(c_COMBC(U_13168,U_13166,tc_HOL_Obool),U_13169),U_13164))))
              | ~ hBOOL(hAPP(U_13167,U_13164)) )
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13168),hAPP(c_Set_OCollect(U_13168),hAPP(hAPP(c_COMBB(tc_fun(U_13166,tc_HOL_Obool),tc_HOL_Obool,U_13168),c_HOL_OEx(U_13166)),hAPP(hAPP(c_COMBB(tc_fun(U_13166,tc_HOL_Obool),tc_fun(U_13166,tc_HOL_Obool),U_13168),hAPP(c_COMBS(U_13166,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13166),c_fconj),U_13167))),U_13169))))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13166),hAPP(c_Set_OCollect(U_13166),U_13167))) ),
    inference(variable_rename,[status(thm)],[f_3365_1]) ).

fof(f_3365_3,plain,
    ! [U_13169,U_13168,U_13167,U_13166] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13168),hAPP(c_Set_OCollect(U_13168),hAPP(hAPP(c_COMBB(tc_fun(U_13166,tc_HOL_Obool),tc_HOL_Obool,U_13168),c_HOL_OEx(U_13166)),hAPP(hAPP(c_COMBB(tc_fun(U_13166,tc_HOL_Obool),tc_fun(U_13166,tc_HOL_Obool),U_13168),hAPP(c_COMBS(U_13166,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13166),c_fconj),U_13167))),U_13169)))))
          | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13168),hAPP(c_Set_OCollect(U_13168),hAPP(hAPP(c_COMBC(U_13168,U_13166,tc_HOL_Obool),U_13169),sK314(U_13169,U_13168,U_13167,U_13166)))))
            & hBOOL(hAPP(U_13167,sK314(U_13169,U_13168,U_13167,U_13166))) ) )
        & ( ! [U_13164] :
              ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13168),hAPP(c_Set_OCollect(U_13168),hAPP(hAPP(c_COMBC(U_13168,U_13166,tc_HOL_Obool),U_13169),U_13164))))
              | ~ hBOOL(hAPP(U_13167,U_13164)) )
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13168),hAPP(c_Set_OCollect(U_13168),hAPP(hAPP(c_COMBB(tc_fun(U_13166,tc_HOL_Obool),tc_HOL_Obool,U_13168),c_HOL_OEx(U_13166)),hAPP(hAPP(c_COMBB(tc_fun(U_13166,tc_HOL_Obool),tc_fun(U_13166,tc_HOL_Obool),U_13168),hAPP(c_COMBS(U_13166,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13166),c_fconj),U_13167))),U_13169))))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13166),hAPP(c_Set_OCollect(U_13166),U_13167))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK314]),skolemize(U_13165,sK314(U_13169,U_13168,U_13167,U_13166))],[f_3365_2]) ).

cnf(f_3365_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13168),hAPP(c_Set_OCollect(U_13168),hAPP(hAPP(c_COMBC(U_13168,U_13166,tc_HOL_Obool),U_13169),U_13164))))
    | ~ hBOOL(hAPP(U_13167,U_13164))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13168),hAPP(c_Set_OCollect(U_13168),hAPP(hAPP(c_COMBB(tc_fun(U_13166,tc_HOL_Obool),tc_HOL_Obool,U_13168),c_HOL_OEx(U_13166)),hAPP(hAPP(c_COMBB(tc_fun(U_13166,tc_HOL_Obool),tc_fun(U_13166,tc_HOL_Obool),U_13168),hAPP(c_COMBS(U_13166,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13166),c_fconj),U_13167))),U_13169)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13166),hAPP(c_Set_OCollect(U_13166),U_13167))) ),
    inference(clausify,[status(thm)],[f_3365_3]) ).

cnf(f_3365_5,plain,
    ( hBOOL(hAPP(U_13167,sK314(U_13169,U_13168,U_13167,U_13166)))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_13168),hAPP(c_Set_OCollect(U_13168),hAPP(hAPP(c_COMBB(tc_fun(U_13166,tc_HOL_Obool),tc_HOL_Obool,U_13168),c_HOL_OEx(U_13166)),hAPP(hAPP(c_COMBB(tc_fun(U_13166,tc_HOL_Obool),tc_fun(U_13166,tc_HOL_Obool),U_13168),hAPP(c_COMBS(U_13166,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13166),c_fconj),U_13167))),U_13169)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13166),hAPP(c_Set_OCollect(U_13166),U_13167))) ),
    inference(clausify,[status(thm)],[f_3365_3]) ).

cnf(f_3365_6,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13168),hAPP(c_Set_OCollect(U_13168),hAPP(hAPP(c_COMBC(U_13168,U_13166,tc_HOL_Obool),U_13169),sK314(U_13169,U_13168,U_13167,U_13166)))))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_13168),hAPP(c_Set_OCollect(U_13168),hAPP(hAPP(c_COMBB(tc_fun(U_13166,tc_HOL_Obool),tc_HOL_Obool,U_13168),c_HOL_OEx(U_13166)),hAPP(hAPP(c_COMBB(tc_fun(U_13166,tc_HOL_Obool),tc_fun(U_13166,tc_HOL_Obool),U_13168),hAPP(c_COMBS(U_13166,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13166),c_fconj),U_13167))),U_13169)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13166),hAPP(c_Set_OCollect(U_13166),U_13167))) ),
    inference(clausify,[status(thm)],[f_3365_3]) ).

fof(f_3366_1,plain,
    ! [V_f_2,T_c,V_P_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),T_c),c_COMBB(T_c,tc_HOL_Obool,T_b)),c_fequal)),V_f_2)))),V_P_2)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2))) ),
    inference(fof_nnf,[status(thm)],[fact_finite__image__set]) ).

fof(f_3366_2,plain,
    ! [U_13173,U_13172,U_13171,U_13170] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13172),hAPP(c_Set_OCollect(U_13172),hAPP(hAPP(c_COMBB(tc_fun(U_13170,tc_HOL_Obool),tc_HOL_Obool,U_13172),c_HOL_OEx(U_13170)),hAPP(hAPP(c_COMBC(U_13172,tc_fun(U_13170,tc_HOL_Obool),tc_fun(U_13170,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13170,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13170,tc_HOL_Obool),tc_fun(U_13170,tc_HOL_Obool)),U_13172),c_COMBS(U_13170,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13170,tc_HOL_Obool),tc_fun(U_13170,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13172),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13170),c_fconj)),hAPP(hAPP(c_COMBC(U_13172,tc_fun(U_13170,U_13172),tc_fun(U_13170,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13172,tc_HOL_Obool),tc_fun(tc_fun(U_13170,U_13172),tc_fun(U_13170,tc_HOL_Obool)),U_13172),c_COMBB(U_13172,tc_HOL_Obool,U_13170)),c_fequal)),U_13173)))),U_13171)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13170),hAPP(c_Set_OCollect(U_13170),U_13171))) ),
    inference(variable_rename,[status(thm)],[f_3366_1]) ).

cnf(f_3366_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13172),hAPP(c_Set_OCollect(U_13172),hAPP(hAPP(c_COMBB(tc_fun(U_13170,tc_HOL_Obool),tc_HOL_Obool,U_13172),c_HOL_OEx(U_13170)),hAPP(hAPP(c_COMBC(U_13172,tc_fun(U_13170,tc_HOL_Obool),tc_fun(U_13170,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13170,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13170,tc_HOL_Obool),tc_fun(U_13170,tc_HOL_Obool)),U_13172),c_COMBS(U_13170,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13170,tc_HOL_Obool),tc_fun(U_13170,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13172),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13170),c_fconj)),hAPP(hAPP(c_COMBC(U_13172,tc_fun(U_13170,U_13172),tc_fun(U_13170,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13172,tc_HOL_Obool),tc_fun(tc_fun(U_13170,U_13172),tc_fun(U_13170,tc_HOL_Obool)),U_13172),c_COMBB(U_13172,tc_HOL_Obool,U_13170)),c_fequal)),U_13173)))),U_13171)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13170),hAPP(c_Set_OCollect(U_13170),U_13171))) ),
    inference(clausify,[status(thm)],[f_3366_2]) ).

fof(f_3367_1,plain,
    ! [T_c,T_b] : c_Fun_Oinj__on(tc_fun(T_b,T_c),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_b,T_c)),c_Set_OCollect(tc_prod(T_b,T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_b,T_c)),c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool)),hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBC(T_c,T_c,tc_HOL_Obool),c_fequal)))),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,T_c),tc_HOL_Obool))),
    inference(fof_nnf,[status(thm)],[fact_inj__graph]) ).

fof(f_3367_2,plain,
    ! [U_13175,U_13174] : c_Fun_Oinj__on(tc_fun(U_13174,U_13175),tc_fun(tc_prod(U_13174,U_13175),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_13174,U_13175),tc_HOL_Obool),tc_fun(tc_prod(U_13174,U_13175),tc_HOL_Obool),tc_fun(U_13174,U_13175)),c_Set_OCollect(tc_prod(U_13174,U_13175))),hAPP(hAPP(c_COMBB(tc_fun(U_13174,tc_fun(U_13175,tc_HOL_Obool)),tc_fun(tc_prod(U_13174,U_13175),tc_HOL_Obool),tc_fun(U_13174,U_13175)),c_Product__Type_Oprod_Oprod__case(U_13174,U_13175,tc_HOL_Obool)),hAPP(c_COMBB(U_13175,tc_fun(U_13175,tc_HOL_Obool),U_13174),hAPP(c_COMBC(U_13175,U_13175,tc_HOL_Obool),c_fequal)))),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_13174,U_13175),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_3367_1]) ).

cnf(f_3367_3,plain,
    c_Fun_Oinj__on(tc_fun(U_13174,U_13175),tc_fun(tc_prod(U_13174,U_13175),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_13174,U_13175),tc_HOL_Obool),tc_fun(tc_prod(U_13174,U_13175),tc_HOL_Obool),tc_fun(U_13174,U_13175)),c_Set_OCollect(tc_prod(U_13174,U_13175))),hAPP(hAPP(c_COMBB(tc_fun(U_13174,tc_fun(U_13175,tc_HOL_Obool)),tc_fun(tc_prod(U_13174,U_13175),tc_HOL_Obool),tc_fun(U_13174,U_13175)),c_Product__Type_Oprod_Oprod__case(U_13174,U_13175,tc_HOL_Obool)),hAPP(c_COMBB(U_13175,tc_fun(U_13175,tc_HOL_Obool),U_13174),hAPP(c_COMBC(U_13175,U_13175,tc_HOL_Obool),c_fequal)))),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_13174,U_13175),tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_3367_2]) ).

fof(f_3368_1,plain,
    ! [V_P_2] : c_Nat__Transfer_Onat__set(hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_P_2))),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J]) ).

fof(f_3368_2,plain,
    ! [U_13176] : c_Nat__Transfer_Onat__set(hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),U_13176))),
    inference(variable_rename,[status(thm)],[f_3368_1]) ).

cnf(f_3368_3,plain,
    c_Nat__Transfer_Onat__set(hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),U_13176))),
    inference(clausify,[status(thm)],[f_3368_2]) ).

fof(f_3369_1,plain,
    ! [T_b] : c_Wellfounded_Ofinite__psubset(T_b) = hAPP(c_Set_OCollect(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBS(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_fconj)),c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool))))),c_Finite__Set_Ofinite(T_b)))),
    inference(fof_nnf,[status(thm)],[fact_finite__psubset__def]) ).

fof(f_3369_2,plain,
    ! [U_13177] : c_Wellfounded_Ofinite__psubset(U_13177) = hAPP(c_Set_OCollect(tc_prod(tc_fun(U_13177,tc_HOL_Obool),tc_fun(U_13177,tc_HOL_Obool))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(U_13177,tc_HOL_Obool),tc_fun(U_13177,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(U_13177,tc_HOL_Obool),tc_fun(tc_fun(U_13177,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_13177,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13177,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(U_13177,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_13177,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(U_13177,tc_HOL_Obool)),c_COMBS(tc_fun(U_13177,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13177,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_13177,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(U_13177,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(U_13177,tc_HOL_Obool)),c_fconj)),c_Orderings_Oord__class_Oless(tc_fun(U_13177,tc_HOL_Obool))))),c_Finite__Set_Ofinite(U_13177)))),
    inference(variable_rename,[status(thm)],[f_3369_1]) ).

cnf(f_3369_3,plain,
    c_Wellfounded_Ofinite__psubset(U_13177) = hAPP(c_Set_OCollect(tc_prod(tc_fun(U_13177,tc_HOL_Obool),tc_fun(U_13177,tc_HOL_Obool))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(U_13177,tc_HOL_Obool),tc_fun(U_13177,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(U_13177,tc_HOL_Obool),tc_fun(tc_fun(U_13177,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_13177,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13177,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(U_13177,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_13177,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(U_13177,tc_HOL_Obool)),c_COMBS(tc_fun(U_13177,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13177,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_13177,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(U_13177,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(U_13177,tc_HOL_Obool)),c_fconj)),c_Orderings_Oord__class_Oless(tc_fun(U_13177,tc_HOL_Obool))))),c_Finite__Set_Ofinite(U_13177)))),
    inference(clausify,[status(thm)],[f_3369_2]) ).

fof(f_3370_1,plain,
    ! [V_f_2,V_r_2,T_b,T_c] : hAPP(hAPP(c_Relation_Oinv__image(T_c,T_b),V_r_2),V_f_2) = hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_c,T_c)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_c,T_c),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_c,T_c)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_c),tc_fun(T_b,tc_prod(T_c,T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_c,T_c)),tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,tc_prod(T_c,T_c))),T_b),c_COMBB(T_c,tc_prod(T_c,T_c),T_b)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_prod(T_c,T_c)),T_b),c_Product__Type_OPair(T_c,T_c)),V_f_2))),V_f_2)))),V_r_2))),
    inference(fof_nnf,[status(thm)],[fact_inv__image__def]) ).

fof(f_3370_2,plain,
    ! [U_13181,U_13180,U_13179,U_13178] : hAPP(hAPP(c_Relation_Oinv__image(U_13178,U_13179),U_13180),U_13181) = hAPP(c_Set_OCollect(tc_prod(U_13179,U_13179)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13179,U_13179,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13179,tc_fun(tc_prod(U_13178,U_13178),tc_HOL_Obool),tc_fun(U_13179,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13179,tc_fun(tc_fun(tc_prod(U_13178,U_13178),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13178,U_13178),tc_HOL_Obool),tc_fun(U_13179,tc_HOL_Obool)),U_13179),c_COMBC(U_13179,tc_fun(tc_prod(U_13178,U_13178),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13179,tc_prod(U_13178,U_13178)),tc_fun(U_13179,tc_fun(tc_fun(tc_prod(U_13178,U_13178),tc_HOL_Obool),tc_HOL_Obool)),U_13179),hAPP(c_COMBB(tc_prod(U_13178,U_13178),tc_fun(tc_fun(tc_prod(U_13178,U_13178),tc_HOL_Obool),tc_HOL_Obool),U_13179),c_member(tc_prod(U_13178,U_13178)))),hAPP(hAPP(c_COMBC(U_13179,tc_fun(U_13179,U_13178),tc_fun(U_13179,tc_prod(U_13178,U_13178))),hAPP(hAPP(c_COMBB(tc_fun(U_13178,tc_prod(U_13178,U_13178)),tc_fun(tc_fun(U_13179,U_13178),tc_fun(U_13179,tc_prod(U_13178,U_13178))),U_13179),c_COMBB(U_13178,tc_prod(U_13178,U_13178),U_13179)),hAPP(hAPP(c_COMBB(U_13178,tc_fun(U_13178,tc_prod(U_13178,U_13178)),U_13179),c_Product__Type_OPair(U_13178,U_13178)),U_13181))),U_13181)))),U_13180))),
    inference(variable_rename,[status(thm)],[f_3370_1]) ).

cnf(f_3370_3,plain,
    hAPP(hAPP(c_Relation_Oinv__image(U_13178,U_13179),U_13180),U_13181) = hAPP(c_Set_OCollect(tc_prod(U_13179,U_13179)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13179,U_13179,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13179,tc_fun(tc_prod(U_13178,U_13178),tc_HOL_Obool),tc_fun(U_13179,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13179,tc_fun(tc_fun(tc_prod(U_13178,U_13178),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13178,U_13178),tc_HOL_Obool),tc_fun(U_13179,tc_HOL_Obool)),U_13179),c_COMBC(U_13179,tc_fun(tc_prod(U_13178,U_13178),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13179,tc_prod(U_13178,U_13178)),tc_fun(U_13179,tc_fun(tc_fun(tc_prod(U_13178,U_13178),tc_HOL_Obool),tc_HOL_Obool)),U_13179),hAPP(c_COMBB(tc_prod(U_13178,U_13178),tc_fun(tc_fun(tc_prod(U_13178,U_13178),tc_HOL_Obool),tc_HOL_Obool),U_13179),c_member(tc_prod(U_13178,U_13178)))),hAPP(hAPP(c_COMBC(U_13179,tc_fun(U_13179,U_13178),tc_fun(U_13179,tc_prod(U_13178,U_13178))),hAPP(hAPP(c_COMBB(tc_fun(U_13178,tc_prod(U_13178,U_13178)),tc_fun(tc_fun(U_13179,U_13178),tc_fun(U_13179,tc_prod(U_13178,U_13178))),U_13179),c_COMBB(U_13178,tc_prod(U_13178,U_13178),U_13179)),hAPP(hAPP(c_COMBB(U_13178,tc_fun(U_13178,tc_prod(U_13178,U_13178)),U_13179),c_Product__Type_OPair(U_13178,U_13178)),U_13181))),U_13181)))),U_13180))),
    inference(clausify,[status(thm)],[f_3370_2]) ).

fof(f_3371_1,plain,
    ! [V_P_2] : hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_P_2)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Nat_Onat),V_P_2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J]) ).

fof(f_3371_2,plain,
    ! [U_13182] : hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),U_13182)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Nat_Onat),U_13182),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))),
    inference(variable_rename,[status(thm)],[f_3371_1]) ).

cnf(f_3371_3,plain,
    hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),U_13182)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Nat_Onat),U_13182),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))),
    inference(clausify,[status(thm)],[f_3371_2]) ).

fof(f_3372_1,plain,
    ! [V_P_2] : hAPP(c_Set_OCollect(tc_Nat_Onat),V_P_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),V_P_2),c_Int_Onat)))),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J]) ).

fof(f_3372_2,plain,
    ! [U_13183] : hAPP(c_Set_OCollect(tc_Nat_Onat),U_13183) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),U_13183),c_Int_Onat)))),
    inference(variable_rename,[status(thm)],[f_3372_1]) ).

cnf(f_3372_3,plain,
    hAPP(c_Set_OCollect(tc_Nat_Onat),U_13183) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),U_13183),c_Int_Onat)))),
    inference(clausify,[status(thm)],[f_3372_2]) ).

fof(f_3373_1,plain,
    ! [V_k_2,V_N_2,T_b] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_k_2),c_Big__Operators_Olinorder__class_OMin(T_b,V_N_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(T_b),V_k_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_N_2)))))
      | V_N_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
      | ~ class_Groups_Olinordered__ab__semigroup__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_add__Min__commute]) ).

fof(f_3373_2,plain,
    ! [U_13186,U_13185,U_13184] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_13184),U_13186),c_Big__Operators_Olinorder__class_OMin(U_13184,U_13185)) = c_Big__Operators_Olinorder__class_OMin(U_13184,hAPP(c_Set_OCollect(U_13184),hAPP(hAPP(c_COMBB(tc_fun(U_13184,tc_HOL_Obool),tc_HOL_Obool,U_13184),c_HOL_OEx(U_13184)),hAPP(hAPP(c_COMBC(U_13184,tc_fun(U_13184,tc_HOL_Obool),tc_fun(U_13184,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13184,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13184,tc_HOL_Obool),tc_fun(U_13184,tc_HOL_Obool)),U_13184),c_COMBS(U_13184,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13184,tc_HOL_Obool),tc_fun(U_13184,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13184),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13184),c_fconj)),hAPP(hAPP(c_COMBC(U_13184,tc_fun(U_13184,U_13184),tc_fun(U_13184,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13184,tc_HOL_Obool),tc_fun(tc_fun(U_13184,U_13184),tc_fun(U_13184,tc_HOL_Obool)),U_13184),c_COMBB(U_13184,tc_HOL_Obool,U_13184)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(U_13184),U_13186))))),hAPP(hAPP(c_COMBC(U_13184,tc_fun(U_13184,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13184)),U_13185)))))
      | U_13185 = c_Orderings_Obot__class_Obot(tc_fun(U_13184,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13184),U_13185))
      | ~ class_Groups_Olinordered__ab__semigroup__add(U_13184) ),
    inference(variable_rename,[status(thm)],[f_3373_1]) ).

cnf(f_3373_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_13184),U_13186),c_Big__Operators_Olinorder__class_OMin(U_13184,U_13185)) = c_Big__Operators_Olinorder__class_OMin(U_13184,hAPP(c_Set_OCollect(U_13184),hAPP(hAPP(c_COMBB(tc_fun(U_13184,tc_HOL_Obool),tc_HOL_Obool,U_13184),c_HOL_OEx(U_13184)),hAPP(hAPP(c_COMBC(U_13184,tc_fun(U_13184,tc_HOL_Obool),tc_fun(U_13184,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13184,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13184,tc_HOL_Obool),tc_fun(U_13184,tc_HOL_Obool)),U_13184),c_COMBS(U_13184,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13184,tc_HOL_Obool),tc_fun(U_13184,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13184),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13184),c_fconj)),hAPP(hAPP(c_COMBC(U_13184,tc_fun(U_13184,U_13184),tc_fun(U_13184,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13184,tc_HOL_Obool),tc_fun(tc_fun(U_13184,U_13184),tc_fun(U_13184,tc_HOL_Obool)),U_13184),c_COMBB(U_13184,tc_HOL_Obool,U_13184)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(U_13184),U_13186))))),hAPP(hAPP(c_COMBC(U_13184,tc_fun(U_13184,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13184)),U_13185)))))
    | U_13185 = c_Orderings_Obot__class_Obot(tc_fun(U_13184,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13184),U_13185))
    | ~ class_Groups_Olinordered__ab__semigroup__add(U_13184) ),
    inference(clausify,[status(thm)],[f_3373_2]) ).

fof(f_3374_1,plain,
    ! [V_k_2,V_N_2,T_b] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_k_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_N_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(T_b),V_k_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_N_2)))))
      | V_N_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
      | ~ class_Groups_Olinordered__ab__semigroup__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_add__Max__commute]) ).

fof(f_3374_2,plain,
    ! [U_13189,U_13188,U_13187] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_13187),U_13189),c_Big__Operators_Olinorder__class_OMax(U_13187,U_13188)) = c_Big__Operators_Olinorder__class_OMax(U_13187,hAPP(c_Set_OCollect(U_13187),hAPP(hAPP(c_COMBB(tc_fun(U_13187,tc_HOL_Obool),tc_HOL_Obool,U_13187),c_HOL_OEx(U_13187)),hAPP(hAPP(c_COMBC(U_13187,tc_fun(U_13187,tc_HOL_Obool),tc_fun(U_13187,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13187,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13187,tc_HOL_Obool),tc_fun(U_13187,tc_HOL_Obool)),U_13187),c_COMBS(U_13187,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13187,tc_HOL_Obool),tc_fun(U_13187,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13187),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13187),c_fconj)),hAPP(hAPP(c_COMBC(U_13187,tc_fun(U_13187,U_13187),tc_fun(U_13187,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13187,tc_HOL_Obool),tc_fun(tc_fun(U_13187,U_13187),tc_fun(U_13187,tc_HOL_Obool)),U_13187),c_COMBB(U_13187,tc_HOL_Obool,U_13187)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(U_13187),U_13189))))),hAPP(hAPP(c_COMBC(U_13187,tc_fun(U_13187,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13187)),U_13188)))))
      | U_13188 = c_Orderings_Obot__class_Obot(tc_fun(U_13187,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13187),U_13188))
      | ~ class_Groups_Olinordered__ab__semigroup__add(U_13187) ),
    inference(variable_rename,[status(thm)],[f_3374_1]) ).

cnf(f_3374_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_13187),U_13189),c_Big__Operators_Olinorder__class_OMax(U_13187,U_13188)) = c_Big__Operators_Olinorder__class_OMax(U_13187,hAPP(c_Set_OCollect(U_13187),hAPP(hAPP(c_COMBB(tc_fun(U_13187,tc_HOL_Obool),tc_HOL_Obool,U_13187),c_HOL_OEx(U_13187)),hAPP(hAPP(c_COMBC(U_13187,tc_fun(U_13187,tc_HOL_Obool),tc_fun(U_13187,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13187,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13187,tc_HOL_Obool),tc_fun(U_13187,tc_HOL_Obool)),U_13187),c_COMBS(U_13187,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13187,tc_HOL_Obool),tc_fun(U_13187,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13187),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13187),c_fconj)),hAPP(hAPP(c_COMBC(U_13187,tc_fun(U_13187,U_13187),tc_fun(U_13187,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13187,tc_HOL_Obool),tc_fun(tc_fun(U_13187,U_13187),tc_fun(U_13187,tc_HOL_Obool)),U_13187),c_COMBB(U_13187,tc_HOL_Obool,U_13187)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(U_13187),U_13189))))),hAPP(hAPP(c_COMBC(U_13187,tc_fun(U_13187,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13187)),U_13188)))))
    | U_13188 = c_Orderings_Obot__class_Obot(tc_fun(U_13187,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13187),U_13188))
    | ~ class_Groups_Olinordered__ab__semigroup__add(U_13187) ),
    inference(clausify,[status(thm)],[f_3374_2]) ).

fof(f_3375_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Odistrib__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sup__Inf1__distrib]) ).

fof(f_3375_2,plain,
    ! [U_13192,U_13191,U_13190] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_13190),U_13192),c_Big__Operators_Olattice__class_OInf__fin(U_13190,U_13191)) = c_Big__Operators_Olattice__class_OInf__fin(U_13190,hAPP(c_Set_OCollect(U_13190),hAPP(hAPP(c_COMBB(tc_fun(U_13190,tc_HOL_Obool),tc_HOL_Obool,U_13190),c_HOL_OEx(U_13190)),hAPP(hAPP(c_COMBC(U_13190,tc_fun(U_13190,tc_HOL_Obool),tc_fun(U_13190,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13190,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13190,tc_HOL_Obool),tc_fun(U_13190,tc_HOL_Obool)),U_13190),c_COMBS(U_13190,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13190,tc_HOL_Obool),tc_fun(U_13190,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13190),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13190),c_fconj)),hAPP(hAPP(c_COMBC(U_13190,tc_fun(U_13190,U_13190),tc_fun(U_13190,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13190,tc_HOL_Obool),tc_fun(tc_fun(U_13190,U_13190),tc_fun(U_13190,tc_HOL_Obool)),U_13190),c_COMBB(U_13190,tc_HOL_Obool,U_13190)),c_fequal)),hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_13190),U_13192))))),hAPP(hAPP(c_COMBC(U_13190,tc_fun(U_13190,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13190)),U_13191)))))
      | U_13191 = c_Orderings_Obot__class_Obot(tc_fun(U_13190,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13190),U_13191))
      | ~ class_Lattices_Odistrib__lattice(U_13190) ),
    inference(variable_rename,[status(thm)],[f_3375_1]) ).

cnf(f_3375_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_13190),U_13192),c_Big__Operators_Olattice__class_OInf__fin(U_13190,U_13191)) = c_Big__Operators_Olattice__class_OInf__fin(U_13190,hAPP(c_Set_OCollect(U_13190),hAPP(hAPP(c_COMBB(tc_fun(U_13190,tc_HOL_Obool),tc_HOL_Obool,U_13190),c_HOL_OEx(U_13190)),hAPP(hAPP(c_COMBC(U_13190,tc_fun(U_13190,tc_HOL_Obool),tc_fun(U_13190,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13190,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13190,tc_HOL_Obool),tc_fun(U_13190,tc_HOL_Obool)),U_13190),c_COMBS(U_13190,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13190,tc_HOL_Obool),tc_fun(U_13190,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13190),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13190),c_fconj)),hAPP(hAPP(c_COMBC(U_13190,tc_fun(U_13190,U_13190),tc_fun(U_13190,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13190,tc_HOL_Obool),tc_fun(tc_fun(U_13190,U_13190),tc_fun(U_13190,tc_HOL_Obool)),U_13190),c_COMBB(U_13190,tc_HOL_Obool,U_13190)),c_fequal)),hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_13190),U_13192))))),hAPP(hAPP(c_COMBC(U_13190,tc_fun(U_13190,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13190)),U_13191)))))
    | U_13191 = c_Orderings_Obot__class_Obot(tc_fun(U_13190,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13190),U_13191))
    | ~ class_Lattices_Odistrib__lattice(U_13190) ),
    inference(clausify,[status(thm)],[f_3375_2]) ).

fof(f_3376_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBS(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal))),c_Lattices_Osemilattice__sup__class_Osup(T_b)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2)))))))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Odistrib__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sup__Inf2__distrib]) ).

fof(f_3376_2,plain,
    ! [U_13195,U_13194,U_13193] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_13193),c_Big__Operators_Olattice__class_OInf__fin(U_13193,U_13194)),c_Big__Operators_Olattice__class_OInf__fin(U_13193,U_13195)) = c_Big__Operators_Olattice__class_OInf__fin(U_13193,hAPP(c_Set_OCollect(U_13193),hAPP(hAPP(c_COMBB(tc_fun(U_13193,tc_HOL_Obool),tc_HOL_Obool,U_13193),c_HOL_OEx(U_13193)),hAPP(hAPP(c_COMBB(tc_fun(U_13193,tc_fun(U_13193,tc_HOL_Obool)),tc_fun(U_13193,tc_HOL_Obool),U_13193),hAPP(c_COMBB(tc_fun(U_13193,tc_HOL_Obool),tc_HOL_Obool,U_13193),c_HOL_OEx(U_13193))),hAPP(hAPP(c_COMBC(U_13193,tc_fun(U_13193,tc_fun(U_13193,tc_HOL_Obool)),tc_fun(U_13193,tc_fun(U_13193,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13193,tc_fun(tc_fun(U_13193,tc_HOL_Obool),tc_fun(U_13193,tc_HOL_Obool))),tc_fun(tc_fun(U_13193,tc_fun(U_13193,tc_HOL_Obool)),tc_fun(U_13193,tc_fun(U_13193,tc_HOL_Obool))),U_13193),c_COMBS(U_13193,tc_fun(U_13193,tc_HOL_Obool),tc_fun(U_13193,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13193,tc_fun(U_13193,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_13193,tc_fun(tc_fun(U_13193,tc_HOL_Obool),tc_fun(U_13193,tc_HOL_Obool))),U_13193),hAPP(c_COMBB(tc_fun(U_13193,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13193,tc_HOL_Obool),tc_fun(U_13193,tc_HOL_Obool)),U_13193),c_COMBS(U_13193,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13193,tc_fun(U_13193,tc_HOL_Obool)),tc_fun(U_13193,tc_fun(U_13193,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_13193),hAPP(c_COMBB(tc_fun(U_13193,tc_HOL_Obool),tc_fun(U_13193,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13193),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13193),c_fconj))),hAPP(hAPP(c_COMBC(U_13193,tc_fun(U_13193,tc_fun(U_13193,U_13193)),tc_fun(U_13193,tc_fun(U_13193,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13193,U_13193),tc_fun(U_13193,tc_HOL_Obool)),tc_fun(tc_fun(U_13193,tc_fun(U_13193,U_13193)),tc_fun(U_13193,tc_fun(U_13193,tc_HOL_Obool))),U_13193),c_COMBB(tc_fun(U_13193,U_13193),tc_fun(U_13193,tc_HOL_Obool),U_13193)),hAPP(hAPP(c_COMBB(tc_fun(U_13193,tc_HOL_Obool),tc_fun(tc_fun(U_13193,U_13193),tc_fun(U_13193,tc_HOL_Obool)),U_13193),c_COMBB(U_13193,tc_HOL_Obool,U_13193)),c_fequal))),c_Lattices_Osemilattice__sup__class_Osup(U_13193)))))),hAPP(hAPP(c_COMBC(U_13193,tc_fun(U_13193,tc_HOL_Obool),tc_fun(U_13193,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13193,tc_HOL_Obool),tc_fun(U_13193,tc_HOL_Obool)),U_13193),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13193)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13193),c_fconj),hAPP(hAPP(c_COMBC(U_13193,tc_fun(U_13193,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13193)),U_13194)))),hAPP(hAPP(c_COMBC(U_13193,tc_fun(U_13193,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13193)),U_13195)))))))
      | U_13195 = c_Orderings_Obot__class_Obot(tc_fun(U_13193,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13193),U_13195))
      | U_13194 = c_Orderings_Obot__class_Obot(tc_fun(U_13193,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13193),U_13194))
      | ~ class_Lattices_Odistrib__lattice(U_13193) ),
    inference(variable_rename,[status(thm)],[f_3376_1]) ).

cnf(f_3376_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_13193),c_Big__Operators_Olattice__class_OInf__fin(U_13193,U_13194)),c_Big__Operators_Olattice__class_OInf__fin(U_13193,U_13195)) = c_Big__Operators_Olattice__class_OInf__fin(U_13193,hAPP(c_Set_OCollect(U_13193),hAPP(hAPP(c_COMBB(tc_fun(U_13193,tc_HOL_Obool),tc_HOL_Obool,U_13193),c_HOL_OEx(U_13193)),hAPP(hAPP(c_COMBB(tc_fun(U_13193,tc_fun(U_13193,tc_HOL_Obool)),tc_fun(U_13193,tc_HOL_Obool),U_13193),hAPP(c_COMBB(tc_fun(U_13193,tc_HOL_Obool),tc_HOL_Obool,U_13193),c_HOL_OEx(U_13193))),hAPP(hAPP(c_COMBC(U_13193,tc_fun(U_13193,tc_fun(U_13193,tc_HOL_Obool)),tc_fun(U_13193,tc_fun(U_13193,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13193,tc_fun(tc_fun(U_13193,tc_HOL_Obool),tc_fun(U_13193,tc_HOL_Obool))),tc_fun(tc_fun(U_13193,tc_fun(U_13193,tc_HOL_Obool)),tc_fun(U_13193,tc_fun(U_13193,tc_HOL_Obool))),U_13193),c_COMBS(U_13193,tc_fun(U_13193,tc_HOL_Obool),tc_fun(U_13193,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13193,tc_fun(U_13193,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_13193,tc_fun(tc_fun(U_13193,tc_HOL_Obool),tc_fun(U_13193,tc_HOL_Obool))),U_13193),hAPP(c_COMBB(tc_fun(U_13193,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13193,tc_HOL_Obool),tc_fun(U_13193,tc_HOL_Obool)),U_13193),c_COMBS(U_13193,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13193,tc_fun(U_13193,tc_HOL_Obool)),tc_fun(U_13193,tc_fun(U_13193,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_13193),hAPP(c_COMBB(tc_fun(U_13193,tc_HOL_Obool),tc_fun(U_13193,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13193),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13193),c_fconj))),hAPP(hAPP(c_COMBC(U_13193,tc_fun(U_13193,tc_fun(U_13193,U_13193)),tc_fun(U_13193,tc_fun(U_13193,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13193,U_13193),tc_fun(U_13193,tc_HOL_Obool)),tc_fun(tc_fun(U_13193,tc_fun(U_13193,U_13193)),tc_fun(U_13193,tc_fun(U_13193,tc_HOL_Obool))),U_13193),c_COMBB(tc_fun(U_13193,U_13193),tc_fun(U_13193,tc_HOL_Obool),U_13193)),hAPP(hAPP(c_COMBB(tc_fun(U_13193,tc_HOL_Obool),tc_fun(tc_fun(U_13193,U_13193),tc_fun(U_13193,tc_HOL_Obool)),U_13193),c_COMBB(U_13193,tc_HOL_Obool,U_13193)),c_fequal))),c_Lattices_Osemilattice__sup__class_Osup(U_13193)))))),hAPP(hAPP(c_COMBC(U_13193,tc_fun(U_13193,tc_HOL_Obool),tc_fun(U_13193,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13193,tc_HOL_Obool),tc_fun(U_13193,tc_HOL_Obool)),U_13193),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13193)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13193),c_fconj),hAPP(hAPP(c_COMBC(U_13193,tc_fun(U_13193,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13193)),U_13194)))),hAPP(hAPP(c_COMBC(U_13193,tc_fun(U_13193,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13193)),U_13195)))))))
    | U_13195 = c_Orderings_Obot__class_Obot(tc_fun(U_13193,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13193),U_13195))
    | U_13194 = c_Orderings_Obot__class_Obot(tc_fun(U_13193,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13193),U_13194))
    | ~ class_Lattices_Odistrib__lattice(U_13193) ),
    inference(clausify,[status(thm)],[f_3376_2]) ).

fof(f_3377_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Odistrib__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_inf__Sup1__distrib]) ).

fof(f_3377_2,plain,
    ! [U_13198,U_13197,U_13196] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_13196),U_13198),c_Big__Operators_Olattice__class_OSup__fin(U_13196,U_13197)) = c_Big__Operators_Olattice__class_OSup__fin(U_13196,hAPP(c_Set_OCollect(U_13196),hAPP(hAPP(c_COMBB(tc_fun(U_13196,tc_HOL_Obool),tc_HOL_Obool,U_13196),c_HOL_OEx(U_13196)),hAPP(hAPP(c_COMBC(U_13196,tc_fun(U_13196,tc_HOL_Obool),tc_fun(U_13196,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13196,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13196,tc_HOL_Obool),tc_fun(U_13196,tc_HOL_Obool)),U_13196),c_COMBS(U_13196,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13196,tc_HOL_Obool),tc_fun(U_13196,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13196),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13196),c_fconj)),hAPP(hAPP(c_COMBC(U_13196,tc_fun(U_13196,U_13196),tc_fun(U_13196,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13196,tc_HOL_Obool),tc_fun(tc_fun(U_13196,U_13196),tc_fun(U_13196,tc_HOL_Obool)),U_13196),c_COMBB(U_13196,tc_HOL_Obool,U_13196)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_13196),U_13198))))),hAPP(hAPP(c_COMBC(U_13196,tc_fun(U_13196,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13196)),U_13197)))))
      | U_13197 = c_Orderings_Obot__class_Obot(tc_fun(U_13196,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13196),U_13197))
      | ~ class_Lattices_Odistrib__lattice(U_13196) ),
    inference(variable_rename,[status(thm)],[f_3377_1]) ).

cnf(f_3377_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_13196),U_13198),c_Big__Operators_Olattice__class_OSup__fin(U_13196,U_13197)) = c_Big__Operators_Olattice__class_OSup__fin(U_13196,hAPP(c_Set_OCollect(U_13196),hAPP(hAPP(c_COMBB(tc_fun(U_13196,tc_HOL_Obool),tc_HOL_Obool,U_13196),c_HOL_OEx(U_13196)),hAPP(hAPP(c_COMBC(U_13196,tc_fun(U_13196,tc_HOL_Obool),tc_fun(U_13196,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13196,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13196,tc_HOL_Obool),tc_fun(U_13196,tc_HOL_Obool)),U_13196),c_COMBS(U_13196,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13196,tc_HOL_Obool),tc_fun(U_13196,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13196),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13196),c_fconj)),hAPP(hAPP(c_COMBC(U_13196,tc_fun(U_13196,U_13196),tc_fun(U_13196,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13196,tc_HOL_Obool),tc_fun(tc_fun(U_13196,U_13196),tc_fun(U_13196,tc_HOL_Obool)),U_13196),c_COMBB(U_13196,tc_HOL_Obool,U_13196)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_13196),U_13198))))),hAPP(hAPP(c_COMBC(U_13196,tc_fun(U_13196,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13196)),U_13197)))))
    | U_13197 = c_Orderings_Obot__class_Obot(tc_fun(U_13196,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13196),U_13197))
    | ~ class_Lattices_Odistrib__lattice(U_13196) ),
    inference(clausify,[status(thm)],[f_3377_2]) ).

fof(f_3378_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBS(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(T_b)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2)))))))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Lattices_Odistrib__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_inf__Sup2__distrib]) ).

fof(f_3378_2,plain,
    ! [U_13201,U_13200,U_13199] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_13199),c_Big__Operators_Olattice__class_OSup__fin(U_13199,U_13200)),c_Big__Operators_Olattice__class_OSup__fin(U_13199,U_13201)) = c_Big__Operators_Olattice__class_OSup__fin(U_13199,hAPP(c_Set_OCollect(U_13199),hAPP(hAPP(c_COMBB(tc_fun(U_13199,tc_HOL_Obool),tc_HOL_Obool,U_13199),c_HOL_OEx(U_13199)),hAPP(hAPP(c_COMBB(tc_fun(U_13199,tc_fun(U_13199,tc_HOL_Obool)),tc_fun(U_13199,tc_HOL_Obool),U_13199),hAPP(c_COMBB(tc_fun(U_13199,tc_HOL_Obool),tc_HOL_Obool,U_13199),c_HOL_OEx(U_13199))),hAPP(hAPP(c_COMBC(U_13199,tc_fun(U_13199,tc_fun(U_13199,tc_HOL_Obool)),tc_fun(U_13199,tc_fun(U_13199,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13199,tc_fun(tc_fun(U_13199,tc_HOL_Obool),tc_fun(U_13199,tc_HOL_Obool))),tc_fun(tc_fun(U_13199,tc_fun(U_13199,tc_HOL_Obool)),tc_fun(U_13199,tc_fun(U_13199,tc_HOL_Obool))),U_13199),c_COMBS(U_13199,tc_fun(U_13199,tc_HOL_Obool),tc_fun(U_13199,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13199,tc_fun(U_13199,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_13199,tc_fun(tc_fun(U_13199,tc_HOL_Obool),tc_fun(U_13199,tc_HOL_Obool))),U_13199),hAPP(c_COMBB(tc_fun(U_13199,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13199,tc_HOL_Obool),tc_fun(U_13199,tc_HOL_Obool)),U_13199),c_COMBS(U_13199,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13199,tc_fun(U_13199,tc_HOL_Obool)),tc_fun(U_13199,tc_fun(U_13199,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_13199),hAPP(c_COMBB(tc_fun(U_13199,tc_HOL_Obool),tc_fun(U_13199,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13199),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13199),c_fconj))),hAPP(hAPP(c_COMBC(U_13199,tc_fun(U_13199,tc_fun(U_13199,U_13199)),tc_fun(U_13199,tc_fun(U_13199,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13199,U_13199),tc_fun(U_13199,tc_HOL_Obool)),tc_fun(tc_fun(U_13199,tc_fun(U_13199,U_13199)),tc_fun(U_13199,tc_fun(U_13199,tc_HOL_Obool))),U_13199),c_COMBB(tc_fun(U_13199,U_13199),tc_fun(U_13199,tc_HOL_Obool),U_13199)),hAPP(hAPP(c_COMBB(tc_fun(U_13199,tc_HOL_Obool),tc_fun(tc_fun(U_13199,U_13199),tc_fun(U_13199,tc_HOL_Obool)),U_13199),c_COMBB(U_13199,tc_HOL_Obool,U_13199)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(U_13199)))))),hAPP(hAPP(c_COMBC(U_13199,tc_fun(U_13199,tc_HOL_Obool),tc_fun(U_13199,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13199,tc_HOL_Obool),tc_fun(U_13199,tc_HOL_Obool)),U_13199),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13199)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13199),c_fconj),hAPP(hAPP(c_COMBC(U_13199,tc_fun(U_13199,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13199)),U_13200)))),hAPP(hAPP(c_COMBC(U_13199,tc_fun(U_13199,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13199)),U_13201)))))))
      | U_13201 = c_Orderings_Obot__class_Obot(tc_fun(U_13199,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13199),U_13201))
      | U_13200 = c_Orderings_Obot__class_Obot(tc_fun(U_13199,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13199),U_13200))
      | ~ class_Lattices_Odistrib__lattice(U_13199) ),
    inference(variable_rename,[status(thm)],[f_3378_1]) ).

cnf(f_3378_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_13199),c_Big__Operators_Olattice__class_OSup__fin(U_13199,U_13200)),c_Big__Operators_Olattice__class_OSup__fin(U_13199,U_13201)) = c_Big__Operators_Olattice__class_OSup__fin(U_13199,hAPP(c_Set_OCollect(U_13199),hAPP(hAPP(c_COMBB(tc_fun(U_13199,tc_HOL_Obool),tc_HOL_Obool,U_13199),c_HOL_OEx(U_13199)),hAPP(hAPP(c_COMBB(tc_fun(U_13199,tc_fun(U_13199,tc_HOL_Obool)),tc_fun(U_13199,tc_HOL_Obool),U_13199),hAPP(c_COMBB(tc_fun(U_13199,tc_HOL_Obool),tc_HOL_Obool,U_13199),c_HOL_OEx(U_13199))),hAPP(hAPP(c_COMBC(U_13199,tc_fun(U_13199,tc_fun(U_13199,tc_HOL_Obool)),tc_fun(U_13199,tc_fun(U_13199,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13199,tc_fun(tc_fun(U_13199,tc_HOL_Obool),tc_fun(U_13199,tc_HOL_Obool))),tc_fun(tc_fun(U_13199,tc_fun(U_13199,tc_HOL_Obool)),tc_fun(U_13199,tc_fun(U_13199,tc_HOL_Obool))),U_13199),c_COMBS(U_13199,tc_fun(U_13199,tc_HOL_Obool),tc_fun(U_13199,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13199,tc_fun(U_13199,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_13199,tc_fun(tc_fun(U_13199,tc_HOL_Obool),tc_fun(U_13199,tc_HOL_Obool))),U_13199),hAPP(c_COMBB(tc_fun(U_13199,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13199,tc_HOL_Obool),tc_fun(U_13199,tc_HOL_Obool)),U_13199),c_COMBS(U_13199,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13199,tc_fun(U_13199,tc_HOL_Obool)),tc_fun(U_13199,tc_fun(U_13199,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_13199),hAPP(c_COMBB(tc_fun(U_13199,tc_HOL_Obool),tc_fun(U_13199,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13199),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13199),c_fconj))),hAPP(hAPP(c_COMBC(U_13199,tc_fun(U_13199,tc_fun(U_13199,U_13199)),tc_fun(U_13199,tc_fun(U_13199,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13199,U_13199),tc_fun(U_13199,tc_HOL_Obool)),tc_fun(tc_fun(U_13199,tc_fun(U_13199,U_13199)),tc_fun(U_13199,tc_fun(U_13199,tc_HOL_Obool))),U_13199),c_COMBB(tc_fun(U_13199,U_13199),tc_fun(U_13199,tc_HOL_Obool),U_13199)),hAPP(hAPP(c_COMBB(tc_fun(U_13199,tc_HOL_Obool),tc_fun(tc_fun(U_13199,U_13199),tc_fun(U_13199,tc_HOL_Obool)),U_13199),c_COMBB(U_13199,tc_HOL_Obool,U_13199)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(U_13199)))))),hAPP(hAPP(c_COMBC(U_13199,tc_fun(U_13199,tc_HOL_Obool),tc_fun(U_13199,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13199,tc_HOL_Obool),tc_fun(U_13199,tc_HOL_Obool)),U_13199),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13199)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13199),c_fconj),hAPP(hAPP(c_COMBC(U_13199,tc_fun(U_13199,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13199)),U_13200)))),hAPP(hAPP(c_COMBC(U_13199,tc_fun(U_13199,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13199)),U_13201)))))))
    | U_13201 = c_Orderings_Obot__class_Obot(tc_fun(U_13199,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13199),U_13201))
    | U_13200 = c_Orderings_Obot__class_Obot(tc_fun(U_13199,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13199),U_13200))
    | ~ class_Lattices_Odistrib__lattice(U_13199) ),
    inference(clausify,[status(thm)],[f_3378_2]) ).

fof(f_3379_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__Sup1__distrib]) ).

fof(f_3379_2,plain,
    ! [U_13204,U_13203,U_13202] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_13202),U_13204),c_Big__Operators_Olattice_OSup__fin(U_13202,c_Orderings_Oord__class_Omax(U_13202),U_13203)) = c_Big__Operators_Olattice_OSup__fin(U_13202,c_Orderings_Oord__class_Omax(U_13202),hAPP(c_Set_OCollect(U_13202),hAPP(hAPP(c_COMBB(tc_fun(U_13202,tc_HOL_Obool),tc_HOL_Obool,U_13202),c_HOL_OEx(U_13202)),hAPP(hAPP(c_COMBC(U_13202,tc_fun(U_13202,tc_HOL_Obool),tc_fun(U_13202,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13202,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13202,tc_HOL_Obool),tc_fun(U_13202,tc_HOL_Obool)),U_13202),c_COMBS(U_13202,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13202,tc_HOL_Obool),tc_fun(U_13202,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13202),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13202),c_fconj)),hAPP(hAPP(c_COMBC(U_13202,tc_fun(U_13202,U_13202),tc_fun(U_13202,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13202,tc_HOL_Obool),tc_fun(tc_fun(U_13202,U_13202),tc_fun(U_13202,tc_HOL_Obool)),U_13202),c_COMBB(U_13202,tc_HOL_Obool,U_13202)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(U_13202),U_13204))))),hAPP(hAPP(c_COMBC(U_13202,tc_fun(U_13202,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13202)),U_13203)))))
      | U_13203 = c_Orderings_Obot__class_Obot(tc_fun(U_13202,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13202),U_13203))
      | ~ class_Orderings_Olinorder(U_13202) ),
    inference(variable_rename,[status(thm)],[f_3379_1]) ).

cnf(f_3379_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_13202),U_13204),c_Big__Operators_Olattice_OSup__fin(U_13202,c_Orderings_Oord__class_Omax(U_13202),U_13203)) = c_Big__Operators_Olattice_OSup__fin(U_13202,c_Orderings_Oord__class_Omax(U_13202),hAPP(c_Set_OCollect(U_13202),hAPP(hAPP(c_COMBB(tc_fun(U_13202,tc_HOL_Obool),tc_HOL_Obool,U_13202),c_HOL_OEx(U_13202)),hAPP(hAPP(c_COMBC(U_13202,tc_fun(U_13202,tc_HOL_Obool),tc_fun(U_13202,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13202,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13202,tc_HOL_Obool),tc_fun(U_13202,tc_HOL_Obool)),U_13202),c_COMBS(U_13202,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13202,tc_HOL_Obool),tc_fun(U_13202,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13202),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13202),c_fconj)),hAPP(hAPP(c_COMBC(U_13202,tc_fun(U_13202,U_13202),tc_fun(U_13202,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13202,tc_HOL_Obool),tc_fun(tc_fun(U_13202,U_13202),tc_fun(U_13202,tc_HOL_Obool)),U_13202),c_COMBB(U_13202,tc_HOL_Obool,U_13202)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(U_13202),U_13204))))),hAPP(hAPP(c_COMBC(U_13202,tc_fun(U_13202,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13202)),U_13203)))))
    | U_13203 = c_Orderings_Obot__class_Obot(tc_fun(U_13202,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13202),U_13203))
    | ~ class_Orderings_Olinorder(U_13202) ),
    inference(clausify,[status(thm)],[f_3379_2]) ).

fof(f_3380_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBS(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal))),c_Orderings_Oord__class_Omin(T_b)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2)))))))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__Sup2__distrib]) ).

fof(f_3380_2,plain,
    ! [U_13207,U_13206,U_13205] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_13205),c_Big__Operators_Olattice_OSup__fin(U_13205,c_Orderings_Oord__class_Omax(U_13205),U_13206)),c_Big__Operators_Olattice_OSup__fin(U_13205,c_Orderings_Oord__class_Omax(U_13205),U_13207)) = c_Big__Operators_Olattice_OSup__fin(U_13205,c_Orderings_Oord__class_Omax(U_13205),hAPP(c_Set_OCollect(U_13205),hAPP(hAPP(c_COMBB(tc_fun(U_13205,tc_HOL_Obool),tc_HOL_Obool,U_13205),c_HOL_OEx(U_13205)),hAPP(hAPP(c_COMBB(tc_fun(U_13205,tc_fun(U_13205,tc_HOL_Obool)),tc_fun(U_13205,tc_HOL_Obool),U_13205),hAPP(c_COMBB(tc_fun(U_13205,tc_HOL_Obool),tc_HOL_Obool,U_13205),c_HOL_OEx(U_13205))),hAPP(hAPP(c_COMBC(U_13205,tc_fun(U_13205,tc_fun(U_13205,tc_HOL_Obool)),tc_fun(U_13205,tc_fun(U_13205,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13205,tc_fun(tc_fun(U_13205,tc_HOL_Obool),tc_fun(U_13205,tc_HOL_Obool))),tc_fun(tc_fun(U_13205,tc_fun(U_13205,tc_HOL_Obool)),tc_fun(U_13205,tc_fun(U_13205,tc_HOL_Obool))),U_13205),c_COMBS(U_13205,tc_fun(U_13205,tc_HOL_Obool),tc_fun(U_13205,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13205,tc_fun(U_13205,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_13205,tc_fun(tc_fun(U_13205,tc_HOL_Obool),tc_fun(U_13205,tc_HOL_Obool))),U_13205),hAPP(c_COMBB(tc_fun(U_13205,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13205,tc_HOL_Obool),tc_fun(U_13205,tc_HOL_Obool)),U_13205),c_COMBS(U_13205,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13205,tc_fun(U_13205,tc_HOL_Obool)),tc_fun(U_13205,tc_fun(U_13205,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_13205),hAPP(c_COMBB(tc_fun(U_13205,tc_HOL_Obool),tc_fun(U_13205,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13205),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13205),c_fconj))),hAPP(hAPP(c_COMBC(U_13205,tc_fun(U_13205,tc_fun(U_13205,U_13205)),tc_fun(U_13205,tc_fun(U_13205,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13205,U_13205),tc_fun(U_13205,tc_HOL_Obool)),tc_fun(tc_fun(U_13205,tc_fun(U_13205,U_13205)),tc_fun(U_13205,tc_fun(U_13205,tc_HOL_Obool))),U_13205),c_COMBB(tc_fun(U_13205,U_13205),tc_fun(U_13205,tc_HOL_Obool),U_13205)),hAPP(hAPP(c_COMBB(tc_fun(U_13205,tc_HOL_Obool),tc_fun(tc_fun(U_13205,U_13205),tc_fun(U_13205,tc_HOL_Obool)),U_13205),c_COMBB(U_13205,tc_HOL_Obool,U_13205)),c_fequal))),c_Orderings_Oord__class_Omin(U_13205)))))),hAPP(hAPP(c_COMBC(U_13205,tc_fun(U_13205,tc_HOL_Obool),tc_fun(U_13205,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13205,tc_HOL_Obool),tc_fun(U_13205,tc_HOL_Obool)),U_13205),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13205)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13205),c_fconj),hAPP(hAPP(c_COMBC(U_13205,tc_fun(U_13205,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13205)),U_13206)))),hAPP(hAPP(c_COMBC(U_13205,tc_fun(U_13205,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13205)),U_13207)))))))
      | U_13207 = c_Orderings_Obot__class_Obot(tc_fun(U_13205,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13205),U_13207))
      | U_13206 = c_Orderings_Obot__class_Obot(tc_fun(U_13205,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13205),U_13206))
      | ~ class_Orderings_Olinorder(U_13205) ),
    inference(variable_rename,[status(thm)],[f_3380_1]) ).

cnf(f_3380_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_13205),c_Big__Operators_Olattice_OSup__fin(U_13205,c_Orderings_Oord__class_Omax(U_13205),U_13206)),c_Big__Operators_Olattice_OSup__fin(U_13205,c_Orderings_Oord__class_Omax(U_13205),U_13207)) = c_Big__Operators_Olattice_OSup__fin(U_13205,c_Orderings_Oord__class_Omax(U_13205),hAPP(c_Set_OCollect(U_13205),hAPP(hAPP(c_COMBB(tc_fun(U_13205,tc_HOL_Obool),tc_HOL_Obool,U_13205),c_HOL_OEx(U_13205)),hAPP(hAPP(c_COMBB(tc_fun(U_13205,tc_fun(U_13205,tc_HOL_Obool)),tc_fun(U_13205,tc_HOL_Obool),U_13205),hAPP(c_COMBB(tc_fun(U_13205,tc_HOL_Obool),tc_HOL_Obool,U_13205),c_HOL_OEx(U_13205))),hAPP(hAPP(c_COMBC(U_13205,tc_fun(U_13205,tc_fun(U_13205,tc_HOL_Obool)),tc_fun(U_13205,tc_fun(U_13205,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13205,tc_fun(tc_fun(U_13205,tc_HOL_Obool),tc_fun(U_13205,tc_HOL_Obool))),tc_fun(tc_fun(U_13205,tc_fun(U_13205,tc_HOL_Obool)),tc_fun(U_13205,tc_fun(U_13205,tc_HOL_Obool))),U_13205),c_COMBS(U_13205,tc_fun(U_13205,tc_HOL_Obool),tc_fun(U_13205,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13205,tc_fun(U_13205,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_13205,tc_fun(tc_fun(U_13205,tc_HOL_Obool),tc_fun(U_13205,tc_HOL_Obool))),U_13205),hAPP(c_COMBB(tc_fun(U_13205,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13205,tc_HOL_Obool),tc_fun(U_13205,tc_HOL_Obool)),U_13205),c_COMBS(U_13205,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13205,tc_fun(U_13205,tc_HOL_Obool)),tc_fun(U_13205,tc_fun(U_13205,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_13205),hAPP(c_COMBB(tc_fun(U_13205,tc_HOL_Obool),tc_fun(U_13205,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13205),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13205),c_fconj))),hAPP(hAPP(c_COMBC(U_13205,tc_fun(U_13205,tc_fun(U_13205,U_13205)),tc_fun(U_13205,tc_fun(U_13205,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13205,U_13205),tc_fun(U_13205,tc_HOL_Obool)),tc_fun(tc_fun(U_13205,tc_fun(U_13205,U_13205)),tc_fun(U_13205,tc_fun(U_13205,tc_HOL_Obool))),U_13205),c_COMBB(tc_fun(U_13205,U_13205),tc_fun(U_13205,tc_HOL_Obool),U_13205)),hAPP(hAPP(c_COMBB(tc_fun(U_13205,tc_HOL_Obool),tc_fun(tc_fun(U_13205,U_13205),tc_fun(U_13205,tc_HOL_Obool)),U_13205),c_COMBB(U_13205,tc_HOL_Obool,U_13205)),c_fequal))),c_Orderings_Oord__class_Omin(U_13205)))))),hAPP(hAPP(c_COMBC(U_13205,tc_fun(U_13205,tc_HOL_Obool),tc_fun(U_13205,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13205,tc_HOL_Obool),tc_fun(U_13205,tc_HOL_Obool)),U_13205),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13205)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13205),c_fconj),hAPP(hAPP(c_COMBC(U_13205,tc_fun(U_13205,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13205)),U_13206)))),hAPP(hAPP(c_COMBC(U_13205,tc_fun(U_13205,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13205)),U_13207)))))))
    | U_13207 = c_Orderings_Obot__class_Obot(tc_fun(U_13205,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13205),U_13207))
    | U_13206 = c_Orderings_Obot__class_Obot(tc_fun(U_13205,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13205),U_13206))
    | ~ class_Orderings_Olinorder(U_13205) ),
    inference(clausify,[status(thm)],[f_3380_2]) ).

fof(f_3381_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBS(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal))),c_Orderings_Oord__class_Omax(T_b)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2)))))))
      | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Osup__Inf2__distrib]) ).

fof(f_3381_2,plain,
    ! [U_13210,U_13209,U_13208] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_13208),c_Big__Operators_Olattice_OInf__fin(U_13208,c_Orderings_Oord__class_Omin(U_13208),U_13209)),c_Big__Operators_Olattice_OInf__fin(U_13208,c_Orderings_Oord__class_Omin(U_13208),U_13210)) = c_Big__Operators_Olattice_OInf__fin(U_13208,c_Orderings_Oord__class_Omin(U_13208),hAPP(c_Set_OCollect(U_13208),hAPP(hAPP(c_COMBB(tc_fun(U_13208,tc_HOL_Obool),tc_HOL_Obool,U_13208),c_HOL_OEx(U_13208)),hAPP(hAPP(c_COMBB(tc_fun(U_13208,tc_fun(U_13208,tc_HOL_Obool)),tc_fun(U_13208,tc_HOL_Obool),U_13208),hAPP(c_COMBB(tc_fun(U_13208,tc_HOL_Obool),tc_HOL_Obool,U_13208),c_HOL_OEx(U_13208))),hAPP(hAPP(c_COMBC(U_13208,tc_fun(U_13208,tc_fun(U_13208,tc_HOL_Obool)),tc_fun(U_13208,tc_fun(U_13208,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13208,tc_fun(tc_fun(U_13208,tc_HOL_Obool),tc_fun(U_13208,tc_HOL_Obool))),tc_fun(tc_fun(U_13208,tc_fun(U_13208,tc_HOL_Obool)),tc_fun(U_13208,tc_fun(U_13208,tc_HOL_Obool))),U_13208),c_COMBS(U_13208,tc_fun(U_13208,tc_HOL_Obool),tc_fun(U_13208,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13208,tc_fun(U_13208,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_13208,tc_fun(tc_fun(U_13208,tc_HOL_Obool),tc_fun(U_13208,tc_HOL_Obool))),U_13208),hAPP(c_COMBB(tc_fun(U_13208,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13208,tc_HOL_Obool),tc_fun(U_13208,tc_HOL_Obool)),U_13208),c_COMBS(U_13208,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13208,tc_fun(U_13208,tc_HOL_Obool)),tc_fun(U_13208,tc_fun(U_13208,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_13208),hAPP(c_COMBB(tc_fun(U_13208,tc_HOL_Obool),tc_fun(U_13208,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13208),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13208),c_fconj))),hAPP(hAPP(c_COMBC(U_13208,tc_fun(U_13208,tc_fun(U_13208,U_13208)),tc_fun(U_13208,tc_fun(U_13208,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13208,U_13208),tc_fun(U_13208,tc_HOL_Obool)),tc_fun(tc_fun(U_13208,tc_fun(U_13208,U_13208)),tc_fun(U_13208,tc_fun(U_13208,tc_HOL_Obool))),U_13208),c_COMBB(tc_fun(U_13208,U_13208),tc_fun(U_13208,tc_HOL_Obool),U_13208)),hAPP(hAPP(c_COMBB(tc_fun(U_13208,tc_HOL_Obool),tc_fun(tc_fun(U_13208,U_13208),tc_fun(U_13208,tc_HOL_Obool)),U_13208),c_COMBB(U_13208,tc_HOL_Obool,U_13208)),c_fequal))),c_Orderings_Oord__class_Omax(U_13208)))))),hAPP(hAPP(c_COMBC(U_13208,tc_fun(U_13208,tc_HOL_Obool),tc_fun(U_13208,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13208,tc_HOL_Obool),tc_fun(U_13208,tc_HOL_Obool)),U_13208),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13208)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13208),c_fconj),hAPP(hAPP(c_COMBC(U_13208,tc_fun(U_13208,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13208)),U_13209)))),hAPP(hAPP(c_COMBC(U_13208,tc_fun(U_13208,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13208)),U_13210)))))))
      | U_13210 = c_Orderings_Obot__class_Obot(tc_fun(U_13208,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13208),U_13210))
      | U_13209 = c_Orderings_Obot__class_Obot(tc_fun(U_13208,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13208),U_13209))
      | ~ class_Orderings_Olinorder(U_13208) ),
    inference(variable_rename,[status(thm)],[f_3381_1]) ).

cnf(f_3381_3,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_13208),c_Big__Operators_Olattice_OInf__fin(U_13208,c_Orderings_Oord__class_Omin(U_13208),U_13209)),c_Big__Operators_Olattice_OInf__fin(U_13208,c_Orderings_Oord__class_Omin(U_13208),U_13210)) = c_Big__Operators_Olattice_OInf__fin(U_13208,c_Orderings_Oord__class_Omin(U_13208),hAPP(c_Set_OCollect(U_13208),hAPP(hAPP(c_COMBB(tc_fun(U_13208,tc_HOL_Obool),tc_HOL_Obool,U_13208),c_HOL_OEx(U_13208)),hAPP(hAPP(c_COMBB(tc_fun(U_13208,tc_fun(U_13208,tc_HOL_Obool)),tc_fun(U_13208,tc_HOL_Obool),U_13208),hAPP(c_COMBB(tc_fun(U_13208,tc_HOL_Obool),tc_HOL_Obool,U_13208),c_HOL_OEx(U_13208))),hAPP(hAPP(c_COMBC(U_13208,tc_fun(U_13208,tc_fun(U_13208,tc_HOL_Obool)),tc_fun(U_13208,tc_fun(U_13208,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13208,tc_fun(tc_fun(U_13208,tc_HOL_Obool),tc_fun(U_13208,tc_HOL_Obool))),tc_fun(tc_fun(U_13208,tc_fun(U_13208,tc_HOL_Obool)),tc_fun(U_13208,tc_fun(U_13208,tc_HOL_Obool))),U_13208),c_COMBS(U_13208,tc_fun(U_13208,tc_HOL_Obool),tc_fun(U_13208,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13208,tc_fun(U_13208,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_13208,tc_fun(tc_fun(U_13208,tc_HOL_Obool),tc_fun(U_13208,tc_HOL_Obool))),U_13208),hAPP(c_COMBB(tc_fun(U_13208,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13208,tc_HOL_Obool),tc_fun(U_13208,tc_HOL_Obool)),U_13208),c_COMBS(U_13208,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13208,tc_fun(U_13208,tc_HOL_Obool)),tc_fun(U_13208,tc_fun(U_13208,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_13208),hAPP(c_COMBB(tc_fun(U_13208,tc_HOL_Obool),tc_fun(U_13208,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13208),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13208),c_fconj))),hAPP(hAPP(c_COMBC(U_13208,tc_fun(U_13208,tc_fun(U_13208,U_13208)),tc_fun(U_13208,tc_fun(U_13208,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13208,U_13208),tc_fun(U_13208,tc_HOL_Obool)),tc_fun(tc_fun(U_13208,tc_fun(U_13208,U_13208)),tc_fun(U_13208,tc_fun(U_13208,tc_HOL_Obool))),U_13208),c_COMBB(tc_fun(U_13208,U_13208),tc_fun(U_13208,tc_HOL_Obool),U_13208)),hAPP(hAPP(c_COMBB(tc_fun(U_13208,tc_HOL_Obool),tc_fun(tc_fun(U_13208,U_13208),tc_fun(U_13208,tc_HOL_Obool)),U_13208),c_COMBB(U_13208,tc_HOL_Obool,U_13208)),c_fequal))),c_Orderings_Oord__class_Omax(U_13208)))))),hAPP(hAPP(c_COMBC(U_13208,tc_fun(U_13208,tc_HOL_Obool),tc_fun(U_13208,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13208,tc_HOL_Obool),tc_fun(U_13208,tc_HOL_Obool)),U_13208),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13208)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13208),c_fconj),hAPP(hAPP(c_COMBC(U_13208,tc_fun(U_13208,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13208)),U_13209)))),hAPP(hAPP(c_COMBC(U_13208,tc_fun(U_13208,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13208)),U_13210)))))))
    | U_13210 = c_Orderings_Obot__class_Obot(tc_fun(U_13208,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13208),U_13210))
    | U_13209 = c_Orderings_Obot__class_Obot(tc_fun(U_13208,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13208),U_13209))
    | ~ class_Orderings_Olinorder(U_13208) ),
    inference(clausify,[status(thm)],[f_3381_2]) ).

fof(f_3382_1,plain,
    ! [V_B_2,V_A_2,T_c,T_b] : c_Nitpick_Oprod(T_b,T_c,V_A_2,V_B_2) = hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2)))),
    inference(fof_nnf,[status(thm)],[fact_Nitpick_Oprod__def]) ).

fof(f_3382_2,plain,
    ! [U_13214,U_13213,U_13212,U_13211] : c_Nitpick_Oprod(U_13211,U_13212,U_13213,U_13214) = hAPP(c_Set_OCollect(tc_prod(U_13211,U_13212)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13211,U_13212,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13211,tc_fun(U_13212,tc_HOL_Obool),tc_fun(U_13212,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13212,tc_HOL_Obool),tc_fun(U_13212,tc_HOL_Obool)),U_13211),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13212)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13211),c_fconj),hAPP(hAPP(c_COMBC(U_13211,tc_fun(U_13211,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13211)),U_13213)))),hAPP(hAPP(c_COMBC(U_13212,tc_fun(U_13212,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13212)),U_13214)))),
    inference(variable_rename,[status(thm)],[f_3382_1]) ).

cnf(f_3382_3,plain,
    c_Nitpick_Oprod(U_13211,U_13212,U_13213,U_13214) = hAPP(c_Set_OCollect(tc_prod(U_13211,U_13212)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13211,U_13212,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13211,tc_fun(U_13212,tc_HOL_Obool),tc_fun(U_13212,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13212,tc_HOL_Obool),tc_fun(U_13212,tc_HOL_Obool)),U_13211),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13212)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13211),c_fconj),hAPP(hAPP(c_COMBC(U_13211,tc_fun(U_13211,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13211)),U_13213)))),hAPP(hAPP(c_COMBC(U_13212,tc_fun(U_13212,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13212)),U_13214)))),
    inference(clausify,[status(thm)],[f_3382_2]) ).

fof(f_3383_1,plain,
    ! [V_d_2] : c_Int_Oint__ge__less__than(V_d_2) = hAPP(c_Set_OCollect(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_d_2)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
    inference(fof_nnf,[status(thm)],[fact_int__ge__less__than__def]) ).

fof(f_3383_2,plain,
    ! [U_13215] : c_Int_Oint__ge__less__than(U_13215) = hAPP(c_Set_OCollect(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_13215)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
    inference(variable_rename,[status(thm)],[f_3383_1]) ).

cnf(f_3383_3,plain,
    c_Int_Oint__ge__less__than(U_13215) = hAPP(c_Set_OCollect(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_13215)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
    inference(clausify,[status(thm)],[f_3383_2]) ).

fof(f_3384_1,plain,
    ! [V_d_2] : c_Int_Oint__ge__less__than2(V_d_2) = hAPP(c_Set_OCollect(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_d_2)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
    inference(fof_nnf,[status(thm)],[fact_int__ge__less__than2__def]) ).

fof(f_3384_2,plain,
    ! [U_13216] : c_Int_Oint__ge__less__than2(U_13216) = hAPP(c_Set_OCollect(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_13216)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
    inference(variable_rename,[status(thm)],[f_3384_1]) ).

cnf(f_3384_3,plain,
    c_Int_Oint__ge__less__than2(U_13216) = hAPP(c_Set_OCollect(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_13216)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
    inference(clausify,[status(thm)],[f_3384_2]) ).

fof(f_3385_1,plain,
    ! [V_r_2,T_b] :
      ( ( c_Predicate_Oreflp(T_b,V_r_2)
        | ~ c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))) )
      & ( c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2)))
        | ~ c_Predicate_Oreflp(T_b,V_r_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_reflp__def]) ).

fof(f_3385_2,plain,
    ! [U_13218,U_13217] :
      ( ( c_Predicate_Oreflp(U_13217,U_13218)
        | ~ c_Relation_Orefl__on(U_13217,c_Orderings_Otop__class_Otop(tc_fun(U_13217,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(U_13217,U_13217)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13217,U_13217,tc_HOL_Obool),U_13218))) )
      & ( c_Relation_Orefl__on(U_13217,c_Orderings_Otop__class_Otop(tc_fun(U_13217,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(U_13217,U_13217)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13217,U_13217,tc_HOL_Obool),U_13218)))
        | ~ c_Predicate_Oreflp(U_13217,U_13218) ) ),
    inference(variable_rename,[status(thm)],[f_3385_1]) ).

fof(f_3385_3,plain,
    ( ! [U_13222,U_13220] :
        ( c_Predicate_Oreflp(U_13220,U_13222)
        | ~ c_Relation_Orefl__on(U_13220,c_Orderings_Otop__class_Otop(tc_fun(U_13220,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(U_13220,U_13220)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13220,U_13220,tc_HOL_Obool),U_13222))) )
    & ! [U_13221,U_13219] :
        ( c_Relation_Orefl__on(U_13219,c_Orderings_Otop__class_Otop(tc_fun(U_13219,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(U_13219,U_13219)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13219,U_13219,tc_HOL_Obool),U_13221)))
        | ~ c_Predicate_Oreflp(U_13219,U_13221) ) ),
    inference(miniscope,[status(thm)],[f_3385_2]) ).

cnf(f_3385_4,plain,
    ( c_Relation_Orefl__on(U_13219,c_Orderings_Otop__class_Otop(tc_fun(U_13219,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(U_13219,U_13219)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13219,U_13219,tc_HOL_Obool),U_13221)))
    | ~ c_Predicate_Oreflp(U_13219,U_13221) ),
    inference(clausify,[status(thm)],[f_3385_3]) ).

cnf(f_3385_5,plain,
    ( c_Predicate_Oreflp(U_13220,U_13222)
    | ~ c_Relation_Orefl__on(U_13220,c_Orderings_Otop__class_Otop(tc_fun(U_13220,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(U_13220,U_13220)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13220,U_13220,tc_HOL_Obool),U_13222))) ),
    inference(clausify,[status(thm)],[f_3385_3]) ).

fof(f_3386_1,plain,
    ! [V_B_2,V_A_2,V_g_2,V_f_2,T_c,T_b,T_d] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_d),c_Fun_Oid(T_d)),hAPP(c_Set_OCollect(T_d),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_d),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_d),hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c))),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),T_d),c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),T_d),hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_d),hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj))),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_b,tc_fun(T_c,T_d)),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_d),tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_c,T_d)),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),T_d),c_COMBB(tc_fun(T_c,T_d),tc_fun(T_c,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_c,T_d),tc_fun(T_c,tc_HOL_Obool)),T_d),c_COMBB(T_d,tc_HOL_Obool,T_c)),c_fequal))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,T_d),tc_fun(T_c,T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_d),tc_fun(tc_fun(T_c,T_d),tc_fun(T_c,T_d)),T_b),c_COMBB(T_d,T_d,T_c)),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,T_d),T_b),c_Groups_Otimes__class_Otimes(T_d)),V_f_2))),V_g_2)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2)))))))
      | ~ c_Fun_Oinj__on(tc_prod(T_b,T_c),T_d,hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,T_d),tc_fun(T_c,T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_d),tc_fun(tc_fun(T_c,T_d),tc_fun(T_c,T_d)),T_b),c_COMBB(T_d,T_d,T_c)),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,T_d),T_b),c_Groups_Otimes__class_Otimes(T_d)),V_f_2))),V_g_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2)))
      | ~ class_Rings_Osemiring__0(T_d) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__mult__setsum__if__inj]) ).

fof(f_3386_2,plain,
    ! [U_13229,U_13228,U_13227,U_13226,U_13225,U_13224,U_13223] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_13223),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13224,U_13223),U_13226),U_13228)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13225,U_13223),U_13227),U_13229)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13223,U_13223),c_Fun_Oid(U_13223)),hAPP(c_Set_OCollect(U_13223),hAPP(hAPP(c_COMBB(tc_fun(U_13224,tc_HOL_Obool),tc_HOL_Obool,U_13223),c_HOL_OEx(U_13224)),hAPP(hAPP(c_COMBB(tc_fun(U_13224,tc_fun(U_13225,tc_HOL_Obool)),tc_fun(U_13224,tc_HOL_Obool),U_13223),hAPP(c_COMBB(tc_fun(U_13225,tc_HOL_Obool),tc_HOL_Obool,U_13224),c_HOL_OEx(U_13225))),hAPP(hAPP(c_COMBC(U_13223,tc_fun(U_13224,tc_fun(U_13225,tc_HOL_Obool)),tc_fun(U_13224,tc_fun(U_13225,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13224,tc_fun(tc_fun(U_13225,tc_HOL_Obool),tc_fun(U_13225,tc_HOL_Obool))),tc_fun(tc_fun(U_13224,tc_fun(U_13225,tc_HOL_Obool)),tc_fun(U_13224,tc_fun(U_13225,tc_HOL_Obool))),U_13223),c_COMBS(U_13224,tc_fun(U_13225,tc_HOL_Obool),tc_fun(U_13225,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13224,tc_fun(U_13225,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_13224,tc_fun(tc_fun(U_13225,tc_HOL_Obool),tc_fun(U_13225,tc_HOL_Obool))),U_13223),hAPP(c_COMBB(tc_fun(U_13225,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13225,tc_HOL_Obool),tc_fun(U_13225,tc_HOL_Obool)),U_13224),c_COMBS(U_13225,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13224,tc_fun(U_13225,tc_HOL_Obool)),tc_fun(U_13224,tc_fun(U_13225,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_13223),hAPP(c_COMBB(tc_fun(U_13225,tc_HOL_Obool),tc_fun(U_13225,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13224),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13225),c_fconj))),hAPP(hAPP(c_COMBC(U_13223,tc_fun(U_13224,tc_fun(U_13225,U_13223)),tc_fun(U_13224,tc_fun(U_13225,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13225,U_13223),tc_fun(U_13225,tc_HOL_Obool)),tc_fun(tc_fun(U_13224,tc_fun(U_13225,U_13223)),tc_fun(U_13224,tc_fun(U_13225,tc_HOL_Obool))),U_13223),c_COMBB(tc_fun(U_13225,U_13223),tc_fun(U_13225,tc_HOL_Obool),U_13224)),hAPP(hAPP(c_COMBB(tc_fun(U_13223,tc_HOL_Obool),tc_fun(tc_fun(U_13225,U_13223),tc_fun(U_13225,tc_HOL_Obool)),U_13223),c_COMBB(U_13223,tc_HOL_Obool,U_13225)),c_fequal))),hAPP(hAPP(c_COMBC(U_13224,tc_fun(U_13225,U_13223),tc_fun(U_13225,U_13223)),hAPP(hAPP(c_COMBB(tc_fun(U_13223,U_13223),tc_fun(tc_fun(U_13225,U_13223),tc_fun(U_13225,U_13223)),U_13224),c_COMBB(U_13223,U_13223,U_13225)),hAPP(hAPP(c_COMBB(U_13223,tc_fun(U_13223,U_13223),U_13224),c_Groups_Otimes__class_Otimes(U_13223)),U_13226))),U_13227)))))),hAPP(hAPP(c_COMBC(U_13224,tc_fun(U_13225,tc_HOL_Obool),tc_fun(U_13225,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13225,tc_HOL_Obool),tc_fun(U_13225,tc_HOL_Obool)),U_13224),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13225)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13224),c_fconj),hAPP(hAPP(c_COMBC(U_13224,tc_fun(U_13224,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13224)),U_13228)))),hAPP(hAPP(c_COMBC(U_13225,tc_fun(U_13225,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13225)),U_13229)))))))
      | ~ c_Fun_Oinj__on(tc_prod(U_13224,U_13225),U_13223,hAPP(c_Product__Type_Oprod_Oprod__case(U_13224,U_13225,U_13223),hAPP(hAPP(c_COMBC(U_13224,tc_fun(U_13225,U_13223),tc_fun(U_13225,U_13223)),hAPP(hAPP(c_COMBB(tc_fun(U_13223,U_13223),tc_fun(tc_fun(U_13225,U_13223),tc_fun(U_13225,U_13223)),U_13224),c_COMBB(U_13223,U_13223,U_13225)),hAPP(hAPP(c_COMBB(U_13223,tc_fun(U_13223,U_13223),U_13224),c_Groups_Otimes__class_Otimes(U_13223)),U_13226))),U_13227)),hAPP(hAPP(c_Product__Type_OSigma(U_13224,U_13225),U_13228),hAPP(c_COMBK(tc_fun(U_13225,tc_HOL_Obool),U_13224),U_13229)))
      | ~ class_Rings_Osemiring__0(U_13223) ),
    inference(variable_rename,[status(thm)],[f_3386_1]) ).

cnf(f_3386_3,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_13223),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13224,U_13223),U_13226),U_13228)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13225,U_13223),U_13227),U_13229)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13223,U_13223),c_Fun_Oid(U_13223)),hAPP(c_Set_OCollect(U_13223),hAPP(hAPP(c_COMBB(tc_fun(U_13224,tc_HOL_Obool),tc_HOL_Obool,U_13223),c_HOL_OEx(U_13224)),hAPP(hAPP(c_COMBB(tc_fun(U_13224,tc_fun(U_13225,tc_HOL_Obool)),tc_fun(U_13224,tc_HOL_Obool),U_13223),hAPP(c_COMBB(tc_fun(U_13225,tc_HOL_Obool),tc_HOL_Obool,U_13224),c_HOL_OEx(U_13225))),hAPP(hAPP(c_COMBC(U_13223,tc_fun(U_13224,tc_fun(U_13225,tc_HOL_Obool)),tc_fun(U_13224,tc_fun(U_13225,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13224,tc_fun(tc_fun(U_13225,tc_HOL_Obool),tc_fun(U_13225,tc_HOL_Obool))),tc_fun(tc_fun(U_13224,tc_fun(U_13225,tc_HOL_Obool)),tc_fun(U_13224,tc_fun(U_13225,tc_HOL_Obool))),U_13223),c_COMBS(U_13224,tc_fun(U_13225,tc_HOL_Obool),tc_fun(U_13225,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13224,tc_fun(U_13225,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_13224,tc_fun(tc_fun(U_13225,tc_HOL_Obool),tc_fun(U_13225,tc_HOL_Obool))),U_13223),hAPP(c_COMBB(tc_fun(U_13225,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13225,tc_HOL_Obool),tc_fun(U_13225,tc_HOL_Obool)),U_13224),c_COMBS(U_13225,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13224,tc_fun(U_13225,tc_HOL_Obool)),tc_fun(U_13224,tc_fun(U_13225,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_13223),hAPP(c_COMBB(tc_fun(U_13225,tc_HOL_Obool),tc_fun(U_13225,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13224),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13225),c_fconj))),hAPP(hAPP(c_COMBC(U_13223,tc_fun(U_13224,tc_fun(U_13225,U_13223)),tc_fun(U_13224,tc_fun(U_13225,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13225,U_13223),tc_fun(U_13225,tc_HOL_Obool)),tc_fun(tc_fun(U_13224,tc_fun(U_13225,U_13223)),tc_fun(U_13224,tc_fun(U_13225,tc_HOL_Obool))),U_13223),c_COMBB(tc_fun(U_13225,U_13223),tc_fun(U_13225,tc_HOL_Obool),U_13224)),hAPP(hAPP(c_COMBB(tc_fun(U_13223,tc_HOL_Obool),tc_fun(tc_fun(U_13225,U_13223),tc_fun(U_13225,tc_HOL_Obool)),U_13223),c_COMBB(U_13223,tc_HOL_Obool,U_13225)),c_fequal))),hAPP(hAPP(c_COMBC(U_13224,tc_fun(U_13225,U_13223),tc_fun(U_13225,U_13223)),hAPP(hAPP(c_COMBB(tc_fun(U_13223,U_13223),tc_fun(tc_fun(U_13225,U_13223),tc_fun(U_13225,U_13223)),U_13224),c_COMBB(U_13223,U_13223,U_13225)),hAPP(hAPP(c_COMBB(U_13223,tc_fun(U_13223,U_13223),U_13224),c_Groups_Otimes__class_Otimes(U_13223)),U_13226))),U_13227)))))),hAPP(hAPP(c_COMBC(U_13224,tc_fun(U_13225,tc_HOL_Obool),tc_fun(U_13225,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13225,tc_HOL_Obool),tc_fun(U_13225,tc_HOL_Obool)),U_13224),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13225)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13224),c_fconj),hAPP(hAPP(c_COMBC(U_13224,tc_fun(U_13224,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13224)),U_13228)))),hAPP(hAPP(c_COMBC(U_13225,tc_fun(U_13225,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13225)),U_13229)))))))
    | ~ c_Fun_Oinj__on(tc_prod(U_13224,U_13225),U_13223,hAPP(c_Product__Type_Oprod_Oprod__case(U_13224,U_13225,U_13223),hAPP(hAPP(c_COMBC(U_13224,tc_fun(U_13225,U_13223),tc_fun(U_13225,U_13223)),hAPP(hAPP(c_COMBB(tc_fun(U_13223,U_13223),tc_fun(tc_fun(U_13225,U_13223),tc_fun(U_13225,U_13223)),U_13224),c_COMBB(U_13223,U_13223,U_13225)),hAPP(hAPP(c_COMBB(U_13223,tc_fun(U_13223,U_13223),U_13224),c_Groups_Otimes__class_Otimes(U_13223)),U_13226))),U_13227)),hAPP(hAPP(c_Product__Type_OSigma(U_13224,U_13225),U_13228),hAPP(c_COMBK(tc_fun(U_13225,tc_HOL_Obool),U_13224),U_13229)))
    | ~ class_Rings_Osemiring__0(U_13223) ),
    inference(clausify,[status(thm)],[f_3386_2]) ).

fof(f_3387_1,plain,
    ! [V_k_2,V_R_2,V_t_2,T_c,V_s_2,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_Nat_Onat,T_b),c_Finite__Set_Ocard(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_OCollect(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_t_2)))),V_R_2)))),V_s_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),V_k_2),V_t_2)
      | ? [B_x] :
          ( hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_s_2))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),V_R_2),B_x)))) != hAPP(V_k_2,B_x)
          & hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_t_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_t_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2)) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__multicount__gen]) ).

fof(f_3387_2,plain,
    ! [U_13236,U_13235,U_13234,U_13233,U_13232,U_13231] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13231,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_13233,tc_HOL_Obool),tc_Nat_Onat,U_13231),c_Finite__Set_Ocard(U_13233)),hAPP(hAPP(c_COMBB(tc_fun(U_13233,tc_HOL_Obool),tc_fun(U_13233,tc_HOL_Obool),U_13231),c_Set_OCollect(U_13233)),hAPP(hAPP(c_COMBB(tc_fun(U_13233,tc_HOL_Obool),tc_fun(U_13233,tc_HOL_Obool),U_13231),hAPP(c_COMBS(U_13233,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13233),c_fconj),hAPP(hAPP(c_COMBC(U_13233,tc_fun(U_13233,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13233)),U_13234)))),U_13235)))),U_13232) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13233,tc_Nat_Onat),U_13236),U_13234)
      | ? [U_13230] :
          ( hAPP(c_Finite__Set_Ocard(U_13231),hAPP(c_Set_OCollect(U_13231),hAPP(hAPP(c_COMBS(U_13231,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13231),c_fconj),hAPP(hAPP(c_COMBC(U_13231,tc_fun(U_13231,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13231)),U_13232))),hAPP(hAPP(c_COMBC(U_13231,U_13233,tc_HOL_Obool),U_13235),U_13230)))) != hAPP(U_13236,U_13230)
          & hBOOL(hAPP(hAPP(c_member(U_13233),U_13230),U_13234)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13233),U_13234))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13231),U_13232)) ),
    inference(variable_rename,[status(thm)],[f_3387_1]) ).

fof(f_3387_3,plain,
    ! [U_13236,U_13235,U_13234,U_13233,U_13232,U_13231] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13231,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_13233,tc_HOL_Obool),tc_Nat_Onat,U_13231),c_Finite__Set_Ocard(U_13233)),hAPP(hAPP(c_COMBB(tc_fun(U_13233,tc_HOL_Obool),tc_fun(U_13233,tc_HOL_Obool),U_13231),c_Set_OCollect(U_13233)),hAPP(hAPP(c_COMBB(tc_fun(U_13233,tc_HOL_Obool),tc_fun(U_13233,tc_HOL_Obool),U_13231),hAPP(c_COMBS(U_13233,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13233),c_fconj),hAPP(hAPP(c_COMBC(U_13233,tc_fun(U_13233,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13233)),U_13234)))),U_13235)))),U_13232) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13233,tc_Nat_Onat),U_13236),U_13234)
      | ( hAPP(c_Finite__Set_Ocard(U_13231),hAPP(c_Set_OCollect(U_13231),hAPP(hAPP(c_COMBS(U_13231,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13231),c_fconj),hAPP(hAPP(c_COMBC(U_13231,tc_fun(U_13231,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13231)),U_13232))),hAPP(hAPP(c_COMBC(U_13231,U_13233,tc_HOL_Obool),U_13235),sK315(U_13236,U_13235,U_13234,U_13233,U_13232,U_13231))))) != hAPP(U_13236,sK315(U_13236,U_13235,U_13234,U_13233,U_13232,U_13231))
        & hBOOL(hAPP(hAPP(c_member(U_13233),sK315(U_13236,U_13235,U_13234,U_13233,U_13232,U_13231)),U_13234)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13233),U_13234))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13231),U_13232)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK315]),skolemize(U_13230,sK315(U_13236,U_13235,U_13234,U_13233,U_13232,U_13231))],[f_3387_2]) ).

cnf(f_3387_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13233),sK315(U_13236,U_13235,U_13234,U_13233,U_13232,U_13231)),U_13234))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13231,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_13233,tc_HOL_Obool),tc_Nat_Onat,U_13231),c_Finite__Set_Ocard(U_13233)),hAPP(hAPP(c_COMBB(tc_fun(U_13233,tc_HOL_Obool),tc_fun(U_13233,tc_HOL_Obool),U_13231),c_Set_OCollect(U_13233)),hAPP(hAPP(c_COMBB(tc_fun(U_13233,tc_HOL_Obool),tc_fun(U_13233,tc_HOL_Obool),U_13231),hAPP(c_COMBS(U_13233,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13233),c_fconj),hAPP(hAPP(c_COMBC(U_13233,tc_fun(U_13233,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13233)),U_13234)))),U_13235)))),U_13232) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13233,tc_Nat_Onat),U_13236),U_13234)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13233),U_13234))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13231),U_13232)) ),
    inference(clausify,[status(thm)],[f_3387_3]) ).

cnf(f_3387_5,plain,
    ( hAPP(c_Finite__Set_Ocard(U_13231),hAPP(c_Set_OCollect(U_13231),hAPP(hAPP(c_COMBS(U_13231,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13231),c_fconj),hAPP(hAPP(c_COMBC(U_13231,tc_fun(U_13231,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13231)),U_13232))),hAPP(hAPP(c_COMBC(U_13231,U_13233,tc_HOL_Obool),U_13235),sK315(U_13236,U_13235,U_13234,U_13233,U_13232,U_13231))))) != hAPP(U_13236,sK315(U_13236,U_13235,U_13234,U_13233,U_13232,U_13231))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13231,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_13233,tc_HOL_Obool),tc_Nat_Onat,U_13231),c_Finite__Set_Ocard(U_13233)),hAPP(hAPP(c_COMBB(tc_fun(U_13233,tc_HOL_Obool),tc_fun(U_13233,tc_HOL_Obool),U_13231),c_Set_OCollect(U_13233)),hAPP(hAPP(c_COMBB(tc_fun(U_13233,tc_HOL_Obool),tc_fun(U_13233,tc_HOL_Obool),U_13231),hAPP(c_COMBS(U_13233,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13233),c_fconj),hAPP(hAPP(c_COMBC(U_13233,tc_fun(U_13233,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13233)),U_13234)))),U_13235)))),U_13232) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13233,tc_Nat_Onat),U_13236),U_13234)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13233),U_13234))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13231),U_13232)) ),
    inference(clausify,[status(thm)],[f_3387_3]) ).

fof(f_3388_1,plain,
    ! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,T_b,c_Fun_Oid(T_b),V_A_2),
    inference(fof_nnf,[status(thm)],[fact_inj__on__id]) ).

fof(f_3388_2,plain,
    ! [U_13238,U_13237] : c_Fun_Oinj__on(U_13237,U_13237,c_Fun_Oid(U_13237),U_13238),
    inference(variable_rename,[status(thm)],[f_3388_1]) ).

cnf(f_3388_3,plain,
    c_Fun_Oinj__on(U_13237,U_13237,c_Fun_Oid(U_13237),U_13238),
    inference(clausify,[status(thm)],[f_3388_2]) ).

fof(f_3389_1,plain,
    c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[fact_of__int__eq__id]) ).

cnf(f_3389_2,plain,
    c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_3389_1]) ).

fof(f_3390_1,plain,
    ! [V_v_2,V_c_2,V_b_2,V_a_2,T_b,T_c,T_d] :
      ( hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,V_v_2)
      | hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) != hAPP(c_Fun_Ocomp(T_c,T_c,T_b,c_Fun_Oid(T_c)),V_c_2) ),
    inference(fof_nnf,[status(thm)],[fact_o__eq__id__dest]) ).

fof(f_3390_2,plain,
    ! [U_13245,U_13244,U_13243,U_13242,U_13241,U_13240,U_13239] :
      ( hAPP(U_13242,hAPP(U_13243,U_13245)) = hAPP(U_13244,U_13245)
      | hAPP(c_Fun_Ocomp(U_13239,U_13240,U_13241,U_13242),U_13243) != hAPP(c_Fun_Ocomp(U_13240,U_13240,U_13241,c_Fun_Oid(U_13240)),U_13244) ),
    inference(variable_rename,[status(thm)],[f_3390_1]) ).

fof(f_3390_3,plain,
    ! [U_13245,U_13244,U_13243,U_13242] :
      ( ! [U_13241,U_13240,U_13239] : hAPP(c_Fun_Ocomp(U_13239,U_13240,U_13241,U_13242),U_13243) != hAPP(c_Fun_Ocomp(U_13240,U_13240,U_13241,c_Fun_Oid(U_13240)),U_13244)
      | hAPP(U_13242,hAPP(U_13243,U_13245)) = hAPP(U_13244,U_13245) ),
    inference(miniscope,[status(thm)],[f_3390_2]) ).

cnf(f_3390_4,plain,
    ( hAPP(c_Fun_Ocomp(U_13239,U_13240,U_13241,U_13242),U_13243) != hAPP(c_Fun_Ocomp(U_13240,U_13240,U_13241,c_Fun_Oid(U_13240)),U_13244)
    | hAPP(U_13242,hAPP(U_13243,U_13245)) = hAPP(U_13244,U_13245) ),
    inference(clausify,[status(thm)],[f_3390_3]) ).

fof(f_3391_1,plain,
    ! [V_f_2,T_c,T_b] : hAPP(c_Fun_Ocomp(T_b,T_c,T_b,V_f_2),c_Fun_Oid(T_b)) = V_f_2,
    inference(fof_nnf,[status(thm)],[fact_o__id]) ).

fof(f_3391_2,plain,
    ! [U_13248,U_13247,U_13246] : hAPP(c_Fun_Ocomp(U_13246,U_13247,U_13246,U_13248),c_Fun_Oid(U_13246)) = U_13248,
    inference(variable_rename,[status(thm)],[f_3391_1]) ).

cnf(f_3391_3,plain,
    hAPP(c_Fun_Ocomp(U_13246,U_13247,U_13246,U_13248),c_Fun_Oid(U_13246)) = U_13248,
    inference(clausify,[status(thm)],[f_3391_2]) ).

fof(f_3392_1,plain,
    ! [V_g_2,T_b,T_c] : hAPP(c_Fun_Ocomp(T_c,T_c,T_b,c_Fun_Oid(T_c)),V_g_2) = V_g_2,
    inference(fof_nnf,[status(thm)],[fact_id__o]) ).

fof(f_3392_2,plain,
    ! [U_13251,U_13250,U_13249] : hAPP(c_Fun_Ocomp(U_13249,U_13249,U_13250,c_Fun_Oid(U_13249)),U_13251) = U_13251,
    inference(variable_rename,[status(thm)],[f_3392_1]) ).

cnf(f_3392_3,plain,
    hAPP(c_Fun_Ocomp(U_13249,U_13249,U_13250,c_Fun_Oid(U_13249)),U_13251) = U_13251,
    inference(clausify,[status(thm)],[f_3392_2]) ).

fof(f_3393_1,plain,
    ! [V_x_1,T_a] : hAPP(c_Fun_Oid(T_a),V_x_1) = V_x_1,
    inference(fof_nnf,[status(thm)],[fact_id__def]) ).

fof(f_3393_2,plain,
    ! [U_13253,U_13252] : hAPP(c_Fun_Oid(U_13252),U_13253) = U_13253,
    inference(variable_rename,[status(thm)],[f_3393_1]) ).

cnf(f_3393_3,plain,
    hAPP(c_Fun_Oid(U_13252),U_13253) = U_13253,
    inference(clausify,[status(thm)],[f_3393_2]) ).

fof(f_3394_1,plain,
    ! [T_b,T_c] : c_Product__Type_Oapsnd(T_c,T_c,T_b,c_Fun_Oid(T_c)) = c_Fun_Oid(tc_prod(T_b,T_c)),
    inference(fof_nnf,[status(thm)],[fact_apsnd__id]) ).

fof(f_3394_2,plain,
    ! [U_13255,U_13254] : c_Product__Type_Oapsnd(U_13254,U_13254,U_13255,c_Fun_Oid(U_13254)) = c_Fun_Oid(tc_prod(U_13255,U_13254)),
    inference(variable_rename,[status(thm)],[f_3394_1]) ).

cnf(f_3394_3,plain,
    c_Product__Type_Oapsnd(U_13254,U_13254,U_13255,c_Fun_Oid(U_13254)) = c_Fun_Oid(tc_prod(U_13255,U_13254)),
    inference(clausify,[status(thm)],[f_3394_2]) ).

fof(f_3395_1,plain,
    ! [V_x_2,V_r_2,T_b] :
      ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_x_2))
      | ~ c_Predicate_Oreflp(T_b,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_reflpE]) ).

fof(f_3395_2,plain,
    ! [U_13258,U_13257,U_13256] :
      ( hBOOL(hAPP(hAPP(U_13257,U_13258),U_13258))
      | ~ c_Predicate_Oreflp(U_13256,U_13257) ),
    inference(variable_rename,[status(thm)],[f_3395_1]) ).

fof(f_3395_3,plain,
    ! [U_13258,U_13257] :
      ( ! [U_13256] : ~ c_Predicate_Oreflp(U_13256,U_13257)
      | hBOOL(hAPP(hAPP(U_13257,U_13258),U_13258)) ),
    inference(miniscope,[status(thm)],[f_3395_2]) ).

cnf(f_3395_4,plain,
    ( ~ c_Predicate_Oreflp(U_13256,U_13257)
    | hBOOL(hAPP(hAPP(U_13257,U_13258),U_13258)) ),
    inference(clausify,[status(thm)],[f_3395_3]) ).

fof(f_3396_1,plain,
    ! [V_x,T_a] : hAPP(c_Fun_Oid(T_a),V_x) = V_x,
    inference(fof_nnf,[status(thm)],[fact_id__apply]) ).

fof(f_3396_2,plain,
    ! [U_13260,U_13259] : hAPP(c_Fun_Oid(U_13259),U_13260) = U_13260,
    inference(variable_rename,[status(thm)],[f_3396_1]) ).

cnf(f_3396_3,plain,
    hAPP(c_Fun_Oid(U_13259),U_13260) = U_13260,
    inference(clausify,[status(thm)],[f_3396_2]) ).

fof(f_3397_1,plain,
    ! [T_c,T_b] : c_Product__Type_Oapfst(T_b,T_b,T_c,c_Fun_Oid(T_b)) = c_Fun_Oid(tc_prod(T_b,T_c)),
    inference(fof_nnf,[status(thm)],[fact_apfst__id]) ).

fof(f_3397_2,plain,
    ! [U_13262,U_13261] : c_Product__Type_Oapfst(U_13261,U_13261,U_13262,c_Fun_Oid(U_13261)) = c_Fun_Oid(tc_prod(U_13261,U_13262)),
    inference(variable_rename,[status(thm)],[f_3397_1]) ).

cnf(f_3397_3,plain,
    c_Product__Type_Oapfst(U_13261,U_13261,U_13262,c_Fun_Oid(U_13261)) = c_Fun_Oid(tc_prod(U_13261,U_13262)),
    inference(clausify,[status(thm)],[f_3397_2]) ).

fof(f_3398_1,plain,
    ! [V_A_2,T_b] : hAPP(c_Set_Ovimage(T_b,T_b,c_Fun_Oid(T_b)),V_A_2) = V_A_2,
    inference(fof_nnf,[status(thm)],[fact_vimage__id]) ).

fof(f_3398_2,plain,
    ! [U_13264,U_13263] : hAPP(c_Set_Ovimage(U_13263,U_13263,c_Fun_Oid(U_13263)),U_13264) = U_13264,
    inference(variable_rename,[status(thm)],[f_3398_1]) ).

cnf(f_3398_3,plain,
    hAPP(c_Set_Ovimage(U_13263,U_13263,c_Fun_Oid(U_13263)),U_13264) = U_13264,
    inference(clausify,[status(thm)],[f_3398_2]) ).

fof(f_3399_1,plain,
    ! [T_c,T_b] : c_Product__Type_Omap__pair(T_b,T_b,T_c,T_c,c_Fun_Oid(T_b),c_Fun_Oid(T_c)) = c_Fun_Oid(tc_prod(T_b,T_c)),
    inference(fof_nnf,[status(thm)],[fact_map__pair_Oid]) ).

fof(f_3399_2,plain,
    ! [U_13266,U_13265] : c_Product__Type_Omap__pair(U_13265,U_13265,U_13266,U_13266,c_Fun_Oid(U_13265),c_Fun_Oid(U_13266)) = c_Fun_Oid(tc_prod(U_13265,U_13266)),
    inference(variable_rename,[status(thm)],[f_3399_1]) ).

cnf(f_3399_3,plain,
    c_Product__Type_Omap__pair(U_13265,U_13265,U_13266,U_13266,c_Fun_Oid(U_13265),c_Fun_Oid(U_13266)) = c_Fun_Oid(tc_prod(U_13265,U_13266)),
    inference(clausify,[status(thm)],[f_3399_2]) ).

fof(f_3400_1,plain,
    ! [T_c,T_b] : c_Product__Type_Omap__pair(T_b,T_b,T_c,T_c,c_COMBI(T_b),c_COMBI(T_c)) = c_Fun_Oid(tc_prod(T_b,T_c)),
    inference(fof_nnf,[status(thm)],[fact_map__pair_Oidentity]) ).

fof(f_3400_2,plain,
    ! [U_13268,U_13267] : c_Product__Type_Omap__pair(U_13267,U_13267,U_13268,U_13268,c_COMBI(U_13267),c_COMBI(U_13268)) = c_Fun_Oid(tc_prod(U_13267,U_13268)),
    inference(variable_rename,[status(thm)],[f_3400_1]) ).

cnf(f_3400_3,plain,
    c_Product__Type_Omap__pair(U_13267,U_13267,U_13268,U_13268,c_COMBI(U_13267),c_COMBI(U_13268)) = c_Fun_Oid(tc_prod(U_13267,U_13268)),
    inference(clausify,[status(thm)],[f_3400_2]) ).

fof(f_3401_1,plain,
    ! [V_Y_2,T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_Fun_Oid(T_b)),V_Y_2) = V_Y_2,
    inference(fof_nnf,[status(thm)],[fact_image__id]) ).

fof(f_3401_2,plain,
    ! [U_13270,U_13269] : hAPP(c_Set_Oimage(U_13269,U_13269,c_Fun_Oid(U_13269)),U_13270) = U_13270,
    inference(variable_rename,[status(thm)],[f_3401_1]) ).

cnf(f_3401_3,plain,
    hAPP(c_Set_Oimage(U_13269,U_13269,c_Fun_Oid(U_13269)),U_13270) = U_13270,
    inference(clausify,[status(thm)],[f_3401_2]) ).

fof(f_3402_1,plain,
    ! [T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_Fun_Oid(T_b)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_surj__id]) ).

fof(f_3402_2,plain,
    ! [U_13271] : hAPP(c_Set_Oimage(U_13271,U_13271,c_Fun_Oid(U_13271)),c_Orderings_Otop__class_Otop(tc_fun(U_13271,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_13271,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3402_1]) ).

cnf(f_3402_3,plain,
    hAPP(c_Set_Oimage(U_13271,U_13271,c_Fun_Oid(U_13271)),c_Orderings_Otop__class_Otop(tc_fun(U_13271,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_13271,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3402_2]) ).

fof(f_3403_1,plain,
    ! [V_F_2,V_f_2,T_c,T_b] :
      ( hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Fun_Oid(T_c)
      | ~ c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding_Oempty]) ).

fof(f_3403_2,plain,
    ! [U_13275,U_13274,U_13273,U_13272] :
      ( hAPP(U_13275,c_Orderings_Obot__class_Obot(tc_fun(U_13272,tc_HOL_Obool))) = c_Fun_Oid(U_13273)
      | ~ c_Finite__Set_Ofolding(U_13272,U_13273,U_13274,U_13275) ),
    inference(variable_rename,[status(thm)],[f_3403_1]) ).

cnf(f_3403_3,plain,
    ( hAPP(U_13275,c_Orderings_Obot__class_Obot(tc_fun(U_13272,tc_HOL_Obool))) = c_Fun_Oid(U_13273)
    | ~ c_Finite__Set_Ofolding(U_13272,U_13273,U_13274,U_13275) ),
    inference(clausify,[status(thm)],[f_3403_2]) ).

fof(f_3404_1,plain,
    ! [V_f_2,T_b,T_d,T_c] : c_Product__Type_Oapsnd(T_c,T_d,T_b,V_f_2) = c_Product__Type_Omap__pair(T_b,T_b,T_c,T_d,c_Fun_Oid(T_b),V_f_2),
    inference(fof_nnf,[status(thm)],[fact_apsnd__def]) ).

fof(f_3404_2,plain,
    ! [U_13279,U_13278,U_13277,U_13276] : c_Product__Type_Oapsnd(U_13276,U_13277,U_13278,U_13279) = c_Product__Type_Omap__pair(U_13278,U_13278,U_13276,U_13277,c_Fun_Oid(U_13278),U_13279),
    inference(variable_rename,[status(thm)],[f_3404_1]) ).

cnf(f_3404_3,plain,
    c_Product__Type_Oapsnd(U_13276,U_13277,U_13278,U_13279) = c_Product__Type_Omap__pair(U_13278,U_13278,U_13276,U_13277,c_Fun_Oid(U_13278),U_13279),
    inference(clausify,[status(thm)],[f_3404_2]) ).

fof(f_3405_1,plain,
    ! [V_f_2,T_c,T_d,T_b] : c_Product__Type_Oapfst(T_b,T_d,T_c,V_f_2) = c_Product__Type_Omap__pair(T_b,T_d,T_c,T_c,V_f_2,c_Fun_Oid(T_c)),
    inference(fof_nnf,[status(thm)],[fact_apfst__def]) ).

fof(f_3405_2,plain,
    ! [U_13283,U_13282,U_13281,U_13280] : c_Product__Type_Oapfst(U_13280,U_13281,U_13282,U_13283) = c_Product__Type_Omap__pair(U_13280,U_13281,U_13282,U_13282,U_13283,c_Fun_Oid(U_13282)),
    inference(variable_rename,[status(thm)],[f_3405_1]) ).

cnf(f_3405_3,plain,
    c_Product__Type_Oapfst(U_13280,U_13281,U_13282,U_13283) = c_Product__Type_Omap__pair(U_13280,U_13281,U_13282,U_13282,U_13283,c_Fun_Oid(U_13282)),
    inference(clausify,[status(thm)],[f_3405_2]) ).

fof(f_3406_1,plain,
    ! [T_c,T_b] : hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_prod(T_b,T_c)),c_Product__Type_OPair(T_b,T_c)) = c_Fun_Oid(tc_prod(T_b,T_c)),
    inference(fof_nnf,[status(thm)],[fact_split__Pair]) ).

fof(f_3406_2,plain,
    ! [U_13285,U_13284] : hAPP(c_Product__Type_Oprod_Oprod__case(U_13284,U_13285,tc_prod(U_13284,U_13285)),c_Product__Type_OPair(U_13284,U_13285)) = c_Fun_Oid(tc_prod(U_13284,U_13285)),
    inference(variable_rename,[status(thm)],[f_3406_1]) ).

cnf(f_3406_3,plain,
    hAPP(c_Product__Type_Oprod_Oprod__case(U_13284,U_13285,tc_prod(U_13284,U_13285)),c_Product__Type_OPair(U_13284,U_13285)) = c_Fun_Oid(tc_prod(U_13284,U_13285)),
    inference(clausify,[status(thm)],[f_3406_2]) ).

fof(f_3407_1,plain,
    ! [V_B_2,V_f_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_c),c_Fun_Oid(T_c)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2))
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
      | ~ class_Groups_Ocomm__monoid__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__reindex__id]) ).

fof(f_3407_2,plain,
    ! [U_13289,U_13288,U_13287,U_13286] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13287,U_13286),U_13288),U_13289) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13286,U_13286),c_Fun_Oid(U_13286)),hAPP(c_Set_Oimage(U_13287,U_13286,U_13288),U_13289))
      | ~ c_Fun_Oinj__on(U_13287,U_13286,U_13288,U_13289)
      | ~ class_Groups_Ocomm__monoid__add(U_13286) ),
    inference(variable_rename,[status(thm)],[f_3407_1]) ).

cnf(f_3407_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13287,U_13286),U_13288),U_13289) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13286,U_13286),c_Fun_Oid(U_13286)),hAPP(c_Set_Oimage(U_13287,U_13286,U_13288),U_13289))
    | ~ c_Fun_Oinj__on(U_13287,U_13286,U_13288,U_13289)
    | ~ class_Groups_Ocomm__monoid__add(U_13286) ),
    inference(clausify,[status(thm)],[f_3407_2]) ).

fof(f_3408_1,plain,
    ! [V_B_2,V_f_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_c),c_Fun_Oid(T_c)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2))
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
      | ~ class_Groups_Ocomm__monoid__mult(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__reindex__id]) ).

fof(f_3408_2,plain,
    ! [U_13293,U_13292,U_13291,U_13290] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13291,U_13290),U_13292),U_13293) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13290,U_13290),c_Fun_Oid(U_13290)),hAPP(c_Set_Oimage(U_13291,U_13290,U_13292),U_13293))
      | ~ c_Fun_Oinj__on(U_13291,U_13290,U_13292,U_13293)
      | ~ class_Groups_Ocomm__monoid__mult(U_13290) ),
    inference(variable_rename,[status(thm)],[f_3408_1]) ).

cnf(f_3408_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13291,U_13290),U_13292),U_13293) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13290,U_13290),c_Fun_Oid(U_13290)),hAPP(c_Set_Oimage(U_13291,U_13290,U_13292),U_13293))
    | ~ c_Fun_Oinj__on(U_13291,U_13290,U_13292,U_13293)
    | ~ class_Groups_Ocomm__monoid__mult(U_13290) ),
    inference(clausify,[status(thm)],[f_3408_2]) ).

fof(f_3409_1,plain,
    ! [V_A_2,T_b] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
        | ! [B_n,B_f] : V_A_2 != hAPP(c_Set_Oimage(tc_Nat_Onat,T_b,B_f),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),B_n))) )
      & ( ? [B_n,B_f] : V_A_2 = hAPP(c_Set_Oimage(tc_Nat_Onat,T_b,B_f),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),B_n)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_finite__conv__nat__seg__image]) ).

fof(f_3409_2,plain,
    ! [U_13299,U_13298] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13298),U_13299))
        | ! [U_13297,U_13296] : U_13299 != hAPP(c_Set_Oimage(tc_Nat_Onat,U_13298,U_13296),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_13297))) )
      & ( ? [U_13295,U_13294] : U_13299 = hAPP(c_Set_Oimage(tc_Nat_Onat,U_13298,U_13294),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_13295)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13298),U_13299)) ) ),
    inference(variable_rename,[status(thm)],[f_3409_1]) ).

fof(f_3409_3,plain,
    ( ! [U_13303,U_13301] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13301),U_13303))
        | ! [U_13297,U_13296] : U_13303 != hAPP(c_Set_Oimage(tc_Nat_Onat,U_13301,U_13296),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_13297))) )
    & ! [U_13302,U_13300] :
        ( ? [U_13295,U_13294] : U_13302 = hAPP(c_Set_Oimage(tc_Nat_Onat,U_13300,U_13294),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_13295)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13300),U_13302)) ) ),
    inference(miniscope,[status(thm)],[f_3409_2]) ).

fof(f_3409_4,plain,
    ( ! [U_13303,U_13301] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13301),U_13303))
        | ! [U_13297,U_13296] : U_13303 != hAPP(c_Set_Oimage(tc_Nat_Onat,U_13301,U_13296),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_13297))) )
    & ! [U_13302,U_13300] :
        ( ? [U_13294] : U_13302 = hAPP(c_Set_Oimage(tc_Nat_Onat,U_13300,U_13294),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),sK316(U_13302,U_13300))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13300),U_13302)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK316]),skolemize(U_13295,sK316(U_13302,U_13300))],[f_3409_3]) ).

fof(f_3409_5,plain,
    ( ! [U_13303,U_13301] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13301),U_13303))
        | ! [U_13297,U_13296] : U_13303 != hAPP(c_Set_Oimage(tc_Nat_Onat,U_13301,U_13296),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_13297))) )
    & ! [U_13302,U_13300] :
        ( U_13302 = hAPP(c_Set_Oimage(tc_Nat_Onat,U_13300,sK317(U_13302,U_13300)),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),sK316(U_13302,U_13300))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13300),U_13302)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK317]),skolemize(U_13294,sK317(U_13302,U_13300))],[f_3409_4]) ).

cnf(f_3409_6,plain,
    ( U_13302 = hAPP(c_Set_Oimage(tc_Nat_Onat,U_13300,sK317(U_13302,U_13300)),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),sK316(U_13302,U_13300))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13300),U_13302)) ),
    inference(clausify,[status(thm)],[f_3409_5]) ).

cnf(f_3409_7,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13301),U_13303))
    | U_13303 != hAPP(c_Set_Oimage(tc_Nat_Onat,U_13301,U_13296),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_13297))) ),
    inference(clausify,[status(thm)],[f_3409_5]) ).

fof(f_3410_1,plain,
    ! [V_s_2,V_r_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_r_2),V_s_2) = hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_d))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_b),c_COMBS(T_d,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_d),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_b),c_COMBC(T_d,tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_b,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_d),tc_fun(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_b,T_d)))),c_Product__Type_OPair(T_b,T_d)))),V_r_2))))),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_d,T_c)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_d,T_c),tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_d,T_c)))),hAPP(c_COMBC(T_d,T_c,tc_prod(T_d,T_c)),c_Product__Type_OPair(T_d,T_c))))),V_s_2))))),
    inference(fof_nnf,[status(thm)],[fact_rel__comp__def]) ).

fof(f_3410_2,plain,
    ! [U_13308,U_13307,U_13306,U_13305,U_13304] : hAPP(hAPP(c_Relation_Orel__comp(U_13304,U_13305,U_13306),U_13307),U_13308) = hAPP(c_Set_OCollect(tc_prod(U_13304,U_13306)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13304,U_13306,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_13306,tc_fun(U_13305,tc_HOL_Obool)),tc_fun(U_13306,tc_HOL_Obool),U_13304),hAPP(c_COMBB(tc_fun(U_13305,tc_HOL_Obool),tc_HOL_Obool,U_13306),c_HOL_OEx(U_13305))),hAPP(hAPP(c_COMBC(U_13304,tc_fun(U_13306,tc_fun(U_13305,tc_HOL_Obool)),tc_fun(U_13306,tc_fun(U_13305,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13305,tc_HOL_Obool),tc_fun(U_13305,tc_HOL_Obool)),tc_fun(tc_fun(U_13306,tc_fun(U_13305,tc_HOL_Obool)),tc_fun(U_13306,tc_fun(U_13305,tc_HOL_Obool))),U_13304),c_COMBB(tc_fun(U_13305,tc_HOL_Obool),tc_fun(U_13305,tc_HOL_Obool),U_13306)),hAPP(hAPP(c_COMBB(tc_fun(U_13305,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13305,tc_HOL_Obool),tc_fun(U_13305,tc_HOL_Obool)),U_13304),c_COMBS(U_13305,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13305,tc_HOL_Obool),tc_fun(U_13305,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13304),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13305),c_fconj)),hAPP(hAPP(c_COMBC(U_13304,tc_fun(tc_prod(U_13304,U_13305),tc_HOL_Obool),tc_fun(U_13305,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13305,tc_fun(tc_fun(tc_prod(U_13304,U_13305),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13304,U_13305),tc_HOL_Obool),tc_fun(U_13305,tc_HOL_Obool)),U_13304),c_COMBC(U_13305,tc_fun(tc_prod(U_13304,U_13305),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13305,tc_prod(U_13304,U_13305)),tc_fun(U_13305,tc_fun(tc_fun(tc_prod(U_13304,U_13305),tc_HOL_Obool),tc_HOL_Obool)),U_13304),hAPP(c_COMBB(tc_prod(U_13304,U_13305),tc_fun(tc_fun(tc_prod(U_13304,U_13305),tc_HOL_Obool),tc_HOL_Obool),U_13305),c_member(tc_prod(U_13304,U_13305)))),c_Product__Type_OPair(U_13304,U_13305)))),U_13307))))),hAPP(hAPP(c_COMBC(U_13306,tc_fun(tc_prod(U_13305,U_13306),tc_HOL_Obool),tc_fun(U_13305,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13305,tc_fun(tc_fun(tc_prod(U_13305,U_13306),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13305,U_13306),tc_HOL_Obool),tc_fun(U_13305,tc_HOL_Obool)),U_13306),c_COMBC(U_13305,tc_fun(tc_prod(U_13305,U_13306),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13305,tc_prod(U_13305,U_13306)),tc_fun(U_13305,tc_fun(tc_fun(tc_prod(U_13305,U_13306),tc_HOL_Obool),tc_HOL_Obool)),U_13306),hAPP(c_COMBB(tc_prod(U_13305,U_13306),tc_fun(tc_fun(tc_prod(U_13305,U_13306),tc_HOL_Obool),tc_HOL_Obool),U_13305),c_member(tc_prod(U_13305,U_13306)))),hAPP(c_COMBC(U_13305,U_13306,tc_prod(U_13305,U_13306)),c_Product__Type_OPair(U_13305,U_13306))))),U_13308))))),
    inference(variable_rename,[status(thm)],[f_3410_1]) ).

cnf(f_3410_3,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_13304,U_13305,U_13306),U_13307),U_13308) = hAPP(c_Set_OCollect(tc_prod(U_13304,U_13306)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13304,U_13306,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_13306,tc_fun(U_13305,tc_HOL_Obool)),tc_fun(U_13306,tc_HOL_Obool),U_13304),hAPP(c_COMBB(tc_fun(U_13305,tc_HOL_Obool),tc_HOL_Obool,U_13306),c_HOL_OEx(U_13305))),hAPP(hAPP(c_COMBC(U_13304,tc_fun(U_13306,tc_fun(U_13305,tc_HOL_Obool)),tc_fun(U_13306,tc_fun(U_13305,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13305,tc_HOL_Obool),tc_fun(U_13305,tc_HOL_Obool)),tc_fun(tc_fun(U_13306,tc_fun(U_13305,tc_HOL_Obool)),tc_fun(U_13306,tc_fun(U_13305,tc_HOL_Obool))),U_13304),c_COMBB(tc_fun(U_13305,tc_HOL_Obool),tc_fun(U_13305,tc_HOL_Obool),U_13306)),hAPP(hAPP(c_COMBB(tc_fun(U_13305,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13305,tc_HOL_Obool),tc_fun(U_13305,tc_HOL_Obool)),U_13304),c_COMBS(U_13305,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13305,tc_HOL_Obool),tc_fun(U_13305,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13304),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13305),c_fconj)),hAPP(hAPP(c_COMBC(U_13304,tc_fun(tc_prod(U_13304,U_13305),tc_HOL_Obool),tc_fun(U_13305,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13305,tc_fun(tc_fun(tc_prod(U_13304,U_13305),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13304,U_13305),tc_HOL_Obool),tc_fun(U_13305,tc_HOL_Obool)),U_13304),c_COMBC(U_13305,tc_fun(tc_prod(U_13304,U_13305),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13305,tc_prod(U_13304,U_13305)),tc_fun(U_13305,tc_fun(tc_fun(tc_prod(U_13304,U_13305),tc_HOL_Obool),tc_HOL_Obool)),U_13304),hAPP(c_COMBB(tc_prod(U_13304,U_13305),tc_fun(tc_fun(tc_prod(U_13304,U_13305),tc_HOL_Obool),tc_HOL_Obool),U_13305),c_member(tc_prod(U_13304,U_13305)))),c_Product__Type_OPair(U_13304,U_13305)))),U_13307))))),hAPP(hAPP(c_COMBC(U_13306,tc_fun(tc_prod(U_13305,U_13306),tc_HOL_Obool),tc_fun(U_13305,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13305,tc_fun(tc_fun(tc_prod(U_13305,U_13306),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13305,U_13306),tc_HOL_Obool),tc_fun(U_13305,tc_HOL_Obool)),U_13306),c_COMBC(U_13305,tc_fun(tc_prod(U_13305,U_13306),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13305,tc_prod(U_13305,U_13306)),tc_fun(U_13305,tc_fun(tc_fun(tc_prod(U_13305,U_13306),tc_HOL_Obool),tc_HOL_Obool)),U_13306),hAPP(c_COMBB(tc_prod(U_13305,U_13306),tc_fun(tc_fun(tc_prod(U_13305,U_13306),tc_HOL_Obool),tc_HOL_Obool),U_13305),c_member(tc_prod(U_13305,U_13306)))),hAPP(c_COMBC(U_13305,U_13306,tc_prod(U_13305,U_13306)),c_Product__Type_OPair(U_13305,U_13306))))),U_13308))))),
    inference(clausify,[status(thm)],[f_3410_2]) ).

fof(f_3411_1,plain,
    ! [V_P_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),hAPP(c_Set_OCollect(tc_prod(T_c,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,tc_HOL_Obool),V_P_2))) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c)),hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),V_P_2))),
    inference(fof_nnf,[status(thm)],[fact_Range__Collect__split]) ).

fof(f_3411_2,plain,
    ! [U_13311,U_13310,U_13309] : hAPP(c_Relation_ORange(U_13309,U_13310),hAPP(c_Set_OCollect(tc_prod(U_13309,U_13310)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13309,U_13310,tc_HOL_Obool),U_13311))) = hAPP(c_Set_OCollect(U_13310),hAPP(hAPP(c_COMBB(tc_fun(U_13309,tc_HOL_Obool),tc_HOL_Obool,U_13310),c_HOL_OEx(U_13309)),hAPP(c_COMBC(U_13309,U_13310,tc_HOL_Obool),U_13311))),
    inference(variable_rename,[status(thm)],[f_3411_1]) ).

cnf(f_3411_3,plain,
    hAPP(c_Relation_ORange(U_13309,U_13310),hAPP(c_Set_OCollect(tc_prod(U_13309,U_13310)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13309,U_13310,tc_HOL_Obool),U_13311))) = hAPP(c_Set_OCollect(U_13310),hAPP(hAPP(c_COMBB(tc_fun(U_13309,tc_HOL_Obool),tc_HOL_Obool,U_13310),c_HOL_OEx(U_13309)),hAPP(c_COMBC(U_13309,U_13310,tc_HOL_Obool),U_13311))),
    inference(clausify,[status(thm)],[f_3411_2]) ).

fof(f_3412_1,plain,
    ! [V_s_2,V_c_2,T_d,V_r_2,V_b_2,V_a_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),V_a_2),V_c_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_b_2),V_c_2)),V_s_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_rel__compI]) ).

fof(f_3412_2,plain,
    ! [U_13319,U_13318,U_13317,U_13316,U_13315,U_13314,U_13313,U_13312] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13312,U_13317)),hAPP(hAPP(c_Product__Type_OPair(U_13312,U_13317),U_13314),U_13318)),hAPP(hAPP(c_Relation_Orel__comp(U_13312,U_13313,U_13317),U_13316),U_13319)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13313,U_13317)),hAPP(hAPP(c_Product__Type_OPair(U_13313,U_13317),U_13315),U_13318)),U_13319))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13312,U_13313)),hAPP(hAPP(c_Product__Type_OPair(U_13312,U_13313),U_13314),U_13315)),U_13316)) ),
    inference(variable_rename,[status(thm)],[f_3412_1]) ).

cnf(f_3412_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13312,U_13317)),hAPP(hAPP(c_Product__Type_OPair(U_13312,U_13317),U_13314),U_13318)),hAPP(hAPP(c_Relation_Orel__comp(U_13312,U_13313,U_13317),U_13316),U_13319)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13313,U_13317)),hAPP(hAPP(c_Product__Type_OPair(U_13313,U_13317),U_13315),U_13318)),U_13319))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13312,U_13313)),hAPP(hAPP(c_Product__Type_OPair(U_13312,U_13313),U_13314),U_13315)),U_13316)) ),
    inference(clausify,[status(thm)],[f_3412_2]) ).

fof(f_3413_1,plain,
    ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_RangeI]) ).

fof(f_3413_2,plain,
    ! [U_13324,U_13323,U_13322,U_13321,U_13320] :
      ( hBOOL(hAPP(hAPP(c_member(U_13321),U_13323),hAPP(c_Relation_ORange(U_13320,U_13321),U_13324)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13320,U_13321)),hAPP(hAPP(c_Product__Type_OPair(U_13320,U_13321),U_13322),U_13323)),U_13324)) ),
    inference(variable_rename,[status(thm)],[f_3413_1]) ).

cnf(f_3413_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13321),U_13323),hAPP(c_Relation_ORange(U_13320,U_13321),U_13324)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13320,U_13321)),hAPP(hAPP(c_Product__Type_OPair(U_13320,U_13321),U_13322),U_13323)),U_13324)) ),
    inference(clausify,[status(thm)],[f_3413_2]) ).

fof(f_3414_1,plain,
    ! [V_s_2,V_r_2,V_I_2,T_e,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)),V_I_2),V_r_2)),V_s_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBC(T_e,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),T_e),c_Relation_Orel__comp(T_b,T_d,T_c)),V_r_2)),V_s_2)),
    inference(fof_nnf,[status(thm)],[fact_rel__comp__UNION__distrib2]) ).

fof(f_3414_2,plain,
    ! [U_13331,U_13330,U_13329,U_13328,U_13327,U_13326,U_13325] : hAPP(hAPP(c_Relation_Orel__comp(U_13325,U_13326,U_13327),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13328,tc_fun(tc_prod(U_13325,U_13326),tc_HOL_Obool)),U_13329),U_13330)),U_13331) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13328,tc_fun(tc_prod(U_13325,U_13327),tc_HOL_Obool)),U_13329),hAPP(hAPP(c_COMBC(U_13328,tc_fun(tc_prod(U_13326,U_13327),tc_HOL_Obool),tc_fun(tc_prod(U_13325,U_13327),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_13325,U_13326),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_13326,U_13327),tc_HOL_Obool),tc_fun(tc_prod(U_13325,U_13327),tc_HOL_Obool)),U_13328),c_Relation_Orel__comp(U_13325,U_13326,U_13327)),U_13330)),U_13331)),
    inference(variable_rename,[status(thm)],[f_3414_1]) ).

cnf(f_3414_3,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_13325,U_13326,U_13327),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13328,tc_fun(tc_prod(U_13325,U_13326),tc_HOL_Obool)),U_13329),U_13330)),U_13331) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13328,tc_fun(tc_prod(U_13325,U_13327),tc_HOL_Obool)),U_13329),hAPP(hAPP(c_COMBC(U_13328,tc_fun(tc_prod(U_13326,U_13327),tc_HOL_Obool),tc_fun(tc_prod(U_13325,U_13327),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_13325,U_13326),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_13326,U_13327),tc_HOL_Obool),tc_fun(tc_prod(U_13325,U_13327),tc_HOL_Obool)),U_13328),c_Relation_Orel__comp(U_13325,U_13326,U_13327)),U_13330)),U_13331)),
    inference(clausify,[status(thm)],[f_3414_2]) ).

fof(f_3415_1,plain,
    ! [V_r_2,V_I_2,T_e,V_s_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_s_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool)),V_I_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),T_e),hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_s_2)),V_r_2)),
    inference(fof_nnf,[status(thm)],[fact_rel__comp__UNION__distrib]) ).

fof(f_3415_2,plain,
    ! [U_13338,U_13337,U_13336,U_13335,U_13334,U_13333,U_13332] : hAPP(hAPP(c_Relation_Orel__comp(U_13332,U_13333,U_13334),U_13335),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13336,tc_fun(tc_prod(U_13333,U_13334),tc_HOL_Obool)),U_13337),U_13338)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13336,tc_fun(tc_prod(U_13332,U_13334),tc_HOL_Obool)),U_13337),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_13333,U_13334),tc_HOL_Obool),tc_fun(tc_prod(U_13332,U_13334),tc_HOL_Obool),U_13336),hAPP(c_Relation_Orel__comp(U_13332,U_13333,U_13334),U_13335)),U_13338)),
    inference(variable_rename,[status(thm)],[f_3415_1]) ).

cnf(f_3415_3,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_13332,U_13333,U_13334),U_13335),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13336,tc_fun(tc_prod(U_13333,U_13334),tc_HOL_Obool)),U_13337),U_13338)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13336,tc_fun(tc_prod(U_13332,U_13334),tc_HOL_Obool)),U_13337),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_13333,U_13334),tc_HOL_Obool),tc_fun(tc_prod(U_13332,U_13334),tc_HOL_Obool),U_13336),hAPP(c_Relation_Orel__comp(U_13332,U_13333,U_13334),U_13335)),U_13338)),
    inference(clausify,[status(thm)],[f_3415_2]) ).

fof(f_3416_1,plain,
    ! [V_R_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_R_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_rel__comp__empty2]) ).

fof(f_3416_2,plain,
    ! [U_13342,U_13341,U_13340,U_13339] : hAPP(hAPP(c_Relation_Orel__comp(U_13339,U_13340,U_13341),U_13342),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13340,U_13341),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13339,U_13341),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3416_1]) ).

cnf(f_3416_3,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_13339,U_13340,U_13341),U_13342),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13340,U_13341),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13339,U_13341),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3416_2]) ).

fof(f_3417_1,plain,
    ! [V_R_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool))),V_R_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_rel__comp__empty1]) ).

fof(f_3417_2,plain,
    ! [U_13346,U_13345,U_13344,U_13343] : hAPP(hAPP(c_Relation_Orel__comp(U_13343,U_13344,U_13345),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13343,U_13344),tc_HOL_Obool))),U_13346) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13343,U_13345),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3417_1]) ).

cnf(f_3417_3,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_13343,U_13344,U_13345),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13343,U_13344),tc_HOL_Obool))),U_13346) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13343,U_13345),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3417_2]) ).

fof(f_3418_1,plain,
    ! [V_T_2,V_S_2,V_R_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_R_2),V_S_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_R_2),V_T_2)),
    inference(fof_nnf,[status(thm)],[fact_rel__comp__distrib]) ).

fof(f_3418_2,plain,
    ! [U_13352,U_13351,U_13350,U_13349,U_13348,U_13347] : hAPP(hAPP(c_Relation_Orel__comp(U_13347,U_13348,U_13349),U_13350),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13348,U_13349),tc_HOL_Obool)),U_13351),U_13352)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13347,U_13349),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13347,U_13348,U_13349),U_13350),U_13351)),hAPP(hAPP(c_Relation_Orel__comp(U_13347,U_13348,U_13349),U_13350),U_13352)),
    inference(variable_rename,[status(thm)],[f_3418_1]) ).

cnf(f_3418_3,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_13347,U_13348,U_13349),U_13350),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13348,U_13349),tc_HOL_Obool)),U_13351),U_13352)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13347,U_13349),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13347,U_13348,U_13349),U_13350),U_13351)),hAPP(hAPP(c_Relation_Orel__comp(U_13347,U_13348,U_13349),U_13350),U_13352)),
    inference(clausify,[status(thm)],[f_3418_2]) ).

fof(f_3419_1,plain,
    ! [V_R_2,V_T_2,V_S_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)),V_S_2),V_T_2)),V_R_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_S_2),V_R_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_T_2),V_R_2)),
    inference(fof_nnf,[status(thm)],[fact_rel__comp__distrib2]) ).

fof(f_3419_2,plain,
    ! [U_13358,U_13357,U_13356,U_13355,U_13354,U_13353] : hAPP(hAPP(c_Relation_Orel__comp(U_13353,U_13354,U_13355),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13353,U_13354),tc_HOL_Obool)),U_13356),U_13357)),U_13358) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13353,U_13355),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13353,U_13354,U_13355),U_13356),U_13358)),hAPP(hAPP(c_Relation_Orel__comp(U_13353,U_13354,U_13355),U_13357),U_13358)),
    inference(variable_rename,[status(thm)],[f_3419_1]) ).

cnf(f_3419_3,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_13353,U_13354,U_13355),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13353,U_13354),tc_HOL_Obool)),U_13356),U_13357)),U_13358) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13353,U_13355),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13353,U_13354,U_13355),U_13356),U_13358)),hAPP(hAPP(c_Relation_Orel__comp(U_13353,U_13354,U_13355),U_13357),U_13358)),
    inference(clausify,[status(thm)],[f_3419_2]) ).

fof(f_3420_1,plain,
    ! [V_T_2,V_S_2,V_R_2,T_e,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_e,T_d),V_R_2),V_S_2)),V_T_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_e,T_c),V_R_2),hAPP(hAPP(c_Relation_Orel__comp(T_e,T_d,T_c),V_S_2),V_T_2)),
    inference(fof_nnf,[status(thm)],[fact_O__assoc]) ).

fof(f_3420_2,plain,
    ! [U_13365,U_13364,U_13363,U_13362,U_13361,U_13360,U_13359] : hAPP(hAPP(c_Relation_Orel__comp(U_13359,U_13360,U_13361),hAPP(hAPP(c_Relation_Orel__comp(U_13359,U_13362,U_13360),U_13363),U_13364)),U_13365) = hAPP(hAPP(c_Relation_Orel__comp(U_13359,U_13362,U_13361),U_13363),hAPP(hAPP(c_Relation_Orel__comp(U_13362,U_13360,U_13361),U_13364),U_13365)),
    inference(variable_rename,[status(thm)],[f_3420_1]) ).

cnf(f_3420_3,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_13359,U_13360,U_13361),hAPP(hAPP(c_Relation_Orel__comp(U_13359,U_13362,U_13360),U_13363),U_13364)),U_13365) = hAPP(hAPP(c_Relation_Orel__comp(U_13359,U_13362,U_13361),U_13363),hAPP(hAPP(c_Relation_Orel__comp(U_13362,U_13360,U_13361),U_13364),U_13365)),
    inference(clausify,[status(thm)],[f_3420_2]) ).

fof(f_3421_1,plain,
    ! [V_s_2,V_s_H_2,T_d,V_r_2,V_r_H_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_H_2),V_s_H_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),V_s_H_2),V_s_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_H_2),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_rel__comp__mono]) ).

fof(f_3421_2,plain,
    ! [U_13372,U_13371,U_13370,U_13369,U_13368,U_13367,U_13366] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13366,U_13370),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13366,U_13367,U_13370),U_13368),U_13371)),hAPP(hAPP(c_Relation_Orel__comp(U_13366,U_13367,U_13370),U_13369),U_13372)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13367,U_13370),tc_HOL_Obool)),U_13371),U_13372))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13366,U_13367),tc_HOL_Obool)),U_13368),U_13369)) ),
    inference(variable_rename,[status(thm)],[f_3421_1]) ).

cnf(f_3421_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13366,U_13370),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13366,U_13367,U_13370),U_13368),U_13371)),hAPP(hAPP(c_Relation_Orel__comp(U_13366,U_13367,U_13370),U_13369),U_13372)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13367,U_13370),tc_HOL_Obool)),U_13371),U_13372))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13366,U_13367),tc_HOL_Obool)),U_13368),U_13369)) ),
    inference(clausify,[status(thm)],[f_3421_2]) ).

fof(f_3422_1,plain,
    ! [V_A_2,T_b] : hAPP(c_Relation_ORange(T_b,T_b),c_Relation_OId__on(T_b,V_A_2)) = V_A_2,
    inference(fof_nnf,[status(thm)],[fact_Range__Id__on]) ).

fof(f_3422_2,plain,
    ! [U_13374,U_13373] : hAPP(c_Relation_ORange(U_13373,U_13373),c_Relation_OId__on(U_13373,U_13374)) = U_13374,
    inference(variable_rename,[status(thm)],[f_3422_1]) ).

cnf(f_3422_3,plain,
    hAPP(c_Relation_ORange(U_13373,U_13373),c_Relation_OId__on(U_13373,U_13374)) = U_13374,
    inference(clausify,[status(thm)],[f_3422_2]) ).

fof(f_3423_1,plain,
    ! [V_C_2,V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_B_2),V_C_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
      | hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_A_2),V_C_2) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
      | hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) ),
    inference(fof_nnf,[status(thm)],[fact_union__comp__emptyR]) ).

fof(f_3423_2,plain,
    ! [U_13378,U_13377,U_13376,U_13375] :
      ( hAPP(hAPP(c_Relation_Orel__comp(U_13375,U_13375,U_13375),U_13376),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13375,U_13375),tc_HOL_Obool)),U_13377),U_13378)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13375,U_13375),tc_HOL_Obool))
      | hAPP(hAPP(c_Relation_Orel__comp(U_13375,U_13375,U_13375),U_13376),U_13378) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13375,U_13375),tc_HOL_Obool))
      | hAPP(hAPP(c_Relation_Orel__comp(U_13375,U_13375,U_13375),U_13376),U_13377) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13375,U_13375),tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_3423_1]) ).

cnf(f_3423_3,plain,
    ( hAPP(hAPP(c_Relation_Orel__comp(U_13375,U_13375,U_13375),U_13376),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13375,U_13375),tc_HOL_Obool)),U_13377),U_13378)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13375,U_13375),tc_HOL_Obool))
    | hAPP(hAPP(c_Relation_Orel__comp(U_13375,U_13375,U_13375),U_13376),U_13378) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13375,U_13375),tc_HOL_Obool))
    | hAPP(hAPP(c_Relation_Orel__comp(U_13375,U_13375,U_13375),U_13376),U_13377) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13375,U_13375),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3423_2]) ).

fof(f_3424_1,plain,
    ! [V_B_2,V_C_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
      | hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_B_2),V_C_2) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
      | hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_A_2),V_C_2) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) ),
    inference(fof_nnf,[status(thm)],[fact_union__comp__emptyL]) ).

fof(f_3424_2,plain,
    ! [U_13382,U_13381,U_13380,U_13379] :
      ( hAPP(hAPP(c_Relation_Orel__comp(U_13379,U_13379,U_13379),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13379,U_13379),tc_HOL_Obool)),U_13380),U_13382)),U_13381) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13379,U_13379),tc_HOL_Obool))
      | hAPP(hAPP(c_Relation_Orel__comp(U_13379,U_13379,U_13379),U_13382),U_13381) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13379,U_13379),tc_HOL_Obool))
      | hAPP(hAPP(c_Relation_Orel__comp(U_13379,U_13379,U_13379),U_13380),U_13381) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13379,U_13379),tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_3424_1]) ).

cnf(f_3424_3,plain,
    ( hAPP(hAPP(c_Relation_Orel__comp(U_13379,U_13379,U_13379),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13379,U_13379),tc_HOL_Obool)),U_13380),U_13382)),U_13381) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13379,U_13379),tc_HOL_Obool))
    | hAPP(hAPP(c_Relation_Orel__comp(U_13379,U_13379,U_13379),U_13382),U_13381) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13379,U_13379),tc_HOL_Obool))
    | hAPP(hAPP(c_Relation_Orel__comp(U_13379,U_13379,U_13379),U_13380),U_13381) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13379,U_13379),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3424_2]) ).

fof(f_3425_1,plain,
    ! [V_S_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_Relation_ORange(T_c,T_b)),
    inference(fof_nnf,[status(thm)],[fact_Range__Union]) ).

fof(f_3425_2,plain,
    ! [U_13385,U_13384,U_13383] : hAPP(c_Relation_ORange(U_13383,U_13384),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(U_13383,U_13384),tc_HOL_Obool),U_13385)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(U_13383,U_13384),tc_HOL_Obool),tc_fun(U_13384,tc_HOL_Obool)),U_13385),c_Relation_ORange(U_13383,U_13384)),
    inference(variable_rename,[status(thm)],[f_3425_1]) ).

cnf(f_3425_3,plain,
    hAPP(c_Relation_ORange(U_13383,U_13384),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(U_13383,U_13384),tc_HOL_Obool),U_13385)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(U_13383,U_13384),tc_HOL_Obool),tc_fun(U_13384,tc_HOL_Obool)),U_13385),c_Relation_ORange(U_13383,U_13384)),
    inference(clausify,[status(thm)],[f_3425_2]) ).

fof(f_3426_1,plain,
    ! [T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Range__empty]) ).

fof(f_3426_2,plain,
    ! [U_13387,U_13386] : hAPP(c_Relation_ORange(U_13386,U_13387),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13386,U_13387),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_13387,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3426_1]) ).

cnf(f_3426_3,plain,
    hAPP(c_Relation_ORange(U_13386,U_13387),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13386,U_13387),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_13387,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3426_2]) ).

fof(f_3427_1,plain,
    ! [V_r_2,T_b,T_c] :
      ( ( hAPP(c_Relation_ORange(T_c,T_b),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
        | V_r_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)) )
      & ( V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool))
        | hAPP(c_Relation_ORange(T_c,T_b),V_r_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Range__empty__iff]) ).

fof(f_3427_2,plain,
    ! [U_13390,U_13389,U_13388] :
      ( ( hAPP(c_Relation_ORange(U_13388,U_13389),U_13390) = c_Orderings_Obot__class_Obot(tc_fun(U_13389,tc_HOL_Obool))
        | U_13390 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13388,U_13389),tc_HOL_Obool)) )
      & ( U_13390 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13388,U_13389),tc_HOL_Obool))
        | hAPP(c_Relation_ORange(U_13388,U_13389),U_13390) != c_Orderings_Obot__class_Obot(tc_fun(U_13389,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_3427_1]) ).

fof(f_3427_3,plain,
    ( ! [U_13396,U_13394,U_13392] :
        ( hAPP(c_Relation_ORange(U_13392,U_13394),U_13396) = c_Orderings_Obot__class_Obot(tc_fun(U_13394,tc_HOL_Obool))
        | U_13396 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13392,U_13394),tc_HOL_Obool)) )
    & ! [U_13395,U_13393,U_13391] :
        ( U_13395 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13391,U_13393),tc_HOL_Obool))
        | hAPP(c_Relation_ORange(U_13391,U_13393),U_13395) != c_Orderings_Obot__class_Obot(tc_fun(U_13393,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_3427_2]) ).

cnf(f_3427_4,plain,
    ( U_13395 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13391,U_13393),tc_HOL_Obool))
    | hAPP(c_Relation_ORange(U_13391,U_13393),U_13395) != c_Orderings_Obot__class_Obot(tc_fun(U_13393,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3427_3]) ).

cnf(f_3427_5,plain,
    ( hAPP(c_Relation_ORange(U_13392,U_13394),U_13396) = c_Orderings_Obot__class_Obot(tc_fun(U_13394,tc_HOL_Obool))
    | U_13396 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13392,U_13394),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3427_3]) ).

fof(f_3428_1,plain,
    ! [V_C_2,V_s_2,T_d,V_B_2,V_A_2,V_r_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_b),V_C_2))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),V_s_2),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_B_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_C_2))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_rel__comp__subset__Sigma]) ).

fof(f_3428_2,plain,
    ! [U_13404,U_13403,U_13402,U_13401,U_13400,U_13399,U_13398,U_13397] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13397,U_13402),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13397,U_13398,U_13402),U_13399),U_13403)),hAPP(hAPP(c_Product__Type_OSigma(U_13397,U_13402),U_13400),hAPP(c_COMBK(tc_fun(U_13402,tc_HOL_Obool),U_13397),U_13404))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13398,U_13402),tc_HOL_Obool)),U_13403),hAPP(hAPP(c_Product__Type_OSigma(U_13398,U_13402),U_13401),hAPP(c_COMBK(tc_fun(U_13402,tc_HOL_Obool),U_13398),U_13404))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13397,U_13398),tc_HOL_Obool)),U_13399),hAPP(hAPP(c_Product__Type_OSigma(U_13397,U_13398),U_13400),hAPP(c_COMBK(tc_fun(U_13398,tc_HOL_Obool),U_13397),U_13401)))) ),
    inference(variable_rename,[status(thm)],[f_3428_1]) ).

cnf(f_3428_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13397,U_13402),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13397,U_13398,U_13402),U_13399),U_13403)),hAPP(hAPP(c_Product__Type_OSigma(U_13397,U_13402),U_13400),hAPP(c_COMBK(tc_fun(U_13402,tc_HOL_Obool),U_13397),U_13404))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13398,U_13402),tc_HOL_Obool)),U_13403),hAPP(hAPP(c_Product__Type_OSigma(U_13398,U_13402),U_13401),hAPP(c_COMBK(tc_fun(U_13402,tc_HOL_Obool),U_13398),U_13404))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13397,U_13398),tc_HOL_Obool)),U_13399),hAPP(hAPP(c_Product__Type_OSigma(U_13397,U_13398),U_13400),hAPP(c_COMBK(tc_fun(U_13398,tc_HOL_Obool),U_13397),U_13401)))) ),
    inference(clausify,[status(thm)],[f_3428_2]) ).

fof(f_3429_1,plain,
    ! [V_B_2,V_A_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_c,T_b),V_A_2)),hAPP(c_Relation_ORange(T_c,T_b),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_Range__Un__eq]) ).

fof(f_3429_2,plain,
    ! [U_13408,U_13407,U_13406,U_13405] : hAPP(c_Relation_ORange(U_13405,U_13406),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13405,U_13406),tc_HOL_Obool)),U_13407),U_13408)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13406,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_13405,U_13406),U_13407)),hAPP(c_Relation_ORange(U_13405,U_13406),U_13408)),
    inference(variable_rename,[status(thm)],[f_3429_1]) ).

cnf(f_3429_3,plain,
    hAPP(c_Relation_ORange(U_13405,U_13406),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13405,U_13406),tc_HOL_Obool)),U_13407),U_13408)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13406,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_13405,U_13406),U_13407)),hAPP(c_Relation_ORange(U_13405,U_13406),U_13408)),
    inference(clausify,[status(thm)],[f_3429_2]) ).

fof(f_3430_1,plain,
    ! [V_r_2,T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Relation_ORange(T_b,T_c),V_r_2)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__Range]) ).

fof(f_3430_2,plain,
    ! [U_13411,U_13410,U_13409] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13410),hAPP(c_Relation_ORange(U_13409,U_13410),U_13411)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13409,U_13410)),U_13411)) ),
    inference(variable_rename,[status(thm)],[f_3430_1]) ).

cnf(f_3430_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13410),hAPP(c_Relation_ORange(U_13409,U_13410),U_13411)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13409,U_13410)),U_13411)) ),
    inference(clausify,[status(thm)],[f_3430_2]) ).

fof(f_3431_1,plain,
    ! [V_R_2,T_b,T_c] : hAPP(c_Set_Oimage(tc_prod(T_c,T_b),T_b,c_Product__Type_Osnd(T_c,T_b)),V_R_2) = hAPP(c_Relation_ORange(T_c,T_b),V_R_2),
    inference(fof_nnf,[status(thm)],[fact_snd__eq__Range]) ).

fof(f_3431_2,plain,
    ! [U_13414,U_13413,U_13412] : hAPP(c_Set_Oimage(tc_prod(U_13412,U_13413),U_13413,c_Product__Type_Osnd(U_13412,U_13413)),U_13414) = hAPP(c_Relation_ORange(U_13412,U_13413),U_13414),
    inference(variable_rename,[status(thm)],[f_3431_1]) ).

cnf(f_3431_3,plain,
    hAPP(c_Set_Oimage(tc_prod(U_13412,U_13413),U_13413,c_Product__Type_Osnd(U_13412,U_13413)),U_13414) = hAPP(c_Relation_ORange(U_13412,U_13413),U_13414),
    inference(clausify,[status(thm)],[f_3431_2]) ).

fof(f_3432_1,plain,
    ! [V_r_2,T_c,V_a_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2)))
        | ! [B_y] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_y),V_a_2)),V_r_2)) )
      & ( ? [B_y] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_y),V_a_2)),V_r_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_Range__iff]) ).

fof(f_3432_2,plain,
    ! [U_13420,U_13419,U_13418,U_13417] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_13417),U_13418),hAPP(c_Relation_ORange(U_13419,U_13417),U_13420)))
        | ! [U_13416] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13419,U_13417)),hAPP(hAPP(c_Product__Type_OPair(U_13419,U_13417),U_13416),U_13418)),U_13420)) )
      & ( ? [U_13415] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_13419,U_13417)),hAPP(hAPP(c_Product__Type_OPair(U_13419,U_13417),U_13415),U_13418)),U_13420))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13417),U_13418),hAPP(c_Relation_ORange(U_13419,U_13417),U_13420))) ) ),
    inference(variable_rename,[status(thm)],[f_3432_1]) ).

fof(f_3432_3,plain,
    ( ! [U_13428,U_13426,U_13424,U_13422] :
        ( hBOOL(hAPP(hAPP(c_member(U_13422),U_13424),hAPP(c_Relation_ORange(U_13426,U_13422),U_13428)))
        | ! [U_13416] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13426,U_13422)),hAPP(hAPP(c_Product__Type_OPair(U_13426,U_13422),U_13416),U_13424)),U_13428)) )
    & ! [U_13427,U_13425,U_13423,U_13421] :
        ( ? [U_13415] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_13425,U_13421)),hAPP(hAPP(c_Product__Type_OPair(U_13425,U_13421),U_13415),U_13423)),U_13427))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13421),U_13423),hAPP(c_Relation_ORange(U_13425,U_13421),U_13427))) ) ),
    inference(miniscope,[status(thm)],[f_3432_2]) ).

fof(f_3432_4,plain,
    ( ! [U_13428,U_13426,U_13424,U_13422] :
        ( hBOOL(hAPP(hAPP(c_member(U_13422),U_13424),hAPP(c_Relation_ORange(U_13426,U_13422),U_13428)))
        | ! [U_13416] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13426,U_13422)),hAPP(hAPP(c_Product__Type_OPair(U_13426,U_13422),U_13416),U_13424)),U_13428)) )
    & ! [U_13427,U_13425,U_13423,U_13421] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13425,U_13421)),hAPP(hAPP(c_Product__Type_OPair(U_13425,U_13421),sK318(U_13427,U_13425,U_13423,U_13421)),U_13423)),U_13427))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13421),U_13423),hAPP(c_Relation_ORange(U_13425,U_13421),U_13427))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK318]),skolemize(U_13415,sK318(U_13427,U_13425,U_13423,U_13421))],[f_3432_3]) ).

cnf(f_3432_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13425,U_13421)),hAPP(hAPP(c_Product__Type_OPair(U_13425,U_13421),sK318(U_13427,U_13425,U_13423,U_13421)),U_13423)),U_13427))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13421),U_13423),hAPP(c_Relation_ORange(U_13425,U_13421),U_13427))) ),
    inference(clausify,[status(thm)],[f_3432_4]) ).

cnf(f_3432_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13422),U_13424),hAPP(c_Relation_ORange(U_13426,U_13422),U_13428)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13426,U_13422)),hAPP(hAPP(c_Product__Type_OPair(U_13426,U_13422),U_13416),U_13424)),U_13428)) ),
    inference(clausify,[status(thm)],[f_3432_4]) ).

fof(f_3433_1,plain,
    ! [V_r_2,V_b_2,V_a_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2)),
    inference(fof_nnf,[status(thm)],[fact_Range__insert]) ).

fof(f_3433_2,plain,
    ! [U_13433,U_13432,U_13431,U_13430,U_13429] : hAPP(c_Relation_ORange(U_13429,U_13430),hAPP(hAPP(c_Set_Oinsert(tc_prod(U_13429,U_13430)),hAPP(hAPP(c_Product__Type_OPair(U_13429,U_13430),U_13431),U_13432)),U_13433)) = hAPP(hAPP(c_Set_Oinsert(U_13430),U_13432),hAPP(c_Relation_ORange(U_13429,U_13430),U_13433)),
    inference(variable_rename,[status(thm)],[f_3433_1]) ).

cnf(f_3433_3,plain,
    hAPP(c_Relation_ORange(U_13429,U_13430),hAPP(hAPP(c_Set_Oinsert(tc_prod(U_13429,U_13430)),hAPP(hAPP(c_Product__Type_OPair(U_13429,U_13430),U_13431),U_13432)),U_13433)) = hAPP(hAPP(c_Set_Oinsert(U_13430),U_13432),hAPP(c_Relation_ORange(U_13429,U_13430),U_13433)),
    inference(clausify,[status(thm)],[f_3433_2]) ).

fof(f_3434_1,plain,
    ! [V_B_2,V_A_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_c,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_c,T_b),V_A_2)),hAPP(c_Relation_ORange(T_c,T_b),V_B_2)))),
    inference(fof_nnf,[status(thm)],[fact_Range__Int__subset]) ).

fof(f_3434_2,plain,
    ! [U_13437,U_13436,U_13435,U_13434] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13434,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_13435,U_13434),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_13435,U_13434),tc_HOL_Obool)),U_13436),U_13437))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13434,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_13435,U_13434),U_13436)),hAPP(c_Relation_ORange(U_13435,U_13434),U_13437)))),
    inference(variable_rename,[status(thm)],[f_3434_1]) ).

cnf(f_3434_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13434,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_13435,U_13434),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_13435,U_13434),tc_HOL_Obool)),U_13436),U_13437))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13434,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_13435,U_13434),U_13436)),hAPP(c_Relation_ORange(U_13435,U_13434),U_13437)))),
    inference(clausify,[status(thm)],[f_3434_2]) ).

fof(f_3435_1,plain,
    ! [V_B_2,V_A_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_c,T_b),V_A_2)),hAPP(c_Relation_ORange(T_c,T_b),V_B_2))),hAPP(c_Relation_ORange(T_c,T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_A_2),V_B_2)))),
    inference(fof_nnf,[status(thm)],[fact_Range__Diff__subset]) ).

fof(f_3435_2,plain,
    ! [U_13441,U_13440,U_13439,U_13438] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13438,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13438,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_13439,U_13438),U_13440)),hAPP(c_Relation_ORange(U_13439,U_13438),U_13441))),hAPP(c_Relation_ORange(U_13439,U_13438),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_13439,U_13438),tc_HOL_Obool)),U_13440),U_13441)))),
    inference(variable_rename,[status(thm)],[f_3435_1]) ).

cnf(f_3435_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13438,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13438,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_13439,U_13438),U_13440)),hAPP(c_Relation_ORange(U_13439,U_13438),U_13441))),hAPP(c_Relation_ORange(U_13439,U_13438),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_13439,U_13438),tc_HOL_Obool)),U_13440),U_13441)))),
    inference(clausify,[status(thm)],[f_3435_2]) ).

fof(f_3436_1,plain,
    ! [V_S_2,V_R_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Wellfounded_Omax__ext(T_b,V_R_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(T_b,V_S_2)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omax__ext(T_b,V_R_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_S_2)),V_R_2)) ),
    inference(fof_nnf,[status(thm)],[fact_max__ext__compat]) ).

fof(f_3436_2,plain,
    ! [U_13444,U_13443,U_13442] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(U_13442,tc_HOL_Obool),tc_fun(U_13442,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(U_13442,tc_HOL_Obool),tc_fun(U_13442,tc_HOL_Obool),tc_fun(U_13442,tc_HOL_Obool)),c_Wellfounded_Omax__ext(U_13442,U_13443)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(U_13442,tc_HOL_Obool),tc_fun(U_13442,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(U_13442,U_13444)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(U_13442,tc_HOL_Obool),tc_fun(U_13442,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_13442,tc_HOL_Obool),tc_fun(U_13442,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_13442,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(U_13442,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(U_13442,tc_HOL_Obool),tc_fun(U_13442,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omax__ext(U_13442,U_13443)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13442,U_13442),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13442,U_13442,U_13442),U_13443),U_13444)),U_13443)) ),
    inference(variable_rename,[status(thm)],[f_3436_1]) ).

cnf(f_3436_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(U_13442,tc_HOL_Obool),tc_fun(U_13442,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(U_13442,tc_HOL_Obool),tc_fun(U_13442,tc_HOL_Obool),tc_fun(U_13442,tc_HOL_Obool)),c_Wellfounded_Omax__ext(U_13442,U_13443)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(U_13442,tc_HOL_Obool),tc_fun(U_13442,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(U_13442,U_13444)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(U_13442,tc_HOL_Obool),tc_fun(U_13442,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_13442,tc_HOL_Obool),tc_fun(U_13442,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_13442,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(U_13442,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(U_13442,tc_HOL_Obool),tc_fun(U_13442,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omax__ext(U_13442,U_13443)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13442,U_13442),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13442,U_13442,U_13442),U_13443),U_13444)),U_13443)) ),
    inference(clausify,[status(thm)],[f_3436_2]) ).

fof(f_3437_1,plain,
    ! [V_S_2,V_R_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Wellfounded_Omin__ext(T_b,V_R_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(T_b,V_S_2)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omin__ext(T_b,V_R_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_S_2)),V_R_2)) ),
    inference(fof_nnf,[status(thm)],[fact_min__ext__compat]) ).

fof(f_3437_2,plain,
    ! [U_13447,U_13446,U_13445] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(U_13445,tc_HOL_Obool),tc_fun(U_13445,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(U_13445,tc_HOL_Obool),tc_fun(U_13445,tc_HOL_Obool),tc_fun(U_13445,tc_HOL_Obool)),c_Wellfounded_Omin__ext(U_13445,U_13446)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(U_13445,tc_HOL_Obool),tc_fun(U_13445,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(U_13445,U_13447)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(U_13445,tc_HOL_Obool),tc_fun(U_13445,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_13445,tc_HOL_Obool),tc_fun(U_13445,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_13445,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(U_13445,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(U_13445,tc_HOL_Obool),tc_fun(U_13445,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omin__ext(U_13445,U_13446)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13445,U_13445),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13445,U_13445,U_13445),U_13446),U_13447)),U_13446)) ),
    inference(variable_rename,[status(thm)],[f_3437_1]) ).

cnf(f_3437_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(U_13445,tc_HOL_Obool),tc_fun(U_13445,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(U_13445,tc_HOL_Obool),tc_fun(U_13445,tc_HOL_Obool),tc_fun(U_13445,tc_HOL_Obool)),c_Wellfounded_Omin__ext(U_13445,U_13446)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(U_13445,tc_HOL_Obool),tc_fun(U_13445,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(U_13445,U_13447)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(U_13445,tc_HOL_Obool),tc_fun(U_13445,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_13445,tc_HOL_Obool),tc_fun(U_13445,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_13445,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(U_13445,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(U_13445,tc_HOL_Obool),tc_fun(U_13445,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omin__ext(U_13445,U_13446)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13445,U_13445),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13445,U_13445,U_13445),U_13446),U_13447)),U_13446)) ),
    inference(clausify,[status(thm)],[f_3437_2]) ).

fof(f_3438_1,plain,
    ! [V_x_2,V_r_2,T_c,T_b] :
      ( ( hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_r_2)),V_x_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) )
      & ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2)))
        | ~ hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_r_2)),V_x_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_RangeP__Range__eq]) ).

fof(f_3438_2,plain,
    ! [U_13451,U_13450,U_13449,U_13448] :
      ( ( hBOOL(hAPP(c_Predicate_ORangeP(U_13448,U_13449,hAPP(hAPP(c_COMBC(U_13448,tc_fun(tc_prod(U_13448,U_13449),tc_HOL_Obool),tc_fun(U_13449,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13449,tc_fun(tc_fun(tc_prod(U_13448,U_13449),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13448,U_13449),tc_HOL_Obool),tc_fun(U_13449,tc_HOL_Obool)),U_13448),c_COMBC(U_13449,tc_fun(tc_prod(U_13448,U_13449),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13449,tc_prod(U_13448,U_13449)),tc_fun(U_13449,tc_fun(tc_fun(tc_prod(U_13448,U_13449),tc_HOL_Obool),tc_HOL_Obool)),U_13448),hAPP(c_COMBB(tc_prod(U_13448,U_13449),tc_fun(tc_fun(tc_prod(U_13448,U_13449),tc_HOL_Obool),tc_HOL_Obool),U_13449),c_member(tc_prod(U_13448,U_13449)))),c_Product__Type_OPair(U_13448,U_13449)))),U_13450)),U_13451))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13449),U_13451),hAPP(c_Relation_ORange(U_13448,U_13449),U_13450))) )
      & ( hBOOL(hAPP(hAPP(c_member(U_13449),U_13451),hAPP(c_Relation_ORange(U_13448,U_13449),U_13450)))
        | ~ hBOOL(hAPP(c_Predicate_ORangeP(U_13448,U_13449,hAPP(hAPP(c_COMBC(U_13448,tc_fun(tc_prod(U_13448,U_13449),tc_HOL_Obool),tc_fun(U_13449,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13449,tc_fun(tc_fun(tc_prod(U_13448,U_13449),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13448,U_13449),tc_HOL_Obool),tc_fun(U_13449,tc_HOL_Obool)),U_13448),c_COMBC(U_13449,tc_fun(tc_prod(U_13448,U_13449),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13449,tc_prod(U_13448,U_13449)),tc_fun(U_13449,tc_fun(tc_fun(tc_prod(U_13448,U_13449),tc_HOL_Obool),tc_HOL_Obool)),U_13448),hAPP(c_COMBB(tc_prod(U_13448,U_13449),tc_fun(tc_fun(tc_prod(U_13448,U_13449),tc_HOL_Obool),tc_HOL_Obool),U_13449),c_member(tc_prod(U_13448,U_13449)))),c_Product__Type_OPair(U_13448,U_13449)))),U_13450)),U_13451)) ) ),
    inference(variable_rename,[status(thm)],[f_3438_1]) ).

fof(f_3438_3,plain,
    ( ! [U_13459,U_13457,U_13455,U_13453] :
        ( hBOOL(hAPP(c_Predicate_ORangeP(U_13453,U_13455,hAPP(hAPP(c_COMBC(U_13453,tc_fun(tc_prod(U_13453,U_13455),tc_HOL_Obool),tc_fun(U_13455,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13455,tc_fun(tc_fun(tc_prod(U_13453,U_13455),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13453,U_13455),tc_HOL_Obool),tc_fun(U_13455,tc_HOL_Obool)),U_13453),c_COMBC(U_13455,tc_fun(tc_prod(U_13453,U_13455),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13455,tc_prod(U_13453,U_13455)),tc_fun(U_13455,tc_fun(tc_fun(tc_prod(U_13453,U_13455),tc_HOL_Obool),tc_HOL_Obool)),U_13453),hAPP(c_COMBB(tc_prod(U_13453,U_13455),tc_fun(tc_fun(tc_prod(U_13453,U_13455),tc_HOL_Obool),tc_HOL_Obool),U_13455),c_member(tc_prod(U_13453,U_13455)))),c_Product__Type_OPair(U_13453,U_13455)))),U_13457)),U_13459))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13455),U_13459),hAPP(c_Relation_ORange(U_13453,U_13455),U_13457))) )
    & ! [U_13458,U_13456,U_13454,U_13452] :
        ( hBOOL(hAPP(hAPP(c_member(U_13454),U_13458),hAPP(c_Relation_ORange(U_13452,U_13454),U_13456)))
        | ~ hBOOL(hAPP(c_Predicate_ORangeP(U_13452,U_13454,hAPP(hAPP(c_COMBC(U_13452,tc_fun(tc_prod(U_13452,U_13454),tc_HOL_Obool),tc_fun(U_13454,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13454,tc_fun(tc_fun(tc_prod(U_13452,U_13454),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13452,U_13454),tc_HOL_Obool),tc_fun(U_13454,tc_HOL_Obool)),U_13452),c_COMBC(U_13454,tc_fun(tc_prod(U_13452,U_13454),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13454,tc_prod(U_13452,U_13454)),tc_fun(U_13454,tc_fun(tc_fun(tc_prod(U_13452,U_13454),tc_HOL_Obool),tc_HOL_Obool)),U_13452),hAPP(c_COMBB(tc_prod(U_13452,U_13454),tc_fun(tc_fun(tc_prod(U_13452,U_13454),tc_HOL_Obool),tc_HOL_Obool),U_13454),c_member(tc_prod(U_13452,U_13454)))),c_Product__Type_OPair(U_13452,U_13454)))),U_13456)),U_13458)) ) ),
    inference(miniscope,[status(thm)],[f_3438_2]) ).

cnf(f_3438_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13454),U_13458),hAPP(c_Relation_ORange(U_13452,U_13454),U_13456)))
    | ~ hBOOL(hAPP(c_Predicate_ORangeP(U_13452,U_13454,hAPP(hAPP(c_COMBC(U_13452,tc_fun(tc_prod(U_13452,U_13454),tc_HOL_Obool),tc_fun(U_13454,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13454,tc_fun(tc_fun(tc_prod(U_13452,U_13454),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13452,U_13454),tc_HOL_Obool),tc_fun(U_13454,tc_HOL_Obool)),U_13452),c_COMBC(U_13454,tc_fun(tc_prod(U_13452,U_13454),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13454,tc_prod(U_13452,U_13454)),tc_fun(U_13454,tc_fun(tc_fun(tc_prod(U_13452,U_13454),tc_HOL_Obool),tc_HOL_Obool)),U_13452),hAPP(c_COMBB(tc_prod(U_13452,U_13454),tc_fun(tc_fun(tc_prod(U_13452,U_13454),tc_HOL_Obool),tc_HOL_Obool),U_13454),c_member(tc_prod(U_13452,U_13454)))),c_Product__Type_OPair(U_13452,U_13454)))),U_13456)),U_13458)) ),
    inference(clausify,[status(thm)],[f_3438_3]) ).

cnf(f_3438_5,plain,
    ( hBOOL(hAPP(c_Predicate_ORangeP(U_13453,U_13455,hAPP(hAPP(c_COMBC(U_13453,tc_fun(tc_prod(U_13453,U_13455),tc_HOL_Obool),tc_fun(U_13455,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13455,tc_fun(tc_fun(tc_prod(U_13453,U_13455),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13453,U_13455),tc_HOL_Obool),tc_fun(U_13455,tc_HOL_Obool)),U_13453),c_COMBC(U_13455,tc_fun(tc_prod(U_13453,U_13455),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13455,tc_prod(U_13453,U_13455)),tc_fun(U_13455,tc_fun(tc_fun(tc_prod(U_13453,U_13455),tc_HOL_Obool),tc_HOL_Obool)),U_13453),hAPP(c_COMBB(tc_prod(U_13453,U_13455),tc_fun(tc_fun(tc_prod(U_13453,U_13455),tc_HOL_Obool),tc_HOL_Obool),U_13455),c_member(tc_prod(U_13453,U_13455)))),c_Product__Type_OPair(U_13453,U_13455)))),U_13457)),U_13459))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13455),U_13459),hAPP(c_Relation_ORange(U_13453,U_13455),U_13457))) ),
    inference(clausify,[status(thm)],[f_3438_3]) ).

fof(f_3439_1,plain,
    ! [V_r_2,T_c,V_b_2,T_b] :
      ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),V_b_2)),V_r_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_RangeE]) ).

fof(f_3439_2,plain,
    ! [U_13464,U_13463,U_13462,U_13461] :
      ( ? [U_13460] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_13463,U_13461)),hAPP(hAPP(c_Product__Type_OPair(U_13463,U_13461),U_13460),U_13462)),U_13464))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13461),U_13462),hAPP(c_Relation_ORange(U_13463,U_13461),U_13464))) ),
    inference(variable_rename,[status(thm)],[f_3439_1]) ).

fof(f_3439_3,plain,
    ! [U_13464,U_13463,U_13462,U_13461] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13463,U_13461)),hAPP(hAPP(c_Product__Type_OPair(U_13463,U_13461),sK319(U_13464,U_13463,U_13462,U_13461)),U_13462)),U_13464))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13461),U_13462),hAPP(c_Relation_ORange(U_13463,U_13461),U_13464))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK319]),skolemize(U_13460,sK319(U_13464,U_13463,U_13462,U_13461))],[f_3439_2]) ).

cnf(f_3439_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13463,U_13461)),hAPP(hAPP(c_Product__Type_OPair(U_13463,U_13461),sK319(U_13464,U_13463,U_13462,U_13461)),U_13462)),U_13464))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13461),U_13462),hAPP(c_Relation_ORange(U_13463,U_13461),U_13464))) ),
    inference(clausify,[status(thm)],[f_3439_3]) ).

fof(f_3440_1,plain,
    ! [V_y_2,V_x_2,V_s_2,V_r_2,T_d,T_c,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_b,T_c,T_d,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_r_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_c,T_d)))),c_Product__Type_OPair(T_c,T_d)))),V_s_2)),V_x_2),V_y_2))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),V_x_2),V_y_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),V_x_2),V_y_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2)))
        | ~ hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_b,T_c,T_d,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_r_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_c,T_d)))),c_Product__Type_OPair(T_c,T_d)))),V_s_2)),V_x_2),V_y_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_pred__comp__rel__comp__eq]) ).

fof(f_3440_2,plain,
    ! [U_13471,U_13470,U_13469,U_13468,U_13467,U_13466,U_13465] :
      ( ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13465,U_13466,U_13467,hAPP(hAPP(c_COMBC(U_13465,tc_fun(tc_prod(U_13465,U_13466),tc_HOL_Obool),tc_fun(U_13466,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13466,tc_fun(tc_fun(tc_prod(U_13465,U_13466),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13465,U_13466),tc_HOL_Obool),tc_fun(U_13466,tc_HOL_Obool)),U_13465),c_COMBC(U_13466,tc_fun(tc_prod(U_13465,U_13466),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13466,tc_prod(U_13465,U_13466)),tc_fun(U_13466,tc_fun(tc_fun(tc_prod(U_13465,U_13466),tc_HOL_Obool),tc_HOL_Obool)),U_13465),hAPP(c_COMBB(tc_prod(U_13465,U_13466),tc_fun(tc_fun(tc_prod(U_13465,U_13466),tc_HOL_Obool),tc_HOL_Obool),U_13466),c_member(tc_prod(U_13465,U_13466)))),c_Product__Type_OPair(U_13465,U_13466)))),U_13468),hAPP(hAPP(c_COMBC(U_13466,tc_fun(tc_prod(U_13466,U_13467),tc_HOL_Obool),tc_fun(U_13467,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13467,tc_fun(tc_fun(tc_prod(U_13466,U_13467),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13466,U_13467),tc_HOL_Obool),tc_fun(U_13467,tc_HOL_Obool)),U_13466),c_COMBC(U_13467,tc_fun(tc_prod(U_13466,U_13467),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13467,tc_prod(U_13466,U_13467)),tc_fun(U_13467,tc_fun(tc_fun(tc_prod(U_13466,U_13467),tc_HOL_Obool),tc_HOL_Obool)),U_13466),hAPP(c_COMBB(tc_prod(U_13466,U_13467),tc_fun(tc_fun(tc_prod(U_13466,U_13467),tc_HOL_Obool),tc_HOL_Obool),U_13467),c_member(tc_prod(U_13466,U_13467)))),c_Product__Type_OPair(U_13466,U_13467)))),U_13469)),U_13470),U_13471))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13465,U_13467)),hAPP(hAPP(c_Product__Type_OPair(U_13465,U_13467),U_13470),U_13471)),hAPP(hAPP(c_Relation_Orel__comp(U_13465,U_13466,U_13467),U_13468),U_13469))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13465,U_13467)),hAPP(hAPP(c_Product__Type_OPair(U_13465,U_13467),U_13470),U_13471)),hAPP(hAPP(c_Relation_Orel__comp(U_13465,U_13466,U_13467),U_13468),U_13469)))
        | ~ hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13465,U_13466,U_13467,hAPP(hAPP(c_COMBC(U_13465,tc_fun(tc_prod(U_13465,U_13466),tc_HOL_Obool),tc_fun(U_13466,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13466,tc_fun(tc_fun(tc_prod(U_13465,U_13466),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13465,U_13466),tc_HOL_Obool),tc_fun(U_13466,tc_HOL_Obool)),U_13465),c_COMBC(U_13466,tc_fun(tc_prod(U_13465,U_13466),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13466,tc_prod(U_13465,U_13466)),tc_fun(U_13466,tc_fun(tc_fun(tc_prod(U_13465,U_13466),tc_HOL_Obool),tc_HOL_Obool)),U_13465),hAPP(c_COMBB(tc_prod(U_13465,U_13466),tc_fun(tc_fun(tc_prod(U_13465,U_13466),tc_HOL_Obool),tc_HOL_Obool),U_13466),c_member(tc_prod(U_13465,U_13466)))),c_Product__Type_OPair(U_13465,U_13466)))),U_13468),hAPP(hAPP(c_COMBC(U_13466,tc_fun(tc_prod(U_13466,U_13467),tc_HOL_Obool),tc_fun(U_13467,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13467,tc_fun(tc_fun(tc_prod(U_13466,U_13467),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13466,U_13467),tc_HOL_Obool),tc_fun(U_13467,tc_HOL_Obool)),U_13466),c_COMBC(U_13467,tc_fun(tc_prod(U_13466,U_13467),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13467,tc_prod(U_13466,U_13467)),tc_fun(U_13467,tc_fun(tc_fun(tc_prod(U_13466,U_13467),tc_HOL_Obool),tc_HOL_Obool)),U_13466),hAPP(c_COMBB(tc_prod(U_13466,U_13467),tc_fun(tc_fun(tc_prod(U_13466,U_13467),tc_HOL_Obool),tc_HOL_Obool),U_13467),c_member(tc_prod(U_13466,U_13467)))),c_Product__Type_OPair(U_13466,U_13467)))),U_13469)),U_13470),U_13471)) ) ),
    inference(variable_rename,[status(thm)],[f_3440_1]) ).

fof(f_3440_3,plain,
    ( ! [U_13485,U_13483,U_13481,U_13479,U_13477,U_13475,U_13473] :
        ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13473,U_13475,U_13477,hAPP(hAPP(c_COMBC(U_13473,tc_fun(tc_prod(U_13473,U_13475),tc_HOL_Obool),tc_fun(U_13475,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13475,tc_fun(tc_fun(tc_prod(U_13473,U_13475),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13473,U_13475),tc_HOL_Obool),tc_fun(U_13475,tc_HOL_Obool)),U_13473),c_COMBC(U_13475,tc_fun(tc_prod(U_13473,U_13475),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13475,tc_prod(U_13473,U_13475)),tc_fun(U_13475,tc_fun(tc_fun(tc_prod(U_13473,U_13475),tc_HOL_Obool),tc_HOL_Obool)),U_13473),hAPP(c_COMBB(tc_prod(U_13473,U_13475),tc_fun(tc_fun(tc_prod(U_13473,U_13475),tc_HOL_Obool),tc_HOL_Obool),U_13475),c_member(tc_prod(U_13473,U_13475)))),c_Product__Type_OPair(U_13473,U_13475)))),U_13479),hAPP(hAPP(c_COMBC(U_13475,tc_fun(tc_prod(U_13475,U_13477),tc_HOL_Obool),tc_fun(U_13477,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13477,tc_fun(tc_fun(tc_prod(U_13475,U_13477),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13475,U_13477),tc_HOL_Obool),tc_fun(U_13477,tc_HOL_Obool)),U_13475),c_COMBC(U_13477,tc_fun(tc_prod(U_13475,U_13477),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13477,tc_prod(U_13475,U_13477)),tc_fun(U_13477,tc_fun(tc_fun(tc_prod(U_13475,U_13477),tc_HOL_Obool),tc_HOL_Obool)),U_13475),hAPP(c_COMBB(tc_prod(U_13475,U_13477),tc_fun(tc_fun(tc_prod(U_13475,U_13477),tc_HOL_Obool),tc_HOL_Obool),U_13477),c_member(tc_prod(U_13475,U_13477)))),c_Product__Type_OPair(U_13475,U_13477)))),U_13481)),U_13483),U_13485))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13473,U_13477)),hAPP(hAPP(c_Product__Type_OPair(U_13473,U_13477),U_13483),U_13485)),hAPP(hAPP(c_Relation_Orel__comp(U_13473,U_13475,U_13477),U_13479),U_13481))) )
    & ! [U_13484,U_13482,U_13480,U_13478,U_13476,U_13474,U_13472] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13472,U_13476)),hAPP(hAPP(c_Product__Type_OPair(U_13472,U_13476),U_13482),U_13484)),hAPP(hAPP(c_Relation_Orel__comp(U_13472,U_13474,U_13476),U_13478),U_13480)))
        | ~ hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13472,U_13474,U_13476,hAPP(hAPP(c_COMBC(U_13472,tc_fun(tc_prod(U_13472,U_13474),tc_HOL_Obool),tc_fun(U_13474,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13474,tc_fun(tc_fun(tc_prod(U_13472,U_13474),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13472,U_13474),tc_HOL_Obool),tc_fun(U_13474,tc_HOL_Obool)),U_13472),c_COMBC(U_13474,tc_fun(tc_prod(U_13472,U_13474),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13474,tc_prod(U_13472,U_13474)),tc_fun(U_13474,tc_fun(tc_fun(tc_prod(U_13472,U_13474),tc_HOL_Obool),tc_HOL_Obool)),U_13472),hAPP(c_COMBB(tc_prod(U_13472,U_13474),tc_fun(tc_fun(tc_prod(U_13472,U_13474),tc_HOL_Obool),tc_HOL_Obool),U_13474),c_member(tc_prod(U_13472,U_13474)))),c_Product__Type_OPair(U_13472,U_13474)))),U_13478),hAPP(hAPP(c_COMBC(U_13474,tc_fun(tc_prod(U_13474,U_13476),tc_HOL_Obool),tc_fun(U_13476,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13476,tc_fun(tc_fun(tc_prod(U_13474,U_13476),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13474,U_13476),tc_HOL_Obool),tc_fun(U_13476,tc_HOL_Obool)),U_13474),c_COMBC(U_13476,tc_fun(tc_prod(U_13474,U_13476),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13476,tc_prod(U_13474,U_13476)),tc_fun(U_13476,tc_fun(tc_fun(tc_prod(U_13474,U_13476),tc_HOL_Obool),tc_HOL_Obool)),U_13474),hAPP(c_COMBB(tc_prod(U_13474,U_13476),tc_fun(tc_fun(tc_prod(U_13474,U_13476),tc_HOL_Obool),tc_HOL_Obool),U_13476),c_member(tc_prod(U_13474,U_13476)))),c_Product__Type_OPair(U_13474,U_13476)))),U_13480)),U_13482),U_13484)) ) ),
    inference(miniscope,[status(thm)],[f_3440_2]) ).

cnf(f_3440_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13472,U_13476)),hAPP(hAPP(c_Product__Type_OPair(U_13472,U_13476),U_13482),U_13484)),hAPP(hAPP(c_Relation_Orel__comp(U_13472,U_13474,U_13476),U_13478),U_13480)))
    | ~ hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13472,U_13474,U_13476,hAPP(hAPP(c_COMBC(U_13472,tc_fun(tc_prod(U_13472,U_13474),tc_HOL_Obool),tc_fun(U_13474,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13474,tc_fun(tc_fun(tc_prod(U_13472,U_13474),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13472,U_13474),tc_HOL_Obool),tc_fun(U_13474,tc_HOL_Obool)),U_13472),c_COMBC(U_13474,tc_fun(tc_prod(U_13472,U_13474),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13474,tc_prod(U_13472,U_13474)),tc_fun(U_13474,tc_fun(tc_fun(tc_prod(U_13472,U_13474),tc_HOL_Obool),tc_HOL_Obool)),U_13472),hAPP(c_COMBB(tc_prod(U_13472,U_13474),tc_fun(tc_fun(tc_prod(U_13472,U_13474),tc_HOL_Obool),tc_HOL_Obool),U_13474),c_member(tc_prod(U_13472,U_13474)))),c_Product__Type_OPair(U_13472,U_13474)))),U_13478),hAPP(hAPP(c_COMBC(U_13474,tc_fun(tc_prod(U_13474,U_13476),tc_HOL_Obool),tc_fun(U_13476,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13476,tc_fun(tc_fun(tc_prod(U_13474,U_13476),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13474,U_13476),tc_HOL_Obool),tc_fun(U_13476,tc_HOL_Obool)),U_13474),c_COMBC(U_13476,tc_fun(tc_prod(U_13474,U_13476),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13476,tc_prod(U_13474,U_13476)),tc_fun(U_13476,tc_fun(tc_fun(tc_prod(U_13474,U_13476),tc_HOL_Obool),tc_HOL_Obool)),U_13474),hAPP(c_COMBB(tc_prod(U_13474,U_13476),tc_fun(tc_fun(tc_prod(U_13474,U_13476),tc_HOL_Obool),tc_HOL_Obool),U_13476),c_member(tc_prod(U_13474,U_13476)))),c_Product__Type_OPair(U_13474,U_13476)))),U_13480)),U_13482),U_13484)) ),
    inference(clausify,[status(thm)],[f_3440_3]) ).

cnf(f_3440_5,plain,
    ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13473,U_13475,U_13477,hAPP(hAPP(c_COMBC(U_13473,tc_fun(tc_prod(U_13473,U_13475),tc_HOL_Obool),tc_fun(U_13475,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13475,tc_fun(tc_fun(tc_prod(U_13473,U_13475),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13473,U_13475),tc_HOL_Obool),tc_fun(U_13475,tc_HOL_Obool)),U_13473),c_COMBC(U_13475,tc_fun(tc_prod(U_13473,U_13475),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13475,tc_prod(U_13473,U_13475)),tc_fun(U_13475,tc_fun(tc_fun(tc_prod(U_13473,U_13475),tc_HOL_Obool),tc_HOL_Obool)),U_13473),hAPP(c_COMBB(tc_prod(U_13473,U_13475),tc_fun(tc_fun(tc_prod(U_13473,U_13475),tc_HOL_Obool),tc_HOL_Obool),U_13475),c_member(tc_prod(U_13473,U_13475)))),c_Product__Type_OPair(U_13473,U_13475)))),U_13479),hAPP(hAPP(c_COMBC(U_13475,tc_fun(tc_prod(U_13475,U_13477),tc_HOL_Obool),tc_fun(U_13477,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13477,tc_fun(tc_fun(tc_prod(U_13475,U_13477),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13475,U_13477),tc_HOL_Obool),tc_fun(U_13477,tc_HOL_Obool)),U_13475),c_COMBC(U_13477,tc_fun(tc_prod(U_13475,U_13477),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13477,tc_prod(U_13475,U_13477)),tc_fun(U_13477,tc_fun(tc_fun(tc_prod(U_13475,U_13477),tc_HOL_Obool),tc_HOL_Obool)),U_13475),hAPP(c_COMBB(tc_prod(U_13475,U_13477),tc_fun(tc_fun(tc_prod(U_13475,U_13477),tc_HOL_Obool),tc_HOL_Obool),U_13477),c_member(tc_prod(U_13475,U_13477)))),c_Product__Type_OPair(U_13475,U_13477)))),U_13481)),U_13483),U_13485))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13473,U_13477)),hAPP(hAPP(c_Product__Type_OPair(U_13473,U_13477),U_13483),U_13485)),hAPP(hAPP(c_Relation_Orel__comp(U_13473,U_13475,U_13477),U_13479),U_13481))) ),
    inference(clausify,[status(thm)],[f_3440_3]) ).

fof(f_3441_1,plain,
    ! [T_d,T_c,T_b,V_c_2,V_s_2,V_b_2,V_a_2,V_r_2] :
      ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_b,T_c,T_d,V_r_2,V_s_2),V_a_2),V_c_2))
      | ~ hBOOL(hAPP(hAPP(V_s_2,V_b_2),V_c_2))
      | ~ hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) ),
    inference(fof_nnf,[status(thm)],[fact_pred__comp_Ointros]) ).

fof(f_3441_2,plain,
    ! [U_13493,U_13492,U_13491,U_13490,U_13489,U_13488,U_13487,U_13486] :
      ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13491,U_13492,U_13493,U_13486,U_13489),U_13487),U_13490))
      | ~ hBOOL(hAPP(hAPP(U_13489,U_13488),U_13490))
      | ~ hBOOL(hAPP(hAPP(U_13486,U_13487),U_13488)) ),
    inference(variable_rename,[status(thm)],[f_3441_1]) ).

cnf(f_3441_3,plain,
    ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13491,U_13492,U_13493,U_13486,U_13489),U_13487),U_13490))
    | ~ hBOOL(hAPP(hAPP(U_13489,U_13488),U_13490))
    | ~ hBOOL(hAPP(hAPP(U_13486,U_13487),U_13488)) ),
    inference(clausify,[status(thm)],[f_3441_2]) ).

fof(f_3442_1,plain,
    ! [T_c,T_b,V_b_2,V_a_2,V_r_2] :
      ( hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_b_2))
      | ~ hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) ),
    inference(fof_nnf,[status(thm)],[fact_RangeP_Ointros]) ).

fof(f_3442_2,plain,
    ! [U_13498,U_13497,U_13496,U_13495,U_13494] :
      ( hBOOL(hAPP(c_Predicate_ORangeP(U_13497,U_13498,U_13494),U_13496))
      | ~ hBOOL(hAPP(hAPP(U_13494,U_13495),U_13496)) ),
    inference(variable_rename,[status(thm)],[f_3442_1]) ).

cnf(f_3442_3,plain,
    ( hBOOL(hAPP(c_Predicate_ORangeP(U_13497,U_13498,U_13494),U_13496))
    | ~ hBOOL(hAPP(hAPP(U_13494,U_13495),U_13496)) ),
    inference(clausify,[status(thm)],[f_3442_2]) ).

fof(f_3443_1,plain,
    ! [V_a3_2,V_a1_2,V_s_2,V_r_2,T_d,T_c,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_b,T_c,T_d,V_r_2,V_s_2),V_a1_2),V_a3_2))
        | ! [B_b] :
            ( ~ hBOOL(hAPP(hAPP(V_s_2,B_b),V_a3_2))
            | ~ hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_b)) ) )
      & ( ? [B_b] :
            ( hBOOL(hAPP(hAPP(V_s_2,B_b),V_a3_2))
            & hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_b)) )
        | ~ hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_b,T_c,T_d,V_r_2,V_s_2),V_a1_2),V_a3_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_pred__comp_Oequations]) ).

fof(f_3443_2,plain,
    ! [U_13507,U_13506,U_13505,U_13504,U_13503,U_13502,U_13501] :
      ( ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13501,U_13502,U_13503,U_13504,U_13505),U_13506),U_13507))
        | ! [U_13500] :
            ( ~ hBOOL(hAPP(hAPP(U_13505,U_13500),U_13507))
            | ~ hBOOL(hAPP(hAPP(U_13504,U_13506),U_13500)) ) )
      & ( ? [U_13499] :
            ( hBOOL(hAPP(hAPP(U_13505,U_13499),U_13507))
            & hBOOL(hAPP(hAPP(U_13504,U_13506),U_13499)) )
        | ~ hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13501,U_13502,U_13503,U_13504,U_13505),U_13506),U_13507)) ) ),
    inference(variable_rename,[status(thm)],[f_3443_1]) ).

fof(f_3443_3,plain,
    ( ! [U_13521,U_13519,U_13517,U_13515] :
        ( ! [U_13513,U_13511,U_13509] : hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13509,U_13511,U_13513,U_13515,U_13517),U_13519),U_13521))
        | ! [U_13500] :
            ( ~ hBOOL(hAPP(hAPP(U_13517,U_13500),U_13521))
            | ~ hBOOL(hAPP(hAPP(U_13515,U_13519),U_13500)) ) )
    & ! [U_13520,U_13518,U_13516,U_13514] :
        ( ! [U_13512,U_13510,U_13508] : ~ hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13508,U_13510,U_13512,U_13514,U_13516),U_13518),U_13520))
        | ? [U_13499] :
            ( hBOOL(hAPP(hAPP(U_13516,U_13499),U_13520))
            & hBOOL(hAPP(hAPP(U_13514,U_13518),U_13499)) ) ) ),
    inference(miniscope,[status(thm)],[f_3443_2]) ).

fof(f_3443_4,plain,
    ( ! [U_13521,U_13519,U_13517,U_13515] :
        ( ! [U_13513,U_13511,U_13509] : hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13509,U_13511,U_13513,U_13515,U_13517),U_13519),U_13521))
        | ! [U_13500] :
            ( ~ hBOOL(hAPP(hAPP(U_13517,U_13500),U_13521))
            | ~ hBOOL(hAPP(hAPP(U_13515,U_13519),U_13500)) ) )
    & ! [U_13520,U_13518,U_13516,U_13514] :
        ( ! [U_13512,U_13510,U_13508] : ~ hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13508,U_13510,U_13512,U_13514,U_13516),U_13518),U_13520))
        | ( hBOOL(hAPP(hAPP(U_13516,sK320(U_13520,U_13518,U_13516,U_13514)),U_13520))
          & hBOOL(hAPP(hAPP(U_13514,U_13518),sK320(U_13520,U_13518,U_13516,U_13514))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK320]),skolemize(U_13499,sK320(U_13520,U_13518,U_13516,U_13514))],[f_3443_3]) ).

cnf(f_3443_5,plain,
    ( hBOOL(hAPP(hAPP(U_13514,U_13518),sK320(U_13520,U_13518,U_13516,U_13514)))
    | ~ hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13508,U_13510,U_13512,U_13514,U_13516),U_13518),U_13520)) ),
    inference(clausify,[status(thm)],[f_3443_4]) ).

cnf(f_3443_6,plain,
    ( hBOOL(hAPP(hAPP(U_13516,sK320(U_13520,U_13518,U_13516,U_13514)),U_13520))
    | ~ hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13508,U_13510,U_13512,U_13514,U_13516),U_13518),U_13520)) ),
    inference(clausify,[status(thm)],[f_3443_4]) ).

cnf(f_3443_7,plain,
    ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13509,U_13511,U_13513,U_13515,U_13517),U_13519),U_13521))
    | ~ hBOOL(hAPP(hAPP(U_13517,U_13500),U_13521))
    | ~ hBOOL(hAPP(hAPP(U_13515,U_13519),U_13500)) ),
    inference(clausify,[status(thm)],[f_3443_4]) ).

fof(f_3444_1,plain,
    ! [V_a2_2,V_r_2,T_c,T_b] :
      ( ( hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_a2_2))
        | ! [B_a] : ~ hBOOL(hAPP(hAPP(V_r_2,B_a),V_a2_2)) )
      & ( ? [B_a] : hBOOL(hAPP(hAPP(V_r_2,B_a),V_a2_2))
        | ~ hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_a2_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_RangeP_Oequations]) ).

fof(f_3444_2,plain,
    ! [U_13527,U_13526,U_13525,U_13524] :
      ( ( hBOOL(hAPP(c_Predicate_ORangeP(U_13524,U_13525,U_13526),U_13527))
        | ! [U_13523] : ~ hBOOL(hAPP(hAPP(U_13526,U_13523),U_13527)) )
      & ( ? [U_13522] : hBOOL(hAPP(hAPP(U_13526,U_13522),U_13527))
        | ~ hBOOL(hAPP(c_Predicate_ORangeP(U_13524,U_13525,U_13526),U_13527)) ) ),
    inference(variable_rename,[status(thm)],[f_3444_1]) ).

fof(f_3444_3,plain,
    ( ! [U_13535,U_13533] :
        ( ! [U_13531,U_13529] : hBOOL(hAPP(c_Predicate_ORangeP(U_13529,U_13531,U_13533),U_13535))
        | ! [U_13523] : ~ hBOOL(hAPP(hAPP(U_13533,U_13523),U_13535)) )
    & ! [U_13534,U_13532] :
        ( ! [U_13530,U_13528] : ~ hBOOL(hAPP(c_Predicate_ORangeP(U_13528,U_13530,U_13532),U_13534))
        | ? [U_13522] : hBOOL(hAPP(hAPP(U_13532,U_13522),U_13534)) ) ),
    inference(miniscope,[status(thm)],[f_3444_2]) ).

fof(f_3444_4,plain,
    ( ! [U_13535,U_13533] :
        ( ! [U_13531,U_13529] : hBOOL(hAPP(c_Predicate_ORangeP(U_13529,U_13531,U_13533),U_13535))
        | ! [U_13523] : ~ hBOOL(hAPP(hAPP(U_13533,U_13523),U_13535)) )
    & ! [U_13534,U_13532] :
        ( ! [U_13530,U_13528] : ~ hBOOL(hAPP(c_Predicate_ORangeP(U_13528,U_13530,U_13532),U_13534))
        | hBOOL(hAPP(hAPP(U_13532,sK321(U_13534,U_13532)),U_13534)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK321]),skolemize(U_13522,sK321(U_13534,U_13532))],[f_3444_3]) ).

cnf(f_3444_5,plain,
    ( ~ hBOOL(hAPP(c_Predicate_ORangeP(U_13528,U_13530,U_13532),U_13534))
    | hBOOL(hAPP(hAPP(U_13532,sK321(U_13534,U_13532)),U_13534)) ),
    inference(clausify,[status(thm)],[f_3444_4]) ).

cnf(f_3444_6,plain,
    ( hBOOL(hAPP(c_Predicate_ORangeP(U_13529,U_13531,U_13533),U_13535))
    | ~ hBOOL(hAPP(hAPP(U_13533,U_13523),U_13535)) ),
    inference(clausify,[status(thm)],[f_3444_4]) ).

fof(f_3445_1,plain,
    ! [V_S_2,V_R_2,T_b] :
      ( c_FunDef_Oreduction__pair(T_b,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_S_2)),V_R_2))
      | ~ c_Wellfounded_Owf(T_b,V_R_2) ),
    inference(fof_nnf,[status(thm)],[fact_reduction__pairI]) ).

fof(f_3445_2,plain,
    ! [U_13538,U_13537,U_13536] :
      ( c_FunDef_Oreduction__pair(U_13536,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(U_13536,U_13536),tc_HOL_Obool),tc_fun(tc_prod(U_13536,U_13536),tc_HOL_Obool)),U_13537),U_13538))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13536,U_13536),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13536,U_13536,U_13536),U_13537),U_13538)),U_13537))
      | ~ c_Wellfounded_Owf(U_13536,U_13537) ),
    inference(variable_rename,[status(thm)],[f_3445_1]) ).

cnf(f_3445_3,plain,
    ( c_FunDef_Oreduction__pair(U_13536,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(U_13536,U_13536),tc_HOL_Obool),tc_fun(tc_prod(U_13536,U_13536),tc_HOL_Obool)),U_13537),U_13538))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13536,U_13536),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13536,U_13536,U_13536),U_13537),U_13538)),U_13537))
    | ~ c_Wellfounded_Owf(U_13536,U_13537) ),
    inference(clausify,[status(thm)],[f_3445_2]) ).

fof(f_3446_1,plain,
    ! [V_P_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_P_2))) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c)),V_P_2)),
    inference(fof_nnf,[status(thm)],[fact_Domain__Collect__split]) ).

fof(f_3446_2,plain,
    ! [U_13541,U_13540,U_13539] : hAPP(c_Relation_ODomain(U_13539,U_13540),hAPP(c_Set_OCollect(tc_prod(U_13539,U_13540)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13539,U_13540,tc_HOL_Obool),U_13541))) = hAPP(c_Set_OCollect(U_13539),hAPP(hAPP(c_COMBB(tc_fun(U_13540,tc_HOL_Obool),tc_HOL_Obool,U_13539),c_HOL_OEx(U_13540)),U_13541)),
    inference(variable_rename,[status(thm)],[f_3446_1]) ).

cnf(f_3446_3,plain,
    hAPP(c_Relation_ODomain(U_13539,U_13540),hAPP(c_Set_OCollect(tc_prod(U_13539,U_13540)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13539,U_13540,tc_HOL_Obool),U_13541))) = hAPP(c_Set_OCollect(U_13539),hAPP(hAPP(c_COMBB(tc_fun(U_13540,tc_HOL_Obool),tc_HOL_Obool,U_13539),c_HOL_OEx(U_13540)),U_13541)),
    inference(clausify,[status(thm)],[f_3446_2]) ).

fof(f_3447_1,plain,
    ! [V_a_2,T_b] : c_HOL_OThe(T_b,hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2)) = V_a_2,
    inference(fof_nnf,[status(thm)],[fact_the__eq__trivial]) ).

fof(f_3447_2,plain,
    ! [U_13543,U_13542] : c_HOL_OThe(U_13542,hAPP(hAPP(c_COMBC(U_13542,U_13542,tc_HOL_Obool),c_fequal),U_13543)) = U_13543,
    inference(variable_rename,[status(thm)],[f_3447_1]) ).

cnf(f_3447_3,plain,
    c_HOL_OThe(U_13542,hAPP(hAPP(c_COMBC(U_13542,U_13542,tc_HOL_Obool),c_fequal),U_13543)) = U_13543,
    inference(clausify,[status(thm)],[f_3447_2]) ).

fof(f_3448_1,plain,
    c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than),
    inference(fof_nnf,[status(thm)],[fact_wf__less__than]) ).

cnf(f_3448_2,plain,
    c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than),
    inference(clausify,[status(thm)],[f_3448_1]) ).

fof(f_3449_1,plain,
    ! [T_b] : c_Wellfounded_Owf(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))),
    inference(fof_nnf,[status(thm)],[fact_wf__empty]) ).

fof(f_3449_2,plain,
    ! [U_13544] : c_Wellfounded_Owf(U_13544,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13544,U_13544),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_3449_1]) ).

cnf(f_3449_3,plain,
    c_Wellfounded_Owf(U_13544,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13544,U_13544),tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_3449_2]) ).

fof(f_3450_1,plain,
    ! [V_f_2,T_c,V_r_2,T_b] :
      ( c_Wellfounded_Owf(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2))
      | ~ c_Wellfounded_Owf(T_b,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_wf__inv__image]) ).

fof(f_3450_2,plain,
    ! [U_13548,U_13547,U_13546,U_13545] :
      ( c_Wellfounded_Owf(U_13547,hAPP(hAPP(c_Relation_Oinv__image(U_13545,U_13547),U_13546),U_13548))
      | ~ c_Wellfounded_Owf(U_13545,U_13546) ),
    inference(variable_rename,[status(thm)],[f_3450_1]) ).

cnf(f_3450_3,plain,
    ( c_Wellfounded_Owf(U_13547,hAPP(hAPP(c_Relation_Oinv__image(U_13545,U_13547),U_13546),U_13548))
    | ~ c_Wellfounded_Owf(U_13545,U_13546) ),
    inference(clausify,[status(thm)],[f_3450_2]) ).

fof(f_3451_1,plain,
    ! [V_rb_2,T_c,V_ra_2,T_b] :
      ( c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Wellfounded_Olex__prod(T_b,T_c,V_ra_2,V_rb_2))
      | ~ c_Wellfounded_Owf(T_c,V_rb_2)
      | ~ c_Wellfounded_Owf(T_b,V_ra_2) ),
    inference(fof_nnf,[status(thm)],[fact_wf__lex__prod]) ).

fof(f_3451_2,plain,
    ! [U_13552,U_13551,U_13550,U_13549] :
      ( c_Wellfounded_Owf(tc_prod(U_13549,U_13551),c_Wellfounded_Olex__prod(U_13549,U_13551,U_13550,U_13552))
      | ~ c_Wellfounded_Owf(U_13551,U_13552)
      | ~ c_Wellfounded_Owf(U_13549,U_13550) ),
    inference(variable_rename,[status(thm)],[f_3451_1]) ).

cnf(f_3451_3,plain,
    ( c_Wellfounded_Owf(tc_prod(U_13549,U_13551),c_Wellfounded_Olex__prod(U_13549,U_13551,U_13550,U_13552))
    | ~ c_Wellfounded_Owf(U_13551,U_13552)
    | ~ c_Wellfounded_Owf(U_13549,U_13550) ),
    inference(clausify,[status(thm)],[f_3451_2]) ).

fof(f_3452_1,plain,
    ! [V_f_2,T_b] : c_Wellfounded_Owf(T_b,hAPP(c_Wellfounded_Omeasure(T_b),V_f_2)),
    inference(fof_nnf,[status(thm)],[fact_wf__measure]) ).

fof(f_3452_2,plain,
    ! [U_13554,U_13553] : c_Wellfounded_Owf(U_13553,hAPP(c_Wellfounded_Omeasure(U_13553),U_13554)),
    inference(variable_rename,[status(thm)],[f_3452_1]) ).

cnf(f_3452_3,plain,
    c_Wellfounded_Owf(U_13553,hAPP(c_Wellfounded_Omeasure(U_13553),U_13554)),
    inference(clausify,[status(thm)],[f_3452_2]) ).

fof(f_3453_1,plain,
    ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_DomainI]) ).

fof(f_3453_2,plain,
    ! [U_13559,U_13558,U_13557,U_13556,U_13555] :
      ( hBOOL(hAPP(hAPP(c_member(U_13555),U_13557),hAPP(c_Relation_ODomain(U_13555,U_13556),U_13559)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13555,U_13556)),hAPP(hAPP(c_Product__Type_OPair(U_13555,U_13556),U_13557),U_13558)),U_13559)) ),
    inference(variable_rename,[status(thm)],[f_3453_1]) ).

cnf(f_3453_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13555),U_13557),hAPP(c_Relation_ODomain(U_13555,U_13556),U_13559)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13555,U_13556)),hAPP(hAPP(c_Product__Type_OPair(U_13555,U_13556),U_13557),U_13558)),U_13559)) ),
    inference(clausify,[status(thm)],[f_3453_2]) ).

fof(f_3454_1,plain,
    ! [V_R_2,T_b] :
      ( ( c_Wellfounded_Owf(T_b,V_R_2)
        | ~ c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2)) )
      & ( c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2))
        | ~ c_Wellfounded_Owf(T_b,V_R_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_wf__comp__self]) ).

fof(f_3454_2,plain,
    ! [U_13561,U_13560] :
      ( ( c_Wellfounded_Owf(U_13560,U_13561)
        | ~ c_Wellfounded_Owf(U_13560,hAPP(hAPP(c_Relation_Orel__comp(U_13560,U_13560,U_13560),U_13561),U_13561)) )
      & ( c_Wellfounded_Owf(U_13560,hAPP(hAPP(c_Relation_Orel__comp(U_13560,U_13560,U_13560),U_13561),U_13561))
        | ~ c_Wellfounded_Owf(U_13560,U_13561) ) ),
    inference(variable_rename,[status(thm)],[f_3454_1]) ).

fof(f_3454_3,plain,
    ( ! [U_13565,U_13563] :
        ( c_Wellfounded_Owf(U_13563,U_13565)
        | ~ c_Wellfounded_Owf(U_13563,hAPP(hAPP(c_Relation_Orel__comp(U_13563,U_13563,U_13563),U_13565),U_13565)) )
    & ! [U_13564,U_13562] :
        ( c_Wellfounded_Owf(U_13562,hAPP(hAPP(c_Relation_Orel__comp(U_13562,U_13562,U_13562),U_13564),U_13564))
        | ~ c_Wellfounded_Owf(U_13562,U_13564) ) ),
    inference(miniscope,[status(thm)],[f_3454_2]) ).

cnf(f_3454_4,plain,
    ( c_Wellfounded_Owf(U_13562,hAPP(hAPP(c_Relation_Orel__comp(U_13562,U_13562,U_13562),U_13564),U_13564))
    | ~ c_Wellfounded_Owf(U_13562,U_13564) ),
    inference(clausify,[status(thm)],[f_3454_3]) ).

cnf(f_3454_5,plain,
    ( c_Wellfounded_Owf(U_13563,U_13565)
    | ~ c_Wellfounded_Owf(U_13563,hAPP(hAPP(c_Relation_Orel__comp(U_13563,U_13563,U_13563),U_13565),U_13565)) ),
    inference(clausify,[status(thm)],[f_3454_3]) ).

fof(f_3455_1,plain,
    ! [V_r_2,T_b] :
      ( c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Omin__ext(T_b,V_r_2))
      | ~ c_Wellfounded_Owf(T_b,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_min__ext__wf]) ).

fof(f_3455_2,plain,
    ! [U_13567,U_13566] :
      ( c_Wellfounded_Owf(tc_fun(U_13566,tc_HOL_Obool),c_Wellfounded_Omin__ext(U_13566,U_13567))
      | ~ c_Wellfounded_Owf(U_13566,U_13567) ),
    inference(variable_rename,[status(thm)],[f_3455_1]) ).

cnf(f_3455_3,plain,
    ( c_Wellfounded_Owf(tc_fun(U_13566,tc_HOL_Obool),c_Wellfounded_Omin__ext(U_13566,U_13567))
    | ~ c_Wellfounded_Owf(U_13566,U_13567) ),
    inference(clausify,[status(thm)],[f_3455_2]) ).

fof(f_3456_1,plain,
    ! [V_p_2,V_r_2,T_b] :
      ( c_Wellfounded_Owf(T_b,V_p_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_p_2),V_r_2))
      | ~ c_Wellfounded_Owf(T_b,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_wf__subset]) ).

fof(f_3456_2,plain,
    ! [U_13570,U_13569,U_13568] :
      ( c_Wellfounded_Owf(U_13568,U_13570)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13568,U_13568),tc_HOL_Obool)),U_13570),U_13569))
      | ~ c_Wellfounded_Owf(U_13568,U_13569) ),
    inference(variable_rename,[status(thm)],[f_3456_1]) ).

cnf(f_3456_3,plain,
    ( c_Wellfounded_Owf(U_13568,U_13570)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13568,U_13568),tc_HOL_Obool)),U_13570),U_13569))
    | ~ c_Wellfounded_Owf(U_13568,U_13569) ),
    inference(clausify,[status(thm)],[f_3456_2]) ).

fof(f_3457_1,plain,
    ! [V_a_2,V_r_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),V_r_2))
      | ~ c_Wellfounded_Owf(T_b,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_wf__irrefl]) ).

fof(f_3457_2,plain,
    ! [U_13573,U_13572,U_13571] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13571,U_13571)),hAPP(hAPP(c_Product__Type_OPair(U_13571,U_13571),U_13573),U_13573)),U_13572))
      | ~ c_Wellfounded_Owf(U_13571,U_13572) ),
    inference(variable_rename,[status(thm)],[f_3457_1]) ).

cnf(f_3457_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13571,U_13571)),hAPP(hAPP(c_Product__Type_OPair(U_13571,U_13571),U_13573),U_13573)),U_13572))
    | ~ c_Wellfounded_Owf(U_13571,U_13572) ),
    inference(clausify,[status(thm)],[f_3457_2]) ).

fof(f_3458_1,plain,
    ! [V_x_2,V_a_2,V_r_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_a_2)),V_r_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_x_2)),V_r_2))
      | ~ c_Wellfounded_Owf(T_b,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_wf__asym]) ).

fof(f_3458_2,plain,
    ! [U_13577,U_13576,U_13575,U_13574] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13574,U_13574)),hAPP(hAPP(c_Product__Type_OPair(U_13574,U_13574),U_13577),U_13576)),U_13575))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13574,U_13574)),hAPP(hAPP(c_Product__Type_OPair(U_13574,U_13574),U_13576),U_13577)),U_13575))
      | ~ c_Wellfounded_Owf(U_13574,U_13575) ),
    inference(variable_rename,[status(thm)],[f_3458_1]) ).

cnf(f_3458_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13574,U_13574)),hAPP(hAPP(c_Product__Type_OPair(U_13574,U_13574),U_13577),U_13576)),U_13575))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13574,U_13574)),hAPP(hAPP(c_Product__Type_OPair(U_13574,U_13574),U_13576),U_13577)),U_13575))
    | ~ c_Wellfounded_Owf(U_13574,U_13575) ),
    inference(clausify,[status(thm)],[f_3458_2]) ).

fof(f_3459_1,plain,
    ! [V_x_2,V_a_2,V_r_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_a_2)),V_r_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_x_2)),V_r_2))
      | ~ c_Wellfounded_Owf(T_b,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_wf__not__sym]) ).

fof(f_3459_2,plain,
    ! [U_13581,U_13580,U_13579,U_13578] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13578,U_13578)),hAPP(hAPP(c_Product__Type_OPair(U_13578,U_13578),U_13581),U_13580)),U_13579))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13578,U_13578)),hAPP(hAPP(c_Product__Type_OPair(U_13578,U_13578),U_13580),U_13581)),U_13579))
      | ~ c_Wellfounded_Owf(U_13578,U_13579) ),
    inference(variable_rename,[status(thm)],[f_3459_1]) ).

cnf(f_3459_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13578,U_13578)),hAPP(hAPP(c_Product__Type_OPair(U_13578,U_13578),U_13581),U_13580)),U_13579))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13578,U_13578)),hAPP(hAPP(c_Product__Type_OPair(U_13578,U_13578),U_13580),U_13581)),U_13579))
    | ~ c_Wellfounded_Owf(U_13578,U_13579) ),
    inference(clausify,[status(thm)],[f_3459_2]) ).

fof(f_3460_1,plain,
    ! [V_a_2,V_r_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),V_r_2))
      | ~ c_Wellfounded_Owf(T_b,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_wf__not__refl]) ).

fof(f_3460_2,plain,
    ! [U_13584,U_13583,U_13582] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13582,U_13582)),hAPP(hAPP(c_Product__Type_OPair(U_13582,U_13582),U_13584),U_13584)),U_13583))
      | ~ c_Wellfounded_Owf(U_13582,U_13583) ),
    inference(variable_rename,[status(thm)],[f_3460_1]) ).

cnf(f_3460_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13582,U_13582)),hAPP(hAPP(c_Product__Type_OPair(U_13582,U_13582),U_13584),U_13584)),U_13583))
    | ~ c_Wellfounded_Owf(U_13582,U_13583) ),
    inference(clausify,[status(thm)],[f_3460_2]) ).

fof(f_3461_1,plain,
    ! [V_r_2,T_b] :
      ( c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Omax__ext(T_b,V_r_2))
      | ~ c_Wellfounded_Owf(T_b,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_max__ext__wf]) ).

fof(f_3461_2,plain,
    ! [U_13586,U_13585] :
      ( c_Wellfounded_Owf(tc_fun(U_13585,tc_HOL_Obool),c_Wellfounded_Omax__ext(U_13585,U_13586))
      | ~ c_Wellfounded_Owf(U_13585,U_13586) ),
    inference(variable_rename,[status(thm)],[f_3461_1]) ).

cnf(f_3461_3,plain,
    ( c_Wellfounded_Owf(tc_fun(U_13585,tc_HOL_Obool),c_Wellfounded_Omax__ext(U_13585,U_13586))
    | ~ c_Wellfounded_Owf(U_13585,U_13586) ),
    inference(clausify,[status(thm)],[f_3461_2]) ).

fof(f_3462_1,plain,
    c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
    inference(fof_nnf,[status(thm)],[fact_wf__pair__less]) ).

cnf(f_3462_2,plain,
    c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
    inference(clausify,[status(thm)],[f_3462_1]) ).

fof(f_3463_1,plain,
    ! [T_b] : c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_b)),
    inference(fof_nnf,[status(thm)],[fact_wf__finite__psubset]) ).

fof(f_3463_2,plain,
    ! [U_13587] : c_Wellfounded_Owf(tc_fun(U_13587,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(U_13587)),
    inference(variable_rename,[status(thm)],[f_3463_1]) ).

cnf(f_3463_3,plain,
    c_Wellfounded_Owf(tc_fun(U_13587,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(U_13587)),
    inference(clausify,[status(thm)],[f_3463_2]) ).

fof(f_3464_1,plain,
    ! [V_f_2,V_R_2,T_b] :
      ( c_Wellfounded_Owf(T_b,c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2))
      | ~ c_Wellfounded_Owf(T_b,V_R_2) ),
    inference(fof_nnf,[status(thm)],[fact_wf__mlex]) ).

fof(f_3464_2,plain,
    ! [U_13590,U_13589,U_13588] :
      ( c_Wellfounded_Owf(U_13588,c_Wellfounded_Omlex__prod(U_13588,U_13590,U_13589))
      | ~ c_Wellfounded_Owf(U_13588,U_13589) ),
    inference(variable_rename,[status(thm)],[f_3464_1]) ).

cnf(f_3464_3,plain,
    ( c_Wellfounded_Owf(U_13588,c_Wellfounded_Omlex__prod(U_13588,U_13590,U_13589))
    | ~ c_Wellfounded_Owf(U_13588,U_13589) ),
    inference(clausify,[status(thm)],[f_3464_2]) ).

fof(f_3465_1,plain,
    ! [V_r_H_2,V_r_2,T_b] :
      ( c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_r_H_2))
      | ~ c_Wellfounded_Owf(T_b,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_wf__Int1]) ).

fof(f_3465_2,plain,
    ! [U_13593,U_13592,U_13591] :
      ( c_Wellfounded_Owf(U_13591,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_13591,U_13591),tc_HOL_Obool)),U_13592),U_13593))
      | ~ c_Wellfounded_Owf(U_13591,U_13592) ),
    inference(variable_rename,[status(thm)],[f_3465_1]) ).

cnf(f_3465_3,plain,
    ( c_Wellfounded_Owf(U_13591,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_13591,U_13591),tc_HOL_Obool)),U_13592),U_13593))
    | ~ c_Wellfounded_Owf(U_13591,U_13592) ),
    inference(clausify,[status(thm)],[f_3465_2]) ).

fof(f_3466_1,plain,
    ! [V_r_H_2,V_r_2,T_b] :
      ( c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_H_2),V_r_2))
      | ~ c_Wellfounded_Owf(T_b,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_wf__Int2]) ).

fof(f_3466_2,plain,
    ! [U_13596,U_13595,U_13594] :
      ( c_Wellfounded_Owf(U_13594,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_13594,U_13594),tc_HOL_Obool)),U_13596),U_13595))
      | ~ c_Wellfounded_Owf(U_13594,U_13595) ),
    inference(variable_rename,[status(thm)],[f_3466_1]) ).

cnf(f_3466_3,plain,
    ( c_Wellfounded_Owf(U_13594,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_13594,U_13594),tc_HOL_Obool)),U_13596),U_13595))
    | ~ c_Wellfounded_Owf(U_13594,U_13595) ),
    inference(clausify,[status(thm)],[f_3466_2]) ).

fof(f_3467_1,plain,
    ! [V_A_2,T_b] : hAPP(c_Relation_ODomain(T_b,T_b),c_Relation_OId__on(T_b,V_A_2)) = V_A_2,
    inference(fof_nnf,[status(thm)],[fact_Domain__Id__on]) ).

fof(f_3467_2,plain,
    ! [U_13598,U_13597] : hAPP(c_Relation_ODomain(U_13597,U_13597),c_Relation_OId__on(U_13597,U_13598)) = U_13598,
    inference(variable_rename,[status(thm)],[f_3467_1]) ).

cnf(f_3467_3,plain,
    hAPP(c_Relation_ODomain(U_13597,U_13597),c_Relation_OId__on(U_13597,U_13598)) = U_13598,
    inference(clausify,[status(thm)],[f_3467_2]) ).

fof(f_3468_1,plain,
    c_Wellfounded_Owf(tc_Nat_Onat,hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)))),
    inference(fof_nnf,[status(thm)],[fact_wf__less]) ).

cnf(f_3468_2,plain,
    c_Wellfounded_Owf(tc_Nat_Onat,hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)))),
    inference(clausify,[status(thm)],[f_3468_1]) ).

fof(f_3469_1,plain,
    ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(V_d_2)),
    inference(fof_nnf,[status(thm)],[fact_wf__int__ge__less__than2]) ).

fof(f_3469_2,plain,
    ! [U_13599] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(U_13599)),
    inference(variable_rename,[status(thm)],[f_3469_1]) ).

cnf(f_3469_3,plain,
    c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(U_13599)),
    inference(clausify,[status(thm)],[f_3469_2]) ).

fof(f_3470_1,plain,
    ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(V_d_2)),
    inference(fof_nnf,[status(thm)],[fact_wf__int__ge__less__than]) ).

fof(f_3470_2,plain,
    ! [U_13600] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(U_13600)),
    inference(variable_rename,[status(thm)],[f_3470_1]) ).

cnf(f_3470_3,plain,
    c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(U_13600)),
    inference(clausify,[status(thm)],[f_3470_2]) ).

fof(f_3471_1,plain,
    ! [V_s_2,V_r_2,T_b] :
      ( c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_b),V_r_2)),hAPP(c_Relation_ORange(T_b,T_b),V_s_2)) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ c_Wellfounded_Owf(T_b,V_s_2)
      | ~ c_Wellfounded_Owf(T_b,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_wf__Un]) ).

fof(f_3471_2,plain,
    ! [U_13603,U_13602,U_13601] :
      ( c_Wellfounded_Owf(U_13601,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13601,U_13601),tc_HOL_Obool)),U_13602),U_13603))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13601,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_13601,U_13601),U_13602)),hAPP(c_Relation_ORange(U_13601,U_13601),U_13603)) != c_Orderings_Obot__class_Obot(tc_fun(U_13601,tc_HOL_Obool))
      | ~ c_Wellfounded_Owf(U_13601,U_13603)
      | ~ c_Wellfounded_Owf(U_13601,U_13602) ),
    inference(variable_rename,[status(thm)],[f_3471_1]) ).

cnf(f_3471_3,plain,
    ( c_Wellfounded_Owf(U_13601,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13601,U_13601),tc_HOL_Obool)),U_13602),U_13603))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13601,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_13601,U_13601),U_13602)),hAPP(c_Relation_ORange(U_13601,U_13601),U_13603)) != c_Orderings_Obot__class_Obot(tc_fun(U_13601,tc_HOL_Obool))
    | ~ c_Wellfounded_Owf(U_13601,U_13603)
    | ~ c_Wellfounded_Owf(U_13601,U_13602) ),
    inference(clausify,[status(thm)],[f_3471_2]) ).

fof(f_3472_1,plain,
    ! [V_r_2,T_b] :
      ( ( c_Wellfounded_Owf(T_b,V_r_2)
        | ? [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2))) )
      & ( ! [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2)))
        | ~ c_Wellfounded_Owf(T_b,V_r_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_wf__acc__iff]) ).

fof(f_3472_2,plain,
    ! [U_13607,U_13606] :
      ( ( c_Wellfounded_Owf(U_13606,U_13607)
        | ? [U_13605] : ~ hBOOL(hAPP(hAPP(c_member(U_13606),U_13605),c_Wellfounded_Oacc(U_13606,U_13607))) )
      & ( ! [U_13604] : hBOOL(hAPP(hAPP(c_member(U_13606),U_13604),c_Wellfounded_Oacc(U_13606,U_13607)))
        | ~ c_Wellfounded_Owf(U_13606,U_13607) ) ),
    inference(variable_rename,[status(thm)],[f_3472_1]) ).

fof(f_3472_3,plain,
    ( ! [U_13611,U_13609] :
        ( c_Wellfounded_Owf(U_13609,U_13611)
        | ? [U_13605] : ~ hBOOL(hAPP(hAPP(c_member(U_13609),U_13605),c_Wellfounded_Oacc(U_13609,U_13611))) )
    & ! [U_13610,U_13608] :
        ( ! [U_13604] : hBOOL(hAPP(hAPP(c_member(U_13608),U_13604),c_Wellfounded_Oacc(U_13608,U_13610)))
        | ~ c_Wellfounded_Owf(U_13608,U_13610) ) ),
    inference(miniscope,[status(thm)],[f_3472_2]) ).

fof(f_3472_4,plain,
    ( ! [U_13611,U_13609] :
        ( c_Wellfounded_Owf(U_13609,U_13611)
        | ~ hBOOL(hAPP(hAPP(c_member(U_13609),sK322(U_13611,U_13609)),c_Wellfounded_Oacc(U_13609,U_13611))) )
    & ! [U_13610,U_13608] :
        ( ! [U_13604] : hBOOL(hAPP(hAPP(c_member(U_13608),U_13604),c_Wellfounded_Oacc(U_13608,U_13610)))
        | ~ c_Wellfounded_Owf(U_13608,U_13610) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK322]),skolemize(U_13605,sK322(U_13611,U_13609))],[f_3472_3]) ).

cnf(f_3472_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13608),U_13604),c_Wellfounded_Oacc(U_13608,U_13610)))
    | ~ c_Wellfounded_Owf(U_13608,U_13610) ),
    inference(clausify,[status(thm)],[f_3472_4]) ).

cnf(f_3472_6,plain,
    ( c_Wellfounded_Owf(U_13609,U_13611)
    | ~ hBOOL(hAPP(hAPP(c_member(U_13609),sK322(U_13611,U_13609)),c_Wellfounded_Oacc(U_13609,U_13611))) ),
    inference(clausify,[status(thm)],[f_3472_4]) ).

fof(f_3473_1,plain,
    ! [V_x_2,V_r_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2)))
      | ~ c_Wellfounded_Owf(T_b,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_acc__wfD]) ).

fof(f_3473_2,plain,
    ! [U_13614,U_13613,U_13612] :
      ( hBOOL(hAPP(hAPP(c_member(U_13612),U_13614),c_Wellfounded_Oacc(U_13612,U_13613)))
      | ~ c_Wellfounded_Owf(U_13612,U_13613) ),
    inference(variable_rename,[status(thm)],[f_3473_1]) ).

cnf(f_3473_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13612),U_13614),c_Wellfounded_Oacc(U_13612,U_13613)))
    | ~ c_Wellfounded_Owf(U_13612,U_13613) ),
    inference(clausify,[status(thm)],[f_3473_2]) ).

fof(f_3474_1,plain,
    ! [V_R_2,T_b] :
      ( c_Wellfounded_Owf(T_b,V_R_2)
      | hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) ),
    inference(fof_nnf,[status(thm)],[fact_wf__no__loop]) ).

fof(f_3474_2,plain,
    ! [U_13616,U_13615] :
      ( c_Wellfounded_Owf(U_13615,U_13616)
      | hAPP(hAPP(c_Relation_Orel__comp(U_13615,U_13615,U_13615),U_13616),U_13616) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13615,U_13615),tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_3474_1]) ).

cnf(f_3474_3,plain,
    ( c_Wellfounded_Owf(U_13615,U_13616)
    | hAPP(hAPP(c_Relation_Orel__comp(U_13615,U_13615,U_13615),U_13616),U_13616) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13615,U_13615),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3474_2]) ).

fof(f_3475_1,plain,
    ! [V_S_2,V_R_2,T_b] :
      ( ( c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2))
        | ~ c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_S_2),V_R_2))),V_S_2)) )
      & ( c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_S_2),V_R_2))),V_S_2))
        | ~ c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_wf__union__merge]) ).

fof(f_3475_2,plain,
    ! [U_13619,U_13618,U_13617] :
      ( ( c_Wellfounded_Owf(U_13617,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13617,U_13617),tc_HOL_Obool)),U_13618),U_13619))
        | ~ c_Wellfounded_Owf(U_13617,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13617,U_13617),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13617,U_13617),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13617,U_13617,U_13617),U_13618),U_13618)),hAPP(hAPP(c_Relation_Orel__comp(U_13617,U_13617,U_13617),U_13619),U_13618))),U_13619)) )
      & ( c_Wellfounded_Owf(U_13617,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13617,U_13617),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13617,U_13617),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13617,U_13617,U_13617),U_13618),U_13618)),hAPP(hAPP(c_Relation_Orel__comp(U_13617,U_13617,U_13617),U_13619),U_13618))),U_13619))
        | ~ c_Wellfounded_Owf(U_13617,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13617,U_13617),tc_HOL_Obool)),U_13618),U_13619)) ) ),
    inference(variable_rename,[status(thm)],[f_3475_1]) ).

fof(f_3475_3,plain,
    ( ! [U_13625,U_13623,U_13621] :
        ( c_Wellfounded_Owf(U_13621,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13621,U_13621),tc_HOL_Obool)),U_13623),U_13625))
        | ~ c_Wellfounded_Owf(U_13621,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13621,U_13621),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13621,U_13621),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13621,U_13621,U_13621),U_13623),U_13623)),hAPP(hAPP(c_Relation_Orel__comp(U_13621,U_13621,U_13621),U_13625),U_13623))),U_13625)) )
    & ! [U_13624,U_13622,U_13620] :
        ( c_Wellfounded_Owf(U_13620,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13620,U_13620),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13620,U_13620),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13620,U_13620,U_13620),U_13622),U_13622)),hAPP(hAPP(c_Relation_Orel__comp(U_13620,U_13620,U_13620),U_13624),U_13622))),U_13624))
        | ~ c_Wellfounded_Owf(U_13620,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13620,U_13620),tc_HOL_Obool)),U_13622),U_13624)) ) ),
    inference(miniscope,[status(thm)],[f_3475_2]) ).

cnf(f_3475_4,plain,
    ( c_Wellfounded_Owf(U_13620,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13620,U_13620),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13620,U_13620),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13620,U_13620,U_13620),U_13622),U_13622)),hAPP(hAPP(c_Relation_Orel__comp(U_13620,U_13620,U_13620),U_13624),U_13622))),U_13624))
    | ~ c_Wellfounded_Owf(U_13620,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13620,U_13620),tc_HOL_Obool)),U_13622),U_13624)) ),
    inference(clausify,[status(thm)],[f_3475_3]) ).

cnf(f_3475_5,plain,
    ( c_Wellfounded_Owf(U_13621,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13621,U_13621),tc_HOL_Obool)),U_13623),U_13625))
    | ~ c_Wellfounded_Owf(U_13621,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13621,U_13621),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13621,U_13621),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13621,U_13621,U_13621),U_13623),U_13623)),hAPP(hAPP(c_Relation_Orel__comp(U_13621,U_13621,U_13621),U_13625),U_13623))),U_13625)) ),
    inference(clausify,[status(thm)],[f_3475_3]) ).

fof(f_3476_1,plain,
    ! [T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Domain__empty]) ).

fof(f_3476_2,plain,
    ! [U_13627,U_13626] : hAPP(c_Relation_ODomain(U_13626,U_13627),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13626,U_13627),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_13626,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3476_1]) ).

cnf(f_3476_3,plain,
    hAPP(c_Relation_ODomain(U_13626,U_13627),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13626,U_13627),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_13626,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3476_2]) ).

fof(f_3477_1,plain,
    ! [V_r_2,T_c,T_b] :
      ( ( hAPP(c_Relation_ODomain(T_b,T_c),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
        | V_r_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) )
      & ( V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))
        | hAPP(c_Relation_ODomain(T_b,T_c),V_r_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Domain__empty__iff]) ).

fof(f_3477_2,plain,
    ! [U_13630,U_13629,U_13628] :
      ( ( hAPP(c_Relation_ODomain(U_13628,U_13629),U_13630) = c_Orderings_Obot__class_Obot(tc_fun(U_13628,tc_HOL_Obool))
        | U_13630 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13628,U_13629),tc_HOL_Obool)) )
      & ( U_13630 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13628,U_13629),tc_HOL_Obool))
        | hAPP(c_Relation_ODomain(U_13628,U_13629),U_13630) != c_Orderings_Obot__class_Obot(tc_fun(U_13628,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_3477_1]) ).

fof(f_3477_3,plain,
    ( ! [U_13636,U_13634,U_13632] :
        ( hAPP(c_Relation_ODomain(U_13632,U_13634),U_13636) = c_Orderings_Obot__class_Obot(tc_fun(U_13632,tc_HOL_Obool))
        | U_13636 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13632,U_13634),tc_HOL_Obool)) )
    & ! [U_13635,U_13633,U_13631] :
        ( U_13635 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13631,U_13633),tc_HOL_Obool))
        | hAPP(c_Relation_ODomain(U_13631,U_13633),U_13635) != c_Orderings_Obot__class_Obot(tc_fun(U_13631,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_3477_2]) ).

cnf(f_3477_4,plain,
    ( U_13635 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13631,U_13633),tc_HOL_Obool))
    | hAPP(c_Relation_ODomain(U_13631,U_13633),U_13635) != c_Orderings_Obot__class_Obot(tc_fun(U_13631,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3477_3]) ).

cnf(f_3477_5,plain,
    ( hAPP(c_Relation_ODomain(U_13632,U_13634),U_13636) = c_Orderings_Obot__class_Obot(tc_fun(U_13632,tc_HOL_Obool))
    | U_13636 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13632,U_13634),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3477_3]) ).

fof(f_3478_1,plain,
    ! [V_s_2,V_r_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)),hAPP(c_Relation_ODomain(T_b,T_c),V_s_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_2),V_s_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Domain__mono]) ).

fof(f_3478_2,plain,
    ! [U_13640,U_13639,U_13638,U_13637] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13637,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_13637,U_13638),U_13639)),hAPP(c_Relation_ODomain(U_13637,U_13638),U_13640)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13637,U_13638),tc_HOL_Obool)),U_13639),U_13640)) ),
    inference(variable_rename,[status(thm)],[f_3478_1]) ).

cnf(f_3478_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13637,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_13637,U_13638),U_13639)),hAPP(c_Relation_ODomain(U_13637,U_13638),U_13640)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13637,U_13638),tc_HOL_Obool)),U_13639),U_13640)) ),
    inference(clausify,[status(thm)],[f_3478_2]) ).

fof(f_3479_1,plain,
    ! [V_B_2,V_A_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_c),V_A_2)),hAPP(c_Relation_ODomain(T_b,T_c),V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_Domain__Un__eq]) ).

fof(f_3479_2,plain,
    ! [U_13644,U_13643,U_13642,U_13641] : hAPP(c_Relation_ODomain(U_13641,U_13642),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13641,U_13642),tc_HOL_Obool)),U_13643),U_13644)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13641,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_13641,U_13642),U_13643)),hAPP(c_Relation_ODomain(U_13641,U_13642),U_13644)),
    inference(variable_rename,[status(thm)],[f_3479_1]) ).

cnf(f_3479_3,plain,
    hAPP(c_Relation_ODomain(U_13641,U_13642),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13641,U_13642),tc_HOL_Obool)),U_13643),U_13644)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13641,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_13641,U_13642),U_13643)),hAPP(c_Relation_ODomain(U_13641,U_13642),U_13644)),
    inference(clausify,[status(thm)],[f_3479_2]) ).

fof(f_3480_1,plain,
    ! [V_r_2,T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__Domain]) ).

fof(f_3480_2,plain,
    ! [U_13647,U_13646,U_13645] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13645),hAPP(c_Relation_ODomain(U_13645,U_13646),U_13647)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13645,U_13646)),U_13647)) ),
    inference(variable_rename,[status(thm)],[f_3480_1]) ).

cnf(f_3480_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13645),hAPP(c_Relation_ODomain(U_13645,U_13646),U_13647)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13645,U_13646)),U_13647)) ),
    inference(clausify,[status(thm)],[f_3480_2]) ).

fof(f_3481_1,plain,
    ! [V_R_2,T_c,T_b] : hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_b,c_Product__Type_Ofst(T_b,T_c)),V_R_2) = hAPP(c_Relation_ODomain(T_b,T_c),V_R_2),
    inference(fof_nnf,[status(thm)],[fact_fst__eq__Domain]) ).

fof(f_3481_2,plain,
    ! [U_13650,U_13649,U_13648] : hAPP(c_Set_Oimage(tc_prod(U_13648,U_13649),U_13648,c_Product__Type_Ofst(U_13648,U_13649)),U_13650) = hAPP(c_Relation_ODomain(U_13648,U_13649),U_13650),
    inference(variable_rename,[status(thm)],[f_3481_1]) ).

cnf(f_3481_3,plain,
    hAPP(c_Set_Oimage(tc_prod(U_13648,U_13649),U_13648,c_Product__Type_Ofst(U_13648,U_13649)),U_13650) = hAPP(c_Relation_ODomain(U_13648,U_13649),U_13650),
    inference(clausify,[status(thm)],[f_3481_2]) ).

fof(f_3482_1,plain,
    ! [V_r_2,T_b] :
      ( ( c_Wellfounded_Owf(T_b,V_r_2)
        | ? [B_f] :
          ! [B_i] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(B_f,hAPP(c_Nat_OSuc,B_i))),hAPP(B_f,B_i))),V_r_2)) )
      & ( ! [B_f] :
          ? [B_i] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(B_f,hAPP(c_Nat_OSuc,B_i))),hAPP(B_f,B_i))),V_r_2))
        | ~ c_Wellfounded_Owf(T_b,V_r_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_wf__iff__no__infinite__down__chain]) ).

fof(f_3482_2,plain,
    ! [U_13656,U_13655] :
      ( ( c_Wellfounded_Owf(U_13655,U_13656)
        | ? [U_13654] :
          ! [U_13653] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_13655,U_13655)),hAPP(hAPP(c_Product__Type_OPair(U_13655,U_13655),hAPP(U_13654,hAPP(c_Nat_OSuc,U_13653))),hAPP(U_13654,U_13653))),U_13656)) )
      & ( ! [U_13652] :
          ? [U_13651] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13655,U_13655)),hAPP(hAPP(c_Product__Type_OPair(U_13655,U_13655),hAPP(U_13652,hAPP(c_Nat_OSuc,U_13651))),hAPP(U_13652,U_13651))),U_13656))
        | ~ c_Wellfounded_Owf(U_13655,U_13656) ) ),
    inference(variable_rename,[status(thm)],[f_3482_1]) ).

fof(f_3482_3,plain,
    ( ! [U_13660,U_13658] :
        ( c_Wellfounded_Owf(U_13658,U_13660)
        | ? [U_13654] :
          ! [U_13653] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_13658,U_13658)),hAPP(hAPP(c_Product__Type_OPair(U_13658,U_13658),hAPP(U_13654,hAPP(c_Nat_OSuc,U_13653))),hAPP(U_13654,U_13653))),U_13660)) )
    & ! [U_13659,U_13657] :
        ( ! [U_13652] :
          ? [U_13651] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13657,U_13657)),hAPP(hAPP(c_Product__Type_OPair(U_13657,U_13657),hAPP(U_13652,hAPP(c_Nat_OSuc,U_13651))),hAPP(U_13652,U_13651))),U_13659))
        | ~ c_Wellfounded_Owf(U_13657,U_13659) ) ),
    inference(miniscope,[status(thm)],[f_3482_2]) ).

fof(f_3482_4,plain,
    ( ! [U_13660,U_13658] :
        ( c_Wellfounded_Owf(U_13658,U_13660)
        | ? [U_13654] :
          ! [U_13653] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_13658,U_13658)),hAPP(hAPP(c_Product__Type_OPair(U_13658,U_13658),hAPP(U_13654,hAPP(c_Nat_OSuc,U_13653))),hAPP(U_13654,U_13653))),U_13660)) )
    & ! [U_13659,U_13657] :
        ( ! [U_13652] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13657,U_13657)),hAPP(hAPP(c_Product__Type_OPair(U_13657,U_13657),hAPP(U_13652,hAPP(c_Nat_OSuc,sK323(U_13659,U_13657,U_13652)))),hAPP(U_13652,sK323(U_13659,U_13657,U_13652)))),U_13659))
        | ~ c_Wellfounded_Owf(U_13657,U_13659) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK323]),skolemize(U_13651,sK323(U_13659,U_13657,U_13652))],[f_3482_3]) ).

fof(f_3482_5,plain,
    ( ! [U_13660,U_13658] :
        ( c_Wellfounded_Owf(U_13658,U_13660)
        | ! [U_13653] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_13658,U_13658)),hAPP(hAPP(c_Product__Type_OPair(U_13658,U_13658),hAPP(sK324(U_13660,U_13658),hAPP(c_Nat_OSuc,U_13653))),hAPP(sK324(U_13660,U_13658),U_13653))),U_13660)) )
    & ! [U_13659,U_13657] :
        ( ! [U_13652] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13657,U_13657)),hAPP(hAPP(c_Product__Type_OPair(U_13657,U_13657),hAPP(U_13652,hAPP(c_Nat_OSuc,sK323(U_13659,U_13657,U_13652)))),hAPP(U_13652,sK323(U_13659,U_13657,U_13652)))),U_13659))
        | ~ c_Wellfounded_Owf(U_13657,U_13659) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK324]),skolemize(U_13654,sK324(U_13660,U_13658))],[f_3482_4]) ).

cnf(f_3482_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13657,U_13657)),hAPP(hAPP(c_Product__Type_OPair(U_13657,U_13657),hAPP(U_13652,hAPP(c_Nat_OSuc,sK323(U_13659,U_13657,U_13652)))),hAPP(U_13652,sK323(U_13659,U_13657,U_13652)))),U_13659))
    | ~ c_Wellfounded_Owf(U_13657,U_13659) ),
    inference(clausify,[status(thm)],[f_3482_5]) ).

cnf(f_3482_7,plain,
    ( c_Wellfounded_Owf(U_13658,U_13660)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_13658,U_13658)),hAPP(hAPP(c_Product__Type_OPair(U_13658,U_13658),hAPP(sK324(U_13660,U_13658),hAPP(c_Nat_OSuc,U_13653))),hAPP(sK324(U_13660,U_13658),U_13653))),U_13660)) ),
    inference(clausify,[status(thm)],[f_3482_5]) ).

fof(f_3483_1,plain,
    ! [V_A_2,V_R_2,T_b] :
      ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Relation_OImage(T_b,T_b,V_R_2),V_A_2)))
      | ~ c_Wellfounded_Owf(T_b,V_R_2) ),
    inference(fof_nnf,[status(thm)],[fact_wfE__pf]) ).

fof(f_3483_2,plain,
    ! [U_13663,U_13662,U_13661] :
      ( U_13663 = c_Orderings_Obot__class_Obot(tc_fun(U_13661,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13661,tc_HOL_Obool)),U_13663),hAPP(c_Relation_OImage(U_13661,U_13661,U_13662),U_13663)))
      | ~ c_Wellfounded_Owf(U_13661,U_13662) ),
    inference(variable_rename,[status(thm)],[f_3483_1]) ).

cnf(f_3483_3,plain,
    ( U_13663 = c_Orderings_Obot__class_Obot(tc_fun(U_13661,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13661,tc_HOL_Obool)),U_13663),hAPP(c_Relation_OImage(U_13661,U_13661,U_13662),U_13663)))
    | ~ c_Wellfounded_Owf(U_13661,U_13662) ),
    inference(clausify,[status(thm)],[f_3483_2]) ).

fof(f_3484_1,plain,
    ! [V_S_2,V_R_2,T_b] :
      ( c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_S_2)),V_R_2))
      | ~ c_Wellfounded_Owf(T_b,V_S_2)
      | ~ c_Wellfounded_Owf(T_b,V_R_2) ),
    inference(fof_nnf,[status(thm)],[fact_wf__union__compatible]) ).

fof(f_3484_2,plain,
    ! [U_13666,U_13665,U_13664] :
      ( c_Wellfounded_Owf(U_13664,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13664,U_13664),tc_HOL_Obool)),U_13665),U_13666))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13664,U_13664),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13664,U_13664,U_13664),U_13665),U_13666)),U_13665))
      | ~ c_Wellfounded_Owf(U_13664,U_13666)
      | ~ c_Wellfounded_Owf(U_13664,U_13665) ),
    inference(variable_rename,[status(thm)],[f_3484_1]) ).

cnf(f_3484_3,plain,
    ( c_Wellfounded_Owf(U_13664,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13664,U_13664),tc_HOL_Obool)),U_13665),U_13666))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13664,U_13664),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13664,U_13664,U_13664),U_13665),U_13666)),U_13665))
    | ~ c_Wellfounded_Owf(U_13664,U_13666)
    | ~ c_Wellfounded_Owf(U_13664,U_13665) ),
    inference(clausify,[status(thm)],[f_3484_2]) ).

fof(f_3485_1,plain,
    ! [V_r_2,T_c,V_a_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)))
        | ! [B_y] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),B_y)),V_r_2)) )
      & ( ? [B_y] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),B_y)),V_r_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_Domain__iff]) ).

fof(f_3485_2,plain,
    ! [U_13672,U_13671,U_13670,U_13669] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_13669),U_13670),hAPP(c_Relation_ODomain(U_13669,U_13671),U_13672)))
        | ! [U_13668] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13669,U_13671)),hAPP(hAPP(c_Product__Type_OPair(U_13669,U_13671),U_13670),U_13668)),U_13672)) )
      & ( ? [U_13667] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_13669,U_13671)),hAPP(hAPP(c_Product__Type_OPair(U_13669,U_13671),U_13670),U_13667)),U_13672))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13669),U_13670),hAPP(c_Relation_ODomain(U_13669,U_13671),U_13672))) ) ),
    inference(variable_rename,[status(thm)],[f_3485_1]) ).

fof(f_3485_3,plain,
    ( ! [U_13680,U_13678,U_13676,U_13674] :
        ( hBOOL(hAPP(hAPP(c_member(U_13674),U_13676),hAPP(c_Relation_ODomain(U_13674,U_13678),U_13680)))
        | ! [U_13668] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13674,U_13678)),hAPP(hAPP(c_Product__Type_OPair(U_13674,U_13678),U_13676),U_13668)),U_13680)) )
    & ! [U_13679,U_13677,U_13675,U_13673] :
        ( ? [U_13667] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_13673,U_13677)),hAPP(hAPP(c_Product__Type_OPair(U_13673,U_13677),U_13675),U_13667)),U_13679))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13673),U_13675),hAPP(c_Relation_ODomain(U_13673,U_13677),U_13679))) ) ),
    inference(miniscope,[status(thm)],[f_3485_2]) ).

fof(f_3485_4,plain,
    ( ! [U_13680,U_13678,U_13676,U_13674] :
        ( hBOOL(hAPP(hAPP(c_member(U_13674),U_13676),hAPP(c_Relation_ODomain(U_13674,U_13678),U_13680)))
        | ! [U_13668] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13674,U_13678)),hAPP(hAPP(c_Product__Type_OPair(U_13674,U_13678),U_13676),U_13668)),U_13680)) )
    & ! [U_13679,U_13677,U_13675,U_13673] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13673,U_13677)),hAPP(hAPP(c_Product__Type_OPair(U_13673,U_13677),U_13675),sK325(U_13679,U_13677,U_13675,U_13673))),U_13679))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13673),U_13675),hAPP(c_Relation_ODomain(U_13673,U_13677),U_13679))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK325]),skolemize(U_13667,sK325(U_13679,U_13677,U_13675,U_13673))],[f_3485_3]) ).

cnf(f_3485_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13673,U_13677)),hAPP(hAPP(c_Product__Type_OPair(U_13673,U_13677),U_13675),sK325(U_13679,U_13677,U_13675,U_13673))),U_13679))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13673),U_13675),hAPP(c_Relation_ODomain(U_13673,U_13677),U_13679))) ),
    inference(clausify,[status(thm)],[f_3485_4]) ).

cnf(f_3485_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13674),U_13676),hAPP(c_Relation_ODomain(U_13674,U_13678),U_13680)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13674,U_13678)),hAPP(hAPP(c_Product__Type_OPair(U_13674,U_13678),U_13676),U_13668)),U_13680)) ),
    inference(clausify,[status(thm)],[f_3485_4]) ).

fof(f_3486_1,plain,
    ! [T_b] :
      ( c_Wellfounded_Owf(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),c_Orderings_Oord__class_Oless(T_b))))
      | ~ class_Orderings_Owellorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_wf]) ).

fof(f_3486_2,plain,
    ! [U_13681] :
      ( c_Wellfounded_Owf(U_13681,hAPP(c_Set_OCollect(tc_prod(U_13681,U_13681)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13681,U_13681,tc_HOL_Obool),c_Orderings_Oord__class_Oless(U_13681))))
      | ~ class_Orderings_Owellorder(U_13681) ),
    inference(variable_rename,[status(thm)],[f_3486_1]) ).

cnf(f_3486_3,plain,
    ( c_Wellfounded_Owf(U_13681,hAPP(c_Set_OCollect(tc_prod(U_13681,U_13681)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13681,U_13681,tc_HOL_Obool),c_Orderings_Oord__class_Oless(U_13681))))
    | ~ class_Orderings_Owellorder(U_13681) ),
    inference(clausify,[status(thm)],[f_3486_2]) ).

fof(f_3487_1,plain,
    ! [V_r_2,V_b_2,V_a_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)),
    inference(fof_nnf,[status(thm)],[fact_Domain__insert]) ).

fof(f_3487_2,plain,
    ! [U_13686,U_13685,U_13684,U_13683,U_13682] : hAPP(c_Relation_ODomain(U_13682,U_13683),hAPP(hAPP(c_Set_Oinsert(tc_prod(U_13682,U_13683)),hAPP(hAPP(c_Product__Type_OPair(U_13682,U_13683),U_13684),U_13685)),U_13686)) = hAPP(hAPP(c_Set_Oinsert(U_13682),U_13684),hAPP(c_Relation_ODomain(U_13682,U_13683),U_13686)),
    inference(variable_rename,[status(thm)],[f_3487_1]) ).

cnf(f_3487_3,plain,
    hAPP(c_Relation_ODomain(U_13682,U_13683),hAPP(hAPP(c_Set_Oinsert(tc_prod(U_13682,U_13683)),hAPP(hAPP(c_Product__Type_OPair(U_13682,U_13683),U_13684),U_13685)),U_13686)) = hAPP(hAPP(c_Set_Oinsert(U_13682),U_13684),hAPP(c_Relation_ODomain(U_13682,U_13683),U_13686)),
    inference(clausify,[status(thm)],[f_3487_2]) ).

fof(f_3488_1,plain,
    ! [V_P_2,T_b] :
      ( ( c_FunDef_Oreduction__pair(T_b,V_P_2)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2)))
        | ~ c_Wellfounded_Owf(T_b,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2)) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2)))
          & c_Wellfounded_Owf(T_b,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2)) )
        | ~ c_FunDef_Oreduction__pair(T_b,V_P_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_reduction__pair__def]) ).

fof(f_3488_2,plain,
    ! [U_13688,U_13687] :
      ( ( c_FunDef_Oreduction__pair(U_13687,U_13688)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13687,U_13687),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13687,U_13687,U_13687),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13687,U_13687),tc_HOL_Obool),tc_fun(tc_prod(U_13687,U_13687),tc_HOL_Obool)),U_13688)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(U_13687,U_13687),tc_HOL_Obool),tc_fun(tc_prod(U_13687,U_13687),tc_HOL_Obool)),U_13688))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13687,U_13687),tc_HOL_Obool),tc_fun(tc_prod(U_13687,U_13687),tc_HOL_Obool)),U_13688)))
        | ~ c_Wellfounded_Owf(U_13687,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13687,U_13687),tc_HOL_Obool),tc_fun(tc_prod(U_13687,U_13687),tc_HOL_Obool)),U_13688)) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13687,U_13687),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13687,U_13687,U_13687),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13687,U_13687),tc_HOL_Obool),tc_fun(tc_prod(U_13687,U_13687),tc_HOL_Obool)),U_13688)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(U_13687,U_13687),tc_HOL_Obool),tc_fun(tc_prod(U_13687,U_13687),tc_HOL_Obool)),U_13688))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13687,U_13687),tc_HOL_Obool),tc_fun(tc_prod(U_13687,U_13687),tc_HOL_Obool)),U_13688)))
          & c_Wellfounded_Owf(U_13687,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13687,U_13687),tc_HOL_Obool),tc_fun(tc_prod(U_13687,U_13687),tc_HOL_Obool)),U_13688)) )
        | ~ c_FunDef_Oreduction__pair(U_13687,U_13688) ) ),
    inference(variable_rename,[status(thm)],[f_3488_1]) ).

fof(f_3488_3,plain,
    ( ! [U_13692,U_13690] :
        ( c_FunDef_Oreduction__pair(U_13690,U_13692)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13690,U_13690),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13690,U_13690,U_13690),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13690,U_13690),tc_HOL_Obool),tc_fun(tc_prod(U_13690,U_13690),tc_HOL_Obool)),U_13692)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(U_13690,U_13690),tc_HOL_Obool),tc_fun(tc_prod(U_13690,U_13690),tc_HOL_Obool)),U_13692))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13690,U_13690),tc_HOL_Obool),tc_fun(tc_prod(U_13690,U_13690),tc_HOL_Obool)),U_13692)))
        | ~ c_Wellfounded_Owf(U_13690,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13690,U_13690),tc_HOL_Obool),tc_fun(tc_prod(U_13690,U_13690),tc_HOL_Obool)),U_13692)) )
    & ! [U_13691,U_13689] :
        ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13689,U_13689),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13689,U_13689,U_13689),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13689,U_13689),tc_HOL_Obool),tc_fun(tc_prod(U_13689,U_13689),tc_HOL_Obool)),U_13691)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(U_13689,U_13689),tc_HOL_Obool),tc_fun(tc_prod(U_13689,U_13689),tc_HOL_Obool)),U_13691))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13689,U_13689),tc_HOL_Obool),tc_fun(tc_prod(U_13689,U_13689),tc_HOL_Obool)),U_13691)))
          & c_Wellfounded_Owf(U_13689,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13689,U_13689),tc_HOL_Obool),tc_fun(tc_prod(U_13689,U_13689),tc_HOL_Obool)),U_13691)) )
        | ~ c_FunDef_Oreduction__pair(U_13689,U_13691) ) ),
    inference(miniscope,[status(thm)],[f_3488_2]) ).

cnf(f_3488_4,plain,
    ( c_Wellfounded_Owf(U_13689,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13689,U_13689),tc_HOL_Obool),tc_fun(tc_prod(U_13689,U_13689),tc_HOL_Obool)),U_13691))
    | ~ c_FunDef_Oreduction__pair(U_13689,U_13691) ),
    inference(clausify,[status(thm)],[f_3488_3]) ).

cnf(f_3488_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13689,U_13689),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13689,U_13689,U_13689),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13689,U_13689),tc_HOL_Obool),tc_fun(tc_prod(U_13689,U_13689),tc_HOL_Obool)),U_13691)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(U_13689,U_13689),tc_HOL_Obool),tc_fun(tc_prod(U_13689,U_13689),tc_HOL_Obool)),U_13691))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13689,U_13689),tc_HOL_Obool),tc_fun(tc_prod(U_13689,U_13689),tc_HOL_Obool)),U_13691)))
    | ~ c_FunDef_Oreduction__pair(U_13689,U_13691) ),
    inference(clausify,[status(thm)],[f_3488_3]) ).

cnf(f_3488_6,plain,
    ( c_FunDef_Oreduction__pair(U_13690,U_13692)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13690,U_13690),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13690,U_13690,U_13690),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13690,U_13690),tc_HOL_Obool),tc_fun(tc_prod(U_13690,U_13690),tc_HOL_Obool)),U_13692)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(U_13690,U_13690),tc_HOL_Obool),tc_fun(tc_prod(U_13690,U_13690),tc_HOL_Obool)),U_13692))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13690,U_13690),tc_HOL_Obool),tc_fun(tc_prod(U_13690,U_13690),tc_HOL_Obool)),U_13692)))
    | ~ c_Wellfounded_Owf(U_13690,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13690,U_13690),tc_HOL_Obool),tc_fun(tc_prod(U_13690,U_13690),tc_HOL_Obool)),U_13692)) ),
    inference(clausify,[status(thm)],[f_3488_3]) ).

fof(f_3489_1,plain,
    ! [V_S_2,V_R_2,V_P_2,T_b] :
      ( c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2))
      | ~ c_Wellfounded_Owf(T_b,V_S_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_S_2),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2)))
      | ~ c_FunDef_Oreduction__pair(T_b,V_P_2) ),
    inference(fof_nnf,[status(thm)],[fact_reduction__pair__lemma]) ).

fof(f_3489_2,plain,
    ! [U_13696,U_13695,U_13694,U_13693] :
      ( c_Wellfounded_Owf(U_13693,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13693,U_13693),tc_HOL_Obool)),U_13695),U_13696))
      | ~ c_Wellfounded_Owf(U_13693,U_13696)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13693,U_13693),tc_HOL_Obool)),U_13696),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(U_13693,U_13693),tc_HOL_Obool),tc_fun(tc_prod(U_13693,U_13693),tc_HOL_Obool)),U_13694)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13693,U_13693),tc_HOL_Obool)),U_13695),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13693,U_13693),tc_HOL_Obool),tc_fun(tc_prod(U_13693,U_13693),tc_HOL_Obool)),U_13694)))
      | ~ c_FunDef_Oreduction__pair(U_13693,U_13694) ),
    inference(variable_rename,[status(thm)],[f_3489_1]) ).

cnf(f_3489_3,plain,
    ( c_Wellfounded_Owf(U_13693,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13693,U_13693),tc_HOL_Obool)),U_13695),U_13696))
    | ~ c_Wellfounded_Owf(U_13693,U_13696)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13693,U_13693),tc_HOL_Obool)),U_13696),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(U_13693,U_13693),tc_HOL_Obool),tc_fun(tc_prod(U_13693,U_13693),tc_HOL_Obool)),U_13694)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13693,U_13693),tc_HOL_Obool)),U_13695),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13693,U_13693),tc_HOL_Obool),tc_fun(tc_prod(U_13693,U_13693),tc_HOL_Obool)),U_13694)))
    | ~ c_FunDef_Oreduction__pair(U_13693,U_13694) ),
    inference(clausify,[status(thm)],[f_3489_2]) ).

fof(f_3490_1,plain,
    ! [V_B_2,V_A_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_c),V_A_2)),hAPP(c_Relation_ODomain(T_b,T_c),V_B_2)))),
    inference(fof_nnf,[status(thm)],[fact_Domain__Int__subset]) ).

fof(f_3490_2,plain,
    ! [U_13700,U_13699,U_13698,U_13697] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13697,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_13697,U_13698),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_13697,U_13698),tc_HOL_Obool)),U_13699),U_13700))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13697,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_13697,U_13698),U_13699)),hAPP(c_Relation_ODomain(U_13697,U_13698),U_13700)))),
    inference(variable_rename,[status(thm)],[f_3490_1]) ).

cnf(f_3490_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13697,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_13697,U_13698),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_13697,U_13698),tc_HOL_Obool)),U_13699),U_13700))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13697,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_13697,U_13698),U_13699)),hAPP(c_Relation_ODomain(U_13697,U_13698),U_13700)))),
    inference(clausify,[status(thm)],[f_3490_2]) ).

fof(f_3491_1,plain,
    ! [V_B_2,V_A_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_c),V_A_2)),hAPP(c_Relation_ODomain(T_b,T_c),V_B_2))),hAPP(c_Relation_ODomain(T_b,T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_A_2),V_B_2)))),
    inference(fof_nnf,[status(thm)],[fact_Domain__Diff__subset]) ).

fof(f_3491_2,plain,
    ! [U_13704,U_13703,U_13702,U_13701] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13701,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13701,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_13701,U_13702),U_13703)),hAPP(c_Relation_ODomain(U_13701,U_13702),U_13704))),hAPP(c_Relation_ODomain(U_13701,U_13702),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_13701,U_13702),tc_HOL_Obool)),U_13703),U_13704)))),
    inference(variable_rename,[status(thm)],[f_3491_1]) ).

cnf(f_3491_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13701,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13701,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_13701,U_13702),U_13703)),hAPP(c_Relation_ODomain(U_13701,U_13702),U_13704))),hAPP(c_Relation_ODomain(U_13701,U_13702),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_13701,U_13702),tc_HOL_Obool)),U_13703),U_13704)))),
    inference(clausify,[status(thm)],[f_3491_2]) ).

fof(f_3492_1,plain,
    ! [V_r_2,T_b] : hAPP(c_Relation_OField(T_b),V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_b),V_r_2)),hAPP(c_Relation_ORange(T_b,T_b),V_r_2)),
    inference(fof_nnf,[status(thm)],[fact_Field__def]) ).

fof(f_3492_2,plain,
    ! [U_13706,U_13705] : hAPP(c_Relation_OField(U_13705),U_13706) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13705,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_13705,U_13705),U_13706)),hAPP(c_Relation_ORange(U_13705,U_13705),U_13706)),
    inference(variable_rename,[status(thm)],[f_3492_1]) ).

cnf(f_3492_3,plain,
    hAPP(c_Relation_OField(U_13705),U_13706) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13705,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_13705,U_13705),U_13706)),hAPP(c_Relation_ORange(U_13705,U_13705),U_13706)),
    inference(clausify,[status(thm)],[f_3492_2]) ).

fof(f_3493_1,plain,
    ! [V_f_2,T_c,V_r_2,T_b] :
      ( c_Wellfounded_Owf(T_c,hAPP(c_Set_Oimage(tc_prod(T_b,T_b),tc_prod(T_c,T_c),c_Product__Type_Omap__pair(T_b,T_c,T_b,T_c,V_f_2,V_f_2)),V_r_2))
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
      | ~ c_Wellfounded_Owf(T_b,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_wf__map__pair__image]) ).

fof(f_3493_2,plain,
    ! [U_13710,U_13709,U_13708,U_13707] :
      ( c_Wellfounded_Owf(U_13709,hAPP(c_Set_Oimage(tc_prod(U_13707,U_13707),tc_prod(U_13709,U_13709),c_Product__Type_Omap__pair(U_13707,U_13709,U_13707,U_13709,U_13710,U_13710)),U_13708))
      | ~ c_Fun_Oinj__on(U_13707,U_13709,U_13710,c_Orderings_Otop__class_Otop(tc_fun(U_13707,tc_HOL_Obool)))
      | ~ c_Wellfounded_Owf(U_13707,U_13708) ),
    inference(variable_rename,[status(thm)],[f_3493_1]) ).

cnf(f_3493_3,plain,
    ( c_Wellfounded_Owf(U_13709,hAPP(c_Set_Oimage(tc_prod(U_13707,U_13707),tc_prod(U_13709,U_13709),c_Product__Type_Omap__pair(U_13707,U_13709,U_13707,U_13709,U_13710,U_13710)),U_13708))
    | ~ c_Fun_Oinj__on(U_13707,U_13709,U_13710,c_Orderings_Otop__class_Otop(tc_fun(U_13707,tc_HOL_Obool)))
    | ~ c_Wellfounded_Owf(U_13707,U_13708) ),
    inference(clausify,[status(thm)],[f_3493_2]) ).

fof(f_3494_1,plain,
    ! [V_S_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_Relation_ODomain(T_b,T_c)),
    inference(fof_nnf,[status(thm)],[fact_Domain__Union]) ).

fof(f_3494_2,plain,
    ! [U_13713,U_13712,U_13711] : hAPP(c_Relation_ODomain(U_13711,U_13712),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(U_13711,U_13712),tc_HOL_Obool),U_13713)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(U_13711,U_13712),tc_HOL_Obool),tc_fun(U_13711,tc_HOL_Obool)),U_13713),c_Relation_ODomain(U_13711,U_13712)),
    inference(variable_rename,[status(thm)],[f_3494_1]) ).

cnf(f_3494_3,plain,
    hAPP(c_Relation_ODomain(U_13711,U_13712),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(U_13711,U_13712),tc_HOL_Obool),U_13713)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(U_13711,U_13712),tc_HOL_Obool),tc_fun(U_13711,tc_HOL_Obool)),U_13713),c_Relation_ODomain(U_13711,U_13712)),
    inference(clausify,[status(thm)],[f_3494_2]) ).

fof(f_3495_1,plain,
    ! [V_x_2,T_b] : c_HOL_OThe(T_b,hAPP(c_fequal,V_x_2)) = V_x_2,
    inference(fof_nnf,[status(thm)],[fact_the__sym__eq__trivial]) ).

fof(f_3495_2,plain,
    ! [U_13715,U_13714] : c_HOL_OThe(U_13714,hAPP(c_fequal,U_13715)) = U_13715,
    inference(variable_rename,[status(thm)],[f_3495_1]) ).

cnf(f_3495_3,plain,
    c_HOL_OThe(U_13714,hAPP(c_fequal,U_13715)) = U_13715,
    inference(clausify,[status(thm)],[f_3495_2]) ).

fof(f_3496_1,plain,
    ! [V_x_2,V_r_2,T_c,T_b] :
      ( ( hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_r_2)),V_x_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) )
      & ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)))
        | ~ hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_r_2)),V_x_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_DomainP__Domain__eq]) ).

fof(f_3496_2,plain,
    ! [U_13719,U_13718,U_13717,U_13716] :
      ( ( hBOOL(hAPP(c_Predicate_ODomainP(U_13716,U_13717,hAPP(hAPP(c_COMBC(U_13716,tc_fun(tc_prod(U_13716,U_13717),tc_HOL_Obool),tc_fun(U_13717,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13717,tc_fun(tc_fun(tc_prod(U_13716,U_13717),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13716,U_13717),tc_HOL_Obool),tc_fun(U_13717,tc_HOL_Obool)),U_13716),c_COMBC(U_13717,tc_fun(tc_prod(U_13716,U_13717),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13717,tc_prod(U_13716,U_13717)),tc_fun(U_13717,tc_fun(tc_fun(tc_prod(U_13716,U_13717),tc_HOL_Obool),tc_HOL_Obool)),U_13716),hAPP(c_COMBB(tc_prod(U_13716,U_13717),tc_fun(tc_fun(tc_prod(U_13716,U_13717),tc_HOL_Obool),tc_HOL_Obool),U_13717),c_member(tc_prod(U_13716,U_13717)))),c_Product__Type_OPair(U_13716,U_13717)))),U_13718)),U_13719))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13716),U_13719),hAPP(c_Relation_ODomain(U_13716,U_13717),U_13718))) )
      & ( hBOOL(hAPP(hAPP(c_member(U_13716),U_13719),hAPP(c_Relation_ODomain(U_13716,U_13717),U_13718)))
        | ~ hBOOL(hAPP(c_Predicate_ODomainP(U_13716,U_13717,hAPP(hAPP(c_COMBC(U_13716,tc_fun(tc_prod(U_13716,U_13717),tc_HOL_Obool),tc_fun(U_13717,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13717,tc_fun(tc_fun(tc_prod(U_13716,U_13717),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13716,U_13717),tc_HOL_Obool),tc_fun(U_13717,tc_HOL_Obool)),U_13716),c_COMBC(U_13717,tc_fun(tc_prod(U_13716,U_13717),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13717,tc_prod(U_13716,U_13717)),tc_fun(U_13717,tc_fun(tc_fun(tc_prod(U_13716,U_13717),tc_HOL_Obool),tc_HOL_Obool)),U_13716),hAPP(c_COMBB(tc_prod(U_13716,U_13717),tc_fun(tc_fun(tc_prod(U_13716,U_13717),tc_HOL_Obool),tc_HOL_Obool),U_13717),c_member(tc_prod(U_13716,U_13717)))),c_Product__Type_OPair(U_13716,U_13717)))),U_13718)),U_13719)) ) ),
    inference(variable_rename,[status(thm)],[f_3496_1]) ).

fof(f_3496_3,plain,
    ( ! [U_13727,U_13725,U_13723,U_13721] :
        ( hBOOL(hAPP(c_Predicate_ODomainP(U_13721,U_13723,hAPP(hAPP(c_COMBC(U_13721,tc_fun(tc_prod(U_13721,U_13723),tc_HOL_Obool),tc_fun(U_13723,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13723,tc_fun(tc_fun(tc_prod(U_13721,U_13723),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13721,U_13723),tc_HOL_Obool),tc_fun(U_13723,tc_HOL_Obool)),U_13721),c_COMBC(U_13723,tc_fun(tc_prod(U_13721,U_13723),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13723,tc_prod(U_13721,U_13723)),tc_fun(U_13723,tc_fun(tc_fun(tc_prod(U_13721,U_13723),tc_HOL_Obool),tc_HOL_Obool)),U_13721),hAPP(c_COMBB(tc_prod(U_13721,U_13723),tc_fun(tc_fun(tc_prod(U_13721,U_13723),tc_HOL_Obool),tc_HOL_Obool),U_13723),c_member(tc_prod(U_13721,U_13723)))),c_Product__Type_OPair(U_13721,U_13723)))),U_13725)),U_13727))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13721),U_13727),hAPP(c_Relation_ODomain(U_13721,U_13723),U_13725))) )
    & ! [U_13726,U_13724,U_13722,U_13720] :
        ( hBOOL(hAPP(hAPP(c_member(U_13720),U_13726),hAPP(c_Relation_ODomain(U_13720,U_13722),U_13724)))
        | ~ hBOOL(hAPP(c_Predicate_ODomainP(U_13720,U_13722,hAPP(hAPP(c_COMBC(U_13720,tc_fun(tc_prod(U_13720,U_13722),tc_HOL_Obool),tc_fun(U_13722,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13722,tc_fun(tc_fun(tc_prod(U_13720,U_13722),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13720,U_13722),tc_HOL_Obool),tc_fun(U_13722,tc_HOL_Obool)),U_13720),c_COMBC(U_13722,tc_fun(tc_prod(U_13720,U_13722),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13722,tc_prod(U_13720,U_13722)),tc_fun(U_13722,tc_fun(tc_fun(tc_prod(U_13720,U_13722),tc_HOL_Obool),tc_HOL_Obool)),U_13720),hAPP(c_COMBB(tc_prod(U_13720,U_13722),tc_fun(tc_fun(tc_prod(U_13720,U_13722),tc_HOL_Obool),tc_HOL_Obool),U_13722),c_member(tc_prod(U_13720,U_13722)))),c_Product__Type_OPair(U_13720,U_13722)))),U_13724)),U_13726)) ) ),
    inference(miniscope,[status(thm)],[f_3496_2]) ).

cnf(f_3496_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13720),U_13726),hAPP(c_Relation_ODomain(U_13720,U_13722),U_13724)))
    | ~ hBOOL(hAPP(c_Predicate_ODomainP(U_13720,U_13722,hAPP(hAPP(c_COMBC(U_13720,tc_fun(tc_prod(U_13720,U_13722),tc_HOL_Obool),tc_fun(U_13722,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13722,tc_fun(tc_fun(tc_prod(U_13720,U_13722),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13720,U_13722),tc_HOL_Obool),tc_fun(U_13722,tc_HOL_Obool)),U_13720),c_COMBC(U_13722,tc_fun(tc_prod(U_13720,U_13722),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13722,tc_prod(U_13720,U_13722)),tc_fun(U_13722,tc_fun(tc_fun(tc_prod(U_13720,U_13722),tc_HOL_Obool),tc_HOL_Obool)),U_13720),hAPP(c_COMBB(tc_prod(U_13720,U_13722),tc_fun(tc_fun(tc_prod(U_13720,U_13722),tc_HOL_Obool),tc_HOL_Obool),U_13722),c_member(tc_prod(U_13720,U_13722)))),c_Product__Type_OPair(U_13720,U_13722)))),U_13724)),U_13726)) ),
    inference(clausify,[status(thm)],[f_3496_3]) ).

cnf(f_3496_5,plain,
    ( hBOOL(hAPP(c_Predicate_ODomainP(U_13721,U_13723,hAPP(hAPP(c_COMBC(U_13721,tc_fun(tc_prod(U_13721,U_13723),tc_HOL_Obool),tc_fun(U_13723,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13723,tc_fun(tc_fun(tc_prod(U_13721,U_13723),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13721,U_13723),tc_HOL_Obool),tc_fun(U_13723,tc_HOL_Obool)),U_13721),c_COMBC(U_13723,tc_fun(tc_prod(U_13721,U_13723),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13723,tc_prod(U_13721,U_13723)),tc_fun(U_13723,tc_fun(tc_fun(tc_prod(U_13721,U_13723),tc_HOL_Obool),tc_HOL_Obool)),U_13721),hAPP(c_COMBB(tc_prod(U_13721,U_13723),tc_fun(tc_fun(tc_prod(U_13721,U_13723),tc_HOL_Obool),tc_HOL_Obool),U_13723),c_member(tc_prod(U_13721,U_13723)))),c_Product__Type_OPair(U_13721,U_13723)))),U_13725)),U_13727))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13721),U_13727),hAPP(c_Relation_ODomain(U_13721,U_13723),U_13725))) ),
    inference(clausify,[status(thm)],[f_3496_3]) ).

fof(f_3497_1,plain,
    ! [V_r_2,T_b] :
      ( c_Wellfounded_Owf(tc_List_Olist(T_b),c_List_Olenlex(T_b,V_r_2))
      | ~ c_Wellfounded_Owf(T_b,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_wf__lenlex]) ).

fof(f_3497_2,plain,
    ! [U_13729,U_13728] :
      ( c_Wellfounded_Owf(tc_List_Olist(U_13728),c_List_Olenlex(U_13728,U_13729))
      | ~ c_Wellfounded_Owf(U_13728,U_13729) ),
    inference(variable_rename,[status(thm)],[f_3497_1]) ).

cnf(f_3497_3,plain,
    ( c_Wellfounded_Owf(tc_List_Olist(U_13728),c_List_Olenlex(U_13728,U_13729))
    | ~ c_Wellfounded_Owf(U_13728,U_13729) ),
    inference(clausify,[status(thm)],[f_3497_2]) ).

fof(f_3498_1,plain,
    ! [V_r_2,T_c,V_a_2,T_b] :
      ( ? [B_y] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),B_y)),V_r_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_DomainE]) ).

fof(f_3498_2,plain,
    ! [U_13734,U_13733,U_13732,U_13731] :
      ( ? [U_13730] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_13731,U_13733)),hAPP(hAPP(c_Product__Type_OPair(U_13731,U_13733),U_13732),U_13730)),U_13734))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13731),U_13732),hAPP(c_Relation_ODomain(U_13731,U_13733),U_13734))) ),
    inference(variable_rename,[status(thm)],[f_3498_1]) ).

fof(f_3498_3,plain,
    ! [U_13734,U_13733,U_13732,U_13731] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13731,U_13733)),hAPP(hAPP(c_Product__Type_OPair(U_13731,U_13733),U_13732),sK326(U_13734,U_13733,U_13732,U_13731))),U_13734))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13731),U_13732),hAPP(c_Relation_ODomain(U_13731,U_13733),U_13734))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK326]),skolemize(U_13730,sK326(U_13734,U_13733,U_13732,U_13731))],[f_3498_2]) ).

cnf(f_3498_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13731,U_13733)),hAPP(hAPP(c_Product__Type_OPair(U_13731,U_13733),U_13732),sK326(U_13734,U_13733,U_13732,U_13731))),U_13734))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13731),U_13732),hAPP(c_Relation_ODomain(U_13731,U_13733),U_13734))) ),
    inference(clausify,[status(thm)],[f_3498_3]) ).

fof(f_3499_1,plain,
    ! [T_c,T_b,V_b_2,V_a_2,V_r_2] :
      ( hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a_2))
      | ~ hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) ),
    inference(fof_nnf,[status(thm)],[fact_DomainP_Ointros]) ).

fof(f_3499_2,plain,
    ! [U_13739,U_13738,U_13737,U_13736,U_13735] :
      ( hBOOL(hAPP(c_Predicate_ODomainP(U_13738,U_13739,U_13735),U_13736))
      | ~ hBOOL(hAPP(hAPP(U_13735,U_13736),U_13737)) ),
    inference(variable_rename,[status(thm)],[f_3499_1]) ).

cnf(f_3499_3,plain,
    ( hBOOL(hAPP(c_Predicate_ODomainP(U_13738,U_13739,U_13735),U_13736))
    | ~ hBOOL(hAPP(hAPP(U_13735,U_13736),U_13737)) ),
    inference(clausify,[status(thm)],[f_3499_2]) ).

fof(f_3500_1,plain,
    ! [V_a1_2,V_r_2,T_c,T_b] :
      ( ( hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a1_2))
        | ! [B_x1] : ~ hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_x1)) )
      & ( ? [B_x1] : hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_x1))
        | ~ hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a1_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_DomainP_Oequations]) ).

fof(f_3500_2,plain,
    ! [U_13745,U_13744,U_13743,U_13742] :
      ( ( hBOOL(hAPP(c_Predicate_ODomainP(U_13742,U_13743,U_13744),U_13745))
        | ! [U_13741] : ~ hBOOL(hAPP(hAPP(U_13744,U_13745),U_13741)) )
      & ( ? [U_13740] : hBOOL(hAPP(hAPP(U_13744,U_13745),U_13740))
        | ~ hBOOL(hAPP(c_Predicate_ODomainP(U_13742,U_13743,U_13744),U_13745)) ) ),
    inference(variable_rename,[status(thm)],[f_3500_1]) ).

fof(f_3500_3,plain,
    ( ! [U_13753,U_13751] :
        ( ! [U_13749,U_13747] : hBOOL(hAPP(c_Predicate_ODomainP(U_13747,U_13749,U_13751),U_13753))
        | ! [U_13741] : ~ hBOOL(hAPP(hAPP(U_13751,U_13753),U_13741)) )
    & ! [U_13752,U_13750] :
        ( ! [U_13748,U_13746] : ~ hBOOL(hAPP(c_Predicate_ODomainP(U_13746,U_13748,U_13750),U_13752))
        | ? [U_13740] : hBOOL(hAPP(hAPP(U_13750,U_13752),U_13740)) ) ),
    inference(miniscope,[status(thm)],[f_3500_2]) ).

fof(f_3500_4,plain,
    ( ! [U_13753,U_13751] :
        ( ! [U_13749,U_13747] : hBOOL(hAPP(c_Predicate_ODomainP(U_13747,U_13749,U_13751),U_13753))
        | ! [U_13741] : ~ hBOOL(hAPP(hAPP(U_13751,U_13753),U_13741)) )
    & ! [U_13752,U_13750] :
        ( ! [U_13748,U_13746] : ~ hBOOL(hAPP(c_Predicate_ODomainP(U_13746,U_13748,U_13750),U_13752))
        | hBOOL(hAPP(hAPP(U_13750,U_13752),sK327(U_13752,U_13750))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK327]),skolemize(U_13740,sK327(U_13752,U_13750))],[f_3500_3]) ).

cnf(f_3500_5,plain,
    ( ~ hBOOL(hAPP(c_Predicate_ODomainP(U_13746,U_13748,U_13750),U_13752))
    | hBOOL(hAPP(hAPP(U_13750,U_13752),sK327(U_13752,U_13750))) ),
    inference(clausify,[status(thm)],[f_3500_4]) ).

cnf(f_3500_6,plain,
    ( hBOOL(hAPP(c_Predicate_ODomainP(U_13747,U_13749,U_13751),U_13753))
    | ~ hBOOL(hAPP(hAPP(U_13751,U_13753),U_13741)) ),
    inference(clausify,[status(thm)],[f_3500_4]) ).

fof(f_3501_1,plain,
    c_Wellfounded_Opred__nat = hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_fequal)),c_Nat_OSuc))),
    inference(fof_nnf,[status(thm)],[fact_pred__nat__def]) ).

cnf(f_3501_2,plain,
    c_Wellfounded_Opred__nat = hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_fequal)),c_Nat_OSuc))),
    inference(clausify,[status(thm)],[f_3501_1]) ).

fof(f_3502_1,plain,
    ! [V_r_2,T_b] :
      ( c_Wellfounded_Owf(tc_List_Olist(T_b),c_List_Olex(T_b,V_r_2))
      | ~ c_Wellfounded_Owf(T_b,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_wf__lex]) ).

fof(f_3502_2,plain,
    ! [U_13755,U_13754] :
      ( c_Wellfounded_Owf(tc_List_Olist(U_13754),c_List_Olex(U_13754,U_13755))
      | ~ c_Wellfounded_Owf(U_13754,U_13755) ),
    inference(variable_rename,[status(thm)],[f_3502_1]) ).

cnf(f_3502_3,plain,
    ( c_Wellfounded_Owf(tc_List_Olist(U_13754),c_List_Olex(U_13754,U_13755))
    | ~ c_Wellfounded_Owf(U_13754,U_13755) ),
    inference(clausify,[status(thm)],[f_3502_2]) ).

fof(f_3503_1,plain,
    ! [V_n_2,V_r_2,T_b] :
      ( c_Wellfounded_Owf(tc_List_Olist(T_b),hAPP(c_List_Olexn(T_b,V_r_2),V_n_2))
      | ~ c_Wellfounded_Owf(T_b,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_wf__lexn]) ).

fof(f_3503_2,plain,
    ! [U_13758,U_13757,U_13756] :
      ( c_Wellfounded_Owf(tc_List_Olist(U_13756),hAPP(c_List_Olexn(U_13756,U_13757),U_13758))
      | ~ c_Wellfounded_Owf(U_13756,U_13757) ),
    inference(variable_rename,[status(thm)],[f_3503_1]) ).

cnf(f_3503_3,plain,
    ( c_Wellfounded_Owf(tc_List_Olist(U_13756),hAPP(c_List_Olexn(U_13756,U_13757),U_13758))
    | ~ c_Wellfounded_Owf(U_13756,U_13757) ),
    inference(clausify,[status(thm)],[f_3503_2]) ).

fof(f_3504_1,plain,
    ! [V_r_2,T_b] : c_List_Olex(T_b,V_r_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_List_Olexn(T_b,V_r_2)),
    inference(fof_nnf,[status(thm)],[fact_lex__def]) ).

fof(f_3504_2,plain,
    ! [U_13760,U_13759] : c_List_Olex(U_13759,U_13760) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(tc_List_Olist(U_13759),tc_List_Olist(U_13759)),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_List_Olexn(U_13759,U_13760)),
    inference(variable_rename,[status(thm)],[f_3504_1]) ).

cnf(f_3504_3,plain,
    c_List_Olex(U_13759,U_13760) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(tc_List_Olist(U_13759),tc_List_Olist(U_13759)),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_List_Olexn(U_13759,U_13760)),
    inference(clausify,[status(thm)],[f_3504_2]) ).

fof(f_3505_1,plain,
    ! [V_r_2,T_b] : hAPP(c_List_Olexn(T_b,V_r_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_lexn_Osimps_I1_J]) ).

fof(f_3505_2,plain,
    ! [U_13762,U_13761] : hAPP(c_List_Olexn(U_13761,U_13762),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(U_13761),tc_List_Olist(U_13761)),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3505_1]) ).

cnf(f_3505_3,plain,
    hAPP(c_List_Olexn(U_13761,U_13762),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(U_13761),tc_List_Olist(U_13761)),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3505_2]) ).

fof(f_3506_1,plain,
    c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat),
    inference(fof_nnf,[status(thm)],[fact_wf__pred__nat]) ).

cnf(f_3506_2,plain,
    c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat),
    inference(clausify,[status(thm)],[f_3506_1]) ).

fof(f_3507_1,plain,
    ! [T_b,V_R_2,T_c,V_P_2] :
      ( c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Recdef_Osame__fst(T_b,T_c,V_P_2,V_R_2))
      | ? [B_x] :
          ( ~ c_Wellfounded_Owf(T_c,hAPP(V_R_2,B_x))
          & hBOOL(hAPP(V_P_2,B_x)) ) ),
    inference(fof_nnf,[status(thm)],[fact_wf__same__fst]) ).

fof(f_3507_2,plain,
    ! [U_13767,U_13766,U_13765,U_13764] :
      ( c_Wellfounded_Owf(tc_prod(U_13767,U_13765),c_Recdef_Osame__fst(U_13767,U_13765,U_13764,U_13766))
      | ? [U_13763] :
          ( ~ c_Wellfounded_Owf(U_13765,hAPP(U_13766,U_13763))
          & hBOOL(hAPP(U_13764,U_13763)) ) ),
    inference(variable_rename,[status(thm)],[f_3507_1]) ).

fof(f_3507_3,plain,
    ! [U_13767,U_13766,U_13765,U_13764] :
      ( c_Wellfounded_Owf(tc_prod(U_13767,U_13765),c_Recdef_Osame__fst(U_13767,U_13765,U_13764,U_13766))
      | ( ~ c_Wellfounded_Owf(U_13765,hAPP(U_13766,sK328(U_13767,U_13766,U_13765,U_13764)))
        & hBOOL(hAPP(U_13764,sK328(U_13767,U_13766,U_13765,U_13764))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK328]),skolemize(U_13763,sK328(U_13767,U_13766,U_13765,U_13764))],[f_3507_2]) ).

cnf(f_3507_4,plain,
    ( hBOOL(hAPP(U_13764,sK328(U_13767,U_13766,U_13765,U_13764)))
    | c_Wellfounded_Owf(tc_prod(U_13767,U_13765),c_Recdef_Osame__fst(U_13767,U_13765,U_13764,U_13766)) ),
    inference(clausify,[status(thm)],[f_3507_3]) ).

cnf(f_3507_5,plain,
    ( ~ c_Wellfounded_Owf(U_13765,hAPP(U_13766,sK328(U_13767,U_13766,U_13765,U_13764)))
    | c_Wellfounded_Owf(tc_prod(U_13767,U_13765),c_Recdef_Osame__fst(U_13767,U_13765,U_13764,U_13766)) ),
    inference(clausify,[status(thm)],[f_3507_3]) ).

fof(f_3508_1,plain,
    ! [T_b,V_g_2,V_f_2,V_P_2] :
      ( c_Wellfounded_Owf(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_P_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),V_g_2)))))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,hAPP(V_g_2,B_x))),hAPP(V_f_2,B_x)))
          & hBOOL(hAPP(V_P_2,B_x)) ) ),
    inference(fof_nnf,[status(thm)],[fact_wf__if__measure]) ).

fof(f_3508_2,plain,
    ! [U_13772,U_13771,U_13770,U_13769] :
      ( c_Wellfounded_Owf(U_13772,hAPP(c_Set_OCollect(tc_prod(U_13772,U_13772)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13772,U_13772,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_13772,tc_HOL_Obool),tc_fun(U_13772,tc_HOL_Obool),U_13772),hAPP(c_COMBS(U_13772,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13772),c_fconj),U_13769))),hAPP(hAPP(c_COMBC(U_13772,tc_fun(U_13772,U_13772),tc_fun(U_13772,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13772,tc_HOL_Obool),tc_fun(tc_fun(U_13772,U_13772),tc_fun(U_13772,tc_HOL_Obool)),U_13772),c_COMBB(U_13772,tc_HOL_Obool,U_13772)),c_fequal)),U_13771)))))
      | ? [U_13768] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_13770,hAPP(U_13771,U_13768))),hAPP(U_13770,U_13768)))
          & hBOOL(hAPP(U_13769,U_13768)) ) ),
    inference(variable_rename,[status(thm)],[f_3508_1]) ).

fof(f_3508_3,plain,
    ! [U_13772,U_13771,U_13770,U_13769] :
      ( c_Wellfounded_Owf(U_13772,hAPP(c_Set_OCollect(tc_prod(U_13772,U_13772)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13772,U_13772,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_13772,tc_HOL_Obool),tc_fun(U_13772,tc_HOL_Obool),U_13772),hAPP(c_COMBS(U_13772,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13772),c_fconj),U_13769))),hAPP(hAPP(c_COMBC(U_13772,tc_fun(U_13772,U_13772),tc_fun(U_13772,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13772,tc_HOL_Obool),tc_fun(tc_fun(U_13772,U_13772),tc_fun(U_13772,tc_HOL_Obool)),U_13772),c_COMBB(U_13772,tc_HOL_Obool,U_13772)),c_fequal)),U_13771)))))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_13770,hAPP(U_13771,sK329(U_13772,U_13771,U_13770,U_13769)))),hAPP(U_13770,sK329(U_13772,U_13771,U_13770,U_13769))))
        & hBOOL(hAPP(U_13769,sK329(U_13772,U_13771,U_13770,U_13769))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK329]),skolemize(U_13768,sK329(U_13772,U_13771,U_13770,U_13769))],[f_3508_2]) ).

cnf(f_3508_4,plain,
    ( hBOOL(hAPP(U_13769,sK329(U_13772,U_13771,U_13770,U_13769)))
    | c_Wellfounded_Owf(U_13772,hAPP(c_Set_OCollect(tc_prod(U_13772,U_13772)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13772,U_13772,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_13772,tc_HOL_Obool),tc_fun(U_13772,tc_HOL_Obool),U_13772),hAPP(c_COMBS(U_13772,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13772),c_fconj),U_13769))),hAPP(hAPP(c_COMBC(U_13772,tc_fun(U_13772,U_13772),tc_fun(U_13772,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13772,tc_HOL_Obool),tc_fun(tc_fun(U_13772,U_13772),tc_fun(U_13772,tc_HOL_Obool)),U_13772),c_COMBB(U_13772,tc_HOL_Obool,U_13772)),c_fequal)),U_13771))))) ),
    inference(clausify,[status(thm)],[f_3508_3]) ).

cnf(f_3508_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_13770,hAPP(U_13771,sK329(U_13772,U_13771,U_13770,U_13769)))),hAPP(U_13770,sK329(U_13772,U_13771,U_13770,U_13769))))
    | c_Wellfounded_Owf(U_13772,hAPP(c_Set_OCollect(tc_prod(U_13772,U_13772)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13772,U_13772,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_13772,tc_HOL_Obool),tc_fun(U_13772,tc_HOL_Obool),U_13772),hAPP(c_COMBS(U_13772,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13772),c_fconj),U_13769))),hAPP(hAPP(c_COMBC(U_13772,tc_fun(U_13772,U_13772),tc_fun(U_13772,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13772,tc_HOL_Obool),tc_fun(tc_fun(U_13772,U_13772),tc_fun(U_13772,tc_HOL_Obool)),U_13772),c_COMBB(U_13772,tc_HOL_Obool,U_13772)),c_fequal)),U_13771))))) ),
    inference(clausify,[status(thm)],[f_3508_3]) ).

fof(f_3509_1,plain,
    ! [V_r_2,T_b] :
      ( ( c_Wellfounded_OwfP(T_b,V_r_2)
        | ~ c_Wellfounded_Owf(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))) )
      & ( c_Wellfounded_Owf(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2)))
        | ~ c_Wellfounded_OwfP(T_b,V_r_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_wfP__def]) ).

fof(f_3509_2,plain,
    ! [U_13774,U_13773] :
      ( ( c_Wellfounded_OwfP(U_13773,U_13774)
        | ~ c_Wellfounded_Owf(U_13773,hAPP(c_Set_OCollect(tc_prod(U_13773,U_13773)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13773,U_13773,tc_HOL_Obool),U_13774))) )
      & ( c_Wellfounded_Owf(U_13773,hAPP(c_Set_OCollect(tc_prod(U_13773,U_13773)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13773,U_13773,tc_HOL_Obool),U_13774)))
        | ~ c_Wellfounded_OwfP(U_13773,U_13774) ) ),
    inference(variable_rename,[status(thm)],[f_3509_1]) ).

fof(f_3509_3,plain,
    ( ! [U_13778,U_13776] :
        ( c_Wellfounded_OwfP(U_13776,U_13778)
        | ~ c_Wellfounded_Owf(U_13776,hAPP(c_Set_OCollect(tc_prod(U_13776,U_13776)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13776,U_13776,tc_HOL_Obool),U_13778))) )
    & ! [U_13777,U_13775] :
        ( c_Wellfounded_Owf(U_13775,hAPP(c_Set_OCollect(tc_prod(U_13775,U_13775)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13775,U_13775,tc_HOL_Obool),U_13777)))
        | ~ c_Wellfounded_OwfP(U_13775,U_13777) ) ),
    inference(miniscope,[status(thm)],[f_3509_2]) ).

cnf(f_3509_4,plain,
    ( c_Wellfounded_Owf(U_13775,hAPP(c_Set_OCollect(tc_prod(U_13775,U_13775)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13775,U_13775,tc_HOL_Obool),U_13777)))
    | ~ c_Wellfounded_OwfP(U_13775,U_13777) ),
    inference(clausify,[status(thm)],[f_3509_3]) ).

cnf(f_3509_5,plain,
    ( c_Wellfounded_OwfP(U_13776,U_13778)
    | ~ c_Wellfounded_Owf(U_13776,hAPP(c_Set_OCollect(tc_prod(U_13776,U_13776)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13776,U_13776,tc_HOL_Obool),U_13778))) ),
    inference(clausify,[status(thm)],[f_3509_3]) ).

fof(f_3510_1,plain,
    ! [T_b] : c_Wellfounded_OwfP(T_b,hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBK(tc_HOL_Obool,T_b),c_fFalse))),
    inference(fof_nnf,[status(thm)],[fact_wfP__empty]) ).

fof(f_3510_2,plain,
    ! [U_13779] : c_Wellfounded_OwfP(U_13779,hAPP(c_COMBK(tc_fun(U_13779,tc_HOL_Obool),U_13779),hAPP(c_COMBK(tc_HOL_Obool,U_13779),c_fFalse))),
    inference(variable_rename,[status(thm)],[f_3510_1]) ).

cnf(f_3510_3,plain,
    c_Wellfounded_OwfP(U_13779,hAPP(c_COMBK(tc_fun(U_13779,tc_HOL_Obool),U_13779),hAPP(c_COMBK(tc_HOL_Obool,U_13779),c_fFalse))),
    inference(clausify,[status(thm)],[f_3510_2]) ).

fof(f_3511_1,plain,
    ! [V_x_2,V_r_2,T_b] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_x_2))
      | ~ c_Wellfounded_OwfP(T_b,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_accp__wfPD]) ).

fof(f_3511_2,plain,
    ! [U_13782,U_13781,U_13780] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_13780,U_13781),U_13782))
      | ~ c_Wellfounded_OwfP(U_13780,U_13781) ),
    inference(variable_rename,[status(thm)],[f_3511_1]) ).

cnf(f_3511_3,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_13780,U_13781),U_13782))
    | ~ c_Wellfounded_OwfP(U_13780,U_13781) ),
    inference(clausify,[status(thm)],[f_3511_2]) ).

fof(f_3512_1,plain,
    ! [V_r_2,T_b] :
      ( ( c_Wellfounded_OwfP(T_b,V_r_2)
        | ? [B_x1] : ~ hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x1)) )
      & ( ! [B_x1] : hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x1))
        | ~ c_Wellfounded_OwfP(T_b,V_r_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_wfP__accp__iff]) ).

fof(f_3512_2,plain,
    ! [U_13786,U_13785] :
      ( ( c_Wellfounded_OwfP(U_13785,U_13786)
        | ? [U_13784] : ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_13785,U_13786),U_13784)) )
      & ( ! [U_13783] : hBOOL(hAPP(c_Wellfounded_Oaccp(U_13785,U_13786),U_13783))
        | ~ c_Wellfounded_OwfP(U_13785,U_13786) ) ),
    inference(variable_rename,[status(thm)],[f_3512_1]) ).

fof(f_3512_3,plain,
    ( ! [U_13790,U_13788] :
        ( c_Wellfounded_OwfP(U_13788,U_13790)
        | ? [U_13784] : ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_13788,U_13790),U_13784)) )
    & ! [U_13789,U_13787] :
        ( ! [U_13783] : hBOOL(hAPP(c_Wellfounded_Oaccp(U_13787,U_13789),U_13783))
        | ~ c_Wellfounded_OwfP(U_13787,U_13789) ) ),
    inference(miniscope,[status(thm)],[f_3512_2]) ).

fof(f_3512_4,plain,
    ( ! [U_13790,U_13788] :
        ( c_Wellfounded_OwfP(U_13788,U_13790)
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_13788,U_13790),sK330(U_13790,U_13788))) )
    & ! [U_13789,U_13787] :
        ( ! [U_13783] : hBOOL(hAPP(c_Wellfounded_Oaccp(U_13787,U_13789),U_13783))
        | ~ c_Wellfounded_OwfP(U_13787,U_13789) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK330]),skolemize(U_13784,sK330(U_13790,U_13788))],[f_3512_3]) ).

cnf(f_3512_5,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_13787,U_13789),U_13783))
    | ~ c_Wellfounded_OwfP(U_13787,U_13789) ),
    inference(clausify,[status(thm)],[f_3512_4]) ).

cnf(f_3512_6,plain,
    ( c_Wellfounded_OwfP(U_13788,U_13790)
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_13788,U_13790),sK330(U_13790,U_13788))) ),
    inference(clausify,[status(thm)],[f_3512_4]) ).

fof(f_3513_1,plain,
    ! [V_p_2,V_r_2,T_b] :
      ( c_Wellfounded_OwfP(T_b,V_p_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),V_p_2),V_r_2))
      | ~ c_Wellfounded_OwfP(T_b,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_wfP__subset]) ).

fof(f_3513_2,plain,
    ! [U_13793,U_13792,U_13791] :
      ( c_Wellfounded_OwfP(U_13791,U_13793)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13791,tc_fun(U_13791,tc_HOL_Obool))),U_13793),U_13792))
      | ~ c_Wellfounded_OwfP(U_13791,U_13792) ),
    inference(variable_rename,[status(thm)],[f_3513_1]) ).

cnf(f_3513_3,plain,
    ( c_Wellfounded_OwfP(U_13791,U_13793)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13791,tc_fun(U_13791,tc_HOL_Obool))),U_13793),U_13792))
    | ~ c_Wellfounded_OwfP(U_13791,U_13792) ),
    inference(clausify,[status(thm)],[f_3513_2]) ).

fof(f_3514_1,plain,
    ! [V_R_2,T_b] :
      ( c_Wellfounded_OwfP(T_b,c_FunDef_Oin__rel(T_b,T_b,V_R_2))
      | ~ c_Wellfounded_Owf(T_b,V_R_2) ),
    inference(fof_nnf,[status(thm)],[fact_wf__in__rel]) ).

fof(f_3514_2,plain,
    ! [U_13795,U_13794] :
      ( c_Wellfounded_OwfP(U_13794,c_FunDef_Oin__rel(U_13794,U_13794,U_13795))
      | ~ c_Wellfounded_Owf(U_13794,U_13795) ),
    inference(variable_rename,[status(thm)],[f_3514_1]) ).

cnf(f_3514_3,plain,
    ( c_Wellfounded_OwfP(U_13794,c_FunDef_Oin__rel(U_13794,U_13794,U_13795))
    | ~ c_Wellfounded_Owf(U_13794,U_13795) ),
    inference(clausify,[status(thm)],[f_3514_2]) ).

fof(f_3515_1,plain,
    ! [V_r_2,T_b] :
      ( ( c_Wellfounded_OwfP(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2))
        | ~ c_Wellfounded_Owf(T_b,V_r_2) )
      & ( c_Wellfounded_Owf(T_b,V_r_2)
        | ~ c_Wellfounded_OwfP(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_wfP__wf__eq]) ).

fof(f_3515_2,plain,
    ! [U_13797,U_13796] :
      ( ( c_Wellfounded_OwfP(U_13796,hAPP(hAPP(c_COMBC(U_13796,tc_fun(tc_prod(U_13796,U_13796),tc_HOL_Obool),tc_fun(U_13796,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13796,tc_fun(tc_fun(tc_prod(U_13796,U_13796),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13796,U_13796),tc_HOL_Obool),tc_fun(U_13796,tc_HOL_Obool)),U_13796),c_COMBC(U_13796,tc_fun(tc_prod(U_13796,U_13796),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13796,tc_prod(U_13796,U_13796)),tc_fun(U_13796,tc_fun(tc_fun(tc_prod(U_13796,U_13796),tc_HOL_Obool),tc_HOL_Obool)),U_13796),hAPP(c_COMBB(tc_prod(U_13796,U_13796),tc_fun(tc_fun(tc_prod(U_13796,U_13796),tc_HOL_Obool),tc_HOL_Obool),U_13796),c_member(tc_prod(U_13796,U_13796)))),c_Product__Type_OPair(U_13796,U_13796)))),U_13797))
        | ~ c_Wellfounded_Owf(U_13796,U_13797) )
      & ( c_Wellfounded_Owf(U_13796,U_13797)
        | ~ c_Wellfounded_OwfP(U_13796,hAPP(hAPP(c_COMBC(U_13796,tc_fun(tc_prod(U_13796,U_13796),tc_HOL_Obool),tc_fun(U_13796,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13796,tc_fun(tc_fun(tc_prod(U_13796,U_13796),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13796,U_13796),tc_HOL_Obool),tc_fun(U_13796,tc_HOL_Obool)),U_13796),c_COMBC(U_13796,tc_fun(tc_prod(U_13796,U_13796),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13796,tc_prod(U_13796,U_13796)),tc_fun(U_13796,tc_fun(tc_fun(tc_prod(U_13796,U_13796),tc_HOL_Obool),tc_HOL_Obool)),U_13796),hAPP(c_COMBB(tc_prod(U_13796,U_13796),tc_fun(tc_fun(tc_prod(U_13796,U_13796),tc_HOL_Obool),tc_HOL_Obool),U_13796),c_member(tc_prod(U_13796,U_13796)))),c_Product__Type_OPair(U_13796,U_13796)))),U_13797)) ) ),
    inference(variable_rename,[status(thm)],[f_3515_1]) ).

fof(f_3515_3,plain,
    ( ! [U_13801,U_13799] :
        ( c_Wellfounded_OwfP(U_13799,hAPP(hAPP(c_COMBC(U_13799,tc_fun(tc_prod(U_13799,U_13799),tc_HOL_Obool),tc_fun(U_13799,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13799,tc_fun(tc_fun(tc_prod(U_13799,U_13799),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13799,U_13799),tc_HOL_Obool),tc_fun(U_13799,tc_HOL_Obool)),U_13799),c_COMBC(U_13799,tc_fun(tc_prod(U_13799,U_13799),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13799,tc_prod(U_13799,U_13799)),tc_fun(U_13799,tc_fun(tc_fun(tc_prod(U_13799,U_13799),tc_HOL_Obool),tc_HOL_Obool)),U_13799),hAPP(c_COMBB(tc_prod(U_13799,U_13799),tc_fun(tc_fun(tc_prod(U_13799,U_13799),tc_HOL_Obool),tc_HOL_Obool),U_13799),c_member(tc_prod(U_13799,U_13799)))),c_Product__Type_OPair(U_13799,U_13799)))),U_13801))
        | ~ c_Wellfounded_Owf(U_13799,U_13801) )
    & ! [U_13800,U_13798] :
        ( c_Wellfounded_Owf(U_13798,U_13800)
        | ~ c_Wellfounded_OwfP(U_13798,hAPP(hAPP(c_COMBC(U_13798,tc_fun(tc_prod(U_13798,U_13798),tc_HOL_Obool),tc_fun(U_13798,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13798,tc_fun(tc_fun(tc_prod(U_13798,U_13798),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13798,U_13798),tc_HOL_Obool),tc_fun(U_13798,tc_HOL_Obool)),U_13798),c_COMBC(U_13798,tc_fun(tc_prod(U_13798,U_13798),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13798,tc_prod(U_13798,U_13798)),tc_fun(U_13798,tc_fun(tc_fun(tc_prod(U_13798,U_13798),tc_HOL_Obool),tc_HOL_Obool)),U_13798),hAPP(c_COMBB(tc_prod(U_13798,U_13798),tc_fun(tc_fun(tc_prod(U_13798,U_13798),tc_HOL_Obool),tc_HOL_Obool),U_13798),c_member(tc_prod(U_13798,U_13798)))),c_Product__Type_OPair(U_13798,U_13798)))),U_13800)) ) ),
    inference(miniscope,[status(thm)],[f_3515_2]) ).

cnf(f_3515_4,plain,
    ( c_Wellfounded_Owf(U_13798,U_13800)
    | ~ c_Wellfounded_OwfP(U_13798,hAPP(hAPP(c_COMBC(U_13798,tc_fun(tc_prod(U_13798,U_13798),tc_HOL_Obool),tc_fun(U_13798,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13798,tc_fun(tc_fun(tc_prod(U_13798,U_13798),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13798,U_13798),tc_HOL_Obool),tc_fun(U_13798,tc_HOL_Obool)),U_13798),c_COMBC(U_13798,tc_fun(tc_prod(U_13798,U_13798),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13798,tc_prod(U_13798,U_13798)),tc_fun(U_13798,tc_fun(tc_fun(tc_prod(U_13798,U_13798),tc_HOL_Obool),tc_HOL_Obool)),U_13798),hAPP(c_COMBB(tc_prod(U_13798,U_13798),tc_fun(tc_fun(tc_prod(U_13798,U_13798),tc_HOL_Obool),tc_HOL_Obool),U_13798),c_member(tc_prod(U_13798,U_13798)))),c_Product__Type_OPair(U_13798,U_13798)))),U_13800)) ),
    inference(clausify,[status(thm)],[f_3515_3]) ).

cnf(f_3515_5,plain,
    ( c_Wellfounded_OwfP(U_13799,hAPP(hAPP(c_COMBC(U_13799,tc_fun(tc_prod(U_13799,U_13799),tc_HOL_Obool),tc_fun(U_13799,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13799,tc_fun(tc_fun(tc_prod(U_13799,U_13799),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13799,U_13799),tc_HOL_Obool),tc_fun(U_13799,tc_HOL_Obool)),U_13799),c_COMBC(U_13799,tc_fun(tc_prod(U_13799,U_13799),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13799,tc_prod(U_13799,U_13799)),tc_fun(U_13799,tc_fun(tc_fun(tc_prod(U_13799,U_13799),tc_HOL_Obool),tc_HOL_Obool)),U_13799),hAPP(c_COMBB(tc_prod(U_13799,U_13799),tc_fun(tc_fun(tc_prod(U_13799,U_13799),tc_HOL_Obool),tc_HOL_Obool),U_13799),c_member(tc_prod(U_13799,U_13799)))),c_Product__Type_OPair(U_13799,U_13799)))),U_13801))
    | ~ c_Wellfounded_Owf(U_13799,U_13801) ),
    inference(clausify,[status(thm)],[f_3515_3]) ).

fof(f_3516_1,plain,
    ! [V_r_2,T_b] :
      ( c_Wellfounded_Oacyclic(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2)))
      | ~ c_Wellfounded_OwfP(T_b,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_wfP__acyclicP]) ).

fof(f_3516_2,plain,
    ! [U_13803,U_13802] :
      ( c_Wellfounded_Oacyclic(U_13802,hAPP(c_Set_OCollect(tc_prod(U_13802,U_13802)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13802,U_13802,tc_HOL_Obool),U_13803)))
      | ~ c_Wellfounded_OwfP(U_13802,U_13803) ),
    inference(variable_rename,[status(thm)],[f_3516_1]) ).

cnf(f_3516_3,plain,
    ( c_Wellfounded_Oacyclic(U_13802,hAPP(c_Set_OCollect(tc_prod(U_13802,U_13802)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13802,U_13802,tc_HOL_Obool),U_13803)))
    | ~ c_Wellfounded_OwfP(U_13802,U_13803) ),
    inference(clausify,[status(thm)],[f_3516_2]) ).

fof(f_3517_1,plain,
    ! [V_f_2,T_c,V_A_2,T_b] :
      ( ? [B_x] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),hAPP(V_f_2,B_x))))))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_pigeonhole__infinite]) ).

fof(f_3517_2,plain,
    ! [U_13808,U_13807,U_13806,U_13805] :
      ( ? [U_13804] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13805),hAPP(c_Set_OCollect(U_13805),hAPP(hAPP(c_COMBS(U_13805,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13805),c_fconj),hAPP(hAPP(c_COMBC(U_13805,tc_fun(U_13805,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13805)),U_13806))),hAPP(hAPP(c_COMBC(U_13805,U_13807,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_13807,tc_fun(U_13807,tc_HOL_Obool),U_13805),c_fequal),U_13808)),hAPP(U_13808,U_13804))))))
          & hBOOL(hAPP(hAPP(c_member(U_13805),U_13804),U_13806)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13807),hAPP(c_Set_Oimage(U_13805,U_13807,U_13808),U_13806)))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_13805),U_13806)) ),
    inference(variable_rename,[status(thm)],[f_3517_1]) ).

fof(f_3517_3,plain,
    ! [U_13808,U_13807,U_13806,U_13805] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13805),hAPP(c_Set_OCollect(U_13805),hAPP(hAPP(c_COMBS(U_13805,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13805),c_fconj),hAPP(hAPP(c_COMBC(U_13805,tc_fun(U_13805,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13805)),U_13806))),hAPP(hAPP(c_COMBC(U_13805,U_13807,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_13807,tc_fun(U_13807,tc_HOL_Obool),U_13805),c_fequal),U_13808)),hAPP(U_13808,sK331(U_13808,U_13807,U_13806,U_13805)))))))
        & hBOOL(hAPP(hAPP(c_member(U_13805),sK331(U_13808,U_13807,U_13806,U_13805)),U_13806)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13807),hAPP(c_Set_Oimage(U_13805,U_13807,U_13808),U_13806)))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_13805),U_13806)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK331]),skolemize(U_13804,sK331(U_13808,U_13807,U_13806,U_13805))],[f_3517_2]) ).

cnf(f_3517_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13805),sK331(U_13808,U_13807,U_13806,U_13805)),U_13806))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13807),hAPP(c_Set_Oimage(U_13805,U_13807,U_13808),U_13806)))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_13805),U_13806)) ),
    inference(clausify,[status(thm)],[f_3517_3]) ).

cnf(f_3517_5,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13805),hAPP(c_Set_OCollect(U_13805),hAPP(hAPP(c_COMBS(U_13805,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13805),c_fconj),hAPP(hAPP(c_COMBC(U_13805,tc_fun(U_13805,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13805)),U_13806))),hAPP(hAPP(c_COMBC(U_13805,U_13807,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_13807,tc_fun(U_13807,tc_HOL_Obool),U_13805),c_fequal),U_13808)),hAPP(U_13808,sK331(U_13808,U_13807,U_13806,U_13805)))))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13807),hAPP(c_Set_Oimage(U_13805,U_13807,U_13808),U_13806)))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_13805),U_13806)) ),
    inference(clausify,[status(thm)],[f_3517_3]) ).

fof(f_3518_1,plain,
    ! [V_r_2,V_A_2,T_b] :
      ( ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
        | ? [B_x] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
        | ? [B_x] :
            ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),B_x))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2)) ) )
      & ( ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2))
              | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
          & ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),B_x))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2)) ) )
        | ~ c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_refl__on__def_H]) ).

fof(f_3518_2,plain,
    ! [U_13815,U_13814,U_13813] :
      ( ( c_Relation_Orefl__on(U_13813,U_13814,U_13815)
        | ? [U_13812] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13813,U_13813)),hAPP(hAPP(c_Product__Type_OPair(U_13813,U_13813),U_13812),U_13812)),U_13815))
            & hBOOL(hAPP(hAPP(c_member(U_13813),U_13812),U_13814)) )
        | ? [U_13811] :
            ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13813,U_13813,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13813,tc_fun(U_13813,tc_HOL_Obool),tc_fun(U_13813,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13813,tc_HOL_Obool),tc_fun(U_13813,tc_HOL_Obool)),U_13813),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13813)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13813),c_fconj),hAPP(hAPP(c_COMBC(U_13813,tc_fun(U_13813,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13813)),U_13814)))),hAPP(hAPP(c_COMBC(U_13813,tc_fun(U_13813,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13813)),U_13814))),U_13811))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_13813,U_13813)),U_13811),U_13815)) ) )
      & ( ( ! [U_13810] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13813,U_13813)),hAPP(hAPP(c_Product__Type_OPair(U_13813,U_13813),U_13810),U_13810)),U_13815))
              | ~ hBOOL(hAPP(hAPP(c_member(U_13813),U_13810),U_13814)) )
          & ! [U_13809] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13813,U_13813,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13813,tc_fun(U_13813,tc_HOL_Obool),tc_fun(U_13813,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13813,tc_HOL_Obool),tc_fun(U_13813,tc_HOL_Obool)),U_13813),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13813)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13813),c_fconj),hAPP(hAPP(c_COMBC(U_13813,tc_fun(U_13813,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13813)),U_13814)))),hAPP(hAPP(c_COMBC(U_13813,tc_fun(U_13813,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13813)),U_13814))),U_13809))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13813,U_13813)),U_13809),U_13815)) ) )
        | ~ c_Relation_Orefl__on(U_13813,U_13814,U_13815) ) ),
    inference(variable_rename,[status(thm)],[f_3518_1]) ).

fof(f_3518_3,plain,
    ( ! [U_13821,U_13819,U_13817] :
        ( c_Relation_Orefl__on(U_13817,U_13819,U_13821)
        | ? [U_13812] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13817,U_13817)),hAPP(hAPP(c_Product__Type_OPair(U_13817,U_13817),U_13812),U_13812)),U_13821))
            & hBOOL(hAPP(hAPP(c_member(U_13817),U_13812),U_13819)) )
        | ? [U_13811] :
            ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13817,U_13817,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13817,tc_fun(U_13817,tc_HOL_Obool),tc_fun(U_13817,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13817,tc_HOL_Obool),tc_fun(U_13817,tc_HOL_Obool)),U_13817),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13817)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13817),c_fconj),hAPP(hAPP(c_COMBC(U_13817,tc_fun(U_13817,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13817)),U_13819)))),hAPP(hAPP(c_COMBC(U_13817,tc_fun(U_13817,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13817)),U_13819))),U_13811))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_13817,U_13817)),U_13811),U_13821)) ) )
    & ! [U_13820,U_13818,U_13816] :
        ( ( ! [U_13810] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13816,U_13816)),hAPP(hAPP(c_Product__Type_OPair(U_13816,U_13816),U_13810),U_13810)),U_13820))
              | ~ hBOOL(hAPP(hAPP(c_member(U_13816),U_13810),U_13818)) )
          & ! [U_13809] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13816,U_13816,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13816,tc_fun(U_13816,tc_HOL_Obool),tc_fun(U_13816,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13816,tc_HOL_Obool),tc_fun(U_13816,tc_HOL_Obool)),U_13816),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13816)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13816),c_fconj),hAPP(hAPP(c_COMBC(U_13816,tc_fun(U_13816,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13816)),U_13818)))),hAPP(hAPP(c_COMBC(U_13816,tc_fun(U_13816,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13816)),U_13818))),U_13809))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13816,U_13816)),U_13809),U_13820)) ) )
        | ~ c_Relation_Orefl__on(U_13816,U_13818,U_13820) ) ),
    inference(miniscope,[status(thm)],[f_3518_2]) ).

fof(f_3518_4,plain,
    ( ! [U_13821,U_13819,U_13817] :
        ( c_Relation_Orefl__on(U_13817,U_13819,U_13821)
        | ? [U_13812] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13817,U_13817)),hAPP(hAPP(c_Product__Type_OPair(U_13817,U_13817),U_13812),U_13812)),U_13821))
            & hBOOL(hAPP(hAPP(c_member(U_13817),U_13812),U_13819)) )
        | ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13817,U_13817,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13817,tc_fun(U_13817,tc_HOL_Obool),tc_fun(U_13817,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13817,tc_HOL_Obool),tc_fun(U_13817,tc_HOL_Obool)),U_13817),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13817)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13817),c_fconj),hAPP(hAPP(c_COMBC(U_13817,tc_fun(U_13817,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13817)),U_13819)))),hAPP(hAPP(c_COMBC(U_13817,tc_fun(U_13817,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13817)),U_13819))),sK332(U_13821,U_13819,U_13817)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_13817,U_13817)),sK332(U_13821,U_13819,U_13817)),U_13821)) ) )
    & ! [U_13820,U_13818,U_13816] :
        ( ( ! [U_13810] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13816,U_13816)),hAPP(hAPP(c_Product__Type_OPair(U_13816,U_13816),U_13810),U_13810)),U_13820))
              | ~ hBOOL(hAPP(hAPP(c_member(U_13816),U_13810),U_13818)) )
          & ! [U_13809] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13816,U_13816,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13816,tc_fun(U_13816,tc_HOL_Obool),tc_fun(U_13816,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13816,tc_HOL_Obool),tc_fun(U_13816,tc_HOL_Obool)),U_13816),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13816)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13816),c_fconj),hAPP(hAPP(c_COMBC(U_13816,tc_fun(U_13816,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13816)),U_13818)))),hAPP(hAPP(c_COMBC(U_13816,tc_fun(U_13816,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13816)),U_13818))),U_13809))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13816,U_13816)),U_13809),U_13820)) ) )
        | ~ c_Relation_Orefl__on(U_13816,U_13818,U_13820) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK332]),skolemize(U_13811,sK332(U_13821,U_13819,U_13817))],[f_3518_3]) ).

fof(f_3518_5,plain,
    ( ! [U_13821,U_13819,U_13817] :
        ( c_Relation_Orefl__on(U_13817,U_13819,U_13821)
        | ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13817,U_13817)),hAPP(hAPP(c_Product__Type_OPair(U_13817,U_13817),sK333(U_13821,U_13819,U_13817)),sK333(U_13821,U_13819,U_13817))),U_13821))
          & hBOOL(hAPP(hAPP(c_member(U_13817),sK333(U_13821,U_13819,U_13817)),U_13819)) )
        | ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13817,U_13817,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13817,tc_fun(U_13817,tc_HOL_Obool),tc_fun(U_13817,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13817,tc_HOL_Obool),tc_fun(U_13817,tc_HOL_Obool)),U_13817),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13817)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13817),c_fconj),hAPP(hAPP(c_COMBC(U_13817,tc_fun(U_13817,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13817)),U_13819)))),hAPP(hAPP(c_COMBC(U_13817,tc_fun(U_13817,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13817)),U_13819))),sK332(U_13821,U_13819,U_13817)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_13817,U_13817)),sK332(U_13821,U_13819,U_13817)),U_13821)) ) )
    & ! [U_13820,U_13818,U_13816] :
        ( ( ! [U_13810] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13816,U_13816)),hAPP(hAPP(c_Product__Type_OPair(U_13816,U_13816),U_13810),U_13810)),U_13820))
              | ~ hBOOL(hAPP(hAPP(c_member(U_13816),U_13810),U_13818)) )
          & ! [U_13809] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13816,U_13816,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13816,tc_fun(U_13816,tc_HOL_Obool),tc_fun(U_13816,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13816,tc_HOL_Obool),tc_fun(U_13816,tc_HOL_Obool)),U_13816),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13816)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13816),c_fconj),hAPP(hAPP(c_COMBC(U_13816,tc_fun(U_13816,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13816)),U_13818)))),hAPP(hAPP(c_COMBC(U_13816,tc_fun(U_13816,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13816)),U_13818))),U_13809))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13816,U_13816)),U_13809),U_13820)) ) )
        | ~ c_Relation_Orefl__on(U_13816,U_13818,U_13820) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK333]),skolemize(U_13812,sK333(U_13821,U_13819,U_13817))],[f_3518_4]) ).

cnf(f_3518_6,plain,
    ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13816,U_13816,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13816,tc_fun(U_13816,tc_HOL_Obool),tc_fun(U_13816,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13816,tc_HOL_Obool),tc_fun(U_13816,tc_HOL_Obool)),U_13816),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13816)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13816),c_fconj),hAPP(hAPP(c_COMBC(U_13816,tc_fun(U_13816,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13816)),U_13818)))),hAPP(hAPP(c_COMBC(U_13816,tc_fun(U_13816,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13816)),U_13818))),U_13809))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13816,U_13816)),U_13809),U_13820))
    | ~ c_Relation_Orefl__on(U_13816,U_13818,U_13820) ),
    inference(clausify,[status(thm)],[f_3518_5]) ).

cnf(f_3518_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13816,U_13816)),hAPP(hAPP(c_Product__Type_OPair(U_13816,U_13816),U_13810),U_13810)),U_13820))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13816),U_13810),U_13818))
    | ~ c_Relation_Orefl__on(U_13816,U_13818,U_13820) ),
    inference(clausify,[status(thm)],[f_3518_5]) ).

cnf(f_3518_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13817),sK333(U_13821,U_13819,U_13817)),U_13819))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_13817,U_13817)),sK332(U_13821,U_13819,U_13817)),U_13821))
    | c_Relation_Orefl__on(U_13817,U_13819,U_13821) ),
    inference(clausify,[status(thm)],[f_3518_5]) ).

cnf(f_3518_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13817,U_13817)),hAPP(hAPP(c_Product__Type_OPair(U_13817,U_13817),sK333(U_13821,U_13819,U_13817)),sK333(U_13821,U_13819,U_13817))),U_13821))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_13817,U_13817)),sK332(U_13821,U_13819,U_13817)),U_13821))
    | c_Relation_Orefl__on(U_13817,U_13819,U_13821) ),
    inference(clausify,[status(thm)],[f_3518_5]) ).

cnf(f_3518_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13817),sK333(U_13821,U_13819,U_13817)),U_13819))
    | ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13817,U_13817,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13817,tc_fun(U_13817,tc_HOL_Obool),tc_fun(U_13817,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13817,tc_HOL_Obool),tc_fun(U_13817,tc_HOL_Obool)),U_13817),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13817)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13817),c_fconj),hAPP(hAPP(c_COMBC(U_13817,tc_fun(U_13817,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13817)),U_13819)))),hAPP(hAPP(c_COMBC(U_13817,tc_fun(U_13817,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13817)),U_13819))),sK332(U_13821,U_13819,U_13817)))
    | c_Relation_Orefl__on(U_13817,U_13819,U_13821) ),
    inference(clausify,[status(thm)],[f_3518_5]) ).

cnf(f_3518_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13817,U_13817)),hAPP(hAPP(c_Product__Type_OPair(U_13817,U_13817),sK333(U_13821,U_13819,U_13817)),sK333(U_13821,U_13819,U_13817))),U_13821))
    | ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13817,U_13817,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13817,tc_fun(U_13817,tc_HOL_Obool),tc_fun(U_13817,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13817,tc_HOL_Obool),tc_fun(U_13817,tc_HOL_Obool)),U_13817),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13817)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13817),c_fconj),hAPP(hAPP(c_COMBC(U_13817,tc_fun(U_13817,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13817)),U_13819)))),hAPP(hAPP(c_COMBC(U_13817,tc_fun(U_13817,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13817)),U_13819))),sK332(U_13821,U_13819,U_13817)))
    | c_Relation_Orefl__on(U_13817,U_13819,U_13821) ),
    inference(clausify,[status(thm)],[f_3518_5]) ).

fof(f_3519_1,plain,
    ! [V_P_2,T_b,B_x] :
      ( hBOOL(hAPP(V_P_2,B_x))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ),
    inference(fof_nnf,[status(thm)],[fact_ball__empty]) ).

fof(f_3519_2,plain,
    ! [U_13824,U_13823,U_13822] :
      ( hBOOL(hAPP(U_13824,U_13822))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13823),U_13822),c_Orderings_Obot__class_Obot(tc_fun(U_13823,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_3519_1]) ).

cnf(f_3519_3,plain,
    ( hBOOL(hAPP(U_13824,U_13822))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13823),U_13822),c_Orderings_Obot__class_Obot(tc_fun(U_13823,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_3519_2]) ).

fof(f_3520_1,plain,
    ! [V_r_2,T_b] :
      ( c_Wellfounded_Oacyclic(T_b,V_r_2)
      | ~ c_Wellfounded_Owf(T_b,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_wf__acyclic]) ).

fof(f_3520_2,plain,
    ! [U_13826,U_13825] :
      ( c_Wellfounded_Oacyclic(U_13825,U_13826)
      | ~ c_Wellfounded_Owf(U_13825,U_13826) ),
    inference(variable_rename,[status(thm)],[f_3520_1]) ).

cnf(f_3520_3,plain,
    ( c_Wellfounded_Oacyclic(U_13825,U_13826)
    | ~ c_Wellfounded_Owf(U_13825,U_13826) ),
    inference(clausify,[status(thm)],[f_3520_2]) ).

fof(f_3521_1,plain,
    ! [V_r_2,V_s_2,T_b] :
      ( c_Wellfounded_Oacyclic(T_b,V_r_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
      | ~ c_Wellfounded_Oacyclic(T_b,V_s_2) ),
    inference(fof_nnf,[status(thm)],[fact_acyclic__subset]) ).

fof(f_3521_2,plain,
    ! [U_13829,U_13828,U_13827] :
      ( c_Wellfounded_Oacyclic(U_13827,U_13829)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13827,U_13827),tc_HOL_Obool)),U_13829),U_13828))
      | ~ c_Wellfounded_Oacyclic(U_13827,U_13828) ),
    inference(variable_rename,[status(thm)],[f_3521_1]) ).

cnf(f_3521_3,plain,
    ( c_Wellfounded_Oacyclic(U_13827,U_13829)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13827,U_13827),tc_HOL_Obool)),U_13829),U_13828))
    | ~ c_Wellfounded_Oacyclic(U_13827,U_13828) ),
    inference(clausify,[status(thm)],[f_3521_2]) ).

fof(f_3522_1,plain,
    ! [T_b] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_HOL_Obool) = c_Set_OBall(T_b),
    inference(fof_nnf,[status(thm)],[fact_INFI__bool__eq]) ).

fof(f_3522_2,plain,
    ! [U_13830] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_13830,tc_HOL_Obool) = c_Set_OBall(U_13830),
    inference(variable_rename,[status(thm)],[f_3522_1]) ).

cnf(f_3522_3,plain,
    c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_13830,tc_HOL_Obool) = c_Set_OBall(U_13830),
    inference(clausify,[status(thm)],[f_3522_2]) ).

fof(f_3523_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( ( hBOOL(hAPP(c_Predicate_OPowp(T_b,V_A_2),V_B_2))
        | ? [B_x] :
            ( ~ hBOOL(hAPP(V_A_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) ) )
      & ( ! [B_x] :
            ( hBOOL(hAPP(V_A_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) )
        | ~ hBOOL(hAPP(c_Predicate_OPowp(T_b,V_A_2),V_B_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Powp__def]) ).

fof(f_3523_2,plain,
    ! [U_13835,U_13834,U_13833] :
      ( ( hBOOL(hAPP(c_Predicate_OPowp(U_13833,U_13834),U_13835))
        | ? [U_13832] :
            ( ~ hBOOL(hAPP(U_13834,U_13832))
            & hBOOL(hAPP(hAPP(c_member(U_13833),U_13832),U_13835)) ) )
      & ( ! [U_13831] :
            ( hBOOL(hAPP(U_13834,U_13831))
            | ~ hBOOL(hAPP(hAPP(c_member(U_13833),U_13831),U_13835)) )
        | ~ hBOOL(hAPP(c_Predicate_OPowp(U_13833,U_13834),U_13835)) ) ),
    inference(variable_rename,[status(thm)],[f_3523_1]) ).

fof(f_3523_3,plain,
    ( ! [U_13841,U_13839,U_13837] :
        ( hBOOL(hAPP(c_Predicate_OPowp(U_13837,U_13839),U_13841))
        | ? [U_13832] :
            ( ~ hBOOL(hAPP(U_13839,U_13832))
            & hBOOL(hAPP(hAPP(c_member(U_13837),U_13832),U_13841)) ) )
    & ! [U_13840,U_13838,U_13836] :
        ( ! [U_13831] :
            ( hBOOL(hAPP(U_13838,U_13831))
            | ~ hBOOL(hAPP(hAPP(c_member(U_13836),U_13831),U_13840)) )
        | ~ hBOOL(hAPP(c_Predicate_OPowp(U_13836,U_13838),U_13840)) ) ),
    inference(miniscope,[status(thm)],[f_3523_2]) ).

fof(f_3523_4,plain,
    ( ! [U_13841,U_13839,U_13837] :
        ( hBOOL(hAPP(c_Predicate_OPowp(U_13837,U_13839),U_13841))
        | ( ~ hBOOL(hAPP(U_13839,sK334(U_13841,U_13839,U_13837)))
          & hBOOL(hAPP(hAPP(c_member(U_13837),sK334(U_13841,U_13839,U_13837)),U_13841)) ) )
    & ! [U_13840,U_13838,U_13836] :
        ( ! [U_13831] :
            ( hBOOL(hAPP(U_13838,U_13831))
            | ~ hBOOL(hAPP(hAPP(c_member(U_13836),U_13831),U_13840)) )
        | ~ hBOOL(hAPP(c_Predicate_OPowp(U_13836,U_13838),U_13840)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK334]),skolemize(U_13832,sK334(U_13841,U_13839,U_13837))],[f_3523_3]) ).

cnf(f_3523_5,plain,
    ( hBOOL(hAPP(U_13838,U_13831))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13836),U_13831),U_13840))
    | ~ hBOOL(hAPP(c_Predicate_OPowp(U_13836,U_13838),U_13840)) ),
    inference(clausify,[status(thm)],[f_3523_4]) ).

cnf(f_3523_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13837),sK334(U_13841,U_13839,U_13837)),U_13841))
    | hBOOL(hAPP(c_Predicate_OPowp(U_13837,U_13839),U_13841)) ),
    inference(clausify,[status(thm)],[f_3523_4]) ).

cnf(f_3523_7,plain,
    ( ~ hBOOL(hAPP(U_13839,sK334(U_13841,U_13839,U_13837)))
    | hBOOL(hAPP(c_Predicate_OPowp(U_13837,U_13839),U_13841)) ),
    inference(clausify,[status(thm)],[f_3523_4]) ).

fof(f_3524_1,plain,
    ! [V_P_2,V_A_2,T_c,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fimplies),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)))),V_P_2))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Set_OCollect(T_b)),hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),V_P_2))),
    inference(fof_nnf,[status(thm)],[fact_Collect__ball__eq]) ).

fof(f_3524_2,plain,
    ! [U_13845,U_13844,U_13843,U_13842] : hAPP(c_Set_OCollect(U_13842),hAPP(hAPP(c_COMBB(tc_fun(U_13843,tc_HOL_Obool),tc_HOL_Obool,U_13842),c_HOL_OAll(U_13843)),hAPP(hAPP(c_COMBB(tc_fun(U_13843,tc_HOL_Obool),tc_fun(U_13843,tc_HOL_Obool),U_13842),hAPP(c_COMBS(U_13843,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13843),c_fimplies),hAPP(hAPP(c_COMBC(U_13843,tc_fun(U_13843,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13843)),U_13844)))),U_13845))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_13843,tc_fun(U_13842,tc_HOL_Obool)),U_13844),hAPP(hAPP(c_COMBB(tc_fun(U_13842,tc_HOL_Obool),tc_fun(U_13842,tc_HOL_Obool),U_13843),c_Set_OCollect(U_13842)),hAPP(c_COMBC(U_13842,U_13843,tc_HOL_Obool),U_13845))),
    inference(variable_rename,[status(thm)],[f_3524_1]) ).

cnf(f_3524_3,plain,
    hAPP(c_Set_OCollect(U_13842),hAPP(hAPP(c_COMBB(tc_fun(U_13843,tc_HOL_Obool),tc_HOL_Obool,U_13842),c_HOL_OAll(U_13843)),hAPP(hAPP(c_COMBB(tc_fun(U_13843,tc_HOL_Obool),tc_fun(U_13843,tc_HOL_Obool),U_13842),hAPP(c_COMBS(U_13843,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13843),c_fimplies),hAPP(hAPP(c_COMBC(U_13843,tc_fun(U_13843,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13843)),U_13844)))),U_13845))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_13843,tc_fun(U_13842,tc_HOL_Obool)),U_13844),hAPP(hAPP(c_COMBB(tc_fun(U_13842,tc_HOL_Obool),tc_fun(U_13842,tc_HOL_Obool),U_13843),c_Set_OCollect(U_13842)),hAPP(c_COMBC(U_13842,U_13843,tc_HOL_Obool),U_13845))),
    inference(clausify,[status(thm)],[f_3524_2]) ).

fof(f_3525_1,plain,
    ! [V_f_2,V_r_2,T_c,T_b] :
      ( ( c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2)
        | ? [B_x] :
            ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_c,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2))),V_f_2)),B_x))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2)) ) )
      & ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_c,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2))),V_f_2)),B_x))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2)) )
        | ~ c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_congruent__def]) ).

fof(f_3525_2,plain,
    ! [U_13851,U_13850,U_13849,U_13848] :
      ( ( c_Equiv__Relations_Ocongruent(U_13848,U_13849,U_13850,U_13851)
        | ? [U_13847] :
            ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13848,U_13848,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13848,tc_fun(U_13848,U_13849),tc_fun(U_13848,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13849,tc_HOL_Obool),tc_fun(tc_fun(U_13848,U_13849),tc_fun(U_13848,tc_HOL_Obool)),U_13848),c_COMBB(U_13849,tc_HOL_Obool,U_13848)),hAPP(hAPP(c_COMBB(U_13849,tc_fun(U_13849,tc_HOL_Obool),U_13848),c_fequal),U_13851))),U_13851)),U_13847))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_13848,U_13848)),U_13847),U_13850)) ) )
      & ( ! [U_13846] :
            ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13848,U_13848,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13848,tc_fun(U_13848,U_13849),tc_fun(U_13848,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13849,tc_HOL_Obool),tc_fun(tc_fun(U_13848,U_13849),tc_fun(U_13848,tc_HOL_Obool)),U_13848),c_COMBB(U_13849,tc_HOL_Obool,U_13848)),hAPP(hAPP(c_COMBB(U_13849,tc_fun(U_13849,tc_HOL_Obool),U_13848),c_fequal),U_13851))),U_13851)),U_13846))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13848,U_13848)),U_13846),U_13850)) )
        | ~ c_Equiv__Relations_Ocongruent(U_13848,U_13849,U_13850,U_13851) ) ),
    inference(variable_rename,[status(thm)],[f_3525_1]) ).

fof(f_3525_3,plain,
    ( ! [U_13859,U_13857,U_13855,U_13853] :
        ( c_Equiv__Relations_Ocongruent(U_13853,U_13855,U_13857,U_13859)
        | ? [U_13847] :
            ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13853,U_13853,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13853,tc_fun(U_13853,U_13855),tc_fun(U_13853,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13855,tc_HOL_Obool),tc_fun(tc_fun(U_13853,U_13855),tc_fun(U_13853,tc_HOL_Obool)),U_13853),c_COMBB(U_13855,tc_HOL_Obool,U_13853)),hAPP(hAPP(c_COMBB(U_13855,tc_fun(U_13855,tc_HOL_Obool),U_13853),c_fequal),U_13859))),U_13859)),U_13847))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_13853,U_13853)),U_13847),U_13857)) ) )
    & ! [U_13858,U_13856,U_13854,U_13852] :
        ( ! [U_13846] :
            ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13852,U_13852,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13852,tc_fun(U_13852,U_13854),tc_fun(U_13852,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13854,tc_HOL_Obool),tc_fun(tc_fun(U_13852,U_13854),tc_fun(U_13852,tc_HOL_Obool)),U_13852),c_COMBB(U_13854,tc_HOL_Obool,U_13852)),hAPP(hAPP(c_COMBB(U_13854,tc_fun(U_13854,tc_HOL_Obool),U_13852),c_fequal),U_13858))),U_13858)),U_13846))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13852,U_13852)),U_13846),U_13856)) )
        | ~ c_Equiv__Relations_Ocongruent(U_13852,U_13854,U_13856,U_13858) ) ),
    inference(miniscope,[status(thm)],[f_3525_2]) ).

fof(f_3525_4,plain,
    ( ! [U_13859,U_13857,U_13855,U_13853] :
        ( c_Equiv__Relations_Ocongruent(U_13853,U_13855,U_13857,U_13859)
        | ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13853,U_13853,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13853,tc_fun(U_13853,U_13855),tc_fun(U_13853,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13855,tc_HOL_Obool),tc_fun(tc_fun(U_13853,U_13855),tc_fun(U_13853,tc_HOL_Obool)),U_13853),c_COMBB(U_13855,tc_HOL_Obool,U_13853)),hAPP(hAPP(c_COMBB(U_13855,tc_fun(U_13855,tc_HOL_Obool),U_13853),c_fequal),U_13859))),U_13859)),sK335(U_13859,U_13857,U_13855,U_13853)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_13853,U_13853)),sK335(U_13859,U_13857,U_13855,U_13853)),U_13857)) ) )
    & ! [U_13858,U_13856,U_13854,U_13852] :
        ( ! [U_13846] :
            ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13852,U_13852,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13852,tc_fun(U_13852,U_13854),tc_fun(U_13852,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13854,tc_HOL_Obool),tc_fun(tc_fun(U_13852,U_13854),tc_fun(U_13852,tc_HOL_Obool)),U_13852),c_COMBB(U_13854,tc_HOL_Obool,U_13852)),hAPP(hAPP(c_COMBB(U_13854,tc_fun(U_13854,tc_HOL_Obool),U_13852),c_fequal),U_13858))),U_13858)),U_13846))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13852,U_13852)),U_13846),U_13856)) )
        | ~ c_Equiv__Relations_Ocongruent(U_13852,U_13854,U_13856,U_13858) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK335]),skolemize(U_13847,sK335(U_13859,U_13857,U_13855,U_13853))],[f_3525_3]) ).

cnf(f_3525_5,plain,
    ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13852,U_13852,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13852,tc_fun(U_13852,U_13854),tc_fun(U_13852,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13854,tc_HOL_Obool),tc_fun(tc_fun(U_13852,U_13854),tc_fun(U_13852,tc_HOL_Obool)),U_13852),c_COMBB(U_13854,tc_HOL_Obool,U_13852)),hAPP(hAPP(c_COMBB(U_13854,tc_fun(U_13854,tc_HOL_Obool),U_13852),c_fequal),U_13858))),U_13858)),U_13846))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13852,U_13852)),U_13846),U_13856))
    | ~ c_Equiv__Relations_Ocongruent(U_13852,U_13854,U_13856,U_13858) ),
    inference(clausify,[status(thm)],[f_3525_4]) ).

cnf(f_3525_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13853,U_13853)),sK335(U_13859,U_13857,U_13855,U_13853)),U_13857))
    | c_Equiv__Relations_Ocongruent(U_13853,U_13855,U_13857,U_13859) ),
    inference(clausify,[status(thm)],[f_3525_4]) ).

cnf(f_3525_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13853,U_13853,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13853,tc_fun(U_13853,U_13855),tc_fun(U_13853,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13855,tc_HOL_Obool),tc_fun(tc_fun(U_13853,U_13855),tc_fun(U_13853,tc_HOL_Obool)),U_13853),c_COMBB(U_13855,tc_HOL_Obool,U_13853)),hAPP(hAPP(c_COMBB(U_13855,tc_fun(U_13855,tc_HOL_Obool),U_13853),c_fequal),U_13859))),U_13859)),sK335(U_13859,U_13857,U_13855,U_13853)))
    | c_Equiv__Relations_Ocongruent(U_13853,U_13855,U_13857,U_13859) ),
    inference(clausify,[status(thm)],[f_3525_4]) ).

fof(f_3526_1,plain,
    ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fimplies),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c)),c_member(T_b))),V_B_2)))),
    inference(fof_nnf,[status(thm)],[fact_INTER__def]) ).

fof(f_3526_2,plain,
    ! [U_13863,U_13862,U_13861,U_13860] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_13860,tc_fun(U_13861,tc_HOL_Obool)),U_13862),U_13863) = hAPP(c_Set_OCollect(U_13861),hAPP(hAPP(c_COMBB(tc_fun(U_13860,tc_HOL_Obool),tc_HOL_Obool,U_13861),c_HOL_OAll(U_13860)),hAPP(hAPP(c_COMBB(tc_fun(U_13860,tc_HOL_Obool),tc_fun(U_13860,tc_HOL_Obool),U_13861),hAPP(c_COMBS(U_13860,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13860),c_fimplies),hAPP(hAPP(c_COMBC(U_13860,tc_fun(U_13860,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13860)),U_13862)))),hAPP(hAPP(c_COMBC(U_13861,tc_fun(U_13860,tc_fun(U_13861,tc_HOL_Obool)),tc_fun(U_13860,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13861,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_13860,tc_fun(U_13861,tc_HOL_Obool)),tc_fun(U_13860,tc_HOL_Obool)),U_13861),c_COMBB(tc_fun(U_13861,tc_HOL_Obool),tc_HOL_Obool,U_13860)),c_member(U_13861))),U_13863)))),
    inference(variable_rename,[status(thm)],[f_3526_1]) ).

cnf(f_3526_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_13860,tc_fun(U_13861,tc_HOL_Obool)),U_13862),U_13863) = hAPP(c_Set_OCollect(U_13861),hAPP(hAPP(c_COMBB(tc_fun(U_13860,tc_HOL_Obool),tc_HOL_Obool,U_13861),c_HOL_OAll(U_13860)),hAPP(hAPP(c_COMBB(tc_fun(U_13860,tc_HOL_Obool),tc_fun(U_13860,tc_HOL_Obool),U_13861),hAPP(c_COMBS(U_13860,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13860),c_fimplies),hAPP(hAPP(c_COMBC(U_13860,tc_fun(U_13860,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13860)),U_13862)))),hAPP(hAPP(c_COMBC(U_13861,tc_fun(U_13860,tc_fun(U_13861,tc_HOL_Obool)),tc_fun(U_13860,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13861,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_13860,tc_fun(U_13861,tc_HOL_Obool)),tc_fun(U_13860,tc_HOL_Obool)),U_13861),c_COMBB(tc_fun(U_13861,tc_HOL_Obool),tc_HOL_Obool,U_13860)),c_member(U_13861))),U_13863)))),
    inference(clausify,[status(thm)],[f_3526_2]) ).

fof(f_3527_1,plain,
    ! [V_r_2,T_b] :
      ( ( ( c_Wellfounded_Owf(T_b,V_r_2)
          | ~ c_Wellfounded_Oacyclic(T_b,V_r_2) )
        & ( c_Wellfounded_Oacyclic(T_b,V_r_2)
          | ~ c_Wellfounded_Owf(T_b,V_r_2) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_wf__iff__acyclic__if__finite]) ).

fof(f_3527_2,plain,
    ! [U_13865,U_13864] :
      ( ( ( c_Wellfounded_Owf(U_13864,U_13865)
          | ~ c_Wellfounded_Oacyclic(U_13864,U_13865) )
        & ( c_Wellfounded_Oacyclic(U_13864,U_13865)
          | ~ c_Wellfounded_Owf(U_13864,U_13865) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13864,U_13864)),U_13865)) ),
    inference(variable_rename,[status(thm)],[f_3527_1]) ).

cnf(f_3527_3,plain,
    ( c_Wellfounded_Oacyclic(U_13864,U_13865)
    | ~ c_Wellfounded_Owf(U_13864,U_13865)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13864,U_13864)),U_13865)) ),
    inference(clausify,[status(thm)],[f_3527_2]) ).

cnf(f_3527_4,plain,
    ( c_Wellfounded_Owf(U_13864,U_13865)
    | ~ c_Wellfounded_Oacyclic(U_13864,U_13865)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13864,U_13864)),U_13865)) ),
    inference(clausify,[status(thm)],[f_3527_2]) ).

fof(f_3528_1,plain,
    ! [V_r_2,T_b] :
      ( c_Wellfounded_Owf(T_b,V_r_2)
      | ~ c_Wellfounded_Oacyclic(T_b,V_r_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__acyclic__wf]) ).

fof(f_3528_2,plain,
    ! [U_13867,U_13866] :
      ( c_Wellfounded_Owf(U_13866,U_13867)
      | ~ c_Wellfounded_Oacyclic(U_13866,U_13867)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13866,U_13866)),U_13867)) ),
    inference(variable_rename,[status(thm)],[f_3528_1]) ).

cnf(f_3528_3,plain,
    ( c_Wellfounded_Owf(U_13866,U_13867)
    | ~ c_Wellfounded_Oacyclic(U_13866,U_13867)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13866,U_13866)),U_13867)) ),
    inference(clausify,[status(thm)],[f_3528_2]) ).

fof(f_3529_1,plain,
    ! [V_A_2,T_b] :
      ( c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_b))))))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__Inf]) ).

fof(f_3529_2,plain,
    ! [U_13869,U_13868] :
      ( c_Complete__Lattice_OSup__class_OSup(U_13868,U_13869) = c_Complete__Lattice_OInf__class_OInf(U_13868,hAPP(c_Set_OCollect(U_13868),hAPP(hAPP(c_COMBB(tc_fun(U_13868,tc_HOL_Obool),tc_HOL_Obool,U_13868),c_HOL_OAll(U_13868)),hAPP(hAPP(c_COMBB(tc_fun(U_13868,tc_HOL_Obool),tc_fun(U_13868,tc_HOL_Obool),U_13868),hAPP(c_COMBS(U_13868,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13868),c_fimplies),hAPP(hAPP(c_COMBC(U_13868,tc_fun(U_13868,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13868)),U_13869)))),hAPP(c_COMBC(U_13868,U_13868,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(U_13868))))))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_13868) ),
    inference(variable_rename,[status(thm)],[f_3529_1]) ).

cnf(f_3529_3,plain,
    ( c_Complete__Lattice_OSup__class_OSup(U_13868,U_13869) = c_Complete__Lattice_OInf__class_OInf(U_13868,hAPP(c_Set_OCollect(U_13868),hAPP(hAPP(c_COMBB(tc_fun(U_13868,tc_HOL_Obool),tc_HOL_Obool,U_13868),c_HOL_OAll(U_13868)),hAPP(hAPP(c_COMBB(tc_fun(U_13868,tc_HOL_Obool),tc_fun(U_13868,tc_HOL_Obool),U_13868),hAPP(c_COMBS(U_13868,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13868),c_fimplies),hAPP(hAPP(c_COMBC(U_13868,tc_fun(U_13868,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13868)),U_13869)))),hAPP(c_COMBC(U_13868,U_13868,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(U_13868))))))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_13868) ),
    inference(clausify,[status(thm)],[f_3529_2]) ).

fof(f_3530_1,plain,
    ! [V_A_2,T_b] :
      ( c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),c_Orderings_Oord__class_Oless__eq(T_b)))))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__Sup]) ).

fof(f_3530_2,plain,
    ! [U_13871,U_13870] :
      ( c_Complete__Lattice_OInf__class_OInf(U_13870,U_13871) = c_Complete__Lattice_OSup__class_OSup(U_13870,hAPP(c_Set_OCollect(U_13870),hAPP(hAPP(c_COMBB(tc_fun(U_13870,tc_HOL_Obool),tc_HOL_Obool,U_13870),c_HOL_OAll(U_13870)),hAPP(hAPP(c_COMBB(tc_fun(U_13870,tc_HOL_Obool),tc_fun(U_13870,tc_HOL_Obool),U_13870),hAPP(c_COMBS(U_13870,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13870),c_fimplies),hAPP(hAPP(c_COMBC(U_13870,tc_fun(U_13870,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13870)),U_13871)))),c_Orderings_Oord__class_Oless__eq(U_13870)))))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_13870) ),
    inference(variable_rename,[status(thm)],[f_3530_1]) ).

cnf(f_3530_3,plain,
    ( c_Complete__Lattice_OInf__class_OInf(U_13870,U_13871) = c_Complete__Lattice_OSup__class_OSup(U_13870,hAPP(c_Set_OCollect(U_13870),hAPP(hAPP(c_COMBB(tc_fun(U_13870,tc_HOL_Obool),tc_HOL_Obool,U_13870),c_HOL_OAll(U_13870)),hAPP(hAPP(c_COMBB(tc_fun(U_13870,tc_HOL_Obool),tc_fun(U_13870,tc_HOL_Obool),U_13870),hAPP(c_COMBS(U_13870,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13870),c_fimplies),hAPP(hAPP(c_COMBC(U_13870,tc_fun(U_13870,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13870)),U_13871)))),c_Orderings_Oord__class_Oless__eq(U_13870)))))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_13870) ),
    inference(clausify,[status(thm)],[f_3530_2]) ).

fof(f_3531_1,plain,
    ! [V_r_2,T_b] :
      ( ( c_Nitpick_Owf_H(T_b,V_r_2)
        | ( ~ c_Nitpick_Ounknown(tc_HOL_Obool)
          & ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) )
        | ~ c_Wellfounded_Oacyclic(T_b,V_r_2) )
      & ( ( ( c_Nitpick_Ounknown(tc_HOL_Obool)
            | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) )
          & c_Wellfounded_Oacyclic(T_b,V_r_2) )
        | ~ c_Nitpick_Owf_H(T_b,V_r_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_Nitpick_Owf_H__def]) ).

fof(f_3531_2,plain,
    ! [U_13873,U_13872] :
      ( ( c_Nitpick_Owf_H(U_13872,U_13873)
        | ( ~ c_Nitpick_Ounknown(tc_HOL_Obool)
          & ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13872,U_13872)),U_13873)) )
        | ~ c_Wellfounded_Oacyclic(U_13872,U_13873) )
      & ( ( ( c_Nitpick_Ounknown(tc_HOL_Obool)
            | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13872,U_13872)),U_13873)) )
          & c_Wellfounded_Oacyclic(U_13872,U_13873) )
        | ~ c_Nitpick_Owf_H(U_13872,U_13873) ) ),
    inference(variable_rename,[status(thm)],[f_3531_1]) ).

fof(f_3531_3,plain,
    ( ! [U_13877,U_13875] :
        ( c_Nitpick_Owf_H(U_13875,U_13877)
        | ( ~ c_Nitpick_Ounknown(tc_HOL_Obool)
          & ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13875,U_13875)),U_13877)) )
        | ~ c_Wellfounded_Oacyclic(U_13875,U_13877) )
    & ! [U_13876,U_13874] :
        ( ( ( c_Nitpick_Ounknown(tc_HOL_Obool)
            | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13874,U_13874)),U_13876)) )
          & c_Wellfounded_Oacyclic(U_13874,U_13876) )
        | ~ c_Nitpick_Owf_H(U_13874,U_13876) ) ),
    inference(miniscope,[status(thm)],[f_3531_2]) ).

cnf(f_3531_4,plain,
    ( c_Wellfounded_Oacyclic(U_13874,U_13876)
    | ~ c_Nitpick_Owf_H(U_13874,U_13876) ),
    inference(clausify,[status(thm)],[f_3531_3]) ).

cnf(f_3531_5,plain,
    ( c_Nitpick_Ounknown(tc_HOL_Obool)
    | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13874,U_13874)),U_13876))
    | ~ c_Nitpick_Owf_H(U_13874,U_13876) ),
    inference(clausify,[status(thm)],[f_3531_3]) ).

cnf(f_3531_6,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13875,U_13875)),U_13877))
    | ~ c_Wellfounded_Oacyclic(U_13875,U_13877)
    | c_Nitpick_Owf_H(U_13875,U_13877) ),
    inference(clausify,[status(thm)],[f_3531_3]) ).

cnf(f_3531_7,plain,
    ( ~ c_Nitpick_Ounknown(tc_HOL_Obool)
    | ~ c_Wellfounded_Oacyclic(U_13875,U_13877)
    | c_Nitpick_Owf_H(U_13875,U_13877) ),
    inference(clausify,[status(thm)],[f_3531_3]) ).

fof(f_3532_1,plain,
    ! [V_x_2,V_P_2] :
      ( hBOOL(hAPP(V_P_2,V_x_2))
      | ? [B_y] :
          ( ~ hBOOL(hAPP(V_P_2,hAPP(c_Int_OAbs__Integ,B_y)))
          & hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Abs__Integ__induct]) ).

fof(f_3532_2,plain,
    ! [U_13880,U_13879] :
      ( hBOOL(hAPP(U_13879,U_13880))
      | ? [U_13878] :
          ( ~ hBOOL(hAPP(U_13879,hAPP(c_Int_OAbs__Integ,U_13878)))
          & hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_13878),c_Int_OInteg)) ) ),
    inference(variable_rename,[status(thm)],[f_3532_1]) ).

fof(f_3532_3,plain,
    ! [U_13880,U_13879] :
      ( hBOOL(hAPP(U_13879,U_13880))
      | ( ~ hBOOL(hAPP(U_13879,hAPP(c_Int_OAbs__Integ,sK336(U_13880,U_13879))))
        & hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),sK336(U_13880,U_13879)),c_Int_OInteg)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK336]),skolemize(U_13878,sK336(U_13880,U_13879))],[f_3532_2]) ).

cnf(f_3532_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),sK336(U_13880,U_13879)),c_Int_OInteg))
    | hBOOL(hAPP(U_13879,U_13880)) ),
    inference(clausify,[status(thm)],[f_3532_3]) ).

cnf(f_3532_5,plain,
    ( ~ hBOOL(hAPP(U_13879,hAPP(c_Int_OAbs__Integ,sK336(U_13880,U_13879))))
    | hBOOL(hAPP(U_13879,U_13880)) ),
    inference(clausify,[status(thm)],[f_3532_3]) ).

fof(f_3533_1,plain,
    ! [V_x_2] :
    ? [B_y] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg))
      & V_x_2 = hAPP(c_Int_OAbs__Integ,B_y) ),
    inference(fof_nnf,[status(thm)],[fact_Abs__Integ__cases]) ).

fof(f_3533_2,plain,
    ! [U_13882] :
    ? [U_13881] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_13881),c_Int_OInteg))
      & U_13882 = hAPP(c_Int_OAbs__Integ,U_13881) ),
    inference(variable_rename,[status(thm)],[f_3533_1]) ).

fof(f_3533_3,plain,
    ! [U_13882] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),sK337(U_13882)),c_Int_OInteg))
      & U_13882 = hAPP(c_Int_OAbs__Integ,sK337(U_13882)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK337]),skolemize(U_13881,sK337(U_13882))],[f_3533_2]) ).

cnf(f_3533_4,plain,
    U_13882 = hAPP(c_Int_OAbs__Integ,sK337(U_13882)),
    inference(clausify,[status(thm)],[f_3533_3]) ).

cnf(f_3533_5,plain,
    hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),sK337(U_13882)),c_Int_OInteg)),
    inference(clausify,[status(thm)],[f_3533_3]) ).

fof(f_3534_1,plain,
    ! [V_A_2,T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_fimplies),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_b,tc_HOL_Obool))),V_A_2)))),c_member(T_b)))),
    inference(fof_nnf,[status(thm)],[fact_Inter__eq]) ).

fof(f_3534_2,plain,
    ! [U_13884,U_13883] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_13883,tc_HOL_Obool),U_13884) = hAPP(c_Set_OCollect(U_13883),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13883,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,U_13883),c_HOL_OAll(tc_fun(U_13883,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13883,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_13883,tc_HOL_Obool),tc_HOL_Obool),U_13883),hAPP(c_COMBS(tc_fun(U_13883,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(U_13883,tc_HOL_Obool)),c_fimplies),hAPP(hAPP(c_COMBC(tc_fun(U_13883,tc_HOL_Obool),tc_fun(tc_fun(U_13883,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(U_13883,tc_HOL_Obool))),U_13884)))),c_member(U_13883)))),
    inference(variable_rename,[status(thm)],[f_3534_1]) ).

cnf(f_3534_3,plain,
    c_Complete__Lattice_OInf__class_OInf(tc_fun(U_13883,tc_HOL_Obool),U_13884) = hAPP(c_Set_OCollect(U_13883),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13883,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,U_13883),c_HOL_OAll(tc_fun(U_13883,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13883,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_13883,tc_HOL_Obool),tc_HOL_Obool),U_13883),hAPP(c_COMBS(tc_fun(U_13883,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(U_13883,tc_HOL_Obool)),c_fimplies),hAPP(hAPP(c_COMBC(tc_fun(U_13883,tc_HOL_Obool),tc_fun(tc_fun(U_13883,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(U_13883,tc_HOL_Obool))),U_13884)))),c_member(U_13883)))),
    inference(clausify,[status(thm)],[f_3534_2]) ).

fof(f_3535_1,plain,
    ! [V_B_2,T_c,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))
      | ? [B_a] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_a)))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__UN__I]) ).

fof(f_3535_2,plain,
    ! [U_13889,U_13888,U_13887,U_13886] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13888),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13886,tc_fun(U_13888,tc_HOL_Obool)),U_13887),U_13889)))
      | ? [U_13885] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13888),hAPP(U_13889,U_13885)))
          & hBOOL(hAPP(hAPP(c_member(U_13886),U_13885),U_13887)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13886),U_13887)) ),
    inference(variable_rename,[status(thm)],[f_3535_1]) ).

fof(f_3535_3,plain,
    ! [U_13889,U_13888,U_13887,U_13886] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13888),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13886,tc_fun(U_13888,tc_HOL_Obool)),U_13887),U_13889)))
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13888),hAPP(U_13889,sK338(U_13889,U_13888,U_13887,U_13886))))
        & hBOOL(hAPP(hAPP(c_member(U_13886),sK338(U_13889,U_13888,U_13887,U_13886)),U_13887)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13886),U_13887)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK338]),skolemize(U_13885,sK338(U_13889,U_13888,U_13887,U_13886))],[f_3535_2]) ).

cnf(f_3535_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13886),sK338(U_13889,U_13888,U_13887,U_13886)),U_13887))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_13888),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13886,tc_fun(U_13888,tc_HOL_Obool)),U_13887),U_13889)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13886),U_13887)) ),
    inference(clausify,[status(thm)],[f_3535_3]) ).

cnf(f_3535_5,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13888),hAPP(U_13889,sK338(U_13889,U_13888,U_13887,U_13886))))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_13888),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13886,tc_fun(U_13888,tc_HOL_Obool)),U_13887),U_13889)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13886),U_13887)) ),
    inference(clausify,[status(thm)],[f_3535_3]) ).

fof(f_3536_1,plain,
    ! [V_k_2,V_N_2] :
      ( c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_k_2),V_N_2)
      | ? [B_x] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),B_x))
          & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_inj__on__diff__nat]) ).

fof(f_3536_2,plain,
    ! [U_13892,U_13891] :
      ( c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),U_13892),U_13891)
      | ? [U_13890] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_13892),U_13890))
          & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_13890),U_13891)) ) ),
    inference(variable_rename,[status(thm)],[f_3536_1]) ).

fof(f_3536_3,plain,
    ! [U_13892,U_13891] :
      ( c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),U_13892),U_13891)
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_13892),sK339(U_13892,U_13891)))
        & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK339(U_13892,U_13891)),U_13891)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK339]),skolemize(U_13890,sK339(U_13892,U_13891))],[f_3536_2]) ).

cnf(f_3536_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK339(U_13892,U_13891)),U_13891))
    | c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),U_13892),U_13891) ),
    inference(clausify,[status(thm)],[f_3536_3]) ).

cnf(f_3536_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_13892),sK339(U_13892,U_13891)))
    | c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),U_13892),U_13891) ),
    inference(clausify,[status(thm)],[f_3536_3]) ).

fof(f_3537_1,plain,
    ! [T_b,V_r_2,T_c] :
      ( c_Wellfounded_OwfP(T_c,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2))
      | ? [B_i,B_j] :
          ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_Predicate_ODomainP(T_c,T_c,hAPP(V_r_2,B_i))),c_Predicate_ORangeP(T_c,T_c,hAPP(V_r_2,B_j))) != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
          & hAPP(V_r_2,B_i) != hAPP(V_r_2,B_j) )
      | ? [B_i] : ~ c_Wellfounded_OwfP(T_c,hAPP(V_r_2,B_i)) ),
    inference(fof_nnf,[status(thm)],[fact_wfP__SUP]) ).

fof(f_3537_2,plain,
    ! [U_13898,U_13897,U_13896] :
      ( c_Wellfounded_OwfP(U_13896,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13898,tc_fun(U_13896,tc_fun(U_13896,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_13898,tc_HOL_Obool))),U_13897))
      | ? [U_13895,U_13894] :
          ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13896,tc_HOL_Obool)),c_Predicate_ODomainP(U_13896,U_13896,hAPP(U_13897,U_13895))),c_Predicate_ORangeP(U_13896,U_13896,hAPP(U_13897,U_13894))) != c_Orderings_Obot__class_Obot(tc_fun(U_13896,tc_HOL_Obool))
          & hAPP(U_13897,U_13895) != hAPP(U_13897,U_13894) )
      | ? [U_13893] : ~ c_Wellfounded_OwfP(U_13896,hAPP(U_13897,U_13893)) ),
    inference(variable_rename,[status(thm)],[f_3537_1]) ).

fof(f_3537_3,plain,
    ! [U_13898,U_13897,U_13896] :
      ( c_Wellfounded_OwfP(U_13896,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13898,tc_fun(U_13896,tc_fun(U_13896,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_13898,tc_HOL_Obool))),U_13897))
      | ? [U_13895,U_13894] :
          ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13896,tc_HOL_Obool)),c_Predicate_ODomainP(U_13896,U_13896,hAPP(U_13897,U_13895))),c_Predicate_ORangeP(U_13896,U_13896,hAPP(U_13897,U_13894))) != c_Orderings_Obot__class_Obot(tc_fun(U_13896,tc_HOL_Obool))
          & hAPP(U_13897,U_13895) != hAPP(U_13897,U_13894) )
      | ~ c_Wellfounded_OwfP(U_13896,hAPP(U_13897,sK340(U_13898,U_13897,U_13896))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK340]),skolemize(U_13893,sK340(U_13898,U_13897,U_13896))],[f_3537_2]) ).

fof(f_3537_4,plain,
    ! [U_13898,U_13897,U_13896] :
      ( c_Wellfounded_OwfP(U_13896,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13898,tc_fun(U_13896,tc_fun(U_13896,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_13898,tc_HOL_Obool))),U_13897))
      | ? [U_13894] :
          ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13896,tc_HOL_Obool)),c_Predicate_ODomainP(U_13896,U_13896,hAPP(U_13897,sK341(U_13898,U_13897,U_13896)))),c_Predicate_ORangeP(U_13896,U_13896,hAPP(U_13897,U_13894))) != c_Orderings_Obot__class_Obot(tc_fun(U_13896,tc_HOL_Obool))
          & hAPP(U_13897,sK341(U_13898,U_13897,U_13896)) != hAPP(U_13897,U_13894) )
      | ~ c_Wellfounded_OwfP(U_13896,hAPP(U_13897,sK340(U_13898,U_13897,U_13896))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK341]),skolemize(U_13895,sK341(U_13898,U_13897,U_13896))],[f_3537_3]) ).

fof(f_3537_5,plain,
    ! [U_13898,U_13897,U_13896] :
      ( c_Wellfounded_OwfP(U_13896,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13898,tc_fun(U_13896,tc_fun(U_13896,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_13898,tc_HOL_Obool))),U_13897))
      | ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13896,tc_HOL_Obool)),c_Predicate_ODomainP(U_13896,U_13896,hAPP(U_13897,sK341(U_13898,U_13897,U_13896)))),c_Predicate_ORangeP(U_13896,U_13896,hAPP(U_13897,sK342(U_13898,U_13897,U_13896)))) != c_Orderings_Obot__class_Obot(tc_fun(U_13896,tc_HOL_Obool))
        & hAPP(U_13897,sK341(U_13898,U_13897,U_13896)) != hAPP(U_13897,sK342(U_13898,U_13897,U_13896)) )
      | ~ c_Wellfounded_OwfP(U_13896,hAPP(U_13897,sK340(U_13898,U_13897,U_13896))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK342]),skolemize(U_13894,sK342(U_13898,U_13897,U_13896))],[f_3537_4]) ).

cnf(f_3537_6,plain,
    ( hAPP(U_13897,sK341(U_13898,U_13897,U_13896)) != hAPP(U_13897,sK342(U_13898,U_13897,U_13896))
    | c_Wellfounded_OwfP(U_13896,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13898,tc_fun(U_13896,tc_fun(U_13896,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_13898,tc_HOL_Obool))),U_13897))
    | ~ c_Wellfounded_OwfP(U_13896,hAPP(U_13897,sK340(U_13898,U_13897,U_13896))) ),
    inference(clausify,[status(thm)],[f_3537_5]) ).

cnf(f_3537_7,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13896,tc_HOL_Obool)),c_Predicate_ODomainP(U_13896,U_13896,hAPP(U_13897,sK341(U_13898,U_13897,U_13896)))),c_Predicate_ORangeP(U_13896,U_13896,hAPP(U_13897,sK342(U_13898,U_13897,U_13896)))) != c_Orderings_Obot__class_Obot(tc_fun(U_13896,tc_HOL_Obool))
    | c_Wellfounded_OwfP(U_13896,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13898,tc_fun(U_13896,tc_fun(U_13896,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_13898,tc_HOL_Obool))),U_13897))
    | ~ c_Wellfounded_OwfP(U_13896,hAPP(U_13897,sK340(U_13898,U_13897,U_13896))) ),
    inference(clausify,[status(thm)],[f_3537_5]) ).

fof(f_3538_1,plain,
    ! [V_c_2,V_z_2,T_d,T_c,T_b,V_p_2] :
      ( hBOOL(hAPP(hAPP(c_member(T_d),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_d,tc_HOL_Obool)),V_c_2),V_p_2)))
      | ? [B_a,B_b] :
          ( ~ hBOOL(hAPP(hAPP(c_member(T_d),V_z_2),hAPP(hAPP(V_c_2,B_a),B_b)))
          & V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b) ) ),
    inference(fof_nnf,[status(thm)],[fact_mem__splitI2]) ).

fof(f_3538_2,plain,
    ! [U_13906,U_13905,U_13904,U_13903,U_13902,U_13901] :
      ( hBOOL(hAPP(hAPP(c_member(U_13904),U_13905),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13902,U_13903,tc_fun(U_13904,tc_HOL_Obool)),U_13906),U_13901)))
      | ? [U_13900,U_13899] :
          ( ~ hBOOL(hAPP(hAPP(c_member(U_13904),U_13905),hAPP(hAPP(U_13906,U_13900),U_13899)))
          & U_13901 = hAPP(hAPP(c_Product__Type_OPair(U_13902,U_13903),U_13900),U_13899) ) ),
    inference(variable_rename,[status(thm)],[f_3538_1]) ).

fof(f_3538_3,plain,
    ! [U_13906,U_13905,U_13904,U_13903,U_13902,U_13901] :
      ( hBOOL(hAPP(hAPP(c_member(U_13904),U_13905),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13902,U_13903,tc_fun(U_13904,tc_HOL_Obool)),U_13906),U_13901)))
      | ? [U_13899] :
          ( ~ hBOOL(hAPP(hAPP(c_member(U_13904),U_13905),hAPP(hAPP(U_13906,sK343(U_13906,U_13905,U_13904,U_13903,U_13902,U_13901)),U_13899)))
          & U_13901 = hAPP(hAPP(c_Product__Type_OPair(U_13902,U_13903),sK343(U_13906,U_13905,U_13904,U_13903,U_13902,U_13901)),U_13899) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK343]),skolemize(U_13900,sK343(U_13906,U_13905,U_13904,U_13903,U_13902,U_13901))],[f_3538_2]) ).

fof(f_3538_4,plain,
    ! [U_13906,U_13905,U_13904,U_13903,U_13902,U_13901] :
      ( hBOOL(hAPP(hAPP(c_member(U_13904),U_13905),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13902,U_13903,tc_fun(U_13904,tc_HOL_Obool)),U_13906),U_13901)))
      | ( ~ hBOOL(hAPP(hAPP(c_member(U_13904),U_13905),hAPP(hAPP(U_13906,sK343(U_13906,U_13905,U_13904,U_13903,U_13902,U_13901)),sK344(U_13906,U_13905,U_13904,U_13903,U_13902,U_13901))))
        & U_13901 = hAPP(hAPP(c_Product__Type_OPair(U_13902,U_13903),sK343(U_13906,U_13905,U_13904,U_13903,U_13902,U_13901)),sK344(U_13906,U_13905,U_13904,U_13903,U_13902,U_13901)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK344]),skolemize(U_13899,sK344(U_13906,U_13905,U_13904,U_13903,U_13902,U_13901))],[f_3538_3]) ).

cnf(f_3538_5,plain,
    ( U_13901 = hAPP(hAPP(c_Product__Type_OPair(U_13902,U_13903),sK343(U_13906,U_13905,U_13904,U_13903,U_13902,U_13901)),sK344(U_13906,U_13905,U_13904,U_13903,U_13902,U_13901))
    | hBOOL(hAPP(hAPP(c_member(U_13904),U_13905),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13902,U_13903,tc_fun(U_13904,tc_HOL_Obool)),U_13906),U_13901))) ),
    inference(clausify,[status(thm)],[f_3538_4]) ).

cnf(f_3538_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_13904),U_13905),hAPP(hAPP(U_13906,sK343(U_13906,U_13905,U_13904,U_13903,U_13902,U_13901)),sK344(U_13906,U_13905,U_13904,U_13903,U_13902,U_13901))))
    | hBOOL(hAPP(hAPP(c_member(U_13904),U_13905),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13902,U_13903,tc_fun(U_13904,tc_HOL_Obool)),U_13906),U_13901))) ),
    inference(clausify,[status(thm)],[f_3538_4]) ).

fof(f_3539_1,plain,
    ! [V_p_2,V_c_2,T_d,T_c,V_z_2,T_b] :
      ( ? [B_x,B_y] :
          ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_c_2,B_x),B_y)))
          & V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),B_x),B_y) )
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_fun(T_b,tc_HOL_Obool)),V_c_2),V_p_2))) ),
    inference(fof_nnf,[status(thm)],[fact_mem__splitE]) ).

fof(f_3539_2,plain,
    ! [U_13914,U_13913,U_13912,U_13911,U_13910,U_13909] :
      ( ? [U_13908,U_13907] :
          ( hBOOL(hAPP(hAPP(c_member(U_13909),U_13910),hAPP(hAPP(U_13913,U_13908),U_13907)))
          & U_13914 = hAPP(hAPP(c_Product__Type_OPair(U_13911,U_13912),U_13908),U_13907) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_13909),U_13910),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13911,U_13912,tc_fun(U_13909,tc_HOL_Obool)),U_13913),U_13914))) ),
    inference(variable_rename,[status(thm)],[f_3539_1]) ).

fof(f_3539_3,plain,
    ! [U_13914,U_13913,U_13912,U_13911,U_13910,U_13909] :
      ( ? [U_13907] :
          ( hBOOL(hAPP(hAPP(c_member(U_13909),U_13910),hAPP(hAPP(U_13913,sK345(U_13914,U_13913,U_13912,U_13911,U_13910,U_13909)),U_13907)))
          & U_13914 = hAPP(hAPP(c_Product__Type_OPair(U_13911,U_13912),sK345(U_13914,U_13913,U_13912,U_13911,U_13910,U_13909)),U_13907) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_13909),U_13910),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13911,U_13912,tc_fun(U_13909,tc_HOL_Obool)),U_13913),U_13914))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK345]),skolemize(U_13908,sK345(U_13914,U_13913,U_13912,U_13911,U_13910,U_13909))],[f_3539_2]) ).

fof(f_3539_4,plain,
    ! [U_13914,U_13913,U_13912,U_13911,U_13910,U_13909] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_13909),U_13910),hAPP(hAPP(U_13913,sK345(U_13914,U_13913,U_13912,U_13911,U_13910,U_13909)),sK346(U_13914,U_13913,U_13912,U_13911,U_13910,U_13909))))
        & U_13914 = hAPP(hAPP(c_Product__Type_OPair(U_13911,U_13912),sK345(U_13914,U_13913,U_13912,U_13911,U_13910,U_13909)),sK346(U_13914,U_13913,U_13912,U_13911,U_13910,U_13909)) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_13909),U_13910),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13911,U_13912,tc_fun(U_13909,tc_HOL_Obool)),U_13913),U_13914))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK346]),skolemize(U_13907,sK346(U_13914,U_13913,U_13912,U_13911,U_13910,U_13909))],[f_3539_3]) ).

cnf(f_3539_5,plain,
    ( U_13914 = hAPP(hAPP(c_Product__Type_OPair(U_13911,U_13912),sK345(U_13914,U_13913,U_13912,U_13911,U_13910,U_13909)),sK346(U_13914,U_13913,U_13912,U_13911,U_13910,U_13909))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13909),U_13910),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13911,U_13912,tc_fun(U_13909,tc_HOL_Obool)),U_13913),U_13914))) ),
    inference(clausify,[status(thm)],[f_3539_4]) ).

cnf(f_3539_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13909),U_13910),hAPP(hAPP(U_13913,sK345(U_13914,U_13913,U_13912,U_13911,U_13910,U_13909)),sK346(U_13914,U_13913,U_13912,U_13911,U_13910,U_13909))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13909),U_13910),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13911,U_13912,tc_fun(U_13909,tc_HOL_Obool)),U_13913),U_13914))) ),
    inference(clausify,[status(thm)],[f_3539_4]) ).

fof(f_3540_1,plain,
    ! [V_P_2,T_c,T_b] : c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_P_2)) = c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(hAPP(c_COMBS(tc_prod(T_b,T_c),T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_HOL_Obool),tc_prod(T_b,T_c)),V_P_2),c_Product__Type_Ofst(T_b,T_c))),c_Product__Type_Osnd(T_b,T_c))),
    inference(fof_nnf,[status(thm)],[fact_Eps__split]) ).

fof(f_3540_2,plain,
    ! [U_13917,U_13916,U_13915] : c_Hilbert__Choice_OEps(tc_prod(U_13915,U_13916),hAPP(c_Product__Type_Oprod_Oprod__case(U_13915,U_13916,tc_HOL_Obool),U_13917)) = c_Hilbert__Choice_OEps(tc_prod(U_13915,U_13916),hAPP(hAPP(c_COMBS(tc_prod(U_13915,U_13916),U_13916,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_13915,tc_fun(U_13916,tc_HOL_Obool),tc_prod(U_13915,U_13916)),U_13917),c_Product__Type_Ofst(U_13915,U_13916))),c_Product__Type_Osnd(U_13915,U_13916))),
    inference(variable_rename,[status(thm)],[f_3540_1]) ).

cnf(f_3540_3,plain,
    c_Hilbert__Choice_OEps(tc_prod(U_13915,U_13916),hAPP(c_Product__Type_Oprod_Oprod__case(U_13915,U_13916,tc_HOL_Obool),U_13917)) = c_Hilbert__Choice_OEps(tc_prod(U_13915,U_13916),hAPP(hAPP(c_COMBS(tc_prod(U_13915,U_13916),U_13916,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_13915,tc_fun(U_13916,tc_HOL_Obool),tc_prod(U_13915,U_13916)),U_13917),c_Product__Type_Ofst(U_13915,U_13916))),c_Product__Type_Osnd(U_13915,U_13916))),
    inference(clausify,[status(thm)],[f_3540_2]) ).

fof(f_3541_1,plain,
    ! [T_b,V_c_2,V_P_2] :
      ( hBOOL(hAPP(V_P_2,V_c_2))
      | V_c_2 != c_Hilbert__Choice_OEps(T_b,V_P_2)
      | ! [B_x1] : ~ hBOOL(hAPP(V_P_2,B_x1)) ),
    inference(fof_nnf,[status(thm)],[fact_exE__some]) ).

fof(f_3541_2,plain,
    ! [U_13921,U_13920,U_13919] :
      ( hBOOL(hAPP(U_13919,U_13920))
      | U_13920 != c_Hilbert__Choice_OEps(U_13921,U_13919)
      | ! [U_13918] : ~ hBOOL(hAPP(U_13919,U_13918)) ),
    inference(variable_rename,[status(thm)],[f_3541_1]) ).

cnf(f_3541_3,plain,
    ( hBOOL(hAPP(U_13919,U_13920))
    | U_13920 != c_Hilbert__Choice_OEps(U_13921,U_13919)
    | ~ hBOOL(hAPP(U_13919,U_13918)) ),
    inference(clausify,[status(thm)],[f_3541_2]) ).

fof(f_3542_1,plain,
    ! [V_x_2,T_b] : c_Hilbert__Choice_OEps(T_b,hAPP(c_fequal,V_x_2)) = V_x_2,
    inference(fof_nnf,[status(thm)],[fact_some__sym__eq__trivial]) ).

fof(f_3542_2,plain,
    ! [U_13923,U_13922] : c_Hilbert__Choice_OEps(U_13922,hAPP(c_fequal,U_13923)) = U_13923,
    inference(variable_rename,[status(thm)],[f_3542_1]) ).

cnf(f_3542_3,plain,
    c_Hilbert__Choice_OEps(U_13922,hAPP(c_fequal,U_13923)) = U_13923,
    inference(clausify,[status(thm)],[f_3542_2]) ).

fof(f_3543_1,plain,
    ! [V_x_2,T_b] : c_Hilbert__Choice_OEps(T_b,hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)) = V_x_2,
    inference(fof_nnf,[status(thm)],[fact_some__eq__trivial]) ).

fof(f_3543_2,plain,
    ! [U_13925,U_13924] : c_Hilbert__Choice_OEps(U_13924,hAPP(hAPP(c_COMBC(U_13924,U_13924,tc_HOL_Obool),c_fequal),U_13925)) = U_13925,
    inference(variable_rename,[status(thm)],[f_3543_1]) ).

cnf(f_3543_3,plain,
    c_Hilbert__Choice_OEps(U_13924,hAPP(hAPP(c_COMBC(U_13924,U_13924,tc_HOL_Obool),c_fequal),U_13925)) = U_13925,
    inference(clausify,[status(thm)],[f_3543_2]) ).

fof(f_3544_1,plain,
    ! [T_b,V_P_2] :
      ( ( hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_b,V_P_2)))
        | ! [B_x1] : ~ hBOOL(hAPP(V_P_2,B_x1)) )
      & ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
        | ~ hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_b,V_P_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_some__eq__ex]) ).

fof(f_3544_2,plain,
    ! [U_13929,U_13928] :
      ( ( hBOOL(hAPP(U_13928,c_Hilbert__Choice_OEps(U_13929,U_13928)))
        | ! [U_13927] : ~ hBOOL(hAPP(U_13928,U_13927)) )
      & ( ? [U_13926] : hBOOL(hAPP(U_13928,U_13926))
        | ~ hBOOL(hAPP(U_13928,c_Hilbert__Choice_OEps(U_13929,U_13928))) ) ),
    inference(variable_rename,[status(thm)],[f_3544_1]) ).

fof(f_3544_3,plain,
    ( ! [U_13933,U_13931] :
        ( hBOOL(hAPP(U_13931,c_Hilbert__Choice_OEps(U_13933,U_13931)))
        | ! [U_13927] : ~ hBOOL(hAPP(U_13931,U_13927)) )
    & ! [U_13932,U_13930] :
        ( ? [U_13926] : hBOOL(hAPP(U_13930,U_13926))
        | ~ hBOOL(hAPP(U_13930,c_Hilbert__Choice_OEps(U_13932,U_13930))) ) ),
    inference(miniscope,[status(thm)],[f_3544_2]) ).

fof(f_3544_4,plain,
    ( ! [U_13933,U_13931] :
        ( hBOOL(hAPP(U_13931,c_Hilbert__Choice_OEps(U_13933,U_13931)))
        | ! [U_13927] : ~ hBOOL(hAPP(U_13931,U_13927)) )
    & ! [U_13932,U_13930] :
        ( hBOOL(hAPP(U_13930,sK347(U_13932,U_13930)))
        | ~ hBOOL(hAPP(U_13930,c_Hilbert__Choice_OEps(U_13932,U_13930))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK347]),skolemize(U_13926,sK347(U_13932,U_13930))],[f_3544_3]) ).

cnf(f_3544_5,plain,
    ( hBOOL(hAPP(U_13930,sK347(U_13932,U_13930)))
    | ~ hBOOL(hAPP(U_13930,c_Hilbert__Choice_OEps(U_13932,U_13930))) ),
    inference(clausify,[status(thm)],[f_3544_4]) ).

cnf(f_3544_6,plain,
    ( hBOOL(hAPP(U_13931,c_Hilbert__Choice_OEps(U_13933,U_13931)))
    | ~ hBOOL(hAPP(U_13931,U_13927)) ),
    inference(clausify,[status(thm)],[f_3544_4]) ).

fof(f_3545_1,plain,
    ! [T_b,V_P_2] :
      ( hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_b,V_P_2)))
      | ! [B_x1] : ~ hBOOL(hAPP(V_P_2,B_x1)) ),
    inference(fof_nnf,[status(thm)],[fact_someI__ex]) ).

fof(f_3545_2,plain,
    ! [U_13936,U_13935] :
      ( hBOOL(hAPP(U_13935,c_Hilbert__Choice_OEps(U_13936,U_13935)))
      | ! [U_13934] : ~ hBOOL(hAPP(U_13935,U_13934)) ),
    inference(variable_rename,[status(thm)],[f_3545_1]) ).

cnf(f_3545_3,plain,
    ( hBOOL(hAPP(U_13935,c_Hilbert__Choice_OEps(U_13936,U_13935)))
    | ~ hBOOL(hAPP(U_13935,U_13934)) ),
    inference(clausify,[status(thm)],[f_3545_2]) ).

fof(f_3546_1,plain,
    ! [T_b,B_P] :
      ( hBOOL(hAPP(B_P,c_Hilbert__Choice_OEps(T_b,B_P)))
      | ! [B_x] : ~ hBOOL(hAPP(B_P,B_x)) ),
    inference(fof_nnf,[status(thm)],[fact_tfl__some]) ).

fof(f_3546_2,plain,
    ! [U_13939,U_13938] :
      ( hBOOL(hAPP(U_13938,c_Hilbert__Choice_OEps(U_13939,U_13938)))
      | ! [U_13937] : ~ hBOOL(hAPP(U_13938,U_13937)) ),
    inference(variable_rename,[status(thm)],[f_3546_1]) ).

cnf(f_3546_3,plain,
    ( hBOOL(hAPP(U_13938,c_Hilbert__Choice_OEps(U_13939,U_13938)))
    | ~ hBOOL(hAPP(U_13938,U_13937)) ),
    inference(clausify,[status(thm)],[f_3546_2]) ).

fof(f_3547_1,plain,
    ! [T_b,V_x_2,V_P_2] :
      ( hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_b,V_P_2)))
      | ~ hBOOL(hAPP(V_P_2,V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_someI]) ).

fof(f_3547_2,plain,
    ! [U_13942,U_13941,U_13940] :
      ( hBOOL(hAPP(U_13940,c_Hilbert__Choice_OEps(U_13942,U_13940)))
      | ~ hBOOL(hAPP(U_13940,U_13941)) ),
    inference(variable_rename,[status(thm)],[f_3547_1]) ).

cnf(f_3547_3,plain,
    ( hBOOL(hAPP(U_13940,c_Hilbert__Choice_OEps(U_13942,U_13940)))
    | ~ hBOOL(hAPP(U_13940,U_13941)) ),
    inference(clausify,[status(thm)],[f_3547_2]) ).

fof(f_3548_1,plain,
    ! [V_P_2,T_c,T_b] : c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),V_P_2) = c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,T_c),V_P_2)),c_Product__Type_OPair(T_b,T_c)))),
    inference(fof_nnf,[status(thm)],[fact_split__paired__Eps]) ).

fof(f_3548_2,plain,
    ! [U_13945,U_13944,U_13943] : c_Hilbert__Choice_OEps(tc_prod(U_13943,U_13944),U_13945) = c_Hilbert__Choice_OEps(tc_prod(U_13943,U_13944),hAPP(c_Product__Type_Oprod_Oprod__case(U_13943,U_13944,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_13944,tc_prod(U_13943,U_13944)),tc_fun(U_13944,tc_HOL_Obool),U_13943),hAPP(c_COMBB(tc_prod(U_13943,U_13944),tc_HOL_Obool,U_13944),U_13945)),c_Product__Type_OPair(U_13943,U_13944)))),
    inference(variable_rename,[status(thm)],[f_3548_1]) ).

cnf(f_3548_3,plain,
    c_Hilbert__Choice_OEps(tc_prod(U_13943,U_13944),U_13945) = c_Hilbert__Choice_OEps(tc_prod(U_13943,U_13944),hAPP(c_Product__Type_Oprod_Oprod__case(U_13943,U_13944,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_13944,tc_prod(U_13943,U_13944)),tc_fun(U_13944,tc_HOL_Obool),U_13943),hAPP(c_COMBB(tc_prod(U_13943,U_13944),tc_HOL_Obool,U_13944),U_13945)),c_Product__Type_OPair(U_13943,U_13944)))),
    inference(clausify,[status(thm)],[f_3548_2]) ).

fof(f_3549_1,plain,
    ! [V_y_2,V_x_2,T_c,T_b] : c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_x_2)))),hAPP(c_fequal,V_y_2)))) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2),
    inference(fof_nnf,[status(thm)],[fact_Eps__split__eq]) ).

fof(f_3549_2,plain,
    ! [U_13949,U_13948,U_13947,U_13946] : c_Hilbert__Choice_OEps(tc_prod(U_13946,U_13947),hAPP(c_Product__Type_Oprod_Oprod__case(U_13946,U_13947,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13946,tc_fun(U_13947,tc_HOL_Obool),tc_fun(U_13947,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13947,tc_HOL_Obool),tc_fun(U_13947,tc_HOL_Obool)),U_13946),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13947)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13946),c_fconj),hAPP(c_fequal,U_13948)))),hAPP(c_fequal,U_13949)))) = hAPP(hAPP(c_Product__Type_OPair(U_13946,U_13947),U_13948),U_13949),
    inference(variable_rename,[status(thm)],[f_3549_1]) ).

cnf(f_3549_3,plain,
    c_Hilbert__Choice_OEps(tc_prod(U_13946,U_13947),hAPP(c_Product__Type_Oprod_Oprod__case(U_13946,U_13947,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13946,tc_fun(U_13947,tc_HOL_Obool),tc_fun(U_13947,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13947,tc_HOL_Obool),tc_fun(U_13947,tc_HOL_Obool)),U_13946),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13947)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13946),c_fconj),hAPP(c_fequal,U_13948)))),hAPP(c_fequal,U_13949)))) = hAPP(hAPP(c_Product__Type_OPair(U_13946,U_13947),U_13948),U_13949),
    inference(clausify,[status(thm)],[f_3549_2]) ).

fof(f_3550_1,plain,
    ! [V_R_2,T_b] :
      ( c_Wellfounded_Owf(T_b,V_R_2)
      | ? [B_A] :
          ( B_A != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_A),hAPP(c_Relation_OImage(T_b,T_b,V_R_2),B_A))) ) ),
    inference(fof_nnf,[status(thm)],[fact_wfI__pf]) ).

fof(f_3550_2,plain,
    ! [U_13952,U_13951] :
      ( c_Wellfounded_Owf(U_13951,U_13952)
      | ? [U_13950] :
          ( U_13950 != c_Orderings_Obot__class_Obot(tc_fun(U_13951,tc_HOL_Obool))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13951,tc_HOL_Obool)),U_13950),hAPP(c_Relation_OImage(U_13951,U_13951,U_13952),U_13950))) ) ),
    inference(variable_rename,[status(thm)],[f_3550_1]) ).

fof(f_3550_3,plain,
    ! [U_13952,U_13951] :
      ( c_Wellfounded_Owf(U_13951,U_13952)
      | ( sK348(U_13952,U_13951) != c_Orderings_Obot__class_Obot(tc_fun(U_13951,tc_HOL_Obool))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13951,tc_HOL_Obool)),sK348(U_13952,U_13951)),hAPP(c_Relation_OImage(U_13951,U_13951,U_13952),sK348(U_13952,U_13951)))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK348]),skolemize(U_13950,sK348(U_13952,U_13951))],[f_3550_2]) ).

cnf(f_3550_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13951,tc_HOL_Obool)),sK348(U_13952,U_13951)),hAPP(c_Relation_OImage(U_13951,U_13951,U_13952),sK348(U_13952,U_13951))))
    | c_Wellfounded_Owf(U_13951,U_13952) ),
    inference(clausify,[status(thm)],[f_3550_3]) ).

cnf(f_3550_5,plain,
    ( sK348(U_13952,U_13951) != c_Orderings_Obot__class_Obot(tc_fun(U_13951,tc_HOL_Obool))
    | c_Wellfounded_Owf(U_13951,U_13952) ),
    inference(clausify,[status(thm)],[f_3550_3]) ).

fof(f_3551_1,plain,
    ! [V_D_2,V_B_2,T_c,V_C_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_C_2),V_D_2)))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_B_2,B_x)),hAPP(V_D_2,B_x)))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Sigma__mono]) ).

fof(f_3551_2,plain,
    ! [U_13959,U_13958,U_13957,U_13956,U_13955,U_13954] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13954,U_13957),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13954,U_13957),U_13955),U_13958)),hAPP(hAPP(c_Product__Type_OSigma(U_13954,U_13957),U_13956),U_13959)))
      | ? [U_13953] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13957,tc_HOL_Obool)),hAPP(U_13958,U_13953)),hAPP(U_13959,U_13953)))
          & hBOOL(hAPP(hAPP(c_member(U_13954),U_13953),U_13955)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13954,tc_HOL_Obool)),U_13955),U_13956)) ),
    inference(variable_rename,[status(thm)],[f_3551_1]) ).

fof(f_3551_3,plain,
    ! [U_13959,U_13958,U_13957,U_13956,U_13955,U_13954] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13954,U_13957),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13954,U_13957),U_13955),U_13958)),hAPP(hAPP(c_Product__Type_OSigma(U_13954,U_13957),U_13956),U_13959)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13957,tc_HOL_Obool)),hAPP(U_13958,sK349(U_13959,U_13958,U_13957,U_13956,U_13955,U_13954))),hAPP(U_13959,sK349(U_13959,U_13958,U_13957,U_13956,U_13955,U_13954))))
        & hBOOL(hAPP(hAPP(c_member(U_13954),sK349(U_13959,U_13958,U_13957,U_13956,U_13955,U_13954)),U_13955)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13954,tc_HOL_Obool)),U_13955),U_13956)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK349]),skolemize(U_13953,sK349(U_13959,U_13958,U_13957,U_13956,U_13955,U_13954))],[f_3551_2]) ).

cnf(f_3551_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13954),sK349(U_13959,U_13958,U_13957,U_13956,U_13955,U_13954)),U_13955))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13954,U_13957),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13954,U_13957),U_13955),U_13958)),hAPP(hAPP(c_Product__Type_OSigma(U_13954,U_13957),U_13956),U_13959)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13954,tc_HOL_Obool)),U_13955),U_13956)) ),
    inference(clausify,[status(thm)],[f_3551_3]) ).

cnf(f_3551_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13957,tc_HOL_Obool)),hAPP(U_13958,sK349(U_13959,U_13958,U_13957,U_13956,U_13955,U_13954))),hAPP(U_13959,sK349(U_13959,U_13958,U_13957,U_13956,U_13955,U_13954))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13954,U_13957),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_13954,U_13957),U_13955),U_13958)),hAPP(hAPP(c_Product__Type_OSigma(U_13954,U_13957),U_13956),U_13959)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13954,tc_HOL_Obool)),U_13955),U_13956)) ),
    inference(clausify,[status(thm)],[f_3551_3]) ).

fof(f_3552_1,plain,
    ! [V_R_2,V_x_2,T_b] :
      ( ? [B_z] :
          ( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_z),c_Wellfounded_Oacc(T_b,V_R_2)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_z),V_x_2)),V_R_2)) )
      | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_R_2))) ),
    inference(fof_nnf,[status(thm)],[fact_not__acc__down]) ).

fof(f_3552_2,plain,
    ! [U_13963,U_13962,U_13961] :
      ( ? [U_13960] :
          ( ~ hBOOL(hAPP(hAPP(c_member(U_13961),U_13960),c_Wellfounded_Oacc(U_13961,U_13963)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_13961,U_13961)),hAPP(hAPP(c_Product__Type_OPair(U_13961,U_13961),U_13960),U_13962)),U_13963)) )
      | hBOOL(hAPP(hAPP(c_member(U_13961),U_13962),c_Wellfounded_Oacc(U_13961,U_13963))) ),
    inference(variable_rename,[status(thm)],[f_3552_1]) ).

fof(f_3552_3,plain,
    ! [U_13963,U_13962,U_13961] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(U_13961),sK350(U_13963,U_13962,U_13961)),c_Wellfounded_Oacc(U_13961,U_13963)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_13961,U_13961)),hAPP(hAPP(c_Product__Type_OPair(U_13961,U_13961),sK350(U_13963,U_13962,U_13961)),U_13962)),U_13963)) )
      | hBOOL(hAPP(hAPP(c_member(U_13961),U_13962),c_Wellfounded_Oacc(U_13961,U_13963))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK350]),skolemize(U_13960,sK350(U_13963,U_13962,U_13961))],[f_3552_2]) ).

cnf(f_3552_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13961,U_13961)),hAPP(hAPP(c_Product__Type_OPair(U_13961,U_13961),sK350(U_13963,U_13962,U_13961)),U_13962)),U_13963))
    | hBOOL(hAPP(hAPP(c_member(U_13961),U_13962),c_Wellfounded_Oacc(U_13961,U_13963))) ),
    inference(clausify,[status(thm)],[f_3552_3]) ).

cnf(f_3552_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_13961),sK350(U_13963,U_13962,U_13961)),c_Wellfounded_Oacc(U_13961,U_13963)))
    | hBOOL(hAPP(hAPP(c_member(U_13961),U_13962),c_Wellfounded_Oacc(U_13961,U_13963))) ),
    inference(clausify,[status(thm)],[f_3552_3]) ).

fof(f_3553_1,plain,
    ! [V_r_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2)))
      | ? [B_y] :
          ( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_y),c_Wellfounded_Oacc(T_b,V_r_2)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_x_2)),V_r_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_acc_OaccI]) ).

fof(f_3553_2,plain,
    ! [U_13967,U_13966,U_13965] :
      ( hBOOL(hAPP(hAPP(c_member(U_13965),U_13966),c_Wellfounded_Oacc(U_13965,U_13967)))
      | ? [U_13964] :
          ( ~ hBOOL(hAPP(hAPP(c_member(U_13965),U_13964),c_Wellfounded_Oacc(U_13965,U_13967)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_13965,U_13965)),hAPP(hAPP(c_Product__Type_OPair(U_13965,U_13965),U_13964),U_13966)),U_13967)) ) ),
    inference(variable_rename,[status(thm)],[f_3553_1]) ).

fof(f_3553_3,plain,
    ! [U_13967,U_13966,U_13965] :
      ( hBOOL(hAPP(hAPP(c_member(U_13965),U_13966),c_Wellfounded_Oacc(U_13965,U_13967)))
      | ( ~ hBOOL(hAPP(hAPP(c_member(U_13965),sK351(U_13967,U_13966,U_13965)),c_Wellfounded_Oacc(U_13965,U_13967)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_13965,U_13965)),hAPP(hAPP(c_Product__Type_OPair(U_13965,U_13965),sK351(U_13967,U_13966,U_13965)),U_13966)),U_13967)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK351]),skolemize(U_13964,sK351(U_13967,U_13966,U_13965))],[f_3553_2]) ).

cnf(f_3553_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13965,U_13965)),hAPP(hAPP(c_Product__Type_OPair(U_13965,U_13965),sK351(U_13967,U_13966,U_13965)),U_13966)),U_13967))
    | hBOOL(hAPP(hAPP(c_member(U_13965),U_13966),c_Wellfounded_Oacc(U_13965,U_13967))) ),
    inference(clausify,[status(thm)],[f_3553_3]) ).

cnf(f_3553_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_13965),sK351(U_13967,U_13966,U_13965)),c_Wellfounded_Oacc(U_13965,U_13967)))
    | hBOOL(hAPP(hAPP(c_member(U_13965),U_13966),c_Wellfounded_Oacc(U_13965,U_13967))) ),
    inference(clausify,[status(thm)],[f_3553_3]) ).

fof(f_3554_1,plain,
    ! [V_R_2,V_a2_2,V_a1_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_a1_2),V_a2_2)),c_Wellfounded_Omax__ext(T_b,V_R_2)))
        | ? [B_x] :
            ( ! [B_xa] :
                ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_xa)),V_R_2))
                | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2)) )
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2)) )
        | V_a2_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2)) )
      & ( ( ! [B_x] :
              ( ? [B_xa] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_xa)),V_R_2))
                  & hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2)) )
              | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2)) )
          & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_a1_2),V_a2_2)),c_Wellfounded_Omax__ext(T_b,V_R_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_max__ext_Osimps]) ).

fof(f_3554_2,plain,
    ! [U_13975,U_13974,U_13973,U_13972] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_13972,tc_HOL_Obool),tc_fun(U_13972,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_13972,tc_HOL_Obool),tc_fun(U_13972,tc_HOL_Obool)),U_13973),U_13974)),c_Wellfounded_Omax__ext(U_13972,U_13975)))
        | ? [U_13971] :
            ( ! [U_13970] :
                ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13972,U_13972)),hAPP(hAPP(c_Product__Type_OPair(U_13972,U_13972),U_13971),U_13970)),U_13975))
                | ~ hBOOL(hAPP(hAPP(c_member(U_13972),U_13970),U_13974)) )
            & hBOOL(hAPP(hAPP(c_member(U_13972),U_13971),U_13973)) )
        | U_13974 = c_Orderings_Obot__class_Obot(tc_fun(U_13972,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13972),U_13974))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13972),U_13973)) )
      & ( ( ! [U_13969] :
              ( ? [U_13968] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13972,U_13972)),hAPP(hAPP(c_Product__Type_OPair(U_13972,U_13972),U_13969),U_13968)),U_13975))
                  & hBOOL(hAPP(hAPP(c_member(U_13972),U_13968),U_13974)) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_13972),U_13969),U_13973)) )
          & U_13974 != c_Orderings_Obot__class_Obot(tc_fun(U_13972,tc_HOL_Obool))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_13972),U_13974))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_13972),U_13973)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_13972,tc_HOL_Obool),tc_fun(U_13972,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_13972,tc_HOL_Obool),tc_fun(U_13972,tc_HOL_Obool)),U_13973),U_13974)),c_Wellfounded_Omax__ext(U_13972,U_13975))) ) ),
    inference(variable_rename,[status(thm)],[f_3554_1]) ).

fof(f_3554_3,plain,
    ( ! [U_13983,U_13981,U_13979,U_13977] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_13977,tc_HOL_Obool),tc_fun(U_13977,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_13977,tc_HOL_Obool),tc_fun(U_13977,tc_HOL_Obool)),U_13979),U_13981)),c_Wellfounded_Omax__ext(U_13977,U_13983)))
        | ? [U_13971] :
            ( ! [U_13970] :
                ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13977,U_13977)),hAPP(hAPP(c_Product__Type_OPair(U_13977,U_13977),U_13971),U_13970)),U_13983))
                | ~ hBOOL(hAPP(hAPP(c_member(U_13977),U_13970),U_13981)) )
            & hBOOL(hAPP(hAPP(c_member(U_13977),U_13971),U_13979)) )
        | U_13981 = c_Orderings_Obot__class_Obot(tc_fun(U_13977,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13977),U_13981))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13977),U_13979)) )
    & ! [U_13982,U_13980,U_13978,U_13976] :
        ( ( ! [U_13969] :
              ( ? [U_13968] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13976,U_13976)),hAPP(hAPP(c_Product__Type_OPair(U_13976,U_13976),U_13969),U_13968)),U_13982))
                  & hBOOL(hAPP(hAPP(c_member(U_13976),U_13968),U_13980)) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_13976),U_13969),U_13978)) )
          & U_13980 != c_Orderings_Obot__class_Obot(tc_fun(U_13976,tc_HOL_Obool))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_13976),U_13980))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_13976),U_13978)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_13976,tc_HOL_Obool),tc_fun(U_13976,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_13976,tc_HOL_Obool),tc_fun(U_13976,tc_HOL_Obool)),U_13978),U_13980)),c_Wellfounded_Omax__ext(U_13976,U_13982))) ) ),
    inference(miniscope,[status(thm)],[f_3554_2]) ).

fof(f_3554_4,plain,
    ( ! [U_13983,U_13981,U_13979,U_13977] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_13977,tc_HOL_Obool),tc_fun(U_13977,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_13977,tc_HOL_Obool),tc_fun(U_13977,tc_HOL_Obool)),U_13979),U_13981)),c_Wellfounded_Omax__ext(U_13977,U_13983)))
        | ? [U_13971] :
            ( ! [U_13970] :
                ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13977,U_13977)),hAPP(hAPP(c_Product__Type_OPair(U_13977,U_13977),U_13971),U_13970)),U_13983))
                | ~ hBOOL(hAPP(hAPP(c_member(U_13977),U_13970),U_13981)) )
            & hBOOL(hAPP(hAPP(c_member(U_13977),U_13971),U_13979)) )
        | U_13981 = c_Orderings_Obot__class_Obot(tc_fun(U_13977,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13977),U_13981))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13977),U_13979)) )
    & ! [U_13982,U_13980,U_13978,U_13976] :
        ( ( ! [U_13969] :
              ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13976,U_13976)),hAPP(hAPP(c_Product__Type_OPair(U_13976,U_13976),U_13969),sK352(U_13982,U_13980,U_13978,U_13976,U_13969))),U_13982))
                & hBOOL(hAPP(hAPP(c_member(U_13976),sK352(U_13982,U_13980,U_13978,U_13976,U_13969)),U_13980)) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_13976),U_13969),U_13978)) )
          & U_13980 != c_Orderings_Obot__class_Obot(tc_fun(U_13976,tc_HOL_Obool))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_13976),U_13980))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_13976),U_13978)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_13976,tc_HOL_Obool),tc_fun(U_13976,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_13976,tc_HOL_Obool),tc_fun(U_13976,tc_HOL_Obool)),U_13978),U_13980)),c_Wellfounded_Omax__ext(U_13976,U_13982))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK352]),skolemize(U_13968,sK352(U_13982,U_13980,U_13978,U_13976,U_13969))],[f_3554_3]) ).

fof(f_3554_5,plain,
    ( ! [U_13983,U_13981,U_13979,U_13977] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_13977,tc_HOL_Obool),tc_fun(U_13977,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_13977,tc_HOL_Obool),tc_fun(U_13977,tc_HOL_Obool)),U_13979),U_13981)),c_Wellfounded_Omax__ext(U_13977,U_13983)))
        | ( ! [U_13970] :
              ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13977,U_13977)),hAPP(hAPP(c_Product__Type_OPair(U_13977,U_13977),sK353(U_13983,U_13981,U_13979,U_13977)),U_13970)),U_13983))
              | ~ hBOOL(hAPP(hAPP(c_member(U_13977),U_13970),U_13981)) )
          & hBOOL(hAPP(hAPP(c_member(U_13977),sK353(U_13983,U_13981,U_13979,U_13977)),U_13979)) )
        | U_13981 = c_Orderings_Obot__class_Obot(tc_fun(U_13977,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13977),U_13981))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13977),U_13979)) )
    & ! [U_13982,U_13980,U_13978,U_13976] :
        ( ( ! [U_13969] :
              ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13976,U_13976)),hAPP(hAPP(c_Product__Type_OPair(U_13976,U_13976),U_13969),sK352(U_13982,U_13980,U_13978,U_13976,U_13969))),U_13982))
                & hBOOL(hAPP(hAPP(c_member(U_13976),sK352(U_13982,U_13980,U_13978,U_13976,U_13969)),U_13980)) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_13976),U_13969),U_13978)) )
          & U_13980 != c_Orderings_Obot__class_Obot(tc_fun(U_13976,tc_HOL_Obool))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_13976),U_13980))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_13976),U_13978)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_13976,tc_HOL_Obool),tc_fun(U_13976,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_13976,tc_HOL_Obool),tc_fun(U_13976,tc_HOL_Obool)),U_13978),U_13980)),c_Wellfounded_Omax__ext(U_13976,U_13982))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK353]),skolemize(U_13971,sK353(U_13983,U_13981,U_13979,U_13977))],[f_3554_4]) ).

cnf(f_3554_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13976),U_13978))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_13976,tc_HOL_Obool),tc_fun(U_13976,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_13976,tc_HOL_Obool),tc_fun(U_13976,tc_HOL_Obool)),U_13978),U_13980)),c_Wellfounded_Omax__ext(U_13976,U_13982))) ),
    inference(clausify,[status(thm)],[f_3554_5]) ).

cnf(f_3554_7,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13976),U_13980))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_13976,tc_HOL_Obool),tc_fun(U_13976,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_13976,tc_HOL_Obool),tc_fun(U_13976,tc_HOL_Obool)),U_13978),U_13980)),c_Wellfounded_Omax__ext(U_13976,U_13982))) ),
    inference(clausify,[status(thm)],[f_3554_5]) ).

cnf(f_3554_8,plain,
    ( U_13980 != c_Orderings_Obot__class_Obot(tc_fun(U_13976,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_13976,tc_HOL_Obool),tc_fun(U_13976,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_13976,tc_HOL_Obool),tc_fun(U_13976,tc_HOL_Obool)),U_13978),U_13980)),c_Wellfounded_Omax__ext(U_13976,U_13982))) ),
    inference(clausify,[status(thm)],[f_3554_5]) ).

cnf(f_3554_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13976),sK352(U_13982,U_13980,U_13978,U_13976,U_13969)),U_13980))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13976),U_13969),U_13978))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_13976,tc_HOL_Obool),tc_fun(U_13976,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_13976,tc_HOL_Obool),tc_fun(U_13976,tc_HOL_Obool)),U_13978),U_13980)),c_Wellfounded_Omax__ext(U_13976,U_13982))) ),
    inference(clausify,[status(thm)],[f_3554_5]) ).

cnf(f_3554_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13976,U_13976)),hAPP(hAPP(c_Product__Type_OPair(U_13976,U_13976),U_13969),sK352(U_13982,U_13980,U_13978,U_13976,U_13969))),U_13982))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13976),U_13969),U_13978))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_13976,tc_HOL_Obool),tc_fun(U_13976,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_13976,tc_HOL_Obool),tc_fun(U_13976,tc_HOL_Obool)),U_13978),U_13980)),c_Wellfounded_Omax__ext(U_13976,U_13982))) ),
    inference(clausify,[status(thm)],[f_3554_5]) ).

cnf(f_3554_11,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13977),sK353(U_13983,U_13981,U_13979,U_13977)),U_13979))
    | U_13981 = c_Orderings_Obot__class_Obot(tc_fun(U_13977,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13977),U_13981))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13977),U_13979))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_13977,tc_HOL_Obool),tc_fun(U_13977,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_13977,tc_HOL_Obool),tc_fun(U_13977,tc_HOL_Obool)),U_13979),U_13981)),c_Wellfounded_Omax__ext(U_13977,U_13983))) ),
    inference(clausify,[status(thm)],[f_3554_5]) ).

cnf(f_3554_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13977,U_13977)),hAPP(hAPP(c_Product__Type_OPair(U_13977,U_13977),sK353(U_13983,U_13981,U_13979,U_13977)),U_13970)),U_13983))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13977),U_13970),U_13981))
    | U_13981 = c_Orderings_Obot__class_Obot(tc_fun(U_13977,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13977),U_13981))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13977),U_13979))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_13977,tc_HOL_Obool),tc_fun(U_13977,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_13977,tc_HOL_Obool),tc_fun(U_13977,tc_HOL_Obool)),U_13979),U_13981)),c_Wellfounded_Omax__ext(U_13977,U_13983))) ),
    inference(clausify,[status(thm)],[f_3554_5]) ).

fof(f_3555_1,plain,
    ! [V_X_2,V_a_2,V_f_2,T_b,V_A_2] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_A_2))))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2))
      | ~ c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
      | V_A_2 != c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_def__coinduct__set]) ).

fof(f_3555_2,plain,
    ! [U_13988,U_13987,U_13986,U_13985,U_13984] :
      ( hBOOL(hAPP(hAPP(c_member(U_13985),U_13987),U_13984))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13985,tc_HOL_Obool)),U_13988),hAPP(U_13986,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13985,tc_HOL_Obool)),U_13988),U_13984))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13985),U_13987),U_13988))
      | ~ c_Orderings_Oorder__class_Omono(tc_fun(U_13985,tc_HOL_Obool),tc_fun(U_13985,tc_HOL_Obool),U_13986)
      | U_13984 != c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_13985,tc_HOL_Obool),U_13986) ),
    inference(variable_rename,[status(thm)],[f_3555_1]) ).

cnf(f_3555_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13985),U_13987),U_13984))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13985,tc_HOL_Obool)),U_13988),hAPP(U_13986,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13985,tc_HOL_Obool)),U_13988),U_13984))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13985),U_13987),U_13988))
    | ~ c_Orderings_Oorder__class_Omono(tc_fun(U_13985,tc_HOL_Obool),tc_fun(U_13985,tc_HOL_Obool),U_13986)
    | U_13984 != c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_13985,tc_HOL_Obool),U_13986) ),
    inference(clausify,[status(thm)],[f_3555_2]) ).

fof(f_3556_1,plain,
    ! [V_f_2,V_A_2,T_b] :
      ( V_A_2 = hAPP(V_f_2,V_A_2)
      | ~ c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
      | V_A_2 != c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2)
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_def__gfp__unfold]) ).

fof(f_3556_2,plain,
    ! [U_13991,U_13990,U_13989] :
      ( U_13990 = hAPP(U_13991,U_13990)
      | ~ c_Orderings_Oorder__class_Omono(U_13989,U_13989,U_13991)
      | U_13990 != c_Inductive_Ocomplete__lattice__class_Ogfp(U_13989,U_13991)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_13989) ),
    inference(variable_rename,[status(thm)],[f_3556_1]) ).

cnf(f_3556_3,plain,
    ( U_13990 = hAPP(U_13991,U_13990)
    | ~ c_Orderings_Oorder__class_Omono(U_13989,U_13989,U_13991)
    | U_13990 != c_Inductive_Ocomplete__lattice__class_Ogfp(U_13989,U_13991)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_13989) ),
    inference(clausify,[status(thm)],[f_3556_2]) ).

fof(f_3557_1,plain,
    ! [V_f_2,T_b] :
      ( c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2) = hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2))
      | ~ c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_gfp__unfold]) ).

fof(f_3557_2,plain,
    ! [U_13993,U_13992] :
      ( c_Inductive_Ocomplete__lattice__class_Ogfp(U_13992,U_13993) = hAPP(U_13993,c_Inductive_Ocomplete__lattice__class_Ogfp(U_13992,U_13993))
      | ~ c_Orderings_Oorder__class_Omono(U_13992,U_13992,U_13993)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_13992) ),
    inference(variable_rename,[status(thm)],[f_3557_1]) ).

cnf(f_3557_3,plain,
    ( c_Inductive_Ocomplete__lattice__class_Ogfp(U_13992,U_13993) = hAPP(U_13993,c_Inductive_Ocomplete__lattice__class_Ogfp(U_13992,U_13993))
    | ~ c_Orderings_Oorder__class_Omono(U_13992,U_13992,U_13993)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_13992) ),
    inference(clausify,[status(thm)],[f_3557_2]) ).

fof(f_3558_1,plain,
    ! [V_f_2,V_X_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_X_2),c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_X_2),hAPP(V_f_2,V_X_2)))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_gfp__upperbound]) ).

fof(f_3558_2,plain,
    ! [U_13996,U_13995,U_13994] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13994),U_13995),c_Inductive_Ocomplete__lattice__class_Ogfp(U_13994,U_13996)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13994),U_13995),hAPP(U_13996,U_13995)))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_13994) ),
    inference(variable_rename,[status(thm)],[f_3558_1]) ).

cnf(f_3558_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13994),U_13995),c_Inductive_Ocomplete__lattice__class_Ogfp(U_13994,U_13996)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13994),U_13995),hAPP(U_13996,U_13995)))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_13994) ),
    inference(clausify,[status(thm)],[f_3558_2]) ).

fof(f_3559_1,plain,
    ! [V_f_2,V_X_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(V_f_2,V_X_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2)) ),
    inference(fof_nnf,[status(thm)],[fact_weak__coinduct]) ).

fof(f_3559_2,plain,
    ! [U_14000,U_13999,U_13998,U_13997] :
      ( hBOOL(hAPP(hAPP(c_member(U_13997),U_13998),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_13997,tc_HOL_Obool),U_14000)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13997,tc_HOL_Obool)),U_13999),hAPP(U_14000,U_13999)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13997),U_13998),U_13999)) ),
    inference(variable_rename,[status(thm)],[f_3559_1]) ).

cnf(f_3559_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13997),U_13998),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_13997,tc_HOL_Obool),U_14000)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13997,tc_HOL_Obool)),U_13999),hAPP(U_14000,U_13999)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13997),U_13998),U_13999)) ),
    inference(clausify,[status(thm)],[f_3559_2]) ).

fof(f_3560_1,plain,
    ! [V_f_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2))),c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2)))
      | ~ c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_gfp__lemma3]) ).

fof(f_3560_2,plain,
    ! [U_14002,U_14001] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14001),hAPP(U_14002,c_Inductive_Ocomplete__lattice__class_Ogfp(U_14001,U_14002))),c_Inductive_Ocomplete__lattice__class_Ogfp(U_14001,U_14002)))
      | ~ c_Orderings_Oorder__class_Omono(U_14001,U_14001,U_14002)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_14001) ),
    inference(variable_rename,[status(thm)],[f_3560_1]) ).

cnf(f_3560_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14001),hAPP(U_14002,c_Inductive_Ocomplete__lattice__class_Ogfp(U_14001,U_14002))),c_Inductive_Ocomplete__lattice__class_Ogfp(U_14001,U_14002)))
    | ~ c_Orderings_Oorder__class_Omono(U_14001,U_14001,U_14002)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_14001) ),
    inference(clausify,[status(thm)],[f_3560_2]) ).

fof(f_3561_1,plain,
    ! [V_f_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2)),hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2))))
      | ~ c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_gfp__lemma2]) ).

fof(f_3561_2,plain,
    ! [U_14004,U_14003] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14003),c_Inductive_Ocomplete__lattice__class_Ogfp(U_14003,U_14004)),hAPP(U_14004,c_Inductive_Ocomplete__lattice__class_Ogfp(U_14003,U_14004))))
      | ~ c_Orderings_Oorder__class_Omono(U_14003,U_14003,U_14004)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_14003) ),
    inference(variable_rename,[status(thm)],[f_3561_1]) ).

cnf(f_3561_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14003),c_Inductive_Ocomplete__lattice__class_Ogfp(U_14003,U_14004)),hAPP(U_14004,c_Inductive_Ocomplete__lattice__class_Ogfp(U_14003,U_14004))))
    | ~ c_Orderings_Oorder__class_Omono(U_14003,U_14003,U_14004)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_14003) ),
    inference(clausify,[status(thm)],[f_3561_2]) ).

fof(f_3562_1,plain,
    ! [V_f_2,V_g_2,T_c,V_X_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_g_2,V_a_2)),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_c,tc_HOL_Obool),V_f_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_g_2),V_X_2)),hAPP(V_f_2,hAPP(c_Set_Oimage(T_b,T_c,V_g_2),V_X_2))))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2)) ),
    inference(fof_nnf,[status(thm)],[fact_weak__coinduct__image]) ).

fof(f_3562_2,plain,
    ! [U_14010,U_14009,U_14008,U_14007,U_14006,U_14005] :
      ( hBOOL(hAPP(hAPP(c_member(U_14008),hAPP(U_14009,U_14006)),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_14008,tc_HOL_Obool),U_14010)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14008,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_14005,U_14008,U_14009),U_14007)),hAPP(U_14010,hAPP(c_Set_Oimage(U_14005,U_14008,U_14009),U_14007))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_14005),U_14006),U_14007)) ),
    inference(variable_rename,[status(thm)],[f_3562_1]) ).

cnf(f_3562_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14008),hAPP(U_14009,U_14006)),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_14008,tc_HOL_Obool),U_14010)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14008,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_14005,U_14008,U_14009),U_14007)),hAPP(U_14010,hAPP(c_Set_Oimage(U_14005,U_14008,U_14009),U_14007))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14005),U_14006),U_14007)) ),
    inference(clausify,[status(thm)],[f_3562_2]) ).

fof(f_3563_1,plain,
    ! [V_X_2,V_a_2,V_f_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_X_2),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)))))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)))
      | ~ c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_gfp__fun__UnI2]) ).

fof(f_3563_2,plain,
    ! [U_14014,U_14013,U_14012,U_14011] :
      ( hBOOL(hAPP(hAPP(c_member(U_14011),U_14013),hAPP(U_14012,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14011,tc_HOL_Obool)),U_14014),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_14011,tc_HOL_Obool),U_14012)))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_14011),U_14013),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_14011,tc_HOL_Obool),U_14012)))
      | ~ c_Orderings_Oorder__class_Omono(tc_fun(U_14011,tc_HOL_Obool),tc_fun(U_14011,tc_HOL_Obool),U_14012) ),
    inference(variable_rename,[status(thm)],[f_3563_1]) ).

cnf(f_3563_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14011),U_14013),hAPP(U_14012,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14011,tc_HOL_Obool)),U_14014),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_14011,tc_HOL_Obool),U_14012)))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14011),U_14013),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_14011,tc_HOL_Obool),U_14012)))
    | ~ c_Orderings_Oorder__class_Omono(tc_fun(U_14011,tc_HOL_Obool),tc_fun(U_14011,tc_HOL_Obool),U_14012) ),
    inference(clausify,[status(thm)],[f_3563_2]) ).

fof(f_3564_1,plain,
    ! [V_X_2,V_f_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_X_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_X_2),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_X_2),V_A_2))))
      | ~ c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
      | V_A_2 != c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2)
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_def__coinduct]) ).

fof(f_3564_2,plain,
    ! [U_14018,U_14017,U_14016,U_14015] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14015),U_14018),U_14016))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14015),U_14018),hAPP(U_14017,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_14015),U_14018),U_14016))))
      | ~ c_Orderings_Oorder__class_Omono(U_14015,U_14015,U_14017)
      | U_14016 != c_Inductive_Ocomplete__lattice__class_Ogfp(U_14015,U_14017)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_14015) ),
    inference(variable_rename,[status(thm)],[f_3564_1]) ).

cnf(f_3564_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14015),U_14018),U_14016))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14015),U_14018),hAPP(U_14017,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_14015),U_14018),U_14016))))
    | ~ c_Orderings_Oorder__class_Omono(U_14015,U_14015,U_14017)
    | U_14016 != c_Inductive_Ocomplete__lattice__class_Ogfp(U_14015,U_14017)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_14015) ),
    inference(clausify,[status(thm)],[f_3564_2]) ).

fof(f_3565_1,plain,
    ! [V_f_2,V_X_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_X_2),c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2))),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_X_2),c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2)))))
      | ~ c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_X_2),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_X_2),c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2)))))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_coinduct__lemma]) ).

fof(f_3565_2,plain,
    ! [U_14021,U_14020,U_14019] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14019),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_14019),U_14020),c_Inductive_Ocomplete__lattice__class_Ogfp(U_14019,U_14021))),hAPP(U_14021,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_14019),U_14020),c_Inductive_Ocomplete__lattice__class_Ogfp(U_14019,U_14021)))))
      | ~ c_Orderings_Oorder__class_Omono(U_14019,U_14019,U_14021)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14019),U_14020),hAPP(U_14021,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_14019),U_14020),c_Inductive_Ocomplete__lattice__class_Ogfp(U_14019,U_14021)))))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_14019) ),
    inference(variable_rename,[status(thm)],[f_3565_1]) ).

cnf(f_3565_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14019),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_14019),U_14020),c_Inductive_Ocomplete__lattice__class_Ogfp(U_14019,U_14021))),hAPP(U_14021,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_14019),U_14020),c_Inductive_Ocomplete__lattice__class_Ogfp(U_14019,U_14021)))))
    | ~ c_Orderings_Oorder__class_Omono(U_14019,U_14019,U_14021)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14019),U_14020),hAPP(U_14021,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_14019),U_14020),c_Inductive_Ocomplete__lattice__class_Ogfp(U_14019,U_14021)))))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_14019) ),
    inference(clausify,[status(thm)],[f_3565_2]) ).

fof(f_3566_1,plain,
    ! [V_X_2,V_f_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_X_2),c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_X_2),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_X_2),c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2)))))
      | ~ c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_coinduct]) ).

fof(f_3566_2,plain,
    ! [U_14024,U_14023,U_14022] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14022),U_14024),c_Inductive_Ocomplete__lattice__class_Ogfp(U_14022,U_14023)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14022),U_14024),hAPP(U_14023,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_14022),U_14024),c_Inductive_Ocomplete__lattice__class_Ogfp(U_14022,U_14023)))))
      | ~ c_Orderings_Oorder__class_Omono(U_14022,U_14022,U_14023)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_14022) ),
    inference(variable_rename,[status(thm)],[f_3566_1]) ).

cnf(f_3566_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14022),U_14024),c_Inductive_Ocomplete__lattice__class_Ogfp(U_14022,U_14023)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14022),U_14024),hAPP(U_14023,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_14022),U_14024),c_Inductive_Ocomplete__lattice__class_Ogfp(U_14022,U_14023)))))
    | ~ c_Orderings_Oorder__class_Omono(U_14022,U_14022,U_14023)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_14022) ),
    inference(clausify,[status(thm)],[f_3566_2]) ).

fof(f_3567_1,plain,
    ! [V_X_2,V_a_2,V_f_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_X_2),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)))))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2))
      | ~ c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_coinduct__set]) ).

fof(f_3567_2,plain,
    ! [U_14028,U_14027,U_14026,U_14025] :
      ( hBOOL(hAPP(hAPP(c_member(U_14025),U_14027),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_14025,tc_HOL_Obool),U_14026)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14025,tc_HOL_Obool)),U_14028),hAPP(U_14026,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14025,tc_HOL_Obool)),U_14028),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_14025,tc_HOL_Obool),U_14026)))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_14025),U_14027),U_14028))
      | ~ c_Orderings_Oorder__class_Omono(tc_fun(U_14025,tc_HOL_Obool),tc_fun(U_14025,tc_HOL_Obool),U_14026) ),
    inference(variable_rename,[status(thm)],[f_3567_1]) ).

cnf(f_3567_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14025),U_14027),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_14025,tc_HOL_Obool),U_14026)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14025,tc_HOL_Obool)),U_14028),hAPP(U_14026,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14025,tc_HOL_Obool)),U_14028),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_14025,tc_HOL_Obool),U_14026)))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14025),U_14027),U_14028))
    | ~ c_Orderings_Oorder__class_Omono(tc_fun(U_14025,tc_HOL_Obool),tc_fun(U_14025,tc_HOL_Obool),U_14026) ),
    inference(clausify,[status(thm)],[f_3567_2]) ).

fof(f_3568_1,plain,
    ! [V_X_2,V_a_2,V_f_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_f_2)),V_X_2))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2))))))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2))
      | ~ c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_coinduct3]) ).

fof(f_3568_2,plain,
    ! [U_14032,U_14031,U_14030,U_14029] :
      ( hBOOL(hAPP(hAPP(c_member(U_14029),U_14031),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_14029,tc_HOL_Obool),U_14030)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14029,tc_HOL_Obool)),U_14032),hAPP(U_14030,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(U_14029,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(U_14029,tc_HOL_Obool),tc_fun(U_14029,tc_HOL_Obool),tc_fun(U_14029,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14029,tc_HOL_Obool),tc_fun(tc_fun(U_14029,tc_HOL_Obool),tc_fun(U_14029,tc_HOL_Obool)),tc_fun(U_14029,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14029,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(U_14029,tc_HOL_Obool),tc_fun(U_14029,tc_HOL_Obool),tc_fun(U_14029,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14029,tc_HOL_Obool),tc_fun(tc_fun(U_14029,tc_HOL_Obool),tc_fun(U_14029,tc_HOL_Obool)),tc_fun(U_14029,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14029,tc_HOL_Obool))),U_14030)),U_14032))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_14029,tc_HOL_Obool),U_14030))))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_14029),U_14031),U_14032))
      | ~ c_Orderings_Oorder__class_Omono(tc_fun(U_14029,tc_HOL_Obool),tc_fun(U_14029,tc_HOL_Obool),U_14030) ),
    inference(variable_rename,[status(thm)],[f_3568_1]) ).

cnf(f_3568_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14029),U_14031),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_14029,tc_HOL_Obool),U_14030)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14029,tc_HOL_Obool)),U_14032),hAPP(U_14030,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(U_14029,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(U_14029,tc_HOL_Obool),tc_fun(U_14029,tc_HOL_Obool),tc_fun(U_14029,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14029,tc_HOL_Obool),tc_fun(tc_fun(U_14029,tc_HOL_Obool),tc_fun(U_14029,tc_HOL_Obool)),tc_fun(U_14029,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14029,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(U_14029,tc_HOL_Obool),tc_fun(U_14029,tc_HOL_Obool),tc_fun(U_14029,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14029,tc_HOL_Obool),tc_fun(tc_fun(U_14029,tc_HOL_Obool),tc_fun(U_14029,tc_HOL_Obool)),tc_fun(U_14029,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14029,tc_HOL_Obool))),U_14030)),U_14032))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_14029,tc_HOL_Obool),U_14030))))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14029),U_14031),U_14032))
    | ~ c_Orderings_Oorder__class_Omono(tc_fun(U_14029,tc_HOL_Obool),tc_fun(U_14029,tc_HOL_Obool),U_14030) ),
    inference(clausify,[status(thm)],[f_3568_2]) ).

fof(f_3569_1,plain,
    ! [V_X_2,V_a_2,V_f_2,T_b,V_A_2] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_f_2)),V_X_2))),V_A_2)))))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2))
      | ~ c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
      | V_A_2 != c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_def__coinduct3]) ).

fof(f_3569_2,plain,
    ! [U_14037,U_14036,U_14035,U_14034,U_14033] :
      ( hBOOL(hAPP(hAPP(c_member(U_14034),U_14036),U_14033))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14034,tc_HOL_Obool)),U_14037),hAPP(U_14035,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(U_14034,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(U_14034,tc_HOL_Obool),tc_fun(U_14034,tc_HOL_Obool),tc_fun(U_14034,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14034,tc_HOL_Obool),tc_fun(tc_fun(U_14034,tc_HOL_Obool),tc_fun(U_14034,tc_HOL_Obool)),tc_fun(U_14034,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14034,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(U_14034,tc_HOL_Obool),tc_fun(U_14034,tc_HOL_Obool),tc_fun(U_14034,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14034,tc_HOL_Obool),tc_fun(tc_fun(U_14034,tc_HOL_Obool),tc_fun(U_14034,tc_HOL_Obool)),tc_fun(U_14034,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14034,tc_HOL_Obool))),U_14035)),U_14037))),U_14033)))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_14034),U_14036),U_14037))
      | ~ c_Orderings_Oorder__class_Omono(tc_fun(U_14034,tc_HOL_Obool),tc_fun(U_14034,tc_HOL_Obool),U_14035)
      | U_14033 != c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_14034,tc_HOL_Obool),U_14035) ),
    inference(variable_rename,[status(thm)],[f_3569_1]) ).

cnf(f_3569_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14034),U_14036),U_14033))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14034,tc_HOL_Obool)),U_14037),hAPP(U_14035,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(U_14034,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(U_14034,tc_HOL_Obool),tc_fun(U_14034,tc_HOL_Obool),tc_fun(U_14034,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14034,tc_HOL_Obool),tc_fun(tc_fun(U_14034,tc_HOL_Obool),tc_fun(U_14034,tc_HOL_Obool)),tc_fun(U_14034,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14034,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(U_14034,tc_HOL_Obool),tc_fun(U_14034,tc_HOL_Obool),tc_fun(U_14034,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14034,tc_HOL_Obool),tc_fun(tc_fun(U_14034,tc_HOL_Obool),tc_fun(U_14034,tc_HOL_Obool)),tc_fun(U_14034,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14034,tc_HOL_Obool))),U_14035)),U_14037))),U_14033)))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14034),U_14036),U_14037))
    | ~ c_Orderings_Oorder__class_Omono(tc_fun(U_14034,tc_HOL_Obool),tc_fun(U_14034,tc_HOL_Obool),U_14035)
    | U_14033 != c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_14034,tc_HOL_Obool),U_14035) ),
    inference(clausify,[status(thm)],[f_3569_2]) ).

fof(f_3570_1,plain,
    ! [V_X_2,V_a_2,V_P_2,T_b,V_A_2] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | ? [B_z] :
          ( ~ hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_A_2)),B_z))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_z),V_X_2)) )
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2))
      | ~ c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_OCollect(T_b)),V_P_2))
      | V_A_2 != c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_OCollect(T_b)),V_P_2)) ),
    inference(fof_nnf,[status(thm)],[fact_def__Collect__coinduct]) ).

fof(f_3570_2,plain,
    ! [U_14043,U_14042,U_14041,U_14040,U_14039] :
      ( hBOOL(hAPP(hAPP(c_member(U_14040),U_14042),U_14039))
      | ? [U_14038] :
          ( ~ hBOOL(hAPP(hAPP(U_14041,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14040,tc_HOL_Obool)),U_14043),U_14039)),U_14038))
          & hBOOL(hAPP(hAPP(c_member(U_14040),U_14038),U_14043)) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_14040),U_14042),U_14043))
      | ~ c_Orderings_Oorder__class_Omono(tc_fun(U_14040,tc_HOL_Obool),tc_fun(U_14040,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_14040,tc_HOL_Obool),tc_fun(U_14040,tc_HOL_Obool),tc_fun(U_14040,tc_HOL_Obool)),c_Set_OCollect(U_14040)),U_14041))
      | U_14039 != c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_14040,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_14040,tc_HOL_Obool),tc_fun(U_14040,tc_HOL_Obool),tc_fun(U_14040,tc_HOL_Obool)),c_Set_OCollect(U_14040)),U_14041)) ),
    inference(variable_rename,[status(thm)],[f_3570_1]) ).

fof(f_3570_3,plain,
    ! [U_14043,U_14042,U_14041,U_14040,U_14039] :
      ( hBOOL(hAPP(hAPP(c_member(U_14040),U_14042),U_14039))
      | ( ~ hBOOL(hAPP(hAPP(U_14041,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14040,tc_HOL_Obool)),U_14043),U_14039)),sK354(U_14043,U_14042,U_14041,U_14040,U_14039)))
        & hBOOL(hAPP(hAPP(c_member(U_14040),sK354(U_14043,U_14042,U_14041,U_14040,U_14039)),U_14043)) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_14040),U_14042),U_14043))
      | ~ c_Orderings_Oorder__class_Omono(tc_fun(U_14040,tc_HOL_Obool),tc_fun(U_14040,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_14040,tc_HOL_Obool),tc_fun(U_14040,tc_HOL_Obool),tc_fun(U_14040,tc_HOL_Obool)),c_Set_OCollect(U_14040)),U_14041))
      | U_14039 != c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_14040,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_14040,tc_HOL_Obool),tc_fun(U_14040,tc_HOL_Obool),tc_fun(U_14040,tc_HOL_Obool)),c_Set_OCollect(U_14040)),U_14041)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK354]),skolemize(U_14038,sK354(U_14043,U_14042,U_14041,U_14040,U_14039))],[f_3570_2]) ).

cnf(f_3570_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14040),sK354(U_14043,U_14042,U_14041,U_14040,U_14039)),U_14043))
    | hBOOL(hAPP(hAPP(c_member(U_14040),U_14042),U_14039))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14040),U_14042),U_14043))
    | ~ c_Orderings_Oorder__class_Omono(tc_fun(U_14040,tc_HOL_Obool),tc_fun(U_14040,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_14040,tc_HOL_Obool),tc_fun(U_14040,tc_HOL_Obool),tc_fun(U_14040,tc_HOL_Obool)),c_Set_OCollect(U_14040)),U_14041))
    | U_14039 != c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_14040,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_14040,tc_HOL_Obool),tc_fun(U_14040,tc_HOL_Obool),tc_fun(U_14040,tc_HOL_Obool)),c_Set_OCollect(U_14040)),U_14041)) ),
    inference(clausify,[status(thm)],[f_3570_3]) ).

cnf(f_3570_5,plain,
    ( ~ hBOOL(hAPP(hAPP(U_14041,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14040,tc_HOL_Obool)),U_14043),U_14039)),sK354(U_14043,U_14042,U_14041,U_14040,U_14039)))
    | hBOOL(hAPP(hAPP(c_member(U_14040),U_14042),U_14039))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14040),U_14042),U_14043))
    | ~ c_Orderings_Oorder__class_Omono(tc_fun(U_14040,tc_HOL_Obool),tc_fun(U_14040,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_14040,tc_HOL_Obool),tc_fun(U_14040,tc_HOL_Obool),tc_fun(U_14040,tc_HOL_Obool)),c_Set_OCollect(U_14040)),U_14041))
    | U_14039 != c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_14040,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_14040,tc_HOL_Obool),tc_fun(U_14040,tc_HOL_Obool),tc_fun(U_14040,tc_HOL_Obool)),c_Set_OCollect(U_14040)),U_14041)) ),
    inference(clausify,[status(thm)],[f_3570_3]) ).

fof(f_3571_1,plain,
    ! [V_A_2,V_f_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2)),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_A_2)),V_A_2))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_lfp__lowerbound]) ).

fof(f_3571_2,plain,
    ! [U_14046,U_14045,U_14044] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14044),c_Inductive_Ocomplete__lattice__class_Olfp(U_14044,U_14045)),U_14046))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14044),hAPP(U_14045,U_14046)),U_14046))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_14044) ),
    inference(variable_rename,[status(thm)],[f_3571_1]) ).

cnf(f_3571_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14044),c_Inductive_Ocomplete__lattice__class_Olfp(U_14044,U_14045)),U_14046))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14044),hAPP(U_14045,U_14046)),U_14046))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_14044) ),
    inference(clausify,[status(thm)],[f_3571_2]) ).

fof(f_3572_1,plain,
    ! [V_f_2,T_b] :
      ( c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2) = hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2))
      | ~ c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_lfp__unfold]) ).

fof(f_3572_2,plain,
    ! [U_14048,U_14047] :
      ( c_Inductive_Ocomplete__lattice__class_Olfp(U_14047,U_14048) = hAPP(U_14048,c_Inductive_Ocomplete__lattice__class_Olfp(U_14047,U_14048))
      | ~ c_Orderings_Oorder__class_Omono(U_14047,U_14047,U_14048)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_14047) ),
    inference(variable_rename,[status(thm)],[f_3572_1]) ).

cnf(f_3572_3,plain,
    ( c_Inductive_Ocomplete__lattice__class_Olfp(U_14047,U_14048) = hAPP(U_14048,c_Inductive_Ocomplete__lattice__class_Olfp(U_14047,U_14048))
    | ~ c_Orderings_Oorder__class_Omono(U_14047,U_14047,U_14048)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_14047) ),
    inference(clausify,[status(thm)],[f_3572_2]) ).

fof(f_3573_1,plain,
    ! [V_f_2,V_h_2,T_b] :
      ( V_h_2 = hAPP(V_f_2,V_h_2)
      | ~ c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
      | V_h_2 != c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2)
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_def__lfp__unfold]) ).

fof(f_3573_2,plain,
    ! [U_14051,U_14050,U_14049] :
      ( U_14050 = hAPP(U_14051,U_14050)
      | ~ c_Orderings_Oorder__class_Omono(U_14049,U_14049,U_14051)
      | U_14050 != c_Inductive_Ocomplete__lattice__class_Olfp(U_14049,U_14051)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_14049) ),
    inference(variable_rename,[status(thm)],[f_3573_1]) ).

cnf(f_3573_3,plain,
    ( U_14050 = hAPP(U_14051,U_14050)
    | ~ c_Orderings_Oorder__class_Omono(U_14049,U_14049,U_14051)
    | U_14050 != c_Inductive_Ocomplete__lattice__class_Olfp(U_14049,U_14051)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_14049) ),
    inference(clausify,[status(thm)],[f_3573_2]) ).

fof(f_3574_1,plain,
    ! [V_t_2,T_b] :
      ( c_Inductive_Ocomplete__lattice__class_Olfp(T_b,hAPP(c_COMBK(T_b,T_b),V_t_2)) = V_t_2
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_lfp__const]) ).

fof(f_3574_2,plain,
    ! [U_14053,U_14052] :
      ( c_Inductive_Ocomplete__lattice__class_Olfp(U_14052,hAPP(c_COMBK(U_14052,U_14052),U_14053)) = U_14053
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_14052) ),
    inference(variable_rename,[status(thm)],[f_3574_1]) ).

cnf(f_3574_3,plain,
    ( c_Inductive_Ocomplete__lattice__class_Olfp(U_14052,hAPP(c_COMBK(U_14052,U_14052),U_14053)) = U_14053
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_14052) ),
    inference(clausify,[status(thm)],[f_3574_2]) ).

fof(f_3575_1,plain,
    ! [V_f_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2)),hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2))))
      | ~ c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_lfp__lemma3]) ).

fof(f_3575_2,plain,
    ! [U_14055,U_14054] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14054),c_Inductive_Ocomplete__lattice__class_Olfp(U_14054,U_14055)),hAPP(U_14055,c_Inductive_Ocomplete__lattice__class_Olfp(U_14054,U_14055))))
      | ~ c_Orderings_Oorder__class_Omono(U_14054,U_14054,U_14055)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_14054) ),
    inference(variable_rename,[status(thm)],[f_3575_1]) ).

cnf(f_3575_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14054),c_Inductive_Ocomplete__lattice__class_Olfp(U_14054,U_14055)),hAPP(U_14055,c_Inductive_Ocomplete__lattice__class_Olfp(U_14054,U_14055))))
    | ~ c_Orderings_Oorder__class_Omono(U_14054,U_14054,U_14055)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_14054) ),
    inference(clausify,[status(thm)],[f_3575_2]) ).

fof(f_3576_1,plain,
    ! [V_f_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2))),c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2)))
      | ~ c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_lfp__lemma2]) ).

fof(f_3576_2,plain,
    ! [U_14057,U_14056] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14056),hAPP(U_14057,c_Inductive_Ocomplete__lattice__class_Olfp(U_14056,U_14057))),c_Inductive_Ocomplete__lattice__class_Olfp(U_14056,U_14057)))
      | ~ c_Orderings_Oorder__class_Omono(U_14056,U_14056,U_14057)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_14056) ),
    inference(variable_rename,[status(thm)],[f_3576_1]) ).

cnf(f_3576_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14056),hAPP(U_14057,c_Inductive_Ocomplete__lattice__class_Olfp(U_14056,U_14057))),c_Inductive_Ocomplete__lattice__class_Olfp(U_14056,U_14057)))
    | ~ c_Orderings_Oorder__class_Omono(U_14056,U_14056,U_14057)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_14056) ),
    inference(clausify,[status(thm)],[f_3576_2]) ).

fof(f_3577_1,plain,
    ! [V_P_2,V_f_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2)),V_P_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2)),V_P_2))),V_P_2))
      | ~ c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_lfp__induct]) ).

fof(f_3577_2,plain,
    ! [U_14060,U_14059,U_14058] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14058),c_Inductive_Ocomplete__lattice__class_Olfp(U_14058,U_14059)),U_14060))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14058),hAPP(U_14059,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_14058),c_Inductive_Ocomplete__lattice__class_Olfp(U_14058,U_14059)),U_14060))),U_14060))
      | ~ c_Orderings_Oorder__class_Omono(U_14058,U_14058,U_14059)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_14058) ),
    inference(variable_rename,[status(thm)],[f_3577_1]) ).

cnf(f_3577_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14058),c_Inductive_Ocomplete__lattice__class_Olfp(U_14058,U_14059)),U_14060))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14058),hAPP(U_14059,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_14058),c_Inductive_Ocomplete__lattice__class_Olfp(U_14058,U_14059)),U_14060))),U_14060))
    | ~ c_Orderings_Oorder__class_Omono(U_14058,U_14058,U_14059)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_14058) ),
    inference(clausify,[status(thm)],[f_3577_2]) ).

fof(f_3578_1,plain,
    ! [V_P_2,V_f_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_A_2),V_P_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_A_2),V_P_2))),V_P_2))
      | ~ c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
      | V_A_2 != c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2)
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_def__lfp__induct]) ).

fof(f_3578_2,plain,
    ! [U_14064,U_14063,U_14062,U_14061] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14061),U_14062),U_14064))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14061),hAPP(U_14063,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_14061),U_14062),U_14064))),U_14064))
      | ~ c_Orderings_Oorder__class_Omono(U_14061,U_14061,U_14063)
      | U_14062 != c_Inductive_Ocomplete__lattice__class_Olfp(U_14061,U_14063)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_14061) ),
    inference(variable_rename,[status(thm)],[f_3578_1]) ).

cnf(f_3578_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14061),U_14062),U_14064))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14061),hAPP(U_14063,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_14061),U_14062),U_14064))),U_14064))
    | ~ c_Orderings_Oorder__class_Omono(U_14061,U_14061,U_14063)
    | U_14062 != c_Inductive_Ocomplete__lattice__class_Olfp(U_14061,U_14063)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_14061) ),
    inference(clausify,[status(thm)],[f_3578_2]) ).

fof(f_3579_1,plain,
    ! [V_f_2,V_X_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_f_2)),V_X_2))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)))),hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_f_2)),V_X_2))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2))))))
      | ~ c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_f_2)),V_X_2))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)))))) ),
    inference(fof_nnf,[status(thm)],[fact_coinduct3__lemma]) ).

fof(f_3579_2,plain,
    ! [U_14067,U_14066,U_14065] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14065,tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(U_14065,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(U_14065,tc_HOL_Obool),tc_fun(U_14065,tc_HOL_Obool),tc_fun(U_14065,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14065,tc_HOL_Obool),tc_fun(tc_fun(U_14065,tc_HOL_Obool),tc_fun(U_14065,tc_HOL_Obool)),tc_fun(U_14065,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14065,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(U_14065,tc_HOL_Obool),tc_fun(U_14065,tc_HOL_Obool),tc_fun(U_14065,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14065,tc_HOL_Obool),tc_fun(tc_fun(U_14065,tc_HOL_Obool),tc_fun(U_14065,tc_HOL_Obool)),tc_fun(U_14065,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14065,tc_HOL_Obool))),U_14067)),U_14066))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_14065,tc_HOL_Obool),U_14067)))),hAPP(U_14067,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(U_14065,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(U_14065,tc_HOL_Obool),tc_fun(U_14065,tc_HOL_Obool),tc_fun(U_14065,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14065,tc_HOL_Obool),tc_fun(tc_fun(U_14065,tc_HOL_Obool),tc_fun(U_14065,tc_HOL_Obool)),tc_fun(U_14065,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14065,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(U_14065,tc_HOL_Obool),tc_fun(U_14065,tc_HOL_Obool),tc_fun(U_14065,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14065,tc_HOL_Obool),tc_fun(tc_fun(U_14065,tc_HOL_Obool),tc_fun(U_14065,tc_HOL_Obool)),tc_fun(U_14065,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14065,tc_HOL_Obool))),U_14067)),U_14066))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_14065,tc_HOL_Obool),U_14067))))))
      | ~ c_Orderings_Oorder__class_Omono(tc_fun(U_14065,tc_HOL_Obool),tc_fun(U_14065,tc_HOL_Obool),U_14067)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14065,tc_HOL_Obool)),U_14066),hAPP(U_14067,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(U_14065,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(U_14065,tc_HOL_Obool),tc_fun(U_14065,tc_HOL_Obool),tc_fun(U_14065,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14065,tc_HOL_Obool),tc_fun(tc_fun(U_14065,tc_HOL_Obool),tc_fun(U_14065,tc_HOL_Obool)),tc_fun(U_14065,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14065,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(U_14065,tc_HOL_Obool),tc_fun(U_14065,tc_HOL_Obool),tc_fun(U_14065,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14065,tc_HOL_Obool),tc_fun(tc_fun(U_14065,tc_HOL_Obool),tc_fun(U_14065,tc_HOL_Obool)),tc_fun(U_14065,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14065,tc_HOL_Obool))),U_14067)),U_14066))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_14065,tc_HOL_Obool),U_14067)))))) ),
    inference(variable_rename,[status(thm)],[f_3579_1]) ).

cnf(f_3579_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14065,tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(U_14065,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(U_14065,tc_HOL_Obool),tc_fun(U_14065,tc_HOL_Obool),tc_fun(U_14065,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14065,tc_HOL_Obool),tc_fun(tc_fun(U_14065,tc_HOL_Obool),tc_fun(U_14065,tc_HOL_Obool)),tc_fun(U_14065,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14065,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(U_14065,tc_HOL_Obool),tc_fun(U_14065,tc_HOL_Obool),tc_fun(U_14065,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14065,tc_HOL_Obool),tc_fun(tc_fun(U_14065,tc_HOL_Obool),tc_fun(U_14065,tc_HOL_Obool)),tc_fun(U_14065,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14065,tc_HOL_Obool))),U_14067)),U_14066))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_14065,tc_HOL_Obool),U_14067)))),hAPP(U_14067,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(U_14065,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(U_14065,tc_HOL_Obool),tc_fun(U_14065,tc_HOL_Obool),tc_fun(U_14065,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14065,tc_HOL_Obool),tc_fun(tc_fun(U_14065,tc_HOL_Obool),tc_fun(U_14065,tc_HOL_Obool)),tc_fun(U_14065,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14065,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(U_14065,tc_HOL_Obool),tc_fun(U_14065,tc_HOL_Obool),tc_fun(U_14065,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14065,tc_HOL_Obool),tc_fun(tc_fun(U_14065,tc_HOL_Obool),tc_fun(U_14065,tc_HOL_Obool)),tc_fun(U_14065,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14065,tc_HOL_Obool))),U_14067)),U_14066))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_14065,tc_HOL_Obool),U_14067))))))
    | ~ c_Orderings_Oorder__class_Omono(tc_fun(U_14065,tc_HOL_Obool),tc_fun(U_14065,tc_HOL_Obool),U_14067)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14065,tc_HOL_Obool)),U_14066),hAPP(U_14067,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(U_14065,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(U_14065,tc_HOL_Obool),tc_fun(U_14065,tc_HOL_Obool),tc_fun(U_14065,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14065,tc_HOL_Obool),tc_fun(tc_fun(U_14065,tc_HOL_Obool),tc_fun(U_14065,tc_HOL_Obool)),tc_fun(U_14065,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14065,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(U_14065,tc_HOL_Obool),tc_fun(U_14065,tc_HOL_Obool),tc_fun(U_14065,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14065,tc_HOL_Obool),tc_fun(tc_fun(U_14065,tc_HOL_Obool),tc_fun(U_14065,tc_HOL_Obool)),tc_fun(U_14065,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14065,tc_HOL_Obool))),U_14067)),U_14066))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_14065,tc_HOL_Obool),U_14067)))))) ),
    inference(clausify,[status(thm)],[f_3579_2]) ).

fof(f_3580_1,plain,
    ! [V_P_2,V_a_2,V_f_2,T_b,V_A_2] :
      ( hBOOL(hAPP(V_P_2,V_a_2))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(V_P_2,B_x))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_P_2))))) )
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | ~ c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
      | V_A_2 != c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(T_b,tc_HOL_Obool),V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_def__lfp__induct__set]) ).

fof(f_3580_2,plain,
    ! [U_14073,U_14072,U_14071,U_14070,U_14069] :
      ( hBOOL(hAPP(U_14073,U_14072))
      | ? [U_14068] :
          ( ~ hBOOL(hAPP(U_14073,U_14068))
          & hBOOL(hAPP(hAPP(c_member(U_14070),U_14068),hAPP(U_14071,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14070,tc_HOL_Obool)),U_14069),hAPP(c_Set_OCollect(U_14070),U_14073))))) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_14070),U_14072),U_14069))
      | ~ c_Orderings_Oorder__class_Omono(tc_fun(U_14070,tc_HOL_Obool),tc_fun(U_14070,tc_HOL_Obool),U_14071)
      | U_14069 != c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(U_14070,tc_HOL_Obool),U_14071) ),
    inference(variable_rename,[status(thm)],[f_3580_1]) ).

fof(f_3580_3,plain,
    ! [U_14073,U_14072,U_14071,U_14070,U_14069] :
      ( hBOOL(hAPP(U_14073,U_14072))
      | ( ~ hBOOL(hAPP(U_14073,sK355(U_14073,U_14072,U_14071,U_14070,U_14069)))
        & hBOOL(hAPP(hAPP(c_member(U_14070),sK355(U_14073,U_14072,U_14071,U_14070,U_14069)),hAPP(U_14071,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14070,tc_HOL_Obool)),U_14069),hAPP(c_Set_OCollect(U_14070),U_14073))))) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_14070),U_14072),U_14069))
      | ~ c_Orderings_Oorder__class_Omono(tc_fun(U_14070,tc_HOL_Obool),tc_fun(U_14070,tc_HOL_Obool),U_14071)
      | U_14069 != c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(U_14070,tc_HOL_Obool),U_14071) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK355]),skolemize(U_14068,sK355(U_14073,U_14072,U_14071,U_14070,U_14069))],[f_3580_2]) ).

cnf(f_3580_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14070),sK355(U_14073,U_14072,U_14071,U_14070,U_14069)),hAPP(U_14071,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14070,tc_HOL_Obool)),U_14069),hAPP(c_Set_OCollect(U_14070),U_14073)))))
    | hBOOL(hAPP(U_14073,U_14072))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14070),U_14072),U_14069))
    | ~ c_Orderings_Oorder__class_Omono(tc_fun(U_14070,tc_HOL_Obool),tc_fun(U_14070,tc_HOL_Obool),U_14071)
    | U_14069 != c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(U_14070,tc_HOL_Obool),U_14071) ),
    inference(clausify,[status(thm)],[f_3580_3]) ).

cnf(f_3580_5,plain,
    ( ~ hBOOL(hAPP(U_14073,sK355(U_14073,U_14072,U_14071,U_14070,U_14069)))
    | hBOOL(hAPP(U_14073,U_14072))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14070),U_14072),U_14069))
    | ~ c_Orderings_Oorder__class_Omono(tc_fun(U_14070,tc_HOL_Obool),tc_fun(U_14070,tc_HOL_Obool),U_14071)
    | U_14069 != c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(U_14070,tc_HOL_Obool),U_14071) ),
    inference(clausify,[status(thm)],[f_3580_3]) ).

fof(f_3581_1,plain,
    ! [V_P_2,V_f_2,V_a_2,T_b] :
      ( hBOOL(hAPP(V_P_2,V_a_2))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(V_P_2,B_x))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)),hAPP(c_Set_OCollect(T_b),V_P_2))))) )
      | ~ c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(T_b,tc_HOL_Obool),V_f_2))) ),
    inference(fof_nnf,[status(thm)],[fact_lfp__induct__set]) ).

fof(f_3581_2,plain,
    ! [U_14078,U_14077,U_14076,U_14075] :
      ( hBOOL(hAPP(U_14078,U_14076))
      | ? [U_14074] :
          ( ~ hBOOL(hAPP(U_14078,U_14074))
          & hBOOL(hAPP(hAPP(c_member(U_14075),U_14074),hAPP(U_14077,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14075,tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(U_14075,tc_HOL_Obool),U_14077)),hAPP(c_Set_OCollect(U_14075),U_14078))))) )
      | ~ c_Orderings_Oorder__class_Omono(tc_fun(U_14075,tc_HOL_Obool),tc_fun(U_14075,tc_HOL_Obool),U_14077)
      | ~ hBOOL(hAPP(hAPP(c_member(U_14075),U_14076),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(U_14075,tc_HOL_Obool),U_14077))) ),
    inference(variable_rename,[status(thm)],[f_3581_1]) ).

fof(f_3581_3,plain,
    ! [U_14078,U_14077,U_14076,U_14075] :
      ( hBOOL(hAPP(U_14078,U_14076))
      | ( ~ hBOOL(hAPP(U_14078,sK356(U_14078,U_14077,U_14076,U_14075)))
        & hBOOL(hAPP(hAPP(c_member(U_14075),sK356(U_14078,U_14077,U_14076,U_14075)),hAPP(U_14077,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14075,tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(U_14075,tc_HOL_Obool),U_14077)),hAPP(c_Set_OCollect(U_14075),U_14078))))) )
      | ~ c_Orderings_Oorder__class_Omono(tc_fun(U_14075,tc_HOL_Obool),tc_fun(U_14075,tc_HOL_Obool),U_14077)
      | ~ hBOOL(hAPP(hAPP(c_member(U_14075),U_14076),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(U_14075,tc_HOL_Obool),U_14077))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK356]),skolemize(U_14074,sK356(U_14078,U_14077,U_14076,U_14075))],[f_3581_2]) ).

cnf(f_3581_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14075),sK356(U_14078,U_14077,U_14076,U_14075)),hAPP(U_14077,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14075,tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(U_14075,tc_HOL_Obool),U_14077)),hAPP(c_Set_OCollect(U_14075),U_14078)))))
    | hBOOL(hAPP(U_14078,U_14076))
    | ~ c_Orderings_Oorder__class_Omono(tc_fun(U_14075,tc_HOL_Obool),tc_fun(U_14075,tc_HOL_Obool),U_14077)
    | ~ hBOOL(hAPP(hAPP(c_member(U_14075),U_14076),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(U_14075,tc_HOL_Obool),U_14077))) ),
    inference(clausify,[status(thm)],[f_3581_3]) ).

cnf(f_3581_5,plain,
    ( ~ hBOOL(hAPP(U_14078,sK356(U_14078,U_14077,U_14076,U_14075)))
    | hBOOL(hAPP(U_14078,U_14076))
    | ~ c_Orderings_Oorder__class_Omono(tc_fun(U_14075,tc_HOL_Obool),tc_fun(U_14075,tc_HOL_Obool),U_14077)
    | ~ hBOOL(hAPP(hAPP(c_member(U_14075),U_14076),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(U_14075,tc_HOL_Obool),U_14077))) ),
    inference(clausify,[status(thm)],[f_3581_3]) ).

fof(f_3582_1,plain,
    ! [V_P_2,V_f_2,V_b_2,V_a_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(V_P_2,V_a_2),V_b_2))
      | ? [B_a,B_b] :
          ( ~ hBOOL(hAPP(hAPP(V_P_2,B_a),B_b))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b)),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),V_f_2)),hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_P_2)))))) )
      | ~ c_Orderings_Oorder__class_Omono(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),V_f_2)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),V_f_2))) ),
    inference(fof_nnf,[status(thm)],[fact_lfp__induct2]) ).

fof(f_3582_2,plain,
    ! [U_14086,U_14085,U_14084,U_14083,U_14082,U_14081] :
      ( hBOOL(hAPP(hAPP(U_14086,U_14083),U_14084))
      | ? [U_14080,U_14079] :
          ( ~ hBOOL(hAPP(hAPP(U_14086,U_14080),U_14079))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14081,U_14082)),hAPP(hAPP(c_Product__Type_OPair(U_14081,U_14082),U_14080),U_14079)),hAPP(U_14085,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14081,U_14082),tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(U_14081,U_14082),tc_HOL_Obool),U_14085)),hAPP(c_Set_OCollect(tc_prod(U_14081,U_14082)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14081,U_14082,tc_HOL_Obool),U_14086)))))) )
      | ~ c_Orderings_Oorder__class_Omono(tc_fun(tc_prod(U_14081,U_14082),tc_HOL_Obool),tc_fun(tc_prod(U_14081,U_14082),tc_HOL_Obool),U_14085)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14081,U_14082)),hAPP(hAPP(c_Product__Type_OPair(U_14081,U_14082),U_14083),U_14084)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(U_14081,U_14082),tc_HOL_Obool),U_14085))) ),
    inference(variable_rename,[status(thm)],[f_3582_1]) ).

fof(f_3582_3,plain,
    ! [U_14086,U_14085,U_14084,U_14083,U_14082,U_14081] :
      ( hBOOL(hAPP(hAPP(U_14086,U_14083),U_14084))
      | ? [U_14079] :
          ( ~ hBOOL(hAPP(hAPP(U_14086,sK357(U_14086,U_14085,U_14084,U_14083,U_14082,U_14081)),U_14079))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14081,U_14082)),hAPP(hAPP(c_Product__Type_OPair(U_14081,U_14082),sK357(U_14086,U_14085,U_14084,U_14083,U_14082,U_14081)),U_14079)),hAPP(U_14085,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14081,U_14082),tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(U_14081,U_14082),tc_HOL_Obool),U_14085)),hAPP(c_Set_OCollect(tc_prod(U_14081,U_14082)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14081,U_14082,tc_HOL_Obool),U_14086)))))) )
      | ~ c_Orderings_Oorder__class_Omono(tc_fun(tc_prod(U_14081,U_14082),tc_HOL_Obool),tc_fun(tc_prod(U_14081,U_14082),tc_HOL_Obool),U_14085)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14081,U_14082)),hAPP(hAPP(c_Product__Type_OPair(U_14081,U_14082),U_14083),U_14084)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(U_14081,U_14082),tc_HOL_Obool),U_14085))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK357]),skolemize(U_14080,sK357(U_14086,U_14085,U_14084,U_14083,U_14082,U_14081))],[f_3582_2]) ).

fof(f_3582_4,plain,
    ! [U_14086,U_14085,U_14084,U_14083,U_14082,U_14081] :
      ( hBOOL(hAPP(hAPP(U_14086,U_14083),U_14084))
      | ( ~ hBOOL(hAPP(hAPP(U_14086,sK357(U_14086,U_14085,U_14084,U_14083,U_14082,U_14081)),sK358(U_14086,U_14085,U_14084,U_14083,U_14082,U_14081)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14081,U_14082)),hAPP(hAPP(c_Product__Type_OPair(U_14081,U_14082),sK357(U_14086,U_14085,U_14084,U_14083,U_14082,U_14081)),sK358(U_14086,U_14085,U_14084,U_14083,U_14082,U_14081))),hAPP(U_14085,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14081,U_14082),tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(U_14081,U_14082),tc_HOL_Obool),U_14085)),hAPP(c_Set_OCollect(tc_prod(U_14081,U_14082)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14081,U_14082,tc_HOL_Obool),U_14086)))))) )
      | ~ c_Orderings_Oorder__class_Omono(tc_fun(tc_prod(U_14081,U_14082),tc_HOL_Obool),tc_fun(tc_prod(U_14081,U_14082),tc_HOL_Obool),U_14085)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14081,U_14082)),hAPP(hAPP(c_Product__Type_OPair(U_14081,U_14082),U_14083),U_14084)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(U_14081,U_14082),tc_HOL_Obool),U_14085))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK358]),skolemize(U_14079,sK358(U_14086,U_14085,U_14084,U_14083,U_14082,U_14081))],[f_3582_3]) ).

cnf(f_3582_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14081,U_14082)),hAPP(hAPP(c_Product__Type_OPair(U_14081,U_14082),sK357(U_14086,U_14085,U_14084,U_14083,U_14082,U_14081)),sK358(U_14086,U_14085,U_14084,U_14083,U_14082,U_14081))),hAPP(U_14085,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14081,U_14082),tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(U_14081,U_14082),tc_HOL_Obool),U_14085)),hAPP(c_Set_OCollect(tc_prod(U_14081,U_14082)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14081,U_14082,tc_HOL_Obool),U_14086))))))
    | hBOOL(hAPP(hAPP(U_14086,U_14083),U_14084))
    | ~ c_Orderings_Oorder__class_Omono(tc_fun(tc_prod(U_14081,U_14082),tc_HOL_Obool),tc_fun(tc_prod(U_14081,U_14082),tc_HOL_Obool),U_14085)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14081,U_14082)),hAPP(hAPP(c_Product__Type_OPair(U_14081,U_14082),U_14083),U_14084)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(U_14081,U_14082),tc_HOL_Obool),U_14085))) ),
    inference(clausify,[status(thm)],[f_3582_4]) ).

cnf(f_3582_6,plain,
    ( ~ hBOOL(hAPP(hAPP(U_14086,sK357(U_14086,U_14085,U_14084,U_14083,U_14082,U_14081)),sK358(U_14086,U_14085,U_14084,U_14083,U_14082,U_14081)))
    | hBOOL(hAPP(hAPP(U_14086,U_14083),U_14084))
    | ~ c_Orderings_Oorder__class_Omono(tc_fun(tc_prod(U_14081,U_14082),tc_HOL_Obool),tc_fun(tc_prod(U_14081,U_14082),tc_HOL_Obool),U_14085)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14081,U_14082)),hAPP(hAPP(c_Product__Type_OPair(U_14081,U_14082),U_14083),U_14084)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(U_14081,U_14082),tc_HOL_Obool),U_14085))) ),
    inference(clausify,[status(thm)],[f_3582_4]) ).

fof(f_3583_1,plain,
    ! [V_f_2,V_r_2,T_b] :
      ( ? [B_k] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_k))),hAPP(V_f_2,B_k))),V_r_2))
      | ~ c_Wellfounded_Owf(T_b,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_wf__no__infinite__down__chainE]) ).

fof(f_3583_2,plain,
    ! [U_14090,U_14089,U_14088] :
      ( ? [U_14087] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14088,U_14088)),hAPP(hAPP(c_Product__Type_OPair(U_14088,U_14088),hAPP(U_14090,hAPP(c_Nat_OSuc,U_14087))),hAPP(U_14090,U_14087))),U_14089))
      | ~ c_Wellfounded_Owf(U_14088,U_14089) ),
    inference(variable_rename,[status(thm)],[f_3583_1]) ).

fof(f_3583_3,plain,
    ! [U_14090,U_14089,U_14088] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14088,U_14088)),hAPP(hAPP(c_Product__Type_OPair(U_14088,U_14088),hAPP(U_14090,hAPP(c_Nat_OSuc,sK359(U_14090,U_14089,U_14088)))),hAPP(U_14090,sK359(U_14090,U_14089,U_14088)))),U_14089))
      | ~ c_Wellfounded_Owf(U_14088,U_14089) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK359]),skolemize(U_14087,sK359(U_14090,U_14089,U_14088))],[f_3583_2]) ).

cnf(f_3583_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14088,U_14088)),hAPP(hAPP(c_Product__Type_OPair(U_14088,U_14088),hAPP(U_14090,hAPP(c_Nat_OSuc,sK359(U_14090,U_14089,U_14088)))),hAPP(U_14090,sK359(U_14090,U_14089,U_14088)))),U_14089))
    | ~ c_Wellfounded_Owf(U_14088,U_14089) ),
    inference(clausify,[status(thm)],[f_3583_3]) ).

fof(f_3584_1,plain,
    ! [V_x_2,V_f_2,T_b,T_c,V_k_2] :
      ( ( hAPP(c_Random_Oiterate(T_c,T_b,V_k_2,V_f_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_c,T_b,tc_prod(T_c,T_b)),hAPP(V_f_2,V_x_2)),c_Random_Oiterate(T_c,T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_k_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),V_f_2))
        | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
      & ( hAPP(c_Random_Oiterate(T_c,T_b,V_k_2,V_f_2),V_x_2) = hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2)
        | V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(fof_nnf,[status(thm)],[fact_iterate_Osimps]) ).

fof(f_3584_2,plain,
    ! [U_14095,U_14094,U_14093,U_14092,U_14091] :
      ( ( hAPP(c_Random_Oiterate(U_14092,U_14093,U_14091,U_14094),U_14095) = hAPP(hAPP(c_Product__Type_Oscomp(U_14093,U_14092,U_14093,tc_prod(U_14092,U_14093)),hAPP(U_14094,U_14095)),c_Random_Oiterate(U_14092,U_14093,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_14091),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),U_14094))
        | U_14091 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
      & ( hAPP(c_Random_Oiterate(U_14092,U_14093,U_14091,U_14094),U_14095) = hAPP(c_Product__Type_OPair(U_14092,U_14093),U_14095)
        | U_14091 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(variable_rename,[status(thm)],[f_3584_1]) ).

fof(f_3584_3,plain,
    ( ! [U_14105,U_14103,U_14101,U_14099,U_14097] :
        ( hAPP(c_Random_Oiterate(U_14099,U_14101,U_14097,U_14103),U_14105) = hAPP(hAPP(c_Product__Type_Oscomp(U_14101,U_14099,U_14101,tc_prod(U_14099,U_14101)),hAPP(U_14103,U_14105)),c_Random_Oiterate(U_14099,U_14101,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_14097),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),U_14103))
        | U_14097 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
    & ! [U_14104,U_14102,U_14100,U_14098,U_14096] :
        ( hAPP(c_Random_Oiterate(U_14098,U_14100,U_14096,U_14102),U_14104) = hAPP(c_Product__Type_OPair(U_14098,U_14100),U_14104)
        | U_14096 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(miniscope,[status(thm)],[f_3584_2]) ).

cnf(f_3584_4,plain,
    ( hAPP(c_Random_Oiterate(U_14098,U_14100,U_14096,U_14102),U_14104) = hAPP(c_Product__Type_OPair(U_14098,U_14100),U_14104)
    | U_14096 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_3584_3]) ).

cnf(f_3584_5,plain,
    ( hAPP(c_Random_Oiterate(U_14099,U_14101,U_14097,U_14103),U_14105) = hAPP(hAPP(c_Product__Type_Oscomp(U_14101,U_14099,U_14101,tc_prod(U_14099,U_14101)),hAPP(U_14103,U_14105)),c_Random_Oiterate(U_14099,U_14101,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_14097),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),U_14103))
    | U_14097 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_3584_3]) ).

fof(f_3585_1,plain,
    ! [V_x_2,V_g_2,V_f_2,T_b,T_e,T_d,T_c] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_c,T_d,T_e,T_b),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_d,T_e),hAPP(V_f_2,V_x_2))),hAPP(c_Product__Type_Osnd(T_d,T_e),hAPP(V_f_2,V_x_2))),
    inference(fof_nnf,[status(thm)],[fact_scomp__unfold]) ).

fof(f_3585_2,plain,
    ! [U_14112,U_14111,U_14110,U_14109,U_14108,U_14107,U_14106] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(U_14106,U_14107,U_14108,U_14109),U_14110),U_14111),U_14112) = hAPP(hAPP(U_14111,hAPP(c_Product__Type_Ofst(U_14107,U_14108),hAPP(U_14110,U_14112))),hAPP(c_Product__Type_Osnd(U_14107,U_14108),hAPP(U_14110,U_14112))),
    inference(variable_rename,[status(thm)],[f_3585_1]) ).

cnf(f_3585_3,plain,
    hAPP(hAPP(hAPP(c_Product__Type_Oscomp(U_14106,U_14107,U_14108,U_14109),U_14110),U_14111),U_14112) = hAPP(hAPP(U_14111,hAPP(c_Product__Type_Ofst(U_14107,U_14108),hAPP(U_14110,U_14112))),hAPP(c_Product__Type_Osnd(U_14107,U_14108),hAPP(U_14110,U_14112))),
    inference(clausify,[status(thm)],[f_3585_2]) ).

fof(f_3586_1,plain,
    ! [V_h_2,V_g_2,V_f_2,T_g,T_f,T_c,T_e,T_d,T_b] : hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_d,T_e,T_c),hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_f,T_g,tc_prod(T_d,T_e)),V_f_2),V_g_2)),V_h_2) = hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_f,T_g,T_c),V_f_2),hAPP(hAPP(c_COMBC(T_f,tc_fun(T_d,tc_fun(T_e,T_c)),tc_fun(T_g,T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_g,tc_prod(T_d,T_e)),tc_fun(tc_fun(T_d,tc_fun(T_e,T_c)),tc_fun(T_g,T_c)),T_f),c_Product__Type_Oscomp(T_g,T_d,T_e,T_c)),V_g_2)),V_h_2)),
    inference(fof_nnf,[status(thm)],[fact_scomp__scomp]) ).

fof(f_3586_2,plain,
    ! [U_14121,U_14120,U_14119,U_14118,U_14117,U_14116,U_14115,U_14114,U_14113] : hAPP(hAPP(c_Product__Type_Oscomp(U_14113,U_14114,U_14115,U_14116),hAPP(hAPP(c_Product__Type_Oscomp(U_14113,U_14117,U_14118,tc_prod(U_14114,U_14115)),U_14119),U_14120)),U_14121) = hAPP(hAPP(c_Product__Type_Oscomp(U_14113,U_14117,U_14118,U_14116),U_14119),hAPP(hAPP(c_COMBC(U_14117,tc_fun(U_14114,tc_fun(U_14115,U_14116)),tc_fun(U_14118,U_14116)),hAPP(hAPP(c_COMBB(tc_fun(U_14118,tc_prod(U_14114,U_14115)),tc_fun(tc_fun(U_14114,tc_fun(U_14115,U_14116)),tc_fun(U_14118,U_14116)),U_14117),c_Product__Type_Oscomp(U_14118,U_14114,U_14115,U_14116)),U_14120)),U_14121)),
    inference(variable_rename,[status(thm)],[f_3586_1]) ).

cnf(f_3586_3,plain,
    hAPP(hAPP(c_Product__Type_Oscomp(U_14113,U_14114,U_14115,U_14116),hAPP(hAPP(c_Product__Type_Oscomp(U_14113,U_14117,U_14118,tc_prod(U_14114,U_14115)),U_14119),U_14120)),U_14121) = hAPP(hAPP(c_Product__Type_Oscomp(U_14113,U_14117,U_14118,U_14116),U_14119),hAPP(hAPP(c_COMBC(U_14117,tc_fun(U_14114,tc_fun(U_14115,U_14116)),tc_fun(U_14118,U_14116)),hAPP(hAPP(c_COMBB(tc_fun(U_14118,tc_prod(U_14114,U_14115)),tc_fun(tc_fun(U_14114,tc_fun(U_14115,U_14116)),tc_fun(U_14118,U_14116)),U_14117),c_Product__Type_Oscomp(U_14118,U_14114,U_14115,U_14116)),U_14120)),U_14121)),
    inference(clausify,[status(thm)],[f_3586_2]) ).

fof(f_3587_1,plain,
    ! [V_x_2,T_d,T_c,T_b] : hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_c,T_d,tc_prod(T_c,T_d)),V_x_2),c_Product__Type_OPair(T_c,T_d)) = V_x_2,
    inference(fof_nnf,[status(thm)],[fact_scomp__Pair]) ).

fof(f_3587_2,plain,
    ! [U_14125,U_14124,U_14123,U_14122] : hAPP(hAPP(c_Product__Type_Oscomp(U_14122,U_14123,U_14124,tc_prod(U_14123,U_14124)),U_14125),c_Product__Type_OPair(U_14123,U_14124)) = U_14125,
    inference(variable_rename,[status(thm)],[f_3587_1]) ).

cnf(f_3587_3,plain,
    hAPP(hAPP(c_Product__Type_Oscomp(U_14122,U_14123,U_14124,tc_prod(U_14123,U_14124)),U_14125),c_Product__Type_OPair(U_14123,U_14124)) = U_14125,
    inference(clausify,[status(thm)],[f_3587_2]) ).

fof(f_3588_1,plain,
    ! [V_f_2,V_x_2,T_c,T_d,T_b] : hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_d,T_b,T_c),hAPP(c_Product__Type_OPair(T_d,T_b),V_x_2)),V_f_2) = hAPP(V_f_2,V_x_2),
    inference(fof_nnf,[status(thm)],[fact_Pair__scomp]) ).

fof(f_3588_2,plain,
    ! [U_14130,U_14129,U_14128,U_14127,U_14126] : hAPP(hAPP(c_Product__Type_Oscomp(U_14126,U_14127,U_14126,U_14128),hAPP(c_Product__Type_OPair(U_14127,U_14126),U_14129)),U_14130) = hAPP(U_14130,U_14129),
    inference(variable_rename,[status(thm)],[f_3588_1]) ).

cnf(f_3588_3,plain,
    hAPP(hAPP(c_Product__Type_Oscomp(U_14126,U_14127,U_14126,U_14128),hAPP(c_Product__Type_OPair(U_14127,U_14126),U_14129)),U_14130) = hAPP(U_14130,U_14129),
    inference(clausify,[status(thm)],[f_3588_2]) ).

fof(f_3589_1,plain,
    ! [V_x_2,V_g_2,V_f_2,T_b,T_e,T_d,T_c] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_c,T_d,T_e,T_b),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,T_b),V_g_2),hAPP(V_f_2,V_x_2)),
    inference(fof_nnf,[status(thm)],[fact_scomp__apply]) ).

fof(f_3589_2,plain,
    ! [U_14137,U_14136,U_14135,U_14134,U_14133,U_14132,U_14131] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(U_14131,U_14132,U_14133,U_14134),U_14135),U_14136),U_14137) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14132,U_14133,U_14134),U_14136),hAPP(U_14135,U_14137)),
    inference(variable_rename,[status(thm)],[f_3589_1]) ).

cnf(f_3589_3,plain,
    hAPP(hAPP(hAPP(c_Product__Type_Oscomp(U_14131,U_14132,U_14133,U_14134),U_14135),U_14136),U_14137) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14132,U_14133,U_14134),U_14136),hAPP(U_14135,U_14137)),
    inference(clausify,[status(thm)],[f_3589_2]) ).

fof(f_3590_1,plain,
    ! [V_x_2,V_g_2,V_f_2,T_b,T_e,T_d,T_c] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_c,T_d,T_e,T_b),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,T_b),V_g_2),hAPP(V_f_2,V_x_2)),
    inference(fof_nnf,[status(thm)],[fact_scomp__def]) ).

fof(f_3590_2,plain,
    ! [U_14144,U_14143,U_14142,U_14141,U_14140,U_14139,U_14138] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(U_14138,U_14139,U_14140,U_14141),U_14142),U_14143),U_14144) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14139,U_14140,U_14141),U_14143),hAPP(U_14142,U_14144)),
    inference(variable_rename,[status(thm)],[f_3590_1]) ).

cnf(f_3590_3,plain,
    hAPP(hAPP(hAPP(c_Product__Type_Oscomp(U_14138,U_14139,U_14140,U_14141),U_14142),U_14143),U_14144) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14139,U_14140,U_14141),U_14143),hAPP(U_14142,U_14144)),
    inference(clausify,[status(thm)],[f_3590_2]) ).

fof(f_3591_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_m_2),V_n_2)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_m_2),V_n_2)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ) ),
    inference(fof_nnf,[status(thm)],[fact_less__eq]) ).

fof(f_3591_2,plain,
    ! [U_14146,U_14145] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_14145),U_14146)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_14145),U_14146)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_14145),U_14146))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_14145),U_14146)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ) ),
    inference(variable_rename,[status(thm)],[f_3591_1]) ).

fof(f_3591_3,plain,
    ( ! [U_14150,U_14148] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_14148),U_14150)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_14148),U_14150)) )
    & ! [U_14149,U_14147] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_14147),U_14149))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_14147),U_14149)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ) ),
    inference(miniscope,[status(thm)],[f_3591_2]) ).

cnf(f_3591_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_14147),U_14149))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_14147),U_14149)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ),
    inference(clausify,[status(thm)],[f_3591_3]) ).

cnf(f_3591_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_14148),U_14150)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_14148),U_14150)) ),
    inference(clausify,[status(thm)],[f_3591_3]) ).

fof(f_3592_1,plain,
    ! [V_r_2,T_b] :
      ( ( c_Wellfounded_Owf(T_b,V_r_2)
        | ? [B_Q] :
            ( ! [B_x] :
                ( ? [B_y] :
                    ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),B_Q))
                    & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_x)),V_r_2)) )
                | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q)) )
            & ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q)) ) )
      & ( ! [B_Q] :
            ( ? [B_x] :
                ( ! [B_y] :
                    ( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_y),B_Q))
                    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_x)),V_r_2)) )
                & hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q)) )
            | ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q)) )
        | ~ c_Wellfounded_Owf(T_b,V_r_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_wf__eq__minimal]) ).

fof(f_3592_2,plain,
    ! [U_14160,U_14159] :
      ( ( c_Wellfounded_Owf(U_14159,U_14160)
        | ? [U_14158] :
            ( ! [U_14157] :
                ( ? [U_14156] :
                    ( hBOOL(hAPP(hAPP(c_member(U_14159),U_14156),U_14158))
                    & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14159,U_14159)),hAPP(hAPP(c_Product__Type_OPair(U_14159,U_14159),U_14156),U_14157)),U_14160)) )
                | ~ hBOOL(hAPP(hAPP(c_member(U_14159),U_14157),U_14158)) )
            & ? [U_14155] : hBOOL(hAPP(hAPP(c_member(U_14159),U_14155),U_14158)) ) )
      & ( ! [U_14154] :
            ( ? [U_14153] :
                ( ! [U_14152] :
                    ( ~ hBOOL(hAPP(hAPP(c_member(U_14159),U_14152),U_14154))
                    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14159,U_14159)),hAPP(hAPP(c_Product__Type_OPair(U_14159,U_14159),U_14152),U_14153)),U_14160)) )
                & hBOOL(hAPP(hAPP(c_member(U_14159),U_14153),U_14154)) )
            | ! [U_14151] : ~ hBOOL(hAPP(hAPP(c_member(U_14159),U_14151),U_14154)) )
        | ~ c_Wellfounded_Owf(U_14159,U_14160) ) ),
    inference(variable_rename,[status(thm)],[f_3592_1]) ).

fof(f_3592_3,plain,
    ( ! [U_14164,U_14162] :
        ( c_Wellfounded_Owf(U_14162,U_14164)
        | ? [U_14158] :
            ( ! [U_14157] :
                ( ? [U_14156] :
                    ( hBOOL(hAPP(hAPP(c_member(U_14162),U_14156),U_14158))
                    & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14162,U_14162)),hAPP(hAPP(c_Product__Type_OPair(U_14162,U_14162),U_14156),U_14157)),U_14164)) )
                | ~ hBOOL(hAPP(hAPP(c_member(U_14162),U_14157),U_14158)) )
            & ? [U_14155] : hBOOL(hAPP(hAPP(c_member(U_14162),U_14155),U_14158)) ) )
    & ! [U_14163,U_14161] :
        ( ! [U_14154] :
            ( ? [U_14153] :
                ( ! [U_14152] :
                    ( ~ hBOOL(hAPP(hAPP(c_member(U_14161),U_14152),U_14154))
                    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14161,U_14161)),hAPP(hAPP(c_Product__Type_OPair(U_14161,U_14161),U_14152),U_14153)),U_14163)) )
                & hBOOL(hAPP(hAPP(c_member(U_14161),U_14153),U_14154)) )
            | ! [U_14151] : ~ hBOOL(hAPP(hAPP(c_member(U_14161),U_14151),U_14154)) )
        | ~ c_Wellfounded_Owf(U_14161,U_14163) ) ),
    inference(miniscope,[status(thm)],[f_3592_2]) ).

fof(f_3592_4,plain,
    ( ! [U_14164,U_14162] :
        ( c_Wellfounded_Owf(U_14162,U_14164)
        | ? [U_14158] :
            ( ! [U_14157] :
                ( ? [U_14156] :
                    ( hBOOL(hAPP(hAPP(c_member(U_14162),U_14156),U_14158))
                    & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14162,U_14162)),hAPP(hAPP(c_Product__Type_OPair(U_14162,U_14162),U_14156),U_14157)),U_14164)) )
                | ~ hBOOL(hAPP(hAPP(c_member(U_14162),U_14157),U_14158)) )
            & ? [U_14155] : hBOOL(hAPP(hAPP(c_member(U_14162),U_14155),U_14158)) ) )
    & ! [U_14163,U_14161] :
        ( ! [U_14154] :
            ( ( ! [U_14152] :
                  ( ~ hBOOL(hAPP(hAPP(c_member(U_14161),U_14152),U_14154))
                  | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14161,U_14161)),hAPP(hAPP(c_Product__Type_OPair(U_14161,U_14161),U_14152),sK360(U_14163,U_14161,U_14154))),U_14163)) )
              & hBOOL(hAPP(hAPP(c_member(U_14161),sK360(U_14163,U_14161,U_14154)),U_14154)) )
            | ! [U_14151] : ~ hBOOL(hAPP(hAPP(c_member(U_14161),U_14151),U_14154)) )
        | ~ c_Wellfounded_Owf(U_14161,U_14163) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK360]),skolemize(U_14153,sK360(U_14163,U_14161,U_14154))],[f_3592_3]) ).

fof(f_3592_5,plain,
    ( ! [U_14164,U_14162] :
        ( c_Wellfounded_Owf(U_14162,U_14164)
        | ( ! [U_14157] :
              ( ? [U_14156] :
                  ( hBOOL(hAPP(hAPP(c_member(U_14162),U_14156),sK361(U_14164,U_14162)))
                  & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14162,U_14162)),hAPP(hAPP(c_Product__Type_OPair(U_14162,U_14162),U_14156),U_14157)),U_14164)) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_14162),U_14157),sK361(U_14164,U_14162))) )
          & ? [U_14155] : hBOOL(hAPP(hAPP(c_member(U_14162),U_14155),sK361(U_14164,U_14162))) ) )
    & ! [U_14163,U_14161] :
        ( ! [U_14154] :
            ( ( ! [U_14152] :
                  ( ~ hBOOL(hAPP(hAPP(c_member(U_14161),U_14152),U_14154))
                  | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14161,U_14161)),hAPP(hAPP(c_Product__Type_OPair(U_14161,U_14161),U_14152),sK360(U_14163,U_14161,U_14154))),U_14163)) )
              & hBOOL(hAPP(hAPP(c_member(U_14161),sK360(U_14163,U_14161,U_14154)),U_14154)) )
            | ! [U_14151] : ~ hBOOL(hAPP(hAPP(c_member(U_14161),U_14151),U_14154)) )
        | ~ c_Wellfounded_Owf(U_14161,U_14163) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK361]),skolemize(U_14158,sK361(U_14164,U_14162))],[f_3592_4]) ).

fof(f_3592_6,plain,
    ( ! [U_14164,U_14162] :
        ( c_Wellfounded_Owf(U_14162,U_14164)
        | ( ! [U_14157] :
              ( ? [U_14156] :
                  ( hBOOL(hAPP(hAPP(c_member(U_14162),U_14156),sK361(U_14164,U_14162)))
                  & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14162,U_14162)),hAPP(hAPP(c_Product__Type_OPair(U_14162,U_14162),U_14156),U_14157)),U_14164)) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_14162),U_14157),sK361(U_14164,U_14162))) )
          & hBOOL(hAPP(hAPP(c_member(U_14162),sK362(U_14164,U_14162)),sK361(U_14164,U_14162))) ) )
    & ! [U_14163,U_14161] :
        ( ! [U_14154] :
            ( ( ! [U_14152] :
                  ( ~ hBOOL(hAPP(hAPP(c_member(U_14161),U_14152),U_14154))
                  | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14161,U_14161)),hAPP(hAPP(c_Product__Type_OPair(U_14161,U_14161),U_14152),sK360(U_14163,U_14161,U_14154))),U_14163)) )
              & hBOOL(hAPP(hAPP(c_member(U_14161),sK360(U_14163,U_14161,U_14154)),U_14154)) )
            | ! [U_14151] : ~ hBOOL(hAPP(hAPP(c_member(U_14161),U_14151),U_14154)) )
        | ~ c_Wellfounded_Owf(U_14161,U_14163) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK362]),skolemize(U_14155,sK362(U_14164,U_14162))],[f_3592_5]) ).

fof(f_3592_7,plain,
    ( ! [U_14164,U_14162] :
        ( c_Wellfounded_Owf(U_14162,U_14164)
        | ( ! [U_14157] :
              ( ( hBOOL(hAPP(hAPP(c_member(U_14162),sK363(U_14164,U_14162,U_14157)),sK361(U_14164,U_14162)))
                & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14162,U_14162)),hAPP(hAPP(c_Product__Type_OPair(U_14162,U_14162),sK363(U_14164,U_14162,U_14157)),U_14157)),U_14164)) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_14162),U_14157),sK361(U_14164,U_14162))) )
          & hBOOL(hAPP(hAPP(c_member(U_14162),sK362(U_14164,U_14162)),sK361(U_14164,U_14162))) ) )
    & ! [U_14163,U_14161] :
        ( ! [U_14154] :
            ( ( ! [U_14152] :
                  ( ~ hBOOL(hAPP(hAPP(c_member(U_14161),U_14152),U_14154))
                  | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14161,U_14161)),hAPP(hAPP(c_Product__Type_OPair(U_14161,U_14161),U_14152),sK360(U_14163,U_14161,U_14154))),U_14163)) )
              & hBOOL(hAPP(hAPP(c_member(U_14161),sK360(U_14163,U_14161,U_14154)),U_14154)) )
            | ! [U_14151] : ~ hBOOL(hAPP(hAPP(c_member(U_14161),U_14151),U_14154)) )
        | ~ c_Wellfounded_Owf(U_14161,U_14163) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK363]),skolemize(U_14156,sK363(U_14164,U_14162,U_14157))],[f_3592_6]) ).

cnf(f_3592_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14161),sK360(U_14163,U_14161,U_14154)),U_14154))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14161),U_14151),U_14154))
    | ~ c_Wellfounded_Owf(U_14161,U_14163) ),
    inference(clausify,[status(thm)],[f_3592_7]) ).

cnf(f_3592_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_14161),U_14152),U_14154))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14161,U_14161)),hAPP(hAPP(c_Product__Type_OPair(U_14161,U_14161),U_14152),sK360(U_14163,U_14161,U_14154))),U_14163))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14161),U_14151),U_14154))
    | ~ c_Wellfounded_Owf(U_14161,U_14163) ),
    inference(clausify,[status(thm)],[f_3592_7]) ).

cnf(f_3592_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14162),sK362(U_14164,U_14162)),sK361(U_14164,U_14162)))
    | c_Wellfounded_Owf(U_14162,U_14164) ),
    inference(clausify,[status(thm)],[f_3592_7]) ).

cnf(f_3592_11,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14162,U_14162)),hAPP(hAPP(c_Product__Type_OPair(U_14162,U_14162),sK363(U_14164,U_14162,U_14157)),U_14157)),U_14164))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14162),U_14157),sK361(U_14164,U_14162)))
    | c_Wellfounded_Owf(U_14162,U_14164) ),
    inference(clausify,[status(thm)],[f_3592_7]) ).

cnf(f_3592_12,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14162),sK363(U_14164,U_14162,U_14157)),sK361(U_14164,U_14162)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14162),U_14157),sK361(U_14164,U_14162)))
    | c_Wellfounded_Owf(U_14162,U_14164) ),
    inference(clausify,[status(thm)],[f_3592_7]) ).

fof(f_3593_1,plain,
    ! [V_r_2,T_b] :
      ( c_Wellfounded_Owf(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2))
      | ~ c_Wellfounded_Owf(T_b,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_wf__trancl]) ).

fof(f_3593_2,plain,
    ! [U_14166,U_14165] :
      ( c_Wellfounded_Owf(U_14165,c_Transitive__Closure_Otrancl(U_14165,U_14166))
      | ~ c_Wellfounded_Owf(U_14165,U_14166) ),
    inference(variable_rename,[status(thm)],[f_3593_1]) ).

cnf(f_3593_3,plain,
    ( c_Wellfounded_Owf(U_14165,c_Transitive__Closure_Otrancl(U_14165,U_14166))
    | ~ c_Wellfounded_Owf(U_14165,U_14166) ),
    inference(clausify,[status(thm)],[f_3593_2]) ).

fof(f_3594_1,plain,
    c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat),
    inference(fof_nnf,[status(thm)],[fact_less__than__def]) ).

cnf(f_3594_2,plain,
    c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat),
    inference(clausify,[status(thm)],[f_3594_1]) ).

fof(f_3595_1,plain,
    ! [V_r_2,T_b] :
      ( ( c_Wellfounded_Oacyclic(T_b,V_r_2)
        | ? [B_x] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) )
      & ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
        | ~ c_Wellfounded_Oacyclic(T_b,V_r_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_acyclic__def]) ).

fof(f_3595_2,plain,
    ! [U_14170,U_14169] :
      ( ( c_Wellfounded_Oacyclic(U_14169,U_14170)
        | ? [U_14168] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_14169,U_14169)),hAPP(hAPP(c_Product__Type_OPair(U_14169,U_14169),U_14168),U_14168)),c_Transitive__Closure_Otrancl(U_14169,U_14170))) )
      & ( ! [U_14167] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14169,U_14169)),hAPP(hAPP(c_Product__Type_OPair(U_14169,U_14169),U_14167),U_14167)),c_Transitive__Closure_Otrancl(U_14169,U_14170)))
        | ~ c_Wellfounded_Oacyclic(U_14169,U_14170) ) ),
    inference(variable_rename,[status(thm)],[f_3595_1]) ).

fof(f_3595_3,plain,
    ( ! [U_14174,U_14172] :
        ( c_Wellfounded_Oacyclic(U_14172,U_14174)
        | ? [U_14168] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_14172,U_14172)),hAPP(hAPP(c_Product__Type_OPair(U_14172,U_14172),U_14168),U_14168)),c_Transitive__Closure_Otrancl(U_14172,U_14174))) )
    & ! [U_14173,U_14171] :
        ( ! [U_14167] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14171,U_14171)),hAPP(hAPP(c_Product__Type_OPair(U_14171,U_14171),U_14167),U_14167)),c_Transitive__Closure_Otrancl(U_14171,U_14173)))
        | ~ c_Wellfounded_Oacyclic(U_14171,U_14173) ) ),
    inference(miniscope,[status(thm)],[f_3595_2]) ).

fof(f_3595_4,plain,
    ( ! [U_14174,U_14172] :
        ( c_Wellfounded_Oacyclic(U_14172,U_14174)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14172,U_14172)),hAPP(hAPP(c_Product__Type_OPair(U_14172,U_14172),sK364(U_14174,U_14172)),sK364(U_14174,U_14172))),c_Transitive__Closure_Otrancl(U_14172,U_14174))) )
    & ! [U_14173,U_14171] :
        ( ! [U_14167] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14171,U_14171)),hAPP(hAPP(c_Product__Type_OPair(U_14171,U_14171),U_14167),U_14167)),c_Transitive__Closure_Otrancl(U_14171,U_14173)))
        | ~ c_Wellfounded_Oacyclic(U_14171,U_14173) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK364]),skolemize(U_14168,sK364(U_14174,U_14172))],[f_3595_3]) ).

cnf(f_3595_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14171,U_14171)),hAPP(hAPP(c_Product__Type_OPair(U_14171,U_14171),U_14167),U_14167)),c_Transitive__Closure_Otrancl(U_14171,U_14173)))
    | ~ c_Wellfounded_Oacyclic(U_14171,U_14173) ),
    inference(clausify,[status(thm)],[f_3595_4]) ).

cnf(f_3595_6,plain,
    ( c_Wellfounded_Oacyclic(U_14172,U_14174)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14172,U_14172)),hAPP(hAPP(c_Product__Type_OPair(U_14172,U_14172),sK364(U_14174,U_14172)),sK364(U_14174,U_14172))),c_Transitive__Closure_Otrancl(U_14172,U_14174))) ),
    inference(clausify,[status(thm)],[f_3595_4]) ).

fof(f_3596_1,plain,
    ! [V_r_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_trancl_Or__into__trancl]) ).

fof(f_3596_2,plain,
    ! [U_14178,U_14177,U_14176,U_14175] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14175,U_14175)),hAPP(hAPP(c_Product__Type_OPair(U_14175,U_14175),U_14176),U_14177)),c_Transitive__Closure_Otrancl(U_14175,U_14178)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14175,U_14175)),hAPP(hAPP(c_Product__Type_OPair(U_14175,U_14175),U_14176),U_14177)),U_14178)) ),
    inference(variable_rename,[status(thm)],[f_3596_1]) ).

cnf(f_3596_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14175,U_14175)),hAPP(hAPP(c_Product__Type_OPair(U_14175,U_14175),U_14176),U_14177)),c_Transitive__Closure_Otrancl(U_14175,U_14178)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14175,U_14175)),hAPP(hAPP(c_Product__Type_OPair(U_14175,U_14175),U_14176),U_14177)),U_14178)) ),
    inference(clausify,[status(thm)],[f_3596_2]) ).

fof(f_3597_1,plain,
    ! [V_r_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),hAPP(c_Relation_OField(T_b),V_r_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_Relation_OField(T_b),V_r_2))))),
    inference(fof_nnf,[status(thm)],[fact_trancl__subset__Field2]) ).

fof(f_3597_2,plain,
    ! [U_14180,U_14179] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14179,U_14179),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_14179,U_14180)),hAPP(hAPP(c_Product__Type_OSigma(U_14179,U_14179),hAPP(c_Relation_OField(U_14179),U_14180)),hAPP(c_COMBK(tc_fun(U_14179,tc_HOL_Obool),U_14179),hAPP(c_Relation_OField(U_14179),U_14180))))),
    inference(variable_rename,[status(thm)],[f_3597_1]) ).

cnf(f_3597_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14179,U_14179),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_14179,U_14180)),hAPP(hAPP(c_Product__Type_OSigma(U_14179,U_14179),hAPP(c_Relation_OField(U_14179),U_14180)),hAPP(c_COMBK(tc_fun(U_14179,tc_HOL_Obool),U_14179),hAPP(c_Relation_OField(U_14179),U_14180))))),
    inference(clausify,[status(thm)],[f_3597_2]) ).

fof(f_3598_1,plain,
    ! [V_r_2,V_p_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_r__into__trancl_H]) ).

fof(f_3598_2,plain,
    ! [U_14183,U_14182,U_14181] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14181,U_14181)),U_14182),c_Transitive__Closure_Otrancl(U_14181,U_14183)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14181,U_14181)),U_14182),U_14183)) ),
    inference(variable_rename,[status(thm)],[f_3598_1]) ).

cnf(f_3598_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14181,U_14181)),U_14182),c_Transitive__Closure_Otrancl(U_14181,U_14183)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14181,U_14181)),U_14182),U_14183)) ),
    inference(clausify,[status(thm)],[f_3598_2]) ).

fof(f_3599_1,plain,
    ! [T_b] : c_Transitive__Closure_Otrancl(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_trancl__empty]) ).

fof(f_3599_2,plain,
    ! [U_14184] : c_Transitive__Closure_Otrancl(U_14184,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14184,U_14184),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14184,U_14184),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3599_1]) ).

cnf(f_3599_3,plain,
    c_Transitive__Closure_Otrancl(U_14184,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14184,U_14184),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14184,U_14184),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3599_2]) ).

fof(f_3600_1,plain,
    ! [V_r_2,T_b] : hAPP(c_Relation_ODomain(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)) = hAPP(c_Relation_ODomain(T_b,T_b),V_r_2),
    inference(fof_nnf,[status(thm)],[fact_trancl__domain]) ).

fof(f_3600_2,plain,
    ! [U_14186,U_14185] : hAPP(c_Relation_ODomain(U_14185,U_14185),c_Transitive__Closure_Otrancl(U_14185,U_14186)) = hAPP(c_Relation_ODomain(U_14185,U_14185),U_14186),
    inference(variable_rename,[status(thm)],[f_3600_1]) ).

cnf(f_3600_3,plain,
    hAPP(c_Relation_ODomain(U_14185,U_14185),c_Transitive__Closure_Otrancl(U_14185,U_14186)) = hAPP(c_Relation_ODomain(U_14185,U_14185),U_14186),
    inference(clausify,[status(thm)],[f_3600_2]) ).

fof(f_3601_1,plain,
    ! [V_r_2,T_b] : hAPP(c_Relation_ORange(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)) = hAPP(c_Relation_ORange(T_b,T_b),V_r_2),
    inference(fof_nnf,[status(thm)],[fact_trancl__range]) ).

fof(f_3601_2,plain,
    ! [U_14188,U_14187] : hAPP(c_Relation_ORange(U_14187,U_14187),c_Transitive__Closure_Otrancl(U_14187,U_14188)) = hAPP(c_Relation_ORange(U_14187,U_14187),U_14188),
    inference(variable_rename,[status(thm)],[f_3601_1]) ).

cnf(f_3601_3,plain,
    hAPP(c_Relation_ORange(U_14187,U_14187),c_Transitive__Closure_Otrancl(U_14187,U_14188)) = hAPP(c_Relation_ORange(U_14187,U_14187),U_14188),
    inference(clausify,[status(thm)],[f_3601_2]) ).

fof(f_3602_1,plain,
    ! [V_r_2,T_b] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_finite__trancl]) ).

fof(f_3602_2,plain,
    ! [U_14190,U_14189] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14189,U_14189)),c_Transitive__Closure_Otrancl(U_14189,U_14190)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14189,U_14189)),U_14190)) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14189,U_14189)),U_14190))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14189,U_14189)),c_Transitive__Closure_Otrancl(U_14189,U_14190))) ) ),
    inference(variable_rename,[status(thm)],[f_3602_1]) ).

fof(f_3602_3,plain,
    ( ! [U_14194,U_14192] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14192,U_14192)),c_Transitive__Closure_Otrancl(U_14192,U_14194)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14192,U_14192)),U_14194)) )
    & ! [U_14193,U_14191] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14191,U_14191)),U_14193))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14191,U_14191)),c_Transitive__Closure_Otrancl(U_14191,U_14193))) ) ),
    inference(miniscope,[status(thm)],[f_3602_2]) ).

cnf(f_3602_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14191,U_14191)),U_14193))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14191,U_14191)),c_Transitive__Closure_Otrancl(U_14191,U_14193))) ),
    inference(clausify,[status(thm)],[f_3602_3]) ).

cnf(f_3602_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14192,U_14192)),c_Transitive__Closure_Otrancl(U_14192,U_14194)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14192,U_14192)),U_14194)) ),
    inference(clausify,[status(thm)],[f_3602_3]) ).

fof(f_3603_1,plain,
    ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_trancl__trans]) ).

fof(f_3603_2,plain,
    ! [U_14199,U_14198,U_14197,U_14196,U_14195] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14195,U_14195)),hAPP(hAPP(c_Product__Type_OPair(U_14195,U_14195),U_14196),U_14199)),c_Transitive__Closure_Otrancl(U_14195,U_14198)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14195,U_14195)),hAPP(hAPP(c_Product__Type_OPair(U_14195,U_14195),U_14197),U_14199)),c_Transitive__Closure_Otrancl(U_14195,U_14198)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14195,U_14195)),hAPP(hAPP(c_Product__Type_OPair(U_14195,U_14195),U_14196),U_14197)),c_Transitive__Closure_Otrancl(U_14195,U_14198))) ),
    inference(variable_rename,[status(thm)],[f_3603_1]) ).

cnf(f_3603_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14195,U_14195)),hAPP(hAPP(c_Product__Type_OPair(U_14195,U_14195),U_14196),U_14199)),c_Transitive__Closure_Otrancl(U_14195,U_14198)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14195,U_14195)),hAPP(hAPP(c_Product__Type_OPair(U_14195,U_14195),U_14197),U_14199)),c_Transitive__Closure_Otrancl(U_14195,U_14198)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14195,U_14195)),hAPP(hAPP(c_Product__Type_OPair(U_14195,U_14195),U_14196),U_14197)),c_Transitive__Closure_Otrancl(U_14195,U_14198))) ),
    inference(clausify,[status(thm)],[f_3603_2]) ).

fof(f_3604_1,plain,
    ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),V_r_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_Transitive__Closure_Otrancl__into__trancl]) ).

fof(f_3604_2,plain,
    ! [U_14204,U_14203,U_14202,U_14201,U_14200] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14200,U_14200)),hAPP(hAPP(c_Product__Type_OPair(U_14200,U_14200),U_14201),U_14204)),c_Transitive__Closure_Otrancl(U_14200,U_14203)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14200,U_14200)),hAPP(hAPP(c_Product__Type_OPair(U_14200,U_14200),U_14202),U_14204)),U_14203))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14200,U_14200)),hAPP(hAPP(c_Product__Type_OPair(U_14200,U_14200),U_14201),U_14202)),c_Transitive__Closure_Otrancl(U_14200,U_14203))) ),
    inference(variable_rename,[status(thm)],[f_3604_1]) ).

cnf(f_3604_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14200,U_14200)),hAPP(hAPP(c_Product__Type_OPair(U_14200,U_14200),U_14201),U_14204)),c_Transitive__Closure_Otrancl(U_14200,U_14203)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14200,U_14200)),hAPP(hAPP(c_Product__Type_OPair(U_14200,U_14200),U_14202),U_14204)),U_14203))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14200,U_14200)),hAPP(hAPP(c_Product__Type_OPair(U_14200,U_14200),U_14201),U_14202)),c_Transitive__Closure_Otrancl(U_14200,U_14203))) ),
    inference(clausify,[status(thm)],[f_3604_2]) ).

fof(f_3605_1,plain,
    ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_trancl__into__trancl2]) ).

fof(f_3605_2,plain,
    ! [U_14209,U_14208,U_14207,U_14206,U_14205] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14205,U_14205)),hAPP(hAPP(c_Product__Type_OPair(U_14205,U_14205),U_14206),U_14209)),c_Transitive__Closure_Otrancl(U_14205,U_14208)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14205,U_14205)),hAPP(hAPP(c_Product__Type_OPair(U_14205,U_14205),U_14207),U_14209)),c_Transitive__Closure_Otrancl(U_14205,U_14208)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14205,U_14205)),hAPP(hAPP(c_Product__Type_OPair(U_14205,U_14205),U_14206),U_14207)),U_14208)) ),
    inference(variable_rename,[status(thm)],[f_3605_1]) ).

cnf(f_3605_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14205,U_14205)),hAPP(hAPP(c_Product__Type_OPair(U_14205,U_14205),U_14206),U_14209)),c_Transitive__Closure_Otrancl(U_14205,U_14208)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14205,U_14205)),hAPP(hAPP(c_Product__Type_OPair(U_14205,U_14205),U_14207),U_14209)),c_Transitive__Closure_Otrancl(U_14205,U_14208)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14205,U_14205)),hAPP(hAPP(c_Product__Type_OPair(U_14205,U_14205),U_14206),U_14207)),U_14208)) ),
    inference(clausify,[status(thm)],[f_3605_2]) ).

fof(f_3606_1,plain,
    ! [V_c_2,V_R_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),V_R_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_R_2)) ),
    inference(fof_nnf,[status(thm)],[fact_r__r__into__trancl]) ).

fof(f_3606_2,plain,
    ! [U_14214,U_14213,U_14212,U_14211,U_14210] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14210,U_14210)),hAPP(hAPP(c_Product__Type_OPair(U_14210,U_14210),U_14211),U_14214)),c_Transitive__Closure_Otrancl(U_14210,U_14213)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14210,U_14210)),hAPP(hAPP(c_Product__Type_OPair(U_14210,U_14210),U_14212),U_14214)),U_14213))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14210,U_14210)),hAPP(hAPP(c_Product__Type_OPair(U_14210,U_14210),U_14211),U_14212)),U_14213)) ),
    inference(variable_rename,[status(thm)],[f_3606_1]) ).

cnf(f_3606_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14210,U_14210)),hAPP(hAPP(c_Product__Type_OPair(U_14210,U_14210),U_14211),U_14214)),c_Transitive__Closure_Otrancl(U_14210,U_14213)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14210,U_14210)),hAPP(hAPP(c_Product__Type_OPair(U_14210,U_14210),U_14212),U_14214)),U_14213))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14210,U_14210)),hAPP(hAPP(c_Product__Type_OPair(U_14210,U_14210),U_14211),U_14212)),U_14213)) ),
    inference(clausify,[status(thm)],[f_3606_2]) ).

fof(f_3607_1,plain,
    ! [V_s_2,V_r_2,V_p_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_s_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_trancl__mono]) ).

fof(f_3607_2,plain,
    ! [U_14218,U_14217,U_14216,U_14215] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14215,U_14215)),U_14216),c_Transitive__Closure_Otrancl(U_14215,U_14218)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14215,U_14215),tc_HOL_Obool)),U_14217),U_14218))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14215,U_14215)),U_14216),c_Transitive__Closure_Otrancl(U_14215,U_14217))) ),
    inference(variable_rename,[status(thm)],[f_3607_1]) ).

cnf(f_3607_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14215,U_14215)),U_14216),c_Transitive__Closure_Otrancl(U_14215,U_14218)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14215,U_14215),tc_HOL_Obool)),U_14217),U_14218))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14215,U_14215)),U_14216),c_Transitive__Closure_Otrancl(U_14215,U_14217))) ),
    inference(clausify,[status(thm)],[f_3607_2]) ).

fof(f_3608_1,plain,
    ! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)),V_r_2)),
    inference(fof_nnf,[status(thm)],[fact_trancl__unfold]) ).

fof(f_3608_2,plain,
    ! [U_14220,U_14219] : c_Transitive__Closure_Otrancl(U_14219,U_14220) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14219,U_14219),tc_HOL_Obool)),U_14220),hAPP(hAPP(c_Relation_Orel__comp(U_14219,U_14219,U_14219),c_Transitive__Closure_Otrancl(U_14219,U_14220)),U_14220)),
    inference(variable_rename,[status(thm)],[f_3608_1]) ).

cnf(f_3608_3,plain,
    c_Transitive__Closure_Otrancl(U_14219,U_14220) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14219,U_14219),tc_HOL_Obool)),U_14220),hAPP(hAPP(c_Relation_Orel__comp(U_14219,U_14219,U_14219),c_Transitive__Closure_Otrancl(U_14219,U_14220)),U_14220)),
    inference(clausify,[status(thm)],[f_3608_2]) ).

fof(f_3609_1,plain,
    ! [V_A_2,V_r_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_trancl__subset__Sigma]) ).

fof(f_3609_2,plain,
    ! [U_14223,U_14222,U_14221] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14221,U_14221),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_14221,U_14222)),hAPP(hAPP(c_Product__Type_OSigma(U_14221,U_14221),U_14223),hAPP(c_COMBK(tc_fun(U_14221,tc_HOL_Obool),U_14221),U_14223))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14221,U_14221),tc_HOL_Obool)),U_14222),hAPP(hAPP(c_Product__Type_OSigma(U_14221,U_14221),U_14223),hAPP(c_COMBK(tc_fun(U_14221,tc_HOL_Obool),U_14221),U_14223)))) ),
    inference(variable_rename,[status(thm)],[f_3609_1]) ).

cnf(f_3609_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14221,U_14221),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_14221,U_14222)),hAPP(hAPP(c_Product__Type_OSigma(U_14221,U_14221),U_14223),hAPP(c_COMBK(tc_fun(U_14221,tc_HOL_Obool),U_14221),U_14223))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14221,U_14221),tc_HOL_Obool)),U_14222),hAPP(hAPP(c_Product__Type_OSigma(U_14221,U_14221),U_14223),hAPP(c_COMBK(tc_fun(U_14221,tc_HOL_Obool),U_14221),U_14223)))) ),
    inference(clausify,[status(thm)],[f_3609_2]) ).

fof(f_3610_1,plain,
    ! [V_s_2,V_r_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),V_s_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),V_s_2)),V_r_2)),V_s_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ),
    inference(fof_nnf,[status(thm)],[fact_trancl__Int__subset]) ).

fof(f_3610_2,plain,
    ! [U_14226,U_14225,U_14224] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14224,U_14224),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_14224,U_14225)),U_14226))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14224,U_14224),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_14224,U_14224,U_14224),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14224,U_14224),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_14224,U_14225)),U_14226)),U_14225)),U_14226))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14224,U_14224),tc_HOL_Obool)),U_14225),U_14226)) ),
    inference(variable_rename,[status(thm)],[f_3610_1]) ).

cnf(f_3610_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14224,U_14224),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_14224,U_14225)),U_14226))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14224,U_14224),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_14224,U_14224,U_14224),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14224,U_14224),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_14224,U_14225)),U_14226)),U_14225)),U_14226))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14224,U_14224),tc_HOL_Obool)),U_14225),U_14226)) ),
    inference(clausify,[status(thm)],[f_3610_2]) ).

fof(f_3611_1,plain,
    ! [V_r_2,V_x_2,V_y_2,T_b] : c_Transitive__Closure_Otrancl(T_b,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),V_r_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b))),hAPP(hAPP(c_COMBC(T_b,T_b,tc_prod(T_b,T_b)),c_Product__Type_OPair(T_b,T_b)),V_y_2))),c_Transitive__Closure_Ortrancl(T_b,V_r_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b))),hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2))),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))))),
    inference(fof_nnf,[status(thm)],[fact_trancl__insert]) ).

fof(f_3611_2,plain,
    ! [U_14230,U_14229,U_14228,U_14227] : c_Transitive__Closure_Otrancl(U_14227,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14227,U_14227)),hAPP(hAPP(c_Product__Type_OPair(U_14227,U_14227),U_14228),U_14229)),U_14230)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14227,U_14227),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_14227,U_14230)),hAPP(c_Set_OCollect(tc_prod(U_14227,U_14227)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14227,U_14227,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14227,tc_fun(U_14227,tc_HOL_Obool),tc_fun(U_14227,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14227,tc_HOL_Obool),tc_fun(U_14227,tc_HOL_Obool)),U_14227),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14227)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14227),c_fconj),hAPP(hAPP(c_COMBC(U_14227,tc_fun(tc_prod(U_14227,U_14227),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(U_14227,U_14227),tc_fun(tc_fun(tc_prod(U_14227,U_14227),tc_HOL_Obool),tc_HOL_Obool),U_14227),c_member(tc_prod(U_14227,U_14227))),hAPP(hAPP(c_COMBC(U_14227,U_14227,tc_prod(U_14227,U_14227)),c_Product__Type_OPair(U_14227,U_14227)),U_14228))),c_Transitive__Closure_Ortrancl(U_14227,U_14230))))),hAPP(hAPP(c_COMBC(U_14227,tc_fun(tc_prod(U_14227,U_14227),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(U_14227,U_14227),tc_fun(tc_fun(tc_prod(U_14227,U_14227),tc_HOL_Obool),tc_HOL_Obool),U_14227),c_member(tc_prod(U_14227,U_14227))),hAPP(c_Product__Type_OPair(U_14227,U_14227),U_14229))),c_Transitive__Closure_Ortrancl(U_14227,U_14230)))))),
    inference(variable_rename,[status(thm)],[f_3611_1]) ).

cnf(f_3611_3,plain,
    c_Transitive__Closure_Otrancl(U_14227,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14227,U_14227)),hAPP(hAPP(c_Product__Type_OPair(U_14227,U_14227),U_14228),U_14229)),U_14230)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14227,U_14227),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_14227,U_14230)),hAPP(c_Set_OCollect(tc_prod(U_14227,U_14227)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14227,U_14227,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14227,tc_fun(U_14227,tc_HOL_Obool),tc_fun(U_14227,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14227,tc_HOL_Obool),tc_fun(U_14227,tc_HOL_Obool)),U_14227),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14227)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14227),c_fconj),hAPP(hAPP(c_COMBC(U_14227,tc_fun(tc_prod(U_14227,U_14227),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(U_14227,U_14227),tc_fun(tc_fun(tc_prod(U_14227,U_14227),tc_HOL_Obool),tc_HOL_Obool),U_14227),c_member(tc_prod(U_14227,U_14227))),hAPP(hAPP(c_COMBC(U_14227,U_14227,tc_prod(U_14227,U_14227)),c_Product__Type_OPair(U_14227,U_14227)),U_14228))),c_Transitive__Closure_Ortrancl(U_14227,U_14230))))),hAPP(hAPP(c_COMBC(U_14227,tc_fun(tc_prod(U_14227,U_14227),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(U_14227,U_14227),tc_fun(tc_fun(tc_prod(U_14227,U_14227),tc_HOL_Obool),tc_HOL_Obool),U_14227),c_member(tc_prod(U_14227,U_14227))),hAPP(c_Product__Type_OPair(U_14227,U_14227),U_14229))),c_Transitive__Closure_Ortrancl(U_14227,U_14230)))))),
    inference(clausify,[status(thm)],[f_3611_2]) ).

fof(f_3612_1,plain,
    ! [V_y_2,V_x_2,V_r_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2)),c_fequal),V_x_2),V_y_2))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b)))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2)),c_fequal),V_x_2),V_y_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_reflcl__set__eq]) ).

fof(f_3612_2,plain,
    ! [U_14234,U_14233,U_14232,U_14231] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14231,tc_fun(U_14231,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_14231,tc_fun(tc_prod(U_14231,U_14231),tc_HOL_Obool),tc_fun(U_14231,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14231,tc_fun(tc_fun(tc_prod(U_14231,U_14231),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14231,U_14231),tc_HOL_Obool),tc_fun(U_14231,tc_HOL_Obool)),U_14231),c_COMBC(U_14231,tc_fun(tc_prod(U_14231,U_14231),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14231,tc_prod(U_14231,U_14231)),tc_fun(U_14231,tc_fun(tc_fun(tc_prod(U_14231,U_14231),tc_HOL_Obool),tc_HOL_Obool)),U_14231),hAPP(c_COMBB(tc_prod(U_14231,U_14231),tc_fun(tc_fun(tc_prod(U_14231,U_14231),tc_HOL_Obool),tc_HOL_Obool),U_14231),c_member(tc_prod(U_14231,U_14231)))),c_Product__Type_OPair(U_14231,U_14231)))),U_14232)),c_fequal),U_14233),U_14234))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14231,U_14231)),hAPP(hAPP(c_Product__Type_OPair(U_14231,U_14231),U_14233),U_14234)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14231,U_14231),tc_HOL_Obool)),U_14232),c_Relation_OId(U_14231)))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14231,U_14231)),hAPP(hAPP(c_Product__Type_OPair(U_14231,U_14231),U_14233),U_14234)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14231,U_14231),tc_HOL_Obool)),U_14232),c_Relation_OId(U_14231))))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14231,tc_fun(U_14231,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_14231,tc_fun(tc_prod(U_14231,U_14231),tc_HOL_Obool),tc_fun(U_14231,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14231,tc_fun(tc_fun(tc_prod(U_14231,U_14231),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14231,U_14231),tc_HOL_Obool),tc_fun(U_14231,tc_HOL_Obool)),U_14231),c_COMBC(U_14231,tc_fun(tc_prod(U_14231,U_14231),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14231,tc_prod(U_14231,U_14231)),tc_fun(U_14231,tc_fun(tc_fun(tc_prod(U_14231,U_14231),tc_HOL_Obool),tc_HOL_Obool)),U_14231),hAPP(c_COMBB(tc_prod(U_14231,U_14231),tc_fun(tc_fun(tc_prod(U_14231,U_14231),tc_HOL_Obool),tc_HOL_Obool),U_14231),c_member(tc_prod(U_14231,U_14231)))),c_Product__Type_OPair(U_14231,U_14231)))),U_14232)),c_fequal),U_14233),U_14234)) ) ),
    inference(variable_rename,[status(thm)],[f_3612_1]) ).

fof(f_3612_3,plain,
    ( ! [U_14242,U_14240,U_14238,U_14236] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14236,tc_fun(U_14236,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_14236,tc_fun(tc_prod(U_14236,U_14236),tc_HOL_Obool),tc_fun(U_14236,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14236,tc_fun(tc_fun(tc_prod(U_14236,U_14236),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14236,U_14236),tc_HOL_Obool),tc_fun(U_14236,tc_HOL_Obool)),U_14236),c_COMBC(U_14236,tc_fun(tc_prod(U_14236,U_14236),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14236,tc_prod(U_14236,U_14236)),tc_fun(U_14236,tc_fun(tc_fun(tc_prod(U_14236,U_14236),tc_HOL_Obool),tc_HOL_Obool)),U_14236),hAPP(c_COMBB(tc_prod(U_14236,U_14236),tc_fun(tc_fun(tc_prod(U_14236,U_14236),tc_HOL_Obool),tc_HOL_Obool),U_14236),c_member(tc_prod(U_14236,U_14236)))),c_Product__Type_OPair(U_14236,U_14236)))),U_14238)),c_fequal),U_14240),U_14242))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14236,U_14236)),hAPP(hAPP(c_Product__Type_OPair(U_14236,U_14236),U_14240),U_14242)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14236,U_14236),tc_HOL_Obool)),U_14238),c_Relation_OId(U_14236)))) )
    & ! [U_14241,U_14239,U_14237,U_14235] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14235,U_14235)),hAPP(hAPP(c_Product__Type_OPair(U_14235,U_14235),U_14239),U_14241)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14235,U_14235),tc_HOL_Obool)),U_14237),c_Relation_OId(U_14235))))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14235,tc_fun(U_14235,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_14235,tc_fun(tc_prod(U_14235,U_14235),tc_HOL_Obool),tc_fun(U_14235,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14235,tc_fun(tc_fun(tc_prod(U_14235,U_14235),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14235,U_14235),tc_HOL_Obool),tc_fun(U_14235,tc_HOL_Obool)),U_14235),c_COMBC(U_14235,tc_fun(tc_prod(U_14235,U_14235),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14235,tc_prod(U_14235,U_14235)),tc_fun(U_14235,tc_fun(tc_fun(tc_prod(U_14235,U_14235),tc_HOL_Obool),tc_HOL_Obool)),U_14235),hAPP(c_COMBB(tc_prod(U_14235,U_14235),tc_fun(tc_fun(tc_prod(U_14235,U_14235),tc_HOL_Obool),tc_HOL_Obool),U_14235),c_member(tc_prod(U_14235,U_14235)))),c_Product__Type_OPair(U_14235,U_14235)))),U_14237)),c_fequal),U_14239),U_14241)) ) ),
    inference(miniscope,[status(thm)],[f_3612_2]) ).

cnf(f_3612_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14235,U_14235)),hAPP(hAPP(c_Product__Type_OPair(U_14235,U_14235),U_14239),U_14241)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14235,U_14235),tc_HOL_Obool)),U_14237),c_Relation_OId(U_14235))))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14235,tc_fun(U_14235,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_14235,tc_fun(tc_prod(U_14235,U_14235),tc_HOL_Obool),tc_fun(U_14235,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14235,tc_fun(tc_fun(tc_prod(U_14235,U_14235),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14235,U_14235),tc_HOL_Obool),tc_fun(U_14235,tc_HOL_Obool)),U_14235),c_COMBC(U_14235,tc_fun(tc_prod(U_14235,U_14235),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14235,tc_prod(U_14235,U_14235)),tc_fun(U_14235,tc_fun(tc_fun(tc_prod(U_14235,U_14235),tc_HOL_Obool),tc_HOL_Obool)),U_14235),hAPP(c_COMBB(tc_prod(U_14235,U_14235),tc_fun(tc_fun(tc_prod(U_14235,U_14235),tc_HOL_Obool),tc_HOL_Obool),U_14235),c_member(tc_prod(U_14235,U_14235)))),c_Product__Type_OPair(U_14235,U_14235)))),U_14237)),c_fequal),U_14239),U_14241)) ),
    inference(clausify,[status(thm)],[f_3612_3]) ).

cnf(f_3612_5,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14236,tc_fun(U_14236,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_14236,tc_fun(tc_prod(U_14236,U_14236),tc_HOL_Obool),tc_fun(U_14236,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14236,tc_fun(tc_fun(tc_prod(U_14236,U_14236),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14236,U_14236),tc_HOL_Obool),tc_fun(U_14236,tc_HOL_Obool)),U_14236),c_COMBC(U_14236,tc_fun(tc_prod(U_14236,U_14236),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14236,tc_prod(U_14236,U_14236)),tc_fun(U_14236,tc_fun(tc_fun(tc_prod(U_14236,U_14236),tc_HOL_Obool),tc_HOL_Obool)),U_14236),hAPP(c_COMBB(tc_prod(U_14236,U_14236),tc_fun(tc_fun(tc_prod(U_14236,U_14236),tc_HOL_Obool),tc_HOL_Obool),U_14236),c_member(tc_prod(U_14236,U_14236)))),c_Product__Type_OPair(U_14236,U_14236)))),U_14238)),c_fequal),U_14240),U_14242))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14236,U_14236)),hAPP(hAPP(c_Product__Type_OPair(U_14236,U_14236),U_14240),U_14242)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14236,U_14236),tc_HOL_Obool)),U_14238),c_Relation_OId(U_14236)))) ),
    inference(clausify,[status(thm)],[f_3612_3]) ).

fof(f_3613_1,plain,
    ! [V_r_2,V_p_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_r__into__rtrancl]) ).

fof(f_3613_2,plain,
    ! [U_14245,U_14244,U_14243] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14243,U_14243)),U_14244),c_Transitive__Closure_Ortrancl(U_14243,U_14245)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14243,U_14243)),U_14244),U_14245)) ),
    inference(variable_rename,[status(thm)],[f_3613_1]) ).

cnf(f_3613_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14243,U_14243)),U_14244),c_Transitive__Closure_Ortrancl(U_14243,U_14245)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14243,U_14243)),U_14244),U_14245)) ),
    inference(clausify,[status(thm)],[f_3613_2]) ).

fof(f_3614_1,plain,
    ! [V_r_2,V_a_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))),
    inference(fof_nnf,[status(thm)],[fact_rtrancl_Ortrancl__refl]) ).

fof(f_3614_2,plain,
    ! [U_14248,U_14247,U_14246] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_14246,U_14246)),hAPP(hAPP(c_Product__Type_OPair(U_14246,U_14246),U_14247),U_14247)),c_Transitive__Closure_Ortrancl(U_14246,U_14248))),
    inference(variable_rename,[status(thm)],[f_3614_1]) ).

cnf(f_3614_3,plain,
    hBOOL(hAPP(hAPP(c_member(tc_prod(U_14246,U_14246)),hAPP(hAPP(c_Product__Type_OPair(U_14246,U_14246),U_14247),U_14247)),c_Transitive__Closure_Ortrancl(U_14246,U_14248))),
    inference(clausify,[status(thm)],[f_3614_2]) ).

fof(f_3615_1,plain,
    ! [V_a_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),c_Relation_OId(T_b))),
    inference(fof_nnf,[status(thm)],[fact_IdI]) ).

fof(f_3615_2,plain,
    ! [U_14250,U_14249] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_14249,U_14249)),hAPP(hAPP(c_Product__Type_OPair(U_14249,U_14249),U_14250),U_14250)),c_Relation_OId(U_14249))),
    inference(variable_rename,[status(thm)],[f_3615_1]) ).

cnf(f_3615_3,plain,
    hBOOL(hAPP(hAPP(c_member(tc_prod(U_14249,U_14249)),hAPP(hAPP(c_Product__Type_OPair(U_14249,U_14249),U_14250),U_14250)),c_Relation_OId(U_14249))),
    inference(clausify,[status(thm)],[f_3615_2]) ).

fof(f_3616_1,plain,
    ! [V_r_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_trancl__into__rtrancl]) ).

fof(f_3616_2,plain,
    ! [U_14254,U_14253,U_14252,U_14251] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14251,U_14251)),hAPP(hAPP(c_Product__Type_OPair(U_14251,U_14251),U_14252),U_14253)),c_Transitive__Closure_Ortrancl(U_14251,U_14254)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14251,U_14251)),hAPP(hAPP(c_Product__Type_OPair(U_14251,U_14251),U_14252),U_14253)),c_Transitive__Closure_Otrancl(U_14251,U_14254))) ),
    inference(variable_rename,[status(thm)],[f_3616_1]) ).

cnf(f_3616_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14251,U_14251)),hAPP(hAPP(c_Product__Type_OPair(U_14251,U_14251),U_14252),U_14253)),c_Transitive__Closure_Ortrancl(U_14251,U_14254)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14251,U_14251)),hAPP(hAPP(c_Product__Type_OPair(U_14251,U_14251),U_14252),U_14253)),c_Transitive__Closure_Otrancl(U_14251,U_14254))) ),
    inference(clausify,[status(thm)],[f_3616_2]) ).

fof(f_3617_1,plain,
    ! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,V_r_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_r_2),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),
    inference(fof_nnf,[status(thm)],[fact_trancl__unfold__left]) ).

fof(f_3617_2,plain,
    ! [U_14256,U_14255] : c_Transitive__Closure_Otrancl(U_14255,U_14256) = hAPP(hAPP(c_Relation_Orel__comp(U_14255,U_14255,U_14255),U_14256),c_Transitive__Closure_Ortrancl(U_14255,U_14256)),
    inference(variable_rename,[status(thm)],[f_3617_1]) ).

cnf(f_3617_3,plain,
    c_Transitive__Closure_Otrancl(U_14255,U_14256) = hAPP(hAPP(c_Relation_Orel__comp(U_14255,U_14255,U_14255),U_14256),c_Transitive__Closure_Ortrancl(U_14255,U_14256)),
    inference(clausify,[status(thm)],[f_3617_2]) ).

fof(f_3618_1,plain,
    ! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,V_r_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_r_2),
    inference(fof_nnf,[status(thm)],[fact_trancl__unfold__right]) ).

fof(f_3618_2,plain,
    ! [U_14258,U_14257] : c_Transitive__Closure_Otrancl(U_14257,U_14258) = hAPP(hAPP(c_Relation_Orel__comp(U_14257,U_14257,U_14257),c_Transitive__Closure_Ortrancl(U_14257,U_14258)),U_14258),
    inference(variable_rename,[status(thm)],[f_3618_1]) ).

cnf(f_3618_3,plain,
    c_Transitive__Closure_Otrancl(U_14257,U_14258) = hAPP(hAPP(c_Relation_Orel__comp(U_14257,U_14257,U_14257),c_Transitive__Closure_Ortrancl(U_14257,U_14258)),U_14258),
    inference(clausify,[status(thm)],[f_3618_2]) ).

fof(f_3619_1,plain,
    ! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))) = c_Transitive__Closure_Ortrancl(T_b,V_r_2),
    inference(fof_nnf,[status(thm)],[fact_trancl__reflcl]) ).

fof(f_3619_2,plain,
    ! [U_14260,U_14259] : c_Transitive__Closure_Otrancl(U_14259,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14259,U_14259),tc_HOL_Obool)),U_14260),c_Relation_OId(U_14259))) = c_Transitive__Closure_Ortrancl(U_14259,U_14260),
    inference(variable_rename,[status(thm)],[f_3619_1]) ).

cnf(f_3619_3,plain,
    c_Transitive__Closure_Otrancl(U_14259,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14259,U_14259),tc_HOL_Obool)),U_14260),c_Relation_OId(U_14259))) = c_Transitive__Closure_Ortrancl(U_14259,U_14260),
    inference(clausify,[status(thm)],[f_3619_2]) ).

fof(f_3620_1,plain,
    ! [V_r_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),c_Relation_OId(T_b)) = c_Transitive__Closure_Ortrancl(T_b,V_r_2),
    inference(fof_nnf,[status(thm)],[fact_reflcl__trancl]) ).

fof(f_3620_2,plain,
    ! [U_14262,U_14261] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14261,U_14261),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_14261,U_14262)),c_Relation_OId(U_14261)) = c_Transitive__Closure_Ortrancl(U_14261,U_14262),
    inference(variable_rename,[status(thm)],[f_3620_1]) ).

cnf(f_3620_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14261,U_14261),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_14261,U_14262)),c_Relation_OId(U_14261)) = c_Transitive__Closure_Ortrancl(U_14261,U_14262),
    inference(clausify,[status(thm)],[f_3620_2]) ).

fof(f_3621_1,plain,
    ! [V_R_2,T_b] : c_Transitive__Closure_Otrancl(T_b,c_Transitive__Closure_Ortrancl(T_b,V_R_2)) = c_Transitive__Closure_Ortrancl(T_b,V_R_2),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__trancl__absorb]) ).

fof(f_3621_2,plain,
    ! [U_14264,U_14263] : c_Transitive__Closure_Otrancl(U_14263,c_Transitive__Closure_Ortrancl(U_14263,U_14264)) = c_Transitive__Closure_Ortrancl(U_14263,U_14264),
    inference(variable_rename,[status(thm)],[f_3621_1]) ).

cnf(f_3621_3,plain,
    c_Transitive__Closure_Otrancl(U_14263,c_Transitive__Closure_Ortrancl(U_14263,U_14264)) = c_Transitive__Closure_Ortrancl(U_14263,U_14264),
    inference(clausify,[status(thm)],[f_3621_2]) ).

fof(f_3622_1,plain,
    ! [V_R_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,c_Transitive__Closure_Otrancl(T_b,V_R_2)) = c_Transitive__Closure_Ortrancl(T_b,V_R_2),
    inference(fof_nnf,[status(thm)],[fact_trancl__rtrancl__absorb]) ).

fof(f_3622_2,plain,
    ! [U_14266,U_14265] : c_Transitive__Closure_Ortrancl(U_14265,c_Transitive__Closure_Otrancl(U_14265,U_14266)) = c_Transitive__Closure_Ortrancl(U_14265,U_14266),
    inference(variable_rename,[status(thm)],[f_3622_1]) ).

cnf(f_3622_3,plain,
    c_Transitive__Closure_Ortrancl(U_14265,c_Transitive__Closure_Otrancl(U_14265,U_14266)) = c_Transitive__Closure_Ortrancl(U_14265,U_14266),
    inference(clausify,[status(thm)],[f_3622_2]) ).

fof(f_3623_1,plain,
    ! [V_R_2,T_b] : hAPP(c_Relation_ODomain(T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_R_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Domain__rtrancl]) ).

fof(f_3623_2,plain,
    ! [U_14268,U_14267] : hAPP(c_Relation_ODomain(U_14267,U_14267),c_Transitive__Closure_Ortrancl(U_14267,U_14268)) = c_Orderings_Otop__class_Otop(tc_fun(U_14267,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3623_1]) ).

cnf(f_3623_3,plain,
    hAPP(c_Relation_ODomain(U_14267,U_14267),c_Transitive__Closure_Ortrancl(U_14267,U_14268)) = c_Orderings_Otop__class_Otop(tc_fun(U_14267,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3623_2]) ).

fof(f_3624_1,plain,
    ! [V_R_2,T_b] : hAPP(c_Relation_ORange(T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_R_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Range__rtrancl]) ).

fof(f_3624_2,plain,
    ! [U_14270,U_14269] : hAPP(c_Relation_ORange(U_14269,U_14269),c_Transitive__Closure_Ortrancl(U_14269,U_14270)) = c_Orderings_Otop__class_Otop(tc_fun(U_14269,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3624_1]) ).

cnf(f_3624_3,plain,
    hAPP(c_Relation_ORange(U_14269,U_14269),c_Transitive__Closure_Ortrancl(U_14269,U_14270)) = c_Orderings_Otop__class_Otop(tc_fun(U_14269,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3624_2]) ).

fof(f_3625_1,plain,
    ! [V_r_2,T_b] : c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),
    inference(fof_nnf,[status(thm)],[fact_refl__rtrancl]) ).

fof(f_3625_2,plain,
    ! [U_14272,U_14271] : c_Relation_Orefl__on(U_14271,c_Orderings_Otop__class_Otop(tc_fun(U_14271,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14271,U_14272)),
    inference(variable_rename,[status(thm)],[f_3625_1]) ).

cnf(f_3625_3,plain,
    c_Relation_Orefl__on(U_14271,c_Orderings_Otop__class_Otop(tc_fun(U_14271,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14271,U_14272)),
    inference(clausify,[status(thm)],[f_3625_2]) ).

fof(f_3626_1,plain,
    ! [V_r_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) = c_Transitive__Closure_Ortrancl(T_b,V_r_2),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__idemp]) ).

fof(f_3626_2,plain,
    ! [U_14274,U_14273] : c_Transitive__Closure_Ortrancl(U_14273,c_Transitive__Closure_Ortrancl(U_14273,U_14274)) = c_Transitive__Closure_Ortrancl(U_14273,U_14274),
    inference(variable_rename,[status(thm)],[f_3626_1]) ).

cnf(f_3626_3,plain,
    c_Transitive__Closure_Ortrancl(U_14273,c_Transitive__Closure_Ortrancl(U_14273,U_14274)) = c_Transitive__Closure_Ortrancl(U_14273,U_14274),
    inference(clausify,[status(thm)],[f_3626_2]) ).

fof(f_3627_1,plain,
    ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__trans]) ).

fof(f_3627_2,plain,
    ! [U_14279,U_14278,U_14277,U_14276,U_14275] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14275,U_14275)),hAPP(hAPP(c_Product__Type_OPair(U_14275,U_14275),U_14276),U_14279)),c_Transitive__Closure_Ortrancl(U_14275,U_14278)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14275,U_14275)),hAPP(hAPP(c_Product__Type_OPair(U_14275,U_14275),U_14277),U_14279)),c_Transitive__Closure_Ortrancl(U_14275,U_14278)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14275,U_14275)),hAPP(hAPP(c_Product__Type_OPair(U_14275,U_14275),U_14276),U_14277)),c_Transitive__Closure_Ortrancl(U_14275,U_14278))) ),
    inference(variable_rename,[status(thm)],[f_3627_1]) ).

cnf(f_3627_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14275,U_14275)),hAPP(hAPP(c_Product__Type_OPair(U_14275,U_14275),U_14276),U_14279)),c_Transitive__Closure_Ortrancl(U_14275,U_14278)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14275,U_14275)),hAPP(hAPP(c_Product__Type_OPair(U_14275,U_14275),U_14277),U_14279)),c_Transitive__Closure_Ortrancl(U_14275,U_14278)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14275,U_14275)),hAPP(hAPP(c_Product__Type_OPair(U_14275,U_14275),U_14276),U_14277)),c_Transitive__Closure_Ortrancl(U_14275,U_14278))) ),
    inference(clausify,[status(thm)],[f_3627_2]) ).

fof(f_3628_1,plain,
    ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),V_r_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_rtrancl_Ortrancl__into__rtrancl]) ).

fof(f_3628_2,plain,
    ! [U_14284,U_14283,U_14282,U_14281,U_14280] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14280,U_14280)),hAPP(hAPP(c_Product__Type_OPair(U_14280,U_14280),U_14281),U_14284)),c_Transitive__Closure_Ortrancl(U_14280,U_14283)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14280,U_14280)),hAPP(hAPP(c_Product__Type_OPair(U_14280,U_14280),U_14282),U_14284)),U_14283))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14280,U_14280)),hAPP(hAPP(c_Product__Type_OPair(U_14280,U_14280),U_14281),U_14282)),c_Transitive__Closure_Ortrancl(U_14280,U_14283))) ),
    inference(variable_rename,[status(thm)],[f_3628_1]) ).

cnf(f_3628_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14280,U_14280)),hAPP(hAPP(c_Product__Type_OPair(U_14280,U_14280),U_14281),U_14284)),c_Transitive__Closure_Ortrancl(U_14280,U_14283)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14280,U_14280)),hAPP(hAPP(c_Product__Type_OPair(U_14280,U_14280),U_14282),U_14284)),U_14283))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14280,U_14280)),hAPP(hAPP(c_Product__Type_OPair(U_14280,U_14280),U_14281),U_14282)),c_Transitive__Closure_Ortrancl(U_14280,U_14283))) ),
    inference(clausify,[status(thm)],[f_3628_2]) ).

fof(f_3629_1,plain,
    ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_converse__rtrancl__into__rtrancl]) ).

fof(f_3629_2,plain,
    ! [U_14289,U_14288,U_14287,U_14286,U_14285] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14285,U_14285)),hAPP(hAPP(c_Product__Type_OPair(U_14285,U_14285),U_14286),U_14289)),c_Transitive__Closure_Ortrancl(U_14285,U_14288)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14285,U_14285)),hAPP(hAPP(c_Product__Type_OPair(U_14285,U_14285),U_14287),U_14289)),c_Transitive__Closure_Ortrancl(U_14285,U_14288)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14285,U_14285)),hAPP(hAPP(c_Product__Type_OPair(U_14285,U_14285),U_14286),U_14287)),U_14288)) ),
    inference(variable_rename,[status(thm)],[f_3629_1]) ).

cnf(f_3629_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14285,U_14285)),hAPP(hAPP(c_Product__Type_OPair(U_14285,U_14285),U_14286),U_14289)),c_Transitive__Closure_Ortrancl(U_14285,U_14288)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14285,U_14285)),hAPP(hAPP(c_Product__Type_OPair(U_14285,U_14285),U_14287),U_14289)),c_Transitive__Closure_Ortrancl(U_14285,U_14288)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14285,U_14285)),hAPP(hAPP(c_Product__Type_OPair(U_14285,U_14285),U_14286),U_14287)),U_14288)) ),
    inference(clausify,[status(thm)],[f_3629_2]) ).

fof(f_3630_1,plain,
    ! [V_r_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))) = c_Transitive__Closure_Ortrancl(T_b,V_r_2),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__r__diff__Id]) ).

fof(f_3630_2,plain,
    ! [U_14291,U_14290] : c_Transitive__Closure_Ortrancl(U_14290,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_14290,U_14290),tc_HOL_Obool)),U_14291),c_Relation_OId(U_14290))) = c_Transitive__Closure_Ortrancl(U_14290,U_14291),
    inference(variable_rename,[status(thm)],[f_3630_1]) ).

cnf(f_3630_3,plain,
    c_Transitive__Closure_Ortrancl(U_14290,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_14290,U_14290),tc_HOL_Obool)),U_14291),c_Relation_OId(U_14290))) = c_Transitive__Closure_Ortrancl(U_14290,U_14291),
    inference(clausify,[status(thm)],[f_3630_2]) ).

fof(f_3631_1,plain,
    ! [V_S_2,V_R_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2))))
      | ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,V_S_2)))
        & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_in__rtrancl__UnI]) ).

fof(f_3631_2,plain,
    ! [U_14295,U_14294,U_14293,U_14292] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14292,U_14292)),U_14293),c_Transitive__Closure_Ortrancl(U_14292,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14292,U_14292),tc_HOL_Obool)),U_14294),U_14295))))
      | ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14292,U_14292)),U_14293),c_Transitive__Closure_Ortrancl(U_14292,U_14295)))
        & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14292,U_14292)),U_14293),c_Transitive__Closure_Ortrancl(U_14292,U_14294))) ) ),
    inference(variable_rename,[status(thm)],[f_3631_1]) ).

cnf(f_3631_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14292,U_14292)),U_14293),c_Transitive__Closure_Ortrancl(U_14292,U_14294)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14292,U_14292)),U_14293),c_Transitive__Closure_Ortrancl(U_14292,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14292,U_14292),tc_HOL_Obool)),U_14294),U_14295)))) ),
    inference(clausify,[status(thm)],[f_3631_2]) ).

cnf(f_3631_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14292,U_14292)),U_14293),c_Transitive__Closure_Ortrancl(U_14292,U_14295)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14292,U_14292)),U_14293),c_Transitive__Closure_Ortrancl(U_14292,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14292,U_14292),tc_HOL_Obool)),U_14294),U_14295)))) ),
    inference(clausify,[status(thm)],[f_3631_2]) ).

fof(f_3632_1,plain,
    ! [V_s_2,V_r_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),c_Transitive__Closure_Ortrancl(T_b,V_s_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__mono]) ).

fof(f_3632_2,plain,
    ! [U_14298,U_14297,U_14296] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14296,U_14296),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14296,U_14297)),c_Transitive__Closure_Ortrancl(U_14296,U_14298)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14296,U_14296),tc_HOL_Obool)),U_14297),U_14298)) ),
    inference(variable_rename,[status(thm)],[f_3632_1]) ).

cnf(f_3632_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14296,U_14296),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14296,U_14297)),c_Transitive__Closure_Ortrancl(U_14296,U_14298)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14296,U_14296),tc_HOL_Obool)),U_14297),U_14298)) ),
    inference(clausify,[status(thm)],[f_3632_2]) ).

fof(f_3633_1,plain,
    ! [V_S_2,V_R_2,T_b] :
      ( c_Transitive__Closure_Ortrancl(T_b,V_S_2) = c_Transitive__Closure_Ortrancl(T_b,V_R_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_S_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)) ),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__subset]) ).

fof(f_3633_2,plain,
    ! [U_14301,U_14300,U_14299] :
      ( c_Transitive__Closure_Ortrancl(U_14299,U_14301) = c_Transitive__Closure_Ortrancl(U_14299,U_14300)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14299,U_14299),tc_HOL_Obool)),U_14301),c_Transitive__Closure_Ortrancl(U_14299,U_14300)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14299,U_14299),tc_HOL_Obool)),U_14300),U_14301)) ),
    inference(variable_rename,[status(thm)],[f_3633_1]) ).

cnf(f_3633_3,plain,
    ( c_Transitive__Closure_Ortrancl(U_14299,U_14301) = c_Transitive__Closure_Ortrancl(U_14299,U_14300)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14299,U_14299),tc_HOL_Obool)),U_14301),c_Transitive__Closure_Ortrancl(U_14299,U_14300)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14299,U_14299),tc_HOL_Obool)),U_14300),U_14301)) ),
    inference(clausify,[status(thm)],[f_3633_2]) ).

fof(f_3634_1,plain,
    ! [V_s_2,V_r_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),c_Transitive__Closure_Ortrancl(T_b,V_s_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Transitive__Closure_Ortrancl(T_b,V_s_2))) ),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__subset__rtrancl]) ).

fof(f_3634_2,plain,
    ! [U_14304,U_14303,U_14302] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14302,U_14302),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14302,U_14303)),c_Transitive__Closure_Ortrancl(U_14302,U_14304)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14302,U_14302),tc_HOL_Obool)),U_14303),c_Transitive__Closure_Ortrancl(U_14302,U_14304))) ),
    inference(variable_rename,[status(thm)],[f_3634_1]) ).

cnf(f_3634_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14302,U_14302),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14302,U_14303)),c_Transitive__Closure_Ortrancl(U_14302,U_14304)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14302,U_14302),tc_HOL_Obool)),U_14303),c_Transitive__Closure_Ortrancl(U_14302,U_14304))) ),
    inference(clausify,[status(thm)],[f_3634_2]) ).

fof(f_3635_1,plain,
    ! [V_R_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)),c_Relation_OId(T_b)) = c_Transitive__Closure_Ortrancl(T_b,V_R_2),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__reflcl__absorb]) ).

fof(f_3635_2,plain,
    ! [U_14306,U_14305] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14305,U_14305),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14305,U_14306)),c_Relation_OId(U_14305)) = c_Transitive__Closure_Ortrancl(U_14305,U_14306),
    inference(variable_rename,[status(thm)],[f_3635_1]) ).

cnf(f_3635_3,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14305,U_14305),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14305,U_14306)),c_Relation_OId(U_14305)) = c_Transitive__Closure_Ortrancl(U_14305,U_14306),
    inference(clausify,[status(thm)],[f_3635_2]) ).

fof(f_3636_1,plain,
    ! [V_S_2,V_R_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)),c_Transitive__Closure_Ortrancl(T_b,V_S_2))) = c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__Un__rtrancl]) ).

fof(f_3636_2,plain,
    ! [U_14309,U_14308,U_14307] : c_Transitive__Closure_Ortrancl(U_14307,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14307,U_14307),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14307,U_14308)),c_Transitive__Closure_Ortrancl(U_14307,U_14309))) = c_Transitive__Closure_Ortrancl(U_14307,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14307,U_14307),tc_HOL_Obool)),U_14308),U_14309)),
    inference(variable_rename,[status(thm)],[f_3636_1]) ).

cnf(f_3636_3,plain,
    c_Transitive__Closure_Ortrancl(U_14307,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14307,U_14307),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14307,U_14308)),c_Transitive__Closure_Ortrancl(U_14307,U_14309))) = c_Transitive__Closure_Ortrancl(U_14307,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14307,U_14307),tc_HOL_Obool)),U_14308),U_14309)),
    inference(clausify,[status(thm)],[f_3636_2]) ).

fof(f_3637_1,plain,
    ! [V_R_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),c_Relation_OId(T_b))) = c_Transitive__Closure_Ortrancl(T_b,V_R_2),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__reflcl]) ).

fof(f_3637_2,plain,
    ! [U_14311,U_14310] : c_Transitive__Closure_Ortrancl(U_14310,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14310,U_14310),tc_HOL_Obool)),U_14311),c_Relation_OId(U_14310))) = c_Transitive__Closure_Ortrancl(U_14310,U_14311),
    inference(variable_rename,[status(thm)],[f_3637_1]) ).

cnf(f_3637_3,plain,
    c_Transitive__Closure_Ortrancl(U_14310,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14310,U_14310),tc_HOL_Obool)),U_14311),c_Relation_OId(U_14310))) = c_Transitive__Closure_Ortrancl(U_14310,U_14311),
    inference(clausify,[status(thm)],[f_3637_2]) ).

fof(f_3638_1,plain,
    ! [V_S_2,V_R_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)),c_Transitive__Closure_Ortrancl(T_b,V_S_2))),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)))),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__Un__subset]) ).

fof(f_3638_2,plain,
    ! [U_14314,U_14313,U_14312] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14312,U_14312),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14312,U_14312),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14312,U_14313)),c_Transitive__Closure_Ortrancl(U_14312,U_14314))),c_Transitive__Closure_Ortrancl(U_14312,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14312,U_14312),tc_HOL_Obool)),U_14313),U_14314)))),
    inference(variable_rename,[status(thm)],[f_3638_1]) ).

cnf(f_3638_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14312,U_14312),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14312,U_14312),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14312,U_14313)),c_Transitive__Closure_Ortrancl(U_14312,U_14314))),c_Transitive__Closure_Ortrancl(U_14312,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14312,U_14312),tc_HOL_Obool)),U_14313),U_14314)))),
    inference(clausify,[status(thm)],[f_3638_2]) ).

fof(f_3639_1,plain,
    ! [V_X_2,V_r_2,T_b] :
      ( hAPP(c_Relation_OImage(T_b,T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_X_2) = V_X_2
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),V_X_2)),V_X_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Image__closed__trancl]) ).

fof(f_3639_2,plain,
    ! [U_14317,U_14316,U_14315] :
      ( hAPP(c_Relation_OImage(U_14315,U_14315,c_Transitive__Closure_Ortrancl(U_14315,U_14316)),U_14317) = U_14317
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14315,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_14315,U_14315,U_14316),U_14317)),U_14317)) ),
    inference(variable_rename,[status(thm)],[f_3639_1]) ).

cnf(f_3639_3,plain,
    ( hAPP(c_Relation_OImage(U_14315,U_14315,c_Transitive__Closure_Ortrancl(U_14315,U_14316)),U_14317) = U_14317
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14315,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_14315,U_14315,U_14316),U_14317)),U_14317)) ),
    inference(clausify,[status(thm)],[f_3639_2]) ).

fof(f_3640_1,plain,
    ! [V_r_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Relation_OId(T_b)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_r_2)),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__unfold]) ).

fof(f_3640_2,plain,
    ! [U_14319,U_14318] : c_Transitive__Closure_Ortrancl(U_14318,U_14319) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14318,U_14318),tc_HOL_Obool)),c_Relation_OId(U_14318)),hAPP(hAPP(c_Relation_Orel__comp(U_14318,U_14318,U_14318),c_Transitive__Closure_Ortrancl(U_14318,U_14319)),U_14319)),
    inference(variable_rename,[status(thm)],[f_3640_1]) ).

cnf(f_3640_3,plain,
    c_Transitive__Closure_Ortrancl(U_14318,U_14319) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14318,U_14318),tc_HOL_Obool)),c_Relation_OId(U_14318)),hAPP(hAPP(c_Relation_Orel__comp(U_14318,U_14318,U_14318),c_Transitive__Closure_Ortrancl(U_14318,U_14319)),U_14319)),
    inference(clausify,[status(thm)],[f_3640_2]) ).

fof(f_3641_1,plain,
    ! [V_R_2,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_R_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)) = c_Transitive__Closure_Ortrancl(T_b,V_R_2),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__idemp__self__comp]) ).

fof(f_3641_2,plain,
    ! [U_14321,U_14320] : hAPP(hAPP(c_Relation_Orel__comp(U_14320,U_14320,U_14320),c_Transitive__Closure_Ortrancl(U_14320,U_14321)),c_Transitive__Closure_Ortrancl(U_14320,U_14321)) = c_Transitive__Closure_Ortrancl(U_14320,U_14321),
    inference(variable_rename,[status(thm)],[f_3641_1]) ).

cnf(f_3641_3,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_14320,U_14320,U_14320),c_Transitive__Closure_Ortrancl(U_14320,U_14321)),c_Transitive__Closure_Ortrancl(U_14320,U_14321)) = c_Transitive__Closure_Ortrancl(U_14320,U_14321),
    inference(clausify,[status(thm)],[f_3641_2]) ).

fof(f_3642_1,plain,
    ! [V_r_2,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_r_2),c_Transitive__Closure_Ortrancl(T_b,V_r_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_r_2),
    inference(fof_nnf,[status(thm)],[fact_r__comp__rtrancl__eq]) ).

fof(f_3642_2,plain,
    ! [U_14323,U_14322] : hAPP(hAPP(c_Relation_Orel__comp(U_14322,U_14322,U_14322),U_14323),c_Transitive__Closure_Ortrancl(U_14322,U_14323)) = hAPP(hAPP(c_Relation_Orel__comp(U_14322,U_14322,U_14322),c_Transitive__Closure_Ortrancl(U_14322,U_14323)),U_14323),
    inference(variable_rename,[status(thm)],[f_3642_1]) ).

cnf(f_3642_3,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_14322,U_14322,U_14322),U_14323),c_Transitive__Closure_Ortrancl(U_14322,U_14323)) = hAPP(hAPP(c_Relation_Orel__comp(U_14322,U_14322,U_14322),c_Transitive__Closure_Ortrancl(U_14322,U_14323)),U_14323),
    inference(clausify,[status(thm)],[f_3642_2]) ).

fof(f_3643_1,plain,
    ! [V_r_2,V_s_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_s_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_s_2)),V_r_2)),V_s_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Relation_OId(T_b)),V_s_2)) ),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__Int__subset]) ).

fof(f_3643_2,plain,
    ! [U_14326,U_14325,U_14324] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14324,U_14324),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14324,U_14326)),U_14325))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14324,U_14324),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_14324,U_14324,U_14324),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14324,U_14324),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14324,U_14326)),U_14325)),U_14326)),U_14325))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14324,U_14324),tc_HOL_Obool)),c_Relation_OId(U_14324)),U_14325)) ),
    inference(variable_rename,[status(thm)],[f_3643_1]) ).

cnf(f_3643_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14324,U_14324),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14324,U_14326)),U_14325))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14324,U_14324),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_14324,U_14324,U_14324),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14324,U_14324),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14324,U_14326)),U_14325)),U_14326)),U_14325))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14324,U_14324),tc_HOL_Obool)),c_Relation_OId(U_14324)),U_14325)) ),
    inference(clausify,[status(thm)],[f_3643_2]) ).

fof(f_3644_1,plain,
    ! [T_b] : c_Transitive__Closure_Ortrancl(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) = c_Relation_OId(T_b),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__empty]) ).

fof(f_3644_2,plain,
    ! [U_14327] : c_Transitive__Closure_Ortrancl(U_14327,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14327,U_14327),tc_HOL_Obool))) = c_Relation_OId(U_14327),
    inference(variable_rename,[status(thm)],[f_3644_1]) ).

cnf(f_3644_3,plain,
    c_Transitive__Closure_Ortrancl(U_14327,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14327,U_14327),tc_HOL_Obool))) = c_Relation_OId(U_14327),
    inference(clausify,[status(thm)],[f_3644_2]) ).

fof(f_3645_1,plain,
    ! [V_R_2,T_c,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_c),V_R_2),c_Relation_OId(T_c)) = V_R_2,
    inference(fof_nnf,[status(thm)],[fact_R__O__Id]) ).

fof(f_3645_2,plain,
    ! [U_14330,U_14329,U_14328] : hAPP(hAPP(c_Relation_Orel__comp(U_14328,U_14329,U_14329),U_14330),c_Relation_OId(U_14329)) = U_14330,
    inference(variable_rename,[status(thm)],[f_3645_1]) ).

cnf(f_3645_3,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_14328,U_14329,U_14329),U_14330),c_Relation_OId(U_14329)) = U_14330,
    inference(clausify,[status(thm)],[f_3645_2]) ).

fof(f_3646_1,plain,
    ! [V_R_2,T_c,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_c),c_Relation_OId(T_b)),V_R_2) = V_R_2,
    inference(fof_nnf,[status(thm)],[fact_Id__O__R]) ).

fof(f_3646_2,plain,
    ! [U_14333,U_14332,U_14331] : hAPP(hAPP(c_Relation_Orel__comp(U_14331,U_14331,U_14332),c_Relation_OId(U_14331)),U_14333) = U_14333,
    inference(variable_rename,[status(thm)],[f_3646_1]) ).

cnf(f_3646_3,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_14331,U_14331,U_14332),c_Relation_OId(U_14331)),U_14333) = U_14333,
    inference(clausify,[status(thm)],[f_3646_2]) ).

fof(f_3647_1,plain,
    ! [V_A_2,T_b] : hAPP(c_Relation_OImage(T_b,T_b,c_Relation_OId(T_b)),V_A_2) = V_A_2,
    inference(fof_nnf,[status(thm)],[fact_Image__Id]) ).

fof(f_3647_2,plain,
    ! [U_14335,U_14334] : hAPP(c_Relation_OImage(U_14334,U_14334,c_Relation_OId(U_14334)),U_14335) = U_14335,
    inference(variable_rename,[status(thm)],[f_3647_1]) ).

cnf(f_3647_3,plain,
    hAPP(c_Relation_OImage(U_14334,U_14334,c_Relation_OId(U_14334)),U_14335) = U_14335,
    inference(clausify,[status(thm)],[f_3647_2]) ).

fof(f_3648_1,plain,
    ! [V_b_2,V_a_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Relation_OId(T_b)))
        | V_a_2 != V_b_2 )
      & ( V_a_2 = V_b_2
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Relation_OId(T_b))) ) ),
    inference(fof_nnf,[status(thm)],[fact_pair__in__Id__conv]) ).

fof(f_3648_2,plain,
    ! [U_14338,U_14337,U_14336] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14336,U_14336)),hAPP(hAPP(c_Product__Type_OPair(U_14336,U_14336),U_14337),U_14338)),c_Relation_OId(U_14336)))
        | U_14337 != U_14338 )
      & ( U_14337 = U_14338
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14336,U_14336)),hAPP(hAPP(c_Product__Type_OPair(U_14336,U_14336),U_14337),U_14338)),c_Relation_OId(U_14336))) ) ),
    inference(variable_rename,[status(thm)],[f_3648_1]) ).

fof(f_3648_3,plain,
    ( ! [U_14344,U_14342] :
        ( ! [U_14340] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_14340,U_14340)),hAPP(hAPP(c_Product__Type_OPair(U_14340,U_14340),U_14342),U_14344)),c_Relation_OId(U_14340)))
        | U_14342 != U_14344 )
    & ! [U_14343,U_14341] :
        ( ! [U_14339] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14339,U_14339)),hAPP(hAPP(c_Product__Type_OPair(U_14339,U_14339),U_14341),U_14343)),c_Relation_OId(U_14339)))
        | U_14341 = U_14343 ) ),
    inference(miniscope,[status(thm)],[f_3648_2]) ).

cnf(f_3648_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14339,U_14339)),hAPP(hAPP(c_Product__Type_OPair(U_14339,U_14339),U_14341),U_14343)),c_Relation_OId(U_14339)))
    | U_14341 = U_14343 ),
    inference(clausify,[status(thm)],[f_3648_3]) ).

cnf(f_3648_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14340,U_14340)),hAPP(hAPP(c_Product__Type_OPair(U_14340,U_14340),U_14342),U_14344)),c_Relation_OId(U_14340)))
    | U_14342 != U_14344 ),
    inference(clausify,[status(thm)],[f_3648_3]) ).

fof(f_3649_1,plain,
    ! [V_z_2,V_r_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__trancl__trancl]) ).

fof(f_3649_2,plain,
    ! [U_14349,U_14348,U_14347,U_14346,U_14345] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14345,U_14345)),hAPP(hAPP(c_Product__Type_OPair(U_14345,U_14345),U_14346),U_14349)),c_Transitive__Closure_Otrancl(U_14345,U_14348)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14345,U_14345)),hAPP(hAPP(c_Product__Type_OPair(U_14345,U_14345),U_14347),U_14349)),c_Transitive__Closure_Otrancl(U_14345,U_14348)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14345,U_14345)),hAPP(hAPP(c_Product__Type_OPair(U_14345,U_14345),U_14346),U_14347)),c_Transitive__Closure_Ortrancl(U_14345,U_14348))) ),
    inference(variable_rename,[status(thm)],[f_3649_1]) ).

cnf(f_3649_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14345,U_14345)),hAPP(hAPP(c_Product__Type_OPair(U_14345,U_14345),U_14346),U_14349)),c_Transitive__Closure_Otrancl(U_14345,U_14348)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14345,U_14345)),hAPP(hAPP(c_Product__Type_OPair(U_14345,U_14345),U_14347),U_14349)),c_Transitive__Closure_Otrancl(U_14345,U_14348)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14345,U_14345)),hAPP(hAPP(c_Product__Type_OPair(U_14345,U_14345),U_14346),U_14347)),c_Transitive__Closure_Ortrancl(U_14345,U_14348))) ),
    inference(clausify,[status(thm)],[f_3649_2]) ).

fof(f_3650_1,plain,
    ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_trancl__rtrancl__trancl]) ).

fof(f_3650_2,plain,
    ! [U_14354,U_14353,U_14352,U_14351,U_14350] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14350,U_14350)),hAPP(hAPP(c_Product__Type_OPair(U_14350,U_14350),U_14351),U_14354)),c_Transitive__Closure_Otrancl(U_14350,U_14353)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14350,U_14350)),hAPP(hAPP(c_Product__Type_OPair(U_14350,U_14350),U_14352),U_14354)),c_Transitive__Closure_Ortrancl(U_14350,U_14353)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14350,U_14350)),hAPP(hAPP(c_Product__Type_OPair(U_14350,U_14350),U_14351),U_14352)),c_Transitive__Closure_Otrancl(U_14350,U_14353))) ),
    inference(variable_rename,[status(thm)],[f_3650_1]) ).

cnf(f_3650_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14350,U_14350)),hAPP(hAPP(c_Product__Type_OPair(U_14350,U_14350),U_14351),U_14354)),c_Transitive__Closure_Otrancl(U_14350,U_14353)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14350,U_14350)),hAPP(hAPP(c_Product__Type_OPair(U_14350,U_14350),U_14352),U_14354)),c_Transitive__Closure_Ortrancl(U_14350,U_14353)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14350,U_14350)),hAPP(hAPP(c_Product__Type_OPair(U_14350,U_14350),U_14351),U_14352)),c_Transitive__Closure_Otrancl(U_14350,U_14353))) ),
    inference(clausify,[status(thm)],[f_3650_2]) ).

fof(f_3651_1,plain,
    ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),V_r_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__into__trancl1]) ).

fof(f_3651_2,plain,
    ! [U_14359,U_14358,U_14357,U_14356,U_14355] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14355,U_14355)),hAPP(hAPP(c_Product__Type_OPair(U_14355,U_14355),U_14356),U_14359)),c_Transitive__Closure_Otrancl(U_14355,U_14358)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14355,U_14355)),hAPP(hAPP(c_Product__Type_OPair(U_14355,U_14355),U_14357),U_14359)),U_14358))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14355,U_14355)),hAPP(hAPP(c_Product__Type_OPair(U_14355,U_14355),U_14356),U_14357)),c_Transitive__Closure_Ortrancl(U_14355,U_14358))) ),
    inference(variable_rename,[status(thm)],[f_3651_1]) ).

cnf(f_3651_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14355,U_14355)),hAPP(hAPP(c_Product__Type_OPair(U_14355,U_14355),U_14356),U_14359)),c_Transitive__Closure_Otrancl(U_14355,U_14358)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14355,U_14355)),hAPP(hAPP(c_Product__Type_OPair(U_14355,U_14355),U_14357),U_14359)),U_14358))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14355,U_14355)),hAPP(hAPP(c_Product__Type_OPair(U_14355,U_14355),U_14356),U_14357)),c_Transitive__Closure_Ortrancl(U_14355,U_14358))) ),
    inference(clausify,[status(thm)],[f_3651_2]) ).

fof(f_3652_1,plain,
    ! [V_R_2,V_b_2,V_a_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2)))
        & V_a_2 != V_b_2 )
      | V_a_2 = V_b_2
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) ),
    inference(fof_nnf,[status(thm)],[fact_rtranclD]) ).

fof(f_3652_2,plain,
    ! [U_14363,U_14362,U_14361,U_14360] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14360,U_14360)),hAPP(hAPP(c_Product__Type_OPair(U_14360,U_14360),U_14361),U_14362)),c_Transitive__Closure_Otrancl(U_14360,U_14363)))
        & U_14361 != U_14362 )
      | U_14361 = U_14362
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14360,U_14360)),hAPP(hAPP(c_Product__Type_OPair(U_14360,U_14360),U_14361),U_14362)),c_Transitive__Closure_Ortrancl(U_14360,U_14363))) ),
    inference(variable_rename,[status(thm)],[f_3652_1]) ).

cnf(f_3652_3,plain,
    ( U_14361 != U_14362
    | U_14361 = U_14362
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14360,U_14360)),hAPP(hAPP(c_Product__Type_OPair(U_14360,U_14360),U_14361),U_14362)),c_Transitive__Closure_Ortrancl(U_14360,U_14363))) ),
    inference(clausify,[status(thm)],[f_3652_2]) ).

cnf(f_3652_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14360,U_14360)),hAPP(hAPP(c_Product__Type_OPair(U_14360,U_14360),U_14361),U_14362)),c_Transitive__Closure_Otrancl(U_14360,U_14363)))
    | U_14361 = U_14362
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14360,U_14360)),hAPP(hAPP(c_Product__Type_OPair(U_14360,U_14360),U_14361),U_14362)),c_Transitive__Closure_Ortrancl(U_14360,U_14363))) ),
    inference(clausify,[status(thm)],[f_3652_2]) ).

fof(f_3653_1,plain,
    ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__into__trancl2]) ).

fof(f_3653_2,plain,
    ! [U_14368,U_14367,U_14366,U_14365,U_14364] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14364,U_14364)),hAPP(hAPP(c_Product__Type_OPair(U_14364,U_14364),U_14365),U_14368)),c_Transitive__Closure_Otrancl(U_14364,U_14367)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14364,U_14364)),hAPP(hAPP(c_Product__Type_OPair(U_14364,U_14364),U_14366),U_14368)),c_Transitive__Closure_Ortrancl(U_14364,U_14367)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14364,U_14364)),hAPP(hAPP(c_Product__Type_OPair(U_14364,U_14364),U_14365),U_14366)),U_14367)) ),
    inference(variable_rename,[status(thm)],[f_3653_1]) ).

cnf(f_3653_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14364,U_14364)),hAPP(hAPP(c_Product__Type_OPair(U_14364,U_14364),U_14365),U_14368)),c_Transitive__Closure_Otrancl(U_14364,U_14367)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14364,U_14364)),hAPP(hAPP(c_Product__Type_OPair(U_14364,U_14364),U_14366),U_14368)),c_Transitive__Closure_Ortrancl(U_14364,U_14367)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14364,U_14364)),hAPP(hAPP(c_Product__Type_OPair(U_14364,U_14364),U_14365),U_14366)),U_14367)) ),
    inference(clausify,[status(thm)],[f_3653_2]) ).

fof(f_3654_1,plain,
    ! [V_R_2,V_y_2,V_x_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2)))
            | V_x_2 = V_y_2 )
          & V_x_2 != V_y_2 ) )
      & ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2)))
          & V_x_2 != V_y_2 )
        | V_x_2 = V_y_2
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__eq__or__trancl]) ).

fof(f_3654_2,plain,
    ! [U_14372,U_14371,U_14370,U_14369] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14369,U_14369)),hAPP(hAPP(c_Product__Type_OPair(U_14369,U_14369),U_14370),U_14371)),c_Transitive__Closure_Ortrancl(U_14369,U_14372)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14369,U_14369)),hAPP(hAPP(c_Product__Type_OPair(U_14369,U_14369),U_14370),U_14371)),c_Transitive__Closure_Otrancl(U_14369,U_14372)))
            | U_14370 = U_14371 )
          & U_14370 != U_14371 ) )
      & ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14369,U_14369)),hAPP(hAPP(c_Product__Type_OPair(U_14369,U_14369),U_14370),U_14371)),c_Transitive__Closure_Otrancl(U_14369,U_14372)))
          & U_14370 != U_14371 )
        | U_14370 = U_14371
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14369,U_14369)),hAPP(hAPP(c_Product__Type_OPair(U_14369,U_14369),U_14370),U_14371)),c_Transitive__Closure_Ortrancl(U_14369,U_14372))) ) ),
    inference(variable_rename,[status(thm)],[f_3654_1]) ).

fof(f_3654_3,plain,
    ( ! [U_14380,U_14378,U_14376,U_14374] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14374,U_14374)),hAPP(hAPP(c_Product__Type_OPair(U_14374,U_14374),U_14376),U_14378)),c_Transitive__Closure_Ortrancl(U_14374,U_14380)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14374,U_14374)),hAPP(hAPP(c_Product__Type_OPair(U_14374,U_14374),U_14376),U_14378)),c_Transitive__Closure_Otrancl(U_14374,U_14380)))
            | U_14376 = U_14378 )
          & U_14376 != U_14378 ) )
    & ! [U_14379,U_14377,U_14375,U_14373] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14373,U_14373)),hAPP(hAPP(c_Product__Type_OPair(U_14373,U_14373),U_14375),U_14377)),c_Transitive__Closure_Otrancl(U_14373,U_14379)))
          & U_14375 != U_14377 )
        | U_14375 = U_14377
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14373,U_14373)),hAPP(hAPP(c_Product__Type_OPair(U_14373,U_14373),U_14375),U_14377)),c_Transitive__Closure_Ortrancl(U_14373,U_14379))) ) ),
    inference(miniscope,[status(thm)],[f_3654_2]) ).

cnf(f_3654_4,plain,
    ( U_14375 != U_14377
    | U_14375 = U_14377
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14373,U_14373)),hAPP(hAPP(c_Product__Type_OPair(U_14373,U_14373),U_14375),U_14377)),c_Transitive__Closure_Ortrancl(U_14373,U_14379))) ),
    inference(clausify,[status(thm)],[f_3654_3]) ).

cnf(f_3654_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14373,U_14373)),hAPP(hAPP(c_Product__Type_OPair(U_14373,U_14373),U_14375),U_14377)),c_Transitive__Closure_Otrancl(U_14373,U_14379)))
    | U_14375 = U_14377
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14373,U_14373)),hAPP(hAPP(c_Product__Type_OPair(U_14373,U_14373),U_14375),U_14377)),c_Transitive__Closure_Ortrancl(U_14373,U_14379))) ),
    inference(clausify,[status(thm)],[f_3654_3]) ).

cnf(f_3654_6,plain,
    ( U_14376 != U_14378
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14374,U_14374)),hAPP(hAPP(c_Product__Type_OPair(U_14374,U_14374),U_14376),U_14378)),c_Transitive__Closure_Ortrancl(U_14374,U_14380))) ),
    inference(clausify,[status(thm)],[f_3654_3]) ).

cnf(f_3654_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14374,U_14374)),hAPP(hAPP(c_Product__Type_OPair(U_14374,U_14374),U_14376),U_14378)),c_Transitive__Closure_Otrancl(U_14374,U_14380)))
    | U_14376 = U_14378
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14374,U_14374)),hAPP(hAPP(c_Product__Type_OPair(U_14374,U_14374),U_14376),U_14378)),c_Transitive__Closure_Ortrancl(U_14374,U_14380))) ),
    inference(clausify,[status(thm)],[f_3654_3]) ).

fof(f_3655_1,plain,
    ! [T_b] : hAPP(c_Relation_ODomain(T_b,T_b),c_Relation_OId(T_b)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Domain__Id]) ).

fof(f_3655_2,plain,
    ! [U_14381] : hAPP(c_Relation_ODomain(U_14381,U_14381),c_Relation_OId(U_14381)) = c_Orderings_Otop__class_Otop(tc_fun(U_14381,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3655_1]) ).

cnf(f_3655_3,plain,
    hAPP(c_Relation_ODomain(U_14381,U_14381),c_Relation_OId(U_14381)) = c_Orderings_Otop__class_Otop(tc_fun(U_14381,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3655_2]) ).

fof(f_3656_1,plain,
    ! [T_b] : hAPP(c_Relation_ORange(T_b,T_b),c_Relation_OId(T_b)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_Range__Id]) ).

fof(f_3656_2,plain,
    ! [U_14382] : hAPP(c_Relation_ORange(U_14382,U_14382),c_Relation_OId(U_14382)) = c_Orderings_Otop__class_Otop(tc_fun(U_14382,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3656_1]) ).

cnf(f_3656_3,plain,
    hAPP(c_Relation_ORange(U_14382,U_14382),c_Relation_OId(U_14382)) = c_Orderings_Otop__class_Otop(tc_fun(U_14382,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3656_2]) ).

fof(f_3657_1,plain,
    ! [T_b] : c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Relation_OId(T_b)),
    inference(fof_nnf,[status(thm)],[fact_refl__Id]) ).

fof(f_3657_2,plain,
    ! [U_14383] : c_Relation_Orefl__on(U_14383,c_Orderings_Otop__class_Otop(tc_fun(U_14383,tc_HOL_Obool)),c_Relation_OId(U_14383)),
    inference(variable_rename,[status(thm)],[f_3657_1]) ).

cnf(f_3657_3,plain,
    c_Relation_Orefl__on(U_14383,c_Orderings_Otop__class_Otop(tc_fun(U_14383,tc_HOL_Obool)),c_Relation_OId(U_14383)),
    inference(clausify,[status(thm)],[f_3657_2]) ).

fof(f_3658_1,plain,
    c_FunDef_Opair__leq = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_HOL_Obool)),c_FunDef_Opair__less),c_Relation_OId(tc_prod(tc_Nat_Onat,tc_Nat_Onat))),
    inference(fof_nnf,[status(thm)],[fact_pair__leq__def]) ).

cnf(f_3658_2,plain,
    c_FunDef_Opair__leq = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_HOL_Obool)),c_FunDef_Opair__less),c_Relation_OId(tc_prod(tc_Nat_Onat,tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_3658_1]) ).

fof(f_3659_1,plain,
    ! [V_y_2,V_R_2,V_x_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
          | V_x_2 != V_y_2 )
        & ( V_x_2 = V_y_2
          | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) ) )
      | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_b),V_R_2))) ),
    inference(fof_nnf,[status(thm)],[fact_Not__Domain__rtrancl]) ).

fof(f_3659_2,plain,
    ! [U_14387,U_14386,U_14385,U_14384] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14384,U_14384)),hAPP(hAPP(c_Product__Type_OPair(U_14384,U_14384),U_14385),U_14387)),c_Transitive__Closure_Ortrancl(U_14384,U_14386)))
          | U_14385 != U_14387 )
        & ( U_14385 = U_14387
          | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14384,U_14384)),hAPP(hAPP(c_Product__Type_OPair(U_14384,U_14384),U_14385),U_14387)),c_Transitive__Closure_Ortrancl(U_14384,U_14386))) ) )
      | hBOOL(hAPP(hAPP(c_member(U_14384),U_14385),hAPP(c_Relation_ODomain(U_14384,U_14384),U_14386))) ),
    inference(variable_rename,[status(thm)],[f_3659_1]) ).

cnf(f_3659_3,plain,
    ( U_14385 = U_14387
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14384,U_14384)),hAPP(hAPP(c_Product__Type_OPair(U_14384,U_14384),U_14385),U_14387)),c_Transitive__Closure_Ortrancl(U_14384,U_14386)))
    | hBOOL(hAPP(hAPP(c_member(U_14384),U_14385),hAPP(c_Relation_ODomain(U_14384,U_14384),U_14386))) ),
    inference(clausify,[status(thm)],[f_3659_2]) ).

cnf(f_3659_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14384,U_14384)),hAPP(hAPP(c_Product__Type_OPair(U_14384,U_14384),U_14385),U_14387)),c_Transitive__Closure_Ortrancl(U_14384,U_14386)))
    | U_14385 != U_14387
    | hBOOL(hAPP(hAPP(c_member(U_14384),U_14385),hAPP(c_Relation_ODomain(U_14384,U_14384),U_14386))) ),
    inference(clausify,[status(thm)],[f_3659_2]) ).

fof(f_3660_1,plain,
    ! [V_b_2,V_r_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_acc__downwards]) ).

fof(f_3660_2,plain,
    ! [U_14391,U_14390,U_14389,U_14388] :
      ( hBOOL(hAPP(hAPP(c_member(U_14388),U_14391),c_Wellfounded_Oacc(U_14388,U_14390)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14388,U_14388)),hAPP(hAPP(c_Product__Type_OPair(U_14388,U_14388),U_14391),U_14389)),c_Transitive__Closure_Ortrancl(U_14388,U_14390)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_14388),U_14389),c_Wellfounded_Oacc(U_14388,U_14390))) ),
    inference(variable_rename,[status(thm)],[f_3660_1]) ).

cnf(f_3660_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14388),U_14391),c_Wellfounded_Oacc(U_14388,U_14390)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14388,U_14388)),hAPP(hAPP(c_Product__Type_OPair(U_14388,U_14388),U_14391),U_14389)),c_Transitive__Closure_Ortrancl(U_14388,U_14390)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14388),U_14389),c_Wellfounded_Oacc(U_14388,U_14390))) ),
    inference(clausify,[status(thm)],[f_3660_2]) ).

fof(f_3661_1,plain,
    ! [V_r_2,V_a_2,V_b_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_acc__downwards__aux]) ).

fof(f_3661_2,plain,
    ! [U_14395,U_14394,U_14393,U_14392] :
      ( hBOOL(hAPP(hAPP(c_member(U_14392),U_14393),c_Wellfounded_Oacc(U_14392,U_14395)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_14392),U_14394),c_Wellfounded_Oacc(U_14392,U_14395)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14392,U_14392)),hAPP(hAPP(c_Product__Type_OPair(U_14392,U_14392),U_14393),U_14394)),c_Transitive__Closure_Ortrancl(U_14392,U_14395))) ),
    inference(variable_rename,[status(thm)],[f_3661_1]) ).

cnf(f_3661_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14392),U_14393),c_Wellfounded_Oacc(U_14392,U_14395)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14392),U_14394),c_Wellfounded_Oacc(U_14392,U_14395)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14392,U_14392)),hAPP(hAPP(c_Product__Type_OPair(U_14392,U_14392),U_14393),U_14394)),c_Transitive__Closure_Ortrancl(U_14392,U_14395))) ),
    inference(clausify,[status(thm)],[f_3661_2]) ).

fof(f_3662_1,plain,
    ! [V_r_2,V_x_2,V_y_2,T_b] :
      ( ( c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),V_r_2))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
        | ~ c_Wellfounded_Owf(T_b,V_r_2) )
      & ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
          & c_Wellfounded_Owf(T_b,V_r_2) )
        | ~ c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),V_r_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_wf__insert]) ).

fof(f_3662_2,plain,
    ! [U_14399,U_14398,U_14397,U_14396] :
      ( ( c_Wellfounded_Owf(U_14396,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14396,U_14396)),hAPP(hAPP(c_Product__Type_OPair(U_14396,U_14396),U_14397),U_14398)),U_14399))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14396,U_14396)),hAPP(hAPP(c_Product__Type_OPair(U_14396,U_14396),U_14398),U_14397)),c_Transitive__Closure_Ortrancl(U_14396,U_14399)))
        | ~ c_Wellfounded_Owf(U_14396,U_14399) )
      & ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14396,U_14396)),hAPP(hAPP(c_Product__Type_OPair(U_14396,U_14396),U_14398),U_14397)),c_Transitive__Closure_Ortrancl(U_14396,U_14399)))
          & c_Wellfounded_Owf(U_14396,U_14399) )
        | ~ c_Wellfounded_Owf(U_14396,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14396,U_14396)),hAPP(hAPP(c_Product__Type_OPair(U_14396,U_14396),U_14397),U_14398)),U_14399)) ) ),
    inference(variable_rename,[status(thm)],[f_3662_1]) ).

fof(f_3662_3,plain,
    ( ! [U_14407,U_14405,U_14403,U_14401] :
        ( c_Wellfounded_Owf(U_14401,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14401,U_14401)),hAPP(hAPP(c_Product__Type_OPair(U_14401,U_14401),U_14403),U_14405)),U_14407))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14401,U_14401)),hAPP(hAPP(c_Product__Type_OPair(U_14401,U_14401),U_14405),U_14403)),c_Transitive__Closure_Ortrancl(U_14401,U_14407)))
        | ~ c_Wellfounded_Owf(U_14401,U_14407) )
    & ! [U_14406,U_14404,U_14402,U_14400] :
        ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14400,U_14400)),hAPP(hAPP(c_Product__Type_OPair(U_14400,U_14400),U_14404),U_14402)),c_Transitive__Closure_Ortrancl(U_14400,U_14406)))
          & c_Wellfounded_Owf(U_14400,U_14406) )
        | ~ c_Wellfounded_Owf(U_14400,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14400,U_14400)),hAPP(hAPP(c_Product__Type_OPair(U_14400,U_14400),U_14402),U_14404)),U_14406)) ) ),
    inference(miniscope,[status(thm)],[f_3662_2]) ).

cnf(f_3662_4,plain,
    ( c_Wellfounded_Owf(U_14400,U_14406)
    | ~ c_Wellfounded_Owf(U_14400,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14400,U_14400)),hAPP(hAPP(c_Product__Type_OPair(U_14400,U_14400),U_14402),U_14404)),U_14406)) ),
    inference(clausify,[status(thm)],[f_3662_3]) ).

cnf(f_3662_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14400,U_14400)),hAPP(hAPP(c_Product__Type_OPair(U_14400,U_14400),U_14404),U_14402)),c_Transitive__Closure_Ortrancl(U_14400,U_14406)))
    | ~ c_Wellfounded_Owf(U_14400,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14400,U_14400)),hAPP(hAPP(c_Product__Type_OPair(U_14400,U_14400),U_14402),U_14404)),U_14406)) ),
    inference(clausify,[status(thm)],[f_3662_3]) ).

cnf(f_3662_6,plain,
    ( c_Wellfounded_Owf(U_14401,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14401,U_14401)),hAPP(hAPP(c_Product__Type_OPair(U_14401,U_14401),U_14403),U_14405)),U_14407))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14401,U_14401)),hAPP(hAPP(c_Product__Type_OPair(U_14401,U_14401),U_14405),U_14403)),c_Transitive__Closure_Ortrancl(U_14401,U_14407)))
    | ~ c_Wellfounded_Owf(U_14401,U_14407) ),
    inference(clausify,[status(thm)],[f_3662_3]) ).

fof(f_3663_1,plain,
    ! [V_r_2,V_x_2,V_y_2,T_b] :
      ( ( c_Wellfounded_Oacyclic(T_b,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),V_r_2))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
        | ~ c_Wellfounded_Oacyclic(T_b,V_r_2) )
      & ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
          & c_Wellfounded_Oacyclic(T_b,V_r_2) )
        | ~ c_Wellfounded_Oacyclic(T_b,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),V_r_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_acyclic__insert]) ).

fof(f_3663_2,plain,
    ! [U_14411,U_14410,U_14409,U_14408] :
      ( ( c_Wellfounded_Oacyclic(U_14408,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14408,U_14408)),hAPP(hAPP(c_Product__Type_OPair(U_14408,U_14408),U_14409),U_14410)),U_14411))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14408,U_14408)),hAPP(hAPP(c_Product__Type_OPair(U_14408,U_14408),U_14410),U_14409)),c_Transitive__Closure_Ortrancl(U_14408,U_14411)))
        | ~ c_Wellfounded_Oacyclic(U_14408,U_14411) )
      & ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14408,U_14408)),hAPP(hAPP(c_Product__Type_OPair(U_14408,U_14408),U_14410),U_14409)),c_Transitive__Closure_Ortrancl(U_14408,U_14411)))
          & c_Wellfounded_Oacyclic(U_14408,U_14411) )
        | ~ c_Wellfounded_Oacyclic(U_14408,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14408,U_14408)),hAPP(hAPP(c_Product__Type_OPair(U_14408,U_14408),U_14409),U_14410)),U_14411)) ) ),
    inference(variable_rename,[status(thm)],[f_3663_1]) ).

fof(f_3663_3,plain,
    ( ! [U_14419,U_14417,U_14415,U_14413] :
        ( c_Wellfounded_Oacyclic(U_14413,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14413,U_14413)),hAPP(hAPP(c_Product__Type_OPair(U_14413,U_14413),U_14415),U_14417)),U_14419))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14413,U_14413)),hAPP(hAPP(c_Product__Type_OPair(U_14413,U_14413),U_14417),U_14415)),c_Transitive__Closure_Ortrancl(U_14413,U_14419)))
        | ~ c_Wellfounded_Oacyclic(U_14413,U_14419) )
    & ! [U_14418,U_14416,U_14414,U_14412] :
        ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14412,U_14412)),hAPP(hAPP(c_Product__Type_OPair(U_14412,U_14412),U_14416),U_14414)),c_Transitive__Closure_Ortrancl(U_14412,U_14418)))
          & c_Wellfounded_Oacyclic(U_14412,U_14418) )
        | ~ c_Wellfounded_Oacyclic(U_14412,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14412,U_14412)),hAPP(hAPP(c_Product__Type_OPair(U_14412,U_14412),U_14414),U_14416)),U_14418)) ) ),
    inference(miniscope,[status(thm)],[f_3663_2]) ).

cnf(f_3663_4,plain,
    ( c_Wellfounded_Oacyclic(U_14412,U_14418)
    | ~ c_Wellfounded_Oacyclic(U_14412,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14412,U_14412)),hAPP(hAPP(c_Product__Type_OPair(U_14412,U_14412),U_14414),U_14416)),U_14418)) ),
    inference(clausify,[status(thm)],[f_3663_3]) ).

cnf(f_3663_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14412,U_14412)),hAPP(hAPP(c_Product__Type_OPair(U_14412,U_14412),U_14416),U_14414)),c_Transitive__Closure_Ortrancl(U_14412,U_14418)))
    | ~ c_Wellfounded_Oacyclic(U_14412,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14412,U_14412)),hAPP(hAPP(c_Product__Type_OPair(U_14412,U_14412),U_14414),U_14416)),U_14418)) ),
    inference(clausify,[status(thm)],[f_3663_3]) ).

cnf(f_3663_6,plain,
    ( c_Wellfounded_Oacyclic(U_14413,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14413,U_14413)),hAPP(hAPP(c_Product__Type_OPair(U_14413,U_14413),U_14415),U_14417)),U_14419))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14413,U_14413)),hAPP(hAPP(c_Product__Type_OPair(U_14413,U_14413),U_14417),U_14415)),c_Transitive__Closure_Ortrancl(U_14413,U_14419)))
    | ~ c_Wellfounded_Oacyclic(U_14413,U_14419) ),
    inference(clausify,[status(thm)],[f_3663_3]) ).

fof(f_3664_1,plain,
    ! [V_r_2,T_b] : c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))),
    inference(fof_nnf,[status(thm)],[fact_refl__reflcl]) ).

fof(f_3664_2,plain,
    ! [U_14421,U_14420] : c_Relation_Orefl__on(U_14420,c_Orderings_Otop__class_Otop(tc_fun(U_14420,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14420,U_14420),tc_HOL_Obool)),U_14421),c_Relation_OId(U_14420))),
    inference(variable_rename,[status(thm)],[f_3664_1]) ).

cnf(f_3664_3,plain,
    c_Relation_Orefl__on(U_14420,c_Orderings_Otop__class_Otop(tc_fun(U_14420,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14420,U_14420),tc_HOL_Obool)),U_14421),c_Relation_OId(U_14420))),
    inference(clausify,[status(thm)],[f_3664_2]) ).

fof(f_3665_1,plain,
    ! [T_b] : c_Relation_OId(T_b) = hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_prod(T_b,T_b)),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(tc_prod(T_b,T_b),tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_HOL_Obool)),tc_prod(T_b,T_b)),c_COMBB(tc_prod(T_b,T_b),tc_HOL_Obool,T_b)),c_fequal)),hAPP(hAPP(c_COMBS(T_b,T_b,tc_prod(T_b,T_b)),c_Product__Type_OPair(T_b,T_b)),c_COMBI(T_b))))),
    inference(fof_nnf,[status(thm)],[fact_Id__def]) ).

fof(f_3665_2,plain,
    ! [U_14422] : c_Relation_OId(U_14422) = hAPP(c_Set_OCollect(tc_prod(U_14422,U_14422)),hAPP(hAPP(c_COMBB(tc_fun(U_14422,tc_HOL_Obool),tc_HOL_Obool,tc_prod(U_14422,U_14422)),c_HOL_OEx(U_14422)),hAPP(hAPP(c_COMBC(tc_prod(U_14422,U_14422),tc_fun(U_14422,tc_prod(U_14422,U_14422)),tc_fun(U_14422,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_14422,U_14422),tc_HOL_Obool),tc_fun(tc_fun(U_14422,tc_prod(U_14422,U_14422)),tc_fun(U_14422,tc_HOL_Obool)),tc_prod(U_14422,U_14422)),c_COMBB(tc_prod(U_14422,U_14422),tc_HOL_Obool,U_14422)),c_fequal)),hAPP(hAPP(c_COMBS(U_14422,U_14422,tc_prod(U_14422,U_14422)),c_Product__Type_OPair(U_14422,U_14422)),c_COMBI(U_14422))))),
    inference(variable_rename,[status(thm)],[f_3665_1]) ).

cnf(f_3665_3,plain,
    c_Relation_OId(U_14422) = hAPP(c_Set_OCollect(tc_prod(U_14422,U_14422)),hAPP(hAPP(c_COMBB(tc_fun(U_14422,tc_HOL_Obool),tc_HOL_Obool,tc_prod(U_14422,U_14422)),c_HOL_OEx(U_14422)),hAPP(hAPP(c_COMBC(tc_prod(U_14422,U_14422),tc_fun(U_14422,tc_prod(U_14422,U_14422)),tc_fun(U_14422,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_14422,U_14422),tc_HOL_Obool),tc_fun(tc_fun(U_14422,tc_prod(U_14422,U_14422)),tc_fun(U_14422,tc_HOL_Obool)),tc_prod(U_14422,U_14422)),c_COMBB(tc_prod(U_14422,U_14422),tc_HOL_Obool,U_14422)),c_fequal)),hAPP(hAPP(c_COMBS(U_14422,U_14422,tc_prod(U_14422,U_14422)),c_Product__Type_OPair(U_14422,U_14422)),c_COMBI(U_14422))))),
    inference(clausify,[status(thm)],[f_3665_2]) ).

fof(f_3666_1,plain,
    ! [V_r_2,T_b] : c_Relation_Oirrefl(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))),
    inference(fof_nnf,[status(thm)],[fact_irrefl__diff__Id]) ).

fof(f_3666_2,plain,
    ! [U_14424,U_14423] : c_Relation_Oirrefl(U_14423,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_14423,U_14423),tc_HOL_Obool)),U_14424),c_Relation_OId(U_14423))),
    inference(variable_rename,[status(thm)],[f_3666_1]) ).

cnf(f_3666_3,plain,
    c_Relation_Oirrefl(U_14423,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_14423,U_14423),tc_HOL_Obool)),U_14424),c_Relation_OId(U_14423))),
    inference(clausify,[status(thm)],[f_3666_2]) ).

fof(f_3667_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_m_2),V_n_2)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_m_2),V_n_2)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ) ),
    inference(fof_nnf,[status(thm)],[fact_pred__nat__trancl__eq__le]) ).

fof(f_3667_2,plain,
    ! [U_14426,U_14425] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_14425),U_14426)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_14425),U_14426)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_14425),U_14426))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_14425),U_14426)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ) ),
    inference(variable_rename,[status(thm)],[f_3667_1]) ).

fof(f_3667_3,plain,
    ( ! [U_14430,U_14428] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_14428),U_14430)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_14428),U_14430)) )
    & ! [U_14429,U_14427] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_14427),U_14429))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_14427),U_14429)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ) ),
    inference(miniscope,[status(thm)],[f_3667_2]) ).

cnf(f_3667_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_14427),U_14429))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_14427),U_14429)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ),
    inference(clausify,[status(thm)],[f_3667_3]) ).

cnf(f_3667_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_14428),U_14430)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_14428),U_14430)) ),
    inference(clausify,[status(thm)],[f_3667_3]) ).

fof(f_3668_1,plain,
    ! [V_A_2,V_r_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | V_a_2 = V_b_2
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_trancl__subset__Sigma__aux]) ).

fof(f_3668_2,plain,
    ! [U_14435,U_14434,U_14433,U_14432,U_14431] :
      ( hBOOL(hAPP(hAPP(c_member(U_14431),U_14432),U_14435))
      | U_14432 = U_14433
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14431,U_14431),tc_HOL_Obool)),U_14434),hAPP(hAPP(c_Product__Type_OSigma(U_14431,U_14431),U_14435),hAPP(c_COMBK(tc_fun(U_14431,tc_HOL_Obool),U_14431),U_14435))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14431,U_14431)),hAPP(hAPP(c_Product__Type_OPair(U_14431,U_14431),U_14432),U_14433)),c_Transitive__Closure_Ortrancl(U_14431,U_14434))) ),
    inference(variable_rename,[status(thm)],[f_3668_1]) ).

cnf(f_3668_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14431),U_14432),U_14435))
    | U_14432 = U_14433
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14431,U_14431),tc_HOL_Obool)),U_14434),hAPP(hAPP(c_Product__Type_OSigma(U_14431,U_14431),U_14435),hAPP(c_COMBK(tc_fun(U_14431,tc_HOL_Obool),U_14431),U_14435))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14431,U_14431)),hAPP(hAPP(c_Product__Type_OPair(U_14431,U_14431),U_14432),U_14433)),c_Transitive__Closure_Ortrancl(U_14431,U_14434))) ),
    inference(clausify,[status(thm)],[f_3668_2]) ).

fof(f_3669_1,plain,
    ! [V_x_2,V_r_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_x_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) ),
    inference(fof_nnf,[status(thm)],[fact_irrefl__tranclI]) ).

fof(f_3669_2,plain,
    ! [U_14438,U_14437,U_14436] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14436,U_14436)),hAPP(hAPP(c_Product__Type_OPair(U_14436,U_14436),U_14438),U_14438)),c_Transitive__Closure_Otrancl(U_14436,U_14437)))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14436,U_14436),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(U_14436,U_14436),U_14437)),c_Transitive__Closure_Ortrancl(U_14436,U_14437)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14436,U_14436),tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_3669_1]) ).

cnf(f_3669_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14436,U_14436)),hAPP(hAPP(c_Product__Type_OPair(U_14436,U_14436),U_14438),U_14438)),c_Transitive__Closure_Otrancl(U_14436,U_14437)))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14436,U_14436),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(U_14436,U_14436),U_14437)),c_Transitive__Closure_Ortrancl(U_14436,U_14437)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14436,U_14436),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3669_2]) ).

fof(f_3670_1,plain,
    ! [V_k_2,V_i_2,V_r_2,V_f_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2))),hAPP(V_f_2,V_i_2))),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
      | ? [B_i] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_i))),hAPP(V_f_2,B_i))),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_sequence__trans]) ).

fof(f_3670_2,plain,
    ! [U_14444,U_14443,U_14442,U_14441,U_14440] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14440,U_14440)),hAPP(hAPP(c_Product__Type_OPair(U_14440,U_14440),hAPP(U_14441,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_14443),U_14444))),hAPP(U_14441,U_14443))),c_Transitive__Closure_Ortrancl(U_14440,U_14442)))
      | ? [U_14439] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14440,U_14440)),hAPP(hAPP(c_Product__Type_OPair(U_14440,U_14440),hAPP(U_14441,hAPP(c_Nat_OSuc,U_14439))),hAPP(U_14441,U_14439))),c_Transitive__Closure_Ortrancl(U_14440,U_14442))) ),
    inference(variable_rename,[status(thm)],[f_3670_1]) ).

fof(f_3670_3,plain,
    ! [U_14444,U_14443,U_14442,U_14441,U_14440] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14440,U_14440)),hAPP(hAPP(c_Product__Type_OPair(U_14440,U_14440),hAPP(U_14441,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_14443),U_14444))),hAPP(U_14441,U_14443))),c_Transitive__Closure_Ortrancl(U_14440,U_14442)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14440,U_14440)),hAPP(hAPP(c_Product__Type_OPair(U_14440,U_14440),hAPP(U_14441,hAPP(c_Nat_OSuc,sK365(U_14444,U_14443,U_14442,U_14441,U_14440)))),hAPP(U_14441,sK365(U_14444,U_14443,U_14442,U_14441,U_14440)))),c_Transitive__Closure_Ortrancl(U_14440,U_14442))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK365]),skolemize(U_14439,sK365(U_14444,U_14443,U_14442,U_14441,U_14440))],[f_3670_2]) ).

cnf(f_3670_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14440,U_14440)),hAPP(hAPP(c_Product__Type_OPair(U_14440,U_14440),hAPP(U_14441,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_14443),U_14444))),hAPP(U_14441,U_14443))),c_Transitive__Closure_Ortrancl(U_14440,U_14442)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14440,U_14440)),hAPP(hAPP(c_Product__Type_OPair(U_14440,U_14440),hAPP(U_14441,hAPP(c_Nat_OSuc,sK365(U_14444,U_14443,U_14442,U_14441,U_14440)))),hAPP(U_14441,sK365(U_14444,U_14443,U_14442,U_14441,U_14440)))),c_Transitive__Closure_Ortrancl(U_14440,U_14442))) ),
    inference(clausify,[status(thm)],[f_3670_3]) ).

fof(f_3671_1,plain,
    ! [V_r_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) = hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__converse]) ).

fof(f_3671_2,plain,
    ! [U_14446,U_14445] : c_Transitive__Closure_Ortrancl(U_14445,hAPP(c_Relation_Oconverse(U_14445,U_14445),U_14446)) = hAPP(c_Relation_Oconverse(U_14445,U_14445),c_Transitive__Closure_Ortrancl(U_14445,U_14446)),
    inference(variable_rename,[status(thm)],[f_3671_1]) ).

cnf(f_3671_3,plain,
    c_Transitive__Closure_Ortrancl(U_14445,hAPP(c_Relation_Oconverse(U_14445,U_14445),U_14446)) = hAPP(c_Relation_Oconverse(U_14445,U_14445),c_Transitive__Closure_Ortrancl(U_14445,U_14446)),
    inference(clausify,[status(thm)],[f_3671_2]) ).

fof(f_3672_1,plain,
    ! [T_b] : hAPP(c_Relation_Oconverse(T_b,T_b),c_Relation_OId(T_b)) = c_Relation_OId(T_b),
    inference(fof_nnf,[status(thm)],[fact_converse__Id]) ).

fof(f_3672_2,plain,
    ! [U_14447] : hAPP(c_Relation_Oconverse(U_14447,U_14447),c_Relation_OId(U_14447)) = c_Relation_OId(U_14447),
    inference(variable_rename,[status(thm)],[f_3672_1]) ).

cnf(f_3672_3,plain,
    hAPP(c_Relation_Oconverse(U_14447,U_14447),c_Relation_OId(U_14447)) = c_Relation_OId(U_14447),
    inference(clausify,[status(thm)],[f_3672_2]) ).

fof(f_3673_1,plain,
    ! [V_r_2,T_b] :
      ( ( c_Wellfounded_Oacyclic(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
        | ~ c_Wellfounded_Oacyclic(T_b,V_r_2) )
      & ( c_Wellfounded_Oacyclic(T_b,V_r_2)
        | ~ c_Wellfounded_Oacyclic(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_acyclic__converse]) ).

fof(f_3673_2,plain,
    ! [U_14449,U_14448] :
      ( ( c_Wellfounded_Oacyclic(U_14448,hAPP(c_Relation_Oconverse(U_14448,U_14448),U_14449))
        | ~ c_Wellfounded_Oacyclic(U_14448,U_14449) )
      & ( c_Wellfounded_Oacyclic(U_14448,U_14449)
        | ~ c_Wellfounded_Oacyclic(U_14448,hAPP(c_Relation_Oconverse(U_14448,U_14448),U_14449)) ) ),
    inference(variable_rename,[status(thm)],[f_3673_1]) ).

fof(f_3673_3,plain,
    ( ! [U_14453,U_14451] :
        ( c_Wellfounded_Oacyclic(U_14451,hAPP(c_Relation_Oconverse(U_14451,U_14451),U_14453))
        | ~ c_Wellfounded_Oacyclic(U_14451,U_14453) )
    & ! [U_14452,U_14450] :
        ( c_Wellfounded_Oacyclic(U_14450,U_14452)
        | ~ c_Wellfounded_Oacyclic(U_14450,hAPP(c_Relation_Oconverse(U_14450,U_14450),U_14452)) ) ),
    inference(miniscope,[status(thm)],[f_3673_2]) ).

cnf(f_3673_4,plain,
    ( c_Wellfounded_Oacyclic(U_14450,U_14452)
    | ~ c_Wellfounded_Oacyclic(U_14450,hAPP(c_Relation_Oconverse(U_14450,U_14450),U_14452)) ),
    inference(clausify,[status(thm)],[f_3673_3]) ).

cnf(f_3673_5,plain,
    ( c_Wellfounded_Oacyclic(U_14451,hAPP(c_Relation_Oconverse(U_14451,U_14451),U_14453))
    | ~ c_Wellfounded_Oacyclic(U_14451,U_14453) ),
    inference(clausify,[status(thm)],[f_3673_3]) ).

fof(f_3674_1,plain,
    ! [V_r_2,V_A_2,T_b] :
      ( ( c_Relation_Orefl__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
        | ~ c_Relation_Orefl__on(T_b,V_A_2,V_r_2) )
      & ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
        | ~ c_Relation_Orefl__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_refl__on__converse]) ).

fof(f_3674_2,plain,
    ! [U_14456,U_14455,U_14454] :
      ( ( c_Relation_Orefl__on(U_14454,U_14455,hAPP(c_Relation_Oconverse(U_14454,U_14454),U_14456))
        | ~ c_Relation_Orefl__on(U_14454,U_14455,U_14456) )
      & ( c_Relation_Orefl__on(U_14454,U_14455,U_14456)
        | ~ c_Relation_Orefl__on(U_14454,U_14455,hAPP(c_Relation_Oconverse(U_14454,U_14454),U_14456)) ) ),
    inference(variable_rename,[status(thm)],[f_3674_1]) ).

fof(f_3674_3,plain,
    ( ! [U_14462,U_14460,U_14458] :
        ( c_Relation_Orefl__on(U_14458,U_14460,hAPP(c_Relation_Oconverse(U_14458,U_14458),U_14462))
        | ~ c_Relation_Orefl__on(U_14458,U_14460,U_14462) )
    & ! [U_14461,U_14459,U_14457] :
        ( c_Relation_Orefl__on(U_14457,U_14459,U_14461)
        | ~ c_Relation_Orefl__on(U_14457,U_14459,hAPP(c_Relation_Oconverse(U_14457,U_14457),U_14461)) ) ),
    inference(miniscope,[status(thm)],[f_3674_2]) ).

cnf(f_3674_4,plain,
    ( c_Relation_Orefl__on(U_14457,U_14459,U_14461)
    | ~ c_Relation_Orefl__on(U_14457,U_14459,hAPP(c_Relation_Oconverse(U_14457,U_14457),U_14461)) ),
    inference(clausify,[status(thm)],[f_3674_3]) ).

cnf(f_3674_5,plain,
    ( c_Relation_Orefl__on(U_14458,U_14460,hAPP(c_Relation_Oconverse(U_14458,U_14458),U_14462))
    | ~ c_Relation_Orefl__on(U_14458,U_14460,U_14462) ),
    inference(clausify,[status(thm)],[f_3674_3]) ).

fof(f_3675_1,plain,
    ! [V_A_2,T_b] : hAPP(c_Relation_Oconverse(T_b,T_b),c_Relation_OId__on(T_b,V_A_2)) = c_Relation_OId__on(T_b,V_A_2),
    inference(fof_nnf,[status(thm)],[fact_converse__Id__on]) ).

fof(f_3675_2,plain,
    ! [U_14464,U_14463] : hAPP(c_Relation_Oconverse(U_14463,U_14463),c_Relation_OId__on(U_14463,U_14464)) = c_Relation_OId__on(U_14463,U_14464),
    inference(variable_rename,[status(thm)],[f_3675_1]) ).

cnf(f_3675_3,plain,
    hAPP(c_Relation_Oconverse(U_14463,U_14463),c_Relation_OId__on(U_14463,U_14464)) = c_Relation_OId__on(U_14463,U_14464),
    inference(clausify,[status(thm)],[f_3675_2]) ).

fof(f_3676_1,plain,
    ! [V_f_2,V_R_2,T_c,T_b] : hAPP(c_Relation_Oconverse(T_b,T_b),hAPP(hAPP(c_Relation_Oinv__image(T_c,T_b),V_R_2),V_f_2)) = hAPP(hAPP(c_Relation_Oinv__image(T_c,T_b),hAPP(c_Relation_Oconverse(T_c,T_c),V_R_2)),V_f_2),
    inference(fof_nnf,[status(thm)],[fact_converse__inv__image]) ).

fof(f_3676_2,plain,
    ! [U_14468,U_14467,U_14466,U_14465] : hAPP(c_Relation_Oconverse(U_14465,U_14465),hAPP(hAPP(c_Relation_Oinv__image(U_14466,U_14465),U_14467),U_14468)) = hAPP(hAPP(c_Relation_Oinv__image(U_14466,U_14465),hAPP(c_Relation_Oconverse(U_14466,U_14466),U_14467)),U_14468),
    inference(variable_rename,[status(thm)],[f_3676_1]) ).

cnf(f_3676_3,plain,
    hAPP(c_Relation_Oconverse(U_14465,U_14465),hAPP(hAPP(c_Relation_Oinv__image(U_14466,U_14465),U_14467),U_14468)) = hAPP(hAPP(c_Relation_Oinv__image(U_14466,U_14465),hAPP(c_Relation_Oconverse(U_14466,U_14466),U_14467)),U_14468),
    inference(clausify,[status(thm)],[f_3676_2]) ).

fof(f_3677_1,plain,
    ! [V_r_2,T_c,T_b] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_c,T_b)),V_r_2)) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_c,T_b)),V_r_2))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_finite__converse]) ).

fof(f_3677_2,plain,
    ! [U_14471,U_14470,U_14469] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14469,U_14470)),hAPP(c_Relation_Oconverse(U_14470,U_14469),U_14471)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14470,U_14469)),U_14471)) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14470,U_14469)),U_14471))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14469,U_14470)),hAPP(c_Relation_Oconverse(U_14470,U_14469),U_14471))) ) ),
    inference(variable_rename,[status(thm)],[f_3677_1]) ).

fof(f_3677_3,plain,
    ( ! [U_14477,U_14475,U_14473] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14473,U_14475)),hAPP(c_Relation_Oconverse(U_14475,U_14473),U_14477)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14475,U_14473)),U_14477)) )
    & ! [U_14476,U_14474,U_14472] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14474,U_14472)),U_14476))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14472,U_14474)),hAPP(c_Relation_Oconverse(U_14474,U_14472),U_14476))) ) ),
    inference(miniscope,[status(thm)],[f_3677_2]) ).

cnf(f_3677_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14474,U_14472)),U_14476))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14472,U_14474)),hAPP(c_Relation_Oconverse(U_14474,U_14472),U_14476))) ),
    inference(clausify,[status(thm)],[f_3677_3]) ).

cnf(f_3677_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14473,U_14475)),hAPP(c_Relation_Oconverse(U_14475,U_14473),U_14477)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14475,U_14473)),U_14477)) ),
    inference(clausify,[status(thm)],[f_3677_3]) ).

fof(f_3678_1,plain,
    ! [V_s_2,V_r_2,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_s_2)),
    inference(fof_nnf,[status(thm)],[fact_converse__Int]) ).

fof(f_3678_2,plain,
    ! [U_14481,U_14480,U_14479,U_14478] : hAPP(c_Relation_Oconverse(U_14478,U_14479),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14478,U_14479),tc_HOL_Obool)),U_14480),U_14481)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14479,U_14478),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(U_14478,U_14479),U_14480)),hAPP(c_Relation_Oconverse(U_14478,U_14479),U_14481)),
    inference(variable_rename,[status(thm)],[f_3678_1]) ).

cnf(f_3678_3,plain,
    hAPP(c_Relation_Oconverse(U_14478,U_14479),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14478,U_14479),tc_HOL_Obool)),U_14480),U_14481)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14479,U_14478),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(U_14478,U_14479),U_14480)),hAPP(c_Relation_Oconverse(U_14478,U_14479),U_14481)),
    inference(clausify,[status(thm)],[f_3678_2]) ).

fof(f_3679_1,plain,
    ! [V_r_2,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2)) = V_r_2,
    inference(fof_nnf,[status(thm)],[fact_converse__converse]) ).

fof(f_3679_2,plain,
    ! [U_14484,U_14483,U_14482] : hAPP(c_Relation_Oconverse(U_14482,U_14483),hAPP(c_Relation_Oconverse(U_14483,U_14482),U_14484)) = U_14484,
    inference(variable_rename,[status(thm)],[f_3679_1]) ).

cnf(f_3679_3,plain,
    hAPP(c_Relation_Oconverse(U_14482,U_14483),hAPP(c_Relation_Oconverse(U_14483,U_14482),U_14484)) = U_14484,
    inference(clausify,[status(thm)],[f_3679_2]) ).

fof(f_3680_1,plain,
    ! [V_r_2,T_b] : hAPP(c_Relation_OField(T_b),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) = hAPP(c_Relation_OField(T_b),V_r_2),
    inference(fof_nnf,[status(thm)],[fact_Field__converse]) ).

fof(f_3680_2,plain,
    ! [U_14486,U_14485] : hAPP(c_Relation_OField(U_14485),hAPP(c_Relation_Oconverse(U_14485,U_14485),U_14486)) = hAPP(c_Relation_OField(U_14485),U_14486),
    inference(variable_rename,[status(thm)],[f_3680_1]) ).

cnf(f_3680_3,plain,
    hAPP(c_Relation_OField(U_14485),hAPP(c_Relation_Oconverse(U_14485,U_14485),U_14486)) = hAPP(c_Relation_OField(U_14485),U_14486),
    inference(clausify,[status(thm)],[f_3680_2]) ).

fof(f_3681_1,plain,
    ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_b_2),V_a_2)),V_r_2)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_b_2),V_a_2)),V_r_2))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_converse__iff]) ).

fof(f_3681_2,plain,
    ! [U_14491,U_14490,U_14489,U_14488,U_14487] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14487,U_14488)),hAPP(hAPP(c_Product__Type_OPair(U_14487,U_14488),U_14489),U_14490)),hAPP(c_Relation_Oconverse(U_14488,U_14487),U_14491)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14488,U_14487)),hAPP(hAPP(c_Product__Type_OPair(U_14488,U_14487),U_14490),U_14489)),U_14491)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14488,U_14487)),hAPP(hAPP(c_Product__Type_OPair(U_14488,U_14487),U_14490),U_14489)),U_14491))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14487,U_14488)),hAPP(hAPP(c_Product__Type_OPair(U_14487,U_14488),U_14489),U_14490)),hAPP(c_Relation_Oconverse(U_14488,U_14487),U_14491))) ) ),
    inference(variable_rename,[status(thm)],[f_3681_1]) ).

fof(f_3681_3,plain,
    ( ! [U_14501,U_14499,U_14497,U_14495,U_14493] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14493,U_14495)),hAPP(hAPP(c_Product__Type_OPair(U_14493,U_14495),U_14497),U_14499)),hAPP(c_Relation_Oconverse(U_14495,U_14493),U_14501)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14495,U_14493)),hAPP(hAPP(c_Product__Type_OPair(U_14495,U_14493),U_14499),U_14497)),U_14501)) )
    & ! [U_14500,U_14498,U_14496,U_14494,U_14492] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14494,U_14492)),hAPP(hAPP(c_Product__Type_OPair(U_14494,U_14492),U_14498),U_14496)),U_14500))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14492,U_14494)),hAPP(hAPP(c_Product__Type_OPair(U_14492,U_14494),U_14496),U_14498)),hAPP(c_Relation_Oconverse(U_14494,U_14492),U_14500))) ) ),
    inference(miniscope,[status(thm)],[f_3681_2]) ).

cnf(f_3681_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14494,U_14492)),hAPP(hAPP(c_Product__Type_OPair(U_14494,U_14492),U_14498),U_14496)),U_14500))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14492,U_14494)),hAPP(hAPP(c_Product__Type_OPair(U_14492,U_14494),U_14496),U_14498)),hAPP(c_Relation_Oconverse(U_14494,U_14492),U_14500))) ),
    inference(clausify,[status(thm)],[f_3681_3]) ).

cnf(f_3681_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14493,U_14495)),hAPP(hAPP(c_Product__Type_OPair(U_14493,U_14495),U_14497),U_14499)),hAPP(c_Relation_Oconverse(U_14495,U_14493),U_14501)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14495,U_14493)),hAPP(hAPP(c_Product__Type_OPair(U_14495,U_14493),U_14499),U_14497)),U_14501)) ),
    inference(clausify,[status(thm)],[f_3681_3]) ).

fof(f_3682_1,plain,
    ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_b_2),V_a_2)),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_converseI]) ).

fof(f_3682_2,plain,
    ! [U_14506,U_14505,U_14504,U_14503,U_14502] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14503,U_14502)),hAPP(hAPP(c_Product__Type_OPair(U_14503,U_14502),U_14505),U_14504)),hAPP(c_Relation_Oconverse(U_14502,U_14503),U_14506)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14502,U_14503)),hAPP(hAPP(c_Product__Type_OPair(U_14502,U_14503),U_14504),U_14505)),U_14506)) ),
    inference(variable_rename,[status(thm)],[f_3682_1]) ).

cnf(f_3682_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14503,U_14502)),hAPP(hAPP(c_Product__Type_OPair(U_14503,U_14502),U_14505),U_14504)),hAPP(c_Relation_Oconverse(U_14502,U_14503),U_14506)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14502,U_14503)),hAPP(hAPP(c_Product__Type_OPair(U_14502,U_14503),U_14504),U_14505)),U_14506)) ),
    inference(clausify,[status(thm)],[f_3682_2]) ).

fof(f_3683_1,plain,
    ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_b_2),V_a_2)),V_r_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_converseD]) ).

fof(f_3683_2,plain,
    ! [U_14511,U_14510,U_14509,U_14508,U_14507] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14508,U_14507)),hAPP(hAPP(c_Product__Type_OPair(U_14508,U_14507),U_14510),U_14509)),U_14511))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14507,U_14508)),hAPP(hAPP(c_Product__Type_OPair(U_14507,U_14508),U_14509),U_14510)),hAPP(c_Relation_Oconverse(U_14508,U_14507),U_14511))) ),
    inference(variable_rename,[status(thm)],[f_3683_1]) ).

cnf(f_3683_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14508,U_14507)),hAPP(hAPP(c_Product__Type_OPair(U_14508,U_14507),U_14510),U_14509)),U_14511))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14507,U_14508)),hAPP(hAPP(c_Product__Type_OPair(U_14507,U_14508),U_14509),U_14510)),hAPP(c_Relation_Oconverse(U_14508,U_14507),U_14511))) ),
    inference(clausify,[status(thm)],[f_3683_2]) ).

fof(f_3684_1,plain,
    ! [V_s_2,V_r_2,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_s_2)),
    inference(fof_nnf,[status(thm)],[fact_converse__Un]) ).

fof(f_3684_2,plain,
    ! [U_14515,U_14514,U_14513,U_14512] : hAPP(c_Relation_Oconverse(U_14512,U_14513),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14512,U_14513),tc_HOL_Obool)),U_14514),U_14515)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14513,U_14512),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(U_14512,U_14513),U_14514)),hAPP(c_Relation_Oconverse(U_14512,U_14513),U_14515)),
    inference(variable_rename,[status(thm)],[f_3684_1]) ).

cnf(f_3684_3,plain,
    hAPP(c_Relation_Oconverse(U_14512,U_14513),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14512,U_14513),tc_HOL_Obool)),U_14514),U_14515)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14513,U_14512),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(U_14512,U_14513),U_14514)),hAPP(c_Relation_Oconverse(U_14512,U_14513),U_14515)),
    inference(clausify,[status(thm)],[f_3684_2]) ).

fof(f_3685_1,plain,
    ! [V_s_2,V_r_2,T_d,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Relation_Orel__comp(T_c,T_d,T_b),V_r_2),V_s_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),hAPP(c_Relation_Oconverse(T_d,T_b),V_s_2)),hAPP(c_Relation_Oconverse(T_c,T_d),V_r_2)),
    inference(fof_nnf,[status(thm)],[fact_converse__rel__comp]) ).

fof(f_3685_2,plain,
    ! [U_14520,U_14519,U_14518,U_14517,U_14516] : hAPP(c_Relation_Oconverse(U_14516,U_14517),hAPP(hAPP(c_Relation_Orel__comp(U_14516,U_14518,U_14517),U_14519),U_14520)) = hAPP(hAPP(c_Relation_Orel__comp(U_14517,U_14518,U_14516),hAPP(c_Relation_Oconverse(U_14518,U_14517),U_14520)),hAPP(c_Relation_Oconverse(U_14516,U_14518),U_14519)),
    inference(variable_rename,[status(thm)],[f_3685_1]) ).

cnf(f_3685_3,plain,
    hAPP(c_Relation_Oconverse(U_14516,U_14517),hAPP(hAPP(c_Relation_Orel__comp(U_14516,U_14518,U_14517),U_14519),U_14520)) = hAPP(hAPP(c_Relation_Orel__comp(U_14517,U_14518,U_14516),hAPP(c_Relation_Oconverse(U_14518,U_14517),U_14520)),hAPP(c_Relation_Oconverse(U_14516,U_14518),U_14519)),
    inference(clausify,[status(thm)],[f_3685_2]) ).

fof(f_3686_1,plain,
    ! [V_r_2,V_S_2,T_d,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_S_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_S_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),T_d),c_Relation_Oconverse(T_c,T_b)),V_r_2)),
    inference(fof_nnf,[status(thm)],[fact_converse__UNION]) ).

fof(f_3686_2,plain,
    ! [U_14525,U_14524,U_14523,U_14522,U_14521] : hAPP(c_Relation_Oconverse(U_14521,U_14522),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14523,tc_fun(tc_prod(U_14521,U_14522),tc_HOL_Obool)),U_14524),U_14525)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14523,tc_fun(tc_prod(U_14522,U_14521),tc_HOL_Obool)),U_14524),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_14521,U_14522),tc_HOL_Obool),tc_fun(tc_prod(U_14522,U_14521),tc_HOL_Obool),U_14523),c_Relation_Oconverse(U_14521,U_14522)),U_14525)),
    inference(variable_rename,[status(thm)],[f_3686_1]) ).

cnf(f_3686_3,plain,
    hAPP(c_Relation_Oconverse(U_14521,U_14522),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14523,tc_fun(tc_prod(U_14521,U_14522),tc_HOL_Obool)),U_14524),U_14525)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14523,tc_fun(tc_prod(U_14522,U_14521),tc_HOL_Obool)),U_14524),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_14521,U_14522),tc_HOL_Obool),tc_fun(tc_prod(U_14522,U_14521),tc_HOL_Obool),U_14523),c_Relation_Oconverse(U_14521,U_14522)),U_14525)),
    inference(clausify,[status(thm)],[f_3686_2]) ).

fof(f_3687_1,plain,
    ! [V_r_2,V_S_2,T_d,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_S_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_S_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),T_d),c_Relation_Oconverse(T_c,T_b)),V_r_2)),
    inference(fof_nnf,[status(thm)],[fact_converse__INTER]) ).

fof(f_3687_2,plain,
    ! [U_14530,U_14529,U_14528,U_14527,U_14526] : hAPP(c_Relation_Oconverse(U_14526,U_14527),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_14528,tc_fun(tc_prod(U_14526,U_14527),tc_HOL_Obool)),U_14529),U_14530)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_14528,tc_fun(tc_prod(U_14527,U_14526),tc_HOL_Obool)),U_14529),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_14526,U_14527),tc_HOL_Obool),tc_fun(tc_prod(U_14527,U_14526),tc_HOL_Obool),U_14528),c_Relation_Oconverse(U_14526,U_14527)),U_14530)),
    inference(variable_rename,[status(thm)],[f_3687_1]) ).

cnf(f_3687_3,plain,
    hAPP(c_Relation_Oconverse(U_14526,U_14527),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_14528,tc_fun(tc_prod(U_14526,U_14527),tc_HOL_Obool)),U_14529),U_14530)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_14528,tc_fun(tc_prod(U_14527,U_14526),tc_HOL_Obool)),U_14529),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_14526,U_14527),tc_HOL_Obool),tc_fun(tc_prod(U_14527,U_14526),tc_HOL_Obool),U_14528),c_Relation_Oconverse(U_14526,U_14527)),U_14530)),
    inference(clausify,[status(thm)],[f_3687_2]) ).

fof(f_3688_1,plain,
    ! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) = hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)),
    inference(fof_nnf,[status(thm)],[fact_trancl__converse]) ).

fof(f_3688_2,plain,
    ! [U_14532,U_14531] : c_Transitive__Closure_Otrancl(U_14531,hAPP(c_Relation_Oconverse(U_14531,U_14531),U_14532)) = hAPP(c_Relation_Oconverse(U_14531,U_14531),c_Transitive__Closure_Otrancl(U_14531,U_14532)),
    inference(variable_rename,[status(thm)],[f_3688_1]) ).

cnf(f_3688_3,plain,
    c_Transitive__Closure_Otrancl(U_14531,hAPP(c_Relation_Oconverse(U_14531,U_14531),U_14532)) = hAPP(c_Relation_Oconverse(U_14531,U_14531),c_Transitive__Closure_Otrancl(U_14531,U_14532)),
    inference(clausify,[status(thm)],[f_3688_2]) ).

fof(f_3689_1,plain,
    ! [V_r_2,T_b] :
      ( c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
      | ~ c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_wf__converse__trancl]) ).

fof(f_3689_2,plain,
    ! [U_14534,U_14533] :
      ( c_Wellfounded_Owf(U_14533,hAPP(c_Relation_Oconverse(U_14533,U_14533),c_Transitive__Closure_Otrancl(U_14533,U_14534)))
      | ~ c_Wellfounded_Owf(U_14533,hAPP(c_Relation_Oconverse(U_14533,U_14533),U_14534)) ),
    inference(variable_rename,[status(thm)],[f_3689_1]) ).

cnf(f_3689_3,plain,
    ( c_Wellfounded_Owf(U_14533,hAPP(c_Relation_Oconverse(U_14533,U_14533),c_Transitive__Closure_Otrancl(U_14533,U_14534)))
    | ~ c_Wellfounded_Owf(U_14533,hAPP(c_Relation_Oconverse(U_14533,U_14533),U_14534)) ),
    inference(clausify,[status(thm)],[f_3689_2]) ).

fof(f_3690_1,plain,
    ! [V_r_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),V_r_2) = V_r_2
      | ~ c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_equiv__comp__eq]) ).

fof(f_3690_2,plain,
    ! [U_14537,U_14536,U_14535] :
      ( hAPP(hAPP(c_Relation_Orel__comp(U_14535,U_14535,U_14535),hAPP(c_Relation_Oconverse(U_14535,U_14535),U_14537)),U_14537) = U_14537
      | ~ c_Equiv__Relations_Oequiv(U_14535,U_14536,U_14537) ),
    inference(variable_rename,[status(thm)],[f_3690_1]) ).

cnf(f_3690_3,plain,
    ( hAPP(hAPP(c_Relation_Orel__comp(U_14535,U_14535,U_14535),hAPP(c_Relation_Oconverse(U_14535,U_14535),U_14537)),U_14537) = U_14537
    | ~ c_Equiv__Relations_Oequiv(U_14535,U_14536,U_14537) ),
    inference(clausify,[status(thm)],[f_3690_2]) ).

fof(f_3691_1,plain,
    ! [V_r_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),V_r_2) = hAPP(c_Relation_ODomain(T_b,T_c),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)),
    inference(fof_nnf,[status(thm)],[fact_Range__def]) ).

fof(f_3691_2,plain,
    ! [U_14540,U_14539,U_14538] : hAPP(c_Relation_ORange(U_14538,U_14539),U_14540) = hAPP(c_Relation_ODomain(U_14539,U_14538),hAPP(c_Relation_Oconverse(U_14538,U_14539),U_14540)),
    inference(variable_rename,[status(thm)],[f_3691_1]) ).

cnf(f_3691_3,plain,
    hAPP(c_Relation_ORange(U_14538,U_14539),U_14540) = hAPP(c_Relation_ODomain(U_14539,U_14538),hAPP(c_Relation_Oconverse(U_14538,U_14539),U_14540)),
    inference(clausify,[status(thm)],[f_3691_2]) ).

fof(f_3692_1,plain,
    ! [V_r_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)) = hAPP(c_Relation_ORange(T_c,T_b),V_r_2),
    inference(fof_nnf,[status(thm)],[fact_Domain__converse]) ).

fof(f_3692_2,plain,
    ! [U_14543,U_14542,U_14541] : hAPP(c_Relation_ODomain(U_14541,U_14542),hAPP(c_Relation_Oconverse(U_14542,U_14541),U_14543)) = hAPP(c_Relation_ORange(U_14542,U_14541),U_14543),
    inference(variable_rename,[status(thm)],[f_3692_1]) ).

cnf(f_3692_3,plain,
    hAPP(c_Relation_ODomain(U_14541,U_14542),hAPP(c_Relation_Oconverse(U_14542,U_14541),U_14543)) = hAPP(c_Relation_ORange(U_14542,U_14541),U_14543),
    inference(clausify,[status(thm)],[f_3692_2]) ).

fof(f_3693_1,plain,
    ! [V_r_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2)) = hAPP(c_Relation_ODomain(T_b,T_c),V_r_2),
    inference(fof_nnf,[status(thm)],[fact_Range__converse]) ).

fof(f_3693_2,plain,
    ! [U_14546,U_14545,U_14544] : hAPP(c_Relation_ORange(U_14544,U_14545),hAPP(c_Relation_Oconverse(U_14545,U_14544),U_14546)) = hAPP(c_Relation_ODomain(U_14545,U_14544),U_14546),
    inference(variable_rename,[status(thm)],[f_3693_1]) ).

cnf(f_3693_3,plain,
    hAPP(c_Relation_ORange(U_14544,U_14545),hAPP(c_Relation_Oconverse(U_14545,U_14544),U_14546)) = hAPP(c_Relation_ODomain(U_14545,U_14544),U_14546),
    inference(clausify,[status(thm)],[f_3693_2]) ).

fof(f_3694_1,plain,
    ! [V_r_2,V_x_2,V_y_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__converseI]) ).

fof(f_3694_2,plain,
    ! [U_14550,U_14549,U_14548,U_14547] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14547,U_14547)),hAPP(hAPP(c_Product__Type_OPair(U_14547,U_14547),U_14549),U_14548)),c_Transitive__Closure_Ortrancl(U_14547,hAPP(c_Relation_Oconverse(U_14547,U_14547),U_14550))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14547,U_14547)),hAPP(hAPP(c_Product__Type_OPair(U_14547,U_14547),U_14548),U_14549)),c_Transitive__Closure_Ortrancl(U_14547,U_14550))) ),
    inference(variable_rename,[status(thm)],[f_3694_1]) ).

cnf(f_3694_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14547,U_14547)),hAPP(hAPP(c_Product__Type_OPair(U_14547,U_14547),U_14549),U_14548)),c_Transitive__Closure_Ortrancl(U_14547,hAPP(c_Relation_Oconverse(U_14547,U_14547),U_14550))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14547,U_14547)),hAPP(hAPP(c_Product__Type_OPair(U_14547,U_14547),U_14548),U_14549)),c_Transitive__Closure_Ortrancl(U_14547,U_14550))) ),
    inference(clausify,[status(thm)],[f_3694_2]) ).

fof(f_3695_1,plain,
    ! [V_r_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__converseD]) ).

fof(f_3695_2,plain,
    ! [U_14554,U_14553,U_14552,U_14551] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14551,U_14551)),hAPP(hAPP(c_Product__Type_OPair(U_14551,U_14551),U_14553),U_14552)),c_Transitive__Closure_Ortrancl(U_14551,U_14554)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14551,U_14551)),hAPP(hAPP(c_Product__Type_OPair(U_14551,U_14551),U_14552),U_14553)),c_Transitive__Closure_Ortrancl(U_14551,hAPP(c_Relation_Oconverse(U_14551,U_14551),U_14554)))) ),
    inference(variable_rename,[status(thm)],[f_3695_1]) ).

cnf(f_3695_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14551,U_14551)),hAPP(hAPP(c_Product__Type_OPair(U_14551,U_14551),U_14553),U_14552)),c_Transitive__Closure_Ortrancl(U_14551,U_14554)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14551,U_14551)),hAPP(hAPP(c_Product__Type_OPair(U_14551,U_14551),U_14552),U_14553)),c_Transitive__Closure_Ortrancl(U_14551,hAPP(c_Relation_Oconverse(U_14551,U_14551),U_14554)))) ),
    inference(clausify,[status(thm)],[f_3695_2]) ).

fof(f_3696_1,plain,
    ! [V_r_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_trancl__converseI]) ).

fof(f_3696_2,plain,
    ! [U_14558,U_14557,U_14556,U_14555] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14555,U_14555)),hAPP(hAPP(c_Product__Type_OPair(U_14555,U_14555),U_14556),U_14557)),c_Transitive__Closure_Otrancl(U_14555,hAPP(c_Relation_Oconverse(U_14555,U_14555),U_14558))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14555,U_14555)),hAPP(hAPP(c_Product__Type_OPair(U_14555,U_14555),U_14556),U_14557)),hAPP(c_Relation_Oconverse(U_14555,U_14555),c_Transitive__Closure_Otrancl(U_14555,U_14558)))) ),
    inference(variable_rename,[status(thm)],[f_3696_1]) ).

cnf(f_3696_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14555,U_14555)),hAPP(hAPP(c_Product__Type_OPair(U_14555,U_14555),U_14556),U_14557)),c_Transitive__Closure_Otrancl(U_14555,hAPP(c_Relation_Oconverse(U_14555,U_14555),U_14558))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14555,U_14555)),hAPP(hAPP(c_Product__Type_OPair(U_14555,U_14555),U_14556),U_14557)),hAPP(c_Relation_Oconverse(U_14555,U_14555),c_Transitive__Closure_Otrancl(U_14555,U_14558)))) ),
    inference(clausify,[status(thm)],[f_3696_2]) ).

fof(f_3697_1,plain,
    ! [V_r_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_trancl__converseD]) ).

fof(f_3697_2,plain,
    ! [U_14562,U_14561,U_14560,U_14559] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14559,U_14559)),hAPP(hAPP(c_Product__Type_OPair(U_14559,U_14559),U_14560),U_14561)),hAPP(c_Relation_Oconverse(U_14559,U_14559),c_Transitive__Closure_Otrancl(U_14559,U_14562))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14559,U_14559)),hAPP(hAPP(c_Product__Type_OPair(U_14559,U_14559),U_14560),U_14561)),c_Transitive__Closure_Otrancl(U_14559,hAPP(c_Relation_Oconverse(U_14559,U_14559),U_14562)))) ),
    inference(variable_rename,[status(thm)],[f_3697_1]) ).

cnf(f_3697_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14559,U_14559)),hAPP(hAPP(c_Product__Type_OPair(U_14559,U_14559),U_14560),U_14561)),hAPP(c_Relation_Oconverse(U_14559,U_14559),c_Transitive__Closure_Otrancl(U_14559,U_14562))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14559,U_14559)),hAPP(hAPP(c_Product__Type_OPair(U_14559,U_14559),U_14560),U_14561)),c_Transitive__Closure_Otrancl(U_14559,hAPP(c_Relation_Oconverse(U_14559,U_14559),U_14562)))) ),
    inference(clausify,[status(thm)],[f_3697_2]) ).

fof(f_3698_1,plain,
    ! [V_B_2,V_A_2,V_r_2,T_c,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2)),V_B_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2))))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2)),V_B_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Image__subset__eq]) ).

fof(f_3698_2,plain,
    ! [U_14567,U_14566,U_14565,U_14564,U_14563] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14563,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_14564,U_14563,U_14565),U_14566)),U_14567))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14564,tc_HOL_Obool)),U_14566),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14564,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_14563,U_14564,hAPP(c_Relation_Oconverse(U_14564,U_14563),U_14565)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14563,tc_HOL_Obool)),U_14567))))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14564,tc_HOL_Obool)),U_14566),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14564,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_14563,U_14564,hAPP(c_Relation_Oconverse(U_14564,U_14563),U_14565)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14563,tc_HOL_Obool)),U_14567)))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14563,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_14564,U_14563,U_14565),U_14566)),U_14567)) ) ),
    inference(variable_rename,[status(thm)],[f_3698_1]) ).

fof(f_3698_3,plain,
    ( ! [U_14577,U_14575,U_14573,U_14571,U_14569] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14569,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_14571,U_14569,U_14573),U_14575)),U_14577))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14571,tc_HOL_Obool)),U_14575),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14571,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_14569,U_14571,hAPP(c_Relation_Oconverse(U_14571,U_14569),U_14573)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14569,tc_HOL_Obool)),U_14577))))) )
    & ! [U_14576,U_14574,U_14572,U_14570,U_14568] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14570,tc_HOL_Obool)),U_14574),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14570,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_14568,U_14570,hAPP(c_Relation_Oconverse(U_14570,U_14568),U_14572)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14568,tc_HOL_Obool)),U_14576)))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14568,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_14570,U_14568,U_14572),U_14574)),U_14576)) ) ),
    inference(miniscope,[status(thm)],[f_3698_2]) ).

cnf(f_3698_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14570,tc_HOL_Obool)),U_14574),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14570,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_14568,U_14570,hAPP(c_Relation_Oconverse(U_14570,U_14568),U_14572)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14568,tc_HOL_Obool)),U_14576)))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14568,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_14570,U_14568,U_14572),U_14574)),U_14576)) ),
    inference(clausify,[status(thm)],[f_3698_3]) ).

cnf(f_3698_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14569,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_14571,U_14569,U_14573),U_14575)),U_14577))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14571,tc_HOL_Obool)),U_14575),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14571,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_14569,U_14571,hAPP(c_Relation_Oconverse(U_14571,U_14569),U_14573)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14569,tc_HOL_Obool)),U_14577))))) ),
    inference(clausify,[status(thm)],[f_3698_3]) ).

fof(f_3699_1,plain,
    ! [V_r_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),V_r_2)))
      | ~ c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_refl__on__comp__subset]) ).

fof(f_3699_2,plain,
    ! [U_14580,U_14579,U_14578] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14578,U_14578),tc_HOL_Obool)),U_14580),hAPP(hAPP(c_Relation_Orel__comp(U_14578,U_14578,U_14578),hAPP(c_Relation_Oconverse(U_14578,U_14578),U_14580)),U_14580)))
      | ~ c_Relation_Orefl__on(U_14578,U_14579,U_14580) ),
    inference(variable_rename,[status(thm)],[f_3699_1]) ).

cnf(f_3699_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14578,U_14578),tc_HOL_Obool)),U_14580),hAPP(hAPP(c_Relation_Orel__comp(U_14578,U_14578,U_14578),hAPP(c_Relation_Oconverse(U_14578,U_14578),U_14580)),U_14580)))
    | ~ c_Relation_Orefl__on(U_14578,U_14579,U_14580) ),
    inference(clausify,[status(thm)],[f_3699_2]) ).

fof(f_3700_1,plain,
    ! [V_A_2,V_r_2,T_b] :
      ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
      | hAPP(c_Relation_ODomain(T_b,T_b),V_r_2) != V_A_2
      | hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),V_r_2) != V_r_2 ),
    inference(fof_nnf,[status(thm)],[fact_comp__equivI]) ).

fof(f_3700_2,plain,
    ! [U_14583,U_14582,U_14581] :
      ( c_Equiv__Relations_Oequiv(U_14581,U_14583,U_14582)
      | hAPP(c_Relation_ODomain(U_14581,U_14581),U_14582) != U_14583
      | hAPP(hAPP(c_Relation_Orel__comp(U_14581,U_14581,U_14581),hAPP(c_Relation_Oconverse(U_14581,U_14581),U_14582)),U_14582) != U_14582 ),
    inference(variable_rename,[status(thm)],[f_3700_1]) ).

cnf(f_3700_3,plain,
    ( c_Equiv__Relations_Oequiv(U_14581,U_14583,U_14582)
    | hAPP(c_Relation_ODomain(U_14581,U_14581),U_14582) != U_14583
    | hAPP(hAPP(c_Relation_Orel__comp(U_14581,U_14581,U_14581),hAPP(c_Relation_Oconverse(U_14581,U_14581),U_14582)),U_14582) != U_14582 ),
    inference(clausify,[status(thm)],[f_3700_2]) ).

fof(f_3701_1,plain,
    ! [V_r_2,T_b] :
      ( c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
      | ~ c_Wellfounded_Oacyclic(T_b,V_r_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__acyclic__wf__converse]) ).

fof(f_3701_2,plain,
    ! [U_14585,U_14584] :
      ( c_Wellfounded_Owf(U_14584,hAPP(c_Relation_Oconverse(U_14584,U_14584),U_14585))
      | ~ c_Wellfounded_Oacyclic(U_14584,U_14585)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14584,U_14584)),U_14585)) ),
    inference(variable_rename,[status(thm)],[f_3701_1]) ).

cnf(f_3701_3,plain,
    ( c_Wellfounded_Owf(U_14584,hAPP(c_Relation_Oconverse(U_14584,U_14584),U_14585))
    | ~ c_Wellfounded_Oacyclic(U_14584,U_14585)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14584,U_14584)),U_14585)) ),
    inference(clausify,[status(thm)],[f_3701_2]) ).

fof(f_3702_1,plain,
    ! [V_r_2,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2) = hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_c,T_b)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_c,T_b),tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_c,T_b)))),hAPP(c_COMBC(T_c,T_b,tc_prod(T_c,T_b)),c_Product__Type_OPair(T_c,T_b))))),V_r_2))),
    inference(fof_nnf,[status(thm)],[fact_converse__def]) ).

fof(f_3702_2,plain,
    ! [U_14588,U_14587,U_14586] : hAPP(c_Relation_Oconverse(U_14586,U_14587),U_14588) = hAPP(c_Set_OCollect(tc_prod(U_14587,U_14586)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14587,U_14586,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14587,tc_fun(tc_prod(U_14586,U_14587),tc_HOL_Obool),tc_fun(U_14586,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14586,tc_fun(tc_fun(tc_prod(U_14586,U_14587),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14586,U_14587),tc_HOL_Obool),tc_fun(U_14586,tc_HOL_Obool)),U_14587),c_COMBC(U_14586,tc_fun(tc_prod(U_14586,U_14587),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14586,tc_prod(U_14586,U_14587)),tc_fun(U_14586,tc_fun(tc_fun(tc_prod(U_14586,U_14587),tc_HOL_Obool),tc_HOL_Obool)),U_14587),hAPP(c_COMBB(tc_prod(U_14586,U_14587),tc_fun(tc_fun(tc_prod(U_14586,U_14587),tc_HOL_Obool),tc_HOL_Obool),U_14586),c_member(tc_prod(U_14586,U_14587)))),hAPP(c_COMBC(U_14586,U_14587,tc_prod(U_14586,U_14587)),c_Product__Type_OPair(U_14586,U_14587))))),U_14588))),
    inference(variable_rename,[status(thm)],[f_3702_1]) ).

cnf(f_3702_3,plain,
    hAPP(c_Relation_Oconverse(U_14586,U_14587),U_14588) = hAPP(c_Set_OCollect(tc_prod(U_14587,U_14586)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14587,U_14586,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14587,tc_fun(tc_prod(U_14586,U_14587),tc_HOL_Obool),tc_fun(U_14586,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14586,tc_fun(tc_fun(tc_prod(U_14586,U_14587),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14586,U_14587),tc_HOL_Obool),tc_fun(U_14586,tc_HOL_Obool)),U_14587),c_COMBC(U_14586,tc_fun(tc_prod(U_14586,U_14587),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14586,tc_prod(U_14586,U_14587)),tc_fun(U_14586,tc_fun(tc_fun(tc_prod(U_14586,U_14587),tc_HOL_Obool),tc_HOL_Obool)),U_14587),hAPP(c_COMBB(tc_prod(U_14586,U_14587),tc_fun(tc_fun(tc_prod(U_14586,U_14587),tc_HOL_Obool),tc_HOL_Obool),U_14586),c_member(tc_prod(U_14586,U_14587)))),hAPP(c_COMBC(U_14586,U_14587,tc_prod(U_14586,U_14587)),c_Product__Type_OPair(U_14586,U_14587))))),U_14588))),
    inference(clausify,[status(thm)],[f_3702_2]) ).

fof(f_3703_1,plain,
    ! [V_B_2,T_d,V_A_2,V_r_2,T_c,T_b] :
      ( hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Relation_OImage(T_c,T_b,V_r_2)),V_B_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))
      | ~ c_Relation_Osingle__valued(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Image__INT__eq]) ).

fof(f_3703_2,plain,
    ! [U_14594,U_14593,U_14592,U_14591,U_14590,U_14589] :
      ( hAPP(c_Relation_OImage(U_14590,U_14589,U_14591),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_14593,tc_fun(U_14590,tc_HOL_Obool)),U_14592),U_14594)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_14593,tc_fun(U_14589,tc_HOL_Obool)),U_14592),hAPP(hAPP(c_COMBB(tc_fun(U_14590,tc_HOL_Obool),tc_fun(U_14589,tc_HOL_Obool),U_14593),c_Relation_OImage(U_14590,U_14589,U_14591)),U_14594))
      | U_14592 = c_Orderings_Obot__class_Obot(tc_fun(U_14593,tc_HOL_Obool))
      | ~ c_Relation_Osingle__valued(U_14589,U_14590,hAPP(c_Relation_Oconverse(U_14590,U_14589),U_14591)) ),
    inference(variable_rename,[status(thm)],[f_3703_1]) ).

cnf(f_3703_3,plain,
    ( hAPP(c_Relation_OImage(U_14590,U_14589,U_14591),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_14593,tc_fun(U_14590,tc_HOL_Obool)),U_14592),U_14594)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_14593,tc_fun(U_14589,tc_HOL_Obool)),U_14592),hAPP(hAPP(c_COMBB(tc_fun(U_14590,tc_HOL_Obool),tc_fun(U_14589,tc_HOL_Obool),U_14593),c_Relation_OImage(U_14590,U_14589,U_14591)),U_14594))
    | U_14592 = c_Orderings_Obot__class_Obot(tc_fun(U_14593,tc_HOL_Obool))
    | ~ c_Relation_Osingle__valued(U_14589,U_14590,hAPP(c_Relation_Oconverse(U_14590,U_14589),U_14591)) ),
    inference(clausify,[status(thm)],[f_3703_2]) ).

fof(f_3704_1,plain,
    ! [V_r_2,V_A_2,T_b] :
      ( ( c_Relation_Ototal__on(T_b,V_A_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b)))
        | ~ c_Relation_Ototal__on(T_b,V_A_2,V_r_2) )
      & ( c_Relation_Ototal__on(T_b,V_A_2,V_r_2)
        | ~ c_Relation_Ototal__on(T_b,V_A_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))) ) ),
    inference(fof_nnf,[status(thm)],[fact_total__on__diff__Id]) ).

fof(f_3704_2,plain,
    ! [U_14597,U_14596,U_14595] :
      ( ( c_Relation_Ototal__on(U_14595,U_14596,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_14595,U_14595),tc_HOL_Obool)),U_14597),c_Relation_OId(U_14595)))
        | ~ c_Relation_Ototal__on(U_14595,U_14596,U_14597) )
      & ( c_Relation_Ototal__on(U_14595,U_14596,U_14597)
        | ~ c_Relation_Ototal__on(U_14595,U_14596,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_14595,U_14595),tc_HOL_Obool)),U_14597),c_Relation_OId(U_14595))) ) ),
    inference(variable_rename,[status(thm)],[f_3704_1]) ).

fof(f_3704_3,plain,
    ( ! [U_14603,U_14601,U_14599] :
        ( c_Relation_Ototal__on(U_14599,U_14601,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_14599,U_14599),tc_HOL_Obool)),U_14603),c_Relation_OId(U_14599)))
        | ~ c_Relation_Ototal__on(U_14599,U_14601,U_14603) )
    & ! [U_14602,U_14600,U_14598] :
        ( c_Relation_Ototal__on(U_14598,U_14600,U_14602)
        | ~ c_Relation_Ototal__on(U_14598,U_14600,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_14598,U_14598),tc_HOL_Obool)),U_14602),c_Relation_OId(U_14598))) ) ),
    inference(miniscope,[status(thm)],[f_3704_2]) ).

cnf(f_3704_4,plain,
    ( c_Relation_Ototal__on(U_14598,U_14600,U_14602)
    | ~ c_Relation_Ototal__on(U_14598,U_14600,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_14598,U_14598),tc_HOL_Obool)),U_14602),c_Relation_OId(U_14598))) ),
    inference(clausify,[status(thm)],[f_3704_3]) ).

cnf(f_3704_5,plain,
    ( c_Relation_Ototal__on(U_14599,U_14601,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_14599,U_14599),tc_HOL_Obool)),U_14603),c_Relation_OId(U_14599)))
    | ~ c_Relation_Ototal__on(U_14599,U_14601,U_14603) ),
    inference(clausify,[status(thm)],[f_3704_3]) ).

fof(f_3705_1,plain,
    ! [T_b] : c_Relation_Osingle__valued(T_b,T_b,c_Relation_OId(T_b)),
    inference(fof_nnf,[status(thm)],[fact_single__valued__Id]) ).

fof(f_3705_2,plain,
    ! [U_14604] : c_Relation_Osingle__valued(U_14604,U_14604,c_Relation_OId(U_14604)),
    inference(variable_rename,[status(thm)],[f_3705_1]) ).

cnf(f_3705_3,plain,
    c_Relation_Osingle__valued(U_14604,U_14604,c_Relation_OId(U_14604)),
    inference(clausify,[status(thm)],[f_3705_2]) ).

fof(f_3706_1,plain,
    ! [V_s_2,V_r_2,T_c,T_b] :
      ( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
      | ~ c_Relation_Osingle__valued(T_b,T_c,V_s_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_2),V_s_2)) ),
    inference(fof_nnf,[status(thm)],[fact_single__valued__subset]) ).

fof(f_3706_2,plain,
    ! [U_14608,U_14607,U_14606,U_14605] :
      ( c_Relation_Osingle__valued(U_14605,U_14606,U_14607)
      | ~ c_Relation_Osingle__valued(U_14605,U_14606,U_14608)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14605,U_14606),tc_HOL_Obool)),U_14607),U_14608)) ),
    inference(variable_rename,[status(thm)],[f_3706_1]) ).

cnf(f_3706_3,plain,
    ( c_Relation_Osingle__valued(U_14605,U_14606,U_14607)
    | ~ c_Relation_Osingle__valued(U_14605,U_14606,U_14608)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14605,U_14606),tc_HOL_Obool)),U_14607),U_14608)) ),
    inference(clausify,[status(thm)],[f_3706_2]) ).

fof(f_3707_1,plain,
    ! [V_s_2,T_d,V_r_2,T_c,T_b] :
      ( c_Relation_Osingle__valued(T_b,T_d,hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2))
      | ~ c_Relation_Osingle__valued(T_c,T_d,V_s_2)
      | ~ c_Relation_Osingle__valued(T_b,T_c,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_single__valued__rel__comp]) ).

fof(f_3707_2,plain,
    ! [U_14613,U_14612,U_14611,U_14610,U_14609] :
      ( c_Relation_Osingle__valued(U_14609,U_14612,hAPP(hAPP(c_Relation_Orel__comp(U_14609,U_14610,U_14612),U_14611),U_14613))
      | ~ c_Relation_Osingle__valued(U_14610,U_14612,U_14613)
      | ~ c_Relation_Osingle__valued(U_14609,U_14610,U_14611) ),
    inference(variable_rename,[status(thm)],[f_3707_1]) ).

cnf(f_3707_3,plain,
    ( c_Relation_Osingle__valued(U_14609,U_14612,hAPP(hAPP(c_Relation_Orel__comp(U_14609,U_14610,U_14612),U_14611),U_14613))
    | ~ c_Relation_Osingle__valued(U_14610,U_14612,U_14613)
    | ~ c_Relation_Osingle__valued(U_14609,U_14610,U_14611) ),
    inference(clausify,[status(thm)],[f_3707_2]) ).

fof(f_3708_1,plain,
    ! [V_A_2,T_b] : c_Relation_Osingle__valued(T_b,T_b,c_Relation_OId__on(T_b,V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_single__valued__Id__on]) ).

fof(f_3708_2,plain,
    ! [U_14615,U_14614] : c_Relation_Osingle__valued(U_14614,U_14614,c_Relation_OId__on(U_14614,U_14615)),
    inference(variable_rename,[status(thm)],[f_3708_1]) ).

cnf(f_3708_3,plain,
    c_Relation_Osingle__valued(U_14614,U_14614,c_Relation_OId__on(U_14614,U_14615)),
    inference(clausify,[status(thm)],[f_3708_2]) ).

fof(f_3709_1,plain,
    ! [V_r_2,T_b] : c_Relation_Ototal__on(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_r_2),
    inference(fof_nnf,[status(thm)],[fact_total__on__empty]) ).

fof(f_3709_2,plain,
    ! [U_14617,U_14616] : c_Relation_Ototal__on(U_14616,c_Orderings_Obot__class_Obot(tc_fun(U_14616,tc_HOL_Obool)),U_14617),
    inference(variable_rename,[status(thm)],[f_3709_1]) ).

cnf(f_3709_3,plain,
    c_Relation_Ototal__on(U_14616,c_Orderings_Obot__class_Obot(tc_fun(U_14616,tc_HOL_Obool)),U_14617),
    inference(clausify,[status(thm)],[f_3709_2]) ).

fof(f_3710_1,plain,
    ! [V_r_2,V_A_2,T_b] :
      ( ( c_Relation_Ototal__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
        | ~ c_Relation_Ototal__on(T_b,V_A_2,V_r_2) )
      & ( c_Relation_Ototal__on(T_b,V_A_2,V_r_2)
        | ~ c_Relation_Ototal__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_total__on__converse]) ).

fof(f_3710_2,plain,
    ! [U_14620,U_14619,U_14618] :
      ( ( c_Relation_Ototal__on(U_14618,U_14619,hAPP(c_Relation_Oconverse(U_14618,U_14618),U_14620))
        | ~ c_Relation_Ototal__on(U_14618,U_14619,U_14620) )
      & ( c_Relation_Ototal__on(U_14618,U_14619,U_14620)
        | ~ c_Relation_Ototal__on(U_14618,U_14619,hAPP(c_Relation_Oconverse(U_14618,U_14618),U_14620)) ) ),
    inference(variable_rename,[status(thm)],[f_3710_1]) ).

fof(f_3710_3,plain,
    ( ! [U_14626,U_14624,U_14622] :
        ( c_Relation_Ototal__on(U_14622,U_14624,hAPP(c_Relation_Oconverse(U_14622,U_14622),U_14626))
        | ~ c_Relation_Ototal__on(U_14622,U_14624,U_14626) )
    & ! [U_14625,U_14623,U_14621] :
        ( c_Relation_Ototal__on(U_14621,U_14623,U_14625)
        | ~ c_Relation_Ototal__on(U_14621,U_14623,hAPP(c_Relation_Oconverse(U_14621,U_14621),U_14625)) ) ),
    inference(miniscope,[status(thm)],[f_3710_2]) ).

cnf(f_3710_4,plain,
    ( c_Relation_Ototal__on(U_14621,U_14623,U_14625)
    | ~ c_Relation_Ototal__on(U_14621,U_14623,hAPP(c_Relation_Oconverse(U_14621,U_14621),U_14625)) ),
    inference(clausify,[status(thm)],[f_3710_3]) ).

cnf(f_3710_5,plain,
    ( c_Relation_Ototal__on(U_14622,U_14624,hAPP(c_Relation_Oconverse(U_14622,U_14622),U_14626))
    | ~ c_Relation_Ototal__on(U_14622,U_14624,U_14626) ),
    inference(clausify,[status(thm)],[f_3710_3]) ).

fof(f_3711_1,plain,
    ! [V_z_2,V_y_2,V_x_2,V_r_2,T_c,T_b] :
      ( V_y_2 = V_z_2
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_z_2)),V_r_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),V_r_2))
      | ~ c_Relation_Osingle__valued(T_b,T_c,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_single__valuedD]) ).

fof(f_3711_2,plain,
    ! [U_14632,U_14631,U_14630,U_14629,U_14628,U_14627] :
      ( U_14631 = U_14632
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14627,U_14628)),hAPP(hAPP(c_Product__Type_OPair(U_14627,U_14628),U_14630),U_14632)),U_14629))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14627,U_14628)),hAPP(hAPP(c_Product__Type_OPair(U_14627,U_14628),U_14630),U_14631)),U_14629))
      | ~ c_Relation_Osingle__valued(U_14627,U_14628,U_14629) ),
    inference(variable_rename,[status(thm)],[f_3711_1]) ).

cnf(f_3711_3,plain,
    ( U_14631 = U_14632
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14627,U_14628)),hAPP(hAPP(c_Product__Type_OPair(U_14627,U_14628),U_14630),U_14632)),U_14629))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14627,U_14628)),hAPP(hAPP(c_Product__Type_OPair(U_14627,U_14628),U_14630),U_14631)),U_14629))
    | ~ c_Relation_Osingle__valued(U_14627,U_14628,U_14629) ),
    inference(clausify,[status(thm)],[f_3711_2]) ).

fof(f_3712_1,plain,
    ! [V_r_2,T_c,T_b] :
      ( ( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
        | ? [B_x,B_y] :
            ( ? [B_z] :
                ( B_y != B_z
                & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_z)),V_r_2)) )
            & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y)),V_r_2)) ) )
      & ( ! [B_x,B_y] :
            ( ! [B_z] :
                ( B_y = B_z
                | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_z)),V_r_2)) )
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y)),V_r_2)) )
        | ~ c_Relation_Osingle__valued(T_b,T_c,V_r_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_single__valued__def]) ).

fof(f_3712_2,plain,
    ! [U_14641,U_14640,U_14639] :
      ( ( c_Relation_Osingle__valued(U_14639,U_14640,U_14641)
        | ? [U_14638,U_14637] :
            ( ? [U_14636] :
                ( U_14637 != U_14636
                & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14639,U_14640)),hAPP(hAPP(c_Product__Type_OPair(U_14639,U_14640),U_14638),U_14636)),U_14641)) )
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14639,U_14640)),hAPP(hAPP(c_Product__Type_OPair(U_14639,U_14640),U_14638),U_14637)),U_14641)) ) )
      & ( ! [U_14635,U_14634] :
            ( ! [U_14633] :
                ( U_14634 = U_14633
                | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14639,U_14640)),hAPP(hAPP(c_Product__Type_OPair(U_14639,U_14640),U_14635),U_14633)),U_14641)) )
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14639,U_14640)),hAPP(hAPP(c_Product__Type_OPair(U_14639,U_14640),U_14635),U_14634)),U_14641)) )
        | ~ c_Relation_Osingle__valued(U_14639,U_14640,U_14641) ) ),
    inference(variable_rename,[status(thm)],[f_3712_1]) ).

fof(f_3712_3,plain,
    ( ! [U_14647,U_14645,U_14643] :
        ( c_Relation_Osingle__valued(U_14643,U_14645,U_14647)
        | ? [U_14638,U_14637] :
            ( ? [U_14636] :
                ( U_14637 != U_14636
                & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14643,U_14645)),hAPP(hAPP(c_Product__Type_OPair(U_14643,U_14645),U_14638),U_14636)),U_14647)) )
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14643,U_14645)),hAPP(hAPP(c_Product__Type_OPair(U_14643,U_14645),U_14638),U_14637)),U_14647)) ) )
    & ! [U_14646,U_14644,U_14642] :
        ( ! [U_14635,U_14634] :
            ( ! [U_14633] :
                ( U_14634 = U_14633
                | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14642,U_14644)),hAPP(hAPP(c_Product__Type_OPair(U_14642,U_14644),U_14635),U_14633)),U_14646)) )
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14642,U_14644)),hAPP(hAPP(c_Product__Type_OPair(U_14642,U_14644),U_14635),U_14634)),U_14646)) )
        | ~ c_Relation_Osingle__valued(U_14642,U_14644,U_14646) ) ),
    inference(miniscope,[status(thm)],[f_3712_2]) ).

fof(f_3712_4,plain,
    ( ! [U_14647,U_14645,U_14643] :
        ( c_Relation_Osingle__valued(U_14643,U_14645,U_14647)
        | ? [U_14637] :
            ( ? [U_14636] :
                ( U_14637 != U_14636
                & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14643,U_14645)),hAPP(hAPP(c_Product__Type_OPair(U_14643,U_14645),sK366(U_14647,U_14645,U_14643)),U_14636)),U_14647)) )
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14643,U_14645)),hAPP(hAPP(c_Product__Type_OPair(U_14643,U_14645),sK366(U_14647,U_14645,U_14643)),U_14637)),U_14647)) ) )
    & ! [U_14646,U_14644,U_14642] :
        ( ! [U_14635,U_14634] :
            ( ! [U_14633] :
                ( U_14634 = U_14633
                | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14642,U_14644)),hAPP(hAPP(c_Product__Type_OPair(U_14642,U_14644),U_14635),U_14633)),U_14646)) )
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14642,U_14644)),hAPP(hAPP(c_Product__Type_OPair(U_14642,U_14644),U_14635),U_14634)),U_14646)) )
        | ~ c_Relation_Osingle__valued(U_14642,U_14644,U_14646) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK366]),skolemize(U_14638,sK366(U_14647,U_14645,U_14643))],[f_3712_3]) ).

fof(f_3712_5,plain,
    ( ! [U_14647,U_14645,U_14643] :
        ( c_Relation_Osingle__valued(U_14643,U_14645,U_14647)
        | ( ? [U_14636] :
              ( sK367(U_14647,U_14645,U_14643) != U_14636
              & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14643,U_14645)),hAPP(hAPP(c_Product__Type_OPair(U_14643,U_14645),sK366(U_14647,U_14645,U_14643)),U_14636)),U_14647)) )
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14643,U_14645)),hAPP(hAPP(c_Product__Type_OPair(U_14643,U_14645),sK366(U_14647,U_14645,U_14643)),sK367(U_14647,U_14645,U_14643))),U_14647)) ) )
    & ! [U_14646,U_14644,U_14642] :
        ( ! [U_14635,U_14634] :
            ( ! [U_14633] :
                ( U_14634 = U_14633
                | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14642,U_14644)),hAPP(hAPP(c_Product__Type_OPair(U_14642,U_14644),U_14635),U_14633)),U_14646)) )
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14642,U_14644)),hAPP(hAPP(c_Product__Type_OPair(U_14642,U_14644),U_14635),U_14634)),U_14646)) )
        | ~ c_Relation_Osingle__valued(U_14642,U_14644,U_14646) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK367]),skolemize(U_14637,sK367(U_14647,U_14645,U_14643))],[f_3712_4]) ).

fof(f_3712_6,plain,
    ( ! [U_14647,U_14645,U_14643] :
        ( c_Relation_Osingle__valued(U_14643,U_14645,U_14647)
        | ( sK367(U_14647,U_14645,U_14643) != sK368(U_14647,U_14645,U_14643)
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14643,U_14645)),hAPP(hAPP(c_Product__Type_OPair(U_14643,U_14645),sK366(U_14647,U_14645,U_14643)),sK368(U_14647,U_14645,U_14643))),U_14647))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14643,U_14645)),hAPP(hAPP(c_Product__Type_OPair(U_14643,U_14645),sK366(U_14647,U_14645,U_14643)),sK367(U_14647,U_14645,U_14643))),U_14647)) ) )
    & ! [U_14646,U_14644,U_14642] :
        ( ! [U_14635,U_14634] :
            ( ! [U_14633] :
                ( U_14634 = U_14633
                | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14642,U_14644)),hAPP(hAPP(c_Product__Type_OPair(U_14642,U_14644),U_14635),U_14633)),U_14646)) )
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14642,U_14644)),hAPP(hAPP(c_Product__Type_OPair(U_14642,U_14644),U_14635),U_14634)),U_14646)) )
        | ~ c_Relation_Osingle__valued(U_14642,U_14644,U_14646) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK368]),skolemize(U_14636,sK368(U_14647,U_14645,U_14643))],[f_3712_5]) ).

cnf(f_3712_7,plain,
    ( U_14634 = U_14633
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14642,U_14644)),hAPP(hAPP(c_Product__Type_OPair(U_14642,U_14644),U_14635),U_14633)),U_14646))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14642,U_14644)),hAPP(hAPP(c_Product__Type_OPair(U_14642,U_14644),U_14635),U_14634)),U_14646))
    | ~ c_Relation_Osingle__valued(U_14642,U_14644,U_14646) ),
    inference(clausify,[status(thm)],[f_3712_6]) ).

cnf(f_3712_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14643,U_14645)),hAPP(hAPP(c_Product__Type_OPair(U_14643,U_14645),sK366(U_14647,U_14645,U_14643)),sK367(U_14647,U_14645,U_14643))),U_14647))
    | c_Relation_Osingle__valued(U_14643,U_14645,U_14647) ),
    inference(clausify,[status(thm)],[f_3712_6]) ).

cnf(f_3712_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14643,U_14645)),hAPP(hAPP(c_Product__Type_OPair(U_14643,U_14645),sK366(U_14647,U_14645,U_14643)),sK368(U_14647,U_14645,U_14643))),U_14647))
    | c_Relation_Osingle__valued(U_14643,U_14645,U_14647) ),
    inference(clausify,[status(thm)],[f_3712_6]) ).

cnf(f_3712_10,plain,
    ( sK367(U_14647,U_14645,U_14643) != sK368(U_14647,U_14645,U_14643)
    | c_Relation_Osingle__valued(U_14643,U_14645,U_14647) ),
    inference(clausify,[status(thm)],[f_3712_6]) ).

fof(f_3713_1,plain,
    ! [V_r_2,V_A_2,T_b] :
      ( ( c_Relation_Ototal__on(T_b,V_A_2,V_r_2)
        | ? [B_x] :
            ( ? [B_xa] :
                ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_xa),B_x)),V_r_2))
                & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_xa)),V_r_2))
                & B_x != B_xa
                & hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2)) )
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
      & ( ! [B_x] :
            ( ! [B_xa] :
                ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_xa),B_x)),V_r_2))
                | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_xa)),V_r_2))
                | B_x = B_xa
                | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2)) )
            | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
        | ~ c_Relation_Ototal__on(T_b,V_A_2,V_r_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_total__on__def]) ).

fof(f_3713_2,plain,
    ! [U_14654,U_14653,U_14652] :
      ( ( c_Relation_Ototal__on(U_14652,U_14653,U_14654)
        | ? [U_14651] :
            ( ? [U_14650] :
                ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14652,U_14652)),hAPP(hAPP(c_Product__Type_OPair(U_14652,U_14652),U_14650),U_14651)),U_14654))
                & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14652,U_14652)),hAPP(hAPP(c_Product__Type_OPair(U_14652,U_14652),U_14651),U_14650)),U_14654))
                & U_14651 != U_14650
                & hBOOL(hAPP(hAPP(c_member(U_14652),U_14650),U_14653)) )
            & hBOOL(hAPP(hAPP(c_member(U_14652),U_14651),U_14653)) ) )
      & ( ! [U_14649] :
            ( ! [U_14648] :
                ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14652,U_14652)),hAPP(hAPP(c_Product__Type_OPair(U_14652,U_14652),U_14648),U_14649)),U_14654))
                | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14652,U_14652)),hAPP(hAPP(c_Product__Type_OPair(U_14652,U_14652),U_14649),U_14648)),U_14654))
                | U_14649 = U_14648
                | ~ hBOOL(hAPP(hAPP(c_member(U_14652),U_14648),U_14653)) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_14652),U_14649),U_14653)) )
        | ~ c_Relation_Ototal__on(U_14652,U_14653,U_14654) ) ),
    inference(variable_rename,[status(thm)],[f_3713_1]) ).

fof(f_3713_3,plain,
    ( ! [U_14660,U_14658,U_14656] :
        ( c_Relation_Ototal__on(U_14656,U_14658,U_14660)
        | ? [U_14651] :
            ( ? [U_14650] :
                ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14656,U_14656)),hAPP(hAPP(c_Product__Type_OPair(U_14656,U_14656),U_14650),U_14651)),U_14660))
                & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14656,U_14656)),hAPP(hAPP(c_Product__Type_OPair(U_14656,U_14656),U_14651),U_14650)),U_14660))
                & U_14651 != U_14650
                & hBOOL(hAPP(hAPP(c_member(U_14656),U_14650),U_14658)) )
            & hBOOL(hAPP(hAPP(c_member(U_14656),U_14651),U_14658)) ) )
    & ! [U_14659,U_14657,U_14655] :
        ( ! [U_14649] :
            ( ! [U_14648] :
                ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14655,U_14655)),hAPP(hAPP(c_Product__Type_OPair(U_14655,U_14655),U_14648),U_14649)),U_14659))
                | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14655,U_14655)),hAPP(hAPP(c_Product__Type_OPair(U_14655,U_14655),U_14649),U_14648)),U_14659))
                | U_14649 = U_14648
                | ~ hBOOL(hAPP(hAPP(c_member(U_14655),U_14648),U_14657)) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_14655),U_14649),U_14657)) )
        | ~ c_Relation_Ototal__on(U_14655,U_14657,U_14659) ) ),
    inference(miniscope,[status(thm)],[f_3713_2]) ).

fof(f_3713_4,plain,
    ( ! [U_14660,U_14658,U_14656] :
        ( c_Relation_Ototal__on(U_14656,U_14658,U_14660)
        | ( ? [U_14650] :
              ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14656,U_14656)),hAPP(hAPP(c_Product__Type_OPair(U_14656,U_14656),U_14650),sK369(U_14660,U_14658,U_14656))),U_14660))
              & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14656,U_14656)),hAPP(hAPP(c_Product__Type_OPair(U_14656,U_14656),sK369(U_14660,U_14658,U_14656)),U_14650)),U_14660))
              & sK369(U_14660,U_14658,U_14656) != U_14650
              & hBOOL(hAPP(hAPP(c_member(U_14656),U_14650),U_14658)) )
          & hBOOL(hAPP(hAPP(c_member(U_14656),sK369(U_14660,U_14658,U_14656)),U_14658)) ) )
    & ! [U_14659,U_14657,U_14655] :
        ( ! [U_14649] :
            ( ! [U_14648] :
                ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14655,U_14655)),hAPP(hAPP(c_Product__Type_OPair(U_14655,U_14655),U_14648),U_14649)),U_14659))
                | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14655,U_14655)),hAPP(hAPP(c_Product__Type_OPair(U_14655,U_14655),U_14649),U_14648)),U_14659))
                | U_14649 = U_14648
                | ~ hBOOL(hAPP(hAPP(c_member(U_14655),U_14648),U_14657)) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_14655),U_14649),U_14657)) )
        | ~ c_Relation_Ototal__on(U_14655,U_14657,U_14659) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK369]),skolemize(U_14651,sK369(U_14660,U_14658,U_14656))],[f_3713_3]) ).

fof(f_3713_5,plain,
    ( ! [U_14660,U_14658,U_14656] :
        ( c_Relation_Ototal__on(U_14656,U_14658,U_14660)
        | ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14656,U_14656)),hAPP(hAPP(c_Product__Type_OPair(U_14656,U_14656),sK370(U_14660,U_14658,U_14656)),sK369(U_14660,U_14658,U_14656))),U_14660))
          & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14656,U_14656)),hAPP(hAPP(c_Product__Type_OPair(U_14656,U_14656),sK369(U_14660,U_14658,U_14656)),sK370(U_14660,U_14658,U_14656))),U_14660))
          & sK369(U_14660,U_14658,U_14656) != sK370(U_14660,U_14658,U_14656)
          & hBOOL(hAPP(hAPP(c_member(U_14656),sK370(U_14660,U_14658,U_14656)),U_14658))
          & hBOOL(hAPP(hAPP(c_member(U_14656),sK369(U_14660,U_14658,U_14656)),U_14658)) ) )
    & ! [U_14659,U_14657,U_14655] :
        ( ! [U_14649] :
            ( ! [U_14648] :
                ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14655,U_14655)),hAPP(hAPP(c_Product__Type_OPair(U_14655,U_14655),U_14648),U_14649)),U_14659))
                | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14655,U_14655)),hAPP(hAPP(c_Product__Type_OPair(U_14655,U_14655),U_14649),U_14648)),U_14659))
                | U_14649 = U_14648
                | ~ hBOOL(hAPP(hAPP(c_member(U_14655),U_14648),U_14657)) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_14655),U_14649),U_14657)) )
        | ~ c_Relation_Ototal__on(U_14655,U_14657,U_14659) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK370]),skolemize(U_14650,sK370(U_14660,U_14658,U_14656))],[f_3713_4]) ).

cnf(f_3713_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14655,U_14655)),hAPP(hAPP(c_Product__Type_OPair(U_14655,U_14655),U_14648),U_14649)),U_14659))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14655,U_14655)),hAPP(hAPP(c_Product__Type_OPair(U_14655,U_14655),U_14649),U_14648)),U_14659))
    | U_14649 = U_14648
    | ~ hBOOL(hAPP(hAPP(c_member(U_14655),U_14648),U_14657))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14655),U_14649),U_14657))
    | ~ c_Relation_Ototal__on(U_14655,U_14657,U_14659) ),
    inference(clausify,[status(thm)],[f_3713_5]) ).

cnf(f_3713_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14656),sK369(U_14660,U_14658,U_14656)),U_14658))
    | c_Relation_Ototal__on(U_14656,U_14658,U_14660) ),
    inference(clausify,[status(thm)],[f_3713_5]) ).

cnf(f_3713_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14656),sK370(U_14660,U_14658,U_14656)),U_14658))
    | c_Relation_Ototal__on(U_14656,U_14658,U_14660) ),
    inference(clausify,[status(thm)],[f_3713_5]) ).

cnf(f_3713_9,plain,
    ( sK369(U_14660,U_14658,U_14656) != sK370(U_14660,U_14658,U_14656)
    | c_Relation_Ototal__on(U_14656,U_14658,U_14660) ),
    inference(clausify,[status(thm)],[f_3713_5]) ).

cnf(f_3713_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14656,U_14656)),hAPP(hAPP(c_Product__Type_OPair(U_14656,U_14656),sK369(U_14660,U_14658,U_14656)),sK370(U_14660,U_14658,U_14656))),U_14660))
    | c_Relation_Ototal__on(U_14656,U_14658,U_14660) ),
    inference(clausify,[status(thm)],[f_3713_5]) ).

cnf(f_3713_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14656,U_14656)),hAPP(hAPP(c_Product__Type_OPair(U_14656,U_14656),sK370(U_14660,U_14658,U_14656)),sK369(U_14660,U_14658,U_14656))),U_14660))
    | c_Relation_Ototal__on(U_14656,U_14658,U_14660) ),
    inference(clausify,[status(thm)],[f_3713_5]) ).

fof(f_3714_1,plain,
    ! [V_z_2,V_y_2,V_x_2,V_r_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_z_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
      | ~ c_Relation_Osingle__valued(T_b,T_b,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_single__valued__confluent]) ).

fof(f_3714_2,plain,
    ! [U_14665,U_14664,U_14663,U_14662,U_14661] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14661,U_14661)),hAPP(hAPP(c_Product__Type_OPair(U_14661,U_14661),U_14665),U_14664)),c_Transitive__Closure_Ortrancl(U_14661,U_14662)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14661,U_14661)),hAPP(hAPP(c_Product__Type_OPair(U_14661,U_14661),U_14664),U_14665)),c_Transitive__Closure_Ortrancl(U_14661,U_14662)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14661,U_14661)),hAPP(hAPP(c_Product__Type_OPair(U_14661,U_14661),U_14663),U_14665)),c_Transitive__Closure_Ortrancl(U_14661,U_14662)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14661,U_14661)),hAPP(hAPP(c_Product__Type_OPair(U_14661,U_14661),U_14663),U_14664)),c_Transitive__Closure_Ortrancl(U_14661,U_14662)))
      | ~ c_Relation_Osingle__valued(U_14661,U_14661,U_14662) ),
    inference(variable_rename,[status(thm)],[f_3714_1]) ).

cnf(f_3714_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14661,U_14661)),hAPP(hAPP(c_Product__Type_OPair(U_14661,U_14661),U_14665),U_14664)),c_Transitive__Closure_Ortrancl(U_14661,U_14662)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14661,U_14661)),hAPP(hAPP(c_Product__Type_OPair(U_14661,U_14661),U_14664),U_14665)),c_Transitive__Closure_Ortrancl(U_14661,U_14662)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14661,U_14661)),hAPP(hAPP(c_Product__Type_OPair(U_14661,U_14661),U_14663),U_14665)),c_Transitive__Closure_Ortrancl(U_14661,U_14662)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14661,U_14661)),hAPP(hAPP(c_Product__Type_OPair(U_14661,U_14661),U_14663),U_14664)),c_Transitive__Closure_Ortrancl(U_14661,U_14662)))
    | ~ c_Relation_Osingle__valued(U_14661,U_14661,U_14662) ),
    inference(clausify,[status(thm)],[f_3714_2]) ).

fof(f_3715_1,plain,
    ! [V_B_2,V_A_2,V_R_2,T_c,T_b] :
      ( hAPP(c_Relation_OImage(T_c,T_b,V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_B_2))
      | ~ c_Relation_Osingle__valued(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_R_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Image__Int__eq]) ).

fof(f_3715_2,plain,
    ! [U_14670,U_14669,U_14668,U_14667,U_14666] :
      ( hAPP(c_Relation_OImage(U_14667,U_14666,U_14668),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14667,tc_HOL_Obool)),U_14669),U_14670)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14666,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_14667,U_14666,U_14668),U_14669)),hAPP(c_Relation_OImage(U_14667,U_14666,U_14668),U_14670))
      | ~ c_Relation_Osingle__valued(U_14666,U_14667,hAPP(c_Relation_Oconverse(U_14667,U_14666),U_14668)) ),
    inference(variable_rename,[status(thm)],[f_3715_1]) ).

cnf(f_3715_3,plain,
    ( hAPP(c_Relation_OImage(U_14667,U_14666,U_14668),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14667,tc_HOL_Obool)),U_14669),U_14670)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14666,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_14667,U_14666,U_14668),U_14669)),hAPP(c_Relation_OImage(U_14667,U_14666,U_14668),U_14670))
    | ~ c_Relation_Osingle__valued(U_14666,U_14667,hAPP(c_Relation_Oconverse(U_14667,U_14666),U_14668)) ),
    inference(clausify,[status(thm)],[f_3715_2]) ).

fof(f_3716_1,plain,
    ! [V_R_2,V_p_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) ),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__imp__UN__rel__pow]) ).

fof(f_3716_2,plain,
    ! [U_14673,U_14672,U_14671] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14671,U_14671)),U_14672),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(U_14671,U_14671),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(U_14671,U_14671),tc_HOL_Obool),tc_fun(tc_prod(U_14671,U_14671),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(U_14671,U_14671),tc_HOL_Obool)),U_14673))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14671,U_14671)),U_14672),c_Transitive__Closure_Ortrancl(U_14671,U_14673))) ),
    inference(variable_rename,[status(thm)],[f_3716_1]) ).

cnf(f_3716_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14671,U_14671)),U_14672),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(U_14671,U_14671),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(U_14671,U_14671),tc_HOL_Obool),tc_fun(tc_prod(U_14671,U_14671),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(U_14671,U_14671),tc_HOL_Obool)),U_14673))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14671,U_14671)),U_14672),c_Transitive__Closure_Ortrancl(U_14671,U_14673))) ),
    inference(clausify,[status(thm)],[f_3716_2]) ).

fof(f_3717_1,plain,
    ! [V_r_2,T_b] :
      ( c_Wellfounded_Oacyclic(T_b,V_r_2)
      | ? [B_x] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_acyclicI]) ).

fof(f_3717_2,plain,
    ! [U_14676,U_14675] :
      ( c_Wellfounded_Oacyclic(U_14675,U_14676)
      | ? [U_14674] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_14675,U_14675)),hAPP(hAPP(c_Product__Type_OPair(U_14675,U_14675),U_14674),U_14674)),c_Transitive__Closure_Otrancl(U_14675,U_14676))) ),
    inference(variable_rename,[status(thm)],[f_3717_1]) ).

fof(f_3717_3,plain,
    ! [U_14676,U_14675] :
      ( c_Wellfounded_Oacyclic(U_14675,U_14676)
      | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14675,U_14675)),hAPP(hAPP(c_Product__Type_OPair(U_14675,U_14675),sK371(U_14676,U_14675)),sK371(U_14676,U_14675))),c_Transitive__Closure_Otrancl(U_14675,U_14676))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK371]),skolemize(U_14674,sK371(U_14676,U_14675))],[f_3717_2]) ).

cnf(f_3717_4,plain,
    ( c_Wellfounded_Oacyclic(U_14675,U_14676)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14675,U_14675)),hAPP(hAPP(c_Product__Type_OPair(U_14675,U_14675),sK371(U_14676,U_14675)),sK371(U_14676,U_14675))),c_Transitive__Closure_Otrancl(U_14675,U_14676))) ),
    inference(clausify,[status(thm)],[f_3717_3]) ).

fof(f_3718_1,plain,
    ! [V_n_2,V_R_2,T_b] :
      ( c_Relation_Osingle__valued(T_b,T_b,hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2))
      | ~ c_Relation_Osingle__valued(T_b,T_b,V_R_2) ),
    inference(fof_nnf,[status(thm)],[fact_single__valued__rel__pow]) ).

fof(f_3718_2,plain,
    ! [U_14679,U_14678,U_14677] :
      ( c_Relation_Osingle__valued(U_14677,U_14677,hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14677,U_14677),tc_HOL_Obool),U_14679),U_14678))
      | ~ c_Relation_Osingle__valued(U_14677,U_14677,U_14678) ),
    inference(variable_rename,[status(thm)],[f_3718_1]) ).

cnf(f_3718_3,plain,
    ( c_Relation_Osingle__valued(U_14677,U_14677,hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14677,U_14677),tc_HOL_Obool),U_14679),U_14678))
    | ~ c_Relation_Osingle__valued(U_14677,U_14677,U_14678) ),
    inference(clausify,[status(thm)],[f_3718_2]) ).

fof(f_3719_1,plain,
    ! [V_f_2,V_n_2,T_c,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_fun(T_b,T_c),tc_fun(T_b,T_c)),V_n_2),c_Fun_Ocomp(T_c,T_c,T_b,V_f_2)) = c_Fun_Ocomp(T_c,T_c,T_b,hAPP(hAPP(c_Nat_Ocompow(T_c,T_c),V_n_2),V_f_2)),
    inference(fof_nnf,[status(thm)],[fact_comp__funpow]) ).

fof(f_3719_2,plain,
    ! [U_14683,U_14682,U_14681,U_14680] : hAPP(hAPP(c_Nat_Ocompow(tc_fun(U_14680,U_14681),tc_fun(U_14680,U_14681)),U_14682),c_Fun_Ocomp(U_14681,U_14681,U_14680,U_14683)) = c_Fun_Ocomp(U_14681,U_14681,U_14680,hAPP(hAPP(c_Nat_Ocompow(U_14681,U_14681),U_14682),U_14683)),
    inference(variable_rename,[status(thm)],[f_3719_1]) ).

cnf(f_3719_3,plain,
    hAPP(hAPP(c_Nat_Ocompow(tc_fun(U_14680,U_14681),tc_fun(U_14680,U_14681)),U_14682),c_Fun_Ocomp(U_14681,U_14681,U_14680,U_14683)) = c_Fun_Ocomp(U_14681,U_14681,U_14680,hAPP(hAPP(c_Nat_Ocompow(U_14681,U_14681),U_14682),U_14683)),
    inference(clausify,[status(thm)],[f_3719_2]) ).

fof(f_3720_1,plain,
    ! [V_x_2,V_n_2,T_b,V_f_2] : hAPP(V_f_2,hAPP(hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),V_f_2),V_x_2)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),V_f_2),hAPP(V_f_2,V_x_2)),
    inference(fof_nnf,[status(thm)],[fact_funpow__swap1]) ).

fof(f_3720_2,plain,
    ! [U_14687,U_14686,U_14685,U_14684] : hAPP(U_14684,hAPP(hAPP(hAPP(c_Nat_Ocompow(U_14685,U_14685),U_14686),U_14684),U_14687)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(U_14685,U_14685),U_14686),U_14684),hAPP(U_14684,U_14687)),
    inference(variable_rename,[status(thm)],[f_3720_1]) ).

cnf(f_3720_3,plain,
    hAPP(U_14684,hAPP(hAPP(hAPP(c_Nat_Ocompow(U_14685,U_14685),U_14686),U_14684),U_14687)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(U_14685,U_14685),U_14686),U_14684),hAPP(U_14684,U_14687)),
    inference(clausify,[status(thm)],[f_3720_2]) ).

fof(f_3721_1,plain,
    ! [V_f_2,V_m_2,V_n_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_m_2),V_f_2)) = hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)),V_f_2),
    inference(fof_nnf,[status(thm)],[fact_funpow__mult]) ).

fof(f_3721_2,plain,
    ! [U_14691,U_14690,U_14689,U_14688] : hAPP(hAPP(c_Nat_Ocompow(U_14688,U_14688),U_14689),hAPP(hAPP(c_Nat_Ocompow(U_14688,U_14688),U_14690),U_14691)) = hAPP(hAPP(c_Nat_Ocompow(U_14688,U_14688),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_14690),U_14689)),U_14691),
    inference(variable_rename,[status(thm)],[f_3721_1]) ).

cnf(f_3721_3,plain,
    hAPP(hAPP(c_Nat_Ocompow(U_14688,U_14688),U_14689),hAPP(hAPP(c_Nat_Ocompow(U_14688,U_14688),U_14690),U_14691)) = hAPP(hAPP(c_Nat_Ocompow(U_14688,U_14688),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_14690),U_14689)),U_14691),
    inference(clausify,[status(thm)],[f_3721_2]) ).

fof(f_3722_1,plain,
    ! [V_R_2,V_n_2,T_b] :
      ( c_Wellfounded_Owf(T_b,V_R_2)
      | ~ c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)) ),
    inference(fof_nnf,[status(thm)],[fact_wf__exp]) ).

fof(f_3722_2,plain,
    ! [U_14694,U_14693,U_14692] :
      ( c_Wellfounded_Owf(U_14692,U_14694)
      | ~ c_Wellfounded_Owf(U_14692,hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14692,U_14692),tc_HOL_Obool),U_14693),U_14694)) ),
    inference(variable_rename,[status(thm)],[f_3722_1]) ).

cnf(f_3722_3,plain,
    ( c_Wellfounded_Owf(U_14692,U_14694)
    | ~ c_Wellfounded_Owf(U_14692,hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14692,U_14692),tc_HOL_Obool),U_14693),U_14694)) ),
    inference(clausify,[status(thm)],[f_3722_2]) ).

fof(f_3723_1,plain,
    ! [V_n_2,V_R_2,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)),V_R_2),
    inference(fof_nnf,[status(thm)],[fact_rel__pow__commute]) ).

fof(f_3723_2,plain,
    ! [U_14697,U_14696,U_14695] : hAPP(hAPP(c_Relation_Orel__comp(U_14695,U_14695,U_14695),U_14696),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14695,U_14695),tc_HOL_Obool),U_14697),U_14696)) = hAPP(hAPP(c_Relation_Orel__comp(U_14695,U_14695,U_14695),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14695,U_14695),tc_HOL_Obool),U_14697),U_14696)),U_14696),
    inference(variable_rename,[status(thm)],[f_3723_1]) ).

cnf(f_3723_3,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_14695,U_14695,U_14695),U_14696),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14695,U_14695),tc_HOL_Obool),U_14697),U_14696)) = hAPP(hAPP(c_Relation_Orel__comp(U_14695,U_14695,U_14695),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14695,U_14695),tc_HOL_Obool),U_14697),U_14696)),U_14696),
    inference(clausify,[status(thm)],[f_3723_2]) ).

fof(f_3724_1,plain,
    ! [V_R_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_R_2) = V_R_2,
    inference(fof_nnf,[status(thm)],[fact_rel__pow__1]) ).

fof(f_3724_2,plain,
    ! [U_14699,U_14698] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14698,U_14698),tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_14699) = U_14699,
    inference(variable_rename,[status(thm)],[f_3724_1]) ).

cnf(f_3724_3,plain,
    hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14698,U_14698),tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_14699) = U_14699,
    inference(clausify,[status(thm)],[f_3724_2]) ).

fof(f_3725_1,plain,
    ! [V_R_2,V_p_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
        | ! [B_n] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),B_n),V_R_2))) )
      & ( ? [B_n] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),B_n),V_R_2)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__power]) ).

fof(f_3725_2,plain,
    ! [U_14704,U_14703,U_14702] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14702,U_14702)),U_14703),c_Transitive__Closure_Ortrancl(U_14702,U_14704)))
        | ! [U_14701] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14702,U_14702)),U_14703),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14702,U_14702),tc_HOL_Obool),U_14701),U_14704))) )
      & ( ? [U_14700] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_14702,U_14702)),U_14703),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14702,U_14702),tc_HOL_Obool),U_14700),U_14704)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14702,U_14702)),U_14703),c_Transitive__Closure_Ortrancl(U_14702,U_14704))) ) ),
    inference(variable_rename,[status(thm)],[f_3725_1]) ).

fof(f_3725_3,plain,
    ( ! [U_14710,U_14708,U_14706] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14706,U_14706)),U_14708),c_Transitive__Closure_Ortrancl(U_14706,U_14710)))
        | ! [U_14701] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14706,U_14706)),U_14708),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14706,U_14706),tc_HOL_Obool),U_14701),U_14710))) )
    & ! [U_14709,U_14707,U_14705] :
        ( ? [U_14700] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_14705,U_14705)),U_14707),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14705,U_14705),tc_HOL_Obool),U_14700),U_14709)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14705,U_14705)),U_14707),c_Transitive__Closure_Ortrancl(U_14705,U_14709))) ) ),
    inference(miniscope,[status(thm)],[f_3725_2]) ).

fof(f_3725_4,plain,
    ( ! [U_14710,U_14708,U_14706] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14706,U_14706)),U_14708),c_Transitive__Closure_Ortrancl(U_14706,U_14710)))
        | ! [U_14701] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14706,U_14706)),U_14708),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14706,U_14706),tc_HOL_Obool),U_14701),U_14710))) )
    & ! [U_14709,U_14707,U_14705] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14705,U_14705)),U_14707),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14705,U_14705),tc_HOL_Obool),sK372(U_14709,U_14707,U_14705)),U_14709)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14705,U_14705)),U_14707),c_Transitive__Closure_Ortrancl(U_14705,U_14709))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK372]),skolemize(U_14700,sK372(U_14709,U_14707,U_14705))],[f_3725_3]) ).

cnf(f_3725_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14705,U_14705)),U_14707),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14705,U_14705),tc_HOL_Obool),sK372(U_14709,U_14707,U_14705)),U_14709)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14705,U_14705)),U_14707),c_Transitive__Closure_Ortrancl(U_14705,U_14709))) ),
    inference(clausify,[status(thm)],[f_3725_4]) ).

cnf(f_3725_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14706,U_14706)),U_14708),c_Transitive__Closure_Ortrancl(U_14706,U_14710)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14706,U_14706)),U_14708),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14706,U_14706),tc_HOL_Obool),U_14701),U_14710))) ),
    inference(clausify,[status(thm)],[f_3725_4]) ).

fof(f_3726_1,plain,
    ! [V_R_2,V_n_2,V_p_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2))) ),
    inference(fof_nnf,[status(thm)],[fact_rel__pow__imp__rtrancl]) ).

fof(f_3726_2,plain,
    ! [U_14714,U_14713,U_14712,U_14711] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14711,U_14711)),U_14712),c_Transitive__Closure_Ortrancl(U_14711,U_14714)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14711,U_14711)),U_14712),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14711,U_14711),tc_HOL_Obool),U_14713),U_14714))) ),
    inference(variable_rename,[status(thm)],[f_3726_1]) ).

cnf(f_3726_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14711,U_14711)),U_14712),c_Transitive__Closure_Ortrancl(U_14711,U_14714)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14711,U_14711)),U_14712),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14711,U_14711),tc_HOL_Obool),U_14713),U_14714))) ),
    inference(clausify,[status(thm)],[f_3726_2]) ).

fof(f_3727_1,plain,
    ! [V_R_2,V_n_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)),V_R_2),
    inference(fof_nnf,[status(thm)],[fact_relpow_Osimps_I2_J]) ).

fof(f_3727_2,plain,
    ! [U_14717,U_14716,U_14715] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14715,U_14715),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_14716)),U_14717) = hAPP(hAPP(c_Relation_Orel__comp(U_14715,U_14715,U_14715),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14715,U_14715),tc_HOL_Obool),U_14716),U_14717)),U_14717),
    inference(variable_rename,[status(thm)],[f_3727_1]) ).

cnf(f_3727_3,plain,
    hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14715,U_14715),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_14716)),U_14717) = hAPP(hAPP(c_Relation_Orel__comp(U_14715,U_14715,U_14715),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14715,U_14715),tc_HOL_Obool),U_14716),U_14717)),U_14717),
    inference(clausify,[status(thm)],[f_3727_2]) ).

fof(f_3728_1,plain,
    ! [V_R_2,V_n_2,V_m_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)),V_R_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_m_2),V_R_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)),
    inference(fof_nnf,[status(thm)],[fact_rel__pow__add]) ).

fof(f_3728_2,plain,
    ! [U_14721,U_14720,U_14719,U_14718] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14718,U_14718),tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_14719),U_14720)),U_14721) = hAPP(hAPP(c_Relation_Orel__comp(U_14718,U_14718,U_14718),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14718,U_14718),tc_HOL_Obool),U_14719),U_14721)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14718,U_14718),tc_HOL_Obool),U_14720),U_14721)),
    inference(variable_rename,[status(thm)],[f_3728_1]) ).

cnf(f_3728_3,plain,
    hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14718,U_14718),tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_14719),U_14720)),U_14721) = hAPP(hAPP(c_Relation_Orel__comp(U_14718,U_14718,U_14718),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14718,U_14718),tc_HOL_Obool),U_14719),U_14721)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14718,U_14718),tc_HOL_Obool),U_14720),U_14721)),
    inference(clausify,[status(thm)],[f_3728_2]) ).

fof(f_3729_1,plain,
    ! [V_R_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_R_2) = c_Relation_OId(T_b),
    inference(fof_nnf,[status(thm)],[fact_relpow_Osimps_I1_J]) ).

fof(f_3729_2,plain,
    ! [U_14723,U_14722] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14722,U_14722),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_14723) = c_Relation_OId(U_14722),
    inference(variable_rename,[status(thm)],[f_3729_1]) ).

cnf(f_3729_3,plain,
    hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14722,U_14722),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_14723) = c_Relation_OId(U_14722),
    inference(clausify,[status(thm)],[f_3729_2]) ).

fof(f_3730_1,plain,
    ! [V_R_2,V_y_2,V_x_2,T_b] :
      ( V_x_2 = V_y_2
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_R_2))) ),
    inference(fof_nnf,[status(thm)],[fact_rel__pow__0__E]) ).

fof(f_3730_2,plain,
    ! [U_14727,U_14726,U_14725,U_14724] :
      ( U_14725 = U_14726
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14724,U_14724)),hAPP(hAPP(c_Product__Type_OPair(U_14724,U_14724),U_14725),U_14726)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14724,U_14724),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_14727))) ),
    inference(variable_rename,[status(thm)],[f_3730_1]) ).

fof(f_3730_3,plain,
    ! [U_14727,U_14726,U_14725] :
      ( ! [U_14724] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14724,U_14724)),hAPP(hAPP(c_Product__Type_OPair(U_14724,U_14724),U_14725),U_14726)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14724,U_14724),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_14727)))
      | U_14725 = U_14726 ),
    inference(miniscope,[status(thm)],[f_3730_2]) ).

cnf(f_3730_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14724,U_14724)),hAPP(hAPP(c_Product__Type_OPair(U_14724,U_14724),U_14725),U_14726)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14724,U_14724),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_14727)))
    | U_14725 = U_14726 ),
    inference(clausify,[status(thm)],[f_3730_3]) ).

fof(f_3731_1,plain,
    ! [V_R_2,V_x_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_R_2))),
    inference(fof_nnf,[status(thm)],[fact_rel__pow__0__I]) ).

fof(f_3731_2,plain,
    ! [U_14730,U_14729,U_14728] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_14728,U_14728)),hAPP(hAPP(c_Product__Type_OPair(U_14728,U_14728),U_14729),U_14729)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14728,U_14728),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_14730))),
    inference(variable_rename,[status(thm)],[f_3731_1]) ).

cnf(f_3731_3,plain,
    hBOOL(hAPP(hAPP(c_member(tc_prod(U_14728,U_14728)),hAPP(hAPP(c_Product__Type_OPair(U_14728,U_14728),U_14729),U_14729)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14728,U_14728),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_14730))),
    inference(clausify,[status(thm)],[f_3731_2]) ).

fof(f_3732_1,plain,
    ! [V_n_2,V_z_2,V_R_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_R_2)) ),
    inference(fof_nnf,[status(thm)],[fact_rel__pow__Suc__I2]) ).

fof(f_3732_2,plain,
    ! [U_14736,U_14735,U_14734,U_14733,U_14732,U_14731] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14731,U_14731)),hAPP(hAPP(c_Product__Type_OPair(U_14731,U_14731),U_14732),U_14735)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14731,U_14731),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_14736)),U_14734)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14731,U_14731)),hAPP(hAPP(c_Product__Type_OPair(U_14731,U_14731),U_14733),U_14735)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14731,U_14731),tc_HOL_Obool),U_14736),U_14734)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14731,U_14731)),hAPP(hAPP(c_Product__Type_OPair(U_14731,U_14731),U_14732),U_14733)),U_14734)) ),
    inference(variable_rename,[status(thm)],[f_3732_1]) ).

cnf(f_3732_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14731,U_14731)),hAPP(hAPP(c_Product__Type_OPair(U_14731,U_14731),U_14732),U_14735)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14731,U_14731),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_14736)),U_14734)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14731,U_14731)),hAPP(hAPP(c_Product__Type_OPair(U_14731,U_14731),U_14733),U_14735)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14731,U_14731),tc_HOL_Obool),U_14736),U_14734)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14731,U_14731)),hAPP(hAPP(c_Product__Type_OPair(U_14731,U_14731),U_14732),U_14733)),U_14734)) ),
    inference(clausify,[status(thm)],[f_3732_2]) ).

fof(f_3733_1,plain,
    ! [V_z_2,V_R_2,V_n_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),V_R_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2))) ),
    inference(fof_nnf,[status(thm)],[fact_rel__pow__Suc__I]) ).

fof(f_3733_2,plain,
    ! [U_14742,U_14741,U_14740,U_14739,U_14738,U_14737] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14737,U_14737)),hAPP(hAPP(c_Product__Type_OPair(U_14737,U_14737),U_14738),U_14742)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14737,U_14737),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_14740)),U_14741)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14737,U_14737)),hAPP(hAPP(c_Product__Type_OPair(U_14737,U_14737),U_14739),U_14742)),U_14741))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14737,U_14737)),hAPP(hAPP(c_Product__Type_OPair(U_14737,U_14737),U_14738),U_14739)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14737,U_14737),tc_HOL_Obool),U_14740),U_14741))) ),
    inference(variable_rename,[status(thm)],[f_3733_1]) ).

cnf(f_3733_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14737,U_14737)),hAPP(hAPP(c_Product__Type_OPair(U_14737,U_14737),U_14738),U_14742)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14737,U_14737),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_14740)),U_14741)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14737,U_14737)),hAPP(hAPP(c_Product__Type_OPair(U_14737,U_14737),U_14739),U_14742)),U_14741))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14737,U_14737)),hAPP(hAPP(c_Product__Type_OPair(U_14737,U_14737),U_14738),U_14739)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14737,U_14737),tc_HOL_Obool),U_14740),U_14741))) ),
    inference(clausify,[status(thm)],[f_3733_2]) ).

fof(f_3734_1,plain,
    ! [V_f_2,V_n_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),hAPP(c_Nat_OSuc,V_n_2)),V_f_2) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,V_f_2),hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),V_f_2)),
    inference(fof_nnf,[status(thm)],[fact_funpow_Osimps_I2_J]) ).

fof(f_3734_2,plain,
    ! [U_14745,U_14744,U_14743] : hAPP(hAPP(c_Nat_Ocompow(U_14743,U_14743),hAPP(c_Nat_OSuc,U_14744)),U_14745) = hAPP(c_Fun_Ocomp(U_14743,U_14743,U_14743,U_14745),hAPP(hAPP(c_Nat_Ocompow(U_14743,U_14743),U_14744),U_14745)),
    inference(variable_rename,[status(thm)],[f_3734_1]) ).

cnf(f_3734_3,plain,
    hAPP(hAPP(c_Nat_Ocompow(U_14743,U_14743),hAPP(c_Nat_OSuc,U_14744)),U_14745) = hAPP(c_Fun_Ocomp(U_14743,U_14743,U_14743,U_14745),hAPP(hAPP(c_Nat_Ocompow(U_14743,U_14743),U_14744),U_14745)),
    inference(clausify,[status(thm)],[f_3734_2]) ).

fof(f_3735_1,plain,
    ! [V_f_2,V_n_2,V_m_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)),V_f_2) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_m_2),V_f_2)),hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),V_f_2)),
    inference(fof_nnf,[status(thm)],[fact_funpow__add]) ).

fof(f_3735_2,plain,
    ! [U_14749,U_14748,U_14747,U_14746] : hAPP(hAPP(c_Nat_Ocompow(U_14746,U_14746),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_14747),U_14748)),U_14749) = hAPP(c_Fun_Ocomp(U_14746,U_14746,U_14746,hAPP(hAPP(c_Nat_Ocompow(U_14746,U_14746),U_14747),U_14749)),hAPP(hAPP(c_Nat_Ocompow(U_14746,U_14746),U_14748),U_14749)),
    inference(variable_rename,[status(thm)],[f_3735_1]) ).

cnf(f_3735_3,plain,
    hAPP(hAPP(c_Nat_Ocompow(U_14746,U_14746),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_14747),U_14748)),U_14749) = hAPP(c_Fun_Ocomp(U_14746,U_14746,U_14746,hAPP(hAPP(c_Nat_Ocompow(U_14746,U_14746),U_14747),U_14749)),hAPP(hAPP(c_Nat_Ocompow(U_14746,U_14746),U_14748),U_14749)),
    inference(clausify,[status(thm)],[f_3735_2]) ).

fof(f_3736_1,plain,
    ! [V_f_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_f_2) = c_Fun_Oid(T_b),
    inference(fof_nnf,[status(thm)],[fact_funpow_Osimps_I1_J]) ).

fof(f_3736_2,plain,
    ! [U_14751,U_14750] : hAPP(hAPP(c_Nat_Ocompow(U_14750,U_14750),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_14751) = c_Fun_Oid(U_14750),
    inference(variable_rename,[status(thm)],[f_3736_1]) ).

cnf(f_3736_3,plain,
    hAPP(hAPP(c_Nat_Ocompow(U_14750,U_14750),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_14751) = c_Fun_Oid(U_14750),
    inference(clausify,[status(thm)],[f_3736_2]) ).

fof(f_3737_1,plain,
    ! [V_R_2,V_p_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_R_2)))
        | ! [B_n] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),B_n),V_R_2)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)) ) )
      & ( ? [B_n] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),B_n),V_R_2)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_R_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_trancl__power]) ).

fof(f_3737_2,plain,
    ! [U_14756,U_14755,U_14754] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14754,U_14754)),U_14755),c_Transitive__Closure_Otrancl(U_14754,U_14756)))
        | ! [U_14753] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14754,U_14754)),U_14755),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14754,U_14754),tc_HOL_Obool),U_14753),U_14756)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_14753)) ) )
      & ( ? [U_14752] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14754,U_14754)),U_14755),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14754,U_14754),tc_HOL_Obool),U_14752),U_14756)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_14752)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14754,U_14754)),U_14755),c_Transitive__Closure_Otrancl(U_14754,U_14756))) ) ),
    inference(variable_rename,[status(thm)],[f_3737_1]) ).

fof(f_3737_3,plain,
    ( ! [U_14762,U_14760,U_14758] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14758,U_14758)),U_14760),c_Transitive__Closure_Otrancl(U_14758,U_14762)))
        | ! [U_14753] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14758,U_14758)),U_14760),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14758,U_14758),tc_HOL_Obool),U_14753),U_14762)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_14753)) ) )
    & ! [U_14761,U_14759,U_14757] :
        ( ? [U_14752] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14757,U_14757)),U_14759),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14757,U_14757),tc_HOL_Obool),U_14752),U_14761)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_14752)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14757,U_14757)),U_14759),c_Transitive__Closure_Otrancl(U_14757,U_14761))) ) ),
    inference(miniscope,[status(thm)],[f_3737_2]) ).

fof(f_3737_4,plain,
    ( ! [U_14762,U_14760,U_14758] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14758,U_14758)),U_14760),c_Transitive__Closure_Otrancl(U_14758,U_14762)))
        | ! [U_14753] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14758,U_14758)),U_14760),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14758,U_14758),tc_HOL_Obool),U_14753),U_14762)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_14753)) ) )
    & ! [U_14761,U_14759,U_14757] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14757,U_14757)),U_14759),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14757,U_14757),tc_HOL_Obool),sK373(U_14761,U_14759,U_14757)),U_14761)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK373(U_14761,U_14759,U_14757))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14757,U_14757)),U_14759),c_Transitive__Closure_Otrancl(U_14757,U_14761))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK373]),skolemize(U_14752,sK373(U_14761,U_14759,U_14757))],[f_3737_3]) ).

cnf(f_3737_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK373(U_14761,U_14759,U_14757)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14757,U_14757)),U_14759),c_Transitive__Closure_Otrancl(U_14757,U_14761))) ),
    inference(clausify,[status(thm)],[f_3737_4]) ).

cnf(f_3737_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14757,U_14757)),U_14759),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14757,U_14757),tc_HOL_Obool),sK373(U_14761,U_14759,U_14757)),U_14761)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14757,U_14757)),U_14759),c_Transitive__Closure_Otrancl(U_14757,U_14761))) ),
    inference(clausify,[status(thm)],[f_3737_4]) ).

cnf(f_3737_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14758,U_14758)),U_14760),c_Transitive__Closure_Otrancl(U_14758,U_14762)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14758,U_14758)),U_14760),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14758,U_14758),tc_HOL_Obool),U_14753),U_14762)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_14753)) ),
    inference(clausify,[status(thm)],[f_3737_4]) ).

fof(f_3738_1,plain,
    ! [V_R_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,V_R_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2)),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__is__UN__rel__pow]) ).

fof(f_3738_2,plain,
    ! [U_14764,U_14763] : c_Transitive__Closure_Ortrancl(U_14763,U_14764) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(U_14763,U_14763),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(U_14763,U_14763),tc_HOL_Obool),tc_fun(tc_prod(U_14763,U_14763),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(U_14763,U_14763),tc_HOL_Obool)),U_14764)),
    inference(variable_rename,[status(thm)],[f_3738_1]) ).

cnf(f_3738_3,plain,
    c_Transitive__Closure_Ortrancl(U_14763,U_14764) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(U_14763,U_14763),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(U_14763,U_14763),tc_HOL_Obool),tc_fun(tc_prod(U_14763,U_14763),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(U_14763,U_14763),tc_HOL_Obool)),U_14764)),
    inference(clausify,[status(thm)],[f_3738_2]) ).

fof(f_3739_1,plain,
    ! [T_b] : c_Nat_Ofunpow(T_b) = c_Nat_Ocompow(T_b,T_b),
    inference(fof_nnf,[status(thm)],[fact_funpow__code__def]) ).

fof(f_3739_2,plain,
    ! [U_14765] : c_Nat_Ofunpow(U_14765) = c_Nat_Ocompow(U_14765,U_14765),
    inference(variable_rename,[status(thm)],[f_3739_1]) ).

cnf(f_3739_3,plain,
    c_Nat_Ofunpow(U_14765) = c_Nat_Ocompow(U_14765,U_14765),
    inference(clausify,[status(thm)],[f_3739_2]) ).

fof(f_3740_1,plain,
    ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
      ( ? [B_y,B_m] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),B_m),V_R_2)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),V_R_2))
          & V_n_2 = hAPP(c_Nat_OSuc,B_m) )
      | ( V_x_2 = V_z_2
        & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2))) ),
    inference(fof_nnf,[status(thm)],[fact_rel__pow__E2]) ).

fof(f_3740_2,plain,
    ! [U_14772,U_14771,U_14770,U_14769,U_14768] :
      ( ? [U_14767,U_14766] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14768,U_14768)),hAPP(hAPP(c_Product__Type_OPair(U_14768,U_14768),U_14767),U_14770)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14768,U_14768),tc_HOL_Obool),U_14766),U_14772)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14768,U_14768)),hAPP(hAPP(c_Product__Type_OPair(U_14768,U_14768),U_14769),U_14767)),U_14772))
          & U_14771 = hAPP(c_Nat_OSuc,U_14766) )
      | ( U_14769 = U_14770
        & U_14771 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14768,U_14768)),hAPP(hAPP(c_Product__Type_OPair(U_14768,U_14768),U_14769),U_14770)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14768,U_14768),tc_HOL_Obool),U_14771),U_14772))) ),
    inference(variable_rename,[status(thm)],[f_3740_1]) ).

fof(f_3740_3,plain,
    ! [U_14772,U_14771,U_14770,U_14769,U_14768] :
      ( ? [U_14766] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14768,U_14768)),hAPP(hAPP(c_Product__Type_OPair(U_14768,U_14768),sK374(U_14772,U_14771,U_14770,U_14769,U_14768)),U_14770)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14768,U_14768),tc_HOL_Obool),U_14766),U_14772)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14768,U_14768)),hAPP(hAPP(c_Product__Type_OPair(U_14768,U_14768),U_14769),sK374(U_14772,U_14771,U_14770,U_14769,U_14768))),U_14772))
          & U_14771 = hAPP(c_Nat_OSuc,U_14766) )
      | ( U_14769 = U_14770
        & U_14771 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14768,U_14768)),hAPP(hAPP(c_Product__Type_OPair(U_14768,U_14768),U_14769),U_14770)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14768,U_14768),tc_HOL_Obool),U_14771),U_14772))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK374]),skolemize(U_14767,sK374(U_14772,U_14771,U_14770,U_14769,U_14768))],[f_3740_2]) ).

fof(f_3740_4,plain,
    ! [U_14772,U_14771,U_14770,U_14769,U_14768] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14768,U_14768)),hAPP(hAPP(c_Product__Type_OPair(U_14768,U_14768),sK374(U_14772,U_14771,U_14770,U_14769,U_14768)),U_14770)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14768,U_14768),tc_HOL_Obool),sK375(U_14772,U_14771,U_14770,U_14769,U_14768)),U_14772)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14768,U_14768)),hAPP(hAPP(c_Product__Type_OPair(U_14768,U_14768),U_14769),sK374(U_14772,U_14771,U_14770,U_14769,U_14768))),U_14772))
        & U_14771 = hAPP(c_Nat_OSuc,sK375(U_14772,U_14771,U_14770,U_14769,U_14768)) )
      | ( U_14769 = U_14770
        & U_14771 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14768,U_14768)),hAPP(hAPP(c_Product__Type_OPair(U_14768,U_14768),U_14769),U_14770)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14768,U_14768),tc_HOL_Obool),U_14771),U_14772))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK375]),skolemize(U_14766,sK375(U_14772,U_14771,U_14770,U_14769,U_14768))],[f_3740_3]) ).

cnf(f_3740_5,plain,
    ( U_14771 = hAPP(c_Nat_OSuc,sK375(U_14772,U_14771,U_14770,U_14769,U_14768))
    | U_14771 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14768,U_14768)),hAPP(hAPP(c_Product__Type_OPair(U_14768,U_14768),U_14769),U_14770)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14768,U_14768),tc_HOL_Obool),U_14771),U_14772))) ),
    inference(clausify,[status(thm)],[f_3740_4]) ).

cnf(f_3740_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14768,U_14768)),hAPP(hAPP(c_Product__Type_OPair(U_14768,U_14768),U_14769),sK374(U_14772,U_14771,U_14770,U_14769,U_14768))),U_14772))
    | U_14771 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14768,U_14768)),hAPP(hAPP(c_Product__Type_OPair(U_14768,U_14768),U_14769),U_14770)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14768,U_14768),tc_HOL_Obool),U_14771),U_14772))) ),
    inference(clausify,[status(thm)],[f_3740_4]) ).

cnf(f_3740_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14768,U_14768)),hAPP(hAPP(c_Product__Type_OPair(U_14768,U_14768),sK374(U_14772,U_14771,U_14770,U_14769,U_14768)),U_14770)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14768,U_14768),tc_HOL_Obool),sK375(U_14772,U_14771,U_14770,U_14769,U_14768)),U_14772)))
    | U_14771 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14768,U_14768)),hAPP(hAPP(c_Product__Type_OPair(U_14768,U_14768),U_14769),U_14770)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14768,U_14768),tc_HOL_Obool),U_14771),U_14772))) ),
    inference(clausify,[status(thm)],[f_3740_4]) ).

cnf(f_3740_8,plain,
    ( U_14771 = hAPP(c_Nat_OSuc,sK375(U_14772,U_14771,U_14770,U_14769,U_14768))
    | U_14769 = U_14770
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14768,U_14768)),hAPP(hAPP(c_Product__Type_OPair(U_14768,U_14768),U_14769),U_14770)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14768,U_14768),tc_HOL_Obool),U_14771),U_14772))) ),
    inference(clausify,[status(thm)],[f_3740_4]) ).

cnf(f_3740_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14768,U_14768)),hAPP(hAPP(c_Product__Type_OPair(U_14768,U_14768),U_14769),sK374(U_14772,U_14771,U_14770,U_14769,U_14768))),U_14772))
    | U_14769 = U_14770
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14768,U_14768)),hAPP(hAPP(c_Product__Type_OPair(U_14768,U_14768),U_14769),U_14770)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14768,U_14768),tc_HOL_Obool),U_14771),U_14772))) ),
    inference(clausify,[status(thm)],[f_3740_4]) ).

cnf(f_3740_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14768,U_14768)),hAPP(hAPP(c_Product__Type_OPair(U_14768,U_14768),sK374(U_14772,U_14771,U_14770,U_14769,U_14768)),U_14770)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14768,U_14768),tc_HOL_Obool),sK375(U_14772,U_14771,U_14770,U_14769,U_14768)),U_14772)))
    | U_14769 = U_14770
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14768,U_14768)),hAPP(hAPP(c_Product__Type_OPair(U_14768,U_14768),U_14769),U_14770)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14768,U_14768),tc_HOL_Obool),U_14771),U_14772))) ),
    inference(clausify,[status(thm)],[f_3740_4]) ).

fof(f_3741_1,plain,
    ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
      ( ? [B_y,B_m] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),V_R_2))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),B_m),V_R_2)))
          & V_n_2 = hAPP(c_Nat_OSuc,B_m) )
      | ( V_x_2 = V_z_2
        & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2))) ),
    inference(fof_nnf,[status(thm)],[fact_rel__pow__E]) ).

fof(f_3741_2,plain,
    ! [U_14779,U_14778,U_14777,U_14776,U_14775] :
      ( ? [U_14774,U_14773] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14775,U_14775)),hAPP(hAPP(c_Product__Type_OPair(U_14775,U_14775),U_14774),U_14777)),U_14779))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14775,U_14775)),hAPP(hAPP(c_Product__Type_OPair(U_14775,U_14775),U_14776),U_14774)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14775,U_14775),tc_HOL_Obool),U_14773),U_14779)))
          & U_14778 = hAPP(c_Nat_OSuc,U_14773) )
      | ( U_14776 = U_14777
        & U_14778 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14775,U_14775)),hAPP(hAPP(c_Product__Type_OPair(U_14775,U_14775),U_14776),U_14777)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14775,U_14775),tc_HOL_Obool),U_14778),U_14779))) ),
    inference(variable_rename,[status(thm)],[f_3741_1]) ).

fof(f_3741_3,plain,
    ! [U_14779,U_14778,U_14777,U_14776,U_14775] :
      ( ? [U_14773] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14775,U_14775)),hAPP(hAPP(c_Product__Type_OPair(U_14775,U_14775),sK376(U_14779,U_14778,U_14777,U_14776,U_14775)),U_14777)),U_14779))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14775,U_14775)),hAPP(hAPP(c_Product__Type_OPair(U_14775,U_14775),U_14776),sK376(U_14779,U_14778,U_14777,U_14776,U_14775))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14775,U_14775),tc_HOL_Obool),U_14773),U_14779)))
          & U_14778 = hAPP(c_Nat_OSuc,U_14773) )
      | ( U_14776 = U_14777
        & U_14778 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14775,U_14775)),hAPP(hAPP(c_Product__Type_OPair(U_14775,U_14775),U_14776),U_14777)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14775,U_14775),tc_HOL_Obool),U_14778),U_14779))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK376]),skolemize(U_14774,sK376(U_14779,U_14778,U_14777,U_14776,U_14775))],[f_3741_2]) ).

fof(f_3741_4,plain,
    ! [U_14779,U_14778,U_14777,U_14776,U_14775] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14775,U_14775)),hAPP(hAPP(c_Product__Type_OPair(U_14775,U_14775),sK376(U_14779,U_14778,U_14777,U_14776,U_14775)),U_14777)),U_14779))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14775,U_14775)),hAPP(hAPP(c_Product__Type_OPair(U_14775,U_14775),U_14776),sK376(U_14779,U_14778,U_14777,U_14776,U_14775))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14775,U_14775),tc_HOL_Obool),sK377(U_14779,U_14778,U_14777,U_14776,U_14775)),U_14779)))
        & U_14778 = hAPP(c_Nat_OSuc,sK377(U_14779,U_14778,U_14777,U_14776,U_14775)) )
      | ( U_14776 = U_14777
        & U_14778 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14775,U_14775)),hAPP(hAPP(c_Product__Type_OPair(U_14775,U_14775),U_14776),U_14777)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14775,U_14775),tc_HOL_Obool),U_14778),U_14779))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK377]),skolemize(U_14773,sK377(U_14779,U_14778,U_14777,U_14776,U_14775))],[f_3741_3]) ).

cnf(f_3741_5,plain,
    ( U_14778 = hAPP(c_Nat_OSuc,sK377(U_14779,U_14778,U_14777,U_14776,U_14775))
    | U_14778 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14775,U_14775)),hAPP(hAPP(c_Product__Type_OPair(U_14775,U_14775),U_14776),U_14777)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14775,U_14775),tc_HOL_Obool),U_14778),U_14779))) ),
    inference(clausify,[status(thm)],[f_3741_4]) ).

cnf(f_3741_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14775,U_14775)),hAPP(hAPP(c_Product__Type_OPair(U_14775,U_14775),U_14776),sK376(U_14779,U_14778,U_14777,U_14776,U_14775))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14775,U_14775),tc_HOL_Obool),sK377(U_14779,U_14778,U_14777,U_14776,U_14775)),U_14779)))
    | U_14778 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14775,U_14775)),hAPP(hAPP(c_Product__Type_OPair(U_14775,U_14775),U_14776),U_14777)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14775,U_14775),tc_HOL_Obool),U_14778),U_14779))) ),
    inference(clausify,[status(thm)],[f_3741_4]) ).

cnf(f_3741_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14775,U_14775)),hAPP(hAPP(c_Product__Type_OPair(U_14775,U_14775),sK376(U_14779,U_14778,U_14777,U_14776,U_14775)),U_14777)),U_14779))
    | U_14778 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14775,U_14775)),hAPP(hAPP(c_Product__Type_OPair(U_14775,U_14775),U_14776),U_14777)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14775,U_14775),tc_HOL_Obool),U_14778),U_14779))) ),
    inference(clausify,[status(thm)],[f_3741_4]) ).

cnf(f_3741_8,plain,
    ( U_14778 = hAPP(c_Nat_OSuc,sK377(U_14779,U_14778,U_14777,U_14776,U_14775))
    | U_14776 = U_14777
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14775,U_14775)),hAPP(hAPP(c_Product__Type_OPair(U_14775,U_14775),U_14776),U_14777)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14775,U_14775),tc_HOL_Obool),U_14778),U_14779))) ),
    inference(clausify,[status(thm)],[f_3741_4]) ).

cnf(f_3741_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14775,U_14775)),hAPP(hAPP(c_Product__Type_OPair(U_14775,U_14775),U_14776),sK376(U_14779,U_14778,U_14777,U_14776,U_14775))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14775,U_14775),tc_HOL_Obool),sK377(U_14779,U_14778,U_14777,U_14776,U_14775)),U_14779)))
    | U_14776 = U_14777
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14775,U_14775)),hAPP(hAPP(c_Product__Type_OPair(U_14775,U_14775),U_14776),U_14777)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14775,U_14775),tc_HOL_Obool),U_14778),U_14779))) ),
    inference(clausify,[status(thm)],[f_3741_4]) ).

cnf(f_3741_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14775,U_14775)),hAPP(hAPP(c_Product__Type_OPair(U_14775,U_14775),sK376(U_14779,U_14778,U_14777,U_14776,U_14775)),U_14777)),U_14779))
    | U_14776 = U_14777
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14775,U_14775)),hAPP(hAPP(c_Product__Type_OPair(U_14775,U_14775),U_14776),U_14777)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14775,U_14775),tc_HOL_Obool),U_14778),U_14779))) ),
    inference(clausify,[status(thm)],[f_3741_4]) ).

fof(f_3742_1,plain,
    ! [V_Q_2,V_P_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_P_2)))
      | ? [B_x] :
          ( ? [B_y] :
              ( B_x != B_y
              & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_Q_2)) )
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),B_x)),c_Transitive__Closure_Ortrancl(T_b,V_P_2))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2),V_Q_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__Un__separatorE]) ).

fof(f_3742_2,plain,
    ! [U_14786,U_14785,U_14784,U_14783,U_14782] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14782,U_14782)),hAPP(hAPP(c_Product__Type_OPair(U_14782,U_14782),U_14783),U_14784)),c_Transitive__Closure_Ortrancl(U_14782,U_14785)))
      | ? [U_14781] :
          ( ? [U_14780] :
              ( U_14781 != U_14780
              & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14782,U_14782)),hAPP(hAPP(c_Product__Type_OPair(U_14782,U_14782),U_14781),U_14780)),U_14786)) )
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14782,U_14782)),hAPP(hAPP(c_Product__Type_OPair(U_14782,U_14782),U_14783),U_14781)),c_Transitive__Closure_Ortrancl(U_14782,U_14785))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14782,U_14782)),hAPP(hAPP(c_Product__Type_OPair(U_14782,U_14782),U_14783),U_14784)),c_Transitive__Closure_Ortrancl(U_14782,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14782,U_14782),tc_HOL_Obool)),U_14785),U_14786)))) ),
    inference(variable_rename,[status(thm)],[f_3742_1]) ).

fof(f_3742_3,plain,
    ! [U_14786,U_14785,U_14784,U_14783,U_14782] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14782,U_14782)),hAPP(hAPP(c_Product__Type_OPair(U_14782,U_14782),U_14783),U_14784)),c_Transitive__Closure_Ortrancl(U_14782,U_14785)))
      | ( ? [U_14780] :
            ( sK378(U_14786,U_14785,U_14784,U_14783,U_14782) != U_14780
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14782,U_14782)),hAPP(hAPP(c_Product__Type_OPair(U_14782,U_14782),sK378(U_14786,U_14785,U_14784,U_14783,U_14782)),U_14780)),U_14786)) )
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14782,U_14782)),hAPP(hAPP(c_Product__Type_OPair(U_14782,U_14782),U_14783),sK378(U_14786,U_14785,U_14784,U_14783,U_14782))),c_Transitive__Closure_Ortrancl(U_14782,U_14785))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14782,U_14782)),hAPP(hAPP(c_Product__Type_OPair(U_14782,U_14782),U_14783),U_14784)),c_Transitive__Closure_Ortrancl(U_14782,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14782,U_14782),tc_HOL_Obool)),U_14785),U_14786)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK378]),skolemize(U_14781,sK378(U_14786,U_14785,U_14784,U_14783,U_14782))],[f_3742_2]) ).

fof(f_3742_4,plain,
    ! [U_14786,U_14785,U_14784,U_14783,U_14782] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14782,U_14782)),hAPP(hAPP(c_Product__Type_OPair(U_14782,U_14782),U_14783),U_14784)),c_Transitive__Closure_Ortrancl(U_14782,U_14785)))
      | ( sK378(U_14786,U_14785,U_14784,U_14783,U_14782) != sK379(U_14786,U_14785,U_14784,U_14783,U_14782)
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14782,U_14782)),hAPP(hAPP(c_Product__Type_OPair(U_14782,U_14782),sK378(U_14786,U_14785,U_14784,U_14783,U_14782)),sK379(U_14786,U_14785,U_14784,U_14783,U_14782))),U_14786))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14782,U_14782)),hAPP(hAPP(c_Product__Type_OPair(U_14782,U_14782),U_14783),sK378(U_14786,U_14785,U_14784,U_14783,U_14782))),c_Transitive__Closure_Ortrancl(U_14782,U_14785))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14782,U_14782)),hAPP(hAPP(c_Product__Type_OPair(U_14782,U_14782),U_14783),U_14784)),c_Transitive__Closure_Ortrancl(U_14782,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14782,U_14782),tc_HOL_Obool)),U_14785),U_14786)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK379]),skolemize(U_14780,sK379(U_14786,U_14785,U_14784,U_14783,U_14782))],[f_3742_3]) ).

cnf(f_3742_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14782,U_14782)),hAPP(hAPP(c_Product__Type_OPair(U_14782,U_14782),U_14783),sK378(U_14786,U_14785,U_14784,U_14783,U_14782))),c_Transitive__Closure_Ortrancl(U_14782,U_14785)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14782,U_14782)),hAPP(hAPP(c_Product__Type_OPair(U_14782,U_14782),U_14783),U_14784)),c_Transitive__Closure_Ortrancl(U_14782,U_14785)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14782,U_14782)),hAPP(hAPP(c_Product__Type_OPair(U_14782,U_14782),U_14783),U_14784)),c_Transitive__Closure_Ortrancl(U_14782,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14782,U_14782),tc_HOL_Obool)),U_14785),U_14786)))) ),
    inference(clausify,[status(thm)],[f_3742_4]) ).

cnf(f_3742_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14782,U_14782)),hAPP(hAPP(c_Product__Type_OPair(U_14782,U_14782),sK378(U_14786,U_14785,U_14784,U_14783,U_14782)),sK379(U_14786,U_14785,U_14784,U_14783,U_14782))),U_14786))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14782,U_14782)),hAPP(hAPP(c_Product__Type_OPair(U_14782,U_14782),U_14783),U_14784)),c_Transitive__Closure_Ortrancl(U_14782,U_14785)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14782,U_14782)),hAPP(hAPP(c_Product__Type_OPair(U_14782,U_14782),U_14783),U_14784)),c_Transitive__Closure_Ortrancl(U_14782,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14782,U_14782),tc_HOL_Obool)),U_14785),U_14786)))) ),
    inference(clausify,[status(thm)],[f_3742_4]) ).

cnf(f_3742_7,plain,
    ( sK378(U_14786,U_14785,U_14784,U_14783,U_14782) != sK379(U_14786,U_14785,U_14784,U_14783,U_14782)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14782,U_14782)),hAPP(hAPP(c_Product__Type_OPair(U_14782,U_14782),U_14783),U_14784)),c_Transitive__Closure_Ortrancl(U_14782,U_14785)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14782,U_14782)),hAPP(hAPP(c_Product__Type_OPair(U_14782,U_14782),U_14783),U_14784)),c_Transitive__Closure_Ortrancl(U_14782,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14782,U_14782),tc_HOL_Obool)),U_14785),U_14786)))) ),
    inference(clausify,[status(thm)],[f_3742_4]) ).

fof(f_3743_1,plain,
    ! [V_Q_2,V_P_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_P_2)))
      | ? [B_x] :
          ( ? [B_y] :
              ( B_y != B_x
              & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_x)),V_Q_2)) )
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_P_2))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2),V_Q_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__Un__separator__converseE]) ).

fof(f_3743_2,plain,
    ! [U_14793,U_14792,U_14791,U_14790,U_14789] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14789,U_14789)),hAPP(hAPP(c_Product__Type_OPair(U_14789,U_14789),U_14790),U_14791)),c_Transitive__Closure_Ortrancl(U_14789,U_14792)))
      | ? [U_14788] :
          ( ? [U_14787] :
              ( U_14787 != U_14788
              & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14789,U_14789)),hAPP(hAPP(c_Product__Type_OPair(U_14789,U_14789),U_14787),U_14788)),U_14793)) )
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14789,U_14789)),hAPP(hAPP(c_Product__Type_OPair(U_14789,U_14789),U_14788),U_14791)),c_Transitive__Closure_Ortrancl(U_14789,U_14792))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14789,U_14789)),hAPP(hAPP(c_Product__Type_OPair(U_14789,U_14789),U_14790),U_14791)),c_Transitive__Closure_Ortrancl(U_14789,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14789,U_14789),tc_HOL_Obool)),U_14792),U_14793)))) ),
    inference(variable_rename,[status(thm)],[f_3743_1]) ).

fof(f_3743_3,plain,
    ! [U_14793,U_14792,U_14791,U_14790,U_14789] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14789,U_14789)),hAPP(hAPP(c_Product__Type_OPair(U_14789,U_14789),U_14790),U_14791)),c_Transitive__Closure_Ortrancl(U_14789,U_14792)))
      | ( ? [U_14787] :
            ( U_14787 != sK380(U_14793,U_14792,U_14791,U_14790,U_14789)
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14789,U_14789)),hAPP(hAPP(c_Product__Type_OPair(U_14789,U_14789),U_14787),sK380(U_14793,U_14792,U_14791,U_14790,U_14789))),U_14793)) )
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14789,U_14789)),hAPP(hAPP(c_Product__Type_OPair(U_14789,U_14789),sK380(U_14793,U_14792,U_14791,U_14790,U_14789)),U_14791)),c_Transitive__Closure_Ortrancl(U_14789,U_14792))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14789,U_14789)),hAPP(hAPP(c_Product__Type_OPair(U_14789,U_14789),U_14790),U_14791)),c_Transitive__Closure_Ortrancl(U_14789,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14789,U_14789),tc_HOL_Obool)),U_14792),U_14793)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK380]),skolemize(U_14788,sK380(U_14793,U_14792,U_14791,U_14790,U_14789))],[f_3743_2]) ).

fof(f_3743_4,plain,
    ! [U_14793,U_14792,U_14791,U_14790,U_14789] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14789,U_14789)),hAPP(hAPP(c_Product__Type_OPair(U_14789,U_14789),U_14790),U_14791)),c_Transitive__Closure_Ortrancl(U_14789,U_14792)))
      | ( sK381(U_14793,U_14792,U_14791,U_14790,U_14789) != sK380(U_14793,U_14792,U_14791,U_14790,U_14789)
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14789,U_14789)),hAPP(hAPP(c_Product__Type_OPair(U_14789,U_14789),sK381(U_14793,U_14792,U_14791,U_14790,U_14789)),sK380(U_14793,U_14792,U_14791,U_14790,U_14789))),U_14793))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14789,U_14789)),hAPP(hAPP(c_Product__Type_OPair(U_14789,U_14789),sK380(U_14793,U_14792,U_14791,U_14790,U_14789)),U_14791)),c_Transitive__Closure_Ortrancl(U_14789,U_14792))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14789,U_14789)),hAPP(hAPP(c_Product__Type_OPair(U_14789,U_14789),U_14790),U_14791)),c_Transitive__Closure_Ortrancl(U_14789,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14789,U_14789),tc_HOL_Obool)),U_14792),U_14793)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK381]),skolemize(U_14787,sK381(U_14793,U_14792,U_14791,U_14790,U_14789))],[f_3743_3]) ).

cnf(f_3743_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14789,U_14789)),hAPP(hAPP(c_Product__Type_OPair(U_14789,U_14789),sK380(U_14793,U_14792,U_14791,U_14790,U_14789)),U_14791)),c_Transitive__Closure_Ortrancl(U_14789,U_14792)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14789,U_14789)),hAPP(hAPP(c_Product__Type_OPair(U_14789,U_14789),U_14790),U_14791)),c_Transitive__Closure_Ortrancl(U_14789,U_14792)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14789,U_14789)),hAPP(hAPP(c_Product__Type_OPair(U_14789,U_14789),U_14790),U_14791)),c_Transitive__Closure_Ortrancl(U_14789,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14789,U_14789),tc_HOL_Obool)),U_14792),U_14793)))) ),
    inference(clausify,[status(thm)],[f_3743_4]) ).

cnf(f_3743_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14789,U_14789)),hAPP(hAPP(c_Product__Type_OPair(U_14789,U_14789),sK381(U_14793,U_14792,U_14791,U_14790,U_14789)),sK380(U_14793,U_14792,U_14791,U_14790,U_14789))),U_14793))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14789,U_14789)),hAPP(hAPP(c_Product__Type_OPair(U_14789,U_14789),U_14790),U_14791)),c_Transitive__Closure_Ortrancl(U_14789,U_14792)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14789,U_14789)),hAPP(hAPP(c_Product__Type_OPair(U_14789,U_14789),U_14790),U_14791)),c_Transitive__Closure_Ortrancl(U_14789,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14789,U_14789),tc_HOL_Obool)),U_14792),U_14793)))) ),
    inference(clausify,[status(thm)],[f_3743_4]) ).

cnf(f_3743_7,plain,
    ( sK381(U_14793,U_14792,U_14791,U_14790,U_14789) != sK380(U_14793,U_14792,U_14791,U_14790,U_14789)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14789,U_14789)),hAPP(hAPP(c_Product__Type_OPair(U_14789,U_14789),U_14790),U_14791)),c_Transitive__Closure_Ortrancl(U_14789,U_14792)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14789,U_14789)),hAPP(hAPP(c_Product__Type_OPair(U_14789,U_14789),U_14790),U_14791)),c_Transitive__Closure_Ortrancl(U_14789,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14789,U_14789),tc_HOL_Obool)),U_14792),U_14793)))) ),
    inference(clausify,[status(thm)],[f_3743_4]) ).

fof(f_3744_1,plain,
    ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
      ( ? [B_y] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),V_R_2))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) ),
    inference(fof_nnf,[status(thm)],[fact_rel__pow__Suc__E]) ).

fof(f_3744_2,plain,
    ! [U_14799,U_14798,U_14797,U_14796,U_14795] :
      ( ? [U_14794] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14795,U_14795)),hAPP(hAPP(c_Product__Type_OPair(U_14795,U_14795),U_14794),U_14797)),U_14799))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14795,U_14795)),hAPP(hAPP(c_Product__Type_OPair(U_14795,U_14795),U_14796),U_14794)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14795,U_14795),tc_HOL_Obool),U_14798),U_14799))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14795,U_14795)),hAPP(hAPP(c_Product__Type_OPair(U_14795,U_14795),U_14796),U_14797)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14795,U_14795),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_14798)),U_14799))) ),
    inference(variable_rename,[status(thm)],[f_3744_1]) ).

fof(f_3744_3,plain,
    ! [U_14799,U_14798,U_14797,U_14796,U_14795] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14795,U_14795)),hAPP(hAPP(c_Product__Type_OPair(U_14795,U_14795),sK382(U_14799,U_14798,U_14797,U_14796,U_14795)),U_14797)),U_14799))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14795,U_14795)),hAPP(hAPP(c_Product__Type_OPair(U_14795,U_14795),U_14796),sK382(U_14799,U_14798,U_14797,U_14796,U_14795))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14795,U_14795),tc_HOL_Obool),U_14798),U_14799))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14795,U_14795)),hAPP(hAPP(c_Product__Type_OPair(U_14795,U_14795),U_14796),U_14797)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14795,U_14795),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_14798)),U_14799))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK382]),skolemize(U_14794,sK382(U_14799,U_14798,U_14797,U_14796,U_14795))],[f_3744_2]) ).

cnf(f_3744_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14795,U_14795)),hAPP(hAPP(c_Product__Type_OPair(U_14795,U_14795),U_14796),sK382(U_14799,U_14798,U_14797,U_14796,U_14795))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14795,U_14795),tc_HOL_Obool),U_14798),U_14799)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14795,U_14795)),hAPP(hAPP(c_Product__Type_OPair(U_14795,U_14795),U_14796),U_14797)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14795,U_14795),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_14798)),U_14799))) ),
    inference(clausify,[status(thm)],[f_3744_3]) ).

cnf(f_3744_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14795,U_14795)),hAPP(hAPP(c_Product__Type_OPair(U_14795,U_14795),sK382(U_14799,U_14798,U_14797,U_14796,U_14795)),U_14797)),U_14799))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14795,U_14795)),hAPP(hAPP(c_Product__Type_OPair(U_14795,U_14795),U_14796),U_14797)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14795,U_14795),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_14798)),U_14799))) ),
    inference(clausify,[status(thm)],[f_3744_3]) ).

fof(f_3745_1,plain,
    ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
      ( ? [B_y] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),V_R_2)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) ),
    inference(fof_nnf,[status(thm)],[fact_rel__pow__Suc__D2]) ).

fof(f_3745_2,plain,
    ! [U_14805,U_14804,U_14803,U_14802,U_14801] :
      ( ? [U_14800] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14801,U_14801)),hAPP(hAPP(c_Product__Type_OPair(U_14801,U_14801),U_14800),U_14803)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14801,U_14801),tc_HOL_Obool),U_14804),U_14805)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14801,U_14801)),hAPP(hAPP(c_Product__Type_OPair(U_14801,U_14801),U_14802),U_14800)),U_14805)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14801,U_14801)),hAPP(hAPP(c_Product__Type_OPair(U_14801,U_14801),U_14802),U_14803)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14801,U_14801),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_14804)),U_14805))) ),
    inference(variable_rename,[status(thm)],[f_3745_1]) ).

fof(f_3745_3,plain,
    ! [U_14805,U_14804,U_14803,U_14802,U_14801] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14801,U_14801)),hAPP(hAPP(c_Product__Type_OPair(U_14801,U_14801),sK383(U_14805,U_14804,U_14803,U_14802,U_14801)),U_14803)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14801,U_14801),tc_HOL_Obool),U_14804),U_14805)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14801,U_14801)),hAPP(hAPP(c_Product__Type_OPair(U_14801,U_14801),U_14802),sK383(U_14805,U_14804,U_14803,U_14802,U_14801))),U_14805)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14801,U_14801)),hAPP(hAPP(c_Product__Type_OPair(U_14801,U_14801),U_14802),U_14803)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14801,U_14801),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_14804)),U_14805))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK383]),skolemize(U_14800,sK383(U_14805,U_14804,U_14803,U_14802,U_14801))],[f_3745_2]) ).

cnf(f_3745_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14801,U_14801)),hAPP(hAPP(c_Product__Type_OPair(U_14801,U_14801),U_14802),sK383(U_14805,U_14804,U_14803,U_14802,U_14801))),U_14805))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14801,U_14801)),hAPP(hAPP(c_Product__Type_OPair(U_14801,U_14801),U_14802),U_14803)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14801,U_14801),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_14804)),U_14805))) ),
    inference(clausify,[status(thm)],[f_3745_3]) ).

cnf(f_3745_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14801,U_14801)),hAPP(hAPP(c_Product__Type_OPair(U_14801,U_14801),sK383(U_14805,U_14804,U_14803,U_14802,U_14801)),U_14803)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14801,U_14801),tc_HOL_Obool),U_14804),U_14805)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14801,U_14801)),hAPP(hAPP(c_Product__Type_OPair(U_14801,U_14801),U_14802),U_14803)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14801,U_14801),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_14804)),U_14805))) ),
    inference(clausify,[status(thm)],[f_3745_3]) ).

fof(f_3746_1,plain,
    ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
      ( ? [B_y] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),V_R_2)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) ),
    inference(fof_nnf,[status(thm)],[fact_rel__pow__Suc__E2]) ).

fof(f_3746_2,plain,
    ! [U_14811,U_14810,U_14809,U_14808,U_14807] :
      ( ? [U_14806] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14807,U_14807)),hAPP(hAPP(c_Product__Type_OPair(U_14807,U_14807),U_14806),U_14809)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14807,U_14807),tc_HOL_Obool),U_14810),U_14811)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14807,U_14807)),hAPP(hAPP(c_Product__Type_OPair(U_14807,U_14807),U_14808),U_14806)),U_14811)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14807,U_14807)),hAPP(hAPP(c_Product__Type_OPair(U_14807,U_14807),U_14808),U_14809)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14807,U_14807),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_14810)),U_14811))) ),
    inference(variable_rename,[status(thm)],[f_3746_1]) ).

fof(f_3746_3,plain,
    ! [U_14811,U_14810,U_14809,U_14808,U_14807] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14807,U_14807)),hAPP(hAPP(c_Product__Type_OPair(U_14807,U_14807),sK384(U_14811,U_14810,U_14809,U_14808,U_14807)),U_14809)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14807,U_14807),tc_HOL_Obool),U_14810),U_14811)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14807,U_14807)),hAPP(hAPP(c_Product__Type_OPair(U_14807,U_14807),U_14808),sK384(U_14811,U_14810,U_14809,U_14808,U_14807))),U_14811)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14807,U_14807)),hAPP(hAPP(c_Product__Type_OPair(U_14807,U_14807),U_14808),U_14809)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14807,U_14807),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_14810)),U_14811))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK384]),skolemize(U_14806,sK384(U_14811,U_14810,U_14809,U_14808,U_14807))],[f_3746_2]) ).

cnf(f_3746_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14807,U_14807)),hAPP(hAPP(c_Product__Type_OPair(U_14807,U_14807),U_14808),sK384(U_14811,U_14810,U_14809,U_14808,U_14807))),U_14811))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14807,U_14807)),hAPP(hAPP(c_Product__Type_OPair(U_14807,U_14807),U_14808),U_14809)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14807,U_14807),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_14810)),U_14811))) ),
    inference(clausify,[status(thm)],[f_3746_3]) ).

cnf(f_3746_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14807,U_14807)),hAPP(hAPP(c_Product__Type_OPair(U_14807,U_14807),sK384(U_14811,U_14810,U_14809,U_14808,U_14807)),U_14809)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14807,U_14807),tc_HOL_Obool),U_14810),U_14811)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14807,U_14807)),hAPP(hAPP(c_Product__Type_OPair(U_14807,U_14807),U_14808),U_14809)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14807,U_14807),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_14810)),U_14811))) ),
    inference(clausify,[status(thm)],[f_3746_3]) ).

fof(f_3747_1,plain,
    ! [V_R_2,V_y_2,V_x_2,T_b] :
      ( ? [B_z] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_z),V_y_2)),V_R_2))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_z)),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2))) ),
    inference(fof_nnf,[status(thm)],[fact_tranclD2]) ).

fof(f_3747_2,plain,
    ! [U_14816,U_14815,U_14814,U_14813] :
      ( ? [U_14812] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14813,U_14813)),hAPP(hAPP(c_Product__Type_OPair(U_14813,U_14813),U_14812),U_14815)),U_14816))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14813,U_14813)),hAPP(hAPP(c_Product__Type_OPair(U_14813,U_14813),U_14814),U_14812)),c_Transitive__Closure_Ortrancl(U_14813,U_14816))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14813,U_14813)),hAPP(hAPP(c_Product__Type_OPair(U_14813,U_14813),U_14814),U_14815)),c_Transitive__Closure_Otrancl(U_14813,U_14816))) ),
    inference(variable_rename,[status(thm)],[f_3747_1]) ).

fof(f_3747_3,plain,
    ! [U_14816,U_14815,U_14814,U_14813] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14813,U_14813)),hAPP(hAPP(c_Product__Type_OPair(U_14813,U_14813),sK385(U_14816,U_14815,U_14814,U_14813)),U_14815)),U_14816))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14813,U_14813)),hAPP(hAPP(c_Product__Type_OPair(U_14813,U_14813),U_14814),sK385(U_14816,U_14815,U_14814,U_14813))),c_Transitive__Closure_Ortrancl(U_14813,U_14816))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14813,U_14813)),hAPP(hAPP(c_Product__Type_OPair(U_14813,U_14813),U_14814),U_14815)),c_Transitive__Closure_Otrancl(U_14813,U_14816))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK385]),skolemize(U_14812,sK385(U_14816,U_14815,U_14814,U_14813))],[f_3747_2]) ).

cnf(f_3747_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14813,U_14813)),hAPP(hAPP(c_Product__Type_OPair(U_14813,U_14813),U_14814),sK385(U_14816,U_14815,U_14814,U_14813))),c_Transitive__Closure_Ortrancl(U_14813,U_14816)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14813,U_14813)),hAPP(hAPP(c_Product__Type_OPair(U_14813,U_14813),U_14814),U_14815)),c_Transitive__Closure_Otrancl(U_14813,U_14816))) ),
    inference(clausify,[status(thm)],[f_3747_3]) ).

cnf(f_3747_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14813,U_14813)),hAPP(hAPP(c_Product__Type_OPair(U_14813,U_14813),sK385(U_14816,U_14815,U_14814,U_14813)),U_14815)),U_14816))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14813,U_14813)),hAPP(hAPP(c_Product__Type_OPair(U_14813,U_14813),U_14814),U_14815)),c_Transitive__Closure_Otrancl(U_14813,U_14816))) ),
    inference(clausify,[status(thm)],[f_3747_3]) ).

fof(f_3748_1,plain,
    ! [V_R_2,V_y_2,V_x_2,T_b] :
      ( ? [B_z] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_z),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_z)),V_R_2)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2))) ),
    inference(fof_nnf,[status(thm)],[fact_tranclD]) ).

fof(f_3748_2,plain,
    ! [U_14821,U_14820,U_14819,U_14818] :
      ( ? [U_14817] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14818,U_14818)),hAPP(hAPP(c_Product__Type_OPair(U_14818,U_14818),U_14817),U_14820)),c_Transitive__Closure_Ortrancl(U_14818,U_14821)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14818,U_14818)),hAPP(hAPP(c_Product__Type_OPair(U_14818,U_14818),U_14819),U_14817)),U_14821)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14818,U_14818)),hAPP(hAPP(c_Product__Type_OPair(U_14818,U_14818),U_14819),U_14820)),c_Transitive__Closure_Otrancl(U_14818,U_14821))) ),
    inference(variable_rename,[status(thm)],[f_3748_1]) ).

fof(f_3748_3,plain,
    ! [U_14821,U_14820,U_14819,U_14818] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14818,U_14818)),hAPP(hAPP(c_Product__Type_OPair(U_14818,U_14818),sK386(U_14821,U_14820,U_14819,U_14818)),U_14820)),c_Transitive__Closure_Ortrancl(U_14818,U_14821)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14818,U_14818)),hAPP(hAPP(c_Product__Type_OPair(U_14818,U_14818),U_14819),sK386(U_14821,U_14820,U_14819,U_14818))),U_14821)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14818,U_14818)),hAPP(hAPP(c_Product__Type_OPair(U_14818,U_14818),U_14819),U_14820)),c_Transitive__Closure_Otrancl(U_14818,U_14821))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK386]),skolemize(U_14817,sK386(U_14821,U_14820,U_14819,U_14818))],[f_3748_2]) ).

cnf(f_3748_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14818,U_14818)),hAPP(hAPP(c_Product__Type_OPair(U_14818,U_14818),U_14819),sK386(U_14821,U_14820,U_14819,U_14818))),U_14821))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14818,U_14818)),hAPP(hAPP(c_Product__Type_OPair(U_14818,U_14818),U_14819),U_14820)),c_Transitive__Closure_Otrancl(U_14818,U_14821))) ),
    inference(clausify,[status(thm)],[f_3748_3]) ).

cnf(f_3748_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14818,U_14818)),hAPP(hAPP(c_Product__Type_OPair(U_14818,U_14818),sK386(U_14821,U_14820,U_14819,U_14818)),U_14820)),c_Transitive__Closure_Ortrancl(U_14818,U_14821)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14818,U_14818)),hAPP(hAPP(c_Product__Type_OPair(U_14818,U_14818),U_14819),U_14820)),c_Transitive__Closure_Otrancl(U_14818,U_14821))) ),
    inference(clausify,[status(thm)],[f_3748_3]) ).

fof(f_3749_1,plain,
    ! [V_p_2,T_b] :
      ( ? [B_x] : V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Relation_OId(T_b))) ),
    inference(fof_nnf,[status(thm)],[fact_IdE]) ).

fof(f_3749_2,plain,
    ! [U_14824,U_14823] :
      ( ? [U_14822] : U_14824 = hAPP(hAPP(c_Product__Type_OPair(U_14823,U_14823),U_14822),U_14822)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14823,U_14823)),U_14824),c_Relation_OId(U_14823))) ),
    inference(variable_rename,[status(thm)],[f_3749_1]) ).

fof(f_3749_3,plain,
    ! [U_14824,U_14823] :
      ( U_14824 = hAPP(hAPP(c_Product__Type_OPair(U_14823,U_14823),sK387(U_14824,U_14823)),sK387(U_14824,U_14823))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14823,U_14823)),U_14824),c_Relation_OId(U_14823))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK387]),skolemize(U_14822,sK387(U_14824,U_14823))],[f_3749_2]) ).

cnf(f_3749_4,plain,
    ( U_14824 = hAPP(hAPP(c_Product__Type_OPair(U_14823,U_14823),sK387(U_14824,U_14823)),sK387(U_14824,U_14823))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14823,U_14823)),U_14824),c_Relation_OId(U_14823))) ),
    inference(clausify,[status(thm)],[f_3749_3]) ).

fof(f_3750_1,plain,
    ! [V_P_H_2,V_P_2] :
      ( hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_P_2)) = hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_P_H_2))
      | ? [B_x] :
          ( ( ( ~ hBOOL(hAPP(V_P_2,B_x))
              & hBOOL(hAPP(V_P_H_2,B_x)) )
            | ( ~ hBOOL(hAPP(V_P_H_2,B_x))
              & hBOOL(hAPP(V_P_2,B_x)) ) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) ),
    inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__cong]) ).

fof(f_3750_2,plain,
    ! [U_14827,U_14826] :
      ( hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),U_14826)) = hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),U_14827))
      | ? [U_14825] :
          ( ( ( ~ hBOOL(hAPP(U_14826,U_14825))
              & hBOOL(hAPP(U_14827,U_14825)) )
            | ( ~ hBOOL(hAPP(U_14827,U_14825))
              & hBOOL(hAPP(U_14826,U_14825)) ) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_14825)) ) ),
    inference(variable_rename,[status(thm)],[f_3750_1]) ).

fof(f_3750_3,plain,
    ! [U_14827,U_14826] :
      ( hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),U_14826)) = hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),U_14827))
      | ( ( ( ~ hBOOL(hAPP(U_14826,sK388(U_14827,U_14826)))
            & hBOOL(hAPP(U_14827,sK388(U_14827,U_14826))) )
          | ( ~ hBOOL(hAPP(U_14827,sK388(U_14827,U_14826)))
            & hBOOL(hAPP(U_14826,sK388(U_14827,U_14826))) ) )
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK388(U_14827,U_14826))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK388]),skolemize(U_14825,sK388(U_14827,U_14826))],[f_3750_2]) ).

cnf(f_3750_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK388(U_14827,U_14826)))
    | hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),U_14826)) = hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),U_14827)) ),
    inference(clausify,[status(thm)],[f_3750_3]) ).

cnf(f_3750_5,plain,
    ( hBOOL(hAPP(U_14827,sK388(U_14827,U_14826)))
    | hBOOL(hAPP(U_14826,sK388(U_14827,U_14826)))
    | hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),U_14826)) = hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),U_14827)) ),
    inference(clausify,[status(thm)],[f_3750_3]) ).

cnf(f_3750_6,plain,
    ( ~ hBOOL(hAPP(U_14826,sK388(U_14827,U_14826)))
    | hBOOL(hAPP(U_14826,sK388(U_14827,U_14826)))
    | hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),U_14826)) = hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),U_14827)) ),
    inference(clausify,[status(thm)],[f_3750_3]) ).

cnf(f_3750_7,plain,
    ( hBOOL(hAPP(U_14827,sK388(U_14827,U_14826)))
    | ~ hBOOL(hAPP(U_14827,sK388(U_14827,U_14826)))
    | hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),U_14826)) = hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),U_14827)) ),
    inference(clausify,[status(thm)],[f_3750_3]) ).

cnf(f_3750_8,plain,
    ( ~ hBOOL(hAPP(U_14826,sK388(U_14827,U_14826)))
    | ~ hBOOL(hAPP(U_14827,sK388(U_14827,U_14826)))
    | hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),U_14826)) = hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),U_14827)) ),
    inference(clausify,[status(thm)],[f_3750_3]) ).

fof(f_3751_1,plain,
    ! [V_Q_2,V_P_2,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_P_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_OCollect(T_b),V_Q_2))))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(V_Q_2,B_x))
          & hBOOL(hAPP(V_P_2,B_x))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Int__Collect__mono]) ).

fof(f_3751_2,plain,
    ! [U_14833,U_14832,U_14831,U_14830,U_14829] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14829,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14829,tc_HOL_Obool)),U_14830),hAPP(c_Set_OCollect(U_14829),U_14832))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14829,tc_HOL_Obool)),U_14831),hAPP(c_Set_OCollect(U_14829),U_14833))))
      | ? [U_14828] :
          ( ~ hBOOL(hAPP(U_14833,U_14828))
          & hBOOL(hAPP(U_14832,U_14828))
          & hBOOL(hAPP(hAPP(c_member(U_14829),U_14828),U_14830)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14829,tc_HOL_Obool)),U_14830),U_14831)) ),
    inference(variable_rename,[status(thm)],[f_3751_1]) ).

fof(f_3751_3,plain,
    ! [U_14833,U_14832,U_14831,U_14830,U_14829] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14829,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14829,tc_HOL_Obool)),U_14830),hAPP(c_Set_OCollect(U_14829),U_14832))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14829,tc_HOL_Obool)),U_14831),hAPP(c_Set_OCollect(U_14829),U_14833))))
      | ( ~ hBOOL(hAPP(U_14833,sK389(U_14833,U_14832,U_14831,U_14830,U_14829)))
        & hBOOL(hAPP(U_14832,sK389(U_14833,U_14832,U_14831,U_14830,U_14829)))
        & hBOOL(hAPP(hAPP(c_member(U_14829),sK389(U_14833,U_14832,U_14831,U_14830,U_14829)),U_14830)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14829,tc_HOL_Obool)),U_14830),U_14831)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK389]),skolemize(U_14828,sK389(U_14833,U_14832,U_14831,U_14830,U_14829))],[f_3751_2]) ).

cnf(f_3751_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14829),sK389(U_14833,U_14832,U_14831,U_14830,U_14829)),U_14830))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14829,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14829,tc_HOL_Obool)),U_14830),hAPP(c_Set_OCollect(U_14829),U_14832))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14829,tc_HOL_Obool)),U_14831),hAPP(c_Set_OCollect(U_14829),U_14833))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14829,tc_HOL_Obool)),U_14830),U_14831)) ),
    inference(clausify,[status(thm)],[f_3751_3]) ).

cnf(f_3751_5,plain,
    ( hBOOL(hAPP(U_14832,sK389(U_14833,U_14832,U_14831,U_14830,U_14829)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14829,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14829,tc_HOL_Obool)),U_14830),hAPP(c_Set_OCollect(U_14829),U_14832))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14829,tc_HOL_Obool)),U_14831),hAPP(c_Set_OCollect(U_14829),U_14833))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14829,tc_HOL_Obool)),U_14830),U_14831)) ),
    inference(clausify,[status(thm)],[f_3751_3]) ).

cnf(f_3751_6,plain,
    ( ~ hBOOL(hAPP(U_14833,sK389(U_14833,U_14832,U_14831,U_14830,U_14829)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14829,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14829,tc_HOL_Obool)),U_14830),hAPP(c_Set_OCollect(U_14829),U_14832))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14829,tc_HOL_Obool)),U_14831),hAPP(c_Set_OCollect(U_14829),U_14833))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14829,tc_HOL_Obool)),U_14830),U_14831)) ),
    inference(clausify,[status(thm)],[f_3751_3]) ).

fof(f_3752_1,plain,
    ! [V_r_2,V_yx_2,T_c,T_b] :
      ( ? [B_x,B_y] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),B_y)),V_r_2))
          & V_yx_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_y),B_x) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_yx_2),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_converseE]) ).

fof(f_3752_2,plain,
    ! [U_14839,U_14838,U_14837,U_14836] :
      ( ? [U_14835,U_14834] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14837,U_14836)),hAPP(hAPP(c_Product__Type_OPair(U_14837,U_14836),U_14835),U_14834)),U_14839))
          & U_14838 = hAPP(hAPP(c_Product__Type_OPair(U_14836,U_14837),U_14834),U_14835) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14836,U_14837)),U_14838),hAPP(c_Relation_Oconverse(U_14837,U_14836),U_14839))) ),
    inference(variable_rename,[status(thm)],[f_3752_1]) ).

fof(f_3752_3,plain,
    ! [U_14839,U_14838,U_14837,U_14836] :
      ( ? [U_14834] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14837,U_14836)),hAPP(hAPP(c_Product__Type_OPair(U_14837,U_14836),sK390(U_14839,U_14838,U_14837,U_14836)),U_14834)),U_14839))
          & U_14838 = hAPP(hAPP(c_Product__Type_OPair(U_14836,U_14837),U_14834),sK390(U_14839,U_14838,U_14837,U_14836)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14836,U_14837)),U_14838),hAPP(c_Relation_Oconverse(U_14837,U_14836),U_14839))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK390]),skolemize(U_14835,sK390(U_14839,U_14838,U_14837,U_14836))],[f_3752_2]) ).

fof(f_3752_4,plain,
    ! [U_14839,U_14838,U_14837,U_14836] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14837,U_14836)),hAPP(hAPP(c_Product__Type_OPair(U_14837,U_14836),sK390(U_14839,U_14838,U_14837,U_14836)),sK391(U_14839,U_14838,U_14837,U_14836))),U_14839))
        & U_14838 = hAPP(hAPP(c_Product__Type_OPair(U_14836,U_14837),sK391(U_14839,U_14838,U_14837,U_14836)),sK390(U_14839,U_14838,U_14837,U_14836)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14836,U_14837)),U_14838),hAPP(c_Relation_Oconverse(U_14837,U_14836),U_14839))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK391]),skolemize(U_14834,sK391(U_14839,U_14838,U_14837,U_14836))],[f_3752_3]) ).

cnf(f_3752_5,plain,
    ( U_14838 = hAPP(hAPP(c_Product__Type_OPair(U_14836,U_14837),sK391(U_14839,U_14838,U_14837,U_14836)),sK390(U_14839,U_14838,U_14837,U_14836))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14836,U_14837)),U_14838),hAPP(c_Relation_Oconverse(U_14837,U_14836),U_14839))) ),
    inference(clausify,[status(thm)],[f_3752_4]) ).

cnf(f_3752_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14837,U_14836)),hAPP(hAPP(c_Product__Type_OPair(U_14837,U_14836),sK390(U_14839,U_14838,U_14837,U_14836)),sK391(U_14839,U_14838,U_14837,U_14836))),U_14839))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14836,U_14837)),U_14838),hAPP(c_Relation_Oconverse(U_14837,U_14836),U_14839))) ),
    inference(clausify,[status(thm)],[f_3752_4]) ).

fof(f_3753_1,plain,
    ! [V_s_2,V_r_2,T_d,V_xz_2,T_c,T_b] :
      ( ? [B_x,B_y,B_z] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_c),B_y),B_z)),V_s_2))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),B_x),B_y)),V_r_2))
          & V_xz_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_z) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_xz_2),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_r_2),V_s_2))) ),
    inference(fof_nnf,[status(thm)],[fact_rel__compE]) ).

fof(f_3753_2,plain,
    ! [U_14848,U_14847,U_14846,U_14845,U_14844,U_14843] :
      ( ? [U_14842,U_14841,U_14840] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14846,U_14844)),hAPP(hAPP(c_Product__Type_OPair(U_14846,U_14844),U_14841),U_14840)),U_14848))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14843,U_14846)),hAPP(hAPP(c_Product__Type_OPair(U_14843,U_14846),U_14842),U_14841)),U_14847))
          & U_14845 = hAPP(hAPP(c_Product__Type_OPair(U_14843,U_14844),U_14842),U_14840) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14843,U_14844)),U_14845),hAPP(hAPP(c_Relation_Orel__comp(U_14843,U_14846,U_14844),U_14847),U_14848))) ),
    inference(variable_rename,[status(thm)],[f_3753_1]) ).

fof(f_3753_3,plain,
    ! [U_14848,U_14847,U_14846,U_14845,U_14844,U_14843] :
      ( ? [U_14841,U_14840] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14846,U_14844)),hAPP(hAPP(c_Product__Type_OPair(U_14846,U_14844),U_14841),U_14840)),U_14848))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14843,U_14846)),hAPP(hAPP(c_Product__Type_OPair(U_14843,U_14846),sK392(U_14848,U_14847,U_14846,U_14845,U_14844,U_14843)),U_14841)),U_14847))
          & U_14845 = hAPP(hAPP(c_Product__Type_OPair(U_14843,U_14844),sK392(U_14848,U_14847,U_14846,U_14845,U_14844,U_14843)),U_14840) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14843,U_14844)),U_14845),hAPP(hAPP(c_Relation_Orel__comp(U_14843,U_14846,U_14844),U_14847),U_14848))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK392]),skolemize(U_14842,sK392(U_14848,U_14847,U_14846,U_14845,U_14844,U_14843))],[f_3753_2]) ).

fof(f_3753_4,plain,
    ! [U_14848,U_14847,U_14846,U_14845,U_14844,U_14843] :
      ( ? [U_14840] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14846,U_14844)),hAPP(hAPP(c_Product__Type_OPair(U_14846,U_14844),sK393(U_14848,U_14847,U_14846,U_14845,U_14844,U_14843)),U_14840)),U_14848))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14843,U_14846)),hAPP(hAPP(c_Product__Type_OPair(U_14843,U_14846),sK392(U_14848,U_14847,U_14846,U_14845,U_14844,U_14843)),sK393(U_14848,U_14847,U_14846,U_14845,U_14844,U_14843))),U_14847))
          & U_14845 = hAPP(hAPP(c_Product__Type_OPair(U_14843,U_14844),sK392(U_14848,U_14847,U_14846,U_14845,U_14844,U_14843)),U_14840) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14843,U_14844)),U_14845),hAPP(hAPP(c_Relation_Orel__comp(U_14843,U_14846,U_14844),U_14847),U_14848))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK393]),skolemize(U_14841,sK393(U_14848,U_14847,U_14846,U_14845,U_14844,U_14843))],[f_3753_3]) ).

fof(f_3753_5,plain,
    ! [U_14848,U_14847,U_14846,U_14845,U_14844,U_14843] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14846,U_14844)),hAPP(hAPP(c_Product__Type_OPair(U_14846,U_14844),sK393(U_14848,U_14847,U_14846,U_14845,U_14844,U_14843)),sK394(U_14848,U_14847,U_14846,U_14845,U_14844,U_14843))),U_14848))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14843,U_14846)),hAPP(hAPP(c_Product__Type_OPair(U_14843,U_14846),sK392(U_14848,U_14847,U_14846,U_14845,U_14844,U_14843)),sK393(U_14848,U_14847,U_14846,U_14845,U_14844,U_14843))),U_14847))
        & U_14845 = hAPP(hAPP(c_Product__Type_OPair(U_14843,U_14844),sK392(U_14848,U_14847,U_14846,U_14845,U_14844,U_14843)),sK394(U_14848,U_14847,U_14846,U_14845,U_14844,U_14843)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14843,U_14844)),U_14845),hAPP(hAPP(c_Relation_Orel__comp(U_14843,U_14846,U_14844),U_14847),U_14848))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK394]),skolemize(U_14840,sK394(U_14848,U_14847,U_14846,U_14845,U_14844,U_14843))],[f_3753_4]) ).

cnf(f_3753_6,plain,
    ( U_14845 = hAPP(hAPP(c_Product__Type_OPair(U_14843,U_14844),sK392(U_14848,U_14847,U_14846,U_14845,U_14844,U_14843)),sK394(U_14848,U_14847,U_14846,U_14845,U_14844,U_14843))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14843,U_14844)),U_14845),hAPP(hAPP(c_Relation_Orel__comp(U_14843,U_14846,U_14844),U_14847),U_14848))) ),
    inference(clausify,[status(thm)],[f_3753_5]) ).

cnf(f_3753_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14843,U_14846)),hAPP(hAPP(c_Product__Type_OPair(U_14843,U_14846),sK392(U_14848,U_14847,U_14846,U_14845,U_14844,U_14843)),sK393(U_14848,U_14847,U_14846,U_14845,U_14844,U_14843))),U_14847))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14843,U_14844)),U_14845),hAPP(hAPP(c_Relation_Orel__comp(U_14843,U_14846,U_14844),U_14847),U_14848))) ),
    inference(clausify,[status(thm)],[f_3753_5]) ).

cnf(f_3753_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14846,U_14844)),hAPP(hAPP(c_Product__Type_OPair(U_14846,U_14844),sK393(U_14848,U_14847,U_14846,U_14845,U_14844,U_14843)),sK394(U_14848,U_14847,U_14846,U_14845,U_14844,U_14843))),U_14848))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14843,U_14844)),U_14845),hAPP(hAPP(c_Relation_Orel__comp(U_14843,U_14846,U_14844),U_14847),U_14848))) ),
    inference(clausify,[status(thm)],[f_3753_5]) ).

fof(f_3754_1,plain,
    ! [V_r_2,V_q_2,T_b] : c_Nitpick_Oplus__frac(T_b,V_q_2,V_r_2) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_b),c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(T_b),V_q_2),hAPP(c_Nitpick_Odenom(T_b),V_r_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,T_b),tc_Int_Oint),c_Nitpick_Ofrac(T_b)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_b),V_q_2))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(c_Nitpick_Odenom(T_b),V_q_2))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_b),V_r_2))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(c_Nitpick_Odenom(T_b),V_r_2)))))),c_COMBI(tc_Int_Oint))),
    inference(fof_nnf,[status(thm)],[fact_Nitpick_Oplus__frac__def]) ).

fof(f_3754_2,plain,
    ! [U_14851,U_14850,U_14849] : c_Nitpick_Oplus__frac(U_14849,U_14850,U_14851) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_14849),c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(U_14849),U_14850),hAPP(c_Nitpick_Odenom(U_14849),U_14851))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,U_14849),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,U_14849),tc_Int_Oint),c_Nitpick_Ofrac(U_14849)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_14849),U_14850))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(c_Nitpick_Odenom(U_14849),U_14850))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_14849),U_14851))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(c_Nitpick_Odenom(U_14849),U_14851)))))),c_COMBI(tc_Int_Oint))),
    inference(variable_rename,[status(thm)],[f_3754_1]) ).

cnf(f_3754_3,plain,
    c_Nitpick_Oplus__frac(U_14849,U_14850,U_14851) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_14849),c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(U_14849),U_14850),hAPP(c_Nitpick_Odenom(U_14849),U_14851))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,U_14849),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,U_14849),tc_Int_Oint),c_Nitpick_Ofrac(U_14849)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_14849),U_14850))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(c_Nitpick_Odenom(U_14849),U_14850))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_14849),U_14851))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(c_Nitpick_Odenom(U_14849),U_14851)))))),c_COMBI(tc_Int_Oint))),
    inference(clausify,[status(thm)],[f_3754_2]) ).

fof(f_3755_1,plain,
    ! [V_r,V_q,T_a] : c_Nitpick_Otimes__frac(T_a,V_q,V_r) = hAPP(hAPP(c_Nitpick_Ofrac(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_a),V_q)),hAPP(c_Nitpick_Onum(T_a),V_r))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Odenom(T_a),V_q)),hAPP(c_Nitpick_Odenom(T_a),V_r))),
    inference(fof_nnf,[status(thm)],[fact_Nitpick_Otimes__frac__def]) ).

fof(f_3755_2,plain,
    ! [U_14854,U_14853,U_14852] : c_Nitpick_Otimes__frac(U_14852,U_14853,U_14854) = hAPP(hAPP(c_Nitpick_Ofrac(U_14852),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_14852),U_14853)),hAPP(c_Nitpick_Onum(U_14852),U_14854))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Odenom(U_14852),U_14853)),hAPP(c_Nitpick_Odenom(U_14852),U_14854))),
    inference(variable_rename,[status(thm)],[f_3755_1]) ).

cnf(f_3755_3,plain,
    c_Nitpick_Otimes__frac(U_14852,U_14853,U_14854) = hAPP(hAPP(c_Nitpick_Ofrac(U_14852),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_14852),U_14853)),hAPP(c_Nitpick_Onum(U_14852),U_14854))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Odenom(U_14852),U_14853)),hAPP(c_Nitpick_Odenom(U_14852),U_14854))),
    inference(clausify,[status(thm)],[f_3755_2]) ).

fof(f_3756_1,plain,
    ! [V_q,T_a,T_b] :
      ( c_Nitpick_Oof__frac(T_a,T_b,V_q) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(c_Nitpick_Onum(T_a),V_q))),hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(c_Nitpick_Odenom(T_a),V_q)))
      | ~ class_Rings_Oring__1(T_b)
      | ~ class_Rings_Oinverse(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Nitpick_Oof__frac__def]) ).

fof(f_3756_2,plain,
    ! [U_14857,U_14856,U_14855] :
      ( c_Nitpick_Oof__frac(U_14856,U_14855,U_14857) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_14855),hAPP(c_Int_Oring__1__class_Oof__int(U_14855),hAPP(c_Nitpick_Onum(U_14856),U_14857))),hAPP(c_Int_Oring__1__class_Oof__int(U_14855),hAPP(c_Nitpick_Odenom(U_14856),U_14857)))
      | ~ class_Rings_Oring__1(U_14855)
      | ~ class_Rings_Oinverse(U_14855) ),
    inference(variable_rename,[status(thm)],[f_3756_1]) ).

cnf(f_3756_3,plain,
    ( c_Nitpick_Oof__frac(U_14856,U_14855,U_14857) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_14855),hAPP(c_Int_Oring__1__class_Oof__int(U_14855),hAPP(c_Nitpick_Onum(U_14856),U_14857))),hAPP(c_Int_Oring__1__class_Oof__int(U_14855),hAPP(c_Nitpick_Odenom(U_14856),U_14857)))
    | ~ class_Rings_Oring__1(U_14855)
    | ~ class_Rings_Oinverse(U_14855) ),
    inference(clausify,[status(thm)],[f_3756_2]) ).

fof(f_3757_1,plain,
    ! [V_q,T_a] : c_Nitpick_Oinverse__frac(T_a,V_q) = hAPP(hAPP(c_Nitpick_Ofrac(T_a),hAPP(c_Nitpick_Odenom(T_a),V_q)),hAPP(c_Nitpick_Onum(T_a),V_q)),
    inference(fof_nnf,[status(thm)],[fact_Nitpick_Oinverse__frac__def]) ).

fof(f_3757_2,plain,
    ! [U_14859,U_14858] : c_Nitpick_Oinverse__frac(U_14858,U_14859) = hAPP(hAPP(c_Nitpick_Ofrac(U_14858),hAPP(c_Nitpick_Odenom(U_14858),U_14859)),hAPP(c_Nitpick_Onum(U_14858),U_14859)),
    inference(variable_rename,[status(thm)],[f_3757_1]) ).

cnf(f_3757_3,plain,
    c_Nitpick_Oinverse__frac(U_14858,U_14859) = hAPP(hAPP(c_Nitpick_Ofrac(U_14858),hAPP(c_Nitpick_Odenom(U_14858),U_14859)),hAPP(c_Nitpick_Onum(U_14858),U_14859)),
    inference(clausify,[status(thm)],[f_3757_2]) ).

fof(f_3758_1,plain,
    ! [V_q,T_a] : c_Nitpick_Ouminus__frac(T_a,V_q) = c_Nitpick_OAbs__Frac(T_a,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_a),V_q))),hAPP(c_Nitpick_Odenom(T_a),V_q))),
    inference(fof_nnf,[status(thm)],[fact_Nitpick_Ouminus__frac__def]) ).

fof(f_3758_2,plain,
    ! [U_14861,U_14860] : c_Nitpick_Ouminus__frac(U_14860,U_14861) = c_Nitpick_OAbs__Frac(U_14860,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_14860),U_14861))),hAPP(c_Nitpick_Odenom(U_14860),U_14861))),
    inference(variable_rename,[status(thm)],[f_3758_1]) ).

cnf(f_3758_3,plain,
    c_Nitpick_Ouminus__frac(U_14860,U_14861) = c_Nitpick_OAbs__Frac(U_14860,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_14860),U_14861))),hAPP(c_Nitpick_Odenom(U_14860),U_14861))),
    inference(clausify,[status(thm)],[f_3758_2]) ).

fof(f_3759_1,plain,
    ! [V_r_2,V_q_2,T_b] :
      ( ( c_Nitpick_Oless__frac(T_b,V_q_2,V_r_2)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_b),c_Nitpick_Oplus__frac(T_b,V_q_2,c_Nitpick_Ouminus__frac(T_b,V_r_2)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_b),c_Nitpick_Oplus__frac(T_b,V_q_2,c_Nitpick_Ouminus__frac(T_b,V_r_2)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ c_Nitpick_Oless__frac(T_b,V_q_2,V_r_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_Nitpick_Oless__frac__def]) ).

fof(f_3759_2,plain,
    ! [U_14864,U_14863,U_14862] :
      ( ( c_Nitpick_Oless__frac(U_14862,U_14863,U_14864)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_14862),c_Nitpick_Oplus__frac(U_14862,U_14863,c_Nitpick_Ouminus__frac(U_14862,U_14864)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_14862),c_Nitpick_Oplus__frac(U_14862,U_14863,c_Nitpick_Ouminus__frac(U_14862,U_14864)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ c_Nitpick_Oless__frac(U_14862,U_14863,U_14864) ) ),
    inference(variable_rename,[status(thm)],[f_3759_1]) ).

fof(f_3759_3,plain,
    ( ! [U_14870,U_14868,U_14866] :
        ( c_Nitpick_Oless__frac(U_14866,U_14868,U_14870)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_14866),c_Nitpick_Oplus__frac(U_14866,U_14868,c_Nitpick_Ouminus__frac(U_14866,U_14870)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_14869,U_14867,U_14865] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_14865),c_Nitpick_Oplus__frac(U_14865,U_14867,c_Nitpick_Ouminus__frac(U_14865,U_14869)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ c_Nitpick_Oless__frac(U_14865,U_14867,U_14869) ) ),
    inference(miniscope,[status(thm)],[f_3759_2]) ).

cnf(f_3759_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_14865),c_Nitpick_Oplus__frac(U_14865,U_14867,c_Nitpick_Ouminus__frac(U_14865,U_14869)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ c_Nitpick_Oless__frac(U_14865,U_14867,U_14869) ),
    inference(clausify,[status(thm)],[f_3759_3]) ).

cnf(f_3759_5,plain,
    ( c_Nitpick_Oless__frac(U_14866,U_14868,U_14870)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_14866),c_Nitpick_Oplus__frac(U_14866,U_14868,c_Nitpick_Ouminus__frac(U_14866,U_14870)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_3759_3]) ).

fof(f_3760_1,plain,
    ! [V_r_2,V_q_2,T_b] :
      ( ( c_Nitpick_Oless__eq__frac(T_b,V_q_2,V_r_2)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_b),c_Nitpick_Oplus__frac(T_b,V_q_2,c_Nitpick_Ouminus__frac(T_b,V_r_2)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_b),c_Nitpick_Oplus__frac(T_b,V_q_2,c_Nitpick_Ouminus__frac(T_b,V_r_2)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ c_Nitpick_Oless__eq__frac(T_b,V_q_2,V_r_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_Nitpick_Oless__eq__frac__def]) ).

fof(f_3760_2,plain,
    ! [U_14873,U_14872,U_14871] :
      ( ( c_Nitpick_Oless__eq__frac(U_14871,U_14872,U_14873)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_14871),c_Nitpick_Oplus__frac(U_14871,U_14872,c_Nitpick_Ouminus__frac(U_14871,U_14873)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_14871),c_Nitpick_Oplus__frac(U_14871,U_14872,c_Nitpick_Ouminus__frac(U_14871,U_14873)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ c_Nitpick_Oless__eq__frac(U_14871,U_14872,U_14873) ) ),
    inference(variable_rename,[status(thm)],[f_3760_1]) ).

fof(f_3760_3,plain,
    ( ! [U_14879,U_14877,U_14875] :
        ( c_Nitpick_Oless__eq__frac(U_14875,U_14877,U_14879)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_14875),c_Nitpick_Oplus__frac(U_14875,U_14877,c_Nitpick_Ouminus__frac(U_14875,U_14879)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_14878,U_14876,U_14874] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_14874),c_Nitpick_Oplus__frac(U_14874,U_14876,c_Nitpick_Ouminus__frac(U_14874,U_14878)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ c_Nitpick_Oless__eq__frac(U_14874,U_14876,U_14878) ) ),
    inference(miniscope,[status(thm)],[f_3760_2]) ).

cnf(f_3760_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_14874),c_Nitpick_Oplus__frac(U_14874,U_14876,c_Nitpick_Ouminus__frac(U_14874,U_14878)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ c_Nitpick_Oless__eq__frac(U_14874,U_14876,U_14878) ),
    inference(clausify,[status(thm)],[f_3760_3]) ).

cnf(f_3760_5,plain,
    ( c_Nitpick_Oless__eq__frac(U_14875,U_14877,U_14879)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_14875),c_Nitpick_Oplus__frac(U_14875,U_14877,c_Nitpick_Ouminus__frac(U_14875,U_14879)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_3760_3]) ).

fof(f_3761_1,plain,
    ! [T_b] : c_Nitpick_Odenom(T_b) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,T_b,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(T_b)),
    inference(fof_nnf,[status(thm)],[fact_Nitpick_Odenom__def]) ).

fof(f_3761_2,plain,
    ! [U_14880] : c_Nitpick_Odenom(U_14880) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,U_14880,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(U_14880)),
    inference(variable_rename,[status(thm)],[f_3761_1]) ).

cnf(f_3761_3,plain,
    c_Nitpick_Odenom(U_14880) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,U_14880,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(U_14880)),
    inference(clausify,[status(thm)],[f_3761_2]) ).

fof(f_3762_1,plain,
    ! [T_b] : c_Nitpick_Onum(T_b) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,T_b,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(T_b)),
    inference(fof_nnf,[status(thm)],[fact_Nitpick_Onum__def]) ).

fof(f_3762_2,plain,
    ! [U_14881] : c_Nitpick_Onum(U_14881) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,U_14881,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(U_14881)),
    inference(variable_rename,[status(thm)],[f_3762_1]) ).

cnf(f_3762_3,plain,
    c_Nitpick_Onum(U_14881) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,U_14881,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(U_14881)),
    inference(clausify,[status(thm)],[f_3762_2]) ).

fof(f_3763_1,plain,
    ! [T_d,T_c,T_b] : c_Product__Type_Ointernal__split(T_b,T_c,T_d) = c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),
    inference(fof_nnf,[status(thm)],[fact_internal__split__def]) ).

fof(f_3763_2,plain,
    ! [U_14884,U_14883,U_14882] : c_Product__Type_Ointernal__split(U_14882,U_14883,U_14884) = c_Product__Type_Oprod_Oprod__case(U_14882,U_14883,U_14884),
    inference(variable_rename,[status(thm)],[f_3763_1]) ).

cnf(f_3763_3,plain,
    c_Product__Type_Ointernal__split(U_14882,U_14883,U_14884) = c_Product__Type_Oprod_Oprod__case(U_14882,U_14883,U_14884),
    inference(clausify,[status(thm)],[f_3763_2]) ).

fof(f_3764_1,plain,
    c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_bool_Osize_I1_J]) ).

cnf(f_3764_2,plain,
    c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_3764_1]) ).

fof(f_3765_1,plain,
    ! [V_b_2,V_a_2,V_c_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Ointernal__split(T_c,T_d,T_b),V_c_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(V_c_2,V_a_2),V_b_2),
    inference(fof_nnf,[status(thm)],[fact_internal__split__conv]) ).

fof(f_3765_2,plain,
    ! [U_14890,U_14889,U_14888,U_14887,U_14886,U_14885] : hAPP(hAPP(c_Product__Type_Ointernal__split(U_14885,U_14886,U_14887),U_14888),hAPP(hAPP(c_Product__Type_OPair(U_14885,U_14886),U_14889),U_14890)) = hAPP(hAPP(U_14888,U_14889),U_14890),
    inference(variable_rename,[status(thm)],[f_3765_1]) ).

cnf(f_3765_3,plain,
    hAPP(hAPP(c_Product__Type_Ointernal__split(U_14885,U_14886,U_14887),U_14888),hAPP(hAPP(c_Product__Type_OPair(U_14885,U_14886),U_14889),U_14890)) = hAPP(hAPP(U_14888,U_14889),U_14890),
    inference(clausify,[status(thm)],[f_3765_2]) ).

fof(f_3766_1,plain,
    c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_bool_Osize_I2_J]) ).

cnf(f_3766_2,plain,
    c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_3766_1]) ).

fof(f_3767_1,plain,
    ! [V_u_2,V_f_2] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),V_f_2)),V_u_2))))
      | ? [B_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_n),hAPP(V_f_2,B_n))) ),
    inference(fof_nnf,[status(thm)],[fact_finite__less__ub]) ).

fof(f_3767_2,plain,
    ! [U_14893,U_14892] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),U_14892)),U_14893))))
      | ? [U_14891] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_14891),hAPP(U_14892,U_14891))) ),
    inference(variable_rename,[status(thm)],[f_3767_1]) ).

fof(f_3767_3,plain,
    ! [U_14893,U_14892] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),U_14892)),U_14893))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK395(U_14893,U_14892)),hAPP(U_14892,sK395(U_14893,U_14892)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK395]),skolemize(U_14891,sK395(U_14893,U_14892))],[f_3767_2]) ).

cnf(f_3767_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),U_14892)),U_14893))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK395(U_14893,U_14892)),hAPP(U_14892,sK395(U_14893,U_14892)))) ),
    inference(clausify,[status(thm)],[f_3767_3]) ).

fof(f_3768_1,plain,
    ! [V_r_2,T_b] : c_List_Olenlex(T_b,V_r_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_List_Olist(T_b)),tc_List_Olist(T_b)),c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_List_Olist(T_b),c_Wellfounded_Oless__than,c_List_Olex(T_b,V_r_2))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_prod(tc_Nat_Onat,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_List_Olist(T_b),tc_prod(tc_Nat_Onat,tc_List_Olist(T_b))),tc_List_Olist(T_b)),c_Product__Type_OPair(tc_Nat_Onat,tc_List_Olist(T_b))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),c_COMBI(tc_List_Olist(T_b)))),
    inference(fof_nnf,[status(thm)],[fact_lenlex__def]) ).

fof(f_3768_2,plain,
    ! [U_14895,U_14894] : c_List_Olenlex(U_14894,U_14895) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_List_Olist(U_14894)),tc_List_Olist(U_14894)),c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_List_Olist(U_14894),c_Wellfounded_Oless__than,c_List_Olex(U_14894,U_14895))),hAPP(hAPP(c_COMBS(tc_List_Olist(U_14894),tc_List_Olist(U_14894),tc_prod(tc_Nat_Onat,tc_List_Olist(U_14894))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_List_Olist(U_14894),tc_prod(tc_Nat_Onat,tc_List_Olist(U_14894))),tc_List_Olist(U_14894)),c_Product__Type_OPair(tc_Nat_Onat,tc_List_Olist(U_14894))),c_Nat_Osize__class_Osize(tc_List_Olist(U_14894)))),c_COMBI(tc_List_Olist(U_14894)))),
    inference(variable_rename,[status(thm)],[f_3768_1]) ).

cnf(f_3768_3,plain,
    c_List_Olenlex(U_14894,U_14895) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_List_Olist(U_14894)),tc_List_Olist(U_14894)),c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_List_Olist(U_14894),c_Wellfounded_Oless__than,c_List_Olex(U_14894,U_14895))),hAPP(hAPP(c_COMBS(tc_List_Olist(U_14894),tc_List_Olist(U_14894),tc_prod(tc_Nat_Onat,tc_List_Olist(U_14894))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_List_Olist(U_14894),tc_prod(tc_Nat_Onat,tc_List_Olist(U_14894))),tc_List_Olist(U_14894)),c_Product__Type_OPair(tc_Nat_Onat,tc_List_Olist(U_14894))),c_Nat_Osize__class_Osize(tc_List_Olist(U_14894)))),c_COMBI(tc_List_Olist(U_14894)))),
    inference(clausify,[status(thm)],[f_3768_2]) ).

fof(f_3769_1,plain,
    ! [V_n_2,V_r_2,V_ys_2,V_xs_2,T_b] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = V_n_2
        & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = V_n_2 )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),hAPP(c_List_Olexn(T_b,V_r_2),V_n_2))) ),
    inference(fof_nnf,[status(thm)],[fact_lexn__length]) ).

fof(f_3769_2,plain,
    ! [U_14900,U_14899,U_14898,U_14897,U_14896] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14896)),U_14898) = U_14900
        & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14896)),U_14897) = U_14900 )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14896),tc_List_Olist(U_14896))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14896),tc_List_Olist(U_14896)),U_14897),U_14898)),hAPP(c_List_Olexn(U_14896,U_14899),U_14900))) ),
    inference(variable_rename,[status(thm)],[f_3769_1]) ).

cnf(f_3769_3,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14896)),U_14897) = U_14900
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14896),tc_List_Olist(U_14896))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14896),tc_List_Olist(U_14896)),U_14897),U_14898)),hAPP(c_List_Olexn(U_14896,U_14899),U_14900))) ),
    inference(clausify,[status(thm)],[f_3769_2]) ).

cnf(f_3769_4,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14896)),U_14898) = U_14900
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14896),tc_List_Olist(U_14896))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14896),tc_List_Olist(U_14896)),U_14897),U_14898)),hAPP(c_List_Olexn(U_14896,U_14899),U_14900))) ),
    inference(clausify,[status(thm)],[f_3769_2]) ).

fof(f_3770_1,plain,
    ! [V_ys,V_xs,T_a] :
      ( V_xs != V_ys
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys) ),
    inference(fof_nnf,[status(thm)],[fact_neq__if__length__neq]) ).

fof(f_3770_2,plain,
    ! [U_14903,U_14902,U_14901] :
      ( U_14902 != U_14903
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14901)),U_14902) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14901)),U_14903) ),
    inference(variable_rename,[status(thm)],[f_3770_1]) ).

fof(f_3770_3,plain,
    ! [U_14903,U_14902] :
      ( ! [U_14901] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14901)),U_14902) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14901)),U_14903)
      | U_14902 != U_14903 ),
    inference(miniscope,[status(thm)],[f_3770_2]) ).

cnf(f_3770_4,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14901)),U_14902) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14901)),U_14903)
    | U_14902 != U_14903 ),
    inference(clausify,[status(thm)],[f_3770_3]) ).

fof(f_3771_1,plain,
    ! [V_r_2,T_b] : c_List_Olenlex(T_b,V_r_2) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fdisj)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBC(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_HOL_Obool)),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))))),c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b))))),c_List_Olex(T_b,V_r_2)))))),
    inference(fof_nnf,[status(thm)],[fact_lenlex__conv]) ).

fof(f_3771_2,plain,
    ! [U_14905,U_14904] : c_List_Olenlex(U_14904,U_14905) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(U_14904),tc_List_Olist(U_14904))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_14904),tc_List_Olist(U_14904),tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_List_Olist(U_14904),tc_fun(tc_List_Olist(U_14904),tc_HOL_Obool),tc_fun(tc_List_Olist(U_14904),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_14904),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(U_14904),tc_HOL_Obool),tc_fun(tc_List_Olist(U_14904),tc_HOL_Obool)),tc_List_Olist(U_14904)),c_COMBS(tc_List_Olist(U_14904),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_14904),tc_HOL_Obool),tc_fun(tc_List_Olist(U_14904),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(U_14904)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_14904)),c_fdisj)),hAPP(hAPP(c_COMBC(tc_List_Olist(U_14904),tc_fun(tc_List_Olist(U_14904),tc_Nat_Onat),tc_fun(tc_List_Olist(U_14904),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_14904),tc_Nat_Onat),tc_fun(tc_List_Olist(U_14904),tc_HOL_Obool)),tc_List_Olist(U_14904)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_14904))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_14904)),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_14904))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_14904)))))),hAPP(hAPP(c_COMBS(tc_List_Olist(U_14904),tc_fun(tc_List_Olist(U_14904),tc_HOL_Obool),tc_fun(tc_List_Olist(U_14904),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_14904),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(U_14904),tc_HOL_Obool),tc_fun(tc_List_Olist(U_14904),tc_HOL_Obool)),tc_List_Olist(U_14904)),c_COMBS(tc_List_Olist(U_14904),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_14904),tc_HOL_Obool),tc_fun(tc_List_Olist(U_14904),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(U_14904)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_14904)),c_fconj)),hAPP(hAPP(c_COMBC(tc_List_Olist(U_14904),tc_fun(tc_List_Olist(U_14904),tc_Nat_Onat),tc_fun(tc_List_Olist(U_14904),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_14904),tc_Nat_Onat),tc_fun(tc_List_Olist(U_14904),tc_HOL_Obool)),tc_List_Olist(U_14904)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_14904))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_14904)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_14904))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_14904)))))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_14904),tc_fun(tc_prod(tc_List_Olist(U_14904),tc_List_Olist(U_14904)),tc_HOL_Obool),tc_fun(tc_List_Olist(U_14904),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_14904),tc_fun(tc_fun(tc_prod(tc_List_Olist(U_14904),tc_List_Olist(U_14904)),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(tc_List_Olist(U_14904),tc_List_Olist(U_14904)),tc_HOL_Obool),tc_fun(tc_List_Olist(U_14904),tc_HOL_Obool)),tc_List_Olist(U_14904)),c_COMBC(tc_List_Olist(U_14904),tc_fun(tc_prod(tc_List_Olist(U_14904),tc_List_Olist(U_14904)),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_14904),tc_prod(tc_List_Olist(U_14904),tc_List_Olist(U_14904))),tc_fun(tc_List_Olist(U_14904),tc_fun(tc_fun(tc_prod(tc_List_Olist(U_14904),tc_List_Olist(U_14904)),tc_HOL_Obool),tc_HOL_Obool)),tc_List_Olist(U_14904)),hAPP(c_COMBB(tc_prod(tc_List_Olist(U_14904),tc_List_Olist(U_14904)),tc_fun(tc_fun(tc_prod(tc_List_Olist(U_14904),tc_List_Olist(U_14904)),tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_14904)),c_member(tc_prod(tc_List_Olist(U_14904),tc_List_Olist(U_14904))))),c_Product__Type_OPair(tc_List_Olist(U_14904),tc_List_Olist(U_14904))))),c_List_Olex(U_14904,U_14905)))))),
    inference(variable_rename,[status(thm)],[f_3771_1]) ).

cnf(f_3771_3,plain,
    c_List_Olenlex(U_14904,U_14905) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(U_14904),tc_List_Olist(U_14904))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_14904),tc_List_Olist(U_14904),tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_List_Olist(U_14904),tc_fun(tc_List_Olist(U_14904),tc_HOL_Obool),tc_fun(tc_List_Olist(U_14904),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_14904),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(U_14904),tc_HOL_Obool),tc_fun(tc_List_Olist(U_14904),tc_HOL_Obool)),tc_List_Olist(U_14904)),c_COMBS(tc_List_Olist(U_14904),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_14904),tc_HOL_Obool),tc_fun(tc_List_Olist(U_14904),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(U_14904)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_14904)),c_fdisj)),hAPP(hAPP(c_COMBC(tc_List_Olist(U_14904),tc_fun(tc_List_Olist(U_14904),tc_Nat_Onat),tc_fun(tc_List_Olist(U_14904),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_14904),tc_Nat_Onat),tc_fun(tc_List_Olist(U_14904),tc_HOL_Obool)),tc_List_Olist(U_14904)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_14904))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_14904)),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_14904))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_14904)))))),hAPP(hAPP(c_COMBS(tc_List_Olist(U_14904),tc_fun(tc_List_Olist(U_14904),tc_HOL_Obool),tc_fun(tc_List_Olist(U_14904),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_14904),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(U_14904),tc_HOL_Obool),tc_fun(tc_List_Olist(U_14904),tc_HOL_Obool)),tc_List_Olist(U_14904)),c_COMBS(tc_List_Olist(U_14904),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_14904),tc_HOL_Obool),tc_fun(tc_List_Olist(U_14904),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(U_14904)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_14904)),c_fconj)),hAPP(hAPP(c_COMBC(tc_List_Olist(U_14904),tc_fun(tc_List_Olist(U_14904),tc_Nat_Onat),tc_fun(tc_List_Olist(U_14904),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_14904),tc_Nat_Onat),tc_fun(tc_List_Olist(U_14904),tc_HOL_Obool)),tc_List_Olist(U_14904)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_14904))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_14904)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_14904))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_14904)))))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_14904),tc_fun(tc_prod(tc_List_Olist(U_14904),tc_List_Olist(U_14904)),tc_HOL_Obool),tc_fun(tc_List_Olist(U_14904),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_14904),tc_fun(tc_fun(tc_prod(tc_List_Olist(U_14904),tc_List_Olist(U_14904)),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(tc_List_Olist(U_14904),tc_List_Olist(U_14904)),tc_HOL_Obool),tc_fun(tc_List_Olist(U_14904),tc_HOL_Obool)),tc_List_Olist(U_14904)),c_COMBC(tc_List_Olist(U_14904),tc_fun(tc_prod(tc_List_Olist(U_14904),tc_List_Olist(U_14904)),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_14904),tc_prod(tc_List_Olist(U_14904),tc_List_Olist(U_14904))),tc_fun(tc_List_Olist(U_14904),tc_fun(tc_fun(tc_prod(tc_List_Olist(U_14904),tc_List_Olist(U_14904)),tc_HOL_Obool),tc_HOL_Obool)),tc_List_Olist(U_14904)),hAPP(c_COMBB(tc_prod(tc_List_Olist(U_14904),tc_List_Olist(U_14904)),tc_fun(tc_fun(tc_prod(tc_List_Olist(U_14904),tc_List_Olist(U_14904)),tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_14904)),c_member(tc_prod(tc_List_Olist(U_14904),tc_List_Olist(U_14904))))),c_Product__Type_OPair(tc_List_Olist(U_14904),tc_List_Olist(U_14904))))),c_List_Olex(U_14904,U_14905)))))),
    inference(clausify,[status(thm)],[f_3771_2]) ).

fof(f_3772_1,plain,
    ! [V_I_2,V_xs_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Osublist(T_b,V_xs_2,V_I_2)) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_I_2)))),
    inference(fof_nnf,[status(thm)],[fact_length__sublist]) ).

fof(f_3772_2,plain,
    ! [U_14908,U_14907,U_14906] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14906)),c_List_Osublist(U_14906,U_14907,U_14908)) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14906)),U_14907)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),U_14908)))),
    inference(variable_rename,[status(thm)],[f_3772_1]) ).

cnf(f_3772_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14906)),c_List_Osublist(U_14906,U_14907,U_14908)) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14906)),U_14907)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),U_14908)))),
    inference(clausify,[status(thm)],[f_3772_2]) ).

fof(f_3773_1,plain,
    ! [V_n_2,V_r_2,T_b] : hAPP(c_List_Olexn(T_b,V_r_2),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_prod(tc_prod(T_b,tc_List_Olist(T_b)),tc_prod(T_b,tc_List_Olist(T_b))),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_Product__Type_Omap__pair(tc_prod(T_b,tc_List_Olist(T_b)),tc_List_Olist(T_b),tc_prod(T_b,tc_List_Olist(T_b)),tc_List_Olist(T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)))),c_Wellfounded_Olex__prod(T_b,tc_List_Olist(T_b),V_r_2,hAPP(c_List_Olexn(T_b,V_r_2),V_n_2)))),hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),hAPP(c_Nat_OSuc,V_n_2))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),hAPP(c_Nat_OSuc,V_n_2)))))),
    inference(fof_nnf,[status(thm)],[fact_lexn_Osimps_I2_J]) ).

fof(f_3773_2,plain,
    ! [U_14911,U_14910,U_14909] : hAPP(c_List_Olexn(U_14909,U_14910),hAPP(c_Nat_OSuc,U_14911)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(U_14909),tc_List_Olist(U_14909)),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_prod(tc_prod(U_14909,tc_List_Olist(U_14909)),tc_prod(U_14909,tc_List_Olist(U_14909))),tc_prod(tc_List_Olist(U_14909),tc_List_Olist(U_14909)),c_Product__Type_Omap__pair(tc_prod(U_14909,tc_List_Olist(U_14909)),tc_List_Olist(U_14909),tc_prod(U_14909,tc_List_Olist(U_14909)),tc_List_Olist(U_14909),hAPP(c_Product__Type_Oprod_Oprod__case(U_14909,tc_List_Olist(U_14909),tc_List_Olist(U_14909)),c_List_Olist_OCons(U_14909)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14909,tc_List_Olist(U_14909),tc_List_Olist(U_14909)),c_List_Olist_OCons(U_14909)))),c_Wellfounded_Olex__prod(U_14909,tc_List_Olist(U_14909),U_14910,hAPP(c_List_Olexn(U_14909,U_14910),U_14911)))),hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(U_14909),tc_List_Olist(U_14909))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_14909),tc_List_Olist(U_14909),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(U_14909),tc_fun(tc_List_Olist(U_14909),tc_HOL_Obool),tc_fun(tc_List_Olist(U_14909),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_14909),tc_HOL_Obool),tc_fun(tc_List_Olist(U_14909),tc_HOL_Obool)),tc_List_Olist(U_14909)),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_14909))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_14909)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_14909),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_14909)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_14909)))),hAPP(c_Nat_OSuc,U_14911))))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_14909),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_14909)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_14909)))),hAPP(c_Nat_OSuc,U_14911)))))),
    inference(variable_rename,[status(thm)],[f_3773_1]) ).

cnf(f_3773_3,plain,
    hAPP(c_List_Olexn(U_14909,U_14910),hAPP(c_Nat_OSuc,U_14911)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(U_14909),tc_List_Olist(U_14909)),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_prod(tc_prod(U_14909,tc_List_Olist(U_14909)),tc_prod(U_14909,tc_List_Olist(U_14909))),tc_prod(tc_List_Olist(U_14909),tc_List_Olist(U_14909)),c_Product__Type_Omap__pair(tc_prod(U_14909,tc_List_Olist(U_14909)),tc_List_Olist(U_14909),tc_prod(U_14909,tc_List_Olist(U_14909)),tc_List_Olist(U_14909),hAPP(c_Product__Type_Oprod_Oprod__case(U_14909,tc_List_Olist(U_14909),tc_List_Olist(U_14909)),c_List_Olist_OCons(U_14909)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14909,tc_List_Olist(U_14909),tc_List_Olist(U_14909)),c_List_Olist_OCons(U_14909)))),c_Wellfounded_Olex__prod(U_14909,tc_List_Olist(U_14909),U_14910,hAPP(c_List_Olexn(U_14909,U_14910),U_14911)))),hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(U_14909),tc_List_Olist(U_14909))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_14909),tc_List_Olist(U_14909),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(U_14909),tc_fun(tc_List_Olist(U_14909),tc_HOL_Obool),tc_fun(tc_List_Olist(U_14909),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_14909),tc_HOL_Obool),tc_fun(tc_List_Olist(U_14909),tc_HOL_Obool)),tc_List_Olist(U_14909)),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_14909))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_14909)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_14909),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_14909)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_14909)))),hAPP(c_Nat_OSuc,U_14911))))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_14909),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_14909)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_14909)))),hAPP(c_Nat_OSuc,U_14911)))))),
    inference(clausify,[status(thm)],[f_3773_2]) ).

fof(f_3774_1,plain,
    ! [V_x,V_ys,V_xs,T_a] :
      ( V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys))) ),
    inference(fof_nnf,[status(thm)],[fact_impossible__Cons]) ).

fof(f_3774_2,plain,
    ! [U_14915,U_14914,U_14913,U_14912] :
      ( U_14913 != hAPP(hAPP(c_List_Olist_OCons(U_14912),U_14915),U_14914)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14912)),U_14913)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14912)),U_14914))) ),
    inference(variable_rename,[status(thm)],[f_3774_1]) ).

cnf(f_3774_3,plain,
    ( U_14913 != hAPP(hAPP(c_List_Olist_OCons(U_14912),U_14915),U_14914)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14912)),U_14913)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14912)),U_14914))) ),
    inference(clausify,[status(thm)],[f_3774_2]) ).

fof(f_3775_1,plain,
    ! [V_list_H_2,V_a_H_2,V_list_2,V_a_2,T_b] :
      ( ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_list_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_H_2),V_list_H_2)
        | V_list_2 != V_list_H_2
        | V_a_2 != V_a_H_2 )
      & ( ( V_list_2 = V_list_H_2
          & V_a_2 = V_a_H_2 )
        | hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_list_2) != hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_H_2),V_list_H_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_list_Oinject]) ).

fof(f_3775_2,plain,
    ! [U_14920,U_14919,U_14918,U_14917,U_14916] :
      ( ( hAPP(hAPP(c_List_Olist_OCons(U_14916),U_14917),U_14918) = hAPP(hAPP(c_List_Olist_OCons(U_14916),U_14919),U_14920)
        | U_14918 != U_14920
        | U_14917 != U_14919 )
      & ( ( U_14918 = U_14920
          & U_14917 = U_14919 )
        | hAPP(hAPP(c_List_Olist_OCons(U_14916),U_14917),U_14918) != hAPP(hAPP(c_List_Olist_OCons(U_14916),U_14919),U_14920) ) ),
    inference(variable_rename,[status(thm)],[f_3775_1]) ).

fof(f_3775_3,plain,
    ( ! [U_14930,U_14928,U_14926,U_14924] :
        ( ! [U_14922] : hAPP(hAPP(c_List_Olist_OCons(U_14922),U_14924),U_14926) = hAPP(hAPP(c_List_Olist_OCons(U_14922),U_14928),U_14930)
        | U_14926 != U_14930
        | U_14924 != U_14928 )
    & ! [U_14929,U_14927,U_14925,U_14923] :
        ( ! [U_14921] : hAPP(hAPP(c_List_Olist_OCons(U_14921),U_14923),U_14925) != hAPP(hAPP(c_List_Olist_OCons(U_14921),U_14927),U_14929)
        | ( U_14925 = U_14929
          & U_14923 = U_14927 ) ) ),
    inference(miniscope,[status(thm)],[f_3775_2]) ).

cnf(f_3775_4,plain,
    ( U_14923 = U_14927
    | hAPP(hAPP(c_List_Olist_OCons(U_14921),U_14923),U_14925) != hAPP(hAPP(c_List_Olist_OCons(U_14921),U_14927),U_14929) ),
    inference(clausify,[status(thm)],[f_3775_3]) ).

cnf(f_3775_5,plain,
    ( U_14925 = U_14929
    | hAPP(hAPP(c_List_Olist_OCons(U_14921),U_14923),U_14925) != hAPP(hAPP(c_List_Olist_OCons(U_14921),U_14927),U_14929) ),
    inference(clausify,[status(thm)],[f_3775_3]) ).

cnf(f_3775_6,plain,
    ( hAPP(hAPP(c_List_Olist_OCons(U_14922),U_14924),U_14926) = hAPP(hAPP(c_List_Olist_OCons(U_14922),U_14928),U_14930)
    | U_14926 != U_14930
    | U_14924 != U_14928 ),
    inference(clausify,[status(thm)],[f_3775_3]) ).

fof(f_3776_1,plain,
    ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) != V_xs,
    inference(fof_nnf,[status(thm)],[fact_not__Cons__self2]) ).

fof(f_3776_2,plain,
    ! [U_14933,U_14932,U_14931] : hAPP(hAPP(c_List_Olist_OCons(U_14931),U_14932),U_14933) != U_14933,
    inference(variable_rename,[status(thm)],[f_3776_1]) ).

cnf(f_3776_3,plain,
    hAPP(hAPP(c_List_Olist_OCons(U_14931),U_14932),U_14933) != U_14933,
    inference(clausify,[status(thm)],[f_3776_2]) ).

fof(f_3777_1,plain,
    ! [V_x,T_a,V_xs] : V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs),
    inference(fof_nnf,[status(thm)],[fact_not__Cons__self]) ).

fof(f_3777_2,plain,
    ! [U_14936,U_14935,U_14934] : U_14934 != hAPP(hAPP(c_List_Olist_OCons(U_14935),U_14936),U_14934),
    inference(variable_rename,[status(thm)],[f_3777_1]) ).

cnf(f_3777_3,plain,
    U_14934 != hAPP(hAPP(c_List_Olist_OCons(U_14935),U_14936),U_14934),
    inference(clausify,[status(thm)],[f_3777_2]) ).

fof(f_3778_1,plain,
    ! [V_list,V_a,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a),V_list)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_list)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(fof_nnf,[status(thm)],[fact_list_Osize_I4_J]) ).

fof(f_3778_2,plain,
    ! [U_14939,U_14938,U_14937] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14937)),hAPP(hAPP(c_List_Olist_OCons(U_14937),U_14938),U_14939)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14937)),U_14939)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_3778_1]) ).

cnf(f_3778_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14937)),hAPP(hAPP(c_List_Olist_OCons(U_14937),U_14938),U_14939)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14937)),U_14939)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_3778_2]) ).

fof(f_3779_1,plain,
    ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olex(T_b,V_r_2)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olex(T_b,V_r_2)))
            | V_x_2 != V_y_2 )
          & ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) ) ) )
      & ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olex(T_b,V_r_2)))
          & V_x_2 = V_y_2 )
        | ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olex(T_b,V_r_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_Cons__in__lex]) ).

fof(f_3779_2,plain,
    ! [U_14945,U_14944,U_14943,U_14942,U_14941,U_14940] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14940),tc_List_Olist(U_14940))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14940),tc_List_Olist(U_14940)),hAPP(hAPP(c_List_Olist_OCons(U_14940),U_14941),U_14942)),hAPP(hAPP(c_List_Olist_OCons(U_14940),U_14943),U_14944))),c_List_Olex(U_14940,U_14945)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14940),tc_List_Olist(U_14940))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14940),tc_List_Olist(U_14940)),U_14942),U_14944)),c_List_Olex(U_14940,U_14945)))
            | U_14941 != U_14943 )
          & ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14940)),U_14942) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14940)),U_14944)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14940,U_14940)),hAPP(hAPP(c_Product__Type_OPair(U_14940,U_14940),U_14941),U_14943)),U_14945)) ) ) )
      & ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14940),tc_List_Olist(U_14940))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14940),tc_List_Olist(U_14940)),U_14942),U_14944)),c_List_Olex(U_14940,U_14945)))
          & U_14941 = U_14943 )
        | ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14940)),U_14942) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14940)),U_14944)
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14940,U_14940)),hAPP(hAPP(c_Product__Type_OPair(U_14940,U_14940),U_14941),U_14943)),U_14945)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14940),tc_List_Olist(U_14940))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14940),tc_List_Olist(U_14940)),hAPP(hAPP(c_List_Olist_OCons(U_14940),U_14941),U_14942)),hAPP(hAPP(c_List_Olist_OCons(U_14940),U_14943),U_14944))),c_List_Olex(U_14940,U_14945))) ) ),
    inference(variable_rename,[status(thm)],[f_3779_1]) ).

fof(f_3779_3,plain,
    ( ! [U_14957,U_14955,U_14953,U_14951,U_14949,U_14947] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14947),tc_List_Olist(U_14947))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14947),tc_List_Olist(U_14947)),hAPP(hAPP(c_List_Olist_OCons(U_14947),U_14949),U_14951)),hAPP(hAPP(c_List_Olist_OCons(U_14947),U_14953),U_14955))),c_List_Olex(U_14947,U_14957)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14947),tc_List_Olist(U_14947))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14947),tc_List_Olist(U_14947)),U_14951),U_14955)),c_List_Olex(U_14947,U_14957)))
            | U_14949 != U_14953 )
          & ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14947)),U_14951) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14947)),U_14955)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14947,U_14947)),hAPP(hAPP(c_Product__Type_OPair(U_14947,U_14947),U_14949),U_14953)),U_14957)) ) ) )
    & ! [U_14956,U_14954,U_14952,U_14950,U_14948,U_14946] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14946),tc_List_Olist(U_14946))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14946),tc_List_Olist(U_14946)),U_14950),U_14954)),c_List_Olex(U_14946,U_14956)))
          & U_14948 = U_14952 )
        | ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14946)),U_14950) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14946)),U_14954)
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14946,U_14946)),hAPP(hAPP(c_Product__Type_OPair(U_14946,U_14946),U_14948),U_14952)),U_14956)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14946),tc_List_Olist(U_14946))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14946),tc_List_Olist(U_14946)),hAPP(hAPP(c_List_Olist_OCons(U_14946),U_14948),U_14950)),hAPP(hAPP(c_List_Olist_OCons(U_14946),U_14952),U_14954))),c_List_Olex(U_14946,U_14956))) ) ),
    inference(miniscope,[status(thm)],[f_3779_2]) ).

cnf(f_3779_4,plain,
    ( U_14948 = U_14952
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14946,U_14946)),hAPP(hAPP(c_Product__Type_OPair(U_14946,U_14946),U_14948),U_14952)),U_14956))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14946),tc_List_Olist(U_14946))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14946),tc_List_Olist(U_14946)),hAPP(hAPP(c_List_Olist_OCons(U_14946),U_14948),U_14950)),hAPP(hAPP(c_List_Olist_OCons(U_14946),U_14952),U_14954))),c_List_Olex(U_14946,U_14956))) ),
    inference(clausify,[status(thm)],[f_3779_3]) ).

cnf(f_3779_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14946),tc_List_Olist(U_14946))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14946),tc_List_Olist(U_14946)),U_14950),U_14954)),c_List_Olex(U_14946,U_14956)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14946,U_14946)),hAPP(hAPP(c_Product__Type_OPair(U_14946,U_14946),U_14948),U_14952)),U_14956))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14946),tc_List_Olist(U_14946))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14946),tc_List_Olist(U_14946)),hAPP(hAPP(c_List_Olist_OCons(U_14946),U_14948),U_14950)),hAPP(hAPP(c_List_Olist_OCons(U_14946),U_14952),U_14954))),c_List_Olex(U_14946,U_14956))) ),
    inference(clausify,[status(thm)],[f_3779_3]) ).

cnf(f_3779_6,plain,
    ( U_14948 = U_14952
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14946)),U_14950) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14946)),U_14954)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14946),tc_List_Olist(U_14946))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14946),tc_List_Olist(U_14946)),hAPP(hAPP(c_List_Olist_OCons(U_14946),U_14948),U_14950)),hAPP(hAPP(c_List_Olist_OCons(U_14946),U_14952),U_14954))),c_List_Olex(U_14946,U_14956))) ),
    inference(clausify,[status(thm)],[f_3779_3]) ).

cnf(f_3779_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14946),tc_List_Olist(U_14946))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14946),tc_List_Olist(U_14946)),U_14950),U_14954)),c_List_Olex(U_14946,U_14956)))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14946)),U_14950) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14946)),U_14954)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14946),tc_List_Olist(U_14946))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14946),tc_List_Olist(U_14946)),hAPP(hAPP(c_List_Olist_OCons(U_14946),U_14948),U_14950)),hAPP(hAPP(c_List_Olist_OCons(U_14946),U_14952),U_14954))),c_List_Olex(U_14946,U_14956))) ),
    inference(clausify,[status(thm)],[f_3779_3]) ).

cnf(f_3779_8,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14947)),U_14951) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14947)),U_14955)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14947,U_14947)),hAPP(hAPP(c_Product__Type_OPair(U_14947,U_14947),U_14949),U_14953)),U_14957))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14947),tc_List_Olist(U_14947))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14947),tc_List_Olist(U_14947)),hAPP(hAPP(c_List_Olist_OCons(U_14947),U_14949),U_14951)),hAPP(hAPP(c_List_Olist_OCons(U_14947),U_14953),U_14955))),c_List_Olex(U_14947,U_14957))) ),
    inference(clausify,[status(thm)],[f_3779_3]) ).

cnf(f_3779_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14947),tc_List_Olist(U_14947))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14947),tc_List_Olist(U_14947)),U_14951),U_14955)),c_List_Olex(U_14947,U_14957)))
    | U_14949 != U_14953
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14947),tc_List_Olist(U_14947))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14947),tc_List_Olist(U_14947)),hAPP(hAPP(c_List_Olist_OCons(U_14947),U_14949),U_14951)),hAPP(hAPP(c_List_Olist_OCons(U_14947),U_14953),U_14955))),c_List_Olex(U_14947,U_14957))) ),
    inference(clausify,[status(thm)],[f_3779_3]) ).

fof(f_3780_1,plain,
    ! [V_XS_2,V_A_2,T_b] : c_List_Oset__Cons(T_b,V_A_2,V_XS_2) = hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_List_Olist(T_b)),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),tc_List_Olist(T_b)),c_COMBS(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),T_b),c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),tc_List_Olist(T_b)),c_COMBB(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_List_Olist(T_b),tc_HOL_Obool,tc_List_Olist(T_b))),c_fequal))),c_List_Olist_OCons(T_b)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(T_b))),V_XS_2)))))),
    inference(fof_nnf,[status(thm)],[fact_set__Cons__def]) ).

fof(f_3780_2,plain,
    ! [U_14960,U_14959,U_14958] : c_List_Oset__Cons(U_14958,U_14959,U_14960) = hAPP(c_Set_OCollect(tc_List_Olist(U_14958)),hAPP(hAPP(c_COMBB(tc_fun(U_14958,tc_HOL_Obool),tc_HOL_Obool,tc_List_Olist(U_14958)),c_HOL_OEx(U_14958)),hAPP(hAPP(c_COMBB(tc_fun(U_14958,tc_fun(tc_List_Olist(U_14958),tc_HOL_Obool)),tc_fun(U_14958,tc_HOL_Obool),tc_List_Olist(U_14958)),hAPP(c_COMBB(tc_fun(tc_List_Olist(U_14958),tc_HOL_Obool),tc_HOL_Obool,U_14958),c_HOL_OEx(tc_List_Olist(U_14958)))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_14958),tc_fun(U_14958,tc_fun(tc_List_Olist(U_14958),tc_HOL_Obool)),tc_fun(U_14958,tc_fun(tc_List_Olist(U_14958),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14958,tc_fun(tc_fun(tc_List_Olist(U_14958),tc_HOL_Obool),tc_fun(tc_List_Olist(U_14958),tc_HOL_Obool))),tc_fun(tc_fun(U_14958,tc_fun(tc_List_Olist(U_14958),tc_HOL_Obool)),tc_fun(U_14958,tc_fun(tc_List_Olist(U_14958),tc_HOL_Obool))),tc_List_Olist(U_14958)),c_COMBS(U_14958,tc_fun(tc_List_Olist(U_14958),tc_HOL_Obool),tc_fun(tc_List_Olist(U_14958),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14958,tc_fun(tc_List_Olist(U_14958),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_14958,tc_fun(tc_fun(tc_List_Olist(U_14958),tc_HOL_Obool),tc_fun(tc_List_Olist(U_14958),tc_HOL_Obool))),tc_List_Olist(U_14958)),hAPP(c_COMBB(tc_fun(tc_List_Olist(U_14958),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(U_14958),tc_HOL_Obool),tc_fun(tc_List_Olist(U_14958),tc_HOL_Obool)),U_14958),c_COMBS(tc_List_Olist(U_14958),tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14958,tc_fun(tc_List_Olist(U_14958),tc_HOL_Obool)),tc_fun(U_14958,tc_fun(tc_List_Olist(U_14958),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_List_Olist(U_14958)),hAPP(c_COMBB(tc_fun(tc_List_Olist(U_14958),tc_HOL_Obool),tc_fun(tc_List_Olist(U_14958),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_14958),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_14958)),c_fconj))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_14958),tc_fun(U_14958,tc_fun(tc_List_Olist(U_14958),tc_List_Olist(U_14958))),tc_fun(U_14958,tc_fun(tc_List_Olist(U_14958),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(U_14958),tc_List_Olist(U_14958)),tc_fun(tc_List_Olist(U_14958),tc_HOL_Obool)),tc_fun(tc_fun(U_14958,tc_fun(tc_List_Olist(U_14958),tc_List_Olist(U_14958))),tc_fun(U_14958,tc_fun(tc_List_Olist(U_14958),tc_HOL_Obool))),tc_List_Olist(U_14958)),c_COMBB(tc_fun(tc_List_Olist(U_14958),tc_List_Olist(U_14958)),tc_fun(tc_List_Olist(U_14958),tc_HOL_Obool),U_14958)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_14958),tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_14958),tc_List_Olist(U_14958)),tc_fun(tc_List_Olist(U_14958),tc_HOL_Obool)),tc_List_Olist(U_14958)),c_COMBB(tc_List_Olist(U_14958),tc_HOL_Obool,tc_List_Olist(U_14958))),c_fequal))),c_List_Olist_OCons(U_14958)))))),hAPP(hAPP(c_COMBC(U_14958,tc_fun(tc_List_Olist(U_14958),tc_HOL_Obool),tc_fun(tc_List_Olist(U_14958),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_14958),tc_HOL_Obool),tc_fun(tc_List_Olist(U_14958),tc_HOL_Obool)),U_14958),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_14958))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14958),c_fconj),hAPP(hAPP(c_COMBC(U_14958,tc_fun(U_14958,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14958)),U_14959)))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_14958),tc_fun(tc_List_Olist(U_14958),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(U_14958))),U_14960)))))),
    inference(variable_rename,[status(thm)],[f_3780_1]) ).

cnf(f_3780_3,plain,
    c_List_Oset__Cons(U_14958,U_14959,U_14960) = hAPP(c_Set_OCollect(tc_List_Olist(U_14958)),hAPP(hAPP(c_COMBB(tc_fun(U_14958,tc_HOL_Obool),tc_HOL_Obool,tc_List_Olist(U_14958)),c_HOL_OEx(U_14958)),hAPP(hAPP(c_COMBB(tc_fun(U_14958,tc_fun(tc_List_Olist(U_14958),tc_HOL_Obool)),tc_fun(U_14958,tc_HOL_Obool),tc_List_Olist(U_14958)),hAPP(c_COMBB(tc_fun(tc_List_Olist(U_14958),tc_HOL_Obool),tc_HOL_Obool,U_14958),c_HOL_OEx(tc_List_Olist(U_14958)))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_14958),tc_fun(U_14958,tc_fun(tc_List_Olist(U_14958),tc_HOL_Obool)),tc_fun(U_14958,tc_fun(tc_List_Olist(U_14958),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14958,tc_fun(tc_fun(tc_List_Olist(U_14958),tc_HOL_Obool),tc_fun(tc_List_Olist(U_14958),tc_HOL_Obool))),tc_fun(tc_fun(U_14958,tc_fun(tc_List_Olist(U_14958),tc_HOL_Obool)),tc_fun(U_14958,tc_fun(tc_List_Olist(U_14958),tc_HOL_Obool))),tc_List_Olist(U_14958)),c_COMBS(U_14958,tc_fun(tc_List_Olist(U_14958),tc_HOL_Obool),tc_fun(tc_List_Olist(U_14958),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14958,tc_fun(tc_List_Olist(U_14958),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_14958,tc_fun(tc_fun(tc_List_Olist(U_14958),tc_HOL_Obool),tc_fun(tc_List_Olist(U_14958),tc_HOL_Obool))),tc_List_Olist(U_14958)),hAPP(c_COMBB(tc_fun(tc_List_Olist(U_14958),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(U_14958),tc_HOL_Obool),tc_fun(tc_List_Olist(U_14958),tc_HOL_Obool)),U_14958),c_COMBS(tc_List_Olist(U_14958),tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14958,tc_fun(tc_List_Olist(U_14958),tc_HOL_Obool)),tc_fun(U_14958,tc_fun(tc_List_Olist(U_14958),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_List_Olist(U_14958)),hAPP(c_COMBB(tc_fun(tc_List_Olist(U_14958),tc_HOL_Obool),tc_fun(tc_List_Olist(U_14958),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_14958),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_14958)),c_fconj))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_14958),tc_fun(U_14958,tc_fun(tc_List_Olist(U_14958),tc_List_Olist(U_14958))),tc_fun(U_14958,tc_fun(tc_List_Olist(U_14958),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(U_14958),tc_List_Olist(U_14958)),tc_fun(tc_List_Olist(U_14958),tc_HOL_Obool)),tc_fun(tc_fun(U_14958,tc_fun(tc_List_Olist(U_14958),tc_List_Olist(U_14958))),tc_fun(U_14958,tc_fun(tc_List_Olist(U_14958),tc_HOL_Obool))),tc_List_Olist(U_14958)),c_COMBB(tc_fun(tc_List_Olist(U_14958),tc_List_Olist(U_14958)),tc_fun(tc_List_Olist(U_14958),tc_HOL_Obool),U_14958)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_14958),tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_14958),tc_List_Olist(U_14958)),tc_fun(tc_List_Olist(U_14958),tc_HOL_Obool)),tc_List_Olist(U_14958)),c_COMBB(tc_List_Olist(U_14958),tc_HOL_Obool,tc_List_Olist(U_14958))),c_fequal))),c_List_Olist_OCons(U_14958)))))),hAPP(hAPP(c_COMBC(U_14958,tc_fun(tc_List_Olist(U_14958),tc_HOL_Obool),tc_fun(tc_List_Olist(U_14958),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_14958),tc_HOL_Obool),tc_fun(tc_List_Olist(U_14958),tc_HOL_Obool)),U_14958),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_14958))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14958),c_fconj),hAPP(hAPP(c_COMBC(U_14958,tc_fun(U_14958,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14958)),U_14959)))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_14958),tc_fun(tc_List_Olist(U_14958),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(U_14958))),U_14960)))))),
    inference(clausify,[status(thm)],[f_3780_2]) ).

fof(f_3781_1,plain,
    ! [V_xs,V_x,T_a,V_i] :
      ( ( hAPP(c_Random_Opick(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a)),V_x),V_xs)),V_i) = hAPP(c_Random_Opick(T_a,V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_i),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a),V_x)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a),V_x))) )
      & ( hAPP(c_Random_Opick(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a)),V_x),V_xs)),V_i) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,T_a),V_x)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a),V_x))) ) ),
    inference(fof_nnf,[status(thm)],[fact_pick_Osimps]) ).

fof(f_3781_2,plain,
    ! [U_14964,U_14963,U_14962,U_14961] :
      ( ( hAPP(c_Random_Opick(U_14962,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,U_14962)),U_14963),U_14964)),U_14961) = hAPP(c_Random_Opick(U_14962,U_14964),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_14961),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_14962),U_14963)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_14961),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_14962),U_14963))) )
      & ( hAPP(c_Random_Opick(U_14962,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,U_14962)),U_14963),U_14964)),U_14961) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,U_14962),U_14963)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_14961),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_14962),U_14963))) ) ),
    inference(variable_rename,[status(thm)],[f_3781_1]) ).

fof(f_3781_3,plain,
    ( ! [U_14972,U_14970,U_14968,U_14966] :
        ( hAPP(c_Random_Opick(U_14968,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,U_14968)),U_14970),U_14972)),U_14966) = hAPP(c_Random_Opick(U_14968,U_14972),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_14966),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_14968),U_14970)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_14966),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_14968),U_14970))) )
    & ! [U_14971,U_14969,U_14967,U_14965] :
        ( hAPP(c_Random_Opick(U_14967,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,U_14967)),U_14969),U_14971)),U_14965) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,U_14967),U_14969)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_14965),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_14967),U_14969))) ) ),
    inference(miniscope,[status(thm)],[f_3781_2]) ).

cnf(f_3781_4,plain,
    ( hAPP(c_Random_Opick(U_14967,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,U_14967)),U_14969),U_14971)),U_14965) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,U_14967),U_14969)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_14965),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_14967),U_14969))) ),
    inference(clausify,[status(thm)],[f_3781_3]) ).

cnf(f_3781_5,plain,
    ( hAPP(c_Random_Opick(U_14968,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,U_14968)),U_14970),U_14972)),U_14966) = hAPP(c_Random_Opick(U_14968,U_14972),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_14966),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_14968),U_14970)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_14966),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_14968),U_14970))) ),
    inference(clausify,[status(thm)],[f_3781_3]) ).

fof(f_3782_1,plain,
    ! [V_xs_2,V_x_2,T_b] : c_Random_Oselect__weight(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b)),hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_b),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),V_x_2)),V_xs_2)) = c_Random_Oselect__weight(T_b,V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_select__weight__cons__zero]) ).

fof(f_3782_2,plain,
    ! [U_14975,U_14974,U_14973] : c_Random_Oselect__weight(U_14973,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,U_14973)),hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,U_14973),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),U_14974)),U_14975)) = c_Random_Oselect__weight(U_14973,U_14975),
    inference(variable_rename,[status(thm)],[f_3782_1]) ).

cnf(f_3782_3,plain,
    c_Random_Oselect__weight(U_14973,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,U_14973)),hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,U_14973),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),U_14974)),U_14975)) = c_Random_Oselect__weight(U_14973,U_14975),
    inference(clausify,[status(thm)],[f_3782_2]) ).

fof(f_3783_1,plain,
    ! [V_r_2,V_y_2,V_b_2,V_x_2,V_a_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_x_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_b_2),V_y_2))),c_List_Olexord(T_b,V_r_2)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2)))
            | V_a_2 != V_b_2 )
          & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) ) )
      & ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2)))
          & V_a_2 = V_b_2 )
        | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_x_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_b_2),V_y_2))),c_List_Olexord(T_b,V_r_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_lexord__cons__cons]) ).

fof(f_3783_2,plain,
    ! [U_14981,U_14980,U_14979,U_14978,U_14977,U_14976] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14976),tc_List_Olist(U_14976))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14976),tc_List_Olist(U_14976)),hAPP(hAPP(c_List_Olist_OCons(U_14976),U_14977),U_14978)),hAPP(hAPP(c_List_Olist_OCons(U_14976),U_14979),U_14980))),c_List_Olexord(U_14976,U_14981)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14976),tc_List_Olist(U_14976))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14976),tc_List_Olist(U_14976)),U_14978),U_14980)),c_List_Olexord(U_14976,U_14981)))
            | U_14977 != U_14979 )
          & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14976,U_14976)),hAPP(hAPP(c_Product__Type_OPair(U_14976,U_14976),U_14977),U_14979)),U_14981)) ) )
      & ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14976),tc_List_Olist(U_14976))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14976),tc_List_Olist(U_14976)),U_14978),U_14980)),c_List_Olexord(U_14976,U_14981)))
          & U_14977 = U_14979 )
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14976,U_14976)),hAPP(hAPP(c_Product__Type_OPair(U_14976,U_14976),U_14977),U_14979)),U_14981))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14976),tc_List_Olist(U_14976))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14976),tc_List_Olist(U_14976)),hAPP(hAPP(c_List_Olist_OCons(U_14976),U_14977),U_14978)),hAPP(hAPP(c_List_Olist_OCons(U_14976),U_14979),U_14980))),c_List_Olexord(U_14976,U_14981))) ) ),
    inference(variable_rename,[status(thm)],[f_3783_1]) ).

fof(f_3783_3,plain,
    ( ! [U_14993,U_14991,U_14989,U_14987,U_14985,U_14983] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14983),tc_List_Olist(U_14983))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14983),tc_List_Olist(U_14983)),hAPP(hAPP(c_List_Olist_OCons(U_14983),U_14985),U_14987)),hAPP(hAPP(c_List_Olist_OCons(U_14983),U_14989),U_14991))),c_List_Olexord(U_14983,U_14993)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14983),tc_List_Olist(U_14983))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14983),tc_List_Olist(U_14983)),U_14987),U_14991)),c_List_Olexord(U_14983,U_14993)))
            | U_14985 != U_14989 )
          & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14983,U_14983)),hAPP(hAPP(c_Product__Type_OPair(U_14983,U_14983),U_14985),U_14989)),U_14993)) ) )
    & ! [U_14992,U_14990,U_14988,U_14986,U_14984,U_14982] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14982),tc_List_Olist(U_14982))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14982),tc_List_Olist(U_14982)),U_14986),U_14990)),c_List_Olexord(U_14982,U_14992)))
          & U_14984 = U_14988 )
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14982,U_14982)),hAPP(hAPP(c_Product__Type_OPair(U_14982,U_14982),U_14984),U_14988)),U_14992))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14982),tc_List_Olist(U_14982))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14982),tc_List_Olist(U_14982)),hAPP(hAPP(c_List_Olist_OCons(U_14982),U_14984),U_14986)),hAPP(hAPP(c_List_Olist_OCons(U_14982),U_14988),U_14990))),c_List_Olexord(U_14982,U_14992))) ) ),
    inference(miniscope,[status(thm)],[f_3783_2]) ).

cnf(f_3783_4,plain,
    ( U_14984 = U_14988
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14982,U_14982)),hAPP(hAPP(c_Product__Type_OPair(U_14982,U_14982),U_14984),U_14988)),U_14992))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14982),tc_List_Olist(U_14982))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14982),tc_List_Olist(U_14982)),hAPP(hAPP(c_List_Olist_OCons(U_14982),U_14984),U_14986)),hAPP(hAPP(c_List_Olist_OCons(U_14982),U_14988),U_14990))),c_List_Olexord(U_14982,U_14992))) ),
    inference(clausify,[status(thm)],[f_3783_3]) ).

cnf(f_3783_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14982),tc_List_Olist(U_14982))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14982),tc_List_Olist(U_14982)),U_14986),U_14990)),c_List_Olexord(U_14982,U_14992)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_14982,U_14982)),hAPP(hAPP(c_Product__Type_OPair(U_14982,U_14982),U_14984),U_14988)),U_14992))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14982),tc_List_Olist(U_14982))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14982),tc_List_Olist(U_14982)),hAPP(hAPP(c_List_Olist_OCons(U_14982),U_14984),U_14986)),hAPP(hAPP(c_List_Olist_OCons(U_14982),U_14988),U_14990))),c_List_Olexord(U_14982,U_14992))) ),
    inference(clausify,[status(thm)],[f_3783_3]) ).

cnf(f_3783_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14983,U_14983)),hAPP(hAPP(c_Product__Type_OPair(U_14983,U_14983),U_14985),U_14989)),U_14993))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14983),tc_List_Olist(U_14983))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14983),tc_List_Olist(U_14983)),hAPP(hAPP(c_List_Olist_OCons(U_14983),U_14985),U_14987)),hAPP(hAPP(c_List_Olist_OCons(U_14983),U_14989),U_14991))),c_List_Olexord(U_14983,U_14993))) ),
    inference(clausify,[status(thm)],[f_3783_3]) ).

cnf(f_3783_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14983),tc_List_Olist(U_14983))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14983),tc_List_Olist(U_14983)),U_14987),U_14991)),c_List_Olexord(U_14983,U_14993)))
    | U_14985 != U_14989
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14983),tc_List_Olist(U_14983))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14983),tc_List_Olist(U_14983)),hAPP(hAPP(c_List_Olist_OCons(U_14983),U_14985),U_14987)),hAPP(hAPP(c_List_Olist_OCons(U_14983),U_14989),U_14991))),c_List_Olexord(U_14983,U_14993))) ),
    inference(clausify,[status(thm)],[f_3783_3]) ).

fof(f_3784_1,plain,
    ! [V_r_2,V_y_2,V_x_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olex(T_b,V_r_2)))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_y_2)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2))) )
      & ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_y_2)
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olex(T_b,V_r_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_lexord__lex]) ).

fof(f_3784_2,plain,
    ! [U_14997,U_14996,U_14995,U_14994] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14994),tc_List_Olist(U_14994))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14994),tc_List_Olist(U_14994)),U_14995),U_14996)),c_List_Olex(U_14994,U_14997)))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14994)),U_14995) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14994)),U_14996)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14994),tc_List_Olist(U_14994))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14994),tc_List_Olist(U_14994)),U_14995),U_14996)),c_List_Olexord(U_14994,U_14997))) )
      & ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14994)),U_14995) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14994)),U_14996)
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14994),tc_List_Olist(U_14994))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14994),tc_List_Olist(U_14994)),U_14995),U_14996)),c_List_Olexord(U_14994,U_14997))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14994),tc_List_Olist(U_14994))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14994),tc_List_Olist(U_14994)),U_14995),U_14996)),c_List_Olex(U_14994,U_14997))) ) ),
    inference(variable_rename,[status(thm)],[f_3784_1]) ).

fof(f_3784_3,plain,
    ( ! [U_15005,U_15003,U_15001,U_14999] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14999),tc_List_Olist(U_14999))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14999),tc_List_Olist(U_14999)),U_15001),U_15003)),c_List_Olex(U_14999,U_15005)))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14999)),U_15001) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14999)),U_15003)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14999),tc_List_Olist(U_14999))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14999),tc_List_Olist(U_14999)),U_15001),U_15003)),c_List_Olexord(U_14999,U_15005))) )
    & ! [U_15004,U_15002,U_15000,U_14998] :
        ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14998)),U_15000) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14998)),U_15002)
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14998),tc_List_Olist(U_14998))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14998),tc_List_Olist(U_14998)),U_15000),U_15002)),c_List_Olexord(U_14998,U_15004))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14998),tc_List_Olist(U_14998))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14998),tc_List_Olist(U_14998)),U_15000),U_15002)),c_List_Olex(U_14998,U_15004))) ) ),
    inference(miniscope,[status(thm)],[f_3784_2]) ).

cnf(f_3784_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14998),tc_List_Olist(U_14998))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14998),tc_List_Olist(U_14998)),U_15000),U_15002)),c_List_Olexord(U_14998,U_15004)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14998),tc_List_Olist(U_14998))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14998),tc_List_Olist(U_14998)),U_15000),U_15002)),c_List_Olex(U_14998,U_15004))) ),
    inference(clausify,[status(thm)],[f_3784_3]) ).

cnf(f_3784_5,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14998)),U_15000) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14998)),U_15002)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14998),tc_List_Olist(U_14998))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14998),tc_List_Olist(U_14998)),U_15000),U_15002)),c_List_Olex(U_14998,U_15004))) ),
    inference(clausify,[status(thm)],[f_3784_3]) ).

cnf(f_3784_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14999),tc_List_Olist(U_14999))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14999),tc_List_Olist(U_14999)),U_15001),U_15003)),c_List_Olex(U_14999,U_15005)))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14999)),U_15001) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_14999)),U_15003)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_14999),tc_List_Olist(U_14999))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_14999),tc_List_Olist(U_14999)),U_15001),U_15003)),c_List_Olexord(U_14999,U_15005))) ),
    inference(clausify,[status(thm)],[f_3784_3]) ).

fof(f_3785_1,plain,
    ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__listrel1__ConsI2]) ).

fof(f_3785_2,plain,
    ! [U_15011,U_15010,U_15009,U_15008,U_15007,U_15006] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15006),tc_List_Olist(U_15006))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15006),tc_List_Olist(U_15006)),hAPP(hAPP(c_List_Olist_OCons(U_15006),U_15007),U_15010)),hAPP(hAPP(c_List_Olist_OCons(U_15006),U_15008),U_15011))),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_15006),c_List_Olistrel1(U_15006,U_15009))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15006),tc_List_Olist(U_15006))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15006),tc_List_Olist(U_15006)),U_15010),U_15011)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_15006),c_List_Olistrel1(U_15006,U_15009))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15006,U_15006)),hAPP(hAPP(c_Product__Type_OPair(U_15006,U_15006),U_15007),U_15008)),c_Transitive__Closure_Ortrancl(U_15006,U_15009))) ),
    inference(variable_rename,[status(thm)],[f_3785_1]) ).

cnf(f_3785_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15006),tc_List_Olist(U_15006))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15006),tc_List_Olist(U_15006)),hAPP(hAPP(c_List_Olist_OCons(U_15006),U_15007),U_15010)),hAPP(hAPP(c_List_Olist_OCons(U_15006),U_15008),U_15011))),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_15006),c_List_Olistrel1(U_15006,U_15009))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15006),tc_List_Olist(U_15006))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15006),tc_List_Olist(U_15006)),U_15010),U_15011)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_15006),c_List_Olistrel1(U_15006,U_15009))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15006,U_15006)),hAPP(hAPP(c_Product__Type_OPair(U_15006,U_15006),U_15007),U_15008)),c_Transitive__Closure_Ortrancl(U_15006,U_15009))) ),
    inference(clausify,[status(thm)],[f_3785_2]) ).

fof(f_3786_1,plain,
    ! [V_list_2,V_a_2,V_fa_2,T_b] : c_List_Olist_Olist__size(T_b,V_fa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_list_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_fa_2,V_a_2)),c_List_Olist_Olist__size(T_b,V_fa_2,V_list_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(fof_nnf,[status(thm)],[fact_list_Osize_I2_J]) ).

fof(f_3786_2,plain,
    ! [U_15015,U_15014,U_15013,U_15012] : c_List_Olist_Olist__size(U_15012,U_15013,hAPP(hAPP(c_List_Olist_OCons(U_15012),U_15014),U_15015)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_15013,U_15014)),c_List_Olist_Olist__size(U_15012,U_15013,U_15015))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_3786_1]) ).

cnf(f_3786_3,plain,
    c_List_Olist_Olist__size(U_15012,U_15013,hAPP(hAPP(c_List_Olist_OCons(U_15012),U_15014),U_15015)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_15013,U_15014)),c_List_Olist_Olist__size(U_15012,U_15013,U_15015))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_3786_2]) ).

fof(f_3787_1,plain,
    ! [V_xs_2,V_r_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),c_Wellfounded_Oacc(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_Cons__acc__listrel1I]) ).

fof(f_3787_2,plain,
    ! [U_15019,U_15018,U_15017,U_15016] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15016)),hAPP(hAPP(c_List_Olist_OCons(U_15016),U_15017),U_15019)),c_Wellfounded_Oacc(tc_List_Olist(U_15016),c_List_Olistrel1(U_15016,U_15018))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15016)),U_15019),c_Wellfounded_Oacc(tc_List_Olist(U_15016),c_List_Olistrel1(U_15016,U_15018))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15016),U_15017),c_Wellfounded_Oacc(U_15016,U_15018))) ),
    inference(variable_rename,[status(thm)],[f_3787_1]) ).

cnf(f_3787_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15016)),hAPP(hAPP(c_List_Olist_OCons(U_15016),U_15017),U_15019)),c_Wellfounded_Oacc(tc_List_Olist(U_15016),c_List_Olistrel1(U_15016,U_15018))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15016)),U_15019),c_Wellfounded_Oacc(tc_List_Olist(U_15016),c_List_Olistrel1(U_15016,U_15018))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15016),U_15017),c_Wellfounded_Oacc(U_15016,U_15018))) ),
    inference(clausify,[status(thm)],[f_3787_2]) ).

fof(f_3788_1,plain,
    ! [V_s_2,V_r_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel1(T_b,V_r_2)),c_List_Olistrel1(T_b,V_s_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ),
    inference(fof_nnf,[status(thm)],[fact_listrel1__mono]) ).

fof(f_3788_2,plain,
    ! [U_15022,U_15021,U_15020] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_15020),tc_List_Olist(U_15020)),tc_HOL_Obool)),c_List_Olistrel1(U_15020,U_15021)),c_List_Olistrel1(U_15020,U_15022)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15020,U_15020),tc_HOL_Obool)),U_15021),U_15022)) ),
    inference(variable_rename,[status(thm)],[f_3788_1]) ).

cnf(f_3788_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_15020),tc_List_Olist(U_15020)),tc_HOL_Obool)),c_List_Olistrel1(U_15020,U_15021)),c_List_Olistrel1(U_15020,U_15022)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15020,U_15020),tc_HOL_Obool)),U_15021),U_15022)) ),
    inference(clausify,[status(thm)],[f_3788_2]) ).

fof(f_3789_1,plain,
    ! [V_r_2,T_b] : c_List_Olistrel1(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) = hAPP(c_Relation_Oconverse(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olistrel1(T_b,V_r_2)),
    inference(fof_nnf,[status(thm)],[fact_listrel1__converse]) ).

fof(f_3789_2,plain,
    ! [U_15024,U_15023] : c_List_Olistrel1(U_15023,hAPP(c_Relation_Oconverse(U_15023,U_15023),U_15024)) = hAPP(c_Relation_Oconverse(tc_List_Olist(U_15023),tc_List_Olist(U_15023)),c_List_Olistrel1(U_15023,U_15024)),
    inference(variable_rename,[status(thm)],[f_3789_1]) ).

cnf(f_3789_3,plain,
    c_List_Olistrel1(U_15023,hAPP(c_Relation_Oconverse(U_15023,U_15023),U_15024)) = hAPP(c_Relation_Oconverse(tc_List_Olist(U_15023),tc_List_Olist(U_15023)),c_List_Olistrel1(U_15023,U_15024)),
    inference(clausify,[status(thm)],[f_3789_2]) ).

fof(f_3790_1,plain,
    ! [V_r_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel1(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))),
    inference(fof_nnf,[status(thm)],[fact_listrel1__rtrancl__subset__rtrancl__listrel1]) ).

fof(f_3790_2,plain,
    ! [U_15026,U_15025] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_15025),tc_List_Olist(U_15025)),tc_HOL_Obool)),c_List_Olistrel1(U_15025,c_Transitive__Closure_Ortrancl(U_15025,U_15026))),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_15025),c_List_Olistrel1(U_15025,U_15026)))),
    inference(variable_rename,[status(thm)],[f_3790_1]) ).

cnf(f_3790_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_15025),tc_List_Olist(U_15025)),tc_HOL_Obool)),c_List_Olistrel1(U_15025,c_Transitive__Closure_Ortrancl(U_15025,U_15026))),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_15025),c_List_Olistrel1(U_15025,U_15026)))),
    inference(clausify,[status(thm)],[f_3790_2]) ).

fof(f_3791_1,plain,
    ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_ys_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__listrel1__ConsI1]) ).

fof(f_3791_2,plain,
    ! [U_15031,U_15030,U_15029,U_15028,U_15027] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15027),tc_List_Olist(U_15027))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15027),tc_List_Olist(U_15027)),hAPP(hAPP(c_List_Olist_OCons(U_15027),U_15031),U_15028)),hAPP(hAPP(c_List_Olist_OCons(U_15027),U_15031),U_15029))),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_15027),c_List_Olistrel1(U_15027,U_15030))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15027),tc_List_Olist(U_15027))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15027),tc_List_Olist(U_15027)),U_15028),U_15029)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_15027),c_List_Olistrel1(U_15027,U_15030)))) ),
    inference(variable_rename,[status(thm)],[f_3791_1]) ).

cnf(f_3791_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15027),tc_List_Olist(U_15027))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15027),tc_List_Olist(U_15027)),hAPP(hAPP(c_List_Olist_OCons(U_15027),U_15031),U_15028)),hAPP(hAPP(c_List_Olist_OCons(U_15027),U_15031),U_15029))),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_15027),c_List_Olistrel1(U_15027,U_15030))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15027),tc_List_Olist(U_15027))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15027),tc_List_Olist(U_15027)),U_15028),U_15029)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_15027),c_List_Olistrel1(U_15027,U_15030)))) ),
    inference(clausify,[status(thm)],[f_3791_2]) ).

fof(f_3792_1,plain,
    ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_ys_2))),c_List_Olistrel1(T_b,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_listrel1I2]) ).

fof(f_3792_2,plain,
    ! [U_15036,U_15035,U_15034,U_15033,U_15032] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15032),tc_List_Olist(U_15032))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15032),tc_List_Olist(U_15032)),hAPP(hAPP(c_List_Olist_OCons(U_15032),U_15036),U_15033)),hAPP(hAPP(c_List_Olist_OCons(U_15032),U_15036),U_15034))),c_List_Olistrel1(U_15032,U_15035)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15032),tc_List_Olist(U_15032))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15032),tc_List_Olist(U_15032)),U_15033),U_15034)),c_List_Olistrel1(U_15032,U_15035))) ),
    inference(variable_rename,[status(thm)],[f_3792_1]) ).

cnf(f_3792_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15032),tc_List_Olist(U_15032))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15032),tc_List_Olist(U_15032)),hAPP(hAPP(c_List_Olist_OCons(U_15032),U_15036),U_15033)),hAPP(hAPP(c_List_Olist_OCons(U_15032),U_15036),U_15034))),c_List_Olistrel1(U_15032,U_15035)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15032),tc_List_Olist(U_15032))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15032),tc_List_Olist(U_15032)),U_15033),U_15034)),c_List_Olistrel1(U_15032,U_15035))) ),
    inference(clausify,[status(thm)],[f_3792_2]) ).

fof(f_3793_1,plain,
    ! [V_r_2,V_y_2,V_x_2,T_b] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_y_2)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__listrel1__eq__len]) ).

fof(f_3793_2,plain,
    ! [U_15040,U_15039,U_15038,U_15037] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15037)),U_15038) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15037)),U_15039)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15037),tc_List_Olist(U_15037))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15037),tc_List_Olist(U_15037)),U_15038),U_15039)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_15037),c_List_Olistrel1(U_15037,U_15040)))) ),
    inference(variable_rename,[status(thm)],[f_3793_1]) ).

cnf(f_3793_3,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15037)),U_15038) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15037)),U_15039)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15037),tc_List_Olist(U_15037))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15037),tc_List_Olist(U_15037)),U_15038),U_15039)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_15037),c_List_Olistrel1(U_15037,U_15040)))) ),
    inference(clausify,[status(thm)],[f_3793_2]) ).

fof(f_3794_1,plain,
    ! [V_r_2,V_ys_2,V_xs_2,T_b] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_listrel1__eq__len]) ).

fof(f_3794_2,plain,
    ! [U_15044,U_15043,U_15042,U_15041] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15041)),U_15042) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15041)),U_15043)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15041),tc_List_Olist(U_15041))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15041),tc_List_Olist(U_15041)),U_15042),U_15043)),c_List_Olistrel1(U_15041,U_15044))) ),
    inference(variable_rename,[status(thm)],[f_3794_1]) ).

cnf(f_3794_3,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15041)),U_15042) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15041)),U_15043)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15041),tc_List_Olist(U_15041))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15041),tc_List_Olist(U_15041)),U_15042),U_15043)),c_List_Olistrel1(U_15041,U_15044))) ),
    inference(clausify,[status(thm)],[f_3794_2]) ).

fof(f_3795_1,plain,
    ! [V_r_2,V_y_2,V_x_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olistrel1(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olistrel1(T_b,V_r_2)))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olistrel1(T_b,V_r_2))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olistrel1(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_in__listrel1__converse]) ).

fof(f_3795_2,plain,
    ! [U_15048,U_15047,U_15046,U_15045] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15045),tc_List_Olist(U_15045))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15045),tc_List_Olist(U_15045)),U_15046),U_15047)),c_List_Olistrel1(U_15045,hAPP(c_Relation_Oconverse(U_15045,U_15045),U_15048))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15045),tc_List_Olist(U_15045))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15045),tc_List_Olist(U_15045)),U_15046),U_15047)),hAPP(c_Relation_Oconverse(tc_List_Olist(U_15045),tc_List_Olist(U_15045)),c_List_Olistrel1(U_15045,U_15048)))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15045),tc_List_Olist(U_15045))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15045),tc_List_Olist(U_15045)),U_15046),U_15047)),hAPP(c_Relation_Oconverse(tc_List_Olist(U_15045),tc_List_Olist(U_15045)),c_List_Olistrel1(U_15045,U_15048))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15045),tc_List_Olist(U_15045))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15045),tc_List_Olist(U_15045)),U_15046),U_15047)),c_List_Olistrel1(U_15045,hAPP(c_Relation_Oconverse(U_15045,U_15045),U_15048)))) ) ),
    inference(variable_rename,[status(thm)],[f_3795_1]) ).

fof(f_3795_3,plain,
    ( ! [U_15056,U_15054,U_15052,U_15050] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15050),tc_List_Olist(U_15050))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15050),tc_List_Olist(U_15050)),U_15052),U_15054)),c_List_Olistrel1(U_15050,hAPP(c_Relation_Oconverse(U_15050,U_15050),U_15056))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15050),tc_List_Olist(U_15050))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15050),tc_List_Olist(U_15050)),U_15052),U_15054)),hAPP(c_Relation_Oconverse(tc_List_Olist(U_15050),tc_List_Olist(U_15050)),c_List_Olistrel1(U_15050,U_15056)))) )
    & ! [U_15055,U_15053,U_15051,U_15049] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15049),tc_List_Olist(U_15049))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15049),tc_List_Olist(U_15049)),U_15051),U_15053)),hAPP(c_Relation_Oconverse(tc_List_Olist(U_15049),tc_List_Olist(U_15049)),c_List_Olistrel1(U_15049,U_15055))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15049),tc_List_Olist(U_15049))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15049),tc_List_Olist(U_15049)),U_15051),U_15053)),c_List_Olistrel1(U_15049,hAPP(c_Relation_Oconverse(U_15049,U_15049),U_15055)))) ) ),
    inference(miniscope,[status(thm)],[f_3795_2]) ).

cnf(f_3795_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15049),tc_List_Olist(U_15049))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15049),tc_List_Olist(U_15049)),U_15051),U_15053)),hAPP(c_Relation_Oconverse(tc_List_Olist(U_15049),tc_List_Olist(U_15049)),c_List_Olistrel1(U_15049,U_15055))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15049),tc_List_Olist(U_15049))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15049),tc_List_Olist(U_15049)),U_15051),U_15053)),c_List_Olistrel1(U_15049,hAPP(c_Relation_Oconverse(U_15049,U_15049),U_15055)))) ),
    inference(clausify,[status(thm)],[f_3795_3]) ).

cnf(f_3795_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15050),tc_List_Olist(U_15050))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15050),tc_List_Olist(U_15050)),U_15052),U_15054)),c_List_Olistrel1(U_15050,hAPP(c_Relation_Oconverse(U_15050,U_15050),U_15056))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15050),tc_List_Olist(U_15050))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15050),tc_List_Olist(U_15050)),U_15052),U_15054)),hAPP(c_Relation_Oconverse(tc_List_Olist(U_15050),tc_List_Olist(U_15050)),c_List_Olistrel1(U_15050,U_15056)))) ),
    inference(clausify,[status(thm)],[f_3795_3]) ).

fof(f_3796_1,plain,
    ! [V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_xs_2))),c_List_Olistrel1(T_b,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_listrel1I1]) ).

fof(f_3796_2,plain,
    ! [U_15061,U_15060,U_15059,U_15058,U_15057] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15057),tc_List_Olist(U_15057))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15057),tc_List_Olist(U_15057)),hAPP(hAPP(c_List_Olist_OCons(U_15057),U_15058),U_15061)),hAPP(hAPP(c_List_Olist_OCons(U_15057),U_15059),U_15061))),c_List_Olistrel1(U_15057,U_15060)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15057,U_15057)),hAPP(hAPP(c_Product__Type_OPair(U_15057,U_15057),U_15058),U_15059)),U_15060)) ),
    inference(variable_rename,[status(thm)],[f_3796_1]) ).

cnf(f_3796_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15057),tc_List_Olist(U_15057))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15057),tc_List_Olist(U_15057)),hAPP(hAPP(c_List_Olist_OCons(U_15057),U_15058),U_15061)),hAPP(hAPP(c_List_Olist_OCons(U_15057),U_15059),U_15061))),c_List_Olistrel1(U_15057,U_15060)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15057,U_15057)),hAPP(hAPP(c_Product__Type_OPair(U_15057,U_15057),U_15058),U_15059)),U_15060)) ),
    inference(clausify,[status(thm)],[f_3796_2]) ).

fof(f_3797_1,plain,
    ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olistrel1(T_b,V_r_2)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
            | V_x_2 != V_y_2 )
          & ( V_xs_2 != V_ys_2
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) ) ) )
      & ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
          & V_x_2 = V_y_2 )
        | ( V_xs_2 = V_ys_2
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olistrel1(T_b,V_r_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_Cons__listrel1__Cons]) ).

fof(f_3797_2,plain,
    ! [U_15067,U_15066,U_15065,U_15064,U_15063,U_15062] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15062),tc_List_Olist(U_15062))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15062),tc_List_Olist(U_15062)),hAPP(hAPP(c_List_Olist_OCons(U_15062),U_15063),U_15064)),hAPP(hAPP(c_List_Olist_OCons(U_15062),U_15065),U_15066))),c_List_Olistrel1(U_15062,U_15067)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15062),tc_List_Olist(U_15062))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15062),tc_List_Olist(U_15062)),U_15064),U_15066)),c_List_Olistrel1(U_15062,U_15067)))
            | U_15063 != U_15065 )
          & ( U_15064 != U_15066
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15062,U_15062)),hAPP(hAPP(c_Product__Type_OPair(U_15062,U_15062),U_15063),U_15065)),U_15067)) ) ) )
      & ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15062),tc_List_Olist(U_15062))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15062),tc_List_Olist(U_15062)),U_15064),U_15066)),c_List_Olistrel1(U_15062,U_15067)))
          & U_15063 = U_15065 )
        | ( U_15064 = U_15066
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15062,U_15062)),hAPP(hAPP(c_Product__Type_OPair(U_15062,U_15062),U_15063),U_15065)),U_15067)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15062),tc_List_Olist(U_15062))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15062),tc_List_Olist(U_15062)),hAPP(hAPP(c_List_Olist_OCons(U_15062),U_15063),U_15064)),hAPP(hAPP(c_List_Olist_OCons(U_15062),U_15065),U_15066))),c_List_Olistrel1(U_15062,U_15067))) ) ),
    inference(variable_rename,[status(thm)],[f_3797_1]) ).

fof(f_3797_3,plain,
    ( ! [U_15079,U_15077,U_15075,U_15073,U_15071,U_15069] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15069),tc_List_Olist(U_15069))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15069),tc_List_Olist(U_15069)),hAPP(hAPP(c_List_Olist_OCons(U_15069),U_15071),U_15073)),hAPP(hAPP(c_List_Olist_OCons(U_15069),U_15075),U_15077))),c_List_Olistrel1(U_15069,U_15079)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15069),tc_List_Olist(U_15069))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15069),tc_List_Olist(U_15069)),U_15073),U_15077)),c_List_Olistrel1(U_15069,U_15079)))
            | U_15071 != U_15075 )
          & ( U_15073 != U_15077
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15069,U_15069)),hAPP(hAPP(c_Product__Type_OPair(U_15069,U_15069),U_15071),U_15075)),U_15079)) ) ) )
    & ! [U_15078,U_15076,U_15074,U_15072,U_15070,U_15068] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15068),tc_List_Olist(U_15068))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15068),tc_List_Olist(U_15068)),U_15072),U_15076)),c_List_Olistrel1(U_15068,U_15078)))
          & U_15070 = U_15074 )
        | ( U_15072 = U_15076
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15068,U_15068)),hAPP(hAPP(c_Product__Type_OPair(U_15068,U_15068),U_15070),U_15074)),U_15078)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15068),tc_List_Olist(U_15068))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15068),tc_List_Olist(U_15068)),hAPP(hAPP(c_List_Olist_OCons(U_15068),U_15070),U_15072)),hAPP(hAPP(c_List_Olist_OCons(U_15068),U_15074),U_15076))),c_List_Olistrel1(U_15068,U_15078))) ) ),
    inference(miniscope,[status(thm)],[f_3797_2]) ).

cnf(f_3797_4,plain,
    ( U_15070 = U_15074
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_15068,U_15068)),hAPP(hAPP(c_Product__Type_OPair(U_15068,U_15068),U_15070),U_15074)),U_15078))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15068),tc_List_Olist(U_15068))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15068),tc_List_Olist(U_15068)),hAPP(hAPP(c_List_Olist_OCons(U_15068),U_15070),U_15072)),hAPP(hAPP(c_List_Olist_OCons(U_15068),U_15074),U_15076))),c_List_Olistrel1(U_15068,U_15078))) ),
    inference(clausify,[status(thm)],[f_3797_3]) ).

cnf(f_3797_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15068),tc_List_Olist(U_15068))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15068),tc_List_Olist(U_15068)),U_15072),U_15076)),c_List_Olistrel1(U_15068,U_15078)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_15068,U_15068)),hAPP(hAPP(c_Product__Type_OPair(U_15068,U_15068),U_15070),U_15074)),U_15078))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15068),tc_List_Olist(U_15068))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15068),tc_List_Olist(U_15068)),hAPP(hAPP(c_List_Olist_OCons(U_15068),U_15070),U_15072)),hAPP(hAPP(c_List_Olist_OCons(U_15068),U_15074),U_15076))),c_List_Olistrel1(U_15068,U_15078))) ),
    inference(clausify,[status(thm)],[f_3797_3]) ).

cnf(f_3797_6,plain,
    ( U_15070 = U_15074
    | U_15072 = U_15076
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15068),tc_List_Olist(U_15068))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15068),tc_List_Olist(U_15068)),hAPP(hAPP(c_List_Olist_OCons(U_15068),U_15070),U_15072)),hAPP(hAPP(c_List_Olist_OCons(U_15068),U_15074),U_15076))),c_List_Olistrel1(U_15068,U_15078))) ),
    inference(clausify,[status(thm)],[f_3797_3]) ).

cnf(f_3797_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15068),tc_List_Olist(U_15068))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15068),tc_List_Olist(U_15068)),U_15072),U_15076)),c_List_Olistrel1(U_15068,U_15078)))
    | U_15072 = U_15076
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15068),tc_List_Olist(U_15068))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15068),tc_List_Olist(U_15068)),hAPP(hAPP(c_List_Olist_OCons(U_15068),U_15070),U_15072)),hAPP(hAPP(c_List_Olist_OCons(U_15068),U_15074),U_15076))),c_List_Olistrel1(U_15068,U_15078))) ),
    inference(clausify,[status(thm)],[f_3797_3]) ).

cnf(f_3797_8,plain,
    ( U_15073 != U_15077
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15069,U_15069)),hAPP(hAPP(c_Product__Type_OPair(U_15069,U_15069),U_15071),U_15075)),U_15079))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15069),tc_List_Olist(U_15069))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15069),tc_List_Olist(U_15069)),hAPP(hAPP(c_List_Olist_OCons(U_15069),U_15071),U_15073)),hAPP(hAPP(c_List_Olist_OCons(U_15069),U_15075),U_15077))),c_List_Olistrel1(U_15069,U_15079))) ),
    inference(clausify,[status(thm)],[f_3797_3]) ).

cnf(f_3797_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15069),tc_List_Olist(U_15069))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15069),tc_List_Olist(U_15069)),U_15073),U_15077)),c_List_Olistrel1(U_15069,U_15079)))
    | U_15071 != U_15075
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15069),tc_List_Olist(U_15069))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15069),tc_List_Olist(U_15069)),hAPP(hAPP(c_List_Olist_OCons(U_15069),U_15071),U_15073)),hAPP(hAPP(c_List_Olist_OCons(U_15069),U_15075),U_15077))),c_List_Olistrel1(U_15069,U_15079))) ),
    inference(clausify,[status(thm)],[f_3797_3]) ).

fof(f_3798_1,plain,
    ! [V_xs_2,V_x_2,V_r_2,T_b] : hAPP(c_Relation_OImage(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))) = c_List_Oset__Cons(T_b,hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),hAPP(c_Relation_OImage(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),V_xs_2),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))))),
    inference(fof_nnf,[status(thm)],[fact_listrel__Cons]) ).

fof(f_3798_2,plain,
    ! [U_15083,U_15082,U_15081,U_15080] : hAPP(c_Relation_OImage(tc_List_Olist(U_15080),tc_List_Olist(U_15080),c_List_Olistrel(U_15080,U_15081)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_15080)),hAPP(hAPP(c_List_Olist_OCons(U_15080),U_15082),U_15083)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_15080),tc_HOL_Obool)))) = c_List_Oset__Cons(U_15080,hAPP(c_Relation_OImage(U_15080,U_15080,U_15081),hAPP(hAPP(c_Set_Oinsert(U_15080),U_15082),c_Orderings_Obot__class_Obot(tc_fun(U_15080,tc_HOL_Obool)))),hAPP(c_Relation_OImage(tc_List_Olist(U_15080),tc_List_Olist(U_15080),c_List_Olistrel(U_15080,U_15081)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_15080)),U_15083),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_15080),tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_3798_1]) ).

cnf(f_3798_3,plain,
    hAPP(c_Relation_OImage(tc_List_Olist(U_15080),tc_List_Olist(U_15080),c_List_Olistrel(U_15080,U_15081)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_15080)),hAPP(hAPP(c_List_Olist_OCons(U_15080),U_15082),U_15083)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_15080),tc_HOL_Obool)))) = c_List_Oset__Cons(U_15080,hAPP(c_Relation_OImage(U_15080,U_15080,U_15081),hAPP(hAPP(c_Set_Oinsert(U_15080),U_15082),c_Orderings_Obot__class_Obot(tc_fun(U_15080,tc_HOL_Obool)))),hAPP(c_Relation_OImage(tc_List_Olist(U_15080),tc_List_Olist(U_15080),c_List_Olistrel(U_15080,U_15081)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_15080)),U_15083),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_15080),tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_3798_2]) ).

fof(f_3799_1,plain,
    ! [V_y_2,V_r_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_y_2),V_y_2)),c_List_Olexord(T_b,V_r_2)))
      | ? [B_x] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_lexord__irreflexive]) ).

fof(f_3799_2,plain,
    ! [U_15087,U_15086,U_15085] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15085),tc_List_Olist(U_15085))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15085),tc_List_Olist(U_15085)),U_15087),U_15087)),c_List_Olexord(U_15085,U_15086)))
      | ? [U_15084] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_15085,U_15085)),hAPP(hAPP(c_Product__Type_OPair(U_15085,U_15085),U_15084),U_15084)),U_15086)) ),
    inference(variable_rename,[status(thm)],[f_3799_1]) ).

fof(f_3799_3,plain,
    ! [U_15087,U_15086,U_15085] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15085),tc_List_Olist(U_15085))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15085),tc_List_Olist(U_15085)),U_15087),U_15087)),c_List_Olexord(U_15085,U_15086)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(U_15085,U_15085)),hAPP(hAPP(c_Product__Type_OPair(U_15085,U_15085),sK396(U_15087,U_15086,U_15085)),sK396(U_15087,U_15086,U_15085))),U_15086)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK396]),skolemize(U_15084,sK396(U_15087,U_15086,U_15085))],[f_3799_2]) ).

cnf(f_3799_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15085),tc_List_Olist(U_15085))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15085),tc_List_Olist(U_15085)),U_15087),U_15087)),c_List_Olexord(U_15085,U_15086)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_15085,U_15085)),hAPP(hAPP(c_Product__Type_OPair(U_15085,U_15085),sK396(U_15087,U_15086,U_15085)),sK396(U_15087,U_15086,U_15085))),U_15086)) ),
    inference(clausify,[status(thm)],[f_3799_3]) ).

fof(f_3800_1,plain,
    ! [V_r_2,V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_xs_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)))),
    inference(fof_nnf,[status(thm)],[fact_listrel__rtrancl__refl]) ).

fof(f_3800_2,plain,
    ! [U_15090,U_15089,U_15088] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15088),tc_List_Olist(U_15088))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15088),tc_List_Olist(U_15088)),U_15089),U_15089)),c_List_Olistrel(U_15088,c_Transitive__Closure_Ortrancl(U_15088,U_15090)))),
    inference(variable_rename,[status(thm)],[f_3800_1]) ).

cnf(f_3800_3,plain,
    hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15088),tc_List_Olist(U_15088))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15088),tc_List_Olist(U_15088)),U_15089),U_15089)),c_List_Olistrel(U_15088,c_Transitive__Closure_Ortrancl(U_15088,U_15090)))),
    inference(clausify,[status(thm)],[f_3800_2]) ).

fof(f_3801_1,plain,
    ! [V_s_2,V_r_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel(T_b,V_r_2)),c_List_Olistrel(T_b,V_s_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ),
    inference(fof_nnf,[status(thm)],[fact_listrel__mono]) ).

fof(f_3801_2,plain,
    ! [U_15093,U_15092,U_15091] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_15091),tc_List_Olist(U_15091)),tc_HOL_Obool)),c_List_Olistrel(U_15091,U_15092)),c_List_Olistrel(U_15091,U_15093)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15091,U_15091),tc_HOL_Obool)),U_15092),U_15093)) ),
    inference(variable_rename,[status(thm)],[f_3801_1]) ).

cnf(f_3801_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_15091),tc_List_Olist(U_15091)),tc_HOL_Obool)),c_List_Olistrel(U_15091,U_15092)),c_List_Olistrel(U_15091,U_15093)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15091,U_15091),tc_HOL_Obool)),U_15092),U_15093)) ),
    inference(clausify,[status(thm)],[f_3801_2]) ).

fof(f_3802_1,plain,
    ! [V_r_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel(T_b,V_r_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))),
    inference(fof_nnf,[status(thm)],[fact_listrel__subset__rtrancl__listrel1]) ).

fof(f_3802_2,plain,
    ! [U_15095,U_15094] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_15094),tc_List_Olist(U_15094)),tc_HOL_Obool)),c_List_Olistrel(U_15094,U_15095)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_15094),c_List_Olistrel1(U_15094,U_15095)))),
    inference(variable_rename,[status(thm)],[f_3802_1]) ).

cnf(f_3802_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_15094),tc_List_Olist(U_15094)),tc_HOL_Obool)),c_List_Olistrel(U_15094,U_15095)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_15094),c_List_Olistrel1(U_15094,U_15095)))),
    inference(clausify,[status(thm)],[f_3802_2]) ).

fof(f_3803_1,plain,
    ! [V_r_2,V_ys_2,V_xs_2,T_b] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_listrel__eq__len]) ).

fof(f_3803_2,plain,
    ! [U_15099,U_15098,U_15097,U_15096] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15096)),U_15097) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15096)),U_15098)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15096),tc_List_Olist(U_15096))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15096),tc_List_Olist(U_15096)),U_15097),U_15098)),c_List_Olistrel(U_15096,U_15099))) ),
    inference(variable_rename,[status(thm)],[f_3803_1]) ).

cnf(f_3803_3,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15096)),U_15097) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15096)),U_15098)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15096),tc_List_Olist(U_15096))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15096),tc_List_Olist(U_15096)),U_15097),U_15098)),c_List_Olistrel(U_15096,U_15099))) ),
    inference(clausify,[status(thm)],[f_3803_2]) ).

fof(f_3804_1,plain,
    ! [V_zs_2,V_r_2,V_ys_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_zs_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_ys_2),V_zs_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_listrel__rtrancl__trans]) ).

fof(f_3804_2,plain,
    ! [U_15104,U_15103,U_15102,U_15101,U_15100] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15100),tc_List_Olist(U_15100))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15100),tc_List_Olist(U_15100)),U_15101),U_15104)),c_List_Olistrel(U_15100,c_Transitive__Closure_Ortrancl(U_15100,U_15103))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15100),tc_List_Olist(U_15100))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15100),tc_List_Olist(U_15100)),U_15102),U_15104)),c_List_Olistrel(U_15100,c_Transitive__Closure_Ortrancl(U_15100,U_15103))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15100),tc_List_Olist(U_15100))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15100),tc_List_Olist(U_15100)),U_15101),U_15102)),c_List_Olistrel(U_15100,c_Transitive__Closure_Ortrancl(U_15100,U_15103)))) ),
    inference(variable_rename,[status(thm)],[f_3804_1]) ).

cnf(f_3804_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15100),tc_List_Olist(U_15100))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15100),tc_List_Olist(U_15100)),U_15101),U_15104)),c_List_Olistrel(U_15100,c_Transitive__Closure_Ortrancl(U_15100,U_15103))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15100),tc_List_Olist(U_15100))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15100),tc_List_Olist(U_15100)),U_15102),U_15104)),c_List_Olistrel(U_15100,c_Transitive__Closure_Ortrancl(U_15100,U_15103))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15100),tc_List_Olist(U_15100))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15100),tc_List_Olist(U_15100)),U_15101),U_15102)),c_List_Olistrel(U_15100,c_Transitive__Closure_Ortrancl(U_15100,U_15103)))) ),
    inference(clausify,[status(thm)],[f_3804_2]) ).

fof(f_3805_1,plain,
    ! [V_r_2,T_b] : c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)),
    inference(fof_nnf,[status(thm)],[fact_listrel__rtrancl__eq__rtrancl__listrel1]) ).

fof(f_3805_2,plain,
    ! [U_15106,U_15105] : c_List_Olistrel(U_15105,c_Transitive__Closure_Ortrancl(U_15105,U_15106)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(U_15105),c_List_Olistrel1(U_15105,U_15106)),
    inference(variable_rename,[status(thm)],[f_3805_1]) ).

cnf(f_3805_3,plain,
    c_List_Olistrel(U_15105,c_Transitive__Closure_Ortrancl(U_15105,U_15106)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(U_15105),c_List_Olistrel1(U_15105,U_15106)),
    inference(clausify,[status(thm)],[f_3805_2]) ).

fof(f_3806_1,plain,
    ! [V_r_2,V_ys_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_listrel__reflcl__if__listrel1]) ).

fof(f_3806_2,plain,
    ! [U_15110,U_15109,U_15108,U_15107] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15107),tc_List_Olist(U_15107))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15107),tc_List_Olist(U_15107)),U_15108),U_15109)),c_List_Olistrel(U_15107,c_Transitive__Closure_Ortrancl(U_15107,U_15110))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15107),tc_List_Olist(U_15107))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15107),tc_List_Olist(U_15107)),U_15108),U_15109)),c_List_Olistrel1(U_15107,U_15110))) ),
    inference(variable_rename,[status(thm)],[f_3806_1]) ).

cnf(f_3806_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15107),tc_List_Olist(U_15107))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15107),tc_List_Olist(U_15107)),U_15108),U_15109)),c_List_Olistrel(U_15107,c_Transitive__Closure_Ortrancl(U_15107,U_15110))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15107),tc_List_Olist(U_15107))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15107),tc_List_Olist(U_15107)),U_15108),U_15109)),c_List_Olistrel1(U_15107,U_15110))) ),
    inference(clausify,[status(thm)],[f_3806_2]) ).

fof(f_3807_1,plain,
    ! [V_r_H_2,V_r_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel1(T_b,V_r_2)),c_List_Olistrel(T_b,V_r_H_2)))
      | ~ c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_r_H_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_r_H_2)) ),
    inference(fof_nnf,[status(thm)],[fact_listrel1__subset__listrel]) ).

fof(f_3807_2,plain,
    ! [U_15113,U_15112,U_15111] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_15111),tc_List_Olist(U_15111)),tc_HOL_Obool)),c_List_Olistrel1(U_15111,U_15112)),c_List_Olistrel(U_15111,U_15113)))
      | ~ c_Relation_Orefl__on(U_15111,c_Orderings_Otop__class_Otop(tc_fun(U_15111,tc_HOL_Obool)),U_15113)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15111,U_15111),tc_HOL_Obool)),U_15112),U_15113)) ),
    inference(variable_rename,[status(thm)],[f_3807_1]) ).

cnf(f_3807_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_15111),tc_List_Olist(U_15111)),tc_HOL_Obool)),c_List_Olistrel1(U_15111,U_15112)),c_List_Olistrel(U_15111,U_15113)))
    | ~ c_Relation_Orefl__on(U_15111,c_Orderings_Otop__class_Otop(tc_fun(U_15111,tc_HOL_Obool)),U_15113)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15111,U_15111),tc_HOL_Obool)),U_15112),U_15113)) ),
    inference(clausify,[status(thm)],[f_3807_2]) ).

fof(f_3808_1,plain,
    ! [V_r_2,V_ys_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__listrel1__if__listrel]) ).

fof(f_3808_2,plain,
    ! [U_15117,U_15116,U_15115,U_15114] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15114),tc_List_Olist(U_15114))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15114),tc_List_Olist(U_15114)),U_15115),U_15116)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_15114),c_List_Olistrel1(U_15114,U_15117))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15114),tc_List_Olist(U_15114))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15114),tc_List_Olist(U_15114)),U_15115),U_15116)),c_List_Olistrel(U_15114,U_15117))) ),
    inference(variable_rename,[status(thm)],[f_3808_1]) ).

cnf(f_3808_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15114),tc_List_Olist(U_15114))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15114),tc_List_Olist(U_15114)),U_15115),U_15116)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_15114),c_List_Olistrel1(U_15114,U_15117))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15114),tc_List_Olist(U_15114))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15114),tc_List_Olist(U_15114)),U_15115),U_15116)),c_List_Olistrel(U_15114,U_15117))) ),
    inference(clausify,[status(thm)],[f_3808_2]) ).

fof(f_3809_1,plain,
    ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olistrel(T_b,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_listrel_OCons]) ).

fof(f_3809_2,plain,
    ! [U_15123,U_15122,U_15121,U_15120,U_15119,U_15118] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15118),tc_List_Olist(U_15118))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15118),tc_List_Olist(U_15118)),hAPP(hAPP(c_List_Olist_OCons(U_15118),U_15119),U_15122)),hAPP(hAPP(c_List_Olist_OCons(U_15118),U_15120),U_15123))),c_List_Olistrel(U_15118,U_15121)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15118),tc_List_Olist(U_15118))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15118),tc_List_Olist(U_15118)),U_15122),U_15123)),c_List_Olistrel(U_15118,U_15121)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15118,U_15118)),hAPP(hAPP(c_Product__Type_OPair(U_15118,U_15118),U_15119),U_15120)),U_15121)) ),
    inference(variable_rename,[status(thm)],[f_3809_1]) ).

cnf(f_3809_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15118),tc_List_Olist(U_15118))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15118),tc_List_Olist(U_15118)),hAPP(hAPP(c_List_Olist_OCons(U_15118),U_15119),U_15122)),hAPP(hAPP(c_List_Olist_OCons(U_15118),U_15120),U_15123))),c_List_Olistrel(U_15118,U_15121)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15118),tc_List_Olist(U_15118))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15118),tc_List_Olist(U_15118)),U_15122),U_15123)),c_List_Olistrel(U_15118,U_15121)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15118,U_15118)),hAPP(hAPP(c_Product__Type_OPair(U_15118,U_15118),U_15119),U_15120)),U_15121)) ),
    inference(clausify,[status(thm)],[f_3809_2]) ).

fof(f_3810_1,plain,
    ! [V_xa_2,V_x_2,V_r_2,T_b] :
      ( ( c_List_Olistrelp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2),V_x_2,V_xa_2)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_xa_2)),c_List_Olistrel(T_b,V_r_2))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_xa_2)),c_List_Olistrel(T_b,V_r_2)))
        | ~ c_List_Olistrelp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2),V_x_2,V_xa_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_listrelp__listrel__eq]) ).

fof(f_3810_2,plain,
    ! [U_15127,U_15126,U_15125,U_15124] :
      ( ( c_List_Olistrelp(U_15124,hAPP(hAPP(c_COMBC(U_15124,tc_fun(tc_prod(U_15124,U_15124),tc_HOL_Obool),tc_fun(U_15124,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15124,tc_fun(tc_fun(tc_prod(U_15124,U_15124),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15124,U_15124),tc_HOL_Obool),tc_fun(U_15124,tc_HOL_Obool)),U_15124),c_COMBC(U_15124,tc_fun(tc_prod(U_15124,U_15124),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15124,tc_prod(U_15124,U_15124)),tc_fun(U_15124,tc_fun(tc_fun(tc_prod(U_15124,U_15124),tc_HOL_Obool),tc_HOL_Obool)),U_15124),hAPP(c_COMBB(tc_prod(U_15124,U_15124),tc_fun(tc_fun(tc_prod(U_15124,U_15124),tc_HOL_Obool),tc_HOL_Obool),U_15124),c_member(tc_prod(U_15124,U_15124)))),c_Product__Type_OPair(U_15124,U_15124)))),U_15125),U_15126,U_15127)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15124),tc_List_Olist(U_15124))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15124),tc_List_Olist(U_15124)),U_15126),U_15127)),c_List_Olistrel(U_15124,U_15125))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15124),tc_List_Olist(U_15124))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15124),tc_List_Olist(U_15124)),U_15126),U_15127)),c_List_Olistrel(U_15124,U_15125)))
        | ~ c_List_Olistrelp(U_15124,hAPP(hAPP(c_COMBC(U_15124,tc_fun(tc_prod(U_15124,U_15124),tc_HOL_Obool),tc_fun(U_15124,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15124,tc_fun(tc_fun(tc_prod(U_15124,U_15124),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15124,U_15124),tc_HOL_Obool),tc_fun(U_15124,tc_HOL_Obool)),U_15124),c_COMBC(U_15124,tc_fun(tc_prod(U_15124,U_15124),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15124,tc_prod(U_15124,U_15124)),tc_fun(U_15124,tc_fun(tc_fun(tc_prod(U_15124,U_15124),tc_HOL_Obool),tc_HOL_Obool)),U_15124),hAPP(c_COMBB(tc_prod(U_15124,U_15124),tc_fun(tc_fun(tc_prod(U_15124,U_15124),tc_HOL_Obool),tc_HOL_Obool),U_15124),c_member(tc_prod(U_15124,U_15124)))),c_Product__Type_OPair(U_15124,U_15124)))),U_15125),U_15126,U_15127) ) ),
    inference(variable_rename,[status(thm)],[f_3810_1]) ).

fof(f_3810_3,plain,
    ( ! [U_15135,U_15133,U_15131,U_15129] :
        ( c_List_Olistrelp(U_15129,hAPP(hAPP(c_COMBC(U_15129,tc_fun(tc_prod(U_15129,U_15129),tc_HOL_Obool),tc_fun(U_15129,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15129,tc_fun(tc_fun(tc_prod(U_15129,U_15129),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15129,U_15129),tc_HOL_Obool),tc_fun(U_15129,tc_HOL_Obool)),U_15129),c_COMBC(U_15129,tc_fun(tc_prod(U_15129,U_15129),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15129,tc_prod(U_15129,U_15129)),tc_fun(U_15129,tc_fun(tc_fun(tc_prod(U_15129,U_15129),tc_HOL_Obool),tc_HOL_Obool)),U_15129),hAPP(c_COMBB(tc_prod(U_15129,U_15129),tc_fun(tc_fun(tc_prod(U_15129,U_15129),tc_HOL_Obool),tc_HOL_Obool),U_15129),c_member(tc_prod(U_15129,U_15129)))),c_Product__Type_OPair(U_15129,U_15129)))),U_15131),U_15133,U_15135)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15129),tc_List_Olist(U_15129))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15129),tc_List_Olist(U_15129)),U_15133),U_15135)),c_List_Olistrel(U_15129,U_15131))) )
    & ! [U_15134,U_15132,U_15130,U_15128] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15128),tc_List_Olist(U_15128))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15128),tc_List_Olist(U_15128)),U_15132),U_15134)),c_List_Olistrel(U_15128,U_15130)))
        | ~ c_List_Olistrelp(U_15128,hAPP(hAPP(c_COMBC(U_15128,tc_fun(tc_prod(U_15128,U_15128),tc_HOL_Obool),tc_fun(U_15128,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15128,tc_fun(tc_fun(tc_prod(U_15128,U_15128),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15128,U_15128),tc_HOL_Obool),tc_fun(U_15128,tc_HOL_Obool)),U_15128),c_COMBC(U_15128,tc_fun(tc_prod(U_15128,U_15128),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15128,tc_prod(U_15128,U_15128)),tc_fun(U_15128,tc_fun(tc_fun(tc_prod(U_15128,U_15128),tc_HOL_Obool),tc_HOL_Obool)),U_15128),hAPP(c_COMBB(tc_prod(U_15128,U_15128),tc_fun(tc_fun(tc_prod(U_15128,U_15128),tc_HOL_Obool),tc_HOL_Obool),U_15128),c_member(tc_prod(U_15128,U_15128)))),c_Product__Type_OPair(U_15128,U_15128)))),U_15130),U_15132,U_15134) ) ),
    inference(miniscope,[status(thm)],[f_3810_2]) ).

cnf(f_3810_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15128),tc_List_Olist(U_15128))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15128),tc_List_Olist(U_15128)),U_15132),U_15134)),c_List_Olistrel(U_15128,U_15130)))
    | ~ c_List_Olistrelp(U_15128,hAPP(hAPP(c_COMBC(U_15128,tc_fun(tc_prod(U_15128,U_15128),tc_HOL_Obool),tc_fun(U_15128,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15128,tc_fun(tc_fun(tc_prod(U_15128,U_15128),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15128,U_15128),tc_HOL_Obool),tc_fun(U_15128,tc_HOL_Obool)),U_15128),c_COMBC(U_15128,tc_fun(tc_prod(U_15128,U_15128),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15128,tc_prod(U_15128,U_15128)),tc_fun(U_15128,tc_fun(tc_fun(tc_prod(U_15128,U_15128),tc_HOL_Obool),tc_HOL_Obool)),U_15128),hAPP(c_COMBB(tc_prod(U_15128,U_15128),tc_fun(tc_fun(tc_prod(U_15128,U_15128),tc_HOL_Obool),tc_HOL_Obool),U_15128),c_member(tc_prod(U_15128,U_15128)))),c_Product__Type_OPair(U_15128,U_15128)))),U_15130),U_15132,U_15134) ),
    inference(clausify,[status(thm)],[f_3810_3]) ).

cnf(f_3810_5,plain,
    ( c_List_Olistrelp(U_15129,hAPP(hAPP(c_COMBC(U_15129,tc_fun(tc_prod(U_15129,U_15129),tc_HOL_Obool),tc_fun(U_15129,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15129,tc_fun(tc_fun(tc_prod(U_15129,U_15129),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15129,U_15129),tc_HOL_Obool),tc_fun(U_15129,tc_HOL_Obool)),U_15129),c_COMBC(U_15129,tc_fun(tc_prod(U_15129,U_15129),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15129,tc_prod(U_15129,U_15129)),tc_fun(U_15129,tc_fun(tc_fun(tc_prod(U_15129,U_15129),tc_HOL_Obool),tc_HOL_Obool)),U_15129),hAPP(c_COMBB(tc_prod(U_15129,U_15129),tc_fun(tc_fun(tc_prod(U_15129,U_15129),tc_HOL_Obool),tc_HOL_Obool),U_15129),c_member(tc_prod(U_15129,U_15129)))),c_Product__Type_OPair(U_15129,U_15129)))),U_15131),U_15133,U_15135)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15129),tc_List_Olist(U_15129))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15129),tc_List_Olist(U_15129)),U_15133),U_15135)),c_List_Olistrel(U_15129,U_15131))) ),
    inference(clausify,[status(thm)],[f_3810_3]) ).

fof(f_3811_1,plain,
    ! [V_r_2,V_ys_2,V_y_2,V_xs_2,T_b] :
      ( ? [B_x,B_xs] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),B_xs),V_ys_2)),c_List_Olistrel(T_b,V_r_2)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),V_y_2)),V_r_2))
          & V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_xs) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olistrel(T_b,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_listrel__Cons2]) ).

fof(f_3811_2,plain,
    ! [U_15142,U_15141,U_15140,U_15139,U_15138] :
      ( ? [U_15137,U_15136] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15138),tc_List_Olist(U_15138))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15138),tc_List_Olist(U_15138)),U_15136),U_15141)),c_List_Olistrel(U_15138,U_15142)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15138,U_15138)),hAPP(hAPP(c_Product__Type_OPair(U_15138,U_15138),U_15137),U_15140)),U_15142))
          & U_15139 = hAPP(hAPP(c_List_Olist_OCons(U_15138),U_15137),U_15136) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15138),tc_List_Olist(U_15138))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15138),tc_List_Olist(U_15138)),U_15139),hAPP(hAPP(c_List_Olist_OCons(U_15138),U_15140),U_15141))),c_List_Olistrel(U_15138,U_15142))) ),
    inference(variable_rename,[status(thm)],[f_3811_1]) ).

fof(f_3811_3,plain,
    ! [U_15142,U_15141,U_15140,U_15139,U_15138] :
      ( ? [U_15136] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15138),tc_List_Olist(U_15138))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15138),tc_List_Olist(U_15138)),U_15136),U_15141)),c_List_Olistrel(U_15138,U_15142)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15138,U_15138)),hAPP(hAPP(c_Product__Type_OPair(U_15138,U_15138),sK397(U_15142,U_15141,U_15140,U_15139,U_15138)),U_15140)),U_15142))
          & U_15139 = hAPP(hAPP(c_List_Olist_OCons(U_15138),sK397(U_15142,U_15141,U_15140,U_15139,U_15138)),U_15136) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15138),tc_List_Olist(U_15138))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15138),tc_List_Olist(U_15138)),U_15139),hAPP(hAPP(c_List_Olist_OCons(U_15138),U_15140),U_15141))),c_List_Olistrel(U_15138,U_15142))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK397]),skolemize(U_15137,sK397(U_15142,U_15141,U_15140,U_15139,U_15138))],[f_3811_2]) ).

fof(f_3811_4,plain,
    ! [U_15142,U_15141,U_15140,U_15139,U_15138] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15138),tc_List_Olist(U_15138))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15138),tc_List_Olist(U_15138)),sK398(U_15142,U_15141,U_15140,U_15139,U_15138)),U_15141)),c_List_Olistrel(U_15138,U_15142)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15138,U_15138)),hAPP(hAPP(c_Product__Type_OPair(U_15138,U_15138),sK397(U_15142,U_15141,U_15140,U_15139,U_15138)),U_15140)),U_15142))
        & U_15139 = hAPP(hAPP(c_List_Olist_OCons(U_15138),sK397(U_15142,U_15141,U_15140,U_15139,U_15138)),sK398(U_15142,U_15141,U_15140,U_15139,U_15138)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15138),tc_List_Olist(U_15138))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15138),tc_List_Olist(U_15138)),U_15139),hAPP(hAPP(c_List_Olist_OCons(U_15138),U_15140),U_15141))),c_List_Olistrel(U_15138,U_15142))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK398]),skolemize(U_15136,sK398(U_15142,U_15141,U_15140,U_15139,U_15138))],[f_3811_3]) ).

cnf(f_3811_5,plain,
    ( U_15139 = hAPP(hAPP(c_List_Olist_OCons(U_15138),sK397(U_15142,U_15141,U_15140,U_15139,U_15138)),sK398(U_15142,U_15141,U_15140,U_15139,U_15138))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15138),tc_List_Olist(U_15138))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15138),tc_List_Olist(U_15138)),U_15139),hAPP(hAPP(c_List_Olist_OCons(U_15138),U_15140),U_15141))),c_List_Olistrel(U_15138,U_15142))) ),
    inference(clausify,[status(thm)],[f_3811_4]) ).

cnf(f_3811_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15138,U_15138)),hAPP(hAPP(c_Product__Type_OPair(U_15138,U_15138),sK397(U_15142,U_15141,U_15140,U_15139,U_15138)),U_15140)),U_15142))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15138),tc_List_Olist(U_15138))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15138),tc_List_Olist(U_15138)),U_15139),hAPP(hAPP(c_List_Olist_OCons(U_15138),U_15140),U_15141))),c_List_Olistrel(U_15138,U_15142))) ),
    inference(clausify,[status(thm)],[f_3811_4]) ).

cnf(f_3811_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15138),tc_List_Olist(U_15138))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15138),tc_List_Olist(U_15138)),sK398(U_15142,U_15141,U_15140,U_15139,U_15138)),U_15141)),c_List_Olistrel(U_15138,U_15142)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15138),tc_List_Olist(U_15138))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15138),tc_List_Olist(U_15138)),U_15139),hAPP(hAPP(c_List_Olist_OCons(U_15138),U_15140),U_15141))),c_List_Olistrel(U_15138,U_15142))) ),
    inference(clausify,[status(thm)],[f_3811_4]) ).

fof(f_3812_1,plain,
    ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2,V_r_2,T_b] :
      ( ( c_List_Olistrelp(T_b,V_r_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a1_2),V_a3_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a2_2),V_a4_2))
        | ~ c_List_Olistrelp(T_b,V_r_2,V_a3_2,V_a4_2)
        | ~ hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2)) )
      & ( ( c_List_Olistrelp(T_b,V_r_2,V_a3_2,V_a4_2)
          & hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2)) )
        | ~ c_List_Olistrelp(T_b,V_r_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a1_2),V_a3_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a2_2),V_a4_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_listrelp_Oequations_I2_J]) ).

fof(f_3812_2,plain,
    ! [U_15148,U_15147,U_15146,U_15145,U_15144,U_15143] :
      ( ( c_List_Olistrelp(U_15143,U_15144,hAPP(hAPP(c_List_Olist_OCons(U_15143),U_15145),U_15146),hAPP(hAPP(c_List_Olist_OCons(U_15143),U_15147),U_15148))
        | ~ c_List_Olistrelp(U_15143,U_15144,U_15146,U_15148)
        | ~ hBOOL(hAPP(hAPP(U_15144,U_15145),U_15147)) )
      & ( ( c_List_Olistrelp(U_15143,U_15144,U_15146,U_15148)
          & hBOOL(hAPP(hAPP(U_15144,U_15145),U_15147)) )
        | ~ c_List_Olistrelp(U_15143,U_15144,hAPP(hAPP(c_List_Olist_OCons(U_15143),U_15145),U_15146),hAPP(hAPP(c_List_Olist_OCons(U_15143),U_15147),U_15148)) ) ),
    inference(variable_rename,[status(thm)],[f_3812_1]) ).

fof(f_3812_3,plain,
    ( ! [U_15160,U_15158,U_15156,U_15154,U_15152,U_15150] :
        ( c_List_Olistrelp(U_15150,U_15152,hAPP(hAPP(c_List_Olist_OCons(U_15150),U_15154),U_15156),hAPP(hAPP(c_List_Olist_OCons(U_15150),U_15158),U_15160))
        | ~ c_List_Olistrelp(U_15150,U_15152,U_15156,U_15160)
        | ~ hBOOL(hAPP(hAPP(U_15152,U_15154),U_15158)) )
    & ! [U_15159,U_15157,U_15155,U_15153,U_15151,U_15149] :
        ( ( c_List_Olistrelp(U_15149,U_15151,U_15155,U_15159)
          & hBOOL(hAPP(hAPP(U_15151,U_15153),U_15157)) )
        | ~ c_List_Olistrelp(U_15149,U_15151,hAPP(hAPP(c_List_Olist_OCons(U_15149),U_15153),U_15155),hAPP(hAPP(c_List_Olist_OCons(U_15149),U_15157),U_15159)) ) ),
    inference(miniscope,[status(thm)],[f_3812_2]) ).

cnf(f_3812_4,plain,
    ( hBOOL(hAPP(hAPP(U_15151,U_15153),U_15157))
    | ~ c_List_Olistrelp(U_15149,U_15151,hAPP(hAPP(c_List_Olist_OCons(U_15149),U_15153),U_15155),hAPP(hAPP(c_List_Olist_OCons(U_15149),U_15157),U_15159)) ),
    inference(clausify,[status(thm)],[f_3812_3]) ).

cnf(f_3812_5,plain,
    ( c_List_Olistrelp(U_15149,U_15151,U_15155,U_15159)
    | ~ c_List_Olistrelp(U_15149,U_15151,hAPP(hAPP(c_List_Olist_OCons(U_15149),U_15153),U_15155),hAPP(hAPP(c_List_Olist_OCons(U_15149),U_15157),U_15159)) ),
    inference(clausify,[status(thm)],[f_3812_3]) ).

cnf(f_3812_6,plain,
    ( c_List_Olistrelp(U_15150,U_15152,hAPP(hAPP(c_List_Olist_OCons(U_15150),U_15154),U_15156),hAPP(hAPP(c_List_Olist_OCons(U_15150),U_15158),U_15160))
    | ~ c_List_Olistrelp(U_15150,U_15152,U_15156,U_15160)
    | ~ hBOOL(hAPP(hAPP(U_15152,U_15154),U_15158)) ),
    inference(clausify,[status(thm)],[f_3812_3]) ).

fof(f_3813_1,plain,
    ! [V_ys_2,V_xs_2,T_b,V_y_2,V_x_2,V_r_2] :
      ( c_List_Olistrelp(T_b,V_r_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))
      | ~ c_List_Olistrelp(T_b,V_r_2,V_xs_2,V_ys_2)
      | ~ hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_listrelp_OCons]) ).

fof(f_3813_2,plain,
    ! [U_15166,U_15165,U_15164,U_15163,U_15162,U_15161] :
      ( c_List_Olistrelp(U_15164,U_15161,hAPP(hAPP(c_List_Olist_OCons(U_15164),U_15162),U_15165),hAPP(hAPP(c_List_Olist_OCons(U_15164),U_15163),U_15166))
      | ~ c_List_Olistrelp(U_15164,U_15161,U_15165,U_15166)
      | ~ hBOOL(hAPP(hAPP(U_15161,U_15162),U_15163)) ),
    inference(variable_rename,[status(thm)],[f_3813_1]) ).

cnf(f_3813_3,plain,
    ( c_List_Olistrelp(U_15164,U_15161,hAPP(hAPP(c_List_Olist_OCons(U_15164),U_15162),U_15165),hAPP(hAPP(c_List_Olist_OCons(U_15164),U_15163),U_15166))
    | ~ c_List_Olistrelp(U_15164,U_15161,U_15165,U_15166)
    | ~ hBOOL(hAPP(hAPP(U_15161,U_15162),U_15163)) ),
    inference(clausify,[status(thm)],[f_3813_2]) ).

fof(f_3814_1,plain,
    ! [V_r_2,V_xs_2,V_ys_2,V_y_2,T_b] :
      ( ? [B_y,B_ys] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_ys_2),B_ys)),c_List_Olistrel(T_b,V_r_2)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),B_y)),V_r_2))
          & V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_y),B_ys) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)),V_xs_2)),c_List_Olistrel(T_b,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_listrel__Cons1]) ).

fof(f_3814_2,plain,
    ! [U_15173,U_15172,U_15171,U_15170,U_15169] :
      ( ? [U_15168,U_15167] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15169),tc_List_Olist(U_15169))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15169),tc_List_Olist(U_15169)),U_15171),U_15167)),c_List_Olistrel(U_15169,U_15173)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15169,U_15169)),hAPP(hAPP(c_Product__Type_OPair(U_15169,U_15169),U_15170),U_15168)),U_15173))
          & U_15172 = hAPP(hAPP(c_List_Olist_OCons(U_15169),U_15168),U_15167) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15169),tc_List_Olist(U_15169))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15169),tc_List_Olist(U_15169)),hAPP(hAPP(c_List_Olist_OCons(U_15169),U_15170),U_15171)),U_15172)),c_List_Olistrel(U_15169,U_15173))) ),
    inference(variable_rename,[status(thm)],[f_3814_1]) ).

fof(f_3814_3,plain,
    ! [U_15173,U_15172,U_15171,U_15170,U_15169] :
      ( ? [U_15167] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15169),tc_List_Olist(U_15169))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15169),tc_List_Olist(U_15169)),U_15171),U_15167)),c_List_Olistrel(U_15169,U_15173)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15169,U_15169)),hAPP(hAPP(c_Product__Type_OPair(U_15169,U_15169),U_15170),sK399(U_15173,U_15172,U_15171,U_15170,U_15169))),U_15173))
          & U_15172 = hAPP(hAPP(c_List_Olist_OCons(U_15169),sK399(U_15173,U_15172,U_15171,U_15170,U_15169)),U_15167) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15169),tc_List_Olist(U_15169))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15169),tc_List_Olist(U_15169)),hAPP(hAPP(c_List_Olist_OCons(U_15169),U_15170),U_15171)),U_15172)),c_List_Olistrel(U_15169,U_15173))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK399]),skolemize(U_15168,sK399(U_15173,U_15172,U_15171,U_15170,U_15169))],[f_3814_2]) ).

fof(f_3814_4,plain,
    ! [U_15173,U_15172,U_15171,U_15170,U_15169] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15169),tc_List_Olist(U_15169))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15169),tc_List_Olist(U_15169)),U_15171),sK400(U_15173,U_15172,U_15171,U_15170,U_15169))),c_List_Olistrel(U_15169,U_15173)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15169,U_15169)),hAPP(hAPP(c_Product__Type_OPair(U_15169,U_15169),U_15170),sK399(U_15173,U_15172,U_15171,U_15170,U_15169))),U_15173))
        & U_15172 = hAPP(hAPP(c_List_Olist_OCons(U_15169),sK399(U_15173,U_15172,U_15171,U_15170,U_15169)),sK400(U_15173,U_15172,U_15171,U_15170,U_15169)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15169),tc_List_Olist(U_15169))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15169),tc_List_Olist(U_15169)),hAPP(hAPP(c_List_Olist_OCons(U_15169),U_15170),U_15171)),U_15172)),c_List_Olistrel(U_15169,U_15173))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK400]),skolemize(U_15167,sK400(U_15173,U_15172,U_15171,U_15170,U_15169))],[f_3814_3]) ).

cnf(f_3814_5,plain,
    ( U_15172 = hAPP(hAPP(c_List_Olist_OCons(U_15169),sK399(U_15173,U_15172,U_15171,U_15170,U_15169)),sK400(U_15173,U_15172,U_15171,U_15170,U_15169))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15169),tc_List_Olist(U_15169))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15169),tc_List_Olist(U_15169)),hAPP(hAPP(c_List_Olist_OCons(U_15169),U_15170),U_15171)),U_15172)),c_List_Olistrel(U_15169,U_15173))) ),
    inference(clausify,[status(thm)],[f_3814_4]) ).

cnf(f_3814_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15169,U_15169)),hAPP(hAPP(c_Product__Type_OPair(U_15169,U_15169),U_15170),sK399(U_15173,U_15172,U_15171,U_15170,U_15169))),U_15173))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15169),tc_List_Olist(U_15169))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15169),tc_List_Olist(U_15169)),hAPP(hAPP(c_List_Olist_OCons(U_15169),U_15170),U_15171)),U_15172)),c_List_Olistrel(U_15169,U_15173))) ),
    inference(clausify,[status(thm)],[f_3814_4]) ).

cnf(f_3814_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15169),tc_List_Olist(U_15169))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15169),tc_List_Olist(U_15169)),U_15171),sK400(U_15173,U_15172,U_15171,U_15170,U_15169))),c_List_Olistrel(U_15169,U_15173)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15169),tc_List_Olist(U_15169))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15169),tc_List_Olist(U_15169)),hAPP(hAPP(c_List_Olist_OCons(U_15169),U_15170),U_15171)),U_15172)),c_List_Olistrel(U_15169,U_15173))) ),
    inference(clausify,[status(thm)],[f_3814_4]) ).

fof(f_3815_1,plain,
    ! [V_A_2,V_r_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel(T_b,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olists(T_b,V_A_2)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_List_Olist(T_b)),c_List_Olists(T_b,V_A_2)))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_listrel__subset]) ).

fof(f_3815_2,plain,
    ! [U_15176,U_15175,U_15174] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_15174),tc_List_Olist(U_15174)),tc_HOL_Obool)),c_List_Olistrel(U_15174,U_15175)),hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(U_15174),tc_List_Olist(U_15174)),c_List_Olists(U_15174,U_15176)),hAPP(c_COMBK(tc_fun(tc_List_Olist(U_15174),tc_HOL_Obool),tc_List_Olist(U_15174)),c_List_Olists(U_15174,U_15176)))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15174,U_15174),tc_HOL_Obool)),U_15175),hAPP(hAPP(c_Product__Type_OSigma(U_15174,U_15174),U_15176),hAPP(c_COMBK(tc_fun(U_15174,tc_HOL_Obool),U_15174),U_15176)))) ),
    inference(variable_rename,[status(thm)],[f_3815_1]) ).

cnf(f_3815_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_15174),tc_List_Olist(U_15174)),tc_HOL_Obool)),c_List_Olistrel(U_15174,U_15175)),hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(U_15174),tc_List_Olist(U_15174)),c_List_Olists(U_15174,U_15176)),hAPP(c_COMBK(tc_fun(tc_List_Olist(U_15174),tc_HOL_Obool),tc_List_Olist(U_15174)),c_List_Olists(U_15174,U_15176)))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15174,U_15174),tc_HOL_Obool)),U_15175),hAPP(hAPP(c_Product__Type_OSigma(U_15174,U_15174),U_15176),hAPP(c_COMBK(tc_fun(U_15174,tc_HOL_Obool),U_15174),U_15176)))) ),
    inference(clausify,[status(thm)],[f_3815_2]) ).

fof(f_3816_1,plain,
    ! [T_b] : c_List_Olists(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_lists__UNIV]) ).

fof(f_3816_2,plain,
    ! [U_15177] : c_List_Olists(U_15177,c_Orderings_Otop__class_Otop(tc_fun(U_15177,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_15177),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3816_1]) ).

cnf(f_3816_3,plain,
    c_List_Olists(U_15177,c_Orderings_Otop__class_Otop(tc_fun(U_15177,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_15177),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3816_2]) ).

fof(f_3817_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),c_List_Olists(T_b,V_A_2)),c_List_Olists(T_b,V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_lists__mono]) ).

fof(f_3817_2,plain,
    ! [U_15180,U_15179,U_15178] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(U_15178),tc_HOL_Obool)),c_List_Olists(U_15178,U_15179)),c_List_Olists(U_15178,U_15180)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15178,tc_HOL_Obool)),U_15179),U_15180)) ),
    inference(variable_rename,[status(thm)],[f_3817_1]) ).

cnf(f_3817_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(U_15178),tc_HOL_Obool)),c_List_Olists(U_15178,U_15179)),c_List_Olists(U_15178,U_15180)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15178,tc_HOL_Obool)),U_15179),U_15180)) ),
    inference(clausify,[status(thm)],[f_3817_2]) ).

fof(f_3818_1,plain,
    ! [V_r_2,V_A_2,T_b] :
      ( c_Equiv__Relations_Oequiv(tc_List_Olist(T_b),c_List_Olists(T_b,V_A_2),c_List_Olistrel(T_b,V_r_2))
      | ~ c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_equiv__listrel]) ).

fof(f_3818_2,plain,
    ! [U_15183,U_15182,U_15181] :
      ( c_Equiv__Relations_Oequiv(tc_List_Olist(U_15181),c_List_Olists(U_15181,U_15182),c_List_Olistrel(U_15181,U_15183))
      | ~ c_Equiv__Relations_Oequiv(U_15181,U_15182,U_15183) ),
    inference(variable_rename,[status(thm)],[f_3818_1]) ).

cnf(f_3818_3,plain,
    ( c_Equiv__Relations_Oequiv(tc_List_Olist(U_15181),c_List_Olists(U_15181,U_15182),c_List_Olistrel(U_15181,U_15183))
    | ~ c_Equiv__Relations_Oequiv(U_15181,U_15182,U_15183) ),
    inference(clausify,[status(thm)],[f_3818_2]) ).

fof(f_3819_1,plain,
    ! [V_r_2,V_A_2,T_b] :
      ( c_Relation_Orefl__on(tc_List_Olist(T_b),c_List_Olists(T_b,V_A_2),c_List_Olistrel(T_b,V_r_2))
      | ~ c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_listrel__refl__on]) ).

fof(f_3819_2,plain,
    ! [U_15186,U_15185,U_15184] :
      ( c_Relation_Orefl__on(tc_List_Olist(U_15184),c_List_Olists(U_15184,U_15185),c_List_Olistrel(U_15184,U_15186))
      | ~ c_Relation_Orefl__on(U_15184,U_15185,U_15186) ),
    inference(variable_rename,[status(thm)],[f_3819_1]) ).

cnf(f_3819_3,plain,
    ( c_Relation_Orefl__on(tc_List_Olist(U_15184),c_List_Olists(U_15184,U_15185),c_List_Olistrel(U_15184,U_15186))
    | ~ c_Relation_Orefl__on(U_15184,U_15185,U_15186) ),
    inference(clausify,[status(thm)],[f_3819_2]) ).

fof(f_3820_1,plain,
    ! [V_A_2,V_xs_2,V_x_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),c_List_Olists(T_b,V_A_2)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2)))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) )
      & ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2)))
          & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),c_List_Olists(T_b,V_A_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_Cons__in__lists__iff]) ).

fof(f_3820_2,plain,
    ! [U_15190,U_15189,U_15188,U_15187] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15187)),hAPP(hAPP(c_List_Olist_OCons(U_15187),U_15188),U_15189)),c_List_Olists(U_15187,U_15190)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15187)),U_15189),c_List_Olists(U_15187,U_15190)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_15187),U_15188),U_15190)) )
      & ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15187)),U_15189),c_List_Olists(U_15187,U_15190)))
          & hBOOL(hAPP(hAPP(c_member(U_15187),U_15188),U_15190)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15187)),hAPP(hAPP(c_List_Olist_OCons(U_15187),U_15188),U_15189)),c_List_Olists(U_15187,U_15190))) ) ),
    inference(variable_rename,[status(thm)],[f_3820_1]) ).

fof(f_3820_3,plain,
    ( ! [U_15198,U_15196,U_15194,U_15192] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15192)),hAPP(hAPP(c_List_Olist_OCons(U_15192),U_15194),U_15196)),c_List_Olists(U_15192,U_15198)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15192)),U_15196),c_List_Olists(U_15192,U_15198)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_15192),U_15194),U_15198)) )
    & ! [U_15197,U_15195,U_15193,U_15191] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15191)),U_15195),c_List_Olists(U_15191,U_15197)))
          & hBOOL(hAPP(hAPP(c_member(U_15191),U_15193),U_15197)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15191)),hAPP(hAPP(c_List_Olist_OCons(U_15191),U_15193),U_15195)),c_List_Olists(U_15191,U_15197))) ) ),
    inference(miniscope,[status(thm)],[f_3820_2]) ).

cnf(f_3820_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15191),U_15193),U_15197))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15191)),hAPP(hAPP(c_List_Olist_OCons(U_15191),U_15193),U_15195)),c_List_Olists(U_15191,U_15197))) ),
    inference(clausify,[status(thm)],[f_3820_3]) ).

cnf(f_3820_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15191)),U_15195),c_List_Olists(U_15191,U_15197)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15191)),hAPP(hAPP(c_List_Olist_OCons(U_15191),U_15193),U_15195)),c_List_Olists(U_15191,U_15197))) ),
    inference(clausify,[status(thm)],[f_3820_3]) ).

cnf(f_3820_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15192)),hAPP(hAPP(c_List_Olist_OCons(U_15192),U_15194),U_15196)),c_List_Olists(U_15192,U_15198)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15192)),U_15196),c_List_Olists(U_15192,U_15198)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15192),U_15194),U_15198)) ),
    inference(clausify,[status(thm)],[f_3820_3]) ).

fof(f_3821_1,plain,
    ! [V_r_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,c_Wellfounded_Oacc(T_b,V_r_2))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_lists__accI]) ).

fof(f_3821_2,plain,
    ! [U_15201,U_15200,U_15199] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15199)),U_15200),c_List_Olists(U_15199,c_Wellfounded_Oacc(U_15199,U_15201))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15199)),U_15200),c_Wellfounded_Oacc(tc_List_Olist(U_15199),c_List_Olistrel1(U_15199,U_15201)))) ),
    inference(variable_rename,[status(thm)],[f_3821_1]) ).

cnf(f_3821_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15199)),U_15200),c_List_Olists(U_15199,c_Wellfounded_Oacc(U_15199,U_15201))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15199)),U_15200),c_Wellfounded_Oacc(tc_List_Olist(U_15199),c_List_Olistrel1(U_15199,U_15201)))) ),
    inference(clausify,[status(thm)],[f_3821_2]) ).

fof(f_3822_1,plain,
    ! [V_r_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,c_Wellfounded_Oacc(T_b,V_r_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_lists__accD]) ).

fof(f_3822_2,plain,
    ! [U_15204,U_15203,U_15202] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15202)),U_15203),c_Wellfounded_Oacc(tc_List_Olist(U_15202),c_List_Olistrel1(U_15202,U_15204))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15202)),U_15203),c_List_Olists(U_15202,c_Wellfounded_Oacc(U_15202,U_15204)))) ),
    inference(variable_rename,[status(thm)],[f_3822_1]) ).

cnf(f_3822_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15202)),U_15203),c_Wellfounded_Oacc(tc_List_Olist(U_15202),c_List_Olistrel1(U_15202,U_15204))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15202)),U_15203),c_List_Olists(U_15202,c_Wellfounded_Oacc(U_15202,U_15204)))) ),
    inference(clausify,[status(thm)],[f_3822_2]) ).

fof(f_3823_1,plain,
    ! [V_r_2,V_ys_2,V_xs_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2)))
        | ? [B_n] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n)),hAPP(hAPP(c_List_Onth(T_b),V_ys_2),B_n))),V_r_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) )
      & ( ( ! [B_n] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n)),hAPP(hAPP(c_List_Onth(T_b),V_ys_2),B_n))),V_r_2))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_listrel__iff__nth]) ).

fof(f_3823_2,plain,
    ! [U_15210,U_15209,U_15208,U_15207] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15207),tc_List_Olist(U_15207))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15207),tc_List_Olist(U_15207)),U_15208),U_15209)),c_List_Olistrel(U_15207,U_15210)))
        | ? [U_15206] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15207,U_15207)),hAPP(hAPP(c_Product__Type_OPair(U_15207,U_15207),hAPP(hAPP(c_List_Onth(U_15207),U_15208),U_15206)),hAPP(hAPP(c_List_Onth(U_15207),U_15209),U_15206))),U_15210))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15206),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15207)),U_15208))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15207)),U_15208) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15207)),U_15209) )
      & ( ( ! [U_15205] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15207,U_15207)),hAPP(hAPP(c_Product__Type_OPair(U_15207,U_15207),hAPP(hAPP(c_List_Onth(U_15207),U_15208),U_15205)),hAPP(hAPP(c_List_Onth(U_15207),U_15209),U_15205))),U_15210))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15205),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15207)),U_15208))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15207)),U_15208) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15207)),U_15209) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15207),tc_List_Olist(U_15207))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15207),tc_List_Olist(U_15207)),U_15208),U_15209)),c_List_Olistrel(U_15207,U_15210))) ) ),
    inference(variable_rename,[status(thm)],[f_3823_1]) ).

fof(f_3823_3,plain,
    ( ! [U_15218,U_15216,U_15214,U_15212] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15212),tc_List_Olist(U_15212))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15212),tc_List_Olist(U_15212)),U_15214),U_15216)),c_List_Olistrel(U_15212,U_15218)))
        | ? [U_15206] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15212,U_15212)),hAPP(hAPP(c_Product__Type_OPair(U_15212,U_15212),hAPP(hAPP(c_List_Onth(U_15212),U_15214),U_15206)),hAPP(hAPP(c_List_Onth(U_15212),U_15216),U_15206))),U_15218))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15206),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15212)),U_15214))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15212)),U_15214) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15212)),U_15216) )
    & ! [U_15217,U_15215,U_15213,U_15211] :
        ( ( ! [U_15205] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15211,U_15211)),hAPP(hAPP(c_Product__Type_OPair(U_15211,U_15211),hAPP(hAPP(c_List_Onth(U_15211),U_15213),U_15205)),hAPP(hAPP(c_List_Onth(U_15211),U_15215),U_15205))),U_15217))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15205),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15211)),U_15213))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15211)),U_15213) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15211)),U_15215) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15211),tc_List_Olist(U_15211))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15211),tc_List_Olist(U_15211)),U_15213),U_15215)),c_List_Olistrel(U_15211,U_15217))) ) ),
    inference(miniscope,[status(thm)],[f_3823_2]) ).

fof(f_3823_4,plain,
    ( ! [U_15218,U_15216,U_15214,U_15212] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15212),tc_List_Olist(U_15212))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15212),tc_List_Olist(U_15212)),U_15214),U_15216)),c_List_Olistrel(U_15212,U_15218)))
        | ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15212,U_15212)),hAPP(hAPP(c_Product__Type_OPair(U_15212,U_15212),hAPP(hAPP(c_List_Onth(U_15212),U_15214),sK401(U_15218,U_15216,U_15214,U_15212))),hAPP(hAPP(c_List_Onth(U_15212),U_15216),sK401(U_15218,U_15216,U_15214,U_15212)))),U_15218))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK401(U_15218,U_15216,U_15214,U_15212)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15212)),U_15214))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15212)),U_15214) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15212)),U_15216) )
    & ! [U_15217,U_15215,U_15213,U_15211] :
        ( ( ! [U_15205] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15211,U_15211)),hAPP(hAPP(c_Product__Type_OPair(U_15211,U_15211),hAPP(hAPP(c_List_Onth(U_15211),U_15213),U_15205)),hAPP(hAPP(c_List_Onth(U_15211),U_15215),U_15205))),U_15217))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15205),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15211)),U_15213))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15211)),U_15213) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15211)),U_15215) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15211),tc_List_Olist(U_15211))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15211),tc_List_Olist(U_15211)),U_15213),U_15215)),c_List_Olistrel(U_15211,U_15217))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK401]),skolemize(U_15206,sK401(U_15218,U_15216,U_15214,U_15212))],[f_3823_3]) ).

cnf(f_3823_5,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15211)),U_15213) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15211)),U_15215)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15211),tc_List_Olist(U_15211))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15211),tc_List_Olist(U_15211)),U_15213),U_15215)),c_List_Olistrel(U_15211,U_15217))) ),
    inference(clausify,[status(thm)],[f_3823_4]) ).

cnf(f_3823_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15211,U_15211)),hAPP(hAPP(c_Product__Type_OPair(U_15211,U_15211),hAPP(hAPP(c_List_Onth(U_15211),U_15213),U_15205)),hAPP(hAPP(c_List_Onth(U_15211),U_15215),U_15205))),U_15217))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15205),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15211)),U_15213)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15211),tc_List_Olist(U_15211))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15211),tc_List_Olist(U_15211)),U_15213),U_15215)),c_List_Olistrel(U_15211,U_15217))) ),
    inference(clausify,[status(thm)],[f_3823_4]) ).

cnf(f_3823_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK401(U_15218,U_15216,U_15214,U_15212)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15212)),U_15214)))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15212)),U_15214) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15212)),U_15216)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15212),tc_List_Olist(U_15212))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15212),tc_List_Olist(U_15212)),U_15214),U_15216)),c_List_Olistrel(U_15212,U_15218))) ),
    inference(clausify,[status(thm)],[f_3823_4]) ).

cnf(f_3823_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15212,U_15212)),hAPP(hAPP(c_Product__Type_OPair(U_15212,U_15212),hAPP(hAPP(c_List_Onth(U_15212),U_15214),sK401(U_15218,U_15216,U_15214,U_15212))),hAPP(hAPP(c_List_Onth(U_15212),U_15216),sK401(U_15218,U_15216,U_15214,U_15212)))),U_15218))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15212)),U_15214) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15212)),U_15216)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15212),tc_List_Olist(U_15212))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15212),tc_List_Olist(U_15212)),U_15214),U_15216)),c_List_Olistrel(U_15212,U_15218))) ),
    inference(clausify,[status(thm)],[f_3823_4]) ).

fof(f_3824_1,plain,
    ! [V_y_2,V_x_2,V_r_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_y_2),V_x_2)),c_List_Olexord(T_b,V_r_2)))
      | V_x_2 = V_y_2
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2)))
      | ? [B_a,B_b] :
          ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_b),B_a)),V_r_2))
          & B_a != B_b
          & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_a),B_b)),V_r_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_lexord__linear]) ).

fof(f_3824_2,plain,
    ! [U_15224,U_15223,U_15222,U_15221] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15221),tc_List_Olist(U_15221))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15221),tc_List_Olist(U_15221)),U_15224),U_15223)),c_List_Olexord(U_15221,U_15222)))
      | U_15223 = U_15224
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15221),tc_List_Olist(U_15221))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15221),tc_List_Olist(U_15221)),U_15223),U_15224)),c_List_Olexord(U_15221,U_15222)))
      | ? [U_15220,U_15219] :
          ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15221,U_15221)),hAPP(hAPP(c_Product__Type_OPair(U_15221,U_15221),U_15219),U_15220)),U_15222))
          & U_15220 != U_15219
          & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15221,U_15221)),hAPP(hAPP(c_Product__Type_OPair(U_15221,U_15221),U_15220),U_15219)),U_15222)) ) ),
    inference(variable_rename,[status(thm)],[f_3824_1]) ).

fof(f_3824_3,plain,
    ! [U_15224,U_15223,U_15222,U_15221] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15221),tc_List_Olist(U_15221))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15221),tc_List_Olist(U_15221)),U_15224),U_15223)),c_List_Olexord(U_15221,U_15222)))
      | U_15223 = U_15224
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15221),tc_List_Olist(U_15221))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15221),tc_List_Olist(U_15221)),U_15223),U_15224)),c_List_Olexord(U_15221,U_15222)))
      | ? [U_15219] :
          ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15221,U_15221)),hAPP(hAPP(c_Product__Type_OPair(U_15221,U_15221),U_15219),sK402(U_15224,U_15223,U_15222,U_15221))),U_15222))
          & sK402(U_15224,U_15223,U_15222,U_15221) != U_15219
          & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15221,U_15221)),hAPP(hAPP(c_Product__Type_OPair(U_15221,U_15221),sK402(U_15224,U_15223,U_15222,U_15221)),U_15219)),U_15222)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK402]),skolemize(U_15220,sK402(U_15224,U_15223,U_15222,U_15221))],[f_3824_2]) ).

fof(f_3824_4,plain,
    ! [U_15224,U_15223,U_15222,U_15221] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15221),tc_List_Olist(U_15221))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15221),tc_List_Olist(U_15221)),U_15224),U_15223)),c_List_Olexord(U_15221,U_15222)))
      | U_15223 = U_15224
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15221),tc_List_Olist(U_15221))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15221),tc_List_Olist(U_15221)),U_15223),U_15224)),c_List_Olexord(U_15221,U_15222)))
      | ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15221,U_15221)),hAPP(hAPP(c_Product__Type_OPair(U_15221,U_15221),sK403(U_15224,U_15223,U_15222,U_15221)),sK402(U_15224,U_15223,U_15222,U_15221))),U_15222))
        & sK402(U_15224,U_15223,U_15222,U_15221) != sK403(U_15224,U_15223,U_15222,U_15221)
        & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15221,U_15221)),hAPP(hAPP(c_Product__Type_OPair(U_15221,U_15221),sK402(U_15224,U_15223,U_15222,U_15221)),sK403(U_15224,U_15223,U_15222,U_15221))),U_15222)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK403]),skolemize(U_15219,sK403(U_15224,U_15223,U_15222,U_15221))],[f_3824_3]) ).

cnf(f_3824_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15221,U_15221)),hAPP(hAPP(c_Product__Type_OPair(U_15221,U_15221),sK402(U_15224,U_15223,U_15222,U_15221)),sK403(U_15224,U_15223,U_15222,U_15221))),U_15222))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15221),tc_List_Olist(U_15221))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15221),tc_List_Olist(U_15221)),U_15224),U_15223)),c_List_Olexord(U_15221,U_15222)))
    | U_15223 = U_15224
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15221),tc_List_Olist(U_15221))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15221),tc_List_Olist(U_15221)),U_15223),U_15224)),c_List_Olexord(U_15221,U_15222))) ),
    inference(clausify,[status(thm)],[f_3824_4]) ).

cnf(f_3824_6,plain,
    ( sK402(U_15224,U_15223,U_15222,U_15221) != sK403(U_15224,U_15223,U_15222,U_15221)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15221),tc_List_Olist(U_15221))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15221),tc_List_Olist(U_15221)),U_15224),U_15223)),c_List_Olexord(U_15221,U_15222)))
    | U_15223 = U_15224
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15221),tc_List_Olist(U_15221))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15221),tc_List_Olist(U_15221)),U_15223),U_15224)),c_List_Olexord(U_15221,U_15222))) ),
    inference(clausify,[status(thm)],[f_3824_4]) ).

cnf(f_3824_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15221,U_15221)),hAPP(hAPP(c_Product__Type_OPair(U_15221,U_15221),sK403(U_15224,U_15223,U_15222,U_15221)),sK402(U_15224,U_15223,U_15222,U_15221))),U_15222))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15221),tc_List_Olist(U_15221))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15221),tc_List_Olist(U_15221)),U_15224),U_15223)),c_List_Olexord(U_15221,U_15222)))
    | U_15223 = U_15224
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15221),tc_List_Olist(U_15221))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15221),tc_List_Olist(U_15221)),U_15223),U_15224)),c_List_Olexord(U_15221,U_15222))) ),
    inference(clausify,[status(thm)],[f_3824_4]) ).

fof(f_3825_1,plain,
    ! [T_b] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_b)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_infinite__UNIV__listI]) ).

fof(f_3825_2,plain,
    ! [U_15225] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(U_15225)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_15225),tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_3825_1]) ).

cnf(f_3825_3,plain,
    ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(U_15225)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_15225),tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_3825_2]) ).

fof(f_3826_1,plain,
    ! [T_b,V_ys_2,V_xs_2] :
      ( ( V_xs_2 = V_ys_2
        | ? [B_i] :
            ( hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) != hAPP(hAPP(c_List_Onth(T_b),V_ys_2),B_i)
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) )
      & ( ( ! [B_i] :
              ( hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) = hAPP(hAPP(c_List_Onth(T_b),V_ys_2),B_i)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) )
        | V_xs_2 != V_ys_2 ) ),
    inference(fof_nnf,[status(thm)],[fact_list__eq__iff__nth__eq]) ).

fof(f_3826_2,plain,
    ! [U_15230,U_15229,U_15228] :
      ( ( U_15228 = U_15229
        | ? [U_15227] :
            ( hAPP(hAPP(c_List_Onth(U_15230),U_15228),U_15227) != hAPP(hAPP(c_List_Onth(U_15230),U_15229),U_15227)
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15227),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15230)),U_15228))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15230)),U_15228) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15230)),U_15229) )
      & ( ( ! [U_15226] :
              ( hAPP(hAPP(c_List_Onth(U_15230),U_15228),U_15226) = hAPP(hAPP(c_List_Onth(U_15230),U_15229),U_15226)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15226),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15230)),U_15228))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15230)),U_15228) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15230)),U_15229) )
        | U_15228 != U_15229 ) ),
    inference(variable_rename,[status(thm)],[f_3826_1]) ).

fof(f_3826_3,plain,
    ( ! [U_15236,U_15234,U_15232] :
        ( U_15232 = U_15234
        | ? [U_15227] :
            ( hAPP(hAPP(c_List_Onth(U_15236),U_15232),U_15227) != hAPP(hAPP(c_List_Onth(U_15236),U_15234),U_15227)
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15227),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15236)),U_15232))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15236)),U_15232) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15236)),U_15234) )
    & ! [U_15235,U_15233,U_15231] :
        ( ( ! [U_15226] :
              ( hAPP(hAPP(c_List_Onth(U_15235),U_15231),U_15226) = hAPP(hAPP(c_List_Onth(U_15235),U_15233),U_15226)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15226),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15235)),U_15231))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15235)),U_15231) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15235)),U_15233) )
        | U_15231 != U_15233 ) ),
    inference(miniscope,[status(thm)],[f_3826_2]) ).

fof(f_3826_4,plain,
    ( ! [U_15236,U_15234,U_15232] :
        ( U_15232 = U_15234
        | ( hAPP(hAPP(c_List_Onth(U_15236),U_15232),sK404(U_15236,U_15234,U_15232)) != hAPP(hAPP(c_List_Onth(U_15236),U_15234),sK404(U_15236,U_15234,U_15232))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK404(U_15236,U_15234,U_15232)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15236)),U_15232))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15236)),U_15232) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15236)),U_15234) )
    & ! [U_15235,U_15233,U_15231] :
        ( ( ! [U_15226] :
              ( hAPP(hAPP(c_List_Onth(U_15235),U_15231),U_15226) = hAPP(hAPP(c_List_Onth(U_15235),U_15233),U_15226)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15226),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15235)),U_15231))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15235)),U_15231) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15235)),U_15233) )
        | U_15231 != U_15233 ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK404]),skolemize(U_15227,sK404(U_15236,U_15234,U_15232))],[f_3826_3]) ).

cnf(f_3826_5,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15235)),U_15231) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15235)),U_15233)
    | U_15231 != U_15233 ),
    inference(clausify,[status(thm)],[f_3826_4]) ).

cnf(f_3826_6,plain,
    ( hAPP(hAPP(c_List_Onth(U_15235),U_15231),U_15226) = hAPP(hAPP(c_List_Onth(U_15235),U_15233),U_15226)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15226),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15235)),U_15231)))
    | U_15231 != U_15233 ),
    inference(clausify,[status(thm)],[f_3826_4]) ).

cnf(f_3826_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK404(U_15236,U_15234,U_15232)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15236)),U_15232)))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15236)),U_15232) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15236)),U_15234)
    | U_15232 = U_15234 ),
    inference(clausify,[status(thm)],[f_3826_4]) ).

cnf(f_3826_8,plain,
    ( hAPP(hAPP(c_List_Onth(U_15236),U_15232),sK404(U_15236,U_15234,U_15232)) != hAPP(hAPP(c_List_Onth(U_15236),U_15234),sK404(U_15236,U_15234,U_15232))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15236)),U_15232) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15236)),U_15234)
    | U_15232 = U_15234 ),
    inference(clausify,[status(thm)],[f_3826_4]) ).

fof(f_3827_1,plain,
    ! [V_n,V_xs,V_x,T_a] : hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n),
    inference(fof_nnf,[status(thm)],[fact_nth__Cons__Suc]) ).

fof(f_3827_2,plain,
    ! [U_15240,U_15239,U_15238,U_15237] : hAPP(hAPP(c_List_Onth(U_15237),hAPP(hAPP(c_List_Olist_OCons(U_15237),U_15238),U_15239)),hAPP(c_Nat_OSuc,U_15240)) = hAPP(hAPP(c_List_Onth(U_15237),U_15239),U_15240),
    inference(variable_rename,[status(thm)],[f_3827_1]) ).

cnf(f_3827_3,plain,
    hAPP(hAPP(c_List_Onth(U_15237),hAPP(hAPP(c_List_Olist_OCons(U_15237),U_15238),U_15239)),hAPP(c_Nat_OSuc,U_15240)) = hAPP(hAPP(c_List_Onth(U_15237),U_15239),U_15240),
    inference(clausify,[status(thm)],[f_3827_2]) ).

fof(f_3828_1,plain,
    ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_x,
    inference(fof_nnf,[status(thm)],[fact_nth__Cons__0]) ).

fof(f_3828_2,plain,
    ! [U_15243,U_15242,U_15241] : hAPP(hAPP(c_List_Onth(U_15241),hAPP(hAPP(c_List_Olist_OCons(U_15241),U_15242),U_15243)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_15242,
    inference(variable_rename,[status(thm)],[f_3828_1]) ).

cnf(f_3828_3,plain,
    hAPP(hAPP(c_List_Onth(U_15241),hAPP(hAPP(c_List_Olist_OCons(U_15241),U_15242),U_15243)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_15242,
    inference(clausify,[status(thm)],[f_3828_2]) ).

fof(f_3829_1,plain,
    ! [V_n_2,V_xs_2,V_x_2,T_b] : hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_n_2) = c_Nat_Onat_Onat__case(T_b,V_x_2,hAPP(c_List_Onth(T_b),V_xs_2),V_n_2),
    inference(fof_nnf,[status(thm)],[fact_nth_Osimps]) ).

fof(f_3829_2,plain,
    ! [U_15247,U_15246,U_15245,U_15244] : hAPP(hAPP(c_List_Onth(U_15244),hAPP(hAPP(c_List_Olist_OCons(U_15244),U_15245),U_15246)),U_15247) = c_Nat_Onat_Onat__case(U_15244,U_15245,hAPP(c_List_Onth(U_15244),U_15246),U_15247),
    inference(variable_rename,[status(thm)],[f_3829_1]) ).

cnf(f_3829_3,plain,
    hAPP(hAPP(c_List_Onth(U_15244),hAPP(hAPP(c_List_Olist_OCons(U_15244),U_15245),U_15246)),U_15247) = c_Nat_Onat_Onat__case(U_15244,U_15245,hAPP(c_List_Onth(U_15244),U_15246),U_15247),
    inference(clausify,[status(thm)],[f_3829_2]) ).

fof(f_3830_1,plain,
    ! [V_xs,V_x,T_a,V_n] :
      ( ( hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_n) = hAPP(hAPP(c_List_Onth(T_a),V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
        | V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_n) = V_x
        | V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(fof_nnf,[status(thm)],[fact_nth__Cons_H]) ).

fof(f_3830_2,plain,
    ! [U_15251,U_15250,U_15249,U_15248] :
      ( ( hAPP(hAPP(c_List_Onth(U_15249),hAPP(hAPP(c_List_Olist_OCons(U_15249),U_15250),U_15251)),U_15248) = hAPP(hAPP(c_List_Onth(U_15249),U_15251),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_15248),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
        | U_15248 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_List_Onth(U_15249),hAPP(hAPP(c_List_Olist_OCons(U_15249),U_15250),U_15251)),U_15248) = U_15250
        | U_15248 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_3830_1]) ).

fof(f_3830_3,plain,
    ( ! [U_15259,U_15257,U_15255,U_15253] :
        ( hAPP(hAPP(c_List_Onth(U_15255),hAPP(hAPP(c_List_Olist_OCons(U_15255),U_15257),U_15259)),U_15253) = hAPP(hAPP(c_List_Onth(U_15255),U_15259),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_15253),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
        | U_15253 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_15258,U_15256,U_15254,U_15252] :
        ( hAPP(hAPP(c_List_Onth(U_15254),hAPP(hAPP(c_List_Olist_OCons(U_15254),U_15256),U_15258)),U_15252) = U_15256
        | U_15252 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_3830_2]) ).

cnf(f_3830_4,plain,
    ( hAPP(hAPP(c_List_Onth(U_15254),hAPP(hAPP(c_List_Olist_OCons(U_15254),U_15256),U_15258)),U_15252) = U_15256
    | U_15252 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_3830_3]) ).

cnf(f_3830_5,plain,
    ( hAPP(hAPP(c_List_Onth(U_15255),hAPP(hAPP(c_List_Olist_OCons(U_15255),U_15257),U_15259)),U_15253) = hAPP(hAPP(c_List_Onth(U_15255),U_15259),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_15253),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | U_15253 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_3830_3]) ).

fof(f_3831_1,plain,
    ! [V_xs,V_x,T_a,V_v] :
      ( ( hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(hAPP(c_List_Onth(T_a),V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = V_x
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(fof_nnf,[status(thm)],[fact_nth__Cons__number__of]) ).

fof(f_3831_2,plain,
    ! [U_15263,U_15262,U_15261,U_15260] :
      ( ( hAPP(hAPP(c_List_Onth(U_15261),hAPP(hAPP(c_List_Olist_OCons(U_15261),U_15262),U_15263)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15260)) = hAPP(hAPP(c_List_Onth(U_15261),U_15263),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15260)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15260) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_List_Onth(U_15261),hAPP(hAPP(c_List_Olist_OCons(U_15261),U_15262),U_15263)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15260)) = U_15262
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15260) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_3831_1]) ).

fof(f_3831_3,plain,
    ( ! [U_15271,U_15269,U_15267,U_15265] :
        ( hAPP(hAPP(c_List_Onth(U_15267),hAPP(hAPP(c_List_Olist_OCons(U_15267),U_15269),U_15271)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15265)) = hAPP(hAPP(c_List_Onth(U_15267),U_15271),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15265)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15265) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_15270,U_15268,U_15266,U_15264] :
        ( hAPP(hAPP(c_List_Onth(U_15266),hAPP(hAPP(c_List_Olist_OCons(U_15266),U_15268),U_15270)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15264)) = U_15268
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15264) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_3831_2]) ).

cnf(f_3831_4,plain,
    ( hAPP(hAPP(c_List_Onth(U_15266),hAPP(hAPP(c_List_Olist_OCons(U_15266),U_15268),U_15270)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15264)) = U_15268
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15264) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_3831_3]) ).

cnf(f_3831_5,plain,
    ( hAPP(hAPP(c_List_Onth(U_15267),hAPP(hAPP(c_List_Olist_OCons(U_15267),U_15269),U_15271)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15265)) = hAPP(hAPP(c_List_Onth(U_15267),U_15271),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15265)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15265) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_3831_3]) ).

fof(f_3832_1,plain,
    ! [V_r_2,V_y_2,V_x_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2)))
        | ( ! [B_i] :
              ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(hAPP(c_List_Onth(T_b),V_x_2),B_i)),hAPP(hAPP(c_List_Onth(T_b),V_y_2),B_i))),V_r_2))
              | hAPP(hAPP(c_List_Otake(T_b),B_i),V_x_2) != hAPP(hAPP(c_List_Otake(T_b),B_i),V_y_2)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_y_2)))) )
          & ( hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2)),V_y_2) != V_x_2
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_y_2))) ) ) )
      & ( ? [B_i] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(hAPP(c_List_Onth(T_b),V_x_2),B_i)),hAPP(hAPP(c_List_Onth(T_b),V_y_2),B_i))),V_r_2))
            & hAPP(hAPP(c_List_Otake(T_b),B_i),V_x_2) = hAPP(hAPP(c_List_Otake(T_b),B_i),V_y_2)
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_y_2)))) )
        | ( hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2)),V_y_2) = V_x_2
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_y_2))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_lexord__take__index__conv]) ).

fof(f_3832_2,plain,
    ! [U_15277,U_15276,U_15275,U_15274] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15274),tc_List_Olist(U_15274))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15274),tc_List_Olist(U_15274)),U_15275),U_15276)),c_List_Olexord(U_15274,U_15277)))
        | ( ! [U_15273] :
              ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15274,U_15274)),hAPP(hAPP(c_Product__Type_OPair(U_15274,U_15274),hAPP(hAPP(c_List_Onth(U_15274),U_15275),U_15273)),hAPP(hAPP(c_List_Onth(U_15274),U_15276),U_15273))),U_15277))
              | hAPP(hAPP(c_List_Otake(U_15274),U_15273),U_15275) != hAPP(hAPP(c_List_Otake(U_15274),U_15273),U_15276)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15273),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15274)),U_15275)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15274)),U_15276)))) )
          & ( hAPP(hAPP(c_List_Otake(U_15274),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15274)),U_15275)),U_15276) != U_15275
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15274)),U_15275)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15274)),U_15276))) ) ) )
      & ( ? [U_15272] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15274,U_15274)),hAPP(hAPP(c_Product__Type_OPair(U_15274,U_15274),hAPP(hAPP(c_List_Onth(U_15274),U_15275),U_15272)),hAPP(hAPP(c_List_Onth(U_15274),U_15276),U_15272))),U_15277))
            & hAPP(hAPP(c_List_Otake(U_15274),U_15272),U_15275) = hAPP(hAPP(c_List_Otake(U_15274),U_15272),U_15276)
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15272),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15274)),U_15275)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15274)),U_15276)))) )
        | ( hAPP(hAPP(c_List_Otake(U_15274),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15274)),U_15275)),U_15276) = U_15275
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15274)),U_15275)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15274)),U_15276))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15274),tc_List_Olist(U_15274))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15274),tc_List_Olist(U_15274)),U_15275),U_15276)),c_List_Olexord(U_15274,U_15277))) ) ),
    inference(variable_rename,[status(thm)],[f_3832_1]) ).

fof(f_3832_3,plain,
    ( ! [U_15285,U_15283,U_15281,U_15279] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15279),tc_List_Olist(U_15279))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15279),tc_List_Olist(U_15279)),U_15281),U_15283)),c_List_Olexord(U_15279,U_15285)))
        | ( ! [U_15273] :
              ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15279,U_15279)),hAPP(hAPP(c_Product__Type_OPair(U_15279,U_15279),hAPP(hAPP(c_List_Onth(U_15279),U_15281),U_15273)),hAPP(hAPP(c_List_Onth(U_15279),U_15283),U_15273))),U_15285))
              | hAPP(hAPP(c_List_Otake(U_15279),U_15273),U_15281) != hAPP(hAPP(c_List_Otake(U_15279),U_15273),U_15283)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15273),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15279)),U_15281)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15279)),U_15283)))) )
          & ( hAPP(hAPP(c_List_Otake(U_15279),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15279)),U_15281)),U_15283) != U_15281
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15279)),U_15281)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15279)),U_15283))) ) ) )
    & ! [U_15284,U_15282,U_15280,U_15278] :
        ( ? [U_15272] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15278,U_15278)),hAPP(hAPP(c_Product__Type_OPair(U_15278,U_15278),hAPP(hAPP(c_List_Onth(U_15278),U_15280),U_15272)),hAPP(hAPP(c_List_Onth(U_15278),U_15282),U_15272))),U_15284))
            & hAPP(hAPP(c_List_Otake(U_15278),U_15272),U_15280) = hAPP(hAPP(c_List_Otake(U_15278),U_15272),U_15282)
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15272),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15278)),U_15280)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15278)),U_15282)))) )
        | ( hAPP(hAPP(c_List_Otake(U_15278),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15278)),U_15280)),U_15282) = U_15280
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15278)),U_15280)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15278)),U_15282))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15278),tc_List_Olist(U_15278))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15278),tc_List_Olist(U_15278)),U_15280),U_15282)),c_List_Olexord(U_15278,U_15284))) ) ),
    inference(miniscope,[status(thm)],[f_3832_2]) ).

fof(f_3832_4,plain,
    ( ! [U_15285,U_15283,U_15281,U_15279] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15279),tc_List_Olist(U_15279))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15279),tc_List_Olist(U_15279)),U_15281),U_15283)),c_List_Olexord(U_15279,U_15285)))
        | ( ! [U_15273] :
              ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15279,U_15279)),hAPP(hAPP(c_Product__Type_OPair(U_15279,U_15279),hAPP(hAPP(c_List_Onth(U_15279),U_15281),U_15273)),hAPP(hAPP(c_List_Onth(U_15279),U_15283),U_15273))),U_15285))
              | hAPP(hAPP(c_List_Otake(U_15279),U_15273),U_15281) != hAPP(hAPP(c_List_Otake(U_15279),U_15273),U_15283)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15273),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15279)),U_15281)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15279)),U_15283)))) )
          & ( hAPP(hAPP(c_List_Otake(U_15279),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15279)),U_15281)),U_15283) != U_15281
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15279)),U_15281)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15279)),U_15283))) ) ) )
    & ! [U_15284,U_15282,U_15280,U_15278] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15278,U_15278)),hAPP(hAPP(c_Product__Type_OPair(U_15278,U_15278),hAPP(hAPP(c_List_Onth(U_15278),U_15280),sK405(U_15284,U_15282,U_15280,U_15278))),hAPP(hAPP(c_List_Onth(U_15278),U_15282),sK405(U_15284,U_15282,U_15280,U_15278)))),U_15284))
          & hAPP(hAPP(c_List_Otake(U_15278),sK405(U_15284,U_15282,U_15280,U_15278)),U_15280) = hAPP(hAPP(c_List_Otake(U_15278),sK405(U_15284,U_15282,U_15280,U_15278)),U_15282)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK405(U_15284,U_15282,U_15280,U_15278)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15278)),U_15280)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15278)),U_15282)))) )
        | ( hAPP(hAPP(c_List_Otake(U_15278),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15278)),U_15280)),U_15282) = U_15280
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15278)),U_15280)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15278)),U_15282))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15278),tc_List_Olist(U_15278))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15278),tc_List_Olist(U_15278)),U_15280),U_15282)),c_List_Olexord(U_15278,U_15284))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK405]),skolemize(U_15272,sK405(U_15284,U_15282,U_15280,U_15278))],[f_3832_3]) ).

cnf(f_3832_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK405(U_15284,U_15282,U_15280,U_15278)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15278)),U_15280)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15278)),U_15282))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15278)),U_15280)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15278)),U_15282)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15278),tc_List_Olist(U_15278))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15278),tc_List_Olist(U_15278)),U_15280),U_15282)),c_List_Olexord(U_15278,U_15284))) ),
    inference(clausify,[status(thm)],[f_3832_4]) ).

cnf(f_3832_6,plain,
    ( hAPP(hAPP(c_List_Otake(U_15278),sK405(U_15284,U_15282,U_15280,U_15278)),U_15280) = hAPP(hAPP(c_List_Otake(U_15278),sK405(U_15284,U_15282,U_15280,U_15278)),U_15282)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15278)),U_15280)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15278)),U_15282)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15278),tc_List_Olist(U_15278))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15278),tc_List_Olist(U_15278)),U_15280),U_15282)),c_List_Olexord(U_15278,U_15284))) ),
    inference(clausify,[status(thm)],[f_3832_4]) ).

cnf(f_3832_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15278,U_15278)),hAPP(hAPP(c_Product__Type_OPair(U_15278,U_15278),hAPP(hAPP(c_List_Onth(U_15278),U_15280),sK405(U_15284,U_15282,U_15280,U_15278))),hAPP(hAPP(c_List_Onth(U_15278),U_15282),sK405(U_15284,U_15282,U_15280,U_15278)))),U_15284))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15278)),U_15280)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15278)),U_15282)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15278),tc_List_Olist(U_15278))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15278),tc_List_Olist(U_15278)),U_15280),U_15282)),c_List_Olexord(U_15278,U_15284))) ),
    inference(clausify,[status(thm)],[f_3832_4]) ).

cnf(f_3832_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK405(U_15284,U_15282,U_15280,U_15278)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15278)),U_15280)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15278)),U_15282))))
    | hAPP(hAPP(c_List_Otake(U_15278),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15278)),U_15280)),U_15282) = U_15280
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15278),tc_List_Olist(U_15278))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15278),tc_List_Olist(U_15278)),U_15280),U_15282)),c_List_Olexord(U_15278,U_15284))) ),
    inference(clausify,[status(thm)],[f_3832_4]) ).

cnf(f_3832_9,plain,
    ( hAPP(hAPP(c_List_Otake(U_15278),sK405(U_15284,U_15282,U_15280,U_15278)),U_15280) = hAPP(hAPP(c_List_Otake(U_15278),sK405(U_15284,U_15282,U_15280,U_15278)),U_15282)
    | hAPP(hAPP(c_List_Otake(U_15278),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15278)),U_15280)),U_15282) = U_15280
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15278),tc_List_Olist(U_15278))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15278),tc_List_Olist(U_15278)),U_15280),U_15282)),c_List_Olexord(U_15278,U_15284))) ),
    inference(clausify,[status(thm)],[f_3832_4]) ).

cnf(f_3832_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15278,U_15278)),hAPP(hAPP(c_Product__Type_OPair(U_15278,U_15278),hAPP(hAPP(c_List_Onth(U_15278),U_15280),sK405(U_15284,U_15282,U_15280,U_15278))),hAPP(hAPP(c_List_Onth(U_15278),U_15282),sK405(U_15284,U_15282,U_15280,U_15278)))),U_15284))
    | hAPP(hAPP(c_List_Otake(U_15278),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15278)),U_15280)),U_15282) = U_15280
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15278),tc_List_Olist(U_15278))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15278),tc_List_Olist(U_15278)),U_15280),U_15282)),c_List_Olexord(U_15278,U_15284))) ),
    inference(clausify,[status(thm)],[f_3832_4]) ).

cnf(f_3832_11,plain,
    ( hAPP(hAPP(c_List_Otake(U_15279),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15279)),U_15281)),U_15283) != U_15281
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15279)),U_15281)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15279)),U_15283)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15279),tc_List_Olist(U_15279))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15279),tc_List_Olist(U_15279)),U_15281),U_15283)),c_List_Olexord(U_15279,U_15285))) ),
    inference(clausify,[status(thm)],[f_3832_4]) ).

cnf(f_3832_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15279,U_15279)),hAPP(hAPP(c_Product__Type_OPair(U_15279,U_15279),hAPP(hAPP(c_List_Onth(U_15279),U_15281),U_15273)),hAPP(hAPP(c_List_Onth(U_15279),U_15283),U_15273))),U_15285))
    | hAPP(hAPP(c_List_Otake(U_15279),U_15273),U_15281) != hAPP(hAPP(c_List_Otake(U_15279),U_15273),U_15283)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15273),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15279)),U_15281)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15279)),U_15283))))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15279),tc_List_Olist(U_15279))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15279),tc_List_Olist(U_15279)),U_15281),U_15283)),c_List_Olexord(U_15279,U_15285))) ),
    inference(clausify,[status(thm)],[f_3832_4]) ).

fof(f_3833_1,plain,
    ! [V_I_2,V_xs_2,T_b] : hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_b),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(T_b),V_xs_2))))),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_I_2))))),
    inference(fof_nnf,[status(thm)],[fact_set__sublist]) ).

fof(f_3833_2,plain,
    ! [U_15288,U_15287,U_15286] : hAPP(c_List_Oset(U_15286),c_List_Osublist(U_15286,U_15287,U_15288)) = hAPP(c_Set_OCollect(U_15286),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,U_15286),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(U_15286,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_15286),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_15286),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(U_15286,tc_fun(tc_Nat_Onat,U_15286),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15286,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,U_15286),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_15286),c_COMBB(U_15286,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(U_15286),U_15287))))),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15286)),U_15287)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),U_15288))))),
    inference(variable_rename,[status(thm)],[f_3833_1]) ).

cnf(f_3833_3,plain,
    hAPP(c_List_Oset(U_15286),c_List_Osublist(U_15286,U_15287,U_15288)) = hAPP(c_Set_OCollect(U_15286),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,U_15286),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(U_15286,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_15286),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_15286),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(U_15286,tc_fun(tc_Nat_Onat,U_15286),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15286,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,U_15286),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_15286),c_COMBB(U_15286,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(U_15286),U_15287))))),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15286)),U_15287)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),U_15288))))),
    inference(clausify,[status(thm)],[f_3833_2]) ).

fof(f_3834_1,plain,
    ! [V_xs_2,T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_List_Oset(T_b),V_xs_2))),
    inference(fof_nnf,[status(thm)],[fact_finite__set]) ).

fof(f_3834_2,plain,
    ! [U_15290,U_15289] : hBOOL(hAPP(c_Finite__Set_Ofinite(U_15289),hAPP(c_List_Oset(U_15289),U_15290))),
    inference(variable_rename,[status(thm)],[f_3834_1]) ).

cnf(f_3834_3,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(U_15289),hAPP(c_List_Oset(U_15289),U_15290))),
    inference(clausify,[status(thm)],[f_3834_2]) ).

fof(f_3835_1,plain,
    ! [V_x_2,V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)))),
    inference(fof_nnf,[status(thm)],[fact_set__subset__Cons]) ).

fof(f_3835_2,plain,
    ! [U_15293,U_15292,U_15291] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15291,tc_HOL_Obool)),hAPP(c_List_Oset(U_15291),U_15292)),hAPP(c_List_Oset(U_15291),hAPP(hAPP(c_List_Olist_OCons(U_15291),U_15293),U_15292)))),
    inference(variable_rename,[status(thm)],[f_3835_1]) ).

cnf(f_3835_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15291,tc_HOL_Obool)),hAPP(c_List_Oset(U_15291),U_15292)),hAPP(c_List_Oset(U_15291),hAPP(hAPP(c_List_Olist_OCons(U_15291),U_15293),U_15292)))),
    inference(clausify,[status(thm)],[f_3835_2]) ).

fof(f_3836_1,plain,
    ! [V_n,V_xs,T_a] :
      ( hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs) = V_xs
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_take__all]) ).

fof(f_3836_2,plain,
    ! [U_15296,U_15295,U_15294] :
      ( hAPP(hAPP(c_List_Otake(U_15294),U_15296),U_15295) = U_15295
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15294)),U_15295)),U_15296)) ),
    inference(variable_rename,[status(thm)],[f_3836_1]) ).

cnf(f_3836_3,plain,
    ( hAPP(hAPP(c_List_Otake(U_15294),U_15296),U_15295) = U_15295
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15294)),U_15295)),U_15296)) ),
    inference(clausify,[status(thm)],[f_3836_2]) ).

fof(f_3837_1,plain,
    ! [V_xs_2,V_n_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2))),
    inference(fof_nnf,[status(thm)],[fact_set__take__subset]) ).

fof(f_3837_2,plain,
    ! [U_15299,U_15298,U_15297] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15297,tc_HOL_Obool)),hAPP(c_List_Oset(U_15297),hAPP(hAPP(c_List_Otake(U_15297),U_15298),U_15299))),hAPP(c_List_Oset(U_15297),U_15299))),
    inference(variable_rename,[status(thm)],[f_3837_1]) ).

cnf(f_3837_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15297,tc_HOL_Obool)),hAPP(c_List_Oset(U_15297),hAPP(hAPP(c_List_Otake(U_15297),U_15298),U_15299))),hAPP(c_List_Oset(U_15297),U_15299))),
    inference(clausify,[status(thm)],[f_3837_2]) ).

fof(f_3838_1,plain,
    ! [V_xs_2,T_b,V_n_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),V_m_2),V_xs_2))),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ),
    inference(fof_nnf,[status(thm)],[fact_set__take__subset__set__take]) ).

fof(f_3838_2,plain,
    ! [U_15303,U_15302,U_15301,U_15300] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15302,tc_HOL_Obool)),hAPP(c_List_Oset(U_15302),hAPP(hAPP(c_List_Otake(U_15302),U_15300),U_15303))),hAPP(c_List_Oset(U_15302),hAPP(hAPP(c_List_Otake(U_15302),U_15301),U_15303))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_15300),U_15301)) ),
    inference(variable_rename,[status(thm)],[f_3838_1]) ).

cnf(f_3838_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15302,tc_HOL_Obool)),hAPP(c_List_Oset(U_15302),hAPP(hAPP(c_List_Otake(U_15302),U_15300),U_15303))),hAPP(c_List_Oset(U_15302),hAPP(hAPP(c_List_Otake(U_15302),U_15301),U_15303))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_15300),U_15301)) ),
    inference(clausify,[status(thm)],[f_3838_2]) ).

fof(f_3839_1,plain,
    ! [V_I_2,V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2))),hAPP(c_List_Oset(T_b),V_xs_2))),
    inference(fof_nnf,[status(thm)],[fact_set__sublist__subset]) ).

fof(f_3839_2,plain,
    ! [U_15306,U_15305,U_15304] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15304,tc_HOL_Obool)),hAPP(c_List_Oset(U_15304),c_List_Osublist(U_15304,U_15305,U_15306))),hAPP(c_List_Oset(U_15304),U_15305))),
    inference(variable_rename,[status(thm)],[f_3839_1]) ).

cnf(f_3839_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15304,tc_HOL_Obool)),hAPP(c_List_Oset(U_15304),c_List_Osublist(U_15304,U_15305,U_15306))),hAPP(c_List_Oset(U_15304),U_15305))),
    inference(clausify,[status(thm)],[f_3839_2]) ).

fof(f_3840_1,plain,
    ! [V_xs,T_a,V_n,V_i] :
      ( hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),V_i) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_nth__take]) ).

fof(f_3840_2,plain,
    ! [U_15310,U_15309,U_15308,U_15307] :
      ( hAPP(hAPP(c_List_Onth(U_15309),hAPP(hAPP(c_List_Otake(U_15309),U_15308),U_15310)),U_15307) = hAPP(hAPP(c_List_Onth(U_15309),U_15310),U_15307)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15307),U_15308)) ),
    inference(variable_rename,[status(thm)],[f_3840_1]) ).

cnf(f_3840_3,plain,
    ( hAPP(hAPP(c_List_Onth(U_15309),hAPP(hAPP(c_List_Otake(U_15309),U_15308),U_15310)),U_15307) = hAPP(hAPP(c_List_Onth(U_15309),U_15310),U_15307)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15307),U_15308)) ),
    inference(clausify,[status(thm)],[f_3840_2]) ).

fof(f_3841_1,plain,
    ! [V_xs_2,V_x_2,V_y_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2)))
      | V_y_2 = V_x_2
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_set__ConsD]) ).

fof(f_3841_2,plain,
    ! [U_15314,U_15313,U_15312,U_15311] :
      ( hBOOL(hAPP(hAPP(c_member(U_15311),U_15312),hAPP(c_List_Oset(U_15311),U_15314)))
      | U_15312 = U_15313
      | ~ hBOOL(hAPP(hAPP(c_member(U_15311),U_15312),hAPP(c_List_Oset(U_15311),hAPP(hAPP(c_List_Olist_OCons(U_15311),U_15313),U_15314)))) ),
    inference(variable_rename,[status(thm)],[f_3841_1]) ).

cnf(f_3841_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15311),U_15312),hAPP(c_List_Oset(U_15311),U_15314)))
    | U_15312 = U_15313
    | ~ hBOOL(hAPP(hAPP(c_member(U_15311),U_15312),hAPP(c_List_Oset(U_15311),hAPP(hAPP(c_List_Olist_OCons(U_15311),U_15313),U_15314)))) ),
    inference(clausify,[status(thm)],[f_3841_2]) ).

fof(f_3842_1,plain,
    ! [V_I_2,V_xs_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_in__set__sublistD]) ).

fof(f_3842_2,plain,
    ! [U_15318,U_15317,U_15316,U_15315] :
      ( hBOOL(hAPP(hAPP(c_member(U_15315),U_15316),hAPP(c_List_Oset(U_15315),U_15317)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15315),U_15316),hAPP(c_List_Oset(U_15315),c_List_Osublist(U_15315,U_15317,U_15318)))) ),
    inference(variable_rename,[status(thm)],[f_3842_1]) ).

cnf(f_3842_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15315),U_15316),hAPP(c_List_Oset(U_15315),U_15317)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15315),U_15316),hAPP(c_List_Oset(U_15315),c_List_Osublist(U_15315,U_15317,U_15318)))) ),
    inference(clausify,[status(thm)],[f_3842_2]) ).

fof(f_3843_1,plain,
    ! [V_xs_2,V_n_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_in__set__takeD]) ).

fof(f_3843_2,plain,
    ! [U_15322,U_15321,U_15320,U_15319] :
      ( hBOOL(hAPP(hAPP(c_member(U_15319),U_15320),hAPP(c_List_Oset(U_15319),U_15322)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15319),U_15320),hAPP(c_List_Oset(U_15319),hAPP(hAPP(c_List_Otake(U_15319),U_15321),U_15322)))) ),
    inference(variable_rename,[status(thm)],[f_3843_1]) ).

cnf(f_3843_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15319),U_15320),hAPP(c_List_Oset(U_15319),U_15322)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15319),U_15320),hAPP(c_List_Oset(U_15319),hAPP(hAPP(c_List_Otake(U_15319),U_15321),U_15322)))) ),
    inference(clausify,[status(thm)],[f_3843_2]) ).

fof(f_3844_1,plain,
    ! [V_I_2,V_xs_2,V_x_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2))))
      | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_notin__set__sublistI]) ).

fof(f_3844_2,plain,
    ! [U_15326,U_15325,U_15324,U_15323] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_15323),U_15324),hAPP(c_List_Oset(U_15323),c_List_Osublist(U_15323,U_15325,U_15326))))
      | hBOOL(hAPP(hAPP(c_member(U_15323),U_15324),hAPP(c_List_Oset(U_15323),U_15325))) ),
    inference(variable_rename,[status(thm)],[f_3844_1]) ).

cnf(f_3844_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_15323),U_15324),hAPP(c_List_Oset(U_15323),c_List_Osublist(U_15323,U_15325,U_15326))))
    | hBOOL(hAPP(hAPP(c_member(U_15323),U_15324),hAPP(c_List_Oset(U_15323),U_15325))) ),
    inference(clausify,[status(thm)],[f_3844_2]) ).

fof(f_3845_1,plain,
    ! [V_xs,V_x,V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_n)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),
    inference(fof_nnf,[status(thm)],[fact_take__Suc__Cons]) ).

fof(f_3845_2,plain,
    ! [U_15330,U_15329,U_15328,U_15327] : hAPP(hAPP(c_List_Otake(U_15327),hAPP(c_Nat_OSuc,U_15328)),hAPP(hAPP(c_List_Olist_OCons(U_15327),U_15329),U_15330)) = hAPP(hAPP(c_List_Olist_OCons(U_15327),U_15329),hAPP(hAPP(c_List_Otake(U_15327),U_15328),U_15330)),
    inference(variable_rename,[status(thm)],[f_3845_1]) ).

cnf(f_3845_3,plain,
    hAPP(hAPP(c_List_Otake(U_15327),hAPP(c_Nat_OSuc,U_15328)),hAPP(hAPP(c_List_Olist_OCons(U_15327),U_15329),U_15330)) = hAPP(hAPP(c_List_Olist_OCons(U_15327),U_15329),hAPP(hAPP(c_List_Otake(U_15327),U_15328),U_15330)),
    inference(clausify,[status(thm)],[f_3845_2]) ).

fof(f_3846_1,plain,
    ! [V_xs,V_n,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n),
    inference(fof_nnf,[status(thm)],[fact_length__take]) ).

fof(f_3846_2,plain,
    ! [U_15333,U_15332,U_15331] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15331)),hAPP(hAPP(c_List_Otake(U_15331),U_15332),U_15333)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15331)),U_15333)),U_15332),
    inference(variable_rename,[status(thm)],[f_3846_1]) ).

cnf(f_3846_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15331)),hAPP(hAPP(c_List_Otake(U_15331),U_15332),U_15333)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15331)),U_15333)),U_15332),
    inference(clausify,[status(thm)],[f_3846_2]) ).

fof(f_3847_1,plain,
    ! [V_xs,V_m,V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(hAPP(c_List_Otake(T_a),V_m),V_xs)) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_n),V_m)),V_xs),
    inference(fof_nnf,[status(thm)],[fact_take__take]) ).

fof(f_3847_2,plain,
    ! [U_15337,U_15336,U_15335,U_15334] : hAPP(hAPP(c_List_Otake(U_15334),U_15335),hAPP(hAPP(c_List_Otake(U_15334),U_15336),U_15337)) = hAPP(hAPP(c_List_Otake(U_15334),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_15335),U_15336)),U_15337),
    inference(variable_rename,[status(thm)],[f_3847_1]) ).

cnf(f_3847_3,plain,
    hAPP(hAPP(c_List_Otake(U_15334),U_15335),hAPP(hAPP(c_List_Otake(U_15334),U_15336),U_15337)) = hAPP(hAPP(c_List_Otake(U_15334),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_15335),U_15336)),U_15337),
    inference(clausify,[status(thm)],[f_3847_2]) ).

fof(f_3848_1,plain,
    ! [V_xs_2,V_x_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_List_Oset_Osimps_I2_J]) ).

fof(f_3848_2,plain,
    ! [U_15340,U_15339,U_15338] : hAPP(c_List_Oset(U_15338),hAPP(hAPP(c_List_Olist_OCons(U_15338),U_15339),U_15340)) = hAPP(hAPP(c_Set_Oinsert(U_15338),U_15339),hAPP(c_List_Oset(U_15338),U_15340)),
    inference(variable_rename,[status(thm)],[f_3848_1]) ).

cnf(f_3848_3,plain,
    hAPP(c_List_Oset(U_15338),hAPP(hAPP(c_List_Olist_OCons(U_15338),U_15339),U_15340)) = hAPP(hAPP(c_Set_Oinsert(U_15338),U_15339),hAPP(c_List_Oset(U_15338),U_15340)),
    inference(clausify,[status(thm)],[f_3848_2]) ).

fof(f_3849_1,plain,
    ! [V_n_2,V_l_2,T_b] : c_List_Osublist(T_b,V_l_2,hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2)) = hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_l_2),
    inference(fof_nnf,[status(thm)],[fact_sublist__upt__eq__take]) ).

fof(f_3849_2,plain,
    ! [U_15343,U_15342,U_15341] : c_List_Osublist(U_15341,U_15342,hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_15343)) = hAPP(hAPP(c_List_Otake(U_15341),U_15343),U_15342),
    inference(variable_rename,[status(thm)],[f_3849_1]) ).

cnf(f_3849_3,plain,
    c_List_Osublist(U_15341,U_15342,hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_15343)) = hAPP(hAPP(c_List_Otake(U_15341),U_15343),U_15342),
    inference(clausify,[status(thm)],[f_3849_2]) ).

fof(f_3850_1,plain,
    ! [V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_List_Oset(T_b),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))),
    inference(fof_nnf,[status(thm)],[fact_card__length]) ).

fof(f_3850_2,plain,
    ! [U_15345,U_15344] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_15344),hAPP(c_List_Oset(U_15344),U_15345))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15344)),U_15345))),
    inference(variable_rename,[status(thm)],[f_3850_1]) ).

cnf(f_3850_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_15344),hAPP(c_List_Oset(U_15344),U_15345))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15344)),U_15345))),
    inference(clausify,[status(thm)],[f_3850_2]) ).

fof(f_3851_1,plain,
    ! [V_P_2,V_xs_2,T_b] :
      ( ( ! [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) )
        | ? [B_i] :
            ( ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ) )
      & ( ! [B_i] :
            ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) )
        | ? [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_all__set__conv__all__nth]) ).

fof(f_3851_2,plain,
    ! [U_15352,U_15351,U_15350] :
      ( ( ! [U_15349] :
            ( hBOOL(hAPP(U_15352,U_15349))
            | ~ hBOOL(hAPP(hAPP(c_member(U_15350),U_15349),hAPP(c_List_Oset(U_15350),U_15351))) )
        | ? [U_15348] :
            ( ~ hBOOL(hAPP(U_15352,hAPP(hAPP(c_List_Onth(U_15350),U_15351),U_15348)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15348),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15350)),U_15351))) ) )
      & ( ! [U_15347] :
            ( hBOOL(hAPP(U_15352,hAPP(hAPP(c_List_Onth(U_15350),U_15351),U_15347)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15347),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15350)),U_15351))) )
        | ? [U_15346] :
            ( ~ hBOOL(hAPP(U_15352,U_15346))
            & hBOOL(hAPP(hAPP(c_member(U_15350),U_15346),hAPP(c_List_Oset(U_15350),U_15351))) ) ) ),
    inference(variable_rename,[status(thm)],[f_3851_1]) ).

fof(f_3851_3,plain,
    ( ! [U_15358,U_15356,U_15354] :
        ( ! [U_15349] :
            ( hBOOL(hAPP(U_15358,U_15349))
            | ~ hBOOL(hAPP(hAPP(c_member(U_15354),U_15349),hAPP(c_List_Oset(U_15354),U_15356))) )
        | ? [U_15348] :
            ( ~ hBOOL(hAPP(U_15358,hAPP(hAPP(c_List_Onth(U_15354),U_15356),U_15348)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15348),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15354)),U_15356))) ) )
    & ! [U_15357,U_15355,U_15353] :
        ( ! [U_15347] :
            ( hBOOL(hAPP(U_15357,hAPP(hAPP(c_List_Onth(U_15353),U_15355),U_15347)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15347),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15353)),U_15355))) )
        | ? [U_15346] :
            ( ~ hBOOL(hAPP(U_15357,U_15346))
            & hBOOL(hAPP(hAPP(c_member(U_15353),U_15346),hAPP(c_List_Oset(U_15353),U_15355))) ) ) ),
    inference(miniscope,[status(thm)],[f_3851_2]) ).

fof(f_3851_4,plain,
    ( ! [U_15358,U_15356,U_15354] :
        ( ! [U_15349] :
            ( hBOOL(hAPP(U_15358,U_15349))
            | ~ hBOOL(hAPP(hAPP(c_member(U_15354),U_15349),hAPP(c_List_Oset(U_15354),U_15356))) )
        | ? [U_15348] :
            ( ~ hBOOL(hAPP(U_15358,hAPP(hAPP(c_List_Onth(U_15354),U_15356),U_15348)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15348),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15354)),U_15356))) ) )
    & ! [U_15357,U_15355,U_15353] :
        ( ! [U_15347] :
            ( hBOOL(hAPP(U_15357,hAPP(hAPP(c_List_Onth(U_15353),U_15355),U_15347)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15347),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15353)),U_15355))) )
        | ( ~ hBOOL(hAPP(U_15357,sK406(U_15357,U_15355,U_15353)))
          & hBOOL(hAPP(hAPP(c_member(U_15353),sK406(U_15357,U_15355,U_15353)),hAPP(c_List_Oset(U_15353),U_15355))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK406]),skolemize(U_15346,sK406(U_15357,U_15355,U_15353))],[f_3851_3]) ).

fof(f_3851_5,plain,
    ( ! [U_15358,U_15356,U_15354] :
        ( ! [U_15349] :
            ( hBOOL(hAPP(U_15358,U_15349))
            | ~ hBOOL(hAPP(hAPP(c_member(U_15354),U_15349),hAPP(c_List_Oset(U_15354),U_15356))) )
        | ( ~ hBOOL(hAPP(U_15358,hAPP(hAPP(c_List_Onth(U_15354),U_15356),sK407(U_15358,U_15356,U_15354))))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK407(U_15358,U_15356,U_15354)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15354)),U_15356))) ) )
    & ! [U_15357,U_15355,U_15353] :
        ( ! [U_15347] :
            ( hBOOL(hAPP(U_15357,hAPP(hAPP(c_List_Onth(U_15353),U_15355),U_15347)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15347),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15353)),U_15355))) )
        | ( ~ hBOOL(hAPP(U_15357,sK406(U_15357,U_15355,U_15353)))
          & hBOOL(hAPP(hAPP(c_member(U_15353),sK406(U_15357,U_15355,U_15353)),hAPP(c_List_Oset(U_15353),U_15355))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK407]),skolemize(U_15348,sK407(U_15358,U_15356,U_15354))],[f_3851_4]) ).

cnf(f_3851_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15353),sK406(U_15357,U_15355,U_15353)),hAPP(c_List_Oset(U_15353),U_15355)))
    | hBOOL(hAPP(U_15357,hAPP(hAPP(c_List_Onth(U_15353),U_15355),U_15347)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15347),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15353)),U_15355))) ),
    inference(clausify,[status(thm)],[f_3851_5]) ).

cnf(f_3851_7,plain,
    ( ~ hBOOL(hAPP(U_15357,sK406(U_15357,U_15355,U_15353)))
    | hBOOL(hAPP(U_15357,hAPP(hAPP(c_List_Onth(U_15353),U_15355),U_15347)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15347),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15353)),U_15355))) ),
    inference(clausify,[status(thm)],[f_3851_5]) ).

cnf(f_3851_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK407(U_15358,U_15356,U_15354)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15354)),U_15356)))
    | hBOOL(hAPP(U_15358,U_15349))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15354),U_15349),hAPP(c_List_Oset(U_15354),U_15356))) ),
    inference(clausify,[status(thm)],[f_3851_5]) ).

cnf(f_3851_9,plain,
    ( ~ hBOOL(hAPP(U_15358,hAPP(hAPP(c_List_Onth(U_15354),U_15356),sK407(U_15358,U_15356,U_15354))))
    | hBOOL(hAPP(U_15358,U_15349))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15354),U_15349),hAPP(c_List_Oset(U_15354),U_15356))) ),
    inference(clausify,[status(thm)],[f_3851_5]) ).

fof(f_3852_1,plain,
    ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),c_List_Olist_Olist__size(T_b,V_f_2,V_xs_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_list__size__estimation]) ).

fof(f_3852_2,plain,
    ! [U_15363,U_15362,U_15361,U_15360,U_15359] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15362),c_List_Olist_Olist__size(U_15359,U_15363,U_15361)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15362),hAPP(U_15363,U_15360)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15359),U_15360),hAPP(c_List_Oset(U_15359),U_15361))) ),
    inference(variable_rename,[status(thm)],[f_3852_1]) ).

cnf(f_3852_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15362),c_List_Olist_Olist__size(U_15359,U_15363,U_15361)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15362),hAPP(U_15363,U_15360)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15359),U_15360),hAPP(c_List_Oset(U_15359),U_15361))) ),
    inference(clausify,[status(thm)],[f_3852_2]) ).

fof(f_3853_1,plain,
    ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),c_List_Olist_Olist__size(T_b,V_f_2,V_xs_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_list__size__estimation_H]) ).

fof(f_3853_2,plain,
    ! [U_15368,U_15367,U_15366,U_15365,U_15364] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_15367),c_List_Olist_Olist__size(U_15364,U_15368,U_15366)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_15367),hAPP(U_15368,U_15365)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15364),U_15365),hAPP(c_List_Oset(U_15364),U_15366))) ),
    inference(variable_rename,[status(thm)],[f_3853_1]) ).

cnf(f_3853_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_15367),c_List_Olist_Olist__size(U_15364,U_15368,U_15366)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_15367),hAPP(U_15368,U_15365)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15364),U_15365),hAPP(c_List_Oset(U_15364),U_15366))) ),
    inference(clausify,[status(thm)],[f_3853_2]) ).

fof(f_3854_1,plain,
    ! [V_A_2,V_xs_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2)))
        | ? [B_x] :
            ( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) ) )
      & ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
            | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_in__lists__conv__set]) ).

fof(f_3854_2,plain,
    ! [U_15373,U_15372,U_15371] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15371)),U_15372),c_List_Olists(U_15371,U_15373)))
        | ? [U_15370] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_15371),U_15370),U_15373))
            & hBOOL(hAPP(hAPP(c_member(U_15371),U_15370),hAPP(c_List_Oset(U_15371),U_15372))) ) )
      & ( ! [U_15369] :
            ( hBOOL(hAPP(hAPP(c_member(U_15371),U_15369),U_15373))
            | ~ hBOOL(hAPP(hAPP(c_member(U_15371),U_15369),hAPP(c_List_Oset(U_15371),U_15372))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15371)),U_15372),c_List_Olists(U_15371,U_15373))) ) ),
    inference(variable_rename,[status(thm)],[f_3854_1]) ).

fof(f_3854_3,plain,
    ( ! [U_15379,U_15377,U_15375] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15375)),U_15377),c_List_Olists(U_15375,U_15379)))
        | ? [U_15370] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_15375),U_15370),U_15379))
            & hBOOL(hAPP(hAPP(c_member(U_15375),U_15370),hAPP(c_List_Oset(U_15375),U_15377))) ) )
    & ! [U_15378,U_15376,U_15374] :
        ( ! [U_15369] :
            ( hBOOL(hAPP(hAPP(c_member(U_15374),U_15369),U_15378))
            | ~ hBOOL(hAPP(hAPP(c_member(U_15374),U_15369),hAPP(c_List_Oset(U_15374),U_15376))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15374)),U_15376),c_List_Olists(U_15374,U_15378))) ) ),
    inference(miniscope,[status(thm)],[f_3854_2]) ).

fof(f_3854_4,plain,
    ( ! [U_15379,U_15377,U_15375] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15375)),U_15377),c_List_Olists(U_15375,U_15379)))
        | ( ~ hBOOL(hAPP(hAPP(c_member(U_15375),sK408(U_15379,U_15377,U_15375)),U_15379))
          & hBOOL(hAPP(hAPP(c_member(U_15375),sK408(U_15379,U_15377,U_15375)),hAPP(c_List_Oset(U_15375),U_15377))) ) )
    & ! [U_15378,U_15376,U_15374] :
        ( ! [U_15369] :
            ( hBOOL(hAPP(hAPP(c_member(U_15374),U_15369),U_15378))
            | ~ hBOOL(hAPP(hAPP(c_member(U_15374),U_15369),hAPP(c_List_Oset(U_15374),U_15376))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15374)),U_15376),c_List_Olists(U_15374,U_15378))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK408]),skolemize(U_15370,sK408(U_15379,U_15377,U_15375))],[f_3854_3]) ).

cnf(f_3854_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15374),U_15369),U_15378))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15374),U_15369),hAPP(c_List_Oset(U_15374),U_15376)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15374)),U_15376),c_List_Olists(U_15374,U_15378))) ),
    inference(clausify,[status(thm)],[f_3854_4]) ).

cnf(f_3854_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15375),sK408(U_15379,U_15377,U_15375)),hAPP(c_List_Oset(U_15375),U_15377)))
    | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15375)),U_15377),c_List_Olists(U_15375,U_15379))) ),
    inference(clausify,[status(thm)],[f_3854_4]) ).

cnf(f_3854_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_15375),sK408(U_15379,U_15377,U_15375)),U_15379))
    | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15375)),U_15377),c_List_Olists(U_15375,U_15379))) ),
    inference(clausify,[status(thm)],[f_3854_4]) ).

fof(f_3855_1,plain,
    ! [V_xs_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_length__pos__if__in__set]) ).

fof(f_3855_2,plain,
    ! [U_15382,U_15381,U_15380] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15380)),U_15382)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15380),U_15381),hAPP(c_List_Oset(U_15380),U_15382))) ),
    inference(variable_rename,[status(thm)],[f_3855_1]) ).

cnf(f_3855_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15380)),U_15382)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15380),U_15381),hAPP(c_List_Oset(U_15380),U_15382))) ),
    inference(clausify,[status(thm)],[f_3855_2]) ).

fof(f_3856_1,plain,
    ! [V_xs_2,T_b,V_n_2] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2)),hAPP(c_List_Oset(T_b),V_xs_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_nth__mem]) ).

fof(f_3856_2,plain,
    ! [U_15385,U_15384,U_15383] :
      ( hBOOL(hAPP(hAPP(c_member(U_15384),hAPP(hAPP(c_List_Onth(U_15384),U_15385),U_15383)),hAPP(c_List_Oset(U_15384),U_15385)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15383),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15384)),U_15385))) ),
    inference(variable_rename,[status(thm)],[f_3856_1]) ).

cnf(f_3856_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15384),hAPP(hAPP(c_List_Onth(U_15384),U_15385),U_15383)),hAPP(c_List_Oset(U_15384),U_15385)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15383),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15384)),U_15385))) ),
    inference(clausify,[status(thm)],[f_3856_2]) ).

fof(f_3857_1,plain,
    ! [V_xs_2,V_x_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
        | ! [B_i] :
            ( hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) != V_x_2
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ) )
      & ( ? [B_i] :
            ( hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) = V_x_2
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) )
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_in__set__conv__nth]) ).

fof(f_3857_2,plain,
    ! [U_15390,U_15389,U_15388] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_15388),U_15389),hAPP(c_List_Oset(U_15388),U_15390)))
        | ! [U_15387] :
            ( hAPP(hAPP(c_List_Onth(U_15388),U_15390),U_15387) != U_15389
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15387),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15388)),U_15390))) ) )
      & ( ? [U_15386] :
            ( hAPP(hAPP(c_List_Onth(U_15388),U_15390),U_15386) = U_15389
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15386),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15388)),U_15390))) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_15388),U_15389),hAPP(c_List_Oset(U_15388),U_15390))) ) ),
    inference(variable_rename,[status(thm)],[f_3857_1]) ).

fof(f_3857_3,plain,
    ( ! [U_15396,U_15394,U_15392] :
        ( hBOOL(hAPP(hAPP(c_member(U_15392),U_15394),hAPP(c_List_Oset(U_15392),U_15396)))
        | ! [U_15387] :
            ( hAPP(hAPP(c_List_Onth(U_15392),U_15396),U_15387) != U_15394
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15387),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15392)),U_15396))) ) )
    & ! [U_15395,U_15393,U_15391] :
        ( ? [U_15386] :
            ( hAPP(hAPP(c_List_Onth(U_15391),U_15395),U_15386) = U_15393
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15386),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15391)),U_15395))) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_15391),U_15393),hAPP(c_List_Oset(U_15391),U_15395))) ) ),
    inference(miniscope,[status(thm)],[f_3857_2]) ).

fof(f_3857_4,plain,
    ( ! [U_15396,U_15394,U_15392] :
        ( hBOOL(hAPP(hAPP(c_member(U_15392),U_15394),hAPP(c_List_Oset(U_15392),U_15396)))
        | ! [U_15387] :
            ( hAPP(hAPP(c_List_Onth(U_15392),U_15396),U_15387) != U_15394
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15387),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15392)),U_15396))) ) )
    & ! [U_15395,U_15393,U_15391] :
        ( ( hAPP(hAPP(c_List_Onth(U_15391),U_15395),sK409(U_15395,U_15393,U_15391)) = U_15393
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK409(U_15395,U_15393,U_15391)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15391)),U_15395))) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_15391),U_15393),hAPP(c_List_Oset(U_15391),U_15395))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK409]),skolemize(U_15386,sK409(U_15395,U_15393,U_15391))],[f_3857_3]) ).

cnf(f_3857_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK409(U_15395,U_15393,U_15391)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15391)),U_15395)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15391),U_15393),hAPP(c_List_Oset(U_15391),U_15395))) ),
    inference(clausify,[status(thm)],[f_3857_4]) ).

cnf(f_3857_6,plain,
    ( hAPP(hAPP(c_List_Onth(U_15391),U_15395),sK409(U_15395,U_15393,U_15391)) = U_15393
    | ~ hBOOL(hAPP(hAPP(c_member(U_15391),U_15393),hAPP(c_List_Oset(U_15391),U_15395))) ),
    inference(clausify,[status(thm)],[f_3857_4]) ).

cnf(f_3857_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15392),U_15394),hAPP(c_List_Oset(U_15392),U_15396)))
    | hAPP(hAPP(c_List_Onth(U_15392),U_15396),U_15387) != U_15394
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15387),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15392)),U_15396))) ),
    inference(clausify,[status(thm)],[f_3857_4]) ).

fof(f_3858_1,plain,
    ! [V_A_2,T_b] : c_List_Olists(T_b,V_A_2) = hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),c_List_Oset(T_b))),V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_lists__eq__set]) ).

fof(f_3858_2,plain,
    ! [U_15398,U_15397] : c_List_Olists(U_15397,U_15398) = hAPP(c_Set_OCollect(tc_List_Olist(U_15397)),hAPP(hAPP(c_COMBC(tc_List_Olist(U_15397),tc_fun(U_15397,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_15397,tc_HOL_Obool),tc_fun(tc_fun(U_15397,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_15397)),c_Orderings_Oord__class_Oless__eq(tc_fun(U_15397,tc_HOL_Obool))),c_List_Oset(U_15397))),U_15398)),
    inference(variable_rename,[status(thm)],[f_3858_1]) ).

cnf(f_3858_3,plain,
    c_List_Olists(U_15397,U_15398) = hAPP(c_Set_OCollect(tc_List_Olist(U_15397)),hAPP(hAPP(c_COMBC(tc_List_Olist(U_15397),tc_fun(U_15397,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_15397,tc_HOL_Obool),tc_fun(tc_fun(U_15397,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_15397)),c_Orderings_Oord__class_Oless__eq(tc_fun(U_15397,tc_HOL_Obool))),c_List_Oset(U_15397))),U_15398)),
    inference(clausify,[status(thm)],[f_3858_2]) ).

fof(f_3859_1,plain,
    ! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_b),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(T_b),V_xs_2))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))))),
    inference(fof_nnf,[status(thm)],[fact_set__conv__nth]) ).

fof(f_3859_2,plain,
    ! [U_15400,U_15399] : hAPP(c_List_Oset(U_15399),U_15400) = hAPP(c_Set_OCollect(U_15399),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,U_15399),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(U_15399,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_15399),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_15399),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(U_15399,tc_fun(tc_Nat_Onat,U_15399),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15399,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,U_15399),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_15399),c_COMBB(U_15399,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(U_15399),U_15400))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15399)),U_15400))))),
    inference(variable_rename,[status(thm)],[f_3859_1]) ).

cnf(f_3859_3,plain,
    hAPP(c_List_Oset(U_15399),U_15400) = hAPP(c_Set_OCollect(U_15399),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,U_15399),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(U_15399,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_15399),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_15399),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(U_15399,tc_fun(tc_Nat_Onat,U_15399),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15399,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,U_15399),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_15399),c_COMBB(U_15399,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(U_15399),U_15400))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15399)),U_15400))))),
    inference(clausify,[status(thm)],[f_3859_2]) ).

fof(f_3860_1,plain,
    ! [V_n_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_b)),hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),c_List_Oset(T_b))),V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_n_2)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__lists__length__eq]) ).

fof(f_3860_2,plain,
    ! [U_15403,U_15402,U_15401] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(U_15401)),hAPP(c_Set_OCollect(tc_List_Olist(U_15401)),hAPP(hAPP(c_COMBS(tc_List_Olist(U_15401),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_15401)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_15401),tc_fun(U_15401,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_15401,tc_HOL_Obool),tc_fun(tc_fun(U_15401,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_15401)),c_Orderings_Oord__class_Oless__eq(tc_fun(U_15401,tc_HOL_Obool))),c_List_Oset(U_15401))),U_15402))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_15401),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_15401)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_15401)))),U_15403)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15401),U_15402)) ),
    inference(variable_rename,[status(thm)],[f_3860_1]) ).

cnf(f_3860_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(U_15401)),hAPP(c_Set_OCollect(tc_List_Olist(U_15401)),hAPP(hAPP(c_COMBS(tc_List_Olist(U_15401),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_15401)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_15401),tc_fun(U_15401,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_15401,tc_HOL_Obool),tc_fun(tc_fun(U_15401,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_15401)),c_Orderings_Oord__class_Oless__eq(tc_fun(U_15401,tc_HOL_Obool))),c_List_Oset(U_15401))),U_15402))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_15401),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_15401)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_15401)))),U_15403)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15401),U_15402)) ),
    inference(clausify,[status(thm)],[f_3860_2]) ).

fof(f_3861_1,plain,
    ! [V_n_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_b)),hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),c_List_Oset(T_b))),V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_n_2)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__lists__length__le]) ).

fof(f_3861_2,plain,
    ! [U_15406,U_15405,U_15404] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(U_15404)),hAPP(c_Set_OCollect(tc_List_Olist(U_15404)),hAPP(hAPP(c_COMBS(tc_List_Olist(U_15404),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_15404)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_15404),tc_fun(U_15404,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_15404,tc_HOL_Obool),tc_fun(tc_fun(U_15404,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_15404)),c_Orderings_Oord__class_Oless__eq(tc_fun(U_15404,tc_HOL_Obool))),c_List_Oset(U_15404))),U_15405))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_15404),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_15404)),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_15404)))),U_15406)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15404),U_15405)) ),
    inference(variable_rename,[status(thm)],[f_3861_1]) ).

cnf(f_3861_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(U_15404)),hAPP(c_Set_OCollect(tc_List_Olist(U_15404)),hAPP(hAPP(c_COMBS(tc_List_Olist(U_15404),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_15404)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_15404),tc_fun(U_15404,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_15404,tc_HOL_Obool),tc_fun(tc_fun(U_15404,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_15404)),c_Orderings_Oord__class_Oless__eq(tc_fun(U_15404,tc_HOL_Obool))),c_List_Oset(U_15404))),U_15405))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_15404),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_15404)),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_15404)))),U_15406)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15404),U_15405)) ),
    inference(clausify,[status(thm)],[f_3861_2]) ).

fof(f_3862_1,plain,
    ! [V_r_2,V_ys_2,V_xs_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2)))
        | ? [B_x] :
            ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2)),B_x))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),hAPP(c_List_Oset(tc_prod(T_b,T_b)),hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_ys_2)))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) )
      & ( ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2)),B_x))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),hAPP(c_List_Oset(tc_prod(T_b,T_b)),hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_ys_2)))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_listrel__iff__zip]) ).

fof(f_3862_2,plain,
    ! [U_15412,U_15411,U_15410,U_15409] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15409),tc_List_Olist(U_15409))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15409),tc_List_Olist(U_15409)),U_15410),U_15411)),c_List_Olistrel(U_15409,U_15412)))
        | ? [U_15408] :
            ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_15409,U_15409,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_15409,tc_fun(tc_prod(U_15409,U_15409),tc_HOL_Obool),tc_fun(U_15409,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15409,tc_fun(tc_fun(tc_prod(U_15409,U_15409),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15409,U_15409),tc_HOL_Obool),tc_fun(U_15409,tc_HOL_Obool)),U_15409),c_COMBC(U_15409,tc_fun(tc_prod(U_15409,U_15409),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15409,tc_prod(U_15409,U_15409)),tc_fun(U_15409,tc_fun(tc_fun(tc_prod(U_15409,U_15409),tc_HOL_Obool),tc_HOL_Obool)),U_15409),hAPP(c_COMBB(tc_prod(U_15409,U_15409),tc_fun(tc_fun(tc_prod(U_15409,U_15409),tc_HOL_Obool),tc_HOL_Obool),U_15409),c_member(tc_prod(U_15409,U_15409)))),c_Product__Type_OPair(U_15409,U_15409)))),U_15412)),U_15408))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15409,U_15409)),U_15408),hAPP(c_List_Oset(tc_prod(U_15409,U_15409)),hAPP(hAPP(c_List_Ozip(U_15409,U_15409),U_15410),U_15411)))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15409)),U_15410) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15409)),U_15411) )
      & ( ( ! [U_15407] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_15409,U_15409,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_15409,tc_fun(tc_prod(U_15409,U_15409),tc_HOL_Obool),tc_fun(U_15409,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15409,tc_fun(tc_fun(tc_prod(U_15409,U_15409),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15409,U_15409),tc_HOL_Obool),tc_fun(U_15409,tc_HOL_Obool)),U_15409),c_COMBC(U_15409,tc_fun(tc_prod(U_15409,U_15409),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15409,tc_prod(U_15409,U_15409)),tc_fun(U_15409,tc_fun(tc_fun(tc_prod(U_15409,U_15409),tc_HOL_Obool),tc_HOL_Obool)),U_15409),hAPP(c_COMBB(tc_prod(U_15409,U_15409),tc_fun(tc_fun(tc_prod(U_15409,U_15409),tc_HOL_Obool),tc_HOL_Obool),U_15409),c_member(tc_prod(U_15409,U_15409)))),c_Product__Type_OPair(U_15409,U_15409)))),U_15412)),U_15407))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15409,U_15409)),U_15407),hAPP(c_List_Oset(tc_prod(U_15409,U_15409)),hAPP(hAPP(c_List_Ozip(U_15409,U_15409),U_15410),U_15411)))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15409)),U_15410) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15409)),U_15411) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15409),tc_List_Olist(U_15409))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15409),tc_List_Olist(U_15409)),U_15410),U_15411)),c_List_Olistrel(U_15409,U_15412))) ) ),
    inference(variable_rename,[status(thm)],[f_3862_1]) ).

fof(f_3862_3,plain,
    ( ! [U_15420,U_15418,U_15416,U_15414] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15414),tc_List_Olist(U_15414))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15414),tc_List_Olist(U_15414)),U_15416),U_15418)),c_List_Olistrel(U_15414,U_15420)))
        | ? [U_15408] :
            ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_15414,U_15414,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_15414,tc_fun(tc_prod(U_15414,U_15414),tc_HOL_Obool),tc_fun(U_15414,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15414,tc_fun(tc_fun(tc_prod(U_15414,U_15414),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15414,U_15414),tc_HOL_Obool),tc_fun(U_15414,tc_HOL_Obool)),U_15414),c_COMBC(U_15414,tc_fun(tc_prod(U_15414,U_15414),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15414,tc_prod(U_15414,U_15414)),tc_fun(U_15414,tc_fun(tc_fun(tc_prod(U_15414,U_15414),tc_HOL_Obool),tc_HOL_Obool)),U_15414),hAPP(c_COMBB(tc_prod(U_15414,U_15414),tc_fun(tc_fun(tc_prod(U_15414,U_15414),tc_HOL_Obool),tc_HOL_Obool),U_15414),c_member(tc_prod(U_15414,U_15414)))),c_Product__Type_OPair(U_15414,U_15414)))),U_15420)),U_15408))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15414,U_15414)),U_15408),hAPP(c_List_Oset(tc_prod(U_15414,U_15414)),hAPP(hAPP(c_List_Ozip(U_15414,U_15414),U_15416),U_15418)))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15414)),U_15416) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15414)),U_15418) )
    & ! [U_15419,U_15417,U_15415,U_15413] :
        ( ( ! [U_15407] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_15413,U_15413,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_15413,tc_fun(tc_prod(U_15413,U_15413),tc_HOL_Obool),tc_fun(U_15413,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15413,tc_fun(tc_fun(tc_prod(U_15413,U_15413),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15413,U_15413),tc_HOL_Obool),tc_fun(U_15413,tc_HOL_Obool)),U_15413),c_COMBC(U_15413,tc_fun(tc_prod(U_15413,U_15413),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15413,tc_prod(U_15413,U_15413)),tc_fun(U_15413,tc_fun(tc_fun(tc_prod(U_15413,U_15413),tc_HOL_Obool),tc_HOL_Obool)),U_15413),hAPP(c_COMBB(tc_prod(U_15413,U_15413),tc_fun(tc_fun(tc_prod(U_15413,U_15413),tc_HOL_Obool),tc_HOL_Obool),U_15413),c_member(tc_prod(U_15413,U_15413)))),c_Product__Type_OPair(U_15413,U_15413)))),U_15419)),U_15407))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15413,U_15413)),U_15407),hAPP(c_List_Oset(tc_prod(U_15413,U_15413)),hAPP(hAPP(c_List_Ozip(U_15413,U_15413),U_15415),U_15417)))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15413)),U_15415) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15413)),U_15417) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15413),tc_List_Olist(U_15413))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15413),tc_List_Olist(U_15413)),U_15415),U_15417)),c_List_Olistrel(U_15413,U_15419))) ) ),
    inference(miniscope,[status(thm)],[f_3862_2]) ).

fof(f_3862_4,plain,
    ( ! [U_15420,U_15418,U_15416,U_15414] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15414),tc_List_Olist(U_15414))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15414),tc_List_Olist(U_15414)),U_15416),U_15418)),c_List_Olistrel(U_15414,U_15420)))
        | ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_15414,U_15414,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_15414,tc_fun(tc_prod(U_15414,U_15414),tc_HOL_Obool),tc_fun(U_15414,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15414,tc_fun(tc_fun(tc_prod(U_15414,U_15414),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15414,U_15414),tc_HOL_Obool),tc_fun(U_15414,tc_HOL_Obool)),U_15414),c_COMBC(U_15414,tc_fun(tc_prod(U_15414,U_15414),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15414,tc_prod(U_15414,U_15414)),tc_fun(U_15414,tc_fun(tc_fun(tc_prod(U_15414,U_15414),tc_HOL_Obool),tc_HOL_Obool)),U_15414),hAPP(c_COMBB(tc_prod(U_15414,U_15414),tc_fun(tc_fun(tc_prod(U_15414,U_15414),tc_HOL_Obool),tc_HOL_Obool),U_15414),c_member(tc_prod(U_15414,U_15414)))),c_Product__Type_OPair(U_15414,U_15414)))),U_15420)),sK410(U_15420,U_15418,U_15416,U_15414)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15414,U_15414)),sK410(U_15420,U_15418,U_15416,U_15414)),hAPP(c_List_Oset(tc_prod(U_15414,U_15414)),hAPP(hAPP(c_List_Ozip(U_15414,U_15414),U_15416),U_15418)))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15414)),U_15416) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15414)),U_15418) )
    & ! [U_15419,U_15417,U_15415,U_15413] :
        ( ( ! [U_15407] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_15413,U_15413,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_15413,tc_fun(tc_prod(U_15413,U_15413),tc_HOL_Obool),tc_fun(U_15413,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15413,tc_fun(tc_fun(tc_prod(U_15413,U_15413),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15413,U_15413),tc_HOL_Obool),tc_fun(U_15413,tc_HOL_Obool)),U_15413),c_COMBC(U_15413,tc_fun(tc_prod(U_15413,U_15413),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15413,tc_prod(U_15413,U_15413)),tc_fun(U_15413,tc_fun(tc_fun(tc_prod(U_15413,U_15413),tc_HOL_Obool),tc_HOL_Obool)),U_15413),hAPP(c_COMBB(tc_prod(U_15413,U_15413),tc_fun(tc_fun(tc_prod(U_15413,U_15413),tc_HOL_Obool),tc_HOL_Obool),U_15413),c_member(tc_prod(U_15413,U_15413)))),c_Product__Type_OPair(U_15413,U_15413)))),U_15419)),U_15407))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15413,U_15413)),U_15407),hAPP(c_List_Oset(tc_prod(U_15413,U_15413)),hAPP(hAPP(c_List_Ozip(U_15413,U_15413),U_15415),U_15417)))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15413)),U_15415) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15413)),U_15417) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15413),tc_List_Olist(U_15413))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15413),tc_List_Olist(U_15413)),U_15415),U_15417)),c_List_Olistrel(U_15413,U_15419))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK410]),skolemize(U_15408,sK410(U_15420,U_15418,U_15416,U_15414))],[f_3862_3]) ).

cnf(f_3862_5,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15413)),U_15415) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15413)),U_15417)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15413),tc_List_Olist(U_15413))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15413),tc_List_Olist(U_15413)),U_15415),U_15417)),c_List_Olistrel(U_15413,U_15419))) ),
    inference(clausify,[status(thm)],[f_3862_4]) ).

cnf(f_3862_6,plain,
    ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_15413,U_15413,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_15413,tc_fun(tc_prod(U_15413,U_15413),tc_HOL_Obool),tc_fun(U_15413,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15413,tc_fun(tc_fun(tc_prod(U_15413,U_15413),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15413,U_15413),tc_HOL_Obool),tc_fun(U_15413,tc_HOL_Obool)),U_15413),c_COMBC(U_15413,tc_fun(tc_prod(U_15413,U_15413),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15413,tc_prod(U_15413,U_15413)),tc_fun(U_15413,tc_fun(tc_fun(tc_prod(U_15413,U_15413),tc_HOL_Obool),tc_HOL_Obool)),U_15413),hAPP(c_COMBB(tc_prod(U_15413,U_15413),tc_fun(tc_fun(tc_prod(U_15413,U_15413),tc_HOL_Obool),tc_HOL_Obool),U_15413),c_member(tc_prod(U_15413,U_15413)))),c_Product__Type_OPair(U_15413,U_15413)))),U_15419)),U_15407))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15413,U_15413)),U_15407),hAPP(c_List_Oset(tc_prod(U_15413,U_15413)),hAPP(hAPP(c_List_Ozip(U_15413,U_15413),U_15415),U_15417))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15413),tc_List_Olist(U_15413))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15413),tc_List_Olist(U_15413)),U_15415),U_15417)),c_List_Olistrel(U_15413,U_15419))) ),
    inference(clausify,[status(thm)],[f_3862_4]) ).

cnf(f_3862_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15414,U_15414)),sK410(U_15420,U_15418,U_15416,U_15414)),hAPP(c_List_Oset(tc_prod(U_15414,U_15414)),hAPP(hAPP(c_List_Ozip(U_15414,U_15414),U_15416),U_15418))))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15414)),U_15416) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15414)),U_15418)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15414),tc_List_Olist(U_15414))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15414),tc_List_Olist(U_15414)),U_15416),U_15418)),c_List_Olistrel(U_15414,U_15420))) ),
    inference(clausify,[status(thm)],[f_3862_4]) ).

cnf(f_3862_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_15414,U_15414,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_15414,tc_fun(tc_prod(U_15414,U_15414),tc_HOL_Obool),tc_fun(U_15414,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15414,tc_fun(tc_fun(tc_prod(U_15414,U_15414),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_15414,U_15414),tc_HOL_Obool),tc_fun(U_15414,tc_HOL_Obool)),U_15414),c_COMBC(U_15414,tc_fun(tc_prod(U_15414,U_15414),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15414,tc_prod(U_15414,U_15414)),tc_fun(U_15414,tc_fun(tc_fun(tc_prod(U_15414,U_15414),tc_HOL_Obool),tc_HOL_Obool)),U_15414),hAPP(c_COMBB(tc_prod(U_15414,U_15414),tc_fun(tc_fun(tc_prod(U_15414,U_15414),tc_HOL_Obool),tc_HOL_Obool),U_15414),c_member(tc_prod(U_15414,U_15414)))),c_Product__Type_OPair(U_15414,U_15414)))),U_15420)),sK410(U_15420,U_15418,U_15416,U_15414)))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15414)),U_15416) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15414)),U_15418)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15414),tc_List_Olist(U_15414))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15414),tc_List_Olist(U_15414)),U_15416),U_15418)),c_List_Olistrel(U_15414,U_15420))) ),
    inference(clausify,[status(thm)],[f_3862_4]) ).

fof(f_3863_1,plain,
    ! [V_ys_2,V_xs_2,T_c,T_b] : hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) = hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_prod(T_b,T_c)),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(T_b,T_c),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(T_b,T_c)),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_prod(T_b,T_c)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(tc_prod(T_b,T_c),tc_fun(tc_Nat_Onat,tc_prod(T_b,T_c)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_prod(T_b,T_c)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(T_b,T_c)),c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_c,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_prod(T_b,T_c)),tc_Nat_Onat),c_Product__Type_OPair(T_b,T_c)),hAPP(c_List_Onth(T_b),V_xs_2))),hAPP(c_List_Onth(T_c),V_ys_2)))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)))))),
    inference(fof_nnf,[status(thm)],[fact_set__zip]) ).

fof(f_3863_2,plain,
    ! [U_15424,U_15423,U_15422,U_15421] : hAPP(c_List_Oset(tc_prod(U_15421,U_15422)),hAPP(hAPP(c_List_Ozip(U_15421,U_15422),U_15423),U_15424)) = hAPP(c_Set_OCollect(tc_prod(U_15421,U_15422)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_prod(U_15421,U_15422)),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(U_15421,U_15422),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(U_15421,U_15422)),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_prod(U_15421,U_15422)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(tc_prod(U_15421,U_15422),tc_fun(tc_Nat_Onat,tc_prod(U_15421,U_15422)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_15421,U_15422),tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_prod(U_15421,U_15422)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(U_15421,U_15422)),c_COMBB(tc_prod(U_15421,U_15422),tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,U_15422,tc_prod(U_15421,U_15422)),hAPP(hAPP(c_COMBB(U_15421,tc_fun(U_15422,tc_prod(U_15421,U_15422)),tc_Nat_Onat),c_Product__Type_OPair(U_15421,U_15422)),hAPP(c_List_Onth(U_15421),U_15423))),hAPP(c_List_Onth(U_15422),U_15424)))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15421)),U_15423)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15422)),U_15424)))))),
    inference(variable_rename,[status(thm)],[f_3863_1]) ).

cnf(f_3863_3,plain,
    hAPP(c_List_Oset(tc_prod(U_15421,U_15422)),hAPP(hAPP(c_List_Ozip(U_15421,U_15422),U_15423),U_15424)) = hAPP(c_Set_OCollect(tc_prod(U_15421,U_15422)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_prod(U_15421,U_15422)),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(U_15421,U_15422),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(U_15421,U_15422)),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_prod(U_15421,U_15422)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(tc_prod(U_15421,U_15422),tc_fun(tc_Nat_Onat,tc_prod(U_15421,U_15422)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_15421,U_15422),tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_prod(U_15421,U_15422)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(U_15421,U_15422)),c_COMBB(tc_prod(U_15421,U_15422),tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,U_15422,tc_prod(U_15421,U_15422)),hAPP(hAPP(c_COMBB(U_15421,tc_fun(U_15422,tc_prod(U_15421,U_15422)),tc_Nat_Onat),c_Product__Type_OPair(U_15421,U_15422)),hAPP(c_List_Onth(U_15421),U_15423))),hAPP(c_List_Onth(U_15422),U_15424)))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15421)),U_15423)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15422)),U_15424)))))),
    inference(clausify,[status(thm)],[f_3863_2]) ).

fof(f_3864_1,plain,
    ! [V_ys,V_xs,V_n,T_b,T_a] : hAPP(hAPP(c_List_Otake(tc_prod(T_a,T_b)),V_n),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)) = hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Otake(T_b),V_n),V_ys)),
    inference(fof_nnf,[status(thm)],[fact_take__zip]) ).

fof(f_3864_2,plain,
    ! [U_15429,U_15428,U_15427,U_15426,U_15425] : hAPP(hAPP(c_List_Otake(tc_prod(U_15425,U_15426)),U_15427),hAPP(hAPP(c_List_Ozip(U_15425,U_15426),U_15428),U_15429)) = hAPP(hAPP(c_List_Ozip(U_15425,U_15426),hAPP(hAPP(c_List_Otake(U_15425),U_15427),U_15428)),hAPP(hAPP(c_List_Otake(U_15426),U_15427),U_15429)),
    inference(variable_rename,[status(thm)],[f_3864_1]) ).

cnf(f_3864_3,plain,
    hAPP(hAPP(c_List_Otake(tc_prod(U_15425,U_15426)),U_15427),hAPP(hAPP(c_List_Ozip(U_15425,U_15426),U_15428),U_15429)) = hAPP(hAPP(c_List_Ozip(U_15425,U_15426),hAPP(hAPP(c_List_Otake(U_15425),U_15427),U_15428)),hAPP(hAPP(c_List_Otake(U_15426),U_15427),U_15429)),
    inference(clausify,[status(thm)],[f_3864_2]) ).

fof(f_3865_1,plain,
    ! [V_ys,V_xs,T_b,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(T_a,T_b))),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys)),
    inference(fof_nnf,[status(thm)],[fact_length__zip]) ).

fof(f_3865_2,plain,
    ! [U_15433,U_15432,U_15431,U_15430] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(U_15430,U_15431))),hAPP(hAPP(c_List_Ozip(U_15430,U_15431),U_15432),U_15433)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15430)),U_15432)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15431)),U_15433)),
    inference(variable_rename,[status(thm)],[f_3865_1]) ).

cnf(f_3865_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(U_15430,U_15431))),hAPP(hAPP(c_List_Ozip(U_15430,U_15431),U_15432),U_15433)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15430)),U_15432)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15431)),U_15433)),
    inference(clausify,[status(thm)],[f_3865_2]) ).

fof(f_3866_1,plain,
    ! [V_ys,V_y,V_xs,V_x,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y),V_ys)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x),V_y)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)),
    inference(fof_nnf,[status(thm)],[fact_zip__Cons__Cons]) ).

fof(f_3866_2,plain,
    ! [U_15439,U_15438,U_15437,U_15436,U_15435,U_15434] : hAPP(hAPP(c_List_Ozip(U_15434,U_15435),hAPP(hAPP(c_List_Olist_OCons(U_15434),U_15436),U_15437)),hAPP(hAPP(c_List_Olist_OCons(U_15435),U_15438),U_15439)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(U_15434,U_15435)),hAPP(hAPP(c_Product__Type_OPair(U_15434,U_15435),U_15436),U_15438)),hAPP(hAPP(c_List_Ozip(U_15434,U_15435),U_15437),U_15439)),
    inference(variable_rename,[status(thm)],[f_3866_1]) ).

cnf(f_3866_3,plain,
    hAPP(hAPP(c_List_Ozip(U_15434,U_15435),hAPP(hAPP(c_List_Olist_OCons(U_15434),U_15436),U_15437)),hAPP(hAPP(c_List_Olist_OCons(U_15435),U_15438),U_15439)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(U_15434,U_15435)),hAPP(hAPP(c_Product__Type_OPair(U_15434,U_15435),U_15436),U_15438)),hAPP(hAPP(c_List_Ozip(U_15434,U_15435),U_15437),U_15439)),
    inference(clausify,[status(thm)],[f_3866_2]) ).

fof(f_3867_1,plain,
    ! [T_b,V_ys_2,V_xs_2] :
      ( ( V_xs_2 = V_ys_2
        | ? [B_x] :
            ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),c_fequal),B_x))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),hAPP(c_List_Oset(tc_prod(T_b,T_b)),hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_ys_2)))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) )
      & ( ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),c_fequal),B_x))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),hAPP(c_List_Oset(tc_prod(T_b,T_b)),hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_ys_2)))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) )
        | V_xs_2 != V_ys_2 ) ),
    inference(fof_nnf,[status(thm)],[fact_list__eq__iff__zip__eq]) ).

fof(f_3867_2,plain,
    ! [U_15444,U_15443,U_15442] :
      ( ( U_15442 = U_15443
        | ? [U_15441] :
            ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_15444,U_15444,tc_HOL_Obool),c_fequal),U_15441))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15444,U_15444)),U_15441),hAPP(c_List_Oset(tc_prod(U_15444,U_15444)),hAPP(hAPP(c_List_Ozip(U_15444,U_15444),U_15442),U_15443)))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15444)),U_15442) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15444)),U_15443) )
      & ( ( ! [U_15440] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_15444,U_15444,tc_HOL_Obool),c_fequal),U_15440))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15444,U_15444)),U_15440),hAPP(c_List_Oset(tc_prod(U_15444,U_15444)),hAPP(hAPP(c_List_Ozip(U_15444,U_15444),U_15442),U_15443)))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15444)),U_15442) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15444)),U_15443) )
        | U_15442 != U_15443 ) ),
    inference(variable_rename,[status(thm)],[f_3867_1]) ).

fof(f_3867_3,plain,
    ( ! [U_15450,U_15448,U_15446] :
        ( U_15446 = U_15448
        | ? [U_15441] :
            ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_15450,U_15450,tc_HOL_Obool),c_fequal),U_15441))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15450,U_15450)),U_15441),hAPP(c_List_Oset(tc_prod(U_15450,U_15450)),hAPP(hAPP(c_List_Ozip(U_15450,U_15450),U_15446),U_15448)))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15450)),U_15446) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15450)),U_15448) )
    & ! [U_15449,U_15447,U_15445] :
        ( ( ! [U_15440] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_15449,U_15449,tc_HOL_Obool),c_fequal),U_15440))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15449,U_15449)),U_15440),hAPP(c_List_Oset(tc_prod(U_15449,U_15449)),hAPP(hAPP(c_List_Ozip(U_15449,U_15449),U_15445),U_15447)))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15449)),U_15445) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15449)),U_15447) )
        | U_15445 != U_15447 ) ),
    inference(miniscope,[status(thm)],[f_3867_2]) ).

fof(f_3867_4,plain,
    ( ! [U_15450,U_15448,U_15446] :
        ( U_15446 = U_15448
        | ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_15450,U_15450,tc_HOL_Obool),c_fequal),sK411(U_15450,U_15448,U_15446)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15450,U_15450)),sK411(U_15450,U_15448,U_15446)),hAPP(c_List_Oset(tc_prod(U_15450,U_15450)),hAPP(hAPP(c_List_Ozip(U_15450,U_15450),U_15446),U_15448)))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15450)),U_15446) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15450)),U_15448) )
    & ! [U_15449,U_15447,U_15445] :
        ( ( ! [U_15440] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_15449,U_15449,tc_HOL_Obool),c_fequal),U_15440))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15449,U_15449)),U_15440),hAPP(c_List_Oset(tc_prod(U_15449,U_15449)),hAPP(hAPP(c_List_Ozip(U_15449,U_15449),U_15445),U_15447)))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15449)),U_15445) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15449)),U_15447) )
        | U_15445 != U_15447 ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK411]),skolemize(U_15441,sK411(U_15450,U_15448,U_15446))],[f_3867_3]) ).

cnf(f_3867_5,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15449)),U_15445) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15449)),U_15447)
    | U_15445 != U_15447 ),
    inference(clausify,[status(thm)],[f_3867_4]) ).

cnf(f_3867_6,plain,
    ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_15449,U_15449,tc_HOL_Obool),c_fequal),U_15440))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15449,U_15449)),U_15440),hAPP(c_List_Oset(tc_prod(U_15449,U_15449)),hAPP(hAPP(c_List_Ozip(U_15449,U_15449),U_15445),U_15447))))
    | U_15445 != U_15447 ),
    inference(clausify,[status(thm)],[f_3867_4]) ).

cnf(f_3867_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15450,U_15450)),sK411(U_15450,U_15448,U_15446)),hAPP(c_List_Oset(tc_prod(U_15450,U_15450)),hAPP(hAPP(c_List_Ozip(U_15450,U_15450),U_15446),U_15448))))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15450)),U_15446) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15450)),U_15448)
    | U_15446 = U_15448 ),
    inference(clausify,[status(thm)],[f_3867_4]) ).

cnf(f_3867_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_15450,U_15450,tc_HOL_Obool),c_fequal),sK411(U_15450,U_15448,U_15446)))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15450)),U_15446) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15450)),U_15448)
    | U_15446 = U_15448 ),
    inference(clausify,[status(thm)],[f_3867_4]) ).

fof(f_3868_1,plain,
    ! [V_xs_2,V_b_2,V_a_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),hAPP(c_List_Oset(tc_prod(T_b,T_b)),hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_xs_2))))
        | V_a_2 != V_b_2
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2))) )
      & ( ( V_a_2 = V_b_2
          & hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),hAPP(c_List_Oset(tc_prod(T_b,T_b)),hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_xs_2)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_zip__same]) ).

fof(f_3868_2,plain,
    ! [U_15454,U_15453,U_15452,U_15451] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15451,U_15451)),hAPP(hAPP(c_Product__Type_OPair(U_15451,U_15451),U_15452),U_15453)),hAPP(c_List_Oset(tc_prod(U_15451,U_15451)),hAPP(hAPP(c_List_Ozip(U_15451,U_15451),U_15454),U_15454))))
        | U_15452 != U_15453
        | ~ hBOOL(hAPP(hAPP(c_member(U_15451),U_15452),hAPP(c_List_Oset(U_15451),U_15454))) )
      & ( ( U_15452 = U_15453
          & hBOOL(hAPP(hAPP(c_member(U_15451),U_15452),hAPP(c_List_Oset(U_15451),U_15454))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15451,U_15451)),hAPP(hAPP(c_Product__Type_OPair(U_15451,U_15451),U_15452),U_15453)),hAPP(c_List_Oset(tc_prod(U_15451,U_15451)),hAPP(hAPP(c_List_Ozip(U_15451,U_15451),U_15454),U_15454)))) ) ),
    inference(variable_rename,[status(thm)],[f_3868_1]) ).

fof(f_3868_3,plain,
    ( ! [U_15462,U_15460,U_15458,U_15456] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15456,U_15456)),hAPP(hAPP(c_Product__Type_OPair(U_15456,U_15456),U_15458),U_15460)),hAPP(c_List_Oset(tc_prod(U_15456,U_15456)),hAPP(hAPP(c_List_Ozip(U_15456,U_15456),U_15462),U_15462))))
        | U_15458 != U_15460
        | ~ hBOOL(hAPP(hAPP(c_member(U_15456),U_15458),hAPP(c_List_Oset(U_15456),U_15462))) )
    & ! [U_15461,U_15459,U_15457,U_15455] :
        ( ( U_15457 = U_15459
          & hBOOL(hAPP(hAPP(c_member(U_15455),U_15457),hAPP(c_List_Oset(U_15455),U_15461))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15455,U_15455)),hAPP(hAPP(c_Product__Type_OPair(U_15455,U_15455),U_15457),U_15459)),hAPP(c_List_Oset(tc_prod(U_15455,U_15455)),hAPP(hAPP(c_List_Ozip(U_15455,U_15455),U_15461),U_15461)))) ) ),
    inference(miniscope,[status(thm)],[f_3868_2]) ).

cnf(f_3868_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15455),U_15457),hAPP(c_List_Oset(U_15455),U_15461)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15455,U_15455)),hAPP(hAPP(c_Product__Type_OPair(U_15455,U_15455),U_15457),U_15459)),hAPP(c_List_Oset(tc_prod(U_15455,U_15455)),hAPP(hAPP(c_List_Ozip(U_15455,U_15455),U_15461),U_15461)))) ),
    inference(clausify,[status(thm)],[f_3868_3]) ).

cnf(f_3868_5,plain,
    ( U_15457 = U_15459
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15455,U_15455)),hAPP(hAPP(c_Product__Type_OPair(U_15455,U_15455),U_15457),U_15459)),hAPP(c_List_Oset(tc_prod(U_15455,U_15455)),hAPP(hAPP(c_List_Ozip(U_15455,U_15455),U_15461),U_15461)))) ),
    inference(clausify,[status(thm)],[f_3868_3]) ).

cnf(f_3868_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15456,U_15456)),hAPP(hAPP(c_Product__Type_OPair(U_15456,U_15456),U_15458),U_15460)),hAPP(c_List_Oset(tc_prod(U_15456,U_15456)),hAPP(hAPP(c_List_Ozip(U_15456,U_15456),U_15462),U_15462))))
    | U_15458 != U_15460
    | ~ hBOOL(hAPP(hAPP(c_member(U_15456),U_15458),hAPP(c_List_Oset(U_15456),U_15462))) ),
    inference(clausify,[status(thm)],[f_3868_3]) ).

fof(f_3869_1,plain,
    ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_set__zip__leftD]) ).

fof(f_3869_2,plain,
    ! [U_15468,U_15467,U_15466,U_15465,U_15464,U_15463] :
      ( hBOOL(hAPP(hAPP(c_member(U_15463),U_15465),hAPP(c_List_Oset(U_15463),U_15467)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15463,U_15464)),hAPP(hAPP(c_Product__Type_OPair(U_15463,U_15464),U_15465),U_15466)),hAPP(c_List_Oset(tc_prod(U_15463,U_15464)),hAPP(hAPP(c_List_Ozip(U_15463,U_15464),U_15467),U_15468)))) ),
    inference(variable_rename,[status(thm)],[f_3869_1]) ).

cnf(f_3869_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15463),U_15465),hAPP(c_List_Oset(U_15463),U_15467)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15463,U_15464)),hAPP(hAPP(c_Product__Type_OPair(U_15463,U_15464),U_15465),U_15466)),hAPP(c_List_Oset(tc_prod(U_15463,U_15464)),hAPP(hAPP(c_List_Ozip(U_15463,U_15464),U_15467),U_15468)))) ),
    inference(clausify,[status(thm)],[f_3869_2]) ).

fof(f_3870_1,plain,
    ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_ys_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_set__zip__rightD]) ).

fof(f_3870_2,plain,
    ! [U_15474,U_15473,U_15472,U_15471,U_15470,U_15469] :
      ( hBOOL(hAPP(hAPP(c_member(U_15470),U_15472),hAPP(c_List_Oset(U_15470),U_15474)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15469,U_15470)),hAPP(hAPP(c_Product__Type_OPair(U_15469,U_15470),U_15471),U_15472)),hAPP(c_List_Oset(tc_prod(U_15469,U_15470)),hAPP(hAPP(c_List_Ozip(U_15469,U_15470),U_15473),U_15474)))) ),
    inference(variable_rename,[status(thm)],[f_3870_1]) ).

fof(f_3870_3,plain,
    ! [U_15474,U_15473,U_15472,U_15471,U_15470] :
      ( ! [U_15469] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15469,U_15470)),hAPP(hAPP(c_Product__Type_OPair(U_15469,U_15470),U_15471),U_15472)),hAPP(c_List_Oset(tc_prod(U_15469,U_15470)),hAPP(hAPP(c_List_Ozip(U_15469,U_15470),U_15473),U_15474))))
      | hBOOL(hAPP(hAPP(c_member(U_15470),U_15472),hAPP(c_List_Oset(U_15470),U_15474))) ),
    inference(miniscope,[status(thm)],[f_3870_2]) ).

cnf(f_3870_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15469,U_15470)),hAPP(hAPP(c_Product__Type_OPair(U_15469,U_15470),U_15471),U_15472)),hAPP(c_List_Oset(tc_prod(U_15469,U_15470)),hAPP(hAPP(c_List_Ozip(U_15469,U_15470),U_15473),U_15474))))
    | hBOOL(hAPP(hAPP(c_member(U_15470),U_15472),hAPP(c_List_Oset(U_15470),U_15474))) ),
    inference(clausify,[status(thm)],[f_3870_3]) ).

fof(f_3871_1,plain,
    ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_ys_2)))
        & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_in__set__zipE]) ).

fof(f_3871_2,plain,
    ! [U_15480,U_15479,U_15478,U_15477,U_15476,U_15475] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_15476),U_15478),hAPP(c_List_Oset(U_15476),U_15480)))
        & hBOOL(hAPP(hAPP(c_member(U_15475),U_15477),hAPP(c_List_Oset(U_15475),U_15479))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15475,U_15476)),hAPP(hAPP(c_Product__Type_OPair(U_15475,U_15476),U_15477),U_15478)),hAPP(c_List_Oset(tc_prod(U_15475,U_15476)),hAPP(hAPP(c_List_Ozip(U_15475,U_15476),U_15479),U_15480)))) ),
    inference(variable_rename,[status(thm)],[f_3871_1]) ).

cnf(f_3871_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15475),U_15477),hAPP(c_List_Oset(U_15475),U_15479)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15475,U_15476)),hAPP(hAPP(c_Product__Type_OPair(U_15475,U_15476),U_15477),U_15478)),hAPP(c_List_Oset(tc_prod(U_15475,U_15476)),hAPP(hAPP(c_List_Ozip(U_15475,U_15476),U_15479),U_15480)))) ),
    inference(clausify,[status(thm)],[f_3871_2]) ).

cnf(f_3871_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15476),U_15478),hAPP(c_List_Oset(U_15476),U_15480)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15475,U_15476)),hAPP(hAPP(c_Product__Type_OPair(U_15475,U_15476),U_15477),U_15478)),hAPP(c_List_Oset(tc_prod(U_15475,U_15476)),hAPP(hAPP(c_List_Ozip(U_15475,U_15476),U_15479),U_15480)))) ),
    inference(clausify,[status(thm)],[f_3871_2]) ).

fof(f_3872_1,plain,
    ! [V_ys,T_b,V_xs,T_a,V_i] :
      ( hAPP(hAPP(c_List_Onth(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)),V_i) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)),hAPP(hAPP(c_List_Onth(T_b),V_ys),V_i))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) ),
    inference(fof_nnf,[status(thm)],[fact_nth__zip]) ).

fof(f_3872_2,plain,
    ! [U_15485,U_15484,U_15483,U_15482,U_15481] :
      ( hAPP(hAPP(c_List_Onth(tc_prod(U_15482,U_15484)),hAPP(hAPP(c_List_Ozip(U_15482,U_15484),U_15483),U_15485)),U_15481) = hAPP(hAPP(c_Product__Type_OPair(U_15482,U_15484),hAPP(hAPP(c_List_Onth(U_15482),U_15483),U_15481)),hAPP(hAPP(c_List_Onth(U_15484),U_15485),U_15481))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15481),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15484)),U_15485)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15481),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15482)),U_15483))) ),
    inference(variable_rename,[status(thm)],[f_3872_1]) ).

cnf(f_3872_3,plain,
    ( hAPP(hAPP(c_List_Onth(tc_prod(U_15482,U_15484)),hAPP(hAPP(c_List_Ozip(U_15482,U_15484),U_15483),U_15485)),U_15481) = hAPP(hAPP(c_Product__Type_OPair(U_15482,U_15484),hAPP(hAPP(c_List_Onth(U_15482),U_15483),U_15481)),hAPP(hAPP(c_List_Onth(U_15484),U_15485),U_15481))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15481),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15484)),U_15485)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15481),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15482)),U_15483))) ),
    inference(clausify,[status(thm)],[f_3872_2]) ).

fof(f_3873_1,plain,
    ! [V_j_2,V_i_2] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,V_i_2,V_j_2) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_j_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    inference(fof_nnf,[status(thm)],[fact_greaterThanLessThan__upto]) ).

fof(f_3873_2,plain,
    ! [U_15487,U_15486] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_15486,U_15487) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_15486),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_15487),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    inference(variable_rename,[status(thm)],[f_3873_1]) ).

cnf(f_3873_3,plain,
    c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_15486,U_15487) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_15486),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_15487),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    inference(clausify,[status(thm)],[f_3873_2]) ).

fof(f_3874_1,plain,
    ! [V_xs_2,T_b] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(T_b),V_xs_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(c_List_Onth(T_b),V_xs_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_listsum__setsum__nth]) ).

fof(f_3874_2,plain,
    ! [U_15489,U_15488] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_15488),U_15489) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_15488),hAPP(c_List_Onth(U_15488),U_15489)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15488)),U_15489)))
      | ~ class_Groups_Ocomm__monoid__add(U_15488) ),
    inference(variable_rename,[status(thm)],[f_3874_1]) ).

cnf(f_3874_3,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_15488),U_15489) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_15488),hAPP(c_List_Onth(U_15488),U_15489)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15488)),U_15489)))
    | ~ class_Groups_Ocomm__monoid__add(U_15488) ),
    inference(clausify,[status(thm)],[f_3874_2]) ).

fof(f_3875_1,plain,
    ! [V_ns_2] :
      ( ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ? [B_x] :
            ( B_x != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2))) ) )
      & ( ! [B_x] :
            ( B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2))) )
        | hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(fof_nnf,[status(thm)],[fact_listsum__eq__0__nat__iff__nat]) ).

fof(f_3875_2,plain,
    ! [U_15492] :
      ( ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_15492) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ? [U_15491] :
            ( U_15491 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_15491),hAPP(c_List_Oset(tc_Nat_Onat),U_15492))) ) )
      & ( ! [U_15490] :
            ( U_15490 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_15490),hAPP(c_List_Oset(tc_Nat_Onat),U_15492))) )
        | hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_15492) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_3875_1]) ).

fof(f_3875_3,plain,
    ( ! [U_15494] :
        ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_15494) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ? [U_15491] :
            ( U_15491 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_15491),hAPP(c_List_Oset(tc_Nat_Onat),U_15494))) ) )
    & ! [U_15493] :
        ( ! [U_15490] :
            ( U_15490 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_15490),hAPP(c_List_Oset(tc_Nat_Onat),U_15493))) )
        | hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_15493) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_3875_2]) ).

fof(f_3875_4,plain,
    ( ! [U_15494] :
        ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_15494) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ( sK412(U_15494) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK412(U_15494)),hAPP(c_List_Oset(tc_Nat_Onat),U_15494))) ) )
    & ! [U_15493] :
        ( ! [U_15490] :
            ( U_15490 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_15490),hAPP(c_List_Oset(tc_Nat_Onat),U_15493))) )
        | hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_15493) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK412]),skolemize(U_15491,sK412(U_15494))],[f_3875_3]) ).

cnf(f_3875_5,plain,
    ( U_15490 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_15490),hAPP(c_List_Oset(tc_Nat_Onat),U_15493)))
    | hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_15493) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_3875_4]) ).

cnf(f_3875_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK412(U_15494)),hAPP(c_List_Oset(tc_Nat_Onat),U_15494)))
    | hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_15494) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_3875_4]) ).

cnf(f_3875_7,plain,
    ( sK412(U_15494) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_15494) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_3875_4]) ).

fof(f_3876_1,plain,
    ! [V_j_2,V_i_2] : hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_i_2,V_j_2)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2),
    inference(fof_nnf,[status(thm)],[fact_set__upto]) ).

fof(f_3876_2,plain,
    ! [U_15496,U_15495] : hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_15495,U_15496)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_15495,U_15496),
    inference(variable_rename,[status(thm)],[f_3876_1]) ).

cnf(f_3876_3,plain,
    hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_15495,U_15496)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_15495,U_15496),
    inference(clausify,[status(thm)],[f_3876_2]) ).

fof(f_3877_1,plain,
    ! [V_j_2,V_i_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_i_2,V_j_2)),
    inference(fof_nnf,[status(thm)],[fact_atLeastAtMost__upto]) ).

fof(f_3877_2,plain,
    ! [U_15498,U_15497] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_15497,U_15498) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_15497,U_15498)),
    inference(variable_rename,[status(thm)],[f_3877_1]) ).

cnf(f_3877_3,plain,
    c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_15497,U_15498) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_15497,U_15498)),
    inference(clausify,[status(thm)],[f_3877_2]) ).

fof(f_3878_1,plain,
    ! [V_ns,V_k] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),V_ns),V_k)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),V_ns))) ),
    inference(fof_nnf,[status(thm)],[fact_elem__le__listsum__nat]) ).

fof(f_3878_2,plain,
    ! [U_15500,U_15499] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),U_15500),U_15499)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_15500)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15499),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),U_15500))) ),
    inference(variable_rename,[status(thm)],[f_3878_1]) ).

cnf(f_3878_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),U_15500),U_15499)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_15500)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15499),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),U_15500))) ),
    inference(clausify,[status(thm)],[f_3878_2]) ).

fof(f_3879_1,plain,
    ! [V_xs,V_x,T_a] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs))
      | ~ class_Groups_Omonoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_listsum__simps_I2_J]) ).

fof(f_3879_2,plain,
    ! [U_15503,U_15502,U_15501] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_15501),hAPP(hAPP(c_List_Olist_OCons(U_15501),U_15502),U_15503)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_15501),U_15502),hAPP(c_List_Omonoid__add__class_Olistsum(U_15501),U_15503))
      | ~ class_Groups_Omonoid__add(U_15501) ),
    inference(variable_rename,[status(thm)],[f_3879_1]) ).

cnf(f_3879_3,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_15501),hAPP(hAPP(c_List_Olist_OCons(U_15501),U_15502),U_15503)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_15501),U_15502),hAPP(c_List_Omonoid__add__class_Olistsum(U_15501),U_15503))
    | ~ class_Groups_Omonoid__add(U_15501) ),
    inference(clausify,[status(thm)],[f_3879_2]) ).

fof(f_3880_1,plain,
    ! [V_j_2,V_i_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_i_2),V_j_2) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_i_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_j_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__upto]) ).

fof(f_3880_2,plain,
    ! [U_15505,U_15504] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_15504),U_15505) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_15504,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_15505),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    inference(variable_rename,[status(thm)],[f_3880_1]) ).

cnf(f_3880_3,plain,
    hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_15504),U_15505) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_15504,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_15505),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    inference(clausify,[status(thm)],[f_3880_2]) ).

fof(f_3881_1,plain,
    ! [V_j_2,V_i_2] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,V_i_2,V_j_2) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_j_2)),
    inference(fof_nnf,[status(thm)],[fact_greaterThanAtMost__upto]) ).

fof(f_3881_2,plain,
    ! [U_15507,U_15506] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_15506,U_15507) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_15506),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_15507)),
    inference(variable_rename,[status(thm)],[f_3881_1]) ).

cnf(f_3881_3,plain,
    c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_15506,U_15507) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_15506),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_15507)),
    inference(clausify,[status(thm)],[f_3881_2]) ).

fof(f_3882_1,plain,
    ! [V_l_2] :
      ( ( c_List_Onat__list(V_l_2)
        | ~ c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),V_l_2)) )
      & ( c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),V_l_2))
        | ~ c_List_Onat__list(V_l_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__list__def]) ).

fof(f_3882_2,plain,
    ! [U_15508] :
      ( ( c_List_Onat__list(U_15508)
        | ~ c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),U_15508)) )
      & ( c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),U_15508))
        | ~ c_List_Onat__list(U_15508) ) ),
    inference(variable_rename,[status(thm)],[f_3882_1]) ).

fof(f_3882_3,plain,
    ( ! [U_15510] :
        ( c_List_Onat__list(U_15510)
        | ~ c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),U_15510)) )
    & ! [U_15509] :
        ( c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),U_15509))
        | ~ c_List_Onat__list(U_15509) ) ),
    inference(miniscope,[status(thm)],[f_3882_2]) ).

cnf(f_3882_4,plain,
    ( c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),U_15509))
    | ~ c_List_Onat__list(U_15509) ),
    inference(clausify,[status(thm)],[f_3882_3]) ).

cnf(f_3882_5,plain,
    ( c_List_Onat__list(U_15510)
    | ~ c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),U_15510)) ),
    inference(clausify,[status(thm)],[f_3882_3]) ).

fof(f_3883_1,plain,
    ! [V_g_2,V_f_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(T_b,V_f_2,V_xs_2)),c_List_Olist_Olist__size(T_b,V_g_2,V_xs_2)))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x)))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__size__pointwise]) ).

fof(f_3883_2,plain,
    ! [U_15515,U_15514,U_15513,U_15512] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(U_15512,U_15514,U_15513)),c_List_Olist_Olist__size(U_15512,U_15515,U_15513)))
      | ? [U_15511] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_15514,U_15511)),hAPP(U_15515,U_15511)))
          & hBOOL(hAPP(hAPP(c_member(U_15512),U_15511),hAPP(c_List_Oset(U_15512),U_15513))) ) ),
    inference(variable_rename,[status(thm)],[f_3883_1]) ).

fof(f_3883_3,plain,
    ! [U_15515,U_15514,U_15513,U_15512] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(U_15512,U_15514,U_15513)),c_List_Olist_Olist__size(U_15512,U_15515,U_15513)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_15514,sK413(U_15515,U_15514,U_15513,U_15512))),hAPP(U_15515,sK413(U_15515,U_15514,U_15513,U_15512))))
        & hBOOL(hAPP(hAPP(c_member(U_15512),sK413(U_15515,U_15514,U_15513,U_15512)),hAPP(c_List_Oset(U_15512),U_15513))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK413]),skolemize(U_15511,sK413(U_15515,U_15514,U_15513,U_15512))],[f_3883_2]) ).

cnf(f_3883_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15512),sK413(U_15515,U_15514,U_15513,U_15512)),hAPP(c_List_Oset(U_15512),U_15513)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(U_15512,U_15514,U_15513)),c_List_Olist_Olist__size(U_15512,U_15515,U_15513))) ),
    inference(clausify,[status(thm)],[f_3883_3]) ).

cnf(f_3883_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_15514,sK413(U_15515,U_15514,U_15513,U_15512))),hAPP(U_15515,sK413(U_15515,U_15514,U_15513,U_15512))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(U_15512,U_15514,U_15513)),c_List_Olist_Olist__size(U_15512,U_15515,U_15513))) ),
    inference(clausify,[status(thm)],[f_3883_3]) ).

fof(f_3884_1,plain,
    ! [V_n,V_ns,V_k] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat,V_ns),V_k),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns)),V_n)),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),V_ns),V_k))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),V_ns))) ),
    inference(fof_nnf,[status(thm)],[fact_listsum__update__nat]) ).

fof(f_3884_2,plain,
    ! [U_15518,U_15517,U_15516] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat,U_15517),U_15516),U_15518)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_15517)),U_15518)),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),U_15517),U_15516))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15516),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),U_15517))) ),
    inference(variable_rename,[status(thm)],[f_3884_1]) ).

cnf(f_3884_3,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat,U_15517),U_15516),U_15518)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_15517)),U_15518)),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),U_15517),U_15516))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15516),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),U_15517))) ),
    inference(clausify,[status(thm)],[f_3884_2]) ).

fof(f_3885_1,plain,
    ! [V_xs,T_a,V_n] :
      ( c_List_Obutlast(T_a,hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) ),
    inference(fof_nnf,[status(thm)],[fact_butlast__take]) ).

fof(f_3885_2,plain,
    ! [U_15521,U_15520,U_15519] :
      ( c_List_Obutlast(U_15520,hAPP(hAPP(c_List_Otake(U_15520),U_15519),U_15521)) = hAPP(hAPP(c_List_Otake(U_15520),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_15519),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_15521)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_15519),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15520)),U_15521))) ),
    inference(variable_rename,[status(thm)],[f_3885_1]) ).

cnf(f_3885_3,plain,
    ( c_List_Obutlast(U_15520,hAPP(hAPP(c_List_Otake(U_15520),U_15519),U_15521)) = hAPP(hAPP(c_List_Otake(U_15520),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_15519),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_15521)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_15519),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15520)),U_15521))) ),
    inference(clausify,[status(thm)],[f_3885_2]) ).

fof(f_3886_1,plain,
    ! [V_x,V_i,V_xs,T_a] :
      ( hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x) = V_xs
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_i)) ),
    inference(fof_nnf,[status(thm)],[fact_list__update__beyond]) ).

fof(f_3886_2,plain,
    ! [U_15525,U_15524,U_15523,U_15522] :
      ( hAPP(hAPP(c_List_Olist__update(U_15522,U_15523),U_15524),U_15525) = U_15523
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15522)),U_15523)),U_15524)) ),
    inference(variable_rename,[status(thm)],[f_3886_1]) ).

cnf(f_3886_3,plain,
    ( hAPP(hAPP(c_List_Olist__update(U_15522,U_15523),U_15524),U_15525) = U_15523
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15522)),U_15523)),U_15524)) ),
    inference(clausify,[status(thm)],[f_3886_2]) ).

fof(f_3887_1,plain,
    ! [V_i,V_xs,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)) = V_xs,
    inference(fof_nnf,[status(thm)],[fact_list__update__id]) ).

fof(f_3887_2,plain,
    ! [U_15528,U_15527,U_15526] : hAPP(hAPP(c_List_Olist__update(U_15526,U_15527),U_15528),hAPP(hAPP(c_List_Onth(U_15526),U_15527),U_15528)) = U_15527,
    inference(variable_rename,[status(thm)],[f_3887_1]) ).

cnf(f_3887_3,plain,
    hAPP(hAPP(c_List_Olist__update(U_15526,U_15527),U_15528),hAPP(hAPP(c_List_Onth(U_15526),U_15527),U_15528)) = U_15527,
    inference(clausify,[status(thm)],[f_3887_2]) ).

fof(f_3888_1,plain,
    ! [V_x,V_xs,T_a,V_j,V_i] :
      ( hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_j) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_j)
      | V_i = V_j ),
    inference(fof_nnf,[status(thm)],[fact_nth__list__update__neq]) ).

fof(f_3888_2,plain,
    ! [U_15533,U_15532,U_15531,U_15530,U_15529] :
      ( hAPP(hAPP(c_List_Onth(U_15531),hAPP(hAPP(c_List_Olist__update(U_15531,U_15532),U_15529),U_15533)),U_15530) = hAPP(hAPP(c_List_Onth(U_15531),U_15532),U_15530)
      | U_15529 = U_15530 ),
    inference(variable_rename,[status(thm)],[f_3888_1]) ).

cnf(f_3888_3,plain,
    ( hAPP(hAPP(c_List_Onth(U_15531),hAPP(hAPP(c_List_Olist__update(U_15531,U_15532),U_15529),U_15533)),U_15530) = hAPP(hAPP(c_List_Onth(U_15531),U_15532),U_15530)
    | U_15529 = U_15530 ),
    inference(clausify,[status(thm)],[f_3888_2]) ).

fof(f_3889_1,plain,
    ! [V_x,V_i,V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs),
    inference(fof_nnf,[status(thm)],[fact_length__list__update]) ).

fof(f_3889_2,plain,
    ! [U_15537,U_15536,U_15535,U_15534] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15534)),hAPP(hAPP(c_List_Olist__update(U_15534,U_15535),U_15536),U_15537)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15534)),U_15535),
    inference(variable_rename,[status(thm)],[f_3889_1]) ).

cnf(f_3889_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15534)),hAPP(hAPP(c_List_Olist__update(U_15534,U_15535),U_15536),U_15537)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15534)),U_15535),
    inference(clausify,[status(thm)],[f_3889_2]) ).

fof(f_3890_1,plain,
    ! [V_x,V_xs,T_a,V_k] :
      ( ( c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = hAPP(hAPP(c_List_Olist__update(T_a,c_List_Obutlast(T_a,V_xs)),V_k),V_x)
        | V_k = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
      & ( c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = c_List_Obutlast(T_a,V_xs)
        | V_k != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
    inference(fof_nnf,[status(thm)],[fact_butlast__list__update]) ).

fof(f_3890_2,plain,
    ! [U_15541,U_15540,U_15539,U_15538] :
      ( ( c_List_Obutlast(U_15539,hAPP(hAPP(c_List_Olist__update(U_15539,U_15540),U_15538),U_15541)) = hAPP(hAPP(c_List_Olist__update(U_15539,c_List_Obutlast(U_15539,U_15540)),U_15538),U_15541)
        | U_15538 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15539)),U_15540)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
      & ( c_List_Obutlast(U_15539,hAPP(hAPP(c_List_Olist__update(U_15539,U_15540),U_15538),U_15541)) = c_List_Obutlast(U_15539,U_15540)
        | U_15538 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15539)),U_15540)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
    inference(variable_rename,[status(thm)],[f_3890_1]) ).

fof(f_3890_3,plain,
    ( ! [U_15549,U_15547,U_15545,U_15543] :
        ( c_List_Obutlast(U_15545,hAPP(hAPP(c_List_Olist__update(U_15545,U_15547),U_15543),U_15549)) = hAPP(hAPP(c_List_Olist__update(U_15545,c_List_Obutlast(U_15545,U_15547)),U_15543),U_15549)
        | U_15543 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15545)),U_15547)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
    & ! [U_15548,U_15546,U_15544,U_15542] :
        ( c_List_Obutlast(U_15544,hAPP(hAPP(c_List_Olist__update(U_15544,U_15546),U_15542),U_15548)) = c_List_Obutlast(U_15544,U_15546)
        | U_15542 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15544)),U_15546)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
    inference(miniscope,[status(thm)],[f_3890_2]) ).

cnf(f_3890_4,plain,
    ( c_List_Obutlast(U_15544,hAPP(hAPP(c_List_Olist__update(U_15544,U_15546),U_15542),U_15548)) = c_List_Obutlast(U_15544,U_15546)
    | U_15542 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15544)),U_15546)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_3890_3]) ).

cnf(f_3890_5,plain,
    ( c_List_Obutlast(U_15545,hAPP(hAPP(c_List_Olist__update(U_15545,U_15547),U_15543),U_15549)) = hAPP(hAPP(c_List_Olist__update(U_15545,c_List_Obutlast(U_15545,U_15547)),U_15543),U_15549)
    | U_15543 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15545)),U_15547)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_3890_3]) ).

fof(f_3891_1,plain,
    ! [V_y,V_ys,V_x,V_i,V_xs,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),hAPP(hAPP(c_List_Olist__update(T_b,V_ys),V_i),V_y)) = hAPP(hAPP(c_List_Olist__update(tc_prod(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)),V_i),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x),V_y)),
    inference(fof_nnf,[status(thm)],[fact_zip__update]) ).

fof(f_3891_2,plain,
    ! [U_15556,U_15555,U_15554,U_15553,U_15552,U_15551,U_15550] : hAPP(hAPP(c_List_Ozip(U_15550,U_15551),hAPP(hAPP(c_List_Olist__update(U_15550,U_15552),U_15553),U_15554)),hAPP(hAPP(c_List_Olist__update(U_15551,U_15555),U_15553),U_15556)) = hAPP(hAPP(c_List_Olist__update(tc_prod(U_15550,U_15551),hAPP(hAPP(c_List_Ozip(U_15550,U_15551),U_15552),U_15555)),U_15553),hAPP(hAPP(c_Product__Type_OPair(U_15550,U_15551),U_15554),U_15556)),
    inference(variable_rename,[status(thm)],[f_3891_1]) ).

cnf(f_3891_3,plain,
    hAPP(hAPP(c_List_Ozip(U_15550,U_15551),hAPP(hAPP(c_List_Olist__update(U_15550,U_15552),U_15553),U_15554)),hAPP(hAPP(c_List_Olist__update(U_15551,U_15555),U_15553),U_15556)) = hAPP(hAPP(c_List_Olist__update(tc_prod(U_15550,U_15551),hAPP(hAPP(c_List_Ozip(U_15550,U_15551),U_15552),U_15555)),U_15553),hAPP(hAPP(c_Product__Type_OPair(U_15550,U_15551),U_15554),U_15556)),
    inference(clausify,[status(thm)],[f_3891_2]) ).

fof(f_3892_1,plain,
    ! [V_xy,V_i,V_ys,V_xs,T_b,T_a] : hAPP(hAPP(c_List_Olist__update(tc_prod(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)),V_i),V_xy) = hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),hAPP(c_Product__Type_Ofst(T_a,T_b),V_xy))),hAPP(hAPP(c_List_Olist__update(T_b,V_ys),V_i),hAPP(c_Product__Type_Osnd(T_a,T_b),V_xy))),
    inference(fof_nnf,[status(thm)],[fact_update__zip]) ).

fof(f_3892_2,plain,
    ! [U_15562,U_15561,U_15560,U_15559,U_15558,U_15557] : hAPP(hAPP(c_List_Olist__update(tc_prod(U_15557,U_15558),hAPP(hAPP(c_List_Ozip(U_15557,U_15558),U_15559),U_15560)),U_15561),U_15562) = hAPP(hAPP(c_List_Ozip(U_15557,U_15558),hAPP(hAPP(c_List_Olist__update(U_15557,U_15559),U_15561),hAPP(c_Product__Type_Ofst(U_15557,U_15558),U_15562))),hAPP(hAPP(c_List_Olist__update(U_15558,U_15560),U_15561),hAPP(c_Product__Type_Osnd(U_15557,U_15558),U_15562))),
    inference(variable_rename,[status(thm)],[f_3892_1]) ).

cnf(f_3892_3,plain,
    hAPP(hAPP(c_List_Olist__update(tc_prod(U_15557,U_15558),hAPP(hAPP(c_List_Ozip(U_15557,U_15558),U_15559),U_15560)),U_15561),U_15562) = hAPP(hAPP(c_List_Ozip(U_15557,U_15558),hAPP(hAPP(c_List_Olist__update(U_15557,U_15559),U_15561),hAPP(c_Product__Type_Ofst(U_15557,U_15558),U_15562))),hAPP(hAPP(c_List_Olist__update(U_15558,U_15560),U_15561),hAPP(c_Product__Type_Osnd(U_15557,U_15558),U_15562))),
    inference(clausify,[status(thm)],[f_3892_2]) ).

fof(f_3893_1,plain,
    ! [V_x_H,V_x,V_xs,T_a,V_i_H,V_i] :
      ( hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_i_H),V_x_H) = hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i_H),V_x_H)),V_i),V_x)
      | V_i = V_i_H ),
    inference(fof_nnf,[status(thm)],[fact_list__update__swap]) ).

fof(f_3893_2,plain,
    ! [U_15568,U_15567,U_15566,U_15565,U_15564,U_15563] :
      ( hAPP(hAPP(c_List_Olist__update(U_15565,hAPP(hAPP(c_List_Olist__update(U_15565,U_15566),U_15563),U_15567)),U_15564),U_15568) = hAPP(hAPP(c_List_Olist__update(U_15565,hAPP(hAPP(c_List_Olist__update(U_15565,U_15566),U_15564),U_15568)),U_15563),U_15567)
      | U_15563 = U_15564 ),
    inference(variable_rename,[status(thm)],[f_3893_1]) ).

cnf(f_3893_3,plain,
    ( hAPP(hAPP(c_List_Olist__update(U_15565,hAPP(hAPP(c_List_Olist__update(U_15565,U_15566),U_15563),U_15567)),U_15564),U_15568) = hAPP(hAPP(c_List_Olist__update(U_15565,hAPP(hAPP(c_List_Olist__update(U_15565,U_15566),U_15564),U_15568)),U_15563),U_15567)
    | U_15563 = U_15564 ),
    inference(clausify,[status(thm)],[f_3893_2]) ).

fof(f_3894_1,plain,
    ! [V_y,V_x,V_i,V_xs,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_i),V_y) = hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_y),
    inference(fof_nnf,[status(thm)],[fact_list__update__overwrite]) ).

fof(f_3894_2,plain,
    ! [U_15573,U_15572,U_15571,U_15570,U_15569] : hAPP(hAPP(c_List_Olist__update(U_15569,hAPP(hAPP(c_List_Olist__update(U_15569,U_15570),U_15571),U_15572)),U_15571),U_15573) = hAPP(hAPP(c_List_Olist__update(U_15569,U_15570),U_15571),U_15573),
    inference(variable_rename,[status(thm)],[f_3894_1]) ).

cnf(f_3894_3,plain,
    hAPP(hAPP(c_List_Olist__update(U_15569,hAPP(hAPP(c_List_Olist__update(U_15569,U_15570),U_15571),U_15572)),U_15571),U_15573) = hAPP(hAPP(c_List_Olist__update(U_15569,U_15570),U_15571),U_15573),
    inference(clausify,[status(thm)],[f_3894_2]) ).

fof(f_3895_1,plain,
    ! [V_v_2,V_i_2,V_xs_2,V_x_2,T_b] : hAPP(hAPP(c_List_Olist__update(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_i_2),V_v_2) = c_Nat_Onat_Onat__case(tc_List_Olist(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_v_2),V_xs_2),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_Nat_Onat),hAPP(c_List_Olist_OCons(T_b),V_x_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,T_b,tc_List_Olist(T_b)),c_List_Olist__update(T_b,V_xs_2)),V_v_2)),V_i_2),
    inference(fof_nnf,[status(thm)],[fact_list__update_Osimps_I2_J]) ).

fof(f_3895_2,plain,
    ! [U_15578,U_15577,U_15576,U_15575,U_15574] : hAPP(hAPP(c_List_Olist__update(U_15574,hAPP(hAPP(c_List_Olist_OCons(U_15574),U_15575),U_15576)),U_15577),U_15578) = c_Nat_Onat_Onat__case(tc_List_Olist(U_15574),hAPP(hAPP(c_List_Olist_OCons(U_15574),U_15578),U_15576),hAPP(hAPP(c_COMBB(tc_List_Olist(U_15574),tc_List_Olist(U_15574),tc_Nat_Onat),hAPP(c_List_Olist_OCons(U_15574),U_15575)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,U_15574,tc_List_Olist(U_15574)),c_List_Olist__update(U_15574,U_15576)),U_15578)),U_15577),
    inference(variable_rename,[status(thm)],[f_3895_1]) ).

cnf(f_3895_3,plain,
    hAPP(hAPP(c_List_Olist__update(U_15574,hAPP(hAPP(c_List_Olist_OCons(U_15574),U_15575),U_15576)),U_15577),U_15578) = c_Nat_Onat_Onat__case(tc_List_Olist(U_15574),hAPP(hAPP(c_List_Olist_OCons(U_15574),U_15578),U_15576),hAPP(hAPP(c_COMBB(tc_List_Olist(U_15574),tc_List_Olist(U_15574),tc_Nat_Onat),hAPP(c_List_Olist_OCons(U_15574),U_15575)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,U_15574,tc_List_Olist(U_15574)),c_List_Olist__update(U_15574,U_15576)),U_15578)),U_15577),
    inference(clausify,[status(thm)],[f_3895_2]) ).

fof(f_3896_1,plain,
    ! [V_y,V_i,V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(c_Nat_OSuc,V_i)),V_y) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_y)),
    inference(fof_nnf,[status(thm)],[fact_list__update__code_I3_J]) ).

fof(f_3896_2,plain,
    ! [U_15583,U_15582,U_15581,U_15580,U_15579] : hAPP(hAPP(c_List_Olist__update(U_15579,hAPP(hAPP(c_List_Olist_OCons(U_15579),U_15580),U_15581)),hAPP(c_Nat_OSuc,U_15582)),U_15583) = hAPP(hAPP(c_List_Olist_OCons(U_15579),U_15580),hAPP(hAPP(c_List_Olist__update(U_15579,U_15581),U_15582),U_15583)),
    inference(variable_rename,[status(thm)],[f_3896_1]) ).

cnf(f_3896_3,plain,
    hAPP(hAPP(c_List_Olist__update(U_15579,hAPP(hAPP(c_List_Olist_OCons(U_15579),U_15580),U_15581)),hAPP(c_Nat_OSuc,U_15582)),U_15583) = hAPP(hAPP(c_List_Olist_OCons(U_15579),U_15580),hAPP(hAPP(c_List_Olist__update(U_15579,U_15581),U_15582),U_15583)),
    inference(clausify,[status(thm)],[f_3896_2]) ).

fof(f_3897_1,plain,
    ! [V_y,V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_y) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs),
    inference(fof_nnf,[status(thm)],[fact_list__update__code_I2_J]) ).

fof(f_3897_2,plain,
    ! [U_15587,U_15586,U_15585,U_15584] : hAPP(hAPP(c_List_Olist__update(U_15584,hAPP(hAPP(c_List_Olist_OCons(U_15584),U_15585),U_15586)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_15587) = hAPP(hAPP(c_List_Olist_OCons(U_15584),U_15587),U_15586),
    inference(variable_rename,[status(thm)],[f_3897_1]) ).

cnf(f_3897_3,plain,
    hAPP(hAPP(c_List_Olist__update(U_15584,hAPP(hAPP(c_List_Olist_OCons(U_15584),U_15585),U_15586)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_15587) = hAPP(hAPP(c_List_Olist_OCons(U_15584),U_15587),U_15586),
    inference(clausify,[status(thm)],[f_3897_2]) ).

fof(f_3898_1,plain,
    ! [V_xs_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_xs_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_in__set__butlastD]) ).

fof(f_3898_2,plain,
    ! [U_15590,U_15589,U_15588] :
      ( hBOOL(hAPP(hAPP(c_member(U_15588),U_15589),hAPP(c_List_Oset(U_15588),U_15590)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15588),U_15589),hAPP(c_List_Oset(U_15588),c_List_Obutlast(U_15588,U_15590)))) ),
    inference(variable_rename,[status(thm)],[f_3898_1]) ).

cnf(f_3898_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15588),U_15589),hAPP(c_List_Oset(U_15588),U_15590)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15588),U_15589),hAPP(c_List_Oset(U_15588),c_List_Obutlast(U_15588,U_15590)))) ),
    inference(clausify,[status(thm)],[f_3898_2]) ).

fof(f_3899_1,plain,
    ! [V_i_2,V_x_2,V_A_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2))),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_set__update__subsetI]) ).

fof(f_3899_2,plain,
    ! [U_15595,U_15594,U_15593,U_15592,U_15591] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15591,tc_HOL_Obool)),hAPP(c_List_Oset(U_15591),hAPP(hAPP(c_List_Olist__update(U_15591,U_15592),U_15595),U_15594))),U_15593))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15591),U_15594),U_15593))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15591,tc_HOL_Obool)),hAPP(c_List_Oset(U_15591),U_15592)),U_15593)) ),
    inference(variable_rename,[status(thm)],[f_3899_1]) ).

cnf(f_3899_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15591,tc_HOL_Obool)),hAPP(c_List_Oset(U_15591),hAPP(hAPP(c_List_Olist__update(U_15591,U_15592),U_15595),U_15594))),U_15593))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15591),U_15594),U_15593))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15591,tc_HOL_Obool)),hAPP(c_List_Oset(U_15591),U_15592)),U_15593)) ),
    inference(clausify,[status(thm)],[f_3899_2]) ).

fof(f_3900_1,plain,
    ! [V_x_2,V_i_2,V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2))),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))),
    inference(fof_nnf,[status(thm)],[fact_set__update__subset__insert]) ).

fof(f_3900_2,plain,
    ! [U_15599,U_15598,U_15597,U_15596] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15596,tc_HOL_Obool)),hAPP(c_List_Oset(U_15596),hAPP(hAPP(c_List_Olist__update(U_15596,U_15597),U_15598),U_15599))),hAPP(hAPP(c_Set_Oinsert(U_15596),U_15599),hAPP(c_List_Oset(U_15596),U_15597)))),
    inference(variable_rename,[status(thm)],[f_3900_1]) ).

cnf(f_3900_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15596,tc_HOL_Obool)),hAPP(c_List_Oset(U_15596),hAPP(hAPP(c_List_Olist__update(U_15596,U_15597),U_15598),U_15599))),hAPP(hAPP(c_Set_Oinsert(U_15596),U_15599),hAPP(c_List_Oset(U_15596),U_15597)))),
    inference(clausify,[status(thm)],[f_3900_2]) ).

fof(f_3901_1,plain,
    ! [V_x,V_j,V_xs,T_a,V_i] :
      ( ( ( hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_j) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_j)
          | V_i = V_j )
        & ( hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_j) = V_x
          | V_i != V_j ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) ),
    inference(fof_nnf,[status(thm)],[fact_nth__list__update]) ).

fof(f_3901_2,plain,
    ! [U_15604,U_15603,U_15602,U_15601,U_15600] :
      ( ( ( hAPP(hAPP(c_List_Onth(U_15601),hAPP(hAPP(c_List_Olist__update(U_15601,U_15602),U_15600),U_15604)),U_15603) = hAPP(hAPP(c_List_Onth(U_15601),U_15602),U_15603)
          | U_15600 = U_15603 )
        & ( hAPP(hAPP(c_List_Onth(U_15601),hAPP(hAPP(c_List_Olist__update(U_15601,U_15602),U_15600),U_15604)),U_15603) = U_15604
          | U_15600 != U_15603 ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15600),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15601)),U_15602))) ),
    inference(variable_rename,[status(thm)],[f_3901_1]) ).

cnf(f_3901_3,plain,
    ( hAPP(hAPP(c_List_Onth(U_15601),hAPP(hAPP(c_List_Olist__update(U_15601,U_15602),U_15600),U_15604)),U_15603) = U_15604
    | U_15600 != U_15603
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15600),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15601)),U_15602))) ),
    inference(clausify,[status(thm)],[f_3901_2]) ).

cnf(f_3901_4,plain,
    ( hAPP(hAPP(c_List_Onth(U_15601),hAPP(hAPP(c_List_Olist__update(U_15601,U_15602),U_15600),U_15604)),U_15603) = hAPP(hAPP(c_List_Onth(U_15601),U_15602),U_15603)
    | U_15600 = U_15603
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15600),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15601)),U_15602))) ),
    inference(clausify,[status(thm)],[f_3901_2]) ).

fof(f_3902_1,plain,
    ! [V_x_2,V_xs_2,T_b,V_i_2] :
      ( ( ( hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2) = V_xs_2
          | hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_i_2) != V_x_2 )
        & ( hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_i_2) = V_x_2
          | hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2) != V_xs_2 ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_list__update__same__conv]) ).

fof(f_3902_2,plain,
    ! [U_15608,U_15607,U_15606,U_15605] :
      ( ( ( hAPP(hAPP(c_List_Olist__update(U_15606,U_15607),U_15605),U_15608) = U_15607
          | hAPP(hAPP(c_List_Onth(U_15606),U_15607),U_15605) != U_15608 )
        & ( hAPP(hAPP(c_List_Onth(U_15606),U_15607),U_15605) = U_15608
          | hAPP(hAPP(c_List_Olist__update(U_15606,U_15607),U_15605),U_15608) != U_15607 ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15605),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15606)),U_15607))) ),
    inference(variable_rename,[status(thm)],[f_3902_1]) ).

cnf(f_3902_3,plain,
    ( hAPP(hAPP(c_List_Onth(U_15606),U_15607),U_15605) = U_15608
    | hAPP(hAPP(c_List_Olist__update(U_15606,U_15607),U_15605),U_15608) != U_15607
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15605),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15606)),U_15607))) ),
    inference(clausify,[status(thm)],[f_3902_2]) ).

cnf(f_3902_4,plain,
    ( hAPP(hAPP(c_List_Olist__update(U_15606,U_15607),U_15605),U_15608) = U_15607
    | hAPP(hAPP(c_List_Onth(U_15606),U_15607),U_15605) != U_15608
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15605),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15606)),U_15607))) ),
    inference(clausify,[status(thm)],[f_3902_2]) ).

fof(f_3903_1,plain,
    ! [V_x,V_xs,T_a,V_i] :
      ( hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_i) = V_x
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) ),
    inference(fof_nnf,[status(thm)],[fact_nth__list__update__eq]) ).

fof(f_3903_2,plain,
    ! [U_15612,U_15611,U_15610,U_15609] :
      ( hAPP(hAPP(c_List_Onth(U_15610),hAPP(hAPP(c_List_Olist__update(U_15610,U_15611),U_15609),U_15612)),U_15609) = U_15612
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15609),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15610)),U_15611))) ),
    inference(variable_rename,[status(thm)],[f_3903_1]) ).

cnf(f_3903_3,plain,
    ( hAPP(hAPP(c_List_Onth(U_15610),hAPP(hAPP(c_List_Olist__update(U_15610,U_15611),U_15609),U_15612)),U_15609) = U_15612
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15609),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15610)),U_15611))) ),
    inference(clausify,[status(thm)],[f_3903_2]) ).

fof(f_3904_1,plain,
    ! [V_xs,T_a,V_n] :
      ( hAPP(hAPP(c_List_Otake(T_a),V_n),c_List_Obutlast(T_a,V_xs)) = hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) ),
    inference(fof_nnf,[status(thm)],[fact_take__butlast]) ).

fof(f_3904_2,plain,
    ! [U_15615,U_15614,U_15613] :
      ( hAPP(hAPP(c_List_Otake(U_15614),U_15613),c_List_Obutlast(U_15614,U_15615)) = hAPP(hAPP(c_List_Otake(U_15614),U_15613),U_15615)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15613),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15614)),U_15615))) ),
    inference(variable_rename,[status(thm)],[f_3904_1]) ).

cnf(f_3904_3,plain,
    ( hAPP(hAPP(c_List_Otake(U_15614),U_15613),c_List_Obutlast(U_15614,U_15615)) = hAPP(hAPP(c_List_Otake(U_15614),U_15613),U_15615)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15613),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15614)),U_15615))) ),
    inference(clausify,[status(thm)],[f_3904_2]) ).

fof(f_3905_1,plain,
    ! [V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Obutlast(T_a,V_xs)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(fof_nnf,[status(thm)],[fact_length__butlast]) ).

fof(f_3905_2,plain,
    ! [U_15617,U_15616] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15616)),c_List_Obutlast(U_15616,U_15617)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15616)),U_15617)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[f_3905_1]) ).

cnf(f_3905_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15616)),c_List_Obutlast(U_15616,U_15617)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15616)),U_15617)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(clausify,[status(thm)],[f_3905_2]) ).

fof(f_3906_1,plain,
    ! [V_x_2,V_xs_2,T_b,V_n_2] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_n_2),V_x_2))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_set__update__memI]) ).

fof(f_3906_2,plain,
    ! [U_15621,U_15620,U_15619,U_15618] :
      ( hBOOL(hAPP(hAPP(c_member(U_15619),U_15621),hAPP(c_List_Oset(U_15619),hAPP(hAPP(c_List_Olist__update(U_15619,U_15620),U_15618),U_15621))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15618),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15619)),U_15620))) ),
    inference(variable_rename,[status(thm)],[f_3906_1]) ).

cnf(f_3906_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15619),U_15621),hAPP(c_List_Oset(U_15619),hAPP(hAPP(c_List_Olist__update(U_15619,U_15620),U_15618),U_15621))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15618),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15619)),U_15620))) ),
    inference(clausify,[status(thm)],[f_3906_2]) ).

fof(f_3907_1,plain,
    ! [V_xs,T_a] : c_List_Obutlast(T_a,V_xs) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs),
    inference(fof_nnf,[status(thm)],[fact_butlast__conv__take]) ).

fof(f_3907_2,plain,
    ! [U_15623,U_15622] : c_List_Obutlast(U_15622,U_15623) = hAPP(hAPP(c_List_Otake(U_15622),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15622)),U_15623)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_15623),
    inference(variable_rename,[status(thm)],[f_3907_1]) ).

cnf(f_3907_3,plain,
    c_List_Obutlast(U_15622,U_15623) = hAPP(hAPP(c_List_Otake(U_15622),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15622)),U_15623)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_15623),
    inference(clausify,[status(thm)],[f_3907_2]) ).

fof(f_3908_1,plain,
    ! [V_r_2,V_ys_2,V_xs_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
        | ! [B_y,B_n] :
            ( V_ys_2 != hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),B_n),B_y)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n)),B_y)),V_r_2)) ) )
      & ( ? [B_y,B_n] :
            ( V_ys_2 = hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),B_n),B_y)
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n)),B_y)),V_r_2)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_listrel1__iff__update]) ).

fof(f_3908_2,plain,
    ! [U_15631,U_15630,U_15629,U_15628] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15628),tc_List_Olist(U_15628))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15628),tc_List_Olist(U_15628)),U_15629),U_15630)),c_List_Olistrel1(U_15628,U_15631)))
        | ! [U_15627,U_15626] :
            ( U_15630 != hAPP(hAPP(c_List_Olist__update(U_15628,U_15629),U_15626),U_15627)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15626),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15628)),U_15629)))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15628,U_15628)),hAPP(hAPP(c_Product__Type_OPair(U_15628,U_15628),hAPP(hAPP(c_List_Onth(U_15628),U_15629),U_15626)),U_15627)),U_15631)) ) )
      & ( ? [U_15625,U_15624] :
            ( U_15630 = hAPP(hAPP(c_List_Olist__update(U_15628,U_15629),U_15624),U_15625)
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15624),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15628)),U_15629)))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15628,U_15628)),hAPP(hAPP(c_Product__Type_OPair(U_15628,U_15628),hAPP(hAPP(c_List_Onth(U_15628),U_15629),U_15624)),U_15625)),U_15631)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15628),tc_List_Olist(U_15628))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15628),tc_List_Olist(U_15628)),U_15629),U_15630)),c_List_Olistrel1(U_15628,U_15631))) ) ),
    inference(variable_rename,[status(thm)],[f_3908_1]) ).

fof(f_3908_3,plain,
    ( ! [U_15639,U_15637,U_15635,U_15633] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15633),tc_List_Olist(U_15633))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15633),tc_List_Olist(U_15633)),U_15635),U_15637)),c_List_Olistrel1(U_15633,U_15639)))
        | ! [U_15627,U_15626] :
            ( U_15637 != hAPP(hAPP(c_List_Olist__update(U_15633,U_15635),U_15626),U_15627)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15626),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15633)),U_15635)))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15633,U_15633)),hAPP(hAPP(c_Product__Type_OPair(U_15633,U_15633),hAPP(hAPP(c_List_Onth(U_15633),U_15635),U_15626)),U_15627)),U_15639)) ) )
    & ! [U_15638,U_15636,U_15634,U_15632] :
        ( ? [U_15625,U_15624] :
            ( U_15636 = hAPP(hAPP(c_List_Olist__update(U_15632,U_15634),U_15624),U_15625)
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15624),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15632)),U_15634)))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15632,U_15632)),hAPP(hAPP(c_Product__Type_OPair(U_15632,U_15632),hAPP(hAPP(c_List_Onth(U_15632),U_15634),U_15624)),U_15625)),U_15638)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15632),tc_List_Olist(U_15632))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15632),tc_List_Olist(U_15632)),U_15634),U_15636)),c_List_Olistrel1(U_15632,U_15638))) ) ),
    inference(miniscope,[status(thm)],[f_3908_2]) ).

fof(f_3908_4,plain,
    ( ! [U_15639,U_15637,U_15635,U_15633] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15633),tc_List_Olist(U_15633))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15633),tc_List_Olist(U_15633)),U_15635),U_15637)),c_List_Olistrel1(U_15633,U_15639)))
        | ! [U_15627,U_15626] :
            ( U_15637 != hAPP(hAPP(c_List_Olist__update(U_15633,U_15635),U_15626),U_15627)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15626),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15633)),U_15635)))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15633,U_15633)),hAPP(hAPP(c_Product__Type_OPair(U_15633,U_15633),hAPP(hAPP(c_List_Onth(U_15633),U_15635),U_15626)),U_15627)),U_15639)) ) )
    & ! [U_15638,U_15636,U_15634,U_15632] :
        ( ? [U_15624] :
            ( U_15636 = hAPP(hAPP(c_List_Olist__update(U_15632,U_15634),U_15624),sK414(U_15638,U_15636,U_15634,U_15632))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15624),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15632)),U_15634)))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15632,U_15632)),hAPP(hAPP(c_Product__Type_OPair(U_15632,U_15632),hAPP(hAPP(c_List_Onth(U_15632),U_15634),U_15624)),sK414(U_15638,U_15636,U_15634,U_15632))),U_15638)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15632),tc_List_Olist(U_15632))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15632),tc_List_Olist(U_15632)),U_15634),U_15636)),c_List_Olistrel1(U_15632,U_15638))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK414]),skolemize(U_15625,sK414(U_15638,U_15636,U_15634,U_15632))],[f_3908_3]) ).

fof(f_3908_5,plain,
    ( ! [U_15639,U_15637,U_15635,U_15633] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15633),tc_List_Olist(U_15633))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15633),tc_List_Olist(U_15633)),U_15635),U_15637)),c_List_Olistrel1(U_15633,U_15639)))
        | ! [U_15627,U_15626] :
            ( U_15637 != hAPP(hAPP(c_List_Olist__update(U_15633,U_15635),U_15626),U_15627)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15626),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15633)),U_15635)))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15633,U_15633)),hAPP(hAPP(c_Product__Type_OPair(U_15633,U_15633),hAPP(hAPP(c_List_Onth(U_15633),U_15635),U_15626)),U_15627)),U_15639)) ) )
    & ! [U_15638,U_15636,U_15634,U_15632] :
        ( ( U_15636 = hAPP(hAPP(c_List_Olist__update(U_15632,U_15634),sK415(U_15638,U_15636,U_15634,U_15632)),sK414(U_15638,U_15636,U_15634,U_15632))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK415(U_15638,U_15636,U_15634,U_15632)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15632)),U_15634)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15632,U_15632)),hAPP(hAPP(c_Product__Type_OPair(U_15632,U_15632),hAPP(hAPP(c_List_Onth(U_15632),U_15634),sK415(U_15638,U_15636,U_15634,U_15632))),sK414(U_15638,U_15636,U_15634,U_15632))),U_15638)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15632),tc_List_Olist(U_15632))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15632),tc_List_Olist(U_15632)),U_15634),U_15636)),c_List_Olistrel1(U_15632,U_15638))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK415]),skolemize(U_15624,sK415(U_15638,U_15636,U_15634,U_15632))],[f_3908_4]) ).

cnf(f_3908_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15632,U_15632)),hAPP(hAPP(c_Product__Type_OPair(U_15632,U_15632),hAPP(hAPP(c_List_Onth(U_15632),U_15634),sK415(U_15638,U_15636,U_15634,U_15632))),sK414(U_15638,U_15636,U_15634,U_15632))),U_15638))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15632),tc_List_Olist(U_15632))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15632),tc_List_Olist(U_15632)),U_15634),U_15636)),c_List_Olistrel1(U_15632,U_15638))) ),
    inference(clausify,[status(thm)],[f_3908_5]) ).

cnf(f_3908_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK415(U_15638,U_15636,U_15634,U_15632)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15632)),U_15634)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15632),tc_List_Olist(U_15632))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15632),tc_List_Olist(U_15632)),U_15634),U_15636)),c_List_Olistrel1(U_15632,U_15638))) ),
    inference(clausify,[status(thm)],[f_3908_5]) ).

cnf(f_3908_8,plain,
    ( U_15636 = hAPP(hAPP(c_List_Olist__update(U_15632,U_15634),sK415(U_15638,U_15636,U_15634,U_15632)),sK414(U_15638,U_15636,U_15634,U_15632))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15632),tc_List_Olist(U_15632))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15632),tc_List_Olist(U_15632)),U_15634),U_15636)),c_List_Olistrel1(U_15632,U_15638))) ),
    inference(clausify,[status(thm)],[f_3908_5]) ).

cnf(f_3908_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15633),tc_List_Olist(U_15633))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15633),tc_List_Olist(U_15633)),U_15635),U_15637)),c_List_Olistrel1(U_15633,U_15639)))
    | U_15637 != hAPP(hAPP(c_List_Olist__update(U_15633,U_15635),U_15626),U_15627)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15626),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15633)),U_15635)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15633,U_15633)),hAPP(hAPP(c_Product__Type_OPair(U_15633,U_15633),hAPP(hAPP(c_List_Onth(U_15633),U_15635),U_15626)),U_15627)),U_15639)) ),
    inference(clausify,[status(thm)],[f_3908_5]) ).

fof(f_3909_1,plain,
    ! [V_i_2,V_a_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_a_2)))
      | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_i_2)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__list__update]) ).

fof(f_3909_2,plain,
    ! [U_15643,U_15642,U_15641,U_15640] :
      ( hBOOL(hAPP(c_List_Odistinct(U_15640),hAPP(hAPP(c_List_Olist__update(U_15640,U_15641),U_15643),U_15642)))
      | hBOOL(hAPP(hAPP(c_member(U_15640),U_15642),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_15640,tc_HOL_Obool)),hAPP(c_List_Oset(U_15640),U_15641)),hAPP(hAPP(c_Set_Oinsert(U_15640),hAPP(hAPP(c_List_Onth(U_15640),U_15641),U_15643)),c_Orderings_Obot__class_Obot(tc_fun(U_15640,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_15640),U_15641)) ),
    inference(variable_rename,[status(thm)],[f_3909_1]) ).

cnf(f_3909_3,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_15640),hAPP(hAPP(c_List_Olist__update(U_15640,U_15641),U_15643),U_15642)))
    | hBOOL(hAPP(hAPP(c_member(U_15640),U_15642),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_15640,tc_HOL_Obool)),hAPP(c_List_Oset(U_15640),U_15641)),hAPP(hAPP(c_Set_Oinsert(U_15640),hAPP(hAPP(c_List_Onth(U_15640),U_15641),U_15643)),c_Orderings_Obot__class_Obot(tc_fun(U_15640,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_15640),U_15641)) ),
    inference(clausify,[status(thm)],[f_3909_2]) ).

fof(f_3910_1,plain,
    ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(V_i,V_j))),
    inference(fof_nnf,[status(thm)],[fact_distinct__upto]) ).

fof(f_3910_2,plain,
    ! [U_15645,U_15644] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(U_15644,U_15645))),
    inference(variable_rename,[status(thm)],[f_3910_1]) ).

cnf(f_3910_3,plain,
    hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(U_15644,U_15645))),
    inference(clausify,[status(thm)],[f_3910_2]) ).

fof(f_3911_1,plain,
    ! [V_i,V_xs,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__take]) ).

fof(f_3911_2,plain,
    ! [U_15648,U_15647,U_15646] :
      ( hBOOL(hAPP(c_List_Odistinct(U_15646),hAPP(hAPP(c_List_Otake(U_15646),U_15648),U_15647)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_15646),U_15647)) ),
    inference(variable_rename,[status(thm)],[f_3911_1]) ).

cnf(f_3911_3,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_15646),hAPP(hAPP(c_List_Otake(U_15646),U_15648),U_15647)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_15646),U_15647)) ),
    inference(clausify,[status(thm)],[f_3911_2]) ).

fof(f_3912_1,plain,
    ! [V_I_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2)))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__sublistI]) ).

fof(f_3912_2,plain,
    ! [U_15651,U_15650,U_15649] :
      ( hBOOL(hAPP(c_List_Odistinct(U_15649),c_List_Osublist(U_15649,U_15650,U_15651)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_15649),U_15650)) ),
    inference(variable_rename,[status(thm)],[f_3912_1]) ).

cnf(f_3912_3,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_15649),c_List_Osublist(U_15649,U_15650,U_15651)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_15649),U_15650)) ),
    inference(clausify,[status(thm)],[f_3912_2]) ).

fof(f_3913_1,plain,
    ! [V_xs,T_b,V_ys,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(tc_prod(T_b,T_a)),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs),V_ys)))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_a),V_ys)) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__zipI2]) ).

fof(f_3913_2,plain,
    ! [U_15655,U_15654,U_15653,U_15652] :
      ( hBOOL(hAPP(c_List_Odistinct(tc_prod(U_15654,U_15652)),hAPP(hAPP(c_List_Ozip(U_15654,U_15652),U_15655),U_15653)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_15652),U_15653)) ),
    inference(variable_rename,[status(thm)],[f_3913_1]) ).

cnf(f_3913_3,plain,
    ( hBOOL(hAPP(c_List_Odistinct(tc_prod(U_15654,U_15652)),hAPP(hAPP(c_List_Ozip(U_15654,U_15652),U_15655),U_15653)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_15652),U_15653)) ),
    inference(clausify,[status(thm)],[f_3913_2]) ).

fof(f_3914_1,plain,
    ! [V_ys,T_b,V_xs,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__zipI1]) ).

fof(f_3914_2,plain,
    ! [U_15659,U_15658,U_15657,U_15656] :
      ( hBOOL(hAPP(c_List_Odistinct(tc_prod(U_15656,U_15658)),hAPP(hAPP(c_List_Ozip(U_15656,U_15658),U_15657),U_15659)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_15656),U_15657)) ),
    inference(variable_rename,[status(thm)],[f_3914_1]) ).

cnf(f_3914_3,plain,
    ( hBOOL(hAPP(c_List_Odistinct(tc_prod(U_15656,U_15658)),hAPP(hAPP(c_List_Ozip(U_15656,U_15658),U_15657),U_15659)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_15656),U_15657)) ),
    inference(clausify,[status(thm)],[f_3914_2]) ).

fof(f_3915_1,plain,
    ! [V_xs_2,V_x_2,T_b] :
      ( ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)))
        | ~ hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
        | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) )
      & ( ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
          & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) )
        | ~ hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_distinct_Osimps_I2_J]) ).

fof(f_3915_2,plain,
    ! [U_15662,U_15661,U_15660] :
      ( ( hBOOL(hAPP(c_List_Odistinct(U_15660),hAPP(hAPP(c_List_Olist_OCons(U_15660),U_15661),U_15662)))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_15660),U_15662))
        | hBOOL(hAPP(hAPP(c_member(U_15660),U_15661),hAPP(c_List_Oset(U_15660),U_15662))) )
      & ( ( hBOOL(hAPP(c_List_Odistinct(U_15660),U_15662))
          & ~ hBOOL(hAPP(hAPP(c_member(U_15660),U_15661),hAPP(c_List_Oset(U_15660),U_15662))) )
        | ~ hBOOL(hAPP(c_List_Odistinct(U_15660),hAPP(hAPP(c_List_Olist_OCons(U_15660),U_15661),U_15662))) ) ),
    inference(variable_rename,[status(thm)],[f_3915_1]) ).

fof(f_3915_3,plain,
    ( ! [U_15668,U_15666,U_15664] :
        ( hBOOL(hAPP(c_List_Odistinct(U_15664),hAPP(hAPP(c_List_Olist_OCons(U_15664),U_15666),U_15668)))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_15664),U_15668))
        | hBOOL(hAPP(hAPP(c_member(U_15664),U_15666),hAPP(c_List_Oset(U_15664),U_15668))) )
    & ! [U_15667,U_15665,U_15663] :
        ( ( hBOOL(hAPP(c_List_Odistinct(U_15663),U_15667))
          & ~ hBOOL(hAPP(hAPP(c_member(U_15663),U_15665),hAPP(c_List_Oset(U_15663),U_15667))) )
        | ~ hBOOL(hAPP(c_List_Odistinct(U_15663),hAPP(hAPP(c_List_Olist_OCons(U_15663),U_15665),U_15667))) ) ),
    inference(miniscope,[status(thm)],[f_3915_2]) ).

cnf(f_3915_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_15663),U_15665),hAPP(c_List_Oset(U_15663),U_15667)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_15663),hAPP(hAPP(c_List_Olist_OCons(U_15663),U_15665),U_15667))) ),
    inference(clausify,[status(thm)],[f_3915_3]) ).

cnf(f_3915_5,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_15663),U_15667))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_15663),hAPP(hAPP(c_List_Olist_OCons(U_15663),U_15665),U_15667))) ),
    inference(clausify,[status(thm)],[f_3915_3]) ).

cnf(f_3915_6,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_15664),hAPP(hAPP(c_List_Olist_OCons(U_15664),U_15666),U_15668)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_15664),U_15668))
    | hBOOL(hAPP(hAPP(c_member(U_15664),U_15666),hAPP(c_List_Oset(U_15664),U_15668))) ),
    inference(clausify,[status(thm)],[f_3915_3]) ).

fof(f_3916_1,plain,
    ! [V_xs_2,T_b] :
      ( hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)
      | ~ hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__card]) ).

fof(f_3916_2,plain,
    ! [U_15670,U_15669] :
      ( hAPP(c_Finite__Set_Ocard(U_15669),hAPP(c_List_Oset(U_15669),U_15670)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15669)),U_15670)
      | ~ hBOOL(hAPP(c_List_Odistinct(U_15669),U_15670)) ),
    inference(variable_rename,[status(thm)],[f_3916_1]) ).

cnf(f_3916_3,plain,
    ( hAPP(c_Finite__Set_Ocard(U_15669),hAPP(c_List_Oset(U_15669),U_15670)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15669)),U_15670)
    | ~ hBOOL(hAPP(c_List_Odistinct(U_15669),U_15670)) ),
    inference(clausify,[status(thm)],[f_3916_2]) ).

fof(f_3917_1,plain,
    ! [V_xs_2,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
      | hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_List_Oset(T_b),V_xs_2)) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) ),
    inference(fof_nnf,[status(thm)],[fact_card__distinct]) ).

fof(f_3917_2,plain,
    ! [U_15672,U_15671] :
      ( hBOOL(hAPP(c_List_Odistinct(U_15671),U_15672))
      | hAPP(c_Finite__Set_Ocard(U_15671),hAPP(c_List_Oset(U_15671),U_15672)) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15671)),U_15672) ),
    inference(variable_rename,[status(thm)],[f_3917_1]) ).

cnf(f_3917_3,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_15671),U_15672))
    | hAPP(c_Finite__Set_Ocard(U_15671),hAPP(c_List_Oset(U_15671),U_15672)) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15671)),U_15672) ),
    inference(clausify,[status(thm)],[f_3917_2]) ).

fof(f_3918_1,plain,
    ! [V_xs_2,T_b] :
      ( ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
        | ? [B_i] :
            ( ? [B_j] :
                ( hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) = hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_j)
                & B_i != B_j
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) )
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ) )
      & ( ! [B_i] :
            ( ! [B_j] :
                ( hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) != hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_j)
                | B_i = B_j
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) )
        | ~ hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__conv__nth]) ).

fof(f_3918_2,plain,
    ! [U_15678,U_15677] :
      ( ( hBOOL(hAPP(c_List_Odistinct(U_15677),U_15678))
        | ? [U_15676] :
            ( ? [U_15675] :
                ( hAPP(hAPP(c_List_Onth(U_15677),U_15678),U_15676) = hAPP(hAPP(c_List_Onth(U_15677),U_15678),U_15675)
                & U_15676 != U_15675
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15675),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15677)),U_15678))) )
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15676),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15677)),U_15678))) ) )
      & ( ! [U_15674] :
            ( ! [U_15673] :
                ( hAPP(hAPP(c_List_Onth(U_15677),U_15678),U_15674) != hAPP(hAPP(c_List_Onth(U_15677),U_15678),U_15673)
                | U_15674 = U_15673
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15673),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15677)),U_15678))) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15674),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15677)),U_15678))) )
        | ~ hBOOL(hAPP(c_List_Odistinct(U_15677),U_15678)) ) ),
    inference(variable_rename,[status(thm)],[f_3918_1]) ).

fof(f_3918_3,plain,
    ( ! [U_15682,U_15680] :
        ( hBOOL(hAPP(c_List_Odistinct(U_15680),U_15682))
        | ? [U_15676] :
            ( ? [U_15675] :
                ( hAPP(hAPP(c_List_Onth(U_15680),U_15682),U_15676) = hAPP(hAPP(c_List_Onth(U_15680),U_15682),U_15675)
                & U_15676 != U_15675
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15675),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15680)),U_15682))) )
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15676),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15680)),U_15682))) ) )
    & ! [U_15681,U_15679] :
        ( ! [U_15674] :
            ( ! [U_15673] :
                ( hAPP(hAPP(c_List_Onth(U_15679),U_15681),U_15674) != hAPP(hAPP(c_List_Onth(U_15679),U_15681),U_15673)
                | U_15674 = U_15673
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15673),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15679)),U_15681))) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15674),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15679)),U_15681))) )
        | ~ hBOOL(hAPP(c_List_Odistinct(U_15679),U_15681)) ) ),
    inference(miniscope,[status(thm)],[f_3918_2]) ).

fof(f_3918_4,plain,
    ( ! [U_15682,U_15680] :
        ( hBOOL(hAPP(c_List_Odistinct(U_15680),U_15682))
        | ( ? [U_15675] :
              ( hAPP(hAPP(c_List_Onth(U_15680),U_15682),sK416(U_15682,U_15680)) = hAPP(hAPP(c_List_Onth(U_15680),U_15682),U_15675)
              & sK416(U_15682,U_15680) != U_15675
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15675),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15680)),U_15682))) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK416(U_15682,U_15680)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15680)),U_15682))) ) )
    & ! [U_15681,U_15679] :
        ( ! [U_15674] :
            ( ! [U_15673] :
                ( hAPP(hAPP(c_List_Onth(U_15679),U_15681),U_15674) != hAPP(hAPP(c_List_Onth(U_15679),U_15681),U_15673)
                | U_15674 = U_15673
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15673),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15679)),U_15681))) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15674),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15679)),U_15681))) )
        | ~ hBOOL(hAPP(c_List_Odistinct(U_15679),U_15681)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK416]),skolemize(U_15676,sK416(U_15682,U_15680))],[f_3918_3]) ).

fof(f_3918_5,plain,
    ( ! [U_15682,U_15680] :
        ( hBOOL(hAPP(c_List_Odistinct(U_15680),U_15682))
        | ( hAPP(hAPP(c_List_Onth(U_15680),U_15682),sK416(U_15682,U_15680)) = hAPP(hAPP(c_List_Onth(U_15680),U_15682),sK417(U_15682,U_15680))
          & sK416(U_15682,U_15680) != sK417(U_15682,U_15680)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK417(U_15682,U_15680)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15680)),U_15682)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK416(U_15682,U_15680)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15680)),U_15682))) ) )
    & ! [U_15681,U_15679] :
        ( ! [U_15674] :
            ( ! [U_15673] :
                ( hAPP(hAPP(c_List_Onth(U_15679),U_15681),U_15674) != hAPP(hAPP(c_List_Onth(U_15679),U_15681),U_15673)
                | U_15674 = U_15673
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15673),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15679)),U_15681))) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15674),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15679)),U_15681))) )
        | ~ hBOOL(hAPP(c_List_Odistinct(U_15679),U_15681)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK417]),skolemize(U_15675,sK417(U_15682,U_15680))],[f_3918_4]) ).

cnf(f_3918_6,plain,
    ( hAPP(hAPP(c_List_Onth(U_15679),U_15681),U_15674) != hAPP(hAPP(c_List_Onth(U_15679),U_15681),U_15673)
    | U_15674 = U_15673
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15673),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15679)),U_15681)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15674),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15679)),U_15681)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_15679),U_15681)) ),
    inference(clausify,[status(thm)],[f_3918_5]) ).

cnf(f_3918_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK416(U_15682,U_15680)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15680)),U_15682)))
    | hBOOL(hAPP(c_List_Odistinct(U_15680),U_15682)) ),
    inference(clausify,[status(thm)],[f_3918_5]) ).

cnf(f_3918_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK417(U_15682,U_15680)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15680)),U_15682)))
    | hBOOL(hAPP(c_List_Odistinct(U_15680),U_15682)) ),
    inference(clausify,[status(thm)],[f_3918_5]) ).

cnf(f_3918_9,plain,
    ( sK416(U_15682,U_15680) != sK417(U_15682,U_15680)
    | hBOOL(hAPP(c_List_Odistinct(U_15680),U_15682)) ),
    inference(clausify,[status(thm)],[f_3918_5]) ).

cnf(f_3918_10,plain,
    ( hAPP(hAPP(c_List_Onth(U_15680),U_15682),sK416(U_15682,U_15680)) = hAPP(hAPP(c_List_Onth(U_15680),U_15682),sK417(U_15682,U_15680))
    | hBOOL(hAPP(c_List_Odistinct(U_15680),U_15682)) ),
    inference(clausify,[status(thm)],[f_3918_5]) ).

fof(f_3919_1,plain,
    ! [V_j_2,V_i_2,V_xs_2,T_b] :
      ( ( ( hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_i_2) = hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_j_2)
          | V_i_2 != V_j_2 )
        & ( V_i_2 = V_j_2
          | hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_i_2) != hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_j_2) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ),
    inference(fof_nnf,[status(thm)],[fact_nth__eq__iff__index__eq]) ).

fof(f_3919_2,plain,
    ! [U_15686,U_15685,U_15684,U_15683] :
      ( ( ( hAPP(hAPP(c_List_Onth(U_15683),U_15684),U_15685) = hAPP(hAPP(c_List_Onth(U_15683),U_15684),U_15686)
          | U_15685 != U_15686 )
        & ( U_15685 = U_15686
          | hAPP(hAPP(c_List_Onth(U_15683),U_15684),U_15685) != hAPP(hAPP(c_List_Onth(U_15683),U_15684),U_15686) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15686),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15683)),U_15684)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15685),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15683)),U_15684)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_15683),U_15684)) ),
    inference(variable_rename,[status(thm)],[f_3919_1]) ).

cnf(f_3919_3,plain,
    ( U_15685 = U_15686
    | hAPP(hAPP(c_List_Onth(U_15683),U_15684),U_15685) != hAPP(hAPP(c_List_Onth(U_15683),U_15684),U_15686)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15686),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15683)),U_15684)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15685),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15683)),U_15684)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_15683),U_15684)) ),
    inference(clausify,[status(thm)],[f_3919_2]) ).

cnf(f_3919_4,plain,
    ( hAPP(hAPP(c_List_Onth(U_15683),U_15684),U_15685) = hAPP(hAPP(c_List_Onth(U_15683),U_15684),U_15686)
    | U_15685 != U_15686
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15686),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15683)),U_15684)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15685),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15683)),U_15684)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_15683),U_15684)) ),
    inference(clausify,[status(thm)],[f_3919_2]) ).

fof(f_3920_1,plain,
    ! [V_xs_2,T_b] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(T_b),V_xs_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_b),c_COMBI(T_b)),hAPP(c_List_Oset(T_b),V_xs_2))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__listsum__conv__Setsum]) ).

fof(f_3920_2,plain,
    ! [U_15688,U_15687] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_15687),U_15688) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15687,U_15687),c_COMBI(U_15687)),hAPP(c_List_Oset(U_15687),U_15688))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_15687),U_15688))
      | ~ class_Groups_Ocomm__monoid__add(U_15687) ),
    inference(variable_rename,[status(thm)],[f_3920_1]) ).

cnf(f_3920_3,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_15687),U_15688) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15687,U_15687),c_COMBI(U_15687)),hAPP(c_List_Oset(U_15687),U_15688))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_15687),U_15688))
    | ~ class_Groups_Ocomm__monoid__add(U_15687) ),
    inference(clausify,[status(thm)],[f_3920_2]) ).

fof(f_3921_1,plain,
    ! [V_A_2,T_b] :
      ( ( c_Nitpick_Ocard_H(T_b,V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) )
      & ( c_Nitpick_Ocard_H(T_b,V_A_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_Hilbert__Choice_OEps(tc_List_Olist(T_b),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_List_Oset(T_b))),V_A_2))),c_List_Odistinct(T_b))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Nitpick_Ocard_H__def]) ).

fof(f_3921_2,plain,
    ! [U_15690,U_15689] :
      ( ( c_Nitpick_Ocard_H(U_15689,U_15690) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(c_Finite__Set_Ofinite(U_15689),U_15690)) )
      & ( c_Nitpick_Ocard_H(U_15689,U_15690) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15689)),c_Hilbert__Choice_OEps(tc_List_Olist(U_15689),hAPP(hAPP(c_COMBS(tc_List_Olist(U_15689),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_15689)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_15689),tc_fun(U_15689,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_15689,tc_HOL_Obool),tc_fun(tc_fun(U_15689,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_15689)),c_fequal),c_List_Oset(U_15689))),U_15690))),c_List_Odistinct(U_15689))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15689),U_15690)) ) ),
    inference(variable_rename,[status(thm)],[f_3921_1]) ).

fof(f_3921_3,plain,
    ( ! [U_15694,U_15692] :
        ( c_Nitpick_Ocard_H(U_15692,U_15694) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(c_Finite__Set_Ofinite(U_15692),U_15694)) )
    & ! [U_15693,U_15691] :
        ( c_Nitpick_Ocard_H(U_15691,U_15693) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15691)),c_Hilbert__Choice_OEps(tc_List_Olist(U_15691),hAPP(hAPP(c_COMBS(tc_List_Olist(U_15691),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_15691)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_15691),tc_fun(U_15691,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_15691,tc_HOL_Obool),tc_fun(tc_fun(U_15691,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_15691)),c_fequal),c_List_Oset(U_15691))),U_15693))),c_List_Odistinct(U_15691))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15691),U_15693)) ) ),
    inference(miniscope,[status(thm)],[f_3921_2]) ).

cnf(f_3921_4,plain,
    ( c_Nitpick_Ocard_H(U_15691,U_15693) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15691)),c_Hilbert__Choice_OEps(tc_List_Olist(U_15691),hAPP(hAPP(c_COMBS(tc_List_Olist(U_15691),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_15691)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_15691),tc_fun(U_15691,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_15691,tc_HOL_Obool),tc_fun(tc_fun(U_15691,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_15691)),c_fequal),c_List_Oset(U_15691))),U_15693))),c_List_Odistinct(U_15691))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15691),U_15693)) ),
    inference(clausify,[status(thm)],[f_3921_3]) ).

cnf(f_3921_5,plain,
    ( c_Nitpick_Ocard_H(U_15692,U_15694) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_15692),U_15694)) ),
    inference(clausify,[status(thm)],[f_3921_3]) ).

fof(f_3922_1,plain,
    ! [V_ys,V_xs,T_a,V_k] :
      ( hAPP(hAPP(c_List_Otake(T_a),V_k),V_xs) = hAPP(hAPP(c_List_Otake(T_a),V_k),V_ys)
      | ? [B_i] :
          ( hAPP(hAPP(c_List_Onth(T_a),V_xs),B_i) != hAPP(hAPP(c_List_Onth(T_a),V_ys),B_i)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_k)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) ),
    inference(fof_nnf,[status(thm)],[fact_nth__take__lemma]) ).

fof(f_3922_2,plain,
    ! [U_15699,U_15698,U_15697,U_15696] :
      ( hAPP(hAPP(c_List_Otake(U_15697),U_15696),U_15698) = hAPP(hAPP(c_List_Otake(U_15697),U_15696),U_15699)
      | ? [U_15695] :
          ( hAPP(hAPP(c_List_Onth(U_15697),U_15698),U_15695) != hAPP(hAPP(c_List_Onth(U_15697),U_15699),U_15695)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_15695),U_15696)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_15696),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15697)),U_15699)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_15696),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15697)),U_15698))) ),
    inference(variable_rename,[status(thm)],[f_3922_1]) ).

fof(f_3922_3,plain,
    ! [U_15699,U_15698,U_15697,U_15696] :
      ( hAPP(hAPP(c_List_Otake(U_15697),U_15696),U_15698) = hAPP(hAPP(c_List_Otake(U_15697),U_15696),U_15699)
      | ( hAPP(hAPP(c_List_Onth(U_15697),U_15698),sK418(U_15699,U_15698,U_15697,U_15696)) != hAPP(hAPP(c_List_Onth(U_15697),U_15699),sK418(U_15699,U_15698,U_15697,U_15696))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK418(U_15699,U_15698,U_15697,U_15696)),U_15696)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_15696),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15697)),U_15699)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_15696),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15697)),U_15698))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK418]),skolemize(U_15695,sK418(U_15699,U_15698,U_15697,U_15696))],[f_3922_2]) ).

cnf(f_3922_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK418(U_15699,U_15698,U_15697,U_15696)),U_15696))
    | hAPP(hAPP(c_List_Otake(U_15697),U_15696),U_15698) = hAPP(hAPP(c_List_Otake(U_15697),U_15696),U_15699)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_15696),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15697)),U_15699)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_15696),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15697)),U_15698))) ),
    inference(clausify,[status(thm)],[f_3922_3]) ).

cnf(f_3922_5,plain,
    ( hAPP(hAPP(c_List_Onth(U_15697),U_15698),sK418(U_15699,U_15698,U_15697,U_15696)) != hAPP(hAPP(c_List_Onth(U_15697),U_15699),sK418(U_15699,U_15698,U_15697,U_15696))
    | hAPP(hAPP(c_List_Otake(U_15697),U_15696),U_15698) = hAPP(hAPP(c_List_Otake(U_15697),U_15696),U_15699)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_15696),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15697)),U_15699)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_15696),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15697)),U_15698))) ),
    inference(clausify,[status(thm)],[f_3922_3]) ).

fof(f_3923_1,plain,
    ! [V_x_2,V_xs_2,T_b] :
      ( hAPP(c_List_Oset(T_b),c_List_Oremove1(T_b,V_x_2,V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ),
    inference(fof_nnf,[status(thm)],[fact_set__remove1__eq]) ).

fof(f_3923_2,plain,
    ! [U_15702,U_15701,U_15700] :
      ( hAPP(c_List_Oset(U_15700),c_List_Oremove1(U_15700,U_15702,U_15701)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_15700,tc_HOL_Obool)),hAPP(c_List_Oset(U_15700),U_15701)),hAPP(hAPP(c_Set_Oinsert(U_15700),U_15702),c_Orderings_Obot__class_Obot(tc_fun(U_15700,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_15700),U_15701)) ),
    inference(variable_rename,[status(thm)],[f_3923_1]) ).

cnf(f_3923_3,plain,
    ( hAPP(c_List_Oset(U_15700),c_List_Oremove1(U_15700,U_15702,U_15701)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_15700,tc_HOL_Obool)),hAPP(c_List_Oset(U_15700),U_15701)),hAPP(hAPP(c_Set_Oinsert(U_15700),U_15702),c_Orderings_Obot__class_Obot(tc_fun(U_15700,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_15700),U_15701)) ),
    inference(clausify,[status(thm)],[f_3923_2]) ).

fof(f_3924_1,plain,
    ! [V_xs,V_x,T_a,V_v] :
      ( ( hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a)
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(fof_nnf,[status(thm)],[fact_take__Cons__number__of]) ).

fof(f_3924_2,plain,
    ! [U_15706,U_15705,U_15704,U_15703] :
      ( ( hAPP(hAPP(c_List_Otake(U_15704),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15703)),hAPP(hAPP(c_List_Olist_OCons(U_15704),U_15705),U_15706)) = hAPP(hAPP(c_List_Olist_OCons(U_15704),U_15705),hAPP(hAPP(c_List_Otake(U_15704),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15703)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_15706))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15703) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_List_Otake(U_15704),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15703)),hAPP(hAPP(c_List_Olist_OCons(U_15704),U_15705),U_15706)) = c_List_Olist_ONil(U_15704)
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15703) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_3924_1]) ).

fof(f_3924_3,plain,
    ( ! [U_15714,U_15712,U_15710,U_15708] :
        ( hAPP(hAPP(c_List_Otake(U_15710),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15708)),hAPP(hAPP(c_List_Olist_OCons(U_15710),U_15712),U_15714)) = hAPP(hAPP(c_List_Olist_OCons(U_15710),U_15712),hAPP(hAPP(c_List_Otake(U_15710),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15708)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_15714))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15708) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_15713,U_15711,U_15709,U_15707] :
        ( hAPP(hAPP(c_List_Otake(U_15709),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15707)),hAPP(hAPP(c_List_Olist_OCons(U_15709),U_15711),U_15713)) = c_List_Olist_ONil(U_15709)
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15707) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_3924_2]) ).

cnf(f_3924_4,plain,
    ( hAPP(hAPP(c_List_Otake(U_15709),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15707)),hAPP(hAPP(c_List_Olist_OCons(U_15709),U_15711),U_15713)) = c_List_Olist_ONil(U_15709)
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15707) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_3924_3]) ).

cnf(f_3924_5,plain,
    ( hAPP(hAPP(c_List_Otake(U_15710),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15708)),hAPP(hAPP(c_List_Olist_OCons(U_15710),U_15712),U_15714)) = hAPP(hAPP(c_List_Olist_OCons(U_15710),U_15712),hAPP(hAPP(c_List_Otake(U_15710),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15708)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_15714))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_15708) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_3924_3]) ).

fof(f_3925_1,plain,
    ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_List_Olists(T_b,V_A_2))),
    inference(fof_nnf,[status(thm)],[fact_lists_ONil]) ).

fof(f_3925_2,plain,
    ! [U_15716,U_15715] : hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15715)),c_List_Olist_ONil(U_15715)),c_List_Olists(U_15715,U_15716))),
    inference(variable_rename,[status(thm)],[f_3925_1]) ).

cnf(f_3925_3,plain,
    hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_15715)),c_List_Olist_ONil(U_15715)),c_List_Olists(U_15715,U_15716))),
    inference(clausify,[status(thm)],[f_3925_2]) ).

fof(f_3926_1,plain,
    ! [V_r_2,V_xs_2,T_b] :
      ( V_xs_2 = c_List_Olist_ONil(T_b)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_xs_2)),c_List_Olistrel(T_b,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_listrel__Nil1]) ).

fof(f_3926_2,plain,
    ! [U_15719,U_15718,U_15717] :
      ( U_15718 = c_List_Olist_ONil(U_15717)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15717),tc_List_Olist(U_15717))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15717),tc_List_Olist(U_15717)),c_List_Olist_ONil(U_15717)),U_15718)),c_List_Olistrel(U_15717,U_15719))) ),
    inference(variable_rename,[status(thm)],[f_3926_1]) ).

cnf(f_3926_3,plain,
    ( U_15718 = c_List_Olist_ONil(U_15717)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15717),tc_List_Olist(U_15717))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15717),tc_List_Olist(U_15717)),c_List_Olist_ONil(U_15717)),U_15718)),c_List_Olistrel(U_15717,U_15719))) ),
    inference(clausify,[status(thm)],[f_3926_2]) ).

fof(f_3927_1,plain,
    ! [V_r_2,V_xs_2,T_b] :
      ( V_xs_2 = c_List_Olist_ONil(T_b)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),c_List_Olist_ONil(T_b))),c_List_Olistrel(T_b,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_listrel__Nil2]) ).

fof(f_3927_2,plain,
    ! [U_15722,U_15721,U_15720] :
      ( U_15721 = c_List_Olist_ONil(U_15720)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15720),tc_List_Olist(U_15720))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15720),tc_List_Olist(U_15720)),U_15721),c_List_Olist_ONil(U_15720))),c_List_Olistrel(U_15720,U_15722))) ),
    inference(variable_rename,[status(thm)],[f_3927_1]) ).

cnf(f_3927_3,plain,
    ( U_15721 = c_List_Olist_ONil(U_15720)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15720),tc_List_Olist(U_15720))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15720),tc_List_Olist(U_15720)),U_15721),c_List_Olist_ONil(U_15720))),c_List_Olistrel(U_15720,U_15722))) ),
    inference(clausify,[status(thm)],[f_3927_2]) ).

fof(f_3928_1,plain,
    ! [T_a,V_xs] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Obutlast(T_a,V_xs)))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
      | V_xs = c_List_Olist_ONil(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__butlast]) ).

fof(f_3928_2,plain,
    ! [U_15724,U_15723] :
      ( hBOOL(hAPP(c_List_Odistinct(U_15724),c_List_Obutlast(U_15724,U_15723)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_15724),U_15723))
      | U_15723 = c_List_Olist_ONil(U_15724) ),
    inference(variable_rename,[status(thm)],[f_3928_1]) ).

cnf(f_3928_3,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_15724),c_List_Obutlast(U_15724,U_15723)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_15724),U_15723))
    | U_15723 = c_List_Olist_ONil(U_15724) ),
    inference(clausify,[status(thm)],[f_3928_2]) ).

fof(f_3929_1,plain,
    ! [T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olist_ONil(T_a))),
    inference(fof_nnf,[status(thm)],[fact_distinct_Osimps_I1_J]) ).

fof(f_3929_2,plain,
    ! [U_15725] : hBOOL(hAPP(c_List_Odistinct(U_15725),c_List_Olist_ONil(U_15725))),
    inference(variable_rename,[status(thm)],[f_3929_1]) ).

cnf(f_3929_3,plain,
    hBOOL(hAPP(c_List_Odistinct(U_15725),c_List_Olist_ONil(U_15725))),
    inference(clausify,[status(thm)],[f_3929_2]) ).

fof(f_3930_1,plain,
    ! [V_x,V_xs,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremove1(T_a,V_x,V_xs)))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__remove1]) ).

fof(f_3930_2,plain,
    ! [U_15728,U_15727,U_15726] :
      ( hBOOL(hAPP(c_List_Odistinct(U_15726),c_List_Oremove1(U_15726,U_15728,U_15727)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_15726),U_15727)) ),
    inference(variable_rename,[status(thm)],[f_3930_1]) ).

cnf(f_3930_3,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_15726),c_List_Oremove1(U_15726,U_15728,U_15727)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_15726),U_15727)) ),
    inference(clausify,[status(thm)],[f_3930_2]) ).

fof(f_3931_1,plain,
    ! [T_a] : c_List_Obutlast(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a),
    inference(fof_nnf,[status(thm)],[fact_butlast_Osimps_I1_J]) ).

fof(f_3931_2,plain,
    ! [U_15729] : c_List_Obutlast(U_15729,c_List_Olist_ONil(U_15729)) = c_List_Olist_ONil(U_15729),
    inference(variable_rename,[status(thm)],[f_3931_1]) ).

cnf(f_3931_3,plain,
    c_List_Obutlast(U_15729,c_List_Olist_ONil(U_15729)) = c_List_Olist_ONil(U_15729),
    inference(clausify,[status(thm)],[f_3931_2]) ).

fof(f_3932_1,plain,
    ! [V_x,T_a,V_xs] :
      ( ( c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Obutlast(T_a,V_xs))
        | V_xs = c_List_Olist_ONil(T_a) )
      & ( c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a)
        | V_xs != c_List_Olist_ONil(T_a) ) ),
    inference(fof_nnf,[status(thm)],[fact_butlast_Osimps_I2_J]) ).

fof(f_3932_2,plain,
    ! [U_15732,U_15731,U_15730] :
      ( ( c_List_Obutlast(U_15731,hAPP(hAPP(c_List_Olist_OCons(U_15731),U_15732),U_15730)) = hAPP(hAPP(c_List_Olist_OCons(U_15731),U_15732),c_List_Obutlast(U_15731,U_15730))
        | U_15730 = c_List_Olist_ONil(U_15731) )
      & ( c_List_Obutlast(U_15731,hAPP(hAPP(c_List_Olist_OCons(U_15731),U_15732),U_15730)) = c_List_Olist_ONil(U_15731)
        | U_15730 != c_List_Olist_ONil(U_15731) ) ),
    inference(variable_rename,[status(thm)],[f_3932_1]) ).

fof(f_3932_3,plain,
    ( ! [U_15738,U_15736,U_15734] :
        ( c_List_Obutlast(U_15736,hAPP(hAPP(c_List_Olist_OCons(U_15736),U_15738),U_15734)) = hAPP(hAPP(c_List_Olist_OCons(U_15736),U_15738),c_List_Obutlast(U_15736,U_15734))
        | U_15734 = c_List_Olist_ONil(U_15736) )
    & ! [U_15737,U_15735,U_15733] :
        ( c_List_Obutlast(U_15735,hAPP(hAPP(c_List_Olist_OCons(U_15735),U_15737),U_15733)) = c_List_Olist_ONil(U_15735)
        | U_15733 != c_List_Olist_ONil(U_15735) ) ),
    inference(miniscope,[status(thm)],[f_3932_2]) ).

cnf(f_3932_4,plain,
    ( c_List_Obutlast(U_15735,hAPP(hAPP(c_List_Olist_OCons(U_15735),U_15737),U_15733)) = c_List_Olist_ONil(U_15735)
    | U_15733 != c_List_Olist_ONil(U_15735) ),
    inference(clausify,[status(thm)],[f_3932_3]) ).

cnf(f_3932_5,plain,
    ( c_List_Obutlast(U_15736,hAPP(hAPP(c_List_Olist_OCons(U_15736),U_15738),U_15734)) = hAPP(hAPP(c_List_Olist_OCons(U_15736),U_15738),c_List_Obutlast(U_15736,U_15734))
    | U_15734 = c_List_Olist_ONil(U_15736) ),
    inference(clausify,[status(thm)],[f_3932_3]) ).

fof(f_3933_1,plain,
    ! [V_xs,T_a,V_y,V_x] :
      ( ( c_List_Oremove1(T_a,V_x,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),c_List_Oremove1(T_a,V_x,V_xs))
        | V_x = V_y )
      & ( c_List_Oremove1(T_a,V_x,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = V_xs
        | V_x != V_y ) ),
    inference(fof_nnf,[status(thm)],[fact_remove1_Osimps_I2_J]) ).

fof(f_3933_2,plain,
    ! [U_15742,U_15741,U_15740,U_15739] :
      ( ( c_List_Oremove1(U_15741,U_15739,hAPP(hAPP(c_List_Olist_OCons(U_15741),U_15740),U_15742)) = hAPP(hAPP(c_List_Olist_OCons(U_15741),U_15740),c_List_Oremove1(U_15741,U_15739,U_15742))
        | U_15739 = U_15740 )
      & ( c_List_Oremove1(U_15741,U_15739,hAPP(hAPP(c_List_Olist_OCons(U_15741),U_15740),U_15742)) = U_15742
        | U_15739 != U_15740 ) ),
    inference(variable_rename,[status(thm)],[f_3933_1]) ).

fof(f_3933_3,plain,
    ( ! [U_15750,U_15748,U_15746,U_15744] :
        ( c_List_Oremove1(U_15748,U_15744,hAPP(hAPP(c_List_Olist_OCons(U_15748),U_15746),U_15750)) = hAPP(hAPP(c_List_Olist_OCons(U_15748),U_15746),c_List_Oremove1(U_15748,U_15744,U_15750))
        | U_15744 = U_15746 )
    & ! [U_15749,U_15747,U_15745,U_15743] :
        ( c_List_Oremove1(U_15747,U_15743,hAPP(hAPP(c_List_Olist_OCons(U_15747),U_15745),U_15749)) = U_15749
        | U_15743 != U_15745 ) ),
    inference(miniscope,[status(thm)],[f_3933_2]) ).

cnf(f_3933_4,plain,
    ( c_List_Oremove1(U_15747,U_15743,hAPP(hAPP(c_List_Olist_OCons(U_15747),U_15745),U_15749)) = U_15749
    | U_15743 != U_15745 ),
    inference(clausify,[status(thm)],[f_3933_3]) ).

cnf(f_3933_5,plain,
    ( c_List_Oremove1(U_15748,U_15744,hAPP(hAPP(c_List_Olist_OCons(U_15748),U_15746),U_15750)) = hAPP(hAPP(c_List_Olist_OCons(U_15748),U_15746),c_List_Oremove1(U_15748,U_15744,U_15750))
    | U_15744 = U_15746 ),
    inference(clausify,[status(thm)],[f_3933_3]) ).

fof(f_3934_1,plain,
    ! [V_list_H,V_a_H,T_a] : hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_H),V_list_H) != c_List_Olist_ONil(T_a),
    inference(fof_nnf,[status(thm)],[fact_list_Osimps_I3_J]) ).

fof(f_3934_2,plain,
    ! [U_15753,U_15752,U_15751] : hAPP(hAPP(c_List_Olist_OCons(U_15751),U_15752),U_15753) != c_List_Olist_ONil(U_15751),
    inference(variable_rename,[status(thm)],[f_3934_1]) ).

cnf(f_3934_3,plain,
    hAPP(hAPP(c_List_Olist_OCons(U_15751),U_15752),U_15753) != c_List_Olist_ONil(U_15751),
    inference(clausify,[status(thm)],[f_3934_2]) ).

fof(f_3935_1,plain,
    ! [V_list_H,V_a_H,T_a] : c_List_Olist_ONil(T_a) != hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_H),V_list_H),
    inference(fof_nnf,[status(thm)],[fact_list_Osimps_I2_J]) ).

fof(f_3935_2,plain,
    ! [U_15756,U_15755,U_15754] : c_List_Olist_ONil(U_15754) != hAPP(hAPP(c_List_Olist_OCons(U_15754),U_15755),U_15756),
    inference(variable_rename,[status(thm)],[f_3935_1]) ).

cnf(f_3935_3,plain,
    c_List_Olist_ONil(U_15754) != hAPP(hAPP(c_List_Olist_OCons(U_15754),U_15755),U_15756),
    inference(clausify,[status(thm)],[f_3935_2]) ).

fof(f_3936_1,plain,
    ! [V_i,V_j] :
      ( c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j),V_i)) ),
    inference(fof_nnf,[status(thm)],[fact_upto__empty]) ).

fof(f_3936_2,plain,
    ! [U_15758,U_15757] :
      ( c_List_Oupto(U_15758,U_15757) = c_List_Olist_ONil(tc_Int_Oint)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_15757),U_15758)) ),
    inference(variable_rename,[status(thm)],[f_3936_1]) ).

cnf(f_3936_3,plain,
    ( c_List_Oupto(U_15758,U_15757) = c_List_Olist_ONil(tc_Int_Oint)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_15757),U_15758)) ),
    inference(clausify,[status(thm)],[f_3936_2]) ).

fof(f_3937_1,plain,
    ! [V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a),
    inference(fof_nnf,[status(thm)],[fact_take__Nil]) ).

fof(f_3937_2,plain,
    ! [U_15760,U_15759] : hAPP(hAPP(c_List_Otake(U_15759),U_15760),c_List_Olist_ONil(U_15759)) = c_List_Olist_ONil(U_15759),
    inference(variable_rename,[status(thm)],[f_3937_1]) ).

cnf(f_3937_3,plain,
    hAPP(hAPP(c_List_Otake(U_15759),U_15760),c_List_Olist_ONil(U_15759)) = c_List_Olist_ONil(U_15759),
    inference(clausify,[status(thm)],[f_3937_2]) ).

fof(f_3938_1,plain,
    ! [V_xs_2,V_n_2,T_b] :
      ( ( hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2) = c_List_Olist_ONil(T_b)
        | ( V_xs_2 != c_List_Olist_ONil(T_b)
          & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( V_xs_2 = c_List_Olist_ONil(T_b)
        | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2) != c_List_Olist_ONil(T_b) ) ),
    inference(fof_nnf,[status(thm)],[fact_take__eq__Nil]) ).

fof(f_3938_2,plain,
    ! [U_15763,U_15762,U_15761] :
      ( ( hAPP(hAPP(c_List_Otake(U_15761),U_15762),U_15763) = c_List_Olist_ONil(U_15761)
        | ( U_15763 != c_List_Olist_ONil(U_15761)
          & U_15762 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( U_15763 = c_List_Olist_ONil(U_15761)
        | U_15762 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_List_Otake(U_15761),U_15762),U_15763) != c_List_Olist_ONil(U_15761) ) ),
    inference(variable_rename,[status(thm)],[f_3938_1]) ).

fof(f_3938_3,plain,
    ( ! [U_15769,U_15767,U_15765] :
        ( hAPP(hAPP(c_List_Otake(U_15765),U_15767),U_15769) = c_List_Olist_ONil(U_15765)
        | ( U_15769 != c_List_Olist_ONil(U_15765)
          & U_15767 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_15768,U_15766,U_15764] :
        ( U_15768 = c_List_Olist_ONil(U_15764)
        | U_15766 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_List_Otake(U_15764),U_15766),U_15768) != c_List_Olist_ONil(U_15764) ) ),
    inference(miniscope,[status(thm)],[f_3938_2]) ).

cnf(f_3938_4,plain,
    ( U_15768 = c_List_Olist_ONil(U_15764)
    | U_15766 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_List_Otake(U_15764),U_15766),U_15768) != c_List_Olist_ONil(U_15764) ),
    inference(clausify,[status(thm)],[f_3938_3]) ).

cnf(f_3938_5,plain,
    ( U_15767 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_List_Otake(U_15765),U_15767),U_15769) = c_List_Olist_ONil(U_15765) ),
    inference(clausify,[status(thm)],[f_3938_3]) ).

cnf(f_3938_6,plain,
    ( U_15769 != c_List_Olist_ONil(U_15765)
    | hAPP(hAPP(c_List_Otake(U_15765),U_15767),U_15769) = c_List_Olist_ONil(U_15765) ),
    inference(clausify,[status(thm)],[f_3938_3]) ).

fof(f_3939_1,plain,
    ! [V_xs,T_a] : hAPP(hAPP(c_List_Otake(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_xs) = c_List_Olist_ONil(T_a),
    inference(fof_nnf,[status(thm)],[fact_take__0]) ).

fof(f_3939_2,plain,
    ! [U_15771,U_15770] : hAPP(hAPP(c_List_Otake(U_15770),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_15771) = c_List_Olist_ONil(U_15770),
    inference(variable_rename,[status(thm)],[f_3939_1]) ).

cnf(f_3939_3,plain,
    hAPP(hAPP(c_List_Otake(U_15770),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_15771) = c_List_Olist_ONil(U_15770),
    inference(clausify,[status(thm)],[f_3939_2]) ).

fof(f_3940_1,plain,
    ! [V_A_2,T_b] : c_List_Osublist(T_b,c_List_Olist_ONil(T_b),V_A_2) = c_List_Olist_ONil(T_b),
    inference(fof_nnf,[status(thm)],[fact_sublist__nil]) ).

fof(f_3940_2,plain,
    ! [U_15773,U_15772] : c_List_Osublist(U_15772,c_List_Olist_ONil(U_15772),U_15773) = c_List_Olist_ONil(U_15772),
    inference(variable_rename,[status(thm)],[f_3940_1]) ).

cnf(f_3940_3,plain,
    c_List_Osublist(U_15772,c_List_Olist_ONil(U_15772),U_15773) = c_List_Olist_ONil(U_15772),
    inference(clausify,[status(thm)],[f_3940_2]) ).

fof(f_3941_1,plain,
    ! [V_x,T_a] : c_List_Oremove1(T_a,V_x,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a),
    inference(fof_nnf,[status(thm)],[fact_remove1_Osimps_I1_J]) ).

fof(f_3941_2,plain,
    ! [U_15775,U_15774] : c_List_Oremove1(U_15774,U_15775,c_List_Olist_ONil(U_15774)) = c_List_Olist_ONil(U_15774),
    inference(variable_rename,[status(thm)],[f_3941_1]) ).

cnf(f_3941_3,plain,
    c_List_Oremove1(U_15774,U_15775,c_List_Olist_ONil(U_15774)) = c_List_Olist_ONil(U_15774),
    inference(clausify,[status(thm)],[f_3941_2]) ).

fof(f_3942_1,plain,
    ! [V_zs,V_y,V_x,T_a] : c_List_Oremove1(T_a,V_x,c_List_Oremove1(T_a,V_y,V_zs)) = c_List_Oremove1(T_a,V_y,c_List_Oremove1(T_a,V_x,V_zs)),
    inference(fof_nnf,[status(thm)],[fact_remove1__commute]) ).

fof(f_3942_2,plain,
    ! [U_15779,U_15778,U_15777,U_15776] : c_List_Oremove1(U_15776,U_15777,c_List_Oremove1(U_15776,U_15778,U_15779)) = c_List_Oremove1(U_15776,U_15778,c_List_Oremove1(U_15776,U_15777,U_15779)),
    inference(variable_rename,[status(thm)],[f_3942_1]) ).

cnf(f_3942_3,plain,
    c_List_Oremove1(U_15776,U_15777,c_List_Oremove1(U_15776,U_15778,U_15779)) = c_List_Oremove1(U_15776,U_15778,c_List_Oremove1(U_15776,U_15777,U_15779)),
    inference(clausify,[status(thm)],[f_3942_2]) ).

fof(f_3943_1,plain,
    ! [V_r_2,T_b] : c_List_Olistrelp(T_b,V_r_2,c_List_Olist_ONil(T_b),c_List_Olist_ONil(T_b)),
    inference(fof_nnf,[status(thm)],[fact_listrelp_ONil]) ).

fof(f_3943_2,plain,
    ! [U_15781,U_15780] : c_List_Olistrelp(U_15780,U_15781,c_List_Olist_ONil(U_15780),c_List_Olist_ONil(U_15780)),
    inference(variable_rename,[status(thm)],[f_3943_1]) ).

cnf(f_3943_3,plain,
    c_List_Olistrelp(U_15780,U_15781,c_List_Olist_ONil(U_15780),c_List_Olist_ONil(U_15780)),
    inference(clausify,[status(thm)],[f_3943_2]) ).

fof(f_3944_1,plain,
    ! [V_r_2,T_b] : c_List_Olistrelp(T_b,V_r_2,c_List_Olist_ONil(T_b),c_List_Olist_ONil(T_b)),
    inference(fof_nnf,[status(thm)],[fact_listrelp_Oequations_I1_J]) ).

fof(f_3944_2,plain,
    ! [U_15783,U_15782] : c_List_Olistrelp(U_15782,U_15783,c_List_Olist_ONil(U_15782),c_List_Olist_ONil(U_15782)),
    inference(variable_rename,[status(thm)],[f_3944_1]) ).

cnf(f_3944_3,plain,
    c_List_Olistrelp(U_15782,U_15783,c_List_Olist_ONil(U_15782),c_List_Olist_ONil(U_15782)),
    inference(clausify,[status(thm)],[f_3944_2]) ).

fof(f_3945_1,plain,
    ! [V_xs,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(tc_prod(T_a,T_b)),
    inference(fof_nnf,[status(thm)],[fact_zip_Osimps_I1_J]) ).

fof(f_3945_2,plain,
    ! [U_15786,U_15785,U_15784] : hAPP(hAPP(c_List_Ozip(U_15784,U_15785),U_15786),c_List_Olist_ONil(U_15785)) = c_List_Olist_ONil(tc_prod(U_15784,U_15785)),
    inference(variable_rename,[status(thm)],[f_3945_1]) ).

cnf(f_3945_3,plain,
    hAPP(hAPP(c_List_Ozip(U_15784,U_15785),U_15786),c_List_Olist_ONil(U_15785)) = c_List_Olist_ONil(tc_prod(U_15784,U_15785)),
    inference(clausify,[status(thm)],[f_3945_2]) ).

fof(f_3946_1,plain,
    ! [V_ys,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),c_List_Olist_ONil(T_a)),V_ys) = c_List_Olist_ONil(tc_prod(T_a,T_b)),
    inference(fof_nnf,[status(thm)],[fact_zip__Nil]) ).

fof(f_3946_2,plain,
    ! [U_15789,U_15788,U_15787] : hAPP(hAPP(c_List_Ozip(U_15787,U_15788),c_List_Olist_ONil(U_15787)),U_15789) = c_List_Olist_ONil(tc_prod(U_15787,U_15788)),
    inference(variable_rename,[status(thm)],[f_3946_1]) ).

cnf(f_3946_3,plain,
    hAPP(hAPP(c_List_Ozip(U_15787,U_15788),c_List_Olist_ONil(U_15787)),U_15789) = c_List_Olist_ONil(tc_prod(U_15787,U_15788)),
    inference(clausify,[status(thm)],[f_3946_2]) ).

fof(f_3947_1,plain,
    ! [V_fa_2,T_b] : c_List_Olist_Olist__size(T_b,V_fa_2,c_List_Olist_ONil(T_b)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_list_Osize_I1_J]) ).

fof(f_3947_2,plain,
    ! [U_15791,U_15790] : c_List_Olist_Olist__size(U_15790,U_15791,c_List_Olist_ONil(U_15790)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_3947_1]) ).

cnf(f_3947_3,plain,
    c_List_Olist_Olist__size(U_15790,U_15791,c_List_Olist_ONil(U_15790)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_3947_2]) ).

fof(f_3948_1,plain,
    ! [T_a] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(T_a),c_List_Olist_ONil(T_a)) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Groups_Omonoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_listsum__simps_I1_J]) ).

fof(f_3948_2,plain,
    ! [U_15792] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_15792),c_List_Olist_ONil(U_15792)) = c_Groups_Ozero__class_Ozero(U_15792)
      | ~ class_Groups_Omonoid__add(U_15792) ),
    inference(variable_rename,[status(thm)],[f_3948_1]) ).

cnf(f_3948_3,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_15792),c_List_Olist_ONil(U_15792)) = c_Groups_Ozero__class_Ozero(U_15792)
    | ~ class_Groups_Omonoid__add(U_15792) ),
    inference(clausify,[status(thm)],[f_3948_2]) ).

fof(f_3949_1,plain,
    ! [V_xs_2,T_b] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | V_xs_2 != c_List_Olist_ONil(T_b) )
      & ( V_xs_2 = c_List_Olist_ONil(T_b)
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(fof_nnf,[status(thm)],[fact_length__0__conv]) ).

fof(f_3949_2,plain,
    ! [U_15794,U_15793] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15793)),U_15794) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_15794 != c_List_Olist_ONil(U_15793) )
      & ( U_15794 = c_List_Olist_ONil(U_15793)
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15793)),U_15794) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_3949_1]) ).

fof(f_3949_3,plain,
    ( ! [U_15798,U_15796] :
        ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15796)),U_15798) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_15798 != c_List_Olist_ONil(U_15796) )
    & ! [U_15797,U_15795] :
        ( U_15797 = c_List_Olist_ONil(U_15795)
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15795)),U_15797) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_3949_2]) ).

cnf(f_3949_4,plain,
    ( U_15797 = c_List_Olist_ONil(U_15795)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15795)),U_15797) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_3949_3]) ).

cnf(f_3949_5,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15796)),U_15798) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_15798 != c_List_Olist_ONil(U_15796) ),
    inference(clausify,[status(thm)],[f_3949_3]) ).

fof(f_3950_1,plain,
    ! [T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_list_Osize_I3_J]) ).

fof(f_3950_2,plain,
    ! [U_15799] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15799)),c_List_Olist_ONil(U_15799)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_3950_1]) ).

cnf(f_3950_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15799)),c_List_Olist_ONil(U_15799)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_3950_2]) ).

fof(f_3951_1,plain,
    ! [T_b] : hAPP(c_List_Oset(T_b),c_List_Olist_ONil(T_b)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    inference(fof_nnf,[status(thm)],[fact_List_Oset_Osimps_I1_J]) ).

fof(f_3951_2,plain,
    ! [U_15800] : hAPP(c_List_Oset(U_15800),c_List_Olist_ONil(U_15800)) = c_Orderings_Obot__class_Obot(tc_fun(U_15800,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3951_1]) ).

cnf(f_3951_3,plain,
    hAPP(c_List_Oset(U_15800),c_List_Olist_ONil(U_15800)) = c_Orderings_Obot__class_Obot(tc_fun(U_15800,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3951_2]) ).

fof(f_3952_1,plain,
    ! [V_xs_2,T_b] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_List_Oset(T_b),V_xs_2)
        | V_xs_2 != c_List_Olist_ONil(T_b) )
      & ( V_xs_2 = c_List_Olist_ONil(T_b)
        | c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) != hAPP(c_List_Oset(T_b),V_xs_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_set__empty2]) ).

fof(f_3952_2,plain,
    ! [U_15802,U_15801] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(U_15801,tc_HOL_Obool)) = hAPP(c_List_Oset(U_15801),U_15802)
        | U_15802 != c_List_Olist_ONil(U_15801) )
      & ( U_15802 = c_List_Olist_ONil(U_15801)
        | c_Orderings_Obot__class_Obot(tc_fun(U_15801,tc_HOL_Obool)) != hAPP(c_List_Oset(U_15801),U_15802) ) ),
    inference(variable_rename,[status(thm)],[f_3952_1]) ).

fof(f_3952_3,plain,
    ( ! [U_15806,U_15804] :
        ( c_Orderings_Obot__class_Obot(tc_fun(U_15804,tc_HOL_Obool)) = hAPP(c_List_Oset(U_15804),U_15806)
        | U_15806 != c_List_Olist_ONil(U_15804) )
    & ! [U_15805,U_15803] :
        ( U_15805 = c_List_Olist_ONil(U_15803)
        | c_Orderings_Obot__class_Obot(tc_fun(U_15803,tc_HOL_Obool)) != hAPP(c_List_Oset(U_15803),U_15805) ) ),
    inference(miniscope,[status(thm)],[f_3952_2]) ).

cnf(f_3952_4,plain,
    ( U_15805 = c_List_Olist_ONil(U_15803)
    | c_Orderings_Obot__class_Obot(tc_fun(U_15803,tc_HOL_Obool)) != hAPP(c_List_Oset(U_15803),U_15805) ),
    inference(clausify,[status(thm)],[f_3952_3]) ).

cnf(f_3952_5,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(U_15804,tc_HOL_Obool)) = hAPP(c_List_Oset(U_15804),U_15806)
    | U_15806 != c_List_Olist_ONil(U_15804) ),
    inference(clausify,[status(thm)],[f_3952_3]) ).

fof(f_3953_1,plain,
    ! [V_xs_2,T_b] :
      ( ( hAPP(c_List_Oset(T_b),V_xs_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
        | V_xs_2 != c_List_Olist_ONil(T_b) )
      & ( V_xs_2 = c_List_Olist_ONil(T_b)
        | hAPP(c_List_Oset(T_b),V_xs_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_set__empty]) ).

fof(f_3953_2,plain,
    ! [U_15808,U_15807] :
      ( ( hAPP(c_List_Oset(U_15807),U_15808) = c_Orderings_Obot__class_Obot(tc_fun(U_15807,tc_HOL_Obool))
        | U_15808 != c_List_Olist_ONil(U_15807) )
      & ( U_15808 = c_List_Olist_ONil(U_15807)
        | hAPP(c_List_Oset(U_15807),U_15808) != c_Orderings_Obot__class_Obot(tc_fun(U_15807,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_3953_1]) ).

fof(f_3953_3,plain,
    ( ! [U_15812,U_15810] :
        ( hAPP(c_List_Oset(U_15810),U_15812) = c_Orderings_Obot__class_Obot(tc_fun(U_15810,tc_HOL_Obool))
        | U_15812 != c_List_Olist_ONil(U_15810) )
    & ! [U_15811,U_15809] :
        ( U_15811 = c_List_Olist_ONil(U_15809)
        | hAPP(c_List_Oset(U_15809),U_15811) != c_Orderings_Obot__class_Obot(tc_fun(U_15809,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_3953_2]) ).

cnf(f_3953_4,plain,
    ( U_15811 = c_List_Olist_ONil(U_15809)
    | hAPP(c_List_Oset(U_15809),U_15811) != c_Orderings_Obot__class_Obot(tc_fun(U_15809,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3953_3]) ).

cnf(f_3953_5,plain,
    ( hAPP(c_List_Oset(U_15810),U_15812) = c_Orderings_Obot__class_Obot(tc_fun(U_15810,tc_HOL_Obool))
    | U_15812 != c_List_Olist_ONil(U_15810) ),
    inference(clausify,[status(thm)],[f_3953_3]) ).

fof(f_3954_1,plain,
    ! [V_x_2,V_k_2,V_xs_2,T_b] :
      ( ( hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_k_2),V_x_2) = c_List_Olist_ONil(T_b)
        | V_xs_2 != c_List_Olist_ONil(T_b) )
      & ( V_xs_2 = c_List_Olist_ONil(T_b)
        | hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_k_2),V_x_2) != c_List_Olist_ONil(T_b) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__update__nonempty]) ).

fof(f_3954_2,plain,
    ! [U_15816,U_15815,U_15814,U_15813] :
      ( ( hAPP(hAPP(c_List_Olist__update(U_15813,U_15814),U_15815),U_15816) = c_List_Olist_ONil(U_15813)
        | U_15814 != c_List_Olist_ONil(U_15813) )
      & ( U_15814 = c_List_Olist_ONil(U_15813)
        | hAPP(hAPP(c_List_Olist__update(U_15813,U_15814),U_15815),U_15816) != c_List_Olist_ONil(U_15813) ) ),
    inference(variable_rename,[status(thm)],[f_3954_1]) ).

fof(f_3954_3,plain,
    ( ! [U_15824,U_15822,U_15820,U_15818] :
        ( hAPP(hAPP(c_List_Olist__update(U_15818,U_15820),U_15822),U_15824) = c_List_Olist_ONil(U_15818)
        | U_15820 != c_List_Olist_ONil(U_15818) )
    & ! [U_15823,U_15821,U_15819,U_15817] :
        ( U_15819 = c_List_Olist_ONil(U_15817)
        | hAPP(hAPP(c_List_Olist__update(U_15817,U_15819),U_15821),U_15823) != c_List_Olist_ONil(U_15817) ) ),
    inference(miniscope,[status(thm)],[f_3954_2]) ).

cnf(f_3954_4,plain,
    ( U_15819 = c_List_Olist_ONil(U_15817)
    | hAPP(hAPP(c_List_Olist__update(U_15817,U_15819),U_15821),U_15823) != c_List_Olist_ONil(U_15817) ),
    inference(clausify,[status(thm)],[f_3954_3]) ).

cnf(f_3954_5,plain,
    ( hAPP(hAPP(c_List_Olist__update(U_15818,U_15820),U_15822),U_15824) = c_List_Olist_ONil(U_15818)
    | U_15820 != c_List_Olist_ONil(U_15818) ),
    inference(clausify,[status(thm)],[f_3954_3]) ).

fof(f_3955_1,plain,
    ! [V_v,V_i,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,c_List_Olist_ONil(T_a)),V_i),V_v) = c_List_Olist_ONil(T_a),
    inference(fof_nnf,[status(thm)],[fact_list__update_Osimps_I1_J]) ).

fof(f_3955_2,plain,
    ! [U_15827,U_15826,U_15825] : hAPP(hAPP(c_List_Olist__update(U_15825,c_List_Olist_ONil(U_15825)),U_15826),U_15827) = c_List_Olist_ONil(U_15825),
    inference(variable_rename,[status(thm)],[f_3955_1]) ).

cnf(f_3955_3,plain,
    hAPP(hAPP(c_List_Olist__update(U_15825,c_List_Olist_ONil(U_15825)),U_15826),U_15827) = c_List_Olist_ONil(U_15825),
    inference(clausify,[status(thm)],[f_3955_2]) ).

fof(f_3956_1,plain,
    ! [V_y,V_i,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,c_List_Olist_ONil(T_a)),V_i),V_y) = c_List_Olist_ONil(T_a),
    inference(fof_nnf,[status(thm)],[fact_list__update__code_I1_J]) ).

fof(f_3956_2,plain,
    ! [U_15830,U_15829,U_15828] : hAPP(hAPP(c_List_Olist__update(U_15828,c_List_Olist_ONil(U_15828)),U_15829),U_15830) = c_List_Olist_ONil(U_15828),
    inference(variable_rename,[status(thm)],[f_3956_1]) ).

cnf(f_3956_3,plain,
    hAPP(hAPP(c_List_Olist__update(U_15828,c_List_Olist_ONil(U_15828)),U_15829),U_15830) = c_List_Olist_ONil(U_15828),
    inference(clausify,[status(thm)],[f_3956_2]) ).

fof(f_3957_1,plain,
    ! [V_xs_2,T_b,V_b_2,V_a_2] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),c_List_Oremove1(T_b,V_b_2,V_xs_2))))
          | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2))) )
        & ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2)))
          | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),c_List_Oremove1(T_b,V_b_2,V_xs_2)))) ) )
      | V_a_2 = V_b_2 ),
    inference(fof_nnf,[status(thm)],[fact_in__set__remove1]) ).

fof(f_3957_2,plain,
    ! [U_15834,U_15833,U_15832,U_15831] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(U_15833),U_15831),hAPP(c_List_Oset(U_15833),c_List_Oremove1(U_15833,U_15832,U_15834))))
          | ~ hBOOL(hAPP(hAPP(c_member(U_15833),U_15831),hAPP(c_List_Oset(U_15833),U_15834))) )
        & ( hBOOL(hAPP(hAPP(c_member(U_15833),U_15831),hAPP(c_List_Oset(U_15833),U_15834)))
          | ~ hBOOL(hAPP(hAPP(c_member(U_15833),U_15831),hAPP(c_List_Oset(U_15833),c_List_Oremove1(U_15833,U_15832,U_15834)))) ) )
      | U_15831 = U_15832 ),
    inference(variable_rename,[status(thm)],[f_3957_1]) ).

cnf(f_3957_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15833),U_15831),hAPP(c_List_Oset(U_15833),U_15834)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15833),U_15831),hAPP(c_List_Oset(U_15833),c_List_Oremove1(U_15833,U_15832,U_15834))))
    | U_15831 = U_15832 ),
    inference(clausify,[status(thm)],[f_3957_2]) ).

cnf(f_3957_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15833),U_15831),hAPP(c_List_Oset(U_15833),c_List_Oremove1(U_15833,U_15832,U_15834))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15833),U_15831),hAPP(c_List_Oset(U_15833),U_15834)))
    | U_15831 = U_15832 ),
    inference(clausify,[status(thm)],[f_3957_2]) ).

fof(f_3958_1,plain,
    ! [V_y_2,V_xs_2,V_x_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Oremove1(T_b,V_y_2,V_xs_2))))
      | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_notin__set__remove1]) ).

fof(f_3958_2,plain,
    ! [U_15838,U_15837,U_15836,U_15835] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_15835),U_15836),hAPP(c_List_Oset(U_15835),c_List_Oremove1(U_15835,U_15838,U_15837))))
      | hBOOL(hAPP(hAPP(c_member(U_15835),U_15836),hAPP(c_List_Oset(U_15835),U_15837))) ),
    inference(variable_rename,[status(thm)],[f_3958_1]) ).

cnf(f_3958_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_15835),U_15836),hAPP(c_List_Oset(U_15835),c_List_Oremove1(U_15835,U_15838,U_15837))))
    | hBOOL(hAPP(hAPP(c_member(U_15835),U_15836),hAPP(c_List_Oset(U_15835),U_15837))) ),
    inference(clausify,[status(thm)],[f_3958_2]) ).

fof(f_3959_1,plain,
    ! [V_xs_2,V_x_2,T_b] :
      ( c_List_Oremove1(T_b,V_x_2,V_xs_2) = V_xs_2
      | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_remove1__idem]) ).

fof(f_3959_2,plain,
    ! [U_15841,U_15840,U_15839] :
      ( c_List_Oremove1(U_15839,U_15840,U_15841) = U_15841
      | hBOOL(hAPP(hAPP(c_member(U_15839),U_15840),hAPP(c_List_Oset(U_15839),U_15841))) ),
    inference(variable_rename,[status(thm)],[f_3959_1]) ).

cnf(f_3959_3,plain,
    ( c_List_Oremove1(U_15839,U_15840,U_15841) = U_15841
    | hBOOL(hAPP(hAPP(c_member(U_15839),U_15840),hAPP(c_List_Oset(U_15839),U_15841))) ),
    inference(clausify,[status(thm)],[f_3959_2]) ).

fof(f_3960_1,plain,
    ! [V_xs_2,T_b] : c_List_Osublist(T_b,V_xs_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) = c_List_Olist_ONil(T_b),
    inference(fof_nnf,[status(thm)],[fact_sublist__empty]) ).

fof(f_3960_2,plain,
    ! [U_15843,U_15842] : c_List_Osublist(U_15842,U_15843,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) = c_List_Olist_ONil(U_15842),
    inference(variable_rename,[status(thm)],[f_3960_1]) ).

cnf(f_3960_3,plain,
    c_List_Osublist(U_15842,U_15843,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) = c_List_Olist_ONil(U_15842),
    inference(clausify,[status(thm)],[f_3960_2]) ).

fof(f_3961_1,plain,
    ! [V_xs_2,V_x_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),c_List_Oremove1(T_b,V_x_2,V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2))),
    inference(fof_nnf,[status(thm)],[fact_set__remove1__subset]) ).

fof(f_3961_2,plain,
    ! [U_15846,U_15845,U_15844] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15844,tc_HOL_Obool)),hAPP(c_List_Oset(U_15844),c_List_Oremove1(U_15844,U_15845,U_15846))),hAPP(c_List_Oset(U_15844),U_15846))),
    inference(variable_rename,[status(thm)],[f_3961_1]) ).

cnf(f_3961_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15844,tc_HOL_Obool)),hAPP(c_List_Oset(U_15844),c_List_Oremove1(U_15844,U_15845,U_15846))),hAPP(c_List_Oset(U_15844),U_15846))),
    inference(clausify,[status(thm)],[f_3961_2]) ).

fof(f_3962_1,plain,
    ! [V_xs_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
        | V_xs_2 = c_List_Olist_ONil(T_b) )
      & ( V_xs_2 != c_List_Olist_ONil(T_b)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_length__greater__0__conv]) ).

fof(f_3962_2,plain,
    ! [U_15848,U_15847] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15847)),U_15848)))
        | U_15848 = c_List_Olist_ONil(U_15847) )
      & ( U_15848 != c_List_Olist_ONil(U_15847)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15847)),U_15848))) ) ),
    inference(variable_rename,[status(thm)],[f_3962_1]) ).

fof(f_3962_3,plain,
    ( ! [U_15852,U_15850] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15850)),U_15852)))
        | U_15852 = c_List_Olist_ONil(U_15850) )
    & ! [U_15851,U_15849] :
        ( U_15851 != c_List_Olist_ONil(U_15849)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15849)),U_15851))) ) ),
    inference(miniscope,[status(thm)],[f_3962_2]) ).

cnf(f_3962_4,plain,
    ( U_15851 != c_List_Olist_ONil(U_15849)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15849)),U_15851))) ),
    inference(clausify,[status(thm)],[f_3962_3]) ).

cnf(f_3962_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15850)),U_15852)))
    | U_15852 = c_List_Olist_ONil(U_15850) ),
    inference(clausify,[status(thm)],[f_3962_3]) ).

fof(f_3963_1,plain,
    ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Otake(T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a)),
    inference(fof_nnf,[status(thm)],[fact_take__1__Cons]) ).

fof(f_3963_2,plain,
    ! [U_15855,U_15854,U_15853] : hAPP(hAPP(c_List_Otake(U_15853),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(U_15853),U_15854),U_15855)) = hAPP(hAPP(c_List_Olist_OCons(U_15853),U_15854),c_List_Olist_ONil(U_15853)),
    inference(variable_rename,[status(thm)],[f_3963_1]) ).

cnf(f_3963_3,plain,
    hAPP(hAPP(c_List_Otake(U_15853),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(U_15853),U_15854),U_15855)) = hAPP(hAPP(c_List_Olist_OCons(U_15853),U_15854),c_List_Olist_ONil(U_15853)),
    inference(clausify,[status(thm)],[f_3963_2]) ).

fof(f_3964_1,plain,
    ! [V_r_2,V_xs_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_xs_2)),c_List_Olistrel1(T_b,V_r_2))),
    inference(fof_nnf,[status(thm)],[fact_not__Nil__listrel1]) ).

fof(f_3964_2,plain,
    ! [U_15858,U_15857,U_15856] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15856),tc_List_Olist(U_15856))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15856),tc_List_Olist(U_15856)),c_List_Olist_ONil(U_15856)),U_15857)),c_List_Olistrel1(U_15856,U_15858))),
    inference(variable_rename,[status(thm)],[f_3964_1]) ).

cnf(f_3964_3,plain,
    ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15856),tc_List_Olist(U_15856))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15856),tc_List_Olist(U_15856)),c_List_Olist_ONil(U_15856)),U_15857)),c_List_Olistrel1(U_15856,U_15858))),
    inference(clausify,[status(thm)],[f_3964_2]) ).

fof(f_3965_1,plain,
    ! [V_r_2,V_xs_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),c_List_Olist_ONil(T_b))),c_List_Olistrel1(T_b,V_r_2))),
    inference(fof_nnf,[status(thm)],[fact_not__listrel1__Nil]) ).

fof(f_3965_2,plain,
    ! [U_15861,U_15860,U_15859] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15859),tc_List_Olist(U_15859))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15859),tc_List_Olist(U_15859)),U_15860),c_List_Olist_ONil(U_15859))),c_List_Olistrel1(U_15859,U_15861))),
    inference(variable_rename,[status(thm)],[f_3965_1]) ).

cnf(f_3965_3,plain,
    ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15859),tc_List_Olist(U_15859))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15859),tc_List_Olist(U_15859)),U_15860),c_List_Olist_ONil(U_15859))),c_List_Olistrel1(U_15859,U_15861))),
    inference(clausify,[status(thm)],[f_3965_2]) ).

fof(f_3966_1,plain,
    ! [V_r_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_List_Olist_ONil(T_b))),c_List_Olistrel(T_b,V_r_2))),
    inference(fof_nnf,[status(thm)],[fact_listrel_ONil]) ).

fof(f_3966_2,plain,
    ! [U_15863,U_15862] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15862),tc_List_Olist(U_15862))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15862),tc_List_Olist(U_15862)),c_List_Olist_ONil(U_15862)),c_List_Olist_ONil(U_15862))),c_List_Olistrel(U_15862,U_15863))),
    inference(variable_rename,[status(thm)],[f_3966_1]) ).

cnf(f_3966_3,plain,
    hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15862),tc_List_Olist(U_15862))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15862),tc_List_Olist(U_15862)),c_List_Olist_ONil(U_15862)),c_List_Olist_ONil(U_15862))),c_List_Olistrel(U_15862,U_15863))),
    inference(clausify,[status(thm)],[f_3966_2]) ).

fof(f_3967_1,plain,
    ! [V_r_2,V_x_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),c_List_Olist_ONil(T_b))),c_List_Olexord(T_b,V_r_2))),
    inference(fof_nnf,[status(thm)],[fact_lexord__Nil__right]) ).

fof(f_3967_2,plain,
    ! [U_15866,U_15865,U_15864] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15864),tc_List_Olist(U_15864))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15864),tc_List_Olist(U_15864)),U_15865),c_List_Olist_ONil(U_15864))),c_List_Olexord(U_15864,U_15866))),
    inference(variable_rename,[status(thm)],[f_3967_1]) ).

cnf(f_3967_3,plain,
    ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15864),tc_List_Olist(U_15864))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15864),tc_List_Olist(U_15864)),U_15865),c_List_Olist_ONil(U_15864))),c_List_Olexord(U_15864,U_15866))),
    inference(clausify,[status(thm)],[f_3967_2]) ).

fof(f_3968_1,plain,
    ! [V_r_2,V_ys_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_ys_2)),c_List_Olex(T_b,V_r_2))),
    inference(fof_nnf,[status(thm)],[fact_Nil__notin__lex]) ).

fof(f_3968_2,plain,
    ! [U_15869,U_15868,U_15867] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15867),tc_List_Olist(U_15867))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15867),tc_List_Olist(U_15867)),c_List_Olist_ONil(U_15867)),U_15868)),c_List_Olex(U_15867,U_15869))),
    inference(variable_rename,[status(thm)],[f_3968_1]) ).

cnf(f_3968_3,plain,
    ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15867),tc_List_Olist(U_15867))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15867),tc_List_Olist(U_15867)),c_List_Olist_ONil(U_15867)),U_15868)),c_List_Olex(U_15867,U_15869))),
    inference(clausify,[status(thm)],[f_3968_2]) ).

fof(f_3969_1,plain,
    ! [V_r_2,V_xs_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),c_List_Olist_ONil(T_b))),c_List_Olex(T_b,V_r_2))),
    inference(fof_nnf,[status(thm)],[fact_Nil2__notin__lex]) ).

fof(f_3969_2,plain,
    ! [U_15872,U_15871,U_15870] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15870),tc_List_Olist(U_15870))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15870),tc_List_Olist(U_15870)),U_15871),c_List_Olist_ONil(U_15870))),c_List_Olex(U_15870,U_15872))),
    inference(variable_rename,[status(thm)],[f_3969_1]) ).

cnf(f_3969_3,plain,
    ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_15870),tc_List_Olist(U_15870))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15870),tc_List_Olist(U_15870)),U_15871),c_List_Olist_ONil(U_15870))),c_List_Olex(U_15870,U_15872))),
    inference(clausify,[status(thm)],[f_3969_2]) ).

fof(f_3970_1,plain,
    ! [V_xs_2,V_x_2,V_n_2,T_b] : hAPP(hAPP(c_List_Otake(T_b),V_n_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_Nat_Onat_Onat__case(tc_List_Olist(T_b),c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_Nat_Onat),hAPP(c_List_Olist_OCons(T_b),V_x_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Otake(T_b)),V_xs_2)),V_n_2),
    inference(fof_nnf,[status(thm)],[fact_take__Cons]) ).

fof(f_3970_2,plain,
    ! [U_15876,U_15875,U_15874,U_15873] : hAPP(hAPP(c_List_Otake(U_15873),U_15874),hAPP(hAPP(c_List_Olist_OCons(U_15873),U_15875),U_15876)) = c_Nat_Onat_Onat__case(tc_List_Olist(U_15873),c_List_Olist_ONil(U_15873),hAPP(hAPP(c_COMBB(tc_List_Olist(U_15873),tc_List_Olist(U_15873),tc_Nat_Onat),hAPP(c_List_Olist_OCons(U_15873),U_15875)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(U_15873),tc_List_Olist(U_15873)),c_List_Otake(U_15873)),U_15876)),U_15874),
    inference(variable_rename,[status(thm)],[f_3970_1]) ).

cnf(f_3970_3,plain,
    hAPP(hAPP(c_List_Otake(U_15873),U_15874),hAPP(hAPP(c_List_Olist_OCons(U_15873),U_15875),U_15876)) = c_Nat_Onat_Onat__case(tc_List_Olist(U_15873),c_List_Olist_ONil(U_15873),hAPP(hAPP(c_COMBB(tc_List_Olist(U_15873),tc_List_Olist(U_15873),tc_Nat_Onat),hAPP(c_List_Olist_OCons(U_15873),U_15875)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(U_15873),tc_List_Olist(U_15873)),c_List_Otake(U_15873)),U_15876)),U_15874),
    inference(clausify,[status(thm)],[f_3970_2]) ).

fof(f_3971_1,plain,
    ! [V_j,V_i] :
      ( ( c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) )
      & ( c_List_Oupto(V_i,V_j) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),V_i),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_j))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) ) ),
    inference(fof_nnf,[status(thm)],[fact_upto_Osimps]) ).

fof(f_3971_2,plain,
    ! [U_15878,U_15877] :
      ( ( c_List_Oupto(U_15877,U_15878) = c_List_Olist_ONil(tc_Int_Oint)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_15877),U_15878)) )
      & ( c_List_Oupto(U_15877,U_15878) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),U_15877),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_15877),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_15878))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_15877),U_15878)) ) ),
    inference(variable_rename,[status(thm)],[f_3971_1]) ).

fof(f_3971_3,plain,
    ( ! [U_15882,U_15880] :
        ( c_List_Oupto(U_15880,U_15882) = c_List_Olist_ONil(tc_Int_Oint)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_15880),U_15882)) )
    & ! [U_15881,U_15879] :
        ( c_List_Oupto(U_15879,U_15881) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),U_15879),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_15879),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_15881))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_15879),U_15881)) ) ),
    inference(miniscope,[status(thm)],[f_3971_2]) ).

cnf(f_3971_4,plain,
    ( c_List_Oupto(U_15879,U_15881) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),U_15879),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_15879),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_15881))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_15879),U_15881)) ),
    inference(clausify,[status(thm)],[f_3971_3]) ).

cnf(f_3971_5,plain,
    ( c_List_Oupto(U_15880,U_15882) = c_List_Olist_ONil(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_15880),U_15882)) ),
    inference(clausify,[status(thm)],[f_3971_3]) ).

fof(f_3972_1,plain,
    ! [V_x_2,T_b,V_A_2] :
      ( ( c_List_Osublist(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)),V_A_2) = c_List_Olist_ONil(T_b)
        | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2)) )
      & ( c_List_Osublist(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)),V_A_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_sublist__singleton]) ).

fof(f_3972_2,plain,
    ! [U_15885,U_15884,U_15883] :
      ( ( c_List_Osublist(U_15884,hAPP(hAPP(c_List_Olist_OCons(U_15884),U_15885),c_List_Olist_ONil(U_15884)),U_15883) = c_List_Olist_ONil(U_15884)
        | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_15883)) )
      & ( c_List_Osublist(U_15884,hAPP(hAPP(c_List_Olist_OCons(U_15884),U_15885),c_List_Olist_ONil(U_15884)),U_15883) = hAPP(hAPP(c_List_Olist_OCons(U_15884),U_15885),c_List_Olist_ONil(U_15884))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_15883)) ) ),
    inference(variable_rename,[status(thm)],[f_3972_1]) ).

fof(f_3972_3,plain,
    ( ! [U_15891,U_15889,U_15887] :
        ( c_List_Osublist(U_15889,hAPP(hAPP(c_List_Olist_OCons(U_15889),U_15891),c_List_Olist_ONil(U_15889)),U_15887) = c_List_Olist_ONil(U_15889)
        | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_15887)) )
    & ! [U_15890,U_15888,U_15886] :
        ( c_List_Osublist(U_15888,hAPP(hAPP(c_List_Olist_OCons(U_15888),U_15890),c_List_Olist_ONil(U_15888)),U_15886) = hAPP(hAPP(c_List_Olist_OCons(U_15888),U_15890),c_List_Olist_ONil(U_15888))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_15886)) ) ),
    inference(miniscope,[status(thm)],[f_3972_2]) ).

cnf(f_3972_4,plain,
    ( c_List_Osublist(U_15888,hAPP(hAPP(c_List_Olist_OCons(U_15888),U_15890),c_List_Olist_ONil(U_15888)),U_15886) = hAPP(hAPP(c_List_Olist_OCons(U_15888),U_15890),c_List_Olist_ONil(U_15888))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_15886)) ),
    inference(clausify,[status(thm)],[f_3972_3]) ).

cnf(f_3972_5,plain,
    ( c_List_Osublist(U_15889,hAPP(hAPP(c_List_Olist_OCons(U_15889),U_15891),c_List_Olist_ONil(U_15889)),U_15887) = c_List_Olist_ONil(U_15889)
    | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_15887)) ),
    inference(clausify,[status(thm)],[f_3972_3]) ).

fof(f_3973_1,plain,
    ! [T_b] : c_List_Olists(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),
    inference(fof_nnf,[status(thm)],[fact_lists__empty]) ).

fof(f_3973_2,plain,
    ! [U_15892] : c_List_Olists(U_15892,c_Orderings_Obot__class_Obot(tc_fun(U_15892,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_15892)),c_List_Olist_ONil(U_15892)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_15892),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_3973_1]) ).

cnf(f_3973_3,plain,
    c_List_Olists(U_15892,c_Orderings_Obot__class_Obot(tc_fun(U_15892,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_15892)),c_List_Olist_ONil(U_15892)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_15892),tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_3973_2]) ).

fof(f_3974_1,plain,
    ! [V_xs,V_x,T_a,V_n] :
      ( ( hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs))
        | V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a)
        | V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(fof_nnf,[status(thm)],[fact_take__Cons_H]) ).

fof(f_3974_2,plain,
    ! [U_15896,U_15895,U_15894,U_15893] :
      ( ( hAPP(hAPP(c_List_Otake(U_15894),U_15893),hAPP(hAPP(c_List_Olist_OCons(U_15894),U_15895),U_15896)) = hAPP(hAPP(c_List_Olist_OCons(U_15894),U_15895),hAPP(hAPP(c_List_Otake(U_15894),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_15893),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_15896))
        | U_15893 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_List_Otake(U_15894),U_15893),hAPP(hAPP(c_List_Olist_OCons(U_15894),U_15895),U_15896)) = c_List_Olist_ONil(U_15894)
        | U_15893 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_3974_1]) ).

fof(f_3974_3,plain,
    ( ! [U_15904,U_15902,U_15900,U_15898] :
        ( hAPP(hAPP(c_List_Otake(U_15900),U_15898),hAPP(hAPP(c_List_Olist_OCons(U_15900),U_15902),U_15904)) = hAPP(hAPP(c_List_Olist_OCons(U_15900),U_15902),hAPP(hAPP(c_List_Otake(U_15900),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_15898),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_15904))
        | U_15898 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_15903,U_15901,U_15899,U_15897] :
        ( hAPP(hAPP(c_List_Otake(U_15899),U_15897),hAPP(hAPP(c_List_Olist_OCons(U_15899),U_15901),U_15903)) = c_List_Olist_ONil(U_15899)
        | U_15897 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_3974_2]) ).

cnf(f_3974_4,plain,
    ( hAPP(hAPP(c_List_Otake(U_15899),U_15897),hAPP(hAPP(c_List_Olist_OCons(U_15899),U_15901),U_15903)) = c_List_Olist_ONil(U_15899)
    | U_15897 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_3974_3]) ).

cnf(f_3974_5,plain,
    ( hAPP(hAPP(c_List_Otake(U_15900),U_15898),hAPP(hAPP(c_List_Olist_OCons(U_15900),U_15902),U_15904)) = hAPP(hAPP(c_List_Olist_OCons(U_15900),U_15902),hAPP(hAPP(c_List_Otake(U_15900),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_15898),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_15904))
    | U_15898 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_3974_3]) ).

fof(f_3975_1,plain,
    ! [V_n,V_m] :
      ( ( c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n)) = c_List_Olist_ONil(tc_Int_Oint)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n))) )
      & ( c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m)),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n))) ) ),
    inference(fof_nnf,[status(thm)],[fact_upto__rec__number__of]) ).

fof(f_3975_2,plain,
    ! [U_15906,U_15905] :
      ( ( c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_15905),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_15906)) = c_List_Olist_ONil(tc_Int_Oint)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_15905)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_15906))) )
      & ( c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_15905),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_15906)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_15905)),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_15905)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_15906)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_15905)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_15906))) ) ),
    inference(variable_rename,[status(thm)],[f_3975_1]) ).

fof(f_3975_3,plain,
    ( ! [U_15910,U_15908] :
        ( c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_15908),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_15910)) = c_List_Olist_ONil(tc_Int_Oint)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_15908)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_15910))) )
    & ! [U_15909,U_15907] :
        ( c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_15907),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_15909)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_15907)),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_15907)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_15909)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_15907)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_15909))) ) ),
    inference(miniscope,[status(thm)],[f_3975_2]) ).

cnf(f_3975_4,plain,
    ( c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_15907),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_15909)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_15907)),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_15907)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_15909)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_15907)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_15909))) ),
    inference(clausify,[status(thm)],[f_3975_3]) ).

cnf(f_3975_5,plain,
    ( c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_15908),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_15910)) = c_List_Olist_ONil(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_15908)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_15910))) ),
    inference(clausify,[status(thm)],[f_3975_3]) ).

fof(f_3976_1,plain,
    ! [V_r_2,T_b] : hAPP(c_Relation_OImage(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),
    inference(fof_nnf,[status(thm)],[fact_listrel__Nil]) ).

fof(f_3976_2,plain,
    ! [U_15912,U_15911] : hAPP(c_Relation_OImage(tc_List_Olist(U_15911),tc_List_Olist(U_15911),c_List_Olistrel(U_15911,U_15912)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_15911)),c_List_Olist_ONil(U_15911)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_15911),tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_15911)),c_List_Olist_ONil(U_15911)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_15911),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_3976_1]) ).

cnf(f_3976_3,plain,
    hAPP(c_Relation_OImage(tc_List_Olist(U_15911),tc_List_Olist(U_15911),c_List_Olistrel(U_15911,U_15912)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_15911)),c_List_Olist_ONil(U_15911)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_15911),tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_15911)),c_List_Olist_ONil(U_15911)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_15911),tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_3976_2]) ).

fof(f_3977_1,plain,
    ! [V_A_2,T_b] : c_List_Oset__Cons(T_b,V_A_2,hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))) = hAPP(c_Set_Oimage(T_b,tc_List_Olist(T_b),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b))),V_A_2),
    inference(fof_nnf,[status(thm)],[fact_set__Cons__sing__Nil]) ).

fof(f_3977_2,plain,
    ! [U_15914,U_15913] : c_List_Oset__Cons(U_15913,U_15914,hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_15913)),c_List_Olist_ONil(U_15913)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_15913),tc_HOL_Obool)))) = hAPP(c_Set_Oimage(U_15913,tc_List_Olist(U_15913),hAPP(hAPP(c_COMBC(U_15913,tc_List_Olist(U_15913),tc_List_Olist(U_15913)),c_List_Olist_OCons(U_15913)),c_List_Olist_ONil(U_15913))),U_15914),
    inference(variable_rename,[status(thm)],[f_3977_1]) ).

cnf(f_3977_3,plain,
    c_List_Oset__Cons(U_15913,U_15914,hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_15913)),c_List_Olist_ONil(U_15913)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_15913),tc_HOL_Obool)))) = hAPP(c_Set_Oimage(U_15913,tc_List_Olist(U_15913),hAPP(hAPP(c_COMBC(U_15913,tc_List_Olist(U_15913),tc_List_Olist(U_15913)),c_List_Olist_OCons(U_15913)),c_List_Olist_ONil(U_15913))),U_15914),
    inference(clausify,[status(thm)],[f_3977_2]) ).

fof(f_3978_1,plain,
    ! [V_xs_2,V_x_2,T_b] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremove1(T_b,V_x_2,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)
        | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) )
      & ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremove1(T_b,V_x_2,V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_length__remove1]) ).

fof(f_3978_2,plain,
    ! [U_15917,U_15916,U_15915] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15915)),c_List_Oremove1(U_15915,U_15916,U_15917)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15915)),U_15917)
        | hBOOL(hAPP(hAPP(c_member(U_15915),U_15916),hAPP(c_List_Oset(U_15915),U_15917))) )
      & ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15915)),c_List_Oremove1(U_15915,U_15916,U_15917)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15915)),U_15917)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | ~ hBOOL(hAPP(hAPP(c_member(U_15915),U_15916),hAPP(c_List_Oset(U_15915),U_15917))) ) ),
    inference(variable_rename,[status(thm)],[f_3978_1]) ).

fof(f_3978_3,plain,
    ( ! [U_15923,U_15921,U_15919] :
        ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15919)),c_List_Oremove1(U_15919,U_15921,U_15923)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15919)),U_15923)
        | hBOOL(hAPP(hAPP(c_member(U_15919),U_15921),hAPP(c_List_Oset(U_15919),U_15923))) )
    & ! [U_15922,U_15920,U_15918] :
        ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15918)),c_List_Oremove1(U_15918,U_15920,U_15922)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15918)),U_15922)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | ~ hBOOL(hAPP(hAPP(c_member(U_15918),U_15920),hAPP(c_List_Oset(U_15918),U_15922))) ) ),
    inference(miniscope,[status(thm)],[f_3978_2]) ).

cnf(f_3978_4,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15918)),c_List_Oremove1(U_15918,U_15920,U_15922)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15918)),U_15922)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15918),U_15920),hAPP(c_List_Oset(U_15918),U_15922))) ),
    inference(clausify,[status(thm)],[f_3978_3]) ).

cnf(f_3978_5,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15919)),c_List_Oremove1(U_15919,U_15921,U_15923)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15919)),U_15923)
    | hBOOL(hAPP(hAPP(c_member(U_15919),U_15921),hAPP(c_List_Oset(U_15919),U_15923))) ),
    inference(clausify,[status(thm)],[f_3978_3]) ).

fof(f_3979_1,plain,
    ! [V_j_2,V_i_2] :
      ( ( ( c_List_Oupto(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Int_Oint)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2)) )
        & ( c_List_Oupto(V_i_2,V_j_2) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),V_i_2),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_j_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2)) ) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_i_2),V_j_2))) ),
    inference(fof_nnf,[status(thm)],[fact_upto_Opsimps]) ).

fof(f_3979_2,plain,
    ! [U_15925,U_15924] :
      ( ( ( c_List_Oupto(U_15924,U_15925) = c_List_Olist_ONil(tc_Int_Oint)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_15924),U_15925)) )
        & ( c_List_Oupto(U_15924,U_15925) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),U_15924),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_15924),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_15925))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_15924),U_15925)) ) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_15924),U_15925))) ),
    inference(variable_rename,[status(thm)],[f_3979_1]) ).

cnf(f_3979_3,plain,
    ( c_List_Oupto(U_15924,U_15925) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),U_15924),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_15924),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_15925))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_15924),U_15925))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_15924),U_15925))) ),
    inference(clausify,[status(thm)],[f_3979_2]) ).

cnf(f_3979_4,plain,
    ( c_List_Oupto(U_15924,U_15925) = c_List_Olist_ONil(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_15924),U_15925))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_15924),U_15925))) ),
    inference(clausify,[status(thm)],[f_3979_2]) ).

fof(f_3980_1,plain,
    ! [V_s_2,T_b,V_xs_2] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Product__Type_Ofst(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect(T_b,V_xs_2),V_s_2))),hAPP(c_List_Oset(T_b),V_xs_2)))
      | V_xs_2 = c_List_Olist_ONil(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_select]) ).

fof(f_3980_2,plain,
    ! [U_15928,U_15927,U_15926] :
      ( hBOOL(hAPP(hAPP(c_member(U_15927),hAPP(c_Product__Type_Ofst(U_15927,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect(U_15927,U_15926),U_15928))),hAPP(c_List_Oset(U_15927),U_15926)))
      | U_15926 = c_List_Olist_ONil(U_15927) ),
    inference(variable_rename,[status(thm)],[f_3980_1]) ).

cnf(f_3980_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15927),hAPP(c_Product__Type_Ofst(U_15927,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect(U_15927,U_15926),U_15928))),hAPP(c_List_Oset(U_15927),U_15926)))
    | U_15926 = c_List_Olist_ONil(U_15927) ),
    inference(clausify,[status(thm)],[f_3980_2]) ).

fof(f_3981_1,plain,
    ! [T_b] : c_List_Olistset(T_b,c_List_Olist_ONil(tc_fun(T_b,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),
    inference(fof_nnf,[status(thm)],[fact_listset_Osimps_I1_J]) ).

fof(f_3981_2,plain,
    ! [U_15929] : c_List_Olistset(U_15929,c_List_Olist_ONil(tc_fun(U_15929,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_15929)),c_List_Olist_ONil(U_15929)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_15929),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_3981_1]) ).

cnf(f_3981_3,plain,
    c_List_Olistset(U_15929,c_List_Olist_ONil(tc_fun(U_15929,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_15929)),c_List_Olist_ONil(U_15929)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_15929),tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_3981_2]) ).

fof(f_3982_1,plain,
    ! [V_ys_2,V_xs_2,V_x_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_ys_2) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(T_b,T_c)),T_c,c_List_Olist_ONil(tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c)))),T_c),c_COMBB(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(T_c))),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c))),T_c),c_List_Olist_OCons(tc_prod(T_b,T_c))),hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2)))),hAPP(c_List_Ozip(T_b,T_c),V_xs_2))),V_ys_2),
    inference(fof_nnf,[status(thm)],[fact_zip__Cons1]) ).

fof(f_3982_2,plain,
    ! [U_15934,U_15933,U_15932,U_15931,U_15930] : hAPP(hAPP(c_List_Ozip(U_15930,U_15931),hAPP(hAPP(c_List_Olist_OCons(U_15930),U_15932),U_15933)),U_15934) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(U_15930,U_15931)),U_15931,c_List_Olist_ONil(tc_prod(U_15930,U_15931)),hAPP(hAPP(c_COMBC(U_15931,tc_fun(tc_List_Olist(U_15931),tc_List_Olist(tc_prod(U_15930,U_15931))),tc_fun(tc_List_Olist(U_15931),tc_List_Olist(tc_prod(U_15930,U_15931)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(U_15930,U_15931)),tc_List_Olist(tc_prod(U_15930,U_15931))),tc_fun(tc_fun(tc_List_Olist(U_15931),tc_List_Olist(tc_prod(U_15930,U_15931))),tc_fun(tc_List_Olist(U_15931),tc_List_Olist(tc_prod(U_15930,U_15931)))),U_15931),c_COMBB(tc_List_Olist(tc_prod(U_15930,U_15931)),tc_List_Olist(tc_prod(U_15930,U_15931)),tc_List_Olist(U_15931))),hAPP(hAPP(c_COMBB(tc_prod(U_15930,U_15931),tc_fun(tc_List_Olist(tc_prod(U_15930,U_15931)),tc_List_Olist(tc_prod(U_15930,U_15931))),U_15931),c_List_Olist_OCons(tc_prod(U_15930,U_15931))),hAPP(c_Product__Type_OPair(U_15930,U_15931),U_15932)))),hAPP(c_List_Ozip(U_15930,U_15931),U_15933))),U_15934),
    inference(variable_rename,[status(thm)],[f_3982_1]) ).

cnf(f_3982_3,plain,
    hAPP(hAPP(c_List_Ozip(U_15930,U_15931),hAPP(hAPP(c_List_Olist_OCons(U_15930),U_15932),U_15933)),U_15934) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(U_15930,U_15931)),U_15931,c_List_Olist_ONil(tc_prod(U_15930,U_15931)),hAPP(hAPP(c_COMBC(U_15931,tc_fun(tc_List_Olist(U_15931),tc_List_Olist(tc_prod(U_15930,U_15931))),tc_fun(tc_List_Olist(U_15931),tc_List_Olist(tc_prod(U_15930,U_15931)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(U_15930,U_15931)),tc_List_Olist(tc_prod(U_15930,U_15931))),tc_fun(tc_fun(tc_List_Olist(U_15931),tc_List_Olist(tc_prod(U_15930,U_15931))),tc_fun(tc_List_Olist(U_15931),tc_List_Olist(tc_prod(U_15930,U_15931)))),U_15931),c_COMBB(tc_List_Olist(tc_prod(U_15930,U_15931)),tc_List_Olist(tc_prod(U_15930,U_15931)),tc_List_Olist(U_15931))),hAPP(hAPP(c_COMBB(tc_prod(U_15930,U_15931),tc_fun(tc_List_Olist(tc_prod(U_15930,U_15931)),tc_List_Olist(tc_prod(U_15930,U_15931))),U_15931),c_List_Olist_OCons(tc_prod(U_15930,U_15931))),hAPP(c_Product__Type_OPair(U_15930,U_15931),U_15932)))),hAPP(c_List_Ozip(U_15930,U_15931),U_15933))),U_15934),
    inference(clausify,[status(thm)],[f_3982_2]) ).

fof(f_3983_1,plain,
    ! [V_list_2,V_a_2,V_f2_2,V_f1_2,T_c,T_b] : hAPP(c_List_Olist_Olist__case(T_b,T_c,V_f1_2,V_f2_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_a_2),V_list_2)) = hAPP(hAPP(V_f2_2,V_a_2),V_list_2),
    inference(fof_nnf,[status(thm)],[fact_list_Osimps_I5_J]) ).

fof(f_3983_2,plain,
    ! [U_15940,U_15939,U_15938,U_15937,U_15936,U_15935] : hAPP(c_List_Olist_Olist__case(U_15935,U_15936,U_15937,U_15938),hAPP(hAPP(c_List_Olist_OCons(U_15936),U_15939),U_15940)) = hAPP(hAPP(U_15938,U_15939),U_15940),
    inference(variable_rename,[status(thm)],[f_3983_1]) ).

cnf(f_3983_3,plain,
    hAPP(c_List_Olist_Olist__case(U_15935,U_15936,U_15937,U_15938),hAPP(hAPP(c_List_Olist_OCons(U_15936),U_15939),U_15940)) = hAPP(hAPP(U_15938,U_15939),U_15940),
    inference(clausify,[status(thm)],[f_3983_2]) ).

fof(f_3984_1,plain,
    ! [V_f2_2,V_f1_2,T_c,T_b] : hAPP(c_List_Olist_Olist__case(T_b,T_c,V_f1_2,V_f2_2),c_List_Olist_ONil(T_c)) = V_f1_2,
    inference(fof_nnf,[status(thm)],[fact_list_Osimps_I4_J]) ).

fof(f_3984_2,plain,
    ! [U_15944,U_15943,U_15942,U_15941] : hAPP(c_List_Olist_Olist__case(U_15941,U_15942,U_15943,U_15944),c_List_Olist_ONil(U_15942)) = U_15943,
    inference(variable_rename,[status(thm)],[f_3984_1]) ).

cnf(f_3984_3,plain,
    hAPP(c_List_Olist_Olist__case(U_15941,U_15942,U_15943,U_15944),c_List_Olist_ONil(U_15942)) = U_15943,
    inference(clausify,[status(thm)],[f_3984_2]) ).

fof(f_3985_1,plain,
    ! [V_As_2,V_A_2,T_b] : c_List_Olistset(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_As_2)) = c_List_Oset__Cons(T_b,V_A_2,c_List_Olistset(T_b,V_As_2)),
    inference(fof_nnf,[status(thm)],[fact_listset_Osimps_I2_J]) ).

fof(f_3985_2,plain,
    ! [U_15947,U_15946,U_15945] : c_List_Olistset(U_15945,hAPP(hAPP(c_List_Olist_OCons(tc_fun(U_15945,tc_HOL_Obool)),U_15946),U_15947)) = c_List_Oset__Cons(U_15945,U_15946,c_List_Olistset(U_15945,U_15947)),
    inference(variable_rename,[status(thm)],[f_3985_1]) ).

cnf(f_3985_3,plain,
    c_List_Olistset(U_15945,hAPP(hAPP(c_List_Olist_OCons(tc_fun(U_15945,tc_HOL_Obool)),U_15946),U_15947)) = c_List_Oset__Cons(U_15945,U_15946,c_List_Olistset(U_15945,U_15947)),
    inference(clausify,[status(thm)],[f_3985_2]) ).

fof(f_3986_1,plain,
    ! [V_ys_2,V_y_2,V_xs_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(T_b,T_c)),T_b,c_List_Olist_ONil(tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_b,T_c)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_b,T_c)))),T_b),c_COMBB(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c))),T_b),c_List_Olist_OCons(tc_prod(T_b,T_c))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_prod(T_b,T_c)),c_Product__Type_OPair(T_b,T_c)),V_y_2)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c))),c_List_Ozip(T_b,T_c)),V_ys_2))),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_zip__Cons]) ).

fof(f_3986_2,plain,
    ! [U_15952,U_15951,U_15950,U_15949,U_15948] : hAPP(hAPP(c_List_Ozip(U_15948,U_15949),U_15950),hAPP(hAPP(c_List_Olist_OCons(U_15949),U_15951),U_15952)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(U_15948,U_15949)),U_15948,c_List_Olist_ONil(tc_prod(U_15948,U_15949)),hAPP(hAPP(c_COMBC(U_15948,tc_fun(tc_List_Olist(U_15948),tc_List_Olist(tc_prod(U_15948,U_15949))),tc_fun(tc_List_Olist(U_15948),tc_List_Olist(tc_prod(U_15948,U_15949)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(U_15948,U_15949)),tc_List_Olist(tc_prod(U_15948,U_15949))),tc_fun(tc_fun(tc_List_Olist(U_15948),tc_List_Olist(tc_prod(U_15948,U_15949))),tc_fun(tc_List_Olist(U_15948),tc_List_Olist(tc_prod(U_15948,U_15949)))),U_15948),c_COMBB(tc_List_Olist(tc_prod(U_15948,U_15949)),tc_List_Olist(tc_prod(U_15948,U_15949)),tc_List_Olist(U_15948))),hAPP(hAPP(c_COMBB(tc_prod(U_15948,U_15949),tc_fun(tc_List_Olist(tc_prod(U_15948,U_15949)),tc_List_Olist(tc_prod(U_15948,U_15949))),U_15948),c_List_Olist_OCons(tc_prod(U_15948,U_15949))),hAPP(hAPP(c_COMBC(U_15948,U_15949,tc_prod(U_15948,U_15949)),c_Product__Type_OPair(U_15948,U_15949)),U_15951)))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_15948),tc_List_Olist(U_15949),tc_List_Olist(tc_prod(U_15948,U_15949))),c_List_Ozip(U_15948,U_15949)),U_15952))),U_15950),
    inference(variable_rename,[status(thm)],[f_3986_1]) ).

cnf(f_3986_3,plain,
    hAPP(hAPP(c_List_Ozip(U_15948,U_15949),U_15950),hAPP(hAPP(c_List_Olist_OCons(U_15949),U_15951),U_15952)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(U_15948,U_15949)),U_15948,c_List_Olist_ONil(tc_prod(U_15948,U_15949)),hAPP(hAPP(c_COMBC(U_15948,tc_fun(tc_List_Olist(U_15948),tc_List_Olist(tc_prod(U_15948,U_15949))),tc_fun(tc_List_Olist(U_15948),tc_List_Olist(tc_prod(U_15948,U_15949)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(U_15948,U_15949)),tc_List_Olist(tc_prod(U_15948,U_15949))),tc_fun(tc_fun(tc_List_Olist(U_15948),tc_List_Olist(tc_prod(U_15948,U_15949))),tc_fun(tc_List_Olist(U_15948),tc_List_Olist(tc_prod(U_15948,U_15949)))),U_15948),c_COMBB(tc_List_Olist(tc_prod(U_15948,U_15949)),tc_List_Olist(tc_prod(U_15948,U_15949)),tc_List_Olist(U_15948))),hAPP(hAPP(c_COMBB(tc_prod(U_15948,U_15949),tc_fun(tc_List_Olist(tc_prod(U_15948,U_15949)),tc_List_Olist(tc_prod(U_15948,U_15949))),U_15948),c_List_Olist_OCons(tc_prod(U_15948,U_15949))),hAPP(hAPP(c_COMBC(U_15948,U_15949,tc_prod(U_15948,U_15949)),c_Product__Type_OPair(U_15948,U_15949)),U_15951)))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_15948),tc_List_Olist(U_15949),tc_List_Olist(tc_prod(U_15948,U_15949))),c_List_Ozip(U_15948,U_15949)),U_15952))),U_15950),
    inference(clausify,[status(thm)],[f_3986_2]) ).

fof(f_3987_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( c_List_Olinorder__class_Osorted__list__of__set(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = c_List_Oremove1(T_b,V_x_2,c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__list__of__set__remove]) ).

fof(f_3987_2,plain,
    ! [U_15955,U_15954,U_15953] :
      ( c_List_Olinorder__class_Osorted__list__of__set(U_15953,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_15953,tc_HOL_Obool)),U_15954),hAPP(hAPP(c_Set_Oinsert(U_15953),U_15955),c_Orderings_Obot__class_Obot(tc_fun(U_15953,tc_HOL_Obool))))) = c_List_Oremove1(U_15953,U_15955,c_List_Olinorder__class_Osorted__list__of__set(U_15953,U_15954))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15953),U_15954))
      | ~ class_Orderings_Olinorder(U_15953) ),
    inference(variable_rename,[status(thm)],[f_3987_1]) ).

cnf(f_3987_3,plain,
    ( c_List_Olinorder__class_Osorted__list__of__set(U_15953,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_15953,tc_HOL_Obool)),U_15954),hAPP(hAPP(c_Set_Oinsert(U_15953),U_15955),c_Orderings_Obot__class_Obot(tc_fun(U_15953,tc_HOL_Obool))))) = c_List_Oremove1(U_15953,U_15955,c_List_Olinorder__class_Osorted__list__of__set(U_15953,U_15954))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15953),U_15954))
    | ~ class_Orderings_Olinorder(U_15953) ),
    inference(clausify,[status(thm)],[f_3987_2]) ).

fof(f_3988_1,plain,
    ! [V_P_2,V_a1_2,V_a0_2] :
      ( hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2))
      | ? [B_i,B_j] :
          ( ~ hBOOL(hAPP(hAPP(V_P_2,B_i),B_j))
          & ( hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_i),c_Groups_Oone__class_Oone(tc_Int_Oint))),B_j))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_i),B_j)) )
          & hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_i),B_j))) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2))) ),
    inference(fof_nnf,[status(thm)],[fact_upto_Opinduct]) ).

fof(f_3988_2,plain,
    ! [U_15960,U_15959,U_15958] :
      ( hBOOL(hAPP(hAPP(U_15960,U_15958),U_15959))
      | ? [U_15957,U_15956] :
          ( ~ hBOOL(hAPP(hAPP(U_15960,U_15957),U_15956))
          & ( hBOOL(hAPP(hAPP(U_15960,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_15957),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_15956))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_15957),U_15956)) )
          & hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_15957),U_15956))) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_15958),U_15959))) ),
    inference(variable_rename,[status(thm)],[f_3988_1]) ).

fof(f_3988_3,plain,
    ! [U_15960,U_15959,U_15958] :
      ( hBOOL(hAPP(hAPP(U_15960,U_15958),U_15959))
      | ? [U_15956] :
          ( ~ hBOOL(hAPP(hAPP(U_15960,sK419(U_15960,U_15959,U_15958)),U_15956))
          & ( hBOOL(hAPP(hAPP(U_15960,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK419(U_15960,U_15959,U_15958)),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_15956))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK419(U_15960,U_15959,U_15958)),U_15956)) )
          & hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),sK419(U_15960,U_15959,U_15958)),U_15956))) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_15958),U_15959))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK419]),skolemize(U_15957,sK419(U_15960,U_15959,U_15958))],[f_3988_2]) ).

fof(f_3988_4,plain,
    ! [U_15960,U_15959,U_15958] :
      ( hBOOL(hAPP(hAPP(U_15960,U_15958),U_15959))
      | ( ~ hBOOL(hAPP(hAPP(U_15960,sK419(U_15960,U_15959,U_15958)),sK420(U_15960,U_15959,U_15958)))
        & ( hBOOL(hAPP(hAPP(U_15960,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK419(U_15960,U_15959,U_15958)),c_Groups_Oone__class_Oone(tc_Int_Oint))),sK420(U_15960,U_15959,U_15958)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK419(U_15960,U_15959,U_15958)),sK420(U_15960,U_15959,U_15958))) )
        & hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),sK419(U_15960,U_15959,U_15958)),sK420(U_15960,U_15959,U_15958)))) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_15958),U_15959))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK420]),skolemize(U_15956,sK420(U_15960,U_15959,U_15958))],[f_3988_3]) ).

cnf(f_3988_5,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),sK419(U_15960,U_15959,U_15958)),sK420(U_15960,U_15959,U_15958))))
    | hBOOL(hAPP(hAPP(U_15960,U_15958),U_15959))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_15958),U_15959))) ),
    inference(clausify,[status(thm)],[f_3988_4]) ).

cnf(f_3988_6,plain,
    ( hBOOL(hAPP(hAPP(U_15960,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK419(U_15960,U_15959,U_15958)),c_Groups_Oone__class_Oone(tc_Int_Oint))),sK420(U_15960,U_15959,U_15958)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK419(U_15960,U_15959,U_15958)),sK420(U_15960,U_15959,U_15958)))
    | hBOOL(hAPP(hAPP(U_15960,U_15958),U_15959))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_15958),U_15959))) ),
    inference(clausify,[status(thm)],[f_3988_4]) ).

cnf(f_3988_7,plain,
    ( ~ hBOOL(hAPP(hAPP(U_15960,sK419(U_15960,U_15959,U_15958)),sK420(U_15960,U_15959,U_15958)))
    | hBOOL(hAPP(hAPP(U_15960,U_15958),U_15959))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_15958),U_15959))) ),
    inference(clausify,[status(thm)],[f_3988_4]) ).

fof(f_3989_1,plain,
    ! [T_b] :
      ( c_List_Olinorder__class_Osorted__list__of__set(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_List_Olist_ONil(T_b)
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__list__of__set__empty]) ).

fof(f_3989_2,plain,
    ! [U_15961] :
      ( c_List_Olinorder__class_Osorted__list__of__set(U_15961,c_Orderings_Obot__class_Obot(tc_fun(U_15961,tc_HOL_Obool))) = c_List_Olist_ONil(U_15961)
      | ~ class_Orderings_Olinorder(U_15961) ),
    inference(variable_rename,[status(thm)],[f_3989_1]) ).

cnf(f_3989_3,plain,
    ( c_List_Olinorder__class_Osorted__list__of__set(U_15961,c_Orderings_Obot__class_Obot(tc_fun(U_15961,tc_HOL_Obool))) = c_List_Olist_ONil(U_15961)
    | ~ class_Orderings_Olinorder(U_15961) ),
    inference(clausify,[status(thm)],[f_3989_2]) ).

fof(f_3990_1,plain,
    ! [V_x_2,V_f_2,T_b,T_c,V_k_2] :
      ( ( hAPP(hAPP(c_Lazy__Sequence_Oanamorph(T_c,T_b,V_f_2),V_k_2),V_x_2) = c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(T_b),T_c),tc_prod(T_b,T_c),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),T_c),c_List_Olist_ONil(T_b)),V_x_2),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_prod(tc_List_Olist(T_b),T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c)),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(T_b),T_c),tc_prod(tc_List_Olist(T_b),T_c)),tc_fun(tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c)),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c))),T_b),c_COMBB(tc_prod(tc_List_Olist(T_b),T_c),tc_prod(tc_List_Olist(T_b),T_c),T_c)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c))),tc_fun(tc_prod(tc_List_Olist(T_b),T_c),tc_prod(tc_List_Olist(T_b),T_c)),T_b),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),T_c,tc_prod(tc_List_Olist(T_b),T_c))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c))),T_b),hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c)),tc_List_Olist(T_b)),c_Product__Type_OPair(tc_List_Olist(T_b),T_c))),c_List_Olist_OCons(T_b))))),hAPP(c_Lazy__Sequence_Oanamorph(T_c,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_k_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))))),hAPP(V_f_2,V_x_2))
        | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
      & ( hAPP(hAPP(c_Lazy__Sequence_Oanamorph(T_c,T_b,V_f_2),V_k_2),V_x_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),T_c),c_List_Olist_ONil(T_b)),V_x_2)
        | V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(fof_nnf,[status(thm)],[fact_anamorph_Osimps]) ).

fof(f_3990_2,plain,
    ! [U_15966,U_15965,U_15964,U_15963,U_15962] :
      ( ( hAPP(hAPP(c_Lazy__Sequence_Oanamorph(U_15963,U_15964,U_15965),U_15962),U_15966) = c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(U_15964),U_15963),tc_prod(U_15964,U_15963),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15964),U_15963),c_List_Olist_ONil(U_15964)),U_15966),hAPP(c_Product__Type_Oprod_Oprod__case(U_15964,U_15963,tc_prod(tc_List_Olist(U_15964),U_15963)),hAPP(hAPP(c_COMBC(U_15964,tc_fun(U_15963,tc_prod(tc_List_Olist(U_15964),U_15963)),tc_fun(U_15963,tc_prod(tc_List_Olist(U_15964),U_15963))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(U_15964),U_15963),tc_prod(tc_List_Olist(U_15964),U_15963)),tc_fun(tc_fun(U_15963,tc_prod(tc_List_Olist(U_15964),U_15963)),tc_fun(U_15963,tc_prod(tc_List_Olist(U_15964),U_15963))),U_15964),c_COMBB(tc_prod(tc_List_Olist(U_15964),U_15963),tc_prod(tc_List_Olist(U_15964),U_15963),U_15963)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_15964),tc_fun(U_15963,tc_prod(tc_List_Olist(U_15964),U_15963))),tc_fun(tc_prod(tc_List_Olist(U_15964),U_15963),tc_prod(tc_List_Olist(U_15964),U_15963)),U_15964),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_15964),U_15963,tc_prod(tc_List_Olist(U_15964),U_15963))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_15964),tc_List_Olist(U_15964)),tc_fun(tc_List_Olist(U_15964),tc_fun(U_15963,tc_prod(tc_List_Olist(U_15964),U_15963))),U_15964),hAPP(c_COMBB(tc_List_Olist(U_15964),tc_fun(U_15963,tc_prod(tc_List_Olist(U_15964),U_15963)),tc_List_Olist(U_15964)),c_Product__Type_OPair(tc_List_Olist(U_15964),U_15963))),c_List_Olist_OCons(U_15964))))),hAPP(c_Lazy__Sequence_Oanamorph(U_15963,U_15964,U_15965),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_15962),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))))),hAPP(U_15965,U_15966))
        | U_15962 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
      & ( hAPP(hAPP(c_Lazy__Sequence_Oanamorph(U_15963,U_15964,U_15965),U_15962),U_15966) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15964),U_15963),c_List_Olist_ONil(U_15964)),U_15966)
        | U_15962 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(variable_rename,[status(thm)],[f_3990_1]) ).

fof(f_3990_3,plain,
    ( ! [U_15976,U_15974,U_15972,U_15970,U_15968] :
        ( hAPP(hAPP(c_Lazy__Sequence_Oanamorph(U_15970,U_15972,U_15974),U_15968),U_15976) = c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(U_15972),U_15970),tc_prod(U_15972,U_15970),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15972),U_15970),c_List_Olist_ONil(U_15972)),U_15976),hAPP(c_Product__Type_Oprod_Oprod__case(U_15972,U_15970,tc_prod(tc_List_Olist(U_15972),U_15970)),hAPP(hAPP(c_COMBC(U_15972,tc_fun(U_15970,tc_prod(tc_List_Olist(U_15972),U_15970)),tc_fun(U_15970,tc_prod(tc_List_Olist(U_15972),U_15970))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(U_15972),U_15970),tc_prod(tc_List_Olist(U_15972),U_15970)),tc_fun(tc_fun(U_15970,tc_prod(tc_List_Olist(U_15972),U_15970)),tc_fun(U_15970,tc_prod(tc_List_Olist(U_15972),U_15970))),U_15972),c_COMBB(tc_prod(tc_List_Olist(U_15972),U_15970),tc_prod(tc_List_Olist(U_15972),U_15970),U_15970)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_15972),tc_fun(U_15970,tc_prod(tc_List_Olist(U_15972),U_15970))),tc_fun(tc_prod(tc_List_Olist(U_15972),U_15970),tc_prod(tc_List_Olist(U_15972),U_15970)),U_15972),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_15972),U_15970,tc_prod(tc_List_Olist(U_15972),U_15970))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_15972),tc_List_Olist(U_15972)),tc_fun(tc_List_Olist(U_15972),tc_fun(U_15970,tc_prod(tc_List_Olist(U_15972),U_15970))),U_15972),hAPP(c_COMBB(tc_List_Olist(U_15972),tc_fun(U_15970,tc_prod(tc_List_Olist(U_15972),U_15970)),tc_List_Olist(U_15972)),c_Product__Type_OPair(tc_List_Olist(U_15972),U_15970))),c_List_Olist_OCons(U_15972))))),hAPP(c_Lazy__Sequence_Oanamorph(U_15970,U_15972,U_15974),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_15968),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))))),hAPP(U_15974,U_15976))
        | U_15968 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
    & ! [U_15975,U_15973,U_15971,U_15969,U_15967] :
        ( hAPP(hAPP(c_Lazy__Sequence_Oanamorph(U_15969,U_15971,U_15973),U_15967),U_15975) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15971),U_15969),c_List_Olist_ONil(U_15971)),U_15975)
        | U_15967 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(miniscope,[status(thm)],[f_3990_2]) ).

cnf(f_3990_4,plain,
    ( hAPP(hAPP(c_Lazy__Sequence_Oanamorph(U_15969,U_15971,U_15973),U_15967),U_15975) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15971),U_15969),c_List_Olist_ONil(U_15971)),U_15975)
    | U_15967 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_3990_3]) ).

cnf(f_3990_5,plain,
    ( hAPP(hAPP(c_Lazy__Sequence_Oanamorph(U_15970,U_15972,U_15974),U_15968),U_15976) = c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(U_15972),U_15970),tc_prod(U_15972,U_15970),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_15972),U_15970),c_List_Olist_ONil(U_15972)),U_15976),hAPP(c_Product__Type_Oprod_Oprod__case(U_15972,U_15970,tc_prod(tc_List_Olist(U_15972),U_15970)),hAPP(hAPP(c_COMBC(U_15972,tc_fun(U_15970,tc_prod(tc_List_Olist(U_15972),U_15970)),tc_fun(U_15970,tc_prod(tc_List_Olist(U_15972),U_15970))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(U_15972),U_15970),tc_prod(tc_List_Olist(U_15972),U_15970)),tc_fun(tc_fun(U_15970,tc_prod(tc_List_Olist(U_15972),U_15970)),tc_fun(U_15970,tc_prod(tc_List_Olist(U_15972),U_15970))),U_15972),c_COMBB(tc_prod(tc_List_Olist(U_15972),U_15970),tc_prod(tc_List_Olist(U_15972),U_15970),U_15970)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_15972),tc_fun(U_15970,tc_prod(tc_List_Olist(U_15972),U_15970))),tc_fun(tc_prod(tc_List_Olist(U_15972),U_15970),tc_prod(tc_List_Olist(U_15972),U_15970)),U_15972),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_15972),U_15970,tc_prod(tc_List_Olist(U_15972),U_15970))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_15972),tc_List_Olist(U_15972)),tc_fun(tc_List_Olist(U_15972),tc_fun(U_15970,tc_prod(tc_List_Olist(U_15972),U_15970))),U_15972),hAPP(c_COMBB(tc_List_Olist(U_15972),tc_fun(U_15970,tc_prod(tc_List_Olist(U_15972),U_15970)),tc_List_Olist(U_15972)),c_Product__Type_OPair(tc_List_Olist(U_15972),U_15970))),c_List_Olist_OCons(U_15972))))),hAPP(c_Lazy__Sequence_Oanamorph(U_15970,U_15972,U_15974),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_15968),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))))),hAPP(U_15974,U_15976))
    | U_15968 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_3990_3]) ).

fof(f_3991_1,plain,
    ! [V_A_2,V_l_2,V_x_2,T_b] : c_List_Osublist(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_l_2),V_A_2) = hAPP(hAPP(c_List_Oappend(T_b),hAPP(hAPP(hAPP(c_If(tc_List_Olist(T_b)),hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))),c_List_Olist_ONil(T_b))),c_List_Osublist(T_b,V_l_2,hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),V_A_2)))),
    inference(fof_nnf,[status(thm)],[fact_sublist__Cons]) ).

fof(f_3991_2,plain,
    ! [U_15980,U_15979,U_15978,U_15977] : c_List_Osublist(U_15977,hAPP(hAPP(c_List_Olist_OCons(U_15977),U_15978),U_15979),U_15980) = hAPP(hAPP(c_List_Oappend(U_15977),hAPP(hAPP(hAPP(c_If(tc_List_Olist(U_15977)),hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_15980)),hAPP(hAPP(c_List_Olist_OCons(U_15977),U_15978),c_List_Olist_ONil(U_15977))),c_List_Olist_ONil(U_15977))),c_List_Osublist(U_15977,U_15979,hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),U_15980)))),
    inference(variable_rename,[status(thm)],[f_3991_1]) ).

cnf(f_3991_3,plain,
    c_List_Osublist(U_15977,hAPP(hAPP(c_List_Olist_OCons(U_15977),U_15978),U_15979),U_15980) = hAPP(hAPP(c_List_Oappend(U_15977),hAPP(hAPP(hAPP(c_If(tc_List_Olist(U_15977)),hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_15980)),hAPP(hAPP(c_List_Olist_OCons(U_15977),U_15978),c_List_Olist_ONil(U_15977))),c_List_Olist_ONil(U_15977))),c_List_Osublist(U_15977,U_15979,hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),U_15980)))),
    inference(clausify,[status(thm)],[f_3991_2]) ).

fof(f_3992_1,plain,
    ! [V_y_2,V_ys_2,V_x_2,V_xs_2,T_b] :
      ( ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))) = hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),c_List_Olist_ONil(T_b)))
        | V_x_2 != V_y_2
        | V_xs_2 != V_ys_2 )
      & ( ( V_x_2 = V_y_2
          & V_xs_2 = V_ys_2 )
        | hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))) != hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),c_List_Olist_ONil(T_b))) ) ),
    inference(fof_nnf,[status(thm)],[fact_append1__eq__conv]) ).

fof(f_3992_2,plain,
    ! [U_15985,U_15984,U_15983,U_15982,U_15981] :
      ( ( hAPP(hAPP(c_List_Oappend(U_15981),U_15982),hAPP(hAPP(c_List_Olist_OCons(U_15981),U_15983),c_List_Olist_ONil(U_15981))) = hAPP(hAPP(c_List_Oappend(U_15981),U_15984),hAPP(hAPP(c_List_Olist_OCons(U_15981),U_15985),c_List_Olist_ONil(U_15981)))
        | U_15983 != U_15985
        | U_15982 != U_15984 )
      & ( ( U_15983 = U_15985
          & U_15982 = U_15984 )
        | hAPP(hAPP(c_List_Oappend(U_15981),U_15982),hAPP(hAPP(c_List_Olist_OCons(U_15981),U_15983),c_List_Olist_ONil(U_15981))) != hAPP(hAPP(c_List_Oappend(U_15981),U_15984),hAPP(hAPP(c_List_Olist_OCons(U_15981),U_15985),c_List_Olist_ONil(U_15981))) ) ),
    inference(variable_rename,[status(thm)],[f_3992_1]) ).

fof(f_3992_3,plain,
    ( ! [U_15995,U_15993,U_15991,U_15989] :
        ( ! [U_15987] : hAPP(hAPP(c_List_Oappend(U_15987),U_15989),hAPP(hAPP(c_List_Olist_OCons(U_15987),U_15991),c_List_Olist_ONil(U_15987))) = hAPP(hAPP(c_List_Oappend(U_15987),U_15993),hAPP(hAPP(c_List_Olist_OCons(U_15987),U_15995),c_List_Olist_ONil(U_15987)))
        | U_15991 != U_15995
        | U_15989 != U_15993 )
    & ! [U_15994,U_15992,U_15990,U_15988] :
        ( ! [U_15986] : hAPP(hAPP(c_List_Oappend(U_15986),U_15988),hAPP(hAPP(c_List_Olist_OCons(U_15986),U_15990),c_List_Olist_ONil(U_15986))) != hAPP(hAPP(c_List_Oappend(U_15986),U_15992),hAPP(hAPP(c_List_Olist_OCons(U_15986),U_15994),c_List_Olist_ONil(U_15986)))
        | ( U_15990 = U_15994
          & U_15988 = U_15992 ) ) ),
    inference(miniscope,[status(thm)],[f_3992_2]) ).

cnf(f_3992_4,plain,
    ( U_15988 = U_15992
    | hAPP(hAPP(c_List_Oappend(U_15986),U_15988),hAPP(hAPP(c_List_Olist_OCons(U_15986),U_15990),c_List_Olist_ONil(U_15986))) != hAPP(hAPP(c_List_Oappend(U_15986),U_15992),hAPP(hAPP(c_List_Olist_OCons(U_15986),U_15994),c_List_Olist_ONil(U_15986))) ),
    inference(clausify,[status(thm)],[f_3992_3]) ).

cnf(f_3992_5,plain,
    ( U_15990 = U_15994
    | hAPP(hAPP(c_List_Oappend(U_15986),U_15988),hAPP(hAPP(c_List_Olist_OCons(U_15986),U_15990),c_List_Olist_ONil(U_15986))) != hAPP(hAPP(c_List_Oappend(U_15986),U_15992),hAPP(hAPP(c_List_Olist_OCons(U_15986),U_15994),c_List_Olist_ONil(U_15986))) ),
    inference(clausify,[status(thm)],[f_3992_3]) ).

cnf(f_3992_6,plain,
    ( hAPP(hAPP(c_List_Oappend(U_15987),U_15989),hAPP(hAPP(c_List_Olist_OCons(U_15987),U_15991),c_List_Olist_ONil(U_15987))) = hAPP(hAPP(c_List_Oappend(U_15987),U_15993),hAPP(hAPP(c_List_Olist_OCons(U_15987),U_15995),c_List_Olist_ONil(U_15987)))
    | U_15991 != U_15995
    | U_15989 != U_15993 ),
    inference(clausify,[status(thm)],[f_3992_3]) ).

fof(f_3993_1,plain,
    ! [V_zs_2,V_ys_2,V_xs_2,V_x_2,T_b] :
      ( ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) = hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_zs_2)
        | ( ! [B_ys_H] :
              ( V_xs_2 != hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2)
              | hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H) != V_ys_2 )
          & ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) != V_zs_2
            | V_ys_2 != c_List_Olist_ONil(T_b) ) ) )
      & ( ? [B_ys_H] :
            ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2)
            & hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H) = V_ys_2 )
        | ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) = V_zs_2
          & V_ys_2 = c_List_Olist_ONil(T_b) )
        | hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) != hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_zs_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_Cons__eq__append__conv]) ).

fof(f_3993_2,plain,
    ! [U_16002,U_16001,U_16000,U_15999,U_15998] :
      ( ( hAPP(hAPP(c_List_Olist_OCons(U_15998),U_15999),U_16000) = hAPP(hAPP(c_List_Oappend(U_15998),U_16001),U_16002)
        | ( ! [U_15997] :
              ( U_16000 != hAPP(hAPP(c_List_Oappend(U_15998),U_15997),U_16002)
              | hAPP(hAPP(c_List_Olist_OCons(U_15998),U_15999),U_15997) != U_16001 )
          & ( hAPP(hAPP(c_List_Olist_OCons(U_15998),U_15999),U_16000) != U_16002
            | U_16001 != c_List_Olist_ONil(U_15998) ) ) )
      & ( ? [U_15996] :
            ( U_16000 = hAPP(hAPP(c_List_Oappend(U_15998),U_15996),U_16002)
            & hAPP(hAPP(c_List_Olist_OCons(U_15998),U_15999),U_15996) = U_16001 )
        | ( hAPP(hAPP(c_List_Olist_OCons(U_15998),U_15999),U_16000) = U_16002
          & U_16001 = c_List_Olist_ONil(U_15998) )
        | hAPP(hAPP(c_List_Olist_OCons(U_15998),U_15999),U_16000) != hAPP(hAPP(c_List_Oappend(U_15998),U_16001),U_16002) ) ),
    inference(variable_rename,[status(thm)],[f_3993_1]) ).

fof(f_3993_3,plain,
    ( ! [U_16012,U_16010,U_16008,U_16006,U_16004] :
        ( hAPP(hAPP(c_List_Olist_OCons(U_16004),U_16006),U_16008) = hAPP(hAPP(c_List_Oappend(U_16004),U_16010),U_16012)
        | ( ! [U_15997] :
              ( U_16008 != hAPP(hAPP(c_List_Oappend(U_16004),U_15997),U_16012)
              | hAPP(hAPP(c_List_Olist_OCons(U_16004),U_16006),U_15997) != U_16010 )
          & ( hAPP(hAPP(c_List_Olist_OCons(U_16004),U_16006),U_16008) != U_16012
            | U_16010 != c_List_Olist_ONil(U_16004) ) ) )
    & ! [U_16011,U_16009,U_16007,U_16005,U_16003] :
        ( ? [U_15996] :
            ( U_16007 = hAPP(hAPP(c_List_Oappend(U_16003),U_15996),U_16011)
            & hAPP(hAPP(c_List_Olist_OCons(U_16003),U_16005),U_15996) = U_16009 )
        | ( hAPP(hAPP(c_List_Olist_OCons(U_16003),U_16005),U_16007) = U_16011
          & U_16009 = c_List_Olist_ONil(U_16003) )
        | hAPP(hAPP(c_List_Olist_OCons(U_16003),U_16005),U_16007) != hAPP(hAPP(c_List_Oappend(U_16003),U_16009),U_16011) ) ),
    inference(miniscope,[status(thm)],[f_3993_2]) ).

fof(f_3993_4,plain,
    ( ! [U_16012,U_16010,U_16008,U_16006,U_16004] :
        ( hAPP(hAPP(c_List_Olist_OCons(U_16004),U_16006),U_16008) = hAPP(hAPP(c_List_Oappend(U_16004),U_16010),U_16012)
        | ( ! [U_15997] :
              ( U_16008 != hAPP(hAPP(c_List_Oappend(U_16004),U_15997),U_16012)
              | hAPP(hAPP(c_List_Olist_OCons(U_16004),U_16006),U_15997) != U_16010 )
          & ( hAPP(hAPP(c_List_Olist_OCons(U_16004),U_16006),U_16008) != U_16012
            | U_16010 != c_List_Olist_ONil(U_16004) ) ) )
    & ! [U_16011,U_16009,U_16007,U_16005,U_16003] :
        ( ( U_16007 = hAPP(hAPP(c_List_Oappend(U_16003),sK421(U_16011,U_16009,U_16007,U_16005,U_16003)),U_16011)
          & hAPP(hAPP(c_List_Olist_OCons(U_16003),U_16005),sK421(U_16011,U_16009,U_16007,U_16005,U_16003)) = U_16009 )
        | ( hAPP(hAPP(c_List_Olist_OCons(U_16003),U_16005),U_16007) = U_16011
          & U_16009 = c_List_Olist_ONil(U_16003) )
        | hAPP(hAPP(c_List_Olist_OCons(U_16003),U_16005),U_16007) != hAPP(hAPP(c_List_Oappend(U_16003),U_16009),U_16011) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK421]),skolemize(U_15996,sK421(U_16011,U_16009,U_16007,U_16005,U_16003))],[f_3993_3]) ).

cnf(f_3993_5,plain,
    ( hAPP(hAPP(c_List_Olist_OCons(U_16003),U_16005),sK421(U_16011,U_16009,U_16007,U_16005,U_16003)) = U_16009
    | U_16009 = c_List_Olist_ONil(U_16003)
    | hAPP(hAPP(c_List_Olist_OCons(U_16003),U_16005),U_16007) != hAPP(hAPP(c_List_Oappend(U_16003),U_16009),U_16011) ),
    inference(clausify,[status(thm)],[f_3993_4]) ).

cnf(f_3993_6,plain,
    ( U_16007 = hAPP(hAPP(c_List_Oappend(U_16003),sK421(U_16011,U_16009,U_16007,U_16005,U_16003)),U_16011)
    | U_16009 = c_List_Olist_ONil(U_16003)
    | hAPP(hAPP(c_List_Olist_OCons(U_16003),U_16005),U_16007) != hAPP(hAPP(c_List_Oappend(U_16003),U_16009),U_16011) ),
    inference(clausify,[status(thm)],[f_3993_4]) ).

cnf(f_3993_7,plain,
    ( hAPP(hAPP(c_List_Olist_OCons(U_16003),U_16005),sK421(U_16011,U_16009,U_16007,U_16005,U_16003)) = U_16009
    | hAPP(hAPP(c_List_Olist_OCons(U_16003),U_16005),U_16007) = U_16011
    | hAPP(hAPP(c_List_Olist_OCons(U_16003),U_16005),U_16007) != hAPP(hAPP(c_List_Oappend(U_16003),U_16009),U_16011) ),
    inference(clausify,[status(thm)],[f_3993_4]) ).

cnf(f_3993_8,plain,
    ( U_16007 = hAPP(hAPP(c_List_Oappend(U_16003),sK421(U_16011,U_16009,U_16007,U_16005,U_16003)),U_16011)
    | hAPP(hAPP(c_List_Olist_OCons(U_16003),U_16005),U_16007) = U_16011
    | hAPP(hAPP(c_List_Olist_OCons(U_16003),U_16005),U_16007) != hAPP(hAPP(c_List_Oappend(U_16003),U_16009),U_16011) ),
    inference(clausify,[status(thm)],[f_3993_4]) ).

cnf(f_3993_9,plain,
    ( hAPP(hAPP(c_List_Olist_OCons(U_16004),U_16006),U_16008) != U_16012
    | U_16010 != c_List_Olist_ONil(U_16004)
    | hAPP(hAPP(c_List_Olist_OCons(U_16004),U_16006),U_16008) = hAPP(hAPP(c_List_Oappend(U_16004),U_16010),U_16012) ),
    inference(clausify,[status(thm)],[f_3993_4]) ).

cnf(f_3993_10,plain,
    ( U_16008 != hAPP(hAPP(c_List_Oappend(U_16004),U_15997),U_16012)
    | hAPP(hAPP(c_List_Olist_OCons(U_16004),U_16006),U_15997) != U_16010
    | hAPP(hAPP(c_List_Olist_OCons(U_16004),U_16006),U_16008) = hAPP(hAPP(c_List_Oappend(U_16004),U_16010),U_16012) ),
    inference(clausify,[status(thm)],[f_3993_4]) ).

fof(f_3994_1,plain,
    ! [V_xs_2,V_x_2,V_zs_2,V_ys_2,T_b] :
      ( ( hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_zs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)
        | ( ! [B_ys_H] :
              ( hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2) != V_xs_2
              | V_ys_2 != hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H) )
          & ( V_zs_2 != hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)
            | V_ys_2 != c_List_Olist_ONil(T_b) ) ) )
      & ( ? [B_ys_H] :
            ( hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2) = V_xs_2
            & V_ys_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H) )
        | ( V_zs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)
          & V_ys_2 = c_List_Olist_ONil(T_b) )
        | hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_zs_2) != hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_append__eq__Cons__conv]) ).

fof(f_3994_2,plain,
    ! [U_16019,U_16018,U_16017,U_16016,U_16015] :
      ( ( hAPP(hAPP(c_List_Oappend(U_16015),U_16016),U_16017) = hAPP(hAPP(c_List_Olist_OCons(U_16015),U_16018),U_16019)
        | ( ! [U_16014] :
              ( hAPP(hAPP(c_List_Oappend(U_16015),U_16014),U_16017) != U_16019
              | U_16016 != hAPP(hAPP(c_List_Olist_OCons(U_16015),U_16018),U_16014) )
          & ( U_16017 != hAPP(hAPP(c_List_Olist_OCons(U_16015),U_16018),U_16019)
            | U_16016 != c_List_Olist_ONil(U_16015) ) ) )
      & ( ? [U_16013] :
            ( hAPP(hAPP(c_List_Oappend(U_16015),U_16013),U_16017) = U_16019
            & U_16016 = hAPP(hAPP(c_List_Olist_OCons(U_16015),U_16018),U_16013) )
        | ( U_16017 = hAPP(hAPP(c_List_Olist_OCons(U_16015),U_16018),U_16019)
          & U_16016 = c_List_Olist_ONil(U_16015) )
        | hAPP(hAPP(c_List_Oappend(U_16015),U_16016),U_16017) != hAPP(hAPP(c_List_Olist_OCons(U_16015),U_16018),U_16019) ) ),
    inference(variable_rename,[status(thm)],[f_3994_1]) ).

fof(f_3994_3,plain,
    ( ! [U_16029,U_16027,U_16025,U_16023,U_16021] :
        ( hAPP(hAPP(c_List_Oappend(U_16021),U_16023),U_16025) = hAPP(hAPP(c_List_Olist_OCons(U_16021),U_16027),U_16029)
        | ( ! [U_16014] :
              ( hAPP(hAPP(c_List_Oappend(U_16021),U_16014),U_16025) != U_16029
              | U_16023 != hAPP(hAPP(c_List_Olist_OCons(U_16021),U_16027),U_16014) )
          & ( U_16025 != hAPP(hAPP(c_List_Olist_OCons(U_16021),U_16027),U_16029)
            | U_16023 != c_List_Olist_ONil(U_16021) ) ) )
    & ! [U_16028,U_16026,U_16024,U_16022,U_16020] :
        ( ? [U_16013] :
            ( hAPP(hAPP(c_List_Oappend(U_16020),U_16013),U_16024) = U_16028
            & U_16022 = hAPP(hAPP(c_List_Olist_OCons(U_16020),U_16026),U_16013) )
        | ( U_16024 = hAPP(hAPP(c_List_Olist_OCons(U_16020),U_16026),U_16028)
          & U_16022 = c_List_Olist_ONil(U_16020) )
        | hAPP(hAPP(c_List_Oappend(U_16020),U_16022),U_16024) != hAPP(hAPP(c_List_Olist_OCons(U_16020),U_16026),U_16028) ) ),
    inference(miniscope,[status(thm)],[f_3994_2]) ).

fof(f_3994_4,plain,
    ( ! [U_16029,U_16027,U_16025,U_16023,U_16021] :
        ( hAPP(hAPP(c_List_Oappend(U_16021),U_16023),U_16025) = hAPP(hAPP(c_List_Olist_OCons(U_16021),U_16027),U_16029)
        | ( ! [U_16014] :
              ( hAPP(hAPP(c_List_Oappend(U_16021),U_16014),U_16025) != U_16029
              | U_16023 != hAPP(hAPP(c_List_Olist_OCons(U_16021),U_16027),U_16014) )
          & ( U_16025 != hAPP(hAPP(c_List_Olist_OCons(U_16021),U_16027),U_16029)
            | U_16023 != c_List_Olist_ONil(U_16021) ) ) )
    & ! [U_16028,U_16026,U_16024,U_16022,U_16020] :
        ( ( hAPP(hAPP(c_List_Oappend(U_16020),sK422(U_16028,U_16026,U_16024,U_16022,U_16020)),U_16024) = U_16028
          & U_16022 = hAPP(hAPP(c_List_Olist_OCons(U_16020),U_16026),sK422(U_16028,U_16026,U_16024,U_16022,U_16020)) )
        | ( U_16024 = hAPP(hAPP(c_List_Olist_OCons(U_16020),U_16026),U_16028)
          & U_16022 = c_List_Olist_ONil(U_16020) )
        | hAPP(hAPP(c_List_Oappend(U_16020),U_16022),U_16024) != hAPP(hAPP(c_List_Olist_OCons(U_16020),U_16026),U_16028) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK422]),skolemize(U_16013,sK422(U_16028,U_16026,U_16024,U_16022,U_16020))],[f_3994_3]) ).

cnf(f_3994_5,plain,
    ( U_16022 = hAPP(hAPP(c_List_Olist_OCons(U_16020),U_16026),sK422(U_16028,U_16026,U_16024,U_16022,U_16020))
    | U_16022 = c_List_Olist_ONil(U_16020)
    | hAPP(hAPP(c_List_Oappend(U_16020),U_16022),U_16024) != hAPP(hAPP(c_List_Olist_OCons(U_16020),U_16026),U_16028) ),
    inference(clausify,[status(thm)],[f_3994_4]) ).

cnf(f_3994_6,plain,
    ( hAPP(hAPP(c_List_Oappend(U_16020),sK422(U_16028,U_16026,U_16024,U_16022,U_16020)),U_16024) = U_16028
    | U_16022 = c_List_Olist_ONil(U_16020)
    | hAPP(hAPP(c_List_Oappend(U_16020),U_16022),U_16024) != hAPP(hAPP(c_List_Olist_OCons(U_16020),U_16026),U_16028) ),
    inference(clausify,[status(thm)],[f_3994_4]) ).

cnf(f_3994_7,plain,
    ( U_16022 = hAPP(hAPP(c_List_Olist_OCons(U_16020),U_16026),sK422(U_16028,U_16026,U_16024,U_16022,U_16020))
    | U_16024 = hAPP(hAPP(c_List_Olist_OCons(U_16020),U_16026),U_16028)
    | hAPP(hAPP(c_List_Oappend(U_16020),U_16022),U_16024) != hAPP(hAPP(c_List_Olist_OCons(U_16020),U_16026),U_16028) ),
    inference(clausify,[status(thm)],[f_3994_4]) ).

cnf(f_3994_8,plain,
    ( hAPP(hAPP(c_List_Oappend(U_16020),sK422(U_16028,U_16026,U_16024,U_16022,U_16020)),U_16024) = U_16028
    | U_16024 = hAPP(hAPP(c_List_Olist_OCons(U_16020),U_16026),U_16028)
    | hAPP(hAPP(c_List_Oappend(U_16020),U_16022),U_16024) != hAPP(hAPP(c_List_Olist_OCons(U_16020),U_16026),U_16028) ),
    inference(clausify,[status(thm)],[f_3994_4]) ).

cnf(f_3994_9,plain,
    ( U_16025 != hAPP(hAPP(c_List_Olist_OCons(U_16021),U_16027),U_16029)
    | U_16023 != c_List_Olist_ONil(U_16021)
    | hAPP(hAPP(c_List_Oappend(U_16021),U_16023),U_16025) = hAPP(hAPP(c_List_Olist_OCons(U_16021),U_16027),U_16029) ),
    inference(clausify,[status(thm)],[f_3994_4]) ).

cnf(f_3994_10,plain,
    ( hAPP(hAPP(c_List_Oappend(U_16021),U_16014),U_16025) != U_16029
    | U_16023 != hAPP(hAPP(c_List_Olist_OCons(U_16021),U_16027),U_16014)
    | hAPP(hAPP(c_List_Oappend(U_16021),U_16023),U_16025) = hAPP(hAPP(c_List_Olist_OCons(U_16021),U_16027),U_16029) ),
    inference(clausify,[status(thm)],[f_3994_4]) ).

fof(f_3995_1,plain,
    ! [V_zs,V_xs,V_ys,V_xs1,V_x,T_a] :
      ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),V_ys),V_zs)
      | V_xs != hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_zs)
      | hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs1) != V_ys ),
    inference(fof_nnf,[status(thm)],[fact_Cons__eq__appendI]) ).

fof(f_3995_2,plain,
    ! [U_16035,U_16034,U_16033,U_16032,U_16031,U_16030] :
      ( hAPP(hAPP(c_List_Olist_OCons(U_16030),U_16031),U_16034) = hAPP(hAPP(c_List_Oappend(U_16030),U_16033),U_16035)
      | U_16034 != hAPP(hAPP(c_List_Oappend(U_16030),U_16032),U_16035)
      | hAPP(hAPP(c_List_Olist_OCons(U_16030),U_16031),U_16032) != U_16033 ),
    inference(variable_rename,[status(thm)],[f_3995_1]) ).

cnf(f_3995_3,plain,
    ( hAPP(hAPP(c_List_Olist_OCons(U_16030),U_16031),U_16034) = hAPP(hAPP(c_List_Oappend(U_16030),U_16033),U_16035)
    | U_16034 != hAPP(hAPP(c_List_Oappend(U_16030),U_16032),U_16035)
    | hAPP(hAPP(c_List_Olist_OCons(U_16030),U_16031),U_16032) != U_16033 ),
    inference(clausify,[status(thm)],[f_3995_2]) ).

fof(f_3996_1,plain,
    ! [V_ys,V_xs,V_x,T_a] : hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_ys) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),
    inference(fof_nnf,[status(thm)],[fact_append__Cons]) ).

fof(f_3996_2,plain,
    ! [U_16039,U_16038,U_16037,U_16036] : hAPP(hAPP(c_List_Oappend(U_16036),hAPP(hAPP(c_List_Olist_OCons(U_16036),U_16037),U_16038)),U_16039) = hAPP(hAPP(c_List_Olist_OCons(U_16036),U_16037),hAPP(hAPP(c_List_Oappend(U_16036),U_16038),U_16039)),
    inference(variable_rename,[status(thm)],[f_3996_1]) ).

cnf(f_3996_3,plain,
    hAPP(hAPP(c_List_Oappend(U_16036),hAPP(hAPP(c_List_Olist_OCons(U_16036),U_16037),U_16038)),U_16039) = hAPP(hAPP(c_List_Olist_OCons(U_16036),U_16037),hAPP(hAPP(c_List_Oappend(U_16036),U_16038),U_16039)),
    inference(clausify,[status(thm)],[f_3996_2]) ).

fof(f_3997_1,plain,
    ! [V_A_2,V_ys_2,V_xs_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)),c_List_Olists(T_b,V_A_2)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_ys_2),c_List_Olists(T_b,V_A_2)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2))) )
      & ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_ys_2),c_List_Olists(T_b,V_A_2)))
          & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)),c_List_Olists(T_b,V_A_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_append__in__lists__conv]) ).

fof(f_3997_2,plain,
    ! [U_16043,U_16042,U_16041,U_16040] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16040)),hAPP(hAPP(c_List_Oappend(U_16040),U_16041),U_16042)),c_List_Olists(U_16040,U_16043)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16040)),U_16042),c_List_Olists(U_16040,U_16043)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16040)),U_16041),c_List_Olists(U_16040,U_16043))) )
      & ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16040)),U_16042),c_List_Olists(U_16040,U_16043)))
          & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16040)),U_16041),c_List_Olists(U_16040,U_16043))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16040)),hAPP(hAPP(c_List_Oappend(U_16040),U_16041),U_16042)),c_List_Olists(U_16040,U_16043))) ) ),
    inference(variable_rename,[status(thm)],[f_3997_1]) ).

fof(f_3997_3,plain,
    ( ! [U_16051,U_16049,U_16047,U_16045] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16045)),hAPP(hAPP(c_List_Oappend(U_16045),U_16047),U_16049)),c_List_Olists(U_16045,U_16051)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16045)),U_16049),c_List_Olists(U_16045,U_16051)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16045)),U_16047),c_List_Olists(U_16045,U_16051))) )
    & ! [U_16050,U_16048,U_16046,U_16044] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16044)),U_16048),c_List_Olists(U_16044,U_16050)))
          & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16044)),U_16046),c_List_Olists(U_16044,U_16050))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16044)),hAPP(hAPP(c_List_Oappend(U_16044),U_16046),U_16048)),c_List_Olists(U_16044,U_16050))) ) ),
    inference(miniscope,[status(thm)],[f_3997_2]) ).

cnf(f_3997_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16044)),U_16046),c_List_Olists(U_16044,U_16050)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16044)),hAPP(hAPP(c_List_Oappend(U_16044),U_16046),U_16048)),c_List_Olists(U_16044,U_16050))) ),
    inference(clausify,[status(thm)],[f_3997_3]) ).

cnf(f_3997_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16044)),U_16048),c_List_Olists(U_16044,U_16050)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16044)),hAPP(hAPP(c_List_Oappend(U_16044),U_16046),U_16048)),c_List_Olists(U_16044,U_16050))) ),
    inference(clausify,[status(thm)],[f_3997_3]) ).

cnf(f_3997_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16045)),hAPP(hAPP(c_List_Oappend(U_16045),U_16047),U_16049)),c_List_Olists(U_16045,U_16051)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16045)),U_16049),c_List_Olists(U_16045,U_16051)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16045)),U_16047),c_List_Olists(U_16045,U_16051))) ),
    inference(clausify,[status(thm)],[f_3997_3]) ).

fof(f_3998_1,plain,
    ! [V_zs,V_ys,V_xs,T_a] : hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_zs) = hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Oappend(T_a),V_ys),V_zs)),
    inference(fof_nnf,[status(thm)],[fact_append__assoc]) ).

fof(f_3998_2,plain,
    ! [U_16055,U_16054,U_16053,U_16052] : hAPP(hAPP(c_List_Oappend(U_16052),hAPP(hAPP(c_List_Oappend(U_16052),U_16053),U_16054)),U_16055) = hAPP(hAPP(c_List_Oappend(U_16052),U_16053),hAPP(hAPP(c_List_Oappend(U_16052),U_16054),U_16055)),
    inference(variable_rename,[status(thm)],[f_3998_1]) ).

cnf(f_3998_3,plain,
    hAPP(hAPP(c_List_Oappend(U_16052),hAPP(hAPP(c_List_Oappend(U_16052),U_16053),U_16054)),U_16055) = hAPP(hAPP(c_List_Oappend(U_16052),U_16053),hAPP(hAPP(c_List_Oappend(U_16052),U_16054),U_16055)),
    inference(clausify,[status(thm)],[f_3998_2]) ).

fof(f_3999_1,plain,
    ! [V_tsa_2,V_zs_2,V_ys_2,V_xs_2,T_b] :
      ( ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),V_tsa_2)
        | ! [B_us] :
            ( ( V_ys_2 != hAPP(hAPP(c_List_Oappend(T_b),B_us),V_tsa_2)
              | hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),B_us) != V_zs_2 )
            & ( hAPP(hAPP(c_List_Oappend(T_b),B_us),V_ys_2) != V_tsa_2
              | V_xs_2 != hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),B_us) ) ) )
      & ( ? [B_us] :
            ( ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),V_tsa_2)
              & hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),B_us) = V_zs_2 )
            | ( hAPP(hAPP(c_List_Oappend(T_b),B_us),V_ys_2) = V_tsa_2
              & V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),B_us) ) )
        | hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) != hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),V_tsa_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_append__eq__append__conv2]) ).

fof(f_3999_2,plain,
    ! [U_16062,U_16061,U_16060,U_16059,U_16058] :
      ( ( hAPP(hAPP(c_List_Oappend(U_16058),U_16059),U_16060) = hAPP(hAPP(c_List_Oappend(U_16058),U_16061),U_16062)
        | ! [U_16057] :
            ( ( U_16060 != hAPP(hAPP(c_List_Oappend(U_16058),U_16057),U_16062)
              | hAPP(hAPP(c_List_Oappend(U_16058),U_16059),U_16057) != U_16061 )
            & ( hAPP(hAPP(c_List_Oappend(U_16058),U_16057),U_16060) != U_16062
              | U_16059 != hAPP(hAPP(c_List_Oappend(U_16058),U_16061),U_16057) ) ) )
      & ( ? [U_16056] :
            ( ( U_16060 = hAPP(hAPP(c_List_Oappend(U_16058),U_16056),U_16062)
              & hAPP(hAPP(c_List_Oappend(U_16058),U_16059),U_16056) = U_16061 )
            | ( hAPP(hAPP(c_List_Oappend(U_16058),U_16056),U_16060) = U_16062
              & U_16059 = hAPP(hAPP(c_List_Oappend(U_16058),U_16061),U_16056) ) )
        | hAPP(hAPP(c_List_Oappend(U_16058),U_16059),U_16060) != hAPP(hAPP(c_List_Oappend(U_16058),U_16061),U_16062) ) ),
    inference(variable_rename,[status(thm)],[f_3999_1]) ).

fof(f_3999_3,plain,
    ( ! [U_16076,U_16074,U_16072,U_16070,U_16068] :
        ( hAPP(hAPP(c_List_Oappend(U_16068),U_16070),U_16072) = hAPP(hAPP(c_List_Oappend(U_16068),U_16074),U_16076)
        | ( ! [U_16066] :
              ( U_16072 != hAPP(hAPP(c_List_Oappend(U_16068),U_16066),U_16076)
              | hAPP(hAPP(c_List_Oappend(U_16068),U_16070),U_16066) != U_16074 )
          & ! [U_16065] :
              ( hAPP(hAPP(c_List_Oappend(U_16068),U_16065),U_16072) != U_16076
              | U_16070 != hAPP(hAPP(c_List_Oappend(U_16068),U_16074),U_16065) ) ) )
    & ! [U_16075,U_16073,U_16071,U_16069,U_16067] :
        ( ? [U_16064] :
            ( U_16071 = hAPP(hAPP(c_List_Oappend(U_16067),U_16064),U_16075)
            & hAPP(hAPP(c_List_Oappend(U_16067),U_16069),U_16064) = U_16073 )
        | ? [U_16063] :
            ( hAPP(hAPP(c_List_Oappend(U_16067),U_16063),U_16071) = U_16075
            & U_16069 = hAPP(hAPP(c_List_Oappend(U_16067),U_16073),U_16063) )
        | hAPP(hAPP(c_List_Oappend(U_16067),U_16069),U_16071) != hAPP(hAPP(c_List_Oappend(U_16067),U_16073),U_16075) ) ),
    inference(miniscope,[status(thm)],[f_3999_2]) ).

fof(f_3999_4,plain,
    ( ! [U_16076,U_16074,U_16072,U_16070,U_16068] :
        ( hAPP(hAPP(c_List_Oappend(U_16068),U_16070),U_16072) = hAPP(hAPP(c_List_Oappend(U_16068),U_16074),U_16076)
        | ( ! [U_16066] :
              ( U_16072 != hAPP(hAPP(c_List_Oappend(U_16068),U_16066),U_16076)
              | hAPP(hAPP(c_List_Oappend(U_16068),U_16070),U_16066) != U_16074 )
          & ! [U_16065] :
              ( hAPP(hAPP(c_List_Oappend(U_16068),U_16065),U_16072) != U_16076
              | U_16070 != hAPP(hAPP(c_List_Oappend(U_16068),U_16074),U_16065) ) ) )
    & ! [U_16075,U_16073,U_16071,U_16069,U_16067] :
        ( ? [U_16064] :
            ( U_16071 = hAPP(hAPP(c_List_Oappend(U_16067),U_16064),U_16075)
            & hAPP(hAPP(c_List_Oappend(U_16067),U_16069),U_16064) = U_16073 )
        | ( hAPP(hAPP(c_List_Oappend(U_16067),sK423(U_16075,U_16073,U_16071,U_16069,U_16067)),U_16071) = U_16075
          & U_16069 = hAPP(hAPP(c_List_Oappend(U_16067),U_16073),sK423(U_16075,U_16073,U_16071,U_16069,U_16067)) )
        | hAPP(hAPP(c_List_Oappend(U_16067),U_16069),U_16071) != hAPP(hAPP(c_List_Oappend(U_16067),U_16073),U_16075) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK423]),skolemize(U_16063,sK423(U_16075,U_16073,U_16071,U_16069,U_16067))],[f_3999_3]) ).

fof(f_3999_5,plain,
    ( ! [U_16076,U_16074,U_16072,U_16070,U_16068] :
        ( hAPP(hAPP(c_List_Oappend(U_16068),U_16070),U_16072) = hAPP(hAPP(c_List_Oappend(U_16068),U_16074),U_16076)
        | ( ! [U_16066] :
              ( U_16072 != hAPP(hAPP(c_List_Oappend(U_16068),U_16066),U_16076)
              | hAPP(hAPP(c_List_Oappend(U_16068),U_16070),U_16066) != U_16074 )
          & ! [U_16065] :
              ( hAPP(hAPP(c_List_Oappend(U_16068),U_16065),U_16072) != U_16076
              | U_16070 != hAPP(hAPP(c_List_Oappend(U_16068),U_16074),U_16065) ) ) )
    & ! [U_16075,U_16073,U_16071,U_16069,U_16067] :
        ( ( U_16071 = hAPP(hAPP(c_List_Oappend(U_16067),sK424(U_16075,U_16073,U_16071,U_16069,U_16067)),U_16075)
          & hAPP(hAPP(c_List_Oappend(U_16067),U_16069),sK424(U_16075,U_16073,U_16071,U_16069,U_16067)) = U_16073 )
        | ( hAPP(hAPP(c_List_Oappend(U_16067),sK423(U_16075,U_16073,U_16071,U_16069,U_16067)),U_16071) = U_16075
          & U_16069 = hAPP(hAPP(c_List_Oappend(U_16067),U_16073),sK423(U_16075,U_16073,U_16071,U_16069,U_16067)) )
        | hAPP(hAPP(c_List_Oappend(U_16067),U_16069),U_16071) != hAPP(hAPP(c_List_Oappend(U_16067),U_16073),U_16075) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK424]),skolemize(U_16064,sK424(U_16075,U_16073,U_16071,U_16069,U_16067))],[f_3999_4]) ).

cnf(f_3999_6,plain,
    ( hAPP(hAPP(c_List_Oappend(U_16067),U_16069),sK424(U_16075,U_16073,U_16071,U_16069,U_16067)) = U_16073
    | U_16069 = hAPP(hAPP(c_List_Oappend(U_16067),U_16073),sK423(U_16075,U_16073,U_16071,U_16069,U_16067))
    | hAPP(hAPP(c_List_Oappend(U_16067),U_16069),U_16071) != hAPP(hAPP(c_List_Oappend(U_16067),U_16073),U_16075) ),
    inference(clausify,[status(thm)],[f_3999_5]) ).

cnf(f_3999_7,plain,
    ( U_16071 = hAPP(hAPP(c_List_Oappend(U_16067),sK424(U_16075,U_16073,U_16071,U_16069,U_16067)),U_16075)
    | U_16069 = hAPP(hAPP(c_List_Oappend(U_16067),U_16073),sK423(U_16075,U_16073,U_16071,U_16069,U_16067))
    | hAPP(hAPP(c_List_Oappend(U_16067),U_16069),U_16071) != hAPP(hAPP(c_List_Oappend(U_16067),U_16073),U_16075) ),
    inference(clausify,[status(thm)],[f_3999_5]) ).

cnf(f_3999_8,plain,
    ( hAPP(hAPP(c_List_Oappend(U_16067),U_16069),sK424(U_16075,U_16073,U_16071,U_16069,U_16067)) = U_16073
    | hAPP(hAPP(c_List_Oappend(U_16067),sK423(U_16075,U_16073,U_16071,U_16069,U_16067)),U_16071) = U_16075
    | hAPP(hAPP(c_List_Oappend(U_16067),U_16069),U_16071) != hAPP(hAPP(c_List_Oappend(U_16067),U_16073),U_16075) ),
    inference(clausify,[status(thm)],[f_3999_5]) ).

cnf(f_3999_9,plain,
    ( U_16071 = hAPP(hAPP(c_List_Oappend(U_16067),sK424(U_16075,U_16073,U_16071,U_16069,U_16067)),U_16075)
    | hAPP(hAPP(c_List_Oappend(U_16067),sK423(U_16075,U_16073,U_16071,U_16069,U_16067)),U_16071) = U_16075
    | hAPP(hAPP(c_List_Oappend(U_16067),U_16069),U_16071) != hAPP(hAPP(c_List_Oappend(U_16067),U_16073),U_16075) ),
    inference(clausify,[status(thm)],[f_3999_5]) ).

cnf(f_3999_10,plain,
    ( hAPP(hAPP(c_List_Oappend(U_16068),U_16065),U_16072) != U_16076
    | U_16070 != hAPP(hAPP(c_List_Oappend(U_16068),U_16074),U_16065)
    | hAPP(hAPP(c_List_Oappend(U_16068),U_16070),U_16072) = hAPP(hAPP(c_List_Oappend(U_16068),U_16074),U_16076) ),
    inference(clausify,[status(thm)],[f_3999_5]) ).

cnf(f_3999_11,plain,
    ( U_16072 != hAPP(hAPP(c_List_Oappend(U_16068),U_16066),U_16076)
    | hAPP(hAPP(c_List_Oappend(U_16068),U_16070),U_16066) != U_16074
    | hAPP(hAPP(c_List_Oappend(U_16068),U_16070),U_16072) = hAPP(hAPP(c_List_Oappend(U_16068),U_16074),U_16076) ),
    inference(clausify,[status(thm)],[f_3999_5]) ).

fof(f_4000_1,plain,
    ! [V_zs_2,V_ys_2,V_xs_2,T_b] :
      ( ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_zs_2)
        | V_ys_2 != V_zs_2 )
      & ( V_ys_2 = V_zs_2
        | hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) != hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_zs_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_same__append__eq]) ).

fof(f_4000_2,plain,
    ! [U_16080,U_16079,U_16078,U_16077] :
      ( ( hAPP(hAPP(c_List_Oappend(U_16077),U_16078),U_16079) = hAPP(hAPP(c_List_Oappend(U_16077),U_16078),U_16080)
        | U_16079 != U_16080 )
      & ( U_16079 = U_16080
        | hAPP(hAPP(c_List_Oappend(U_16077),U_16078),U_16079) != hAPP(hAPP(c_List_Oappend(U_16077),U_16078),U_16080) ) ),
    inference(variable_rename,[status(thm)],[f_4000_1]) ).

fof(f_4000_3,plain,
    ( ! [U_16088,U_16086] :
        ( ! [U_16084,U_16082] : hAPP(hAPP(c_List_Oappend(U_16082),U_16084),U_16086) = hAPP(hAPP(c_List_Oappend(U_16082),U_16084),U_16088)
        | U_16086 != U_16088 )
    & ! [U_16087,U_16085] :
        ( ! [U_16083,U_16081] : hAPP(hAPP(c_List_Oappend(U_16081),U_16083),U_16085) != hAPP(hAPP(c_List_Oappend(U_16081),U_16083),U_16087)
        | U_16085 = U_16087 ) ),
    inference(miniscope,[status(thm)],[f_4000_2]) ).

cnf(f_4000_4,plain,
    ( hAPP(hAPP(c_List_Oappend(U_16081),U_16083),U_16085) != hAPP(hAPP(c_List_Oappend(U_16081),U_16083),U_16087)
    | U_16085 = U_16087 ),
    inference(clausify,[status(thm)],[f_4000_3]) ).

cnf(f_4000_5,plain,
    ( hAPP(hAPP(c_List_Oappend(U_16082),U_16084),U_16086) = hAPP(hAPP(c_List_Oappend(U_16082),U_16084),U_16088)
    | U_16086 != U_16088 ),
    inference(clausify,[status(thm)],[f_4000_3]) ).

fof(f_4001_1,plain,
    ! [V_zs_2,V_xs_2,V_ys_2,T_b] :
      ( ( hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_xs_2) = hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),V_xs_2)
        | V_ys_2 != V_zs_2 )
      & ( V_ys_2 = V_zs_2
        | hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_xs_2) != hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),V_xs_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_append__same__eq]) ).

fof(f_4001_2,plain,
    ! [U_16092,U_16091,U_16090,U_16089] :
      ( ( hAPP(hAPP(c_List_Oappend(U_16089),U_16090),U_16091) = hAPP(hAPP(c_List_Oappend(U_16089),U_16092),U_16091)
        | U_16090 != U_16092 )
      & ( U_16090 = U_16092
        | hAPP(hAPP(c_List_Oappend(U_16089),U_16090),U_16091) != hAPP(hAPP(c_List_Oappend(U_16089),U_16092),U_16091) ) ),
    inference(variable_rename,[status(thm)],[f_4001_1]) ).

fof(f_4001_3,plain,
    ( ! [U_16100,U_16098,U_16096] :
        ( ! [U_16094] : hAPP(hAPP(c_List_Oappend(U_16094),U_16096),U_16098) = hAPP(hAPP(c_List_Oappend(U_16094),U_16100),U_16098)
        | U_16096 != U_16100 )
    & ! [U_16099,U_16097,U_16095] :
        ( ! [U_16093] : hAPP(hAPP(c_List_Oappend(U_16093),U_16095),U_16097) != hAPP(hAPP(c_List_Oappend(U_16093),U_16099),U_16097)
        | U_16095 = U_16099 ) ),
    inference(miniscope,[status(thm)],[f_4001_2]) ).

cnf(f_4001_4,plain,
    ( hAPP(hAPP(c_List_Oappend(U_16093),U_16095),U_16097) != hAPP(hAPP(c_List_Oappend(U_16093),U_16099),U_16097)
    | U_16095 = U_16099 ),
    inference(clausify,[status(thm)],[f_4001_3]) ).

cnf(f_4001_5,plain,
    ( hAPP(hAPP(c_List_Oappend(U_16094),U_16096),U_16098) = hAPP(hAPP(c_List_Oappend(U_16094),U_16100),U_16098)
    | U_16096 != U_16100 ),
    inference(clausify,[status(thm)],[f_4001_3]) ).

fof(f_4002_1,plain,
    ! [V_us,V_ys,V_zs,V_xs1,V_xs,T_a] :
      ( hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys) = hAPP(hAPP(c_List_Oappend(T_a),V_zs),V_us)
      | V_ys != hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_us)
      | hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_xs1) != V_zs ),
    inference(fof_nnf,[status(thm)],[fact_append__eq__appendI]) ).

fof(f_4002_2,plain,
    ! [U_16106,U_16105,U_16104,U_16103,U_16102,U_16101] :
      ( hAPP(hAPP(c_List_Oappend(U_16101),U_16102),U_16105) = hAPP(hAPP(c_List_Oappend(U_16101),U_16104),U_16106)
      | U_16105 != hAPP(hAPP(c_List_Oappend(U_16101),U_16103),U_16106)
      | hAPP(hAPP(c_List_Oappend(U_16101),U_16102),U_16103) != U_16104 ),
    inference(variable_rename,[status(thm)],[f_4002_1]) ).

cnf(f_4002_3,plain,
    ( hAPP(hAPP(c_List_Oappend(U_16101),U_16102),U_16105) = hAPP(hAPP(c_List_Oappend(U_16101),U_16104),U_16106)
    | U_16105 != hAPP(hAPP(c_List_Oappend(U_16101),U_16103),U_16106)
    | hAPP(hAPP(c_List_Oappend(U_16101),U_16102),U_16103) != U_16104 ),
    inference(clausify,[status(thm)],[f_4002_2]) ).

fof(f_4003_1,plain,
    ! [V_ys,V_xs,T_a] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs)),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_ys))
      | ~ class_Groups_Omonoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_listsum__append]) ).

fof(f_4003_2,plain,
    ! [U_16109,U_16108,U_16107] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_16107),hAPP(hAPP(c_List_Oappend(U_16107),U_16108),U_16109)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_16107),hAPP(c_List_Omonoid__add__class_Olistsum(U_16107),U_16108)),hAPP(c_List_Omonoid__add__class_Olistsum(U_16107),U_16109))
      | ~ class_Groups_Omonoid__add(U_16107) ),
    inference(variable_rename,[status(thm)],[f_4003_1]) ).

cnf(f_4003_3,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_16107),hAPP(hAPP(c_List_Oappend(U_16107),U_16108),U_16109)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_16107),hAPP(c_List_Omonoid__add__class_Olistsum(U_16107),U_16108)),hAPP(c_List_Omonoid__add__class_Olistsum(U_16107),U_16109))
    | ~ class_Groups_Omonoid__add(U_16107) ),
    inference(clausify,[status(thm)],[f_4003_2]) ).

fof(f_4004_1,plain,
    ! [V_ys,V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys)),
    inference(fof_nnf,[status(thm)],[fact_length__append]) ).

fof(f_4004_2,plain,
    ! [U_16112,U_16111,U_16110] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16110)),hAPP(hAPP(c_List_Oappend(U_16110),U_16111),U_16112)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16110)),U_16111)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16110)),U_16112)),
    inference(variable_rename,[status(thm)],[f_4004_1]) ).

cnf(f_4004_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16110)),hAPP(hAPP(c_List_Oappend(U_16110),U_16111),U_16112)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16110)),U_16111)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16110)),U_16112)),
    inference(clausify,[status(thm)],[f_4004_2]) ).

fof(f_4005_1,plain,
    ! [V_vs,V_ys,V_us,T_b,V_xs,T_a] :
      ( hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),hAPP(hAPP(c_List_Oappend(T_b),V_us),V_vs)) = hAPP(hAPP(c_List_Oappend(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_us)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_ys),V_vs))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_vs)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_us) ),
    inference(fof_nnf,[status(thm)],[fact_zip__append]) ).

fof(f_4005_2,plain,
    ! [U_16118,U_16117,U_16116,U_16115,U_16114,U_16113] :
      ( hAPP(hAPP(c_List_Ozip(U_16113,U_16115),hAPP(hAPP(c_List_Oappend(U_16113),U_16114),U_16117)),hAPP(hAPP(c_List_Oappend(U_16115),U_16116),U_16118)) = hAPP(hAPP(c_List_Oappend(tc_prod(U_16113,U_16115)),hAPP(hAPP(c_List_Ozip(U_16113,U_16115),U_16114),U_16116)),hAPP(hAPP(c_List_Ozip(U_16113,U_16115),U_16117),U_16118))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16113)),U_16117) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16115)),U_16118)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16113)),U_16114) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16115)),U_16116) ),
    inference(variable_rename,[status(thm)],[f_4005_1]) ).

cnf(f_4005_3,plain,
    ( hAPP(hAPP(c_List_Ozip(U_16113,U_16115),hAPP(hAPP(c_List_Oappend(U_16113),U_16114),U_16117)),hAPP(hAPP(c_List_Oappend(U_16115),U_16116),U_16118)) = hAPP(hAPP(c_List_Oappend(tc_prod(U_16113,U_16115)),hAPP(hAPP(c_List_Ozip(U_16113,U_16115),U_16114),U_16116)),hAPP(hAPP(c_List_Ozip(U_16113,U_16115),U_16117),U_16118))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16113)),U_16117) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16115)),U_16118)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16113)),U_16114) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16115)),U_16116) ),
    inference(clausify,[status(thm)],[f_4005_2]) ).

fof(f_4006_1,plain,
    ! [V_ys_2,V_xs_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_ys_2)),
    inference(fof_nnf,[status(thm)],[fact_set__append]) ).

fof(f_4006_2,plain,
    ! [U_16121,U_16120,U_16119] : hAPP(c_List_Oset(U_16119),hAPP(hAPP(c_List_Oappend(U_16119),U_16120),U_16121)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16119,tc_HOL_Obool)),hAPP(c_List_Oset(U_16119),U_16120)),hAPP(c_List_Oset(U_16119),U_16121)),
    inference(variable_rename,[status(thm)],[f_4006_1]) ).

cnf(f_4006_3,plain,
    hAPP(c_List_Oset(U_16119),hAPP(hAPP(c_List_Oappend(U_16119),U_16120),U_16121)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16119,tc_HOL_Obool)),hAPP(c_List_Oset(U_16119),U_16120)),hAPP(c_List_Oset(U_16119),U_16121)),
    inference(clausify,[status(thm)],[f_4006_2]) ).

fof(f_4007_1,plain,
    ! [T_a,V_ys,V_xs] :
      ( V_xs = hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys)
      | V_xs != V_ys ),
    inference(fof_nnf,[status(thm)],[fact_eq__Nil__appendI]) ).

fof(f_4007_2,plain,
    ! [U_16124,U_16123,U_16122] :
      ( U_16122 = hAPP(hAPP(c_List_Oappend(U_16124),c_List_Olist_ONil(U_16124)),U_16123)
      | U_16122 != U_16123 ),
    inference(variable_rename,[status(thm)],[f_4007_1]) ).

cnf(f_4007_3,plain,
    ( U_16122 = hAPP(hAPP(c_List_Oappend(U_16124),c_List_Olist_ONil(U_16124)),U_16123)
    | U_16122 != U_16123 ),
    inference(clausify,[status(thm)],[f_4007_2]) ).

fof(f_4008_1,plain,
    ! [V_ys_2,V_xs_2,T_b] :
      ( ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_ys_2
        | V_xs_2 != c_List_Olist_ONil(T_b) )
      & ( V_xs_2 = c_List_Olist_ONil(T_b)
        | hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) != V_ys_2 ) ),
    inference(fof_nnf,[status(thm)],[fact_append__self__conv2]) ).

fof(f_4008_2,plain,
    ! [U_16127,U_16126,U_16125] :
      ( ( hAPP(hAPP(c_List_Oappend(U_16125),U_16126),U_16127) = U_16127
        | U_16126 != c_List_Olist_ONil(U_16125) )
      & ( U_16126 = c_List_Olist_ONil(U_16125)
        | hAPP(hAPP(c_List_Oappend(U_16125),U_16126),U_16127) != U_16127 ) ),
    inference(variable_rename,[status(thm)],[f_4008_1]) ).

fof(f_4008_3,plain,
    ( ! [U_16133,U_16131,U_16129] :
        ( hAPP(hAPP(c_List_Oappend(U_16129),U_16131),U_16133) = U_16133
        | U_16131 != c_List_Olist_ONil(U_16129) )
    & ! [U_16132,U_16130,U_16128] :
        ( U_16130 = c_List_Olist_ONil(U_16128)
        | hAPP(hAPP(c_List_Oappend(U_16128),U_16130),U_16132) != U_16132 ) ),
    inference(miniscope,[status(thm)],[f_4008_2]) ).

cnf(f_4008_4,plain,
    ( U_16130 = c_List_Olist_ONil(U_16128)
    | hAPP(hAPP(c_List_Oappend(U_16128),U_16130),U_16132) != U_16132 ),
    inference(clausify,[status(thm)],[f_4008_3]) ).

cnf(f_4008_5,plain,
    ( hAPP(hAPP(c_List_Oappend(U_16129),U_16131),U_16133) = U_16133
    | U_16131 != c_List_Olist_ONil(U_16129) ),
    inference(clausify,[status(thm)],[f_4008_3]) ).

fof(f_4009_1,plain,
    ! [V_ys_2,V_xs_2,T_b] :
      ( ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_xs_2
        | V_ys_2 != c_List_Olist_ONil(T_b) )
      & ( V_ys_2 = c_List_Olist_ONil(T_b)
        | hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) != V_xs_2 ) ),
    inference(fof_nnf,[status(thm)],[fact_append__self__conv]) ).

fof(f_4009_2,plain,
    ! [U_16136,U_16135,U_16134] :
      ( ( hAPP(hAPP(c_List_Oappend(U_16134),U_16135),U_16136) = U_16135
        | U_16136 != c_List_Olist_ONil(U_16134) )
      & ( U_16136 = c_List_Olist_ONil(U_16134)
        | hAPP(hAPP(c_List_Oappend(U_16134),U_16135),U_16136) != U_16135 ) ),
    inference(variable_rename,[status(thm)],[f_4009_1]) ).

fof(f_4009_3,plain,
    ( ! [U_16142,U_16140,U_16138] :
        ( hAPP(hAPP(c_List_Oappend(U_16138),U_16140),U_16142) = U_16140
        | U_16142 != c_List_Olist_ONil(U_16138) )
    & ! [U_16141,U_16139,U_16137] :
        ( U_16141 = c_List_Olist_ONil(U_16137)
        | hAPP(hAPP(c_List_Oappend(U_16137),U_16139),U_16141) != U_16139 ) ),
    inference(miniscope,[status(thm)],[f_4009_2]) ).

cnf(f_4009_4,plain,
    ( U_16141 = c_List_Olist_ONil(U_16137)
    | hAPP(hAPP(c_List_Oappend(U_16137),U_16139),U_16141) != U_16139 ),
    inference(clausify,[status(thm)],[f_4009_3]) ).

cnf(f_4009_5,plain,
    ( hAPP(hAPP(c_List_Oappend(U_16138),U_16140),U_16142) = U_16140
    | U_16142 != c_List_Olist_ONil(U_16138) ),
    inference(clausify,[status(thm)],[f_4009_3]) ).

fof(f_4010_1,plain,
    ! [V_ys_2,V_xs_2,T_b] :
      ( ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = c_List_Olist_ONil(T_b)
        | V_ys_2 != c_List_Olist_ONil(T_b)
        | V_xs_2 != c_List_Olist_ONil(T_b) )
      & ( ( V_ys_2 = c_List_Olist_ONil(T_b)
          & V_xs_2 = c_List_Olist_ONil(T_b) )
        | hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) != c_List_Olist_ONil(T_b) ) ),
    inference(fof_nnf,[status(thm)],[fact_append__is__Nil__conv]) ).

fof(f_4010_2,plain,
    ! [U_16145,U_16144,U_16143] :
      ( ( hAPP(hAPP(c_List_Oappend(U_16143),U_16144),U_16145) = c_List_Olist_ONil(U_16143)
        | U_16145 != c_List_Olist_ONil(U_16143)
        | U_16144 != c_List_Olist_ONil(U_16143) )
      & ( ( U_16145 = c_List_Olist_ONil(U_16143)
          & U_16144 = c_List_Olist_ONil(U_16143) )
        | hAPP(hAPP(c_List_Oappend(U_16143),U_16144),U_16145) != c_List_Olist_ONil(U_16143) ) ),
    inference(variable_rename,[status(thm)],[f_4010_1]) ).

fof(f_4010_3,plain,
    ( ! [U_16151,U_16149,U_16147] :
        ( hAPP(hAPP(c_List_Oappend(U_16147),U_16149),U_16151) = c_List_Olist_ONil(U_16147)
        | U_16151 != c_List_Olist_ONil(U_16147)
        | U_16149 != c_List_Olist_ONil(U_16147) )
    & ! [U_16150,U_16148,U_16146] :
        ( ( U_16150 = c_List_Olist_ONil(U_16146)
          & U_16148 = c_List_Olist_ONil(U_16146) )
        | hAPP(hAPP(c_List_Oappend(U_16146),U_16148),U_16150) != c_List_Olist_ONil(U_16146) ) ),
    inference(miniscope,[status(thm)],[f_4010_2]) ).

cnf(f_4010_4,plain,
    ( U_16148 = c_List_Olist_ONil(U_16146)
    | hAPP(hAPP(c_List_Oappend(U_16146),U_16148),U_16150) != c_List_Olist_ONil(U_16146) ),
    inference(clausify,[status(thm)],[f_4010_3]) ).

cnf(f_4010_5,plain,
    ( U_16150 = c_List_Olist_ONil(U_16146)
    | hAPP(hAPP(c_List_Oappend(U_16146),U_16148),U_16150) != c_List_Olist_ONil(U_16146) ),
    inference(clausify,[status(thm)],[f_4010_3]) ).

cnf(f_4010_6,plain,
    ( hAPP(hAPP(c_List_Oappend(U_16147),U_16149),U_16151) = c_List_Olist_ONil(U_16147)
    | U_16151 != c_List_Olist_ONil(U_16147)
    | U_16149 != c_List_Olist_ONil(U_16147) ),
    inference(clausify,[status(thm)],[f_4010_3]) ).

fof(f_4011_1,plain,
    ! [V_xs_2,T_b,V_ys_2] :
      ( ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
        | V_xs_2 != c_List_Olist_ONil(T_b) )
      & ( V_xs_2 = c_List_Olist_ONil(T_b)
        | V_ys_2 != hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_self__append__conv2]) ).

fof(f_4011_2,plain,
    ! [U_16154,U_16153,U_16152] :
      ( ( U_16152 = hAPP(hAPP(c_List_Oappend(U_16153),U_16154),U_16152)
        | U_16154 != c_List_Olist_ONil(U_16153) )
      & ( U_16154 = c_List_Olist_ONil(U_16153)
        | U_16152 != hAPP(hAPP(c_List_Oappend(U_16153),U_16154),U_16152) ) ),
    inference(variable_rename,[status(thm)],[f_4011_1]) ).

fof(f_4011_3,plain,
    ( ! [U_16160,U_16158] :
        ( ! [U_16156] : U_16156 = hAPP(hAPP(c_List_Oappend(U_16158),U_16160),U_16156)
        | U_16160 != c_List_Olist_ONil(U_16158) )
    & ! [U_16159,U_16157] :
        ( ! [U_16155] : U_16155 != hAPP(hAPP(c_List_Oappend(U_16157),U_16159),U_16155)
        | U_16159 = c_List_Olist_ONil(U_16157) ) ),
    inference(miniscope,[status(thm)],[f_4011_2]) ).

cnf(f_4011_4,plain,
    ( U_16155 != hAPP(hAPP(c_List_Oappend(U_16157),U_16159),U_16155)
    | U_16159 = c_List_Olist_ONil(U_16157) ),
    inference(clausify,[status(thm)],[f_4011_3]) ).

cnf(f_4011_5,plain,
    ( U_16156 = hAPP(hAPP(c_List_Oappend(U_16158),U_16160),U_16156)
    | U_16160 != c_List_Olist_ONil(U_16158) ),
    inference(clausify,[status(thm)],[f_4011_3]) ).

fof(f_4012_1,plain,
    ! [V_ys_2,T_b,V_xs_2] :
      ( ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
        | V_ys_2 != c_List_Olist_ONil(T_b) )
      & ( V_ys_2 = c_List_Olist_ONil(T_b)
        | V_xs_2 != hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_self__append__conv]) ).

fof(f_4012_2,plain,
    ! [U_16163,U_16162,U_16161] :
      ( ( U_16161 = hAPP(hAPP(c_List_Oappend(U_16162),U_16161),U_16163)
        | U_16163 != c_List_Olist_ONil(U_16162) )
      & ( U_16163 = c_List_Olist_ONil(U_16162)
        | U_16161 != hAPP(hAPP(c_List_Oappend(U_16162),U_16161),U_16163) ) ),
    inference(variable_rename,[status(thm)],[f_4012_1]) ).

fof(f_4012_3,plain,
    ( ! [U_16169,U_16167] :
        ( ! [U_16165] : U_16165 = hAPP(hAPP(c_List_Oappend(U_16167),U_16165),U_16169)
        | U_16169 != c_List_Olist_ONil(U_16167) )
    & ! [U_16168,U_16166] :
        ( ! [U_16164] : U_16164 != hAPP(hAPP(c_List_Oappend(U_16166),U_16164),U_16168)
        | U_16168 = c_List_Olist_ONil(U_16166) ) ),
    inference(miniscope,[status(thm)],[f_4012_2]) ).

cnf(f_4012_4,plain,
    ( U_16164 != hAPP(hAPP(c_List_Oappend(U_16166),U_16164),U_16168)
    | U_16168 = c_List_Olist_ONil(U_16166) ),
    inference(clausify,[status(thm)],[f_4012_3]) ).

cnf(f_4012_5,plain,
    ( U_16165 = hAPP(hAPP(c_List_Oappend(U_16167),U_16165),U_16169)
    | U_16169 != c_List_Olist_ONil(U_16167) ),
    inference(clausify,[status(thm)],[f_4012_3]) ).

fof(f_4013_1,plain,
    ! [V_xs,T_a] : hAPP(hAPP(c_List_Oappend(T_a),V_xs),c_List_Olist_ONil(T_a)) = V_xs,
    inference(fof_nnf,[status(thm)],[fact_append__Nil2]) ).

fof(f_4013_2,plain,
    ! [U_16171,U_16170] : hAPP(hAPP(c_List_Oappend(U_16170),U_16171),c_List_Olist_ONil(U_16170)) = U_16171,
    inference(variable_rename,[status(thm)],[f_4013_1]) ).

cnf(f_4013_3,plain,
    hAPP(hAPP(c_List_Oappend(U_16170),U_16171),c_List_Olist_ONil(U_16170)) = U_16171,
    inference(clausify,[status(thm)],[f_4013_2]) ).

fof(f_4014_1,plain,
    ! [V_ys_2,V_xs_2,T_b] :
      ( ( c_List_Olist_ONil(T_b) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
        | V_ys_2 != c_List_Olist_ONil(T_b)
        | V_xs_2 != c_List_Olist_ONil(T_b) )
      & ( ( V_ys_2 = c_List_Olist_ONil(T_b)
          & V_xs_2 = c_List_Olist_ONil(T_b) )
        | c_List_Olist_ONil(T_b) != hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_Nil__is__append__conv]) ).

fof(f_4014_2,plain,
    ! [U_16174,U_16173,U_16172] :
      ( ( c_List_Olist_ONil(U_16172) = hAPP(hAPP(c_List_Oappend(U_16172),U_16173),U_16174)
        | U_16174 != c_List_Olist_ONil(U_16172)
        | U_16173 != c_List_Olist_ONil(U_16172) )
      & ( ( U_16174 = c_List_Olist_ONil(U_16172)
          & U_16173 = c_List_Olist_ONil(U_16172) )
        | c_List_Olist_ONil(U_16172) != hAPP(hAPP(c_List_Oappend(U_16172),U_16173),U_16174) ) ),
    inference(variable_rename,[status(thm)],[f_4014_1]) ).

fof(f_4014_3,plain,
    ( ! [U_16180,U_16178,U_16176] :
        ( c_List_Olist_ONil(U_16176) = hAPP(hAPP(c_List_Oappend(U_16176),U_16178),U_16180)
        | U_16180 != c_List_Olist_ONil(U_16176)
        | U_16178 != c_List_Olist_ONil(U_16176) )
    & ! [U_16179,U_16177,U_16175] :
        ( ( U_16179 = c_List_Olist_ONil(U_16175)
          & U_16177 = c_List_Olist_ONil(U_16175) )
        | c_List_Olist_ONil(U_16175) != hAPP(hAPP(c_List_Oappend(U_16175),U_16177),U_16179) ) ),
    inference(miniscope,[status(thm)],[f_4014_2]) ).

cnf(f_4014_4,plain,
    ( U_16177 = c_List_Olist_ONil(U_16175)
    | c_List_Olist_ONil(U_16175) != hAPP(hAPP(c_List_Oappend(U_16175),U_16177),U_16179) ),
    inference(clausify,[status(thm)],[f_4014_3]) ).

cnf(f_4014_5,plain,
    ( U_16179 = c_List_Olist_ONil(U_16175)
    | c_List_Olist_ONil(U_16175) != hAPP(hAPP(c_List_Oappend(U_16175),U_16177),U_16179) ),
    inference(clausify,[status(thm)],[f_4014_3]) ).

cnf(f_4014_6,plain,
    ( c_List_Olist_ONil(U_16176) = hAPP(hAPP(c_List_Oappend(U_16176),U_16178),U_16180)
    | U_16180 != c_List_Olist_ONil(U_16176)
    | U_16178 != c_List_Olist_ONil(U_16176) ),
    inference(clausify,[status(thm)],[f_4014_3]) ).

fof(f_4015_1,plain,
    ! [V_ys,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) = V_ys,
    inference(fof_nnf,[status(thm)],[fact_append__Nil]) ).

fof(f_4015_2,plain,
    ! [U_16182,U_16181] : hAPP(hAPP(c_List_Oappend(U_16181),c_List_Olist_ONil(U_16181)),U_16182) = U_16182,
    inference(variable_rename,[status(thm)],[f_4015_1]) ).

cnf(f_4015_3,plain,
    hAPP(hAPP(c_List_Oappend(U_16181),c_List_Olist_ONil(U_16181)),U_16182) = U_16182,
    inference(clausify,[status(thm)],[f_4015_2]) ).

fof(f_4016_1,plain,
    ! [V_xs,T_a,V_ys] :
      ( ( c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),V_xs),c_List_Obutlast(T_a,V_ys))
        | V_ys = c_List_Olist_ONil(T_a) )
      & ( c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Obutlast(T_a,V_xs)
        | V_ys != c_List_Olist_ONil(T_a) ) ),
    inference(fof_nnf,[status(thm)],[fact_butlast__append]) ).

fof(f_4016_2,plain,
    ! [U_16185,U_16184,U_16183] :
      ( ( c_List_Obutlast(U_16184,hAPP(hAPP(c_List_Oappend(U_16184),U_16185),U_16183)) = hAPP(hAPP(c_List_Oappend(U_16184),U_16185),c_List_Obutlast(U_16184,U_16183))
        | U_16183 = c_List_Olist_ONil(U_16184) )
      & ( c_List_Obutlast(U_16184,hAPP(hAPP(c_List_Oappend(U_16184),U_16185),U_16183)) = c_List_Obutlast(U_16184,U_16185)
        | U_16183 != c_List_Olist_ONil(U_16184) ) ),
    inference(variable_rename,[status(thm)],[f_4016_1]) ).

fof(f_4016_3,plain,
    ( ! [U_16191,U_16189,U_16187] :
        ( c_List_Obutlast(U_16189,hAPP(hAPP(c_List_Oappend(U_16189),U_16191),U_16187)) = hAPP(hAPP(c_List_Oappend(U_16189),U_16191),c_List_Obutlast(U_16189,U_16187))
        | U_16187 = c_List_Olist_ONil(U_16189) )
    & ! [U_16190,U_16188,U_16186] :
        ( c_List_Obutlast(U_16188,hAPP(hAPP(c_List_Oappend(U_16188),U_16190),U_16186)) = c_List_Obutlast(U_16188,U_16190)
        | U_16186 != c_List_Olist_ONil(U_16188) ) ),
    inference(miniscope,[status(thm)],[f_4016_2]) ).

cnf(f_4016_4,plain,
    ( c_List_Obutlast(U_16188,hAPP(hAPP(c_List_Oappend(U_16188),U_16190),U_16186)) = c_List_Obutlast(U_16188,U_16190)
    | U_16186 != c_List_Olist_ONil(U_16188) ),
    inference(clausify,[status(thm)],[f_4016_3]) ).

cnf(f_4016_5,plain,
    ( c_List_Obutlast(U_16189,hAPP(hAPP(c_List_Oappend(U_16189),U_16191),U_16187)) = hAPP(hAPP(c_List_Oappend(U_16189),U_16191),c_List_Obutlast(U_16189,U_16187))
    | U_16187 = c_List_Olist_ONil(U_16189) ),
    inference(clausify,[status(thm)],[f_4016_3]) ).

fof(f_4017_1,plain,
    ! [V_ys,V_x,V_xs,T_a] : hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)) = V_x,
    inference(fof_nnf,[status(thm)],[fact_nth__append__length]) ).

fof(f_4017_2,plain,
    ! [U_16195,U_16194,U_16193,U_16192] : hAPP(hAPP(c_List_Onth(U_16192),hAPP(hAPP(c_List_Oappend(U_16192),U_16193),hAPP(hAPP(c_List_Olist_OCons(U_16192),U_16194),U_16195))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16192)),U_16193)) = U_16194,
    inference(variable_rename,[status(thm)],[f_4017_1]) ).

cnf(f_4017_3,plain,
    hAPP(hAPP(c_List_Onth(U_16192),hAPP(hAPP(c_List_Oappend(U_16192),U_16193),hAPP(hAPP(c_List_Olist_OCons(U_16192),U_16194),U_16195))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16192)),U_16193)) = U_16194,
    inference(clausify,[status(thm)],[f_4017_2]) ).

fof(f_4018_1,plain,
    ! [V_n,V_ys,V_xs,T_a] : hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n)) = hAPP(hAPP(c_List_Onth(T_a),V_ys),V_n),
    inference(fof_nnf,[status(thm)],[fact_nth__append__length__plus]) ).

fof(f_4018_2,plain,
    ! [U_16199,U_16198,U_16197,U_16196] : hAPP(hAPP(c_List_Onth(U_16196),hAPP(hAPP(c_List_Oappend(U_16196),U_16197),U_16198)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16196)),U_16197)),U_16199)) = hAPP(hAPP(c_List_Onth(U_16196),U_16198),U_16199),
    inference(variable_rename,[status(thm)],[f_4018_1]) ).

cnf(f_4018_3,plain,
    hAPP(hAPP(c_List_Onth(U_16196),hAPP(hAPP(c_List_Oappend(U_16196),U_16197),U_16198)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16196)),U_16197)),U_16199)) = hAPP(hAPP(c_List_Onth(U_16196),U_16198),U_16199),
    inference(clausify,[status(thm)],[f_4018_2]) ).

fof(f_4019_1,plain,
    ! [V_ys,V_xs,V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_ys)),
    inference(fof_nnf,[status(thm)],[fact_take__append]) ).

fof(f_4019_2,plain,
    ! [U_16203,U_16202,U_16201,U_16200] : hAPP(hAPP(c_List_Otake(U_16200),U_16201),hAPP(hAPP(c_List_Oappend(U_16200),U_16202),U_16203)) = hAPP(hAPP(c_List_Oappend(U_16200),hAPP(hAPP(c_List_Otake(U_16200),U_16201),U_16202)),hAPP(hAPP(c_List_Otake(U_16200),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_16201),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16200)),U_16202))),U_16203)),
    inference(variable_rename,[status(thm)],[f_4019_1]) ).

cnf(f_4019_3,plain,
    hAPP(hAPP(c_List_Otake(U_16200),U_16201),hAPP(hAPP(c_List_Oappend(U_16200),U_16202),U_16203)) = hAPP(hAPP(c_List_Oappend(U_16200),hAPP(hAPP(c_List_Otake(U_16200),U_16201),U_16202)),hAPP(hAPP(c_List_Otake(U_16200),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_16201),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16200)),U_16202))),U_16203)),
    inference(clausify,[status(thm)],[f_4019_2]) ).

fof(f_4020_1,plain,
    ! [V_x,V_ys,V_xs,T_a,V_i] :
      ( hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_i),V_x) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_ys)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) ),
    inference(fof_nnf,[status(thm)],[fact_list__update__append1]) ).

fof(f_4020_2,plain,
    ! [U_16208,U_16207,U_16206,U_16205,U_16204] :
      ( hAPP(hAPP(c_List_Olist__update(U_16205,hAPP(hAPP(c_List_Oappend(U_16205),U_16206),U_16207)),U_16204),U_16208) = hAPP(hAPP(c_List_Oappend(U_16205),hAPP(hAPP(c_List_Olist__update(U_16205,U_16206),U_16204),U_16208)),U_16207)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16204),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16205)),U_16206))) ),
    inference(variable_rename,[status(thm)],[f_4020_1]) ).

cnf(f_4020_3,plain,
    ( hAPP(hAPP(c_List_Olist__update(U_16205,hAPP(hAPP(c_List_Oappend(U_16205),U_16206),U_16207)),U_16204),U_16208) = hAPP(hAPP(c_List_Oappend(U_16205),hAPP(hAPP(c_List_Olist__update(U_16205,U_16206),U_16204),U_16208)),U_16207)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16204),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16205)),U_16206))) ),
    inference(clausify,[status(thm)],[f_4020_2]) ).

fof(f_4021_1,plain,
    ! [V_y,V_ys,V_x,V_xs,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_y) = hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys)),
    inference(fof_nnf,[status(thm)],[fact_list__update__length]) ).

fof(f_4021_2,plain,
    ! [U_16213,U_16212,U_16211,U_16210,U_16209] : hAPP(hAPP(c_List_Olist__update(U_16209,hAPP(hAPP(c_List_Oappend(U_16209),U_16210),hAPP(hAPP(c_List_Olist_OCons(U_16209),U_16211),U_16212))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16209)),U_16210)),U_16213) = hAPP(hAPP(c_List_Oappend(U_16209),U_16210),hAPP(hAPP(c_List_Olist_OCons(U_16209),U_16213),U_16212)),
    inference(variable_rename,[status(thm)],[f_4021_1]) ).

cnf(f_4021_3,plain,
    hAPP(hAPP(c_List_Olist__update(U_16209,hAPP(hAPP(c_List_Oappend(U_16209),U_16210),hAPP(hAPP(c_List_Olist_OCons(U_16209),U_16211),U_16212))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16209)),U_16210)),U_16213) = hAPP(hAPP(c_List_Oappend(U_16209),U_16210),hAPP(hAPP(c_List_Olist_OCons(U_16209),U_16213),U_16212)),
    inference(clausify,[status(thm)],[f_4021_2]) ).

fof(f_4022_1,plain,
    ! [V_ys_2,V_xs_2,V_x_2,T_b] :
      ( ( c_List_Oremove1(T_b,V_x_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),c_List_Oremove1(T_b,V_x_2,V_ys_2))
        | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) )
      & ( c_List_Oremove1(T_b,V_x_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),c_List_Oremove1(T_b,V_x_2,V_xs_2)),V_ys_2)
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_remove1__append]) ).

fof(f_4022_2,plain,
    ! [U_16217,U_16216,U_16215,U_16214] :
      ( ( c_List_Oremove1(U_16214,U_16215,hAPP(hAPP(c_List_Oappend(U_16214),U_16216),U_16217)) = hAPP(hAPP(c_List_Oappend(U_16214),U_16216),c_List_Oremove1(U_16214,U_16215,U_16217))
        | hBOOL(hAPP(hAPP(c_member(U_16214),U_16215),hAPP(c_List_Oset(U_16214),U_16216))) )
      & ( c_List_Oremove1(U_16214,U_16215,hAPP(hAPP(c_List_Oappend(U_16214),U_16216),U_16217)) = hAPP(hAPP(c_List_Oappend(U_16214),c_List_Oremove1(U_16214,U_16215,U_16216)),U_16217)
        | ~ hBOOL(hAPP(hAPP(c_member(U_16214),U_16215),hAPP(c_List_Oset(U_16214),U_16216))) ) ),
    inference(variable_rename,[status(thm)],[f_4022_1]) ).

fof(f_4022_3,plain,
    ( ! [U_16225,U_16223,U_16221,U_16219] :
        ( c_List_Oremove1(U_16219,U_16221,hAPP(hAPP(c_List_Oappend(U_16219),U_16223),U_16225)) = hAPP(hAPP(c_List_Oappend(U_16219),U_16223),c_List_Oremove1(U_16219,U_16221,U_16225))
        | hBOOL(hAPP(hAPP(c_member(U_16219),U_16221),hAPP(c_List_Oset(U_16219),U_16223))) )
    & ! [U_16224,U_16222,U_16220,U_16218] :
        ( c_List_Oremove1(U_16218,U_16220,hAPP(hAPP(c_List_Oappend(U_16218),U_16222),U_16224)) = hAPP(hAPP(c_List_Oappend(U_16218),c_List_Oremove1(U_16218,U_16220,U_16222)),U_16224)
        | ~ hBOOL(hAPP(hAPP(c_member(U_16218),U_16220),hAPP(c_List_Oset(U_16218),U_16222))) ) ),
    inference(miniscope,[status(thm)],[f_4022_2]) ).

cnf(f_4022_4,plain,
    ( c_List_Oremove1(U_16218,U_16220,hAPP(hAPP(c_List_Oappend(U_16218),U_16222),U_16224)) = hAPP(hAPP(c_List_Oappend(U_16218),c_List_Oremove1(U_16218,U_16220,U_16222)),U_16224)
    | ~ hBOOL(hAPP(hAPP(c_member(U_16218),U_16220),hAPP(c_List_Oset(U_16218),U_16222))) ),
    inference(clausify,[status(thm)],[f_4022_3]) ).

cnf(f_4022_5,plain,
    ( c_List_Oremove1(U_16219,U_16221,hAPP(hAPP(c_List_Oappend(U_16219),U_16223),U_16225)) = hAPP(hAPP(c_List_Oappend(U_16219),U_16223),c_List_Oremove1(U_16219,U_16221,U_16225))
    | hBOOL(hAPP(hAPP(c_member(U_16219),U_16221),hAPP(c_List_Oset(U_16219),U_16223))) ),
    inference(clausify,[status(thm)],[f_4022_3]) ).

fof(f_4023_1,plain,
    ! [V_ys_2,V_xs_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)))))
      | ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_ys_2))))
        & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_xs_2)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_in__set__butlast__appendI]) ).

fof(f_4023_2,plain,
    ! [U_16229,U_16228,U_16227,U_16226] :
      ( hBOOL(hAPP(hAPP(c_member(U_16226),U_16227),hAPP(c_List_Oset(U_16226),c_List_Obutlast(U_16226,hAPP(hAPP(c_List_Oappend(U_16226),U_16228),U_16229)))))
      | ( ~ hBOOL(hAPP(hAPP(c_member(U_16226),U_16227),hAPP(c_List_Oset(U_16226),c_List_Obutlast(U_16226,U_16229))))
        & ~ hBOOL(hAPP(hAPP(c_member(U_16226),U_16227),hAPP(c_List_Oset(U_16226),c_List_Obutlast(U_16226,U_16228)))) ) ),
    inference(variable_rename,[status(thm)],[f_4023_1]) ).

cnf(f_4023_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_16226),U_16227),hAPP(c_List_Oset(U_16226),c_List_Obutlast(U_16226,U_16228))))
    | hBOOL(hAPP(hAPP(c_member(U_16226),U_16227),hAPP(c_List_Oset(U_16226),c_List_Obutlast(U_16226,hAPP(hAPP(c_List_Oappend(U_16226),U_16228),U_16229))))) ),
    inference(clausify,[status(thm)],[f_4023_2]) ).

cnf(f_4023_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_16226),U_16227),hAPP(c_List_Oset(U_16226),c_List_Obutlast(U_16226,U_16229))))
    | hBOOL(hAPP(hAPP(c_member(U_16226),U_16227),hAPP(c_List_Oset(U_16226),c_List_Obutlast(U_16226,hAPP(hAPP(c_List_Oappend(U_16226),U_16228),U_16229))))) ),
    inference(clausify,[status(thm)],[f_4023_2]) ).

fof(f_4024_1,plain,
    ! [V_x,V_xs,T_a] : c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a)))) = V_xs,
    inference(fof_nnf,[status(thm)],[fact_butlast__snoc]) ).

fof(f_4024_2,plain,
    ! [U_16232,U_16231,U_16230] : c_List_Obutlast(U_16230,hAPP(hAPP(c_List_Oappend(U_16230),U_16231),hAPP(hAPP(c_List_Olist_OCons(U_16230),U_16232),c_List_Olist_ONil(U_16230)))) = U_16231,
    inference(variable_rename,[status(thm)],[f_4024_1]) ).

cnf(f_4024_3,plain,
    c_List_Obutlast(U_16230,hAPP(hAPP(c_List_Oappend(U_16230),U_16231),hAPP(hAPP(c_List_Olist_OCons(U_16230),U_16232),c_List_Olist_ONil(U_16230)))) = U_16231,
    inference(clausify,[status(thm)],[f_4024_2]) ).

fof(f_4025_1,plain,
    ! [V_vs_2,V_us_2,V_r_2,V_ys_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_us_2)),hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_vs_2))),c_List_Olistrel1(T_b,V_r_2)))
      | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_us_2),V_vs_2)),c_List_Olistrel1(T_b,V_r_2)))
          | V_xs_2 != V_ys_2 )
        & ( V_us_2 != V_vs_2
          | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_append__listrel1I]) ).

fof(f_4025_2,plain,
    ! [U_16238,U_16237,U_16236,U_16235,U_16234,U_16233] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16233),tc_List_Olist(U_16233))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16233),tc_List_Olist(U_16233)),hAPP(hAPP(c_List_Oappend(U_16233),U_16234),U_16237)),hAPP(hAPP(c_List_Oappend(U_16233),U_16235),U_16238))),c_List_Olistrel1(U_16233,U_16236)))
      | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16233),tc_List_Olist(U_16233))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16233),tc_List_Olist(U_16233)),U_16237),U_16238)),c_List_Olistrel1(U_16233,U_16236)))
          | U_16234 != U_16235 )
        & ( U_16237 != U_16238
          | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16233),tc_List_Olist(U_16233))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16233),tc_List_Olist(U_16233)),U_16234),U_16235)),c_List_Olistrel1(U_16233,U_16236))) ) ) ),
    inference(variable_rename,[status(thm)],[f_4025_1]) ).

cnf(f_4025_3,plain,
    ( U_16237 != U_16238
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16233),tc_List_Olist(U_16233))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16233),tc_List_Olist(U_16233)),U_16234),U_16235)),c_List_Olistrel1(U_16233,U_16236)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16233),tc_List_Olist(U_16233))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16233),tc_List_Olist(U_16233)),hAPP(hAPP(c_List_Oappend(U_16233),U_16234),U_16237)),hAPP(hAPP(c_List_Oappend(U_16233),U_16235),U_16238))),c_List_Olistrel1(U_16233,U_16236))) ),
    inference(clausify,[status(thm)],[f_4025_2]) ).

cnf(f_4025_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16233),tc_List_Olist(U_16233))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16233),tc_List_Olist(U_16233)),U_16237),U_16238)),c_List_Olistrel1(U_16233,U_16236)))
    | U_16234 != U_16235
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16233),tc_List_Olist(U_16233))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16233),tc_List_Olist(U_16233)),hAPP(hAPP(c_List_Oappend(U_16233),U_16234),U_16237)),hAPP(hAPP(c_List_Oappend(U_16233),U_16235),U_16238))),c_List_Olistrel1(U_16233,U_16236))) ),
    inference(clausify,[status(thm)],[f_4025_2]) ).

fof(f_4026_1,plain,
    ! [V_x_2,V_r_2,V_v_2,V_u_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_u_2)),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_v_2))),c_List_Olexord(T_b,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_u_2),V_v_2)),c_List_Olexord(T_b,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_lexord__append__leftI]) ).

fof(f_4026_2,plain,
    ! [U_16243,U_16242,U_16241,U_16240,U_16239] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16239),tc_List_Olist(U_16239))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16239),tc_List_Olist(U_16239)),hAPP(hAPP(c_List_Oappend(U_16239),U_16243),U_16240)),hAPP(hAPP(c_List_Oappend(U_16239),U_16243),U_16241))),c_List_Olexord(U_16239,U_16242)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16239),tc_List_Olist(U_16239))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16239),tc_List_Olist(U_16239)),U_16240),U_16241)),c_List_Olexord(U_16239,U_16242))) ),
    inference(variable_rename,[status(thm)],[f_4026_1]) ).

cnf(f_4026_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16239),tc_List_Olist(U_16239))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16239),tc_List_Olist(U_16239)),hAPP(hAPP(c_List_Oappend(U_16239),U_16243),U_16240)),hAPP(hAPP(c_List_Oappend(U_16239),U_16243),U_16241))),c_List_Olexord(U_16239,U_16242)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16239),tc_List_Olist(U_16239))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16239),tc_List_Olist(U_16239)),U_16240),U_16241)),c_List_Olexord(U_16239,U_16242))) ),
    inference(clausify,[status(thm)],[f_4026_2]) ).

fof(f_4027_1,plain,
    ! [V_ys_2,V_xs_2,T_b] :
      ( ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_ys_2)) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_List_Odistinct(T_b),V_ys_2))
        | ~ hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) )
      & ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_ys_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
          & hBOOL(hAPP(c_List_Odistinct(T_b),V_ys_2))
          & hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) )
        | ~ hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__append]) ).

fof(f_4027_2,plain,
    ! [U_16246,U_16245,U_16244] :
      ( ( hBOOL(hAPP(c_List_Odistinct(U_16244),hAPP(hAPP(c_List_Oappend(U_16244),U_16245),U_16246)))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16244,tc_HOL_Obool)),hAPP(c_List_Oset(U_16244),U_16245)),hAPP(c_List_Oset(U_16244),U_16246)) != c_Orderings_Obot__class_Obot(tc_fun(U_16244,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_16244),U_16246))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_16244),U_16245)) )
      & ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16244,tc_HOL_Obool)),hAPP(c_List_Oset(U_16244),U_16245)),hAPP(c_List_Oset(U_16244),U_16246)) = c_Orderings_Obot__class_Obot(tc_fun(U_16244,tc_HOL_Obool))
          & hBOOL(hAPP(c_List_Odistinct(U_16244),U_16246))
          & hBOOL(hAPP(c_List_Odistinct(U_16244),U_16245)) )
        | ~ hBOOL(hAPP(c_List_Odistinct(U_16244),hAPP(hAPP(c_List_Oappend(U_16244),U_16245),U_16246))) ) ),
    inference(variable_rename,[status(thm)],[f_4027_1]) ).

fof(f_4027_3,plain,
    ( ! [U_16252,U_16250,U_16248] :
        ( hBOOL(hAPP(c_List_Odistinct(U_16248),hAPP(hAPP(c_List_Oappend(U_16248),U_16250),U_16252)))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16248,tc_HOL_Obool)),hAPP(c_List_Oset(U_16248),U_16250)),hAPP(c_List_Oset(U_16248),U_16252)) != c_Orderings_Obot__class_Obot(tc_fun(U_16248,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_16248),U_16252))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_16248),U_16250)) )
    & ! [U_16251,U_16249,U_16247] :
        ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16247,tc_HOL_Obool)),hAPP(c_List_Oset(U_16247),U_16249)),hAPP(c_List_Oset(U_16247),U_16251)) = c_Orderings_Obot__class_Obot(tc_fun(U_16247,tc_HOL_Obool))
          & hBOOL(hAPP(c_List_Odistinct(U_16247),U_16251))
          & hBOOL(hAPP(c_List_Odistinct(U_16247),U_16249)) )
        | ~ hBOOL(hAPP(c_List_Odistinct(U_16247),hAPP(hAPP(c_List_Oappend(U_16247),U_16249),U_16251))) ) ),
    inference(miniscope,[status(thm)],[f_4027_2]) ).

cnf(f_4027_4,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_16247),U_16249))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_16247),hAPP(hAPP(c_List_Oappend(U_16247),U_16249),U_16251))) ),
    inference(clausify,[status(thm)],[f_4027_3]) ).

cnf(f_4027_5,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_16247),U_16251))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_16247),hAPP(hAPP(c_List_Oappend(U_16247),U_16249),U_16251))) ),
    inference(clausify,[status(thm)],[f_4027_3]) ).

cnf(f_4027_6,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16247,tc_HOL_Obool)),hAPP(c_List_Oset(U_16247),U_16249)),hAPP(c_List_Oset(U_16247),U_16251)) = c_Orderings_Obot__class_Obot(tc_fun(U_16247,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_16247),hAPP(hAPP(c_List_Oappend(U_16247),U_16249),U_16251))) ),
    inference(clausify,[status(thm)],[f_4027_3]) ).

cnf(f_4027_7,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_16248),hAPP(hAPP(c_List_Oappend(U_16248),U_16250),U_16252)))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16248,tc_HOL_Obool)),hAPP(c_List_Oset(U_16248),U_16250)),hAPP(c_List_Oset(U_16248),U_16252)) != c_Orderings_Obot__class_Obot(tc_fun(U_16248,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_16248),U_16252))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_16248),U_16250)) ),
    inference(clausify,[status(thm)],[f_4027_3]) ).

fof(f_4028_1,plain,
    ! [V_ys,V_xs,T_a,V_n] :
      ( ( hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_n) = hAPP(hAPP(c_List_Onth(T_a),V_ys),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) )
      & ( hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_n) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) ) ),
    inference(fof_nnf,[status(thm)],[fact_nth__append]) ).

fof(f_4028_2,plain,
    ! [U_16256,U_16255,U_16254,U_16253] :
      ( ( hAPP(hAPP(c_List_Onth(U_16254),hAPP(hAPP(c_List_Oappend(U_16254),U_16255),U_16256)),U_16253) = hAPP(hAPP(c_List_Onth(U_16254),U_16256),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_16253),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16254)),U_16255)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16253),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16254)),U_16255))) )
      & ( hAPP(hAPP(c_List_Onth(U_16254),hAPP(hAPP(c_List_Oappend(U_16254),U_16255),U_16256)),U_16253) = hAPP(hAPP(c_List_Onth(U_16254),U_16255),U_16253)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16253),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16254)),U_16255))) ) ),
    inference(variable_rename,[status(thm)],[f_4028_1]) ).

fof(f_4028_3,plain,
    ( ! [U_16264,U_16262,U_16260,U_16258] :
        ( hAPP(hAPP(c_List_Onth(U_16260),hAPP(hAPP(c_List_Oappend(U_16260),U_16262),U_16264)),U_16258) = hAPP(hAPP(c_List_Onth(U_16260),U_16264),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_16258),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16260)),U_16262)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16258),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16260)),U_16262))) )
    & ! [U_16263,U_16261,U_16259,U_16257] :
        ( hAPP(hAPP(c_List_Onth(U_16259),hAPP(hAPP(c_List_Oappend(U_16259),U_16261),U_16263)),U_16257) = hAPP(hAPP(c_List_Onth(U_16259),U_16261),U_16257)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16257),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16259)),U_16261))) ) ),
    inference(miniscope,[status(thm)],[f_4028_2]) ).

cnf(f_4028_4,plain,
    ( hAPP(hAPP(c_List_Onth(U_16259),hAPP(hAPP(c_List_Oappend(U_16259),U_16261),U_16263)),U_16257) = hAPP(hAPP(c_List_Onth(U_16259),U_16261),U_16257)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16257),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16259)),U_16261))) ),
    inference(clausify,[status(thm)],[f_4028_3]) ).

cnf(f_4028_5,plain,
    ( hAPP(hAPP(c_List_Onth(U_16260),hAPP(hAPP(c_List_Oappend(U_16260),U_16262),U_16264)),U_16258) = hAPP(hAPP(c_List_Onth(U_16260),U_16264),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_16258),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16260)),U_16262)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16258),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16260)),U_16262))) ),
    inference(clausify,[status(thm)],[f_4028_3]) ).

fof(f_4029_1,plain,
    ! [V_x,V_ys,V_xs,T_a,V_n] :
      ( ( hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_n),V_x) = hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist__update(T_a,V_ys),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_x))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) )
      & ( hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_n),V_x) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_n),V_x)),V_ys)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__update__append]) ).

fof(f_4029_2,plain,
    ! [U_16269,U_16268,U_16267,U_16266,U_16265] :
      ( ( hAPP(hAPP(c_List_Olist__update(U_16266,hAPP(hAPP(c_List_Oappend(U_16266),U_16267),U_16268)),U_16265),U_16269) = hAPP(hAPP(c_List_Oappend(U_16266),U_16267),hAPP(hAPP(c_List_Olist__update(U_16266,U_16268),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_16265),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16266)),U_16267))),U_16269))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16265),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16266)),U_16267))) )
      & ( hAPP(hAPP(c_List_Olist__update(U_16266,hAPP(hAPP(c_List_Oappend(U_16266),U_16267),U_16268)),U_16265),U_16269) = hAPP(hAPP(c_List_Oappend(U_16266),hAPP(hAPP(c_List_Olist__update(U_16266,U_16267),U_16265),U_16269)),U_16268)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16265),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16266)),U_16267))) ) ),
    inference(variable_rename,[status(thm)],[f_4029_1]) ).

fof(f_4029_3,plain,
    ( ! [U_16279,U_16277,U_16275,U_16273,U_16271] :
        ( hAPP(hAPP(c_List_Olist__update(U_16273,hAPP(hAPP(c_List_Oappend(U_16273),U_16275),U_16277)),U_16271),U_16279) = hAPP(hAPP(c_List_Oappend(U_16273),U_16275),hAPP(hAPP(c_List_Olist__update(U_16273,U_16277),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_16271),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16273)),U_16275))),U_16279))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16271),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16273)),U_16275))) )
    & ! [U_16278,U_16276,U_16274,U_16272,U_16270] :
        ( hAPP(hAPP(c_List_Olist__update(U_16272,hAPP(hAPP(c_List_Oappend(U_16272),U_16274),U_16276)),U_16270),U_16278) = hAPP(hAPP(c_List_Oappend(U_16272),hAPP(hAPP(c_List_Olist__update(U_16272,U_16274),U_16270),U_16278)),U_16276)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16270),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16272)),U_16274))) ) ),
    inference(miniscope,[status(thm)],[f_4029_2]) ).

cnf(f_4029_4,plain,
    ( hAPP(hAPP(c_List_Olist__update(U_16272,hAPP(hAPP(c_List_Oappend(U_16272),U_16274),U_16276)),U_16270),U_16278) = hAPP(hAPP(c_List_Oappend(U_16272),hAPP(hAPP(c_List_Olist__update(U_16272,U_16274),U_16270),U_16278)),U_16276)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16270),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16272)),U_16274))) ),
    inference(clausify,[status(thm)],[f_4029_3]) ).

cnf(f_4029_5,plain,
    ( hAPP(hAPP(c_List_Olist__update(U_16273,hAPP(hAPP(c_List_Oappend(U_16273),U_16275),U_16277)),U_16271),U_16279) = hAPP(hAPP(c_List_Oappend(U_16273),U_16275),hAPP(hAPP(c_List_Olist__update(U_16273,U_16277),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_16271),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16273)),U_16275))),U_16279))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16271),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16273)),U_16275))) ),
    inference(clausify,[status(thm)],[f_4029_3]) ).

fof(f_4030_1,plain,
    ! [V_A_2,V_l_H_2,V_l_2,T_b] : c_List_Osublist(T_b,hAPP(hAPP(c_List_Oappend(T_b),V_l_2),V_l_H_2),V_A_2) = hAPP(hAPP(c_List_Oappend(T_b),c_List_Osublist(T_b,V_l_2,V_A_2)),c_List_Osublist(T_b,V_l_H_2,hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_l_2)))),V_A_2)))),
    inference(fof_nnf,[status(thm)],[fact_sublist__append]) ).

fof(f_4030_2,plain,
    ! [U_16283,U_16282,U_16281,U_16280] : c_List_Osublist(U_16280,hAPP(hAPP(c_List_Oappend(U_16280),U_16281),U_16282),U_16283) = hAPP(hAPP(c_List_Oappend(U_16280),c_List_Osublist(U_16280,U_16281,U_16283)),c_List_Osublist(U_16280,U_16282,hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16280)),U_16281)))),U_16283)))),
    inference(variable_rename,[status(thm)],[f_4030_1]) ).

cnf(f_4030_3,plain,
    c_List_Osublist(U_16280,hAPP(hAPP(c_List_Oappend(U_16280),U_16281),U_16282),U_16283) = hAPP(hAPP(c_List_Oappend(U_16280),c_List_Osublist(U_16280,U_16281,U_16283)),c_List_Osublist(U_16280,U_16282,hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16280)),U_16281)))),U_16283)))),
    inference(clausify,[status(thm)],[f_4030_2]) ).

fof(f_4031_1,plain,
    ! [V_ys_2,V_vs_2,V_us_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
      | V_ys_2 != hAPP(hAPP(c_List_Oappend(T_b),V_us_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_vs_2))
      | V_xs_2 != hAPP(hAPP(c_List_Oappend(T_b),V_us_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_vs_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_listrel1I]) ).

fof(f_4031_2,plain,
    ! [U_16291,U_16290,U_16289,U_16288,U_16287,U_16286,U_16285,U_16284] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16284),tc_List_Olist(U_16284))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16284),tc_List_Olist(U_16284)),U_16288),U_16291)),c_List_Olistrel1(U_16284,U_16287)))
      | U_16291 != hAPP(hAPP(c_List_Oappend(U_16284),U_16289),hAPP(hAPP(c_List_Olist_OCons(U_16284),U_16286),U_16290))
      | U_16288 != hAPP(hAPP(c_List_Oappend(U_16284),U_16289),hAPP(hAPP(c_List_Olist_OCons(U_16284),U_16285),U_16290))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16284,U_16284)),hAPP(hAPP(c_Product__Type_OPair(U_16284,U_16284),U_16285),U_16286)),U_16287)) ),
    inference(variable_rename,[status(thm)],[f_4031_1]) ).

cnf(f_4031_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16284),tc_List_Olist(U_16284))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16284),tc_List_Olist(U_16284)),U_16288),U_16291)),c_List_Olistrel1(U_16284,U_16287)))
    | U_16291 != hAPP(hAPP(c_List_Oappend(U_16284),U_16289),hAPP(hAPP(c_List_Olist_OCons(U_16284),U_16286),U_16290))
    | U_16288 != hAPP(hAPP(c_List_Oappend(U_16284),U_16289),hAPP(hAPP(c_List_Olist_OCons(U_16284),U_16285),U_16290))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16284,U_16284)),hAPP(hAPP(c_Product__Type_OPair(U_16284,U_16284),U_16285),U_16286)),U_16287)) ),
    inference(clausify,[status(thm)],[f_4031_2]) ).

fof(f_4032_1,plain,
    ! [V_y_2,V_x_2,V_u_2,V_r_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_u_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_x_2))),hAPP(hAPP(c_List_Oappend(T_b),V_u_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_b_2),V_y_2)))),c_List_Olexord(T_b,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) ),
    inference(fof_nnf,[status(thm)],[fact_lexord__append__left__rightI]) ).

fof(f_4032_2,plain,
    ! [U_16298,U_16297,U_16296,U_16295,U_16294,U_16293,U_16292] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16292),tc_List_Olist(U_16292))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16292),tc_List_Olist(U_16292)),hAPP(hAPP(c_List_Oappend(U_16292),U_16296),hAPP(hAPP(c_List_Olist_OCons(U_16292),U_16293),U_16297))),hAPP(hAPP(c_List_Oappend(U_16292),U_16296),hAPP(hAPP(c_List_Olist_OCons(U_16292),U_16294),U_16298)))),c_List_Olexord(U_16292,U_16295)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16292,U_16292)),hAPP(hAPP(c_Product__Type_OPair(U_16292,U_16292),U_16293),U_16294)),U_16295)) ),
    inference(variable_rename,[status(thm)],[f_4032_1]) ).

cnf(f_4032_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16292),tc_List_Olist(U_16292))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16292),tc_List_Olist(U_16292)),hAPP(hAPP(c_List_Oappend(U_16292),U_16296),hAPP(hAPP(c_List_Olist_OCons(U_16292),U_16293),U_16297))),hAPP(hAPP(c_List_Oappend(U_16292),U_16296),hAPP(hAPP(c_List_Olist_OCons(U_16292),U_16294),U_16298)))),c_List_Olexord(U_16292,U_16295)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16292,U_16292)),hAPP(hAPP(c_Product__Type_OPair(U_16292,U_16292),U_16293),U_16294)),U_16295)) ),
    inference(clausify,[status(thm)],[f_4032_2]) ).

fof(f_4033_1,plain,
    ! [V_xs,T_a,V_i] :
      ( hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_i)),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)),c_List_Olist_ONil(T_a)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) ),
    inference(fof_nnf,[status(thm)],[fact_take__Suc__conv__app__nth]) ).

fof(f_4033_2,plain,
    ! [U_16301,U_16300,U_16299] :
      ( hAPP(hAPP(c_List_Otake(U_16300),hAPP(c_Nat_OSuc,U_16299)),U_16301) = hAPP(hAPP(c_List_Oappend(U_16300),hAPP(hAPP(c_List_Otake(U_16300),U_16299),U_16301)),hAPP(hAPP(c_List_Olist_OCons(U_16300),hAPP(hAPP(c_List_Onth(U_16300),U_16301),U_16299)),c_List_Olist_ONil(U_16300)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16299),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16300)),U_16301))) ),
    inference(variable_rename,[status(thm)],[f_4033_1]) ).

cnf(f_4033_3,plain,
    ( hAPP(hAPP(c_List_Otake(U_16300),hAPP(c_Nat_OSuc,U_16299)),U_16301) = hAPP(hAPP(c_List_Oappend(U_16300),hAPP(hAPP(c_List_Otake(U_16300),U_16299),U_16301)),hAPP(hAPP(c_List_Olist_OCons(U_16300),hAPP(hAPP(c_List_Onth(U_16300),U_16301),U_16299)),c_List_Olist_ONil(U_16300)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16299),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16300)),U_16301))) ),
    inference(clausify,[status(thm)],[f_4033_2]) ).

fof(f_4034_1,plain,
    ! [V_r_2,V_y_2,V_ys_2,V_x_2,V_xs_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)))),hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),c_List_Olist_ONil(T_b))))),c_List_Olistrel1(T_b,V_r_2)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
            | V_xs_2 != V_ys_2 )
          & ( V_x_2 != V_y_2
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) ) ) )
      & ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
          & V_xs_2 = V_ys_2 )
        | ( V_x_2 = V_y_2
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)))),hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),c_List_Olist_ONil(T_b))))),c_List_Olistrel1(T_b,V_r_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_snoc__listrel1__snoc__iff]) ).

fof(f_4034_2,plain,
    ! [U_16307,U_16306,U_16305,U_16304,U_16303,U_16302] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16302),tc_List_Olist(U_16302))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16302),tc_List_Olist(U_16302)),hAPP(hAPP(c_List_Oappend(U_16302),U_16303),hAPP(hAPP(c_List_Olist_OCons(U_16302),U_16304),c_List_Olist_ONil(U_16302)))),hAPP(hAPP(c_List_Oappend(U_16302),U_16305),hAPP(hAPP(c_List_Olist_OCons(U_16302),U_16306),c_List_Olist_ONil(U_16302))))),c_List_Olistrel1(U_16302,U_16307)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16302,U_16302)),hAPP(hAPP(c_Product__Type_OPair(U_16302,U_16302),U_16304),U_16306)),U_16307))
            | U_16303 != U_16305 )
          & ( U_16304 != U_16306
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16302),tc_List_Olist(U_16302))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16302),tc_List_Olist(U_16302)),U_16303),U_16305)),c_List_Olistrel1(U_16302,U_16307))) ) ) )
      & ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16302,U_16302)),hAPP(hAPP(c_Product__Type_OPair(U_16302,U_16302),U_16304),U_16306)),U_16307))
          & U_16303 = U_16305 )
        | ( U_16304 = U_16306
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16302),tc_List_Olist(U_16302))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16302),tc_List_Olist(U_16302)),U_16303),U_16305)),c_List_Olistrel1(U_16302,U_16307))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16302),tc_List_Olist(U_16302))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16302),tc_List_Olist(U_16302)),hAPP(hAPP(c_List_Oappend(U_16302),U_16303),hAPP(hAPP(c_List_Olist_OCons(U_16302),U_16304),c_List_Olist_ONil(U_16302)))),hAPP(hAPP(c_List_Oappend(U_16302),U_16305),hAPP(hAPP(c_List_Olist_OCons(U_16302),U_16306),c_List_Olist_ONil(U_16302))))),c_List_Olistrel1(U_16302,U_16307))) ) ),
    inference(variable_rename,[status(thm)],[f_4034_1]) ).

fof(f_4034_3,plain,
    ( ! [U_16319,U_16317,U_16315,U_16313,U_16311,U_16309] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16309),tc_List_Olist(U_16309))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16309),tc_List_Olist(U_16309)),hAPP(hAPP(c_List_Oappend(U_16309),U_16311),hAPP(hAPP(c_List_Olist_OCons(U_16309),U_16313),c_List_Olist_ONil(U_16309)))),hAPP(hAPP(c_List_Oappend(U_16309),U_16315),hAPP(hAPP(c_List_Olist_OCons(U_16309),U_16317),c_List_Olist_ONil(U_16309))))),c_List_Olistrel1(U_16309,U_16319)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16309,U_16309)),hAPP(hAPP(c_Product__Type_OPair(U_16309,U_16309),U_16313),U_16317)),U_16319))
            | U_16311 != U_16315 )
          & ( U_16313 != U_16317
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16309),tc_List_Olist(U_16309))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16309),tc_List_Olist(U_16309)),U_16311),U_16315)),c_List_Olistrel1(U_16309,U_16319))) ) ) )
    & ! [U_16318,U_16316,U_16314,U_16312,U_16310,U_16308] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16308,U_16308)),hAPP(hAPP(c_Product__Type_OPair(U_16308,U_16308),U_16312),U_16316)),U_16318))
          & U_16310 = U_16314 )
        | ( U_16312 = U_16316
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16308),tc_List_Olist(U_16308))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16308),tc_List_Olist(U_16308)),U_16310),U_16314)),c_List_Olistrel1(U_16308,U_16318))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16308),tc_List_Olist(U_16308))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16308),tc_List_Olist(U_16308)),hAPP(hAPP(c_List_Oappend(U_16308),U_16310),hAPP(hAPP(c_List_Olist_OCons(U_16308),U_16312),c_List_Olist_ONil(U_16308)))),hAPP(hAPP(c_List_Oappend(U_16308),U_16314),hAPP(hAPP(c_List_Olist_OCons(U_16308),U_16316),c_List_Olist_ONil(U_16308))))),c_List_Olistrel1(U_16308,U_16318))) ) ),
    inference(miniscope,[status(thm)],[f_4034_2]) ).

cnf(f_4034_4,plain,
    ( U_16310 = U_16314
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16308),tc_List_Olist(U_16308))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16308),tc_List_Olist(U_16308)),U_16310),U_16314)),c_List_Olistrel1(U_16308,U_16318)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16308),tc_List_Olist(U_16308))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16308),tc_List_Olist(U_16308)),hAPP(hAPP(c_List_Oappend(U_16308),U_16310),hAPP(hAPP(c_List_Olist_OCons(U_16308),U_16312),c_List_Olist_ONil(U_16308)))),hAPP(hAPP(c_List_Oappend(U_16308),U_16314),hAPP(hAPP(c_List_Olist_OCons(U_16308),U_16316),c_List_Olist_ONil(U_16308))))),c_List_Olistrel1(U_16308,U_16318))) ),
    inference(clausify,[status(thm)],[f_4034_3]) ).

cnf(f_4034_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16308,U_16308)),hAPP(hAPP(c_Product__Type_OPair(U_16308,U_16308),U_16312),U_16316)),U_16318))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16308),tc_List_Olist(U_16308))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16308),tc_List_Olist(U_16308)),U_16310),U_16314)),c_List_Olistrel1(U_16308,U_16318)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16308),tc_List_Olist(U_16308))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16308),tc_List_Olist(U_16308)),hAPP(hAPP(c_List_Oappend(U_16308),U_16310),hAPP(hAPP(c_List_Olist_OCons(U_16308),U_16312),c_List_Olist_ONil(U_16308)))),hAPP(hAPP(c_List_Oappend(U_16308),U_16314),hAPP(hAPP(c_List_Olist_OCons(U_16308),U_16316),c_List_Olist_ONil(U_16308))))),c_List_Olistrel1(U_16308,U_16318))) ),
    inference(clausify,[status(thm)],[f_4034_3]) ).

cnf(f_4034_6,plain,
    ( U_16310 = U_16314
    | U_16312 = U_16316
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16308),tc_List_Olist(U_16308))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16308),tc_List_Olist(U_16308)),hAPP(hAPP(c_List_Oappend(U_16308),U_16310),hAPP(hAPP(c_List_Olist_OCons(U_16308),U_16312),c_List_Olist_ONil(U_16308)))),hAPP(hAPP(c_List_Oappend(U_16308),U_16314),hAPP(hAPP(c_List_Olist_OCons(U_16308),U_16316),c_List_Olist_ONil(U_16308))))),c_List_Olistrel1(U_16308,U_16318))) ),
    inference(clausify,[status(thm)],[f_4034_3]) ).

cnf(f_4034_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16308,U_16308)),hAPP(hAPP(c_Product__Type_OPair(U_16308,U_16308),U_16312),U_16316)),U_16318))
    | U_16312 = U_16316
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16308),tc_List_Olist(U_16308))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16308),tc_List_Olist(U_16308)),hAPP(hAPP(c_List_Oappend(U_16308),U_16310),hAPP(hAPP(c_List_Olist_OCons(U_16308),U_16312),c_List_Olist_ONil(U_16308)))),hAPP(hAPP(c_List_Oappend(U_16308),U_16314),hAPP(hAPP(c_List_Olist_OCons(U_16308),U_16316),c_List_Olist_ONil(U_16308))))),c_List_Olistrel1(U_16308,U_16318))) ),
    inference(clausify,[status(thm)],[f_4034_3]) ).

cnf(f_4034_8,plain,
    ( U_16313 != U_16317
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16309),tc_List_Olist(U_16309))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16309),tc_List_Olist(U_16309)),U_16311),U_16315)),c_List_Olistrel1(U_16309,U_16319)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16309),tc_List_Olist(U_16309))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16309),tc_List_Olist(U_16309)),hAPP(hAPP(c_List_Oappend(U_16309),U_16311),hAPP(hAPP(c_List_Olist_OCons(U_16309),U_16313),c_List_Olist_ONil(U_16309)))),hAPP(hAPP(c_List_Oappend(U_16309),U_16315),hAPP(hAPP(c_List_Olist_OCons(U_16309),U_16317),c_List_Olist_ONil(U_16309))))),c_List_Olistrel1(U_16309,U_16319))) ),
    inference(clausify,[status(thm)],[f_4034_3]) ).

cnf(f_4034_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16309,U_16309)),hAPP(hAPP(c_Product__Type_OPair(U_16309,U_16309),U_16313),U_16317)),U_16319))
    | U_16311 != U_16315
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16309),tc_List_Olist(U_16309))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16309),tc_List_Olist(U_16309)),hAPP(hAPP(c_List_Oappend(U_16309),U_16311),hAPP(hAPP(c_List_Olist_OCons(U_16309),U_16313),c_List_Olist_ONil(U_16309)))),hAPP(hAPP(c_List_Oappend(U_16309),U_16315),hAPP(hAPP(c_List_Olist_OCons(U_16309),U_16317),c_List_Olist_ONil(U_16309))))),c_List_Olistrel1(U_16309,U_16319))) ),
    inference(clausify,[status(thm)],[f_4034_3]) ).

fof(f_4035_1,plain,
    ! [V_r_2,V_ys_2,V_xs_2,T_b] :
      ( ? [B_x,B_y] :
          ( ? [B_us,B_vs] :
              ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),B_y),B_vs))
              & V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_vs)) )
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_r_2)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_listrel1E]) ).

fof(f_4035_2,plain,
    ! [U_16327,U_16326,U_16325,U_16324] :
      ( ? [U_16323,U_16322] :
          ( ? [U_16321,U_16320] :
              ( U_16326 = hAPP(hAPP(c_List_Oappend(U_16324),U_16321),hAPP(hAPP(c_List_Olist_OCons(U_16324),U_16322),U_16320))
              & U_16325 = hAPP(hAPP(c_List_Oappend(U_16324),U_16321),hAPP(hAPP(c_List_Olist_OCons(U_16324),U_16323),U_16320)) )
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16324,U_16324)),hAPP(hAPP(c_Product__Type_OPair(U_16324,U_16324),U_16323),U_16322)),U_16327)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16324),tc_List_Olist(U_16324))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16324),tc_List_Olist(U_16324)),U_16325),U_16326)),c_List_Olistrel1(U_16324,U_16327))) ),
    inference(variable_rename,[status(thm)],[f_4035_1]) ).

fof(f_4035_3,plain,
    ! [U_16327,U_16326,U_16325,U_16324] :
      ( ? [U_16322] :
          ( ? [U_16321,U_16320] :
              ( U_16326 = hAPP(hAPP(c_List_Oappend(U_16324),U_16321),hAPP(hAPP(c_List_Olist_OCons(U_16324),U_16322),U_16320))
              & U_16325 = hAPP(hAPP(c_List_Oappend(U_16324),U_16321),hAPP(hAPP(c_List_Olist_OCons(U_16324),sK425(U_16327,U_16326,U_16325,U_16324)),U_16320)) )
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16324,U_16324)),hAPP(hAPP(c_Product__Type_OPair(U_16324,U_16324),sK425(U_16327,U_16326,U_16325,U_16324)),U_16322)),U_16327)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16324),tc_List_Olist(U_16324))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16324),tc_List_Olist(U_16324)),U_16325),U_16326)),c_List_Olistrel1(U_16324,U_16327))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK425]),skolemize(U_16323,sK425(U_16327,U_16326,U_16325,U_16324))],[f_4035_2]) ).

fof(f_4035_4,plain,
    ! [U_16327,U_16326,U_16325,U_16324] :
      ( ( ? [U_16321,U_16320] :
            ( U_16326 = hAPP(hAPP(c_List_Oappend(U_16324),U_16321),hAPP(hAPP(c_List_Olist_OCons(U_16324),sK426(U_16327,U_16326,U_16325,U_16324)),U_16320))
            & U_16325 = hAPP(hAPP(c_List_Oappend(U_16324),U_16321),hAPP(hAPP(c_List_Olist_OCons(U_16324),sK425(U_16327,U_16326,U_16325,U_16324)),U_16320)) )
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16324,U_16324)),hAPP(hAPP(c_Product__Type_OPair(U_16324,U_16324),sK425(U_16327,U_16326,U_16325,U_16324)),sK426(U_16327,U_16326,U_16325,U_16324))),U_16327)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16324),tc_List_Olist(U_16324))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16324),tc_List_Olist(U_16324)),U_16325),U_16326)),c_List_Olistrel1(U_16324,U_16327))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK426]),skolemize(U_16322,sK426(U_16327,U_16326,U_16325,U_16324))],[f_4035_3]) ).

fof(f_4035_5,plain,
    ! [U_16327,U_16326,U_16325,U_16324] :
      ( ( ? [U_16320] :
            ( U_16326 = hAPP(hAPP(c_List_Oappend(U_16324),sK427(U_16327,U_16326,U_16325,U_16324)),hAPP(hAPP(c_List_Olist_OCons(U_16324),sK426(U_16327,U_16326,U_16325,U_16324)),U_16320))
            & U_16325 = hAPP(hAPP(c_List_Oappend(U_16324),sK427(U_16327,U_16326,U_16325,U_16324)),hAPP(hAPP(c_List_Olist_OCons(U_16324),sK425(U_16327,U_16326,U_16325,U_16324)),U_16320)) )
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16324,U_16324)),hAPP(hAPP(c_Product__Type_OPair(U_16324,U_16324),sK425(U_16327,U_16326,U_16325,U_16324)),sK426(U_16327,U_16326,U_16325,U_16324))),U_16327)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16324),tc_List_Olist(U_16324))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16324),tc_List_Olist(U_16324)),U_16325),U_16326)),c_List_Olistrel1(U_16324,U_16327))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK427]),skolemize(U_16321,sK427(U_16327,U_16326,U_16325,U_16324))],[f_4035_4]) ).

fof(f_4035_6,plain,
    ! [U_16327,U_16326,U_16325,U_16324] :
      ( ( U_16326 = hAPP(hAPP(c_List_Oappend(U_16324),sK427(U_16327,U_16326,U_16325,U_16324)),hAPP(hAPP(c_List_Olist_OCons(U_16324),sK426(U_16327,U_16326,U_16325,U_16324)),sK428(U_16327,U_16326,U_16325,U_16324)))
        & U_16325 = hAPP(hAPP(c_List_Oappend(U_16324),sK427(U_16327,U_16326,U_16325,U_16324)),hAPP(hAPP(c_List_Olist_OCons(U_16324),sK425(U_16327,U_16326,U_16325,U_16324)),sK428(U_16327,U_16326,U_16325,U_16324)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_16324,U_16324)),hAPP(hAPP(c_Product__Type_OPair(U_16324,U_16324),sK425(U_16327,U_16326,U_16325,U_16324)),sK426(U_16327,U_16326,U_16325,U_16324))),U_16327)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16324),tc_List_Olist(U_16324))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16324),tc_List_Olist(U_16324)),U_16325),U_16326)),c_List_Olistrel1(U_16324,U_16327))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK428]),skolemize(U_16320,sK428(U_16327,U_16326,U_16325,U_16324))],[f_4035_5]) ).

cnf(f_4035_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16324,U_16324)),hAPP(hAPP(c_Product__Type_OPair(U_16324,U_16324),sK425(U_16327,U_16326,U_16325,U_16324)),sK426(U_16327,U_16326,U_16325,U_16324))),U_16327))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16324),tc_List_Olist(U_16324))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16324),tc_List_Olist(U_16324)),U_16325),U_16326)),c_List_Olistrel1(U_16324,U_16327))) ),
    inference(clausify,[status(thm)],[f_4035_6]) ).

cnf(f_4035_8,plain,
    ( U_16325 = hAPP(hAPP(c_List_Oappend(U_16324),sK427(U_16327,U_16326,U_16325,U_16324)),hAPP(hAPP(c_List_Olist_OCons(U_16324),sK425(U_16327,U_16326,U_16325,U_16324)),sK428(U_16327,U_16326,U_16325,U_16324)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16324),tc_List_Olist(U_16324))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16324),tc_List_Olist(U_16324)),U_16325),U_16326)),c_List_Olistrel1(U_16324,U_16327))) ),
    inference(clausify,[status(thm)],[f_4035_6]) ).

cnf(f_4035_9,plain,
    ( U_16326 = hAPP(hAPP(c_List_Oappend(U_16324),sK427(U_16327,U_16326,U_16325,U_16324)),hAPP(hAPP(c_List_Olist_OCons(U_16324),sK426(U_16327,U_16326,U_16325,U_16324)),sK428(U_16327,U_16326,U_16325,U_16324)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16324),tc_List_Olist(U_16324))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16324),tc_List_Olist(U_16324)),U_16325),U_16326)),c_List_Olistrel1(U_16324,U_16327))) ),
    inference(clausify,[status(thm)],[f_4035_6]) ).

fof(f_4036_1,plain,
    ! [V_r_2,V_v_2,V_u_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_u_2),V_v_2)),c_List_Olexord(T_b,V_r_2)))
      | ? [B_a] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_a),B_a)),V_r_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_u_2)),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_v_2))),c_List_Olexord(T_b,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_lexord__append__leftD]) ).

fof(f_4036_2,plain,
    ! [U_16333,U_16332,U_16331,U_16330,U_16329] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16329),tc_List_Olist(U_16329))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16329),tc_List_Olist(U_16329)),U_16331),U_16332)),c_List_Olexord(U_16329,U_16333)))
      | ? [U_16328] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_16329,U_16329)),hAPP(hAPP(c_Product__Type_OPair(U_16329,U_16329),U_16328),U_16328)),U_16333))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16329),tc_List_Olist(U_16329))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16329),tc_List_Olist(U_16329)),hAPP(hAPP(c_List_Oappend(U_16329),U_16330),U_16331)),hAPP(hAPP(c_List_Oappend(U_16329),U_16330),U_16332))),c_List_Olexord(U_16329,U_16333))) ),
    inference(variable_rename,[status(thm)],[f_4036_1]) ).

fof(f_4036_3,plain,
    ! [U_16333,U_16332,U_16331,U_16330,U_16329] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16329),tc_List_Olist(U_16329))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16329),tc_List_Olist(U_16329)),U_16331),U_16332)),c_List_Olexord(U_16329,U_16333)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(U_16329,U_16329)),hAPP(hAPP(c_Product__Type_OPair(U_16329,U_16329),sK429(U_16333,U_16332,U_16331,U_16330,U_16329)),sK429(U_16333,U_16332,U_16331,U_16330,U_16329))),U_16333))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16329),tc_List_Olist(U_16329))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16329),tc_List_Olist(U_16329)),hAPP(hAPP(c_List_Oappend(U_16329),U_16330),U_16331)),hAPP(hAPP(c_List_Oappend(U_16329),U_16330),U_16332))),c_List_Olexord(U_16329,U_16333))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK429]),skolemize(U_16328,sK429(U_16333,U_16332,U_16331,U_16330,U_16329))],[f_4036_2]) ).

cnf(f_4036_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16329),tc_List_Olist(U_16329))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16329),tc_List_Olist(U_16329)),U_16331),U_16332)),c_List_Olexord(U_16329,U_16333)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_16329,U_16329)),hAPP(hAPP(c_Product__Type_OPair(U_16329,U_16329),sK429(U_16333,U_16332,U_16331,U_16330,U_16329)),sK429(U_16333,U_16332,U_16331,U_16330,U_16329))),U_16333))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16329),tc_List_Olist(U_16329))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16329),tc_List_Olist(U_16329)),hAPP(hAPP(c_List_Oappend(U_16329),U_16330),U_16331)),hAPP(hAPP(c_List_Oappend(U_16329),U_16330),U_16332))),c_List_Olexord(U_16329,U_16333))) ),
    inference(clausify,[status(thm)],[f_4036_3]) ).

fof(f_4037_1,plain,
    ! [V_xs_2,T_b] : hAPP(c_List_Orotate1(T_b),V_xs_2) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Oappend(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b)))),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_rotate1__def]) ).

fof(f_4037_2,plain,
    ! [U_16335,U_16334] : hAPP(c_List_Orotate1(U_16334),U_16335) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(U_16334),U_16334,c_List_Olist_ONil(U_16334),hAPP(hAPP(c_COMBB(tc_List_Olist(U_16334),tc_fun(tc_List_Olist(U_16334),tc_List_Olist(U_16334)),U_16334),hAPP(c_COMBC(tc_List_Olist(U_16334),tc_List_Olist(U_16334),tc_List_Olist(U_16334)),c_List_Oappend(U_16334))),hAPP(hAPP(c_COMBC(U_16334,tc_List_Olist(U_16334),tc_List_Olist(U_16334)),c_List_Olist_OCons(U_16334)),c_List_Olist_ONil(U_16334)))),U_16335),
    inference(variable_rename,[status(thm)],[f_4037_1]) ).

cnf(f_4037_3,plain,
    hAPP(c_List_Orotate1(U_16334),U_16335) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(U_16334),U_16334,c_List_Olist_ONil(U_16334),hAPP(hAPP(c_COMBB(tc_List_Olist(U_16334),tc_fun(tc_List_Olist(U_16334),tc_List_Olist(U_16334)),U_16334),hAPP(c_COMBC(tc_List_Olist(U_16334),tc_List_Olist(U_16334),tc_List_Olist(U_16334)),c_List_Oappend(U_16334))),hAPP(hAPP(c_COMBC(U_16334,tc_List_Olist(U_16334),tc_List_Olist(U_16334)),c_List_Olist_OCons(U_16334)),c_List_Olist_ONil(U_16334)))),U_16335),
    inference(clausify,[status(thm)],[f_4037_2]) ).

fof(f_4038_1,plain,
    ! [V_a,V_xs,T_a,V_i] :
      ( hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_a) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_i)),V_xs)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) ),
    inference(fof_nnf,[status(thm)],[fact_upd__conv__take__nth__drop]) ).

fof(f_4038_2,plain,
    ! [U_16339,U_16338,U_16337,U_16336] :
      ( hAPP(hAPP(c_List_Olist__update(U_16337,U_16338),U_16336),U_16339) = hAPP(hAPP(c_List_Oappend(U_16337),hAPP(hAPP(c_List_Otake(U_16337),U_16336),U_16338)),hAPP(hAPP(c_List_Olist_OCons(U_16337),U_16339),hAPP(hAPP(c_List_Odrop(U_16337),hAPP(c_Nat_OSuc,U_16336)),U_16338)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16336),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16337)),U_16338))) ),
    inference(variable_rename,[status(thm)],[f_4038_1]) ).

cnf(f_4038_3,plain,
    ( hAPP(hAPP(c_List_Olist__update(U_16337,U_16338),U_16336),U_16339) = hAPP(hAPP(c_List_Oappend(U_16337),hAPP(hAPP(c_List_Otake(U_16337),U_16336),U_16338)),hAPP(hAPP(c_List_Olist_OCons(U_16337),U_16339),hAPP(hAPP(c_List_Odrop(U_16337),hAPP(c_Nat_OSuc,U_16336)),U_16338)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16336),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16337)),U_16338))) ),
    inference(clausify,[status(thm)],[f_4038_2]) ).

fof(f_4039_1,plain,
    ! [V_xs,V_n,T_a] : hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = V_xs,
    inference(fof_nnf,[status(thm)],[fact_append__take__drop__id]) ).

fof(f_4039_2,plain,
    ! [U_16342,U_16341,U_16340] : hAPP(hAPP(c_List_Oappend(U_16340),hAPP(hAPP(c_List_Otake(U_16340),U_16341),U_16342)),hAPP(hAPP(c_List_Odrop(U_16340),U_16341),U_16342)) = U_16342,
    inference(variable_rename,[status(thm)],[f_4039_1]) ).

cnf(f_4039_3,plain,
    hAPP(hAPP(c_List_Oappend(U_16340),hAPP(hAPP(c_List_Otake(U_16340),U_16341),U_16342)),hAPP(hAPP(c_List_Odrop(U_16340),U_16341),U_16342)) = U_16342,
    inference(clausify,[status(thm)],[f_4039_2]) ).

fof(f_4040_1,plain,
    ! [V_xs,V_x,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_n)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs),
    inference(fof_nnf,[status(thm)],[fact_drop__Suc__Cons]) ).

fof(f_4040_2,plain,
    ! [U_16346,U_16345,U_16344,U_16343] : hAPP(hAPP(c_List_Odrop(U_16343),hAPP(c_Nat_OSuc,U_16344)),hAPP(hAPP(c_List_Olist_OCons(U_16343),U_16345),U_16346)) = hAPP(hAPP(c_List_Odrop(U_16343),U_16344),U_16346),
    inference(variable_rename,[status(thm)],[f_4040_1]) ).

cnf(f_4040_3,plain,
    hAPP(hAPP(c_List_Odrop(U_16343),hAPP(c_Nat_OSuc,U_16344)),hAPP(hAPP(c_List_Olist_OCons(U_16343),U_16345),U_16346)) = hAPP(hAPP(c_List_Odrop(U_16343),U_16344),U_16346),
    inference(clausify,[status(thm)],[f_4040_2]) ).

fof(f_4041_1,plain,
    ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Odrop(T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_xs,
    inference(fof_nnf,[status(thm)],[fact_drop__1__Cons]) ).

fof(f_4041_2,plain,
    ! [U_16349,U_16348,U_16347] : hAPP(hAPP(c_List_Odrop(U_16347),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(U_16347),U_16348),U_16349)) = U_16349,
    inference(variable_rename,[status(thm)],[f_4041_1]) ).

cnf(f_4041_3,plain,
    hAPP(hAPP(c_List_Odrop(U_16347),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(U_16347),U_16348),U_16349)) = U_16349,
    inference(clausify,[status(thm)],[f_4041_2]) ).

fof(f_4042_1,plain,
    ! [V_ys,V_y,V_xs,V_n,T_a] :
      ( hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) = V_y
      | hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) != hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys) ),
    inference(fof_nnf,[status(thm)],[fact_nth__via__drop]) ).

fof(f_4042_2,plain,
    ! [U_16354,U_16353,U_16352,U_16351,U_16350] :
      ( hAPP(hAPP(c_List_Onth(U_16350),U_16352),U_16351) = U_16353
      | hAPP(hAPP(c_List_Odrop(U_16350),U_16351),U_16352) != hAPP(hAPP(c_List_Olist_OCons(U_16350),U_16353),U_16354) ),
    inference(variable_rename,[status(thm)],[f_4042_1]) ).

cnf(f_4042_3,plain,
    ( hAPP(hAPP(c_List_Onth(U_16350),U_16352),U_16351) = U_16353
    | hAPP(hAPP(c_List_Odrop(U_16350),U_16351),U_16352) != hAPP(hAPP(c_List_Olist_OCons(U_16350),U_16353),U_16354) ),
    inference(clausify,[status(thm)],[f_4042_2]) ).

fof(f_4043_1,plain,
    ! [V_xs_2,T_b] :
      ( ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate1(T_b),V_xs_2)))
        | ~ hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) )
      & ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
        | ~ hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate1(T_b),V_xs_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_distinct1__rotate]) ).

fof(f_4043_2,plain,
    ! [U_16356,U_16355] :
      ( ( hBOOL(hAPP(c_List_Odistinct(U_16355),hAPP(c_List_Orotate1(U_16355),U_16356)))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_16355),U_16356)) )
      & ( hBOOL(hAPP(c_List_Odistinct(U_16355),U_16356))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_16355),hAPP(c_List_Orotate1(U_16355),U_16356))) ) ),
    inference(variable_rename,[status(thm)],[f_4043_1]) ).

fof(f_4043_3,plain,
    ( ! [U_16360,U_16358] :
        ( hBOOL(hAPP(c_List_Odistinct(U_16358),hAPP(c_List_Orotate1(U_16358),U_16360)))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_16358),U_16360)) )
    & ! [U_16359,U_16357] :
        ( hBOOL(hAPP(c_List_Odistinct(U_16357),U_16359))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_16357),hAPP(c_List_Orotate1(U_16357),U_16359))) ) ),
    inference(miniscope,[status(thm)],[f_4043_2]) ).

cnf(f_4043_4,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_16357),U_16359))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_16357),hAPP(c_List_Orotate1(U_16357),U_16359))) ),
    inference(clausify,[status(thm)],[f_4043_3]) ).

cnf(f_4043_5,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_16358),hAPP(c_List_Orotate1(U_16358),U_16360)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_16358),U_16360)) ),
    inference(clausify,[status(thm)],[f_4043_3]) ).

fof(f_4044_1,plain,
    ! [V_i,V_xs,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs)))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__drop]) ).

fof(f_4044_2,plain,
    ! [U_16363,U_16362,U_16361] :
      ( hBOOL(hAPP(c_List_Odistinct(U_16361),hAPP(hAPP(c_List_Odrop(U_16361),U_16363),U_16362)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_16361),U_16362)) ),
    inference(variable_rename,[status(thm)],[f_4044_1]) ).

cnf(f_4044_3,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_16361),hAPP(hAPP(c_List_Odrop(U_16361),U_16363),U_16362)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_16361),U_16362)) ),
    inference(clausify,[status(thm)],[f_4044_2]) ).

fof(f_4045_1,plain,
    ! [V_xs,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),c_List_Obutlast(T_a,V_xs)) = c_List_Obutlast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)),
    inference(fof_nnf,[status(thm)],[fact_drop__butlast]) ).

fof(f_4045_2,plain,
    ! [U_16366,U_16365,U_16364] : hAPP(hAPP(c_List_Odrop(U_16364),U_16365),c_List_Obutlast(U_16364,U_16366)) = c_List_Obutlast(U_16364,hAPP(hAPP(c_List_Odrop(U_16364),U_16365),U_16366)),
    inference(variable_rename,[status(thm)],[f_4045_1]) ).

cnf(f_4045_3,plain,
    hAPP(hAPP(c_List_Odrop(U_16364),U_16365),c_List_Obutlast(U_16364,U_16366)) = c_List_Obutlast(U_16364,hAPP(hAPP(c_List_Odrop(U_16364),U_16365),U_16366)),
    inference(clausify,[status(thm)],[f_4045_2]) ).

fof(f_4046_1,plain,
    ! [V_xs,V_n,T_a] : c_List_Obutlast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),V_n),c_List_Obutlast(T_a,V_xs)),
    inference(fof_nnf,[status(thm)],[fact_butlast__drop]) ).

fof(f_4046_2,plain,
    ! [U_16369,U_16368,U_16367] : c_List_Obutlast(U_16367,hAPP(hAPP(c_List_Odrop(U_16367),U_16368),U_16369)) = hAPP(hAPP(c_List_Odrop(U_16367),U_16368),c_List_Obutlast(U_16367,U_16369)),
    inference(variable_rename,[status(thm)],[f_4046_1]) ).

cnf(f_4046_3,plain,
    c_List_Obutlast(U_16367,hAPP(hAPP(c_List_Odrop(U_16367),U_16368),U_16369)) = hAPP(hAPP(c_List_Odrop(U_16367),U_16368),c_List_Obutlast(U_16367,U_16369)),
    inference(clausify,[status(thm)],[f_4046_2]) ).

fof(f_4047_1,plain,
    ! [V_xs,V_m,V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(hAPP(c_List_Odrop(T_a),V_m),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),V_m),hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),V_xs)),
    inference(fof_nnf,[status(thm)],[fact_take__drop]) ).

fof(f_4047_2,plain,
    ! [U_16373,U_16372,U_16371,U_16370] : hAPP(hAPP(c_List_Otake(U_16370),U_16371),hAPP(hAPP(c_List_Odrop(U_16370),U_16372),U_16373)) = hAPP(hAPP(c_List_Odrop(U_16370),U_16372),hAPP(hAPP(c_List_Otake(U_16370),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_16371),U_16372)),U_16373)),
    inference(variable_rename,[status(thm)],[f_4047_1]) ).

cnf(f_4047_3,plain,
    hAPP(hAPP(c_List_Otake(U_16370),U_16371),hAPP(hAPP(c_List_Odrop(U_16370),U_16372),U_16373)) = hAPP(hAPP(c_List_Odrop(U_16370),U_16372),hAPP(hAPP(c_List_Otake(U_16370),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_16371),U_16372)),U_16373)),
    inference(clausify,[status(thm)],[f_4047_2]) ).

fof(f_4048_1,plain,
    ! [V_xs,V_m,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(hAPP(c_List_Otake(T_a),V_m),V_xs)) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)),
    inference(fof_nnf,[status(thm)],[fact_drop__take]) ).

fof(f_4048_2,plain,
    ! [U_16377,U_16376,U_16375,U_16374] : hAPP(hAPP(c_List_Odrop(U_16374),U_16375),hAPP(hAPP(c_List_Otake(U_16374),U_16376),U_16377)) = hAPP(hAPP(c_List_Otake(U_16374),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_16376),U_16375)),hAPP(hAPP(c_List_Odrop(U_16374),U_16375),U_16377)),
    inference(variable_rename,[status(thm)],[f_4048_1]) ).

cnf(f_4048_3,plain,
    hAPP(hAPP(c_List_Odrop(U_16374),U_16375),hAPP(hAPP(c_List_Otake(U_16374),U_16376),U_16377)) = hAPP(hAPP(c_List_Otake(U_16374),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_16376),U_16375)),hAPP(hAPP(c_List_Odrop(U_16374),U_16375),U_16377)),
    inference(clausify,[status(thm)],[f_4048_2]) ).

fof(f_4049_1,plain,
    ! [V_xs,V_m,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(hAPP(c_List_Odrop(T_a),V_m),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),V_xs),
    inference(fof_nnf,[status(thm)],[fact_drop__drop]) ).

fof(f_4049_2,plain,
    ! [U_16381,U_16380,U_16379,U_16378] : hAPP(hAPP(c_List_Odrop(U_16378),U_16379),hAPP(hAPP(c_List_Odrop(U_16378),U_16380),U_16381)) = hAPP(hAPP(c_List_Odrop(U_16378),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_16379),U_16380)),U_16381),
    inference(variable_rename,[status(thm)],[f_4049_1]) ).

cnf(f_4049_3,plain,
    hAPP(hAPP(c_List_Odrop(U_16378),U_16379),hAPP(hAPP(c_List_Odrop(U_16378),U_16380),U_16381)) = hAPP(hAPP(c_List_Odrop(U_16378),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_16379),U_16380)),U_16381),
    inference(clausify,[status(thm)],[f_4049_2]) ).

fof(f_4050_1,plain,
    ! [V_xs,T_a] : hAPP(hAPP(c_List_Odrop(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_xs) = V_xs,
    inference(fof_nnf,[status(thm)],[fact_drop__0]) ).

fof(f_4050_2,plain,
    ! [U_16383,U_16382] : hAPP(hAPP(c_List_Odrop(U_16382),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_16383) = U_16383,
    inference(variable_rename,[status(thm)],[f_4050_1]) ).

cnf(f_4050_3,plain,
    hAPP(hAPP(c_List_Odrop(U_16382),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_16383) = U_16383,
    inference(clausify,[status(thm)],[f_4050_2]) ).

fof(f_4051_1,plain,
    ! [V_ys,V_xs,V_n,T_b,T_a] : hAPP(hAPP(c_List_Odrop(tc_prod(T_a,T_b)),V_n),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)) = hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Odrop(T_b),V_n),V_ys)),
    inference(fof_nnf,[status(thm)],[fact_drop__zip]) ).

fof(f_4051_2,plain,
    ! [U_16388,U_16387,U_16386,U_16385,U_16384] : hAPP(hAPP(c_List_Odrop(tc_prod(U_16384,U_16385)),U_16386),hAPP(hAPP(c_List_Ozip(U_16384,U_16385),U_16387),U_16388)) = hAPP(hAPP(c_List_Ozip(U_16384,U_16385),hAPP(hAPP(c_List_Odrop(U_16384),U_16386),U_16387)),hAPP(hAPP(c_List_Odrop(U_16385),U_16386),U_16388)),
    inference(variable_rename,[status(thm)],[f_4051_1]) ).

cnf(f_4051_3,plain,
    hAPP(hAPP(c_List_Odrop(tc_prod(U_16384,U_16385)),U_16386),hAPP(hAPP(c_List_Ozip(U_16384,U_16385),U_16387),U_16388)) = hAPP(hAPP(c_List_Ozip(U_16384,U_16385),hAPP(hAPP(c_List_Odrop(U_16384),U_16386),U_16387)),hAPP(hAPP(c_List_Odrop(U_16385),U_16386),U_16388)),
    inference(clausify,[status(thm)],[f_4051_2]) ).

fof(f_4052_1,plain,
    ! [V_xs,V_n,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n),
    inference(fof_nnf,[status(thm)],[fact_length__drop]) ).

fof(f_4052_2,plain,
    ! [U_16391,U_16390,U_16389] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16389)),hAPP(hAPP(c_List_Odrop(U_16389),U_16390),U_16391)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16389)),U_16391)),U_16390),
    inference(variable_rename,[status(thm)],[f_4052_1]) ).

cnf(f_4052_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16389)),hAPP(hAPP(c_List_Odrop(U_16389),U_16390),U_16391)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16389)),U_16391)),U_16390),
    inference(clausify,[status(thm)],[f_4052_2]) ).

fof(f_4053_1,plain,
    ! [V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Orotate1(T_a),V_xs)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs),
    inference(fof_nnf,[status(thm)],[fact_length__rotate1]) ).

fof(f_4053_2,plain,
    ! [U_16393,U_16392] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16392)),hAPP(c_List_Orotate1(U_16392),U_16393)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16392)),U_16393),
    inference(variable_rename,[status(thm)],[f_4053_1]) ).

cnf(f_4053_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16392)),hAPP(c_List_Orotate1(U_16392),U_16393)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16392)),U_16393),
    inference(clausify,[status(thm)],[f_4053_2]) ).

fof(f_4054_1,plain,
    ! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_Orotate1(T_b),V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_set__rotate1]) ).

fof(f_4054_2,plain,
    ! [U_16395,U_16394] : hAPP(c_List_Oset(U_16394),hAPP(c_List_Orotate1(U_16394),U_16395)) = hAPP(c_List_Oset(U_16394),U_16395),
    inference(variable_rename,[status(thm)],[f_4054_1]) ).

cnf(f_4054_3,plain,
    hAPP(c_List_Oset(U_16394),hAPP(c_List_Orotate1(U_16394),U_16395)) = hAPP(c_List_Oset(U_16394),U_16395),
    inference(clausify,[status(thm)],[f_4054_2]) ).

fof(f_4055_1,plain,
    ! [V_xs_2,V_n_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_in__set__dropD]) ).

fof(f_4055_2,plain,
    ! [U_16399,U_16398,U_16397,U_16396] :
      ( hBOOL(hAPP(hAPP(c_member(U_16396),U_16397),hAPP(c_List_Oset(U_16396),U_16399)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_16396),U_16397),hAPP(c_List_Oset(U_16396),hAPP(hAPP(c_List_Odrop(U_16396),U_16398),U_16399)))) ),
    inference(variable_rename,[status(thm)],[f_4055_1]) ).

cnf(f_4055_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16396),U_16397),hAPP(c_List_Oset(U_16396),U_16399)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16396),U_16397),hAPP(c_List_Oset(U_16396),hAPP(hAPP(c_List_Odrop(U_16396),U_16398),U_16399)))) ),
    inference(clausify,[status(thm)],[f_4055_2]) ).

fof(f_4056_1,plain,
    ! [V_xs_2,V_n_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2))),
    inference(fof_nnf,[status(thm)],[fact_set__drop__subset]) ).

fof(f_4056_2,plain,
    ! [U_16402,U_16401,U_16400] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16400,tc_HOL_Obool)),hAPP(c_List_Oset(U_16400),hAPP(hAPP(c_List_Odrop(U_16400),U_16401),U_16402))),hAPP(c_List_Oset(U_16400),U_16402))),
    inference(variable_rename,[status(thm)],[f_4056_1]) ).

cnf(f_4056_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16400,tc_HOL_Obool)),hAPP(c_List_Oset(U_16400),hAPP(hAPP(c_List_Odrop(U_16400),U_16401),U_16402))),hAPP(c_List_Oset(U_16400),U_16402))),
    inference(clausify,[status(thm)],[f_4056_2]) ).

fof(f_4057_1,plain,
    ! [V_xs_2,T_b] :
      ( ( hAPP(c_List_Orotate1(T_b),V_xs_2) = c_List_Olist_ONil(T_b)
        | V_xs_2 != c_List_Olist_ONil(T_b) )
      & ( V_xs_2 = c_List_Olist_ONil(T_b)
        | hAPP(c_List_Orotate1(T_b),V_xs_2) != c_List_Olist_ONil(T_b) ) ),
    inference(fof_nnf,[status(thm)],[fact_rotate1__is__Nil__conv]) ).

fof(f_4057_2,plain,
    ! [U_16404,U_16403] :
      ( ( hAPP(c_List_Orotate1(U_16403),U_16404) = c_List_Olist_ONil(U_16403)
        | U_16404 != c_List_Olist_ONil(U_16403) )
      & ( U_16404 = c_List_Olist_ONil(U_16403)
        | hAPP(c_List_Orotate1(U_16403),U_16404) != c_List_Olist_ONil(U_16403) ) ),
    inference(variable_rename,[status(thm)],[f_4057_1]) ).

fof(f_4057_3,plain,
    ( ! [U_16408,U_16406] :
        ( hAPP(c_List_Orotate1(U_16406),U_16408) = c_List_Olist_ONil(U_16406)
        | U_16408 != c_List_Olist_ONil(U_16406) )
    & ! [U_16407,U_16405] :
        ( U_16407 = c_List_Olist_ONil(U_16405)
        | hAPP(c_List_Orotate1(U_16405),U_16407) != c_List_Olist_ONil(U_16405) ) ),
    inference(miniscope,[status(thm)],[f_4057_2]) ).

cnf(f_4057_4,plain,
    ( U_16407 = c_List_Olist_ONil(U_16405)
    | hAPP(c_List_Orotate1(U_16405),U_16407) != c_List_Olist_ONil(U_16405) ),
    inference(clausify,[status(thm)],[f_4057_3]) ).

cnf(f_4057_5,plain,
    ( hAPP(c_List_Orotate1(U_16406),U_16408) = c_List_Olist_ONil(U_16406)
    | U_16408 != c_List_Olist_ONil(U_16406) ),
    inference(clausify,[status(thm)],[f_4057_3]) ).

fof(f_4058_1,plain,
    ! [V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a),
    inference(fof_nnf,[status(thm)],[fact_drop__Nil]) ).

fof(f_4058_2,plain,
    ! [U_16410,U_16409] : hAPP(hAPP(c_List_Odrop(U_16409),U_16410),c_List_Olist_ONil(U_16409)) = c_List_Olist_ONil(U_16409),
    inference(variable_rename,[status(thm)],[f_4058_1]) ).

cnf(f_4058_3,plain,
    hAPP(hAPP(c_List_Odrop(U_16409),U_16410),c_List_Olist_ONil(U_16409)) = c_List_Olist_ONil(U_16409),
    inference(clausify,[status(thm)],[f_4058_2]) ).

fof(f_4059_1,plain,
    ! [V_xs_2,T_b,V_m_2,V_n_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Odrop(T_b),V_m_2),V_xs_2))),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ),
    inference(fof_nnf,[status(thm)],[fact_set__drop__subset__set__drop]) ).

fof(f_4059_2,plain,
    ! [U_16414,U_16413,U_16412,U_16411] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16413,tc_HOL_Obool)),hAPP(c_List_Oset(U_16413),hAPP(hAPP(c_List_Odrop(U_16413),U_16412),U_16414))),hAPP(c_List_Oset(U_16413),hAPP(hAPP(c_List_Odrop(U_16413),U_16411),U_16414))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_16411),U_16412)) ),
    inference(variable_rename,[status(thm)],[f_4059_1]) ).

cnf(f_4059_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16413,tc_HOL_Obool)),hAPP(c_List_Oset(U_16413),hAPP(hAPP(c_List_Odrop(U_16413),U_16412),U_16414))),hAPP(c_List_Oset(U_16413),hAPP(hAPP(c_List_Odrop(U_16413),U_16411),U_16414))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_16411),U_16412)) ),
    inference(clausify,[status(thm)],[f_4059_2]) ).

fof(f_4060_1,plain,
    ! [V_n,V_xs,T_a] :
      ( hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = c_List_Olist_ONil(T_a)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_drop__all]) ).

fof(f_4060_2,plain,
    ! [U_16417,U_16416,U_16415] :
      ( hAPP(hAPP(c_List_Odrop(U_16415),U_16417),U_16416) = c_List_Olist_ONil(U_16415)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16415)),U_16416)),U_16417)) ),
    inference(variable_rename,[status(thm)],[f_4060_1]) ).

cnf(f_4060_3,plain,
    ( hAPP(hAPP(c_List_Odrop(U_16415),U_16417),U_16416) = c_List_Olist_ONil(U_16415)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16415)),U_16416)),U_16417)) ),
    inference(clausify,[status(thm)],[f_4060_2]) ).

fof(f_4061_1,plain,
    ! [V_xs_2,V_n_2,T_b] :
      ( ( hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2) = c_List_Olist_ONil(T_b)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),V_n_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),V_n_2))
        | hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2) != c_List_Olist_ONil(T_b) ) ),
    inference(fof_nnf,[status(thm)],[fact_drop__eq__Nil]) ).

fof(f_4061_2,plain,
    ! [U_16420,U_16419,U_16418] :
      ( ( hAPP(hAPP(c_List_Odrop(U_16418),U_16419),U_16420) = c_List_Olist_ONil(U_16418)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16418)),U_16420)),U_16419)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16418)),U_16420)),U_16419))
        | hAPP(hAPP(c_List_Odrop(U_16418),U_16419),U_16420) != c_List_Olist_ONil(U_16418) ) ),
    inference(variable_rename,[status(thm)],[f_4061_1]) ).

fof(f_4061_3,plain,
    ( ! [U_16426,U_16424,U_16422] :
        ( hAPP(hAPP(c_List_Odrop(U_16422),U_16424),U_16426) = c_List_Olist_ONil(U_16422)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16422)),U_16426)),U_16424)) )
    & ! [U_16425,U_16423,U_16421] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16421)),U_16425)),U_16423))
        | hAPP(hAPP(c_List_Odrop(U_16421),U_16423),U_16425) != c_List_Olist_ONil(U_16421) ) ),
    inference(miniscope,[status(thm)],[f_4061_2]) ).

cnf(f_4061_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16421)),U_16425)),U_16423))
    | hAPP(hAPP(c_List_Odrop(U_16421),U_16423),U_16425) != c_List_Olist_ONil(U_16421) ),
    inference(clausify,[status(thm)],[f_4061_3]) ).

cnf(f_4061_5,plain,
    ( hAPP(hAPP(c_List_Odrop(U_16422),U_16424),U_16426) = c_List_Olist_ONil(U_16422)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16422)),U_16426)),U_16424)) ),
    inference(clausify,[status(thm)],[f_4061_3]) ).

fof(f_4062_1,plain,
    ! [V_ys,V_xs,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Odrop(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_ys)),
    inference(fof_nnf,[status(thm)],[fact_drop__append]) ).

fof(f_4062_2,plain,
    ! [U_16430,U_16429,U_16428,U_16427] : hAPP(hAPP(c_List_Odrop(U_16427),U_16428),hAPP(hAPP(c_List_Oappend(U_16427),U_16429),U_16430)) = hAPP(hAPP(c_List_Oappend(U_16427),hAPP(hAPP(c_List_Odrop(U_16427),U_16428),U_16429)),hAPP(hAPP(c_List_Odrop(U_16427),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_16428),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16427)),U_16429))),U_16430)),
    inference(variable_rename,[status(thm)],[f_4062_1]) ).

cnf(f_4062_3,plain,
    hAPP(hAPP(c_List_Odrop(U_16427),U_16428),hAPP(hAPP(c_List_Oappend(U_16427),U_16429),U_16430)) = hAPP(hAPP(c_List_Oappend(U_16427),hAPP(hAPP(c_List_Odrop(U_16427),U_16428),U_16429)),hAPP(hAPP(c_List_Odrop(U_16427),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_16428),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16427)),U_16429))),U_16430)),
    inference(clausify,[status(thm)],[f_4062_2]) ).

fof(f_4063_1,plain,
    ! [V_zs_2,V_ys_2,V_xs_2,T_b] :
      ( ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_zs_2
        | V_ys_2 != hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),V_zs_2)
        | V_xs_2 != hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),V_zs_2) )
      & ( ( V_ys_2 = hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),V_zs_2)
          & V_xs_2 = hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),V_zs_2) )
        | hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) != V_zs_2 ) ),
    inference(fof_nnf,[status(thm)],[fact_append__eq__conv__conj]) ).

fof(f_4063_2,plain,
    ! [U_16434,U_16433,U_16432,U_16431] :
      ( ( hAPP(hAPP(c_List_Oappend(U_16431),U_16432),U_16433) = U_16434
        | U_16433 != hAPP(hAPP(c_List_Odrop(U_16431),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16431)),U_16432)),U_16434)
        | U_16432 != hAPP(hAPP(c_List_Otake(U_16431),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16431)),U_16432)),U_16434) )
      & ( ( U_16433 = hAPP(hAPP(c_List_Odrop(U_16431),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16431)),U_16432)),U_16434)
          & U_16432 = hAPP(hAPP(c_List_Otake(U_16431),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16431)),U_16432)),U_16434) )
        | hAPP(hAPP(c_List_Oappend(U_16431),U_16432),U_16433) != U_16434 ) ),
    inference(variable_rename,[status(thm)],[f_4063_1]) ).

fof(f_4063_3,plain,
    ( ! [U_16442,U_16440,U_16438,U_16436] :
        ( hAPP(hAPP(c_List_Oappend(U_16436),U_16438),U_16440) = U_16442
        | U_16440 != hAPP(hAPP(c_List_Odrop(U_16436),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16436)),U_16438)),U_16442)
        | U_16438 != hAPP(hAPP(c_List_Otake(U_16436),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16436)),U_16438)),U_16442) )
    & ! [U_16441,U_16439,U_16437,U_16435] :
        ( ( U_16439 = hAPP(hAPP(c_List_Odrop(U_16435),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16435)),U_16437)),U_16441)
          & U_16437 = hAPP(hAPP(c_List_Otake(U_16435),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16435)),U_16437)),U_16441) )
        | hAPP(hAPP(c_List_Oappend(U_16435),U_16437),U_16439) != U_16441 ) ),
    inference(miniscope,[status(thm)],[f_4063_2]) ).

cnf(f_4063_4,plain,
    ( U_16437 = hAPP(hAPP(c_List_Otake(U_16435),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16435)),U_16437)),U_16441)
    | hAPP(hAPP(c_List_Oappend(U_16435),U_16437),U_16439) != U_16441 ),
    inference(clausify,[status(thm)],[f_4063_3]) ).

cnf(f_4063_5,plain,
    ( U_16439 = hAPP(hAPP(c_List_Odrop(U_16435),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16435)),U_16437)),U_16441)
    | hAPP(hAPP(c_List_Oappend(U_16435),U_16437),U_16439) != U_16441 ),
    inference(clausify,[status(thm)],[f_4063_3]) ).

cnf(f_4063_6,plain,
    ( hAPP(hAPP(c_List_Oappend(U_16436),U_16438),U_16440) = U_16442
    | U_16440 != hAPP(hAPP(c_List_Odrop(U_16436),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16436)),U_16438)),U_16442)
    | U_16438 != hAPP(hAPP(c_List_Otake(U_16436),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16436)),U_16438)),U_16442) ),
    inference(clausify,[status(thm)],[f_4063_3]) ).

fof(f_4064_1,plain,
    ! [V_xs_2,V_x_2,V_n_2,T_b] : hAPP(hAPP(c_List_Odrop(T_b),V_n_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_Nat_Onat_Onat__case(tc_List_Olist(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Odrop(T_b)),V_xs_2),V_n_2),
    inference(fof_nnf,[status(thm)],[fact_drop__Cons]) ).

fof(f_4064_2,plain,
    ! [U_16446,U_16445,U_16444,U_16443] : hAPP(hAPP(c_List_Odrop(U_16443),U_16444),hAPP(hAPP(c_List_Olist_OCons(U_16443),U_16445),U_16446)) = c_Nat_Onat_Onat__case(tc_List_Olist(U_16443),hAPP(hAPP(c_List_Olist_OCons(U_16443),U_16445),U_16446),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(U_16443),tc_List_Olist(U_16443)),c_List_Odrop(U_16443)),U_16446),U_16444),
    inference(variable_rename,[status(thm)],[f_4064_1]) ).

cnf(f_4064_3,plain,
    hAPP(hAPP(c_List_Odrop(U_16443),U_16444),hAPP(hAPP(c_List_Olist_OCons(U_16443),U_16445),U_16446)) = c_Nat_Onat_Onat__case(tc_List_Olist(U_16443),hAPP(hAPP(c_List_Olist_OCons(U_16443),U_16445),U_16446),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(U_16443),tc_List_Olist(U_16443)),c_List_Odrop(U_16443)),U_16446),U_16444),
    inference(clausify,[status(thm)],[f_4064_2]) ).

fof(f_4065_1,plain,
    ! [V_xs,V_x,T_a,V_n] :
      ( ( hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs)
        | V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)
        | V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(fof_nnf,[status(thm)],[fact_drop__Cons_H]) ).

fof(f_4065_2,plain,
    ! [U_16450,U_16449,U_16448,U_16447] :
      ( ( hAPP(hAPP(c_List_Odrop(U_16448),U_16447),hAPP(hAPP(c_List_Olist_OCons(U_16448),U_16449),U_16450)) = hAPP(hAPP(c_List_Odrop(U_16448),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_16447),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_16450)
        | U_16447 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_List_Odrop(U_16448),U_16447),hAPP(hAPP(c_List_Olist_OCons(U_16448),U_16449),U_16450)) = hAPP(hAPP(c_List_Olist_OCons(U_16448),U_16449),U_16450)
        | U_16447 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_4065_1]) ).

fof(f_4065_3,plain,
    ( ! [U_16458,U_16456,U_16454,U_16452] :
        ( hAPP(hAPP(c_List_Odrop(U_16454),U_16452),hAPP(hAPP(c_List_Olist_OCons(U_16454),U_16456),U_16458)) = hAPP(hAPP(c_List_Odrop(U_16454),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_16452),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_16458)
        | U_16452 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_16457,U_16455,U_16453,U_16451] :
        ( hAPP(hAPP(c_List_Odrop(U_16453),U_16451),hAPP(hAPP(c_List_Olist_OCons(U_16453),U_16455),U_16457)) = hAPP(hAPP(c_List_Olist_OCons(U_16453),U_16455),U_16457)
        | U_16451 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_4065_2]) ).

cnf(f_4065_4,plain,
    ( hAPP(hAPP(c_List_Odrop(U_16453),U_16451),hAPP(hAPP(c_List_Olist_OCons(U_16453),U_16455),U_16457)) = hAPP(hAPP(c_List_Olist_OCons(U_16453),U_16455),U_16457)
    | U_16451 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4065_3]) ).

cnf(f_4065_5,plain,
    ( hAPP(hAPP(c_List_Odrop(U_16454),U_16452),hAPP(hAPP(c_List_Olist_OCons(U_16454),U_16456),U_16458)) = hAPP(hAPP(c_List_Odrop(U_16454),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_16452),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_16458)
    | U_16452 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4065_3]) ).

fof(f_4066_1,plain,
    ! [V_xs,T_a,V_i,V_n] :
      ( hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)),V_i) = hAPP(hAPP(c_List_Onth(T_a),V_xs),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_i))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_i)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) ),
    inference(fof_nnf,[status(thm)],[fact_nth__drop]) ).

fof(f_4066_2,plain,
    ! [U_16462,U_16461,U_16460,U_16459] :
      ( hAPP(hAPP(c_List_Onth(U_16461),hAPP(hAPP(c_List_Odrop(U_16461),U_16459),U_16462)),U_16460) = hAPP(hAPP(c_List_Onth(U_16461),U_16462),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_16459),U_16460))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_16459),U_16460)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16461)),U_16462))) ),
    inference(variable_rename,[status(thm)],[f_4066_1]) ).

cnf(f_4066_3,plain,
    ( hAPP(hAPP(c_List_Onth(U_16461),hAPP(hAPP(c_List_Odrop(U_16461),U_16459),U_16462)),U_16460) = hAPP(hAPP(c_List_Onth(U_16461),U_16462),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_16459),U_16460))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_16459),U_16460)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16461)),U_16462))) ),
    inference(clausify,[status(thm)],[f_4066_2]) ).

fof(f_4067_1,plain,
    ! [V_ys_092_060_094isub_0622_2,V_ys_092_060_094isub_0621_2,V_xs_092_060_094isub_0622_2,V_xs_092_060_094isub_0621_2,T_b] :
      ( ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_092_060_094isub_0621_2),V_xs_092_060_094isub_0622_2) = hAPP(hAPP(c_List_Oappend(T_b),V_ys_092_060_094isub_0621_2),V_ys_092_060_094isub_0622_2)
        | ( ( hAPP(hAPP(c_List_Oappend(T_b),hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_092_060_094isub_0621_2)),V_xs_092_060_094isub_0621_2)),V_xs_092_060_094isub_0622_2) != V_ys_092_060_094isub_0622_2
            | hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_092_060_094isub_0621_2)),V_xs_092_060_094isub_0621_2) != V_ys_092_060_094isub_0621_2 )
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_092_060_094isub_0621_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_092_060_094isub_0621_2))) )
        | ( ( V_xs_092_060_094isub_0622_2 != hAPP(hAPP(c_List_Oappend(T_b),hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_092_060_094isub_0621_2)),V_ys_092_060_094isub_0621_2)),V_ys_092_060_094isub_0622_2)
            | V_xs_092_060_094isub_0621_2 != hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_092_060_094isub_0621_2)),V_ys_092_060_094isub_0621_2) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_092_060_094isub_0621_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_092_060_094isub_0621_2))) ) )
      & ( ( ( ( hAPP(hAPP(c_List_Oappend(T_b),hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_092_060_094isub_0621_2)),V_xs_092_060_094isub_0621_2)),V_xs_092_060_094isub_0622_2) = V_ys_092_060_094isub_0622_2
              & hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_092_060_094isub_0621_2)),V_xs_092_060_094isub_0621_2) = V_ys_092_060_094isub_0621_2 )
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_092_060_094isub_0621_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_092_060_094isub_0621_2))) )
          & ( ( V_xs_092_060_094isub_0622_2 = hAPP(hAPP(c_List_Oappend(T_b),hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_092_060_094isub_0621_2)),V_ys_092_060_094isub_0621_2)),V_ys_092_060_094isub_0622_2)
              & V_xs_092_060_094isub_0621_2 = hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_092_060_094isub_0621_2)),V_ys_092_060_094isub_0621_2) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_092_060_094isub_0621_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_092_060_094isub_0621_2))) ) )
        | hAPP(hAPP(c_List_Oappend(T_b),V_xs_092_060_094isub_0621_2),V_xs_092_060_094isub_0622_2) != hAPP(hAPP(c_List_Oappend(T_b),V_ys_092_060_094isub_0621_2),V_ys_092_060_094isub_0622_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_append__eq__append__conv__if]) ).

fof(f_4067_2,plain,
    ! [U_16467,U_16466,U_16465,U_16464,U_16463] :
      ( ( hAPP(hAPP(c_List_Oappend(U_16463),U_16464),U_16465) = hAPP(hAPP(c_List_Oappend(U_16463),U_16466),U_16467)
        | ( ( hAPP(hAPP(c_List_Oappend(U_16463),hAPP(hAPP(c_List_Odrop(U_16463),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16463)),U_16466)),U_16464)),U_16465) != U_16467
            | hAPP(hAPP(c_List_Otake(U_16463),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16463)),U_16466)),U_16464) != U_16466 )
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16463)),U_16464)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16463)),U_16466))) )
        | ( ( U_16465 != hAPP(hAPP(c_List_Oappend(U_16463),hAPP(hAPP(c_List_Odrop(U_16463),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16463)),U_16464)),U_16466)),U_16467)
            | U_16464 != hAPP(hAPP(c_List_Otake(U_16463),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16463)),U_16464)),U_16466) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16463)),U_16464)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16463)),U_16466))) ) )
      & ( ( ( ( hAPP(hAPP(c_List_Oappend(U_16463),hAPP(hAPP(c_List_Odrop(U_16463),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16463)),U_16466)),U_16464)),U_16465) = U_16467
              & hAPP(hAPP(c_List_Otake(U_16463),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16463)),U_16466)),U_16464) = U_16466 )
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16463)),U_16464)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16463)),U_16466))) )
          & ( ( U_16465 = hAPP(hAPP(c_List_Oappend(U_16463),hAPP(hAPP(c_List_Odrop(U_16463),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16463)),U_16464)),U_16466)),U_16467)
              & U_16464 = hAPP(hAPP(c_List_Otake(U_16463),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16463)),U_16464)),U_16466) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16463)),U_16464)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16463)),U_16466))) ) )
        | hAPP(hAPP(c_List_Oappend(U_16463),U_16464),U_16465) != hAPP(hAPP(c_List_Oappend(U_16463),U_16466),U_16467) ) ),
    inference(variable_rename,[status(thm)],[f_4067_1]) ).

fof(f_4067_3,plain,
    ( ! [U_16477,U_16475,U_16473,U_16471,U_16469] :
        ( hAPP(hAPP(c_List_Oappend(U_16469),U_16471),U_16473) = hAPP(hAPP(c_List_Oappend(U_16469),U_16475),U_16477)
        | ( ( hAPP(hAPP(c_List_Oappend(U_16469),hAPP(hAPP(c_List_Odrop(U_16469),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16469)),U_16475)),U_16471)),U_16473) != U_16477
            | hAPP(hAPP(c_List_Otake(U_16469),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16469)),U_16475)),U_16471) != U_16475 )
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16469)),U_16471)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16469)),U_16475))) )
        | ( ( U_16473 != hAPP(hAPP(c_List_Oappend(U_16469),hAPP(hAPP(c_List_Odrop(U_16469),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16469)),U_16471)),U_16475)),U_16477)
            | U_16471 != hAPP(hAPP(c_List_Otake(U_16469),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16469)),U_16471)),U_16475) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16469)),U_16471)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16469)),U_16475))) ) )
    & ! [U_16476,U_16474,U_16472,U_16470,U_16468] :
        ( ( ( ( hAPP(hAPP(c_List_Oappend(U_16468),hAPP(hAPP(c_List_Odrop(U_16468),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16468)),U_16474)),U_16470)),U_16472) = U_16476
              & hAPP(hAPP(c_List_Otake(U_16468),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16468)),U_16474)),U_16470) = U_16474 )
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16468)),U_16470)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16468)),U_16474))) )
          & ( ( U_16472 = hAPP(hAPP(c_List_Oappend(U_16468),hAPP(hAPP(c_List_Odrop(U_16468),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16468)),U_16470)),U_16474)),U_16476)
              & U_16470 = hAPP(hAPP(c_List_Otake(U_16468),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16468)),U_16470)),U_16474) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16468)),U_16470)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16468)),U_16474))) ) )
        | hAPP(hAPP(c_List_Oappend(U_16468),U_16470),U_16472) != hAPP(hAPP(c_List_Oappend(U_16468),U_16474),U_16476) ) ),
    inference(miniscope,[status(thm)],[f_4067_2]) ).

cnf(f_4067_4,plain,
    ( U_16470 = hAPP(hAPP(c_List_Otake(U_16468),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16468)),U_16470)),U_16474)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16468)),U_16470)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16468)),U_16474)))
    | hAPP(hAPP(c_List_Oappend(U_16468),U_16470),U_16472) != hAPP(hAPP(c_List_Oappend(U_16468),U_16474),U_16476) ),
    inference(clausify,[status(thm)],[f_4067_3]) ).

cnf(f_4067_5,plain,
    ( U_16472 = hAPP(hAPP(c_List_Oappend(U_16468),hAPP(hAPP(c_List_Odrop(U_16468),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16468)),U_16470)),U_16474)),U_16476)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16468)),U_16470)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16468)),U_16474)))
    | hAPP(hAPP(c_List_Oappend(U_16468),U_16470),U_16472) != hAPP(hAPP(c_List_Oappend(U_16468),U_16474),U_16476) ),
    inference(clausify,[status(thm)],[f_4067_3]) ).

cnf(f_4067_6,plain,
    ( hAPP(hAPP(c_List_Otake(U_16468),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16468)),U_16474)),U_16470) = U_16474
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16468)),U_16470)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16468)),U_16474)))
    | hAPP(hAPP(c_List_Oappend(U_16468),U_16470),U_16472) != hAPP(hAPP(c_List_Oappend(U_16468),U_16474),U_16476) ),
    inference(clausify,[status(thm)],[f_4067_3]) ).

cnf(f_4067_7,plain,
    ( hAPP(hAPP(c_List_Oappend(U_16468),hAPP(hAPP(c_List_Odrop(U_16468),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16468)),U_16474)),U_16470)),U_16472) = U_16476
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16468)),U_16470)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16468)),U_16474)))
    | hAPP(hAPP(c_List_Oappend(U_16468),U_16470),U_16472) != hAPP(hAPP(c_List_Oappend(U_16468),U_16474),U_16476) ),
    inference(clausify,[status(thm)],[f_4067_3]) ).

cnf(f_4067_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16469)),U_16471)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16469)),U_16475)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16469)),U_16471)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16469)),U_16475)))
    | hAPP(hAPP(c_List_Oappend(U_16469),U_16471),U_16473) = hAPP(hAPP(c_List_Oappend(U_16469),U_16475),U_16477) ),
    inference(clausify,[status(thm)],[f_4067_3]) ).

cnf(f_4067_9,plain,
    ( hAPP(hAPP(c_List_Oappend(U_16469),hAPP(hAPP(c_List_Odrop(U_16469),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16469)),U_16475)),U_16471)),U_16473) != U_16477
    | hAPP(hAPP(c_List_Otake(U_16469),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16469)),U_16475)),U_16471) != U_16475
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16469)),U_16471)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16469)),U_16475)))
    | hAPP(hAPP(c_List_Oappend(U_16469),U_16471),U_16473) = hAPP(hAPP(c_List_Oappend(U_16469),U_16475),U_16477) ),
    inference(clausify,[status(thm)],[f_4067_3]) ).

cnf(f_4067_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16469)),U_16471)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16469)),U_16475)))
    | U_16473 != hAPP(hAPP(c_List_Oappend(U_16469),hAPP(hAPP(c_List_Odrop(U_16469),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16469)),U_16471)),U_16475)),U_16477)
    | U_16471 != hAPP(hAPP(c_List_Otake(U_16469),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16469)),U_16471)),U_16475)
    | hAPP(hAPP(c_List_Oappend(U_16469),U_16471),U_16473) = hAPP(hAPP(c_List_Oappend(U_16469),U_16475),U_16477) ),
    inference(clausify,[status(thm)],[f_4067_3]) ).

cnf(f_4067_11,plain,
    ( hAPP(hAPP(c_List_Oappend(U_16469),hAPP(hAPP(c_List_Odrop(U_16469),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16469)),U_16475)),U_16471)),U_16473) != U_16477
    | hAPP(hAPP(c_List_Otake(U_16469),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16469)),U_16475)),U_16471) != U_16475
    | U_16473 != hAPP(hAPP(c_List_Oappend(U_16469),hAPP(hAPP(c_List_Odrop(U_16469),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16469)),U_16471)),U_16475)),U_16477)
    | U_16471 != hAPP(hAPP(c_List_Otake(U_16469),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16469)),U_16471)),U_16475)
    | hAPP(hAPP(c_List_Oappend(U_16469),U_16471),U_16473) = hAPP(hAPP(c_List_Oappend(U_16469),U_16475),U_16477) ),
    inference(clausify,[status(thm)],[f_4067_3]) ).

fof(f_4068_1,plain,
    ! [V_xs,T_a,V_i] :
      ( hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_i)),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) ),
    inference(fof_nnf,[status(thm)],[fact_nth__drop_H]) ).

fof(f_4068_2,plain,
    ! [U_16480,U_16479,U_16478] :
      ( hAPP(hAPP(c_List_Olist_OCons(U_16479),hAPP(hAPP(c_List_Onth(U_16479),U_16480),U_16478)),hAPP(hAPP(c_List_Odrop(U_16479),hAPP(c_Nat_OSuc,U_16478)),U_16480)) = hAPP(hAPP(c_List_Odrop(U_16479),U_16478),U_16480)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16478),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16479)),U_16480))) ),
    inference(variable_rename,[status(thm)],[f_4068_1]) ).

cnf(f_4068_3,plain,
    ( hAPP(hAPP(c_List_Olist_OCons(U_16479),hAPP(hAPP(c_List_Onth(U_16479),U_16480),U_16478)),hAPP(hAPP(c_List_Odrop(U_16479),hAPP(c_Nat_OSuc,U_16478)),U_16480)) = hAPP(hAPP(c_List_Odrop(U_16479),U_16478),U_16480)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16478),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16479)),U_16480))) ),
    inference(clausify,[status(thm)],[f_4068_2]) ).

fof(f_4069_1,plain,
    ! [V_xs,V_x,T_b,T_a] :
      ( hAPP(c_List_Orotate1(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x),V_xs)) = hAPP(hAPP(c_List_Oappend(T_b),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x),c_List_Olist_ONil(T_b)))
      & hAPP(c_List_Orotate1(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_rotate__simps]) ).

fof(f_4069_2,plain,
    ! [U_16484,U_16483,U_16482,U_16481] :
      ( hAPP(c_List_Orotate1(U_16482),hAPP(hAPP(c_List_Olist_OCons(U_16482),U_16483),U_16484)) = hAPP(hAPP(c_List_Oappend(U_16482),U_16484),hAPP(hAPP(c_List_Olist_OCons(U_16482),U_16483),c_List_Olist_ONil(U_16482)))
      & hAPP(c_List_Orotate1(U_16481),c_List_Olist_ONil(U_16481)) = c_List_Olist_ONil(U_16481) ),
    inference(variable_rename,[status(thm)],[f_4069_1]) ).

fof(f_4069_3,plain,
    ( ! [U_16484,U_16483,U_16482] : hAPP(c_List_Orotate1(U_16482),hAPP(hAPP(c_List_Olist_OCons(U_16482),U_16483),U_16484)) = hAPP(hAPP(c_List_Oappend(U_16482),U_16484),hAPP(hAPP(c_List_Olist_OCons(U_16482),U_16483),c_List_Olist_ONil(U_16482)))
    & ! [U_16481] : hAPP(c_List_Orotate1(U_16481),c_List_Olist_ONil(U_16481)) = c_List_Olist_ONil(U_16481) ),
    inference(miniscope,[status(thm)],[f_4069_2]) ).

cnf(f_4069_4,plain,
    hAPP(c_List_Orotate1(U_16481),c_List_Olist_ONil(U_16481)) = c_List_Olist_ONil(U_16481),
    inference(clausify,[status(thm)],[f_4069_3]) ).

cnf(f_4069_5,plain,
    hAPP(c_List_Orotate1(U_16482),hAPP(hAPP(c_List_Olist_OCons(U_16482),U_16483),U_16484)) = hAPP(hAPP(c_List_Oappend(U_16482),U_16484),hAPP(hAPP(c_List_Olist_OCons(U_16482),U_16483),c_List_Olist_ONil(U_16482))),
    inference(clausify,[status(thm)],[f_4069_3]) ).

fof(f_4070_1,plain,
    ! [V_xs,V_x,T_a,V_v] :
      ( ( hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs)
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(fof_nnf,[status(thm)],[fact_drop__Cons__number__of]) ).

fof(f_4070_2,plain,
    ! [U_16488,U_16487,U_16486,U_16485] :
      ( ( hAPP(hAPP(c_List_Odrop(U_16486),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_16485)),hAPP(hAPP(c_List_Olist_OCons(U_16486),U_16487),U_16488)) = hAPP(hAPP(c_List_Odrop(U_16486),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_16485)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_16488)
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_16485) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_List_Odrop(U_16486),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_16485)),hAPP(hAPP(c_List_Olist_OCons(U_16486),U_16487),U_16488)) = hAPP(hAPP(c_List_Olist_OCons(U_16486),U_16487),U_16488)
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_16485) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_4070_1]) ).

fof(f_4070_3,plain,
    ( ! [U_16496,U_16494,U_16492,U_16490] :
        ( hAPP(hAPP(c_List_Odrop(U_16492),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_16490)),hAPP(hAPP(c_List_Olist_OCons(U_16492),U_16494),U_16496)) = hAPP(hAPP(c_List_Odrop(U_16492),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_16490)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_16496)
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_16490) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_16495,U_16493,U_16491,U_16489] :
        ( hAPP(hAPP(c_List_Odrop(U_16491),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_16489)),hAPP(hAPP(c_List_Olist_OCons(U_16491),U_16493),U_16495)) = hAPP(hAPP(c_List_Olist_OCons(U_16491),U_16493),U_16495)
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_16489) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_4070_2]) ).

cnf(f_4070_4,plain,
    ( hAPP(hAPP(c_List_Odrop(U_16491),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_16489)),hAPP(hAPP(c_List_Olist_OCons(U_16491),U_16493),U_16495)) = hAPP(hAPP(c_List_Olist_OCons(U_16491),U_16493),U_16495)
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_16489) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4070_3]) ).

cnf(f_4070_5,plain,
    ( hAPP(hAPP(c_List_Odrop(U_16492),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_16490)),hAPP(hAPP(c_List_Olist_OCons(U_16492),U_16494),U_16496)) = hAPP(hAPP(c_List_Odrop(U_16492),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_16490)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_16496)
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_16490) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4070_3]) ).

fof(f_4071_1,plain,
    ! [V_xs,T_a,V_j,V_i] :
      ( hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)),hAPP(hAPP(c_List_Otake(T_a),V_j),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) ),
    inference(fof_nnf,[status(thm)],[fact_take__add]) ).

fof(f_4071_2,plain,
    ! [U_16500,U_16499,U_16498,U_16497] :
      ( hAPP(hAPP(c_List_Otake(U_16499),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_16497),U_16498)),U_16500) = hAPP(hAPP(c_List_Oappend(U_16499),hAPP(hAPP(c_List_Otake(U_16499),U_16497),U_16500)),hAPP(hAPP(c_List_Otake(U_16499),U_16498),hAPP(hAPP(c_List_Odrop(U_16499),U_16497),U_16500)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_16497),U_16498)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16499)),U_16500))) ),
    inference(variable_rename,[status(thm)],[f_4071_1]) ).

cnf(f_4071_3,plain,
    ( hAPP(hAPP(c_List_Otake(U_16499),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_16497),U_16498)),U_16500) = hAPP(hAPP(c_List_Oappend(U_16499),hAPP(hAPP(c_List_Otake(U_16499),U_16497),U_16500)),hAPP(hAPP(c_List_Otake(U_16499),U_16498),hAPP(hAPP(c_List_Odrop(U_16499),U_16497),U_16500)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_16497),U_16498)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16499)),U_16500))) ),
    inference(clausify,[status(thm)],[f_4071_2]) ).

fof(f_4072_1,plain,
    ! [V_xs,T_a] :
      ( hAPP(c_List_Orotate1(T_a),V_xs) = V_xs
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(fof_nnf,[status(thm)],[fact_rotate1__length01]) ).

fof(f_4072_2,plain,
    ! [U_16502,U_16501] :
      ( hAPP(c_List_Orotate1(U_16501),U_16502) = U_16502
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16501)),U_16502)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(variable_rename,[status(thm)],[f_4072_1]) ).

cnf(f_4072_3,plain,
    ( hAPP(c_List_Orotate1(U_16501),U_16502) = U_16502
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16501)),U_16502)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(clausify,[status(thm)],[f_4072_2]) ).

fof(f_4073_1,plain,
    ! [V_zs,V_ys,V_xs,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),hAPP(hAPP(c_List_Oappend(T_b),V_ys),V_zs)) = hAPP(hAPP(c_List_Oappend(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys)),V_xs)),V_ys)),hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys)),V_xs)),V_zs)),
    inference(fof_nnf,[status(thm)],[fact_zip__append2]) ).

fof(f_4073_2,plain,
    ! [U_16507,U_16506,U_16505,U_16504,U_16503] : hAPP(hAPP(c_List_Ozip(U_16503,U_16504),U_16505),hAPP(hAPP(c_List_Oappend(U_16504),U_16506),U_16507)) = hAPP(hAPP(c_List_Oappend(tc_prod(U_16503,U_16504)),hAPP(hAPP(c_List_Ozip(U_16503,U_16504),hAPP(hAPP(c_List_Otake(U_16503),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16504)),U_16506)),U_16505)),U_16506)),hAPP(hAPP(c_List_Ozip(U_16503,U_16504),hAPP(hAPP(c_List_Odrop(U_16503),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16504)),U_16506)),U_16505)),U_16507)),
    inference(variable_rename,[status(thm)],[f_4073_1]) ).

cnf(f_4073_3,plain,
    hAPP(hAPP(c_List_Ozip(U_16503,U_16504),U_16505),hAPP(hAPP(c_List_Oappend(U_16504),U_16506),U_16507)) = hAPP(hAPP(c_List_Oappend(tc_prod(U_16503,U_16504)),hAPP(hAPP(c_List_Ozip(U_16503,U_16504),hAPP(hAPP(c_List_Otake(U_16503),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16504)),U_16506)),U_16505)),U_16506)),hAPP(hAPP(c_List_Ozip(U_16503,U_16504),hAPP(hAPP(c_List_Odrop(U_16503),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16504)),U_16506)),U_16505)),U_16507)),
    inference(clausify,[status(thm)],[f_4073_2]) ).

fof(f_4074_1,plain,
    ! [V_zs,V_ys,V_xs,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_zs) = hAPP(hAPP(c_List_Oappend(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_zs))),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_ys),hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_zs))),
    inference(fof_nnf,[status(thm)],[fact_zip__append1]) ).

fof(f_4074_2,plain,
    ! [U_16512,U_16511,U_16510,U_16509,U_16508] : hAPP(hAPP(c_List_Ozip(U_16508,U_16509),hAPP(hAPP(c_List_Oappend(U_16508),U_16510),U_16511)),U_16512) = hAPP(hAPP(c_List_Oappend(tc_prod(U_16508,U_16509)),hAPP(hAPP(c_List_Ozip(U_16508,U_16509),U_16510),hAPP(hAPP(c_List_Otake(U_16509),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16508)),U_16510)),U_16512))),hAPP(hAPP(c_List_Ozip(U_16508,U_16509),U_16511),hAPP(hAPP(c_List_Odrop(U_16509),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16508)),U_16510)),U_16512))),
    inference(variable_rename,[status(thm)],[f_4074_1]) ).

cnf(f_4074_3,plain,
    hAPP(hAPP(c_List_Ozip(U_16508,U_16509),hAPP(hAPP(c_List_Oappend(U_16508),U_16510),U_16511)),U_16512) = hAPP(hAPP(c_List_Oappend(tc_prod(U_16508,U_16509)),hAPP(hAPP(c_List_Ozip(U_16508,U_16509),U_16510),hAPP(hAPP(c_List_Otake(U_16509),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16508)),U_16510)),U_16512))),hAPP(hAPP(c_List_Ozip(U_16508,U_16509),U_16511),hAPP(hAPP(c_List_Odrop(U_16509),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16508)),U_16510)),U_16512))),
    inference(clausify,[status(thm)],[f_4074_2]) ).

fof(f_4075_1,plain,
    ! [V_xs,T_a,V_i] :
      ( V_xs = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_i)),V_xs)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) ),
    inference(fof_nnf,[status(thm)],[fact_id__take__nth__drop]) ).

fof(f_4075_2,plain,
    ! [U_16515,U_16514,U_16513] :
      ( U_16515 = hAPP(hAPP(c_List_Oappend(U_16514),hAPP(hAPP(c_List_Otake(U_16514),U_16513),U_16515)),hAPP(hAPP(c_List_Olist_OCons(U_16514),hAPP(hAPP(c_List_Onth(U_16514),U_16515),U_16513)),hAPP(hAPP(c_List_Odrop(U_16514),hAPP(c_Nat_OSuc,U_16513)),U_16515)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16513),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16514)),U_16515))) ),
    inference(variable_rename,[status(thm)],[f_4075_1]) ).

cnf(f_4075_3,plain,
    ( U_16515 = hAPP(hAPP(c_List_Oappend(U_16514),hAPP(hAPP(c_List_Otake(U_16514),U_16513),U_16515)),hAPP(hAPP(c_List_Olist_OCons(U_16514),hAPP(hAPP(c_List_Onth(U_16514),U_16515),U_16513)),hAPP(hAPP(c_List_Odrop(U_16514),hAPP(c_Nat_OSuc,U_16513)),U_16515)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16513),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16514)),U_16515))) ),
    inference(clausify,[status(thm)],[f_4075_2]) ).

fof(f_4076_1,plain,
    ! [V_xs,T_a,V_n] :
      ( hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs))),c_List_Olist_ONil(T_a))) = hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_n)),V_xs)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) ),
    inference(fof_nnf,[status(thm)],[fact_take__hd__drop]) ).

fof(f_4076_2,plain,
    ! [U_16518,U_16517,U_16516] :
      ( hAPP(hAPP(c_List_Oappend(U_16517),hAPP(hAPP(c_List_Otake(U_16517),U_16516),U_16518)),hAPP(hAPP(c_List_Olist_OCons(U_16517),hAPP(c_List_Ohd(U_16517),hAPP(hAPP(c_List_Odrop(U_16517),U_16516),U_16518))),c_List_Olist_ONil(U_16517))) = hAPP(hAPP(c_List_Otake(U_16517),hAPP(c_Nat_OSuc,U_16516)),U_16518)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16516),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16517)),U_16518))) ),
    inference(variable_rename,[status(thm)],[f_4076_1]) ).

cnf(f_4076_3,plain,
    ( hAPP(hAPP(c_List_Oappend(U_16517),hAPP(hAPP(c_List_Otake(U_16517),U_16516),U_16518)),hAPP(hAPP(c_List_Olist_OCons(U_16517),hAPP(c_List_Ohd(U_16517),hAPP(hAPP(c_List_Odrop(U_16517),U_16516),U_16518))),c_List_Olist_ONil(U_16517))) = hAPP(hAPP(c_List_Otake(U_16517),hAPP(c_Nat_OSuc,U_16516)),U_16518)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16516),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16517)),U_16518))) ),
    inference(clausify,[status(thm)],[f_4076_2]) ).

fof(f_4077_1,plain,
    ! [V_n,T_a,V_xs] :
      ( hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
      | V_xs = c_List_Olist_ONil(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_hd__drop__conv__nth]) ).

fof(f_4077_2,plain,
    ! [U_16521,U_16520,U_16519] :
      ( hAPP(c_List_Ohd(U_16520),hAPP(hAPP(c_List_Odrop(U_16520),U_16521),U_16519)) = hAPP(hAPP(c_List_Onth(U_16520),U_16519),U_16521)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16521),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16520)),U_16519)))
      | U_16519 = c_List_Olist_ONil(U_16520) ),
    inference(variable_rename,[status(thm)],[f_4077_1]) ).

cnf(f_4077_3,plain,
    ( hAPP(c_List_Ohd(U_16520),hAPP(hAPP(c_List_Odrop(U_16520),U_16521),U_16519)) = hAPP(hAPP(c_List_Onth(U_16520),U_16519),U_16521)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16521),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16520)),U_16519)))
    | U_16519 = c_List_Olist_ONil(U_16520) ),
    inference(clausify,[status(thm)],[f_4077_2]) ).

fof(f_4078_1,plain,
    ! [V_xs,V_x,T_a] : hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x,
    inference(fof_nnf,[status(thm)],[fact_hd_Osimps]) ).

fof(f_4078_2,plain,
    ! [U_16524,U_16523,U_16522] : hAPP(c_List_Ohd(U_16522),hAPP(hAPP(c_List_Olist_OCons(U_16522),U_16523),U_16524)) = U_16523,
    inference(variable_rename,[status(thm)],[f_4078_1]) ).

cnf(f_4078_3,plain,
    hAPP(c_List_Ohd(U_16522),hAPP(hAPP(c_List_Olist_OCons(U_16522),U_16523),U_16524)) = U_16523,
    inference(clausify,[status(thm)],[f_4078_2]) ).

fof(f_4079_1,plain,
    ! [V_ys,T_a,V_xs] :
      ( ( hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(c_List_Ohd(T_a),V_xs)
        | V_xs = c_List_Olist_ONil(T_a) )
      & ( hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(c_List_Ohd(T_a),V_ys)
        | V_xs != c_List_Olist_ONil(T_a) ) ),
    inference(fof_nnf,[status(thm)],[fact_hd__append]) ).

fof(f_4079_2,plain,
    ! [U_16527,U_16526,U_16525] :
      ( ( hAPP(c_List_Ohd(U_16526),hAPP(hAPP(c_List_Oappend(U_16526),U_16525),U_16527)) = hAPP(c_List_Ohd(U_16526),U_16525)
        | U_16525 = c_List_Olist_ONil(U_16526) )
      & ( hAPP(c_List_Ohd(U_16526),hAPP(hAPP(c_List_Oappend(U_16526),U_16525),U_16527)) = hAPP(c_List_Ohd(U_16526),U_16527)
        | U_16525 != c_List_Olist_ONil(U_16526) ) ),
    inference(variable_rename,[status(thm)],[f_4079_1]) ).

fof(f_4079_3,plain,
    ( ! [U_16533,U_16531,U_16529] :
        ( hAPP(c_List_Ohd(U_16531),hAPP(hAPP(c_List_Oappend(U_16531),U_16529),U_16533)) = hAPP(c_List_Ohd(U_16531),U_16529)
        | U_16529 = c_List_Olist_ONil(U_16531) )
    & ! [U_16532,U_16530,U_16528] :
        ( hAPP(c_List_Ohd(U_16530),hAPP(hAPP(c_List_Oappend(U_16530),U_16528),U_16532)) = hAPP(c_List_Ohd(U_16530),U_16532)
        | U_16528 != c_List_Olist_ONil(U_16530) ) ),
    inference(miniscope,[status(thm)],[f_4079_2]) ).

cnf(f_4079_4,plain,
    ( hAPP(c_List_Ohd(U_16530),hAPP(hAPP(c_List_Oappend(U_16530),U_16528),U_16532)) = hAPP(c_List_Ohd(U_16530),U_16532)
    | U_16528 != c_List_Olist_ONil(U_16530) ),
    inference(clausify,[status(thm)],[f_4079_3]) ).

cnf(f_4079_5,plain,
    ( hAPP(c_List_Ohd(U_16531),hAPP(hAPP(c_List_Oappend(U_16531),U_16529),U_16533)) = hAPP(c_List_Ohd(U_16531),U_16529)
    | U_16529 = c_List_Olist_ONil(U_16531) ),
    inference(clausify,[status(thm)],[f_4079_3]) ).

fof(f_4080_1,plain,
    ! [V_ys,T_a,V_xs] :
      ( hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(c_List_Ohd(T_a),V_xs)
      | V_xs = c_List_Olist_ONil(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_hd__append2]) ).

fof(f_4080_2,plain,
    ! [U_16536,U_16535,U_16534] :
      ( hAPP(c_List_Ohd(U_16535),hAPP(hAPP(c_List_Oappend(U_16535),U_16534),U_16536)) = hAPP(c_List_Ohd(U_16535),U_16534)
      | U_16534 = c_List_Olist_ONil(U_16535) ),
    inference(variable_rename,[status(thm)],[f_4080_1]) ).

cnf(f_4080_3,plain,
    ( hAPP(c_List_Ohd(U_16535),hAPP(hAPP(c_List_Oappend(U_16535),U_16534),U_16536)) = hAPP(c_List_Ohd(U_16535),U_16534)
    | U_16534 = c_List_Olist_ONil(U_16535) ),
    inference(clausify,[status(thm)],[f_4080_2]) ).

fof(f_4081_1,plain,
    ! [T_b,V_xs_2] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_List_Ohd(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_xs_2)))
      | V_xs_2 = c_List_Olist_ONil(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_hd__in__set]) ).

fof(f_4081_2,plain,
    ! [U_16538,U_16537] :
      ( hBOOL(hAPP(hAPP(c_member(U_16538),hAPP(c_List_Ohd(U_16538),U_16537)),hAPP(c_List_Oset(U_16538),U_16537)))
      | U_16537 = c_List_Olist_ONil(U_16538) ),
    inference(variable_rename,[status(thm)],[f_4081_1]) ).

cnf(f_4081_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16538),hAPP(c_List_Ohd(U_16538),U_16537)),hAPP(c_List_Oset(U_16538),U_16537)))
    | U_16537 = c_List_Olist_ONil(U_16538) ),
    inference(clausify,[status(thm)],[f_4081_2]) ).

fof(f_4082_1,plain,
    ! [T_a,V_xs] :
      ( hAPP(c_List_Ohd(T_a),V_xs) = hAPP(hAPP(c_List_Onth(T_a),V_xs),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
      | V_xs = c_List_Olist_ONil(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_hd__conv__nth]) ).

fof(f_4082_2,plain,
    ! [U_16540,U_16539] :
      ( hAPP(c_List_Ohd(U_16540),U_16539) = hAPP(hAPP(c_List_Onth(U_16540),U_16539),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
      | U_16539 = c_List_Olist_ONil(U_16540) ),
    inference(variable_rename,[status(thm)],[f_4082_1]) ).

cnf(f_4082_3,plain,
    ( hAPP(c_List_Ohd(U_16540),U_16539) = hAPP(hAPP(c_List_Onth(U_16540),U_16539),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | U_16539 = c_List_Olist_ONil(U_16540) ),
    inference(clausify,[status(thm)],[f_4082_2]) ).

fof(f_4083_1,plain,
    ! [T_a,V_xs] :
      ( hAPP(c_List_Orotate1(T_a),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Otl(T_a),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(c_List_Ohd(T_a),V_xs)),c_List_Olist_ONil(T_a)))
      | V_xs = c_List_Olist_ONil(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_rotate1__hd__tl]) ).

fof(f_4083_2,plain,
    ! [U_16542,U_16541] :
      ( hAPP(c_List_Orotate1(U_16542),U_16541) = hAPP(hAPP(c_List_Oappend(U_16542),hAPP(c_List_Otl(U_16542),U_16541)),hAPP(hAPP(c_List_Olist_OCons(U_16542),hAPP(c_List_Ohd(U_16542),U_16541)),c_List_Olist_ONil(U_16542)))
      | U_16541 = c_List_Olist_ONil(U_16542) ),
    inference(variable_rename,[status(thm)],[f_4083_1]) ).

cnf(f_4083_3,plain,
    ( hAPP(c_List_Orotate1(U_16542),U_16541) = hAPP(hAPP(c_List_Oappend(U_16542),hAPP(c_List_Otl(U_16542),U_16541)),hAPP(hAPP(c_List_Olist_OCons(U_16542),hAPP(c_List_Ohd(U_16542),U_16541)),c_List_Olist_ONil(U_16542)))
    | U_16541 = c_List_Olist_ONil(U_16542) ),
    inference(clausify,[status(thm)],[f_4083_2]) ).

fof(f_4084_1,plain,
    ! [V_n,T_a,V_xs] :
      ( hAPP(c_List_Ohd(T_a),hAPP(c_List_Orotate(T_a,V_n),V_xs)) = hAPP(hAPP(c_List_Onth(T_a),V_xs),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
      | V_xs = c_List_Olist_ONil(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_hd__rotate__conv__nth]) ).

fof(f_4084_2,plain,
    ! [U_16545,U_16544,U_16543] :
      ( hAPP(c_List_Ohd(U_16544),hAPP(c_List_Orotate(U_16544,U_16545),U_16543)) = hAPP(hAPP(c_List_Onth(U_16544),U_16543),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_16545,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16544)),U_16543)))
      | U_16543 = c_List_Olist_ONil(U_16544) ),
    inference(variable_rename,[status(thm)],[f_4084_1]) ).

cnf(f_4084_3,plain,
    ( hAPP(c_List_Ohd(U_16544),hAPP(c_List_Orotate(U_16544,U_16545),U_16543)) = hAPP(hAPP(c_List_Onth(U_16544),U_16543),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_16545,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16544)),U_16543)))
    | U_16543 = c_List_Olist_ONil(U_16544) ),
    inference(clausify,[status(thm)],[f_4084_2]) ).

fof(f_4085_1,plain,
    ! [V_xs,V_n,T_a] : hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs)),
    inference(fof_nnf,[status(thm)],[fact_tl__drop]) ).

fof(f_4085_2,plain,
    ! [U_16548,U_16547,U_16546] : hAPP(c_List_Otl(U_16546),hAPP(hAPP(c_List_Odrop(U_16546),U_16547),U_16548)) = hAPP(hAPP(c_List_Odrop(U_16546),U_16547),hAPP(c_List_Otl(U_16546),U_16548)),
    inference(variable_rename,[status(thm)],[f_4085_1]) ).

cnf(f_4085_3,plain,
    hAPP(c_List_Otl(U_16546),hAPP(hAPP(c_List_Odrop(U_16546),U_16547),U_16548)) = hAPP(hAPP(c_List_Odrop(U_16546),U_16547),hAPP(c_List_Otl(U_16546),U_16548)),
    inference(clausify,[status(thm)],[f_4085_2]) ).

fof(f_4086_1,plain,
    ! [V_xs,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs)) = hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)),
    inference(fof_nnf,[status(thm)],[fact_drop__tl]) ).

fof(f_4086_2,plain,
    ! [U_16551,U_16550,U_16549] : hAPP(hAPP(c_List_Odrop(U_16549),U_16550),hAPP(c_List_Otl(U_16549),U_16551)) = hAPP(c_List_Otl(U_16549),hAPP(hAPP(c_List_Odrop(U_16549),U_16550),U_16551)),
    inference(variable_rename,[status(thm)],[f_4086_1]) ).

cnf(f_4086_3,plain,
    hAPP(hAPP(c_List_Odrop(U_16549),U_16550),hAPP(c_List_Otl(U_16549),U_16551)) = hAPP(c_List_Otl(U_16549),hAPP(hAPP(c_List_Odrop(U_16549),U_16550),U_16551)),
    inference(clausify,[status(thm)],[f_4086_2]) ).

fof(f_4087_1,plain,
    ! [V_xs,V_x,T_a] : hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_xs,
    inference(fof_nnf,[status(thm)],[fact_tl_Osimps_I2_J]) ).

fof(f_4087_2,plain,
    ! [U_16554,U_16553,U_16552] : hAPP(c_List_Otl(U_16552),hAPP(hAPP(c_List_Olist_OCons(U_16552),U_16553),U_16554)) = U_16554,
    inference(variable_rename,[status(thm)],[f_4087_1]) ).

cnf(f_4087_3,plain,
    hAPP(c_List_Otl(U_16552),hAPP(hAPP(c_List_Olist_OCons(U_16552),U_16553),U_16554)) = U_16554,
    inference(clausify,[status(thm)],[f_4087_2]) ).

fof(f_4088_1,plain,
    ! [V_xs_2,V_n_2,T_b] :
      ( ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2)))
        | ~ hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) )
      & ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
        | ~ hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__rotate]) ).

fof(f_4088_2,plain,
    ! [U_16557,U_16556,U_16555] :
      ( ( hBOOL(hAPP(c_List_Odistinct(U_16555),hAPP(c_List_Orotate(U_16555,U_16556),U_16557)))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_16555),U_16557)) )
      & ( hBOOL(hAPP(c_List_Odistinct(U_16555),U_16557))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_16555),hAPP(c_List_Orotate(U_16555,U_16556),U_16557))) ) ),
    inference(variable_rename,[status(thm)],[f_4088_1]) ).

fof(f_4088_3,plain,
    ( ! [U_16563,U_16561,U_16559] :
        ( hBOOL(hAPP(c_List_Odistinct(U_16559),hAPP(c_List_Orotate(U_16559,U_16561),U_16563)))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_16559),U_16563)) )
    & ! [U_16562,U_16560,U_16558] :
        ( hBOOL(hAPP(c_List_Odistinct(U_16558),U_16562))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_16558),hAPP(c_List_Orotate(U_16558,U_16560),U_16562))) ) ),
    inference(miniscope,[status(thm)],[f_4088_2]) ).

cnf(f_4088_4,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_16558),U_16562))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_16558),hAPP(c_List_Orotate(U_16558,U_16560),U_16562))) ),
    inference(clausify,[status(thm)],[f_4088_3]) ).

cnf(f_4088_5,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_16559),hAPP(c_List_Orotate(U_16559,U_16561),U_16563)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_16559),U_16563)) ),
    inference(clausify,[status(thm)],[f_4088_3]) ).

fof(f_4089_1,plain,
    ! [V_xs,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Otl(T_a),V_xs)))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__tl]) ).

fof(f_4089_2,plain,
    ! [U_16565,U_16564] :
      ( hBOOL(hAPP(c_List_Odistinct(U_16564),hAPP(c_List_Otl(U_16564),U_16565)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_16564),U_16565)) ),
    inference(variable_rename,[status(thm)],[f_4089_1]) ).

cnf(f_4089_3,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_16564),hAPP(c_List_Otl(U_16564),U_16565)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_16564),U_16565)) ),
    inference(clausify,[status(thm)],[f_4089_2]) ).

fof(f_4090_1,plain,
    ! [T_b] : c_List_Orotate(T_b,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(T_b)),
    inference(fof_nnf,[status(thm)],[fact_rotate0]) ).

fof(f_4090_2,plain,
    ! [U_16566] : c_List_Orotate(U_16566,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(U_16566)),
    inference(variable_rename,[status(thm)],[f_4090_1]) ).

cnf(f_4090_3,plain,
    c_List_Orotate(U_16566,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(U_16566)),
    inference(clausify,[status(thm)],[f_4090_2]) ).

fof(f_4091_1,plain,
    ! [V_xs,V_n,V_m,T_a] : hAPP(c_List_Orotate(T_a,V_m),hAPP(c_List_Orotate(T_a,V_n),V_xs)) = hAPP(c_List_Orotate(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_xs),
    inference(fof_nnf,[status(thm)],[fact_rotate__rotate]) ).

fof(f_4091_2,plain,
    ! [U_16570,U_16569,U_16568,U_16567] : hAPP(c_List_Orotate(U_16567,U_16568),hAPP(c_List_Orotate(U_16567,U_16569),U_16570)) = hAPP(c_List_Orotate(U_16567,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_16568),U_16569)),U_16570),
    inference(variable_rename,[status(thm)],[f_4091_1]) ).

cnf(f_4091_3,plain,
    hAPP(c_List_Orotate(U_16567,U_16568),hAPP(c_List_Orotate(U_16567,U_16569),U_16570)) = hAPP(c_List_Orotate(U_16567,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_16568),U_16569)),U_16570),
    inference(clausify,[status(thm)],[f_4091_2]) ).

fof(f_4092_1,plain,
    ! [V_n_2,V_m_2,T_b] : c_List_Orotate(T_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)) = hAPP(c_Fun_Ocomp(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Orotate(T_b,V_m_2)),c_List_Orotate(T_b,V_n_2)),
    inference(fof_nnf,[status(thm)],[fact_rotate__add]) ).

fof(f_4092_2,plain,
    ! [U_16573,U_16572,U_16571] : c_List_Orotate(U_16571,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_16572),U_16573)) = hAPP(c_Fun_Ocomp(tc_List_Olist(U_16571),tc_List_Olist(U_16571),tc_List_Olist(U_16571),c_List_Orotate(U_16571,U_16572)),c_List_Orotate(U_16571,U_16573)),
    inference(variable_rename,[status(thm)],[f_4092_1]) ).

cnf(f_4092_3,plain,
    c_List_Orotate(U_16571,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_16572),U_16573)) = hAPP(c_Fun_Ocomp(tc_List_Olist(U_16571),tc_List_Olist(U_16571),tc_List_Olist(U_16571),c_List_Orotate(U_16571,U_16572)),c_List_Orotate(U_16571,U_16573)),
    inference(clausify,[status(thm)],[f_4092_2]) ).

fof(f_4093_1,plain,
    ! [V_xs,V_n,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Orotate(T_a,V_n),V_xs)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs),
    inference(fof_nnf,[status(thm)],[fact_length__rotate]) ).

fof(f_4093_2,plain,
    ! [U_16576,U_16575,U_16574] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16574)),hAPP(c_List_Orotate(U_16574,U_16575),U_16576)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16574)),U_16576),
    inference(variable_rename,[status(thm)],[f_4093_1]) ).

cnf(f_4093_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16574)),hAPP(c_List_Orotate(U_16574,U_16575),U_16576)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16574)),U_16576),
    inference(clausify,[status(thm)],[f_4093_2]) ).

fof(f_4094_1,plain,
    ! [V_xs_2,V_n_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_set__rotate]) ).

fof(f_4094_2,plain,
    ! [U_16579,U_16578,U_16577] : hAPP(c_List_Oset(U_16577),hAPP(c_List_Orotate(U_16577,U_16578),U_16579)) = hAPP(c_List_Oset(U_16577),U_16579),
    inference(variable_rename,[status(thm)],[f_4094_1]) ).

cnf(f_4094_3,plain,
    hAPP(c_List_Oset(U_16577),hAPP(c_List_Orotate(U_16577,U_16578),U_16579)) = hAPP(c_List_Oset(U_16577),U_16579),
    inference(clausify,[status(thm)],[f_4094_2]) ).

fof(f_4095_1,plain,
    ! [V_xs_2,V_n_2,T_b] :
      ( ( hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2) = c_List_Olist_ONil(T_b)
        | V_xs_2 != c_List_Olist_ONil(T_b) )
      & ( V_xs_2 = c_List_Olist_ONil(T_b)
        | hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2) != c_List_Olist_ONil(T_b) ) ),
    inference(fof_nnf,[status(thm)],[fact_rotate__is__Nil__conv]) ).

fof(f_4095_2,plain,
    ! [U_16582,U_16581,U_16580] :
      ( ( hAPP(c_List_Orotate(U_16580,U_16581),U_16582) = c_List_Olist_ONil(U_16580)
        | U_16582 != c_List_Olist_ONil(U_16580) )
      & ( U_16582 = c_List_Olist_ONil(U_16580)
        | hAPP(c_List_Orotate(U_16580,U_16581),U_16582) != c_List_Olist_ONil(U_16580) ) ),
    inference(variable_rename,[status(thm)],[f_4095_1]) ).

fof(f_4095_3,plain,
    ( ! [U_16588,U_16586,U_16584] :
        ( hAPP(c_List_Orotate(U_16584,U_16586),U_16588) = c_List_Olist_ONil(U_16584)
        | U_16588 != c_List_Olist_ONil(U_16584) )
    & ! [U_16587,U_16585,U_16583] :
        ( U_16587 = c_List_Olist_ONil(U_16583)
        | hAPP(c_List_Orotate(U_16583,U_16585),U_16587) != c_List_Olist_ONil(U_16583) ) ),
    inference(miniscope,[status(thm)],[f_4095_2]) ).

cnf(f_4095_4,plain,
    ( U_16587 = c_List_Olist_ONil(U_16583)
    | hAPP(c_List_Orotate(U_16583,U_16585),U_16587) != c_List_Olist_ONil(U_16583) ),
    inference(clausify,[status(thm)],[f_4095_3]) ).

cnf(f_4095_5,plain,
    ( hAPP(c_List_Orotate(U_16584,U_16586),U_16588) = c_List_Olist_ONil(U_16584)
    | U_16588 != c_List_Olist_ONil(U_16584) ),
    inference(clausify,[status(thm)],[f_4095_3]) ).

fof(f_4096_1,plain,
    ! [T_a] : hAPP(c_List_Otl(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a),
    inference(fof_nnf,[status(thm)],[fact_tl_Osimps_I1_J]) ).

fof(f_4096_2,plain,
    ! [U_16589] : hAPP(c_List_Otl(U_16589),c_List_Olist_ONil(U_16589)) = c_List_Olist_ONil(U_16589),
    inference(variable_rename,[status(thm)],[f_4096_1]) ).

cnf(f_4096_3,plain,
    hAPP(c_List_Otl(U_16589),c_List_Olist_ONil(U_16589)) = c_List_Olist_ONil(U_16589),
    inference(clausify,[status(thm)],[f_4096_2]) ).

fof(f_4097_1,plain,
    ! [V_xs,V_n,T_a] : hAPP(c_List_Orotate1(T_a),hAPP(c_List_Orotate(T_a,V_n),V_xs)) = hAPP(c_List_Orotate(T_a,V_n),hAPP(c_List_Orotate1(T_a),V_xs)),
    inference(fof_nnf,[status(thm)],[fact_rotate1__rotate__swap]) ).

fof(f_4097_2,plain,
    ! [U_16592,U_16591,U_16590] : hAPP(c_List_Orotate1(U_16590),hAPP(c_List_Orotate(U_16590,U_16591),U_16592)) = hAPP(c_List_Orotate(U_16590,U_16591),hAPP(c_List_Orotate1(U_16590),U_16592)),
    inference(variable_rename,[status(thm)],[f_4097_1]) ).

cnf(f_4097_3,plain,
    hAPP(c_List_Orotate1(U_16590),hAPP(c_List_Orotate(U_16590,U_16591),U_16592)) = hAPP(c_List_Orotate(U_16590,U_16591),hAPP(c_List_Orotate1(U_16590),U_16592)),
    inference(clausify,[status(thm)],[f_4097_2]) ).

fof(f_4098_1,plain,
    ! [V_n_2,T_b] : c_List_Orotate(T_b,V_n_2) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_n_2),c_List_Orotate1(T_b)),
    inference(fof_nnf,[status(thm)],[fact_rotate__def]) ).

fof(f_4098_2,plain,
    ! [U_16594,U_16593] : c_List_Orotate(U_16593,U_16594) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(U_16593),tc_List_Olist(U_16593)),U_16594),c_List_Orotate1(U_16593)),
    inference(variable_rename,[status(thm)],[f_4098_1]) ).

cnf(f_4098_3,plain,
    c_List_Orotate(U_16593,U_16594) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(U_16593),tc_List_Olist(U_16593)),U_16594),c_List_Orotate1(U_16593)),
    inference(clausify,[status(thm)],[f_4098_2]) ).

fof(f_4099_1,plain,
    ! [V_ys,T_a,V_xs] :
      ( hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Otl(T_a),V_xs)),V_ys)
      | V_xs = c_List_Olist_ONil(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_tl__append2]) ).

fof(f_4099_2,plain,
    ! [U_16597,U_16596,U_16595] :
      ( hAPP(c_List_Otl(U_16596),hAPP(hAPP(c_List_Oappend(U_16596),U_16595),U_16597)) = hAPP(hAPP(c_List_Oappend(U_16596),hAPP(c_List_Otl(U_16596),U_16595)),U_16597)
      | U_16595 = c_List_Olist_ONil(U_16596) ),
    inference(variable_rename,[status(thm)],[f_4099_1]) ).

cnf(f_4099_3,plain,
    ( hAPP(c_List_Otl(U_16596),hAPP(hAPP(c_List_Oappend(U_16596),U_16595),U_16597)) = hAPP(hAPP(c_List_Oappend(U_16596),hAPP(c_List_Otl(U_16596),U_16595)),U_16597)
    | U_16595 = c_List_Olist_ONil(U_16596) ),
    inference(clausify,[status(thm)],[f_4099_2]) ).

fof(f_4100_1,plain,
    ! [V_xs,V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs)) = hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_n)),V_xs)),
    inference(fof_nnf,[status(thm)],[fact_take__tl]) ).

fof(f_4100_2,plain,
    ! [U_16600,U_16599,U_16598] : hAPP(hAPP(c_List_Otake(U_16598),U_16599),hAPP(c_List_Otl(U_16598),U_16600)) = hAPP(c_List_Otl(U_16598),hAPP(hAPP(c_List_Otake(U_16598),hAPP(c_Nat_OSuc,U_16599)),U_16600)),
    inference(variable_rename,[status(thm)],[f_4100_1]) ).

cnf(f_4100_3,plain,
    hAPP(hAPP(c_List_Otake(U_16598),U_16599),hAPP(c_List_Otl(U_16598),U_16600)) = hAPP(c_List_Otl(U_16598),hAPP(hAPP(c_List_Otake(U_16598),hAPP(c_Nat_OSuc,U_16599)),U_16600)),
    inference(clausify,[status(thm)],[f_4100_2]) ).

fof(f_4101_1,plain,
    ! [V_xs,V_n,T_a] : hAPP(c_List_Orotate(T_a,V_n),V_xs) = hAPP(c_List_Orotate(T_a,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_xs),
    inference(fof_nnf,[status(thm)],[fact_rotate__conv__mod]) ).

fof(f_4101_2,plain,
    ! [U_16603,U_16602,U_16601] : hAPP(c_List_Orotate(U_16601,U_16602),U_16603) = hAPP(c_List_Orotate(U_16601,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_16602,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16601)),U_16603))),U_16603),
    inference(variable_rename,[status(thm)],[f_4101_1]) ).

cnf(f_4101_3,plain,
    hAPP(c_List_Orotate(U_16601,U_16602),U_16603) = hAPP(c_List_Orotate(U_16601,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_16602,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16601)),U_16603))),U_16603),
    inference(clausify,[status(thm)],[f_4101_2]) ).

fof(f_4102_1,plain,
    ! [V_xs,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_n)),V_xs) = hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs)),
    inference(fof_nnf,[status(thm)],[fact_drop__Suc]) ).

fof(f_4102_2,plain,
    ! [U_16606,U_16605,U_16604] : hAPP(hAPP(c_List_Odrop(U_16604),hAPP(c_Nat_OSuc,U_16605)),U_16606) = hAPP(hAPP(c_List_Odrop(U_16604),U_16605),hAPP(c_List_Otl(U_16604),U_16606)),
    inference(variable_rename,[status(thm)],[f_4102_1]) ).

cnf(f_4102_3,plain,
    hAPP(hAPP(c_List_Odrop(U_16604),hAPP(c_Nat_OSuc,U_16605)),U_16606) = hAPP(hAPP(c_List_Odrop(U_16604),U_16605),hAPP(c_List_Otl(U_16604),U_16606)),
    inference(clausify,[status(thm)],[f_4102_2]) ).

fof(f_4103_1,plain,
    ! [V_xs,V_n,T_a] : hAPP(c_List_Orotate(T_a,hAPP(c_Nat_OSuc,V_n)),V_xs) = hAPP(c_List_Orotate1(T_a),hAPP(c_List_Orotate(T_a,V_n),V_xs)),
    inference(fof_nnf,[status(thm)],[fact_rotate__Suc]) ).

fof(f_4103_2,plain,
    ! [U_16609,U_16608,U_16607] : hAPP(c_List_Orotate(U_16607,hAPP(c_Nat_OSuc,U_16608)),U_16609) = hAPP(c_List_Orotate1(U_16607),hAPP(c_List_Orotate(U_16607,U_16608),U_16609)),
    inference(variable_rename,[status(thm)],[f_4103_1]) ).

cnf(f_4103_3,plain,
    hAPP(c_List_Orotate(U_16607,hAPP(c_Nat_OSuc,U_16608)),U_16609) = hAPP(c_List_Orotate1(U_16607),hAPP(c_List_Orotate(U_16607,U_16608),U_16609)),
    inference(clausify,[status(thm)],[f_4103_2]) ).

fof(f_4104_1,plain,
    ! [V_ys_2,V_xs_2,T_b] : hAPP(c_List_Otl(T_b),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,hAPP(c_List_Otl(T_b),V_ys_2),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Oappend(T_b)),V_ys_2))),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_tl__append]) ).

fof(f_4104_2,plain,
    ! [U_16612,U_16611,U_16610] : hAPP(c_List_Otl(U_16610),hAPP(hAPP(c_List_Oappend(U_16610),U_16611),U_16612)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(U_16610),U_16610,hAPP(c_List_Otl(U_16610),U_16612),hAPP(c_COMBK(tc_fun(tc_List_Olist(U_16610),tc_List_Olist(U_16610)),U_16610),hAPP(hAPP(c_COMBC(tc_List_Olist(U_16610),tc_List_Olist(U_16610),tc_List_Olist(U_16610)),c_List_Oappend(U_16610)),U_16612))),U_16611),
    inference(variable_rename,[status(thm)],[f_4104_1]) ).

cnf(f_4104_3,plain,
    hAPP(c_List_Otl(U_16610),hAPP(hAPP(c_List_Oappend(U_16610),U_16611),U_16612)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(U_16610),U_16610,hAPP(c_List_Otl(U_16610),U_16612),hAPP(c_COMBK(tc_fun(tc_List_Olist(U_16610),tc_List_Olist(U_16610)),U_16610),hAPP(hAPP(c_COMBC(tc_List_Olist(U_16610),tc_List_Olist(U_16610),tc_List_Olist(U_16610)),c_List_Oappend(U_16610)),U_16612))),U_16611),
    inference(clausify,[status(thm)],[f_4104_2]) ).

fof(f_4105_1,plain,
    ! [V_xs,T_a,V_n] :
      ( hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs
      | c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(fof_nnf,[status(thm)],[fact_rotate__id]) ).

fof(f_4105_2,plain,
    ! [U_16615,U_16614,U_16613] :
      ( hAPP(c_List_Orotate(U_16614,U_16613),U_16615) = U_16615
      | c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_16613,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16614)),U_16615)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[f_4105_1]) ).

cnf(f_4105_3,plain,
    ( hAPP(c_List_Orotate(U_16614,U_16613),U_16615) = U_16615
    | c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_16613,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16614)),U_16615)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4105_2]) ).

fof(f_4106_1,plain,
    ! [V_n,V_xs,T_a] :
      ( hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(fof_nnf,[status(thm)],[fact_rotate__length01]) ).

fof(f_4106_2,plain,
    ! [U_16618,U_16617,U_16616] :
      ( hAPP(c_List_Orotate(U_16616,U_16618),U_16617) = U_16617
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16616)),U_16617)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(variable_rename,[status(thm)],[f_4106_1]) ).

cnf(f_4106_3,plain,
    ( hAPP(c_List_Orotate(U_16616,U_16618),U_16617) = U_16617
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16616)),U_16617)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(clausify,[status(thm)],[f_4106_2]) ).

fof(f_4107_1,plain,
    ! [V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Otl(T_a),V_xs)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(fof_nnf,[status(thm)],[fact_length__tl]) ).

fof(f_4107_2,plain,
    ! [U_16620,U_16619] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16619)),hAPP(c_List_Otl(U_16619),U_16620)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16619)),U_16620)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[f_4107_1]) ).

cnf(f_4107_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16619)),hAPP(c_List_Otl(U_16619),U_16620)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16619)),U_16620)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(clausify,[status(thm)],[f_4107_2]) ).

fof(f_4108_1,plain,
    ! [V_xs,V_n,T_a] : hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_List_Otl(T_a),V_xs)),
    inference(fof_nnf,[status(thm)],[fact_tl__take]) ).

fof(f_4108_2,plain,
    ! [U_16623,U_16622,U_16621] : hAPP(c_List_Otl(U_16621),hAPP(hAPP(c_List_Otake(U_16621),U_16622),U_16623)) = hAPP(hAPP(c_List_Otake(U_16621),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_16622),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_List_Otl(U_16621),U_16623)),
    inference(variable_rename,[status(thm)],[f_4108_1]) ).

cnf(f_4108_3,plain,
    hAPP(c_List_Otl(U_16621),hAPP(hAPP(c_List_Otake(U_16621),U_16622),U_16623)) = hAPP(hAPP(c_List_Otake(U_16621),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_16622),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_List_Otl(U_16621),U_16623)),
    inference(clausify,[status(thm)],[f_4108_2]) ).

fof(f_4109_1,plain,
    ! [V_n,T_a,V_xs] :
      ( hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_n)),V_xs) = hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(c_List_Ohd(T_a),V_xs)),hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs)))
      | V_xs = c_List_Olist_ONil(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_take__Suc]) ).

fof(f_4109_2,plain,
    ! [U_16626,U_16625,U_16624] :
      ( hAPP(hAPP(c_List_Otake(U_16625),hAPP(c_Nat_OSuc,U_16626)),U_16624) = hAPP(hAPP(c_List_Olist_OCons(U_16625),hAPP(c_List_Ohd(U_16625),U_16624)),hAPP(hAPP(c_List_Otake(U_16625),U_16626),hAPP(c_List_Otl(U_16625),U_16624)))
      | U_16624 = c_List_Olist_ONil(U_16625) ),
    inference(variable_rename,[status(thm)],[f_4109_1]) ).

cnf(f_4109_3,plain,
    ( hAPP(hAPP(c_List_Otake(U_16625),hAPP(c_Nat_OSuc,U_16626)),U_16624) = hAPP(hAPP(c_List_Olist_OCons(U_16625),hAPP(c_List_Ohd(U_16625),U_16624)),hAPP(hAPP(c_List_Otake(U_16625),U_16626),hAPP(c_List_Otl(U_16625),U_16624)))
    | U_16624 = c_List_Olist_ONil(U_16625) ),
    inference(clausify,[status(thm)],[f_4109_2]) ).

fof(f_4110_1,plain,
    ! [V_xs,V_n,T_a] : hAPP(c_List_Orotate(T_a,V_n),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Odrop(T_a),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_xs)),hAPP(hAPP(c_List_Otake(T_a),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_xs)),
    inference(fof_nnf,[status(thm)],[fact_rotate__drop__take]) ).

fof(f_4110_2,plain,
    ! [U_16629,U_16628,U_16627] : hAPP(c_List_Orotate(U_16627,U_16628),U_16629) = hAPP(hAPP(c_List_Oappend(U_16627),hAPP(hAPP(c_List_Odrop(U_16627),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_16628,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16627)),U_16629))),U_16629)),hAPP(hAPP(c_List_Otake(U_16627),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_16628,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16627)),U_16629))),U_16629)),
    inference(variable_rename,[status(thm)],[f_4110_1]) ).

cnf(f_4110_3,plain,
    hAPP(c_List_Orotate(U_16627,U_16628),U_16629) = hAPP(hAPP(c_List_Oappend(U_16627),hAPP(hAPP(c_List_Odrop(U_16627),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_16628,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16627)),U_16629))),U_16629)),hAPP(hAPP(c_List_Otake(U_16627),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_16628,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16627)),U_16629))),U_16629)),
    inference(clausify,[status(thm)],[f_4110_2]) ).

fof(f_4111_1,plain,
    ! [V_xs_2,T_b] :
      ( hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),hAPP(c_List_Ohd(T_b),V_xs_2)),hAPP(c_List_Otl(T_b),V_xs_2))
      | V_xs_2 = c_List_Olist_ONil(T_b)
      | ~ class_Lattices_Oab__semigroup__idem__mult(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_fold1__set]) ).

fof(f_4111_2,plain,
    ! [U_16631,U_16630] :
      ( hAPP(c_Finite__Set_Ofold1(U_16630,c_Groups_Otimes__class_Otimes(U_16630)),hAPP(c_List_Oset(U_16630),U_16631)) = hAPP(c_List_Ofoldl(U_16630,U_16630,c_Groups_Otimes__class_Otimes(U_16630),hAPP(c_List_Ohd(U_16630),U_16631)),hAPP(c_List_Otl(U_16630),U_16631))
      | U_16631 = c_List_Olist_ONil(U_16630)
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_16630) ),
    inference(variable_rename,[status(thm)],[f_4111_1]) ).

cnf(f_4111_3,plain,
    ( hAPP(c_Finite__Set_Ofold1(U_16630,c_Groups_Otimes__class_Otimes(U_16630)),hAPP(c_List_Oset(U_16630),U_16631)) = hAPP(c_List_Ofoldl(U_16630,U_16630,c_Groups_Otimes__class_Otimes(U_16630),hAPP(c_List_Ohd(U_16630),U_16631)),hAPP(c_List_Otl(U_16630),U_16631))
    | U_16631 = c_List_Olist_ONil(U_16630)
    | ~ class_Lattices_Oab__semigroup__idem__mult(U_16630) ),
    inference(clausify,[status(thm)],[f_4111_2]) ).

fof(f_4112_1,plain,
    ! [V_r_2,V_x_2,T_b,V_y_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_y_2))),c_List_Olexord(T_b,V_r_2)))
      | ! [B_b,B_z] : V_y_2 != hAPP(hAPP(c_List_Olist_OCons(T_b),B_b),B_z) ),
    inference(fof_nnf,[status(thm)],[fact_lexord__append__rightI]) ).

fof(f_4112_2,plain,
    ! [U_16637,U_16636,U_16635,U_16634] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16635),tc_List_Olist(U_16635))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16635),tc_List_Olist(U_16635)),U_16636),hAPP(hAPP(c_List_Oappend(U_16635),U_16636),U_16634))),c_List_Olexord(U_16635,U_16637)))
      | ! [U_16633,U_16632] : U_16634 != hAPP(hAPP(c_List_Olist_OCons(U_16635),U_16633),U_16632) ),
    inference(variable_rename,[status(thm)],[f_4112_1]) ).

cnf(f_4112_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16635),tc_List_Olist(U_16635))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16635),tc_List_Olist(U_16635)),U_16636),hAPP(hAPP(c_List_Oappend(U_16635),U_16636),U_16634))),c_List_Olexord(U_16635,U_16637)))
    | U_16634 != hAPP(hAPP(c_List_Olist_OCons(U_16635),U_16633),U_16632) ),
    inference(clausify,[status(thm)],[f_4112_2]) ).

fof(f_4113_1,plain,
    ! [V_a_2,V_f_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),c_List_Olist_ONil(T_c)) = V_a_2,
    inference(fof_nnf,[status(thm)],[fact_foldl__Nil]) ).

fof(f_4113_2,plain,
    ! [U_16641,U_16640,U_16639,U_16638] : hAPP(c_List_Ofoldl(U_16638,U_16639,U_16640,U_16641),c_List_Olist_ONil(U_16639)) = U_16641,
    inference(variable_rename,[status(thm)],[f_4113_1]) ).

cnf(f_4113_3,plain,
    hAPP(c_List_Ofoldl(U_16638,U_16639,U_16640,U_16641),c_List_Olist_ONil(U_16639)) = U_16641,
    inference(clausify,[status(thm)],[f_4113_2]) ).

fof(f_4114_1,plain,
    ! [V_ns_2,V_n_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_ns_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ),
    inference(fof_nnf,[status(thm)],[fact_start__le__sum]) ).

fof(f_4114_2,plain,
    ! [U_16644,U_16643,U_16642] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_16642),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_16643),U_16644)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_16642),U_16643)) ),
    inference(variable_rename,[status(thm)],[f_4114_1]) ).

cnf(f_4114_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_16642),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_16643),U_16644)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_16642),U_16643)) ),
    inference(clausify,[status(thm)],[f_4114_2]) ).

fof(f_4115_1,plain,
    ! [V_zs_2,V_y_2,V_x_2,T_b] :
      ( hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_y_2)),V_zs_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_y_2),V_zs_2))
      | ~ class_Groups_Osemigroup__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_foldl__assoc]) ).

fof(f_4115_2,plain,
    ! [U_16648,U_16647,U_16646,U_16645] :
      ( hAPP(c_List_Ofoldl(U_16645,U_16645,c_Groups_Oplus__class_Oplus(U_16645),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_16645),U_16646),U_16647)),U_16648) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_16645),U_16646),hAPP(c_List_Ofoldl(U_16645,U_16645,c_Groups_Oplus__class_Oplus(U_16645),U_16647),U_16648))
      | ~ class_Groups_Osemigroup__add(U_16645) ),
    inference(variable_rename,[status(thm)],[f_4115_1]) ).

cnf(f_4115_3,plain,
    ( hAPP(c_List_Ofoldl(U_16645,U_16645,c_Groups_Oplus__class_Oplus(U_16645),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_16645),U_16646),U_16647)),U_16648) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_16645),U_16646),hAPP(c_List_Ofoldl(U_16645,U_16645,c_Groups_Oplus__class_Oplus(U_16645),U_16647),U_16648))
    | ~ class_Groups_Osemigroup__add(U_16645) ),
    inference(clausify,[status(thm)],[f_4115_2]) ).

fof(f_4116_1,plain,
    ! [V_zs_2,V_x_2,T_b] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_zs_2)) = hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_zs_2)
      | ~ class_Groups_Omonoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_foldl__absorb0]) ).

fof(f_4116_2,plain,
    ! [U_16651,U_16650,U_16649] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_16649),U_16650),hAPP(c_List_Ofoldl(U_16649,U_16649,c_Groups_Oplus__class_Oplus(U_16649),c_Groups_Ozero__class_Ozero(U_16649)),U_16651)) = hAPP(c_List_Ofoldl(U_16649,U_16649,c_Groups_Oplus__class_Oplus(U_16649),U_16650),U_16651)
      | ~ class_Groups_Omonoid__add(U_16649) ),
    inference(variable_rename,[status(thm)],[f_4116_1]) ).

cnf(f_4116_3,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_16649),U_16650),hAPP(c_List_Ofoldl(U_16649,U_16649,c_Groups_Oplus__class_Oplus(U_16649),c_Groups_Ozero__class_Ozero(U_16649)),U_16651)) = hAPP(c_List_Ofoldl(U_16649,U_16649,c_Groups_Oplus__class_Oplus(U_16649),U_16650),U_16651)
    | ~ class_Groups_Omonoid__add(U_16649) ),
    inference(clausify,[status(thm)],[f_4116_2]) ).

fof(f_4117_1,plain,
    ! [V_xs_2,V_x_2,V_a_2,V_f_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,hAPP(hAPP(V_f_2,V_a_2),V_x_2)),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_foldl__Cons]) ).

fof(f_4117_2,plain,
    ! [U_16657,U_16656,U_16655,U_16654,U_16653,U_16652] : hAPP(c_List_Ofoldl(U_16652,U_16653,U_16654,U_16655),hAPP(hAPP(c_List_Olist_OCons(U_16653),U_16656),U_16657)) = hAPP(c_List_Ofoldl(U_16652,U_16653,U_16654,hAPP(hAPP(U_16654,U_16655),U_16656)),U_16657),
    inference(variable_rename,[status(thm)],[f_4117_1]) ).

cnf(f_4117_3,plain,
    hAPP(c_List_Ofoldl(U_16652,U_16653,U_16654,U_16655),hAPP(hAPP(c_List_Olist_OCons(U_16653),U_16656),U_16657)) = hAPP(c_List_Ofoldl(U_16652,U_16653,U_16654,hAPP(hAPP(U_16654,U_16655),U_16656)),U_16657),
    inference(clausify,[status(thm)],[f_4117_2]) ).

fof(f_4118_1,plain,
    ! [V_ys_2,V_xs_2,V_a_2,V_f_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2)) = hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),V_xs_2)),V_ys_2),
    inference(fof_nnf,[status(thm)],[fact_foldl__append]) ).

fof(f_4118_2,plain,
    ! [U_16663,U_16662,U_16661,U_16660,U_16659,U_16658] : hAPP(c_List_Ofoldl(U_16658,U_16659,U_16660,U_16661),hAPP(hAPP(c_List_Oappend(U_16659),U_16662),U_16663)) = hAPP(c_List_Ofoldl(U_16658,U_16659,U_16660,hAPP(c_List_Ofoldl(U_16658,U_16659,U_16660,U_16661),U_16662)),U_16663),
    inference(variable_rename,[status(thm)],[f_4118_1]) ).

cnf(f_4118_3,plain,
    hAPP(c_List_Ofoldl(U_16658,U_16659,U_16660,U_16661),hAPP(hAPP(c_List_Oappend(U_16659),U_16662),U_16663)) = hAPP(c_List_Ofoldl(U_16658,U_16659,U_16660,hAPP(c_List_Ofoldl(U_16658,U_16659,U_16660,U_16661),U_16662)),U_16663),
    inference(clausify,[status(thm)],[f_4118_2]) ).

fof(f_4119_1,plain,
    ! [T_b] :
      ( c_List_Omonoid__add__class_Olistsum(T_b) = c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),c_Groups_Ozero__class_Ozero(T_b))
      | ~ class_Groups_Omonoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_listsum__foldl]) ).

fof(f_4119_2,plain,
    ! [U_16664] :
      ( c_List_Omonoid__add__class_Olistsum(U_16664) = c_List_Ofoldl(U_16664,U_16664,c_Groups_Oplus__class_Oplus(U_16664),c_Groups_Ozero__class_Ozero(U_16664))
      | ~ class_Groups_Omonoid__add(U_16664) ),
    inference(variable_rename,[status(thm)],[f_4119_1]) ).

cnf(f_4119_3,plain,
    ( c_List_Omonoid__add__class_Olistsum(U_16664) = c_List_Ofoldl(U_16664,U_16664,c_Groups_Oplus__class_Oplus(U_16664),c_Groups_Ozero__class_Ozero(U_16664))
    | ~ class_Groups_Omonoid__add(U_16664) ),
    inference(clausify,[status(thm)],[f_4119_2]) ).

fof(f_4120_1,plain,
    ! [V_ns_2,V_m_2] :
      ( ( hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_ns_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ? [B_x] :
            ( B_x != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2))) )
        | V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ( ! [B_x] :
              ( B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2))) )
          & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_ns_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(fof_nnf,[status(thm)],[fact_sum__eq__0__conv]) ).

fof(f_4120_2,plain,
    ! [U_16668,U_16667] :
      ( ( hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_16667),U_16668) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ? [U_16666] :
            ( U_16666 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_16666),hAPP(c_List_Oset(tc_Nat_Onat),U_16668))) )
        | U_16667 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ( ! [U_16665] :
              ( U_16665 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_16665),hAPP(c_List_Oset(tc_Nat_Onat),U_16668))) )
          & U_16667 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_16667),U_16668) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_4120_1]) ).

fof(f_4120_3,plain,
    ( ! [U_16672,U_16670] :
        ( hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_16670),U_16672) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ? [U_16666] :
            ( U_16666 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_16666),hAPP(c_List_Oset(tc_Nat_Onat),U_16672))) )
        | U_16670 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_16671,U_16669] :
        ( ( ! [U_16665] :
              ( U_16665 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_16665),hAPP(c_List_Oset(tc_Nat_Onat),U_16671))) )
          & U_16669 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_16669),U_16671) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_4120_2]) ).

fof(f_4120_4,plain,
    ( ! [U_16672,U_16670] :
        ( hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_16670),U_16672) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ( sK430(U_16672,U_16670) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK430(U_16672,U_16670)),hAPP(c_List_Oset(tc_Nat_Onat),U_16672))) )
        | U_16670 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_16671,U_16669] :
        ( ( ! [U_16665] :
              ( U_16665 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_16665),hAPP(c_List_Oset(tc_Nat_Onat),U_16671))) )
          & U_16669 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_16669),U_16671) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK430]),skolemize(U_16666,sK430(U_16672,U_16670))],[f_4120_3]) ).

cnf(f_4120_5,plain,
    ( U_16669 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_16669),U_16671) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4120_4]) ).

cnf(f_4120_6,plain,
    ( U_16665 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_16665),hAPP(c_List_Oset(tc_Nat_Onat),U_16671)))
    | hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_16669),U_16671) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4120_4]) ).

cnf(f_4120_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK430(U_16672,U_16670)),hAPP(c_List_Oset(tc_Nat_Onat),U_16672)))
    | U_16670 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_16670),U_16672) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4120_4]) ).

cnf(f_4120_8,plain,
    ( sK430(U_16672,U_16670) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_16670 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_16670),U_16672) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4120_4]) ).

fof(f_4121_1,plain,
    ! [V_xs_2,V_y_2,V_f_2,T_c,T_b] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_c,T_b,hAPP(c_COMBC(T_b,T_c,T_c),V_f_2),V_y_2),V_xs_2)
      | ~ c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofold__set]) ).

fof(f_4121_2,plain,
    ! [U_16677,U_16676,U_16675,U_16674,U_16673] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_16673,U_16674,U_16675),U_16676),hAPP(c_List_Oset(U_16673),U_16677)) = hAPP(c_List_Ofoldl(U_16674,U_16673,hAPP(c_COMBC(U_16673,U_16674,U_16674),U_16675),U_16676),U_16677)
      | ~ c_Finite__Set_Ofun__left__comm__idem(U_16673,U_16674,U_16675) ),
    inference(variable_rename,[status(thm)],[f_4121_1]) ).

cnf(f_4121_3,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_16673,U_16674,U_16675),U_16676),hAPP(c_List_Oset(U_16673),U_16677)) = hAPP(c_List_Ofoldl(U_16674,U_16673,hAPP(c_COMBC(U_16673,U_16674,U_16674),U_16675),U_16676),U_16677)
    | ~ c_Finite__Set_Ofun__left__comm__idem(U_16673,U_16674,U_16675) ),
    inference(clausify,[status(thm)],[f_4121_2]) ).

fof(f_4122_1,plain,
    ! [V_xs_2,T_b] :
      ( c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Orderings_Obot__class_Obot(T_b)),V_xs_2)
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__set__fold]) ).

fof(f_4122_2,plain,
    ! [U_16679,U_16678] :
      ( c_Complete__Lattice_OSup__class_OSup(U_16678,hAPP(c_List_Oset(U_16678),U_16679)) = hAPP(c_List_Ofoldl(U_16678,U_16678,c_Lattices_Osemilattice__sup__class_Osup(U_16678),c_Orderings_Obot__class_Obot(U_16678)),U_16679)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16678) ),
    inference(variable_rename,[status(thm)],[f_4122_1]) ).

cnf(f_4122_3,plain,
    ( c_Complete__Lattice_OSup__class_OSup(U_16678,hAPP(c_List_Oset(U_16678),U_16679)) = hAPP(c_List_Ofoldl(U_16678,U_16678,c_Lattices_Osemilattice__sup__class_Osup(U_16678),c_Orderings_Obot__class_Obot(U_16678)),U_16679)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16678) ),
    inference(clausify,[status(thm)],[f_4122_2]) ).

fof(f_4123_1,plain,
    ! [V_xs_2,T_b] :
      ( c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Orderings_Otop__class_Otop(T_b)),V_xs_2)
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__set__fold]) ).

fof(f_4123_2,plain,
    ! [U_16681,U_16680] :
      ( c_Complete__Lattice_OInf__class_OInf(U_16680,hAPP(c_List_Oset(U_16680),U_16681)) = hAPP(c_List_Ofoldl(U_16680,U_16680,c_Lattices_Osemilattice__inf__class_Oinf(U_16680),c_Orderings_Otop__class_Otop(U_16680)),U_16681)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16680) ),
    inference(variable_rename,[status(thm)],[f_4123_1]) ).

cnf(f_4123_3,plain,
    ( c_Complete__Lattice_OInf__class_OInf(U_16680,hAPP(c_List_Oset(U_16680),U_16681)) = hAPP(c_List_Ofoldl(U_16680,U_16680,c_Lattices_Osemilattice__inf__class_Oinf(U_16680),c_Orderings_Otop__class_Otop(U_16680)),U_16681)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16680) ),
    inference(clausify,[status(thm)],[f_4123_2]) ).

fof(f_4124_1,plain,
    ! [V_xs_2,V_x_2,T_b] :
      ( c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_xs_2)
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__fin__set__fold]) ).

fof(f_4124_2,plain,
    ! [U_16684,U_16683,U_16682] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_16682,hAPP(c_List_Oset(U_16682),hAPP(hAPP(c_List_Olist_OCons(U_16682),U_16683),U_16684))) = hAPP(c_List_Ofoldl(U_16682,U_16682,c_Lattices_Osemilattice__sup__class_Osup(U_16682),U_16683),U_16684)
      | ~ class_Lattices_Olattice(U_16682) ),
    inference(variable_rename,[status(thm)],[f_4124_1]) ).

cnf(f_4124_3,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_16682,hAPP(c_List_Oset(U_16682),hAPP(hAPP(c_List_Olist_OCons(U_16682),U_16683),U_16684))) = hAPP(c_List_Ofoldl(U_16682,U_16682,c_Lattices_Osemilattice__sup__class_Osup(U_16682),U_16683),U_16684)
    | ~ class_Lattices_Olattice(U_16682) ),
    inference(clausify,[status(thm)],[f_4124_2]) ).

fof(f_4125_1,plain,
    ! [V_xs_2,V_x_2,T_b] :
      ( c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_xs_2)
      | ~ class_Lattices_Olattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__fin__set__fold]) ).

fof(f_4125_2,plain,
    ! [U_16687,U_16686,U_16685] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_16685,hAPP(c_List_Oset(U_16685),hAPP(hAPP(c_List_Olist_OCons(U_16685),U_16686),U_16687))) = hAPP(c_List_Ofoldl(U_16685,U_16685,c_Lattices_Osemilattice__inf__class_Oinf(U_16685),U_16686),U_16687)
      | ~ class_Lattices_Olattice(U_16685) ),
    inference(variable_rename,[status(thm)],[f_4125_1]) ).

cnf(f_4125_3,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_16685,hAPP(c_List_Oset(U_16685),hAPP(hAPP(c_List_Olist_OCons(U_16685),U_16686),U_16687))) = hAPP(c_List_Ofoldl(U_16685,U_16685,c_Lattices_Osemilattice__inf__class_Oinf(U_16685),U_16686),U_16687)
    | ~ class_Lattices_Olattice(U_16685) ),
    inference(clausify,[status(thm)],[f_4125_2]) ).

fof(f_4126_1,plain,
    ! [V_xs_2,V_x_2,T_b] :
      ( c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Orderings_Oord__class_Omin(T_b),V_x_2),V_xs_2)
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Min__fin__set__fold]) ).

fof(f_4126_2,plain,
    ! [U_16690,U_16689,U_16688] :
      ( c_Big__Operators_Olinorder__class_OMin(U_16688,hAPP(c_List_Oset(U_16688),hAPP(hAPP(c_List_Olist_OCons(U_16688),U_16689),U_16690))) = hAPP(c_List_Ofoldl(U_16688,U_16688,c_Orderings_Oord__class_Omin(U_16688),U_16689),U_16690)
      | ~ class_Orderings_Olinorder(U_16688) ),
    inference(variable_rename,[status(thm)],[f_4126_1]) ).

cnf(f_4126_3,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_16688,hAPP(c_List_Oset(U_16688),hAPP(hAPP(c_List_Olist_OCons(U_16688),U_16689),U_16690))) = hAPP(c_List_Ofoldl(U_16688,U_16688,c_Orderings_Oord__class_Omin(U_16688),U_16689),U_16690)
    | ~ class_Orderings_Olinorder(U_16688) ),
    inference(clausify,[status(thm)],[f_4126_2]) ).

fof(f_4127_1,plain,
    ! [V_xs_2,V_x_2,T_b] :
      ( c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_x_2),V_xs_2)
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Max__fin__set__fold]) ).

fof(f_4127_2,plain,
    ! [U_16693,U_16692,U_16691] :
      ( c_Big__Operators_Olinorder__class_OMax(U_16691,hAPP(c_List_Oset(U_16691),hAPP(hAPP(c_List_Olist_OCons(U_16691),U_16692),U_16693))) = hAPP(c_List_Ofoldl(U_16691,U_16691,c_Orderings_Oord__class_Omax(U_16691),U_16692),U_16693)
      | ~ class_Orderings_Olinorder(U_16691) ),
    inference(variable_rename,[status(thm)],[f_4127_1]) ).

cnf(f_4127_3,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_16691,hAPP(c_List_Oset(U_16691),hAPP(hAPP(c_List_Olist_OCons(U_16691),U_16692),U_16693))) = hAPP(c_List_Ofoldl(U_16691,U_16691,c_Orderings_Oord__class_Omax(U_16691),U_16692),U_16693)
    | ~ class_Orderings_Olinorder(U_16691) ),
    inference(clausify,[status(thm)],[f_4127_2]) ).

fof(f_4128_1,plain,
    ! [V_xs_2,V_x_2,T_b] :
      ( c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Orderings_Oord__class_Omin(T_b),V_x_2),V_xs_2)
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin__set__fold]) ).

fof(f_4128_2,plain,
    ! [U_16696,U_16695,U_16694] :
      ( c_Big__Operators_Olattice_OInf__fin(U_16694,c_Orderings_Oord__class_Omin(U_16694),hAPP(c_List_Oset(U_16694),hAPP(hAPP(c_List_Olist_OCons(U_16694),U_16695),U_16696))) = hAPP(c_List_Ofoldl(U_16694,U_16694,c_Orderings_Oord__class_Omin(U_16694),U_16695),U_16696)
      | ~ class_Orderings_Olinorder(U_16694) ),
    inference(variable_rename,[status(thm)],[f_4128_1]) ).

cnf(f_4128_3,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_16694,c_Orderings_Oord__class_Omin(U_16694),hAPP(c_List_Oset(U_16694),hAPP(hAPP(c_List_Olist_OCons(U_16694),U_16695),U_16696))) = hAPP(c_List_Ofoldl(U_16694,U_16694,c_Orderings_Oord__class_Omin(U_16694),U_16695),U_16696)
    | ~ class_Orderings_Olinorder(U_16694) ),
    inference(clausify,[status(thm)],[f_4128_2]) ).

fof(f_4129_1,plain,
    ! [V_xs_2,V_x_2,T_b] :
      ( c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_x_2),V_xs_2)
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin__set__fold]) ).

fof(f_4129_2,plain,
    ! [U_16699,U_16698,U_16697] :
      ( c_Big__Operators_Olattice_OSup__fin(U_16697,c_Orderings_Oord__class_Omax(U_16697),hAPP(c_List_Oset(U_16697),hAPP(hAPP(c_List_Olist_OCons(U_16697),U_16698),U_16699))) = hAPP(c_List_Ofoldl(U_16697,U_16697,c_Orderings_Oord__class_Omax(U_16697),U_16698),U_16699)
      | ~ class_Orderings_Olinorder(U_16697) ),
    inference(variable_rename,[status(thm)],[f_4129_1]) ).

cnf(f_4129_3,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_16697,c_Orderings_Oord__class_Omax(U_16697),hAPP(c_List_Oset(U_16697),hAPP(hAPP(c_List_Olist_OCons(U_16697),U_16698),U_16699))) = hAPP(c_List_Ofoldl(U_16697,U_16697,c_Orderings_Oord__class_Omax(U_16697),U_16698),U_16699)
    | ~ class_Orderings_Olinorder(U_16697) ),
    inference(clausify,[status(thm)],[f_4129_2]) ).

fof(f_4130_1,plain,
    ! [V_f_2,V_xs_2,T_c,T_b] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),hAPP(c_List_Oset(T_c),V_xs_2)),V_f_2) = hAPP(c_List_Ofoldl(T_b,T_c,hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_f_2)),c_Orderings_Obot__class_Obot(T_b)),V_xs_2)
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_SUPR__set__fold]) ).

fof(f_4130_2,plain,
    ! [U_16703,U_16702,U_16701,U_16700] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16701,U_16700),hAPP(c_List_Oset(U_16701),U_16702)),U_16703) = hAPP(c_List_Ofoldl(U_16700,U_16701,hAPP(c_COMBC(U_16701,U_16700,U_16700),hAPP(hAPP(c_COMBB(U_16700,tc_fun(U_16700,U_16700),U_16701),c_Lattices_Osemilattice__sup__class_Osup(U_16700)),U_16703)),c_Orderings_Obot__class_Obot(U_16700)),U_16702)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16700) ),
    inference(variable_rename,[status(thm)],[f_4130_1]) ).

cnf(f_4130_3,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16701,U_16700),hAPP(c_List_Oset(U_16701),U_16702)),U_16703) = hAPP(c_List_Ofoldl(U_16700,U_16701,hAPP(c_COMBC(U_16701,U_16700,U_16700),hAPP(hAPP(c_COMBB(U_16700,tc_fun(U_16700,U_16700),U_16701),c_Lattices_Osemilattice__sup__class_Osup(U_16700)),U_16703)),c_Orderings_Obot__class_Obot(U_16700)),U_16702)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16700) ),
    inference(clausify,[status(thm)],[f_4130_2]) ).

fof(f_4131_1,plain,
    ! [V_f_2,V_xs_2,T_c,T_b] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),hAPP(c_List_Oset(T_c),V_xs_2)),V_f_2) = hAPP(c_List_Ofoldl(T_b,T_c,hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_f_2)),c_Orderings_Otop__class_Otop(T_b)),V_xs_2)
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_INFI__set__fold]) ).

fof(f_4131_2,plain,
    ! [U_16707,U_16706,U_16705,U_16704] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16705,U_16704),hAPP(c_List_Oset(U_16705),U_16706)),U_16707) = hAPP(c_List_Ofoldl(U_16704,U_16705,hAPP(c_COMBC(U_16705,U_16704,U_16704),hAPP(hAPP(c_COMBB(U_16704,tc_fun(U_16704,U_16704),U_16705),c_Lattices_Osemilattice__inf__class_Oinf(U_16704)),U_16707)),c_Orderings_Otop__class_Otop(U_16704)),U_16706)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16704) ),
    inference(variable_rename,[status(thm)],[f_4131_1]) ).

cnf(f_4131_3,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16705,U_16704),hAPP(c_List_Oset(U_16705),U_16706)),U_16707) = hAPP(c_List_Ofoldl(U_16704,U_16705,hAPP(c_COMBC(U_16705,U_16704,U_16704),hAPP(hAPP(c_COMBB(U_16704,tc_fun(U_16704,U_16704),U_16705),c_Lattices_Osemilattice__inf__class_Oinf(U_16704)),U_16707)),c_Orderings_Otop__class_Otop(U_16704)),U_16706)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16704) ),
    inference(clausify,[status(thm)],[f_4131_2]) ).

fof(f_4132_1,plain,
    ! [V_ns_2,V_n_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_ns_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_n_2),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2))) ),
    inference(fof_nnf,[status(thm)],[fact_elem__le__sum]) ).

fof(f_4132_2,plain,
    ! [U_16709,U_16708] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_16708),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_16709)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_16708),hAPP(c_List_Oset(tc_Nat_Onat),U_16709))) ),
    inference(variable_rename,[status(thm)],[f_4132_1]) ).

cnf(f_4132_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_16708),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_16709)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_16708),hAPP(c_List_Oset(tc_Nat_Onat),U_16709))) ),
    inference(clausify,[status(thm)],[f_4132_2]) ).

fof(f_4133_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( c_List_Olinorder__class_Osorted__list__of__set(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),c_List_Olinorder__class_Osorted__list__of__set(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__list__of__set__insert]) ).

fof(f_4133_2,plain,
    ! [U_16712,U_16711,U_16710] :
      ( c_List_Olinorder__class_Osorted__list__of__set(U_16710,hAPP(hAPP(c_Set_Oinsert(U_16710),U_16712),U_16711)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16710,U_16710,c_COMBI(U_16710)),U_16712),c_List_Olinorder__class_Osorted__list__of__set(U_16710,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16710,tc_HOL_Obool)),U_16711),hAPP(hAPP(c_Set_Oinsert(U_16710),U_16712),c_Orderings_Obot__class_Obot(tc_fun(U_16710,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16710),U_16711))
      | ~ class_Orderings_Olinorder(U_16710) ),
    inference(variable_rename,[status(thm)],[f_4133_1]) ).

cnf(f_4133_3,plain,
    ( c_List_Olinorder__class_Osorted__list__of__set(U_16710,hAPP(hAPP(c_Set_Oinsert(U_16710),U_16712),U_16711)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16710,U_16710,c_COMBI(U_16710)),U_16712),c_List_Olinorder__class_Osorted__list__of__set(U_16710,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16710,tc_HOL_Obool)),U_16711),hAPP(hAPP(c_Set_Oinsert(U_16710),U_16712),c_Orderings_Obot__class_Obot(tc_fun(U_16710,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16710),U_16711))
    | ~ class_Orderings_Olinorder(U_16710) ),
    inference(clausify,[status(thm)],[f_4133_2]) ).

fof(f_4134_1,plain,
    ! [V_r_2,V_y_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_y_2)),c_List_Olexord(T_b,V_r_2)))
        | ! [B_a,B_x] : V_y_2 != hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_x) )
      & ( ? [B_a,B_x] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_x)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_y_2)),c_List_Olexord(T_b,V_r_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_lexord__Nil__left]) ).

fof(f_4134_2,plain,
    ! [U_16719,U_16718,U_16717] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16717),tc_List_Olist(U_16717))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16717),tc_List_Olist(U_16717)),c_List_Olist_ONil(U_16717)),U_16718)),c_List_Olexord(U_16717,U_16719)))
        | ! [U_16716,U_16715] : U_16718 != hAPP(hAPP(c_List_Olist_OCons(U_16717),U_16716),U_16715) )
      & ( ? [U_16714,U_16713] : U_16718 = hAPP(hAPP(c_List_Olist_OCons(U_16717),U_16714),U_16713)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16717),tc_List_Olist(U_16717))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16717),tc_List_Olist(U_16717)),c_List_Olist_ONil(U_16717)),U_16718)),c_List_Olexord(U_16717,U_16719))) ) ),
    inference(variable_rename,[status(thm)],[f_4134_1]) ).

fof(f_4134_3,plain,
    ( ! [U_16725,U_16723,U_16721] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16721),tc_List_Olist(U_16721))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16721),tc_List_Olist(U_16721)),c_List_Olist_ONil(U_16721)),U_16723)),c_List_Olexord(U_16721,U_16725)))
        | ! [U_16716,U_16715] : U_16723 != hAPP(hAPP(c_List_Olist_OCons(U_16721),U_16716),U_16715) )
    & ! [U_16724,U_16722,U_16720] :
        ( ? [U_16714,U_16713] : U_16722 = hAPP(hAPP(c_List_Olist_OCons(U_16720),U_16714),U_16713)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16720),tc_List_Olist(U_16720))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16720),tc_List_Olist(U_16720)),c_List_Olist_ONil(U_16720)),U_16722)),c_List_Olexord(U_16720,U_16724))) ) ),
    inference(miniscope,[status(thm)],[f_4134_2]) ).

fof(f_4134_4,plain,
    ( ! [U_16725,U_16723,U_16721] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16721),tc_List_Olist(U_16721))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16721),tc_List_Olist(U_16721)),c_List_Olist_ONil(U_16721)),U_16723)),c_List_Olexord(U_16721,U_16725)))
        | ! [U_16716,U_16715] : U_16723 != hAPP(hAPP(c_List_Olist_OCons(U_16721),U_16716),U_16715) )
    & ! [U_16724,U_16722,U_16720] :
        ( ? [U_16713] : U_16722 = hAPP(hAPP(c_List_Olist_OCons(U_16720),sK431(U_16724,U_16722,U_16720)),U_16713)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16720),tc_List_Olist(U_16720))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16720),tc_List_Olist(U_16720)),c_List_Olist_ONil(U_16720)),U_16722)),c_List_Olexord(U_16720,U_16724))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK431]),skolemize(U_16714,sK431(U_16724,U_16722,U_16720))],[f_4134_3]) ).

fof(f_4134_5,plain,
    ( ! [U_16725,U_16723,U_16721] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16721),tc_List_Olist(U_16721))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16721),tc_List_Olist(U_16721)),c_List_Olist_ONil(U_16721)),U_16723)),c_List_Olexord(U_16721,U_16725)))
        | ! [U_16716,U_16715] : U_16723 != hAPP(hAPP(c_List_Olist_OCons(U_16721),U_16716),U_16715) )
    & ! [U_16724,U_16722,U_16720] :
        ( U_16722 = hAPP(hAPP(c_List_Olist_OCons(U_16720),sK431(U_16724,U_16722,U_16720)),sK432(U_16724,U_16722,U_16720))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16720),tc_List_Olist(U_16720))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16720),tc_List_Olist(U_16720)),c_List_Olist_ONil(U_16720)),U_16722)),c_List_Olexord(U_16720,U_16724))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK432]),skolemize(U_16713,sK432(U_16724,U_16722,U_16720))],[f_4134_4]) ).

cnf(f_4134_6,plain,
    ( U_16722 = hAPP(hAPP(c_List_Olist_OCons(U_16720),sK431(U_16724,U_16722,U_16720)),sK432(U_16724,U_16722,U_16720))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16720),tc_List_Olist(U_16720))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16720),tc_List_Olist(U_16720)),c_List_Olist_ONil(U_16720)),U_16722)),c_List_Olexord(U_16720,U_16724))) ),
    inference(clausify,[status(thm)],[f_4134_5]) ).

cnf(f_4134_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_16721),tc_List_Olist(U_16721))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_16721),tc_List_Olist(U_16721)),c_List_Olist_ONil(U_16721)),U_16723)),c_List_Olexord(U_16721,U_16725)))
    | U_16723 != hAPP(hAPP(c_List_Olist_OCons(U_16721),U_16716),U_16715) ),
    inference(clausify,[status(thm)],[f_4134_5]) ).

fof(f_4135_1,plain,
    ! [V_x_2,V_f_2,T_b,T_c] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),c_List_Olist_ONil(T_b)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))
      | ~ class_Orderings_Olinorder(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_insort__key_Osimps_I1_J]) ).

fof(f_4135_2,plain,
    ! [U_16729,U_16728,U_16727,U_16726] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16727,U_16726,U_16728),U_16729),c_List_Olist_ONil(U_16727)) = hAPP(hAPP(c_List_Olist_OCons(U_16727),U_16729),c_List_Olist_ONil(U_16727))
      | ~ class_Orderings_Olinorder(U_16726) ),
    inference(variable_rename,[status(thm)],[f_4135_1]) ).

cnf(f_4135_3,plain,
    ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16727,U_16726,U_16728),U_16729),c_List_Olist_ONil(U_16727)) = hAPP(hAPP(c_List_Olist_OCons(U_16727),U_16729),c_List_Olist_ONil(U_16727))
    | ~ class_Orderings_Olinorder(U_16726) ),
    inference(clausify,[status(thm)],[f_4135_2]) ).

fof(f_4136_1,plain,
    ! [V_ys_2,T_c,V_y_2,V_x_2,V_f_2,T_b] :
      ( ( ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)) = hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_ys_2))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) )
        & ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)) = hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) ) )
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_insort__key_Osimps_I2_J]) ).

fof(f_4136_2,plain,
    ! [U_16735,U_16734,U_16733,U_16732,U_16731,U_16730] :
      ( ( ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16734,U_16730,U_16731),U_16732),hAPP(hAPP(c_List_Olist_OCons(U_16734),U_16733),U_16735)) = hAPP(hAPP(c_List_Olist_OCons(U_16734),U_16733),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16734,U_16730,U_16731),U_16732),U_16735))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16730),hAPP(U_16731,U_16732)),hAPP(U_16731,U_16733))) )
        & ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16734,U_16730,U_16731),U_16732),hAPP(hAPP(c_List_Olist_OCons(U_16734),U_16733),U_16735)) = hAPP(hAPP(c_List_Olist_OCons(U_16734),U_16732),hAPP(hAPP(c_List_Olist_OCons(U_16734),U_16733),U_16735))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16730),hAPP(U_16731,U_16732)),hAPP(U_16731,U_16733))) ) )
      | ~ class_Orderings_Olinorder(U_16730) ),
    inference(variable_rename,[status(thm)],[f_4136_1]) ).

cnf(f_4136_3,plain,
    ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16734,U_16730,U_16731),U_16732),hAPP(hAPP(c_List_Olist_OCons(U_16734),U_16733),U_16735)) = hAPP(hAPP(c_List_Olist_OCons(U_16734),U_16732),hAPP(hAPP(c_List_Olist_OCons(U_16734),U_16733),U_16735))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16730),hAPP(U_16731,U_16732)),hAPP(U_16731,U_16733)))
    | ~ class_Orderings_Olinorder(U_16730) ),
    inference(clausify,[status(thm)],[f_4136_2]) ).

cnf(f_4136_4,plain,
    ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16734,U_16730,U_16731),U_16732),hAPP(hAPP(c_List_Olist_OCons(U_16734),U_16733),U_16735)) = hAPP(hAPP(c_List_Olist_OCons(U_16734),U_16733),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16734,U_16730,U_16731),U_16732),U_16735))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16730),hAPP(U_16731,U_16732)),hAPP(U_16731,U_16733)))
    | ~ class_Orderings_Olinorder(U_16730) ),
    inference(clausify,[status(thm)],[f_4136_2]) ).

fof(f_4137_1,plain,
    ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
      ( hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))
      | ~ class_Orderings_Olinorder(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_set__insort]) ).

fof(f_4137_2,plain,
    ! [U_16740,U_16739,U_16738,U_16737,U_16736] :
      ( hAPP(c_List_Oset(U_16737),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16737,U_16736,U_16738),U_16739),U_16740)) = hAPP(hAPP(c_Set_Oinsert(U_16737),U_16739),hAPP(c_List_Oset(U_16737),U_16740))
      | ~ class_Orderings_Olinorder(U_16736) ),
    inference(variable_rename,[status(thm)],[f_4137_1]) ).

cnf(f_4137_3,plain,
    ( hAPP(c_List_Oset(U_16737),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16737,U_16736,U_16738),U_16739),U_16740)) = hAPP(hAPP(c_Set_Oinsert(U_16737),U_16739),hAPP(c_List_Oset(U_16737),U_16740))
    | ~ class_Orderings_Olinorder(U_16736) ),
    inference(clausify,[status(thm)],[f_4137_2]) ).

fof(f_4138_1,plain,
    ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),V_xs_2)) = hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))
      | ~ class_Orderings_Olinorder(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_length__insort]) ).

fof(f_4138_2,plain,
    ! [U_16745,U_16744,U_16743,U_16742,U_16741] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16742)),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16742,U_16741,U_16743),U_16744),U_16745)) = hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16742)),U_16745))
      | ~ class_Orderings_Olinorder(U_16741) ),
    inference(variable_rename,[status(thm)],[f_4138_1]) ).

cnf(f_4138_3,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16742)),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16742,U_16741,U_16743),U_16744),U_16745)) = hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16742)),U_16745))
    | ~ class_Orderings_Olinorder(U_16741) ),
    inference(clausify,[status(thm)],[f_4138_2]) ).

fof(f_4139_1,plain,
    ! [V_xs_2,V_y_2,V_x_2,T_b] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_y_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),V_xs_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_insort__left__comm]) ).

fof(f_4139_2,plain,
    ! [U_16749,U_16748,U_16747,U_16746] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16746,U_16746,c_COMBI(U_16746)),U_16747),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16746,U_16746,c_COMBI(U_16746)),U_16748),U_16749)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16746,U_16746,c_COMBI(U_16746)),U_16748),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16746,U_16746,c_COMBI(U_16746)),U_16747),U_16749))
      | ~ class_Orderings_Olinorder(U_16746) ),
    inference(variable_rename,[status(thm)],[f_4139_1]) ).

cnf(f_4139_3,plain,
    ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16746,U_16746,c_COMBI(U_16746)),U_16747),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16746,U_16746,c_COMBI(U_16746)),U_16748),U_16749)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16746,U_16746,c_COMBI(U_16746)),U_16748),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16746,U_16746,c_COMBI(U_16746)),U_16747),U_16749))
    | ~ class_Orderings_Olinorder(U_16746) ),
    inference(clausify,[status(thm)],[f_4139_2]) ).

fof(f_4140_1,plain,
    ! [T_b] :
      ( c_Finite__Set_Ofun__left__comm(T_b,tc_List_Olist(T_b),c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm__insort]) ).

fof(f_4140_2,plain,
    ! [U_16750] :
      ( c_Finite__Set_Ofun__left__comm(U_16750,tc_List_Olist(U_16750),c_List_Olinorder__class_Oinsort__key(U_16750,U_16750,c_COMBI(U_16750)))
      | ~ class_Orderings_Olinorder(U_16750) ),
    inference(variable_rename,[status(thm)],[f_4140_1]) ).

cnf(f_4140_3,plain,
    ( c_Finite__Set_Ofun__left__comm(U_16750,tc_List_Olist(U_16750),c_List_Olinorder__class_Oinsort__key(U_16750,U_16750,c_COMBI(U_16750)))
    | ~ class_Orderings_Olinorder(U_16750) ),
    inference(clausify,[status(thm)],[f_4140_2]) ).

fof(f_4141_1,plain,
    ! [V_xs_2,T_c,V_y_2,V_x_2,V_f_2,T_b] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_y_2),V_xs_2))
      | hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_insort__key__left__comm]) ).

fof(f_4141_2,plain,
    ! [U_16756,U_16755,U_16754,U_16753,U_16752,U_16751] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16755,U_16751,U_16752),U_16754),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16755,U_16751,U_16752),U_16753),U_16756)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16755,U_16751,U_16752),U_16753),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16755,U_16751,U_16752),U_16754),U_16756))
      | hAPP(U_16752,U_16753) = hAPP(U_16752,U_16754)
      | ~ class_Orderings_Olinorder(U_16751) ),
    inference(variable_rename,[status(thm)],[f_4141_1]) ).

cnf(f_4141_3,plain,
    ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16755,U_16751,U_16752),U_16754),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16755,U_16751,U_16752),U_16753),U_16756)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16755,U_16751,U_16752),U_16753),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16755,U_16751,U_16752),U_16754),U_16756))
    | hAPP(U_16752,U_16753) = hAPP(U_16752,U_16754)
    | ~ class_Orderings_Olinorder(U_16751) ),
    inference(clausify,[status(thm)],[f_4141_2]) ).

fof(f_4142_1,plain,
    ! [V_xs_2,V_x_2,T_b] :
      ( c_List_Oremove1(T_b,V_x_2,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),V_xs_2)) = V_xs_2
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_remove1__insort]) ).

fof(f_4142_2,plain,
    ! [U_16759,U_16758,U_16757] :
      ( c_List_Oremove1(U_16757,U_16758,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16757,U_16757,c_COMBI(U_16757)),U_16758),U_16759)) = U_16759
      | ~ class_Orderings_Olinorder(U_16757) ),
    inference(variable_rename,[status(thm)],[f_4142_1]) ).

cnf(f_4142_3,plain,
    ( c_List_Oremove1(U_16757,U_16758,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16757,U_16757,c_COMBI(U_16757)),U_16758),U_16759)) = U_16759
    | ~ class_Orderings_Olinorder(U_16757) ),
    inference(clausify,[status(thm)],[f_4142_2]) ).

fof(f_4143_1,plain,
    ! [V_xs_2,V_a_2,V_f_2,T_b,T_c] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_a_2),V_xs_2) != c_List_Olist_ONil(T_b)
      | ~ class_Orderings_Olinorder(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_insort__not__Nil]) ).

fof(f_4143_2,plain,
    ! [U_16764,U_16763,U_16762,U_16761,U_16760] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16761,U_16760,U_16762),U_16763),U_16764) != c_List_Olist_ONil(U_16761)
      | ~ class_Orderings_Olinorder(U_16760) ),
    inference(variable_rename,[status(thm)],[f_4143_1]) ).

cnf(f_4143_3,plain,
    ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16761,U_16760,U_16762),U_16763),U_16764) != c_List_Olist_ONil(U_16761)
    | ~ class_Orderings_Olinorder(U_16760) ),
    inference(clausify,[status(thm)],[f_4143_2]) ).

fof(f_4144_1,plain,
    ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
      ( ( ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),V_xs_2)))
          | ~ hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
          | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) )
        & ( ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
            & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) )
          | ~ hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),V_xs_2))) ) )
      | ~ class_Orderings_Olinorder(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__insort]) ).

fof(f_4144_2,plain,
    ! [U_16769,U_16768,U_16767,U_16766,U_16765] :
      ( ( ( hBOOL(hAPP(c_List_Odistinct(U_16766),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16766,U_16765,U_16767),U_16768),U_16769)))
          | ~ hBOOL(hAPP(c_List_Odistinct(U_16766),U_16769))
          | hBOOL(hAPP(hAPP(c_member(U_16766),U_16768),hAPP(c_List_Oset(U_16766),U_16769))) )
        & ( ( hBOOL(hAPP(c_List_Odistinct(U_16766),U_16769))
            & ~ hBOOL(hAPP(hAPP(c_member(U_16766),U_16768),hAPP(c_List_Oset(U_16766),U_16769))) )
          | ~ hBOOL(hAPP(c_List_Odistinct(U_16766),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16766,U_16765,U_16767),U_16768),U_16769))) ) )
      | ~ class_Orderings_Olinorder(U_16765) ),
    inference(variable_rename,[status(thm)],[f_4144_1]) ).

cnf(f_4144_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_16766),U_16768),hAPP(c_List_Oset(U_16766),U_16769)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_16766),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16766,U_16765,U_16767),U_16768),U_16769)))
    | ~ class_Orderings_Olinorder(U_16765) ),
    inference(clausify,[status(thm)],[f_4144_2]) ).

cnf(f_4144_4,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_16766),U_16769))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_16766),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16766,U_16765,U_16767),U_16768),U_16769)))
    | ~ class_Orderings_Olinorder(U_16765) ),
    inference(clausify,[status(thm)],[f_4144_2]) ).

cnf(f_4144_5,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_16766),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16766,U_16765,U_16767),U_16768),U_16769)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_16766),U_16769))
    | hBOOL(hAPP(hAPP(c_member(U_16766),U_16768),hAPP(c_List_Oset(U_16766),U_16769)))
    | ~ class_Orderings_Olinorder(U_16765) ),
    inference(clausify,[status(thm)],[f_4144_2]) ).

fof(f_4145_1,plain,
    ! [V_xs_2,T_c,V_x_2,V_f_2,T_b] :
      ( c_List_Olinorder__class_Oinsort__insert__key(T_c,T_b,V_f_2,V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_xs_2)
      | hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_List_Oset(T_c),V_xs_2))))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_insort__insert__insort__key]) ).

fof(f_4145_2,plain,
    ! [U_16774,U_16773,U_16772,U_16771,U_16770] :
      ( c_List_Olinorder__class_Oinsort__insert__key(U_16773,U_16770,U_16771,U_16772,U_16774) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16773,U_16770,U_16771),U_16772),U_16774)
      | hBOOL(hAPP(hAPP(c_member(U_16770),hAPP(U_16771,U_16772)),hAPP(c_Set_Oimage(U_16773,U_16770,U_16771),hAPP(c_List_Oset(U_16773),U_16774))))
      | ~ class_Orderings_Olinorder(U_16770) ),
    inference(variable_rename,[status(thm)],[f_4145_1]) ).

cnf(f_4145_3,plain,
    ( c_List_Olinorder__class_Oinsort__insert__key(U_16773,U_16770,U_16771,U_16772,U_16774) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16773,U_16770,U_16771),U_16772),U_16774)
    | hBOOL(hAPP(hAPP(c_member(U_16770),hAPP(U_16771,U_16772)),hAPP(c_Set_Oimage(U_16773,U_16770,U_16771),hAPP(c_List_Oset(U_16773),U_16774))))
    | ~ class_Orderings_Olinorder(U_16770) ),
    inference(clausify,[status(thm)],[f_4145_2]) ).

fof(f_4146_1,plain,
    ! [V_xs_2,V_x_2,T_b] :
      ( c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),V_xs_2)
      | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_insort__insert__insort]) ).

fof(f_4146_2,plain,
    ! [U_16777,U_16776,U_16775] :
      ( c_List_Olinorder__class_Oinsort__insert__key(U_16775,U_16775,c_COMBI(U_16775),U_16776,U_16777) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16775,U_16775,c_COMBI(U_16775)),U_16776),U_16777)
      | hBOOL(hAPP(hAPP(c_member(U_16775),U_16776),hAPP(c_List_Oset(U_16775),U_16777)))
      | ~ class_Orderings_Olinorder(U_16775) ),
    inference(variable_rename,[status(thm)],[f_4146_1]) ).

cnf(f_4146_3,plain,
    ( c_List_Olinorder__class_Oinsort__insert__key(U_16775,U_16775,c_COMBI(U_16775),U_16776,U_16777) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_16775,U_16775,c_COMBI(U_16775)),U_16776),U_16777)
    | hBOOL(hAPP(hAPP(c_member(U_16775),U_16776),hAPP(c_List_Oset(U_16775),U_16777)))
    | ~ class_Orderings_Olinorder(U_16775) ),
    inference(clausify,[status(thm)],[f_4146_2]) ).

fof(f_4147_1,plain,
    ! [V_x_2,V_f_2,V_xs_2,T_b,T_c] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Oinsort__insert__key(T_b,T_c,V_f_2,V_x_2,V_xs_2)))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
      | ~ class_Orderings_Olinorder(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__insort__insert]) ).

fof(f_4147_2,plain,
    ! [U_16782,U_16781,U_16780,U_16779,U_16778] :
      ( hBOOL(hAPP(c_List_Odistinct(U_16779),c_List_Olinorder__class_Oinsort__insert__key(U_16779,U_16778,U_16781,U_16782,U_16780)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_16779),U_16780))
      | ~ class_Orderings_Olinorder(U_16778) ),
    inference(variable_rename,[status(thm)],[f_4147_1]) ).

cnf(f_4147_3,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_16779),c_List_Olinorder__class_Oinsort__insert__key(U_16779,U_16778,U_16781,U_16782,U_16780)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_16779),U_16780))
    | ~ class_Orderings_Olinorder(U_16778) ),
    inference(clausify,[status(thm)],[f_4147_2]) ).

fof(f_4148_1,plain,
    ! [V_xs_2,V_x_2,T_b] :
      ( c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2) = V_xs_2
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_insort__insert__triv]) ).

fof(f_4148_2,plain,
    ! [U_16785,U_16784,U_16783] :
      ( c_List_Olinorder__class_Oinsort__insert__key(U_16783,U_16783,c_COMBI(U_16783),U_16784,U_16785) = U_16785
      | ~ hBOOL(hAPP(hAPP(c_member(U_16783),U_16784),hAPP(c_List_Oset(U_16783),U_16785)))
      | ~ class_Orderings_Olinorder(U_16783) ),
    inference(variable_rename,[status(thm)],[f_4148_1]) ).

cnf(f_4148_3,plain,
    ( c_List_Olinorder__class_Oinsort__insert__key(U_16783,U_16783,c_COMBI(U_16783),U_16784,U_16785) = U_16785
    | ~ hBOOL(hAPP(hAPP(c_member(U_16783),U_16784),hAPP(c_List_Oset(U_16783),U_16785)))
    | ~ class_Orderings_Olinorder(U_16783) ),
    inference(clausify,[status(thm)],[f_4148_2]) ).

fof(f_4149_1,plain,
    ! [V_xs_2,V_x_2,T_b] :
      ( hAPP(c_List_Oset(T_b),c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_set__insort__insert]) ).

fof(f_4149_2,plain,
    ! [U_16788,U_16787,U_16786] :
      ( hAPP(c_List_Oset(U_16786),c_List_Olinorder__class_Oinsort__insert__key(U_16786,U_16786,c_COMBI(U_16786),U_16787,U_16788)) = hAPP(hAPP(c_Set_Oinsert(U_16786),U_16787),hAPP(c_List_Oset(U_16786),U_16788))
      | ~ class_Orderings_Olinorder(U_16786) ),
    inference(variable_rename,[status(thm)],[f_4149_1]) ).

cnf(f_4149_3,plain,
    ( hAPP(c_List_Oset(U_16786),c_List_Olinorder__class_Oinsort__insert__key(U_16786,U_16786,c_COMBI(U_16786),U_16787,U_16788)) = hAPP(hAPP(c_Set_Oinsert(U_16786),U_16787),hAPP(c_List_Oset(U_16786),U_16788))
    | ~ class_Orderings_Olinorder(U_16786) ),
    inference(clausify,[status(thm)],[f_4149_2]) ).

fof(f_4150_1,plain,
    ! [V_xs_2,T_c,V_x_2,V_f_2,T_b] :
      ( c_List_Olinorder__class_Oinsort__insert__key(T_c,T_b,V_f_2,V_x_2,V_xs_2) = V_xs_2
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_List_Oset(T_c),V_xs_2))))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_insort__insert__key__triv]) ).

fof(f_4150_2,plain,
    ! [U_16793,U_16792,U_16791,U_16790,U_16789] :
      ( c_List_Olinorder__class_Oinsort__insert__key(U_16792,U_16789,U_16790,U_16791,U_16793) = U_16793
      | ~ hBOOL(hAPP(hAPP(c_member(U_16789),hAPP(U_16790,U_16791)),hAPP(c_Set_Oimage(U_16792,U_16789,U_16790),hAPP(c_List_Oset(U_16792),U_16793))))
      | ~ class_Orderings_Olinorder(U_16789) ),
    inference(variable_rename,[status(thm)],[f_4150_1]) ).

cnf(f_4150_3,plain,
    ( c_List_Olinorder__class_Oinsort__insert__key(U_16792,U_16789,U_16790,U_16791,U_16793) = U_16793
    | ~ hBOOL(hAPP(hAPP(c_member(U_16789),hAPP(U_16790,U_16791)),hAPP(c_Set_Oimage(U_16792,U_16789,U_16790),hAPP(c_List_Oset(U_16792),U_16793))))
    | ~ class_Orderings_Olinorder(U_16789) ),
    inference(clausify,[status(thm)],[f_4150_2]) ).

fof(f_4151_1,plain,
    ! [V_x,V_k,T_a,V_xs] :
      ( ( ( c_List_Olast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = c_List_Olast(T_a,V_xs)
          | V_k = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
        & ( c_List_Olast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = V_x
          | V_k != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) )
      | V_xs = c_List_Olist_ONil(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_last__list__update]) ).

fof(f_4151_2,plain,
    ! [U_16797,U_16796,U_16795,U_16794] :
      ( ( ( c_List_Olast(U_16795,hAPP(hAPP(c_List_Olist__update(U_16795,U_16794),U_16796),U_16797)) = c_List_Olast(U_16795,U_16794)
          | U_16796 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16795)),U_16794)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
        & ( c_List_Olast(U_16795,hAPP(hAPP(c_List_Olist__update(U_16795,U_16794),U_16796),U_16797)) = U_16797
          | U_16796 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16795)),U_16794)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) )
      | U_16794 = c_List_Olist_ONil(U_16795) ),
    inference(variable_rename,[status(thm)],[f_4151_1]) ).

cnf(f_4151_3,plain,
    ( c_List_Olast(U_16795,hAPP(hAPP(c_List_Olist__update(U_16795,U_16794),U_16796),U_16797)) = U_16797
    | U_16796 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16795)),U_16794)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | U_16794 = c_List_Olist_ONil(U_16795) ),
    inference(clausify,[status(thm)],[f_4151_2]) ).

cnf(f_4151_4,plain,
    ( c_List_Olast(U_16795,hAPP(hAPP(c_List_Olist__update(U_16795,U_16794),U_16796),U_16797)) = c_List_Olast(U_16795,U_16794)
    | U_16796 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16795)),U_16794)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | U_16794 = c_List_Olist_ONil(U_16795) ),
    inference(clausify,[status(thm)],[f_4151_2]) ).

fof(f_4152_1,plain,
    ! [T_a,V_xs] :
      ( c_List_Olast(T_a,V_xs) = hAPP(hAPP(c_List_Onth(T_a),V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
      | V_xs = c_List_Olist_ONil(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_last__conv__nth]) ).

fof(f_4152_2,plain,
    ! [U_16799,U_16798] :
      ( c_List_Olast(U_16799,U_16798) = hAPP(hAPP(c_List_Onth(U_16799),U_16798),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16799)),U_16798)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
      | U_16798 = c_List_Olist_ONil(U_16799) ),
    inference(variable_rename,[status(thm)],[f_4152_1]) ).

cnf(f_4152_3,plain,
    ( c_List_Olast(U_16799,U_16798) = hAPP(hAPP(c_List_Onth(U_16799),U_16798),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16799)),U_16798)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | U_16798 = c_List_Olist_ONil(U_16799) ),
    inference(clausify,[status(thm)],[f_4152_2]) ).

fof(f_4153_1,plain,
    ! [V_x,T_a,V_xs] :
      ( c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x
      | V_xs != c_List_Olist_ONil(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_last__ConsL]) ).

fof(f_4153_2,plain,
    ! [U_16802,U_16801,U_16800] :
      ( c_List_Olast(U_16801,hAPP(hAPP(c_List_Olist_OCons(U_16801),U_16802),U_16800)) = U_16802
      | U_16800 != c_List_Olist_ONil(U_16801) ),
    inference(variable_rename,[status(thm)],[f_4153_1]) ).

cnf(f_4153_3,plain,
    ( c_List_Olast(U_16801,hAPP(hAPP(c_List_Olist_OCons(U_16801),U_16802),U_16800)) = U_16802
    | U_16800 != c_List_Olist_ONil(U_16801) ),
    inference(clausify,[status(thm)],[f_4153_2]) ).

fof(f_4154_1,plain,
    ! [V_x,T_a,V_xs] :
      ( c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs)
      | V_xs = c_List_Olist_ONil(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_last__ConsR]) ).

fof(f_4154_2,plain,
    ! [U_16805,U_16804,U_16803] :
      ( c_List_Olast(U_16804,hAPP(hAPP(c_List_Olist_OCons(U_16804),U_16805),U_16803)) = c_List_Olast(U_16804,U_16803)
      | U_16803 = c_List_Olist_ONil(U_16804) ),
    inference(variable_rename,[status(thm)],[f_4154_1]) ).

cnf(f_4154_3,plain,
    ( c_List_Olast(U_16804,hAPP(hAPP(c_List_Olist_OCons(U_16804),U_16805),U_16803)) = c_List_Olast(U_16804,U_16803)
    | U_16803 = c_List_Olist_ONil(U_16804) ),
    inference(clausify,[status(thm)],[f_4154_2]) ).

fof(f_4155_1,plain,
    ! [V_x,T_a,V_xs] :
      ( ( c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs)
        | V_xs = c_List_Olist_ONil(T_a) )
      & ( c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x
        | V_xs != c_List_Olist_ONil(T_a) ) ),
    inference(fof_nnf,[status(thm)],[fact_last_Osimps]) ).

fof(f_4155_2,plain,
    ! [U_16808,U_16807,U_16806] :
      ( ( c_List_Olast(U_16807,hAPP(hAPP(c_List_Olist_OCons(U_16807),U_16808),U_16806)) = c_List_Olast(U_16807,U_16806)
        | U_16806 = c_List_Olist_ONil(U_16807) )
      & ( c_List_Olast(U_16807,hAPP(hAPP(c_List_Olist_OCons(U_16807),U_16808),U_16806)) = U_16808
        | U_16806 != c_List_Olist_ONil(U_16807) ) ),
    inference(variable_rename,[status(thm)],[f_4155_1]) ).

fof(f_4155_3,plain,
    ( ! [U_16814,U_16812,U_16810] :
        ( c_List_Olast(U_16812,hAPP(hAPP(c_List_Olist_OCons(U_16812),U_16814),U_16810)) = c_List_Olast(U_16812,U_16810)
        | U_16810 = c_List_Olist_ONil(U_16812) )
    & ! [U_16813,U_16811,U_16809] :
        ( c_List_Olast(U_16811,hAPP(hAPP(c_List_Olist_OCons(U_16811),U_16813),U_16809)) = U_16813
        | U_16809 != c_List_Olist_ONil(U_16811) ) ),
    inference(miniscope,[status(thm)],[f_4155_2]) ).

cnf(f_4155_4,plain,
    ( c_List_Olast(U_16811,hAPP(hAPP(c_List_Olist_OCons(U_16811),U_16813),U_16809)) = U_16813
    | U_16809 != c_List_Olist_ONil(U_16811) ),
    inference(clausify,[status(thm)],[f_4155_3]) ).

cnf(f_4155_5,plain,
    ( c_List_Olast(U_16812,hAPP(hAPP(c_List_Olist_OCons(U_16812),U_16814),U_16810)) = c_List_Olast(U_16812,U_16810)
    | U_16810 = c_List_Olist_ONil(U_16812) ),
    inference(clausify,[status(thm)],[f_4155_3]) ).

fof(f_4156_1,plain,
    ! [V_xs,T_a,V_ys] :
      ( c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs)
      | V_ys != c_List_Olist_ONil(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_last__appendL]) ).

fof(f_4156_2,plain,
    ! [U_16817,U_16816,U_16815] :
      ( c_List_Olast(U_16816,hAPP(hAPP(c_List_Oappend(U_16816),U_16817),U_16815)) = c_List_Olast(U_16816,U_16817)
      | U_16815 != c_List_Olist_ONil(U_16816) ),
    inference(variable_rename,[status(thm)],[f_4156_1]) ).

cnf(f_4156_3,plain,
    ( c_List_Olast(U_16816,hAPP(hAPP(c_List_Oappend(U_16816),U_16817),U_16815)) = c_List_Olast(U_16816,U_16817)
    | U_16815 != c_List_Olist_ONil(U_16816) ),
    inference(clausify,[status(thm)],[f_4156_2]) ).

fof(f_4157_1,plain,
    ! [V_xs,T_a,V_ys] :
      ( c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys)
      | V_ys = c_List_Olist_ONil(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_last__appendR]) ).

fof(f_4157_2,plain,
    ! [U_16820,U_16819,U_16818] :
      ( c_List_Olast(U_16819,hAPP(hAPP(c_List_Oappend(U_16819),U_16820),U_16818)) = c_List_Olast(U_16819,U_16818)
      | U_16818 = c_List_Olist_ONil(U_16819) ),
    inference(variable_rename,[status(thm)],[f_4157_1]) ).

cnf(f_4157_3,plain,
    ( c_List_Olast(U_16819,hAPP(hAPP(c_List_Oappend(U_16819),U_16820),U_16818)) = c_List_Olast(U_16819,U_16818)
    | U_16818 = c_List_Olist_ONil(U_16819) ),
    inference(clausify,[status(thm)],[f_4157_2]) ).

fof(f_4158_1,plain,
    ! [V_xs,T_a,V_ys] :
      ( ( c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys)
        | V_ys = c_List_Olist_ONil(T_a) )
      & ( c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs)
        | V_ys != c_List_Olist_ONil(T_a) ) ),
    inference(fof_nnf,[status(thm)],[fact_last__append]) ).

fof(f_4158_2,plain,
    ! [U_16823,U_16822,U_16821] :
      ( ( c_List_Olast(U_16822,hAPP(hAPP(c_List_Oappend(U_16822),U_16823),U_16821)) = c_List_Olast(U_16822,U_16821)
        | U_16821 = c_List_Olist_ONil(U_16822) )
      & ( c_List_Olast(U_16822,hAPP(hAPP(c_List_Oappend(U_16822),U_16823),U_16821)) = c_List_Olast(U_16822,U_16823)
        | U_16821 != c_List_Olist_ONil(U_16822) ) ),
    inference(variable_rename,[status(thm)],[f_4158_1]) ).

fof(f_4158_3,plain,
    ( ! [U_16829,U_16827,U_16825] :
        ( c_List_Olast(U_16827,hAPP(hAPP(c_List_Oappend(U_16827),U_16829),U_16825)) = c_List_Olast(U_16827,U_16825)
        | U_16825 = c_List_Olist_ONil(U_16827) )
    & ! [U_16828,U_16826,U_16824] :
        ( c_List_Olast(U_16826,hAPP(hAPP(c_List_Oappend(U_16826),U_16828),U_16824)) = c_List_Olast(U_16826,U_16828)
        | U_16824 != c_List_Olist_ONil(U_16826) ) ),
    inference(miniscope,[status(thm)],[f_4158_2]) ).

cnf(f_4158_4,plain,
    ( c_List_Olast(U_16826,hAPP(hAPP(c_List_Oappend(U_16826),U_16828),U_16824)) = c_List_Olast(U_16826,U_16828)
    | U_16824 != c_List_Olist_ONil(U_16826) ),
    inference(clausify,[status(thm)],[f_4158_3]) ).

cnf(f_4158_5,plain,
    ( c_List_Olast(U_16827,hAPP(hAPP(c_List_Oappend(U_16827),U_16829),U_16825)) = c_List_Olast(U_16827,U_16825)
    | U_16825 = c_List_Olist_ONil(U_16827) ),
    inference(clausify,[status(thm)],[f_4158_3]) ).

fof(f_4159_1,plain,
    ! [T_b,V_as_2] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),c_List_Olast(T_b,V_as_2)),hAPP(c_List_Oset(T_b),V_as_2)))
      | V_as_2 = c_List_Olist_ONil(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_last__in__set]) ).

fof(f_4159_2,plain,
    ! [U_16831,U_16830] :
      ( hBOOL(hAPP(hAPP(c_member(U_16831),c_List_Olast(U_16831,U_16830)),hAPP(c_List_Oset(U_16831),U_16830)))
      | U_16830 = c_List_Olist_ONil(U_16831) ),
    inference(variable_rename,[status(thm)],[f_4159_1]) ).

cnf(f_4159_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16831),c_List_Olast(U_16831,U_16830)),hAPP(c_List_Oset(U_16831),U_16830)))
    | U_16830 = c_List_Olist_ONil(U_16831) ),
    inference(clausify,[status(thm)],[f_4159_2]) ).

fof(f_4160_1,plain,
    ! [V_x,V_xs,T_a] : c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a)))) = V_x,
    inference(fof_nnf,[status(thm)],[fact_last__snoc]) ).

fof(f_4160_2,plain,
    ! [U_16834,U_16833,U_16832] : c_List_Olast(U_16832,hAPP(hAPP(c_List_Oappend(U_16832),U_16833),hAPP(hAPP(c_List_Olist_OCons(U_16832),U_16834),c_List_Olist_ONil(U_16832)))) = U_16834,
    inference(variable_rename,[status(thm)],[f_4160_1]) ).

cnf(f_4160_3,plain,
    c_List_Olast(U_16832,hAPP(hAPP(c_List_Oappend(U_16832),U_16833),hAPP(hAPP(c_List_Olist_OCons(U_16832),U_16834),c_List_Olist_ONil(U_16832)))) = U_16834,
    inference(clausify,[status(thm)],[f_4160_2]) ).

fof(f_4161_1,plain,
    ! [V_xs,T_a,V_n] :
      ( c_List_Olast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = c_List_Olast(T_a,V_xs)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) ),
    inference(fof_nnf,[status(thm)],[fact_last__drop]) ).

fof(f_4161_2,plain,
    ! [U_16837,U_16836,U_16835] :
      ( c_List_Olast(U_16836,hAPP(hAPP(c_List_Odrop(U_16836),U_16835),U_16837)) = c_List_Olast(U_16836,U_16837)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16835),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16836)),U_16837))) ),
    inference(variable_rename,[status(thm)],[f_4161_1]) ).

cnf(f_4161_3,plain,
    ( c_List_Olast(U_16836,hAPP(hAPP(c_List_Odrop(U_16836),U_16835),U_16837)) = c_List_Olast(U_16836,U_16837)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_16835),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16836)),U_16837))) ),
    inference(clausify,[status(thm)],[f_4161_2]) ).

fof(f_4162_1,plain,
    ! [V_ys_2,V_x_2,V_xs_2,T_b] :
      ( ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))) = V_ys_2
        | c_List_Olast(T_b,V_ys_2) != V_x_2
        | c_List_Obutlast(T_b,V_ys_2) != V_xs_2
        | V_ys_2 = c_List_Olist_ONil(T_b) )
      & ( ( c_List_Olast(T_b,V_ys_2) = V_x_2
          & c_List_Obutlast(T_b,V_ys_2) = V_xs_2
          & V_ys_2 != c_List_Olist_ONil(T_b) )
        | hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))) != V_ys_2 ) ),
    inference(fof_nnf,[status(thm)],[fact_snoc__eq__iff__butlast]) ).

fof(f_4162_2,plain,
    ! [U_16841,U_16840,U_16839,U_16838] :
      ( ( hAPP(hAPP(c_List_Oappend(U_16838),U_16839),hAPP(hAPP(c_List_Olist_OCons(U_16838),U_16840),c_List_Olist_ONil(U_16838))) = U_16841
        | c_List_Olast(U_16838,U_16841) != U_16840
        | c_List_Obutlast(U_16838,U_16841) != U_16839
        | U_16841 = c_List_Olist_ONil(U_16838) )
      & ( ( c_List_Olast(U_16838,U_16841) = U_16840
          & c_List_Obutlast(U_16838,U_16841) = U_16839
          & U_16841 != c_List_Olist_ONil(U_16838) )
        | hAPP(hAPP(c_List_Oappend(U_16838),U_16839),hAPP(hAPP(c_List_Olist_OCons(U_16838),U_16840),c_List_Olist_ONil(U_16838))) != U_16841 ) ),
    inference(variable_rename,[status(thm)],[f_4162_1]) ).

fof(f_4162_3,plain,
    ( ! [U_16849,U_16847,U_16845,U_16843] :
        ( hAPP(hAPP(c_List_Oappend(U_16843),U_16845),hAPP(hAPP(c_List_Olist_OCons(U_16843),U_16847),c_List_Olist_ONil(U_16843))) = U_16849
        | c_List_Olast(U_16843,U_16849) != U_16847
        | c_List_Obutlast(U_16843,U_16849) != U_16845
        | U_16849 = c_List_Olist_ONil(U_16843) )
    & ! [U_16848,U_16846,U_16844,U_16842] :
        ( ( c_List_Olast(U_16842,U_16848) = U_16846
          & c_List_Obutlast(U_16842,U_16848) = U_16844
          & U_16848 != c_List_Olist_ONil(U_16842) )
        | hAPP(hAPP(c_List_Oappend(U_16842),U_16844),hAPP(hAPP(c_List_Olist_OCons(U_16842),U_16846),c_List_Olist_ONil(U_16842))) != U_16848 ) ),
    inference(miniscope,[status(thm)],[f_4162_2]) ).

cnf(f_4162_4,plain,
    ( U_16848 != c_List_Olist_ONil(U_16842)
    | hAPP(hAPP(c_List_Oappend(U_16842),U_16844),hAPP(hAPP(c_List_Olist_OCons(U_16842),U_16846),c_List_Olist_ONil(U_16842))) != U_16848 ),
    inference(clausify,[status(thm)],[f_4162_3]) ).

cnf(f_4162_5,plain,
    ( c_List_Obutlast(U_16842,U_16848) = U_16844
    | hAPP(hAPP(c_List_Oappend(U_16842),U_16844),hAPP(hAPP(c_List_Olist_OCons(U_16842),U_16846),c_List_Olist_ONil(U_16842))) != U_16848 ),
    inference(clausify,[status(thm)],[f_4162_3]) ).

cnf(f_4162_6,plain,
    ( c_List_Olast(U_16842,U_16848) = U_16846
    | hAPP(hAPP(c_List_Oappend(U_16842),U_16844),hAPP(hAPP(c_List_Olist_OCons(U_16842),U_16846),c_List_Olist_ONil(U_16842))) != U_16848 ),
    inference(clausify,[status(thm)],[f_4162_3]) ).

cnf(f_4162_7,plain,
    ( hAPP(hAPP(c_List_Oappend(U_16843),U_16845),hAPP(hAPP(c_List_Olist_OCons(U_16843),U_16847),c_List_Olist_ONil(U_16843))) = U_16849
    | c_List_Olast(U_16843,U_16849) != U_16847
    | c_List_Obutlast(U_16843,U_16849) != U_16845
    | U_16849 = c_List_Olist_ONil(U_16843) ),
    inference(clausify,[status(thm)],[f_4162_3]) ).

fof(f_4163_1,plain,
    ! [T_a,V_xs] :
      ( hAPP(hAPP(c_List_Oappend(T_a),c_List_Obutlast(T_a,V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),c_List_Olast(T_a,V_xs)),c_List_Olist_ONil(T_a))) = V_xs
      | V_xs = c_List_Olist_ONil(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_append__butlast__last__id]) ).

fof(f_4163_2,plain,
    ! [U_16851,U_16850] :
      ( hAPP(hAPP(c_List_Oappend(U_16851),c_List_Obutlast(U_16851,U_16850)),hAPP(hAPP(c_List_Olist_OCons(U_16851),c_List_Olast(U_16851,U_16850)),c_List_Olist_ONil(U_16851))) = U_16850
      | U_16850 = c_List_Olist_ONil(U_16851) ),
    inference(variable_rename,[status(thm)],[f_4163_1]) ).

cnf(f_4163_3,plain,
    ( hAPP(hAPP(c_List_Oappend(U_16851),c_List_Obutlast(U_16851,U_16850)),hAPP(hAPP(c_List_Olist_OCons(U_16851),c_List_Olast(U_16851,U_16850)),c_List_Olist_ONil(U_16851))) = U_16850
    | U_16850 = c_List_Olist_ONil(U_16851) ),
    inference(clausify,[status(thm)],[f_4163_2]) ).

fof(f_4164_1,plain,
    ! [V_A_2,V_a_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_a_2),c_List_Olists(T_b,V_A_2)))
        | ( ! [B_a,B_l] :
              ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_l),c_List_Olists(T_b,V_A_2)))
              | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
              | V_a_2 != hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_l) )
          & V_a_2 != c_List_Olist_ONil(T_b) ) )
      & ( ? [B_a,B_l] :
            ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_l),c_List_Olists(T_b,V_A_2)))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
            & V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_l) )
        | V_a_2 = c_List_Olist_ONil(T_b)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_a_2),c_List_Olists(T_b,V_A_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_lists_Osimps]) ).

fof(f_4164_2,plain,
    ! [U_16858,U_16857,U_16856] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16856)),U_16857),c_List_Olists(U_16856,U_16858)))
        | ( ! [U_16855,U_16854] :
              ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16856)),U_16854),c_List_Olists(U_16856,U_16858)))
              | ~ hBOOL(hAPP(hAPP(c_member(U_16856),U_16855),U_16858))
              | U_16857 != hAPP(hAPP(c_List_Olist_OCons(U_16856),U_16855),U_16854) )
          & U_16857 != c_List_Olist_ONil(U_16856) ) )
      & ( ? [U_16853,U_16852] :
            ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16856)),U_16852),c_List_Olists(U_16856,U_16858)))
            & hBOOL(hAPP(hAPP(c_member(U_16856),U_16853),U_16858))
            & U_16857 = hAPP(hAPP(c_List_Olist_OCons(U_16856),U_16853),U_16852) )
        | U_16857 = c_List_Olist_ONil(U_16856)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16856)),U_16857),c_List_Olists(U_16856,U_16858))) ) ),
    inference(variable_rename,[status(thm)],[f_4164_1]) ).

fof(f_4164_3,plain,
    ( ! [U_16864,U_16862,U_16860] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16860)),U_16862),c_List_Olists(U_16860,U_16864)))
        | ( ! [U_16855] :
              ( ! [U_16854] :
                  ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16860)),U_16854),c_List_Olists(U_16860,U_16864)))
                  | U_16862 != hAPP(hAPP(c_List_Olist_OCons(U_16860),U_16855),U_16854) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_16860),U_16855),U_16864)) )
          & U_16862 != c_List_Olist_ONil(U_16860) ) )
    & ! [U_16863,U_16861,U_16859] :
        ( ? [U_16853] :
            ( ? [U_16852] :
                ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16859)),U_16852),c_List_Olists(U_16859,U_16863)))
                & U_16861 = hAPP(hAPP(c_List_Olist_OCons(U_16859),U_16853),U_16852) )
            & hBOOL(hAPP(hAPP(c_member(U_16859),U_16853),U_16863)) )
        | U_16861 = c_List_Olist_ONil(U_16859)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16859)),U_16861),c_List_Olists(U_16859,U_16863))) ) ),
    inference(miniscope,[status(thm)],[f_4164_2]) ).

fof(f_4164_4,plain,
    ( ! [U_16864,U_16862,U_16860] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16860)),U_16862),c_List_Olists(U_16860,U_16864)))
        | ( ! [U_16855] :
              ( ! [U_16854] :
                  ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16860)),U_16854),c_List_Olists(U_16860,U_16864)))
                  | U_16862 != hAPP(hAPP(c_List_Olist_OCons(U_16860),U_16855),U_16854) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_16860),U_16855),U_16864)) )
          & U_16862 != c_List_Olist_ONil(U_16860) ) )
    & ! [U_16863,U_16861,U_16859] :
        ( ( ? [U_16852] :
              ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16859)),U_16852),c_List_Olists(U_16859,U_16863)))
              & U_16861 = hAPP(hAPP(c_List_Olist_OCons(U_16859),sK433(U_16863,U_16861,U_16859)),U_16852) )
          & hBOOL(hAPP(hAPP(c_member(U_16859),sK433(U_16863,U_16861,U_16859)),U_16863)) )
        | U_16861 = c_List_Olist_ONil(U_16859)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16859)),U_16861),c_List_Olists(U_16859,U_16863))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK433]),skolemize(U_16853,sK433(U_16863,U_16861,U_16859))],[f_4164_3]) ).

fof(f_4164_5,plain,
    ( ! [U_16864,U_16862,U_16860] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16860)),U_16862),c_List_Olists(U_16860,U_16864)))
        | ( ! [U_16855] :
              ( ! [U_16854] :
                  ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16860)),U_16854),c_List_Olists(U_16860,U_16864)))
                  | U_16862 != hAPP(hAPP(c_List_Olist_OCons(U_16860),U_16855),U_16854) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_16860),U_16855),U_16864)) )
          & U_16862 != c_List_Olist_ONil(U_16860) ) )
    & ! [U_16863,U_16861,U_16859] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16859)),sK434(U_16863,U_16861,U_16859)),c_List_Olists(U_16859,U_16863)))
          & U_16861 = hAPP(hAPP(c_List_Olist_OCons(U_16859),sK433(U_16863,U_16861,U_16859)),sK434(U_16863,U_16861,U_16859))
          & hBOOL(hAPP(hAPP(c_member(U_16859),sK433(U_16863,U_16861,U_16859)),U_16863)) )
        | U_16861 = c_List_Olist_ONil(U_16859)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16859)),U_16861),c_List_Olists(U_16859,U_16863))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK434]),skolemize(U_16852,sK434(U_16863,U_16861,U_16859))],[f_4164_4]) ).

cnf(f_4164_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16859),sK433(U_16863,U_16861,U_16859)),U_16863))
    | U_16861 = c_List_Olist_ONil(U_16859)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16859)),U_16861),c_List_Olists(U_16859,U_16863))) ),
    inference(clausify,[status(thm)],[f_4164_5]) ).

cnf(f_4164_7,plain,
    ( U_16861 = hAPP(hAPP(c_List_Olist_OCons(U_16859),sK433(U_16863,U_16861,U_16859)),sK434(U_16863,U_16861,U_16859))
    | U_16861 = c_List_Olist_ONil(U_16859)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16859)),U_16861),c_List_Olists(U_16859,U_16863))) ),
    inference(clausify,[status(thm)],[f_4164_5]) ).

cnf(f_4164_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16859)),sK434(U_16863,U_16861,U_16859)),c_List_Olists(U_16859,U_16863)))
    | U_16861 = c_List_Olist_ONil(U_16859)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16859)),U_16861),c_List_Olists(U_16859,U_16863))) ),
    inference(clausify,[status(thm)],[f_4164_5]) ).

cnf(f_4164_9,plain,
    ( U_16862 != c_List_Olist_ONil(U_16860)
    | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16860)),U_16862),c_List_Olists(U_16860,U_16864))) ),
    inference(clausify,[status(thm)],[f_4164_5]) ).

cnf(f_4164_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16860)),U_16854),c_List_Olists(U_16860,U_16864)))
    | U_16862 != hAPP(hAPP(c_List_Olist_OCons(U_16860),U_16855),U_16854)
    | ~ hBOOL(hAPP(hAPP(c_member(U_16860),U_16855),U_16864))
    | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_16860)),U_16862),c_List_Olists(U_16860,U_16864))) ),
    inference(clausify,[status(thm)],[f_4164_5]) ).

fof(f_4165_1,plain,
    ! [T_b,V_xs_2] :
      ( c_Random_Oselect__weight(T_b,hAPP(hAPP(c_List_Omap(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,T_b)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_b),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),V_xs_2)) = c_Random_Oselect(T_b,V_xs_2)
      | V_xs_2 = c_List_Olist_ONil(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_select__weigth__select]) ).

fof(f_4165_2,plain,
    ! [U_16866,U_16865] :
      ( c_Random_Oselect__weight(U_16866,hAPP(hAPP(c_List_Omap(U_16866,tc_prod(tc_Code__Numeral_Ocode__numeral,U_16866)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,U_16866),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),U_16865)) = c_Random_Oselect(U_16866,U_16865)
      | U_16865 = c_List_Olist_ONil(U_16866) ),
    inference(variable_rename,[status(thm)],[f_4165_1]) ).

cnf(f_4165_3,plain,
    ( c_Random_Oselect__weight(U_16866,hAPP(hAPP(c_List_Omap(U_16866,tc_prod(tc_Code__Numeral_Ocode__numeral,U_16866)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,U_16866),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),U_16865)) = c_Random_Oselect(U_16866,U_16865)
    | U_16865 = c_List_Olist_ONil(U_16866) ),
    inference(clausify,[status(thm)],[f_4165_2]) ).

fof(f_4166_1,plain,
    ! [V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_c),hAPP(c_List_Omap(T_b,T_c),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_inj__mapI]) ).

fof(f_4166_2,plain,
    ! [U_16869,U_16868,U_16867] :
      ( c_Fun_Oinj__on(tc_List_Olist(U_16867),tc_List_Olist(U_16868),hAPP(c_List_Omap(U_16867,U_16868),U_16869),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_16867),tc_HOL_Obool)))
      | ~ c_Fun_Oinj__on(U_16867,U_16868,U_16869,c_Orderings_Otop__class_Otop(tc_fun(U_16867,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_4166_1]) ).

cnf(f_4166_3,plain,
    ( c_Fun_Oinj__on(tc_List_Olist(U_16867),tc_List_Olist(U_16868),hAPP(c_List_Omap(U_16867,U_16868),U_16869),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_16867),tc_HOL_Obool)))
    | ~ c_Fun_Oinj__on(U_16867,U_16868,U_16869,c_Orderings_Otop__class_Otop(tc_fun(U_16867,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4166_2]) ).

fof(f_4167_1,plain,
    ! [V_f_2,T_c,T_b,V_xs_2] :
      ( c_List_Olast(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) = hAPP(V_f_2,c_List_Olast(T_b,V_xs_2))
      | V_xs_2 = c_List_Olist_ONil(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_last__map]) ).

fof(f_4167_2,plain,
    ! [U_16873,U_16872,U_16871,U_16870] :
      ( c_List_Olast(U_16872,hAPP(hAPP(c_List_Omap(U_16871,U_16872),U_16873),U_16870)) = hAPP(U_16873,c_List_Olast(U_16871,U_16870))
      | U_16870 = c_List_Olist_ONil(U_16871) ),
    inference(variable_rename,[status(thm)],[f_4167_1]) ).

cnf(f_4167_3,plain,
    ( c_List_Olast(U_16872,hAPP(hAPP(c_List_Omap(U_16871,U_16872),U_16873),U_16870)) = hAPP(U_16873,c_List_Olast(U_16871,U_16870))
    | U_16870 = c_List_Olist_ONil(U_16871) ),
    inference(clausify,[status(thm)],[f_4167_2]) ).

fof(f_4168_1,plain,
    ! [V_xs_2,V_f_2,T_d,V_a_2,V_g_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_g_2,V_a_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_d,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_d,T_c),tc_fun(T_d,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_b),tc_fun(tc_fun(T_d,T_c),tc_fun(T_d,T_b)),T_b),c_COMBB(T_c,T_b,T_d)),V_g_2)),V_f_2),V_a_2),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_foldl__map]) ).

fof(f_4168_2,plain,
    ! [U_16880,U_16879,U_16878,U_16877,U_16876,U_16875,U_16874] : hAPP(c_List_Ofoldl(U_16874,U_16875,U_16876,U_16877),hAPP(hAPP(c_List_Omap(U_16878,U_16875),U_16879),U_16880)) = hAPP(c_List_Ofoldl(U_16874,U_16878,hAPP(hAPP(c_COMBC(U_16874,tc_fun(U_16878,U_16875),tc_fun(U_16878,U_16874)),hAPP(hAPP(c_COMBB(tc_fun(U_16875,U_16874),tc_fun(tc_fun(U_16878,U_16875),tc_fun(U_16878,U_16874)),U_16874),c_COMBB(U_16875,U_16874,U_16878)),U_16876)),U_16879),U_16877),U_16880),
    inference(variable_rename,[status(thm)],[f_4168_1]) ).

cnf(f_4168_3,plain,
    hAPP(c_List_Ofoldl(U_16874,U_16875,U_16876,U_16877),hAPP(hAPP(c_List_Omap(U_16878,U_16875),U_16879),U_16880)) = hAPP(c_List_Ofoldl(U_16874,U_16878,hAPP(hAPP(c_COMBC(U_16874,tc_fun(U_16878,U_16875),tc_fun(U_16878,U_16874)),hAPP(hAPP(c_COMBB(tc_fun(U_16875,U_16874),tc_fun(tc_fun(U_16878,U_16875),tc_fun(U_16878,U_16874)),U_16874),c_COMBB(U_16875,U_16874,U_16878)),U_16876)),U_16879),U_16877),U_16880),
    inference(clausify,[status(thm)],[f_4168_2]) ).

fof(f_4169_1,plain,
    ! [V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Otl(T_c),V_xs_2)) = hAPP(c_List_Otl(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_map__tl]) ).

fof(f_4169_2,plain,
    ! [U_16884,U_16883,U_16882,U_16881] : hAPP(hAPP(c_List_Omap(U_16881,U_16882),U_16883),hAPP(c_List_Otl(U_16881),U_16884)) = hAPP(c_List_Otl(U_16882),hAPP(hAPP(c_List_Omap(U_16881,U_16882),U_16883),U_16884)),
    inference(variable_rename,[status(thm)],[f_4169_1]) ).

cnf(f_4169_3,plain,
    hAPP(hAPP(c_List_Omap(U_16881,U_16882),U_16883),hAPP(c_List_Otl(U_16881),U_16884)) = hAPP(c_List_Otl(U_16882),hAPP(hAPP(c_List_Omap(U_16881,U_16882),U_16883),U_16884)),
    inference(clausify,[status(thm)],[f_4169_2]) ).

fof(f_4170_1,plain,
    ! [V_xs_2,V_f_2,T_c,V_n_2,T_b] : hAPP(c_List_Orotate(T_b,V_n_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Orotate(T_c,V_n_2),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_rotate__map]) ).

fof(f_4170_2,plain,
    ! [U_16889,U_16888,U_16887,U_16886,U_16885] : hAPP(c_List_Orotate(U_16885,U_16886),hAPP(hAPP(c_List_Omap(U_16887,U_16885),U_16888),U_16889)) = hAPP(hAPP(c_List_Omap(U_16887,U_16885),U_16888),hAPP(c_List_Orotate(U_16887,U_16886),U_16889)),
    inference(variable_rename,[status(thm)],[f_4170_1]) ).

cnf(f_4170_3,plain,
    hAPP(c_List_Orotate(U_16885,U_16886),hAPP(hAPP(c_List_Omap(U_16887,U_16885),U_16888),U_16889)) = hAPP(hAPP(c_List_Omap(U_16887,U_16885),U_16888),hAPP(c_List_Orotate(U_16887,U_16886),U_16889)),
    inference(clausify,[status(thm)],[f_4170_2]) ).

fof(f_4171_1,plain,
    ! [V_xs_2,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,tc_prod(T_b,T_b)),hAPP(hAPP(c_COMBS(T_b,T_b,tc_prod(T_b,T_b)),c_Product__Type_OPair(T_b,T_b)),c_COMBI(T_b))),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_zip__same__conv__map]) ).

fof(f_4171_2,plain,
    ! [U_16891,U_16890] : hAPP(hAPP(c_List_Ozip(U_16890,U_16890),U_16891),U_16891) = hAPP(hAPP(c_List_Omap(U_16890,tc_prod(U_16890,U_16890)),hAPP(hAPP(c_COMBS(U_16890,U_16890,tc_prod(U_16890,U_16890)),c_Product__Type_OPair(U_16890,U_16890)),c_COMBI(U_16890))),U_16891),
    inference(variable_rename,[status(thm)],[f_4171_1]) ).

cnf(f_4171_3,plain,
    hAPP(hAPP(c_List_Ozip(U_16890,U_16890),U_16891),U_16891) = hAPP(hAPP(c_List_Omap(U_16890,tc_prod(U_16890,U_16890)),hAPP(hAPP(c_COMBS(U_16890,U_16890,tc_prod(U_16890,U_16890)),c_Product__Type_OPair(U_16890,U_16890)),c_COMBI(U_16890))),U_16891),
    inference(clausify,[status(thm)],[f_4171_2]) ).

fof(f_4172_1,plain,
    ! [V_ys_2,V_g_2,T_e,V_xs_2,V_f_2,T_d,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Omap(T_d,T_b),V_f_2),V_xs_2)),hAPP(hAPP(c_List_Omap(T_e,T_c),V_g_2),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_d,T_e),tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_e,T_c),tc_fun(T_e,tc_prod(T_b,T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(tc_fun(T_e,T_c),tc_fun(T_e,tc_prod(T_b,T_c))),T_d),c_COMBB(T_c,tc_prod(T_b,T_c),T_e)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_prod(T_b,T_c)),T_d),c_Product__Type_OPair(T_b,T_c)),V_f_2))),V_g_2))),hAPP(hAPP(c_List_Ozip(T_d,T_e),V_xs_2),V_ys_2)),
    inference(fof_nnf,[status(thm)],[fact_zip__map__map]) ).

fof(f_4172_2,plain,
    ! [U_16899,U_16898,U_16897,U_16896,U_16895,U_16894,U_16893,U_16892] : hAPP(hAPP(c_List_Ozip(U_16892,U_16893),hAPP(hAPP(c_List_Omap(U_16894,U_16892),U_16895),U_16896)),hAPP(hAPP(c_List_Omap(U_16897,U_16893),U_16898),U_16899)) = hAPP(hAPP(c_List_Omap(tc_prod(U_16894,U_16897),tc_prod(U_16892,U_16893)),hAPP(c_Product__Type_Oprod_Oprod__case(U_16894,U_16897,tc_prod(U_16892,U_16893)),hAPP(hAPP(c_COMBC(U_16894,tc_fun(U_16897,U_16893),tc_fun(U_16897,tc_prod(U_16892,U_16893))),hAPP(hAPP(c_COMBB(tc_fun(U_16893,tc_prod(U_16892,U_16893)),tc_fun(tc_fun(U_16897,U_16893),tc_fun(U_16897,tc_prod(U_16892,U_16893))),U_16894),c_COMBB(U_16893,tc_prod(U_16892,U_16893),U_16897)),hAPP(hAPP(c_COMBB(U_16892,tc_fun(U_16893,tc_prod(U_16892,U_16893)),U_16894),c_Product__Type_OPair(U_16892,U_16893)),U_16895))),U_16898))),hAPP(hAPP(c_List_Ozip(U_16894,U_16897),U_16896),U_16899)),
    inference(variable_rename,[status(thm)],[f_4172_1]) ).

cnf(f_4172_3,plain,
    hAPP(hAPP(c_List_Ozip(U_16892,U_16893),hAPP(hAPP(c_List_Omap(U_16894,U_16892),U_16895),U_16896)),hAPP(hAPP(c_List_Omap(U_16897,U_16893),U_16898),U_16899)) = hAPP(hAPP(c_List_Omap(tc_prod(U_16894,U_16897),tc_prod(U_16892,U_16893)),hAPP(c_Product__Type_Oprod_Oprod__case(U_16894,U_16897,tc_prod(U_16892,U_16893)),hAPP(hAPP(c_COMBC(U_16894,tc_fun(U_16897,U_16893),tc_fun(U_16897,tc_prod(U_16892,U_16893))),hAPP(hAPP(c_COMBB(tc_fun(U_16893,tc_prod(U_16892,U_16893)),tc_fun(tc_fun(U_16897,U_16893),tc_fun(U_16897,tc_prod(U_16892,U_16893))),U_16894),c_COMBB(U_16893,tc_prod(U_16892,U_16893),U_16897)),hAPP(hAPP(c_COMBB(U_16892,tc_fun(U_16893,tc_prod(U_16892,U_16893)),U_16894),c_Product__Type_OPair(U_16892,U_16893)),U_16895))),U_16898))),hAPP(hAPP(c_List_Ozip(U_16894,U_16897),U_16896),U_16899)),
    inference(clausify,[status(thm)],[f_4172_2]) ).

fof(f_4173_1,plain,
    ! [V_ys_2,V_xs_2,V_f_2,T_d,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Omap(T_d,T_b),V_f_2),V_xs_2)),V_ys_2) = hAPP(hAPP(c_List_Omap(tc_prod(T_d,T_c),tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_c,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_prod(T_b,T_c)),T_d),c_Product__Type_OPair(T_b,T_c)),V_f_2))),hAPP(hAPP(c_List_Ozip(T_d,T_c),V_xs_2),V_ys_2)),
    inference(fof_nnf,[status(thm)],[fact_zip__map1]) ).

fof(f_4173_2,plain,
    ! [U_16905,U_16904,U_16903,U_16902,U_16901,U_16900] : hAPP(hAPP(c_List_Ozip(U_16900,U_16901),hAPP(hAPP(c_List_Omap(U_16902,U_16900),U_16903),U_16904)),U_16905) = hAPP(hAPP(c_List_Omap(tc_prod(U_16902,U_16901),tc_prod(U_16900,U_16901)),hAPP(c_Product__Type_Oprod_Oprod__case(U_16902,U_16901,tc_prod(U_16900,U_16901)),hAPP(hAPP(c_COMBB(U_16900,tc_fun(U_16901,tc_prod(U_16900,U_16901)),U_16902),c_Product__Type_OPair(U_16900,U_16901)),U_16903))),hAPP(hAPP(c_List_Ozip(U_16902,U_16901),U_16904),U_16905)),
    inference(variable_rename,[status(thm)],[f_4173_1]) ).

cnf(f_4173_3,plain,
    hAPP(hAPP(c_List_Ozip(U_16900,U_16901),hAPP(hAPP(c_List_Omap(U_16902,U_16900),U_16903),U_16904)),U_16905) = hAPP(hAPP(c_List_Omap(tc_prod(U_16902,U_16901),tc_prod(U_16900,U_16901)),hAPP(c_Product__Type_Oprod_Oprod__case(U_16902,U_16901,tc_prod(U_16900,U_16901)),hAPP(hAPP(c_COMBB(U_16900,tc_fun(U_16901,tc_prod(U_16900,U_16901)),U_16902),c_Product__Type_OPair(U_16900,U_16901)),U_16903))),hAPP(hAPP(c_List_Ozip(U_16902,U_16901),U_16904),U_16905)),
    inference(clausify,[status(thm)],[f_4173_2]) ).

fof(f_4174_1,plain,
    ! [V_ys_2,V_xs_2,V_g_2,T_e,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_d),T_b),V_f_2),hAPP(hAPP(c_List_Ozip(T_c,T_d),hAPP(hAPP(c_List_Omap(T_e,T_c),V_g_2),V_xs_2)),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_e,T_d),T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_e,T_d,T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,T_b),T_e),hAPP(c_COMBB(tc_prod(T_c,T_d),T_b,T_d),V_f_2)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_d,tc_prod(T_c,T_d)),T_e),c_Product__Type_OPair(T_c,T_d)),V_g_2)))),hAPP(hAPP(c_List_Ozip(T_e,T_d),V_xs_2),V_ys_2)),
    inference(fof_nnf,[status(thm)],[fact_map__zip__map]) ).

fof(f_4174_2,plain,
    ! [U_16913,U_16912,U_16911,U_16910,U_16909,U_16908,U_16907,U_16906] : hAPP(hAPP(c_List_Omap(tc_prod(U_16906,U_16907),U_16908),U_16909),hAPP(hAPP(c_List_Ozip(U_16906,U_16907),hAPP(hAPP(c_List_Omap(U_16910,U_16906),U_16911),U_16912)),U_16913)) = hAPP(hAPP(c_List_Omap(tc_prod(U_16910,U_16907),U_16908),hAPP(c_Product__Type_Oprod_Oprod__case(U_16910,U_16907,U_16908),hAPP(hAPP(c_COMBB(tc_fun(U_16907,tc_prod(U_16906,U_16907)),tc_fun(U_16907,U_16908),U_16910),hAPP(c_COMBB(tc_prod(U_16906,U_16907),U_16908,U_16907),U_16909)),hAPP(hAPP(c_COMBB(U_16906,tc_fun(U_16907,tc_prod(U_16906,U_16907)),U_16910),c_Product__Type_OPair(U_16906,U_16907)),U_16911)))),hAPP(hAPP(c_List_Ozip(U_16910,U_16907),U_16912),U_16913)),
    inference(variable_rename,[status(thm)],[f_4174_1]) ).

cnf(f_4174_3,plain,
    hAPP(hAPP(c_List_Omap(tc_prod(U_16906,U_16907),U_16908),U_16909),hAPP(hAPP(c_List_Ozip(U_16906,U_16907),hAPP(hAPP(c_List_Omap(U_16910,U_16906),U_16911),U_16912)),U_16913)) = hAPP(hAPP(c_List_Omap(tc_prod(U_16910,U_16907),U_16908),hAPP(c_Product__Type_Oprod_Oprod__case(U_16910,U_16907,U_16908),hAPP(hAPP(c_COMBB(tc_fun(U_16907,tc_prod(U_16906,U_16907)),tc_fun(U_16907,U_16908),U_16910),hAPP(c_COMBB(tc_prod(U_16906,U_16907),U_16908,U_16907),U_16909)),hAPP(hAPP(c_COMBB(U_16906,tc_fun(U_16907,tc_prod(U_16906,U_16907)),U_16910),c_Product__Type_OPair(U_16906,U_16907)),U_16911)))),hAPP(hAPP(c_List_Ozip(U_16910,U_16907),U_16912),U_16913)),
    inference(clausify,[status(thm)],[f_4174_2]) ).

fof(f_4175_1,plain,
    ! [V_ys_2,V_g_2,T_e,V_xs_2,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_d),T_b),V_f_2),hAPP(hAPP(c_List_Ozip(T_c,T_d),V_xs_2),hAPP(hAPP(c_List_Omap(T_e,T_d),V_g_2),V_ys_2))) = hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_e),T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_e,T_b),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_prod(T_c,T_d)),tc_fun(T_e,T_b),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),T_b,T_e),V_f_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_e,T_d),tc_fun(T_e,tc_prod(T_c,T_d))),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(tc_fun(T_e,T_d),tc_fun(T_e,tc_prod(T_c,T_d))),T_c),c_COMBB(T_d,tc_prod(T_c,T_d),T_e)),c_Product__Type_OPair(T_c,T_d))),V_g_2)))),hAPP(hAPP(c_List_Ozip(T_c,T_e),V_xs_2),V_ys_2)),
    inference(fof_nnf,[status(thm)],[fact_map__zip__map2]) ).

fof(f_4175_2,plain,
    ! [U_16921,U_16920,U_16919,U_16918,U_16917,U_16916,U_16915,U_16914] : hAPP(hAPP(c_List_Omap(tc_prod(U_16914,U_16915),U_16916),U_16917),hAPP(hAPP(c_List_Ozip(U_16914,U_16915),U_16918),hAPP(hAPP(c_List_Omap(U_16919,U_16915),U_16920),U_16921))) = hAPP(hAPP(c_List_Omap(tc_prod(U_16914,U_16919),U_16916),hAPP(c_Product__Type_Oprod_Oprod__case(U_16914,U_16919,U_16916),hAPP(hAPP(c_COMBB(tc_fun(U_16919,tc_prod(U_16914,U_16915)),tc_fun(U_16919,U_16916),U_16914),hAPP(c_COMBB(tc_prod(U_16914,U_16915),U_16916,U_16919),U_16917)),hAPP(hAPP(c_COMBC(U_16914,tc_fun(U_16919,U_16915),tc_fun(U_16919,tc_prod(U_16914,U_16915))),hAPP(hAPP(c_COMBB(tc_fun(U_16915,tc_prod(U_16914,U_16915)),tc_fun(tc_fun(U_16919,U_16915),tc_fun(U_16919,tc_prod(U_16914,U_16915))),U_16914),c_COMBB(U_16915,tc_prod(U_16914,U_16915),U_16919)),c_Product__Type_OPair(U_16914,U_16915))),U_16920)))),hAPP(hAPP(c_List_Ozip(U_16914,U_16919),U_16918),U_16921)),
    inference(variable_rename,[status(thm)],[f_4175_1]) ).

cnf(f_4175_3,plain,
    hAPP(hAPP(c_List_Omap(tc_prod(U_16914,U_16915),U_16916),U_16917),hAPP(hAPP(c_List_Ozip(U_16914,U_16915),U_16918),hAPP(hAPP(c_List_Omap(U_16919,U_16915),U_16920),U_16921))) = hAPP(hAPP(c_List_Omap(tc_prod(U_16914,U_16919),U_16916),hAPP(c_Product__Type_Oprod_Oprod__case(U_16914,U_16919,U_16916),hAPP(hAPP(c_COMBB(tc_fun(U_16919,tc_prod(U_16914,U_16915)),tc_fun(U_16919,U_16916),U_16914),hAPP(c_COMBB(tc_prod(U_16914,U_16915),U_16916,U_16919),U_16917)),hAPP(hAPP(c_COMBC(U_16914,tc_fun(U_16919,U_16915),tc_fun(U_16919,tc_prod(U_16914,U_16915))),hAPP(hAPP(c_COMBB(tc_fun(U_16915,tc_prod(U_16914,U_16915)),tc_fun(tc_fun(U_16919,U_16915),tc_fun(U_16919,tc_prod(U_16914,U_16915))),U_16914),c_COMBB(U_16915,tc_prod(U_16914,U_16915),U_16919)),c_Product__Type_OPair(U_16914,U_16915))),U_16920)))),hAPP(hAPP(c_List_Ozip(U_16914,U_16919),U_16918),U_16921)),
    inference(clausify,[status(thm)],[f_4175_2]) ).

fof(f_4176_1,plain,
    ! [V_ys_2,V_f_2,T_d,V_xs_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_d),tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_d,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_d,T_c),tc_fun(T_d,tc_prod(T_b,T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(tc_fun(T_d,T_c),tc_fun(T_d,tc_prod(T_b,T_c))),T_b),c_COMBB(T_c,tc_prod(T_b,T_c),T_d)),c_Product__Type_OPair(T_b,T_c))),V_f_2))),hAPP(hAPP(c_List_Ozip(T_b,T_d),V_xs_2),V_ys_2)),
    inference(fof_nnf,[status(thm)],[fact_zip__map2]) ).

fof(f_4176_2,plain,
    ! [U_16927,U_16926,U_16925,U_16924,U_16923,U_16922] : hAPP(hAPP(c_List_Ozip(U_16922,U_16923),U_16924),hAPP(hAPP(c_List_Omap(U_16925,U_16923),U_16926),U_16927)) = hAPP(hAPP(c_List_Omap(tc_prod(U_16922,U_16925),tc_prod(U_16922,U_16923)),hAPP(c_Product__Type_Oprod_Oprod__case(U_16922,U_16925,tc_prod(U_16922,U_16923)),hAPP(hAPP(c_COMBC(U_16922,tc_fun(U_16925,U_16923),tc_fun(U_16925,tc_prod(U_16922,U_16923))),hAPP(hAPP(c_COMBB(tc_fun(U_16923,tc_prod(U_16922,U_16923)),tc_fun(tc_fun(U_16925,U_16923),tc_fun(U_16925,tc_prod(U_16922,U_16923))),U_16922),c_COMBB(U_16923,tc_prod(U_16922,U_16923),U_16925)),c_Product__Type_OPair(U_16922,U_16923))),U_16926))),hAPP(hAPP(c_List_Ozip(U_16922,U_16925),U_16924),U_16927)),
    inference(variable_rename,[status(thm)],[f_4176_1]) ).

cnf(f_4176_3,plain,
    hAPP(hAPP(c_List_Ozip(U_16922,U_16923),U_16924),hAPP(hAPP(c_List_Omap(U_16925,U_16923),U_16926),U_16927)) = hAPP(hAPP(c_List_Omap(tc_prod(U_16922,U_16925),tc_prod(U_16922,U_16923)),hAPP(c_Product__Type_Oprod_Oprod__case(U_16922,U_16925,tc_prod(U_16922,U_16923)),hAPP(hAPP(c_COMBC(U_16922,tc_fun(U_16925,U_16923),tc_fun(U_16925,tc_prod(U_16922,U_16923))),hAPP(hAPP(c_COMBB(tc_fun(U_16923,tc_prod(U_16922,U_16923)),tc_fun(tc_fun(U_16925,U_16923),tc_fun(U_16925,tc_prod(U_16922,U_16923))),U_16922),c_COMBB(U_16923,tc_prod(U_16922,U_16923),U_16925)),c_Product__Type_OPair(U_16922,U_16923))),U_16926))),hAPP(hAPP(c_List_Ozip(U_16922,U_16925),U_16924),U_16927)),
    inference(clausify,[status(thm)],[f_4176_2]) ).

fof(f_4177_1,plain,
    ! [V_xs_2,V_f_2,T_c,T_b] :
      ( ( c_List_Olist_ONil(T_b) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)
        | V_xs_2 != c_List_Olist_ONil(T_c) )
      & ( V_xs_2 = c_List_Olist_ONil(T_c)
        | c_List_Olist_ONil(T_b) != hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_Nil__is__map__conv]) ).

fof(f_4177_2,plain,
    ! [U_16931,U_16930,U_16929,U_16928] :
      ( ( c_List_Olist_ONil(U_16928) = hAPP(hAPP(c_List_Omap(U_16929,U_16928),U_16930),U_16931)
        | U_16931 != c_List_Olist_ONil(U_16929) )
      & ( U_16931 = c_List_Olist_ONil(U_16929)
        | c_List_Olist_ONil(U_16928) != hAPP(hAPP(c_List_Omap(U_16929,U_16928),U_16930),U_16931) ) ),
    inference(variable_rename,[status(thm)],[f_4177_1]) ).

fof(f_4177_3,plain,
    ( ! [U_16939,U_16937,U_16935] :
        ( ! [U_16933] : c_List_Olist_ONil(U_16933) = hAPP(hAPP(c_List_Omap(U_16935,U_16933),U_16937),U_16939)
        | U_16939 != c_List_Olist_ONil(U_16935) )
    & ! [U_16938,U_16936,U_16934] :
        ( ! [U_16932] : c_List_Olist_ONil(U_16932) != hAPP(hAPP(c_List_Omap(U_16934,U_16932),U_16936),U_16938)
        | U_16938 = c_List_Olist_ONil(U_16934) ) ),
    inference(miniscope,[status(thm)],[f_4177_2]) ).

cnf(f_4177_4,plain,
    ( c_List_Olist_ONil(U_16932) != hAPP(hAPP(c_List_Omap(U_16934,U_16932),U_16936),U_16938)
    | U_16938 = c_List_Olist_ONil(U_16934) ),
    inference(clausify,[status(thm)],[f_4177_3]) ).

cnf(f_4177_5,plain,
    ( c_List_Olist_ONil(U_16933) = hAPP(hAPP(c_List_Omap(U_16935,U_16933),U_16937),U_16939)
    | U_16939 != c_List_Olist_ONil(U_16935) ),
    inference(clausify,[status(thm)],[f_4177_3]) ).

fof(f_4178_1,plain,
    ! [V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Olist_ONil(T_c)) = c_List_Olist_ONil(T_b),
    inference(fof_nnf,[status(thm)],[fact_map_Osimps_I1_J]) ).

fof(f_4178_2,plain,
    ! [U_16942,U_16941,U_16940] : hAPP(hAPP(c_List_Omap(U_16940,U_16941),U_16942),c_List_Olist_ONil(U_16940)) = c_List_Olist_ONil(U_16941),
    inference(variable_rename,[status(thm)],[f_4178_1]) ).

cnf(f_4178_3,plain,
    hAPP(hAPP(c_List_Omap(U_16940,U_16941),U_16942),c_List_Olist_ONil(U_16940)) = c_List_Olist_ONil(U_16941),
    inference(clausify,[status(thm)],[f_4178_2]) ).

fof(f_4179_1,plain,
    ! [V_xs_2,V_f_2,T_b,T_c] :
      ( ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = c_List_Olist_ONil(T_b)
        | V_xs_2 != c_List_Olist_ONil(T_c) )
      & ( V_xs_2 = c_List_Olist_ONil(T_c)
        | hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) != c_List_Olist_ONil(T_b) ) ),
    inference(fof_nnf,[status(thm)],[fact_map__is__Nil__conv]) ).

fof(f_4179_2,plain,
    ! [U_16946,U_16945,U_16944,U_16943] :
      ( ( hAPP(hAPP(c_List_Omap(U_16943,U_16944),U_16945),U_16946) = c_List_Olist_ONil(U_16944)
        | U_16946 != c_List_Olist_ONil(U_16943) )
      & ( U_16946 = c_List_Olist_ONil(U_16943)
        | hAPP(hAPP(c_List_Omap(U_16943,U_16944),U_16945),U_16946) != c_List_Olist_ONil(U_16944) ) ),
    inference(variable_rename,[status(thm)],[f_4179_1]) ).

fof(f_4179_3,plain,
    ( ! [U_16954,U_16952,U_16950,U_16948] :
        ( hAPP(hAPP(c_List_Omap(U_16948,U_16950),U_16952),U_16954) = c_List_Olist_ONil(U_16950)
        | U_16954 != c_List_Olist_ONil(U_16948) )
    & ! [U_16953,U_16951,U_16949,U_16947] :
        ( U_16953 = c_List_Olist_ONil(U_16947)
        | hAPP(hAPP(c_List_Omap(U_16947,U_16949),U_16951),U_16953) != c_List_Olist_ONil(U_16949) ) ),
    inference(miniscope,[status(thm)],[f_4179_2]) ).

cnf(f_4179_4,plain,
    ( U_16953 = c_List_Olist_ONil(U_16947)
    | hAPP(hAPP(c_List_Omap(U_16947,U_16949),U_16951),U_16953) != c_List_Olist_ONil(U_16949) ),
    inference(clausify,[status(thm)],[f_4179_3]) ).

cnf(f_4179_5,plain,
    ( hAPP(hAPP(c_List_Omap(U_16948,U_16950),U_16952),U_16954) = c_List_Olist_ONil(U_16950)
    | U_16954 != c_List_Olist_ONil(U_16948) ),
    inference(clausify,[status(thm)],[f_4179_3]) ).

fof(f_4180_1,plain,
    ! [V_y_2,V_k_2,V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Olist__update(T_c,V_xs_2),V_k_2),V_y_2)) = hAPP(hAPP(c_List_Olist__update(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)),V_k_2),hAPP(V_f_2,V_y_2)),
    inference(fof_nnf,[status(thm)],[fact_map__update]) ).

fof(f_4180_2,plain,
    ! [U_16960,U_16959,U_16958,U_16957,U_16956,U_16955] : hAPP(hAPP(c_List_Omap(U_16955,U_16956),U_16957),hAPP(hAPP(c_List_Olist__update(U_16955,U_16958),U_16959),U_16960)) = hAPP(hAPP(c_List_Olist__update(U_16956,hAPP(hAPP(c_List_Omap(U_16955,U_16956),U_16957),U_16958)),U_16959),hAPP(U_16957,U_16960)),
    inference(variable_rename,[status(thm)],[f_4180_1]) ).

cnf(f_4180_3,plain,
    hAPP(hAPP(c_List_Omap(U_16955,U_16956),U_16957),hAPP(hAPP(c_List_Olist__update(U_16955,U_16958),U_16959),U_16960)) = hAPP(hAPP(c_List_Olist__update(U_16956,hAPP(hAPP(c_List_Omap(U_16955,U_16956),U_16957),U_16958)),U_16959),hAPP(U_16957,U_16960)),
    inference(clausify,[status(thm)],[f_4180_2]) ).

fof(f_4181_1,plain,
    ! [V_g_2,V_xs_2,V_f_2,T_b,T_c] :
      ( ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_xs_2)
        | ? [B_x] :
            ( hAPP(V_f_2,B_x) != hAPP(V_g_2,B_x)
            & hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2))) ) )
      & ( ! [B_x] :
            ( hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x)
            | ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2))) )
        | hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) != hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_xs_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_map__eq__conv]) ).

fof(f_4181_2,plain,
    ! [U_16967,U_16966,U_16965,U_16964,U_16963] :
      ( ( hAPP(hAPP(c_List_Omap(U_16963,U_16964),U_16965),U_16966) = hAPP(hAPP(c_List_Omap(U_16963,U_16964),U_16967),U_16966)
        | ? [U_16962] :
            ( hAPP(U_16965,U_16962) != hAPP(U_16967,U_16962)
            & hBOOL(hAPP(hAPP(c_member(U_16963),U_16962),hAPP(c_List_Oset(U_16963),U_16966))) ) )
      & ( ! [U_16961] :
            ( hAPP(U_16965,U_16961) = hAPP(U_16967,U_16961)
            | ~ hBOOL(hAPP(hAPP(c_member(U_16963),U_16961),hAPP(c_List_Oset(U_16963),U_16966))) )
        | hAPP(hAPP(c_List_Omap(U_16963,U_16964),U_16965),U_16966) != hAPP(hAPP(c_List_Omap(U_16963,U_16964),U_16967),U_16966) ) ),
    inference(variable_rename,[status(thm)],[f_4181_1]) ).

fof(f_4181_3,plain,
    ( ! [U_16977,U_16975,U_16973,U_16971,U_16969] :
        ( hAPP(hAPP(c_List_Omap(U_16969,U_16971),U_16973),U_16975) = hAPP(hAPP(c_List_Omap(U_16969,U_16971),U_16977),U_16975)
        | ? [U_16962] :
            ( hAPP(U_16973,U_16962) != hAPP(U_16977,U_16962)
            & hBOOL(hAPP(hAPP(c_member(U_16969),U_16962),hAPP(c_List_Oset(U_16969),U_16975))) ) )
    & ! [U_16976,U_16974,U_16972,U_16970,U_16968] :
        ( ! [U_16961] :
            ( hAPP(U_16972,U_16961) = hAPP(U_16976,U_16961)
            | ~ hBOOL(hAPP(hAPP(c_member(U_16968),U_16961),hAPP(c_List_Oset(U_16968),U_16974))) )
        | hAPP(hAPP(c_List_Omap(U_16968,U_16970),U_16972),U_16974) != hAPP(hAPP(c_List_Omap(U_16968,U_16970),U_16976),U_16974) ) ),
    inference(miniscope,[status(thm)],[f_4181_2]) ).

fof(f_4181_4,plain,
    ( ! [U_16977,U_16975,U_16973,U_16971,U_16969] :
        ( hAPP(hAPP(c_List_Omap(U_16969,U_16971),U_16973),U_16975) = hAPP(hAPP(c_List_Omap(U_16969,U_16971),U_16977),U_16975)
        | ( hAPP(U_16973,sK435(U_16977,U_16975,U_16973,U_16971,U_16969)) != hAPP(U_16977,sK435(U_16977,U_16975,U_16973,U_16971,U_16969))
          & hBOOL(hAPP(hAPP(c_member(U_16969),sK435(U_16977,U_16975,U_16973,U_16971,U_16969)),hAPP(c_List_Oset(U_16969),U_16975))) ) )
    & ! [U_16976,U_16974,U_16972,U_16970,U_16968] :
        ( ! [U_16961] :
            ( hAPP(U_16972,U_16961) = hAPP(U_16976,U_16961)
            | ~ hBOOL(hAPP(hAPP(c_member(U_16968),U_16961),hAPP(c_List_Oset(U_16968),U_16974))) )
        | hAPP(hAPP(c_List_Omap(U_16968,U_16970),U_16972),U_16974) != hAPP(hAPP(c_List_Omap(U_16968,U_16970),U_16976),U_16974) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK435]),skolemize(U_16962,sK435(U_16977,U_16975,U_16973,U_16971,U_16969))],[f_4181_3]) ).

cnf(f_4181_5,plain,
    ( hAPP(U_16972,U_16961) = hAPP(U_16976,U_16961)
    | ~ hBOOL(hAPP(hAPP(c_member(U_16968),U_16961),hAPP(c_List_Oset(U_16968),U_16974)))
    | hAPP(hAPP(c_List_Omap(U_16968,U_16970),U_16972),U_16974) != hAPP(hAPP(c_List_Omap(U_16968,U_16970),U_16976),U_16974) ),
    inference(clausify,[status(thm)],[f_4181_4]) ).

cnf(f_4181_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16969),sK435(U_16977,U_16975,U_16973,U_16971,U_16969)),hAPP(c_List_Oset(U_16969),U_16975)))
    | hAPP(hAPP(c_List_Omap(U_16969,U_16971),U_16973),U_16975) = hAPP(hAPP(c_List_Omap(U_16969,U_16971),U_16977),U_16975) ),
    inference(clausify,[status(thm)],[f_4181_4]) ).

cnf(f_4181_7,plain,
    ( hAPP(U_16973,sK435(U_16977,U_16975,U_16973,U_16971,U_16969)) != hAPP(U_16977,sK435(U_16977,U_16975,U_16973,U_16971,U_16969))
    | hAPP(hAPP(c_List_Omap(U_16969,U_16971),U_16973),U_16975) = hAPP(hAPP(c_List_Omap(U_16969,U_16971),U_16977),U_16975) ),
    inference(clausify,[status(thm)],[f_4181_4]) ).

fof(f_4182_1,plain,
    ! [V_ys_2,V_g_2,T_d,V_xs_2,V_f_2,T_b,T_c] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_d)),V_ys_2)
      | hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) != hAPP(hAPP(c_List_Omap(T_d,T_b),V_g_2),V_ys_2) ),
    inference(fof_nnf,[status(thm)],[fact_map__eq__imp__length__eq]) ).

fof(f_4182_2,plain,
    ! [U_16984,U_16983,U_16982,U_16981,U_16980,U_16979,U_16978] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16978)),U_16981) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16982)),U_16984)
      | hAPP(hAPP(c_List_Omap(U_16978,U_16979),U_16980),U_16981) != hAPP(hAPP(c_List_Omap(U_16982,U_16979),U_16983),U_16984) ),
    inference(variable_rename,[status(thm)],[f_4182_1]) ).

cnf(f_4182_3,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16978)),U_16981) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16982)),U_16984)
    | hAPP(hAPP(c_List_Omap(U_16978,U_16979),U_16980),U_16981) != hAPP(hAPP(c_List_Omap(U_16982,U_16979),U_16983),U_16984) ),
    inference(clausify,[status(thm)],[f_4182_2]) ).

fof(f_4183_1,plain,
    ! [V_xs_2,V_f_2,T_c,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_length__map]) ).

fof(f_4183_2,plain,
    ! [U_16988,U_16987,U_16986,U_16985] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16985)),hAPP(hAPP(c_List_Omap(U_16986,U_16985),U_16987),U_16988)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16986)),U_16988),
    inference(variable_rename,[status(thm)],[f_4183_1]) ).

cnf(f_4183_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16985)),hAPP(hAPP(c_List_Omap(U_16986,U_16985),U_16987),U_16988)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_16986)),U_16988),
    inference(clausify,[status(thm)],[f_4183_2]) ).

fof(f_4184_1,plain,
    ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Ominus__class_Ominus(T_b)),V_f_2)),V_g_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_xs_2)))
      | ~ class_Groups_Oab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_listsum__subtractf]) ).

fof(f_4184_2,plain,
    ! [U_16993,U_16992,U_16991,U_16990,U_16989] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_16989),hAPP(hAPP(c_List_Omap(U_16990,U_16989),hAPP(hAPP(c_COMBS(U_16990,U_16989,U_16989),hAPP(hAPP(c_COMBB(U_16989,tc_fun(U_16989,U_16989),U_16990),c_Groups_Ominus__class_Ominus(U_16989)),U_16991)),U_16992)),U_16993)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_16989),hAPP(c_List_Omonoid__add__class_Olistsum(U_16989),hAPP(hAPP(c_List_Omap(U_16990,U_16989),U_16991),U_16993))),hAPP(c_List_Omonoid__add__class_Olistsum(U_16989),hAPP(hAPP(c_List_Omap(U_16990,U_16989),U_16992),U_16993)))
      | ~ class_Groups_Oab__group__add(U_16989) ),
    inference(variable_rename,[status(thm)],[f_4184_1]) ).

cnf(f_4184_3,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_16989),hAPP(hAPP(c_List_Omap(U_16990,U_16989),hAPP(hAPP(c_COMBS(U_16990,U_16989,U_16989),hAPP(hAPP(c_COMBB(U_16989,tc_fun(U_16989,U_16989),U_16990),c_Groups_Ominus__class_Ominus(U_16989)),U_16991)),U_16992)),U_16993)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_16989),hAPP(c_List_Omonoid__add__class_Olistsum(U_16989),hAPP(hAPP(c_List_Omap(U_16990,U_16989),U_16991),U_16993))),hAPP(c_List_Omonoid__add__class_Olistsum(U_16989),hAPP(hAPP(c_List_Omap(U_16990,U_16989),U_16992),U_16993)))
    | ~ class_Groups_Oab__group__add(U_16989) ),
    inference(clausify,[status(thm)],[f_4184_2]) ).

fof(f_4185_1,plain,
    ! [V_xs_2,T_c,T_b] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(c_COMBK(T_b,T_c),c_Groups_Ozero__class_Ozero(T_b))),V_xs_2)) = c_Groups_Ozero__class_Ozero(T_b)
      | ~ class_Groups_Omonoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_listsum__0]) ).

fof(f_4185_2,plain,
    ! [U_16996,U_16995,U_16994] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_16994),hAPP(hAPP(c_List_Omap(U_16995,U_16994),hAPP(c_COMBK(U_16994,U_16995),c_Groups_Ozero__class_Ozero(U_16994))),U_16996)) = c_Groups_Ozero__class_Ozero(U_16994)
      | ~ class_Groups_Omonoid__add(U_16994) ),
    inference(variable_rename,[status(thm)],[f_4185_1]) ).

cnf(f_4185_3,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_16994),hAPP(hAPP(c_List_Omap(U_16995,U_16994),hAPP(c_COMBK(U_16994,U_16995),c_Groups_Ozero__class_Ozero(U_16994))),U_16996)) = c_Groups_Ozero__class_Ozero(U_16994)
    | ~ class_Groups_Omonoid__add(U_16994) ),
    inference(clausify,[status(thm)],[f_4185_2]) ).

fof(f_4186_1,plain,
    ! [V_xs_2,V_f_2,V_c_2,T_c,T_b] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2)),V_f_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)))
      | ~ class_Rings_Osemiring__0(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_listsum__const__mult]) ).

fof(f_4186_2,plain,
    ! [U_17001,U_17000,U_16999,U_16998,U_16997] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_16997),hAPP(hAPP(c_List_Omap(U_16998,U_16997),hAPP(hAPP(c_COMBB(U_16997,U_16997,U_16998),hAPP(c_Groups_Otimes__class_Otimes(U_16997),U_16999)),U_17000)),U_17001)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_16997),U_16999),hAPP(c_List_Omonoid__add__class_Olistsum(U_16997),hAPP(hAPP(c_List_Omap(U_16998,U_16997),U_17000),U_17001)))
      | ~ class_Rings_Osemiring__0(U_16997) ),
    inference(variable_rename,[status(thm)],[f_4186_1]) ).

cnf(f_4186_3,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_16997),hAPP(hAPP(c_List_Omap(U_16998,U_16997),hAPP(hAPP(c_COMBB(U_16997,U_16997,U_16998),hAPP(c_Groups_Otimes__class_Otimes(U_16997),U_16999)),U_17000)),U_17001)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_16997),U_16999),hAPP(c_List_Omonoid__add__class_Olistsum(U_16997),hAPP(hAPP(c_List_Omap(U_16998,U_16997),U_17000),U_17001)))
    | ~ class_Rings_Osemiring__0(U_16997) ),
    inference(clausify,[status(thm)],[f_4186_2]) ).

fof(f_4187_1,plain,
    ! [V_xs_2,V_c_2,V_f_2,T_c,T_b] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Otimes__class_Otimes(T_b)),V_f_2)),V_c_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))),V_c_2)
      | ~ class_Rings_Osemiring__0(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_listsum__mult__const]) ).

fof(f_4187_2,plain,
    ! [U_17006,U_17005,U_17004,U_17003,U_17002] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_17002),hAPP(hAPP(c_List_Omap(U_17003,U_17002),hAPP(hAPP(c_COMBC(U_17003,U_17002,U_17002),hAPP(hAPP(c_COMBB(U_17002,tc_fun(U_17002,U_17002),U_17003),c_Groups_Otimes__class_Otimes(U_17002)),U_17004)),U_17005)),U_17006)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_17002),hAPP(c_List_Omonoid__add__class_Olistsum(U_17002),hAPP(hAPP(c_List_Omap(U_17003,U_17002),U_17004),U_17006))),U_17005)
      | ~ class_Rings_Osemiring__0(U_17002) ),
    inference(variable_rename,[status(thm)],[f_4187_1]) ).

cnf(f_4187_3,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_17002),hAPP(hAPP(c_List_Omap(U_17003,U_17002),hAPP(hAPP(c_COMBC(U_17003,U_17002,U_17002),hAPP(hAPP(c_COMBB(U_17002,tc_fun(U_17002,U_17002),U_17003),c_Groups_Otimes__class_Otimes(U_17002)),U_17004)),U_17005)),U_17006)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_17002),hAPP(c_List_Omonoid__add__class_Olistsum(U_17002),hAPP(hAPP(c_List_Omap(U_17003,U_17002),U_17004),U_17006))),U_17005)
    | ~ class_Rings_Osemiring__0(U_17002) ),
    inference(clausify,[status(thm)],[f_4187_2]) ).

fof(f_4188_1,plain,
    ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Oplus__class_Oplus(T_b)),V_f_2)),V_g_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_xs_2)))
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_listsum__addf]) ).

fof(f_4188_2,plain,
    ! [U_17011,U_17010,U_17009,U_17008,U_17007] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_17007),hAPP(hAPP(c_List_Omap(U_17008,U_17007),hAPP(hAPP(c_COMBS(U_17008,U_17007,U_17007),hAPP(hAPP(c_COMBB(U_17007,tc_fun(U_17007,U_17007),U_17008),c_Groups_Oplus__class_Oplus(U_17007)),U_17009)),U_17010)),U_17011)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_17007),hAPP(c_List_Omonoid__add__class_Olistsum(U_17007),hAPP(hAPP(c_List_Omap(U_17008,U_17007),U_17009),U_17011))),hAPP(c_List_Omonoid__add__class_Olistsum(U_17007),hAPP(hAPP(c_List_Omap(U_17008,U_17007),U_17010),U_17011)))
      | ~ class_Groups_Ocomm__monoid__add(U_17007) ),
    inference(variable_rename,[status(thm)],[f_4188_1]) ).

cnf(f_4188_3,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_17007),hAPP(hAPP(c_List_Omap(U_17008,U_17007),hAPP(hAPP(c_COMBS(U_17008,U_17007,U_17007),hAPP(hAPP(c_COMBB(U_17007,tc_fun(U_17007,U_17007),U_17008),c_Groups_Oplus__class_Oplus(U_17007)),U_17009)),U_17010)),U_17011)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_17007),hAPP(c_List_Omonoid__add__class_Olistsum(U_17007),hAPP(hAPP(c_List_Omap(U_17008,U_17007),U_17009),U_17011))),hAPP(c_List_Omonoid__add__class_Olistsum(U_17007),hAPP(hAPP(c_List_Omap(U_17008,U_17007),U_17010),U_17011)))
    | ~ class_Groups_Ocomm__monoid__add(U_17007) ),
    inference(clausify,[status(thm)],[f_4188_2]) ).

fof(f_4189_1,plain,
    ! [V_ys_2,V_xs_2,V_f_2,T_c,T_b] :
      ( ( ( hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2)
          | V_xs_2 != V_ys_2 )
        & ( V_xs_2 = V_ys_2
          | hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2) != hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2) ) )
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_inj__map__eq__map]) ).

fof(f_4189_2,plain,
    ! [U_17016,U_17015,U_17014,U_17013,U_17012] :
      ( ( ( hAPP(hAPP(c_List_Omap(U_17012,U_17013),U_17014),U_17015) = hAPP(hAPP(c_List_Omap(U_17012,U_17013),U_17014),U_17016)
          | U_17015 != U_17016 )
        & ( U_17015 = U_17016
          | hAPP(hAPP(c_List_Omap(U_17012,U_17013),U_17014),U_17015) != hAPP(hAPP(c_List_Omap(U_17012,U_17013),U_17014),U_17016) ) )
      | ~ c_Fun_Oinj__on(U_17012,U_17013,U_17014,c_Orderings_Otop__class_Otop(tc_fun(U_17012,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_4189_1]) ).

cnf(f_4189_3,plain,
    ( U_17015 = U_17016
    | hAPP(hAPP(c_List_Omap(U_17012,U_17013),U_17014),U_17015) != hAPP(hAPP(c_List_Omap(U_17012,U_17013),U_17014),U_17016)
    | ~ c_Fun_Oinj__on(U_17012,U_17013,U_17014,c_Orderings_Otop__class_Otop(tc_fun(U_17012,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4189_2]) ).

cnf(f_4189_4,plain,
    ( hAPP(hAPP(c_List_Omap(U_17012,U_17013),U_17014),U_17015) = hAPP(hAPP(c_List_Omap(U_17012,U_17013),U_17014),U_17016)
    | U_17015 != U_17016
    | ~ c_Fun_Oinj__on(U_17012,U_17013,U_17014,c_Orderings_Otop__class_Otop(tc_fun(U_17012,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4189_2]) ).

fof(f_4190_1,plain,
    ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
      ( V_xs_2 = V_ys_2
      | ~ c_Fun_Oinj__on(T_c,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
      | hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) != hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_ys_2) ),
    inference(fof_nnf,[status(thm)],[fact_map__injective]) ).

fof(f_4190_2,plain,
    ! [U_17021,U_17020,U_17019,U_17018,U_17017] :
      ( U_17020 = U_17021
      | ~ c_Fun_Oinj__on(U_17017,U_17018,U_17019,c_Orderings_Otop__class_Otop(tc_fun(U_17017,tc_HOL_Obool)))
      | hAPP(hAPP(c_List_Omap(U_17017,U_17018),U_17019),U_17020) != hAPP(hAPP(c_List_Omap(U_17017,U_17018),U_17019),U_17021) ),
    inference(variable_rename,[status(thm)],[f_4190_1]) ).

cnf(f_4190_3,plain,
    ( U_17020 = U_17021
    | ~ c_Fun_Oinj__on(U_17017,U_17018,U_17019,c_Orderings_Otop__class_Otop(tc_fun(U_17017,tc_HOL_Obool)))
    | hAPP(hAPP(c_List_Omap(U_17017,U_17018),U_17019),U_17020) != hAPP(hAPP(c_List_Omap(U_17017,U_17018),U_17019),U_17021) ),
    inference(clausify,[status(thm)],[f_4190_2]) ).

fof(f_4191_1,plain,
    ! [V_xs_2,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_b),c_COMBI(T_b)),V_xs_2) = V_xs_2,
    inference(fof_nnf,[status(thm)],[fact_map__ident]) ).

fof(f_4191_2,plain,
    ! [U_17023,U_17022] : hAPP(hAPP(c_List_Omap(U_17022,U_17022),c_COMBI(U_17022)),U_17023) = U_17023,
    inference(variable_rename,[status(thm)],[f_4191_1]) ).

cnf(f_4191_3,plain,
    hAPP(hAPP(c_List_Omap(U_17022,U_17022),c_COMBI(U_17022)),U_17023) = U_17023,
    inference(clausify,[status(thm)],[f_4191_2]) ).

fof(f_4192_1,plain,
    ! [V_xs_2,V_f_2,T_c,V_n_2,T_b] : hAPP(hAPP(c_List_Otake(T_b),V_n_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Otake(T_c),V_n_2),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_take__map]) ).

fof(f_4192_2,plain,
    ! [U_17028,U_17027,U_17026,U_17025,U_17024] : hAPP(hAPP(c_List_Otake(U_17024),U_17025),hAPP(hAPP(c_List_Omap(U_17026,U_17024),U_17027),U_17028)) = hAPP(hAPP(c_List_Omap(U_17026,U_17024),U_17027),hAPP(hAPP(c_List_Otake(U_17026),U_17025),U_17028)),
    inference(variable_rename,[status(thm)],[f_4192_1]) ).

cnf(f_4192_3,plain,
    hAPP(hAPP(c_List_Otake(U_17024),U_17025),hAPP(hAPP(c_List_Omap(U_17026,U_17024),U_17027),U_17028)) = hAPP(hAPP(c_List_Omap(U_17026,U_17024),U_17027),hAPP(hAPP(c_List_Otake(U_17026),U_17025),U_17028)),
    inference(clausify,[status(thm)],[f_4192_2]) ).

fof(f_4193_1,plain,
    ! [V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Obutlast(T_c,V_xs_2)) = c_List_Obutlast(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_map__butlast]) ).

fof(f_4193_2,plain,
    ! [U_17032,U_17031,U_17030,U_17029] : hAPP(hAPP(c_List_Omap(U_17029,U_17030),U_17031),c_List_Obutlast(U_17029,U_17032)) = c_List_Obutlast(U_17030,hAPP(hAPP(c_List_Omap(U_17029,U_17030),U_17031),U_17032)),
    inference(variable_rename,[status(thm)],[f_4193_1]) ).

cnf(f_4193_3,plain,
    hAPP(hAPP(c_List_Omap(U_17029,U_17030),U_17031),c_List_Obutlast(U_17029,U_17032)) = c_List_Obutlast(U_17030,hAPP(hAPP(c_List_Omap(U_17029,U_17030),U_17031),U_17032)),
    inference(clausify,[status(thm)],[f_4193_2]) ).

fof(f_4194_1,plain,
    ! [V_xs_2,V_f_2,T_c,T_b] : hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_List_Oset(T_c),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_set__map]) ).

fof(f_4194_2,plain,
    ! [U_17036,U_17035,U_17034,U_17033] : hAPP(c_List_Oset(U_17033),hAPP(hAPP(c_List_Omap(U_17034,U_17033),U_17035),U_17036)) = hAPP(c_Set_Oimage(U_17034,U_17033,U_17035),hAPP(c_List_Oset(U_17034),U_17036)),
    inference(variable_rename,[status(thm)],[f_4194_1]) ).

cnf(f_4194_3,plain,
    hAPP(c_List_Oset(U_17033),hAPP(hAPP(c_List_Omap(U_17034,U_17033),U_17035),U_17036)) = hAPP(c_Set_Oimage(U_17034,U_17033,U_17035),hAPP(c_List_Oset(U_17034),U_17036)),
    inference(clausify,[status(thm)],[f_4194_2]) ).

fof(f_4195_1,plain,
    ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),hAPP(V_f_2,V_x_2)),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_map_Osimps_I2_J]) ).

fof(f_4195_2,plain,
    ! [U_17041,U_17040,U_17039,U_17038,U_17037] : hAPP(hAPP(c_List_Omap(U_17037,U_17038),U_17039),hAPP(hAPP(c_List_Olist_OCons(U_17037),U_17040),U_17041)) = hAPP(hAPP(c_List_Olist_OCons(U_17038),hAPP(U_17039,U_17040)),hAPP(hAPP(c_List_Omap(U_17037,U_17038),U_17039),U_17041)),
    inference(variable_rename,[status(thm)],[f_4195_1]) ).

cnf(f_4195_3,plain,
    hAPP(hAPP(c_List_Omap(U_17037,U_17038),U_17039),hAPP(hAPP(c_List_Olist_OCons(U_17037),U_17040),U_17041)) = hAPP(hAPP(c_List_Olist_OCons(U_17038),hAPP(U_17039,U_17040)),hAPP(hAPP(c_List_Omap(U_17037,U_17038),U_17039),U_17041)),
    inference(clausify,[status(thm)],[f_4195_2]) ).

fof(f_4196_1,plain,
    ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_ys_2)),
    inference(fof_nnf,[status(thm)],[fact_map__append]) ).

fof(f_4196_2,plain,
    ! [U_17046,U_17045,U_17044,U_17043,U_17042] : hAPP(hAPP(c_List_Omap(U_17042,U_17043),U_17044),hAPP(hAPP(c_List_Oappend(U_17042),U_17045),U_17046)) = hAPP(hAPP(c_List_Oappend(U_17043),hAPP(hAPP(c_List_Omap(U_17042,U_17043),U_17044),U_17045)),hAPP(hAPP(c_List_Omap(U_17042,U_17043),U_17044),U_17046)),
    inference(variable_rename,[status(thm)],[f_4196_1]) ).

cnf(f_4196_3,plain,
    hAPP(hAPP(c_List_Omap(U_17042,U_17043),U_17044),hAPP(hAPP(c_List_Oappend(U_17042),U_17045),U_17046)) = hAPP(hAPP(c_List_Oappend(U_17043),hAPP(hAPP(c_List_Omap(U_17042,U_17043),U_17044),U_17045)),hAPP(hAPP(c_List_Omap(U_17042,U_17043),U_17044),U_17046)),
    inference(clausify,[status(thm)],[f_4196_2]) ).

fof(f_4197_1,plain,
    ! [V_f_2,T_c,T_b,V_xs_2] :
      ( hAPP(c_List_Ohd(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) = hAPP(V_f_2,hAPP(c_List_Ohd(T_b),V_xs_2))
      | V_xs_2 = c_List_Olist_ONil(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_hd__map]) ).

fof(f_4197_2,plain,
    ! [U_17050,U_17049,U_17048,U_17047] :
      ( hAPP(c_List_Ohd(U_17049),hAPP(hAPP(c_List_Omap(U_17048,U_17049),U_17050),U_17047)) = hAPP(U_17050,hAPP(c_List_Ohd(U_17048),U_17047))
      | U_17047 = c_List_Olist_ONil(U_17048) ),
    inference(variable_rename,[status(thm)],[f_4197_1]) ).

cnf(f_4197_3,plain,
    ( hAPP(c_List_Ohd(U_17049),hAPP(hAPP(c_List_Omap(U_17048,U_17049),U_17050),U_17047)) = hAPP(U_17050,hAPP(c_List_Ohd(U_17048),U_17047))
    | U_17047 = c_List_Olist_ONil(U_17048) ),
    inference(clausify,[status(thm)],[f_4197_2]) ).

fof(f_4198_1,plain,
    ! [V_xs_2,V_f_2,T_c,V_n_2,T_b] : hAPP(hAPP(c_List_Odrop(T_b),V_n_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Odrop(T_c),V_n_2),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_drop__map]) ).

fof(f_4198_2,plain,
    ! [U_17055,U_17054,U_17053,U_17052,U_17051] : hAPP(hAPP(c_List_Odrop(U_17051),U_17052),hAPP(hAPP(c_List_Omap(U_17053,U_17051),U_17054),U_17055)) = hAPP(hAPP(c_List_Omap(U_17053,U_17051),U_17054),hAPP(hAPP(c_List_Odrop(U_17053),U_17052),U_17055)),
    inference(variable_rename,[status(thm)],[f_4198_1]) ).

cnf(f_4198_3,plain,
    hAPP(hAPP(c_List_Odrop(U_17051),U_17052),hAPP(hAPP(c_List_Omap(U_17053,U_17051),U_17054),U_17055)) = hAPP(hAPP(c_List_Omap(U_17053,U_17051),U_17054),hAPP(hAPP(c_List_Odrop(U_17053),U_17052),U_17055)),
    inference(clausify,[status(thm)],[f_4198_2]) ).

fof(f_4199_1,plain,
    ! [T_b] : hAPP(c_List_Omap(T_b,T_b),c_COMBI(T_b)) = c_Fun_Oid(tc_List_Olist(T_b)),
    inference(fof_nnf,[status(thm)],[fact_List_Omap_Oidentity]) ).

fof(f_4199_2,plain,
    ! [U_17056] : hAPP(c_List_Omap(U_17056,U_17056),c_COMBI(U_17056)) = c_Fun_Oid(tc_List_Olist(U_17056)),
    inference(variable_rename,[status(thm)],[f_4199_1]) ).

cnf(f_4199_3,plain,
    hAPP(c_List_Omap(U_17056,U_17056),c_COMBI(U_17056)) = c_Fun_Oid(tc_List_Olist(U_17056)),
    inference(clausify,[status(thm)],[f_4199_2]) ).

fof(f_4200_1,plain,
    ! [T_b] : hAPP(c_List_Omap(T_b,T_b),c_Fun_Oid(T_b)) = c_Fun_Oid(tc_List_Olist(T_b)),
    inference(fof_nnf,[status(thm)],[fact_List_Omap_Oid]) ).

fof(f_4200_2,plain,
    ! [U_17057] : hAPP(c_List_Omap(U_17057,U_17057),c_Fun_Oid(U_17057)) = c_Fun_Oid(tc_List_Olist(U_17057)),
    inference(variable_rename,[status(thm)],[f_4200_1]) ).

cnf(f_4200_3,plain,
    hAPP(c_List_Omap(U_17057,U_17057),c_Fun_Oid(U_17057)) = c_Fun_Oid(tc_List_Olist(U_17057)),
    inference(clausify,[status(thm)],[f_4200_2]) ).

fof(f_4201_1,plain,
    ! [V_xs_2,V_g_2,T_d,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_g_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_d,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2)),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_map__map]) ).

fof(f_4201_2,plain,
    ! [U_17063,U_17062,U_17061,U_17060,U_17059,U_17058] : hAPP(hAPP(c_List_Omap(U_17058,U_17059),U_17060),hAPP(hAPP(c_List_Omap(U_17061,U_17058),U_17062),U_17063)) = hAPP(hAPP(c_List_Omap(U_17061,U_17059),hAPP(c_Fun_Ocomp(U_17058,U_17059,U_17061,U_17060),U_17062)),U_17063),
    inference(variable_rename,[status(thm)],[f_4201_1]) ).

cnf(f_4201_3,plain,
    hAPP(hAPP(c_List_Omap(U_17058,U_17059),U_17060),hAPP(hAPP(c_List_Omap(U_17061,U_17058),U_17062),U_17063)) = hAPP(hAPP(c_List_Omap(U_17061,U_17059),hAPP(c_Fun_Ocomp(U_17058,U_17059,U_17061,U_17060),U_17062)),U_17063),
    inference(clausify,[status(thm)],[f_4201_2]) ).

fof(f_4202_1,plain,
    ! [V_list_2,V_g_2,T_d,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_g_2),V_list_2)) = hAPP(hAPP(c_List_Omap(T_d,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2)),V_list_2),
    inference(fof_nnf,[status(thm)],[fact_List_Omap_Ocompositionality]) ).

fof(f_4202_2,plain,
    ! [U_17069,U_17068,U_17067,U_17066,U_17065,U_17064] : hAPP(hAPP(c_List_Omap(U_17064,U_17065),U_17066),hAPP(hAPP(c_List_Omap(U_17067,U_17064),U_17068),U_17069)) = hAPP(hAPP(c_List_Omap(U_17067,U_17065),hAPP(c_Fun_Ocomp(U_17064,U_17065,U_17067,U_17066),U_17068)),U_17069),
    inference(variable_rename,[status(thm)],[f_4202_1]) ).

cnf(f_4202_3,plain,
    hAPP(hAPP(c_List_Omap(U_17064,U_17065),U_17066),hAPP(hAPP(c_List_Omap(U_17067,U_17064),U_17068),U_17069)) = hAPP(hAPP(c_List_Omap(U_17067,U_17065),hAPP(c_Fun_Ocomp(U_17064,U_17065,U_17067,U_17066),U_17068)),U_17069),
    inference(clausify,[status(thm)],[f_4202_2]) ).

fof(f_4203_1,plain,
    ! [V_g_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(tc_List_Olist(T_d),tc_List_Olist(T_c),tc_List_Olist(T_b),hAPP(c_List_Omap(T_d,T_c),V_f_2)),hAPP(c_List_Omap(T_b,T_d),V_g_2)) = hAPP(c_List_Omap(T_b,T_c),hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),V_g_2)),
    inference(fof_nnf,[status(thm)],[fact_map__comp__map]) ).

fof(f_4203_2,plain,
    ! [U_17074,U_17073,U_17072,U_17071,U_17070] : hAPP(c_Fun_Ocomp(tc_List_Olist(U_17070),tc_List_Olist(U_17071),tc_List_Olist(U_17072),hAPP(c_List_Omap(U_17070,U_17071),U_17073)),hAPP(c_List_Omap(U_17072,U_17070),U_17074)) = hAPP(c_List_Omap(U_17072,U_17071),hAPP(c_Fun_Ocomp(U_17070,U_17071,U_17072,U_17073),U_17074)),
    inference(variable_rename,[status(thm)],[f_4203_1]) ).

cnf(f_4203_3,plain,
    hAPP(c_Fun_Ocomp(tc_List_Olist(U_17070),tc_List_Olist(U_17071),tc_List_Olist(U_17072),hAPP(c_List_Omap(U_17070,U_17071),U_17073)),hAPP(c_List_Omap(U_17072,U_17070),U_17074)) = hAPP(c_List_Omap(U_17072,U_17071),hAPP(c_Fun_Ocomp(U_17070,U_17071,U_17072,U_17073),U_17074)),
    inference(clausify,[status(thm)],[f_4203_2]) ).

fof(f_4204_1,plain,
    ! [V_g_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(tc_List_Olist(T_d),tc_List_Olist(T_c),tc_List_Olist(T_b),hAPP(c_List_Omap(T_d,T_c),V_f_2)),hAPP(c_List_Omap(T_b,T_d),V_g_2)) = hAPP(c_List_Omap(T_b,T_c),hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),V_g_2)),
    inference(fof_nnf,[status(thm)],[fact_List_Omap_Ocomp]) ).

fof(f_4204_2,plain,
    ! [U_17079,U_17078,U_17077,U_17076,U_17075] : hAPP(c_Fun_Ocomp(tc_List_Olist(U_17075),tc_List_Olist(U_17076),tc_List_Olist(U_17077),hAPP(c_List_Omap(U_17075,U_17076),U_17078)),hAPP(c_List_Omap(U_17077,U_17075),U_17079)) = hAPP(c_List_Omap(U_17077,U_17076),hAPP(c_Fun_Ocomp(U_17075,U_17076,U_17077,U_17078),U_17079)),
    inference(variable_rename,[status(thm)],[f_4204_1]) ).

cnf(f_4204_3,plain,
    hAPP(c_Fun_Ocomp(tc_List_Olist(U_17075),tc_List_Olist(U_17076),tc_List_Olist(U_17077),hAPP(c_List_Omap(U_17075,U_17076),U_17078)),hAPP(c_List_Omap(U_17077,U_17075),U_17079)) = hAPP(c_List_Omap(U_17077,U_17076),hAPP(c_Fun_Ocomp(U_17075,U_17076,U_17077,U_17078),U_17079)),
    inference(clausify,[status(thm)],[f_4204_2]) ).

fof(f_4205_1,plain,
    ! [V_xs_2,V_g_2,T_c,V_f_2,T_b] : c_List_Olist_Olist__size(T_b,V_f_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_xs_2)) = c_List_Olist_Olist__size(T_c,hAPP(c_Fun_Ocomp(T_b,tc_Nat_Onat,T_c,V_f_2),V_g_2),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_list__size__map]) ).

fof(f_4205_2,plain,
    ! [U_17084,U_17083,U_17082,U_17081,U_17080] : c_List_Olist_Olist__size(U_17080,U_17081,hAPP(hAPP(c_List_Omap(U_17082,U_17080),U_17083),U_17084)) = c_List_Olist_Olist__size(U_17082,hAPP(c_Fun_Ocomp(U_17080,tc_Nat_Onat,U_17082,U_17081),U_17083),U_17084),
    inference(variable_rename,[status(thm)],[f_4205_1]) ).

cnf(f_4205_3,plain,
    c_List_Olist_Olist__size(U_17080,U_17081,hAPP(hAPP(c_List_Omap(U_17082,U_17080),U_17083),U_17084)) = c_List_Olist_Olist__size(U_17082,hAPP(c_Fun_Ocomp(U_17080,tc_Nat_Onat,U_17082,U_17081),U_17083),U_17084),
    inference(clausify,[status(thm)],[f_4205_2]) ).

fof(f_4206_1,plain,
    ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
      ( V_xs_2 = V_ys_2
      | ~ c_Fun_Oinj__on(T_c,T_b,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_List_Oset(T_c),V_xs_2)),hAPP(c_List_Oset(T_c),V_ys_2)))
      | hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) != hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_ys_2) ),
    inference(fof_nnf,[status(thm)],[fact_map__inj__on]) ).

fof(f_4206_2,plain,
    ! [U_17089,U_17088,U_17087,U_17086,U_17085] :
      ( U_17088 = U_17089
      | ~ c_Fun_Oinj__on(U_17085,U_17086,U_17087,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_17085,tc_HOL_Obool)),hAPP(c_List_Oset(U_17085),U_17088)),hAPP(c_List_Oset(U_17085),U_17089)))
      | hAPP(hAPP(c_List_Omap(U_17085,U_17086),U_17087),U_17088) != hAPP(hAPP(c_List_Omap(U_17085,U_17086),U_17087),U_17089) ),
    inference(variable_rename,[status(thm)],[f_4206_1]) ).

cnf(f_4206_3,plain,
    ( U_17088 = U_17089
    | ~ c_Fun_Oinj__on(U_17085,U_17086,U_17087,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_17085,tc_HOL_Obool)),hAPP(c_List_Oset(U_17085),U_17088)),hAPP(c_List_Oset(U_17085),U_17089)))
    | hAPP(hAPP(c_List_Omap(U_17085,U_17086),U_17087),U_17088) != hAPP(hAPP(c_List_Omap(U_17085,U_17086),U_17087),U_17089) ),
    inference(clausify,[status(thm)],[f_4206_2]) ).

fof(f_4207_1,plain,
    ! [V_ys_2,V_xs_2,V_f_2,T_c,T_b] :
      ( ( ( hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2)
          | V_xs_2 != V_ys_2 )
        & ( V_xs_2 = V_ys_2
          | hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2) != hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2) ) )
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_ys_2))) ),
    inference(fof_nnf,[status(thm)],[fact_inj__on__map__eq__map]) ).

fof(f_4207_2,plain,
    ! [U_17094,U_17093,U_17092,U_17091,U_17090] :
      ( ( ( hAPP(hAPP(c_List_Omap(U_17090,U_17091),U_17092),U_17093) = hAPP(hAPP(c_List_Omap(U_17090,U_17091),U_17092),U_17094)
          | U_17093 != U_17094 )
        & ( U_17093 = U_17094
          | hAPP(hAPP(c_List_Omap(U_17090,U_17091),U_17092),U_17093) != hAPP(hAPP(c_List_Omap(U_17090,U_17091),U_17092),U_17094) ) )
      | ~ c_Fun_Oinj__on(U_17090,U_17091,U_17092,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_17090,tc_HOL_Obool)),hAPP(c_List_Oset(U_17090),U_17093)),hAPP(c_List_Oset(U_17090),U_17094))) ),
    inference(variable_rename,[status(thm)],[f_4207_1]) ).

cnf(f_4207_3,plain,
    ( U_17093 = U_17094
    | hAPP(hAPP(c_List_Omap(U_17090,U_17091),U_17092),U_17093) != hAPP(hAPP(c_List_Omap(U_17090,U_17091),U_17092),U_17094)
    | ~ c_Fun_Oinj__on(U_17090,U_17091,U_17092,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_17090,tc_HOL_Obool)),hAPP(c_List_Oset(U_17090),U_17093)),hAPP(c_List_Oset(U_17090),U_17094))) ),
    inference(clausify,[status(thm)],[f_4207_2]) ).

cnf(f_4207_4,plain,
    ( hAPP(hAPP(c_List_Omap(U_17090,U_17091),U_17092),U_17093) = hAPP(hAPP(c_List_Omap(U_17090,U_17091),U_17092),U_17094)
    | U_17093 != U_17094
    | ~ c_Fun_Oinj__on(U_17090,U_17091,U_17092,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_17090,tc_HOL_Obool)),hAPP(c_List_Oset(U_17090),U_17093)),hAPP(c_List_Oset(U_17090),U_17094))) ),
    inference(clausify,[status(thm)],[f_4207_2]) ).

fof(f_4208_1,plain,
    ! [V_f_2,T_c,V_xs_2,T_b,V_n_2] :
      ( hAPP(hAPP(c_List_Onth(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)),V_n_2) = hAPP(V_f_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_nth__map]) ).

fof(f_4208_2,plain,
    ! [U_17099,U_17098,U_17097,U_17096,U_17095] :
      ( hAPP(hAPP(c_List_Onth(U_17098),hAPP(hAPP(c_List_Omap(U_17096,U_17098),U_17099),U_17097)),U_17095) = hAPP(U_17099,hAPP(hAPP(c_List_Onth(U_17096),U_17097),U_17095))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_17095),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17096)),U_17097))) ),
    inference(variable_rename,[status(thm)],[f_4208_1]) ).

cnf(f_4208_3,plain,
    ( hAPP(hAPP(c_List_Onth(U_17098),hAPP(hAPP(c_List_Omap(U_17096,U_17098),U_17099),U_17097)),U_17095) = hAPP(U_17099,hAPP(hAPP(c_List_Onth(U_17096),U_17097),U_17095))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_17095),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17096)),U_17097))) ),
    inference(clausify,[status(thm)],[f_4208_2]) ).

fof(f_4209_1,plain,
    ! [V_v_2,V_f_2,T_c,V_xs_2,V_y_2,T_b] :
      ( hAPP(hAPP(c_List_Omap(T_b,T_c),c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_y_2,V_v_2)),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)
      | hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_map__fun__upd]) ).

fof(f_4209_2,plain,
    ! [U_17105,U_17104,U_17103,U_17102,U_17101,U_17100] :
      ( hAPP(hAPP(c_List_Omap(U_17100,U_17103),c_Fun_Ofun__upd(U_17100,U_17103,U_17104,U_17101,U_17105)),U_17102) = hAPP(hAPP(c_List_Omap(U_17100,U_17103),U_17104),U_17102)
      | hBOOL(hAPP(hAPP(c_member(U_17100),U_17101),hAPP(c_List_Oset(U_17100),U_17102))) ),
    inference(variable_rename,[status(thm)],[f_4209_1]) ).

cnf(f_4209_3,plain,
    ( hAPP(hAPP(c_List_Omap(U_17100,U_17103),c_Fun_Ofun__upd(U_17100,U_17103,U_17104,U_17101,U_17105)),U_17102) = hAPP(hAPP(c_List_Omap(U_17100,U_17103),U_17104),U_17102)
    | hBOOL(hAPP(hAPP(c_member(U_17100),U_17101),hAPP(c_List_Oset(U_17100),U_17102))) ),
    inference(clausify,[status(thm)],[f_4209_2]) ).

fof(f_4210_1,plain,
    ! [V_xs_2,V_f_2,T_c,T_b] :
      ( ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)))
        | ~ c_Fun_Oinj__on(T_c,T_b,V_f_2,hAPP(c_List_Oset(T_c),V_xs_2))
        | ~ hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2)) )
      & ( ( c_Fun_Oinj__on(T_c,T_b,V_f_2,hAPP(c_List_Oset(T_c),V_xs_2))
          & hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2)) )
        | ~ hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__map]) ).

fof(f_4210_2,plain,
    ! [U_17109,U_17108,U_17107,U_17106] :
      ( ( hBOOL(hAPP(c_List_Odistinct(U_17106),hAPP(hAPP(c_List_Omap(U_17107,U_17106),U_17108),U_17109)))
        | ~ c_Fun_Oinj__on(U_17107,U_17106,U_17108,hAPP(c_List_Oset(U_17107),U_17109))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_17107),U_17109)) )
      & ( ( c_Fun_Oinj__on(U_17107,U_17106,U_17108,hAPP(c_List_Oset(U_17107),U_17109))
          & hBOOL(hAPP(c_List_Odistinct(U_17107),U_17109)) )
        | ~ hBOOL(hAPP(c_List_Odistinct(U_17106),hAPP(hAPP(c_List_Omap(U_17107,U_17106),U_17108),U_17109))) ) ),
    inference(variable_rename,[status(thm)],[f_4210_1]) ).

fof(f_4210_3,plain,
    ( ! [U_17117,U_17115,U_17113,U_17111] :
        ( hBOOL(hAPP(c_List_Odistinct(U_17111),hAPP(hAPP(c_List_Omap(U_17113,U_17111),U_17115),U_17117)))
        | ~ c_Fun_Oinj__on(U_17113,U_17111,U_17115,hAPP(c_List_Oset(U_17113),U_17117))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_17113),U_17117)) )
    & ! [U_17116,U_17114,U_17112,U_17110] :
        ( ( c_Fun_Oinj__on(U_17112,U_17110,U_17114,hAPP(c_List_Oset(U_17112),U_17116))
          & hBOOL(hAPP(c_List_Odistinct(U_17112),U_17116)) )
        | ~ hBOOL(hAPP(c_List_Odistinct(U_17110),hAPP(hAPP(c_List_Omap(U_17112,U_17110),U_17114),U_17116))) ) ),
    inference(miniscope,[status(thm)],[f_4210_2]) ).

cnf(f_4210_4,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_17112),U_17116))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17110),hAPP(hAPP(c_List_Omap(U_17112,U_17110),U_17114),U_17116))) ),
    inference(clausify,[status(thm)],[f_4210_3]) ).

cnf(f_4210_5,plain,
    ( c_Fun_Oinj__on(U_17112,U_17110,U_17114,hAPP(c_List_Oset(U_17112),U_17116))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17110),hAPP(hAPP(c_List_Omap(U_17112,U_17110),U_17114),U_17116))) ),
    inference(clausify,[status(thm)],[f_4210_3]) ).

cnf(f_4210_6,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_17111),hAPP(hAPP(c_List_Omap(U_17113,U_17111),U_17115),U_17117)))
    | ~ c_Fun_Oinj__on(U_17113,U_17111,U_17115,hAPP(c_List_Oset(U_17113),U_17117))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17113),U_17117)) ),
    inference(clausify,[status(thm)],[f_4210_3]) ).

fof(f_4211_1,plain,
    ! [V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_b,T_b),c_Groups_Oabs__class_Oabs(T_b)),V_xs_2))))
      | ~ class_Groups_Oordered__ab__group__add__abs(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_listsum__abs]) ).

fof(f_4211_2,plain,
    ! [U_17119,U_17118] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17118),hAPP(c_Groups_Oabs__class_Oabs(U_17118),hAPP(c_List_Omonoid__add__class_Olistsum(U_17118),U_17119))),hAPP(c_List_Omonoid__add__class_Olistsum(U_17118),hAPP(hAPP(c_List_Omap(U_17118,U_17118),c_Groups_Oabs__class_Oabs(U_17118)),U_17119))))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_17118) ),
    inference(variable_rename,[status(thm)],[f_4211_1]) ).

cnf(f_4211_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17118),hAPP(c_Groups_Oabs__class_Oabs(U_17118),hAPP(c_List_Omonoid__add__class_Olistsum(U_17118),U_17119))),hAPP(c_List_Omonoid__add__class_Olistsum(U_17118),hAPP(hAPP(c_List_Omap(U_17118,U_17118),c_Groups_Oabs__class_Oabs(U_17118)),U_17119))))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_17118) ),
    inference(clausify,[status(thm)],[f_4211_2]) ).

fof(f_4212_1,plain,
    ! [V_xs_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(c_Fun_Ocomp(T_b,T_b,T_c,c_Groups_Ouminus__class_Ouminus(T_b)),V_f_2)),V_xs_2))
      | ~ class_Groups_Oab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_uminus__listsum__map]) ).

fof(f_4212_2,plain,
    ! [U_17123,U_17122,U_17121,U_17120] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_17120),hAPP(c_List_Omonoid__add__class_Olistsum(U_17120),hAPP(hAPP(c_List_Omap(U_17121,U_17120),U_17122),U_17123))) = hAPP(c_List_Omonoid__add__class_Olistsum(U_17120),hAPP(hAPP(c_List_Omap(U_17121,U_17120),hAPP(c_Fun_Ocomp(U_17120,U_17120,U_17121,c_Groups_Ouminus__class_Ouminus(U_17120)),U_17122)),U_17123))
      | ~ class_Groups_Oab__group__add(U_17120) ),
    inference(variable_rename,[status(thm)],[f_4212_1]) ).

cnf(f_4212_3,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_17120),hAPP(c_List_Omonoid__add__class_Olistsum(U_17120),hAPP(hAPP(c_List_Omap(U_17121,U_17120),U_17122),U_17123))) = hAPP(c_List_Omonoid__add__class_Olistsum(U_17120),hAPP(hAPP(c_List_Omap(U_17121,U_17120),hAPP(c_Fun_Ocomp(U_17120,U_17120,U_17121,c_Groups_Ouminus__class_Ouminus(U_17120)),U_17122)),U_17123))
    | ~ class_Groups_Oab__group__add(U_17120) ),
    inference(clausify,[status(thm)],[f_4212_2]) ).

fof(f_4213_1,plain,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_c),hAPP(c_List_Omap(T_b,T_c),V_f_2),V_A_2)
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),c_List_Oset(T_b)),V_A_2))) ),
    inference(fof_nnf,[status(thm)],[fact_inj__on__mapI]) ).

fof(f_4213_2,plain,
    ! [U_17127,U_17126,U_17125,U_17124] :
      ( c_Fun_Oinj__on(tc_List_Olist(U_17124),tc_List_Olist(U_17125),hAPP(c_List_Omap(U_17124,U_17125),U_17126),U_17127)
      | ~ c_Fun_Oinj__on(U_17124,U_17125,U_17126,c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17124,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_List_Olist(U_17124),tc_fun(U_17124,tc_HOL_Obool),c_List_Oset(U_17124)),U_17127))) ),
    inference(variable_rename,[status(thm)],[f_4213_1]) ).

cnf(f_4213_3,plain,
    ( c_Fun_Oinj__on(tc_List_Olist(U_17124),tc_List_Olist(U_17125),hAPP(c_List_Omap(U_17124,U_17125),U_17126),U_17127)
    | ~ c_Fun_Oinj__on(U_17124,U_17125,U_17126,c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17124,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_List_Olist(U_17124),tc_fun(U_17124,tc_HOL_Obool),c_List_Oset(U_17124)),U_17127))) ),
    inference(clausify,[status(thm)],[f_4213_2]) ).

fof(f_4214_1,plain,
    ! [V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
      | ~ c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_c),hAPP(c_List_Omap(T_b,T_c),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_inj__mapD]) ).

fof(f_4214_2,plain,
    ! [U_17130,U_17129,U_17128] :
      ( c_Fun_Oinj__on(U_17128,U_17129,U_17130,c_Orderings_Otop__class_Otop(tc_fun(U_17128,tc_HOL_Obool)))
      | ~ c_Fun_Oinj__on(tc_List_Olist(U_17128),tc_List_Olist(U_17129),hAPP(c_List_Omap(U_17128,U_17129),U_17130),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_17128),tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_4214_1]) ).

cnf(f_4214_3,plain,
    ( c_Fun_Oinj__on(U_17128,U_17129,U_17130,c_Orderings_Otop__class_Otop(tc_fun(U_17128,tc_HOL_Obool)))
    | ~ c_Fun_Oinj__on(tc_List_Olist(U_17128),tc_List_Olist(U_17129),hAPP(c_List_Omap(U_17128,U_17129),U_17130),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_17128),tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4214_2]) ).

fof(f_4215_1,plain,
    ! [V_f_2,T_c,T_b] :
      ( ( c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_c),hAPP(c_List_Omap(T_b,T_c),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))
        | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) )
      & ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
        | ~ c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_c),hAPP(c_List_Omap(T_b,T_c),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))) ) ),
    inference(fof_nnf,[status(thm)],[fact_inj__map]) ).

fof(f_4215_2,plain,
    ! [U_17133,U_17132,U_17131] :
      ( ( c_Fun_Oinj__on(tc_List_Olist(U_17131),tc_List_Olist(U_17132),hAPP(c_List_Omap(U_17131,U_17132),U_17133),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_17131),tc_HOL_Obool)))
        | ~ c_Fun_Oinj__on(U_17131,U_17132,U_17133,c_Orderings_Otop__class_Otop(tc_fun(U_17131,tc_HOL_Obool))) )
      & ( c_Fun_Oinj__on(U_17131,U_17132,U_17133,c_Orderings_Otop__class_Otop(tc_fun(U_17131,tc_HOL_Obool)))
        | ~ c_Fun_Oinj__on(tc_List_Olist(U_17131),tc_List_Olist(U_17132),hAPP(c_List_Omap(U_17131,U_17132),U_17133),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_17131),tc_HOL_Obool))) ) ),
    inference(variable_rename,[status(thm)],[f_4215_1]) ).

fof(f_4215_3,plain,
    ( ! [U_17139,U_17137,U_17135] :
        ( c_Fun_Oinj__on(tc_List_Olist(U_17135),tc_List_Olist(U_17137),hAPP(c_List_Omap(U_17135,U_17137),U_17139),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_17135),tc_HOL_Obool)))
        | ~ c_Fun_Oinj__on(U_17135,U_17137,U_17139,c_Orderings_Otop__class_Otop(tc_fun(U_17135,tc_HOL_Obool))) )
    & ! [U_17138,U_17136,U_17134] :
        ( c_Fun_Oinj__on(U_17134,U_17136,U_17138,c_Orderings_Otop__class_Otop(tc_fun(U_17134,tc_HOL_Obool)))
        | ~ c_Fun_Oinj__on(tc_List_Olist(U_17134),tc_List_Olist(U_17136),hAPP(c_List_Omap(U_17134,U_17136),U_17138),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_17134),tc_HOL_Obool))) ) ),
    inference(miniscope,[status(thm)],[f_4215_2]) ).

cnf(f_4215_4,plain,
    ( c_Fun_Oinj__on(U_17134,U_17136,U_17138,c_Orderings_Otop__class_Otop(tc_fun(U_17134,tc_HOL_Obool)))
    | ~ c_Fun_Oinj__on(tc_List_Olist(U_17134),tc_List_Olist(U_17136),hAPP(c_List_Omap(U_17134,U_17136),U_17138),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_17134),tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4215_3]) ).

cnf(f_4215_5,plain,
    ( c_Fun_Oinj__on(tc_List_Olist(U_17135),tc_List_Olist(U_17137),hAPP(c_List_Omap(U_17135,U_17137),U_17139),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_17135),tc_HOL_Obool)))
    | ~ c_Fun_Oinj__on(U_17135,U_17137,U_17139,c_Orderings_Otop__class_Otop(tc_fun(U_17135,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4215_3]) ).

fof(f_4216_1,plain,
    ! [V_f_2,V_xs_2,T_b,T_c] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(c_List_Oset(T_b),V_xs_2))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
      | ~ class_Groups_Ocomm__monoid__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_listsum__distinct__conv__setsum__set]) ).

fof(f_4216_2,plain,
    ! [U_17143,U_17142,U_17141,U_17140] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_17140),hAPP(hAPP(c_List_Omap(U_17141,U_17140),U_17143),U_17142)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_17141,U_17140),U_17143),hAPP(c_List_Oset(U_17141),U_17142))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17141),U_17142))
      | ~ class_Groups_Ocomm__monoid__add(U_17140) ),
    inference(variable_rename,[status(thm)],[f_4216_1]) ).

cnf(f_4216_3,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_17140),hAPP(hAPP(c_List_Omap(U_17141,U_17140),U_17143),U_17142)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_17141,U_17140),U_17143),hAPP(c_List_Oset(U_17141),U_17142))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17141),U_17142))
    | ~ class_Groups_Ocomm__monoid__add(U_17140) ),
    inference(clausify,[status(thm)],[f_4216_2]) ).

fof(f_4217_1,plain,
    ! [V_xs_2,V_r_2,T_c,T_b] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(c_COMBK(T_b,T_c),V_r_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2))),V_r_2)
      | ~ class_Rings_Osemiring__1(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_listsum__triv]) ).

fof(f_4217_2,plain,
    ! [U_17147,U_17146,U_17145,U_17144] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_17144),hAPP(hAPP(c_List_Omap(U_17145,U_17144),hAPP(c_COMBK(U_17144,U_17145),U_17146)),U_17147)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_17144),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_17144),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17145)),U_17147))),U_17146)
      | ~ class_Rings_Osemiring__1(U_17144) ),
    inference(variable_rename,[status(thm)],[f_4217_1]) ).

cnf(f_4217_3,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_17144),hAPP(hAPP(c_List_Omap(U_17145,U_17144),hAPP(c_COMBK(U_17144,U_17145),U_17146)),U_17147)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_17144),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_17144),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17145)),U_17147))),U_17146)
    | ~ class_Rings_Osemiring__1(U_17144) ),
    inference(clausify,[status(thm)],[f_4217_2]) ).

fof(f_4218_1,plain,
    ! [V_f_2,V_xs_2,V_x_2,T_b,T_c] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_f_2,V_x_2)),hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),c_List_Oremove1(T_b,V_x_2,V_xs_2))))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
      | ~ class_Groups_Ocomm__monoid__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_listsum__map__remove1]) ).

fof(f_4218_2,plain,
    ! [U_17152,U_17151,U_17150,U_17149,U_17148] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_17148),hAPP(hAPP(c_List_Omap(U_17149,U_17148),U_17152),U_17151)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_17148),hAPP(U_17152,U_17150)),hAPP(c_List_Omonoid__add__class_Olistsum(U_17148),hAPP(hAPP(c_List_Omap(U_17149,U_17148),U_17152),c_List_Oremove1(U_17149,U_17150,U_17151))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_17149),U_17150),hAPP(c_List_Oset(U_17149),U_17151)))
      | ~ class_Groups_Ocomm__monoid__add(U_17148) ),
    inference(variable_rename,[status(thm)],[f_4218_1]) ).

cnf(f_4218_3,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_17148),hAPP(hAPP(c_List_Omap(U_17149,U_17148),U_17152),U_17151)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_17148),hAPP(U_17152,U_17150)),hAPP(c_List_Omonoid__add__class_Olistsum(U_17148),hAPP(hAPP(c_List_Omap(U_17149,U_17148),U_17152),c_List_Oremove1(U_17149,U_17150,U_17151))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_17149),U_17150),hAPP(c_List_Oset(U_17149),U_17151)))
    | ~ class_Groups_Ocomm__monoid__add(U_17148) ),
    inference(clausify,[status(thm)],[f_4218_2]) ).

fof(f_4219_1,plain,
    ! [V_f_2,V_A_2,T_b,T_c] :
      ( ( ( c_Nitpick_Osetsum_H(T_b,T_c,V_f_2,V_A_2) = c_Groups_Ozero__class_Ozero(T_c)
          | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) )
        & ( c_Nitpick_Osetsum_H(T_b,T_c,V_f_2,V_A_2) = hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),c_Hilbert__Choice_OEps(tc_List_Olist(T_b),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_List_Oset(T_b))),V_A_2))),c_List_Odistinct(T_b)))))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) )
      | ~ class_Groups_Ocomm__monoid__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_Nitpick_Osetsum_H__def]) ).

fof(f_4219_2,plain,
    ! [U_17156,U_17155,U_17154,U_17153] :
      ( ( ( c_Nitpick_Osetsum_H(U_17154,U_17153,U_17156,U_17155) = c_Groups_Ozero__class_Ozero(U_17153)
          | hBOOL(hAPP(c_Finite__Set_Ofinite(U_17154),U_17155)) )
        & ( c_Nitpick_Osetsum_H(U_17154,U_17153,U_17156,U_17155) = hAPP(c_List_Omonoid__add__class_Olistsum(U_17153),hAPP(hAPP(c_List_Omap(U_17154,U_17153),U_17156),c_Hilbert__Choice_OEps(tc_List_Olist(U_17154),hAPP(hAPP(c_COMBS(tc_List_Olist(U_17154),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_17154)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17154),tc_fun(U_17154,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_17154,tc_HOL_Obool),tc_fun(tc_fun(U_17154,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_17154)),c_fequal),c_List_Oset(U_17154))),U_17155))),c_List_Odistinct(U_17154)))))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17154),U_17155)) ) )
      | ~ class_Groups_Ocomm__monoid__add(U_17153) ),
    inference(variable_rename,[status(thm)],[f_4219_1]) ).

cnf(f_4219_3,plain,
    ( c_Nitpick_Osetsum_H(U_17154,U_17153,U_17156,U_17155) = hAPP(c_List_Omonoid__add__class_Olistsum(U_17153),hAPP(hAPP(c_List_Omap(U_17154,U_17153),U_17156),c_Hilbert__Choice_OEps(tc_List_Olist(U_17154),hAPP(hAPP(c_COMBS(tc_List_Olist(U_17154),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_17154)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17154),tc_fun(U_17154,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_17154,tc_HOL_Obool),tc_fun(tc_fun(U_17154,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_17154)),c_fequal),c_List_Oset(U_17154))),U_17155))),c_List_Odistinct(U_17154)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17154),U_17155))
    | ~ class_Groups_Ocomm__monoid__add(U_17153) ),
    inference(clausify,[status(thm)],[f_4219_2]) ).

cnf(f_4219_4,plain,
    ( c_Nitpick_Osetsum_H(U_17154,U_17153,U_17156,U_17155) = c_Groups_Ozero__class_Ozero(U_17153)
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_17154),U_17155))
    | ~ class_Groups_Ocomm__monoid__add(U_17153) ),
    inference(clausify,[status(thm)],[f_4219_2]) ).

fof(f_4220_1,plain,
    ! [V_xs_2,T_b,V_l_2] :
      ( hAPP(c_Random_Opick(T_b,hAPP(hAPP(c_List_Omap(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,T_b)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_b),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),V_xs_2)),hAPP(c_Code__Numeral_Oof__nat,V_l_2)) = hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_l_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_l_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_pick__same]) ).

fof(f_4220_2,plain,
    ! [U_17159,U_17158,U_17157] :
      ( hAPP(c_Random_Opick(U_17158,hAPP(hAPP(c_List_Omap(U_17158,tc_prod(tc_Code__Numeral_Ocode__numeral,U_17158)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,U_17158),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),U_17159)),hAPP(c_Code__Numeral_Oof__nat,U_17157)) = hAPP(hAPP(c_List_Onth(U_17158),U_17159),U_17157)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_17157),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17158)),U_17159))) ),
    inference(variable_rename,[status(thm)],[f_4220_1]) ).

cnf(f_4220_3,plain,
    ( hAPP(c_Random_Opick(U_17158,hAPP(hAPP(c_List_Omap(U_17158,tc_prod(tc_Code__Numeral_Ocode__numeral,U_17158)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,U_17158),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),U_17159)),hAPP(c_Code__Numeral_Oof__nat,U_17157)) = hAPP(hAPP(c_List_Onth(U_17158),U_17159),U_17157)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_17157),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17158)),U_17159))) ),
    inference(clausify,[status(thm)],[f_4220_2]) ).

fof(f_4221_1,plain,
    c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(fof_nnf,[status(thm)],[fact_zero__code__numeral__def]) ).

cnf(f_4221_2,plain,
    c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(clausify,[status(thm)],[f_4221_1]) ).

fof(f_4222_1,plain,
    ! [V_m_2,V_n_2] :
      ( ( hAPP(c_Code__Numeral_Oof__nat,V_n_2) = hAPP(c_Code__Numeral_Oof__nat,V_m_2)
        | V_n_2 != V_m_2 )
      & ( V_n_2 = V_m_2
        | hAPP(c_Code__Numeral_Oof__nat,V_n_2) != hAPP(c_Code__Numeral_Oof__nat,V_m_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_Code__Numeral_Oof__nat__inject]) ).

fof(f_4222_2,plain,
    ! [U_17161,U_17160] :
      ( ( hAPP(c_Code__Numeral_Oof__nat,U_17160) = hAPP(c_Code__Numeral_Oof__nat,U_17161)
        | U_17160 != U_17161 )
      & ( U_17160 = U_17161
        | hAPP(c_Code__Numeral_Oof__nat,U_17160) != hAPP(c_Code__Numeral_Oof__nat,U_17161) ) ),
    inference(variable_rename,[status(thm)],[f_4222_1]) ).

fof(f_4222_3,plain,
    ( ! [U_17165,U_17163] :
        ( hAPP(c_Code__Numeral_Oof__nat,U_17163) = hAPP(c_Code__Numeral_Oof__nat,U_17165)
        | U_17163 != U_17165 )
    & ! [U_17164,U_17162] :
        ( U_17162 = U_17164
        | hAPP(c_Code__Numeral_Oof__nat,U_17162) != hAPP(c_Code__Numeral_Oof__nat,U_17164) ) ),
    inference(miniscope,[status(thm)],[f_4222_2]) ).

cnf(f_4222_4,plain,
    ( U_17162 = U_17164
    | hAPP(c_Code__Numeral_Oof__nat,U_17162) != hAPP(c_Code__Numeral_Oof__nat,U_17164) ),
    inference(clausify,[status(thm)],[f_4222_3]) ).

cnf(f_4222_5,plain,
    ( hAPP(c_Code__Numeral_Oof__nat,U_17163) = hAPP(c_Code__Numeral_Oof__nat,U_17165)
    | U_17163 != U_17165 ),
    inference(clausify,[status(thm)],[f_4222_3]) ).

fof(f_4223_1,plain,
    ! [V_m,V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,V_n)),hAPP(c_Code__Numeral_Oof__nat,V_m)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m)),
    inference(fof_nnf,[status(thm)],[fact_times__code__numeral__code]) ).

fof(f_4223_2,plain,
    ! [U_17167,U_17166] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_17166)),hAPP(c_Code__Numeral_Oof__nat,U_17167)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_17166),U_17167)),
    inference(variable_rename,[status(thm)],[f_4223_1]) ).

cnf(f_4223_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_17166)),hAPP(c_Code__Numeral_Oof__nat,U_17167)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_17166),U_17167)),
    inference(clausify,[status(thm)],[f_4223_2]) ).

fof(f_4224_1,plain,
    c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[fact_Code__Numeral_Oof__nat__code]) ).

cnf(f_4224_2,plain,
    c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_4224_1]) ).

fof(f_4225_1,plain,
    c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(fof_nnf,[status(thm)],[fact_one__code__numeral__def]) ).

cnf(f_4225_2,plain,
    c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(clausify,[status(thm)],[f_4225_1]) ).

fof(f_4226_1,plain,
    ! [V_m_2,V_n_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,V_n_2)),hAPP(c_Code__Numeral_Oof__nat,V_m_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,V_n_2)),hAPP(c_Code__Numeral_Oof__nat,V_m_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_less__code__numeral__code]) ).

fof(f_4226_2,plain,
    ! [U_17169,U_17168] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_17168)),hAPP(c_Code__Numeral_Oof__nat,U_17169)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_17168),U_17169)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_17168),U_17169))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_17168)),hAPP(c_Code__Numeral_Oof__nat,U_17169))) ) ),
    inference(variable_rename,[status(thm)],[f_4226_1]) ).

fof(f_4226_3,plain,
    ( ! [U_17173,U_17171] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_17171)),hAPP(c_Code__Numeral_Oof__nat,U_17173)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_17171),U_17173)) )
    & ! [U_17172,U_17170] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_17170),U_17172))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_17170)),hAPP(c_Code__Numeral_Oof__nat,U_17172))) ) ),
    inference(miniscope,[status(thm)],[f_4226_2]) ).

cnf(f_4226_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_17170),U_17172))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_17170)),hAPP(c_Code__Numeral_Oof__nat,U_17172))) ),
    inference(clausify,[status(thm)],[f_4226_3]) ).

cnf(f_4226_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_17171)),hAPP(c_Code__Numeral_Oof__nat,U_17173)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_17171),U_17173)) ),
    inference(clausify,[status(thm)],[f_4226_3]) ).

fof(f_4227_1,plain,
    ! [V_y_2,V_x_2] :
      ( ( ( hAPP(c_Code__Numeral_Oof__nat,V_x_2) = hAPP(c_Code__Numeral_Oof__nat,V_y_2)
          | V_x_2 != V_y_2 )
        & ( V_x_2 = V_y_2
          | hAPP(c_Code__Numeral_Oof__nat,V_x_2) != hAPP(c_Code__Numeral_Oof__nat,V_y_2) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ),
    inference(fof_nnf,[status(thm)],[fact_code__numeral_Oof__nat__inject]) ).

fof(f_4227_2,plain,
    ! [U_17175,U_17174] :
      ( ( ( hAPP(c_Code__Numeral_Oof__nat,U_17174) = hAPP(c_Code__Numeral_Oof__nat,U_17175)
          | U_17174 != U_17175 )
        & ( U_17174 = U_17175
          | hAPP(c_Code__Numeral_Oof__nat,U_17174) != hAPP(c_Code__Numeral_Oof__nat,U_17175) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_17175),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_17174),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_4227_1]) ).

cnf(f_4227_3,plain,
    ( U_17174 = U_17175
    | hAPP(c_Code__Numeral_Oof__nat,U_17174) != hAPP(c_Code__Numeral_Oof__nat,U_17175)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_17175),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_17174),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_4227_2]) ).

cnf(f_4227_4,plain,
    ( hAPP(c_Code__Numeral_Oof__nat,U_17174) = hAPP(c_Code__Numeral_Oof__nat,U_17175)
    | U_17174 != U_17175
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_17175),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_17174),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_4227_2]) ).

fof(f_4228_1,plain,
    ! [V_ys_2,T_c,V_xs_2,T_b] :
      ( hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) = V_xs_2
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2) ),
    inference(fof_nnf,[status(thm)],[fact_map__fst__zip]) ).

fof(f_4228_2,plain,
    ! [U_17179,U_17178,U_17177,U_17176] :
      ( hAPP(hAPP(c_List_Omap(tc_prod(U_17176,U_17178),U_17176),c_Product__Type_Ofst(U_17176,U_17178)),hAPP(hAPP(c_List_Ozip(U_17176,U_17178),U_17177),U_17179)) = U_17177
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17176)),U_17177) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17178)),U_17179) ),
    inference(variable_rename,[status(thm)],[f_4228_1]) ).

cnf(f_4228_3,plain,
    ( hAPP(hAPP(c_List_Omap(tc_prod(U_17176,U_17178),U_17176),c_Product__Type_Ofst(U_17176,U_17178)),hAPP(hAPP(c_List_Ozip(U_17176,U_17178),U_17177),U_17179)) = U_17177
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17176)),U_17177) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17178)),U_17179) ),
    inference(clausify,[status(thm)],[f_4228_2]) ).

fof(f_4229_1,plain,
    ! [V_ys_2,T_c,V_xs_2,T_b] :
      ( hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_c),c_Product__Type_Osnd(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) = V_ys_2
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2) ),
    inference(fof_nnf,[status(thm)],[fact_map__snd__zip]) ).

fof(f_4229_2,plain,
    ! [U_17183,U_17182,U_17181,U_17180] :
      ( hAPP(hAPP(c_List_Omap(tc_prod(U_17180,U_17182),U_17182),c_Product__Type_Osnd(U_17180,U_17182)),hAPP(hAPP(c_List_Ozip(U_17180,U_17182),U_17181),U_17183)) = U_17183
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17180)),U_17181) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17182)),U_17183) ),
    inference(variable_rename,[status(thm)],[f_4229_1]) ).

cnf(f_4229_3,plain,
    ( hAPP(hAPP(c_List_Omap(tc_prod(U_17180,U_17182),U_17182),c_Product__Type_Osnd(U_17180,U_17182)),hAPP(hAPP(c_List_Ozip(U_17180,U_17182),U_17181),U_17183)) = U_17183
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17180)),U_17181) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17182)),U_17183) ),
    inference(clausify,[status(thm)],[f_4229_2]) ).

fof(f_4230_1,plain,
    c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral,tc_Int_Oint,c_Code__Numeral_Oof__nat),c_Int_Onat),
    inference(fof_nnf,[status(thm)],[fact_number__of__code__numeral__def]) ).

cnf(f_4230_2,plain,
    c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral,tc_Int_Oint,c_Code__Numeral_Oof__nat),c_Int_Onat),
    inference(clausify,[status(thm)],[f_4230_1]) ).

fof(f_4231_1,plain,
    ! [V_zs_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_zs_2)),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_c),c_Product__Type_Osnd(T_b,T_c)),V_zs_2)) = V_zs_2,
    inference(fof_nnf,[status(thm)],[fact_zip__map__fst__snd]) ).

fof(f_4231_2,plain,
    ! [U_17186,U_17185,U_17184] : hAPP(hAPP(c_List_Ozip(U_17184,U_17185),hAPP(hAPP(c_List_Omap(tc_prod(U_17184,U_17185),U_17184),c_Product__Type_Ofst(U_17184,U_17185)),U_17186)),hAPP(hAPP(c_List_Omap(tc_prod(U_17184,U_17185),U_17185),c_Product__Type_Osnd(U_17184,U_17185)),U_17186)) = U_17186,
    inference(variable_rename,[status(thm)],[f_4231_1]) ).

cnf(f_4231_3,plain,
    hAPP(hAPP(c_List_Ozip(U_17184,U_17185),hAPP(hAPP(c_List_Omap(tc_prod(U_17184,U_17185),U_17184),c_Product__Type_Ofst(U_17184,U_17185)),U_17186)),hAPP(hAPP(c_List_Omap(tc_prod(U_17184,U_17185),U_17185),c_Product__Type_Osnd(U_17184,U_17185)),U_17186)) = U_17186,
    inference(clausify,[status(thm)],[f_4231_2]) ).

fof(f_4232_1,plain,
    ! [V_m,V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,V_n)),hAPP(c_Code__Numeral_Oof__nat,V_m)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),
    inference(fof_nnf,[status(thm)],[fact_plus__code__numeral__code]) ).

fof(f_4232_2,plain,
    ! [U_17188,U_17187] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_17187)),hAPP(c_Code__Numeral_Oof__nat,U_17188)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_17187),U_17188)),
    inference(variable_rename,[status(thm)],[f_4232_1]) ).

cnf(f_4232_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_17187)),hAPP(c_Code__Numeral_Oof__nat,U_17188)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_17187),U_17188)),
    inference(clausify,[status(thm)],[f_4232_2]) ).

fof(f_4233_1,plain,
    ! [V_m_2,V_n_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,V_n_2)),hAPP(c_Code__Numeral_Oof__nat,V_m_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,V_n_2)),hAPP(c_Code__Numeral_Oof__nat,V_m_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_less__eq__code__numeral__code]) ).

fof(f_4233_2,plain,
    ! [U_17190,U_17189] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_17189)),hAPP(c_Code__Numeral_Oof__nat,U_17190)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_17189),U_17190)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_17189),U_17190))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_17189)),hAPP(c_Code__Numeral_Oof__nat,U_17190))) ) ),
    inference(variable_rename,[status(thm)],[f_4233_1]) ).

fof(f_4233_3,plain,
    ( ! [U_17194,U_17192] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_17192)),hAPP(c_Code__Numeral_Oof__nat,U_17194)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_17192),U_17194)) )
    & ! [U_17193,U_17191] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_17191),U_17193))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_17191)),hAPP(c_Code__Numeral_Oof__nat,U_17193))) ) ),
    inference(miniscope,[status(thm)],[f_4233_2]) ).

cnf(f_4233_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_17191),U_17193))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_17191)),hAPP(c_Code__Numeral_Oof__nat,U_17193))) ),
    inference(clausify,[status(thm)],[f_4233_3]) ).

cnf(f_4233_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_17192)),hAPP(c_Code__Numeral_Oof__nat,U_17194)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_17192),U_17194)) ),
    inference(clausify,[status(thm)],[f_4233_3]) ).

fof(f_4234_1,plain,
    ! [V_m,V_n] : hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,hAPP(c_Code__Numeral_Oof__nat,V_n)),hAPP(c_Code__Numeral_Oof__nat,V_m)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m)),
    inference(fof_nnf,[status(thm)],[fact_subtract__code__numeral__code]) ).

fof(f_4234_2,plain,
    ! [U_17196,U_17195] : hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,hAPP(c_Code__Numeral_Oof__nat,U_17195)),hAPP(c_Code__Numeral_Oof__nat,U_17196)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_17195),U_17196)),
    inference(variable_rename,[status(thm)],[f_4234_1]) ).

cnf(f_4234_3,plain,
    hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,hAPP(c_Code__Numeral_Oof__nat,U_17195)),hAPP(c_Code__Numeral_Oof__nat,U_17196)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_17195),U_17196)),
    inference(clausify,[status(thm)],[f_4234_2]) ).

fof(f_4235_1,plain,
    ! [V_xs_2,T_b,V_i_2] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Random_Opick(T_b,V_xs_2),V_i_2)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),T_b),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i_2),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_pick__member]) ).

fof(f_4235_2,plain,
    ! [U_17199,U_17198,U_17197] :
      ( hBOOL(hAPP(hAPP(c_member(U_17198),hAPP(c_Random_Opick(U_17198,U_17199),U_17197)),hAPP(c_List_Oset(U_17198),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,U_17198),U_17198),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,U_17198)),U_17199))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_17197),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,U_17198),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_17198)),U_17199)))) ),
    inference(variable_rename,[status(thm)],[f_4235_1]) ).

cnf(f_4235_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_17198),hAPP(c_Random_Opick(U_17198,U_17199),U_17197)),hAPP(c_List_Oset(U_17198),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,U_17198),U_17198),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,U_17198)),U_17199))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_17197),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,U_17198),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_17198)),U_17199)))) ),
    inference(clausify,[status(thm)],[f_4235_2]) ).

fof(f_4236_1,plain,
    ! [V_zs_2,V_ys_2,T_c,V_xs_2,T_b] :
      ( ( ( hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2) = V_zs_2
          | hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_c),c_Product__Type_Osnd(T_b,T_c)),V_zs_2) != V_ys_2
          | hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_zs_2) != V_xs_2 )
        & ( ( hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_c),c_Product__Type_Osnd(T_b,T_c)),V_zs_2) = V_ys_2
            & hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_zs_2) = V_xs_2 )
          | hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2) != V_zs_2 ) )
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2) ),
    inference(fof_nnf,[status(thm)],[fact_zip__eq__conv]) ).

fof(f_4236_2,plain,
    ! [U_17204,U_17203,U_17202,U_17201,U_17200] :
      ( ( ( hAPP(hAPP(c_List_Ozip(U_17200,U_17202),U_17201),U_17203) = U_17204
          | hAPP(hAPP(c_List_Omap(tc_prod(U_17200,U_17202),U_17202),c_Product__Type_Osnd(U_17200,U_17202)),U_17204) != U_17203
          | hAPP(hAPP(c_List_Omap(tc_prod(U_17200,U_17202),U_17200),c_Product__Type_Ofst(U_17200,U_17202)),U_17204) != U_17201 )
        & ( ( hAPP(hAPP(c_List_Omap(tc_prod(U_17200,U_17202),U_17202),c_Product__Type_Osnd(U_17200,U_17202)),U_17204) = U_17203
            & hAPP(hAPP(c_List_Omap(tc_prod(U_17200,U_17202),U_17200),c_Product__Type_Ofst(U_17200,U_17202)),U_17204) = U_17201 )
          | hAPP(hAPP(c_List_Ozip(U_17200,U_17202),U_17201),U_17203) != U_17204 ) )
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17200)),U_17201) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17202)),U_17203) ),
    inference(variable_rename,[status(thm)],[f_4236_1]) ).

cnf(f_4236_3,plain,
    ( hAPP(hAPP(c_List_Omap(tc_prod(U_17200,U_17202),U_17200),c_Product__Type_Ofst(U_17200,U_17202)),U_17204) = U_17201
    | hAPP(hAPP(c_List_Ozip(U_17200,U_17202),U_17201),U_17203) != U_17204
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17200)),U_17201) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17202)),U_17203) ),
    inference(clausify,[status(thm)],[f_4236_2]) ).

cnf(f_4236_4,plain,
    ( hAPP(hAPP(c_List_Omap(tc_prod(U_17200,U_17202),U_17202),c_Product__Type_Osnd(U_17200,U_17202)),U_17204) = U_17203
    | hAPP(hAPP(c_List_Ozip(U_17200,U_17202),U_17201),U_17203) != U_17204
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17200)),U_17201) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17202)),U_17203) ),
    inference(clausify,[status(thm)],[f_4236_2]) ).

cnf(f_4236_5,plain,
    ( hAPP(hAPP(c_List_Ozip(U_17200,U_17202),U_17201),U_17203) = U_17204
    | hAPP(hAPP(c_List_Omap(tc_prod(U_17200,U_17202),U_17202),c_Product__Type_Osnd(U_17200,U_17202)),U_17204) != U_17203
    | hAPP(hAPP(c_List_Omap(tc_prod(U_17200,U_17202),U_17200),c_Product__Type_Ofst(U_17200,U_17202)),U_17204) != U_17201
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17200)),U_17201) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17202)),U_17203) ),
    inference(clausify,[status(thm)],[f_4236_2]) ).

fof(f_4237_1,plain,
    ! [V_xs_2,V_f_2,T_b] : c_List_Olist_Olist__size(T_b,V_f_2,V_xs_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(T_b,tc_Nat_Onat),V_f_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_list__size__conv__listsum]) ).

fof(f_4237_2,plain,
    ! [U_17207,U_17206,U_17205] : c_List_Olist_Olist__size(U_17205,U_17206,U_17207) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(U_17205,tc_Nat_Onat),U_17206),U_17207))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17205)),U_17207)),
    inference(variable_rename,[status(thm)],[f_4237_1]) ).

cnf(f_4237_3,plain,
    c_List_Olist_Olist__size(U_17205,U_17206,U_17207) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(U_17205,tc_Nat_Onat),U_17206),U_17207))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17205)),U_17207)),
    inference(clausify,[status(thm)],[f_4237_2]) ).

fof(f_4238_1,plain,
    ! [V_i_2] :
      ( ( V_i_2 != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),V_i_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),V_i_2))
        | V_i_2 = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(fof_nnf,[status(thm)],[fact_code__numeral__not__eq__zero]) ).

fof(f_4238_2,plain,
    ! [U_17208] :
      ( ( U_17208 != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),U_17208)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),U_17208))
        | U_17208 = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(variable_rename,[status(thm)],[f_4238_1]) ).

fof(f_4238_3,plain,
    ( ! [U_17210] :
        ( U_17210 != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),U_17210)) )
    & ! [U_17209] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),U_17209))
        | U_17209 = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(miniscope,[status(thm)],[f_4238_2]) ).

cnf(f_4238_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),U_17209))
    | U_17209 = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_4238_3]) ).

cnf(f_4238_5,plain,
    ( U_17210 != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),U_17210)) ),
    inference(clausify,[status(thm)],[f_4238_3]) ).

fof(f_4239_1,plain,
    ! [V_j_2,V_i_2,V_f_2,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),V_f_2),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_i_2,V_j_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(tc_Int_Oint,T_b),V_f_2),c_List_Oupto(V_i_2,V_j_2)))
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__set__upto__conv__listsum__int]) ).

fof(f_4239_2,plain,
    ! [U_17214,U_17213,U_17212,U_17211] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_17211),U_17212),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_17213,U_17214))) = hAPP(c_List_Omonoid__add__class_Olistsum(U_17211),hAPP(hAPP(c_List_Omap(tc_Int_Oint,U_17211),U_17212),c_List_Oupto(U_17213,U_17214)))
      | ~ class_Groups_Ocomm__monoid__add(U_17211) ),
    inference(variable_rename,[status(thm)],[f_4239_1]) ).

cnf(f_4239_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_17211),U_17212),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_17213,U_17214))) = hAPP(c_List_Omonoid__add__class_Olistsum(U_17211),hAPP(hAPP(c_List_Omap(tc_Int_Oint,U_17211),U_17212),c_List_Oupto(U_17213,U_17214)))
    | ~ class_Groups_Ocomm__monoid__add(U_17211) ),
    inference(clausify,[status(thm)],[f_4239_2]) ).

fof(f_4240_1,plain,
    ! [V_l_2,V_k_2,V_f_2,T_b] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(tc_Int_Oint,T_b),V_f_2),c_List_Oupto(V_k_2,V_l_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),V_f_2),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_k_2,V_l_2)))
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_interv__listsum__conv__setsum__set__int]) ).

fof(f_4240_2,plain,
    ! [U_17218,U_17217,U_17216,U_17215] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_17215),hAPP(hAPP(c_List_Omap(tc_Int_Oint,U_17215),U_17216),c_List_Oupto(U_17217,U_17218))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_17215),U_17216),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_17217,U_17218)))
      | ~ class_Groups_Ocomm__monoid__add(U_17215) ),
    inference(variable_rename,[status(thm)],[f_4240_1]) ).

cnf(f_4240_3,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_17215),hAPP(hAPP(c_List_Omap(tc_Int_Oint,U_17215),U_17216),c_List_Oupto(U_17217,U_17218))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_17215),U_17216),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_17217,U_17218)))
    | ~ class_Groups_Ocomm__monoid__add(U_17215) ),
    inference(clausify,[status(thm)],[f_4240_2]) ).

fof(f_4241_1,plain,
    ! [V_s_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Product__Type_Ofst(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect__weight(T_b,V_xs_2),V_s_2))),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),T_b),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_select__weight__member]) ).

fof(f_4241_2,plain,
    ! [U_17221,U_17220,U_17219] :
      ( hBOOL(hAPP(hAPP(c_member(U_17219),hAPP(c_Product__Type_Ofst(U_17219,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect__weight(U_17219,U_17220),U_17221))),hAPP(c_List_Oset(U_17219),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,U_17219),U_17219),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,U_17219)),U_17220))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,U_17219),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_17219)),U_17220)))) ),
    inference(variable_rename,[status(thm)],[f_4241_1]) ).

cnf(f_4241_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_17219),hAPP(c_Product__Type_Ofst(U_17219,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect__weight(U_17219,U_17220),U_17221))),hAPP(c_List_Oset(U_17219),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,U_17219),U_17219),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,U_17219)),U_17220))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,U_17219),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_17219)),U_17220)))) ),
    inference(clausify,[status(thm)],[f_4241_2]) ).

fof(f_4242_1,plain,
    ! [V_xs_2,T_b] : c_Random_Oselect__weight(T_b,V_xs_2) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Orange(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Opick(T_b,V_xs_2))),
    inference(fof_nnf,[status(thm)],[fact_select__weight__def]) ).

fof(f_4242_2,plain,
    ! [U_17223,U_17222] : c_Random_Oselect__weight(U_17222,U_17223) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(U_17222,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Orange(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,U_17222),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_17222)),U_17223)))),hAPP(hAPP(c_COMBB(U_17222,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(U_17222,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(U_17222,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Opick(U_17222,U_17223))),
    inference(variable_rename,[status(thm)],[f_4242_1]) ).

cnf(f_4242_3,plain,
    c_Random_Oselect__weight(U_17222,U_17223) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(U_17222,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Orange(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,U_17222),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_17222)),U_17223)))),hAPP(hAPP(c_COMBB(U_17222,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(U_17222,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(U_17222,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Opick(U_17222,U_17223))),
    inference(clausify,[status(thm)],[f_4242_2]) ).

fof(f_4243_1,plain,
    ! [V_xs_2,T_b] : c_Random_Oselect(T_b,V_xs_2) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Orange(hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Code__Numeral_Ocode__numeral),hAPP(c_List_Onth(T_b),V_xs_2)),c_Code__Numeral_Onat__of))),
    inference(fof_nnf,[status(thm)],[fact_select__def]) ).

fof(f_4243_2,plain,
    ! [U_17225,U_17224] : c_Random_Oselect(U_17224,U_17225) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(U_17224,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Orange(hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17224)),U_17225)))),hAPP(hAPP(c_COMBB(U_17224,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(U_17224,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(U_17224,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_17224,tc_Code__Numeral_Ocode__numeral),hAPP(c_List_Onth(U_17224),U_17225)),c_Code__Numeral_Onat__of))),
    inference(variable_rename,[status(thm)],[f_4243_1]) ).

cnf(f_4243_3,plain,
    c_Random_Oselect(U_17224,U_17225) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(U_17224,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Orange(hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17224)),U_17225)))),hAPP(hAPP(c_COMBB(U_17224,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(U_17224,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(U_17224,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_17224,tc_Code__Numeral_Ocode__numeral),hAPP(c_List_Onth(U_17224),U_17225)),c_Code__Numeral_Onat__of))),
    inference(clausify,[status(thm)],[f_4243_2]) ).

fof(f_4244_1,plain,
    ! [V_g_2,V_f_2,V_xs_2,T_b,T_c] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_g_2),V_xs_2))))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x)))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) )
      | ~ class_Groups_Oordered__ab__semigroup__add(T_c)
      | ~ class_Groups_Omonoid__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_listsum__mono]) ).

fof(f_4244_2,plain,
    ! [U_17231,U_17230,U_17229,U_17228,U_17227] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17227),hAPP(c_List_Omonoid__add__class_Olistsum(U_17227),hAPP(hAPP(c_List_Omap(U_17228,U_17227),U_17230),U_17229))),hAPP(c_List_Omonoid__add__class_Olistsum(U_17227),hAPP(hAPP(c_List_Omap(U_17228,U_17227),U_17231),U_17229))))
      | ? [U_17226] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17227),hAPP(U_17230,U_17226)),hAPP(U_17231,U_17226)))
          & hBOOL(hAPP(hAPP(c_member(U_17228),U_17226),hAPP(c_List_Oset(U_17228),U_17229))) )
      | ~ class_Groups_Oordered__ab__semigroup__add(U_17227)
      | ~ class_Groups_Omonoid__add(U_17227) ),
    inference(variable_rename,[status(thm)],[f_4244_1]) ).

fof(f_4244_3,plain,
    ! [U_17231,U_17230,U_17229,U_17228,U_17227] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17227),hAPP(c_List_Omonoid__add__class_Olistsum(U_17227),hAPP(hAPP(c_List_Omap(U_17228,U_17227),U_17230),U_17229))),hAPP(c_List_Omonoid__add__class_Olistsum(U_17227),hAPP(hAPP(c_List_Omap(U_17228,U_17227),U_17231),U_17229))))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17227),hAPP(U_17230,sK436(U_17231,U_17230,U_17229,U_17228,U_17227))),hAPP(U_17231,sK436(U_17231,U_17230,U_17229,U_17228,U_17227))))
        & hBOOL(hAPP(hAPP(c_member(U_17228),sK436(U_17231,U_17230,U_17229,U_17228,U_17227)),hAPP(c_List_Oset(U_17228),U_17229))) )
      | ~ class_Groups_Oordered__ab__semigroup__add(U_17227)
      | ~ class_Groups_Omonoid__add(U_17227) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK436]),skolemize(U_17226,sK436(U_17231,U_17230,U_17229,U_17228,U_17227))],[f_4244_2]) ).

cnf(f_4244_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_17228),sK436(U_17231,U_17230,U_17229,U_17228,U_17227)),hAPP(c_List_Oset(U_17228),U_17229)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17227),hAPP(c_List_Omonoid__add__class_Olistsum(U_17227),hAPP(hAPP(c_List_Omap(U_17228,U_17227),U_17230),U_17229))),hAPP(c_List_Omonoid__add__class_Olistsum(U_17227),hAPP(hAPP(c_List_Omap(U_17228,U_17227),U_17231),U_17229))))
    | ~ class_Groups_Oordered__ab__semigroup__add(U_17227)
    | ~ class_Groups_Omonoid__add(U_17227) ),
    inference(clausify,[status(thm)],[f_4244_3]) ).

cnf(f_4244_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17227),hAPP(U_17230,sK436(U_17231,U_17230,U_17229,U_17228,U_17227))),hAPP(U_17231,sK436(U_17231,U_17230,U_17229,U_17228,U_17227))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17227),hAPP(c_List_Omonoid__add__class_Olistsum(U_17227),hAPP(hAPP(c_List_Omap(U_17228,U_17227),U_17230),U_17229))),hAPP(c_List_Omonoid__add__class_Olistsum(U_17227),hAPP(hAPP(c_List_Omap(U_17228,U_17227),U_17231),U_17229))))
    | ~ class_Groups_Oordered__ab__semigroup__add(U_17227)
    | ~ class_Groups_Omonoid__add(U_17227) ),
    inference(clausify,[status(thm)],[f_4244_3]) ).

fof(f_4245_1,plain,
    ! [V_n] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_n)) = V_n,
    inference(fof_nnf,[status(thm)],[fact_nat__of__of__nat]) ).

fof(f_4245_2,plain,
    ! [U_17232] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,U_17232)) = U_17232,
    inference(variable_rename,[status(thm)],[f_4245_1]) ).

cnf(f_4245_3,plain,
    hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,U_17232)) = U_17232,
    inference(clausify,[status(thm)],[f_4245_2]) ).

fof(f_4246_1,plain,
    ! [V_k] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_k)) = V_k,
    inference(fof_nnf,[status(thm)],[fact_of__nat__nat__of]) ).

fof(f_4246_2,plain,
    ! [U_17233] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,U_17233)) = U_17233,
    inference(variable_rename,[status(thm)],[f_4246_1]) ).

cnf(f_4246_3,plain,
    hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,U_17233)) = U_17233,
    inference(clausify,[status(thm)],[f_4246_2]) ).

fof(f_4247_1,plain,
    ! [V_x] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_x)) = V_x,
    inference(fof_nnf,[status(thm)],[fact_nat__of__inverse]) ).

fof(f_4247_2,plain,
    ! [U_17234] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,U_17234)) = U_17234,
    inference(variable_rename,[status(thm)],[f_4247_1]) ).

cnf(f_4247_3,plain,
    hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,U_17234)) = U_17234,
    inference(clausify,[status(thm)],[f_4247_2]) ).

fof(f_4248_1,plain,
    ! [V_m,V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),V_n),V_m) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n)),hAPP(c_Code__Numeral_Onat__of,V_m))),
    inference(fof_nnf,[status(thm)],[fact_times__code__numeral__def]) ).

fof(f_4248_2,plain,
    ! [U_17236,U_17235] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),U_17235),U_17236) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_17235)),hAPP(c_Code__Numeral_Onat__of,U_17236))),
    inference(variable_rename,[status(thm)],[f_4248_1]) ).

cnf(f_4248_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),U_17235),U_17236) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_17235)),hAPP(c_Code__Numeral_Onat__of,U_17236))),
    inference(clausify,[status(thm)],[f_4248_2]) ).

fof(f_4249_1,plain,
    ! [V_y_2,V_x_2] :
      ( ( hAPP(c_Code__Numeral_Onat__of,V_x_2) = hAPP(c_Code__Numeral_Onat__of,V_y_2)
        | V_x_2 != V_y_2 )
      & ( V_x_2 = V_y_2
        | hAPP(c_Code__Numeral_Onat__of,V_x_2) != hAPP(c_Code__Numeral_Onat__of,V_y_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_code__numeral_Onat__of__inject]) ).

fof(f_4249_2,plain,
    ! [U_17238,U_17237] :
      ( ( hAPP(c_Code__Numeral_Onat__of,U_17237) = hAPP(c_Code__Numeral_Onat__of,U_17238)
        | U_17237 != U_17238 )
      & ( U_17237 = U_17238
        | hAPP(c_Code__Numeral_Onat__of,U_17237) != hAPP(c_Code__Numeral_Onat__of,U_17238) ) ),
    inference(variable_rename,[status(thm)],[f_4249_1]) ).

fof(f_4249_3,plain,
    ( ! [U_17242,U_17240] :
        ( hAPP(c_Code__Numeral_Onat__of,U_17240) = hAPP(c_Code__Numeral_Onat__of,U_17242)
        | U_17240 != U_17242 )
    & ! [U_17241,U_17239] :
        ( U_17239 = U_17241
        | hAPP(c_Code__Numeral_Onat__of,U_17239) != hAPP(c_Code__Numeral_Onat__of,U_17241) ) ),
    inference(miniscope,[status(thm)],[f_4249_2]) ).

cnf(f_4249_4,plain,
    ( U_17239 = U_17241
    | hAPP(c_Code__Numeral_Onat__of,U_17239) != hAPP(c_Code__Numeral_Onat__of,U_17241) ),
    inference(clausify,[status(thm)],[f_4249_3]) ).

cnf(f_4249_5,plain,
    ( hAPP(c_Code__Numeral_Onat__of,U_17240) = hAPP(c_Code__Numeral_Onat__of,U_17242)
    | U_17240 != U_17242 ),
    inference(clausify,[status(thm)],[f_4249_3]) ).

fof(f_4250_1,plain,
    ! [V_l_2,V_k_2] :
      ( ( hAPP(c_Code__Numeral_Onat__of,V_k_2) = hAPP(c_Code__Numeral_Onat__of,V_l_2)
        | V_k_2 != V_l_2 )
      & ( V_k_2 = V_l_2
        | hAPP(c_Code__Numeral_Onat__of,V_k_2) != hAPP(c_Code__Numeral_Onat__of,V_l_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_Code__Numeral_Onat__of__inject]) ).

fof(f_4250_2,plain,
    ! [U_17244,U_17243] :
      ( ( hAPP(c_Code__Numeral_Onat__of,U_17243) = hAPP(c_Code__Numeral_Onat__of,U_17244)
        | U_17243 != U_17244 )
      & ( U_17243 = U_17244
        | hAPP(c_Code__Numeral_Onat__of,U_17243) != hAPP(c_Code__Numeral_Onat__of,U_17244) ) ),
    inference(variable_rename,[status(thm)],[f_4250_1]) ).

fof(f_4250_3,plain,
    ( ! [U_17248,U_17246] :
        ( hAPP(c_Code__Numeral_Onat__of,U_17246) = hAPP(c_Code__Numeral_Onat__of,U_17248)
        | U_17246 != U_17248 )
    & ! [U_17247,U_17245] :
        ( U_17245 = U_17247
        | hAPP(c_Code__Numeral_Onat__of,U_17245) != hAPP(c_Code__Numeral_Onat__of,U_17247) ) ),
    inference(miniscope,[status(thm)],[f_4250_2]) ).

cnf(f_4250_4,plain,
    ( U_17245 = U_17247
    | hAPP(c_Code__Numeral_Onat__of,U_17245) != hAPP(c_Code__Numeral_Onat__of,U_17247) ),
    inference(clausify,[status(thm)],[f_4250_3]) ).

cnf(f_4250_5,plain,
    ( hAPP(c_Code__Numeral_Onat__of,U_17246) = hAPP(c_Code__Numeral_Onat__of,U_17248)
    | U_17246 != U_17248 ),
    inference(clausify,[status(thm)],[f_4250_3]) ).

fof(f_4251_1,plain,
    c_Typedef_Otype__definition(tc_Code__Numeral_Ocode__numeral,tc_Nat_Onat,c_Code__Numeral_Onat__of,c_Code__Numeral_Oof__nat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    inference(fof_nnf,[status(thm)],[fact_type__definition__code__numeral]) ).

cnf(f_4251_2,plain,
    c_Typedef_Otype__definition(tc_Code__Numeral_Ocode__numeral,tc_Nat_Onat,c_Code__Numeral_Onat__of,c_Code__Numeral_Oof__nat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_4251_1]) ).

fof(f_4252_1,plain,
    ! [V_m_2,V_n_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n_2)),hAPP(c_Code__Numeral_Onat__of,V_m_2))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n_2)),hAPP(c_Code__Numeral_Onat__of,V_m_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_less__code__numeral__def]) ).

fof(f_4252_2,plain,
    ! [U_17250,U_17249] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_17249),U_17250))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_17249)),hAPP(c_Code__Numeral_Onat__of,U_17250))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_17249)),hAPP(c_Code__Numeral_Onat__of,U_17250)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_17249),U_17250)) ) ),
    inference(variable_rename,[status(thm)],[f_4252_1]) ).

fof(f_4252_3,plain,
    ( ! [U_17254,U_17252] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_17252),U_17254))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_17252)),hAPP(c_Code__Numeral_Onat__of,U_17254))) )
    & ! [U_17253,U_17251] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_17251)),hAPP(c_Code__Numeral_Onat__of,U_17253)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_17251),U_17253)) ) ),
    inference(miniscope,[status(thm)],[f_4252_2]) ).

cnf(f_4252_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_17251)),hAPP(c_Code__Numeral_Onat__of,U_17253)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_17251),U_17253)) ),
    inference(clausify,[status(thm)],[f_4252_3]) ).

cnf(f_4252_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_17252),U_17254))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_17252)),hAPP(c_Code__Numeral_Onat__of,U_17254))) ),
    inference(clausify,[status(thm)],[f_4252_3]) ).

fof(f_4253_1,plain,
    ! [V_x_2] : hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_x_2)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_nat__of]) ).

fof(f_4253_2,plain,
    ! [U_17255] : hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_17255)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_4253_1]) ).

cnf(f_4253_3,plain,
    hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_17255)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_4253_2]) ).

fof(f_4254_1,plain,
    ! [V_k] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),V_k)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_k),
    inference(fof_nnf,[status(thm)],[fact_nat__of__number]) ).

fof(f_4254_2,plain,
    ! [U_17256] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),U_17256)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_17256),
    inference(variable_rename,[status(thm)],[f_4254_1]) ).

cnf(f_4254_3,plain,
    hAPP(c_Code__Numeral_Onat__of,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),U_17256)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_17256),
    inference(clausify,[status(thm)],[f_4254_2]) ).

fof(f_4255_1,plain,
    c_Code__Numeral_Oint__of = hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Int_Oint,tc_Code__Numeral_Ocode__numeral,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_Code__Numeral_Onat__of),
    inference(fof_nnf,[status(thm)],[fact_int__of__def]) ).

cnf(f_4255_2,plain,
    c_Code__Numeral_Oint__of = hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Int_Oint,tc_Code__Numeral_Ocode__numeral,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_Code__Numeral_Onat__of),
    inference(clausify,[status(thm)],[f_4255_1]) ).

fof(f_4256_1,plain,
    ! [V_m_2,V_n_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n_2)),hAPP(c_Code__Numeral_Onat__of,V_m_2))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n_2)),hAPP(c_Code__Numeral_Onat__of,V_m_2)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_less__eq__code__numeral__def]) ).

fof(f_4256_2,plain,
    ! [U_17258,U_17257] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_17257),U_17258))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_17257)),hAPP(c_Code__Numeral_Onat__of,U_17258))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_17257)),hAPP(c_Code__Numeral_Onat__of,U_17258)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_17257),U_17258)) ) ),
    inference(variable_rename,[status(thm)],[f_4256_1]) ).

fof(f_4256_3,plain,
    ( ! [U_17262,U_17260] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_17260),U_17262))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_17260)),hAPP(c_Code__Numeral_Onat__of,U_17262))) )
    & ! [U_17261,U_17259] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_17259)),hAPP(c_Code__Numeral_Onat__of,U_17261)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_17259),U_17261)) ) ),
    inference(miniscope,[status(thm)],[f_4256_2]) ).

cnf(f_4256_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_17259)),hAPP(c_Code__Numeral_Onat__of,U_17261)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_17259),U_17261)) ),
    inference(clausify,[status(thm)],[f_4256_3]) ).

cnf(f_4256_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_17260),U_17262))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_17260)),hAPP(c_Code__Numeral_Onat__of,U_17262))) ),
    inference(clausify,[status(thm)],[f_4256_3]) ).

fof(f_4257_1,plain,
    ! [V_i] : hAPP(c_Code__Numeral_Onat__of,V_i) = c_Code__Numeral_Onat__of__aux(V_i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(fof_nnf,[status(thm)],[fact_nat__of__code]) ).

fof(f_4257_2,plain,
    ! [U_17263] : hAPP(c_Code__Numeral_Onat__of,U_17263) = c_Code__Numeral_Onat__of__aux(U_17263,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[f_4257_1]) ).

cnf(f_4257_3,plain,
    hAPP(c_Code__Numeral_Onat__of,U_17263) = c_Code__Numeral_Onat__of__aux(U_17263,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(clausify,[status(thm)],[f_4257_2]) ).

fof(f_4258_1,plain,
    ! [V_n,V_i] : c_Code__Numeral_Onat__of__aux(V_i,V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_i)),V_n),
    inference(fof_nnf,[status(thm)],[fact_nat__of__aux__def]) ).

fof(f_4258_2,plain,
    ! [U_17265,U_17264] : c_Code__Numeral_Onat__of__aux(U_17264,U_17265) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_17264)),U_17265),
    inference(variable_rename,[status(thm)],[f_4258_1]) ).

cnf(f_4258_3,plain,
    c_Code__Numeral_Onat__of__aux(U_17264,U_17265) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_17264)),U_17265),
    inference(clausify,[status(thm)],[f_4258_2]) ).

fof(f_4259_1,plain,
    ! [V_k] : c_Code__Numeral_OSuc__code__numeral(V_k) = hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,V_k))),
    inference(fof_nnf,[status(thm)],[fact_Suc__code__numeral__def]) ).

fof(f_4259_2,plain,
    ! [U_17266] : c_Code__Numeral_OSuc__code__numeral(U_17266) = hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,U_17266))),
    inference(variable_rename,[status(thm)],[f_4259_1]) ).

cnf(f_4259_3,plain,
    c_Code__Numeral_OSuc__code__numeral(U_17266) = hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,U_17266))),
    inference(clausify,[status(thm)],[f_4259_2]) ).

fof(f_4260_1,plain,
    ! [V_m,V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_n),V_m) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n)),hAPP(c_Code__Numeral_Onat__of,V_m))),
    inference(fof_nnf,[status(thm)],[fact_minus__code__numeral__def]) ).

fof(f_4260_2,plain,
    ! [U_17268,U_17267] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_17267),U_17268) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_17267)),hAPP(c_Code__Numeral_Onat__of,U_17268))),
    inference(variable_rename,[status(thm)],[f_4260_1]) ).

cnf(f_4260_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_17267),U_17268) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_17267)),hAPP(c_Code__Numeral_Onat__of,U_17268))),
    inference(clausify,[status(thm)],[f_4260_2]) ).

fof(f_4261_1,plain,
    ! [V_y_2] :
      ( hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_y_2)) = V_y_2
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__inverse]) ).

fof(f_4261_2,plain,
    ! [U_17269] :
      ( hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,U_17269)) = U_17269
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_17269),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_4261_1]) ).

cnf(f_4261_3,plain,
    ( hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,U_17269)) = U_17269
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_17269),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_4261_2]) ).

fof(f_4262_1,plain,
    ! [V_m,V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),V_n),V_m) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n)),hAPP(c_Code__Numeral_Onat__of,V_m))),
    inference(fof_nnf,[status(thm)],[fact_plus__code__numeral__def]) ).

fof(f_4262_2,plain,
    ! [U_17271,U_17270] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),U_17270),U_17271) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_17270)),hAPP(c_Code__Numeral_Onat__of,U_17271))),
    inference(variable_rename,[status(thm)],[f_4262_1]) ).

cnf(f_4262_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),U_17270),U_17271) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_17270)),hAPP(c_Code__Numeral_Onat__of,U_17271))),
    inference(clausify,[status(thm)],[f_4262_2]) ).

fof(f_4263_1,plain,
    ! [V_m,V_n] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_n),V_m) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n)),hAPP(c_Code__Numeral_Onat__of,V_m))),
    inference(fof_nnf,[status(thm)],[fact_div__code__numeral__def]) ).

fof(f_4263_2,plain,
    ! [U_17273,U_17272] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),U_17272),U_17273) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_17272)),hAPP(c_Code__Numeral_Onat__of,U_17273))),
    inference(variable_rename,[status(thm)],[f_4263_1]) ).

cnf(f_4263_3,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),U_17272),U_17273) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_17272)),hAPP(c_Code__Numeral_Onat__of,U_17273))),
    inference(clausify,[status(thm)],[f_4263_2]) ).

fof(f_4264_1,plain,
    ! [V_m,V_n] : c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,V_n,V_m) = hAPP(c_Code__Numeral_Oof__nat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Code__Numeral_Onat__of,V_n),hAPP(c_Code__Numeral_Onat__of,V_m))),
    inference(fof_nnf,[status(thm)],[fact_mod__code__numeral__def]) ).

fof(f_4264_2,plain,
    ! [U_17275,U_17274] : c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,U_17274,U_17275) = hAPP(c_Code__Numeral_Oof__nat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Code__Numeral_Onat__of,U_17274),hAPP(c_Code__Numeral_Onat__of,U_17275))),
    inference(variable_rename,[status(thm)],[f_4264_1]) ).

cnf(f_4264_3,plain,
    c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,U_17274,U_17275) = hAPP(c_Code__Numeral_Oof__nat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Code__Numeral_Onat__of,U_17274),hAPP(c_Code__Numeral_Onat__of,U_17275))),
    inference(clausify,[status(thm)],[f_4264_2]) ).

fof(f_4265_1,plain,
    ! [V_k] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_k)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Code__Numeral_Onat__of,V_k)))
      | V_k = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(fof_nnf,[status(thm)],[fact_code__numeral__decr]) ).

fof(f_4265_2,plain,
    ! [U_17276] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_17276)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Code__Numeral_Onat__of,U_17276)))
      | U_17276 = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(variable_rename,[status(thm)],[f_4265_1]) ).

cnf(f_4265_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_17276)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Code__Numeral_Onat__of,U_17276)))
    | U_17276 = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_4265_2]) ).

fof(f_4266_1,plain,
    ! [V_i_2,V_xq_2] : hAPP(c_New__DSequence_Opos__not__seq(V_xq_2),V_i_2) = c_Lazy__Sequence_Ohb__not__seq(hAPP(V_xq_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_i_2))),
    inference(fof_nnf,[status(thm)],[fact_New__DSequence_Opos__not__seq__def]) ).

fof(f_4266_2,plain,
    ! [U_17278,U_17277] : hAPP(c_New__DSequence_Opos__not__seq(U_17277),U_17278) = c_Lazy__Sequence_Ohb__not__seq(hAPP(U_17277,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),U_17278))),
    inference(variable_rename,[status(thm)],[f_4266_1]) ).

cnf(f_4266_3,plain,
    hAPP(c_New__DSequence_Opos__not__seq(U_17277),U_17278) = c_Lazy__Sequence_Ohb__not__seq(hAPP(U_17277,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),U_17278))),
    inference(clausify,[status(thm)],[f_4266_2]) ).

fof(f_4267_1,plain,
    ! [V_no_2,V_yes_2,V_xs_2,V_P_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_yes_2)),hAPP(c_List_Oset(T_b),V_no_2)) = hAPP(c_List_Oset(T_b),V_xs_2)
      | c_List_Opartition(T_b,V_P_2,V_xs_2) != hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_yes_2),V_no_2) ),
    inference(fof_nnf,[status(thm)],[fact_partition__set]) ).

fof(f_4267_2,plain,
    ! [U_17283,U_17282,U_17281,U_17280,U_17279] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_17279,tc_HOL_Obool)),hAPP(c_List_Oset(U_17279),U_17282)),hAPP(c_List_Oset(U_17279),U_17283)) = hAPP(c_List_Oset(U_17279),U_17281)
      | c_List_Opartition(U_17279,U_17280,U_17281) != hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17279),tc_List_Olist(U_17279)),U_17282),U_17283) ),
    inference(variable_rename,[status(thm)],[f_4267_1]) ).

cnf(f_4267_3,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_17279,tc_HOL_Obool)),hAPP(c_List_Oset(U_17279),U_17282)),hAPP(c_List_Oset(U_17279),U_17283)) = hAPP(c_List_Oset(U_17279),U_17281)
    | c_List_Opartition(U_17279,U_17280,U_17281) != hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17279),tc_List_Olist(U_17279)),U_17282),U_17283) ),
    inference(clausify,[status(thm)],[f_4267_2]) ).

fof(f_4268_1,plain,
    ! [V_no_2,V_yes_2,V_xs_2,V_P_2,T_b] :
      ( ( ! [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_no_2))) )
        & ! [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_yes_2))) ) )
      | c_List_Opartition(T_b,V_P_2,V_xs_2) != hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_yes_2),V_no_2) ),
    inference(fof_nnf,[status(thm)],[fact_partition__P]) ).

fof(f_4268_2,plain,
    ! [U_17290,U_17289,U_17288,U_17287,U_17286] :
      ( ( ! [U_17285] :
            ( ~ hBOOL(hAPP(U_17287,U_17285))
            | ~ hBOOL(hAPP(hAPP(c_member(U_17286),U_17285),hAPP(c_List_Oset(U_17286),U_17290))) )
        & ! [U_17284] :
            ( hBOOL(hAPP(U_17287,U_17284))
            | ~ hBOOL(hAPP(hAPP(c_member(U_17286),U_17284),hAPP(c_List_Oset(U_17286),U_17289))) ) )
      | c_List_Opartition(U_17286,U_17287,U_17288) != hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17286),tc_List_Olist(U_17286)),U_17289),U_17290) ),
    inference(variable_rename,[status(thm)],[f_4268_1]) ).

cnf(f_4268_3,plain,
    ( hBOOL(hAPP(U_17287,U_17284))
    | ~ hBOOL(hAPP(hAPP(c_member(U_17286),U_17284),hAPP(c_List_Oset(U_17286),U_17289)))
    | c_List_Opartition(U_17286,U_17287,U_17288) != hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17286),tc_List_Olist(U_17286)),U_17289),U_17290) ),
    inference(clausify,[status(thm)],[f_4268_2]) ).

cnf(f_4268_4,plain,
    ( ~ hBOOL(hAPP(U_17287,U_17285))
    | ~ hBOOL(hAPP(hAPP(c_member(U_17286),U_17285),hAPP(c_List_Oset(U_17286),U_17290)))
    | c_List_Opartition(U_17286,U_17287,U_17288) != hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17286),tc_List_Olist(U_17286)),U_17289),U_17290) ),
    inference(clausify,[status(thm)],[f_4268_2]) ).

fof(f_4269_1,plain,
    ! [V_P_2,T_b] : c_List_Opartition(T_b,V_P_2,c_List_Olist_ONil(T_b)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_List_Olist_ONil(T_b)),
    inference(fof_nnf,[status(thm)],[fact_partition_Osimps_I1_J]) ).

fof(f_4269_2,plain,
    ! [U_17292,U_17291] : c_List_Opartition(U_17291,U_17292,c_List_Olist_ONil(U_17291)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17291),tc_List_Olist(U_17291)),c_List_Olist_ONil(U_17291)),c_List_Olist_ONil(U_17291)),
    inference(variable_rename,[status(thm)],[f_4269_1]) ).

cnf(f_4269_3,plain,
    c_List_Opartition(U_17291,U_17292,c_List_Olist_ONil(U_17291)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17291),tc_List_Olist(U_17291)),c_List_Olist_ONil(U_17291)),c_List_Olist_ONil(U_17291)),
    inference(clausify,[status(thm)],[f_4269_2]) ).

fof(f_4270_1,plain,
    ! [V_xs_2,V_x_2,V_P_2,T_b] : c_List_Opartition(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_fun(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_List_Olist(T_b)),c_COMBS(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_List_Olist(T_b)),hAPP(c_If(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(V_P_2,V_x_2)))),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_List_Olist(T_b)),c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(c_List_Olist_OCons(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_List_Olist(T_b)),c_COMBB(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_List_Olist(T_b))),c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(c_List_Olist_OCons(T_b),V_x_2)))),c_List_Opartition(T_b,V_P_2,V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_partition_Osimps_I2_J]) ).

fof(f_4270_2,plain,
    ! [U_17296,U_17295,U_17294,U_17293] : c_List_Opartition(U_17293,U_17294,hAPP(hAPP(c_List_Olist_OCons(U_17293),U_17295),U_17296)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_17293),tc_List_Olist(U_17293),tc_prod(tc_List_Olist(U_17293),tc_List_Olist(U_17293))),hAPP(hAPP(c_COMBS(tc_List_Olist(U_17293),tc_fun(tc_List_Olist(U_17293),tc_prod(tc_List_Olist(U_17293),tc_List_Olist(U_17293))),tc_fun(tc_List_Olist(U_17293),tc_prod(tc_List_Olist(U_17293),tc_List_Olist(U_17293)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_17293),tc_fun(tc_prod(tc_List_Olist(U_17293),tc_List_Olist(U_17293)),tc_prod(tc_List_Olist(U_17293),tc_List_Olist(U_17293)))),tc_fun(tc_fun(tc_List_Olist(U_17293),tc_prod(tc_List_Olist(U_17293),tc_List_Olist(U_17293))),tc_fun(tc_List_Olist(U_17293),tc_prod(tc_List_Olist(U_17293),tc_List_Olist(U_17293)))),tc_List_Olist(U_17293)),c_COMBS(tc_List_Olist(U_17293),tc_prod(tc_List_Olist(U_17293),tc_List_Olist(U_17293)),tc_prod(tc_List_Olist(U_17293),tc_List_Olist(U_17293)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_17293),tc_prod(tc_List_Olist(U_17293),tc_List_Olist(U_17293))),tc_fun(tc_List_Olist(U_17293),tc_fun(tc_prod(tc_List_Olist(U_17293),tc_List_Olist(U_17293)),tc_prod(tc_List_Olist(U_17293),tc_List_Olist(U_17293)))),tc_List_Olist(U_17293)),hAPP(c_COMBB(tc_prod(tc_List_Olist(U_17293),tc_List_Olist(U_17293)),tc_fun(tc_prod(tc_List_Olist(U_17293),tc_List_Olist(U_17293)),tc_prod(tc_List_Olist(U_17293),tc_List_Olist(U_17293))),tc_List_Olist(U_17293)),hAPP(c_If(tc_prod(tc_List_Olist(U_17293),tc_List_Olist(U_17293))),hAPP(U_17294,U_17295)))),hAPP(hAPP(c_COMBB(tc_List_Olist(U_17293),tc_fun(tc_List_Olist(U_17293),tc_prod(tc_List_Olist(U_17293),tc_List_Olist(U_17293))),tc_List_Olist(U_17293)),c_Product__Type_OPair(tc_List_Olist(U_17293),tc_List_Olist(U_17293))),hAPP(c_List_Olist_OCons(U_17293),U_17295))))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17293),tc_fun(tc_List_Olist(U_17293),tc_List_Olist(U_17293)),tc_fun(tc_List_Olist(U_17293),tc_prod(tc_List_Olist(U_17293),tc_List_Olist(U_17293)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_17293),tc_prod(tc_List_Olist(U_17293),tc_List_Olist(U_17293))),tc_fun(tc_fun(tc_List_Olist(U_17293),tc_List_Olist(U_17293)),tc_fun(tc_List_Olist(U_17293),tc_prod(tc_List_Olist(U_17293),tc_List_Olist(U_17293)))),tc_List_Olist(U_17293)),c_COMBB(tc_List_Olist(U_17293),tc_prod(tc_List_Olist(U_17293),tc_List_Olist(U_17293)),tc_List_Olist(U_17293))),c_Product__Type_OPair(tc_List_Olist(U_17293),tc_List_Olist(U_17293)))),hAPP(c_List_Olist_OCons(U_17293),U_17295)))),c_List_Opartition(U_17293,U_17294,U_17296)),
    inference(variable_rename,[status(thm)],[f_4270_1]) ).

cnf(f_4270_3,plain,
    c_List_Opartition(U_17293,U_17294,hAPP(hAPP(c_List_Olist_OCons(U_17293),U_17295),U_17296)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_17293),tc_List_Olist(U_17293),tc_prod(tc_List_Olist(U_17293),tc_List_Olist(U_17293))),hAPP(hAPP(c_COMBS(tc_List_Olist(U_17293),tc_fun(tc_List_Olist(U_17293),tc_prod(tc_List_Olist(U_17293),tc_List_Olist(U_17293))),tc_fun(tc_List_Olist(U_17293),tc_prod(tc_List_Olist(U_17293),tc_List_Olist(U_17293)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_17293),tc_fun(tc_prod(tc_List_Olist(U_17293),tc_List_Olist(U_17293)),tc_prod(tc_List_Olist(U_17293),tc_List_Olist(U_17293)))),tc_fun(tc_fun(tc_List_Olist(U_17293),tc_prod(tc_List_Olist(U_17293),tc_List_Olist(U_17293))),tc_fun(tc_List_Olist(U_17293),tc_prod(tc_List_Olist(U_17293),tc_List_Olist(U_17293)))),tc_List_Olist(U_17293)),c_COMBS(tc_List_Olist(U_17293),tc_prod(tc_List_Olist(U_17293),tc_List_Olist(U_17293)),tc_prod(tc_List_Olist(U_17293),tc_List_Olist(U_17293)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_17293),tc_prod(tc_List_Olist(U_17293),tc_List_Olist(U_17293))),tc_fun(tc_List_Olist(U_17293),tc_fun(tc_prod(tc_List_Olist(U_17293),tc_List_Olist(U_17293)),tc_prod(tc_List_Olist(U_17293),tc_List_Olist(U_17293)))),tc_List_Olist(U_17293)),hAPP(c_COMBB(tc_prod(tc_List_Olist(U_17293),tc_List_Olist(U_17293)),tc_fun(tc_prod(tc_List_Olist(U_17293),tc_List_Olist(U_17293)),tc_prod(tc_List_Olist(U_17293),tc_List_Olist(U_17293))),tc_List_Olist(U_17293)),hAPP(c_If(tc_prod(tc_List_Olist(U_17293),tc_List_Olist(U_17293))),hAPP(U_17294,U_17295)))),hAPP(hAPP(c_COMBB(tc_List_Olist(U_17293),tc_fun(tc_List_Olist(U_17293),tc_prod(tc_List_Olist(U_17293),tc_List_Olist(U_17293))),tc_List_Olist(U_17293)),c_Product__Type_OPair(tc_List_Olist(U_17293),tc_List_Olist(U_17293))),hAPP(c_List_Olist_OCons(U_17293),U_17295))))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17293),tc_fun(tc_List_Olist(U_17293),tc_List_Olist(U_17293)),tc_fun(tc_List_Olist(U_17293),tc_prod(tc_List_Olist(U_17293),tc_List_Olist(U_17293)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_17293),tc_prod(tc_List_Olist(U_17293),tc_List_Olist(U_17293))),tc_fun(tc_fun(tc_List_Olist(U_17293),tc_List_Olist(U_17293)),tc_fun(tc_List_Olist(U_17293),tc_prod(tc_List_Olist(U_17293),tc_List_Olist(U_17293)))),tc_List_Olist(U_17293)),c_COMBB(tc_List_Olist(U_17293),tc_prod(tc_List_Olist(U_17293),tc_List_Olist(U_17293)),tc_List_Olist(U_17293))),c_Product__Type_OPair(tc_List_Olist(U_17293),tc_List_Olist(U_17293)))),hAPP(c_List_Olist_OCons(U_17293),U_17295)))),c_List_Opartition(U_17293,U_17294,U_17296)),
    inference(clausify,[status(thm)],[f_4270_2]) ).

fof(f_4271_1,plain,
    ! [V_B_2,V_A_2,T_b] : c_List_Olistsp(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(T_b))),c_List_Olists(T_b,V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(T_b))),c_List_Olists(T_b,V_B_2))),
    inference(fof_nnf,[status(thm)],[fact_lists__Int__eq]) ).

fof(f_4271_2,plain,
    ! [U_17299,U_17298,U_17297] : c_List_Olistsp(U_17297,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17297,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_17297,tc_fun(U_17297,tc_HOL_Obool),tc_HOL_Obool),c_member(U_17297)),U_17298)),hAPP(hAPP(c_COMBC(U_17297,tc_fun(U_17297,tc_HOL_Obool),tc_HOL_Obool),c_member(U_17297)),U_17299))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(U_17297),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17297),tc_fun(tc_List_Olist(U_17297),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(U_17297))),c_List_Olists(U_17297,U_17298))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17297),tc_fun(tc_List_Olist(U_17297),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(U_17297))),c_List_Olists(U_17297,U_17299))),
    inference(variable_rename,[status(thm)],[f_4271_1]) ).

cnf(f_4271_3,plain,
    c_List_Olistsp(U_17297,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17297,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_17297,tc_fun(U_17297,tc_HOL_Obool),tc_HOL_Obool),c_member(U_17297)),U_17298)),hAPP(hAPP(c_COMBC(U_17297,tc_fun(U_17297,tc_HOL_Obool),tc_HOL_Obool),c_member(U_17297)),U_17299))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(U_17297),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17297),tc_fun(tc_List_Olist(U_17297),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(U_17297))),c_List_Olists(U_17297,U_17298))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17297),tc_fun(tc_List_Olist(U_17297),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(U_17297))),c_List_Olists(U_17297,U_17299))),
    inference(clausify,[status(thm)],[f_4271_2]) ).

fof(f_4272_1,plain,
    ! [V_B_2,V_A_2,V_l_2,T_b] :
      ( hBOOL(hAPP(c_List_Olistsp(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_l_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_l_2),c_List_Olists(T_b,V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_l_2),c_List_Olists(T_b,V_A_2))) ),
    inference(fof_nnf,[status(thm)],[fact_lists__IntI]) ).

fof(f_4272_2,plain,
    ! [U_17303,U_17302,U_17301,U_17300] :
      ( hBOOL(hAPP(c_List_Olistsp(U_17300,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17300,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_17300,tc_fun(U_17300,tc_HOL_Obool),tc_HOL_Obool),c_member(U_17300)),U_17302)),hAPP(hAPP(c_COMBC(U_17300,tc_fun(U_17300,tc_HOL_Obool),tc_HOL_Obool),c_member(U_17300)),U_17303))),U_17301))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17300)),U_17301),c_List_Olists(U_17300,U_17303)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17300)),U_17301),c_List_Olists(U_17300,U_17302))) ),
    inference(variable_rename,[status(thm)],[f_4272_1]) ).

cnf(f_4272_3,plain,
    ( hBOOL(hAPP(c_List_Olistsp(U_17300,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17300,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_17300,tc_fun(U_17300,tc_HOL_Obool),tc_HOL_Obool),c_member(U_17300)),U_17302)),hAPP(hAPP(c_COMBC(U_17300,tc_fun(U_17300,tc_HOL_Obool),tc_HOL_Obool),c_member(U_17300)),U_17303))),U_17301))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17300)),U_17301),c_List_Olists(U_17300,U_17303)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17300)),U_17301),c_List_Olists(U_17300,U_17302))) ),
    inference(clausify,[status(thm)],[f_4272_2]) ).

fof(f_4273_1,plain,
    ! [V_A_2,T_b] : hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),c_List_Olist_ONil(T_b))),
    inference(fof_nnf,[status(thm)],[fact_listsp_ONil]) ).

fof(f_4273_2,plain,
    ! [U_17305,U_17304] : hBOOL(hAPP(c_List_Olistsp(U_17304,U_17305),c_List_Olist_ONil(U_17304))),
    inference(variable_rename,[status(thm)],[f_4273_1]) ).

cnf(f_4273_3,plain,
    hBOOL(hAPP(c_List_Olistsp(U_17304,U_17305),c_List_Olist_ONil(U_17304))),
    inference(clausify,[status(thm)],[f_4273_2]) ).

fof(f_4274_1,plain,
    ! [V_A_2,T_b] : hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),c_List_Olist_ONil(T_b))),
    inference(fof_nnf,[status(thm)],[fact_listsp_Oequations_I1_J]) ).

fof(f_4274_2,plain,
    ! [U_17307,U_17306] : hBOOL(hAPP(c_List_Olistsp(U_17306,U_17307),c_List_Olist_ONil(U_17306))),
    inference(variable_rename,[status(thm)],[f_4274_1]) ).

cnf(f_4274_3,plain,
    hBOOL(hAPP(c_List_Olistsp(U_17306,U_17307),c_List_Olist_ONil(U_17306))),
    inference(clausify,[status(thm)],[f_4274_2]) ).

fof(f_4275_1,plain,
    ! [V_xs_2,V_A_2,T_b] :
      ( ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_xs_2))
        | ? [B_x] :
            ( ~ hBOOL(hAPP(V_A_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) ) )
      & ( ! [B_x] :
            ( hBOOL(hAPP(V_A_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) )
        | ~ hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_xs_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_in__listsp__conv__set]) ).

fof(f_4275_2,plain,
    ! [U_17312,U_17311,U_17310] :
      ( ( hBOOL(hAPP(c_List_Olistsp(U_17310,U_17311),U_17312))
        | ? [U_17309] :
            ( ~ hBOOL(hAPP(U_17311,U_17309))
            & hBOOL(hAPP(hAPP(c_member(U_17310),U_17309),hAPP(c_List_Oset(U_17310),U_17312))) ) )
      & ( ! [U_17308] :
            ( hBOOL(hAPP(U_17311,U_17308))
            | ~ hBOOL(hAPP(hAPP(c_member(U_17310),U_17308),hAPP(c_List_Oset(U_17310),U_17312))) )
        | ~ hBOOL(hAPP(c_List_Olistsp(U_17310,U_17311),U_17312)) ) ),
    inference(variable_rename,[status(thm)],[f_4275_1]) ).

fof(f_4275_3,plain,
    ( ! [U_17318,U_17316,U_17314] :
        ( hBOOL(hAPP(c_List_Olistsp(U_17314,U_17316),U_17318))
        | ? [U_17309] :
            ( ~ hBOOL(hAPP(U_17316,U_17309))
            & hBOOL(hAPP(hAPP(c_member(U_17314),U_17309),hAPP(c_List_Oset(U_17314),U_17318))) ) )
    & ! [U_17317,U_17315,U_17313] :
        ( ! [U_17308] :
            ( hBOOL(hAPP(U_17315,U_17308))
            | ~ hBOOL(hAPP(hAPP(c_member(U_17313),U_17308),hAPP(c_List_Oset(U_17313),U_17317))) )
        | ~ hBOOL(hAPP(c_List_Olistsp(U_17313,U_17315),U_17317)) ) ),
    inference(miniscope,[status(thm)],[f_4275_2]) ).

fof(f_4275_4,plain,
    ( ! [U_17318,U_17316,U_17314] :
        ( hBOOL(hAPP(c_List_Olistsp(U_17314,U_17316),U_17318))
        | ( ~ hBOOL(hAPP(U_17316,sK437(U_17318,U_17316,U_17314)))
          & hBOOL(hAPP(hAPP(c_member(U_17314),sK437(U_17318,U_17316,U_17314)),hAPP(c_List_Oset(U_17314),U_17318))) ) )
    & ! [U_17317,U_17315,U_17313] :
        ( ! [U_17308] :
            ( hBOOL(hAPP(U_17315,U_17308))
            | ~ hBOOL(hAPP(hAPP(c_member(U_17313),U_17308),hAPP(c_List_Oset(U_17313),U_17317))) )
        | ~ hBOOL(hAPP(c_List_Olistsp(U_17313,U_17315),U_17317)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK437]),skolemize(U_17309,sK437(U_17318,U_17316,U_17314))],[f_4275_3]) ).

cnf(f_4275_5,plain,
    ( hBOOL(hAPP(U_17315,U_17308))
    | ~ hBOOL(hAPP(hAPP(c_member(U_17313),U_17308),hAPP(c_List_Oset(U_17313),U_17317)))
    | ~ hBOOL(hAPP(c_List_Olistsp(U_17313,U_17315),U_17317)) ),
    inference(clausify,[status(thm)],[f_4275_4]) ).

cnf(f_4275_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_17314),sK437(U_17318,U_17316,U_17314)),hAPP(c_List_Oset(U_17314),U_17318)))
    | hBOOL(hAPP(c_List_Olistsp(U_17314,U_17316),U_17318)) ),
    inference(clausify,[status(thm)],[f_4275_4]) ).

cnf(f_4275_7,plain,
    ( ~ hBOOL(hAPP(U_17316,sK437(U_17318,U_17316,U_17314)))
    | hBOOL(hAPP(c_List_Olistsp(U_17314,U_17316),U_17318)) ),
    inference(clausify,[status(thm)],[f_4275_4]) ).

fof(f_4276_1,plain,
    ! [V_x_2,V_B_2,V_A_2,T_b] :
      ( ( hBOOL(hAPP(c_List_Olistsp(T_b,hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_A_2)),V_B_2)),V_x_2))
        | ~ hBOOL(hAPP(c_List_Olistsp(T_b,V_B_2),V_x_2))
        | ~ hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_x_2)) )
      & ( ( hBOOL(hAPP(c_List_Olistsp(T_b,V_B_2),V_x_2))
          & hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_x_2)) )
        | ~ hBOOL(hAPP(c_List_Olistsp(T_b,hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_A_2)),V_B_2)),V_x_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_listsp__conj__eq]) ).

fof(f_4276_2,plain,
    ! [U_17322,U_17321,U_17320,U_17319] :
      ( ( hBOOL(hAPP(c_List_Olistsp(U_17319,hAPP(hAPP(c_COMBS(U_17319,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_17319),c_fconj),U_17320)),U_17321)),U_17322))
        | ~ hBOOL(hAPP(c_List_Olistsp(U_17319,U_17321),U_17322))
        | ~ hBOOL(hAPP(c_List_Olistsp(U_17319,U_17320),U_17322)) )
      & ( ( hBOOL(hAPP(c_List_Olistsp(U_17319,U_17321),U_17322))
          & hBOOL(hAPP(c_List_Olistsp(U_17319,U_17320),U_17322)) )
        | ~ hBOOL(hAPP(c_List_Olistsp(U_17319,hAPP(hAPP(c_COMBS(U_17319,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_17319),c_fconj),U_17320)),U_17321)),U_17322)) ) ),
    inference(variable_rename,[status(thm)],[f_4276_1]) ).

fof(f_4276_3,plain,
    ( ! [U_17330,U_17328,U_17326,U_17324] :
        ( hBOOL(hAPP(c_List_Olistsp(U_17324,hAPP(hAPP(c_COMBS(U_17324,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_17324),c_fconj),U_17326)),U_17328)),U_17330))
        | ~ hBOOL(hAPP(c_List_Olistsp(U_17324,U_17328),U_17330))
        | ~ hBOOL(hAPP(c_List_Olistsp(U_17324,U_17326),U_17330)) )
    & ! [U_17329,U_17327,U_17325,U_17323] :
        ( ( hBOOL(hAPP(c_List_Olistsp(U_17323,U_17327),U_17329))
          & hBOOL(hAPP(c_List_Olistsp(U_17323,U_17325),U_17329)) )
        | ~ hBOOL(hAPP(c_List_Olistsp(U_17323,hAPP(hAPP(c_COMBS(U_17323,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_17323),c_fconj),U_17325)),U_17327)),U_17329)) ) ),
    inference(miniscope,[status(thm)],[f_4276_2]) ).

cnf(f_4276_4,plain,
    ( hBOOL(hAPP(c_List_Olistsp(U_17323,U_17325),U_17329))
    | ~ hBOOL(hAPP(c_List_Olistsp(U_17323,hAPP(hAPP(c_COMBS(U_17323,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_17323),c_fconj),U_17325)),U_17327)),U_17329)) ),
    inference(clausify,[status(thm)],[f_4276_3]) ).

cnf(f_4276_5,plain,
    ( hBOOL(hAPP(c_List_Olistsp(U_17323,U_17327),U_17329))
    | ~ hBOOL(hAPP(c_List_Olistsp(U_17323,hAPP(hAPP(c_COMBS(U_17323,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_17323),c_fconj),U_17325)),U_17327)),U_17329)) ),
    inference(clausify,[status(thm)],[f_4276_3]) ).

cnf(f_4276_6,plain,
    ( hBOOL(hAPP(c_List_Olistsp(U_17324,hAPP(hAPP(c_COMBS(U_17324,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_17324),c_fconj),U_17326)),U_17328)),U_17330))
    | ~ hBOOL(hAPP(c_List_Olistsp(U_17324,U_17328),U_17330))
    | ~ hBOOL(hAPP(c_List_Olistsp(U_17324,U_17326),U_17330)) ),
    inference(clausify,[status(thm)],[f_4276_3]) ).

fof(f_4277_1,plain,
    ! [V_B_2,V_l_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_List_Olistsp(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_l_2))
      | ~ hBOOL(hAPP(c_List_Olistsp(T_b,V_B_2),V_l_2))
      | ~ hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_l_2)) ),
    inference(fof_nnf,[status(thm)],[fact_listsp__infI]) ).

fof(f_4277_2,plain,
    ! [U_17334,U_17333,U_17332,U_17331] :
      ( hBOOL(hAPP(c_List_Olistsp(U_17331,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17331,tc_HOL_Obool)),U_17332),U_17334)),U_17333))
      | ~ hBOOL(hAPP(c_List_Olistsp(U_17331,U_17334),U_17333))
      | ~ hBOOL(hAPP(c_List_Olistsp(U_17331,U_17332),U_17333)) ),
    inference(variable_rename,[status(thm)],[f_4277_1]) ).

cnf(f_4277_3,plain,
    ( hBOOL(hAPP(c_List_Olistsp(U_17331,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17331,tc_HOL_Obool)),U_17332),U_17334)),U_17333))
    | ~ hBOOL(hAPP(c_List_Olistsp(U_17331,U_17334),U_17333))
    | ~ hBOOL(hAPP(c_List_Olistsp(U_17331,U_17332),U_17333)) ),
    inference(clausify,[status(thm)],[f_4277_2]) ).

fof(f_4278_1,plain,
    ! [V_B_2,V_A_2,T_b] : c_List_Olistsp(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),c_List_Olistsp(T_b,V_A_2)),c_List_Olistsp(T_b,V_B_2)),
    inference(fof_nnf,[status(thm)],[fact_listsp__inf__eq]) ).

fof(f_4278_2,plain,
    ! [U_17337,U_17336,U_17335] : c_List_Olistsp(U_17335,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17335,tc_HOL_Obool)),U_17336),U_17337)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(U_17335),tc_HOL_Obool)),c_List_Olistsp(U_17335,U_17336)),c_List_Olistsp(U_17335,U_17337)),
    inference(variable_rename,[status(thm)],[f_4278_1]) ).

cnf(f_4278_3,plain,
    c_List_Olistsp(U_17335,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17335,tc_HOL_Obool)),U_17336),U_17337)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(U_17335),tc_HOL_Obool)),c_List_Olistsp(U_17335,U_17336)),c_List_Olistsp(U_17335,U_17337)),
    inference(clausify,[status(thm)],[f_4278_2]) ).

fof(f_4279_1,plain,
    ! [V_a2_2,V_a1_2,V_A_2,T_b] :
      ( ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a1_2),V_a2_2)))
        | ~ hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_a2_2))
        | ~ hBOOL(hAPP(V_A_2,V_a1_2)) )
      & ( ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_a2_2))
          & hBOOL(hAPP(V_A_2,V_a1_2)) )
        | ~ hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a1_2),V_a2_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_listsp_Oequations_I2_J]) ).

fof(f_4279_2,plain,
    ! [U_17341,U_17340,U_17339,U_17338] :
      ( ( hBOOL(hAPP(c_List_Olistsp(U_17338,U_17339),hAPP(hAPP(c_List_Olist_OCons(U_17338),U_17340),U_17341)))
        | ~ hBOOL(hAPP(c_List_Olistsp(U_17338,U_17339),U_17341))
        | ~ hBOOL(hAPP(U_17339,U_17340)) )
      & ( ( hBOOL(hAPP(c_List_Olistsp(U_17338,U_17339),U_17341))
          & hBOOL(hAPP(U_17339,U_17340)) )
        | ~ hBOOL(hAPP(c_List_Olistsp(U_17338,U_17339),hAPP(hAPP(c_List_Olist_OCons(U_17338),U_17340),U_17341))) ) ),
    inference(variable_rename,[status(thm)],[f_4279_1]) ).

fof(f_4279_3,plain,
    ( ! [U_17349,U_17347,U_17345,U_17343] :
        ( hBOOL(hAPP(c_List_Olistsp(U_17343,U_17345),hAPP(hAPP(c_List_Olist_OCons(U_17343),U_17347),U_17349)))
        | ~ hBOOL(hAPP(c_List_Olistsp(U_17343,U_17345),U_17349))
        | ~ hBOOL(hAPP(U_17345,U_17347)) )
    & ! [U_17348,U_17346,U_17344,U_17342] :
        ( ( hBOOL(hAPP(c_List_Olistsp(U_17342,U_17344),U_17348))
          & hBOOL(hAPP(U_17344,U_17346)) )
        | ~ hBOOL(hAPP(c_List_Olistsp(U_17342,U_17344),hAPP(hAPP(c_List_Olist_OCons(U_17342),U_17346),U_17348))) ) ),
    inference(miniscope,[status(thm)],[f_4279_2]) ).

cnf(f_4279_4,plain,
    ( hBOOL(hAPP(U_17344,U_17346))
    | ~ hBOOL(hAPP(c_List_Olistsp(U_17342,U_17344),hAPP(hAPP(c_List_Olist_OCons(U_17342),U_17346),U_17348))) ),
    inference(clausify,[status(thm)],[f_4279_3]) ).

cnf(f_4279_5,plain,
    ( hBOOL(hAPP(c_List_Olistsp(U_17342,U_17344),U_17348))
    | ~ hBOOL(hAPP(c_List_Olistsp(U_17342,U_17344),hAPP(hAPP(c_List_Olist_OCons(U_17342),U_17346),U_17348))) ),
    inference(clausify,[status(thm)],[f_4279_3]) ).

cnf(f_4279_6,plain,
    ( hBOOL(hAPP(c_List_Olistsp(U_17343,U_17345),hAPP(hAPP(c_List_Olist_OCons(U_17343),U_17347),U_17349)))
    | ~ hBOOL(hAPP(c_List_Olistsp(U_17343,U_17345),U_17349))
    | ~ hBOOL(hAPP(U_17345,U_17347)) ),
    inference(clausify,[status(thm)],[f_4279_3]) ).

fof(f_4280_1,plain,
    ! [V_ys_2,V_xs_2,V_A_2,T_b] :
      ( ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)))
        | ~ hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_ys_2))
        | ~ hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_xs_2)) )
      & ( ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_ys_2))
          & hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_xs_2)) )
        | ~ hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_append__in__listsp__conv]) ).

fof(f_4280_2,plain,
    ! [U_17353,U_17352,U_17351,U_17350] :
      ( ( hBOOL(hAPP(c_List_Olistsp(U_17350,U_17351),hAPP(hAPP(c_List_Oappend(U_17350),U_17352),U_17353)))
        | ~ hBOOL(hAPP(c_List_Olistsp(U_17350,U_17351),U_17353))
        | ~ hBOOL(hAPP(c_List_Olistsp(U_17350,U_17351),U_17352)) )
      & ( ( hBOOL(hAPP(c_List_Olistsp(U_17350,U_17351),U_17353))
          & hBOOL(hAPP(c_List_Olistsp(U_17350,U_17351),U_17352)) )
        | ~ hBOOL(hAPP(c_List_Olistsp(U_17350,U_17351),hAPP(hAPP(c_List_Oappend(U_17350),U_17352),U_17353))) ) ),
    inference(variable_rename,[status(thm)],[f_4280_1]) ).

fof(f_4280_3,plain,
    ( ! [U_17361,U_17359,U_17357,U_17355] :
        ( hBOOL(hAPP(c_List_Olistsp(U_17355,U_17357),hAPP(hAPP(c_List_Oappend(U_17355),U_17359),U_17361)))
        | ~ hBOOL(hAPP(c_List_Olistsp(U_17355,U_17357),U_17361))
        | ~ hBOOL(hAPP(c_List_Olistsp(U_17355,U_17357),U_17359)) )
    & ! [U_17360,U_17358,U_17356,U_17354] :
        ( ( hBOOL(hAPP(c_List_Olistsp(U_17354,U_17356),U_17360))
          & hBOOL(hAPP(c_List_Olistsp(U_17354,U_17356),U_17358)) )
        | ~ hBOOL(hAPP(c_List_Olistsp(U_17354,U_17356),hAPP(hAPP(c_List_Oappend(U_17354),U_17358),U_17360))) ) ),
    inference(miniscope,[status(thm)],[f_4280_2]) ).

cnf(f_4280_4,plain,
    ( hBOOL(hAPP(c_List_Olistsp(U_17354,U_17356),U_17358))
    | ~ hBOOL(hAPP(c_List_Olistsp(U_17354,U_17356),hAPP(hAPP(c_List_Oappend(U_17354),U_17358),U_17360))) ),
    inference(clausify,[status(thm)],[f_4280_3]) ).

cnf(f_4280_5,plain,
    ( hBOOL(hAPP(c_List_Olistsp(U_17354,U_17356),U_17360))
    | ~ hBOOL(hAPP(c_List_Olistsp(U_17354,U_17356),hAPP(hAPP(c_List_Oappend(U_17354),U_17358),U_17360))) ),
    inference(clausify,[status(thm)],[f_4280_3]) ).

cnf(f_4280_6,plain,
    ( hBOOL(hAPP(c_List_Olistsp(U_17355,U_17357),hAPP(hAPP(c_List_Oappend(U_17355),U_17359),U_17361)))
    | ~ hBOOL(hAPP(c_List_Olistsp(U_17355,U_17357),U_17361))
    | ~ hBOOL(hAPP(c_List_Olistsp(U_17355,U_17357),U_17359)) ),
    inference(clausify,[status(thm)],[f_4280_3]) ).

fof(f_4281_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),c_List_Olistsp(T_b,V_A_2)),c_List_Olistsp(T_b,V_B_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
    inference(fof_nnf,[status(thm)],[fact_listsp__mono]) ).

fof(f_4281_2,plain,
    ! [U_17364,U_17363,U_17362] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(U_17362),tc_HOL_Obool)),c_List_Olistsp(U_17362,U_17363)),c_List_Olistsp(U_17362,U_17364)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17362,tc_HOL_Obool)),U_17363),U_17364)) ),
    inference(variable_rename,[status(thm)],[f_4281_1]) ).

cnf(f_4281_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(U_17362),tc_HOL_Obool)),c_List_Olistsp(U_17362,U_17363)),c_List_Olistsp(U_17362,U_17364)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17362,tc_HOL_Obool)),U_17363),U_17364)) ),
    inference(clausify,[status(thm)],[f_4281_2]) ).

fof(f_4282_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( ( hBOOL(hAPP(c_List_Olistsp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)),V_x_2))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_x_2),c_List_Olists(T_b,V_A_2))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_x_2),c_List_Olists(T_b,V_A_2)))
        | ~ hBOOL(hAPP(c_List_Olistsp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)),V_x_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_listsp__lists__eq]) ).

fof(f_4282_2,plain,
    ! [U_17367,U_17366,U_17365] :
      ( ( hBOOL(hAPP(c_List_Olistsp(U_17365,hAPP(hAPP(c_COMBC(U_17365,tc_fun(U_17365,tc_HOL_Obool),tc_HOL_Obool),c_member(U_17365)),U_17366)),U_17367))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17365)),U_17367),c_List_Olists(U_17365,U_17366))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17365)),U_17367),c_List_Olists(U_17365,U_17366)))
        | ~ hBOOL(hAPP(c_List_Olistsp(U_17365,hAPP(hAPP(c_COMBC(U_17365,tc_fun(U_17365,tc_HOL_Obool),tc_HOL_Obool),c_member(U_17365)),U_17366)),U_17367)) ) ),
    inference(variable_rename,[status(thm)],[f_4282_1]) ).

fof(f_4282_3,plain,
    ( ! [U_17373,U_17371,U_17369] :
        ( hBOOL(hAPP(c_List_Olistsp(U_17369,hAPP(hAPP(c_COMBC(U_17369,tc_fun(U_17369,tc_HOL_Obool),tc_HOL_Obool),c_member(U_17369)),U_17371)),U_17373))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17369)),U_17373),c_List_Olists(U_17369,U_17371))) )
    & ! [U_17372,U_17370,U_17368] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17368)),U_17372),c_List_Olists(U_17368,U_17370)))
        | ~ hBOOL(hAPP(c_List_Olistsp(U_17368,hAPP(hAPP(c_COMBC(U_17368,tc_fun(U_17368,tc_HOL_Obool),tc_HOL_Obool),c_member(U_17368)),U_17370)),U_17372)) ) ),
    inference(miniscope,[status(thm)],[f_4282_2]) ).

cnf(f_4282_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17368)),U_17372),c_List_Olists(U_17368,U_17370)))
    | ~ hBOOL(hAPP(c_List_Olistsp(U_17368,hAPP(hAPP(c_COMBC(U_17368,tc_fun(U_17368,tc_HOL_Obool),tc_HOL_Obool),c_member(U_17368)),U_17370)),U_17372)) ),
    inference(clausify,[status(thm)],[f_4282_3]) ).

cnf(f_4282_5,plain,
    ( hBOOL(hAPP(c_List_Olistsp(U_17369,hAPP(hAPP(c_COMBC(U_17369,tc_fun(U_17369,tc_HOL_Obool),tc_HOL_Obool),c_member(U_17369)),U_17371)),U_17373))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17369)),U_17373),c_List_Olists(U_17369,U_17371))) ),
    inference(clausify,[status(thm)],[f_4282_3]) ).

fof(f_4283_1,plain,
    ! [V_ys_2,V_xs_2,V_x_2,T_c,T_b] : c_Enum_Oproduct(T_b,T_c,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Omap(T_c,tc_prod(T_b,T_c)),hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2)),V_ys_2)),c_Enum_Oproduct(T_b,T_c,V_xs_2,V_ys_2)),
    inference(fof_nnf,[status(thm)],[fact_product_Osimps_I2_J]) ).

fof(f_4283_2,plain,
    ! [U_17378,U_17377,U_17376,U_17375,U_17374] : c_Enum_Oproduct(U_17374,U_17375,hAPP(hAPP(c_List_Olist_OCons(U_17374),U_17376),U_17377),U_17378) = hAPP(hAPP(c_List_Oappend(tc_prod(U_17374,U_17375)),hAPP(hAPP(c_List_Omap(U_17375,tc_prod(U_17374,U_17375)),hAPP(c_Product__Type_OPair(U_17374,U_17375),U_17376)),U_17378)),c_Enum_Oproduct(U_17374,U_17375,U_17377,U_17378)),
    inference(variable_rename,[status(thm)],[f_4283_1]) ).

cnf(f_4283_3,plain,
    c_Enum_Oproduct(U_17374,U_17375,hAPP(hAPP(c_List_Olist_OCons(U_17374),U_17376),U_17377),U_17378) = hAPP(hAPP(c_List_Oappend(tc_prod(U_17374,U_17375)),hAPP(hAPP(c_List_Omap(U_17375,tc_prod(U_17374,U_17375)),hAPP(c_Product__Type_OPair(U_17374,U_17375),U_17376)),U_17378)),c_Enum_Oproduct(U_17374,U_17375,U_17377,U_17378)),
    inference(clausify,[status(thm)],[f_4283_2]) ).

fof(f_4284_1,plain,
    ! [V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
      ( ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
        | ? [B_x] :
            ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_P_2),B_x))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),B_x),hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2) )
      & ( ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_P_2),B_x))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),B_x),hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2) )
        | ~ c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__all2__def]) ).

fof(f_4284_2,plain,
    ! [U_17385,U_17384,U_17383,U_17382,U_17381] :
      ( ( c_List_Olist__all2(U_17381,U_17382,U_17383,U_17384,U_17385)
        | ? [U_17380] :
            ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_17381,U_17382,tc_HOL_Obool),U_17383),U_17380))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_17381,U_17382)),U_17380),hAPP(c_List_Oset(tc_prod(U_17381,U_17382)),hAPP(hAPP(c_List_Ozip(U_17381,U_17382),U_17384),U_17385)))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17381)),U_17384) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17382)),U_17385) )
      & ( ( ! [U_17379] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_17381,U_17382,tc_HOL_Obool),U_17383),U_17379))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17381,U_17382)),U_17379),hAPP(c_List_Oset(tc_prod(U_17381,U_17382)),hAPP(hAPP(c_List_Ozip(U_17381,U_17382),U_17384),U_17385)))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17381)),U_17384) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17382)),U_17385) )
        | ~ c_List_Olist__all2(U_17381,U_17382,U_17383,U_17384,U_17385) ) ),
    inference(variable_rename,[status(thm)],[f_4284_1]) ).

fof(f_4284_3,plain,
    ( ! [U_17395,U_17393,U_17391,U_17389,U_17387] :
        ( c_List_Olist__all2(U_17387,U_17389,U_17391,U_17393,U_17395)
        | ? [U_17380] :
            ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_17387,U_17389,tc_HOL_Obool),U_17391),U_17380))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_17387,U_17389)),U_17380),hAPP(c_List_Oset(tc_prod(U_17387,U_17389)),hAPP(hAPP(c_List_Ozip(U_17387,U_17389),U_17393),U_17395)))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17387)),U_17393) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17389)),U_17395) )
    & ! [U_17394,U_17392,U_17390,U_17388,U_17386] :
        ( ( ! [U_17379] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_17386,U_17388,tc_HOL_Obool),U_17390),U_17379))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17386,U_17388)),U_17379),hAPP(c_List_Oset(tc_prod(U_17386,U_17388)),hAPP(hAPP(c_List_Ozip(U_17386,U_17388),U_17392),U_17394)))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17386)),U_17392) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17388)),U_17394) )
        | ~ c_List_Olist__all2(U_17386,U_17388,U_17390,U_17392,U_17394) ) ),
    inference(miniscope,[status(thm)],[f_4284_2]) ).

fof(f_4284_4,plain,
    ( ! [U_17395,U_17393,U_17391,U_17389,U_17387] :
        ( c_List_Olist__all2(U_17387,U_17389,U_17391,U_17393,U_17395)
        | ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_17387,U_17389,tc_HOL_Obool),U_17391),sK438(U_17395,U_17393,U_17391,U_17389,U_17387)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_17387,U_17389)),sK438(U_17395,U_17393,U_17391,U_17389,U_17387)),hAPP(c_List_Oset(tc_prod(U_17387,U_17389)),hAPP(hAPP(c_List_Ozip(U_17387,U_17389),U_17393),U_17395)))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17387)),U_17393) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17389)),U_17395) )
    & ! [U_17394,U_17392,U_17390,U_17388,U_17386] :
        ( ( ! [U_17379] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_17386,U_17388,tc_HOL_Obool),U_17390),U_17379))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17386,U_17388)),U_17379),hAPP(c_List_Oset(tc_prod(U_17386,U_17388)),hAPP(hAPP(c_List_Ozip(U_17386,U_17388),U_17392),U_17394)))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17386)),U_17392) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17388)),U_17394) )
        | ~ c_List_Olist__all2(U_17386,U_17388,U_17390,U_17392,U_17394) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK438]),skolemize(U_17380,sK438(U_17395,U_17393,U_17391,U_17389,U_17387))],[f_4284_3]) ).

cnf(f_4284_5,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17386)),U_17392) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17388)),U_17394)
    | ~ c_List_Olist__all2(U_17386,U_17388,U_17390,U_17392,U_17394) ),
    inference(clausify,[status(thm)],[f_4284_4]) ).

cnf(f_4284_6,plain,
    ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_17386,U_17388,tc_HOL_Obool),U_17390),U_17379))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17386,U_17388)),U_17379),hAPP(c_List_Oset(tc_prod(U_17386,U_17388)),hAPP(hAPP(c_List_Ozip(U_17386,U_17388),U_17392),U_17394))))
    | ~ c_List_Olist__all2(U_17386,U_17388,U_17390,U_17392,U_17394) ),
    inference(clausify,[status(thm)],[f_4284_4]) ).

cnf(f_4284_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17387,U_17389)),sK438(U_17395,U_17393,U_17391,U_17389,U_17387)),hAPP(c_List_Oset(tc_prod(U_17387,U_17389)),hAPP(hAPP(c_List_Ozip(U_17387,U_17389),U_17393),U_17395))))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17387)),U_17393) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17389)),U_17395)
    | c_List_Olist__all2(U_17387,U_17389,U_17391,U_17393,U_17395) ),
    inference(clausify,[status(thm)],[f_4284_4]) ).

cnf(f_4284_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_17387,U_17389,tc_HOL_Obool),U_17391),sK438(U_17395,U_17393,U_17391,U_17389,U_17387)))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17387)),U_17393) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17389)),U_17395)
    | c_List_Olist__all2(U_17387,U_17389,U_17391,U_17393,U_17395) ),
    inference(clausify,[status(thm)],[f_4284_4]) ).

fof(f_4285_1,plain,
    ! [V_bs_2,V_as_2,V_f_2,T_d,V_P_2,T_c,T_b] :
      ( ( c_List_Olist__all2(T_b,T_c,V_P_2,hAPP(hAPP(c_List_Omap(T_d,T_b),V_f_2),V_as_2),V_bs_2)
        | ~ c_List_Olist__all2(T_d,T_c,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),V_P_2),V_f_2),V_as_2,V_bs_2) )
      & ( c_List_Olist__all2(T_d,T_c,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),V_P_2),V_f_2),V_as_2,V_bs_2)
        | ~ c_List_Olist__all2(T_b,T_c,V_P_2,hAPP(hAPP(c_List_Omap(T_d,T_b),V_f_2),V_as_2),V_bs_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__all2__map1]) ).

fof(f_4285_2,plain,
    ! [U_17402,U_17401,U_17400,U_17399,U_17398,U_17397,U_17396] :
      ( ( c_List_Olist__all2(U_17396,U_17397,U_17398,hAPP(hAPP(c_List_Omap(U_17399,U_17396),U_17400),U_17401),U_17402)
        | ~ c_List_Olist__all2(U_17399,U_17397,hAPP(hAPP(c_COMBB(U_17396,tc_fun(U_17397,tc_HOL_Obool),U_17399),U_17398),U_17400),U_17401,U_17402) )
      & ( c_List_Olist__all2(U_17399,U_17397,hAPP(hAPP(c_COMBB(U_17396,tc_fun(U_17397,tc_HOL_Obool),U_17399),U_17398),U_17400),U_17401,U_17402)
        | ~ c_List_Olist__all2(U_17396,U_17397,U_17398,hAPP(hAPP(c_List_Omap(U_17399,U_17396),U_17400),U_17401),U_17402) ) ),
    inference(variable_rename,[status(thm)],[f_4285_1]) ).

fof(f_4285_3,plain,
    ( ! [U_17416,U_17414,U_17412,U_17410,U_17408,U_17406,U_17404] :
        ( c_List_Olist__all2(U_17404,U_17406,U_17408,hAPP(hAPP(c_List_Omap(U_17410,U_17404),U_17412),U_17414),U_17416)
        | ~ c_List_Olist__all2(U_17410,U_17406,hAPP(hAPP(c_COMBB(U_17404,tc_fun(U_17406,tc_HOL_Obool),U_17410),U_17408),U_17412),U_17414,U_17416) )
    & ! [U_17415,U_17413,U_17411,U_17409,U_17407,U_17405,U_17403] :
        ( c_List_Olist__all2(U_17409,U_17405,hAPP(hAPP(c_COMBB(U_17403,tc_fun(U_17405,tc_HOL_Obool),U_17409),U_17407),U_17411),U_17413,U_17415)
        | ~ c_List_Olist__all2(U_17403,U_17405,U_17407,hAPP(hAPP(c_List_Omap(U_17409,U_17403),U_17411),U_17413),U_17415) ) ),
    inference(miniscope,[status(thm)],[f_4285_2]) ).

cnf(f_4285_4,plain,
    ( c_List_Olist__all2(U_17409,U_17405,hAPP(hAPP(c_COMBB(U_17403,tc_fun(U_17405,tc_HOL_Obool),U_17409),U_17407),U_17411),U_17413,U_17415)
    | ~ c_List_Olist__all2(U_17403,U_17405,U_17407,hAPP(hAPP(c_List_Omap(U_17409,U_17403),U_17411),U_17413),U_17415) ),
    inference(clausify,[status(thm)],[f_4285_3]) ).

cnf(f_4285_5,plain,
    ( c_List_Olist__all2(U_17404,U_17406,U_17408,hAPP(hAPP(c_List_Omap(U_17410,U_17404),U_17412),U_17414),U_17416)
    | ~ c_List_Olist__all2(U_17410,U_17406,hAPP(hAPP(c_COMBB(U_17404,tc_fun(U_17406,tc_HOL_Obool),U_17410),U_17408),U_17412),U_17414,U_17416) ),
    inference(clausify,[status(thm)],[f_4285_3]) ).

fof(f_4286_1,plain,
    ! [V_bs_2,V_f_2,T_d,V_as_2,V_P_2,T_c,T_b] :
      ( ( c_List_Olist__all2(T_b,T_c,V_P_2,V_as_2,hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_bs_2))
        | ~ c_List_Olist__all2(T_b,T_d,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_d,T_c),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_d,T_c),tc_fun(T_d,tc_HOL_Obool)),T_b),c_COMBB(T_c,tc_HOL_Obool,T_d)),V_P_2)),V_f_2),V_as_2,V_bs_2) )
      & ( c_List_Olist__all2(T_b,T_d,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_d,T_c),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_d,T_c),tc_fun(T_d,tc_HOL_Obool)),T_b),c_COMBB(T_c,tc_HOL_Obool,T_d)),V_P_2)),V_f_2),V_as_2,V_bs_2)
        | ~ c_List_Olist__all2(T_b,T_c,V_P_2,V_as_2,hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_bs_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__all2__map2]) ).

fof(f_4286_2,plain,
    ! [U_17423,U_17422,U_17421,U_17420,U_17419,U_17418,U_17417] :
      ( ( c_List_Olist__all2(U_17417,U_17418,U_17419,U_17420,hAPP(hAPP(c_List_Omap(U_17421,U_17418),U_17422),U_17423))
        | ~ c_List_Olist__all2(U_17417,U_17421,hAPP(hAPP(c_COMBC(U_17417,tc_fun(U_17421,U_17418),tc_fun(U_17421,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17418,tc_HOL_Obool),tc_fun(tc_fun(U_17421,U_17418),tc_fun(U_17421,tc_HOL_Obool)),U_17417),c_COMBB(U_17418,tc_HOL_Obool,U_17421)),U_17419)),U_17422),U_17420,U_17423) )
      & ( c_List_Olist__all2(U_17417,U_17421,hAPP(hAPP(c_COMBC(U_17417,tc_fun(U_17421,U_17418),tc_fun(U_17421,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17418,tc_HOL_Obool),tc_fun(tc_fun(U_17421,U_17418),tc_fun(U_17421,tc_HOL_Obool)),U_17417),c_COMBB(U_17418,tc_HOL_Obool,U_17421)),U_17419)),U_17422),U_17420,U_17423)
        | ~ c_List_Olist__all2(U_17417,U_17418,U_17419,U_17420,hAPP(hAPP(c_List_Omap(U_17421,U_17418),U_17422),U_17423)) ) ),
    inference(variable_rename,[status(thm)],[f_4286_1]) ).

fof(f_4286_3,plain,
    ( ! [U_17437,U_17435,U_17433,U_17431,U_17429,U_17427,U_17425] :
        ( c_List_Olist__all2(U_17425,U_17427,U_17429,U_17431,hAPP(hAPP(c_List_Omap(U_17433,U_17427),U_17435),U_17437))
        | ~ c_List_Olist__all2(U_17425,U_17433,hAPP(hAPP(c_COMBC(U_17425,tc_fun(U_17433,U_17427),tc_fun(U_17433,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17427,tc_HOL_Obool),tc_fun(tc_fun(U_17433,U_17427),tc_fun(U_17433,tc_HOL_Obool)),U_17425),c_COMBB(U_17427,tc_HOL_Obool,U_17433)),U_17429)),U_17435),U_17431,U_17437) )
    & ! [U_17436,U_17434,U_17432,U_17430,U_17428,U_17426,U_17424] :
        ( c_List_Olist__all2(U_17424,U_17432,hAPP(hAPP(c_COMBC(U_17424,tc_fun(U_17432,U_17426),tc_fun(U_17432,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17426,tc_HOL_Obool),tc_fun(tc_fun(U_17432,U_17426),tc_fun(U_17432,tc_HOL_Obool)),U_17424),c_COMBB(U_17426,tc_HOL_Obool,U_17432)),U_17428)),U_17434),U_17430,U_17436)
        | ~ c_List_Olist__all2(U_17424,U_17426,U_17428,U_17430,hAPP(hAPP(c_List_Omap(U_17432,U_17426),U_17434),U_17436)) ) ),
    inference(miniscope,[status(thm)],[f_4286_2]) ).

cnf(f_4286_4,plain,
    ( c_List_Olist__all2(U_17424,U_17432,hAPP(hAPP(c_COMBC(U_17424,tc_fun(U_17432,U_17426),tc_fun(U_17432,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17426,tc_HOL_Obool),tc_fun(tc_fun(U_17432,U_17426),tc_fun(U_17432,tc_HOL_Obool)),U_17424),c_COMBB(U_17426,tc_HOL_Obool,U_17432)),U_17428)),U_17434),U_17430,U_17436)
    | ~ c_List_Olist__all2(U_17424,U_17426,U_17428,U_17430,hAPP(hAPP(c_List_Omap(U_17432,U_17426),U_17434),U_17436)) ),
    inference(clausify,[status(thm)],[f_4286_3]) ).

cnf(f_4286_5,plain,
    ( c_List_Olist__all2(U_17425,U_17427,U_17429,U_17431,hAPP(hAPP(c_List_Omap(U_17433,U_17427),U_17435),U_17437))
    | ~ c_List_Olist__all2(U_17425,U_17433,hAPP(hAPP(c_COMBC(U_17425,tc_fun(U_17433,U_17427),tc_fun(U_17433,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17427,tc_HOL_Obool),tc_fun(tc_fun(U_17433,U_17427),tc_fun(U_17433,tc_HOL_Obool)),U_17425),c_COMBB(U_17427,tc_HOL_Obool,U_17433)),U_17429)),U_17435),U_17431,U_17437) ),
    inference(clausify,[status(thm)],[f_4286_3]) ).

fof(f_4287_1,plain,
    ! [V_n_2,V_bs_2,V_as_2,V_P_2,T_c,T_b] :
      ( c_List_Olist__all2(T_b,T_c,V_P_2,hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_as_2),hAPP(hAPP(c_List_Odrop(T_c),V_n_2),V_bs_2))
      | ~ c_List_Olist__all2(T_b,T_c,V_P_2,V_as_2,V_bs_2) ),
    inference(fof_nnf,[status(thm)],[fact_list__all2__dropI]) ).

fof(f_4287_2,plain,
    ! [U_17443,U_17442,U_17441,U_17440,U_17439,U_17438] :
      ( c_List_Olist__all2(U_17438,U_17439,U_17440,hAPP(hAPP(c_List_Odrop(U_17438),U_17443),U_17441),hAPP(hAPP(c_List_Odrop(U_17439),U_17443),U_17442))
      | ~ c_List_Olist__all2(U_17438,U_17439,U_17440,U_17441,U_17442) ),
    inference(variable_rename,[status(thm)],[f_4287_1]) ).

cnf(f_4287_3,plain,
    ( c_List_Olist__all2(U_17438,U_17439,U_17440,hAPP(hAPP(c_List_Odrop(U_17438),U_17443),U_17441),hAPP(hAPP(c_List_Odrop(U_17439),U_17443),U_17442))
    | ~ c_List_Olist__all2(U_17438,U_17439,U_17440,U_17441,U_17442) ),
    inference(clausify,[status(thm)],[f_4287_2]) ).

fof(f_4288_1,plain,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,V_P_2,T_c,T_b] :
      ( c_List_Olist__all2(T_b,T_c,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_a_2),V_c_2),hAPP(hAPP(c_List_Oappend(T_c),V_b_2),V_d_2))
      | ~ c_List_Olist__all2(T_b,T_c,V_P_2,V_c_2,V_d_2)
      | ~ c_List_Olist__all2(T_b,T_c,V_P_2,V_a_2,V_b_2) ),
    inference(fof_nnf,[status(thm)],[fact_list__all2__appendI]) ).

fof(f_4288_2,plain,
    ! [U_17450,U_17449,U_17448,U_17447,U_17446,U_17445,U_17444] :
      ( c_List_Olist__all2(U_17444,U_17445,U_17446,hAPP(hAPP(c_List_Oappend(U_17444),U_17447),U_17449),hAPP(hAPP(c_List_Oappend(U_17445),U_17448),U_17450))
      | ~ c_List_Olist__all2(U_17444,U_17445,U_17446,U_17449,U_17450)
      | ~ c_List_Olist__all2(U_17444,U_17445,U_17446,U_17447,U_17448) ),
    inference(variable_rename,[status(thm)],[f_4288_1]) ).

cnf(f_4288_3,plain,
    ( c_List_Olist__all2(U_17444,U_17445,U_17446,hAPP(hAPP(c_List_Oappend(U_17444),U_17447),U_17449),hAPP(hAPP(c_List_Oappend(U_17445),U_17448),U_17450))
    | ~ c_List_Olist__all2(U_17444,U_17445,U_17446,U_17449,U_17450)
    | ~ c_List_Olist__all2(U_17444,U_17445,U_17446,U_17447,U_17448) ),
    inference(clausify,[status(thm)],[f_4288_2]) ).

fof(f_4289_1,plain,
    ! [V_vs_2,V_us_2,V_P_2,V_ys_2,T_c,V_xs_2,T_b] :
      ( ( ( c_List_Olist__all2(T_b,T_c,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_us_2),hAPP(hAPP(c_List_Oappend(T_c),V_ys_2),V_vs_2))
          | ~ c_List_Olist__all2(T_b,T_c,V_P_2,V_us_2,V_vs_2)
          | ~ c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2) )
        & ( ( c_List_Olist__all2(T_b,T_c,V_P_2,V_us_2,V_vs_2)
            & c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2) )
          | ~ c_List_Olist__all2(T_b,T_c,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_us_2),hAPP(hAPP(c_List_Oappend(T_c),V_ys_2),V_vs_2)) ) )
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2) ),
    inference(fof_nnf,[status(thm)],[fact_list__all2__append]) ).

fof(f_4289_2,plain,
    ! [U_17457,U_17456,U_17455,U_17454,U_17453,U_17452,U_17451] :
      ( ( ( c_List_Olist__all2(U_17451,U_17453,U_17455,hAPP(hAPP(c_List_Oappend(U_17451),U_17452),U_17456),hAPP(hAPP(c_List_Oappend(U_17453),U_17454),U_17457))
          | ~ c_List_Olist__all2(U_17451,U_17453,U_17455,U_17456,U_17457)
          | ~ c_List_Olist__all2(U_17451,U_17453,U_17455,U_17452,U_17454) )
        & ( ( c_List_Olist__all2(U_17451,U_17453,U_17455,U_17456,U_17457)
            & c_List_Olist__all2(U_17451,U_17453,U_17455,U_17452,U_17454) )
          | ~ c_List_Olist__all2(U_17451,U_17453,U_17455,hAPP(hAPP(c_List_Oappend(U_17451),U_17452),U_17456),hAPP(hAPP(c_List_Oappend(U_17453),U_17454),U_17457)) ) )
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17451)),U_17452) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17453)),U_17454) ),
    inference(variable_rename,[status(thm)],[f_4289_1]) ).

cnf(f_4289_3,plain,
    ( c_List_Olist__all2(U_17451,U_17453,U_17455,U_17452,U_17454)
    | ~ c_List_Olist__all2(U_17451,U_17453,U_17455,hAPP(hAPP(c_List_Oappend(U_17451),U_17452),U_17456),hAPP(hAPP(c_List_Oappend(U_17453),U_17454),U_17457))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17451)),U_17452) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17453)),U_17454) ),
    inference(clausify,[status(thm)],[f_4289_2]) ).

cnf(f_4289_4,plain,
    ( c_List_Olist__all2(U_17451,U_17453,U_17455,U_17456,U_17457)
    | ~ c_List_Olist__all2(U_17451,U_17453,U_17455,hAPP(hAPP(c_List_Oappend(U_17451),U_17452),U_17456),hAPP(hAPP(c_List_Oappend(U_17453),U_17454),U_17457))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17451)),U_17452) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17453)),U_17454) ),
    inference(clausify,[status(thm)],[f_4289_2]) ).

cnf(f_4289_5,plain,
    ( c_List_Olist__all2(U_17451,U_17453,U_17455,hAPP(hAPP(c_List_Oappend(U_17451),U_17452),U_17456),hAPP(hAPP(c_List_Oappend(U_17453),U_17454),U_17457))
    | ~ c_List_Olist__all2(U_17451,U_17453,U_17455,U_17456,U_17457)
    | ~ c_List_Olist__all2(U_17451,U_17453,U_17455,U_17452,U_17454)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17451)),U_17452) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17453)),U_17454) ),
    inference(clausify,[status(thm)],[f_4289_2]) ).

fof(f_4290_1,plain,
    ! [V_ys_2,V_y_2,V_xs_2,V_x_2,V_P_2,T_c,T_b] :
      ( ( c_List_Olist__all2(T_b,T_c,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2))
        | ~ c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
        | ~ hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2)) )
      & ( ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
          & hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2)) )
        | ~ c_List_Olist__all2(T_b,T_c,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__all2__Cons]) ).

fof(f_4290_2,plain,
    ! [U_17464,U_17463,U_17462,U_17461,U_17460,U_17459,U_17458] :
      ( ( c_List_Olist__all2(U_17458,U_17459,U_17460,hAPP(hAPP(c_List_Olist_OCons(U_17458),U_17461),U_17462),hAPP(hAPP(c_List_Olist_OCons(U_17459),U_17463),U_17464))
        | ~ c_List_Olist__all2(U_17458,U_17459,U_17460,U_17462,U_17464)
        | ~ hBOOL(hAPP(hAPP(U_17460,U_17461),U_17463)) )
      & ( ( c_List_Olist__all2(U_17458,U_17459,U_17460,U_17462,U_17464)
          & hBOOL(hAPP(hAPP(U_17460,U_17461),U_17463)) )
        | ~ c_List_Olist__all2(U_17458,U_17459,U_17460,hAPP(hAPP(c_List_Olist_OCons(U_17458),U_17461),U_17462),hAPP(hAPP(c_List_Olist_OCons(U_17459),U_17463),U_17464)) ) ),
    inference(variable_rename,[status(thm)],[f_4290_1]) ).

fof(f_4290_3,plain,
    ( ! [U_17478,U_17476,U_17474,U_17472,U_17470,U_17468,U_17466] :
        ( c_List_Olist__all2(U_17466,U_17468,U_17470,hAPP(hAPP(c_List_Olist_OCons(U_17466),U_17472),U_17474),hAPP(hAPP(c_List_Olist_OCons(U_17468),U_17476),U_17478))
        | ~ c_List_Olist__all2(U_17466,U_17468,U_17470,U_17474,U_17478)
        | ~ hBOOL(hAPP(hAPP(U_17470,U_17472),U_17476)) )
    & ! [U_17477,U_17475,U_17473,U_17471,U_17469,U_17467,U_17465] :
        ( ( c_List_Olist__all2(U_17465,U_17467,U_17469,U_17473,U_17477)
          & hBOOL(hAPP(hAPP(U_17469,U_17471),U_17475)) )
        | ~ c_List_Olist__all2(U_17465,U_17467,U_17469,hAPP(hAPP(c_List_Olist_OCons(U_17465),U_17471),U_17473),hAPP(hAPP(c_List_Olist_OCons(U_17467),U_17475),U_17477)) ) ),
    inference(miniscope,[status(thm)],[f_4290_2]) ).

cnf(f_4290_4,plain,
    ( hBOOL(hAPP(hAPP(U_17469,U_17471),U_17475))
    | ~ c_List_Olist__all2(U_17465,U_17467,U_17469,hAPP(hAPP(c_List_Olist_OCons(U_17465),U_17471),U_17473),hAPP(hAPP(c_List_Olist_OCons(U_17467),U_17475),U_17477)) ),
    inference(clausify,[status(thm)],[f_4290_3]) ).

cnf(f_4290_5,plain,
    ( c_List_Olist__all2(U_17465,U_17467,U_17469,U_17473,U_17477)
    | ~ c_List_Olist__all2(U_17465,U_17467,U_17469,hAPP(hAPP(c_List_Olist_OCons(U_17465),U_17471),U_17473),hAPP(hAPP(c_List_Olist_OCons(U_17467),U_17475),U_17477)) ),
    inference(clausify,[status(thm)],[f_4290_3]) ).

cnf(f_4290_6,plain,
    ( c_List_Olist__all2(U_17466,U_17468,U_17470,hAPP(hAPP(c_List_Olist_OCons(U_17466),U_17472),U_17474),hAPP(hAPP(c_List_Olist_OCons(U_17468),U_17476),U_17478))
    | ~ c_List_Olist__all2(U_17466,U_17468,U_17470,U_17474,U_17478)
    | ~ hBOOL(hAPP(hAPP(U_17470,U_17472),U_17476)) ),
    inference(clausify,[status(thm)],[f_4290_3]) ).

fof(f_4291_1,plain,
    ! [V_n_2,V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
      ( c_List_Olist__all2(T_b,T_c,V_P_2,hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2),hAPP(hAPP(c_List_Otake(T_c),V_n_2),V_ys_2))
      | ~ c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2) ),
    inference(fof_nnf,[status(thm)],[fact_list__all2__takeI]) ).

fof(f_4291_2,plain,
    ! [U_17484,U_17483,U_17482,U_17481,U_17480,U_17479] :
      ( c_List_Olist__all2(U_17479,U_17480,U_17481,hAPP(hAPP(c_List_Otake(U_17479),U_17484),U_17482),hAPP(hAPP(c_List_Otake(U_17480),U_17484),U_17483))
      | ~ c_List_Olist__all2(U_17479,U_17480,U_17481,U_17482,U_17483) ),
    inference(variable_rename,[status(thm)],[f_4291_1]) ).

cnf(f_4291_3,plain,
    ( c_List_Olist__all2(U_17479,U_17480,U_17481,hAPP(hAPP(c_List_Otake(U_17479),U_17484),U_17482),hAPP(hAPP(c_List_Otake(U_17480),U_17484),U_17483))
    | ~ c_List_Olist__all2(U_17479,U_17480,U_17481,U_17482,U_17483) ),
    inference(clausify,[status(thm)],[f_4291_2]) ).

fof(f_4292_1,plain,
    ! [T_b,V_ys_2,V_xs_2] :
      ( ( V_xs_2 = V_ys_2
        | ~ c_List_Olist__all2(T_b,T_b,c_fequal,V_xs_2,V_ys_2) )
      & ( c_List_Olist__all2(T_b,T_b,c_fequal,V_xs_2,V_ys_2)
        | V_xs_2 != V_ys_2 ) ),
    inference(fof_nnf,[status(thm)],[fact_list__all2__eq]) ).

fof(f_4292_2,plain,
    ! [U_17487,U_17486,U_17485] :
      ( ( U_17485 = U_17486
        | ~ c_List_Olist__all2(U_17487,U_17487,c_fequal,U_17485,U_17486) )
      & ( c_List_Olist__all2(U_17487,U_17487,c_fequal,U_17485,U_17486)
        | U_17485 != U_17486 ) ),
    inference(variable_rename,[status(thm)],[f_4292_1]) ).

fof(f_4292_3,plain,
    ( ! [U_17493,U_17491,U_17489] :
        ( U_17489 = U_17491
        | ~ c_List_Olist__all2(U_17493,U_17493,c_fequal,U_17489,U_17491) )
    & ! [U_17492,U_17490,U_17488] :
        ( c_List_Olist__all2(U_17492,U_17492,c_fequal,U_17488,U_17490)
        | U_17488 != U_17490 ) ),
    inference(miniscope,[status(thm)],[f_4292_2]) ).

cnf(f_4292_4,plain,
    ( c_List_Olist__all2(U_17492,U_17492,c_fequal,U_17488,U_17490)
    | U_17488 != U_17490 ),
    inference(clausify,[status(thm)],[f_4292_3]) ).

cnf(f_4292_5,plain,
    ( U_17489 = U_17491
    | ~ c_List_Olist__all2(U_17493,U_17493,c_fequal,U_17489,U_17491) ),
    inference(clausify,[status(thm)],[f_4292_3]) ).

fof(f_4293_1,plain,
    ! [V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)
      | ~ c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2) ),
    inference(fof_nnf,[status(thm)],[fact_list__all2__lengthD]) ).

fof(f_4293_2,plain,
    ! [U_17498,U_17497,U_17496,U_17495,U_17494] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17494)),U_17497) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17495)),U_17498)
      | ~ c_List_Olist__all2(U_17494,U_17495,U_17496,U_17497,U_17498) ),
    inference(variable_rename,[status(thm)],[f_4293_1]) ).

cnf(f_4293_3,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17494)),U_17497) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17495)),U_17498)
    | ~ c_List_Olist__all2(U_17494,U_17495,U_17496,U_17497,U_17498) ),
    inference(clausify,[status(thm)],[f_4293_2]) ).

fof(f_4294_1,plain,
    ! [V_xs_2,V_P_2,T_c,T_b] :
      ( ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,c_List_Olist_ONil(T_c))
        | V_xs_2 != c_List_Olist_ONil(T_b) )
      & ( V_xs_2 = c_List_Olist_ONil(T_b)
        | ~ c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,c_List_Olist_ONil(T_c)) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__all2__Nil2]) ).

fof(f_4294_2,plain,
    ! [U_17502,U_17501,U_17500,U_17499] :
      ( ( c_List_Olist__all2(U_17499,U_17500,U_17501,U_17502,c_List_Olist_ONil(U_17500))
        | U_17502 != c_List_Olist_ONil(U_17499) )
      & ( U_17502 = c_List_Olist_ONil(U_17499)
        | ~ c_List_Olist__all2(U_17499,U_17500,U_17501,U_17502,c_List_Olist_ONil(U_17500)) ) ),
    inference(variable_rename,[status(thm)],[f_4294_1]) ).

fof(f_4294_3,plain,
    ( ! [U_17510,U_17508,U_17506,U_17504] :
        ( c_List_Olist__all2(U_17504,U_17506,U_17508,U_17510,c_List_Olist_ONil(U_17506))
        | U_17510 != c_List_Olist_ONil(U_17504) )
    & ! [U_17509,U_17507,U_17505,U_17503] :
        ( U_17509 = c_List_Olist_ONil(U_17503)
        | ~ c_List_Olist__all2(U_17503,U_17505,U_17507,U_17509,c_List_Olist_ONil(U_17505)) ) ),
    inference(miniscope,[status(thm)],[f_4294_2]) ).

cnf(f_4294_4,plain,
    ( U_17509 = c_List_Olist_ONil(U_17503)
    | ~ c_List_Olist__all2(U_17503,U_17505,U_17507,U_17509,c_List_Olist_ONil(U_17505)) ),
    inference(clausify,[status(thm)],[f_4294_3]) ).

cnf(f_4294_5,plain,
    ( c_List_Olist__all2(U_17504,U_17506,U_17508,U_17510,c_List_Olist_ONil(U_17506))
    | U_17510 != c_List_Olist_ONil(U_17504) ),
    inference(clausify,[status(thm)],[f_4294_3]) ).

fof(f_4295_1,plain,
    ! [V_ys_2,V_P_2,T_c,T_b] :
      ( ( c_List_Olist__all2(T_b,T_c,V_P_2,c_List_Olist_ONil(T_b),V_ys_2)
        | V_ys_2 != c_List_Olist_ONil(T_c) )
      & ( V_ys_2 = c_List_Olist_ONil(T_c)
        | ~ c_List_Olist__all2(T_b,T_c,V_P_2,c_List_Olist_ONil(T_b),V_ys_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__all2__Nil]) ).

fof(f_4295_2,plain,
    ! [U_17514,U_17513,U_17512,U_17511] :
      ( ( c_List_Olist__all2(U_17511,U_17512,U_17513,c_List_Olist_ONil(U_17511),U_17514)
        | U_17514 != c_List_Olist_ONil(U_17512) )
      & ( U_17514 = c_List_Olist_ONil(U_17512)
        | ~ c_List_Olist__all2(U_17511,U_17512,U_17513,c_List_Olist_ONil(U_17511),U_17514) ) ),
    inference(variable_rename,[status(thm)],[f_4295_1]) ).

fof(f_4295_3,plain,
    ( ! [U_17522,U_17520,U_17518] :
        ( ! [U_17516] : c_List_Olist__all2(U_17516,U_17518,U_17520,c_List_Olist_ONil(U_17516),U_17522)
        | U_17522 != c_List_Olist_ONil(U_17518) )
    & ! [U_17521,U_17519,U_17517] :
        ( ! [U_17515] : ~ c_List_Olist__all2(U_17515,U_17517,U_17519,c_List_Olist_ONil(U_17515),U_17521)
        | U_17521 = c_List_Olist_ONil(U_17517) ) ),
    inference(miniscope,[status(thm)],[f_4295_2]) ).

cnf(f_4295_4,plain,
    ( ~ c_List_Olist__all2(U_17515,U_17517,U_17519,c_List_Olist_ONil(U_17515),U_17521)
    | U_17521 = c_List_Olist_ONil(U_17517) ),
    inference(clausify,[status(thm)],[f_4295_3]) ).

cnf(f_4295_5,plain,
    ( c_List_Olist__all2(U_17516,U_17518,U_17520,c_List_Olist_ONil(U_17516),U_17522)
    | U_17522 != c_List_Olist_ONil(U_17518) ),
    inference(clausify,[status(thm)],[f_4295_3]) ).

fof(f_4296_1,plain,
    ! [V_uu,T_b,T_a] : c_Enum_Oproduct(T_a,T_b,c_List_Olist_ONil(T_a),V_uu) = c_List_Olist_ONil(tc_prod(T_a,T_b)),
    inference(fof_nnf,[status(thm)],[fact_product_Osimps_I1_J]) ).

fof(f_4296_2,plain,
    ! [U_17525,U_17524,U_17523] : c_Enum_Oproduct(U_17523,U_17524,c_List_Olist_ONil(U_17523),U_17525) = c_List_Olist_ONil(tc_prod(U_17523,U_17524)),
    inference(variable_rename,[status(thm)],[f_4296_1]) ).

cnf(f_4296_3,plain,
    c_Enum_Oproduct(U_17523,U_17524,c_List_Olist_ONil(U_17523),U_17525) = c_List_Olist_ONil(tc_prod(U_17523,U_17524)),
    inference(clausify,[status(thm)],[f_4296_2]) ).

fof(f_4297_1,plain,
    ! [V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
      ( ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
        | ? [B_i] :
            ( ~ hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i)),hAPP(hAPP(c_List_Onth(T_c),V_ys_2),B_i)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2) )
      & ( ( ! [B_i] :
              ( hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i)),hAPP(hAPP(c_List_Onth(T_c),V_ys_2),B_i)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2) )
        | ~ c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__all2__conv__all__nth]) ).

fof(f_4297_2,plain,
    ! [U_17532,U_17531,U_17530,U_17529,U_17528] :
      ( ( c_List_Olist__all2(U_17528,U_17529,U_17530,U_17531,U_17532)
        | ? [U_17527] :
            ( ~ hBOOL(hAPP(hAPP(U_17530,hAPP(hAPP(c_List_Onth(U_17528),U_17531),U_17527)),hAPP(hAPP(c_List_Onth(U_17529),U_17532),U_17527)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_17527),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17528)),U_17531))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17528)),U_17531) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17529)),U_17532) )
      & ( ( ! [U_17526] :
              ( hBOOL(hAPP(hAPP(U_17530,hAPP(hAPP(c_List_Onth(U_17528),U_17531),U_17526)),hAPP(hAPP(c_List_Onth(U_17529),U_17532),U_17526)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_17526),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17528)),U_17531))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17528)),U_17531) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17529)),U_17532) )
        | ~ c_List_Olist__all2(U_17528,U_17529,U_17530,U_17531,U_17532) ) ),
    inference(variable_rename,[status(thm)],[f_4297_1]) ).

fof(f_4297_3,plain,
    ( ! [U_17542,U_17540,U_17538,U_17536,U_17534] :
        ( c_List_Olist__all2(U_17534,U_17536,U_17538,U_17540,U_17542)
        | ? [U_17527] :
            ( ~ hBOOL(hAPP(hAPP(U_17538,hAPP(hAPP(c_List_Onth(U_17534),U_17540),U_17527)),hAPP(hAPP(c_List_Onth(U_17536),U_17542),U_17527)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_17527),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17534)),U_17540))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17534)),U_17540) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17536)),U_17542) )
    & ! [U_17541,U_17539,U_17537,U_17535,U_17533] :
        ( ( ! [U_17526] :
              ( hBOOL(hAPP(hAPP(U_17537,hAPP(hAPP(c_List_Onth(U_17533),U_17539),U_17526)),hAPP(hAPP(c_List_Onth(U_17535),U_17541),U_17526)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_17526),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17533)),U_17539))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17533)),U_17539) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17535)),U_17541) )
        | ~ c_List_Olist__all2(U_17533,U_17535,U_17537,U_17539,U_17541) ) ),
    inference(miniscope,[status(thm)],[f_4297_2]) ).

fof(f_4297_4,plain,
    ( ! [U_17542,U_17540,U_17538,U_17536,U_17534] :
        ( c_List_Olist__all2(U_17534,U_17536,U_17538,U_17540,U_17542)
        | ( ~ hBOOL(hAPP(hAPP(U_17538,hAPP(hAPP(c_List_Onth(U_17534),U_17540),sK439(U_17542,U_17540,U_17538,U_17536,U_17534))),hAPP(hAPP(c_List_Onth(U_17536),U_17542),sK439(U_17542,U_17540,U_17538,U_17536,U_17534))))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK439(U_17542,U_17540,U_17538,U_17536,U_17534)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17534)),U_17540))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17534)),U_17540) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17536)),U_17542) )
    & ! [U_17541,U_17539,U_17537,U_17535,U_17533] :
        ( ( ! [U_17526] :
              ( hBOOL(hAPP(hAPP(U_17537,hAPP(hAPP(c_List_Onth(U_17533),U_17539),U_17526)),hAPP(hAPP(c_List_Onth(U_17535),U_17541),U_17526)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_17526),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17533)),U_17539))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17533)),U_17539) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17535)),U_17541) )
        | ~ c_List_Olist__all2(U_17533,U_17535,U_17537,U_17539,U_17541) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK439]),skolemize(U_17527,sK439(U_17542,U_17540,U_17538,U_17536,U_17534))],[f_4297_3]) ).

cnf(f_4297_5,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17533)),U_17539) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17535)),U_17541)
    | ~ c_List_Olist__all2(U_17533,U_17535,U_17537,U_17539,U_17541) ),
    inference(clausify,[status(thm)],[f_4297_4]) ).

cnf(f_4297_6,plain,
    ( hBOOL(hAPP(hAPP(U_17537,hAPP(hAPP(c_List_Onth(U_17533),U_17539),U_17526)),hAPP(hAPP(c_List_Onth(U_17535),U_17541),U_17526)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_17526),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17533)),U_17539)))
    | ~ c_List_Olist__all2(U_17533,U_17535,U_17537,U_17539,U_17541) ),
    inference(clausify,[status(thm)],[f_4297_4]) ).

cnf(f_4297_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK439(U_17542,U_17540,U_17538,U_17536,U_17534)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17534)),U_17540)))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17534)),U_17540) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17536)),U_17542)
    | c_List_Olist__all2(U_17534,U_17536,U_17538,U_17540,U_17542) ),
    inference(clausify,[status(thm)],[f_4297_4]) ).

cnf(f_4297_8,plain,
    ( ~ hBOOL(hAPP(hAPP(U_17538,hAPP(hAPP(c_List_Onth(U_17534),U_17540),sK439(U_17542,U_17540,U_17538,U_17536,U_17534))),hAPP(hAPP(c_List_Onth(U_17536),U_17542),sK439(U_17542,U_17540,U_17538,U_17536,U_17534))))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17534)),U_17540) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17536)),U_17542)
    | c_List_Olist__all2(U_17534,U_17536,U_17538,U_17540,U_17542) ),
    inference(clausify,[status(thm)],[f_4297_4]) ).

fof(f_4298_1,plain,
    ! [V_p_2,V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_p_2)),hAPP(hAPP(c_List_Onth(T_c),V_ys_2),V_p_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_p_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
      | ~ c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2) ),
    inference(fof_nnf,[status(thm)],[fact_list__all2__nthD]) ).

fof(f_4298_2,plain,
    ! [U_17548,U_17547,U_17546,U_17545,U_17544,U_17543] :
      ( hBOOL(hAPP(hAPP(U_17545,hAPP(hAPP(c_List_Onth(U_17543),U_17546),U_17548)),hAPP(hAPP(c_List_Onth(U_17544),U_17547),U_17548)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_17548),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17543)),U_17546)))
      | ~ c_List_Olist__all2(U_17543,U_17544,U_17545,U_17546,U_17547) ),
    inference(variable_rename,[status(thm)],[f_4298_1]) ).

cnf(f_4298_3,plain,
    ( hBOOL(hAPP(hAPP(U_17545,hAPP(hAPP(c_List_Onth(U_17543),U_17546),U_17548)),hAPP(hAPP(c_List_Onth(U_17544),U_17547),U_17548)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_17548),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17543)),U_17546)))
    | ~ c_List_Olist__all2(U_17543,U_17544,U_17545,U_17546,U_17547) ),
    inference(clausify,[status(thm)],[f_4298_2]) ).

fof(f_4299_1,plain,
    ! [V_p_2,V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_p_2)),hAPP(hAPP(c_List_Onth(T_c),V_ys_2),V_p_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_p_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)))
      | ~ c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2) ),
    inference(fof_nnf,[status(thm)],[fact_list__all2__nthD2]) ).

fof(f_4299_2,plain,
    ! [U_17554,U_17553,U_17552,U_17551,U_17550,U_17549] :
      ( hBOOL(hAPP(hAPP(U_17551,hAPP(hAPP(c_List_Onth(U_17549),U_17552),U_17554)),hAPP(hAPP(c_List_Onth(U_17550),U_17553),U_17554)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_17554),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17550)),U_17553)))
      | ~ c_List_Olist__all2(U_17549,U_17550,U_17551,U_17552,U_17553) ),
    inference(variable_rename,[status(thm)],[f_4299_1]) ).

cnf(f_4299_3,plain,
    ( hBOOL(hAPP(hAPP(U_17551,hAPP(hAPP(c_List_Onth(U_17549),U_17552),U_17554)),hAPP(hAPP(c_List_Onth(U_17550),U_17553),U_17554)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_17554),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17550)),U_17553)))
    | ~ c_List_Olist__all2(U_17549,U_17550,U_17551,U_17552,U_17553) ),
    inference(clausify,[status(thm)],[f_4299_2]) ).

fof(f_4300_1,plain,
    ! [V_y_2,V_x_2,V_ys_2,V_P_2,T_c,V_xs_2,T_b,V_i_2] :
      ( c_List_Olist__all2(T_b,T_c,V_P_2,hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2),hAPP(hAPP(c_List_Olist__update(T_c,V_ys_2),V_i_2),V_y_2))
      | ~ hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
      | ~ c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_list__all2__update__cong]) ).

fof(f_4300_2,plain,
    ! [U_17562,U_17561,U_17560,U_17559,U_17558,U_17557,U_17556,U_17555] :
      ( c_List_Olist__all2(U_17556,U_17558,U_17559,hAPP(hAPP(c_List_Olist__update(U_17556,U_17557),U_17555),U_17561),hAPP(hAPP(c_List_Olist__update(U_17558,U_17560),U_17555),U_17562))
      | ~ hBOOL(hAPP(hAPP(U_17559,U_17561),U_17562))
      | ~ c_List_Olist__all2(U_17556,U_17558,U_17559,U_17557,U_17560)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_17555),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17556)),U_17557))) ),
    inference(variable_rename,[status(thm)],[f_4300_1]) ).

cnf(f_4300_3,plain,
    ( c_List_Olist__all2(U_17556,U_17558,U_17559,hAPP(hAPP(c_List_Olist__update(U_17556,U_17557),U_17555),U_17561),hAPP(hAPP(c_List_Olist__update(U_17558,U_17560),U_17555),U_17562))
    | ~ hBOOL(hAPP(hAPP(U_17559,U_17561),U_17562))
    | ~ c_List_Olist__all2(U_17556,U_17558,U_17559,U_17557,U_17560)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_17555),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17556)),U_17557))) ),
    inference(clausify,[status(thm)],[f_4300_2]) ).

fof(f_4301_1,plain,
    ! [V_i_2,V_y_2,V_x_2,V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
      ( c_List_Olist__all2(T_b,T_c,V_P_2,hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2),hAPP(hAPP(c_List_Olist__update(T_c,V_ys_2),V_i_2),V_y_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)))
      | ~ hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
      | ~ c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2) ),
    inference(fof_nnf,[status(thm)],[fact_list__all2__update__cong2]) ).

fof(f_4301_2,plain,
    ! [U_17570,U_17569,U_17568,U_17567,U_17566,U_17565,U_17564,U_17563] :
      ( c_List_Olist__all2(U_17563,U_17564,U_17565,hAPP(hAPP(c_List_Olist__update(U_17563,U_17566),U_17570),U_17568),hAPP(hAPP(c_List_Olist__update(U_17564,U_17567),U_17570),U_17569))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_17570),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17564)),U_17567)))
      | ~ hBOOL(hAPP(hAPP(U_17565,U_17568),U_17569))
      | ~ c_List_Olist__all2(U_17563,U_17564,U_17565,U_17566,U_17567) ),
    inference(variable_rename,[status(thm)],[f_4301_1]) ).

cnf(f_4301_3,plain,
    ( c_List_Olist__all2(U_17563,U_17564,U_17565,hAPP(hAPP(c_List_Olist__update(U_17563,U_17566),U_17570),U_17568),hAPP(hAPP(c_List_Olist__update(U_17564,U_17567),U_17570),U_17569))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_17570),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17564)),U_17567)))
    | ~ hBOOL(hAPP(hAPP(U_17565,U_17568),U_17569))
    | ~ c_List_Olist__all2(U_17563,U_17564,U_17565,U_17566,U_17567) ),
    inference(clausify,[status(thm)],[f_4301_2]) ).

fof(f_4302_1,plain,
    ! [V_ys,T_b,V_xs,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),c_Enum_Oproduct(T_a,T_b,V_xs,V_ys)))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_b),V_ys))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__product]) ).

fof(f_4302_2,plain,
    ! [U_17574,U_17573,U_17572,U_17571] :
      ( hBOOL(hAPP(c_List_Odistinct(tc_prod(U_17571,U_17573)),c_Enum_Oproduct(U_17571,U_17573,U_17572,U_17574)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17573),U_17574))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17571),U_17572)) ),
    inference(variable_rename,[status(thm)],[f_4302_1]) ).

cnf(f_4302_3,plain,
    ( hBOOL(hAPP(c_List_Odistinct(tc_prod(U_17571,U_17573)),c_Enum_Oproduct(U_17571,U_17573,U_17572,U_17574)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17573),U_17574))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17571),U_17572)) ),
    inference(clausify,[status(thm)],[f_4302_2]) ).

fof(f_4303_1,plain,
    ! [V_ys_2,V_xs_2,T_c,T_b] : hAPP(c_List_Oset(tc_prod(T_b,T_c)),c_Enum_Oproduct(T_b,T_c,V_xs_2,V_ys_2)) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_List_Oset(T_c),V_ys_2))),
    inference(fof_nnf,[status(thm)],[fact_product__list__set]) ).

fof(f_4303_2,plain,
    ! [U_17578,U_17577,U_17576,U_17575] : hAPP(c_List_Oset(tc_prod(U_17575,U_17576)),c_Enum_Oproduct(U_17575,U_17576,U_17577,U_17578)) = hAPP(hAPP(c_Product__Type_OSigma(U_17575,U_17576),hAPP(c_List_Oset(U_17575),U_17577)),hAPP(c_COMBK(tc_fun(U_17576,tc_HOL_Obool),U_17575),hAPP(c_List_Oset(U_17576),U_17578))),
    inference(variable_rename,[status(thm)],[f_4303_1]) ).

cnf(f_4303_3,plain,
    hAPP(c_List_Oset(tc_prod(U_17575,U_17576)),c_Enum_Oproduct(U_17575,U_17576,U_17577,U_17578)) = hAPP(hAPP(c_Product__Type_OSigma(U_17575,U_17576),hAPP(c_List_Oset(U_17575),U_17577)),hAPP(c_COMBK(tc_fun(U_17576,tc_HOL_Obool),U_17575),hAPP(c_List_Oset(U_17576),U_17578))),
    inference(clausify,[status(thm)],[f_4303_2]) ).

fof(f_4304_1,plain,
    ! [V_xs_2,T_b] : hAPP(c_Set_Oimage(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),c_List_Oset(T_b)),hAPP(c_List_Oset(tc_List_Olist(T_b)),c_Enum_Osublists(T_b,V_xs_2))) = hAPP(c_Set_OPow(T_b),hAPP(c_List_Oset(T_b),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_sublists__powset]) ).

fof(f_4304_2,plain,
    ! [U_17580,U_17579] : hAPP(c_Set_Oimage(tc_List_Olist(U_17579),tc_fun(U_17579,tc_HOL_Obool),c_List_Oset(U_17579)),hAPP(c_List_Oset(tc_List_Olist(U_17579)),c_Enum_Osublists(U_17579,U_17580))) = hAPP(c_Set_OPow(U_17579),hAPP(c_List_Oset(U_17579),U_17580)),
    inference(variable_rename,[status(thm)],[f_4304_1]) ).

cnf(f_4304_3,plain,
    hAPP(c_Set_Oimage(tc_List_Olist(U_17579),tc_fun(U_17579,tc_HOL_Obool),c_List_Oset(U_17579)),hAPP(c_List_Oset(tc_List_Olist(U_17579)),c_Enum_Osublists(U_17579,U_17580))) = hAPP(c_Set_OPow(U_17579),hAPP(c_List_Oset(U_17579),U_17580)),
    inference(clausify,[status(thm)],[f_4304_2]) ).

fof(f_4305_1,plain,
    ! [V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_Enum_Osublists(T_a,V_xs)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),
    inference(fof_nnf,[status(thm)],[fact_length__sublists]) ).

fof(f_4305_2,plain,
    ! [U_17582,U_17581] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_17581))),c_Enum_Osublists(U_17581,U_17582)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17581)),U_17582)),
    inference(variable_rename,[status(thm)],[f_4305_1]) ).

cnf(f_4305_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_17581))),c_Enum_Osublists(U_17581,U_17582)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17581)),U_17582)),
    inference(clausify,[status(thm)],[f_4305_2]) ).

fof(f_4306_1,plain,
    ! [T_a] : c_Enum_Osublists(T_a,c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_List_Olist_ONil(tc_List_Olist(T_a))),
    inference(fof_nnf,[status(thm)],[fact_sublists_Osimps_I1_J]) ).

fof(f_4306_2,plain,
    ! [U_17583] : c_Enum_Osublists(U_17583,c_List_Olist_ONil(U_17583)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_17583)),c_List_Olist_ONil(U_17583)),c_List_Olist_ONil(tc_List_Olist(U_17583))),
    inference(variable_rename,[status(thm)],[f_4306_1]) ).

cnf(f_4306_3,plain,
    c_Enum_Osublists(U_17583,c_List_Olist_ONil(U_17583)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_17583)),c_List_Olist_ONil(U_17583)),c_List_Olist_ONil(tc_List_Olist(U_17583))),
    inference(clausify,[status(thm)],[f_4306_2]) ).

fof(f_4307_1,plain,
    ! [V_xs_2,V_x_2,T_b] : c_Enum_Osublists(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),c_Enum_Osublists(T_b,V_xs_2)),hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(T_b)),tc_fun(tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),tc_List_Olist(tc_List_Olist(T_b))),c_List_Oappend(tc_List_Olist(T_b))),hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(c_List_Olist_OCons(T_b),V_x_2)))),c_COMBI(tc_List_Olist(tc_List_Olist(T_b))))),
    inference(fof_nnf,[status(thm)],[fact_sublists_Osimps_I2_J]) ).

fof(f_4307_2,plain,
    ! [U_17586,U_17585,U_17584] : c_Enum_Osublists(U_17584,hAPP(hAPP(c_List_Olist_OCons(U_17584),U_17585),U_17586)) = hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(U_17584)),tc_List_Olist(tc_List_Olist(U_17584))),c_Enum_Osublists(U_17584,U_17586)),hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(U_17584)),tc_List_Olist(tc_List_Olist(U_17584)),tc_List_Olist(tc_List_Olist(U_17584))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(U_17584)),tc_fun(tc_List_Olist(tc_List_Olist(U_17584)),tc_List_Olist(tc_List_Olist(U_17584))),tc_List_Olist(tc_List_Olist(U_17584))),c_List_Oappend(tc_List_Olist(U_17584))),hAPP(c_List_Omap(tc_List_Olist(U_17584),tc_List_Olist(U_17584)),hAPP(c_List_Olist_OCons(U_17584),U_17585)))),c_COMBI(tc_List_Olist(tc_List_Olist(U_17584))))),
    inference(variable_rename,[status(thm)],[f_4307_1]) ).

cnf(f_4307_3,plain,
    c_Enum_Osublists(U_17584,hAPP(hAPP(c_List_Olist_OCons(U_17584),U_17585),U_17586)) = hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(U_17584)),tc_List_Olist(tc_List_Olist(U_17584))),c_Enum_Osublists(U_17584,U_17586)),hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(U_17584)),tc_List_Olist(tc_List_Olist(U_17584)),tc_List_Olist(tc_List_Olist(U_17584))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(U_17584)),tc_fun(tc_List_Olist(tc_List_Olist(U_17584)),tc_List_Olist(tc_List_Olist(U_17584))),tc_List_Olist(tc_List_Olist(U_17584))),c_List_Oappend(tc_List_Olist(U_17584))),hAPP(c_List_Omap(tc_List_Olist(U_17584),tc_List_Olist(U_17584)),hAPP(c_List_Olist_OCons(U_17584),U_17585)))),c_COMBI(tc_List_Olist(tc_List_Olist(U_17584))))),
    inference(clausify,[status(thm)],[f_4307_2]) ).

fof(f_4308_1,plain,
    ! [V_xs_2,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool)),c_List_Oset(T_b)),c_Enum_Osublists(T_b,V_xs_2))))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__set__sublists]) ).

fof(f_4308_2,plain,
    ! [U_17588,U_17587] :
      ( hBOOL(hAPP(c_List_Odistinct(tc_fun(U_17587,tc_HOL_Obool)),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_17587),tc_fun(U_17587,tc_HOL_Obool)),c_List_Oset(U_17587)),c_Enum_Osublists(U_17587,U_17588))))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17587),U_17588)) ),
    inference(variable_rename,[status(thm)],[f_4308_1]) ).

cnf(f_4308_3,plain,
    ( hBOOL(hAPP(c_List_Odistinct(tc_fun(U_17587,tc_HOL_Obool)),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_17587),tc_fun(U_17587,tc_HOL_Obool)),c_List_Oset(U_17587)),c_Enum_Osublists(U_17587,U_17588))))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17587),U_17588)) ),
    inference(clausify,[status(thm)],[f_4308_2]) ).

fof(f_4309_1,plain,
    ! [V_xs_2,V_n_2,T_b] : hAPP(c_List_Oset(tc_List_Olist(T_b)),c_Enum_On__lists(T_b,V_n_2,V_xs_2)) = hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_n_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),c_List_Oset(T_b))),hAPP(c_List_Oset(T_b),V_xs_2)))),
    inference(fof_nnf,[status(thm)],[fact_set__n__lists]) ).

fof(f_4309_2,plain,
    ! [U_17591,U_17590,U_17589] : hAPP(c_List_Oset(tc_List_Olist(U_17589)),c_Enum_On__lists(U_17589,U_17590,U_17591)) = hAPP(c_Set_OCollect(tc_List_Olist(U_17589)),hAPP(hAPP(c_COMBS(tc_List_Olist(U_17589),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_17589)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17589),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_17589)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_17589)))),U_17590))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17589),tc_fun(U_17589,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_17589,tc_HOL_Obool),tc_fun(tc_fun(U_17589,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_17589)),c_Orderings_Oord__class_Oless__eq(tc_fun(U_17589,tc_HOL_Obool))),c_List_Oset(U_17589))),hAPP(c_List_Oset(U_17589),U_17591)))),
    inference(variable_rename,[status(thm)],[f_4309_1]) ).

cnf(f_4309_3,plain,
    hAPP(c_List_Oset(tc_List_Olist(U_17589)),c_Enum_On__lists(U_17589,U_17590,U_17591)) = hAPP(c_Set_OCollect(tc_List_Olist(U_17589)),hAPP(hAPP(c_COMBS(tc_List_Olist(U_17589),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_17589)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17589),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_17589)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_17589)))),U_17590))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17589),tc_fun(U_17589,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_17589,tc_HOL_Obool),tc_fun(tc_fun(U_17589,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_17589)),c_Orderings_Oord__class_Oless__eq(tc_fun(U_17589,tc_HOL_Obool))),c_List_Oset(U_17589))),hAPP(c_List_Oset(U_17589),U_17591)))),
    inference(clausify,[status(thm)],[f_4309_2]) ).

fof(f_4310_1,plain,
    ! [V_P_2,T_b] : c_Enum_Oenum__the(T_b,V_P_2) = c_HOL_OThe(T_b,V_P_2),
    inference(fof_nnf,[status(thm)],[fact_enum__the__def]) ).

fof(f_4310_2,plain,
    ! [U_17593,U_17592] : c_Enum_Oenum__the(U_17592,U_17593) = c_HOL_OThe(U_17592,U_17593),
    inference(variable_rename,[status(thm)],[f_4310_1]) ).

cnf(f_4310_3,plain,
    c_Enum_Oenum__the(U_17592,U_17593) = c_HOL_OThe(U_17592,U_17593),
    inference(clausify,[status(thm)],[f_4310_2]) ).

fof(f_4311_1,plain,
    ! [V_n,V_xs,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n,V_xs)))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__n__lists]) ).

fof(f_4311_2,plain,
    ! [U_17596,U_17595,U_17594] :
      ( hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(U_17594)),c_Enum_On__lists(U_17594,U_17596,U_17595)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17594),U_17595)) ),
    inference(variable_rename,[status(thm)],[f_4311_1]) ).

cnf(f_4311_3,plain,
    ( hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(U_17594)),c_Enum_On__lists(U_17594,U_17596,U_17595)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17594),U_17595)) ),
    inference(clausify,[status(thm)],[f_4311_2]) ).

fof(f_4312_1,plain,
    ! [V_xs,T_a] : c_Enum_On__lists(T_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_xs) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_List_Olist_ONil(tc_List_Olist(T_a))),
    inference(fof_nnf,[status(thm)],[fact_n__lists_Osimps_I1_J]) ).

fof(f_4312_2,plain,
    ! [U_17598,U_17597] : c_Enum_On__lists(U_17597,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_17598) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_17597)),c_List_Olist_ONil(U_17597)),c_List_Olist_ONil(tc_List_Olist(U_17597))),
    inference(variable_rename,[status(thm)],[f_4312_1]) ).

cnf(f_4312_3,plain,
    c_Enum_On__lists(U_17597,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_17598) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_17597)),c_List_Olist_ONil(U_17597)),c_List_Olist_ONil(tc_List_Olist(U_17597))),
    inference(clausify,[status(thm)],[f_4312_2]) ).

fof(f_4313_1,plain,
    ! [T_a,V_n] :
      ( ( c_Enum_On__lists(T_a,V_n,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(tc_List_Olist(T_a))
        | V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( c_Enum_On__lists(T_a,V_n,c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_List_Olist_ONil(tc_List_Olist(T_a)))
        | V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(fof_nnf,[status(thm)],[fact_n__lists__Nil]) ).

fof(f_4313_2,plain,
    ! [U_17600,U_17599] :
      ( ( c_Enum_On__lists(U_17600,U_17599,c_List_Olist_ONil(U_17600)) = c_List_Olist_ONil(tc_List_Olist(U_17600))
        | U_17599 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( c_Enum_On__lists(U_17600,U_17599,c_List_Olist_ONil(U_17600)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_17600)),c_List_Olist_ONil(U_17600)),c_List_Olist_ONil(tc_List_Olist(U_17600)))
        | U_17599 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_4313_1]) ).

fof(f_4313_3,plain,
    ( ! [U_17604,U_17602] :
        ( c_Enum_On__lists(U_17604,U_17602,c_List_Olist_ONil(U_17604)) = c_List_Olist_ONil(tc_List_Olist(U_17604))
        | U_17602 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_17603,U_17601] :
        ( c_Enum_On__lists(U_17603,U_17601,c_List_Olist_ONil(U_17603)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_17603)),c_List_Olist_ONil(U_17603)),c_List_Olist_ONil(tc_List_Olist(U_17603)))
        | U_17601 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_4313_2]) ).

cnf(f_4313_4,plain,
    ( c_Enum_On__lists(U_17603,U_17601,c_List_Olist_ONil(U_17603)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_17603)),c_List_Olist_ONil(U_17603)),c_List_Olist_ONil(tc_List_Olist(U_17603)))
    | U_17601 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4313_3]) ).

cnf(f_4313_5,plain,
    ( c_Enum_On__lists(U_17604,U_17602,c_List_Olist_ONil(U_17604)) = c_List_Olist_ONil(tc_List_Olist(U_17604))
    | U_17602 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4313_3]) ).

fof(f_4314_1,plain,
    ! [V_xs,V_n,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_Enum_On__lists(T_a,V_n,V_xs)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n),
    inference(fof_nnf,[status(thm)],[fact_length__n__lists]) ).

fof(f_4314_2,plain,
    ! [U_17607,U_17606,U_17605] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_17605))),c_Enum_On__lists(U_17605,U_17606,U_17607)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17605)),U_17607)),U_17606),
    inference(variable_rename,[status(thm)],[f_4314_1]) ).

cnf(f_4314_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_17605))),c_Enum_On__lists(U_17605,U_17606,U_17607)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17605)),U_17607)),U_17606),
    inference(clausify,[status(thm)],[f_4314_2]) ).

fof(f_4315_1,plain,
    ! [V_xs_2,V_n_2,V_ys_2,T_b] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = V_n_2
      | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_ys_2),hAPP(c_List_Oset(tc_List_Olist(T_b)),c_Enum_On__lists(T_b,V_n_2,V_xs_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_length__n__lists__elem]) ).

fof(f_4315_2,plain,
    ! [U_17611,U_17610,U_17609,U_17608] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17608)),U_17609) = U_17610
      | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17608)),U_17609),hAPP(c_List_Oset(tc_List_Olist(U_17608)),c_Enum_On__lists(U_17608,U_17610,U_17611)))) ),
    inference(variable_rename,[status(thm)],[f_4315_1]) ).

cnf(f_4315_3,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17608)),U_17609) = U_17610
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17608)),U_17609),hAPP(c_List_Oset(tc_List_Olist(U_17608)),c_Enum_On__lists(U_17608,U_17610,U_17611)))) ),
    inference(clausify,[status(thm)],[f_4315_2]) ).

fof(f_4316_1,plain,
    ! [V_P_2,V_b_2,V_a_2,T_c,T_b] :
      ( c_List_Olist__all2(T_b,T_c,V_P_2,V_a_2,V_b_2)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_a_2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_b_2)
      | ? [B_x] :
          ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_P_2),B_x))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),B_x),hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_a_2),V_b_2)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__all2I]) ).

fof(f_4316_2,plain,
    ! [U_17617,U_17616,U_17615,U_17614,U_17613] :
      ( c_List_Olist__all2(U_17613,U_17614,U_17617,U_17615,U_17616)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17613)),U_17615) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17614)),U_17616)
      | ? [U_17612] :
          ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_17613,U_17614,tc_HOL_Obool),U_17617),U_17612))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_17613,U_17614)),U_17612),hAPP(c_List_Oset(tc_prod(U_17613,U_17614)),hAPP(hAPP(c_List_Ozip(U_17613,U_17614),U_17615),U_17616)))) ) ),
    inference(variable_rename,[status(thm)],[f_4316_1]) ).

fof(f_4316_3,plain,
    ! [U_17617,U_17616,U_17615,U_17614,U_17613] :
      ( c_List_Olist__all2(U_17613,U_17614,U_17617,U_17615,U_17616)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17613)),U_17615) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17614)),U_17616)
      | ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_17613,U_17614,tc_HOL_Obool),U_17617),sK440(U_17617,U_17616,U_17615,U_17614,U_17613)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_17613,U_17614)),sK440(U_17617,U_17616,U_17615,U_17614,U_17613)),hAPP(c_List_Oset(tc_prod(U_17613,U_17614)),hAPP(hAPP(c_List_Ozip(U_17613,U_17614),U_17615),U_17616)))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK440]),skolemize(U_17612,sK440(U_17617,U_17616,U_17615,U_17614,U_17613))],[f_4316_2]) ).

cnf(f_4316_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17613,U_17614)),sK440(U_17617,U_17616,U_17615,U_17614,U_17613)),hAPP(c_List_Oset(tc_prod(U_17613,U_17614)),hAPP(hAPP(c_List_Ozip(U_17613,U_17614),U_17615),U_17616))))
    | c_List_Olist__all2(U_17613,U_17614,U_17617,U_17615,U_17616)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17613)),U_17615) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17614)),U_17616) ),
    inference(clausify,[status(thm)],[f_4316_3]) ).

cnf(f_4316_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_17613,U_17614,tc_HOL_Obool),U_17617),sK440(U_17617,U_17616,U_17615,U_17614,U_17613)))
    | c_List_Olist__all2(U_17613,U_17614,U_17617,U_17615,U_17616)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17613)),U_17615) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17614)),U_17616) ),
    inference(clausify,[status(thm)],[f_4316_3]) ).

fof(f_4317_1,plain,
    ! [V_x_2,V_P_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(V_P_2,V_x_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
      | ? [B_i] :
          ( ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_all__nth__imp__all__set]) ).

fof(f_4317_2,plain,
    ! [U_17622,U_17621,U_17620,U_17619] :
      ( hBOOL(hAPP(U_17621,U_17622))
      | ~ hBOOL(hAPP(hAPP(c_member(U_17619),U_17622),hAPP(c_List_Oset(U_17619),U_17620)))
      | ? [U_17618] :
          ( ~ hBOOL(hAPP(U_17621,hAPP(hAPP(c_List_Onth(U_17619),U_17620),U_17618)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_17618),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17619)),U_17620))) ) ),
    inference(variable_rename,[status(thm)],[f_4317_1]) ).

fof(f_4317_3,plain,
    ! [U_17622,U_17621,U_17620,U_17619] :
      ( hBOOL(hAPP(U_17621,U_17622))
      | ~ hBOOL(hAPP(hAPP(c_member(U_17619),U_17622),hAPP(c_List_Oset(U_17619),U_17620)))
      | ( ~ hBOOL(hAPP(U_17621,hAPP(hAPP(c_List_Onth(U_17619),U_17620),sK441(U_17622,U_17621,U_17620,U_17619))))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK441(U_17622,U_17621,U_17620,U_17619)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17619)),U_17620))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK441]),skolemize(U_17618,sK441(U_17622,U_17621,U_17620,U_17619))],[f_4317_2]) ).

cnf(f_4317_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK441(U_17622,U_17621,U_17620,U_17619)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17619)),U_17620)))
    | hBOOL(hAPP(U_17621,U_17622))
    | ~ hBOOL(hAPP(hAPP(c_member(U_17619),U_17622),hAPP(c_List_Oset(U_17619),U_17620))) ),
    inference(clausify,[status(thm)],[f_4317_3]) ).

cnf(f_4317_5,plain,
    ( ~ hBOOL(hAPP(U_17621,hAPP(hAPP(c_List_Onth(U_17619),U_17620),sK441(U_17622,U_17621,U_17620,U_17619))))
    | hBOOL(hAPP(U_17621,U_17622))
    | ~ hBOOL(hAPP(hAPP(c_member(U_17619),U_17622),hAPP(c_List_Oset(U_17619),U_17620))) ),
    inference(clausify,[status(thm)],[f_4317_3]) ).

fof(f_4318_1,plain,
    ! [V_xs_2,V_y_2,V_f_2,T_c,T_b] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_c,T_b,hAPP(c_COMBC(T_b,T_c,T_c),V_f_2),V_y_2),c_List_Oremdups(T_b,V_xs_2))
      | ~ c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__set__remdups]) ).

fof(f_4318_2,plain,
    ! [U_17627,U_17626,U_17625,U_17624,U_17623] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_17623,U_17624,U_17625),U_17626),hAPP(c_List_Oset(U_17623),U_17627)) = hAPP(c_List_Ofoldl(U_17624,U_17623,hAPP(c_COMBC(U_17623,U_17624,U_17624),U_17625),U_17626),c_List_Oremdups(U_17623,U_17627))
      | ~ c_Finite__Set_Ofun__left__comm(U_17623,U_17624,U_17625) ),
    inference(variable_rename,[status(thm)],[f_4318_1]) ).

cnf(f_4318_3,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_17623,U_17624,U_17625),U_17626),hAPP(c_List_Oset(U_17623),U_17627)) = hAPP(c_List_Ofoldl(U_17624,U_17623,hAPP(c_COMBC(U_17623,U_17624,U_17624),U_17625),U_17626),c_List_Oremdups(U_17623,U_17627))
    | ~ c_Finite__Set_Ofun__left__comm(U_17623,U_17624,U_17625) ),
    inference(clausify,[status(thm)],[f_4318_2]) ).

fof(f_4319_1,plain,
    ! [V_xs_2,V_x_2,V_f_2,T_c,T_b] :
      ( hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),hAPP(c_List_OremoveAll(T_b,V_x_2),V_xs_2)) = hAPP(c_List_OremoveAll(T_c,hAPP(V_f_2,V_x_2)),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_map__removeAll__inj__on]) ).

fof(f_4319_2,plain,
    ! [U_17632,U_17631,U_17630,U_17629,U_17628] :
      ( hAPP(hAPP(c_List_Omap(U_17628,U_17629),U_17630),hAPP(c_List_OremoveAll(U_17628,U_17631),U_17632)) = hAPP(c_List_OremoveAll(U_17629,hAPP(U_17630,U_17631)),hAPP(hAPP(c_List_Omap(U_17628,U_17629),U_17630),U_17632))
      | ~ c_Fun_Oinj__on(U_17628,U_17629,U_17630,hAPP(hAPP(c_Set_Oinsert(U_17628),U_17631),hAPP(c_List_Oset(U_17628),U_17632))) ),
    inference(variable_rename,[status(thm)],[f_4319_1]) ).

cnf(f_4319_3,plain,
    ( hAPP(hAPP(c_List_Omap(U_17628,U_17629),U_17630),hAPP(c_List_OremoveAll(U_17628,U_17631),U_17632)) = hAPP(c_List_OremoveAll(U_17629,hAPP(U_17630,U_17631)),hAPP(hAPP(c_List_Omap(U_17628,U_17629),U_17630),U_17632))
    | ~ c_Fun_Oinj__on(U_17628,U_17629,U_17630,hAPP(hAPP(c_Set_Oinsert(U_17628),U_17631),hAPP(c_List_Oset(U_17628),U_17632))) ),
    inference(clausify,[status(thm)],[f_4319_2]) ).

fof(f_4320_1,plain,
    ! [V_xs,T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremdups(T_a,V_xs))),
    inference(fof_nnf,[status(thm)],[fact_distinct__remdups]) ).

fof(f_4320_2,plain,
    ! [U_17634,U_17633] : hBOOL(hAPP(c_List_Odistinct(U_17633),c_List_Oremdups(U_17633,U_17634))),
    inference(variable_rename,[status(thm)],[f_4320_1]) ).

cnf(f_4320_3,plain,
    hBOOL(hAPP(c_List_Odistinct(U_17633),c_List_Oremdups(U_17633,U_17634))),
    inference(clausify,[status(thm)],[f_4320_2]) ).

fof(f_4321_1,plain,
    ! [V_xs,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oremdups(T_a,V_xs))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),
    inference(fof_nnf,[status(thm)],[fact_length__remdups__leq]) ).

fof(f_4321_2,plain,
    ! [U_17636,U_17635] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17635)),c_List_Oremdups(U_17635,U_17636))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17635)),U_17636))),
    inference(variable_rename,[status(thm)],[f_4321_1]) ).

cnf(f_4321_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17635)),c_List_Oremdups(U_17635,U_17636))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17635)),U_17636))),
    inference(clausify,[status(thm)],[f_4321_2]) ).

fof(f_4322_1,plain,
    ! [V_xs_2,T_b] :
      ( ( c_List_Oremdups(T_b,V_xs_2) = V_xs_2
        | ~ hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) )
      & ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
        | c_List_Oremdups(T_b,V_xs_2) != V_xs_2 ) ),
    inference(fof_nnf,[status(thm)],[fact_remdups__id__iff__distinct]) ).

fof(f_4322_2,plain,
    ! [U_17638,U_17637] :
      ( ( c_List_Oremdups(U_17637,U_17638) = U_17638
        | ~ hBOOL(hAPP(c_List_Odistinct(U_17637),U_17638)) )
      & ( hBOOL(hAPP(c_List_Odistinct(U_17637),U_17638))
        | c_List_Oremdups(U_17637,U_17638) != U_17638 ) ),
    inference(variable_rename,[status(thm)],[f_4322_1]) ).

fof(f_4322_3,plain,
    ( ! [U_17642,U_17640] :
        ( c_List_Oremdups(U_17640,U_17642) = U_17642
        | ~ hBOOL(hAPP(c_List_Odistinct(U_17640),U_17642)) )
    & ! [U_17641,U_17639] :
        ( hBOOL(hAPP(c_List_Odistinct(U_17639),U_17641))
        | c_List_Oremdups(U_17639,U_17641) != U_17641 ) ),
    inference(miniscope,[status(thm)],[f_4322_2]) ).

cnf(f_4322_4,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_17639),U_17641))
    | c_List_Oremdups(U_17639,U_17641) != U_17641 ),
    inference(clausify,[status(thm)],[f_4322_3]) ).

cnf(f_4322_5,plain,
    ( c_List_Oremdups(U_17640,U_17642) = U_17642
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17640),U_17642)) ),
    inference(clausify,[status(thm)],[f_4322_3]) ).

fof(f_4323_1,plain,
    ! [V_x,V_xs,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_OremoveAll(T_a,V_x),V_xs)))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__removeAll]) ).

fof(f_4323_2,plain,
    ! [U_17645,U_17644,U_17643] :
      ( hBOOL(hAPP(c_List_Odistinct(U_17643),hAPP(c_List_OremoveAll(U_17643,U_17645),U_17644)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17643),U_17644)) ),
    inference(variable_rename,[status(thm)],[f_4323_1]) ).

cnf(f_4323_3,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_17643),hAPP(c_List_OremoveAll(U_17643,U_17645),U_17644)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17643),U_17644)) ),
    inference(clausify,[status(thm)],[f_4323_2]) ).

fof(f_4324_1,plain,
    ! [V_xs,T_a] :
      ( c_List_Oremdups(T_a,V_xs) = V_xs
      | ~ hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__remdups__id]) ).

fof(f_4324_2,plain,
    ! [U_17647,U_17646] :
      ( c_List_Oremdups(U_17646,U_17647) = U_17647
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17646),U_17647)) ),
    inference(variable_rename,[status(thm)],[f_4324_1]) ).

cnf(f_4324_3,plain,
    ( c_List_Oremdups(U_17646,U_17647) = U_17647
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17646),U_17647)) ),
    inference(clausify,[status(thm)],[f_4324_2]) ).

fof(f_4325_1,plain,
    ! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),c_List_Oremdups(T_b,V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_set__remdups]) ).

fof(f_4325_2,plain,
    ! [U_17649,U_17648] : hAPP(c_List_Oset(U_17648),c_List_Oremdups(U_17648,U_17649)) = hAPP(c_List_Oset(U_17648),U_17649),
    inference(variable_rename,[status(thm)],[f_4325_1]) ).

cnf(f_4325_3,plain,
    hAPP(c_List_Oset(U_17648),c_List_Oremdups(U_17648,U_17649)) = hAPP(c_List_Oset(U_17648),U_17649),
    inference(clausify,[status(thm)],[f_4325_2]) ).

fof(f_4326_1,plain,
    ! [V_xs_2,T_b] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremdups(T_b,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)
        | c_List_Oremdups(T_b,V_xs_2) != V_xs_2 )
      & ( c_List_Oremdups(T_b,V_xs_2) = V_xs_2
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremdups(T_b,V_xs_2)) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_length__remdups__eq]) ).

fof(f_4326_2,plain,
    ! [U_17651,U_17650] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17650)),c_List_Oremdups(U_17650,U_17651)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17650)),U_17651)
        | c_List_Oremdups(U_17650,U_17651) != U_17651 )
      & ( c_List_Oremdups(U_17650,U_17651) = U_17651
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17650)),c_List_Oremdups(U_17650,U_17651)) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17650)),U_17651) ) ),
    inference(variable_rename,[status(thm)],[f_4326_1]) ).

fof(f_4326_3,plain,
    ( ! [U_17655,U_17653] :
        ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17653)),c_List_Oremdups(U_17653,U_17655)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17653)),U_17655)
        | c_List_Oremdups(U_17653,U_17655) != U_17655 )
    & ! [U_17654,U_17652] :
        ( c_List_Oremdups(U_17652,U_17654) = U_17654
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17652)),c_List_Oremdups(U_17652,U_17654)) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17652)),U_17654) ) ),
    inference(miniscope,[status(thm)],[f_4326_2]) ).

cnf(f_4326_4,plain,
    ( c_List_Oremdups(U_17652,U_17654) = U_17654
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17652)),c_List_Oremdups(U_17652,U_17654)) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17652)),U_17654) ),
    inference(clausify,[status(thm)],[f_4326_3]) ).

cnf(f_4326_5,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17653)),c_List_Oremdups(U_17653,U_17655)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17653)),U_17655)
    | c_List_Oremdups(U_17653,U_17655) != U_17655 ),
    inference(clausify,[status(thm)],[f_4326_3]) ).

fof(f_4327_1,plain,
    ! [V_xs,T_a] : c_List_Oremdups(T_a,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,V_xs),
    inference(fof_nnf,[status(thm)],[fact_remdups__remdups]) ).

fof(f_4327_2,plain,
    ! [U_17657,U_17656] : c_List_Oremdups(U_17656,c_List_Oremdups(U_17656,U_17657)) = c_List_Oremdups(U_17656,U_17657),
    inference(variable_rename,[status(thm)],[f_4327_1]) ).

cnf(f_4327_3,plain,
    c_List_Oremdups(U_17656,c_List_Oremdups(U_17656,U_17657)) = c_List_Oremdups(U_17656,U_17657),
    inference(clausify,[status(thm)],[f_4327_2]) ).

fof(f_4328_1,plain,
    ! [T_a] : c_List_Oremdups(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a),
    inference(fof_nnf,[status(thm)],[fact_remdups_Osimps_I1_J]) ).

fof(f_4328_2,plain,
    ! [U_17658] : c_List_Oremdups(U_17658,c_List_Olist_ONil(U_17658)) = c_List_Olist_ONil(U_17658),
    inference(variable_rename,[status(thm)],[f_4328_1]) ).

cnf(f_4328_3,plain,
    c_List_Oremdups(U_17658,c_List_Olist_ONil(U_17658)) = c_List_Olist_ONil(U_17658),
    inference(clausify,[status(thm)],[f_4328_2]) ).

fof(f_4329_1,plain,
    ! [V_x_2,T_b] :
      ( ( c_List_Olist_ONil(T_b) = c_List_Oremdups(T_b,V_x_2)
        | V_x_2 != c_List_Olist_ONil(T_b) )
      & ( V_x_2 = c_List_Olist_ONil(T_b)
        | c_List_Olist_ONil(T_b) != c_List_Oremdups(T_b,V_x_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_remdups__eq__nil__right__iff]) ).

fof(f_4329_2,plain,
    ! [U_17660,U_17659] :
      ( ( c_List_Olist_ONil(U_17659) = c_List_Oremdups(U_17659,U_17660)
        | U_17660 != c_List_Olist_ONil(U_17659) )
      & ( U_17660 = c_List_Olist_ONil(U_17659)
        | c_List_Olist_ONil(U_17659) != c_List_Oremdups(U_17659,U_17660) ) ),
    inference(variable_rename,[status(thm)],[f_4329_1]) ).

fof(f_4329_3,plain,
    ( ! [U_17664,U_17662] :
        ( c_List_Olist_ONil(U_17662) = c_List_Oremdups(U_17662,U_17664)
        | U_17664 != c_List_Olist_ONil(U_17662) )
    & ! [U_17663,U_17661] :
        ( U_17663 = c_List_Olist_ONil(U_17661)
        | c_List_Olist_ONil(U_17661) != c_List_Oremdups(U_17661,U_17663) ) ),
    inference(miniscope,[status(thm)],[f_4329_2]) ).

cnf(f_4329_4,plain,
    ( U_17663 = c_List_Olist_ONil(U_17661)
    | c_List_Olist_ONil(U_17661) != c_List_Oremdups(U_17661,U_17663) ),
    inference(clausify,[status(thm)],[f_4329_3]) ).

cnf(f_4329_5,plain,
    ( c_List_Olist_ONil(U_17662) = c_List_Oremdups(U_17662,U_17664)
    | U_17664 != c_List_Olist_ONil(U_17662) ),
    inference(clausify,[status(thm)],[f_4329_3]) ).

fof(f_4330_1,plain,
    ! [V_x,T_a] : hAPP(c_List_OremoveAll(T_a,V_x),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a),
    inference(fof_nnf,[status(thm)],[fact_removeAll_Osimps_I1_J]) ).

fof(f_4330_2,plain,
    ! [U_17666,U_17665] : hAPP(c_List_OremoveAll(U_17665,U_17666),c_List_Olist_ONil(U_17665)) = c_List_Olist_ONil(U_17665),
    inference(variable_rename,[status(thm)],[f_4330_1]) ).

cnf(f_4330_3,plain,
    hAPP(c_List_OremoveAll(U_17665,U_17666),c_List_Olist_ONil(U_17665)) = c_List_Olist_ONil(U_17665),
    inference(clausify,[status(thm)],[f_4330_2]) ).

fof(f_4331_1,plain,
    ! [V_x_2,T_b] :
      ( ( c_List_Oremdups(T_b,V_x_2) = c_List_Olist_ONil(T_b)
        | V_x_2 != c_List_Olist_ONil(T_b) )
      & ( V_x_2 = c_List_Olist_ONil(T_b)
        | c_List_Oremdups(T_b,V_x_2) != c_List_Olist_ONil(T_b) ) ),
    inference(fof_nnf,[status(thm)],[fact_remdups__eq__nil__iff]) ).

fof(f_4331_2,plain,
    ! [U_17668,U_17667] :
      ( ( c_List_Oremdups(U_17667,U_17668) = c_List_Olist_ONil(U_17667)
        | U_17668 != c_List_Olist_ONil(U_17667) )
      & ( U_17668 = c_List_Olist_ONil(U_17667)
        | c_List_Oremdups(U_17667,U_17668) != c_List_Olist_ONil(U_17667) ) ),
    inference(variable_rename,[status(thm)],[f_4331_1]) ).

fof(f_4331_3,plain,
    ( ! [U_17672,U_17670] :
        ( c_List_Oremdups(U_17670,U_17672) = c_List_Olist_ONil(U_17670)
        | U_17672 != c_List_Olist_ONil(U_17670) )
    & ! [U_17671,U_17669] :
        ( U_17671 = c_List_Olist_ONil(U_17669)
        | c_List_Oremdups(U_17669,U_17671) != c_List_Olist_ONil(U_17669) ) ),
    inference(miniscope,[status(thm)],[f_4331_2]) ).

cnf(f_4331_4,plain,
    ( U_17671 = c_List_Olist_ONil(U_17669)
    | c_List_Oremdups(U_17669,U_17671) != c_List_Olist_ONil(U_17669) ),
    inference(clausify,[status(thm)],[f_4331_3]) ).

cnf(f_4331_5,plain,
    ( c_List_Oremdups(U_17670,U_17672) = c_List_Olist_ONil(U_17670)
    | U_17672 != c_List_Olist_ONil(U_17670) ),
    inference(clausify,[status(thm)],[f_4331_3]) ).

fof(f_4332_1,plain,
    ! [V_xs,T_a,V_y,V_x] :
      ( ( hAPP(c_List_OremoveAll(T_a,V_x),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),hAPP(c_List_OremoveAll(T_a,V_x),V_xs))
        | V_x = V_y )
      & ( hAPP(c_List_OremoveAll(T_a,V_x),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = hAPP(c_List_OremoveAll(T_a,V_x),V_xs)
        | V_x != V_y ) ),
    inference(fof_nnf,[status(thm)],[fact_removeAll_Osimps_I2_J]) ).

fof(f_4332_2,plain,
    ! [U_17676,U_17675,U_17674,U_17673] :
      ( ( hAPP(c_List_OremoveAll(U_17675,U_17673),hAPP(hAPP(c_List_Olist_OCons(U_17675),U_17674),U_17676)) = hAPP(hAPP(c_List_Olist_OCons(U_17675),U_17674),hAPP(c_List_OremoveAll(U_17675,U_17673),U_17676))
        | U_17673 = U_17674 )
      & ( hAPP(c_List_OremoveAll(U_17675,U_17673),hAPP(hAPP(c_List_Olist_OCons(U_17675),U_17674),U_17676)) = hAPP(c_List_OremoveAll(U_17675,U_17673),U_17676)
        | U_17673 != U_17674 ) ),
    inference(variable_rename,[status(thm)],[f_4332_1]) ).

fof(f_4332_3,plain,
    ( ! [U_17684,U_17682,U_17680,U_17678] :
        ( hAPP(c_List_OremoveAll(U_17682,U_17678),hAPP(hAPP(c_List_Olist_OCons(U_17682),U_17680),U_17684)) = hAPP(hAPP(c_List_Olist_OCons(U_17682),U_17680),hAPP(c_List_OremoveAll(U_17682,U_17678),U_17684))
        | U_17678 = U_17680 )
    & ! [U_17683,U_17681,U_17679,U_17677] :
        ( hAPP(c_List_OremoveAll(U_17681,U_17677),hAPP(hAPP(c_List_Olist_OCons(U_17681),U_17679),U_17683)) = hAPP(c_List_OremoveAll(U_17681,U_17677),U_17683)
        | U_17677 != U_17679 ) ),
    inference(miniscope,[status(thm)],[f_4332_2]) ).

cnf(f_4332_4,plain,
    ( hAPP(c_List_OremoveAll(U_17681,U_17677),hAPP(hAPP(c_List_Olist_OCons(U_17681),U_17679),U_17683)) = hAPP(c_List_OremoveAll(U_17681,U_17677),U_17683)
    | U_17677 != U_17679 ),
    inference(clausify,[status(thm)],[f_4332_3]) ).

cnf(f_4332_5,plain,
    ( hAPP(c_List_OremoveAll(U_17682,U_17678),hAPP(hAPP(c_List_Olist_OCons(U_17682),U_17680),U_17684)) = hAPP(hAPP(c_List_Olist_OCons(U_17682),U_17680),hAPP(c_List_OremoveAll(U_17682,U_17678),U_17684))
    | U_17678 = U_17680 ),
    inference(clausify,[status(thm)],[f_4332_3]) ).

fof(f_4333_1,plain,
    ! [V_ys,V_xs,V_x,T_a] : hAPP(c_List_OremoveAll(T_a,V_x),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_OremoveAll(T_a,V_x),V_xs)),hAPP(c_List_OremoveAll(T_a,V_x),V_ys)),
    inference(fof_nnf,[status(thm)],[fact_removeAll__append]) ).

fof(f_4333_2,plain,
    ! [U_17688,U_17687,U_17686,U_17685] : hAPP(c_List_OremoveAll(U_17685,U_17686),hAPP(hAPP(c_List_Oappend(U_17685),U_17687),U_17688)) = hAPP(hAPP(c_List_Oappend(U_17685),hAPP(c_List_OremoveAll(U_17685,U_17686),U_17687)),hAPP(c_List_OremoveAll(U_17685,U_17686),U_17688)),
    inference(variable_rename,[status(thm)],[f_4333_1]) ).

cnf(f_4333_3,plain,
    hAPP(c_List_OremoveAll(U_17685,U_17686),hAPP(hAPP(c_List_Oappend(U_17685),U_17687),U_17688)) = hAPP(hAPP(c_List_Oappend(U_17685),hAPP(c_List_OremoveAll(U_17685,U_17686),U_17687)),hAPP(c_List_OremoveAll(U_17685,U_17686),U_17688)),
    inference(clausify,[status(thm)],[f_4333_2]) ).

fof(f_4334_1,plain,
    ! [V_xs_2,V_f_2,T_c,T_b] : c_List_Oremdups(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Oremdups(T_c,V_xs_2))) = c_List_Oremdups(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_remdups__map__remdups]) ).

fof(f_4334_2,plain,
    ! [U_17692,U_17691,U_17690,U_17689] : c_List_Oremdups(U_17689,hAPP(hAPP(c_List_Omap(U_17690,U_17689),U_17691),c_List_Oremdups(U_17690,U_17692))) = c_List_Oremdups(U_17689,hAPP(hAPP(c_List_Omap(U_17690,U_17689),U_17691),U_17692)),
    inference(variable_rename,[status(thm)],[f_4334_1]) ).

cnf(f_4334_3,plain,
    c_List_Oremdups(U_17689,hAPP(hAPP(c_List_Omap(U_17690,U_17689),U_17691),c_List_Oremdups(U_17690,U_17692))) = c_List_Oremdups(U_17689,hAPP(hAPP(c_List_Omap(U_17690,U_17689),U_17691),U_17692)),
    inference(clausify,[status(thm)],[f_4334_2]) ).

fof(f_4335_1,plain,
    ! [V_x,V_xs,T_a] :
      ( c_List_Oremove1(T_a,V_x,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,c_List_Oremove1(T_a,V_x,V_xs))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) ),
    inference(fof_nnf,[status(thm)],[fact_remove1__remdups]) ).

fof(f_4335_2,plain,
    ! [U_17695,U_17694,U_17693] :
      ( c_List_Oremove1(U_17693,U_17695,c_List_Oremdups(U_17693,U_17694)) = c_List_Oremdups(U_17693,c_List_Oremove1(U_17693,U_17695,U_17694))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17693),U_17694)) ),
    inference(variable_rename,[status(thm)],[f_4335_1]) ).

cnf(f_4335_3,plain,
    ( c_List_Oremove1(U_17693,U_17695,c_List_Oremdups(U_17693,U_17694)) = c_List_Oremdups(U_17693,c_List_Oremove1(U_17693,U_17695,U_17694))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17693),U_17694)) ),
    inference(clausify,[status(thm)],[f_4335_2]) ).

fof(f_4336_1,plain,
    ! [V_xs_2,V_x_2,T_b] :
      ( hAPP(c_List_OremoveAll(T_b,V_x_2),V_xs_2) = V_xs_2
      | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_removeAll__id]) ).

fof(f_4336_2,plain,
    ! [U_17698,U_17697,U_17696] :
      ( hAPP(c_List_OremoveAll(U_17696,U_17697),U_17698) = U_17698
      | hBOOL(hAPP(hAPP(c_member(U_17696),U_17697),hAPP(c_List_Oset(U_17696),U_17698))) ),
    inference(variable_rename,[status(thm)],[f_4336_1]) ).

cnf(f_4336_3,plain,
    ( hAPP(c_List_OremoveAll(U_17696,U_17697),U_17698) = U_17698
    | hBOOL(hAPP(hAPP(c_member(U_17696),U_17697),hAPP(c_List_Oset(U_17696),U_17698))) ),
    inference(clausify,[status(thm)],[f_4336_2]) ).

fof(f_4337_1,plain,
    ! [V_x,V_xs,T_a] :
      ( c_List_Oremove1(T_a,V_x,V_xs) = hAPP(c_List_OremoveAll(T_a,V_x),V_xs)
      | ~ hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__remove1__removeAll]) ).

fof(f_4337_2,plain,
    ! [U_17701,U_17700,U_17699] :
      ( c_List_Oremove1(U_17699,U_17701,U_17700) = hAPP(c_List_OremoveAll(U_17699,U_17701),U_17700)
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17699),U_17700)) ),
    inference(variable_rename,[status(thm)],[f_4337_1]) ).

cnf(f_4337_3,plain,
    ( c_List_Oremove1(U_17699,U_17701,U_17700) = hAPP(c_List_OremoveAll(U_17699,U_17701),U_17700)
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17699),U_17700)) ),
    inference(clausify,[status(thm)],[f_4337_2]) ).

fof(f_4338_1,plain,
    ! [V_xs_2,V_x_2,T_b] :
      ( ( c_List_Oremdups(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Oremdups(T_b,V_xs_2))
        | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) )
      & ( c_List_Oremdups(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_List_Oremdups(T_b,V_xs_2)
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_remdups_Osimps_I2_J]) ).

fof(f_4338_2,plain,
    ! [U_17704,U_17703,U_17702] :
      ( ( c_List_Oremdups(U_17702,hAPP(hAPP(c_List_Olist_OCons(U_17702),U_17703),U_17704)) = hAPP(hAPP(c_List_Olist_OCons(U_17702),U_17703),c_List_Oremdups(U_17702,U_17704))
        | hBOOL(hAPP(hAPP(c_member(U_17702),U_17703),hAPP(c_List_Oset(U_17702),U_17704))) )
      & ( c_List_Oremdups(U_17702,hAPP(hAPP(c_List_Olist_OCons(U_17702),U_17703),U_17704)) = c_List_Oremdups(U_17702,U_17704)
        | ~ hBOOL(hAPP(hAPP(c_member(U_17702),U_17703),hAPP(c_List_Oset(U_17702),U_17704))) ) ),
    inference(variable_rename,[status(thm)],[f_4338_1]) ).

fof(f_4338_3,plain,
    ( ! [U_17710,U_17708,U_17706] :
        ( c_List_Oremdups(U_17706,hAPP(hAPP(c_List_Olist_OCons(U_17706),U_17708),U_17710)) = hAPP(hAPP(c_List_Olist_OCons(U_17706),U_17708),c_List_Oremdups(U_17706,U_17710))
        | hBOOL(hAPP(hAPP(c_member(U_17706),U_17708),hAPP(c_List_Oset(U_17706),U_17710))) )
    & ! [U_17709,U_17707,U_17705] :
        ( c_List_Oremdups(U_17705,hAPP(hAPP(c_List_Olist_OCons(U_17705),U_17707),U_17709)) = c_List_Oremdups(U_17705,U_17709)
        | ~ hBOOL(hAPP(hAPP(c_member(U_17705),U_17707),hAPP(c_List_Oset(U_17705),U_17709))) ) ),
    inference(miniscope,[status(thm)],[f_4338_2]) ).

cnf(f_4338_4,plain,
    ( c_List_Oremdups(U_17705,hAPP(hAPP(c_List_Olist_OCons(U_17705),U_17707),U_17709)) = c_List_Oremdups(U_17705,U_17709)
    | ~ hBOOL(hAPP(hAPP(c_member(U_17705),U_17707),hAPP(c_List_Oset(U_17705),U_17709))) ),
    inference(clausify,[status(thm)],[f_4338_3]) ).

cnf(f_4338_5,plain,
    ( c_List_Oremdups(U_17706,hAPP(hAPP(c_List_Olist_OCons(U_17706),U_17708),U_17710)) = hAPP(hAPP(c_List_Olist_OCons(U_17706),U_17708),c_List_Oremdups(U_17706,U_17710))
    | hBOOL(hAPP(hAPP(c_member(U_17706),U_17708),hAPP(c_List_Oset(U_17706),U_17710))) ),
    inference(clausify,[status(thm)],[f_4338_3]) ).

fof(f_4339_1,plain,
    ! [V_xs_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremdups(T_b,V_xs_2)) = hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_List_Oset(T_b),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_length__remdups__card__conv]) ).

fof(f_4339_2,plain,
    ! [U_17712,U_17711] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17711)),c_List_Oremdups(U_17711,U_17712)) = hAPP(c_Finite__Set_Ocard(U_17711),hAPP(c_List_Oset(U_17711),U_17712)),
    inference(variable_rename,[status(thm)],[f_4339_1]) ).

cnf(f_4339_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17711)),c_List_Oremdups(U_17711,U_17712)) = hAPP(c_Finite__Set_Ocard(U_17711),hAPP(c_List_Oset(U_17711),U_17712)),
    inference(clausify,[status(thm)],[f_4339_2]) ).

fof(f_4340_1,plain,
    ! [V_xs_2,V_x_2,V_f_2,T_c,T_b] :
      ( hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),hAPP(c_List_OremoveAll(T_b,V_x_2),V_xs_2)) = hAPP(c_List_OremoveAll(T_c,hAPP(V_f_2,V_x_2)),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_map__removeAll__inj]) ).

fof(f_4340_2,plain,
    ! [U_17717,U_17716,U_17715,U_17714,U_17713] :
      ( hAPP(hAPP(c_List_Omap(U_17713,U_17714),U_17715),hAPP(c_List_OremoveAll(U_17713,U_17716),U_17717)) = hAPP(c_List_OremoveAll(U_17714,hAPP(U_17715,U_17716)),hAPP(hAPP(c_List_Omap(U_17713,U_17714),U_17715),U_17717))
      | ~ c_Fun_Oinj__on(U_17713,U_17714,U_17715,c_Orderings_Otop__class_Otop(tc_fun(U_17713,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_4340_1]) ).

cnf(f_4340_3,plain,
    ( hAPP(hAPP(c_List_Omap(U_17713,U_17714),U_17715),hAPP(c_List_OremoveAll(U_17713,U_17716),U_17717)) = hAPP(c_List_OremoveAll(U_17714,hAPP(U_17715,U_17716)),hAPP(hAPP(c_List_Omap(U_17713,U_17714),U_17715),U_17717))
    | ~ c_Fun_Oinj__on(U_17713,U_17714,U_17715,c_Orderings_Otop__class_Otop(tc_fun(U_17713,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4340_2]) ).

fof(f_4341_1,plain,
    ! [V_xs_2,V_x_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_OremoveAll(T_b,V_x_2),V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),
    inference(fof_nnf,[status(thm)],[fact_set__removeAll]) ).

fof(f_4341_2,plain,
    ! [U_17720,U_17719,U_17718] : hAPP(c_List_Oset(U_17718),hAPP(c_List_OremoveAll(U_17718,U_17719),U_17720)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_17718,tc_HOL_Obool)),hAPP(c_List_Oset(U_17718),U_17720)),hAPP(hAPP(c_Set_Oinsert(U_17718),U_17719),c_Orderings_Obot__class_Obot(tc_fun(U_17718,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_4341_1]) ).

cnf(f_4341_3,plain,
    hAPP(c_List_Oset(U_17718),hAPP(c_List_OremoveAll(U_17718,U_17719),U_17720)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_17718,tc_HOL_Obool)),hAPP(c_List_Oset(U_17718),U_17720)),hAPP(hAPP(c_Set_Oinsert(U_17718),U_17719),c_Orderings_Obot__class_Obot(tc_fun(U_17718,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_4341_2]) ).

fof(f_4342_1,plain,
    ! [V_xss_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremdups(T_b,c_List_Oconcat(T_b,V_xss_2))) = hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2)),c_List_Oset(T_b))),
    inference(fof_nnf,[status(thm)],[fact_length__remdups__concat]) ).

fof(f_4342_2,plain,
    ! [U_17722,U_17721] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17721)),c_List_Oremdups(U_17721,c_List_Oconcat(U_17721,U_17722))) = hAPP(c_Finite__Set_Ocard(U_17721),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(U_17721),tc_fun(U_17721,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(U_17721)),U_17722)),c_List_Oset(U_17721))),
    inference(variable_rename,[status(thm)],[f_4342_1]) ).

cnf(f_4342_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17721)),c_List_Oremdups(U_17721,c_List_Oconcat(U_17721,U_17722))) = hAPP(c_Finite__Set_Ocard(U_17721),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(U_17721),tc_fun(U_17721,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(U_17721)),U_17722)),c_List_Oset(U_17721))),
    inference(clausify,[status(thm)],[f_4342_2]) ).

fof(f_4343_1,plain,
    ! [V_xs_2,T_b] :
      ( c_List_Olinorder__class_Osorted__list__of__set(T_b,hAPP(c_List_Oset(T_b),V_xs_2)) = c_List_Olinorder__class_Osort__key(T_b,T_b,c_COMBI(T_b),c_List_Oremdups(T_b,V_xs_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__list__of__set__sort__remdups]) ).

fof(f_4343_2,plain,
    ! [U_17724,U_17723] :
      ( c_List_Olinorder__class_Osorted__list__of__set(U_17723,hAPP(c_List_Oset(U_17723),U_17724)) = c_List_Olinorder__class_Osort__key(U_17723,U_17723,c_COMBI(U_17723),c_List_Oremdups(U_17723,U_17724))
      | ~ class_Orderings_Olinorder(U_17723) ),
    inference(variable_rename,[status(thm)],[f_4343_1]) ).

cnf(f_4343_3,plain,
    ( c_List_Olinorder__class_Osorted__list__of__set(U_17723,hAPP(c_List_Oset(U_17723),U_17724)) = c_List_Olinorder__class_Osort__key(U_17723,U_17723,c_COMBI(U_17723),c_List_Oremdups(U_17723,U_17724))
    | ~ class_Orderings_Olinorder(U_17723) ),
    inference(clausify,[status(thm)],[f_4343_2]) ).

fof(f_4344_1,plain,
    ! [V_f_2,T_b,T_c] :
      ( c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b)
      | ~ class_Orderings_Olinorder(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_sort__key__simps_I1_J]) ).

fof(f_4344_2,plain,
    ! [U_17727,U_17726,U_17725] :
      ( c_List_Olinorder__class_Osort__key(U_17726,U_17725,U_17727,c_List_Olist_ONil(U_17726)) = c_List_Olist_ONil(U_17726)
      | ~ class_Orderings_Olinorder(U_17725) ),
    inference(variable_rename,[status(thm)],[f_4344_1]) ).

cnf(f_4344_3,plain,
    ( c_List_Olinorder__class_Osort__key(U_17726,U_17725,U_17727,c_List_Olist_ONil(U_17726)) = c_List_Olist_ONil(U_17726)
    | ~ class_Orderings_Olinorder(U_17725) ),
    inference(clausify,[status(thm)],[f_4344_2]) ).

fof(f_4345_1,plain,
    ! [V_xss_2,V_xs_2,T_b] : hAPP(c_List_Ofoldl(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Oappend(T_b),V_xs_2),V_xss_2) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),c_List_Oconcat(T_b,V_xss_2)),
    inference(fof_nnf,[status(thm)],[fact_foldl__conv__concat]) ).

fof(f_4345_2,plain,
    ! [U_17730,U_17729,U_17728] : hAPP(c_List_Ofoldl(tc_List_Olist(U_17728),tc_List_Olist(U_17728),c_List_Oappend(U_17728),U_17729),U_17730) = hAPP(hAPP(c_List_Oappend(U_17728),U_17729),c_List_Oconcat(U_17728,U_17730)),
    inference(variable_rename,[status(thm)],[f_4345_1]) ).

cnf(f_4345_3,plain,
    hAPP(c_List_Ofoldl(tc_List_Olist(U_17728),tc_List_Olist(U_17728),c_List_Oappend(U_17728),U_17729),U_17730) = hAPP(hAPP(c_List_Oappend(U_17728),U_17729),c_List_Oconcat(U_17728,U_17730)),
    inference(clausify,[status(thm)],[f_4345_2]) ).

fof(f_4346_1,plain,
    ! [V_xss_2,T_b] : c_List_Oconcat(T_b,V_xss_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Oappend(T_b),c_List_Olist_ONil(T_b)),V_xss_2),
    inference(fof_nnf,[status(thm)],[fact_concat__conv__foldl]) ).

fof(f_4346_2,plain,
    ! [U_17732,U_17731] : c_List_Oconcat(U_17731,U_17732) = hAPP(c_List_Ofoldl(tc_List_Olist(U_17731),tc_List_Olist(U_17731),c_List_Oappend(U_17731),c_List_Olist_ONil(U_17731)),U_17732),
    inference(variable_rename,[status(thm)],[f_4346_1]) ).

cnf(f_4346_3,plain,
    c_List_Oconcat(U_17731,U_17732) = hAPP(c_List_Ofoldl(tc_List_Olist(U_17731),tc_List_Olist(U_17731),c_List_Oappend(U_17731),c_List_Olist_ONil(U_17731)),U_17732),
    inference(clausify,[status(thm)],[f_4346_2]) ).

fof(f_4347_1,plain,
    ! [V_xs_2,V_f_2,T_b,T_c] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)
      | ~ class_Orderings_Olinorder(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_length__sort]) ).

fof(f_4347_2,plain,
    ! [U_17736,U_17735,U_17734,U_17733] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17734)),c_List_Olinorder__class_Osort__key(U_17734,U_17733,U_17735,U_17736)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17734)),U_17736)
      | ~ class_Orderings_Olinorder(U_17733) ),
    inference(variable_rename,[status(thm)],[f_4347_1]) ).

cnf(f_4347_3,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17734)),c_List_Olinorder__class_Osort__key(U_17734,U_17733,U_17735,U_17736)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17734)),U_17736)
    | ~ class_Orderings_Olinorder(U_17733) ),
    inference(clausify,[status(thm)],[f_4347_2]) ).

fof(f_4348_1,plain,
    ! [V_xs_2,V_f_2,T_b,T_c] :
      ( hAPP(c_List_Oset(T_b),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2)
      | ~ class_Orderings_Olinorder(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_set__sort]) ).

fof(f_4348_2,plain,
    ! [U_17740,U_17739,U_17738,U_17737] :
      ( hAPP(c_List_Oset(U_17738),c_List_Olinorder__class_Osort__key(U_17738,U_17737,U_17739,U_17740)) = hAPP(c_List_Oset(U_17738),U_17740)
      | ~ class_Orderings_Olinorder(U_17737) ),
    inference(variable_rename,[status(thm)],[f_4348_1]) ).

cnf(f_4348_3,plain,
    ( hAPP(c_List_Oset(U_17738),c_List_Olinorder__class_Osort__key(U_17738,U_17737,U_17739,U_17740)) = hAPP(c_List_Oset(U_17738),U_17740)
    | ~ class_Orderings_Olinorder(U_17737) ),
    inference(clausify,[status(thm)],[f_4348_2]) ).

fof(f_4349_1,plain,
    ! [V_xs_2,V_f_2,T_b,T_c] :
      ( ( ( hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2)))
          | ~ hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) )
        & ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
          | ~ hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2))) ) )
      | ~ class_Orderings_Olinorder(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__sort]) ).

fof(f_4349_2,plain,
    ! [U_17744,U_17743,U_17742,U_17741] :
      ( ( ( hBOOL(hAPP(c_List_Odistinct(U_17742),c_List_Olinorder__class_Osort__key(U_17742,U_17741,U_17743,U_17744)))
          | ~ hBOOL(hAPP(c_List_Odistinct(U_17742),U_17744)) )
        & ( hBOOL(hAPP(c_List_Odistinct(U_17742),U_17744))
          | ~ hBOOL(hAPP(c_List_Odistinct(U_17742),c_List_Olinorder__class_Osort__key(U_17742,U_17741,U_17743,U_17744))) ) )
      | ~ class_Orderings_Olinorder(U_17741) ),
    inference(variable_rename,[status(thm)],[f_4349_1]) ).

cnf(f_4349_3,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_17742),U_17744))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17742),c_List_Olinorder__class_Osort__key(U_17742,U_17741,U_17743,U_17744)))
    | ~ class_Orderings_Olinorder(U_17741) ),
    inference(clausify,[status(thm)],[f_4349_2]) ).

cnf(f_4349_4,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_17742),c_List_Olinorder__class_Osort__key(U_17742,U_17741,U_17743,U_17744)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17742),U_17744))
    | ~ class_Orderings_Olinorder(U_17741) ),
    inference(clausify,[status(thm)],[f_4349_2]) ).

fof(f_4350_1,plain,
    ! [T_a] : c_List_Oconcat(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(T_a),
    inference(fof_nnf,[status(thm)],[fact_concat_Osimps_I1_J]) ).

fof(f_4350_2,plain,
    ! [U_17745] : c_List_Oconcat(U_17745,c_List_Olist_ONil(tc_List_Olist(U_17745))) = c_List_Olist_ONil(U_17745),
    inference(variable_rename,[status(thm)],[f_4350_1]) ).

cnf(f_4350_3,plain,
    c_List_Oconcat(U_17745,c_List_Olist_ONil(tc_List_Olist(U_17745))) = c_List_Olist_ONil(U_17745),
    inference(clausify,[status(thm)],[f_4350_2]) ).

fof(f_4351_1,plain,
    ! [V_xs,V_x,T_a] : c_List_Oconcat(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),V_x),V_xs)) = hAPP(hAPP(c_List_Oappend(T_a),V_x),c_List_Oconcat(T_a,V_xs)),
    inference(fof_nnf,[status(thm)],[fact_concat_Osimps_I2_J]) ).

fof(f_4351_2,plain,
    ! [U_17748,U_17747,U_17746] : c_List_Oconcat(U_17746,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_17746)),U_17747),U_17748)) = hAPP(hAPP(c_List_Oappend(U_17746),U_17747),c_List_Oconcat(U_17746,U_17748)),
    inference(variable_rename,[status(thm)],[f_4351_1]) ).

cnf(f_4351_3,plain,
    c_List_Oconcat(U_17746,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_17746)),U_17747),U_17748)) = hAPP(hAPP(c_List_Oappend(U_17746),U_17747),c_List_Oconcat(U_17746,U_17748)),
    inference(clausify,[status(thm)],[f_4351_2]) ).

fof(f_4352_1,plain,
    ! [V_xss_2,T_b] :
      ( ( c_List_Olist_ONil(T_b) = c_List_Oconcat(T_b,V_xss_2)
        | ? [B_x] :
            ( B_x != c_List_Olist_ONil(T_b)
            & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2))) ) )
      & ( ! [B_x] :
            ( B_x = c_List_Olist_ONil(T_b)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2))) )
        | c_List_Olist_ONil(T_b) != c_List_Oconcat(T_b,V_xss_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_Nil__eq__concat__conv]) ).

fof(f_4352_2,plain,
    ! [U_17752,U_17751] :
      ( ( c_List_Olist_ONil(U_17751) = c_List_Oconcat(U_17751,U_17752)
        | ? [U_17750] :
            ( U_17750 != c_List_Olist_ONil(U_17751)
            & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17751)),U_17750),hAPP(c_List_Oset(tc_List_Olist(U_17751)),U_17752))) ) )
      & ( ! [U_17749] :
            ( U_17749 = c_List_Olist_ONil(U_17751)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17751)),U_17749),hAPP(c_List_Oset(tc_List_Olist(U_17751)),U_17752))) )
        | c_List_Olist_ONil(U_17751) != c_List_Oconcat(U_17751,U_17752) ) ),
    inference(variable_rename,[status(thm)],[f_4352_1]) ).

fof(f_4352_3,plain,
    ( ! [U_17756,U_17754] :
        ( c_List_Olist_ONil(U_17754) = c_List_Oconcat(U_17754,U_17756)
        | ? [U_17750] :
            ( U_17750 != c_List_Olist_ONil(U_17754)
            & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17754)),U_17750),hAPP(c_List_Oset(tc_List_Olist(U_17754)),U_17756))) ) )
    & ! [U_17755,U_17753] :
        ( ! [U_17749] :
            ( U_17749 = c_List_Olist_ONil(U_17753)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17753)),U_17749),hAPP(c_List_Oset(tc_List_Olist(U_17753)),U_17755))) )
        | c_List_Olist_ONil(U_17753) != c_List_Oconcat(U_17753,U_17755) ) ),
    inference(miniscope,[status(thm)],[f_4352_2]) ).

fof(f_4352_4,plain,
    ( ! [U_17756,U_17754] :
        ( c_List_Olist_ONil(U_17754) = c_List_Oconcat(U_17754,U_17756)
        | ( sK442(U_17756,U_17754) != c_List_Olist_ONil(U_17754)
          & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17754)),sK442(U_17756,U_17754)),hAPP(c_List_Oset(tc_List_Olist(U_17754)),U_17756))) ) )
    & ! [U_17755,U_17753] :
        ( ! [U_17749] :
            ( U_17749 = c_List_Olist_ONil(U_17753)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17753)),U_17749),hAPP(c_List_Oset(tc_List_Olist(U_17753)),U_17755))) )
        | c_List_Olist_ONil(U_17753) != c_List_Oconcat(U_17753,U_17755) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK442]),skolemize(U_17750,sK442(U_17756,U_17754))],[f_4352_3]) ).

cnf(f_4352_5,plain,
    ( U_17749 = c_List_Olist_ONil(U_17753)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17753)),U_17749),hAPP(c_List_Oset(tc_List_Olist(U_17753)),U_17755)))
    | c_List_Olist_ONil(U_17753) != c_List_Oconcat(U_17753,U_17755) ),
    inference(clausify,[status(thm)],[f_4352_4]) ).

cnf(f_4352_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17754)),sK442(U_17756,U_17754)),hAPP(c_List_Oset(tc_List_Olist(U_17754)),U_17756)))
    | c_List_Olist_ONil(U_17754) = c_List_Oconcat(U_17754,U_17756) ),
    inference(clausify,[status(thm)],[f_4352_4]) ).

cnf(f_4352_7,plain,
    ( sK442(U_17756,U_17754) != c_List_Olist_ONil(U_17754)
    | c_List_Olist_ONil(U_17754) = c_List_Oconcat(U_17754,U_17756) ),
    inference(clausify,[status(thm)],[f_4352_4]) ).

fof(f_4353_1,plain,
    ! [V_xss_2,T_b] :
      ( ( c_List_Oconcat(T_b,V_xss_2) = c_List_Olist_ONil(T_b)
        | ? [B_x] :
            ( B_x != c_List_Olist_ONil(T_b)
            & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2))) ) )
      & ( ! [B_x] :
            ( B_x = c_List_Olist_ONil(T_b)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2))) )
        | c_List_Oconcat(T_b,V_xss_2) != c_List_Olist_ONil(T_b) ) ),
    inference(fof_nnf,[status(thm)],[fact_concat__eq__Nil__conv]) ).

fof(f_4353_2,plain,
    ! [U_17760,U_17759] :
      ( ( c_List_Oconcat(U_17759,U_17760) = c_List_Olist_ONil(U_17759)
        | ? [U_17758] :
            ( U_17758 != c_List_Olist_ONil(U_17759)
            & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17759)),U_17758),hAPP(c_List_Oset(tc_List_Olist(U_17759)),U_17760))) ) )
      & ( ! [U_17757] :
            ( U_17757 = c_List_Olist_ONil(U_17759)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17759)),U_17757),hAPP(c_List_Oset(tc_List_Olist(U_17759)),U_17760))) )
        | c_List_Oconcat(U_17759,U_17760) != c_List_Olist_ONil(U_17759) ) ),
    inference(variable_rename,[status(thm)],[f_4353_1]) ).

fof(f_4353_3,plain,
    ( ! [U_17764,U_17762] :
        ( c_List_Oconcat(U_17762,U_17764) = c_List_Olist_ONil(U_17762)
        | ? [U_17758] :
            ( U_17758 != c_List_Olist_ONil(U_17762)
            & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17762)),U_17758),hAPP(c_List_Oset(tc_List_Olist(U_17762)),U_17764))) ) )
    & ! [U_17763,U_17761] :
        ( ! [U_17757] :
            ( U_17757 = c_List_Olist_ONil(U_17761)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17761)),U_17757),hAPP(c_List_Oset(tc_List_Olist(U_17761)),U_17763))) )
        | c_List_Oconcat(U_17761,U_17763) != c_List_Olist_ONil(U_17761) ) ),
    inference(miniscope,[status(thm)],[f_4353_2]) ).

fof(f_4353_4,plain,
    ( ! [U_17764,U_17762] :
        ( c_List_Oconcat(U_17762,U_17764) = c_List_Olist_ONil(U_17762)
        | ( sK443(U_17764,U_17762) != c_List_Olist_ONil(U_17762)
          & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17762)),sK443(U_17764,U_17762)),hAPP(c_List_Oset(tc_List_Olist(U_17762)),U_17764))) ) )
    & ! [U_17763,U_17761] :
        ( ! [U_17757] :
            ( U_17757 = c_List_Olist_ONil(U_17761)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17761)),U_17757),hAPP(c_List_Oset(tc_List_Olist(U_17761)),U_17763))) )
        | c_List_Oconcat(U_17761,U_17763) != c_List_Olist_ONil(U_17761) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK443]),skolemize(U_17758,sK443(U_17764,U_17762))],[f_4353_3]) ).

cnf(f_4353_5,plain,
    ( U_17757 = c_List_Olist_ONil(U_17761)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17761)),U_17757),hAPP(c_List_Oset(tc_List_Olist(U_17761)),U_17763)))
    | c_List_Oconcat(U_17761,U_17763) != c_List_Olist_ONil(U_17761) ),
    inference(clausify,[status(thm)],[f_4353_4]) ).

cnf(f_4353_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17762)),sK443(U_17764,U_17762)),hAPP(c_List_Oset(tc_List_Olist(U_17762)),U_17764)))
    | c_List_Oconcat(U_17762,U_17764) = c_List_Olist_ONil(U_17762) ),
    inference(clausify,[status(thm)],[f_4353_4]) ).

cnf(f_4353_7,plain,
    ( sK443(U_17764,U_17762) != c_List_Olist_ONil(U_17762)
    | c_List_Oconcat(U_17762,U_17764) = c_List_Olist_ONil(U_17762) ),
    inference(clausify,[status(thm)],[f_4353_4]) ).

fof(f_4354_1,plain,
    ! [V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Oconcat(T_c,V_xs_2)) = c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_List_Olist(T_b)),hAPP(c_List_Omap(T_c,T_b),V_f_2)),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_map__concat]) ).

fof(f_4354_2,plain,
    ! [U_17768,U_17767,U_17766,U_17765] : hAPP(hAPP(c_List_Omap(U_17765,U_17766),U_17767),c_List_Oconcat(U_17765,U_17768)) = c_List_Oconcat(U_17766,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_17765),tc_List_Olist(U_17766)),hAPP(c_List_Omap(U_17765,U_17766),U_17767)),U_17768)),
    inference(variable_rename,[status(thm)],[f_4354_1]) ).

cnf(f_4354_3,plain,
    hAPP(hAPP(c_List_Omap(U_17765,U_17766),U_17767),c_List_Oconcat(U_17765,U_17768)) = c_List_Oconcat(U_17766,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_17765),tc_List_Olist(U_17766)),hAPP(c_List_Omap(U_17765,U_17766),U_17767)),U_17768)),
    inference(clausify,[status(thm)],[f_4354_2]) ).

fof(f_4355_1,plain,
    ! [V_xss_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oconcat(T_b,V_xss_2)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xss_2)),
    inference(fof_nnf,[status(thm)],[fact_length__concat]) ).

fof(f_4355_2,plain,
    ! [U_17770,U_17769] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17769)),c_List_Oconcat(U_17769,U_17770)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_17769),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_17769))),U_17770)),
    inference(variable_rename,[status(thm)],[f_4355_1]) ).

cnf(f_4355_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17769)),c_List_Oconcat(U_17769,U_17770)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_17769),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_17769))),U_17770)),
    inference(clausify,[status(thm)],[f_4355_2]) ).

fof(f_4356_1,plain,
    ! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),c_List_Oconcat(T_b,V_xs_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)),c_List_Oset(T_b)),
    inference(fof_nnf,[status(thm)],[fact_set__concat]) ).

fof(f_4356_2,plain,
    ! [U_17772,U_17771] : hAPP(c_List_Oset(U_17771),c_List_Oconcat(U_17771,U_17772)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(U_17771),tc_fun(U_17771,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(U_17771)),U_17772)),c_List_Oset(U_17771)),
    inference(variable_rename,[status(thm)],[f_4356_1]) ).

cnf(f_4356_3,plain,
    hAPP(c_List_Oset(U_17771),c_List_Oconcat(U_17771,U_17772)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(U_17771),tc_fun(U_17771,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(U_17771)),U_17772)),c_List_Oset(U_17771)),
    inference(clausify,[status(thm)],[f_4356_2]) ).

fof(f_4357_1,plain,
    ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
      ( c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2))
      | ~ class_Orderings_Olinorder(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_sort__key__simps_I2_J]) ).

fof(f_4357_2,plain,
    ! [U_17777,U_17776,U_17775,U_17774,U_17773] :
      ( c_List_Olinorder__class_Osort__key(U_17774,U_17773,U_17775,hAPP(hAPP(c_List_Olist_OCons(U_17774),U_17776),U_17777)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17774,U_17773,U_17775),U_17776),c_List_Olinorder__class_Osort__key(U_17774,U_17773,U_17775,U_17777))
      | ~ class_Orderings_Olinorder(U_17773) ),
    inference(variable_rename,[status(thm)],[f_4357_1]) ).

cnf(f_4357_3,plain,
    ( c_List_Olinorder__class_Osort__key(U_17774,U_17773,U_17775,hAPP(hAPP(c_List_Olist_OCons(U_17774),U_17776),U_17777)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17774,U_17773,U_17775),U_17776),c_List_Olinorder__class_Osort__key(U_17774,U_17773,U_17775,U_17777))
    | ~ class_Orderings_Olinorder(U_17773) ),
    inference(clausify,[status(thm)],[f_4357_2]) ).

fof(f_4358_1,plain,
    ! [V_ys,V_xs,T_a] : c_List_Oconcat(T_a,hAPP(hAPP(c_List_Oappend(tc_List_Olist(T_a)),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),c_List_Oconcat(T_a,V_xs)),c_List_Oconcat(T_a,V_ys)),
    inference(fof_nnf,[status(thm)],[fact_concat__append]) ).

fof(f_4358_2,plain,
    ! [U_17780,U_17779,U_17778] : c_List_Oconcat(U_17778,hAPP(hAPP(c_List_Oappend(tc_List_Olist(U_17778)),U_17779),U_17780)) = hAPP(hAPP(c_List_Oappend(U_17778),c_List_Oconcat(U_17778,U_17779)),c_List_Oconcat(U_17778,U_17780)),
    inference(variable_rename,[status(thm)],[f_4358_1]) ).

cnf(f_4358_3,plain,
    c_List_Oconcat(U_17778,hAPP(hAPP(c_List_Oappend(tc_List_Olist(U_17778)),U_17779),U_17780)) = hAPP(hAPP(c_List_Oappend(U_17778),c_List_Oconcat(U_17778,U_17779)),c_List_Oconcat(U_17778,U_17780)),
    inference(clausify,[status(thm)],[f_4358_2]) ).

fof(f_4359_1,plain,
    ! [V_xs_2,T_b] :
      ( c_List_Olinorder__class_Osort__key(T_b,T_b,c_COMBI(T_b),V_xs_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_b),T_b,hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b))),c_List_Olist_ONil(T_b)),V_xs_2)
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sort__foldl__insort]) ).

fof(f_4359_2,plain,
    ! [U_17782,U_17781] :
      ( c_List_Olinorder__class_Osort__key(U_17781,U_17781,c_COMBI(U_17781),U_17782) = hAPP(c_List_Ofoldl(tc_List_Olist(U_17781),U_17781,hAPP(c_COMBC(U_17781,tc_List_Olist(U_17781),tc_List_Olist(U_17781)),c_List_Olinorder__class_Oinsort__key(U_17781,U_17781,c_COMBI(U_17781))),c_List_Olist_ONil(U_17781)),U_17782)
      | ~ class_Orderings_Olinorder(U_17781) ),
    inference(variable_rename,[status(thm)],[f_4359_1]) ).

cnf(f_4359_3,plain,
    ( c_List_Olinorder__class_Osort__key(U_17781,U_17781,c_COMBI(U_17781),U_17782) = hAPP(c_List_Ofoldl(tc_List_Olist(U_17781),U_17781,hAPP(c_COMBC(U_17781,tc_List_Olist(U_17781),tc_List_Olist(U_17781)),c_List_Olinorder__class_Oinsort__key(U_17781,U_17781,c_COMBI(U_17781))),c_List_Olist_ONil(U_17781)),U_17782)
    | ~ class_Orderings_Olinorder(U_17781) ),
    inference(clausify,[status(thm)],[f_4359_2]) ).

fof(f_4360_1,plain,
    ! [V_ys_2,V_xs_2,T_b] :
      ( ( ( c_List_Oconcat(T_b,V_xs_2) = c_List_Oconcat(T_b,V_ys_2)
          | V_xs_2 != V_ys_2 )
        & ( V_xs_2 = V_ys_2
          | c_List_Oconcat(T_b,V_xs_2) != c_List_Oconcat(T_b,V_ys_2) ) )
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_ys_2)
      | ? [B_x] :
          ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),B_x))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),B_x),hAPP(c_List_Oset(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_concat__eq__concat__iff]) ).

fof(f_4360_2,plain,
    ! [U_17786,U_17785,U_17784] :
      ( ( ( c_List_Oconcat(U_17784,U_17785) = c_List_Oconcat(U_17784,U_17786)
          | U_17785 != U_17786 )
        & ( U_17785 = U_17786
          | c_List_Oconcat(U_17784,U_17785) != c_List_Oconcat(U_17784,U_17786) ) )
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_17784))),U_17785) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_17784))),U_17786)
      | ? [U_17783] :
          ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_17784),tc_List_Olist(U_17784),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17784),tc_fun(tc_List_Olist(U_17784),tc_Nat_Onat),tc_fun(tc_List_Olist(U_17784),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_17784),tc_Nat_Onat),tc_fun(tc_List_Olist(U_17784),tc_HOL_Obool)),tc_List_Olist(U_17784)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_17784))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_17784)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_17784))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_17784)))),U_17783))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17784),tc_List_Olist(U_17784))),U_17783),hAPP(c_List_Oset(tc_prod(tc_List_Olist(U_17784),tc_List_Olist(U_17784))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(U_17784),tc_List_Olist(U_17784)),U_17785),U_17786)))) ) ),
    inference(variable_rename,[status(thm)],[f_4360_1]) ).

fof(f_4360_3,plain,
    ! [U_17786,U_17785,U_17784] :
      ( ( ( c_List_Oconcat(U_17784,U_17785) = c_List_Oconcat(U_17784,U_17786)
          | U_17785 != U_17786 )
        & ( U_17785 = U_17786
          | c_List_Oconcat(U_17784,U_17785) != c_List_Oconcat(U_17784,U_17786) ) )
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_17784))),U_17785) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_17784))),U_17786)
      | ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_17784),tc_List_Olist(U_17784),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17784),tc_fun(tc_List_Olist(U_17784),tc_Nat_Onat),tc_fun(tc_List_Olist(U_17784),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_17784),tc_Nat_Onat),tc_fun(tc_List_Olist(U_17784),tc_HOL_Obool)),tc_List_Olist(U_17784)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_17784))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_17784)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_17784))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_17784)))),sK444(U_17786,U_17785,U_17784)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17784),tc_List_Olist(U_17784))),sK444(U_17786,U_17785,U_17784)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(U_17784),tc_List_Olist(U_17784))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(U_17784),tc_List_Olist(U_17784)),U_17785),U_17786)))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK444]),skolemize(U_17783,sK444(U_17786,U_17785,U_17784))],[f_4360_2]) ).

cnf(f_4360_4,plain,
    ( U_17785 = U_17786
    | c_List_Oconcat(U_17784,U_17785) != c_List_Oconcat(U_17784,U_17786)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_17784))),U_17785) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_17784))),U_17786)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17784),tc_List_Olist(U_17784))),sK444(U_17786,U_17785,U_17784)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(U_17784),tc_List_Olist(U_17784))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(U_17784),tc_List_Olist(U_17784)),U_17785),U_17786)))) ),
    inference(clausify,[status(thm)],[f_4360_3]) ).

cnf(f_4360_5,plain,
    ( c_List_Oconcat(U_17784,U_17785) = c_List_Oconcat(U_17784,U_17786)
    | U_17785 != U_17786
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_17784))),U_17785) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_17784))),U_17786)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17784),tc_List_Olist(U_17784))),sK444(U_17786,U_17785,U_17784)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(U_17784),tc_List_Olist(U_17784))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(U_17784),tc_List_Olist(U_17784)),U_17785),U_17786)))) ),
    inference(clausify,[status(thm)],[f_4360_3]) ).

cnf(f_4360_6,plain,
    ( U_17785 = U_17786
    | c_List_Oconcat(U_17784,U_17785) != c_List_Oconcat(U_17784,U_17786)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_17784))),U_17785) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_17784))),U_17786)
    | ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_17784),tc_List_Olist(U_17784),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17784),tc_fun(tc_List_Olist(U_17784),tc_Nat_Onat),tc_fun(tc_List_Olist(U_17784),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_17784),tc_Nat_Onat),tc_fun(tc_List_Olist(U_17784),tc_HOL_Obool)),tc_List_Olist(U_17784)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_17784))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_17784)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_17784))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_17784)))),sK444(U_17786,U_17785,U_17784))) ),
    inference(clausify,[status(thm)],[f_4360_3]) ).

cnf(f_4360_7,plain,
    ( c_List_Oconcat(U_17784,U_17785) = c_List_Oconcat(U_17784,U_17786)
    | U_17785 != U_17786
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_17784))),U_17785) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_17784))),U_17786)
    | ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_17784),tc_List_Olist(U_17784),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17784),tc_fun(tc_List_Olist(U_17784),tc_Nat_Onat),tc_fun(tc_List_Olist(U_17784),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_17784),tc_Nat_Onat),tc_fun(tc_List_Olist(U_17784),tc_HOL_Obool)),tc_List_Olist(U_17784)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_17784))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_17784)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_17784))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_17784)))),sK444(U_17786,U_17785,U_17784))) ),
    inference(clausify,[status(thm)],[f_4360_3]) ).

fof(f_4361_1,plain,
    ! [V_ys_2,V_xs_2,T_b] :
      ( V_xs_2 = V_ys_2
      | ? [B_x] :
          ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),B_x))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),B_x),hAPP(c_List_Oset(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)))) )
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_ys_2)
      | c_List_Oconcat(T_b,V_xs_2) != c_List_Oconcat(T_b,V_ys_2) ),
    inference(fof_nnf,[status(thm)],[fact_concat__injective]) ).

fof(f_4361_2,plain,
    ! [U_17790,U_17789,U_17788] :
      ( U_17789 = U_17790
      | ? [U_17787] :
          ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_17788),tc_List_Olist(U_17788),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17788),tc_fun(tc_List_Olist(U_17788),tc_Nat_Onat),tc_fun(tc_List_Olist(U_17788),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_17788),tc_Nat_Onat),tc_fun(tc_List_Olist(U_17788),tc_HOL_Obool)),tc_List_Olist(U_17788)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_17788))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_17788)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_17788))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_17788)))),U_17787))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17788),tc_List_Olist(U_17788))),U_17787),hAPP(c_List_Oset(tc_prod(tc_List_Olist(U_17788),tc_List_Olist(U_17788))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(U_17788),tc_List_Olist(U_17788)),U_17789),U_17790)))) )
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_17788))),U_17789) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_17788))),U_17790)
      | c_List_Oconcat(U_17788,U_17789) != c_List_Oconcat(U_17788,U_17790) ),
    inference(variable_rename,[status(thm)],[f_4361_1]) ).

fof(f_4361_3,plain,
    ! [U_17790,U_17789,U_17788] :
      ( U_17789 = U_17790
      | ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_17788),tc_List_Olist(U_17788),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17788),tc_fun(tc_List_Olist(U_17788),tc_Nat_Onat),tc_fun(tc_List_Olist(U_17788),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_17788),tc_Nat_Onat),tc_fun(tc_List_Olist(U_17788),tc_HOL_Obool)),tc_List_Olist(U_17788)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_17788))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_17788)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_17788))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_17788)))),sK445(U_17790,U_17789,U_17788)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17788),tc_List_Olist(U_17788))),sK445(U_17790,U_17789,U_17788)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(U_17788),tc_List_Olist(U_17788))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(U_17788),tc_List_Olist(U_17788)),U_17789),U_17790)))) )
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_17788))),U_17789) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_17788))),U_17790)
      | c_List_Oconcat(U_17788,U_17789) != c_List_Oconcat(U_17788,U_17790) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK445]),skolemize(U_17787,sK445(U_17790,U_17789,U_17788))],[f_4361_2]) ).

cnf(f_4361_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17788),tc_List_Olist(U_17788))),sK445(U_17790,U_17789,U_17788)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(U_17788),tc_List_Olist(U_17788))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(U_17788),tc_List_Olist(U_17788)),U_17789),U_17790))))
    | U_17789 = U_17790
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_17788))),U_17789) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_17788))),U_17790)
    | c_List_Oconcat(U_17788,U_17789) != c_List_Oconcat(U_17788,U_17790) ),
    inference(clausify,[status(thm)],[f_4361_3]) ).

cnf(f_4361_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_17788),tc_List_Olist(U_17788),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17788),tc_fun(tc_List_Olist(U_17788),tc_Nat_Onat),tc_fun(tc_List_Olist(U_17788),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_17788),tc_Nat_Onat),tc_fun(tc_List_Olist(U_17788),tc_HOL_Obool)),tc_List_Olist(U_17788)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_17788))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_17788)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_17788))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_17788)))),sK445(U_17790,U_17789,U_17788)))
    | U_17789 = U_17790
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_17788))),U_17789) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_17788))),U_17790)
    | c_List_Oconcat(U_17788,U_17789) != c_List_Oconcat(U_17788,U_17790) ),
    inference(clausify,[status(thm)],[f_4361_3]) ).

fof(f_4362_1,plain,
    ! [V_xs_2,V_f_2,T_c,T_b] : c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(T_c,tc_List_Olist(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_c),c_List_Olist_OCons(T_b)),V_f_2)),c_List_Olist_ONil(T_b))),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_concat__map__singleton]) ).

fof(f_4362_2,plain,
    ! [U_17794,U_17793,U_17792,U_17791] : c_List_Oconcat(U_17791,hAPP(hAPP(c_List_Omap(U_17792,tc_List_Olist(U_17791)),hAPP(hAPP(c_COMBC(U_17792,tc_List_Olist(U_17791),tc_List_Olist(U_17791)),hAPP(hAPP(c_COMBB(U_17791,tc_fun(tc_List_Olist(U_17791),tc_List_Olist(U_17791)),U_17792),c_List_Olist_OCons(U_17791)),U_17793)),c_List_Olist_ONil(U_17791))),U_17794)) = hAPP(hAPP(c_List_Omap(U_17792,U_17791),U_17793),U_17794),
    inference(variable_rename,[status(thm)],[f_4362_1]) ).

cnf(f_4362_3,plain,
    c_List_Oconcat(U_17791,hAPP(hAPP(c_List_Omap(U_17792,tc_List_Olist(U_17791)),hAPP(hAPP(c_COMBC(U_17792,tc_List_Olist(U_17791),tc_List_Olist(U_17791)),hAPP(hAPP(c_COMBB(U_17791,tc_fun(tc_List_Olist(U_17791),tc_List_Olist(U_17791)),U_17792),c_List_Olist_OCons(U_17791)),U_17793)),c_List_Olist_ONil(U_17791))),U_17794)) = hAPP(hAPP(c_List_Omap(U_17792,U_17791),U_17793),U_17794),
    inference(clausify,[status(thm)],[f_4362_2]) ).

fof(f_4363_1,plain,
    ! [V_xs_2,V_n_2,T_b] : c_Enum_On__lists(T_b,hAPP(c_Nat_OSuc,V_n_2),V_xs_2) = c_List_Oconcat(tc_List_Olist(T_b),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),tc_List_Olist(T_b)),c_List_Omap(T_b,tc_List_Olist(T_b))),hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)))),V_xs_2)),c_Enum_On__lists(T_b,V_n_2,V_xs_2))),
    inference(fof_nnf,[status(thm)],[fact_n__lists_Osimps_I2_J]) ).

fof(f_4363_2,plain,
    ! [U_17797,U_17796,U_17795] : c_Enum_On__lists(U_17795,hAPP(c_Nat_OSuc,U_17796),U_17797) = c_List_Oconcat(tc_List_Olist(U_17795),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_17795),tc_List_Olist(tc_List_Olist(U_17795))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17795),tc_List_Olist(U_17795),tc_List_Olist(tc_List_Olist(U_17795))),hAPP(hAPP(c_COMBB(tc_fun(U_17795,tc_List_Olist(U_17795)),tc_fun(tc_List_Olist(U_17795),tc_List_Olist(tc_List_Olist(U_17795))),tc_List_Olist(U_17795)),c_List_Omap(U_17795,tc_List_Olist(U_17795))),hAPP(c_COMBC(U_17795,tc_List_Olist(U_17795),tc_List_Olist(U_17795)),c_List_Olist_OCons(U_17795)))),U_17797)),c_Enum_On__lists(U_17795,U_17796,U_17797))),
    inference(variable_rename,[status(thm)],[f_4363_1]) ).

cnf(f_4363_3,plain,
    c_Enum_On__lists(U_17795,hAPP(c_Nat_OSuc,U_17796),U_17797) = c_List_Oconcat(tc_List_Olist(U_17795),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_17795),tc_List_Olist(tc_List_Olist(U_17795))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17795),tc_List_Olist(U_17795),tc_List_Olist(tc_List_Olist(U_17795))),hAPP(hAPP(c_COMBB(tc_fun(U_17795,tc_List_Olist(U_17795)),tc_fun(tc_List_Olist(U_17795),tc_List_Olist(tc_List_Olist(U_17795))),tc_List_Olist(U_17795)),c_List_Omap(U_17795,tc_List_Olist(U_17795))),hAPP(c_COMBC(U_17795,tc_List_Olist(U_17795),tc_List_Olist(U_17795)),c_List_Olist_OCons(U_17795)))),U_17797)),c_Enum_On__lists(U_17795,U_17796,U_17797))),
    inference(clausify,[status(thm)],[f_4363_2]) ).

fof(f_4364_1,plain,
    ! [V_xss_2,V_xs_2,V_x_2,T_b] : c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_xss_2)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),c_COMBK(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b))))),V_xss_2)))),c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),V_xs_2),c_List_Oconcat(tc_List_Olist(T_b),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_b)),T_b,c_List_Olist_ONil(tc_List_Olist(T_b)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_OCons(tc_List_Olist(T_b))),c_List_Olist_ONil(tc_List_Olist(T_b)))))),V_xss_2))))),
    inference(fof_nnf,[status(thm)],[fact_transpose_Osimps_I3_J]) ).

fof(f_4364_2,plain,
    ! [U_17801,U_17800,U_17799,U_17798] : c_List_Otranspose(U_17798,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_17798)),hAPP(hAPP(c_List_Olist_OCons(U_17798),U_17799),U_17800)),U_17801)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_17798)),hAPP(hAPP(c_List_Olist_OCons(U_17798),U_17799),c_List_Oconcat(U_17798,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_17798),tc_List_Olist(U_17798)),c_List_Olist_Olist__case(tc_List_Olist(U_17798),U_17798,c_List_Olist_ONil(U_17798),hAPP(hAPP(c_COMBB(tc_List_Olist(U_17798),tc_fun(tc_List_Olist(U_17798),tc_List_Olist(U_17798)),U_17798),c_COMBK(tc_List_Olist(U_17798),tc_List_Olist(U_17798))),hAPP(hAPP(c_COMBC(U_17798,tc_List_Olist(U_17798),tc_List_Olist(U_17798)),c_List_Olist_OCons(U_17798)),c_List_Olist_ONil(U_17798))))),U_17801)))),c_List_Otranspose(U_17798,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_17798)),U_17800),c_List_Oconcat(tc_List_Olist(U_17798),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_17798),tc_List_Olist(tc_List_Olist(U_17798))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(U_17798)),U_17798,c_List_Olist_ONil(tc_List_Olist(U_17798)),hAPP(c_COMBK(tc_fun(tc_List_Olist(U_17798),tc_List_Olist(tc_List_Olist(U_17798))),U_17798),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17798),tc_List_Olist(tc_List_Olist(U_17798)),tc_List_Olist(tc_List_Olist(U_17798))),c_List_Olist_OCons(tc_List_Olist(U_17798))),c_List_Olist_ONil(tc_List_Olist(U_17798)))))),U_17801))))),
    inference(variable_rename,[status(thm)],[f_4364_1]) ).

cnf(f_4364_3,plain,
    c_List_Otranspose(U_17798,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_17798)),hAPP(hAPP(c_List_Olist_OCons(U_17798),U_17799),U_17800)),U_17801)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_17798)),hAPP(hAPP(c_List_Olist_OCons(U_17798),U_17799),c_List_Oconcat(U_17798,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_17798),tc_List_Olist(U_17798)),c_List_Olist_Olist__case(tc_List_Olist(U_17798),U_17798,c_List_Olist_ONil(U_17798),hAPP(hAPP(c_COMBB(tc_List_Olist(U_17798),tc_fun(tc_List_Olist(U_17798),tc_List_Olist(U_17798)),U_17798),c_COMBK(tc_List_Olist(U_17798),tc_List_Olist(U_17798))),hAPP(hAPP(c_COMBC(U_17798,tc_List_Olist(U_17798),tc_List_Olist(U_17798)),c_List_Olist_OCons(U_17798)),c_List_Olist_ONil(U_17798))))),U_17801)))),c_List_Otranspose(U_17798,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_17798)),U_17800),c_List_Oconcat(tc_List_Olist(U_17798),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_17798),tc_List_Olist(tc_List_Olist(U_17798))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(U_17798)),U_17798,c_List_Olist_ONil(tc_List_Olist(U_17798)),hAPP(c_COMBK(tc_fun(tc_List_Olist(U_17798),tc_List_Olist(tc_List_Olist(U_17798))),U_17798),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17798),tc_List_Olist(tc_List_Olist(U_17798)),tc_List_Olist(tc_List_Olist(U_17798))),c_List_Olist_OCons(tc_List_Olist(U_17798))),c_List_Olist_ONil(tc_List_Olist(U_17798)))))),U_17801))))),
    inference(clausify,[status(thm)],[f_4364_2]) ).

fof(f_4365_1,plain,
    ! [V_xss_2,T_b] : c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),c_COMBK(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b))))),V_xss_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),T_b),c_List_Ohd(T_b)),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_b)))),V_xss_2)),
    inference(fof_nnf,[status(thm)],[fact_transpose__aux__filter__head]) ).

fof(f_4365_2,plain,
    ! [U_17803,U_17802] : c_List_Oconcat(U_17802,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_17802),tc_List_Olist(U_17802)),c_List_Olist_Olist__case(tc_List_Olist(U_17802),U_17802,c_List_Olist_ONil(U_17802),hAPP(hAPP(c_COMBB(tc_List_Olist(U_17802),tc_fun(tc_List_Olist(U_17802),tc_List_Olist(U_17802)),U_17802),c_COMBK(tc_List_Olist(U_17802),tc_List_Olist(U_17802))),hAPP(hAPP(c_COMBC(U_17802,tc_List_Olist(U_17802),tc_List_Olist(U_17802)),c_List_Olist_OCons(U_17802)),c_List_Olist_ONil(U_17802))))),U_17803)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(U_17802),U_17802),c_List_Ohd(U_17802)),hAPP(c_List_Ofilter(tc_List_Olist(U_17802),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_17802)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17802),tc_List_Olist(U_17802),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(U_17802)))),U_17803)),
    inference(variable_rename,[status(thm)],[f_4365_1]) ).

cnf(f_4365_3,plain,
    c_List_Oconcat(U_17802,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_17802),tc_List_Olist(U_17802)),c_List_Olist_Olist__case(tc_List_Olist(U_17802),U_17802,c_List_Olist_ONil(U_17802),hAPP(hAPP(c_COMBB(tc_List_Olist(U_17802),tc_fun(tc_List_Olist(U_17802),tc_List_Olist(U_17802)),U_17802),c_COMBK(tc_List_Olist(U_17802),tc_List_Olist(U_17802))),hAPP(hAPP(c_COMBC(U_17802,tc_List_Olist(U_17802),tc_List_Olist(U_17802)),c_List_Olist_OCons(U_17802)),c_List_Olist_ONil(U_17802))))),U_17803)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(U_17802),U_17802),c_List_Ohd(U_17802)),hAPP(c_List_Ofilter(tc_List_Olist(U_17802),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_17802)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17802),tc_List_Olist(U_17802),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(U_17802)))),U_17803)),
    inference(clausify,[status(thm)],[f_4365_2]) ).

fof(f_4366_1,plain,
    ! [V_xs_2,V_p_2,T_b] : hAPP(c_List_Ofilter(T_b,V_p_2),c_List_Oconcat(T_b,V_xs_2)) = c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Ofilter(T_b,V_p_2)),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_filter__concat]) ).

fof(f_4366_2,plain,
    ! [U_17806,U_17805,U_17804] : hAPP(c_List_Ofilter(U_17804,U_17805),c_List_Oconcat(U_17804,U_17806)) = c_List_Oconcat(U_17804,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_17804),tc_List_Olist(U_17804)),c_List_Ofilter(U_17804,U_17805)),U_17806)),
    inference(variable_rename,[status(thm)],[f_4366_1]) ).

cnf(f_4366_3,plain,
    hAPP(c_List_Ofilter(U_17804,U_17805),c_List_Oconcat(U_17804,U_17806)) = c_List_Oconcat(U_17804,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_17804),tc_List_Olist(U_17804)),c_List_Ofilter(U_17804,U_17805)),U_17806)),
    inference(clausify,[status(thm)],[f_4366_2]) ).

fof(f_4367_1,plain,
    ! [V_xs_2,V_f_2,V_P_2,T_b,T_c] :
      ( hAPP(c_List_Ofilter(T_b,V_P_2),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2)) = c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2))
      | ~ class_Orderings_Olinorder(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_filter__sort]) ).

fof(f_4367_2,plain,
    ! [U_17811,U_17810,U_17809,U_17808,U_17807] :
      ( hAPP(c_List_Ofilter(U_17808,U_17809),c_List_Olinorder__class_Osort__key(U_17808,U_17807,U_17810,U_17811)) = c_List_Olinorder__class_Osort__key(U_17808,U_17807,U_17810,hAPP(c_List_Ofilter(U_17808,U_17809),U_17811))
      | ~ class_Orderings_Olinorder(U_17807) ),
    inference(variable_rename,[status(thm)],[f_4367_1]) ).

cnf(f_4367_3,plain,
    ( hAPP(c_List_Ofilter(U_17808,U_17809),c_List_Olinorder__class_Osort__key(U_17808,U_17807,U_17810,U_17811)) = c_List_Olinorder__class_Osort__key(U_17808,U_17807,U_17810,hAPP(c_List_Ofilter(U_17808,U_17809),U_17811))
    | ~ class_Orderings_Olinorder(U_17807) ),
    inference(clausify,[status(thm)],[f_4367_2]) ).

fof(f_4368_1,plain,
    ! [V_P_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__filter]) ).

fof(f_4368_2,plain,
    ! [U_17814,U_17813,U_17812] :
      ( hBOOL(hAPP(c_List_Odistinct(U_17812),hAPP(c_List_Ofilter(U_17812,U_17814),U_17813)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17812),U_17813)) ),
    inference(variable_rename,[status(thm)],[f_4368_1]) ).

cnf(f_4368_3,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_17812),hAPP(c_List_Ofilter(U_17812,U_17814),U_17813)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17812),U_17813)) ),
    inference(clausify,[status(thm)],[f_4368_2]) ).

fof(f_4369_1,plain,
    ! [V_xs_2,V_P_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2))),
    inference(fof_nnf,[status(thm)],[fact_filter__is__subset]) ).

fof(f_4369_2,plain,
    ! [U_17817,U_17816,U_17815] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17815,tc_HOL_Obool)),hAPP(c_List_Oset(U_17815),hAPP(c_List_Ofilter(U_17815,U_17816),U_17817))),hAPP(c_List_Oset(U_17815),U_17817))),
    inference(variable_rename,[status(thm)],[f_4369_1]) ).

cnf(f_4369_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17815,tc_HOL_Obool)),hAPP(c_List_Oset(U_17815),hAPP(c_List_Ofilter(U_17815,U_17816),U_17817))),hAPP(c_List_Oset(U_17815),U_17817))),
    inference(clausify,[status(thm)],[f_4369_2]) ).

fof(f_4370_1,plain,
    ! [V_xs_2,V_P_2,T_b] :
      ( ( hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) = V_xs_2
        | ? [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) ) )
      & ( ! [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) )
        | hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) != V_xs_2 ) ),
    inference(fof_nnf,[status(thm)],[fact_filter__id__conv]) ).

fof(f_4370_2,plain,
    ! [U_17822,U_17821,U_17820] :
      ( ( hAPP(c_List_Ofilter(U_17820,U_17821),U_17822) = U_17822
        | ? [U_17819] :
            ( ~ hBOOL(hAPP(U_17821,U_17819))
            & hBOOL(hAPP(hAPP(c_member(U_17820),U_17819),hAPP(c_List_Oset(U_17820),U_17822))) ) )
      & ( ! [U_17818] :
            ( hBOOL(hAPP(U_17821,U_17818))
            | ~ hBOOL(hAPP(hAPP(c_member(U_17820),U_17818),hAPP(c_List_Oset(U_17820),U_17822))) )
        | hAPP(c_List_Ofilter(U_17820,U_17821),U_17822) != U_17822 ) ),
    inference(variable_rename,[status(thm)],[f_4370_1]) ).

fof(f_4370_3,plain,
    ( ! [U_17828,U_17826,U_17824] :
        ( hAPP(c_List_Ofilter(U_17824,U_17826),U_17828) = U_17828
        | ? [U_17819] :
            ( ~ hBOOL(hAPP(U_17826,U_17819))
            & hBOOL(hAPP(hAPP(c_member(U_17824),U_17819),hAPP(c_List_Oset(U_17824),U_17828))) ) )
    & ! [U_17827,U_17825,U_17823] :
        ( ! [U_17818] :
            ( hBOOL(hAPP(U_17825,U_17818))
            | ~ hBOOL(hAPP(hAPP(c_member(U_17823),U_17818),hAPP(c_List_Oset(U_17823),U_17827))) )
        | hAPP(c_List_Ofilter(U_17823,U_17825),U_17827) != U_17827 ) ),
    inference(miniscope,[status(thm)],[f_4370_2]) ).

fof(f_4370_4,plain,
    ( ! [U_17828,U_17826,U_17824] :
        ( hAPP(c_List_Ofilter(U_17824,U_17826),U_17828) = U_17828
        | ( ~ hBOOL(hAPP(U_17826,sK446(U_17828,U_17826,U_17824)))
          & hBOOL(hAPP(hAPP(c_member(U_17824),sK446(U_17828,U_17826,U_17824)),hAPP(c_List_Oset(U_17824),U_17828))) ) )
    & ! [U_17827,U_17825,U_17823] :
        ( ! [U_17818] :
            ( hBOOL(hAPP(U_17825,U_17818))
            | ~ hBOOL(hAPP(hAPP(c_member(U_17823),U_17818),hAPP(c_List_Oset(U_17823),U_17827))) )
        | hAPP(c_List_Ofilter(U_17823,U_17825),U_17827) != U_17827 ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK446]),skolemize(U_17819,sK446(U_17828,U_17826,U_17824))],[f_4370_3]) ).

cnf(f_4370_5,plain,
    ( hBOOL(hAPP(U_17825,U_17818))
    | ~ hBOOL(hAPP(hAPP(c_member(U_17823),U_17818),hAPP(c_List_Oset(U_17823),U_17827)))
    | hAPP(c_List_Ofilter(U_17823,U_17825),U_17827) != U_17827 ),
    inference(clausify,[status(thm)],[f_4370_4]) ).

cnf(f_4370_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_17824),sK446(U_17828,U_17826,U_17824)),hAPP(c_List_Oset(U_17824),U_17828)))
    | hAPP(c_List_Ofilter(U_17824,U_17826),U_17828) = U_17828 ),
    inference(clausify,[status(thm)],[f_4370_4]) ).

cnf(f_4370_7,plain,
    ( ~ hBOOL(hAPP(U_17826,sK446(U_17828,U_17826,U_17824)))
    | hAPP(c_List_Ofilter(U_17824,U_17826),U_17828) = U_17828 ),
    inference(clausify,[status(thm)],[f_4370_4]) ).

fof(f_4371_1,plain,
    ! [V_xs_2,V_P_2,T_b] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_P_2)),V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_sum__length__filter__compl]) ).

fof(f_4371_2,plain,
    ! [U_17831,U_17830,U_17829] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17829)),hAPP(c_List_Ofilter(U_17829,U_17830),U_17831))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17829)),hAPP(c_List_Ofilter(U_17829,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_17829),c_fNot),U_17830)),U_17831))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17829)),U_17831),
    inference(variable_rename,[status(thm)],[f_4371_1]) ).

cnf(f_4371_3,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17829)),hAPP(c_List_Ofilter(U_17829,U_17830),U_17831))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17829)),hAPP(c_List_Ofilter(U_17829,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_17829),c_fNot),U_17830)),U_17831))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17829)),U_17831),
    inference(clausify,[status(thm)],[f_4371_2]) ).

fof(f_4372_1,plain,
    ! [V_xs_2,V_P_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))),
    inference(fof_nnf,[status(thm)],[fact_length__filter__le]) ).

fof(f_4372_2,plain,
    ! [U_17834,U_17833,U_17832] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17832)),hAPP(c_List_Ofilter(U_17832,U_17833),U_17834))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17832)),U_17834))),
    inference(variable_rename,[status(thm)],[f_4372_1]) ).

cnf(f_4372_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17832)),hAPP(c_List_Ofilter(U_17832,U_17833),U_17834))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17832)),U_17834))),
    inference(clausify,[status(thm)],[f_4372_2]) ).

fof(f_4373_1,plain,
    ! [V_xs_2,V_Q_2,V_P_2,T_b] : hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(c_List_Ofilter(T_b,V_Q_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Q_2)),V_P_2)),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_filter__filter]) ).

fof(f_4373_2,plain,
    ! [U_17838,U_17837,U_17836,U_17835] : hAPP(c_List_Ofilter(U_17835,U_17836),hAPP(c_List_Ofilter(U_17835,U_17837),U_17838)) = hAPP(c_List_Ofilter(U_17835,hAPP(hAPP(c_COMBS(U_17835,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_17835),c_fconj),U_17837)),U_17836)),U_17838),
    inference(variable_rename,[status(thm)],[f_4373_1]) ).

cnf(f_4373_3,plain,
    hAPP(c_List_Ofilter(U_17835,U_17836),hAPP(c_List_Ofilter(U_17835,U_17837),U_17838)) = hAPP(c_List_Ofilter(U_17835,hAPP(hAPP(c_COMBS(U_17835,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_17835),c_fconj),U_17837)),U_17836)),U_17838),
    inference(clausify,[status(thm)],[f_4373_2]) ).

fof(f_4374_1,plain,
    ! [V_xs_2,T_b,V_x_2,V_P_2] :
      ( c_List_Oremove1(T_b,V_x_2,hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)
      | hBOOL(hAPP(V_P_2,V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_remove1__filter__not]) ).

fof(f_4374_2,plain,
    ! [U_17842,U_17841,U_17840,U_17839] :
      ( c_List_Oremove1(U_17841,U_17840,hAPP(c_List_Ofilter(U_17841,U_17839),U_17842)) = hAPP(c_List_Ofilter(U_17841,U_17839),U_17842)
      | hBOOL(hAPP(U_17839,U_17840)) ),
    inference(variable_rename,[status(thm)],[f_4374_1]) ).

cnf(f_4374_3,plain,
    ( c_List_Oremove1(U_17841,U_17840,hAPP(c_List_Ofilter(U_17841,U_17839),U_17842)) = hAPP(c_List_Ofilter(U_17841,U_17839),U_17842)
    | hBOOL(hAPP(U_17839,U_17840)) ),
    inference(clausify,[status(thm)],[f_4374_2]) ).

fof(f_4375_1,plain,
    ! [V_xs_2,V_x_2,V_Q_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Q_2),c_List_Oremove1(T_b,V_x_2,V_xs_2)) = c_List_Oremove1(T_b,V_x_2,hAPP(c_List_Ofilter(T_b,V_Q_2),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_filter__remove1]) ).

fof(f_4375_2,plain,
    ! [U_17846,U_17845,U_17844,U_17843] : hAPP(c_List_Ofilter(U_17843,U_17844),c_List_Oremove1(U_17843,U_17845,U_17846)) = c_List_Oremove1(U_17843,U_17845,hAPP(c_List_Ofilter(U_17843,U_17844),U_17846)),
    inference(variable_rename,[status(thm)],[f_4375_1]) ).

cnf(f_4375_3,plain,
    hAPP(c_List_Ofilter(U_17843,U_17844),c_List_Oremove1(U_17843,U_17845,U_17846)) = c_List_Oremove1(U_17843,U_17845,hAPP(c_List_Ofilter(U_17843,U_17844),U_17846)),
    inference(clausify,[status(thm)],[f_4375_2]) ).

fof(f_4376_1,plain,
    ! [V_xs_2,V_f_2,T_b,V_x_2,V_P_2,T_c] :
      ( hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)
      | hBOOL(hAPP(V_P_2,V_x_2))
      | ~ class_Orderings_Olinorder(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_filter__insort__triv]) ).

fof(f_4376_2,plain,
    ! [U_17852,U_17851,U_17850,U_17849,U_17848,U_17847] :
      ( hAPP(c_List_Ofilter(U_17850,U_17848),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17850,U_17847,U_17851),U_17849),U_17852)) = hAPP(c_List_Ofilter(U_17850,U_17848),U_17852)
      | hBOOL(hAPP(U_17848,U_17849))
      | ~ class_Orderings_Olinorder(U_17847) ),
    inference(variable_rename,[status(thm)],[f_4376_1]) ).

cnf(f_4376_3,plain,
    ( hAPP(c_List_Ofilter(U_17850,U_17848),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17850,U_17847,U_17851),U_17849),U_17852)) = hAPP(c_List_Ofilter(U_17850,U_17848),U_17852)
    | hBOOL(hAPP(U_17848,U_17849))
    | ~ class_Orderings_Olinorder(U_17847) ),
    inference(clausify,[status(thm)],[f_4376_2]) ).

fof(f_4377_1,plain,
    ! [V_xs_2,V_P_2,T_b] : hAPP(c_Product__Type_Ofst(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Opartition(T_b,V_P_2,V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_partition__filter1]) ).

fof(f_4377_2,plain,
    ! [U_17855,U_17854,U_17853] : hAPP(c_Product__Type_Ofst(tc_List_Olist(U_17853),tc_List_Olist(U_17853)),c_List_Opartition(U_17853,U_17854,U_17855)) = hAPP(c_List_Ofilter(U_17853,U_17854),U_17855),
    inference(variable_rename,[status(thm)],[f_4377_1]) ).

cnf(f_4377_3,plain,
    hAPP(c_Product__Type_Ofst(tc_List_Olist(U_17853),tc_List_Olist(U_17853)),c_List_Opartition(U_17853,U_17854,U_17855)) = hAPP(c_List_Ofilter(U_17853,U_17854),U_17855),
    inference(clausify,[status(thm)],[f_4377_2]) ).

fof(f_4378_1,plain,
    ! [V_xs_2,V_P_2,T_b] : hAPP(c_Product__Type_Osnd(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Opartition(T_b,V_P_2,V_xs_2)) = hAPP(c_List_Ofilter(T_b,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,T_b,c_fNot),V_P_2)),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_partition__filter2]) ).

fof(f_4378_2,plain,
    ! [U_17858,U_17857,U_17856] : hAPP(c_Product__Type_Osnd(tc_List_Olist(U_17856),tc_List_Olist(U_17856)),c_List_Opartition(U_17856,U_17857,U_17858)) = hAPP(c_List_Ofilter(U_17856,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,U_17856,c_fNot),U_17857)),U_17858),
    inference(variable_rename,[status(thm)],[f_4378_1]) ).

cnf(f_4378_3,plain,
    hAPP(c_Product__Type_Osnd(tc_List_Olist(U_17856),tc_List_Olist(U_17856)),c_List_Opartition(U_17856,U_17857,U_17858)) = hAPP(c_List_Ofilter(U_17856,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,U_17856,c_fNot),U_17857)),U_17858),
    inference(clausify,[status(thm)],[f_4378_2]) ).

fof(f_4379_1,plain,
    ! [V_xs_2,V_f_2,T_b] : c_List_Opartition(T_b,V_f_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_f_2),V_xs_2)),hAPP(c_List_Ofilter(T_b,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,T_b,c_fNot),V_f_2)),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_partition__filter__conv]) ).

fof(f_4379_2,plain,
    ! [U_17861,U_17860,U_17859] : c_List_Opartition(U_17859,U_17860,U_17861) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17859),tc_List_Olist(U_17859)),hAPP(c_List_Ofilter(U_17859,U_17860),U_17861)),hAPP(c_List_Ofilter(U_17859,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,U_17859,c_fNot),U_17860)),U_17861)),
    inference(variable_rename,[status(thm)],[f_4379_1]) ).

cnf(f_4379_3,plain,
    c_List_Opartition(U_17859,U_17860,U_17861) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17859),tc_List_Olist(U_17859)),hAPP(c_List_Ofilter(U_17859,U_17860),U_17861)),hAPP(c_List_Ofilter(U_17859,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,U_17859,c_fNot),U_17860)),U_17861)),
    inference(clausify,[status(thm)],[f_4379_2]) ).

fof(f_4380_1,plain,
    ! [V_xs_2,V_f_2,T_c,V_P_2,T_b] : hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Ofilter(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_P_2),V_f_2)),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_filter__map]) ).

fof(f_4380_2,plain,
    ! [U_17866,U_17865,U_17864,U_17863,U_17862] : hAPP(c_List_Ofilter(U_17862,U_17863),hAPP(hAPP(c_List_Omap(U_17864,U_17862),U_17865),U_17866)) = hAPP(hAPP(c_List_Omap(U_17864,U_17862),U_17865),hAPP(c_List_Ofilter(U_17864,hAPP(c_Fun_Ocomp(U_17862,tc_HOL_Obool,U_17864,U_17863),U_17865)),U_17866)),
    inference(variable_rename,[status(thm)],[f_4380_1]) ).

cnf(f_4380_3,plain,
    hAPP(c_List_Ofilter(U_17862,U_17863),hAPP(hAPP(c_List_Omap(U_17864,U_17862),U_17865),U_17866)) = hAPP(hAPP(c_List_Omap(U_17864,U_17862),U_17865),hAPP(c_List_Ofilter(U_17864,hAPP(c_Fun_Ocomp(U_17862,tc_HOL_Obool,U_17864,U_17863),U_17865)),U_17866)),
    inference(clausify,[status(thm)],[f_4380_2]) ).

fof(f_4381_1,plain,
    ! [T_a] : c_List_Otranspose(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(tc_List_Olist(T_a)),
    inference(fof_nnf,[status(thm)],[fact_transpose_Osimps_I1_J]) ).

fof(f_4381_2,plain,
    ! [U_17867] : c_List_Otranspose(U_17867,c_List_Olist_ONil(tc_List_Olist(U_17867))) = c_List_Olist_ONil(tc_List_Olist(U_17867)),
    inference(variable_rename,[status(thm)],[f_4381_1]) ).

cnf(f_4381_3,plain,
    c_List_Otranspose(U_17867,c_List_Olist_ONil(tc_List_Olist(U_17867))) = c_List_Olist_ONil(tc_List_Olist(U_17867)),
    inference(clausify,[status(thm)],[f_4381_2]) ).

fof(f_4382_1,plain,
    ! [V_P_2,T_b] : hAPP(c_List_Ofilter(T_b,V_P_2),c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b),
    inference(fof_nnf,[status(thm)],[fact_filter_Osimps_I1_J]) ).

fof(f_4382_2,plain,
    ! [U_17869,U_17868] : hAPP(c_List_Ofilter(U_17868,U_17869),c_List_Olist_ONil(U_17868)) = c_List_Olist_ONil(U_17868),
    inference(variable_rename,[status(thm)],[f_4382_1]) ).

cnf(f_4382_3,plain,
    hAPP(c_List_Ofilter(U_17868,U_17869),c_List_Olist_ONil(U_17868)) = c_List_Olist_ONil(U_17868),
    inference(clausify,[status(thm)],[f_4382_2]) ).

fof(f_4383_1,plain,
    ! [V_xs_2,T_b,V_x_2,V_P_2] :
      ( ( hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)
        | hBOOL(hAPP(V_P_2,V_x_2)) )
      & ( hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2))
        | ~ hBOOL(hAPP(V_P_2,V_x_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_filter_Osimps_I2_J]) ).

fof(f_4383_2,plain,
    ! [U_17873,U_17872,U_17871,U_17870] :
      ( ( hAPP(c_List_Ofilter(U_17872,U_17870),hAPP(hAPP(c_List_Olist_OCons(U_17872),U_17871),U_17873)) = hAPP(c_List_Ofilter(U_17872,U_17870),U_17873)
        | hBOOL(hAPP(U_17870,U_17871)) )
      & ( hAPP(c_List_Ofilter(U_17872,U_17870),hAPP(hAPP(c_List_Olist_OCons(U_17872),U_17871),U_17873)) = hAPP(hAPP(c_List_Olist_OCons(U_17872),U_17871),hAPP(c_List_Ofilter(U_17872,U_17870),U_17873))
        | ~ hBOOL(hAPP(U_17870,U_17871)) ) ),
    inference(variable_rename,[status(thm)],[f_4383_1]) ).

fof(f_4383_3,plain,
    ( ! [U_17881,U_17879,U_17877,U_17875] :
        ( hAPP(c_List_Ofilter(U_17879,U_17875),hAPP(hAPP(c_List_Olist_OCons(U_17879),U_17877),U_17881)) = hAPP(c_List_Ofilter(U_17879,U_17875),U_17881)
        | hBOOL(hAPP(U_17875,U_17877)) )
    & ! [U_17880,U_17878,U_17876,U_17874] :
        ( hAPP(c_List_Ofilter(U_17878,U_17874),hAPP(hAPP(c_List_Olist_OCons(U_17878),U_17876),U_17880)) = hAPP(hAPP(c_List_Olist_OCons(U_17878),U_17876),hAPP(c_List_Ofilter(U_17878,U_17874),U_17880))
        | ~ hBOOL(hAPP(U_17874,U_17876)) ) ),
    inference(miniscope,[status(thm)],[f_4383_2]) ).

cnf(f_4383_4,plain,
    ( hAPP(c_List_Ofilter(U_17878,U_17874),hAPP(hAPP(c_List_Olist_OCons(U_17878),U_17876),U_17880)) = hAPP(hAPP(c_List_Olist_OCons(U_17878),U_17876),hAPP(c_List_Ofilter(U_17878,U_17874),U_17880))
    | ~ hBOOL(hAPP(U_17874,U_17876)) ),
    inference(clausify,[status(thm)],[f_4383_3]) ).

cnf(f_4383_5,plain,
    ( hAPP(c_List_Ofilter(U_17879,U_17875),hAPP(hAPP(c_List_Olist_OCons(U_17879),U_17877),U_17881)) = hAPP(c_List_Ofilter(U_17879,U_17875),U_17881)
    | hBOOL(hAPP(U_17875,U_17877)) ),
    inference(clausify,[status(thm)],[f_4383_3]) ).

fof(f_4384_1,plain,
    ! [V_ys_2,V_xs_2,V_P_2,T_b] : hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)),hAPP(c_List_Ofilter(T_b,V_P_2),V_ys_2)),
    inference(fof_nnf,[status(thm)],[fact_filter__append]) ).

fof(f_4384_2,plain,
    ! [U_17885,U_17884,U_17883,U_17882] : hAPP(c_List_Ofilter(U_17882,U_17883),hAPP(hAPP(c_List_Oappend(U_17882),U_17884),U_17885)) = hAPP(hAPP(c_List_Oappend(U_17882),hAPP(c_List_Ofilter(U_17882,U_17883),U_17884)),hAPP(c_List_Ofilter(U_17882,U_17883),U_17885)),
    inference(variable_rename,[status(thm)],[f_4384_1]) ).

cnf(f_4384_3,plain,
    hAPP(c_List_Ofilter(U_17882,U_17883),hAPP(hAPP(c_List_Oappend(U_17882),U_17884),U_17885)) = hAPP(hAPP(c_List_Oappend(U_17882),hAPP(c_List_Ofilter(U_17882,U_17883),U_17884)),hAPP(c_List_Ofilter(U_17882,U_17883),U_17885)),
    inference(clausify,[status(thm)],[f_4384_2]) ).

fof(f_4385_1,plain,
    ! [V_xs_2,V_P_2,T_b] :
      ( ( hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) = c_List_Olist_ONil(T_b)
        | ? [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) ) )
      & ( ! [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) )
        | hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) != c_List_Olist_ONil(T_b) ) ),
    inference(fof_nnf,[status(thm)],[fact_filter__empty__conv]) ).

fof(f_4385_2,plain,
    ! [U_17890,U_17889,U_17888] :
      ( ( hAPP(c_List_Ofilter(U_17888,U_17889),U_17890) = c_List_Olist_ONil(U_17888)
        | ? [U_17887] :
            ( hBOOL(hAPP(U_17889,U_17887))
            & hBOOL(hAPP(hAPP(c_member(U_17888),U_17887),hAPP(c_List_Oset(U_17888),U_17890))) ) )
      & ( ! [U_17886] :
            ( ~ hBOOL(hAPP(U_17889,U_17886))
            | ~ hBOOL(hAPP(hAPP(c_member(U_17888),U_17886),hAPP(c_List_Oset(U_17888),U_17890))) )
        | hAPP(c_List_Ofilter(U_17888,U_17889),U_17890) != c_List_Olist_ONil(U_17888) ) ),
    inference(variable_rename,[status(thm)],[f_4385_1]) ).

fof(f_4385_3,plain,
    ( ! [U_17896,U_17894,U_17892] :
        ( hAPP(c_List_Ofilter(U_17892,U_17894),U_17896) = c_List_Olist_ONil(U_17892)
        | ? [U_17887] :
            ( hBOOL(hAPP(U_17894,U_17887))
            & hBOOL(hAPP(hAPP(c_member(U_17892),U_17887),hAPP(c_List_Oset(U_17892),U_17896))) ) )
    & ! [U_17895,U_17893,U_17891] :
        ( ! [U_17886] :
            ( ~ hBOOL(hAPP(U_17893,U_17886))
            | ~ hBOOL(hAPP(hAPP(c_member(U_17891),U_17886),hAPP(c_List_Oset(U_17891),U_17895))) )
        | hAPP(c_List_Ofilter(U_17891,U_17893),U_17895) != c_List_Olist_ONil(U_17891) ) ),
    inference(miniscope,[status(thm)],[f_4385_2]) ).

fof(f_4385_4,plain,
    ( ! [U_17896,U_17894,U_17892] :
        ( hAPP(c_List_Ofilter(U_17892,U_17894),U_17896) = c_List_Olist_ONil(U_17892)
        | ( hBOOL(hAPP(U_17894,sK447(U_17896,U_17894,U_17892)))
          & hBOOL(hAPP(hAPP(c_member(U_17892),sK447(U_17896,U_17894,U_17892)),hAPP(c_List_Oset(U_17892),U_17896))) ) )
    & ! [U_17895,U_17893,U_17891] :
        ( ! [U_17886] :
            ( ~ hBOOL(hAPP(U_17893,U_17886))
            | ~ hBOOL(hAPP(hAPP(c_member(U_17891),U_17886),hAPP(c_List_Oset(U_17891),U_17895))) )
        | hAPP(c_List_Ofilter(U_17891,U_17893),U_17895) != c_List_Olist_ONil(U_17891) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK447]),skolemize(U_17887,sK447(U_17896,U_17894,U_17892))],[f_4385_3]) ).

cnf(f_4385_5,plain,
    ( ~ hBOOL(hAPP(U_17893,U_17886))
    | ~ hBOOL(hAPP(hAPP(c_member(U_17891),U_17886),hAPP(c_List_Oset(U_17891),U_17895)))
    | hAPP(c_List_Ofilter(U_17891,U_17893),U_17895) != c_List_Olist_ONil(U_17891) ),
    inference(clausify,[status(thm)],[f_4385_4]) ).

cnf(f_4385_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_17892),sK447(U_17896,U_17894,U_17892)),hAPP(c_List_Oset(U_17892),U_17896)))
    | hAPP(c_List_Ofilter(U_17892,U_17894),U_17896) = c_List_Olist_ONil(U_17892) ),
    inference(clausify,[status(thm)],[f_4385_4]) ).

cnf(f_4385_7,plain,
    ( hBOOL(hAPP(U_17894,sK447(U_17896,U_17894,U_17892)))
    | hAPP(c_List_Ofilter(U_17892,U_17894),U_17896) = c_List_Olist_ONil(U_17892) ),
    inference(clausify,[status(thm)],[f_4385_4]) ).

fof(f_4386_1,plain,
    ! [V_xs_2,V_f_2,T_c,V_P_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),hAPP(c_List_Ofilter(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_P_2),V_f_2)),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_length__filter__map]) ).

fof(f_4386_2,plain,
    ! [U_17901,U_17900,U_17899,U_17898,U_17897] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17897)),hAPP(c_List_Ofilter(U_17897,U_17898),hAPP(hAPP(c_List_Omap(U_17899,U_17897),U_17900),U_17901))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17899)),hAPP(c_List_Ofilter(U_17899,hAPP(c_Fun_Ocomp(U_17897,tc_HOL_Obool,U_17899,U_17898),U_17900)),U_17901)),
    inference(variable_rename,[status(thm)],[f_4386_1]) ).

cnf(f_4386_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17897)),hAPP(c_List_Ofilter(U_17897,U_17898),hAPP(hAPP(c_List_Omap(U_17899,U_17897),U_17900),U_17901))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17899)),hAPP(c_List_Ofilter(U_17899,hAPP(c_Fun_Ocomp(U_17897,tc_HOL_Obool,U_17899,U_17898),U_17900)),U_17901)),
    inference(clausify,[status(thm)],[f_4386_2]) ).

fof(f_4387_1,plain,
    ! [V_xs_2,T_b,V_x_2,V_P_2] :
      ( hAPP(c_List_OremoveAll(T_b,V_x_2),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)
      | hBOOL(hAPP(V_P_2,V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_removeAll__filter__not]) ).

fof(f_4387_2,plain,
    ! [U_17905,U_17904,U_17903,U_17902] :
      ( hAPP(c_List_OremoveAll(U_17904,U_17903),hAPP(c_List_Ofilter(U_17904,U_17902),U_17905)) = hAPP(c_List_Ofilter(U_17904,U_17902),U_17905)
      | hBOOL(hAPP(U_17902,U_17903)) ),
    inference(variable_rename,[status(thm)],[f_4387_1]) ).

cnf(f_4387_3,plain,
    ( hAPP(c_List_OremoveAll(U_17904,U_17903),hAPP(c_List_Ofilter(U_17904,U_17902),U_17905)) = hAPP(c_List_Ofilter(U_17904,U_17902),U_17905)
    | hBOOL(hAPP(U_17902,U_17903)) ),
    inference(clausify,[status(thm)],[f_4387_2]) ).

fof(f_4388_1,plain,
    ! [V_xs_2,V_P_2,T_b] : c_List_Oremdups(T_b,hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_P_2),c_List_Oremdups(T_b,V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_remdups__filter]) ).

fof(f_4388_2,plain,
    ! [U_17908,U_17907,U_17906] : c_List_Oremdups(U_17906,hAPP(c_List_Ofilter(U_17906,U_17907),U_17908)) = hAPP(c_List_Ofilter(U_17906,U_17907),c_List_Oremdups(U_17906,U_17908)),
    inference(variable_rename,[status(thm)],[f_4388_1]) ).

cnf(f_4388_3,plain,
    c_List_Oremdups(U_17906,hAPP(c_List_Ofilter(U_17906,U_17907),U_17908)) = hAPP(c_List_Ofilter(U_17906,U_17907),c_List_Oremdups(U_17906,U_17908)),
    inference(clausify,[status(thm)],[f_4388_2]) ).

fof(f_4389_1,plain,
    ! [V_x_2,T_b] : c_List_OremoveAll(T_b,V_x_2) = c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(c_fequal,V_x_2))),
    inference(fof_nnf,[status(thm)],[fact_removeAll__filter__not__eq]) ).

fof(f_4389_2,plain,
    ! [U_17910,U_17909] : c_List_OremoveAll(U_17909,U_17910) = c_List_Ofilter(U_17909,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_17909),c_fNot),hAPP(c_fequal,U_17910))),
    inference(variable_rename,[status(thm)],[f_4389_1]) ).

cnf(f_4389_3,plain,
    c_List_OremoveAll(U_17909,U_17910) = c_List_Ofilter(U_17909,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_17909),c_fNot),hAPP(c_fequal,U_17910))),
    inference(clausify,[status(thm)],[f_4389_2]) ).

fof(f_4390_1,plain,
    ! [V_xss,T_a] : c_List_Otranspose(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),V_xss)) = c_List_Otranspose(T_a,V_xss),
    inference(fof_nnf,[status(thm)],[fact_transpose_Osimps_I2_J]) ).

fof(f_4390_2,plain,
    ! [U_17912,U_17911] : c_List_Otranspose(U_17911,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_17911)),c_List_Olist_ONil(U_17911)),U_17912)) = c_List_Otranspose(U_17911,U_17912),
    inference(variable_rename,[status(thm)],[f_4390_1]) ).

cnf(f_4390_3,plain,
    c_List_Otranspose(U_17911,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_17911)),c_List_Olist_ONil(U_17911)),U_17912)) = c_List_Otranspose(U_17911,U_17912),
    inference(clausify,[status(thm)],[f_4390_2]) ).

fof(f_4391_1,plain,
    ! [V_xs_2,T_b,V_i_2] :
      ( hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),c_List_Otranspose(T_b,V_xs_2)),V_i_2) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,T_b),c_List_Onth(T_b)),V_i_2)),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_xs_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_nth__transpose]) ).

fof(f_4391_2,plain,
    ! [U_17915,U_17914,U_17913] :
      ( hAPP(hAPP(c_List_Onth(tc_List_Olist(U_17914)),c_List_Otranspose(U_17914,U_17915)),U_17913) = hAPP(hAPP(c_List_Omap(tc_List_Olist(U_17914),U_17914),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17914),tc_Nat_Onat,U_17914),c_List_Onth(U_17914)),U_17913)),hAPP(c_List_Ofilter(tc_List_Olist(U_17914),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_17914)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_17913)),c_Nat_Osize__class_Osize(tc_List_Olist(U_17914)))),U_17915))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_17913),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_17914))),c_List_Otranspose(U_17914,U_17915)))) ),
    inference(variable_rename,[status(thm)],[f_4391_1]) ).

cnf(f_4391_3,plain,
    ( hAPP(hAPP(c_List_Onth(tc_List_Olist(U_17914)),c_List_Otranspose(U_17914,U_17915)),U_17913) = hAPP(hAPP(c_List_Omap(tc_List_Olist(U_17914),U_17914),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17914),tc_Nat_Onat,U_17914),c_List_Onth(U_17914)),U_17913)),hAPP(c_List_Ofilter(tc_List_Olist(U_17914),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_17914)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_17913)),c_Nat_Osize__class_Osize(tc_List_Olist(U_17914)))),U_17915))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_17913),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_17914))),c_List_Otranspose(U_17914,U_17915)))) ),
    inference(clausify,[status(thm)],[f_4391_2]) ).

fof(f_4392_1,plain,
    ! [V_xs_2,V_f_2,T_c,T_b] : c_List_Otranspose(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_List_Olist(T_b)),hAPP(c_List_Omap(T_c,T_b),V_f_2)),V_xs_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_List_Olist(T_b)),hAPP(c_List_Omap(T_c,T_b),V_f_2)),c_List_Otranspose(T_c,V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_transpose__map__map]) ).

fof(f_4392_2,plain,
    ! [U_17919,U_17918,U_17917,U_17916] : c_List_Otranspose(U_17916,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_17917),tc_List_Olist(U_17916)),hAPP(c_List_Omap(U_17917,U_17916),U_17918)),U_17919)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(U_17917),tc_List_Olist(U_17916)),hAPP(c_List_Omap(U_17917,U_17916),U_17918)),c_List_Otranspose(U_17917,U_17919)),
    inference(variable_rename,[status(thm)],[f_4392_1]) ).

cnf(f_4392_3,plain,
    c_List_Otranspose(U_17916,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_17917),tc_List_Olist(U_17916)),hAPP(c_List_Omap(U_17917,U_17916),U_17918)),U_17919)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(U_17917),tc_List_Olist(U_17916)),hAPP(c_List_Omap(U_17917,U_17916),U_17918)),c_List_Otranspose(U_17917,U_17919)),
    inference(clausify,[status(thm)],[f_4392_2]) ).

fof(f_4393_1,plain,
    ! [V_xs_2,V_P_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),hAPP(c_List_Oset(T_b),V_xs_2)))),V_P_2)),
    inference(fof_nnf,[status(thm)],[fact_set__filter]) ).

fof(f_4393_2,plain,
    ! [U_17922,U_17921,U_17920] : hAPP(c_List_Oset(U_17920),hAPP(c_List_Ofilter(U_17920,U_17921),U_17922)) = hAPP(c_Set_OCollect(U_17920),hAPP(hAPP(c_COMBS(U_17920,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_17920),c_fconj),hAPP(hAPP(c_COMBC(U_17920,tc_fun(U_17920,tc_HOL_Obool),tc_HOL_Obool),c_member(U_17920)),hAPP(c_List_Oset(U_17920),U_17922)))),U_17921)),
    inference(variable_rename,[status(thm)],[f_4393_1]) ).

cnf(f_4393_3,plain,
    hAPP(c_List_Oset(U_17920),hAPP(c_List_Ofilter(U_17920,U_17921),U_17922)) = hAPP(c_Set_OCollect(U_17920),hAPP(hAPP(c_COMBS(U_17920,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_17920),c_fconj),hAPP(hAPP(c_COMBC(U_17920,tc_fun(U_17920,tc_HOL_Obool),tc_HOL_Obool),c_member(U_17920)),hAPP(c_List_Oset(U_17920),U_17922)))),U_17921)),
    inference(clausify,[status(thm)],[f_4393_2]) ).

fof(f_4394_1,plain,
    ! [V_P_2,V_xs_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
      | hBOOL(hAPP(V_P_2,V_x_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_length__filter__less]) ).

fof(f_4394_2,plain,
    ! [U_17926,U_17925,U_17924,U_17923] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17923)),hAPP(c_List_Ofilter(U_17923,U_17926),U_17925))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17923)),U_17925)))
      | hBOOL(hAPP(U_17926,U_17924))
      | ~ hBOOL(hAPP(hAPP(c_member(U_17923),U_17924),hAPP(c_List_Oset(U_17923),U_17925))) ),
    inference(variable_rename,[status(thm)],[f_4394_1]) ).

cnf(f_4394_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17923)),hAPP(c_List_Ofilter(U_17923,U_17926),U_17925))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17923)),U_17925)))
    | hBOOL(hAPP(U_17926,U_17924))
    | ~ hBOOL(hAPP(hAPP(c_member(U_17923),U_17924),hAPP(c_List_Oset(U_17923),U_17925))) ),
    inference(clausify,[status(thm)],[f_4394_2]) ).

fof(f_4395_1,plain,
    ! [V_y_2,V_xs_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_List_Oset(T_b),hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_y_2))),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_set__minus__filter__out]) ).

fof(f_4395_2,plain,
    ! [U_17929,U_17928,U_17927] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_17927,tc_HOL_Obool)),hAPP(c_List_Oset(U_17927),U_17928)),hAPP(hAPP(c_Set_Oinsert(U_17927),U_17929),c_Orderings_Obot__class_Obot(tc_fun(U_17927,tc_HOL_Obool)))) = hAPP(c_List_Oset(U_17927),hAPP(c_List_Ofilter(U_17927,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_17927),c_fNot),hAPP(hAPP(c_COMBC(U_17927,U_17927,tc_HOL_Obool),c_fequal),U_17929))),U_17928)),
    inference(variable_rename,[status(thm)],[f_4395_1]) ).

cnf(f_4395_3,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_17927,tc_HOL_Obool)),hAPP(c_List_Oset(U_17927),U_17928)),hAPP(hAPP(c_Set_Oinsert(U_17927),U_17929),c_Orderings_Obot__class_Obot(tc_fun(U_17927,tc_HOL_Obool)))) = hAPP(c_List_Oset(U_17927),hAPP(c_List_Ofilter(U_17927,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_17927),c_fNot),hAPP(hAPP(c_COMBC(U_17927,U_17927,tc_HOL_Obool),c_fequal),U_17929))),U_17928)),
    inference(clausify,[status(thm)],[f_4395_2]) ).

fof(f_4396_1,plain,
    ! [V_s_2,V_xs_2,T_b] :
      ( hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_s_2)))),V_xs_2) = c_List_Osublist(T_b,V_xs_2,V_s_2)
      | ~ hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ),
    inference(fof_nnf,[status(thm)],[fact_filter__in__sublist]) ).

fof(f_4396_2,plain,
    ! [U_17932,U_17931,U_17930] :
      ( hAPP(c_List_Ofilter(U_17930,hAPP(hAPP(c_COMBC(U_17930,tc_fun(U_17930,tc_HOL_Obool),tc_HOL_Obool),c_member(U_17930)),hAPP(c_List_Oset(U_17930),c_List_Osublist(U_17930,U_17931,U_17932)))),U_17931) = c_List_Osublist(U_17930,U_17931,U_17932)
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17930),U_17931)) ),
    inference(variable_rename,[status(thm)],[f_4396_1]) ).

cnf(f_4396_3,plain,
    ( hAPP(c_List_Ofilter(U_17930,hAPP(hAPP(c_COMBC(U_17930,tc_fun(U_17930,tc_HOL_Obool),tc_HOL_Obool),c_member(U_17930)),hAPP(c_List_Oset(U_17930),c_List_Osublist(U_17930,U_17931,U_17932)))),U_17931) = c_List_Osublist(U_17930,U_17931,U_17932)
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17930),U_17931)) ),
    inference(clausify,[status(thm)],[f_4396_2]) ).

fof(f_4397_1,plain,
    ! [V_xs_2,T_b] :
      ( ( c_List_Otranspose(T_b,V_xs_2) = c_List_Olist_ONil(tc_List_Olist(T_b))
        | ? [B_x] :
            ( B_x != c_List_Olist_ONil(T_b)
            & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2))) ) )
      & ( ! [B_x] :
            ( B_x = c_List_Olist_ONil(T_b)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2))) )
        | c_List_Otranspose(T_b,V_xs_2) != c_List_Olist_ONil(tc_List_Olist(T_b)) ) ),
    inference(fof_nnf,[status(thm)],[fact_transpose__empty]) ).

fof(f_4397_2,plain,
    ! [U_17936,U_17935] :
      ( ( c_List_Otranspose(U_17935,U_17936) = c_List_Olist_ONil(tc_List_Olist(U_17935))
        | ? [U_17934] :
            ( U_17934 != c_List_Olist_ONil(U_17935)
            & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17935)),U_17934),hAPP(c_List_Oset(tc_List_Olist(U_17935)),U_17936))) ) )
      & ( ! [U_17933] :
            ( U_17933 = c_List_Olist_ONil(U_17935)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17935)),U_17933),hAPP(c_List_Oset(tc_List_Olist(U_17935)),U_17936))) )
        | c_List_Otranspose(U_17935,U_17936) != c_List_Olist_ONil(tc_List_Olist(U_17935)) ) ),
    inference(variable_rename,[status(thm)],[f_4397_1]) ).

fof(f_4397_3,plain,
    ( ! [U_17940,U_17938] :
        ( c_List_Otranspose(U_17938,U_17940) = c_List_Olist_ONil(tc_List_Olist(U_17938))
        | ? [U_17934] :
            ( U_17934 != c_List_Olist_ONil(U_17938)
            & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17938)),U_17934),hAPP(c_List_Oset(tc_List_Olist(U_17938)),U_17940))) ) )
    & ! [U_17939,U_17937] :
        ( ! [U_17933] :
            ( U_17933 = c_List_Olist_ONil(U_17937)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17937)),U_17933),hAPP(c_List_Oset(tc_List_Olist(U_17937)),U_17939))) )
        | c_List_Otranspose(U_17937,U_17939) != c_List_Olist_ONil(tc_List_Olist(U_17937)) ) ),
    inference(miniscope,[status(thm)],[f_4397_2]) ).

fof(f_4397_4,plain,
    ( ! [U_17940,U_17938] :
        ( c_List_Otranspose(U_17938,U_17940) = c_List_Olist_ONil(tc_List_Olist(U_17938))
        | ( sK448(U_17940,U_17938) != c_List_Olist_ONil(U_17938)
          & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17938)),sK448(U_17940,U_17938)),hAPP(c_List_Oset(tc_List_Olist(U_17938)),U_17940))) ) )
    & ! [U_17939,U_17937] :
        ( ! [U_17933] :
            ( U_17933 = c_List_Olist_ONil(U_17937)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17937)),U_17933),hAPP(c_List_Oset(tc_List_Olist(U_17937)),U_17939))) )
        | c_List_Otranspose(U_17937,U_17939) != c_List_Olist_ONil(tc_List_Olist(U_17937)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK448]),skolemize(U_17934,sK448(U_17940,U_17938))],[f_4397_3]) ).

cnf(f_4397_5,plain,
    ( U_17933 = c_List_Olist_ONil(U_17937)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17937)),U_17933),hAPP(c_List_Oset(tc_List_Olist(U_17937)),U_17939)))
    | c_List_Otranspose(U_17937,U_17939) != c_List_Olist_ONil(tc_List_Olist(U_17937)) ),
    inference(clausify,[status(thm)],[f_4397_4]) ).

cnf(f_4397_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_17938)),sK448(U_17940,U_17938)),hAPP(c_List_Oset(tc_List_Olist(U_17938)),U_17940)))
    | c_List_Otranspose(U_17938,U_17940) = c_List_Olist_ONil(tc_List_Olist(U_17938)) ),
    inference(clausify,[status(thm)],[f_4397_4]) ).

cnf(f_4397_7,plain,
    ( sK448(U_17940,U_17938) != c_List_Olist_ONil(U_17938)
    | c_List_Otranspose(U_17938,U_17940) = c_List_Olist_ONil(tc_List_Olist(U_17938)) ),
    inference(clausify,[status(thm)],[f_4397_4]) ).

fof(f_4398_1,plain,
    ! [V_xs_2,V_p_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_p_2),V_xs_2)) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,tc_Nat_Onat),V_p_2),hAPP(c_List_Onth(T_b),V_xs_2))))),
    inference(fof_nnf,[status(thm)],[fact_length__filter__conv__card]) ).

fof(f_4398_2,plain,
    ! [U_17943,U_17942,U_17941] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17941)),hAPP(c_List_Ofilter(U_17941,U_17942),U_17943)) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17941)),U_17943)))),hAPP(hAPP(c_COMBB(U_17941,tc_HOL_Obool,tc_Nat_Onat),U_17942),hAPP(c_List_Onth(U_17941),U_17943))))),
    inference(variable_rename,[status(thm)],[f_4398_1]) ).

cnf(f_4398_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17941)),hAPP(c_List_Ofilter(U_17941,U_17942),U_17943)) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17941)),U_17943)))),hAPP(hAPP(c_COMBB(U_17941,tc_HOL_Obool,tc_Nat_Onat),U_17942),hAPP(c_List_Onth(U_17941),U_17943))))),
    inference(clausify,[status(thm)],[f_4398_2]) ).

fof(f_4399_1,plain,
    ! [V_xss_2,T_b] : c_List_Oconcat(tc_List_Olist(T_b),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_b)),T_b,c_List_Olist_ONil(tc_List_Olist(T_b)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_OCons(tc_List_Olist(T_b))),c_List_Olist_ONil(tc_List_Olist(T_b)))))),V_xss_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Otl(T_b)),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_b)))),V_xss_2)),
    inference(fof_nnf,[status(thm)],[fact_transpose__aux__filter__tail]) ).

fof(f_4399_2,plain,
    ! [U_17945,U_17944] : c_List_Oconcat(tc_List_Olist(U_17944),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_17944),tc_List_Olist(tc_List_Olist(U_17944))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(U_17944)),U_17944,c_List_Olist_ONil(tc_List_Olist(U_17944)),hAPP(c_COMBK(tc_fun(tc_List_Olist(U_17944),tc_List_Olist(tc_List_Olist(U_17944))),U_17944),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17944),tc_List_Olist(tc_List_Olist(U_17944)),tc_List_Olist(tc_List_Olist(U_17944))),c_List_Olist_OCons(tc_List_Olist(U_17944))),c_List_Olist_ONil(tc_List_Olist(U_17944)))))),U_17945)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(U_17944),tc_List_Olist(U_17944)),c_List_Otl(U_17944)),hAPP(c_List_Ofilter(tc_List_Olist(U_17944),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_17944)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17944),tc_List_Olist(U_17944),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(U_17944)))),U_17945)),
    inference(variable_rename,[status(thm)],[f_4399_1]) ).

cnf(f_4399_3,plain,
    c_List_Oconcat(tc_List_Olist(U_17944),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_17944),tc_List_Olist(tc_List_Olist(U_17944))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(U_17944)),U_17944,c_List_Olist_ONil(tc_List_Olist(U_17944)),hAPP(c_COMBK(tc_fun(tc_List_Olist(U_17944),tc_List_Olist(tc_List_Olist(U_17944))),U_17944),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17944),tc_List_Olist(tc_List_Olist(U_17944)),tc_List_Olist(tc_List_Olist(U_17944))),c_List_Olist_OCons(tc_List_Olist(U_17944))),c_List_Olist_ONil(tc_List_Olist(U_17944)))))),U_17945)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(U_17944),tc_List_Olist(U_17944)),c_List_Otl(U_17944)),hAPP(c_List_Ofilter(tc_List_Olist(U_17944),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_17944)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17944),tc_List_Olist(U_17944),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(U_17944)))),U_17945)),
    inference(clausify,[status(thm)],[f_4399_2]) ).

fof(f_4400_1,plain,
    ! [V_xss_2,V_xs_2,V_x_2,T_b] :
      ( c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_xss_2)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),c_COMBK(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b))))),V_xss_2)))),c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),V_xs_2),c_List_Oconcat(tc_List_Olist(T_b),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_b)),T_b,c_List_Olist_ONil(tc_List_Olist(T_b)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_OCons(tc_List_Olist(T_b))),c_List_Olist_ONil(tc_List_Olist(T_b)))))),V_xss_2)))))
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_b)),c_List_Otranspose__rel(T_b)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_xss_2))) ),
    inference(fof_nnf,[status(thm)],[fact_transpose_Opsimps_I3_J]) ).

fof(f_4400_2,plain,
    ! [U_17949,U_17948,U_17947,U_17946] :
      ( c_List_Otranspose(U_17946,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_17946)),hAPP(hAPP(c_List_Olist_OCons(U_17946),U_17947),U_17948)),U_17949)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_17946)),hAPP(hAPP(c_List_Olist_OCons(U_17946),U_17947),c_List_Oconcat(U_17946,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_17946),tc_List_Olist(U_17946)),c_List_Olist_Olist__case(tc_List_Olist(U_17946),U_17946,c_List_Olist_ONil(U_17946),hAPP(hAPP(c_COMBB(tc_List_Olist(U_17946),tc_fun(tc_List_Olist(U_17946),tc_List_Olist(U_17946)),U_17946),c_COMBK(tc_List_Olist(U_17946),tc_List_Olist(U_17946))),hAPP(hAPP(c_COMBC(U_17946,tc_List_Olist(U_17946),tc_List_Olist(U_17946)),c_List_Olist_OCons(U_17946)),c_List_Olist_ONil(U_17946))))),U_17949)))),c_List_Otranspose(U_17946,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_17946)),U_17948),c_List_Oconcat(tc_List_Olist(U_17946),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_17946),tc_List_Olist(tc_List_Olist(U_17946))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(U_17946)),U_17946,c_List_Olist_ONil(tc_List_Olist(U_17946)),hAPP(c_COMBK(tc_fun(tc_List_Olist(U_17946),tc_List_Olist(tc_List_Olist(U_17946))),U_17946),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17946),tc_List_Olist(tc_List_Olist(U_17946)),tc_List_Olist(tc_List_Olist(U_17946))),c_List_Olist_OCons(tc_List_Olist(U_17946))),c_List_Olist_ONil(tc_List_Olist(U_17946)))))),U_17949)))))
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(U_17946)),c_List_Otranspose__rel(U_17946)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_17946)),hAPP(hAPP(c_List_Olist_OCons(U_17946),U_17947),U_17948)),U_17949))) ),
    inference(variable_rename,[status(thm)],[f_4400_1]) ).

cnf(f_4400_3,plain,
    ( c_List_Otranspose(U_17946,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_17946)),hAPP(hAPP(c_List_Olist_OCons(U_17946),U_17947),U_17948)),U_17949)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_17946)),hAPP(hAPP(c_List_Olist_OCons(U_17946),U_17947),c_List_Oconcat(U_17946,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_17946),tc_List_Olist(U_17946)),c_List_Olist_Olist__case(tc_List_Olist(U_17946),U_17946,c_List_Olist_ONil(U_17946),hAPP(hAPP(c_COMBB(tc_List_Olist(U_17946),tc_fun(tc_List_Olist(U_17946),tc_List_Olist(U_17946)),U_17946),c_COMBK(tc_List_Olist(U_17946),tc_List_Olist(U_17946))),hAPP(hAPP(c_COMBC(U_17946,tc_List_Olist(U_17946),tc_List_Olist(U_17946)),c_List_Olist_OCons(U_17946)),c_List_Olist_ONil(U_17946))))),U_17949)))),c_List_Otranspose(U_17946,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_17946)),U_17948),c_List_Oconcat(tc_List_Olist(U_17946),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_17946),tc_List_Olist(tc_List_Olist(U_17946))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(U_17946)),U_17946,c_List_Olist_ONil(tc_List_Olist(U_17946)),hAPP(c_COMBK(tc_fun(tc_List_Olist(U_17946),tc_List_Olist(tc_List_Olist(U_17946))),U_17946),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17946),tc_List_Olist(tc_List_Olist(U_17946)),tc_List_Olist(tc_List_Olist(U_17946))),c_List_Olist_OCons(tc_List_Olist(U_17946))),c_List_Olist_ONil(tc_List_Olist(U_17946)))))),U_17949)))))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(U_17946)),c_List_Otranspose__rel(U_17946)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_17946)),hAPP(hAPP(c_List_Olist_OCons(U_17946),U_17947),U_17948)),U_17949))) ),
    inference(clausify,[status(thm)],[f_4400_2]) ).

fof(f_4401_1,plain,
    ! [V_xss_2,T_b] :
      ( c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_xss_2)) = c_List_Otranspose(T_b,V_xss_2)
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_b)),c_List_Otranspose__rel(T_b)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_xss_2))) ),
    inference(fof_nnf,[status(thm)],[fact_transpose_Opsimps_I2_J]) ).

fof(f_4401_2,plain,
    ! [U_17951,U_17950] :
      ( c_List_Otranspose(U_17950,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_17950)),c_List_Olist_ONil(U_17950)),U_17951)) = c_List_Otranspose(U_17950,U_17951)
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(U_17950)),c_List_Otranspose__rel(U_17950)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_17950)),c_List_Olist_ONil(U_17950)),U_17951))) ),
    inference(variable_rename,[status(thm)],[f_4401_1]) ).

cnf(f_4401_3,plain,
    ( c_List_Otranspose(U_17950,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_17950)),c_List_Olist_ONil(U_17950)),U_17951)) = c_List_Otranspose(U_17950,U_17951)
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(U_17950)),c_List_Otranspose__rel(U_17950)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_17950)),c_List_Olist_ONil(U_17950)),U_17951))) ),
    inference(clausify,[status(thm)],[f_4401_2]) ).

fof(f_4402_1,plain,
    ! [V_is_2,V_xs_2,V_P_2,T_b] : hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(T_b,tc_Nat_Onat)),V_P_2),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_prod(T_b,tc_Nat_Onat)),c_Nat_OSuc),c_Product__Type_Osnd(T_b,tc_Nat_Onat)))),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),V_is_2))) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(T_b,tc_Nat_Onat)),V_P_2),c_Product__Type_Osnd(T_b,tc_Nat_Onat))),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),V_is_2)))),
    inference(fof_nnf,[status(thm)],[fact_sublist__shift__lemma__Suc]) ).

fof(f_4402_2,plain,
    ! [U_17955,U_17954,U_17953,U_17952] : hAPP(hAPP(c_List_Omap(tc_prod(U_17952,tc_Nat_Onat),U_17952),c_Product__Type_Ofst(U_17952,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_17952,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(U_17952,tc_Nat_Onat)),U_17953),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_prod(U_17952,tc_Nat_Onat)),c_Nat_OSuc),c_Product__Type_Osnd(U_17952,tc_Nat_Onat)))),hAPP(hAPP(c_List_Ozip(U_17952,tc_Nat_Onat),U_17954),U_17955))) = hAPP(hAPP(c_List_Omap(tc_prod(U_17952,tc_Nat_Onat),U_17952),c_Product__Type_Ofst(U_17952,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_17952,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(U_17952,tc_Nat_Onat)),U_17953),c_Product__Type_Osnd(U_17952,tc_Nat_Onat))),hAPP(hAPP(c_List_Ozip(U_17952,tc_Nat_Onat),U_17954),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),U_17955)))),
    inference(variable_rename,[status(thm)],[f_4402_1]) ).

cnf(f_4402_3,plain,
    hAPP(hAPP(c_List_Omap(tc_prod(U_17952,tc_Nat_Onat),U_17952),c_Product__Type_Ofst(U_17952,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_17952,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(U_17952,tc_Nat_Onat)),U_17953),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_prod(U_17952,tc_Nat_Onat)),c_Nat_OSuc),c_Product__Type_Osnd(U_17952,tc_Nat_Onat)))),hAPP(hAPP(c_List_Ozip(U_17952,tc_Nat_Onat),U_17954),U_17955))) = hAPP(hAPP(c_List_Omap(tc_prod(U_17952,tc_Nat_Onat),U_17952),c_Product__Type_Ofst(U_17952,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_17952,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(U_17952,tc_Nat_Onat)),U_17953),c_Product__Type_Osnd(U_17952,tc_Nat_Onat))),hAPP(hAPP(c_List_Ozip(U_17952,tc_Nat_Onat),U_17954),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),U_17955)))),
    inference(clausify,[status(thm)],[f_4402_2]) ).

fof(f_4403_1,plain,
    ! [V_xs_2,T_b] : c_Random_Oselect__weight(T_b,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),V_xs_2)) = c_Random_Oselect__weight(T_b,V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_select__weigth__drop__zero]) ).

fof(f_4403_2,plain,
    ! [U_17957,U_17956] : c_Random_Oselect__weight(U_17956,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,U_17956),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,U_17956,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_17956,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,U_17956)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),U_17957)) = c_Random_Oselect__weight(U_17956,U_17957),
    inference(variable_rename,[status(thm)],[f_4403_1]) ).

cnf(f_4403_3,plain,
    c_Random_Oselect__weight(U_17956,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,U_17956),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,U_17956,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_17956,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,U_17956)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),U_17957)) = c_Random_Oselect__weight(U_17956,U_17957),
    inference(clausify,[status(thm)],[f_4403_2]) ).

fof(f_4404_1,plain,
    ! [V_xs_2,T_b] : c_Random_Opick(T_b,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),V_xs_2)) = c_Random_Opick(T_b,V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_pick__drop__zero]) ).

fof(f_4404_2,plain,
    ! [U_17959,U_17958] : c_Random_Opick(U_17958,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,U_17958),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,U_17958,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_17958,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,U_17958)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),U_17959)) = c_Random_Opick(U_17958,U_17959),
    inference(variable_rename,[status(thm)],[f_4404_1]) ).

cnf(f_4404_3,plain,
    c_Random_Opick(U_17958,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,U_17958),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,U_17958,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_17958,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,U_17958)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),U_17959)) = c_Random_Opick(U_17958,U_17959),
    inference(clausify,[status(thm)],[f_4404_2]) ).

fof(f_4405_1,plain,
    ! [T_b] :
      ( c_List_Otranspose(T_b,c_List_Olist_ONil(tc_List_Olist(T_b))) = c_List_Olist_ONil(tc_List_Olist(T_b))
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_b)),c_List_Otranspose__rel(T_b)),c_List_Olist_ONil(tc_List_Olist(T_b)))) ),
    inference(fof_nnf,[status(thm)],[fact_transpose_Opsimps_I1_J]) ).

fof(f_4405_2,plain,
    ! [U_17960] :
      ( c_List_Otranspose(U_17960,c_List_Olist_ONil(tc_List_Olist(U_17960))) = c_List_Olist_ONil(tc_List_Olist(U_17960))
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(U_17960)),c_List_Otranspose__rel(U_17960)),c_List_Olist_ONil(tc_List_Olist(U_17960)))) ),
    inference(variable_rename,[status(thm)],[f_4405_1]) ).

cnf(f_4405_3,plain,
    ( c_List_Otranspose(U_17960,c_List_Olist_ONil(tc_List_Olist(U_17960))) = c_List_Olist_ONil(tc_List_Olist(U_17960))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(U_17960)),c_List_Otranspose__rel(U_17960)),c_List_Olist_ONil(tc_List_Olist(U_17960)))) ),
    inference(clausify,[status(thm)],[f_4405_2]) ).

fof(f_4406_1,plain,
    ! [V_xs_2,T_b] : c_List_Ofoldr(tc_List_Olist(T_b),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_b)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_b)))),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_transpose__max__length]) ).

fof(f_4406_2,plain,
    ! [U_17962,U_17961] : c_List_Ofoldr(tc_List_Olist(U_17961),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(U_17961)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_17961))),c_List_Otranspose(U_17961,U_17962),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_17961))),hAPP(c_List_Ofilter(tc_List_Olist(U_17961),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_17961)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17961),tc_List_Olist(U_17961),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(U_17961)))),U_17962)),
    inference(variable_rename,[status(thm)],[f_4406_1]) ).

cnf(f_4406_3,plain,
    c_List_Ofoldr(tc_List_Olist(U_17961),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(U_17961)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_17961))),c_List_Otranspose(U_17961,U_17962),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_17961))),hAPP(c_List_Ofilter(tc_List_Olist(U_17961),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_17961)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17961),tc_List_Olist(U_17961),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(U_17961)))),U_17962)),
    inference(clausify,[status(thm)],[f_4406_2]) ).

fof(f_4407_1,plain,
    ! [V_xss_2,T_c,V_xs_2,T_b] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))),c_List_Ofoldr(tc_List_Olist(T_c),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_c)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_c))),V_xss_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),c_List_Ofoldr(tc_List_Olist(T_c),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_c)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_c)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_c)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_List_Ofilter(tc_List_Olist(T_c),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_c)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_List_Olist(T_c),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_c)))),V_xss_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
    inference(fof_nnf,[status(thm)],[fact_transpose__aux__max]) ).

fof(f_4407_2,plain,
    ! [U_17966,U_17965,U_17964,U_17963] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17963)),U_17964))),c_List_Ofoldr(tc_List_Olist(U_17965),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(U_17965)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_17965))),U_17966,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17963)),U_17964)),c_List_Ofoldr(tc_List_Olist(U_17965),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(U_17965)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17965),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(U_17965)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_17965)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_List_Ofilter(tc_List_Olist(U_17965),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_17965)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17965),tc_List_Olist(U_17965),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(U_17965)))),U_17966),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
    inference(variable_rename,[status(thm)],[f_4407_1]) ).

cnf(f_4407_3,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17963)),U_17964))),c_List_Ofoldr(tc_List_Olist(U_17965),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(U_17965)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_17965))),U_17966,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17963)),U_17964)),c_List_Ofoldr(tc_List_Olist(U_17965),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(U_17965)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17965),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(U_17965)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_17965)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_List_Ofilter(tc_List_Olist(U_17965),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_17965)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17965),tc_List_Olist(U_17965),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(U_17965)))),U_17966),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
    inference(clausify,[status(thm)],[f_4407_2]) ).

fof(f_4408_1,plain,
    ! [V_a_2,V_f_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_f_2,c_List_Olist_ONil(T_c),V_a_2) = V_a_2,
    inference(fof_nnf,[status(thm)],[fact_foldr_Osimps_I1_J]) ).

fof(f_4408_2,plain,
    ! [U_17970,U_17969,U_17968,U_17967] : c_List_Ofoldr(U_17967,U_17968,U_17969,c_List_Olist_ONil(U_17967),U_17970) = U_17970,
    inference(variable_rename,[status(thm)],[f_4408_1]) ).

cnf(f_4408_3,plain,
    c_List_Ofoldr(U_17967,U_17968,U_17969,c_List_Olist_ONil(U_17967),U_17970) = U_17970,
    inference(clausify,[status(thm)],[f_4408_2]) ).

fof(f_4409_1,plain,
    ! [V_a_2,V_xs_2,V_x_2,V_f_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2),V_a_2) = hAPP(hAPP(V_f_2,V_x_2),c_List_Ofoldr(T_c,T_b,V_f_2,V_xs_2,V_a_2)),
    inference(fof_nnf,[status(thm)],[fact_foldr_Osimps_I2_J]) ).

fof(f_4409_2,plain,
    ! [U_17976,U_17975,U_17974,U_17973,U_17972,U_17971] : c_List_Ofoldr(U_17971,U_17972,U_17973,hAPP(hAPP(c_List_Olist_OCons(U_17971),U_17974),U_17975),U_17976) = hAPP(hAPP(U_17973,U_17974),c_List_Ofoldr(U_17971,U_17972,U_17973,U_17975,U_17976)),
    inference(variable_rename,[status(thm)],[f_4409_1]) ).

cnf(f_4409_3,plain,
    c_List_Ofoldr(U_17971,U_17972,U_17973,hAPP(hAPP(c_List_Olist_OCons(U_17971),U_17974),U_17975),U_17976) = hAPP(hAPP(U_17973,U_17974),c_List_Ofoldr(U_17971,U_17972,U_17973,U_17975,U_17976)),
    inference(clausify,[status(thm)],[f_4409_2]) ).

fof(f_4410_1,plain,
    ! [V_a_2,V_ys_2,V_xs_2,V_f_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_f_2,hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2),V_a_2) = c_List_Ofoldr(T_c,T_b,V_f_2,V_xs_2,c_List_Ofoldr(T_c,T_b,V_f_2,V_ys_2,V_a_2)),
    inference(fof_nnf,[status(thm)],[fact_foldr__append]) ).

fof(f_4410_2,plain,
    ! [U_17982,U_17981,U_17980,U_17979,U_17978,U_17977] : c_List_Ofoldr(U_17977,U_17978,U_17979,hAPP(hAPP(c_List_Oappend(U_17977),U_17980),U_17981),U_17982) = c_List_Ofoldr(U_17977,U_17978,U_17979,U_17980,c_List_Ofoldr(U_17977,U_17978,U_17979,U_17981,U_17982)),
    inference(variable_rename,[status(thm)],[f_4410_1]) ).

cnf(f_4410_3,plain,
    c_List_Ofoldr(U_17977,U_17978,U_17979,hAPP(hAPP(c_List_Oappend(U_17977),U_17980),U_17981),U_17982) = c_List_Ofoldr(U_17977,U_17978,U_17979,U_17980,c_List_Ofoldr(U_17977,U_17978,U_17979,U_17981,U_17982)),
    inference(clausify,[status(thm)],[f_4410_2]) ).

fof(f_4411_1,plain,
    ! [V_a_2,V_xs_2,T_b] :
      ( c_List_Ofoldr(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_xs_2,V_a_2) = hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_xs_2)
      | ~ class_Groups_Oab__semigroup__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_foldr__conv__foldl]) ).

fof(f_4411_2,plain,
    ! [U_17985,U_17984,U_17983] :
      ( c_List_Ofoldr(U_17983,U_17983,c_Groups_Oplus__class_Oplus(U_17983),U_17984,U_17985) = hAPP(c_List_Ofoldl(U_17983,U_17983,c_Groups_Oplus__class_Oplus(U_17983),U_17985),U_17984)
      | ~ class_Groups_Oab__semigroup__add(U_17983) ),
    inference(variable_rename,[status(thm)],[f_4411_1]) ).

cnf(f_4411_3,plain,
    ( c_List_Ofoldr(U_17983,U_17983,c_Groups_Oplus__class_Oplus(U_17983),U_17984,U_17985) = hAPP(c_List_Ofoldl(U_17983,U_17983,c_Groups_Oplus__class_Oplus(U_17983),U_17985),U_17984)
    | ~ class_Groups_Oab__semigroup__add(U_17983) ),
    inference(clausify,[status(thm)],[f_4411_2]) ).

fof(f_4412_1,plain,
    ! [V_a_2,V_xs_2,V_f_2,T_d,V_g_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_g_2,hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2),V_a_2) = c_List_Ofoldr(T_d,T_b,hAPP(c_Fun_Ocomp(T_c,tc_fun(T_b,T_b),T_d,V_g_2),V_f_2),V_xs_2,V_a_2),
    inference(fof_nnf,[status(thm)],[fact_foldr__map]) ).

fof(f_4412_2,plain,
    ! [U_17992,U_17991,U_17990,U_17989,U_17988,U_17987,U_17986] : c_List_Ofoldr(U_17986,U_17987,U_17988,hAPP(hAPP(c_List_Omap(U_17989,U_17986),U_17990),U_17991),U_17992) = c_List_Ofoldr(U_17989,U_17987,hAPP(c_Fun_Ocomp(U_17986,tc_fun(U_17987,U_17987),U_17989,U_17988),U_17990),U_17991,U_17992),
    inference(variable_rename,[status(thm)],[f_4412_1]) ).

cnf(f_4412_3,plain,
    c_List_Ofoldr(U_17986,U_17987,U_17988,hAPP(hAPP(c_List_Omap(U_17989,U_17986),U_17990),U_17991),U_17992) = c_List_Ofoldr(U_17989,U_17987,hAPP(c_Fun_Ocomp(U_17986,tc_fun(U_17987,U_17987),U_17989,U_17988),U_17990),U_17991,U_17992),
    inference(clausify,[status(thm)],[f_4412_2]) ).

fof(f_4413_1,plain,
    ! [V_xs_2,V_a_2,T_b] :
      ( hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_xs_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),c_List_Ofoldr(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_xs_2,c_Groups_Ozero__class_Ozero(T_b)))
      | ~ class_Groups_Omonoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_foldl__foldr1__lemma]) ).

fof(f_4413_2,plain,
    ! [U_17995,U_17994,U_17993] :
      ( hAPP(c_List_Ofoldl(U_17993,U_17993,c_Groups_Oplus__class_Oplus(U_17993),U_17994),U_17995) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_17993),U_17994),c_List_Ofoldr(U_17993,U_17993,c_Groups_Oplus__class_Oplus(U_17993),U_17995,c_Groups_Ozero__class_Ozero(U_17993)))
      | ~ class_Groups_Omonoid__add(U_17993) ),
    inference(variable_rename,[status(thm)],[f_4413_1]) ).

cnf(f_4413_3,plain,
    ( hAPP(c_List_Ofoldl(U_17993,U_17993,c_Groups_Oplus__class_Oplus(U_17993),U_17994),U_17995) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_17993),U_17994),c_List_Ofoldr(U_17993,U_17993,c_Groups_Oplus__class_Oplus(U_17993),U_17995,c_Groups_Ozero__class_Ozero(U_17993)))
    | ~ class_Groups_Omonoid__add(U_17993) ),
    inference(clausify,[status(thm)],[f_4413_2]) ).

fof(f_4414_1,plain,
    ! [V_xs_2,T_b] :
      ( hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_xs_2) = c_List_Ofoldr(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_xs_2,c_Groups_Ozero__class_Ozero(T_b))
      | ~ class_Groups_Omonoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_foldl__foldr1]) ).

fof(f_4414_2,plain,
    ! [U_17997,U_17996] :
      ( hAPP(c_List_Ofoldl(U_17996,U_17996,c_Groups_Oplus__class_Oplus(U_17996),c_Groups_Ozero__class_Ozero(U_17996)),U_17997) = c_List_Ofoldr(U_17996,U_17996,c_Groups_Oplus__class_Oplus(U_17996),U_17997,c_Groups_Ozero__class_Ozero(U_17996))
      | ~ class_Groups_Omonoid__add(U_17996) ),
    inference(variable_rename,[status(thm)],[f_4414_1]) ).

cnf(f_4414_3,plain,
    ( hAPP(c_List_Ofoldl(U_17996,U_17996,c_Groups_Oplus__class_Oplus(U_17996),c_Groups_Ozero__class_Ozero(U_17996)),U_17997) = c_List_Ofoldr(U_17996,U_17996,c_Groups_Oplus__class_Oplus(U_17996),U_17997,c_Groups_Ozero__class_Ozero(U_17996))
    | ~ class_Groups_Omonoid__add(U_17996) ),
    inference(clausify,[status(thm)],[f_4414_2]) ).

fof(f_4415_1,plain,
    ! [V_xs_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2)) = c_List_Ofoldr(tc_List_Olist(T_b),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_b)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(fof_nnf,[status(thm)],[fact_length__transpose]) ).

fof(f_4415_2,plain,
    ! [U_17999,U_17998] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_17998))),c_List_Otranspose(U_17998,U_17999)) = c_List_Ofoldr(tc_List_Olist(U_17998),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(U_17998)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_17998))),U_17999,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[f_4415_1]) ).

cnf(f_4415_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_17998))),c_List_Otranspose(U_17998,U_17999)) = c_List_Ofoldr(tc_List_Olist(U_17998),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(U_17998)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_17998))),U_17999,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(clausify,[status(thm)],[f_4415_2]) ).

fof(f_4416_1,plain,
    ! [V_A_2,V_xs_2,T_b] : c_List_Osublist(T_b,V_xs_2,V_A_2) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_b,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(T_b,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(T_b,tc_Nat_Onat))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))))),
    inference(fof_nnf,[status(thm)],[fact_sublist__def]) ).

fof(f_4416_2,plain,
    ! [U_18002,U_18001,U_18000] : c_List_Osublist(U_18000,U_18001,U_18002) = hAPP(hAPP(c_List_Omap(tc_prod(U_18000,tc_Nat_Onat),U_18000),c_Product__Type_Ofst(U_18000,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_18000,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(U_18000,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(U_18000,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(U_18000,tc_Nat_Onat))),U_18002)),hAPP(hAPP(c_List_Ozip(U_18000,tc_Nat_Onat),U_18001),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18000)),U_18001))))),
    inference(variable_rename,[status(thm)],[f_4416_1]) ).

cnf(f_4416_3,plain,
    c_List_Osublist(U_18000,U_18001,U_18002) = hAPP(hAPP(c_List_Omap(tc_prod(U_18000,tc_Nat_Onat),U_18000),c_Product__Type_Ofst(U_18000,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_18000,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(U_18000,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(U_18000,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(U_18000,tc_Nat_Onat))),U_18002)),hAPP(hAPP(c_List_Ozip(U_18000,tc_Nat_Onat),U_18001),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18000)),U_18001))))),
    inference(clausify,[status(thm)],[f_4416_2]) ).

fof(f_4417_1,plain,
    ! [V_i_2,V_xs_2,V_A_2,T_b] : hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_b,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(T_b,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(T_b,tc_Nat_Onat))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),c_List_Oupt(V_i_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))))) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_b,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(T_b,tc_Nat_Onat)),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(T_b,tc_Nat_Onat),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_prod(T_b,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Product__Type_Osnd(T_b,tc_Nat_Onat))),V_i_2))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))))),
    inference(fof_nnf,[status(thm)],[fact_sublist__shift__lemma]) ).

fof(f_4417_2,plain,
    ! [U_18006,U_18005,U_18004,U_18003] : hAPP(hAPP(c_List_Omap(tc_prod(U_18003,tc_Nat_Onat),U_18003),c_Product__Type_Ofst(U_18003,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_18003,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(U_18003,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(U_18003,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(U_18003,tc_Nat_Onat))),U_18004)),hAPP(hAPP(c_List_Ozip(U_18003,tc_Nat_Onat),U_18005),c_List_Oupt(U_18006,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_18006),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18003)),U_18005)))))) = hAPP(hAPP(c_List_Omap(tc_prod(U_18003,tc_Nat_Onat),U_18003),c_Product__Type_Ofst(U_18003,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_18003,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(U_18003,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(U_18003,tc_Nat_Onat)),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(U_18003,tc_Nat_Onat),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_prod(U_18003,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Product__Type_Osnd(U_18003,tc_Nat_Onat))),U_18006))),U_18004)),hAPP(hAPP(c_List_Ozip(U_18003,tc_Nat_Onat),U_18005),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18003)),U_18005))))),
    inference(variable_rename,[status(thm)],[f_4417_1]) ).

cnf(f_4417_3,plain,
    hAPP(hAPP(c_List_Omap(tc_prod(U_18003,tc_Nat_Onat),U_18003),c_Product__Type_Ofst(U_18003,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_18003,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(U_18003,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(U_18003,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(U_18003,tc_Nat_Onat))),U_18004)),hAPP(hAPP(c_List_Ozip(U_18003,tc_Nat_Onat),U_18005),c_List_Oupt(U_18006,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_18006),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18003)),U_18005)))))) = hAPP(hAPP(c_List_Omap(tc_prod(U_18003,tc_Nat_Onat),U_18003),c_Product__Type_Ofst(U_18003,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_18003,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(U_18003,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(U_18003,tc_Nat_Onat)),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(U_18003,tc_Nat_Onat),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_prod(U_18003,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Product__Type_Osnd(U_18003,tc_Nat_Onat))),U_18006))),U_18004)),hAPP(hAPP(c_List_Ozip(U_18003,tc_Nat_Onat),U_18005),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18003)),U_18005))))),
    inference(clausify,[status(thm)],[f_4417_2]) ).

fof(f_4418_1,plain,
    ! [V_j_2,V_i_2] : hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_i_2,V_j_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2),
    inference(fof_nnf,[status(thm)],[fact_set__upt]) ).

fof(f_4418_2,plain,
    ! [U_18008,U_18007] : hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_18007,U_18008)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_18007),U_18008),
    inference(variable_rename,[status(thm)],[f_4418_1]) ).

cnf(f_4418_3,plain,
    hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_18007,U_18008)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_18007),U_18008),
    inference(clausify,[status(thm)],[f_4418_2]) ).

fof(f_4419_1,plain,
    ! [V_j_2,V_i_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_i_2,V_j_2)),
    inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__upt]) ).

fof(f_4419_2,plain,
    ! [U_18010,U_18009] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_18009),U_18010) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_18009,U_18010)),
    inference(variable_rename,[status(thm)],[f_4419_1]) ).

cnf(f_4419_3,plain,
    hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_18009),U_18010) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_18009,U_18010)),
    inference(clausify,[status(thm)],[f_4419_2]) ).

fof(f_4420_1,plain,
    ! [V_j,V_i] :
      ( ( c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = c_List_Olist_ONil(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) )
      & ( c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(V_i,V_j)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_j),c_List_Olist_ONil(tc_Nat_Onat)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) ) ),
    inference(fof_nnf,[status(thm)],[fact_upt__Suc]) ).

fof(f_4420_2,plain,
    ! [U_18012,U_18011] :
      ( ( c_List_Oupt(U_18011,hAPP(c_Nat_OSuc,U_18012)) = c_List_Olist_ONil(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18011),U_18012)) )
      & ( c_List_Oupt(U_18011,hAPP(c_Nat_OSuc,U_18012)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(U_18011,U_18012)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_18012),c_List_Olist_ONil(tc_Nat_Onat)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18011),U_18012)) ) ),
    inference(variable_rename,[status(thm)],[f_4420_1]) ).

fof(f_4420_3,plain,
    ( ! [U_18016,U_18014] :
        ( c_List_Oupt(U_18014,hAPP(c_Nat_OSuc,U_18016)) = c_List_Olist_ONil(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18014),U_18016)) )
    & ! [U_18015,U_18013] :
        ( c_List_Oupt(U_18013,hAPP(c_Nat_OSuc,U_18015)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(U_18013,U_18015)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_18015),c_List_Olist_ONil(tc_Nat_Onat)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18013),U_18015)) ) ),
    inference(miniscope,[status(thm)],[f_4420_2]) ).

cnf(f_4420_4,plain,
    ( c_List_Oupt(U_18013,hAPP(c_Nat_OSuc,U_18015)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(U_18013,U_18015)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_18015),c_List_Olist_ONil(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18013),U_18015)) ),
    inference(clausify,[status(thm)],[f_4420_3]) ).

cnf(f_4420_5,plain,
    ( c_List_Oupt(U_18014,hAPP(c_Nat_OSuc,U_18016)) = c_List_Olist_ONil(tc_Nat_Onat)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18014),U_18016)) ),
    inference(clausify,[status(thm)],[f_4420_3]) ).

fof(f_4421_1,plain,
    ! [V_j,V_i] :
      ( c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(V_i,V_j)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_j),c_List_Olist_ONil(tc_Nat_Onat)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) ),
    inference(fof_nnf,[status(thm)],[fact_upt__Suc__append]) ).

fof(f_4421_2,plain,
    ! [U_18018,U_18017] :
      ( c_List_Oupt(U_18017,hAPP(c_Nat_OSuc,U_18018)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(U_18017,U_18018)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_18018),c_List_Olist_ONil(tc_Nat_Onat)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18017),U_18018)) ),
    inference(variable_rename,[status(thm)],[f_4421_1]) ).

cnf(f_4421_3,plain,
    ( c_List_Oupt(U_18017,hAPP(c_Nat_OSuc,U_18018)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(U_18017,U_18018)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_18018),c_List_Olist_ONil(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18017),U_18018)) ),
    inference(clausify,[status(thm)],[f_4421_2]) ).

fof(f_4422_1,plain,
    ! [V_k,V_j,V_i] :
      ( c_List_Oupt(V_i,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(V_i,V_j)),c_List_Oupt(V_j,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) ),
    inference(fof_nnf,[status(thm)],[fact_upt__add__eq__append]) ).

fof(f_4422_2,plain,
    ! [U_18021,U_18020,U_18019] :
      ( c_List_Oupt(U_18019,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_18020),U_18021)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(U_18019,U_18020)),c_List_Oupt(U_18020,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_18020),U_18021)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18019),U_18020)) ),
    inference(variable_rename,[status(thm)],[f_4422_1]) ).

cnf(f_4422_3,plain,
    ( c_List_Oupt(U_18019,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_18020),U_18021)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(U_18019,U_18020)),c_List_Oupt(U_18020,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_18020),U_18021)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18019),U_18020)) ),
    inference(clausify,[status(thm)],[f_4422_2]) ).

fof(f_4423_1,plain,
    ! [V_j,V_i] :
      ( ( c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) )
      & ( c_List_Oupt(V_i,V_j) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_i),c_List_Oupt(hAPP(c_Nat_OSuc,V_i),V_j))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) ) ),
    inference(fof_nnf,[status(thm)],[fact_upt__rec]) ).

fof(f_4423_2,plain,
    ! [U_18023,U_18022] :
      ( ( c_List_Oupt(U_18022,U_18023) = c_List_Olist_ONil(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18022),U_18023)) )
      & ( c_List_Oupt(U_18022,U_18023) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_18022),c_List_Oupt(hAPP(c_Nat_OSuc,U_18022),U_18023))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18022),U_18023)) ) ),
    inference(variable_rename,[status(thm)],[f_4423_1]) ).

fof(f_4423_3,plain,
    ( ! [U_18027,U_18025] :
        ( c_List_Oupt(U_18025,U_18027) = c_List_Olist_ONil(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18025),U_18027)) )
    & ! [U_18026,U_18024] :
        ( c_List_Oupt(U_18024,U_18026) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_18024),c_List_Oupt(hAPP(c_Nat_OSuc,U_18024),U_18026))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18024),U_18026)) ) ),
    inference(miniscope,[status(thm)],[f_4423_2]) ).

cnf(f_4423_4,plain,
    ( c_List_Oupt(U_18024,U_18026) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_18024),c_List_Oupt(hAPP(c_Nat_OSuc,U_18024),U_18026))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18024),U_18026)) ),
    inference(clausify,[status(thm)],[f_4423_3]) ).

cnf(f_4423_5,plain,
    ( c_List_Oupt(U_18025,U_18027) = c_List_Olist_ONil(tc_Nat_Onat)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18025),U_18027)) ),
    inference(clausify,[status(thm)],[f_4423_3]) ).

fof(f_4424_1,plain,
    ! [V_j,V_i] :
      ( c_List_Oupt(V_i,V_j) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_i),c_List_Oupt(hAPP(c_Nat_OSuc,V_i),V_j))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) ),
    inference(fof_nnf,[status(thm)],[fact_upt__conv__Cons]) ).

fof(f_4424_2,plain,
    ! [U_18029,U_18028] :
      ( c_List_Oupt(U_18028,U_18029) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_18028),c_List_Oupt(hAPP(c_Nat_OSuc,U_18028),U_18029))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18028),U_18029)) ),
    inference(variable_rename,[status(thm)],[f_4424_1]) ).

cnf(f_4424_3,plain,
    ( c_List_Oupt(U_18028,U_18029) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_18028),c_List_Oupt(hAPP(c_Nat_OSuc,U_18028),U_18029))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18028),U_18029)) ),
    inference(clausify,[status(thm)],[f_4424_2]) ).

fof(f_4425_1,plain,
    ! [V_i,V_j] :
      ( c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i)) ),
    inference(fof_nnf,[status(thm)],[fact_upt__conv__Nil]) ).

fof(f_4425_2,plain,
    ! [U_18031,U_18030] :
      ( c_List_Oupt(U_18031,U_18030) = c_List_Olist_ONil(tc_Nat_Onat)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18030),U_18031)) ),
    inference(variable_rename,[status(thm)],[f_4425_1]) ).

cnf(f_4425_3,plain,
    ( c_List_Oupt(U_18031,U_18030) = c_List_Olist_ONil(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18030),U_18031)) ),
    inference(clausify,[status(thm)],[f_4425_2]) ).

fof(f_4426_1,plain,
    ! [V_j_2,V_i_2] :
      ( ( c_List_Oupt(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Nat_Onat)
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
          & V_j_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
        | V_j_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_List_Oupt(V_i_2,V_j_2) != c_List_Olist_ONil(tc_Nat_Onat) ) ),
    inference(fof_nnf,[status(thm)],[fact_upt__eq__Nil__conv]) ).

fof(f_4426_2,plain,
    ! [U_18033,U_18032] :
      ( ( c_List_Oupt(U_18032,U_18033) = c_List_Olist_ONil(tc_Nat_Onat)
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18033),U_18032))
          & U_18033 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18033),U_18032))
        | U_18033 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_List_Oupt(U_18032,U_18033) != c_List_Olist_ONil(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_4426_1]) ).

fof(f_4426_3,plain,
    ( ! [U_18037,U_18035] :
        ( c_List_Oupt(U_18035,U_18037) = c_List_Olist_ONil(tc_Nat_Onat)
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18037),U_18035))
          & U_18037 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_18036,U_18034] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18036),U_18034))
        | U_18036 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_List_Oupt(U_18034,U_18036) != c_List_Olist_ONil(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_4426_2]) ).

cnf(f_4426_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18036),U_18034))
    | U_18036 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_List_Oupt(U_18034,U_18036) != c_List_Olist_ONil(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4426_3]) ).

cnf(f_4426_5,plain,
    ( U_18037 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_List_Oupt(U_18035,U_18037) = c_List_Olist_ONil(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4426_3]) ).

cnf(f_4426_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18037),U_18035))
    | c_List_Oupt(U_18035,U_18037) = c_List_Olist_ONil(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4426_3]) ).

fof(f_4427_1,plain,
    ! [V_i] : c_List_Oupt(V_i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_upt__0]) ).

fof(f_4427_2,plain,
    ! [U_18038] : c_List_Oupt(U_18038,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_4427_1]) ).

cnf(f_4427_3,plain,
    c_List_Oupt(U_18038,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_4427_2]) ).

fof(f_4428_1,plain,
    ! [V_n,V_m,V_i] :
      ( hAPP(hAPP(c_List_Otake(tc_Nat_Onat),V_m),c_List_Oupt(V_i,V_n)) = c_List_Oupt(V_i,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m)),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_take__upt]) ).

fof(f_4428_2,plain,
    ! [U_18041,U_18040,U_18039] :
      ( hAPP(hAPP(c_List_Otake(tc_Nat_Onat),U_18040),c_List_Oupt(U_18039,U_18041)) = c_List_Oupt(U_18039,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_18039),U_18040))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_18039),U_18040)),U_18041)) ),
    inference(variable_rename,[status(thm)],[f_4428_1]) ).

cnf(f_4428_3,plain,
    ( hAPP(hAPP(c_List_Otake(tc_Nat_Onat),U_18040),c_List_Oupt(U_18039,U_18041)) = c_List_Oupt(U_18039,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_18039),U_18040))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_18039),U_18040)),U_18041)) ),
    inference(clausify,[status(thm)],[f_4428_2]) ).

fof(f_4429_1,plain,
    ! [V_n_2,V_m_2] : c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)) = c_List_Oupt(V_m_2,V_n_2),
    inference(fof_nnf,[status(thm)],[fact_sorted__list__of__set__range]) ).

fof(f_4429_2,plain,
    ! [U_18043,U_18042] : c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_18042),U_18043)) = c_List_Oupt(U_18042,U_18043),
    inference(variable_rename,[status(thm)],[f_4429_1]) ).

cnf(f_4429_3,plain,
    c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_18042),U_18043)) = c_List_Oupt(U_18042,U_18043),
    inference(clausify,[status(thm)],[f_4429_2]) ).

fof(f_4430_1,plain,
    ! [V_j,V_i] :
      ( hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(V_i,V_j)) = V_i
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) ),
    inference(fof_nnf,[status(thm)],[fact_hd__upt]) ).

fof(f_4430_2,plain,
    ! [U_18045,U_18044] :
      ( hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(U_18044,U_18045)) = U_18044
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18044),U_18045)) ),
    inference(variable_rename,[status(thm)],[f_4430_1]) ).

cnf(f_4430_3,plain,
    ( hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(U_18044,U_18045)) = U_18044
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18044),U_18045)) ),
    inference(clausify,[status(thm)],[f_4430_2]) ).

fof(f_4431_1,plain,
    ! [V_j,V_i,V_m] : hAPP(hAPP(c_List_Odrop(tc_Nat_Onat),V_m),c_List_Oupt(V_i,V_j)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m),V_j),
    inference(fof_nnf,[status(thm)],[fact_drop__upt]) ).

fof(f_4431_2,plain,
    ! [U_18048,U_18047,U_18046] : hAPP(hAPP(c_List_Odrop(tc_Nat_Onat),U_18046),c_List_Oupt(U_18047,U_18048)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_18047),U_18046),U_18048),
    inference(variable_rename,[status(thm)],[f_4431_1]) ).

cnf(f_4431_3,plain,
    hAPP(hAPP(c_List_Odrop(tc_Nat_Onat),U_18046),c_List_Oupt(U_18047,U_18048)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_18047),U_18046),U_18048),
    inference(clausify,[status(thm)],[f_4431_2]) ).

fof(f_4432_1,plain,
    ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(V_i,V_j))),
    inference(fof_nnf,[status(thm)],[fact_distinct__upt]) ).

fof(f_4432_2,plain,
    ! [U_18050,U_18049] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(U_18049,U_18050))),
    inference(variable_rename,[status(thm)],[f_4432_1]) ).

cnf(f_4432_3,plain,
    hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(U_18049,U_18050))),
    inference(clausify,[status(thm)],[f_4432_2]) ).

fof(f_4433_1,plain,
    ! [V_j,V_i] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),c_List_Oupt(V_i,V_j)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_i),
    inference(fof_nnf,[status(thm)],[fact_length__upt]) ).

fof(f_4433_2,plain,
    ! [U_18052,U_18051] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),c_List_Oupt(U_18051,U_18052)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_18052),U_18051),
    inference(variable_rename,[status(thm)],[f_4433_1]) ).

cnf(f_4433_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),c_List_Oupt(U_18051,U_18052)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_18052),U_18051),
    inference(clausify,[status(thm)],[f_4433_2]) ).

fof(f_4434_1,plain,
    ! [V_n,V_m] :
      ( ( c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n)) = c_List_Olist_ONil(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n))) )
      & ( c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m)),c_List_Oupt(hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n))) ) ),
    inference(fof_nnf,[status(thm)],[fact_upt__rec__number__of]) ).

fof(f_4434_2,plain,
    ! [U_18054,U_18053] :
      ( ( c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18053),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18054)) = c_List_Olist_ONil(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18053)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18054))) )
      & ( c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18053),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18054)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18053)),c_List_Oupt(hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18053)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18054)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18053)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18054))) ) ),
    inference(variable_rename,[status(thm)],[f_4434_1]) ).

fof(f_4434_3,plain,
    ( ! [U_18058,U_18056] :
        ( c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18056),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18058)) = c_List_Olist_ONil(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18056)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18058))) )
    & ! [U_18057,U_18055] :
        ( c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18055),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18057)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18055)),c_List_Oupt(hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18055)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18057)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18055)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18057))) ) ),
    inference(miniscope,[status(thm)],[f_4434_2]) ).

cnf(f_4434_4,plain,
    ( c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18055),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18057)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18055)),c_List_Oupt(hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18055)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18057)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18055)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18057))) ),
    inference(clausify,[status(thm)],[f_4434_3]) ).

cnf(f_4434_5,plain,
    ( c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18056),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18058)) = c_List_Olist_ONil(tc_Nat_Onat)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18056)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18058))) ),
    inference(clausify,[status(thm)],[f_4434_3]) ).

fof(f_4435_1,plain,
    ! [V_xs_2,V_x_2,V_j_2,V_i_2] :
      ( ( c_List_Oupt(V_i_2,V_j_2) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_x_2),V_xs_2)
        | c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_j_2) != V_xs_2
        | V_i_2 != V_x_2
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_j_2)) )
      & ( ( c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_j_2) = V_xs_2
          & V_i_2 = V_x_2
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_j_2)) )
        | c_List_Oupt(V_i_2,V_j_2) != hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_x_2),V_xs_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_upt__eq__Cons__conv]) ).

fof(f_4435_2,plain,
    ! [U_18062,U_18061,U_18060,U_18059] :
      ( ( c_List_Oupt(U_18059,U_18060) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_18061),U_18062)
        | c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_18059),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_18060) != U_18062
        | U_18059 != U_18061
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18059),U_18060)) )
      & ( ( c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_18059),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_18060) = U_18062
          & U_18059 = U_18061
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18059),U_18060)) )
        | c_List_Oupt(U_18059,U_18060) != hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_18061),U_18062) ) ),
    inference(variable_rename,[status(thm)],[f_4435_1]) ).

fof(f_4435_3,plain,
    ( ! [U_18070,U_18068,U_18066,U_18064] :
        ( c_List_Oupt(U_18064,U_18066) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_18068),U_18070)
        | c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_18064),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_18066) != U_18070
        | U_18064 != U_18068
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18064),U_18066)) )
    & ! [U_18069,U_18067,U_18065,U_18063] :
        ( ( c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_18063),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_18065) = U_18069
          & U_18063 = U_18067
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18063),U_18065)) )
        | c_List_Oupt(U_18063,U_18065) != hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_18067),U_18069) ) ),
    inference(miniscope,[status(thm)],[f_4435_2]) ).

cnf(f_4435_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18063),U_18065))
    | c_List_Oupt(U_18063,U_18065) != hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_18067),U_18069) ),
    inference(clausify,[status(thm)],[f_4435_3]) ).

cnf(f_4435_5,plain,
    ( U_18063 = U_18067
    | c_List_Oupt(U_18063,U_18065) != hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_18067),U_18069) ),
    inference(clausify,[status(thm)],[f_4435_3]) ).

cnf(f_4435_6,plain,
    ( c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_18063),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_18065) = U_18069
    | c_List_Oupt(U_18063,U_18065) != hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_18067),U_18069) ),
    inference(clausify,[status(thm)],[f_4435_3]) ).

cnf(f_4435_7,plain,
    ( c_List_Oupt(U_18064,U_18066) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_18068),U_18070)
    | c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_18064),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_18066) != U_18070
    | U_18064 != U_18068
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18064),U_18066)) ),
    inference(clausify,[status(thm)],[f_4435_3]) ).

fof(f_4436_1,plain,
    ! [V_j,V_i] :
      ( c_List_Olast(tc_Nat_Onat,c_List_Oupt(V_i,V_j)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),c_Groups_Oone__class_Oone(tc_Nat_Onat))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) ),
    inference(fof_nnf,[status(thm)],[fact_last__upt]) ).

fof(f_4436_2,plain,
    ! [U_18072,U_18071] :
      ( c_List_Olast(tc_Nat_Onat,c_List_Oupt(U_18071,U_18072)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_18072),c_Groups_Oone__class_Oone(tc_Nat_Onat))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18071),U_18072)) ),
    inference(variable_rename,[status(thm)],[f_4436_1]) ).

cnf(f_4436_3,plain,
    ( c_List_Olast(tc_Nat_Onat,c_List_Oupt(U_18071,U_18072)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_18072),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18071),U_18072)) ),
    inference(clausify,[status(thm)],[f_4436_2]) ).

fof(f_4437_1,plain,
    ! [V_n_2,V_m_2] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),c_List_Oupt(V_m_2,V_n_2)) = c_List_Oupt(hAPP(c_Nat_OSuc,V_m_2),hAPP(c_Nat_OSuc,V_n_2)),
    inference(fof_nnf,[status(thm)],[fact_map__Suc__upt]) ).

fof(f_4437_2,plain,
    ! [U_18074,U_18073] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),c_List_Oupt(U_18073,U_18074)) = c_List_Oupt(hAPP(c_Nat_OSuc,U_18073),hAPP(c_Nat_OSuc,U_18074)),
    inference(variable_rename,[status(thm)],[f_4437_1]) ).

cnf(f_4437_3,plain,
    hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),c_List_Oupt(U_18073,U_18074)) = c_List_Oupt(hAPP(c_Nat_OSuc,U_18073),hAPP(c_Nat_OSuc,U_18074)),
    inference(clausify,[status(thm)],[f_4437_2]) ).

fof(f_4438_1,plain,
    ! [V_m_2,V_n_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_n_2,V_m_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_n_2,hAPP(c_Nat_OSuc,V_m_2))),
    inference(fof_nnf,[status(thm)],[fact_atLeastAtMost__upt]) ).

fof(f_4438_2,plain,
    ! [U_18076,U_18075] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_18075,U_18076) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_18075,hAPP(c_Nat_OSuc,U_18076))),
    inference(variable_rename,[status(thm)],[f_4438_1]) ).

cnf(f_4438_3,plain,
    c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_18075,U_18076) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_18075,hAPP(c_Nat_OSuc,U_18076))),
    inference(clausify,[status(thm)],[f_4438_2]) ).

fof(f_4439_1,plain,
    ! [V_n_2] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)),
    inference(fof_nnf,[status(thm)],[fact_atLeast__upt]) ).

fof(f_4439_2,plain,
    ! [U_18077] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_18077) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_18077)),
    inference(variable_rename,[status(thm)],[f_4439_1]) ).

cnf(f_4439_3,plain,
    hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_18077) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_18077)),
    inference(clausify,[status(thm)],[f_4439_2]) ).

fof(f_4440_1,plain,
    ! [V_j,V_k,V_i] :
      ( hAPP(hAPP(c_List_Onth(tc_Nat_Onat),c_List_Oupt(V_i,V_j)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),V_j)) ),
    inference(fof_nnf,[status(thm)],[fact_nth__upt]) ).

fof(f_4440_2,plain,
    ! [U_18080,U_18079,U_18078] :
      ( hAPP(hAPP(c_List_Onth(tc_Nat_Onat),c_List_Oupt(U_18078,U_18080)),U_18079) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_18078),U_18079)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_18078),U_18079)),U_18080)) ),
    inference(variable_rename,[status(thm)],[f_4440_1]) ).

cnf(f_4440_3,plain,
    ( hAPP(hAPP(c_List_Onth(tc_Nat_Onat),c_List_Oupt(U_18078,U_18080)),U_18079) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_18078),U_18079)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_18078),U_18079)),U_18080)) ),
    inference(clausify,[status(thm)],[f_4440_2]) ).

fof(f_4441_1,plain,
    ! [V_m_2,V_n_2] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_n_2,V_m_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,V_n_2),hAPP(c_Nat_OSuc,V_m_2))),
    inference(fof_nnf,[status(thm)],[fact_greaterThanAtMost__upt]) ).

fof(f_4441_2,plain,
    ! [U_18082,U_18081] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_18081,U_18082) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,U_18081),hAPP(c_Nat_OSuc,U_18082))),
    inference(variable_rename,[status(thm)],[f_4441_1]) ).

cnf(f_4441_3,plain,
    c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_18081,U_18082) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,U_18081),hAPP(c_Nat_OSuc,U_18082))),
    inference(clausify,[status(thm)],[f_4441_2]) ).

fof(f_4442_1,plain,
    ! [V_m_2,V_n_2] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,V_n_2,V_m_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,V_n_2),V_m_2)),
    inference(fof_nnf,[status(thm)],[fact_greaterThanLessThan__upt]) ).

fof(f_4442_2,plain,
    ! [U_18084,U_18083] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_18083,U_18084) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,U_18083),U_18084)),
    inference(variable_rename,[status(thm)],[f_4442_1]) ).

cnf(f_4442_3,plain,
    c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_18083,U_18084) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,U_18083),U_18084)),
    inference(clausify,[status(thm)],[f_4442_2]) ).

fof(f_4443_1,plain,
    ! [V_n_2] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2))),
    inference(fof_nnf,[status(thm)],[fact_atMost__upto]) ).

fof(f_4443_2,plain,
    ! [U_18085] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_18085) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_18085))),
    inference(variable_rename,[status(thm)],[f_4443_1]) ).

cnf(f_4443_3,plain,
    hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_18085) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_18085))),
    inference(clausify,[status(thm)],[f_4443_2]) ).

fof(f_4444_1,plain,
    ! [V_xs_2,T_b] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),hAPP(c_List_Onth(T_b),V_xs_2)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) = V_xs_2,
    inference(fof_nnf,[status(thm)],[fact_map__nth]) ).

fof(f_4444_2,plain,
    ! [U_18087,U_18086] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,U_18086),hAPP(c_List_Onth(U_18086),U_18087)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18086)),U_18087))) = U_18087,
    inference(variable_rename,[status(thm)],[f_4444_1]) ).

cnf(f_4444_3,plain,
    hAPP(hAPP(c_List_Omap(tc_Nat_Onat,U_18086),hAPP(c_List_Onth(U_18086),U_18087)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18086)),U_18087))) = U_18087,
    inference(clausify,[status(thm)],[f_4444_2]) ).

fof(f_4445_1,plain,
    ! [V_n_2,V_m_2,V_f_2,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_m_2,V_n_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),V_f_2),c_List_Oupt(V_m_2,V_n_2)))
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__set__upt__conv__listsum__nat]) ).

fof(f_4445_2,plain,
    ! [U_18091,U_18090,U_18089,U_18088] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_18088),U_18089),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_18090,U_18091))) = hAPP(c_List_Omonoid__add__class_Olistsum(U_18088),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,U_18088),U_18089),c_List_Oupt(U_18090,U_18091)))
      | ~ class_Groups_Ocomm__monoid__add(U_18088) ),
    inference(variable_rename,[status(thm)],[f_4445_1]) ).

cnf(f_4445_3,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_18088),U_18089),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_18090,U_18091))) = hAPP(c_List_Omonoid__add__class_Olistsum(U_18088),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,U_18088),U_18089),c_List_Oupt(U_18090,U_18091)))
    | ~ class_Groups_Ocomm__monoid__add(U_18088) ),
    inference(clausify,[status(thm)],[f_4445_2]) ).

fof(f_4446_1,plain,
    ! [V_n_2,V_m_2,V_f_2,T_b] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),V_f_2),c_List_Oupt(V_m_2,V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_m_2,V_n_2)))
      | ~ class_Groups_Ocomm__monoid__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_interv__listsum__conv__setsum__set__nat]) ).

fof(f_4446_2,plain,
    ! [U_18095,U_18094,U_18093,U_18092] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18092),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,U_18092),U_18093),c_List_Oupt(U_18094,U_18095))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_18092),U_18093),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_18094,U_18095)))
      | ~ class_Groups_Ocomm__monoid__add(U_18092) ),
    inference(variable_rename,[status(thm)],[f_4446_1]) ).

cnf(f_4446_3,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18092),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,U_18092),U_18093),c_List_Oupt(U_18094,U_18095))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_18092),U_18093),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_18094,U_18095)))
    | ~ class_Groups_Ocomm__monoid__add(U_18092) ),
    inference(clausify,[status(thm)],[f_4446_2]) ).

fof(f_4447_1,plain,
    ! [V_f_2,T_b,V_m_2,V_n_2,V_i_2] :
      ( hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),V_f_2),c_List_Oupt(V_m_2,V_n_2))),V_i_2) = hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_i_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_m_2))) ),
    inference(fof_nnf,[status(thm)],[fact_nth__map__upt]) ).

fof(f_4447_2,plain,
    ! [U_18100,U_18099,U_18098,U_18097,U_18096] :
      ( hAPP(hAPP(c_List_Onth(U_18099),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,U_18099),U_18100),c_List_Oupt(U_18098,U_18097))),U_18096) = hAPP(U_18100,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_18098),U_18096))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18096),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_18097),U_18098))) ),
    inference(variable_rename,[status(thm)],[f_4447_1]) ).

cnf(f_4447_3,plain,
    ( hAPP(hAPP(c_List_Onth(U_18099),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,U_18099),U_18100),c_List_Oupt(U_18098,U_18097))),U_18096) = hAPP(U_18100,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_18098),U_18096))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18096),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_18097),U_18098))) ),
    inference(clausify,[status(thm)],[f_4447_2]) ).

fof(f_4448_1,plain,
    ! [V_n_2,T_b,V_xs_2] :
      ( c_List_Otranspose(T_b,V_xs_2) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(T_b)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(T_b)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,T_b)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_Nat_Onat,T_b),tc_Nat_Onat),c_List_Onth(T_b)),hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2))
      | ? [B_i] :
          ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),B_i)) != V_n_2
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2))) )
      | ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        & V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_b)) ) ),
    inference(fof_nnf,[status(thm)],[fact_transpose__rectangle]) ).

fof(f_4448_2,plain,
    ! [U_18104,U_18103,U_18102] :
      ( c_List_Otranspose(U_18103,U_18102) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(U_18103)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(U_18103)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,U_18103),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(U_18103)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,U_18103)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,U_18103),hAPP(hAPP(c_COMBB(tc_List_Olist(U_18103),tc_fun(tc_Nat_Onat,U_18103),tc_Nat_Onat),c_List_Onth(U_18103)),hAPP(c_List_Onth(tc_List_Olist(U_18103)),U_18102))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_18103))),U_18102)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_18104))
      | ? [U_18101] :
          ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18103)),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_18103)),U_18102),U_18101)) != U_18104
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18101),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_18103))),U_18102))) )
      | ( U_18104 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        & U_18102 = c_List_Olist_ONil(tc_List_Olist(U_18103)) ) ),
    inference(variable_rename,[status(thm)],[f_4448_1]) ).

fof(f_4448_3,plain,
    ! [U_18104,U_18103,U_18102] :
      ( c_List_Otranspose(U_18103,U_18102) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(U_18103)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(U_18103)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,U_18103),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(U_18103)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,U_18103)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,U_18103),hAPP(hAPP(c_COMBB(tc_List_Olist(U_18103),tc_fun(tc_Nat_Onat,U_18103),tc_Nat_Onat),c_List_Onth(U_18103)),hAPP(c_List_Onth(tc_List_Olist(U_18103)),U_18102))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_18103))),U_18102)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_18104))
      | ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18103)),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_18103)),U_18102),sK449(U_18104,U_18103,U_18102))) != U_18104
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK449(U_18104,U_18103,U_18102)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_18103))),U_18102))) )
      | ( U_18104 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        & U_18102 = c_List_Olist_ONil(tc_List_Olist(U_18103)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK449]),skolemize(U_18101,sK449(U_18104,U_18103,U_18102))],[f_4448_2]) ).

cnf(f_4448_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK449(U_18104,U_18103,U_18102)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_18103))),U_18102)))
    | c_List_Otranspose(U_18103,U_18102) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(U_18103)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(U_18103)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,U_18103),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(U_18103)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,U_18103)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,U_18103),hAPP(hAPP(c_COMBB(tc_List_Olist(U_18103),tc_fun(tc_Nat_Onat,U_18103),tc_Nat_Onat),c_List_Onth(U_18103)),hAPP(c_List_Onth(tc_List_Olist(U_18103)),U_18102))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_18103))),U_18102)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_18104))
    | U_18102 = c_List_Olist_ONil(tc_List_Olist(U_18103)) ),
    inference(clausify,[status(thm)],[f_4448_3]) ).

cnf(f_4448_5,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18103)),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_18103)),U_18102),sK449(U_18104,U_18103,U_18102))) != U_18104
    | c_List_Otranspose(U_18103,U_18102) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(U_18103)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(U_18103)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,U_18103),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(U_18103)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,U_18103)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,U_18103),hAPP(hAPP(c_COMBB(tc_List_Olist(U_18103),tc_fun(tc_Nat_Onat,U_18103),tc_Nat_Onat),c_List_Onth(U_18103)),hAPP(c_List_Onth(tc_List_Olist(U_18103)),U_18102))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_18103))),U_18102)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_18104))
    | U_18102 = c_List_Olist_ONil(tc_List_Olist(U_18103)) ),
    inference(clausify,[status(thm)],[f_4448_3]) ).

cnf(f_4448_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK449(U_18104,U_18103,U_18102)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_18103))),U_18102)))
    | c_List_Otranspose(U_18103,U_18102) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(U_18103)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(U_18103)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,U_18103),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(U_18103)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,U_18103)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,U_18103),hAPP(hAPP(c_COMBB(tc_List_Olist(U_18103),tc_fun(tc_Nat_Onat,U_18103),tc_Nat_Onat),c_List_Onth(U_18103)),hAPP(c_List_Onth(tc_List_Olist(U_18103)),U_18102))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_18103))),U_18102)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_18104))
    | U_18104 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4448_3]) ).

cnf(f_4448_7,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18103)),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_18103)),U_18102),sK449(U_18104,U_18103,U_18102))) != U_18104
    | c_List_Otranspose(U_18103,U_18102) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(U_18103)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(U_18103)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,U_18103),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(U_18103)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,U_18103)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,U_18103),hAPP(hAPP(c_COMBB(tc_List_Olist(U_18103),tc_fun(tc_Nat_Onat,U_18103),tc_Nat_Onat),c_List_Onth(U_18103)),hAPP(c_List_Onth(tc_List_Olist(U_18103)),U_18102))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_18103))),U_18102)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_18104))
    | U_18104 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4448_3]) ).

fof(f_4449_1,plain,
    ! [V_f_2,V_xs_2,V_a_2,T_b,T_c] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_a_2),c_List_Oremove1(T_b,V_a_2,V_xs_2)) = V_xs_2
      | hAPP(c_List_Ohd(T_b),hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(T_c,tc_HOL_Obool,T_b),hAPP(c_fequal,hAPP(V_f_2,V_a_2))),V_f_2)),V_xs_2)) != V_a_2
      | ~ c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2)))
      | ~ class_Orderings_Olinorder(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_insort__key__remove1]) ).

fof(f_4449_2,plain,
    ! [U_18109,U_18108,U_18107,U_18106,U_18105] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18106,U_18105,U_18109),U_18107),c_List_Oremove1(U_18106,U_18107,U_18108)) = U_18108
      | hAPP(c_List_Ohd(U_18106),hAPP(c_List_Ofilter(U_18106,hAPP(hAPP(c_COMBB(U_18105,tc_HOL_Obool,U_18106),hAPP(c_fequal,hAPP(U_18109,U_18107))),U_18109)),U_18108)) != U_18107
      | ~ c_List_Olinorder__class_Osorted(U_18105,hAPP(hAPP(c_List_Omap(U_18106,U_18105),U_18109),U_18108))
      | ~ hBOOL(hAPP(hAPP(c_member(U_18106),U_18107),hAPP(c_List_Oset(U_18106),U_18108)))
      | ~ class_Orderings_Olinorder(U_18105) ),
    inference(variable_rename,[status(thm)],[f_4449_1]) ).

cnf(f_4449_3,plain,
    ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18106,U_18105,U_18109),U_18107),c_List_Oremove1(U_18106,U_18107,U_18108)) = U_18108
    | hAPP(c_List_Ohd(U_18106),hAPP(c_List_Ofilter(U_18106,hAPP(hAPP(c_COMBB(U_18105,tc_HOL_Obool,U_18106),hAPP(c_fequal,hAPP(U_18109,U_18107))),U_18109)),U_18108)) != U_18107
    | ~ c_List_Olinorder__class_Osorted(U_18105,hAPP(hAPP(c_List_Omap(U_18106,U_18105),U_18109),U_18108))
    | ~ hBOOL(hAPP(hAPP(c_member(U_18106),U_18107),hAPP(c_List_Oset(U_18106),U_18108)))
    | ~ class_Orderings_Olinorder(U_18105) ),
    inference(clausify,[status(thm)],[f_4449_2]) ).

fof(f_4450_1,plain,
    ! [T_a] :
      ( c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sorted_ONil]) ).

fof(f_4450_2,plain,
    ! [U_18110] :
      ( c_List_Olinorder__class_Osorted(U_18110,c_List_Olist_ONil(U_18110))
      | ~ class_Orderings_Olinorder(U_18110) ),
    inference(variable_rename,[status(thm)],[f_4450_1]) ).

cnf(f_4450_3,plain,
    ( c_List_Olinorder__class_Osorted(U_18110,c_List_Olist_ONil(U_18110))
    | ~ class_Orderings_Olinorder(U_18110) ),
    inference(clausify,[status(thm)],[f_4450_2]) ).

fof(f_4451_1,plain,
    ! [V_x,T_a] :
      ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a)))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__single]) ).

fof(f_4451_2,plain,
    ! [U_18112,U_18111] :
      ( c_List_Olinorder__class_Osorted(U_18111,hAPP(hAPP(c_List_Olist_OCons(U_18111),U_18112),c_List_Olist_ONil(U_18111)))
      | ~ class_Orderings_Olinorder(U_18111) ),
    inference(variable_rename,[status(thm)],[f_4451_1]) ).

cnf(f_4451_3,plain,
    ( c_List_Olinorder__class_Osorted(U_18111,hAPP(hAPP(c_List_Olist_OCons(U_18111),U_18112),c_List_Olist_ONil(U_18111)))
    | ~ class_Orderings_Olinorder(U_18111) ),
    inference(clausify,[status(thm)],[f_4451_2]) ).

fof(f_4452_1,plain,
    ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(V_i,V_j)),
    inference(fof_nnf,[status(thm)],[fact_sorted__upt]) ).

fof(f_4452_2,plain,
    ! [U_18114,U_18113] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(U_18113,U_18114)),
    inference(variable_rename,[status(thm)],[f_4452_1]) ).

cnf(f_4452_3,plain,
    c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(U_18113,U_18114)),
    inference(clausify,[status(thm)],[f_4452_2]) ).

fof(f_4453_1,plain,
    ! [V_xs_2,T_b] :
      ( c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Osort__key(T_b,T_b,c_COMBI(T_b),V_xs_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__sort]) ).

fof(f_4453_2,plain,
    ! [U_18116,U_18115] :
      ( c_List_Olinorder__class_Osorted(U_18115,c_List_Olinorder__class_Osort__key(U_18115,U_18115,c_COMBI(U_18115),U_18116))
      | ~ class_Orderings_Olinorder(U_18115) ),
    inference(variable_rename,[status(thm)],[f_4453_1]) ).

cnf(f_4453_3,plain,
    ( c_List_Olinorder__class_Osorted(U_18115,c_List_Olinorder__class_Osort__key(U_18115,U_18115,c_COMBI(U_18115),U_18116))
    | ~ class_Orderings_Olinorder(U_18115) ),
    inference(clausify,[status(thm)],[f_4453_2]) ).

fof(f_4454_1,plain,
    ! [V_x_2,V_xs_2,T_b] :
      ( c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2))
      | ~ c_List_Olinorder__class_Osorted(T_b,V_xs_2)
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__insort__insert]) ).

fof(f_4454_2,plain,
    ! [U_18119,U_18118,U_18117] :
      ( c_List_Olinorder__class_Osorted(U_18117,c_List_Olinorder__class_Oinsort__insert__key(U_18117,U_18117,c_COMBI(U_18117),U_18119,U_18118))
      | ~ c_List_Olinorder__class_Osorted(U_18117,U_18118)
      | ~ class_Orderings_Olinorder(U_18117) ),
    inference(variable_rename,[status(thm)],[f_4454_1]) ).

cnf(f_4454_3,plain,
    ( c_List_Olinorder__class_Osorted(U_18117,c_List_Olinorder__class_Oinsort__insert__key(U_18117,U_18117,c_COMBI(U_18117),U_18119,U_18118))
    | ~ c_List_Olinorder__class_Osorted(U_18117,U_18118)
    | ~ class_Orderings_Olinorder(U_18117) ),
    inference(clausify,[status(thm)],[f_4454_2]) ).

fof(f_4455_1,plain,
    ! [V_n,V_xs,T_a] :
      ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs))
      | ~ c_List_Olinorder__class_Osorted(T_a,V_xs)
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__drop]) ).

fof(f_4455_2,plain,
    ! [U_18122,U_18121,U_18120] :
      ( c_List_Olinorder__class_Osorted(U_18120,hAPP(hAPP(c_List_Odrop(U_18120),U_18122),U_18121))
      | ~ c_List_Olinorder__class_Osorted(U_18120,U_18121)
      | ~ class_Orderings_Olinorder(U_18120) ),
    inference(variable_rename,[status(thm)],[f_4455_1]) ).

cnf(f_4455_3,plain,
    ( c_List_Olinorder__class_Osorted(U_18120,hAPP(hAPP(c_List_Odrop(U_18120),U_18122),U_18121))
    | ~ c_List_Olinorder__class_Osorted(U_18120,U_18121)
    | ~ class_Orderings_Olinorder(U_18120) ),
    inference(clausify,[status(thm)],[f_4455_2]) ).

fof(f_4456_1,plain,
    ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(V_i,V_j)),
    inference(fof_nnf,[status(thm)],[fact_sorted__upto]) ).

fof(f_4456_2,plain,
    ! [U_18124,U_18123] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(U_18123,U_18124)),
    inference(variable_rename,[status(thm)],[f_4456_1]) ).

cnf(f_4456_3,plain,
    c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(U_18123,U_18124)),
    inference(clausify,[status(thm)],[f_4456_2]) ).

fof(f_4457_1,plain,
    ! [V_n,V_xs,T_a] :
      ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs))
      | ~ c_List_Olinorder__class_Osorted(T_a,V_xs)
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__take]) ).

fof(f_4457_2,plain,
    ! [U_18127,U_18126,U_18125] :
      ( c_List_Olinorder__class_Osorted(U_18125,hAPP(hAPP(c_List_Otake(U_18125),U_18127),U_18126))
      | ~ c_List_Olinorder__class_Osorted(U_18125,U_18126)
      | ~ class_Orderings_Olinorder(U_18125) ),
    inference(variable_rename,[status(thm)],[f_4457_1]) ).

cnf(f_4457_3,plain,
    ( c_List_Olinorder__class_Osorted(U_18125,hAPP(hAPP(c_List_Otake(U_18125),U_18127),U_18126))
    | ~ c_List_Olinorder__class_Osorted(U_18125,U_18126)
    | ~ class_Orderings_Olinorder(U_18125) ),
    inference(clausify,[status(thm)],[f_4457_2]) ).

fof(f_4458_1,plain,
    ! [V_a,V_xs,T_a] :
      ( c_List_Olinorder__class_Osorted(T_a,c_List_Oremove1(T_a,V_a,V_xs))
      | ~ c_List_Olinorder__class_Osorted(T_a,V_xs)
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__remove1]) ).

fof(f_4458_2,plain,
    ! [U_18130,U_18129,U_18128] :
      ( c_List_Olinorder__class_Osorted(U_18128,c_List_Oremove1(U_18128,U_18130,U_18129))
      | ~ c_List_Olinorder__class_Osorted(U_18128,U_18129)
      | ~ class_Orderings_Olinorder(U_18128) ),
    inference(variable_rename,[status(thm)],[f_4458_1]) ).

cnf(f_4458_3,plain,
    ( c_List_Olinorder__class_Osorted(U_18128,c_List_Oremove1(U_18128,U_18130,U_18129))
    | ~ c_List_Olinorder__class_Osorted(U_18128,U_18129)
    | ~ class_Orderings_Olinorder(U_18128) ),
    inference(clausify,[status(thm)],[f_4458_2]) ).

fof(f_4459_1,plain,
    ! [V_xs,T_a] :
      ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Otl(T_a),V_xs))
      | ~ c_List_Olinorder__class_Osorted(T_a,V_xs)
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__tl]) ).

fof(f_4459_2,plain,
    ! [U_18132,U_18131] :
      ( c_List_Olinorder__class_Osorted(U_18131,hAPP(c_List_Otl(U_18131),U_18132))
      | ~ c_List_Olinorder__class_Osorted(U_18131,U_18132)
      | ~ class_Orderings_Olinorder(U_18131) ),
    inference(variable_rename,[status(thm)],[f_4459_1]) ).

cnf(f_4459_3,plain,
    ( c_List_Olinorder__class_Osorted(U_18131,hAPP(c_List_Otl(U_18131),U_18132))
    | ~ c_List_Olinorder__class_Osorted(U_18131,U_18132)
    | ~ class_Orderings_Olinorder(U_18131) ),
    inference(clausify,[status(thm)],[f_4459_2]) ).

fof(f_4460_1,plain,
    ! [V_xs_2,V_x_2,T_b] :
      ( ( ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),V_xs_2))
          | ~ c_List_Olinorder__class_Osorted(T_b,V_xs_2) )
        & ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
          | ~ c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),V_xs_2)) ) )
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__insort]) ).

fof(f_4460_2,plain,
    ! [U_18135,U_18134,U_18133] :
      ( ( ( c_List_Olinorder__class_Osorted(U_18133,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18133,U_18133,c_COMBI(U_18133)),U_18134),U_18135))
          | ~ c_List_Olinorder__class_Osorted(U_18133,U_18135) )
        & ( c_List_Olinorder__class_Osorted(U_18133,U_18135)
          | ~ c_List_Olinorder__class_Osorted(U_18133,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18133,U_18133,c_COMBI(U_18133)),U_18134),U_18135)) ) )
      | ~ class_Orderings_Olinorder(U_18133) ),
    inference(variable_rename,[status(thm)],[f_4460_1]) ).

cnf(f_4460_3,plain,
    ( c_List_Olinorder__class_Osorted(U_18133,U_18135)
    | ~ c_List_Olinorder__class_Osorted(U_18133,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18133,U_18133,c_COMBI(U_18133)),U_18134),U_18135))
    | ~ class_Orderings_Olinorder(U_18133) ),
    inference(clausify,[status(thm)],[f_4460_2]) ).

cnf(f_4460_4,plain,
    ( c_List_Olinorder__class_Osorted(U_18133,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18133,U_18133,c_COMBI(U_18133)),U_18134),U_18135))
    | ~ c_List_Olinorder__class_Osorted(U_18133,U_18135)
    | ~ class_Orderings_Olinorder(U_18133) ),
    inference(clausify,[status(thm)],[f_4460_2]) ).

fof(f_4461_1,plain,
    ! [V_xs,T_a] :
      ( c_List_Olinorder__class_Osorted(T_a,c_List_Obutlast(T_a,V_xs))
      | ~ c_List_Olinorder__class_Osorted(T_a,V_xs)
      | V_xs = c_List_Olist_ONil(T_a)
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__butlast]) ).

fof(f_4461_2,plain,
    ! [U_18137,U_18136] :
      ( c_List_Olinorder__class_Osorted(U_18136,c_List_Obutlast(U_18136,U_18137))
      | ~ c_List_Olinorder__class_Osorted(U_18136,U_18137)
      | U_18137 = c_List_Olist_ONil(U_18136)
      | ~ class_Orderings_Olinorder(U_18136) ),
    inference(variable_rename,[status(thm)],[f_4461_1]) ).

cnf(f_4461_3,plain,
    ( c_List_Olinorder__class_Osorted(U_18136,c_List_Obutlast(U_18136,U_18137))
    | ~ c_List_Olinorder__class_Osorted(U_18136,U_18137)
    | U_18137 = c_List_Olist_ONil(U_18136)
    | ~ class_Orderings_Olinorder(U_18136) ),
    inference(clausify,[status(thm)],[f_4461_2]) ).

fof(f_4462_1,plain,
    ! [T_a] :
      ( c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sorted_Oequations_I1_J]) ).

fof(f_4462_2,plain,
    ! [U_18138] :
      ( c_List_Olinorder__class_Osorted(U_18138,c_List_Olist_ONil(U_18138))
      | ~ class_Orderings_Olinorder(U_18138) ),
    inference(variable_rename,[status(thm)],[f_4462_1]) ).

cnf(f_4462_3,plain,
    ( c_List_Olinorder__class_Osorted(U_18138,c_List_Olist_ONil(U_18138))
    | ~ class_Orderings_Olinorder(U_18138) ),
    inference(clausify,[status(thm)],[f_4462_2]) ).

fof(f_4463_1,plain,
    ! [V_zs,V_y,V_x,T_a] :
      ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_zs)))
      | ~ c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_zs))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__many]) ).

fof(f_4463_2,plain,
    ! [U_18142,U_18141,U_18140,U_18139] :
      ( c_List_Olinorder__class_Osorted(U_18139,hAPP(hAPP(c_List_Olist_OCons(U_18139),U_18140),hAPP(hAPP(c_List_Olist_OCons(U_18139),U_18141),U_18142)))
      | ~ c_List_Olinorder__class_Osorted(U_18139,hAPP(hAPP(c_List_Olist_OCons(U_18139),U_18141),U_18142))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18139),U_18140),U_18141))
      | ~ class_Orderings_Olinorder(U_18139) ),
    inference(variable_rename,[status(thm)],[f_4463_1]) ).

cnf(f_4463_3,plain,
    ( c_List_Olinorder__class_Osorted(U_18139,hAPP(hAPP(c_List_Olist_OCons(U_18139),U_18140),hAPP(hAPP(c_List_Olist_OCons(U_18139),U_18141),U_18142)))
    | ~ c_List_Olinorder__class_Osorted(U_18139,hAPP(hAPP(c_List_Olist_OCons(U_18139),U_18141),U_18142))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18139),U_18140),U_18141))
    | ~ class_Orderings_Olinorder(U_18139) ),
    inference(clausify,[status(thm)],[f_4463_2]) ).

fof(f_4464_1,plain,
    ! [V_zs_2,V_y_2,V_x_2,T_b] :
      ( ( ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_zs_2)))
          | ~ c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_zs_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) )
        & ( ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_zs_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) )
          | ~ c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_zs_2))) ) )
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__many__eq]) ).

fof(f_4464_2,plain,
    ! [U_18146,U_18145,U_18144,U_18143] :
      ( ( ( c_List_Olinorder__class_Osorted(U_18143,hAPP(hAPP(c_List_Olist_OCons(U_18143),U_18144),hAPP(hAPP(c_List_Olist_OCons(U_18143),U_18145),U_18146)))
          | ~ c_List_Olinorder__class_Osorted(U_18143,hAPP(hAPP(c_List_Olist_OCons(U_18143),U_18145),U_18146))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18143),U_18144),U_18145)) )
        & ( ( c_List_Olinorder__class_Osorted(U_18143,hAPP(hAPP(c_List_Olist_OCons(U_18143),U_18145),U_18146))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18143),U_18144),U_18145)) )
          | ~ c_List_Olinorder__class_Osorted(U_18143,hAPP(hAPP(c_List_Olist_OCons(U_18143),U_18144),hAPP(hAPP(c_List_Olist_OCons(U_18143),U_18145),U_18146))) ) )
      | ~ class_Orderings_Olinorder(U_18143) ),
    inference(variable_rename,[status(thm)],[f_4464_1]) ).

cnf(f_4464_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18143),U_18144),U_18145))
    | ~ c_List_Olinorder__class_Osorted(U_18143,hAPP(hAPP(c_List_Olist_OCons(U_18143),U_18144),hAPP(hAPP(c_List_Olist_OCons(U_18143),U_18145),U_18146)))
    | ~ class_Orderings_Olinorder(U_18143) ),
    inference(clausify,[status(thm)],[f_4464_2]) ).

cnf(f_4464_4,plain,
    ( c_List_Olinorder__class_Osorted(U_18143,hAPP(hAPP(c_List_Olist_OCons(U_18143),U_18145),U_18146))
    | ~ c_List_Olinorder__class_Osorted(U_18143,hAPP(hAPP(c_List_Olist_OCons(U_18143),U_18144),hAPP(hAPP(c_List_Olist_OCons(U_18143),U_18145),U_18146)))
    | ~ class_Orderings_Olinorder(U_18143) ),
    inference(clausify,[status(thm)],[f_4464_2]) ).

cnf(f_4464_5,plain,
    ( c_List_Olinorder__class_Osorted(U_18143,hAPP(hAPP(c_List_Olist_OCons(U_18143),U_18144),hAPP(hAPP(c_List_Olist_OCons(U_18143),U_18145),U_18146)))
    | ~ c_List_Olinorder__class_Osorted(U_18143,hAPP(hAPP(c_List_Olist_OCons(U_18143),U_18145),U_18146))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18143),U_18144),U_18145))
    | ~ class_Orderings_Olinorder(U_18143) ),
    inference(clausify,[status(thm)],[f_4464_2]) ).

fof(f_4465_1,plain,
    ! [V_l,T_a] :
      ( c_List_Olinorder__class_Osorted(T_a,c_List_Oremdups(T_a,V_l))
      | ~ c_List_Olinorder__class_Osorted(T_a,V_l)
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__remdups]) ).

fof(f_4465_2,plain,
    ! [U_18148,U_18147] :
      ( c_List_Olinorder__class_Osorted(U_18147,c_List_Oremdups(U_18147,U_18148))
      | ~ c_List_Olinorder__class_Osorted(U_18147,U_18148)
      | ~ class_Orderings_Olinorder(U_18147) ),
    inference(variable_rename,[status(thm)],[f_4465_1]) ).

cnf(f_4465_3,plain,
    ( c_List_Olinorder__class_Osorted(U_18147,c_List_Oremdups(U_18147,U_18148))
    | ~ c_List_Olinorder__class_Osorted(U_18147,U_18148)
    | ~ class_Orderings_Olinorder(U_18147) ),
    inference(clausify,[status(thm)],[f_4465_2]) ).

fof(f_4466_1,plain,
    ! [V_ys_2,V_xs_2,T_b] :
      ( V_xs_2 = V_ys_2
      | hAPP(c_List_Oset(T_b),V_xs_2) != hAPP(c_List_Oset(T_b),V_ys_2)
      | ~ hBOOL(hAPP(c_List_Odistinct(T_b),V_ys_2))
      | ~ c_List_Olinorder__class_Osorted(T_b,V_ys_2)
      | ~ hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
      | ~ c_List_Olinorder__class_Osorted(T_b,V_xs_2)
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__distinct__set__unique]) ).

fof(f_4466_2,plain,
    ! [U_18151,U_18150,U_18149] :
      ( U_18150 = U_18151
      | hAPP(c_List_Oset(U_18149),U_18150) != hAPP(c_List_Oset(U_18149),U_18151)
      | ~ hBOOL(hAPP(c_List_Odistinct(U_18149),U_18151))
      | ~ c_List_Olinorder__class_Osorted(U_18149,U_18151)
      | ~ hBOOL(hAPP(c_List_Odistinct(U_18149),U_18150))
      | ~ c_List_Olinorder__class_Osorted(U_18149,U_18150)
      | ~ class_Orderings_Olinorder(U_18149) ),
    inference(variable_rename,[status(thm)],[f_4466_1]) ).

cnf(f_4466_3,plain,
    ( U_18150 = U_18151
    | hAPP(c_List_Oset(U_18149),U_18150) != hAPP(c_List_Oset(U_18149),U_18151)
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18149),U_18151))
    | ~ c_List_Olinorder__class_Osorted(U_18149,U_18151)
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18149),U_18150))
    | ~ c_List_Olinorder__class_Osorted(U_18149,U_18150)
    | ~ class_Orderings_Olinorder(U_18149) ),
    inference(clausify,[status(thm)],[f_4466_2]) ).

fof(f_4467_1,plain,
    ! [V_xs_2,V_f_2,T_c,T_b] :
      ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Olinorder__class_Osort__key(T_c,T_b,V_f_2,V_xs_2)))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__sort__key]) ).

fof(f_4467_2,plain,
    ! [U_18155,U_18154,U_18153,U_18152] :
      ( c_List_Olinorder__class_Osorted(U_18152,hAPP(hAPP(c_List_Omap(U_18153,U_18152),U_18154),c_List_Olinorder__class_Osort__key(U_18153,U_18152,U_18154,U_18155)))
      | ~ class_Orderings_Olinorder(U_18152) ),
    inference(variable_rename,[status(thm)],[f_4467_1]) ).

cnf(f_4467_3,plain,
    ( c_List_Olinorder__class_Osorted(U_18152,hAPP(hAPP(c_List_Omap(U_18153,U_18152),U_18154),c_List_Olinorder__class_Osort__key(U_18153,U_18152,U_18154,U_18155)))
    | ~ class_Orderings_Olinorder(U_18152) ),
    inference(clausify,[status(thm)],[f_4467_2]) ).

fof(f_4468_1,plain,
    ! [V_x_2,V_xs_2,V_f_2,T_c,T_b] :
      ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Olinorder__class_Oinsort__insert__key(T_c,T_b,V_f_2,V_x_2,V_xs_2)))
      | ~ c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__insort__insert__key]) ).

fof(f_4468_2,plain,
    ! [U_18160,U_18159,U_18158,U_18157,U_18156] :
      ( c_List_Olinorder__class_Osorted(U_18156,hAPP(hAPP(c_List_Omap(U_18157,U_18156),U_18158),c_List_Olinorder__class_Oinsort__insert__key(U_18157,U_18156,U_18158,U_18160,U_18159)))
      | ~ c_List_Olinorder__class_Osorted(U_18156,hAPP(hAPP(c_List_Omap(U_18157,U_18156),U_18158),U_18159))
      | ~ class_Orderings_Olinorder(U_18156) ),
    inference(variable_rename,[status(thm)],[f_4468_1]) ).

cnf(f_4468_3,plain,
    ( c_List_Olinorder__class_Osorted(U_18156,hAPP(hAPP(c_List_Omap(U_18157,U_18156),U_18158),c_List_Olinorder__class_Oinsort__insert__key(U_18157,U_18156,U_18158,U_18160,U_18159)))
    | ~ c_List_Olinorder__class_Osorted(U_18156,hAPP(hAPP(c_List_Omap(U_18157,U_18156),U_18158),U_18159))
    | ~ class_Orderings_Olinorder(U_18156) ),
    inference(clausify,[status(thm)],[f_4468_2]) ).

fof(f_4469_1,plain,
    ! [V_x_2,V_xs_2,V_f_2,T_c,T_b] :
      ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Oremove1(T_c,V_x_2,V_xs_2)))
      | ~ c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__map__remove1]) ).

fof(f_4469_2,plain,
    ! [U_18165,U_18164,U_18163,U_18162,U_18161] :
      ( c_List_Olinorder__class_Osorted(U_18161,hAPP(hAPP(c_List_Omap(U_18162,U_18161),U_18163),c_List_Oremove1(U_18162,U_18165,U_18164)))
      | ~ c_List_Olinorder__class_Osorted(U_18161,hAPP(hAPP(c_List_Omap(U_18162,U_18161),U_18163),U_18164))
      | ~ class_Orderings_Olinorder(U_18161) ),
    inference(variable_rename,[status(thm)],[f_4469_1]) ).

cnf(f_4469_3,plain,
    ( c_List_Olinorder__class_Osorted(U_18161,hAPP(hAPP(c_List_Omap(U_18162,U_18161),U_18163),c_List_Oremove1(U_18162,U_18165,U_18164)))
    | ~ c_List_Olinorder__class_Osorted(U_18161,hAPP(hAPP(c_List_Omap(U_18162,U_18161),U_18163),U_18164))
    | ~ class_Orderings_Olinorder(U_18161) ),
    inference(clausify,[status(thm)],[f_4469_2]) ).

fof(f_4470_1,plain,
    ! [V_xs_2,V_x_2,V_f_2,T_c,T_b] :
      ( ( ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_xs_2)))
          | ~ c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) )
        & ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
          | ~ c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_xs_2))) ) )
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__insort__key]) ).

fof(f_4470_2,plain,
    ! [U_18170,U_18169,U_18168,U_18167,U_18166] :
      ( ( ( c_List_Olinorder__class_Osorted(U_18166,hAPP(hAPP(c_List_Omap(U_18167,U_18166),U_18168),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18167,U_18166,U_18168),U_18169),U_18170)))
          | ~ c_List_Olinorder__class_Osorted(U_18166,hAPP(hAPP(c_List_Omap(U_18167,U_18166),U_18168),U_18170)) )
        & ( c_List_Olinorder__class_Osorted(U_18166,hAPP(hAPP(c_List_Omap(U_18167,U_18166),U_18168),U_18170))
          | ~ c_List_Olinorder__class_Osorted(U_18166,hAPP(hAPP(c_List_Omap(U_18167,U_18166),U_18168),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18167,U_18166,U_18168),U_18169),U_18170))) ) )
      | ~ class_Orderings_Olinorder(U_18166) ),
    inference(variable_rename,[status(thm)],[f_4470_1]) ).

cnf(f_4470_3,plain,
    ( c_List_Olinorder__class_Osorted(U_18166,hAPP(hAPP(c_List_Omap(U_18167,U_18166),U_18168),U_18170))
    | ~ c_List_Olinorder__class_Osorted(U_18166,hAPP(hAPP(c_List_Omap(U_18167,U_18166),U_18168),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18167,U_18166,U_18168),U_18169),U_18170)))
    | ~ class_Orderings_Olinorder(U_18166) ),
    inference(clausify,[status(thm)],[f_4470_2]) ).

cnf(f_4470_4,plain,
    ( c_List_Olinorder__class_Osorted(U_18166,hAPP(hAPP(c_List_Omap(U_18167,U_18166),U_18168),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18167,U_18166,U_18168),U_18169),U_18170)))
    | ~ c_List_Olinorder__class_Osorted(U_18166,hAPP(hAPP(c_List_Omap(U_18167,U_18166),U_18168),U_18170))
    | ~ class_Orderings_Olinorder(U_18166) ),
    inference(clausify,[status(thm)],[f_4470_2]) ).

fof(f_4471_1,plain,
    ! [V_P_2,V_xs_2,V_f_2,T_c,T_b] :
      ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Ofilter(T_c,V_P_2),V_xs_2)))
      | ~ c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__filter]) ).

fof(f_4471_2,plain,
    ! [U_18175,U_18174,U_18173,U_18172,U_18171] :
      ( c_List_Olinorder__class_Osorted(U_18171,hAPP(hAPP(c_List_Omap(U_18172,U_18171),U_18173),hAPP(c_List_Ofilter(U_18172,U_18175),U_18174)))
      | ~ c_List_Olinorder__class_Osorted(U_18171,hAPP(hAPP(c_List_Omap(U_18172,U_18171),U_18173),U_18174))
      | ~ class_Orderings_Olinorder(U_18171) ),
    inference(variable_rename,[status(thm)],[f_4471_1]) ).

cnf(f_4471_3,plain,
    ( c_List_Olinorder__class_Osorted(U_18171,hAPP(hAPP(c_List_Omap(U_18172,U_18171),U_18173),hAPP(c_List_Ofilter(U_18172,U_18175),U_18174)))
    | ~ c_List_Olinorder__class_Osorted(U_18171,hAPP(hAPP(c_List_Omap(U_18172,U_18171),U_18173),U_18174))
    | ~ class_Orderings_Olinorder(U_18171) ),
    inference(clausify,[status(thm)],[f_4471_2]) ).

fof(f_4472_1,plain,
    ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
      ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Ofilter(T_c,hAPP(hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_c),c_fequal),V_f_2)),hAPP(V_g_2,V_xs_2))),V_xs_2)))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__map__same]) ).

fof(f_4472_2,plain,
    ! [U_18180,U_18179,U_18178,U_18177,U_18176] :
      ( c_List_Olinorder__class_Osorted(U_18176,hAPP(hAPP(c_List_Omap(U_18177,U_18176),U_18178),hAPP(c_List_Ofilter(U_18177,hAPP(hAPP(c_COMBC(U_18177,U_18176,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_18176,tc_fun(U_18176,tc_HOL_Obool),U_18177),c_fequal),U_18178)),hAPP(U_18179,U_18180))),U_18180)))
      | ~ class_Orderings_Olinorder(U_18176) ),
    inference(variable_rename,[status(thm)],[f_4472_1]) ).

cnf(f_4472_3,plain,
    ( c_List_Olinorder__class_Osorted(U_18176,hAPP(hAPP(c_List_Omap(U_18177,U_18176),U_18178),hAPP(c_List_Ofilter(U_18177,hAPP(hAPP(c_COMBC(U_18177,U_18176,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_18176,tc_fun(U_18176,tc_HOL_Obool),U_18177),c_fequal),U_18178)),hAPP(U_18179,U_18180))),U_18180)))
    | ~ class_Orderings_Olinorder(U_18176) ),
    inference(clausify,[status(thm)],[f_4472_2]) ).

fof(f_4473_1,plain,
    ! [V_xs_2,V_g_2,T_b] :
      ( c_List_Olinorder__class_Osorted(T_b,hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),hAPP(V_g_2,V_xs_2))),V_xs_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__same]) ).

fof(f_4473_2,plain,
    ! [U_18183,U_18182,U_18181] :
      ( c_List_Olinorder__class_Osorted(U_18181,hAPP(c_List_Ofilter(U_18181,hAPP(hAPP(c_COMBC(U_18181,U_18181,tc_HOL_Obool),c_fequal),hAPP(U_18182,U_18183))),U_18183))
      | ~ class_Orderings_Olinorder(U_18181) ),
    inference(variable_rename,[status(thm)],[f_4473_1]) ).

cnf(f_4473_3,plain,
    ( c_List_Olinorder__class_Osorted(U_18181,hAPP(c_List_Ofilter(U_18181,hAPP(hAPP(c_COMBC(U_18181,U_18181,tc_HOL_Obool),c_fequal),hAPP(U_18182,U_18183))),U_18183))
    | ~ class_Orderings_Olinorder(U_18181) ),
    inference(clausify,[status(thm)],[f_4473_2]) ).

fof(f_4474_1,plain,
    ! [V_xs_2,V_x_2,T_b] :
      ( ( ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
          | ? [B_x] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x))
              & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) )
          | ~ c_List_Olinorder__class_Osorted(T_b,V_xs_2) )
        & ( ( ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x))
                | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) )
            & c_List_Olinorder__class_Osorted(T_b,V_xs_2) )
          | ~ c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) ) )
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__Cons]) ).

fof(f_4474_2,plain,
    ! [U_18188,U_18187,U_18186] :
      ( ( ( c_List_Olinorder__class_Osorted(U_18186,hAPP(hAPP(c_List_Olist_OCons(U_18186),U_18187),U_18188))
          | ? [U_18185] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18186),U_18187),U_18185))
              & hBOOL(hAPP(hAPP(c_member(U_18186),U_18185),hAPP(c_List_Oset(U_18186),U_18188))) )
          | ~ c_List_Olinorder__class_Osorted(U_18186,U_18188) )
        & ( ( ! [U_18184] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18186),U_18187),U_18184))
                | ~ hBOOL(hAPP(hAPP(c_member(U_18186),U_18184),hAPP(c_List_Oset(U_18186),U_18188))) )
            & c_List_Olinorder__class_Osorted(U_18186,U_18188) )
          | ~ c_List_Olinorder__class_Osorted(U_18186,hAPP(hAPP(c_List_Olist_OCons(U_18186),U_18187),U_18188)) ) )
      | ~ class_Orderings_Olinorder(U_18186) ),
    inference(variable_rename,[status(thm)],[f_4474_1]) ).

fof(f_4474_3,plain,
    ! [U_18188,U_18187,U_18186] :
      ( ( ( c_List_Olinorder__class_Osorted(U_18186,hAPP(hAPP(c_List_Olist_OCons(U_18186),U_18187),U_18188))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18186),U_18187),sK450(U_18188,U_18187,U_18186)))
            & hBOOL(hAPP(hAPP(c_member(U_18186),sK450(U_18188,U_18187,U_18186)),hAPP(c_List_Oset(U_18186),U_18188))) )
          | ~ c_List_Olinorder__class_Osorted(U_18186,U_18188) )
        & ( ( ! [U_18184] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18186),U_18187),U_18184))
                | ~ hBOOL(hAPP(hAPP(c_member(U_18186),U_18184),hAPP(c_List_Oset(U_18186),U_18188))) )
            & c_List_Olinorder__class_Osorted(U_18186,U_18188) )
          | ~ c_List_Olinorder__class_Osorted(U_18186,hAPP(hAPP(c_List_Olist_OCons(U_18186),U_18187),U_18188)) ) )
      | ~ class_Orderings_Olinorder(U_18186) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK450]),skolemize(U_18185,sK450(U_18188,U_18187,U_18186))],[f_4474_2]) ).

cnf(f_4474_4,plain,
    ( c_List_Olinorder__class_Osorted(U_18186,U_18188)
    | ~ c_List_Olinorder__class_Osorted(U_18186,hAPP(hAPP(c_List_Olist_OCons(U_18186),U_18187),U_18188))
    | ~ class_Orderings_Olinorder(U_18186) ),
    inference(clausify,[status(thm)],[f_4474_3]) ).

cnf(f_4474_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18186),U_18187),U_18184))
    | ~ hBOOL(hAPP(hAPP(c_member(U_18186),U_18184),hAPP(c_List_Oset(U_18186),U_18188)))
    | ~ c_List_Olinorder__class_Osorted(U_18186,hAPP(hAPP(c_List_Olist_OCons(U_18186),U_18187),U_18188))
    | ~ class_Orderings_Olinorder(U_18186) ),
    inference(clausify,[status(thm)],[f_4474_3]) ).

cnf(f_4474_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18186),sK450(U_18188,U_18187,U_18186)),hAPP(c_List_Oset(U_18186),U_18188)))
    | ~ c_List_Olinorder__class_Osorted(U_18186,U_18188)
    | c_List_Olinorder__class_Osorted(U_18186,hAPP(hAPP(c_List_Olist_OCons(U_18186),U_18187),U_18188))
    | ~ class_Orderings_Olinorder(U_18186) ),
    inference(clausify,[status(thm)],[f_4474_3]) ).

cnf(f_4474_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18186),U_18187),sK450(U_18188,U_18187,U_18186)))
    | ~ c_List_Olinorder__class_Osorted(U_18186,U_18188)
    | c_List_Olinorder__class_Osorted(U_18186,hAPP(hAPP(c_List_Olist_OCons(U_18186),U_18187),U_18188))
    | ~ class_Orderings_Olinorder(U_18186) ),
    inference(clausify,[status(thm)],[f_4474_3]) ).

fof(f_4475_1,plain,
    ! [V_ys_2,V_xs_2,T_b] :
      ( ( ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))
          | ? [B_x] :
              ( ? [B_xa] :
                  ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),B_xa))
                  & hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(c_List_Oset(T_b),V_ys_2))) )
              & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) )
          | ~ c_List_Olinorder__class_Osorted(T_b,V_ys_2)
          | ~ c_List_Olinorder__class_Osorted(T_b,V_xs_2) )
        & ( ( ! [B_x] :
                ( ! [B_xa] :
                    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),B_xa))
                    | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(c_List_Oset(T_b),V_ys_2))) )
                | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) )
            & c_List_Olinorder__class_Osorted(T_b,V_ys_2)
            & c_List_Olinorder__class_Osorted(T_b,V_xs_2) )
          | ~ c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) ) )
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__append]) ).

fof(f_4475_2,plain,
    ! [U_18195,U_18194,U_18193] :
      ( ( ( c_List_Olinorder__class_Osorted(U_18193,hAPP(hAPP(c_List_Oappend(U_18193),U_18194),U_18195))
          | ? [U_18192] :
              ( ? [U_18191] :
                  ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18193),U_18192),U_18191))
                  & hBOOL(hAPP(hAPP(c_member(U_18193),U_18191),hAPP(c_List_Oset(U_18193),U_18195))) )
              & hBOOL(hAPP(hAPP(c_member(U_18193),U_18192),hAPP(c_List_Oset(U_18193),U_18194))) )
          | ~ c_List_Olinorder__class_Osorted(U_18193,U_18195)
          | ~ c_List_Olinorder__class_Osorted(U_18193,U_18194) )
        & ( ( ! [U_18190] :
                ( ! [U_18189] :
                    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18193),U_18190),U_18189))
                    | ~ hBOOL(hAPP(hAPP(c_member(U_18193),U_18189),hAPP(c_List_Oset(U_18193),U_18195))) )
                | ~ hBOOL(hAPP(hAPP(c_member(U_18193),U_18190),hAPP(c_List_Oset(U_18193),U_18194))) )
            & c_List_Olinorder__class_Osorted(U_18193,U_18195)
            & c_List_Olinorder__class_Osorted(U_18193,U_18194) )
          | ~ c_List_Olinorder__class_Osorted(U_18193,hAPP(hAPP(c_List_Oappend(U_18193),U_18194),U_18195)) ) )
      | ~ class_Orderings_Olinorder(U_18193) ),
    inference(variable_rename,[status(thm)],[f_4475_1]) ).

fof(f_4475_3,plain,
    ! [U_18195,U_18194,U_18193] :
      ( ( ( c_List_Olinorder__class_Osorted(U_18193,hAPP(hAPP(c_List_Oappend(U_18193),U_18194),U_18195))
          | ( ? [U_18191] :
                ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18193),sK451(U_18195,U_18194,U_18193)),U_18191))
                & hBOOL(hAPP(hAPP(c_member(U_18193),U_18191),hAPP(c_List_Oset(U_18193),U_18195))) )
            & hBOOL(hAPP(hAPP(c_member(U_18193),sK451(U_18195,U_18194,U_18193)),hAPP(c_List_Oset(U_18193),U_18194))) )
          | ~ c_List_Olinorder__class_Osorted(U_18193,U_18195)
          | ~ c_List_Olinorder__class_Osorted(U_18193,U_18194) )
        & ( ( ! [U_18190] :
                ( ! [U_18189] :
                    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18193),U_18190),U_18189))
                    | ~ hBOOL(hAPP(hAPP(c_member(U_18193),U_18189),hAPP(c_List_Oset(U_18193),U_18195))) )
                | ~ hBOOL(hAPP(hAPP(c_member(U_18193),U_18190),hAPP(c_List_Oset(U_18193),U_18194))) )
            & c_List_Olinorder__class_Osorted(U_18193,U_18195)
            & c_List_Olinorder__class_Osorted(U_18193,U_18194) )
          | ~ c_List_Olinorder__class_Osorted(U_18193,hAPP(hAPP(c_List_Oappend(U_18193),U_18194),U_18195)) ) )
      | ~ class_Orderings_Olinorder(U_18193) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK451]),skolemize(U_18192,sK451(U_18195,U_18194,U_18193))],[f_4475_2]) ).

fof(f_4475_4,plain,
    ! [U_18195,U_18194,U_18193] :
      ( ( ( c_List_Olinorder__class_Osorted(U_18193,hAPP(hAPP(c_List_Oappend(U_18193),U_18194),U_18195))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18193),sK451(U_18195,U_18194,U_18193)),sK452(U_18195,U_18194,U_18193)))
            & hBOOL(hAPP(hAPP(c_member(U_18193),sK452(U_18195,U_18194,U_18193)),hAPP(c_List_Oset(U_18193),U_18195)))
            & hBOOL(hAPP(hAPP(c_member(U_18193),sK451(U_18195,U_18194,U_18193)),hAPP(c_List_Oset(U_18193),U_18194))) )
          | ~ c_List_Olinorder__class_Osorted(U_18193,U_18195)
          | ~ c_List_Olinorder__class_Osorted(U_18193,U_18194) )
        & ( ( ! [U_18190] :
                ( ! [U_18189] :
                    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18193),U_18190),U_18189))
                    | ~ hBOOL(hAPP(hAPP(c_member(U_18193),U_18189),hAPP(c_List_Oset(U_18193),U_18195))) )
                | ~ hBOOL(hAPP(hAPP(c_member(U_18193),U_18190),hAPP(c_List_Oset(U_18193),U_18194))) )
            & c_List_Olinorder__class_Osorted(U_18193,U_18195)
            & c_List_Olinorder__class_Osorted(U_18193,U_18194) )
          | ~ c_List_Olinorder__class_Osorted(U_18193,hAPP(hAPP(c_List_Oappend(U_18193),U_18194),U_18195)) ) )
      | ~ class_Orderings_Olinorder(U_18193) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK452]),skolemize(U_18191,sK452(U_18195,U_18194,U_18193))],[f_4475_3]) ).

cnf(f_4475_5,plain,
    ( c_List_Olinorder__class_Osorted(U_18193,U_18194)
    | ~ c_List_Olinorder__class_Osorted(U_18193,hAPP(hAPP(c_List_Oappend(U_18193),U_18194),U_18195))
    | ~ class_Orderings_Olinorder(U_18193) ),
    inference(clausify,[status(thm)],[f_4475_4]) ).

cnf(f_4475_6,plain,
    ( c_List_Olinorder__class_Osorted(U_18193,U_18195)
    | ~ c_List_Olinorder__class_Osorted(U_18193,hAPP(hAPP(c_List_Oappend(U_18193),U_18194),U_18195))
    | ~ class_Orderings_Olinorder(U_18193) ),
    inference(clausify,[status(thm)],[f_4475_4]) ).

cnf(f_4475_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18193),U_18190),U_18189))
    | ~ hBOOL(hAPP(hAPP(c_member(U_18193),U_18189),hAPP(c_List_Oset(U_18193),U_18195)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_18193),U_18190),hAPP(c_List_Oset(U_18193),U_18194)))
    | ~ c_List_Olinorder__class_Osorted(U_18193,hAPP(hAPP(c_List_Oappend(U_18193),U_18194),U_18195))
    | ~ class_Orderings_Olinorder(U_18193) ),
    inference(clausify,[status(thm)],[f_4475_4]) ).

cnf(f_4475_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18193),sK451(U_18195,U_18194,U_18193)),hAPP(c_List_Oset(U_18193),U_18194)))
    | ~ c_List_Olinorder__class_Osorted(U_18193,U_18195)
    | ~ c_List_Olinorder__class_Osorted(U_18193,U_18194)
    | c_List_Olinorder__class_Osorted(U_18193,hAPP(hAPP(c_List_Oappend(U_18193),U_18194),U_18195))
    | ~ class_Orderings_Olinorder(U_18193) ),
    inference(clausify,[status(thm)],[f_4475_4]) ).

cnf(f_4475_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18193),sK452(U_18195,U_18194,U_18193)),hAPP(c_List_Oset(U_18193),U_18195)))
    | ~ c_List_Olinorder__class_Osorted(U_18193,U_18195)
    | ~ c_List_Olinorder__class_Osorted(U_18193,U_18194)
    | c_List_Olinorder__class_Osorted(U_18193,hAPP(hAPP(c_List_Oappend(U_18193),U_18194),U_18195))
    | ~ class_Orderings_Olinorder(U_18193) ),
    inference(clausify,[status(thm)],[f_4475_4]) ).

cnf(f_4475_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18193),sK451(U_18195,U_18194,U_18193)),sK452(U_18195,U_18194,U_18193)))
    | ~ c_List_Olinorder__class_Osorted(U_18193,U_18195)
    | ~ c_List_Olinorder__class_Osorted(U_18193,U_18194)
    | c_List_Olinorder__class_Osorted(U_18193,hAPP(hAPP(c_List_Oappend(U_18193),U_18194),U_18195))
    | ~ class_Orderings_Olinorder(U_18193) ),
    inference(clausify,[status(thm)],[f_4475_4]) ).

fof(f_4476_1,plain,
    ! [V_x_2,V_P_2,V_xs_2,V_f_2,T_c,T_b] :
      ( hAPP(c_List_Ofilter(T_c,V_P_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),hAPP(c_List_Ofilter(T_c,V_P_2),V_xs_2))
      | ~ hBOOL(hAPP(V_P_2,V_x_2))
      | ~ c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_filter__insort]) ).

fof(f_4476_2,plain,
    ! [U_18201,U_18200,U_18199,U_18198,U_18197,U_18196] :
      ( hAPP(c_List_Ofilter(U_18197,U_18200),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18197,U_18196,U_18198),U_18201),U_18199)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18197,U_18196,U_18198),U_18201),hAPP(c_List_Ofilter(U_18197,U_18200),U_18199))
      | ~ hBOOL(hAPP(U_18200,U_18201))
      | ~ c_List_Olinorder__class_Osorted(U_18196,hAPP(hAPP(c_List_Omap(U_18197,U_18196),U_18198),U_18199))
      | ~ class_Orderings_Olinorder(U_18196) ),
    inference(variable_rename,[status(thm)],[f_4476_1]) ).

cnf(f_4476_3,plain,
    ( hAPP(c_List_Ofilter(U_18197,U_18200),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18197,U_18196,U_18198),U_18201),U_18199)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18197,U_18196,U_18198),U_18201),hAPP(c_List_Ofilter(U_18197,U_18200),U_18199))
    | ~ hBOOL(hAPP(U_18200,U_18201))
    | ~ c_List_Olinorder__class_Osorted(U_18196,hAPP(hAPP(c_List_Omap(U_18197,U_18196),U_18198),U_18199))
    | ~ class_Orderings_Olinorder(U_18196) ),
    inference(clausify,[status(thm)],[f_4476_2]) ).

fof(f_4477_1,plain,
    ! [V_a1_2,V_a2_2,T_b] :
      ( ( ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a2_2),V_a1_2))
          | ~ c_List_Olinorder__class_Osorted(T_b,V_a1_2)
          | ? [B_x] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a2_2),B_x))
              & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_a1_2))) ) )
        & ( ( c_List_Olinorder__class_Osorted(T_b,V_a1_2)
            & ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a2_2),B_x))
                | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_a1_2))) ) )
          | ~ c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a2_2),V_a1_2)) ) )
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sorted_Oequations_I2_J]) ).

fof(f_4477_2,plain,
    ! [U_18206,U_18205,U_18204] :
      ( ( ( c_List_Olinorder__class_Osorted(U_18204,hAPP(hAPP(c_List_Olist_OCons(U_18204),U_18205),U_18206))
          | ~ c_List_Olinorder__class_Osorted(U_18204,U_18206)
          | ? [U_18203] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18204),U_18205),U_18203))
              & hBOOL(hAPP(hAPP(c_member(U_18204),U_18203),hAPP(c_List_Oset(U_18204),U_18206))) ) )
        & ( ( c_List_Olinorder__class_Osorted(U_18204,U_18206)
            & ! [U_18202] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18204),U_18205),U_18202))
                | ~ hBOOL(hAPP(hAPP(c_member(U_18204),U_18202),hAPP(c_List_Oset(U_18204),U_18206))) ) )
          | ~ c_List_Olinorder__class_Osorted(U_18204,hAPP(hAPP(c_List_Olist_OCons(U_18204),U_18205),U_18206)) ) )
      | ~ class_Orderings_Olinorder(U_18204) ),
    inference(variable_rename,[status(thm)],[f_4477_1]) ).

fof(f_4477_3,plain,
    ! [U_18206,U_18205,U_18204] :
      ( ( ( c_List_Olinorder__class_Osorted(U_18204,hAPP(hAPP(c_List_Olist_OCons(U_18204),U_18205),U_18206))
          | ~ c_List_Olinorder__class_Osorted(U_18204,U_18206)
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18204),U_18205),sK453(U_18206,U_18205,U_18204)))
            & hBOOL(hAPP(hAPP(c_member(U_18204),sK453(U_18206,U_18205,U_18204)),hAPP(c_List_Oset(U_18204),U_18206))) ) )
        & ( ( c_List_Olinorder__class_Osorted(U_18204,U_18206)
            & ! [U_18202] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18204),U_18205),U_18202))
                | ~ hBOOL(hAPP(hAPP(c_member(U_18204),U_18202),hAPP(c_List_Oset(U_18204),U_18206))) ) )
          | ~ c_List_Olinorder__class_Osorted(U_18204,hAPP(hAPP(c_List_Olist_OCons(U_18204),U_18205),U_18206)) ) )
      | ~ class_Orderings_Olinorder(U_18204) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK453]),skolemize(U_18203,sK453(U_18206,U_18205,U_18204))],[f_4477_2]) ).

cnf(f_4477_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18204),U_18205),U_18202))
    | ~ hBOOL(hAPP(hAPP(c_member(U_18204),U_18202),hAPP(c_List_Oset(U_18204),U_18206)))
    | ~ c_List_Olinorder__class_Osorted(U_18204,hAPP(hAPP(c_List_Olist_OCons(U_18204),U_18205),U_18206))
    | ~ class_Orderings_Olinorder(U_18204) ),
    inference(clausify,[status(thm)],[f_4477_3]) ).

cnf(f_4477_5,plain,
    ( c_List_Olinorder__class_Osorted(U_18204,U_18206)
    | ~ c_List_Olinorder__class_Osorted(U_18204,hAPP(hAPP(c_List_Olist_OCons(U_18204),U_18205),U_18206))
    | ~ class_Orderings_Olinorder(U_18204) ),
    inference(clausify,[status(thm)],[f_4477_3]) ).

cnf(f_4477_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18204),sK453(U_18206,U_18205,U_18204)),hAPP(c_List_Oset(U_18204),U_18206)))
    | ~ c_List_Olinorder__class_Osorted(U_18204,U_18206)
    | c_List_Olinorder__class_Osorted(U_18204,hAPP(hAPP(c_List_Olist_OCons(U_18204),U_18205),U_18206))
    | ~ class_Orderings_Olinorder(U_18204) ),
    inference(clausify,[status(thm)],[f_4477_3]) ).

cnf(f_4477_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18204),U_18205),sK453(U_18206,U_18205,U_18204)))
    | ~ c_List_Olinorder__class_Osorted(U_18204,U_18206)
    | c_List_Olinorder__class_Osorted(U_18204,hAPP(hAPP(c_List_Olist_OCons(U_18204),U_18205),U_18206))
    | ~ class_Orderings_Olinorder(U_18204) ),
    inference(clausify,[status(thm)],[f_4477_3]) ).

fof(f_4478_1,plain,
    ! [V_A_2,T_b] :
      ( ( hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2)))
        & c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2))
        & hAPP(c_List_Oset(T_b),c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2)) = V_A_2 )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__list__of__set]) ).

fof(f_4478_2,plain,
    ! [U_18208,U_18207] :
      ( ( hBOOL(hAPP(c_List_Odistinct(U_18207),c_List_Olinorder__class_Osorted__list__of__set(U_18207,U_18208)))
        & c_List_Olinorder__class_Osorted(U_18207,c_List_Olinorder__class_Osorted__list__of__set(U_18207,U_18208))
        & hAPP(c_List_Oset(U_18207),c_List_Olinorder__class_Osorted__list__of__set(U_18207,U_18208)) = U_18208 )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_18207),U_18208))
      | ~ class_Orderings_Olinorder(U_18207) ),
    inference(variable_rename,[status(thm)],[f_4478_1]) ).

cnf(f_4478_3,plain,
    ( hAPP(c_List_Oset(U_18207),c_List_Olinorder__class_Osorted__list__of__set(U_18207,U_18208)) = U_18208
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_18207),U_18208))
    | ~ class_Orderings_Olinorder(U_18207) ),
    inference(clausify,[status(thm)],[f_4478_2]) ).

cnf(f_4478_4,plain,
    ( c_List_Olinorder__class_Osorted(U_18207,c_List_Olinorder__class_Osorted__list__of__set(U_18207,U_18208))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_18207),U_18208))
    | ~ class_Orderings_Olinorder(U_18207) ),
    inference(clausify,[status(thm)],[f_4478_2]) ).

cnf(f_4478_5,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_18207),c_List_Olinorder__class_Osorted__list__of__set(U_18207,U_18208)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_18207),U_18208))
    | ~ class_Orderings_Olinorder(U_18207) ),
    inference(clausify,[status(thm)],[f_4478_2]) ).

fof(f_4479_1,plain,
    ! [V_xs_2,V_a_2,T_b] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_a_2),c_List_Oremove1(T_b,V_a_2,V_xs_2)) = V_xs_2
      | ~ c_List_Olinorder__class_Osorted(T_b,V_xs_2)
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2)))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_insort__remove1]) ).

fof(f_4479_2,plain,
    ! [U_18211,U_18210,U_18209] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18209,U_18209,c_COMBI(U_18209)),U_18210),c_List_Oremove1(U_18209,U_18210,U_18211)) = U_18211
      | ~ c_List_Olinorder__class_Osorted(U_18209,U_18211)
      | ~ hBOOL(hAPP(hAPP(c_member(U_18209),U_18210),hAPP(c_List_Oset(U_18209),U_18211)))
      | ~ class_Orderings_Olinorder(U_18209) ),
    inference(variable_rename,[status(thm)],[f_4479_1]) ).

cnf(f_4479_3,plain,
    ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18209,U_18209,c_COMBI(U_18209)),U_18210),c_List_Oremove1(U_18209,U_18210,U_18211)) = U_18211
    | ~ c_List_Olinorder__class_Osorted(U_18209,U_18211)
    | ~ hBOOL(hAPP(hAPP(c_member(U_18209),U_18210),hAPP(c_List_Oset(U_18209),U_18211)))
    | ~ class_Orderings_Olinorder(U_18209) ),
    inference(clausify,[status(thm)],[f_4479_2]) ).

fof(f_4480_1,plain,
    ! [V_xs_2,T_b] :
      ( ( ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
          | ? [B_j] :
              ( ? [B_i] :
                  ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i)),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_j)))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j)) )
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ) )
        & ( ! [B_j] :
              ( ! [B_i] :
                  ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i)),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_j)))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j)) )
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) )
          | ~ c_List_Olinorder__class_Osorted(T_b,V_xs_2) ) )
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__equals__nth__mono]) ).

fof(f_4480_2,plain,
    ! [U_18217,U_18216] :
      ( ( ( c_List_Olinorder__class_Osorted(U_18216,U_18217)
          | ? [U_18215] :
              ( ? [U_18214] :
                  ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18216),hAPP(hAPP(c_List_Onth(U_18216),U_18217),U_18214)),hAPP(hAPP(c_List_Onth(U_18216),U_18217),U_18215)))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18214),U_18215)) )
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18215),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18216)),U_18217))) ) )
        & ( ! [U_18213] :
              ( ! [U_18212] :
                  ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18216),hAPP(hAPP(c_List_Onth(U_18216),U_18217),U_18212)),hAPP(hAPP(c_List_Onth(U_18216),U_18217),U_18213)))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18212),U_18213)) )
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18213),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18216)),U_18217))) )
          | ~ c_List_Olinorder__class_Osorted(U_18216,U_18217) ) )
      | ~ class_Orderings_Olinorder(U_18216) ),
    inference(variable_rename,[status(thm)],[f_4480_1]) ).

fof(f_4480_3,plain,
    ! [U_18217,U_18216] :
      ( ( ( c_List_Olinorder__class_Osorted(U_18216,U_18217)
          | ( ? [U_18214] :
                ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18216),hAPP(hAPP(c_List_Onth(U_18216),U_18217),U_18214)),hAPP(hAPP(c_List_Onth(U_18216),U_18217),sK454(U_18217,U_18216))))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18214),sK454(U_18217,U_18216))) )
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK454(U_18217,U_18216)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18216)),U_18217))) ) )
        & ( ! [U_18213] :
              ( ! [U_18212] :
                  ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18216),hAPP(hAPP(c_List_Onth(U_18216),U_18217),U_18212)),hAPP(hAPP(c_List_Onth(U_18216),U_18217),U_18213)))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18212),U_18213)) )
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18213),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18216)),U_18217))) )
          | ~ c_List_Olinorder__class_Osorted(U_18216,U_18217) ) )
      | ~ class_Orderings_Olinorder(U_18216) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK454]),skolemize(U_18215,sK454(U_18217,U_18216))],[f_4480_2]) ).

fof(f_4480_4,plain,
    ! [U_18217,U_18216] :
      ( ( ( c_List_Olinorder__class_Osorted(U_18216,U_18217)
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18216),hAPP(hAPP(c_List_Onth(U_18216),U_18217),sK455(U_18217,U_18216))),hAPP(hAPP(c_List_Onth(U_18216),U_18217),sK454(U_18217,U_18216))))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK455(U_18217,U_18216)),sK454(U_18217,U_18216)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK454(U_18217,U_18216)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18216)),U_18217))) ) )
        & ( ! [U_18213] :
              ( ! [U_18212] :
                  ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18216),hAPP(hAPP(c_List_Onth(U_18216),U_18217),U_18212)),hAPP(hAPP(c_List_Onth(U_18216),U_18217),U_18213)))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18212),U_18213)) )
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18213),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18216)),U_18217))) )
          | ~ c_List_Olinorder__class_Osorted(U_18216,U_18217) ) )
      | ~ class_Orderings_Olinorder(U_18216) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK455]),skolemize(U_18214,sK455(U_18217,U_18216))],[f_4480_3]) ).

cnf(f_4480_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18216),hAPP(hAPP(c_List_Onth(U_18216),U_18217),U_18212)),hAPP(hAPP(c_List_Onth(U_18216),U_18217),U_18213)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18212),U_18213))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18213),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18216)),U_18217)))
    | ~ c_List_Olinorder__class_Osorted(U_18216,U_18217)
    | ~ class_Orderings_Olinorder(U_18216) ),
    inference(clausify,[status(thm)],[f_4480_4]) ).

cnf(f_4480_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK454(U_18217,U_18216)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18216)),U_18217)))
    | c_List_Olinorder__class_Osorted(U_18216,U_18217)
    | ~ class_Orderings_Olinorder(U_18216) ),
    inference(clausify,[status(thm)],[f_4480_4]) ).

cnf(f_4480_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK455(U_18217,U_18216)),sK454(U_18217,U_18216)))
    | c_List_Olinorder__class_Osorted(U_18216,U_18217)
    | ~ class_Orderings_Olinorder(U_18216) ),
    inference(clausify,[status(thm)],[f_4480_4]) ).

cnf(f_4480_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18216),hAPP(hAPP(c_List_Onth(U_18216),U_18217),sK455(U_18217,U_18216))),hAPP(hAPP(c_List_Onth(U_18216),U_18217),sK454(U_18217,U_18216))))
    | c_List_Olinorder__class_Osorted(U_18216,U_18217)
    | ~ class_Orderings_Olinorder(U_18216) ),
    inference(clausify,[status(thm)],[f_4480_4]) ).

fof(f_4481_1,plain,
    ! [V_j,V_i,V_xs,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_j)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
      | ~ c_List_Olinorder__class_Osorted(T_a,V_xs)
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__nth__mono]) ).

fof(f_4481_2,plain,
    ! [U_18221,U_18220,U_18219,U_18218] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18218),hAPP(hAPP(c_List_Onth(U_18218),U_18219),U_18220)),hAPP(hAPP(c_List_Onth(U_18218),U_18219),U_18221)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18221),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18218)),U_18219)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18220),U_18221))
      | ~ c_List_Olinorder__class_Osorted(U_18218,U_18219)
      | ~ class_Orderings_Olinorder(U_18218) ),
    inference(variable_rename,[status(thm)],[f_4481_1]) ).

cnf(f_4481_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18218),hAPP(hAPP(c_List_Onth(U_18218),U_18219),U_18220)),hAPP(hAPP(c_List_Onth(U_18218),U_18219),U_18221)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18221),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18218)),U_18219)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18220),U_18221))
    | ~ c_List_Olinorder__class_Osorted(U_18218,U_18219)
    | ~ class_Orderings_Olinorder(U_18218) ),
    inference(clausify,[status(thm)],[f_4481_2]) ).

fof(f_4482_1,plain,
    ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
      ( V_xs_2 = V_ys_2
      | hAPP(c_List_Oset(T_b),V_xs_2) != hAPP(c_List_Oset(T_b),V_ys_2)
      | ~ hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2)))
      | ~ c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)))
      | ~ c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_ys_2)))
      | ~ class_Orderings_Olinorder(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_map__sorted__distinct__set__unique]) ).

fof(f_4482_2,plain,
    ! [U_18226,U_18225,U_18224,U_18223,U_18222] :
      ( U_18225 = U_18226
      | hAPP(c_List_Oset(U_18223),U_18225) != hAPP(c_List_Oset(U_18223),U_18226)
      | ~ hBOOL(hAPP(c_List_Odistinct(U_18222),hAPP(hAPP(c_List_Omap(U_18223,U_18222),U_18224),U_18226)))
      | ~ c_List_Olinorder__class_Osorted(U_18222,hAPP(hAPP(c_List_Omap(U_18223,U_18222),U_18224),U_18226))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_18222),hAPP(hAPP(c_List_Omap(U_18223,U_18222),U_18224),U_18225)))
      | ~ c_List_Olinorder__class_Osorted(U_18222,hAPP(hAPP(c_List_Omap(U_18223,U_18222),U_18224),U_18225))
      | ~ c_Fun_Oinj__on(U_18223,U_18222,U_18224,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_18223,tc_HOL_Obool)),hAPP(c_List_Oset(U_18223),U_18225)),hAPP(c_List_Oset(U_18223),U_18226)))
      | ~ class_Orderings_Olinorder(U_18222) ),
    inference(variable_rename,[status(thm)],[f_4482_1]) ).

cnf(f_4482_3,plain,
    ( U_18225 = U_18226
    | hAPP(c_List_Oset(U_18223),U_18225) != hAPP(c_List_Oset(U_18223),U_18226)
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18222),hAPP(hAPP(c_List_Omap(U_18223,U_18222),U_18224),U_18226)))
    | ~ c_List_Olinorder__class_Osorted(U_18222,hAPP(hAPP(c_List_Omap(U_18223,U_18222),U_18224),U_18226))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18222),hAPP(hAPP(c_List_Omap(U_18223,U_18222),U_18224),U_18225)))
    | ~ c_List_Olinorder__class_Osorted(U_18222,hAPP(hAPP(c_List_Omap(U_18223,U_18222),U_18224),U_18225))
    | ~ c_Fun_Oinj__on(U_18223,U_18222,U_18224,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_18223,tc_HOL_Obool)),hAPP(c_List_Oset(U_18223),U_18225)),hAPP(c_List_Oset(U_18223),U_18226)))
    | ~ class_Orderings_Olinorder(U_18222) ),
    inference(clausify,[status(thm)],[f_4482_2]) ).

fof(f_4483_1,plain,
    ! [V_i_2,V_xs_2,T_b] :
      ( hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,T_b),c_List_Onth(T_b)),V_i_2)),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),c_List_Otranspose(T_b,V_xs_2))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),V_i_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2)))
      | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_transpose__column]) ).

fof(f_4483_2,plain,
    ! [U_18229,U_18228,U_18227] :
      ( hAPP(hAPP(c_List_Omap(tc_List_Olist(U_18227),U_18227),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18227),tc_Nat_Onat,U_18227),c_List_Onth(U_18227)),U_18229)),hAPP(c_List_Ofilter(tc_List_Olist(U_18227),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_18227)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18229)),c_Nat_Osize__class_Osize(tc_List_Olist(U_18227)))),c_List_Otranspose(U_18227,U_18228))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(U_18227)),U_18228),U_18229)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18229),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_18227))),U_18228)))
      | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_18227),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_18227))),U_18228))) ),
    inference(variable_rename,[status(thm)],[f_4483_1]) ).

cnf(f_4483_3,plain,
    ( hAPP(hAPP(c_List_Omap(tc_List_Olist(U_18227),U_18227),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18227),tc_Nat_Onat,U_18227),c_List_Onth(U_18227)),U_18229)),hAPP(c_List_Ofilter(tc_List_Olist(U_18227),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_18227)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18229)),c_Nat_Osize__class_Osize(tc_List_Olist(U_18227)))),c_List_Otranspose(U_18227,U_18228))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(U_18227)),U_18228),U_18229)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18229),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_18227))),U_18228)))
    | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_18227),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_18227))),U_18228))) ),
    inference(clausify,[status(thm)],[f_4483_2]) ).

fof(f_4484_1,plain,
    ! [V_j_2,V_i_2,V_xs_2,T_b] :
      ( hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),c_List_Otranspose(T_b,V_xs_2)),V_i_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),V_j_2)),V_i_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_xs_2))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2))))
      | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_nth__nth__transpose__sorted]) ).

fof(f_4484_2,plain,
    ! [U_18233,U_18232,U_18231,U_18230] :
      ( hAPP(hAPP(c_List_Onth(U_18230),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_18230)),c_List_Otranspose(U_18230,U_18231)),U_18232)),U_18233) = hAPP(hAPP(c_List_Onth(U_18230),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_18230)),U_18231),U_18233)),U_18232)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18233),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_18230))),hAPP(c_List_Ofilter(tc_List_Olist(U_18230),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_18230)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18232)),c_Nat_Osize__class_Osize(tc_List_Olist(U_18230)))),U_18231))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18232),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_18230))),c_List_Otranspose(U_18230,U_18231))))
      | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_18230),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_18230))),U_18231))) ),
    inference(variable_rename,[status(thm)],[f_4484_1]) ).

cnf(f_4484_3,plain,
    ( hAPP(hAPP(c_List_Onth(U_18230),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_18230)),c_List_Otranspose(U_18230,U_18231)),U_18232)),U_18233) = hAPP(hAPP(c_List_Onth(U_18230),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_18230)),U_18231),U_18233)),U_18232)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18233),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_18230))),hAPP(c_List_Ofilter(tc_List_Olist(U_18230),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_18230)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18232)),c_Nat_Osize__class_Osize(tc_List_Olist(U_18230)))),U_18231))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18232),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_18230))),c_List_Otranspose(U_18230,U_18231))))
    | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_18230),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_18230))),U_18231))) ),
    inference(clausify,[status(thm)],[f_4484_2]) ).

fof(f_4485_1,plain,
    ! [V_A_2,T_b] : c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Orev(T_b),V_A_2),
    inference(fof_nnf,[status(thm)],[fact_inj__on__rev]) ).

fof(f_4485_2,plain,
    ! [U_18235,U_18234] : c_Fun_Oinj__on(tc_List_Olist(U_18234),tc_List_Olist(U_18234),c_List_Orev(U_18234),U_18235),
    inference(variable_rename,[status(thm)],[f_4485_1]) ).

cnf(f_4485_3,plain,
    c_Fun_Oinj__on(tc_List_Olist(U_18234),tc_List_Olist(U_18234),c_List_Orev(U_18234),U_18235),
    inference(clausify,[status(thm)],[f_4485_2]) ).

fof(f_4486_1,plain,
    ! [V_xs_2,T_b] :
      ( ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orev(T_b),V_xs_2)))
        | ~ hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) )
      & ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
        | ~ hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orev(T_b),V_xs_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__rev]) ).

fof(f_4486_2,plain,
    ! [U_18237,U_18236] :
      ( ( hBOOL(hAPP(c_List_Odistinct(U_18236),hAPP(c_List_Orev(U_18236),U_18237)))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_18236),U_18237)) )
      & ( hBOOL(hAPP(c_List_Odistinct(U_18236),U_18237))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_18236),hAPP(c_List_Orev(U_18236),U_18237))) ) ),
    inference(variable_rename,[status(thm)],[f_4486_1]) ).

fof(f_4486_3,plain,
    ( ! [U_18241,U_18239] :
        ( hBOOL(hAPP(c_List_Odistinct(U_18239),hAPP(c_List_Orev(U_18239),U_18241)))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_18239),U_18241)) )
    & ! [U_18240,U_18238] :
        ( hBOOL(hAPP(c_List_Odistinct(U_18238),U_18240))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_18238),hAPP(c_List_Orev(U_18238),U_18240))) ) ),
    inference(miniscope,[status(thm)],[f_4486_2]) ).

cnf(f_4486_4,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_18238),U_18240))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18238),hAPP(c_List_Orev(U_18238),U_18240))) ),
    inference(clausify,[status(thm)],[f_4486_3]) ).

cnf(f_4486_5,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_18239),hAPP(c_List_Orev(U_18239),U_18241)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18239),U_18241)) ),
    inference(clausify,[status(thm)],[f_4486_3]) ).

fof(f_4487_1,plain,
    ! [T_a] : hAPP(c_List_Orev(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a),
    inference(fof_nnf,[status(thm)],[fact_rev_Osimps_I1_J]) ).

fof(f_4487_2,plain,
    ! [U_18242] : hAPP(c_List_Orev(U_18242),c_List_Olist_ONil(U_18242)) = c_List_Olist_ONil(U_18242),
    inference(variable_rename,[status(thm)],[f_4487_1]) ).

cnf(f_4487_3,plain,
    hAPP(c_List_Orev(U_18242),c_List_Olist_ONil(U_18242)) = c_List_Olist_ONil(U_18242),
    inference(clausify,[status(thm)],[f_4487_2]) ).

fof(f_4488_1,plain,
    ! [V_xs_2,T_b] :
      ( ( c_List_Olist_ONil(T_b) = hAPP(c_List_Orev(T_b),V_xs_2)
        | V_xs_2 != c_List_Olist_ONil(T_b) )
      & ( V_xs_2 = c_List_Olist_ONil(T_b)
        | c_List_Olist_ONil(T_b) != hAPP(c_List_Orev(T_b),V_xs_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_Nil__is__rev__conv]) ).

fof(f_4488_2,plain,
    ! [U_18244,U_18243] :
      ( ( c_List_Olist_ONil(U_18243) = hAPP(c_List_Orev(U_18243),U_18244)
        | U_18244 != c_List_Olist_ONil(U_18243) )
      & ( U_18244 = c_List_Olist_ONil(U_18243)
        | c_List_Olist_ONil(U_18243) != hAPP(c_List_Orev(U_18243),U_18244) ) ),
    inference(variable_rename,[status(thm)],[f_4488_1]) ).

fof(f_4488_3,plain,
    ( ! [U_18248,U_18246] :
        ( c_List_Olist_ONil(U_18246) = hAPP(c_List_Orev(U_18246),U_18248)
        | U_18248 != c_List_Olist_ONil(U_18246) )
    & ! [U_18247,U_18245] :
        ( U_18247 = c_List_Olist_ONil(U_18245)
        | c_List_Olist_ONil(U_18245) != hAPP(c_List_Orev(U_18245),U_18247) ) ),
    inference(miniscope,[status(thm)],[f_4488_2]) ).

cnf(f_4488_4,plain,
    ( U_18247 = c_List_Olist_ONil(U_18245)
    | c_List_Olist_ONil(U_18245) != hAPP(c_List_Orev(U_18245),U_18247) ),
    inference(clausify,[status(thm)],[f_4488_3]) ).

cnf(f_4488_5,plain,
    ( c_List_Olist_ONil(U_18246) = hAPP(c_List_Orev(U_18246),U_18248)
    | U_18248 != c_List_Olist_ONil(U_18246) ),
    inference(clausify,[status(thm)],[f_4488_3]) ).

fof(f_4489_1,plain,
    ! [V_xs_2,T_b] :
      ( ( hAPP(c_List_Orev(T_b),V_xs_2) = c_List_Olist_ONil(T_b)
        | V_xs_2 != c_List_Olist_ONil(T_b) )
      & ( V_xs_2 = c_List_Olist_ONil(T_b)
        | hAPP(c_List_Orev(T_b),V_xs_2) != c_List_Olist_ONil(T_b) ) ),
    inference(fof_nnf,[status(thm)],[fact_rev__is__Nil__conv]) ).

fof(f_4489_2,plain,
    ! [U_18250,U_18249] :
      ( ( hAPP(c_List_Orev(U_18249),U_18250) = c_List_Olist_ONil(U_18249)
        | U_18250 != c_List_Olist_ONil(U_18249) )
      & ( U_18250 = c_List_Olist_ONil(U_18249)
        | hAPP(c_List_Orev(U_18249),U_18250) != c_List_Olist_ONil(U_18249) ) ),
    inference(variable_rename,[status(thm)],[f_4489_1]) ).

fof(f_4489_3,plain,
    ( ! [U_18254,U_18252] :
        ( hAPP(c_List_Orev(U_18252),U_18254) = c_List_Olist_ONil(U_18252)
        | U_18254 != c_List_Olist_ONil(U_18252) )
    & ! [U_18253,U_18251] :
        ( U_18253 = c_List_Olist_ONil(U_18251)
        | hAPP(c_List_Orev(U_18251),U_18253) != c_List_Olist_ONil(U_18251) ) ),
    inference(miniscope,[status(thm)],[f_4489_2]) ).

cnf(f_4489_4,plain,
    ( U_18253 = c_List_Olist_ONil(U_18251)
    | hAPP(c_List_Orev(U_18251),U_18253) != c_List_Olist_ONil(U_18251) ),
    inference(clausify,[status(thm)],[f_4489_3]) ).

cnf(f_4489_5,plain,
    ( hAPP(c_List_Orev(U_18252),U_18254) = c_List_Olist_ONil(U_18252)
    | U_18254 != c_List_Olist_ONil(U_18252) ),
    inference(clausify,[status(thm)],[f_4489_3]) ).

fof(f_4490_1,plain,
    ! [V_x_2,V_xs_2,T_b] :
      ( ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))
        | V_xs_2 != hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) )
      & ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))
        | hAPP(c_List_Orev(T_b),V_xs_2) != hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ) ),
    inference(fof_nnf,[status(thm)],[fact_rev__singleton__conv]) ).

fof(f_4490_2,plain,
    ! [U_18257,U_18256,U_18255] :
      ( ( hAPP(c_List_Orev(U_18255),U_18256) = hAPP(hAPP(c_List_Olist_OCons(U_18255),U_18257),c_List_Olist_ONil(U_18255))
        | U_18256 != hAPP(hAPP(c_List_Olist_OCons(U_18255),U_18257),c_List_Olist_ONil(U_18255)) )
      & ( U_18256 = hAPP(hAPP(c_List_Olist_OCons(U_18255),U_18257),c_List_Olist_ONil(U_18255))
        | hAPP(c_List_Orev(U_18255),U_18256) != hAPP(hAPP(c_List_Olist_OCons(U_18255),U_18257),c_List_Olist_ONil(U_18255)) ) ),
    inference(variable_rename,[status(thm)],[f_4490_1]) ).

fof(f_4490_3,plain,
    ( ! [U_18263,U_18261,U_18259] :
        ( hAPP(c_List_Orev(U_18259),U_18261) = hAPP(hAPP(c_List_Olist_OCons(U_18259),U_18263),c_List_Olist_ONil(U_18259))
        | U_18261 != hAPP(hAPP(c_List_Olist_OCons(U_18259),U_18263),c_List_Olist_ONil(U_18259)) )
    & ! [U_18262,U_18260,U_18258] :
        ( U_18260 = hAPP(hAPP(c_List_Olist_OCons(U_18258),U_18262),c_List_Olist_ONil(U_18258))
        | hAPP(c_List_Orev(U_18258),U_18260) != hAPP(hAPP(c_List_Olist_OCons(U_18258),U_18262),c_List_Olist_ONil(U_18258)) ) ),
    inference(miniscope,[status(thm)],[f_4490_2]) ).

cnf(f_4490_4,plain,
    ( U_18260 = hAPP(hAPP(c_List_Olist_OCons(U_18258),U_18262),c_List_Olist_ONil(U_18258))
    | hAPP(c_List_Orev(U_18258),U_18260) != hAPP(hAPP(c_List_Olist_OCons(U_18258),U_18262),c_List_Olist_ONil(U_18258)) ),
    inference(clausify,[status(thm)],[f_4490_3]) ).

cnf(f_4490_5,plain,
    ( hAPP(c_List_Orev(U_18259),U_18261) = hAPP(hAPP(c_List_Olist_OCons(U_18259),U_18263),c_List_Olist_ONil(U_18259))
    | U_18261 != hAPP(hAPP(c_List_Olist_OCons(U_18259),U_18263),c_List_Olist_ONil(U_18259)) ),
    inference(clausify,[status(thm)],[f_4490_3]) ).

fof(f_4491_1,plain,
    ! [V_xs_2,V_x_2,T_b] :
      ( ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) = hAPP(c_List_Orev(T_b),V_xs_2)
        | V_xs_2 != hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) )
      & ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))
        | hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) != hAPP(c_List_Orev(T_b),V_xs_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_singleton__rev__conv]) ).

fof(f_4491_2,plain,
    ! [U_18266,U_18265,U_18264] :
      ( ( hAPP(hAPP(c_List_Olist_OCons(U_18264),U_18265),c_List_Olist_ONil(U_18264)) = hAPP(c_List_Orev(U_18264),U_18266)
        | U_18266 != hAPP(hAPP(c_List_Olist_OCons(U_18264),U_18265),c_List_Olist_ONil(U_18264)) )
      & ( U_18266 = hAPP(hAPP(c_List_Olist_OCons(U_18264),U_18265),c_List_Olist_ONil(U_18264))
        | hAPP(hAPP(c_List_Olist_OCons(U_18264),U_18265),c_List_Olist_ONil(U_18264)) != hAPP(c_List_Orev(U_18264),U_18266) ) ),
    inference(variable_rename,[status(thm)],[f_4491_1]) ).

fof(f_4491_3,plain,
    ( ! [U_18272,U_18270,U_18268] :
        ( hAPP(hAPP(c_List_Olist_OCons(U_18268),U_18270),c_List_Olist_ONil(U_18268)) = hAPP(c_List_Orev(U_18268),U_18272)
        | U_18272 != hAPP(hAPP(c_List_Olist_OCons(U_18268),U_18270),c_List_Olist_ONil(U_18268)) )
    & ! [U_18271,U_18269,U_18267] :
        ( U_18271 = hAPP(hAPP(c_List_Olist_OCons(U_18267),U_18269),c_List_Olist_ONil(U_18267))
        | hAPP(hAPP(c_List_Olist_OCons(U_18267),U_18269),c_List_Olist_ONil(U_18267)) != hAPP(c_List_Orev(U_18267),U_18271) ) ),
    inference(miniscope,[status(thm)],[f_4491_2]) ).

cnf(f_4491_4,plain,
    ( U_18271 = hAPP(hAPP(c_List_Olist_OCons(U_18267),U_18269),c_List_Olist_ONil(U_18267))
    | hAPP(hAPP(c_List_Olist_OCons(U_18267),U_18269),c_List_Olist_ONil(U_18267)) != hAPP(c_List_Orev(U_18267),U_18271) ),
    inference(clausify,[status(thm)],[f_4491_3]) ).

cnf(f_4491_5,plain,
    ( hAPP(hAPP(c_List_Olist_OCons(U_18268),U_18270),c_List_Olist_ONil(U_18268)) = hAPP(c_List_Orev(U_18268),U_18272)
    | U_18272 != hAPP(hAPP(c_List_Olist_OCons(U_18268),U_18270),c_List_Olist_ONil(U_18268)) ),
    inference(clausify,[status(thm)],[f_4491_3]) ).

fof(f_4492_1,plain,
    ! [V_ys,V_xs,T_a] : hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Orev(T_a),V_ys)),hAPP(c_List_Orev(T_a),V_xs)),
    inference(fof_nnf,[status(thm)],[fact_rev__append]) ).

fof(f_4492_2,plain,
    ! [U_18275,U_18274,U_18273] : hAPP(c_List_Orev(U_18273),hAPP(hAPP(c_List_Oappend(U_18273),U_18274),U_18275)) = hAPP(hAPP(c_List_Oappend(U_18273),hAPP(c_List_Orev(U_18273),U_18275)),hAPP(c_List_Orev(U_18273),U_18274)),
    inference(variable_rename,[status(thm)],[f_4492_1]) ).

cnf(f_4492_3,plain,
    hAPP(c_List_Orev(U_18273),hAPP(hAPP(c_List_Oappend(U_18273),U_18274),U_18275)) = hAPP(hAPP(c_List_Oappend(U_18273),hAPP(c_List_Orev(U_18273),U_18275)),hAPP(c_List_Orev(U_18273),U_18274)),
    inference(clausify,[status(thm)],[f_4492_2]) ).

fof(f_4493_1,plain,
    ! [V_xs_2,T_b] : hAPP(c_List_Orev(T_b),c_List_Oconcat(T_b,V_xs_2)) = c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Orev(T_b)),hAPP(c_List_Orev(tc_List_Olist(T_b)),V_xs_2))),
    inference(fof_nnf,[status(thm)],[fact_rev__concat]) ).

fof(f_4493_2,plain,
    ! [U_18277,U_18276] : hAPP(c_List_Orev(U_18276),c_List_Oconcat(U_18276,U_18277)) = c_List_Oconcat(U_18276,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_18276),tc_List_Olist(U_18276)),c_List_Orev(U_18276)),hAPP(c_List_Orev(tc_List_Olist(U_18276)),U_18277))),
    inference(variable_rename,[status(thm)],[f_4493_1]) ).

cnf(f_4493_3,plain,
    hAPP(c_List_Orev(U_18276),c_List_Oconcat(U_18276,U_18277)) = c_List_Oconcat(U_18276,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_18276),tc_List_Olist(U_18276)),c_List_Orev(U_18276)),hAPP(c_List_Orev(tc_List_Olist(U_18276)),U_18277))),
    inference(clausify,[status(thm)],[f_4493_2]) ).

fof(f_4494_1,plain,
    ! [V_xs_2,V_f_2,T_c,T_b] : hAPP(c_List_Orev(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Orev(T_c),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_rev__map]) ).

fof(f_4494_2,plain,
    ! [U_18281,U_18280,U_18279,U_18278] : hAPP(c_List_Orev(U_18278),hAPP(hAPP(c_List_Omap(U_18279,U_18278),U_18280),U_18281)) = hAPP(hAPP(c_List_Omap(U_18279,U_18278),U_18280),hAPP(c_List_Orev(U_18279),U_18281)),
    inference(variable_rename,[status(thm)],[f_4494_1]) ).

cnf(f_4494_3,plain,
    hAPP(c_List_Orev(U_18278),hAPP(hAPP(c_List_Omap(U_18279,U_18278),U_18280),U_18281)) = hAPP(hAPP(c_List_Omap(U_18279,U_18278),U_18280),hAPP(c_List_Orev(U_18279),U_18281)),
    inference(clausify,[status(thm)],[f_4494_2]) ).

fof(f_4495_1,plain,
    ! [V_xs_2,V_P_2,T_b] : hAPP(c_List_Orev(T_b),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(c_List_Orev(T_b),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_rev__filter]) ).

fof(f_4495_2,plain,
    ! [U_18284,U_18283,U_18282] : hAPP(c_List_Orev(U_18282),hAPP(c_List_Ofilter(U_18282,U_18283),U_18284)) = hAPP(c_List_Ofilter(U_18282,U_18283),hAPP(c_List_Orev(U_18282),U_18284)),
    inference(variable_rename,[status(thm)],[f_4495_1]) ).

cnf(f_4495_3,plain,
    hAPP(c_List_Orev(U_18282),hAPP(c_List_Ofilter(U_18282,U_18283),U_18284)) = hAPP(c_List_Ofilter(U_18282,U_18283),hAPP(c_List_Orev(U_18282),U_18284)),
    inference(clausify,[status(thm)],[f_4495_2]) ).

fof(f_4496_1,plain,
    ! [V_ys,T_b,V_xs,T_a] :
      ( hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(c_List_Orev(T_a),V_xs)),hAPP(c_List_Orev(T_b),V_ys)) = hAPP(c_List_Orev(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys) ),
    inference(fof_nnf,[status(thm)],[fact_zip__rev]) ).

fof(f_4496_2,plain,
    ! [U_18288,U_18287,U_18286,U_18285] :
      ( hAPP(hAPP(c_List_Ozip(U_18285,U_18287),hAPP(c_List_Orev(U_18285),U_18286)),hAPP(c_List_Orev(U_18287),U_18288)) = hAPP(c_List_Orev(tc_prod(U_18285,U_18287)),hAPP(hAPP(c_List_Ozip(U_18285,U_18287),U_18286),U_18288))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18285)),U_18286) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18287)),U_18288) ),
    inference(variable_rename,[status(thm)],[f_4496_1]) ).

cnf(f_4496_3,plain,
    ( hAPP(hAPP(c_List_Ozip(U_18285,U_18287),hAPP(c_List_Orev(U_18285),U_18286)),hAPP(c_List_Orev(U_18287),U_18288)) = hAPP(c_List_Orev(tc_prod(U_18285,U_18287)),hAPP(hAPP(c_List_Ozip(U_18285,U_18287),U_18286),U_18288))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18285)),U_18286) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18287)),U_18288) ),
    inference(clausify,[status(thm)],[f_4496_2]) ).

fof(f_4497_1,plain,
    ! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_Orev(T_b),V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_set__rev]) ).

fof(f_4497_2,plain,
    ! [U_18290,U_18289] : hAPP(c_List_Oset(U_18289),hAPP(c_List_Orev(U_18289),U_18290)) = hAPP(c_List_Oset(U_18289),U_18290),
    inference(variable_rename,[status(thm)],[f_4497_1]) ).

cnf(f_4497_3,plain,
    hAPP(c_List_Oset(U_18289),hAPP(c_List_Orev(U_18289),U_18290)) = hAPP(c_List_Oset(U_18289),U_18290),
    inference(clausify,[status(thm)],[f_4497_2]) ).

fof(f_4498_1,plain,
    ! [V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
      ( ( c_List_Olist__all2(T_b,T_c,V_P_2,hAPP(c_List_Orev(T_b),V_xs_2),V_ys_2)
        | ~ c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,hAPP(c_List_Orev(T_c),V_ys_2)) )
      & ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,hAPP(c_List_Orev(T_c),V_ys_2))
        | ~ c_List_Olist__all2(T_b,T_c,V_P_2,hAPP(c_List_Orev(T_b),V_xs_2),V_ys_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__all2__rev1]) ).

fof(f_4498_2,plain,
    ! [U_18295,U_18294,U_18293,U_18292,U_18291] :
      ( ( c_List_Olist__all2(U_18291,U_18292,U_18293,hAPP(c_List_Orev(U_18291),U_18294),U_18295)
        | ~ c_List_Olist__all2(U_18291,U_18292,U_18293,U_18294,hAPP(c_List_Orev(U_18292),U_18295)) )
      & ( c_List_Olist__all2(U_18291,U_18292,U_18293,U_18294,hAPP(c_List_Orev(U_18292),U_18295))
        | ~ c_List_Olist__all2(U_18291,U_18292,U_18293,hAPP(c_List_Orev(U_18291),U_18294),U_18295) ) ),
    inference(variable_rename,[status(thm)],[f_4498_1]) ).

fof(f_4498_3,plain,
    ( ! [U_18305,U_18303,U_18301,U_18299,U_18297] :
        ( c_List_Olist__all2(U_18297,U_18299,U_18301,hAPP(c_List_Orev(U_18297),U_18303),U_18305)
        | ~ c_List_Olist__all2(U_18297,U_18299,U_18301,U_18303,hAPP(c_List_Orev(U_18299),U_18305)) )
    & ! [U_18304,U_18302,U_18300,U_18298,U_18296] :
        ( c_List_Olist__all2(U_18296,U_18298,U_18300,U_18302,hAPP(c_List_Orev(U_18298),U_18304))
        | ~ c_List_Olist__all2(U_18296,U_18298,U_18300,hAPP(c_List_Orev(U_18296),U_18302),U_18304) ) ),
    inference(miniscope,[status(thm)],[f_4498_2]) ).

cnf(f_4498_4,plain,
    ( c_List_Olist__all2(U_18296,U_18298,U_18300,U_18302,hAPP(c_List_Orev(U_18298),U_18304))
    | ~ c_List_Olist__all2(U_18296,U_18298,U_18300,hAPP(c_List_Orev(U_18296),U_18302),U_18304) ),
    inference(clausify,[status(thm)],[f_4498_3]) ).

cnf(f_4498_5,plain,
    ( c_List_Olist__all2(U_18297,U_18299,U_18301,hAPP(c_List_Orev(U_18297),U_18303),U_18305)
    | ~ c_List_Olist__all2(U_18297,U_18299,U_18301,U_18303,hAPP(c_List_Orev(U_18299),U_18305)) ),
    inference(clausify,[status(thm)],[f_4498_3]) ).

fof(f_4499_1,plain,
    ! [V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
      ( ( c_List_Olist__all2(T_b,T_c,V_P_2,hAPP(c_List_Orev(T_b),V_xs_2),hAPP(c_List_Orev(T_c),V_ys_2))
        | ~ c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2) )
      & ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
        | ~ c_List_Olist__all2(T_b,T_c,V_P_2,hAPP(c_List_Orev(T_b),V_xs_2),hAPP(c_List_Orev(T_c),V_ys_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__all2__rev]) ).

fof(f_4499_2,plain,
    ! [U_18310,U_18309,U_18308,U_18307,U_18306] :
      ( ( c_List_Olist__all2(U_18306,U_18307,U_18308,hAPP(c_List_Orev(U_18306),U_18309),hAPP(c_List_Orev(U_18307),U_18310))
        | ~ c_List_Olist__all2(U_18306,U_18307,U_18308,U_18309,U_18310) )
      & ( c_List_Olist__all2(U_18306,U_18307,U_18308,U_18309,U_18310)
        | ~ c_List_Olist__all2(U_18306,U_18307,U_18308,hAPP(c_List_Orev(U_18306),U_18309),hAPP(c_List_Orev(U_18307),U_18310)) ) ),
    inference(variable_rename,[status(thm)],[f_4499_1]) ).

fof(f_4499_3,plain,
    ( ! [U_18320,U_18318,U_18316,U_18314,U_18312] :
        ( c_List_Olist__all2(U_18312,U_18314,U_18316,hAPP(c_List_Orev(U_18312),U_18318),hAPP(c_List_Orev(U_18314),U_18320))
        | ~ c_List_Olist__all2(U_18312,U_18314,U_18316,U_18318,U_18320) )
    & ! [U_18319,U_18317,U_18315,U_18313,U_18311] :
        ( c_List_Olist__all2(U_18311,U_18313,U_18315,U_18317,U_18319)
        | ~ c_List_Olist__all2(U_18311,U_18313,U_18315,hAPP(c_List_Orev(U_18311),U_18317),hAPP(c_List_Orev(U_18313),U_18319)) ) ),
    inference(miniscope,[status(thm)],[f_4499_2]) ).

cnf(f_4499_4,plain,
    ( c_List_Olist__all2(U_18311,U_18313,U_18315,U_18317,U_18319)
    | ~ c_List_Olist__all2(U_18311,U_18313,U_18315,hAPP(c_List_Orev(U_18311),U_18317),hAPP(c_List_Orev(U_18313),U_18319)) ),
    inference(clausify,[status(thm)],[f_4499_3]) ).

cnf(f_4499_5,plain,
    ( c_List_Olist__all2(U_18312,U_18314,U_18316,hAPP(c_List_Orev(U_18312),U_18318),hAPP(c_List_Orev(U_18314),U_18320))
    | ~ c_List_Olist__all2(U_18312,U_18314,U_18316,U_18318,U_18320) ),
    inference(clausify,[status(thm)],[f_4499_3]) ).

fof(f_4500_1,plain,
    ! [V_ys_2,V_xs_2,T_b] :
      ( ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(c_List_Orev(T_b),V_ys_2)
        | V_xs_2 != V_ys_2 )
      & ( V_xs_2 = V_ys_2
        | hAPP(c_List_Orev(T_b),V_xs_2) != hAPP(c_List_Orev(T_b),V_ys_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_rev__is__rev__conv]) ).

fof(f_4500_2,plain,
    ! [U_18323,U_18322,U_18321] :
      ( ( hAPP(c_List_Orev(U_18321),U_18322) = hAPP(c_List_Orev(U_18321),U_18323)
        | U_18322 != U_18323 )
      & ( U_18322 = U_18323
        | hAPP(c_List_Orev(U_18321),U_18322) != hAPP(c_List_Orev(U_18321),U_18323) ) ),
    inference(variable_rename,[status(thm)],[f_4500_1]) ).

fof(f_4500_3,plain,
    ( ! [U_18329,U_18327] :
        ( ! [U_18325] : hAPP(c_List_Orev(U_18325),U_18327) = hAPP(c_List_Orev(U_18325),U_18329)
        | U_18327 != U_18329 )
    & ! [U_18328,U_18326] :
        ( ! [U_18324] : hAPP(c_List_Orev(U_18324),U_18326) != hAPP(c_List_Orev(U_18324),U_18328)
        | U_18326 = U_18328 ) ),
    inference(miniscope,[status(thm)],[f_4500_2]) ).

cnf(f_4500_4,plain,
    ( hAPP(c_List_Orev(U_18324),U_18326) != hAPP(c_List_Orev(U_18324),U_18328)
    | U_18326 = U_18328 ),
    inference(clausify,[status(thm)],[f_4500_3]) ).

cnf(f_4500_5,plain,
    ( hAPP(c_List_Orev(U_18325),U_18327) = hAPP(c_List_Orev(U_18325),U_18329)
    | U_18327 != U_18329 ),
    inference(clausify,[status(thm)],[f_4500_3]) ).

fof(f_4501_1,plain,
    ! [V_ys_2,V_xs_2,T_b] :
      ( ( hAPP(c_List_Orev(T_b),V_xs_2) = V_ys_2
        | V_xs_2 != hAPP(c_List_Orev(T_b),V_ys_2) )
      & ( V_xs_2 = hAPP(c_List_Orev(T_b),V_ys_2)
        | hAPP(c_List_Orev(T_b),V_xs_2) != V_ys_2 ) ),
    inference(fof_nnf,[status(thm)],[fact_rev__swap]) ).

fof(f_4501_2,plain,
    ! [U_18332,U_18331,U_18330] :
      ( ( hAPP(c_List_Orev(U_18330),U_18331) = U_18332
        | U_18331 != hAPP(c_List_Orev(U_18330),U_18332) )
      & ( U_18331 = hAPP(c_List_Orev(U_18330),U_18332)
        | hAPP(c_List_Orev(U_18330),U_18331) != U_18332 ) ),
    inference(variable_rename,[status(thm)],[f_4501_1]) ).

fof(f_4501_3,plain,
    ( ! [U_18338,U_18336,U_18334] :
        ( hAPP(c_List_Orev(U_18334),U_18336) = U_18338
        | U_18336 != hAPP(c_List_Orev(U_18334),U_18338) )
    & ! [U_18337,U_18335,U_18333] :
        ( U_18335 = hAPP(c_List_Orev(U_18333),U_18337)
        | hAPP(c_List_Orev(U_18333),U_18335) != U_18337 ) ),
    inference(miniscope,[status(thm)],[f_4501_2]) ).

cnf(f_4501_4,plain,
    ( U_18335 = hAPP(c_List_Orev(U_18333),U_18337)
    | hAPP(c_List_Orev(U_18333),U_18335) != U_18337 ),
    inference(clausify,[status(thm)],[f_4501_3]) ).

cnf(f_4501_5,plain,
    ( hAPP(c_List_Orev(U_18334),U_18336) = U_18338
    | U_18336 != hAPP(c_List_Orev(U_18334),U_18338) ),
    inference(clausify,[status(thm)],[f_4501_3]) ).

fof(f_4502_1,plain,
    ! [V_xs,T_a] : hAPP(c_List_Orev(T_a),hAPP(c_List_Orev(T_a),V_xs)) = V_xs,
    inference(fof_nnf,[status(thm)],[fact_rev__rev__ident]) ).

fof(f_4502_2,plain,
    ! [U_18340,U_18339] : hAPP(c_List_Orev(U_18339),hAPP(c_List_Orev(U_18339),U_18340)) = U_18340,
    inference(variable_rename,[status(thm)],[f_4502_1]) ).

cnf(f_4502_3,plain,
    hAPP(c_List_Orev(U_18339),hAPP(c_List_Orev(U_18339),U_18340)) = U_18340,
    inference(clausify,[status(thm)],[f_4502_2]) ).

fof(f_4503_1,plain,
    ! [V_xs,T_a] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs)
      | ~ class_Groups_Ocomm__monoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_listsum__rev]) ).

fof(f_4503_2,plain,
    ! [U_18342,U_18341] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18341),hAPP(c_List_Orev(U_18341),U_18342)) = hAPP(c_List_Omonoid__add__class_Olistsum(U_18341),U_18342)
      | ~ class_Groups_Ocomm__monoid__add(U_18341) ),
    inference(variable_rename,[status(thm)],[f_4503_1]) ).

cnf(f_4503_3,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18341),hAPP(c_List_Orev(U_18341),U_18342)) = hAPP(c_List_Omonoid__add__class_Olistsum(U_18341),U_18342)
    | ~ class_Groups_Ocomm__monoid__add(U_18341) ),
    inference(clausify,[status(thm)],[f_4503_2]) ).

fof(f_4504_1,plain,
    ! [V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs),
    inference(fof_nnf,[status(thm)],[fact_length__rev]) ).

fof(f_4504_2,plain,
    ! [U_18344,U_18343] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18343)),hAPP(c_List_Orev(U_18343),U_18344)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18343)),U_18344),
    inference(variable_rename,[status(thm)],[f_4504_1]) ).

cnf(f_4504_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18343)),hAPP(c_List_Orev(U_18343),U_18344)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18343)),U_18344),
    inference(clausify,[status(thm)],[f_4504_2]) ).

fof(f_4505_1,plain,
    ! [V_a_2,V_xs_2,V_f_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_f_2,V_xs_2,V_a_2) = hAPP(c_List_Ofoldl(T_b,T_c,hAPP(c_COMBC(T_c,T_b,T_b),V_f_2),V_a_2),hAPP(c_List_Orev(T_c),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_foldr__foldl]) ).

fof(f_4505_2,plain,
    ! [U_18349,U_18348,U_18347,U_18346,U_18345] : c_List_Ofoldr(U_18345,U_18346,U_18347,U_18348,U_18349) = hAPP(c_List_Ofoldl(U_18346,U_18345,hAPP(c_COMBC(U_18345,U_18346,U_18346),U_18347),U_18349),hAPP(c_List_Orev(U_18345),U_18348)),
    inference(variable_rename,[status(thm)],[f_4505_1]) ).

cnf(f_4505_3,plain,
    c_List_Ofoldr(U_18345,U_18346,U_18347,U_18348,U_18349) = hAPP(c_List_Ofoldl(U_18346,U_18345,hAPP(c_COMBC(U_18345,U_18346,U_18346),U_18347),U_18349),hAPP(c_List_Orev(U_18345),U_18348)),
    inference(clausify,[status(thm)],[f_4505_2]) ).

fof(f_4506_1,plain,
    ! [V_xs_2,V_a_2,V_f_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),V_xs_2) = c_List_Ofoldr(T_c,T_b,hAPP(c_COMBC(T_b,T_c,T_b),V_f_2),hAPP(c_List_Orev(T_c),V_xs_2),V_a_2),
    inference(fof_nnf,[status(thm)],[fact_foldl__foldr]) ).

fof(f_4506_2,plain,
    ! [U_18354,U_18353,U_18352,U_18351,U_18350] : hAPP(c_List_Ofoldl(U_18350,U_18351,U_18352,U_18353),U_18354) = c_List_Ofoldr(U_18351,U_18350,hAPP(c_COMBC(U_18350,U_18351,U_18350),U_18352),hAPP(c_List_Orev(U_18351),U_18354),U_18353),
    inference(variable_rename,[status(thm)],[f_4506_1]) ).

cnf(f_4506_3,plain,
    hAPP(c_List_Ofoldl(U_18350,U_18351,U_18352,U_18353),U_18354) = c_List_Ofoldr(U_18351,U_18350,hAPP(c_COMBC(U_18350,U_18351,U_18350),U_18352),hAPP(c_List_Orev(U_18351),U_18354),U_18353),
    inference(clausify,[status(thm)],[f_4506_2]) ).

fof(f_4507_1,plain,
    ! [V_xs,V_x,T_a] : hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Orev(T_a),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))),
    inference(fof_nnf,[status(thm)],[fact_rev_Osimps_I2_J]) ).

fof(f_4507_2,plain,
    ! [U_18357,U_18356,U_18355] : hAPP(c_List_Orev(U_18355),hAPP(hAPP(c_List_Olist_OCons(U_18355),U_18356),U_18357)) = hAPP(hAPP(c_List_Oappend(U_18355),hAPP(c_List_Orev(U_18355),U_18357)),hAPP(hAPP(c_List_Olist_OCons(U_18355),U_18356),c_List_Olist_ONil(U_18355))),
    inference(variable_rename,[status(thm)],[f_4507_1]) ).

cnf(f_4507_3,plain,
    hAPP(c_List_Orev(U_18355),hAPP(hAPP(c_List_Olist_OCons(U_18355),U_18356),U_18357)) = hAPP(hAPP(c_List_Oappend(U_18355),hAPP(c_List_Orev(U_18355),U_18357)),hAPP(hAPP(c_List_Olist_OCons(U_18355),U_18356),c_List_Olist_ONil(U_18355))),
    inference(clausify,[status(thm)],[f_4507_2]) ).

fof(f_4508_1,plain,
    ! [V_ys_2,V_y_2,V_xs_2,T_b] :
      ( ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)
        | V_xs_2 != hAPP(hAPP(c_List_Oappend(T_b),hAPP(c_List_Orev(T_b),V_ys_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),c_List_Olist_ONil(T_b))) )
      & ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),hAPP(c_List_Orev(T_b),V_ys_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),c_List_Olist_ONil(T_b)))
        | hAPP(c_List_Orev(T_b),V_xs_2) != hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_rev__eq__Cons__iff]) ).

fof(f_4508_2,plain,
    ! [U_18361,U_18360,U_18359,U_18358] :
      ( ( hAPP(c_List_Orev(U_18358),U_18359) = hAPP(hAPP(c_List_Olist_OCons(U_18358),U_18360),U_18361)
        | U_18359 != hAPP(hAPP(c_List_Oappend(U_18358),hAPP(c_List_Orev(U_18358),U_18361)),hAPP(hAPP(c_List_Olist_OCons(U_18358),U_18360),c_List_Olist_ONil(U_18358))) )
      & ( U_18359 = hAPP(hAPP(c_List_Oappend(U_18358),hAPP(c_List_Orev(U_18358),U_18361)),hAPP(hAPP(c_List_Olist_OCons(U_18358),U_18360),c_List_Olist_ONil(U_18358)))
        | hAPP(c_List_Orev(U_18358),U_18359) != hAPP(hAPP(c_List_Olist_OCons(U_18358),U_18360),U_18361) ) ),
    inference(variable_rename,[status(thm)],[f_4508_1]) ).

fof(f_4508_3,plain,
    ( ! [U_18369,U_18367,U_18365,U_18363] :
        ( hAPP(c_List_Orev(U_18363),U_18365) = hAPP(hAPP(c_List_Olist_OCons(U_18363),U_18367),U_18369)
        | U_18365 != hAPP(hAPP(c_List_Oappend(U_18363),hAPP(c_List_Orev(U_18363),U_18369)),hAPP(hAPP(c_List_Olist_OCons(U_18363),U_18367),c_List_Olist_ONil(U_18363))) )
    & ! [U_18368,U_18366,U_18364,U_18362] :
        ( U_18364 = hAPP(hAPP(c_List_Oappend(U_18362),hAPP(c_List_Orev(U_18362),U_18368)),hAPP(hAPP(c_List_Olist_OCons(U_18362),U_18366),c_List_Olist_ONil(U_18362)))
        | hAPP(c_List_Orev(U_18362),U_18364) != hAPP(hAPP(c_List_Olist_OCons(U_18362),U_18366),U_18368) ) ),
    inference(miniscope,[status(thm)],[f_4508_2]) ).

cnf(f_4508_4,plain,
    ( U_18364 = hAPP(hAPP(c_List_Oappend(U_18362),hAPP(c_List_Orev(U_18362),U_18368)),hAPP(hAPP(c_List_Olist_OCons(U_18362),U_18366),c_List_Olist_ONil(U_18362)))
    | hAPP(c_List_Orev(U_18362),U_18364) != hAPP(hAPP(c_List_Olist_OCons(U_18362),U_18366),U_18368) ),
    inference(clausify,[status(thm)],[f_4508_3]) ).

cnf(f_4508_5,plain,
    ( hAPP(c_List_Orev(U_18363),U_18365) = hAPP(hAPP(c_List_Olist_OCons(U_18363),U_18367),U_18369)
    | U_18365 != hAPP(hAPP(c_List_Oappend(U_18363),hAPP(c_List_Orev(U_18363),U_18369)),hAPP(hAPP(c_List_Olist_OCons(U_18363),U_18367),c_List_Olist_ONil(U_18363))) ),
    inference(clausify,[status(thm)],[f_4508_3]) ).

fof(f_4509_1,plain,
    ! [T_a,V_xs] :
      ( c_List_Olast(T_a,hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Ohd(T_a),V_xs)
      | V_xs = c_List_Olist_ONil(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_last__rev]) ).

fof(f_4509_2,plain,
    ! [U_18371,U_18370] :
      ( c_List_Olast(U_18371,hAPP(c_List_Orev(U_18371),U_18370)) = hAPP(c_List_Ohd(U_18371),U_18370)
      | U_18370 = c_List_Olist_ONil(U_18371) ),
    inference(variable_rename,[status(thm)],[f_4509_1]) ).

cnf(f_4509_3,plain,
    ( c_List_Olast(U_18371,hAPP(c_List_Orev(U_18371),U_18370)) = hAPP(c_List_Ohd(U_18371),U_18370)
    | U_18370 = c_List_Olist_ONil(U_18371) ),
    inference(clausify,[status(thm)],[f_4509_2]) ).

fof(f_4510_1,plain,
    ! [T_a,V_xs] :
      ( hAPP(c_List_Ohd(T_a),hAPP(c_List_Orev(T_a),V_xs)) = c_List_Olast(T_a,V_xs)
      | V_xs = c_List_Olist_ONil(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_hd__rev]) ).

fof(f_4510_2,plain,
    ! [U_18373,U_18372] :
      ( hAPP(c_List_Ohd(U_18373),hAPP(c_List_Orev(U_18373),U_18372)) = c_List_Olast(U_18373,U_18372)
      | U_18372 = c_List_Olist_ONil(U_18373) ),
    inference(variable_rename,[status(thm)],[f_4510_1]) ).

cnf(f_4510_3,plain,
    ( hAPP(c_List_Ohd(U_18373),hAPP(c_List_Orev(U_18373),U_18372)) = c_List_Olast(U_18373,U_18372)
    | U_18372 = c_List_Olist_ONil(U_18373) ),
    inference(clausify,[status(thm)],[f_4510_2]) ).

fof(f_4511_1,plain,
    ! [V_xs_2,T_b] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2)))),
    inference(fof_nnf,[status(thm)],[fact_sorted__transpose]) ).

fof(f_4511_2,plain,
    ! [U_18375,U_18374] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_18374),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_18374))),c_List_Otranspose(U_18374,U_18375)))),
    inference(variable_rename,[status(thm)],[f_4511_1]) ).

cnf(f_4511_3,plain,
    c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_18374),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_18374))),c_List_Otranspose(U_18374,U_18375)))),
    inference(clausify,[status(thm)],[f_4511_2]) ).

fof(f_4512_1,plain,
    ! [V_xs_2,T_b] : hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_b),T_b,hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b)),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_rev__foldl__cons]) ).

fof(f_4512_2,plain,
    ! [U_18377,U_18376] : hAPP(c_List_Orev(U_18376),U_18377) = hAPP(c_List_Ofoldl(tc_List_Olist(U_18376),U_18376,hAPP(c_COMBC(U_18376,tc_List_Olist(U_18376),tc_List_Olist(U_18376)),c_List_Olist_OCons(U_18376)),c_List_Olist_ONil(U_18376)),U_18377),
    inference(variable_rename,[status(thm)],[f_4512_1]) ).

cnf(f_4512_3,plain,
    hAPP(c_List_Orev(U_18376),U_18377) = hAPP(c_List_Ofoldl(tc_List_Olist(U_18376),U_18376,hAPP(c_COMBC(U_18376,tc_List_Olist(U_18376),tc_List_Olist(U_18376)),c_List_Olist_OCons(U_18376)),c_List_Olist_ONil(U_18376)),U_18377),
    inference(clausify,[status(thm)],[f_4512_2]) ).

fof(f_4513_1,plain,
    ! [V_xs,V_i,T_a] : hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs)) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_i)),hAPP(c_List_Orev(T_a),V_xs)),
    inference(fof_nnf,[status(thm)],[fact_rev__drop]) ).

fof(f_4513_2,plain,
    ! [U_18380,U_18379,U_18378] : hAPP(c_List_Orev(U_18378),hAPP(hAPP(c_List_Odrop(U_18378),U_18379),U_18380)) = hAPP(hAPP(c_List_Otake(U_18378),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18378)),U_18380)),U_18379)),hAPP(c_List_Orev(U_18378),U_18380)),
    inference(variable_rename,[status(thm)],[f_4513_1]) ).

cnf(f_4513_3,plain,
    hAPP(c_List_Orev(U_18378),hAPP(hAPP(c_List_Odrop(U_18378),U_18379),U_18380)) = hAPP(hAPP(c_List_Otake(U_18378),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18378)),U_18380)),U_18379)),hAPP(c_List_Orev(U_18378),U_18380)),
    inference(clausify,[status(thm)],[f_4513_2]) ).

fof(f_4514_1,plain,
    ! [V_xs,V_i,T_a] : hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_i)),hAPP(c_List_Orev(T_a),V_xs)),
    inference(fof_nnf,[status(thm)],[fact_rev__take]) ).

fof(f_4514_2,plain,
    ! [U_18383,U_18382,U_18381] : hAPP(c_List_Orev(U_18381),hAPP(hAPP(c_List_Otake(U_18381),U_18382),U_18383)) = hAPP(hAPP(c_List_Odrop(U_18381),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18381)),U_18383)),U_18382)),hAPP(c_List_Orev(U_18381),U_18383)),
    inference(variable_rename,[status(thm)],[f_4514_1]) ).

cnf(f_4514_3,plain,
    hAPP(c_List_Orev(U_18381),hAPP(hAPP(c_List_Otake(U_18381),U_18382),U_18383)) = hAPP(hAPP(c_List_Odrop(U_18381),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18381)),U_18383)),U_18382)),hAPP(c_List_Orev(U_18381),U_18383)),
    inference(clausify,[status(thm)],[f_4514_2]) ).

fof(f_4515_1,plain,
    ! [V_xs,V_n,T_a] : hAPP(c_List_Orotate(T_a,V_n),hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Orev(T_a),hAPP(c_List_Orotate(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))),V_xs)),
    inference(fof_nnf,[status(thm)],[fact_rotate__rev]) ).

fof(f_4515_2,plain,
    ! [U_18386,U_18385,U_18384] : hAPP(c_List_Orotate(U_18384,U_18385),hAPP(c_List_Orev(U_18384),U_18386)) = hAPP(c_List_Orev(U_18384),hAPP(c_List_Orotate(U_18384,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18384)),U_18386)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_18385,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18384)),U_18386)))),U_18386)),
    inference(variable_rename,[status(thm)],[f_4515_1]) ).

cnf(f_4515_3,plain,
    hAPP(c_List_Orotate(U_18384,U_18385),hAPP(c_List_Orev(U_18384),U_18386)) = hAPP(c_List_Orev(U_18384),hAPP(c_List_Orotate(U_18384,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18384)),U_18386)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_18385,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18384)),U_18386)))),U_18386)),
    inference(clausify,[status(thm)],[f_4515_2]) ).

fof(f_4516_1,plain,
    ! [V_xs,T_a,V_n] :
      ( hAPP(hAPP(c_List_Onth(T_a),hAPP(c_List_Orev(T_a),V_xs)),V_n) = hAPP(hAPP(c_List_Onth(T_a),V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_OSuc,V_n)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) ),
    inference(fof_nnf,[status(thm)],[fact_rev__nth]) ).

fof(f_4516_2,plain,
    ! [U_18389,U_18388,U_18387] :
      ( hAPP(hAPP(c_List_Onth(U_18388),hAPP(c_List_Orev(U_18388),U_18389)),U_18387) = hAPP(hAPP(c_List_Onth(U_18388),U_18389),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18388)),U_18389)),hAPP(c_Nat_OSuc,U_18387)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18387),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18388)),U_18389))) ),
    inference(variable_rename,[status(thm)],[f_4516_1]) ).

cnf(f_4516_3,plain,
    ( hAPP(hAPP(c_List_Onth(U_18388),hAPP(c_List_Orev(U_18388),U_18389)),U_18387) = hAPP(hAPP(c_List_Onth(U_18388),U_18389),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18388)),U_18389)),hAPP(c_Nat_OSuc,U_18387)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18387),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18388)),U_18389))) ),
    inference(clausify,[status(thm)],[f_4516_2]) ).

fof(f_4517_1,plain,
    ! [V_y,V_xs,T_a,V_k] :
      ( hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_y)) = hAPP(hAPP(c_List_Olist__update(T_a,hAPP(c_List_Orev(T_a),V_xs)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_k)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_y)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) ),
    inference(fof_nnf,[status(thm)],[fact_rev__update]) ).

fof(f_4517_2,plain,
    ! [U_18393,U_18392,U_18391,U_18390] :
      ( hAPP(c_List_Orev(U_18391),hAPP(hAPP(c_List_Olist__update(U_18391,U_18392),U_18390),U_18393)) = hAPP(hAPP(c_List_Olist__update(U_18391,hAPP(c_List_Orev(U_18391),U_18392)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18391)),U_18392)),U_18390)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_18393)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18390),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18391)),U_18392))) ),
    inference(variable_rename,[status(thm)],[f_4517_1]) ).

cnf(f_4517_3,plain,
    ( hAPP(c_List_Orev(U_18391),hAPP(hAPP(c_List_Olist__update(U_18391,U_18392),U_18390),U_18393)) = hAPP(hAPP(c_List_Olist__update(U_18391,hAPP(c_List_Orev(U_18391),U_18392)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18391)),U_18392)),U_18390)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_18393)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18390),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18391)),U_18392))) ),
    inference(clausify,[status(thm)],[f_4517_2]) ).

fof(f_4518_1,plain,
    ! [V_j,V_i,V_xs,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_j)),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
      | ~ c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),V_xs))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__rev__nth__mono]) ).

fof(f_4518_2,plain,
    ! [U_18397,U_18396,U_18395,U_18394] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18394),hAPP(hAPP(c_List_Onth(U_18394),U_18395),U_18397)),hAPP(hAPP(c_List_Onth(U_18394),U_18395),U_18396)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18397),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18394)),U_18395)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18396),U_18397))
      | ~ c_List_Olinorder__class_Osorted(U_18394,hAPP(c_List_Orev(U_18394),U_18395))
      | ~ class_Orderings_Olinorder(U_18394) ),
    inference(variable_rename,[status(thm)],[f_4518_1]) ).

cnf(f_4518_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18394),hAPP(hAPP(c_List_Onth(U_18394),U_18395),U_18397)),hAPP(hAPP(c_List_Onth(U_18394),U_18395),U_18396)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18397),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18394)),U_18395)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18396),U_18397))
    | ~ c_List_Olinorder__class_Osorted(U_18394,hAPP(c_List_Orev(U_18394),U_18395))
    | ~ class_Orderings_Olinorder(U_18394) ),
    inference(clausify,[status(thm)],[f_4518_2]) ).

fof(f_4519_1,plain,
    ! [V_y_2,V_xs_2,T_b] :
      ( ( ( c_List_Ofoldr(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_xs_2,V_y_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_y_2)
          | V_xs_2 = c_List_Olist_ONil(T_b) )
        & ( c_List_Ofoldr(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_xs_2,V_y_2) = V_y_2
          | V_xs_2 != c_List_Olist_ONil(T_b) ) )
      | ~ c_List_Olinorder__class_Osorted(T_b,hAPP(c_List_Orev(T_b),V_xs_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_foldr__max__sorted]) ).

fof(f_4519_2,plain,
    ! [U_18400,U_18399,U_18398] :
      ( ( ( c_List_Ofoldr(U_18398,U_18398,c_Orderings_Oord__class_Omax(U_18398),U_18399,U_18400) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_18398),hAPP(hAPP(c_List_Onth(U_18398),U_18399),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_18400)
          | U_18399 = c_List_Olist_ONil(U_18398) )
        & ( c_List_Ofoldr(U_18398,U_18398,c_Orderings_Oord__class_Omax(U_18398),U_18399,U_18400) = U_18400
          | U_18399 != c_List_Olist_ONil(U_18398) ) )
      | ~ c_List_Olinorder__class_Osorted(U_18398,hAPP(c_List_Orev(U_18398),U_18399))
      | ~ class_Orderings_Olinorder(U_18398) ),
    inference(variable_rename,[status(thm)],[f_4519_1]) ).

cnf(f_4519_3,plain,
    ( c_List_Ofoldr(U_18398,U_18398,c_Orderings_Oord__class_Omax(U_18398),U_18399,U_18400) = U_18400
    | U_18399 != c_List_Olist_ONil(U_18398)
    | ~ c_List_Olinorder__class_Osorted(U_18398,hAPP(c_List_Orev(U_18398),U_18399))
    | ~ class_Orderings_Olinorder(U_18398) ),
    inference(clausify,[status(thm)],[f_4519_2]) ).

cnf(f_4519_4,plain,
    ( c_List_Ofoldr(U_18398,U_18398,c_Orderings_Oord__class_Omax(U_18398),U_18399,U_18400) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_18398),hAPP(hAPP(c_List_Onth(U_18398),U_18399),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_18400)
    | U_18399 = c_List_Olist_ONil(U_18398)
    | ~ c_List_Olinorder__class_Osorted(U_18398,hAPP(c_List_Orev(U_18398),U_18399))
    | ~ class_Orderings_Olinorder(U_18398) ),
    inference(clausify,[status(thm)],[f_4519_2]) ).

fof(f_4520_1,plain,
    ! [V_xs_2,T_b] :
      ( ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          | V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_b)) )
        & ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          | V_xs_2 != c_List_Olist_ONil(tc_List_Olist(T_b)) ) )
      | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_length__transpose__sorted]) ).

fof(f_4520_2,plain,
    ! [U_18402,U_18401] :
      ( ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_18401))),c_List_Otranspose(U_18401,U_18402)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18401)),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_18401)),U_18402),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          | U_18402 = c_List_Olist_ONil(tc_List_Olist(U_18401)) )
        & ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_18401))),c_List_Otranspose(U_18401,U_18402)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          | U_18402 != c_List_Olist_ONil(tc_List_Olist(U_18401)) ) )
      | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_18401),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_18401))),U_18402))) ),
    inference(variable_rename,[status(thm)],[f_4520_1]) ).

cnf(f_4520_3,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_18401))),c_List_Otranspose(U_18401,U_18402)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_18402 != c_List_Olist_ONil(tc_List_Olist(U_18401))
    | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_18401),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_18401))),U_18402))) ),
    inference(clausify,[status(thm)],[f_4520_2]) ).

cnf(f_4520_4,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_18401))),c_List_Otranspose(U_18401,U_18402)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18401)),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_18401)),U_18402),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | U_18402 = c_List_Olist_ONil(tc_List_Olist(U_18401))
    | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_18401),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_18401))),U_18402))) ),
    inference(clausify,[status(thm)],[f_4520_2]) ).

fof(f_4521_1,plain,
    ! [V_i_2,V_xs_2,T_b] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),c_List_Otranspose(T_b,V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),V_i_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2)))
      | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_transpose__column__length]) ).

fof(f_4521_2,plain,
    ! [U_18405,U_18404,U_18403] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_18403))),hAPP(c_List_Ofilter(tc_List_Olist(U_18403),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_18403)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18405)),c_Nat_Osize__class_Osize(tc_List_Olist(U_18403)))),c_List_Otranspose(U_18403,U_18404))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18403)),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_18403)),U_18404),U_18405))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18405),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_18403))),U_18404)))
      | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_18403),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_18403))),U_18404))) ),
    inference(variable_rename,[status(thm)],[f_4521_1]) ).

cnf(f_4521_3,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_18403))),hAPP(c_List_Ofilter(tc_List_Olist(U_18403),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_18403)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18405)),c_Nat_Osize__class_Osize(tc_List_Olist(U_18403)))),c_List_Otranspose(U_18403,U_18404))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18403)),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_18403)),U_18404),U_18405))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18405),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_18403))),U_18404)))
    | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_18403),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_18403))),U_18404))) ),
    inference(clausify,[status(thm)],[f_4521_2]) ).

fof(f_4522_1,plain,
    ! [V_xs_2,T_b] :
      ( c_List_Otranspose(T_b,c_List_Otranspose(T_b,V_xs_2)) = c_List_OtakeWhile(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_b))),V_xs_2)
      | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_transpose__transpose]) ).

fof(f_4522_2,plain,
    ! [U_18407,U_18406] :
      ( c_List_Otranspose(U_18406,c_List_Otranspose(U_18406,U_18407)) = c_List_OtakeWhile(tc_List_Olist(U_18406),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_18406)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18406),tc_List_Olist(U_18406),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(U_18406))),U_18407)
      | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_18406),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_18406))),U_18407))) ),
    inference(variable_rename,[status(thm)],[f_4522_1]) ).

cnf(f_4522_3,plain,
    ( c_List_Otranspose(U_18406,c_List_Otranspose(U_18406,U_18407)) = c_List_OtakeWhile(tc_List_Olist(U_18406),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_18406)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18406),tc_List_Olist(U_18406),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(U_18406))),U_18407)
    | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_18406),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_18406))),U_18407))) ),
    inference(clausify,[status(thm)],[f_4522_2]) ).

fof(f_4523_1,plain,
    c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)),
    inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__list__functions_I2_J]) ).

cnf(f_4523_2,plain,
    c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)),
    inference(clausify,[status(thm)],[f_4523_1]) ).

fof(f_4524_1,plain,
    ! [V_P_2,V_xs_2,T_b] :
      ( c_List_Olinorder__class_Osorted(T_b,c_List_OtakeWhile(T_b,V_P_2,V_xs_2))
      | ~ c_List_Olinorder__class_Osorted(T_b,V_xs_2)
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__takeWhile]) ).

fof(f_4524_2,plain,
    ! [U_18410,U_18409,U_18408] :
      ( c_List_Olinorder__class_Osorted(U_18408,c_List_OtakeWhile(U_18408,U_18410,U_18409))
      | ~ c_List_Olinorder__class_Osorted(U_18408,U_18409)
      | ~ class_Orderings_Olinorder(U_18408) ),
    inference(variable_rename,[status(thm)],[f_4524_1]) ).

cnf(f_4524_3,plain,
    ( c_List_Olinorder__class_Osorted(U_18408,c_List_OtakeWhile(U_18408,U_18410,U_18409))
    | ~ c_List_Olinorder__class_Osorted(U_18408,U_18409)
    | ~ class_Orderings_Olinorder(U_18408) ),
    inference(clausify,[status(thm)],[f_4524_2]) ).

fof(f_4525_1,plain,
    ! [V_xs_2,V_P_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))),
    inference(fof_nnf,[status(thm)],[fact_length__takeWhile__le]) ).

fof(f_4525_2,plain,
    ! [U_18413,U_18412,U_18411] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18411)),c_List_OtakeWhile(U_18411,U_18412,U_18413))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18411)),U_18413))),
    inference(variable_rename,[status(thm)],[f_4525_1]) ).

cnf(f_4525_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18411)),c_List_OtakeWhile(U_18411,U_18412,U_18413))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18411)),U_18413))),
    inference(clausify,[status(thm)],[f_4525_2]) ).

fof(f_4526_1,plain,
    ! [V_xs_2,V_P_2,T_b] :
      ( ( c_List_OtakeWhile(T_b,V_P_2,V_xs_2) = V_xs_2
        | ? [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) ) )
      & ( ! [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) )
        | c_List_OtakeWhile(T_b,V_P_2,V_xs_2) != V_xs_2 ) ),
    inference(fof_nnf,[status(thm)],[fact_takeWhile__eq__all__conv]) ).

fof(f_4526_2,plain,
    ! [U_18418,U_18417,U_18416] :
      ( ( c_List_OtakeWhile(U_18416,U_18417,U_18418) = U_18418
        | ? [U_18415] :
            ( ~ hBOOL(hAPP(U_18417,U_18415))
            & hBOOL(hAPP(hAPP(c_member(U_18416),U_18415),hAPP(c_List_Oset(U_18416),U_18418))) ) )
      & ( ! [U_18414] :
            ( hBOOL(hAPP(U_18417,U_18414))
            | ~ hBOOL(hAPP(hAPP(c_member(U_18416),U_18414),hAPP(c_List_Oset(U_18416),U_18418))) )
        | c_List_OtakeWhile(U_18416,U_18417,U_18418) != U_18418 ) ),
    inference(variable_rename,[status(thm)],[f_4526_1]) ).

fof(f_4526_3,plain,
    ( ! [U_18424,U_18422,U_18420] :
        ( c_List_OtakeWhile(U_18420,U_18422,U_18424) = U_18424
        | ? [U_18415] :
            ( ~ hBOOL(hAPP(U_18422,U_18415))
            & hBOOL(hAPP(hAPP(c_member(U_18420),U_18415),hAPP(c_List_Oset(U_18420),U_18424))) ) )
    & ! [U_18423,U_18421,U_18419] :
        ( ! [U_18414] :
            ( hBOOL(hAPP(U_18421,U_18414))
            | ~ hBOOL(hAPP(hAPP(c_member(U_18419),U_18414),hAPP(c_List_Oset(U_18419),U_18423))) )
        | c_List_OtakeWhile(U_18419,U_18421,U_18423) != U_18423 ) ),
    inference(miniscope,[status(thm)],[f_4526_2]) ).

fof(f_4526_4,plain,
    ( ! [U_18424,U_18422,U_18420] :
        ( c_List_OtakeWhile(U_18420,U_18422,U_18424) = U_18424
        | ( ~ hBOOL(hAPP(U_18422,sK456(U_18424,U_18422,U_18420)))
          & hBOOL(hAPP(hAPP(c_member(U_18420),sK456(U_18424,U_18422,U_18420)),hAPP(c_List_Oset(U_18420),U_18424))) ) )
    & ! [U_18423,U_18421,U_18419] :
        ( ! [U_18414] :
            ( hBOOL(hAPP(U_18421,U_18414))
            | ~ hBOOL(hAPP(hAPP(c_member(U_18419),U_18414),hAPP(c_List_Oset(U_18419),U_18423))) )
        | c_List_OtakeWhile(U_18419,U_18421,U_18423) != U_18423 ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK456]),skolemize(U_18415,sK456(U_18424,U_18422,U_18420))],[f_4526_3]) ).

cnf(f_4526_5,plain,
    ( hBOOL(hAPP(U_18421,U_18414))
    | ~ hBOOL(hAPP(hAPP(c_member(U_18419),U_18414),hAPP(c_List_Oset(U_18419),U_18423)))
    | c_List_OtakeWhile(U_18419,U_18421,U_18423) != U_18423 ),
    inference(clausify,[status(thm)],[f_4526_4]) ).

cnf(f_4526_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18420),sK456(U_18424,U_18422,U_18420)),hAPP(c_List_Oset(U_18420),U_18424)))
    | c_List_OtakeWhile(U_18420,U_18422,U_18424) = U_18424 ),
    inference(clausify,[status(thm)],[f_4526_4]) ).

cnf(f_4526_7,plain,
    ( ~ hBOOL(hAPP(U_18422,sK456(U_18424,U_18422,U_18420)))
    | c_List_OtakeWhile(U_18420,U_18422,U_18424) = U_18424 ),
    inference(clausify,[status(thm)],[f_4526_4]) ).

fof(f_4527_1,plain,
    ! [V_xs_2,V_P_2,V_x_2,T_b] :
      ( ( hBOOL(hAPP(V_P_2,V_x_2))
        & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) )
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_OtakeWhile(T_b,V_P_2,V_xs_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_set__takeWhileD]) ).

fof(f_4527_2,plain,
    ! [U_18428,U_18427,U_18426,U_18425] :
      ( ( hBOOL(hAPP(U_18427,U_18426))
        & hBOOL(hAPP(hAPP(c_member(U_18425),U_18426),hAPP(c_List_Oset(U_18425),U_18428))) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_18425),U_18426),hAPP(c_List_Oset(U_18425),c_List_OtakeWhile(U_18425,U_18427,U_18428)))) ),
    inference(variable_rename,[status(thm)],[f_4527_1]) ).

cnf(f_4527_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18425),U_18426),hAPP(c_List_Oset(U_18425),U_18428)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_18425),U_18426),hAPP(c_List_Oset(U_18425),c_List_OtakeWhile(U_18425,U_18427,U_18428)))) ),
    inference(clausify,[status(thm)],[f_4527_2]) ).

cnf(f_4527_4,plain,
    ( hBOOL(hAPP(U_18427,U_18426))
    | ~ hBOOL(hAPP(hAPP(c_member(U_18425),U_18426),hAPP(c_List_Oset(U_18425),c_List_OtakeWhile(U_18425,U_18427,U_18428)))) ),
    inference(clausify,[status(thm)],[f_4527_2]) ).

fof(f_4528_1,plain,
    ! [V_ys_2,V_P_2,V_xs_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),c_List_OtakeWhile(T_c,V_P_2,V_ys_2)) = c_List_OtakeWhile(tc_prod(T_b,T_c),hAPP(c_Fun_Ocomp(T_c,tc_HOL_Obool,tc_prod(T_b,T_c),V_P_2),c_Product__Type_Osnd(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)),
    inference(fof_nnf,[status(thm)],[fact_zip__takeWhile__snd]) ).

fof(f_4528_2,plain,
    ! [U_18433,U_18432,U_18431,U_18430,U_18429] : hAPP(hAPP(c_List_Ozip(U_18429,U_18430),U_18431),c_List_OtakeWhile(U_18430,U_18432,U_18433)) = c_List_OtakeWhile(tc_prod(U_18429,U_18430),hAPP(c_Fun_Ocomp(U_18430,tc_HOL_Obool,tc_prod(U_18429,U_18430),U_18432),c_Product__Type_Osnd(U_18429,U_18430)),hAPP(hAPP(c_List_Ozip(U_18429,U_18430),U_18431),U_18433)),
    inference(variable_rename,[status(thm)],[f_4528_1]) ).

cnf(f_4528_3,plain,
    hAPP(hAPP(c_List_Ozip(U_18429,U_18430),U_18431),c_List_OtakeWhile(U_18430,U_18432,U_18433)) = c_List_OtakeWhile(tc_prod(U_18429,U_18430),hAPP(c_Fun_Ocomp(U_18430,tc_HOL_Obool,tc_prod(U_18429,U_18430),U_18432),c_Product__Type_Osnd(U_18429,U_18430)),hAPP(hAPP(c_List_Ozip(U_18429,U_18430),U_18431),U_18433)),
    inference(clausify,[status(thm)],[f_4528_2]) ).

fof(f_4529_1,plain,
    ! [V_ys_2,V_xs_2,V_P_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),c_List_OtakeWhile(T_b,V_P_2,V_xs_2)),V_ys_2) = c_List_OtakeWhile(tc_prod(T_b,T_c),hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,tc_prod(T_b,T_c),V_P_2),c_Product__Type_Ofst(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)),
    inference(fof_nnf,[status(thm)],[fact_zip__takeWhile__fst]) ).

fof(f_4529_2,plain,
    ! [U_18438,U_18437,U_18436,U_18435,U_18434] : hAPP(hAPP(c_List_Ozip(U_18434,U_18435),c_List_OtakeWhile(U_18434,U_18436,U_18437)),U_18438) = c_List_OtakeWhile(tc_prod(U_18434,U_18435),hAPP(c_Fun_Ocomp(U_18434,tc_HOL_Obool,tc_prod(U_18434,U_18435),U_18436),c_Product__Type_Ofst(U_18434,U_18435)),hAPP(hAPP(c_List_Ozip(U_18434,U_18435),U_18437),U_18438)),
    inference(variable_rename,[status(thm)],[f_4529_1]) ).

cnf(f_4529_3,plain,
    hAPP(hAPP(c_List_Ozip(U_18434,U_18435),c_List_OtakeWhile(U_18434,U_18436,U_18437)),U_18438) = c_List_OtakeWhile(tc_prod(U_18434,U_18435),hAPP(c_Fun_Ocomp(U_18434,tc_HOL_Obool,tc_prod(U_18434,U_18435),U_18436),c_Product__Type_Ofst(U_18434,U_18435)),hAPP(hAPP(c_List_Ozip(U_18434,U_18435),U_18437),U_18438)),
    inference(clausify,[status(thm)],[f_4529_2]) ).

fof(f_4530_1,plain,
    ! [V_xs_2,V_f_2,T_c,V_P_2,T_b] : c_List_OtakeWhile(T_b,V_P_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_OtakeWhile(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_P_2),V_f_2),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_takeWhile__map]) ).

fof(f_4530_2,plain,
    ! [U_18443,U_18442,U_18441,U_18440,U_18439] : c_List_OtakeWhile(U_18439,U_18440,hAPP(hAPP(c_List_Omap(U_18441,U_18439),U_18442),U_18443)) = hAPP(hAPP(c_List_Omap(U_18441,U_18439),U_18442),c_List_OtakeWhile(U_18441,hAPP(c_Fun_Ocomp(U_18439,tc_HOL_Obool,U_18441,U_18440),U_18442),U_18443)),
    inference(variable_rename,[status(thm)],[f_4530_1]) ).

cnf(f_4530_3,plain,
    c_List_OtakeWhile(U_18439,U_18440,hAPP(hAPP(c_List_Omap(U_18441,U_18439),U_18442),U_18443)) = hAPP(hAPP(c_List_Omap(U_18441,U_18439),U_18442),c_List_OtakeWhile(U_18441,hAPP(c_Fun_Ocomp(U_18439,tc_HOL_Obool,U_18441,U_18440),U_18442),U_18443)),
    inference(clausify,[status(thm)],[f_4530_2]) ).

fof(f_4531_1,plain,
    ! [V_l_2,V_xs_2,T_b,V_x_2,V_P_2] :
      ( c_List_OtakeWhile(T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_l_2))) = c_List_OtakeWhile(T_b,V_P_2,V_xs_2)
      | hBOOL(hAPP(V_P_2,V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_takeWhile__tail]) ).

fof(f_4531_2,plain,
    ! [U_18448,U_18447,U_18446,U_18445,U_18444] :
      ( c_List_OtakeWhile(U_18446,U_18444,hAPP(hAPP(c_List_Oappend(U_18446),U_18447),hAPP(hAPP(c_List_Olist_OCons(U_18446),U_18445),U_18448))) = c_List_OtakeWhile(U_18446,U_18444,U_18447)
      | hBOOL(hAPP(U_18444,U_18445)) ),
    inference(variable_rename,[status(thm)],[f_4531_1]) ).

cnf(f_4531_3,plain,
    ( c_List_OtakeWhile(U_18446,U_18444,hAPP(hAPP(c_List_Oappend(U_18446),U_18447),hAPP(hAPP(c_List_Olist_OCons(U_18446),U_18445),U_18448))) = c_List_OtakeWhile(U_18446,U_18444,U_18447)
    | hBOOL(hAPP(U_18444,U_18445)) ),
    inference(clausify,[status(thm)],[f_4531_2]) ).

fof(f_4532_1,plain,
    ! [V_xs_2,T_b,V_x_2,V_P_2] :
      ( ( c_List_OtakeWhile(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_List_Olist_ONil(T_b)
        | hBOOL(hAPP(V_P_2,V_x_2)) )
      & ( c_List_OtakeWhile(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))
        | ~ hBOOL(hAPP(V_P_2,V_x_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_takeWhile_Osimps_I2_J]) ).

fof(f_4532_2,plain,
    ! [U_18452,U_18451,U_18450,U_18449] :
      ( ( c_List_OtakeWhile(U_18451,U_18449,hAPP(hAPP(c_List_Olist_OCons(U_18451),U_18450),U_18452)) = c_List_Olist_ONil(U_18451)
        | hBOOL(hAPP(U_18449,U_18450)) )
      & ( c_List_OtakeWhile(U_18451,U_18449,hAPP(hAPP(c_List_Olist_OCons(U_18451),U_18450),U_18452)) = hAPP(hAPP(c_List_Olist_OCons(U_18451),U_18450),c_List_OtakeWhile(U_18451,U_18449,U_18452))
        | ~ hBOOL(hAPP(U_18449,U_18450)) ) ),
    inference(variable_rename,[status(thm)],[f_4532_1]) ).

fof(f_4532_3,plain,
    ( ! [U_18460,U_18458,U_18456,U_18454] :
        ( c_List_OtakeWhile(U_18458,U_18454,hAPP(hAPP(c_List_Olist_OCons(U_18458),U_18456),U_18460)) = c_List_Olist_ONil(U_18458)
        | hBOOL(hAPP(U_18454,U_18456)) )
    & ! [U_18459,U_18457,U_18455,U_18453] :
        ( c_List_OtakeWhile(U_18457,U_18453,hAPP(hAPP(c_List_Olist_OCons(U_18457),U_18455),U_18459)) = hAPP(hAPP(c_List_Olist_OCons(U_18457),U_18455),c_List_OtakeWhile(U_18457,U_18453,U_18459))
        | ~ hBOOL(hAPP(U_18453,U_18455)) ) ),
    inference(miniscope,[status(thm)],[f_4532_2]) ).

cnf(f_4532_4,plain,
    ( c_List_OtakeWhile(U_18457,U_18453,hAPP(hAPP(c_List_Olist_OCons(U_18457),U_18455),U_18459)) = hAPP(hAPP(c_List_Olist_OCons(U_18457),U_18455),c_List_OtakeWhile(U_18457,U_18453,U_18459))
    | ~ hBOOL(hAPP(U_18453,U_18455)) ),
    inference(clausify,[status(thm)],[f_4532_3]) ).

cnf(f_4532_5,plain,
    ( c_List_OtakeWhile(U_18458,U_18454,hAPP(hAPP(c_List_Olist_OCons(U_18458),U_18456),U_18460)) = c_List_Olist_ONil(U_18458)
    | hBOOL(hAPP(U_18454,U_18456)) ),
    inference(clausify,[status(thm)],[f_4532_3]) ).

fof(f_4533_1,plain,
    ! [V_P_2,T_b] : c_List_OtakeWhile(T_b,V_P_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b),
    inference(fof_nnf,[status(thm)],[fact_takeWhile_Osimps_I1_J]) ).

fof(f_4533_2,plain,
    ! [U_18462,U_18461] : c_List_OtakeWhile(U_18461,U_18462,c_List_Olist_ONil(U_18461)) = c_List_Olist_ONil(U_18461),
    inference(variable_rename,[status(thm)],[f_4533_1]) ).

cnf(f_4533_3,plain,
    c_List_OtakeWhile(U_18461,U_18462,c_List_Olist_ONil(U_18461)) = c_List_Olist_ONil(U_18461),
    inference(clausify,[status(thm)],[f_4533_2]) ).

fof(f_4534_1,plain,
    ! [V_xs_2,V_P_2,T_b] : c_List_OtakeWhile(T_b,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_takeWhile__eq__take]) ).

fof(f_4534_2,plain,
    ! [U_18465,U_18464,U_18463] : c_List_OtakeWhile(U_18463,U_18464,U_18465) = hAPP(hAPP(c_List_Otake(U_18463),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18463)),c_List_OtakeWhile(U_18463,U_18464,U_18465))),U_18465),
    inference(variable_rename,[status(thm)],[f_4534_1]) ).

cnf(f_4534_3,plain,
    c_List_OtakeWhile(U_18463,U_18464,U_18465) = hAPP(hAPP(c_List_Otake(U_18463),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18463)),c_List_OtakeWhile(U_18463,U_18464,U_18465))),U_18465),
    inference(clausify,[status(thm)],[f_4534_2]) ).

fof(f_4535_1,plain,
    ! [V_P_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),c_List_OtakeWhile(T_b,V_P_2,V_xs_2)))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__takeWhile]) ).

fof(f_4535_2,plain,
    ! [U_18468,U_18467,U_18466] :
      ( hBOOL(hAPP(c_List_Odistinct(U_18466),c_List_OtakeWhile(U_18466,U_18468,U_18467)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_18466),U_18467)) ),
    inference(variable_rename,[status(thm)],[f_4535_1]) ).

cnf(f_4535_3,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_18466),c_List_OtakeWhile(U_18466,U_18468,U_18467)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18466),U_18467)) ),
    inference(clausify,[status(thm)],[f_4535_2]) ).

fof(f_4536_1,plain,
    ! [V_l_2] : c_List_Oreturn__list(V_l_2) = hAPP(hAPP(c_List_Omap(tc_Int_Oint,tc_Nat_Onat),c_Int_Onat),V_l_2),
    inference(fof_nnf,[status(thm)],[fact_return__list__def]) ).

fof(f_4536_2,plain,
    ! [U_18469] : c_List_Oreturn__list(U_18469) = hAPP(hAPP(c_List_Omap(tc_Int_Oint,tc_Nat_Onat),c_Int_Onat),U_18469),
    inference(variable_rename,[status(thm)],[f_4536_1]) ).

cnf(f_4536_3,plain,
    c_List_Oreturn__list(U_18469) = hAPP(hAPP(c_List_Omap(tc_Int_Oint,tc_Nat_Onat),c_Int_Onat),U_18469),
    inference(clausify,[status(thm)],[f_4536_2]) ).

fof(f_4537_1,plain,
    ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_b] :
      ( c_List_OtakeWhile(T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = c_List_OtakeWhile(T_b,V_P_2,V_xs_2)
      | hBOOL(hAPP(V_P_2,V_x_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_takeWhile__append1]) ).

fof(f_4537_2,plain,
    ! [U_18474,U_18473,U_18472,U_18471,U_18470] :
      ( c_List_OtakeWhile(U_18470,U_18473,hAPP(hAPP(c_List_Oappend(U_18470),U_18472),U_18474)) = c_List_OtakeWhile(U_18470,U_18473,U_18472)
      | hBOOL(hAPP(U_18473,U_18471))
      | ~ hBOOL(hAPP(hAPP(c_member(U_18470),U_18471),hAPP(c_List_Oset(U_18470),U_18472))) ),
    inference(variable_rename,[status(thm)],[f_4537_1]) ).

cnf(f_4537_3,plain,
    ( c_List_OtakeWhile(U_18470,U_18473,hAPP(hAPP(c_List_Oappend(U_18470),U_18472),U_18474)) = c_List_OtakeWhile(U_18470,U_18473,U_18472)
    | hBOOL(hAPP(U_18473,U_18471))
    | ~ hBOOL(hAPP(hAPP(c_member(U_18470),U_18471),hAPP(c_List_Oset(U_18470),U_18472))) ),
    inference(clausify,[status(thm)],[f_4537_2]) ).

fof(f_4538_1,plain,
    ! [V_xs_2,V_P_2,T_b,V_j_2] :
      ( hAPP(hAPP(c_List_Onth(T_b),c_List_OtakeWhile(T_b,V_P_2,V_xs_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_j_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_P_2,V_xs_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_takeWhile__nth]) ).

fof(f_4538_2,plain,
    ! [U_18478,U_18477,U_18476,U_18475] :
      ( hAPP(hAPP(c_List_Onth(U_18476),c_List_OtakeWhile(U_18476,U_18477,U_18478)),U_18475) = hAPP(hAPP(c_List_Onth(U_18476),U_18478),U_18475)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18475),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18476)),c_List_OtakeWhile(U_18476,U_18477,U_18478)))) ),
    inference(variable_rename,[status(thm)],[f_4538_1]) ).

cnf(f_4538_3,plain,
    ( hAPP(hAPP(c_List_Onth(U_18476),c_List_OtakeWhile(U_18476,U_18477,U_18478)),U_18475) = hAPP(hAPP(c_List_Onth(U_18476),U_18478),U_18475)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18475),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18476)),c_List_OtakeWhile(U_18476,U_18477,U_18478)))) ),
    inference(clausify,[status(thm)],[f_4538_2]) ).

fof(f_4539_1,plain,
    ! [V_xs_2,V_P_2,T_b] :
      ( ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_P_2,V_xs_2)))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_nth__length__takeWhile]) ).

fof(f_4539_2,plain,
    ! [U_18481,U_18480,U_18479] :
      ( ~ hBOOL(hAPP(U_18480,hAPP(hAPP(c_List_Onth(U_18479),U_18481),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18479)),c_List_OtakeWhile(U_18479,U_18480,U_18481)))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18479)),c_List_OtakeWhile(U_18479,U_18480,U_18481))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18479)),U_18481))) ),
    inference(variable_rename,[status(thm)],[f_4539_1]) ).

cnf(f_4539_3,plain,
    ( ~ hBOOL(hAPP(U_18480,hAPP(hAPP(c_List_Onth(U_18479),U_18481),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18479)),c_List_OtakeWhile(U_18479,U_18480,U_18481)))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18479)),c_List_OtakeWhile(U_18479,U_18480,U_18481))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18479)),U_18481))) ),
    inference(clausify,[status(thm)],[f_4539_2]) ).

fof(f_4540_1,plain,
    ! [T_b,V_xs_2] :
      ( c_List_OtakeWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),c_List_Olast(T_b,V_xs_2))),V_xs_2) = c_List_Obutlast(T_b,V_xs_2)
      | ~ hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
      | V_xs_2 = c_List_Olist_ONil(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_takeWhile__not__last]) ).

fof(f_4540_2,plain,
    ! [U_18483,U_18482] :
      ( c_List_OtakeWhile(U_18483,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_18483),c_fNot),hAPP(hAPP(c_COMBC(U_18483,U_18483,tc_HOL_Obool),c_fequal),c_List_Olast(U_18483,U_18482))),U_18482) = c_List_Obutlast(U_18483,U_18482)
      | ~ hBOOL(hAPP(c_List_Odistinct(U_18483),U_18482))
      | U_18482 = c_List_Olist_ONil(U_18483) ),
    inference(variable_rename,[status(thm)],[f_4540_1]) ).

cnf(f_4540_3,plain,
    ( c_List_OtakeWhile(U_18483,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_18483),c_fNot),hAPP(hAPP(c_COMBC(U_18483,U_18483,tc_HOL_Obool),c_fequal),c_List_Olast(U_18483,U_18482))),U_18482) = c_List_Obutlast(U_18483,U_18482)
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18483),U_18482))
    | U_18482 = c_List_Olist_ONil(U_18483) ),
    inference(clausify,[status(thm)],[f_4540_2]) ).

fof(f_4541_1,plain,
    ! [V_t_2,V_xs_2,V_f_2,T_c,T_b] :
      ( hAPP(c_List_Ofilter(T_c,hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,T_c),hAPP(c_Orderings_Oord__class_Oless(T_b),V_t_2)),V_f_2)),V_xs_2) = c_List_OtakeWhile(T_c,hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,T_c),hAPP(c_Orderings_Oord__class_Oless(T_b),V_t_2)),V_f_2),V_xs_2)
      | ~ c_List_Olinorder__class_Osorted(T_b,hAPP(c_List_Orev(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_filter__equals__takeWhile__sorted__rev]) ).

fof(f_4541_2,plain,
    ! [U_18488,U_18487,U_18486,U_18485,U_18484] :
      ( hAPP(c_List_Ofilter(U_18485,hAPP(hAPP(c_COMBB(U_18484,tc_HOL_Obool,U_18485),hAPP(c_Orderings_Oord__class_Oless(U_18484),U_18488)),U_18486)),U_18487) = c_List_OtakeWhile(U_18485,hAPP(hAPP(c_COMBB(U_18484,tc_HOL_Obool,U_18485),hAPP(c_Orderings_Oord__class_Oless(U_18484),U_18488)),U_18486),U_18487)
      | ~ c_List_Olinorder__class_Osorted(U_18484,hAPP(c_List_Orev(U_18484),hAPP(hAPP(c_List_Omap(U_18485,U_18484),U_18486),U_18487)))
      | ~ class_Orderings_Olinorder(U_18484) ),
    inference(variable_rename,[status(thm)],[f_4541_1]) ).

cnf(f_4541_3,plain,
    ( hAPP(c_List_Ofilter(U_18485,hAPP(hAPP(c_COMBB(U_18484,tc_HOL_Obool,U_18485),hAPP(c_Orderings_Oord__class_Oless(U_18484),U_18488)),U_18486)),U_18487) = c_List_OtakeWhile(U_18485,hAPP(hAPP(c_COMBB(U_18484,tc_HOL_Obool,U_18485),hAPP(c_Orderings_Oord__class_Oless(U_18484),U_18488)),U_18486),U_18487)
    | ~ c_List_Olinorder__class_Osorted(U_18484,hAPP(c_List_Orev(U_18484),hAPP(hAPP(c_List_Omap(U_18485,U_18484),U_18486),U_18487)))
    | ~ class_Orderings_Olinorder(U_18484) ),
    inference(clausify,[status(thm)],[f_4541_2]) ).

fof(f_4542_1,plain,
    ! [V_l] :
      ( c_List_Oembed__list(c_List_Oreturn__list(V_l)) = V_l
      | ~ c_List_Onat__list(V_l) ),
    inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__list__return__embed]) ).

fof(f_4542_2,plain,
    ! [U_18489] :
      ( c_List_Oembed__list(c_List_Oreturn__list(U_18489)) = U_18489
      | ~ c_List_Onat__list(U_18489) ),
    inference(variable_rename,[status(thm)],[f_4542_1]) ).

cnf(f_4542_3,plain,
    ( c_List_Oembed__list(c_List_Oreturn__list(U_18489)) = U_18489
    | ~ c_List_Onat__list(U_18489) ),
    inference(clausify,[status(thm)],[f_4542_2]) ).

fof(f_4543_1,plain,
    ! [V_m,V_l] : hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),V_l),V_m) = c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint),c_List_Oembed__list(V_l)),c_List_Oembed__list(V_m))),
    inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__list__functions_I1_J]) ).

fof(f_4543_2,plain,
    ! [U_18491,U_18490] : hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),U_18490),U_18491) = c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint),c_List_Oembed__list(U_18490)),c_List_Oembed__list(U_18491))),
    inference(variable_rename,[status(thm)],[f_4543_1]) ).

cnf(f_4543_3,plain,
    hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),U_18490),U_18491) = c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint),c_List_Oembed__list(U_18490)),c_List_Oembed__list(U_18491))),
    inference(clausify,[status(thm)],[f_4543_2]) ).

fof(f_4544_1,plain,
    ! [V_l_2] : c_List_Oembed__list(V_l_2) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_l_2),
    inference(fof_nnf,[status(thm)],[fact_embed__list__def]) ).

fof(f_4544_2,plain,
    ! [U_18492] : c_List_Oembed__list(U_18492) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_18492),
    inference(variable_rename,[status(thm)],[f_4544_1]) ).

cnf(f_4544_3,plain,
    c_List_Oembed__list(U_18492) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_18492),
    inference(clausify,[status(thm)],[f_4544_2]) ).

fof(f_4545_1,plain,
    ! [V_x_2,V_xs_2,T_b] :
      ( c_List_OtakeWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)),hAPP(c_List_Orev(T_b),V_xs_2)) = hAPP(c_List_Orev(T_b),hAPP(c_List_Otl(T_b),c_List_OdropWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)),V_xs_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ),
    inference(fof_nnf,[status(thm)],[fact_takeWhile__neq__rev]) ).

fof(f_4545_2,plain,
    ! [U_18495,U_18494,U_18493] :
      ( c_List_OtakeWhile(U_18493,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_18493),c_fNot),hAPP(hAPP(c_COMBC(U_18493,U_18493,tc_HOL_Obool),c_fequal),U_18495)),hAPP(c_List_Orev(U_18493),U_18494)) = hAPP(c_List_Orev(U_18493),hAPP(c_List_Otl(U_18493),c_List_OdropWhile(U_18493,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_18493),c_fNot),hAPP(hAPP(c_COMBC(U_18493,U_18493,tc_HOL_Obool),c_fequal),U_18495)),U_18494)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_18493),U_18495),hAPP(c_List_Oset(U_18493),U_18494)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_18493),U_18494)) ),
    inference(variable_rename,[status(thm)],[f_4545_1]) ).

cnf(f_4545_3,plain,
    ( c_List_OtakeWhile(U_18493,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_18493),c_fNot),hAPP(hAPP(c_COMBC(U_18493,U_18493,tc_HOL_Obool),c_fequal),U_18495)),hAPP(c_List_Orev(U_18493),U_18494)) = hAPP(c_List_Orev(U_18493),hAPP(c_List_Otl(U_18493),c_List_OdropWhile(U_18493,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_18493),c_fNot),hAPP(hAPP(c_COMBC(U_18493,U_18493,tc_HOL_Obool),c_fequal),U_18495)),U_18494)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_18493),U_18495),hAPP(c_List_Oset(U_18493),U_18494)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18493),U_18494)) ),
    inference(clausify,[status(thm)],[f_4545_2]) ).

fof(f_4546_1,plain,
    ! [V_x_2,V_xs_2,T_b] :
      ( c_List_OdropWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)),hAPP(c_List_Orev(T_b),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),hAPP(c_List_Orev(T_b),c_List_OtakeWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)),V_xs_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ),
    inference(fof_nnf,[status(thm)],[fact_dropWhile__neq__rev]) ).

fof(f_4546_2,plain,
    ! [U_18498,U_18497,U_18496] :
      ( c_List_OdropWhile(U_18496,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_18496),c_fNot),hAPP(hAPP(c_COMBC(U_18496,U_18496,tc_HOL_Obool),c_fequal),U_18498)),hAPP(c_List_Orev(U_18496),U_18497)) = hAPP(hAPP(c_List_Olist_OCons(U_18496),U_18498),hAPP(c_List_Orev(U_18496),c_List_OtakeWhile(U_18496,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_18496),c_fNot),hAPP(hAPP(c_COMBC(U_18496,U_18496,tc_HOL_Obool),c_fequal),U_18498)),U_18497)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_18496),U_18498),hAPP(c_List_Oset(U_18496),U_18497)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_18496),U_18497)) ),
    inference(variable_rename,[status(thm)],[f_4546_1]) ).

cnf(f_4546_3,plain,
    ( c_List_OdropWhile(U_18496,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_18496),c_fNot),hAPP(hAPP(c_COMBC(U_18496,U_18496,tc_HOL_Obool),c_fequal),U_18498)),hAPP(c_List_Orev(U_18496),U_18497)) = hAPP(hAPP(c_List_Olist_OCons(U_18496),U_18498),hAPP(c_List_Orev(U_18496),c_List_OtakeWhile(U_18496,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_18496),c_fNot),hAPP(hAPP(c_COMBC(U_18496,U_18496,tc_HOL_Obool),c_fequal),U_18498)),U_18497)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_18496),U_18498),hAPP(c_List_Oset(U_18496),U_18497)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18496),U_18497)) ),
    inference(clausify,[status(thm)],[f_4546_2]) ).

fof(f_4547_1,plain,
    ! [V_xs_2,V_P_2,T_b] : hAPP(hAPP(c_List_Oappend(T_b),c_List_OtakeWhile(T_b,V_P_2,V_xs_2)),c_List_OdropWhile(T_b,V_P_2,V_xs_2)) = V_xs_2,
    inference(fof_nnf,[status(thm)],[fact_takeWhile__dropWhile__id]) ).

fof(f_4547_2,plain,
    ! [U_18501,U_18500,U_18499] : hAPP(hAPP(c_List_Oappend(U_18499),c_List_OtakeWhile(U_18499,U_18500,U_18501)),c_List_OdropWhile(U_18499,U_18500,U_18501)) = U_18501,
    inference(variable_rename,[status(thm)],[f_4547_1]) ).

cnf(f_4547_3,plain,
    hAPP(hAPP(c_List_Oappend(U_18499),c_List_OtakeWhile(U_18499,U_18500,U_18501)),c_List_OdropWhile(U_18499,U_18500,U_18501)) = U_18501,
    inference(clausify,[status(thm)],[f_4547_2]) ).

fof(f_4548_1,plain,
    ! [V_P_2,V_xs_2,T_b] :
      ( c_List_Olinorder__class_Osorted(T_b,c_List_OdropWhile(T_b,V_P_2,V_xs_2))
      | ~ c_List_Olinorder__class_Osorted(T_b,V_xs_2)
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__dropWhile]) ).

fof(f_4548_2,plain,
    ! [U_18504,U_18503,U_18502] :
      ( c_List_Olinorder__class_Osorted(U_18502,c_List_OdropWhile(U_18502,U_18504,U_18503))
      | ~ c_List_Olinorder__class_Osorted(U_18502,U_18503)
      | ~ class_Orderings_Olinorder(U_18502) ),
    inference(variable_rename,[status(thm)],[f_4548_1]) ).

cnf(f_4548_3,plain,
    ( c_List_Olinorder__class_Osorted(U_18502,c_List_OdropWhile(U_18502,U_18504,U_18503))
    | ~ c_List_Olinorder__class_Osorted(U_18502,U_18503)
    | ~ class_Orderings_Olinorder(U_18502) ),
    inference(clausify,[status(thm)],[f_4548_2]) ).

fof(f_4549_1,plain,
    ! [V_xs_2,V_P_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OdropWhile(T_b,V_P_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))),
    inference(fof_nnf,[status(thm)],[fact_length__dropWhile__le]) ).

fof(f_4549_2,plain,
    ! [U_18507,U_18506,U_18505] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18505)),c_List_OdropWhile(U_18505,U_18506,U_18507))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18505)),U_18507))),
    inference(variable_rename,[status(thm)],[f_4549_1]) ).

cnf(f_4549_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18505)),c_List_OdropWhile(U_18505,U_18506,U_18507))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18505)),U_18507))),
    inference(clausify,[status(thm)],[f_4549_2]) ).

fof(f_4550_1,plain,
    ! [V_xs_2,V_P_2,T_b] :
      ( ( c_List_OdropWhile(T_b,V_P_2,V_xs_2) = c_List_Olist_ONil(T_b)
        | ? [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) ) )
      & ( ! [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) )
        | c_List_OdropWhile(T_b,V_P_2,V_xs_2) != c_List_Olist_ONil(T_b) ) ),
    inference(fof_nnf,[status(thm)],[fact_dropWhile__eq__Nil__conv]) ).

fof(f_4550_2,plain,
    ! [U_18512,U_18511,U_18510] :
      ( ( c_List_OdropWhile(U_18510,U_18511,U_18512) = c_List_Olist_ONil(U_18510)
        | ? [U_18509] :
            ( ~ hBOOL(hAPP(U_18511,U_18509))
            & hBOOL(hAPP(hAPP(c_member(U_18510),U_18509),hAPP(c_List_Oset(U_18510),U_18512))) ) )
      & ( ! [U_18508] :
            ( hBOOL(hAPP(U_18511,U_18508))
            | ~ hBOOL(hAPP(hAPP(c_member(U_18510),U_18508),hAPP(c_List_Oset(U_18510),U_18512))) )
        | c_List_OdropWhile(U_18510,U_18511,U_18512) != c_List_Olist_ONil(U_18510) ) ),
    inference(variable_rename,[status(thm)],[f_4550_1]) ).

fof(f_4550_3,plain,
    ( ! [U_18518,U_18516,U_18514] :
        ( c_List_OdropWhile(U_18514,U_18516,U_18518) = c_List_Olist_ONil(U_18514)
        | ? [U_18509] :
            ( ~ hBOOL(hAPP(U_18516,U_18509))
            & hBOOL(hAPP(hAPP(c_member(U_18514),U_18509),hAPP(c_List_Oset(U_18514),U_18518))) ) )
    & ! [U_18517,U_18515,U_18513] :
        ( ! [U_18508] :
            ( hBOOL(hAPP(U_18515,U_18508))
            | ~ hBOOL(hAPP(hAPP(c_member(U_18513),U_18508),hAPP(c_List_Oset(U_18513),U_18517))) )
        | c_List_OdropWhile(U_18513,U_18515,U_18517) != c_List_Olist_ONil(U_18513) ) ),
    inference(miniscope,[status(thm)],[f_4550_2]) ).

fof(f_4550_4,plain,
    ( ! [U_18518,U_18516,U_18514] :
        ( c_List_OdropWhile(U_18514,U_18516,U_18518) = c_List_Olist_ONil(U_18514)
        | ( ~ hBOOL(hAPP(U_18516,sK457(U_18518,U_18516,U_18514)))
          & hBOOL(hAPP(hAPP(c_member(U_18514),sK457(U_18518,U_18516,U_18514)),hAPP(c_List_Oset(U_18514),U_18518))) ) )
    & ! [U_18517,U_18515,U_18513] :
        ( ! [U_18508] :
            ( hBOOL(hAPP(U_18515,U_18508))
            | ~ hBOOL(hAPP(hAPP(c_member(U_18513),U_18508),hAPP(c_List_Oset(U_18513),U_18517))) )
        | c_List_OdropWhile(U_18513,U_18515,U_18517) != c_List_Olist_ONil(U_18513) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK457]),skolemize(U_18509,sK457(U_18518,U_18516,U_18514))],[f_4550_3]) ).

cnf(f_4550_5,plain,
    ( hBOOL(hAPP(U_18515,U_18508))
    | ~ hBOOL(hAPP(hAPP(c_member(U_18513),U_18508),hAPP(c_List_Oset(U_18513),U_18517)))
    | c_List_OdropWhile(U_18513,U_18515,U_18517) != c_List_Olist_ONil(U_18513) ),
    inference(clausify,[status(thm)],[f_4550_4]) ).

cnf(f_4550_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18514),sK457(U_18518,U_18516,U_18514)),hAPP(c_List_Oset(U_18514),U_18518)))
    | c_List_OdropWhile(U_18514,U_18516,U_18518) = c_List_Olist_ONil(U_18514) ),
    inference(clausify,[status(thm)],[f_4550_4]) ).

cnf(f_4550_7,plain,
    ( ~ hBOOL(hAPP(U_18516,sK457(U_18518,U_18516,U_18514)))
    | c_List_OdropWhile(U_18514,U_18516,U_18518) = c_List_Olist_ONil(U_18514) ),
    inference(clausify,[status(thm)],[f_4550_4]) ).

fof(f_4551_1,plain,
    ! [V_xs_2,T_b,V_x_2,V_P_2] :
      ( ( c_List_OdropWhile(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)
        | hBOOL(hAPP(V_P_2,V_x_2)) )
      & ( c_List_OdropWhile(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_List_OdropWhile(T_b,V_P_2,V_xs_2)
        | ~ hBOOL(hAPP(V_P_2,V_x_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_dropWhile_Osimps_I2_J]) ).

fof(f_4551_2,plain,
    ! [U_18522,U_18521,U_18520,U_18519] :
      ( ( c_List_OdropWhile(U_18521,U_18519,hAPP(hAPP(c_List_Olist_OCons(U_18521),U_18520),U_18522)) = hAPP(hAPP(c_List_Olist_OCons(U_18521),U_18520),U_18522)
        | hBOOL(hAPP(U_18519,U_18520)) )
      & ( c_List_OdropWhile(U_18521,U_18519,hAPP(hAPP(c_List_Olist_OCons(U_18521),U_18520),U_18522)) = c_List_OdropWhile(U_18521,U_18519,U_18522)
        | ~ hBOOL(hAPP(U_18519,U_18520)) ) ),
    inference(variable_rename,[status(thm)],[f_4551_1]) ).

fof(f_4551_3,plain,
    ( ! [U_18530,U_18528,U_18526,U_18524] :
        ( c_List_OdropWhile(U_18528,U_18524,hAPP(hAPP(c_List_Olist_OCons(U_18528),U_18526),U_18530)) = hAPP(hAPP(c_List_Olist_OCons(U_18528),U_18526),U_18530)
        | hBOOL(hAPP(U_18524,U_18526)) )
    & ! [U_18529,U_18527,U_18525,U_18523] :
        ( c_List_OdropWhile(U_18527,U_18523,hAPP(hAPP(c_List_Olist_OCons(U_18527),U_18525),U_18529)) = c_List_OdropWhile(U_18527,U_18523,U_18529)
        | ~ hBOOL(hAPP(U_18523,U_18525)) ) ),
    inference(miniscope,[status(thm)],[f_4551_2]) ).

cnf(f_4551_4,plain,
    ( c_List_OdropWhile(U_18527,U_18523,hAPP(hAPP(c_List_Olist_OCons(U_18527),U_18525),U_18529)) = c_List_OdropWhile(U_18527,U_18523,U_18529)
    | ~ hBOOL(hAPP(U_18523,U_18525)) ),
    inference(clausify,[status(thm)],[f_4551_3]) ).

cnf(f_4551_5,plain,
    ( c_List_OdropWhile(U_18528,U_18524,hAPP(hAPP(c_List_Olist_OCons(U_18528),U_18526),U_18530)) = hAPP(hAPP(c_List_Olist_OCons(U_18528),U_18526),U_18530)
    | hBOOL(hAPP(U_18524,U_18526)) ),
    inference(clausify,[status(thm)],[f_4551_3]) ).

fof(f_4552_1,plain,
    ! [V_P_2,T_b] : c_List_OdropWhile(T_b,V_P_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b),
    inference(fof_nnf,[status(thm)],[fact_dropWhile_Osimps_I1_J]) ).

fof(f_4552_2,plain,
    ! [U_18532,U_18531] : c_List_OdropWhile(U_18531,U_18532,c_List_Olist_ONil(U_18531)) = c_List_Olist_ONil(U_18531),
    inference(variable_rename,[status(thm)],[f_4552_1]) ).

cnf(f_4552_3,plain,
    c_List_OdropWhile(U_18531,U_18532,c_List_Olist_ONil(U_18531)) = c_List_Olist_ONil(U_18531),
    inference(clausify,[status(thm)],[f_4552_2]) ).

fof(f_4553_1,plain,
    ! [V_P_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),c_List_OdropWhile(T_b,V_P_2,V_xs_2)))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__dropWhile]) ).

fof(f_4553_2,plain,
    ! [U_18535,U_18534,U_18533] :
      ( hBOOL(hAPP(c_List_Odistinct(U_18533),c_List_OdropWhile(U_18533,U_18535,U_18534)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_18533),U_18534)) ),
    inference(variable_rename,[status(thm)],[f_4553_1]) ).

cnf(f_4553_3,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_18533),c_List_OdropWhile(U_18533,U_18535,U_18534)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18533),U_18534)) ),
    inference(clausify,[status(thm)],[f_4553_2]) ).

fof(f_4554_1,plain,
    ! [V_xs_2,V_P_2,T_b] :
      ( ~ hBOOL(hAPP(V_P_2,hAPP(c_List_Ohd(T_b),c_List_OdropWhile(T_b,V_P_2,V_xs_2))))
      | c_List_OdropWhile(T_b,V_P_2,V_xs_2) = c_List_Olist_ONil(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_hd__dropWhile]) ).

fof(f_4554_2,plain,
    ! [U_18538,U_18537,U_18536] :
      ( ~ hBOOL(hAPP(U_18537,hAPP(c_List_Ohd(U_18536),c_List_OdropWhile(U_18536,U_18537,U_18538))))
      | c_List_OdropWhile(U_18536,U_18537,U_18538) = c_List_Olist_ONil(U_18536) ),
    inference(variable_rename,[status(thm)],[f_4554_1]) ).

cnf(f_4554_3,plain,
    ( ~ hBOOL(hAPP(U_18537,hAPP(c_List_Ohd(U_18536),c_List_OdropWhile(U_18536,U_18537,U_18538))))
    | c_List_OdropWhile(U_18536,U_18537,U_18538) = c_List_Olist_ONil(U_18536) ),
    inference(clausify,[status(thm)],[f_4554_2]) ).

fof(f_4555_1,plain,
    ! [V_xs_2,V_f_2,T_c,V_P_2,T_b] : c_List_OdropWhile(T_b,V_P_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_OdropWhile(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_P_2),V_f_2),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_dropWhile__map]) ).

fof(f_4555_2,plain,
    ! [U_18543,U_18542,U_18541,U_18540,U_18539] : c_List_OdropWhile(U_18539,U_18540,hAPP(hAPP(c_List_Omap(U_18541,U_18539),U_18542),U_18543)) = hAPP(hAPP(c_List_Omap(U_18541,U_18539),U_18542),c_List_OdropWhile(U_18541,hAPP(c_Fun_Ocomp(U_18539,tc_HOL_Obool,U_18541,U_18540),U_18542),U_18543)),
    inference(variable_rename,[status(thm)],[f_4555_1]) ).

cnf(f_4555_3,plain,
    c_List_OdropWhile(U_18539,U_18540,hAPP(hAPP(c_List_Omap(U_18541,U_18539),U_18542),U_18543)) = hAPP(hAPP(c_List_Omap(U_18541,U_18539),U_18542),c_List_OdropWhile(U_18541,hAPP(c_Fun_Ocomp(U_18539,tc_HOL_Obool,U_18541,U_18540),U_18542),U_18543)),
    inference(clausify,[status(thm)],[f_4555_2]) ).

fof(f_4556_1,plain,
    ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_b] :
      ( c_List_OdropWhile(T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),c_List_OdropWhile(T_b,V_P_2,V_xs_2)),V_ys_2)
      | hBOOL(hAPP(V_P_2,V_x_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_dropWhile__append1]) ).

fof(f_4556_2,plain,
    ! [U_18548,U_18547,U_18546,U_18545,U_18544] :
      ( c_List_OdropWhile(U_18544,U_18547,hAPP(hAPP(c_List_Oappend(U_18544),U_18546),U_18548)) = hAPP(hAPP(c_List_Oappend(U_18544),c_List_OdropWhile(U_18544,U_18547,U_18546)),U_18548)
      | hBOOL(hAPP(U_18547,U_18545))
      | ~ hBOOL(hAPP(hAPP(c_member(U_18544),U_18545),hAPP(c_List_Oset(U_18544),U_18546))) ),
    inference(variable_rename,[status(thm)],[f_4556_1]) ).

cnf(f_4556_3,plain,
    ( c_List_OdropWhile(U_18544,U_18547,hAPP(hAPP(c_List_Oappend(U_18544),U_18546),U_18548)) = hAPP(hAPP(c_List_Oappend(U_18544),c_List_OdropWhile(U_18544,U_18547,U_18546)),U_18548)
    | hBOOL(hAPP(U_18547,U_18545))
    | ~ hBOOL(hAPP(hAPP(c_member(U_18544),U_18545),hAPP(c_List_Oset(U_18544),U_18546))) ),
    inference(clausify,[status(thm)],[f_4556_2]) ).

fof(f_4557_1,plain,
    ! [V_ys_2,V_y_2,V_xs_2,V_P_2,T_b] :
      ( ( c_List_OdropWhile(T_b,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)
        | hBOOL(hAPP(V_P_2,V_y_2))
        | V_xs_2 != hAPP(hAPP(c_List_Oappend(T_b),c_List_OtakeWhile(T_b,V_P_2,V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)) )
      & ( ( ~ hBOOL(hAPP(V_P_2,V_y_2))
          & V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),c_List_OtakeWhile(T_b,V_P_2,V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)) )
        | c_List_OdropWhile(T_b,V_P_2,V_xs_2) != hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_dropWhile__eq__Cons__conv]) ).

fof(f_4557_2,plain,
    ! [U_18553,U_18552,U_18551,U_18550,U_18549] :
      ( ( c_List_OdropWhile(U_18549,U_18550,U_18551) = hAPP(hAPP(c_List_Olist_OCons(U_18549),U_18552),U_18553)
        | hBOOL(hAPP(U_18550,U_18552))
        | U_18551 != hAPP(hAPP(c_List_Oappend(U_18549),c_List_OtakeWhile(U_18549,U_18550,U_18551)),hAPP(hAPP(c_List_Olist_OCons(U_18549),U_18552),U_18553)) )
      & ( ( ~ hBOOL(hAPP(U_18550,U_18552))
          & U_18551 = hAPP(hAPP(c_List_Oappend(U_18549),c_List_OtakeWhile(U_18549,U_18550,U_18551)),hAPP(hAPP(c_List_Olist_OCons(U_18549),U_18552),U_18553)) )
        | c_List_OdropWhile(U_18549,U_18550,U_18551) != hAPP(hAPP(c_List_Olist_OCons(U_18549),U_18552),U_18553) ) ),
    inference(variable_rename,[status(thm)],[f_4557_1]) ).

fof(f_4557_3,plain,
    ( ! [U_18563,U_18561,U_18559,U_18557,U_18555] :
        ( c_List_OdropWhile(U_18555,U_18557,U_18559) = hAPP(hAPP(c_List_Olist_OCons(U_18555),U_18561),U_18563)
        | hBOOL(hAPP(U_18557,U_18561))
        | U_18559 != hAPP(hAPP(c_List_Oappend(U_18555),c_List_OtakeWhile(U_18555,U_18557,U_18559)),hAPP(hAPP(c_List_Olist_OCons(U_18555),U_18561),U_18563)) )
    & ! [U_18562,U_18560,U_18558,U_18556,U_18554] :
        ( ( ~ hBOOL(hAPP(U_18556,U_18560))
          & U_18558 = hAPP(hAPP(c_List_Oappend(U_18554),c_List_OtakeWhile(U_18554,U_18556,U_18558)),hAPP(hAPP(c_List_Olist_OCons(U_18554),U_18560),U_18562)) )
        | c_List_OdropWhile(U_18554,U_18556,U_18558) != hAPP(hAPP(c_List_Olist_OCons(U_18554),U_18560),U_18562) ) ),
    inference(miniscope,[status(thm)],[f_4557_2]) ).

cnf(f_4557_4,plain,
    ( U_18558 = hAPP(hAPP(c_List_Oappend(U_18554),c_List_OtakeWhile(U_18554,U_18556,U_18558)),hAPP(hAPP(c_List_Olist_OCons(U_18554),U_18560),U_18562))
    | c_List_OdropWhile(U_18554,U_18556,U_18558) != hAPP(hAPP(c_List_Olist_OCons(U_18554),U_18560),U_18562) ),
    inference(clausify,[status(thm)],[f_4557_3]) ).

cnf(f_4557_5,plain,
    ( ~ hBOOL(hAPP(U_18556,U_18560))
    | c_List_OdropWhile(U_18554,U_18556,U_18558) != hAPP(hAPP(c_List_Olist_OCons(U_18554),U_18560),U_18562) ),
    inference(clausify,[status(thm)],[f_4557_3]) ).

cnf(f_4557_6,plain,
    ( c_List_OdropWhile(U_18555,U_18557,U_18559) = hAPP(hAPP(c_List_Olist_OCons(U_18555),U_18561),U_18563)
    | hBOOL(hAPP(U_18557,U_18561))
    | U_18559 != hAPP(hAPP(c_List_Oappend(U_18555),c_List_OtakeWhile(U_18555,U_18557,U_18559)),hAPP(hAPP(c_List_Olist_OCons(U_18555),U_18561),U_18563)) ),
    inference(clausify,[status(thm)],[f_4557_3]) ).

fof(f_4558_1,plain,
    ! [V_xs_2,V_P_2,T_b] : c_List_OdropWhile(T_b,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_dropWhile__eq__drop]) ).

fof(f_4558_2,plain,
    ! [U_18566,U_18565,U_18564] : c_List_OdropWhile(U_18564,U_18565,U_18566) = hAPP(hAPP(c_List_Odrop(U_18564),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18564)),c_List_OtakeWhile(U_18564,U_18565,U_18566))),U_18566),
    inference(variable_rename,[status(thm)],[f_4558_1]) ).

cnf(f_4558_3,plain,
    c_List_OdropWhile(U_18564,U_18565,U_18566) = hAPP(hAPP(c_List_Odrop(U_18564),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18564)),c_List_OtakeWhile(U_18564,U_18565,U_18566))),U_18566),
    inference(clausify,[status(thm)],[f_4558_2]) ).

fof(f_4559_1,plain,
    ! [V_xs_2,V_P_2,T_b,V_j_2] :
      ( hAPP(hAPP(c_List_Onth(T_b),c_List_OdropWhile(T_b,V_P_2,V_xs_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_b),V_xs_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OdropWhile(T_b,V_P_2,V_xs_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_dropWhile__nth]) ).

fof(f_4559_2,plain,
    ! [U_18570,U_18569,U_18568,U_18567] :
      ( hAPP(hAPP(c_List_Onth(U_18568),c_List_OdropWhile(U_18568,U_18569,U_18570)),U_18567) = hAPP(hAPP(c_List_Onth(U_18568),U_18570),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_18567),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18568)),c_List_OtakeWhile(U_18568,U_18569,U_18570))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18567),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18568)),c_List_OdropWhile(U_18568,U_18569,U_18570)))) ),
    inference(variable_rename,[status(thm)],[f_4559_1]) ).

cnf(f_4559_3,plain,
    ( hAPP(hAPP(c_List_Onth(U_18568),c_List_OdropWhile(U_18568,U_18569,U_18570)),U_18567) = hAPP(hAPP(c_List_Onth(U_18568),U_18570),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_18567),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18568)),c_List_OtakeWhile(U_18568,U_18569,U_18570))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18567),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18568)),c_List_OdropWhile(U_18568,U_18569,U_18570)))) ),
    inference(clausify,[status(thm)],[f_4559_2]) ).

fof(f_4560_1,plain,
    ! [V_f_2,V_P_2,V_xs_2,T_b,T_c] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))
      | ? [B_x] :
          ( hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_c)
          & ~ hBOOL(hAPP(V_P_2,B_x))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) )
      | ~ class_Groups_Omonoid__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_listsum__map__filter]) ).

fof(f_4560_2,plain,
    ! [U_18576,U_18575,U_18574,U_18573,U_18572] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18572),hAPP(hAPP(c_List_Omap(U_18573,U_18572),U_18576),hAPP(c_List_Ofilter(U_18573,U_18575),U_18574))) = hAPP(c_List_Omonoid__add__class_Olistsum(U_18572),hAPP(hAPP(c_List_Omap(U_18573,U_18572),U_18576),U_18574))
      | ? [U_18571] :
          ( hAPP(U_18576,U_18571) != c_Groups_Ozero__class_Ozero(U_18572)
          & ~ hBOOL(hAPP(U_18575,U_18571))
          & hBOOL(hAPP(hAPP(c_member(U_18573),U_18571),hAPP(c_List_Oset(U_18573),U_18574))) )
      | ~ class_Groups_Omonoid__add(U_18572) ),
    inference(variable_rename,[status(thm)],[f_4560_1]) ).

fof(f_4560_3,plain,
    ! [U_18576,U_18575,U_18574,U_18573,U_18572] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18572),hAPP(hAPP(c_List_Omap(U_18573,U_18572),U_18576),hAPP(c_List_Ofilter(U_18573,U_18575),U_18574))) = hAPP(c_List_Omonoid__add__class_Olistsum(U_18572),hAPP(hAPP(c_List_Omap(U_18573,U_18572),U_18576),U_18574))
      | ( hAPP(U_18576,sK458(U_18576,U_18575,U_18574,U_18573,U_18572)) != c_Groups_Ozero__class_Ozero(U_18572)
        & ~ hBOOL(hAPP(U_18575,sK458(U_18576,U_18575,U_18574,U_18573,U_18572)))
        & hBOOL(hAPP(hAPP(c_member(U_18573),sK458(U_18576,U_18575,U_18574,U_18573,U_18572)),hAPP(c_List_Oset(U_18573),U_18574))) )
      | ~ class_Groups_Omonoid__add(U_18572) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK458]),skolemize(U_18571,sK458(U_18576,U_18575,U_18574,U_18573,U_18572))],[f_4560_2]) ).

cnf(f_4560_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18573),sK458(U_18576,U_18575,U_18574,U_18573,U_18572)),hAPP(c_List_Oset(U_18573),U_18574)))
    | hAPP(c_List_Omonoid__add__class_Olistsum(U_18572),hAPP(hAPP(c_List_Omap(U_18573,U_18572),U_18576),hAPP(c_List_Ofilter(U_18573,U_18575),U_18574))) = hAPP(c_List_Omonoid__add__class_Olistsum(U_18572),hAPP(hAPP(c_List_Omap(U_18573,U_18572),U_18576),U_18574))
    | ~ class_Groups_Omonoid__add(U_18572) ),
    inference(clausify,[status(thm)],[f_4560_3]) ).

cnf(f_4560_5,plain,
    ( ~ hBOOL(hAPP(U_18575,sK458(U_18576,U_18575,U_18574,U_18573,U_18572)))
    | hAPP(c_List_Omonoid__add__class_Olistsum(U_18572),hAPP(hAPP(c_List_Omap(U_18573,U_18572),U_18576),hAPP(c_List_Ofilter(U_18573,U_18575),U_18574))) = hAPP(c_List_Omonoid__add__class_Olistsum(U_18572),hAPP(hAPP(c_List_Omap(U_18573,U_18572),U_18576),U_18574))
    | ~ class_Groups_Omonoid__add(U_18572) ),
    inference(clausify,[status(thm)],[f_4560_3]) ).

cnf(f_4560_6,plain,
    ( hAPP(U_18576,sK458(U_18576,U_18575,U_18574,U_18573,U_18572)) != c_Groups_Ozero__class_Ozero(U_18572)
    | hAPP(c_List_Omonoid__add__class_Olistsum(U_18572),hAPP(hAPP(c_List_Omap(U_18573,U_18572),U_18576),hAPP(c_List_Ofilter(U_18573,U_18575),U_18574))) = hAPP(c_List_Omonoid__add__class_Olistsum(U_18572),hAPP(hAPP(c_List_Omap(U_18573,U_18572),U_18576),U_18574))
    | ~ class_Groups_Omonoid__add(U_18572) ),
    inference(clausify,[status(thm)],[f_4560_3]) ).

fof(f_4561_1,plain,
    ! [V_xs,T_a] :
      ( c_List_Olinorder__class_Osorted(T_a,V_xs)
      | ? [B_i,B_j] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),B_i)),hAPP(hAPP(c_List_Onth(T_a),V_xs),B_j)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j)) )
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__nth__monoI]) ).

fof(f_4561_2,plain,
    ! [U_18580,U_18579] :
      ( c_List_Olinorder__class_Osorted(U_18579,U_18580)
      | ? [U_18578,U_18577] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18579),hAPP(hAPP(c_List_Onth(U_18579),U_18580),U_18578)),hAPP(hAPP(c_List_Onth(U_18579),U_18580),U_18577)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18577),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18579)),U_18580)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18578),U_18577)) )
      | ~ class_Orderings_Olinorder(U_18579) ),
    inference(variable_rename,[status(thm)],[f_4561_1]) ).

fof(f_4561_3,plain,
    ! [U_18580,U_18579] :
      ( c_List_Olinorder__class_Osorted(U_18579,U_18580)
      | ? [U_18577] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18579),hAPP(hAPP(c_List_Onth(U_18579),U_18580),sK459(U_18580,U_18579))),hAPP(hAPP(c_List_Onth(U_18579),U_18580),U_18577)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18577),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18579)),U_18580)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK459(U_18580,U_18579)),U_18577)) )
      | ~ class_Orderings_Olinorder(U_18579) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK459]),skolemize(U_18578,sK459(U_18580,U_18579))],[f_4561_2]) ).

fof(f_4561_4,plain,
    ! [U_18580,U_18579] :
      ( c_List_Olinorder__class_Osorted(U_18579,U_18580)
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18579),hAPP(hAPP(c_List_Onth(U_18579),U_18580),sK459(U_18580,U_18579))),hAPP(hAPP(c_List_Onth(U_18579),U_18580),sK460(U_18580,U_18579))))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK460(U_18580,U_18579)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18579)),U_18580)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK459(U_18580,U_18579)),sK460(U_18580,U_18579))) )
      | ~ class_Orderings_Olinorder(U_18579) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK460]),skolemize(U_18577,sK460(U_18580,U_18579))],[f_4561_3]) ).

cnf(f_4561_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK459(U_18580,U_18579)),sK460(U_18580,U_18579)))
    | c_List_Olinorder__class_Osorted(U_18579,U_18580)
    | ~ class_Orderings_Olinorder(U_18579) ),
    inference(clausify,[status(thm)],[f_4561_4]) ).

cnf(f_4561_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK460(U_18580,U_18579)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18579)),U_18580)))
    | c_List_Olinorder__class_Osorted(U_18579,U_18580)
    | ~ class_Orderings_Olinorder(U_18579) ),
    inference(clausify,[status(thm)],[f_4561_4]) ).

cnf(f_4561_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18579),hAPP(hAPP(c_List_Onth(U_18579),U_18580),sK459(U_18580,U_18579))),hAPP(hAPP(c_List_Onth(U_18579),U_18580),sK460(U_18580,U_18579))))
    | c_List_Olinorder__class_Osorted(U_18579,U_18580)
    | ~ class_Orderings_Olinorder(U_18579) ),
    inference(clausify,[status(thm)],[f_4561_4]) ).

fof(f_4562_1,plain,
    ! [V_xs_2,V_P_2,T_b] :
      ( c_List_OtakeWhile(T_b,V_P_2,V_xs_2) = hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)
      | ? [B_x] :
          ( hBOOL(hAPP(V_P_2,B_x))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),c_List_OdropWhile(T_b,V_P_2,V_xs_2)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_takeWhile__eq__filter]) ).

fof(f_4562_2,plain,
    ! [U_18584,U_18583,U_18582] :
      ( c_List_OtakeWhile(U_18582,U_18583,U_18584) = hAPP(c_List_Ofilter(U_18582,U_18583),U_18584)
      | ? [U_18581] :
          ( hBOOL(hAPP(U_18583,U_18581))
          & hBOOL(hAPP(hAPP(c_member(U_18582),U_18581),hAPP(c_List_Oset(U_18582),c_List_OdropWhile(U_18582,U_18583,U_18584)))) ) ),
    inference(variable_rename,[status(thm)],[f_4562_1]) ).

fof(f_4562_3,plain,
    ! [U_18584,U_18583,U_18582] :
      ( c_List_OtakeWhile(U_18582,U_18583,U_18584) = hAPP(c_List_Ofilter(U_18582,U_18583),U_18584)
      | ( hBOOL(hAPP(U_18583,sK461(U_18584,U_18583,U_18582)))
        & hBOOL(hAPP(hAPP(c_member(U_18582),sK461(U_18584,U_18583,U_18582)),hAPP(c_List_Oset(U_18582),c_List_OdropWhile(U_18582,U_18583,U_18584)))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK461]),skolemize(U_18581,sK461(U_18584,U_18583,U_18582))],[f_4562_2]) ).

cnf(f_4562_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18582),sK461(U_18584,U_18583,U_18582)),hAPP(c_List_Oset(U_18582),c_List_OdropWhile(U_18582,U_18583,U_18584))))
    | c_List_OtakeWhile(U_18582,U_18583,U_18584) = hAPP(c_List_Ofilter(U_18582,U_18583),U_18584) ),
    inference(clausify,[status(thm)],[f_4562_3]) ).

cnf(f_4562_5,plain,
    ( hBOOL(hAPP(U_18583,sK461(U_18584,U_18583,U_18582)))
    | c_List_OtakeWhile(U_18582,U_18583,U_18584) = hAPP(c_List_Ofilter(U_18582,U_18583),U_18584) ),
    inference(clausify,[status(thm)],[f_4562_3]) ).

fof(f_4563_1,plain,
    ! [V_P_2,V_xs_2,T_b,V_n_2] :
      ( c_List_OtakeWhile(T_b,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2)
      | ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) )
      | ? [B_i] :
          ( ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_takeWhile__eq__take__P__nth]) ).

fof(f_4563_2,plain,
    ! [U_18589,U_18588,U_18587,U_18586] :
      ( c_List_OtakeWhile(U_18587,U_18589,U_18588) = hAPP(hAPP(c_List_Otake(U_18587),U_18586),U_18588)
      | ( hBOOL(hAPP(U_18589,hAPP(hAPP(c_List_Onth(U_18587),U_18588),U_18586)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18586),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18587)),U_18588))) )
      | ? [U_18585] :
          ( ~ hBOOL(hAPP(U_18589,hAPP(hAPP(c_List_Onth(U_18587),U_18588),U_18585)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18585),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18587)),U_18588)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18585),U_18586)) ) ),
    inference(variable_rename,[status(thm)],[f_4563_1]) ).

fof(f_4563_3,plain,
    ! [U_18589,U_18588,U_18587,U_18586] :
      ( c_List_OtakeWhile(U_18587,U_18589,U_18588) = hAPP(hAPP(c_List_Otake(U_18587),U_18586),U_18588)
      | ( hBOOL(hAPP(U_18589,hAPP(hAPP(c_List_Onth(U_18587),U_18588),U_18586)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18586),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18587)),U_18588))) )
      | ( ~ hBOOL(hAPP(U_18589,hAPP(hAPP(c_List_Onth(U_18587),U_18588),sK462(U_18589,U_18588,U_18587,U_18586))))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK462(U_18589,U_18588,U_18587,U_18586)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18587)),U_18588)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK462(U_18589,U_18588,U_18587,U_18586)),U_18586)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK462]),skolemize(U_18585,sK462(U_18589,U_18588,U_18587,U_18586))],[f_4563_2]) ).

cnf(f_4563_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18586),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18587)),U_18588)))
    | c_List_OtakeWhile(U_18587,U_18589,U_18588) = hAPP(hAPP(c_List_Otake(U_18587),U_18586),U_18588)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK462(U_18589,U_18588,U_18587,U_18586)),U_18586)) ),
    inference(clausify,[status(thm)],[f_4563_3]) ).

cnf(f_4563_5,plain,
    ( hBOOL(hAPP(U_18589,hAPP(hAPP(c_List_Onth(U_18587),U_18588),U_18586)))
    | c_List_OtakeWhile(U_18587,U_18589,U_18588) = hAPP(hAPP(c_List_Otake(U_18587),U_18586),U_18588)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK462(U_18589,U_18588,U_18587,U_18586)),U_18586)) ),
    inference(clausify,[status(thm)],[f_4563_3]) ).

cnf(f_4563_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18586),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18587)),U_18588)))
    | c_List_OtakeWhile(U_18587,U_18589,U_18588) = hAPP(hAPP(c_List_Otake(U_18587),U_18586),U_18588)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK462(U_18589,U_18588,U_18587,U_18586)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18587)),U_18588))) ),
    inference(clausify,[status(thm)],[f_4563_3]) ).

cnf(f_4563_7,plain,
    ( hBOOL(hAPP(U_18589,hAPP(hAPP(c_List_Onth(U_18587),U_18588),U_18586)))
    | c_List_OtakeWhile(U_18587,U_18589,U_18588) = hAPP(hAPP(c_List_Otake(U_18587),U_18586),U_18588)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK462(U_18589,U_18588,U_18587,U_18586)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18587)),U_18588))) ),
    inference(clausify,[status(thm)],[f_4563_3]) ).

cnf(f_4563_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18586),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18587)),U_18588)))
    | c_List_OtakeWhile(U_18587,U_18589,U_18588) = hAPP(hAPP(c_List_Otake(U_18587),U_18586),U_18588)
    | ~ hBOOL(hAPP(U_18589,hAPP(hAPP(c_List_Onth(U_18587),U_18588),sK462(U_18589,U_18588,U_18587,U_18586)))) ),
    inference(clausify,[status(thm)],[f_4563_3]) ).

cnf(f_4563_9,plain,
    ( hBOOL(hAPP(U_18589,hAPP(hAPP(c_List_Onth(U_18587),U_18588),U_18586)))
    | c_List_OtakeWhile(U_18587,U_18589,U_18588) = hAPP(hAPP(c_List_Otake(U_18587),U_18586),U_18588)
    | ~ hBOOL(hAPP(U_18589,hAPP(hAPP(c_List_Onth(U_18587),U_18588),sK462(U_18589,U_18588,U_18587,U_18586)))) ),
    inference(clausify,[status(thm)],[f_4563_3]) ).

fof(f_4564_1,plain,
    ! [V_xs_2,T_b,V_P_2,V_j_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
      | ? [B_i] :
          ( ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_j_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_length__takeWhile__less__P__nth]) ).

fof(f_4564_2,plain,
    ! [U_18594,U_18593,U_18592,U_18591] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18591),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18593)),c_List_OtakeWhile(U_18593,U_18592,U_18594))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18591),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18593)),U_18594)))
      | ? [U_18590] :
          ( ~ hBOOL(hAPP(U_18592,hAPP(hAPP(c_List_Onth(U_18593),U_18594),U_18590)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18590),U_18591)) ) ),
    inference(variable_rename,[status(thm)],[f_4564_1]) ).

fof(f_4564_3,plain,
    ! [U_18594,U_18593,U_18592,U_18591] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18591),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18593)),c_List_OtakeWhile(U_18593,U_18592,U_18594))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18591),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18593)),U_18594)))
      | ( ~ hBOOL(hAPP(U_18592,hAPP(hAPP(c_List_Onth(U_18593),U_18594),sK463(U_18594,U_18593,U_18592,U_18591))))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK463(U_18594,U_18593,U_18592,U_18591)),U_18591)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK463]),skolemize(U_18590,sK463(U_18594,U_18593,U_18592,U_18591))],[f_4564_2]) ).

cnf(f_4564_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK463(U_18594,U_18593,U_18592,U_18591)),U_18591))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18591),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18593)),c_List_OtakeWhile(U_18593,U_18592,U_18594))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18591),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18593)),U_18594))) ),
    inference(clausify,[status(thm)],[f_4564_3]) ).

cnf(f_4564_5,plain,
    ( ~ hBOOL(hAPP(U_18592,hAPP(hAPP(c_List_Onth(U_18593),U_18594),sK463(U_18594,U_18593,U_18592,U_18591))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18591),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18593)),c_List_OtakeWhile(U_18593,U_18592,U_18594))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18591),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18593)),U_18594))) ),
    inference(clausify,[status(thm)],[f_4564_3]) ).

fof(f_4565_1,plain,
    ! [V_a_2,T_b] :
      ( ( ( c_List_Olinorder__class_Osorted(T_b,V_a_2)
          | ( ! [B_xs,B_x] :
                ( ~ c_List_Olinorder__class_Osorted(T_b,B_xs)
                | ? [B_xa] :
                    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),B_xa))
                    & hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(c_List_Oset(T_b),B_xs))) )
                | V_a_2 != hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_xs) )
            & V_a_2 != c_List_Olist_ONil(T_b) ) )
        & ( ? [B_xs,B_x] :
              ( c_List_Olinorder__class_Osorted(T_b,B_xs)
              & ! [B_xa] :
                  ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),B_xa))
                  | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(c_List_Oset(T_b),B_xs))) )
              & V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_xs) )
          | V_a_2 = c_List_Olist_ONil(T_b)
          | ~ c_List_Olinorder__class_Osorted(T_b,V_a_2) ) )
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sorted_Osimps]) ).

fof(f_4565_2,plain,
    ! [U_18602,U_18601] :
      ( ( ( c_List_Olinorder__class_Osorted(U_18601,U_18602)
          | ( ! [U_18600,U_18599] :
                ( ~ c_List_Olinorder__class_Osorted(U_18601,U_18600)
                | ? [U_18598] :
                    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18601),U_18599),U_18598))
                    & hBOOL(hAPP(hAPP(c_member(U_18601),U_18598),hAPP(c_List_Oset(U_18601),U_18600))) )
                | U_18602 != hAPP(hAPP(c_List_Olist_OCons(U_18601),U_18599),U_18600) )
            & U_18602 != c_List_Olist_ONil(U_18601) ) )
        & ( ? [U_18597,U_18596] :
              ( c_List_Olinorder__class_Osorted(U_18601,U_18597)
              & ! [U_18595] :
                  ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18601),U_18596),U_18595))
                  | ~ hBOOL(hAPP(hAPP(c_member(U_18601),U_18595),hAPP(c_List_Oset(U_18601),U_18597))) )
              & U_18602 = hAPP(hAPP(c_List_Olist_OCons(U_18601),U_18596),U_18597) )
          | U_18602 = c_List_Olist_ONil(U_18601)
          | ~ c_List_Olinorder__class_Osorted(U_18601,U_18602) ) )
      | ~ class_Orderings_Olinorder(U_18601) ),
    inference(variable_rename,[status(thm)],[f_4565_1]) ).

fof(f_4565_3,plain,
    ! [U_18602,U_18601] :
      ( ( ( c_List_Olinorder__class_Osorted(U_18601,U_18602)
          | ( ! [U_18600] :
                ( ! [U_18599] :
                    ( ? [U_18598] :
                        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18601),U_18599),U_18598))
                        & hBOOL(hAPP(hAPP(c_member(U_18601),U_18598),hAPP(c_List_Oset(U_18601),U_18600))) )
                    | U_18602 != hAPP(hAPP(c_List_Olist_OCons(U_18601),U_18599),U_18600) )
                | ~ c_List_Olinorder__class_Osorted(U_18601,U_18600) )
            & U_18602 != c_List_Olist_ONil(U_18601) ) )
        & ( ? [U_18597] :
              ( ? [U_18596] :
                  ( ! [U_18595] :
                      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18601),U_18596),U_18595))
                      | ~ hBOOL(hAPP(hAPP(c_member(U_18601),U_18595),hAPP(c_List_Oset(U_18601),U_18597))) )
                  & U_18602 = hAPP(hAPP(c_List_Olist_OCons(U_18601),U_18596),U_18597) )
              & c_List_Olinorder__class_Osorted(U_18601,U_18597) )
          | U_18602 = c_List_Olist_ONil(U_18601)
          | ~ c_List_Olinorder__class_Osorted(U_18601,U_18602) ) )
      | ~ class_Orderings_Olinorder(U_18601) ),
    inference(miniscope,[status(thm)],[f_4565_2]) ).

fof(f_4565_4,plain,
    ! [U_18602,U_18601] :
      ( ( ( c_List_Olinorder__class_Osorted(U_18601,U_18602)
          | ( ! [U_18600] :
                ( ! [U_18599] :
                    ( ? [U_18598] :
                        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18601),U_18599),U_18598))
                        & hBOOL(hAPP(hAPP(c_member(U_18601),U_18598),hAPP(c_List_Oset(U_18601),U_18600))) )
                    | U_18602 != hAPP(hAPP(c_List_Olist_OCons(U_18601),U_18599),U_18600) )
                | ~ c_List_Olinorder__class_Osorted(U_18601,U_18600) )
            & U_18602 != c_List_Olist_ONil(U_18601) ) )
        & ( ( ? [U_18596] :
                ( ! [U_18595] :
                    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18601),U_18596),U_18595))
                    | ~ hBOOL(hAPP(hAPP(c_member(U_18601),U_18595),hAPP(c_List_Oset(U_18601),sK464(U_18602,U_18601)))) )
                & U_18602 = hAPP(hAPP(c_List_Olist_OCons(U_18601),U_18596),sK464(U_18602,U_18601)) )
            & c_List_Olinorder__class_Osorted(U_18601,sK464(U_18602,U_18601)) )
          | U_18602 = c_List_Olist_ONil(U_18601)
          | ~ c_List_Olinorder__class_Osorted(U_18601,U_18602) ) )
      | ~ class_Orderings_Olinorder(U_18601) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK464]),skolemize(U_18597,sK464(U_18602,U_18601))],[f_4565_3]) ).

fof(f_4565_5,plain,
    ! [U_18602,U_18601] :
      ( ( ( c_List_Olinorder__class_Osorted(U_18601,U_18602)
          | ( ! [U_18600] :
                ( ! [U_18599] :
                    ( ? [U_18598] :
                        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18601),U_18599),U_18598))
                        & hBOOL(hAPP(hAPP(c_member(U_18601),U_18598),hAPP(c_List_Oset(U_18601),U_18600))) )
                    | U_18602 != hAPP(hAPP(c_List_Olist_OCons(U_18601),U_18599),U_18600) )
                | ~ c_List_Olinorder__class_Osorted(U_18601,U_18600) )
            & U_18602 != c_List_Olist_ONil(U_18601) ) )
        & ( ( ! [U_18595] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18601),sK465(U_18602,U_18601)),U_18595))
                | ~ hBOOL(hAPP(hAPP(c_member(U_18601),U_18595),hAPP(c_List_Oset(U_18601),sK464(U_18602,U_18601)))) )
            & U_18602 = hAPP(hAPP(c_List_Olist_OCons(U_18601),sK465(U_18602,U_18601)),sK464(U_18602,U_18601))
            & c_List_Olinorder__class_Osorted(U_18601,sK464(U_18602,U_18601)) )
          | U_18602 = c_List_Olist_ONil(U_18601)
          | ~ c_List_Olinorder__class_Osorted(U_18601,U_18602) ) )
      | ~ class_Orderings_Olinorder(U_18601) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK465]),skolemize(U_18596,sK465(U_18602,U_18601))],[f_4565_4]) ).

fof(f_4565_6,plain,
    ! [U_18602,U_18601] :
      ( ( ( c_List_Olinorder__class_Osorted(U_18601,U_18602)
          | ( ! [U_18600] :
                ( ! [U_18599] :
                    ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18601),U_18599),sK466(U_18602,U_18601,U_18600,U_18599)))
                      & hBOOL(hAPP(hAPP(c_member(U_18601),sK466(U_18602,U_18601,U_18600,U_18599)),hAPP(c_List_Oset(U_18601),U_18600))) )
                    | U_18602 != hAPP(hAPP(c_List_Olist_OCons(U_18601),U_18599),U_18600) )
                | ~ c_List_Olinorder__class_Osorted(U_18601,U_18600) )
            & U_18602 != c_List_Olist_ONil(U_18601) ) )
        & ( ( ! [U_18595] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18601),sK465(U_18602,U_18601)),U_18595))
                | ~ hBOOL(hAPP(hAPP(c_member(U_18601),U_18595),hAPP(c_List_Oset(U_18601),sK464(U_18602,U_18601)))) )
            & U_18602 = hAPP(hAPP(c_List_Olist_OCons(U_18601),sK465(U_18602,U_18601)),sK464(U_18602,U_18601))
            & c_List_Olinorder__class_Osorted(U_18601,sK464(U_18602,U_18601)) )
          | U_18602 = c_List_Olist_ONil(U_18601)
          | ~ c_List_Olinorder__class_Osorted(U_18601,U_18602) ) )
      | ~ class_Orderings_Olinorder(U_18601) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK466]),skolemize(U_18598,sK466(U_18602,U_18601,U_18600,U_18599))],[f_4565_5]) ).

cnf(f_4565_7,plain,
    ( c_List_Olinorder__class_Osorted(U_18601,sK464(U_18602,U_18601))
    | U_18602 = c_List_Olist_ONil(U_18601)
    | ~ c_List_Olinorder__class_Osorted(U_18601,U_18602)
    | ~ class_Orderings_Olinorder(U_18601) ),
    inference(clausify,[status(thm)],[f_4565_6]) ).

cnf(f_4565_8,plain,
    ( U_18602 = hAPP(hAPP(c_List_Olist_OCons(U_18601),sK465(U_18602,U_18601)),sK464(U_18602,U_18601))
    | U_18602 = c_List_Olist_ONil(U_18601)
    | ~ c_List_Olinorder__class_Osorted(U_18601,U_18602)
    | ~ class_Orderings_Olinorder(U_18601) ),
    inference(clausify,[status(thm)],[f_4565_6]) ).

cnf(f_4565_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18601),sK465(U_18602,U_18601)),U_18595))
    | ~ hBOOL(hAPP(hAPP(c_member(U_18601),U_18595),hAPP(c_List_Oset(U_18601),sK464(U_18602,U_18601))))
    | U_18602 = c_List_Olist_ONil(U_18601)
    | ~ c_List_Olinorder__class_Osorted(U_18601,U_18602)
    | ~ class_Orderings_Olinorder(U_18601) ),
    inference(clausify,[status(thm)],[f_4565_6]) ).

cnf(f_4565_10,plain,
    ( U_18602 != c_List_Olist_ONil(U_18601)
    | c_List_Olinorder__class_Osorted(U_18601,U_18602)
    | ~ class_Orderings_Olinorder(U_18601) ),
    inference(clausify,[status(thm)],[f_4565_6]) ).

cnf(f_4565_11,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18601),sK466(U_18602,U_18601,U_18600,U_18599)),hAPP(c_List_Oset(U_18601),U_18600)))
    | U_18602 != hAPP(hAPP(c_List_Olist_OCons(U_18601),U_18599),U_18600)
    | ~ c_List_Olinorder__class_Osorted(U_18601,U_18600)
    | c_List_Olinorder__class_Osorted(U_18601,U_18602)
    | ~ class_Orderings_Olinorder(U_18601) ),
    inference(clausify,[status(thm)],[f_4565_6]) ).

cnf(f_4565_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18601),U_18599),sK466(U_18602,U_18601,U_18600,U_18599)))
    | U_18602 != hAPP(hAPP(c_List_Olist_OCons(U_18601),U_18599),U_18600)
    | ~ c_List_Olinorder__class_Osorted(U_18601,U_18600)
    | c_List_Olinorder__class_Osorted(U_18601,U_18602)
    | ~ class_Orderings_Olinorder(U_18601) ),
    inference(clausify,[status(thm)],[f_4565_6]) ).

fof(f_4566_1,plain,
    ! [V_xs_2,V_x_2,T_b] :
      ( c_List_Oinsert(T_b,V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)
      | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_not__in__set__insert]) ).

fof(f_4566_2,plain,
    ! [U_18605,U_18604,U_18603] :
      ( c_List_Oinsert(U_18603,U_18604,U_18605) = hAPP(hAPP(c_List_Olist_OCons(U_18603),U_18604),U_18605)
      | hBOOL(hAPP(hAPP(c_member(U_18603),U_18604),hAPP(c_List_Oset(U_18603),U_18605))) ),
    inference(variable_rename,[status(thm)],[f_4566_1]) ).

cnf(f_4566_3,plain,
    ( c_List_Oinsert(U_18603,U_18604,U_18605) = hAPP(hAPP(c_List_Olist_OCons(U_18603),U_18604),U_18605)
    | hBOOL(hAPP(hAPP(c_member(U_18603),U_18604),hAPP(c_List_Oset(U_18603),U_18605))) ),
    inference(clausify,[status(thm)],[f_4566_2]) ).

fof(f_4567_1,plain,
    ! [V_xs_2,V_x_2,T_b] :
      ( ( c_List_Oinsert(T_b,V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)
        | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) )
      & ( c_List_Oinsert(T_b,V_x_2,V_xs_2) = V_xs_2
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_List_Oinsert__def]) ).

fof(f_4567_2,plain,
    ! [U_18608,U_18607,U_18606] :
      ( ( c_List_Oinsert(U_18606,U_18607,U_18608) = hAPP(hAPP(c_List_Olist_OCons(U_18606),U_18607),U_18608)
        | hBOOL(hAPP(hAPP(c_member(U_18606),U_18607),hAPP(c_List_Oset(U_18606),U_18608))) )
      & ( c_List_Oinsert(U_18606,U_18607,U_18608) = U_18608
        | ~ hBOOL(hAPP(hAPP(c_member(U_18606),U_18607),hAPP(c_List_Oset(U_18606),U_18608))) ) ),
    inference(variable_rename,[status(thm)],[f_4567_1]) ).

fof(f_4567_3,plain,
    ( ! [U_18614,U_18612,U_18610] :
        ( c_List_Oinsert(U_18610,U_18612,U_18614) = hAPP(hAPP(c_List_Olist_OCons(U_18610),U_18612),U_18614)
        | hBOOL(hAPP(hAPP(c_member(U_18610),U_18612),hAPP(c_List_Oset(U_18610),U_18614))) )
    & ! [U_18613,U_18611,U_18609] :
        ( c_List_Oinsert(U_18609,U_18611,U_18613) = U_18613
        | ~ hBOOL(hAPP(hAPP(c_member(U_18609),U_18611),hAPP(c_List_Oset(U_18609),U_18613))) ) ),
    inference(miniscope,[status(thm)],[f_4567_2]) ).

cnf(f_4567_4,plain,
    ( c_List_Oinsert(U_18609,U_18611,U_18613) = U_18613
    | ~ hBOOL(hAPP(hAPP(c_member(U_18609),U_18611),hAPP(c_List_Oset(U_18609),U_18613))) ),
    inference(clausify,[status(thm)],[f_4567_3]) ).

cnf(f_4567_5,plain,
    ( c_List_Oinsert(U_18610,U_18612,U_18614) = hAPP(hAPP(c_List_Olist_OCons(U_18610),U_18612),U_18614)
    | hBOOL(hAPP(hAPP(c_member(U_18610),U_18612),hAPP(c_List_Oset(U_18610),U_18614))) ),
    inference(clausify,[status(thm)],[f_4567_3]) ).

fof(f_4568_1,plain,
    ! [V_xs,V_x,T_a] : c_List_Oinsert(T_a,V_x,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,c_List_Oinsert(T_a,V_x,V_xs)),
    inference(fof_nnf,[status(thm)],[fact_insert__remdups]) ).

fof(f_4568_2,plain,
    ! [U_18617,U_18616,U_18615] : c_List_Oinsert(U_18615,U_18616,c_List_Oremdups(U_18615,U_18617)) = c_List_Oremdups(U_18615,c_List_Oinsert(U_18615,U_18616,U_18617)),
    inference(variable_rename,[status(thm)],[f_4568_1]) ).

cnf(f_4568_3,plain,
    c_List_Oinsert(U_18615,U_18616,c_List_Oremdups(U_18615,U_18617)) = c_List_Oremdups(U_18615,c_List_Oinsert(U_18615,U_18616,U_18617)),
    inference(clausify,[status(thm)],[f_4568_2]) ).

fof(f_4569_1,plain,
    ! [V_x,V_xs,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oinsert(T_a,V_x,V_xs)))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__insert]) ).

fof(f_4569_2,plain,
    ! [U_18620,U_18619,U_18618] :
      ( hBOOL(hAPP(c_List_Odistinct(U_18618),c_List_Oinsert(U_18618,U_18620,U_18619)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_18618),U_18619)) ),
    inference(variable_rename,[status(thm)],[f_4569_1]) ).

cnf(f_4569_3,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_18618),c_List_Oinsert(U_18618,U_18620,U_18619)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18618),U_18619)) ),
    inference(clausify,[status(thm)],[f_4569_2]) ).

fof(f_4570_1,plain,
    ! [V_xs_2,V_x_2,T_b] :
      ( c_List_Oinsert(T_b,V_x_2,V_xs_2) = V_xs_2
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_in__set__insert]) ).

fof(f_4570_2,plain,
    ! [U_18623,U_18622,U_18621] :
      ( c_List_Oinsert(U_18621,U_18622,U_18623) = U_18623
      | ~ hBOOL(hAPP(hAPP(c_member(U_18621),U_18622),hAPP(c_List_Oset(U_18621),U_18623))) ),
    inference(variable_rename,[status(thm)],[f_4570_1]) ).

cnf(f_4570_3,plain,
    ( c_List_Oinsert(U_18621,U_18622,U_18623) = U_18623
    | ~ hBOOL(hAPP(hAPP(c_member(U_18621),U_18622),hAPP(c_List_Oset(U_18621),U_18623))) ),
    inference(clausify,[status(thm)],[f_4570_2]) ).

fof(f_4571_1,plain,
    ! [V_xs_2,V_x_2,T_b] : hAPP(c_List_Oset(T_b),c_List_Oinsert(T_b,V_x_2,V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_List_Oset__insert]) ).

fof(f_4571_2,plain,
    ! [U_18626,U_18625,U_18624] : hAPP(c_List_Oset(U_18624),c_List_Oinsert(U_18624,U_18625,U_18626)) = hAPP(hAPP(c_Set_Oinsert(U_18624),U_18625),hAPP(c_List_Oset(U_18624),U_18626)),
    inference(variable_rename,[status(thm)],[f_4571_1]) ).

cnf(f_4571_3,plain,
    hAPP(c_List_Oset(U_18624),c_List_Oinsert(U_18624,U_18625,U_18626)) = hAPP(hAPP(c_Set_Oinsert(U_18624),U_18625),hAPP(c_List_Oset(U_18624),U_18626)),
    inference(clausify,[status(thm)],[f_4571_2]) ).

fof(f_4572_1,plain,
    ! [V_x,T_a] : c_List_Oinsert(T_a,V_x,c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a)),
    inference(fof_nnf,[status(thm)],[fact_insert__Nil]) ).

fof(f_4572_2,plain,
    ! [U_18628,U_18627] : c_List_Oinsert(U_18627,U_18628,c_List_Olist_ONil(U_18627)) = hAPP(hAPP(c_List_Olist_OCons(U_18627),U_18628),c_List_Olist_ONil(U_18627)),
    inference(variable_rename,[status(thm)],[f_4572_1]) ).

cnf(f_4572_3,plain,
    c_List_Oinsert(U_18627,U_18628,c_List_Olist_ONil(U_18627)) = hAPP(hAPP(c_List_Olist_OCons(U_18627),U_18628),c_List_Olist_ONil(U_18627)),
    inference(clausify,[status(thm)],[f_4572_2]) ).

fof(f_4573_1,plain,
    ! [V_xs_2,V_f_2,T_c,T_b] : c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(T_c,tc_List_Olist(T_b)),V_f_2),V_xs_2)) = c_List_Omaps(T_c,T_b,V_f_2,V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_concat__map__maps]) ).

fof(f_4573_2,plain,
    ! [U_18632,U_18631,U_18630,U_18629] : c_List_Oconcat(U_18629,hAPP(hAPP(c_List_Omap(U_18630,tc_List_Olist(U_18629)),U_18631),U_18632)) = c_List_Omaps(U_18630,U_18629,U_18631,U_18632),
    inference(variable_rename,[status(thm)],[f_4573_1]) ).

cnf(f_4573_3,plain,
    c_List_Oconcat(U_18629,hAPP(hAPP(c_List_Omap(U_18630,tc_List_Olist(U_18629)),U_18631),U_18632)) = c_List_Omaps(U_18630,U_18629,U_18631,U_18632),
    inference(clausify,[status(thm)],[f_4573_2]) ).

fof(f_4574_1,plain,
    ! [V_xs_2,V_f_2,T_b,T_c] : c_List_Omaps(T_c,T_b,V_f_2,V_xs_2) = c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(T_c,tc_List_Olist(T_b)),V_f_2),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_maps__def]) ).

fof(f_4574_2,plain,
    ! [U_18636,U_18635,U_18634,U_18633] : c_List_Omaps(U_18633,U_18634,U_18635,U_18636) = c_List_Oconcat(U_18634,hAPP(hAPP(c_List_Omap(U_18633,tc_List_Olist(U_18634)),U_18635),U_18636)),
    inference(variable_rename,[status(thm)],[f_4574_1]) ).

cnf(f_4574_3,plain,
    c_List_Omaps(U_18633,U_18634,U_18635,U_18636) = c_List_Oconcat(U_18634,hAPP(hAPP(c_List_Omap(U_18633,tc_List_Olist(U_18634)),U_18635),U_18636)),
    inference(clausify,[status(thm)],[f_4574_2]) ).

fof(f_4575_1,plain,
    ! [V_f_2,T_b,T_c] : c_List_Omaps(T_c,T_b,V_f_2,c_List_Olist_ONil(T_c)) = c_List_Olist_ONil(T_b),
    inference(fof_nnf,[status(thm)],[fact_maps__simps_I2_J]) ).

fof(f_4575_2,plain,
    ! [U_18639,U_18638,U_18637] : c_List_Omaps(U_18637,U_18638,U_18639,c_List_Olist_ONil(U_18637)) = c_List_Olist_ONil(U_18638),
    inference(variable_rename,[status(thm)],[f_4575_1]) ).

cnf(f_4575_3,plain,
    c_List_Omaps(U_18637,U_18638,U_18639,c_List_Olist_ONil(U_18637)) = c_List_Olist_ONil(U_18638),
    inference(clausify,[status(thm)],[f_4575_2]) ).

fof(f_4576_1,plain,
    ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] : c_List_Omaps(T_c,T_b,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Oappend(T_b),hAPP(V_f_2,V_x_2)),c_List_Omaps(T_c,T_b,V_f_2,V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_maps__simps_I1_J]) ).

fof(f_4576_2,plain,
    ! [U_18644,U_18643,U_18642,U_18641,U_18640] : c_List_Omaps(U_18640,U_18641,U_18642,hAPP(hAPP(c_List_Olist_OCons(U_18640),U_18643),U_18644)) = hAPP(hAPP(c_List_Oappend(U_18641),hAPP(U_18642,U_18643)),c_List_Omaps(U_18640,U_18641,U_18642,U_18644)),
    inference(variable_rename,[status(thm)],[f_4576_1]) ).

cnf(f_4576_3,plain,
    c_List_Omaps(U_18640,U_18641,U_18642,hAPP(hAPP(c_List_Olist_OCons(U_18640),U_18643),U_18644)) = hAPP(hAPP(c_List_Oappend(U_18641),hAPP(U_18642,U_18643)),c_List_Omaps(U_18640,U_18641,U_18642,U_18644)),
    inference(clausify,[status(thm)],[f_4576_2]) ).

fof(f_4577_1,plain,
    ! [V_xs_2,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Oconcat(T_b,V_xs_2)))
      | ? [B_ys] :
          ( ? [B_zs] :
              ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),B_ys)),hAPP(c_List_Oset(T_b),B_zs)) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
              & B_ys != B_zs
              & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_zs),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2))) )
          & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2))) )
      | ? [B_ys] :
          ( ~ hBOOL(hAPP(c_List_Odistinct(T_b),B_ys))
          & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2))) )
      | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_b)),V_xs_2)) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__concat]) ).

fof(f_4577_2,plain,
    ! [U_18649,U_18648] :
      ( hBOOL(hAPP(c_List_Odistinct(U_18648),c_List_Oconcat(U_18648,U_18649)))
      | ? [U_18647] :
          ( ? [U_18646] :
              ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_18648,tc_HOL_Obool)),hAPP(c_List_Oset(U_18648),U_18647)),hAPP(c_List_Oset(U_18648),U_18646)) != c_Orderings_Obot__class_Obot(tc_fun(U_18648,tc_HOL_Obool))
              & U_18647 != U_18646
              & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_18648)),U_18646),hAPP(c_List_Oset(tc_List_Olist(U_18648)),U_18649))) )
          & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_18648)),U_18647),hAPP(c_List_Oset(tc_List_Olist(U_18648)),U_18649))) )
      | ? [U_18645] :
          ( ~ hBOOL(hAPP(c_List_Odistinct(U_18648),U_18645))
          & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_18648)),U_18645),hAPP(c_List_Oset(tc_List_Olist(U_18648)),U_18649))) )
      | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(U_18648)),U_18649)) ),
    inference(variable_rename,[status(thm)],[f_4577_1]) ).

fof(f_4577_3,plain,
    ! [U_18649,U_18648] :
      ( hBOOL(hAPP(c_List_Odistinct(U_18648),c_List_Oconcat(U_18648,U_18649)))
      | ? [U_18647] :
          ( ? [U_18646] :
              ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_18648,tc_HOL_Obool)),hAPP(c_List_Oset(U_18648),U_18647)),hAPP(c_List_Oset(U_18648),U_18646)) != c_Orderings_Obot__class_Obot(tc_fun(U_18648,tc_HOL_Obool))
              & U_18647 != U_18646
              & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_18648)),U_18646),hAPP(c_List_Oset(tc_List_Olist(U_18648)),U_18649))) )
          & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_18648)),U_18647),hAPP(c_List_Oset(tc_List_Olist(U_18648)),U_18649))) )
      | ( ~ hBOOL(hAPP(c_List_Odistinct(U_18648),sK467(U_18649,U_18648)))
        & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_18648)),sK467(U_18649,U_18648)),hAPP(c_List_Oset(tc_List_Olist(U_18648)),U_18649))) )
      | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(U_18648)),U_18649)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK467]),skolemize(U_18645,sK467(U_18649,U_18648))],[f_4577_2]) ).

fof(f_4577_4,plain,
    ! [U_18649,U_18648] :
      ( hBOOL(hAPP(c_List_Odistinct(U_18648),c_List_Oconcat(U_18648,U_18649)))
      | ( ? [U_18646] :
            ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_18648,tc_HOL_Obool)),hAPP(c_List_Oset(U_18648),sK468(U_18649,U_18648))),hAPP(c_List_Oset(U_18648),U_18646)) != c_Orderings_Obot__class_Obot(tc_fun(U_18648,tc_HOL_Obool))
            & sK468(U_18649,U_18648) != U_18646
            & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_18648)),U_18646),hAPP(c_List_Oset(tc_List_Olist(U_18648)),U_18649))) )
        & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_18648)),sK468(U_18649,U_18648)),hAPP(c_List_Oset(tc_List_Olist(U_18648)),U_18649))) )
      | ( ~ hBOOL(hAPP(c_List_Odistinct(U_18648),sK467(U_18649,U_18648)))
        & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_18648)),sK467(U_18649,U_18648)),hAPP(c_List_Oset(tc_List_Olist(U_18648)),U_18649))) )
      | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(U_18648)),U_18649)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK468]),skolemize(U_18647,sK468(U_18649,U_18648))],[f_4577_3]) ).

fof(f_4577_5,plain,
    ! [U_18649,U_18648] :
      ( hBOOL(hAPP(c_List_Odistinct(U_18648),c_List_Oconcat(U_18648,U_18649)))
      | ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_18648,tc_HOL_Obool)),hAPP(c_List_Oset(U_18648),sK468(U_18649,U_18648))),hAPP(c_List_Oset(U_18648),sK469(U_18649,U_18648))) != c_Orderings_Obot__class_Obot(tc_fun(U_18648,tc_HOL_Obool))
        & sK468(U_18649,U_18648) != sK469(U_18649,U_18648)
        & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_18648)),sK469(U_18649,U_18648)),hAPP(c_List_Oset(tc_List_Olist(U_18648)),U_18649)))
        & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_18648)),sK468(U_18649,U_18648)),hAPP(c_List_Oset(tc_List_Olist(U_18648)),U_18649))) )
      | ( ~ hBOOL(hAPP(c_List_Odistinct(U_18648),sK467(U_18649,U_18648)))
        & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_18648)),sK467(U_18649,U_18648)),hAPP(c_List_Oset(tc_List_Olist(U_18648)),U_18649))) )
      | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(U_18648)),U_18649)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK469]),skolemize(U_18646,sK469(U_18649,U_18648))],[f_4577_4]) ).

cnf(f_4577_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_18648)),sK468(U_18649,U_18648)),hAPP(c_List_Oset(tc_List_Olist(U_18648)),U_18649)))
    | hBOOL(hAPP(c_List_Odistinct(U_18648),c_List_Oconcat(U_18648,U_18649)))
    | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_18648)),sK467(U_18649,U_18648)),hAPP(c_List_Oset(tc_List_Olist(U_18648)),U_18649)))
    | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(U_18648)),U_18649)) ),
    inference(clausify,[status(thm)],[f_4577_5]) ).

cnf(f_4577_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_18648)),sK469(U_18649,U_18648)),hAPP(c_List_Oset(tc_List_Olist(U_18648)),U_18649)))
    | hBOOL(hAPP(c_List_Odistinct(U_18648),c_List_Oconcat(U_18648,U_18649)))
    | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_18648)),sK467(U_18649,U_18648)),hAPP(c_List_Oset(tc_List_Olist(U_18648)),U_18649)))
    | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(U_18648)),U_18649)) ),
    inference(clausify,[status(thm)],[f_4577_5]) ).

cnf(f_4577_8,plain,
    ( sK468(U_18649,U_18648) != sK469(U_18649,U_18648)
    | hBOOL(hAPP(c_List_Odistinct(U_18648),c_List_Oconcat(U_18648,U_18649)))
    | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_18648)),sK467(U_18649,U_18648)),hAPP(c_List_Oset(tc_List_Olist(U_18648)),U_18649)))
    | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(U_18648)),U_18649)) ),
    inference(clausify,[status(thm)],[f_4577_5]) ).

cnf(f_4577_9,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_18648,tc_HOL_Obool)),hAPP(c_List_Oset(U_18648),sK468(U_18649,U_18648))),hAPP(c_List_Oset(U_18648),sK469(U_18649,U_18648))) != c_Orderings_Obot__class_Obot(tc_fun(U_18648,tc_HOL_Obool))
    | hBOOL(hAPP(c_List_Odistinct(U_18648),c_List_Oconcat(U_18648,U_18649)))
    | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_18648)),sK467(U_18649,U_18648)),hAPP(c_List_Oset(tc_List_Olist(U_18648)),U_18649)))
    | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(U_18648)),U_18649)) ),
    inference(clausify,[status(thm)],[f_4577_5]) ).

cnf(f_4577_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_18648)),sK468(U_18649,U_18648)),hAPP(c_List_Oset(tc_List_Olist(U_18648)),U_18649)))
    | hBOOL(hAPP(c_List_Odistinct(U_18648),c_List_Oconcat(U_18648,U_18649)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18648),sK467(U_18649,U_18648)))
    | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(U_18648)),U_18649)) ),
    inference(clausify,[status(thm)],[f_4577_5]) ).

cnf(f_4577_11,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_18648)),sK469(U_18649,U_18648)),hAPP(c_List_Oset(tc_List_Olist(U_18648)),U_18649)))
    | hBOOL(hAPP(c_List_Odistinct(U_18648),c_List_Oconcat(U_18648,U_18649)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18648),sK467(U_18649,U_18648)))
    | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(U_18648)),U_18649)) ),
    inference(clausify,[status(thm)],[f_4577_5]) ).

cnf(f_4577_12,plain,
    ( sK468(U_18649,U_18648) != sK469(U_18649,U_18648)
    | hBOOL(hAPP(c_List_Odistinct(U_18648),c_List_Oconcat(U_18648,U_18649)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18648),sK467(U_18649,U_18648)))
    | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(U_18648)),U_18649)) ),
    inference(clausify,[status(thm)],[f_4577_5]) ).

cnf(f_4577_13,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_18648,tc_HOL_Obool)),hAPP(c_List_Oset(U_18648),sK468(U_18649,U_18648))),hAPP(c_List_Oset(U_18648),sK469(U_18649,U_18648))) != c_Orderings_Obot__class_Obot(tc_fun(U_18648,tc_HOL_Obool))
    | hBOOL(hAPP(c_List_Odistinct(U_18648),c_List_Oconcat(U_18648,U_18649)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18648),sK467(U_18649,U_18648)))
    | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(U_18648)),U_18649)) ),
    inference(clausify,[status(thm)],[f_4577_5]) ).

fof(f_4578_1,plain,
    ! [V_fs_2,T_b,V_y_2,V_x_2,V_f_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_List_Omeasures(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_b,tc_Nat_Onat)),V_f_2),V_fs_2))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_List_Omeasures(T_b,V_fs_2)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) ),
    inference(fof_nnf,[status(thm)],[fact_measures__lesseq]) ).

fof(f_4578_2,plain,
    ! [U_18654,U_18653,U_18652,U_18651,U_18650] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_18653,U_18653)),hAPP(hAPP(c_Product__Type_OPair(U_18653,U_18653),U_18651),U_18652)),c_List_Omeasures(U_18653,hAPP(hAPP(c_List_Olist_OCons(tc_fun(U_18653,tc_Nat_Onat)),U_18650),U_18654))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18653,U_18653)),hAPP(hAPP(c_Product__Type_OPair(U_18653,U_18653),U_18651),U_18652)),c_List_Omeasures(U_18653,U_18654)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(U_18650,U_18651)),hAPP(U_18650,U_18652))) ),
    inference(variable_rename,[status(thm)],[f_4578_1]) ).

cnf(f_4578_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_18653,U_18653)),hAPP(hAPP(c_Product__Type_OPair(U_18653,U_18653),U_18651),U_18652)),c_List_Omeasures(U_18653,hAPP(hAPP(c_List_Olist_OCons(tc_fun(U_18653,tc_Nat_Onat)),U_18650),U_18654))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18653,U_18653)),hAPP(hAPP(c_Product__Type_OPair(U_18653,U_18653),U_18651),U_18652)),c_List_Omeasures(U_18653,U_18654)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(U_18650,U_18651)),hAPP(U_18650,U_18652))) ),
    inference(clausify,[status(thm)],[f_4578_2]) ).

fof(f_4579_1,plain,
    ! [V_fs_2,T_b] : c_Wellfounded_Owf(T_b,c_List_Omeasures(T_b,V_fs_2)),
    inference(fof_nnf,[status(thm)],[fact_wf__measures]) ).

fof(f_4579_2,plain,
    ! [U_18656,U_18655] : c_Wellfounded_Owf(U_18655,c_List_Omeasures(U_18655,U_18656)),
    inference(variable_rename,[status(thm)],[f_4579_1]) ).

cnf(f_4579_3,plain,
    c_Wellfounded_Owf(U_18655,c_List_Omeasures(U_18655,U_18656)),
    inference(clausify,[status(thm)],[f_4579_2]) ).

fof(f_4580_1,plain,
    ! [V_y_2,V_x_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_List_Omeasures(T_b,c_List_Olist_ONil(tc_fun(T_b,tc_Nat_Onat))))),
    inference(fof_nnf,[status(thm)],[fact_in__measures_I1_J]) ).

fof(f_4580_2,plain,
    ! [U_18659,U_18658,U_18657] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18657,U_18657)),hAPP(hAPP(c_Product__Type_OPair(U_18657,U_18657),U_18658),U_18659)),c_List_Omeasures(U_18657,c_List_Olist_ONil(tc_fun(U_18657,tc_Nat_Onat))))),
    inference(variable_rename,[status(thm)],[f_4580_1]) ).

cnf(f_4580_3,plain,
    ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18657,U_18657)),hAPP(hAPP(c_Product__Type_OPair(U_18657,U_18657),U_18658),U_18659)),c_List_Omeasures(U_18657,c_List_Olist_ONil(tc_fun(U_18657,tc_Nat_Onat))))),
    inference(clausify,[status(thm)],[f_4580_2]) ).

fof(f_4581_1,plain,
    ! [V_fs_2,T_b] : c_List_Omeasures(T_b,V_fs_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_List_Olist(tc_Nat_Onat),T_b),c_List_Olex(tc_Nat_Onat,c_Wellfounded_Oless__than)),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(tc_fun(T_b,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_Nat_Onat),tc_Nat_Onat),tc_fun(tc_List_Olist(tc_fun(T_b,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),T_b),c_List_Omap(tc_fun(T_b,tc_Nat_Onat),tc_Nat_Onat)),hAPP(c_COMBC(tc_fun(T_b,tc_Nat_Onat),T_b,tc_Nat_Onat),c_COMBI(tc_fun(T_b,tc_Nat_Onat))))),V_fs_2)),
    inference(fof_nnf,[status(thm)],[fact_measures__def]) ).

fof(f_4581_2,plain,
    ! [U_18661,U_18660] : c_List_Omeasures(U_18660,U_18661) = hAPP(hAPP(c_Relation_Oinv__image(tc_List_Olist(tc_Nat_Onat),U_18660),c_List_Olex(tc_Nat_Onat,c_Wellfounded_Oless__than)),hAPP(hAPP(c_COMBC(U_18660,tc_List_Olist(tc_fun(U_18660,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_18660,tc_Nat_Onat),tc_Nat_Onat),tc_fun(tc_List_Olist(tc_fun(U_18660,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),U_18660),c_List_Omap(tc_fun(U_18660,tc_Nat_Onat),tc_Nat_Onat)),hAPP(c_COMBC(tc_fun(U_18660,tc_Nat_Onat),U_18660,tc_Nat_Onat),c_COMBI(tc_fun(U_18660,tc_Nat_Onat))))),U_18661)),
    inference(variable_rename,[status(thm)],[f_4581_1]) ).

cnf(f_4581_3,plain,
    c_List_Omeasures(U_18660,U_18661) = hAPP(hAPP(c_Relation_Oinv__image(tc_List_Olist(tc_Nat_Onat),U_18660),c_List_Olex(tc_Nat_Onat,c_Wellfounded_Oless__than)),hAPP(hAPP(c_COMBC(U_18660,tc_List_Olist(tc_fun(U_18660,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_18660,tc_Nat_Onat),tc_Nat_Onat),tc_fun(tc_List_Olist(tc_fun(U_18660,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),U_18660),c_List_Omap(tc_fun(U_18660,tc_Nat_Onat),tc_Nat_Onat)),hAPP(c_COMBC(tc_fun(U_18660,tc_Nat_Onat),U_18660,tc_Nat_Onat),c_COMBI(tc_fun(U_18660,tc_Nat_Onat))))),U_18661)),
    inference(clausify,[status(thm)],[f_4581_2]) ).

fof(f_4582_1,plain,
    ! [V_fs_2,T_b,V_y_2,V_x_2,V_f_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_List_Omeasures(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_b,tc_Nat_Onat)),V_f_2),V_fs_2))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) ),
    inference(fof_nnf,[status(thm)],[fact_measures__less]) ).

fof(f_4582_2,plain,
    ! [U_18666,U_18665,U_18664,U_18663,U_18662] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_18665,U_18665)),hAPP(hAPP(c_Product__Type_OPair(U_18665,U_18665),U_18663),U_18664)),c_List_Omeasures(U_18665,hAPP(hAPP(c_List_Olist_OCons(tc_fun(U_18665,tc_Nat_Onat)),U_18662),U_18666))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_18662,U_18663)),hAPP(U_18662,U_18664))) ),
    inference(variable_rename,[status(thm)],[f_4582_1]) ).

cnf(f_4582_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_18665,U_18665)),hAPP(hAPP(c_Product__Type_OPair(U_18665,U_18665),U_18663),U_18664)),c_List_Omeasures(U_18665,hAPP(hAPP(c_List_Olist_OCons(tc_fun(U_18665,tc_Nat_Onat)),U_18662),U_18666))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_18662,U_18663)),hAPP(U_18662,U_18664))) ),
    inference(clausify,[status(thm)],[f_4582_2]) ).

fof(f_4583_1,plain,
    ! [V_fs_2,V_f_2,V_y_2,V_x_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_List_Omeasures(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_b,tc_Nat_Onat)),V_f_2),V_fs_2))))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_List_Omeasures(T_b,V_fs_2)))
            | hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) )
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) ) )
      & ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_List_Omeasures(T_b,V_fs_2)))
          & hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) )
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_List_Omeasures(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_b,tc_Nat_Onat)),V_f_2),V_fs_2)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_in__measures_I2_J]) ).

fof(f_4583_2,plain,
    ! [U_18671,U_18670,U_18669,U_18668,U_18667] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_18667,U_18667)),hAPP(hAPP(c_Product__Type_OPair(U_18667,U_18667),U_18668),U_18669)),c_List_Omeasures(U_18667,hAPP(hAPP(c_List_Olist_OCons(tc_fun(U_18667,tc_Nat_Onat)),U_18670),U_18671))))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18667,U_18667)),hAPP(hAPP(c_Product__Type_OPair(U_18667,U_18667),U_18668),U_18669)),c_List_Omeasures(U_18667,U_18671)))
            | hAPP(U_18670,U_18668) != hAPP(U_18670,U_18669) )
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_18670,U_18668)),hAPP(U_18670,U_18669))) ) )
      & ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_18667,U_18667)),hAPP(hAPP(c_Product__Type_OPair(U_18667,U_18667),U_18668),U_18669)),c_List_Omeasures(U_18667,U_18671)))
          & hAPP(U_18670,U_18668) = hAPP(U_18670,U_18669) )
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_18670,U_18668)),hAPP(U_18670,U_18669)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18667,U_18667)),hAPP(hAPP(c_Product__Type_OPair(U_18667,U_18667),U_18668),U_18669)),c_List_Omeasures(U_18667,hAPP(hAPP(c_List_Olist_OCons(tc_fun(U_18667,tc_Nat_Onat)),U_18670),U_18671)))) ) ),
    inference(variable_rename,[status(thm)],[f_4583_1]) ).

fof(f_4583_3,plain,
    ( ! [U_18681,U_18679,U_18677,U_18675,U_18673] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_18673,U_18673)),hAPP(hAPP(c_Product__Type_OPair(U_18673,U_18673),U_18675),U_18677)),c_List_Omeasures(U_18673,hAPP(hAPP(c_List_Olist_OCons(tc_fun(U_18673,tc_Nat_Onat)),U_18679),U_18681))))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18673,U_18673)),hAPP(hAPP(c_Product__Type_OPair(U_18673,U_18673),U_18675),U_18677)),c_List_Omeasures(U_18673,U_18681)))
            | hAPP(U_18679,U_18675) != hAPP(U_18679,U_18677) )
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_18679,U_18675)),hAPP(U_18679,U_18677))) ) )
    & ! [U_18680,U_18678,U_18676,U_18674,U_18672] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_18672,U_18672)),hAPP(hAPP(c_Product__Type_OPair(U_18672,U_18672),U_18674),U_18676)),c_List_Omeasures(U_18672,U_18680)))
          & hAPP(U_18678,U_18674) = hAPP(U_18678,U_18676) )
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_18678,U_18674)),hAPP(U_18678,U_18676)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18672,U_18672)),hAPP(hAPP(c_Product__Type_OPair(U_18672,U_18672),U_18674),U_18676)),c_List_Omeasures(U_18672,hAPP(hAPP(c_List_Olist_OCons(tc_fun(U_18672,tc_Nat_Onat)),U_18678),U_18680)))) ) ),
    inference(miniscope,[status(thm)],[f_4583_2]) ).

cnf(f_4583_4,plain,
    ( hAPP(U_18678,U_18674) = hAPP(U_18678,U_18676)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_18678,U_18674)),hAPP(U_18678,U_18676)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18672,U_18672)),hAPP(hAPP(c_Product__Type_OPair(U_18672,U_18672),U_18674),U_18676)),c_List_Omeasures(U_18672,hAPP(hAPP(c_List_Olist_OCons(tc_fun(U_18672,tc_Nat_Onat)),U_18678),U_18680)))) ),
    inference(clausify,[status(thm)],[f_4583_3]) ).

cnf(f_4583_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_18672,U_18672)),hAPP(hAPP(c_Product__Type_OPair(U_18672,U_18672),U_18674),U_18676)),c_List_Omeasures(U_18672,U_18680)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_18678,U_18674)),hAPP(U_18678,U_18676)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18672,U_18672)),hAPP(hAPP(c_Product__Type_OPair(U_18672,U_18672),U_18674),U_18676)),c_List_Omeasures(U_18672,hAPP(hAPP(c_List_Olist_OCons(tc_fun(U_18672,tc_Nat_Onat)),U_18678),U_18680)))) ),
    inference(clausify,[status(thm)],[f_4583_3]) ).

cnf(f_4583_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_18679,U_18675)),hAPP(U_18679,U_18677)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_18673,U_18673)),hAPP(hAPP(c_Product__Type_OPair(U_18673,U_18673),U_18675),U_18677)),c_List_Omeasures(U_18673,hAPP(hAPP(c_List_Olist_OCons(tc_fun(U_18673,tc_Nat_Onat)),U_18679),U_18681)))) ),
    inference(clausify,[status(thm)],[f_4583_3]) ).

cnf(f_4583_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18673,U_18673)),hAPP(hAPP(c_Product__Type_OPair(U_18673,U_18673),U_18675),U_18677)),c_List_Omeasures(U_18673,U_18681)))
    | hAPP(U_18679,U_18675) != hAPP(U_18679,U_18677)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_18673,U_18673)),hAPP(hAPP(c_Product__Type_OPair(U_18673,U_18673),U_18675),U_18677)),c_List_Omeasures(U_18673,hAPP(hAPP(c_List_Olist_OCons(tc_fun(U_18673,tc_Nat_Onat)),U_18679),U_18681)))) ),
    inference(clausify,[status(thm)],[f_4583_3]) ).

fof(f_4584_1,plain,
    ! [V_s_2,V_g_2,V_h_2,V_f_2,T_c,T_d,V_xs_2,T_b] :
      ( hAPP(c_List_Ofoldl(T_d,T_b,hAPP(c_COMBC(T_b,T_d,T_d),V_f_2),hAPP(V_h_2,V_s_2)),V_xs_2) = hAPP(V_h_2,hAPP(c_List_Ofoldl(T_c,T_b,hAPP(c_COMBC(T_b,T_c,T_c),V_g_2),V_s_2),V_xs_2))
      | ? [B_x] :
          ( hAPP(c_Fun_Ocomp(T_d,T_d,T_c,hAPP(V_f_2,B_x)),V_h_2) != hAPP(c_Fun_Ocomp(T_c,T_d,T_c,V_h_2),hAPP(V_g_2,B_x))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_foldl__apply]) ).

fof(f_4584_2,plain,
    ! [U_18690,U_18689,U_18688,U_18687,U_18686,U_18685,U_18684,U_18683] :
      ( hAPP(c_List_Ofoldl(U_18685,U_18683,hAPP(c_COMBC(U_18683,U_18685,U_18685),U_18687),hAPP(U_18688,U_18690)),U_18684) = hAPP(U_18688,hAPP(c_List_Ofoldl(U_18686,U_18683,hAPP(c_COMBC(U_18683,U_18686,U_18686),U_18689),U_18690),U_18684))
      | ? [U_18682] :
          ( hAPP(c_Fun_Ocomp(U_18685,U_18685,U_18686,hAPP(U_18687,U_18682)),U_18688) != hAPP(c_Fun_Ocomp(U_18686,U_18685,U_18686,U_18688),hAPP(U_18689,U_18682))
          & hBOOL(hAPP(hAPP(c_member(U_18683),U_18682),hAPP(c_List_Oset(U_18683),U_18684))) ) ),
    inference(variable_rename,[status(thm)],[f_4584_1]) ).

fof(f_4584_3,plain,
    ! [U_18690,U_18689,U_18688,U_18687,U_18686,U_18685,U_18684,U_18683] :
      ( hAPP(c_List_Ofoldl(U_18685,U_18683,hAPP(c_COMBC(U_18683,U_18685,U_18685),U_18687),hAPP(U_18688,U_18690)),U_18684) = hAPP(U_18688,hAPP(c_List_Ofoldl(U_18686,U_18683,hAPP(c_COMBC(U_18683,U_18686,U_18686),U_18689),U_18690),U_18684))
      | ( hAPP(c_Fun_Ocomp(U_18685,U_18685,U_18686,hAPP(U_18687,sK470(U_18690,U_18689,U_18688,U_18687,U_18686,U_18685,U_18684,U_18683))),U_18688) != hAPP(c_Fun_Ocomp(U_18686,U_18685,U_18686,U_18688),hAPP(U_18689,sK470(U_18690,U_18689,U_18688,U_18687,U_18686,U_18685,U_18684,U_18683)))
        & hBOOL(hAPP(hAPP(c_member(U_18683),sK470(U_18690,U_18689,U_18688,U_18687,U_18686,U_18685,U_18684,U_18683)),hAPP(c_List_Oset(U_18683),U_18684))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK470]),skolemize(U_18682,sK470(U_18690,U_18689,U_18688,U_18687,U_18686,U_18685,U_18684,U_18683))],[f_4584_2]) ).

cnf(f_4584_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18683),sK470(U_18690,U_18689,U_18688,U_18687,U_18686,U_18685,U_18684,U_18683)),hAPP(c_List_Oset(U_18683),U_18684)))
    | hAPP(c_List_Ofoldl(U_18685,U_18683,hAPP(c_COMBC(U_18683,U_18685,U_18685),U_18687),hAPP(U_18688,U_18690)),U_18684) = hAPP(U_18688,hAPP(c_List_Ofoldl(U_18686,U_18683,hAPP(c_COMBC(U_18683,U_18686,U_18686),U_18689),U_18690),U_18684)) ),
    inference(clausify,[status(thm)],[f_4584_3]) ).

cnf(f_4584_5,plain,
    ( hAPP(c_Fun_Ocomp(U_18685,U_18685,U_18686,hAPP(U_18687,sK470(U_18690,U_18689,U_18688,U_18687,U_18686,U_18685,U_18684,U_18683))),U_18688) != hAPP(c_Fun_Ocomp(U_18686,U_18685,U_18686,U_18688),hAPP(U_18689,sK470(U_18690,U_18689,U_18688,U_18687,U_18686,U_18685,U_18684,U_18683)))
    | hAPP(c_List_Ofoldl(U_18685,U_18683,hAPP(c_COMBC(U_18683,U_18685,U_18685),U_18687),hAPP(U_18688,U_18690)),U_18684) = hAPP(U_18688,hAPP(c_List_Ofoldl(U_18686,U_18683,hAPP(c_COMBC(U_18683,U_18686,U_18686),U_18689),U_18690),U_18684)) ),
    inference(clausify,[status(thm)],[f_4584_3]) ).

fof(f_4585_1,plain,
    ! [V_g_2,V_f_2,T_b,T_c] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,T_c)),V_f_2),V_g_2))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBS(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),V_g_2))))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) )
        & ( ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBS(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),V_g_2))))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,T_c)),V_f_2),V_g_2)) ) )
      | ~ class_Enum_Oenum(T_b)
      | ~ class_Orderings_Oorder(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_order__fun_I2_J]) ).

fof(f_4585_2,plain,
    ! [U_18694,U_18693,U_18692,U_18691] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_18692,U_18691)),U_18693),U_18694))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(U_18692),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_18692),c_fNot),hAPP(hAPP(c_COMBS(U_18692,U_18691,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_18691,tc_fun(U_18691,tc_HOL_Obool),U_18692),c_fequal),U_18693)),U_18694))))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18692,U_18691)),U_18693),U_18694)) )
        & ( ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(U_18692),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_18692),c_fNot),hAPP(hAPP(c_COMBS(U_18692,U_18691,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_18691,tc_fun(U_18691,tc_HOL_Obool),U_18692),c_fequal),U_18693)),U_18694))))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18692,U_18691)),U_18693),U_18694)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_18692,U_18691)),U_18693),U_18694)) ) )
      | ~ class_Enum_Oenum(U_18692)
      | ~ class_Orderings_Oorder(U_18691) ),
    inference(variable_rename,[status(thm)],[f_4585_1]) ).

cnf(f_4585_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18692,U_18691)),U_18693),U_18694))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_18692,U_18691)),U_18693),U_18694))
    | ~ class_Enum_Oenum(U_18692)
    | ~ class_Orderings_Oorder(U_18691) ),
    inference(clausify,[status(thm)],[f_4585_2]) ).

cnf(f_4585_4,plain,
    ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(U_18692),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_18692),c_fNot),hAPP(hAPP(c_COMBS(U_18692,U_18691,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_18691,tc_fun(U_18691,tc_HOL_Obool),U_18692),c_fequal),U_18693)),U_18694))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_18692,U_18691)),U_18693),U_18694))
    | ~ class_Enum_Oenum(U_18692)
    | ~ class_Orderings_Oorder(U_18691) ),
    inference(clausify,[status(thm)],[f_4585_2]) ).

cnf(f_4585_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_18692,U_18691)),U_18693),U_18694))
    | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(U_18692),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_18692),c_fNot),hAPP(hAPP(c_COMBS(U_18692,U_18691,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_18691,tc_fun(U_18691,tc_HOL_Obool),U_18692),c_fequal),U_18693)),U_18694))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18692,U_18691)),U_18693),U_18694))
    | ~ class_Enum_Oenum(U_18692)
    | ~ class_Orderings_Oorder(U_18691) ),
    inference(clausify,[status(thm)],[f_4585_2]) ).

fof(f_4586_1,plain,
    ! [V_P_2,T_b,T_c] :
      ( ( ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(T_b,T_c)),V_P_2))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_Enum_Oenum__class_Oenum__ex(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,T_c),V_P_2)),c_Product__Type_OPair(T_b,T_c))))) )
        & ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_Enum_Oenum__class_Oenum__ex(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,T_c),V_P_2)),c_Product__Type_OPair(T_b,T_c)))))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(T_b,T_c)),V_P_2)) ) )
      | ~ class_Enum_Oenum(T_b)
      | ~ class_Enum_Oenum(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_enum__ex__prod__def]) ).

fof(f_4586_2,plain,
    ! [U_18697,U_18696,U_18695] :
      ( ( ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(U_18696,U_18695)),U_18697))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(U_18696),hAPP(hAPP(c_COMBB(tc_fun(U_18695,tc_HOL_Obool),tc_HOL_Obool,U_18696),c_Enum_Oenum__class_Oenum__ex(U_18695)),hAPP(hAPP(c_COMBB(tc_fun(U_18695,tc_prod(U_18696,U_18695)),tc_fun(U_18695,tc_HOL_Obool),U_18696),hAPP(c_COMBB(tc_prod(U_18696,U_18695),tc_HOL_Obool,U_18695),U_18697)),c_Product__Type_OPair(U_18696,U_18695))))) )
        & ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(U_18696),hAPP(hAPP(c_COMBB(tc_fun(U_18695,tc_HOL_Obool),tc_HOL_Obool,U_18696),c_Enum_Oenum__class_Oenum__ex(U_18695)),hAPP(hAPP(c_COMBB(tc_fun(U_18695,tc_prod(U_18696,U_18695)),tc_fun(U_18695,tc_HOL_Obool),U_18696),hAPP(c_COMBB(tc_prod(U_18696,U_18695),tc_HOL_Obool,U_18695),U_18697)),c_Product__Type_OPair(U_18696,U_18695)))))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(U_18696,U_18695)),U_18697)) ) )
      | ~ class_Enum_Oenum(U_18696)
      | ~ class_Enum_Oenum(U_18695) ),
    inference(variable_rename,[status(thm)],[f_4586_1]) ).

cnf(f_4586_3,plain,
    ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(U_18696),hAPP(hAPP(c_COMBB(tc_fun(U_18695,tc_HOL_Obool),tc_HOL_Obool,U_18696),c_Enum_Oenum__class_Oenum__ex(U_18695)),hAPP(hAPP(c_COMBB(tc_fun(U_18695,tc_prod(U_18696,U_18695)),tc_fun(U_18695,tc_HOL_Obool),U_18696),hAPP(c_COMBB(tc_prod(U_18696,U_18695),tc_HOL_Obool,U_18695),U_18697)),c_Product__Type_OPair(U_18696,U_18695)))))
    | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(U_18696,U_18695)),U_18697))
    | ~ class_Enum_Oenum(U_18696)
    | ~ class_Enum_Oenum(U_18695) ),
    inference(clausify,[status(thm)],[f_4586_2]) ).

cnf(f_4586_4,plain,
    ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(U_18696,U_18695)),U_18697))
    | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(U_18696),hAPP(hAPP(c_COMBB(tc_fun(U_18695,tc_HOL_Obool),tc_HOL_Obool,U_18696),c_Enum_Oenum__class_Oenum__ex(U_18695)),hAPP(hAPP(c_COMBB(tc_fun(U_18695,tc_prod(U_18696,U_18695)),tc_fun(U_18695,tc_HOL_Obool),U_18696),hAPP(c_COMBB(tc_prod(U_18696,U_18695),tc_HOL_Obool,U_18695),U_18697)),c_Product__Type_OPair(U_18696,U_18695)))))
    | ~ class_Enum_Oenum(U_18696)
    | ~ class_Enum_Oenum(U_18695) ),
    inference(clausify,[status(thm)],[f_4586_2]) ).

fof(f_4587_1,plain,
    ! [V_P_2,T_b] :
      ( ( ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),V_P_2)) )
        & ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),V_P_2))
          | ! [B_x1] : ~ hBOOL(hAPP(V_P_2,B_x1)) ) )
      | ~ class_Enum_Oenum(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_exists__code]) ).

fof(f_4587_2,plain,
    ! [U_18701,U_18700] :
      ( ( ( ? [U_18699] : hBOOL(hAPP(U_18701,U_18699))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(U_18700),U_18701)) )
        & ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(U_18700),U_18701))
          | ! [U_18698] : ~ hBOOL(hAPP(U_18701,U_18698)) ) )
      | ~ class_Enum_Oenum(U_18700) ),
    inference(variable_rename,[status(thm)],[f_4587_1]) ).

fof(f_4587_3,plain,
    ! [U_18701,U_18700] :
      ( ( ( hBOOL(hAPP(U_18701,sK471(U_18701,U_18700)))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(U_18700),U_18701)) )
        & ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(U_18700),U_18701))
          | ! [U_18698] : ~ hBOOL(hAPP(U_18701,U_18698)) ) )
      | ~ class_Enum_Oenum(U_18700) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK471]),skolemize(U_18699,sK471(U_18701,U_18700))],[f_4587_2]) ).

cnf(f_4587_4,plain,
    ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(U_18700),U_18701))
    | ~ hBOOL(hAPP(U_18701,U_18698))
    | ~ class_Enum_Oenum(U_18700) ),
    inference(clausify,[status(thm)],[f_4587_3]) ).

cnf(f_4587_5,plain,
    ( hBOOL(hAPP(U_18701,sK471(U_18701,U_18700)))
    | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(U_18700),U_18701))
    | ~ class_Enum_Oenum(U_18700) ),
    inference(clausify,[status(thm)],[f_4587_3]) ).

fof(f_4588_1,plain,
    ! [V_P_2,T_b] :
      ( ( ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),V_P_2))
          | ! [B_x1] : ~ hBOOL(hAPP(V_P_2,B_x1)) )
        & ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),V_P_2)) ) )
      | ~ class_Enum_Oenum(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_enum__ex]) ).

fof(f_4588_2,plain,
    ! [U_18705,U_18704] :
      ( ( ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(U_18704),U_18705))
          | ! [U_18703] : ~ hBOOL(hAPP(U_18705,U_18703)) )
        & ( ? [U_18702] : hBOOL(hAPP(U_18705,U_18702))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(U_18704),U_18705)) ) )
      | ~ class_Enum_Oenum(U_18704) ),
    inference(variable_rename,[status(thm)],[f_4588_1]) ).

fof(f_4588_3,plain,
    ! [U_18705,U_18704] :
      ( ( ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(U_18704),U_18705))
          | ! [U_18703] : ~ hBOOL(hAPP(U_18705,U_18703)) )
        & ( hBOOL(hAPP(U_18705,sK472(U_18705,U_18704)))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(U_18704),U_18705)) ) )
      | ~ class_Enum_Oenum(U_18704) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK472]),skolemize(U_18702,sK472(U_18705,U_18704))],[f_4588_2]) ).

cnf(f_4588_4,plain,
    ( hBOOL(hAPP(U_18705,sK472(U_18705,U_18704)))
    | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(U_18704),U_18705))
    | ~ class_Enum_Oenum(U_18704) ),
    inference(clausify,[status(thm)],[f_4588_3]) ).

cnf(f_4588_5,plain,
    ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(U_18704),U_18705))
    | ~ hBOOL(hAPP(U_18705,U_18703))
    | ~ class_Enum_Oenum(U_18704) ),
    inference(clausify,[status(thm)],[f_4588_3]) ).

fof(f_4589_1,plain,
    ! [V_P_2,V_ys_2,T_c,V_xs_2,T_b] :
      ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)))
      | ( ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Otake(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2))),V_xs_2)),hAPP(hAPP(c_List_Otake(T_c),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2))),V_ys_2))))
        & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Otake(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2))),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),hAPP(hAPP(c_List_Otake(T_c),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2))),V_ys_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_zip__obtain__same__length]) ).

fof(f_4589_2,plain,
    ! [U_18710,U_18709,U_18708,U_18707,U_18706] :
      ( hBOOL(hAPP(U_18710,hAPP(hAPP(c_List_Ozip(U_18706,U_18708),U_18707),U_18709)))
      | ( ~ hBOOL(hAPP(U_18710,hAPP(hAPP(c_List_Ozip(U_18706,U_18708),hAPP(hAPP(c_List_Otake(U_18706),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18706)),U_18707)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18708)),U_18709))),U_18707)),hAPP(hAPP(c_List_Otake(U_18708),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18706)),U_18707)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18708)),U_18709))),U_18709))))
        & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18706)),hAPP(hAPP(c_List_Otake(U_18706),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18706)),U_18707)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18708)),U_18709))),U_18707)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18708)),hAPP(hAPP(c_List_Otake(U_18708),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18706)),U_18707)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18708)),U_18709))),U_18709)) ) ),
    inference(variable_rename,[status(thm)],[f_4589_1]) ).

cnf(f_4589_3,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18706)),hAPP(hAPP(c_List_Otake(U_18706),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18706)),U_18707)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18708)),U_18709))),U_18707)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18708)),hAPP(hAPP(c_List_Otake(U_18708),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18706)),U_18707)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18708)),U_18709))),U_18709))
    | hBOOL(hAPP(U_18710,hAPP(hAPP(c_List_Ozip(U_18706,U_18708),U_18707),U_18709))) ),
    inference(clausify,[status(thm)],[f_4589_2]) ).

cnf(f_4589_4,plain,
    ( ~ hBOOL(hAPP(U_18710,hAPP(hAPP(c_List_Ozip(U_18706,U_18708),hAPP(hAPP(c_List_Otake(U_18706),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18706)),U_18707)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18708)),U_18709))),U_18707)),hAPP(hAPP(c_List_Otake(U_18708),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18706)),U_18707)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18708)),U_18709))),U_18709))))
    | hBOOL(hAPP(U_18710,hAPP(hAPP(c_List_Ozip(U_18706,U_18708),U_18707),U_18709))) ),
    inference(clausify,[status(thm)],[f_4589_2]) ).

fof(f_4590_1,plain,
    ! [V_seed_2,V_size_2,V_nrandom_2,V_R_2] : c_New__Random__Sequence_Opos__not__random__dseq(V_R_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__not__seq(hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2)),
    inference(fof_nnf,[status(thm)],[fact_pos__not__random__dseq__def]) ).

fof(f_4590_2,plain,
    ! [U_18714,U_18713,U_18712,U_18711] : c_New__Random__Sequence_Opos__not__random__dseq(U_18711,U_18712,U_18713,U_18714) = c_New__DSequence_Opos__not__seq(hAPP(hAPP(hAPP(U_18711,U_18712),U_18713),U_18714)),
    inference(variable_rename,[status(thm)],[f_4590_1]) ).

cnf(f_4590_3,plain,
    c_New__Random__Sequence_Opos__not__random__dseq(U_18711,U_18712,U_18713,U_18714) = c_New__DSequence_Opos__not__seq(hAPP(hAPP(hAPP(U_18711,U_18712),U_18713),U_18714)),
    inference(clausify,[status(thm)],[f_4590_2]) ).

fof(f_4591_1,plain,
    ! [V_ys_2,V_P_2,V_xs_2,T_b] :
      ( c_List_OdropWhile(T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = c_List_OdropWhile(T_b,V_P_2,V_ys_2)
      | ? [B_x] :
          ( ~ hBOOL(hAPP(V_P_2,B_x))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_dropWhile__append2]) ).

fof(f_4591_2,plain,
    ! [U_18719,U_18718,U_18717,U_18716] :
      ( c_List_OdropWhile(U_18716,U_18718,hAPP(hAPP(c_List_Oappend(U_18716),U_18717),U_18719)) = c_List_OdropWhile(U_18716,U_18718,U_18719)
      | ? [U_18715] :
          ( ~ hBOOL(hAPP(U_18718,U_18715))
          & hBOOL(hAPP(hAPP(c_member(U_18716),U_18715),hAPP(c_List_Oset(U_18716),U_18717))) ) ),
    inference(variable_rename,[status(thm)],[f_4591_1]) ).

fof(f_4591_3,plain,
    ! [U_18719,U_18718,U_18717,U_18716] :
      ( c_List_OdropWhile(U_18716,U_18718,hAPP(hAPP(c_List_Oappend(U_18716),U_18717),U_18719)) = c_List_OdropWhile(U_18716,U_18718,U_18719)
      | ( ~ hBOOL(hAPP(U_18718,sK473(U_18719,U_18718,U_18717,U_18716)))
        & hBOOL(hAPP(hAPP(c_member(U_18716),sK473(U_18719,U_18718,U_18717,U_18716)),hAPP(c_List_Oset(U_18716),U_18717))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK473]),skolemize(U_18715,sK473(U_18719,U_18718,U_18717,U_18716))],[f_4591_2]) ).

cnf(f_4591_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18716),sK473(U_18719,U_18718,U_18717,U_18716)),hAPP(c_List_Oset(U_18716),U_18717)))
    | c_List_OdropWhile(U_18716,U_18718,hAPP(hAPP(c_List_Oappend(U_18716),U_18717),U_18719)) = c_List_OdropWhile(U_18716,U_18718,U_18719) ),
    inference(clausify,[status(thm)],[f_4591_3]) ).

cnf(f_4591_5,plain,
    ( ~ hBOOL(hAPP(U_18718,sK473(U_18719,U_18718,U_18717,U_18716)))
    | c_List_OdropWhile(U_18716,U_18718,hAPP(hAPP(c_List_Oappend(U_18716),U_18717),U_18719)) = c_List_OdropWhile(U_18716,U_18718,U_18719) ),
    inference(clausify,[status(thm)],[f_4591_3]) ).

fof(f_4592_1,plain,
    ! [V_P_2,V_b_2,T_c,V_a_2,T_b] :
      ( c_List_Olist__all2(T_b,T_c,V_P_2,V_a_2,V_b_2)
      | ? [B_n] :
          ( ~ hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_a_2),B_n)),hAPP(hAPP(c_List_Onth(T_c),V_b_2),B_n)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_a_2))) )
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_a_2) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_b_2) ),
    inference(fof_nnf,[status(thm)],[fact_list__all2__all__nthI]) ).

fof(f_4592_2,plain,
    ! [U_18725,U_18724,U_18723,U_18722,U_18721] :
      ( c_List_Olist__all2(U_18721,U_18723,U_18725,U_18722,U_18724)
      | ? [U_18720] :
          ( ~ hBOOL(hAPP(hAPP(U_18725,hAPP(hAPP(c_List_Onth(U_18721),U_18722),U_18720)),hAPP(hAPP(c_List_Onth(U_18723),U_18724),U_18720)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18720),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18721)),U_18722))) )
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18721)),U_18722) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18723)),U_18724) ),
    inference(variable_rename,[status(thm)],[f_4592_1]) ).

fof(f_4592_3,plain,
    ! [U_18725,U_18724,U_18723,U_18722,U_18721] :
      ( c_List_Olist__all2(U_18721,U_18723,U_18725,U_18722,U_18724)
      | ( ~ hBOOL(hAPP(hAPP(U_18725,hAPP(hAPP(c_List_Onth(U_18721),U_18722),sK474(U_18725,U_18724,U_18723,U_18722,U_18721))),hAPP(hAPP(c_List_Onth(U_18723),U_18724),sK474(U_18725,U_18724,U_18723,U_18722,U_18721))))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK474(U_18725,U_18724,U_18723,U_18722,U_18721)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18721)),U_18722))) )
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18721)),U_18722) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18723)),U_18724) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK474]),skolemize(U_18720,sK474(U_18725,U_18724,U_18723,U_18722,U_18721))],[f_4592_2]) ).

cnf(f_4592_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK474(U_18725,U_18724,U_18723,U_18722,U_18721)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18721)),U_18722)))
    | c_List_Olist__all2(U_18721,U_18723,U_18725,U_18722,U_18724)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18721)),U_18722) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18723)),U_18724) ),
    inference(clausify,[status(thm)],[f_4592_3]) ).

cnf(f_4592_5,plain,
    ( ~ hBOOL(hAPP(hAPP(U_18725,hAPP(hAPP(c_List_Onth(U_18721),U_18722),sK474(U_18725,U_18724,U_18723,U_18722,U_18721))),hAPP(hAPP(c_List_Onth(U_18723),U_18724),sK474(U_18725,U_18724,U_18723,U_18722,U_18721))))
    | c_List_Olist__all2(U_18721,U_18723,U_18725,U_18722,U_18724)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18721)),U_18722) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18723)),U_18724) ),
    inference(clausify,[status(thm)],[f_4592_3]) ).

fof(f_4593_1,plain,
    ! [V_A_2,T_b] :
      ( ? [B_x] :
          ( ! [B_y] :
              ( B_y = B_x
              | ~ hBOOL(hAPP(c_List_Odistinct(T_b),B_y))
              | ~ c_List_Olinorder__class_Osorted(T_b,B_y)
              | hAPP(c_List_Oset(T_b),B_y) != V_A_2 )
          & hBOOL(hAPP(c_List_Odistinct(T_b),B_x))
          & c_List_Olinorder__class_Osorted(T_b,B_x)
          & hAPP(c_List_Oset(T_b),B_x) = V_A_2 )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_finite__sorted__distinct__unique]) ).

fof(f_4593_2,plain,
    ! [U_18729,U_18728] :
      ( ? [U_18727] :
          ( ! [U_18726] :
              ( U_18726 = U_18727
              | ~ hBOOL(hAPP(c_List_Odistinct(U_18728),U_18726))
              | ~ c_List_Olinorder__class_Osorted(U_18728,U_18726)
              | hAPP(c_List_Oset(U_18728),U_18726) != U_18729 )
          & hBOOL(hAPP(c_List_Odistinct(U_18728),U_18727))
          & c_List_Olinorder__class_Osorted(U_18728,U_18727)
          & hAPP(c_List_Oset(U_18728),U_18727) = U_18729 )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_18728),U_18729))
      | ~ class_Orderings_Olinorder(U_18728) ),
    inference(variable_rename,[status(thm)],[f_4593_1]) ).

fof(f_4593_3,plain,
    ! [U_18729,U_18728] :
      ( ( ! [U_18726] :
            ( U_18726 = sK475(U_18729,U_18728)
            | ~ hBOOL(hAPP(c_List_Odistinct(U_18728),U_18726))
            | ~ c_List_Olinorder__class_Osorted(U_18728,U_18726)
            | hAPP(c_List_Oset(U_18728),U_18726) != U_18729 )
        & hBOOL(hAPP(c_List_Odistinct(U_18728),sK475(U_18729,U_18728)))
        & c_List_Olinorder__class_Osorted(U_18728,sK475(U_18729,U_18728))
        & hAPP(c_List_Oset(U_18728),sK475(U_18729,U_18728)) = U_18729 )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_18728),U_18729))
      | ~ class_Orderings_Olinorder(U_18728) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK475]),skolemize(U_18727,sK475(U_18729,U_18728))],[f_4593_2]) ).

cnf(f_4593_4,plain,
    ( hAPP(c_List_Oset(U_18728),sK475(U_18729,U_18728)) = U_18729
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_18728),U_18729))
    | ~ class_Orderings_Olinorder(U_18728) ),
    inference(clausify,[status(thm)],[f_4593_3]) ).

cnf(f_4593_5,plain,
    ( c_List_Olinorder__class_Osorted(U_18728,sK475(U_18729,U_18728))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_18728),U_18729))
    | ~ class_Orderings_Olinorder(U_18728) ),
    inference(clausify,[status(thm)],[f_4593_3]) ).

cnf(f_4593_6,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_18728),sK475(U_18729,U_18728)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_18728),U_18729))
    | ~ class_Orderings_Olinorder(U_18728) ),
    inference(clausify,[status(thm)],[f_4593_3]) ).

cnf(f_4593_7,plain,
    ( U_18726 = sK475(U_18729,U_18728)
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18728),U_18726))
    | ~ c_List_Olinorder__class_Osorted(U_18728,U_18726)
    | hAPP(c_List_Oset(U_18728),U_18726) != U_18729
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_18728),U_18729))
    | ~ class_Orderings_Olinorder(U_18728) ),
    inference(clausify,[status(thm)],[f_4593_3]) ).

fof(f_4594_1,plain,
    ! [V_ys_2,V_P_2,V_xs_2,T_b] :
      ( c_List_OtakeWhile(T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),c_List_OtakeWhile(T_b,V_P_2,V_ys_2))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(V_P_2,B_x))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_takeWhile__append2]) ).

fof(f_4594_2,plain,
    ! [U_18734,U_18733,U_18732,U_18731] :
      ( c_List_OtakeWhile(U_18731,U_18733,hAPP(hAPP(c_List_Oappend(U_18731),U_18732),U_18734)) = hAPP(hAPP(c_List_Oappend(U_18731),U_18732),c_List_OtakeWhile(U_18731,U_18733,U_18734))
      | ? [U_18730] :
          ( ~ hBOOL(hAPP(U_18733,U_18730))
          & hBOOL(hAPP(hAPP(c_member(U_18731),U_18730),hAPP(c_List_Oset(U_18731),U_18732))) ) ),
    inference(variable_rename,[status(thm)],[f_4594_1]) ).

fof(f_4594_3,plain,
    ! [U_18734,U_18733,U_18732,U_18731] :
      ( c_List_OtakeWhile(U_18731,U_18733,hAPP(hAPP(c_List_Oappend(U_18731),U_18732),U_18734)) = hAPP(hAPP(c_List_Oappend(U_18731),U_18732),c_List_OtakeWhile(U_18731,U_18733,U_18734))
      | ( ~ hBOOL(hAPP(U_18733,sK476(U_18734,U_18733,U_18732,U_18731)))
        & hBOOL(hAPP(hAPP(c_member(U_18731),sK476(U_18734,U_18733,U_18732,U_18731)),hAPP(c_List_Oset(U_18731),U_18732))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK476]),skolemize(U_18730,sK476(U_18734,U_18733,U_18732,U_18731))],[f_4594_2]) ).

cnf(f_4594_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18731),sK476(U_18734,U_18733,U_18732,U_18731)),hAPP(c_List_Oset(U_18731),U_18732)))
    | c_List_OtakeWhile(U_18731,U_18733,hAPP(hAPP(c_List_Oappend(U_18731),U_18732),U_18734)) = hAPP(hAPP(c_List_Oappend(U_18731),U_18732),c_List_OtakeWhile(U_18731,U_18733,U_18734)) ),
    inference(clausify,[status(thm)],[f_4594_3]) ).

cnf(f_4594_5,plain,
    ( ~ hBOOL(hAPP(U_18733,sK476(U_18734,U_18733,U_18732,U_18731)))
    | c_List_OtakeWhile(U_18731,U_18733,hAPP(hAPP(c_List_Oappend(U_18731),U_18732),U_18734)) = hAPP(hAPP(c_List_Oappend(U_18731),U_18732),c_List_OtakeWhile(U_18731,U_18733,U_18734)) ),
    inference(clausify,[status(thm)],[f_4594_3]) ).

fof(f_4595_1,plain,
    ! [V_a_2,V_f_2,V_xs_2,T_b,T_c] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_a_2),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_xs_2)
      | ? [B_x] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_a_2)),hAPP(V_f_2,B_x)))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) )
      | ~ class_Orderings_Olinorder(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_insort__is__Cons]) ).

fof(f_4595_2,plain,
    ! [U_18740,U_18739,U_18738,U_18737,U_18736] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18737,U_18736,U_18739),U_18740),U_18738) = hAPP(hAPP(c_List_Olist_OCons(U_18737),U_18740),U_18738)
      | ? [U_18735] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18736),hAPP(U_18739,U_18740)),hAPP(U_18739,U_18735)))
          & hBOOL(hAPP(hAPP(c_member(U_18737),U_18735),hAPP(c_List_Oset(U_18737),U_18738))) )
      | ~ class_Orderings_Olinorder(U_18736) ),
    inference(variable_rename,[status(thm)],[f_4595_1]) ).

fof(f_4595_3,plain,
    ! [U_18740,U_18739,U_18738,U_18737,U_18736] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18737,U_18736,U_18739),U_18740),U_18738) = hAPP(hAPP(c_List_Olist_OCons(U_18737),U_18740),U_18738)
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18736),hAPP(U_18739,U_18740)),hAPP(U_18739,sK477(U_18740,U_18739,U_18738,U_18737,U_18736))))
        & hBOOL(hAPP(hAPP(c_member(U_18737),sK477(U_18740,U_18739,U_18738,U_18737,U_18736)),hAPP(c_List_Oset(U_18737),U_18738))) )
      | ~ class_Orderings_Olinorder(U_18736) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK477]),skolemize(U_18735,sK477(U_18740,U_18739,U_18738,U_18737,U_18736))],[f_4595_2]) ).

cnf(f_4595_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18737),sK477(U_18740,U_18739,U_18738,U_18737,U_18736)),hAPP(c_List_Oset(U_18737),U_18738)))
    | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18737,U_18736,U_18739),U_18740),U_18738) = hAPP(hAPP(c_List_Olist_OCons(U_18737),U_18740),U_18738)
    | ~ class_Orderings_Olinorder(U_18736) ),
    inference(clausify,[status(thm)],[f_4595_3]) ).

cnf(f_4595_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18736),hAPP(U_18739,U_18740)),hAPP(U_18739,sK477(U_18740,U_18739,U_18738,U_18737,U_18736))))
    | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18737,U_18736,U_18739),U_18740),U_18738) = hAPP(hAPP(c_List_Olist_OCons(U_18737),U_18740),U_18738)
    | ~ class_Orderings_Olinorder(U_18736) ),
    inference(clausify,[status(thm)],[f_4595_3]) ).

fof(f_4596_1,plain,
    ! [V_xs_2,V_x_2,V_ys_2,V_P_2,T_b] :
      ( ( hAPP(c_List_Ofilter(T_b,V_P_2),V_ys_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)
        | ! [B_us,B_vs] :
            ( V_xs_2 != hAPP(c_List_Ofilter(T_b,V_P_2),B_vs)
            | ~ hBOOL(hAPP(V_P_2,V_x_2))
            | ? [B_x] :
                ( hBOOL(hAPP(V_P_2,B_x))
                & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),B_us))) )
            | V_ys_2 != hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_vs)) ) )
      & ( ? [B_us,B_vs] :
            ( V_xs_2 = hAPP(c_List_Ofilter(T_b,V_P_2),B_vs)
            & hBOOL(hAPP(V_P_2,V_x_2))
            & ! [B_x] :
                ( ~ hBOOL(hAPP(V_P_2,B_x))
                | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),B_us))) )
            & V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_vs)) )
        | hAPP(c_List_Ofilter(T_b,V_P_2),V_ys_2) != hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_filter__eq__Cons__iff]) ).

fof(f_4596_2,plain,
    ! [U_18751,U_18750,U_18749,U_18748,U_18747] :
      ( ( hAPP(c_List_Ofilter(U_18747,U_18748),U_18749) = hAPP(hAPP(c_List_Olist_OCons(U_18747),U_18750),U_18751)
        | ! [U_18746,U_18745] :
            ( U_18751 != hAPP(c_List_Ofilter(U_18747,U_18748),U_18745)
            | ~ hBOOL(hAPP(U_18748,U_18750))
            | ? [U_18744] :
                ( hBOOL(hAPP(U_18748,U_18744))
                & hBOOL(hAPP(hAPP(c_member(U_18747),U_18744),hAPP(c_List_Oset(U_18747),U_18746))) )
            | U_18749 != hAPP(hAPP(c_List_Oappend(U_18747),U_18746),hAPP(hAPP(c_List_Olist_OCons(U_18747),U_18750),U_18745)) ) )
      & ( ? [U_18743,U_18742] :
            ( U_18751 = hAPP(c_List_Ofilter(U_18747,U_18748),U_18742)
            & hBOOL(hAPP(U_18748,U_18750))
            & ! [U_18741] :
                ( ~ hBOOL(hAPP(U_18748,U_18741))
                | ~ hBOOL(hAPP(hAPP(c_member(U_18747),U_18741),hAPP(c_List_Oset(U_18747),U_18743))) )
            & U_18749 = hAPP(hAPP(c_List_Oappend(U_18747),U_18743),hAPP(hAPP(c_List_Olist_OCons(U_18747),U_18750),U_18742)) )
        | hAPP(c_List_Ofilter(U_18747,U_18748),U_18749) != hAPP(hAPP(c_List_Olist_OCons(U_18747),U_18750),U_18751) ) ),
    inference(variable_rename,[status(thm)],[f_4596_1]) ).

fof(f_4596_3,plain,
    ( ! [U_18761,U_18759,U_18757,U_18755,U_18753] :
        ( hAPP(c_List_Ofilter(U_18753,U_18755),U_18757) = hAPP(hAPP(c_List_Olist_OCons(U_18753),U_18759),U_18761)
        | ! [U_18746] :
            ( ! [U_18745] :
                ( U_18761 != hAPP(c_List_Ofilter(U_18753,U_18755),U_18745)
                | U_18757 != hAPP(hAPP(c_List_Oappend(U_18753),U_18746),hAPP(hAPP(c_List_Olist_OCons(U_18753),U_18759),U_18745)) )
            | ? [U_18744] :
                ( hBOOL(hAPP(U_18755,U_18744))
                & hBOOL(hAPP(hAPP(c_member(U_18753),U_18744),hAPP(c_List_Oset(U_18753),U_18746))) ) )
        | ~ hBOOL(hAPP(U_18755,U_18759)) )
    & ! [U_18760,U_18758,U_18756,U_18754,U_18752] :
        ( ( ? [U_18743] :
              ( ? [U_18742] :
                  ( U_18760 = hAPP(c_List_Ofilter(U_18752,U_18754),U_18742)
                  & U_18756 = hAPP(hAPP(c_List_Oappend(U_18752),U_18743),hAPP(hAPP(c_List_Olist_OCons(U_18752),U_18758),U_18742)) )
              & ! [U_18741] :
                  ( ~ hBOOL(hAPP(U_18754,U_18741))
                  | ~ hBOOL(hAPP(hAPP(c_member(U_18752),U_18741),hAPP(c_List_Oset(U_18752),U_18743))) ) )
          & hBOOL(hAPP(U_18754,U_18758)) )
        | hAPP(c_List_Ofilter(U_18752,U_18754),U_18756) != hAPP(hAPP(c_List_Olist_OCons(U_18752),U_18758),U_18760) ) ),
    inference(miniscope,[status(thm)],[f_4596_2]) ).

fof(f_4596_4,plain,
    ( ! [U_18761,U_18759,U_18757,U_18755,U_18753] :
        ( hAPP(c_List_Ofilter(U_18753,U_18755),U_18757) = hAPP(hAPP(c_List_Olist_OCons(U_18753),U_18759),U_18761)
        | ! [U_18746] :
            ( ! [U_18745] :
                ( U_18761 != hAPP(c_List_Ofilter(U_18753,U_18755),U_18745)
                | U_18757 != hAPP(hAPP(c_List_Oappend(U_18753),U_18746),hAPP(hAPP(c_List_Olist_OCons(U_18753),U_18759),U_18745)) )
            | ? [U_18744] :
                ( hBOOL(hAPP(U_18755,U_18744))
                & hBOOL(hAPP(hAPP(c_member(U_18753),U_18744),hAPP(c_List_Oset(U_18753),U_18746))) ) )
        | ~ hBOOL(hAPP(U_18755,U_18759)) )
    & ! [U_18760,U_18758,U_18756,U_18754,U_18752] :
        ( ( ? [U_18742] :
              ( U_18760 = hAPP(c_List_Ofilter(U_18752,U_18754),U_18742)
              & U_18756 = hAPP(hAPP(c_List_Oappend(U_18752),sK478(U_18760,U_18758,U_18756,U_18754,U_18752)),hAPP(hAPP(c_List_Olist_OCons(U_18752),U_18758),U_18742)) )
          & ! [U_18741] :
              ( ~ hBOOL(hAPP(U_18754,U_18741))
              | ~ hBOOL(hAPP(hAPP(c_member(U_18752),U_18741),hAPP(c_List_Oset(U_18752),sK478(U_18760,U_18758,U_18756,U_18754,U_18752)))) )
          & hBOOL(hAPP(U_18754,U_18758)) )
        | hAPP(c_List_Ofilter(U_18752,U_18754),U_18756) != hAPP(hAPP(c_List_Olist_OCons(U_18752),U_18758),U_18760) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK478]),skolemize(U_18743,sK478(U_18760,U_18758,U_18756,U_18754,U_18752))],[f_4596_3]) ).

fof(f_4596_5,plain,
    ( ! [U_18761,U_18759,U_18757,U_18755,U_18753] :
        ( hAPP(c_List_Ofilter(U_18753,U_18755),U_18757) = hAPP(hAPP(c_List_Olist_OCons(U_18753),U_18759),U_18761)
        | ! [U_18746] :
            ( ! [U_18745] :
                ( U_18761 != hAPP(c_List_Ofilter(U_18753,U_18755),U_18745)
                | U_18757 != hAPP(hAPP(c_List_Oappend(U_18753),U_18746),hAPP(hAPP(c_List_Olist_OCons(U_18753),U_18759),U_18745)) )
            | ? [U_18744] :
                ( hBOOL(hAPP(U_18755,U_18744))
                & hBOOL(hAPP(hAPP(c_member(U_18753),U_18744),hAPP(c_List_Oset(U_18753),U_18746))) ) )
        | ~ hBOOL(hAPP(U_18755,U_18759)) )
    & ! [U_18760,U_18758,U_18756,U_18754,U_18752] :
        ( ( U_18760 = hAPP(c_List_Ofilter(U_18752,U_18754),sK479(U_18760,U_18758,U_18756,U_18754,U_18752))
          & U_18756 = hAPP(hAPP(c_List_Oappend(U_18752),sK478(U_18760,U_18758,U_18756,U_18754,U_18752)),hAPP(hAPP(c_List_Olist_OCons(U_18752),U_18758),sK479(U_18760,U_18758,U_18756,U_18754,U_18752)))
          & ! [U_18741] :
              ( ~ hBOOL(hAPP(U_18754,U_18741))
              | ~ hBOOL(hAPP(hAPP(c_member(U_18752),U_18741),hAPP(c_List_Oset(U_18752),sK478(U_18760,U_18758,U_18756,U_18754,U_18752)))) )
          & hBOOL(hAPP(U_18754,U_18758)) )
        | hAPP(c_List_Ofilter(U_18752,U_18754),U_18756) != hAPP(hAPP(c_List_Olist_OCons(U_18752),U_18758),U_18760) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK479]),skolemize(U_18742,sK479(U_18760,U_18758,U_18756,U_18754,U_18752))],[f_4596_4]) ).

fof(f_4596_6,plain,
    ( ! [U_18761,U_18759,U_18757,U_18755,U_18753] :
        ( hAPP(c_List_Ofilter(U_18753,U_18755),U_18757) = hAPP(hAPP(c_List_Olist_OCons(U_18753),U_18759),U_18761)
        | ! [U_18746] :
            ( ! [U_18745] :
                ( U_18761 != hAPP(c_List_Ofilter(U_18753,U_18755),U_18745)
                | U_18757 != hAPP(hAPP(c_List_Oappend(U_18753),U_18746),hAPP(hAPP(c_List_Olist_OCons(U_18753),U_18759),U_18745)) )
            | ( hBOOL(hAPP(U_18755,sK480(U_18761,U_18759,U_18757,U_18755,U_18753,U_18746)))
              & hBOOL(hAPP(hAPP(c_member(U_18753),sK480(U_18761,U_18759,U_18757,U_18755,U_18753,U_18746)),hAPP(c_List_Oset(U_18753),U_18746))) ) )
        | ~ hBOOL(hAPP(U_18755,U_18759)) )
    & ! [U_18760,U_18758,U_18756,U_18754,U_18752] :
        ( ( U_18760 = hAPP(c_List_Ofilter(U_18752,U_18754),sK479(U_18760,U_18758,U_18756,U_18754,U_18752))
          & U_18756 = hAPP(hAPP(c_List_Oappend(U_18752),sK478(U_18760,U_18758,U_18756,U_18754,U_18752)),hAPP(hAPP(c_List_Olist_OCons(U_18752),U_18758),sK479(U_18760,U_18758,U_18756,U_18754,U_18752)))
          & ! [U_18741] :
              ( ~ hBOOL(hAPP(U_18754,U_18741))
              | ~ hBOOL(hAPP(hAPP(c_member(U_18752),U_18741),hAPP(c_List_Oset(U_18752),sK478(U_18760,U_18758,U_18756,U_18754,U_18752)))) )
          & hBOOL(hAPP(U_18754,U_18758)) )
        | hAPP(c_List_Ofilter(U_18752,U_18754),U_18756) != hAPP(hAPP(c_List_Olist_OCons(U_18752),U_18758),U_18760) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK480]),skolemize(U_18744,sK480(U_18761,U_18759,U_18757,U_18755,U_18753,U_18746))],[f_4596_5]) ).

cnf(f_4596_7,plain,
    ( hBOOL(hAPP(U_18754,U_18758))
    | hAPP(c_List_Ofilter(U_18752,U_18754),U_18756) != hAPP(hAPP(c_List_Olist_OCons(U_18752),U_18758),U_18760) ),
    inference(clausify,[status(thm)],[f_4596_6]) ).

cnf(f_4596_8,plain,
    ( ~ hBOOL(hAPP(U_18754,U_18741))
    | ~ hBOOL(hAPP(hAPP(c_member(U_18752),U_18741),hAPP(c_List_Oset(U_18752),sK478(U_18760,U_18758,U_18756,U_18754,U_18752))))
    | hAPP(c_List_Ofilter(U_18752,U_18754),U_18756) != hAPP(hAPP(c_List_Olist_OCons(U_18752),U_18758),U_18760) ),
    inference(clausify,[status(thm)],[f_4596_6]) ).

cnf(f_4596_9,plain,
    ( U_18756 = hAPP(hAPP(c_List_Oappend(U_18752),sK478(U_18760,U_18758,U_18756,U_18754,U_18752)),hAPP(hAPP(c_List_Olist_OCons(U_18752),U_18758),sK479(U_18760,U_18758,U_18756,U_18754,U_18752)))
    | hAPP(c_List_Ofilter(U_18752,U_18754),U_18756) != hAPP(hAPP(c_List_Olist_OCons(U_18752),U_18758),U_18760) ),
    inference(clausify,[status(thm)],[f_4596_6]) ).

cnf(f_4596_10,plain,
    ( U_18760 = hAPP(c_List_Ofilter(U_18752,U_18754),sK479(U_18760,U_18758,U_18756,U_18754,U_18752))
    | hAPP(c_List_Ofilter(U_18752,U_18754),U_18756) != hAPP(hAPP(c_List_Olist_OCons(U_18752),U_18758),U_18760) ),
    inference(clausify,[status(thm)],[f_4596_6]) ).

cnf(f_4596_11,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18753),sK480(U_18761,U_18759,U_18757,U_18755,U_18753,U_18746)),hAPP(c_List_Oset(U_18753),U_18746)))
    | U_18761 != hAPP(c_List_Ofilter(U_18753,U_18755),U_18745)
    | U_18757 != hAPP(hAPP(c_List_Oappend(U_18753),U_18746),hAPP(hAPP(c_List_Olist_OCons(U_18753),U_18759),U_18745))
    | ~ hBOOL(hAPP(U_18755,U_18759))
    | hAPP(c_List_Ofilter(U_18753,U_18755),U_18757) = hAPP(hAPP(c_List_Olist_OCons(U_18753),U_18759),U_18761) ),
    inference(clausify,[status(thm)],[f_4596_6]) ).

cnf(f_4596_12,plain,
    ( hBOOL(hAPP(U_18755,sK480(U_18761,U_18759,U_18757,U_18755,U_18753,U_18746)))
    | U_18761 != hAPP(c_List_Ofilter(U_18753,U_18755),U_18745)
    | U_18757 != hAPP(hAPP(c_List_Oappend(U_18753),U_18746),hAPP(hAPP(c_List_Olist_OCons(U_18753),U_18759),U_18745))
    | ~ hBOOL(hAPP(U_18755,U_18759))
    | hAPP(c_List_Ofilter(U_18753,U_18755),U_18757) = hAPP(hAPP(c_List_Olist_OCons(U_18753),U_18759),U_18761) ),
    inference(clausify,[status(thm)],[f_4596_6]) ).

fof(f_4597_1,plain,
    ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_b] :
      ( ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) = hAPP(c_List_Ofilter(T_b,V_P_2),V_ys_2)
        | ! [B_us,B_vs] :
            ( V_xs_2 != hAPP(c_List_Ofilter(T_b,V_P_2),B_vs)
            | ~ hBOOL(hAPP(V_P_2,V_x_2))
            | ? [B_x] :
                ( hBOOL(hAPP(V_P_2,B_x))
                & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),B_us))) )
            | V_ys_2 != hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_vs)) ) )
      & ( ? [B_us,B_vs] :
            ( V_xs_2 = hAPP(c_List_Ofilter(T_b,V_P_2),B_vs)
            & hBOOL(hAPP(V_P_2,V_x_2))
            & ! [B_x] :
                ( ~ hBOOL(hAPP(V_P_2,B_x))
                | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),B_us))) )
            & V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_vs)) )
        | hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) != hAPP(c_List_Ofilter(T_b,V_P_2),V_ys_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_Cons__eq__filter__iff]) ).

fof(f_4597_2,plain,
    ! [U_18772,U_18771,U_18770,U_18769,U_18768] :
      ( ( hAPP(hAPP(c_List_Olist_OCons(U_18768),U_18769),U_18770) = hAPP(c_List_Ofilter(U_18768,U_18771),U_18772)
        | ! [U_18767,U_18766] :
            ( U_18770 != hAPP(c_List_Ofilter(U_18768,U_18771),U_18766)
            | ~ hBOOL(hAPP(U_18771,U_18769))
            | ? [U_18765] :
                ( hBOOL(hAPP(U_18771,U_18765))
                & hBOOL(hAPP(hAPP(c_member(U_18768),U_18765),hAPP(c_List_Oset(U_18768),U_18767))) )
            | U_18772 != hAPP(hAPP(c_List_Oappend(U_18768),U_18767),hAPP(hAPP(c_List_Olist_OCons(U_18768),U_18769),U_18766)) ) )
      & ( ? [U_18764,U_18763] :
            ( U_18770 = hAPP(c_List_Ofilter(U_18768,U_18771),U_18763)
            & hBOOL(hAPP(U_18771,U_18769))
            & ! [U_18762] :
                ( ~ hBOOL(hAPP(U_18771,U_18762))
                | ~ hBOOL(hAPP(hAPP(c_member(U_18768),U_18762),hAPP(c_List_Oset(U_18768),U_18764))) )
            & U_18772 = hAPP(hAPP(c_List_Oappend(U_18768),U_18764),hAPP(hAPP(c_List_Olist_OCons(U_18768),U_18769),U_18763)) )
        | hAPP(hAPP(c_List_Olist_OCons(U_18768),U_18769),U_18770) != hAPP(c_List_Ofilter(U_18768,U_18771),U_18772) ) ),
    inference(variable_rename,[status(thm)],[f_4597_1]) ).

fof(f_4597_3,plain,
    ( ! [U_18782,U_18780,U_18778,U_18776,U_18774] :
        ( hAPP(hAPP(c_List_Olist_OCons(U_18774),U_18776),U_18778) = hAPP(c_List_Ofilter(U_18774,U_18780),U_18782)
        | ! [U_18767] :
            ( ! [U_18766] :
                ( U_18778 != hAPP(c_List_Ofilter(U_18774,U_18780),U_18766)
                | U_18782 != hAPP(hAPP(c_List_Oappend(U_18774),U_18767),hAPP(hAPP(c_List_Olist_OCons(U_18774),U_18776),U_18766)) )
            | ? [U_18765] :
                ( hBOOL(hAPP(U_18780,U_18765))
                & hBOOL(hAPP(hAPP(c_member(U_18774),U_18765),hAPP(c_List_Oset(U_18774),U_18767))) ) )
        | ~ hBOOL(hAPP(U_18780,U_18776)) )
    & ! [U_18781,U_18779,U_18777,U_18775,U_18773] :
        ( ( ? [U_18764] :
              ( ? [U_18763] :
                  ( U_18777 = hAPP(c_List_Ofilter(U_18773,U_18779),U_18763)
                  & U_18781 = hAPP(hAPP(c_List_Oappend(U_18773),U_18764),hAPP(hAPP(c_List_Olist_OCons(U_18773),U_18775),U_18763)) )
              & ! [U_18762] :
                  ( ~ hBOOL(hAPP(U_18779,U_18762))
                  | ~ hBOOL(hAPP(hAPP(c_member(U_18773),U_18762),hAPP(c_List_Oset(U_18773),U_18764))) ) )
          & hBOOL(hAPP(U_18779,U_18775)) )
        | hAPP(hAPP(c_List_Olist_OCons(U_18773),U_18775),U_18777) != hAPP(c_List_Ofilter(U_18773,U_18779),U_18781) ) ),
    inference(miniscope,[status(thm)],[f_4597_2]) ).

fof(f_4597_4,plain,
    ( ! [U_18782,U_18780,U_18778,U_18776,U_18774] :
        ( hAPP(hAPP(c_List_Olist_OCons(U_18774),U_18776),U_18778) = hAPP(c_List_Ofilter(U_18774,U_18780),U_18782)
        | ! [U_18767] :
            ( ! [U_18766] :
                ( U_18778 != hAPP(c_List_Ofilter(U_18774,U_18780),U_18766)
                | U_18782 != hAPP(hAPP(c_List_Oappend(U_18774),U_18767),hAPP(hAPP(c_List_Olist_OCons(U_18774),U_18776),U_18766)) )
            | ? [U_18765] :
                ( hBOOL(hAPP(U_18780,U_18765))
                & hBOOL(hAPP(hAPP(c_member(U_18774),U_18765),hAPP(c_List_Oset(U_18774),U_18767))) ) )
        | ~ hBOOL(hAPP(U_18780,U_18776)) )
    & ! [U_18781,U_18779,U_18777,U_18775,U_18773] :
        ( ( ? [U_18763] :
              ( U_18777 = hAPP(c_List_Ofilter(U_18773,U_18779),U_18763)
              & U_18781 = hAPP(hAPP(c_List_Oappend(U_18773),sK481(U_18781,U_18779,U_18777,U_18775,U_18773)),hAPP(hAPP(c_List_Olist_OCons(U_18773),U_18775),U_18763)) )
          & ! [U_18762] :
              ( ~ hBOOL(hAPP(U_18779,U_18762))
              | ~ hBOOL(hAPP(hAPP(c_member(U_18773),U_18762),hAPP(c_List_Oset(U_18773),sK481(U_18781,U_18779,U_18777,U_18775,U_18773)))) )
          & hBOOL(hAPP(U_18779,U_18775)) )
        | hAPP(hAPP(c_List_Olist_OCons(U_18773),U_18775),U_18777) != hAPP(c_List_Ofilter(U_18773,U_18779),U_18781) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK481]),skolemize(U_18764,sK481(U_18781,U_18779,U_18777,U_18775,U_18773))],[f_4597_3]) ).

fof(f_4597_5,plain,
    ( ! [U_18782,U_18780,U_18778,U_18776,U_18774] :
        ( hAPP(hAPP(c_List_Olist_OCons(U_18774),U_18776),U_18778) = hAPP(c_List_Ofilter(U_18774,U_18780),U_18782)
        | ! [U_18767] :
            ( ! [U_18766] :
                ( U_18778 != hAPP(c_List_Ofilter(U_18774,U_18780),U_18766)
                | U_18782 != hAPP(hAPP(c_List_Oappend(U_18774),U_18767),hAPP(hAPP(c_List_Olist_OCons(U_18774),U_18776),U_18766)) )
            | ? [U_18765] :
                ( hBOOL(hAPP(U_18780,U_18765))
                & hBOOL(hAPP(hAPP(c_member(U_18774),U_18765),hAPP(c_List_Oset(U_18774),U_18767))) ) )
        | ~ hBOOL(hAPP(U_18780,U_18776)) )
    & ! [U_18781,U_18779,U_18777,U_18775,U_18773] :
        ( ( U_18777 = hAPP(c_List_Ofilter(U_18773,U_18779),sK482(U_18781,U_18779,U_18777,U_18775,U_18773))
          & U_18781 = hAPP(hAPP(c_List_Oappend(U_18773),sK481(U_18781,U_18779,U_18777,U_18775,U_18773)),hAPP(hAPP(c_List_Olist_OCons(U_18773),U_18775),sK482(U_18781,U_18779,U_18777,U_18775,U_18773)))
          & ! [U_18762] :
              ( ~ hBOOL(hAPP(U_18779,U_18762))
              | ~ hBOOL(hAPP(hAPP(c_member(U_18773),U_18762),hAPP(c_List_Oset(U_18773),sK481(U_18781,U_18779,U_18777,U_18775,U_18773)))) )
          & hBOOL(hAPP(U_18779,U_18775)) )
        | hAPP(hAPP(c_List_Olist_OCons(U_18773),U_18775),U_18777) != hAPP(c_List_Ofilter(U_18773,U_18779),U_18781) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK482]),skolemize(U_18763,sK482(U_18781,U_18779,U_18777,U_18775,U_18773))],[f_4597_4]) ).

fof(f_4597_6,plain,
    ( ! [U_18782,U_18780,U_18778,U_18776,U_18774] :
        ( hAPP(hAPP(c_List_Olist_OCons(U_18774),U_18776),U_18778) = hAPP(c_List_Ofilter(U_18774,U_18780),U_18782)
        | ! [U_18767] :
            ( ! [U_18766] :
                ( U_18778 != hAPP(c_List_Ofilter(U_18774,U_18780),U_18766)
                | U_18782 != hAPP(hAPP(c_List_Oappend(U_18774),U_18767),hAPP(hAPP(c_List_Olist_OCons(U_18774),U_18776),U_18766)) )
            | ( hBOOL(hAPP(U_18780,sK483(U_18782,U_18780,U_18778,U_18776,U_18774,U_18767)))
              & hBOOL(hAPP(hAPP(c_member(U_18774),sK483(U_18782,U_18780,U_18778,U_18776,U_18774,U_18767)),hAPP(c_List_Oset(U_18774),U_18767))) ) )
        | ~ hBOOL(hAPP(U_18780,U_18776)) )
    & ! [U_18781,U_18779,U_18777,U_18775,U_18773] :
        ( ( U_18777 = hAPP(c_List_Ofilter(U_18773,U_18779),sK482(U_18781,U_18779,U_18777,U_18775,U_18773))
          & U_18781 = hAPP(hAPP(c_List_Oappend(U_18773),sK481(U_18781,U_18779,U_18777,U_18775,U_18773)),hAPP(hAPP(c_List_Olist_OCons(U_18773),U_18775),sK482(U_18781,U_18779,U_18777,U_18775,U_18773)))
          & ! [U_18762] :
              ( ~ hBOOL(hAPP(U_18779,U_18762))
              | ~ hBOOL(hAPP(hAPP(c_member(U_18773),U_18762),hAPP(c_List_Oset(U_18773),sK481(U_18781,U_18779,U_18777,U_18775,U_18773)))) )
          & hBOOL(hAPP(U_18779,U_18775)) )
        | hAPP(hAPP(c_List_Olist_OCons(U_18773),U_18775),U_18777) != hAPP(c_List_Ofilter(U_18773,U_18779),U_18781) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK483]),skolemize(U_18765,sK483(U_18782,U_18780,U_18778,U_18776,U_18774,U_18767))],[f_4597_5]) ).

cnf(f_4597_7,plain,
    ( hBOOL(hAPP(U_18779,U_18775))
    | hAPP(hAPP(c_List_Olist_OCons(U_18773),U_18775),U_18777) != hAPP(c_List_Ofilter(U_18773,U_18779),U_18781) ),
    inference(clausify,[status(thm)],[f_4597_6]) ).

cnf(f_4597_8,plain,
    ( ~ hBOOL(hAPP(U_18779,U_18762))
    | ~ hBOOL(hAPP(hAPP(c_member(U_18773),U_18762),hAPP(c_List_Oset(U_18773),sK481(U_18781,U_18779,U_18777,U_18775,U_18773))))
    | hAPP(hAPP(c_List_Olist_OCons(U_18773),U_18775),U_18777) != hAPP(c_List_Ofilter(U_18773,U_18779),U_18781) ),
    inference(clausify,[status(thm)],[f_4597_6]) ).

cnf(f_4597_9,plain,
    ( U_18781 = hAPP(hAPP(c_List_Oappend(U_18773),sK481(U_18781,U_18779,U_18777,U_18775,U_18773)),hAPP(hAPP(c_List_Olist_OCons(U_18773),U_18775),sK482(U_18781,U_18779,U_18777,U_18775,U_18773)))
    | hAPP(hAPP(c_List_Olist_OCons(U_18773),U_18775),U_18777) != hAPP(c_List_Ofilter(U_18773,U_18779),U_18781) ),
    inference(clausify,[status(thm)],[f_4597_6]) ).

cnf(f_4597_10,plain,
    ( U_18777 = hAPP(c_List_Ofilter(U_18773,U_18779),sK482(U_18781,U_18779,U_18777,U_18775,U_18773))
    | hAPP(hAPP(c_List_Olist_OCons(U_18773),U_18775),U_18777) != hAPP(c_List_Ofilter(U_18773,U_18779),U_18781) ),
    inference(clausify,[status(thm)],[f_4597_6]) ).

cnf(f_4597_11,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18774),sK483(U_18782,U_18780,U_18778,U_18776,U_18774,U_18767)),hAPP(c_List_Oset(U_18774),U_18767)))
    | U_18778 != hAPP(c_List_Ofilter(U_18774,U_18780),U_18766)
    | U_18782 != hAPP(hAPP(c_List_Oappend(U_18774),U_18767),hAPP(hAPP(c_List_Olist_OCons(U_18774),U_18776),U_18766))
    | ~ hBOOL(hAPP(U_18780,U_18776))
    | hAPP(hAPP(c_List_Olist_OCons(U_18774),U_18776),U_18778) = hAPP(c_List_Ofilter(U_18774,U_18780),U_18782) ),
    inference(clausify,[status(thm)],[f_4597_6]) ).

cnf(f_4597_12,plain,
    ( hBOOL(hAPP(U_18780,sK483(U_18782,U_18780,U_18778,U_18776,U_18774,U_18767)))
    | U_18778 != hAPP(c_List_Ofilter(U_18774,U_18780),U_18766)
    | U_18782 != hAPP(hAPP(c_List_Oappend(U_18774),U_18767),hAPP(hAPP(c_List_Olist_OCons(U_18774),U_18776),U_18766))
    | ~ hBOOL(hAPP(U_18780,U_18776))
    | hAPP(hAPP(c_List_Olist_OCons(U_18774),U_18776),U_18778) = hAPP(c_List_Ofilter(U_18774,U_18780),U_18782) ),
    inference(clausify,[status(thm)],[f_4597_6]) ).

fof(f_4598_1,plain,
    ! [V_g_2,V_f_2,T_b,T_c] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),hAPP(hAPP(c_COMBS(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_Orderings_Oord__class_Oless__eq(T_c)),V_f_2)),V_g_2))) )
        & ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),hAPP(hAPP(c_COMBS(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_Orderings_Oord__class_Oless__eq(T_c)),V_f_2)),V_g_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) ) )
      | ~ class_Enum_Oenum(T_b)
      | ~ class_Orderings_Oorder(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_order__fun_I1_J]) ).

fof(f_4598_2,plain,
    ! [U_18786,U_18785,U_18784,U_18783] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18784,U_18783)),U_18785),U_18786))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(U_18784),hAPP(hAPP(c_COMBS(U_18784,U_18783,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_18783,tc_fun(U_18783,tc_HOL_Obool),U_18784),c_Orderings_Oord__class_Oless__eq(U_18783)),U_18785)),U_18786))) )
        & ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(U_18784),hAPP(hAPP(c_COMBS(U_18784,U_18783,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_18783,tc_fun(U_18783,tc_HOL_Obool),U_18784),c_Orderings_Oord__class_Oless__eq(U_18783)),U_18785)),U_18786)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18784,U_18783)),U_18785),U_18786)) ) )
      | ~ class_Enum_Oenum(U_18784)
      | ~ class_Orderings_Oorder(U_18783) ),
    inference(variable_rename,[status(thm)],[f_4598_1]) ).

cnf(f_4598_3,plain,
    ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(U_18784),hAPP(hAPP(c_COMBS(U_18784,U_18783,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_18783,tc_fun(U_18783,tc_HOL_Obool),U_18784),c_Orderings_Oord__class_Oless__eq(U_18783)),U_18785)),U_18786)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18784,U_18783)),U_18785),U_18786))
    | ~ class_Enum_Oenum(U_18784)
    | ~ class_Orderings_Oorder(U_18783) ),
    inference(clausify,[status(thm)],[f_4598_2]) ).

cnf(f_4598_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18784,U_18783)),U_18785),U_18786))
    | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(U_18784),hAPP(hAPP(c_COMBS(U_18784,U_18783,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_18783,tc_fun(U_18783,tc_HOL_Obool),U_18784),c_Orderings_Oord__class_Oless__eq(U_18783)),U_18785)),U_18786)))
    | ~ class_Enum_Oenum(U_18784)
    | ~ class_Orderings_Oorder(U_18783) ),
    inference(clausify,[status(thm)],[f_4598_2]) ).

fof(f_4599_1,plain,
    ! [V_P_2,T_b] :
      ( ( ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),V_P_2))
          | ? [B_x1] : ~ hBOOL(hAPP(V_P_2,B_x1)) )
        & ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),V_P_2)) ) )
      | ~ class_Enum_Oenum(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_enum__all]) ).

fof(f_4599_2,plain,
    ! [U_18790,U_18789] :
      ( ( ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(U_18789),U_18790))
          | ? [U_18788] : ~ hBOOL(hAPP(U_18790,U_18788)) )
        & ( ! [U_18787] : hBOOL(hAPP(U_18790,U_18787))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(U_18789),U_18790)) ) )
      | ~ class_Enum_Oenum(U_18789) ),
    inference(variable_rename,[status(thm)],[f_4599_1]) ).

fof(f_4599_3,plain,
    ! [U_18790,U_18789] :
      ( ( ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(U_18789),U_18790))
          | ~ hBOOL(hAPP(U_18790,sK484(U_18790,U_18789))) )
        & ( ! [U_18787] : hBOOL(hAPP(U_18790,U_18787))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(U_18789),U_18790)) ) )
      | ~ class_Enum_Oenum(U_18789) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK484]),skolemize(U_18788,sK484(U_18790,U_18789))],[f_4599_2]) ).

cnf(f_4599_4,plain,
    ( hBOOL(hAPP(U_18790,U_18787))
    | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(U_18789),U_18790))
    | ~ class_Enum_Oenum(U_18789) ),
    inference(clausify,[status(thm)],[f_4599_3]) ).

cnf(f_4599_5,plain,
    ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(U_18789),U_18790))
    | ~ hBOOL(hAPP(U_18790,sK484(U_18790,U_18789)))
    | ~ class_Enum_Oenum(U_18789) ),
    inference(clausify,[status(thm)],[f_4599_3]) ).

fof(f_4600_1,plain,
    ! [V_P_2,T_b] :
      ( ( ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),V_P_2)) )
        & ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),V_P_2))
          | ? [B_x1] : ~ hBOOL(hAPP(V_P_2,B_x1)) ) )
      | ~ class_Enum_Oenum(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_all__code]) ).

fof(f_4600_2,plain,
    ! [U_18794,U_18793] :
      ( ( ( ! [U_18792] : hBOOL(hAPP(U_18794,U_18792))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(U_18793),U_18794)) )
        & ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(U_18793),U_18794))
          | ? [U_18791] : ~ hBOOL(hAPP(U_18794,U_18791)) ) )
      | ~ class_Enum_Oenum(U_18793) ),
    inference(variable_rename,[status(thm)],[f_4600_1]) ).

fof(f_4600_3,plain,
    ! [U_18794,U_18793] :
      ( ( ( ! [U_18792] : hBOOL(hAPP(U_18794,U_18792))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(U_18793),U_18794)) )
        & ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(U_18793),U_18794))
          | ~ hBOOL(hAPP(U_18794,sK485(U_18794,U_18793))) ) )
      | ~ class_Enum_Oenum(U_18793) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK485]),skolemize(U_18791,sK485(U_18794,U_18793))],[f_4600_2]) ).

cnf(f_4600_4,plain,
    ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(U_18793),U_18794))
    | ~ hBOOL(hAPP(U_18794,sK485(U_18794,U_18793)))
    | ~ class_Enum_Oenum(U_18793) ),
    inference(clausify,[status(thm)],[f_4600_3]) ).

cnf(f_4600_5,plain,
    ( hBOOL(hAPP(U_18794,U_18792))
    | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(U_18793),U_18794))
    | ~ class_Enum_Oenum(U_18793) ),
    inference(clausify,[status(thm)],[f_4600_3]) ).

fof(f_4601_1,plain,
    ! [V_P_2,T_b,T_c] :
      ( ( ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(T_b,T_c)),V_P_2))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_Enum_Oenum__class_Oenum__all(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,T_c),V_P_2)),c_Product__Type_OPair(T_b,T_c))))) )
        & ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_Enum_Oenum__class_Oenum__all(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,T_c),V_P_2)),c_Product__Type_OPair(T_b,T_c)))))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(T_b,T_c)),V_P_2)) ) )
      | ~ class_Enum_Oenum(T_b)
      | ~ class_Enum_Oenum(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_enum__all__prod__def]) ).

fof(f_4601_2,plain,
    ! [U_18797,U_18796,U_18795] :
      ( ( ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(U_18796,U_18795)),U_18797))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(U_18796),hAPP(hAPP(c_COMBB(tc_fun(U_18795,tc_HOL_Obool),tc_HOL_Obool,U_18796),c_Enum_Oenum__class_Oenum__all(U_18795)),hAPP(hAPP(c_COMBB(tc_fun(U_18795,tc_prod(U_18796,U_18795)),tc_fun(U_18795,tc_HOL_Obool),U_18796),hAPP(c_COMBB(tc_prod(U_18796,U_18795),tc_HOL_Obool,U_18795),U_18797)),c_Product__Type_OPair(U_18796,U_18795))))) )
        & ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(U_18796),hAPP(hAPP(c_COMBB(tc_fun(U_18795,tc_HOL_Obool),tc_HOL_Obool,U_18796),c_Enum_Oenum__class_Oenum__all(U_18795)),hAPP(hAPP(c_COMBB(tc_fun(U_18795,tc_prod(U_18796,U_18795)),tc_fun(U_18795,tc_HOL_Obool),U_18796),hAPP(c_COMBB(tc_prod(U_18796,U_18795),tc_HOL_Obool,U_18795),U_18797)),c_Product__Type_OPair(U_18796,U_18795)))))
          | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(U_18796,U_18795)),U_18797)) ) )
      | ~ class_Enum_Oenum(U_18796)
      | ~ class_Enum_Oenum(U_18795) ),
    inference(variable_rename,[status(thm)],[f_4601_1]) ).

cnf(f_4601_3,plain,
    ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(U_18796),hAPP(hAPP(c_COMBB(tc_fun(U_18795,tc_HOL_Obool),tc_HOL_Obool,U_18796),c_Enum_Oenum__class_Oenum__all(U_18795)),hAPP(hAPP(c_COMBB(tc_fun(U_18795,tc_prod(U_18796,U_18795)),tc_fun(U_18795,tc_HOL_Obool),U_18796),hAPP(c_COMBB(tc_prod(U_18796,U_18795),tc_HOL_Obool,U_18795),U_18797)),c_Product__Type_OPair(U_18796,U_18795)))))
    | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(U_18796,U_18795)),U_18797))
    | ~ class_Enum_Oenum(U_18796)
    | ~ class_Enum_Oenum(U_18795) ),
    inference(clausify,[status(thm)],[f_4601_2]) ).

cnf(f_4601_4,plain,
    ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(U_18796,U_18795)),U_18797))
    | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(U_18796),hAPP(hAPP(c_COMBB(tc_fun(U_18795,tc_HOL_Obool),tc_HOL_Obool,U_18796),c_Enum_Oenum__class_Oenum__all(U_18795)),hAPP(hAPP(c_COMBB(tc_fun(U_18795,tc_prod(U_18796,U_18795)),tc_fun(U_18795,tc_HOL_Obool),U_18796),hAPP(c_COMBB(tc_prod(U_18796,U_18795),tc_HOL_Obool,U_18795),U_18797)),c_Product__Type_OPair(U_18796,U_18795)))))
    | ~ class_Enum_Oenum(U_18796)
    | ~ class_Enum_Oenum(U_18795) ),
    inference(clausify,[status(thm)],[f_4601_2]) ).

fof(f_4602_1,plain,
    ! [V_P_2,V_xs_2,T_b,V_n_2] :
      ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2)))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(V_P_2,B_x))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_list__ball__nth]) ).

fof(f_4602_2,plain,
    ! [U_18802,U_18801,U_18800,U_18799] :
      ( hBOOL(hAPP(U_18802,hAPP(hAPP(c_List_Onth(U_18800),U_18801),U_18799)))
      | ? [U_18798] :
          ( ~ hBOOL(hAPP(U_18802,U_18798))
          & hBOOL(hAPP(hAPP(c_member(U_18800),U_18798),hAPP(c_List_Oset(U_18800),U_18801))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18799),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18800)),U_18801))) ),
    inference(variable_rename,[status(thm)],[f_4602_1]) ).

fof(f_4602_3,plain,
    ! [U_18802,U_18801,U_18800,U_18799] :
      ( hBOOL(hAPP(U_18802,hAPP(hAPP(c_List_Onth(U_18800),U_18801),U_18799)))
      | ( ~ hBOOL(hAPP(U_18802,sK486(U_18802,U_18801,U_18800,U_18799)))
        & hBOOL(hAPP(hAPP(c_member(U_18800),sK486(U_18802,U_18801,U_18800,U_18799)),hAPP(c_List_Oset(U_18800),U_18801))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18799),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18800)),U_18801))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK486]),skolemize(U_18798,sK486(U_18802,U_18801,U_18800,U_18799))],[f_4602_2]) ).

cnf(f_4602_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18800),sK486(U_18802,U_18801,U_18800,U_18799)),hAPP(c_List_Oset(U_18800),U_18801)))
    | hBOOL(hAPP(U_18802,hAPP(hAPP(c_List_Onth(U_18800),U_18801),U_18799)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18799),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18800)),U_18801))) ),
    inference(clausify,[status(thm)],[f_4602_3]) ).

cnf(f_4602_5,plain,
    ( ~ hBOOL(hAPP(U_18802,sK486(U_18802,U_18801,U_18800,U_18799)))
    | hBOOL(hAPP(U_18802,hAPP(hAPP(c_List_Onth(U_18800),U_18801),U_18799)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18799),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18800)),U_18801))) ),
    inference(clausify,[status(thm)],[f_4602_3]) ).

fof(f_4603_1,plain,
    ! [V_x_2,V_xs_2,T_b] :
      ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
      | ~ c_List_Olinorder__class_Osorted(T_b,V_xs_2)
      | ? [B_x] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) )
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sorted_OCons]) ).

fof(f_4603_2,plain,
    ! [U_18806,U_18805,U_18804] :
      ( c_List_Olinorder__class_Osorted(U_18804,hAPP(hAPP(c_List_Olist_OCons(U_18804),U_18806),U_18805))
      | ~ c_List_Olinorder__class_Osorted(U_18804,U_18805)
      | ? [U_18803] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18804),U_18806),U_18803))
          & hBOOL(hAPP(hAPP(c_member(U_18804),U_18803),hAPP(c_List_Oset(U_18804),U_18805))) )
      | ~ class_Orderings_Olinorder(U_18804) ),
    inference(variable_rename,[status(thm)],[f_4603_1]) ).

fof(f_4603_3,plain,
    ! [U_18806,U_18805,U_18804] :
      ( c_List_Olinorder__class_Osorted(U_18804,hAPP(hAPP(c_List_Olist_OCons(U_18804),U_18806),U_18805))
      | ~ c_List_Olinorder__class_Osorted(U_18804,U_18805)
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18804),U_18806),sK487(U_18806,U_18805,U_18804)))
        & hBOOL(hAPP(hAPP(c_member(U_18804),sK487(U_18806,U_18805,U_18804)),hAPP(c_List_Oset(U_18804),U_18805))) )
      | ~ class_Orderings_Olinorder(U_18804) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK487]),skolemize(U_18803,sK487(U_18806,U_18805,U_18804))],[f_4603_2]) ).

cnf(f_4603_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18804),sK487(U_18806,U_18805,U_18804)),hAPP(c_List_Oset(U_18804),U_18805)))
    | c_List_Olinorder__class_Osorted(U_18804,hAPP(hAPP(c_List_Olist_OCons(U_18804),U_18806),U_18805))
    | ~ c_List_Olinorder__class_Osorted(U_18804,U_18805)
    | ~ class_Orderings_Olinorder(U_18804) ),
    inference(clausify,[status(thm)],[f_4603_3]) ).

cnf(f_4603_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18804),U_18806),sK487(U_18806,U_18805,U_18804)))
    | c_List_Olinorder__class_Osorted(U_18804,hAPP(hAPP(c_List_Olist_OCons(U_18804),U_18806),U_18805))
    | ~ c_List_Olinorder__class_Osorted(U_18804,U_18805)
    | ~ class_Orderings_Olinorder(U_18804) ),
    inference(clausify,[status(thm)],[f_4603_3]) ).

fof(f_4604_1,plain,
    ! [V_xs_2,V_P_2,T_b] :
      ( ( c_List_Olist__ex(T_b,V_P_2,V_xs_2)
        | ! [B_n] :
            ( ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ) )
      & ( ? [B_n] :
            ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) )
        | ~ c_List_Olist__ex(T_b,V_P_2,V_xs_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__ex__length]) ).

fof(f_4604_2,plain,
    ! [U_18811,U_18810,U_18809] :
      ( ( c_List_Olist__ex(U_18809,U_18810,U_18811)
        | ! [U_18808] :
            ( ~ hBOOL(hAPP(U_18810,hAPP(hAPP(c_List_Onth(U_18809),U_18811),U_18808)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18808),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18809)),U_18811))) ) )
      & ( ? [U_18807] :
            ( hBOOL(hAPP(U_18810,hAPP(hAPP(c_List_Onth(U_18809),U_18811),U_18807)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18807),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18809)),U_18811))) )
        | ~ c_List_Olist__ex(U_18809,U_18810,U_18811) ) ),
    inference(variable_rename,[status(thm)],[f_4604_1]) ).

fof(f_4604_3,plain,
    ( ! [U_18817,U_18815,U_18813] :
        ( c_List_Olist__ex(U_18813,U_18815,U_18817)
        | ! [U_18808] :
            ( ~ hBOOL(hAPP(U_18815,hAPP(hAPP(c_List_Onth(U_18813),U_18817),U_18808)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18808),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18813)),U_18817))) ) )
    & ! [U_18816,U_18814,U_18812] :
        ( ? [U_18807] :
            ( hBOOL(hAPP(U_18814,hAPP(hAPP(c_List_Onth(U_18812),U_18816),U_18807)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18807),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18812)),U_18816))) )
        | ~ c_List_Olist__ex(U_18812,U_18814,U_18816) ) ),
    inference(miniscope,[status(thm)],[f_4604_2]) ).

fof(f_4604_4,plain,
    ( ! [U_18817,U_18815,U_18813] :
        ( c_List_Olist__ex(U_18813,U_18815,U_18817)
        | ! [U_18808] :
            ( ~ hBOOL(hAPP(U_18815,hAPP(hAPP(c_List_Onth(U_18813),U_18817),U_18808)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18808),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18813)),U_18817))) ) )
    & ! [U_18816,U_18814,U_18812] :
        ( ( hBOOL(hAPP(U_18814,hAPP(hAPP(c_List_Onth(U_18812),U_18816),sK488(U_18816,U_18814,U_18812))))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK488(U_18816,U_18814,U_18812)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18812)),U_18816))) )
        | ~ c_List_Olist__ex(U_18812,U_18814,U_18816) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK488]),skolemize(U_18807,sK488(U_18816,U_18814,U_18812))],[f_4604_3]) ).

cnf(f_4604_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK488(U_18816,U_18814,U_18812)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18812)),U_18816)))
    | ~ c_List_Olist__ex(U_18812,U_18814,U_18816) ),
    inference(clausify,[status(thm)],[f_4604_4]) ).

cnf(f_4604_6,plain,
    ( hBOOL(hAPP(U_18814,hAPP(hAPP(c_List_Onth(U_18812),U_18816),sK488(U_18816,U_18814,U_18812))))
    | ~ c_List_Olist__ex(U_18812,U_18814,U_18816) ),
    inference(clausify,[status(thm)],[f_4604_4]) ).

cnf(f_4604_7,plain,
    ( c_List_Olist__ex(U_18813,U_18815,U_18817)
    | ~ hBOOL(hAPP(U_18815,hAPP(hAPP(c_List_Onth(U_18813),U_18817),U_18808)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18808),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18813)),U_18817))) ),
    inference(clausify,[status(thm)],[f_4604_4]) ).

fof(f_4605_1,plain,
    ! [V_xs_2,V_x_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
        | ! [B_ys] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),B_ys)))
            | ! [B_zs] : V_xs_2 != hAPP(hAPP(c_List_Oappend(T_b),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_zs)) ) )
      & ( ? [B_ys] :
            ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),B_ys)))
            & ? [B_zs] : V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_zs)) )
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_in__set__conv__decomp__first]) ).

fof(f_4605_2,plain,
    ! [U_18824,U_18823,U_18822] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_18822),U_18823),hAPP(c_List_Oset(U_18822),U_18824)))
        | ! [U_18821] :
            ( hBOOL(hAPP(hAPP(c_member(U_18822),U_18823),hAPP(c_List_Oset(U_18822),U_18821)))
            | ! [U_18820] : U_18824 != hAPP(hAPP(c_List_Oappend(U_18822),U_18821),hAPP(hAPP(c_List_Olist_OCons(U_18822),U_18823),U_18820)) ) )
      & ( ? [U_18819] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_18822),U_18823),hAPP(c_List_Oset(U_18822),U_18819)))
            & ? [U_18818] : U_18824 = hAPP(hAPP(c_List_Oappend(U_18822),U_18819),hAPP(hAPP(c_List_Olist_OCons(U_18822),U_18823),U_18818)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_18822),U_18823),hAPP(c_List_Oset(U_18822),U_18824))) ) ),
    inference(variable_rename,[status(thm)],[f_4605_1]) ).

fof(f_4605_3,plain,
    ( ! [U_18830,U_18828,U_18826] :
        ( hBOOL(hAPP(hAPP(c_member(U_18826),U_18828),hAPP(c_List_Oset(U_18826),U_18830)))
        | ! [U_18821] :
            ( hBOOL(hAPP(hAPP(c_member(U_18826),U_18828),hAPP(c_List_Oset(U_18826),U_18821)))
            | ! [U_18820] : U_18830 != hAPP(hAPP(c_List_Oappend(U_18826),U_18821),hAPP(hAPP(c_List_Olist_OCons(U_18826),U_18828),U_18820)) ) )
    & ! [U_18829,U_18827,U_18825] :
        ( ? [U_18819] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_18825),U_18827),hAPP(c_List_Oset(U_18825),U_18819)))
            & ? [U_18818] : U_18829 = hAPP(hAPP(c_List_Oappend(U_18825),U_18819),hAPP(hAPP(c_List_Olist_OCons(U_18825),U_18827),U_18818)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_18825),U_18827),hAPP(c_List_Oset(U_18825),U_18829))) ) ),
    inference(miniscope,[status(thm)],[f_4605_2]) ).

fof(f_4605_4,plain,
    ( ! [U_18830,U_18828,U_18826] :
        ( hBOOL(hAPP(hAPP(c_member(U_18826),U_18828),hAPP(c_List_Oset(U_18826),U_18830)))
        | ! [U_18821] :
            ( hBOOL(hAPP(hAPP(c_member(U_18826),U_18828),hAPP(c_List_Oset(U_18826),U_18821)))
            | ! [U_18820] : U_18830 != hAPP(hAPP(c_List_Oappend(U_18826),U_18821),hAPP(hAPP(c_List_Olist_OCons(U_18826),U_18828),U_18820)) ) )
    & ! [U_18829,U_18827,U_18825] :
        ( ( ~ hBOOL(hAPP(hAPP(c_member(U_18825),U_18827),hAPP(c_List_Oset(U_18825),sK489(U_18829,U_18827,U_18825))))
          & ? [U_18818] : U_18829 = hAPP(hAPP(c_List_Oappend(U_18825),sK489(U_18829,U_18827,U_18825)),hAPP(hAPP(c_List_Olist_OCons(U_18825),U_18827),U_18818)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_18825),U_18827),hAPP(c_List_Oset(U_18825),U_18829))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK489]),skolemize(U_18819,sK489(U_18829,U_18827,U_18825))],[f_4605_3]) ).

fof(f_4605_5,plain,
    ( ! [U_18830,U_18828,U_18826] :
        ( hBOOL(hAPP(hAPP(c_member(U_18826),U_18828),hAPP(c_List_Oset(U_18826),U_18830)))
        | ! [U_18821] :
            ( hBOOL(hAPP(hAPP(c_member(U_18826),U_18828),hAPP(c_List_Oset(U_18826),U_18821)))
            | ! [U_18820] : U_18830 != hAPP(hAPP(c_List_Oappend(U_18826),U_18821),hAPP(hAPP(c_List_Olist_OCons(U_18826),U_18828),U_18820)) ) )
    & ! [U_18829,U_18827,U_18825] :
        ( ( ~ hBOOL(hAPP(hAPP(c_member(U_18825),U_18827),hAPP(c_List_Oset(U_18825),sK489(U_18829,U_18827,U_18825))))
          & U_18829 = hAPP(hAPP(c_List_Oappend(U_18825),sK489(U_18829,U_18827,U_18825)),hAPP(hAPP(c_List_Olist_OCons(U_18825),U_18827),sK490(U_18829,U_18827,U_18825))) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_18825),U_18827),hAPP(c_List_Oset(U_18825),U_18829))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK490]),skolemize(U_18818,sK490(U_18829,U_18827,U_18825))],[f_4605_4]) ).

cnf(f_4605_6,plain,
    ( U_18829 = hAPP(hAPP(c_List_Oappend(U_18825),sK489(U_18829,U_18827,U_18825)),hAPP(hAPP(c_List_Olist_OCons(U_18825),U_18827),sK490(U_18829,U_18827,U_18825)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_18825),U_18827),hAPP(c_List_Oset(U_18825),U_18829))) ),
    inference(clausify,[status(thm)],[f_4605_5]) ).

cnf(f_4605_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_18825),U_18827),hAPP(c_List_Oset(U_18825),sK489(U_18829,U_18827,U_18825))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_18825),U_18827),hAPP(c_List_Oset(U_18825),U_18829))) ),
    inference(clausify,[status(thm)],[f_4605_5]) ).

cnf(f_4605_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18826),U_18828),hAPP(c_List_Oset(U_18826),U_18830)))
    | hBOOL(hAPP(hAPP(c_member(U_18826),U_18828),hAPP(c_List_Oset(U_18826),U_18821)))
    | U_18830 != hAPP(hAPP(c_List_Oappend(U_18826),U_18821),hAPP(hAPP(c_List_Olist_OCons(U_18826),U_18828),U_18820)) ),
    inference(clausify,[status(thm)],[f_4605_5]) ).

fof(f_4606_1,plain,
    ! [V_P_2,T_b] : ~ c_List_Olist__ex(T_b,V_P_2,c_List_Olist_ONil(T_b)),
    inference(fof_nnf,[status(thm)],[fact_list__ex__simps_I2_J]) ).

fof(f_4606_2,plain,
    ! [U_18832,U_18831] : ~ c_List_Olist__ex(U_18831,U_18832,c_List_Olist_ONil(U_18831)),
    inference(variable_rename,[status(thm)],[f_4606_1]) ).

cnf(f_4606_3,plain,
    ~ c_List_Olist__ex(U_18831,U_18832,c_List_Olist_ONil(U_18831)),
    inference(clausify,[status(thm)],[f_4606_2]) ).

fof(f_4607_1,plain,
    ! [V_ys_2,V_xs_2,V_P_2,T_b] :
      ( ( c_List_Olist__ex(T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))
        | ( ~ c_List_Olist__ex(T_b,V_P_2,V_ys_2)
          & ~ c_List_Olist__ex(T_b,V_P_2,V_xs_2) ) )
      & ( c_List_Olist__ex(T_b,V_P_2,V_ys_2)
        | c_List_Olist__ex(T_b,V_P_2,V_xs_2)
        | ~ c_List_Olist__ex(T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__ex__append]) ).

fof(f_4607_2,plain,
    ! [U_18836,U_18835,U_18834,U_18833] :
      ( ( c_List_Olist__ex(U_18833,U_18834,hAPP(hAPP(c_List_Oappend(U_18833),U_18835),U_18836))
        | ( ~ c_List_Olist__ex(U_18833,U_18834,U_18836)
          & ~ c_List_Olist__ex(U_18833,U_18834,U_18835) ) )
      & ( c_List_Olist__ex(U_18833,U_18834,U_18836)
        | c_List_Olist__ex(U_18833,U_18834,U_18835)
        | ~ c_List_Olist__ex(U_18833,U_18834,hAPP(hAPP(c_List_Oappend(U_18833),U_18835),U_18836)) ) ),
    inference(variable_rename,[status(thm)],[f_4607_1]) ).

fof(f_4607_3,plain,
    ( ! [U_18844,U_18842,U_18840,U_18838] :
        ( c_List_Olist__ex(U_18838,U_18840,hAPP(hAPP(c_List_Oappend(U_18838),U_18842),U_18844))
        | ( ~ c_List_Olist__ex(U_18838,U_18840,U_18844)
          & ~ c_List_Olist__ex(U_18838,U_18840,U_18842) ) )
    & ! [U_18843,U_18841,U_18839,U_18837] :
        ( c_List_Olist__ex(U_18837,U_18839,U_18843)
        | c_List_Olist__ex(U_18837,U_18839,U_18841)
        | ~ c_List_Olist__ex(U_18837,U_18839,hAPP(hAPP(c_List_Oappend(U_18837),U_18841),U_18843)) ) ),
    inference(miniscope,[status(thm)],[f_4607_2]) ).

cnf(f_4607_4,plain,
    ( c_List_Olist__ex(U_18837,U_18839,U_18843)
    | c_List_Olist__ex(U_18837,U_18839,U_18841)
    | ~ c_List_Olist__ex(U_18837,U_18839,hAPP(hAPP(c_List_Oappend(U_18837),U_18841),U_18843)) ),
    inference(clausify,[status(thm)],[f_4607_3]) ).

cnf(f_4607_5,plain,
    ( ~ c_List_Olist__ex(U_18838,U_18840,U_18842)
    | c_List_Olist__ex(U_18838,U_18840,hAPP(hAPP(c_List_Oappend(U_18838),U_18842),U_18844)) ),
    inference(clausify,[status(thm)],[f_4607_3]) ).

cnf(f_4607_6,plain,
    ( ~ c_List_Olist__ex(U_18838,U_18840,U_18844)
    | c_List_Olist__ex(U_18838,U_18840,hAPP(hAPP(c_List_Oappend(U_18838),U_18842),U_18844)) ),
    inference(clausify,[status(thm)],[f_4607_3]) ).

fof(f_4608_1,plain,
    ! [V_xs_2,V_P_2,T_b] :
      ( ( c_List_Olist__ex(T_b,V_P_2,V_xs_2)
        | ! [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) ) )
      & ( ? [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) )
        | ~ c_List_Olist__ex(T_b,V_P_2,V_xs_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__ex__iff]) ).

fof(f_4608_2,plain,
    ! [U_18849,U_18848,U_18847] :
      ( ( c_List_Olist__ex(U_18847,U_18848,U_18849)
        | ! [U_18846] :
            ( ~ hBOOL(hAPP(U_18848,U_18846))
            | ~ hBOOL(hAPP(hAPP(c_member(U_18847),U_18846),hAPP(c_List_Oset(U_18847),U_18849))) ) )
      & ( ? [U_18845] :
            ( hBOOL(hAPP(U_18848,U_18845))
            & hBOOL(hAPP(hAPP(c_member(U_18847),U_18845),hAPP(c_List_Oset(U_18847),U_18849))) )
        | ~ c_List_Olist__ex(U_18847,U_18848,U_18849) ) ),
    inference(variable_rename,[status(thm)],[f_4608_1]) ).

fof(f_4608_3,plain,
    ( ! [U_18855,U_18853,U_18851] :
        ( c_List_Olist__ex(U_18851,U_18853,U_18855)
        | ! [U_18846] :
            ( ~ hBOOL(hAPP(U_18853,U_18846))
            | ~ hBOOL(hAPP(hAPP(c_member(U_18851),U_18846),hAPP(c_List_Oset(U_18851),U_18855))) ) )
    & ! [U_18854,U_18852,U_18850] :
        ( ? [U_18845] :
            ( hBOOL(hAPP(U_18852,U_18845))
            & hBOOL(hAPP(hAPP(c_member(U_18850),U_18845),hAPP(c_List_Oset(U_18850),U_18854))) )
        | ~ c_List_Olist__ex(U_18850,U_18852,U_18854) ) ),
    inference(miniscope,[status(thm)],[f_4608_2]) ).

fof(f_4608_4,plain,
    ( ! [U_18855,U_18853,U_18851] :
        ( c_List_Olist__ex(U_18851,U_18853,U_18855)
        | ! [U_18846] :
            ( ~ hBOOL(hAPP(U_18853,U_18846))
            | ~ hBOOL(hAPP(hAPP(c_member(U_18851),U_18846),hAPP(c_List_Oset(U_18851),U_18855))) ) )
    & ! [U_18854,U_18852,U_18850] :
        ( ( hBOOL(hAPP(U_18852,sK491(U_18854,U_18852,U_18850)))
          & hBOOL(hAPP(hAPP(c_member(U_18850),sK491(U_18854,U_18852,U_18850)),hAPP(c_List_Oset(U_18850),U_18854))) )
        | ~ c_List_Olist__ex(U_18850,U_18852,U_18854) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK491]),skolemize(U_18845,sK491(U_18854,U_18852,U_18850))],[f_4608_3]) ).

cnf(f_4608_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18850),sK491(U_18854,U_18852,U_18850)),hAPP(c_List_Oset(U_18850),U_18854)))
    | ~ c_List_Olist__ex(U_18850,U_18852,U_18854) ),
    inference(clausify,[status(thm)],[f_4608_4]) ).

cnf(f_4608_6,plain,
    ( hBOOL(hAPP(U_18852,sK491(U_18854,U_18852,U_18850)))
    | ~ c_List_Olist__ex(U_18850,U_18852,U_18854) ),
    inference(clausify,[status(thm)],[f_4608_4]) ).

cnf(f_4608_7,plain,
    ( c_List_Olist__ex(U_18851,U_18853,U_18855)
    | ~ hBOOL(hAPP(U_18853,U_18846))
    | ~ hBOOL(hAPP(hAPP(c_member(U_18851),U_18846),hAPP(c_List_Oset(U_18851),U_18855))) ),
    inference(clausify,[status(thm)],[f_4608_4]) ).

fof(f_4609_1,plain,
    ! [V_xs_2,V_P_2,T_b] :
      ( ( c_List_Olist__ex(T_b,V_P_2,hAPP(c_List_Orev(T_b),V_xs_2))
        | ~ c_List_Olist__ex(T_b,V_P_2,V_xs_2) )
      & ( c_List_Olist__ex(T_b,V_P_2,V_xs_2)
        | ~ c_List_Olist__ex(T_b,V_P_2,hAPP(c_List_Orev(T_b),V_xs_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__ex__rev]) ).

fof(f_4609_2,plain,
    ! [U_18858,U_18857,U_18856] :
      ( ( c_List_Olist__ex(U_18856,U_18857,hAPP(c_List_Orev(U_18856),U_18858))
        | ~ c_List_Olist__ex(U_18856,U_18857,U_18858) )
      & ( c_List_Olist__ex(U_18856,U_18857,U_18858)
        | ~ c_List_Olist__ex(U_18856,U_18857,hAPP(c_List_Orev(U_18856),U_18858)) ) ),
    inference(variable_rename,[status(thm)],[f_4609_1]) ).

fof(f_4609_3,plain,
    ( ! [U_18864,U_18862,U_18860] :
        ( c_List_Olist__ex(U_18860,U_18862,hAPP(c_List_Orev(U_18860),U_18864))
        | ~ c_List_Olist__ex(U_18860,U_18862,U_18864) )
    & ! [U_18863,U_18861,U_18859] :
        ( c_List_Olist__ex(U_18859,U_18861,U_18863)
        | ~ c_List_Olist__ex(U_18859,U_18861,hAPP(c_List_Orev(U_18859),U_18863)) ) ),
    inference(miniscope,[status(thm)],[f_4609_2]) ).

cnf(f_4609_4,plain,
    ( c_List_Olist__ex(U_18859,U_18861,U_18863)
    | ~ c_List_Olist__ex(U_18859,U_18861,hAPP(c_List_Orev(U_18859),U_18863)) ),
    inference(clausify,[status(thm)],[f_4609_3]) ).

cnf(f_4609_5,plain,
    ( c_List_Olist__ex(U_18860,U_18862,hAPP(c_List_Orev(U_18860),U_18864))
    | ~ c_List_Olist__ex(U_18860,U_18862,U_18864) ),
    inference(clausify,[status(thm)],[f_4609_3]) ).

fof(f_4610_1,plain,
    ! [V_xs_2,V_x_2,V_P_2,T_b] :
      ( ( c_List_Olist__ex(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
        | ( ~ c_List_Olist__ex(T_b,V_P_2,V_xs_2)
          & ~ hBOOL(hAPP(V_P_2,V_x_2)) ) )
      & ( c_List_Olist__ex(T_b,V_P_2,V_xs_2)
        | hBOOL(hAPP(V_P_2,V_x_2))
        | ~ c_List_Olist__ex(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__ex__simps_I1_J]) ).

fof(f_4610_2,plain,
    ! [U_18868,U_18867,U_18866,U_18865] :
      ( ( c_List_Olist__ex(U_18865,U_18866,hAPP(hAPP(c_List_Olist_OCons(U_18865),U_18867),U_18868))
        | ( ~ c_List_Olist__ex(U_18865,U_18866,U_18868)
          & ~ hBOOL(hAPP(U_18866,U_18867)) ) )
      & ( c_List_Olist__ex(U_18865,U_18866,U_18868)
        | hBOOL(hAPP(U_18866,U_18867))
        | ~ c_List_Olist__ex(U_18865,U_18866,hAPP(hAPP(c_List_Olist_OCons(U_18865),U_18867),U_18868)) ) ),
    inference(variable_rename,[status(thm)],[f_4610_1]) ).

fof(f_4610_3,plain,
    ( ! [U_18876,U_18874,U_18872,U_18870] :
        ( c_List_Olist__ex(U_18870,U_18872,hAPP(hAPP(c_List_Olist_OCons(U_18870),U_18874),U_18876))
        | ( ~ c_List_Olist__ex(U_18870,U_18872,U_18876)
          & ~ hBOOL(hAPP(U_18872,U_18874)) ) )
    & ! [U_18875,U_18873,U_18871,U_18869] :
        ( c_List_Olist__ex(U_18869,U_18871,U_18875)
        | hBOOL(hAPP(U_18871,U_18873))
        | ~ c_List_Olist__ex(U_18869,U_18871,hAPP(hAPP(c_List_Olist_OCons(U_18869),U_18873),U_18875)) ) ),
    inference(miniscope,[status(thm)],[f_4610_2]) ).

cnf(f_4610_4,plain,
    ( c_List_Olist__ex(U_18869,U_18871,U_18875)
    | hBOOL(hAPP(U_18871,U_18873))
    | ~ c_List_Olist__ex(U_18869,U_18871,hAPP(hAPP(c_List_Olist_OCons(U_18869),U_18873),U_18875)) ),
    inference(clausify,[status(thm)],[f_4610_3]) ).

cnf(f_4610_5,plain,
    ( ~ hBOOL(hAPP(U_18872,U_18874))
    | c_List_Olist__ex(U_18870,U_18872,hAPP(hAPP(c_List_Olist_OCons(U_18870),U_18874),U_18876)) ),
    inference(clausify,[status(thm)],[f_4610_3]) ).

cnf(f_4610_6,plain,
    ( ~ c_List_Olist__ex(U_18870,U_18872,U_18876)
    | c_List_Olist__ex(U_18870,U_18872,hAPP(hAPP(c_List_Olist_OCons(U_18870),U_18874),U_18876)) ),
    inference(clausify,[status(thm)],[f_4610_3]) ).

fof(f_4611_1,plain,
    ! [V_xs_2,V_x_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
        | ! [B_ys,B_zs] : V_xs_2 != hAPP(hAPP(c_List_Oappend(T_b),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_zs)) )
      & ( ? [B_ys,B_zs] : V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_zs))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_in__set__conv__decomp]) ).

fof(f_4611_2,plain,
    ! [U_18883,U_18882,U_18881] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_18881),U_18882),hAPP(c_List_Oset(U_18881),U_18883)))
        | ! [U_18880,U_18879] : U_18883 != hAPP(hAPP(c_List_Oappend(U_18881),U_18880),hAPP(hAPP(c_List_Olist_OCons(U_18881),U_18882),U_18879)) )
      & ( ? [U_18878,U_18877] : U_18883 = hAPP(hAPP(c_List_Oappend(U_18881),U_18878),hAPP(hAPP(c_List_Olist_OCons(U_18881),U_18882),U_18877))
        | ~ hBOOL(hAPP(hAPP(c_member(U_18881),U_18882),hAPP(c_List_Oset(U_18881),U_18883))) ) ),
    inference(variable_rename,[status(thm)],[f_4611_1]) ).

fof(f_4611_3,plain,
    ( ! [U_18889,U_18887,U_18885] :
        ( hBOOL(hAPP(hAPP(c_member(U_18885),U_18887),hAPP(c_List_Oset(U_18885),U_18889)))
        | ! [U_18880,U_18879] : U_18889 != hAPP(hAPP(c_List_Oappend(U_18885),U_18880),hAPP(hAPP(c_List_Olist_OCons(U_18885),U_18887),U_18879)) )
    & ! [U_18888,U_18886,U_18884] :
        ( ? [U_18878,U_18877] : U_18888 = hAPP(hAPP(c_List_Oappend(U_18884),U_18878),hAPP(hAPP(c_List_Olist_OCons(U_18884),U_18886),U_18877))
        | ~ hBOOL(hAPP(hAPP(c_member(U_18884),U_18886),hAPP(c_List_Oset(U_18884),U_18888))) ) ),
    inference(miniscope,[status(thm)],[f_4611_2]) ).

fof(f_4611_4,plain,
    ( ! [U_18889,U_18887,U_18885] :
        ( hBOOL(hAPP(hAPP(c_member(U_18885),U_18887),hAPP(c_List_Oset(U_18885),U_18889)))
        | ! [U_18880,U_18879] : U_18889 != hAPP(hAPP(c_List_Oappend(U_18885),U_18880),hAPP(hAPP(c_List_Olist_OCons(U_18885),U_18887),U_18879)) )
    & ! [U_18888,U_18886,U_18884] :
        ( ? [U_18877] : U_18888 = hAPP(hAPP(c_List_Oappend(U_18884),sK492(U_18888,U_18886,U_18884)),hAPP(hAPP(c_List_Olist_OCons(U_18884),U_18886),U_18877))
        | ~ hBOOL(hAPP(hAPP(c_member(U_18884),U_18886),hAPP(c_List_Oset(U_18884),U_18888))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK492]),skolemize(U_18878,sK492(U_18888,U_18886,U_18884))],[f_4611_3]) ).

fof(f_4611_5,plain,
    ( ! [U_18889,U_18887,U_18885] :
        ( hBOOL(hAPP(hAPP(c_member(U_18885),U_18887),hAPP(c_List_Oset(U_18885),U_18889)))
        | ! [U_18880,U_18879] : U_18889 != hAPP(hAPP(c_List_Oappend(U_18885),U_18880),hAPP(hAPP(c_List_Olist_OCons(U_18885),U_18887),U_18879)) )
    & ! [U_18888,U_18886,U_18884] :
        ( U_18888 = hAPP(hAPP(c_List_Oappend(U_18884),sK492(U_18888,U_18886,U_18884)),hAPP(hAPP(c_List_Olist_OCons(U_18884),U_18886),sK493(U_18888,U_18886,U_18884)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_18884),U_18886),hAPP(c_List_Oset(U_18884),U_18888))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK493]),skolemize(U_18877,sK493(U_18888,U_18886,U_18884))],[f_4611_4]) ).

cnf(f_4611_6,plain,
    ( U_18888 = hAPP(hAPP(c_List_Oappend(U_18884),sK492(U_18888,U_18886,U_18884)),hAPP(hAPP(c_List_Olist_OCons(U_18884),U_18886),sK493(U_18888,U_18886,U_18884)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_18884),U_18886),hAPP(c_List_Oset(U_18884),U_18888))) ),
    inference(clausify,[status(thm)],[f_4611_5]) ).

cnf(f_4611_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18885),U_18887),hAPP(c_List_Oset(U_18885),U_18889)))
    | U_18889 != hAPP(hAPP(c_List_Oappend(U_18885),U_18880),hAPP(hAPP(c_List_Olist_OCons(U_18885),U_18887),U_18879)) ),
    inference(clausify,[status(thm)],[f_4611_5]) ).

fof(f_4612_1,plain,
    ! [V_xs_2,V_x_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
        | ! [B_ys,B_zs] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),B_zs)))
            | V_xs_2 != hAPP(hAPP(c_List_Oappend(T_b),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_zs)) ) )
      & ( ? [B_ys,B_zs] :
            ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),B_zs)))
            & V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_zs)) )
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_in__set__conv__decomp__last]) ).

fof(f_4612_2,plain,
    ! [U_18896,U_18895,U_18894] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_18894),U_18895),hAPP(c_List_Oset(U_18894),U_18896)))
        | ! [U_18893,U_18892] :
            ( hBOOL(hAPP(hAPP(c_member(U_18894),U_18895),hAPP(c_List_Oset(U_18894),U_18892)))
            | U_18896 != hAPP(hAPP(c_List_Oappend(U_18894),U_18893),hAPP(hAPP(c_List_Olist_OCons(U_18894),U_18895),U_18892)) ) )
      & ( ? [U_18891,U_18890] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_18894),U_18895),hAPP(c_List_Oset(U_18894),U_18890)))
            & U_18896 = hAPP(hAPP(c_List_Oappend(U_18894),U_18891),hAPP(hAPP(c_List_Olist_OCons(U_18894),U_18895),U_18890)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_18894),U_18895),hAPP(c_List_Oset(U_18894),U_18896))) ) ),
    inference(variable_rename,[status(thm)],[f_4612_1]) ).

fof(f_4612_3,plain,
    ( ! [U_18902,U_18900,U_18898] :
        ( hBOOL(hAPP(hAPP(c_member(U_18898),U_18900),hAPP(c_List_Oset(U_18898),U_18902)))
        | ! [U_18893,U_18892] :
            ( hBOOL(hAPP(hAPP(c_member(U_18898),U_18900),hAPP(c_List_Oset(U_18898),U_18892)))
            | U_18902 != hAPP(hAPP(c_List_Oappend(U_18898),U_18893),hAPP(hAPP(c_List_Olist_OCons(U_18898),U_18900),U_18892)) ) )
    & ! [U_18901,U_18899,U_18897] :
        ( ? [U_18891,U_18890] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_18897),U_18899),hAPP(c_List_Oset(U_18897),U_18890)))
            & U_18901 = hAPP(hAPP(c_List_Oappend(U_18897),U_18891),hAPP(hAPP(c_List_Olist_OCons(U_18897),U_18899),U_18890)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_18897),U_18899),hAPP(c_List_Oset(U_18897),U_18901))) ) ),
    inference(miniscope,[status(thm)],[f_4612_2]) ).

fof(f_4612_4,plain,
    ( ! [U_18902,U_18900,U_18898] :
        ( hBOOL(hAPP(hAPP(c_member(U_18898),U_18900),hAPP(c_List_Oset(U_18898),U_18902)))
        | ! [U_18893,U_18892] :
            ( hBOOL(hAPP(hAPP(c_member(U_18898),U_18900),hAPP(c_List_Oset(U_18898),U_18892)))
            | U_18902 != hAPP(hAPP(c_List_Oappend(U_18898),U_18893),hAPP(hAPP(c_List_Olist_OCons(U_18898),U_18900),U_18892)) ) )
    & ! [U_18901,U_18899,U_18897] :
        ( ? [U_18890] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_18897),U_18899),hAPP(c_List_Oset(U_18897),U_18890)))
            & U_18901 = hAPP(hAPP(c_List_Oappend(U_18897),sK494(U_18901,U_18899,U_18897)),hAPP(hAPP(c_List_Olist_OCons(U_18897),U_18899),U_18890)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_18897),U_18899),hAPP(c_List_Oset(U_18897),U_18901))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK494]),skolemize(U_18891,sK494(U_18901,U_18899,U_18897))],[f_4612_3]) ).

fof(f_4612_5,plain,
    ( ! [U_18902,U_18900,U_18898] :
        ( hBOOL(hAPP(hAPP(c_member(U_18898),U_18900),hAPP(c_List_Oset(U_18898),U_18902)))
        | ! [U_18893,U_18892] :
            ( hBOOL(hAPP(hAPP(c_member(U_18898),U_18900),hAPP(c_List_Oset(U_18898),U_18892)))
            | U_18902 != hAPP(hAPP(c_List_Oappend(U_18898),U_18893),hAPP(hAPP(c_List_Olist_OCons(U_18898),U_18900),U_18892)) ) )
    & ! [U_18901,U_18899,U_18897] :
        ( ( ~ hBOOL(hAPP(hAPP(c_member(U_18897),U_18899),hAPP(c_List_Oset(U_18897),sK495(U_18901,U_18899,U_18897))))
          & U_18901 = hAPP(hAPP(c_List_Oappend(U_18897),sK494(U_18901,U_18899,U_18897)),hAPP(hAPP(c_List_Olist_OCons(U_18897),U_18899),sK495(U_18901,U_18899,U_18897))) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_18897),U_18899),hAPP(c_List_Oset(U_18897),U_18901))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK495]),skolemize(U_18890,sK495(U_18901,U_18899,U_18897))],[f_4612_4]) ).

cnf(f_4612_6,plain,
    ( U_18901 = hAPP(hAPP(c_List_Oappend(U_18897),sK494(U_18901,U_18899,U_18897)),hAPP(hAPP(c_List_Olist_OCons(U_18897),U_18899),sK495(U_18901,U_18899,U_18897)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_18897),U_18899),hAPP(c_List_Oset(U_18897),U_18901))) ),
    inference(clausify,[status(thm)],[f_4612_5]) ).

cnf(f_4612_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_18897),U_18899),hAPP(c_List_Oset(U_18897),sK495(U_18901,U_18899,U_18897))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_18897),U_18899),hAPP(c_List_Oset(U_18897),U_18901))) ),
    inference(clausify,[status(thm)],[f_4612_5]) ).

cnf(f_4612_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18898),U_18900),hAPP(c_List_Oset(U_18898),U_18902)))
    | hBOOL(hAPP(hAPP(c_member(U_18898),U_18900),hAPP(c_List_Oset(U_18898),U_18892)))
    | U_18902 != hAPP(hAPP(c_List_Oappend(U_18898),U_18893),hAPP(hAPP(c_List_Olist_OCons(U_18898),U_18900),U_18892)) ),
    inference(clausify,[status(thm)],[f_4612_5]) ).

fof(f_4613_1,plain,
    ! [V_xs_2,V_P_2,T_b] :
      ( ( c_List_Olist__all(T_b,V_P_2,V_xs_2)
        | ? [B_n] :
            ( ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ) )
      & ( ! [B_n] :
            ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) )
        | ~ c_List_Olist__all(T_b,V_P_2,V_xs_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__all__length]) ).

fof(f_4613_2,plain,
    ! [U_18907,U_18906,U_18905] :
      ( ( c_List_Olist__all(U_18905,U_18906,U_18907)
        | ? [U_18904] :
            ( ~ hBOOL(hAPP(U_18906,hAPP(hAPP(c_List_Onth(U_18905),U_18907),U_18904)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18904),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18905)),U_18907))) ) )
      & ( ! [U_18903] :
            ( hBOOL(hAPP(U_18906,hAPP(hAPP(c_List_Onth(U_18905),U_18907),U_18903)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18903),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18905)),U_18907))) )
        | ~ c_List_Olist__all(U_18905,U_18906,U_18907) ) ),
    inference(variable_rename,[status(thm)],[f_4613_1]) ).

fof(f_4613_3,plain,
    ( ! [U_18913,U_18911,U_18909] :
        ( c_List_Olist__all(U_18909,U_18911,U_18913)
        | ? [U_18904] :
            ( ~ hBOOL(hAPP(U_18911,hAPP(hAPP(c_List_Onth(U_18909),U_18913),U_18904)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18904),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18909)),U_18913))) ) )
    & ! [U_18912,U_18910,U_18908] :
        ( ! [U_18903] :
            ( hBOOL(hAPP(U_18910,hAPP(hAPP(c_List_Onth(U_18908),U_18912),U_18903)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18903),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18908)),U_18912))) )
        | ~ c_List_Olist__all(U_18908,U_18910,U_18912) ) ),
    inference(miniscope,[status(thm)],[f_4613_2]) ).

fof(f_4613_4,plain,
    ( ! [U_18913,U_18911,U_18909] :
        ( c_List_Olist__all(U_18909,U_18911,U_18913)
        | ( ~ hBOOL(hAPP(U_18911,hAPP(hAPP(c_List_Onth(U_18909),U_18913),sK496(U_18913,U_18911,U_18909))))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK496(U_18913,U_18911,U_18909)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18909)),U_18913))) ) )
    & ! [U_18912,U_18910,U_18908] :
        ( ! [U_18903] :
            ( hBOOL(hAPP(U_18910,hAPP(hAPP(c_List_Onth(U_18908),U_18912),U_18903)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18903),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18908)),U_18912))) )
        | ~ c_List_Olist__all(U_18908,U_18910,U_18912) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK496]),skolemize(U_18904,sK496(U_18913,U_18911,U_18909))],[f_4613_3]) ).

cnf(f_4613_5,plain,
    ( hBOOL(hAPP(U_18910,hAPP(hAPP(c_List_Onth(U_18908),U_18912),U_18903)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18903),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18908)),U_18912)))
    | ~ c_List_Olist__all(U_18908,U_18910,U_18912) ),
    inference(clausify,[status(thm)],[f_4613_4]) ).

cnf(f_4613_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK496(U_18913,U_18911,U_18909)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18909)),U_18913)))
    | c_List_Olist__all(U_18909,U_18911,U_18913) ),
    inference(clausify,[status(thm)],[f_4613_4]) ).

cnf(f_4613_7,plain,
    ( ~ hBOOL(hAPP(U_18911,hAPP(hAPP(c_List_Onth(U_18909),U_18913),sK496(U_18913,U_18911,U_18909))))
    | c_List_Olist__all(U_18909,U_18911,U_18913) ),
    inference(clausify,[status(thm)],[f_4613_4]) ).

fof(f_4614_1,plain,
    c_FunDef_Ois__measure(tc_Int_Oint,hAPP(c_Fun_Ocomp(tc_Int_Oint,tc_Nat_Onat,tc_Int_Oint,c_Int_Onat),c_Groups_Oabs__class_Oabs(tc_Int_Oint))),
    inference(fof_nnf,[status(thm)],[fact_measure__function__int]) ).

cnf(f_4614_2,plain,
    c_FunDef_Ois__measure(tc_Int_Oint,hAPP(c_Fun_Ocomp(tc_Int_Oint,tc_Nat_Onat,tc_Int_Oint,c_Int_Onat),c_Groups_Oabs__class_Oabs(tc_Int_Oint))),
    inference(clausify,[status(thm)],[f_4614_1]) ).

fof(f_4615_1,plain,
    ! [V_P_2,T_b] : c_List_Olist__all(T_b,V_P_2,c_List_Olist_ONil(T_b)),
    inference(fof_nnf,[status(thm)],[fact_list__all__simps_I2_J]) ).

fof(f_4615_2,plain,
    ! [U_18915,U_18914] : c_List_Olist__all(U_18914,U_18915,c_List_Olist_ONil(U_18914)),
    inference(variable_rename,[status(thm)],[f_4615_1]) ).

cnf(f_4615_3,plain,
    c_List_Olist__all(U_18914,U_18915,c_List_Olist_ONil(U_18914)),
    inference(clausify,[status(thm)],[f_4615_2]) ).

fof(f_4616_1,plain,
    ! [V_ys_2,V_xs_2,V_P_2,T_b] :
      ( ( c_List_Olist__all(T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))
        | ~ c_List_Olist__all(T_b,V_P_2,V_ys_2)
        | ~ c_List_Olist__all(T_b,V_P_2,V_xs_2) )
      & ( ( c_List_Olist__all(T_b,V_P_2,V_ys_2)
          & c_List_Olist__all(T_b,V_P_2,V_xs_2) )
        | ~ c_List_Olist__all(T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__all__append]) ).

fof(f_4616_2,plain,
    ! [U_18919,U_18918,U_18917,U_18916] :
      ( ( c_List_Olist__all(U_18916,U_18917,hAPP(hAPP(c_List_Oappend(U_18916),U_18918),U_18919))
        | ~ c_List_Olist__all(U_18916,U_18917,U_18919)
        | ~ c_List_Olist__all(U_18916,U_18917,U_18918) )
      & ( ( c_List_Olist__all(U_18916,U_18917,U_18919)
          & c_List_Olist__all(U_18916,U_18917,U_18918) )
        | ~ c_List_Olist__all(U_18916,U_18917,hAPP(hAPP(c_List_Oappend(U_18916),U_18918),U_18919)) ) ),
    inference(variable_rename,[status(thm)],[f_4616_1]) ).

fof(f_4616_3,plain,
    ( ! [U_18927,U_18925,U_18923,U_18921] :
        ( c_List_Olist__all(U_18921,U_18923,hAPP(hAPP(c_List_Oappend(U_18921),U_18925),U_18927))
        | ~ c_List_Olist__all(U_18921,U_18923,U_18927)
        | ~ c_List_Olist__all(U_18921,U_18923,U_18925) )
    & ! [U_18926,U_18924,U_18922,U_18920] :
        ( ( c_List_Olist__all(U_18920,U_18922,U_18926)
          & c_List_Olist__all(U_18920,U_18922,U_18924) )
        | ~ c_List_Olist__all(U_18920,U_18922,hAPP(hAPP(c_List_Oappend(U_18920),U_18924),U_18926)) ) ),
    inference(miniscope,[status(thm)],[f_4616_2]) ).

cnf(f_4616_4,plain,
    ( c_List_Olist__all(U_18920,U_18922,U_18924)
    | ~ c_List_Olist__all(U_18920,U_18922,hAPP(hAPP(c_List_Oappend(U_18920),U_18924),U_18926)) ),
    inference(clausify,[status(thm)],[f_4616_3]) ).

cnf(f_4616_5,plain,
    ( c_List_Olist__all(U_18920,U_18922,U_18926)
    | ~ c_List_Olist__all(U_18920,U_18922,hAPP(hAPP(c_List_Oappend(U_18920),U_18924),U_18926)) ),
    inference(clausify,[status(thm)],[f_4616_3]) ).

cnf(f_4616_6,plain,
    ( c_List_Olist__all(U_18921,U_18923,hAPP(hAPP(c_List_Oappend(U_18921),U_18925),U_18927))
    | ~ c_List_Olist__all(U_18921,U_18923,U_18927)
    | ~ c_List_Olist__all(U_18921,U_18923,U_18925) ),
    inference(clausify,[status(thm)],[f_4616_3]) ).

fof(f_4617_1,plain,
    ! [T_b] :
      ( c_FunDef_Ois__measure(T_b,c_Nat_Osize__class_Osize(T_b))
      | ~ class_Nat_Osize(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_measure__size]) ).

fof(f_4617_2,plain,
    ! [U_18928] :
      ( c_FunDef_Ois__measure(U_18928,c_Nat_Osize__class_Osize(U_18928))
      | ~ class_Nat_Osize(U_18928) ),
    inference(variable_rename,[status(thm)],[f_4617_1]) ).

cnf(f_4617_3,plain,
    ( c_FunDef_Ois__measure(U_18928,c_Nat_Osize__class_Osize(U_18928))
    | ~ class_Nat_Osize(U_18928) ),
    inference(clausify,[status(thm)],[f_4617_2]) ).

fof(f_4618_1,plain,
    ! [V_f_2,T_b] : c_FunDef_Ois__measure(T_b,V_f_2),
    inference(fof_nnf,[status(thm)],[fact_is__measure_Ointros]) ).

fof(f_4618_2,plain,
    ! [U_18930,U_18929] : c_FunDef_Ois__measure(U_18929,U_18930),
    inference(variable_rename,[status(thm)],[f_4618_1]) ).

cnf(f_4618_3,plain,
    c_FunDef_Ois__measure(U_18929,U_18930),
    inference(clausify,[status(thm)],[f_4618_2]) ).

fof(f_4619_1,plain,
    ! [V_a_2,T_b] : c_FunDef_Ois__measure(T_b,V_a_2),
    inference(fof_nnf,[status(thm)],[fact_is__measure_Oequations]) ).

fof(f_4619_2,plain,
    ! [U_18932,U_18931] : c_FunDef_Ois__measure(U_18931,U_18932),
    inference(variable_rename,[status(thm)],[f_4619_1]) ).

cnf(f_4619_3,plain,
    c_FunDef_Ois__measure(U_18931,U_18932),
    inference(clausify,[status(thm)],[f_4619_2]) ).

fof(f_4620_1,plain,
    ! [V_a_2,T_b] : c_FunDef_Ois__measure(T_b,V_a_2),
    inference(fof_nnf,[status(thm)],[fact_is__measure_Osimps]) ).

fof(f_4620_2,plain,
    ! [U_18934,U_18933] : c_FunDef_Ois__measure(U_18933,U_18934),
    inference(variable_rename,[status(thm)],[f_4620_1]) ).

cnf(f_4620_3,plain,
    c_FunDef_Ois__measure(U_18933,U_18934),
    inference(clausify,[status(thm)],[f_4620_2]) ).

fof(f_4621_1,plain,
    ! [V_xs_2,V_P_2,T_b] :
      ( ( c_List_Olist__all(T_b,V_P_2,V_xs_2)
        | ? [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) ) )
      & ( ! [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) )
        | ~ c_List_Olist__all(T_b,V_P_2,V_xs_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__all__iff]) ).

fof(f_4621_2,plain,
    ! [U_18939,U_18938,U_18937] :
      ( ( c_List_Olist__all(U_18937,U_18938,U_18939)
        | ? [U_18936] :
            ( ~ hBOOL(hAPP(U_18938,U_18936))
            & hBOOL(hAPP(hAPP(c_member(U_18937),U_18936),hAPP(c_List_Oset(U_18937),U_18939))) ) )
      & ( ! [U_18935] :
            ( hBOOL(hAPP(U_18938,U_18935))
            | ~ hBOOL(hAPP(hAPP(c_member(U_18937),U_18935),hAPP(c_List_Oset(U_18937),U_18939))) )
        | ~ c_List_Olist__all(U_18937,U_18938,U_18939) ) ),
    inference(variable_rename,[status(thm)],[f_4621_1]) ).

fof(f_4621_3,plain,
    ( ! [U_18945,U_18943,U_18941] :
        ( c_List_Olist__all(U_18941,U_18943,U_18945)
        | ? [U_18936] :
            ( ~ hBOOL(hAPP(U_18943,U_18936))
            & hBOOL(hAPP(hAPP(c_member(U_18941),U_18936),hAPP(c_List_Oset(U_18941),U_18945))) ) )
    & ! [U_18944,U_18942,U_18940] :
        ( ! [U_18935] :
            ( hBOOL(hAPP(U_18942,U_18935))
            | ~ hBOOL(hAPP(hAPP(c_member(U_18940),U_18935),hAPP(c_List_Oset(U_18940),U_18944))) )
        | ~ c_List_Olist__all(U_18940,U_18942,U_18944) ) ),
    inference(miniscope,[status(thm)],[f_4621_2]) ).

fof(f_4621_4,plain,
    ( ! [U_18945,U_18943,U_18941] :
        ( c_List_Olist__all(U_18941,U_18943,U_18945)
        | ( ~ hBOOL(hAPP(U_18943,sK497(U_18945,U_18943,U_18941)))
          & hBOOL(hAPP(hAPP(c_member(U_18941),sK497(U_18945,U_18943,U_18941)),hAPP(c_List_Oset(U_18941),U_18945))) ) )
    & ! [U_18944,U_18942,U_18940] :
        ( ! [U_18935] :
            ( hBOOL(hAPP(U_18942,U_18935))
            | ~ hBOOL(hAPP(hAPP(c_member(U_18940),U_18935),hAPP(c_List_Oset(U_18940),U_18944))) )
        | ~ c_List_Olist__all(U_18940,U_18942,U_18944) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK497]),skolemize(U_18936,sK497(U_18945,U_18943,U_18941))],[f_4621_3]) ).

cnf(f_4621_5,plain,
    ( hBOOL(hAPP(U_18942,U_18935))
    | ~ hBOOL(hAPP(hAPP(c_member(U_18940),U_18935),hAPP(c_List_Oset(U_18940),U_18944)))
    | ~ c_List_Olist__all(U_18940,U_18942,U_18944) ),
    inference(clausify,[status(thm)],[f_4621_4]) ).

cnf(f_4621_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18941),sK497(U_18945,U_18943,U_18941)),hAPP(c_List_Oset(U_18941),U_18945)))
    | c_List_Olist__all(U_18941,U_18943,U_18945) ),
    inference(clausify,[status(thm)],[f_4621_4]) ).

cnf(f_4621_7,plain,
    ( ~ hBOOL(hAPP(U_18943,sK497(U_18945,U_18943,U_18941)))
    | c_List_Olist__all(U_18941,U_18943,U_18945) ),
    inference(clausify,[status(thm)],[f_4621_4]) ).

fof(f_4622_1,plain,
    ! [T_c,V_f_2,T_b] :
      ( c_FunDef_Ois__measure(tc_prod(T_b,T_c),hAPP(hAPP(c_COMBB(T_b,tc_Nat_Onat,tc_prod(T_b,T_c)),V_f_2),c_Product__Type_Ofst(T_b,T_c)))
      | ~ c_FunDef_Ois__measure(T_b,V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_measure__fst]) ).

fof(f_4622_2,plain,
    ! [U_18948,U_18947,U_18946] :
      ( c_FunDef_Ois__measure(tc_prod(U_18946,U_18948),hAPP(hAPP(c_COMBB(U_18946,tc_Nat_Onat,tc_prod(U_18946,U_18948)),U_18947),c_Product__Type_Ofst(U_18946,U_18948)))
      | ~ c_FunDef_Ois__measure(U_18946,U_18947) ),
    inference(variable_rename,[status(thm)],[f_4622_1]) ).

cnf(f_4622_3,plain,
    ( c_FunDef_Ois__measure(tc_prod(U_18946,U_18948),hAPP(hAPP(c_COMBB(U_18946,tc_Nat_Onat,tc_prod(U_18946,U_18948)),U_18947),c_Product__Type_Ofst(U_18946,U_18948)))
    | ~ c_FunDef_Ois__measure(U_18946,U_18947) ),
    inference(clausify,[status(thm)],[f_4622_2]) ).

fof(f_4623_1,plain,
    ! [T_c,V_f_2,T_b] :
      ( c_FunDef_Ois__measure(tc_prod(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,tc_Nat_Onat,tc_prod(T_c,T_b)),V_f_2),c_Product__Type_Osnd(T_c,T_b)))
      | ~ c_FunDef_Ois__measure(T_b,V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_measure__snd]) ).

fof(f_4623_2,plain,
    ! [U_18951,U_18950,U_18949] :
      ( c_FunDef_Ois__measure(tc_prod(U_18951,U_18949),hAPP(hAPP(c_COMBB(U_18949,tc_Nat_Onat,tc_prod(U_18951,U_18949)),U_18950),c_Product__Type_Osnd(U_18951,U_18949)))
      | ~ c_FunDef_Ois__measure(U_18949,U_18950) ),
    inference(variable_rename,[status(thm)],[f_4623_1]) ).

cnf(f_4623_3,plain,
    ( c_FunDef_Ois__measure(tc_prod(U_18951,U_18949),hAPP(hAPP(c_COMBB(U_18949,tc_Nat_Onat,tc_prod(U_18951,U_18949)),U_18950),c_Product__Type_Osnd(U_18951,U_18949)))
    | ~ c_FunDef_Ois__measure(U_18949,U_18950) ),
    inference(clausify,[status(thm)],[f_4623_2]) ).

fof(f_4624_1,plain,
    ! [V_xs_2,V_P_2,T_b] :
      ( ( c_List_Olist__all(T_b,V_P_2,hAPP(c_List_Orev(T_b),V_xs_2))
        | ~ c_List_Olist__all(T_b,V_P_2,V_xs_2) )
      & ( c_List_Olist__all(T_b,V_P_2,V_xs_2)
        | ~ c_List_Olist__all(T_b,V_P_2,hAPP(c_List_Orev(T_b),V_xs_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__all__rev]) ).

fof(f_4624_2,plain,
    ! [U_18954,U_18953,U_18952] :
      ( ( c_List_Olist__all(U_18952,U_18953,hAPP(c_List_Orev(U_18952),U_18954))
        | ~ c_List_Olist__all(U_18952,U_18953,U_18954) )
      & ( c_List_Olist__all(U_18952,U_18953,U_18954)
        | ~ c_List_Olist__all(U_18952,U_18953,hAPP(c_List_Orev(U_18952),U_18954)) ) ),
    inference(variable_rename,[status(thm)],[f_4624_1]) ).

fof(f_4624_3,plain,
    ( ! [U_18960,U_18958,U_18956] :
        ( c_List_Olist__all(U_18956,U_18958,hAPP(c_List_Orev(U_18956),U_18960))
        | ~ c_List_Olist__all(U_18956,U_18958,U_18960) )
    & ! [U_18959,U_18957,U_18955] :
        ( c_List_Olist__all(U_18955,U_18957,U_18959)
        | ~ c_List_Olist__all(U_18955,U_18957,hAPP(c_List_Orev(U_18955),U_18959)) ) ),
    inference(miniscope,[status(thm)],[f_4624_2]) ).

cnf(f_4624_4,plain,
    ( c_List_Olist__all(U_18955,U_18957,U_18959)
    | ~ c_List_Olist__all(U_18955,U_18957,hAPP(c_List_Orev(U_18955),U_18959)) ),
    inference(clausify,[status(thm)],[f_4624_3]) ).

cnf(f_4624_5,plain,
    ( c_List_Olist__all(U_18956,U_18958,hAPP(c_List_Orev(U_18956),U_18960))
    | ~ c_List_Olist__all(U_18956,U_18958,U_18960) ),
    inference(clausify,[status(thm)],[f_4624_3]) ).

fof(f_4625_1,plain,
    ! [V_xs_2,V_x_2,V_P_2,T_b] :
      ( ( c_List_Olist__all(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
        | ~ c_List_Olist__all(T_b,V_P_2,V_xs_2)
        | ~ hBOOL(hAPP(V_P_2,V_x_2)) )
      & ( ( c_List_Olist__all(T_b,V_P_2,V_xs_2)
          & hBOOL(hAPP(V_P_2,V_x_2)) )
        | ~ c_List_Olist__all(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__all__simps_I1_J]) ).

fof(f_4625_2,plain,
    ! [U_18964,U_18963,U_18962,U_18961] :
      ( ( c_List_Olist__all(U_18961,U_18962,hAPP(hAPP(c_List_Olist_OCons(U_18961),U_18963),U_18964))
        | ~ c_List_Olist__all(U_18961,U_18962,U_18964)
        | ~ hBOOL(hAPP(U_18962,U_18963)) )
      & ( ( c_List_Olist__all(U_18961,U_18962,U_18964)
          & hBOOL(hAPP(U_18962,U_18963)) )
        | ~ c_List_Olist__all(U_18961,U_18962,hAPP(hAPP(c_List_Olist_OCons(U_18961),U_18963),U_18964)) ) ),
    inference(variable_rename,[status(thm)],[f_4625_1]) ).

fof(f_4625_3,plain,
    ( ! [U_18972,U_18970,U_18968,U_18966] :
        ( c_List_Olist__all(U_18966,U_18968,hAPP(hAPP(c_List_Olist_OCons(U_18966),U_18970),U_18972))
        | ~ c_List_Olist__all(U_18966,U_18968,U_18972)
        | ~ hBOOL(hAPP(U_18968,U_18970)) )
    & ! [U_18971,U_18969,U_18967,U_18965] :
        ( ( c_List_Olist__all(U_18965,U_18967,U_18971)
          & hBOOL(hAPP(U_18967,U_18969)) )
        | ~ c_List_Olist__all(U_18965,U_18967,hAPP(hAPP(c_List_Olist_OCons(U_18965),U_18969),U_18971)) ) ),
    inference(miniscope,[status(thm)],[f_4625_2]) ).

cnf(f_4625_4,plain,
    ( hBOOL(hAPP(U_18967,U_18969))
    | ~ c_List_Olist__all(U_18965,U_18967,hAPP(hAPP(c_List_Olist_OCons(U_18965),U_18969),U_18971)) ),
    inference(clausify,[status(thm)],[f_4625_3]) ).

cnf(f_4625_5,plain,
    ( c_List_Olist__all(U_18965,U_18967,U_18971)
    | ~ c_List_Olist__all(U_18965,U_18967,hAPP(hAPP(c_List_Olist_OCons(U_18965),U_18969),U_18971)) ),
    inference(clausify,[status(thm)],[f_4625_3]) ).

cnf(f_4625_6,plain,
    ( c_List_Olist__all(U_18966,U_18968,hAPP(hAPP(c_List_Olist_OCons(U_18966),U_18970),U_18972))
    | ~ c_List_Olist__all(U_18966,U_18968,U_18972)
    | ~ hBOOL(hAPP(U_18968,U_18970)) ),
    inference(clausify,[status(thm)],[f_4625_3]) ).

fof(f_4626_1,plain,
    ! [V_P_2,V_xs_2,T_b] :
      ( ( ! [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) )
        | ~ c_List_Olist__all(T_b,V_P_2,V_xs_2) )
      & ( c_List_Olist__all(T_b,V_P_2,V_xs_2)
        | ? [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_Ball__set__list__all]) ).

fof(f_4626_2,plain,
    ! [U_18977,U_18976,U_18975] :
      ( ( ! [U_18974] :
            ( hBOOL(hAPP(U_18977,U_18974))
            | ~ hBOOL(hAPP(hAPP(c_member(U_18975),U_18974),hAPP(c_List_Oset(U_18975),U_18976))) )
        | ~ c_List_Olist__all(U_18975,U_18977,U_18976) )
      & ( c_List_Olist__all(U_18975,U_18977,U_18976)
        | ? [U_18973] :
            ( ~ hBOOL(hAPP(U_18977,U_18973))
            & hBOOL(hAPP(hAPP(c_member(U_18975),U_18973),hAPP(c_List_Oset(U_18975),U_18976))) ) ) ),
    inference(variable_rename,[status(thm)],[f_4626_1]) ).

fof(f_4626_3,plain,
    ( ! [U_18983,U_18981,U_18979] :
        ( ! [U_18974] :
            ( hBOOL(hAPP(U_18983,U_18974))
            | ~ hBOOL(hAPP(hAPP(c_member(U_18979),U_18974),hAPP(c_List_Oset(U_18979),U_18981))) )
        | ~ c_List_Olist__all(U_18979,U_18983,U_18981) )
    & ! [U_18982,U_18980,U_18978] :
        ( c_List_Olist__all(U_18978,U_18982,U_18980)
        | ? [U_18973] :
            ( ~ hBOOL(hAPP(U_18982,U_18973))
            & hBOOL(hAPP(hAPP(c_member(U_18978),U_18973),hAPP(c_List_Oset(U_18978),U_18980))) ) ) ),
    inference(miniscope,[status(thm)],[f_4626_2]) ).

fof(f_4626_4,plain,
    ( ! [U_18983,U_18981,U_18979] :
        ( ! [U_18974] :
            ( hBOOL(hAPP(U_18983,U_18974))
            | ~ hBOOL(hAPP(hAPP(c_member(U_18979),U_18974),hAPP(c_List_Oset(U_18979),U_18981))) )
        | ~ c_List_Olist__all(U_18979,U_18983,U_18981) )
    & ! [U_18982,U_18980,U_18978] :
        ( c_List_Olist__all(U_18978,U_18982,U_18980)
        | ( ~ hBOOL(hAPP(U_18982,sK498(U_18982,U_18980,U_18978)))
          & hBOOL(hAPP(hAPP(c_member(U_18978),sK498(U_18982,U_18980,U_18978)),hAPP(c_List_Oset(U_18978),U_18980))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK498]),skolemize(U_18973,sK498(U_18982,U_18980,U_18978))],[f_4626_3]) ).

cnf(f_4626_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18978),sK498(U_18982,U_18980,U_18978)),hAPP(c_List_Oset(U_18978),U_18980)))
    | c_List_Olist__all(U_18978,U_18982,U_18980) ),
    inference(clausify,[status(thm)],[f_4626_4]) ).

cnf(f_4626_6,plain,
    ( ~ hBOOL(hAPP(U_18982,sK498(U_18982,U_18980,U_18978)))
    | c_List_Olist__all(U_18978,U_18982,U_18980) ),
    inference(clausify,[status(thm)],[f_4626_4]) ).

cnf(f_4626_7,plain,
    ( hBOOL(hAPP(U_18983,U_18974))
    | ~ hBOOL(hAPP(hAPP(c_member(U_18979),U_18974),hAPP(c_List_Oset(U_18979),U_18981)))
    | ~ c_List_Olist__all(U_18979,U_18983,U_18981) ),
    inference(clausify,[status(thm)],[f_4626_4]) ).

fof(f_4627_1,plain,
    ! [V_xs_2,V_P_2,T_b] :
      ( ( c_List_Olist__all(T_b,V_P_2,V_xs_2)
        | ? [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) ) )
      & ( ! [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) )
        | ~ c_List_Olist__all(T_b,V_P_2,V_xs_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__all__iff__raw]) ).

fof(f_4627_2,plain,
    ! [U_18988,U_18987,U_18986] :
      ( ( c_List_Olist__all(U_18986,U_18987,U_18988)
        | ? [U_18985] :
            ( ~ hBOOL(hAPP(U_18987,U_18985))
            & hBOOL(hAPP(hAPP(c_member(U_18986),U_18985),hAPP(c_List_Oset(U_18986),U_18988))) ) )
      & ( ! [U_18984] :
            ( hBOOL(hAPP(U_18987,U_18984))
            | ~ hBOOL(hAPP(hAPP(c_member(U_18986),U_18984),hAPP(c_List_Oset(U_18986),U_18988))) )
        | ~ c_List_Olist__all(U_18986,U_18987,U_18988) ) ),
    inference(variable_rename,[status(thm)],[f_4627_1]) ).

fof(f_4627_3,plain,
    ( ! [U_18994,U_18992,U_18990] :
        ( c_List_Olist__all(U_18990,U_18992,U_18994)
        | ? [U_18985] :
            ( ~ hBOOL(hAPP(U_18992,U_18985))
            & hBOOL(hAPP(hAPP(c_member(U_18990),U_18985),hAPP(c_List_Oset(U_18990),U_18994))) ) )
    & ! [U_18993,U_18991,U_18989] :
        ( ! [U_18984] :
            ( hBOOL(hAPP(U_18991,U_18984))
            | ~ hBOOL(hAPP(hAPP(c_member(U_18989),U_18984),hAPP(c_List_Oset(U_18989),U_18993))) )
        | ~ c_List_Olist__all(U_18989,U_18991,U_18993) ) ),
    inference(miniscope,[status(thm)],[f_4627_2]) ).

fof(f_4627_4,plain,
    ( ! [U_18994,U_18992,U_18990] :
        ( c_List_Olist__all(U_18990,U_18992,U_18994)
        | ( ~ hBOOL(hAPP(U_18992,sK499(U_18994,U_18992,U_18990)))
          & hBOOL(hAPP(hAPP(c_member(U_18990),sK499(U_18994,U_18992,U_18990)),hAPP(c_List_Oset(U_18990),U_18994))) ) )
    & ! [U_18993,U_18991,U_18989] :
        ( ! [U_18984] :
            ( hBOOL(hAPP(U_18991,U_18984))
            | ~ hBOOL(hAPP(hAPP(c_member(U_18989),U_18984),hAPP(c_List_Oset(U_18989),U_18993))) )
        | ~ c_List_Olist__all(U_18989,U_18991,U_18993) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK499]),skolemize(U_18985,sK499(U_18994,U_18992,U_18990))],[f_4627_3]) ).

cnf(f_4627_5,plain,
    ( hBOOL(hAPP(U_18991,U_18984))
    | ~ hBOOL(hAPP(hAPP(c_member(U_18989),U_18984),hAPP(c_List_Oset(U_18989),U_18993)))
    | ~ c_List_Olist__all(U_18989,U_18991,U_18993) ),
    inference(clausify,[status(thm)],[f_4627_4]) ).

cnf(f_4627_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18990),sK499(U_18994,U_18992,U_18990)),hAPP(c_List_Oset(U_18990),U_18994)))
    | c_List_Olist__all(U_18990,U_18992,U_18994) ),
    inference(clausify,[status(thm)],[f_4627_4]) ).

cnf(f_4627_7,plain,
    ( ~ hBOOL(hAPP(U_18992,sK499(U_18994,U_18992,U_18990)))
    | c_List_Olist__all(U_18990,U_18992,U_18994) ),
    inference(clausify,[status(thm)],[f_4627_4]) ).

fof(f_4628_1,plain,
    ! [V_xs_2,V_x_2,V_P_2,T_b] :
      ( ( c_List_Olist__ex1(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
        | ( ~ c_List_Olist__ex1(T_b,V_P_2,V_xs_2)
          & ~ hBOOL(hAPP(V_P_2,V_x_2)) )
        | ( ~ c_List_Olist__all(T_b,hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_P_2))),hAPP(c_fequal,V_x_2)),V_xs_2)
          & hBOOL(hAPP(V_P_2,V_x_2)) ) )
      & ( ( ( c_List_Olist__ex1(T_b,V_P_2,V_xs_2)
            | hBOOL(hAPP(V_P_2,V_x_2)) )
          & ( c_List_Olist__all(T_b,hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_P_2))),hAPP(c_fequal,V_x_2)),V_xs_2)
            | ~ hBOOL(hAPP(V_P_2,V_x_2)) ) )
        | ~ c_List_Olist__ex1(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__ex1__simps_I2_J]) ).

fof(f_4628_2,plain,
    ! [U_18998,U_18997,U_18996,U_18995] :
      ( ( c_List_Olist__ex1(U_18995,U_18996,hAPP(hAPP(c_List_Olist_OCons(U_18995),U_18997),U_18998))
        | ( ~ c_List_Olist__ex1(U_18995,U_18996,U_18998)
          & ~ hBOOL(hAPP(U_18996,U_18997)) )
        | ( ~ c_List_Olist__all(U_18995,hAPP(hAPP(c_COMBS(U_18995,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_18995),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_18995),c_fNot),U_18996))),hAPP(c_fequal,U_18997)),U_18998)
          & hBOOL(hAPP(U_18996,U_18997)) ) )
      & ( ( ( c_List_Olist__ex1(U_18995,U_18996,U_18998)
            | hBOOL(hAPP(U_18996,U_18997)) )
          & ( c_List_Olist__all(U_18995,hAPP(hAPP(c_COMBS(U_18995,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_18995),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_18995),c_fNot),U_18996))),hAPP(c_fequal,U_18997)),U_18998)
            | ~ hBOOL(hAPP(U_18996,U_18997)) ) )
        | ~ c_List_Olist__ex1(U_18995,U_18996,hAPP(hAPP(c_List_Olist_OCons(U_18995),U_18997),U_18998)) ) ),
    inference(variable_rename,[status(thm)],[f_4628_1]) ).

fof(f_4628_3,plain,
    ( ! [U_19006,U_19004,U_19002,U_19000] :
        ( c_List_Olist__ex1(U_19000,U_19002,hAPP(hAPP(c_List_Olist_OCons(U_19000),U_19004),U_19006))
        | ( ~ c_List_Olist__ex1(U_19000,U_19002,U_19006)
          & ~ hBOOL(hAPP(U_19002,U_19004)) )
        | ( ~ c_List_Olist__all(U_19000,hAPP(hAPP(c_COMBS(U_19000,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_19000),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_19000),c_fNot),U_19002))),hAPP(c_fequal,U_19004)),U_19006)
          & hBOOL(hAPP(U_19002,U_19004)) ) )
    & ! [U_19005,U_19003,U_19001,U_18999] :
        ( ( ( c_List_Olist__ex1(U_18999,U_19001,U_19005)
            | hBOOL(hAPP(U_19001,U_19003)) )
          & ( c_List_Olist__all(U_18999,hAPP(hAPP(c_COMBS(U_18999,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_18999),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_18999),c_fNot),U_19001))),hAPP(c_fequal,U_19003)),U_19005)
            | ~ hBOOL(hAPP(U_19001,U_19003)) ) )
        | ~ c_List_Olist__ex1(U_18999,U_19001,hAPP(hAPP(c_List_Olist_OCons(U_18999),U_19003),U_19005)) ) ),
    inference(miniscope,[status(thm)],[f_4628_2]) ).

cnf(f_4628_4,plain,
    ( c_List_Olist__all(U_18999,hAPP(hAPP(c_COMBS(U_18999,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_18999),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_18999),c_fNot),U_19001))),hAPP(c_fequal,U_19003)),U_19005)
    | ~ hBOOL(hAPP(U_19001,U_19003))
    | ~ c_List_Olist__ex1(U_18999,U_19001,hAPP(hAPP(c_List_Olist_OCons(U_18999),U_19003),U_19005)) ),
    inference(clausify,[status(thm)],[f_4628_3]) ).

cnf(f_4628_5,plain,
    ( c_List_Olist__ex1(U_18999,U_19001,U_19005)
    | hBOOL(hAPP(U_19001,U_19003))
    | ~ c_List_Olist__ex1(U_18999,U_19001,hAPP(hAPP(c_List_Olist_OCons(U_18999),U_19003),U_19005)) ),
    inference(clausify,[status(thm)],[f_4628_3]) ).

cnf(f_4628_6,plain,
    ( ~ hBOOL(hAPP(U_19002,U_19004))
    | hBOOL(hAPP(U_19002,U_19004))
    | c_List_Olist__ex1(U_19000,U_19002,hAPP(hAPP(c_List_Olist_OCons(U_19000),U_19004),U_19006)) ),
    inference(clausify,[status(thm)],[f_4628_3]) ).

cnf(f_4628_7,plain,
    ( ~ c_List_Olist__ex1(U_19000,U_19002,U_19006)
    | hBOOL(hAPP(U_19002,U_19004))
    | c_List_Olist__ex1(U_19000,U_19002,hAPP(hAPP(c_List_Olist_OCons(U_19000),U_19004),U_19006)) ),
    inference(clausify,[status(thm)],[f_4628_3]) ).

cnf(f_4628_8,plain,
    ( ~ hBOOL(hAPP(U_19002,U_19004))
    | ~ c_List_Olist__all(U_19000,hAPP(hAPP(c_COMBS(U_19000,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_19000),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_19000),c_fNot),U_19002))),hAPP(c_fequal,U_19004)),U_19006)
    | c_List_Olist__ex1(U_19000,U_19002,hAPP(hAPP(c_List_Olist_OCons(U_19000),U_19004),U_19006)) ),
    inference(clausify,[status(thm)],[f_4628_3]) ).

cnf(f_4628_9,plain,
    ( ~ c_List_Olist__ex1(U_19000,U_19002,U_19006)
    | ~ c_List_Olist__all(U_19000,hAPP(hAPP(c_COMBS(U_19000,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_19000),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_19000),c_fNot),U_19002))),hAPP(c_fequal,U_19004)),U_19006)
    | c_List_Olist__ex1(U_19000,U_19002,hAPP(hAPP(c_List_Olist_OCons(U_19000),U_19004),U_19006)) ),
    inference(clausify,[status(thm)],[f_4628_3]) ).

fof(f_4629_1,plain,
    c_Nat__Transfer_Otransfer__morphism(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_COMBK(tc_HOL_Obool,tc_Nat_Onat),c_fTrue)),
    inference(fof_nnf,[status(thm)],[fact_transfer__morphism__int__nat]) ).

cnf(f_4629_2,plain,
    c_Nat__Transfer_Otransfer__morphism(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_COMBK(tc_HOL_Obool,tc_Nat_Onat),c_fTrue)),
    inference(clausify,[status(thm)],[f_4629_1]) ).

fof(f_4630_1,plain,
    ! [V_P_2,T_b] : ~ c_List_Olist__ex1(T_b,V_P_2,c_List_Olist_ONil(T_b)),
    inference(fof_nnf,[status(thm)],[fact_list__ex1__simps_I1_J]) ).

fof(f_4630_2,plain,
    ! [U_19008,U_19007] : ~ c_List_Olist__ex1(U_19007,U_19008,c_List_Olist_ONil(U_19007)),
    inference(variable_rename,[status(thm)],[f_4630_1]) ).

cnf(f_4630_3,plain,
    ~ c_List_Olist__ex1(U_19007,U_19008,c_List_Olist_ONil(U_19007)),
    inference(clausify,[status(thm)],[f_4630_2]) ).

fof(f_4631_1,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_bool_Osize_I4_J]) ).

cnf(f_4631_2,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_4631_1]) ).

fof(f_4632_1,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_bool_Osize_I3_J]) ).

cnf(f_4632_2,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_4632_1]) ).

fof(f_4633_1,plain,
    ! [V_xs_2,V_P_2,T_b] :
      ( ( c_List_Olist__ex1(T_b,V_P_2,V_xs_2)
        | ! [B_x] :
            ( ? [B_y] :
                ( B_y != B_x
                & hBOOL(hAPP(V_P_2,B_y))
                & hBOOL(hAPP(hAPP(c_member(T_b),B_y),hAPP(c_List_Oset(T_b),V_xs_2))) )
            | ~ hBOOL(hAPP(V_P_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) ) )
      & ( ? [B_x] :
            ( ! [B_y] :
                ( B_y = B_x
                | ~ hBOOL(hAPP(V_P_2,B_y))
                | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_y),hAPP(c_List_Oset(T_b),V_xs_2))) )
            & hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) )
        | ~ c_List_Olist__ex1(T_b,V_P_2,V_xs_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__ex1__iff]) ).

fof(f_4633_2,plain,
    ! [U_19015,U_19014,U_19013] :
      ( ( c_List_Olist__ex1(U_19013,U_19014,U_19015)
        | ! [U_19012] :
            ( ? [U_19011] :
                ( U_19011 != U_19012
                & hBOOL(hAPP(U_19014,U_19011))
                & hBOOL(hAPP(hAPP(c_member(U_19013),U_19011),hAPP(c_List_Oset(U_19013),U_19015))) )
            | ~ hBOOL(hAPP(U_19014,U_19012))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19013),U_19012),hAPP(c_List_Oset(U_19013),U_19015))) ) )
      & ( ? [U_19010] :
            ( ! [U_19009] :
                ( U_19009 = U_19010
                | ~ hBOOL(hAPP(U_19014,U_19009))
                | ~ hBOOL(hAPP(hAPP(c_member(U_19013),U_19009),hAPP(c_List_Oset(U_19013),U_19015))) )
            & hBOOL(hAPP(U_19014,U_19010))
            & hBOOL(hAPP(hAPP(c_member(U_19013),U_19010),hAPP(c_List_Oset(U_19013),U_19015))) )
        | ~ c_List_Olist__ex1(U_19013,U_19014,U_19015) ) ),
    inference(variable_rename,[status(thm)],[f_4633_1]) ).

fof(f_4633_3,plain,
    ( ! [U_19021,U_19019,U_19017] :
        ( c_List_Olist__ex1(U_19017,U_19019,U_19021)
        | ! [U_19012] :
            ( ? [U_19011] :
                ( U_19011 != U_19012
                & hBOOL(hAPP(U_19019,U_19011))
                & hBOOL(hAPP(hAPP(c_member(U_19017),U_19011),hAPP(c_List_Oset(U_19017),U_19021))) )
            | ~ hBOOL(hAPP(U_19019,U_19012))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19017),U_19012),hAPP(c_List_Oset(U_19017),U_19021))) ) )
    & ! [U_19020,U_19018,U_19016] :
        ( ? [U_19010] :
            ( ! [U_19009] :
                ( U_19009 = U_19010
                | ~ hBOOL(hAPP(U_19018,U_19009))
                | ~ hBOOL(hAPP(hAPP(c_member(U_19016),U_19009),hAPP(c_List_Oset(U_19016),U_19020))) )
            & hBOOL(hAPP(U_19018,U_19010))
            & hBOOL(hAPP(hAPP(c_member(U_19016),U_19010),hAPP(c_List_Oset(U_19016),U_19020))) )
        | ~ c_List_Olist__ex1(U_19016,U_19018,U_19020) ) ),
    inference(miniscope,[status(thm)],[f_4633_2]) ).

fof(f_4633_4,plain,
    ( ! [U_19021,U_19019,U_19017] :
        ( c_List_Olist__ex1(U_19017,U_19019,U_19021)
        | ! [U_19012] :
            ( ? [U_19011] :
                ( U_19011 != U_19012
                & hBOOL(hAPP(U_19019,U_19011))
                & hBOOL(hAPP(hAPP(c_member(U_19017),U_19011),hAPP(c_List_Oset(U_19017),U_19021))) )
            | ~ hBOOL(hAPP(U_19019,U_19012))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19017),U_19012),hAPP(c_List_Oset(U_19017),U_19021))) ) )
    & ! [U_19020,U_19018,U_19016] :
        ( ( ! [U_19009] :
              ( U_19009 = sK500(U_19020,U_19018,U_19016)
              | ~ hBOOL(hAPP(U_19018,U_19009))
              | ~ hBOOL(hAPP(hAPP(c_member(U_19016),U_19009),hAPP(c_List_Oset(U_19016),U_19020))) )
          & hBOOL(hAPP(U_19018,sK500(U_19020,U_19018,U_19016)))
          & hBOOL(hAPP(hAPP(c_member(U_19016),sK500(U_19020,U_19018,U_19016)),hAPP(c_List_Oset(U_19016),U_19020))) )
        | ~ c_List_Olist__ex1(U_19016,U_19018,U_19020) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK500]),skolemize(U_19010,sK500(U_19020,U_19018,U_19016))],[f_4633_3]) ).

fof(f_4633_5,plain,
    ( ! [U_19021,U_19019,U_19017] :
        ( c_List_Olist__ex1(U_19017,U_19019,U_19021)
        | ! [U_19012] :
            ( ( sK501(U_19021,U_19019,U_19017,U_19012) != U_19012
              & hBOOL(hAPP(U_19019,sK501(U_19021,U_19019,U_19017,U_19012)))
              & hBOOL(hAPP(hAPP(c_member(U_19017),sK501(U_19021,U_19019,U_19017,U_19012)),hAPP(c_List_Oset(U_19017),U_19021))) )
            | ~ hBOOL(hAPP(U_19019,U_19012))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19017),U_19012),hAPP(c_List_Oset(U_19017),U_19021))) ) )
    & ! [U_19020,U_19018,U_19016] :
        ( ( ! [U_19009] :
              ( U_19009 = sK500(U_19020,U_19018,U_19016)
              | ~ hBOOL(hAPP(U_19018,U_19009))
              | ~ hBOOL(hAPP(hAPP(c_member(U_19016),U_19009),hAPP(c_List_Oset(U_19016),U_19020))) )
          & hBOOL(hAPP(U_19018,sK500(U_19020,U_19018,U_19016)))
          & hBOOL(hAPP(hAPP(c_member(U_19016),sK500(U_19020,U_19018,U_19016)),hAPP(c_List_Oset(U_19016),U_19020))) )
        | ~ c_List_Olist__ex1(U_19016,U_19018,U_19020) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK501]),skolemize(U_19011,sK501(U_19021,U_19019,U_19017,U_19012))],[f_4633_4]) ).

cnf(f_4633_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19016),sK500(U_19020,U_19018,U_19016)),hAPP(c_List_Oset(U_19016),U_19020)))
    | ~ c_List_Olist__ex1(U_19016,U_19018,U_19020) ),
    inference(clausify,[status(thm)],[f_4633_5]) ).

cnf(f_4633_7,plain,
    ( hBOOL(hAPP(U_19018,sK500(U_19020,U_19018,U_19016)))
    | ~ c_List_Olist__ex1(U_19016,U_19018,U_19020) ),
    inference(clausify,[status(thm)],[f_4633_5]) ).

cnf(f_4633_8,plain,
    ( U_19009 = sK500(U_19020,U_19018,U_19016)
    | ~ hBOOL(hAPP(U_19018,U_19009))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19016),U_19009),hAPP(c_List_Oset(U_19016),U_19020)))
    | ~ c_List_Olist__ex1(U_19016,U_19018,U_19020) ),
    inference(clausify,[status(thm)],[f_4633_5]) ).

cnf(f_4633_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19017),sK501(U_19021,U_19019,U_19017,U_19012)),hAPP(c_List_Oset(U_19017),U_19021)))
    | ~ hBOOL(hAPP(U_19019,U_19012))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19017),U_19012),hAPP(c_List_Oset(U_19017),U_19021)))
    | c_List_Olist__ex1(U_19017,U_19019,U_19021) ),
    inference(clausify,[status(thm)],[f_4633_5]) ).

cnf(f_4633_10,plain,
    ( hBOOL(hAPP(U_19019,sK501(U_19021,U_19019,U_19017,U_19012)))
    | ~ hBOOL(hAPP(U_19019,U_19012))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19017),U_19012),hAPP(c_List_Oset(U_19017),U_19021)))
    | c_List_Olist__ex1(U_19017,U_19019,U_19021) ),
    inference(clausify,[status(thm)],[f_4633_5]) ).

cnf(f_4633_11,plain,
    ( sK501(U_19021,U_19019,U_19017,U_19012) != U_19012
    | ~ hBOOL(hAPP(U_19019,U_19012))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19017),U_19012),hAPP(c_List_Oset(U_19017),U_19021)))
    | c_List_Olist__ex1(U_19017,U_19019,U_19021) ),
    inference(clausify,[status(thm)],[f_4633_5]) ).

fof(f_4634_1,plain,
    ! [V_f_2,V_x_2,T_b,T_c,V_i_2] :
      ( ( hAPP(c_New__DSequence_Opos__decr__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = hAPP(c_Lazy__Sequence_Obind(T_c,T_b,hAPP(V_x_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_i_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b)),V_f_2),V_i_2))
        | V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
      & ( hAPP(c_New__DSequence_Opos__decr__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Oempty(T_b)
        | V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(fof_nnf,[status(thm)],[fact_New__DSequence_Opos__decr__bind__def]) ).

fof(f_4634_2,plain,
    ! [U_19026,U_19025,U_19024,U_19023,U_19022] :
      ( ( hAPP(c_New__DSequence_Opos__decr__bind(U_19023,U_19024,U_19025,U_19026),U_19022) = hAPP(c_Lazy__Sequence_Obind(U_19023,U_19024,hAPP(U_19025,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_19022),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBC(U_19023,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_19024)),U_19026),U_19022))
        | U_19022 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
      & ( hAPP(c_New__DSequence_Opos__decr__bind(U_19023,U_19024,U_19025,U_19026),U_19022) = c_Lazy__Sequence_Oempty(U_19024)
        | U_19022 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(variable_rename,[status(thm)],[f_4634_1]) ).

fof(f_4634_3,plain,
    ( ! [U_19036,U_19034,U_19032,U_19030,U_19028] :
        ( hAPP(c_New__DSequence_Opos__decr__bind(U_19030,U_19032,U_19034,U_19036),U_19028) = hAPP(c_Lazy__Sequence_Obind(U_19030,U_19032,hAPP(U_19034,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_19028),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBC(U_19030,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_19032)),U_19036),U_19028))
        | U_19028 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
    & ! [U_19035,U_19033,U_19031,U_19029,U_19027] :
        ( hAPP(c_New__DSequence_Opos__decr__bind(U_19029,U_19031,U_19033,U_19035),U_19027) = c_Lazy__Sequence_Oempty(U_19031)
        | U_19027 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(miniscope,[status(thm)],[f_4634_2]) ).

cnf(f_4634_4,plain,
    ( hAPP(c_New__DSequence_Opos__decr__bind(U_19029,U_19031,U_19033,U_19035),U_19027) = c_Lazy__Sequence_Oempty(U_19031)
    | U_19027 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_4634_3]) ).

cnf(f_4634_5,plain,
    ( hAPP(c_New__DSequence_Opos__decr__bind(U_19030,U_19032,U_19034,U_19036),U_19028) = hAPP(c_Lazy__Sequence_Obind(U_19030,U_19032,hAPP(U_19034,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_19028),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBC(U_19030,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_19032)),U_19036),U_19028))
    | U_19028 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_4634_3]) ).

fof(f_4635_1,plain,
    ! [V_f_2,V_x_2,T_b,T_c,V_i_2] :
      ( ( hAPP(c_New__DSequence_Oneg__decr__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohb__bind(T_c,T_b,hAPP(V_x_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_i_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b))),V_f_2),V_i_2))
        | V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
      & ( hAPP(c_New__DSequence_Oneg__decr__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohit__bound(T_b)
        | V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(fof_nnf,[status(thm)],[fact_New__DSequence_Oneg__decr__bind__def]) ).

fof(f_4635_2,plain,
    ! [U_19041,U_19040,U_19039,U_19038,U_19037] :
      ( ( hAPP(c_New__DSequence_Oneg__decr__bind(U_19038,U_19039,U_19040,U_19041),U_19037) = c_Lazy__Sequence_Ohb__bind(U_19038,U_19039,hAPP(U_19040,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_19037),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(U_19038,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_19039))),U_19041),U_19037))
        | U_19037 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
      & ( hAPP(c_New__DSequence_Oneg__decr__bind(U_19038,U_19039,U_19040,U_19041),U_19037) = c_Lazy__Sequence_Ohit__bound(U_19039)
        | U_19037 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(variable_rename,[status(thm)],[f_4635_1]) ).

fof(f_4635_3,plain,
    ( ! [U_19051,U_19049,U_19047,U_19045,U_19043] :
        ( hAPP(c_New__DSequence_Oneg__decr__bind(U_19045,U_19047,U_19049,U_19051),U_19043) = c_Lazy__Sequence_Ohb__bind(U_19045,U_19047,hAPP(U_19049,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_19043),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(U_19045,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_19047))),U_19051),U_19043))
        | U_19043 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
    & ! [U_19050,U_19048,U_19046,U_19044,U_19042] :
        ( hAPP(c_New__DSequence_Oneg__decr__bind(U_19044,U_19046,U_19048,U_19050),U_19042) = c_Lazy__Sequence_Ohit__bound(U_19046)
        | U_19042 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(miniscope,[status(thm)],[f_4635_2]) ).

cnf(f_4635_4,plain,
    ( hAPP(c_New__DSequence_Oneg__decr__bind(U_19044,U_19046,U_19048,U_19050),U_19042) = c_Lazy__Sequence_Ohit__bound(U_19046)
    | U_19042 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_4635_3]) ).

cnf(f_4635_5,plain,
    ( hAPP(c_New__DSequence_Oneg__decr__bind(U_19045,U_19047,U_19049,U_19051),U_19043) = c_Lazy__Sequence_Ohb__bind(U_19045,U_19047,hAPP(U_19049,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_19043),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(U_19045,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_19047))),U_19051),U_19043))
    | U_19043 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_4635_3]) ).

fof(f_4636_1,plain,
    ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_b,T_c] : c_New__Random__Sequence_Oneg__decr__bind(T_c,T_b,V_R_2,V_f_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Oneg__decr__bind(T_c,T_b,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_c,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b))))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)),
    inference(fof_nnf,[status(thm)],[fact_New__Random__Sequence_Oneg__decr__bind__def]) ).

fof(f_4636_2,plain,
    ! [U_19058,U_19057,U_19056,U_19055,U_19054,U_19053,U_19052] : c_New__Random__Sequence_Oneg__decr__bind(U_19052,U_19053,U_19054,U_19055,U_19056,U_19057,U_19058) = c_New__DSequence_Oneg__decr__bind(U_19052,U_19053,hAPP(hAPP(hAPP(U_19054,U_19056),U_19057),U_19058),hAPP(hAPP(c_COMBC(U_19052,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_19053)))),hAPP(hAPP(c_COMBC(U_19052,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_19053))))),hAPP(hAPP(c_COMBC(U_19052,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_19053)))))),U_19055),U_19056)),U_19057)),U_19058)),
    inference(variable_rename,[status(thm)],[f_4636_1]) ).

cnf(f_4636_3,plain,
    c_New__Random__Sequence_Oneg__decr__bind(U_19052,U_19053,U_19054,U_19055,U_19056,U_19057,U_19058) = c_New__DSequence_Oneg__decr__bind(U_19052,U_19053,hAPP(hAPP(hAPP(U_19054,U_19056),U_19057),U_19058),hAPP(hAPP(c_COMBC(U_19052,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_19053)))),hAPP(hAPP(c_COMBC(U_19052,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_19053))))),hAPP(hAPP(c_COMBC(U_19052,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_19053)))))),U_19055),U_19056)),U_19057)),U_19058)),
    inference(clausify,[status(thm)],[f_4636_2]) ).

fof(f_4637_1,plain,
    ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_b,T_c] : c_New__Random__Sequence_Opos__decr__bind(T_c,T_b,V_R_2,V_f_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__decr__bind(T_c,T_b,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_c,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b)))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)),
    inference(fof_nnf,[status(thm)],[fact_New__Random__Sequence_Opos__decr__bind__def]) ).

fof(f_4637_2,plain,
    ! [U_19065,U_19064,U_19063,U_19062,U_19061,U_19060,U_19059] : c_New__Random__Sequence_Opos__decr__bind(U_19059,U_19060,U_19061,U_19062,U_19063,U_19064,U_19065) = c_New__DSequence_Opos__decr__bind(U_19059,U_19060,hAPP(hAPP(hAPP(U_19061,U_19063),U_19064),U_19065),hAPP(hAPP(c_COMBC(U_19059,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_19060))),hAPP(hAPP(c_COMBC(U_19059,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_19060)))),hAPP(hAPP(c_COMBC(U_19059,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_19060))))),U_19062),U_19063)),U_19064)),U_19065)),
    inference(variable_rename,[status(thm)],[f_4637_1]) ).

cnf(f_4637_3,plain,
    c_New__Random__Sequence_Opos__decr__bind(U_19059,U_19060,U_19061,U_19062,U_19063,U_19064,U_19065) = c_New__DSequence_Opos__decr__bind(U_19059,U_19060,hAPP(hAPP(hAPP(U_19061,U_19063),U_19064),U_19065),hAPP(hAPP(c_COMBC(U_19059,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_19060))),hAPP(hAPP(c_COMBC(U_19059,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_19060)))),hAPP(hAPP(c_COMBC(U_19059,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_19060))))),U_19062),U_19063)),U_19064)),U_19065)),
    inference(clausify,[status(thm)],[f_4637_2]) ).

fof(f_4638_1,plain,
    ! [V_i_2,V_f_2,V_x_2,T_b,T_c] : hAPP(c_New__DSequence_Oneg__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohb__bind(T_c,T_b,hAPP(V_x_2,V_i_2),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b))),V_f_2),V_i_2)),
    inference(fof_nnf,[status(thm)],[fact_New__DSequence_Oneg__bind__def]) ).

fof(f_4638_2,plain,
    ! [U_19070,U_19069,U_19068,U_19067,U_19066] : hAPP(c_New__DSequence_Oneg__bind(U_19066,U_19067,U_19068,U_19069),U_19070) = c_Lazy__Sequence_Ohb__bind(U_19066,U_19067,hAPP(U_19068,U_19070),hAPP(hAPP(c_COMBC(U_19066,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_19067))),U_19069),U_19070)),
    inference(variable_rename,[status(thm)],[f_4638_1]) ).

cnf(f_4638_3,plain,
    hAPP(c_New__DSequence_Oneg__bind(U_19066,U_19067,U_19068,U_19069),U_19070) = c_Lazy__Sequence_Ohb__bind(U_19066,U_19067,hAPP(U_19068,U_19070),hAPP(hAPP(c_COMBC(U_19066,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_19067))),U_19069),U_19070)),
    inference(clausify,[status(thm)],[f_4638_2]) ).

fof(f_4639_1,plain,
    ! [V_i_1,T_a] : hAPP(c_New__DSequence_Opos__empty(T_a),V_i_1) = c_Lazy__Sequence_Oempty(T_a),
    inference(fof_nnf,[status(thm)],[fact_New__DSequence_Opos__empty__def]) ).

fof(f_4639_2,plain,
    ! [U_19072,U_19071] : hAPP(c_New__DSequence_Opos__empty(U_19071),U_19072) = c_Lazy__Sequence_Oempty(U_19071),
    inference(variable_rename,[status(thm)],[f_4639_1]) ).

cnf(f_4639_3,plain,
    hAPP(c_New__DSequence_Opos__empty(U_19071),U_19072) = c_Lazy__Sequence_Oempty(U_19071),
    inference(clausify,[status(thm)],[f_4639_2]) ).

fof(f_4640_1,plain,
    ! [V_seed_2,V_size_2,V_nrandom_2,T_b] : c_New__Random__Sequence_Opos__empty(T_b,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__empty(T_b),
    inference(fof_nnf,[status(thm)],[fact_pos__empty__def]) ).

fof(f_4640_2,plain,
    ! [U_19076,U_19075,U_19074,U_19073] : c_New__Random__Sequence_Opos__empty(U_19073,U_19074,U_19075,U_19076) = c_New__DSequence_Opos__empty(U_19073),
    inference(variable_rename,[status(thm)],[f_4640_1]) ).

cnf(f_4640_3,plain,
    c_New__Random__Sequence_Opos__empty(U_19073,U_19074,U_19075,U_19076) = c_New__DSequence_Opos__empty(U_19073),
    inference(clausify,[status(thm)],[f_4640_2]) ).

fof(f_4641_1,plain,
    ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_b,T_c] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(T_c,T_b,V_R_2,V_f_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Oneg__bind(T_c,T_b,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_c,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b))))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)),
    inference(fof_nnf,[status(thm)],[fact_neg__bind__def]) ).

fof(f_4641_2,plain,
    ! [U_19083,U_19082,U_19081,U_19080,U_19079,U_19078,U_19077] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(U_19077,U_19078,U_19079,U_19080),U_19081),U_19082),U_19083) = c_New__DSequence_Oneg__bind(U_19077,U_19078,hAPP(hAPP(hAPP(U_19079,U_19081),U_19082),U_19083),hAPP(hAPP(c_COMBC(U_19077,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_19078)))),hAPP(hAPP(c_COMBC(U_19077,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_19078))))),hAPP(hAPP(c_COMBC(U_19077,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_19078)))))),U_19080),U_19081)),U_19082)),U_19083)),
    inference(variable_rename,[status(thm)],[f_4641_1]) ).

cnf(f_4641_3,plain,
    hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(U_19077,U_19078,U_19079,U_19080),U_19081),U_19082),U_19083) = c_New__DSequence_Oneg__bind(U_19077,U_19078,hAPP(hAPP(hAPP(U_19079,U_19081),U_19082),U_19083),hAPP(hAPP(c_COMBC(U_19077,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_19078)))),hAPP(hAPP(c_COMBC(U_19077,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_19078))))),hAPP(hAPP(c_COMBC(U_19077,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_19078)))))),U_19080),U_19081)),U_19082)),U_19083)),
    inference(clausify,[status(thm)],[f_4641_2]) ).

fof(f_4642_1,plain,
    ! [V_i_2,V_f_2,V_x_2,T_b,T_c] : hAPP(c_New__DSequence_Opos__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = hAPP(c_Lazy__Sequence_Obind(T_c,T_b,hAPP(V_x_2,V_i_2)),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b)),V_f_2),V_i_2)),
    inference(fof_nnf,[status(thm)],[fact_New__DSequence_Opos__bind__def]) ).

fof(f_4642_2,plain,
    ! [U_19088,U_19087,U_19086,U_19085,U_19084] : hAPP(c_New__DSequence_Opos__bind(U_19084,U_19085,U_19086,U_19087),U_19088) = hAPP(c_Lazy__Sequence_Obind(U_19084,U_19085,hAPP(U_19086,U_19088)),hAPP(hAPP(c_COMBC(U_19084,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_19085)),U_19087),U_19088)),
    inference(variable_rename,[status(thm)],[f_4642_1]) ).

cnf(f_4642_3,plain,
    hAPP(c_New__DSequence_Opos__bind(U_19084,U_19085,U_19086,U_19087),U_19088) = hAPP(c_Lazy__Sequence_Obind(U_19084,U_19085,hAPP(U_19086,U_19088)),hAPP(hAPP(c_COMBC(U_19084,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_19085)),U_19087),U_19088)),
    inference(clausify,[status(thm)],[f_4642_2]) ).

fof(f_4643_1,plain,
    ! [V_P_2,V_f_2,T_b,T_c] : c_New__Random__Sequence_Oneg__map(T_c,T_b,V_f_2,V_P_2) = c_New__Random__Sequence_Oneg__bind(T_c,T_b,V_P_2,hAPP(c_Fun_Ocomp(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)))))),T_c,c_New__Random__Sequence_Oneg__single(T_b)),V_f_2)),
    inference(fof_nnf,[status(thm)],[fact_neg__map__def]) ).

fof(f_4643_2,plain,
    ! [U_19092,U_19091,U_19090,U_19089] : c_New__Random__Sequence_Oneg__map(U_19089,U_19090,U_19091,U_19092) = c_New__Random__Sequence_Oneg__bind(U_19089,U_19090,U_19092,hAPP(c_Fun_Ocomp(U_19090,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_19090)))))),U_19089,c_New__Random__Sequence_Oneg__single(U_19090)),U_19091)),
    inference(variable_rename,[status(thm)],[f_4643_1]) ).

cnf(f_4643_3,plain,
    c_New__Random__Sequence_Oneg__map(U_19089,U_19090,U_19091,U_19092) = c_New__Random__Sequence_Oneg__bind(U_19089,U_19090,U_19092,hAPP(c_Fun_Ocomp(U_19090,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_19090)))))),U_19089,c_New__Random__Sequence_Oneg__single(U_19090)),U_19091)),
    inference(clausify,[status(thm)],[f_4643_2]) ).

fof(f_4644_1,plain,
    ! [V_seed_2,V_size_2,V_nrandom_2,V_x_2,T_b] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(T_b),V_x_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Oneg__single(T_b,V_x_2),
    inference(fof_nnf,[status(thm)],[fact_neg__single__def]) ).

fof(f_4644_2,plain,
    ! [U_19097,U_19096,U_19095,U_19094,U_19093] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(U_19093),U_19094),U_19095),U_19096),U_19097) = c_New__DSequence_Oneg__single(U_19093,U_19094),
    inference(variable_rename,[status(thm)],[f_4644_1]) ).

cnf(f_4644_3,plain,
    hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(U_19093),U_19094),U_19095),U_19096),U_19097) = c_New__DSequence_Oneg__single(U_19093,U_19094),
    inference(clausify,[status(thm)],[f_4644_2]) ).

fof(f_4645_1,plain,
    ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_b,T_c] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(T_c,T_b,V_R_2,V_f_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Opos__bind(T_c,T_b,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_c,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b)))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)),
    inference(fof_nnf,[status(thm)],[fact_pos__bind__def]) ).

fof(f_4645_2,plain,
    ! [U_19104,U_19103,U_19102,U_19101,U_19100,U_19099,U_19098] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(U_19098,U_19099,U_19100,U_19101),U_19102),U_19103),U_19104) = c_New__DSequence_Opos__bind(U_19098,U_19099,hAPP(hAPP(hAPP(U_19100,U_19102),U_19103),U_19104),hAPP(hAPP(c_COMBC(U_19098,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_19099))),hAPP(hAPP(c_COMBC(U_19098,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_19099)))),hAPP(hAPP(c_COMBC(U_19098,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_19099))))),U_19101),U_19102)),U_19103)),U_19104)),
    inference(variable_rename,[status(thm)],[f_4645_1]) ).

cnf(f_4645_3,plain,
    hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(U_19098,U_19099,U_19100,U_19101),U_19102),U_19103),U_19104) = c_New__DSequence_Opos__bind(U_19098,U_19099,hAPP(hAPP(hAPP(U_19100,U_19102),U_19103),U_19104),hAPP(hAPP(c_COMBC(U_19098,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_19099))),hAPP(hAPP(c_COMBC(U_19098,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_19099)))),hAPP(hAPP(c_COMBC(U_19098,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_19099))))),U_19101),U_19102)),U_19103)),U_19104)),
    inference(clausify,[status(thm)],[f_4645_2]) ).

fof(f_4646_1,plain,
    ! [V_i_1,V_x,T_a] : hAPP(c_New__DSequence_Oneg__single(T_a,V_x),V_i_1) = c_Lazy__Sequence_Ohb__single(T_a,V_x),
    inference(fof_nnf,[status(thm)],[fact_New__DSequence_Oneg__single__def]) ).

fof(f_4646_2,plain,
    ! [U_19107,U_19106,U_19105] : hAPP(c_New__DSequence_Oneg__single(U_19105,U_19106),U_19107) = c_Lazy__Sequence_Ohb__single(U_19105,U_19106),
    inference(variable_rename,[status(thm)],[f_4646_1]) ).

cnf(f_4646_3,plain,
    hAPP(c_New__DSequence_Oneg__single(U_19105,U_19106),U_19107) = c_Lazy__Sequence_Ohb__single(U_19105,U_19106),
    inference(clausify,[status(thm)],[f_4646_2]) ).

fof(f_4647_1,plain,
    ! [V_P_2,V_f_2,T_b,T_c] : c_New__Random__Sequence_Opos__map(T_c,T_b,V_f_2,V_P_2) = c_New__Random__Sequence_Opos__bind(T_c,T_b,V_P_2,hAPP(c_Fun_Ocomp(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))))),T_c,c_New__Random__Sequence_Opos__single(T_b)),V_f_2)),
    inference(fof_nnf,[status(thm)],[fact_pos__map__def]) ).

fof(f_4647_2,plain,
    ! [U_19111,U_19110,U_19109,U_19108] : c_New__Random__Sequence_Opos__map(U_19108,U_19109,U_19110,U_19111) = c_New__Random__Sequence_Opos__bind(U_19108,U_19109,U_19111,hAPP(c_Fun_Ocomp(U_19109,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_19109))))),U_19108,c_New__Random__Sequence_Opos__single(U_19109)),U_19110)),
    inference(variable_rename,[status(thm)],[f_4647_1]) ).

cnf(f_4647_3,plain,
    c_New__Random__Sequence_Opos__map(U_19108,U_19109,U_19110,U_19111) = c_New__Random__Sequence_Opos__bind(U_19108,U_19109,U_19111,hAPP(c_Fun_Ocomp(U_19109,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_19109))))),U_19108,c_New__Random__Sequence_Opos__single(U_19109)),U_19110)),
    inference(clausify,[status(thm)],[f_4647_2]) ).

fof(f_4648_1,plain,
    ! [V_seed_2,V_size_2,V_nrandom_2,V_x_2,T_b] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(T_b),V_x_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Opos__single(T_b,V_x_2),
    inference(fof_nnf,[status(thm)],[fact_pos__single__def]) ).

fof(f_4648_2,plain,
    ! [U_19116,U_19115,U_19114,U_19113,U_19112] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(U_19112),U_19113),U_19114),U_19115),U_19116) = c_New__DSequence_Opos__single(U_19112,U_19113),
    inference(variable_rename,[status(thm)],[f_4648_1]) ).

cnf(f_4648_3,plain,
    hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(U_19112),U_19113),U_19114),U_19115),U_19116) = c_New__DSequence_Opos__single(U_19112,U_19113),
    inference(clausify,[status(thm)],[f_4648_2]) ).

fof(f_4649_1,plain,
    ! [V_ys,V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Osplice(T_a,V_xs,V_ys)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys)),
    inference(fof_nnf,[status(thm)],[fact_length__splice]) ).

fof(f_4649_2,plain,
    ! [U_19119,U_19118,U_19117] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19117)),c_List_Osplice(U_19117,U_19118,U_19119)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19117)),U_19118)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19117)),U_19119)),
    inference(variable_rename,[status(thm)],[f_4649_1]) ).

cnf(f_4649_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19117)),c_List_Osplice(U_19117,U_19118,U_19119)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19117)),U_19118)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19117)),U_19119)),
    inference(clausify,[status(thm)],[f_4649_2]) ).

fof(f_4650_1,plain,
    ! [V_ys,V_y,V_xs,V_x,T_a] : c_List_Osplice(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),c_List_Osplice(T_a,V_xs,V_ys))),
    inference(fof_nnf,[status(thm)],[fact_splice_Osimps_I3_J]) ).

fof(f_4650_2,plain,
    ! [U_19124,U_19123,U_19122,U_19121,U_19120] : c_List_Osplice(U_19120,hAPP(hAPP(c_List_Olist_OCons(U_19120),U_19121),U_19122),hAPP(hAPP(c_List_Olist_OCons(U_19120),U_19123),U_19124)) = hAPP(hAPP(c_List_Olist_OCons(U_19120),U_19121),hAPP(hAPP(c_List_Olist_OCons(U_19120),U_19123),c_List_Osplice(U_19120,U_19122,U_19124))),
    inference(variable_rename,[status(thm)],[f_4650_1]) ).

cnf(f_4650_3,plain,
    c_List_Osplice(U_19120,hAPP(hAPP(c_List_Olist_OCons(U_19120),U_19121),U_19122),hAPP(hAPP(c_List_Olist_OCons(U_19120),U_19123),U_19124)) = hAPP(hAPP(c_List_Olist_OCons(U_19120),U_19121),hAPP(hAPP(c_List_Olist_OCons(U_19120),U_19123),c_List_Osplice(U_19120,U_19122,U_19124))),
    inference(clausify,[status(thm)],[f_4650_2]) ).

fof(f_4651_1,plain,
    ! [V_xs,T_a] : c_List_Osplice(T_a,V_xs,c_List_Olist_ONil(T_a)) = V_xs,
    inference(fof_nnf,[status(thm)],[fact_splice__Nil2]) ).

fof(f_4651_2,plain,
    ! [U_19126,U_19125] : c_List_Osplice(U_19125,U_19126,c_List_Olist_ONil(U_19125)) = U_19126,
    inference(variable_rename,[status(thm)],[f_4651_1]) ).

cnf(f_4651_3,plain,
    c_List_Osplice(U_19125,U_19126,c_List_Olist_ONil(U_19125)) = U_19126,
    inference(clausify,[status(thm)],[f_4651_2]) ).

fof(f_4652_1,plain,
    ! [V_ys,T_a] : c_List_Osplice(T_a,c_List_Olist_ONil(T_a),V_ys) = V_ys,
    inference(fof_nnf,[status(thm)],[fact_splice_Osimps_I1_J]) ).

fof(f_4652_2,plain,
    ! [U_19128,U_19127] : c_List_Osplice(U_19127,c_List_Olist_ONil(U_19127),U_19128) = U_19128,
    inference(variable_rename,[status(thm)],[f_4652_1]) ).

cnf(f_4652_3,plain,
    c_List_Osplice(U_19127,c_List_Olist_ONil(U_19127),U_19128) = U_19128,
    inference(clausify,[status(thm)],[f_4652_2]) ).

fof(f_4653_1,plain,
    ! [V_va,V_v,T_a] : c_List_Osplice(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_v),V_va),c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_v),V_va),
    inference(fof_nnf,[status(thm)],[fact_splice_Osimps_I2_J]) ).

fof(f_4653_2,plain,
    ! [U_19131,U_19130,U_19129] : c_List_Osplice(U_19129,hAPP(hAPP(c_List_Olist_OCons(U_19129),U_19130),U_19131),c_List_Olist_ONil(U_19129)) = hAPP(hAPP(c_List_Olist_OCons(U_19129),U_19130),U_19131),
    inference(variable_rename,[status(thm)],[f_4653_1]) ).

cnf(f_4653_3,plain,
    c_List_Osplice(U_19129,hAPP(hAPP(c_List_Olist_OCons(U_19129),U_19130),U_19131),c_List_Olist_ONil(U_19129)) = hAPP(hAPP(c_List_Olist_OCons(U_19129),U_19130),U_19131),
    inference(clausify,[status(thm)],[f_4653_2]) ).

fof(f_4654_1,plain,
    ! [V_i_1,V_x,T_a] : hAPP(c_New__DSequence_Opos__single(T_a,V_x),V_i_1) = hAPP(c_Lazy__Sequence_Osingle(T_a),V_x),
    inference(fof_nnf,[status(thm)],[fact_New__DSequence_Opos__single__def]) ).

fof(f_4654_2,plain,
    ! [U_19134,U_19133,U_19132] : hAPP(c_New__DSequence_Opos__single(U_19132,U_19133),U_19134) = hAPP(c_Lazy__Sequence_Osingle(U_19132),U_19133),
    inference(variable_rename,[status(thm)],[f_4654_1]) ).

cnf(f_4654_3,plain,
    hAPP(c_New__DSequence_Opos__single(U_19132,U_19133),U_19134) = hAPP(c_Lazy__Sequence_Osingle(U_19132),U_19133),
    inference(clausify,[status(thm)],[f_4654_2]) ).

fof(f_4655_1,plain,
    ! [V_r_2,T_b] :
      ( ( c_Wellfounded_Oacyclic(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),c_Predicate_Oconversep(T_b,T_b,V_r_2))))
        | ~ c_Wellfounded_Oacyclic(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))) )
      & ( c_Wellfounded_Oacyclic(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2)))
        | ~ c_Wellfounded_Oacyclic(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),c_Predicate_Oconversep(T_b,T_b,V_r_2)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_acyclicP__converse]) ).

fof(f_4655_2,plain,
    ! [U_19136,U_19135] :
      ( ( c_Wellfounded_Oacyclic(U_19135,hAPP(c_Set_OCollect(tc_prod(U_19135,U_19135)),hAPP(c_Product__Type_Oprod_Oprod__case(U_19135,U_19135,tc_HOL_Obool),c_Predicate_Oconversep(U_19135,U_19135,U_19136))))
        | ~ c_Wellfounded_Oacyclic(U_19135,hAPP(c_Set_OCollect(tc_prod(U_19135,U_19135)),hAPP(c_Product__Type_Oprod_Oprod__case(U_19135,U_19135,tc_HOL_Obool),U_19136))) )
      & ( c_Wellfounded_Oacyclic(U_19135,hAPP(c_Set_OCollect(tc_prod(U_19135,U_19135)),hAPP(c_Product__Type_Oprod_Oprod__case(U_19135,U_19135,tc_HOL_Obool),U_19136)))
        | ~ c_Wellfounded_Oacyclic(U_19135,hAPP(c_Set_OCollect(tc_prod(U_19135,U_19135)),hAPP(c_Product__Type_Oprod_Oprod__case(U_19135,U_19135,tc_HOL_Obool),c_Predicate_Oconversep(U_19135,U_19135,U_19136)))) ) ),
    inference(variable_rename,[status(thm)],[f_4655_1]) ).

fof(f_4655_3,plain,
    ( ! [U_19140,U_19138] :
        ( c_Wellfounded_Oacyclic(U_19138,hAPP(c_Set_OCollect(tc_prod(U_19138,U_19138)),hAPP(c_Product__Type_Oprod_Oprod__case(U_19138,U_19138,tc_HOL_Obool),c_Predicate_Oconversep(U_19138,U_19138,U_19140))))
        | ~ c_Wellfounded_Oacyclic(U_19138,hAPP(c_Set_OCollect(tc_prod(U_19138,U_19138)),hAPP(c_Product__Type_Oprod_Oprod__case(U_19138,U_19138,tc_HOL_Obool),U_19140))) )
    & ! [U_19139,U_19137] :
        ( c_Wellfounded_Oacyclic(U_19137,hAPP(c_Set_OCollect(tc_prod(U_19137,U_19137)),hAPP(c_Product__Type_Oprod_Oprod__case(U_19137,U_19137,tc_HOL_Obool),U_19139)))
        | ~ c_Wellfounded_Oacyclic(U_19137,hAPP(c_Set_OCollect(tc_prod(U_19137,U_19137)),hAPP(c_Product__Type_Oprod_Oprod__case(U_19137,U_19137,tc_HOL_Obool),c_Predicate_Oconversep(U_19137,U_19137,U_19139)))) ) ),
    inference(miniscope,[status(thm)],[f_4655_2]) ).

cnf(f_4655_4,plain,
    ( c_Wellfounded_Oacyclic(U_19137,hAPP(c_Set_OCollect(tc_prod(U_19137,U_19137)),hAPP(c_Product__Type_Oprod_Oprod__case(U_19137,U_19137,tc_HOL_Obool),U_19139)))
    | ~ c_Wellfounded_Oacyclic(U_19137,hAPP(c_Set_OCollect(tc_prod(U_19137,U_19137)),hAPP(c_Product__Type_Oprod_Oprod__case(U_19137,U_19137,tc_HOL_Obool),c_Predicate_Oconversep(U_19137,U_19137,U_19139)))) ),
    inference(clausify,[status(thm)],[f_4655_3]) ).

cnf(f_4655_5,plain,
    ( c_Wellfounded_Oacyclic(U_19138,hAPP(c_Set_OCollect(tc_prod(U_19138,U_19138)),hAPP(c_Product__Type_Oprod_Oprod__case(U_19138,U_19138,tc_HOL_Obool),c_Predicate_Oconversep(U_19138,U_19138,U_19140))))
    | ~ c_Wellfounded_Oacyclic(U_19138,hAPP(c_Set_OCollect(tc_prod(U_19138,U_19138)),hAPP(c_Product__Type_Oprod_Oprod__case(U_19138,U_19138,tc_HOL_Obool),U_19140))) ),
    inference(clausify,[status(thm)],[f_4655_3]) ).

fof(f_4656_1,plain,
    ! [V_s_2,V_r_2,T_b,T_c] : c_Predicate_Oconversep(T_c,T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool))),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),c_Predicate_Oconversep(T_c,T_b,V_r_2)),c_Predicate_Oconversep(T_c,T_b,V_s_2)),
    inference(fof_nnf,[status(thm)],[fact_converse__meet]) ).

fof(f_4656_2,plain,
    ! [U_19144,U_19143,U_19142,U_19141] : c_Predicate_Oconversep(U_19141,U_19142,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_19141,tc_fun(U_19142,tc_HOL_Obool))),U_19143),U_19144)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_19142,tc_fun(U_19141,tc_HOL_Obool))),c_Predicate_Oconversep(U_19141,U_19142,U_19143)),c_Predicate_Oconversep(U_19141,U_19142,U_19144)),
    inference(variable_rename,[status(thm)],[f_4656_1]) ).

cnf(f_4656_3,plain,
    c_Predicate_Oconversep(U_19141,U_19142,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_19141,tc_fun(U_19142,tc_HOL_Obool))),U_19143),U_19144)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_19142,tc_fun(U_19141,tc_HOL_Obool))),c_Predicate_Oconversep(U_19141,U_19142,U_19143)),c_Predicate_Oconversep(U_19141,U_19142,U_19144)),
    inference(clausify,[status(thm)],[f_4656_2]) ).

fof(f_4657_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_b,hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot)),c_fequal)),V_x_2),V_y_2))
        | V_x_2 = V_y_2 )
      & ( V_x_2 != V_y_2
        | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_b,hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot)),c_fequal)),V_x_2),V_y_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_conversep__noteq]) ).

fof(f_4657_2,plain,
    ! [U_19147,U_19146,U_19145] :
      ( ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_19145,U_19145,hAPP(hAPP(c_COMBB(tc_fun(U_19145,tc_HOL_Obool),tc_fun(U_19145,tc_HOL_Obool),U_19145),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_19145),c_fNot)),c_fequal)),U_19146),U_19147))
        | U_19146 = U_19147 )
      & ( U_19146 != U_19147
        | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_19145,U_19145,hAPP(hAPP(c_COMBB(tc_fun(U_19145,tc_HOL_Obool),tc_fun(U_19145,tc_HOL_Obool),U_19145),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_19145),c_fNot)),c_fequal)),U_19146),U_19147)) ) ),
    inference(variable_rename,[status(thm)],[f_4657_1]) ).

fof(f_4657_3,plain,
    ( ! [U_19153,U_19151] :
        ( ! [U_19149] : hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_19149,U_19149,hAPP(hAPP(c_COMBB(tc_fun(U_19149,tc_HOL_Obool),tc_fun(U_19149,tc_HOL_Obool),U_19149),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_19149),c_fNot)),c_fequal)),U_19151),U_19153))
        | U_19151 = U_19153 )
    & ! [U_19152,U_19150] :
        ( ! [U_19148] : ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_19148,U_19148,hAPP(hAPP(c_COMBB(tc_fun(U_19148,tc_HOL_Obool),tc_fun(U_19148,tc_HOL_Obool),U_19148),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_19148),c_fNot)),c_fequal)),U_19150),U_19152))
        | U_19150 != U_19152 ) ),
    inference(miniscope,[status(thm)],[f_4657_2]) ).

cnf(f_4657_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_19148,U_19148,hAPP(hAPP(c_COMBB(tc_fun(U_19148,tc_HOL_Obool),tc_fun(U_19148,tc_HOL_Obool),U_19148),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_19148),c_fNot)),c_fequal)),U_19150),U_19152))
    | U_19150 != U_19152 ),
    inference(clausify,[status(thm)],[f_4657_3]) ).

cnf(f_4657_5,plain,
    ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_19149,U_19149,hAPP(hAPP(c_COMBB(tc_fun(U_19149,tc_HOL_Obool),tc_fun(U_19149,tc_HOL_Obool),U_19149),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_19149),c_fNot)),c_fequal)),U_19151),U_19153))
    | U_19151 = U_19153 ),
    inference(clausify,[status(thm)],[f_4657_3]) ).

fof(f_4658_1,plain,
    ! [T_b] : c_Predicate_Oconversep(T_b,T_b,c_fequal) = c_fequal,
    inference(fof_nnf,[status(thm)],[fact_conversep__eq]) ).

fof(f_4658_2,plain,
    ! [U_19154] : c_Predicate_Oconversep(U_19154,U_19154,c_fequal) = c_fequal,
    inference(variable_rename,[status(thm)],[f_4658_1]) ).

cnf(f_4658_3,plain,
    c_Predicate_Oconversep(U_19154,U_19154,c_fequal) = c_fequal,
    inference(clausify,[status(thm)],[f_4658_2]) ).

fof(f_4659_1,plain,
    ! [V_r_2,T_b,T_c] : c_Predicate_Oconversep(T_c,T_b,c_Predicate_Oconversep(T_b,T_c,V_r_2)) = V_r_2,
    inference(fof_nnf,[status(thm)],[fact_conversep__conversep]) ).

fof(f_4659_2,plain,
    ! [U_19157,U_19156,U_19155] : c_Predicate_Oconversep(U_19155,U_19156,c_Predicate_Oconversep(U_19156,U_19155,U_19157)) = U_19157,
    inference(variable_rename,[status(thm)],[f_4659_1]) ).

cnf(f_4659_3,plain,
    c_Predicate_Oconversep(U_19155,U_19156,c_Predicate_Oconversep(U_19156,U_19155,U_19157)) = U_19157,
    inference(clausify,[status(thm)],[f_4659_2]) ).

fof(f_4660_1,plain,
    ! [V_b_2,V_a_2,V_r_2,T_c,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a_2),V_b_2))
        | ~ hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2)) )
      & ( hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2))
        | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a_2),V_b_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_conversep__iff]) ).

fof(f_4660_2,plain,
    ! [U_19162,U_19161,U_19160,U_19159,U_19158] :
      ( ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_19158,U_19159,U_19160),U_19161),U_19162))
        | ~ hBOOL(hAPP(hAPP(U_19160,U_19162),U_19161)) )
      & ( hBOOL(hAPP(hAPP(U_19160,U_19162),U_19161))
        | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_19158,U_19159,U_19160),U_19161),U_19162)) ) ),
    inference(variable_rename,[status(thm)],[f_4660_1]) ).

fof(f_4660_3,plain,
    ( ! [U_19172,U_19170,U_19168] :
        ( ! [U_19166,U_19164] : hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_19164,U_19166,U_19168),U_19170),U_19172))
        | ~ hBOOL(hAPP(hAPP(U_19168,U_19172),U_19170)) )
    & ! [U_19171,U_19169,U_19167] :
        ( ! [U_19165,U_19163] : ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_19163,U_19165,U_19167),U_19169),U_19171))
        | hBOOL(hAPP(hAPP(U_19167,U_19171),U_19169)) ) ),
    inference(miniscope,[status(thm)],[f_4660_2]) ).

cnf(f_4660_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_19163,U_19165,U_19167),U_19169),U_19171))
    | hBOOL(hAPP(hAPP(U_19167,U_19171),U_19169)) ),
    inference(clausify,[status(thm)],[f_4660_3]) ).

cnf(f_4660_5,plain,
    ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_19164,U_19166,U_19168),U_19170),U_19172))
    | ~ hBOOL(hAPP(hAPP(U_19168,U_19172),U_19170)) ),
    inference(clausify,[status(thm)],[f_4660_3]) ).

fof(f_4661_1,plain,
    ! [V_a1_2,V_a2_2,V_r_2,T_c,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a2_2),V_a1_2))
        | ~ hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2)) )
      & ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2))
        | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a2_2),V_a1_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_conversep_Oequations]) ).

fof(f_4661_2,plain,
    ! [U_19177,U_19176,U_19175,U_19174,U_19173] :
      ( ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_19173,U_19174,U_19175),U_19176),U_19177))
        | ~ hBOOL(hAPP(hAPP(U_19175,U_19177),U_19176)) )
      & ( hBOOL(hAPP(hAPP(U_19175,U_19177),U_19176))
        | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_19173,U_19174,U_19175),U_19176),U_19177)) ) ),
    inference(variable_rename,[status(thm)],[f_4661_1]) ).

fof(f_4661_3,plain,
    ( ! [U_19187,U_19185,U_19183] :
        ( ! [U_19181,U_19179] : hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_19179,U_19181,U_19183),U_19185),U_19187))
        | ~ hBOOL(hAPP(hAPP(U_19183,U_19187),U_19185)) )
    & ! [U_19186,U_19184,U_19182] :
        ( ! [U_19180,U_19178] : ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_19178,U_19180,U_19182),U_19184),U_19186))
        | hBOOL(hAPP(hAPP(U_19182,U_19186),U_19184)) ) ),
    inference(miniscope,[status(thm)],[f_4661_2]) ).

cnf(f_4661_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_19178,U_19180,U_19182),U_19184),U_19186))
    | hBOOL(hAPP(hAPP(U_19182,U_19186),U_19184)) ),
    inference(clausify,[status(thm)],[f_4661_3]) ).

cnf(f_4661_5,plain,
    ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_19179,U_19181,U_19183),U_19185),U_19187))
    | ~ hBOOL(hAPP(hAPP(U_19183,U_19187),U_19185)) ),
    inference(clausify,[status(thm)],[f_4661_3]) ).

fof(f_4662_1,plain,
    ! [T_c,T_b,V_b_2,V_a_2,V_r_2] :
      ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_b_2),V_a_2))
      | ~ hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) ),
    inference(fof_nnf,[status(thm)],[fact_conversep_Ointros]) ).

fof(f_4662_2,plain,
    ! [U_19192,U_19191,U_19190,U_19189,U_19188] :
      ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_19191,U_19192,U_19188),U_19190),U_19189))
      | ~ hBOOL(hAPP(hAPP(U_19188,U_19189),U_19190)) ),
    inference(variable_rename,[status(thm)],[f_4662_1]) ).

cnf(f_4662_3,plain,
    ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_19191,U_19192,U_19188),U_19190),U_19189))
    | ~ hBOOL(hAPP(hAPP(U_19188,U_19189),U_19190)) ),
    inference(clausify,[status(thm)],[f_4662_2]) ).

fof(f_4663_1,plain,
    ! [V_b_2,V_a_2,V_r_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2))
      | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a_2),V_b_2)) ),
    inference(fof_nnf,[status(thm)],[fact_conversepD]) ).

fof(f_4663_2,plain,
    ! [U_19197,U_19196,U_19195,U_19194,U_19193] :
      ( hBOOL(hAPP(hAPP(U_19195,U_19197),U_19196))
      | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_19193,U_19194,U_19195),U_19196),U_19197)) ),
    inference(variable_rename,[status(thm)],[f_4663_1]) ).

fof(f_4663_3,plain,
    ! [U_19197,U_19196,U_19195] :
      ( ! [U_19194,U_19193] : ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_19193,U_19194,U_19195),U_19196),U_19197))
      | hBOOL(hAPP(hAPP(U_19195,U_19197),U_19196)) ),
    inference(miniscope,[status(thm)],[f_4663_2]) ).

cnf(f_4663_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_19193,U_19194,U_19195),U_19196),U_19197))
    | hBOOL(hAPP(hAPP(U_19195,U_19197),U_19196)) ),
    inference(clausify,[status(thm)],[f_4663_3]) ).

fof(f_4664_1,plain,
    ! [V_s_2,V_r_2,T_d,T_b,T_c] : c_Predicate_Oconversep(T_c,T_b,c_Predicate_Opred__comp(T_c,T_d,T_b,V_r_2,V_s_2)) = c_Predicate_Opred__comp(T_b,T_d,T_c,c_Predicate_Oconversep(T_d,T_b,V_s_2),c_Predicate_Oconversep(T_c,T_d,V_r_2)),
    inference(fof_nnf,[status(thm)],[fact_converse__pred__comp]) ).

fof(f_4664_2,plain,
    ! [U_19202,U_19201,U_19200,U_19199,U_19198] : c_Predicate_Oconversep(U_19198,U_19199,c_Predicate_Opred__comp(U_19198,U_19200,U_19199,U_19201,U_19202)) = c_Predicate_Opred__comp(U_19199,U_19200,U_19198,c_Predicate_Oconversep(U_19200,U_19199,U_19202),c_Predicate_Oconversep(U_19198,U_19200,U_19201)),
    inference(variable_rename,[status(thm)],[f_4664_1]) ).

cnf(f_4664_3,plain,
    c_Predicate_Oconversep(U_19198,U_19199,c_Predicate_Opred__comp(U_19198,U_19200,U_19199,U_19201,U_19202)) = c_Predicate_Opred__comp(U_19199,U_19200,U_19198,c_Predicate_Oconversep(U_19200,U_19199,U_19202),c_Predicate_Oconversep(U_19198,U_19200,U_19201)),
    inference(clausify,[status(thm)],[f_4664_2]) ).

fof(f_4665_1,plain,
    ! [V_s_2,V_r_2,T_b,T_c] : c_Predicate_Oconversep(T_c,T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool))),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),c_Predicate_Oconversep(T_c,T_b,V_r_2)),c_Predicate_Oconversep(T_c,T_b,V_s_2)),
    inference(fof_nnf,[status(thm)],[fact_converse__join]) ).

fof(f_4665_2,plain,
    ! [U_19206,U_19205,U_19204,U_19203] : c_Predicate_Oconversep(U_19203,U_19204,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_19203,tc_fun(U_19204,tc_HOL_Obool))),U_19205),U_19206)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_19204,tc_fun(U_19203,tc_HOL_Obool))),c_Predicate_Oconversep(U_19203,U_19204,U_19205)),c_Predicate_Oconversep(U_19203,U_19204,U_19206)),
    inference(variable_rename,[status(thm)],[f_4665_1]) ).

cnf(f_4665_3,plain,
    c_Predicate_Oconversep(U_19203,U_19204,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_19203,tc_fun(U_19204,tc_HOL_Obool))),U_19205),U_19206)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_19204,tc_fun(U_19203,tc_HOL_Obool))),c_Predicate_Oconversep(U_19203,U_19204,U_19205)),c_Predicate_Oconversep(U_19203,U_19204,U_19206)),
    inference(clausify,[status(thm)],[f_4665_2]) ).

fof(f_4666_1,plain,
    ! [V_y_2,V_x_2,V_r_2,T_c,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_r_2)),V_x_2),V_y_2))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2)))
        | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_r_2)),V_x_2),V_y_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_conversep__converse__eq]) ).

fof(f_4666_2,plain,
    ! [U_19211,U_19210,U_19209,U_19208,U_19207] :
      ( ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_19207,U_19208,hAPP(hAPP(c_COMBC(U_19207,tc_fun(tc_prod(U_19207,U_19208),tc_HOL_Obool),tc_fun(U_19208,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_19208,tc_fun(tc_fun(tc_prod(U_19207,U_19208),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_19207,U_19208),tc_HOL_Obool),tc_fun(U_19208,tc_HOL_Obool)),U_19207),c_COMBC(U_19208,tc_fun(tc_prod(U_19207,U_19208),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_19208,tc_prod(U_19207,U_19208)),tc_fun(U_19208,tc_fun(tc_fun(tc_prod(U_19207,U_19208),tc_HOL_Obool),tc_HOL_Obool)),U_19207),hAPP(c_COMBB(tc_prod(U_19207,U_19208),tc_fun(tc_fun(tc_prod(U_19207,U_19208),tc_HOL_Obool),tc_HOL_Obool),U_19208),c_member(tc_prod(U_19207,U_19208)))),c_Product__Type_OPair(U_19207,U_19208)))),U_19209)),U_19210),U_19211))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19208,U_19207)),hAPP(hAPP(c_Product__Type_OPair(U_19208,U_19207),U_19210),U_19211)),hAPP(c_Relation_Oconverse(U_19207,U_19208),U_19209))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19208,U_19207)),hAPP(hAPP(c_Product__Type_OPair(U_19208,U_19207),U_19210),U_19211)),hAPP(c_Relation_Oconverse(U_19207,U_19208),U_19209)))
        | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_19207,U_19208,hAPP(hAPP(c_COMBC(U_19207,tc_fun(tc_prod(U_19207,U_19208),tc_HOL_Obool),tc_fun(U_19208,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_19208,tc_fun(tc_fun(tc_prod(U_19207,U_19208),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_19207,U_19208),tc_HOL_Obool),tc_fun(U_19208,tc_HOL_Obool)),U_19207),c_COMBC(U_19208,tc_fun(tc_prod(U_19207,U_19208),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_19208,tc_prod(U_19207,U_19208)),tc_fun(U_19208,tc_fun(tc_fun(tc_prod(U_19207,U_19208),tc_HOL_Obool),tc_HOL_Obool)),U_19207),hAPP(c_COMBB(tc_prod(U_19207,U_19208),tc_fun(tc_fun(tc_prod(U_19207,U_19208),tc_HOL_Obool),tc_HOL_Obool),U_19208),c_member(tc_prod(U_19207,U_19208)))),c_Product__Type_OPair(U_19207,U_19208)))),U_19209)),U_19210),U_19211)) ) ),
    inference(variable_rename,[status(thm)],[f_4666_1]) ).

fof(f_4666_3,plain,
    ( ! [U_19221,U_19219,U_19217,U_19215,U_19213] :
        ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_19213,U_19215,hAPP(hAPP(c_COMBC(U_19213,tc_fun(tc_prod(U_19213,U_19215),tc_HOL_Obool),tc_fun(U_19215,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_19215,tc_fun(tc_fun(tc_prod(U_19213,U_19215),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_19213,U_19215),tc_HOL_Obool),tc_fun(U_19215,tc_HOL_Obool)),U_19213),c_COMBC(U_19215,tc_fun(tc_prod(U_19213,U_19215),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_19215,tc_prod(U_19213,U_19215)),tc_fun(U_19215,tc_fun(tc_fun(tc_prod(U_19213,U_19215),tc_HOL_Obool),tc_HOL_Obool)),U_19213),hAPP(c_COMBB(tc_prod(U_19213,U_19215),tc_fun(tc_fun(tc_prod(U_19213,U_19215),tc_HOL_Obool),tc_HOL_Obool),U_19215),c_member(tc_prod(U_19213,U_19215)))),c_Product__Type_OPair(U_19213,U_19215)))),U_19217)),U_19219),U_19221))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19215,U_19213)),hAPP(hAPP(c_Product__Type_OPair(U_19215,U_19213),U_19219),U_19221)),hAPP(c_Relation_Oconverse(U_19213,U_19215),U_19217))) )
    & ! [U_19220,U_19218,U_19216,U_19214,U_19212] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19214,U_19212)),hAPP(hAPP(c_Product__Type_OPair(U_19214,U_19212),U_19218),U_19220)),hAPP(c_Relation_Oconverse(U_19212,U_19214),U_19216)))
        | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_19212,U_19214,hAPP(hAPP(c_COMBC(U_19212,tc_fun(tc_prod(U_19212,U_19214),tc_HOL_Obool),tc_fun(U_19214,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_19214,tc_fun(tc_fun(tc_prod(U_19212,U_19214),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_19212,U_19214),tc_HOL_Obool),tc_fun(U_19214,tc_HOL_Obool)),U_19212),c_COMBC(U_19214,tc_fun(tc_prod(U_19212,U_19214),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_19214,tc_prod(U_19212,U_19214)),tc_fun(U_19214,tc_fun(tc_fun(tc_prod(U_19212,U_19214),tc_HOL_Obool),tc_HOL_Obool)),U_19212),hAPP(c_COMBB(tc_prod(U_19212,U_19214),tc_fun(tc_fun(tc_prod(U_19212,U_19214),tc_HOL_Obool),tc_HOL_Obool),U_19214),c_member(tc_prod(U_19212,U_19214)))),c_Product__Type_OPair(U_19212,U_19214)))),U_19216)),U_19218),U_19220)) ) ),
    inference(miniscope,[status(thm)],[f_4666_2]) ).

cnf(f_4666_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19214,U_19212)),hAPP(hAPP(c_Product__Type_OPair(U_19214,U_19212),U_19218),U_19220)),hAPP(c_Relation_Oconverse(U_19212,U_19214),U_19216)))
    | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_19212,U_19214,hAPP(hAPP(c_COMBC(U_19212,tc_fun(tc_prod(U_19212,U_19214),tc_HOL_Obool),tc_fun(U_19214,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_19214,tc_fun(tc_fun(tc_prod(U_19212,U_19214),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_19212,U_19214),tc_HOL_Obool),tc_fun(U_19214,tc_HOL_Obool)),U_19212),c_COMBC(U_19214,tc_fun(tc_prod(U_19212,U_19214),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_19214,tc_prod(U_19212,U_19214)),tc_fun(U_19214,tc_fun(tc_fun(tc_prod(U_19212,U_19214),tc_HOL_Obool),tc_HOL_Obool)),U_19212),hAPP(c_COMBB(tc_prod(U_19212,U_19214),tc_fun(tc_fun(tc_prod(U_19212,U_19214),tc_HOL_Obool),tc_HOL_Obool),U_19214),c_member(tc_prod(U_19212,U_19214)))),c_Product__Type_OPair(U_19212,U_19214)))),U_19216)),U_19218),U_19220)) ),
    inference(clausify,[status(thm)],[f_4666_3]) ).

cnf(f_4666_5,plain,
    ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_19213,U_19215,hAPP(hAPP(c_COMBC(U_19213,tc_fun(tc_prod(U_19213,U_19215),tc_HOL_Obool),tc_fun(U_19215,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_19215,tc_fun(tc_fun(tc_prod(U_19213,U_19215),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_19213,U_19215),tc_HOL_Obool),tc_fun(U_19215,tc_HOL_Obool)),U_19213),c_COMBC(U_19215,tc_fun(tc_prod(U_19213,U_19215),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_19215,tc_prod(U_19213,U_19215)),tc_fun(U_19215,tc_fun(tc_fun(tc_prod(U_19213,U_19215),tc_HOL_Obool),tc_HOL_Obool)),U_19213),hAPP(c_COMBB(tc_prod(U_19213,U_19215),tc_fun(tc_fun(tc_prod(U_19213,U_19215),tc_HOL_Obool),tc_HOL_Obool),U_19215),c_member(tc_prod(U_19213,U_19215)))),c_Product__Type_OPair(U_19213,U_19215)))),U_19217)),U_19219),U_19221))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19215,U_19213)),hAPP(hAPP(c_Product__Type_OPair(U_19215,U_19213),U_19219),U_19221)),hAPP(c_Relation_Oconverse(U_19213,U_19215),U_19217))) ),
    inference(clausify,[status(thm)],[f_4666_3]) ).

fof(f_4667_1,plain,
    ! [V_s2_2,V_s1_2,T_c,T_b] : c_Lazy__Sequence_Oproduct(T_b,T_c,V_s1_2,V_s2_2) = hAPP(c_Lazy__Sequence_Obind(T_b,tc_prod(T_b,T_c),V_s1_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_b,T_c))),tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_b,T_c)),T_b),c_Lazy__Sequence_Obind(T_c,tc_prod(T_b,T_c),V_s2_2)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_b,T_c))),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_b,T_c)),T_c),c_Lazy__Sequence_Osingle(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),
    inference(fof_nnf,[status(thm)],[fact_]) ).

fof(f_4667_2,plain,
    ! [U_19225,U_19224,U_19223,U_19222] : c_Lazy__Sequence_Oproduct(U_19222,U_19223,U_19224,U_19225) = hAPP(c_Lazy__Sequence_Obind(U_19222,tc_prod(U_19222,U_19223),U_19224),hAPP(hAPP(c_COMBB(tc_fun(U_19223,tc_Lazy__Sequence_Olazy__sequence(tc_prod(U_19222,U_19223))),tc_Lazy__Sequence_Olazy__sequence(tc_prod(U_19222,U_19223)),U_19222),c_Lazy__Sequence_Obind(U_19223,tc_prod(U_19222,U_19223),U_19225)),hAPP(hAPP(c_COMBB(tc_fun(U_19223,tc_prod(U_19222,U_19223)),tc_fun(U_19223,tc_Lazy__Sequence_Olazy__sequence(tc_prod(U_19222,U_19223))),U_19222),hAPP(c_COMBB(tc_prod(U_19222,U_19223),tc_Lazy__Sequence_Olazy__sequence(tc_prod(U_19222,U_19223)),U_19223),c_Lazy__Sequence_Osingle(tc_prod(U_19222,U_19223)))),c_Product__Type_OPair(U_19222,U_19223)))),
    inference(variable_rename,[status(thm)],[f_4667_1]) ).

cnf(f_4667_3,plain,
    c_Lazy__Sequence_Oproduct(U_19222,U_19223,U_19224,U_19225) = hAPP(c_Lazy__Sequence_Obind(U_19222,tc_prod(U_19222,U_19223),U_19224),hAPP(hAPP(c_COMBB(tc_fun(U_19223,tc_Lazy__Sequence_Olazy__sequence(tc_prod(U_19222,U_19223))),tc_Lazy__Sequence_Olazy__sequence(tc_prod(U_19222,U_19223)),U_19222),c_Lazy__Sequence_Obind(U_19223,tc_prod(U_19222,U_19223),U_19225)),hAPP(hAPP(c_COMBB(tc_fun(U_19223,tc_prod(U_19222,U_19223)),tc_fun(U_19223,tc_Lazy__Sequence_Olazy__sequence(tc_prod(U_19222,U_19223))),U_19222),hAPP(c_COMBB(tc_prod(U_19222,U_19223),tc_Lazy__Sequence_Olazy__sequence(tc_prod(U_19222,U_19223)),U_19223),c_Lazy__Sequence_Osingle(tc_prod(U_19222,U_19223)))),c_Product__Type_OPair(U_19222,U_19223)))),
    inference(clausify,[status(thm)],[f_4667_2]) ).

fof(f_4668_1,plain,
    ! [V_x,T_a,V_n] :
      ( hAPP(c_List_Otl(T_a),c_List_Oreplicate(T_a,V_n,V_x)) = c_List_Oreplicate(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_x)
      | V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(fof_nnf,[status(thm)],[fact_tl__replicate]) ).

fof(f_4668_2,plain,
    ! [U_19228,U_19227,U_19226] :
      ( hAPP(c_List_Otl(U_19227),c_List_Oreplicate(U_19227,U_19226,U_19228)) = c_List_Oreplicate(U_19227,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19226),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_19228)
      | U_19226 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[f_4668_1]) ).

cnf(f_4668_3,plain,
    ( hAPP(c_List_Otl(U_19227),c_List_Oreplicate(U_19227,U_19226,U_19228)) = c_List_Oreplicate(U_19227,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19226),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_19228)
    | U_19226 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4668_2]) ).

fof(f_4669_1,plain,
    ! [V_xs_2,V_x_2,T_b] : c_List_Oreplicate(T_b,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,hAPP(c_fequal,V_x_2)),V_xs_2)),V_x_2) = hAPP(c_List_Ofilter(T_b,hAPP(c_fequal,V_x_2)),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_replicate__length__filter]) ).

fof(f_4669_2,plain,
    ! [U_19231,U_19230,U_19229] : c_List_Oreplicate(U_19229,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19229)),hAPP(c_List_Ofilter(U_19229,hAPP(c_fequal,U_19230)),U_19231)),U_19230) = hAPP(c_List_Ofilter(U_19229,hAPP(c_fequal,U_19230)),U_19231),
    inference(variable_rename,[status(thm)],[f_4669_1]) ).

cnf(f_4669_3,plain,
    c_List_Oreplicate(U_19229,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19229)),hAPP(c_List_Ofilter(U_19229,hAPP(c_fequal,U_19230)),U_19231)),U_19230) = hAPP(c_List_Ofilter(U_19229,hAPP(c_fequal,U_19230)),U_19231),
    inference(clausify,[status(thm)],[f_4669_2]) ).

fof(f_4670_1,plain,
    ! [V_x,V_n,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oreplicate(T_a,V_n,V_x)) = V_n,
    inference(fof_nnf,[status(thm)],[fact_length__replicate]) ).

fof(f_4670_2,plain,
    ! [U_19234,U_19233,U_19232] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19232)),c_List_Oreplicate(U_19232,U_19233,U_19234)) = U_19233,
    inference(variable_rename,[status(thm)],[f_4670_1]) ).

cnf(f_4670_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19232)),c_List_Oreplicate(U_19232,U_19233,U_19234)) = U_19233,
    inference(clausify,[status(thm)],[f_4670_2]) ).

fof(f_4671_1,plain,
    ! [V_lst_2,V_k_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(c_COMBK(T_b,T_c),V_k_2)),V_lst_2) = c_List_Oreplicate(T_b,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_lst_2),V_k_2),
    inference(fof_nnf,[status(thm)],[fact_map__replicate__const]) ).

fof(f_4671_2,plain,
    ! [U_19238,U_19237,U_19236,U_19235] : hAPP(hAPP(c_List_Omap(U_19235,U_19236),hAPP(c_COMBK(U_19236,U_19235),U_19237)),U_19238) = c_List_Oreplicate(U_19236,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19235)),U_19238),U_19237),
    inference(variable_rename,[status(thm)],[f_4671_1]) ).

cnf(f_4671_3,plain,
    hAPP(hAPP(c_List_Omap(U_19235,U_19236),hAPP(c_COMBK(U_19236,U_19235),U_19237)),U_19238) = c_List_Oreplicate(U_19236,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19235)),U_19238),U_19237),
    inference(clausify,[status(thm)],[f_4671_2]) ).

fof(f_4672_1,plain,
    ! [V_xs,V_x,V_n,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_n,V_x)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_n,V_x)),V_xs)),
    inference(fof_nnf,[status(thm)],[fact_replicate__app__Cons__same]) ).

fof(f_4672_2,plain,
    ! [U_19242,U_19241,U_19240,U_19239] : hAPP(hAPP(c_List_Oappend(U_19239),c_List_Oreplicate(U_19239,U_19240,U_19241)),hAPP(hAPP(c_List_Olist_OCons(U_19239),U_19241),U_19242)) = hAPP(hAPP(c_List_Olist_OCons(U_19239),U_19241),hAPP(hAPP(c_List_Oappend(U_19239),c_List_Oreplicate(U_19239,U_19240,U_19241)),U_19242)),
    inference(variable_rename,[status(thm)],[f_4672_1]) ).

cnf(f_4672_3,plain,
    hAPP(hAPP(c_List_Oappend(U_19239),c_List_Oreplicate(U_19239,U_19240,U_19241)),hAPP(hAPP(c_List_Olist_OCons(U_19239),U_19241),U_19242)) = hAPP(hAPP(c_List_Olist_OCons(U_19239),U_19241),hAPP(hAPP(c_List_Oappend(U_19239),c_List_Oreplicate(U_19239,U_19240,U_19241)),U_19242)),
    inference(clausify,[status(thm)],[f_4672_2]) ).

fof(f_4673_1,plain,
    ! [V_x,V_n,T_a] : c_List_Oreplicate(T_a,hAPP(c_Nat_OSuc,V_n),V_x) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Oreplicate(T_a,V_n,V_x)),
    inference(fof_nnf,[status(thm)],[fact_replicate__Suc]) ).

fof(f_4673_2,plain,
    ! [U_19245,U_19244,U_19243] : c_List_Oreplicate(U_19243,hAPP(c_Nat_OSuc,U_19244),U_19245) = hAPP(hAPP(c_List_Olist_OCons(U_19243),U_19245),c_List_Oreplicate(U_19243,U_19244,U_19245)),
    inference(variable_rename,[status(thm)],[f_4673_1]) ).

cnf(f_4673_3,plain,
    c_List_Oreplicate(U_19243,hAPP(c_Nat_OSuc,U_19244),U_19245) = hAPP(hAPP(c_List_Olist_OCons(U_19243),U_19245),c_List_Oreplicate(U_19243,U_19244,U_19245)),
    inference(clausify,[status(thm)],[f_4673_2]) ).

fof(f_4674_1,plain,
    ! [V_x,V_n,T_a] : hAPP(c_List_Orev(T_a),c_List_Oreplicate(T_a,V_n,V_x)) = c_List_Oreplicate(T_a,V_n,V_x),
    inference(fof_nnf,[status(thm)],[fact_rev__replicate]) ).

fof(f_4674_2,plain,
    ! [U_19248,U_19247,U_19246] : hAPP(c_List_Orev(U_19246),c_List_Oreplicate(U_19246,U_19247,U_19248)) = c_List_Oreplicate(U_19246,U_19247,U_19248),
    inference(variable_rename,[status(thm)],[f_4674_1]) ).

cnf(f_4674_3,plain,
    hAPP(c_List_Orev(U_19246),c_List_Oreplicate(U_19246,U_19247,U_19248)) = c_List_Oreplicate(U_19246,U_19247,U_19248),
    inference(clausify,[status(thm)],[f_4674_2]) ).

fof(f_4675_1,plain,
    ! [V_x,V_k,V_i,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_i),c_List_Oreplicate(T_a,V_k,V_x)) = c_List_Oreplicate(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_i),V_k),V_x),
    inference(fof_nnf,[status(thm)],[fact_take__replicate]) ).

fof(f_4675_2,plain,
    ! [U_19252,U_19251,U_19250,U_19249] : hAPP(hAPP(c_List_Otake(U_19249),U_19250),c_List_Oreplicate(U_19249,U_19251,U_19252)) = c_List_Oreplicate(U_19249,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_19250),U_19251),U_19252),
    inference(variable_rename,[status(thm)],[f_4675_1]) ).

cnf(f_4675_3,plain,
    hAPP(hAPP(c_List_Otake(U_19249),U_19250),c_List_Oreplicate(U_19249,U_19251,U_19252)) = c_List_Oreplicate(U_19249,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_19250),U_19251),U_19252),
    inference(clausify,[status(thm)],[f_4675_2]) ).

fof(f_4676_1,plain,
    ! [V_x,V_k,V_i,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_i),c_List_Oreplicate(T_a,V_k,V_x)) = c_List_Oreplicate(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_k),V_i),V_x),
    inference(fof_nnf,[status(thm)],[fact_drop__replicate]) ).

fof(f_4676_2,plain,
    ! [U_19256,U_19255,U_19254,U_19253] : hAPP(hAPP(c_List_Odrop(U_19253),U_19254),c_List_Oreplicate(U_19253,U_19255,U_19256)) = c_List_Oreplicate(U_19253,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19255),U_19254),U_19256),
    inference(variable_rename,[status(thm)],[f_4676_1]) ).

cnf(f_4676_3,plain,
    hAPP(hAPP(c_List_Odrop(U_19253),U_19254),c_List_Oreplicate(U_19253,U_19255,U_19256)) = c_List_Oreplicate(U_19253,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19255),U_19254),U_19256),
    inference(clausify,[status(thm)],[f_4676_2]) ).

fof(f_4677_1,plain,
    ! [V_x,T_a,V_n] :
      ( hAPP(c_List_Ohd(T_a),c_List_Oreplicate(T_a,V_n,V_x)) = V_x
      | V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(fof_nnf,[status(thm)],[fact_hd__replicate]) ).

fof(f_4677_2,plain,
    ! [U_19259,U_19258,U_19257] :
      ( hAPP(c_List_Ohd(U_19258),c_List_Oreplicate(U_19258,U_19257,U_19259)) = U_19259
      | U_19257 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[f_4677_1]) ).

cnf(f_4677_3,plain,
    ( hAPP(c_List_Ohd(U_19258),c_List_Oreplicate(U_19258,U_19257,U_19259)) = U_19259
    | U_19257 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4677_2]) ).

fof(f_4678_1,plain,
    ! [V_x,T_a,V_n] :
      ( c_List_Olast(T_a,c_List_Oreplicate(T_a,V_n,V_x)) = V_x
      | V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(fof_nnf,[status(thm)],[fact_last__replicate]) ).

fof(f_4678_2,plain,
    ! [U_19262,U_19261,U_19260] :
      ( c_List_Olast(U_19261,c_List_Oreplicate(U_19261,U_19260,U_19262)) = U_19262
      | U_19260 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[f_4678_1]) ).

cnf(f_4678_3,plain,
    ( c_List_Olast(U_19261,c_List_Oreplicate(U_19261,U_19260,U_19262)) = U_19262
    | U_19260 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4678_2]) ).

fof(f_4679_1,plain,
    ! [V_y,V_j,V_x,V_i,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),c_List_Oreplicate(T_a,V_i,V_x)),c_List_Oreplicate(T_b,V_j,V_y)) = c_List_Oreplicate(tc_prod(T_a,T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_i),V_j),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x),V_y)),
    inference(fof_nnf,[status(thm)],[fact_zip__replicate]) ).

fof(f_4679_2,plain,
    ! [U_19268,U_19267,U_19266,U_19265,U_19264,U_19263] : hAPP(hAPP(c_List_Ozip(U_19263,U_19264),c_List_Oreplicate(U_19263,U_19265,U_19266)),c_List_Oreplicate(U_19264,U_19267,U_19268)) = c_List_Oreplicate(tc_prod(U_19263,U_19264),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_19265),U_19267),hAPP(hAPP(c_Product__Type_OPair(U_19263,U_19264),U_19266),U_19268)),
    inference(variable_rename,[status(thm)],[f_4679_1]) ).

cnf(f_4679_3,plain,
    hAPP(hAPP(c_List_Ozip(U_19263,U_19264),c_List_Oreplicate(U_19263,U_19265,U_19266)),c_List_Oreplicate(U_19264,U_19267,U_19268)) = c_List_Oreplicate(tc_prod(U_19263,U_19264),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_19265),U_19267),hAPP(hAPP(c_Product__Type_OPair(U_19263,U_19264),U_19266),U_19268)),
    inference(clausify,[status(thm)],[f_4679_2]) ).

fof(f_4680_1,plain,
    ! [V_P_2,V_a_2,V_n_2,T_b] :
      ( ( ? [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_n_2,V_a_2)))) )
        | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(V_P_2,V_a_2)) )
      & ( ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & hBOOL(hAPP(V_P_2,V_a_2)) )
        | ! [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_n_2,V_a_2)))) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_Bex__set__replicate]) ).

fof(f_4680_2,plain,
    ! [U_19274,U_19273,U_19272,U_19271] :
      ( ( ? [U_19270] :
            ( hBOOL(hAPP(U_19274,U_19270))
            & hBOOL(hAPP(hAPP(c_member(U_19271),U_19270),hAPP(c_List_Oset(U_19271),c_List_Oreplicate(U_19271,U_19272,U_19273)))) )
        | U_19272 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(U_19274,U_19273)) )
      & ( ( U_19272 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & hBOOL(hAPP(U_19274,U_19273)) )
        | ! [U_19269] :
            ( ~ hBOOL(hAPP(U_19274,U_19269))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19271),U_19269),hAPP(c_List_Oset(U_19271),c_List_Oreplicate(U_19271,U_19272,U_19273)))) ) ) ),
    inference(variable_rename,[status(thm)],[f_4680_1]) ).

fof(f_4680_3,plain,
    ( ! [U_19282,U_19280,U_19278] :
        ( ! [U_19276] :
          ? [U_19270] :
            ( hBOOL(hAPP(U_19282,U_19270))
            & hBOOL(hAPP(hAPP(c_member(U_19276),U_19270),hAPP(c_List_Oset(U_19276),c_List_Oreplicate(U_19276,U_19278,U_19280)))) )
        | U_19278 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(U_19282,U_19280)) )
    & ! [U_19281,U_19279,U_19277] :
        ( ! [U_19275,U_19269] :
            ( ~ hBOOL(hAPP(U_19281,U_19269))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19275),U_19269),hAPP(c_List_Oset(U_19275),c_List_Oreplicate(U_19275,U_19277,U_19279)))) )
        | ( U_19277 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & hBOOL(hAPP(U_19281,U_19279)) ) ) ),
    inference(miniscope,[status(thm)],[f_4680_2]) ).

fof(f_4680_4,plain,
    ( ! [U_19282,U_19280,U_19278] :
        ( ! [U_19276] :
            ( hBOOL(hAPP(U_19282,sK502(U_19282,U_19280,U_19278,U_19276)))
            & hBOOL(hAPP(hAPP(c_member(U_19276),sK502(U_19282,U_19280,U_19278,U_19276)),hAPP(c_List_Oset(U_19276),c_List_Oreplicate(U_19276,U_19278,U_19280)))) )
        | U_19278 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(U_19282,U_19280)) )
    & ! [U_19281,U_19279,U_19277] :
        ( ! [U_19275,U_19269] :
            ( ~ hBOOL(hAPP(U_19281,U_19269))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19275),U_19269),hAPP(c_List_Oset(U_19275),c_List_Oreplicate(U_19275,U_19277,U_19279)))) )
        | ( U_19277 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & hBOOL(hAPP(U_19281,U_19279)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK502]),skolemize(U_19270,sK502(U_19282,U_19280,U_19278,U_19276))],[f_4680_3]) ).

cnf(f_4680_5,plain,
    ( hBOOL(hAPP(U_19281,U_19279))
    | ~ hBOOL(hAPP(U_19281,U_19269))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19275),U_19269),hAPP(c_List_Oset(U_19275),c_List_Oreplicate(U_19275,U_19277,U_19279)))) ),
    inference(clausify,[status(thm)],[f_4680_4]) ).

cnf(f_4680_6,plain,
    ( U_19277 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(U_19281,U_19269))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19275),U_19269),hAPP(c_List_Oset(U_19275),c_List_Oreplicate(U_19275,U_19277,U_19279)))) ),
    inference(clausify,[status(thm)],[f_4680_4]) ).

cnf(f_4680_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19276),sK502(U_19282,U_19280,U_19278,U_19276)),hAPP(c_List_Oset(U_19276),c_List_Oreplicate(U_19276,U_19278,U_19280))))
    | U_19278 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(U_19282,U_19280)) ),
    inference(clausify,[status(thm)],[f_4680_4]) ).

cnf(f_4680_8,plain,
    ( hBOOL(hAPP(U_19282,sK502(U_19282,U_19280,U_19278,U_19276)))
    | U_19278 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(U_19282,U_19280)) ),
    inference(clausify,[status(thm)],[f_4680_4]) ).

fof(f_4681_1,plain,
    ! [V_P_2,V_a_2,V_n_2,T_b] :
      ( ( ! [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_n_2,V_a_2)))) )
        | ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & ~ hBOOL(hAPP(V_P_2,V_a_2)) ) )
      & ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(V_P_2,V_a_2))
        | ? [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_n_2,V_a_2)))) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_Ball__set__replicate]) ).

fof(f_4681_2,plain,
    ! [U_19288,U_19287,U_19286,U_19285] :
      ( ( ! [U_19284] :
            ( hBOOL(hAPP(U_19288,U_19284))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19285),U_19284),hAPP(c_List_Oset(U_19285),c_List_Oreplicate(U_19285,U_19286,U_19287)))) )
        | ( U_19286 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & ~ hBOOL(hAPP(U_19288,U_19287)) ) )
      & ( U_19286 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(U_19288,U_19287))
        | ? [U_19283] :
            ( ~ hBOOL(hAPP(U_19288,U_19283))
            & hBOOL(hAPP(hAPP(c_member(U_19285),U_19283),hAPP(c_List_Oset(U_19285),c_List_Oreplicate(U_19285,U_19286,U_19287)))) ) ) ),
    inference(variable_rename,[status(thm)],[f_4681_1]) ).

fof(f_4681_3,plain,
    ( ! [U_19296,U_19294,U_19292] :
        ( ! [U_19290,U_19284] :
            ( hBOOL(hAPP(U_19296,U_19284))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19290),U_19284),hAPP(c_List_Oset(U_19290),c_List_Oreplicate(U_19290,U_19292,U_19294)))) )
        | ( U_19292 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & ~ hBOOL(hAPP(U_19296,U_19294)) ) )
    & ! [U_19295,U_19293,U_19291] :
        ( ! [U_19289] :
          ? [U_19283] :
            ( ~ hBOOL(hAPP(U_19295,U_19283))
            & hBOOL(hAPP(hAPP(c_member(U_19289),U_19283),hAPP(c_List_Oset(U_19289),c_List_Oreplicate(U_19289,U_19291,U_19293)))) )
        | U_19291 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(U_19295,U_19293)) ) ),
    inference(miniscope,[status(thm)],[f_4681_2]) ).

fof(f_4681_4,plain,
    ( ! [U_19296,U_19294,U_19292] :
        ( ! [U_19290,U_19284] :
            ( hBOOL(hAPP(U_19296,U_19284))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19290),U_19284),hAPP(c_List_Oset(U_19290),c_List_Oreplicate(U_19290,U_19292,U_19294)))) )
        | ( U_19292 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & ~ hBOOL(hAPP(U_19296,U_19294)) ) )
    & ! [U_19295,U_19293,U_19291] :
        ( ! [U_19289] :
            ( ~ hBOOL(hAPP(U_19295,sK503(U_19295,U_19293,U_19291,U_19289)))
            & hBOOL(hAPP(hAPP(c_member(U_19289),sK503(U_19295,U_19293,U_19291,U_19289)),hAPP(c_List_Oset(U_19289),c_List_Oreplicate(U_19289,U_19291,U_19293)))) )
        | U_19291 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(U_19295,U_19293)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK503]),skolemize(U_19283,sK503(U_19295,U_19293,U_19291,U_19289))],[f_4681_3]) ).

cnf(f_4681_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19289),sK503(U_19295,U_19293,U_19291,U_19289)),hAPP(c_List_Oset(U_19289),c_List_Oreplicate(U_19289,U_19291,U_19293))))
    | U_19291 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(U_19295,U_19293)) ),
    inference(clausify,[status(thm)],[f_4681_4]) ).

cnf(f_4681_6,plain,
    ( ~ hBOOL(hAPP(U_19295,sK503(U_19295,U_19293,U_19291,U_19289)))
    | U_19291 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(U_19295,U_19293)) ),
    inference(clausify,[status(thm)],[f_4681_4]) ).

cnf(f_4681_7,plain,
    ( ~ hBOOL(hAPP(U_19296,U_19294))
    | hBOOL(hAPP(U_19296,U_19284))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19290),U_19284),hAPP(c_List_Oset(U_19290),c_List_Oreplicate(U_19290,U_19292,U_19294)))) ),
    inference(clausify,[status(thm)],[f_4681_4]) ).

cnf(f_4681_8,plain,
    ( U_19292 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(U_19296,U_19284))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19290),U_19284),hAPP(c_List_Oset(U_19290),c_List_Oreplicate(U_19290,U_19292,U_19294)))) ),
    inference(clausify,[status(thm)],[f_4681_4]) ).

fof(f_4682_1,plain,
    ! [V_y_2,V_n_2,V_x_2,V_m_2,T_b] :
      ( ( c_List_Oreplicate(T_b,V_m_2,V_x_2) = c_List_Oreplicate(T_b,V_n_2,V_y_2)
        | ( V_x_2 != V_y_2
          & V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | V_m_2 != V_n_2 )
      & ( ( ( V_x_2 = V_y_2
            | V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & V_m_2 = V_n_2 )
        | c_List_Oreplicate(T_b,V_m_2,V_x_2) != c_List_Oreplicate(T_b,V_n_2,V_y_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_replicate__eq__replicate]) ).

fof(f_4682_2,plain,
    ! [U_19301,U_19300,U_19299,U_19298,U_19297] :
      ( ( c_List_Oreplicate(U_19297,U_19298,U_19299) = c_List_Oreplicate(U_19297,U_19300,U_19301)
        | ( U_19299 != U_19301
          & U_19298 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | U_19298 != U_19300 )
      & ( ( ( U_19299 = U_19301
            | U_19298 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & U_19298 = U_19300 )
        | c_List_Oreplicate(U_19297,U_19298,U_19299) != c_List_Oreplicate(U_19297,U_19300,U_19301) ) ),
    inference(variable_rename,[status(thm)],[f_4682_1]) ).

fof(f_4682_3,plain,
    ( ! [U_19311,U_19309,U_19307,U_19305] :
        ( ! [U_19303] : c_List_Oreplicate(U_19303,U_19305,U_19307) = c_List_Oreplicate(U_19303,U_19309,U_19311)
        | ( U_19307 != U_19311
          & U_19305 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | U_19305 != U_19309 )
    & ! [U_19310,U_19308,U_19306,U_19304] :
        ( ! [U_19302] : c_List_Oreplicate(U_19302,U_19304,U_19306) != c_List_Oreplicate(U_19302,U_19308,U_19310)
        | ( ( U_19306 = U_19310
            | U_19304 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & U_19304 = U_19308 ) ) ),
    inference(miniscope,[status(thm)],[f_4682_2]) ).

cnf(f_4682_4,plain,
    ( U_19304 = U_19308
    | c_List_Oreplicate(U_19302,U_19304,U_19306) != c_List_Oreplicate(U_19302,U_19308,U_19310) ),
    inference(clausify,[status(thm)],[f_4682_3]) ).

cnf(f_4682_5,plain,
    ( U_19306 = U_19310
    | U_19304 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_List_Oreplicate(U_19302,U_19304,U_19306) != c_List_Oreplicate(U_19302,U_19308,U_19310) ),
    inference(clausify,[status(thm)],[f_4682_3]) ).

cnf(f_4682_6,plain,
    ( U_19305 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_19305 != U_19309
    | c_List_Oreplicate(U_19303,U_19305,U_19307) = c_List_Oreplicate(U_19303,U_19309,U_19311) ),
    inference(clausify,[status(thm)],[f_4682_3]) ).

cnf(f_4682_7,plain,
    ( U_19307 != U_19311
    | U_19305 != U_19309
    | c_List_Oreplicate(U_19303,U_19305,U_19307) = c_List_Oreplicate(U_19303,U_19309,U_19311) ),
    inference(clausify,[status(thm)],[f_4682_3]) ).

fof(f_4683_1,plain,
    ! [V_x,T_a,V_n,V_i] :
      ( hAPP(hAPP(c_List_Onth(T_a),c_List_Oreplicate(T_a,V_n,V_x)),V_i) = V_x
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_nth__replicate]) ).

fof(f_4683_2,plain,
    ! [U_19315,U_19314,U_19313,U_19312] :
      ( hAPP(hAPP(c_List_Onth(U_19314),c_List_Oreplicate(U_19314,U_19313,U_19315)),U_19312) = U_19315
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19312),U_19313)) ),
    inference(variable_rename,[status(thm)],[f_4683_1]) ).

cnf(f_4683_3,plain,
    ( hAPP(hAPP(c_List_Onth(U_19314),c_List_Oreplicate(U_19314,U_19313,U_19315)),U_19312) = U_19315
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19312),U_19313)) ),
    inference(clausify,[status(thm)],[f_4683_2]) ).

fof(f_4684_1,plain,
    ! [V_x,V_m,V_n,T_a] : c_List_Oreplicate(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m),V_x) = hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_n,V_x)),c_List_Oreplicate(T_a,V_m,V_x)),
    inference(fof_nnf,[status(thm)],[fact_replicate__add]) ).

fof(f_4684_2,plain,
    ! [U_19319,U_19318,U_19317,U_19316] : c_List_Oreplicate(U_19316,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19317),U_19318),U_19319) = hAPP(hAPP(c_List_Oappend(U_19316),c_List_Oreplicate(U_19316,U_19317,U_19319)),c_List_Oreplicate(U_19316,U_19318,U_19319)),
    inference(variable_rename,[status(thm)],[f_4684_1]) ).

cnf(f_4684_3,plain,
    c_List_Oreplicate(U_19316,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19317),U_19318),U_19319) = hAPP(hAPP(c_List_Oappend(U_19316),c_List_Oreplicate(U_19316,U_19317,U_19319)),c_List_Oreplicate(U_19316,U_19318,U_19319)),
    inference(clausify,[status(thm)],[f_4684_2]) ).

fof(f_4685_1,plain,
    ! [V_k,V_x,V_n,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_n,V_x)),c_List_Oreplicate(T_a,V_k,V_x)) = hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_k,V_x)),c_List_Oreplicate(T_a,V_n,V_x)),
    inference(fof_nnf,[status(thm)],[fact_append__replicate__commute]) ).

fof(f_4685_2,plain,
    ! [U_19323,U_19322,U_19321,U_19320] : hAPP(hAPP(c_List_Oappend(U_19320),c_List_Oreplicate(U_19320,U_19321,U_19322)),c_List_Oreplicate(U_19320,U_19323,U_19322)) = hAPP(hAPP(c_List_Oappend(U_19320),c_List_Oreplicate(U_19320,U_19323,U_19322)),c_List_Oreplicate(U_19320,U_19321,U_19322)),
    inference(variable_rename,[status(thm)],[f_4685_1]) ).

cnf(f_4685_3,plain,
    hAPP(hAPP(c_List_Oappend(U_19320),c_List_Oreplicate(U_19320,U_19321,U_19322)),c_List_Oreplicate(U_19320,U_19323,U_19322)) = hAPP(hAPP(c_List_Oappend(U_19320),c_List_Oreplicate(U_19320,U_19323,U_19322)),c_List_Oreplicate(U_19320,U_19321,U_19322)),
    inference(clausify,[status(thm)],[f_4685_2]) ).

fof(f_4686_1,plain,
    ! [V_n_2,T_b,V_x_2,V_P_2] :
      ( ( hAPP(c_List_Ofilter(T_b,V_P_2),c_List_Oreplicate(T_b,V_n_2,V_x_2)) = c_List_Olist_ONil(T_b)
        | hBOOL(hAPP(V_P_2,V_x_2)) )
      & ( hAPP(c_List_Ofilter(T_b,V_P_2),c_List_Oreplicate(T_b,V_n_2,V_x_2)) = c_List_Oreplicate(T_b,V_n_2,V_x_2)
        | ~ hBOOL(hAPP(V_P_2,V_x_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_filter__replicate]) ).

fof(f_4686_2,plain,
    ! [U_19327,U_19326,U_19325,U_19324] :
      ( ( hAPP(c_List_Ofilter(U_19326,U_19324),c_List_Oreplicate(U_19326,U_19327,U_19325)) = c_List_Olist_ONil(U_19326)
        | hBOOL(hAPP(U_19324,U_19325)) )
      & ( hAPP(c_List_Ofilter(U_19326,U_19324),c_List_Oreplicate(U_19326,U_19327,U_19325)) = c_List_Oreplicate(U_19326,U_19327,U_19325)
        | ~ hBOOL(hAPP(U_19324,U_19325)) ) ),
    inference(variable_rename,[status(thm)],[f_4686_1]) ).

fof(f_4686_3,plain,
    ( ! [U_19335,U_19333,U_19331,U_19329] :
        ( hAPP(c_List_Ofilter(U_19333,U_19329),c_List_Oreplicate(U_19333,U_19335,U_19331)) = c_List_Olist_ONil(U_19333)
        | hBOOL(hAPP(U_19329,U_19331)) )
    & ! [U_19334,U_19332,U_19330,U_19328] :
        ( hAPP(c_List_Ofilter(U_19332,U_19328),c_List_Oreplicate(U_19332,U_19334,U_19330)) = c_List_Oreplicate(U_19332,U_19334,U_19330)
        | ~ hBOOL(hAPP(U_19328,U_19330)) ) ),
    inference(miniscope,[status(thm)],[f_4686_2]) ).

cnf(f_4686_4,plain,
    ( hAPP(c_List_Ofilter(U_19332,U_19328),c_List_Oreplicate(U_19332,U_19334,U_19330)) = c_List_Oreplicate(U_19332,U_19334,U_19330)
    | ~ hBOOL(hAPP(U_19328,U_19330)) ),
    inference(clausify,[status(thm)],[f_4686_3]) ).

cnf(f_4686_5,plain,
    ( hAPP(c_List_Ofilter(U_19333,U_19329),c_List_Oreplicate(U_19333,U_19335,U_19331)) = c_List_Olist_ONil(U_19333)
    | hBOOL(hAPP(U_19329,U_19331)) ),
    inference(clausify,[status(thm)],[f_4686_3]) ).

fof(f_4687_1,plain,
    ! [V_i,T_a] : c_List_Oconcat(T_a,c_List_Oreplicate(tc_List_Olist(T_a),V_i,c_List_Olist_ONil(T_a))) = c_List_Olist_ONil(T_a),
    inference(fof_nnf,[status(thm)],[fact_concat__replicate__trivial]) ).

fof(f_4687_2,plain,
    ! [U_19337,U_19336] : c_List_Oconcat(U_19336,c_List_Oreplicate(tc_List_Olist(U_19336),U_19337,c_List_Olist_ONil(U_19336))) = c_List_Olist_ONil(U_19336),
    inference(variable_rename,[status(thm)],[f_4687_1]) ).

cnf(f_4687_3,plain,
    c_List_Oconcat(U_19336,c_List_Oreplicate(tc_List_Olist(U_19336),U_19337,c_List_Olist_ONil(U_19336))) = c_List_Olist_ONil(U_19336),
    inference(clausify,[status(thm)],[f_4687_2]) ).

fof(f_4688_1,plain,
    ! [V_x,T_a] : c_List_Oreplicate(T_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x) = c_List_Olist_ONil(T_a),
    inference(fof_nnf,[status(thm)],[fact_replicate__0]) ).

fof(f_4688_2,plain,
    ! [U_19339,U_19338] : c_List_Oreplicate(U_19338,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_19339) = c_List_Olist_ONil(U_19338),
    inference(variable_rename,[status(thm)],[f_4688_1]) ).

cnf(f_4688_3,plain,
    c_List_Oreplicate(U_19338,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_19339) = c_List_Olist_ONil(U_19338),
    inference(clausify,[status(thm)],[f_4688_2]) ).

fof(f_4689_1,plain,
    ! [V_x_2,V_n_2,T_b] :
      ( ( c_List_Olist_ONil(T_b) = c_List_Oreplicate(T_b,V_n_2,V_x_2)
        | V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_List_Olist_ONil(T_b) != c_List_Oreplicate(T_b,V_n_2,V_x_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_empty__replicate]) ).

fof(f_4689_2,plain,
    ! [U_19342,U_19341,U_19340] :
      ( ( c_List_Olist_ONil(U_19340) = c_List_Oreplicate(U_19340,U_19341,U_19342)
        | U_19341 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( U_19341 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_List_Olist_ONil(U_19340) != c_List_Oreplicate(U_19340,U_19341,U_19342) ) ),
    inference(variable_rename,[status(thm)],[f_4689_1]) ).

fof(f_4689_3,plain,
    ( ! [U_19348,U_19346] :
        ( ! [U_19344] : c_List_Olist_ONil(U_19344) = c_List_Oreplicate(U_19344,U_19346,U_19348)
        | U_19346 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_19347,U_19345] :
        ( ! [U_19343] : c_List_Olist_ONil(U_19343) != c_List_Oreplicate(U_19343,U_19345,U_19347)
        | U_19345 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_4689_2]) ).

cnf(f_4689_4,plain,
    ( c_List_Olist_ONil(U_19343) != c_List_Oreplicate(U_19343,U_19345,U_19347)
    | U_19345 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4689_3]) ).

cnf(f_4689_5,plain,
    ( c_List_Olist_ONil(U_19344) = c_List_Oreplicate(U_19344,U_19346,U_19348)
    | U_19346 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4689_3]) ).

fof(f_4690_1,plain,
    ! [V_x_2,V_n_2,T_b] :
      ( ( c_List_Oreplicate(T_b,V_n_2,V_x_2) = c_List_Olist_ONil(T_b)
        | V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_List_Oreplicate(T_b,V_n_2,V_x_2) != c_List_Olist_ONil(T_b) ) ),
    inference(fof_nnf,[status(thm)],[fact_replicate__empty]) ).

fof(f_4690_2,plain,
    ! [U_19351,U_19350,U_19349] :
      ( ( c_List_Oreplicate(U_19349,U_19350,U_19351) = c_List_Olist_ONil(U_19349)
        | U_19350 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( U_19350 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_List_Oreplicate(U_19349,U_19350,U_19351) != c_List_Olist_ONil(U_19349) ) ),
    inference(variable_rename,[status(thm)],[f_4690_1]) ).

fof(f_4690_3,plain,
    ( ! [U_19357,U_19355] :
        ( ! [U_19353] : c_List_Oreplicate(U_19353,U_19355,U_19357) = c_List_Olist_ONil(U_19353)
        | U_19355 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_19356,U_19354] :
        ( ! [U_19352] : c_List_Oreplicate(U_19352,U_19354,U_19356) != c_List_Olist_ONil(U_19352)
        | U_19354 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_4690_2]) ).

cnf(f_4690_4,plain,
    ( c_List_Oreplicate(U_19352,U_19354,U_19356) != c_List_Olist_ONil(U_19352)
    | U_19354 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4690_3]) ).

cnf(f_4690_5,plain,
    ( c_List_Oreplicate(U_19353,U_19355,U_19357) = c_List_Olist_ONil(U_19353)
    | U_19355 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4690_3]) ).

fof(f_4691_1,plain,
    ! [V_x_2,V_n_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Oreplicate(T_c,V_n_2,V_x_2)) = c_List_Oreplicate(T_b,V_n_2,hAPP(V_f_2,V_x_2)),
    inference(fof_nnf,[status(thm)],[fact_map__replicate]) ).

fof(f_4691_2,plain,
    ! [U_19362,U_19361,U_19360,U_19359,U_19358] : hAPP(hAPP(c_List_Omap(U_19358,U_19359),U_19360),c_List_Oreplicate(U_19358,U_19361,U_19362)) = c_List_Oreplicate(U_19359,U_19361,hAPP(U_19360,U_19362)),
    inference(variable_rename,[status(thm)],[f_4691_1]) ).

cnf(f_4691_3,plain,
    hAPP(hAPP(c_List_Omap(U_19358,U_19359),U_19360),c_List_Oreplicate(U_19358,U_19361,U_19362)) = c_List_Oreplicate(U_19359,U_19361,hAPP(U_19360,U_19362)),
    inference(clausify,[status(thm)],[f_4691_2]) ).

fof(f_4692_1,plain,
    ! [V_y_2,V_n_2,V_x_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_n_2,V_y_2))))
        | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | V_x_2 != V_y_2 )
      & ( ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & V_x_2 = V_y_2 )
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_n_2,V_y_2)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_in__set__replicate]) ).

fof(f_4692_2,plain,
    ! [U_19366,U_19365,U_19364,U_19363] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_19363),U_19364),hAPP(c_List_Oset(U_19363),c_List_Oreplicate(U_19363,U_19365,U_19366))))
        | U_19365 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_19364 != U_19366 )
      & ( ( U_19365 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_19364 = U_19366 )
        | ~ hBOOL(hAPP(hAPP(c_member(U_19363),U_19364),hAPP(c_List_Oset(U_19363),c_List_Oreplicate(U_19363,U_19365,U_19366)))) ) ),
    inference(variable_rename,[status(thm)],[f_4692_1]) ).

fof(f_4692_3,plain,
    ( ! [U_19374,U_19372,U_19370] :
        ( ! [U_19368] : hBOOL(hAPP(hAPP(c_member(U_19368),U_19370),hAPP(c_List_Oset(U_19368),c_List_Oreplicate(U_19368,U_19372,U_19374))))
        | U_19372 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_19370 != U_19374 )
    & ! [U_19373,U_19371,U_19369] :
        ( ! [U_19367] : ~ hBOOL(hAPP(hAPP(c_member(U_19367),U_19369),hAPP(c_List_Oset(U_19367),c_List_Oreplicate(U_19367,U_19371,U_19373))))
        | ( U_19371 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_19369 = U_19373 ) ) ),
    inference(miniscope,[status(thm)],[f_4692_2]) ).

cnf(f_4692_4,plain,
    ( U_19369 = U_19373
    | ~ hBOOL(hAPP(hAPP(c_member(U_19367),U_19369),hAPP(c_List_Oset(U_19367),c_List_Oreplicate(U_19367,U_19371,U_19373)))) ),
    inference(clausify,[status(thm)],[f_4692_3]) ).

cnf(f_4692_5,plain,
    ( U_19371 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(U_19367),U_19369),hAPP(c_List_Oset(U_19367),c_List_Oreplicate(U_19367,U_19371,U_19373)))) ),
    inference(clausify,[status(thm)],[f_4692_3]) ).

cnf(f_4692_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19368),U_19370),hAPP(c_List_Oset(U_19368),c_List_Oreplicate(U_19368,U_19372,U_19374))))
    | U_19372 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_19370 != U_19374 ),
    inference(clausify,[status(thm)],[f_4692_3]) ).

fof(f_4693_1,plain,
    ! [V_x,V_i,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_i,V_x)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Oreplicate(T_a,V_i,V_x)),
    inference(fof_nnf,[status(thm)],[fact_replicate__append__same]) ).

fof(f_4693_2,plain,
    ! [U_19377,U_19376,U_19375] : hAPP(hAPP(c_List_Oappend(U_19375),c_List_Oreplicate(U_19375,U_19376,U_19377)),hAPP(hAPP(c_List_Olist_OCons(U_19375),U_19377),c_List_Olist_ONil(U_19375))) = hAPP(hAPP(c_List_Olist_OCons(U_19375),U_19377),c_List_Oreplicate(U_19375,U_19376,U_19377)),
    inference(variable_rename,[status(thm)],[f_4693_1]) ).

cnf(f_4693_3,plain,
    hAPP(hAPP(c_List_Oappend(U_19375),c_List_Oreplicate(U_19375,U_19376,U_19377)),hAPP(hAPP(c_List_Olist_OCons(U_19375),U_19377),c_List_Olist_ONil(U_19375))) = hAPP(hAPP(c_List_Olist_OCons(U_19375),U_19377),c_List_Oreplicate(U_19375,U_19376,U_19377)),
    inference(clausify,[status(thm)],[f_4693_2]) ).

fof(f_4694_1,plain,
    ! [V_i_2,V_x_2,T_b] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),hAPP(c_COMBK(T_b,tc_Nat_Onat),V_x_2)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i_2)) = c_List_Oreplicate(T_b,V_i_2,V_x_2),
    inference(fof_nnf,[status(thm)],[fact_map__replicate__trivial]) ).

fof(f_4694_2,plain,
    ! [U_19380,U_19379,U_19378] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,U_19378),hAPP(c_COMBK(U_19378,tc_Nat_Onat),U_19379)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_19380)) = c_List_Oreplicate(U_19378,U_19380,U_19379),
    inference(variable_rename,[status(thm)],[f_4694_1]) ).

cnf(f_4694_3,plain,
    hAPP(hAPP(c_List_Omap(tc_Nat_Onat,U_19378),hAPP(c_COMBK(U_19378,tc_Nat_Onat),U_19379)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_19380)) = c_List_Oreplicate(U_19378,U_19380,U_19379),
    inference(clausify,[status(thm)],[f_4694_2]) ).

fof(f_4695_1,plain,
    ! [V_x_2,T_b,V_n_2] :
      ( ( hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_n_2,V_x_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))
        | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_n_2,V_x_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
        | V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(fof_nnf,[status(thm)],[fact_set__replicate__conv__if]) ).

fof(f_4695_2,plain,
    ! [U_19383,U_19382,U_19381] :
      ( ( hAPP(c_List_Oset(U_19382),c_List_Oreplicate(U_19382,U_19381,U_19383)) = hAPP(hAPP(c_Set_Oinsert(U_19382),U_19383),c_Orderings_Obot__class_Obot(tc_fun(U_19382,tc_HOL_Obool)))
        | U_19381 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(c_List_Oset(U_19382),c_List_Oreplicate(U_19382,U_19381,U_19383)) = c_Orderings_Obot__class_Obot(tc_fun(U_19382,tc_HOL_Obool))
        | U_19381 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_4695_1]) ).

fof(f_4695_3,plain,
    ( ! [U_19389,U_19387,U_19385] :
        ( hAPP(c_List_Oset(U_19387),c_List_Oreplicate(U_19387,U_19385,U_19389)) = hAPP(hAPP(c_Set_Oinsert(U_19387),U_19389),c_Orderings_Obot__class_Obot(tc_fun(U_19387,tc_HOL_Obool)))
        | U_19385 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_19388,U_19386,U_19384] :
        ( hAPP(c_List_Oset(U_19386),c_List_Oreplicate(U_19386,U_19384,U_19388)) = c_Orderings_Obot__class_Obot(tc_fun(U_19386,tc_HOL_Obool))
        | U_19384 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_4695_2]) ).

cnf(f_4695_4,plain,
    ( hAPP(c_List_Oset(U_19386),c_List_Oreplicate(U_19386,U_19384,U_19388)) = c_Orderings_Obot__class_Obot(tc_fun(U_19386,tc_HOL_Obool))
    | U_19384 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4695_3]) ).

cnf(f_4695_5,plain,
    ( hAPP(c_List_Oset(U_19387),c_List_Oreplicate(U_19387,U_19385,U_19389)) = hAPP(hAPP(c_Set_Oinsert(U_19387),U_19389),c_Orderings_Obot__class_Obot(tc_fun(U_19387,tc_HOL_Obool)))
    | U_19385 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4695_3]) ).

fof(f_4696_1,plain,
    ! [V_x_2,T_b,V_n_2] :
      ( hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_n_2,V_x_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))
      | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(fof_nnf,[status(thm)],[fact_set__replicate]) ).

fof(f_4696_2,plain,
    ! [U_19392,U_19391,U_19390] :
      ( hAPP(c_List_Oset(U_19391),c_List_Oreplicate(U_19391,U_19390,U_19392)) = hAPP(hAPP(c_Set_Oinsert(U_19391),U_19392),c_Orderings_Obot__class_Obot(tc_fun(U_19391,tc_HOL_Obool)))
      | U_19390 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[f_4696_1]) ).

cnf(f_4696_3,plain,
    ( hAPP(c_List_Oset(U_19391),c_List_Oreplicate(U_19391,U_19390,U_19392)) = hAPP(hAPP(c_Set_Oinsert(U_19391),U_19392),c_Orderings_Obot__class_Obot(tc_fun(U_19391,tc_HOL_Obool)))
    | U_19390 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4696_2]) ).

fof(f_4697_1,plain,
    ! [V_x_2,V_n_2,T_b] : hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,hAPP(c_Nat_OSuc,V_n_2),V_x_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),
    inference(fof_nnf,[status(thm)],[fact_set__replicate__Suc]) ).

fof(f_4697_2,plain,
    ! [U_19395,U_19394,U_19393] : hAPP(c_List_Oset(U_19393),c_List_Oreplicate(U_19393,hAPP(c_Nat_OSuc,U_19394),U_19395)) = hAPP(hAPP(c_Set_Oinsert(U_19393),U_19395),c_Orderings_Obot__class_Obot(tc_fun(U_19393,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_4697_1]) ).

cnf(f_4697_3,plain,
    hAPP(c_List_Oset(U_19393),c_List_Oreplicate(U_19393,hAPP(c_Nat_OSuc,U_19394),U_19395)) = hAPP(hAPP(c_Set_Oinsert(U_19393),U_19395),c_Orderings_Obot__class_Obot(tc_fun(U_19393,tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_4697_2]) ).

fof(f_4698_1,plain,
    ! [V_d_2,T_b] :
      ( c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(T_b),V_d_2) = c_Lazy__Sequence_Oappend(tc_List_Olist(T_b),hAPP(c_Lazy__Sequence_Osingle(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),hAPP(hAPP(hAPP(c_If(tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_b))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)),hAPP(c_Lazy__Sequence_Obind(tc_prod(T_b,tc_List_Olist(T_b)),tc_List_Olist(T_b),c_Lazy__Sequence_Oproduct(T_b,tc_List_Olist(T_b),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_d_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_d_2),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_List_Olist(T_b),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_b))),T_b),hAPP(c_COMBB(tc_List_Olist(T_b),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_b)),tc_List_Olist(T_b)),c_Lazy__Sequence_Osingle(tc_List_Olist(T_b)))),c_List_Olist_OCons(T_b))))),c_Lazy__Sequence_Oempty(tc_List_Olist(T_b))))
      | ~ class_Lazy__Sequence_Osmall__lazy(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_small__lazy__list_Osimps]) ).

fof(f_4698_2,plain,
    ! [U_19397,U_19396] :
      ( c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(U_19396),U_19397) = c_Lazy__Sequence_Oappend(tc_List_Olist(U_19396),hAPP(c_Lazy__Sequence_Osingle(tc_List_Olist(U_19396)),c_List_Olist_ONil(U_19396)),hAPP(hAPP(hAPP(c_If(tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(U_19396))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_19397)),hAPP(c_Lazy__Sequence_Obind(tc_prod(U_19396,tc_List_Olist(U_19396)),tc_List_Olist(U_19396),c_Lazy__Sequence_Oproduct(U_19396,tc_List_Olist(U_19396),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(U_19396,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_19397),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(U_19396),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_19397),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Product__Type_Oprod_Oprod__case(U_19396,tc_List_Olist(U_19396),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(U_19396))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_19396),tc_List_Olist(U_19396)),tc_fun(tc_List_Olist(U_19396),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(U_19396))),U_19396),hAPP(c_COMBB(tc_List_Olist(U_19396),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(U_19396)),tc_List_Olist(U_19396)),c_Lazy__Sequence_Osingle(tc_List_Olist(U_19396)))),c_List_Olist_OCons(U_19396))))),c_Lazy__Sequence_Oempty(tc_List_Olist(U_19396))))
      | ~ class_Lazy__Sequence_Osmall__lazy(U_19396) ),
    inference(variable_rename,[status(thm)],[f_4698_1]) ).

cnf(f_4698_3,plain,
    ( c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(U_19396),U_19397) = c_Lazy__Sequence_Oappend(tc_List_Olist(U_19396),hAPP(c_Lazy__Sequence_Osingle(tc_List_Olist(U_19396)),c_List_Olist_ONil(U_19396)),hAPP(hAPP(hAPP(c_If(tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(U_19396))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_19397)),hAPP(c_Lazy__Sequence_Obind(tc_prod(U_19396,tc_List_Olist(U_19396)),tc_List_Olist(U_19396),c_Lazy__Sequence_Oproduct(U_19396,tc_List_Olist(U_19396),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(U_19396,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_19397),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(U_19396),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_19397),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Product__Type_Oprod_Oprod__case(U_19396,tc_List_Olist(U_19396),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(U_19396))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_19396),tc_List_Olist(U_19396)),tc_fun(tc_List_Olist(U_19396),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(U_19396))),U_19396),hAPP(c_COMBB(tc_List_Olist(U_19396),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(U_19396)),tc_List_Olist(U_19396)),c_Lazy__Sequence_Osingle(tc_List_Olist(U_19396)))),c_List_Olist_OCons(U_19396))))),c_Lazy__Sequence_Oempty(tc_List_Olist(U_19396))))
    | ~ class_Lazy__Sequence_Osmall__lazy(U_19396) ),
    inference(clausify,[status(thm)],[f_4698_2]) ).

fof(f_4699_1,plain,
    ! [V_R_2,T_b] : c_Predicate_Opred__comp(T_b,T_b,T_b,c_fequal,c_Predicate_Opred__comp(T_b,T_b,T_b,V_R_2,c_fequal)) = V_R_2,
    inference(fof_nnf,[status(thm)],[fact_eq__comp__r]) ).

fof(f_4699_2,plain,
    ! [U_19399,U_19398] : c_Predicate_Opred__comp(U_19398,U_19398,U_19398,c_fequal,c_Predicate_Opred__comp(U_19398,U_19398,U_19398,U_19399,c_fequal)) = U_19399,
    inference(variable_rename,[status(thm)],[f_4699_1]) ).

cnf(f_4699_3,plain,
    c_Predicate_Opred__comp(U_19398,U_19398,U_19398,c_fequal,c_Predicate_Opred__comp(U_19398,U_19398,U_19398,U_19399,c_fequal)) = U_19399,
    inference(clausify,[status(thm)],[f_4699_2]) ).

fof(f_4700_1,plain,
    ! [V_d,T_b,T_a] :
      ( c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_prod(T_a,T_b),V_d) = c_Lazy__Sequence_Oproduct(T_a,T_b,c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(T_a,V_d),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(T_b,V_d))
      | ~ class_Lazy__Sequence_Osmall__lazy(T_b)
      | ~ class_Lazy__Sequence_Osmall__lazy(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_small__lazy__prod__def]) ).

fof(f_4700_2,plain,
    ! [U_19402,U_19401,U_19400] :
      ( c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_prod(U_19400,U_19401),U_19402) = c_Lazy__Sequence_Oproduct(U_19400,U_19401,c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(U_19400,U_19402),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(U_19401,U_19402))
      | ~ class_Lazy__Sequence_Osmall__lazy(U_19401)
      | ~ class_Lazy__Sequence_Osmall__lazy(U_19400) ),
    inference(variable_rename,[status(thm)],[f_4700_1]) ).

cnf(f_4700_3,plain,
    ( c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_prod(U_19400,U_19401),U_19402) = c_Lazy__Sequence_Oproduct(U_19400,U_19401,c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(U_19400,U_19402),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(U_19401,U_19402))
    | ~ class_Lazy__Sequence_Osmall__lazy(U_19401)
    | ~ class_Lazy__Sequence_Osmall__lazy(U_19400) ),
    inference(clausify,[status(thm)],[f_4700_2]) ).

fof(f_4701_1,plain,
    ! [V_i_2,V_yq_2,V_xq_2,T_b] : hAPP(c_New__DSequence_Opos__union(T_b,V_xq_2,V_yq_2),V_i_2) = c_Lazy__Sequence_Oappend(T_b,hAPP(V_xq_2,V_i_2),hAPP(V_yq_2,V_i_2)),
    inference(fof_nnf,[status(thm)],[fact_New__DSequence_Opos__union__def]) ).

fof(f_4701_2,plain,
    ! [U_19406,U_19405,U_19404,U_19403] : hAPP(c_New__DSequence_Opos__union(U_19403,U_19404,U_19405),U_19406) = c_Lazy__Sequence_Oappend(U_19403,hAPP(U_19404,U_19406),hAPP(U_19405,U_19406)),
    inference(variable_rename,[status(thm)],[f_4701_1]) ).

cnf(f_4701_3,plain,
    hAPP(c_New__DSequence_Opos__union(U_19403,U_19404,U_19405),U_19406) = c_Lazy__Sequence_Oappend(U_19403,hAPP(U_19404,U_19406),hAPP(U_19405,U_19406)),
    inference(clausify,[status(thm)],[f_4701_2]) ).

fof(f_4702_1,plain,
    ! [V_lazy__sequence,V_a,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_a)),c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_a,V_lazy__sequence)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_a)),V_lazy__sequence)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(fof_nnf,[status(thm)],[fact_lazy__sequence_Osize_I4_J]) ).

fof(f_4702_2,plain,
    ! [U_19409,U_19408,U_19407] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(U_19407)),c_Lazy__Sequence_Olazy__sequence_OInsert(U_19407,U_19408,U_19409)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(U_19407)),U_19409)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_4702_1]) ).

cnf(f_4702_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(U_19407)),c_Lazy__Sequence_Olazy__sequence_OInsert(U_19407,U_19408,U_19409)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(U_19407)),U_19409)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_4702_2]) ).

fof(f_4703_1,plain,
    ! [V_yq,V_xq,V_x,T_a] : c_Lazy__Sequence_Oappend(T_a,c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_x,V_xq),V_yq) = c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_x,c_Lazy__Sequence_Oappend(T_a,V_xq,V_yq)),
    inference(fof_nnf,[status(thm)],[fact__01]) ).

fof(f_4703_2,plain,
    ! [U_19413,U_19412,U_19411,U_19410] : c_Lazy__Sequence_Oappend(U_19410,c_Lazy__Sequence_Olazy__sequence_OInsert(U_19410,U_19411,U_19412),U_19413) = c_Lazy__Sequence_Olazy__sequence_OInsert(U_19410,U_19411,c_Lazy__Sequence_Oappend(U_19410,U_19412,U_19413)),
    inference(variable_rename,[status(thm)],[f_4703_1]) ).

cnf(f_4703_3,plain,
    c_Lazy__Sequence_Oappend(U_19410,c_Lazy__Sequence_Olazy__sequence_OInsert(U_19410,U_19411,U_19412),U_19413) = c_Lazy__Sequence_Olazy__sequence_OInsert(U_19410,U_19411,c_Lazy__Sequence_Oappend(U_19410,U_19412,U_19413)),
    inference(clausify,[status(thm)],[f_4703_2]) ).

fof(f_4704_1,plain,
    ! [V_lazy__sequence_H_2,V_a_H_2,V_lazy__sequence_2,V_a_2,T_b] :
      ( ( c_Lazy__Sequence_Olazy__sequence_OInsert(T_b,V_a_2,V_lazy__sequence_2) = c_Lazy__Sequence_Olazy__sequence_OInsert(T_b,V_a_H_2,V_lazy__sequence_H_2)
        | V_lazy__sequence_2 != V_lazy__sequence_H_2
        | V_a_2 != V_a_H_2 )
      & ( ( V_lazy__sequence_2 = V_lazy__sequence_H_2
          & V_a_2 = V_a_H_2 )
        | c_Lazy__Sequence_Olazy__sequence_OInsert(T_b,V_a_2,V_lazy__sequence_2) != c_Lazy__Sequence_Olazy__sequence_OInsert(T_b,V_a_H_2,V_lazy__sequence_H_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_lazy__sequence_Oinject]) ).

fof(f_4704_2,plain,
    ! [U_19418,U_19417,U_19416,U_19415,U_19414] :
      ( ( c_Lazy__Sequence_Olazy__sequence_OInsert(U_19414,U_19415,U_19416) = c_Lazy__Sequence_Olazy__sequence_OInsert(U_19414,U_19417,U_19418)
        | U_19416 != U_19418
        | U_19415 != U_19417 )
      & ( ( U_19416 = U_19418
          & U_19415 = U_19417 )
        | c_Lazy__Sequence_Olazy__sequence_OInsert(U_19414,U_19415,U_19416) != c_Lazy__Sequence_Olazy__sequence_OInsert(U_19414,U_19417,U_19418) ) ),
    inference(variable_rename,[status(thm)],[f_4704_1]) ).

fof(f_4704_3,plain,
    ( ! [U_19428,U_19426,U_19424,U_19422] :
        ( ! [U_19420] : c_Lazy__Sequence_Olazy__sequence_OInsert(U_19420,U_19422,U_19424) = c_Lazy__Sequence_Olazy__sequence_OInsert(U_19420,U_19426,U_19428)
        | U_19424 != U_19428
        | U_19422 != U_19426 )
    & ! [U_19427,U_19425,U_19423,U_19421] :
        ( ! [U_19419] : c_Lazy__Sequence_Olazy__sequence_OInsert(U_19419,U_19421,U_19423) != c_Lazy__Sequence_Olazy__sequence_OInsert(U_19419,U_19425,U_19427)
        | ( U_19423 = U_19427
          & U_19421 = U_19425 ) ) ),
    inference(miniscope,[status(thm)],[f_4704_2]) ).

cnf(f_4704_4,plain,
    ( U_19421 = U_19425
    | c_Lazy__Sequence_Olazy__sequence_OInsert(U_19419,U_19421,U_19423) != c_Lazy__Sequence_Olazy__sequence_OInsert(U_19419,U_19425,U_19427) ),
    inference(clausify,[status(thm)],[f_4704_3]) ).

cnf(f_4704_5,plain,
    ( U_19423 = U_19427
    | c_Lazy__Sequence_Olazy__sequence_OInsert(U_19419,U_19421,U_19423) != c_Lazy__Sequence_Olazy__sequence_OInsert(U_19419,U_19425,U_19427) ),
    inference(clausify,[status(thm)],[f_4704_3]) ).

cnf(f_4704_6,plain,
    ( c_Lazy__Sequence_Olazy__sequence_OInsert(U_19420,U_19422,U_19424) = c_Lazy__Sequence_Olazy__sequence_OInsert(U_19420,U_19426,U_19428)
    | U_19424 != U_19428
    | U_19422 != U_19426 ),
    inference(clausify,[status(thm)],[f_4704_3]) ).

fof(f_4705_1,plain,
    ! [V_seed_2,V_size_2,V_nrandom_2,V_R2_2,V_R1_2,T_b] : c_New__Random__Sequence_Opos__union(T_b,V_R1_2,V_R2_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__union(T_b,hAPP(hAPP(hAPP(V_R1_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(hAPP(V_R2_2,V_nrandom_2),V_size_2),V_seed_2)),
    inference(fof_nnf,[status(thm)],[fact_pos__union__def]) ).

fof(f_4705_2,plain,
    ! [U_19434,U_19433,U_19432,U_19431,U_19430,U_19429] : c_New__Random__Sequence_Opos__union(U_19429,U_19430,U_19431,U_19432,U_19433,U_19434) = c_New__DSequence_Opos__union(U_19429,hAPP(hAPP(hAPP(U_19430,U_19432),U_19433),U_19434),hAPP(hAPP(hAPP(U_19431,U_19432),U_19433),U_19434)),
    inference(variable_rename,[status(thm)],[f_4705_1]) ).

cnf(f_4705_3,plain,
    c_New__Random__Sequence_Opos__union(U_19429,U_19430,U_19431,U_19432,U_19433,U_19434) = c_New__DSequence_Opos__union(U_19429,hAPP(hAPP(hAPP(U_19430,U_19432),U_19433),U_19434),hAPP(hAPP(hAPP(U_19431,U_19432),U_19433),U_19434)),
    inference(clausify,[status(thm)],[f_4705_2]) ).

fof(f_4706_1,plain,
    ! [V_lazy__sequence_2,V_a_2,V_fa_2,T_b] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_b,V_fa_2),c_Lazy__Sequence_Olazy__sequence_OInsert(T_b,V_a_2,V_lazy__sequence_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_fa_2,V_a_2)),hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_b,V_fa_2),V_lazy__sequence_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(fof_nnf,[status(thm)],[fact_lazy__sequence_Osize_I2_J]) ).

fof(f_4706_2,plain,
    ! [U_19438,U_19437,U_19436,U_19435] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(U_19435,U_19436),c_Lazy__Sequence_Olazy__sequence_OInsert(U_19435,U_19437,U_19438)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_19436,U_19437)),hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(U_19435,U_19436),U_19438))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_4706_1]) ).

cnf(f_4706_3,plain,
    hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(U_19435,U_19436),c_Lazy__Sequence_Olazy__sequence_OInsert(U_19435,U_19437,U_19438)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_19436,U_19437)),hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(U_19435,U_19436),U_19438))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_4706_2]) ).

fof(f_4707_1,plain,
    ! [V_i,V_d] :
      ( ( c_Lazy__Sequence_Osmall__lazy_H(V_d,V_i) = c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),V_i),c_Lazy__Sequence_Osmall__lazy_H(V_d,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d),V_i)) )
      & ( c_Lazy__Sequence_Osmall__lazy_H(V_d,V_i) = c_Lazy__Sequence_Oempty(tc_Int_Oint)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d),V_i)) ) ),
    inference(fof_nnf,[status(thm)],[fact_small__lazy_H_Osimps]) ).

fof(f_4707_2,plain,
    ! [U_19440,U_19439] :
      ( ( c_Lazy__Sequence_Osmall__lazy_H(U_19439,U_19440) = c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),U_19440),c_Lazy__Sequence_Osmall__lazy_H(U_19439,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_19440),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_19439),U_19440)) )
      & ( c_Lazy__Sequence_Osmall__lazy_H(U_19439,U_19440) = c_Lazy__Sequence_Oempty(tc_Int_Oint)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_19439),U_19440)) ) ),
    inference(variable_rename,[status(thm)],[f_4707_1]) ).

fof(f_4707_3,plain,
    ( ! [U_19444,U_19442] :
        ( c_Lazy__Sequence_Osmall__lazy_H(U_19442,U_19444) = c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),U_19444),c_Lazy__Sequence_Osmall__lazy_H(U_19442,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_19444),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_19442),U_19444)) )
    & ! [U_19443,U_19441] :
        ( c_Lazy__Sequence_Osmall__lazy_H(U_19441,U_19443) = c_Lazy__Sequence_Oempty(tc_Int_Oint)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_19441),U_19443)) ) ),
    inference(miniscope,[status(thm)],[f_4707_2]) ).

cnf(f_4707_4,plain,
    ( c_Lazy__Sequence_Osmall__lazy_H(U_19441,U_19443) = c_Lazy__Sequence_Oempty(tc_Int_Oint)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_19441),U_19443)) ),
    inference(clausify,[status(thm)],[f_4707_3]) ).

cnf(f_4707_5,plain,
    ( c_Lazy__Sequence_Osmall__lazy_H(U_19442,U_19444) = c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),U_19444),c_Lazy__Sequence_Osmall__lazy_H(U_19442,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_19444),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_19442),U_19444)) ),
    inference(clausify,[status(thm)],[f_4707_3]) ).

fof(f_4708_1,plain,
    ! [V_i_2,V_d_2] :
      ( ( ( c_Lazy__Sequence_Osmall__lazy_H(V_d_2,V_i_2) = c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),V_i_2),c_Lazy__Sequence_Osmall__lazy_H(V_d_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint))))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) )
        & ( c_Lazy__Sequence_Osmall__lazy_H(V_d_2,V_i_2) = c_Lazy__Sequence_Oempty(tc_Int_Oint)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) ) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_d_2),V_i_2))) ),
    inference(fof_nnf,[status(thm)],[fact_small__lazy_H_Opsimps]) ).

fof(f_4708_2,plain,
    ! [U_19446,U_19445] :
      ( ( ( c_Lazy__Sequence_Osmall__lazy_H(U_19445,U_19446) = c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),U_19446),c_Lazy__Sequence_Osmall__lazy_H(U_19445,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_19446),c_Groups_Oone__class_Oone(tc_Int_Oint))))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_19445),U_19446)) )
        & ( c_Lazy__Sequence_Osmall__lazy_H(U_19445,U_19446) = c_Lazy__Sequence_Oempty(tc_Int_Oint)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_19445),U_19446)) ) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_19445),U_19446))) ),
    inference(variable_rename,[status(thm)],[f_4708_1]) ).

cnf(f_4708_3,plain,
    ( c_Lazy__Sequence_Osmall__lazy_H(U_19445,U_19446) = c_Lazy__Sequence_Oempty(tc_Int_Oint)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_19445),U_19446))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_19445),U_19446))) ),
    inference(clausify,[status(thm)],[f_4708_2]) ).

cnf(f_4708_4,plain,
    ( c_Lazy__Sequence_Osmall__lazy_H(U_19445,U_19446) = c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),U_19446),c_Lazy__Sequence_Osmall__lazy_H(U_19445,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_19446),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_19445),U_19446))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_19445),U_19446))) ),
    inference(clausify,[status(thm)],[f_4708_2]) ).

fof(f_4709_1,plain,
    ! [V_d] : c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_Int_Oint,V_d) = c_Lazy__Sequence_Osmall__lazy_H(V_d,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_d)),
    inference(fof_nnf,[status(thm)],[fact_small__lazy__int__def]) ).

fof(f_4709_2,plain,
    ! [U_19447] : c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_Int_Oint,U_19447) = c_Lazy__Sequence_Osmall__lazy_H(U_19447,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_19447)),
    inference(variable_rename,[status(thm)],[f_4709_1]) ).

cnf(f_4709_3,plain,
    c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_Int_Oint,U_19447) = c_Lazy__Sequence_Osmall__lazy_H(U_19447,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_19447)),
    inference(clausify,[status(thm)],[f_4709_2]) ).

fof(f_4710_1,plain,
    ! [V_P_2,V_a1_2,V_a0_2] :
      ( hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2))
      | ? [B_d,B_i] :
          ( ~ hBOOL(hAPP(hAPP(V_P_2,B_d),B_i))
          & ( hBOOL(hAPP(hAPP(V_P_2,B_d),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_i),c_Groups_Oone__class_Oone(tc_Int_Oint))))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_d),B_i)) )
          & hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_d),B_i))) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2))) ),
    inference(fof_nnf,[status(thm)],[fact_small__lazy_H_Opinduct]) ).

fof(f_4710_2,plain,
    ! [U_19452,U_19451,U_19450] :
      ( hBOOL(hAPP(hAPP(U_19452,U_19450),U_19451))
      | ? [U_19449,U_19448] :
          ( ~ hBOOL(hAPP(hAPP(U_19452,U_19449),U_19448))
          & ( hBOOL(hAPP(hAPP(U_19452,U_19449),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_19448),c_Groups_Oone__class_Oone(tc_Int_Oint))))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_19449),U_19448)) )
          & hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_19449),U_19448))) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_19450),U_19451))) ),
    inference(variable_rename,[status(thm)],[f_4710_1]) ).

fof(f_4710_3,plain,
    ! [U_19452,U_19451,U_19450] :
      ( hBOOL(hAPP(hAPP(U_19452,U_19450),U_19451))
      | ? [U_19448] :
          ( ~ hBOOL(hAPP(hAPP(U_19452,sK504(U_19452,U_19451,U_19450)),U_19448))
          & ( hBOOL(hAPP(hAPP(U_19452,sK504(U_19452,U_19451,U_19450)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_19448),c_Groups_Oone__class_Oone(tc_Int_Oint))))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK504(U_19452,U_19451,U_19450)),U_19448)) )
          & hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),sK504(U_19452,U_19451,U_19450)),U_19448))) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_19450),U_19451))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK504]),skolemize(U_19449,sK504(U_19452,U_19451,U_19450))],[f_4710_2]) ).

fof(f_4710_4,plain,
    ! [U_19452,U_19451,U_19450] :
      ( hBOOL(hAPP(hAPP(U_19452,U_19450),U_19451))
      | ( ~ hBOOL(hAPP(hAPP(U_19452,sK504(U_19452,U_19451,U_19450)),sK505(U_19452,U_19451,U_19450)))
        & ( hBOOL(hAPP(hAPP(U_19452,sK504(U_19452,U_19451,U_19450)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK505(U_19452,U_19451,U_19450)),c_Groups_Oone__class_Oone(tc_Int_Oint))))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK504(U_19452,U_19451,U_19450)),sK505(U_19452,U_19451,U_19450))) )
        & hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),sK504(U_19452,U_19451,U_19450)),sK505(U_19452,U_19451,U_19450)))) )
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_19450),U_19451))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK505]),skolemize(U_19448,sK505(U_19452,U_19451,U_19450))],[f_4710_3]) ).

cnf(f_4710_5,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),sK504(U_19452,U_19451,U_19450)),sK505(U_19452,U_19451,U_19450))))
    | hBOOL(hAPP(hAPP(U_19452,U_19450),U_19451))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_19450),U_19451))) ),
    inference(clausify,[status(thm)],[f_4710_4]) ).

cnf(f_4710_6,plain,
    ( hBOOL(hAPP(hAPP(U_19452,sK504(U_19452,U_19451,U_19450)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK505(U_19452,U_19451,U_19450)),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK504(U_19452,U_19451,U_19450)),sK505(U_19452,U_19451,U_19450)))
    | hBOOL(hAPP(hAPP(U_19452,U_19450),U_19451))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_19450),U_19451))) ),
    inference(clausify,[status(thm)],[f_4710_4]) ).

cnf(f_4710_7,plain,
    ( ~ hBOOL(hAPP(hAPP(U_19452,sK504(U_19452,U_19451,U_19450)),sK505(U_19452,U_19451,U_19450)))
    | hBOOL(hAPP(hAPP(U_19452,U_19450),U_19451))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_19450),U_19451))) ),
    inference(clausify,[status(thm)],[f_4710_4]) ).

fof(f_4711_1,plain,
    ! [V_xq_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_b)),V_xq_2) = c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(T_b,tc_Lazy__Sequence_Olazy__sequence(T_b)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),T_b),hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(T_b)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_b)))),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(c_Lazy__Sequence_Oyield(T_b),V_xq_2)),
    inference(fof_nnf,[status(thm)],[fact_size__code]) ).

fof(f_4711_2,plain,
    ! [U_19454,U_19453] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(U_19453)),U_19454) = c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(U_19453,tc_Lazy__Sequence_Olazy__sequence(U_19453)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(U_19453,tc_Lazy__Sequence_Olazy__sequence(U_19453),tc_Nat_Onat),hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(U_19453),tc_Nat_Onat),U_19453),hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(U_19453),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(U_19453)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(U_19453)))),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(c_Lazy__Sequence_Oyield(U_19453),U_19454)),
    inference(variable_rename,[status(thm)],[f_4711_1]) ).

cnf(f_4711_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(U_19453)),U_19454) = c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(U_19453,tc_Lazy__Sequence_Olazy__sequence(U_19453)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(U_19453,tc_Lazy__Sequence_Olazy__sequence(U_19453),tc_Nat_Onat),hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(U_19453),tc_Nat_Onat),U_19453),hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(U_19453),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(U_19453)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(U_19453)))),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(c_Lazy__Sequence_Oyield(U_19453),U_19454)),
    inference(clausify,[status(thm)],[f_4711_2]) ).

fof(f_4712_1,plain,
    ! [V_xq_2,V_s_2,T_b] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_b,V_s_2),V_xq_2) = c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(T_b,tc_Lazy__Sequence_Olazy__sequence(T_b)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),hAPP(hAPP(c_COMBC(T_b,tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat)),T_b),c_COMBC(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),T_b),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(T_b)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat)),T_b),c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Lazy__Sequence_Olazy__sequence(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),T_b),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_s_2))),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_b,V_s_2))))),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Lazy__Sequence_Oyield(T_b),V_xq_2)),
    inference(fof_nnf,[status(thm)],[fact_lazy__sequence__size__code]) ).

fof(f_4712_2,plain,
    ! [U_19457,U_19456,U_19455] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(U_19455,U_19456),U_19457) = c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(U_19455,tc_Lazy__Sequence_Olazy__sequence(U_19455)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(U_19455,tc_Lazy__Sequence_Olazy__sequence(U_19455),tc_Nat_Onat),hAPP(hAPP(c_COMBC(U_19455,tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(U_19455),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(U_19455),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(U_19455),tc_Nat_Onat)),U_19455),c_COMBC(tc_Lazy__Sequence_Olazy__sequence(U_19455),tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(U_19455),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(U_19455),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),U_19455),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(U_19455)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat))),hAPP(hAPP(c_COMBC(U_19455,tc_fun(tc_Lazy__Sequence_Olazy__sequence(U_19455),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(U_19455),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_Lazy__Sequence_Olazy__sequence(U_19455),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(U_19455),tc_Nat_Onat)),U_19455),c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Lazy__Sequence_Olazy__sequence(U_19455))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),U_19455),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_19456))),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(U_19455,U_19456))))),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Lazy__Sequence_Oyield(U_19455),U_19457)),
    inference(variable_rename,[status(thm)],[f_4712_1]) ).

cnf(f_4712_3,plain,
    hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(U_19455,U_19456),U_19457) = c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(U_19455,tc_Lazy__Sequence_Olazy__sequence(U_19455)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(U_19455,tc_Lazy__Sequence_Olazy__sequence(U_19455),tc_Nat_Onat),hAPP(hAPP(c_COMBC(U_19455,tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(U_19455),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(U_19455),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(U_19455),tc_Nat_Onat)),U_19455),c_COMBC(tc_Lazy__Sequence_Olazy__sequence(U_19455),tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(U_19455),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(U_19455),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),U_19455),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(U_19455)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat))),hAPP(hAPP(c_COMBC(U_19455,tc_fun(tc_Lazy__Sequence_Olazy__sequence(U_19455),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(U_19455),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_Lazy__Sequence_Olazy__sequence(U_19455),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(U_19455),tc_Nat_Onat)),U_19455),c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Lazy__Sequence_Olazy__sequence(U_19455))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),U_19455),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_19456))),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(U_19455,U_19456))))),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Lazy__Sequence_Oyield(U_19455),U_19457)),
    inference(clausify,[status(thm)],[f_4712_2]) ).

fof(f_4713_1,plain,
    ! [V_xq_2,V_g_2,V_f_2,T_c,T_b] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(T_b,T_c,V_f_2,V_g_2,V_xq_2) = c_Option_Ooption_Ooption__case(T_b,tc_prod(T_c,tc_Lazy__Sequence_Olazy__sequence(T_c)),V_f_2,hAPP(c_Product__Type_Oprod_Oprod__case(T_c,tc_Lazy__Sequence_Olazy__sequence(T_c),T_b),V_g_2),hAPP(c_Lazy__Sequence_Oyield(T_c),V_xq_2)),
    inference(fof_nnf,[status(thm)],[fact_seq__case]) ).

fof(f_4713_2,plain,
    ! [U_19462,U_19461,U_19460,U_19459,U_19458] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(U_19458,U_19459,U_19460,U_19461,U_19462) = c_Option_Ooption_Ooption__case(U_19458,tc_prod(U_19459,tc_Lazy__Sequence_Olazy__sequence(U_19459)),U_19460,hAPP(c_Product__Type_Oprod_Oprod__case(U_19459,tc_Lazy__Sequence_Olazy__sequence(U_19459),U_19458),U_19461),hAPP(c_Lazy__Sequence_Oyield(U_19459),U_19462)),
    inference(variable_rename,[status(thm)],[f_4713_1]) ).

cnf(f_4713_3,plain,
    c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(U_19458,U_19459,U_19460,U_19461,U_19462) = c_Option_Ooption_Ooption__case(U_19458,tc_prod(U_19459,tc_Lazy__Sequence_Olazy__sequence(U_19459)),U_19460,hAPP(c_Product__Type_Oprod_Oprod__case(U_19459,tc_Lazy__Sequence_Olazy__sequence(U_19459),U_19458),U_19461),hAPP(c_Lazy__Sequence_Oyield(U_19459),U_19462)),
    inference(clausify,[status(thm)],[f_4713_2]) ).

fof(f_4714_1,plain,
    ! [T_b] : c_Lazy__Sequence_Oyieldn(T_b) = c_Lazy__Sequence_Oanamorph(tc_Lazy__Sequence_Olazy__sequence(T_b),T_b,c_Lazy__Sequence_Oyield(T_b)),
    inference(fof_nnf,[status(thm)],[fact_yieldn__def]) ).

fof(f_4714_2,plain,
    ! [U_19463] : c_Lazy__Sequence_Oyieldn(U_19463) = c_Lazy__Sequence_Oanamorph(tc_Lazy__Sequence_Olazy__sequence(U_19463),U_19463,c_Lazy__Sequence_Oyield(U_19463)),
    inference(variable_rename,[status(thm)],[f_4714_1]) ).

cnf(f_4714_3,plain,
    c_Lazy__Sequence_Oyieldn(U_19463) = c_Lazy__Sequence_Oanamorph(tc_Lazy__Sequence_Olazy__sequence(U_19463),U_19463,c_Lazy__Sequence_Oyield(U_19463)),
    inference(clausify,[status(thm)],[f_4714_2]) ).

fof(f_4715_1,plain,
    ! [V_lazy__sequence_2,V_a_2,V_f2_2,V_f1_2,T_c,T_b] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(T_b,T_c,V_f1_2,V_f2_2,c_Lazy__Sequence_Olazy__sequence_OInsert(T_c,V_a_2,V_lazy__sequence_2)) = hAPP(hAPP(V_f2_2,V_a_2),V_lazy__sequence_2),
    inference(fof_nnf,[status(thm)],[fact_lazy__sequence_Osimps_I5_J]) ).

fof(f_4715_2,plain,
    ! [U_19469,U_19468,U_19467,U_19466,U_19465,U_19464] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(U_19464,U_19465,U_19466,U_19467,c_Lazy__Sequence_Olazy__sequence_OInsert(U_19465,U_19468,U_19469)) = hAPP(hAPP(U_19467,U_19468),U_19469),
    inference(variable_rename,[status(thm)],[f_4715_1]) ).

cnf(f_4715_3,plain,
    c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(U_19464,U_19465,U_19466,U_19467,c_Lazy__Sequence_Olazy__sequence_OInsert(U_19465,U_19468,U_19469)) = hAPP(hAPP(U_19467,U_19468),U_19469),
    inference(clausify,[status(thm)],[f_4715_2]) ).

fof(f_4716_1,plain,
    ! [V_r_2,V_A_2,T_c,V_S_2,T_b] :
      ( c_Relation_Orefl__on(T_c,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_S_2),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_S_2),V_r_2))
      | ? [B_x] :
          ( ~ c_Relation_Orefl__on(T_c,hAPP(V_A_2,B_x),hAPP(V_r_2,B_x))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_refl__on__INTER]) ).

fof(f_4716_2,plain,
    ! [U_19475,U_19474,U_19473,U_19472,U_19471] :
      ( c_Relation_Orefl__on(U_19473,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_19471,tc_fun(U_19473,tc_HOL_Obool)),U_19472),U_19474),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_19471,tc_fun(tc_prod(U_19473,U_19473),tc_HOL_Obool)),U_19472),U_19475))
      | ? [U_19470] :
          ( ~ c_Relation_Orefl__on(U_19473,hAPP(U_19474,U_19470),hAPP(U_19475,U_19470))
          & hBOOL(hAPP(hAPP(c_member(U_19471),U_19470),U_19472)) ) ),
    inference(variable_rename,[status(thm)],[f_4716_1]) ).

fof(f_4716_3,plain,
    ! [U_19475,U_19474,U_19473,U_19472,U_19471] :
      ( c_Relation_Orefl__on(U_19473,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_19471,tc_fun(U_19473,tc_HOL_Obool)),U_19472),U_19474),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_19471,tc_fun(tc_prod(U_19473,U_19473),tc_HOL_Obool)),U_19472),U_19475))
      | ( ~ c_Relation_Orefl__on(U_19473,hAPP(U_19474,sK506(U_19475,U_19474,U_19473,U_19472,U_19471)),hAPP(U_19475,sK506(U_19475,U_19474,U_19473,U_19472,U_19471)))
        & hBOOL(hAPP(hAPP(c_member(U_19471),sK506(U_19475,U_19474,U_19473,U_19472,U_19471)),U_19472)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK506]),skolemize(U_19470,sK506(U_19475,U_19474,U_19473,U_19472,U_19471))],[f_4716_2]) ).

cnf(f_4716_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19471),sK506(U_19475,U_19474,U_19473,U_19472,U_19471)),U_19472))
    | c_Relation_Orefl__on(U_19473,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_19471,tc_fun(U_19473,tc_HOL_Obool)),U_19472),U_19474),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_19471,tc_fun(tc_prod(U_19473,U_19473),tc_HOL_Obool)),U_19472),U_19475)) ),
    inference(clausify,[status(thm)],[f_4716_3]) ).

cnf(f_4716_5,plain,
    ( ~ c_Relation_Orefl__on(U_19473,hAPP(U_19474,sK506(U_19475,U_19474,U_19473,U_19472,U_19471)),hAPP(U_19475,sK506(U_19475,U_19474,U_19473,U_19472,U_19471)))
    | c_Relation_Orefl__on(U_19473,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_19471,tc_fun(U_19473,tc_HOL_Obool)),U_19472),U_19474),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_19471,tc_fun(tc_prod(U_19473,U_19473),tc_HOL_Obool)),U_19472),U_19475)) ),
    inference(clausify,[status(thm)],[f_4716_3]) ).

fof(f_4717_1,plain,
    ! [V_xs_2,V_x_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
        | ~ hBOOL(hAPP(hAPP(c_List_Omember(T_b),V_xs_2),V_x_2)) )
      & ( hBOOL(hAPP(hAPP(c_List_Omember(T_b),V_xs_2),V_x_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_in__set__member]) ).

fof(f_4717_2,plain,
    ! [U_19478,U_19477,U_19476] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_19476),U_19477),hAPP(c_List_Oset(U_19476),U_19478)))
        | ~ hBOOL(hAPP(hAPP(c_List_Omember(U_19476),U_19478),U_19477)) )
      & ( hBOOL(hAPP(hAPP(c_List_Omember(U_19476),U_19478),U_19477))
        | ~ hBOOL(hAPP(hAPP(c_member(U_19476),U_19477),hAPP(c_List_Oset(U_19476),U_19478))) ) ),
    inference(variable_rename,[status(thm)],[f_4717_1]) ).

fof(f_4717_3,plain,
    ( ! [U_19484,U_19482,U_19480] :
        ( hBOOL(hAPP(hAPP(c_member(U_19480),U_19482),hAPP(c_List_Oset(U_19480),U_19484)))
        | ~ hBOOL(hAPP(hAPP(c_List_Omember(U_19480),U_19484),U_19482)) )
    & ! [U_19483,U_19481,U_19479] :
        ( hBOOL(hAPP(hAPP(c_List_Omember(U_19479),U_19483),U_19481))
        | ~ hBOOL(hAPP(hAPP(c_member(U_19479),U_19481),hAPP(c_List_Oset(U_19479),U_19483))) ) ),
    inference(miniscope,[status(thm)],[f_4717_2]) ).

cnf(f_4717_4,plain,
    ( hBOOL(hAPP(hAPP(c_List_Omember(U_19479),U_19483),U_19481))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19479),U_19481),hAPP(c_List_Oset(U_19479),U_19483))) ),
    inference(clausify,[status(thm)],[f_4717_3]) ).

cnf(f_4717_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19480),U_19482),hAPP(c_List_Oset(U_19480),U_19484)))
    | ~ hBOOL(hAPP(hAPP(c_List_Omember(U_19480),U_19484),U_19482)) ),
    inference(clausify,[status(thm)],[f_4717_3]) ).

fof(f_4718_1,plain,
    ! [V_y,T_a] : ~ hBOOL(hAPP(hAPP(c_List_Omember(T_a),c_List_Olist_ONil(T_a)),V_y)),
    inference(fof_nnf,[status(thm)],[fact_member__rec_I2_J]) ).

fof(f_4718_2,plain,
    ! [U_19486,U_19485] : ~ hBOOL(hAPP(hAPP(c_List_Omember(U_19485),c_List_Olist_ONil(U_19485)),U_19486)),
    inference(variable_rename,[status(thm)],[f_4718_1]) ).

cnf(f_4718_3,plain,
    ~ hBOOL(hAPP(hAPP(c_List_Omember(U_19485),c_List_Olist_ONil(U_19485)),U_19486)),
    inference(clausify,[status(thm)],[f_4718_2]) ).

fof(f_4719_1,plain,
    ! [T_b] : c_List_Omember(T_b) = c_List_Oset(T_b),
    inference(fof_nnf,[status(thm)],[fact_member__set]) ).

fof(f_4719_2,plain,
    ! [U_19487] : c_List_Omember(U_19487) = c_List_Oset(U_19487),
    inference(variable_rename,[status(thm)],[f_4719_1]) ).

cnf(f_4719_3,plain,
    c_List_Omember(U_19487) = c_List_Oset(U_19487),
    inference(clausify,[status(thm)],[f_4719_2]) ).

fof(f_4720_1,plain,
    ! [V_y_2,V_xs_2,V_x_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_List_Omember(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_y_2))
        | ( ~ hBOOL(hAPP(hAPP(c_List_Omember(T_b),V_xs_2),V_y_2))
          & V_x_2 != V_y_2 ) )
      & ( hBOOL(hAPP(hAPP(c_List_Omember(T_b),V_xs_2),V_y_2))
        | V_x_2 = V_y_2
        | ~ hBOOL(hAPP(hAPP(c_List_Omember(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_y_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_member__rec_I1_J]) ).

fof(f_4720_2,plain,
    ! [U_19491,U_19490,U_19489,U_19488] :
      ( ( hBOOL(hAPP(hAPP(c_List_Omember(U_19488),hAPP(hAPP(c_List_Olist_OCons(U_19488),U_19489),U_19490)),U_19491))
        | ( ~ hBOOL(hAPP(hAPP(c_List_Omember(U_19488),U_19490),U_19491))
          & U_19489 != U_19491 ) )
      & ( hBOOL(hAPP(hAPP(c_List_Omember(U_19488),U_19490),U_19491))
        | U_19489 = U_19491
        | ~ hBOOL(hAPP(hAPP(c_List_Omember(U_19488),hAPP(hAPP(c_List_Olist_OCons(U_19488),U_19489),U_19490)),U_19491)) ) ),
    inference(variable_rename,[status(thm)],[f_4720_1]) ).

fof(f_4720_3,plain,
    ( ! [U_19499,U_19497,U_19495,U_19493] :
        ( hBOOL(hAPP(hAPP(c_List_Omember(U_19493),hAPP(hAPP(c_List_Olist_OCons(U_19493),U_19495),U_19497)),U_19499))
        | ( ~ hBOOL(hAPP(hAPP(c_List_Omember(U_19493),U_19497),U_19499))
          & U_19495 != U_19499 ) )
    & ! [U_19498,U_19496,U_19494,U_19492] :
        ( hBOOL(hAPP(hAPP(c_List_Omember(U_19492),U_19496),U_19498))
        | U_19494 = U_19498
        | ~ hBOOL(hAPP(hAPP(c_List_Omember(U_19492),hAPP(hAPP(c_List_Olist_OCons(U_19492),U_19494),U_19496)),U_19498)) ) ),
    inference(miniscope,[status(thm)],[f_4720_2]) ).

cnf(f_4720_4,plain,
    ( hBOOL(hAPP(hAPP(c_List_Omember(U_19492),U_19496),U_19498))
    | U_19494 = U_19498
    | ~ hBOOL(hAPP(hAPP(c_List_Omember(U_19492),hAPP(hAPP(c_List_Olist_OCons(U_19492),U_19494),U_19496)),U_19498)) ),
    inference(clausify,[status(thm)],[f_4720_3]) ).

cnf(f_4720_5,plain,
    ( U_19495 != U_19499
    | hBOOL(hAPP(hAPP(c_List_Omember(U_19493),hAPP(hAPP(c_List_Olist_OCons(U_19493),U_19495),U_19497)),U_19499)) ),
    inference(clausify,[status(thm)],[f_4720_3]) ).

cnf(f_4720_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_List_Omember(U_19493),U_19497),U_19499))
    | hBOOL(hAPP(hAPP(c_List_Omember(U_19493),hAPP(hAPP(c_List_Olist_OCons(U_19493),U_19495),U_19497)),U_19499)) ),
    inference(clausify,[status(thm)],[f_4720_3]) ).

fof(f_4721_1,plain,
    ! [V_x_2,V_xs_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_List_Omember(T_b),V_xs_2),V_x_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) )
      & ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
        | ~ hBOOL(hAPP(hAPP(c_List_Omember(T_b),V_xs_2),V_x_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_List_Omember__def]) ).

fof(f_4721_2,plain,
    ! [U_19502,U_19501,U_19500] :
      ( ( hBOOL(hAPP(hAPP(c_List_Omember(U_19500),U_19501),U_19502))
        | ~ hBOOL(hAPP(hAPP(c_member(U_19500),U_19502),hAPP(c_List_Oset(U_19500),U_19501))) )
      & ( hBOOL(hAPP(hAPP(c_member(U_19500),U_19502),hAPP(c_List_Oset(U_19500),U_19501)))
        | ~ hBOOL(hAPP(hAPP(c_List_Omember(U_19500),U_19501),U_19502)) ) ),
    inference(variable_rename,[status(thm)],[f_4721_1]) ).

fof(f_4721_3,plain,
    ( ! [U_19508,U_19506,U_19504] :
        ( hBOOL(hAPP(hAPP(c_List_Omember(U_19504),U_19506),U_19508))
        | ~ hBOOL(hAPP(hAPP(c_member(U_19504),U_19508),hAPP(c_List_Oset(U_19504),U_19506))) )
    & ! [U_19507,U_19505,U_19503] :
        ( hBOOL(hAPP(hAPP(c_member(U_19503),U_19507),hAPP(c_List_Oset(U_19503),U_19505)))
        | ~ hBOOL(hAPP(hAPP(c_List_Omember(U_19503),U_19505),U_19507)) ) ),
    inference(miniscope,[status(thm)],[f_4721_2]) ).

cnf(f_4721_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19503),U_19507),hAPP(c_List_Oset(U_19503),U_19505)))
    | ~ hBOOL(hAPP(hAPP(c_List_Omember(U_19503),U_19505),U_19507)) ),
    inference(clausify,[status(thm)],[f_4721_3]) ).

cnf(f_4721_5,plain,
    ( hBOOL(hAPP(hAPP(c_List_Omember(U_19504),U_19506),U_19508))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19504),U_19508),hAPP(c_List_Oset(U_19504),U_19506))) ),
    inference(clausify,[status(thm)],[f_4721_3]) ).

fof(f_4722_1,plain,
    ! [V_xs_2,V_P_2,T_b] :
      ( ( c_List_Olist__ex1(T_b,V_P_2,V_xs_2)
        | ! [B_x] :
            ( ? [B_y] :
                ( B_y != B_x
                & hBOOL(hAPP(V_P_2,B_y))
                & hBOOL(hAPP(hAPP(c_member(T_b),B_y),hAPP(c_List_Oset(T_b),V_xs_2))) )
            | ~ hBOOL(hAPP(V_P_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) ) )
      & ( ? [B_x] :
            ( ! [B_y] :
                ( B_y = B_x
                | ~ hBOOL(hAPP(V_P_2,B_y))
                | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_y),hAPP(c_List_Oset(T_b),V_xs_2))) )
            & hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) )
        | ~ c_List_Olist__ex1(T_b,V_P_2,V_xs_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__ex1__iff__raw]) ).

fof(f_4722_2,plain,
    ! [U_19515,U_19514,U_19513] :
      ( ( c_List_Olist__ex1(U_19513,U_19514,U_19515)
        | ! [U_19512] :
            ( ? [U_19511] :
                ( U_19511 != U_19512
                & hBOOL(hAPP(U_19514,U_19511))
                & hBOOL(hAPP(hAPP(c_member(U_19513),U_19511),hAPP(c_List_Oset(U_19513),U_19515))) )
            | ~ hBOOL(hAPP(U_19514,U_19512))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19513),U_19512),hAPP(c_List_Oset(U_19513),U_19515))) ) )
      & ( ? [U_19510] :
            ( ! [U_19509] :
                ( U_19509 = U_19510
                | ~ hBOOL(hAPP(U_19514,U_19509))
                | ~ hBOOL(hAPP(hAPP(c_member(U_19513),U_19509),hAPP(c_List_Oset(U_19513),U_19515))) )
            & hBOOL(hAPP(U_19514,U_19510))
            & hBOOL(hAPP(hAPP(c_member(U_19513),U_19510),hAPP(c_List_Oset(U_19513),U_19515))) )
        | ~ c_List_Olist__ex1(U_19513,U_19514,U_19515) ) ),
    inference(variable_rename,[status(thm)],[f_4722_1]) ).

fof(f_4722_3,plain,
    ( ! [U_19521,U_19519,U_19517] :
        ( c_List_Olist__ex1(U_19517,U_19519,U_19521)
        | ! [U_19512] :
            ( ? [U_19511] :
                ( U_19511 != U_19512
                & hBOOL(hAPP(U_19519,U_19511))
                & hBOOL(hAPP(hAPP(c_member(U_19517),U_19511),hAPP(c_List_Oset(U_19517),U_19521))) )
            | ~ hBOOL(hAPP(U_19519,U_19512))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19517),U_19512),hAPP(c_List_Oset(U_19517),U_19521))) ) )
    & ! [U_19520,U_19518,U_19516] :
        ( ? [U_19510] :
            ( ! [U_19509] :
                ( U_19509 = U_19510
                | ~ hBOOL(hAPP(U_19518,U_19509))
                | ~ hBOOL(hAPP(hAPP(c_member(U_19516),U_19509),hAPP(c_List_Oset(U_19516),U_19520))) )
            & hBOOL(hAPP(U_19518,U_19510))
            & hBOOL(hAPP(hAPP(c_member(U_19516),U_19510),hAPP(c_List_Oset(U_19516),U_19520))) )
        | ~ c_List_Olist__ex1(U_19516,U_19518,U_19520) ) ),
    inference(miniscope,[status(thm)],[f_4722_2]) ).

fof(f_4722_4,plain,
    ( ! [U_19521,U_19519,U_19517] :
        ( c_List_Olist__ex1(U_19517,U_19519,U_19521)
        | ! [U_19512] :
            ( ? [U_19511] :
                ( U_19511 != U_19512
                & hBOOL(hAPP(U_19519,U_19511))
                & hBOOL(hAPP(hAPP(c_member(U_19517),U_19511),hAPP(c_List_Oset(U_19517),U_19521))) )
            | ~ hBOOL(hAPP(U_19519,U_19512))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19517),U_19512),hAPP(c_List_Oset(U_19517),U_19521))) ) )
    & ! [U_19520,U_19518,U_19516] :
        ( ( ! [U_19509] :
              ( U_19509 = sK507(U_19520,U_19518,U_19516)
              | ~ hBOOL(hAPP(U_19518,U_19509))
              | ~ hBOOL(hAPP(hAPP(c_member(U_19516),U_19509),hAPP(c_List_Oset(U_19516),U_19520))) )
          & hBOOL(hAPP(U_19518,sK507(U_19520,U_19518,U_19516)))
          & hBOOL(hAPP(hAPP(c_member(U_19516),sK507(U_19520,U_19518,U_19516)),hAPP(c_List_Oset(U_19516),U_19520))) )
        | ~ c_List_Olist__ex1(U_19516,U_19518,U_19520) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK507]),skolemize(U_19510,sK507(U_19520,U_19518,U_19516))],[f_4722_3]) ).

fof(f_4722_5,plain,
    ( ! [U_19521,U_19519,U_19517] :
        ( c_List_Olist__ex1(U_19517,U_19519,U_19521)
        | ! [U_19512] :
            ( ( sK508(U_19521,U_19519,U_19517,U_19512) != U_19512
              & hBOOL(hAPP(U_19519,sK508(U_19521,U_19519,U_19517,U_19512)))
              & hBOOL(hAPP(hAPP(c_member(U_19517),sK508(U_19521,U_19519,U_19517,U_19512)),hAPP(c_List_Oset(U_19517),U_19521))) )
            | ~ hBOOL(hAPP(U_19519,U_19512))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19517),U_19512),hAPP(c_List_Oset(U_19517),U_19521))) ) )
    & ! [U_19520,U_19518,U_19516] :
        ( ( ! [U_19509] :
              ( U_19509 = sK507(U_19520,U_19518,U_19516)
              | ~ hBOOL(hAPP(U_19518,U_19509))
              | ~ hBOOL(hAPP(hAPP(c_member(U_19516),U_19509),hAPP(c_List_Oset(U_19516),U_19520))) )
          & hBOOL(hAPP(U_19518,sK507(U_19520,U_19518,U_19516)))
          & hBOOL(hAPP(hAPP(c_member(U_19516),sK507(U_19520,U_19518,U_19516)),hAPP(c_List_Oset(U_19516),U_19520))) )
        | ~ c_List_Olist__ex1(U_19516,U_19518,U_19520) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK508]),skolemize(U_19511,sK508(U_19521,U_19519,U_19517,U_19512))],[f_4722_4]) ).

cnf(f_4722_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19516),sK507(U_19520,U_19518,U_19516)),hAPP(c_List_Oset(U_19516),U_19520)))
    | ~ c_List_Olist__ex1(U_19516,U_19518,U_19520) ),
    inference(clausify,[status(thm)],[f_4722_5]) ).

cnf(f_4722_7,plain,
    ( hBOOL(hAPP(U_19518,sK507(U_19520,U_19518,U_19516)))
    | ~ c_List_Olist__ex1(U_19516,U_19518,U_19520) ),
    inference(clausify,[status(thm)],[f_4722_5]) ).

cnf(f_4722_8,plain,
    ( U_19509 = sK507(U_19520,U_19518,U_19516)
    | ~ hBOOL(hAPP(U_19518,U_19509))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19516),U_19509),hAPP(c_List_Oset(U_19516),U_19520)))
    | ~ c_List_Olist__ex1(U_19516,U_19518,U_19520) ),
    inference(clausify,[status(thm)],[f_4722_5]) ).

cnf(f_4722_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19517),sK508(U_19521,U_19519,U_19517,U_19512)),hAPP(c_List_Oset(U_19517),U_19521)))
    | ~ hBOOL(hAPP(U_19519,U_19512))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19517),U_19512),hAPP(c_List_Oset(U_19517),U_19521)))
    | c_List_Olist__ex1(U_19517,U_19519,U_19521) ),
    inference(clausify,[status(thm)],[f_4722_5]) ).

cnf(f_4722_10,plain,
    ( hBOOL(hAPP(U_19519,sK508(U_19521,U_19519,U_19517,U_19512)))
    | ~ hBOOL(hAPP(U_19519,U_19512))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19517),U_19512),hAPP(c_List_Oset(U_19517),U_19521)))
    | c_List_Olist__ex1(U_19517,U_19519,U_19521) ),
    inference(clausify,[status(thm)],[f_4722_5]) ).

cnf(f_4722_11,plain,
    ( sK508(U_19521,U_19519,U_19517,U_19512) != U_19512
    | ~ hBOOL(hAPP(U_19519,U_19512))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19517),U_19512),hAPP(c_List_Oset(U_19517),U_19521)))
    | c_List_Olist__ex1(U_19517,U_19519,U_19521) ),
    inference(clausify,[status(thm)],[f_4722_5]) ).

fof(f_4723_1,plain,
    ! [V_f_2,V_S_2,T_b,T_c] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2)),V_S_2)
      | ? [B_T1] :
          ( ? [B_T2] :
              ( ? [B_x] :
                  ( hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_c)
                  & hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_T2))
                  & hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_T1)) )
              & B_T1 != B_T2
              & hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_T2),V_S_2)) )
          & hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_T1),V_S_2)) )
      | ? [B_x] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_x))
          & hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_S_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_S_2))
      | ~ class_Groups_Ocomm__monoid__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setsum__UNION__zero]) ).

fof(f_4723_2,plain,
    ! [U_19529,U_19528,U_19527,U_19526] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_19527,U_19526),U_19529),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_19527,tc_HOL_Obool),U_19528)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(U_19527,tc_HOL_Obool),U_19526),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_19527,U_19526),U_19529)),U_19528)
      | ? [U_19525] :
          ( ? [U_19524] :
              ( ? [U_19523] :
                  ( hAPP(U_19529,U_19523) != c_Groups_Ozero__class_Ozero(U_19526)
                  & hBOOL(hAPP(hAPP(c_member(U_19527),U_19523),U_19524))
                  & hBOOL(hAPP(hAPP(c_member(U_19527),U_19523),U_19525)) )
              & U_19525 != U_19524
              & hBOOL(hAPP(hAPP(c_member(tc_fun(U_19527,tc_HOL_Obool)),U_19524),U_19528)) )
          & hBOOL(hAPP(hAPP(c_member(tc_fun(U_19527,tc_HOL_Obool)),U_19525),U_19528)) )
      | ? [U_19522] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19527),U_19522))
          & hBOOL(hAPP(hAPP(c_member(tc_fun(U_19527,tc_HOL_Obool)),U_19522),U_19528)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_19527,tc_HOL_Obool)),U_19528))
      | ~ class_Groups_Ocomm__monoid__add(U_19526) ),
    inference(variable_rename,[status(thm)],[f_4723_1]) ).

fof(f_4723_3,plain,
    ! [U_19529,U_19528,U_19527,U_19526] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_19527,U_19526),U_19529),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_19527,tc_HOL_Obool),U_19528)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(U_19527,tc_HOL_Obool),U_19526),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_19527,U_19526),U_19529)),U_19528)
      | ? [U_19525] :
          ( ? [U_19524] :
              ( ? [U_19523] :
                  ( hAPP(U_19529,U_19523) != c_Groups_Ozero__class_Ozero(U_19526)
                  & hBOOL(hAPP(hAPP(c_member(U_19527),U_19523),U_19524))
                  & hBOOL(hAPP(hAPP(c_member(U_19527),U_19523),U_19525)) )
              & U_19525 != U_19524
              & hBOOL(hAPP(hAPP(c_member(tc_fun(U_19527,tc_HOL_Obool)),U_19524),U_19528)) )
          & hBOOL(hAPP(hAPP(c_member(tc_fun(U_19527,tc_HOL_Obool)),U_19525),U_19528)) )
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19527),sK509(U_19529,U_19528,U_19527,U_19526)))
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_19527,tc_HOL_Obool)),sK509(U_19529,U_19528,U_19527,U_19526)),U_19528)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_19527,tc_HOL_Obool)),U_19528))
      | ~ class_Groups_Ocomm__monoid__add(U_19526) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK509]),skolemize(U_19522,sK509(U_19529,U_19528,U_19527,U_19526))],[f_4723_2]) ).

fof(f_4723_4,plain,
    ! [U_19529,U_19528,U_19527,U_19526] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_19527,U_19526),U_19529),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_19527,tc_HOL_Obool),U_19528)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(U_19527,tc_HOL_Obool),U_19526),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_19527,U_19526),U_19529)),U_19528)
      | ( ? [U_19524] :
            ( ? [U_19523] :
                ( hAPP(U_19529,U_19523) != c_Groups_Ozero__class_Ozero(U_19526)
                & hBOOL(hAPP(hAPP(c_member(U_19527),U_19523),U_19524))
                & hBOOL(hAPP(hAPP(c_member(U_19527),U_19523),sK510(U_19529,U_19528,U_19527,U_19526))) )
            & sK510(U_19529,U_19528,U_19527,U_19526) != U_19524
            & hBOOL(hAPP(hAPP(c_member(tc_fun(U_19527,tc_HOL_Obool)),U_19524),U_19528)) )
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_19527,tc_HOL_Obool)),sK510(U_19529,U_19528,U_19527,U_19526)),U_19528)) )
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19527),sK509(U_19529,U_19528,U_19527,U_19526)))
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_19527,tc_HOL_Obool)),sK509(U_19529,U_19528,U_19527,U_19526)),U_19528)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_19527,tc_HOL_Obool)),U_19528))
      | ~ class_Groups_Ocomm__monoid__add(U_19526) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK510]),skolemize(U_19525,sK510(U_19529,U_19528,U_19527,U_19526))],[f_4723_3]) ).

fof(f_4723_5,plain,
    ! [U_19529,U_19528,U_19527,U_19526] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_19527,U_19526),U_19529),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_19527,tc_HOL_Obool),U_19528)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(U_19527,tc_HOL_Obool),U_19526),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_19527,U_19526),U_19529)),U_19528)
      | ( ? [U_19523] :
            ( hAPP(U_19529,U_19523) != c_Groups_Ozero__class_Ozero(U_19526)
            & hBOOL(hAPP(hAPP(c_member(U_19527),U_19523),sK511(U_19529,U_19528,U_19527,U_19526)))
            & hBOOL(hAPP(hAPP(c_member(U_19527),U_19523),sK510(U_19529,U_19528,U_19527,U_19526))) )
        & sK510(U_19529,U_19528,U_19527,U_19526) != sK511(U_19529,U_19528,U_19527,U_19526)
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_19527,tc_HOL_Obool)),sK511(U_19529,U_19528,U_19527,U_19526)),U_19528))
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_19527,tc_HOL_Obool)),sK510(U_19529,U_19528,U_19527,U_19526)),U_19528)) )
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19527),sK509(U_19529,U_19528,U_19527,U_19526)))
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_19527,tc_HOL_Obool)),sK509(U_19529,U_19528,U_19527,U_19526)),U_19528)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_19527,tc_HOL_Obool)),U_19528))
      | ~ class_Groups_Ocomm__monoid__add(U_19526) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK511]),skolemize(U_19524,sK511(U_19529,U_19528,U_19527,U_19526))],[f_4723_4]) ).

fof(f_4723_6,plain,
    ! [U_19529,U_19528,U_19527,U_19526] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_19527,U_19526),U_19529),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_19527,tc_HOL_Obool),U_19528)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(U_19527,tc_HOL_Obool),U_19526),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_19527,U_19526),U_19529)),U_19528)
      | ( hAPP(U_19529,sK512(U_19529,U_19528,U_19527,U_19526)) != c_Groups_Ozero__class_Ozero(U_19526)
        & hBOOL(hAPP(hAPP(c_member(U_19527),sK512(U_19529,U_19528,U_19527,U_19526)),sK511(U_19529,U_19528,U_19527,U_19526)))
        & hBOOL(hAPP(hAPP(c_member(U_19527),sK512(U_19529,U_19528,U_19527,U_19526)),sK510(U_19529,U_19528,U_19527,U_19526)))
        & sK510(U_19529,U_19528,U_19527,U_19526) != sK511(U_19529,U_19528,U_19527,U_19526)
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_19527,tc_HOL_Obool)),sK511(U_19529,U_19528,U_19527,U_19526)),U_19528))
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_19527,tc_HOL_Obool)),sK510(U_19529,U_19528,U_19527,U_19526)),U_19528)) )
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19527),sK509(U_19529,U_19528,U_19527,U_19526)))
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_19527,tc_HOL_Obool)),sK509(U_19529,U_19528,U_19527,U_19526)),U_19528)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_19527,tc_HOL_Obool)),U_19528))
      | ~ class_Groups_Ocomm__monoid__add(U_19526) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK512]),skolemize(U_19523,sK512(U_19529,U_19528,U_19527,U_19526))],[f_4723_5]) ).

cnf(f_4723_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_19527,tc_HOL_Obool)),sK510(U_19529,U_19528,U_19527,U_19526)),U_19528))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_19527,U_19526),U_19529),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_19527,tc_HOL_Obool),U_19528)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(U_19527,tc_HOL_Obool),U_19526),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_19527,U_19526),U_19529)),U_19528)
    | hBOOL(hAPP(hAPP(c_member(tc_fun(U_19527,tc_HOL_Obool)),sK509(U_19529,U_19528,U_19527,U_19526)),U_19528))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_19527,tc_HOL_Obool)),U_19528))
    | ~ class_Groups_Ocomm__monoid__add(U_19526) ),
    inference(clausify,[status(thm)],[f_4723_6]) ).

cnf(f_4723_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_19527,tc_HOL_Obool)),sK511(U_19529,U_19528,U_19527,U_19526)),U_19528))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_19527,U_19526),U_19529),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_19527,tc_HOL_Obool),U_19528)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(U_19527,tc_HOL_Obool),U_19526),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_19527,U_19526),U_19529)),U_19528)
    | hBOOL(hAPP(hAPP(c_member(tc_fun(U_19527,tc_HOL_Obool)),sK509(U_19529,U_19528,U_19527,U_19526)),U_19528))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_19527,tc_HOL_Obool)),U_19528))
    | ~ class_Groups_Ocomm__monoid__add(U_19526) ),
    inference(clausify,[status(thm)],[f_4723_6]) ).

cnf(f_4723_9,plain,
    ( sK510(U_19529,U_19528,U_19527,U_19526) != sK511(U_19529,U_19528,U_19527,U_19526)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_19527,U_19526),U_19529),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_19527,tc_HOL_Obool),U_19528)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(U_19527,tc_HOL_Obool),U_19526),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_19527,U_19526),U_19529)),U_19528)
    | hBOOL(hAPP(hAPP(c_member(tc_fun(U_19527,tc_HOL_Obool)),sK509(U_19529,U_19528,U_19527,U_19526)),U_19528))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_19527,tc_HOL_Obool)),U_19528))
    | ~ class_Groups_Ocomm__monoid__add(U_19526) ),
    inference(clausify,[status(thm)],[f_4723_6]) ).

cnf(f_4723_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19527),sK512(U_19529,U_19528,U_19527,U_19526)),sK510(U_19529,U_19528,U_19527,U_19526)))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_19527,U_19526),U_19529),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_19527,tc_HOL_Obool),U_19528)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(U_19527,tc_HOL_Obool),U_19526),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_19527,U_19526),U_19529)),U_19528)
    | hBOOL(hAPP(hAPP(c_member(tc_fun(U_19527,tc_HOL_Obool)),sK509(U_19529,U_19528,U_19527,U_19526)),U_19528))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_19527,tc_HOL_Obool)),U_19528))
    | ~ class_Groups_Ocomm__monoid__add(U_19526) ),
    inference(clausify,[status(thm)],[f_4723_6]) ).

cnf(f_4723_11,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19527),sK512(U_19529,U_19528,U_19527,U_19526)),sK511(U_19529,U_19528,U_19527,U_19526)))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_19527,U_19526),U_19529),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_19527,tc_HOL_Obool),U_19528)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(U_19527,tc_HOL_Obool),U_19526),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_19527,U_19526),U_19529)),U_19528)
    | hBOOL(hAPP(hAPP(c_member(tc_fun(U_19527,tc_HOL_Obool)),sK509(U_19529,U_19528,U_19527,U_19526)),U_19528))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_19527,tc_HOL_Obool)),U_19528))
    | ~ class_Groups_Ocomm__monoid__add(U_19526) ),
    inference(clausify,[status(thm)],[f_4723_6]) ).

cnf(f_4723_12,plain,
    ( hAPP(U_19529,sK512(U_19529,U_19528,U_19527,U_19526)) != c_Groups_Ozero__class_Ozero(U_19526)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_19527,U_19526),U_19529),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_19527,tc_HOL_Obool),U_19528)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(U_19527,tc_HOL_Obool),U_19526),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_19527,U_19526),U_19529)),U_19528)
    | hBOOL(hAPP(hAPP(c_member(tc_fun(U_19527,tc_HOL_Obool)),sK509(U_19529,U_19528,U_19527,U_19526)),U_19528))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_19527,tc_HOL_Obool)),U_19528))
    | ~ class_Groups_Ocomm__monoid__add(U_19526) ),
    inference(clausify,[status(thm)],[f_4723_6]) ).

cnf(f_4723_13,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_19527,tc_HOL_Obool)),sK510(U_19529,U_19528,U_19527,U_19526)),U_19528))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_19527,U_19526),U_19529),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_19527,tc_HOL_Obool),U_19528)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(U_19527,tc_HOL_Obool),U_19526),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_19527,U_19526),U_19529)),U_19528)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19527),sK509(U_19529,U_19528,U_19527,U_19526)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_19527,tc_HOL_Obool)),U_19528))
    | ~ class_Groups_Ocomm__monoid__add(U_19526) ),
    inference(clausify,[status(thm)],[f_4723_6]) ).

cnf(f_4723_14,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_19527,tc_HOL_Obool)),sK511(U_19529,U_19528,U_19527,U_19526)),U_19528))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_19527,U_19526),U_19529),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_19527,tc_HOL_Obool),U_19528)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(U_19527,tc_HOL_Obool),U_19526),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_19527,U_19526),U_19529)),U_19528)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19527),sK509(U_19529,U_19528,U_19527,U_19526)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_19527,tc_HOL_Obool)),U_19528))
    | ~ class_Groups_Ocomm__monoid__add(U_19526) ),
    inference(clausify,[status(thm)],[f_4723_6]) ).

cnf(f_4723_15,plain,
    ( sK510(U_19529,U_19528,U_19527,U_19526) != sK511(U_19529,U_19528,U_19527,U_19526)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_19527,U_19526),U_19529),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_19527,tc_HOL_Obool),U_19528)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(U_19527,tc_HOL_Obool),U_19526),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_19527,U_19526),U_19529)),U_19528)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19527),sK509(U_19529,U_19528,U_19527,U_19526)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_19527,tc_HOL_Obool)),U_19528))
    | ~ class_Groups_Ocomm__monoid__add(U_19526) ),
    inference(clausify,[status(thm)],[f_4723_6]) ).

cnf(f_4723_16,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19527),sK512(U_19529,U_19528,U_19527,U_19526)),sK510(U_19529,U_19528,U_19527,U_19526)))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_19527,U_19526),U_19529),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_19527,tc_HOL_Obool),U_19528)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(U_19527,tc_HOL_Obool),U_19526),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_19527,U_19526),U_19529)),U_19528)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19527),sK509(U_19529,U_19528,U_19527,U_19526)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_19527,tc_HOL_Obool)),U_19528))
    | ~ class_Groups_Ocomm__monoid__add(U_19526) ),
    inference(clausify,[status(thm)],[f_4723_6]) ).

cnf(f_4723_17,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19527),sK512(U_19529,U_19528,U_19527,U_19526)),sK511(U_19529,U_19528,U_19527,U_19526)))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_19527,U_19526),U_19529),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_19527,tc_HOL_Obool),U_19528)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(U_19527,tc_HOL_Obool),U_19526),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_19527,U_19526),U_19529)),U_19528)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19527),sK509(U_19529,U_19528,U_19527,U_19526)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_19527,tc_HOL_Obool)),U_19528))
    | ~ class_Groups_Ocomm__monoid__add(U_19526) ),
    inference(clausify,[status(thm)],[f_4723_6]) ).

cnf(f_4723_18,plain,
    ( hAPP(U_19529,sK512(U_19529,U_19528,U_19527,U_19526)) != c_Groups_Ozero__class_Ozero(U_19526)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_19527,U_19526),U_19529),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_19527,tc_HOL_Obool),U_19528)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(U_19527,tc_HOL_Obool),U_19526),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_19527,U_19526),U_19529)),U_19528)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19527),sK509(U_19529,U_19528,U_19527,U_19526)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_19527,tc_HOL_Obool)),U_19528))
    | ~ class_Groups_Ocomm__monoid__add(U_19526) ),
    inference(clausify,[status(thm)],[f_4723_6]) ).

fof(f_4724_1,plain,
    ! [V_d_2,T_b,V_P_2] :
      ( ( c_FunDef_OTHE__default(T_b,V_d_2,V_P_2) = V_d_2
        | ? [B_x] :
            ( ! [B_y] :
                ( B_y = B_x
                | ~ hBOOL(hAPP(V_P_2,B_y)) )
            & hBOOL(hAPP(V_P_2,B_x)) ) )
      & ( c_FunDef_OTHE__default(T_b,V_d_2,V_P_2) = c_HOL_OThe(T_b,V_P_2)
        | ! [B_x] :
            ( ? [B_y] :
                ( B_y != B_x
                & hBOOL(hAPP(V_P_2,B_y)) )
            | ~ hBOOL(hAPP(V_P_2,B_x)) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_THE__default__def]) ).

fof(f_4724_2,plain,
    ! [U_19536,U_19535,U_19534] :
      ( ( c_FunDef_OTHE__default(U_19535,U_19536,U_19534) = U_19536
        | ? [U_19533] :
            ( ! [U_19532] :
                ( U_19532 = U_19533
                | ~ hBOOL(hAPP(U_19534,U_19532)) )
            & hBOOL(hAPP(U_19534,U_19533)) ) )
      & ( c_FunDef_OTHE__default(U_19535,U_19536,U_19534) = c_HOL_OThe(U_19535,U_19534)
        | ! [U_19531] :
            ( ? [U_19530] :
                ( U_19530 != U_19531
                & hBOOL(hAPP(U_19534,U_19530)) )
            | ~ hBOOL(hAPP(U_19534,U_19531)) ) ) ),
    inference(variable_rename,[status(thm)],[f_4724_1]) ).

fof(f_4724_3,plain,
    ( ! [U_19542,U_19540,U_19538] :
        ( c_FunDef_OTHE__default(U_19540,U_19542,U_19538) = U_19542
        | ? [U_19533] :
            ( ! [U_19532] :
                ( U_19532 = U_19533
                | ~ hBOOL(hAPP(U_19538,U_19532)) )
            & hBOOL(hAPP(U_19538,U_19533)) ) )
    & ! [U_19541,U_19539,U_19537] :
        ( c_FunDef_OTHE__default(U_19539,U_19541,U_19537) = c_HOL_OThe(U_19539,U_19537)
        | ! [U_19531] :
            ( ? [U_19530] :
                ( U_19530 != U_19531
                & hBOOL(hAPP(U_19537,U_19530)) )
            | ~ hBOOL(hAPP(U_19537,U_19531)) ) ) ),
    inference(miniscope,[status(thm)],[f_4724_2]) ).

fof(f_4724_4,plain,
    ( ! [U_19542,U_19540,U_19538] :
        ( c_FunDef_OTHE__default(U_19540,U_19542,U_19538) = U_19542
        | ? [U_19533] :
            ( ! [U_19532] :
                ( U_19532 = U_19533
                | ~ hBOOL(hAPP(U_19538,U_19532)) )
            & hBOOL(hAPP(U_19538,U_19533)) ) )
    & ! [U_19541,U_19539,U_19537] :
        ( c_FunDef_OTHE__default(U_19539,U_19541,U_19537) = c_HOL_OThe(U_19539,U_19537)
        | ! [U_19531] :
            ( ( sK513(U_19541,U_19539,U_19537,U_19531) != U_19531
              & hBOOL(hAPP(U_19537,sK513(U_19541,U_19539,U_19537,U_19531))) )
            | ~ hBOOL(hAPP(U_19537,U_19531)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK513]),skolemize(U_19530,sK513(U_19541,U_19539,U_19537,U_19531))],[f_4724_3]) ).

fof(f_4724_5,plain,
    ( ! [U_19542,U_19540,U_19538] :
        ( c_FunDef_OTHE__default(U_19540,U_19542,U_19538) = U_19542
        | ( ! [U_19532] :
              ( U_19532 = sK514(U_19542,U_19540,U_19538)
              | ~ hBOOL(hAPP(U_19538,U_19532)) )
          & hBOOL(hAPP(U_19538,sK514(U_19542,U_19540,U_19538))) ) )
    & ! [U_19541,U_19539,U_19537] :
        ( c_FunDef_OTHE__default(U_19539,U_19541,U_19537) = c_HOL_OThe(U_19539,U_19537)
        | ! [U_19531] :
            ( ( sK513(U_19541,U_19539,U_19537,U_19531) != U_19531
              & hBOOL(hAPP(U_19537,sK513(U_19541,U_19539,U_19537,U_19531))) )
            | ~ hBOOL(hAPP(U_19537,U_19531)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK514]),skolemize(U_19533,sK514(U_19542,U_19540,U_19538))],[f_4724_4]) ).

cnf(f_4724_6,plain,
    ( hBOOL(hAPP(U_19537,sK513(U_19541,U_19539,U_19537,U_19531)))
    | ~ hBOOL(hAPP(U_19537,U_19531))
    | c_FunDef_OTHE__default(U_19539,U_19541,U_19537) = c_HOL_OThe(U_19539,U_19537) ),
    inference(clausify,[status(thm)],[f_4724_5]) ).

cnf(f_4724_7,plain,
    ( sK513(U_19541,U_19539,U_19537,U_19531) != U_19531
    | ~ hBOOL(hAPP(U_19537,U_19531))
    | c_FunDef_OTHE__default(U_19539,U_19541,U_19537) = c_HOL_OThe(U_19539,U_19537) ),
    inference(clausify,[status(thm)],[f_4724_5]) ).

cnf(f_4724_8,plain,
    ( hBOOL(hAPP(U_19538,sK514(U_19542,U_19540,U_19538)))
    | c_FunDef_OTHE__default(U_19540,U_19542,U_19538) = U_19542 ),
    inference(clausify,[status(thm)],[f_4724_5]) ).

cnf(f_4724_9,plain,
    ( U_19532 = sK514(U_19542,U_19540,U_19538)
    | ~ hBOOL(hAPP(U_19538,U_19532))
    | c_FunDef_OTHE__default(U_19540,U_19542,U_19538) = U_19542 ),
    inference(clausify,[status(thm)],[f_4724_5]) ).

fof(f_4725_1,plain,
    ! [T_d,T_c,V_c_2,V_b_2,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_INF2__I]) ).

fof(f_4725_2,plain,
    ! [U_19550,U_19549,U_19548,U_19547,U_19546,U_19545,U_19544] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_19544,tc_fun(U_19549,tc_fun(U_19550,tc_HOL_Obool))),U_19545),U_19546),U_19547),U_19548))
      | ? [U_19543] :
          ( ~ hBOOL(hAPP(hAPP(hAPP(U_19546,U_19543),U_19547),U_19548))
          & hBOOL(hAPP(hAPP(c_member(U_19544),U_19543),U_19545)) ) ),
    inference(variable_rename,[status(thm)],[f_4725_1]) ).

fof(f_4725_3,plain,
    ! [U_19550,U_19549,U_19548,U_19547,U_19546,U_19545,U_19544] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_19544,tc_fun(U_19549,tc_fun(U_19550,tc_HOL_Obool))),U_19545),U_19546),U_19547),U_19548))
      | ( ~ hBOOL(hAPP(hAPP(hAPP(U_19546,sK515(U_19550,U_19549,U_19548,U_19547,U_19546,U_19545,U_19544)),U_19547),U_19548))
        & hBOOL(hAPP(hAPP(c_member(U_19544),sK515(U_19550,U_19549,U_19548,U_19547,U_19546,U_19545,U_19544)),U_19545)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK515]),skolemize(U_19543,sK515(U_19550,U_19549,U_19548,U_19547,U_19546,U_19545,U_19544))],[f_4725_2]) ).

cnf(f_4725_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19544),sK515(U_19550,U_19549,U_19548,U_19547,U_19546,U_19545,U_19544)),U_19545))
    | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_19544,tc_fun(U_19549,tc_fun(U_19550,tc_HOL_Obool))),U_19545),U_19546),U_19547),U_19548)) ),
    inference(clausify,[status(thm)],[f_4725_3]) ).

cnf(f_4725_5,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(U_19546,sK515(U_19550,U_19549,U_19548,U_19547,U_19546,U_19545,U_19544)),U_19547),U_19548))
    | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_19544,tc_fun(U_19549,tc_fun(U_19550,tc_HOL_Obool))),U_19545),U_19546),U_19547),U_19548)) ),
    inference(clausify,[status(thm)],[f_4725_3]) ).

fof(f_4726_1,plain,
    ! [V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
      ( ? [B_x] :
          ( hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) ),
    inference(fof_nnf,[status(thm)],[fact_SUP2__E]) ).

fof(f_4726_2,plain,
    ! [U_19558,U_19557,U_19556,U_19555,U_19554,U_19553,U_19552] :
      ( ? [U_19551] :
          ( hBOOL(hAPP(hAPP(hAPP(U_19556,U_19551),U_19557),U_19558))
          & hBOOL(hAPP(hAPP(c_member(U_19552),U_19551),U_19555)) )
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_19552,tc_fun(U_19553,tc_fun(U_19554,tc_HOL_Obool))),U_19555),U_19556),U_19557),U_19558)) ),
    inference(variable_rename,[status(thm)],[f_4726_1]) ).

fof(f_4726_3,plain,
    ! [U_19558,U_19557,U_19556,U_19555,U_19554,U_19553,U_19552] :
      ( ( hBOOL(hAPP(hAPP(hAPP(U_19556,sK516(U_19558,U_19557,U_19556,U_19555,U_19554,U_19553,U_19552)),U_19557),U_19558))
        & hBOOL(hAPP(hAPP(c_member(U_19552),sK516(U_19558,U_19557,U_19556,U_19555,U_19554,U_19553,U_19552)),U_19555)) )
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_19552,tc_fun(U_19553,tc_fun(U_19554,tc_HOL_Obool))),U_19555),U_19556),U_19557),U_19558)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK516]),skolemize(U_19551,sK516(U_19558,U_19557,U_19556,U_19555,U_19554,U_19553,U_19552))],[f_4726_2]) ).

cnf(f_4726_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19552),sK516(U_19558,U_19557,U_19556,U_19555,U_19554,U_19553,U_19552)),U_19555))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_19552,tc_fun(U_19553,tc_fun(U_19554,tc_HOL_Obool))),U_19555),U_19556),U_19557),U_19558)) ),
    inference(clausify,[status(thm)],[f_4726_3]) ).

cnf(f_4726_5,plain,
    ( hBOOL(hAPP(hAPP(hAPP(U_19556,sK516(U_19558,U_19557,U_19556,U_19555,U_19554,U_19553,U_19552)),U_19557),U_19558))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_19552,tc_fun(U_19553,tc_fun(U_19554,tc_HOL_Obool))),U_19555),U_19556),U_19557),U_19558)) ),
    inference(clausify,[status(thm)],[f_4726_3]) ).

fof(f_4727_1,plain,
    ! [V_M_2,T_b] :
      ( ? [B_n] :
        ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),B_x)),B_n))
          | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),V_M_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_b)),V_M_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__maxlen]) ).

fof(f_4727_2,plain,
    ! [U_19562,U_19561] :
      ( ? [U_19560] :
        ! [U_19559] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19561)),U_19559)),U_19560))
          | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19561)),U_19559),U_19562)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(U_19561)),U_19562)) ),
    inference(variable_rename,[status(thm)],[f_4727_1]) ).

fof(f_4727_3,plain,
    ! [U_19562,U_19561] :
      ( ! [U_19559] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19561)),U_19559)),sK517(U_19562,U_19561)))
          | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19561)),U_19559),U_19562)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(U_19561)),U_19562)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK517]),skolemize(U_19560,sK517(U_19562,U_19561))],[f_4727_2]) ).

cnf(f_4727_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19561)),U_19559)),sK517(U_19562,U_19561)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19561)),U_19559),U_19562))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(U_19561)),U_19562)) ),
    inference(clausify,[status(thm)],[f_4727_3]) ).

fof(f_4728_1,plain,
    ! [T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_a)),c_Lazy__Sequence_Olazy__sequence_OEmpty(T_a)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_lazy__sequence_Osize_I3_J]) ).

fof(f_4728_2,plain,
    ! [U_19563] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(U_19563)),c_Lazy__Sequence_Olazy__sequence_OEmpty(U_19563)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_4728_1]) ).

cnf(f_4728_3,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(U_19563)),c_Lazy__Sequence_Olazy__sequence_OEmpty(U_19563)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_4728_2]) ).

fof(f_4729_1,plain,
    ! [V_fa_2,T_b] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_b,V_fa_2),c_Lazy__Sequence_Olazy__sequence_OEmpty(T_b)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_lazy__sequence_Osize_I1_J]) ).

fof(f_4729_2,plain,
    ! [U_19565,U_19564] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(U_19564,U_19565),c_Lazy__Sequence_Olazy__sequence_OEmpty(U_19564)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_4729_1]) ).

cnf(f_4729_3,plain,
    hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(U_19564,U_19565),c_Lazy__Sequence_Olazy__sequence_OEmpty(U_19564)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_4729_2]) ).

fof(f_4730_1,plain,
    ! [V_yq,T_a] : c_Lazy__Sequence_Oappend(T_a,c_Lazy__Sequence_Olazy__sequence_OEmpty(T_a),V_yq) = V_yq,
    inference(fof_nnf,[status(thm)],[fact__02]) ).

fof(f_4730_2,plain,
    ! [U_19567,U_19566] : c_Lazy__Sequence_Oappend(U_19566,c_Lazy__Sequence_Olazy__sequence_OEmpty(U_19566),U_19567) = U_19567,
    inference(variable_rename,[status(thm)],[f_4730_1]) ).

cnf(f_4730_3,plain,
    c_Lazy__Sequence_Oappend(U_19566,c_Lazy__Sequence_Olazy__sequence_OEmpty(U_19566),U_19567) = U_19567,
    inference(clausify,[status(thm)],[f_4730_2]) ).

fof(f_4731_1,plain,
    ! [V_lazy__sequence_H,V_a_H,T_a] : c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_a_H,V_lazy__sequence_H) != c_Lazy__Sequence_Olazy__sequence_OEmpty(T_a),
    inference(fof_nnf,[status(thm)],[fact_lazy__sequence_Osimps_I3_J]) ).

fof(f_4731_2,plain,
    ! [U_19570,U_19569,U_19568] : c_Lazy__Sequence_Olazy__sequence_OInsert(U_19568,U_19569,U_19570) != c_Lazy__Sequence_Olazy__sequence_OEmpty(U_19568),
    inference(variable_rename,[status(thm)],[f_4731_1]) ).

cnf(f_4731_3,plain,
    c_Lazy__Sequence_Olazy__sequence_OInsert(U_19568,U_19569,U_19570) != c_Lazy__Sequence_Olazy__sequence_OEmpty(U_19568),
    inference(clausify,[status(thm)],[f_4731_2]) ).

fof(f_4732_1,plain,
    ! [V_lazy__sequence_H,V_a_H,T_a] : c_Lazy__Sequence_Olazy__sequence_OEmpty(T_a) != c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_a_H,V_lazy__sequence_H),
    inference(fof_nnf,[status(thm)],[fact_lazy__sequence_Osimps_I2_J]) ).

fof(f_4732_2,plain,
    ! [U_19573,U_19572,U_19571] : c_Lazy__Sequence_Olazy__sequence_OEmpty(U_19571) != c_Lazy__Sequence_Olazy__sequence_OInsert(U_19571,U_19572,U_19573),
    inference(variable_rename,[status(thm)],[f_4732_1]) ).

cnf(f_4732_3,plain,
    c_Lazy__Sequence_Olazy__sequence_OEmpty(U_19571) != c_Lazy__Sequence_Olazy__sequence_OInsert(U_19571,U_19572,U_19573),
    inference(clausify,[status(thm)],[f_4732_2]) ).

fof(f_4733_1,plain,
    ! [V_f2_2,V_f1_2,T_c,T_b] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(T_b,T_c,V_f1_2,V_f2_2,c_Lazy__Sequence_Olazy__sequence_OEmpty(T_c)) = V_f1_2,
    inference(fof_nnf,[status(thm)],[fact_lazy__sequence_Osimps_I4_J]) ).

fof(f_4733_2,plain,
    ! [U_19577,U_19576,U_19575,U_19574] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(U_19574,U_19575,U_19576,U_19577,c_Lazy__Sequence_Olazy__sequence_OEmpty(U_19575)) = U_19576,
    inference(variable_rename,[status(thm)],[f_4733_1]) ).

cnf(f_4733_3,plain,
    c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(U_19574,U_19575,U_19576,U_19577,c_Lazy__Sequence_Olazy__sequence_OEmpty(U_19575)) = U_19576,
    inference(clausify,[status(thm)],[f_4733_2]) ).

fof(f_4734_1,plain,
    ! [V_j_2,V_i_2,V_P_2] :
      ( ( c_List_Olist__all(tc_Int_Oint,V_P_2,c_List_Oupto(V_i_2,V_j_2))
        | ~ c_List_Oall__interval__int(V_P_2,V_i_2,V_j_2) )
      & ( c_List_Oall__interval__int(V_P_2,V_i_2,V_j_2)
        | ~ c_List_Olist__all(tc_Int_Oint,V_P_2,c_List_Oupto(V_i_2,V_j_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__all__iff__all__interval__int]) ).

fof(f_4734_2,plain,
    ! [U_19580,U_19579,U_19578] :
      ( ( c_List_Olist__all(tc_Int_Oint,U_19578,c_List_Oupto(U_19579,U_19580))
        | ~ c_List_Oall__interval__int(U_19578,U_19579,U_19580) )
      & ( c_List_Oall__interval__int(U_19578,U_19579,U_19580)
        | ~ c_List_Olist__all(tc_Int_Oint,U_19578,c_List_Oupto(U_19579,U_19580)) ) ),
    inference(variable_rename,[status(thm)],[f_4734_1]) ).

fof(f_4734_3,plain,
    ( ! [U_19586,U_19584,U_19582] :
        ( c_List_Olist__all(tc_Int_Oint,U_19582,c_List_Oupto(U_19584,U_19586))
        | ~ c_List_Oall__interval__int(U_19582,U_19584,U_19586) )
    & ! [U_19585,U_19583,U_19581] :
        ( c_List_Oall__interval__int(U_19581,U_19583,U_19585)
        | ~ c_List_Olist__all(tc_Int_Oint,U_19581,c_List_Oupto(U_19583,U_19585)) ) ),
    inference(miniscope,[status(thm)],[f_4734_2]) ).

cnf(f_4734_4,plain,
    ( c_List_Oall__interval__int(U_19581,U_19583,U_19585)
    | ~ c_List_Olist__all(tc_Int_Oint,U_19581,c_List_Oupto(U_19583,U_19585)) ),
    inference(clausify,[status(thm)],[f_4734_3]) ).

cnf(f_4734_5,plain,
    ( c_List_Olist__all(tc_Int_Oint,U_19582,c_List_Oupto(U_19584,U_19586))
    | ~ c_List_Oall__interval__int(U_19582,U_19584,U_19586) ),
    inference(clausify,[status(thm)],[f_4734_3]) ).

fof(f_4735_1,plain,
    ! [V_j_2,V_i_2,V_P_2] :
      ( ( c_List_Olist__ex(tc_Int_Oint,V_P_2,c_List_Oupto(V_i_2,V_j_2))
        | c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint,c_fNot),V_P_2),V_i_2,V_j_2) )
      & ( ~ c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint,c_fNot),V_P_2),V_i_2,V_j_2)
        | ~ c_List_Olist__ex(tc_Int_Oint,V_P_2,c_List_Oupto(V_i_2,V_j_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__ex__iff__not__all__inverval__int]) ).

fof(f_4735_2,plain,
    ! [U_19589,U_19588,U_19587] :
      ( ( c_List_Olist__ex(tc_Int_Oint,U_19587,c_List_Oupto(U_19588,U_19589))
        | c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint,c_fNot),U_19587),U_19588,U_19589) )
      & ( ~ c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint,c_fNot),U_19587),U_19588,U_19589)
        | ~ c_List_Olist__ex(tc_Int_Oint,U_19587,c_List_Oupto(U_19588,U_19589)) ) ),
    inference(variable_rename,[status(thm)],[f_4735_1]) ).

fof(f_4735_3,plain,
    ( ! [U_19595,U_19593,U_19591] :
        ( c_List_Olist__ex(tc_Int_Oint,U_19591,c_List_Oupto(U_19593,U_19595))
        | c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint,c_fNot),U_19591),U_19593,U_19595) )
    & ! [U_19594,U_19592,U_19590] :
        ( ~ c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint,c_fNot),U_19590),U_19592,U_19594)
        | ~ c_List_Olist__ex(tc_Int_Oint,U_19590,c_List_Oupto(U_19592,U_19594)) ) ),
    inference(miniscope,[status(thm)],[f_4735_2]) ).

cnf(f_4735_4,plain,
    ( ~ c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint,c_fNot),U_19590),U_19592,U_19594)
    | ~ c_List_Olist__ex(tc_Int_Oint,U_19590,c_List_Oupto(U_19592,U_19594)) ),
    inference(clausify,[status(thm)],[f_4735_3]) ).

cnf(f_4735_5,plain,
    ( c_List_Olist__ex(tc_Int_Oint,U_19591,c_List_Oupto(U_19593,U_19595))
    | c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint,c_fNot),U_19591),U_19593,U_19595) ),
    inference(clausify,[status(thm)],[f_4735_3]) ).

fof(f_4736_1,plain,
    ! [V_j_2,V_i_2,V_P_2] :
      ( ( c_List_Oall__interval__int(V_P_2,V_i_2,V_j_2)
        | ? [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2))) ) )
      & ( ! [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2))) )
        | ~ c_List_Oall__interval__int(V_P_2,V_i_2,V_j_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_all__interval__int__def]) ).

fof(f_4736_2,plain,
    ! [U_19600,U_19599,U_19598] :
      ( ( c_List_Oall__interval__int(U_19598,U_19599,U_19600)
        | ? [U_19597] :
            ( ~ hBOOL(hAPP(U_19598,U_19597))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_19597),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_19599,U_19600))) ) )
      & ( ! [U_19596] :
            ( hBOOL(hAPP(U_19598,U_19596))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_19596),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_19599,U_19600))) )
        | ~ c_List_Oall__interval__int(U_19598,U_19599,U_19600) ) ),
    inference(variable_rename,[status(thm)],[f_4736_1]) ).

fof(f_4736_3,plain,
    ( ! [U_19606,U_19604,U_19602] :
        ( c_List_Oall__interval__int(U_19602,U_19604,U_19606)
        | ? [U_19597] :
            ( ~ hBOOL(hAPP(U_19602,U_19597))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_19597),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_19604,U_19606))) ) )
    & ! [U_19605,U_19603,U_19601] :
        ( ! [U_19596] :
            ( hBOOL(hAPP(U_19601,U_19596))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_19596),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_19603,U_19605))) )
        | ~ c_List_Oall__interval__int(U_19601,U_19603,U_19605) ) ),
    inference(miniscope,[status(thm)],[f_4736_2]) ).

fof(f_4736_4,plain,
    ( ! [U_19606,U_19604,U_19602] :
        ( c_List_Oall__interval__int(U_19602,U_19604,U_19606)
        | ( ~ hBOOL(hAPP(U_19602,sK518(U_19606,U_19604,U_19602)))
          & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK518(U_19606,U_19604,U_19602)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_19604,U_19606))) ) )
    & ! [U_19605,U_19603,U_19601] :
        ( ! [U_19596] :
            ( hBOOL(hAPP(U_19601,U_19596))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_19596),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_19603,U_19605))) )
        | ~ c_List_Oall__interval__int(U_19601,U_19603,U_19605) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK518]),skolemize(U_19597,sK518(U_19606,U_19604,U_19602))],[f_4736_3]) ).

cnf(f_4736_5,plain,
    ( hBOOL(hAPP(U_19601,U_19596))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_19596),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_19603,U_19605)))
    | ~ c_List_Oall__interval__int(U_19601,U_19603,U_19605) ),
    inference(clausify,[status(thm)],[f_4736_4]) ).

cnf(f_4736_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK518(U_19606,U_19604,U_19602)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_19604,U_19606)))
    | c_List_Oall__interval__int(U_19602,U_19604,U_19606) ),
    inference(clausify,[status(thm)],[f_4736_4]) ).

cnf(f_4736_7,plain,
    ( ~ hBOOL(hAPP(U_19602,sK518(U_19606,U_19604,U_19602)))
    | c_List_Oall__interval__int(U_19602,U_19604,U_19606) ),
    inference(clausify,[status(thm)],[f_4736_4]) ).

fof(f_4737_1,plain,
    ! [V_code__numeral_2,V_f2_2,V_f1_2,T_b] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(T_b,V_f1_2,V_f2_2,c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2)) = hAPP(hAPP(V_f2_2,V_code__numeral_2),c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(T_b,V_f1_2,V_f2_2,V_code__numeral_2)),
    inference(fof_nnf,[status(thm)],[fact_code__numeral_Orecs_I2_J]) ).

fof(f_4737_2,plain,
    ! [U_19610,U_19609,U_19608,U_19607] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(U_19607,U_19608,U_19609,c_Code__Numeral_OSuc__code__numeral(U_19610)) = hAPP(hAPP(U_19609,U_19610),c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(U_19607,U_19608,U_19609,U_19610)),
    inference(variable_rename,[status(thm)],[f_4737_1]) ).

cnf(f_4737_3,plain,
    c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(U_19607,U_19608,U_19609,c_Code__Numeral_OSuc__code__numeral(U_19610)) = hAPP(hAPP(U_19609,U_19610),c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(U_19607,U_19608,U_19609,U_19610)),
    inference(clausify,[status(thm)],[f_4737_2]) ).

fof(f_4738_1,plain,
    ! [V_size_2,V_g_2,T_b,V_nrandom_2] :
      ( ( c_Random__Sequence_ORandom(T_b,V_g_2,V_nrandom_2,V_size_2) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm)),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(V_g_2,V_size_2)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random__Sequence_ORandom(T_b,V_g_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_nrandom_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),V_size_2))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b))))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b))))),c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b))))),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Ounion(T_b)),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Osingle(T_b)),c_Product__Type_Ofst(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm)))))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_nrandom_2),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) )
      & ( c_Random__Sequence_ORandom(T_b,V_g_2,V_nrandom_2,V_size_2) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(T_b))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_nrandom_2),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) ) ),
    inference(fof_nnf,[status(thm)],[fact_Random_Osimps]) ).

fof(f_4738_2,plain,
    ! [U_19614,U_19613,U_19612,U_19611] :
      ( ( c_Random__Sequence_ORandom(U_19612,U_19613,U_19611,U_19614) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(U_19612,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm)),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19612)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(U_19613,U_19614)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19612)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19612)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19612)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_prod(U_19612,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19612)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19612)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random__Sequence_ORandom(U_19612,U_19613,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_19611),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),U_19614))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19612)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19612))))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19612)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19612)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_prod(U_19612,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19612)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19612)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19612))))),c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19612)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19612)))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19612)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19612))))),tc_prod(U_19612,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Ounion(U_19612)),hAPP(hAPP(c_COMBB(U_19612,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19612)))),tc_prod(U_19612,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Osingle(U_19612)),c_Product__Type_Ofst(U_19612,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm)))))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_19611),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) )
      & ( c_Random__Sequence_ORandom(U_19612,U_19613,U_19611,U_19614) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19612)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(U_19612))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_19611),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) ) ),
    inference(variable_rename,[status(thm)],[f_4738_1]) ).

fof(f_4738_3,plain,
    ( ! [U_19622,U_19620,U_19618,U_19616] :
        ( c_Random__Sequence_ORandom(U_19618,U_19620,U_19616,U_19622) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(U_19618,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm)),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19618)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(U_19620,U_19622)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19618)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19618)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19618)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_prod(U_19618,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19618)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19618)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random__Sequence_ORandom(U_19618,U_19620,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_19616),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),U_19622))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19618)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19618))))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19618)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19618)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_prod(U_19618,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19618)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19618)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19618))))),c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19618)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19618)))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19618)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19618))))),tc_prod(U_19618,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Ounion(U_19618)),hAPP(hAPP(c_COMBB(U_19618,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19618)))),tc_prod(U_19618,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Osingle(U_19618)),c_Product__Type_Ofst(U_19618,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm)))))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_19616),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) )
    & ! [U_19621,U_19619,U_19617,U_19615] :
        ( c_Random__Sequence_ORandom(U_19617,U_19619,U_19615,U_19621) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19617)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(U_19617))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_19615),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) ) ),
    inference(miniscope,[status(thm)],[f_4738_2]) ).

cnf(f_4738_4,plain,
    ( c_Random__Sequence_ORandom(U_19617,U_19619,U_19615,U_19621) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19617)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(U_19617))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_19615),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) ),
    inference(clausify,[status(thm)],[f_4738_3]) ).

cnf(f_4738_5,plain,
    ( c_Random__Sequence_ORandom(U_19618,U_19620,U_19616,U_19622) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(U_19618,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm)),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19618)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(U_19620,U_19622)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19618)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19618)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19618)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_prod(U_19618,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19618)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19618)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random__Sequence_ORandom(U_19618,U_19620,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_19616),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),U_19622))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19618)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19618))))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19618)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19618)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_prod(U_19618,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19618)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19618)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19618))))),c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19618)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19618)))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19618)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19618))))),tc_prod(U_19618,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Ounion(U_19618)),hAPP(hAPP(c_COMBB(U_19618,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19618)))),tc_prod(U_19618,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Osingle(U_19618)),c_Product__Type_Ofst(U_19618,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm)))))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_19616),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) ),
    inference(clausify,[status(thm)],[f_4738_3]) ).

fof(f_4739_1,plain,
    ! [V_f2_2,V_f1_2,T_b] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(T_b,V_f1_2,V_f2_2,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = V_f1_2,
    inference(fof_nnf,[status(thm)],[fact_code__numeral_Orecs_I1_J]) ).

fof(f_4739_2,plain,
    ! [U_19625,U_19624,U_19623] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(U_19623,U_19624,U_19625,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = U_19624,
    inference(variable_rename,[status(thm)],[f_4739_1]) ).

cnf(f_4739_3,plain,
    c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(U_19623,U_19624,U_19625,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = U_19624,
    inference(clausify,[status(thm)],[f_4739_2]) ).

fof(f_4740_1,plain,
    ! [V_size_2,V_nrandom_2,T_b] : c_Random__Sequence_Oempty(T_b,V_nrandom_2,V_size_2) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(T_b)),
    inference(fof_nnf,[status(thm)],[fact_Random__Sequence_Oempty__def]) ).

fof(f_4740_2,plain,
    ! [U_19628,U_19627,U_19626] : c_Random__Sequence_Oempty(U_19626,U_19627,U_19628) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19626)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(U_19626)),
    inference(variable_rename,[status(thm)],[f_4740_1]) ).

cnf(f_4740_3,plain,
    c_Random__Sequence_Oempty(U_19626,U_19627,U_19628) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19626)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(U_19626)),
    inference(clausify,[status(thm)],[f_4740_2]) ).

fof(f_4741_1,plain,
    ! [V_size_2,V_nrandom_2,V_x_2,T_b] : hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(T_b),V_x_2),V_nrandom_2),V_size_2) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_DSequence_Osingle(T_b),V_x_2)),
    inference(fof_nnf,[status(thm)],[fact_Random__Sequence_Osingle__def]) ).

fof(f_4741_2,plain,
    ! [U_19632,U_19631,U_19630,U_19629] : hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(U_19629),U_19630),U_19631),U_19632) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19629)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_DSequence_Osingle(U_19629),U_19630)),
    inference(variable_rename,[status(thm)],[f_4741_1]) ).

cnf(f_4741_3,plain,
    hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(U_19629),U_19630),U_19631),U_19632) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19629)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_DSequence_Osingle(U_19629),U_19630)),
    inference(clausify,[status(thm)],[f_4741_2]) ).

fof(f_4742_1,plain,
    ! [V_P_2,V_f_2,T_b,T_c] : c_Random__Sequence_Omap(T_c,T_b,V_f_2,V_P_2) = c_Random__Sequence_Obind(T_c,T_b,V_P_2,hAPP(c_Fun_Ocomp(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))))),T_c,c_Random__Sequence_Osingle(T_b)),V_f_2)),
    inference(fof_nnf,[status(thm)],[fact_Random__Sequence_Omap__def]) ).

fof(f_4742_2,plain,
    ! [U_19636,U_19635,U_19634,U_19633] : c_Random__Sequence_Omap(U_19633,U_19634,U_19635,U_19636) = c_Random__Sequence_Obind(U_19633,U_19634,U_19636,hAPP(c_Fun_Ocomp(U_19634,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19634)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))))),U_19633,c_Random__Sequence_Osingle(U_19634)),U_19635)),
    inference(variable_rename,[status(thm)],[f_4742_1]) ).

cnf(f_4742_3,plain,
    c_Random__Sequence_Omap(U_19633,U_19634,U_19635,U_19636) = c_Random__Sequence_Obind(U_19633,U_19634,U_19636,hAPP(c_Fun_Ocomp(U_19634,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_19634)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))))),U_19633,c_Random__Sequence_Osingle(U_19634)),U_19635)),
    inference(clausify,[status(thm)],[f_4742_2]) ).

fof(f_4743_1,plain,
    ! [T_d,V_f_2,V_Q_2,V_p_2,T_b,T_c,V_P_2] :
      ( hBOOL(hAPP(V_Q_2,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,T_d),V_f_2),V_p_2)))
      | ? [B_x,B_y] :
          ( ~ hBOOL(hAPP(V_Q_2,hAPP(hAPP(V_f_2,B_x),B_y)))
          & hBOOL(hAPP(hAPP(V_P_2,B_y),B_x)) )
      | ~ hBOOL(hAPP(hAPP(V_P_2,hAPP(c_Product__Type_Osnd(T_c,T_b),V_p_2)),hAPP(c_Product__Type_Ofst(T_c,T_b),V_p_2))) ),
    inference(fof_nnf,[status(thm)],[fact_exE__realizer]) ).

fof(f_4743_2,plain,
    ! [U_19645,U_19644,U_19643,U_19642,U_19641,U_19640,U_19639] :
      ( hBOOL(hAPP(U_19643,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_19640,U_19641,U_19645),U_19644),U_19642)))
      | ? [U_19638,U_19637] :
          ( ~ hBOOL(hAPP(U_19643,hAPP(hAPP(U_19644,U_19638),U_19637)))
          & hBOOL(hAPP(hAPP(U_19639,U_19637),U_19638)) )
      | ~ hBOOL(hAPP(hAPP(U_19639,hAPP(c_Product__Type_Osnd(U_19640,U_19641),U_19642)),hAPP(c_Product__Type_Ofst(U_19640,U_19641),U_19642))) ),
    inference(variable_rename,[status(thm)],[f_4743_1]) ).

fof(f_4743_3,plain,
    ! [U_19645,U_19644,U_19643,U_19642,U_19641,U_19640,U_19639] :
      ( hBOOL(hAPP(U_19643,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_19640,U_19641,U_19645),U_19644),U_19642)))
      | ? [U_19637] :
          ( ~ hBOOL(hAPP(U_19643,hAPP(hAPP(U_19644,sK519(U_19645,U_19644,U_19643,U_19642,U_19641,U_19640,U_19639)),U_19637)))
          & hBOOL(hAPP(hAPP(U_19639,U_19637),sK519(U_19645,U_19644,U_19643,U_19642,U_19641,U_19640,U_19639))) )
      | ~ hBOOL(hAPP(hAPP(U_19639,hAPP(c_Product__Type_Osnd(U_19640,U_19641),U_19642)),hAPP(c_Product__Type_Ofst(U_19640,U_19641),U_19642))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK519]),skolemize(U_19638,sK519(U_19645,U_19644,U_19643,U_19642,U_19641,U_19640,U_19639))],[f_4743_2]) ).

fof(f_4743_4,plain,
    ! [U_19645,U_19644,U_19643,U_19642,U_19641,U_19640,U_19639] :
      ( hBOOL(hAPP(U_19643,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_19640,U_19641,U_19645),U_19644),U_19642)))
      | ( ~ hBOOL(hAPP(U_19643,hAPP(hAPP(U_19644,sK519(U_19645,U_19644,U_19643,U_19642,U_19641,U_19640,U_19639)),sK520(U_19645,U_19644,U_19643,U_19642,U_19641,U_19640,U_19639))))
        & hBOOL(hAPP(hAPP(U_19639,sK520(U_19645,U_19644,U_19643,U_19642,U_19641,U_19640,U_19639)),sK519(U_19645,U_19644,U_19643,U_19642,U_19641,U_19640,U_19639))) )
      | ~ hBOOL(hAPP(hAPP(U_19639,hAPP(c_Product__Type_Osnd(U_19640,U_19641),U_19642)),hAPP(c_Product__Type_Ofst(U_19640,U_19641),U_19642))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK520]),skolemize(U_19637,sK520(U_19645,U_19644,U_19643,U_19642,U_19641,U_19640,U_19639))],[f_4743_3]) ).

cnf(f_4743_5,plain,
    ( hBOOL(hAPP(hAPP(U_19639,sK520(U_19645,U_19644,U_19643,U_19642,U_19641,U_19640,U_19639)),sK519(U_19645,U_19644,U_19643,U_19642,U_19641,U_19640,U_19639)))
    | hBOOL(hAPP(U_19643,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_19640,U_19641,U_19645),U_19644),U_19642)))
    | ~ hBOOL(hAPP(hAPP(U_19639,hAPP(c_Product__Type_Osnd(U_19640,U_19641),U_19642)),hAPP(c_Product__Type_Ofst(U_19640,U_19641),U_19642))) ),
    inference(clausify,[status(thm)],[f_4743_4]) ).

cnf(f_4743_6,plain,
    ( ~ hBOOL(hAPP(U_19643,hAPP(hAPP(U_19644,sK519(U_19645,U_19644,U_19643,U_19642,U_19641,U_19640,U_19639)),sK520(U_19645,U_19644,U_19643,U_19642,U_19641,U_19640,U_19639))))
    | hBOOL(hAPP(U_19643,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_19640,U_19641,U_19645),U_19644),U_19642)))
    | ~ hBOOL(hAPP(hAPP(U_19639,hAPP(c_Product__Type_Osnd(U_19640,U_19641),U_19642)),hAPP(c_Product__Type_Ofst(U_19640,U_19641),U_19642))) ),
    inference(clausify,[status(thm)],[f_4743_4]) ).

fof(f_4744_1,plain,
    ! [V_A_2,V_P_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,hAPP(c_Set_OCollect(tc_prod(T_c,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,tc_HOL_Obool),V_P_2))),V_A_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)))),hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),V_P_2)))),
    inference(fof_nnf,[status(thm)],[fact_Image__Collect__split]) ).

fof(f_4744_2,plain,
    ! [U_19649,U_19648,U_19647,U_19646] : hAPP(c_Relation_OImage(U_19646,U_19647,hAPP(c_Set_OCollect(tc_prod(U_19646,U_19647)),hAPP(c_Product__Type_Oprod_Oprod__case(U_19646,U_19647,tc_HOL_Obool),U_19648))),U_19649) = hAPP(c_Set_OCollect(U_19647),hAPP(hAPP(c_COMBB(tc_fun(U_19646,tc_HOL_Obool),tc_HOL_Obool,U_19647),c_HOL_OEx(U_19646)),hAPP(hAPP(c_COMBB(tc_fun(U_19646,tc_HOL_Obool),tc_fun(U_19646,tc_HOL_Obool),U_19647),hAPP(c_COMBS(U_19646,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_19646),c_fconj),hAPP(hAPP(c_COMBC(U_19646,tc_fun(U_19646,tc_HOL_Obool),tc_HOL_Obool),c_member(U_19646)),U_19649)))),hAPP(c_COMBC(U_19646,U_19647,tc_HOL_Obool),U_19648)))),
    inference(variable_rename,[status(thm)],[f_4744_1]) ).

cnf(f_4744_3,plain,
    hAPP(c_Relation_OImage(U_19646,U_19647,hAPP(c_Set_OCollect(tc_prod(U_19646,U_19647)),hAPP(c_Product__Type_Oprod_Oprod__case(U_19646,U_19647,tc_HOL_Obool),U_19648))),U_19649) = hAPP(c_Set_OCollect(U_19647),hAPP(hAPP(c_COMBB(tc_fun(U_19646,tc_HOL_Obool),tc_HOL_Obool,U_19647),c_HOL_OEx(U_19646)),hAPP(hAPP(c_COMBB(tc_fun(U_19646,tc_HOL_Obool),tc_fun(U_19646,tc_HOL_Obool),U_19647),hAPP(c_COMBS(U_19646,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_19646),c_fconj),hAPP(hAPP(c_COMBC(U_19646,tc_fun(U_19646,tc_HOL_Obool),tc_HOL_Obool),c_member(U_19646)),U_19649)))),hAPP(c_COMBC(U_19646,U_19647,tc_HOL_Obool),U_19648)))),
    inference(clausify,[status(thm)],[f_4744_2]) ).

fof(f_4745_1,plain,
    ! [V_z_2,V_r_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_z_2)),c_List_Olexord(T_b,V_r_2)))
      | ~ c_Relation_Otrans(T_b,V_r_2)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_y_2),V_z_2)),c_List_Olexord(T_b,V_r_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_lexord__trans]) ).

fof(f_4745_2,plain,
    ! [U_19654,U_19653,U_19652,U_19651,U_19650] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19650),tc_List_Olist(U_19650))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19650),tc_List_Olist(U_19650)),U_19651),U_19654)),c_List_Olexord(U_19650,U_19653)))
      | ~ c_Relation_Otrans(U_19650,U_19653)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19650),tc_List_Olist(U_19650))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19650),tc_List_Olist(U_19650)),U_19652),U_19654)),c_List_Olexord(U_19650,U_19653)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19650),tc_List_Olist(U_19650))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19650),tc_List_Olist(U_19650)),U_19651),U_19652)),c_List_Olexord(U_19650,U_19653))) ),
    inference(variable_rename,[status(thm)],[f_4745_1]) ).

cnf(f_4745_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19650),tc_List_Olist(U_19650))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19650),tc_List_Olist(U_19650)),U_19651),U_19654)),c_List_Olexord(U_19650,U_19653)))
    | ~ c_Relation_Otrans(U_19650,U_19653)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19650),tc_List_Olist(U_19650))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19650),tc_List_Olist(U_19650)),U_19652),U_19654)),c_List_Olexord(U_19650,U_19653)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19650),tc_List_Olist(U_19650))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19650),tc_List_Olist(U_19650)),U_19651),U_19652)),c_List_Olexord(U_19650,U_19653))) ),
    inference(clausify,[status(thm)],[f_4745_2]) ).

fof(f_4746_1,plain,
    c_Relation_Otrans(tc_Nat_Onat,c_Wellfounded_Oless__than),
    inference(fof_nnf,[status(thm)],[fact_trans__less__than]) ).

cnf(f_4746_2,plain,
    c_Relation_Otrans(tc_Nat_Onat,c_Wellfounded_Oless__than),
    inference(clausify,[status(thm)],[f_4746_1]) ).

fof(f_4747_1,plain,
    ! [V_R2_2,T_c,V_R1_2,T_b] :
      ( c_Relation_Otrans(tc_prod(T_b,T_c),c_Wellfounded_Olex__prod(T_b,T_c,V_R1_2,V_R2_2))
      | ~ c_Relation_Otrans(T_c,V_R2_2)
      | ~ c_Relation_Otrans(T_b,V_R1_2) ),
    inference(fof_nnf,[status(thm)],[fact_trans__lex__prod]) ).

fof(f_4747_2,plain,
    ! [U_19658,U_19657,U_19656,U_19655] :
      ( c_Relation_Otrans(tc_prod(U_19655,U_19657),c_Wellfounded_Olex__prod(U_19655,U_19657,U_19656,U_19658))
      | ~ c_Relation_Otrans(U_19657,U_19658)
      | ~ c_Relation_Otrans(U_19655,U_19656) ),
    inference(variable_rename,[status(thm)],[f_4747_1]) ).

cnf(f_4747_3,plain,
    ( c_Relation_Otrans(tc_prod(U_19655,U_19657),c_Wellfounded_Olex__prod(U_19655,U_19657,U_19656,U_19658))
    | ~ c_Relation_Otrans(U_19657,U_19658)
    | ~ c_Relation_Otrans(U_19655,U_19656) ),
    inference(clausify,[status(thm)],[f_4747_2]) ).

fof(f_4748_1,plain,
    ! [V_c_2,V_b_2,V_a_2,V_r_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),V_r_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),V_r_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
      | ~ c_Relation_Otrans(T_b,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_transD]) ).

fof(f_4748_2,plain,
    ! [U_19663,U_19662,U_19661,U_19660,U_19659] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19659,U_19659)),hAPP(hAPP(c_Product__Type_OPair(U_19659,U_19659),U_19661),U_19663)),U_19660))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19659,U_19659)),hAPP(hAPP(c_Product__Type_OPair(U_19659,U_19659),U_19662),U_19663)),U_19660))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19659,U_19659)),hAPP(hAPP(c_Product__Type_OPair(U_19659,U_19659),U_19661),U_19662)),U_19660))
      | ~ c_Relation_Otrans(U_19659,U_19660) ),
    inference(variable_rename,[status(thm)],[f_4748_1]) ).

cnf(f_4748_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19659,U_19659)),hAPP(hAPP(c_Product__Type_OPair(U_19659,U_19659),U_19661),U_19663)),U_19660))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19659,U_19659)),hAPP(hAPP(c_Product__Type_OPair(U_19659,U_19659),U_19662),U_19663)),U_19660))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19659,U_19659)),hAPP(hAPP(c_Product__Type_OPair(U_19659,U_19659),U_19661),U_19662)),U_19660))
    | ~ c_Relation_Otrans(U_19659,U_19660) ),
    inference(clausify,[status(thm)],[f_4748_2]) ).

fof(f_4749_1,plain,
    ! [V_r_2,T_b] :
      ( ( c_Relation_Otrans(T_b,V_r_2)
        | ? [B_x,B_y] :
            ( ? [B_z] :
                ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_z)),V_r_2))
                & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_z)),V_r_2)) )
            & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_r_2)) ) )
      & ( ! [B_x,B_y] :
            ( ! [B_z] :
                ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_z)),V_r_2))
                | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_z)),V_r_2)) )
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_r_2)) )
        | ~ c_Relation_Otrans(T_b,V_r_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_trans__def]) ).

fof(f_4749_2,plain,
    ! [U_19671,U_19670] :
      ( ( c_Relation_Otrans(U_19670,U_19671)
        | ? [U_19669,U_19668] :
            ( ? [U_19667] :
                ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19670,U_19670)),hAPP(hAPP(c_Product__Type_OPair(U_19670,U_19670),U_19669),U_19667)),U_19671))
                & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19670,U_19670)),hAPP(hAPP(c_Product__Type_OPair(U_19670,U_19670),U_19668),U_19667)),U_19671)) )
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19670,U_19670)),hAPP(hAPP(c_Product__Type_OPair(U_19670,U_19670),U_19669),U_19668)),U_19671)) ) )
      & ( ! [U_19666,U_19665] :
            ( ! [U_19664] :
                ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19670,U_19670)),hAPP(hAPP(c_Product__Type_OPair(U_19670,U_19670),U_19666),U_19664)),U_19671))
                | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19670,U_19670)),hAPP(hAPP(c_Product__Type_OPair(U_19670,U_19670),U_19665),U_19664)),U_19671)) )
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19670,U_19670)),hAPP(hAPP(c_Product__Type_OPair(U_19670,U_19670),U_19666),U_19665)),U_19671)) )
        | ~ c_Relation_Otrans(U_19670,U_19671) ) ),
    inference(variable_rename,[status(thm)],[f_4749_1]) ).

fof(f_4749_3,plain,
    ( ! [U_19675,U_19673] :
        ( c_Relation_Otrans(U_19673,U_19675)
        | ? [U_19669,U_19668] :
            ( ? [U_19667] :
                ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19673,U_19673)),hAPP(hAPP(c_Product__Type_OPair(U_19673,U_19673),U_19669),U_19667)),U_19675))
                & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19673,U_19673)),hAPP(hAPP(c_Product__Type_OPair(U_19673,U_19673),U_19668),U_19667)),U_19675)) )
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19673,U_19673)),hAPP(hAPP(c_Product__Type_OPair(U_19673,U_19673),U_19669),U_19668)),U_19675)) ) )
    & ! [U_19674,U_19672] :
        ( ! [U_19666,U_19665] :
            ( ! [U_19664] :
                ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19672,U_19672)),hAPP(hAPP(c_Product__Type_OPair(U_19672,U_19672),U_19666),U_19664)),U_19674))
                | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19672,U_19672)),hAPP(hAPP(c_Product__Type_OPair(U_19672,U_19672),U_19665),U_19664)),U_19674)) )
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19672,U_19672)),hAPP(hAPP(c_Product__Type_OPair(U_19672,U_19672),U_19666),U_19665)),U_19674)) )
        | ~ c_Relation_Otrans(U_19672,U_19674) ) ),
    inference(miniscope,[status(thm)],[f_4749_2]) ).

fof(f_4749_4,plain,
    ( ! [U_19675,U_19673] :
        ( c_Relation_Otrans(U_19673,U_19675)
        | ? [U_19668] :
            ( ? [U_19667] :
                ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19673,U_19673)),hAPP(hAPP(c_Product__Type_OPair(U_19673,U_19673),sK521(U_19675,U_19673)),U_19667)),U_19675))
                & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19673,U_19673)),hAPP(hAPP(c_Product__Type_OPair(U_19673,U_19673),U_19668),U_19667)),U_19675)) )
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19673,U_19673)),hAPP(hAPP(c_Product__Type_OPair(U_19673,U_19673),sK521(U_19675,U_19673)),U_19668)),U_19675)) ) )
    & ! [U_19674,U_19672] :
        ( ! [U_19666,U_19665] :
            ( ! [U_19664] :
                ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19672,U_19672)),hAPP(hAPP(c_Product__Type_OPair(U_19672,U_19672),U_19666),U_19664)),U_19674))
                | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19672,U_19672)),hAPP(hAPP(c_Product__Type_OPair(U_19672,U_19672),U_19665),U_19664)),U_19674)) )
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19672,U_19672)),hAPP(hAPP(c_Product__Type_OPair(U_19672,U_19672),U_19666),U_19665)),U_19674)) )
        | ~ c_Relation_Otrans(U_19672,U_19674) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK521]),skolemize(U_19669,sK521(U_19675,U_19673))],[f_4749_3]) ).

fof(f_4749_5,plain,
    ( ! [U_19675,U_19673] :
        ( c_Relation_Otrans(U_19673,U_19675)
        | ( ? [U_19667] :
              ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19673,U_19673)),hAPP(hAPP(c_Product__Type_OPair(U_19673,U_19673),sK521(U_19675,U_19673)),U_19667)),U_19675))
              & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19673,U_19673)),hAPP(hAPP(c_Product__Type_OPair(U_19673,U_19673),sK522(U_19675,U_19673)),U_19667)),U_19675)) )
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19673,U_19673)),hAPP(hAPP(c_Product__Type_OPair(U_19673,U_19673),sK521(U_19675,U_19673)),sK522(U_19675,U_19673))),U_19675)) ) )
    & ! [U_19674,U_19672] :
        ( ! [U_19666,U_19665] :
            ( ! [U_19664] :
                ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19672,U_19672)),hAPP(hAPP(c_Product__Type_OPair(U_19672,U_19672),U_19666),U_19664)),U_19674))
                | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19672,U_19672)),hAPP(hAPP(c_Product__Type_OPair(U_19672,U_19672),U_19665),U_19664)),U_19674)) )
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19672,U_19672)),hAPP(hAPP(c_Product__Type_OPair(U_19672,U_19672),U_19666),U_19665)),U_19674)) )
        | ~ c_Relation_Otrans(U_19672,U_19674) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK522]),skolemize(U_19668,sK522(U_19675,U_19673))],[f_4749_4]) ).

fof(f_4749_6,plain,
    ( ! [U_19675,U_19673] :
        ( c_Relation_Otrans(U_19673,U_19675)
        | ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19673,U_19673)),hAPP(hAPP(c_Product__Type_OPair(U_19673,U_19673),sK521(U_19675,U_19673)),sK523(U_19675,U_19673))),U_19675))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19673,U_19673)),hAPP(hAPP(c_Product__Type_OPair(U_19673,U_19673),sK522(U_19675,U_19673)),sK523(U_19675,U_19673))),U_19675))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19673,U_19673)),hAPP(hAPP(c_Product__Type_OPair(U_19673,U_19673),sK521(U_19675,U_19673)),sK522(U_19675,U_19673))),U_19675)) ) )
    & ! [U_19674,U_19672] :
        ( ! [U_19666,U_19665] :
            ( ! [U_19664] :
                ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19672,U_19672)),hAPP(hAPP(c_Product__Type_OPair(U_19672,U_19672),U_19666),U_19664)),U_19674))
                | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19672,U_19672)),hAPP(hAPP(c_Product__Type_OPair(U_19672,U_19672),U_19665),U_19664)),U_19674)) )
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19672,U_19672)),hAPP(hAPP(c_Product__Type_OPair(U_19672,U_19672),U_19666),U_19665)),U_19674)) )
        | ~ c_Relation_Otrans(U_19672,U_19674) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK523]),skolemize(U_19667,sK523(U_19675,U_19673))],[f_4749_5]) ).

cnf(f_4749_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19672,U_19672)),hAPP(hAPP(c_Product__Type_OPair(U_19672,U_19672),U_19666),U_19664)),U_19674))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19672,U_19672)),hAPP(hAPP(c_Product__Type_OPair(U_19672,U_19672),U_19665),U_19664)),U_19674))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19672,U_19672)),hAPP(hAPP(c_Product__Type_OPair(U_19672,U_19672),U_19666),U_19665)),U_19674))
    | ~ c_Relation_Otrans(U_19672,U_19674) ),
    inference(clausify,[status(thm)],[f_4749_6]) ).

cnf(f_4749_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19673,U_19673)),hAPP(hAPP(c_Product__Type_OPair(U_19673,U_19673),sK521(U_19675,U_19673)),sK522(U_19675,U_19673))),U_19675))
    | c_Relation_Otrans(U_19673,U_19675) ),
    inference(clausify,[status(thm)],[f_4749_6]) ).

cnf(f_4749_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19673,U_19673)),hAPP(hAPP(c_Product__Type_OPair(U_19673,U_19673),sK522(U_19675,U_19673)),sK523(U_19675,U_19673))),U_19675))
    | c_Relation_Otrans(U_19673,U_19675) ),
    inference(clausify,[status(thm)],[f_4749_6]) ).

cnf(f_4749_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19673,U_19673)),hAPP(hAPP(c_Product__Type_OPair(U_19673,U_19673),sK521(U_19675,U_19673)),sK523(U_19675,U_19673))),U_19675))
    | c_Relation_Otrans(U_19673,U_19675) ),
    inference(clausify,[status(thm)],[f_4749_6]) ).

fof(f_4750_1,plain,
    ! [V_r_2,T_b] : c_Relation_Otrans(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)),
    inference(fof_nnf,[status(thm)],[fact_trans__rtrancl]) ).

fof(f_4750_2,plain,
    ! [U_19677,U_19676] : c_Relation_Otrans(U_19676,c_Transitive__Closure_Ortrancl(U_19676,U_19677)),
    inference(variable_rename,[status(thm)],[f_4750_1]) ).

cnf(f_4750_3,plain,
    c_Relation_Otrans(U_19676,c_Transitive__Closure_Ortrancl(U_19676,U_19677)),
    inference(clausify,[status(thm)],[f_4750_2]) ).

fof(f_4751_1,plain,
    ! [T_b] : c_Relation_Otrans(T_b,c_Relation_OId(T_b)),
    inference(fof_nnf,[status(thm)],[fact_trans__Id]) ).

fof(f_4751_2,plain,
    ! [U_19678] : c_Relation_Otrans(U_19678,c_Relation_OId(U_19678)),
    inference(variable_rename,[status(thm)],[f_4751_1]) ).

cnf(f_4751_3,plain,
    c_Relation_Otrans(U_19678,c_Relation_OId(U_19678)),
    inference(clausify,[status(thm)],[f_4751_2]) ).

fof(f_4752_1,plain,
    ! [V_r_2,T_b] : c_Relation_Otrans(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)),
    inference(fof_nnf,[status(thm)],[fact_trans__trancl]) ).

fof(f_4752_2,plain,
    ! [U_19680,U_19679] : c_Relation_Otrans(U_19679,c_Transitive__Closure_Otrancl(U_19679,U_19680)),
    inference(variable_rename,[status(thm)],[f_4752_1]) ).

cnf(f_4752_3,plain,
    c_Relation_Otrans(U_19679,c_Transitive__Closure_Otrancl(U_19679,U_19680)),
    inference(clausify,[status(thm)],[f_4752_2]) ).

fof(f_4753_1,plain,
    ! [V_r_2,T_b] :
      ( c_Transitive__Closure_Otrancl(T_b,V_r_2) = V_r_2
      | ~ c_Relation_Otrans(T_b,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_trancl__id]) ).

fof(f_4753_2,plain,
    ! [U_19682,U_19681] :
      ( c_Transitive__Closure_Otrancl(U_19681,U_19682) = U_19682
      | ~ c_Relation_Otrans(U_19681,U_19682) ),
    inference(variable_rename,[status(thm)],[f_4753_1]) ).

cnf(f_4753_3,plain,
    ( c_Transitive__Closure_Otrancl(U_19681,U_19682) = U_19682
    | ~ c_Relation_Otrans(U_19681,U_19682) ),
    inference(clausify,[status(thm)],[f_4753_2]) ).

fof(f_4754_1,plain,
    ! [V_A_2,T_b] : c_Relation_Otrans(T_b,c_Relation_OId__on(T_b,V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_trans__Id__on]) ).

fof(f_4754_2,plain,
    ! [U_19684,U_19683] : c_Relation_Otrans(U_19683,c_Relation_OId__on(U_19683,U_19684)),
    inference(variable_rename,[status(thm)],[f_4754_1]) ).

cnf(f_4754_3,plain,
    c_Relation_Otrans(U_19683,c_Relation_OId__on(U_19683,U_19684)),
    inference(clausify,[status(thm)],[f_4754_2]) ).

fof(f_4755_1,plain,
    ! [T_b] : c_Relation_Otrans(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_b)),
    inference(fof_nnf,[status(thm)],[fact_trans__finite__psubset]) ).

fof(f_4755_2,plain,
    ! [U_19685] : c_Relation_Otrans(tc_fun(U_19685,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(U_19685)),
    inference(variable_rename,[status(thm)],[f_4755_1]) ).

cnf(f_4755_3,plain,
    c_Relation_Otrans(tc_fun(U_19685,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(U_19685)),
    inference(clausify,[status(thm)],[f_4755_2]) ).

fof(f_4756_1,plain,
    ! [V_r_2,T_b] :
      ( c_Relation_Otrans(tc_List_Olist(T_b),c_List_Olexord(T_b,V_r_2))
      | ~ c_Relation_Otrans(T_b,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_lexord__transI]) ).

fof(f_4756_2,plain,
    ! [U_19687,U_19686] :
      ( c_Relation_Otrans(tc_List_Olist(U_19686),c_List_Olexord(U_19686,U_19687))
      | ~ c_Relation_Otrans(U_19686,U_19687) ),
    inference(variable_rename,[status(thm)],[f_4756_1]) ).

cnf(f_4756_3,plain,
    ( c_Relation_Otrans(tc_List_Olist(U_19686),c_List_Olexord(U_19686,U_19687))
    | ~ c_Relation_Otrans(U_19686,U_19687) ),
    inference(clausify,[status(thm)],[f_4756_2]) ).

fof(f_4757_1,plain,
    ! [V_r_2,T_b] :
      ( c_Relation_Otrans(tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2))
      | ~ c_Relation_Otrans(T_b,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_listrel__trans]) ).

fof(f_4757_2,plain,
    ! [U_19689,U_19688] :
      ( c_Relation_Otrans(tc_List_Olist(U_19688),c_List_Olistrel(U_19688,U_19689))
      | ~ c_Relation_Otrans(U_19688,U_19689) ),
    inference(variable_rename,[status(thm)],[f_4757_1]) ).

cnf(f_4757_3,plain,
    ( c_Relation_Otrans(tc_List_Olist(U_19688),c_List_Olistrel(U_19688,U_19689))
    | ~ c_Relation_Otrans(U_19688,U_19689) ),
    inference(clausify,[status(thm)],[f_4757_2]) ).

fof(f_4758_1,plain,
    ! [V_P_2,T_b,B_x] :
      ( ~ hBOOL(hAPP(V_P_2,B_x))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ),
    inference(fof_nnf,[status(thm)],[fact_bex__empty]) ).

fof(f_4758_2,plain,
    ! [U_19692,U_19691,U_19690] :
      ( ~ hBOOL(hAPP(U_19692,U_19690))
      | ~ hBOOL(hAPP(hAPP(c_member(U_19691),U_19690),c_Orderings_Obot__class_Obot(tc_fun(U_19691,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_4758_1]) ).

cnf(f_4758_3,plain,
    ( ~ hBOOL(hAPP(U_19692,U_19690))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19691),U_19690),c_Orderings_Obot__class_Obot(tc_fun(U_19691,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_4758_2]) ).

fof(f_4759_1,plain,
    ! [V_r_2,T_b] :
      ( ( c_Relation_Otrans(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
        | ~ c_Relation_Otrans(T_b,V_r_2) )
      & ( c_Relation_Otrans(T_b,V_r_2)
        | ~ c_Relation_Otrans(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_trans__converse]) ).

fof(f_4759_2,plain,
    ! [U_19694,U_19693] :
      ( ( c_Relation_Otrans(U_19693,hAPP(c_Relation_Oconverse(U_19693,U_19693),U_19694))
        | ~ c_Relation_Otrans(U_19693,U_19694) )
      & ( c_Relation_Otrans(U_19693,U_19694)
        | ~ c_Relation_Otrans(U_19693,hAPP(c_Relation_Oconverse(U_19693,U_19693),U_19694)) ) ),
    inference(variable_rename,[status(thm)],[f_4759_1]) ).

fof(f_4759_3,plain,
    ( ! [U_19698,U_19696] :
        ( c_Relation_Otrans(U_19696,hAPP(c_Relation_Oconverse(U_19696,U_19696),U_19698))
        | ~ c_Relation_Otrans(U_19696,U_19698) )
    & ! [U_19697,U_19695] :
        ( c_Relation_Otrans(U_19695,U_19697)
        | ~ c_Relation_Otrans(U_19695,hAPP(c_Relation_Oconverse(U_19695,U_19695),U_19697)) ) ),
    inference(miniscope,[status(thm)],[f_4759_2]) ).

cnf(f_4759_4,plain,
    ( c_Relation_Otrans(U_19695,U_19697)
    | ~ c_Relation_Otrans(U_19695,hAPP(c_Relation_Oconverse(U_19695,U_19695),U_19697)) ),
    inference(clausify,[status(thm)],[f_4759_3]) ).

cnf(f_4759_5,plain,
    ( c_Relation_Otrans(U_19696,hAPP(c_Relation_Oconverse(U_19696,U_19696),U_19698))
    | ~ c_Relation_Otrans(U_19696,U_19698) ),
    inference(clausify,[status(thm)],[f_4759_3]) ).

fof(f_4760_1,plain,
    ! [V_Q_2,T_c,V_A_2,T_b] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),V_Q_2)))))
          | ? [B_x] :
              ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),V_Q_2),B_x))))
              & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
        & ( ! [B_x] :
              ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),V_Q_2),B_x))))
              | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),V_Q_2))))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__Collect__bex]) ).

fof(f_4760_2,plain,
    ! [U_19704,U_19703,U_19702,U_19701] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_19703),hAPP(c_Set_OCollect(U_19703),hAPP(hAPP(c_COMBB(tc_fun(U_19701,tc_HOL_Obool),tc_HOL_Obool,U_19703),c_HOL_OEx(U_19701)),hAPP(hAPP(c_COMBB(tc_fun(U_19701,tc_HOL_Obool),tc_fun(U_19701,tc_HOL_Obool),U_19703),hAPP(c_COMBS(U_19701,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_19701),c_fconj),hAPP(hAPP(c_COMBC(U_19701,tc_fun(U_19701,tc_HOL_Obool),tc_HOL_Obool),c_member(U_19701)),U_19702)))),U_19704)))))
          | ? [U_19700] :
              ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19703),hAPP(c_Set_OCollect(U_19703),hAPP(hAPP(c_COMBC(U_19703,U_19701,tc_HOL_Obool),U_19704),U_19700))))
              & hBOOL(hAPP(hAPP(c_member(U_19701),U_19700),U_19702)) ) )
        & ( ! [U_19699] :
              ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_19703),hAPP(c_Set_OCollect(U_19703),hAPP(hAPP(c_COMBC(U_19703,U_19701,tc_HOL_Obool),U_19704),U_19699))))
              | ~ hBOOL(hAPP(hAPP(c_member(U_19701),U_19699),U_19702)) )
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19703),hAPP(c_Set_OCollect(U_19703),hAPP(hAPP(c_COMBB(tc_fun(U_19701,tc_HOL_Obool),tc_HOL_Obool,U_19703),c_HOL_OEx(U_19701)),hAPP(hAPP(c_COMBB(tc_fun(U_19701,tc_HOL_Obool),tc_fun(U_19701,tc_HOL_Obool),U_19703),hAPP(c_COMBS(U_19701,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_19701),c_fconj),hAPP(hAPP(c_COMBC(U_19701,tc_fun(U_19701,tc_HOL_Obool),tc_HOL_Obool),c_member(U_19701)),U_19702)))),U_19704))))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19701),U_19702)) ),
    inference(variable_rename,[status(thm)],[f_4760_1]) ).

fof(f_4760_3,plain,
    ! [U_19704,U_19703,U_19702,U_19701] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_19703),hAPP(c_Set_OCollect(U_19703),hAPP(hAPP(c_COMBB(tc_fun(U_19701,tc_HOL_Obool),tc_HOL_Obool,U_19703),c_HOL_OEx(U_19701)),hAPP(hAPP(c_COMBB(tc_fun(U_19701,tc_HOL_Obool),tc_fun(U_19701,tc_HOL_Obool),U_19703),hAPP(c_COMBS(U_19701,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_19701),c_fconj),hAPP(hAPP(c_COMBC(U_19701,tc_fun(U_19701,tc_HOL_Obool),tc_HOL_Obool),c_member(U_19701)),U_19702)))),U_19704)))))
          | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19703),hAPP(c_Set_OCollect(U_19703),hAPP(hAPP(c_COMBC(U_19703,U_19701,tc_HOL_Obool),U_19704),sK524(U_19704,U_19703,U_19702,U_19701)))))
            & hBOOL(hAPP(hAPP(c_member(U_19701),sK524(U_19704,U_19703,U_19702,U_19701)),U_19702)) ) )
        & ( ! [U_19699] :
              ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_19703),hAPP(c_Set_OCollect(U_19703),hAPP(hAPP(c_COMBC(U_19703,U_19701,tc_HOL_Obool),U_19704),U_19699))))
              | ~ hBOOL(hAPP(hAPP(c_member(U_19701),U_19699),U_19702)) )
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19703),hAPP(c_Set_OCollect(U_19703),hAPP(hAPP(c_COMBB(tc_fun(U_19701,tc_HOL_Obool),tc_HOL_Obool,U_19703),c_HOL_OEx(U_19701)),hAPP(hAPP(c_COMBB(tc_fun(U_19701,tc_HOL_Obool),tc_fun(U_19701,tc_HOL_Obool),U_19703),hAPP(c_COMBS(U_19701,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_19701),c_fconj),hAPP(hAPP(c_COMBC(U_19701,tc_fun(U_19701,tc_HOL_Obool),tc_HOL_Obool),c_member(U_19701)),U_19702)))),U_19704))))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19701),U_19702)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK524]),skolemize(U_19700,sK524(U_19704,U_19703,U_19702,U_19701))],[f_4760_2]) ).

cnf(f_4760_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_19703),hAPP(c_Set_OCollect(U_19703),hAPP(hAPP(c_COMBC(U_19703,U_19701,tc_HOL_Obool),U_19704),U_19699))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19701),U_19699),U_19702))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19703),hAPP(c_Set_OCollect(U_19703),hAPP(hAPP(c_COMBB(tc_fun(U_19701,tc_HOL_Obool),tc_HOL_Obool,U_19703),c_HOL_OEx(U_19701)),hAPP(hAPP(c_COMBB(tc_fun(U_19701,tc_HOL_Obool),tc_fun(U_19701,tc_HOL_Obool),U_19703),hAPP(c_COMBS(U_19701,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_19701),c_fconj),hAPP(hAPP(c_COMBC(U_19701,tc_fun(U_19701,tc_HOL_Obool),tc_HOL_Obool),c_member(U_19701)),U_19702)))),U_19704)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19701),U_19702)) ),
    inference(clausify,[status(thm)],[f_4760_3]) ).

cnf(f_4760_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19701),sK524(U_19704,U_19703,U_19702,U_19701)),U_19702))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_19703),hAPP(c_Set_OCollect(U_19703),hAPP(hAPP(c_COMBB(tc_fun(U_19701,tc_HOL_Obool),tc_HOL_Obool,U_19703),c_HOL_OEx(U_19701)),hAPP(hAPP(c_COMBB(tc_fun(U_19701,tc_HOL_Obool),tc_fun(U_19701,tc_HOL_Obool),U_19703),hAPP(c_COMBS(U_19701,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_19701),c_fconj),hAPP(hAPP(c_COMBC(U_19701,tc_fun(U_19701,tc_HOL_Obool),tc_HOL_Obool),c_member(U_19701)),U_19702)))),U_19704)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19701),U_19702)) ),
    inference(clausify,[status(thm)],[f_4760_3]) ).

cnf(f_4760_6,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19703),hAPP(c_Set_OCollect(U_19703),hAPP(hAPP(c_COMBC(U_19703,U_19701,tc_HOL_Obool),U_19704),sK524(U_19704,U_19703,U_19702,U_19701)))))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_19703),hAPP(c_Set_OCollect(U_19703),hAPP(hAPP(c_COMBB(tc_fun(U_19701,tc_HOL_Obool),tc_HOL_Obool,U_19703),c_HOL_OEx(U_19701)),hAPP(hAPP(c_COMBB(tc_fun(U_19701,tc_HOL_Obool),tc_fun(U_19701,tc_HOL_Obool),U_19703),hAPP(c_COMBS(U_19701,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_19701),c_fconj),hAPP(hAPP(c_COMBC(U_19701,tc_fun(U_19701,tc_HOL_Obool),tc_HOL_Obool),c_member(U_19701)),U_19702)))),U_19704)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19701),U_19702)) ),
    inference(clausify,[status(thm)],[f_4760_3]) ).

fof(f_4761_1,plain,
    ! [V_P_2,T_b] :
      ( ( ? [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) )
        | ! [B_x1] : ~ hBOOL(hAPP(V_P_2,B_x1)) )
      & ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
        | ! [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_bex__UNIV]) ).

fof(f_4761_2,plain,
    ! [U_19710,U_19709] :
      ( ( ? [U_19708] :
            ( hBOOL(hAPP(U_19710,U_19708))
            & hBOOL(hAPP(hAPP(c_member(U_19709),U_19708),c_Orderings_Otop__class_Otop(tc_fun(U_19709,tc_HOL_Obool)))) )
        | ! [U_19707] : ~ hBOOL(hAPP(U_19710,U_19707)) )
      & ( ? [U_19706] : hBOOL(hAPP(U_19710,U_19706))
        | ! [U_19705] :
            ( ~ hBOOL(hAPP(U_19710,U_19705))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19709),U_19705),c_Orderings_Otop__class_Otop(tc_fun(U_19709,tc_HOL_Obool)))) ) ) ),
    inference(variable_rename,[status(thm)],[f_4761_1]) ).

fof(f_4761_3,plain,
    ( ! [U_19714] :
        ( ! [U_19712] :
          ? [U_19708] :
            ( hBOOL(hAPP(U_19714,U_19708))
            & hBOOL(hAPP(hAPP(c_member(U_19712),U_19708),c_Orderings_Otop__class_Otop(tc_fun(U_19712,tc_HOL_Obool)))) )
        | ! [U_19707] : ~ hBOOL(hAPP(U_19714,U_19707)) )
    & ! [U_19713] :
        ( ! [U_19711,U_19705] :
            ( ~ hBOOL(hAPP(U_19713,U_19705))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19711),U_19705),c_Orderings_Otop__class_Otop(tc_fun(U_19711,tc_HOL_Obool)))) )
        | ? [U_19706] : hBOOL(hAPP(U_19713,U_19706)) ) ),
    inference(miniscope,[status(thm)],[f_4761_2]) ).

fof(f_4761_4,plain,
    ( ! [U_19714] :
        ( ! [U_19712] :
          ? [U_19708] :
            ( hBOOL(hAPP(U_19714,U_19708))
            & hBOOL(hAPP(hAPP(c_member(U_19712),U_19708),c_Orderings_Otop__class_Otop(tc_fun(U_19712,tc_HOL_Obool)))) )
        | ! [U_19707] : ~ hBOOL(hAPP(U_19714,U_19707)) )
    & ! [U_19713] :
        ( ! [U_19711,U_19705] :
            ( ~ hBOOL(hAPP(U_19713,U_19705))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19711),U_19705),c_Orderings_Otop__class_Otop(tc_fun(U_19711,tc_HOL_Obool)))) )
        | hBOOL(hAPP(U_19713,sK525(U_19713))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK525]),skolemize(U_19706,sK525(U_19713))],[f_4761_3]) ).

fof(f_4761_5,plain,
    ( ! [U_19714] :
        ( ! [U_19712] :
            ( hBOOL(hAPP(U_19714,sK526(U_19714,U_19712)))
            & hBOOL(hAPP(hAPP(c_member(U_19712),sK526(U_19714,U_19712)),c_Orderings_Otop__class_Otop(tc_fun(U_19712,tc_HOL_Obool)))) )
        | ! [U_19707] : ~ hBOOL(hAPP(U_19714,U_19707)) )
    & ! [U_19713] :
        ( ! [U_19711,U_19705] :
            ( ~ hBOOL(hAPP(U_19713,U_19705))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19711),U_19705),c_Orderings_Otop__class_Otop(tc_fun(U_19711,tc_HOL_Obool)))) )
        | hBOOL(hAPP(U_19713,sK525(U_19713))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK526]),skolemize(U_19708,sK526(U_19714,U_19712))],[f_4761_4]) ).

cnf(f_4761_6,plain,
    ( ~ hBOOL(hAPP(U_19713,U_19705))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19711),U_19705),c_Orderings_Otop__class_Otop(tc_fun(U_19711,tc_HOL_Obool))))
    | hBOOL(hAPP(U_19713,sK525(U_19713))) ),
    inference(clausify,[status(thm)],[f_4761_5]) ).

cnf(f_4761_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19712),sK526(U_19714,U_19712)),c_Orderings_Otop__class_Otop(tc_fun(U_19712,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(U_19714,U_19707)) ),
    inference(clausify,[status(thm)],[f_4761_5]) ).

cnf(f_4761_8,plain,
    ( hBOOL(hAPP(U_19714,sK526(U_19714,U_19712)))
    | ~ hBOOL(hAPP(U_19714,U_19707)) ),
    inference(clausify,[status(thm)],[f_4761_5]) ).

fof(f_4762_1,plain,
    ! [V_s_2,V_r_2,T_b] :
      ( c_Relation_Otrans(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
      | ~ c_Relation_Otrans(T_b,V_s_2)
      | ~ c_Relation_Otrans(T_b,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_trans__Int]) ).

fof(f_4762_2,plain,
    ! [U_19717,U_19716,U_19715] :
      ( c_Relation_Otrans(U_19715,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_19715,U_19715),tc_HOL_Obool)),U_19716),U_19717))
      | ~ c_Relation_Otrans(U_19715,U_19717)
      | ~ c_Relation_Otrans(U_19715,U_19716) ),
    inference(variable_rename,[status(thm)],[f_4762_1]) ).

cnf(f_4762_3,plain,
    ( c_Relation_Otrans(U_19715,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_19715,U_19715),tc_HOL_Obool)),U_19716),U_19717))
    | ~ c_Relation_Otrans(U_19715,U_19717)
    | ~ c_Relation_Otrans(U_19715,U_19716) ),
    inference(clausify,[status(thm)],[f_4762_2]) ).

fof(f_4763_1,plain,
    ! [T_b] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_HOL_Obool) = c_Set_OBex(T_b),
    inference(fof_nnf,[status(thm)],[fact_SUPR__bool__eq]) ).

fof(f_4763_2,plain,
    ! [U_19718] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_19718,tc_HOL_Obool) = c_Set_OBex(U_19718),
    inference(variable_rename,[status(thm)],[f_4763_1]) ).

cnf(f_4763_3,plain,
    c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_19718,tc_HOL_Obool) = c_Set_OBex(U_19718),
    inference(clausify,[status(thm)],[f_4763_2]) ).

fof(f_4764_1,plain,
    ! [V_r_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_r_2),V_r_2)),V_r_2))
      | ~ c_Relation_Otrans(T_b,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_trans__O__subset]) ).

fof(f_4764_2,plain,
    ! [U_19720,U_19719] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_19719,U_19719),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_19719,U_19719,U_19719),U_19720),U_19720)),U_19720))
      | ~ c_Relation_Otrans(U_19719,U_19720) ),
    inference(variable_rename,[status(thm)],[f_4764_1]) ).

cnf(f_4764_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_19719,U_19719),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_19719,U_19719,U_19719),U_19720),U_19720)),U_19720))
    | ~ c_Relation_Otrans(U_19719,U_19720) ),
    inference(clausify,[status(thm)],[f_4764_2]) ).

fof(f_4765_1,plain,
    ! [V_r_2,T_b] :
      ( c_Relation_Otrans(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b)))
      | ~ c_Relation_Otrans(T_b,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_trans__reflclI]) ).

fof(f_4765_2,plain,
    ! [U_19722,U_19721] :
      ( c_Relation_Otrans(U_19721,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_19721,U_19721),tc_HOL_Obool)),U_19722),c_Relation_OId(U_19721)))
      | ~ c_Relation_Otrans(U_19721,U_19722) ),
    inference(variable_rename,[status(thm)],[f_4765_1]) ).

cnf(f_4765_3,plain,
    ( c_Relation_Otrans(U_19721,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_19721,U_19721),tc_HOL_Obool)),U_19722),c_Relation_OId(U_19721)))
    | ~ c_Relation_Otrans(U_19721,U_19722) ),
    inference(clausify,[status(thm)],[f_4765_2]) ).

fof(f_4766_1,plain,
    ! [V_f_2,T_c,V_r_2,T_b] :
      ( c_Relation_Otrans(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2))
      | ~ c_Relation_Otrans(T_b,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_trans__inv__image]) ).

fof(f_4766_2,plain,
    ! [U_19726,U_19725,U_19724,U_19723] :
      ( c_Relation_Otrans(U_19725,hAPP(hAPP(c_Relation_Oinv__image(U_19723,U_19725),U_19724),U_19726))
      | ~ c_Relation_Otrans(U_19723,U_19724) ),
    inference(variable_rename,[status(thm)],[f_4766_1]) ).

cnf(f_4766_3,plain,
    ( c_Relation_Otrans(U_19725,hAPP(hAPP(c_Relation_Oinv__image(U_19723,U_19725),U_19724),U_19726))
    | ~ c_Relation_Otrans(U_19723,U_19724) ),
    inference(clausify,[status(thm)],[f_4766_2]) ).

fof(f_4767_1,plain,
    ! [V_A_2,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_b,tc_HOL_Obool))),V_A_2)))),c_member(T_b)))),
    inference(fof_nnf,[status(thm)],[fact_Union__eq]) ).

fof(f_4767_2,plain,
    ! [U_19728,U_19727] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_19727,tc_HOL_Obool),U_19728) = hAPP(c_Set_OCollect(U_19727),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_19727,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,U_19727),c_HOL_OEx(tc_fun(U_19727,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_19727,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_19727,tc_HOL_Obool),tc_HOL_Obool),U_19727),hAPP(c_COMBS(tc_fun(U_19727,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(U_19727,tc_HOL_Obool)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(U_19727,tc_HOL_Obool),tc_fun(tc_fun(U_19727,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(U_19727,tc_HOL_Obool))),U_19728)))),c_member(U_19727)))),
    inference(variable_rename,[status(thm)],[f_4767_1]) ).

cnf(f_4767_3,plain,
    c_Complete__Lattice_OSup__class_OSup(tc_fun(U_19727,tc_HOL_Obool),U_19728) = hAPP(c_Set_OCollect(U_19727),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_19727,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,U_19727),c_HOL_OEx(tc_fun(U_19727,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_19727,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_19727,tc_HOL_Obool),tc_HOL_Obool),U_19727),hAPP(c_COMBS(tc_fun(U_19727,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(U_19727,tc_HOL_Obool)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(U_19727,tc_HOL_Obool),tc_fun(tc_fun(U_19727,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(U_19727,tc_HOL_Obool))),U_19728)))),c_member(U_19727)))),
    inference(clausify,[status(thm)],[f_4767_2]) ).

fof(f_4768_1,plain,
    ! [V_P_2,V_xs_2,T_b] :
      ( ( ? [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) )
        | ~ c_List_Olist__ex(T_b,V_P_2,V_xs_2) )
      & ( c_List_Olist__ex(T_b,V_P_2,V_xs_2)
        | ! [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ),
    inference(fof_nnf,[status(thm)],[fact_Bex__set__list__ex]) ).

fof(f_4768_2,plain,
    ! [U_19733,U_19732,U_19731] :
      ( ( ? [U_19730] :
            ( hBOOL(hAPP(U_19733,U_19730))
            & hBOOL(hAPP(hAPP(c_member(U_19731),U_19730),hAPP(c_List_Oset(U_19731),U_19732))) )
        | ~ c_List_Olist__ex(U_19731,U_19733,U_19732) )
      & ( c_List_Olist__ex(U_19731,U_19733,U_19732)
        | ! [U_19729] :
            ( ~ hBOOL(hAPP(U_19733,U_19729))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19731),U_19729),hAPP(c_List_Oset(U_19731),U_19732))) ) ) ),
    inference(variable_rename,[status(thm)],[f_4768_1]) ).

fof(f_4768_3,plain,
    ( ! [U_19739,U_19737,U_19735] :
        ( ? [U_19730] :
            ( hBOOL(hAPP(U_19739,U_19730))
            & hBOOL(hAPP(hAPP(c_member(U_19735),U_19730),hAPP(c_List_Oset(U_19735),U_19737))) )
        | ~ c_List_Olist__ex(U_19735,U_19739,U_19737) )
    & ! [U_19738,U_19736,U_19734] :
        ( c_List_Olist__ex(U_19734,U_19738,U_19736)
        | ! [U_19729] :
            ( ~ hBOOL(hAPP(U_19738,U_19729))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19734),U_19729),hAPP(c_List_Oset(U_19734),U_19736))) ) ) ),
    inference(miniscope,[status(thm)],[f_4768_2]) ).

fof(f_4768_4,plain,
    ( ! [U_19739,U_19737,U_19735] :
        ( ( hBOOL(hAPP(U_19739,sK527(U_19739,U_19737,U_19735)))
          & hBOOL(hAPP(hAPP(c_member(U_19735),sK527(U_19739,U_19737,U_19735)),hAPP(c_List_Oset(U_19735),U_19737))) )
        | ~ c_List_Olist__ex(U_19735,U_19739,U_19737) )
    & ! [U_19738,U_19736,U_19734] :
        ( c_List_Olist__ex(U_19734,U_19738,U_19736)
        | ! [U_19729] :
            ( ~ hBOOL(hAPP(U_19738,U_19729))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19734),U_19729),hAPP(c_List_Oset(U_19734),U_19736))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK527]),skolemize(U_19730,sK527(U_19739,U_19737,U_19735))],[f_4768_3]) ).

cnf(f_4768_5,plain,
    ( c_List_Olist__ex(U_19734,U_19738,U_19736)
    | ~ hBOOL(hAPP(U_19738,U_19729))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19734),U_19729),hAPP(c_List_Oset(U_19734),U_19736))) ),
    inference(clausify,[status(thm)],[f_4768_4]) ).

cnf(f_4768_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19735),sK527(U_19739,U_19737,U_19735)),hAPP(c_List_Oset(U_19735),U_19737)))
    | ~ c_List_Olist__ex(U_19735,U_19739,U_19737) ),
    inference(clausify,[status(thm)],[f_4768_4]) ).

cnf(f_4768_7,plain,
    ( hBOOL(hAPP(U_19739,sK527(U_19739,U_19737,U_19735)))
    | ~ c_List_Olist__ex(U_19735,U_19739,U_19737) ),
    inference(clausify,[status(thm)],[f_4768_4]) ).

fof(f_4769_1,plain,
    ! [V_xs_2,V_P_2,T_b] :
      ( ( c_List_Olist__ex(T_b,V_P_2,V_xs_2)
        | ! [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) ) )
      & ( ? [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) )
        | ~ c_List_Olist__ex(T_b,V_P_2,V_xs_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__ex__iff__raw]) ).

fof(f_4769_2,plain,
    ! [U_19744,U_19743,U_19742] :
      ( ( c_List_Olist__ex(U_19742,U_19743,U_19744)
        | ! [U_19741] :
            ( ~ hBOOL(hAPP(U_19743,U_19741))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19742),U_19741),hAPP(c_List_Oset(U_19742),U_19744))) ) )
      & ( ? [U_19740] :
            ( hBOOL(hAPP(U_19743,U_19740))
            & hBOOL(hAPP(hAPP(c_member(U_19742),U_19740),hAPP(c_List_Oset(U_19742),U_19744))) )
        | ~ c_List_Olist__ex(U_19742,U_19743,U_19744) ) ),
    inference(variable_rename,[status(thm)],[f_4769_1]) ).

fof(f_4769_3,plain,
    ( ! [U_19750,U_19748,U_19746] :
        ( c_List_Olist__ex(U_19746,U_19748,U_19750)
        | ! [U_19741] :
            ( ~ hBOOL(hAPP(U_19748,U_19741))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19746),U_19741),hAPP(c_List_Oset(U_19746),U_19750))) ) )
    & ! [U_19749,U_19747,U_19745] :
        ( ? [U_19740] :
            ( hBOOL(hAPP(U_19747,U_19740))
            & hBOOL(hAPP(hAPP(c_member(U_19745),U_19740),hAPP(c_List_Oset(U_19745),U_19749))) )
        | ~ c_List_Olist__ex(U_19745,U_19747,U_19749) ) ),
    inference(miniscope,[status(thm)],[f_4769_2]) ).

fof(f_4769_4,plain,
    ( ! [U_19750,U_19748,U_19746] :
        ( c_List_Olist__ex(U_19746,U_19748,U_19750)
        | ! [U_19741] :
            ( ~ hBOOL(hAPP(U_19748,U_19741))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19746),U_19741),hAPP(c_List_Oset(U_19746),U_19750))) ) )
    & ! [U_19749,U_19747,U_19745] :
        ( ( hBOOL(hAPP(U_19747,sK528(U_19749,U_19747,U_19745)))
          & hBOOL(hAPP(hAPP(c_member(U_19745),sK528(U_19749,U_19747,U_19745)),hAPP(c_List_Oset(U_19745),U_19749))) )
        | ~ c_List_Olist__ex(U_19745,U_19747,U_19749) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK528]),skolemize(U_19740,sK528(U_19749,U_19747,U_19745))],[f_4769_3]) ).

cnf(f_4769_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19745),sK528(U_19749,U_19747,U_19745)),hAPP(c_List_Oset(U_19745),U_19749)))
    | ~ c_List_Olist__ex(U_19745,U_19747,U_19749) ),
    inference(clausify,[status(thm)],[f_4769_4]) ).

cnf(f_4769_6,plain,
    ( hBOOL(hAPP(U_19747,sK528(U_19749,U_19747,U_19745)))
    | ~ c_List_Olist__ex(U_19745,U_19747,U_19749) ),
    inference(clausify,[status(thm)],[f_4769_4]) ).

cnf(f_4769_7,plain,
    ( c_List_Olist__ex(U_19746,U_19748,U_19750)
    | ~ hBOOL(hAPP(U_19748,U_19741))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19746),U_19741),hAPP(c_List_Oset(U_19746),U_19750))) ),
    inference(clausify,[status(thm)],[f_4769_4]) ).

fof(f_4770_1,plain,
    ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_OCollect(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c)),c_fequal)),V_B_2))))),
    inference(fof_nnf,[status(thm)],[fact_UN__eq]) ).

fof(f_4770_2,plain,
    ! [U_19754,U_19753,U_19752,U_19751] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_19751,tc_fun(U_19752,tc_HOL_Obool)),U_19753),U_19754) = c_Complete__Lattice_OSup__class_OSup(tc_fun(U_19752,tc_HOL_Obool),hAPP(c_Set_OCollect(tc_fun(U_19752,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_19751,tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_19752,tc_HOL_Obool)),c_HOL_OEx(U_19751)),hAPP(hAPP(c_COMBB(tc_fun(U_19751,tc_HOL_Obool),tc_fun(U_19751,tc_HOL_Obool),tc_fun(U_19752,tc_HOL_Obool)),hAPP(c_COMBS(U_19751,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_19751),c_fconj),hAPP(hAPP(c_COMBC(U_19751,tc_fun(U_19751,tc_HOL_Obool),tc_HOL_Obool),c_member(U_19751)),U_19753)))),hAPP(hAPP(c_COMBC(tc_fun(U_19752,tc_HOL_Obool),tc_fun(U_19751,tc_fun(U_19752,tc_HOL_Obool)),tc_fun(U_19751,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_19752,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_19751,tc_fun(U_19752,tc_HOL_Obool)),tc_fun(U_19751,tc_HOL_Obool)),tc_fun(U_19752,tc_HOL_Obool)),c_COMBB(tc_fun(U_19752,tc_HOL_Obool),tc_HOL_Obool,U_19751)),c_fequal)),U_19754))))),
    inference(variable_rename,[status(thm)],[f_4770_1]) ).

cnf(f_4770_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_19751,tc_fun(U_19752,tc_HOL_Obool)),U_19753),U_19754) = c_Complete__Lattice_OSup__class_OSup(tc_fun(U_19752,tc_HOL_Obool),hAPP(c_Set_OCollect(tc_fun(U_19752,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_19751,tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_19752,tc_HOL_Obool)),c_HOL_OEx(U_19751)),hAPP(hAPP(c_COMBB(tc_fun(U_19751,tc_HOL_Obool),tc_fun(U_19751,tc_HOL_Obool),tc_fun(U_19752,tc_HOL_Obool)),hAPP(c_COMBS(U_19751,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_19751),c_fconj),hAPP(hAPP(c_COMBC(U_19751,tc_fun(U_19751,tc_HOL_Obool),tc_HOL_Obool),c_member(U_19751)),U_19753)))),hAPP(hAPP(c_COMBC(tc_fun(U_19752,tc_HOL_Obool),tc_fun(U_19751,tc_fun(U_19752,tc_HOL_Obool)),tc_fun(U_19751,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_19752,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_19751,tc_fun(U_19752,tc_HOL_Obool)),tc_fun(U_19751,tc_HOL_Obool)),tc_fun(U_19752,tc_HOL_Obool)),c_COMBB(tc_fun(U_19752,tc_HOL_Obool),tc_HOL_Obool,U_19751)),c_fequal)),U_19754))))),
    inference(clausify,[status(thm)],[f_4770_2]) ).

fof(f_4771_1,plain,
    ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_OCollect(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c)),c_fequal)),V_B_2))))),
    inference(fof_nnf,[status(thm)],[fact_INT__eq]) ).

fof(f_4771_2,plain,
    ! [U_19758,U_19757,U_19756,U_19755] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_19755,tc_fun(U_19756,tc_HOL_Obool)),U_19757),U_19758) = c_Complete__Lattice_OInf__class_OInf(tc_fun(U_19756,tc_HOL_Obool),hAPP(c_Set_OCollect(tc_fun(U_19756,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_19755,tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_19756,tc_HOL_Obool)),c_HOL_OEx(U_19755)),hAPP(hAPP(c_COMBB(tc_fun(U_19755,tc_HOL_Obool),tc_fun(U_19755,tc_HOL_Obool),tc_fun(U_19756,tc_HOL_Obool)),hAPP(c_COMBS(U_19755,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_19755),c_fconj),hAPP(hAPP(c_COMBC(U_19755,tc_fun(U_19755,tc_HOL_Obool),tc_HOL_Obool),c_member(U_19755)),U_19757)))),hAPP(hAPP(c_COMBC(tc_fun(U_19756,tc_HOL_Obool),tc_fun(U_19755,tc_fun(U_19756,tc_HOL_Obool)),tc_fun(U_19755,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_19756,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_19755,tc_fun(U_19756,tc_HOL_Obool)),tc_fun(U_19755,tc_HOL_Obool)),tc_fun(U_19756,tc_HOL_Obool)),c_COMBB(tc_fun(U_19756,tc_HOL_Obool),tc_HOL_Obool,U_19755)),c_fequal)),U_19758))))),
    inference(variable_rename,[status(thm)],[f_4771_1]) ).

cnf(f_4771_3,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_19755,tc_fun(U_19756,tc_HOL_Obool)),U_19757),U_19758) = c_Complete__Lattice_OInf__class_OInf(tc_fun(U_19756,tc_HOL_Obool),hAPP(c_Set_OCollect(tc_fun(U_19756,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_19755,tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_19756,tc_HOL_Obool)),c_HOL_OEx(U_19755)),hAPP(hAPP(c_COMBB(tc_fun(U_19755,tc_HOL_Obool),tc_fun(U_19755,tc_HOL_Obool),tc_fun(U_19756,tc_HOL_Obool)),hAPP(c_COMBS(U_19755,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_19755),c_fconj),hAPP(hAPP(c_COMBC(U_19755,tc_fun(U_19755,tc_HOL_Obool),tc_HOL_Obool),c_member(U_19755)),U_19757)))),hAPP(hAPP(c_COMBC(tc_fun(U_19756,tc_HOL_Obool),tc_fun(U_19755,tc_fun(U_19756,tc_HOL_Obool)),tc_fun(U_19755,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_19756,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_19755,tc_fun(U_19756,tc_HOL_Obool)),tc_fun(U_19755,tc_HOL_Obool)),tc_fun(U_19756,tc_HOL_Obool)),c_COMBB(tc_fun(U_19756,tc_HOL_Obool),tc_HOL_Obool,U_19755)),c_fequal)),U_19758))))),
    inference(clausify,[status(thm)],[f_4771_2]) ).

fof(f_4772_1,plain,
    ! [V_x_2,V_A_2,T_c,T_b] :
      ( hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,T_b),V_A_2),V_x_2) = c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_fun(T_c,T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_fun(T_c,T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_c,T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_c,T_b))),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_fun(T_c,T_b))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),T_c,T_b),c_COMBI(tc_fun(T_c,T_b))),V_x_2))))))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__fun__def]) ).

fof(f_4772_2,plain,
    ! [U_19762,U_19761,U_19760,U_19759] :
      ( hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(U_19760,U_19759),U_19761),U_19762) = c_Complete__Lattice_OSup__class_OSup(U_19759,hAPP(c_Set_OCollect(U_19759),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_19760,U_19759),tc_HOL_Obool),tc_HOL_Obool,U_19759),c_HOL_OEx(tc_fun(U_19760,U_19759))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_19760,U_19759),tc_HOL_Obool),tc_fun(tc_fun(U_19760,U_19759),tc_HOL_Obool),U_19759),hAPP(c_COMBS(tc_fun(U_19760,U_19759),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(U_19760,U_19759)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(U_19760,U_19759),tc_fun(tc_fun(U_19760,U_19759),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(U_19760,U_19759))),U_19761)))),hAPP(hAPP(c_COMBC(U_19759,tc_fun(tc_fun(U_19760,U_19759),U_19759),tc_fun(tc_fun(U_19760,U_19759),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_19759,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(U_19760,U_19759),U_19759),tc_fun(tc_fun(U_19760,U_19759),tc_HOL_Obool)),U_19759),c_COMBB(U_19759,tc_HOL_Obool,tc_fun(U_19760,U_19759))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(U_19760,U_19759),U_19760,U_19759),c_COMBI(tc_fun(U_19760,U_19759))),U_19762))))))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_19759) ),
    inference(variable_rename,[status(thm)],[f_4772_1]) ).

cnf(f_4772_3,plain,
    ( hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(U_19760,U_19759),U_19761),U_19762) = c_Complete__Lattice_OSup__class_OSup(U_19759,hAPP(c_Set_OCollect(U_19759),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_19760,U_19759),tc_HOL_Obool),tc_HOL_Obool,U_19759),c_HOL_OEx(tc_fun(U_19760,U_19759))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_19760,U_19759),tc_HOL_Obool),tc_fun(tc_fun(U_19760,U_19759),tc_HOL_Obool),U_19759),hAPP(c_COMBS(tc_fun(U_19760,U_19759),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(U_19760,U_19759)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(U_19760,U_19759),tc_fun(tc_fun(U_19760,U_19759),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(U_19760,U_19759))),U_19761)))),hAPP(hAPP(c_COMBC(U_19759,tc_fun(tc_fun(U_19760,U_19759),U_19759),tc_fun(tc_fun(U_19760,U_19759),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_19759,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(U_19760,U_19759),U_19759),tc_fun(tc_fun(U_19760,U_19759),tc_HOL_Obool)),U_19759),c_COMBB(U_19759,tc_HOL_Obool,tc_fun(U_19760,U_19759))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(U_19760,U_19759),U_19760,U_19759),c_COMBI(tc_fun(U_19760,U_19759))),U_19762))))))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_19759) ),
    inference(clausify,[status(thm)],[f_4772_2]) ).

fof(f_4773_1,plain,
    ! [V_x_2,V_A_2,T_c,T_b] :
      ( hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,T_b),V_A_2),V_x_2) = c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_fun(T_c,T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_fun(T_c,T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_c,T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_c,T_b))),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_fun(T_c,T_b))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),T_c,T_b),c_COMBI(tc_fun(T_c,T_b))),V_x_2))))))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Sup__apply]) ).

fof(f_4773_2,plain,
    ! [U_19766,U_19765,U_19764,U_19763] :
      ( hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(U_19764,U_19763),U_19765),U_19766) = c_Complete__Lattice_OSup__class_OSup(U_19763,hAPP(c_Set_OCollect(U_19763),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_19764,U_19763),tc_HOL_Obool),tc_HOL_Obool,U_19763),c_HOL_OEx(tc_fun(U_19764,U_19763))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_19764,U_19763),tc_HOL_Obool),tc_fun(tc_fun(U_19764,U_19763),tc_HOL_Obool),U_19763),hAPP(c_COMBS(tc_fun(U_19764,U_19763),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(U_19764,U_19763)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(U_19764,U_19763),tc_fun(tc_fun(U_19764,U_19763),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(U_19764,U_19763))),U_19765)))),hAPP(hAPP(c_COMBC(U_19763,tc_fun(tc_fun(U_19764,U_19763),U_19763),tc_fun(tc_fun(U_19764,U_19763),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_19763,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(U_19764,U_19763),U_19763),tc_fun(tc_fun(U_19764,U_19763),tc_HOL_Obool)),U_19763),c_COMBB(U_19763,tc_HOL_Obool,tc_fun(U_19764,U_19763))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(U_19764,U_19763),U_19764,U_19763),c_COMBI(tc_fun(U_19764,U_19763))),U_19766))))))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_19763) ),
    inference(variable_rename,[status(thm)],[f_4773_1]) ).

cnf(f_4773_3,plain,
    ( hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(U_19764,U_19763),U_19765),U_19766) = c_Complete__Lattice_OSup__class_OSup(U_19763,hAPP(c_Set_OCollect(U_19763),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_19764,U_19763),tc_HOL_Obool),tc_HOL_Obool,U_19763),c_HOL_OEx(tc_fun(U_19764,U_19763))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_19764,U_19763),tc_HOL_Obool),tc_fun(tc_fun(U_19764,U_19763),tc_HOL_Obool),U_19763),hAPP(c_COMBS(tc_fun(U_19764,U_19763),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(U_19764,U_19763)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(U_19764,U_19763),tc_fun(tc_fun(U_19764,U_19763),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(U_19764,U_19763))),U_19765)))),hAPP(hAPP(c_COMBC(U_19763,tc_fun(tc_fun(U_19764,U_19763),U_19763),tc_fun(tc_fun(U_19764,U_19763),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_19763,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(U_19764,U_19763),U_19763),tc_fun(tc_fun(U_19764,U_19763),tc_HOL_Obool)),U_19763),c_COMBB(U_19763,tc_HOL_Obool,tc_fun(U_19764,U_19763))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(U_19764,U_19763),U_19764,U_19763),c_COMBI(tc_fun(U_19764,U_19763))),U_19766))))))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_19763) ),
    inference(clausify,[status(thm)],[f_4773_2]) ).

fof(f_4774_1,plain,
    ! [V_x_2,V_A_2,T_c,T_b] :
      ( hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,T_b),V_A_2),V_x_2) = c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_fun(T_c,T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_fun(T_c,T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_c,T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_c,T_b))),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_fun(T_c,T_b))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),T_c,T_b),c_COMBI(tc_fun(T_c,T_b))),V_x_2))))))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__fun__def]) ).

fof(f_4774_2,plain,
    ! [U_19770,U_19769,U_19768,U_19767] :
      ( hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(U_19768,U_19767),U_19769),U_19770) = c_Complete__Lattice_OInf__class_OInf(U_19767,hAPP(c_Set_OCollect(U_19767),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_19768,U_19767),tc_HOL_Obool),tc_HOL_Obool,U_19767),c_HOL_OEx(tc_fun(U_19768,U_19767))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_19768,U_19767),tc_HOL_Obool),tc_fun(tc_fun(U_19768,U_19767),tc_HOL_Obool),U_19767),hAPP(c_COMBS(tc_fun(U_19768,U_19767),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(U_19768,U_19767)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(U_19768,U_19767),tc_fun(tc_fun(U_19768,U_19767),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(U_19768,U_19767))),U_19769)))),hAPP(hAPP(c_COMBC(U_19767,tc_fun(tc_fun(U_19768,U_19767),U_19767),tc_fun(tc_fun(U_19768,U_19767),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_19767,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(U_19768,U_19767),U_19767),tc_fun(tc_fun(U_19768,U_19767),tc_HOL_Obool)),U_19767),c_COMBB(U_19767,tc_HOL_Obool,tc_fun(U_19768,U_19767))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(U_19768,U_19767),U_19768,U_19767),c_COMBI(tc_fun(U_19768,U_19767))),U_19770))))))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_19767) ),
    inference(variable_rename,[status(thm)],[f_4774_1]) ).

cnf(f_4774_3,plain,
    ( hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(U_19768,U_19767),U_19769),U_19770) = c_Complete__Lattice_OInf__class_OInf(U_19767,hAPP(c_Set_OCollect(U_19767),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_19768,U_19767),tc_HOL_Obool),tc_HOL_Obool,U_19767),c_HOL_OEx(tc_fun(U_19768,U_19767))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_19768,U_19767),tc_HOL_Obool),tc_fun(tc_fun(U_19768,U_19767),tc_HOL_Obool),U_19767),hAPP(c_COMBS(tc_fun(U_19768,U_19767),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(U_19768,U_19767)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(U_19768,U_19767),tc_fun(tc_fun(U_19768,U_19767),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(U_19768,U_19767))),U_19769)))),hAPP(hAPP(c_COMBC(U_19767,tc_fun(tc_fun(U_19768,U_19767),U_19767),tc_fun(tc_fun(U_19768,U_19767),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_19767,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(U_19768,U_19767),U_19767),tc_fun(tc_fun(U_19768,U_19767),tc_HOL_Obool)),U_19767),c_COMBB(U_19767,tc_HOL_Obool,tc_fun(U_19768,U_19767))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(U_19768,U_19767),U_19768,U_19767),c_COMBI(tc_fun(U_19768,U_19767))),U_19770))))))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_19767) ),
    inference(clausify,[status(thm)],[f_4774_2]) ).

fof(f_4775_1,plain,
    ! [V_x_2,V_A_2,T_c,T_b] :
      ( hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,T_b),V_A_2),V_x_2) = c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_fun(T_c,T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_fun(T_c,T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_c,T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_c,T_b))),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_fun(T_c,T_b))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),T_c,T_b),c_COMBI(tc_fun(T_c,T_b))),V_x_2))))))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Inf__apply]) ).

fof(f_4775_2,plain,
    ! [U_19774,U_19773,U_19772,U_19771] :
      ( hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(U_19772,U_19771),U_19773),U_19774) = c_Complete__Lattice_OInf__class_OInf(U_19771,hAPP(c_Set_OCollect(U_19771),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_19772,U_19771),tc_HOL_Obool),tc_HOL_Obool,U_19771),c_HOL_OEx(tc_fun(U_19772,U_19771))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_19772,U_19771),tc_HOL_Obool),tc_fun(tc_fun(U_19772,U_19771),tc_HOL_Obool),U_19771),hAPP(c_COMBS(tc_fun(U_19772,U_19771),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(U_19772,U_19771)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(U_19772,U_19771),tc_fun(tc_fun(U_19772,U_19771),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(U_19772,U_19771))),U_19773)))),hAPP(hAPP(c_COMBC(U_19771,tc_fun(tc_fun(U_19772,U_19771),U_19771),tc_fun(tc_fun(U_19772,U_19771),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_19771,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(U_19772,U_19771),U_19771),tc_fun(tc_fun(U_19772,U_19771),tc_HOL_Obool)),U_19771),c_COMBB(U_19771,tc_HOL_Obool,tc_fun(U_19772,U_19771))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(U_19772,U_19771),U_19772,U_19771),c_COMBI(tc_fun(U_19772,U_19771))),U_19774))))))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_19771) ),
    inference(variable_rename,[status(thm)],[f_4775_1]) ).

cnf(f_4775_3,plain,
    ( hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(U_19772,U_19771),U_19773),U_19774) = c_Complete__Lattice_OInf__class_OInf(U_19771,hAPP(c_Set_OCollect(U_19771),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_19772,U_19771),tc_HOL_Obool),tc_HOL_Obool,U_19771),c_HOL_OEx(tc_fun(U_19772,U_19771))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_19772,U_19771),tc_HOL_Obool),tc_fun(tc_fun(U_19772,U_19771),tc_HOL_Obool),U_19771),hAPP(c_COMBS(tc_fun(U_19772,U_19771),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(U_19772,U_19771)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(U_19772,U_19771),tc_fun(tc_fun(U_19772,U_19771),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(U_19772,U_19771))),U_19773)))),hAPP(hAPP(c_COMBC(U_19771,tc_fun(tc_fun(U_19772,U_19771),U_19771),tc_fun(tc_fun(U_19772,U_19771),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_19771,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(U_19772,U_19771),U_19771),tc_fun(tc_fun(U_19772,U_19771),tc_HOL_Obool)),U_19771),c_COMBB(U_19771,tc_HOL_Obool,tc_fun(U_19772,U_19771))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(U_19772,U_19771),U_19772,U_19771),c_COMBI(tc_fun(U_19772,U_19771))),U_19774))))))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_19771) ),
    inference(clausify,[status(thm)],[f_4775_2]) ).

fof(f_4776_1,plain,
    ! [V_R_2,V_Y_2,V_X_2,T_b] :
      ( c_Wellfounded_Omax__extp(T_b,V_R_2,V_X_2,V_Y_2)
      | ? [B_x] :
          ( ! [B_xa] :
              ( ~ hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa))
              | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_Y_2)) )
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_X_2)) )
      | V_Y_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Y_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2)) ),
    inference(fof_nnf,[status(thm)],[fact_max__extp_Ointros]) ).

fof(f_4776_2,plain,
    ! [U_19780,U_19779,U_19778,U_19777] :
      ( c_Wellfounded_Omax__extp(U_19777,U_19780,U_19778,U_19779)
      | ? [U_19776] :
          ( ! [U_19775] :
              ( ~ hBOOL(hAPP(hAPP(U_19780,U_19776),U_19775))
              | ~ hBOOL(hAPP(hAPP(c_member(U_19777),U_19775),U_19779)) )
          & hBOOL(hAPP(hAPP(c_member(U_19777),U_19776),U_19778)) )
      | U_19779 = c_Orderings_Obot__class_Obot(tc_fun(U_19777,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19777),U_19779))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19777),U_19778)) ),
    inference(variable_rename,[status(thm)],[f_4776_1]) ).

fof(f_4776_3,plain,
    ! [U_19780,U_19779,U_19778,U_19777] :
      ( c_Wellfounded_Omax__extp(U_19777,U_19780,U_19778,U_19779)
      | ( ! [U_19775] :
            ( ~ hBOOL(hAPP(hAPP(U_19780,sK529(U_19780,U_19779,U_19778,U_19777)),U_19775))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19777),U_19775),U_19779)) )
        & hBOOL(hAPP(hAPP(c_member(U_19777),sK529(U_19780,U_19779,U_19778,U_19777)),U_19778)) )
      | U_19779 = c_Orderings_Obot__class_Obot(tc_fun(U_19777,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19777),U_19779))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19777),U_19778)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK529]),skolemize(U_19776,sK529(U_19780,U_19779,U_19778,U_19777))],[f_4776_2]) ).

cnf(f_4776_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19777),sK529(U_19780,U_19779,U_19778,U_19777)),U_19778))
    | c_Wellfounded_Omax__extp(U_19777,U_19780,U_19778,U_19779)
    | U_19779 = c_Orderings_Obot__class_Obot(tc_fun(U_19777,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19777),U_19779))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19777),U_19778)) ),
    inference(clausify,[status(thm)],[f_4776_3]) ).

cnf(f_4776_5,plain,
    ( ~ hBOOL(hAPP(hAPP(U_19780,sK529(U_19780,U_19779,U_19778,U_19777)),U_19775))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19777),U_19775),U_19779))
    | c_Wellfounded_Omax__extp(U_19777,U_19780,U_19778,U_19779)
    | U_19779 = c_Orderings_Obot__class_Obot(tc_fun(U_19777,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19777),U_19779))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19777),U_19778)) ),
    inference(clausify,[status(thm)],[f_4776_3]) ).

fof(f_4777_1,plain,
    ! [V_r_2,T_b] :
      ( ( c_Predicate_Otransp(T_b,V_r_2)
        | ~ c_Relation_Otrans(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))) )
      & ( c_Relation_Otrans(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2)))
        | ~ c_Predicate_Otransp(T_b,V_r_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_transp__def]) ).

fof(f_4777_2,plain,
    ! [U_19782,U_19781] :
      ( ( c_Predicate_Otransp(U_19781,U_19782)
        | ~ c_Relation_Otrans(U_19781,hAPP(c_Set_OCollect(tc_prod(U_19781,U_19781)),hAPP(c_Product__Type_Oprod_Oprod__case(U_19781,U_19781,tc_HOL_Obool),U_19782))) )
      & ( c_Relation_Otrans(U_19781,hAPP(c_Set_OCollect(tc_prod(U_19781,U_19781)),hAPP(c_Product__Type_Oprod_Oprod__case(U_19781,U_19781,tc_HOL_Obool),U_19782)))
        | ~ c_Predicate_Otransp(U_19781,U_19782) ) ),
    inference(variable_rename,[status(thm)],[f_4777_1]) ).

fof(f_4777_3,plain,
    ( ! [U_19786,U_19784] :
        ( c_Predicate_Otransp(U_19784,U_19786)
        | ~ c_Relation_Otrans(U_19784,hAPP(c_Set_OCollect(tc_prod(U_19784,U_19784)),hAPP(c_Product__Type_Oprod_Oprod__case(U_19784,U_19784,tc_HOL_Obool),U_19786))) )
    & ! [U_19785,U_19783] :
        ( c_Relation_Otrans(U_19783,hAPP(c_Set_OCollect(tc_prod(U_19783,U_19783)),hAPP(c_Product__Type_Oprod_Oprod__case(U_19783,U_19783,tc_HOL_Obool),U_19785)))
        | ~ c_Predicate_Otransp(U_19783,U_19785) ) ),
    inference(miniscope,[status(thm)],[f_4777_2]) ).

cnf(f_4777_4,plain,
    ( c_Relation_Otrans(U_19783,hAPP(c_Set_OCollect(tc_prod(U_19783,U_19783)),hAPP(c_Product__Type_Oprod_Oprod__case(U_19783,U_19783,tc_HOL_Obool),U_19785)))
    | ~ c_Predicate_Otransp(U_19783,U_19785) ),
    inference(clausify,[status(thm)],[f_4777_3]) ).

cnf(f_4777_5,plain,
    ( c_Predicate_Otransp(U_19784,U_19786)
    | ~ c_Relation_Otrans(U_19784,hAPP(c_Set_OCollect(tc_prod(U_19784,U_19784)),hAPP(c_Product__Type_Oprod_Oprod__case(U_19784,U_19784,tc_HOL_Obool),U_19786))) ),
    inference(clausify,[status(thm)],[f_4777_3]) ).

fof(f_4778_1,plain,
    ! [V_z_2,V_y_2,V_x_2,V_r_2,T_b] :
      ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_z_2))
      | ~ hBOOL(hAPP(hAPP(V_r_2,V_y_2),V_z_2))
      | ~ hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2))
      | ~ c_Predicate_Otransp(T_b,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_transpE]) ).

fof(f_4778_2,plain,
    ! [U_19791,U_19790,U_19789,U_19788,U_19787] :
      ( hBOOL(hAPP(hAPP(U_19788,U_19789),U_19791))
      | ~ hBOOL(hAPP(hAPP(U_19788,U_19790),U_19791))
      | ~ hBOOL(hAPP(hAPP(U_19788,U_19789),U_19790))
      | ~ c_Predicate_Otransp(U_19787,U_19788) ),
    inference(variable_rename,[status(thm)],[f_4778_1]) ).

fof(f_4778_3,plain,
    ! [U_19791,U_19790,U_19789,U_19788] :
      ( ! [U_19787] : ~ c_Predicate_Otransp(U_19787,U_19788)
      | hBOOL(hAPP(hAPP(U_19788,U_19789),U_19791))
      | ~ hBOOL(hAPP(hAPP(U_19788,U_19790),U_19791))
      | ~ hBOOL(hAPP(hAPP(U_19788,U_19789),U_19790)) ),
    inference(miniscope,[status(thm)],[f_4778_2]) ).

cnf(f_4778_4,plain,
    ( ~ c_Predicate_Otransp(U_19787,U_19788)
    | hBOOL(hAPP(hAPP(U_19788,U_19789),U_19791))
    | ~ hBOOL(hAPP(hAPP(U_19788,U_19790),U_19791))
    | ~ hBOOL(hAPP(hAPP(U_19788,U_19789),U_19790)) ),
    inference(clausify,[status(thm)],[f_4778_3]) ).

fof(f_4779_1,plain,
    ! [V_R_2,T_b] :
      ( ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
        | ~ c_Predicate_Otransp(T_b,V_R_2)
        | ~ c_Predicate_Osymp(T_b,V_R_2)
        | ~ c_Predicate_Oreflp(T_b,V_R_2) )
      & ( ( c_Predicate_Otransp(T_b,V_R_2)
          & c_Predicate_Osymp(T_b,V_R_2)
          & c_Predicate_Oreflp(T_b,V_R_2) )
        | ~ c_Equiv__Relations_Oequivp(T_b,V_R_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_equivp__reflp__symp__transp]) ).

fof(f_4779_2,plain,
    ! [U_19793,U_19792] :
      ( ( c_Equiv__Relations_Oequivp(U_19792,U_19793)
        | ~ c_Predicate_Otransp(U_19792,U_19793)
        | ~ c_Predicate_Osymp(U_19792,U_19793)
        | ~ c_Predicate_Oreflp(U_19792,U_19793) )
      & ( ( c_Predicate_Otransp(U_19792,U_19793)
          & c_Predicate_Osymp(U_19792,U_19793)
          & c_Predicate_Oreflp(U_19792,U_19793) )
        | ~ c_Equiv__Relations_Oequivp(U_19792,U_19793) ) ),
    inference(variable_rename,[status(thm)],[f_4779_1]) ).

fof(f_4779_3,plain,
    ( ! [U_19797,U_19795] :
        ( c_Equiv__Relations_Oequivp(U_19795,U_19797)
        | ~ c_Predicate_Otransp(U_19795,U_19797)
        | ~ c_Predicate_Osymp(U_19795,U_19797)
        | ~ c_Predicate_Oreflp(U_19795,U_19797) )
    & ! [U_19796,U_19794] :
        ( ( c_Predicate_Otransp(U_19794,U_19796)
          & c_Predicate_Osymp(U_19794,U_19796)
          & c_Predicate_Oreflp(U_19794,U_19796) )
        | ~ c_Equiv__Relations_Oequivp(U_19794,U_19796) ) ),
    inference(miniscope,[status(thm)],[f_4779_2]) ).

cnf(f_4779_4,plain,
    ( c_Predicate_Oreflp(U_19794,U_19796)
    | ~ c_Equiv__Relations_Oequivp(U_19794,U_19796) ),
    inference(clausify,[status(thm)],[f_4779_3]) ).

cnf(f_4779_5,plain,
    ( c_Predicate_Osymp(U_19794,U_19796)
    | ~ c_Equiv__Relations_Oequivp(U_19794,U_19796) ),
    inference(clausify,[status(thm)],[f_4779_3]) ).

cnf(f_4779_6,plain,
    ( c_Predicate_Otransp(U_19794,U_19796)
    | ~ c_Equiv__Relations_Oequivp(U_19794,U_19796) ),
    inference(clausify,[status(thm)],[f_4779_3]) ).

cnf(f_4779_7,plain,
    ( c_Equiv__Relations_Oequivp(U_19795,U_19797)
    | ~ c_Predicate_Otransp(U_19795,U_19797)
    | ~ c_Predicate_Osymp(U_19795,U_19797)
    | ~ c_Predicate_Oreflp(U_19795,U_19797) ),
    inference(clausify,[status(thm)],[f_4779_3]) ).

fof(f_4780_1,plain,
    ! [V_R_2,T_b] :
      ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
      | ~ c_Predicate_Otransp(T_b,V_R_2)
      | ~ c_Predicate_Osymp(T_b,V_R_2)
      | ~ c_Predicate_Oreflp(T_b,V_R_2) ),
    inference(fof_nnf,[status(thm)],[fact_equivpI]) ).

fof(f_4780_2,plain,
    ! [U_19799,U_19798] :
      ( c_Equiv__Relations_Oequivp(U_19798,U_19799)
      | ~ c_Predicate_Otransp(U_19798,U_19799)
      | ~ c_Predicate_Osymp(U_19798,U_19799)
      | ~ c_Predicate_Oreflp(U_19798,U_19799) ),
    inference(variable_rename,[status(thm)],[f_4780_1]) ).

cnf(f_4780_3,plain,
    ( c_Equiv__Relations_Oequivp(U_19798,U_19799)
    | ~ c_Predicate_Otransp(U_19798,U_19799)
    | ~ c_Predicate_Osymp(U_19798,U_19799)
    | ~ c_Predicate_Oreflp(U_19798,U_19799) ),
    inference(clausify,[status(thm)],[f_4780_2]) ).

fof(f_4781_1,plain,
    ! [V_y_2,V_x_2,V_r_2,T_b] :
      ( hBOOL(hAPP(hAPP(V_r_2,V_y_2),V_x_2))
      | ~ hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2))
      | ~ c_Predicate_Osymp(T_b,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_sympE]) ).

fof(f_4781_2,plain,
    ! [U_19803,U_19802,U_19801,U_19800] :
      ( hBOOL(hAPP(hAPP(U_19801,U_19803),U_19802))
      | ~ hBOOL(hAPP(hAPP(U_19801,U_19802),U_19803))
      | ~ c_Predicate_Osymp(U_19800,U_19801) ),
    inference(variable_rename,[status(thm)],[f_4781_1]) ).

fof(f_4781_3,plain,
    ! [U_19803,U_19802,U_19801] :
      ( ! [U_19800] : ~ c_Predicate_Osymp(U_19800,U_19801)
      | hBOOL(hAPP(hAPP(U_19801,U_19803),U_19802))
      | ~ hBOOL(hAPP(hAPP(U_19801,U_19802),U_19803)) ),
    inference(miniscope,[status(thm)],[f_4781_2]) ).

cnf(f_4781_4,plain,
    ( ~ c_Predicate_Osymp(U_19800,U_19801)
    | hBOOL(hAPP(hAPP(U_19801,U_19803),U_19802))
    | ~ hBOOL(hAPP(hAPP(U_19801,U_19802),U_19803)) ),
    inference(clausify,[status(thm)],[f_4781_3]) ).

fof(f_4782_1,plain,
    ! [V_R_2,T_b] :
      ( ( c_Predicate_Otransp(T_b,V_R_2)
        & c_Predicate_Osymp(T_b,V_R_2)
        & c_Predicate_Oreflp(T_b,V_R_2) )
      | ~ c_Equiv__Relations_Oequivp(T_b,V_R_2) ),
    inference(fof_nnf,[status(thm)],[fact_equivpE]) ).

fof(f_4782_2,plain,
    ! [U_19805,U_19804] :
      ( ( c_Predicate_Otransp(U_19804,U_19805)
        & c_Predicate_Osymp(U_19804,U_19805)
        & c_Predicate_Oreflp(U_19804,U_19805) )
      | ~ c_Equiv__Relations_Oequivp(U_19804,U_19805) ),
    inference(variable_rename,[status(thm)],[f_4782_1]) ).

cnf(f_4782_3,plain,
    ( c_Predicate_Oreflp(U_19804,U_19805)
    | ~ c_Equiv__Relations_Oequivp(U_19804,U_19805) ),
    inference(clausify,[status(thm)],[f_4782_2]) ).

cnf(f_4782_4,plain,
    ( c_Predicate_Osymp(U_19804,U_19805)
    | ~ c_Equiv__Relations_Oequivp(U_19804,U_19805) ),
    inference(clausify,[status(thm)],[f_4782_2]) ).

cnf(f_4782_5,plain,
    ( c_Predicate_Otransp(U_19804,U_19805)
    | ~ c_Equiv__Relations_Oequivp(U_19804,U_19805) ),
    inference(clausify,[status(thm)],[f_4782_2]) ).

fof(f_4783_1,plain,
    ! [V_a2_2,V_a1_2,V_R_2,T_b] :
      ( ( c_Wellfounded_Omax__extp(T_b,V_R_2,V_a1_2,V_a2_2)
        | ? [B_x] :
            ( ! [B_xa] :
                ( ~ hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa))
                | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2)) )
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2)) )
        | V_a2_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2)) )
      & ( ( ! [B_x] :
              ( ? [B_xa] :
                  ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa))
                  & hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2)) )
              | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2)) )
          & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2)) )
        | ~ c_Wellfounded_Omax__extp(T_b,V_R_2,V_a1_2,V_a2_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_max__extp_Osimps]) ).

fof(f_4783_2,plain,
    ! [U_19813,U_19812,U_19811,U_19810] :
      ( ( c_Wellfounded_Omax__extp(U_19810,U_19811,U_19812,U_19813)
        | ? [U_19809] :
            ( ! [U_19808] :
                ( ~ hBOOL(hAPP(hAPP(U_19811,U_19809),U_19808))
                | ~ hBOOL(hAPP(hAPP(c_member(U_19810),U_19808),U_19813)) )
            & hBOOL(hAPP(hAPP(c_member(U_19810),U_19809),U_19812)) )
        | U_19813 = c_Orderings_Obot__class_Obot(tc_fun(U_19810,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19810),U_19813))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19810),U_19812)) )
      & ( ( ! [U_19807] :
              ( ? [U_19806] :
                  ( hBOOL(hAPP(hAPP(U_19811,U_19807),U_19806))
                  & hBOOL(hAPP(hAPP(c_member(U_19810),U_19806),U_19813)) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_19810),U_19807),U_19812)) )
          & U_19813 != c_Orderings_Obot__class_Obot(tc_fun(U_19810,tc_HOL_Obool))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_19810),U_19813))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_19810),U_19812)) )
        | ~ c_Wellfounded_Omax__extp(U_19810,U_19811,U_19812,U_19813) ) ),
    inference(variable_rename,[status(thm)],[f_4783_1]) ).

fof(f_4783_3,plain,
    ( ! [U_19821,U_19819,U_19817,U_19815] :
        ( c_Wellfounded_Omax__extp(U_19815,U_19817,U_19819,U_19821)
        | ? [U_19809] :
            ( ! [U_19808] :
                ( ~ hBOOL(hAPP(hAPP(U_19817,U_19809),U_19808))
                | ~ hBOOL(hAPP(hAPP(c_member(U_19815),U_19808),U_19821)) )
            & hBOOL(hAPP(hAPP(c_member(U_19815),U_19809),U_19819)) )
        | U_19821 = c_Orderings_Obot__class_Obot(tc_fun(U_19815,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19815),U_19821))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19815),U_19819)) )
    & ! [U_19820,U_19818,U_19816,U_19814] :
        ( ( ! [U_19807] :
              ( ? [U_19806] :
                  ( hBOOL(hAPP(hAPP(U_19816,U_19807),U_19806))
                  & hBOOL(hAPP(hAPP(c_member(U_19814),U_19806),U_19820)) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_19814),U_19807),U_19818)) )
          & U_19820 != c_Orderings_Obot__class_Obot(tc_fun(U_19814,tc_HOL_Obool))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_19814),U_19820))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_19814),U_19818)) )
        | ~ c_Wellfounded_Omax__extp(U_19814,U_19816,U_19818,U_19820) ) ),
    inference(miniscope,[status(thm)],[f_4783_2]) ).

fof(f_4783_4,plain,
    ( ! [U_19821,U_19819,U_19817,U_19815] :
        ( c_Wellfounded_Omax__extp(U_19815,U_19817,U_19819,U_19821)
        | ? [U_19809] :
            ( ! [U_19808] :
                ( ~ hBOOL(hAPP(hAPP(U_19817,U_19809),U_19808))
                | ~ hBOOL(hAPP(hAPP(c_member(U_19815),U_19808),U_19821)) )
            & hBOOL(hAPP(hAPP(c_member(U_19815),U_19809),U_19819)) )
        | U_19821 = c_Orderings_Obot__class_Obot(tc_fun(U_19815,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19815),U_19821))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19815),U_19819)) )
    & ! [U_19820,U_19818,U_19816,U_19814] :
        ( ( ! [U_19807] :
              ( ( hBOOL(hAPP(hAPP(U_19816,U_19807),sK530(U_19820,U_19818,U_19816,U_19814,U_19807)))
                & hBOOL(hAPP(hAPP(c_member(U_19814),sK530(U_19820,U_19818,U_19816,U_19814,U_19807)),U_19820)) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_19814),U_19807),U_19818)) )
          & U_19820 != c_Orderings_Obot__class_Obot(tc_fun(U_19814,tc_HOL_Obool))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_19814),U_19820))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_19814),U_19818)) )
        | ~ c_Wellfounded_Omax__extp(U_19814,U_19816,U_19818,U_19820) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK530]),skolemize(U_19806,sK530(U_19820,U_19818,U_19816,U_19814,U_19807))],[f_4783_3]) ).

fof(f_4783_5,plain,
    ( ! [U_19821,U_19819,U_19817,U_19815] :
        ( c_Wellfounded_Omax__extp(U_19815,U_19817,U_19819,U_19821)
        | ( ! [U_19808] :
              ( ~ hBOOL(hAPP(hAPP(U_19817,sK531(U_19821,U_19819,U_19817,U_19815)),U_19808))
              | ~ hBOOL(hAPP(hAPP(c_member(U_19815),U_19808),U_19821)) )
          & hBOOL(hAPP(hAPP(c_member(U_19815),sK531(U_19821,U_19819,U_19817,U_19815)),U_19819)) )
        | U_19821 = c_Orderings_Obot__class_Obot(tc_fun(U_19815,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19815),U_19821))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19815),U_19819)) )
    & ! [U_19820,U_19818,U_19816,U_19814] :
        ( ( ! [U_19807] :
              ( ( hBOOL(hAPP(hAPP(U_19816,U_19807),sK530(U_19820,U_19818,U_19816,U_19814,U_19807)))
                & hBOOL(hAPP(hAPP(c_member(U_19814),sK530(U_19820,U_19818,U_19816,U_19814,U_19807)),U_19820)) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_19814),U_19807),U_19818)) )
          & U_19820 != c_Orderings_Obot__class_Obot(tc_fun(U_19814,tc_HOL_Obool))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_19814),U_19820))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_19814),U_19818)) )
        | ~ c_Wellfounded_Omax__extp(U_19814,U_19816,U_19818,U_19820) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK531]),skolemize(U_19809,sK531(U_19821,U_19819,U_19817,U_19815))],[f_4783_4]) ).

cnf(f_4783_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_19814),U_19818))
    | ~ c_Wellfounded_Omax__extp(U_19814,U_19816,U_19818,U_19820) ),
    inference(clausify,[status(thm)],[f_4783_5]) ).

cnf(f_4783_7,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_19814),U_19820))
    | ~ c_Wellfounded_Omax__extp(U_19814,U_19816,U_19818,U_19820) ),
    inference(clausify,[status(thm)],[f_4783_5]) ).

cnf(f_4783_8,plain,
    ( U_19820 != c_Orderings_Obot__class_Obot(tc_fun(U_19814,tc_HOL_Obool))
    | ~ c_Wellfounded_Omax__extp(U_19814,U_19816,U_19818,U_19820) ),
    inference(clausify,[status(thm)],[f_4783_5]) ).

cnf(f_4783_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19814),sK530(U_19820,U_19818,U_19816,U_19814,U_19807)),U_19820))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19814),U_19807),U_19818))
    | ~ c_Wellfounded_Omax__extp(U_19814,U_19816,U_19818,U_19820) ),
    inference(clausify,[status(thm)],[f_4783_5]) ).

cnf(f_4783_10,plain,
    ( hBOOL(hAPP(hAPP(U_19816,U_19807),sK530(U_19820,U_19818,U_19816,U_19814,U_19807)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19814),U_19807),U_19818))
    | ~ c_Wellfounded_Omax__extp(U_19814,U_19816,U_19818,U_19820) ),
    inference(clausify,[status(thm)],[f_4783_5]) ).

cnf(f_4783_11,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19815),sK531(U_19821,U_19819,U_19817,U_19815)),U_19819))
    | U_19821 = c_Orderings_Obot__class_Obot(tc_fun(U_19815,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19815),U_19821))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19815),U_19819))
    | c_Wellfounded_Omax__extp(U_19815,U_19817,U_19819,U_19821) ),
    inference(clausify,[status(thm)],[f_4783_5]) ).

cnf(f_4783_12,plain,
    ( ~ hBOOL(hAPP(hAPP(U_19817,sK531(U_19821,U_19819,U_19817,U_19815)),U_19808))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19815),U_19808),U_19821))
    | U_19821 = c_Orderings_Obot__class_Obot(tc_fun(U_19815,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19815),U_19821))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_19815),U_19819))
    | c_Wellfounded_Omax__extp(U_19815,U_19817,U_19819,U_19821) ),
    inference(clausify,[status(thm)],[f_4783_5]) ).

fof(f_4784_1,plain,
    ! [V_r_2,T_b] :
      ( c_Relation_Otrans(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b)))
      | ~ c_Relation_Oantisym(T_b,V_r_2)
      | ~ c_Relation_Otrans(T_b,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_trans__diff__Id]) ).

fof(f_4784_2,plain,
    ! [U_19823,U_19822] :
      ( c_Relation_Otrans(U_19822,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_19822,U_19822),tc_HOL_Obool)),U_19823),c_Relation_OId(U_19822)))
      | ~ c_Relation_Oantisym(U_19822,U_19823)
      | ~ c_Relation_Otrans(U_19822,U_19823) ),
    inference(variable_rename,[status(thm)],[f_4784_1]) ).

cnf(f_4784_3,plain,
    ( c_Relation_Otrans(U_19822,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_19822,U_19822),tc_HOL_Obool)),U_19823),c_Relation_OId(U_19822)))
    | ~ c_Relation_Oantisym(U_19822,U_19823)
    | ~ c_Relation_Otrans(U_19822,U_19823) ),
    inference(clausify,[status(thm)],[f_4784_2]) ).

fof(f_4785_1,plain,
    ! [V_A_2,T_b] : c_Relation_Oantisym(T_b,c_Relation_OId__on(T_b,V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_antisym__Id__on]) ).

fof(f_4785_2,plain,
    ! [U_19825,U_19824] : c_Relation_Oantisym(U_19824,c_Relation_OId__on(U_19824,U_19825)),
    inference(variable_rename,[status(thm)],[f_4785_1]) ).

cnf(f_4785_3,plain,
    c_Relation_Oantisym(U_19824,c_Relation_OId__on(U_19824,U_19825)),
    inference(clausify,[status(thm)],[f_4785_2]) ).

fof(f_4786_1,plain,
    ! [V_r_2,T_b] :
      ( ( c_Relation_Oantisym(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
        | ~ c_Relation_Oantisym(T_b,V_r_2) )
      & ( c_Relation_Oantisym(T_b,V_r_2)
        | ~ c_Relation_Oantisym(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_antisym__converse]) ).

fof(f_4786_2,plain,
    ! [U_19827,U_19826] :
      ( ( c_Relation_Oantisym(U_19826,hAPP(c_Relation_Oconverse(U_19826,U_19826),U_19827))
        | ~ c_Relation_Oantisym(U_19826,U_19827) )
      & ( c_Relation_Oantisym(U_19826,U_19827)
        | ~ c_Relation_Oantisym(U_19826,hAPP(c_Relation_Oconverse(U_19826,U_19826),U_19827)) ) ),
    inference(variable_rename,[status(thm)],[f_4786_1]) ).

fof(f_4786_3,plain,
    ( ! [U_19831,U_19829] :
        ( c_Relation_Oantisym(U_19829,hAPP(c_Relation_Oconverse(U_19829,U_19829),U_19831))
        | ~ c_Relation_Oantisym(U_19829,U_19831) )
    & ! [U_19830,U_19828] :
        ( c_Relation_Oantisym(U_19828,U_19830)
        | ~ c_Relation_Oantisym(U_19828,hAPP(c_Relation_Oconverse(U_19828,U_19828),U_19830)) ) ),
    inference(miniscope,[status(thm)],[f_4786_2]) ).

cnf(f_4786_4,plain,
    ( c_Relation_Oantisym(U_19828,U_19830)
    | ~ c_Relation_Oantisym(U_19828,hAPP(c_Relation_Oconverse(U_19828,U_19828),U_19830)) ),
    inference(clausify,[status(thm)],[f_4786_3]) ).

cnf(f_4786_5,plain,
    ( c_Relation_Oantisym(U_19829,hAPP(c_Relation_Oconverse(U_19829,U_19829),U_19831))
    | ~ c_Relation_Oantisym(U_19829,U_19831) ),
    inference(clausify,[status(thm)],[f_4786_3]) ).

fof(f_4787_1,plain,
    ! [T_b] : c_Relation_Oantisym(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))),
    inference(fof_nnf,[status(thm)],[fact_antisym__empty]) ).

fof(f_4787_2,plain,
    ! [U_19832] : c_Relation_Oantisym(U_19832,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_19832,U_19832),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_4787_1]) ).

cnf(f_4787_3,plain,
    c_Relation_Oantisym(U_19832,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_19832,U_19832),tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_4787_2]) ).

fof(f_4788_1,plain,
    ! [T_b] : c_Relation_Oantisym(T_b,c_Relation_OId(T_b)),
    inference(fof_nnf,[status(thm)],[fact_antisym__Id]) ).

fof(f_4788_2,plain,
    ! [U_19833] : c_Relation_Oantisym(U_19833,c_Relation_OId(U_19833)),
    inference(variable_rename,[status(thm)],[f_4788_1]) ).

cnf(f_4788_3,plain,
    c_Relation_Oantisym(U_19833,c_Relation_OId(U_19833)),
    inference(clausify,[status(thm)],[f_4788_2]) ).

fof(f_4789_1,plain,
    ! [V_s_2,V_r_2,T_b] :
      ( c_Relation_Oantisym(T_b,V_r_2)
      | ~ c_Relation_Oantisym(T_b,V_s_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ),
    inference(fof_nnf,[status(thm)],[fact_antisym__subset]) ).

fof(f_4789_2,plain,
    ! [U_19836,U_19835,U_19834] :
      ( c_Relation_Oantisym(U_19834,U_19835)
      | ~ c_Relation_Oantisym(U_19834,U_19836)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_19834,U_19834),tc_HOL_Obool)),U_19835),U_19836)) ),
    inference(variable_rename,[status(thm)],[f_4789_1]) ).

cnf(f_4789_3,plain,
    ( c_Relation_Oantisym(U_19834,U_19835)
    | ~ c_Relation_Oantisym(U_19834,U_19836)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_19834,U_19834),tc_HOL_Obool)),U_19835),U_19836)) ),
    inference(clausify,[status(thm)],[f_4789_2]) ).

fof(f_4790_1,plain,
    ! [V_r_2,T_b] :
      ( ( c_Relation_Oantisym(T_b,V_r_2)
        | ? [B_x,B_y] :
            ( B_x != B_y
            & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_x)),V_r_2))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_r_2)) ) )
      & ( ! [B_x,B_y] :
            ( B_x = B_y
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_x)),V_r_2))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_r_2)) )
        | ~ c_Relation_Oantisym(T_b,V_r_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_antisym__def]) ).

fof(f_4790_2,plain,
    ! [U_19842,U_19841] :
      ( ( c_Relation_Oantisym(U_19841,U_19842)
        | ? [U_19840,U_19839] :
            ( U_19840 != U_19839
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19841,U_19841)),hAPP(hAPP(c_Product__Type_OPair(U_19841,U_19841),U_19839),U_19840)),U_19842))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19841,U_19841)),hAPP(hAPP(c_Product__Type_OPair(U_19841,U_19841),U_19840),U_19839)),U_19842)) ) )
      & ( ! [U_19838,U_19837] :
            ( U_19838 = U_19837
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19841,U_19841)),hAPP(hAPP(c_Product__Type_OPair(U_19841,U_19841),U_19837),U_19838)),U_19842))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19841,U_19841)),hAPP(hAPP(c_Product__Type_OPair(U_19841,U_19841),U_19838),U_19837)),U_19842)) )
        | ~ c_Relation_Oantisym(U_19841,U_19842) ) ),
    inference(variable_rename,[status(thm)],[f_4790_1]) ).

fof(f_4790_3,plain,
    ( ! [U_19846,U_19844] :
        ( c_Relation_Oantisym(U_19844,U_19846)
        | ? [U_19840,U_19839] :
            ( U_19840 != U_19839
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19844,U_19844)),hAPP(hAPP(c_Product__Type_OPair(U_19844,U_19844),U_19839),U_19840)),U_19846))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19844,U_19844)),hAPP(hAPP(c_Product__Type_OPair(U_19844,U_19844),U_19840),U_19839)),U_19846)) ) )
    & ! [U_19845,U_19843] :
        ( ! [U_19838,U_19837] :
            ( U_19838 = U_19837
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19843,U_19843)),hAPP(hAPP(c_Product__Type_OPair(U_19843,U_19843),U_19837),U_19838)),U_19845))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19843,U_19843)),hAPP(hAPP(c_Product__Type_OPair(U_19843,U_19843),U_19838),U_19837)),U_19845)) )
        | ~ c_Relation_Oantisym(U_19843,U_19845) ) ),
    inference(miniscope,[status(thm)],[f_4790_2]) ).

fof(f_4790_4,plain,
    ( ! [U_19846,U_19844] :
        ( c_Relation_Oantisym(U_19844,U_19846)
        | ? [U_19839] :
            ( sK532(U_19846,U_19844) != U_19839
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19844,U_19844)),hAPP(hAPP(c_Product__Type_OPair(U_19844,U_19844),U_19839),sK532(U_19846,U_19844))),U_19846))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19844,U_19844)),hAPP(hAPP(c_Product__Type_OPair(U_19844,U_19844),sK532(U_19846,U_19844)),U_19839)),U_19846)) ) )
    & ! [U_19845,U_19843] :
        ( ! [U_19838,U_19837] :
            ( U_19838 = U_19837
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19843,U_19843)),hAPP(hAPP(c_Product__Type_OPair(U_19843,U_19843),U_19837),U_19838)),U_19845))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19843,U_19843)),hAPP(hAPP(c_Product__Type_OPair(U_19843,U_19843),U_19838),U_19837)),U_19845)) )
        | ~ c_Relation_Oantisym(U_19843,U_19845) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK532]),skolemize(U_19840,sK532(U_19846,U_19844))],[f_4790_3]) ).

fof(f_4790_5,plain,
    ( ! [U_19846,U_19844] :
        ( c_Relation_Oantisym(U_19844,U_19846)
        | ( sK532(U_19846,U_19844) != sK533(U_19846,U_19844)
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19844,U_19844)),hAPP(hAPP(c_Product__Type_OPair(U_19844,U_19844),sK533(U_19846,U_19844)),sK532(U_19846,U_19844))),U_19846))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19844,U_19844)),hAPP(hAPP(c_Product__Type_OPair(U_19844,U_19844),sK532(U_19846,U_19844)),sK533(U_19846,U_19844))),U_19846)) ) )
    & ! [U_19845,U_19843] :
        ( ! [U_19838,U_19837] :
            ( U_19838 = U_19837
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19843,U_19843)),hAPP(hAPP(c_Product__Type_OPair(U_19843,U_19843),U_19837),U_19838)),U_19845))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19843,U_19843)),hAPP(hAPP(c_Product__Type_OPair(U_19843,U_19843),U_19838),U_19837)),U_19845)) )
        | ~ c_Relation_Oantisym(U_19843,U_19845) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK533]),skolemize(U_19839,sK533(U_19846,U_19844))],[f_4790_4]) ).

cnf(f_4790_6,plain,
    ( U_19838 = U_19837
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19843,U_19843)),hAPP(hAPP(c_Product__Type_OPair(U_19843,U_19843),U_19837),U_19838)),U_19845))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19843,U_19843)),hAPP(hAPP(c_Product__Type_OPair(U_19843,U_19843),U_19838),U_19837)),U_19845))
    | ~ c_Relation_Oantisym(U_19843,U_19845) ),
    inference(clausify,[status(thm)],[f_4790_5]) ).

cnf(f_4790_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19844,U_19844)),hAPP(hAPP(c_Product__Type_OPair(U_19844,U_19844),sK532(U_19846,U_19844)),sK533(U_19846,U_19844))),U_19846))
    | c_Relation_Oantisym(U_19844,U_19846) ),
    inference(clausify,[status(thm)],[f_4790_5]) ).

cnf(f_4790_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19844,U_19844)),hAPP(hAPP(c_Product__Type_OPair(U_19844,U_19844),sK533(U_19846,U_19844)),sK532(U_19846,U_19844))),U_19846))
    | c_Relation_Oantisym(U_19844,U_19846) ),
    inference(clausify,[status(thm)],[f_4790_5]) ).

cnf(f_4790_9,plain,
    ( sK532(U_19846,U_19844) != sK533(U_19846,U_19844)
    | c_Relation_Oantisym(U_19844,U_19846) ),
    inference(clausify,[status(thm)],[f_4790_5]) ).

fof(f_4791_1,plain,
    ! [V_b_2,V_a_2,V_r_2,T_b] :
      ( V_a_2 = V_b_2
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_a_2)),V_r_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
      | ~ c_Relation_Oantisym(T_b,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_antisymD]) ).

fof(f_4791_2,plain,
    ! [U_19850,U_19849,U_19848,U_19847] :
      ( U_19849 = U_19850
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19847,U_19847)),hAPP(hAPP(c_Product__Type_OPair(U_19847,U_19847),U_19850),U_19849)),U_19848))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19847,U_19847)),hAPP(hAPP(c_Product__Type_OPair(U_19847,U_19847),U_19849),U_19850)),U_19848))
      | ~ c_Relation_Oantisym(U_19847,U_19848) ),
    inference(variable_rename,[status(thm)],[f_4791_1]) ).

cnf(f_4791_3,plain,
    ( U_19849 = U_19850
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19847,U_19847)),hAPP(hAPP(c_Product__Type_OPair(U_19847,U_19847),U_19850),U_19849)),U_19848))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19847,U_19847)),hAPP(hAPP(c_Product__Type_OPair(U_19847,U_19847),U_19849),U_19850)),U_19848))
    | ~ c_Relation_Oantisym(U_19847,U_19848) ),
    inference(clausify,[status(thm)],[f_4791_2]) ).

fof(f_4792_1,plain,
    ! [V_r_2,T_b] :
      ( ( c_Relation_Oantisym(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b)))
        | ~ c_Relation_Oantisym(T_b,V_r_2) )
      & ( c_Relation_Oantisym(T_b,V_r_2)
        | ~ c_Relation_Oantisym(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))) ) ),
    inference(fof_nnf,[status(thm)],[fact_antisym__reflcl]) ).

fof(f_4792_2,plain,
    ! [U_19852,U_19851] :
      ( ( c_Relation_Oantisym(U_19851,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_19851,U_19851),tc_HOL_Obool)),U_19852),c_Relation_OId(U_19851)))
        | ~ c_Relation_Oantisym(U_19851,U_19852) )
      & ( c_Relation_Oantisym(U_19851,U_19852)
        | ~ c_Relation_Oantisym(U_19851,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_19851,U_19851),tc_HOL_Obool)),U_19852),c_Relation_OId(U_19851))) ) ),
    inference(variable_rename,[status(thm)],[f_4792_1]) ).

fof(f_4792_3,plain,
    ( ! [U_19856,U_19854] :
        ( c_Relation_Oantisym(U_19854,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_19854,U_19854),tc_HOL_Obool)),U_19856),c_Relation_OId(U_19854)))
        | ~ c_Relation_Oantisym(U_19854,U_19856) )
    & ! [U_19855,U_19853] :
        ( c_Relation_Oantisym(U_19853,U_19855)
        | ~ c_Relation_Oantisym(U_19853,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_19853,U_19853),tc_HOL_Obool)),U_19855),c_Relation_OId(U_19853))) ) ),
    inference(miniscope,[status(thm)],[f_4792_2]) ).

cnf(f_4792_4,plain,
    ( c_Relation_Oantisym(U_19853,U_19855)
    | ~ c_Relation_Oantisym(U_19853,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_19853,U_19853),tc_HOL_Obool)),U_19855),c_Relation_OId(U_19853))) ),
    inference(clausify,[status(thm)],[f_4792_3]) ).

cnf(f_4792_5,plain,
    ( c_Relation_Oantisym(U_19854,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_19854,U_19854),tc_HOL_Obool)),U_19856),c_Relation_OId(U_19854)))
    | ~ c_Relation_Oantisym(U_19854,U_19856) ),
    inference(clausify,[status(thm)],[f_4792_3]) ).

fof(f_4793_1,plain,
    ! [V_r_2,T_b] :
      ( c_Relation_Oantisym(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2))
      | ~ c_Wellfounded_Oacyclic(T_b,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_acyclic__impl__antisym__rtrancl]) ).

fof(f_4793_2,plain,
    ! [U_19858,U_19857] :
      ( c_Relation_Oantisym(U_19857,c_Transitive__Closure_Ortrancl(U_19857,U_19858))
      | ~ c_Wellfounded_Oacyclic(U_19857,U_19858) ),
    inference(variable_rename,[status(thm)],[f_4793_1]) ).

cnf(f_4793_3,plain,
    ( c_Relation_Oantisym(U_19857,c_Transitive__Closure_Ortrancl(U_19857,U_19858))
    | ~ c_Wellfounded_Oacyclic(U_19857,U_19858) ),
    inference(clausify,[status(thm)],[f_4793_2]) ).

fof(f_4794_1,plain,
    ! [V_x_2,V_A_2,V_L_2,T_d,T_b,T_c] : c_Partial__Function_Ofun__lub(T_c,T_b,T_d,V_L_2,V_A_2,V_x_2) = hAPP(V_L_2,hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(tc_fun(T_d,T_c))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool),tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool),T_c),hAPP(c_COMBS(tc_fun(T_d,T_c),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_d,T_c)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_d,T_c),tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_d,T_c))),V_A_2)))),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_fun(T_d,T_c),T_c),tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_d,T_c),T_c),tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool)),T_c),c_COMBB(T_c,tc_HOL_Obool,tc_fun(T_d,T_c))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(T_d,T_c),T_d,T_c),c_COMBI(tc_fun(T_d,T_c))),V_x_2)))))),
    inference(fof_nnf,[status(thm)],[fact_fun__lub__def]) ).

fof(f_4794_2,plain,
    ! [U_19864,U_19863,U_19862,U_19861,U_19860,U_19859] : c_Partial__Function_Ofun__lub(U_19859,U_19860,U_19861,U_19862,U_19863,U_19864) = hAPP(U_19862,hAPP(c_Set_OCollect(U_19859),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_19861,U_19859),tc_HOL_Obool),tc_HOL_Obool,U_19859),c_HOL_OEx(tc_fun(U_19861,U_19859))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_19861,U_19859),tc_HOL_Obool),tc_fun(tc_fun(U_19861,U_19859),tc_HOL_Obool),U_19859),hAPP(c_COMBS(tc_fun(U_19861,U_19859),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(U_19861,U_19859)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(U_19861,U_19859),tc_fun(tc_fun(U_19861,U_19859),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(U_19861,U_19859))),U_19863)))),hAPP(hAPP(c_COMBC(U_19859,tc_fun(tc_fun(U_19861,U_19859),U_19859),tc_fun(tc_fun(U_19861,U_19859),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_19859,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(U_19861,U_19859),U_19859),tc_fun(tc_fun(U_19861,U_19859),tc_HOL_Obool)),U_19859),c_COMBB(U_19859,tc_HOL_Obool,tc_fun(U_19861,U_19859))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(U_19861,U_19859),U_19861,U_19859),c_COMBI(tc_fun(U_19861,U_19859))),U_19864)))))),
    inference(variable_rename,[status(thm)],[f_4794_1]) ).

cnf(f_4794_3,plain,
    c_Partial__Function_Ofun__lub(U_19859,U_19860,U_19861,U_19862,U_19863,U_19864) = hAPP(U_19862,hAPP(c_Set_OCollect(U_19859),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_19861,U_19859),tc_HOL_Obool),tc_HOL_Obool,U_19859),c_HOL_OEx(tc_fun(U_19861,U_19859))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_19861,U_19859),tc_HOL_Obool),tc_fun(tc_fun(U_19861,U_19859),tc_HOL_Obool),U_19859),hAPP(c_COMBS(tc_fun(U_19861,U_19859),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(U_19861,U_19859)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(U_19861,U_19859),tc_fun(tc_fun(U_19861,U_19859),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(U_19861,U_19859))),U_19863)))),hAPP(hAPP(c_COMBC(U_19859,tc_fun(tc_fun(U_19861,U_19859),U_19859),tc_fun(tc_fun(U_19861,U_19859),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_19859,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(U_19861,U_19859),U_19859),tc_fun(tc_fun(U_19861,U_19859),tc_HOL_Obool)),U_19859),c_COMBB(U_19859,tc_HOL_Obool,tc_fun(U_19861,U_19859))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(U_19861,U_19859),U_19861,U_19859),c_COMBI(tc_fun(U_19861,U_19859))),U_19864)))))),
    inference(clausify,[status(thm)],[f_4794_2]) ).

fof(f_4795_1,plain,
    ! [V_r_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),V_r_2)),V_r_2))
      | ~ c_Relation_Otrans(T_b,V_r_2)
      | ~ c_Relation_Osym(T_b,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_sym__trans__comp__subset]) ).

fof(f_4795_2,plain,
    ! [U_19866,U_19865] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_19865,U_19865),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_19865,U_19865,U_19865),hAPP(c_Relation_Oconverse(U_19865,U_19865),U_19866)),U_19866)),U_19866))
      | ~ c_Relation_Otrans(U_19865,U_19866)
      | ~ c_Relation_Osym(U_19865,U_19866) ),
    inference(variable_rename,[status(thm)],[f_4795_1]) ).

cnf(f_4795_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_19865,U_19865),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_19865,U_19865,U_19865),hAPP(c_Relation_Oconverse(U_19865,U_19865),U_19866)),U_19866)),U_19866))
    | ~ c_Relation_Otrans(U_19865,U_19866)
    | ~ c_Relation_Osym(U_19865,U_19866) ),
    inference(clausify,[status(thm)],[f_4795_2]) ).

fof(f_4796_1,plain,
    ! [V_b_2,V_a_2,V_r_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_a_2)),V_r_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
      | ~ c_Relation_Osym(T_b,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_symD]) ).

fof(f_4796_2,plain,
    ! [U_19870,U_19869,U_19868,U_19867] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19867,U_19867)),hAPP(hAPP(c_Product__Type_OPair(U_19867,U_19867),U_19870),U_19869)),U_19868))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19867,U_19867)),hAPP(hAPP(c_Product__Type_OPair(U_19867,U_19867),U_19869),U_19870)),U_19868))
      | ~ c_Relation_Osym(U_19867,U_19868) ),
    inference(variable_rename,[status(thm)],[f_4796_1]) ).

cnf(f_4796_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19867,U_19867)),hAPP(hAPP(c_Product__Type_OPair(U_19867,U_19867),U_19870),U_19869)),U_19868))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19867,U_19867)),hAPP(hAPP(c_Product__Type_OPair(U_19867,U_19867),U_19869),U_19870)),U_19868))
    | ~ c_Relation_Osym(U_19867,U_19868) ),
    inference(clausify,[status(thm)],[f_4796_2]) ).

fof(f_4797_1,plain,
    ! [V_r_2,T_b] :
      ( ( c_Relation_Osym(T_b,V_r_2)
        | ? [B_x,B_y] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_x)),V_r_2))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_r_2)) ) )
      & ( ! [B_x,B_y] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_x)),V_r_2))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_r_2)) )
        | ~ c_Relation_Osym(T_b,V_r_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_sym__def]) ).

fof(f_4797_2,plain,
    ! [U_19876,U_19875] :
      ( ( c_Relation_Osym(U_19875,U_19876)
        | ? [U_19874,U_19873] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19875,U_19875)),hAPP(hAPP(c_Product__Type_OPair(U_19875,U_19875),U_19873),U_19874)),U_19876))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19875,U_19875)),hAPP(hAPP(c_Product__Type_OPair(U_19875,U_19875),U_19874),U_19873)),U_19876)) ) )
      & ( ! [U_19872,U_19871] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19875,U_19875)),hAPP(hAPP(c_Product__Type_OPair(U_19875,U_19875),U_19871),U_19872)),U_19876))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19875,U_19875)),hAPP(hAPP(c_Product__Type_OPair(U_19875,U_19875),U_19872),U_19871)),U_19876)) )
        | ~ c_Relation_Osym(U_19875,U_19876) ) ),
    inference(variable_rename,[status(thm)],[f_4797_1]) ).

fof(f_4797_3,plain,
    ( ! [U_19880,U_19878] :
        ( c_Relation_Osym(U_19878,U_19880)
        | ? [U_19874,U_19873] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19878,U_19878)),hAPP(hAPP(c_Product__Type_OPair(U_19878,U_19878),U_19873),U_19874)),U_19880))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19878,U_19878)),hAPP(hAPP(c_Product__Type_OPair(U_19878,U_19878),U_19874),U_19873)),U_19880)) ) )
    & ! [U_19879,U_19877] :
        ( ! [U_19872,U_19871] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19877,U_19877)),hAPP(hAPP(c_Product__Type_OPair(U_19877,U_19877),U_19871),U_19872)),U_19879))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19877,U_19877)),hAPP(hAPP(c_Product__Type_OPair(U_19877,U_19877),U_19872),U_19871)),U_19879)) )
        | ~ c_Relation_Osym(U_19877,U_19879) ) ),
    inference(miniscope,[status(thm)],[f_4797_2]) ).

fof(f_4797_4,plain,
    ( ! [U_19880,U_19878] :
        ( c_Relation_Osym(U_19878,U_19880)
        | ? [U_19873] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19878,U_19878)),hAPP(hAPP(c_Product__Type_OPair(U_19878,U_19878),U_19873),sK534(U_19880,U_19878))),U_19880))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19878,U_19878)),hAPP(hAPP(c_Product__Type_OPair(U_19878,U_19878),sK534(U_19880,U_19878)),U_19873)),U_19880)) ) )
    & ! [U_19879,U_19877] :
        ( ! [U_19872,U_19871] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19877,U_19877)),hAPP(hAPP(c_Product__Type_OPair(U_19877,U_19877),U_19871),U_19872)),U_19879))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19877,U_19877)),hAPP(hAPP(c_Product__Type_OPair(U_19877,U_19877),U_19872),U_19871)),U_19879)) )
        | ~ c_Relation_Osym(U_19877,U_19879) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK534]),skolemize(U_19874,sK534(U_19880,U_19878))],[f_4797_3]) ).

fof(f_4797_5,plain,
    ( ! [U_19880,U_19878] :
        ( c_Relation_Osym(U_19878,U_19880)
        | ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19878,U_19878)),hAPP(hAPP(c_Product__Type_OPair(U_19878,U_19878),sK535(U_19880,U_19878)),sK534(U_19880,U_19878))),U_19880))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19878,U_19878)),hAPP(hAPP(c_Product__Type_OPair(U_19878,U_19878),sK534(U_19880,U_19878)),sK535(U_19880,U_19878))),U_19880)) ) )
    & ! [U_19879,U_19877] :
        ( ! [U_19872,U_19871] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19877,U_19877)),hAPP(hAPP(c_Product__Type_OPair(U_19877,U_19877),U_19871),U_19872)),U_19879))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19877,U_19877)),hAPP(hAPP(c_Product__Type_OPair(U_19877,U_19877),U_19872),U_19871)),U_19879)) )
        | ~ c_Relation_Osym(U_19877,U_19879) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK535]),skolemize(U_19873,sK535(U_19880,U_19878))],[f_4797_4]) ).

cnf(f_4797_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19877,U_19877)),hAPP(hAPP(c_Product__Type_OPair(U_19877,U_19877),U_19871),U_19872)),U_19879))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19877,U_19877)),hAPP(hAPP(c_Product__Type_OPair(U_19877,U_19877),U_19872),U_19871)),U_19879))
    | ~ c_Relation_Osym(U_19877,U_19879) ),
    inference(clausify,[status(thm)],[f_4797_5]) ).

cnf(f_4797_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19878,U_19878)),hAPP(hAPP(c_Product__Type_OPair(U_19878,U_19878),sK534(U_19880,U_19878)),sK535(U_19880,U_19878))),U_19880))
    | c_Relation_Osym(U_19878,U_19880) ),
    inference(clausify,[status(thm)],[f_4797_5]) ).

cnf(f_4797_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19878,U_19878)),hAPP(hAPP(c_Product__Type_OPair(U_19878,U_19878),sK535(U_19880,U_19878)),sK534(U_19880,U_19878))),U_19880))
    | c_Relation_Osym(U_19878,U_19880) ),
    inference(clausify,[status(thm)],[f_4797_5]) ).

fof(f_4798_1,plain,
    ! [V_r_2,T_b] :
      ( c_Relation_Osym(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2))
      | ~ c_Relation_Osym(T_b,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_sym__rtrancl]) ).

fof(f_4798_2,plain,
    ! [U_19882,U_19881] :
      ( c_Relation_Osym(U_19881,c_Transitive__Closure_Ortrancl(U_19881,U_19882))
      | ~ c_Relation_Osym(U_19881,U_19882) ),
    inference(variable_rename,[status(thm)],[f_4798_1]) ).

cnf(f_4798_3,plain,
    ( c_Relation_Osym(U_19881,c_Transitive__Closure_Ortrancl(U_19881,U_19882))
    | ~ c_Relation_Osym(U_19881,U_19882) ),
    inference(clausify,[status(thm)],[f_4798_2]) ).

fof(f_4799_1,plain,
    ! [T_b] : c_Relation_Osym(T_b,c_Relation_OId(T_b)),
    inference(fof_nnf,[status(thm)],[fact_sym__Id]) ).

fof(f_4799_2,plain,
    ! [U_19883] : c_Relation_Osym(U_19883,c_Relation_OId(U_19883)),
    inference(variable_rename,[status(thm)],[f_4799_1]) ).

cnf(f_4799_3,plain,
    c_Relation_Osym(U_19883,c_Relation_OId(U_19883)),
    inference(clausify,[status(thm)],[f_4799_2]) ).

fof(f_4800_1,plain,
    ! [V_s_2,V_r_2,T_b] :
      ( c_Relation_Osym(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
      | ~ c_Relation_Osym(T_b,V_s_2)
      | ~ c_Relation_Osym(T_b,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_sym__Un]) ).

fof(f_4800_2,plain,
    ! [U_19886,U_19885,U_19884] :
      ( c_Relation_Osym(U_19884,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_19884,U_19884),tc_HOL_Obool)),U_19885),U_19886))
      | ~ c_Relation_Osym(U_19884,U_19886)
      | ~ c_Relation_Osym(U_19884,U_19885) ),
    inference(variable_rename,[status(thm)],[f_4800_1]) ).

cnf(f_4800_3,plain,
    ( c_Relation_Osym(U_19884,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_19884,U_19884),tc_HOL_Obool)),U_19885),U_19886))
    | ~ c_Relation_Osym(U_19884,U_19886)
    | ~ c_Relation_Osym(U_19884,U_19885) ),
    inference(clausify,[status(thm)],[f_4800_2]) ).

fof(f_4801_1,plain,
    ! [V_r_2,T_b] :
      ( c_Relation_Osym(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2))
      | ~ c_Relation_Osym(T_b,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_sym__trancl]) ).

fof(f_4801_2,plain,
    ! [U_19888,U_19887] :
      ( c_Relation_Osym(U_19887,c_Transitive__Closure_Otrancl(U_19887,U_19888))
      | ~ c_Relation_Osym(U_19887,U_19888) ),
    inference(variable_rename,[status(thm)],[f_4801_1]) ).

cnf(f_4801_3,plain,
    ( c_Relation_Osym(U_19887,c_Transitive__Closure_Otrancl(U_19887,U_19888))
    | ~ c_Relation_Osym(U_19887,U_19888) ),
    inference(clausify,[status(thm)],[f_4801_2]) ).

fof(f_4802_1,plain,
    ! [V_A_2,T_b] : c_Relation_Osym(T_b,c_Relation_OId__on(T_b,V_A_2)),
    inference(fof_nnf,[status(thm)],[fact_sym__Id__on]) ).

fof(f_4802_2,plain,
    ! [U_19890,U_19889] : c_Relation_Osym(U_19889,c_Relation_OId__on(U_19889,U_19890)),
    inference(variable_rename,[status(thm)],[f_4802_1]) ).

cnf(f_4802_3,plain,
    c_Relation_Osym(U_19889,c_Relation_OId__on(U_19889,U_19890)),
    inference(clausify,[status(thm)],[f_4802_2]) ).

fof(f_4803_1,plain,
    ! [V_r_2,T_b] :
      ( c_Relation_Osym(tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2))
      | ~ c_Relation_Osym(T_b,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_listrel__sym]) ).

fof(f_4803_2,plain,
    ! [U_19892,U_19891] :
      ( c_Relation_Osym(tc_List_Olist(U_19891),c_List_Olistrel(U_19891,U_19892))
      | ~ c_Relation_Osym(U_19891,U_19892) ),
    inference(variable_rename,[status(thm)],[f_4803_1]) ).

cnf(f_4803_3,plain,
    ( c_Relation_Osym(tc_List_Olist(U_19891),c_List_Olistrel(U_19891,U_19892))
    | ~ c_Relation_Osym(U_19891,U_19892) ),
    inference(clausify,[status(thm)],[f_4803_2]) ).

fof(f_4804_1,plain,
    ! [V_r_2,T_b] :
      ( ( c_Relation_Osym(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
        | ~ c_Relation_Osym(T_b,V_r_2) )
      & ( c_Relation_Osym(T_b,V_r_2)
        | ~ c_Relation_Osym(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_sym__converse]) ).

fof(f_4804_2,plain,
    ! [U_19894,U_19893] :
      ( ( c_Relation_Osym(U_19893,hAPP(c_Relation_Oconverse(U_19893,U_19893),U_19894))
        | ~ c_Relation_Osym(U_19893,U_19894) )
      & ( c_Relation_Osym(U_19893,U_19894)
        | ~ c_Relation_Osym(U_19893,hAPP(c_Relation_Oconverse(U_19893,U_19893),U_19894)) ) ),
    inference(variable_rename,[status(thm)],[f_4804_1]) ).

fof(f_4804_3,plain,
    ( ! [U_19898,U_19896] :
        ( c_Relation_Osym(U_19896,hAPP(c_Relation_Oconverse(U_19896,U_19896),U_19898))
        | ~ c_Relation_Osym(U_19896,U_19898) )
    & ! [U_19897,U_19895] :
        ( c_Relation_Osym(U_19895,U_19897)
        | ~ c_Relation_Osym(U_19895,hAPP(c_Relation_Oconverse(U_19895,U_19895),U_19897)) ) ),
    inference(miniscope,[status(thm)],[f_4804_2]) ).

cnf(f_4804_4,plain,
    ( c_Relation_Osym(U_19895,U_19897)
    | ~ c_Relation_Osym(U_19895,hAPP(c_Relation_Oconverse(U_19895,U_19895),U_19897)) ),
    inference(clausify,[status(thm)],[f_4804_3]) ).

cnf(f_4804_5,plain,
    ( c_Relation_Osym(U_19896,hAPP(c_Relation_Oconverse(U_19896,U_19896),U_19898))
    | ~ c_Relation_Osym(U_19896,U_19898) ),
    inference(clausify,[status(thm)],[f_4804_3]) ).

fof(f_4805_1,plain,
    ! [V_r_2,T_b] :
      ( ( c_Relation_Osym(T_b,V_r_2)
        | hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2) != V_r_2 )
      & ( hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2) = V_r_2
        | ~ c_Relation_Osym(T_b,V_r_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_sym__conv__converse__eq]) ).

fof(f_4805_2,plain,
    ! [U_19900,U_19899] :
      ( ( c_Relation_Osym(U_19899,U_19900)
        | hAPP(c_Relation_Oconverse(U_19899,U_19899),U_19900) != U_19900 )
      & ( hAPP(c_Relation_Oconverse(U_19899,U_19899),U_19900) = U_19900
        | ~ c_Relation_Osym(U_19899,U_19900) ) ),
    inference(variable_rename,[status(thm)],[f_4805_1]) ).

fof(f_4805_3,plain,
    ( ! [U_19904,U_19902] :
        ( c_Relation_Osym(U_19902,U_19904)
        | hAPP(c_Relation_Oconverse(U_19902,U_19902),U_19904) != U_19904 )
    & ! [U_19903,U_19901] :
        ( hAPP(c_Relation_Oconverse(U_19901,U_19901),U_19903) = U_19903
        | ~ c_Relation_Osym(U_19901,U_19903) ) ),
    inference(miniscope,[status(thm)],[f_4805_2]) ).

cnf(f_4805_4,plain,
    ( hAPP(c_Relation_Oconverse(U_19901,U_19901),U_19903) = U_19903
    | ~ c_Relation_Osym(U_19901,U_19903) ),
    inference(clausify,[status(thm)],[f_4805_3]) ).

cnf(f_4805_5,plain,
    ( c_Relation_Osym(U_19902,U_19904)
    | hAPP(c_Relation_Oconverse(U_19902,U_19902),U_19904) != U_19904 ),
    inference(clausify,[status(thm)],[f_4805_3]) ).

fof(f_4806_1,plain,
    ! [V_s_2,V_r_2,T_b] :
      ( c_Relation_Osym(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
      | ~ c_Relation_Osym(T_b,V_s_2)
      | ~ c_Relation_Osym(T_b,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_sym__Int]) ).

fof(f_4806_2,plain,
    ! [U_19907,U_19906,U_19905] :
      ( c_Relation_Osym(U_19905,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_19905,U_19905),tc_HOL_Obool)),U_19906),U_19907))
      | ~ c_Relation_Osym(U_19905,U_19907)
      | ~ c_Relation_Osym(U_19905,U_19906) ),
    inference(variable_rename,[status(thm)],[f_4806_1]) ).

cnf(f_4806_3,plain,
    ( c_Relation_Osym(U_19905,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_19905,U_19905),tc_HOL_Obool)),U_19906),U_19907))
    | ~ c_Relation_Osym(U_19905,U_19907)
    | ~ c_Relation_Osym(U_19905,U_19906) ),
    inference(clausify,[status(thm)],[f_4806_2]) ).

fof(f_4807_1,plain,
    ! [V_r_2,T_b] : c_Relation_Osym(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))),
    inference(fof_nnf,[status(thm)],[fact_sym__Un__converse]) ).

fof(f_4807_2,plain,
    ! [U_19909,U_19908] : c_Relation_Osym(U_19908,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_19908,U_19908),tc_HOL_Obool)),U_19909),hAPP(c_Relation_Oconverse(U_19908,U_19908),U_19909))),
    inference(variable_rename,[status(thm)],[f_4807_1]) ).

cnf(f_4807_3,plain,
    c_Relation_Osym(U_19908,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_19908,U_19908),tc_HOL_Obool)),U_19909),hAPP(c_Relation_Oconverse(U_19908,U_19908),U_19909))),
    inference(clausify,[status(thm)],[f_4807_2]) ).

fof(f_4808_1,plain,
    ! [V_f_2,T_c,V_r_2,T_b] :
      ( c_Relation_Osym(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2))
      | ~ c_Relation_Osym(T_b,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_sym__inv__image]) ).

fof(f_4808_2,plain,
    ! [U_19913,U_19912,U_19911,U_19910] :
      ( c_Relation_Osym(U_19912,hAPP(hAPP(c_Relation_Oinv__image(U_19910,U_19912),U_19911),U_19913))
      | ~ c_Relation_Osym(U_19910,U_19911) ),
    inference(variable_rename,[status(thm)],[f_4808_1]) ).

cnf(f_4808_3,plain,
    ( c_Relation_Osym(U_19912,hAPP(hAPP(c_Relation_Oinv__image(U_19910,U_19912),U_19911),U_19913))
    | ~ c_Relation_Osym(U_19910,U_19911) ),
    inference(clausify,[status(thm)],[f_4808_2]) ).

fof(f_4809_1,plain,
    ! [V_r_2,T_b] : c_Relation_Osym(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))),
    inference(fof_nnf,[status(thm)],[fact_sym__Int__converse]) ).

fof(f_4809_2,plain,
    ! [U_19915,U_19914] : c_Relation_Osym(U_19914,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_19914,U_19914),tc_HOL_Obool)),U_19915),hAPP(c_Relation_Oconverse(U_19914,U_19914),U_19915))),
    inference(variable_rename,[status(thm)],[f_4809_1]) ).

cnf(f_4809_3,plain,
    c_Relation_Osym(U_19914,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_19914,U_19914),tc_HOL_Obool)),U_19915),hAPP(c_Relation_Oconverse(U_19914,U_19914),U_19915))),
    inference(clausify,[status(thm)],[f_4809_2]) ).

fof(f_4810_1,plain,
    ! [V_r_2,V_A_2,T_b] :
      ( ( c_Relation_Otrans(T_b,V_r_2)
        & c_Relation_Osym(T_b,V_r_2)
        & c_Relation_Orefl__on(T_b,V_A_2,V_r_2) )
      | ~ c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_equivE]) ).

fof(f_4810_2,plain,
    ! [U_19918,U_19917,U_19916] :
      ( ( c_Relation_Otrans(U_19916,U_19918)
        & c_Relation_Osym(U_19916,U_19918)
        & c_Relation_Orefl__on(U_19916,U_19917,U_19918) )
      | ~ c_Equiv__Relations_Oequiv(U_19916,U_19917,U_19918) ),
    inference(variable_rename,[status(thm)],[f_4810_1]) ).

cnf(f_4810_3,plain,
    ( c_Relation_Orefl__on(U_19916,U_19917,U_19918)
    | ~ c_Equiv__Relations_Oequiv(U_19916,U_19917,U_19918) ),
    inference(clausify,[status(thm)],[f_4810_2]) ).

cnf(f_4810_4,plain,
    ( c_Relation_Osym(U_19916,U_19918)
    | ~ c_Equiv__Relations_Oequiv(U_19916,U_19917,U_19918) ),
    inference(clausify,[status(thm)],[f_4810_2]) ).

cnf(f_4810_5,plain,
    ( c_Relation_Otrans(U_19916,U_19918)
    | ~ c_Equiv__Relations_Oequiv(U_19916,U_19917,U_19918) ),
    inference(clausify,[status(thm)],[f_4810_2]) ).

fof(f_4811_1,plain,
    ! [V_r_2,V_A_2,T_b] :
      ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
      | ~ c_Relation_Otrans(T_b,V_r_2)
      | ~ c_Relation_Osym(T_b,V_r_2)
      | ~ c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ),
    inference(fof_nnf,[status(thm)],[fact_equivI]) ).

fof(f_4811_2,plain,
    ! [U_19921,U_19920,U_19919] :
      ( c_Equiv__Relations_Oequiv(U_19919,U_19920,U_19921)
      | ~ c_Relation_Otrans(U_19919,U_19921)
      | ~ c_Relation_Osym(U_19919,U_19921)
      | ~ c_Relation_Orefl__on(U_19919,U_19920,U_19921) ),
    inference(variable_rename,[status(thm)],[f_4811_1]) ).

cnf(f_4811_3,plain,
    ( c_Equiv__Relations_Oequiv(U_19919,U_19920,U_19921)
    | ~ c_Relation_Otrans(U_19919,U_19921)
    | ~ c_Relation_Osym(U_19919,U_19921)
    | ~ c_Relation_Orefl__on(U_19919,U_19920,U_19921) ),
    inference(clausify,[status(thm)],[f_4811_2]) ).

fof(f_4812_1,plain,
    ! [V_r_2,V_A_2,T_b] :
      ( ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
        | ~ c_Relation_Otrans(T_b,V_r_2)
        | ~ c_Relation_Osym(T_b,V_r_2)
        | ~ c_Relation_Orefl__on(T_b,V_A_2,V_r_2) )
      & ( ( c_Relation_Otrans(T_b,V_r_2)
          & c_Relation_Osym(T_b,V_r_2)
          & c_Relation_Orefl__on(T_b,V_A_2,V_r_2) )
        | ~ c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_equiv__def]) ).

fof(f_4812_2,plain,
    ! [U_19924,U_19923,U_19922] :
      ( ( c_Equiv__Relations_Oequiv(U_19922,U_19923,U_19924)
        | ~ c_Relation_Otrans(U_19922,U_19924)
        | ~ c_Relation_Osym(U_19922,U_19924)
        | ~ c_Relation_Orefl__on(U_19922,U_19923,U_19924) )
      & ( ( c_Relation_Otrans(U_19922,U_19924)
          & c_Relation_Osym(U_19922,U_19924)
          & c_Relation_Orefl__on(U_19922,U_19923,U_19924) )
        | ~ c_Equiv__Relations_Oequiv(U_19922,U_19923,U_19924) ) ),
    inference(variable_rename,[status(thm)],[f_4812_1]) ).

fof(f_4812_3,plain,
    ( ! [U_19930,U_19928,U_19926] :
        ( c_Equiv__Relations_Oequiv(U_19926,U_19928,U_19930)
        | ~ c_Relation_Otrans(U_19926,U_19930)
        | ~ c_Relation_Osym(U_19926,U_19930)
        | ~ c_Relation_Orefl__on(U_19926,U_19928,U_19930) )
    & ! [U_19929,U_19927,U_19925] :
        ( ( c_Relation_Otrans(U_19925,U_19929)
          & c_Relation_Osym(U_19925,U_19929)
          & c_Relation_Orefl__on(U_19925,U_19927,U_19929) )
        | ~ c_Equiv__Relations_Oequiv(U_19925,U_19927,U_19929) ) ),
    inference(miniscope,[status(thm)],[f_4812_2]) ).

cnf(f_4812_4,plain,
    ( c_Relation_Orefl__on(U_19925,U_19927,U_19929)
    | ~ c_Equiv__Relations_Oequiv(U_19925,U_19927,U_19929) ),
    inference(clausify,[status(thm)],[f_4812_3]) ).

cnf(f_4812_5,plain,
    ( c_Relation_Osym(U_19925,U_19929)
    | ~ c_Equiv__Relations_Oequiv(U_19925,U_19927,U_19929) ),
    inference(clausify,[status(thm)],[f_4812_3]) ).

cnf(f_4812_6,plain,
    ( c_Relation_Otrans(U_19925,U_19929)
    | ~ c_Equiv__Relations_Oequiv(U_19925,U_19927,U_19929) ),
    inference(clausify,[status(thm)],[f_4812_3]) ).

cnf(f_4812_7,plain,
    ( c_Equiv__Relations_Oequiv(U_19926,U_19928,U_19930)
    | ~ c_Relation_Otrans(U_19926,U_19930)
    | ~ c_Relation_Osym(U_19926,U_19930)
    | ~ c_Relation_Orefl__on(U_19926,U_19928,U_19930) ),
    inference(clausify,[status(thm)],[f_4812_3]) ).

fof(f_4813_1,plain,
    ! [V_r_2,T_b] :
      ( ( c_Predicate_Osymp(T_b,V_r_2)
        | ~ c_Relation_Osym(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))) )
      & ( c_Relation_Osym(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2)))
        | ~ c_Predicate_Osymp(T_b,V_r_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_symp__def]) ).

fof(f_4813_2,plain,
    ! [U_19932,U_19931] :
      ( ( c_Predicate_Osymp(U_19931,U_19932)
        | ~ c_Relation_Osym(U_19931,hAPP(c_Set_OCollect(tc_prod(U_19931,U_19931)),hAPP(c_Product__Type_Oprod_Oprod__case(U_19931,U_19931,tc_HOL_Obool),U_19932))) )
      & ( c_Relation_Osym(U_19931,hAPP(c_Set_OCollect(tc_prod(U_19931,U_19931)),hAPP(c_Product__Type_Oprod_Oprod__case(U_19931,U_19931,tc_HOL_Obool),U_19932)))
        | ~ c_Predicate_Osymp(U_19931,U_19932) ) ),
    inference(variable_rename,[status(thm)],[f_4813_1]) ).

fof(f_4813_3,plain,
    ( ! [U_19936,U_19934] :
        ( c_Predicate_Osymp(U_19934,U_19936)
        | ~ c_Relation_Osym(U_19934,hAPP(c_Set_OCollect(tc_prod(U_19934,U_19934)),hAPP(c_Product__Type_Oprod_Oprod__case(U_19934,U_19934,tc_HOL_Obool),U_19936))) )
    & ! [U_19935,U_19933] :
        ( c_Relation_Osym(U_19933,hAPP(c_Set_OCollect(tc_prod(U_19933,U_19933)),hAPP(c_Product__Type_Oprod_Oprod__case(U_19933,U_19933,tc_HOL_Obool),U_19935)))
        | ~ c_Predicate_Osymp(U_19933,U_19935) ) ),
    inference(miniscope,[status(thm)],[f_4813_2]) ).

cnf(f_4813_4,plain,
    ( c_Relation_Osym(U_19933,hAPP(c_Set_OCollect(tc_prod(U_19933,U_19933)),hAPP(c_Product__Type_Oprod_Oprod__case(U_19933,U_19933,tc_HOL_Obool),U_19935)))
    | ~ c_Predicate_Osymp(U_19933,U_19935) ),
    inference(clausify,[status(thm)],[f_4813_3]) ).

cnf(f_4813_5,plain,
    ( c_Predicate_Osymp(U_19934,U_19936)
    | ~ c_Relation_Osym(U_19934,hAPP(c_Set_OCollect(tc_prod(U_19934,U_19934)),hAPP(c_Product__Type_Oprod_Oprod__case(U_19934,U_19934,tc_HOL_Obool),U_19936))) ),
    inference(clausify,[status(thm)],[f_4813_3]) ).

fof(f_4814_1,plain,
    ! [V_R_2,T_b] :
      ( ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
        | ~ c_Predicate_Otransp(T_b,V_R_2)
        | ~ c_Predicate_Osymp(T_b,V_R_2)
        | ! [B_x] : ~ hBOOL(hAPP(hAPP(V_R_2,B_x),B_x)) )
      & ( ( c_Predicate_Otransp(T_b,V_R_2)
          & c_Predicate_Osymp(T_b,V_R_2)
          & ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x)) )
        | ~ c_Equiv__Relations_Opart__equivp(T_b,V_R_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_part__equivp__refl__symp__transp]) ).

fof(f_4814_2,plain,
    ! [U_19940,U_19939] :
      ( ( c_Equiv__Relations_Opart__equivp(U_19939,U_19940)
        | ~ c_Predicate_Otransp(U_19939,U_19940)
        | ~ c_Predicate_Osymp(U_19939,U_19940)
        | ! [U_19938] : ~ hBOOL(hAPP(hAPP(U_19940,U_19938),U_19938)) )
      & ( ( c_Predicate_Otransp(U_19939,U_19940)
          & c_Predicate_Osymp(U_19939,U_19940)
          & ? [U_19937] : hBOOL(hAPP(hAPP(U_19940,U_19937),U_19937)) )
        | ~ c_Equiv__Relations_Opart__equivp(U_19939,U_19940) ) ),
    inference(variable_rename,[status(thm)],[f_4814_1]) ).

fof(f_4814_3,plain,
    ( ! [U_19944,U_19942] :
        ( c_Equiv__Relations_Opart__equivp(U_19942,U_19944)
        | ~ c_Predicate_Otransp(U_19942,U_19944)
        | ~ c_Predicate_Osymp(U_19942,U_19944)
        | ! [U_19938] : ~ hBOOL(hAPP(hAPP(U_19944,U_19938),U_19938)) )
    & ! [U_19943,U_19941] :
        ( ( c_Predicate_Otransp(U_19941,U_19943)
          & c_Predicate_Osymp(U_19941,U_19943)
          & ? [U_19937] : hBOOL(hAPP(hAPP(U_19943,U_19937),U_19937)) )
        | ~ c_Equiv__Relations_Opart__equivp(U_19941,U_19943) ) ),
    inference(miniscope,[status(thm)],[f_4814_2]) ).

fof(f_4814_4,plain,
    ( ! [U_19944,U_19942] :
        ( c_Equiv__Relations_Opart__equivp(U_19942,U_19944)
        | ~ c_Predicate_Otransp(U_19942,U_19944)
        | ~ c_Predicate_Osymp(U_19942,U_19944)
        | ! [U_19938] : ~ hBOOL(hAPP(hAPP(U_19944,U_19938),U_19938)) )
    & ! [U_19943,U_19941] :
        ( ( c_Predicate_Otransp(U_19941,U_19943)
          & c_Predicate_Osymp(U_19941,U_19943)
          & hBOOL(hAPP(hAPP(U_19943,sK536(U_19943,U_19941)),sK536(U_19943,U_19941))) )
        | ~ c_Equiv__Relations_Opart__equivp(U_19941,U_19943) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK536]),skolemize(U_19937,sK536(U_19943,U_19941))],[f_4814_3]) ).

cnf(f_4814_5,plain,
    ( hBOOL(hAPP(hAPP(U_19943,sK536(U_19943,U_19941)),sK536(U_19943,U_19941)))
    | ~ c_Equiv__Relations_Opart__equivp(U_19941,U_19943) ),
    inference(clausify,[status(thm)],[f_4814_4]) ).

cnf(f_4814_6,plain,
    ( c_Predicate_Osymp(U_19941,U_19943)
    | ~ c_Equiv__Relations_Opart__equivp(U_19941,U_19943) ),
    inference(clausify,[status(thm)],[f_4814_4]) ).

cnf(f_4814_7,plain,
    ( c_Predicate_Otransp(U_19941,U_19943)
    | ~ c_Equiv__Relations_Opart__equivp(U_19941,U_19943) ),
    inference(clausify,[status(thm)],[f_4814_4]) ).

cnf(f_4814_8,plain,
    ( c_Equiv__Relations_Opart__equivp(U_19942,U_19944)
    | ~ c_Predicate_Otransp(U_19942,U_19944)
    | ~ c_Predicate_Osymp(U_19942,U_19944)
    | ~ hBOOL(hAPP(hAPP(U_19944,U_19938),U_19938)) ),
    inference(clausify,[status(thm)],[f_4814_4]) ).

fof(f_4815_1,plain,
    ! [T_b,V_R_2] :
      ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
      | ~ c_Predicate_Otransp(T_b,V_R_2)
      | ~ c_Predicate_Osymp(T_b,V_R_2)
      | ! [B_x] : ~ hBOOL(hAPP(hAPP(V_R_2,B_x),B_x)) ),
    inference(fof_nnf,[status(thm)],[fact_part__equivpI]) ).

fof(f_4815_2,plain,
    ! [U_19947,U_19946] :
      ( c_Equiv__Relations_Opart__equivp(U_19947,U_19946)
      | ~ c_Predicate_Otransp(U_19947,U_19946)
      | ~ c_Predicate_Osymp(U_19947,U_19946)
      | ! [U_19945] : ~ hBOOL(hAPP(hAPP(U_19946,U_19945),U_19945)) ),
    inference(variable_rename,[status(thm)],[f_4815_1]) ).

cnf(f_4815_3,plain,
    ( c_Equiv__Relations_Opart__equivp(U_19947,U_19946)
    | ~ c_Predicate_Otransp(U_19947,U_19946)
    | ~ c_Predicate_Osymp(U_19947,U_19946)
    | ~ hBOOL(hAPP(hAPP(U_19946,U_19945),U_19945)) ),
    inference(clausify,[status(thm)],[f_4815_2]) ).

fof(f_4816_1,plain,
    ! [V_R_2,T_b] :
      ( ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
        | ? [B_x,B_y] :
            ( ( ~ hBOOL(hAPP(hAPP(V_R_2,B_x),B_y))
              & hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y)
              & hBOOL(hAPP(hAPP(V_R_2,B_y),B_y))
              & hBOOL(hAPP(hAPP(V_R_2,B_x),B_x)) )
            | ( ( hAPP(V_R_2,B_x) != hAPP(V_R_2,B_y)
                | ~ hBOOL(hAPP(hAPP(V_R_2,B_y),B_y))
                | ~ hBOOL(hAPP(hAPP(V_R_2,B_x),B_x)) )
              & hBOOL(hAPP(hAPP(V_R_2,B_x),B_y)) ) )
        | ! [B_x] : ~ hBOOL(hAPP(hAPP(V_R_2,B_x),B_x)) )
      & ( ( ! [B_x,B_y] :
              ( ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_y))
                | hAPP(V_R_2,B_x) != hAPP(V_R_2,B_y)
                | ~ hBOOL(hAPP(hAPP(V_R_2,B_y),B_y))
                | ~ hBOOL(hAPP(hAPP(V_R_2,B_x),B_x)) )
              & ( ( hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y)
                  & hBOOL(hAPP(hAPP(V_R_2,B_y),B_y))
                  & hBOOL(hAPP(hAPP(V_R_2,B_x),B_x)) )
                | ~ hBOOL(hAPP(hAPP(V_R_2,B_x),B_y)) ) )
          & ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x)) )
        | ~ c_Equiv__Relations_Opart__equivp(T_b,V_R_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_part__equivp__def]) ).

fof(f_4816_2,plain,
    ! [U_19955,U_19954] :
      ( ( c_Equiv__Relations_Opart__equivp(U_19954,U_19955)
        | ? [U_19953,U_19952] :
            ( ( ~ hBOOL(hAPP(hAPP(U_19955,U_19953),U_19952))
              & hAPP(U_19955,U_19953) = hAPP(U_19955,U_19952)
              & hBOOL(hAPP(hAPP(U_19955,U_19952),U_19952))
              & hBOOL(hAPP(hAPP(U_19955,U_19953),U_19953)) )
            | ( ( hAPP(U_19955,U_19953) != hAPP(U_19955,U_19952)
                | ~ hBOOL(hAPP(hAPP(U_19955,U_19952),U_19952))
                | ~ hBOOL(hAPP(hAPP(U_19955,U_19953),U_19953)) )
              & hBOOL(hAPP(hAPP(U_19955,U_19953),U_19952)) ) )
        | ! [U_19951] : ~ hBOOL(hAPP(hAPP(U_19955,U_19951),U_19951)) )
      & ( ( ! [U_19950,U_19949] :
              ( ( hBOOL(hAPP(hAPP(U_19955,U_19950),U_19949))
                | hAPP(U_19955,U_19950) != hAPP(U_19955,U_19949)
                | ~ hBOOL(hAPP(hAPP(U_19955,U_19949),U_19949))
                | ~ hBOOL(hAPP(hAPP(U_19955,U_19950),U_19950)) )
              & ( ( hAPP(U_19955,U_19950) = hAPP(U_19955,U_19949)
                  & hBOOL(hAPP(hAPP(U_19955,U_19949),U_19949))
                  & hBOOL(hAPP(hAPP(U_19955,U_19950),U_19950)) )
                | ~ hBOOL(hAPP(hAPP(U_19955,U_19950),U_19949)) ) )
          & ? [U_19948] : hBOOL(hAPP(hAPP(U_19955,U_19948),U_19948)) )
        | ~ c_Equiv__Relations_Opart__equivp(U_19954,U_19955) ) ),
    inference(variable_rename,[status(thm)],[f_4816_1]) ).

fof(f_4816_3,plain,
    ( ! [U_19967] :
        ( ! [U_19965] : c_Equiv__Relations_Opart__equivp(U_19965,U_19967)
        | ? [U_19963,U_19961] :
            ( ~ hBOOL(hAPP(hAPP(U_19967,U_19963),U_19961))
            & hAPP(U_19967,U_19963) = hAPP(U_19967,U_19961)
            & hBOOL(hAPP(hAPP(U_19967,U_19961),U_19961))
            & hBOOL(hAPP(hAPP(U_19967,U_19963),U_19963)) )
        | ? [U_19962,U_19960] :
            ( ( hAPP(U_19967,U_19962) != hAPP(U_19967,U_19960)
              | ~ hBOOL(hAPP(hAPP(U_19967,U_19960),U_19960))
              | ~ hBOOL(hAPP(hAPP(U_19967,U_19962),U_19962)) )
            & hBOOL(hAPP(hAPP(U_19967,U_19962),U_19960)) )
        | ! [U_19951] : ~ hBOOL(hAPP(hAPP(U_19967,U_19951),U_19951)) )
    & ! [U_19966] :
        ( ! [U_19964] : ~ c_Equiv__Relations_Opart__equivp(U_19964,U_19966)
        | ( ! [U_19959,U_19957] :
              ( hBOOL(hAPP(hAPP(U_19966,U_19959),U_19957))
              | hAPP(U_19966,U_19959) != hAPP(U_19966,U_19957)
              | ~ hBOOL(hAPP(hAPP(U_19966,U_19957),U_19957))
              | ~ hBOOL(hAPP(hAPP(U_19966,U_19959),U_19959)) )
          & ! [U_19958,U_19956] :
              ( ( hAPP(U_19966,U_19958) = hAPP(U_19966,U_19956)
                & hBOOL(hAPP(hAPP(U_19966,U_19956),U_19956))
                & hBOOL(hAPP(hAPP(U_19966,U_19958),U_19958)) )
              | ~ hBOOL(hAPP(hAPP(U_19966,U_19958),U_19956)) )
          & ? [U_19948] : hBOOL(hAPP(hAPP(U_19966,U_19948),U_19948)) ) ) ),
    inference(miniscope,[status(thm)],[f_4816_2]) ).

fof(f_4816_4,plain,
    ( ! [U_19967] :
        ( ! [U_19965] : c_Equiv__Relations_Opart__equivp(U_19965,U_19967)
        | ? [U_19963,U_19961] :
            ( ~ hBOOL(hAPP(hAPP(U_19967,U_19963),U_19961))
            & hAPP(U_19967,U_19963) = hAPP(U_19967,U_19961)
            & hBOOL(hAPP(hAPP(U_19967,U_19961),U_19961))
            & hBOOL(hAPP(hAPP(U_19967,U_19963),U_19963)) )
        | ? [U_19962,U_19960] :
            ( ( hAPP(U_19967,U_19962) != hAPP(U_19967,U_19960)
              | ~ hBOOL(hAPP(hAPP(U_19967,U_19960),U_19960))
              | ~ hBOOL(hAPP(hAPP(U_19967,U_19962),U_19962)) )
            & hBOOL(hAPP(hAPP(U_19967,U_19962),U_19960)) )
        | ! [U_19951] : ~ hBOOL(hAPP(hAPP(U_19967,U_19951),U_19951)) )
    & ! [U_19966] :
        ( ! [U_19964] : ~ c_Equiv__Relations_Opart__equivp(U_19964,U_19966)
        | ( ! [U_19959,U_19957] :
              ( hBOOL(hAPP(hAPP(U_19966,U_19959),U_19957))
              | hAPP(U_19966,U_19959) != hAPP(U_19966,U_19957)
              | ~ hBOOL(hAPP(hAPP(U_19966,U_19957),U_19957))
              | ~ hBOOL(hAPP(hAPP(U_19966,U_19959),U_19959)) )
          & ! [U_19958,U_19956] :
              ( ( hAPP(U_19966,U_19958) = hAPP(U_19966,U_19956)
                & hBOOL(hAPP(hAPP(U_19966,U_19956),U_19956))
                & hBOOL(hAPP(hAPP(U_19966,U_19958),U_19958)) )
              | ~ hBOOL(hAPP(hAPP(U_19966,U_19958),U_19956)) )
          & hBOOL(hAPP(hAPP(U_19966,sK537(U_19966)),sK537(U_19966))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK537]),skolemize(U_19948,sK537(U_19966))],[f_4816_3]) ).

fof(f_4816_5,plain,
    ( ! [U_19967] :
        ( ! [U_19965] : c_Equiv__Relations_Opart__equivp(U_19965,U_19967)
        | ? [U_19963,U_19961] :
            ( ~ hBOOL(hAPP(hAPP(U_19967,U_19963),U_19961))
            & hAPP(U_19967,U_19963) = hAPP(U_19967,U_19961)
            & hBOOL(hAPP(hAPP(U_19967,U_19961),U_19961))
            & hBOOL(hAPP(hAPP(U_19967,U_19963),U_19963)) )
        | ? [U_19960] :
            ( ( hAPP(U_19967,sK538(U_19967)) != hAPP(U_19967,U_19960)
              | ~ hBOOL(hAPP(hAPP(U_19967,U_19960),U_19960))
              | ~ hBOOL(hAPP(hAPP(U_19967,sK538(U_19967)),sK538(U_19967))) )
            & hBOOL(hAPP(hAPP(U_19967,sK538(U_19967)),U_19960)) )
        | ! [U_19951] : ~ hBOOL(hAPP(hAPP(U_19967,U_19951),U_19951)) )
    & ! [U_19966] :
        ( ! [U_19964] : ~ c_Equiv__Relations_Opart__equivp(U_19964,U_19966)
        | ( ! [U_19959,U_19957] :
              ( hBOOL(hAPP(hAPP(U_19966,U_19959),U_19957))
              | hAPP(U_19966,U_19959) != hAPP(U_19966,U_19957)
              | ~ hBOOL(hAPP(hAPP(U_19966,U_19957),U_19957))
              | ~ hBOOL(hAPP(hAPP(U_19966,U_19959),U_19959)) )
          & ! [U_19958,U_19956] :
              ( ( hAPP(U_19966,U_19958) = hAPP(U_19966,U_19956)
                & hBOOL(hAPP(hAPP(U_19966,U_19956),U_19956))
                & hBOOL(hAPP(hAPP(U_19966,U_19958),U_19958)) )
              | ~ hBOOL(hAPP(hAPP(U_19966,U_19958),U_19956)) )
          & hBOOL(hAPP(hAPP(U_19966,sK537(U_19966)),sK537(U_19966))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK538]),skolemize(U_19962,sK538(U_19967))],[f_4816_4]) ).

fof(f_4816_6,plain,
    ( ! [U_19967] :
        ( ! [U_19965] : c_Equiv__Relations_Opart__equivp(U_19965,U_19967)
        | ? [U_19963,U_19961] :
            ( ~ hBOOL(hAPP(hAPP(U_19967,U_19963),U_19961))
            & hAPP(U_19967,U_19963) = hAPP(U_19967,U_19961)
            & hBOOL(hAPP(hAPP(U_19967,U_19961),U_19961))
            & hBOOL(hAPP(hAPP(U_19967,U_19963),U_19963)) )
        | ( ( hAPP(U_19967,sK538(U_19967)) != hAPP(U_19967,sK539(U_19967))
            | ~ hBOOL(hAPP(hAPP(U_19967,sK539(U_19967)),sK539(U_19967)))
            | ~ hBOOL(hAPP(hAPP(U_19967,sK538(U_19967)),sK538(U_19967))) )
          & hBOOL(hAPP(hAPP(U_19967,sK538(U_19967)),sK539(U_19967))) )
        | ! [U_19951] : ~ hBOOL(hAPP(hAPP(U_19967,U_19951),U_19951)) )
    & ! [U_19966] :
        ( ! [U_19964] : ~ c_Equiv__Relations_Opart__equivp(U_19964,U_19966)
        | ( ! [U_19959,U_19957] :
              ( hBOOL(hAPP(hAPP(U_19966,U_19959),U_19957))
              | hAPP(U_19966,U_19959) != hAPP(U_19966,U_19957)
              | ~ hBOOL(hAPP(hAPP(U_19966,U_19957),U_19957))
              | ~ hBOOL(hAPP(hAPP(U_19966,U_19959),U_19959)) )
          & ! [U_19958,U_19956] :
              ( ( hAPP(U_19966,U_19958) = hAPP(U_19966,U_19956)
                & hBOOL(hAPP(hAPP(U_19966,U_19956),U_19956))
                & hBOOL(hAPP(hAPP(U_19966,U_19958),U_19958)) )
              | ~ hBOOL(hAPP(hAPP(U_19966,U_19958),U_19956)) )
          & hBOOL(hAPP(hAPP(U_19966,sK537(U_19966)),sK537(U_19966))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK539]),skolemize(U_19960,sK539(U_19967))],[f_4816_5]) ).

fof(f_4816_7,plain,
    ( ! [U_19967] :
        ( ! [U_19965] : c_Equiv__Relations_Opart__equivp(U_19965,U_19967)
        | ? [U_19961] :
            ( ~ hBOOL(hAPP(hAPP(U_19967,sK540(U_19967)),U_19961))
            & hAPP(U_19967,sK540(U_19967)) = hAPP(U_19967,U_19961)
            & hBOOL(hAPP(hAPP(U_19967,U_19961),U_19961))
            & hBOOL(hAPP(hAPP(U_19967,sK540(U_19967)),sK540(U_19967))) )
        | ( ( hAPP(U_19967,sK538(U_19967)) != hAPP(U_19967,sK539(U_19967))
            | ~ hBOOL(hAPP(hAPP(U_19967,sK539(U_19967)),sK539(U_19967)))
            | ~ hBOOL(hAPP(hAPP(U_19967,sK538(U_19967)),sK538(U_19967))) )
          & hBOOL(hAPP(hAPP(U_19967,sK538(U_19967)),sK539(U_19967))) )
        | ! [U_19951] : ~ hBOOL(hAPP(hAPP(U_19967,U_19951),U_19951)) )
    & ! [U_19966] :
        ( ! [U_19964] : ~ c_Equiv__Relations_Opart__equivp(U_19964,U_19966)
        | ( ! [U_19959,U_19957] :
              ( hBOOL(hAPP(hAPP(U_19966,U_19959),U_19957))
              | hAPP(U_19966,U_19959) != hAPP(U_19966,U_19957)
              | ~ hBOOL(hAPP(hAPP(U_19966,U_19957),U_19957))
              | ~ hBOOL(hAPP(hAPP(U_19966,U_19959),U_19959)) )
          & ! [U_19958,U_19956] :
              ( ( hAPP(U_19966,U_19958) = hAPP(U_19966,U_19956)
                & hBOOL(hAPP(hAPP(U_19966,U_19956),U_19956))
                & hBOOL(hAPP(hAPP(U_19966,U_19958),U_19958)) )
              | ~ hBOOL(hAPP(hAPP(U_19966,U_19958),U_19956)) )
          & hBOOL(hAPP(hAPP(U_19966,sK537(U_19966)),sK537(U_19966))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK540]),skolemize(U_19963,sK540(U_19967))],[f_4816_6]) ).

fof(f_4816_8,plain,
    ( ! [U_19967] :
        ( ! [U_19965] : c_Equiv__Relations_Opart__equivp(U_19965,U_19967)
        | ( ~ hBOOL(hAPP(hAPP(U_19967,sK540(U_19967)),sK541(U_19967)))
          & hAPP(U_19967,sK540(U_19967)) = hAPP(U_19967,sK541(U_19967))
          & hBOOL(hAPP(hAPP(U_19967,sK541(U_19967)),sK541(U_19967)))
          & hBOOL(hAPP(hAPP(U_19967,sK540(U_19967)),sK540(U_19967))) )
        | ( ( hAPP(U_19967,sK538(U_19967)) != hAPP(U_19967,sK539(U_19967))
            | ~ hBOOL(hAPP(hAPP(U_19967,sK539(U_19967)),sK539(U_19967)))
            | ~ hBOOL(hAPP(hAPP(U_19967,sK538(U_19967)),sK538(U_19967))) )
          & hBOOL(hAPP(hAPP(U_19967,sK538(U_19967)),sK539(U_19967))) )
        | ! [U_19951] : ~ hBOOL(hAPP(hAPP(U_19967,U_19951),U_19951)) )
    & ! [U_19966] :
        ( ! [U_19964] : ~ c_Equiv__Relations_Opart__equivp(U_19964,U_19966)
        | ( ! [U_19959,U_19957] :
              ( hBOOL(hAPP(hAPP(U_19966,U_19959),U_19957))
              | hAPP(U_19966,U_19959) != hAPP(U_19966,U_19957)
              | ~ hBOOL(hAPP(hAPP(U_19966,U_19957),U_19957))
              | ~ hBOOL(hAPP(hAPP(U_19966,U_19959),U_19959)) )
          & ! [U_19958,U_19956] :
              ( ( hAPP(U_19966,U_19958) = hAPP(U_19966,U_19956)
                & hBOOL(hAPP(hAPP(U_19966,U_19956),U_19956))
                & hBOOL(hAPP(hAPP(U_19966,U_19958),U_19958)) )
              | ~ hBOOL(hAPP(hAPP(U_19966,U_19958),U_19956)) )
          & hBOOL(hAPP(hAPP(U_19966,sK537(U_19966)),sK537(U_19966))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK541]),skolemize(U_19961,sK541(U_19967))],[f_4816_7]) ).

cnf(f_4816_9,plain,
    ( hBOOL(hAPP(hAPP(U_19966,sK537(U_19966)),sK537(U_19966)))
    | ~ c_Equiv__Relations_Opart__equivp(U_19964,U_19966) ),
    inference(clausify,[status(thm)],[f_4816_8]) ).

cnf(f_4816_10,plain,
    ( hBOOL(hAPP(hAPP(U_19966,U_19958),U_19958))
    | ~ hBOOL(hAPP(hAPP(U_19966,U_19958),U_19956))
    | ~ c_Equiv__Relations_Opart__equivp(U_19964,U_19966) ),
    inference(clausify,[status(thm)],[f_4816_8]) ).

cnf(f_4816_11,plain,
    ( hBOOL(hAPP(hAPP(U_19966,U_19956),U_19956))
    | ~ hBOOL(hAPP(hAPP(U_19966,U_19958),U_19956))
    | ~ c_Equiv__Relations_Opart__equivp(U_19964,U_19966) ),
    inference(clausify,[status(thm)],[f_4816_8]) ).

cnf(f_4816_12,plain,
    ( hAPP(U_19966,U_19958) = hAPP(U_19966,U_19956)
    | ~ hBOOL(hAPP(hAPP(U_19966,U_19958),U_19956))
    | ~ c_Equiv__Relations_Opart__equivp(U_19964,U_19966) ),
    inference(clausify,[status(thm)],[f_4816_8]) ).

cnf(f_4816_13,plain,
    ( hBOOL(hAPP(hAPP(U_19966,U_19959),U_19957))
    | hAPP(U_19966,U_19959) != hAPP(U_19966,U_19957)
    | ~ hBOOL(hAPP(hAPP(U_19966,U_19957),U_19957))
    | ~ hBOOL(hAPP(hAPP(U_19966,U_19959),U_19959))
    | ~ c_Equiv__Relations_Opart__equivp(U_19964,U_19966) ),
    inference(clausify,[status(thm)],[f_4816_8]) ).

cnf(f_4816_14,plain,
    ( hBOOL(hAPP(hAPP(U_19967,sK540(U_19967)),sK540(U_19967)))
    | hBOOL(hAPP(hAPP(U_19967,sK538(U_19967)),sK539(U_19967)))
    | ~ hBOOL(hAPP(hAPP(U_19967,U_19951),U_19951))
    | c_Equiv__Relations_Opart__equivp(U_19965,U_19967) ),
    inference(clausify,[status(thm)],[f_4816_8]) ).

cnf(f_4816_15,plain,
    ( hBOOL(hAPP(hAPP(U_19967,sK541(U_19967)),sK541(U_19967)))
    | hBOOL(hAPP(hAPP(U_19967,sK538(U_19967)),sK539(U_19967)))
    | ~ hBOOL(hAPP(hAPP(U_19967,U_19951),U_19951))
    | c_Equiv__Relations_Opart__equivp(U_19965,U_19967) ),
    inference(clausify,[status(thm)],[f_4816_8]) ).

cnf(f_4816_16,plain,
    ( hAPP(U_19967,sK540(U_19967)) = hAPP(U_19967,sK541(U_19967))
    | hBOOL(hAPP(hAPP(U_19967,sK538(U_19967)),sK539(U_19967)))
    | ~ hBOOL(hAPP(hAPP(U_19967,U_19951),U_19951))
    | c_Equiv__Relations_Opart__equivp(U_19965,U_19967) ),
    inference(clausify,[status(thm)],[f_4816_8]) ).

cnf(f_4816_17,plain,
    ( ~ hBOOL(hAPP(hAPP(U_19967,sK540(U_19967)),sK541(U_19967)))
    | hBOOL(hAPP(hAPP(U_19967,sK538(U_19967)),sK539(U_19967)))
    | ~ hBOOL(hAPP(hAPP(U_19967,U_19951),U_19951))
    | c_Equiv__Relations_Opart__equivp(U_19965,U_19967) ),
    inference(clausify,[status(thm)],[f_4816_8]) ).

cnf(f_4816_18,plain,
    ( hBOOL(hAPP(hAPP(U_19967,sK540(U_19967)),sK540(U_19967)))
    | hAPP(U_19967,sK538(U_19967)) != hAPP(U_19967,sK539(U_19967))
    | ~ hBOOL(hAPP(hAPP(U_19967,sK539(U_19967)),sK539(U_19967)))
    | ~ hBOOL(hAPP(hAPP(U_19967,sK538(U_19967)),sK538(U_19967)))
    | ~ hBOOL(hAPP(hAPP(U_19967,U_19951),U_19951))
    | c_Equiv__Relations_Opart__equivp(U_19965,U_19967) ),
    inference(clausify,[status(thm)],[f_4816_8]) ).

cnf(f_4816_19,plain,
    ( hBOOL(hAPP(hAPP(U_19967,sK541(U_19967)),sK541(U_19967)))
    | hAPP(U_19967,sK538(U_19967)) != hAPP(U_19967,sK539(U_19967))
    | ~ hBOOL(hAPP(hAPP(U_19967,sK539(U_19967)),sK539(U_19967)))
    | ~ hBOOL(hAPP(hAPP(U_19967,sK538(U_19967)),sK538(U_19967)))
    | ~ hBOOL(hAPP(hAPP(U_19967,U_19951),U_19951))
    | c_Equiv__Relations_Opart__equivp(U_19965,U_19967) ),
    inference(clausify,[status(thm)],[f_4816_8]) ).

cnf(f_4816_20,plain,
    ( hAPP(U_19967,sK540(U_19967)) = hAPP(U_19967,sK541(U_19967))
    | hAPP(U_19967,sK538(U_19967)) != hAPP(U_19967,sK539(U_19967))
    | ~ hBOOL(hAPP(hAPP(U_19967,sK539(U_19967)),sK539(U_19967)))
    | ~ hBOOL(hAPP(hAPP(U_19967,sK538(U_19967)),sK538(U_19967)))
    | ~ hBOOL(hAPP(hAPP(U_19967,U_19951),U_19951))
    | c_Equiv__Relations_Opart__equivp(U_19965,U_19967) ),
    inference(clausify,[status(thm)],[f_4816_8]) ).

cnf(f_4816_21,plain,
    ( ~ hBOOL(hAPP(hAPP(U_19967,sK540(U_19967)),sK541(U_19967)))
    | hAPP(U_19967,sK538(U_19967)) != hAPP(U_19967,sK539(U_19967))
    | ~ hBOOL(hAPP(hAPP(U_19967,sK539(U_19967)),sK539(U_19967)))
    | ~ hBOOL(hAPP(hAPP(U_19967,sK538(U_19967)),sK538(U_19967)))
    | ~ hBOOL(hAPP(hAPP(U_19967,U_19951),U_19951))
    | c_Equiv__Relations_Opart__equivp(U_19965,U_19967) ),
    inference(clausify,[status(thm)],[f_4816_8]) ).

fof(f_4817_1,plain,
    ! [V_y_2,V_x_2,V_R_2,T_b] :
      ( hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2))
      | ~ hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
      | ~ c_Equiv__Relations_Opart__equivp(T_b,V_R_2) ),
    inference(fof_nnf,[status(thm)],[fact_part__equivp__symp]) ).

fof(f_4817_2,plain,
    ! [U_19971,U_19970,U_19969,U_19968] :
      ( hBOOL(hAPP(hAPP(U_19969,U_19971),U_19970))
      | ~ hBOOL(hAPP(hAPP(U_19969,U_19970),U_19971))
      | ~ c_Equiv__Relations_Opart__equivp(U_19968,U_19969) ),
    inference(variable_rename,[status(thm)],[f_4817_1]) ).

fof(f_4817_3,plain,
    ! [U_19971,U_19970,U_19969] :
      ( ! [U_19968] : ~ c_Equiv__Relations_Opart__equivp(U_19968,U_19969)
      | hBOOL(hAPP(hAPP(U_19969,U_19971),U_19970))
      | ~ hBOOL(hAPP(hAPP(U_19969,U_19970),U_19971)) ),
    inference(miniscope,[status(thm)],[f_4817_2]) ).

cnf(f_4817_4,plain,
    ( ~ c_Equiv__Relations_Opart__equivp(U_19968,U_19969)
    | hBOOL(hAPP(hAPP(U_19969,U_19971),U_19970))
    | ~ hBOOL(hAPP(hAPP(U_19969,U_19970),U_19971)) ),
    inference(clausify,[status(thm)],[f_4817_3]) ).

fof(f_4818_1,plain,
    ! [V_z_2,V_y_2,V_x_2,V_R_2,T_b] :
      ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_z_2))
      | ~ hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_z_2))
      | ~ hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
      | ~ c_Equiv__Relations_Opart__equivp(T_b,V_R_2) ),
    inference(fof_nnf,[status(thm)],[fact_part__equivp__transp]) ).

fof(f_4818_2,plain,
    ! [U_19976,U_19975,U_19974,U_19973,U_19972] :
      ( hBOOL(hAPP(hAPP(U_19973,U_19974),U_19976))
      | ~ hBOOL(hAPP(hAPP(U_19973,U_19975),U_19976))
      | ~ hBOOL(hAPP(hAPP(U_19973,U_19974),U_19975))
      | ~ c_Equiv__Relations_Opart__equivp(U_19972,U_19973) ),
    inference(variable_rename,[status(thm)],[f_4818_1]) ).

fof(f_4818_3,plain,
    ! [U_19976,U_19975,U_19974,U_19973] :
      ( ! [U_19972] : ~ c_Equiv__Relations_Opart__equivp(U_19972,U_19973)
      | hBOOL(hAPP(hAPP(U_19973,U_19974),U_19976))
      | ~ hBOOL(hAPP(hAPP(U_19973,U_19975),U_19976))
      | ~ hBOOL(hAPP(hAPP(U_19973,U_19974),U_19975)) ),
    inference(miniscope,[status(thm)],[f_4818_2]) ).

cnf(f_4818_4,plain,
    ( ~ c_Equiv__Relations_Opart__equivp(U_19972,U_19973)
    | hBOOL(hAPP(hAPP(U_19973,U_19974),U_19976))
    | ~ hBOOL(hAPP(hAPP(U_19973,U_19975),U_19976))
    | ~ hBOOL(hAPP(hAPP(U_19973,U_19974),U_19975)) ),
    inference(clausify,[status(thm)],[f_4818_3]) ).

fof(f_4819_1,plain,
    ! [V_R_2,T_b] :
      ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
      | ~ c_Equiv__Relations_Oequivp(T_b,V_R_2) ),
    inference(fof_nnf,[status(thm)],[fact_equivp__implies__part__equivp]) ).

fof(f_4819_2,plain,
    ! [U_19978,U_19977] :
      ( c_Equiv__Relations_Opart__equivp(U_19977,U_19978)
      | ~ c_Equiv__Relations_Oequivp(U_19977,U_19978) ),
    inference(variable_rename,[status(thm)],[f_4819_1]) ).

cnf(f_4819_3,plain,
    ( c_Equiv__Relations_Opart__equivp(U_19977,U_19978)
    | ~ c_Equiv__Relations_Oequivp(U_19977,U_19978) ),
    inference(clausify,[status(thm)],[f_4819_2]) ).

fof(f_4820_1,plain,
    ! [V_R_2,T_b] :
      ( ( c_Predicate_Otransp(T_b,V_R_2)
        & c_Predicate_Osymp(T_b,V_R_2)
        & ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x)) )
      | ~ c_Equiv__Relations_Opart__equivp(T_b,V_R_2) ),
    inference(fof_nnf,[status(thm)],[fact_part__equivpE]) ).

fof(f_4820_2,plain,
    ! [U_19981,U_19980] :
      ( ( c_Predicate_Otransp(U_19980,U_19981)
        & c_Predicate_Osymp(U_19980,U_19981)
        & ? [U_19979] : hBOOL(hAPP(hAPP(U_19981,U_19979),U_19979)) )
      | ~ c_Equiv__Relations_Opart__equivp(U_19980,U_19981) ),
    inference(variable_rename,[status(thm)],[f_4820_1]) ).

fof(f_4820_3,plain,
    ! [U_19981,U_19980] :
      ( ( c_Predicate_Otransp(U_19980,U_19981)
        & c_Predicate_Osymp(U_19980,U_19981)
        & hBOOL(hAPP(hAPP(U_19981,sK542(U_19981,U_19980)),sK542(U_19981,U_19980))) )
      | ~ c_Equiv__Relations_Opart__equivp(U_19980,U_19981) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK542]),skolemize(U_19979,sK542(U_19981,U_19980))],[f_4820_2]) ).

cnf(f_4820_4,plain,
    ( hBOOL(hAPP(hAPP(U_19981,sK542(U_19981,U_19980)),sK542(U_19981,U_19980)))
    | ~ c_Equiv__Relations_Opart__equivp(U_19980,U_19981) ),
    inference(clausify,[status(thm)],[f_4820_3]) ).

cnf(f_4820_5,plain,
    ( c_Predicate_Osymp(U_19980,U_19981)
    | ~ c_Equiv__Relations_Opart__equivp(U_19980,U_19981) ),
    inference(clausify,[status(thm)],[f_4820_3]) ).

cnf(f_4820_6,plain,
    ( c_Predicate_Otransp(U_19980,U_19981)
    | ~ c_Equiv__Relations_Opart__equivp(U_19980,U_19981) ),
    inference(clausify,[status(thm)],[f_4820_3]) ).

fof(f_4821_1,plain,
    ! [V_R_2,T_b] :
      ( ? [B_d] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_d),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBS(T_b,T_b,tc_HOL_Obool),V_R_2),c_COMBI(T_b))))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b)),c_fequal)),V_R_2)))))
      | ~ c_Equiv__Relations_Opart__equivp(T_b,V_R_2) ),
    inference(fof_nnf,[status(thm)],[fact_part__equivp__typedef]) ).

fof(f_4821_2,plain,
    ! [U_19984,U_19983] :
      ( ? [U_19982] : hBOOL(hAPP(hAPP(c_member(tc_fun(U_19983,tc_HOL_Obool)),U_19982),hAPP(hAPP(c_COMBB(tc_fun(U_19983,tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_19983,tc_HOL_Obool)),c_HOL_OEx(U_19983)),hAPP(hAPP(c_COMBB(tc_fun(U_19983,tc_HOL_Obool),tc_fun(U_19983,tc_HOL_Obool),tc_fun(U_19983,tc_HOL_Obool)),hAPP(c_COMBS(U_19983,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_19983),c_fconj),hAPP(hAPP(c_COMBS(U_19983,U_19983,tc_HOL_Obool),U_19984),c_COMBI(U_19983))))),hAPP(hAPP(c_COMBC(tc_fun(U_19983,tc_HOL_Obool),tc_fun(U_19983,tc_fun(U_19983,tc_HOL_Obool)),tc_fun(U_19983,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_19983,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_19983,tc_fun(U_19983,tc_HOL_Obool)),tc_fun(U_19983,tc_HOL_Obool)),tc_fun(U_19983,tc_HOL_Obool)),c_COMBB(tc_fun(U_19983,tc_HOL_Obool),tc_HOL_Obool,U_19983)),c_fequal)),U_19984)))))
      | ~ c_Equiv__Relations_Opart__equivp(U_19983,U_19984) ),
    inference(variable_rename,[status(thm)],[f_4821_1]) ).

fof(f_4821_3,plain,
    ! [U_19984,U_19983] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_19983,tc_HOL_Obool)),sK543(U_19984,U_19983)),hAPP(hAPP(c_COMBB(tc_fun(U_19983,tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_19983,tc_HOL_Obool)),c_HOL_OEx(U_19983)),hAPP(hAPP(c_COMBB(tc_fun(U_19983,tc_HOL_Obool),tc_fun(U_19983,tc_HOL_Obool),tc_fun(U_19983,tc_HOL_Obool)),hAPP(c_COMBS(U_19983,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_19983),c_fconj),hAPP(hAPP(c_COMBS(U_19983,U_19983,tc_HOL_Obool),U_19984),c_COMBI(U_19983))))),hAPP(hAPP(c_COMBC(tc_fun(U_19983,tc_HOL_Obool),tc_fun(U_19983,tc_fun(U_19983,tc_HOL_Obool)),tc_fun(U_19983,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_19983,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_19983,tc_fun(U_19983,tc_HOL_Obool)),tc_fun(U_19983,tc_HOL_Obool)),tc_fun(U_19983,tc_HOL_Obool)),c_COMBB(tc_fun(U_19983,tc_HOL_Obool),tc_HOL_Obool,U_19983)),c_fequal)),U_19984)))))
      | ~ c_Equiv__Relations_Opart__equivp(U_19983,U_19984) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK543]),skolemize(U_19982,sK543(U_19984,U_19983))],[f_4821_2]) ).

cnf(f_4821_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_19983,tc_HOL_Obool)),sK543(U_19984,U_19983)),hAPP(hAPP(c_COMBB(tc_fun(U_19983,tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_19983,tc_HOL_Obool)),c_HOL_OEx(U_19983)),hAPP(hAPP(c_COMBB(tc_fun(U_19983,tc_HOL_Obool),tc_fun(U_19983,tc_HOL_Obool),tc_fun(U_19983,tc_HOL_Obool)),hAPP(c_COMBS(U_19983,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_19983),c_fconj),hAPP(hAPP(c_COMBS(U_19983,U_19983,tc_HOL_Obool),U_19984),c_COMBI(U_19983))))),hAPP(hAPP(c_COMBC(tc_fun(U_19983,tc_HOL_Obool),tc_fun(U_19983,tc_fun(U_19983,tc_HOL_Obool)),tc_fun(U_19983,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_19983,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_19983,tc_fun(U_19983,tc_HOL_Obool)),tc_fun(U_19983,tc_HOL_Obool)),tc_fun(U_19983,tc_HOL_Obool)),c_COMBB(tc_fun(U_19983,tc_HOL_Obool),tc_HOL_Obool,U_19983)),c_fequal)),U_19984)))))
    | ~ c_Equiv__Relations_Opart__equivp(U_19983,U_19984) ),
    inference(clausify,[status(thm)],[f_4821_3]) ).

fof(f_4822_1,plain,
    ! [V_f_2,T_c,T_b] :
      ( ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
        | hAPP(c_Fun_Ocomp(T_c,T_b,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)),V_f_2) != c_Fun_Oid(T_b) )
      & ( hAPP(c_Fun_Ocomp(T_c,T_b,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)),V_f_2) = c_Fun_Oid(T_b)
        | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ),
    inference(fof_nnf,[status(thm)],[fact_inj__iff]) ).

fof(f_4822_2,plain,
    ! [U_19987,U_19986,U_19985] :
      ( ( c_Fun_Oinj__on(U_19985,U_19986,U_19987,c_Orderings_Otop__class_Otop(tc_fun(U_19985,tc_HOL_Obool)))
        | hAPP(c_Fun_Ocomp(U_19986,U_19985,U_19985,c_Hilbert__Choice_Oinv__into(U_19985,U_19986,c_Orderings_Otop__class_Otop(tc_fun(U_19985,tc_HOL_Obool)),U_19987)),U_19987) != c_Fun_Oid(U_19985) )
      & ( hAPP(c_Fun_Ocomp(U_19986,U_19985,U_19985,c_Hilbert__Choice_Oinv__into(U_19985,U_19986,c_Orderings_Otop__class_Otop(tc_fun(U_19985,tc_HOL_Obool)),U_19987)),U_19987) = c_Fun_Oid(U_19985)
        | ~ c_Fun_Oinj__on(U_19985,U_19986,U_19987,c_Orderings_Otop__class_Otop(tc_fun(U_19985,tc_HOL_Obool))) ) ),
    inference(variable_rename,[status(thm)],[f_4822_1]) ).

fof(f_4822_3,plain,
    ( ! [U_19993,U_19991,U_19989] :
        ( c_Fun_Oinj__on(U_19989,U_19991,U_19993,c_Orderings_Otop__class_Otop(tc_fun(U_19989,tc_HOL_Obool)))
        | hAPP(c_Fun_Ocomp(U_19991,U_19989,U_19989,c_Hilbert__Choice_Oinv__into(U_19989,U_19991,c_Orderings_Otop__class_Otop(tc_fun(U_19989,tc_HOL_Obool)),U_19993)),U_19993) != c_Fun_Oid(U_19989) )
    & ! [U_19992,U_19990,U_19988] :
        ( hAPP(c_Fun_Ocomp(U_19990,U_19988,U_19988,c_Hilbert__Choice_Oinv__into(U_19988,U_19990,c_Orderings_Otop__class_Otop(tc_fun(U_19988,tc_HOL_Obool)),U_19992)),U_19992) = c_Fun_Oid(U_19988)
        | ~ c_Fun_Oinj__on(U_19988,U_19990,U_19992,c_Orderings_Otop__class_Otop(tc_fun(U_19988,tc_HOL_Obool))) ) ),
    inference(miniscope,[status(thm)],[f_4822_2]) ).

cnf(f_4822_4,plain,
    ( hAPP(c_Fun_Ocomp(U_19990,U_19988,U_19988,c_Hilbert__Choice_Oinv__into(U_19988,U_19990,c_Orderings_Otop__class_Otop(tc_fun(U_19988,tc_HOL_Obool)),U_19992)),U_19992) = c_Fun_Oid(U_19988)
    | ~ c_Fun_Oinj__on(U_19988,U_19990,U_19992,c_Orderings_Otop__class_Otop(tc_fun(U_19988,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4822_3]) ).

cnf(f_4822_5,plain,
    ( c_Fun_Oinj__on(U_19989,U_19991,U_19993,c_Orderings_Otop__class_Otop(tc_fun(U_19989,tc_HOL_Obool)))
    | hAPP(c_Fun_Ocomp(U_19991,U_19989,U_19989,c_Hilbert__Choice_Oinv__into(U_19989,U_19991,c_Orderings_Otop__class_Otop(tc_fun(U_19989,tc_HOL_Obool)),U_19993)),U_19993) != c_Fun_Oid(U_19989) ),
    inference(clausify,[status(thm)],[f_4822_3]) ).

fof(f_4823_1,plain,
    ! [V_f_2,T_c,T_b] :
      ( hAPP(c_Fun_Ocomp(T_c,T_b,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)),V_f_2) = c_Fun_Oid(T_b)
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_inv__o__cancel]) ).

fof(f_4823_2,plain,
    ! [U_19996,U_19995,U_19994] :
      ( hAPP(c_Fun_Ocomp(U_19995,U_19994,U_19994,c_Hilbert__Choice_Oinv__into(U_19994,U_19995,c_Orderings_Otop__class_Otop(tc_fun(U_19994,tc_HOL_Obool)),U_19996)),U_19996) = c_Fun_Oid(U_19994)
      | ~ c_Fun_Oinj__on(U_19994,U_19995,U_19996,c_Orderings_Otop__class_Otop(tc_fun(U_19994,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_4823_1]) ).

cnf(f_4823_3,plain,
    ( hAPP(c_Fun_Ocomp(U_19995,U_19994,U_19994,c_Hilbert__Choice_Oinv__into(U_19994,U_19995,c_Orderings_Otop__class_Otop(tc_fun(U_19994,tc_HOL_Obool)),U_19996)),U_19996) = c_Fun_Oid(U_19994)
    | ~ c_Fun_Oinj__on(U_19994,U_19995,U_19996,c_Orderings_Otop__class_Otop(tc_fun(U_19994,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4823_2]) ).

fof(f_4824_1,plain,
    ! [T_b] : c_Hilbert__Choice_Oinv__into(T_b,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Fun_Oid(T_b)) = c_Fun_Oid(T_b),
    inference(fof_nnf,[status(thm)],[fact_inv__id]) ).

fof(f_4824_2,plain,
    ! [U_19997] : c_Hilbert__Choice_Oinv__into(U_19997,U_19997,c_Orderings_Otop__class_Otop(tc_fun(U_19997,tc_HOL_Obool)),c_Fun_Oid(U_19997)) = c_Fun_Oid(U_19997),
    inference(variable_rename,[status(thm)],[f_4824_1]) ).

cnf(f_4824_3,plain,
    c_Hilbert__Choice_Oinv__into(U_19997,U_19997,c_Orderings_Otop__class_Otop(tc_fun(U_19997,tc_HOL_Obool)),c_Fun_Oid(U_19997)) = c_Fun_Oid(U_19997),
    inference(clausify,[status(thm)],[f_4824_2]) ).

fof(f_4825_1,plain,
    ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),V_y_2) = V_x_2
      | hAPP(V_f_2,V_x_2) != V_y_2
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_inv__f__eq]) ).

fof(f_4825_2,plain,
    ! [U_20002,U_20001,U_20000,U_19999,U_19998] :
      ( hAPP(c_Hilbert__Choice_Oinv__into(U_19998,U_19999,c_Orderings_Otop__class_Otop(tc_fun(U_19998,tc_HOL_Obool)),U_20000),U_20002) = U_20001
      | hAPP(U_20000,U_20001) != U_20002
      | ~ c_Fun_Oinj__on(U_19998,U_19999,U_20000,c_Orderings_Otop__class_Otop(tc_fun(U_19998,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_4825_1]) ).

cnf(f_4825_3,plain,
    ( hAPP(c_Hilbert__Choice_Oinv__into(U_19998,U_19999,c_Orderings_Otop__class_Otop(tc_fun(U_19998,tc_HOL_Obool)),U_20000),U_20002) = U_20001
    | hAPP(U_20000,U_20001) != U_20002
    | ~ c_Fun_Oinj__on(U_19998,U_19999,U_20000,c_Orderings_Otop__class_Otop(tc_fun(U_19998,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4825_2]) ).

fof(f_4826_1,plain,
    ! [V_x_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_inv__f__f]) ).

fof(f_4826_2,plain,
    ! [U_20006,U_20005,U_20004,U_20003] :
      ( hAPP(c_Hilbert__Choice_Oinv__into(U_20003,U_20004,c_Orderings_Otop__class_Otop(tc_fun(U_20003,tc_HOL_Obool)),U_20005),hAPP(U_20005,U_20006)) = U_20006
      | ~ c_Fun_Oinj__on(U_20003,U_20004,U_20005,c_Orderings_Otop__class_Otop(tc_fun(U_20003,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_4826_1]) ).

cnf(f_4826_3,plain,
    ( hAPP(c_Hilbert__Choice_Oinv__into(U_20003,U_20004,c_Orderings_Otop__class_Otop(tc_fun(U_20003,tc_HOL_Obool)),U_20005),hAPP(U_20005,U_20006)) = U_20006
    | ~ c_Fun_Oinj__on(U_20003,U_20004,U_20005,c_Orderings_Otop__class_Otop(tc_fun(U_20003,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4826_2]) ).

fof(f_4827_1,plain,
    ! [V_x_2,V_A_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_inv__into__f__f]) ).

fof(f_4827_2,plain,
    ! [U_20011,U_20010,U_20009,U_20008,U_20007] :
      ( hAPP(c_Hilbert__Choice_Oinv__into(U_20007,U_20008,U_20010,U_20009),hAPP(U_20009,U_20011)) = U_20011
      | ~ hBOOL(hAPP(hAPP(c_member(U_20007),U_20011),U_20010))
      | ~ c_Fun_Oinj__on(U_20007,U_20008,U_20009,U_20010) ),
    inference(variable_rename,[status(thm)],[f_4827_1]) ).

cnf(f_4827_3,plain,
    ( hAPP(c_Hilbert__Choice_Oinv__into(U_20007,U_20008,U_20010,U_20009),hAPP(U_20009,U_20011)) = U_20011
    | ~ hBOOL(hAPP(hAPP(c_member(U_20007),U_20011),U_20010))
    | ~ c_Fun_Oinj__on(U_20007,U_20008,U_20009,U_20010) ),
    inference(clausify,[status(thm)],[f_4827_2]) ).

fof(f_4828_1,plain,
    ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),V_y_2) = V_x_2
      | hAPP(V_f_2,V_x_2) != V_y_2
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_inv__into__f__eq]) ).

fof(f_4828_2,plain,
    ! [U_20017,U_20016,U_20015,U_20014,U_20013,U_20012] :
      ( hAPP(c_Hilbert__Choice_Oinv__into(U_20012,U_20013,U_20015,U_20014),U_20017) = U_20016
      | hAPP(U_20014,U_20016) != U_20017
      | ~ hBOOL(hAPP(hAPP(c_member(U_20012),U_20016),U_20015))
      | ~ c_Fun_Oinj__on(U_20012,U_20013,U_20014,U_20015) ),
    inference(variable_rename,[status(thm)],[f_4828_1]) ).

cnf(f_4828_3,plain,
    ( hAPP(c_Hilbert__Choice_Oinv__into(U_20012,U_20013,U_20015,U_20014),U_20017) = U_20016
    | hAPP(U_20014,U_20016) != U_20017
    | ~ hBOOL(hAPP(hAPP(c_member(U_20012),U_20016),U_20015))
    | ~ c_Fun_Oinj__on(U_20012,U_20013,U_20014,U_20015) ),
    inference(clausify,[status(thm)],[f_4828_2]) ).

fof(f_4829_1,plain,
    ! [V_A_2,V_f_2,T_c,V_y_2,T_b] :
      ( hAPP(V_f_2,hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_b,V_A_2,V_f_2),V_y_2)) = V_y_2
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) ),
    inference(fof_nnf,[status(thm)],[fact_f__inv__into__f]) ).

fof(f_4829_2,plain,
    ! [U_20022,U_20021,U_20020,U_20019,U_20018] :
      ( hAPP(U_20021,hAPP(c_Hilbert__Choice_Oinv__into(U_20020,U_20018,U_20022,U_20021),U_20019)) = U_20019
      | ~ hBOOL(hAPP(hAPP(c_member(U_20018),U_20019),hAPP(c_Set_Oimage(U_20020,U_20018,U_20021),U_20022))) ),
    inference(variable_rename,[status(thm)],[f_4829_1]) ).

cnf(f_4829_3,plain,
    ( hAPP(U_20021,hAPP(c_Hilbert__Choice_Oinv__into(U_20020,U_20018,U_20022,U_20021),U_20019)) = U_20019
    | ~ hBOOL(hAPP(hAPP(c_member(U_20018),U_20019),hAPP(c_Set_Oimage(U_20020,U_20018,U_20021),U_20022))) ),
    inference(clausify,[status(thm)],[f_4829_2]) ).

fof(f_4830_1,plain,
    ! [V_A_2,V_f_2,T_c,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_c),hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_b,V_A_2,V_f_2),V_x_2)),V_A_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) ),
    inference(fof_nnf,[status(thm)],[fact_inv__into__into]) ).

fof(f_4830_2,plain,
    ! [U_20027,U_20026,U_20025,U_20024,U_20023] :
      ( hBOOL(hAPP(hAPP(c_member(U_20025),hAPP(c_Hilbert__Choice_Oinv__into(U_20025,U_20023,U_20027,U_20026),U_20024)),U_20027))
      | ~ hBOOL(hAPP(hAPP(c_member(U_20023),U_20024),hAPP(c_Set_Oimage(U_20025,U_20023,U_20026),U_20027))) ),
    inference(variable_rename,[status(thm)],[f_4830_1]) ).

cnf(f_4830_3,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20025),hAPP(c_Hilbert__Choice_Oinv__into(U_20025,U_20023,U_20027,U_20026),U_20024)),U_20027))
    | ~ hBOOL(hAPP(hAPP(c_member(U_20023),U_20024),hAPP(c_Set_Oimage(U_20025,U_20023,U_20026),U_20027))) ),
    inference(clausify,[status(thm)],[f_4830_2]) ).

fof(f_4831_1,plain,
    ! [V_y_2,V_x_2,V_f_2,V_A_2,T_c,T_b] :
      ( V_x_2 = V_y_2
      | ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
      | hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),V_x_2) != hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),V_y_2) ),
    inference(fof_nnf,[status(thm)],[fact_inv__into__injective]) ).

fof(f_4831_2,plain,
    ! [U_20033,U_20032,U_20031,U_20030,U_20029,U_20028] :
      ( U_20032 = U_20033
      | ~ hBOOL(hAPP(hAPP(c_member(U_20029),U_20033),hAPP(c_Set_Oimage(U_20028,U_20029,U_20031),U_20030)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_20029),U_20032),hAPP(c_Set_Oimage(U_20028,U_20029,U_20031),U_20030)))
      | hAPP(c_Hilbert__Choice_Oinv__into(U_20028,U_20029,U_20030,U_20031),U_20032) != hAPP(c_Hilbert__Choice_Oinv__into(U_20028,U_20029,U_20030,U_20031),U_20033) ),
    inference(variable_rename,[status(thm)],[f_4831_1]) ).

cnf(f_4831_3,plain,
    ( U_20032 = U_20033
    | ~ hBOOL(hAPP(hAPP(c_member(U_20029),U_20033),hAPP(c_Set_Oimage(U_20028,U_20029,U_20031),U_20030)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_20029),U_20032),hAPP(c_Set_Oimage(U_20028,U_20029,U_20031),U_20030)))
    | hAPP(c_Hilbert__Choice_Oinv__into(U_20028,U_20029,U_20030,U_20031),U_20032) != hAPP(c_Hilbert__Choice_Oinv__into(U_20028,U_20029,U_20030,U_20031),U_20033) ),
    inference(clausify,[status(thm)],[f_4831_2]) ).

fof(f_4832_1,plain,
    ! [V_A_2,V_f_2,T_b,T_c] :
      ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Oimage(T_b,T_c,c_Hilbert__Choice_Oinv__into(T_c,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2)),V_A_2)) = V_A_2
      | hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ),
    inference(fof_nnf,[status(thm)],[fact_image__surj__f__inv__f]) ).

fof(f_4832_2,plain,
    ! [U_20037,U_20036,U_20035,U_20034] :
      ( hAPP(c_Set_Oimage(U_20034,U_20035,U_20036),hAPP(c_Set_Oimage(U_20035,U_20034,c_Hilbert__Choice_Oinv__into(U_20034,U_20035,c_Orderings_Otop__class_Otop(tc_fun(U_20034,tc_HOL_Obool)),U_20036)),U_20037)) = U_20037
      | hAPP(c_Set_Oimage(U_20034,U_20035,U_20036),c_Orderings_Otop__class_Otop(tc_fun(U_20034,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_20035,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_4832_1]) ).

cnf(f_4832_3,plain,
    ( hAPP(c_Set_Oimage(U_20034,U_20035,U_20036),hAPP(c_Set_Oimage(U_20035,U_20034,c_Hilbert__Choice_Oinv__into(U_20034,U_20035,c_Orderings_Otop__class_Otop(tc_fun(U_20034,tc_HOL_Obool)),U_20036)),U_20037)) = U_20037
    | hAPP(c_Set_Oimage(U_20034,U_20035,U_20036),c_Orderings_Otop__class_Otop(tc_fun(U_20034,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_20035,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4832_2]) ).

fof(f_4833_1,plain,
    ! [V_y_2,V_f_2,T_b,T_c] :
      ( hAPP(V_f_2,hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2),V_y_2)) = V_y_2
      | hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ),
    inference(fof_nnf,[status(thm)],[fact_surj__f__inv__f]) ).

fof(f_4833_2,plain,
    ! [U_20041,U_20040,U_20039,U_20038] :
      ( hAPP(U_20040,hAPP(c_Hilbert__Choice_Oinv__into(U_20038,U_20039,c_Orderings_Otop__class_Otop(tc_fun(U_20038,tc_HOL_Obool)),U_20040),U_20041)) = U_20041
      | hAPP(c_Set_Oimage(U_20038,U_20039,U_20040),c_Orderings_Otop__class_Otop(tc_fun(U_20038,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_20039,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_4833_1]) ).

cnf(f_4833_3,plain,
    ( hAPP(U_20040,hAPP(c_Hilbert__Choice_Oinv__into(U_20038,U_20039,c_Orderings_Otop__class_Otop(tc_fun(U_20038,tc_HOL_Obool)),U_20040),U_20041)) = U_20041
    | hAPP(c_Set_Oimage(U_20038,U_20039,U_20040),c_Orderings_Otop__class_Otop(tc_fun(U_20038,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_20039,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4833_2]) ).

fof(f_4834_1,plain,
    ! [V_f_2,T_b,T_c] :
      ( ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
        | ? [B_x] : hAPP(V_f_2,hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2),B_x)) != B_x )
      & ( ! [B_x] : hAPP(V_f_2,hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2),B_x)) = B_x
        | hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_surj__iff__all]) ).

fof(f_4834_2,plain,
    ! [U_20046,U_20045,U_20044] :
      ( ( hAPP(c_Set_Oimage(U_20044,U_20045,U_20046),c_Orderings_Otop__class_Otop(tc_fun(U_20044,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_20045,tc_HOL_Obool))
        | ? [U_20043] : hAPP(U_20046,hAPP(c_Hilbert__Choice_Oinv__into(U_20044,U_20045,c_Orderings_Otop__class_Otop(tc_fun(U_20044,tc_HOL_Obool)),U_20046),U_20043)) != U_20043 )
      & ( ! [U_20042] : hAPP(U_20046,hAPP(c_Hilbert__Choice_Oinv__into(U_20044,U_20045,c_Orderings_Otop__class_Otop(tc_fun(U_20044,tc_HOL_Obool)),U_20046),U_20042)) = U_20042
        | hAPP(c_Set_Oimage(U_20044,U_20045,U_20046),c_Orderings_Otop__class_Otop(tc_fun(U_20044,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_20045,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_4834_1]) ).

fof(f_4834_3,plain,
    ( ! [U_20052,U_20050,U_20048] :
        ( hAPP(c_Set_Oimage(U_20048,U_20050,U_20052),c_Orderings_Otop__class_Otop(tc_fun(U_20048,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_20050,tc_HOL_Obool))
        | ? [U_20043] : hAPP(U_20052,hAPP(c_Hilbert__Choice_Oinv__into(U_20048,U_20050,c_Orderings_Otop__class_Otop(tc_fun(U_20048,tc_HOL_Obool)),U_20052),U_20043)) != U_20043 )
    & ! [U_20051,U_20049,U_20047] :
        ( ! [U_20042] : hAPP(U_20051,hAPP(c_Hilbert__Choice_Oinv__into(U_20047,U_20049,c_Orderings_Otop__class_Otop(tc_fun(U_20047,tc_HOL_Obool)),U_20051),U_20042)) = U_20042
        | hAPP(c_Set_Oimage(U_20047,U_20049,U_20051),c_Orderings_Otop__class_Otop(tc_fun(U_20047,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_20049,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_4834_2]) ).

fof(f_4834_4,plain,
    ( ! [U_20052,U_20050,U_20048] :
        ( hAPP(c_Set_Oimage(U_20048,U_20050,U_20052),c_Orderings_Otop__class_Otop(tc_fun(U_20048,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_20050,tc_HOL_Obool))
        | hAPP(U_20052,hAPP(c_Hilbert__Choice_Oinv__into(U_20048,U_20050,c_Orderings_Otop__class_Otop(tc_fun(U_20048,tc_HOL_Obool)),U_20052),sK544(U_20052,U_20050,U_20048))) != sK544(U_20052,U_20050,U_20048) )
    & ! [U_20051,U_20049,U_20047] :
        ( ! [U_20042] : hAPP(U_20051,hAPP(c_Hilbert__Choice_Oinv__into(U_20047,U_20049,c_Orderings_Otop__class_Otop(tc_fun(U_20047,tc_HOL_Obool)),U_20051),U_20042)) = U_20042
        | hAPP(c_Set_Oimage(U_20047,U_20049,U_20051),c_Orderings_Otop__class_Otop(tc_fun(U_20047,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_20049,tc_HOL_Obool)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK544]),skolemize(U_20043,sK544(U_20052,U_20050,U_20048))],[f_4834_3]) ).

cnf(f_4834_5,plain,
    ( hAPP(U_20051,hAPP(c_Hilbert__Choice_Oinv__into(U_20047,U_20049,c_Orderings_Otop__class_Otop(tc_fun(U_20047,tc_HOL_Obool)),U_20051),U_20042)) = U_20042
    | hAPP(c_Set_Oimage(U_20047,U_20049,U_20051),c_Orderings_Otop__class_Otop(tc_fun(U_20047,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_20049,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4834_4]) ).

cnf(f_4834_6,plain,
    ( hAPP(c_Set_Oimage(U_20048,U_20050,U_20052),c_Orderings_Otop__class_Otop(tc_fun(U_20048,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_20050,tc_HOL_Obool))
    | hAPP(U_20052,hAPP(c_Hilbert__Choice_Oinv__into(U_20048,U_20050,c_Orderings_Otop__class_Otop(tc_fun(U_20048,tc_HOL_Obool)),U_20052),sK544(U_20052,U_20050,U_20048))) != sK544(U_20052,U_20050,U_20048) ),
    inference(clausify,[status(thm)],[f_4834_4]) ).

fof(f_4835_1,plain,
    ! [V_B_H_2,V_A_H_2,V_A_2,V_f_2,T_b,T_c] :
      ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Oimage(T_b,T_c,c_Hilbert__Choice_Oinv__into(T_c,T_b,V_A_2,V_f_2)),V_B_H_2)) = V_B_H_2
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_H_2),V_A_H_2))
      | hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) != V_A_H_2 ),
    inference(fof_nnf,[status(thm)],[fact_image__inv__into__cancel]) ).

fof(f_4835_2,plain,
    ! [U_20058,U_20057,U_20056,U_20055,U_20054,U_20053] :
      ( hAPP(c_Set_Oimage(U_20053,U_20054,U_20055),hAPP(c_Set_Oimage(U_20054,U_20053,c_Hilbert__Choice_Oinv__into(U_20053,U_20054,U_20056,U_20055)),U_20058)) = U_20058
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20054,tc_HOL_Obool)),U_20058),U_20057))
      | hAPP(c_Set_Oimage(U_20053,U_20054,U_20055),U_20056) != U_20057 ),
    inference(variable_rename,[status(thm)],[f_4835_1]) ).

cnf(f_4835_3,plain,
    ( hAPP(c_Set_Oimage(U_20053,U_20054,U_20055),hAPP(c_Set_Oimage(U_20054,U_20053,c_Hilbert__Choice_Oinv__into(U_20053,U_20054,U_20056,U_20055)),U_20058)) = U_20058
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20054,tc_HOL_Obool)),U_20058),U_20057))
    | hAPP(c_Set_Oimage(U_20053,U_20054,U_20055),U_20056) != U_20057 ),
    inference(clausify,[status(thm)],[f_4835_2]) ).

fof(f_4836_1,plain,
    ! [V_x_2,V_f_2,V_A_2,T_c,T_b] : hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),V_x_2) = c_Hilbert__Choice_OEps(T_b,hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),V_x_2))),
    inference(fof_nnf,[status(thm)],[fact_inv__into__def]) ).

fof(f_4836_2,plain,
    ! [U_20063,U_20062,U_20061,U_20060,U_20059] : hAPP(c_Hilbert__Choice_Oinv__into(U_20059,U_20060,U_20061,U_20062),U_20063) = c_Hilbert__Choice_OEps(U_20059,hAPP(hAPP(c_COMBS(U_20059,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_20059),c_fconj),hAPP(hAPP(c_COMBC(U_20059,tc_fun(U_20059,tc_HOL_Obool),tc_HOL_Obool),c_member(U_20059)),U_20061))),hAPP(hAPP(c_COMBC(U_20059,U_20060,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_20060,tc_fun(U_20060,tc_HOL_Obool),U_20059),c_fequal),U_20062)),U_20063))),
    inference(variable_rename,[status(thm)],[f_4836_1]) ).

cnf(f_4836_3,plain,
    hAPP(c_Hilbert__Choice_Oinv__into(U_20059,U_20060,U_20061,U_20062),U_20063) = c_Hilbert__Choice_OEps(U_20059,hAPP(hAPP(c_COMBS(U_20059,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_20059),c_fconj),hAPP(hAPP(c_COMBC(U_20059,tc_fun(U_20059,tc_HOL_Obool),tc_HOL_Obool),c_member(U_20059)),U_20061))),hAPP(hAPP(c_COMBC(U_20059,U_20060,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_20060,tc_fun(U_20060,tc_HOL_Obool),U_20059),c_fequal),U_20062)),U_20063))),
    inference(clausify,[status(thm)],[f_4836_2]) ).

fof(f_4837_1,plain,
    ! [V_y_2,V_f_2,T_c,T_b] : hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),V_y_2) = c_Hilbert__Choice_OEps(T_b,hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),V_y_2)),
    inference(fof_nnf,[status(thm)],[fact_inv__def]) ).

fof(f_4837_2,plain,
    ! [U_20067,U_20066,U_20065,U_20064] : hAPP(c_Hilbert__Choice_Oinv__into(U_20064,U_20065,c_Orderings_Otop__class_Otop(tc_fun(U_20064,tc_HOL_Obool)),U_20066),U_20067) = c_Hilbert__Choice_OEps(U_20064,hAPP(hAPP(c_COMBC(U_20064,U_20065,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_20065,tc_fun(U_20065,tc_HOL_Obool),U_20064),c_fequal),U_20066)),U_20067)),
    inference(variable_rename,[status(thm)],[f_4837_1]) ).

cnf(f_4837_3,plain,
    hAPP(c_Hilbert__Choice_Oinv__into(U_20064,U_20065,c_Orderings_Otop__class_Otop(tc_fun(U_20064,tc_HOL_Obool)),U_20066),U_20067) = c_Hilbert__Choice_OEps(U_20064,hAPP(hAPP(c_COMBC(U_20064,U_20065,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_20065,tc_fun(U_20065,tc_HOL_Obool),U_20064),c_fequal),U_20066)),U_20067)),
    inference(clausify,[status(thm)],[f_4837_2]) ).

fof(f_4838_1,plain,
    ! [V_g_2,T_d,V_f_2,T_c,T_b] :
      ( hAPP(c_Fun_Ocomp(T_c,T_d,T_b,hAPP(c_Fun_Ocomp(T_b,T_d,T_c,V_g_2),c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2))),V_f_2) = V_g_2
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_o__inv__o__cancel]) ).

fof(f_4838_2,plain,
    ! [U_20072,U_20071,U_20070,U_20069,U_20068] :
      ( hAPP(c_Fun_Ocomp(U_20069,U_20071,U_20068,hAPP(c_Fun_Ocomp(U_20068,U_20071,U_20069,U_20072),c_Hilbert__Choice_Oinv__into(U_20068,U_20069,c_Orderings_Otop__class_Otop(tc_fun(U_20068,tc_HOL_Obool)),U_20070))),U_20070) = U_20072
      | ~ c_Fun_Oinj__on(U_20068,U_20069,U_20070,c_Orderings_Otop__class_Otop(tc_fun(U_20068,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_4838_1]) ).

cnf(f_4838_3,plain,
    ( hAPP(c_Fun_Ocomp(U_20069,U_20071,U_20068,hAPP(c_Fun_Ocomp(U_20068,U_20071,U_20069,U_20072),c_Hilbert__Choice_Oinv__into(U_20068,U_20069,c_Orderings_Otop__class_Otop(tc_fun(U_20068,tc_HOL_Obool)),U_20070))),U_20070) = U_20072
    | ~ c_Fun_Oinj__on(U_20068,U_20069,U_20070,c_Orderings_Otop__class_Otop(tc_fun(U_20068,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4838_2]) ).

fof(f_4839_1,plain,
    ! [V_f_2,T_b,T_c] :
      ( c_Fun_Oinj__on(T_b,T_c,c_Hilbert__Choice_Oinv__into(T_c,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
      | hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ),
    inference(fof_nnf,[status(thm)],[fact_surj__imp__inj__inv]) ).

fof(f_4839_2,plain,
    ! [U_20075,U_20074,U_20073] :
      ( c_Fun_Oinj__on(U_20074,U_20073,c_Hilbert__Choice_Oinv__into(U_20073,U_20074,c_Orderings_Otop__class_Otop(tc_fun(U_20073,tc_HOL_Obool)),U_20075),c_Orderings_Otop__class_Otop(tc_fun(U_20074,tc_HOL_Obool)))
      | hAPP(c_Set_Oimage(U_20073,U_20074,U_20075),c_Orderings_Otop__class_Otop(tc_fun(U_20073,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_20074,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_4839_1]) ).

cnf(f_4839_3,plain,
    ( c_Fun_Oinj__on(U_20074,U_20073,c_Hilbert__Choice_Oinv__into(U_20073,U_20074,c_Orderings_Otop__class_Otop(tc_fun(U_20073,tc_HOL_Obool)),U_20075),c_Orderings_Otop__class_Otop(tc_fun(U_20074,tc_HOL_Obool)))
    | hAPP(c_Set_Oimage(U_20073,U_20074,U_20075),c_Orderings_Otop__class_Otop(tc_fun(U_20073,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_20074,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4839_2]) ).

fof(f_4840_1,plain,
    ! [V_X_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Set_Oimage(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_X_2)) = V_X_2
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_inv__image__comp]) ).

fof(f_4840_2,plain,
    ! [U_20079,U_20078,U_20077,U_20076] :
      ( hAPP(c_Set_Oimage(U_20077,U_20076,c_Hilbert__Choice_Oinv__into(U_20076,U_20077,c_Orderings_Otop__class_Otop(tc_fun(U_20076,tc_HOL_Obool)),U_20078)),hAPP(c_Set_Oimage(U_20076,U_20077,U_20078),U_20079)) = U_20079
      | ~ c_Fun_Oinj__on(U_20076,U_20077,U_20078,c_Orderings_Otop__class_Otop(tc_fun(U_20076,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_4840_1]) ).

cnf(f_4840_3,plain,
    ( hAPP(c_Set_Oimage(U_20077,U_20076,c_Hilbert__Choice_Oinv__into(U_20076,U_20077,c_Orderings_Otop__class_Otop(tc_fun(U_20076,tc_HOL_Obool)),U_20078)),hAPP(c_Set_Oimage(U_20076,U_20077,U_20078),U_20079)) = U_20079
    | ~ c_Fun_Oinj__on(U_20076,U_20077,U_20078,c_Orderings_Otop__class_Otop(tc_fun(U_20076,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4840_2]) ).

fof(f_4841_1,plain,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Set_Oimage(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = V_A_2
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_image__inv__f__f]) ).

fof(f_4841_2,plain,
    ! [U_20083,U_20082,U_20081,U_20080] :
      ( hAPP(c_Set_Oimage(U_20081,U_20080,c_Hilbert__Choice_Oinv__into(U_20080,U_20081,c_Orderings_Otop__class_Otop(tc_fun(U_20080,tc_HOL_Obool)),U_20082)),hAPP(c_Set_Oimage(U_20080,U_20081,U_20082),U_20083)) = U_20083
      | ~ c_Fun_Oinj__on(U_20080,U_20081,U_20082,c_Orderings_Otop__class_Otop(tc_fun(U_20080,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_4841_1]) ).

cnf(f_4841_3,plain,
    ( hAPP(c_Set_Oimage(U_20081,U_20080,c_Hilbert__Choice_Oinv__into(U_20080,U_20081,c_Orderings_Otop__class_Otop(tc_fun(U_20080,tc_HOL_Obool)),U_20082)),hAPP(c_Set_Oimage(U_20080,U_20081,U_20082),U_20083)) = U_20083
    | ~ c_Fun_Oinj__on(U_20080,U_20081,U_20082,c_Orderings_Otop__class_Otop(tc_fun(U_20080,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4841_2]) ).

fof(f_4842_1,plain,
    ! [V_f_2,T_c,T_b] :
      ( hAPP(c_Set_Oimage(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_inj__imp__surj__inv]) ).

fof(f_4842_2,plain,
    ! [U_20086,U_20085,U_20084] :
      ( hAPP(c_Set_Oimage(U_20085,U_20084,c_Hilbert__Choice_Oinv__into(U_20084,U_20085,c_Orderings_Otop__class_Otop(tc_fun(U_20084,tc_HOL_Obool)),U_20086)),c_Orderings_Otop__class_Otop(tc_fun(U_20085,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_20084,tc_HOL_Obool))
      | ~ c_Fun_Oinj__on(U_20084,U_20085,U_20086,c_Orderings_Otop__class_Otop(tc_fun(U_20084,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_4842_1]) ).

cnf(f_4842_3,plain,
    ( hAPP(c_Set_Oimage(U_20085,U_20084,c_Hilbert__Choice_Oinv__into(U_20084,U_20085,c_Orderings_Otop__class_Otop(tc_fun(U_20084,tc_HOL_Obool)),U_20086)),c_Orderings_Otop__class_Otop(tc_fun(U_20085,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_20084,tc_HOL_Obool))
    | ~ c_Fun_Oinj__on(U_20084,U_20085,U_20086,c_Orderings_Otop__class_Otop(tc_fun(U_20084,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4842_2]) ).

fof(f_4843_1,plain,
    ! [V_S_2,V_A_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Set_Oimage(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_S_2)) = V_S_2
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_A_2))
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_inv__into__image__cancel]) ).

fof(f_4843_2,plain,
    ! [U_20091,U_20090,U_20089,U_20088,U_20087] :
      ( hAPP(c_Set_Oimage(U_20088,U_20087,c_Hilbert__Choice_Oinv__into(U_20087,U_20088,U_20090,U_20089)),hAPP(c_Set_Oimage(U_20087,U_20088,U_20089),U_20091)) = U_20091
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20087,tc_HOL_Obool)),U_20091),U_20090))
      | ~ c_Fun_Oinj__on(U_20087,U_20088,U_20089,U_20090) ),
    inference(variable_rename,[status(thm)],[f_4843_1]) ).

cnf(f_4843_3,plain,
    ( hAPP(c_Set_Oimage(U_20088,U_20087,c_Hilbert__Choice_Oinv__into(U_20087,U_20088,U_20090,U_20089)),hAPP(c_Set_Oimage(U_20087,U_20088,U_20089),U_20091)) = U_20091
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20087,tc_HOL_Obool)),U_20091),U_20090))
    | ~ c_Fun_Oinj__on(U_20087,U_20088,U_20089,U_20090) ),
    inference(clausify,[status(thm)],[f_4843_2]) ).

fof(f_4844_1,plain,
    ! [V_A_2,V_f_2,T_c,V_B_2,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,c_Hilbert__Choice_Oinv__into(T_c,T_b,V_A_2,V_f_2),V_B_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) ),
    inference(fof_nnf,[status(thm)],[fact_inj__on__inv__into]) ).

fof(f_4844_2,plain,
    ! [U_20096,U_20095,U_20094,U_20093,U_20092] :
      ( c_Fun_Oinj__on(U_20092,U_20094,c_Hilbert__Choice_Oinv__into(U_20094,U_20092,U_20096,U_20095),U_20093)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20092,tc_HOL_Obool)),U_20093),hAPP(c_Set_Oimage(U_20094,U_20092,U_20095),U_20096))) ),
    inference(variable_rename,[status(thm)],[f_4844_1]) ).

cnf(f_4844_3,plain,
    ( c_Fun_Oinj__on(U_20092,U_20094,c_Hilbert__Choice_Oinv__into(U_20094,U_20092,U_20096,U_20095),U_20093)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20092,tc_HOL_Obool)),U_20093),hAPP(c_Set_Oimage(U_20094,U_20092,U_20095),U_20096))) ),
    inference(clausify,[status(thm)],[f_4844_2]) ).

fof(f_4845_1,plain,
    ! [V_x_2,V_A_2,V_g_2,T_d,V_f_2,T_c,T_b] :
      ( hAPP(c_Hilbert__Choice_Oinv__into(T_d,T_c,V_A_2,hAPP(c_Fun_Ocomp(T_b,T_c,T_d,V_f_2),V_g_2)),V_x_2) = hAPP(hAPP(c_Fun_Ocomp(T_b,T_d,T_c,c_Hilbert__Choice_Oinv__into(T_d,T_b,V_A_2,V_g_2)),c_Hilbert__Choice_Oinv__into(T_b,T_c,hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2),V_f_2)),V_x_2)
      | ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2))))
      | ~ c_Fun_Oinj__on(T_d,T_b,V_g_2,V_A_2)
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_inv__into__comp]) ).

fof(f_4845_2,plain,
    ! [U_20103,U_20102,U_20101,U_20100,U_20099,U_20098,U_20097] :
      ( hAPP(c_Hilbert__Choice_Oinv__into(U_20100,U_20098,U_20102,hAPP(c_Fun_Ocomp(U_20097,U_20098,U_20100,U_20099),U_20101)),U_20103) = hAPP(hAPP(c_Fun_Ocomp(U_20097,U_20100,U_20098,c_Hilbert__Choice_Oinv__into(U_20100,U_20097,U_20102,U_20101)),c_Hilbert__Choice_Oinv__into(U_20097,U_20098,hAPP(c_Set_Oimage(U_20100,U_20097,U_20101),U_20102),U_20099)),U_20103)
      | ~ hBOOL(hAPP(hAPP(c_member(U_20098),U_20103),hAPP(c_Set_Oimage(U_20097,U_20098,U_20099),hAPP(c_Set_Oimage(U_20100,U_20097,U_20101),U_20102))))
      | ~ c_Fun_Oinj__on(U_20100,U_20097,U_20101,U_20102)
      | ~ c_Fun_Oinj__on(U_20097,U_20098,U_20099,hAPP(c_Set_Oimage(U_20100,U_20097,U_20101),U_20102)) ),
    inference(variable_rename,[status(thm)],[f_4845_1]) ).

cnf(f_4845_3,plain,
    ( hAPP(c_Hilbert__Choice_Oinv__into(U_20100,U_20098,U_20102,hAPP(c_Fun_Ocomp(U_20097,U_20098,U_20100,U_20099),U_20101)),U_20103) = hAPP(hAPP(c_Fun_Ocomp(U_20097,U_20100,U_20098,c_Hilbert__Choice_Oinv__into(U_20100,U_20097,U_20102,U_20101)),c_Hilbert__Choice_Oinv__into(U_20097,U_20098,hAPP(c_Set_Oimage(U_20100,U_20097,U_20101),U_20102),U_20099)),U_20103)
    | ~ hBOOL(hAPP(hAPP(c_member(U_20098),U_20103),hAPP(c_Set_Oimage(U_20097,U_20098,U_20099),hAPP(c_Set_Oimage(U_20100,U_20097,U_20101),U_20102))))
    | ~ c_Fun_Oinj__on(U_20100,U_20097,U_20101,U_20102)
    | ~ c_Fun_Oinj__on(U_20097,U_20098,U_20099,hAPP(c_Set_Oimage(U_20100,U_20097,U_20101),U_20102)) ),
    inference(clausify,[status(thm)],[f_4845_2]) ).

fof(f_4846_1,plain,
    ! [V_f_2,T_b,T_c] :
      ( ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
        | hAPP(c_Fun_Ocomp(T_c,T_b,T_b,V_f_2),c_Hilbert__Choice_Oinv__into(T_c,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2)) != c_Fun_Oid(T_b) )
      & ( hAPP(c_Fun_Ocomp(T_c,T_b,T_b,V_f_2),c_Hilbert__Choice_Oinv__into(T_c,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2)) = c_Fun_Oid(T_b)
        | hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_surj__iff]) ).

fof(f_4846_2,plain,
    ! [U_20106,U_20105,U_20104] :
      ( ( hAPP(c_Set_Oimage(U_20104,U_20105,U_20106),c_Orderings_Otop__class_Otop(tc_fun(U_20104,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_20105,tc_HOL_Obool))
        | hAPP(c_Fun_Ocomp(U_20104,U_20105,U_20105,U_20106),c_Hilbert__Choice_Oinv__into(U_20104,U_20105,c_Orderings_Otop__class_Otop(tc_fun(U_20104,tc_HOL_Obool)),U_20106)) != c_Fun_Oid(U_20105) )
      & ( hAPP(c_Fun_Ocomp(U_20104,U_20105,U_20105,U_20106),c_Hilbert__Choice_Oinv__into(U_20104,U_20105,c_Orderings_Otop__class_Otop(tc_fun(U_20104,tc_HOL_Obool)),U_20106)) = c_Fun_Oid(U_20105)
        | hAPP(c_Set_Oimage(U_20104,U_20105,U_20106),c_Orderings_Otop__class_Otop(tc_fun(U_20104,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_20105,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_4846_1]) ).

fof(f_4846_3,plain,
    ( ! [U_20112,U_20110,U_20108] :
        ( hAPP(c_Set_Oimage(U_20108,U_20110,U_20112),c_Orderings_Otop__class_Otop(tc_fun(U_20108,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_20110,tc_HOL_Obool))
        | hAPP(c_Fun_Ocomp(U_20108,U_20110,U_20110,U_20112),c_Hilbert__Choice_Oinv__into(U_20108,U_20110,c_Orderings_Otop__class_Otop(tc_fun(U_20108,tc_HOL_Obool)),U_20112)) != c_Fun_Oid(U_20110) )
    & ! [U_20111,U_20109,U_20107] :
        ( hAPP(c_Fun_Ocomp(U_20107,U_20109,U_20109,U_20111),c_Hilbert__Choice_Oinv__into(U_20107,U_20109,c_Orderings_Otop__class_Otop(tc_fun(U_20107,tc_HOL_Obool)),U_20111)) = c_Fun_Oid(U_20109)
        | hAPP(c_Set_Oimage(U_20107,U_20109,U_20111),c_Orderings_Otop__class_Otop(tc_fun(U_20107,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_20109,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_4846_2]) ).

cnf(f_4846_4,plain,
    ( hAPP(c_Fun_Ocomp(U_20107,U_20109,U_20109,U_20111),c_Hilbert__Choice_Oinv__into(U_20107,U_20109,c_Orderings_Otop__class_Otop(tc_fun(U_20107,tc_HOL_Obool)),U_20111)) = c_Fun_Oid(U_20109)
    | hAPP(c_Set_Oimage(U_20107,U_20109,U_20111),c_Orderings_Otop__class_Otop(tc_fun(U_20107,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_20109,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4846_3]) ).

cnf(f_4846_5,plain,
    ( hAPP(c_Set_Oimage(U_20108,U_20110,U_20112),c_Orderings_Otop__class_Otop(tc_fun(U_20108,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_20110,tc_HOL_Obool))
    | hAPP(c_Fun_Ocomp(U_20108,U_20110,U_20110,U_20112),c_Hilbert__Choice_Oinv__into(U_20108,U_20110,c_Orderings_Otop__class_Otop(tc_fun(U_20108,tc_HOL_Obool)),U_20112)) != c_Fun_Oid(U_20110) ),
    inference(clausify,[status(thm)],[f_4846_3]) ).

fof(f_4847_1,plain,
    ! [V_x_2,V_P_2,V_f_2,T_c,T_b] :
      ( hBOOL(hAPP(V_P_2,V_x_2))
      | ? [B_y] :
          ( ~ hBOOL(hAPP(V_P_2,hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),B_y)))
          & hBOOL(hAPP(hAPP(c_member(T_c),B_y),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) )
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_inj__transfer]) ).

fof(f_4847_2,plain,
    ! [U_20118,U_20117,U_20116,U_20115,U_20114] :
      ( hBOOL(hAPP(U_20117,U_20118))
      | ? [U_20113] :
          ( ~ hBOOL(hAPP(U_20117,hAPP(c_Hilbert__Choice_Oinv__into(U_20114,U_20115,c_Orderings_Otop__class_Otop(tc_fun(U_20114,tc_HOL_Obool)),U_20116),U_20113)))
          & hBOOL(hAPP(hAPP(c_member(U_20115),U_20113),hAPP(c_Set_Oimage(U_20114,U_20115,U_20116),c_Orderings_Otop__class_Otop(tc_fun(U_20114,tc_HOL_Obool))))) )
      | ~ c_Fun_Oinj__on(U_20114,U_20115,U_20116,c_Orderings_Otop__class_Otop(tc_fun(U_20114,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_4847_1]) ).

fof(f_4847_3,plain,
    ! [U_20118,U_20117,U_20116,U_20115,U_20114] :
      ( hBOOL(hAPP(U_20117,U_20118))
      | ( ~ hBOOL(hAPP(U_20117,hAPP(c_Hilbert__Choice_Oinv__into(U_20114,U_20115,c_Orderings_Otop__class_Otop(tc_fun(U_20114,tc_HOL_Obool)),U_20116),sK545(U_20118,U_20117,U_20116,U_20115,U_20114))))
        & hBOOL(hAPP(hAPP(c_member(U_20115),sK545(U_20118,U_20117,U_20116,U_20115,U_20114)),hAPP(c_Set_Oimage(U_20114,U_20115,U_20116),c_Orderings_Otop__class_Otop(tc_fun(U_20114,tc_HOL_Obool))))) )
      | ~ c_Fun_Oinj__on(U_20114,U_20115,U_20116,c_Orderings_Otop__class_Otop(tc_fun(U_20114,tc_HOL_Obool))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK545]),skolemize(U_20113,sK545(U_20118,U_20117,U_20116,U_20115,U_20114))],[f_4847_2]) ).

cnf(f_4847_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20115),sK545(U_20118,U_20117,U_20116,U_20115,U_20114)),hAPP(c_Set_Oimage(U_20114,U_20115,U_20116),c_Orderings_Otop__class_Otop(tc_fun(U_20114,tc_HOL_Obool)))))
    | hBOOL(hAPP(U_20117,U_20118))
    | ~ c_Fun_Oinj__on(U_20114,U_20115,U_20116,c_Orderings_Otop__class_Otop(tc_fun(U_20114,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4847_3]) ).

cnf(f_4847_5,plain,
    ( ~ hBOOL(hAPP(U_20117,hAPP(c_Hilbert__Choice_Oinv__into(U_20114,U_20115,c_Orderings_Otop__class_Otop(tc_fun(U_20114,tc_HOL_Obool)),U_20116),sK545(U_20118,U_20117,U_20116,U_20115,U_20114))))
    | hBOOL(hAPP(U_20117,U_20118))
    | ~ c_Fun_Oinj__on(U_20114,U_20115,U_20116,c_Orderings_Otop__class_Otop(tc_fun(U_20114,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4847_3]) ).

fof(f_4848_1,plain,
    ! [V_g_2,V_A_2,T_c,V_I_2,T_b,T_d] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Otimes__class_Otimes(T_d)),V_g_2),c_Groups_Oone__class_Oone(T_d)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_b,c_Groups_Otimes__class_Otimes(T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),T_d,T_b),hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Otimes__class_Otimes(T_d)),V_g_2),c_Groups_Oone__class_Oone(T_d))),V_A_2)),c_Groups_Oone__class_Oone(T_d)),V_I_2)
      | ? [B_x] :
          ( ? [B_xa] :
              ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_A_2,B_x)),hAPP(V_A_2,B_xa)) != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
              & B_x != B_xa
              & hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_I_2)) )
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2)) )
      | ? [B_x] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_A_2,B_x)))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_I_2))
      | ~ class_Groups_Ocomm__monoid__mult(T_d) ),
    inference(fof_nnf,[status(thm)],[fact_fold__image__UN__disjoint]) ).

fof(f_4848_2,plain,
    ! [U_20127,U_20126,U_20125,U_20124,U_20123,U_20122] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_20122,U_20125,c_Groups_Otimes__class_Otimes(U_20122)),U_20127),c_Groups_Oone__class_Oone(U_20122)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_20123,tc_fun(U_20125,tc_HOL_Obool)),U_20124),U_20126)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_20122,U_20123,c_Groups_Otimes__class_Otimes(U_20122)),hAPP(hAPP(c_COMBB(tc_fun(U_20125,tc_HOL_Obool),U_20122,U_20123),hAPP(hAPP(c_Finite__Set_Ofold__image(U_20122,U_20125,c_Groups_Otimes__class_Otimes(U_20122)),U_20127),c_Groups_Oone__class_Oone(U_20122))),U_20126)),c_Groups_Oone__class_Oone(U_20122)),U_20124)
      | ? [U_20121] :
          ( ? [U_20120] :
              ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_20125,tc_HOL_Obool)),hAPP(U_20126,U_20121)),hAPP(U_20126,U_20120)) != c_Orderings_Obot__class_Obot(tc_fun(U_20125,tc_HOL_Obool))
              & U_20121 != U_20120
              & hBOOL(hAPP(hAPP(c_member(U_20123),U_20120),U_20124)) )
          & hBOOL(hAPP(hAPP(c_member(U_20123),U_20121),U_20124)) )
      | ? [U_20119] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20125),hAPP(U_20126,U_20119)))
          & hBOOL(hAPP(hAPP(c_member(U_20123),U_20119),U_20124)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20123),U_20124))
      | ~ class_Groups_Ocomm__monoid__mult(U_20122) ),
    inference(variable_rename,[status(thm)],[f_4848_1]) ).

fof(f_4848_3,plain,
    ! [U_20127,U_20126,U_20125,U_20124,U_20123,U_20122] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_20122,U_20125,c_Groups_Otimes__class_Otimes(U_20122)),U_20127),c_Groups_Oone__class_Oone(U_20122)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_20123,tc_fun(U_20125,tc_HOL_Obool)),U_20124),U_20126)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_20122,U_20123,c_Groups_Otimes__class_Otimes(U_20122)),hAPP(hAPP(c_COMBB(tc_fun(U_20125,tc_HOL_Obool),U_20122,U_20123),hAPP(hAPP(c_Finite__Set_Ofold__image(U_20122,U_20125,c_Groups_Otimes__class_Otimes(U_20122)),U_20127),c_Groups_Oone__class_Oone(U_20122))),U_20126)),c_Groups_Oone__class_Oone(U_20122)),U_20124)
      | ? [U_20121] :
          ( ? [U_20120] :
              ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_20125,tc_HOL_Obool)),hAPP(U_20126,U_20121)),hAPP(U_20126,U_20120)) != c_Orderings_Obot__class_Obot(tc_fun(U_20125,tc_HOL_Obool))
              & U_20121 != U_20120
              & hBOOL(hAPP(hAPP(c_member(U_20123),U_20120),U_20124)) )
          & hBOOL(hAPP(hAPP(c_member(U_20123),U_20121),U_20124)) )
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20125),hAPP(U_20126,sK546(U_20127,U_20126,U_20125,U_20124,U_20123,U_20122))))
        & hBOOL(hAPP(hAPP(c_member(U_20123),sK546(U_20127,U_20126,U_20125,U_20124,U_20123,U_20122)),U_20124)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20123),U_20124))
      | ~ class_Groups_Ocomm__monoid__mult(U_20122) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK546]),skolemize(U_20119,sK546(U_20127,U_20126,U_20125,U_20124,U_20123,U_20122))],[f_4848_2]) ).

fof(f_4848_4,plain,
    ! [U_20127,U_20126,U_20125,U_20124,U_20123,U_20122] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_20122,U_20125,c_Groups_Otimes__class_Otimes(U_20122)),U_20127),c_Groups_Oone__class_Oone(U_20122)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_20123,tc_fun(U_20125,tc_HOL_Obool)),U_20124),U_20126)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_20122,U_20123,c_Groups_Otimes__class_Otimes(U_20122)),hAPP(hAPP(c_COMBB(tc_fun(U_20125,tc_HOL_Obool),U_20122,U_20123),hAPP(hAPP(c_Finite__Set_Ofold__image(U_20122,U_20125,c_Groups_Otimes__class_Otimes(U_20122)),U_20127),c_Groups_Oone__class_Oone(U_20122))),U_20126)),c_Groups_Oone__class_Oone(U_20122)),U_20124)
      | ( ? [U_20120] :
            ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_20125,tc_HOL_Obool)),hAPP(U_20126,sK547(U_20127,U_20126,U_20125,U_20124,U_20123,U_20122))),hAPP(U_20126,U_20120)) != c_Orderings_Obot__class_Obot(tc_fun(U_20125,tc_HOL_Obool))
            & sK547(U_20127,U_20126,U_20125,U_20124,U_20123,U_20122) != U_20120
            & hBOOL(hAPP(hAPP(c_member(U_20123),U_20120),U_20124)) )
        & hBOOL(hAPP(hAPP(c_member(U_20123),sK547(U_20127,U_20126,U_20125,U_20124,U_20123,U_20122)),U_20124)) )
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20125),hAPP(U_20126,sK546(U_20127,U_20126,U_20125,U_20124,U_20123,U_20122))))
        & hBOOL(hAPP(hAPP(c_member(U_20123),sK546(U_20127,U_20126,U_20125,U_20124,U_20123,U_20122)),U_20124)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20123),U_20124))
      | ~ class_Groups_Ocomm__monoid__mult(U_20122) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK547]),skolemize(U_20121,sK547(U_20127,U_20126,U_20125,U_20124,U_20123,U_20122))],[f_4848_3]) ).

fof(f_4848_5,plain,
    ! [U_20127,U_20126,U_20125,U_20124,U_20123,U_20122] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_20122,U_20125,c_Groups_Otimes__class_Otimes(U_20122)),U_20127),c_Groups_Oone__class_Oone(U_20122)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_20123,tc_fun(U_20125,tc_HOL_Obool)),U_20124),U_20126)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_20122,U_20123,c_Groups_Otimes__class_Otimes(U_20122)),hAPP(hAPP(c_COMBB(tc_fun(U_20125,tc_HOL_Obool),U_20122,U_20123),hAPP(hAPP(c_Finite__Set_Ofold__image(U_20122,U_20125,c_Groups_Otimes__class_Otimes(U_20122)),U_20127),c_Groups_Oone__class_Oone(U_20122))),U_20126)),c_Groups_Oone__class_Oone(U_20122)),U_20124)
      | ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_20125,tc_HOL_Obool)),hAPP(U_20126,sK547(U_20127,U_20126,U_20125,U_20124,U_20123,U_20122))),hAPP(U_20126,sK548(U_20127,U_20126,U_20125,U_20124,U_20123,U_20122))) != c_Orderings_Obot__class_Obot(tc_fun(U_20125,tc_HOL_Obool))
        & sK547(U_20127,U_20126,U_20125,U_20124,U_20123,U_20122) != sK548(U_20127,U_20126,U_20125,U_20124,U_20123,U_20122)
        & hBOOL(hAPP(hAPP(c_member(U_20123),sK548(U_20127,U_20126,U_20125,U_20124,U_20123,U_20122)),U_20124))
        & hBOOL(hAPP(hAPP(c_member(U_20123),sK547(U_20127,U_20126,U_20125,U_20124,U_20123,U_20122)),U_20124)) )
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20125),hAPP(U_20126,sK546(U_20127,U_20126,U_20125,U_20124,U_20123,U_20122))))
        & hBOOL(hAPP(hAPP(c_member(U_20123),sK546(U_20127,U_20126,U_20125,U_20124,U_20123,U_20122)),U_20124)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20123),U_20124))
      | ~ class_Groups_Ocomm__monoid__mult(U_20122) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK548]),skolemize(U_20120,sK548(U_20127,U_20126,U_20125,U_20124,U_20123,U_20122))],[f_4848_4]) ).

cnf(f_4848_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20123),sK547(U_20127,U_20126,U_20125,U_20124,U_20123,U_20122)),U_20124))
    | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_20122,U_20125,c_Groups_Otimes__class_Otimes(U_20122)),U_20127),c_Groups_Oone__class_Oone(U_20122)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_20123,tc_fun(U_20125,tc_HOL_Obool)),U_20124),U_20126)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_20122,U_20123,c_Groups_Otimes__class_Otimes(U_20122)),hAPP(hAPP(c_COMBB(tc_fun(U_20125,tc_HOL_Obool),U_20122,U_20123),hAPP(hAPP(c_Finite__Set_Ofold__image(U_20122,U_20125,c_Groups_Otimes__class_Otimes(U_20122)),U_20127),c_Groups_Oone__class_Oone(U_20122))),U_20126)),c_Groups_Oone__class_Oone(U_20122)),U_20124)
    | hBOOL(hAPP(hAPP(c_member(U_20123),sK546(U_20127,U_20126,U_20125,U_20124,U_20123,U_20122)),U_20124))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20123),U_20124))
    | ~ class_Groups_Ocomm__monoid__mult(U_20122) ),
    inference(clausify,[status(thm)],[f_4848_5]) ).

cnf(f_4848_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20123),sK548(U_20127,U_20126,U_20125,U_20124,U_20123,U_20122)),U_20124))
    | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_20122,U_20125,c_Groups_Otimes__class_Otimes(U_20122)),U_20127),c_Groups_Oone__class_Oone(U_20122)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_20123,tc_fun(U_20125,tc_HOL_Obool)),U_20124),U_20126)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_20122,U_20123,c_Groups_Otimes__class_Otimes(U_20122)),hAPP(hAPP(c_COMBB(tc_fun(U_20125,tc_HOL_Obool),U_20122,U_20123),hAPP(hAPP(c_Finite__Set_Ofold__image(U_20122,U_20125,c_Groups_Otimes__class_Otimes(U_20122)),U_20127),c_Groups_Oone__class_Oone(U_20122))),U_20126)),c_Groups_Oone__class_Oone(U_20122)),U_20124)
    | hBOOL(hAPP(hAPP(c_member(U_20123),sK546(U_20127,U_20126,U_20125,U_20124,U_20123,U_20122)),U_20124))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20123),U_20124))
    | ~ class_Groups_Ocomm__monoid__mult(U_20122) ),
    inference(clausify,[status(thm)],[f_4848_5]) ).

cnf(f_4848_8,plain,
    ( sK547(U_20127,U_20126,U_20125,U_20124,U_20123,U_20122) != sK548(U_20127,U_20126,U_20125,U_20124,U_20123,U_20122)
    | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_20122,U_20125,c_Groups_Otimes__class_Otimes(U_20122)),U_20127),c_Groups_Oone__class_Oone(U_20122)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_20123,tc_fun(U_20125,tc_HOL_Obool)),U_20124),U_20126)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_20122,U_20123,c_Groups_Otimes__class_Otimes(U_20122)),hAPP(hAPP(c_COMBB(tc_fun(U_20125,tc_HOL_Obool),U_20122,U_20123),hAPP(hAPP(c_Finite__Set_Ofold__image(U_20122,U_20125,c_Groups_Otimes__class_Otimes(U_20122)),U_20127),c_Groups_Oone__class_Oone(U_20122))),U_20126)),c_Groups_Oone__class_Oone(U_20122)),U_20124)
    | hBOOL(hAPP(hAPP(c_member(U_20123),sK546(U_20127,U_20126,U_20125,U_20124,U_20123,U_20122)),U_20124))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20123),U_20124))
    | ~ class_Groups_Ocomm__monoid__mult(U_20122) ),
    inference(clausify,[status(thm)],[f_4848_5]) ).

cnf(f_4848_9,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_20125,tc_HOL_Obool)),hAPP(U_20126,sK547(U_20127,U_20126,U_20125,U_20124,U_20123,U_20122))),hAPP(U_20126,sK548(U_20127,U_20126,U_20125,U_20124,U_20123,U_20122))) != c_Orderings_Obot__class_Obot(tc_fun(U_20125,tc_HOL_Obool))
    | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_20122,U_20125,c_Groups_Otimes__class_Otimes(U_20122)),U_20127),c_Groups_Oone__class_Oone(U_20122)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_20123,tc_fun(U_20125,tc_HOL_Obool)),U_20124),U_20126)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_20122,U_20123,c_Groups_Otimes__class_Otimes(U_20122)),hAPP(hAPP(c_COMBB(tc_fun(U_20125,tc_HOL_Obool),U_20122,U_20123),hAPP(hAPP(c_Finite__Set_Ofold__image(U_20122,U_20125,c_Groups_Otimes__class_Otimes(U_20122)),U_20127),c_Groups_Oone__class_Oone(U_20122))),U_20126)),c_Groups_Oone__class_Oone(U_20122)),U_20124)
    | hBOOL(hAPP(hAPP(c_member(U_20123),sK546(U_20127,U_20126,U_20125,U_20124,U_20123,U_20122)),U_20124))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20123),U_20124))
    | ~ class_Groups_Ocomm__monoid__mult(U_20122) ),
    inference(clausify,[status(thm)],[f_4848_5]) ).

cnf(f_4848_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20123),sK547(U_20127,U_20126,U_20125,U_20124,U_20123,U_20122)),U_20124))
    | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_20122,U_20125,c_Groups_Otimes__class_Otimes(U_20122)),U_20127),c_Groups_Oone__class_Oone(U_20122)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_20123,tc_fun(U_20125,tc_HOL_Obool)),U_20124),U_20126)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_20122,U_20123,c_Groups_Otimes__class_Otimes(U_20122)),hAPP(hAPP(c_COMBB(tc_fun(U_20125,tc_HOL_Obool),U_20122,U_20123),hAPP(hAPP(c_Finite__Set_Ofold__image(U_20122,U_20125,c_Groups_Otimes__class_Otimes(U_20122)),U_20127),c_Groups_Oone__class_Oone(U_20122))),U_20126)),c_Groups_Oone__class_Oone(U_20122)),U_20124)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20125),hAPP(U_20126,sK546(U_20127,U_20126,U_20125,U_20124,U_20123,U_20122))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20123),U_20124))
    | ~ class_Groups_Ocomm__monoid__mult(U_20122) ),
    inference(clausify,[status(thm)],[f_4848_5]) ).

cnf(f_4848_11,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20123),sK548(U_20127,U_20126,U_20125,U_20124,U_20123,U_20122)),U_20124))
    | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_20122,U_20125,c_Groups_Otimes__class_Otimes(U_20122)),U_20127),c_Groups_Oone__class_Oone(U_20122)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_20123,tc_fun(U_20125,tc_HOL_Obool)),U_20124),U_20126)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_20122,U_20123,c_Groups_Otimes__class_Otimes(U_20122)),hAPP(hAPP(c_COMBB(tc_fun(U_20125,tc_HOL_Obool),U_20122,U_20123),hAPP(hAPP(c_Finite__Set_Ofold__image(U_20122,U_20125,c_Groups_Otimes__class_Otimes(U_20122)),U_20127),c_Groups_Oone__class_Oone(U_20122))),U_20126)),c_Groups_Oone__class_Oone(U_20122)),U_20124)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20125),hAPP(U_20126,sK546(U_20127,U_20126,U_20125,U_20124,U_20123,U_20122))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20123),U_20124))
    | ~ class_Groups_Ocomm__monoid__mult(U_20122) ),
    inference(clausify,[status(thm)],[f_4848_5]) ).

cnf(f_4848_12,plain,
    ( sK547(U_20127,U_20126,U_20125,U_20124,U_20123,U_20122) != sK548(U_20127,U_20126,U_20125,U_20124,U_20123,U_20122)
    | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_20122,U_20125,c_Groups_Otimes__class_Otimes(U_20122)),U_20127),c_Groups_Oone__class_Oone(U_20122)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_20123,tc_fun(U_20125,tc_HOL_Obool)),U_20124),U_20126)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_20122,U_20123,c_Groups_Otimes__class_Otimes(U_20122)),hAPP(hAPP(c_COMBB(tc_fun(U_20125,tc_HOL_Obool),U_20122,U_20123),hAPP(hAPP(c_Finite__Set_Ofold__image(U_20122,U_20125,c_Groups_Otimes__class_Otimes(U_20122)),U_20127),c_Groups_Oone__class_Oone(U_20122))),U_20126)),c_Groups_Oone__class_Oone(U_20122)),U_20124)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20125),hAPP(U_20126,sK546(U_20127,U_20126,U_20125,U_20124,U_20123,U_20122))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20123),U_20124))
    | ~ class_Groups_Ocomm__monoid__mult(U_20122) ),
    inference(clausify,[status(thm)],[f_4848_5]) ).

cnf(f_4848_13,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_20125,tc_HOL_Obool)),hAPP(U_20126,sK547(U_20127,U_20126,U_20125,U_20124,U_20123,U_20122))),hAPP(U_20126,sK548(U_20127,U_20126,U_20125,U_20124,U_20123,U_20122))) != c_Orderings_Obot__class_Obot(tc_fun(U_20125,tc_HOL_Obool))
    | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_20122,U_20125,c_Groups_Otimes__class_Otimes(U_20122)),U_20127),c_Groups_Oone__class_Oone(U_20122)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_20123,tc_fun(U_20125,tc_HOL_Obool)),U_20124),U_20126)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_20122,U_20123,c_Groups_Otimes__class_Otimes(U_20122)),hAPP(hAPP(c_COMBB(tc_fun(U_20125,tc_HOL_Obool),U_20122,U_20123),hAPP(hAPP(c_Finite__Set_Ofold__image(U_20122,U_20125,c_Groups_Otimes__class_Otimes(U_20122)),U_20127),c_Groups_Oone__class_Oone(U_20122))),U_20126)),c_Groups_Oone__class_Oone(U_20122)),U_20124)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20125),hAPP(U_20126,sK546(U_20127,U_20126,U_20125,U_20124,U_20123,U_20122))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20123),U_20124))
    | ~ class_Groups_Ocomm__monoid__mult(U_20122) ),
    inference(clausify,[status(thm)],[f_4848_5]) ).

fof(f_4849_1,plain,
    ! [V_P_2,V_y_2] :
      ( hBOOL(hAPP(V_P_2,V_y_2))
      | ? [B_x] : ~ hBOOL(hAPP(V_P_2,hAPP(c_Code__Numeral_Onat__of,B_x)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ),
    inference(fof_nnf,[status(thm)],[fact_nat__of__induct]) ).

fof(f_4849_2,plain,
    ! [U_20130,U_20129] :
      ( hBOOL(hAPP(U_20130,U_20129))
      | ? [U_20128] : ~ hBOOL(hAPP(U_20130,hAPP(c_Code__Numeral_Onat__of,U_20128)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_20129),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_4849_1]) ).

fof(f_4849_3,plain,
    ! [U_20130,U_20129] :
      ( hBOOL(hAPP(U_20130,U_20129))
      | ~ hBOOL(hAPP(U_20130,hAPP(c_Code__Numeral_Onat__of,sK549(U_20130,U_20129))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_20129),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK549]),skolemize(U_20128,sK549(U_20130,U_20129))],[f_4849_2]) ).

cnf(f_4849_4,plain,
    ( hBOOL(hAPP(U_20130,U_20129))
    | ~ hBOOL(hAPP(U_20130,hAPP(c_Code__Numeral_Onat__of,sK549(U_20130,U_20129))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_20129),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_4849_3]) ).

fof(f_4850_1,plain,
    ! [V_y_2] :
      ( ? [B_x] : V_y_2 = hAPP(c_Code__Numeral_Onat__of,B_x)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ),
    inference(fof_nnf,[status(thm)],[fact_nat__of__cases]) ).

fof(f_4850_2,plain,
    ! [U_20132] :
      ( ? [U_20131] : U_20132 = hAPP(c_Code__Numeral_Onat__of,U_20131)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_20132),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_4850_1]) ).

fof(f_4850_3,plain,
    ! [U_20132] :
      ( U_20132 = hAPP(c_Code__Numeral_Onat__of,sK550(U_20132))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_20132),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK550]),skolemize(U_20131,sK550(U_20132))],[f_4850_2]) ).

cnf(f_4850_4,plain,
    ( U_20132 = hAPP(c_Code__Numeral_Onat__of,sK550(U_20132))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_20132),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_4850_3]) ).

fof(f_4851_1,plain,
    ! [V_x_2,V_P_2] :
      ( hBOOL(hAPP(V_P_2,V_x_2))
      | ? [B_y] :
          ( ~ hBOOL(hAPP(V_P_2,hAPP(c_Code__Numeral_Oof__nat,B_y)))
          & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_y),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__induct]) ).

fof(f_4851_2,plain,
    ! [U_20135,U_20134] :
      ( hBOOL(hAPP(U_20134,U_20135))
      | ? [U_20133] :
          ( ~ hBOOL(hAPP(U_20134,hAPP(c_Code__Numeral_Oof__nat,U_20133)))
          & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_20133),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ) ),
    inference(variable_rename,[status(thm)],[f_4851_1]) ).

fof(f_4851_3,plain,
    ! [U_20135,U_20134] :
      ( hBOOL(hAPP(U_20134,U_20135))
      | ( ~ hBOOL(hAPP(U_20134,hAPP(c_Code__Numeral_Oof__nat,sK551(U_20135,U_20134))))
        & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK551(U_20135,U_20134)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK551]),skolemize(U_20133,sK551(U_20135,U_20134))],[f_4851_2]) ).

cnf(f_4851_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK551(U_20135,U_20134)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
    | hBOOL(hAPP(U_20134,U_20135)) ),
    inference(clausify,[status(thm)],[f_4851_3]) ).

cnf(f_4851_5,plain,
    ( ~ hBOOL(hAPP(U_20134,hAPP(c_Code__Numeral_Oof__nat,sK551(U_20135,U_20134))))
    | hBOOL(hAPP(U_20134,U_20135)) ),
    inference(clausify,[status(thm)],[f_4851_3]) ).

fof(f_4852_1,plain,
    ! [V_x_2] :
    ? [B_y] :
      ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_y),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
      & V_x_2 = hAPP(c_Code__Numeral_Oof__nat,B_y) ),
    inference(fof_nnf,[status(thm)],[fact_of__nat__cases]) ).

fof(f_4852_2,plain,
    ! [U_20137] :
    ? [U_20136] :
      ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_20136),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
      & U_20137 = hAPP(c_Code__Numeral_Oof__nat,U_20136) ),
    inference(variable_rename,[status(thm)],[f_4852_1]) ).

fof(f_4852_3,plain,
    ! [U_20137] :
      ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK552(U_20137)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
      & U_20137 = hAPP(c_Code__Numeral_Oof__nat,sK552(U_20137)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK552]),skolemize(U_20136,sK552(U_20137))],[f_4852_2]) ).

cnf(f_4852_4,plain,
    U_20137 = hAPP(c_Code__Numeral_Oof__nat,sK552(U_20137)),
    inference(clausify,[status(thm)],[f_4852_3]) ).

cnf(f_4852_5,plain,
    hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK552(U_20137)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_4852_3]) ).

fof(f_4853_1,plain,
    ! [V_f2_2,V_f1_2,T_c,T_b] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(T_b,T_c,V_f1_2,V_f2_2,c_Lazy__Sequence_Olazy__sequence_OEmpty(T_c)) = V_f1_2,
    inference(fof_nnf,[status(thm)],[fact_lazy__sequence_Orecs_I1_J]) ).

fof(f_4853_2,plain,
    ! [U_20141,U_20140,U_20139,U_20138] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(U_20138,U_20139,U_20140,U_20141,c_Lazy__Sequence_Olazy__sequence_OEmpty(U_20139)) = U_20140,
    inference(variable_rename,[status(thm)],[f_4853_1]) ).

cnf(f_4853_3,plain,
    c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(U_20138,U_20139,U_20140,U_20141,c_Lazy__Sequence_Olazy__sequence_OEmpty(U_20139)) = U_20140,
    inference(clausify,[status(thm)],[f_4853_2]) ).

fof(f_4854_1,plain,
    ! [V_m_2,V_Q_2,V_n_2,V_P_2] :
      ( c_Orderings_Oord__class_OLeast(tc_Nat_Onat,V_P_2) = hAPP(c_Nat_OSuc,c_Orderings_Oord__class_OLeast(tc_Nat_Onat,V_Q_2))
      | ? [B_k] :
          ( ( ~ hBOOL(hAPP(V_P_2,hAPP(c_Nat_OSuc,B_k)))
            & hBOOL(hAPP(V_Q_2,B_k)) )
          | ( ~ hBOOL(hAPP(V_Q_2,B_k))
            & hBOOL(hAPP(V_P_2,hAPP(c_Nat_OSuc,B_k))) ) )
      | hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
      | ~ hBOOL(hAPP(V_Q_2,V_m_2))
      | ~ hBOOL(hAPP(V_P_2,V_n_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Least__Suc2]) ).

fof(f_4854_2,plain,
    ! [U_20146,U_20145,U_20144,U_20143] :
      ( c_Orderings_Oord__class_OLeast(tc_Nat_Onat,U_20143) = hAPP(c_Nat_OSuc,c_Orderings_Oord__class_OLeast(tc_Nat_Onat,U_20145))
      | ? [U_20142] :
          ( ( ~ hBOOL(hAPP(U_20143,hAPP(c_Nat_OSuc,U_20142)))
            & hBOOL(hAPP(U_20145,U_20142)) )
          | ( ~ hBOOL(hAPP(U_20145,U_20142))
            & hBOOL(hAPP(U_20143,hAPP(c_Nat_OSuc,U_20142))) ) )
      | hBOOL(hAPP(U_20143,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
      | ~ hBOOL(hAPP(U_20145,U_20146))
      | ~ hBOOL(hAPP(U_20143,U_20144)) ),
    inference(variable_rename,[status(thm)],[f_4854_1]) ).

fof(f_4854_3,plain,
    ! [U_20146,U_20145,U_20144,U_20143] :
      ( c_Orderings_Oord__class_OLeast(tc_Nat_Onat,U_20143) = hAPP(c_Nat_OSuc,c_Orderings_Oord__class_OLeast(tc_Nat_Onat,U_20145))
      | ? [U_20148] :
          ( ~ hBOOL(hAPP(U_20143,hAPP(c_Nat_OSuc,U_20148)))
          & hBOOL(hAPP(U_20145,U_20148)) )
      | ? [U_20147] :
          ( ~ hBOOL(hAPP(U_20145,U_20147))
          & hBOOL(hAPP(U_20143,hAPP(c_Nat_OSuc,U_20147))) )
      | hBOOL(hAPP(U_20143,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
      | ~ hBOOL(hAPP(U_20145,U_20146))
      | ~ hBOOL(hAPP(U_20143,U_20144)) ),
    inference(miniscope,[status(thm)],[f_4854_2]) ).

fof(f_4854_4,plain,
    ! [U_20146,U_20145,U_20144,U_20143] :
      ( c_Orderings_Oord__class_OLeast(tc_Nat_Onat,U_20143) = hAPP(c_Nat_OSuc,c_Orderings_Oord__class_OLeast(tc_Nat_Onat,U_20145))
      | ? [U_20148] :
          ( ~ hBOOL(hAPP(U_20143,hAPP(c_Nat_OSuc,U_20148)))
          & hBOOL(hAPP(U_20145,U_20148)) )
      | ( ~ hBOOL(hAPP(U_20145,sK553(U_20146,U_20145,U_20144,U_20143)))
        & hBOOL(hAPP(U_20143,hAPP(c_Nat_OSuc,sK553(U_20146,U_20145,U_20144,U_20143)))) )
      | hBOOL(hAPP(U_20143,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
      | ~ hBOOL(hAPP(U_20145,U_20146))
      | ~ hBOOL(hAPP(U_20143,U_20144)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK553]),skolemize(U_20147,sK553(U_20146,U_20145,U_20144,U_20143))],[f_4854_3]) ).

fof(f_4854_5,plain,
    ! [U_20146,U_20145,U_20144,U_20143] :
      ( c_Orderings_Oord__class_OLeast(tc_Nat_Onat,U_20143) = hAPP(c_Nat_OSuc,c_Orderings_Oord__class_OLeast(tc_Nat_Onat,U_20145))
      | ( ~ hBOOL(hAPP(U_20143,hAPP(c_Nat_OSuc,sK554(U_20146,U_20145,U_20144,U_20143))))
        & hBOOL(hAPP(U_20145,sK554(U_20146,U_20145,U_20144,U_20143))) )
      | ( ~ hBOOL(hAPP(U_20145,sK553(U_20146,U_20145,U_20144,U_20143)))
        & hBOOL(hAPP(U_20143,hAPP(c_Nat_OSuc,sK553(U_20146,U_20145,U_20144,U_20143)))) )
      | hBOOL(hAPP(U_20143,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
      | ~ hBOOL(hAPP(U_20145,U_20146))
      | ~ hBOOL(hAPP(U_20143,U_20144)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK554]),skolemize(U_20148,sK554(U_20146,U_20145,U_20144,U_20143))],[f_4854_4]) ).

cnf(f_4854_6,plain,
    ( hBOOL(hAPP(U_20145,sK554(U_20146,U_20145,U_20144,U_20143)))
    | hBOOL(hAPP(U_20143,hAPP(c_Nat_OSuc,sK553(U_20146,U_20145,U_20144,U_20143))))
    | c_Orderings_Oord__class_OLeast(tc_Nat_Onat,U_20143) = hAPP(c_Nat_OSuc,c_Orderings_Oord__class_OLeast(tc_Nat_Onat,U_20145))
    | hBOOL(hAPP(U_20143,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(U_20145,U_20146))
    | ~ hBOOL(hAPP(U_20143,U_20144)) ),
    inference(clausify,[status(thm)],[f_4854_5]) ).

cnf(f_4854_7,plain,
    ( ~ hBOOL(hAPP(U_20143,hAPP(c_Nat_OSuc,sK554(U_20146,U_20145,U_20144,U_20143))))
    | hBOOL(hAPP(U_20143,hAPP(c_Nat_OSuc,sK553(U_20146,U_20145,U_20144,U_20143))))
    | c_Orderings_Oord__class_OLeast(tc_Nat_Onat,U_20143) = hAPP(c_Nat_OSuc,c_Orderings_Oord__class_OLeast(tc_Nat_Onat,U_20145))
    | hBOOL(hAPP(U_20143,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(U_20145,U_20146))
    | ~ hBOOL(hAPP(U_20143,U_20144)) ),
    inference(clausify,[status(thm)],[f_4854_5]) ).

cnf(f_4854_8,plain,
    ( hBOOL(hAPP(U_20145,sK554(U_20146,U_20145,U_20144,U_20143)))
    | ~ hBOOL(hAPP(U_20145,sK553(U_20146,U_20145,U_20144,U_20143)))
    | c_Orderings_Oord__class_OLeast(tc_Nat_Onat,U_20143) = hAPP(c_Nat_OSuc,c_Orderings_Oord__class_OLeast(tc_Nat_Onat,U_20145))
    | hBOOL(hAPP(U_20143,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(U_20145,U_20146))
    | ~ hBOOL(hAPP(U_20143,U_20144)) ),
    inference(clausify,[status(thm)],[f_4854_5]) ).

cnf(f_4854_9,plain,
    ( ~ hBOOL(hAPP(U_20143,hAPP(c_Nat_OSuc,sK554(U_20146,U_20145,U_20144,U_20143))))
    | ~ hBOOL(hAPP(U_20145,sK553(U_20146,U_20145,U_20144,U_20143)))
    | c_Orderings_Oord__class_OLeast(tc_Nat_Onat,U_20143) = hAPP(c_Nat_OSuc,c_Orderings_Oord__class_OLeast(tc_Nat_Onat,U_20145))
    | hBOOL(hAPP(U_20143,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(U_20145,U_20146))
    | ~ hBOOL(hAPP(U_20143,U_20144)) ),
    inference(clausify,[status(thm)],[f_4854_5]) ).

fof(f_4855_1,plain,
    ! [V_lazy__sequence_2,V_a_2,V_f2_2,V_f1_2,T_c,T_b] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(T_b,T_c,V_f1_2,V_f2_2,c_Lazy__Sequence_Olazy__sequence_OInsert(T_c,V_a_2,V_lazy__sequence_2)) = hAPP(hAPP(hAPP(V_f2_2,V_a_2),V_lazy__sequence_2),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(T_b,T_c,V_f1_2,V_f2_2,V_lazy__sequence_2)),
    inference(fof_nnf,[status(thm)],[fact_lazy__sequence_Orecs_I2_J]) ).

fof(f_4855_2,plain,
    ! [U_20154,U_20153,U_20152,U_20151,U_20150,U_20149] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(U_20149,U_20150,U_20151,U_20152,c_Lazy__Sequence_Olazy__sequence_OInsert(U_20150,U_20153,U_20154)) = hAPP(hAPP(hAPP(U_20152,U_20153),U_20154),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(U_20149,U_20150,U_20151,U_20152,U_20154)),
    inference(variable_rename,[status(thm)],[f_4855_1]) ).

cnf(f_4855_3,plain,
    c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(U_20149,U_20150,U_20151,U_20152,c_Lazy__Sequence_Olazy__sequence_OInsert(U_20150,U_20153,U_20154)) = hAPP(hAPP(hAPP(U_20152,U_20153),U_20154),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(U_20149,U_20150,U_20151,U_20152,U_20154)),
    inference(clausify,[status(thm)],[f_4855_2]) ).

fof(f_4856_1,plain,
    ! [V_l,V_k] :
      ( ( c_Quickcheck_Obeyond(V_k,V_l) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l)) )
      & ( c_Quickcheck_Obeyond(V_k,V_l) = V_l
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l)) ) ),
    inference(fof_nnf,[status(thm)],[fact_beyond__def]) ).

fof(f_4856_2,plain,
    ! [U_20156,U_20155] :
      ( ( c_Quickcheck_Obeyond(U_20155,U_20156) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_20155),U_20156)) )
      & ( c_Quickcheck_Obeyond(U_20155,U_20156) = U_20156
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_20155),U_20156)) ) ),
    inference(variable_rename,[status(thm)],[f_4856_1]) ).

fof(f_4856_3,plain,
    ( ! [U_20160,U_20158] :
        ( c_Quickcheck_Obeyond(U_20158,U_20160) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_20158),U_20160)) )
    & ! [U_20159,U_20157] :
        ( c_Quickcheck_Obeyond(U_20157,U_20159) = U_20159
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_20157),U_20159)) ) ),
    inference(miniscope,[status(thm)],[f_4856_2]) ).

cnf(f_4856_4,plain,
    ( c_Quickcheck_Obeyond(U_20157,U_20159) = U_20159
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_20157),U_20159)) ),
    inference(clausify,[status(thm)],[f_4856_3]) ).

cnf(f_4856_5,plain,
    ( c_Quickcheck_Obeyond(U_20158,U_20160) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_20158),U_20160)) ),
    inference(clausify,[status(thm)],[f_4856_3]) ).

fof(f_4857_1,plain,
    ! [V_P_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(c_Set_OCollect(T_b),V_P_2)) = hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,T_c),V_P_2),c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)))
      | ~ c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_bij__image__Collect__eq]) ).

fof(f_4857_2,plain,
    ! [U_20164,U_20163,U_20162,U_20161] :
      ( hAPP(c_Set_Oimage(U_20161,U_20162,U_20163),hAPP(c_Set_OCollect(U_20161),U_20164)) = hAPP(c_Set_OCollect(U_20162),hAPP(hAPP(c_COMBB(U_20161,tc_HOL_Obool,U_20162),U_20164),c_Hilbert__Choice_Oinv__into(U_20161,U_20162,c_Orderings_Otop__class_Otop(tc_fun(U_20161,tc_HOL_Obool)),U_20163)))
      | ~ c_Fun_Obij__betw(U_20161,U_20162,U_20163,c_Orderings_Otop__class_Otop(tc_fun(U_20161,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20162,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_4857_1]) ).

cnf(f_4857_3,plain,
    ( hAPP(c_Set_Oimage(U_20161,U_20162,U_20163),hAPP(c_Set_OCollect(U_20161),U_20164)) = hAPP(c_Set_OCollect(U_20162),hAPP(hAPP(c_COMBB(U_20161,tc_HOL_Obool,U_20162),U_20164),c_Hilbert__Choice_Oinv__into(U_20161,U_20162,c_Orderings_Otop__class_Otop(tc_fun(U_20161,tc_HOL_Obool)),U_20163)))
    | ~ c_Fun_Obij__betw(U_20161,U_20162,U_20163,c_Orderings_Otop__class_Otop(tc_fun(U_20161,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20162,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4857_2]) ).

fof(f_4858_1,plain,
    ! [V_A_2,T_b] : c_Fun_Obij__betw(T_b,T_b,c_Fun_Oid(T_b),V_A_2,V_A_2),
    inference(fof_nnf,[status(thm)],[fact_bij__betw__id]) ).

fof(f_4858_2,plain,
    ! [U_20166,U_20165] : c_Fun_Obij__betw(U_20165,U_20165,c_Fun_Oid(U_20165),U_20166,U_20166),
    inference(variable_rename,[status(thm)],[f_4858_1]) ).

cnf(f_4858_3,plain,
    c_Fun_Obij__betw(U_20165,U_20165,c_Fun_Oid(U_20165),U_20166,U_20166),
    inference(clausify,[status(thm)],[f_4858_2]) ).

fof(f_4859_1,plain,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Obij__betw(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),V_B_2,V_A_2)
      | ~ c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2) ),
    inference(fof_nnf,[status(thm)],[fact_bij__betw__inv__into]) ).

fof(f_4859_2,plain,
    ! [U_20171,U_20170,U_20169,U_20168,U_20167] :
      ( c_Fun_Obij__betw(U_20168,U_20167,c_Hilbert__Choice_Oinv__into(U_20167,U_20168,U_20170,U_20169),U_20171,U_20170)
      | ~ c_Fun_Obij__betw(U_20167,U_20168,U_20169,U_20170,U_20171) ),
    inference(variable_rename,[status(thm)],[f_4859_1]) ).

cnf(f_4859_3,plain,
    ( c_Fun_Obij__betw(U_20168,U_20167,c_Hilbert__Choice_Oinv__into(U_20167,U_20168,U_20170,U_20169),U_20171,U_20170)
    | ~ c_Fun_Obij__betw(U_20167,U_20168,U_20169,U_20170,U_20171) ),
    inference(clausify,[status(thm)],[f_4859_2]) ).

fof(f_4860_1,plain,
    ! [V_a_2,V_A_H_2,V_A_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_b,V_A_H_2,c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2)),V_a_2) = hAPP(V_f_2,V_a_2)
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
      | ~ c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2) ),
    inference(fof_nnf,[status(thm)],[fact_inv__into__inv__into__eq]) ).

fof(f_4860_2,plain,
    ! [U_20177,U_20176,U_20175,U_20174,U_20173,U_20172] :
      ( hAPP(c_Hilbert__Choice_Oinv__into(U_20173,U_20172,U_20176,c_Hilbert__Choice_Oinv__into(U_20172,U_20173,U_20175,U_20174)),U_20177) = hAPP(U_20174,U_20177)
      | ~ hBOOL(hAPP(hAPP(c_member(U_20172),U_20177),U_20175))
      | ~ c_Fun_Obij__betw(U_20172,U_20173,U_20174,U_20175,U_20176) ),
    inference(variable_rename,[status(thm)],[f_4860_1]) ).

cnf(f_4860_3,plain,
    ( hAPP(c_Hilbert__Choice_Oinv__into(U_20173,U_20172,U_20176,c_Hilbert__Choice_Oinv__into(U_20172,U_20173,U_20175,U_20174)),U_20177) = hAPP(U_20174,U_20177)
    | ~ hBOOL(hAPP(hAPP(c_member(U_20172),U_20177),U_20175))
    | ~ c_Fun_Obij__betw(U_20172,U_20173,U_20174,U_20175,U_20176) ),
    inference(clausify,[status(thm)],[f_4860_2]) ).

fof(f_4861_1,plain,
    ! [V_f_2,T_c,T_b] :
      ( c_Fun_Obij__betw(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
      | ~ c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_bij__imp__bij__inv]) ).

fof(f_4861_2,plain,
    ! [U_20180,U_20179,U_20178] :
      ( c_Fun_Obij__betw(U_20179,U_20178,c_Hilbert__Choice_Oinv__into(U_20178,U_20179,c_Orderings_Otop__class_Otop(tc_fun(U_20178,tc_HOL_Obool)),U_20180),c_Orderings_Otop__class_Otop(tc_fun(U_20179,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20178,tc_HOL_Obool)))
      | ~ c_Fun_Obij__betw(U_20178,U_20179,U_20180,c_Orderings_Otop__class_Otop(tc_fun(U_20178,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20179,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_4861_1]) ).

cnf(f_4861_3,plain,
    ( c_Fun_Obij__betw(U_20179,U_20178,c_Hilbert__Choice_Oinv__into(U_20178,U_20179,c_Orderings_Otop__class_Otop(tc_fun(U_20178,tc_HOL_Obool)),U_20180),c_Orderings_Otop__class_Otop(tc_fun(U_20179,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20178,tc_HOL_Obool)))
    | ~ c_Fun_Obij__betw(U_20178,U_20179,U_20180,c_Orderings_Otop__class_Otop(tc_fun(U_20178,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20179,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4861_2]) ).

fof(f_4862_1,plain,
    ! [V_f_2,T_c,T_b] :
      ( c_Hilbert__Choice_Oinv__into(T_c,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)) = V_f_2
      | ~ c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_inv__inv__eq]) ).

fof(f_4862_2,plain,
    ! [U_20183,U_20182,U_20181] :
      ( c_Hilbert__Choice_Oinv__into(U_20182,U_20181,c_Orderings_Otop__class_Otop(tc_fun(U_20182,tc_HOL_Obool)),c_Hilbert__Choice_Oinv__into(U_20181,U_20182,c_Orderings_Otop__class_Otop(tc_fun(U_20181,tc_HOL_Obool)),U_20183)) = U_20183
      | ~ c_Fun_Obij__betw(U_20181,U_20182,U_20183,c_Orderings_Otop__class_Otop(tc_fun(U_20181,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20182,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_4862_1]) ).

cnf(f_4862_3,plain,
    ( c_Hilbert__Choice_Oinv__into(U_20182,U_20181,c_Orderings_Otop__class_Otop(tc_fun(U_20182,tc_HOL_Obool)),c_Hilbert__Choice_Oinv__into(U_20181,U_20182,c_Orderings_Otop__class_Otop(tc_fun(U_20181,tc_HOL_Obool)),U_20183)) = U_20183
    | ~ c_Fun_Obij__betw(U_20181,U_20182,U_20183,c_Orderings_Otop__class_Otop(tc_fun(U_20181,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20182,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4862_2]) ).

fof(f_4863_1,plain,
    ! [V_g_2,T_d,V_f_2,T_c,T_b] :
      ( c_Hilbert__Choice_Oinv__into(T_d,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Fun_Ocomp(T_b,T_c,T_d,V_f_2),V_g_2)) = hAPP(c_Fun_Ocomp(T_b,T_d,T_c,c_Hilbert__Choice_Oinv__into(T_d,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)),V_g_2)),c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2))
      | ~ c_Fun_Obij__betw(T_d,T_b,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
      | ~ c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_o__inv__distrib]) ).

fof(f_4863_2,plain,
    ! [U_20188,U_20187,U_20186,U_20185,U_20184] :
      ( c_Hilbert__Choice_Oinv__into(U_20187,U_20185,c_Orderings_Otop__class_Otop(tc_fun(U_20187,tc_HOL_Obool)),hAPP(c_Fun_Ocomp(U_20184,U_20185,U_20187,U_20186),U_20188)) = hAPP(c_Fun_Ocomp(U_20184,U_20187,U_20185,c_Hilbert__Choice_Oinv__into(U_20187,U_20184,c_Orderings_Otop__class_Otop(tc_fun(U_20187,tc_HOL_Obool)),U_20188)),c_Hilbert__Choice_Oinv__into(U_20184,U_20185,c_Orderings_Otop__class_Otop(tc_fun(U_20184,tc_HOL_Obool)),U_20186))
      | ~ c_Fun_Obij__betw(U_20187,U_20184,U_20188,c_Orderings_Otop__class_Otop(tc_fun(U_20187,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20184,tc_HOL_Obool)))
      | ~ c_Fun_Obij__betw(U_20184,U_20185,U_20186,c_Orderings_Otop__class_Otop(tc_fun(U_20184,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20185,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_4863_1]) ).

cnf(f_4863_3,plain,
    ( c_Hilbert__Choice_Oinv__into(U_20187,U_20185,c_Orderings_Otop__class_Otop(tc_fun(U_20187,tc_HOL_Obool)),hAPP(c_Fun_Ocomp(U_20184,U_20185,U_20187,U_20186),U_20188)) = hAPP(c_Fun_Ocomp(U_20184,U_20187,U_20185,c_Hilbert__Choice_Oinv__into(U_20187,U_20184,c_Orderings_Otop__class_Otop(tc_fun(U_20187,tc_HOL_Obool)),U_20188)),c_Hilbert__Choice_Oinv__into(U_20184,U_20185,c_Orderings_Otop__class_Otop(tc_fun(U_20184,tc_HOL_Obool)),U_20186))
    | ~ c_Fun_Obij__betw(U_20187,U_20184,U_20188,c_Orderings_Otop__class_Otop(tc_fun(U_20187,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20184,tc_HOL_Obool)))
    | ~ c_Fun_Obij__betw(U_20184,U_20185,U_20186,c_Orderings_Otop__class_Otop(tc_fun(U_20184,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20185,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4863_2]) ).

fof(f_4864_1,plain,
    ! [V_B_2,V_A_2,T_d,V_f_2,T_c,T_b] :
      ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_d),c_Set_Oimage(T_b,T_c,V_f_2)),V_B_2))
      | ~ c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_bij__image__INT]) ).

fof(f_4864_2,plain,
    ! [U_20194,U_20193,U_20192,U_20191,U_20190,U_20189] :
      ( hAPP(c_Set_Oimage(U_20189,U_20190,U_20191),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_20192,tc_fun(U_20189,tc_HOL_Obool)),U_20193),U_20194)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_20192,tc_fun(U_20190,tc_HOL_Obool)),U_20193),hAPP(hAPP(c_COMBB(tc_fun(U_20189,tc_HOL_Obool),tc_fun(U_20190,tc_HOL_Obool),U_20192),c_Set_Oimage(U_20189,U_20190,U_20191)),U_20194))
      | ~ c_Fun_Obij__betw(U_20189,U_20190,U_20191,c_Orderings_Otop__class_Otop(tc_fun(U_20189,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20190,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_4864_1]) ).

cnf(f_4864_3,plain,
    ( hAPP(c_Set_Oimage(U_20189,U_20190,U_20191),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_20192,tc_fun(U_20189,tc_HOL_Obool)),U_20193),U_20194)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_20192,tc_fun(U_20190,tc_HOL_Obool)),U_20193),hAPP(hAPP(c_COMBB(tc_fun(U_20189,tc_HOL_Obool),tc_fun(U_20190,tc_HOL_Obool),U_20192),c_Set_Oimage(U_20189,U_20190,U_20191)),U_20194))
    | ~ c_Fun_Obij__betw(U_20189,U_20190,U_20191,c_Orderings_Otop__class_Otop(tc_fun(U_20189,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20190,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4864_2]) ).

fof(f_4865_1,plain,
    ! [V_A_2,V_f_2,T_d,V_A_H_H_2,V_A_H_2,V_f_H_2,T_c,T_b] :
      ( ( ( c_Fun_Obij__betw(T_d,T_b,V_f_2,V_A_2,V_A_H_2)
          | ~ c_Fun_Obij__betw(T_d,T_c,hAPP(c_Fun_Ocomp(T_b,T_c,T_d,V_f_H_2),V_f_2),V_A_2,V_A_H_H_2) )
        & ( c_Fun_Obij__betw(T_d,T_c,hAPP(c_Fun_Ocomp(T_b,T_c,T_d,V_f_H_2),V_f_2),V_A_2,V_A_H_H_2)
          | ~ c_Fun_Obij__betw(T_d,T_b,V_f_2,V_A_2,V_A_H_2) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_d,T_b,V_f_2),V_A_2)),V_A_H_2))
      | ~ c_Fun_Obij__betw(T_b,T_c,V_f_H_2,V_A_H_2,V_A_H_H_2) ),
    inference(fof_nnf,[status(thm)],[fact_bij__betw__comp__iff2]) ).

fof(f_4865_2,plain,
    ! [U_20202,U_20201,U_20200,U_20199,U_20198,U_20197,U_20196,U_20195] :
      ( ( ( c_Fun_Obij__betw(U_20200,U_20195,U_20201,U_20202,U_20198)
          | ~ c_Fun_Obij__betw(U_20200,U_20196,hAPP(c_Fun_Ocomp(U_20195,U_20196,U_20200,U_20197),U_20201),U_20202,U_20199) )
        & ( c_Fun_Obij__betw(U_20200,U_20196,hAPP(c_Fun_Ocomp(U_20195,U_20196,U_20200,U_20197),U_20201),U_20202,U_20199)
          | ~ c_Fun_Obij__betw(U_20200,U_20195,U_20201,U_20202,U_20198) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20195,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_20200,U_20195,U_20201),U_20202)),U_20198))
      | ~ c_Fun_Obij__betw(U_20195,U_20196,U_20197,U_20198,U_20199) ),
    inference(variable_rename,[status(thm)],[f_4865_1]) ).

cnf(f_4865_3,plain,
    ( c_Fun_Obij__betw(U_20200,U_20196,hAPP(c_Fun_Ocomp(U_20195,U_20196,U_20200,U_20197),U_20201),U_20202,U_20199)
    | ~ c_Fun_Obij__betw(U_20200,U_20195,U_20201,U_20202,U_20198)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20195,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_20200,U_20195,U_20201),U_20202)),U_20198))
    | ~ c_Fun_Obij__betw(U_20195,U_20196,U_20197,U_20198,U_20199) ),
    inference(clausify,[status(thm)],[f_4865_2]) ).

cnf(f_4865_4,plain,
    ( c_Fun_Obij__betw(U_20200,U_20195,U_20201,U_20202,U_20198)
    | ~ c_Fun_Obij__betw(U_20200,U_20196,hAPP(c_Fun_Ocomp(U_20195,U_20196,U_20200,U_20197),U_20201),U_20202,U_20199)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20195,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_20200,U_20195,U_20201),U_20202)),U_20198))
    | ~ c_Fun_Obij__betw(U_20195,U_20196,U_20197,U_20198,U_20199) ),
    inference(clausify,[status(thm)],[f_4865_2]) ).

fof(f_4866_1,plain,
    ! [V_A_H_H_2,V_f_H_2,T_d,V_A_H_2,V_A_2,V_f_2,T_c,T_b] :
      ( ( ( c_Fun_Obij__betw(T_c,T_d,V_f_H_2,V_A_H_2,V_A_H_H_2)
          | ~ c_Fun_Obij__betw(T_b,T_d,hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_f_H_2),V_f_2),V_A_2,V_A_H_H_2) )
        & ( c_Fun_Obij__betw(T_b,T_d,hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_f_H_2),V_f_2),V_A_2,V_A_H_H_2)
          | ~ c_Fun_Obij__betw(T_c,T_d,V_f_H_2,V_A_H_2,V_A_H_H_2) ) )
      | ~ c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2) ),
    inference(fof_nnf,[status(thm)],[fact_bij__betw__comp__iff]) ).

fof(f_4866_2,plain,
    ! [U_20210,U_20209,U_20208,U_20207,U_20206,U_20205,U_20204,U_20203] :
      ( ( ( c_Fun_Obij__betw(U_20204,U_20208,U_20209,U_20207,U_20210)
          | ~ c_Fun_Obij__betw(U_20203,U_20208,hAPP(c_Fun_Ocomp(U_20204,U_20208,U_20203,U_20209),U_20205),U_20206,U_20210) )
        & ( c_Fun_Obij__betw(U_20203,U_20208,hAPP(c_Fun_Ocomp(U_20204,U_20208,U_20203,U_20209),U_20205),U_20206,U_20210)
          | ~ c_Fun_Obij__betw(U_20204,U_20208,U_20209,U_20207,U_20210) ) )
      | ~ c_Fun_Obij__betw(U_20203,U_20204,U_20205,U_20206,U_20207) ),
    inference(variable_rename,[status(thm)],[f_4866_1]) ).

cnf(f_4866_3,plain,
    ( c_Fun_Obij__betw(U_20203,U_20208,hAPP(c_Fun_Ocomp(U_20204,U_20208,U_20203,U_20209),U_20205),U_20206,U_20210)
    | ~ c_Fun_Obij__betw(U_20204,U_20208,U_20209,U_20207,U_20210)
    | ~ c_Fun_Obij__betw(U_20203,U_20204,U_20205,U_20206,U_20207) ),
    inference(clausify,[status(thm)],[f_4866_2]) ).

cnf(f_4866_4,plain,
    ( c_Fun_Obij__betw(U_20204,U_20208,U_20209,U_20207,U_20210)
    | ~ c_Fun_Obij__betw(U_20203,U_20208,hAPP(c_Fun_Ocomp(U_20204,U_20208,U_20203,U_20209),U_20205),U_20206,U_20210)
    | ~ c_Fun_Obij__betw(U_20203,U_20204,U_20205,U_20206,U_20207) ),
    inference(clausify,[status(thm)],[f_4866_2]) ).

fof(f_4867_1,plain,
    ! [V_C_2,V_g_2,T_d,V_B_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Obij__betw(T_b,T_d,hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_g_2),V_f_2),V_A_2,V_C_2)
      | ~ c_Fun_Obij__betw(T_c,T_d,V_g_2,V_B_2,V_C_2)
      | ~ c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2) ),
    inference(fof_nnf,[status(thm)],[fact_bij__betw__trans]) ).

fof(f_4867_2,plain,
    ! [U_20218,U_20217,U_20216,U_20215,U_20214,U_20213,U_20212,U_20211] :
      ( c_Fun_Obij__betw(U_20211,U_20216,hAPP(c_Fun_Ocomp(U_20212,U_20216,U_20211,U_20217),U_20213),U_20214,U_20218)
      | ~ c_Fun_Obij__betw(U_20212,U_20216,U_20217,U_20215,U_20218)
      | ~ c_Fun_Obij__betw(U_20211,U_20212,U_20213,U_20214,U_20215) ),
    inference(variable_rename,[status(thm)],[f_4867_1]) ).

cnf(f_4867_3,plain,
    ( c_Fun_Obij__betw(U_20211,U_20216,hAPP(c_Fun_Ocomp(U_20212,U_20216,U_20211,U_20217),U_20213),U_20214,U_20218)
    | ~ c_Fun_Obij__betw(U_20212,U_20216,U_20217,U_20215,U_20218)
    | ~ c_Fun_Obij__betw(U_20211,U_20212,U_20213,U_20214,U_20215) ),
    inference(clausify,[status(thm)],[f_4867_2]) ).

fof(f_4868_1,plain,
    ! [V_g_2,T_d,V_f_2,T_c,T_b] :
      ( c_Fun_Obij__betw(T_b,T_d,hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_g_2),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)))
      | ~ c_Fun_Obij__betw(T_c,T_d,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)))
      | ~ c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_bij__comp]) ).

fof(f_4868_2,plain,
    ! [U_20223,U_20222,U_20221,U_20220,U_20219] :
      ( c_Fun_Obij__betw(U_20219,U_20222,hAPP(c_Fun_Ocomp(U_20220,U_20222,U_20219,U_20223),U_20221),c_Orderings_Otop__class_Otop(tc_fun(U_20219,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20222,tc_HOL_Obool)))
      | ~ c_Fun_Obij__betw(U_20220,U_20222,U_20223,c_Orderings_Otop__class_Otop(tc_fun(U_20220,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20222,tc_HOL_Obool)))
      | ~ c_Fun_Obij__betw(U_20219,U_20220,U_20221,c_Orderings_Otop__class_Otop(tc_fun(U_20219,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20220,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_4868_1]) ).

cnf(f_4868_3,plain,
    ( c_Fun_Obij__betw(U_20219,U_20222,hAPP(c_Fun_Ocomp(U_20220,U_20222,U_20219,U_20223),U_20221),c_Orderings_Otop__class_Otop(tc_fun(U_20219,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20222,tc_HOL_Obool)))
    | ~ c_Fun_Obij__betw(U_20220,U_20222,U_20223,c_Orderings_Otop__class_Otop(tc_fun(U_20220,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20222,tc_HOL_Obool)))
    | ~ c_Fun_Obij__betw(U_20219,U_20220,U_20221,c_Orderings_Otop__class_Otop(tc_fun(U_20219,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20220,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4868_2]) ).

fof(f_4869_1,plain,
    ! [V_F_2,V_h_2,T_c,T_b] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_c,V_h_2),V_F_2)))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2)) )
        & ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_c,V_h_2),V_F_2))) ) )
      | ~ c_Fun_Obij__betw(T_b,T_c,V_h_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_finite__vimage__iff]) ).

fof(f_4869_2,plain,
    ! [U_20227,U_20226,U_20225,U_20224] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_20224),hAPP(c_Set_Ovimage(U_20224,U_20225,U_20226),U_20227)))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20225),U_20227)) )
        & ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_20225),U_20227))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20224),hAPP(c_Set_Ovimage(U_20224,U_20225,U_20226),U_20227))) ) )
      | ~ c_Fun_Obij__betw(U_20224,U_20225,U_20226,c_Orderings_Otop__class_Otop(tc_fun(U_20224,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20225,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_4869_1]) ).

cnf(f_4869_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_20225),U_20227))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20224),hAPP(c_Set_Ovimage(U_20224,U_20225,U_20226),U_20227)))
    | ~ c_Fun_Obij__betw(U_20224,U_20225,U_20226,c_Orderings_Otop__class_Otop(tc_fun(U_20224,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20225,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4869_2]) ).

cnf(f_4869_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_20224),hAPP(c_Set_Ovimage(U_20224,U_20225,U_20226),U_20227)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20225),U_20227))
    | ~ c_Fun_Obij__betw(U_20224,U_20225,U_20226,c_Orderings_Otop__class_Otop(tc_fun(U_20224,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20225,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4869_2]) ).

fof(f_4870_1,plain,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))
      | ~ c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_bij__image__Compl__eq]) ).

fof(f_4870_2,plain,
    ! [U_20231,U_20230,U_20229,U_20228] :
      ( hAPP(c_Set_Oimage(U_20228,U_20229,U_20230),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_20228,tc_HOL_Obool)),U_20231)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_20229,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_20228,U_20229,U_20230),U_20231))
      | ~ c_Fun_Obij__betw(U_20228,U_20229,U_20230,c_Orderings_Otop__class_Otop(tc_fun(U_20228,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20229,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_4870_1]) ).

cnf(f_4870_3,plain,
    ( hAPP(c_Set_Oimage(U_20228,U_20229,U_20230),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_20228,tc_HOL_Obool)),U_20231)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_20229,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_20228,U_20229,U_20230),U_20231))
    | ~ c_Fun_Obij__betw(U_20228,U_20229,U_20230,c_Orderings_Otop__class_Otop(tc_fun(U_20228,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20229,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4870_2]) ).

fof(f_4871_1,plain,
    ! [V_f_2,T_c,T_b] :
      ( ( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
        | hAPP(c_Set_Oimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))
        | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) )
      & ( ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))
          & c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) )
        | ~ c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) ) ),
    inference(fof_nnf,[status(thm)],[fact_bij__def]) ).

fof(f_4871_2,plain,
    ! [U_20234,U_20233,U_20232] :
      ( ( c_Fun_Obij__betw(U_20232,U_20233,U_20234,c_Orderings_Otop__class_Otop(tc_fun(U_20232,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20233,tc_HOL_Obool)))
        | hAPP(c_Set_Oimage(U_20232,U_20233,U_20234),c_Orderings_Otop__class_Otop(tc_fun(U_20232,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_20233,tc_HOL_Obool))
        | ~ c_Fun_Oinj__on(U_20232,U_20233,U_20234,c_Orderings_Otop__class_Otop(tc_fun(U_20232,tc_HOL_Obool))) )
      & ( ( hAPP(c_Set_Oimage(U_20232,U_20233,U_20234),c_Orderings_Otop__class_Otop(tc_fun(U_20232,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_20233,tc_HOL_Obool))
          & c_Fun_Oinj__on(U_20232,U_20233,U_20234,c_Orderings_Otop__class_Otop(tc_fun(U_20232,tc_HOL_Obool))) )
        | ~ c_Fun_Obij__betw(U_20232,U_20233,U_20234,c_Orderings_Otop__class_Otop(tc_fun(U_20232,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20233,tc_HOL_Obool))) ) ),
    inference(variable_rename,[status(thm)],[f_4871_1]) ).

fof(f_4871_3,plain,
    ( ! [U_20240,U_20238,U_20236] :
        ( c_Fun_Obij__betw(U_20236,U_20238,U_20240,c_Orderings_Otop__class_Otop(tc_fun(U_20236,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20238,tc_HOL_Obool)))
        | hAPP(c_Set_Oimage(U_20236,U_20238,U_20240),c_Orderings_Otop__class_Otop(tc_fun(U_20236,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_20238,tc_HOL_Obool))
        | ~ c_Fun_Oinj__on(U_20236,U_20238,U_20240,c_Orderings_Otop__class_Otop(tc_fun(U_20236,tc_HOL_Obool))) )
    & ! [U_20239,U_20237,U_20235] :
        ( ( hAPP(c_Set_Oimage(U_20235,U_20237,U_20239),c_Orderings_Otop__class_Otop(tc_fun(U_20235,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_20237,tc_HOL_Obool))
          & c_Fun_Oinj__on(U_20235,U_20237,U_20239,c_Orderings_Otop__class_Otop(tc_fun(U_20235,tc_HOL_Obool))) )
        | ~ c_Fun_Obij__betw(U_20235,U_20237,U_20239,c_Orderings_Otop__class_Otop(tc_fun(U_20235,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20237,tc_HOL_Obool))) ) ),
    inference(miniscope,[status(thm)],[f_4871_2]) ).

cnf(f_4871_4,plain,
    ( c_Fun_Oinj__on(U_20235,U_20237,U_20239,c_Orderings_Otop__class_Otop(tc_fun(U_20235,tc_HOL_Obool)))
    | ~ c_Fun_Obij__betw(U_20235,U_20237,U_20239,c_Orderings_Otop__class_Otop(tc_fun(U_20235,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20237,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4871_3]) ).

cnf(f_4871_5,plain,
    ( hAPP(c_Set_Oimage(U_20235,U_20237,U_20239),c_Orderings_Otop__class_Otop(tc_fun(U_20235,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_20237,tc_HOL_Obool))
    | ~ c_Fun_Obij__betw(U_20235,U_20237,U_20239,c_Orderings_Otop__class_Otop(tc_fun(U_20235,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20237,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4871_3]) ).

cnf(f_4871_6,plain,
    ( c_Fun_Obij__betw(U_20236,U_20238,U_20240,c_Orderings_Otop__class_Otop(tc_fun(U_20236,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20238,tc_HOL_Obool)))
    | hAPP(c_Set_Oimage(U_20236,U_20238,U_20240),c_Orderings_Otop__class_Otop(tc_fun(U_20236,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_20238,tc_HOL_Obool))
    | ~ c_Fun_Oinj__on(U_20236,U_20238,U_20240,c_Orderings_Otop__class_Otop(tc_fun(U_20236,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4871_3]) ).

fof(f_4872_1,plain,
    ! [V_f_2,T_c,T_b] :
      ( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
      | hAPP(c_Set_Oimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_bijI]) ).

fof(f_4872_2,plain,
    ! [U_20243,U_20242,U_20241] :
      ( c_Fun_Obij__betw(U_20241,U_20242,U_20243,c_Orderings_Otop__class_Otop(tc_fun(U_20241,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20242,tc_HOL_Obool)))
      | hAPP(c_Set_Oimage(U_20241,U_20242,U_20243),c_Orderings_Otop__class_Otop(tc_fun(U_20241,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_20242,tc_HOL_Obool))
      | ~ c_Fun_Oinj__on(U_20241,U_20242,U_20243,c_Orderings_Otop__class_Otop(tc_fun(U_20241,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_4872_1]) ).

cnf(f_4872_3,plain,
    ( c_Fun_Obij__betw(U_20241,U_20242,U_20243,c_Orderings_Otop__class_Otop(tc_fun(U_20241,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20242,tc_HOL_Obool)))
    | hAPP(c_Set_Oimage(U_20241,U_20242,U_20243),c_Orderings_Otop__class_Otop(tc_fun(U_20241,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_20242,tc_HOL_Obool))
    | ~ c_Fun_Oinj__on(U_20241,U_20242,U_20243,c_Orderings_Otop__class_Otop(tc_fun(U_20241,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4872_2]) ).

fof(f_4873_1,plain,
    ! [V_D_2,V_C_2,V_B_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Obij__betw(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_D_2))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_D_2) != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
      | ~ c_Fun_Obij__betw(T_b,T_c,V_f_2,V_C_2,V_D_2)
      | ~ c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2) ),
    inference(fof_nnf,[status(thm)],[fact_bij__betw__combine]) ).

fof(f_4873_2,plain,
    ! [U_20250,U_20249,U_20248,U_20247,U_20246,U_20245,U_20244] :
      ( c_Fun_Obij__betw(U_20244,U_20245,U_20246,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_20244,tc_HOL_Obool)),U_20247),U_20249),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_20245,tc_HOL_Obool)),U_20248),U_20250))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_20245,tc_HOL_Obool)),U_20248),U_20250) != c_Orderings_Obot__class_Obot(tc_fun(U_20245,tc_HOL_Obool))
      | ~ c_Fun_Obij__betw(U_20244,U_20245,U_20246,U_20249,U_20250)
      | ~ c_Fun_Obij__betw(U_20244,U_20245,U_20246,U_20247,U_20248) ),
    inference(variable_rename,[status(thm)],[f_4873_1]) ).

cnf(f_4873_3,plain,
    ( c_Fun_Obij__betw(U_20244,U_20245,U_20246,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_20244,tc_HOL_Obool)),U_20247),U_20249),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_20245,tc_HOL_Obool)),U_20248),U_20250))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_20245,tc_HOL_Obool)),U_20248),U_20250) != c_Orderings_Obot__class_Obot(tc_fun(U_20245,tc_HOL_Obool))
    | ~ c_Fun_Obij__betw(U_20244,U_20245,U_20246,U_20249,U_20250)
    | ~ c_Fun_Obij__betw(U_20244,U_20245,U_20246,U_20247,U_20248) ),
    inference(clausify,[status(thm)],[f_4873_2]) ).

fof(f_4874_1,plain,
    ! [V_f_2,V_B_H_2,V_A_H_2,T_c,V_B_2,V_A_2,T_b] :
      ( c_Fun_Obij__betw(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_H_2),V_B_H_2))
      | ~ c_Fun_Obij__betw(T_b,T_c,V_f_2,V_B_2,V_B_H_2)
      | ~ c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_H_2),V_B_H_2) != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
    inference(fof_nnf,[status(thm)],[fact_bij__betw__Disj__Un]) ).

fof(f_4874_2,plain,
    ! [U_20257,U_20256,U_20255,U_20254,U_20253,U_20252,U_20251] :
      ( c_Fun_Obij__betw(U_20251,U_20254,U_20257,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_20251,tc_HOL_Obool)),U_20252),U_20253),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_20254,tc_HOL_Obool)),U_20255),U_20256))
      | ~ c_Fun_Obij__betw(U_20251,U_20254,U_20257,U_20253,U_20256)
      | ~ c_Fun_Obij__betw(U_20251,U_20254,U_20257,U_20252,U_20255)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_20254,tc_HOL_Obool)),U_20255),U_20256) != c_Orderings_Obot__class_Obot(tc_fun(U_20254,tc_HOL_Obool))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_20251,tc_HOL_Obool)),U_20252),U_20253) != c_Orderings_Obot__class_Obot(tc_fun(U_20251,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_4874_1]) ).

cnf(f_4874_3,plain,
    ( c_Fun_Obij__betw(U_20251,U_20254,U_20257,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_20251,tc_HOL_Obool)),U_20252),U_20253),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_20254,tc_HOL_Obool)),U_20255),U_20256))
    | ~ c_Fun_Obij__betw(U_20251,U_20254,U_20257,U_20253,U_20256)
    | ~ c_Fun_Obij__betw(U_20251,U_20254,U_20257,U_20252,U_20255)
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_20254,tc_HOL_Obool)),U_20255),U_20256) != c_Orderings_Obot__class_Obot(tc_fun(U_20254,tc_HOL_Obool))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_20251,tc_HOL_Obool)),U_20252),U_20253) != c_Orderings_Obot__class_Obot(tc_fun(U_20251,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4874_2]) ).

fof(f_4875_1,plain,
    ! [V_B_H_2,V_B_2,V_A_H_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_B_2,V_B_H_2)
      | hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2) != V_B_H_2
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
      | ~ c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2) ),
    inference(fof_nnf,[status(thm)],[fact_bij__betw__subset]) ).

fof(f_4875_2,plain,
    ! [U_20264,U_20263,U_20262,U_20261,U_20260,U_20259,U_20258] :
      ( c_Fun_Obij__betw(U_20258,U_20259,U_20260,U_20263,U_20264)
      | hAPP(c_Set_Oimage(U_20258,U_20259,U_20260),U_20263) != U_20264
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20258,tc_HOL_Obool)),U_20263),U_20261))
      | ~ c_Fun_Obij__betw(U_20258,U_20259,U_20260,U_20261,U_20262) ),
    inference(variable_rename,[status(thm)],[f_4875_1]) ).

cnf(f_4875_3,plain,
    ( c_Fun_Obij__betw(U_20258,U_20259,U_20260,U_20263,U_20264)
    | hAPP(c_Set_Oimage(U_20258,U_20259,U_20260),U_20263) != U_20264
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20258,tc_HOL_Obool)),U_20263),U_20261))
    | ~ c_Fun_Obij__betw(U_20258,U_20259,U_20260,U_20261,U_20262) ),
    inference(clausify,[status(thm)],[f_4875_2]) ).

fof(f_4876_1,plain,
    ! [V_f_2,T_c,T_b] :
      ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))
      | ~ c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_bij__is__surj]) ).

fof(f_4876_2,plain,
    ! [U_20267,U_20266,U_20265] :
      ( hAPP(c_Set_Oimage(U_20265,U_20266,U_20267),c_Orderings_Otop__class_Otop(tc_fun(U_20265,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_20266,tc_HOL_Obool))
      | ~ c_Fun_Obij__betw(U_20265,U_20266,U_20267,c_Orderings_Otop__class_Otop(tc_fun(U_20265,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20266,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_4876_1]) ).

cnf(f_4876_3,plain,
    ( hAPP(c_Set_Oimage(U_20265,U_20266,U_20267),c_Orderings_Otop__class_Otop(tc_fun(U_20265,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_20266,tc_HOL_Obool))
    | ~ c_Fun_Obij__betw(U_20265,U_20266,U_20267,c_Orderings_Otop__class_Otop(tc_fun(U_20265,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20266,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4876_2]) ).

fof(f_4877_1,plain,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))
      | ~ c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_bij__betw__imp__surj]) ).

fof(f_4877_2,plain,
    ! [U_20271,U_20270,U_20269,U_20268] :
      ( hAPP(c_Set_Oimage(U_20268,U_20269,U_20270),c_Orderings_Otop__class_Otop(tc_fun(U_20268,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_20269,tc_HOL_Obool))
      | ~ c_Fun_Obij__betw(U_20268,U_20269,U_20270,U_20271,c_Orderings_Otop__class_Otop(tc_fun(U_20269,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_4877_1]) ).

cnf(f_4877_3,plain,
    ( hAPP(c_Set_Oimage(U_20268,U_20269,U_20270),c_Orderings_Otop__class_Otop(tc_fun(U_20268,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_20269,tc_HOL_Obool))
    | ~ c_Fun_Obij__betw(U_20268,U_20269,U_20270,U_20271,c_Orderings_Otop__class_Otop(tc_fun(U_20269,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4877_2]) ).

fof(f_4878_1,plain,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_inj__on__imp__bij__betw]) ).

fof(f_4878_2,plain,
    ! [U_20275,U_20274,U_20273,U_20272] :
      ( c_Fun_Obij__betw(U_20272,U_20273,U_20274,U_20275,hAPP(c_Set_Oimage(U_20272,U_20273,U_20274),U_20275))
      | ~ c_Fun_Oinj__on(U_20272,U_20273,U_20274,U_20275) ),
    inference(variable_rename,[status(thm)],[f_4878_1]) ).

cnf(f_4878_3,plain,
    ( c_Fun_Obij__betw(U_20272,U_20273,U_20274,U_20275,hAPP(c_Set_Oimage(U_20272,U_20273,U_20274),U_20275))
    | ~ c_Fun_Oinj__on(U_20272,U_20273,U_20274,U_20275) ),
    inference(clausify,[status(thm)],[f_4878_2]) ).

fof(f_4879_1,plain,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
      ( ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
        | hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) != V_B_2
        | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) )
      & ( ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) = V_B_2
          & c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) )
        | ~ c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_bij__betw__def]) ).

fof(f_4879_2,plain,
    ! [U_20280,U_20279,U_20278,U_20277,U_20276] :
      ( ( c_Fun_Obij__betw(U_20276,U_20277,U_20278,U_20279,U_20280)
        | hAPP(c_Set_Oimage(U_20276,U_20277,U_20278),U_20279) != U_20280
        | ~ c_Fun_Oinj__on(U_20276,U_20277,U_20278,U_20279) )
      & ( ( hAPP(c_Set_Oimage(U_20276,U_20277,U_20278),U_20279) = U_20280
          & c_Fun_Oinj__on(U_20276,U_20277,U_20278,U_20279) )
        | ~ c_Fun_Obij__betw(U_20276,U_20277,U_20278,U_20279,U_20280) ) ),
    inference(variable_rename,[status(thm)],[f_4879_1]) ).

fof(f_4879_3,plain,
    ( ! [U_20290,U_20288,U_20286,U_20284,U_20282] :
        ( c_Fun_Obij__betw(U_20282,U_20284,U_20286,U_20288,U_20290)
        | hAPP(c_Set_Oimage(U_20282,U_20284,U_20286),U_20288) != U_20290
        | ~ c_Fun_Oinj__on(U_20282,U_20284,U_20286,U_20288) )
    & ! [U_20289,U_20287,U_20285,U_20283,U_20281] :
        ( ( hAPP(c_Set_Oimage(U_20281,U_20283,U_20285),U_20287) = U_20289
          & c_Fun_Oinj__on(U_20281,U_20283,U_20285,U_20287) )
        | ~ c_Fun_Obij__betw(U_20281,U_20283,U_20285,U_20287,U_20289) ) ),
    inference(miniscope,[status(thm)],[f_4879_2]) ).

cnf(f_4879_4,plain,
    ( c_Fun_Oinj__on(U_20281,U_20283,U_20285,U_20287)
    | ~ c_Fun_Obij__betw(U_20281,U_20283,U_20285,U_20287,U_20289) ),
    inference(clausify,[status(thm)],[f_4879_3]) ).

cnf(f_4879_5,plain,
    ( hAPP(c_Set_Oimage(U_20281,U_20283,U_20285),U_20287) = U_20289
    | ~ c_Fun_Obij__betw(U_20281,U_20283,U_20285,U_20287,U_20289) ),
    inference(clausify,[status(thm)],[f_4879_3]) ).

cnf(f_4879_6,plain,
    ( c_Fun_Obij__betw(U_20282,U_20284,U_20286,U_20288,U_20290)
    | hAPP(c_Set_Oimage(U_20282,U_20284,U_20286),U_20288) != U_20290
    | ~ c_Fun_Oinj__on(U_20282,U_20284,U_20286,U_20288) ),
    inference(clausify,[status(thm)],[f_4879_3]) ).

fof(f_4880_1,plain,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
      | ~ c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2) ),
    inference(fof_nnf,[status(thm)],[fact_bij__betw__imp__inj__on]) ).

fof(f_4880_2,plain,
    ! [U_20295,U_20294,U_20293,U_20292,U_20291] :
      ( c_Fun_Oinj__on(U_20291,U_20292,U_20293,U_20294)
      | ~ c_Fun_Obij__betw(U_20291,U_20292,U_20293,U_20294,U_20295) ),
    inference(variable_rename,[status(thm)],[f_4880_1]) ).

cnf(f_4880_3,plain,
    ( c_Fun_Oinj__on(U_20291,U_20292,U_20293,U_20294)
    | ~ c_Fun_Obij__betw(U_20291,U_20292,U_20293,U_20294,U_20295) ),
    inference(clausify,[status(thm)],[f_4880_2]) ).

fof(f_4881_1,plain,
    ! [V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
      | ~ c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_bij__is__inj]) ).

fof(f_4881_2,plain,
    ! [U_20298,U_20297,U_20296] :
      ( c_Fun_Oinj__on(U_20296,U_20297,U_20298,c_Orderings_Otop__class_Otop(tc_fun(U_20296,tc_HOL_Obool)))
      | ~ c_Fun_Obij__betw(U_20296,U_20297,U_20298,c_Orderings_Otop__class_Otop(tc_fun(U_20296,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20297,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_4881_1]) ).

cnf(f_4881_3,plain,
    ( c_Fun_Oinj__on(U_20296,U_20297,U_20298,c_Orderings_Otop__class_Otop(tc_fun(U_20296,tc_HOL_Obool)))
    | ~ c_Fun_Obij__betw(U_20296,U_20297,U_20298,c_Orderings_Otop__class_Otop(tc_fun(U_20296,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20297,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4881_2]) ).

fof(f_4882_1,plain,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2)
      | ~ c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2) ),
    inference(fof_nnf,[status(thm)],[fact_bij__betw__same__card]) ).

fof(f_4882_2,plain,
    ! [U_20303,U_20302,U_20301,U_20300,U_20299] :
      ( hAPP(c_Finite__Set_Ocard(U_20299),U_20302) = hAPP(c_Finite__Set_Ocard(U_20300),U_20303)
      | ~ c_Fun_Obij__betw(U_20299,U_20300,U_20301,U_20302,U_20303) ),
    inference(variable_rename,[status(thm)],[f_4882_1]) ).

cnf(f_4882_3,plain,
    ( hAPP(c_Finite__Set_Ocard(U_20299),U_20302) = hAPP(c_Finite__Set_Ocard(U_20300),U_20303)
    | ~ c_Fun_Obij__betw(U_20299,U_20300,U_20301,U_20302,U_20303) ),
    inference(clausify,[status(thm)],[f_4882_2]) ).

fof(f_4883_1,plain,
    ! [V_k] : c_Quickcheck_Obeyond(V_k,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[fact_beyond__zero]) ).

fof(f_4883_2,plain,
    ! [U_20304] : c_Quickcheck_Obeyond(U_20304,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
    inference(variable_rename,[status(thm)],[f_4883_1]) ).

cnf(f_4883_3,plain,
    c_Quickcheck_Obeyond(U_20304,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_4883_2]) ).

fof(f_4884_1,plain,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Obij__betw(T_c,T_b,c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_B_2,V_A_2)
      | ~ c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2) ),
    inference(fof_nnf,[status(thm)],[fact_bij__betw__the__inv__into]) ).

fof(f_4884_2,plain,
    ! [U_20309,U_20308,U_20307,U_20306,U_20305] :
      ( c_Fun_Obij__betw(U_20306,U_20305,c_Fun_Othe__inv__into(U_20305,U_20306,U_20308,U_20307),U_20309,U_20308)
      | ~ c_Fun_Obij__betw(U_20305,U_20306,U_20307,U_20308,U_20309) ),
    inference(variable_rename,[status(thm)],[f_4884_1]) ).

cnf(f_4884_3,plain,
    ( c_Fun_Obij__betw(U_20306,U_20305,c_Fun_Othe__inv__into(U_20305,U_20306,U_20308,U_20307),U_20309,U_20308)
    | ~ c_Fun_Obij__betw(U_20305,U_20306,U_20307,U_20308,U_20309) ),
    inference(clausify,[status(thm)],[f_4884_2]) ).

fof(f_4885_1,plain,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
      | ~ c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_bij__betw__empty1]) ).

fof(f_4885_2,plain,
    ! [U_20313,U_20312,U_20311,U_20310] :
      ( U_20313 = c_Orderings_Obot__class_Obot(tc_fun(U_20311,tc_HOL_Obool))
      | ~ c_Fun_Obij__betw(U_20310,U_20311,U_20312,c_Orderings_Obot__class_Obot(tc_fun(U_20310,tc_HOL_Obool)),U_20313) ),
    inference(variable_rename,[status(thm)],[f_4885_1]) ).

fof(f_4885_3,plain,
    ! [U_20313,U_20312,U_20311] :
      ( ! [U_20310] : ~ c_Fun_Obij__betw(U_20310,U_20311,U_20312,c_Orderings_Obot__class_Obot(tc_fun(U_20310,tc_HOL_Obool)),U_20313)
      | U_20313 = c_Orderings_Obot__class_Obot(tc_fun(U_20311,tc_HOL_Obool)) ),
    inference(miniscope,[status(thm)],[f_4885_2]) ).

cnf(f_4885_4,plain,
    ( ~ c_Fun_Obij__betw(U_20310,U_20311,U_20312,c_Orderings_Obot__class_Obot(tc_fun(U_20310,tc_HOL_Obool)),U_20313)
    | U_20313 = c_Orderings_Obot__class_Obot(tc_fun(U_20311,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4885_3]) ).

fof(f_4886_1,plain,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_bij__betw__empty2]) ).

fof(f_4886_2,plain,
    ! [U_20317,U_20316,U_20315,U_20314] :
      ( U_20317 = c_Orderings_Obot__class_Obot(tc_fun(U_20314,tc_HOL_Obool))
      | ~ c_Fun_Obij__betw(U_20314,U_20315,U_20316,U_20317,c_Orderings_Obot__class_Obot(tc_fun(U_20315,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_4886_1]) ).

cnf(f_4886_3,plain,
    ( U_20317 = c_Orderings_Obot__class_Obot(tc_fun(U_20314,tc_HOL_Obool))
    | ~ c_Fun_Obij__betw(U_20314,U_20315,U_20316,U_20317,c_Orderings_Obot__class_Obot(tc_fun(U_20315,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4886_2]) ).

fof(f_4887_1,plain,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) )
        & ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) )
      | ~ c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2) ),
    inference(fof_nnf,[status(thm)],[fact_bij__betw__finite]) ).

fof(f_4887_2,plain,
    ! [U_20322,U_20321,U_20320,U_20319,U_20318] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_20318),U_20321))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20319),U_20322)) )
        & ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_20319),U_20322))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20318),U_20321)) ) )
      | ~ c_Fun_Obij__betw(U_20318,U_20319,U_20320,U_20321,U_20322) ),
    inference(variable_rename,[status(thm)],[f_4887_1]) ).

cnf(f_4887_3,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_20319),U_20322))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20318),U_20321))
    | ~ c_Fun_Obij__betw(U_20318,U_20319,U_20320,U_20321,U_20322) ),
    inference(clausify,[status(thm)],[f_4887_2]) ).

cnf(f_4887_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_20318),U_20321))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20319),U_20322))
    | ~ c_Fun_Obij__betw(U_20318,U_20319,U_20320,U_20321,U_20322) ),
    inference(clausify,[status(thm)],[f_4887_2]) ).

fof(f_4888_1,plain,
    ! [V_B_2,T_c,V_A_2,T_b] :
      ( ( ( ? [B_f] : c_Fun_Obij__betw(T_b,T_c,B_f,V_A_2,V_B_2)
          | hAPP(c_Finite__Set_Ocard(T_b),V_A_2) != hAPP(c_Finite__Set_Ocard(T_c),V_B_2) )
        & ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2)
          | ! [B_f] : ~ c_Fun_Obij__betw(T_b,T_c,B_f,V_A_2,V_B_2) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_BIJ]) ).

fof(f_4888_2,plain,
    ! [U_20328,U_20327,U_20326,U_20325] :
      ( ( ( ? [U_20324] : c_Fun_Obij__betw(U_20325,U_20327,U_20324,U_20326,U_20328)
          | hAPP(c_Finite__Set_Ocard(U_20325),U_20326) != hAPP(c_Finite__Set_Ocard(U_20327),U_20328) )
        & ( hAPP(c_Finite__Set_Ocard(U_20325),U_20326) = hAPP(c_Finite__Set_Ocard(U_20327),U_20328)
          | ! [U_20323] : ~ c_Fun_Obij__betw(U_20325,U_20327,U_20323,U_20326,U_20328) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20327),U_20328))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20325),U_20326)) ),
    inference(variable_rename,[status(thm)],[f_4888_1]) ).

fof(f_4888_3,plain,
    ! [U_20328,U_20327,U_20326,U_20325] :
      ( ( ( c_Fun_Obij__betw(U_20325,U_20327,sK555(U_20328,U_20327,U_20326,U_20325),U_20326,U_20328)
          | hAPP(c_Finite__Set_Ocard(U_20325),U_20326) != hAPP(c_Finite__Set_Ocard(U_20327),U_20328) )
        & ( hAPP(c_Finite__Set_Ocard(U_20325),U_20326) = hAPP(c_Finite__Set_Ocard(U_20327),U_20328)
          | ! [U_20323] : ~ c_Fun_Obij__betw(U_20325,U_20327,U_20323,U_20326,U_20328) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20327),U_20328))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20325),U_20326)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK555]),skolemize(U_20324,sK555(U_20328,U_20327,U_20326,U_20325))],[f_4888_2]) ).

cnf(f_4888_4,plain,
    ( hAPP(c_Finite__Set_Ocard(U_20325),U_20326) = hAPP(c_Finite__Set_Ocard(U_20327),U_20328)
    | ~ c_Fun_Obij__betw(U_20325,U_20327,U_20323,U_20326,U_20328)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20327),U_20328))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20325),U_20326)) ),
    inference(clausify,[status(thm)],[f_4888_3]) ).

cnf(f_4888_5,plain,
    ( c_Fun_Obij__betw(U_20325,U_20327,sK555(U_20328,U_20327,U_20326,U_20325),U_20326,U_20328)
    | hAPP(c_Finite__Set_Ocard(U_20325),U_20326) != hAPP(c_Finite__Set_Ocard(U_20327),U_20328)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20327),U_20328))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20325),U_20326)) ),
    inference(clausify,[status(thm)],[f_4888_3]) ).

fof(f_4889_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( ( c_Fun_Obij__betw(T_b,T_b,c_Fun_Oid(T_b),V_A_2,V_B_2)
        | V_A_2 != V_B_2 )
      & ( V_A_2 = V_B_2
        | ~ c_Fun_Obij__betw(T_b,T_b,c_Fun_Oid(T_b),V_A_2,V_B_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_bij__betw__id__iff]) ).

fof(f_4889_2,plain,
    ! [U_20331,U_20330,U_20329] :
      ( ( c_Fun_Obij__betw(U_20329,U_20329,c_Fun_Oid(U_20329),U_20330,U_20331)
        | U_20330 != U_20331 )
      & ( U_20330 = U_20331
        | ~ c_Fun_Obij__betw(U_20329,U_20329,c_Fun_Oid(U_20329),U_20330,U_20331) ) ),
    inference(variable_rename,[status(thm)],[f_4889_1]) ).

fof(f_4889_3,plain,
    ( ! [U_20337,U_20335] :
        ( ! [U_20333] : c_Fun_Obij__betw(U_20333,U_20333,c_Fun_Oid(U_20333),U_20335,U_20337)
        | U_20335 != U_20337 )
    & ! [U_20336,U_20334] :
        ( ! [U_20332] : ~ c_Fun_Obij__betw(U_20332,U_20332,c_Fun_Oid(U_20332),U_20334,U_20336)
        | U_20334 = U_20336 ) ),
    inference(miniscope,[status(thm)],[f_4889_2]) ).

cnf(f_4889_4,plain,
    ( ~ c_Fun_Obij__betw(U_20332,U_20332,c_Fun_Oid(U_20332),U_20334,U_20336)
    | U_20334 = U_20336 ),
    inference(clausify,[status(thm)],[f_4889_3]) ).

cnf(f_4889_5,plain,
    ( c_Fun_Obij__betw(U_20333,U_20333,c_Fun_Oid(U_20333),U_20335,U_20337)
    | U_20335 != U_20337 ),
    inference(clausify,[status(thm)],[f_4889_3]) ).

fof(f_4890_1,plain,
    ! [T_b] : c_Fun_Obij__betw(T_b,T_b,c_Fun_Oid(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),
    inference(fof_nnf,[status(thm)],[fact_bij__id]) ).

fof(f_4890_2,plain,
    ! [U_20338] : c_Fun_Obij__betw(U_20338,U_20338,c_Fun_Oid(U_20338),c_Orderings_Otop__class_Otop(tc_fun(U_20338,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20338,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_4890_1]) ).

cnf(f_4890_3,plain,
    c_Fun_Obij__betw(U_20338,U_20338,c_Fun_Oid(U_20338),c_Orderings_Otop__class_Otop(tc_fun(U_20338,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20338,tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_4890_2]) ).

fof(f_4891_1,plain,
    ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)),V_A_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)),V_A_2)) ) )
      | ~ c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_vimage__subset__eq]) ).

fof(f_4891_2,plain,
    ! [U_20343,U_20342,U_20341,U_20340,U_20339] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20339,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_20339,U_20340,U_20341),U_20342)),U_20343))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20340,tc_HOL_Obool)),U_20342),hAPP(c_Set_Oimage(U_20339,U_20340,U_20341),U_20343))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20340,tc_HOL_Obool)),U_20342),hAPP(c_Set_Oimage(U_20339,U_20340,U_20341),U_20343)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20339,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_20339,U_20340,U_20341),U_20342)),U_20343)) ) )
      | ~ c_Fun_Obij__betw(U_20339,U_20340,U_20341,c_Orderings_Otop__class_Otop(tc_fun(U_20339,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20340,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_4891_1]) ).

cnf(f_4891_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20340,tc_HOL_Obool)),U_20342),hAPP(c_Set_Oimage(U_20339,U_20340,U_20341),U_20343)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20339,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_20339,U_20340,U_20341),U_20342)),U_20343))
    | ~ c_Fun_Obij__betw(U_20339,U_20340,U_20341,c_Orderings_Otop__class_Otop(tc_fun(U_20339,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20340,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4891_2]) ).

cnf(f_4891_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20339,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_20339,U_20340,U_20341),U_20342)),U_20343))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20340,tc_HOL_Obool)),U_20342),hAPP(c_Set_Oimage(U_20339,U_20340,U_20341),U_20343)))
    | ~ c_Fun_Obij__betw(U_20339,U_20340,U_20341,c_Orderings_Otop__class_Otop(tc_fun(U_20339,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20340,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4891_2]) ).

fof(f_4892_1,plain,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2) = hAPP(c_Set_Oimage(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)),V_A_2)
      | ~ c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) ),
    inference(fof_nnf,[status(thm)],[fact_bij__vimage__eq__inv__image]) ).

fof(f_4892_2,plain,
    ! [U_20347,U_20346,U_20345,U_20344] :
      ( hAPP(c_Set_Ovimage(U_20344,U_20345,U_20346),U_20347) = hAPP(c_Set_Oimage(U_20345,U_20344,c_Hilbert__Choice_Oinv__into(U_20344,U_20345,c_Orderings_Otop__class_Otop(tc_fun(U_20344,tc_HOL_Obool)),U_20346)),U_20347)
      | ~ c_Fun_Obij__betw(U_20344,U_20345,U_20346,c_Orderings_Otop__class_Otop(tc_fun(U_20344,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20345,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_4892_1]) ).

cnf(f_4892_3,plain,
    ( hAPP(c_Set_Ovimage(U_20344,U_20345,U_20346),U_20347) = hAPP(c_Set_Oimage(U_20345,U_20344,c_Hilbert__Choice_Oinv__into(U_20344,U_20345,c_Orderings_Otop__class_Otop(tc_fun(U_20344,tc_HOL_Obool)),U_20346)),U_20347)
    | ~ c_Fun_Obij__betw(U_20344,U_20345,U_20346,c_Orderings_Otop__class_Otop(tc_fun(U_20344,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_20345,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4892_2]) ).

fof(f_4893_1,plain,
    ! [V_M_2,T_b] :
      ( ? [B_h] : c_Fun_Obij__betw(tc_Nat_Onat,T_b,B_h,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_M_2)),V_M_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_M_2)) ),
    inference(fof_nnf,[status(thm)],[fact_ex__bij__betw__nat__finite__1]) ).

fof(f_4893_2,plain,
    ! [U_20350,U_20349] :
      ( ? [U_20348] : c_Fun_Obij__betw(tc_Nat_Onat,U_20349,U_20348,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_20349),U_20350)),U_20350)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20349),U_20350)) ),
    inference(variable_rename,[status(thm)],[f_4893_1]) ).

fof(f_4893_3,plain,
    ! [U_20350,U_20349] :
      ( c_Fun_Obij__betw(tc_Nat_Onat,U_20349,sK556(U_20350,U_20349),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_20349),U_20350)),U_20350)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20349),U_20350)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK556]),skolemize(U_20348,sK556(U_20350,U_20349))],[f_4893_2]) ).

cnf(f_4893_4,plain,
    ( c_Fun_Obij__betw(tc_Nat_Onat,U_20349,sK556(U_20350,U_20349),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_20349),U_20350)),U_20350)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20349),U_20350)) ),
    inference(clausify,[status(thm)],[f_4893_3]) ).

fof(f_4894_1,plain,
    ! [V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b] :
      ( ? [B_h] : c_Fun_Obij__betw(T_b,T_c,B_h,V_A_2,V_B_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_g_2),V_B_2)),V_A_2))
      | ~ c_Fun_Oinj__on(T_c,T_b,V_g_2,V_B_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),V_B_2))
      | ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ),
    inference(fof_nnf,[status(thm)],[fact_Cantor__Bernstein]) ).

fof(f_4894_2,plain,
    ! [U_20357,U_20356,U_20355,U_20354,U_20353,U_20352] :
      ( ? [U_20351] : c_Fun_Obij__betw(U_20352,U_20353,U_20351,U_20355,U_20356)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20352,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_20353,U_20352,U_20357),U_20356)),U_20355))
      | ~ c_Fun_Oinj__on(U_20353,U_20352,U_20357,U_20356)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20353,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_20352,U_20353,U_20354),U_20355)),U_20356))
      | ~ c_Fun_Oinj__on(U_20352,U_20353,U_20354,U_20355) ),
    inference(variable_rename,[status(thm)],[f_4894_1]) ).

fof(f_4894_3,plain,
    ! [U_20357,U_20356,U_20355,U_20354,U_20353,U_20352] :
      ( c_Fun_Obij__betw(U_20352,U_20353,sK557(U_20357,U_20356,U_20355,U_20354,U_20353,U_20352),U_20355,U_20356)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20352,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_20353,U_20352,U_20357),U_20356)),U_20355))
      | ~ c_Fun_Oinj__on(U_20353,U_20352,U_20357,U_20356)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20353,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_20352,U_20353,U_20354),U_20355)),U_20356))
      | ~ c_Fun_Oinj__on(U_20352,U_20353,U_20354,U_20355) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK557]),skolemize(U_20351,sK557(U_20357,U_20356,U_20355,U_20354,U_20353,U_20352))],[f_4894_2]) ).

cnf(f_4894_4,plain,
    ( c_Fun_Obij__betw(U_20352,U_20353,sK557(U_20357,U_20356,U_20355,U_20354,U_20353,U_20352),U_20355,U_20356)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20352,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_20353,U_20352,U_20357),U_20356)),U_20355))
    | ~ c_Fun_Oinj__on(U_20353,U_20352,U_20357,U_20356)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20353,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_20352,U_20353,U_20354),U_20355)),U_20356))
    | ~ c_Fun_Oinj__on(U_20352,U_20353,U_20354,U_20355) ),
    inference(clausify,[status(thm)],[f_4894_3]) ).

fof(f_4895_1,plain,
    ! [V_M_2,T_b] :
      ( ? [B_h] : c_Fun_Obij__betw(tc_Nat_Onat,T_b,B_h,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),V_M_2)),V_M_2)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_M_2)) ),
    inference(fof_nnf,[status(thm)],[fact_ex__bij__betw__nat__finite]) ).

fof(f_4895_2,plain,
    ! [U_20360,U_20359] :
      ( ? [U_20358] : c_Fun_Obij__betw(tc_Nat_Onat,U_20359,U_20358,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_20359),U_20360)),U_20360)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20359),U_20360)) ),
    inference(variable_rename,[status(thm)],[f_4895_1]) ).

fof(f_4895_3,plain,
    ! [U_20360,U_20359] :
      ( c_Fun_Obij__betw(tc_Nat_Onat,U_20359,sK558(U_20360,U_20359),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_20359),U_20360)),U_20360)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20359),U_20360)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK558]),skolemize(U_20358,sK558(U_20360,U_20359))],[f_4895_2]) ).

cnf(f_4895_4,plain,
    ( c_Fun_Obij__betw(tc_Nat_Onat,U_20359,sK558(U_20360,U_20359),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_20359),U_20360)),U_20360)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20359),U_20360)) ),
    inference(clausify,[status(thm)],[f_4895_3]) ).

fof(f_4896_1,plain,
    ! [V_M_2,T_b] :
      ( ? [B_h] : c_Fun_Obij__betw(T_b,tc_Nat_Onat,B_h,V_M_2,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),V_M_2)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_M_2)) ),
    inference(fof_nnf,[status(thm)],[fact_ex__bij__betw__finite__nat]) ).

fof(f_4896_2,plain,
    ! [U_20363,U_20362] :
      ( ? [U_20361] : c_Fun_Obij__betw(U_20362,tc_Nat_Onat,U_20361,U_20363,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_20362),U_20363)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20362),U_20363)) ),
    inference(variable_rename,[status(thm)],[f_4896_1]) ).

fof(f_4896_3,plain,
    ! [U_20363,U_20362] :
      ( c_Fun_Obij__betw(U_20362,tc_Nat_Onat,sK559(U_20363,U_20362),U_20363,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_20362),U_20363)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20362),U_20363)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK559]),skolemize(U_20361,sK559(U_20363,U_20362))],[f_4896_2]) ).

cnf(f_4896_4,plain,
    ( c_Fun_Obij__betw(U_20362,tc_Nat_Onat,sK559(U_20363,U_20362),U_20363,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_20362),U_20363)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20362),U_20363)) ),
    inference(clausify,[status(thm)],[f_4896_3]) ).

fof(f_4897_1,plain,
    ! [V_y_2,V_x_2,V_c_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Ocurry(T_c,T_d,T_b,V_c_2),V_x_2),V_y_2) = hAPP(V_c_2,hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2)),
    inference(fof_nnf,[status(thm)],[fact_curry__def]) ).

fof(f_4897_2,plain,
    ! [U_20369,U_20368,U_20367,U_20366,U_20365,U_20364] : hAPP(hAPP(c_Product__Type_Ocurry(U_20364,U_20365,U_20366,U_20367),U_20368),U_20369) = hAPP(U_20367,hAPP(hAPP(c_Product__Type_OPair(U_20364,U_20365),U_20368),U_20369)),
    inference(variable_rename,[status(thm)],[f_4897_1]) ).

cnf(f_4897_3,plain,
    hAPP(hAPP(c_Product__Type_Ocurry(U_20364,U_20365,U_20366,U_20367),U_20368),U_20369) = hAPP(U_20367,hAPP(hAPP(c_Product__Type_OPair(U_20364,U_20365),U_20368),U_20369)),
    inference(clausify,[status(thm)],[f_4897_2]) ).

fof(f_4898_1,plain,
    ! [V_r_2,V_A_2,T_c,V_S_2,T_b] :
      ( c_Relation_Orefl__on(T_c,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_S_2),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_S_2),V_r_2))
      | ? [B_x] :
          ( ~ c_Relation_Orefl__on(T_c,hAPP(V_A_2,B_x),hAPP(V_r_2,B_x))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_refl__on__UNION]) ).

fof(f_4898_2,plain,
    ! [U_20375,U_20374,U_20373,U_20372,U_20371] :
      ( c_Relation_Orefl__on(U_20373,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_20371,tc_fun(U_20373,tc_HOL_Obool)),U_20372),U_20374),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_20371,tc_fun(tc_prod(U_20373,U_20373),tc_HOL_Obool)),U_20372),U_20375))
      | ? [U_20370] :
          ( ~ c_Relation_Orefl__on(U_20373,hAPP(U_20374,U_20370),hAPP(U_20375,U_20370))
          & hBOOL(hAPP(hAPP(c_member(U_20371),U_20370),U_20372)) ) ),
    inference(variable_rename,[status(thm)],[f_4898_1]) ).

fof(f_4898_3,plain,
    ! [U_20375,U_20374,U_20373,U_20372,U_20371] :
      ( c_Relation_Orefl__on(U_20373,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_20371,tc_fun(U_20373,tc_HOL_Obool)),U_20372),U_20374),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_20371,tc_fun(tc_prod(U_20373,U_20373),tc_HOL_Obool)),U_20372),U_20375))
      | ( ~ c_Relation_Orefl__on(U_20373,hAPP(U_20374,sK560(U_20375,U_20374,U_20373,U_20372,U_20371)),hAPP(U_20375,sK560(U_20375,U_20374,U_20373,U_20372,U_20371)))
        & hBOOL(hAPP(hAPP(c_member(U_20371),sK560(U_20375,U_20374,U_20373,U_20372,U_20371)),U_20372)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK560]),skolemize(U_20370,sK560(U_20375,U_20374,U_20373,U_20372,U_20371))],[f_4898_2]) ).

cnf(f_4898_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20371),sK560(U_20375,U_20374,U_20373,U_20372,U_20371)),U_20372))
    | c_Relation_Orefl__on(U_20373,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_20371,tc_fun(U_20373,tc_HOL_Obool)),U_20372),U_20374),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_20371,tc_fun(tc_prod(U_20373,U_20373),tc_HOL_Obool)),U_20372),U_20375)) ),
    inference(clausify,[status(thm)],[f_4898_3]) ).

cnf(f_4898_5,plain,
    ( ~ c_Relation_Orefl__on(U_20373,hAPP(U_20374,sK560(U_20375,U_20374,U_20373,U_20372,U_20371)),hAPP(U_20375,sK560(U_20375,U_20374,U_20373,U_20372,U_20371)))
    | c_Relation_Orefl__on(U_20373,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_20371,tc_fun(U_20373,tc_HOL_Obool)),U_20372),U_20374),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_20371,tc_fun(tc_prod(U_20373,U_20373),tc_HOL_Obool)),U_20372),U_20375)) ),
    inference(clausify,[status(thm)],[f_4898_3]) ).

fof(f_4899_1,plain,
    ! [V_b_2,V_a_2,T_c,T_b,V_f_2] :
      ( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2))
      | ~ hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ),
    inference(fof_nnf,[status(thm)],[fact_curryI]) ).

fof(f_4899_2,plain,
    ! [U_20380,U_20379,U_20378,U_20377,U_20376] :
      ( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(U_20377,U_20378,tc_HOL_Obool,U_20376),U_20379),U_20380))
      | ~ hBOOL(hAPP(U_20376,hAPP(hAPP(c_Product__Type_OPair(U_20377,U_20378),U_20379),U_20380))) ),
    inference(variable_rename,[status(thm)],[f_4899_1]) ).

cnf(f_4899_3,plain,
    ( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(U_20377,U_20378,tc_HOL_Obool,U_20376),U_20379),U_20380))
    | ~ hBOOL(hAPP(U_20376,hAPP(hAPP(c_Product__Type_OPair(U_20377,U_20378),U_20379),U_20380))) ),
    inference(clausify,[status(thm)],[f_4899_2]) ).

fof(f_4900_1,plain,
    ! [V_f_2,T_d,T_c,T_b] : hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),c_Product__Type_Ocurry(T_b,T_c,T_d,V_f_2)) = V_f_2,
    inference(fof_nnf,[status(thm)],[fact_split__curry]) ).

fof(f_4900_2,plain,
    ! [U_20384,U_20383,U_20382,U_20381] : hAPP(c_Product__Type_Oprod_Oprod__case(U_20381,U_20382,U_20383),c_Product__Type_Ocurry(U_20381,U_20382,U_20383,U_20384)) = U_20384,
    inference(variable_rename,[status(thm)],[f_4900_1]) ).

cnf(f_4900_3,plain,
    hAPP(c_Product__Type_Oprod_Oprod__case(U_20381,U_20382,U_20383),c_Product__Type_Ocurry(U_20381,U_20382,U_20383,U_20384)) = U_20384,
    inference(clausify,[status(thm)],[f_4900_2]) ).

fof(f_4901_1,plain,
    ! [V_f_2,T_d,T_c,T_b] : c_Product__Type_Ocurry(T_b,T_c,T_d,hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_f_2)) = V_f_2,
    inference(fof_nnf,[status(thm)],[fact_curry__split]) ).

fof(f_4901_2,plain,
    ! [U_20388,U_20387,U_20386,U_20385] : c_Product__Type_Ocurry(U_20385,U_20386,U_20387,hAPP(c_Product__Type_Oprod_Oprod__case(U_20385,U_20386,U_20387),U_20388)) = U_20388,
    inference(variable_rename,[status(thm)],[f_4901_1]) ).

cnf(f_4901_3,plain,
    c_Product__Type_Ocurry(U_20385,U_20386,U_20387,hAPP(c_Product__Type_Oprod_Oprod__case(U_20385,U_20386,U_20387),U_20388)) = U_20388,
    inference(clausify,[status(thm)],[f_4901_2]) ).

fof(f_4902_1,plain,
    ! [V_b_2,V_a_2,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Ocurry(T_c,T_d,T_b,V_f_2),V_a_2),V_b_2) = hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)),
    inference(fof_nnf,[status(thm)],[fact_curry__conv]) ).

fof(f_4902_2,plain,
    ! [U_20394,U_20393,U_20392,U_20391,U_20390,U_20389] : hAPP(hAPP(c_Product__Type_Ocurry(U_20389,U_20390,U_20391,U_20392),U_20393),U_20394) = hAPP(U_20392,hAPP(hAPP(c_Product__Type_OPair(U_20389,U_20390),U_20393),U_20394)),
    inference(variable_rename,[status(thm)],[f_4902_1]) ).

cnf(f_4902_3,plain,
    hAPP(hAPP(c_Product__Type_Ocurry(U_20389,U_20390,U_20391,U_20392),U_20393),U_20394) = hAPP(U_20392,hAPP(hAPP(c_Product__Type_OPair(U_20389,U_20390),U_20393),U_20394)),
    inference(clausify,[status(thm)],[f_4902_2]) ).

fof(f_4903_1,plain,
    ! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
      ( hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)))
      | ~ hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2)) ),
    inference(fof_nnf,[status(thm)],[fact_curryD]) ).

fof(f_4903_2,plain,
    ! [U_20399,U_20398,U_20397,U_20396,U_20395] :
      ( hBOOL(hAPP(U_20397,hAPP(hAPP(c_Product__Type_OPair(U_20395,U_20396),U_20398),U_20399)))
      | ~ hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(U_20395,U_20396,tc_HOL_Obool,U_20397),U_20398),U_20399)) ),
    inference(variable_rename,[status(thm)],[f_4903_1]) ).

cnf(f_4903_3,plain,
    ( hBOOL(hAPP(U_20397,hAPP(hAPP(c_Product__Type_OPair(U_20395,U_20396),U_20398),U_20399)))
    | ~ hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(U_20395,U_20396,tc_HOL_Obool,U_20397),U_20398),U_20399)) ),
    inference(clausify,[status(thm)],[f_4903_2]) ).

fof(f_4904_1,plain,
    ! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
      ( hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)))
      | ~ hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2)) ),
    inference(fof_nnf,[status(thm)],[fact_curryE]) ).

fof(f_4904_2,plain,
    ! [U_20404,U_20403,U_20402,U_20401,U_20400] :
      ( hBOOL(hAPP(U_20402,hAPP(hAPP(c_Product__Type_OPair(U_20400,U_20401),U_20403),U_20404)))
      | ~ hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(U_20400,U_20401,tc_HOL_Obool,U_20402),U_20403),U_20404)) ),
    inference(variable_rename,[status(thm)],[f_4904_1]) ).

cnf(f_4904_3,plain,
    ( hBOOL(hAPP(U_20402,hAPP(hAPP(c_Product__Type_OPair(U_20400,U_20401),U_20403),U_20404)))
    | ~ hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(U_20400,U_20401,tc_HOL_Obool,U_20402),U_20403),U_20404)) ),
    inference(clausify,[status(thm)],[f_4904_2]) ).

fof(f_4905_1,plain,
    ! [V_P_2,V_R_2,T_b] :
      ( ( ( ? [B_x] :
              ( hBOOL(hAPP(V_P_2,B_x))
              & hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Quotient_ORespects(T_b,V_R_2))) )
          | ! [B_x1] : ~ hBOOL(hAPP(V_P_2,B_x1)) )
        & ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
          | ! [B_x] :
              ( ~ hBOOL(hAPP(V_P_2,B_x))
              | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Quotient_ORespects(T_b,V_R_2))) ) ) )
      | ~ c_Equiv__Relations_Oequivp(T_b,V_R_2) ),
    inference(fof_nnf,[status(thm)],[fact_bex__reg__eqv]) ).

fof(f_4905_2,plain,
    ! [U_20411,U_20410,U_20409] :
      ( ( ( ? [U_20408] :
              ( hBOOL(hAPP(U_20411,U_20408))
              & hBOOL(hAPP(hAPP(c_member(U_20409),U_20408),c_Quotient_ORespects(U_20409,U_20410))) )
          | ! [U_20407] : ~ hBOOL(hAPP(U_20411,U_20407)) )
        & ( ? [U_20406] : hBOOL(hAPP(U_20411,U_20406))
          | ! [U_20405] :
              ( ~ hBOOL(hAPP(U_20411,U_20405))
              | ~ hBOOL(hAPP(hAPP(c_member(U_20409),U_20405),c_Quotient_ORespects(U_20409,U_20410))) ) ) )
      | ~ c_Equiv__Relations_Oequivp(U_20409,U_20410) ),
    inference(variable_rename,[status(thm)],[f_4905_1]) ).

fof(f_4905_3,plain,
    ! [U_20411,U_20410,U_20409] :
      ( ( ( ? [U_20408] :
              ( hBOOL(hAPP(U_20411,U_20408))
              & hBOOL(hAPP(hAPP(c_member(U_20409),U_20408),c_Quotient_ORespects(U_20409,U_20410))) )
          | ! [U_20407] : ~ hBOOL(hAPP(U_20411,U_20407)) )
        & ( hBOOL(hAPP(U_20411,sK561(U_20411,U_20410,U_20409)))
          | ! [U_20405] :
              ( ~ hBOOL(hAPP(U_20411,U_20405))
              | ~ hBOOL(hAPP(hAPP(c_member(U_20409),U_20405),c_Quotient_ORespects(U_20409,U_20410))) ) ) )
      | ~ c_Equiv__Relations_Oequivp(U_20409,U_20410) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK561]),skolemize(U_20406,sK561(U_20411,U_20410,U_20409))],[f_4905_2]) ).

fof(f_4905_4,plain,
    ! [U_20411,U_20410,U_20409] :
      ( ( ( ( hBOOL(hAPP(U_20411,sK562(U_20411,U_20410,U_20409)))
            & hBOOL(hAPP(hAPP(c_member(U_20409),sK562(U_20411,U_20410,U_20409)),c_Quotient_ORespects(U_20409,U_20410))) )
          | ! [U_20407] : ~ hBOOL(hAPP(U_20411,U_20407)) )
        & ( hBOOL(hAPP(U_20411,sK561(U_20411,U_20410,U_20409)))
          | ! [U_20405] :
              ( ~ hBOOL(hAPP(U_20411,U_20405))
              | ~ hBOOL(hAPP(hAPP(c_member(U_20409),U_20405),c_Quotient_ORespects(U_20409,U_20410))) ) ) )
      | ~ c_Equiv__Relations_Oequivp(U_20409,U_20410) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK562]),skolemize(U_20408,sK562(U_20411,U_20410,U_20409))],[f_4905_3]) ).

cnf(f_4905_5,plain,
    ( hBOOL(hAPP(U_20411,sK561(U_20411,U_20410,U_20409)))
    | ~ hBOOL(hAPP(U_20411,U_20405))
    | ~ hBOOL(hAPP(hAPP(c_member(U_20409),U_20405),c_Quotient_ORespects(U_20409,U_20410)))
    | ~ c_Equiv__Relations_Oequivp(U_20409,U_20410) ),
    inference(clausify,[status(thm)],[f_4905_4]) ).

cnf(f_4905_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20409),sK562(U_20411,U_20410,U_20409)),c_Quotient_ORespects(U_20409,U_20410)))
    | ~ hBOOL(hAPP(U_20411,U_20407))
    | ~ c_Equiv__Relations_Oequivp(U_20409,U_20410) ),
    inference(clausify,[status(thm)],[f_4905_4]) ).

cnf(f_4905_7,plain,
    ( hBOOL(hAPP(U_20411,sK562(U_20411,U_20410,U_20409)))
    | ~ hBOOL(hAPP(U_20411,U_20407))
    | ~ c_Equiv__Relations_Oequivp(U_20409,U_20410) ),
    inference(clausify,[status(thm)],[f_4905_4]) ).

fof(f_4906_1,plain,
    ! [V_r_2,V_f_2,T_b] :
      ( ? [B_i] :
        ! [B_k] : hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_i),B_k)) = hAPP(V_f_2,B_i)
      | ~ c_Wellfounded_Owf(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2))
      | ? [B_i] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_i))),hAPP(V_f_2,B_i))),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_wf__weak__decr__stable]) ).

fof(f_4906_2,plain,
    ! [U_20417,U_20416,U_20415] :
      ( ? [U_20414] :
        ! [U_20413] : hAPP(U_20416,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20414),U_20413)) = hAPP(U_20416,U_20414)
      | ~ c_Wellfounded_Owf(U_20415,c_Transitive__Closure_Otrancl(U_20415,U_20417))
      | ? [U_20412] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_20415,U_20415)),hAPP(hAPP(c_Product__Type_OPair(U_20415,U_20415),hAPP(U_20416,hAPP(c_Nat_OSuc,U_20412))),hAPP(U_20416,U_20412))),c_Transitive__Closure_Ortrancl(U_20415,U_20417))) ),
    inference(variable_rename,[status(thm)],[f_4906_1]) ).

fof(f_4906_3,plain,
    ! [U_20417,U_20416,U_20415] :
      ( ? [U_20414] :
        ! [U_20413] : hAPP(U_20416,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20414),U_20413)) = hAPP(U_20416,U_20414)
      | ~ c_Wellfounded_Owf(U_20415,c_Transitive__Closure_Otrancl(U_20415,U_20417))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_20415,U_20415)),hAPP(hAPP(c_Product__Type_OPair(U_20415,U_20415),hAPP(U_20416,hAPP(c_Nat_OSuc,sK563(U_20417,U_20416,U_20415)))),hAPP(U_20416,sK563(U_20417,U_20416,U_20415)))),c_Transitive__Closure_Ortrancl(U_20415,U_20417))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK563]),skolemize(U_20412,sK563(U_20417,U_20416,U_20415))],[f_4906_2]) ).

fof(f_4906_4,plain,
    ! [U_20417,U_20416,U_20415] :
      ( ! [U_20413] : hAPP(U_20416,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK564(U_20417,U_20416,U_20415)),U_20413)) = hAPP(U_20416,sK564(U_20417,U_20416,U_20415))
      | ~ c_Wellfounded_Owf(U_20415,c_Transitive__Closure_Otrancl(U_20415,U_20417))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_20415,U_20415)),hAPP(hAPP(c_Product__Type_OPair(U_20415,U_20415),hAPP(U_20416,hAPP(c_Nat_OSuc,sK563(U_20417,U_20416,U_20415)))),hAPP(U_20416,sK563(U_20417,U_20416,U_20415)))),c_Transitive__Closure_Ortrancl(U_20415,U_20417))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK564]),skolemize(U_20414,sK564(U_20417,U_20416,U_20415))],[f_4906_3]) ).

cnf(f_4906_5,plain,
    ( hAPP(U_20416,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK564(U_20417,U_20416,U_20415)),U_20413)) = hAPP(U_20416,sK564(U_20417,U_20416,U_20415))
    | ~ c_Wellfounded_Owf(U_20415,c_Transitive__Closure_Otrancl(U_20415,U_20417))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_20415,U_20415)),hAPP(hAPP(c_Product__Type_OPair(U_20415,U_20415),hAPP(U_20416,hAPP(c_Nat_OSuc,sK563(U_20417,U_20416,U_20415)))),hAPP(U_20416,sK563(U_20417,U_20416,U_20415)))),c_Transitive__Closure_Ortrancl(U_20415,U_20417))) ),
    inference(clausify,[status(thm)],[f_4906_4]) ).

fof(f_4907_1,plain,
    ! [V_x_2,V_R_2,T_b] :
      ( ( hBOOL(hAPP(c_Quotient_ORespects(T_b,V_R_2),V_x_2))
        | ~ hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) )
      & ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2))
        | ~ hBOOL(hAPP(c_Quotient_ORespects(T_b,V_R_2),V_x_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Respects__def]) ).

fof(f_4907_2,plain,
    ! [U_20420,U_20419,U_20418] :
      ( ( hBOOL(hAPP(c_Quotient_ORespects(U_20418,U_20419),U_20420))
        | ~ hBOOL(hAPP(hAPP(U_20419,U_20420),U_20420)) )
      & ( hBOOL(hAPP(hAPP(U_20419,U_20420),U_20420))
        | ~ hBOOL(hAPP(c_Quotient_ORespects(U_20418,U_20419),U_20420)) ) ),
    inference(variable_rename,[status(thm)],[f_4907_1]) ).

fof(f_4907_3,plain,
    ( ! [U_20426,U_20424] :
        ( ! [U_20422] : hBOOL(hAPP(c_Quotient_ORespects(U_20422,U_20424),U_20426))
        | ~ hBOOL(hAPP(hAPP(U_20424,U_20426),U_20426)) )
    & ! [U_20425,U_20423] :
        ( ! [U_20421] : ~ hBOOL(hAPP(c_Quotient_ORespects(U_20421,U_20423),U_20425))
        | hBOOL(hAPP(hAPP(U_20423,U_20425),U_20425)) ) ),
    inference(miniscope,[status(thm)],[f_4907_2]) ).

cnf(f_4907_4,plain,
    ( ~ hBOOL(hAPP(c_Quotient_ORespects(U_20421,U_20423),U_20425))
    | hBOOL(hAPP(hAPP(U_20423,U_20425),U_20425)) ),
    inference(clausify,[status(thm)],[f_4907_3]) ).

cnf(f_4907_5,plain,
    ( hBOOL(hAPP(c_Quotient_ORespects(U_20422,U_20424),U_20426))
    | ~ hBOOL(hAPP(hAPP(U_20424,U_20426),U_20426)) ),
    inference(clausify,[status(thm)],[f_4907_3]) ).

fof(f_4908_1,plain,
    ! [V_R_2,V_x_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Quotient_ORespects(T_b,V_R_2)))
        | ~ hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) )
      & ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Quotient_ORespects(T_b,V_R_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_in__respects]) ).

fof(f_4908_2,plain,
    ! [U_20429,U_20428,U_20427] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_20427),U_20428),c_Quotient_ORespects(U_20427,U_20429)))
        | ~ hBOOL(hAPP(hAPP(U_20429,U_20428),U_20428)) )
      & ( hBOOL(hAPP(hAPP(U_20429,U_20428),U_20428))
        | ~ hBOOL(hAPP(hAPP(c_member(U_20427),U_20428),c_Quotient_ORespects(U_20427,U_20429))) ) ),
    inference(variable_rename,[status(thm)],[f_4908_1]) ).

fof(f_4908_3,plain,
    ( ! [U_20435,U_20433] :
        ( ! [U_20431] : hBOOL(hAPP(hAPP(c_member(U_20431),U_20433),c_Quotient_ORespects(U_20431,U_20435)))
        | ~ hBOOL(hAPP(hAPP(U_20435,U_20433),U_20433)) )
    & ! [U_20434,U_20432] :
        ( ! [U_20430] : ~ hBOOL(hAPP(hAPP(c_member(U_20430),U_20432),c_Quotient_ORespects(U_20430,U_20434)))
        | hBOOL(hAPP(hAPP(U_20434,U_20432),U_20432)) ) ),
    inference(miniscope,[status(thm)],[f_4908_2]) ).

cnf(f_4908_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_20430),U_20432),c_Quotient_ORespects(U_20430,U_20434)))
    | hBOOL(hAPP(hAPP(U_20434,U_20432),U_20432)) ),
    inference(clausify,[status(thm)],[f_4908_3]) ).

cnf(f_4908_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20431),U_20433),c_Quotient_ORespects(U_20431,U_20435)))
    | ~ hBOOL(hAPP(hAPP(U_20435,U_20433),U_20433)) ),
    inference(clausify,[status(thm)],[f_4908_3]) ).

fof(f_4909_1,plain,
    ! [V_P_2,V_Q_2,V_R_2,T_b] :
      ( ? [B_x] :
          ( hBOOL(hAPP(V_P_2,B_x))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Quotient_ORespects(T_b,V_R_2))) )
      | ! [B_x1] : ~ hBOOL(hAPP(V_Q_2,B_x1))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(V_P_2,B_x))
          & hBOOL(hAPP(V_Q_2,B_x)) )
      | ~ c_Equiv__Relations_Oequivp(T_b,V_R_2) ),
    inference(fof_nnf,[status(thm)],[fact_bex__reg__right]) ).

fof(f_4909_2,plain,
    ! [U_20442,U_20441,U_20440,U_20439] :
      ( ? [U_20438] :
          ( hBOOL(hAPP(U_20442,U_20438))
          & hBOOL(hAPP(hAPP(c_member(U_20439),U_20438),c_Quotient_ORespects(U_20439,U_20440))) )
      | ! [U_20437] : ~ hBOOL(hAPP(U_20441,U_20437))
      | ? [U_20436] :
          ( ~ hBOOL(hAPP(U_20442,U_20436))
          & hBOOL(hAPP(U_20441,U_20436)) )
      | ~ c_Equiv__Relations_Oequivp(U_20439,U_20440) ),
    inference(variable_rename,[status(thm)],[f_4909_1]) ).

fof(f_4909_3,plain,
    ! [U_20442,U_20441,U_20440,U_20439] :
      ( ? [U_20438] :
          ( hBOOL(hAPP(U_20442,U_20438))
          & hBOOL(hAPP(hAPP(c_member(U_20439),U_20438),c_Quotient_ORespects(U_20439,U_20440))) )
      | ! [U_20437] : ~ hBOOL(hAPP(U_20441,U_20437))
      | ( ~ hBOOL(hAPP(U_20442,sK565(U_20442,U_20441,U_20440,U_20439)))
        & hBOOL(hAPP(U_20441,sK565(U_20442,U_20441,U_20440,U_20439))) )
      | ~ c_Equiv__Relations_Oequivp(U_20439,U_20440) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK565]),skolemize(U_20436,sK565(U_20442,U_20441,U_20440,U_20439))],[f_4909_2]) ).

fof(f_4909_4,plain,
    ! [U_20442,U_20441,U_20440,U_20439] :
      ( ( hBOOL(hAPP(U_20442,sK566(U_20442,U_20441,U_20440,U_20439)))
        & hBOOL(hAPP(hAPP(c_member(U_20439),sK566(U_20442,U_20441,U_20440,U_20439)),c_Quotient_ORespects(U_20439,U_20440))) )
      | ! [U_20437] : ~ hBOOL(hAPP(U_20441,U_20437))
      | ( ~ hBOOL(hAPP(U_20442,sK565(U_20442,U_20441,U_20440,U_20439)))
        & hBOOL(hAPP(U_20441,sK565(U_20442,U_20441,U_20440,U_20439))) )
      | ~ c_Equiv__Relations_Oequivp(U_20439,U_20440) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK566]),skolemize(U_20438,sK566(U_20442,U_20441,U_20440,U_20439))],[f_4909_3]) ).

cnf(f_4909_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20439),sK566(U_20442,U_20441,U_20440,U_20439)),c_Quotient_ORespects(U_20439,U_20440)))
    | ~ hBOOL(hAPP(U_20441,U_20437))
    | hBOOL(hAPP(U_20441,sK565(U_20442,U_20441,U_20440,U_20439)))
    | ~ c_Equiv__Relations_Oequivp(U_20439,U_20440) ),
    inference(clausify,[status(thm)],[f_4909_4]) ).

cnf(f_4909_6,plain,
    ( hBOOL(hAPP(U_20442,sK566(U_20442,U_20441,U_20440,U_20439)))
    | ~ hBOOL(hAPP(U_20441,U_20437))
    | hBOOL(hAPP(U_20441,sK565(U_20442,U_20441,U_20440,U_20439)))
    | ~ c_Equiv__Relations_Oequivp(U_20439,U_20440) ),
    inference(clausify,[status(thm)],[f_4909_4]) ).

cnf(f_4909_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20439),sK566(U_20442,U_20441,U_20440,U_20439)),c_Quotient_ORespects(U_20439,U_20440)))
    | ~ hBOOL(hAPP(U_20441,U_20437))
    | ~ hBOOL(hAPP(U_20442,sK565(U_20442,U_20441,U_20440,U_20439)))
    | ~ c_Equiv__Relations_Oequivp(U_20439,U_20440) ),
    inference(clausify,[status(thm)],[f_4909_4]) ).

cnf(f_4909_8,plain,
    ( hBOOL(hAPP(U_20442,sK566(U_20442,U_20441,U_20440,U_20439)))
    | ~ hBOOL(hAPP(U_20441,U_20437))
    | ~ hBOOL(hAPP(U_20442,sK565(U_20442,U_20441,U_20440,U_20439)))
    | ~ c_Equiv__Relations_Oequivp(U_20439,U_20440) ),
    inference(clausify,[status(thm)],[f_4909_4]) ).

fof(f_4910_1,plain,
    ! [V_P_2,T_c,V_R_2,T_b] :
      ( c_Quotient_OBabs(T_b,T_c,c_Quotient_ORespects(T_b,V_R_2),V_P_2) = V_P_2
      | ~ c_Equiv__Relations_Oequivp(T_b,V_R_2) ),
    inference(fof_nnf,[status(thm)],[fact_babs__reg__eqv]) ).

fof(f_4910_2,plain,
    ! [U_20446,U_20445,U_20444,U_20443] :
      ( c_Quotient_OBabs(U_20443,U_20445,c_Quotient_ORespects(U_20443,U_20444),U_20446) = U_20446
      | ~ c_Equiv__Relations_Oequivp(U_20443,U_20444) ),
    inference(variable_rename,[status(thm)],[f_4910_1]) ).

cnf(f_4910_3,plain,
    ( c_Quotient_OBabs(U_20443,U_20445,c_Quotient_ORespects(U_20443,U_20444),U_20446) = U_20446
    | ~ c_Equiv__Relations_Oequivp(U_20443,U_20444) ),
    inference(clausify,[status(thm)],[f_4910_2]) ).

fof(f_4911_1,plain,
    ! [V_m_2,T_c,V_p_2,V_x_2,T_b] :
      ( hAPP(c_Quotient_OBabs(T_b,T_c,V_p_2,V_m_2),V_x_2) = hAPP(V_m_2,V_x_2)
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_p_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Babs__def]) ).

fof(f_4911_2,plain,
    ! [U_20451,U_20450,U_20449,U_20448,U_20447] :
      ( hAPP(c_Quotient_OBabs(U_20447,U_20450,U_20449,U_20451),U_20448) = hAPP(U_20451,U_20448)
      | ~ hBOOL(hAPP(hAPP(c_member(U_20447),U_20448),U_20449)) ),
    inference(variable_rename,[status(thm)],[f_4911_1]) ).

cnf(f_4911_3,plain,
    ( hAPP(c_Quotient_OBabs(U_20447,U_20450,U_20449,U_20451),U_20448) = hAPP(U_20451,U_20448)
    | ~ hBOOL(hAPP(hAPP(c_member(U_20447),U_20448),U_20449)) ),
    inference(clausify,[status(thm)],[f_4911_2]) ).

fof(f_4912_1,plain,
    ! [V_g_2,V_f_2,T_c,V_A_2,V_B_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_f_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_g_2)))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x)))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_INT__anti__mono]) ).

fof(f_4912_2,plain,
    ! [U_20458,U_20457,U_20456,U_20455,U_20454,U_20453] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20456,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_20453,tc_fun(U_20456,tc_HOL_Obool)),U_20455),U_20457)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_20453,tc_fun(U_20456,tc_HOL_Obool)),U_20455),U_20458)))
      | ? [U_20452] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20456,tc_HOL_Obool)),hAPP(U_20457,U_20452)),hAPP(U_20458,U_20452)))
          & hBOOL(hAPP(hAPP(c_member(U_20453),U_20452),U_20455)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20453,tc_HOL_Obool)),U_20454),U_20455)) ),
    inference(variable_rename,[status(thm)],[f_4912_1]) ).

fof(f_4912_3,plain,
    ! [U_20458,U_20457,U_20456,U_20455,U_20454,U_20453] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20456,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_20453,tc_fun(U_20456,tc_HOL_Obool)),U_20455),U_20457)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_20453,tc_fun(U_20456,tc_HOL_Obool)),U_20455),U_20458)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20456,tc_HOL_Obool)),hAPP(U_20457,sK567(U_20458,U_20457,U_20456,U_20455,U_20454,U_20453))),hAPP(U_20458,sK567(U_20458,U_20457,U_20456,U_20455,U_20454,U_20453))))
        & hBOOL(hAPP(hAPP(c_member(U_20453),sK567(U_20458,U_20457,U_20456,U_20455,U_20454,U_20453)),U_20455)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20453,tc_HOL_Obool)),U_20454),U_20455)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK567]),skolemize(U_20452,sK567(U_20458,U_20457,U_20456,U_20455,U_20454,U_20453))],[f_4912_2]) ).

cnf(f_4912_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20453),sK567(U_20458,U_20457,U_20456,U_20455,U_20454,U_20453)),U_20455))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20456,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_20453,tc_fun(U_20456,tc_HOL_Obool)),U_20455),U_20457)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_20453,tc_fun(U_20456,tc_HOL_Obool)),U_20455),U_20458)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20453,tc_HOL_Obool)),U_20454),U_20455)) ),
    inference(clausify,[status(thm)],[f_4912_3]) ).

cnf(f_4912_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20456,tc_HOL_Obool)),hAPP(U_20457,sK567(U_20458,U_20457,U_20456,U_20455,U_20454,U_20453))),hAPP(U_20458,sK567(U_20458,U_20457,U_20456,U_20455,U_20454,U_20453))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20456,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_20453,tc_fun(U_20456,tc_HOL_Obool)),U_20455),U_20457)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_20453,tc_fun(U_20456,tc_HOL_Obool)),U_20455),U_20458)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20453,tc_HOL_Obool)),U_20454),U_20455)) ),
    inference(clausify,[status(thm)],[f_4912_3]) ).

fof(f_4913_1,plain,
    ! [V_B_2,V_C_2,T_c,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(V_B_2,B_x)))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_INT__greatest]) ).

fof(f_4913_2,plain,
    ! [U_20464,U_20463,U_20462,U_20461,U_20460] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20462,tc_HOL_Obool)),U_20463),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_20460,tc_fun(U_20462,tc_HOL_Obool)),U_20461),U_20464)))
      | ? [U_20459] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20462,tc_HOL_Obool)),U_20463),hAPP(U_20464,U_20459)))
          & hBOOL(hAPP(hAPP(c_member(U_20460),U_20459),U_20461)) ) ),
    inference(variable_rename,[status(thm)],[f_4913_1]) ).

fof(f_4913_3,plain,
    ! [U_20464,U_20463,U_20462,U_20461,U_20460] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20462,tc_HOL_Obool)),U_20463),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_20460,tc_fun(U_20462,tc_HOL_Obool)),U_20461),U_20464)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20462,tc_HOL_Obool)),U_20463),hAPP(U_20464,sK568(U_20464,U_20463,U_20462,U_20461,U_20460))))
        & hBOOL(hAPP(hAPP(c_member(U_20460),sK568(U_20464,U_20463,U_20462,U_20461,U_20460)),U_20461)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK568]),skolemize(U_20459,sK568(U_20464,U_20463,U_20462,U_20461,U_20460))],[f_4913_2]) ).

cnf(f_4913_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20460),sK568(U_20464,U_20463,U_20462,U_20461,U_20460)),U_20461))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20462,tc_HOL_Obool)),U_20463),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_20460,tc_fun(U_20462,tc_HOL_Obool)),U_20461),U_20464))) ),
    inference(clausify,[status(thm)],[f_4913_3]) ).

cnf(f_4913_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20462,tc_HOL_Obool)),U_20463),hAPP(U_20464,sK568(U_20464,U_20463,U_20462,U_20461,U_20460))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_20462,tc_HOL_Obool)),U_20463),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_20460,tc_fun(U_20462,tc_HOL_Obool)),U_20461),U_20464))) ),
    inference(clausify,[status(thm)],[f_4913_3]) ).

fof(f_4914_1,plain,
    ! [V_r_2,V_zb_2,V_za_2,V_xb_2,V_xa_2,T_c,T_b] :
      ( ? [B_a,B_b] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_za_2),V_zb_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_b,T_c),V_r_2)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_xa_2),V_xb_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b))),V_r_2)) )
      | hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_xa_2),V_xb_2) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_za_2),V_zb_2)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_xa_2),V_xb_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_za_2),V_zb_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_b,T_c),V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_converse__rtranclE2]) ).

fof(f_4914_2,plain,
    ! [U_20473,U_20472,U_20471,U_20470,U_20469,U_20468,U_20467] :
      ( ? [U_20466,U_20465] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20467,U_20468),tc_prod(U_20467,U_20468))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20467,U_20468),tc_prod(U_20467,U_20468)),hAPP(hAPP(c_Product__Type_OPair(U_20467,U_20468),U_20466),U_20465)),hAPP(hAPP(c_Product__Type_OPair(U_20467,U_20468),U_20471),U_20472))),c_Transitive__Closure_Ortrancl(tc_prod(U_20467,U_20468),U_20473)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20467,U_20468),tc_prod(U_20467,U_20468))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20467,U_20468),tc_prod(U_20467,U_20468)),hAPP(hAPP(c_Product__Type_OPair(U_20467,U_20468),U_20469),U_20470)),hAPP(hAPP(c_Product__Type_OPair(U_20467,U_20468),U_20466),U_20465))),U_20473)) )
      | hAPP(hAPP(c_Product__Type_OPair(U_20467,U_20468),U_20469),U_20470) = hAPP(hAPP(c_Product__Type_OPair(U_20467,U_20468),U_20471),U_20472)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20467,U_20468),tc_prod(U_20467,U_20468))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20467,U_20468),tc_prod(U_20467,U_20468)),hAPP(hAPP(c_Product__Type_OPair(U_20467,U_20468),U_20469),U_20470)),hAPP(hAPP(c_Product__Type_OPair(U_20467,U_20468),U_20471),U_20472))),c_Transitive__Closure_Ortrancl(tc_prod(U_20467,U_20468),U_20473))) ),
    inference(variable_rename,[status(thm)],[f_4914_1]) ).

fof(f_4914_3,plain,
    ! [U_20473,U_20472,U_20471,U_20470,U_20469,U_20468,U_20467] :
      ( ? [U_20465] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20467,U_20468),tc_prod(U_20467,U_20468))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20467,U_20468),tc_prod(U_20467,U_20468)),hAPP(hAPP(c_Product__Type_OPair(U_20467,U_20468),sK569(U_20473,U_20472,U_20471,U_20470,U_20469,U_20468,U_20467)),U_20465)),hAPP(hAPP(c_Product__Type_OPair(U_20467,U_20468),U_20471),U_20472))),c_Transitive__Closure_Ortrancl(tc_prod(U_20467,U_20468),U_20473)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20467,U_20468),tc_prod(U_20467,U_20468))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20467,U_20468),tc_prod(U_20467,U_20468)),hAPP(hAPP(c_Product__Type_OPair(U_20467,U_20468),U_20469),U_20470)),hAPP(hAPP(c_Product__Type_OPair(U_20467,U_20468),sK569(U_20473,U_20472,U_20471,U_20470,U_20469,U_20468,U_20467)),U_20465))),U_20473)) )
      | hAPP(hAPP(c_Product__Type_OPair(U_20467,U_20468),U_20469),U_20470) = hAPP(hAPP(c_Product__Type_OPair(U_20467,U_20468),U_20471),U_20472)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20467,U_20468),tc_prod(U_20467,U_20468))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20467,U_20468),tc_prod(U_20467,U_20468)),hAPP(hAPP(c_Product__Type_OPair(U_20467,U_20468),U_20469),U_20470)),hAPP(hAPP(c_Product__Type_OPair(U_20467,U_20468),U_20471),U_20472))),c_Transitive__Closure_Ortrancl(tc_prod(U_20467,U_20468),U_20473))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK569]),skolemize(U_20466,sK569(U_20473,U_20472,U_20471,U_20470,U_20469,U_20468,U_20467))],[f_4914_2]) ).

fof(f_4914_4,plain,
    ! [U_20473,U_20472,U_20471,U_20470,U_20469,U_20468,U_20467] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20467,U_20468),tc_prod(U_20467,U_20468))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20467,U_20468),tc_prod(U_20467,U_20468)),hAPP(hAPP(c_Product__Type_OPair(U_20467,U_20468),sK569(U_20473,U_20472,U_20471,U_20470,U_20469,U_20468,U_20467)),sK570(U_20473,U_20472,U_20471,U_20470,U_20469,U_20468,U_20467))),hAPP(hAPP(c_Product__Type_OPair(U_20467,U_20468),U_20471),U_20472))),c_Transitive__Closure_Ortrancl(tc_prod(U_20467,U_20468),U_20473)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20467,U_20468),tc_prod(U_20467,U_20468))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20467,U_20468),tc_prod(U_20467,U_20468)),hAPP(hAPP(c_Product__Type_OPair(U_20467,U_20468),U_20469),U_20470)),hAPP(hAPP(c_Product__Type_OPair(U_20467,U_20468),sK569(U_20473,U_20472,U_20471,U_20470,U_20469,U_20468,U_20467)),sK570(U_20473,U_20472,U_20471,U_20470,U_20469,U_20468,U_20467)))),U_20473)) )
      | hAPP(hAPP(c_Product__Type_OPair(U_20467,U_20468),U_20469),U_20470) = hAPP(hAPP(c_Product__Type_OPair(U_20467,U_20468),U_20471),U_20472)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20467,U_20468),tc_prod(U_20467,U_20468))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20467,U_20468),tc_prod(U_20467,U_20468)),hAPP(hAPP(c_Product__Type_OPair(U_20467,U_20468),U_20469),U_20470)),hAPP(hAPP(c_Product__Type_OPair(U_20467,U_20468),U_20471),U_20472))),c_Transitive__Closure_Ortrancl(tc_prod(U_20467,U_20468),U_20473))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK570]),skolemize(U_20465,sK570(U_20473,U_20472,U_20471,U_20470,U_20469,U_20468,U_20467))],[f_4914_3]) ).

cnf(f_4914_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20467,U_20468),tc_prod(U_20467,U_20468))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20467,U_20468),tc_prod(U_20467,U_20468)),hAPP(hAPP(c_Product__Type_OPair(U_20467,U_20468),U_20469),U_20470)),hAPP(hAPP(c_Product__Type_OPair(U_20467,U_20468),sK569(U_20473,U_20472,U_20471,U_20470,U_20469,U_20468,U_20467)),sK570(U_20473,U_20472,U_20471,U_20470,U_20469,U_20468,U_20467)))),U_20473))
    | hAPP(hAPP(c_Product__Type_OPair(U_20467,U_20468),U_20469),U_20470) = hAPP(hAPP(c_Product__Type_OPair(U_20467,U_20468),U_20471),U_20472)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20467,U_20468),tc_prod(U_20467,U_20468))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20467,U_20468),tc_prod(U_20467,U_20468)),hAPP(hAPP(c_Product__Type_OPair(U_20467,U_20468),U_20469),U_20470)),hAPP(hAPP(c_Product__Type_OPair(U_20467,U_20468),U_20471),U_20472))),c_Transitive__Closure_Ortrancl(tc_prod(U_20467,U_20468),U_20473))) ),
    inference(clausify,[status(thm)],[f_4914_4]) ).

cnf(f_4914_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20467,U_20468),tc_prod(U_20467,U_20468))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20467,U_20468),tc_prod(U_20467,U_20468)),hAPP(hAPP(c_Product__Type_OPair(U_20467,U_20468),sK569(U_20473,U_20472,U_20471,U_20470,U_20469,U_20468,U_20467)),sK570(U_20473,U_20472,U_20471,U_20470,U_20469,U_20468,U_20467))),hAPP(hAPP(c_Product__Type_OPair(U_20467,U_20468),U_20471),U_20472))),c_Transitive__Closure_Ortrancl(tc_prod(U_20467,U_20468),U_20473)))
    | hAPP(hAPP(c_Product__Type_OPair(U_20467,U_20468),U_20469),U_20470) = hAPP(hAPP(c_Product__Type_OPair(U_20467,U_20468),U_20471),U_20472)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20467,U_20468),tc_prod(U_20467,U_20468))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20467,U_20468),tc_prod(U_20467,U_20468)),hAPP(hAPP(c_Product__Type_OPair(U_20467,U_20468),U_20469),U_20470)),hAPP(hAPP(c_Product__Type_OPair(U_20467,U_20468),U_20471),U_20472))),c_Transitive__Closure_Ortrancl(tc_prod(U_20467,U_20468),U_20473))) ),
    inference(clausify,[status(thm)],[f_4914_4]) ).

fof(f_4915_1,plain,
    ! [V_P_2,V_r_2,V_by_2,V_bx_2,V_ay_2,V_ax_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(V_P_2,V_ax_2),V_ay_2))
      | ? [B_a,B_b,B_aa,B_ba] :
          ( ~ hBOOL(hAPP(hAPP(V_P_2,B_a),B_b))
          & hBOOL(hAPP(hAPP(V_P_2,B_aa),B_ba))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_aa),B_ba)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_bx_2),V_by_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_b,T_c),V_r_2)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_aa),B_ba))),V_r_2)) )
      | ~ hBOOL(hAPP(hAPP(V_P_2,V_bx_2),V_by_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_ax_2),V_ay_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_bx_2),V_by_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_b,T_c),V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_converse__rtrancl__induct2]) ).

fof(f_4915_2,plain,
    ! [U_20485,U_20484,U_20483,U_20482,U_20481,U_20480,U_20479,U_20478] :
      ( hBOOL(hAPP(hAPP(U_20485,U_20480),U_20481))
      | ? [U_20477,U_20476,U_20475,U_20474] :
          ( ~ hBOOL(hAPP(hAPP(U_20485,U_20477),U_20476))
          & hBOOL(hAPP(hAPP(U_20485,U_20475),U_20474))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20478,U_20479),tc_prod(U_20478,U_20479))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20478,U_20479),tc_prod(U_20478,U_20479)),hAPP(hAPP(c_Product__Type_OPair(U_20478,U_20479),U_20475),U_20474)),hAPP(hAPP(c_Product__Type_OPair(U_20478,U_20479),U_20482),U_20483))),c_Transitive__Closure_Ortrancl(tc_prod(U_20478,U_20479),U_20484)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20478,U_20479),tc_prod(U_20478,U_20479))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20478,U_20479),tc_prod(U_20478,U_20479)),hAPP(hAPP(c_Product__Type_OPair(U_20478,U_20479),U_20477),U_20476)),hAPP(hAPP(c_Product__Type_OPair(U_20478,U_20479),U_20475),U_20474))),U_20484)) )
      | ~ hBOOL(hAPP(hAPP(U_20485,U_20482),U_20483))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20478,U_20479),tc_prod(U_20478,U_20479))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20478,U_20479),tc_prod(U_20478,U_20479)),hAPP(hAPP(c_Product__Type_OPair(U_20478,U_20479),U_20480),U_20481)),hAPP(hAPP(c_Product__Type_OPair(U_20478,U_20479),U_20482),U_20483))),c_Transitive__Closure_Ortrancl(tc_prod(U_20478,U_20479),U_20484))) ),
    inference(variable_rename,[status(thm)],[f_4915_1]) ).

fof(f_4915_3,plain,
    ! [U_20485,U_20484,U_20483,U_20482,U_20481,U_20480,U_20479,U_20478] :
      ( hBOOL(hAPP(hAPP(U_20485,U_20480),U_20481))
      | ? [U_20476,U_20475,U_20474] :
          ( ~ hBOOL(hAPP(hAPP(U_20485,sK571(U_20485,U_20484,U_20483,U_20482,U_20481,U_20480,U_20479,U_20478)),U_20476))
          & hBOOL(hAPP(hAPP(U_20485,U_20475),U_20474))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20478,U_20479),tc_prod(U_20478,U_20479))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20478,U_20479),tc_prod(U_20478,U_20479)),hAPP(hAPP(c_Product__Type_OPair(U_20478,U_20479),U_20475),U_20474)),hAPP(hAPP(c_Product__Type_OPair(U_20478,U_20479),U_20482),U_20483))),c_Transitive__Closure_Ortrancl(tc_prod(U_20478,U_20479),U_20484)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20478,U_20479),tc_prod(U_20478,U_20479))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20478,U_20479),tc_prod(U_20478,U_20479)),hAPP(hAPP(c_Product__Type_OPair(U_20478,U_20479),sK571(U_20485,U_20484,U_20483,U_20482,U_20481,U_20480,U_20479,U_20478)),U_20476)),hAPP(hAPP(c_Product__Type_OPair(U_20478,U_20479),U_20475),U_20474))),U_20484)) )
      | ~ hBOOL(hAPP(hAPP(U_20485,U_20482),U_20483))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20478,U_20479),tc_prod(U_20478,U_20479))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20478,U_20479),tc_prod(U_20478,U_20479)),hAPP(hAPP(c_Product__Type_OPair(U_20478,U_20479),U_20480),U_20481)),hAPP(hAPP(c_Product__Type_OPair(U_20478,U_20479),U_20482),U_20483))),c_Transitive__Closure_Ortrancl(tc_prod(U_20478,U_20479),U_20484))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK571]),skolemize(U_20477,sK571(U_20485,U_20484,U_20483,U_20482,U_20481,U_20480,U_20479,U_20478))],[f_4915_2]) ).

fof(f_4915_4,plain,
    ! [U_20485,U_20484,U_20483,U_20482,U_20481,U_20480,U_20479,U_20478] :
      ( hBOOL(hAPP(hAPP(U_20485,U_20480),U_20481))
      | ? [U_20475,U_20474] :
          ( ~ hBOOL(hAPP(hAPP(U_20485,sK571(U_20485,U_20484,U_20483,U_20482,U_20481,U_20480,U_20479,U_20478)),sK572(U_20485,U_20484,U_20483,U_20482,U_20481,U_20480,U_20479,U_20478)))
          & hBOOL(hAPP(hAPP(U_20485,U_20475),U_20474))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20478,U_20479),tc_prod(U_20478,U_20479))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20478,U_20479),tc_prod(U_20478,U_20479)),hAPP(hAPP(c_Product__Type_OPair(U_20478,U_20479),U_20475),U_20474)),hAPP(hAPP(c_Product__Type_OPair(U_20478,U_20479),U_20482),U_20483))),c_Transitive__Closure_Ortrancl(tc_prod(U_20478,U_20479),U_20484)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20478,U_20479),tc_prod(U_20478,U_20479))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20478,U_20479),tc_prod(U_20478,U_20479)),hAPP(hAPP(c_Product__Type_OPair(U_20478,U_20479),sK571(U_20485,U_20484,U_20483,U_20482,U_20481,U_20480,U_20479,U_20478)),sK572(U_20485,U_20484,U_20483,U_20482,U_20481,U_20480,U_20479,U_20478))),hAPP(hAPP(c_Product__Type_OPair(U_20478,U_20479),U_20475),U_20474))),U_20484)) )
      | ~ hBOOL(hAPP(hAPP(U_20485,U_20482),U_20483))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20478,U_20479),tc_prod(U_20478,U_20479))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20478,U_20479),tc_prod(U_20478,U_20479)),hAPP(hAPP(c_Product__Type_OPair(U_20478,U_20479),U_20480),U_20481)),hAPP(hAPP(c_Product__Type_OPair(U_20478,U_20479),U_20482),U_20483))),c_Transitive__Closure_Ortrancl(tc_prod(U_20478,U_20479),U_20484))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK572]),skolemize(U_20476,sK572(U_20485,U_20484,U_20483,U_20482,U_20481,U_20480,U_20479,U_20478))],[f_4915_3]) ).

fof(f_4915_5,plain,
    ! [U_20485,U_20484,U_20483,U_20482,U_20481,U_20480,U_20479,U_20478] :
      ( hBOOL(hAPP(hAPP(U_20485,U_20480),U_20481))
      | ? [U_20474] :
          ( ~ hBOOL(hAPP(hAPP(U_20485,sK571(U_20485,U_20484,U_20483,U_20482,U_20481,U_20480,U_20479,U_20478)),sK572(U_20485,U_20484,U_20483,U_20482,U_20481,U_20480,U_20479,U_20478)))
          & hBOOL(hAPP(hAPP(U_20485,sK573(U_20485,U_20484,U_20483,U_20482,U_20481,U_20480,U_20479,U_20478)),U_20474))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20478,U_20479),tc_prod(U_20478,U_20479))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20478,U_20479),tc_prod(U_20478,U_20479)),hAPP(hAPP(c_Product__Type_OPair(U_20478,U_20479),sK573(U_20485,U_20484,U_20483,U_20482,U_20481,U_20480,U_20479,U_20478)),U_20474)),hAPP(hAPP(c_Product__Type_OPair(U_20478,U_20479),U_20482),U_20483))),c_Transitive__Closure_Ortrancl(tc_prod(U_20478,U_20479),U_20484)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20478,U_20479),tc_prod(U_20478,U_20479))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20478,U_20479),tc_prod(U_20478,U_20479)),hAPP(hAPP(c_Product__Type_OPair(U_20478,U_20479),sK571(U_20485,U_20484,U_20483,U_20482,U_20481,U_20480,U_20479,U_20478)),sK572(U_20485,U_20484,U_20483,U_20482,U_20481,U_20480,U_20479,U_20478))),hAPP(hAPP(c_Product__Type_OPair(U_20478,U_20479),sK573(U_20485,U_20484,U_20483,U_20482,U_20481,U_20480,U_20479,U_20478)),U_20474))),U_20484)) )
      | ~ hBOOL(hAPP(hAPP(U_20485,U_20482),U_20483))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20478,U_20479),tc_prod(U_20478,U_20479))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20478,U_20479),tc_prod(U_20478,U_20479)),hAPP(hAPP(c_Product__Type_OPair(U_20478,U_20479),U_20480),U_20481)),hAPP(hAPP(c_Product__Type_OPair(U_20478,U_20479),U_20482),U_20483))),c_Transitive__Closure_Ortrancl(tc_prod(U_20478,U_20479),U_20484))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK573]),skolemize(U_20475,sK573(U_20485,U_20484,U_20483,U_20482,U_20481,U_20480,U_20479,U_20478))],[f_4915_4]) ).

fof(f_4915_6,plain,
    ! [U_20485,U_20484,U_20483,U_20482,U_20481,U_20480,U_20479,U_20478] :
      ( hBOOL(hAPP(hAPP(U_20485,U_20480),U_20481))
      | ( ~ hBOOL(hAPP(hAPP(U_20485,sK571(U_20485,U_20484,U_20483,U_20482,U_20481,U_20480,U_20479,U_20478)),sK572(U_20485,U_20484,U_20483,U_20482,U_20481,U_20480,U_20479,U_20478)))
        & hBOOL(hAPP(hAPP(U_20485,sK573(U_20485,U_20484,U_20483,U_20482,U_20481,U_20480,U_20479,U_20478)),sK574(U_20485,U_20484,U_20483,U_20482,U_20481,U_20480,U_20479,U_20478)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20478,U_20479),tc_prod(U_20478,U_20479))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20478,U_20479),tc_prod(U_20478,U_20479)),hAPP(hAPP(c_Product__Type_OPair(U_20478,U_20479),sK573(U_20485,U_20484,U_20483,U_20482,U_20481,U_20480,U_20479,U_20478)),sK574(U_20485,U_20484,U_20483,U_20482,U_20481,U_20480,U_20479,U_20478))),hAPP(hAPP(c_Product__Type_OPair(U_20478,U_20479),U_20482),U_20483))),c_Transitive__Closure_Ortrancl(tc_prod(U_20478,U_20479),U_20484)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20478,U_20479),tc_prod(U_20478,U_20479))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20478,U_20479),tc_prod(U_20478,U_20479)),hAPP(hAPP(c_Product__Type_OPair(U_20478,U_20479),sK571(U_20485,U_20484,U_20483,U_20482,U_20481,U_20480,U_20479,U_20478)),sK572(U_20485,U_20484,U_20483,U_20482,U_20481,U_20480,U_20479,U_20478))),hAPP(hAPP(c_Product__Type_OPair(U_20478,U_20479),sK573(U_20485,U_20484,U_20483,U_20482,U_20481,U_20480,U_20479,U_20478)),sK574(U_20485,U_20484,U_20483,U_20482,U_20481,U_20480,U_20479,U_20478)))),U_20484)) )
      | ~ hBOOL(hAPP(hAPP(U_20485,U_20482),U_20483))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20478,U_20479),tc_prod(U_20478,U_20479))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20478,U_20479),tc_prod(U_20478,U_20479)),hAPP(hAPP(c_Product__Type_OPair(U_20478,U_20479),U_20480),U_20481)),hAPP(hAPP(c_Product__Type_OPair(U_20478,U_20479),U_20482),U_20483))),c_Transitive__Closure_Ortrancl(tc_prod(U_20478,U_20479),U_20484))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK574]),skolemize(U_20474,sK574(U_20485,U_20484,U_20483,U_20482,U_20481,U_20480,U_20479,U_20478))],[f_4915_5]) ).

cnf(f_4915_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20478,U_20479),tc_prod(U_20478,U_20479))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20478,U_20479),tc_prod(U_20478,U_20479)),hAPP(hAPP(c_Product__Type_OPair(U_20478,U_20479),sK571(U_20485,U_20484,U_20483,U_20482,U_20481,U_20480,U_20479,U_20478)),sK572(U_20485,U_20484,U_20483,U_20482,U_20481,U_20480,U_20479,U_20478))),hAPP(hAPP(c_Product__Type_OPair(U_20478,U_20479),sK573(U_20485,U_20484,U_20483,U_20482,U_20481,U_20480,U_20479,U_20478)),sK574(U_20485,U_20484,U_20483,U_20482,U_20481,U_20480,U_20479,U_20478)))),U_20484))
    | hBOOL(hAPP(hAPP(U_20485,U_20480),U_20481))
    | ~ hBOOL(hAPP(hAPP(U_20485,U_20482),U_20483))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20478,U_20479),tc_prod(U_20478,U_20479))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20478,U_20479),tc_prod(U_20478,U_20479)),hAPP(hAPP(c_Product__Type_OPair(U_20478,U_20479),U_20480),U_20481)),hAPP(hAPP(c_Product__Type_OPair(U_20478,U_20479),U_20482),U_20483))),c_Transitive__Closure_Ortrancl(tc_prod(U_20478,U_20479),U_20484))) ),
    inference(clausify,[status(thm)],[f_4915_6]) ).

cnf(f_4915_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20478,U_20479),tc_prod(U_20478,U_20479))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20478,U_20479),tc_prod(U_20478,U_20479)),hAPP(hAPP(c_Product__Type_OPair(U_20478,U_20479),sK573(U_20485,U_20484,U_20483,U_20482,U_20481,U_20480,U_20479,U_20478)),sK574(U_20485,U_20484,U_20483,U_20482,U_20481,U_20480,U_20479,U_20478))),hAPP(hAPP(c_Product__Type_OPair(U_20478,U_20479),U_20482),U_20483))),c_Transitive__Closure_Ortrancl(tc_prod(U_20478,U_20479),U_20484)))
    | hBOOL(hAPP(hAPP(U_20485,U_20480),U_20481))
    | ~ hBOOL(hAPP(hAPP(U_20485,U_20482),U_20483))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20478,U_20479),tc_prod(U_20478,U_20479))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20478,U_20479),tc_prod(U_20478,U_20479)),hAPP(hAPP(c_Product__Type_OPair(U_20478,U_20479),U_20480),U_20481)),hAPP(hAPP(c_Product__Type_OPair(U_20478,U_20479),U_20482),U_20483))),c_Transitive__Closure_Ortrancl(tc_prod(U_20478,U_20479),U_20484))) ),
    inference(clausify,[status(thm)],[f_4915_6]) ).

cnf(f_4915_9,plain,
    ( hBOOL(hAPP(hAPP(U_20485,sK573(U_20485,U_20484,U_20483,U_20482,U_20481,U_20480,U_20479,U_20478)),sK574(U_20485,U_20484,U_20483,U_20482,U_20481,U_20480,U_20479,U_20478)))
    | hBOOL(hAPP(hAPP(U_20485,U_20480),U_20481))
    | ~ hBOOL(hAPP(hAPP(U_20485,U_20482),U_20483))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20478,U_20479),tc_prod(U_20478,U_20479))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20478,U_20479),tc_prod(U_20478,U_20479)),hAPP(hAPP(c_Product__Type_OPair(U_20478,U_20479),U_20480),U_20481)),hAPP(hAPP(c_Product__Type_OPair(U_20478,U_20479),U_20482),U_20483))),c_Transitive__Closure_Ortrancl(tc_prod(U_20478,U_20479),U_20484))) ),
    inference(clausify,[status(thm)],[f_4915_6]) ).

cnf(f_4915_10,plain,
    ( ~ hBOOL(hAPP(hAPP(U_20485,sK571(U_20485,U_20484,U_20483,U_20482,U_20481,U_20480,U_20479,U_20478)),sK572(U_20485,U_20484,U_20483,U_20482,U_20481,U_20480,U_20479,U_20478)))
    | hBOOL(hAPP(hAPP(U_20485,U_20480),U_20481))
    | ~ hBOOL(hAPP(hAPP(U_20485,U_20482),U_20483))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20478,U_20479),tc_prod(U_20478,U_20479))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20478,U_20479),tc_prod(U_20478,U_20479)),hAPP(hAPP(c_Product__Type_OPair(U_20478,U_20479),U_20480),U_20481)),hAPP(hAPP(c_Product__Type_OPair(U_20478,U_20479),U_20482),U_20483))),c_Transitive__Closure_Ortrancl(tc_prod(U_20478,U_20479),U_20484))) ),
    inference(clausify,[status(thm)],[f_4915_6]) ).

fof(f_4916_1,plain,
    ! [V_P_2,V_r_2,V_by_2,V_bx_2,V_ay_2,V_ax_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(V_P_2,V_bx_2),V_by_2))
      | ? [B_a,B_b] :
          ( ? [B_aa,B_ba] :
              ( ~ hBOOL(hAPP(hAPP(V_P_2,B_aa),B_ba))
              & hBOOL(hAPP(hAPP(V_P_2,B_a),B_b))
              & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_aa),B_ba))),V_r_2)) )
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_ax_2),V_ay_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b))),c_Transitive__Closure_Ortrancl(tc_prod(T_b,T_c),V_r_2))) )
      | ~ hBOOL(hAPP(hAPP(V_P_2,V_ax_2),V_ay_2))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_ax_2),V_ay_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_bx_2),V_by_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_b,T_c),V_r_2))) ),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__induct2]) ).

fof(f_4916_2,plain,
    ! [U_20497,U_20496,U_20495,U_20494,U_20493,U_20492,U_20491,U_20490] :
      ( hBOOL(hAPP(hAPP(U_20497,U_20494),U_20495))
      | ? [U_20489,U_20488] :
          ( ? [U_20487,U_20486] :
              ( ~ hBOOL(hAPP(hAPP(U_20497,U_20487),U_20486))
              & hBOOL(hAPP(hAPP(U_20497,U_20489),U_20488))
              & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20490,U_20491),tc_prod(U_20490,U_20491))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20490,U_20491),tc_prod(U_20490,U_20491)),hAPP(hAPP(c_Product__Type_OPair(U_20490,U_20491),U_20489),U_20488)),hAPP(hAPP(c_Product__Type_OPair(U_20490,U_20491),U_20487),U_20486))),U_20496)) )
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20490,U_20491),tc_prod(U_20490,U_20491))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20490,U_20491),tc_prod(U_20490,U_20491)),hAPP(hAPP(c_Product__Type_OPair(U_20490,U_20491),U_20492),U_20493)),hAPP(hAPP(c_Product__Type_OPair(U_20490,U_20491),U_20489),U_20488))),c_Transitive__Closure_Ortrancl(tc_prod(U_20490,U_20491),U_20496))) )
      | ~ hBOOL(hAPP(hAPP(U_20497,U_20492),U_20493))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20490,U_20491),tc_prod(U_20490,U_20491))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20490,U_20491),tc_prod(U_20490,U_20491)),hAPP(hAPP(c_Product__Type_OPair(U_20490,U_20491),U_20492),U_20493)),hAPP(hAPP(c_Product__Type_OPair(U_20490,U_20491),U_20494),U_20495))),c_Transitive__Closure_Ortrancl(tc_prod(U_20490,U_20491),U_20496))) ),
    inference(variable_rename,[status(thm)],[f_4916_1]) ).

fof(f_4916_3,plain,
    ! [U_20497,U_20496,U_20495,U_20494,U_20493,U_20492,U_20491,U_20490] :
      ( hBOOL(hAPP(hAPP(U_20497,U_20494),U_20495))
      | ? [U_20488] :
          ( ? [U_20487,U_20486] :
              ( ~ hBOOL(hAPP(hAPP(U_20497,U_20487),U_20486))
              & hBOOL(hAPP(hAPP(U_20497,sK575(U_20497,U_20496,U_20495,U_20494,U_20493,U_20492,U_20491,U_20490)),U_20488))
              & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20490,U_20491),tc_prod(U_20490,U_20491))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20490,U_20491),tc_prod(U_20490,U_20491)),hAPP(hAPP(c_Product__Type_OPair(U_20490,U_20491),sK575(U_20497,U_20496,U_20495,U_20494,U_20493,U_20492,U_20491,U_20490)),U_20488)),hAPP(hAPP(c_Product__Type_OPair(U_20490,U_20491),U_20487),U_20486))),U_20496)) )
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20490,U_20491),tc_prod(U_20490,U_20491))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20490,U_20491),tc_prod(U_20490,U_20491)),hAPP(hAPP(c_Product__Type_OPair(U_20490,U_20491),U_20492),U_20493)),hAPP(hAPP(c_Product__Type_OPair(U_20490,U_20491),sK575(U_20497,U_20496,U_20495,U_20494,U_20493,U_20492,U_20491,U_20490)),U_20488))),c_Transitive__Closure_Ortrancl(tc_prod(U_20490,U_20491),U_20496))) )
      | ~ hBOOL(hAPP(hAPP(U_20497,U_20492),U_20493))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20490,U_20491),tc_prod(U_20490,U_20491))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20490,U_20491),tc_prod(U_20490,U_20491)),hAPP(hAPP(c_Product__Type_OPair(U_20490,U_20491),U_20492),U_20493)),hAPP(hAPP(c_Product__Type_OPair(U_20490,U_20491),U_20494),U_20495))),c_Transitive__Closure_Ortrancl(tc_prod(U_20490,U_20491),U_20496))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK575]),skolemize(U_20489,sK575(U_20497,U_20496,U_20495,U_20494,U_20493,U_20492,U_20491,U_20490))],[f_4916_2]) ).

fof(f_4916_4,plain,
    ! [U_20497,U_20496,U_20495,U_20494,U_20493,U_20492,U_20491,U_20490] :
      ( hBOOL(hAPP(hAPP(U_20497,U_20494),U_20495))
      | ( ? [U_20487,U_20486] :
            ( ~ hBOOL(hAPP(hAPP(U_20497,U_20487),U_20486))
            & hBOOL(hAPP(hAPP(U_20497,sK575(U_20497,U_20496,U_20495,U_20494,U_20493,U_20492,U_20491,U_20490)),sK576(U_20497,U_20496,U_20495,U_20494,U_20493,U_20492,U_20491,U_20490)))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20490,U_20491),tc_prod(U_20490,U_20491))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20490,U_20491),tc_prod(U_20490,U_20491)),hAPP(hAPP(c_Product__Type_OPair(U_20490,U_20491),sK575(U_20497,U_20496,U_20495,U_20494,U_20493,U_20492,U_20491,U_20490)),sK576(U_20497,U_20496,U_20495,U_20494,U_20493,U_20492,U_20491,U_20490))),hAPP(hAPP(c_Product__Type_OPair(U_20490,U_20491),U_20487),U_20486))),U_20496)) )
        & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20490,U_20491),tc_prod(U_20490,U_20491))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20490,U_20491),tc_prod(U_20490,U_20491)),hAPP(hAPP(c_Product__Type_OPair(U_20490,U_20491),U_20492),U_20493)),hAPP(hAPP(c_Product__Type_OPair(U_20490,U_20491),sK575(U_20497,U_20496,U_20495,U_20494,U_20493,U_20492,U_20491,U_20490)),sK576(U_20497,U_20496,U_20495,U_20494,U_20493,U_20492,U_20491,U_20490)))),c_Transitive__Closure_Ortrancl(tc_prod(U_20490,U_20491),U_20496))) )
      | ~ hBOOL(hAPP(hAPP(U_20497,U_20492),U_20493))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20490,U_20491),tc_prod(U_20490,U_20491))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20490,U_20491),tc_prod(U_20490,U_20491)),hAPP(hAPP(c_Product__Type_OPair(U_20490,U_20491),U_20492),U_20493)),hAPP(hAPP(c_Product__Type_OPair(U_20490,U_20491),U_20494),U_20495))),c_Transitive__Closure_Ortrancl(tc_prod(U_20490,U_20491),U_20496))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK576]),skolemize(U_20488,sK576(U_20497,U_20496,U_20495,U_20494,U_20493,U_20492,U_20491,U_20490))],[f_4916_3]) ).

fof(f_4916_5,plain,
    ! [U_20497,U_20496,U_20495,U_20494,U_20493,U_20492,U_20491,U_20490] :
      ( hBOOL(hAPP(hAPP(U_20497,U_20494),U_20495))
      | ( ? [U_20486] :
            ( ~ hBOOL(hAPP(hAPP(U_20497,sK577(U_20497,U_20496,U_20495,U_20494,U_20493,U_20492,U_20491,U_20490)),U_20486))
            & hBOOL(hAPP(hAPP(U_20497,sK575(U_20497,U_20496,U_20495,U_20494,U_20493,U_20492,U_20491,U_20490)),sK576(U_20497,U_20496,U_20495,U_20494,U_20493,U_20492,U_20491,U_20490)))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20490,U_20491),tc_prod(U_20490,U_20491))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20490,U_20491),tc_prod(U_20490,U_20491)),hAPP(hAPP(c_Product__Type_OPair(U_20490,U_20491),sK575(U_20497,U_20496,U_20495,U_20494,U_20493,U_20492,U_20491,U_20490)),sK576(U_20497,U_20496,U_20495,U_20494,U_20493,U_20492,U_20491,U_20490))),hAPP(hAPP(c_Product__Type_OPair(U_20490,U_20491),sK577(U_20497,U_20496,U_20495,U_20494,U_20493,U_20492,U_20491,U_20490)),U_20486))),U_20496)) )
        & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20490,U_20491),tc_prod(U_20490,U_20491))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20490,U_20491),tc_prod(U_20490,U_20491)),hAPP(hAPP(c_Product__Type_OPair(U_20490,U_20491),U_20492),U_20493)),hAPP(hAPP(c_Product__Type_OPair(U_20490,U_20491),sK575(U_20497,U_20496,U_20495,U_20494,U_20493,U_20492,U_20491,U_20490)),sK576(U_20497,U_20496,U_20495,U_20494,U_20493,U_20492,U_20491,U_20490)))),c_Transitive__Closure_Ortrancl(tc_prod(U_20490,U_20491),U_20496))) )
      | ~ hBOOL(hAPP(hAPP(U_20497,U_20492),U_20493))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20490,U_20491),tc_prod(U_20490,U_20491))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20490,U_20491),tc_prod(U_20490,U_20491)),hAPP(hAPP(c_Product__Type_OPair(U_20490,U_20491),U_20492),U_20493)),hAPP(hAPP(c_Product__Type_OPair(U_20490,U_20491),U_20494),U_20495))),c_Transitive__Closure_Ortrancl(tc_prod(U_20490,U_20491),U_20496))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK577]),skolemize(U_20487,sK577(U_20497,U_20496,U_20495,U_20494,U_20493,U_20492,U_20491,U_20490))],[f_4916_4]) ).

fof(f_4916_6,plain,
    ! [U_20497,U_20496,U_20495,U_20494,U_20493,U_20492,U_20491,U_20490] :
      ( hBOOL(hAPP(hAPP(U_20497,U_20494),U_20495))
      | ( ~ hBOOL(hAPP(hAPP(U_20497,sK577(U_20497,U_20496,U_20495,U_20494,U_20493,U_20492,U_20491,U_20490)),sK578(U_20497,U_20496,U_20495,U_20494,U_20493,U_20492,U_20491,U_20490)))
        & hBOOL(hAPP(hAPP(U_20497,sK575(U_20497,U_20496,U_20495,U_20494,U_20493,U_20492,U_20491,U_20490)),sK576(U_20497,U_20496,U_20495,U_20494,U_20493,U_20492,U_20491,U_20490)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20490,U_20491),tc_prod(U_20490,U_20491))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20490,U_20491),tc_prod(U_20490,U_20491)),hAPP(hAPP(c_Product__Type_OPair(U_20490,U_20491),sK575(U_20497,U_20496,U_20495,U_20494,U_20493,U_20492,U_20491,U_20490)),sK576(U_20497,U_20496,U_20495,U_20494,U_20493,U_20492,U_20491,U_20490))),hAPP(hAPP(c_Product__Type_OPair(U_20490,U_20491),sK577(U_20497,U_20496,U_20495,U_20494,U_20493,U_20492,U_20491,U_20490)),sK578(U_20497,U_20496,U_20495,U_20494,U_20493,U_20492,U_20491,U_20490)))),U_20496))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20490,U_20491),tc_prod(U_20490,U_20491))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20490,U_20491),tc_prod(U_20490,U_20491)),hAPP(hAPP(c_Product__Type_OPair(U_20490,U_20491),U_20492),U_20493)),hAPP(hAPP(c_Product__Type_OPair(U_20490,U_20491),sK575(U_20497,U_20496,U_20495,U_20494,U_20493,U_20492,U_20491,U_20490)),sK576(U_20497,U_20496,U_20495,U_20494,U_20493,U_20492,U_20491,U_20490)))),c_Transitive__Closure_Ortrancl(tc_prod(U_20490,U_20491),U_20496))) )
      | ~ hBOOL(hAPP(hAPP(U_20497,U_20492),U_20493))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20490,U_20491),tc_prod(U_20490,U_20491))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20490,U_20491),tc_prod(U_20490,U_20491)),hAPP(hAPP(c_Product__Type_OPair(U_20490,U_20491),U_20492),U_20493)),hAPP(hAPP(c_Product__Type_OPair(U_20490,U_20491),U_20494),U_20495))),c_Transitive__Closure_Ortrancl(tc_prod(U_20490,U_20491),U_20496))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK578]),skolemize(U_20486,sK578(U_20497,U_20496,U_20495,U_20494,U_20493,U_20492,U_20491,U_20490))],[f_4916_5]) ).

cnf(f_4916_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20490,U_20491),tc_prod(U_20490,U_20491))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20490,U_20491),tc_prod(U_20490,U_20491)),hAPP(hAPP(c_Product__Type_OPair(U_20490,U_20491),U_20492),U_20493)),hAPP(hAPP(c_Product__Type_OPair(U_20490,U_20491),sK575(U_20497,U_20496,U_20495,U_20494,U_20493,U_20492,U_20491,U_20490)),sK576(U_20497,U_20496,U_20495,U_20494,U_20493,U_20492,U_20491,U_20490)))),c_Transitive__Closure_Ortrancl(tc_prod(U_20490,U_20491),U_20496)))
    | hBOOL(hAPP(hAPP(U_20497,U_20494),U_20495))
    | ~ hBOOL(hAPP(hAPP(U_20497,U_20492),U_20493))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20490,U_20491),tc_prod(U_20490,U_20491))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20490,U_20491),tc_prod(U_20490,U_20491)),hAPP(hAPP(c_Product__Type_OPair(U_20490,U_20491),U_20492),U_20493)),hAPP(hAPP(c_Product__Type_OPair(U_20490,U_20491),U_20494),U_20495))),c_Transitive__Closure_Ortrancl(tc_prod(U_20490,U_20491),U_20496))) ),
    inference(clausify,[status(thm)],[f_4916_6]) ).

cnf(f_4916_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20490,U_20491),tc_prod(U_20490,U_20491))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20490,U_20491),tc_prod(U_20490,U_20491)),hAPP(hAPP(c_Product__Type_OPair(U_20490,U_20491),sK575(U_20497,U_20496,U_20495,U_20494,U_20493,U_20492,U_20491,U_20490)),sK576(U_20497,U_20496,U_20495,U_20494,U_20493,U_20492,U_20491,U_20490))),hAPP(hAPP(c_Product__Type_OPair(U_20490,U_20491),sK577(U_20497,U_20496,U_20495,U_20494,U_20493,U_20492,U_20491,U_20490)),sK578(U_20497,U_20496,U_20495,U_20494,U_20493,U_20492,U_20491,U_20490)))),U_20496))
    | hBOOL(hAPP(hAPP(U_20497,U_20494),U_20495))
    | ~ hBOOL(hAPP(hAPP(U_20497,U_20492),U_20493))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20490,U_20491),tc_prod(U_20490,U_20491))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20490,U_20491),tc_prod(U_20490,U_20491)),hAPP(hAPP(c_Product__Type_OPair(U_20490,U_20491),U_20492),U_20493)),hAPP(hAPP(c_Product__Type_OPair(U_20490,U_20491),U_20494),U_20495))),c_Transitive__Closure_Ortrancl(tc_prod(U_20490,U_20491),U_20496))) ),
    inference(clausify,[status(thm)],[f_4916_6]) ).

cnf(f_4916_9,plain,
    ( hBOOL(hAPP(hAPP(U_20497,sK575(U_20497,U_20496,U_20495,U_20494,U_20493,U_20492,U_20491,U_20490)),sK576(U_20497,U_20496,U_20495,U_20494,U_20493,U_20492,U_20491,U_20490)))
    | hBOOL(hAPP(hAPP(U_20497,U_20494),U_20495))
    | ~ hBOOL(hAPP(hAPP(U_20497,U_20492),U_20493))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20490,U_20491),tc_prod(U_20490,U_20491))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20490,U_20491),tc_prod(U_20490,U_20491)),hAPP(hAPP(c_Product__Type_OPair(U_20490,U_20491),U_20492),U_20493)),hAPP(hAPP(c_Product__Type_OPair(U_20490,U_20491),U_20494),U_20495))),c_Transitive__Closure_Ortrancl(tc_prod(U_20490,U_20491),U_20496))) ),
    inference(clausify,[status(thm)],[f_4916_6]) ).

cnf(f_4916_10,plain,
    ( ~ hBOOL(hAPP(hAPP(U_20497,sK577(U_20497,U_20496,U_20495,U_20494,U_20493,U_20492,U_20491,U_20490)),sK578(U_20497,U_20496,U_20495,U_20494,U_20493,U_20492,U_20491,U_20490)))
    | hBOOL(hAPP(hAPP(U_20497,U_20494),U_20495))
    | ~ hBOOL(hAPP(hAPP(U_20497,U_20492),U_20493))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_20490,U_20491),tc_prod(U_20490,U_20491))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_20490,U_20491),tc_prod(U_20490,U_20491)),hAPP(hAPP(c_Product__Type_OPair(U_20490,U_20491),U_20492),U_20493)),hAPP(hAPP(c_Product__Type_OPair(U_20490,U_20491),U_20494),U_20495))),c_Transitive__Closure_Ortrancl(tc_prod(U_20490,U_20491),U_20496))) ),
    inference(clausify,[status(thm)],[f_4916_6]) ).

fof(f_4917_1,plain,
    ! [T_c,V_f_2,V_r_2,T_b] :
      ( c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2)
      | ? [B_y,B_z] :
          ( hAPP(V_f_2,B_y) != hAPP(V_f_2,B_z)
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_z)),V_r_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_congruentI]) ).

fof(f_4917_2,plain,
    ! [U_20503,U_20502,U_20501,U_20500] :
      ( c_Equiv__Relations_Ocongruent(U_20500,U_20503,U_20501,U_20502)
      | ? [U_20499,U_20498] :
          ( hAPP(U_20502,U_20499) != hAPP(U_20502,U_20498)
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_20500,U_20500)),hAPP(hAPP(c_Product__Type_OPair(U_20500,U_20500),U_20499),U_20498)),U_20501)) ) ),
    inference(variable_rename,[status(thm)],[f_4917_1]) ).

fof(f_4917_3,plain,
    ! [U_20503,U_20502,U_20501,U_20500] :
      ( c_Equiv__Relations_Ocongruent(U_20500,U_20503,U_20501,U_20502)
      | ? [U_20498] :
          ( hAPP(U_20502,sK579(U_20503,U_20502,U_20501,U_20500)) != hAPP(U_20502,U_20498)
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_20500,U_20500)),hAPP(hAPP(c_Product__Type_OPair(U_20500,U_20500),sK579(U_20503,U_20502,U_20501,U_20500)),U_20498)),U_20501)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK579]),skolemize(U_20499,sK579(U_20503,U_20502,U_20501,U_20500))],[f_4917_2]) ).

fof(f_4917_4,plain,
    ! [U_20503,U_20502,U_20501,U_20500] :
      ( c_Equiv__Relations_Ocongruent(U_20500,U_20503,U_20501,U_20502)
      | ( hAPP(U_20502,sK579(U_20503,U_20502,U_20501,U_20500)) != hAPP(U_20502,sK580(U_20503,U_20502,U_20501,U_20500))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_20500,U_20500)),hAPP(hAPP(c_Product__Type_OPair(U_20500,U_20500),sK579(U_20503,U_20502,U_20501,U_20500)),sK580(U_20503,U_20502,U_20501,U_20500))),U_20501)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK580]),skolemize(U_20498,sK580(U_20503,U_20502,U_20501,U_20500))],[f_4917_3]) ).

cnf(f_4917_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_20500,U_20500)),hAPP(hAPP(c_Product__Type_OPair(U_20500,U_20500),sK579(U_20503,U_20502,U_20501,U_20500)),sK580(U_20503,U_20502,U_20501,U_20500))),U_20501))
    | c_Equiv__Relations_Ocongruent(U_20500,U_20503,U_20501,U_20502) ),
    inference(clausify,[status(thm)],[f_4917_4]) ).

cnf(f_4917_6,plain,
    ( hAPP(U_20502,sK579(U_20503,U_20502,U_20501,U_20500)) != hAPP(U_20502,sK580(U_20503,U_20502,U_20501,U_20500))
    | c_Equiv__Relations_Ocongruent(U_20500,U_20503,U_20501,U_20502) ),
    inference(clausify,[status(thm)],[f_4917_4]) ).

fof(f_4918_1,plain,
    ! [T_d,V_f_2,V_r2_2,T_c,V_r1_2,T_b] :
      ( c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2)
      | ? [B_y1,B_z1] :
          ( ? [B_y2,B_z2] :
              ( hAPP(hAPP(V_f_2,B_y1),B_y2) != hAPP(hAPP(V_f_2,B_z1),B_z2)
              & hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_y2),B_z2)),V_r2_2)) )
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y1),B_z1)),V_r1_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_congruent2I_H]) ).

fof(f_4918_2,plain,
    ! [U_20513,U_20512,U_20511,U_20510,U_20509,U_20508] :
      ( c_Equiv__Relations_Ocongruent2(U_20508,U_20510,U_20513,U_20509,U_20511,U_20512)
      | ? [U_20507,U_20506] :
          ( ? [U_20505,U_20504] :
              ( hAPP(hAPP(U_20512,U_20507),U_20505) != hAPP(hAPP(U_20512,U_20506),U_20504)
              & hBOOL(hAPP(hAPP(c_member(tc_prod(U_20510,U_20510)),hAPP(hAPP(c_Product__Type_OPair(U_20510,U_20510),U_20505),U_20504)),U_20511)) )
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_20508,U_20508)),hAPP(hAPP(c_Product__Type_OPair(U_20508,U_20508),U_20507),U_20506)),U_20509)) ) ),
    inference(variable_rename,[status(thm)],[f_4918_1]) ).

fof(f_4918_3,plain,
    ! [U_20513,U_20512,U_20511,U_20510,U_20509,U_20508] :
      ( c_Equiv__Relations_Ocongruent2(U_20508,U_20510,U_20513,U_20509,U_20511,U_20512)
      | ? [U_20506] :
          ( ? [U_20505,U_20504] :
              ( hAPP(hAPP(U_20512,sK581(U_20513,U_20512,U_20511,U_20510,U_20509,U_20508)),U_20505) != hAPP(hAPP(U_20512,U_20506),U_20504)
              & hBOOL(hAPP(hAPP(c_member(tc_prod(U_20510,U_20510)),hAPP(hAPP(c_Product__Type_OPair(U_20510,U_20510),U_20505),U_20504)),U_20511)) )
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_20508,U_20508)),hAPP(hAPP(c_Product__Type_OPair(U_20508,U_20508),sK581(U_20513,U_20512,U_20511,U_20510,U_20509,U_20508)),U_20506)),U_20509)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK581]),skolemize(U_20507,sK581(U_20513,U_20512,U_20511,U_20510,U_20509,U_20508))],[f_4918_2]) ).

fof(f_4918_4,plain,
    ! [U_20513,U_20512,U_20511,U_20510,U_20509,U_20508] :
      ( c_Equiv__Relations_Ocongruent2(U_20508,U_20510,U_20513,U_20509,U_20511,U_20512)
      | ( ? [U_20505,U_20504] :
            ( hAPP(hAPP(U_20512,sK581(U_20513,U_20512,U_20511,U_20510,U_20509,U_20508)),U_20505) != hAPP(hAPP(U_20512,sK582(U_20513,U_20512,U_20511,U_20510,U_20509,U_20508)),U_20504)
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_20510,U_20510)),hAPP(hAPP(c_Product__Type_OPair(U_20510,U_20510),U_20505),U_20504)),U_20511)) )
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_20508,U_20508)),hAPP(hAPP(c_Product__Type_OPair(U_20508,U_20508),sK581(U_20513,U_20512,U_20511,U_20510,U_20509,U_20508)),sK582(U_20513,U_20512,U_20511,U_20510,U_20509,U_20508))),U_20509)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK582]),skolemize(U_20506,sK582(U_20513,U_20512,U_20511,U_20510,U_20509,U_20508))],[f_4918_3]) ).

fof(f_4918_5,plain,
    ! [U_20513,U_20512,U_20511,U_20510,U_20509,U_20508] :
      ( c_Equiv__Relations_Ocongruent2(U_20508,U_20510,U_20513,U_20509,U_20511,U_20512)
      | ( ? [U_20504] :
            ( hAPP(hAPP(U_20512,sK581(U_20513,U_20512,U_20511,U_20510,U_20509,U_20508)),sK583(U_20513,U_20512,U_20511,U_20510,U_20509,U_20508)) != hAPP(hAPP(U_20512,sK582(U_20513,U_20512,U_20511,U_20510,U_20509,U_20508)),U_20504)
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_20510,U_20510)),hAPP(hAPP(c_Product__Type_OPair(U_20510,U_20510),sK583(U_20513,U_20512,U_20511,U_20510,U_20509,U_20508)),U_20504)),U_20511)) )
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_20508,U_20508)),hAPP(hAPP(c_Product__Type_OPair(U_20508,U_20508),sK581(U_20513,U_20512,U_20511,U_20510,U_20509,U_20508)),sK582(U_20513,U_20512,U_20511,U_20510,U_20509,U_20508))),U_20509)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK583]),skolemize(U_20505,sK583(U_20513,U_20512,U_20511,U_20510,U_20509,U_20508))],[f_4918_4]) ).

fof(f_4918_6,plain,
    ! [U_20513,U_20512,U_20511,U_20510,U_20509,U_20508] :
      ( c_Equiv__Relations_Ocongruent2(U_20508,U_20510,U_20513,U_20509,U_20511,U_20512)
      | ( hAPP(hAPP(U_20512,sK581(U_20513,U_20512,U_20511,U_20510,U_20509,U_20508)),sK583(U_20513,U_20512,U_20511,U_20510,U_20509,U_20508)) != hAPP(hAPP(U_20512,sK582(U_20513,U_20512,U_20511,U_20510,U_20509,U_20508)),sK584(U_20513,U_20512,U_20511,U_20510,U_20509,U_20508))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_20510,U_20510)),hAPP(hAPP(c_Product__Type_OPair(U_20510,U_20510),sK583(U_20513,U_20512,U_20511,U_20510,U_20509,U_20508)),sK584(U_20513,U_20512,U_20511,U_20510,U_20509,U_20508))),U_20511))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_20508,U_20508)),hAPP(hAPP(c_Product__Type_OPair(U_20508,U_20508),sK581(U_20513,U_20512,U_20511,U_20510,U_20509,U_20508)),sK582(U_20513,U_20512,U_20511,U_20510,U_20509,U_20508))),U_20509)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK584]),skolemize(U_20504,sK584(U_20513,U_20512,U_20511,U_20510,U_20509,U_20508))],[f_4918_5]) ).

cnf(f_4918_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_20508,U_20508)),hAPP(hAPP(c_Product__Type_OPair(U_20508,U_20508),sK581(U_20513,U_20512,U_20511,U_20510,U_20509,U_20508)),sK582(U_20513,U_20512,U_20511,U_20510,U_20509,U_20508))),U_20509))
    | c_Equiv__Relations_Ocongruent2(U_20508,U_20510,U_20513,U_20509,U_20511,U_20512) ),
    inference(clausify,[status(thm)],[f_4918_6]) ).

cnf(f_4918_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_20510,U_20510)),hAPP(hAPP(c_Product__Type_OPair(U_20510,U_20510),sK583(U_20513,U_20512,U_20511,U_20510,U_20509,U_20508)),sK584(U_20513,U_20512,U_20511,U_20510,U_20509,U_20508))),U_20511))
    | c_Equiv__Relations_Ocongruent2(U_20508,U_20510,U_20513,U_20509,U_20511,U_20512) ),
    inference(clausify,[status(thm)],[f_4918_6]) ).

cnf(f_4918_9,plain,
    ( hAPP(hAPP(U_20512,sK581(U_20513,U_20512,U_20511,U_20510,U_20509,U_20508)),sK583(U_20513,U_20512,U_20511,U_20510,U_20509,U_20508)) != hAPP(hAPP(U_20512,sK582(U_20513,U_20512,U_20511,U_20510,U_20509,U_20508)),sK584(U_20513,U_20512,U_20511,U_20510,U_20509,U_20508))
    | c_Equiv__Relations_Ocongruent2(U_20508,U_20510,U_20513,U_20509,U_20511,U_20512) ),
    inference(clausify,[status(thm)],[f_4918_6]) ).

fof(f_4919_1,plain,
    ! [V_xqq,V_xq,T_a] : c_Lazy__Sequence_Oflat(T_a,c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Lazy__Sequence_Olazy__sequence(T_a),V_xq,V_xqq)) = c_Lazy__Sequence_Oappend(T_a,V_xq,c_Lazy__Sequence_Oflat(T_a,V_xqq)),
    inference(fof_nnf,[status(thm)],[fact__03]) ).

fof(f_4919_2,plain,
    ! [U_20516,U_20515,U_20514] : c_Lazy__Sequence_Oflat(U_20514,c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Lazy__Sequence_Olazy__sequence(U_20514),U_20515,U_20516)) = c_Lazy__Sequence_Oappend(U_20514,U_20515,c_Lazy__Sequence_Oflat(U_20514,U_20516)),
    inference(variable_rename,[status(thm)],[f_4919_1]) ).

cnf(f_4919_3,plain,
    c_Lazy__Sequence_Oflat(U_20514,c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Lazy__Sequence_Olazy__sequence(U_20514),U_20515,U_20516)) = c_Lazy__Sequence_Oappend(U_20514,U_20515,c_Lazy__Sequence_Oflat(U_20514,U_20516)),
    inference(clausify,[status(thm)],[f_4919_2]) ).

fof(f_4920_1,plain,
    ! [T_a] : c_Lazy__Sequence_Oflat(T_a,c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Lazy__Sequence_Olazy__sequence(T_a))) = c_Lazy__Sequence_Olazy__sequence_OEmpty(T_a),
    inference(fof_nnf,[status(thm)],[fact__04]) ).

fof(f_4920_2,plain,
    ! [U_20517] : c_Lazy__Sequence_Oflat(U_20517,c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Lazy__Sequence_Olazy__sequence(U_20517))) = c_Lazy__Sequence_Olazy__sequence_OEmpty(U_20517),
    inference(variable_rename,[status(thm)],[f_4920_1]) ).

cnf(f_4920_3,plain,
    c_Lazy__Sequence_Oflat(U_20517,c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Lazy__Sequence_Olazy__sequence(U_20517))) = c_Lazy__Sequence_Olazy__sequence_OEmpty(U_20517),
    inference(clausify,[status(thm)],[f_4920_2]) ).

fof(f_4921_1,plain,
    ! [V_f_2,V_xq_2,T_b,T_c] : hAPP(c_Lazy__Sequence_Obind(T_c,T_b,V_xq_2),V_f_2) = c_Lazy__Sequence_Oflat(T_b,c_Lazy__Sequence_Omap(T_c,tc_Lazy__Sequence_Olazy__sequence(T_b),V_f_2,V_xq_2)),
    inference(fof_nnf,[status(thm)],[fact__05]) ).

fof(f_4921_2,plain,
    ! [U_20521,U_20520,U_20519,U_20518] : hAPP(c_Lazy__Sequence_Obind(U_20518,U_20519,U_20520),U_20521) = c_Lazy__Sequence_Oflat(U_20519,c_Lazy__Sequence_Omap(U_20518,tc_Lazy__Sequence_Olazy__sequence(U_20519),U_20521,U_20520)),
    inference(variable_rename,[status(thm)],[f_4921_1]) ).

cnf(f_4921_3,plain,
    hAPP(c_Lazy__Sequence_Obind(U_20518,U_20519,U_20520),U_20521) = c_Lazy__Sequence_Oflat(U_20519,c_Lazy__Sequence_Omap(U_20518,tc_Lazy__Sequence_Olazy__sequence(U_20519),U_20521,U_20520)),
    inference(clausify,[status(thm)],[f_4921_2]) ).

fof(f_4922_1,plain,
    ! [V_j_2,V_i_2,V_P_2] :
      ( ( c_List_Olist__all(tc_Nat_Onat,V_P_2,c_List_Oupt(V_i_2,V_j_2))
        | ~ c_List_Oall__interval__nat(V_P_2,V_i_2,V_j_2) )
      & ( c_List_Oall__interval__nat(V_P_2,V_i_2,V_j_2)
        | ~ c_List_Olist__all(tc_Nat_Onat,V_P_2,c_List_Oupt(V_i_2,V_j_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__all__iff__all__interval__nat]) ).

fof(f_4922_2,plain,
    ! [U_20524,U_20523,U_20522] :
      ( ( c_List_Olist__all(tc_Nat_Onat,U_20522,c_List_Oupt(U_20523,U_20524))
        | ~ c_List_Oall__interval__nat(U_20522,U_20523,U_20524) )
      & ( c_List_Oall__interval__nat(U_20522,U_20523,U_20524)
        | ~ c_List_Olist__all(tc_Nat_Onat,U_20522,c_List_Oupt(U_20523,U_20524)) ) ),
    inference(variable_rename,[status(thm)],[f_4922_1]) ).

fof(f_4922_3,plain,
    ( ! [U_20530,U_20528,U_20526] :
        ( c_List_Olist__all(tc_Nat_Onat,U_20526,c_List_Oupt(U_20528,U_20530))
        | ~ c_List_Oall__interval__nat(U_20526,U_20528,U_20530) )
    & ! [U_20529,U_20527,U_20525] :
        ( c_List_Oall__interval__nat(U_20525,U_20527,U_20529)
        | ~ c_List_Olist__all(tc_Nat_Onat,U_20525,c_List_Oupt(U_20527,U_20529)) ) ),
    inference(miniscope,[status(thm)],[f_4922_2]) ).

cnf(f_4922_4,plain,
    ( c_List_Oall__interval__nat(U_20525,U_20527,U_20529)
    | ~ c_List_Olist__all(tc_Nat_Onat,U_20525,c_List_Oupt(U_20527,U_20529)) ),
    inference(clausify,[status(thm)],[f_4922_3]) ).

cnf(f_4922_5,plain,
    ( c_List_Olist__all(tc_Nat_Onat,U_20526,c_List_Oupt(U_20528,U_20530))
    | ~ c_List_Oall__interval__nat(U_20526,U_20528,U_20530) ),
    inference(clausify,[status(thm)],[f_4922_3]) ).

fof(f_4923_1,plain,
    ! [V_xq_2,V_x_2,V_f_2,T_b,T_c] : c_Lazy__Sequence_Omap(T_c,T_b,V_f_2,c_Lazy__Sequence_Olazy__sequence_OInsert(T_c,V_x_2,V_xq_2)) = c_Lazy__Sequence_Olazy__sequence_OInsert(T_b,hAPP(V_f_2,V_x_2),c_Lazy__Sequence_Omap(T_c,T_b,V_f_2,V_xq_2)),
    inference(fof_nnf,[status(thm)],[fact__06]) ).

fof(f_4923_2,plain,
    ! [U_20535,U_20534,U_20533,U_20532,U_20531] : c_Lazy__Sequence_Omap(U_20531,U_20532,U_20533,c_Lazy__Sequence_Olazy__sequence_OInsert(U_20531,U_20534,U_20535)) = c_Lazy__Sequence_Olazy__sequence_OInsert(U_20532,hAPP(U_20533,U_20534),c_Lazy__Sequence_Omap(U_20531,U_20532,U_20533,U_20535)),
    inference(variable_rename,[status(thm)],[f_4923_1]) ).

cnf(f_4923_3,plain,
    c_Lazy__Sequence_Omap(U_20531,U_20532,U_20533,c_Lazy__Sequence_Olazy__sequence_OInsert(U_20531,U_20534,U_20535)) = c_Lazy__Sequence_Olazy__sequence_OInsert(U_20532,hAPP(U_20533,U_20534),c_Lazy__Sequence_Omap(U_20531,U_20532,U_20533,U_20535)),
    inference(clausify,[status(thm)],[f_4923_2]) ).

fof(f_4924_1,plain,
    ! [V_f_2,T_b,T_c] : c_Lazy__Sequence_Omap(T_c,T_b,V_f_2,c_Lazy__Sequence_Olazy__sequence_OEmpty(T_c)) = c_Lazy__Sequence_Olazy__sequence_OEmpty(T_b),
    inference(fof_nnf,[status(thm)],[fact__07]) ).

fof(f_4924_2,plain,
    ! [U_20538,U_20537,U_20536] : c_Lazy__Sequence_Omap(U_20536,U_20537,U_20538,c_Lazy__Sequence_Olazy__sequence_OEmpty(U_20536)) = c_Lazy__Sequence_Olazy__sequence_OEmpty(U_20537),
    inference(variable_rename,[status(thm)],[f_4924_1]) ).

cnf(f_4924_3,plain,
    c_Lazy__Sequence_Omap(U_20536,U_20537,U_20538,c_Lazy__Sequence_Olazy__sequence_OEmpty(U_20536)) = c_Lazy__Sequence_Olazy__sequence_OEmpty(U_20537),
    inference(clausify,[status(thm)],[f_4924_2]) ).

fof(f_4925_1,plain,
    ! [V_j_2,V_i_2,V_P_2] :
      ( ( c_List_Oall__interval__nat(V_P_2,V_i_2,V_j_2)
        | ? [B_x] :
            ( ~ hBOOL(hAPP(V_P_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2))) ) )
      & ( ! [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2))) )
        | ~ c_List_Oall__interval__nat(V_P_2,V_i_2,V_j_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_all__interval__nat__def]) ).

fof(f_4925_2,plain,
    ! [U_20543,U_20542,U_20541] :
      ( ( c_List_Oall__interval__nat(U_20541,U_20542,U_20543)
        | ? [U_20540] :
            ( ~ hBOOL(hAPP(U_20541,U_20540))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_20540),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_20542),U_20543))) ) )
      & ( ! [U_20539] :
            ( hBOOL(hAPP(U_20541,U_20539))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_20539),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_20542),U_20543))) )
        | ~ c_List_Oall__interval__nat(U_20541,U_20542,U_20543) ) ),
    inference(variable_rename,[status(thm)],[f_4925_1]) ).

fof(f_4925_3,plain,
    ( ! [U_20549,U_20547,U_20545] :
        ( c_List_Oall__interval__nat(U_20545,U_20547,U_20549)
        | ? [U_20540] :
            ( ~ hBOOL(hAPP(U_20545,U_20540))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_20540),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_20547),U_20549))) ) )
    & ! [U_20548,U_20546,U_20544] :
        ( ! [U_20539] :
            ( hBOOL(hAPP(U_20544,U_20539))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_20539),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_20546),U_20548))) )
        | ~ c_List_Oall__interval__nat(U_20544,U_20546,U_20548) ) ),
    inference(miniscope,[status(thm)],[f_4925_2]) ).

fof(f_4925_4,plain,
    ( ! [U_20549,U_20547,U_20545] :
        ( c_List_Oall__interval__nat(U_20545,U_20547,U_20549)
        | ( ~ hBOOL(hAPP(U_20545,sK585(U_20549,U_20547,U_20545)))
          & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK585(U_20549,U_20547,U_20545)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_20547),U_20549))) ) )
    & ! [U_20548,U_20546,U_20544] :
        ( ! [U_20539] :
            ( hBOOL(hAPP(U_20544,U_20539))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_20539),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_20546),U_20548))) )
        | ~ c_List_Oall__interval__nat(U_20544,U_20546,U_20548) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK585]),skolemize(U_20540,sK585(U_20549,U_20547,U_20545))],[f_4925_3]) ).

cnf(f_4925_5,plain,
    ( hBOOL(hAPP(U_20544,U_20539))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_20539),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_20546),U_20548)))
    | ~ c_List_Oall__interval__nat(U_20544,U_20546,U_20548) ),
    inference(clausify,[status(thm)],[f_4925_4]) ).

cnf(f_4925_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK585(U_20549,U_20547,U_20545)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_20547),U_20549)))
    | c_List_Oall__interval__nat(U_20545,U_20547,U_20549) ),
    inference(clausify,[status(thm)],[f_4925_4]) ).

cnf(f_4925_7,plain,
    ( ~ hBOOL(hAPP(U_20545,sK585(U_20549,U_20547,U_20545)))
    | c_List_Oall__interval__nat(U_20545,U_20547,U_20549) ),
    inference(clausify,[status(thm)],[f_4925_4]) ).

fof(f_4926_1,plain,
    ! [V_j_2,V_i_2,V_P_2] :
      ( ( c_List_Olist__ex(tc_Nat_Onat,V_P_2,c_List_Oupt(V_i_2,V_j_2))
        | c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat,c_fNot),V_P_2),V_i_2,V_j_2) )
      & ( ~ c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat,c_fNot),V_P_2),V_i_2,V_j_2)
        | ~ c_List_Olist__ex(tc_Nat_Onat,V_P_2,c_List_Oupt(V_i_2,V_j_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_list__ex__iff__not__all__inverval__nat]) ).

fof(f_4926_2,plain,
    ! [U_20552,U_20551,U_20550] :
      ( ( c_List_Olist__ex(tc_Nat_Onat,U_20550,c_List_Oupt(U_20551,U_20552))
        | c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat,c_fNot),U_20550),U_20551,U_20552) )
      & ( ~ c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat,c_fNot),U_20550),U_20551,U_20552)
        | ~ c_List_Olist__ex(tc_Nat_Onat,U_20550,c_List_Oupt(U_20551,U_20552)) ) ),
    inference(variable_rename,[status(thm)],[f_4926_1]) ).

fof(f_4926_3,plain,
    ( ! [U_20558,U_20556,U_20554] :
        ( c_List_Olist__ex(tc_Nat_Onat,U_20554,c_List_Oupt(U_20556,U_20558))
        | c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat,c_fNot),U_20554),U_20556,U_20558) )
    & ! [U_20557,U_20555,U_20553] :
        ( ~ c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat,c_fNot),U_20553),U_20555,U_20557)
        | ~ c_List_Olist__ex(tc_Nat_Onat,U_20553,c_List_Oupt(U_20555,U_20557)) ) ),
    inference(miniscope,[status(thm)],[f_4926_2]) ).

cnf(f_4926_4,plain,
    ( ~ c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat,c_fNot),U_20553),U_20555,U_20557)
    | ~ c_List_Olist__ex(tc_Nat_Onat,U_20553,c_List_Oupt(U_20555,U_20557)) ),
    inference(clausify,[status(thm)],[f_4926_3]) ).

cnf(f_4926_5,plain,
    ( c_List_Olist__ex(tc_Nat_Onat,U_20554,c_List_Oupt(U_20556,U_20558))
    | c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat,c_fNot),U_20554),U_20556,U_20558) ),
    inference(clausify,[status(thm)],[f_4926_3]) ).

fof(f_4927_1,plain,
    ! [V_i_2,V_xq_2,V_f_2,T_b,T_c] : c_New__DSequence_Opos__map(T_c,T_b,V_f_2,V_xq_2,V_i_2) = c_Lazy__Sequence_Omap(T_c,T_b,V_f_2,hAPP(V_xq_2,V_i_2)),
    inference(fof_nnf,[status(thm)],[fact_New__DSequence_Opos__map__def]) ).

fof(f_4927_2,plain,
    ! [U_20563,U_20562,U_20561,U_20560,U_20559] : c_New__DSequence_Opos__map(U_20559,U_20560,U_20561,U_20562,U_20563) = c_Lazy__Sequence_Omap(U_20559,U_20560,U_20561,hAPP(U_20562,U_20563)),
    inference(variable_rename,[status(thm)],[f_4927_1]) ).

cnf(f_4927_3,plain,
    c_New__DSequence_Opos__map(U_20559,U_20560,U_20561,U_20562,U_20563) = c_Lazy__Sequence_Omap(U_20559,U_20560,U_20561,hAPP(U_20562,U_20563)),
    inference(clausify,[status(thm)],[f_4927_2]) ).

fof(f_4928_1,plain,
    ! [V_h_2,V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
      ( hAPP(hAPP(V_F_2,V_g_2),V_A_2) = hAPP(hAPP(V_F_2,V_h_2),V_A_2)
      | ? [B_x] :
          ( hAPP(V_g_2,B_x) != hAPP(V_h_2,B_x)
          & hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
      | ~ c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2) ),
    inference(fof_nnf,[status(thm)],[fact_folding__image_Ocong]) ).

fof(f_4928_2,plain,
    ! [U_20572,U_20571,U_20570,U_20569,U_20568,U_20567,U_20566,U_20565] :
      ( hAPP(hAPP(U_20569,U_20571),U_20570) = hAPP(hAPP(U_20569,U_20572),U_20570)
      | ? [U_20564] :
          ( hAPP(U_20571,U_20564) != hAPP(U_20572,U_20564)
          & hBOOL(hAPP(hAPP(c_member(U_20566),U_20564),U_20570)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20566),U_20570))
      | ~ c_Finite__Set_Ofolding__image(U_20565,U_20566,U_20567,U_20568,U_20569) ),
    inference(variable_rename,[status(thm)],[f_4928_1]) ).

fof(f_4928_3,plain,
    ! [U_20572,U_20571,U_20570,U_20569,U_20568,U_20567,U_20566] :
      ( ! [U_20565] : ~ c_Finite__Set_Ofolding__image(U_20565,U_20566,U_20567,U_20568,U_20569)
      | hAPP(hAPP(U_20569,U_20571),U_20570) = hAPP(hAPP(U_20569,U_20572),U_20570)
      | ? [U_20564] :
          ( hAPP(U_20571,U_20564) != hAPP(U_20572,U_20564)
          & hBOOL(hAPP(hAPP(c_member(U_20566),U_20564),U_20570)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20566),U_20570)) ),
    inference(miniscope,[status(thm)],[f_4928_2]) ).

fof(f_4928_4,plain,
    ! [U_20572,U_20571,U_20570,U_20569,U_20568,U_20567,U_20566] :
      ( ! [U_20565] : ~ c_Finite__Set_Ofolding__image(U_20565,U_20566,U_20567,U_20568,U_20569)
      | hAPP(hAPP(U_20569,U_20571),U_20570) = hAPP(hAPP(U_20569,U_20572),U_20570)
      | ( hAPP(U_20571,sK586(U_20572,U_20571,U_20570,U_20569,U_20568,U_20567,U_20566)) != hAPP(U_20572,sK586(U_20572,U_20571,U_20570,U_20569,U_20568,U_20567,U_20566))
        & hBOOL(hAPP(hAPP(c_member(U_20566),sK586(U_20572,U_20571,U_20570,U_20569,U_20568,U_20567,U_20566)),U_20570)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20566),U_20570)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK586]),skolemize(U_20564,sK586(U_20572,U_20571,U_20570,U_20569,U_20568,U_20567,U_20566))],[f_4928_3]) ).

cnf(f_4928_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20566),sK586(U_20572,U_20571,U_20570,U_20569,U_20568,U_20567,U_20566)),U_20570))
    | hAPP(hAPP(U_20569,U_20571),U_20570) = hAPP(hAPP(U_20569,U_20572),U_20570)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20566),U_20570))
    | ~ c_Finite__Set_Ofolding__image(U_20565,U_20566,U_20567,U_20568,U_20569) ),
    inference(clausify,[status(thm)],[f_4928_4]) ).

cnf(f_4928_6,plain,
    ( hAPP(U_20571,sK586(U_20572,U_20571,U_20570,U_20569,U_20568,U_20567,U_20566)) != hAPP(U_20572,sK586(U_20572,U_20571,U_20570,U_20569,U_20568,U_20567,U_20566))
    | hAPP(hAPP(U_20569,U_20571),U_20570) = hAPP(hAPP(U_20569,U_20572),U_20570)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20566),U_20570))
    | ~ c_Finite__Set_Ofolding__image(U_20565,U_20566,U_20567,U_20568,U_20569) ),
    inference(clausify,[status(thm)],[f_4928_4]) ).

fof(f_4929_1,plain,
    ! [V_n,V_m,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_i))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n))) ),
    inference(fof_nnf,[status(thm)],[fact_power__dvd__imp__le]) ).

fof(f_4929_2,plain,
    ! [U_20575,U_20574,U_20573] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20574),U_20575))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_20573))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_20573),U_20574)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_20573),U_20575))) ),
    inference(variable_rename,[status(thm)],[f_4929_1]) ).

cnf(f_4929_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20574),U_20575))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_20573))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_20573),U_20574)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_20573),U_20575))) ),
    inference(clausify,[status(thm)],[f_4929_2]) ).

fof(f_4930_1,plain,
    ! [V_f_2,V_A_2,T_b] :
      ( ? [B_x1] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,V_A_2),B_x1))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    inference(fof_nnf,[status(thm)],[fact_finite__nonempty__imp__fold1Set]) ).

fof(f_4930_2,plain,
    ! [U_20579,U_20578,U_20577] :
      ( ? [U_20576] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_20577,U_20579,U_20578),U_20576))
      | U_20578 = c_Orderings_Obot__class_Obot(tc_fun(U_20577,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20577),U_20578)) ),
    inference(variable_rename,[status(thm)],[f_4930_1]) ).

fof(f_4930_3,plain,
    ! [U_20579,U_20578,U_20577] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_20577,U_20579,U_20578),sK587(U_20579,U_20578,U_20577)))
      | U_20578 = c_Orderings_Obot__class_Obot(tc_fun(U_20577,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20577),U_20578)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK587]),skolemize(U_20576,sK587(U_20579,U_20578,U_20577))],[f_4930_2]) ).

cnf(f_4930_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_20577,U_20579,U_20578),sK587(U_20579,U_20578,U_20577)))
    | U_20578 = c_Orderings_Obot__class_Obot(tc_fun(U_20577,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20577),U_20578)) ),
    inference(clausify,[status(thm)],[f_4930_3]) ).

fof(f_4931_1,plain,
    ! [V_x] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_x)),
    inference(fof_nnf,[status(thm)],[fact_dvd_Oorder__refl]) ).

fof(f_4931_2,plain,
    ! [U_20580] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20580),U_20580)),
    inference(variable_rename,[status(thm)],[f_4931_1]) ).

cnf(f_4931_3,plain,
    hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20580),U_20580)),
    inference(clausify,[status(thm)],[f_4931_2]) ).

fof(f_4932_1,plain,
    ! [V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__0__right]) ).

fof(f_4932_2,plain,
    ! [U_20582,U_20581] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20581),U_20582),c_Groups_Ozero__class_Ozero(U_20581)))
      | ~ class_Rings_Ocomm__semiring__1(U_20581) ),
    inference(variable_rename,[status(thm)],[f_4932_1]) ).

cnf(f_4932_3,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20581),U_20582),c_Groups_Ozero__class_Ozero(U_20581)))
    | ~ class_Rings_Ocomm__semiring__1(U_20581) ),
    inference(clausify,[status(thm)],[f_4932_2]) ).

fof(f_4933_1,plain,
    ! [V_k] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k)),
    inference(fof_nnf,[status(thm)],[fact_dvd__1__left]) ).

fof(f_4933_2,plain,
    ! [U_20583] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_20583)),
    inference(variable_rename,[status(thm)],[f_4933_1]) ).

cnf(f_4933_3,plain,
    hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_20583)),
    inference(clausify,[status(thm)],[f_4933_2]) ).

fof(f_4934_1,plain,
    ! [V_n,V_k] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__imp__le]) ).

fof(f_4934_2,plain,
    ! [U_20585,U_20584] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20584),U_20585))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_20585))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20584),U_20585)) ),
    inference(variable_rename,[status(thm)],[f_4934_1]) ).

cnf(f_4934_3,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20584),U_20585))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_20585))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20584),U_20585)) ),
    inference(clausify,[status(thm)],[f_4934_2]) ).

fof(f_4935_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
          | c_Divides_Odiv__class_Omod(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)) != c_Groups_Ozero__class_Ozero(T_b) )
        & ( c_Divides_Odiv__class_Omod(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)) = c_Groups_Ozero__class_Ozero(T_b)
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2))) ) )
      | ~ class_Int_Onumber(T_b)
      | ~ class_Divides_Osemiring__div(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__eq__mod__eq__0__number__of]) ).

fof(f_4935_2,plain,
    ! [U_20588,U_20587,U_20586] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20586),hAPP(c_Int_Onumber__class_Onumber__of(U_20586),U_20587)),hAPP(c_Int_Onumber__class_Onumber__of(U_20586),U_20588)))
          | c_Divides_Odiv__class_Omod(U_20586,hAPP(c_Int_Onumber__class_Onumber__of(U_20586),U_20588),hAPP(c_Int_Onumber__class_Onumber__of(U_20586),U_20587)) != c_Groups_Ozero__class_Ozero(U_20586) )
        & ( c_Divides_Odiv__class_Omod(U_20586,hAPP(c_Int_Onumber__class_Onumber__of(U_20586),U_20588),hAPP(c_Int_Onumber__class_Onumber__of(U_20586),U_20587)) = c_Groups_Ozero__class_Ozero(U_20586)
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20586),hAPP(c_Int_Onumber__class_Onumber__of(U_20586),U_20587)),hAPP(c_Int_Onumber__class_Onumber__of(U_20586),U_20588))) ) )
      | ~ class_Int_Onumber(U_20586)
      | ~ class_Divides_Osemiring__div(U_20586) ),
    inference(variable_rename,[status(thm)],[f_4935_1]) ).

cnf(f_4935_3,plain,
    ( c_Divides_Odiv__class_Omod(U_20586,hAPP(c_Int_Onumber__class_Onumber__of(U_20586),U_20588),hAPP(c_Int_Onumber__class_Onumber__of(U_20586),U_20587)) = c_Groups_Ozero__class_Ozero(U_20586)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20586),hAPP(c_Int_Onumber__class_Onumber__of(U_20586),U_20587)),hAPP(c_Int_Onumber__class_Onumber__of(U_20586),U_20588)))
    | ~ class_Int_Onumber(U_20586)
    | ~ class_Divides_Osemiring__div(U_20586) ),
    inference(clausify,[status(thm)],[f_4935_2]) ).

cnf(f_4935_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20586),hAPP(c_Int_Onumber__class_Onumber__of(U_20586),U_20587)),hAPP(c_Int_Onumber__class_Onumber__of(U_20586),U_20588)))
    | c_Divides_Odiv__class_Omod(U_20586,hAPP(c_Int_Onumber__class_Onumber__of(U_20586),U_20588),hAPP(c_Int_Onumber__class_Onumber__of(U_20586),U_20587)) != c_Groups_Ozero__class_Ozero(U_20586)
    | ~ class_Int_Onumber(U_20586)
    | ~ class_Divides_Osemiring__div(U_20586) ),
    inference(clausify,[status(thm)],[f_4935_2]) ).

fof(f_4936_1,plain,
    ! [V_a,V_n,V_m,T_a] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_le__imp__power__dvd]) ).

fof(f_4936_2,plain,
    ! [U_20592,U_20591,U_20590,U_20589] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20589),hAPP(hAPP(c_Power_Opower__class_Opower(U_20589),U_20592),U_20590)),hAPP(hAPP(c_Power_Opower__class_Opower(U_20589),U_20592),U_20591)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20590),U_20591))
      | ~ class_Rings_Ocomm__semiring__1(U_20589) ),
    inference(variable_rename,[status(thm)],[f_4936_1]) ).

cnf(f_4936_3,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20589),hAPP(hAPP(c_Power_Opower__class_Opower(U_20589),U_20592),U_20590)),hAPP(hAPP(c_Power_Opower__class_Opower(U_20589),U_20592),U_20591)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20590),U_20591))
    | ~ class_Rings_Ocomm__semiring__1(U_20589) ),
    inference(clausify,[status(thm)],[f_4936_2]) ).

fof(f_4937_1,plain,
    ! [V_m,V_n,V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_m)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__power__le]) ).

fof(f_4937_2,plain,
    ! [U_20597,U_20596,U_20595,U_20594,U_20593] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20593),hAPP(hAPP(c_Power_Opower__class_Opower(U_20593),U_20594),U_20596)),hAPP(hAPP(c_Power_Opower__class_Opower(U_20593),U_20595),U_20597)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20596),U_20597))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20593),U_20594),U_20595))
      | ~ class_Rings_Ocomm__semiring__1(U_20593) ),
    inference(variable_rename,[status(thm)],[f_4937_1]) ).

cnf(f_4937_3,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20593),hAPP(hAPP(c_Power_Opower__class_Opower(U_20593),U_20594),U_20596)),hAPP(hAPP(c_Power_Opower__class_Opower(U_20593),U_20595),U_20597)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20596),U_20597))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20593),U_20594),U_20595))
    | ~ class_Rings_Ocomm__semiring__1(U_20593) ),
    inference(clausify,[status(thm)],[f_4937_2]) ).

fof(f_4938_1,plain,
    ! [V_m,V_b,V_n,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_b))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__le__dvd]) ).

fof(f_4938_2,plain,
    ! [U_20602,U_20601,U_20600,U_20599,U_20598] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20598),hAPP(hAPP(c_Power_Opower__class_Opower(U_20598),U_20599),U_20602)),U_20601))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20602),U_20600))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20598),hAPP(hAPP(c_Power_Opower__class_Opower(U_20598),U_20599),U_20600)),U_20601))
      | ~ class_Rings_Ocomm__semiring__1(U_20598) ),
    inference(variable_rename,[status(thm)],[f_4938_1]) ).

cnf(f_4938_3,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20598),hAPP(hAPP(c_Power_Opower__class_Opower(U_20598),U_20599),U_20602)),U_20601))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20602),U_20600))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20598),hAPP(hAPP(c_Power_Opower__class_Opower(U_20598),U_20599),U_20600)),U_20601))
    | ~ class_Rings_Ocomm__semiring__1(U_20598) ),
    inference(clausify,[status(thm)],[f_4938_2]) ).

fof(f_4939_1,plain,
    ! [V_d_2,V_c_2,V_b_2,V_a_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2,V_d_2)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_d_2))
            | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2),V_a_2)) )
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) ) )
      & ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_d_2))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2),V_a_2)) )
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2,V_d_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_OatLeastatMost__subset__iff]) ).

fof(f_4939_2,plain,
    ! [U_20606,U_20605,U_20604,U_20603] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20603,U_20604)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20605,U_20606)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20604),U_20606))
            | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20605),U_20603)) )
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20603),U_20604)) ) )
      & ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20604),U_20606))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20605),U_20603)) )
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20603),U_20604))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20603,U_20604)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20605,U_20606))) ) ),
    inference(variable_rename,[status(thm)],[f_4939_1]) ).

fof(f_4939_3,plain,
    ( ! [U_20614,U_20612,U_20610,U_20608] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20608,U_20610)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20612,U_20614)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20610),U_20614))
            | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20612),U_20608)) )
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20608),U_20610)) ) )
    & ! [U_20613,U_20611,U_20609,U_20607] :
        ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20609),U_20613))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20611),U_20607)) )
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20607),U_20609))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20607,U_20609)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20611,U_20613))) ) ),
    inference(miniscope,[status(thm)],[f_4939_2]) ).

cnf(f_4939_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20611),U_20607))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20607),U_20609))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20607,U_20609)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20611,U_20613))) ),
    inference(clausify,[status(thm)],[f_4939_3]) ).

cnf(f_4939_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20609),U_20613))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20607),U_20609))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20607,U_20609)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20611,U_20613))) ),
    inference(clausify,[status(thm)],[f_4939_3]) ).

cnf(f_4939_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20608),U_20610))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20608,U_20610)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20612,U_20614))) ),
    inference(clausify,[status(thm)],[f_4939_3]) ).

cnf(f_4939_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20610),U_20614))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20612),U_20608))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20608,U_20610)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20612,U_20614))) ),
    inference(clausify,[status(thm)],[f_4939_3]) ).

fof(f_4940_1,plain,
    ! [V_n,V_m,V_k] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n))) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__diffD]) ).

fof(f_4940_2,plain,
    ! [U_20617,U_20616,U_20615] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20615),U_20616))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20617),U_20616))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20615),U_20617))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20615),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_20616),U_20617))) ),
    inference(variable_rename,[status(thm)],[f_4940_1]) ).

cnf(f_4940_3,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20615),U_20616))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20617),U_20616))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20615),U_20617))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20615),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_20616),U_20617))) ),
    inference(clausify,[status(thm)],[f_4940_2]) ).

fof(f_4941_1,plain,
    ! [V_n,V_m,V_k] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n))) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__diffD1]) ).

fof(f_4941_2,plain,
    ! [U_20620,U_20619,U_20618] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20618),U_20620))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20620),U_20619))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20618),U_20619))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20618),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_20619),U_20620))) ),
    inference(variable_rename,[status(thm)],[f_4941_1]) ).

cnf(f_4941_3,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20618),U_20620))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20620),U_20619))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20618),U_20619))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20618),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_20619),U_20620))) ),
    inference(clausify,[status(thm)],[f_4941_2]) ).

fof(f_4942_1,plain,
    ! [V_k_2,V_i_2] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_i_2),c_SetInterval_Oord_OlessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2)))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2)) )
      & ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_i_2),c_SetInterval_Oord_OlessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_OlessThan__iff]) ).

fof(f_4942_2,plain,
    ! [U_20622,U_20621] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_20621),c_SetInterval_Oord_OlessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_20622)))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20622),U_20621))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20621),U_20622)) )
      & ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20622),U_20621))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20621),U_20622)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_20621),c_SetInterval_Oord_OlessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_20622))) ) ),
    inference(variable_rename,[status(thm)],[f_4942_1]) ).

fof(f_4942_3,plain,
    ( ! [U_20626,U_20624] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_20624),c_SetInterval_Oord_OlessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_20626)))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20626),U_20624))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20624),U_20626)) )
    & ! [U_20625,U_20623] :
        ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20625),U_20623))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20623),U_20625)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_20623),c_SetInterval_Oord_OlessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_20625))) ) ),
    inference(miniscope,[status(thm)],[f_4942_2]) ).

cnf(f_4942_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20623),U_20625))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_20623),c_SetInterval_Oord_OlessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_20625))) ),
    inference(clausify,[status(thm)],[f_4942_3]) ).

cnf(f_4942_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20625),U_20623))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_20623),c_SetInterval_Oord_OlessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_20625))) ),
    inference(clausify,[status(thm)],[f_4942_3]) ).

cnf(f_4942_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_20624),c_SetInterval_Oord_OlessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_20626)))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20626),U_20624))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20624),U_20626)) ),
    inference(clausify,[status(thm)],[f_4942_3]) ).

fof(f_4943_1,plain,
    ! [V_k_2,V_i_2] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_i_2),c_SetInterval_Oord_OgreaterThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2)))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2)) )
      & ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_i_2),c_SetInterval_Oord_OgreaterThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_OgreaterThan__iff]) ).

fof(f_4943_2,plain,
    ! [U_20628,U_20627] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_20627),c_SetInterval_Oord_OgreaterThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_20628)))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20627),U_20628))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20628),U_20627)) )
      & ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20627),U_20628))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20628),U_20627)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_20627),c_SetInterval_Oord_OgreaterThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_20628))) ) ),
    inference(variable_rename,[status(thm)],[f_4943_1]) ).

fof(f_4943_3,plain,
    ( ! [U_20632,U_20630] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_20630),c_SetInterval_Oord_OgreaterThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_20632)))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20630),U_20632))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20632),U_20630)) )
    & ! [U_20631,U_20629] :
        ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20629),U_20631))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20631),U_20629)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_20629),c_SetInterval_Oord_OgreaterThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_20631))) ) ),
    inference(miniscope,[status(thm)],[f_4943_2]) ).

cnf(f_4943_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20631),U_20629))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_20629),c_SetInterval_Oord_OgreaterThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_20631))) ),
    inference(clausify,[status(thm)],[f_4943_3]) ).

cnf(f_4943_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20629),U_20631))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_20629),c_SetInterval_Oord_OgreaterThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_20631))) ),
    inference(clausify,[status(thm)],[f_4943_3]) ).

cnf(f_4943_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_20630),c_SetInterval_Oord_OgreaterThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_20632)))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20630),U_20632))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20632),U_20630)) ),
    inference(clausify,[status(thm)],[f_4943_3]) ).

fof(f_4944_1,plain,
    ! [V_k_2,V_i_2] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_i_2),c_SetInterval_Oord_OatLeast(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2)) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_i_2),c_SetInterval_Oord_OatLeast(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_OatLeast__iff]) ).

fof(f_4944_2,plain,
    ! [U_20634,U_20633] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_20633),c_SetInterval_Oord_OatLeast(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20634)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20634),U_20633)) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20634),U_20633))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_20633),c_SetInterval_Oord_OatLeast(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20634))) ) ),
    inference(variable_rename,[status(thm)],[f_4944_1]) ).

fof(f_4944_3,plain,
    ( ! [U_20638,U_20636] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_20636),c_SetInterval_Oord_OatLeast(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20638)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20638),U_20636)) )
    & ! [U_20637,U_20635] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20637),U_20635))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_20635),c_SetInterval_Oord_OatLeast(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20637))) ) ),
    inference(miniscope,[status(thm)],[f_4944_2]) ).

cnf(f_4944_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20637),U_20635))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_20635),c_SetInterval_Oord_OatLeast(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20637))) ),
    inference(clausify,[status(thm)],[f_4944_3]) ).

cnf(f_4944_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_20636),c_SetInterval_Oord_OatLeast(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20638)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20638),U_20636)) ),
    inference(clausify,[status(thm)],[f_4944_3]) ).

fof(f_4945_1,plain,
    ! [V_k_2,V_i_2] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_i_2),c_SetInterval_Oord_OatMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2)) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_i_2),c_SetInterval_Oord_OatMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_OatMost__iff]) ).

fof(f_4945_2,plain,
    ! [U_20640,U_20639] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_20639),c_SetInterval_Oord_OatMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20640)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20639),U_20640)) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20639),U_20640))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_20639),c_SetInterval_Oord_OatMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20640))) ) ),
    inference(variable_rename,[status(thm)],[f_4945_1]) ).

fof(f_4945_3,plain,
    ( ! [U_20644,U_20642] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_20642),c_SetInterval_Oord_OatMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20644)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20642),U_20644)) )
    & ! [U_20643,U_20641] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20641),U_20643))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_20641),c_SetInterval_Oord_OatMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20643))) ) ),
    inference(miniscope,[status(thm)],[f_4945_2]) ).

cnf(f_4945_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20641),U_20643))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_20641),c_SetInterval_Oord_OatMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20643))) ),
    inference(clausify,[status(thm)],[f_4945_3]) ).

cnf(f_4945_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_20642),c_SetInterval_Oord_OatMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20644)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20642),U_20644)) ),
    inference(clausify,[status(thm)],[f_4945_3]) ).

fof(f_4946_1,plain,
    ! [V_m_2] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
        | V_m_2 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__1__iff__1]) ).

fof(f_4946_2,plain,
    ! [U_20645] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20645),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
        | U_20645 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( U_20645 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20645),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
    inference(variable_rename,[status(thm)],[f_4946_1]) ).

fof(f_4946_3,plain,
    ( ! [U_20647] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20647),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
        | U_20647 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
    & ! [U_20646] :
        ( U_20646 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20646),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
    inference(miniscope,[status(thm)],[f_4946_2]) ).

cnf(f_4946_4,plain,
    ( U_20646 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20646),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
    inference(clausify,[status(thm)],[f_4946_3]) ).

cnf(f_4946_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20647),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
    | U_20647 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_4946_3]) ).

fof(f_4947_1,plain,
    ! [V_n,V_m] :
      ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_n),V_m))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) ),
    inference(fof_nnf,[status(thm)],[fact_nat__dvd__not__less]) ).

fof(f_4947_2,plain,
    ! [U_20649,U_20648] :
      ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20649),U_20648))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20648),U_20649))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_20648)) ),
    inference(variable_rename,[status(thm)],[f_4947_1]) ).

cnf(f_4947_3,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20649),U_20648))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20648),U_20649))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_20648)) ),
    inference(clausify,[status(thm)],[f_4947_2]) ).

fof(f_4948_1,plain,
    ! [V_x,V_y,T_a] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
      | ~ class_Divides_Oring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__div__neg]) ).

fof(f_4948_2,plain,
    ! [U_20652,U_20651,U_20650] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_20650),U_20652),hAPP(c_Groups_Ouminus__class_Ouminus(U_20650),U_20651)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_20650),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_20650),U_20652),U_20651))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20650),U_20651),U_20652))
      | ~ class_Divides_Oring__div(U_20650) ),
    inference(variable_rename,[status(thm)],[f_4948_1]) ).

cnf(f_4948_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_20650),U_20652),hAPP(c_Groups_Ouminus__class_Ouminus(U_20650),U_20651)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_20650),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_20650),U_20652),U_20651))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20650),U_20651),U_20652))
    | ~ class_Divides_Oring__div(U_20650) ),
    inference(clausify,[status(thm)],[f_4948_2]) ).

fof(f_4949_1,plain,
    ! [V_x,V_y,T_a] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),V_y) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
      | ~ class_Divides_Oring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__neg__div]) ).

fof(f_4949_2,plain,
    ! [U_20655,U_20654,U_20653] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_20653),hAPP(c_Groups_Ouminus__class_Ouminus(U_20653),U_20655)),U_20654) = hAPP(c_Groups_Ouminus__class_Ouminus(U_20653),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_20653),U_20655),U_20654))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20653),U_20654),U_20655))
      | ~ class_Divides_Oring__div(U_20653) ),
    inference(variable_rename,[status(thm)],[f_4949_1]) ).

cnf(f_4949_3,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_20653),hAPP(c_Groups_Ouminus__class_Ouminus(U_20653),U_20655)),U_20654) = hAPP(c_Groups_Ouminus__class_Ouminus(U_20653),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_20653),U_20655),U_20654))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20653),U_20654),U_20655))
    | ~ class_Divides_Oring__div(U_20653) ),
    inference(clausify,[status(thm)],[f_4949_2]) ).

fof(f_4950_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),V_y_2)) )
        & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),V_y_2))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2))) ) )
      | ~ class_Rings_Ocomm__ring__1(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__minus__iff]) ).

fof(f_4950_2,plain,
    ! [U_20658,U_20657,U_20656] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20656),U_20657),hAPP(c_Groups_Ouminus__class_Ouminus(U_20656),U_20658)))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20656),U_20657),U_20658)) )
        & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20656),U_20657),U_20658))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20656),U_20657),hAPP(c_Groups_Ouminus__class_Ouminus(U_20656),U_20658))) ) )
      | ~ class_Rings_Ocomm__ring__1(U_20656) ),
    inference(variable_rename,[status(thm)],[f_4950_1]) ).

cnf(f_4950_3,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20656),U_20657),U_20658))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20656),U_20657),hAPP(c_Groups_Ouminus__class_Ouminus(U_20656),U_20658)))
    | ~ class_Rings_Ocomm__ring__1(U_20656) ),
    inference(clausify,[status(thm)],[f_4950_2]) ).

cnf(f_4950_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20656),U_20657),hAPP(c_Groups_Ouminus__class_Ouminus(U_20656),U_20658)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20656),U_20657),U_20658))
    | ~ class_Rings_Ocomm__ring__1(U_20656) ),
    inference(clausify,[status(thm)],[f_4950_2]) ).

fof(f_4951_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)),V_y_2))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),V_y_2)) )
        & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),V_y_2))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)),V_y_2)) ) )
      | ~ class_Rings_Ocomm__ring__1(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_minus__dvd__iff]) ).

fof(f_4951_2,plain,
    ! [U_20661,U_20660,U_20659] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20659),hAPP(c_Groups_Ouminus__class_Ouminus(U_20659),U_20660)),U_20661))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20659),U_20660),U_20661)) )
        & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20659),U_20660),U_20661))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20659),hAPP(c_Groups_Ouminus__class_Ouminus(U_20659),U_20660)),U_20661)) ) )
      | ~ class_Rings_Ocomm__ring__1(U_20659) ),
    inference(variable_rename,[status(thm)],[f_4951_1]) ).

cnf(f_4951_3,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20659),U_20660),U_20661))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20659),hAPP(c_Groups_Ouminus__class_Ouminus(U_20659),U_20660)),U_20661))
    | ~ class_Rings_Ocomm__ring__1(U_20659) ),
    inference(clausify,[status(thm)],[f_4951_2]) ).

cnf(f_4951_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20659),hAPP(c_Groups_Ouminus__class_Ouminus(U_20659),U_20660)),U_20661))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20659),U_20660),U_20661))
    | ~ class_Rings_Ocomm__ring__1(U_20659) ),
    inference(clausify,[status(thm)],[f_4951_2]) ).

fof(f_4952_1,plain,
    ! [V_n,V_m,V_k] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m)) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__diff__nat]) ).

fof(f_4952_2,plain,
    ! [U_20664,U_20663,U_20662] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20662),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_20663),U_20664)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20662),U_20664))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20662),U_20663)) ),
    inference(variable_rename,[status(thm)],[f_4952_1]) ).

cnf(f_4952_3,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20662),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_20663),U_20664)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20662),U_20664))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20662),U_20663)) ),
    inference(clausify,[status(thm)],[f_4952_2]) ).

fof(f_4953_1,plain,
    ! [V_z,V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_y),V_z)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_z))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y))
      | ~ class_Rings_Ocomm__ring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__diff]) ).

fof(f_4953_2,plain,
    ! [U_20668,U_20667,U_20666,U_20665] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20665),U_20666),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_20665),U_20667),U_20668)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20665),U_20666),U_20668))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20665),U_20666),U_20667))
      | ~ class_Rings_Ocomm__ring__1(U_20665) ),
    inference(variable_rename,[status(thm)],[f_4953_1]) ).

cnf(f_4953_3,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20665),U_20666),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_20665),U_20667),U_20668)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20665),U_20666),U_20668))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20665),U_20666),U_20667))
    | ~ class_Rings_Ocomm__ring__1(U_20665) ),
    inference(clausify,[status(thm)],[f_4953_2]) ).

fof(f_4954_1,plain,
    ! [V_n,V_x,V_y,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),V_y)),V_n) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_div__power]) ).

fof(f_4954_2,plain,
    ! [U_20672,U_20671,U_20670,U_20669] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_20669),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_20669),U_20671),U_20670)),U_20672) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_20669),hAPP(hAPP(c_Power_Opower__class_Opower(U_20669),U_20671),U_20672)),hAPP(hAPP(c_Power_Opower__class_Opower(U_20669),U_20670),U_20672))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20669),U_20670),U_20671))
      | ~ class_Divides_Osemiring__div(U_20669) ),
    inference(variable_rename,[status(thm)],[f_4954_1]) ).

cnf(f_4954_3,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_20669),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_20669),U_20671),U_20670)),U_20672) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_20669),hAPP(hAPP(c_Power_Opower__class_Opower(U_20669),U_20671),U_20672)),hAPP(hAPP(c_Power_Opower__class_Opower(U_20669),U_20670),U_20672))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20669),U_20670),U_20671))
    | ~ class_Divides_Osemiring__div(U_20669) ),
    inference(clausify,[status(thm)],[f_4954_2]) ).

fof(f_4955_1,plain,
    ! [V_b,V_a,T_a] :
      ( c_Divides_Odiv__class_Omod(T_a,V_b,V_a) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__imp__mod__0]) ).

fof(f_4955_2,plain,
    ! [U_20675,U_20674,U_20673] :
      ( c_Divides_Odiv__class_Omod(U_20673,U_20675,U_20674) = c_Groups_Ozero__class_Ozero(U_20673)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20673),U_20674),U_20675))
      | ~ class_Divides_Osemiring__div(U_20673) ),
    inference(variable_rename,[status(thm)],[f_4955_1]) ).

cnf(f_4955_3,plain,
    ( c_Divides_Odiv__class_Omod(U_20673,U_20675,U_20674) = c_Groups_Ozero__class_Ozero(U_20673)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20673),U_20674),U_20675))
    | ~ class_Divides_Osemiring__div(U_20673) ),
    inference(clausify,[status(thm)],[f_4955_2]) ).

fof(f_4956_1,plain,
    ! [V_b_2,V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
          | c_Divides_Odiv__class_Omod(T_b,V_b_2,V_a_2) != c_Groups_Ozero__class_Ozero(T_b) )
        & ( c_Divides_Odiv__class_Omod(T_b,V_b_2,V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2)) ) )
      | ~ class_Divides_Osemiring__div(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__eq__mod__eq__0]) ).

fof(f_4956_2,plain,
    ! [U_20678,U_20677,U_20676] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20676),U_20677),U_20678))
          | c_Divides_Odiv__class_Omod(U_20676,U_20678,U_20677) != c_Groups_Ozero__class_Ozero(U_20676) )
        & ( c_Divides_Odiv__class_Omod(U_20676,U_20678,U_20677) = c_Groups_Ozero__class_Ozero(U_20676)
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20676),U_20677),U_20678)) ) )
      | ~ class_Divides_Osemiring__div(U_20676) ),
    inference(variable_rename,[status(thm)],[f_4956_1]) ).

cnf(f_4956_3,plain,
    ( c_Divides_Odiv__class_Omod(U_20676,U_20678,U_20677) = c_Groups_Ozero__class_Ozero(U_20676)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20676),U_20677),U_20678))
    | ~ class_Divides_Osemiring__div(U_20676) ),
    inference(clausify,[status(thm)],[f_4956_2]) ).

cnf(f_4956_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20676),U_20677),U_20678))
    | c_Divides_Odiv__class_Omod(U_20676,U_20678,U_20677) != c_Groups_Ozero__class_Ozero(U_20676)
    | ~ class_Divides_Osemiring__div(U_20676) ),
    inference(clausify,[status(thm)],[f_4956_2]) ).

fof(f_4957_1,plain,
    ! [V_m_2,V_n_2,V_k_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),c_Divides_Odiv__class_Omod(T_b,V_m_2,V_n_2)))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),V_m_2)) )
        & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),V_m_2))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),c_Divides_Odiv__class_Omod(T_b,V_m_2,V_n_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),V_n_2))
      | ~ class_Divides_Osemiring__div(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__mod__iff]) ).

fof(f_4957_2,plain,
    ! [U_20682,U_20681,U_20680,U_20679] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20679),U_20680),c_Divides_Odiv__class_Omod(U_20679,U_20682,U_20681)))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20679),U_20680),U_20682)) )
        & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20679),U_20680),U_20682))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20679),U_20680),c_Divides_Odiv__class_Omod(U_20679,U_20682,U_20681))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20679),U_20680),U_20681))
      | ~ class_Divides_Osemiring__div(U_20679) ),
    inference(variable_rename,[status(thm)],[f_4957_1]) ).

cnf(f_4957_3,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20679),U_20680),U_20682))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20679),U_20680),c_Divides_Odiv__class_Omod(U_20679,U_20682,U_20681)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20679),U_20680),U_20681))
    | ~ class_Divides_Osemiring__div(U_20679) ),
    inference(clausify,[status(thm)],[f_4957_2]) ).

cnf(f_4957_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20679),U_20680),c_Divides_Odiv__class_Omod(U_20679,U_20682,U_20681)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20679),U_20680),U_20682))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20679),U_20680),U_20681))
    | ~ class_Divides_Osemiring__div(U_20679) ),
    inference(clausify,[status(thm)],[f_4957_2]) ).

fof(f_4958_1,plain,
    ! [V_a,V_b,V_c,T_a] :
      ( c_Divides_Odiv__class_Omod(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,V_a,V_c)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_b))
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mod__mod__cancel]) ).

fof(f_4958_2,plain,
    ! [U_20686,U_20685,U_20684,U_20683] :
      ( c_Divides_Odiv__class_Omod(U_20683,c_Divides_Odiv__class_Omod(U_20683,U_20686,U_20685),U_20684) = c_Divides_Odiv__class_Omod(U_20683,U_20686,U_20684)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20683),U_20684),U_20685))
      | ~ class_Divides_Osemiring__div(U_20683) ),
    inference(variable_rename,[status(thm)],[f_4958_1]) ).

cnf(f_4958_3,plain,
    ( c_Divides_Odiv__class_Omod(U_20683,c_Divides_Odiv__class_Omod(U_20683,U_20686,U_20685),U_20684) = c_Divides_Odiv__class_Omod(U_20683,U_20686,U_20684)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20683),U_20684),U_20685))
    | ~ class_Divides_Osemiring__div(U_20683) ),
    inference(clausify,[status(thm)],[f_4958_2]) ).

fof(f_4959_1,plain,
    ! [V_n,V_m,V_k,T_a] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),c_Divides_Odiv__class_Omod(T_a,V_m,V_n)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_m))
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__mod]) ).

fof(f_4959_2,plain,
    ! [U_20690,U_20689,U_20688,U_20687] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20687),U_20688),c_Divides_Odiv__class_Omod(U_20687,U_20689,U_20690)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20687),U_20688),U_20690))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20687),U_20688),U_20689))
      | ~ class_Divides_Osemiring__div(U_20687) ),
    inference(variable_rename,[status(thm)],[f_4959_1]) ).

cnf(f_4959_3,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20687),U_20688),c_Divides_Odiv__class_Omod(U_20687,U_20689,U_20690)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20687),U_20688),U_20690))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20687),U_20688),U_20689))
    | ~ class_Divides_Osemiring__div(U_20687) ),
    inference(clausify,[status(thm)],[f_4959_2]) ).

fof(f_4960_1,plain,
    ! [V_n,V_m,V_k,T_a] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_m))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_n))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),c_Divides_Odiv__class_Omod(T_a,V_m,V_n)))
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__mod__imp__dvd]) ).

fof(f_4960_2,plain,
    ! [U_20694,U_20693,U_20692,U_20691] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20691),U_20692),U_20693))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20691),U_20692),U_20694))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20691),U_20692),c_Divides_Odiv__class_Omod(U_20691,U_20693,U_20694)))
      | ~ class_Divides_Osemiring__div(U_20691) ),
    inference(variable_rename,[status(thm)],[f_4960_1]) ).

cnf(f_4960_3,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20691),U_20692),U_20693))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20691),U_20692),U_20694))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20691),U_20692),c_Divides_Odiv__class_Omod(U_20691,U_20693,U_20694)))
    | ~ class_Divides_Osemiring__div(U_20691) ),
    inference(clausify,[status(thm)],[f_4960_2]) ).

fof(f_4961_1,plain,
    ! [V_a,T_a] :
      ( V_a = c_Groups_Ozero__class_Ozero(T_a)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__0__left]) ).

fof(f_4961_2,plain,
    ! [U_20696,U_20695] :
      ( U_20696 = c_Groups_Ozero__class_Ozero(U_20695)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20695),c_Groups_Ozero__class_Ozero(U_20695)),U_20696))
      | ~ class_Rings_Ocomm__semiring__1(U_20695) ),
    inference(variable_rename,[status(thm)],[f_4961_1]) ).

cnf(f_4961_3,plain,
    ( U_20696 = c_Groups_Ozero__class_Ozero(U_20695)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20695),c_Groups_Ozero__class_Ozero(U_20695)),U_20696))
    | ~ class_Rings_Ocomm__semiring__1(U_20695) ),
    inference(clausify,[status(thm)],[f_4961_2]) ).

fof(f_4962_1,plain,
    ! [V_c_2,V_b_2,V_a_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_b_2),V_a_2)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_c_2),V_a_2)))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_b_2),V_c_2)) )
        & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_b_2),V_c_2))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_b_2),V_a_2)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_c_2),V_a_2))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_c_2))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
      | ~ class_Divides_Osemiring__div(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_div__dvd__div]) ).

fof(f_4962_2,plain,
    ! [U_20700,U_20699,U_20698,U_20697] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20697),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_20697),U_20699),U_20698)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_20697),U_20700),U_20698)))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20697),U_20699),U_20700)) )
        & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20697),U_20699),U_20700))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20697),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_20697),U_20699),U_20698)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_20697),U_20700),U_20698))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20697),U_20698),U_20700))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20697),U_20698),U_20699))
      | ~ class_Divides_Osemiring__div(U_20697) ),
    inference(variable_rename,[status(thm)],[f_4962_1]) ).

cnf(f_4962_3,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20697),U_20699),U_20700))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20697),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_20697),U_20699),U_20698)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_20697),U_20700),U_20698)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20697),U_20698),U_20700))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20697),U_20698),U_20699))
    | ~ class_Divides_Osemiring__div(U_20697) ),
    inference(clausify,[status(thm)],[f_4962_2]) ).

cnf(f_4962_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20697),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_20697),U_20699),U_20698)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_20697),U_20700),U_20698)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20697),U_20699),U_20700))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20697),U_20698),U_20700))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20697),U_20698),U_20699))
    | ~ class_Divides_Osemiring__div(U_20697) ),
    inference(clausify,[status(thm)],[f_4962_2]) ).

fof(f_4963_1,plain,
    ! [V_n,V_y,V_x,T_a] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_n)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__power__same]) ).

fof(f_4963_2,plain,
    ! [U_20704,U_20703,U_20702,U_20701] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20701),hAPP(hAPP(c_Power_Opower__class_Opower(U_20701),U_20702),U_20704)),hAPP(hAPP(c_Power_Opower__class_Opower(U_20701),U_20703),U_20704)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20701),U_20702),U_20703))
      | ~ class_Rings_Ocomm__semiring__1(U_20701) ),
    inference(variable_rename,[status(thm)],[f_4963_1]) ).

cnf(f_4963_3,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20701),hAPP(hAPP(c_Power_Opower__class_Opower(U_20701),U_20702),U_20704)),hAPP(hAPP(c_Power_Opower__class_Opower(U_20701),U_20703),U_20704)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20701),U_20702),U_20703))
    | ~ class_Rings_Ocomm__semiring__1(U_20701) ),
    inference(clausify,[status(thm)],[f_4963_2]) ).

fof(f_4964_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_c))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__trans]) ).

fof(f_4964_2,plain,
    ! [U_20708,U_20707,U_20706,U_20705] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20705),U_20706),U_20708))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20705),U_20707),U_20708))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20705),U_20706),U_20707))
      | ~ class_Rings_Ocomm__semiring__1(U_20705) ),
    inference(variable_rename,[status(thm)],[f_4964_1]) ).

cnf(f_4964_3,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20705),U_20706),U_20708))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20705),U_20707),U_20708))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20705),U_20706),U_20707))
    | ~ class_Rings_Ocomm__semiring__1(U_20705) ),
    inference(clausify,[status(thm)],[f_4964_2]) ).

fof(f_4965_1,plain,
    ! [V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_a))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__refl]) ).

fof(f_4965_2,plain,
    ! [U_20710,U_20709] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20709),U_20710),U_20710))
      | ~ class_Rings_Ocomm__semiring__1(U_20709) ),
    inference(variable_rename,[status(thm)],[f_4965_1]) ).

cnf(f_4965_3,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_20709),U_20710),U_20710))
    | ~ class_Rings_Ocomm__semiring__1(U_20709) ),
    inference(clausify,[status(thm)],[f_4965_2]) ).

fof(f_4966_1,plain,
    ! [V_y,V_x] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Oless__asym]) ).

fof(f_4966_2,plain,
    ! [U_20712,U_20711] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20711),U_20712))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20712),U_20711))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20712),U_20711))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20711),U_20712)) ),
    inference(variable_rename,[status(thm)],[f_4966_1]) ).

cnf(f_4966_3,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20711),U_20712))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20712),U_20711))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20712),U_20711))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20711),U_20712)) ),
    inference(clausify,[status(thm)],[f_4966_2]) ).

fof(f_4967_1,plain,
    ! [V_z,V_y,V_x] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z)) )
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Oless__trans]) ).

fof(f_4967_2,plain,
    ! [U_20715,U_20714,U_20713] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20715),U_20713))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20713),U_20715)) )
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20715),U_20714))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20714),U_20715))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20714),U_20713))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20713),U_20714)) ),
    inference(variable_rename,[status(thm)],[f_4967_1]) ).

cnf(f_4967_3,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20713),U_20715))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20715),U_20714))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20714),U_20715))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20714),U_20713))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20713),U_20714)) ),
    inference(clausify,[status(thm)],[f_4967_2]) ).

cnf(f_4967_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20715),U_20713))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20715),U_20714))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20714),U_20715))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20714),U_20713))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20713),U_20714)) ),
    inference(clausify,[status(thm)],[f_4967_2]) ).

fof(f_4968_1,plain,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Oless__asym_H]) ).

fof(f_4968_2,plain,
    ! [U_20717,U_20716] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20716),U_20717))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20717),U_20716))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20717),U_20716))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20716),U_20717)) ),
    inference(variable_rename,[status(thm)],[f_4968_1]) ).

cnf(f_4968_3,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20716),U_20717))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20717),U_20716))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20717),U_20716))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20716),U_20717)) ),
    inference(clausify,[status(thm)],[f_4968_2]) ).

fof(f_4969_1,plain,
    ! [V_z,V_y,V_x] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z)) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Oless__le__trans]) ).

fof(f_4969_2,plain,
    ! [U_20720,U_20719,U_20718] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20720),U_20718))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20718),U_20720)) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20719),U_20720))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20719),U_20718))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20718),U_20719)) ),
    inference(variable_rename,[status(thm)],[f_4969_1]) ).

cnf(f_4969_3,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20718),U_20720))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20719),U_20720))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20719),U_20718))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20718),U_20719)) ),
    inference(clausify,[status(thm)],[f_4969_2]) ).

cnf(f_4969_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20720),U_20718))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20719),U_20720))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20719),U_20718))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20718),U_20719)) ),
    inference(clausify,[status(thm)],[f_4969_2]) ).

fof(f_4970_1,plain,
    ! [V_c,V_b,V_a] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_a))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)) )
      | V_b != V_c
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Oord__less__eq__trans]) ).

fof(f_4970_2,plain,
    ! [U_20723,U_20722,U_20721] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20723),U_20721))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20721),U_20723)) )
      | U_20722 != U_20723
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20722),U_20721))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20721),U_20722)) ),
    inference(variable_rename,[status(thm)],[f_4970_1]) ).

cnf(f_4970_3,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20721),U_20723))
    | U_20722 != U_20723
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20722),U_20721))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20721),U_20722)) ),
    inference(clausify,[status(thm)],[f_4970_2]) ).

cnf(f_4970_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20723),U_20721))
    | U_20722 != U_20723
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20722),U_20721))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20721),U_20722)) ),
    inference(clausify,[status(thm)],[f_4970_2]) ).

fof(f_4971_1,plain,
    ! [V_y,V_x] :
      ( V_y != V_x
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Oless__imp__not__eq2]) ).

fof(f_4971_2,plain,
    ! [U_20725,U_20724] :
      ( U_20725 != U_20724
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20725),U_20724))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20724),U_20725)) ),
    inference(variable_rename,[status(thm)],[f_4971_1]) ).

cnf(f_4971_3,plain,
    ( U_20725 != U_20724
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20725),U_20724))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20724),U_20725)) ),
    inference(clausify,[status(thm)],[f_4971_2]) ).

fof(f_4972_1,plain,
    ! [V_y,V_x] :
      ( V_x != V_y
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Oless__imp__not__eq]) ).

fof(f_4972_2,plain,
    ! [U_20727,U_20726] :
      ( U_20726 != U_20727
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20727),U_20726))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20726),U_20727)) ),
    inference(variable_rename,[status(thm)],[f_4972_1]) ).

cnf(f_4972_3,plain,
    ( U_20726 != U_20727
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20727),U_20726))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20726),U_20727)) ),
    inference(clausify,[status(thm)],[f_4972_2]) ).

fof(f_4973_1,plain,
    ! [V_y,V_x] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Oless__imp__not__less]) ).

fof(f_4973_2,plain,
    ! [U_20729,U_20728] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20728),U_20729))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20729),U_20728))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20729),U_20728))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20728),U_20729)) ),
    inference(variable_rename,[status(thm)],[f_4973_1]) ).

cnf(f_4973_3,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20728),U_20729))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20729),U_20728))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20729),U_20728))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20728),U_20729)) ),
    inference(clausify,[status(thm)],[f_4973_2]) ).

fof(f_4974_1,plain,
    ! [V_y,V_x] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Oless__imp__le]) ).

fof(f_4974_2,plain,
    ! [U_20731,U_20730] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20730),U_20731))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20731),U_20730))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20730),U_20731)) ),
    inference(variable_rename,[status(thm)],[f_4974_1]) ).

cnf(f_4974_3,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20730),U_20731))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20731),U_20730))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20730),U_20731)) ),
    inference(clausify,[status(thm)],[f_4974_2]) ).

fof(f_4975_1,plain,
    ! [V_y,V_x] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Oless__not__sym]) ).

fof(f_4975_2,plain,
    ! [U_20733,U_20732] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20732),U_20733))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20733),U_20732))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20733),U_20732))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20732),U_20733)) ),
    inference(variable_rename,[status(thm)],[f_4975_1]) ).

cnf(f_4975_3,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20732),U_20733))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20733),U_20732))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20733),U_20732))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20732),U_20733)) ),
    inference(clausify,[status(thm)],[f_4975_2]) ).

fof(f_4976_1,plain,
    ! [V_y,V_x] :
      ( V_x != V_y
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Oless__imp__neq]) ).

fof(f_4976_2,plain,
    ! [U_20735,U_20734] :
      ( U_20734 != U_20735
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20735),U_20734))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20734),U_20735)) ),
    inference(variable_rename,[status(thm)],[f_4976_1]) ).

cnf(f_4976_3,plain,
    ( U_20734 != U_20735
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20735),U_20734))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20734),U_20735)) ),
    inference(clausify,[status(thm)],[f_4976_2]) ).

fof(f_4977_1,plain,
    ! [V_z,V_y,V_x] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z)) )
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_y))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Ole__less__trans]) ).

fof(f_4977_2,plain,
    ! [U_20738,U_20737,U_20736] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20738),U_20736))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20736),U_20738)) )
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20738),U_20737))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20737),U_20738))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20736),U_20737)) ),
    inference(variable_rename,[status(thm)],[f_4977_1]) ).

cnf(f_4977_3,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20736),U_20738))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20738),U_20737))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20737),U_20738))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20736),U_20737)) ),
    inference(clausify,[status(thm)],[f_4977_2]) ).

cnf(f_4977_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20738),U_20736))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20738),U_20737))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20737),U_20738))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20736),U_20737)) ),
    inference(clausify,[status(thm)],[f_4977_2]) ).

fof(f_4978_1,plain,
    ! [V_c,V_b,V_a] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_a))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)) )
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_b))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_c))
      | V_a != V_b ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Oord__eq__less__trans]) ).

fof(f_4978_2,plain,
    ! [U_20741,U_20740,U_20739] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20741),U_20739))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20739),U_20741)) )
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20741),U_20740))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20740),U_20741))
      | U_20739 != U_20740 ),
    inference(variable_rename,[status(thm)],[f_4978_1]) ).

cnf(f_4978_3,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20739),U_20741))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20741),U_20740))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20740),U_20741))
    | U_20739 != U_20740 ),
    inference(clausify,[status(thm)],[f_4978_2]) ).

cnf(f_4978_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20741),U_20739))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20741),U_20740))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20740),U_20741))
    | U_20739 != U_20740 ),
    inference(clausify,[status(thm)],[f_4978_2]) ).

fof(f_4979_1,plain,
    ! [V_z,V_y,V_x] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Oorder__trans]) ).

fof(f_4979_2,plain,
    ! [U_20744,U_20743,U_20742] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20742),U_20744))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20743),U_20744))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20742),U_20743)) ),
    inference(variable_rename,[status(thm)],[f_4979_1]) ).

cnf(f_4979_3,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20742),U_20744))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20743),U_20744))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20742),U_20743)) ),
    inference(clausify,[status(thm)],[f_4979_2]) ).

fof(f_4980_1,plain,
    ! [V_y,V_x] :
      ( V_x = V_y
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Oantisym]) ).

fof(f_4980_2,plain,
    ! [U_20746,U_20745] :
      ( U_20745 = U_20746
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20746),U_20745))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20745),U_20746)) ),
    inference(variable_rename,[status(thm)],[f_4980_1]) ).

cnf(f_4980_3,plain,
    ( U_20745 = U_20746
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20746),U_20745))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20745),U_20746)) ),
    inference(clausify,[status(thm)],[f_4980_2]) ).

fof(f_4981_1,plain,
    ! [V_n,V_m] :
      ( V_m = V_n
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_n),V_m))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__antisym]) ).

fof(f_4981_2,plain,
    ! [U_20748,U_20747] :
      ( U_20747 = U_20748
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20748),U_20747))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20747),U_20748)) ),
    inference(variable_rename,[status(thm)],[f_4981_1]) ).

cnf(f_4981_3,plain,
    ( U_20747 = U_20748
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20748),U_20747))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20747),U_20748)) ),
    inference(clausify,[status(thm)],[f_4981_2]) ).

fof(f_4982_1,plain,
    ! [V_c,V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c))
      | V_b != V_c
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Oord__le__eq__trans]) ).

fof(f_4982_2,plain,
    ! [U_20751,U_20750,U_20749] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20749),U_20751))
      | U_20750 != U_20751
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20749),U_20750)) ),
    inference(variable_rename,[status(thm)],[f_4982_1]) ).

cnf(f_4982_3,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20749),U_20751))
    | U_20750 != U_20751
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20749),U_20750)) ),
    inference(clausify,[status(thm)],[f_4982_2]) ).

fof(f_4983_1,plain,
    ! [V_c,V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_c))
      | V_a != V_b ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Oord__eq__le__trans]) ).

fof(f_4983_2,plain,
    ! [U_20754,U_20753,U_20752] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20752),U_20754))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20753),U_20754))
      | U_20752 != U_20753 ),
    inference(variable_rename,[status(thm)],[f_4983_1]) ).

cnf(f_4983_3,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20752),U_20754))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20753),U_20754))
    | U_20752 != U_20753 ),
    inference(clausify,[status(thm)],[f_4983_2]) ).

fof(f_4984_1,plain,
    ! [V_b,V_a] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) )
      | V_a = V_b
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Ole__neq__trans]) ).

fof(f_4984_2,plain,
    ! [U_20756,U_20755] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20756),U_20755))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20755),U_20756)) )
      | U_20755 = U_20756
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20755),U_20756)) ),
    inference(variable_rename,[status(thm)],[f_4984_1]) ).

cnf(f_4984_3,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20755),U_20756))
    | U_20755 = U_20756
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20755),U_20756)) ),
    inference(clausify,[status(thm)],[f_4984_2]) ).

cnf(f_4984_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20756),U_20755))
    | U_20755 = U_20756
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20755),U_20756)) ),
    inference(clausify,[status(thm)],[f_4984_2]) ).

fof(f_4985_1,plain,
    ! [V_y,V_x] :
      ( V_x = V_y
      | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Ole__imp__less__or__eq]) ).

fof(f_4985_2,plain,
    ! [U_20758,U_20757] :
      ( U_20757 = U_20758
      | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20758),U_20757))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20757),U_20758)) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20757),U_20758)) ),
    inference(variable_rename,[status(thm)],[f_4985_1]) ).

cnf(f_4985_3,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20757),U_20758))
    | U_20757 = U_20758
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20757),U_20758)) ),
    inference(clausify,[status(thm)],[f_4985_2]) ).

cnf(f_4985_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20758),U_20757))
    | U_20757 = U_20758
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_20757),U_20758)) ),
    inference(clausify,[status(thm)],[f_4985_2]) ).

fof(f_4986_1,plain,
    class_Lattices_Obounded__lattice(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Lattices_Obounded__lattice]) ).

cnf(f_4986_2,plain,
    class_Lattices_Obounded__lattice(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_4986_1]) ).

fof(f_4987_1,plain,
    ! [T_2,T_1] :
      ( class_Lattices_Obounded__lattice(tc_fun(T_2,T_1))
      | ~ class_Lattices_Obounded__lattice(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Obounded__lattice]) ).

fof(f_4987_2,plain,
    ! [U_20760,U_20759] :
      ( class_Lattices_Obounded__lattice(tc_fun(U_20760,U_20759))
      | ~ class_Lattices_Obounded__lattice(U_20759) ),
    inference(variable_rename,[status(thm)],[f_4987_1]) ).

cnf(f_4987_3,plain,
    ( class_Lattices_Obounded__lattice(tc_fun(U_20760,U_20759))
    | ~ class_Lattices_Obounded__lattice(U_20759) ),
    inference(clausify,[status(thm)],[f_4987_2]) ).

fof(f_4988_1,plain,
    ! [T_2,T_1] :
      ( class_Complete__Lattice_Ocomplete__lattice(tc_fun(T_2,T_1))
      | ~ class_Complete__Lattice_Ocomplete__lattice(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_fun__Complete__Lattice_Ocomplete__lattice]) ).

fof(f_4988_2,plain,
    ! [U_20762,U_20761] :
      ( class_Complete__Lattice_Ocomplete__lattice(tc_fun(U_20762,U_20761))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_20761) ),
    inference(variable_rename,[status(thm)],[f_4988_1]) ).

cnf(f_4988_3,plain,
    ( class_Complete__Lattice_Ocomplete__lattice(tc_fun(U_20762,U_20761))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_20761) ),
    inference(clausify,[status(thm)],[f_4988_2]) ).

fof(f_4989_1,plain,
    ! [T_2,T_1] :
      ( class_Lattices_Obounded__lattice__top(tc_fun(T_2,T_1))
      | ~ class_Lattices_Obounded__lattice(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Obounded__lattice__top]) ).

fof(f_4989_2,plain,
    ! [U_20764,U_20763] :
      ( class_Lattices_Obounded__lattice__top(tc_fun(U_20764,U_20763))
      | ~ class_Lattices_Obounded__lattice(U_20763) ),
    inference(variable_rename,[status(thm)],[f_4989_1]) ).

cnf(f_4989_3,plain,
    ( class_Lattices_Obounded__lattice__top(tc_fun(U_20764,U_20763))
    | ~ class_Lattices_Obounded__lattice(U_20763) ),
    inference(clausify,[status(thm)],[f_4989_2]) ).

fof(f_4990_1,plain,
    ! [T_2,T_1] :
      ( class_Lattices_Obounded__lattice__bot(tc_fun(T_2,T_1))
      | ~ class_Lattices_Obounded__lattice(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Obounded__lattice__bot]) ).

fof(f_4990_2,plain,
    ! [U_20766,U_20765] :
      ( class_Lattices_Obounded__lattice__bot(tc_fun(U_20766,U_20765))
      | ~ class_Lattices_Obounded__lattice(U_20765) ),
    inference(variable_rename,[status(thm)],[f_4990_1]) ).

cnf(f_4990_3,plain,
    ( class_Lattices_Obounded__lattice__bot(tc_fun(U_20766,U_20765))
    | ~ class_Lattices_Obounded__lattice(U_20765) ),
    inference(clausify,[status(thm)],[f_4990_2]) ).

fof(f_4991_1,plain,
    ! [T_2,T_1] :
      ( class_Lattices_Osemilattice__sup(tc_fun(T_2,T_1))
      | ~ class_Lattices_Olattice(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Osemilattice__sup]) ).

fof(f_4991_2,plain,
    ! [U_20768,U_20767] :
      ( class_Lattices_Osemilattice__sup(tc_fun(U_20768,U_20767))
      | ~ class_Lattices_Olattice(U_20767) ),
    inference(variable_rename,[status(thm)],[f_4991_1]) ).

cnf(f_4991_3,plain,
    ( class_Lattices_Osemilattice__sup(tc_fun(U_20768,U_20767))
    | ~ class_Lattices_Olattice(U_20767) ),
    inference(clausify,[status(thm)],[f_4991_2]) ).

fof(f_4992_1,plain,
    ! [T_2,T_1] :
      ( class_Lattices_Osemilattice__inf(tc_fun(T_2,T_1))
      | ~ class_Lattices_Olattice(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Osemilattice__inf]) ).

fof(f_4992_2,plain,
    ! [U_20770,U_20769] :
      ( class_Lattices_Osemilattice__inf(tc_fun(U_20770,U_20769))
      | ~ class_Lattices_Olattice(U_20769) ),
    inference(variable_rename,[status(thm)],[f_4992_1]) ).

cnf(f_4992_3,plain,
    ( class_Lattices_Osemilattice__inf(tc_fun(U_20770,U_20769))
    | ~ class_Lattices_Olattice(U_20769) ),
    inference(clausify,[status(thm)],[f_4992_2]) ).

fof(f_4993_1,plain,
    ! [T_2,T_1] :
      ( class_Lattices_Odistrib__lattice(tc_fun(T_2,T_1))
      | ~ class_Lattices_Odistrib__lattice(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Odistrib__lattice]) ).

fof(f_4993_2,plain,
    ! [U_20772,U_20771] :
      ( class_Lattices_Odistrib__lattice(tc_fun(U_20772,U_20771))
      | ~ class_Lattices_Odistrib__lattice(U_20771) ),
    inference(variable_rename,[status(thm)],[f_4993_1]) ).

cnf(f_4993_3,plain,
    ( class_Lattices_Odistrib__lattice(tc_fun(U_20772,U_20771))
    | ~ class_Lattices_Odistrib__lattice(U_20771) ),
    inference(clausify,[status(thm)],[f_4993_2]) ).

fof(f_4994_1,plain,
    ! [T_2,T_1] :
      ( class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1))
      | ~ class_Lattices_Oboolean__algebra(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Oboolean__algebra]) ).

fof(f_4994_2,plain,
    ! [U_20774,U_20773] :
      ( class_Lattices_Oboolean__algebra(tc_fun(U_20774,U_20773))
      | ~ class_Lattices_Oboolean__algebra(U_20773) ),
    inference(variable_rename,[status(thm)],[f_4994_1]) ).

cnf(f_4994_3,plain,
    ( class_Lattices_Oboolean__algebra(tc_fun(U_20774,U_20773))
    | ~ class_Lattices_Oboolean__algebra(U_20773) ),
    inference(clausify,[status(thm)],[f_4994_2]) ).

fof(f_4995_1,plain,
    ! [T_2,T_1] :
      ( class_Orderings_Opreorder(tc_fun(T_2,T_1))
      | ~ class_Orderings_Opreorder(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Opreorder]) ).

fof(f_4995_2,plain,
    ! [U_20776,U_20775] :
      ( class_Orderings_Opreorder(tc_fun(U_20776,U_20775))
      | ~ class_Orderings_Opreorder(U_20775) ),
    inference(variable_rename,[status(thm)],[f_4995_1]) ).

cnf(f_4995_3,plain,
    ( class_Orderings_Opreorder(tc_fun(U_20776,U_20775))
    | ~ class_Orderings_Opreorder(U_20775) ),
    inference(clausify,[status(thm)],[f_4995_2]) ).

fof(f_4996_1,plain,
    ! [T_1,T_2] :
      ( class_Finite__Set_Ofinite(tc_fun(T_2,T_1))
      | ~ class_Finite__Set_Ofinite(T_1)
      | ~ class_Finite__Set_Ofinite(T_2) ),
    inference(fof_nnf,[status(thm)],[arity_fun__Finite__Set_Ofinite]) ).

fof(f_4996_2,plain,
    ! [U_20778,U_20777] :
      ( class_Finite__Set_Ofinite(tc_fun(U_20777,U_20778))
      | ~ class_Finite__Set_Ofinite(U_20778)
      | ~ class_Finite__Set_Ofinite(U_20777) ),
    inference(variable_rename,[status(thm)],[f_4996_1]) ).

cnf(f_4996_3,plain,
    ( class_Finite__Set_Ofinite(tc_fun(U_20777,U_20778))
    | ~ class_Finite__Set_Ofinite(U_20778)
    | ~ class_Finite__Set_Ofinite(U_20777) ),
    inference(clausify,[status(thm)],[f_4996_2]) ).

fof(f_4997_1,plain,
    ! [T_2,T_1] :
      ( class_Lattices_Olattice(tc_fun(T_2,T_1))
      | ~ class_Lattices_Olattice(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Olattice]) ).

fof(f_4997_2,plain,
    ! [U_20780,U_20779] :
      ( class_Lattices_Olattice(tc_fun(U_20780,U_20779))
      | ~ class_Lattices_Olattice(U_20779) ),
    inference(variable_rename,[status(thm)],[f_4997_1]) ).

cnf(f_4997_3,plain,
    ( class_Lattices_Olattice(tc_fun(U_20780,U_20779))
    | ~ class_Lattices_Olattice(U_20779) ),
    inference(clausify,[status(thm)],[f_4997_2]) ).

fof(f_4998_1,plain,
    ! [T_2,T_1] :
      ( class_Orderings_Oorder(tc_fun(T_2,T_1))
      | ~ class_Orderings_Oorder(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oorder]) ).

fof(f_4998_2,plain,
    ! [U_20782,U_20781] :
      ( class_Orderings_Oorder(tc_fun(U_20782,U_20781))
      | ~ class_Orderings_Oorder(U_20781) ),
    inference(variable_rename,[status(thm)],[f_4998_1]) ).

cnf(f_4998_3,plain,
    ( class_Orderings_Oorder(tc_fun(U_20782,U_20781))
    | ~ class_Orderings_Oorder(U_20781) ),
    inference(clausify,[status(thm)],[f_4998_2]) ).

fof(f_4999_1,plain,
    ! [T_2,T_1] :
      ( class_Orderings_Otop(tc_fun(T_2,T_1))
      | ~ class_Orderings_Otop(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Otop]) ).

fof(f_4999_2,plain,
    ! [U_20784,U_20783] :
      ( class_Orderings_Otop(tc_fun(U_20784,U_20783))
      | ~ class_Orderings_Otop(U_20783) ),
    inference(variable_rename,[status(thm)],[f_4999_1]) ).

cnf(f_4999_3,plain,
    ( class_Orderings_Otop(tc_fun(U_20784,U_20783))
    | ~ class_Orderings_Otop(U_20783) ),
    inference(clausify,[status(thm)],[f_4999_2]) ).

fof(f_5000_1,plain,
    ! [T_2,T_1] :
      ( class_Orderings_Oord(tc_fun(T_2,T_1))
      | ~ class_Orderings_Oord(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oord]) ).

fof(f_5000_2,plain,
    ! [U_20786,U_20785] :
      ( class_Orderings_Oord(tc_fun(U_20786,U_20785))
      | ~ class_Orderings_Oord(U_20785) ),
    inference(variable_rename,[status(thm)],[f_5000_1]) ).

cnf(f_5000_3,plain,
    ( class_Orderings_Oord(tc_fun(U_20786,U_20785))
    | ~ class_Orderings_Oord(U_20785) ),
    inference(clausify,[status(thm)],[f_5000_2]) ).

fof(f_5001_1,plain,
    ! [T_2,T_1] :
      ( class_Orderings_Obot(tc_fun(T_2,T_1))
      | ~ class_Orderings_Obot(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Obot]) ).

fof(f_5001_2,plain,
    ! [U_20788,U_20787] :
      ( class_Orderings_Obot(tc_fun(U_20788,U_20787))
      | ~ class_Orderings_Obot(U_20787) ),
    inference(variable_rename,[status(thm)],[f_5001_1]) ).

cnf(f_5001_3,plain,
    ( class_Orderings_Obot(tc_fun(U_20788,U_20787))
    | ~ class_Orderings_Obot(U_20787) ),
    inference(clausify,[status(thm)],[f_5001_2]) ).

fof(f_5002_1,plain,
    ! [T_2,T_1] :
      ( class_Groups_Ouminus(tc_fun(T_2,T_1))
      | ~ class_Groups_Ouminus(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_fun__Groups_Ouminus]) ).

fof(f_5002_2,plain,
    ! [U_20790,U_20789] :
      ( class_Groups_Ouminus(tc_fun(U_20790,U_20789))
      | ~ class_Groups_Ouminus(U_20789) ),
    inference(variable_rename,[status(thm)],[f_5002_1]) ).

cnf(f_5002_3,plain,
    ( class_Groups_Ouminus(tc_fun(U_20790,U_20789))
    | ~ class_Groups_Ouminus(U_20789) ),
    inference(clausify,[status(thm)],[f_5002_2]) ).

fof(f_5003_1,plain,
    ! [T_2,T_1] :
      ( class_Groups_Ominus(tc_fun(T_2,T_1))
      | ~ class_Groups_Ominus(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_fun__Groups_Ominus]) ).

fof(f_5003_2,plain,
    ! [U_20792,U_20791] :
      ( class_Groups_Ominus(tc_fun(U_20792,U_20791))
      | ~ class_Groups_Ominus(U_20791) ),
    inference(variable_rename,[status(thm)],[f_5003_1]) ).

cnf(f_5003_3,plain,
    ( class_Groups_Ominus(tc_fun(U_20792,U_20791))
    | ~ class_Groups_Ominus(U_20791) ),
    inference(clausify,[status(thm)],[f_5003_2]) ).

fof(f_5004_1,plain,
    ! [T_1,T_2] :
      ( class_Enum_Oenum(tc_fun(T_2,T_1))
      | ~ class_Enum_Oenum(T_1)
      | ~ class_Enum_Oenum(T_2) ),
    inference(fof_nnf,[status(thm)],[arity_fun__Enum_Oenum]) ).

fof(f_5004_2,plain,
    ! [U_20794,U_20793] :
      ( class_Enum_Oenum(tc_fun(U_20793,U_20794))
      | ~ class_Enum_Oenum(U_20794)
      | ~ class_Enum_Oenum(U_20793) ),
    inference(variable_rename,[status(thm)],[f_5004_1]) ).

cnf(f_5004_3,plain,
    ( class_Enum_Oenum(tc_fun(U_20793,U_20794))
    | ~ class_Enum_Oenum(U_20794)
    | ~ class_Enum_Oenum(U_20793) ),
    inference(clausify,[status(thm)],[f_5004_2]) ).

fof(f_5005_1,plain,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct]) ).

cnf(f_5005_2,plain,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5005_1]) ).

fof(f_5006_1,plain,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add]) ).

cnf(f_5006_2,plain,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5006_1]) ).

fof(f_5007_1,plain,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le]) ).

cnf(f_5007_2,plain,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5007_1]) ).

fof(f_5008_1,plain,
    class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__comm__semiring__strict]) ).

cnf(f_5008_2,plain,
    class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5008_1]) ).

fof(f_5009_1,plain,
    class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring__1__strict]) ).

cnf(f_5009_2,plain,
    class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5009_1]) ).

fof(f_5010_1,plain,
    class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Olinordered__ab__semigroup__add]) ).

cnf(f_5010_2,plain,
    class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5010_1]) ).

fof(f_5011_1,plain,
    class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring__strict]) ).

cnf(f_5011_2,plain,
    class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5011_1]) ).

fof(f_5012_1,plain,
    class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oordered__ab__semigroup__add]) ).

cnf(f_5012_2,plain,
    class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5012_1]) ).

fof(f_5013_1,plain,
    class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oordered__ab__group__add__abs]) ).

cnf(f_5013_2,plain,
    class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5013_1]) ).

fof(f_5014_1,plain,
    class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oordered__comm__monoid__add]) ).

cnf(f_5014_2,plain,
    class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5014_1]) ).

fof(f_5015_1,plain,
    class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Olinordered__ab__group__add]) ).

cnf(f_5015_2,plain,
    class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5015_1]) ).

fof(f_5016_1,plain,
    class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ocancel__ab__semigroup__add]) ).

cnf(f_5016_2,plain,
    class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5016_1]) ).

fof(f_5017_1,plain,
    class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oring__1__no__zero__divisors]) ).

cnf(f_5017_2,plain,
    class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5017_1]) ).

fof(f_5018_1,plain,
    class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oordered__cancel__semiring]) ).

cnf(f_5018_2,plain,
    class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5018_1]) ).

fof(f_5019_1,plain,
    class_Rings_Olinordered__ring__strict(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__ring__strict]) ).

cnf(f_5019_2,plain,
    class_Rings_Olinordered__ring__strict(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5019_1]) ).

fof(f_5020_1,plain,
    class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oring__no__zero__divisors]) ).

cnf(f_5020_2,plain,
    class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5020_1]) ).

fof(f_5021_1,plain,
    class_Rings_Oordered__comm__semiring(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oordered__comm__semiring]) ).

cnf(f_5021_2,plain,
    class_Rings_Oordered__comm__semiring(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5021_1]) ).

fof(f_5022_1,plain,
    class_Rings_Olinordered__semiring__1(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring__1]) ).

cnf(f_5022_2,plain,
    class_Rings_Olinordered__semiring__1(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5022_1]) ).

fof(f_5023_1,plain,
    class_Groups_Oordered__ab__group__add(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oordered__ab__group__add]) ).

cnf(f_5023_2,plain,
    class_Groups_Oordered__ab__group__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5023_1]) ).

fof(f_5024_1,plain,
    class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ocancel__semigroup__add]) ).

cnf(f_5024_2,plain,
    class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5024_1]) ).

fof(f_5025_1,plain,
    class_Rings_Olinordered__semiring(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring]) ).

cnf(f_5025_2,plain,
    class_Rings_Olinordered__semiring(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5025_1]) ).

fof(f_5026_1,plain,
    class_Rings_Olinordered__semidom(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semidom]) ).

cnf(f_5026_2,plain,
    class_Rings_Olinordered__semidom(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5026_1]) ).

fof(f_5027_1,plain,
    class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Lazy__Sequence_Osmall__lazy]) ).

cnf(f_5027_2,plain,
    class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5027_1]) ).

fof(f_5028_1,plain,
    class_Lattices_Osemilattice__sup(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Lattices_Osemilattice__sup]) ).

cnf(f_5028_2,plain,
    class_Lattices_Osemilattice__sup(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5028_1]) ).

fof(f_5029_1,plain,
    class_Lattices_Osemilattice__inf(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Lattices_Osemilattice__inf]) ).

cnf(f_5029_2,plain,
    class_Lattices_Osemilattice__inf(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5029_1]) ).

fof(f_5030_1,plain,
    class_Lattices_Odistrib__lattice(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Lattices_Odistrib__lattice]) ).

cnf(f_5030_2,plain,
    class_Lattices_Odistrib__lattice(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5030_1]) ).

fof(f_5031_1,plain,
    class_Groups_Oab__semigroup__mult(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oab__semigroup__mult]) ).

cnf(f_5031_2,plain,
    class_Groups_Oab__semigroup__mult(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5031_1]) ).

fof(f_5032_1,plain,
    class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ocomm__monoid__mult]) ).

cnf(f_5032_2,plain,
    class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5032_1]) ).

fof(f_5033_1,plain,
    class_Groups_Oab__semigroup__add(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oab__semigroup__add]) ).

cnf(f_5033_2,plain,
    class_Groups_Oab__semigroup__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5033_1]) ).

fof(f_5034_1,plain,
    class_Rings_Oordered__semiring(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oordered__semiring]) ).

cnf(f_5034_2,plain,
    class_Rings_Oordered__semiring(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5034_1]) ).

fof(f_5035_1,plain,
    class_Rings_Oordered__ring__abs(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oordered__ring__abs]) ).

cnf(f_5035_2,plain,
    class_Rings_Oordered__ring__abs(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5035_1]) ).

fof(f_5036_1,plain,
    class_Rings_Ono__zero__divisors(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ono__zero__divisors]) ).

cnf(f_5036_2,plain,
    class_Rings_Ono__zero__divisors(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5036_1]) ).

fof(f_5037_1,plain,
    class_Groups_Ocomm__monoid__add(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ocomm__monoid__add]) ).

cnf(f_5037_2,plain,
    class_Groups_Ocomm__monoid__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5037_1]) ).

fof(f_5038_1,plain,
    class_Rings_Olinordered__ring(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__ring]) ).

cnf(f_5038_2,plain,
    class_Rings_Olinordered__ring(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5038_1]) ).

fof(f_5039_1,plain,
    class_Rings_Olinordered__idom(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__idom]) ).

cnf(f_5039_2,plain,
    class_Rings_Olinordered__idom(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5039_1]) ).

fof(f_5040_1,plain,
    class_Rings_Ocomm__semiring__1(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ocomm__semiring__1]) ).

cnf(f_5040_2,plain,
    class_Rings_Ocomm__semiring__1(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5040_1]) ).

fof(f_5041_1,plain,
    class_Groups_Osemigroup__add(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Osemigroup__add]) ).

cnf(f_5041_2,plain,
    class_Groups_Osemigroup__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5041_1]) ).

fof(f_5042_1,plain,
    class_Divides_Osemiring__div(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Divides_Osemiring__div]) ).

cnf(f_5042_2,plain,
    class_Divides_Osemiring__div(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5042_1]) ).

fof(f_5043_1,plain,
    class_Rings_Ocomm__semiring(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ocomm__semiring]) ).

cnf(f_5043_2,plain,
    class_Rings_Ocomm__semiring(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5043_1]) ).

fof(f_5044_1,plain,
    class_Nat_Osemiring__char__0(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Nat_Osemiring__char__0]) ).

cnf(f_5044_2,plain,
    class_Nat_Osemiring__char__0(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5044_1]) ).

fof(f_5045_1,plain,
    class_Groups_Oab__group__add(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oab__group__add]) ).

cnf(f_5045_2,plain,
    class_Groups_Oab__group__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5045_1]) ).

fof(f_5046_1,plain,
    class_Rings_Ozero__neq__one(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ozero__neq__one]) ).

cnf(f_5046_2,plain,
    class_Rings_Ozero__neq__one(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5046_1]) ).

fof(f_5047_1,plain,
    class_Rings_Oordered__ring(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oordered__ring]) ).

cnf(f_5047_2,plain,
    class_Rings_Oordered__ring(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5047_1]) ).

fof(f_5048_1,plain,
    class_Orderings_Opreorder(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Orderings_Opreorder]) ).

cnf(f_5048_2,plain,
    class_Orderings_Opreorder(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5048_1]) ).

fof(f_5049_1,plain,
    class_Orderings_Olinorder(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Orderings_Olinorder]) ).

cnf(f_5049_2,plain,
    class_Orderings_Olinorder(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5049_1]) ).

fof(f_5050_1,plain,
    class_Groups_Omonoid__mult(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Omonoid__mult]) ).

cnf(f_5050_2,plain,
    class_Groups_Omonoid__mult(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5050_1]) ).

fof(f_5051_1,plain,
    class_Rings_Ocomm__ring__1(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ocomm__ring__1]) ).

cnf(f_5051_2,plain,
    class_Rings_Ocomm__ring__1(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5051_1]) ).

fof(f_5052_1,plain,
    class_Groups_Omonoid__add(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Omonoid__add]) ).

cnf(f_5052_2,plain,
    class_Groups_Omonoid__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5052_1]) ).

fof(f_5053_1,plain,
    class_Rings_Osemiring__1(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Osemiring__1]) ).

cnf(f_5053_2,plain,
    class_Rings_Osemiring__1(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5053_1]) ).

fof(f_5054_1,plain,
    class_Rings_Osemiring__0(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Osemiring__0]) ).

cnf(f_5054_2,plain,
    class_Rings_Osemiring__0(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5054_1]) ).

fof(f_5055_1,plain,
    class_Lattices_Olattice(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Lattices_Olattice]) ).

cnf(f_5055_2,plain,
    class_Lattices_Olattice(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5055_1]) ).

fof(f_5056_1,plain,
    class_Groups_Ogroup__add(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ogroup__add]) ).

cnf(f_5056_2,plain,
    class_Groups_Ogroup__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5056_1]) ).

fof(f_5057_1,plain,
    class_Divides_Oring__div(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Divides_Oring__div]) ).

cnf(f_5057_2,plain,
    class_Divides_Oring__div(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5057_1]) ).

fof(f_5058_1,plain,
    class_Rings_Omult__zero(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Omult__zero]) ).

cnf(f_5058_2,plain,
    class_Rings_Omult__zero(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5058_1]) ).

fof(f_5059_1,plain,
    class_Orderings_Oorder(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Orderings_Oorder]) ).

cnf(f_5059_2,plain,
    class_Orderings_Oorder(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5059_1]) ).

fof(f_5060_1,plain,
    class_Int_Oring__char__0(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Int_Oring__char__0]) ).

cnf(f_5060_2,plain,
    class_Int_Oring__char__0(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5060_1]) ).

fof(f_5061_1,plain,
    class_Int_Onumber__ring(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Int_Onumber__ring]) ).

cnf(f_5061_2,plain,
    class_Int_Onumber__ring(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5061_1]) ).

fof(f_5062_1,plain,
    class_Rings_Osemiring(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Osemiring]) ).

cnf(f_5062_2,plain,
    class_Rings_Osemiring(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5062_1]) ).

fof(f_5063_1,plain,
    class_Orderings_Oord(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Orderings_Oord]) ).

cnf(f_5063_2,plain,
    class_Orderings_Oord(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5063_1]) ).

fof(f_5064_1,plain,
    class_Groups_Ouminus(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ouminus]) ).

cnf(f_5064_2,plain,
    class_Groups_Ouminus(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5064_1]) ).

fof(f_5065_1,plain,
    class_Groups_Osgn__if(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Osgn__if]) ).

cnf(f_5065_2,plain,
    class_Groups_Osgn__if(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5065_1]) ).

fof(f_5066_1,plain,
    class_Groups_Oabs__if(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oabs__if]) ).

cnf(f_5066_2,plain,
    class_Groups_Oabs__if(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5066_1]) ).

fof(f_5067_1,plain,
    class_Rings_Oring__1(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oring__1]) ).

cnf(f_5067_2,plain,
    class_Rings_Oring__1(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5067_1]) ).

fof(f_5068_1,plain,
    class_Groups_Ominus(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ominus]) ).

cnf(f_5068_2,plain,
    class_Groups_Ominus(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5068_1]) ).

fof(f_5069_1,plain,
    class_Power_Opower(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Power_Opower]) ).

cnf(f_5069_2,plain,
    class_Power_Opower(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5069_1]) ).

fof(f_5070_1,plain,
    class_Groups_Ozero(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ozero]) ).

cnf(f_5070_2,plain,
    class_Groups_Ozero(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5070_1]) ).

fof(f_5071_1,plain,
    class_Rings_Oring(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oring]) ).

cnf(f_5071_2,plain,
    class_Rings_Oring(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5071_1]) ).

fof(f_5072_1,plain,
    class_Rings_Oidom(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oidom]) ).

cnf(f_5072_2,plain,
    class_Rings_Oidom(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5072_1]) ).

fof(f_5073_1,plain,
    class_Int_Onumber(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Int_Onumber]) ).

cnf(f_5073_2,plain,
    class_Int_Onumber(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5073_1]) ).

fof(f_5074_1,plain,
    class_Groups_Oone(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oone]) ).

cnf(f_5074_2,plain,
    class_Groups_Oone(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_5074_1]) ).

fof(f_5075_1,plain,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct]) ).

cnf(f_5075_2,plain,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5075_1]) ).

fof(f_5076_1,plain,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add]) ).

cnf(f_5076_2,plain,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5076_1]) ).

fof(f_5077_1,plain,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le]) ).

cnf(f_5077_2,plain,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5077_1]) ).

fof(f_5078_1,plain,
    class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict]) ).

cnf(f_5078_2,plain,
    class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5078_1]) ).

fof(f_5079_1,plain,
    class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add]) ).

cnf(f_5079_2,plain,
    class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5079_1]) ).

fof(f_5080_1,plain,
    class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semiring__strict]) ).

cnf(f_5080_2,plain,
    class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5080_1]) ).

fof(f_5081_1,plain,
    class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Oordered__ab__semigroup__add]) ).

cnf(f_5081_2,plain,
    class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5081_1]) ).

fof(f_5082_1,plain,
    class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Oordered__comm__monoid__add]) ).

cnf(f_5082_2,plain,
    class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5082_1]) ).

fof(f_5083_1,plain,
    class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add]) ).

cnf(f_5083_2,plain,
    class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5083_1]) ).

fof(f_5084_1,plain,
    class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Oordered__cancel__semiring]) ).

cnf(f_5084_2,plain,
    class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5084_1]) ).

fof(f_5085_1,plain,
    class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Oordered__comm__semiring]) ).

cnf(f_5085_2,plain,
    class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5085_1]) ).

fof(f_5086_1,plain,
    class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Ocancel__semigroup__add]) ).

cnf(f_5086_2,plain,
    class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5086_1]) ).

fof(f_5087_1,plain,
    class_Rings_Olinordered__semiring(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semiring]) ).

cnf(f_5087_2,plain,
    class_Rings_Olinordered__semiring(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5087_1]) ).

fof(f_5088_1,plain,
    class_Rings_Olinordered__semidom(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semidom]) ).

cnf(f_5088_2,plain,
    class_Rings_Olinordered__semidom(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5088_1]) ).

fof(f_5089_1,plain,
    class_Lattices_Osemilattice__sup(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Lattices_Osemilattice__sup]) ).

cnf(f_5089_2,plain,
    class_Lattices_Osemilattice__sup(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5089_1]) ).

fof(f_5090_1,plain,
    class_Lattices_Osemilattice__inf(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Lattices_Osemilattice__inf]) ).

cnf(f_5090_2,plain,
    class_Lattices_Osemilattice__inf(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5090_1]) ).

fof(f_5091_1,plain,
    class_Lattices_Odistrib__lattice(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Lattices_Odistrib__lattice]) ).

cnf(f_5091_2,plain,
    class_Lattices_Odistrib__lattice(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5091_1]) ).

fof(f_5092_1,plain,
    class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Oab__semigroup__mult]) ).

cnf(f_5092_2,plain,
    class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5092_1]) ).

fof(f_5093_1,plain,
    class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Ocomm__monoid__mult]) ).

cnf(f_5093_2,plain,
    class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5093_1]) ).

fof(f_5094_1,plain,
    class_Groups_Oab__semigroup__add(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Oab__semigroup__add]) ).

cnf(f_5094_2,plain,
    class_Groups_Oab__semigroup__add(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5094_1]) ).

fof(f_5095_1,plain,
    class_Rings_Oordered__semiring(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Oordered__semiring]) ).

cnf(f_5095_2,plain,
    class_Rings_Oordered__semiring(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5095_1]) ).

fof(f_5096_1,plain,
    class_Rings_Ono__zero__divisors(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Ono__zero__divisors]) ).

cnf(f_5096_2,plain,
    class_Rings_Ono__zero__divisors(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5096_1]) ).

fof(f_5097_1,plain,
    class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Ocomm__monoid__add]) ).

cnf(f_5097_2,plain,
    class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5097_1]) ).

fof(f_5098_1,plain,
    class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Ocomm__semiring__1]) ).

cnf(f_5098_2,plain,
    class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5098_1]) ).

fof(f_5099_1,plain,
    class_Groups_Osemigroup__add(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Osemigroup__add]) ).

cnf(f_5099_2,plain,
    class_Groups_Osemigroup__add(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5099_1]) ).

fof(f_5100_1,plain,
    class_Divides_Osemiring__div(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Divides_Osemiring__div]) ).

cnf(f_5100_2,plain,
    class_Divides_Osemiring__div(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5100_1]) ).

fof(f_5101_1,plain,
    class_Rings_Ocomm__semiring(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Ocomm__semiring]) ).

cnf(f_5101_2,plain,
    class_Rings_Ocomm__semiring(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5101_1]) ).

fof(f_5102_1,plain,
    class_Orderings_Owellorder(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Orderings_Owellorder]) ).

cnf(f_5102_2,plain,
    class_Orderings_Owellorder(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5102_1]) ).

fof(f_5103_1,plain,
    class_Nat_Osemiring__char__0(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Nat_Osemiring__char__0]) ).

cnf(f_5103_2,plain,
    class_Nat_Osemiring__char__0(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5103_1]) ).

fof(f_5104_1,plain,
    class_Rings_Ozero__neq__one(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Ozero__neq__one]) ).

cnf(f_5104_2,plain,
    class_Rings_Ozero__neq__one(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5104_1]) ).

fof(f_5105_1,plain,
    class_Orderings_Opreorder(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Orderings_Opreorder]) ).

cnf(f_5105_2,plain,
    class_Orderings_Opreorder(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5105_1]) ).

fof(f_5106_1,plain,
    class_Orderings_Olinorder(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Orderings_Olinorder]) ).

cnf(f_5106_2,plain,
    class_Orderings_Olinorder(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5106_1]) ).

fof(f_5107_1,plain,
    class_Groups_Omonoid__mult(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__mult]) ).

cnf(f_5107_2,plain,
    class_Groups_Omonoid__mult(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5107_1]) ).

fof(f_5108_1,plain,
    class_Groups_Omonoid__add(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__add]) ).

cnf(f_5108_2,plain,
    class_Groups_Omonoid__add(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5108_1]) ).

fof(f_5109_1,plain,
    class_Rings_Osemiring__1(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Osemiring__1]) ).

cnf(f_5109_2,plain,
    class_Rings_Osemiring__1(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5109_1]) ).

fof(f_5110_1,plain,
    class_Rings_Osemiring__0(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Osemiring__0]) ).

cnf(f_5110_2,plain,
    class_Rings_Osemiring__0(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5110_1]) ).

fof(f_5111_1,plain,
    class_Lattices_Olattice(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Lattices_Olattice]) ).

cnf(f_5111_2,plain,
    class_Lattices_Olattice(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5111_1]) ).

fof(f_5112_1,plain,
    class_Rings_Omult__zero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Omult__zero]) ).

cnf(f_5112_2,plain,
    class_Rings_Omult__zero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5112_1]) ).

fof(f_5113_1,plain,
    class_Orderings_Oorder(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Orderings_Oorder]) ).

cnf(f_5113_2,plain,
    class_Orderings_Oorder(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5113_1]) ).

fof(f_5114_1,plain,
    class_Rings_Osemiring(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Osemiring]) ).

cnf(f_5114_2,plain,
    class_Rings_Osemiring(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5114_1]) ).

fof(f_5115_1,plain,
    class_Orderings_Oord(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Orderings_Oord]) ).

cnf(f_5115_2,plain,
    class_Orderings_Oord(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5115_1]) ).

fof(f_5116_1,plain,
    class_Orderings_Obot(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Orderings_Obot]) ).

cnf(f_5116_2,plain,
    class_Orderings_Obot(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5116_1]) ).

fof(f_5117_1,plain,
    class_Groups_Ominus(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Ominus]) ).

cnf(f_5117_2,plain,
    class_Groups_Ominus(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5117_1]) ).

fof(f_5118_1,plain,
    class_Power_Opower(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Power_Opower]) ).

cnf(f_5118_2,plain,
    class_Power_Opower(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5118_1]) ).

fof(f_5119_1,plain,
    class_Groups_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Ozero]) ).

cnf(f_5119_2,plain,
    class_Groups_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5119_1]) ).

fof(f_5120_1,plain,
    class_Int_Onumber(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Int_Onumber]) ).

cnf(f_5120_2,plain,
    class_Int_Onumber(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5120_1]) ).

fof(f_5121_1,plain,
    class_Groups_Oone(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Oone]) ).

cnf(f_5121_2,plain,
    class_Groups_Oone(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5121_1]) ).

fof(f_5122_1,plain,
    class_Nat_Osize(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Nat_Osize]) ).

cnf(f_5122_2,plain,
    class_Nat_Osize(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_5122_1]) ).

fof(f_5123_1,plain,
    class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice]) ).

cnf(f_5123_2,plain,
    class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_5123_1]) ).

fof(f_5124_1,plain,
    class_Lattices_Obounded__lattice__top(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Lattices_Obounded__lattice__top]) ).

cnf(f_5124_2,plain,
    class_Lattices_Obounded__lattice__top(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_5124_1]) ).

fof(f_5125_1,plain,
    class_Lattices_Obounded__lattice__bot(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Lattices_Obounded__lattice__bot]) ).

cnf(f_5125_2,plain,
    class_Lattices_Obounded__lattice__bot(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_5125_1]) ).

fof(f_5126_1,plain,
    class_Lattices_Osemilattice__sup(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Lattices_Osemilattice__sup]) ).

cnf(f_5126_2,plain,
    class_Lattices_Osemilattice__sup(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_5126_1]) ).

fof(f_5127_1,plain,
    class_Lattices_Osemilattice__inf(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Lattices_Osemilattice__inf]) ).

cnf(f_5127_2,plain,
    class_Lattices_Osemilattice__inf(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_5127_1]) ).

fof(f_5128_1,plain,
    class_Lattices_Odistrib__lattice(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Lattices_Odistrib__lattice]) ).

cnf(f_5128_2,plain,
    class_Lattices_Odistrib__lattice(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_5128_1]) ).

fof(f_5129_1,plain,
    class_Lattices_Oboolean__algebra(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Lattices_Oboolean__algebra]) ).

cnf(f_5129_2,plain,
    class_Lattices_Oboolean__algebra(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_5129_1]) ).

fof(f_5130_1,plain,
    class_Orderings_Opreorder(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Orderings_Opreorder]) ).

cnf(f_5130_2,plain,
    class_Orderings_Opreorder(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_5130_1]) ).

fof(f_5131_1,plain,
    class_Finite__Set_Ofinite(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Finite__Set_Ofinite]) ).

cnf(f_5131_2,plain,
    class_Finite__Set_Ofinite(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_5131_1]) ).

fof(f_5132_1,plain,
    class_Lattices_Olattice(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Lattices_Olattice]) ).

cnf(f_5132_2,plain,
    class_Lattices_Olattice(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_5132_1]) ).

fof(f_5133_1,plain,
    class_Orderings_Oorder(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Orderings_Oorder]) ).

cnf(f_5133_2,plain,
    class_Orderings_Oorder(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_5133_1]) ).

fof(f_5134_1,plain,
    class_Orderings_Otop(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Orderings_Otop]) ).

cnf(f_5134_2,plain,
    class_Orderings_Otop(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_5134_1]) ).

fof(f_5135_1,plain,
    class_Orderings_Oord(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Orderings_Oord]) ).

cnf(f_5135_2,plain,
    class_Orderings_Oord(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_5135_1]) ).

fof(f_5136_1,plain,
    class_Orderings_Obot(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Orderings_Obot]) ).

cnf(f_5136_2,plain,
    class_Orderings_Obot(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_5136_1]) ).

fof(f_5137_1,plain,
    class_Groups_Ouminus(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Groups_Ouminus]) ).

cnf(f_5137_2,plain,
    class_Groups_Ouminus(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_5137_1]) ).

fof(f_5138_1,plain,
    class_Groups_Ominus(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Groups_Ominus]) ).

cnf(f_5138_2,plain,
    class_Groups_Ominus(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_5138_1]) ).

fof(f_5139_1,plain,
    class_Enum_Oenum(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Enum_Oenum]) ).

cnf(f_5139_2,plain,
    class_Enum_Oenum(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_5139_1]) ).

fof(f_5140_1,plain,
    class_Nat_Osize(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Nat_Osize]) ).

cnf(f_5140_2,plain,
    class_Nat_Osize(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_5140_1]) ).

fof(f_5141_1,plain,
    ! [T_1] :
      ( class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(T_1))
      | ~ class_Lazy__Sequence_Osmall__lazy(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_List__Olist__Lazy__Sequence_Osmall__lazy]) ).

fof(f_5141_2,plain,
    ! [U_20795] :
      ( class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(U_20795))
      | ~ class_Lazy__Sequence_Osmall__lazy(U_20795) ),
    inference(variable_rename,[status(thm)],[f_5141_1]) ).

cnf(f_5141_3,plain,
    ( class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(U_20795))
    | ~ class_Lazy__Sequence_Osmall__lazy(U_20795) ),
    inference(clausify,[status(thm)],[f_5141_2]) ).

fof(f_5142_1,plain,
    ! [T_1] : class_Nat_Osize(tc_List_Olist(T_1)),
    inference(fof_nnf,[status(thm)],[arity_List__Olist__Nat_Osize]) ).

fof(f_5142_2,plain,
    ! [U_20796] : class_Nat_Osize(tc_List_Olist(U_20796)),
    inference(variable_rename,[status(thm)],[f_5142_1]) ).

cnf(f_5142_3,plain,
    class_Nat_Osize(tc_List_Olist(U_20796)),
    inference(clausify,[status(thm)],[f_5142_2]) ).

fof(f_5143_1,plain,
    ! [T_1,T_2] :
      ( class_Finite__Set_Ofinite(tc_sum(T_2,T_1))
      | ~ class_Finite__Set_Ofinite(T_1)
      | ~ class_Finite__Set_Ofinite(T_2) ),
    inference(fof_nnf,[status(thm)],[arity_sum__Finite__Set_Ofinite]) ).

fof(f_5143_2,plain,
    ! [U_20798,U_20797] :
      ( class_Finite__Set_Ofinite(tc_sum(U_20797,U_20798))
      | ~ class_Finite__Set_Ofinite(U_20798)
      | ~ class_Finite__Set_Ofinite(U_20797) ),
    inference(variable_rename,[status(thm)],[f_5143_1]) ).

cnf(f_5143_3,plain,
    ( class_Finite__Set_Ofinite(tc_sum(U_20797,U_20798))
    | ~ class_Finite__Set_Ofinite(U_20798)
    | ~ class_Finite__Set_Ofinite(U_20797) ),
    inference(clausify,[status(thm)],[f_5143_2]) ).

fof(f_5144_1,plain,
    ! [T_1,T_2] :
      ( class_Enum_Oenum(tc_sum(T_2,T_1))
      | ~ class_Enum_Oenum(T_1)
      | ~ class_Enum_Oenum(T_2) ),
    inference(fof_nnf,[status(thm)],[arity_sum__Enum_Oenum]) ).

fof(f_5144_2,plain,
    ! [U_20800,U_20799] :
      ( class_Enum_Oenum(tc_sum(U_20799,U_20800))
      | ~ class_Enum_Oenum(U_20800)
      | ~ class_Enum_Oenum(U_20799) ),
    inference(variable_rename,[status(thm)],[f_5144_1]) ).

cnf(f_5144_3,plain,
    ( class_Enum_Oenum(tc_sum(U_20799,U_20800))
    | ~ class_Enum_Oenum(U_20800)
    | ~ class_Enum_Oenum(U_20799) ),
    inference(clausify,[status(thm)],[f_5144_2]) ).

fof(f_5145_1,plain,
    ! [T_1,T_2] : class_Nat_Osize(tc_sum(T_2,T_1)),
    inference(fof_nnf,[status(thm)],[arity_sum__Nat_Osize]) ).

fof(f_5145_2,plain,
    ! [U_20802,U_20801] : class_Nat_Osize(tc_sum(U_20801,U_20802)),
    inference(variable_rename,[status(thm)],[f_5145_1]) ).

cnf(f_5145_3,plain,
    class_Nat_Osize(tc_sum(U_20801,U_20802)),
    inference(clausify,[status(thm)],[f_5145_2]) ).

fof(f_5146_1,plain,
    ! [T_1] :
      ( class_Finite__Set_Ofinite(tc_Option_Ooption(T_1))
      | ~ class_Finite__Set_Ofinite(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_Option__Ooption__Finite__Set_Ofinite]) ).

fof(f_5146_2,plain,
    ! [U_20803] :
      ( class_Finite__Set_Ofinite(tc_Option_Ooption(U_20803))
      | ~ class_Finite__Set_Ofinite(U_20803) ),
    inference(variable_rename,[status(thm)],[f_5146_1]) ).

cnf(f_5146_3,plain,
    ( class_Finite__Set_Ofinite(tc_Option_Ooption(U_20803))
    | ~ class_Finite__Set_Ofinite(U_20803) ),
    inference(clausify,[status(thm)],[f_5146_2]) ).

fof(f_5147_1,plain,
    ! [T_1] :
      ( class_Enum_Oenum(tc_Option_Ooption(T_1))
      | ~ class_Enum_Oenum(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_Option__Ooption__Enum_Oenum]) ).

fof(f_5147_2,plain,
    ! [U_20804] :
      ( class_Enum_Oenum(tc_Option_Ooption(U_20804))
      | ~ class_Enum_Oenum(U_20804) ),
    inference(variable_rename,[status(thm)],[f_5147_1]) ).

cnf(f_5147_3,plain,
    ( class_Enum_Oenum(tc_Option_Ooption(U_20804))
    | ~ class_Enum_Oenum(U_20804) ),
    inference(clausify,[status(thm)],[f_5147_2]) ).

fof(f_5148_1,plain,
    ! [T_1] : class_Nat_Osize(tc_Option_Ooption(T_1)),
    inference(fof_nnf,[status(thm)],[arity_Option__Ooption__Nat_Osize]) ).

fof(f_5148_2,plain,
    ! [U_20805] : class_Nat_Osize(tc_Option_Ooption(U_20805)),
    inference(variable_rename,[status(thm)],[f_5148_1]) ).

cnf(f_5148_3,plain,
    class_Nat_Osize(tc_Option_Ooption(U_20805)),
    inference(clausify,[status(thm)],[f_5148_2]) ).

fof(f_5149_1,plain,
    ! [T_1,T_2] : class_Nat_Osize(tc_Nitpick_Opair__box(T_2,T_1)),
    inference(fof_nnf,[status(thm)],[arity_Nitpick__Opair____box__Nat_Osize]) ).

fof(f_5149_2,plain,
    ! [U_20807,U_20806] : class_Nat_Osize(tc_Nitpick_Opair__box(U_20806,U_20807)),
    inference(variable_rename,[status(thm)],[f_5149_1]) ).

cnf(f_5149_3,plain,
    class_Nat_Osize(tc_Nitpick_Opair__box(U_20806,U_20807)),
    inference(clausify,[status(thm)],[f_5149_2]) ).

fof(f_5150_1,plain,
    ! [T_1,T_2] :
      ( class_Lazy__Sequence_Osmall__lazy(tc_prod(T_2,T_1))
      | ~ class_Lazy__Sequence_Osmall__lazy(T_1)
      | ~ class_Lazy__Sequence_Osmall__lazy(T_2) ),
    inference(fof_nnf,[status(thm)],[arity_prod__Lazy__Sequence_Osmall__lazy]) ).

fof(f_5150_2,plain,
    ! [U_20809,U_20808] :
      ( class_Lazy__Sequence_Osmall__lazy(tc_prod(U_20808,U_20809))
      | ~ class_Lazy__Sequence_Osmall__lazy(U_20809)
      | ~ class_Lazy__Sequence_Osmall__lazy(U_20808) ),
    inference(variable_rename,[status(thm)],[f_5150_1]) ).

cnf(f_5150_3,plain,
    ( class_Lazy__Sequence_Osmall__lazy(tc_prod(U_20808,U_20809))
    | ~ class_Lazy__Sequence_Osmall__lazy(U_20809)
    | ~ class_Lazy__Sequence_Osmall__lazy(U_20808) ),
    inference(clausify,[status(thm)],[f_5150_2]) ).

fof(f_5151_1,plain,
    ! [T_1,T_2] :
      ( class_Finite__Set_Ofinite(tc_prod(T_2,T_1))
      | ~ class_Finite__Set_Ofinite(T_1)
      | ~ class_Finite__Set_Ofinite(T_2) ),
    inference(fof_nnf,[status(thm)],[arity_prod__Finite__Set_Ofinite]) ).

fof(f_5151_2,plain,
    ! [U_20811,U_20810] :
      ( class_Finite__Set_Ofinite(tc_prod(U_20810,U_20811))
      | ~ class_Finite__Set_Ofinite(U_20811)
      | ~ class_Finite__Set_Ofinite(U_20810) ),
    inference(variable_rename,[status(thm)],[f_5151_1]) ).

cnf(f_5151_3,plain,
    ( class_Finite__Set_Ofinite(tc_prod(U_20810,U_20811))
    | ~ class_Finite__Set_Ofinite(U_20811)
    | ~ class_Finite__Set_Ofinite(U_20810) ),
    inference(clausify,[status(thm)],[f_5151_2]) ).

fof(f_5152_1,plain,
    ! [T_1,T_2] :
      ( class_Enum_Oenum(tc_prod(T_2,T_1))
      | ~ class_Enum_Oenum(T_1)
      | ~ class_Enum_Oenum(T_2) ),
    inference(fof_nnf,[status(thm)],[arity_prod__Enum_Oenum]) ).

fof(f_5152_2,plain,
    ! [U_20813,U_20812] :
      ( class_Enum_Oenum(tc_prod(U_20812,U_20813))
      | ~ class_Enum_Oenum(U_20813)
      | ~ class_Enum_Oenum(U_20812) ),
    inference(variable_rename,[status(thm)],[f_5152_1]) ).

cnf(f_5152_3,plain,
    ( class_Enum_Oenum(tc_prod(U_20812,U_20813))
    | ~ class_Enum_Oenum(U_20813)
    | ~ class_Enum_Oenum(U_20812) ),
    inference(clausify,[status(thm)],[f_5152_2]) ).

fof(f_5153_1,plain,
    ! [T_1,T_2] : class_Nat_Osize(tc_prod(T_2,T_1)),
    inference(fof_nnf,[status(thm)],[arity_prod__Nat_Osize]) ).

fof(f_5153_2,plain,
    ! [U_20815,U_20814] : class_Nat_Osize(tc_prod(U_20814,U_20815)),
    inference(variable_rename,[status(thm)],[f_5153_1]) ).

cnf(f_5153_3,plain,
    class_Nat_Osize(tc_prod(U_20814,U_20815)),
    inference(clausify,[status(thm)],[f_5153_2]) ).

fof(f_5154_1,plain,
    class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit),
    inference(fof_nnf,[status(thm)],[arity_Product____Type__Ounit__Lazy__Sequence_Osmall__lazy]) ).

cnf(f_5154_2,plain,
    class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit),
    inference(clausify,[status(thm)],[f_5154_1]) ).

fof(f_5155_1,plain,
    class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
    inference(fof_nnf,[status(thm)],[arity_Product____Type__Ounit__Finite__Set_Ofinite]) ).

cnf(f_5155_2,plain,
    class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
    inference(clausify,[status(thm)],[f_5155_1]) ).

fof(f_5156_1,plain,
    class_Enum_Oenum(tc_Product__Type_Ounit),
    inference(fof_nnf,[status(thm)],[arity_Product____Type__Ounit__Enum_Oenum]) ).

cnf(f_5156_2,plain,
    class_Enum_Oenum(tc_Product__Type_Ounit),
    inference(clausify,[status(thm)],[f_5156_1]) ).

fof(f_5157_1,plain,
    class_Nat_Osize(tc_Product__Type_Ounit),
    inference(fof_nnf,[status(thm)],[arity_Product____Type__Ounit__Nat_Osize]) ).

cnf(f_5157_2,plain,
    class_Nat_Osize(tc_Product__Type_Ounit),
    inference(clausify,[status(thm)],[f_5157_1]) ).

fof(f_5158_1,plain,
    class_Nat_Osize(tc_Code__Evaluation_Oterm),
    inference(fof_nnf,[status(thm)],[arity_Code____Evaluation__Oterm__Nat_Osize]) ).

cnf(f_5158_2,plain,
    class_Nat_Osize(tc_Code__Evaluation_Oterm),
    inference(clausify,[status(thm)],[f_5158_1]) ).

fof(f_5159_1,plain,
    ! [T_1] : class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(T_1)),
    inference(fof_nnf,[status(thm)],[arity_Hoare____Mirabelle__Otriple__Nat_Osize]) ).

fof(f_5159_2,plain,
    ! [U_20816] : class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(U_20816)),
    inference(variable_rename,[status(thm)],[f_5159_1]) ).

cnf(f_5159_3,plain,
    class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(U_20816)),
    inference(clausify,[status(thm)],[f_5159_2]) ).

fof(f_5160_1,plain,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add]) ).

cnf(f_5160_2,plain,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5160_1]) ).

fof(f_5161_1,plain,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le]) ).

cnf(f_5161_2,plain,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5161_1]) ).

fof(f_5162_1,plain,
    class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict]) ).

cnf(f_5162_2,plain,
    class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5162_1]) ).

fof(f_5163_1,plain,
    class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add]) ).

cnf(f_5163_2,plain,
    class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5163_1]) ).

fof(f_5164_1,plain,
    class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict]) ).

cnf(f_5164_2,plain,
    class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5164_1]) ).

fof(f_5165_1,plain,
    class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add]) ).

cnf(f_5165_2,plain,
    class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5165_1]) ).

fof(f_5166_1,plain,
    class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add]) ).

cnf(f_5166_2,plain,
    class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5166_1]) ).

fof(f_5167_1,plain,
    class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add]) ).

cnf(f_5167_2,plain,
    class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5167_1]) ).

fof(f_5168_1,plain,
    class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring]) ).

cnf(f_5168_2,plain,
    class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5168_1]) ).

fof(f_5169_1,plain,
    class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring]) ).

cnf(f_5169_2,plain,
    class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5169_1]) ).

fof(f_5170_1,plain,
    class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add]) ).

cnf(f_5170_2,plain,
    class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5170_1]) ).

fof(f_5171_1,plain,
    class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring]) ).

cnf(f_5171_2,plain,
    class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5171_1]) ).

fof(f_5172_1,plain,
    class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom]) ).

cnf(f_5172_2,plain,
    class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5172_1]) ).

fof(f_5173_1,plain,
    class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult]) ).

cnf(f_5173_2,plain,
    class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5173_1]) ).

fof(f_5174_1,plain,
    class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult]) ).

cnf(f_5174_2,plain,
    class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5174_1]) ).

fof(f_5175_1,plain,
    class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add]) ).

cnf(f_5175_2,plain,
    class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5175_1]) ).

fof(f_5176_1,plain,
    class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring]) ).

cnf(f_5176_2,plain,
    class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5176_1]) ).

fof(f_5177_1,plain,
    class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors]) ).

cnf(f_5177_2,plain,
    class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5177_1]) ).

fof(f_5178_1,plain,
    class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add]) ).

cnf(f_5178_2,plain,
    class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5178_1]) ).

fof(f_5179_1,plain,
    class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1]) ).

cnf(f_5179_2,plain,
    class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5179_1]) ).

fof(f_5180_1,plain,
    class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add]) ).

cnf(f_5180_2,plain,
    class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5180_1]) ).

fof(f_5181_1,plain,
    class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div]) ).

cnf(f_5181_2,plain,
    class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5181_1]) ).

fof(f_5182_1,plain,
    class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring]) ).

cnf(f_5182_2,plain,
    class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5182_1]) ).

fof(f_5183_1,plain,
    class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Nat_Osemiring__char__0]) ).

cnf(f_5183_2,plain,
    class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5183_1]) ).

fof(f_5184_1,plain,
    class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one]) ).

cnf(f_5184_2,plain,
    class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5184_1]) ).

fof(f_5185_1,plain,
    class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder]) ).

cnf(f_5185_2,plain,
    class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5185_1]) ).

fof(f_5186_1,plain,
    class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder]) ).

cnf(f_5186_2,plain,
    class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5186_1]) ).

fof(f_5187_1,plain,
    class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult]) ).

cnf(f_5187_2,plain,
    class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5187_1]) ).

fof(f_5188_1,plain,
    class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add]) ).

cnf(f_5188_2,plain,
    class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5188_1]) ).

fof(f_5189_1,plain,
    class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1]) ).

cnf(f_5189_2,plain,
    class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5189_1]) ).

fof(f_5190_1,plain,
    class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0]) ).

cnf(f_5190_2,plain,
    class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5190_1]) ).

fof(f_5191_1,plain,
    class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero]) ).

cnf(f_5191_2,plain,
    class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5191_1]) ).

fof(f_5192_1,plain,
    class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Orderings_Oorder]) ).

cnf(f_5192_2,plain,
    class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5192_1]) ).

fof(f_5193_1,plain,
    class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Osemiring]) ).

cnf(f_5193_2,plain,
    class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5193_1]) ).

fof(f_5194_1,plain,
    class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Orderings_Oord]) ).

cnf(f_5194_2,plain,
    class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5194_1]) ).

fof(f_5195_1,plain,
    class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Ominus]) ).

cnf(f_5195_2,plain,
    class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5195_1]) ).

fof(f_5196_1,plain,
    class_Power_Opower(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Power_Opower]) ).

cnf(f_5196_2,plain,
    class_Power_Opower(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5196_1]) ).

fof(f_5197_1,plain,
    class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Ozero]) ).

cnf(f_5197_2,plain,
    class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5197_1]) ).

fof(f_5198_1,plain,
    class_Int_Onumber(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Int_Onumber]) ).

cnf(f_5198_2,plain,
    class_Int_Onumber(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5198_1]) ).

fof(f_5199_1,plain,
    class_Groups_Oone(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Groups_Oone]) ).

cnf(f_5199_2,plain,
    class_Groups_Oone(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5199_1]) ).

fof(f_5200_1,plain,
    class_Nat_Osize(tc_Code__Numeral_Ocode__numeral),
    inference(fof_nnf,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Nat_Osize]) ).

cnf(f_5200_2,plain,
    class_Nat_Osize(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_5200_1]) ).

fof(f_5201_1,plain,
    ! [T_1] : class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(T_1)),
    inference(fof_nnf,[status(thm)],[arity_Lazy____Sequence__Olazy____sequence__Nat_Osize]) ).

fof(f_5201_2,plain,
    ! [U_20817] : class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(U_20817)),
    inference(variable_rename,[status(thm)],[f_5201_1]) ).

cnf(f_5201_3,plain,
    class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(U_20817)),
    inference(clausify,[status(thm)],[f_5201_2]) ).

fof(f_5202_1,plain,
    ! [V_P,T_a] : hAPP(c_COMBI(T_a),V_P) = V_P,
    inference(fof_nnf,[status(thm)],[help_c__COMBI__1]) ).

fof(f_5202_2,plain,
    ! [U_20819,U_20818] : hAPP(c_COMBI(U_20818),U_20819) = U_20819,
    inference(variable_rename,[status(thm)],[f_5202_1]) ).

cnf(f_5202_3,plain,
    hAPP(c_COMBI(U_20818),U_20819) = U_20819,
    inference(clausify,[status(thm)],[f_5202_2]) ).

fof(f_5203_1,plain,
    ! [V_Q,V_P,T_b,T_a] : hAPP(hAPP(c_COMBK(T_a,T_b),V_P),V_Q) = V_P,
    inference(fof_nnf,[status(thm)],[help_c__COMBK__1]) ).

fof(f_5203_2,plain,
    ! [U_20823,U_20822,U_20821,U_20820] : hAPP(hAPP(c_COMBK(U_20820,U_20821),U_20822),U_20823) = U_20822,
    inference(variable_rename,[status(thm)],[f_5203_1]) ).

cnf(f_5203_3,plain,
    hAPP(hAPP(c_COMBK(U_20820,U_20821),U_20822),U_20823) = U_20822,
    inference(clausify,[status(thm)],[f_5203_2]) ).

fof(f_5204_1,plain,
    ! [V_R_2,V_Q_2,V_P_2,T_d,T_b,T_c] : hAPP(hAPP(hAPP(c_COMBB(T_c,T_b,T_d),V_P_2),V_Q_2),V_R_2) = hAPP(V_P_2,hAPP(V_Q_2,V_R_2)),
    inference(fof_nnf,[status(thm)],[help_c__COMBB__1]) ).

fof(f_5204_2,plain,
    ! [U_20829,U_20828,U_20827,U_20826,U_20825,U_20824] : hAPP(hAPP(hAPP(c_COMBB(U_20824,U_20825,U_20826),U_20827),U_20828),U_20829) = hAPP(U_20827,hAPP(U_20828,U_20829)),
    inference(variable_rename,[status(thm)],[f_5204_1]) ).

cnf(f_5204_3,plain,
    hAPP(hAPP(hAPP(c_COMBB(U_20824,U_20825,U_20826),U_20827),U_20828),U_20829) = hAPP(U_20827,hAPP(U_20828,U_20829)),
    inference(clausify,[status(thm)],[f_5204_2]) ).

fof(f_5205_1,plain,
    ! [V_R_2,V_Q_2,V_P_2,T_b,T_d,T_c] : hAPP(hAPP(hAPP(c_COMBC(T_c,T_d,T_b),V_P_2),V_Q_2),V_R_2) = hAPP(hAPP(V_P_2,V_R_2),V_Q_2),
    inference(fof_nnf,[status(thm)],[help_c__COMBC__1]) ).

fof(f_5205_2,plain,
    ! [U_20835,U_20834,U_20833,U_20832,U_20831,U_20830] : hAPP(hAPP(hAPP(c_COMBC(U_20830,U_20831,U_20832),U_20833),U_20834),U_20835) = hAPP(hAPP(U_20833,U_20835),U_20834),
    inference(variable_rename,[status(thm)],[f_5205_1]) ).

cnf(f_5205_3,plain,
    hAPP(hAPP(hAPP(c_COMBC(U_20830,U_20831,U_20832),U_20833),U_20834),U_20835) = hAPP(hAPP(U_20833,U_20835),U_20834),
    inference(clausify,[status(thm)],[f_5205_2]) ).

fof(f_5206_1,plain,
    ! [V_R_2,V_Q_2,V_P_2,T_b,T_d,T_c] : hAPP(hAPP(hAPP(c_COMBS(T_c,T_d,T_b),V_P_2),V_Q_2),V_R_2) = hAPP(hAPP(V_P_2,V_R_2),hAPP(V_Q_2,V_R_2)),
    inference(fof_nnf,[status(thm)],[help_c__COMBS__1]) ).

fof(f_5206_2,plain,
    ! [U_20841,U_20840,U_20839,U_20838,U_20837,U_20836] : hAPP(hAPP(hAPP(c_COMBS(U_20836,U_20837,U_20838),U_20839),U_20840),U_20841) = hAPP(hAPP(U_20839,U_20841),hAPP(U_20840,U_20841)),
    inference(variable_rename,[status(thm)],[f_5206_1]) ).

cnf(f_5206_3,plain,
    hAPP(hAPP(hAPP(c_COMBS(U_20836,U_20837,U_20838),U_20839),U_20840),U_20841) = hAPP(hAPP(U_20839,U_20841),hAPP(U_20840,U_20841)),
    inference(clausify,[status(thm)],[f_5206_2]) ).

fof(f_5207_1,plain,
    ! [V_y_2,V_x_2] :
      ( V_x_2 = V_y_2
      | ~ hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) ),
    inference(fof_nnf,[status(thm)],[help_c__fequal__1]) ).

fof(f_5207_2,plain,
    ! [U_20843,U_20842] :
      ( U_20842 = U_20843
      | ~ hBOOL(hAPP(hAPP(c_fequal,U_20842),U_20843)) ),
    inference(variable_rename,[status(thm)],[f_5207_1]) ).

cnf(f_5207_3,plain,
    ( U_20842 = U_20843
    | ~ hBOOL(hAPP(hAPP(c_fequal,U_20842),U_20843)) ),
    inference(clausify,[status(thm)],[f_5207_2]) ).

fof(f_5208_1,plain,
    ! [V_y_2,V_x_2] :
      ( hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2))
      | V_x_2 != V_y_2 ),
    inference(fof_nnf,[status(thm)],[help_c__fequal__2]) ).

fof(f_5208_2,plain,
    ! [U_20845,U_20844] :
      ( hBOOL(hAPP(hAPP(c_fequal,U_20844),U_20845))
      | U_20844 != U_20845 ),
    inference(variable_rename,[status(thm)],[f_5208_1]) ).

cnf(f_5208_3,plain,
    ( hBOOL(hAPP(hAPP(c_fequal,U_20844),U_20845))
    | U_20844 != U_20845 ),
    inference(clausify,[status(thm)],[f_5208_2]) ).

fof(f_5209_1,plain,
    ~ hBOOL(c_fFalse),
    inference(fof_nnf,[status(thm)],[help_c__fFalse__1]) ).

cnf(f_5209_2,plain,
    ~ hBOOL(c_fFalse),
    inference(clausify,[status(thm)],[f_5209_1]) ).

fof(f_5210_1,plain,
    hBOOL(c_fTrue),
    inference(fof_nnf,[status(thm)],[help_c__fTrue__1]) ).

cnf(f_5210_2,plain,
    hBOOL(c_fTrue),
    inference(clausify,[status(thm)],[f_5210_1]) ).

fof(f_5211_1,plain,
    ! [V_P_2] :
      ( ~ hBOOL(V_P_2)
      | ~ hBOOL(hAPP(c_fNot,V_P_2)) ),
    inference(fof_nnf,[status(thm)],[help_c__fNot__1]) ).

fof(f_5211_2,plain,
    ! [U_20846] :
      ( ~ hBOOL(U_20846)
      | ~ hBOOL(hAPP(c_fNot,U_20846)) ),
    inference(variable_rename,[status(thm)],[f_5211_1]) ).

cnf(f_5211_3,plain,
    ( ~ hBOOL(U_20846)
    | ~ hBOOL(hAPP(c_fNot,U_20846)) ),
    inference(clausify,[status(thm)],[f_5211_2]) ).

fof(f_5212_1,plain,
    ! [V_P_2] :
      ( hBOOL(hAPP(c_fNot,V_P_2))
      | hBOOL(V_P_2) ),
    inference(fof_nnf,[status(thm)],[help_c__fNot__2]) ).

fof(f_5212_2,plain,
    ! [U_20847] :
      ( hBOOL(hAPP(c_fNot,U_20847))
      | hBOOL(U_20847) ),
    inference(variable_rename,[status(thm)],[f_5212_1]) ).

cnf(f_5212_3,plain,
    ( hBOOL(hAPP(c_fNot,U_20847))
    | hBOOL(U_20847) ),
    inference(clausify,[status(thm)],[f_5212_2]) ).

fof(f_5213_1,plain,
    ! [V_Q_2,V_P_2] :
      ( hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2))
      | ~ hBOOL(V_Q_2)
      | ~ hBOOL(V_P_2) ),
    inference(fof_nnf,[status(thm)],[help_c__fconj__1]) ).

fof(f_5213_2,plain,
    ! [U_20849,U_20848] :
      ( hBOOL(hAPP(hAPP(c_fconj,U_20848),U_20849))
      | ~ hBOOL(U_20849)
      | ~ hBOOL(U_20848) ),
    inference(variable_rename,[status(thm)],[f_5213_1]) ).

fof(f_5213_3,plain,
    ! [U_20849] :
      ( ! [U_20848] :
          ( hBOOL(hAPP(hAPP(c_fconj,U_20848),U_20849))
          | ~ hBOOL(U_20848) )
      | ~ hBOOL(U_20849) ),
    inference(miniscope,[status(thm)],[f_5213_2]) ).

cnf(f_5213_4,plain,
    ( hBOOL(hAPP(hAPP(c_fconj,U_20848),U_20849))
    | ~ hBOOL(U_20848)
    | ~ hBOOL(U_20849) ),
    inference(clausify,[status(thm)],[f_5213_3]) ).

fof(f_5214_1,plain,
    ! [V_Q_2,V_P_2] :
      ( hBOOL(V_P_2)
      | ~ hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2)) ),
    inference(fof_nnf,[status(thm)],[help_c__fconj__2]) ).

fof(f_5214_2,plain,
    ! [U_20851,U_20850] :
      ( hBOOL(U_20850)
      | ~ hBOOL(hAPP(hAPP(c_fconj,U_20850),U_20851)) ),
    inference(variable_rename,[status(thm)],[f_5214_1]) ).

cnf(f_5214_3,plain,
    ( hBOOL(U_20850)
    | ~ hBOOL(hAPP(hAPP(c_fconj,U_20850),U_20851)) ),
    inference(clausify,[status(thm)],[f_5214_2]) ).

fof(f_5215_1,plain,
    ! [V_Q_2,V_P_2] :
      ( hBOOL(V_Q_2)
      | ~ hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2)) ),
    inference(fof_nnf,[status(thm)],[help_c__fconj__3]) ).

fof(f_5215_2,plain,
    ! [U_20853,U_20852] :
      ( hBOOL(U_20853)
      | ~ hBOOL(hAPP(hAPP(c_fconj,U_20852),U_20853)) ),
    inference(variable_rename,[status(thm)],[f_5215_1]) ).

fof(f_5215_3,plain,
    ! [U_20853] :
      ( ! [U_20852] : ~ hBOOL(hAPP(hAPP(c_fconj,U_20852),U_20853))
      | hBOOL(U_20853) ),
    inference(miniscope,[status(thm)],[f_5215_2]) ).

cnf(f_5215_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_fconj,U_20852),U_20853))
    | hBOOL(U_20853) ),
    inference(clausify,[status(thm)],[f_5215_3]) ).

fof(f_5216_1,plain,
    ! [V_Q_2,V_P_2] :
      ( hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2))
      | ~ hBOOL(V_P_2) ),
    inference(fof_nnf,[status(thm)],[help_c__fdisj__1]) ).

fof(f_5216_2,plain,
    ! [U_20855,U_20854] :
      ( hBOOL(hAPP(hAPP(c_fdisj,U_20854),U_20855))
      | ~ hBOOL(U_20854) ),
    inference(variable_rename,[status(thm)],[f_5216_1]) ).

cnf(f_5216_3,plain,
    ( hBOOL(hAPP(hAPP(c_fdisj,U_20854),U_20855))
    | ~ hBOOL(U_20854) ),
    inference(clausify,[status(thm)],[f_5216_2]) ).

fof(f_5217_1,plain,
    ! [V_P_2,V_Q_2] :
      ( hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2))
      | ~ hBOOL(V_Q_2) ),
    inference(fof_nnf,[status(thm)],[help_c__fdisj__2]) ).

fof(f_5217_2,plain,
    ! [U_20857,U_20856] :
      ( hBOOL(hAPP(hAPP(c_fdisj,U_20857),U_20856))
      | ~ hBOOL(U_20856) ),
    inference(variable_rename,[status(thm)],[f_5217_1]) ).

cnf(f_5217_3,plain,
    ( hBOOL(hAPP(hAPP(c_fdisj,U_20857),U_20856))
    | ~ hBOOL(U_20856) ),
    inference(clausify,[status(thm)],[f_5217_2]) ).

fof(f_5218_1,plain,
    ! [V_Q_2,V_P_2] :
      ( hBOOL(V_Q_2)
      | hBOOL(V_P_2)
      | ~ hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2)) ),
    inference(fof_nnf,[status(thm)],[help_c__fdisj__3]) ).

fof(f_5218_2,plain,
    ! [U_20859,U_20858] :
      ( hBOOL(U_20859)
      | hBOOL(U_20858)
      | ~ hBOOL(hAPP(hAPP(c_fdisj,U_20858),U_20859)) ),
    inference(variable_rename,[status(thm)],[f_5218_1]) ).

fof(f_5218_3,plain,
    ! [U_20859] :
      ( ! [U_20858] :
          ( hBOOL(U_20858)
          | ~ hBOOL(hAPP(hAPP(c_fdisj,U_20858),U_20859)) )
      | hBOOL(U_20859) ),
    inference(miniscope,[status(thm)],[f_5218_2]) ).

cnf(f_5218_4,plain,
    ( hBOOL(U_20858)
    | ~ hBOOL(hAPP(hAPP(c_fdisj,U_20858),U_20859))
    | hBOOL(U_20859) ),
    inference(clausify,[status(thm)],[f_5218_3]) ).

fof(f_5219_1,plain,
    ! [V_Q_2,V_P_2] :
      ( hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2))
      | hBOOL(V_P_2) ),
    inference(fof_nnf,[status(thm)],[help_c__fimplies__1]) ).

fof(f_5219_2,plain,
    ! [U_20861,U_20860] :
      ( hBOOL(hAPP(hAPP(c_fimplies,U_20860),U_20861))
      | hBOOL(U_20860) ),
    inference(variable_rename,[status(thm)],[f_5219_1]) ).

cnf(f_5219_3,plain,
    ( hBOOL(hAPP(hAPP(c_fimplies,U_20860),U_20861))
    | hBOOL(U_20860) ),
    inference(clausify,[status(thm)],[f_5219_2]) ).

fof(f_5220_1,plain,
    ! [V_P_2,V_Q_2] :
      ( hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2))
      | ~ hBOOL(V_Q_2) ),
    inference(fof_nnf,[status(thm)],[help_c__fimplies__2]) ).

fof(f_5220_2,plain,
    ! [U_20863,U_20862] :
      ( hBOOL(hAPP(hAPP(c_fimplies,U_20863),U_20862))
      | ~ hBOOL(U_20862) ),
    inference(variable_rename,[status(thm)],[f_5220_1]) ).

cnf(f_5220_3,plain,
    ( hBOOL(hAPP(hAPP(c_fimplies,U_20863),U_20862))
    | ~ hBOOL(U_20862) ),
    inference(clausify,[status(thm)],[f_5220_2]) ).

fof(f_5221_1,plain,
    ! [V_Q_2,V_P_2] :
      ( hBOOL(V_Q_2)
      | ~ hBOOL(V_P_2)
      | ~ hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2)) ),
    inference(fof_nnf,[status(thm)],[help_c__fimplies__3]) ).

fof(f_5221_2,plain,
    ! [U_20865,U_20864] :
      ( hBOOL(U_20865)
      | ~ hBOOL(U_20864)
      | ~ hBOOL(hAPP(hAPP(c_fimplies,U_20864),U_20865)) ),
    inference(variable_rename,[status(thm)],[f_5221_1]) ).

fof(f_5221_3,plain,
    ! [U_20865] :
      ( ! [U_20864] :
          ( ~ hBOOL(U_20864)
          | ~ hBOOL(hAPP(hAPP(c_fimplies,U_20864),U_20865)) )
      | hBOOL(U_20865) ),
    inference(miniscope,[status(thm)],[f_5221_2]) ).

cnf(f_5221_4,plain,
    ( ~ hBOOL(U_20864)
    | ~ hBOOL(hAPP(hAPP(c_fimplies,U_20864),U_20865))
    | hBOOL(U_20865) ),
    inference(clausify,[status(thm)],[f_5221_3]) ).

fof(f_5222_1,plain,
    c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G_H,v_ts),
    inference(fof_nnf,[status(thm)],[conj_0]) ).

cnf(f_5222_2,plain,
    c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G_H,v_ts),
    inference(clausify,[status(thm)],[f_5222_1]) ).

fof(f_5223_1,negated_conjecture,
    ~ ! [B_G] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_G_H),B_G))
       => c_Hoare__Mirabelle_Ohoare__derivs(t_a,B_G,v_ts) ),
    inference(negate,[status(cth)],[conj_1]) ).

fof(f_5223_2,negated_conjecture,
    ? [B_G] :
      ( ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,B_G,v_ts)
      & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_G_H),B_G)) ),
    inference(fof_nnf,[status(thm)],[f_5223_1]) ).

fof(f_5223_3,negated_conjecture,
    ? [U_20866] :
      ( ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,U_20866,v_ts)
      & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_G_H),U_20866)) ),
    inference(variable_rename,[status(thm)],[f_5223_2]) ).

fof(f_5223_4,negated_conjecture,
    ( ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,sK588,v_ts)
    & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_G_H),sK588)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK588]),skolemize(U_20866,sK588)],[f_5223_3]) ).

cnf(f_5223_5,negated_conjecture,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_G_H),sK588)),
    inference(clausify,[status(thm)],[f_5223_4]) ).

cnf(f_5223_6,negated_conjecture,
    ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,sK588,v_ts),
    inference(clausify,[status(thm)],[f_5223_4]) ).

cnf(f_619_3_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_619_3]) ).

cnf(f_619_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_619_6]) ).

cnf(f_715_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_715_6]) ).

cnf(f_722_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_722_7]) ).

cnf(f_722_8_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_722_8]) ).

cnf(f_722_13_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_722_13]) ).

cnf(f_1054_4_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1054_4]) ).

cnf(f_1054_5_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1054_5]) ).

cnf(f_1054_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1054_6]) ).

cnf(f_1054_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1054_7]) ).

cnf(f_1054_8_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1054_8]) ).

cnf(f_1054_9_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1054_9]) ).

cnf(f_1054_10_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1054_10]) ).

cnf(f_1556_5_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1556_5]) ).

cnf(f_1557_5_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1557_5]) ).

cnf(f_1576_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1576_6]) ).

cnf(f_1576_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1576_7]) ).

cnf(f_1576_12_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1576_12]) ).

cnf(f_1577_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1577_6]) ).

cnf(f_1577_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1577_7]) ).

cnf(f_1577_12_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1577_12]) ).

cnf(f_1588_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1588_6]) ).

cnf(f_1588_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1588_7]) ).

cnf(f_1588_12_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1588_12]) ).

cnf(f_1589_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1589_6]) ).

cnf(f_1589_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1589_7]) ).

cnf(f_1589_12_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1589_12]) ).

cnf(f_1734_5_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1734_5]) ).

cnf(f_1735_5_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1735_5]) ).

cnf(f_1736_5_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1736_5]) ).

cnf(f_1737_5_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1737_5]) ).

cnf(f_1740_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1740_6]) ).

cnf(f_1740_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1740_7]) ).

cnf(f_1740_12_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1740_12]) ).

cnf(f_1741_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1741_6]) ).

cnf(f_1741_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1741_7]) ).

cnf(f_1741_12_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1741_12]) ).

cnf(f_1742_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1742_6]) ).

cnf(f_1742_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1742_7]) ).

cnf(f_1742_12_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1742_12]) ).

cnf(f_1743_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1743_6]) ).

cnf(f_1743_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1743_7]) ).

cnf(f_1743_12_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1743_12]) ).

cnf(f_1744_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1744_6]) ).

cnf(f_1744_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1744_7]) ).

cnf(f_1744_12_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1744_12]) ).

cnf(f_1745_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1745_6]) ).

cnf(f_1745_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1745_7]) ).

cnf(f_1745_12_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1745_12]) ).

cnf(f_1746_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1746_6]) ).

cnf(f_1746_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1746_7]) ).

cnf(f_1746_12_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1746_12]) ).

cnf(f_1747_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1747_6]) ).

cnf(f_1747_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1747_7]) ).

cnf(f_1747_12_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1747_12]) ).

cnf(f_1846_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1846_7]) ).

cnf(f_1846_8_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1846_8]) ).

cnf(f_1846_13_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1846_13]) ).

cnf(f_1910_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1910_6]) ).

cnf(f_1923_3_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1923_3]) ).

cnf(f_1979_8_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_1979_8]) ).

cnf(f_2112_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2112_6]) ).

cnf(f_2113_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2113_6]) ).

cnf(f_2341_3_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2341_3]) ).

cnf(f_2425_8_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2425_8]) ).

cnf(f_2961_3_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2961_3]) ).

cnf(f_3025_10_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_3025_10]) ).

cnf(f_3025_11_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_3025_11]) ).

cnf(f_3025_16_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_3025_16]) ).

cnf(f_3652_3_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_3652_3]) ).

cnf(f_3654_4_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_3654_4]) ).

cnf(f_3750_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_3750_6]) ).

cnf(f_3750_7_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_3750_7]) ).

cnf(f_4067_8_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_4067_8]) ).

cnf(f_4628_6_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_4628_6]) ).

cnf(f_4966_3_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_4966_3]) ).

cnf(f_4968_3_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_4968_3]) ).

cnf(f_4973_3_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_4973_3]) ).

cnf(f_4974_3_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_4974_3]) ).

cnf(f_4975_3_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_4975_3]) ).

cnf(f_4984_3_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_4984_3]) ).

cnf(f_4985_3_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_4985_3]) ).

cnf(equality_1,axiom,
    Eq_x_0 = Eq_x_0,
    theory(equality,[reflexivity]) ).

cnf(equality_2,axiom,
    ( Eq_x_1 = Eq_x_0
    | Eq_x_0 != Eq_x_1 ),
    theory(equality,[symmetry]) ).

cnf(equality_3,axiom,
    ( Eq_x_0 = Eq_x_2
    | Eq_x_1 != Eq_x_2
    | Eq_x_0 != Eq_x_1 ),
    theory(equality,[transitivity]) ).

cnf(equality_4,axiom,
    ( hAPP(Eq_x_0,Eq_x_1) = hAPP(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_5,axiom,
    ( tc_Hoare__Mirabelle_Otriple(Eq_x_0) = tc_Hoare__Mirabelle_Otriple(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_6,axiom,
    ( tc_fun(Eq_x_0,Eq_x_1) = tc_fun(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_7,axiom,
    ( c_Orderings_Oord__class_Oless__eq(Eq_x_0) = c_Orderings_Oord__class_Oless__eq(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_8,axiom,
    ( c_Predicate_OPowp(Eq_x_0,Eq_x_1) = c_Predicate_OPowp(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_9,axiom,
    ( c_SetInterval_Oord__class_OgreaterThan(Eq_x_0) = c_SetInterval_Oord__class_OgreaterThan(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_10,axiom,
    ( c_SetInterval_Oord__class_OlessThan(Eq_x_0) = c_SetInterval_Oord__class_OlessThan(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_11,axiom,
    ( c_SetInterval_Oord__class_OatLeast(Eq_x_0) = c_SetInterval_Oord__class_OatLeast(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_12,axiom,
    ( c_SetInterval_Oord__class_OatMost(Eq_x_0) = c_SetInterval_Oord__class_OatMost(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_13,axiom,
    ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(Eq_x_0,Eq_x_1) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_14,axiom,
    ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI(Eq_x_0,Eq_x_1) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_15,axiom,
    ( c_Orderings_Otop__class_Otop(Eq_x_0) = c_Orderings_Otop__class_Otop(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_16,axiom,
    ( c_Orderings_Obot__class_Obot(Eq_x_0) = c_Orderings_Obot__class_Obot(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_17,axiom,
    ( c_Complete__Lattice_OInf__class_OInf(Eq_x_0,Eq_x_1) = c_Complete__Lattice_OInf__class_OInf(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_18,axiom,
    ( c_Complete__Lattice_OSup__class_OSup(Eq_x_0,Eq_x_1) = c_Complete__Lattice_OSup__class_OSup(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_19,axiom,
    ( c_Set_OPow(Eq_x_0) = c_Set_OPow(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_20,axiom,
    ( c_SetInterval_Oord__class_OgreaterThanLessThan(Eq_x_0,Eq_x_1,Eq_x_2) = c_SetInterval_Oord__class_OgreaterThanLessThan(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_21,axiom,
    ( c_SetInterval_Oord__class_OgreaterThanAtMost(Eq_x_0,Eq_x_1,Eq_x_2) = c_SetInterval_Oord__class_OgreaterThanAtMost(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_22,axiom,
    ( c_SetInterval_Oord__class_OatLeastLessThan(Eq_x_0,Eq_x_1) = c_SetInterval_Oord__class_OatLeastLessThan(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_23,axiom,
    ( c_Groups_Ouminus__class_Ouminus(Eq_x_0) = c_Groups_Ouminus__class_Ouminus(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_24,axiom,
    ( c_SetInterval_Oord__class_OatLeastAtMost(Eq_x_0,Eq_x_1,Eq_x_2) = c_SetInterval_Oord__class_OatLeastAtMost(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_25,axiom,
    ( c_member(Eq_x_0) = c_member(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_26,axiom,
    ( c_Lattices_Osemilattice__sup__class_Osup(Eq_x_0) = c_Lattices_Osemilattice__sup__class_Osup(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_27,axiom,
    ( c_Lattices_Osemilattice__inf__class_Oinf(Eq_x_0) = c_Lattices_Osemilattice__inf__class_Oinf(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_28,axiom,
    ( c_Orderings_Oord__class_Oless(Eq_x_0) = c_Orderings_Oord__class_Oless(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_29,axiom,
    ( c_Set_Oinsert(Eq_x_0) = c_Set_Oinsert(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_30,axiom,
    ( c_Set_Othe__elem(Eq_x_0,Eq_x_1) = c_Set_Othe__elem(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_31,axiom,
    ( c_Set_Oimage(Eq_x_0,Eq_x_1,Eq_x_2) = c_Set_Oimage(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_32,axiom,
    ( c_Orderings_Oord__class_Omax(Eq_x_0) = c_Orderings_Oord__class_Omax(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_33,axiom,
    ( c_Orderings_Oord_Omax(Eq_x_0,Eq_x_1) = c_Orderings_Oord_Omax(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_34,axiom,
    ( c_Big__Operators_Olattice_OSup__fin(Eq_x_0,Eq_x_1,Eq_x_2) = c_Big__Operators_Olattice_OSup__fin(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_35,axiom,
    ( c_Orderings_Oord__class_Omin(Eq_x_0) = c_Orderings_Oord__class_Omin(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_36,axiom,
    ( c_Orderings_Oord_Omin(Eq_x_0,Eq_x_1) = c_Orderings_Oord_Omin(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_37,axiom,
    ( c_Finite__Set_Ofinite(Eq_x_0) = c_Finite__Set_Ofinite(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_38,axiom,
    ( c_Big__Operators_Olattice_OInf__fin(Eq_x_0,Eq_x_1,Eq_x_2) = c_Big__Operators_Olattice_OInf__fin(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_39,axiom,
    ( c_Groups_Ominus__class_Ominus(Eq_x_0) = c_Groups_Ominus__class_Ominus(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_40,axiom,
    ( c_Fun_Ooverride__on(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_Fun_Ooverride__on(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_41,axiom,
    ( tc_prod(Eq_x_0,Eq_x_1) = tc_prod(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_42,axiom,
    ( tc_sum(Eq_x_0,Eq_x_1) = tc_sum(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_43,axiom,
    ( tc_Option_Ooption(Eq_x_0) = tc_Option_Ooption(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_44,axiom,
    ( c_SetInterval_Oord_OatMost(Eq_x_0,Eq_x_1,Eq_x_2) = c_SetInterval_Oord_OatMost(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_45,axiom,
    ( c_SetInterval_Oord_OatLeast(Eq_x_0,Eq_x_1,Eq_x_2) = c_SetInterval_Oord_OatLeast(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_46,axiom,
    ( c_SetInterval_Oord_OlessThan(Eq_x_0,Eq_x_1,Eq_x_2) = c_SetInterval_Oord_OlessThan(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_47,axiom,
    ( c_SetInterval_Oord_OgreaterThan(Eq_x_0,Eq_x_1,Eq_x_2) = c_SetInterval_Oord_OgreaterThan(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_48,axiom,
    ( c_SetInterval_Oord_OatLeastAtMost(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_SetInterval_Oord_OatLeastAtMost(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_49,axiom,
    ( c_SetInterval_Oord_OgreaterThanLessThan(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_SetInterval_Oord_OgreaterThanLessThan(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_50,axiom,
    ( c_SetInterval_Oord_OatLeastLessThan(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_SetInterval_Oord_OatLeastLessThan(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_51,axiom,
    ( c_SetInterval_Oord_OgreaterThanAtMost(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_SetInterval_Oord_OgreaterThanAtMost(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_52,axiom,
    ( c_Big__Operators_Olattice__class_OInf__fin(Eq_x_0,Eq_x_1) = c_Big__Operators_Olattice__class_OInf__fin(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_53,axiom,
    ( c_Big__Operators_Olattice__class_OSup__fin(Eq_x_0,Eq_x_1) = c_Big__Operators_Olattice__class_OSup__fin(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_54,axiom,
    ( c_Big__Operators_Olinorder__class_OMax(Eq_x_0,Eq_x_1) = c_Big__Operators_Olinorder__class_OMax(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_55,axiom,
    ( c_Big__Operators_Olinorder__class_OMin(Eq_x_0,Eq_x_1) = c_Big__Operators_Olinorder__class_OMin(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_56,axiom,
    ( c_Fun_Ofun__upd(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_Fun_Ofun__upd(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_57,axiom,
    ( c_Fun_Othe__inv__into(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Fun_Othe__inv__into(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_58,axiom,
    ( c_Finite__Set_Ofold1(Eq_x_0,Eq_x_1) = c_Finite__Set_Ofold1(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_59,axiom,
    ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum(Eq_x_0,Eq_x_1) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_60,axiom,
    ( c_Groups_Oplus__class_Oplus(Eq_x_0) = c_Groups_Oplus__class_Oplus(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_61,axiom,
    ( c_Groups_Otimes__class_Otimes(Eq_x_0) = c_Groups_Otimes__class_Otimes(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_62,axiom,
    ( c_Finite__Set_Ofold__graph(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_Finite__Set_Ofold__graph(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_63,axiom,
    ( c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(Eq_x_0,Eq_x_1) = c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_64,axiom,
    ( c_Finite__Set_Ofold(Eq_x_0,Eq_x_1,Eq_x_2) = c_Finite__Set_Ofold(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_65,axiom,
    ( c_Finite__Set_Ofold1Set(Eq_x_0,Eq_x_1,Eq_x_2) = c_Finite__Set_Ofold1Set(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_66,axiom,
    ( c_Finite__Set_Ocard(Eq_x_0) = c_Finite__Set_Ocard(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_67,axiom,
    ( c_Groups_Oone__class_Oone(Eq_x_0) = c_Groups_Oone__class_Oone(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_68,axiom,
    ( c_Groups_Ozero__class_Ozero(Eq_x_0) = c_Groups_Ozero__class_Ozero(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_69,axiom,
    ( c_Int_Oring__1__class_OInts(Eq_x_0) = c_Int_Oring__1__class_OInts(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_70,axiom,
    ( c_Sum__Type_OPlus(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Sum__Type_OPlus(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_71,axiom,
    ( c_Rings_Oinverse__class_Odivide(Eq_x_0) = c_Rings_Oinverse__class_Odivide(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_72,axiom,
    ( c_Finite__Set_Ofold__image(Eq_x_0,Eq_x_1,Eq_x_2) = c_Finite__Set_Ofold__image(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_73,axiom,
    ( c_Groups_Osgn__class_Osgn(Eq_x_0,Eq_x_1) = c_Groups_Osgn__class_Osgn(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_74,axiom,
    ( c_Power_Opower__class_Opower(Eq_x_0) = c_Power_Opower__class_Opower(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_75,axiom,
    ( c_Power_Opower_Opower(Eq_x_0,Eq_x_1,Eq_x_2) = c_Power_Opower_Opower(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_76,axiom,
    ( c_Int_Onumber__class_Onumber__of(Eq_x_0) = c_Int_Onumber__class_Onumber__of(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_77,axiom,
    ( c_Int_Opred(Eq_x_0) = c_Int_Opred(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_78,axiom,
    ( c_Int_Osucc(Eq_x_0) = c_Int_Osucc(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_79,axiom,
    ( c_Nat__Transfer_Otsub(Eq_x_0,Eq_x_1) = c_Nat__Transfer_Otsub(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_80,axiom,
    ( c_Divides_Odiv__class_Odiv(Eq_x_0) = c_Divides_Odiv__class_Odiv(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_81,axiom,
    ( c_SMT_Oz3div(Eq_x_0,Eq_x_1) = c_SMT_Oz3div(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_82,axiom,
    ( c_Nat_Osemiring__1__class_ONats(Eq_x_0) = c_Nat_Osemiring__1__class_ONats(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_83,axiom,
    ( c_Int_Onat__aux(Eq_x_0,Eq_x_1) = c_Int_Onat__aux(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_84,axiom,
    ( c_Int_OBit1(Eq_x_0) = c_Int_OBit1(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_85,axiom,
    ( c_Nat_Osemiring__1__class_Oof__nat(Eq_x_0) = c_Nat_Osemiring__1__class_Oof__nat(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_86,axiom,
    ( c_Int_OBit0(Eq_x_0) = c_Int_OBit0(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_87,axiom,
    ( c_Divides_Odiv__class_Omod(Eq_x_0,Eq_x_1,Eq_x_2) = c_Divides_Odiv__class_Omod(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_88,axiom,
    ( c_SMT_Oz3mod(Eq_x_0,Eq_x_1) = c_SMT_Oz3mod(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_89,axiom,
    ( c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(Eq_x_0) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_90,axiom,
    ( c_Int_Oring__1__class_Oof__int(Eq_x_0) = c_Int_Oring__1__class_Oof__int(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_91,axiom,
    ( c_Code__Numeral_Onat__of__aux(Eq_x_0,Eq_x_1) = c_Code__Numeral_Onat__of__aux(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_92,axiom,
    ( c_Code__Numeral_OSuc__code__numeral(Eq_x_0) = c_Code__Numeral_OSuc__code__numeral(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_93,axiom,
    ( c_Nat_Osize__class_Osize(Eq_x_0) = c_Nat_Osize__class_Osize(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_94,axiom,
    ( c_Groups_Oabs__class_Oabs(Eq_x_0) = c_Groups_Oabs__class_Oabs(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_95,axiom,
    ( c_Nitpick_Oint__lcm(Eq_x_0,Eq_x_1) = c_Nitpick_Oint__lcm(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_96,axiom,
    ( c_Nitpick_Onat__lcm(Eq_x_0,Eq_x_1) = c_Nitpick_Onat__lcm(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_97,axiom,
    ( c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_98,axiom,
    ( c_Nitpick_Onat__gcd(Eq_x_0,Eq_x_1) = c_Nitpick_Onat__gcd(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_99,axiom,
    ( c_Random_Olog(Eq_x_0,Eq_x_1) = c_Random_Olog(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_100,axiom,
    ( c_Random_Ominus__shift(Eq_x_0,Eq_x_1,Eq_x_2) = c_Random_Ominus__shift(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_101,axiom,
    ( c_Random_Oinc__shift(Eq_x_0,Eq_x_1) = c_Random_Oinc__shift(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_102,axiom,
    ( c_Nitpick_Opair__box_OPairBox(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Nitpick_Opair__box_OPairBox(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_103,axiom,
    ( c_Nitpick_Opair__box_Opair__box__size(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_Nitpick_Opair__box_Opair__box__size(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_104,axiom,
    ( c_COMBB(Eq_x_0,Eq_x_1,Eq_x_2) = c_COMBB(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_105,axiom,
    ( c_COMBC(Eq_x_0,Eq_x_1,Eq_x_2) = c_COMBC(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_106,axiom,
    ( c_Divides_OnegDivAlg(Eq_x_0,Eq_x_1) = c_Divides_OnegDivAlg(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_107,axiom,
    ( c_Product__Type_OPair(Eq_x_0,Eq_x_1) = c_Product__Type_OPair(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_108,axiom,
    ( c_Divides_Oadjust(Eq_x_0) = c_Divides_Oadjust(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_109,axiom,
    ( c_Fun_Ocomp(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Fun_Ocomp(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_110,axiom,
    ( c_COMBK(Eq_x_0,Eq_x_1) = c_COMBK(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_111,axiom,
    ( c_COMBS(Eq_x_0,Eq_x_1,Eq_x_2) = c_COMBS(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_112,axiom,
    ( c_COMBI(Eq_x_0) = c_COMBI(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_113,axiom,
    ( c_HOL_OLet(Eq_x_0,Eq_x_1) = c_HOL_OLet(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_114,axiom,
    ( c_If(Eq_x_0) = c_If(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_115,axiom,
    ( c_Nitpick_Onorm__frac(Eq_x_0,Eq_x_1) = c_Nitpick_Onorm__frac(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_116,axiom,
    ( c_Nat_Onat_Onat__case(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Nat_Onat_Onat__case(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_117,axiom,
    ( c_Divides_OposDivAlg(Eq_x_0,Eq_x_1) = c_Divides_OposDivAlg(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_118,axiom,
    ( c_FunDef_Oin__rel(Eq_x_0,Eq_x_1,Eq_x_2) = c_FunDef_Oin__rel(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_119,axiom,
    ( c_Code__Numeral_Odiv__mod__code__numeral(Eq_x_0,Eq_x_1) = c_Code__Numeral_Odiv__mod__code__numeral(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_120,axiom,
    ( c_Product__Type_Oprod_Oprod__case(Eq_x_0,Eq_x_1,Eq_x_2) = c_Product__Type_Oprod_Oprod__case(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_121,axiom,
    ( c_Divides_Odivmod__nat(Eq_x_0,Eq_x_1) = c_Divides_Odivmod__nat(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_122,axiom,
    ( c_Nat_Onat_Onat__rec(Eq_x_0,Eq_x_1,Eq_x_2) = c_Nat_Onat_Onat__rec(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_123,axiom,
    ( c_Divides_Odivmod__int(Eq_x_0,Eq_x_1) = c_Divides_Odivmod__int(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_124,axiom,
    ( c_Nat_Osemiring__1__class_Oof__nat__aux(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Nat_Osemiring__1__class_Oof__nat__aux(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_125,axiom,
    ( c_Product__Type_Oapsnd(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Product__Type_Oapsnd(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_126,axiom,
    ( c_Divides_Opdivmod(Eq_x_0,Eq_x_1) = c_Divides_Opdivmod(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_127,axiom,
    ( c_Divides_Odivmod__nat__rel(Eq_x_0,Eq_x_1) = c_Divides_Odivmod__nat__rel(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_128,axiom,
    ( tc_Nitpick_Opair__box(Eq_x_0,Eq_x_1) = tc_Nitpick_Opair__box(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_129,axiom,
    ( c_Nitpick_Opair__box_Opair__box__case(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_Nitpick_Opair__box_Opair__box__case(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_130,axiom,
    ( c_Nitpick_Opair__box_Opair__box__rec(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_Nitpick_Opair__box_Opair__box__rec(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_131,axiom,
    ( c_Wellfounded_Oaccp(Eq_x_0,Eq_x_1) = c_Wellfounded_Oaccp(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_132,axiom,
    ( c_Divides_Odivmod__int__rel(Eq_x_0,Eq_x_1) = c_Divides_Odivmod__int__rel(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_133,axiom,
    ( c_Nat_Onat_Onat__size(Eq_x_0) = c_Nat_Onat_Onat__size(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_134,axiom,
    ( c_Product__Type_Osnd(Eq_x_0,Eq_x_1) = c_Product__Type_Osnd(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_135,axiom,
    ( c_Wellfounded_Omeasure(Eq_x_0) = c_Wellfounded_Omeasure(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_136,axiom,
    ( c_Product__Type_Ofst(Eq_x_0,Eq_x_1) = c_Product__Type_Ofst(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_137,axiom,
    ( c_Product__Type_Oprod_Oprod__size(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_Product__Type_Oprod_Oprod__size(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_138,axiom,
    ( c_Random_Orange(Eq_x_0) = c_Random_Orange(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_139,axiom,
    ( c_Wellfounded_Omlex__prod(Eq_x_0,Eq_x_1,Eq_x_2) = c_Wellfounded_Omlex__prod(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_140,axiom,
    ( c_Orderings_Oord__class_OLeast(Eq_x_0,Eq_x_1) = c_Orderings_Oord__class_OLeast(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_141,axiom,
    ( c_Product__Type_Oprod_Oprod__rec(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_Product__Type_Oprod_Oprod__rec(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_142,axiom,
    ( c_Wellfounded_Olex__prod(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Wellfounded_Olex__prod(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_143,axiom,
    ( c_Recdef_Osame__fst(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Recdef_Osame__fst(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_144,axiom,
    ( c_Wellfounded_Ofinite__psubset(Eq_x_0) = c_Wellfounded_Ofinite__psubset(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_145,axiom,
    ( c_Product__Type_Oapfst(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Product__Type_Oapfst(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_146,axiom,
    ( c_Wellfounded_Omin__ext(Eq_x_0,Eq_x_1) = c_Wellfounded_Omin__ext(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_147,axiom,
    ( c_Wellfounded_Omax__ext(Eq_x_0,Eq_x_1) = c_Wellfounded_Omax__ext(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_148,axiom,
    ( c_Relation_Oinv__image(Eq_x_0,Eq_x_1) = c_Relation_Oinv__image(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_149,axiom,
    ( c_FunDef_Orp__inv__image(Eq_x_0,Eq_x_1) = c_FunDef_Orp__inv__image(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_150,axiom,
    ( c_Relation_OImage(Eq_x_0,Eq_x_1,Eq_x_2) = c_Relation_OImage(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_151,axiom,
    ( c_Relation_OField(Eq_x_0) = c_Relation_OField(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_152,axiom,
    ( c_Relation_OId__on(Eq_x_0,Eq_x_1) = c_Relation_OId__on(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_153,axiom,
    ( c_Equiv__Relations_Oquotient(Eq_x_0) = c_Equiv__Relations_Oquotient(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_154,axiom,
    ( c_Wellfounded_Oacc(Eq_x_0,Eq_x_1) = c_Wellfounded_Oacc(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_155,axiom,
    ( c_Nitpick_Ozero__frac(Eq_x_0) = c_Nitpick_Ozero__frac(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_156,axiom,
    ( c_Nitpick_OAbs__Frac(Eq_x_0,Eq_x_1) = c_Nitpick_OAbs__Frac(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_157,axiom,
    ( c_HOL_OThe(Eq_x_0,Eq_x_1) = c_HOL_OThe(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_158,axiom,
    ( c_Nitpick_Oone__frac(Eq_x_0) = c_Nitpick_Oone__frac(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_159,axiom,
    ( c_Nitpick_Onumber__of__frac(Eq_x_0,Eq_x_1) = c_Nitpick_Onumber__of__frac(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_160,axiom,
    ( c_Nitpick_Ofrac(Eq_x_0) = c_Nitpick_Ofrac(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_161,axiom,
    ( c_Partial__Function_Oflat__lub(Eq_x_0,Eq_x_1,Eq_x_2) = c_Partial__Function_Oflat__lub(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_162,axiom,
    ( c_Set_Ovimage(Eq_x_0,Eq_x_1,Eq_x_2) = c_Set_Ovimage(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_163,axiom,
    ( c_Product__Type_OSigma(Eq_x_0,Eq_x_1) = c_Product__Type_OSigma(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_164,axiom,
    ( c_Product__Type_Omap__pair(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = c_Product__Type_Omap__pair(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_165,axiom,
    ( c_Set_OCollect(Eq_x_0) = c_Set_OCollect(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_166,axiom,
    ( c_HOL_OEx(Eq_x_0) = c_HOL_OEx(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_167,axiom,
    ( c_Nitpick_Oprod(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Nitpick_Oprod(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_168,axiom,
    ( c_Int_Oint__ge__less__than(Eq_x_0) = c_Int_Oint__ge__less__than(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_169,axiom,
    ( c_Int_Oint__ge__less__than2(Eq_x_0) = c_Int_Oint__ge__less__than2(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_170,axiom,
    ( c_Fun_Oid(Eq_x_0) = c_Fun_Oid(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_171,axiom,
    ( c_Relation_Orel__comp(Eq_x_0,Eq_x_1,Eq_x_2) = c_Relation_Orel__comp(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_172,axiom,
    ( c_Relation_ORange(Eq_x_0,Eq_x_1) = c_Relation_ORange(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_173,axiom,
    ( c_Predicate_ORangeP(Eq_x_0,Eq_x_1,Eq_x_2) = c_Predicate_ORangeP(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_174,axiom,
    ( c_Predicate_Opred__comp(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_Predicate_Opred__comp(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_175,axiom,
    ( c_Relation_ODomain(Eq_x_0,Eq_x_1) = c_Relation_ODomain(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_176,axiom,
    ( c_Predicate_ODomainP(Eq_x_0,Eq_x_1,Eq_x_2) = c_Predicate_ODomainP(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_177,axiom,
    ( tc_List_Olist(Eq_x_0) = tc_List_Olist(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_178,axiom,
    ( c_List_Olenlex(Eq_x_0,Eq_x_1) = c_List_Olenlex(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_179,axiom,
    ( c_List_Olex(Eq_x_0,Eq_x_1) = c_List_Olex(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_180,axiom,
    ( c_List_Olexn(Eq_x_0,Eq_x_1) = c_List_Olexn(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_181,axiom,
    ( c_Set_OBall(Eq_x_0) = c_Set_OBall(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_182,axiom,
    ( c_HOL_OAll(Eq_x_0) = c_HOL_OAll(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_183,axiom,
    ( c_Hilbert__Choice_OEps(Eq_x_0,Eq_x_1) = c_Hilbert__Choice_OEps(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_184,axiom,
    ( c_Inductive_Ocomplete__lattice__class_Ogfp(Eq_x_0,Eq_x_1) = c_Inductive_Ocomplete__lattice__class_Ogfp(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_185,axiom,
    ( c_Inductive_Ocomplete__lattice__class_Olfp(Eq_x_0,Eq_x_1) = c_Inductive_Ocomplete__lattice__class_Olfp(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_186,axiom,
    ( c_Random_Oiterate(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Random_Oiterate(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_187,axiom,
    ( c_Product__Type_Oscomp(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Product__Type_Oscomp(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_188,axiom,
    ( c_Transitive__Closure_Otrancl(Eq_x_0,Eq_x_1) = c_Transitive__Closure_Otrancl(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_189,axiom,
    ( c_Transitive__Closure_Ortrancl(Eq_x_0,Eq_x_1) = c_Transitive__Closure_Ortrancl(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_190,axiom,
    ( c_Relation_OId(Eq_x_0) = c_Relation_OId(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_191,axiom,
    ( c_Relation_Oconverse(Eq_x_0,Eq_x_1) = c_Relation_Oconverse(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_192,axiom,
    ( c_Nat_Ocompow(Eq_x_0,Eq_x_1) = c_Nat_Ocompow(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_193,axiom,
    ( c_Nat_Ofunpow(Eq_x_0) = c_Nat_Ofunpow(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_194,axiom,
    ( c_Nitpick_Oplus__frac(Eq_x_0,Eq_x_1,Eq_x_2) = c_Nitpick_Oplus__frac(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_195,axiom,
    ( c_Nitpick_Odenom(Eq_x_0) = c_Nitpick_Odenom(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_196,axiom,
    ( c_Nitpick_Onum(Eq_x_0) = c_Nitpick_Onum(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_197,axiom,
    ( c_Nitpick_Otimes__frac(Eq_x_0,Eq_x_1,Eq_x_2) = c_Nitpick_Otimes__frac(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_198,axiom,
    ( c_Nitpick_Oof__frac(Eq_x_0,Eq_x_1,Eq_x_2) = c_Nitpick_Oof__frac(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_199,axiom,
    ( c_Nitpick_Oinverse__frac(Eq_x_0,Eq_x_1) = c_Nitpick_Oinverse__frac(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_200,axiom,
    ( c_Nitpick_Ouminus__frac(Eq_x_0,Eq_x_1) = c_Nitpick_Ouminus__frac(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_201,axiom,
    ( c_Nitpick_ORep__Frac(Eq_x_0) = c_Nitpick_ORep__Frac(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_202,axiom,
    ( c_Product__Type_Ointernal__split(Eq_x_0,Eq_x_1,Eq_x_2) = c_Product__Type_Ointernal__split(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_203,axiom,
    ( c_HOL_Obool_Obool__size(Eq_x_0) = c_HOL_Obool_Obool__size(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_204,axiom,
    ( c_List_Osublist(Eq_x_0,Eq_x_1,Eq_x_2) = c_List_Osublist(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_205,axiom,
    ( c_List_Olist_OCons(Eq_x_0) = c_List_Olist_OCons(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_206,axiom,
    ( c_List_Oset__Cons(Eq_x_0,Eq_x_1,Eq_x_2) = c_List_Oset__Cons(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_207,axiom,
    ( c_Random_Opick(Eq_x_0,Eq_x_1) = c_Random_Opick(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_208,axiom,
    ( c_Random_Oselect__weight(Eq_x_0,Eq_x_1) = c_Random_Oselect__weight(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_209,axiom,
    ( c_List_Olexord(Eq_x_0,Eq_x_1) = c_List_Olexord(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_210,axiom,
    ( c_List_Olistrel1(Eq_x_0,Eq_x_1) = c_List_Olistrel1(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_211,axiom,
    ( c_List_Olist_Olist__size(Eq_x_0,Eq_x_1,Eq_x_2) = c_List_Olist_Olist__size(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_212,axiom,
    ( c_List_Olistrel(Eq_x_0,Eq_x_1) = c_List_Olistrel(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_213,axiom,
    ( c_List_Olists(Eq_x_0,Eq_x_1) = c_List_Olists(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_214,axiom,
    ( c_List_Onth(Eq_x_0) = c_List_Onth(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_215,axiom,
    ( c_List_Otake(Eq_x_0) = c_List_Otake(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_216,axiom,
    ( c_List_Oset(Eq_x_0) = c_List_Oset(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_217,axiom,
    ( c_List_Ozip(Eq_x_0,Eq_x_1) = c_List_Ozip(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_218,axiom,
    ( c_List_Oupto(Eq_x_0,Eq_x_1) = c_List_Oupto(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_219,axiom,
    ( c_List_Omonoid__add__class_Olistsum(Eq_x_0) = c_List_Omonoid__add__class_Olistsum(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_220,axiom,
    ( c_List_Olist__update(Eq_x_0,Eq_x_1) = c_List_Olist__update(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_221,axiom,
    ( c_List_Obutlast(Eq_x_0,Eq_x_1) = c_List_Obutlast(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_222,axiom,
    ( c_List_Odistinct(Eq_x_0) = c_List_Odistinct(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_223,axiom,
    ( c_Nitpick_Ocard_H(Eq_x_0,Eq_x_1) = c_Nitpick_Ocard_H(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_224,axiom,
    ( c_List_Oremove1(Eq_x_0,Eq_x_1,Eq_x_2) = c_List_Oremove1(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_225,axiom,
    ( c_List_Olist_ONil(Eq_x_0) = c_List_Olist_ONil(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_226,axiom,
    ( c_Random_Oselect(Eq_x_0,Eq_x_1) = c_Random_Oselect(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_227,axiom,
    ( c_List_Olistset(Eq_x_0,Eq_x_1) = c_List_Olistset(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_228,axiom,
    ( c_List_Olist_Olist__case(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_List_Olist_Olist__case(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_229,axiom,
    ( c_List_Olinorder__class_Osorted__list__of__set(Eq_x_0,Eq_x_1) = c_List_Olinorder__class_Osorted__list__of__set(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_230,axiom,
    ( c_Lazy__Sequence_Oanamorph(Eq_x_0,Eq_x_1,Eq_x_2) = c_Lazy__Sequence_Oanamorph(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_231,axiom,
    ( c_Option_Ooption_Ooption__case(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_Option_Ooption_Ooption__case(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_232,axiom,
    ( c_List_Oappend(Eq_x_0) = c_List_Oappend(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_233,axiom,
    ( c_List_Orotate1(Eq_x_0) = c_List_Orotate1(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_234,axiom,
    ( c_List_Odrop(Eq_x_0) = c_List_Odrop(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_235,axiom,
    ( c_List_Ohd(Eq_x_0) = c_List_Ohd(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_236,axiom,
    ( c_List_Otl(Eq_x_0) = c_List_Otl(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_237,axiom,
    ( c_List_Orotate(Eq_x_0,Eq_x_1) = c_List_Orotate(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_238,axiom,
    ( c_List_Ofoldl(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_List_Ofoldl(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_239,axiom,
    ( c_List_Olinorder__class_Oinsort__key(Eq_x_0,Eq_x_1,Eq_x_2) = c_List_Olinorder__class_Oinsort__key(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_240,axiom,
    ( c_List_Olinorder__class_Oinsort__insert__key(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_List_Olinorder__class_Oinsort__insert__key(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_241,axiom,
    ( c_List_Olast(Eq_x_0,Eq_x_1) = c_List_Olast(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_242,axiom,
    ( c_List_Omap(Eq_x_0,Eq_x_1) = c_List_Omap(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_243,axiom,
    ( c_Nitpick_Osetsum_H(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Nitpick_Osetsum_H(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_244,axiom,
    ( c_New__DSequence_Opos__not__seq(Eq_x_0) = c_New__DSequence_Opos__not__seq(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_245,axiom,
    ( c_Lazy__Sequence_Ohb__not__seq(Eq_x_0) = c_Lazy__Sequence_Ohb__not__seq(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_246,axiom,
    ( c_List_Opartition(Eq_x_0,Eq_x_1,Eq_x_2) = c_List_Opartition(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_247,axiom,
    ( c_List_Olistsp(Eq_x_0,Eq_x_1) = c_List_Olistsp(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_248,axiom,
    ( c_Enum_Oproduct(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Enum_Oproduct(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_249,axiom,
    ( c_Enum_Osublists(Eq_x_0,Eq_x_1) = c_Enum_Osublists(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_250,axiom,
    ( c_Enum_On__lists(Eq_x_0,Eq_x_1,Eq_x_2) = c_Enum_On__lists(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_251,axiom,
    ( c_Enum_Oenum__the(Eq_x_0,Eq_x_1) = c_Enum_Oenum__the(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_252,axiom,
    ( c_List_Oremdups(Eq_x_0,Eq_x_1) = c_List_Oremdups(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_253,axiom,
    ( c_List_OremoveAll(Eq_x_0,Eq_x_1) = c_List_OremoveAll(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_254,axiom,
    ( c_List_Oconcat(Eq_x_0,Eq_x_1) = c_List_Oconcat(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_255,axiom,
    ( c_List_Olinorder__class_Osort__key(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_List_Olinorder__class_Osort__key(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_256,axiom,
    ( c_List_Otranspose(Eq_x_0,Eq_x_1) = c_List_Otranspose(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_257,axiom,
    ( c_List_Ofilter(Eq_x_0,Eq_x_1) = c_List_Ofilter(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_258,axiom,
    ( c_List_Otranspose__rel(Eq_x_0) = c_List_Otranspose__rel(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_259,axiom,
    ( c_List_Ofoldr(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_List_Ofoldr(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_260,axiom,
    ( c_List_Oupt(Eq_x_0,Eq_x_1) = c_List_Oupt(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_261,axiom,
    ( c_List_Orev(Eq_x_0) = c_List_Orev(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_262,axiom,
    ( c_List_OtakeWhile(Eq_x_0,Eq_x_1,Eq_x_2) = c_List_OtakeWhile(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_263,axiom,
    ( c_List_Oreturn__list(Eq_x_0) = c_List_Oreturn__list(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_264,axiom,
    ( c_List_Oembed__list(Eq_x_0) = c_List_Oembed__list(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_265,axiom,
    ( c_List_OdropWhile(Eq_x_0,Eq_x_1,Eq_x_2) = c_List_OdropWhile(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_266,axiom,
    ( c_List_Oinsert(Eq_x_0,Eq_x_1,Eq_x_2) = c_List_Oinsert(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_267,axiom,
    ( c_List_Omaps(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_List_Omaps(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_268,axiom,
    ( c_List_Omeasures(Eq_x_0,Eq_x_1) = c_List_Omeasures(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_269,axiom,
    ( c_Enum_Oenum__class_Oenum__ex(Eq_x_0) = c_Enum_Oenum__class_Oenum__ex(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_270,axiom,
    ( c_New__Random__Sequence_Opos__not__random__dseq(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_New__Random__Sequence_Opos__not__random__dseq(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_271,axiom,
    ( c_Enum_Oenum__class_Oenum__all(Eq_x_0) = c_Enum_Oenum__class_Oenum__all(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_272,axiom,
    ( c_New__DSequence_Opos__decr__bind(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_New__DSequence_Opos__decr__bind(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_273,axiom,
    ( c_Lazy__Sequence_Oempty(Eq_x_0) = c_Lazy__Sequence_Oempty(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_274,axiom,
    ( c_Lazy__Sequence_Obind(Eq_x_0,Eq_x_1,Eq_x_2) = c_Lazy__Sequence_Obind(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_275,axiom,
    ( tc_Lazy__Sequence_Olazy__sequence(Eq_x_0) = tc_Lazy__Sequence_Olazy__sequence(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_276,axiom,
    ( c_New__DSequence_Oneg__decr__bind(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_New__DSequence_Oneg__decr__bind(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_277,axiom,
    ( c_Lazy__Sequence_Ohit__bound(Eq_x_0) = c_Lazy__Sequence_Ohit__bound(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_278,axiom,
    ( c_Lazy__Sequence_Ohb__bind(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Lazy__Sequence_Ohb__bind(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_279,axiom,
    ( c_New__Random__Sequence_Oneg__decr__bind(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = c_New__Random__Sequence_Oneg__decr__bind(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_280,axiom,
    ( c_New__Random__Sequence_Opos__decr__bind(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = c_New__Random__Sequence_Opos__decr__bind(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_281,axiom,
    ( c_New__DSequence_Oneg__bind(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_New__DSequence_Oneg__bind(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_282,axiom,
    ( c_New__DSequence_Opos__empty(Eq_x_0) = c_New__DSequence_Opos__empty(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_283,axiom,
    ( c_New__Random__Sequence_Opos__empty(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_New__Random__Sequence_Opos__empty(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_284,axiom,
    ( c_New__Random__Sequence_Oneg__bind(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_New__Random__Sequence_Oneg__bind(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_285,axiom,
    ( c_New__DSequence_Opos__bind(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_New__DSequence_Opos__bind(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_286,axiom,
    ( c_New__Random__Sequence_Oneg__map(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_New__Random__Sequence_Oneg__map(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_287,axiom,
    ( c_New__Random__Sequence_Oneg__single(Eq_x_0) = c_New__Random__Sequence_Oneg__single(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_288,axiom,
    ( c_New__DSequence_Oneg__single(Eq_x_0,Eq_x_1) = c_New__DSequence_Oneg__single(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_289,axiom,
    ( c_New__Random__Sequence_Opos__bind(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_New__Random__Sequence_Opos__bind(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_290,axiom,
    ( c_Lazy__Sequence_Ohb__single(Eq_x_0,Eq_x_1) = c_Lazy__Sequence_Ohb__single(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_291,axiom,
    ( c_New__Random__Sequence_Opos__map(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_New__Random__Sequence_Opos__map(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_292,axiom,
    ( c_New__Random__Sequence_Opos__single(Eq_x_0) = c_New__Random__Sequence_Opos__single(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_293,axiom,
    ( c_New__DSequence_Opos__single(Eq_x_0,Eq_x_1) = c_New__DSequence_Opos__single(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_294,axiom,
    ( c_List_Osplice(Eq_x_0,Eq_x_1,Eq_x_2) = c_List_Osplice(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_295,axiom,
    ( c_Lazy__Sequence_Osingle(Eq_x_0) = c_Lazy__Sequence_Osingle(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_296,axiom,
    ( c_Predicate_Oconversep(Eq_x_0,Eq_x_1,Eq_x_2) = c_Predicate_Oconversep(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_297,axiom,
    ( c_Lazy__Sequence_Oproduct(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Lazy__Sequence_Oproduct(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_298,axiom,
    ( c_List_Oreplicate(Eq_x_0,Eq_x_1,Eq_x_2) = c_List_Oreplicate(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_299,axiom,
    ( c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(Eq_x_0,Eq_x_1) = c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_300,axiom,
    ( c_Lazy__Sequence_Oappend(Eq_x_0,Eq_x_1,Eq_x_2) = c_Lazy__Sequence_Oappend(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_301,axiom,
    ( c_New__DSequence_Opos__union(Eq_x_0,Eq_x_1,Eq_x_2) = c_New__DSequence_Opos__union(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_302,axiom,
    ( c_Lazy__Sequence_Olazy__sequence_OInsert(Eq_x_0,Eq_x_1,Eq_x_2) = c_Lazy__Sequence_Olazy__sequence_OInsert(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_303,axiom,
    ( c_New__Random__Sequence_Opos__union(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = c_New__Random__Sequence_Opos__union(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_304,axiom,
    ( c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(Eq_x_0,Eq_x_1) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_305,axiom,
    ( c_Lazy__Sequence_Osmall__lazy_H(Eq_x_0,Eq_x_1) = c_Lazy__Sequence_Osmall__lazy_H(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_306,axiom,
    ( c_Lazy__Sequence_Oyield(Eq_x_0) = c_Lazy__Sequence_Oyield(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_307,axiom,
    ( c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_308,axiom,
    ( c_Lazy__Sequence_Oyieldn(Eq_x_0) = c_Lazy__Sequence_Oyieldn(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_309,axiom,
    ( c_List_Omember(Eq_x_0) = c_List_Omember(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_310,axiom,
    ( c_FunDef_OTHE__default(Eq_x_0,Eq_x_1,Eq_x_2) = c_FunDef_OTHE__default(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_311,axiom,
    ( c_Lazy__Sequence_Olazy__sequence_OEmpty(Eq_x_0) = c_Lazy__Sequence_Olazy__sequence_OEmpty(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_312,axiom,
    ( c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_313,axiom,
    ( c_Random__Sequence_ORandom(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Random__Sequence_ORandom(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_314,axiom,
    ( c_DSequence_Oempty(Eq_x_0) = c_DSequence_Oempty(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_315,axiom,
    ( c_DSequence_Ounion(Eq_x_0) = c_DSequence_Ounion(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_316,axiom,
    ( c_DSequence_Osingle(Eq_x_0) = c_DSequence_Osingle(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_317,axiom,
    ( c_Random__Sequence_Oempty(Eq_x_0,Eq_x_1,Eq_x_2) = c_Random__Sequence_Oempty(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_318,axiom,
    ( c_Random__Sequence_Osingle(Eq_x_0) = c_Random__Sequence_Osingle(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_319,axiom,
    ( c_Random__Sequence_Omap(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Random__Sequence_Omap(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_320,axiom,
    ( c_Random__Sequence_Obind(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Random__Sequence_Obind(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_321,axiom,
    ( c_Set_OBex(Eq_x_0) = c_Set_OBex(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_322,axiom,
    ( c_Partial__Function_Ofun__lub(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = c_Partial__Function_Ofun__lub(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_323,axiom,
    ( c_Hilbert__Choice_Oinv__into(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Hilbert__Choice_Oinv__into(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_324,axiom,
    ( c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_325,axiom,
    ( c_Quickcheck_Obeyond(Eq_x_0,Eq_x_1) = c_Quickcheck_Obeyond(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_326,axiom,
    ( c_Product__Type_Ocurry(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Product__Type_Ocurry(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_327,axiom,
    ( c_Quotient_ORespects(Eq_x_0,Eq_x_1) = c_Quotient_ORespects(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_328,axiom,
    ( c_Quotient_OBabs(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Quotient_OBabs(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_329,axiom,
    ( c_Lazy__Sequence_Oflat(Eq_x_0,Eq_x_1) = c_Lazy__Sequence_Oflat(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_330,axiom,
    ( c_Lazy__Sequence_Omap(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_Lazy__Sequence_Omap(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_331,axiom,
    ( c_New__DSequence_Opos__map(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_New__DSequence_Opos__map(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_332,axiom,
    ( c_Rings_Odvd__class_Odvd(Eq_x_0) = c_Rings_Odvd__class_Odvd(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_333,axiom,
    ( sK1(Eq_x_0,Eq_x_1) = sK1(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_334,axiom,
    ( sK2(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK2(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_335,axiom,
    ( sK3(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK3(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_336,axiom,
    ( sK4(Eq_x_0,Eq_x_1,Eq_x_2) = sK4(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_337,axiom,
    ( sK5(Eq_x_0,Eq_x_1,Eq_x_2) = sK5(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_338,axiom,
    ( sK6(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK6(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_339,axiom,
    ( sK7(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK7(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_340,axiom,
    ( sK8(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK8(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_341,axiom,
    ( sK9(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK9(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_342,axiom,
    ( sK10(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK10(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_343,axiom,
    ( sK11(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK11(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_344,axiom,
    ( sK12(Eq_x_0,Eq_x_1,Eq_x_2) = sK12(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_345,axiom,
    ( sK13(Eq_x_0,Eq_x_1,Eq_x_2) = sK13(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_346,axiom,
    ( sK14(Eq_x_0,Eq_x_1,Eq_x_2) = sK14(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_347,axiom,
    ( sK15(Eq_x_0,Eq_x_1,Eq_x_2) = sK15(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_348,axiom,
    ( sK16(Eq_x_0,Eq_x_1,Eq_x_2) = sK16(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_349,axiom,
    ( sK17(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK17(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_350,axiom,
    ( sK18(Eq_x_0,Eq_x_1,Eq_x_2) = sK18(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_351,axiom,
    ( sK19(Eq_x_0,Eq_x_1,Eq_x_2) = sK19(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_352,axiom,
    ( sK20(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK20(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_353,axiom,
    ( sK21(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK21(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_354,axiom,
    ( sK22(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK22(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_355,axiom,
    ( sK23(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK23(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_356,axiom,
    ( sK24(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK24(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_357,axiom,
    ( sK25(Eq_x_0,Eq_x_1,Eq_x_2) = sK25(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_358,axiom,
    ( sK26(Eq_x_0,Eq_x_1,Eq_x_2) = sK26(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_359,axiom,
    ( sK27(Eq_x_0,Eq_x_1,Eq_x_2) = sK27(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_360,axiom,
    ( sK28(Eq_x_0,Eq_x_1,Eq_x_2) = sK28(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_361,axiom,
    ( sK29(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK29(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_362,axiom,
    ( sK30(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK30(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_363,axiom,
    ( sK31(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK31(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_364,axiom,
    ( sK32(Eq_x_0,Eq_x_1) = sK32(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_365,axiom,
    ( sK33(Eq_x_0,Eq_x_1) = sK33(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_366,axiom,
    ( sK34(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK34(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_367,axiom,
    ( sK35(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK35(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_368,axiom,
    ( sK36(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK36(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_369,axiom,
    ( sK37(Eq_x_0,Eq_x_1) = sK37(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_370,axiom,
    ( sK38(Eq_x_0,Eq_x_1) = sK38(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_371,axiom,
    ( sK39(Eq_x_0,Eq_x_1) = sK39(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_372,axiom,
    ( sK40(Eq_x_0,Eq_x_1) = sK40(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_373,axiom,
    ( sK41(Eq_x_0,Eq_x_1) = sK41(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_374,axiom,
    ( sK42(Eq_x_0,Eq_x_1,Eq_x_2) = sK42(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_375,axiom,
    ( sK43(Eq_x_0,Eq_x_1,Eq_x_2) = sK43(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_376,axiom,
    ( sK44(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK44(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_377,axiom,
    ( sK45(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK45(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_378,axiom,
    ( sK46(Eq_x_0,Eq_x_1) = sK46(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_379,axiom,
    ( sK47(Eq_x_0,Eq_x_1) = sK47(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_380,axiom,
    ( sK48(Eq_x_0,Eq_x_1) = sK48(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_381,axiom,
    ( sK49(Eq_x_0,Eq_x_1) = sK49(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_382,axiom,
    ( sK50(Eq_x_0,Eq_x_1) = sK50(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_383,axiom,
    ( sK51(Eq_x_0,Eq_x_1) = sK51(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_384,axiom,
    ( sK52(Eq_x_0,Eq_x_1) = sK52(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_385,axiom,
    ( sK53(Eq_x_0,Eq_x_1) = sK53(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_386,axiom,
    ( sK54(Eq_x_0,Eq_x_1,Eq_x_2) = sK54(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_387,axiom,
    ( sK55(Eq_x_0,Eq_x_1,Eq_x_2) = sK55(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_388,axiom,
    ( sK56(Eq_x_0,Eq_x_1,Eq_x_2) = sK56(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_389,axiom,
    ( sK57(Eq_x_0,Eq_x_1,Eq_x_2) = sK57(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_390,axiom,
    ( sK58(Eq_x_0,Eq_x_1,Eq_x_2) = sK58(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_391,axiom,
    ( sK59(Eq_x_0,Eq_x_1,Eq_x_2) = sK59(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_392,axiom,
    ( sK60(Eq_x_0,Eq_x_1,Eq_x_2) = sK60(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_393,axiom,
    ( sK61(Eq_x_0,Eq_x_1,Eq_x_2) = sK61(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_394,axiom,
    ( sK62(Eq_x_0,Eq_x_1,Eq_x_2) = sK62(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_395,axiom,
    ( sK63(Eq_x_0,Eq_x_1,Eq_x_2) = sK63(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_396,axiom,
    ( sK64(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK64(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_397,axiom,
    ( sK65(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK65(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_398,axiom,
    ( sK66(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK66(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_399,axiom,
    ( sK67(Eq_x_0,Eq_x_1,Eq_x_2) = sK67(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_400,axiom,
    ( sK68(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK68(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_401,axiom,
    ( sK69(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK69(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_402,axiom,
    ( sK70(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK70(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_403,axiom,
    ( sK71(Eq_x_0,Eq_x_1,Eq_x_2) = sK71(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_404,axiom,
    ( sK72(Eq_x_0,Eq_x_1,Eq_x_2) = sK72(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_405,axiom,
    ( sK73(Eq_x_0,Eq_x_1,Eq_x_2) = sK73(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_406,axiom,
    ( sK74(Eq_x_0,Eq_x_1,Eq_x_2) = sK74(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_407,axiom,
    ( sK75(Eq_x_0,Eq_x_1,Eq_x_2) = sK75(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_408,axiom,
    ( sK76(Eq_x_0,Eq_x_1,Eq_x_2) = sK76(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_409,axiom,
    ( sK77(Eq_x_0,Eq_x_1,Eq_x_2) = sK77(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_410,axiom,
    ( sK78(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK78(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_411,axiom,
    ( sK79(Eq_x_0,Eq_x_1,Eq_x_2) = sK79(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_412,axiom,
    ( sK80(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7) = sK80(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
    | Eq_x_7 != Eq_y_7
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_413,axiom,
    ( sK81(Eq_x_0) = sK81(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_414,axiom,
    ( sK82(Eq_x_0,Eq_x_1) = sK82(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_415,axiom,
    ( sK83(Eq_x_0,Eq_x_1) = sK83(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_416,axiom,
    ( sK84(Eq_x_0,Eq_x_1) = sK84(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_417,axiom,
    ( sK85(Eq_x_0) = sK85(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_418,axiom,
    ( sK86(Eq_x_0,Eq_x_1) = sK86(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_419,axiom,
    ( sK87(Eq_x_0,Eq_x_1) = sK87(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_420,axiom,
    ( sK88(Eq_x_0,Eq_x_1,Eq_x_2) = sK88(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_421,axiom,
    ( sK89(Eq_x_0,Eq_x_1,Eq_x_2) = sK89(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_422,axiom,
    ( sK90(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7) = sK90(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
    | Eq_x_7 != Eq_y_7
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_423,axiom,
    ( sK91(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK91(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_424,axiom,
    ( sK92(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK92(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_425,axiom,
    ( sK93(Eq_x_0,Eq_x_1) = sK93(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_426,axiom,
    ( sK94(Eq_x_0,Eq_x_1,Eq_x_2) = sK94(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_427,axiom,
    ( sK95(Eq_x_0,Eq_x_1) = sK95(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_428,axiom,
    ( sK96(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK96(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_429,axiom,
    ( sK97(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK97(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_430,axiom,
    ( sK98(Eq_x_0,Eq_x_1,Eq_x_2) = sK98(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_431,axiom,
    ( sK99(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK99(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_432,axiom,
    ( sK100(Eq_x_0) = sK100(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_433,axiom,
    ( sK101(Eq_x_0,Eq_x_1) = sK101(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_434,axiom,
    ( sK102(Eq_x_0,Eq_x_1,Eq_x_2) = sK102(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_435,axiom,
    ( sK103(Eq_x_0,Eq_x_1,Eq_x_2) = sK103(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_436,axiom,
    ( sK104(Eq_x_0,Eq_x_1,Eq_x_2) = sK104(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_437,axiom,
    ( sK105(Eq_x_0,Eq_x_1,Eq_x_2) = sK105(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_438,axiom,
    ( sK106(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK106(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_439,axiom,
    ( sK107(Eq_x_0,Eq_x_1,Eq_x_2) = sK107(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_440,axiom,
    ( sK108(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK108(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_441,axiom,
    ( sK109(Eq_x_0,Eq_x_1) = sK109(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_442,axiom,
    ( sK110(Eq_x_0,Eq_x_1) = sK110(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_443,axiom,
    ( sK111(Eq_x_0,Eq_x_1) = sK111(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_444,axiom,
    ( sK112(Eq_x_0,Eq_x_1) = sK112(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_445,axiom,
    ( sK113(Eq_x_0,Eq_x_1) = sK113(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_446,axiom,
    ( sK114(Eq_x_0,Eq_x_1) = sK114(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_447,axiom,
    ( sK115(Eq_x_0,Eq_x_1) = sK115(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_448,axiom,
    ( sK116(Eq_x_0,Eq_x_1) = sK116(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_449,axiom,
    ( sK117(Eq_x_0,Eq_x_1,Eq_x_2) = sK117(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_450,axiom,
    ( sK118(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK118(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_451,axiom,
    ( sK119(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK119(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_452,axiom,
    ( sK120(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK120(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_453,axiom,
    ( sK121(Eq_x_0,Eq_x_1,Eq_x_2) = sK121(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_454,axiom,
    ( sK122(Eq_x_0,Eq_x_1,Eq_x_2) = sK122(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_455,axiom,
    ( sK123(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK123(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_456,axiom,
    ( sK124(Eq_x_0,Eq_x_1) = sK124(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_457,axiom,
    ( sK125(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK125(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_458,axiom,
    ( sK126(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK126(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_459,axiom,
    ( sK127(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK127(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_460,axiom,
    ( sK128(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK128(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_461,axiom,
    ( sK129(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK129(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_462,axiom,
    ( sK130(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK130(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_463,axiom,
    ( sK131(Eq_x_0,Eq_x_1,Eq_x_2) = sK131(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_464,axiom,
    ( sK132(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK132(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_465,axiom,
    ( sK133(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK133(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_466,axiom,
    ( sK134(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK134(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_467,axiom,
    ( sK135(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK135(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_468,axiom,
    ( sK136(Eq_x_0,Eq_x_1,Eq_x_2) = sK136(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_469,axiom,
    ( sK137(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK137(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_470,axiom,
    ( sK138(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK138(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_471,axiom,
    ( sK139(Eq_x_0,Eq_x_1,Eq_x_2) = sK139(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_472,axiom,
    ( sK140(Eq_x_0,Eq_x_1,Eq_x_2) = sK140(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_473,axiom,
    ( sK141(Eq_x_0,Eq_x_1,Eq_x_2) = sK141(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_474,axiom,
    ( sK142(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK142(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_475,axiom,
    ( sK143(Eq_x_0,Eq_x_1) = sK143(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_476,axiom,
    ( sK144(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK144(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_477,axiom,
    ( sK145(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK145(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_478,axiom,
    ( sK146(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK146(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_479,axiom,
    ( sK147(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK147(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_480,axiom,
    ( sK148(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK148(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_481,axiom,
    ( sK149(Eq_x_0,Eq_x_1,Eq_x_2) = sK149(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_482,axiom,
    ( sK150(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK150(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_483,axiom,
    ( sK151(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK151(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_484,axiom,
    ( sK152(Eq_x_0,Eq_x_1,Eq_x_2) = sK152(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_485,axiom,
    ( sK153(Eq_x_0,Eq_x_1,Eq_x_2) = sK153(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_486,axiom,
    ( sK154(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK154(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_487,axiom,
    ( sK155(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK155(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_488,axiom,
    ( sK156(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK156(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_489,axiom,
    ( sK157(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK157(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_490,axiom,
    ( sK158(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK158(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_491,axiom,
    ( sK159(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK159(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_492,axiom,
    ( sK160(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK160(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_493,axiom,
    ( sK161(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK161(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_494,axiom,
    ( sK162(Eq_x_0,Eq_x_1) = sK162(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_495,axiom,
    ( sK163(Eq_x_0,Eq_x_1) = sK163(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_496,axiom,
    ( sK164(Eq_x_0,Eq_x_1) = sK164(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_497,axiom,
    ( sK165(Eq_x_0,Eq_x_1) = sK165(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_498,axiom,
    ( sK166(Eq_x_0,Eq_x_1) = sK166(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_499,axiom,
    ( sK167(Eq_x_0,Eq_x_1) = sK167(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_500,axiom,
    ( sK168(Eq_x_0,Eq_x_1,Eq_x_2) = sK168(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_501,axiom,
    ( sK169(Eq_x_0,Eq_x_1,Eq_x_2) = sK169(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_502,axiom,
    ( sK170(Eq_x_0,Eq_x_1,Eq_x_2) = sK170(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_503,axiom,
    ( sK171(Eq_x_0,Eq_x_1,Eq_x_2) = sK171(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_504,axiom,
    ( sK172(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK172(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_505,axiom,
    ( sK173(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK173(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_506,axiom,
    ( sK174(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK174(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_507,axiom,
    ( sK175(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK175(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_508,axiom,
    ( sK176(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK176(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_509,axiom,
    ( sK177(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK177(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_510,axiom,
    ( sK178(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK178(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_511,axiom,
    ( sK179(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK179(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_512,axiom,
    ( sK180(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK180(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_513,axiom,
    ( sK181(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK181(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_514,axiom,
    ( sK182(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK182(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_515,axiom,
    ( sK183(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK183(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_516,axiom,
    ( sK184(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK184(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_517,axiom,
    ( sK185(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK185(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_518,axiom,
    ( sK186(Eq_x_0,Eq_x_1,Eq_x_2) = sK186(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_519,axiom,
    ( sK187(Eq_x_0,Eq_x_1,Eq_x_2) = sK187(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_520,axiom,
    ( sK188(Eq_x_0,Eq_x_1,Eq_x_2) = sK188(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_521,axiom,
    ( sK189(Eq_x_0,Eq_x_1,Eq_x_2) = sK189(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_522,axiom,
    ( sK190(Eq_x_0,Eq_x_1,Eq_x_2) = sK190(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_523,axiom,
    ( sK191(Eq_x_0,Eq_x_1,Eq_x_2) = sK191(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_524,axiom,
    ( sK192(Eq_x_0) = sK192(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_525,axiom,
    ( sK193(Eq_x_0) = sK193(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_526,axiom,
    ( sK194(Eq_x_0) = sK194(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_527,axiom,
    ( sK195(Eq_x_0) = sK195(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_528,axiom,
    ( sK196(Eq_x_0,Eq_x_1,Eq_x_2) = sK196(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_529,axiom,
    ( sK197(Eq_x_0,Eq_x_1,Eq_x_2) = sK197(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_530,axiom,
    ( sK198(Eq_x_0,Eq_x_1,Eq_x_2) = sK198(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_531,axiom,
    ( sK199(Eq_x_0) = sK199(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_532,axiom,
    ( sK200(Eq_x_0) = sK200(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_533,axiom,
    ( sK201(Eq_x_0) = sK201(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_534,axiom,
    ( sK202(Eq_x_0) = sK202(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_535,axiom,
    ( sK203(Eq_x_0,Eq_x_1) = sK203(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_536,axiom,
    ( sK204(Eq_x_0,Eq_x_1) = sK204(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_537,axiom,
    ( sK205(Eq_x_0,Eq_x_1) = sK205(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_538,axiom,
    ( sK206(Eq_x_0,Eq_x_1) = sK206(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_539,axiom,
    ( sK207(Eq_x_0) = sK207(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_540,axiom,
    ( sK208(Eq_x_0,Eq_x_1,Eq_x_2) = sK208(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_541,axiom,
    ( sK209(Eq_x_0,Eq_x_1,Eq_x_2) = sK209(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_542,axiom,
    ( sK210(Eq_x_0,Eq_x_1,Eq_x_2) = sK210(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_543,axiom,
    ( sK211(Eq_x_0,Eq_x_1,Eq_x_2) = sK211(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_544,axiom,
    ( sK212(Eq_x_0,Eq_x_1,Eq_x_2) = sK212(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_545,axiom,
    ( sK213(Eq_x_0,Eq_x_1,Eq_x_2) = sK213(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_546,axiom,
    ( sK214(Eq_x_0,Eq_x_1,Eq_x_2) = sK214(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_547,axiom,
    ( sK215(Eq_x_0,Eq_x_1,Eq_x_2) = sK215(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_548,axiom,
    ( sK216(Eq_x_0,Eq_x_1) = sK216(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_549,axiom,
    ( sK217(Eq_x_0,Eq_x_1,Eq_x_2) = sK217(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_550,axiom,
    ( sK218(Eq_x_0,Eq_x_1,Eq_x_2) = sK218(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_551,axiom,
    ( sK219(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK219(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_552,axiom,
    ( sK220(Eq_x_0) = sK220(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_553,axiom,
    ( sK221(Eq_x_0) = sK221(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_554,axiom,
    ( sK222(Eq_x_0,Eq_x_1,Eq_x_2) = sK222(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_555,axiom,
    ( sK223(Eq_x_0,Eq_x_1,Eq_x_2) = sK223(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_556,axiom,
    ( sK224(Eq_x_0,Eq_x_1,Eq_x_2) = sK224(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_557,axiom,
    ( sK225(Eq_x_0,Eq_x_1,Eq_x_2) = sK225(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_558,axiom,
    ( sK226(Eq_x_0,Eq_x_1,Eq_x_2) = sK226(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_559,axiom,
    ( sK227(Eq_x_0,Eq_x_1,Eq_x_2) = sK227(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_560,axiom,
    ( sK228(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK228(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_561,axiom,
    ( sK229(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK229(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_562,axiom,
    ( sK230(Eq_x_0,Eq_x_1,Eq_x_2) = sK230(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_563,axiom,
    ( sK231(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK231(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_564,axiom,
    ( sK232(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK232(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_565,axiom,
    ( sK233(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK233(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_566,axiom,
    ( sK234(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK234(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_567,axiom,
    ( sK235(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK235(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_568,axiom,
    ( sK236(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK236(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_569,axiom,
    ( sK237(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK237(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_570,axiom,
    ( sK238(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK238(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_571,axiom,
    ( sK239(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK239(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_572,axiom,
    ( sK240(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK240(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_573,axiom,
    ( sK241(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK241(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_574,axiom,
    ( sK242(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK242(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_575,axiom,
    ( sK243(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK243(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_576,axiom,
    ( sK244(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK244(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_577,axiom,
    ( sK245(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK245(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_578,axiom,
    ( sK246(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK246(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_579,axiom,
    ( sK247(Eq_x_0,Eq_x_1) = sK247(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_580,axiom,
    ( sK248(Eq_x_0,Eq_x_1,Eq_x_2) = sK248(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_581,axiom,
    ( sK249(Eq_x_0,Eq_x_1,Eq_x_2) = sK249(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_582,axiom,
    ( sK250(Eq_x_0,Eq_x_1,Eq_x_2) = sK250(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_583,axiom,
    ( sK251(Eq_x_0,Eq_x_1,Eq_x_2) = sK251(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_584,axiom,
    ( sK252(Eq_x_0,Eq_x_1,Eq_x_2) = sK252(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_585,axiom,
    ( sK253(Eq_x_0,Eq_x_1,Eq_x_2) = sK253(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_586,axiom,
    ( sK254(Eq_x_0,Eq_x_1,Eq_x_2) = sK254(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_587,axiom,
    ( sK255(Eq_x_0,Eq_x_1,Eq_x_2) = sK255(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_588,axiom,
    ( sK256(Eq_x_0,Eq_x_1,Eq_x_2) = sK256(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_589,axiom,
    ( sK257(Eq_x_0,Eq_x_1,Eq_x_2) = sK257(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_590,axiom,
    ( sK258(Eq_x_0,Eq_x_1,Eq_x_2) = sK258(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_591,axiom,
    ( sK259(Eq_x_0,Eq_x_1,Eq_x_2) = sK259(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_592,axiom,
    ( sK260(Eq_x_0,Eq_x_1,Eq_x_2) = sK260(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_593,axiom,
    ( sK261(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK261(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_594,axiom,
    ( sK262(Eq_x_0,Eq_x_1,Eq_x_2) = sK262(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_595,axiom,
    ( sK263(Eq_x_0,Eq_x_1,Eq_x_2) = sK263(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_596,axiom,
    ( sK264(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK264(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_597,axiom,
    ( sK265(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK265(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_598,axiom,
    ( sK266(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK266(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_599,axiom,
    ( sK267(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK267(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_600,axiom,
    ( sK268(Eq_x_0,Eq_x_1,Eq_x_2) = sK268(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_601,axiom,
    ( sK269(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7) = sK269(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
    | Eq_x_7 != Eq_y_7
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_602,axiom,
    ( sK270(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK270(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_603,axiom,
    ( sK271(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK271(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_604,axiom,
    ( sK272(Eq_x_0,Eq_x_1,Eq_x_2) = sK272(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_605,axiom,
    ( sK273(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7) = sK273(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
    | Eq_x_7 != Eq_y_7
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_606,axiom,
    ( sK274(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK274(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_607,axiom,
    ( sK275(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK275(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_608,axiom,
    ( sK276(Eq_x_0,Eq_x_1) = sK276(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_609,axiom,
    ( sK277(Eq_x_0) = sK277(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_610,axiom,
    ( sK278(Eq_x_0) = sK278(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_611,axiom,
    ( sK279(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK279(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_612,axiom,
    ( sK280(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK280(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_613,axiom,
    ( sK281(Eq_x_0) = sK281(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_614,axiom,
    ( sK282(Eq_x_0) = sK282(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_615,axiom,
    ( sK283(Eq_x_0) = sK283(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_616,axiom,
    ( sK284(Eq_x_0) = sK284(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_617,axiom,
    ( sK285(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK285(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_618,axiom,
    ( sK286(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK286(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_619,axiom,
    ( sK287(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7,Eq_x_8,Eq_x_9,Eq_x_10) = sK287(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7,Eq_y_8,Eq_y_9,Eq_y_10)
    | Eq_x_10 != Eq_y_10
    | Eq_x_9 != Eq_y_9
    | Eq_x_8 != Eq_y_8
    | Eq_x_7 != Eq_y_7
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_620,axiom,
    ( sK288(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7,Eq_x_8,Eq_x_9,Eq_x_10) = sK288(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7,Eq_y_8,Eq_y_9,Eq_y_10)
    | Eq_x_10 != Eq_y_10
    | Eq_x_9 != Eq_y_9
    | Eq_x_8 != Eq_y_8
    | Eq_x_7 != Eq_y_7
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_621,axiom,
    ( sK289(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK289(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_622,axiom,
    ( sK290(Eq_x_0,Eq_x_1,Eq_x_2) = sK290(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_623,axiom,
    ( sK291(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK291(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_624,axiom,
    ( sK292(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK292(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_625,axiom,
    ( sK293(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK293(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_626,axiom,
    ( sK294(Eq_x_0,Eq_x_1,Eq_x_2) = sK294(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_627,axiom,
    ( sK295(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK295(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_628,axiom,
    ( sK296(Eq_x_0) = sK296(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_629,axiom,
    ( sK297(Eq_x_0,Eq_x_1) = sK297(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_630,axiom,
    ( sK298(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK298(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_631,axiom,
    ( sK299(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK299(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_632,axiom,
    ( sK300(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK300(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_633,axiom,
    ( sK301(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK301(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_634,axiom,
    ( sK302(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK302(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_635,axiom,
    ( sK303(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK303(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_636,axiom,
    ( sK304(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK304(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_637,axiom,
    ( sK305(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK305(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_638,axiom,
    ( sK306(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK306(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_639,axiom,
    ( sK307(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7) = sK307(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
    | Eq_x_7 != Eq_y_7
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_640,axiom,
    ( sK308(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7) = sK308(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
    | Eq_x_7 != Eq_y_7
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_641,axiom,
    ( sK309(Eq_x_0,Eq_x_1,Eq_x_2) = sK309(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_642,axiom,
    ( sK310(Eq_x_0) = sK310(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_643,axiom,
    ( sK311(Eq_x_0) = sK311(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_644,axiom,
    ( sK312(Eq_x_0,Eq_x_1,Eq_x_2) = sK312(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_645,axiom,
    ( sK313(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK313(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_646,axiom,
    ( sK314(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK314(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_647,axiom,
    ( sK315(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK315(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_648,axiom,
    ( sK316(Eq_x_0,Eq_x_1) = sK316(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_649,axiom,
    ( sK317(Eq_x_0,Eq_x_1) = sK317(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_650,axiom,
    ( sK318(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK318(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_651,axiom,
    ( sK319(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK319(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_652,axiom,
    ( sK320(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK320(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_653,axiom,
    ( sK321(Eq_x_0,Eq_x_1) = sK321(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_654,axiom,
    ( sK322(Eq_x_0,Eq_x_1) = sK322(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_655,axiom,
    ( sK323(Eq_x_0,Eq_x_1,Eq_x_2) = sK323(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_656,axiom,
    ( sK324(Eq_x_0,Eq_x_1) = sK324(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_657,axiom,
    ( sK325(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK325(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_658,axiom,
    ( sK326(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK326(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_659,axiom,
    ( sK327(Eq_x_0,Eq_x_1) = sK327(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_660,axiom,
    ( sK328(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK328(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_661,axiom,
    ( sK329(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK329(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_662,axiom,
    ( sK330(Eq_x_0,Eq_x_1) = sK330(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_663,axiom,
    ( sK331(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK331(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_664,axiom,
    ( sK332(Eq_x_0,Eq_x_1,Eq_x_2) = sK332(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_665,axiom,
    ( sK333(Eq_x_0,Eq_x_1,Eq_x_2) = sK333(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_666,axiom,
    ( sK334(Eq_x_0,Eq_x_1,Eq_x_2) = sK334(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_667,axiom,
    ( sK335(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK335(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_668,axiom,
    ( sK336(Eq_x_0,Eq_x_1) = sK336(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_669,axiom,
    ( sK337(Eq_x_0) = sK337(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_670,axiom,
    ( sK338(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK338(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_671,axiom,
    ( sK339(Eq_x_0,Eq_x_1) = sK339(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_672,axiom,
    ( sK340(Eq_x_0,Eq_x_1,Eq_x_2) = sK340(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_673,axiom,
    ( sK341(Eq_x_0,Eq_x_1,Eq_x_2) = sK341(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_674,axiom,
    ( sK342(Eq_x_0,Eq_x_1,Eq_x_2) = sK342(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_675,axiom,
    ( sK343(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK343(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_676,axiom,
    ( sK344(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK344(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_677,axiom,
    ( sK345(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK345(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_678,axiom,
    ( sK346(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK346(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_679,axiom,
    ( sK347(Eq_x_0,Eq_x_1) = sK347(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_680,axiom,
    ( sK348(Eq_x_0,Eq_x_1) = sK348(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_681,axiom,
    ( sK349(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK349(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_682,axiom,
    ( sK350(Eq_x_0,Eq_x_1,Eq_x_2) = sK350(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_683,axiom,
    ( sK351(Eq_x_0,Eq_x_1,Eq_x_2) = sK351(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_684,axiom,
    ( sK352(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK352(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_685,axiom,
    ( sK353(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK353(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_686,axiom,
    ( sK354(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK354(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_687,axiom,
    ( sK355(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK355(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_688,axiom,
    ( sK356(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK356(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_689,axiom,
    ( sK357(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK357(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_690,axiom,
    ( sK358(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK358(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_691,axiom,
    ( sK359(Eq_x_0,Eq_x_1,Eq_x_2) = sK359(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_692,axiom,
    ( sK360(Eq_x_0,Eq_x_1,Eq_x_2) = sK360(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_693,axiom,
    ( sK361(Eq_x_0,Eq_x_1) = sK361(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_694,axiom,
    ( sK362(Eq_x_0,Eq_x_1) = sK362(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_695,axiom,
    ( sK363(Eq_x_0,Eq_x_1,Eq_x_2) = sK363(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_696,axiom,
    ( sK364(Eq_x_0,Eq_x_1) = sK364(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_697,axiom,
    ( sK365(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK365(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_698,axiom,
    ( sK366(Eq_x_0,Eq_x_1,Eq_x_2) = sK366(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_699,axiom,
    ( sK367(Eq_x_0,Eq_x_1,Eq_x_2) = sK367(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_700,axiom,
    ( sK368(Eq_x_0,Eq_x_1,Eq_x_2) = sK368(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_701,axiom,
    ( sK369(Eq_x_0,Eq_x_1,Eq_x_2) = sK369(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_702,axiom,
    ( sK370(Eq_x_0,Eq_x_1,Eq_x_2) = sK370(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_703,axiom,
    ( sK371(Eq_x_0,Eq_x_1) = sK371(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_704,axiom,
    ( sK372(Eq_x_0,Eq_x_1,Eq_x_2) = sK372(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_705,axiom,
    ( sK373(Eq_x_0,Eq_x_1,Eq_x_2) = sK373(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_706,axiom,
    ( sK374(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK374(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_707,axiom,
    ( sK375(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK375(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_708,axiom,
    ( sK376(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK376(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_709,axiom,
    ( sK377(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK377(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_710,axiom,
    ( sK378(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK378(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_711,axiom,
    ( sK379(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK379(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_712,axiom,
    ( sK380(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK380(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_713,axiom,
    ( sK381(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK381(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_714,axiom,
    ( sK382(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK382(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_715,axiom,
    ( sK383(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK383(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_716,axiom,
    ( sK384(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK384(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_717,axiom,
    ( sK385(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK385(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_718,axiom,
    ( sK386(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK386(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_719,axiom,
    ( sK387(Eq_x_0,Eq_x_1) = sK387(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_720,axiom,
    ( sK388(Eq_x_0,Eq_x_1) = sK388(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_721,axiom,
    ( sK389(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK389(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_722,axiom,
    ( sK390(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK390(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_723,axiom,
    ( sK391(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK391(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_724,axiom,
    ( sK392(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK392(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_725,axiom,
    ( sK393(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK393(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_726,axiom,
    ( sK394(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK394(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_727,axiom,
    ( sK395(Eq_x_0,Eq_x_1) = sK395(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_728,axiom,
    ( sK396(Eq_x_0,Eq_x_1,Eq_x_2) = sK396(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_729,axiom,
    ( sK397(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK397(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_730,axiom,
    ( sK398(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK398(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_731,axiom,
    ( sK399(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK399(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_732,axiom,
    ( sK400(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK400(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_733,axiom,
    ( sK401(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK401(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_734,axiom,
    ( sK402(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK402(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_735,axiom,
    ( sK403(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK403(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_736,axiom,
    ( sK404(Eq_x_0,Eq_x_1,Eq_x_2) = sK404(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_737,axiom,
    ( sK405(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK405(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_738,axiom,
    ( sK406(Eq_x_0,Eq_x_1,Eq_x_2) = sK406(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_739,axiom,
    ( sK407(Eq_x_0,Eq_x_1,Eq_x_2) = sK407(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_740,axiom,
    ( sK408(Eq_x_0,Eq_x_1,Eq_x_2) = sK408(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_741,axiom,
    ( sK409(Eq_x_0,Eq_x_1,Eq_x_2) = sK409(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_742,axiom,
    ( sK410(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK410(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_743,axiom,
    ( sK411(Eq_x_0,Eq_x_1,Eq_x_2) = sK411(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_744,axiom,
    ( sK412(Eq_x_0) = sK412(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_745,axiom,
    ( sK413(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK413(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_746,axiom,
    ( sK414(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK414(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_747,axiom,
    ( sK415(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK415(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_748,axiom,
    ( sK416(Eq_x_0,Eq_x_1) = sK416(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_749,axiom,
    ( sK417(Eq_x_0,Eq_x_1) = sK417(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_750,axiom,
    ( sK418(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK418(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_751,axiom,
    ( sK419(Eq_x_0,Eq_x_1,Eq_x_2) = sK419(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_752,axiom,
    ( sK420(Eq_x_0,Eq_x_1,Eq_x_2) = sK420(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_753,axiom,
    ( sK421(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK421(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_754,axiom,
    ( sK422(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK422(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_755,axiom,
    ( sK423(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK423(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_756,axiom,
    ( sK424(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK424(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_757,axiom,
    ( sK425(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK425(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_758,axiom,
    ( sK426(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK426(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_759,axiom,
    ( sK427(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK427(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_760,axiom,
    ( sK428(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK428(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_761,axiom,
    ( sK429(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK429(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_762,axiom,
    ( sK430(Eq_x_0,Eq_x_1) = sK430(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_763,axiom,
    ( sK431(Eq_x_0,Eq_x_1,Eq_x_2) = sK431(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_764,axiom,
    ( sK432(Eq_x_0,Eq_x_1,Eq_x_2) = sK432(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_765,axiom,
    ( sK433(Eq_x_0,Eq_x_1,Eq_x_2) = sK433(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_766,axiom,
    ( sK434(Eq_x_0,Eq_x_1,Eq_x_2) = sK434(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_767,axiom,
    ( sK435(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK435(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_768,axiom,
    ( sK436(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK436(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_769,axiom,
    ( sK437(Eq_x_0,Eq_x_1,Eq_x_2) = sK437(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_770,axiom,
    ( sK438(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK438(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_771,axiom,
    ( sK439(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK439(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_772,axiom,
    ( sK440(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK440(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_773,axiom,
    ( sK441(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK441(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_774,axiom,
    ( sK442(Eq_x_0,Eq_x_1) = sK442(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_775,axiom,
    ( sK443(Eq_x_0,Eq_x_1) = sK443(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_776,axiom,
    ( sK444(Eq_x_0,Eq_x_1,Eq_x_2) = sK444(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_777,axiom,
    ( sK445(Eq_x_0,Eq_x_1,Eq_x_2) = sK445(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_778,axiom,
    ( sK446(Eq_x_0,Eq_x_1,Eq_x_2) = sK446(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_779,axiom,
    ( sK447(Eq_x_0,Eq_x_1,Eq_x_2) = sK447(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_780,axiom,
    ( sK448(Eq_x_0,Eq_x_1) = sK448(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_781,axiom,
    ( sK449(Eq_x_0,Eq_x_1,Eq_x_2) = sK449(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_782,axiom,
    ( sK450(Eq_x_0,Eq_x_1,Eq_x_2) = sK450(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_783,axiom,
    ( sK451(Eq_x_0,Eq_x_1,Eq_x_2) = sK451(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_784,axiom,
    ( sK452(Eq_x_0,Eq_x_1,Eq_x_2) = sK452(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_785,axiom,
    ( sK453(Eq_x_0,Eq_x_1,Eq_x_2) = sK453(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_786,axiom,
    ( sK454(Eq_x_0,Eq_x_1) = sK454(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_787,axiom,
    ( sK455(Eq_x_0,Eq_x_1) = sK455(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_788,axiom,
    ( sK456(Eq_x_0,Eq_x_1,Eq_x_2) = sK456(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_789,axiom,
    ( sK457(Eq_x_0,Eq_x_1,Eq_x_2) = sK457(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_790,axiom,
    ( sK458(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK458(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_791,axiom,
    ( sK459(Eq_x_0,Eq_x_1) = sK459(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_792,axiom,
    ( sK460(Eq_x_0,Eq_x_1) = sK460(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_793,axiom,
    ( sK461(Eq_x_0,Eq_x_1,Eq_x_2) = sK461(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_794,axiom,
    ( sK462(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK462(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_795,axiom,
    ( sK463(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK463(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_796,axiom,
    ( sK464(Eq_x_0,Eq_x_1) = sK464(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_797,axiom,
    ( sK465(Eq_x_0,Eq_x_1) = sK465(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_798,axiom,
    ( sK466(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK466(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_799,axiom,
    ( sK467(Eq_x_0,Eq_x_1) = sK467(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_800,axiom,
    ( sK468(Eq_x_0,Eq_x_1) = sK468(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_801,axiom,
    ( sK469(Eq_x_0,Eq_x_1) = sK469(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_802,axiom,
    ( sK470(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7) = sK470(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
    | Eq_x_7 != Eq_y_7
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_803,axiom,
    ( sK471(Eq_x_0,Eq_x_1) = sK471(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_804,axiom,
    ( sK472(Eq_x_0,Eq_x_1) = sK472(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_805,axiom,
    ( sK473(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK473(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_806,axiom,
    ( sK474(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK474(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_807,axiom,
    ( sK475(Eq_x_0,Eq_x_1) = sK475(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_808,axiom,
    ( sK476(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK476(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_809,axiom,
    ( sK477(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK477(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_810,axiom,
    ( sK478(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK478(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_811,axiom,
    ( sK479(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK479(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_812,axiom,
    ( sK480(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK480(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_813,axiom,
    ( sK481(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK481(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_814,axiom,
    ( sK482(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK482(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_815,axiom,
    ( sK483(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK483(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_816,axiom,
    ( sK484(Eq_x_0,Eq_x_1) = sK484(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_817,axiom,
    ( sK485(Eq_x_0,Eq_x_1) = sK485(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_818,axiom,
    ( sK486(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK486(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_819,axiom,
    ( sK487(Eq_x_0,Eq_x_1,Eq_x_2) = sK487(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_820,axiom,
    ( sK488(Eq_x_0,Eq_x_1,Eq_x_2) = sK488(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_821,axiom,
    ( sK489(Eq_x_0,Eq_x_1,Eq_x_2) = sK489(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_822,axiom,
    ( sK490(Eq_x_0,Eq_x_1,Eq_x_2) = sK490(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_823,axiom,
    ( sK491(Eq_x_0,Eq_x_1,Eq_x_2) = sK491(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_824,axiom,
    ( sK492(Eq_x_0,Eq_x_1,Eq_x_2) = sK492(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_825,axiom,
    ( sK493(Eq_x_0,Eq_x_1,Eq_x_2) = sK493(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_826,axiom,
    ( sK494(Eq_x_0,Eq_x_1,Eq_x_2) = sK494(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_827,axiom,
    ( sK495(Eq_x_0,Eq_x_1,Eq_x_2) = sK495(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_828,axiom,
    ( sK496(Eq_x_0,Eq_x_1,Eq_x_2) = sK496(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_829,axiom,
    ( sK497(Eq_x_0,Eq_x_1,Eq_x_2) = sK497(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_830,axiom,
    ( sK498(Eq_x_0,Eq_x_1,Eq_x_2) = sK498(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_831,axiom,
    ( sK499(Eq_x_0,Eq_x_1,Eq_x_2) = sK499(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_832,axiom,
    ( sK500(Eq_x_0,Eq_x_1,Eq_x_2) = sK500(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_833,axiom,
    ( sK501(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK501(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_834,axiom,
    ( sK502(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK502(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_835,axiom,
    ( sK503(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK503(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_836,axiom,
    ( sK504(Eq_x_0,Eq_x_1,Eq_x_2) = sK504(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_837,axiom,
    ( sK505(Eq_x_0,Eq_x_1,Eq_x_2) = sK505(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_838,axiom,
    ( sK506(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK506(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_839,axiom,
    ( sK507(Eq_x_0,Eq_x_1,Eq_x_2) = sK507(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_840,axiom,
    ( sK508(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK508(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_841,axiom,
    ( sK509(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK509(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_842,axiom,
    ( sK510(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK510(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_843,axiom,
    ( sK511(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK511(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_844,axiom,
    ( sK512(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK512(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_845,axiom,
    ( sK513(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK513(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_846,axiom,
    ( sK514(Eq_x_0,Eq_x_1,Eq_x_2) = sK514(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_847,axiom,
    ( sK515(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK515(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_848,axiom,
    ( sK516(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK516(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_849,axiom,
    ( sK517(Eq_x_0,Eq_x_1) = sK517(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_850,axiom,
    ( sK518(Eq_x_0,Eq_x_1,Eq_x_2) = sK518(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_851,axiom,
    ( sK519(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK519(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_852,axiom,
    ( sK520(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK520(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_853,axiom,
    ( sK521(Eq_x_0,Eq_x_1) = sK521(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_854,axiom,
    ( sK522(Eq_x_0,Eq_x_1) = sK522(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_855,axiom,
    ( sK523(Eq_x_0,Eq_x_1) = sK523(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_856,axiom,
    ( sK524(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK524(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_857,axiom,
    ( sK525(Eq_x_0) = sK525(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_858,axiom,
    ( sK526(Eq_x_0,Eq_x_1) = sK526(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_859,axiom,
    ( sK527(Eq_x_0,Eq_x_1,Eq_x_2) = sK527(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_860,axiom,
    ( sK528(Eq_x_0,Eq_x_1,Eq_x_2) = sK528(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_861,axiom,
    ( sK529(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK529(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_862,axiom,
    ( sK530(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK530(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_863,axiom,
    ( sK531(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK531(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_864,axiom,
    ( sK532(Eq_x_0,Eq_x_1) = sK532(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_865,axiom,
    ( sK533(Eq_x_0,Eq_x_1) = sK533(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_866,axiom,
    ( sK534(Eq_x_0,Eq_x_1) = sK534(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_867,axiom,
    ( sK535(Eq_x_0,Eq_x_1) = sK535(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_868,axiom,
    ( sK536(Eq_x_0,Eq_x_1) = sK536(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_869,axiom,
    ( sK537(Eq_x_0) = sK537(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_870,axiom,
    ( sK538(Eq_x_0) = sK538(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_871,axiom,
    ( sK539(Eq_x_0) = sK539(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_872,axiom,
    ( sK540(Eq_x_0) = sK540(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_873,axiom,
    ( sK541(Eq_x_0) = sK541(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_874,axiom,
    ( sK542(Eq_x_0,Eq_x_1) = sK542(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_875,axiom,
    ( sK543(Eq_x_0,Eq_x_1) = sK543(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_876,axiom,
    ( sK544(Eq_x_0,Eq_x_1,Eq_x_2) = sK544(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_877,axiom,
    ( sK545(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK545(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_878,axiom,
    ( sK546(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK546(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_879,axiom,
    ( sK547(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK547(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_880,axiom,
    ( sK548(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK548(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_881,axiom,
    ( sK549(Eq_x_0,Eq_x_1) = sK549(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_882,axiom,
    ( sK550(Eq_x_0) = sK550(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_883,axiom,
    ( sK551(Eq_x_0,Eq_x_1) = sK551(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_884,axiom,
    ( sK552(Eq_x_0) = sK552(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_885,axiom,
    ( sK553(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK553(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_886,axiom,
    ( sK554(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK554(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_887,axiom,
    ( sK555(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK555(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_888,axiom,
    ( sK556(Eq_x_0,Eq_x_1) = sK556(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_889,axiom,
    ( sK557(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK557(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_890,axiom,
    ( sK558(Eq_x_0,Eq_x_1) = sK558(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_891,axiom,
    ( sK559(Eq_x_0,Eq_x_1) = sK559(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_892,axiom,
    ( sK560(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK560(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_893,axiom,
    ( sK561(Eq_x_0,Eq_x_1,Eq_x_2) = sK561(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_894,axiom,
    ( sK562(Eq_x_0,Eq_x_1,Eq_x_2) = sK562(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_895,axiom,
    ( sK563(Eq_x_0,Eq_x_1,Eq_x_2) = sK563(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_896,axiom,
    ( sK564(Eq_x_0,Eq_x_1,Eq_x_2) = sK564(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_897,axiom,
    ( sK565(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK565(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_898,axiom,
    ( sK566(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK566(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_899,axiom,
    ( sK567(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK567(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_900,axiom,
    ( sK568(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK568(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_901,axiom,
    ( sK569(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK569(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_902,axiom,
    ( sK570(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK570(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_903,axiom,
    ( sK571(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7) = sK571(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
    | Eq_x_7 != Eq_y_7
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_904,axiom,
    ( sK572(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7) = sK572(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
    | Eq_x_7 != Eq_y_7
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_905,axiom,
    ( sK573(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7) = sK573(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
    | Eq_x_7 != Eq_y_7
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_906,axiom,
    ( sK574(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7) = sK574(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
    | Eq_x_7 != Eq_y_7
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_907,axiom,
    ( sK575(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7) = sK575(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
    | Eq_x_7 != Eq_y_7
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_908,axiom,
    ( sK576(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7) = sK576(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
    | Eq_x_7 != Eq_y_7
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_909,axiom,
    ( sK577(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7) = sK577(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
    | Eq_x_7 != Eq_y_7
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_910,axiom,
    ( sK578(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7) = sK578(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
    | Eq_x_7 != Eq_y_7
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_911,axiom,
    ( sK579(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK579(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_912,axiom,
    ( sK580(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK580(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_913,axiom,
    ( sK581(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK581(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_914,axiom,
    ( sK582(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK582(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_915,axiom,
    ( sK583(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK583(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_916,axiom,
    ( sK584(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK584(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_917,axiom,
    ( sK585(Eq_x_0,Eq_x_1,Eq_x_2) = sK585(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_918,axiom,
    ( sK586(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK586(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_919,axiom,
    ( sK587(Eq_x_0,Eq_x_1,Eq_x_2) = sK587(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_920,axiom,
    ( hBOOL(Eq_y_0)
    | ~ hBOOL(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_921,axiom,
    ( c_Hoare__Mirabelle_Ohoare__derivs(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_922,axiom,
    ( class_Orderings_Opreorder(Eq_y_0)
    | ~ class_Orderings_Opreorder(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_923,axiom,
    ( class_Orderings_Oord(Eq_y_0)
    | ~ class_Orderings_Oord(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_924,axiom,
    ( class_Orderings_Olinorder(Eq_y_0)
    | ~ class_Orderings_Olinorder(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_925,axiom,
    ( class_Orderings_Oorder(Eq_y_0)
    | ~ class_Orderings_Oorder(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_926,axiom,
    ( c_Orderings_Oorder__class_Ostrict__mono(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ c_Orderings_Oorder__class_Ostrict__mono(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_927,axiom,
    ( class_Complete__Lattice_Ocomplete__lattice(Eq_y_0)
    | ~ class_Complete__Lattice_Ocomplete__lattice(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_928,axiom,
    ( class_Orderings_Otop(Eq_y_0)
    | ~ class_Orderings_Otop(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_929,axiom,
    ( class_Orderings_Obot(Eq_y_0)
    | ~ class_Orderings_Obot(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_930,axiom,
    ( class_Lattices_Oboolean__algebra(Eq_y_0)
    | ~ class_Lattices_Oboolean__algebra(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_931,axiom,
    ( class_Groups_Ouminus(Eq_y_0)
    | ~ class_Groups_Ouminus(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_932,axiom,
    ( class_Groups_Oordered__ab__group__add(Eq_y_0)
    | ~ class_Groups_Oordered__ab__group__add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_933,axiom,
    ( class_Lattices_Olattice(Eq_y_0)
    | ~ class_Lattices_Olattice(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_934,axiom,
    ( class_Lattices_Odistrib__lattice(Eq_y_0)
    | ~ class_Lattices_Odistrib__lattice(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_935,axiom,
    ( class_Lattices_Osemilattice__sup(Eq_y_0)
    | ~ class_Lattices_Osemilattice__sup(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_936,axiom,
    ( class_Lattices_Osemilattice__inf(Eq_y_0)
    | ~ class_Lattices_Osemilattice__inf(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_937,axiom,
    ( class_Lattices_Obounded__lattice__bot(Eq_y_0)
    | ~ class_Lattices_Obounded__lattice__bot(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_938,axiom,
    ( class_Lattices_Obounded__lattice__top(Eq_y_0)
    | ~ class_Lattices_Obounded__lattice__top(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_939,axiom,
    ( class_Groups_Ogroup__add(Eq_y_0)
    | ~ class_Groups_Ogroup__add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_940,axiom,
    ( class_Rings_Olinordered__idom(Eq_y_0)
    | ~ class_Rings_Olinordered__idom(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_941,axiom,
    ( c_Orderings_Oorder__class_Omono(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ c_Orderings_Oorder__class_Omono(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_942,axiom,
    ( class_Groups_Olinordered__ab__group__add(Eq_y_0)
    | ~ class_Groups_Olinordered__ab__group__add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_943,axiom,
    ( c_Fun_Oinj__on(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ c_Fun_Oinj__on(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_944,axiom,
    ( class_Groups_Ominus(Eq_y_0)
    | ~ class_Groups_Ominus(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_945,axiom,
    ( class_Groups_Oab__group__add(Eq_y_0)
    | ~ class_Groups_Oab__group__add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_946,axiom,
    ( class_Finite__Set_Ofinite(Eq_y_0)
    | ~ class_Finite__Set_Ofinite(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_947,axiom,
    ( c_Finite__Set_Ofolding__one(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ c_Finite__Set_Ofolding__one(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_948,axiom,
    ( c_Finite__Set_Ofolding__image__simple(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ c_Finite__Set_Ofolding__image__simple(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_949,axiom,
    ( c_Finite__Set_Ofolding__one__idem(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ c_Finite__Set_Ofolding__one__idem(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_950,axiom,
    ( class_Rings_Oring(Eq_y_0)
    | ~ class_Rings_Oring(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_951,axiom,
    ( c_Big__Operators_Osemilattice__big(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ c_Big__Operators_Osemilattice__big(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_952,axiom,
    ( class_Groups_Ocomm__monoid__add(Eq_y_0)
    | ~ class_Groups_Ocomm__monoid__add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_953,axiom,
    ( class_Groups_Oordered__cancel__ab__semigroup__add(Eq_y_0)
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_954,axiom,
    ( class_Groups_Oab__semigroup__mult(Eq_y_0)
    | ~ class_Groups_Oab__semigroup__mult(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_955,axiom,
    ( class_Lattices_Oab__semigroup__idem__mult(Eq_y_0)
    | ~ class_Lattices_Oab__semigroup__idem__mult(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_956,axiom,
    ( class_Groups_Oab__semigroup__add(Eq_y_0)
    | ~ class_Groups_Oab__semigroup__add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_957,axiom,
    ( class_Groups_Ocancel__semigroup__add(Eq_y_0)
    | ~ class_Groups_Ocancel__semigroup__add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_958,axiom,
    ( class_Groups_Ocancel__ab__semigroup__add(Eq_y_0)
    | ~ class_Groups_Ocancel__ab__semigroup__add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_959,axiom,
    ( class_Rings_Ocomm__semiring(Eq_y_0)
    | ~ class_Rings_Ocomm__semiring(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_960,axiom,
    ( class_Rings_Osemiring(Eq_y_0)
    | ~ class_Rings_Osemiring(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_961,axiom,
    ( class_Rings_Oordered__ring(Eq_y_0)
    | ~ class_Rings_Oordered__ring(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_962,axiom,
    ( class_Groups_Oordered__ab__semigroup__add__imp__le(Eq_y_0)
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_963,axiom,
    ( class_Groups_Oordered__ab__semigroup__add(Eq_y_0)
    | ~ class_Groups_Oordered__ab__semigroup__add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_964,axiom,
    ( class_Rings_Oidom(Eq_y_0)
    | ~ class_Rings_Oidom(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_965,axiom,
    ( class_Rings_Ocomm__ring__1(Eq_y_0)
    | ~ class_Rings_Ocomm__ring__1(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_966,axiom,
    ( class_Rings_Ocomm__semiring__1(Eq_y_0)
    | ~ class_Rings_Ocomm__semiring__1(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_967,axiom,
    ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(Eq_y_0)
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_968,axiom,
    ( class_Groups_Ocomm__monoid__mult(Eq_y_0)
    | ~ class_Groups_Ocomm__monoid__mult(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_969,axiom,
    ( c_Finite__Set_Ofun__left__comm(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ c_Finite__Set_Ofun__left__comm(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_970,axiom,
    ( class_Groups_Oone(Eq_y_0)
    | ~ class_Groups_Oone(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_971,axiom,
    ( class_Groups_Omonoid__mult(Eq_y_0)
    | ~ class_Groups_Omonoid__mult(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_972,axiom,
    ( class_Rings_Olinordered__semidom(Eq_y_0)
    | ~ class_Rings_Olinordered__semidom(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_973,axiom,
    ( class_Rings_Oring__1__no__zero__divisors(Eq_y_0)
    | ~ class_Rings_Oring__1__no__zero__divisors(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_974,axiom,
    ( class_Groups_Ozero(Eq_y_0)
    | ~ class_Groups_Ozero(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_975,axiom,
    ( class_Groups_Omonoid__add(Eq_y_0)
    | ~ class_Groups_Omonoid__add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_976,axiom,
    ( class_Rings_Ono__zero__divisors(Eq_y_0)
    | ~ class_Rings_Ono__zero__divisors(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_977,axiom,
    ( class_Rings_Oring__no__zero__divisors(Eq_y_0)
    | ~ class_Rings_Oring__no__zero__divisors(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_978,axiom,
    ( class_Rings_Omult__zero(Eq_y_0)
    | ~ class_Rings_Omult__zero(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_979,axiom,
    ( class_Rings_Ozero__neq__one(Eq_y_0)
    | ~ class_Rings_Ozero__neq__one(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_980,axiom,
    ( class_Rings_Olinordered__ring__strict(Eq_y_0)
    | ~ class_Rings_Olinordered__ring__strict(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_981,axiom,
    ( class_Rings_Olinordered__ring(Eq_y_0)
    | ~ class_Rings_Olinordered__ring(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_982,axiom,
    ( class_Groups_Oordered__comm__monoid__add(Eq_y_0)
    | ~ class_Groups_Oordered__comm__monoid__add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_983,axiom,
    ( class_Rings_Oordered__cancel__semiring(Eq_y_0)
    | ~ class_Rings_Oordered__cancel__semiring(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_984,axiom,
    ( class_Rings_Oordered__semiring(Eq_y_0)
    | ~ class_Rings_Oordered__semiring(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_985,axiom,
    ( class_Rings_Oordered__comm__semiring(Eq_y_0)
    | ~ class_Rings_Oordered__comm__semiring(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_986,axiom,
    ( class_Rings_Olinordered__semiring__strict(Eq_y_0)
    | ~ class_Rings_Olinordered__semiring__strict(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_987,axiom,
    ( class_Rings_Olinordered__comm__semiring__strict(Eq_y_0)
    | ~ class_Rings_Olinordered__comm__semiring__strict(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_988,axiom,
    ( class_Rings_Olinordered__semiring(Eq_y_0)
    | ~ class_Rings_Olinordered__semiring(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_989,axiom,
    ( class_Rings_Olinordered__semiring__1(Eq_y_0)
    | ~ class_Rings_Olinordered__semiring__1(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_990,axiom,
    ( class_Rings_Olinordered__semiring__1__strict(Eq_y_0)
    | ~ class_Rings_Olinordered__semiring__1__strict(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_991,axiom,
    ( class_Rings_Oring__1(Eq_y_0)
    | ~ class_Rings_Oring__1(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_992,axiom,
    ( class_Int_Oring__char__0(Eq_y_0)
    | ~ class_Int_Oring__char__0(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_993,axiom,
    ( class_Fields_Ofield(Eq_y_0)
    | ~ class_Fields_Ofield(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_994,axiom,
    ( class_Rings_Odivision__ring(Eq_y_0)
    | ~ class_Rings_Odivision__ring(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_995,axiom,
    ( class_Rings_Odivision__ring__inverse__zero(Eq_y_0)
    | ~ class_Rings_Odivision__ring__inverse__zero(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_996,axiom,
    ( class_Fields_Olinordered__field__inverse__zero(Eq_y_0)
    | ~ class_Fields_Olinordered__field__inverse__zero(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_997,axiom,
    ( class_Fields_Olinordered__field(Eq_y_0)
    | ~ class_Fields_Olinordered__field(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_998,axiom,
    ( class_Fields_Ofield__inverse__zero(Eq_y_0)
    | ~ class_Fields_Ofield__inverse__zero(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_999,axiom,
    ( c_Big__Operators_Ocomm__monoid__big(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ c_Big__Operators_Ocomm__monoid__big(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1000,axiom,
    ( class_Groups_Osgn__if(Eq_y_0)
    | ~ class_Groups_Osgn__if(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1001,axiom,
    ( c_Finite__Set_Ofun__left__comm__idem(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ c_Finite__Set_Ofun__left__comm__idem(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1002,axiom,
    ( class_Power_Opower(Eq_y_0)
    | ~ class_Power_Opower(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1003,axiom,
    ( class_Rings_Osemiring__0(Eq_y_0)
    | ~ class_Rings_Osemiring__0(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1004,axiom,
    ( c_Finite__Set_Ofolding__image__simple__idem(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ c_Finite__Set_Ofolding__image__simple__idem(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1005,axiom,
    ( class_Int_Onumber__ring(Eq_y_0)
    | ~ class_Int_Onumber__ring(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1006,axiom,
    ( class_Int_Onumber(Eq_y_0)
    | ~ class_Int_Onumber(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1007,axiom,
    ( c_Nitpick_Ofold__graph_H(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ c_Nitpick_Ofold__graph_H(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1008,axiom,
    ( class_Divides_Osemiring__div(Eq_y_0)
    | ~ class_Divides_Osemiring__div(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1009,axiom,
    ( c_Int_Oiszero(Eq_y_0,Eq_y_1)
    | ~ c_Int_Oiszero(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1010,axiom,
    ( class_Rings_Osemiring__1(Eq_y_0)
    | ~ class_Rings_Osemiring__1(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1011,axiom,
    ( c_Nat__Transfer_Otransfer__morphism(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ c_Nat__Transfer_Otransfer__morphism(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1012,axiom,
    ( class_Nat_Osemiring__char__0(Eq_y_0)
    | ~ class_Nat_Osemiring__char__0(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1013,axiom,
    ( c_Nat__Transfer_Onat__set(Eq_y_0)
    | ~ c_Nat__Transfer_Onat__set(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1014,axiom,
    ( class_Divides_Oring__div(Eq_y_0)
    | ~ class_Divides_Oring__div(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1015,axiom,
    ( c_Nat__Transfer_Ois__nat(Eq_y_0)
    | ~ c_Nat__Transfer_Ois__nat(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1016,axiom,
    ( class_Groups_Oordered__ab__group__add__abs(Eq_y_0)
    | ~ class_Groups_Oordered__ab__group__add__abs(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1017,axiom,
    ( class_Rings_Oordered__ring__abs(Eq_y_0)
    | ~ class_Rings_Oordered__ring__abs(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1018,axiom,
    ( class_Groups_Oabs__if(Eq_y_0)
    | ~ class_Groups_Oabs__if(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1019,axiom,
    ( c_Nitpick_Orefl_H(Eq_y_0,Eq_y_1)
    | ~ c_Nitpick_Orefl_H(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1020,axiom,
    ( c_Finite__Set_Ofolding(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ c_Finite__Set_Ofolding(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1021,axiom,
    ( c_Finite__Set_Ofolding__image(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ c_Finite__Set_Ofolding__image(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1022,axiom,
    ( class_Orderings_Owellorder(Eq_y_0)
    | ~ class_Orderings_Owellorder(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1023,axiom,
    ( c_Finite__Set_Ofolding__idem(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ c_Finite__Set_Ofolding__idem(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1024,axiom,
    ( c_FunDef_Oreduction__pair(Eq_y_0,Eq_y_1)
    | ~ c_FunDef_Oreduction__pair(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1025,axiom,
    ( c_Wellfounded_Omax__extp(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ c_Wellfounded_Omax__extp(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1026,axiom,
    ( c_Relation_Oirrefl(Eq_y_0,Eq_y_1)
    | ~ c_Relation_Oirrefl(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1027,axiom,
    ( c_Equiv__Relations_Oequiv(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ c_Equiv__Relations_Oequiv(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1028,axiom,
    ( c_Equiv__Relations_Ocongruent2(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ c_Equiv__Relations_Ocongruent2(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1029,axiom,
    ( c_Equiv__Relations_Ocongruent(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ c_Equiv__Relations_Ocongruent(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1030,axiom,
    ( c_Equiv__Relations_Oequivp(Eq_y_0,Eq_y_1)
    | ~ c_Equiv__Relations_Oequivp(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1031,axiom,
    ( c_Typedef_Otype__definition(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ c_Typedef_Otype__definition(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1032,axiom,
    ( c_Relation_Orefl__on(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ c_Relation_Orefl__on(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1033,axiom,
    ( class_Groups_Olinordered__ab__semigroup__add(Eq_y_0)
    | ~ class_Groups_Olinordered__ab__semigroup__add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1034,axiom,
    ( c_Predicate_Oreflp(Eq_y_0,Eq_y_1)
    | ~ c_Predicate_Oreflp(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1035,axiom,
    ( c_Wellfounded_Owf(Eq_y_0,Eq_y_1)
    | ~ c_Wellfounded_Owf(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1036,axiom,
    ( c_Wellfounded_OwfP(Eq_y_0,Eq_y_1)
    | ~ c_Wellfounded_OwfP(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1037,axiom,
    ( c_Wellfounded_Oacyclic(Eq_y_0,Eq_y_1)
    | ~ c_Wellfounded_Oacyclic(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1038,axiom,
    ( c_Nitpick_Owf_H(Eq_y_0,Eq_y_1)
    | ~ c_Nitpick_Owf_H(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1039,axiom,
    ( c_Nitpick_Ounknown(Eq_y_0)
    | ~ c_Nitpick_Ounknown(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1040,axiom,
    ( c_Relation_Osingle__valued(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ c_Relation_Osingle__valued(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1041,axiom,
    ( c_Relation_Ototal__on(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ c_Relation_Ototal__on(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1042,axiom,
    ( class_Rings_Oinverse(Eq_y_0)
    | ~ class_Rings_Oinverse(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1043,axiom,
    ( c_Nitpick_Oless__frac(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ c_Nitpick_Oless__frac(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1044,axiom,
    ( c_Nitpick_Oless__eq__frac(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ c_Nitpick_Oless__eq__frac(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1045,axiom,
    ( c_List_Olistrelp(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ c_List_Olistrelp(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1046,axiom,
    ( c_List_Onat__list(Eq_y_0)
    | ~ c_List_Onat__list(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1047,axiom,
    ( class_Groups_Osemigroup__add(Eq_y_0)
    | ~ class_Groups_Osemigroup__add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1048,axiom,
    ( c_List_Olist__all2(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ c_List_Olist__all2(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1049,axiom,
    ( c_List_Olinorder__class_Osorted(Eq_y_0,Eq_y_1)
    | ~ c_List_Olinorder__class_Osorted(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1050,axiom,
    ( class_Enum_Oenum(Eq_y_0)
    | ~ class_Enum_Oenum(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1051,axiom,
    ( c_List_Olist__ex(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ c_List_Olist__ex(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1052,axiom,
    ( c_List_Olist__all(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ c_List_Olist__all(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1053,axiom,
    ( c_FunDef_Ois__measure(Eq_y_0,Eq_y_1)
    | ~ c_FunDef_Ois__measure(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1054,axiom,
    ( class_Nat_Osize(Eq_y_0)
    | ~ class_Nat_Osize(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1055,axiom,
    ( c_List_Olist__ex1(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ c_List_Olist__ex1(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1056,axiom,
    ( class_Lazy__Sequence_Osmall__lazy(Eq_y_0)
    | ~ class_Lazy__Sequence_Osmall__lazy(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1057,axiom,
    ( c_List_Oall__interval__int(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ c_List_Oall__interval__int(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1058,axiom,
    ( c_Relation_Otrans(Eq_y_0,Eq_y_1)
    | ~ c_Relation_Otrans(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1059,axiom,
    ( c_Predicate_Otransp(Eq_y_0,Eq_y_1)
    | ~ c_Predicate_Otransp(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1060,axiom,
    ( c_Predicate_Osymp(Eq_y_0,Eq_y_1)
    | ~ c_Predicate_Osymp(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1061,axiom,
    ( c_Relation_Oantisym(Eq_y_0,Eq_y_1)
    | ~ c_Relation_Oantisym(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1062,axiom,
    ( c_Relation_Osym(Eq_y_0,Eq_y_1)
    | ~ c_Relation_Osym(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1063,axiom,
    ( c_Equiv__Relations_Opart__equivp(Eq_y_0,Eq_y_1)
    | ~ c_Equiv__Relations_Opart__equivp(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1064,axiom,
    ( c_Fun_Obij__betw(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ c_Fun_Obij__betw(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1065,axiom,
    ( c_List_Oall__interval__nat(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ c_List_Oall__interval__nat(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1066,axiom,
    ( class_Lattices_Obounded__lattice(Eq_y_0)
    | ~ class_Lattices_Obounded__lattice(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(sat_proved,plain,
    $false,
    inference(cadical,[status(thm)],[]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02  % Problem  : SWW311+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.03  This is a FOF_THM_RFO_SEQ problem
% 0.00/0.03  % Command  : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37  % Computer : n017.cluster.edu
% 0.09/0.37  % Model    : x86_64 x86_64
% 0.09/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37  % Memory   : 8046.5625MB
% 0.09/0.37  % OS       : Linux 6.8.0-71-generic
% 0.09/0.37  % CPULimit : 300
% 0.09/0.37  % WCLimit  : 300
% 0.09/0.37  % DateTime : Sun Sep 20 05:16:26 UTC 2026
% 0.09/0.37  % CPUTime  : 
% 166.34/166.64  % SZS status Theorem for theBenchmark
% 166.34/166.64  % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------